LMFDB - Embedded newform 22.9.d.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,9,Mod(7,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.96232942134$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	22.7
Dual form			22.9.d.a.19.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.65003 - 9.15298i) q^{2} +(10.6908 - 32.9028i) q^{3} +(-39.5542 - 121.735i) q^{4} +(-864.151 + 627.842i) q^{5} +(-230.065 - 316.657i) q^{6} +(-1443.95 + 469.167i) q^{7} +(-1377.28 - 447.504i) q^{8} +(4339.66 + 3152.95i) q^{9} +O(q^{10})$	\(q+(6.65003 - 9.15298i) q^{2} +(10.6908 - 32.9028i) q^{3} +(-39.5542 - 121.735i) q^{4} +(-864.151 + 627.842i) q^{5} +(-230.065 - 316.657i) q^{6} +(-1443.95 + 469.167i) q^{7} +(-1377.28 - 447.504i) q^{8} +(4339.66 + 3152.95i) q^{9} +12084.7i q^{10} +(-9251.29 - 11347.8i) q^{11} -4428.29 q^{12} +(-17502.9 + 24090.7i) q^{13} +(-5308.02 + 16336.4i) q^{14} +(11419.3 + 35145.1i) q^{15} +(-13254.9 + 9630.27i) q^{16} +(11437.6 + 15742.5i) q^{17} +(57717.8 - 18753.6i) q^{18} +(-122312. - 39741.6i) q^{19} +(110611. + 80363.8i) q^{20} +52525.7i q^{21} +(-165388. + 9213.70i) q^{22} -330077. q^{23} +(-29448.3 + 40532.0i) q^{24} +(231861. - 713595. i) q^{25} +(104107. + 320408. i) q^{26} +(333769. - 242498. i) q^{27} +(114228. + 157222. i) q^{28} +(1.13306e6 - 368153. i) q^{29} +(397621. + 129195. i) q^{30} +(-1.21661e6 - 883920. i) q^{31} +185364. i q^{32} +(-472277. + 183076. i) q^{33} +220151. q^{34} +(953227. - 1.31200e6i) q^{35} +(212173. - 653002. i) q^{36} +(593777. + 1.82746e6i) q^{37} +(-1.17713e6 + 855238. i) q^{38} +(605532. + 833443. i) q^{39} +(1.47114e6 - 478002. i) q^{40} +(-2.24851e6 - 730584. i) q^{41} +(480766. + 349297. i) q^{42} +839962. i q^{43} +(-1.01550e6 + 1.57506e6i) q^{44} -5.72968e6 q^{45} +(-2.19502e6 + 3.02119e6i) q^{46} +(-884649. + 2.72267e6i) q^{47} +(175157. + 539079. i) q^{48} +(-2.79895e6 + 2.03356e6i) q^{49} +(-4.98964e6 - 6.86765e6i) q^{50} +(640247. - 208029. i) q^{51} +(3.62501e6 + 1.17784e6i) q^{52} +(6.77508e6 + 4.92238e6i) q^{53} -4.66760e6i q^{54} +(1.51191e7 + 3.99786e6i) q^{55} +2.19867e6 q^{56} +(-2.61522e6 + 3.59954e6i) q^{57} +(4.16518e6 - 1.28191e7i) q^{58} +(-2.13217e6 - 6.56216e6i) q^{59} +(3.82671e6 - 2.78027e6i) q^{60} +(7.62554e6 + 1.04957e7i) q^{61} +(-1.61810e7 + 5.25753e6i) q^{62} +(-7.74551e6 - 2.51667e6i) q^{63} +(1.69663e6 + 1.23268e6i) q^{64} -3.18071e7i q^{65} +(-1.46496e6 + 5.54021e6i) q^{66} +6.19194e6 q^{67} +(1.46401e6 - 2.01504e6i) q^{68} +(-3.52877e6 + 1.08604e7i) q^{69} +(-5.66976e6 - 1.74497e7i) q^{70} +(2.06518e7 - 1.50044e7i) q^{71} +(-4.56596e6 - 6.28450e6i) q^{72} +(-1.34645e7 + 4.37489e6i) q^{73} +(2.06753e7 + 6.71781e6i) q^{74} +(-2.10005e7 - 1.52577e7i) q^{75} +1.64616e7i q^{76} +(1.86824e7 + 1.20452e7i) q^{77} +1.16553e7 q^{78} +(-3.00155e7 + 4.13128e7i) q^{79} +(5.40797e6 - 1.66440e7i) q^{80} +(6.46494e6 + 1.98970e7i) q^{81} +(-2.16397e7 + 1.57221e7i) q^{82} +(1.82124e7 + 2.50672e7i) q^{83} +(6.39422e6 - 2.07761e6i) q^{84} +(-1.97676e7 - 6.42288e6i) q^{85} +(7.68815e6 + 5.58577e6i) q^{86} -4.12166e7i q^{87} +(7.66340e6 + 1.97691e7i) q^{88} -4.52461e7 q^{89} +(-3.81025e7 + 5.24436e7i) q^{90} +(1.39708e7 - 4.29976e7i) q^{91} +(1.30559e7 + 4.01820e7i) q^{92} +(-4.20899e7 + 3.05801e7i) q^{93} +(1.90376e7 + 2.62030e7i) q^{94} +(1.30648e8 - 4.24500e7i) q^{95} +(6.09898e6 + 1.98168e6i) q^{96} +(-9.87571e7 - 7.17513e7i) q^{97} +3.91420e7i q^{98} +(-4.36845e6 - 7.84144e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9}+O(q^{10}) $ 32 * q - 182 * q^3 + 1024 * q^4 + 1410 * q^5 + 4480 * q^6 - 10950 * q^7 - 1402 * q^9	\( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9} - 47598 q^{11} - 21504 q^{12} + 24990 q^{13} + 106752 q^{14} + 273582 q^{15} - 131072 q^{16} - 553530 q^{17} + 152320 q^{18} + 442680 q^{19} - 180480 q^{20} - 359040 q^{22} - 317064 q^{23} + 573440 q^{24} - 918738 q^{25} - 782592 q^{26} + 714484 q^{27} + 51200 q^{28} + 2380710 q^{29} + 4488960 q^{30} + 181654 q^{31} - 628628 q^{33} - 3865088 q^{34} - 12788370 q^{35} + 5097216 q^{36} - 6976698 q^{37} - 15360 q^{38} + 17382010 q^{39} + 3768320 q^{40} + 5153790 q^{41} - 15355648 q^{42} + 2744064 q^{44} + 5954792 q^{45} - 15447040 q^{46} - 13476378 q^{47} - 2981888 q^{48} + 19896222 q^{49} + 13816320 q^{50} + 37405440 q^{51} + 18368000 q^{52} - 847422 q^{53} - 47212238 q^{55} + 1572864 q^{56} - 119710960 q^{57} - 29125376 q^{58} - 49425120 q^{59} + 12710144 q^{60} + 26432690 q^{61} + 64485120 q^{62} + 289643740 q^{63} + 16777216 q^{64} - 78840064 q^{66} - 133260476 q^{67} - 70851840 q^{68} - 33873776 q^{69} - 50942720 q^{70} + 38304066 q^{71} + 61603840 q^{72} + 208728710 q^{73} + 56355840 q^{74} - 62835924 q^{75} + 92206590 q^{77} - 74988544 q^{78} - 247776110 q^{79} - 22609920 q^{80} - 622273104 q^{81} + 17468928 q^{82} + 434637000 q^{83} + 159336960 q^{84} + 286821150 q^{85} - 7040640 q^{86} + 101498880 q^{88} - 336205452 q^{89} - 270179840 q^{90} - 167007498 q^{91} + 29901312 q^{92} + 65388262 q^{93} + 429944320 q^{94} + 1032904950 q^{95} - 75153432 q^{97} - 459062342 q^{99}+O(q^{100}) \) 32 * q - 182 * q^3 + 1024 * q^4 + 1410 * q^5 + 4480 * q^6 - 10950 * q^7 - 1402 * q^9 - 47598 * q^11 - 21504 * q^12 + 24990 * q^13 + 106752 * q^14 + 273582 * q^15 - 131072 * q^16 - 553530 * q^17 + 152320 * q^18 + 442680 * q^19 - 180480 * q^20 - 359040 * q^22 - 317064 * q^23 + 573440 * q^24 - 918738 * q^25 - 782592 * q^26 + 714484 * q^27 + 51200 * q^28 + 2380710 * q^29 + 4488960 * q^30 + 181654 * q^31 - 628628 * q^33 - 3865088 * q^34 - 12788370 * q^35 + 5097216 * q^36 - 6976698 * q^37 - 15360 * q^38 + 17382010 * q^39 + 3768320 * q^40 + 5153790 * q^41 - 15355648 * q^42 + 2744064 * q^44 + 5954792 * q^45 - 15447040 * q^46 - 13476378 * q^47 - 2981888 * q^48 + 19896222 * q^49 + 13816320 * q^50 + 37405440 * q^51 + 18368000 * q^52 - 847422 * q^53 - 47212238 * q^55 + 1572864 * q^56 - 119710960 * q^57 - 29125376 * q^58 - 49425120 * q^59 + 12710144 * q^60 + 26432690 * q^61 + 64485120 * q^62 + 289643740 * q^63 + 16777216 * q^64 - 78840064 * q^66 - 133260476 * q^67 - 70851840 * q^68 - 33873776 * q^69 - 50942720 * q^70 + 38304066 * q^71 + 61603840 * q^72 + 208728710 * q^73 + 56355840 * q^74 - 62835924 * q^75 + 92206590 * q^77 - 74988544 * q^78 - 247776110 * q^79 - 22609920 * q^80 - 622273104 * q^81 + 17468928 * q^82 + 434637000 * q^83 + 159336960 * q^84 + 286821150 * q^85 - 7040640 * q^86 + 101498880 * q^88 - 336205452 * q^89 - 270179840 * q^90 - 167007498 * q^91 + 29901312 * q^92 + 65388262 * q^93 + 429944320 * q^94 + 1032904950 * q^95 - 75153432 * q^97 - 459062342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	6.65003	−	9.15298i	0.415627	−	0.572061i
$2$	6.65003	−	9.15298i	0.415627	−	0.572061i
$3$	10.6908	−	32.9028i	0.131985	−	0.406207i	−0.863124	−	0.504992i	$-0.831496\pi$
$3$	10.6908	−	32.9028i	0.131985	−	0.406207i	0.995109	+	0.0987848i	$0.0314956\pi$
$4$	−39.5542	−	121.735i	−0.154508	−	0.475528i
$5$	−864.151	+	627.842i	−1.38264	+	1.00455i	−0.386014	+	0.922493i	$0.626148\pi$
$5$	−864.151	+	627.842i	−1.38264	+	1.00455i	−0.996628	+	0.0820548i	$0.973852\pi$
$6$	−230.065	−	316.657i	−0.177519	−	0.244334i
$7$	−1443.95	+	469.167i	−0.601395	+	0.195405i	−0.593862	−	0.804567i	$-0.702398\pi$
$7$	−1443.95	+	469.167i	−0.601395	+	0.195405i	−0.00753237	+	0.999972i	$0.502398\pi$
$8$	−1377.28	−	447.504i	−0.336249	−	0.109254i
$9$	4339.66	+	3152.95i	0.661433	+	0.480559i
$10$			12084.7i			1.20847i
$11$	−9251.29	−	11347.8i	−0.631876	−	0.775070i
$11$	−9251.29	−	11347.8i	−0.631876	−	0.775070i
$12$	−4428.29			−0.213556
$13$	−17502.9	+	24090.7i	−0.612827	+	0.843484i	−0.996806	−	0.0798579i	$-0.974553\pi$
$13$	−17502.9	+	24090.7i	−0.612827	+	0.843484i	0.383979	+	0.923342i	$0.374553\pi$
$14$	−5308.02	+	16336.4i	−0.138172	+	0.425250i
$15$	11419.3	+	35145.1i	0.225567	+	0.694223i
$16$	−13254.9	+	9630.27i	−0.202254	+	0.146946i
$17$	11437.6	+	15742.5i	0.136942	+	0.188485i	0.871980	−	0.489541i	$-0.162836\pi$
$17$	11437.6	+	15742.5i	0.136942	+	0.188485i	−0.735038	+	0.678026i	$0.762836\pi$
$18$	57717.8	−	18753.6i	0.549819	−	0.178647i
$19$	−122312.	−	39741.6i	−0.938545	−	0.304952i	−0.200493	−	0.979695i	$-0.564254\pi$
$19$	−122312.	−	39741.6i	−0.938545	−	0.304952i	−0.738052	+	0.674743i	$0.764254\pi$
$20$	110611.	+	80363.8i	0.691321	+	0.502274i
$21$			52525.7i			0.270081i
$22$	−165388.	+	9213.70i	−0.706012	+	0.0393318i
$23$	−330077.			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$23$	−330077.			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$24$	−29448.3	+	40532.0i	−0.0887595	+	0.122167i
$25$	231861.	−	713595.i	0.593564	−	1.82680i
$26$	104107.	+	320408.i	0.227817	+	0.701149i
$27$	333769.	−	242498.i	0.628046	−	0.456302i
$28$	114228.	+	157222.i	0.185841	+	0.255788i
$29$	1.13306e6	−	368153.i	1.60199	−	0.520519i	0.634394	−	0.773010i	$-0.281250\pi$
$29$	1.13306e6	−	368153.i	1.60199	−	0.520519i	0.967599	+	0.252491i	$0.0812497\pi$
$30$	397621.	+	129195.i	0.490890	+	0.159500i
$31$	−1.21661e6	−	883920.i	−1.31736	−	0.957119i	−0.999961	−	0.00882793i	$-0.997190\pi$
$31$	−1.21661e6	−	883920.i	−1.31736	−	0.957119i	−0.317401	−	0.948291i	$-0.602810\pi$
$32$			185364.i			0.176777i
$33$	−472277.	+	183076.i	−0.398237	+	0.154375i
$34$	220151.			0.164742
$35$	953227.	−	1.31200e6i	0.635220	−	0.874305i
$36$	212173.	−	653002.i	0.126322	−	0.388781i
$37$	593777.	+	1.82746e6i	0.316823	+	0.975080i	0.974998	+	0.222215i	$0.0713286\pi$
$37$	593777.	+	1.82746e6i	0.316823	+	0.975080i	−0.658175	+	0.752865i	$0.728671\pi$
$38$	−1.17713e6	+	855238.i	−0.564536	+	0.410159i
$39$	605532.	+	833443.i	0.261745	+	0.360261i
$40$	1.47114e6	−	478002.i	0.574663	−	0.186719i
$41$	−2.24851e6	−	730584.i	−0.795717	−	0.258544i	−0.117180	−	0.993111i	$-0.537386\pi$
$41$	−2.24851e6	−	730584.i	−0.795717	−	0.258544i	−0.678537	+	0.734567i	$0.737386\pi$
$42$	480766.	+	349297.i	0.154503	+	0.112253i
$43$			839962.i			0.245689i	0.992426	+	0.122844i	$0.0392016\pi$
$43$			839962.i			0.245689i	−0.992426	+	0.122844i	$0.960798\pi$
$44$	−1.01550e6	+	1.57506e6i	−0.270937	+	0.420230i
$45$	−5.72968e6			−1.39727
$46$	−2.19502e6	+	3.02119e6i	−0.490239	+	0.674756i
$47$	−884649.	+	2.72267e6i	−0.181292	+	0.557961i	−0.999865	−	0.0164427i	$-0.994766\pi$
$47$	−884649.	+	2.72267e6i	−0.181292	+	0.557961i	0.818572	+	0.574403i	$0.194766\pi$
