LMFDB - Embedded newform 32.6.g.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,6,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, 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:	$5.13228223402$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	32.5
Dual form			32.6.g.a.13.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.48012 + 3.45378i) q^{2} +(-4.24511 - 10.2486i) q^{3} +(8.14287 + 30.9466i) q^{4} +(36.3338 + 15.0500i) q^{5} +(16.3778 - 60.5765i) q^{6} +(153.750 + 153.750i) q^{7} +(-70.4017 + 166.768i) q^{8} +(84.8142 - 84.8142i) q^{9} +O(q^{10})$	\(q+(4.48012 + 3.45378i) q^{2} +(-4.24511 - 10.2486i) q^{3} +(8.14287 + 30.9466i) q^{4} +(36.3338 + 15.0500i) q^{5} +(16.3778 - 60.5765i) q^{6} +(153.750 + 153.750i) q^{7} +(-70.4017 + 166.768i) q^{8} +(84.8142 - 84.8142i) q^{9} +(110.801 + 192.914i) q^{10} +(167.030 - 403.247i) q^{11} +(282.592 - 214.825i) q^{12} +(-1073.76 + 444.766i) q^{13} +(157.800 + 1219.84i) q^{14} -436.259i q^{15} +(-891.387 + 503.989i) q^{16} -1210.04i q^{17} +(672.907 - 87.0482i) q^{18} +(781.235 - 323.598i) q^{19} +(-169.884 + 1246.96i) q^{20} +(923.038 - 2228.41i) q^{21} +(2141.04 - 1229.71i) q^{22} +(-353.658 + 353.658i) q^{23} +(2008.00 + 13.5699i) q^{24} +(-1116.06 - 1116.06i) q^{25} +(-6346.69 - 1715.92i) q^{26} +(-3719.68 - 1540.74i) q^{27} +(-3506.08 + 6010.02i) q^{28} +(-470.174 - 1135.10i) q^{29} +(1506.74 - 1954.49i) q^{30} +6693.08 q^{31} +(-5734.18 - 820.724i) q^{32} -4841.77 q^{33} +(4179.21 - 5421.12i) q^{34} +(3272.40 + 7900.27i) q^{35} +(3315.34 + 1934.08i) q^{36} +(-7625.91 - 3158.75i) q^{37} +(4617.66 + 1248.45i) q^{38} +(9116.44 + 9116.44i) q^{39} +(-5067.81 + 4999.78i) q^{40} +(1105.80 - 1105.80i) q^{41} +(11831.7 - 6795.57i) q^{42} +(2796.73 - 6751.90i) q^{43} +(13839.2 + 1885.44i) q^{44} +(4358.07 - 1805.17i) q^{45} +(-2805.89 + 362.974i) q^{46} +21741.1i q^{47} +(8949.21 + 6995.98i) q^{48} +30471.3i q^{49} +(-1145.46 - 8854.73i) q^{50} +(-12401.2 + 5136.75i) q^{51} +(-22507.5 - 29607.6i) q^{52} +(2074.15 - 5007.43i) q^{53} +(-11343.2 - 19749.6i) q^{54} +(12137.7 - 12137.7i) q^{55} +(-36464.9 + 14816.4i) q^{56} +(-6632.85 - 6632.85i) q^{57} +(1813.95 - 6709.26i) q^{58} +(3873.01 + 1604.25i) q^{59} +(13500.7 - 3552.40i) q^{60} +(-8145.63 - 19665.3i) q^{61} +(29985.8 + 23116.4i) q^{62} +26080.4 q^{63} +(-22855.2 - 23481.5i) q^{64} -45707.5 q^{65} +(-21691.7 - 16722.4i) q^{66} +(-6148.97 - 14844.9i) q^{67} +(37446.7 - 9853.20i) q^{68} +(5125.82 + 2123.18i) q^{69} +(-12625.0 + 46696.2i) q^{70} +(-31210.6 - 31210.6i) q^{71} +(8173.24 + 20115.4i) q^{72} +(-12349.9 + 12349.9i) q^{73} +(-23255.3 - 40489.7i) q^{74} +(-6700.28 + 16175.9i) q^{75} +(16375.8 + 21541.6i) q^{76} +(87680.2 - 36318.3i) q^{77} +(9356.57 + 72328.9i) q^{78} -1696.53i q^{79} +(-39972.5 + 4896.49i) q^{80} +15515.4i q^{81} +(8773.30 - 1134.93i) q^{82} +(24602.9 - 10190.8i) q^{83} +(76478.0 + 10419.2i) q^{84} +(18211.1 - 43965.4i) q^{85} +(35849.2 - 20590.0i) q^{86} +(-9637.25 + 9637.25i) q^{87} +(55489.5 + 56244.6i) q^{88} +(98244.6 + 98244.6i) q^{89} +(25759.3 + 6964.42i) q^{90} +(-233474. - 96707.9i) q^{91} +(-13824.3 - 8064.73i) q^{92} +(-28412.8 - 68594.6i) q^{93} +(-75088.8 + 97402.5i) q^{94} +33255.4 q^{95} +(15931.0 + 62251.4i) q^{96} -18431.3 q^{97} +(-105241. + 136515. i) q^{98} +(-20034.5 - 48367.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 76 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} - 4 q^{13} + 2476 q^{14} + 4176 q^{16} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 4 q^{21} - 12384 q^{22} + 1668 q^{23} + 21456 q^{24} - 4 q^{25} + 12976 q^{26} - 7468 q^{27} - 2184 q^{28} - 4 q^{29} - 32316 q^{30} + 23056 q^{31} - 18584 q^{32} - 8 q^{33} - 6256 q^{34} - 4780 q^{35} + 65584 q^{36} - 4 q^{37} + 404 q^{38} - 44908 q^{39} - 28952 q^{40} - 4 q^{