$48$	175157.	+	539079.i	0.0329962	+	0.101552i
$49$	−2.79895e6	+	2.03356e6i	−0.485524	+	0.352754i
$50$	−4.98964e6	−	6.86765e6i	−0.798342	−	1.09882i
$51$	640247.	−	208029.i	0.0946383	−	0.0307498i
$52$	3.62501e6	+	1.17784e6i	0.495787	+	0.161091i
$53$	6.77508e6	+	4.92238e6i	0.858640	+	0.623838i	0.927515	−	0.373787i	$-0.121941\pi$
$53$	6.77508e6	+	4.92238e6i	0.858640	+	0.623838i	−0.0688749	+	0.997625i	$0.521941\pi$
$54$		−	4.66760e6i		−	0.548932i
$55$	1.51191e7	+	3.99786e6i	1.65225	+	0.436894i
$56$	2.19867e6			0.223567
$57$	−2.61522e6	+	3.59954e6i	−0.247747	+	0.340995i
$58$	4.16518e6	−	1.28191e7i	0.368063	−	1.13278i
$59$	−2.13217e6	−	6.56216e6i	−0.175960	−	0.541550i	0.823716	−	0.567003i	$-0.191897\pi$
$59$	−2.13217e6	−	6.56216e6i	−0.175960	−	0.541550i	−0.999676	+	0.0254528i	$0.991897\pi$
$60$	3.82671e6	−	2.78027e6i	0.295271	−	0.214527i
$61$	7.62554e6	+	1.04957e7i	0.550746	+	0.758036i	0.990113	−	0.140271i	$-0.0447974\pi$
$61$	7.62554e6	+	1.04957e7i	0.550746	+	0.758036i	−0.439367	+	0.898307i	$0.644797\pi$
$62$	−1.61810e7	+	5.25753e6i	−1.09506	+	0.355807i
$63$	−7.74551e6	−	2.51667e6i	−0.491686	−	0.159758i
$64$	1.69663e6	+	1.23268e6i	0.101127	+	0.0734732i
$65$		−	3.18071e7i		−	1.78185i
$66$	−1.46496e6	+	5.54021e6i	−0.0772059	+	0.291978i
$67$	6.19194e6			0.307275			0.153638	−	0.988127i	$-0.450901\pi$
$67$	6.19194e6			0.307275			0.153638	+	0.988127i	$0.450901\pi$
$68$	1.46401e6	−	2.01504e6i	0.0684712	−	0.0942426i
$69$	−3.52877e6	+	1.08604e7i	−0.155678	+	0.479128i
$70$	−5.66976e6	−	1.74497e7i	−0.236142	−	0.726769i
$71$	2.06518e7	−	1.50044e7i	0.812690	−	0.590454i	−0.101919	−	0.994793i	$-0.532498\pi$
$71$	2.06518e7	−	1.50044e7i	0.812690	−	0.590454i	0.914609	+	0.404339i	$0.132498\pi$
$72$	−4.56596e6	−	6.28450e6i	−0.169903	−	0.233852i
$73$	−1.34645e7	+	4.37489e6i	−0.474132	+	0.154055i	−0.536329	−	0.844009i	$-0.680189\pi$
$73$	−1.34645e7	+	4.37489e6i	−0.474132	+	0.154055i	0.0621967	+	0.998064i	$0.480189\pi$
$74$	2.06753e7	+	6.71781e6i	0.689485	+	0.224027i
$75$	−2.10005e7	−	1.52577e7i	−0.663718	−	0.482220i
$76$			1.64616e7i			0.493422i
$77$	1.86824e7	+	1.20452e7i	0.531459	+	0.342651i
$78$	1.16553e7			0.314880
$79$	−3.00155e7	+	4.13128e7i	−0.770615	+	1.06066i	0.225642	+	0.974210i	$0.427552\pi$
$79$	−3.00155e7	+	4.13128e7i	−0.770615	+	1.06066i	−0.996256	+	0.0864496i	$0.972448\pi$
$80$	5.40797e6	−	1.66440e7i	0.132031	−	0.406348i
$81$	6.46494e6	+	1.98970e7i	0.150184	+	0.462220i
$82$	−2.16397e7	+	1.57221e7i	−0.478625	+	0.347741i
$83$	1.82124e7	+	2.50672e7i	0.383755	+	0.528193i	0.956574	−	0.291488i	$-0.0941504\pi$
$83$	1.82124e7	+	2.50672e7i	0.383755	+	0.528193i	−0.572819	+	0.819682i	$0.694150\pi$
$84$	6.39422e6	−	2.07761e6i	0.128431	−	0.0417298i
$85$	−1.97676e7	−	6.42288e6i	−0.378685	−	0.123042i
$86$	7.68815e6	+	5.58577e6i	0.140549	+	0.102115i
$87$		−	4.12166e7i		−	0.719441i
$88$	7.66340e6	+	1.97691e7i	0.127788	+	0.329652i
$89$	−4.52461e7			−0.721143			−0.360571	−	0.932732i	$-0.617418\pi$
$89$	−4.52461e7			−0.721143			−0.360571	+	0.932732i	$0.617418\pi$
$90$	−3.81025e7	+	5.24436e7i	−0.580743	+	0.799324i
$91$	1.39708e7	−	4.29976e7i	0.203730	−	0.627016i
$92$	1.30559e7	+	4.01820e7i	0.182245	+	0.560893i
$93$	−4.20899e7	+	3.05801e7i	−0.562660	+	0.408796i
$94$	1.90376e7	+	2.62030e7i	0.243838	+	0.335614i
$95$	1.30648e8	−	4.24500e7i	1.60401	−	0.521175i
$96$	6.09898e6	+	1.98168e6i	0.0718079	+	0.0233318i
$97$	−9.87571e7	−	7.17513e7i	−1.11553	−	0.810480i	−0.132005	−	0.991249i	$-0.542141\pi$
$97$	−9.87571e7	−	7.17513e7i	−1.11553	−	0.810480i	−0.983526	+	0.180769i	$0.942141\pi$
$98$			3.91420e7i			0.424364i
$99$	−4.36845e6	−	7.84144e7i	−0.0454765	−	0.816310i
$100$	−9.60407e7			−0.960407
$101$	−7.53110e7	+	1.03657e8i	−0.723724	+	0.996120i	0.275668	+	0.961253i	$0.411101\pi$
$101$	−7.53110e7	+	1.03657e8i	−0.723724	+	0.996120i	−0.999392	+	0.0348675i	$0.988899\pi$
$102$	2.35358e6	−	7.24357e6i	0.0217434	−	0.0669194i
$103$	7.91455e6	+	2.43585e7i	0.0703198	+	0.216422i	0.980040	−	0.198799i	$-0.0637042\pi$
$103$	7.91455e6	+	2.43585e7i	0.0703198	+	0.216422i	−0.909720	+	0.415221i	$0.863704\pi$
$104$	3.48871e7	−	2.53470e7i	0.298217	−	0.216667i
$105$	−3.29778e7	−	4.53901e7i	−0.271309	−	0.373425i
$106$	9.01090e7	−	2.92782e7i	0.713748	−	0.231911i
$107$	7.15149e7	+	2.32366e7i	0.545583	+	0.177271i	0.568824	−	0.822459i	$-0.307398\pi$
$107$	7.15149e7	+	2.32366e7i	0.545583	+	0.177271i	−0.0232408	+	0.999730i	$0.507398\pi$
$108$	−4.27225e7	−	3.10397e7i	−0.314023	−	0.228151i
$109$			1.44679e8i			1.02495i	0.858703	+	0.512473i	$0.171270\pi$
$109$			1.44679e8i			1.02495i	−0.858703	+	0.512473i	$0.828730\pi$
$110$	1.37135e8	−	1.11799e8i	0.936651	−	0.763605i
$111$	6.64763e7			0.437900
$112$	1.46212e7	−	2.01244e7i	0.0929206	−	0.127894i
$113$	8.70674e7	−	2.67966e8i	0.534001	−	1.64349i	−0.211797	−	0.977314i	$-0.567932\pi$
$113$	8.70674e7	−	2.67966e8i	0.534001	−	1.64349i	0.745798	−	0.666172i	$-0.232068\pi$
$114$	1.55552e7	+	4.78741e7i	0.0920995	+	0.283453i
$115$	2.85236e8	−	2.07236e8i	1.63085	−	1.18488i
$116$	−8.96345e7	−	1.23371e8i	−0.495043	−	0.681368i
$117$	−1.51914e8	+	4.93598e7i	−0.810688	+	0.263408i
$118$	−7.42424e7	−	2.41228e7i	−0.382934	−	0.124423i
$119$	−2.39011e7	−	1.73652e7i	−0.119187	−	0.0865947i
$120$		−	5.35147e7i		−	0.258076i
$121$	−4.31861e7	+	2.09964e8i	−0.201466	+	0.979495i
$122$	1.46777e8			0.662548
$123$	−4.80764e7	+	6.61716e7i	−0.210045	+	0.289102i
$124$	−5.94821e7	+	1.83067e8i	−0.251594	+	0.774326i
$125$	1.18726e8	+	3.65401e8i	0.486302	+	1.49668i
$126$	−7.45429e7	+	5.41586e7i	−0.295750	+	0.214875i
$127$	−1.58455e8	−	2.18095e8i	−0.609105	−	0.838361i	0.387399	−	0.921912i	$-0.373374\pi$
$127$	−1.58455e8	−	2.18095e8i	−0.609105	−	0.838361i	−0.996503	+	0.0835515i	$0.973374\pi$
$128$	2.25653e7	−	7.33191e6i	0.0840623	−	0.0273135i
$129$	2.76371e7	+	8.97982e6i	0.0998005	+	0.0324272i
$130$	−2.91130e8	−	2.11518e8i	−1.01933	−	0.740585i
$131$		−	3.69121e7i		−	0.125338i	−0.998034	−	0.0626691i	$-0.980039\pi$
$131$		−	3.69121e7i		−	0.125338i	0.998034	−	0.0626691i	$-0.0199613\pi$
$132$	4.09674e7	+	5.02513e7i	0.134941	+	0.165520i
$133$	1.95258e8			0.624025
$134$	4.11766e7	−	5.66747e7i	0.127712	−	0.175780i
$135$	−1.36177e8	+	4.19109e8i	−0.409985	+	1.26180i
$136$	−8.70788e6	−	2.68001e7i	−0.0254540	−	0.0783395i
$137$	1.51095e8	−	1.09777e8i	0.428912	−	0.311623i	−0.352302	−	0.935887i	$-0.614601\pi$
$137$	1.51095e8	−	1.09777e8i	0.428912	−	0.311623i	0.781214	+	0.624264i	$0.214601\pi$
$138$	7.59390e7	+	1.04521e8i	0.209386	+	0.288196i
$139$	−4.16550e8	+	1.35345e8i	−1.11585	+	0.362563i	−0.808184	−	0.588930i	$-0.799549\pi$
$139$	−4.16550e8	+	1.35345e8i	−1.11585	+	0.362563i	−0.307671	+	0.951493i	$0.599549\pi$
$140$	−1.97421e8	−	6.41460e7i	−0.513904	−	0.166977i
$141$	8.01258e7	+	5.82148e7i	0.202720	+	0.147284i
$142$		−	2.88806e8i		−	0.710317i
$143$	4.35302e8	−	2.42506e7i	1.04099	−	0.0579933i
$144$	−8.78857e7			−0.204394
$145$	−7.47992e8	+	1.02952e9i	−1.69210	+	2.32897i
$146$	−4.94962e7	+	1.52334e8i	−0.108933	+	0.335262i
$147$	3.69867e7	+	1.13833e8i	0.0792094	+	0.243781i
$148$	1.98979e8	−	1.44567e8i	0.414726	−	0.301316i
$149$	−3.88236e8	−	5.34361e8i	−0.787681	−	1.08415i	−0.994393	−	0.105748i	$-0.966276\pi$
$149$	−3.88236e8	−	5.34361e8i	−0.787681	−	1.08415i	0.206712	−	0.978402i	$-0.433724\pi$
$150$	−2.79307e8	+	9.07525e7i	−0.551718	+	0.179264i
$151$	−8.58104e8	−	2.78815e8i	−1.65056	−	0.536301i	−0.671701	−	0.740822i	$-0.734436\pi$
$151$	−8.58104e8	−	2.78815e8i	−1.65056	−	0.536301i	−0.978862	+	0.204522i	$0.934436\pi$
$152$	1.50673e8	+	1.09470e8i	0.282268	+	0.205080i
$153$			1.04379e8i			0.190479i
$154$	2.34488e8	−	9.08986e7i	0.416906	−	0.161612i
$155$	1.60630e9			2.78291
$156$	7.75081e7	−	1.06681e8i	0.130873	−	0.180131i
$157$	1.46345e8	−	4.50403e8i	0.240868	−	0.741315i	−0.755421	−	0.655240i	$-0.772567\pi$
$157$	1.46345e8	−	4.50403e8i	0.240868	−	0.741315i	0.996289	−	0.0860753i	$-0.0274326\pi$
$158$	1.78531e8	+	5.49463e8i	0.286474	+	0.881678i
$159$	2.34391e8	−	1.70295e8i	0.366735	−	0.266448i
$160$	−1.16379e8	−	1.60182e8i	−0.177581	−	0.244419i
$161$	4.76614e8	−	1.54861e8i	0.709355	−	0.230483i
$162$	2.25109e8	+	7.31425e7i	0.326839	+	0.106196i
$163$	−3.90491e8	−	2.83708e8i	−0.553172	−	0.401903i	0.275782	−	0.961220i	$-0.411063\pi$
$163$	−3.90491e8	−	2.83708e8i	−0.553172	−	0.401903i	−0.828954	+	0.559317i	$0.811063\pi$
$164$			3.02620e8i			0.418333i
$165$	2.93175e8	−	4.54721e8i	0.395541	−	0.613493i
$166$	3.50552e8			0.461658
$167$	5.07907e8	−	6.99074e8i	0.653008	−	0.898788i	−0.346217	−	0.938154i	$-0.612534\pi$
$167$	5.07907e8	−	6.99074e8i	0.653008	−	0.898788i	0.999225	+	0.0393662i	$0.0125339\pi$
$168$	2.35055e7	−	7.23424e7i	0.0295074	−	0.0908146i
$169$	−2.19359e7	−	6.75118e7i	−0.0268911	−	0.0827624i
$170$	−1.90243e8	+	1.38220e8i	−0.227779	+	0.165491i
$171$	−4.05490e8	−	5.58109e8i	−0.474237	−	0.652732i
$172$	1.02253e8	−	3.32240e7i	0.116832	−	0.0379610i
$173$	−9.05244e8	−	2.94131e8i	−1.01060	−	0.328365i	−0.243509	−	0.969899i	$-0.578299\pi$
$173$	−9.05244e8	−	2.94131e8i	−1.01060	−	0.328365i	−0.767095	+	0.641533i	$0.778299\pi$
$174$	−3.77255e8	−	2.74092e8i	−0.411565	−	0.299019i
$175$			1.13918e9i			1.21461i
$176$	2.31908e8	+	6.13218e7i	0.241693	+	0.0639094i
$177$	−2.38708e8			−0.243205
$178$	−3.00888e8	+	4.14137e8i	−0.299726	+	0.412538i
$179$	1.91175e8	−	5.88377e8i	0.186217	−	0.573117i	−0.813750	−	0.581215i	$-0.802578\pi$
$179$	1.91175e8	−	5.88377e8i	0.186217	−	0.573117i	0.999967	+	0.00809762i	$0.00257758\pi$
$180$	2.26633e8	+	6.97504e8i	0.215890	+	0.664441i
$181$	2.40035e8	−	1.74396e8i	0.223645	−	0.162488i	−0.470321	−	0.882496i	$-0.655862\pi$
$181$	2.40035e8	−	1.74396e8i	0.223645	−	0.162488i	0.693966	+	0.720008i	$0.255862\pi$
$182$	−3.00650e8	−	4.13810e8i	−0.274016	−	0.377151i
$183$	4.26859e8	−	1.38695e8i	0.380610	−	0.123668i
$184$	4.54608e8	+	1.47711e8i	0.396612	+	0.128867i
$185$	−1.66047e9	−	1.20640e9i	−1.41757	−	1.02992i
$186$			5.88607e8i			0.491783i
$187$	7.28300e7	−	2.75429e8i	0.0595585	−	0.225239i
$188$	3.66436e8			0.293337
$189$	−3.68174e8	+	5.06748e8i	−0.288540	+	0.397141i
$190$	4.80267e8	−	1.47811e9i	0.368526	−	1.13421i
$191$	6.58090e8	+	2.02539e9i	0.494484	+	1.52186i	0.817760	+	0.575559i	$0.195216\pi$
$191$	6.58090e8	+	2.02539e9i	0.494484	+	1.52186i	−0.323276	+	0.946305i	$0.604784\pi$
$192$	5.86967e7	−	4.26456e7i	0.0431925	−	0.0313812i
$193$	1.08850e9	+	1.49820e9i	0.784513	+	1.07979i	0.994770	+	0.102143i	$0.0325701\pi$
$193$	1.08850e9	+	1.49820e9i	0.784513	+	1.07979i	−0.210257	+	0.977646i	$0.567430\pi$
$194$	−1.31348e9	+	4.26774e8i	−0.927289	+	0.301295i
$195$	−1.04654e9	−	3.40042e8i	−0.723799	−	0.235177i
$196$	3.58266e8	+	2.60295e8i	0.242762	+	0.176377i
$197$		−	3.43133e8i		−	0.227823i	−0.993491	−	0.113911i	$-0.963662\pi$
$197$		−	3.43133e8i		−	0.227823i	0.993491	−	0.113911i	$-0.0363380\pi$
$198$	−7.46776e8	−	4.81474e8i	−0.485881	−	0.313265i
$199$	4.34496e8			0.277060			0.138530	−	0.990358i	$-0.455762\pi$
$199$	4.34496e8			0.277060			0.138530	+	0.990358i	$0.455762\pi$
$200$	−6.38674e8	+	8.79059e8i	−0.399171	+	0.549412i
$201$	6.61965e7	−	2.03732e8i	0.0405556	−	0.124817i
$202$	4.47947e8	+	1.37864e9i	0.269043	+	0.828029i
$203$	−1.46335e9	+	1.06319e9i	−0.861718	+	0.626075i
$204$	−5.06489e7	−	6.97122e7i	−0.0292448	−	0.0402521i
$205$	2.40174e9	−	7.80373e8i	1.35991	−	0.441862i
$206$	2.75585e8	+	8.95429e7i	0.153033	+	0.0497236i
$207$	−1.43242e9	−	1.04072e9i	−0.780171	−	0.566827i
$208$		−	4.87879e8i		−	0.260651i
$209$	6.80565e8	+	1.75563e9i	0.356685	+	0.920130i
$210$	−6.34758e8			−0.326386
$211$	−1.49139e9	+	2.05272e9i	−0.752422	+	1.03562i	0.245385	+	0.969426i	$0.421086\pi$
$211$	−1.49139e9	+	2.05272e9i	−0.752422	+	1.03562i	−0.997807	+	0.0661942i	$0.978914\pi$
$212$	3.31245e8	−	1.01947e9i	0.163986	−	0.504696i
$213$	−2.72903e8	−	8.39910e8i	−0.132584	−	0.408051i
$214$	6.88260e8	−	5.00050e8i	0.328169	−	0.238429i
$215$	−5.27363e8	−	7.25854e8i	−0.246806	−	0.339700i
$216$	−5.68211e8	+	1.84623e8i	−0.261033	+	0.0848147i
$217$	2.17143e9	+	7.05541e8i	0.979280	+	0.318188i
$218$	1.32425e9	+	9.62123e8i	0.586332	+	0.425995i
$219$			4.89791e8i			0.212929i
$220$	−1.11345e8	−	1.99866e9i	−0.0475314	−	0.853196i
$221$	−5.79439e8			−0.242906
$222$	4.42069e8	−	6.08456e8i	0.182003	−	0.250506i
$223$	−1.45996e9	+	4.49328e9i	−0.590364	+	1.81695i	−0.0137973	+	0.999905i	$0.504392\pi$
$223$	−1.45996e9	+	4.49328e9i	−0.590364	+	1.81695i	−0.576567	+	0.817050i	$0.695608\pi$
$224$	−8.69667e7	−	2.67656e8i	−0.0345431	−	0.106313i
$225$	3.25613e9	−	2.36571e9i	1.27049	−	0.923065i
$226$	−1.87369e9	−	2.57891e9i	−0.718230	−	0.988558i
$227$	−5.82710e8	+	1.89334e8i	−0.219457	+	0.0713058i	−0.416682	−	0.909052i	$-0.636807\pi$
$227$	−5.82710e8	+	1.89334e8i	−0.219457	+	0.0713058i	0.197225	+	0.980358i	$0.436807\pi$
$228$	5.41634e8	+	1.75987e8i	0.200432	+	0.0651242i
$229$	4.91616e8	+	3.57180e8i	0.178766	+	0.129881i	0.673570	−	0.739124i	$-0.264760\pi$
$229$	4.91616e8	+	3.57180e8i	0.178766	+	0.129881i	−0.494804	+	0.869005i	$0.664760\pi$
$230$		−	3.98889e9i		−	1.42541i
$231$	5.96050e8	−	4.85930e8i	0.209332	−	0.170658i
$232$	−1.72529e9			−0.595538
$233$	−2.52553e8	+	3.47609e8i	−0.0856897	+	0.117942i	−0.849710	−	0.527251i	$-0.823223\pi$
$233$	−2.52553e8	+	3.47609e8i	−0.0856897	+	0.117942i	0.764020	+	0.645193i	$0.223223\pi$
$234$	−5.58442e8	+	1.71871e9i	−0.186258	+	0.573243i
$235$	−9.44937e8	−	2.90822e9i	−0.309836	−	0.953577i
$236$	−7.14510e8	+	5.19122e8i	−0.230335	+	0.167348i
$237$	1.03842e9	+	1.42926e9i	0.329138	+	0.453020i
$238$	−3.17886e8	+	1.03288e8i	−0.0990750	+	0.0321914i
$239$	−5.43864e9	−	1.76712e9i	−1.66686	−	0.541595i	−0.684566	−	0.728951i	$-0.740008\pi$
$239$	−5.43864e9	−	1.76712e9i	−1.66686	−	0.541595i	−0.982292	+	0.187356i	$0.940008\pi$
$240$	−4.89819e8	−	3.55874e8i	−0.147635	−	0.107263i
$241$		−	1.76141e9i		−	0.522146i	−0.965319	−	0.261073i	$-0.915924\pi$
$241$		−	1.76141e9i		−	0.522146i	0.965319	−	0.261073i	$-0.0840764\pi$
$242$	1.63460e9	+	1.79155e9i	0.476597	+	0.522356i
$243$	3.43060e9			0.983886
$244$	9.76069e8	−	1.34344e9i	0.275373	−	0.379018i
$245$	1.14196e9	−	3.51460e9i	0.316948	−	0.975465i
$246$	2.85957e8	+	8.80086e8i	0.0780837	+	0.240317i
$247$	3.09823e9	−	2.25099e9i	0.832388	−	0.604765i
$248$	1.28005e9	+	1.76184e9i	0.338393	+	0.465758i
$249$	1.01948e9	−	3.31250e8i	0.265206	−	0.0861705i
$250$	4.13404e9	+	1.34323e9i	1.05832	+	0.343867i
$251$	4.19223e9	+	3.04583e9i	1.05621	+	0.767381i	0.973383	−	0.229183i	$-0.0736055\pi$
$251$	4.19223e9	+	3.04583e9i	1.05621	+	0.767381i	0.0828258	+	0.996564i	$0.473606\pi$
$252$			1.04245e9i			0.258495i
$253$	3.05364e9	+	3.74565e9i	0.745308	+	0.914208i
$254$	−3.04995e9			−0.732754
$255$	−4.22661e8	+	5.81742e8i	−0.0999611	+	0.137585i
$256$	8.29511e7	−	2.55297e8i	0.0193136	−	0.0594410i
$257$	−2.48258e9	−	7.64059e9i	−0.569076	−	1.75144i	−0.655519	−	0.755179i	$-0.727550\pi$
$257$	−2.48258e9	−	7.64059e9i	−0.569076	−	1.75144i	0.0864425	−	0.996257i	$-0.472450\pi$
$258$	2.65979e8	−	1.93245e8i	0.0600301	−	0.0436144i
$259$	−1.71477e9	−	2.36017e9i	−0.381071	−	0.524499i
$260$	−3.87205e9	+	1.25810e9i	−0.847320	+	0.275311i
$261$	6.07786e9	+	1.97482e9i	1.30975	+	0.425564i
$262$	−3.37856e8	−	2.45467e8i	−0.0717012	−	0.0520939i
$263$			4.55854e9i			0.952803i	0.879228	+	0.476401i	$0.158059\pi$
$263$			4.55854e9i			0.952803i	−0.879228	+	0.476401i	$0.841941\pi$
$264$	7.32384e8	−	4.08009e7i	0.150773	−	0.00839952i
$265$	−8.94517e9			−1.81387
$266$	1.29847e9	−	1.78719e9i	0.259362	−	0.356981i
$267$	−4.83715e8	+	1.48872e9i	−0.0951797	+	0.292933i
$268$	−2.44917e8	−	7.53777e8i	−0.0474766	−	0.146118i
$269$	−6.16850e9	+	4.48168e9i	−1.17807	+	0.855916i	−0.991952	−	0.126611i	$-0.959590\pi$
$269$	−6.16850e9	+	4.48168e9i	−1.17807	+	0.855916i	−0.186116	+	0.982528i	$0.559590\pi$
$270$	2.93052e9	+	4.03351e9i	0.551428	+	0.758976i
$271$	−1.94626e9	+	6.32378e8i	−0.360847	+	0.117246i	−0.483829	−	0.875162i	$-0.660754\pi$
$271$	−1.94626e9	+	6.32378e8i	−0.360847	+	0.117246i	0.122982	+	0.992409i	$0.460754\pi$
$272$	−3.03209e8	−	9.85184e7i	−0.0553944	−	0.0179987i
$273$	−1.26538e9	−	9.19354e8i	−0.227809	−	0.165513i
$274$		−	2.11299e9i		−	0.374883i
$275$	−1.02427e10	+	3.97056e9i	−1.79096	+	0.694258i
$276$	1.46168e9			0.251892
$277$	−2.42658e9	+	3.33989e9i	−0.412168	+	0.567301i	−0.963746	−	0.266823i	$-0.914026\pi$
$277$	−2.42658e9	+	3.33989e9i	−0.412168	+	0.567301i	0.551577	+	0.834124i	$0.314026\pi$
$278$	−1.53126e9	+	4.71272e9i	−0.256371	+	0.789028i
$279$	−2.49273e9	−	7.67183e9i	−0.411394	−	1.26614i
$280$	−1.89998e9	+	1.38042e9i	−0.309113	+	0.224584i
$281$	1.99277e9	+	2.74282e9i	0.319619	+	0.439918i	0.938351	−	0.345684i	$-0.112353\pi$
$281$	1.99277e9	+	2.74282e9i	0.319619	+	0.439918i	−0.618732	+	0.785602i	$0.712353\pi$
$282$	1.06568e9	−	3.46260e8i	0.168512	−	0.0547527i
$283$	3.38836e9	+	1.10094e9i	0.528255	+	0.171640i	0.560988	−	0.827824i	$-0.310421\pi$
$283$	3.38836e9	+	1.10094e9i	0.528255	+	0.171640i	−0.0327335	+	0.999464i	$0.510421\pi$
$284$	−2.64343e9	−	1.92057e9i	−0.406345	−	0.295227i
$285$		−	4.75249e9i		−	0.720347i
$286$	2.67280e9	−	4.14558e9i	0.399487	−	0.619613i
$287$	3.58949e9			0.529061
$288$	−5.84443e8	+	8.04416e8i	−0.0849517	+	0.116926i
$289$	2.03862e9	−	6.27423e9i	0.292244	−	0.899433i
$290$	4.44903e9	+	1.36927e10i	0.629033	+	1.93597i
$291$	−3.41660e9	+	2.48231e9i	−0.476456	+	0.346165i
$292$	1.06516e9	+	1.46606e9i	0.146515	+	0.201661i
$293$	9.64201e9	−	3.13288e9i	1.30827	−	0.425083i	0.429819	−	0.902915i	$-0.358578\pi$
$293$	9.64201e9	−	3.13288e9i	1.30827	−	0.425083i	0.878451	+	0.477833i	$0.158578\pi$
$294$	1.28788e9	+	4.18457e8i	0.172380	+	0.0560095i
$295$	5.96252e9	+	4.33203e9i	0.787303	+	0.572009i
$296$		−	2.78263e9i		−	0.362484i
$297$	−5.83961e9	−	1.54413e9i	−0.750512	−	0.198453i
$298$	−7.47277e9			−0.947582
$299$	5.77732e9	−	7.95180e9i	0.722839	−	0.994903i
$300$	−1.02675e9	+	3.16000e9i	−0.126759	+	0.390124i
$301$	−3.94083e8	−	1.21286e9i	−0.0480088	−	0.147756i
$302$	−8.25841e9	+	6.00008e9i	−0.992815	+	0.721323i
$303$	2.60546e9	+	3.58611e9i	0.309111	+	0.425454i
$304$	2.00396e9	−	6.51127e8i	0.234636	−	0.0762380i
$305$	−1.31792e10	−	4.28219e9i	−1.52297	−	0.494842i
$306$	9.55380e8	+	6.94124e8i	0.108966	+	0.0791683i
$307$			9.83433e9i			1.10711i	0.832812	+	0.553556i	$0.186729\pi$
$307$			9.83433e9i			1.10711i	−0.832812	+	0.553556i	$0.813271\pi$
$308$	7.27362e8	−	2.75075e9i	0.0808254	−	0.305666i
$309$	8.86074e8			0.0971932
$310$	1.06819e10	−	1.47024e10i	1.15665	−	1.59200i
$311$	3.58476e9	−	1.10328e10i	0.383194	−	1.17935i	−0.554588	−	0.832125i	$-0.687124\pi$
$311$	3.58476e9	−	1.10328e10i	0.383194	−	1.17935i	0.937782	−	0.347225i	$-0.112876\pi$
$312$	−4.61016e8	−	1.41886e9i	−0.0486516	−	0.149734i
$313$	4.17139e9	−	3.03069e9i	0.434614	−	0.315766i	−0.348877	−	0.937168i	$-0.613437\pi$
$313$	4.17139e9	−	3.03069e9i	0.434614	−	0.315766i	0.783491	+	0.621403i	$0.213437\pi$
$314$	−3.14934e9	−	4.33469e9i	−0.323967	−	0.445902i
$315$	8.27336e9	−	2.68818e9i	0.840310	−	0.273033i
$316$	6.21646e9	+	2.01985e9i	0.623440	+	0.202568i
$317$	1.04313e10	+	7.57882e9i	1.03301	+	0.750524i	0.968908	−	0.247420i	$-0.0795826\pi$
$317$	1.04313e10	+	7.57882e9i	1.03301	+	0.750524i	0.0640990	+	0.997944i	$0.479583\pi$
$318$		−	3.27784e9i		−	0.320538i
$319$	−1.46600e10	−	9.45183e9i	−1.41570	−	0.912753i
$320$	−2.24007e9			−0.213630
$321$	1.52910e9	−	2.10462e9i	0.144017	−	0.198223i
$322$	1.75206e9	−	5.39228e9i	0.162976	−	0.501590i
$323$	−7.73323e8	−	2.38004e9i	−0.0710478	−	0.218663i
$324$	2.16646e9	−	1.57402e9i	0.196594	−	0.142834i
$325$	1.31328e10	+	1.80757e10i	1.17713	+	1.62018i
$326$	−5.19355e9	+	1.68749e9i	−0.459826	+	0.149407i
$327$	4.76035e9	+	1.54673e9i	0.416340	+	0.135277i
$328$	2.76988e9	+	2.01243e9i	0.239312	+	0.173871i
$329$		−	4.34645e9i		−	0.370980i
$330$	−2.21243e9	−	5.70734e9i	−0.186558	−	0.481258i
$331$	5.68069e9			0.473249			0.236624	−	0.971601i	$-0.423959\pi$
$331$	5.68069e9			0.473249			0.236624	+	0.971601i	$0.423959\pi$
$332$	2.33118e9	−	3.20860e9i	0.191878	−	0.264097i
$333$	−3.18509e9	+	9.80269e9i	−0.259027	+	0.797202i
$334$	−3.02102e9	−	9.29773e9i	−0.242754	−	0.747121i
$335$	−5.35077e9	+	3.88756e9i	−0.424851	+	0.308673i
$336$	−5.05836e8	−	6.96224e8i	−0.0396874	−	0.0546251i
$337$	−1.77889e10	+	5.77997e9i	−1.37921	+	0.448132i	−0.902409	−	0.430880i	$-0.858203\pi$
$337$	−1.77889e10	+	5.77997e9i	−1.37921	+	0.448132i	−0.476800	+	0.879012i	$0.658203\pi$
$338$	−7.63809e8	−	2.48177e8i	−0.0585218	−	0.0190149i
$339$	−7.88600e9	−	5.72952e9i	−0.597115	−	0.433830i
$340$			2.66046e9i			0.199086i
$341$	1.22468e9	+	2.19833e10i	0.0905745	+	1.62583i
$342$	−7.80488e9			−0.570508
$343$	8.23203e9	−	1.13304e10i	0.594744	−	0.818595i
$344$	3.75887e8	−	1.15686e9i	0.0268425	−	0.0826127i
$345$	−3.76926e9	−	1.16006e10i	−0.266060	−	0.818848i
$346$	−8.71208e9	+	6.32970e9i	−0.607879	+	0.441650i
$347$	4.69700e8	+	6.46487e8i	0.0323969	+	0.0445904i	0.824908	−	0.565267i	$-0.191227\pi$
$347$	4.69700e8	+	6.46487e8i	0.0323969	+	0.0445904i	−0.792511	+	0.609857i	$0.791227\pi$
$348$	−5.01751e9	+	1.63029e9i	−0.342115	+	0.111160i
$349$	−1.01174e10	−	3.28734e9i	−0.681973	−	0.221586i	−0.0525141	−	0.998620i	$-0.516723\pi$
$349$	−1.01174e10	−	3.28734e9i	−0.681973	−	0.221586i	−0.629459	+	0.777034i	$0.716723\pi$
$350$	1.04269e10	+	7.57555e9i	0.694834	+	0.504827i
$351$			1.22852e10i			0.809380i
$352$	2.10347e9	−	1.71485e9i	0.137014	−	0.111701i
$353$	3.09645e9			0.199419			0.0997093	−	0.995017i	$-0.468209\pi$
$353$	3.09645e9			0.199419			0.0997093	+	0.995017i	$0.468209\pi$
$354$	−1.58741e9	+	2.18489e9i	−0.101083	+	0.139128i
$355$	−8.42587e9	+	2.59322e10i	−0.530520	+	1.63277i
$356$	1.78967e9	+	5.50805e9i	0.111423	+	0.342924i
$357$	−8.26883e8	+	6.00766e8i	−0.0509063	+	0.0369856i
$358$	−4.11408e9	−	5.66255e9i	−0.250461	−	0.344731i
$359$	1.10011e10	−	3.57447e9i	0.662305	−	0.215196i	0.0414732	−	0.999140i	$-0.486795\pi$
$359$	1.10011e10	−	3.57447e9i	0.662305	−	0.215196i	0.620832	+	0.783944i	$0.286795\pi$
$360$	7.89135e9	+	2.56406e9i	0.469831	+	0.152657i
$361$	−3.59124e8	−	2.60919e8i	−0.0211454	−	0.0153630i
$362$		−	3.35677e9i		−	0.195473i
$363$	6.44669e9	+	3.66561e9i	0.371287	+	0.211115i
$364$	−5.78693e9			−0.329642
$365$	8.88864e9	−	1.22342e10i	0.500800	−	0.689291i
$366$	1.56915e9	−	4.82935e9i	0.0874462	−	0.269132i
$367$	−3.30334e9	−	1.01666e10i	−0.182091	−	0.560419i	0.817795	−	0.575510i	$-0.195196\pi$
$367$	−3.30334e9	−	1.01666e10i	−0.182091	−	0.560419i	−0.999886	+	0.0150907i	$0.995196\pi$
$368$	4.37515e9	−	3.17873e9i	0.238562	−	0.173326i
$369$	−7.45426e9	−	1.02599e10i	−0.402068	−	0.553399i
$370$	−2.20843e10	+	7.17563e9i	−1.17836	+	0.382872i
$371$	−1.20923e10	−	3.92902e9i	−0.638282	−	0.207391i
$372$	5.38751e9	+	3.91425e9i	0.281330	+	0.204398i
$373$			1.95937e10i			1.01224i	0.862464	+	0.506118i	$0.168920\pi$
$373$			1.95937e10i			1.01224i	−0.862464	+	0.506118i	$0.831080\pi$
$374$	−2.03668e9	−	2.49823e9i	−0.104096	−	0.127687i
$375$	1.32920e10			0.672148
$376$	2.43681e9	−	3.35399e9i	0.121919	−	0.167807i
$377$	−1.09628e10	+	3.37400e10i	−0.542695	+	1.67024i
$378$	2.18989e9	+	6.73977e9i	0.107264	+	0.330125i
$379$	1.75711e10	−	1.27662e10i	0.851613	−	0.618733i	−0.0739771	−	0.997260i	$-0.523569\pi$
$379$	1.75711e10	−	1.27662e10i	0.851613	−	0.618733i	0.925590	+	0.378527i	$0.123569\pi$
$380$	−1.03353e10	−	1.42253e10i	−0.495666	−	0.682226i
$381$	−8.86994e9	+	2.88202e9i	−0.420940	+	0.136772i
$382$	2.29147e10	+	7.44544e9i	1.07612	+	0.349653i
$383$	2.36477e10	+	1.71811e10i	1.09899	+	0.798464i	0.980895	−	0.194538i	$-0.0623208\pi$
$383$	2.36477e10	+	1.71811e10i	1.09899	+	0.798464i	0.118096	+	0.993002i	$0.462321\pi$
$384$		−	8.20844e8i		−	0.0377517i
$385$	−2.37069e10	+	1.32071e9i	−1.07903	+	0.0601124i
$386$	2.09515e10			0.943771
$387$	−2.64836e9	+	3.64515e9i	−0.118068	+	0.162507i
$388$	−4.82840e9	+	1.48603e10i	−0.213047	+	0.655692i
$389$	−1.00160e10	−	3.08260e10i	−0.437416	−	1.34623i	−0.890590	−	0.454807i	$-0.849708\pi$
$389$	−1.00160e10	−	3.08260e10i	−0.437416	−	1.34623i	0.453174	−	0.891422i	$-0.350292\pi$
$390$	−1.00719e10	+	7.31769e9i	−0.435366	+	0.316312i
$391$	−3.77528e9	−	5.19623e9i	−0.161526	−	0.222321i
$392$	4.76496e9	−	1.54823e9i	0.201797	−	0.0655678i
$393$	−1.21451e9	−	3.94618e8i	−0.0509133	−	0.0165427i
$394$	−3.14069e9	−	2.28184e9i	−0.130329	−	0.0946893i
$395$		−	5.45455e10i		−	2.24063i
$396$	−9.37301e9	+	3.63341e9i	−0.381152	+	0.147752i
$397$	7.06636e9			0.284468			0.142234	−	0.989833i	$-0.454571\pi$
$397$	7.06636e9			0.284468			0.142234	+	0.989833i	$0.454571\pi$
$398$	2.88942e9	−	3.97694e9i	0.115154	−	0.158495i
$399$	2.08745e9	−	6.42453e9i	0.0823617	−	0.253483i
$400$	3.79881e9	+	1.16915e10i	0.148391	+	0.456701i
$401$	2.73892e8	−	1.98995e8i	0.0105926	−	0.00769597i	−0.582476	−	0.812848i	$-0.697916\pi$
$401$	2.73892e8	−	1.98995e8i	0.0105926	−	0.00769597i	0.593069	+	0.805152i	$0.297916\pi$
$402$	−1.42455e9	−	1.96072e9i	−0.0545471	−	0.0750777i
$403$	4.25886e10	−	1.38379e10i	1.61463	−	0.524625i
$404$	1.55975e10	+	5.06795e9i	0.585505	+	0.190242i
$405$	−1.80789e10	−	1.31351e10i	−0.671973	−	0.488217i
$406$			2.04643e10i			0.753169i
$407$	1.52444e10	−	2.36444e10i	0.555562	−	0.861689i
$408$	−9.74891e8			−0.0351816
$409$	−1.31114e9	+	1.80463e9i	−0.0468549	+	0.0644903i	−0.831802	−	0.555073i	$-0.812690\pi$
$409$	−1.31114e9	+	1.80463e9i	−0.0468549	+	0.0644903i	0.784947	+	0.619563i	$0.212690\pi$
$410$	8.82891e9	−	2.71726e10i	0.312444	−	0.961602i
$411$	−1.99665e9	−	6.14505e9i	−0.0699736	−	0.215357i
$412$	2.65223e9	−	1.92696e9i	0.0920498	−	0.0668781i
$413$	6.15750e9	+	8.47508e9i	0.211643	+	0.291302i
$414$	−1.90513e10	+	6.19015e9i	−0.648520	+	0.210717i
$415$	−3.14765e10	−	1.02273e10i	−1.06119	−	0.344802i
$416$	−4.46555e9	−	3.24441e9i	−0.149108	−	0.108333i
$417$			1.51526e10i			0.501121i
$418$	2.05951e10	+	5.44582e9i	0.674619	+	0.178385i
$419$	−2.81081e10			−0.911960			−0.455980	−	0.889990i	$-0.650711\pi$
$419$	−2.81081e10			−0.911960			−0.455980	+	0.889990i	$0.650711\pi$
$420$	−4.22116e9	+	5.80993e9i	−0.135655	+	0.186713i
$421$	8.10853e9	−	2.49555e10i	0.258115	−	0.794397i	−0.735085	−	0.677975i	$-0.762858\pi$
$421$	8.10853e9	−	2.49555e10i	0.258115	−	0.794397i	0.993200	−	0.116422i	$-0.0371424\pi$
$422$	8.87074e9	+	2.73013e10i	0.279711	+	0.860863i
$423$	−1.24235e10	+	9.02621e9i	−0.388046	+	0.281932i
$424$	−7.12837e9	−	9.81136e9i	−0.220560	−	0.303575i
$425$	1.38857e10	−	4.51173e9i	0.425609	−	0.138289i
$426$	−9.50250e9	−	3.08755e9i	−0.288536	−	0.0937509i
$427$	−1.59351e10	−	1.15775e10i	−0.479340	−	0.348261i
$428$		−	9.62498e9i		−	0.286830i
$429$	3.85579e9	−	1.45819e10i	0.113837	−	0.430511i
$430$	−1.01507e10			−0.296908
$431$	−1.45476e10	+	2.00230e10i	−0.421581	+	0.580257i	−0.965995	−	0.258560i	$-0.916752\pi$
$431$	−1.45476e10	+	2.00230e10i	−0.421581	+	0.580257i	0.544414	+	0.838817i	$0.316752\pi$
$432$	−2.08877e9	+	6.42858e9i	−0.0599730	+	0.184578i
$433$	9.07110e9	+	2.79180e10i	0.258053	+	0.794205i	0.993213	+	0.116311i	$0.0371070\pi$
$433$	9.07110e9	+	2.79180e10i	0.258053	+	0.794205i	−0.735160	+	0.677894i	$0.762893\pi$
$434$	2.08979e10	−	1.51832e10i	0.589038	−	0.427961i
$435$	2.58775e10	+	3.56174e10i	0.722713	+	0.994729i
$436$	1.76126e10	−	5.72268e9i	0.487391	−	0.158363i
$437$	4.03724e10	+	1.31178e10i	1.10703	+	0.359696i
$438$	4.48305e9	+	3.25712e9i	0.121808	+	0.0884989i
$439$			3.37729e10i			0.909307i	0.890668	+	0.454653i	$0.150237\pi$
$439$			3.37729e10i			0.909307i	−0.890668	+	0.454653i	$0.849763\pi$
$440$	−1.90342e10	−	1.22720e10i	−0.507836	−	0.327421i
$441$	−1.85582e10			−0.490661
$442$	−3.85329e9	+	5.30359e9i	−0.100958	+	0.138957i
$443$	7.28059e9	−	2.24073e10i	0.189039	−	0.581802i	−0.810956	−	0.585108i	$-0.801052\pi$
$443$	7.28059e9	−	2.24073e10i	0.189039	−	0.581802i	0.999995	+	0.00330556i	$0.00105219\pi$
$444$	−2.62941e9	−	8.09250e9i	−0.0676592	−	0.208234i
$445$	3.90995e10	−	2.84074e10i	0.997082	−	0.724422i
$446$	3.14182e10	+	4.32434e10i	0.794038	+	1.09290i
$447$	−2.17325e10	+	7.06131e9i	−0.544351	+	0.176870i
$448$	−3.02818e9	−	9.83915e8i	−0.0751743	−	0.0244256i
$449$	−2.45445e10	−	1.78326e10i	−0.603905	−	0.438763i	0.243358	−	0.969937i	$-0.421751\pi$
$449$	−2.45445e10	−	1.78326e10i	−0.603905	−	0.438763i	−0.847263	+	0.531174i	$0.821751\pi$
$450$		−	4.55353e10i		−	1.11045i
$451$	1.25111e10	+	3.22744e10i	0.302404	+	0.780104i
$452$	−3.60648e10			−0.864031
$453$	−1.83476e10	+	2.52533e10i	−0.435698	+	0.599687i
$454$	−2.14207e9	+	6.59261e9i	−0.0504208	+	0.155179i
$455$	1.49229e10	+	4.59279e10i	0.348182	+	1.07159i
$456$	5.21269e9	−	3.78724e9i	0.120560	−	0.0875918i
$457$	−1.82289e10	−	2.50899e10i	−0.417922	−	0.575220i	0.547207	−	0.836998i	$-0.315691\pi$
$457$	−1.82289e10	−	2.50899e10i	−0.417922	−	0.575220i	−0.965128	+	0.261778i	$0.915691\pi$
$458$	6.53853e9	−	2.12450e9i	0.148600	−	0.0482830i
$459$	7.63502e9	+	2.48077e9i	0.172012	+	0.0558902i
$460$	−3.65103e10	−	2.65263e10i	−0.815424	−	0.592440i
$461$			6.82285e10i			1.51064i	0.655354	+	0.755322i	$0.272519\pi$
$461$			6.82285e10i			1.51064i	−0.655354	+	0.755322i	$0.727481\pi$
$462$	−4.83956e8	−	8.68709e9i	−0.0106228	−	0.190681i
$463$	−1.83777e10			−0.399915			−0.199957	−	0.979805i	$-0.564080\pi$
$463$	−1.83777e10			−0.399915			−0.199957	+	0.979805i	$0.564080\pi$
$464$	−1.14732e10	+	1.57915e10i	−0.247522	+	0.340684i
$465$	1.71725e10	−	5.28516e10i	0.367301	−	1.13044i
$466$	1.50218e9	+	4.62322e9i	0.0318550	+	0.0980395i
$467$	−3.03732e10	+	2.20674e10i	−0.638591	+	0.463964i	−0.859366	−	0.511361i	$-0.829141\pi$
$467$	−3.03732e10	+	2.20674e10i	−0.638591	+	0.463964i	0.220775	+	0.975325i	$0.429141\pi$
$468$	1.20176e10	+	1.65409e10i	0.250516	+	0.344806i
$469$	−8.94084e9	+	2.90506e9i	−0.184794	+	0.0600431i
$470$	−3.29027e10	−	1.06907e10i	−0.674280	−	0.219087i
$471$	−1.32550e10	−	9.63030e9i	−0.269337	−	0.195684i
$472$			9.99207e9i			0.201320i
$473$	9.53171e9	−	7.77073e9i	0.190426	−	0.155245i
$474$	1.99875e10			0.395954
$475$	−5.67188e10	+	7.80668e10i	−1.11417	+	1.53353i
$476$	−1.16857e9	+	3.59647e9i	−0.0227628	+	0.0700566i
$477$	1.38815e10	+	4.27230e10i	0.268141	+	0.825254i
$478$	−5.23415e10	+	3.80283e10i	−1.00262	+	0.728444i
$479$	−3.66993e10	−	5.05122e10i	−0.697133	−	0.959521i	−0.999979	−	0.00648141i	$-0.997937\pi$
$479$	−3.66993e10	−	5.05122e10i	−0.697133	−	0.959521i	0.302846	−	0.953039i	$-0.402063\pi$
$480$	−6.51462e9	+	2.11673e9i	−0.122723	+	0.0398750i
$481$	−5.44176e10	−	1.76814e10i	−1.01662	−	0.330320i
$482$	−1.61221e10	−	1.17134e10i	−0.298700	−	0.217018i
$483$		−	1.73375e10i		−	0.318565i
$484$	2.72682e10	−	3.04766e9i	0.496906	−	0.0555374i
$485$	1.30390e11			2.35655
$486$	2.28136e10	−	3.14002e10i	0.408929	−	0.562843i
$487$	1.69779e10	−	5.22527e10i	0.301834	−	0.928950i	−0.679005	−	0.734133i	$-0.737589\pi$
$487$	1.69779e10	−	5.22527e10i	0.301834	−	0.928950i	0.980840	−	0.194817i	$-0.0624113\pi$
$488$	−5.80563e9	−	1.78679e10i	−0.102369	−	0.315060i
$489$	−1.35094e10	+	9.81516e9i	−0.236266	+	0.171657i
$490$	−2.45750e10	−	3.38246e10i	−0.426294	−	0.586743i
$491$	3.21368e10	−	1.04419e10i	0.552939	−	0.179661i	−0.0192028	−	0.999816i	$-0.506113\pi$
$491$	3.21368e10	−	1.04419e10i	0.552939	−	0.179661i	0.572141	+	0.820155i	$0.306113\pi$
$492$	9.95703e9	+	3.23524e9i	0.169930	+	0.0552135i
$493$	1.87551e10	+	1.36264e10i	0.317491	+	0.230671i
$494$		−	4.33272e10i		−	0.727533i
$495$	5.30069e10	+	6.50192e10i	0.882900	+	1.08298i
$496$	2.46385e10			0.407087
$497$	−2.27806e10	+	3.13548e10i	−0.373370	+	0.513899i
$498$	3.74767e9	−	1.15341e10i	0.0609318	−	0.187529i
$499$	−1.42181e10	−	4.37589e10i	−0.229319	−	0.705771i	−0.997824	−	0.0659279i	$-0.978999\pi$
$499$	−1.42181e10	−	4.37589e10i	−0.229319	−	0.705771i	0.768505	−	0.639843i	$-0.221001\pi$
$500$	3.97861e10	−	2.89063e10i	0.636578	−	0.462501i
$501$	−1.75716e10	−	2.41852e10i	−0.278907	−	0.383883i
$502$	5.57569e10	−	1.81165e10i	0.877978	−	0.285272i
$503$	8.49854e10	+	2.76134e10i	1.32762	+	0.431368i	0.885103	−	0.465394i	$-0.154087\pi$
$503$	8.49854e10	+	2.76134e10i	1.32762	+	0.431368i	0.442512	+	0.896763i	$0.354087\pi$
$504$	9.54149e9	+	6.93230e9i	0.147875	+	0.107437i
$505$		−	1.36858e11i		−	2.10429i
$506$	5.45906e10	−	3.04123e9i	0.832753	−	0.0463925i
$507$	−2.45584e9			−0.0371679
$508$	−2.02823e10	+	2.79162e10i	−0.304552	+	0.419180i
$509$	−1.73249e10	+	5.33205e10i	−0.258106	+	0.794370i	0.735095	+	0.677964i	$0.237137\pi$
$509$	−1.73249e10	+	5.33205e10i	−0.258106	+	0.794370i	−0.993202	+	0.116406i	$0.962863\pi$
$510$	2.51397e9	+	7.73721e9i	0.0371603	+	0.114368i
$511$	1.73895e10	−	1.26342e10i	0.255038	−	0.185296i
$512$	−1.78510e9	−	2.45699e9i	−0.0259767	−	0.0357538i
$513$	−5.04613e10	+	1.63959e10i	−0.728599	+	0.236736i
$514$	−8.64434e10	−	2.80872e10i	−1.23845	−	0.402398i
$515$	−2.21327e10	−	1.60803e10i	−0.314633	−	0.228594i
$516$		−	3.71959e9i		−	0.0524682i
$517$	3.90805e10	−	1.51494e10i	0.547013	−	0.212048i
$518$	−3.30059e10			−0.458429
$519$	−1.93555e10	+	2.66405e10i	−0.266768	+	0.367175i
$520$	−1.42338e10	+	4.38072e10i	−0.194674	+	0.599146i
$521$	−1.77647e9	−	5.46740e9i	−0.0241105	−	0.0742045i	0.938277	−	0.345884i	$-0.112421\pi$
$521$	−1.77647e9	−	5.46740e9i	−0.0241105	−	0.0742045i	−0.962388	+	0.271680i	$0.912421\pi$
$522$	5.84934e10	−	4.24980e10i	0.787817	−	0.572382i
$523$	5.43980e9	+	7.48724e9i	0.0727069	+	0.100073i	0.843822	−	0.536624i	$-0.180301\pi$
$523$	5.43980e9	+	7.48724e9i	0.0727069	+	0.100073i	−0.771115	+	0.636696i	$0.780301\pi$
$524$	−4.49350e9	+	1.46003e9i	−0.0596019	+	0.0193658i
$525$	3.74820e10	+	1.21786e10i	0.493385	+	0.160310i
$526$	4.17243e10	+	3.03145e10i	0.545062	+	0.396011i
$527$		−	2.92624e10i		−	0.379373i
$528$	4.49693e9	−	6.97482e9i	0.0578602	−	0.0897424i
$529$	3.06399e10			0.391259
$530$	−5.94857e10	+	8.18750e10i	−0.753892	+	1.03764i
$531$	1.14372e10	−	3.52002e10i	0.143861	−	0.442758i
$532$	−7.72327e9	−	2.37698e10i	−0.0964172	−	0.296742i
$533$	5.69558e10	−	4.13808e10i	0.705714	−	0.512732i
$534$	1.04095e10	+	1.43275e10i	0.128016	+	0.176200i
$535$	−7.63885e10	+	2.48201e10i	−0.932423	+	0.302963i
$536$	−8.52801e9	−	2.77092e9i	−0.103321	−	0.0335710i
$537$	−1.73154e10	−	1.25804e10i	−0.208226	−	0.151285i
$538$			8.62634e10i			1.02967i
$539$	4.89703e10	+	1.29489e10i	0.580200	+	0.153419i
$540$	5.64067e10			0.663369
$541$	6.57919e10	−	9.05548e10i	0.768040	−	1.05712i	−0.228463	−	0.973553i	$-0.573370\pi$
$541$	6.57919e10	−	9.05548e10i	0.768040	−	1.05712i	0.996502	−	0.0835633i	$-0.0266301\pi$
$542$	−7.15454e9	+	2.20194e10i	−0.0829058	+	0.255158i
$543$	−3.17194e9	−	9.76223e9i	−0.0364860	−	0.112292i
$544$	−2.91808e9	+	2.12011e9i	−0.0333198	+	0.0242082i
$545$	−9.08359e10	−	1.25025e11i	−1.02961	−	1.41713i
$546$	−1.68297e10	+	5.46829e9i	−0.189367	+	0.0615291i
$547$	−4.53252e10	−	1.47270e10i	−0.506279	−	0.164500i	0.0447302	−	0.998999i	$-0.485757\pi$
$547$	−4.53252e10	−	1.47270e10i	−0.506279	−	0.164500i	−0.551009	+	0.834499i	$0.685757\pi$
$548$	−1.93402e10	−	1.40515e10i	−0.214456	−	0.155812i
$549$			6.95905e10i			0.766056i
$550$	−3.17721e10	+	1.20156e11i	−0.347212	+	1.31309i
$551$	−1.53218e11			−1.66228
$552$	9.72019e9	−	1.33787e10i	0.104693	−	0.144098i
$553$	2.39582e10	−	7.37359e10i	0.256185	−	0.788457i
$554$	1.44332e10	+	4.44208e10i	0.153223	+	0.471571i
$555$	−5.74455e10	+	4.17366e10i	−0.605458	+	0.439891i
$556$	3.29526e10	+	4.53553e10i	0.344818	+	0.474601i
$557$	−4.68151e10	+	1.52112e10i	−0.486368	+	0.158031i	−0.541928	−	0.840425i	$-0.682306\pi$
$557$	−4.68151e10	+	1.52112e10i	−0.486368	+	0.158031i	0.0555600	+	0.998455i	$0.482306\pi$
$558$	−8.67968e10	−	2.82020e10i	−0.895297	−	0.290899i
$559$	−2.02353e10	−	1.47018e10i	−0.207235	−	0.150565i
$560$			2.65704e10i			0.270175i
$561$	−8.28378e9	−	5.34086e9i	−0.0836329	−	0.0539212i
$562$	3.83570e10			0.384503
$563$	−9.36267e10	+	1.28866e11i	−0.931893	+	1.28264i	0.0272238	+	0.999629i	$0.491333\pi$
$563$	−9.36267e10	+	1.28866e11i	−0.931893	+	1.28264i	−0.959117	+	0.283011i	$0.908667\pi$
$564$	3.91748e9	−	1.20568e10i	0.0387160	−	0.119156i
$565$	9.30010e10	+	2.86228e11i	0.912628	+	2.80878i
$566$	3.26096e10	−	2.36923e10i	0.317746	−	0.230856i
$567$	−1.86701e10	−	2.56972e10i	−0.180640	−	0.248630i
$568$	−3.51578e10	+	1.14235e10i	−0.337776	+	0.109750i
$569$	−1.01467e11	−	3.29685e10i	−0.967997	−	0.314521i	−0.217990	−	0.975951i	$-0.569950\pi$
$569$	−1.01467e11	−	3.29685e10i	−0.967997	−	0.314521i	−0.750007	+	0.661430i	$0.769950\pi$
$570$	−4.34995e10	−	3.16042e10i	−0.412083	−	0.299396i
$571$		−	6.23163e10i		−	0.586216i	−0.956079	−	0.293108i	$-0.905311\pi$
$571$		−	6.23163e10i		−	0.586216i	0.956079	−	0.293108i	$-0.0946895\pi$
$572$	−2.01701e10	−	5.20323e10i	−0.188419	−	0.486059i
$573$	7.36765e10			0.683456
$574$	2.38702e10	−	3.28546e10i	0.219892	−	0.302655i
$575$	−7.65320e10	+	2.35541e11i	−0.700119	+	2.15474i
$576$	3.47625e9	+	1.06988e10i	0.0315806	+	0.0971951i
$577$	9.88277e10	−	7.18025e10i	0.891611	−	0.647793i	−0.0446868	−	0.999001i	$-0.514229\pi$
$577$	9.88277e10	−	7.18025e10i	0.891611	−	0.647793i	0.936297	+	0.351208i	$0.114229\pi$
$578$	−4.38710e10	−	6.03833e10i	−0.393067	−	0.541010i
$579$	6.09317e10	−	1.97979e10i	0.542162	−	0.176159i
$580$	1.54915e11	+	5.03351e10i	1.36893	+	0.444794i
$581$	−3.80584e10	−	2.76511e10i	−0.334000	−	0.242665i
$582$			4.77795e10i			0.416437i
$583$	−6.82002e9	−	1.22421e11i	−0.0590353	−	1.05969i
$584$	2.05022e10			0.176258
$585$	1.00286e11	−	1.38032e11i	0.856284	−	1.17857i
$586$	3.54445e10	−	1.09087e11i	0.300579	−	0.925086i
$587$	−4.87817e9	−	1.50135e10i	−0.0410870	−	0.126453i	0.928409	−	0.371560i	$-0.121177\pi$
$587$	−4.87817e9	−	1.50135e10i	−0.0410870	−	0.126453i	−0.969496	+	0.245107i	$0.921177\pi$
$588$	1.23946e10	−	9.00518e9i	0.103686	−	0.0753326i
$589$	1.13678e11	+	1.56464e11i	0.944528	+	1.30003i
$590$	7.93019e10	−	2.57668e10i	0.654449	−	0.212643i
$591$	−1.12900e10	−	3.66835e9i	−0.0925432	−	0.0300691i
$592$	−2.54694e10	−	1.85046e10i	−0.207363	−	0.150658i
$593$			1.32893e11i			1.07469i	0.843362	+	0.537346i	$0.180573\pi$
$593$			1.32893e11i			1.07469i	−0.843362	+	0.537346i	$0.819427\pi$
$594$	−5.29670e10	+	4.31813e10i	−0.425461	+	0.346857i
$595$	3.15568e10			0.251782
$596$	−4.96942e10	+	6.83982e10i	−0.393841	+	0.542075i
$597$	4.64509e9	−	1.42961e10i	0.0365677	−	0.112544i
$598$	−3.43633e10	−	1.05759e11i	−0.268714	−	0.827017i
$599$	−2.59646e10	+	1.88644e10i	−0.201685	+	0.146533i	−0.684044	−	0.729441i	$-0.739780\pi$
$599$	−2.59646e10	+	1.88644e10i	−0.201685	+	0.146533i	0.482358	+	0.875974i	$0.339780\pi$
$600$	2.20956e10	+	3.04119e10i	0.170490	+	0.234660i
$601$	7.64325e10	−	2.48344e10i	0.585842	−	0.190352i	−0.00107418	−	0.999999i	$-0.500342\pi$
$601$	7.64325e10	−	2.48344e10i	0.585842	−	0.190352i	0.586916	+	0.809648i	$0.300342\pi$
$602$	−1.37220e10	−	4.45854e9i	−0.104479	−	0.0339474i
$603$	2.68709e10	+	1.95229e10i	0.203242	+	0.147664i
$604$			1.15490e11i			0.867753i
$605$	−9.45047e10	−	2.08554e11i	−0.705394	−	1.55667i
$606$	5.01500e10			0.371861
$607$	8.64392e10	−	1.18973e11i	0.636731	−	0.876385i	−0.361705	−	0.932293i	$-0.617805\pi$
$607$	8.64392e10	−	1.18973e11i	0.636731	−	0.876385i	0.998436	+	0.0559079i	$0.0178053\pi$
$608$	7.36666e9	−	2.26722e10i	0.0539084	−	0.165913i
$609$	1.93375e10	+	5.95147e10i	0.140582	+	0.432668i
$610$	−1.26837e11	+	9.21526e10i	−0.916067	+	0.665561i
$611$	−5.01072e10	−	6.89666e10i	−0.359530	−	0.494851i
$612$	1.27066e10	−	4.12863e9i	0.0905783	−	0.0294307i
$613$	1.05128e10	+	3.41581e9i	0.0744520	+	0.0241909i	0.346006	−	0.938232i	$-0.387538\pi$
$613$	1.05128e10	+	3.41581e9i	0.0744520	+	0.0241909i	−0.271554	+	0.962423i	$0.587538\pi$
$614$	9.00135e10	+	6.53986e10i	0.633336	+	0.460145i
$615$		−	8.73666e10i		−	0.610724i
$616$	−2.03406e10	−	2.49501e10i	−0.141267	−	0.173280i
$617$	−1.45058e11			−1.00093			−0.500463	−	0.865758i	$-0.666837\pi$
$617$	−1.45058e11			−1.00093			−0.500463	+	0.865758i	$0.666837\pi$
$618$	5.89242e9	−	8.11022e9i	0.0403961	−	0.0556005i
$619$	3.90587e10	−	1.20210e11i	0.266045	−	0.818802i	−0.725406	−	0.688321i	$-0.758348\pi$
$619$	3.90587e10	−	1.20210e11i	0.266045	−	0.818802i	0.991451	−	0.130481i	$-0.0416521\pi$
$620$	−6.35358e10	−	1.95543e11i	−0.429983	−	1.32335i
$621$	−1.10170e11	+	8.00429e10i	−0.740790	+	0.538216i
$622$	−7.71439e10	−	1.06180e11i	−0.515395	−	0.709380i
$623$	6.53331e10	−	2.12280e10i	0.433691	−	0.140915i
$624$	−1.60526e10	−	5.21580e9i	−0.105878	−	0.0344019i
$625$	−9.48946e10	−	6.89449e10i	−0.621901	−	0.451837i
$626$		−	5.83349e10i		−	0.379867i
$627$	6.50410e10	−	3.62342e9i	0.420840	−	0.0234449i
$628$	−6.06185e10			−0.389733
$629$	−2.19773e10	+	3.02492e10i	−0.140402	+	0.193246i
$630$	3.04133e10	−	9.36024e10i	0.193064	−	0.594189i
$631$	7.92672e10	+	2.43959e11i	0.500007	+	1.53886i	0.809006	+	0.587801i	$0.200006\pi$
$631$	7.92672e10	+	2.43959e11i	0.500007	+	1.53886i	−0.308999	+	0.951062i	$0.599994\pi$
$632$	5.98273e10	−	4.34671e10i	0.375000	−	0.272453i
$633$	5.15961e10	+	7.10160e10i	0.321368	+	0.442325i
$634$	1.38738e11	−	4.50786e10i	0.858691	−	0.279006i
$635$	2.73859e11	+	8.89821e10i	1.68435	+	0.547278i
$636$	−3.00020e10	−	2.17977e10i	−0.183367	−	0.133224i
$637$		−	1.03022e11i		−	0.625709i
$638$	−1.84002e11	+	7.13276e10i	−1.11055	+	0.430502i
$639$	1.36930e11			0.821288
$640$	−1.48965e10	+	2.05033e10i	−0.0887903	+	0.122209i
$641$	−6.01248e10	+	1.85045e11i	−0.356140	+	1.09609i	0.599205	+	0.800596i	$0.295484\pi$
$641$	−6.01248e10	+	1.85045e11i	−0.356140	+	1.09609i	−0.955345	+	0.295492i	$0.904516\pi$
$642$	−9.09501e9	−	2.79916e10i	−0.0535381	−	0.164773i
$643$	4.28796e10	−	3.11539e10i	0.250846	−	0.182250i	−0.455256	−	0.890361i	$-0.650452\pi$
$643$	4.28796e10	−	3.11539e10i	0.250846	−	0.182250i	0.706102	+	0.708111i	$0.250452\pi$
$644$	−3.77042e10	−	5.18954e10i	−0.219203	−	0.301707i
$645$	−2.95205e10	+	9.59179e9i	−0.170563	+	0.0554193i
$646$	−2.69271e10	−	8.74915e9i	−0.154618	−	0.0502384i
$647$	9.12846e10	+	6.63221e10i	0.520931	+	0.378479i	0.816955	−	0.576702i	$-0.195661\pi$
$647$	9.12846e10	+	6.63221e10i	0.520931	+	0.378479i	−0.296023	+	0.955181i	$0.595661\pi$
$648$		−	3.02968e10i		−	0.171829i
$649$	−5.47407e10	+	8.49039e10i	−0.308554	+	0.478574i
$650$	2.52780e11			1.41609
$651$	4.64285e10	−	6.39033e10i	0.258500	−	0.355795i
$652$	−1.90917e10	+	5.87583e10i	−0.105646	+	0.325146i
$653$	−7.30779e10	−	2.24911e11i	−0.401914	−	1.23696i	−0.923445	−	0.383731i	$-0.874639\pi$
$653$	−7.30779e10	−	2.24911e11i	−0.401914	−	1.23696i	0.521531	−	0.853232i	$-0.325361\pi$
$654$	4.58137e10	−	3.32856e10i	0.250429	−	0.181947i
$655$	2.31750e10	+	3.18976e10i	0.125908	+	0.173298i
$656$	3.68395e10	−	1.19699e10i	0.198929	−	0.0646360i
$657$	−7.22253e10	−	2.34674e10i	−0.387639	−	0.125952i
$658$	−3.97829e10	−	2.89040e10i	−0.212223	−	0.154189i
$659$			2.80842e11i			1.48909i	0.667572	+	0.744545i	$0.267334\pi$
$659$			2.80842e11i			1.48909i	−0.667572	+	0.744545i	$0.732666\pi$
$660$	−6.69519e10	−	1.77037e10i	−0.352848	−	0.0933012i
$661$	−2.20199e11			−1.15348			−0.576739	−	0.816928i	$-0.695675\pi$
$661$	−2.20199e11			−1.15348			−0.576739	+	0.816928i	$0.695675\pi$
$662$	3.77768e10	−	5.19953e10i	0.196695	−	0.270727i
$663$	−6.19464e9	+	1.90651e10i	−0.0320599	+	0.0986702i
$664$	−1.38658e10	−	4.26746e10i	−0.0713301	−	0.219531i
$665$	−1.68732e11	+	1.22591e11i	−0.862803	+	0.626863i
$666$	6.85429e10	+	9.43412e10i	0.348390	+	0.479518i
$667$	−3.73997e11	+	1.21519e11i	−1.88958	+	0.613961i
$668$	−1.05192e11	−	3.41789e10i	−0.528294	−	0.171653i
$669$	1.32233e11	+	9.60731e10i	0.660140	+	0.479620i
$670$			7.48279e10i			0.371334i
$671$	4.85565e10	−	1.83631e11i	0.239528	−	0.905851i
$672$	−9.73635e9			−0.0477441
$673$	1.04694e11	−	1.44099e11i	0.510342	−	0.702425i	−0.473635	−	0.880721i	$-0.657059\pi$
$673$	1.04694e11	−	1.44099e11i	0.510342	−	0.702425i	0.983977	+	0.178296i	$0.0570585\pi$
$674$	−6.53929e10	+	2.01259e11i	−0.316877	+	0.975248i
$675$	−9.56569e10	−	2.94402e11i	−0.460788	−	1.41816i
$676$	−7.35091e9	+	5.34075e9i	−0.0352009	+	0.0255750i
$677$	1.27085e11	+	1.74918e11i	0.604979	+	0.832682i	0.996153	−	0.0876352i	$-0.0279310\pi$
$677$	1.27085e11	+	1.74918e11i	0.604979	+	0.832682i	−0.391174	+	0.920317i	$0.627931\pi$
$678$	−1.04884e11	+	3.40790e10i	−0.496354	+	0.161275i
$679$	1.76264e11	+	5.72715e10i	0.829246	+	0.269438i
$680$	2.43512e10	+	1.76922e10i	0.113890	+	0.0827456i
$681$			2.11969e10i			0.0985561i
$682$	2.09357e11	+	1.34980e11i	0.967719	+	0.623924i
$683$	−2.90792e10			−0.133629			−0.0668143	−	0.997765i	$-0.521284\pi$
$683$	−2.90792e10			−0.133629			−0.0668143	+	0.997765i	$0.521284\pi$
$684$	−5.19027e10	+	7.14380e10i	−0.237119	+	0.326366i
$685$	−6.16464e10	+	1.89728e11i	−0.279992	+	0.861726i
$686$	−4.89638e10	−	1.50695e11i	−0.221095	−	0.680461i
$687$	1.70080e10	−	1.23570e10i	0.0763529	−	0.0554736i
$688$	−8.08906e9	−	1.11336e10i	−0.0361031	−	0.0496916i
$689$	−2.37168e11	+	7.70605e10i	−1.05239	+	0.341944i
$690$	−1.31246e11	−	4.26443e10i	−0.579013	−	0.188133i
$691$	6.04056e10	+	4.38872e10i	0.264951	+	0.192498i	0.712327	−	0.701848i	$-0.247641\pi$
$691$	6.04056e10	+	4.38872e10i	0.264951	+	0.192498i	−0.447376	+	0.894346i	$0.647641\pi$
$692$			1.21834e11i			0.531306i
$693$	4.30973e10	+	1.11177e11i	0.186860	+	0.482038i
$694$	9.04080e9			0.0389735
$695$	2.74986e11	−	3.78486e11i	1.17862	−	1.62222i
$696$	−1.84446e10	+	5.67667e10i	−0.0786018	+	0.241912i
$697$	−1.42163e10	−	4.37531e10i	−0.0602357	−	0.185386i
$698$	−9.73700e10	+	7.07435e10i	−0.410207	+	0.298033i
$699$	8.73732e9	+	1.20259e10i	0.0365990	+	0.0503742i
$700$	1.38678e11	−	4.50592e10i	0.577584	−	0.187668i
$701$	−8.53683e10	−	2.77378e10i	−0.353529	−	0.114868i	0.126868	−	0.991920i	$-0.459507\pi$
$701$	−8.53683e10	−	2.77378e10i	−0.353529	−	0.114868i	−0.480397	+	0.877051i	$0.659507\pi$
$702$	1.12446e11	+	8.16967e10i	0.463015	+	0.336400i
$703$		−	2.47118e11i		−	1.01177i
$704$	−1.70789e9	−	3.06569e10i	−0.00695294	−	0.124806i
$705$	−1.05790e11			−0.428243
$706$	2.05915e10	−	2.83418e10i	0.0828838	−	0.114080i
$707$	6.01129e10	−	1.85008e11i	0.240597	−	0.740481i
$708$	9.44189e9	+	2.90591e10i	0.0375773	+	0.115651i
$709$	−3.08057e9	+	2.23816e9i	−0.0121912	+	0.00885741i	−0.593864	−	0.804565i	$-0.702398\pi$
$709$	−3.08057e9	+	2.23816e9i	−0.0121912	+	0.00885741i	0.581673	+	0.813423i	$0.302398\pi$
$710$	1.81324e11	+	2.49572e11i	0.713547	+	0.982114i
$711$	−2.60514e11	+	8.46462e10i	−1.01942	+	0.331230i
$712$	6.23164e10	+	2.02478e10i	0.242484	+	0.0787877i
$713$	4.01576e11	+	2.91762e11i	1.55385	+	1.12894i
$714$			1.15636e10i			0.0444937i
$715$	−3.60941e11	+	2.94257e11i	−1.38106	+	1.12591i
$716$	−7.91880e10			−0.301306
$717$	−1.16286e11	+	1.60054e11i	−0.439999	+	0.605607i
$718$	4.04405e10	−	1.24463e11i	0.152167	−	0.468320i
$719$	2.66870e10	+	8.21340e10i	0.0998582	+	0.307332i	0.988489	−	0.151291i	$-0.0483430\pi$
$719$	2.66870e10	+	8.21340e10i	0.0998582	+	0.307332i	−0.888631	+	0.458623i	$0.848343\pi$
$720$	7.59465e10	−	5.51784e10i	0.282604	−	0.205324i
$721$	−2.28564e10	−	3.14592e10i	−0.0845799	−	0.116414i
$722$	−4.77637e9	+	1.55194e9i	−0.0175772	+	0.00571118i
$723$	−5.79552e10	−	1.88308e10i	−0.212099	−	0.0689153i
$724$	−3.07245e10	−	2.23226e10i	−0.111823	−	0.0812440i
$725$		−	8.93906e11i		−	3.23549i
$726$	7.64219e10	−	3.46300e10i	0.275088	−	0.124654i
$727$	−7.97401e10			−0.285456			−0.142728	−	0.989762i	$-0.545587\pi$
$727$	−7.97401e10			−0.285456			−0.142728	+	0.989762i	$0.545587\pi$
$728$	−3.84832e10	+	5.29676e10i	−0.137008	+	0.188575i
$729$	−5.74080e9	+	1.76684e10i	−0.0203265	+	0.0625585i
$730$	−5.28694e10	−	1.62715e11i	−0.186171	−	0.572976i
$731$	−1.32231e10	+	9.60712e9i	−0.0463087	+	0.0336453i
$732$	−3.37681e10	−	4.64778e10i	−0.117615	−	0.161883i
$733$	−1.36694e10	+	4.44146e9i	−0.0473515	+	0.0153854i	−0.332597	−	0.943069i	$-0.607925\pi$
$733$	−1.36694e10	+	4.44146e9i	−0.0473515	+	0.0153854i	0.285245	+	0.958454i	$0.407925\pi$
$734$	−1.15022e11	−	3.73730e10i	−0.396276	−	0.128758i
$735$	−1.03432e11	−	7.51475e10i	−0.354408	−	0.257493i
$736$		−	6.11843e10i		−	0.208511i
$737$	−5.72834e10	−	7.02649e10i	−0.194160	−	0.238160i
$738$	−1.43480e11			−0.483688
$739$	1.70163e11	−	2.34209e11i	0.570540	−	0.785281i	−0.422079	−	0.906559i	$-0.638699\pi$
$739$	1.70163e11	−	2.34209e11i	0.570540	−	0.785281i	0.992619	+	0.121278i	$0.0386994\pi$
$740$	−8.11830e10	+	2.49855e11i	−0.270731	+	0.833224i
$741$	−4.09415e10	−	1.26005e11i	−0.135797	−	0.417941i
$742$	−1.16376e11	+	8.45524e10i	−0.383928	+	0.278940i
$743$	−2.37298e11	−	3.26612e11i	−0.778643	−	1.07171i	−0.995430	−	0.0954913i	$-0.969558\pi$
$743$	−2.37298e11	−	3.26612e11i	−0.778643	−	1.07171i	0.216787	−	0.976219i	$-0.430442\pi$
$744$	7.16542e10	−	2.32819e10i	0.233857	−	0.0759846i
$745$	6.70989e11	+	2.18017e11i	2.17816	+	0.707728i
$746$	1.79341e11	+	1.30299e11i	0.579061	+	0.420712i
$747$			1.66206e11i			0.533782i
$748$	−3.64102e10	+	2.02840e9i	−0.116310	+	0.00647960i
$749$	−1.14166e11			−0.362751
$750$	8.83921e10	−	1.21661e11i	0.279363	−	0.384510i
$751$	6.25580e10	−	1.92534e11i	0.196663	−	0.605267i	−0.803290	−	0.595588i	$-0.796919\pi$
$751$	6.25580e10	−	1.92534e11i	0.196663	−	0.605267i	0.999953	−	0.00967907i	$-0.00308099\pi$
$752$	−1.44941e10	−	4.46082e10i	−0.0453231	−	0.139490i
$753$	1.45034e11	−	1.05374e11i	0.451119	−	0.327757i
$754$	2.35919e11	+	3.24714e11i	0.729923	+	1.00465i
$755$	9.16583e11	−	2.97816e11i	2.82088	−	0.916558i
$756$	7.62518e10	+	2.47757e10i	0.233433	+	0.0758471i
$757$	1.07893e11	+	7.83885e10i	0.328555	+	0.238709i	0.739817	−	0.672808i	$-0.234912\pi$
$757$	1.07893e11	+	7.83885e10i	0.328555	+	0.238709i	−0.411262	+	0.911517i	$0.634912\pi$
$758$		−	2.45723e11i		−	0.744337i
$759$	1.55888e11	−	6.04293e10i	0.469727	−	0.182088i
$760$	−1.98935e11			−0.596288
$761$	−2.29557e11	+	3.15959e11i	−0.684467	+	0.942089i	−0.999977	−	0.00683388i	$-0.997825\pi$
$761$	−2.29557e11	+	3.15959e11i	−0.684467	+	0.942089i	0.315509	+	0.948923i	$0.397825\pi$
$762$	−3.26063e10	+	1.00352e11i	−0.0967123	+	0.297650i
$763$	−6.78789e10	−	2.08910e11i	−0.200279	−	0.616397i
$764$	2.20532e11	−	1.60226e11i	0.647287	−	0.470282i
$765$	−6.55336e10	−	9.01993e10i	−0.191346	−	0.263364i
$766$	3.14516e11	−	1.02193e11i	0.913541	−	0.296827i
$767$	1.95407e11	+	6.34915e10i	0.564622	+	0.183457i
$768$	−7.51317e9	−	5.45864e9i	−0.0215963	−	0.0156906i
$769$			1.60123e11i			0.457876i	0.973441	+	0.228938i	$0.0735253\pi$
$769$			1.60123e11i			0.457876i	−0.973441	+	0.228938i	$0.926475\pi$
$770$	−1.45563e11	+	2.25772e11i	−0.414085	+	0.642254i
$771$	−2.77937e11			−0.786555
$772$	1.39328e11	−	1.91769e11i	0.392257	−	0.539895i
$773$	1.76912e11	−	5.44480e11i	0.495496	−	1.52498i	−0.320686	−	0.947186i	$-0.603913\pi$
$773$	1.76912e11	−	5.44480e11i	0.495496	−	1.52498i	0.816182	−	0.577795i	$-0.196087\pi$
$774$	1.57523e10	+	4.84807e10i	0.0438916	+	0.135084i
$775$	−9.12845e11	+	6.63221e11i	−2.53041	+	1.83845i
$776$	1.03907e11	+	1.43016e11i	0.286548	+	0.394400i
$777$	−9.59883e10	+	3.11885e10i	−0.263351	+	0.0855678i
$778$	−3.48756e11	−	1.13318e11i	−0.951927	−	0.309300i
$779$	2.45985e11	+	1.78719e11i	0.667973	+	0.485311i
$780$			1.40851e11i			0.380524i
$781$	−3.61323e11	−	9.55423e10i	−0.971162	−	0.256798i
$782$	−7.26667e10			−0.194316
$783$	2.88904e11	−	3.97642e11i	0.768611	−	1.05790i
$784$	1.75162e10	−	5.39093e10i	0.0463635	−	0.142692i
$785$	1.56318e11	+	4.81098e11i	0.411653	+	1.26694i
$786$	−1.16885e10	+	8.49216e9i	−0.0306244	+	0.0222499i
$787$	1.63132e11	+	2.24533e11i	0.425247	+	0.585303i	0.966854	−	0.255329i	$-0.0821839\pi$
$787$	1.63132e11	+	2.24533e11i	0.425247	+	0.585303i	−0.541607	+	0.840632i	$0.682184\pi$
$788$	−4.17713e10	+	1.35723e10i	−0.108336	+	0.0352006i
$789$	1.49989e11	+	4.87343e10i	0.387035	+	0.125755i
$790$	−4.99254e11	−	3.62729e11i	−1.28178	−	0.931267i
$791$			4.27778e11i			1.09273i
$792$	−2.90742e10	+	1.09953e11i	−0.0738937	+	0.279452i
$793$	−3.86317e11			−0.976903
$794$	4.69915e10	−	6.46783e10i	0.118233	−	0.162733i
$795$	−9.56306e10	+	2.94321e11i	−0.239402	+	0.736805i
$796$	−1.71861e10	−	5.28935e10i	−0.0428081	−	0.131750i
$797$	−1.16831e11	+	8.48824e10i	−0.289550	+	0.210370i	−0.723072	−	0.690773i	$-0.757271\pi$
$797$	−1.16831e11	+	8.48824e10i	−0.289550	+	0.210370i	0.433522	+	0.901143i	$0.357271\pi$
$798$	−4.49219e10	−	6.18297e10i	−0.110776	−	0.152470i
$799$	−5.29798e10	+	1.72142e10i	−0.129994	+	0.0422376i
$800$	1.32275e11	+	4.29786e10i	0.322936	+	0.104928i
$801$	−1.96353e11	−	1.42659e11i	−0.476988	−	0.346552i
$802$		−	3.83025e9i		−	0.00925827i
$803$	1.74210e11	+	1.12319e11i	0.418996	+	0.270142i
$804$	−2.74197e10			−0.0656203
$805$	−3.14638e11	+	4.33062e11i	−0.749252	+	1.03126i
$806$	1.56558e11	−	4.81835e11i	0.370966	−	1.14172i
$807$	8.15136e10	+	2.50873e11i	0.192192	+	0.591507i
$808$	1.50111e11	−	1.09062e11i	0.352182	−	0.255875i
$809$	1.86795e11	+	2.57101e11i	0.436084	+	0.600218i	0.969336	−	0.245738i	$-0.0790303\pi$
$809$	1.86795e11	+	2.57101e11i	0.436084	+	0.600218i	−0.533252	+	0.845956i	$0.679030\pi$
$810$	−2.40450e11	+	7.81271e10i	−0.558580	+	0.181494i
$811$	−5.67544e11	−	1.84406e11i	−1.31195	−	0.426277i	−0.432224	−	0.901766i	$-0.642271\pi$
$811$	−5.67544e11	−	1.84406e11i	−1.31195	−	0.426277i	−0.879722	+	0.475489i	$0.842271\pi$
$812$	1.87309e11	+	1.36088e11i	0.430859	+	0.313037i
$813$			7.07979e10i			0.162053i
$814$	−1.15041e11	−	2.96768e11i	−0.262032	−	0.675957i
$815$	5.15567e11			1.16857
$816$	−6.48306e9	+	8.92316e9i	−0.0146224	+	0.0201260i
$817$	3.33814e10	−	1.02738e11i	0.0749233	−	0.230590i
$818$	7.79861e9	+	2.40017e10i	0.0174182	+	0.0536078i
$819$	1.96198e11	−	1.42546e11i	0.436072	−	0.316825i
$820$	−1.89998e11	−	2.61509e11i	−0.420236	−	0.578405i
$821$	−2.21916e11	+	7.21050e10i	−0.488446	+	0.158706i	−0.542878	−	0.839812i	$-0.682665\pi$
$821$	−2.21916e11	+	7.21050e10i	−0.488446	+	0.158706i	0.0544315	+	0.998518i	$0.482665\pi$
$822$	−6.95233e10	−	2.25895e10i	−0.152280	−	0.0494788i
$823$	−4.09894e11	−	2.97806e11i	−0.893455	−	0.649133i	0.0433219	−	0.999061i	$-0.486206\pi$
$823$	−4.09894e11	−	2.97806e11i	−0.893455	−	0.649133i	−0.936776	+	0.349928i	$0.886206\pi$
$824$		−	3.70902e10i		−	0.0804544i
$825$	2.11398e10	+	3.79463e11i	0.0456336	+	0.819131i
$826$	1.18520e11			0.254607
$827$	−4.16269e10	+	5.72945e10i	−0.0889922	+	0.122487i	−0.851192	−	0.524855i	$-0.824120\pi$
$827$	−4.16269e10	+	5.72945e10i	−0.0889922	+	0.122487i	0.762199	+	0.647342i	$0.224120\pi$
$828$	−7.00335e10	+	2.15541e11i	−0.148999	+	0.458573i
$829$	−6.92913e10	−	2.13257e11i	−0.146710	−	0.451528i	0.850517	−	0.525948i	$-0.176289\pi$
$829$	−6.92913e10	−	2.13257e11i	−0.146710	−	0.451528i	−0.997227	+	0.0744201i	$0.976289\pi$
$830$	−3.02930e11	+	2.20092e11i	−0.638308	+	0.463758i
$831$	8.39498e10	+	1.15547e11i	0.176042	+	0.242301i
$832$	−5.93921e10	+	1.92977e10i	−0.123947	+	0.0402728i
$833$	−6.40264e10	−	2.08034e10i	−0.132978	−	0.0432071i
$834$	1.38691e11	+	1.00765e11i	0.286672	+	0.208279i
$835$			9.22991e11i			1.89868i
$836$	1.86803e11	−	1.52291e11i	0.382437	−	0.311782i
$837$	−6.20416e11			−1.26410
$838$	−1.86920e11	+	2.57273e11i	−0.379035	+	0.521697i
$839$	−1.13893e11	+	3.50528e11i	−0.229853	+	0.707416i	0.767909	+	0.640559i	$0.221297\pi$
$839$	−1.13893e11	+	3.50528e11i	−0.229853	+	0.707416i	−0.997763	+	0.0668571i	$0.978703\pi$
$840$	2.51073e10	+	7.72724e10i	0.0504294	+	0.155206i
$841$	7.43579e11	−	5.40242e11i	1.48643	−	1.07995i
$842$	−1.74495e11	−	2.40172e11i	−0.347164	−	0.477831i
$843$	1.11551e11	−	3.62450e10i	0.220883	−	0.0717691i
$844$	3.08879e11	+	1.00361e11i	0.608722	+	0.197786i
$845$	6.13427e10	+	4.45681e10i	0.120320	+	0.0874173i
$846$			1.73737e11i			0.339165i
$847$	−3.61495e10	−	3.23438e11i	−0.0702375	−	0.628431i
$848$	−1.37207e11			−0.265334
$849$	7.24482e10	−	9.97164e10i	0.139443	−	0.191927i
$850$	5.10444e10	−	1.57098e11i	0.0977850	−	0.300951i
$851$	−1.95992e11	−	6.03201e11i	−0.373697	−	1.15012i
$852$	−9.14522e10	+	6.64439e10i	−0.173554	+	0.126095i
$853$	3.60009e11	+	4.95510e11i	0.680013	+	0.935957i	0.999934	−	0.0114870i	$-0.00365650\pi$
$853$	3.60009e11	+	4.95510e11i	0.680013	+	0.935957i	−0.319921	+	0.947444i	$0.603657\pi$
$854$	−2.11938e11	+	6.88628e10i	−0.398453	+	0.129465i
$855$	7.00809e11	+	2.27707e11i	1.31140	+	0.426100i
$856$	−8.80973e10	−	6.40064e10i	−0.164084	−	0.119214i
$857$		−	9.39923e11i		−	1.74248i	−0.490854	−	0.871242i	$-0.663315\pi$
$857$		−	9.39923e11i		−	1.74248i	0.490854	−	0.871242i	$-0.336685\pi$
$858$	−1.07827e11	−	1.32262e11i	−0.198965	−	0.244054i
$859$	3.87113e11			0.710993			0.355497	−	0.934678i	$-0.384312\pi$
$859$	3.87113e11			0.710993			0.355497	+	0.934678i	$0.384312\pi$
$860$	−6.75025e10	+	9.29093e10i	−0.123403	+	0.169850i
$861$	3.83744e10	−	1.18104e11i	0.0698279	−	0.214908i
$862$	8.65285e10	+	2.66307e11i	0.156722	+	0.482341i
$863$	−5.91932e10	+	4.30064e10i	−0.106716	+	0.0775335i	−0.639863	−	0.768489i	$-0.721009\pi$
$863$	−5.91932e10	+	4.30064e10i	−0.106716	+	0.0775335i	0.533148	+	0.846022i	$0.321009\pi$
$864$	4.49503e10	+	6.18687e10i	0.0806635	+	0.111024i
$865$	9.66935e11	−	3.14176e11i	1.72716	−	0.561189i
$866$	3.15856e11	+	1.02628e11i	0.561588	+	0.182471i
$867$	−1.84645e11	−	1.34152e11i	−0.326784	−	0.237423i
$868$		−	2.92247e11i		−	0.514838i
$869$	7.46491e11	−	4.15869e10i	1.30902	−	0.0729251i
$870$	4.98092e11			0.869425
$871$	−1.08377e11	+	1.49168e11i	−0.188306	+	0.259182i
$872$	6.47447e10	−	1.99264e11i	0.111979	−	0.344637i
$873$	−2.02344e11	−	6.22752e11i	−0.348365	−	1.07216i
$874$	3.88545e11	−	2.82294e11i	0.665879	−	0.483790i
$875$	−3.42869e11	−	4.71918e11i	−0.584919	−	0.805072i
$876$	5.96248e10	−	1.93733e10i	0.101254	−	0.0328993i
$877$	−7.16927e11	−	2.32944e11i	−1.21193	−	0.393779i	−0.367791	−	0.929908i	$-0.619886\pi$
$877$	−7.16927e11	−	2.32944e11i	−1.21193	−	0.393779i	−0.844136	+	0.536129i	$0.819886\pi$
$878$	3.09123e11	+	2.24591e11i	0.520179	+	0.377932i
$879$		−	3.50742e11i		−	0.587532i
$880$	−2.38904e11	+	9.26101e10i	−0.398375	+	0.154429i
$881$	7.39966e11			1.22831			0.614155	−	0.789185i	$-0.289497\pi$
$881$	7.39966e11			1.22831			0.614155	+	0.789185i	$0.289497\pi$
$882$	−1.23413e11	+	1.69863e11i	−0.203932	+	0.280688i
$883$	−2.59033e11	+	7.97222e11i	−0.426101	+	1.31140i	0.475835	+	0.879534i	$0.342146\pi$
$883$	−2.59033e11	+	7.97222e11i	−0.426101	+	1.31140i	−0.901936	+	0.431869i	$0.857854\pi$
$884$	2.29192e10	+	7.05381e10i	0.0375311	+	0.115509i
$885$	2.06279e11	−	1.49871e11i	0.336266	−	0.244312i
$886$	−1.56678e11	−	2.15649e11i	−0.254257	−	0.349955i
$887$	−9.63422e11	+	3.13035e11i	−1.55640	+	0.505706i	−0.955844	−	0.293874i	$-0.905055\pi$
$887$	−9.63422e11	+	3.13035e11i	−1.55640	+	0.505706i	−0.600559	+	0.799580i	$0.705055\pi$
$888$	−9.15562e10	−	2.97484e10i	−0.147243	−	0.0478423i
$889$	3.31125e11	+	2.40576e11i	0.530132	+	0.385164i
$890$		−	5.46787e11i		−	0.871481i
$891$	1.65979e11	−	2.57436e11i	0.263355	−	0.408469i
$892$	6.04738e11			0.955230
$893$	2.16407e11	−	2.97858e11i	0.340302	−	0.468386i
$894$	−7.98896e10	+	2.45875e11i	−0.125066	+	0.384914i
$895$	2.04204e11	+	6.28474e11i	0.318252	+	0.979480i
$896$	−2.91433e10	+	2.11738e10i	−0.0452174	+	0.0328524i
$897$	−1.99872e11	−	2.75101e11i	−0.308733	−	0.424934i
$898$	−3.26443e11	+	1.06068e11i	−0.501998	+	0.163109i
$899$	−1.70391e12	−	5.53634e11i	−2.60860	−	0.847587i
$900$	−4.16784e11	−	3.02811e11i	−0.635245	−	0.461532i
$901$			1.62957e11i			0.247271i
$902$	3.78606e11	+	1.00112e11i	0.571955	+	0.151238i
$903$	−4.41195e10			−0.0663559
$904$	−2.39832e11	+	3.30100e11i	−0.359115	+	0.494279i
$905$	−9.79335e10	+	3.01408e11i	−0.145995	+	0.449325i
$906$	1.09131e11	+	3.35870e11i	0.161970	+	0.498492i
$907$	3.20853e11	−	2.33113e11i	0.474107	−	0.344459i	−0.324933	−	0.945737i	$-0.605342\pi$
$907$	3.20853e11	−	2.33113e11i	0.474107	−	0.344459i	0.799040	+	0.601278i	$0.205342\pi$
$908$	4.60972e10	+	6.34474e10i	0.0678159	+	0.0933405i
$909$	−6.53648e11	+	2.12383e11i	−0.957390	+	0.311075i
$910$	5.19614e11	+	1.68833e11i	0.757732	+	0.246202i
$911$	−5.76110e11	−	4.18568e11i	−0.836434	−	0.607705i	0.0849384	−	0.996386i	$-0.472931\pi$
$911$	−5.76110e11	−	4.18568e11i	−0.836434	−	0.607705i	−0.921372	+	0.388681i	$0.872931\pi$
$912$		−	7.28969e10i		−	0.105373i
$913$	1.15969e11	−	4.38574e11i	0.166901	−	0.631190i
$914$	−3.50870e11			−0.502760
$915$	−2.81792e11	+	3.87853e11i	−0.402017	+	0.553328i
$916$	2.40359e10	−	7.39750e10i	0.0341412	−	0.105076i
$917$	1.73180e10	+	5.32992e10i	0.0244917	+	0.0753778i
$918$	7.34795e10	−	5.33860e10i	0.103466	−	0.0751721i
$919$	−4.80094e11	−	6.60793e11i	−0.673076	−	0.926410i	0.326749	−	0.945111i	$-0.394047\pi$
$919$	−4.80094e11	−	6.60793e11i	−0.673076	−	0.926410i	−0.999825	+	0.0187012i	$0.994047\pi$
$920$	−4.85589e11	+	1.57777e11i	−0.677825	+	0.220239i
$921$	3.23577e11	+	1.05136e11i	0.449716	+	0.146122i
$922$	6.24494e11	+	4.53722e11i	0.864181	+	0.627864i
$923$			7.60139e11i			1.04734i
$924$	−8.27311e10	−	5.33398e10i	−0.113496	−	0.0731751i
$925$	1.44174e12			1.96933
$926$	−1.22212e11	+	1.68211e11i	−0.166215	+	0.228776i
$927$	−4.24546e10	+	1.30662e11i	−0.0574917	+	0.176941i
$928$	6.82423e10	+	2.10028e11i	0.0920157	+	0.283195i
$929$	−6.03702e10	+	4.38616e10i	−0.0810513	+	0.0588872i	−0.627573	−	0.778558i	$-0.715952\pi$
$929$	−6.03702e10	+	4.38616e10i	−0.0810513	+	0.0588872i	0.546522	+	0.837445i	$0.315952\pi$
$930$	−3.69552e11	−	5.08645e11i	−0.494019	−	0.679959i
$931$	4.23163e11	−	1.37494e11i	0.563260	−	0.183014i
$932$	5.23058e10	+	1.69952e10i	0.0693244	+	0.0225249i
$933$	−3.24685e11	−	2.35897e11i	−0.428485	−	0.311312i
$934$			4.24754e11i			0.558149i
$935$	1.09990e11	+	2.83738e11i	0.143915	+	0.371254i
$936$	2.31316e11			0.301372
$937$	−4.73540e11	+	6.51771e11i	−0.614325	+	0.845545i	−0.996924	−	0.0783687i	$-0.975029\pi$
$937$	−4.73540e11	+	6.51771e11i	−0.614325	+	0.845545i	0.382600	+	0.923914i	$0.375029\pi$
$938$	−3.28670e10	+	1.01154e11i	−0.0424569	+	0.130669i
$939$	−5.51229e10	−	1.69651e11i	−0.0709038	−	0.218219i
$940$	−3.16656e11	+	2.30064e11i	−0.405580	+	0.294671i
$941$	−1.47513e11	−	2.03035e11i	−0.188136	−	0.258947i	0.704521	−	0.709683i	$-0.251162\pi$
$941$	−1.47513e11	−	2.03035e11i	−0.188136	−	0.258947i	−0.892658	+	0.450736i	$0.851162\pi$
$942$	−1.76292e11	+	5.72807e10i	−0.223887	+	0.0727453i
$943$	7.42180e11	+	2.41149e11i	0.938561	+	0.304957i
$944$	9.14572e10	+	6.64476e10i	0.115168	+	0.0836741i
$945$		−	6.69061e11i		−	0.838955i
$946$	−7.73916e9	−	1.38919e11i	−0.00966338	−	0.173459i
$947$	1.26120e12			1.56813			0.784067	−	0.620676i	$-0.213142\pi$
$947$	1.26120e12			1.56813			0.784067	+	0.620676i	$0.213142\pi$
$948$	1.32917e11	−	1.82945e11i	0.164569	−	0.226510i
$949$	1.30275e11	−	4.00944e11i	0.160618	−	0.494332i
$950$	3.37362e11	+	1.03829e12i	0.414192	+	1.27475i
$951$	3.60883e11	−	2.62197e11i	0.441209	−	0.320557i
$952$	2.51475e10	+	3.46125e10i	0.0306159	+	0.0421391i
$953$	−1.58585e11	+	5.15273e10i	−0.192260	+	0.0624692i	−0.403565	−	0.914951i	$-0.632229\pi$
$953$	−1.58585e11	+	5.15273e10i	−0.192260	+	0.0624692i	0.211304	+	0.977420i	$0.432229\pi$
$954$	4.83355e11	+	1.57052e11i	0.583543	+	0.189605i
$955$	−1.84032e12	−	1.33707e12i	−2.21248	−	1.60746i
$956$			7.31971e11i			0.876319i
$957$	−4.67718e11	+	3.81307e11i	−0.557617	+	0.454597i
$958$	−7.06389e11			−0.838652
$959$	−1.66670e11	+	2.29401e11i	−0.197053	+	0.271220i
$960$	−2.39481e10	+	7.37045e10i	−0.0281959	+	0.0867779i
$961$	4.35271e11	+	1.33963e12i	0.510348	+	1.57069i
$962$	−5.23716e11	+	3.80502e11i	−0.611499	+	0.444280i
$963$	2.37087e11	+	3.26322e11i	0.275678	+	0.379438i
$964$	−2.14426e11	+	6.96711e10i	−0.248295	+	0.0806760i
$965$	−1.88126e12	−	6.11259e11i	−2.16940	−	0.704881i
$966$	−1.58690e11	−	1.15295e11i	−0.182239	−	0.132404i
$967$			1.68783e12i			1.93029i	0.261724	+	0.965143i	$0.415709\pi$
$967$			1.68783e12i			1.93029i	−0.261724	+	0.965143i	$0.584291\pi$
$968$	1.53439e11	−	2.69852e11i	0.174757	−	0.307344i
$969$	−8.65774e10			−0.0981995
$970$	8.67094e11	−	1.19345e12i	0.979444	−	1.34809i
$971$	1.20113e11	−	3.69668e11i	0.135117	−	0.415849i	−0.860491	−	0.509466i	$-0.829843\pi$
$971$	1.20113e11	−	3.69668e11i	0.135117	−	0.415849i	0.995608	+	0.0936171i	$0.0298430\pi$
$972$	−1.35694e11	−	4.17625e11i	−0.152019	−	0.467866i
$973$	5.37977e11	−	3.90863e11i	0.600223	−	0.436087i
$974$	−3.65364e11	−	5.02880e11i	−0.405966	−	0.558765i
$975$	7.35140e11	−	2.38861e11i	0.813489	−	0.264319i
$976$	−2.02152e11	−	6.56832e10i	−0.222781	−	0.0723860i
$977$	9.64249e11	+	7.00568e11i	1.05831	+	0.768904i	0.973774	−	0.227517i	$-0.0730608\pi$
$977$	9.64249e11	+	7.00568e11i	1.05831	+	0.768904i	0.0845311	+	0.996421i	$0.473061\pi$
$978$			1.88923e11i			0.206504i
$979$	4.18585e11	+	5.13444e11i	0.455673	+	0.558936i
$980$	−4.73020e11			−0.512832
$981$	−4.56167e11	+	6.27860e11i	−0.492547	+	0.677933i
$982$	1.18136e11	−	3.63587e11i	0.127039	−	0.390987i
$983$	2.21609e11	+	6.82041e11i	0.237341	+	0.730460i	0.996802	+	0.0799079i	$0.0254626\pi$
$983$	2.21609e11	+	6.82041e11i	0.237341	+	0.730460i	−0.759461	+	0.650552i	$0.774537\pi$
$984$	9.58266e10	−	6.96221e10i	0.102213	−	0.0742620i
$985$	2.15433e11	+	2.96518e11i	0.228859	+	0.314997i
$986$	2.49444e11	−	8.10492e10i	0.263916	−	0.0857514i
$987$	−1.43010e11	−	4.64668e10i	−0.150695	−	0.0489637i
$988$	−3.96573e11	−	2.88127e11i	−0.416194	−	0.302383i
$989$		−	2.77252e11i		−	0.289794i
$990$	9.47617e11	−	5.27915e10i	0.986489	−	0.0549571i
$991$	−1.82757e12			−1.89487			−0.947436	−	0.319946i	$-0.896335\pi$
$991$	−1.82757e12			−1.89487			−0.947436	+	0.319946i	$0.896335\pi$
$992$	1.63847e11	−	2.25516e11i	0.169196	−	0.232879i
$993$	6.07309e10	−	1.86910e11i	0.0624615	−	0.192237i
$994$	1.35498e11	+	4.17020e11i	0.138799	+	0.427181i
$995$	−3.75471e11	+	2.72795e11i	−0.383075	+	0.278320i
$996$	−8.06496e10	−	1.11005e11i	−0.0819530	−	0.112799i
$997$	1.38677e12	−	4.50590e11i	1.40354	−	0.456038i	0.493207	−	0.869912i	$-0.335824\pi$
$997$	1.38677e12	−	4.50590e11i	1.40354	−	0.456038i	0.910334	+	0.413874i	$0.135824\pi$
$998$	−4.95075e11	−	1.60860e11i	−0.499056	−	0.162153i
$999$	6.41338e11	+	4.65959e11i	0.643910	+	0.467828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.9.d.a.7.7	✓	32
11.5	even	5		242.9.b.e.241.24		32
11.6	odd	10		242.9.b.e.241.23		32
11.8	odd	10	inner	22.9.d.a.19.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.9.d.a.7.7	✓	32	1.1	even	1	trivial
22.9.d.a.19.7	yes	32	11.8	odd	10	inner
242.9.b.e.241.23		32	11.6	odd	10
242.9.b.e.241.24		32	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(6.65003 - 9.15298i) q^{2} +(10.6908 - 32.9028i) q^{3} +(-39.5542 - 121.735i) q^{4} +(-864.151 + 627.842i) q^{5} +(-230.065 - 316.657i) q^{6} +(-1443.95 + 469.167i) q^{7} +(-1377.28 - 447.504i) q^{8} +(4339.66 + 3152.95i) q^{9} +O(q^{10})\)	\(q+(6.65003 - 9.15298i) q^{2} +(10.6908 - 32.9028i) q^{3} +(-39.5542 - 121.735i) q^{4} +(-864.151 + 627.842i) q^{5} +(-230.065 - 316.657i) q^{6} +(-1443.95 + 469.167i) q^{7} +(-1377.28 - 447.504i) q^{8} +(4339.66 + 3152.95i) q^{9} +12084.7i q^{10} +(-9251.29 - 11347.8i) q^{11} -4428.29 q^{12} +(-17502.9 + 24090.7i) q^{13} +(-5308.02 + 16336.4i) q^{14} +(11419.3 + 35145.1i) q^{15} +(-13254.9 + 9630.27i) q^{16} +(11437.6 + 15742.5i) q^{17} +(57717.8 - 18753.6i) q^{18} +(-122312. - 39741.6i) q^{19} +(110611. + 80363.8i) q^{20} +52525.7i q^{21} +(-165388. + 9213.70i) q^{22} -330077. q^{23} +(-29448.3 + 40532.0i) q^{24} +(231861. - 713595. i) q^{25} +(104107. + 320408. i) q^{26} +(333769. - 242498. i) q^{27} +(114228. + 157222. i) q^{28} +(1.13306e6 - 368153. i) q^{29} +(397621. + 129195. i) q^{30} +(-1.21661e6 - 883920. i) q^{31} +185364. i q^{32} +(-472277. + 183076. i) q^{33} +220151. q^{34} +(953227. - 1.31200e6i) q^{35} +(212173. - 653002. i) q^{36} +(593777. + 1.82746e6i) q^{37} +(-1.17713e6 + 855238. i) q^{38} +(605532. + 833443. i) q^{39} +(1.47114e6 - 478002. i) q^{40} +(-2.24851e6 - 730584. i) q^{41} +(480766. + 349297. i) q^{42} +839962. i q^{43} +(-1.01550e6 + 1.57506e6i) q^{44} -5.72968e6 q^{45} +(-2.19502e6 + 3.02119e6i) q^{46} +(-884649. + 2.72267e6i) q^{47} +(175157. + 539079. i) q^{48} +(-2.79895e6 + 2.03356e6i) q^{49} +(-4.98964e6 - 6.86765e6i) q^{50} +(640247. - 208029. i) q^{51} +(3.62501e6 + 1.17784e6i) q^{52} +(6.77508e6 + 4.92238e6i) q^{53} -4.66760e6i q^{54} +(1.51191e7 + 3.99786e6i) q^{55} +2.19867e6 q^{56} +(-2.61522e6 + 3.59954e6i) q^{57} +(4.16518e6 - 1.28191e7i) q^{58} +(-2.13217e6 - 6.56216e6i) q^{59} +(3.82671e6 - 2.78027e6i) q^{60} +(7.62554e6 + 1.04957e7i) q^{61} +(-1.61810e7 + 5.25753e6i) q^{62} +(-7.74551e6 - 2.51667e6i) q^{63} +(1.69663e6 + 1.23268e6i) q^{64} -3.18071e7i q^{65} +(-1.46496e6 + 5.54021e6i) q^{66} +6.19194e6 q^{67} +(1.46401e6 - 2.01504e6i) q^{68} +(-3.52877e6 + 1.08604e7i) q^{69} +(-5.66976e6 - 1.74497e7i) q^{70} +(2.06518e7 - 1.50044e7i) q^{71} +(-4.56596e6 - 6.28450e6i) q^{72} +(-1.34645e7 + 4.37489e6i) q^{73} +(2.06753e7 + 6.71781e6i) q^{74} +(-2.10005e7 - 1.52577e7i) q^{75} +1.64616e7i q^{76} +(1.86824e7 + 1.20452e7i) q^{77} +1.16553e7 q^{78} +(-3.00155e7 + 4.13128e7i) q^{79} +(5.40797e6 - 1.66440e7i) q^{80} +(6.46494e6 + 1.98970e7i) q^{81} +(-2.16397e7 + 1.57221e7i) q^{82} +(1.82124e7 + 2.50672e7i) q^{83} +(6.39422e6 - 2.07761e6i) q^{84} +(-1.97676e7 - 6.42288e6i) q^{85} +(7.68815e6 + 5.58577e6i) q^{86} -4.12166e7i q^{87} +(7.66340e6 + 1.97691e7i) q^{88} -4.52461e7 q^{89} +(-3.81025e7 + 5.24436e7i) q^{90} +(1.39708e7 - 4.29976e7i) q^{91} +(1.30559e7 + 4.01820e7i) q^{92} +(-4.20899e7 + 3.05801e7i) q^{93} +(1.90376e7 + 2.62030e7i) q^{94} +(1.30648e8 - 4.24500e7i) q^{95} +(6.09898e6 + 1.98168e6i) q^{96} +(-9.87571e7 - 7.17513e7i) q^{97} +3.91420e7i q^{98} +(-4.36845e6 - 7.84144e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9}+O(q^{10}) \) 32 * q - 182 * q^3 + 1024 * q^4 + 1410 * q^5 + 4480 * q^6 - 10950 * q^7 - 1402 * q^9	\( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9} - 47598 q^{11} - 21504 q^{12} + 24990 q^{13} + 106752 q^{14} + 273582 q^{15} - 131072 q^{16} - 553530 q^{17} + 152320 q^{18} + 442680 q^{19} - 180480 q^{20} - 359040 q^{22} - 317064 q^{23} + 573440 q^{24} - 918738 q^{25} - 782592 q^{26} + 714484 q^{27} + 51200 q^{28} + 2380710 q^{29} + 4488960 q^{30} + 181654 q^{31} - 628628 q^{33} - 3865088 q^{34} - 12788370 q^{35} + 5097216 q^{36} - 6976698 q^{37} - 15360 q^{38} + 17382010 q^{39} + 3768320 q^{40} + 5153790 q^{41} - 15355648 q^{42} + 2744064 q^{44} + 5954792 q^{45} - 15447040 q^{46} - 13476378 q^{47} - 2981888 q^{48} + 19896222 q^{49} + 13816320 q^{50} + 37405440 q^{51} + 18368000 q^{52} - 847422 q^{53} - 47212238 q^{55} + 1572864 q^{56} - 119710960 q^{57} - 29125376 q^{58} - 49425120 q^{59} + 12710144 q^{60} + 26432690 q^{61} + 64485120 q^{62} + 289643740 q^{63} + 16777216 q^{64} - 78840064 q^{66} - 133260476 q^{67} - 70851840 q^{68} - 33873776 q^{69} - 50942720 q^{70} + 38304066 q^{71} + 61603840 q^{72} + 208728710 q^{73} + 56355840 q^{74} - 62835924 q^{75} + 92206590 q^{77} - 74988544 q^{78} - 247776110 q^{79} - 22609920 q^{80} - 622273104 q^{81} + 17468928 q^{82} + 434637000 q^{83} + 159336960 q^{84} + 286821150 q^{85} - 7040640 q^{86} + 101498880 q^{88} - 336205452 q^{89} - 270179840 q^{90} - 167007498 q^{91} + 29901312 q^{92} + 65388262 q^{93} + 429944320 q^{94} + 1032904950 q^{95} - 75153432 q^{97} - 459062342 q^{99}+O(q^{100}) \) 32 * q - 182 * q^3 + 1024 * q^4 + 1410 * q^5 + 4480 * q^6 - 10950 * q^7 - 1402 * q^9 - 47598 * q^11 - 21504 * q^12 + 24990 * q^13 + 106752 * q^14 + 273582 * q^15 - 131072 * q^16 - 553530 * q^17 + 152320 * q^18 + 442680 * q^19 - 180480 * q^20 - 359040 * q^22 - 317064 * q^23 + 573440 * q^24 - 918738 * q^25 - 782592 * q^26 + 714484 * q^27 + 51200 * q^28 + 2380710 * q^29 + 4488960 * q^30 + 181654 * q^31 - 628628 * q^33 - 3865088 * q^34 - 12788370 * q^35 + 5097216 * q^36 - 6976698 * q^37 - 15360 * q^38 + 17382010 * q^39 + 3768320 * q^40 + 5153790 * q^41 - 15355648 * q^42 + 2744064 * q^44 + 5954792 * q^45 - 15447040 * q^46 - 13476378 * q^47 - 2981888 * q^48 + 19896222 * q^49 + 13816320 * q^50 + 37405440 * q^51 + 18368000 * q^52 - 847422 * q^53 - 47212238 * q^55 + 1572864 * q^56 - 119710960 * q^57 - 29125376 * q^58 - 49425120 * q^59 + 12710144 * q^60 + 26432690 * q^61 + 64485120 * q^62 + 289643740 * q^63 + 16777216 * q^64 - 78840064 * q^66 - 133260476 * q^67 - 70851840 * q^68 - 33873776 * q^69 - 50942720 * q^70 + 38304066 * q^71 + 61603840 * q^72 + 208728710 * q^73 + 56355840 * q^74 - 62835924 * q^75 + 92206590 * q^77 - 74988544 * q^78 - 247776110 * q^79 - 22609920 * q^80 - 622273104 * q^81 + 17468928 * q^82 + 434637000 * q^83 + 159336960 * q^84 + 286821150 * q^85 - 7040640 * q^86 + 101498880 * q^88 - 336205452 * q^89 - 270179840 * q^90 - 167007498 * q^91 + 29901312 * q^92 + 65388262 * q^93 + 429944320 * q^94 + 1032904950 * q^95 - 75153432 * q^97 - 459062342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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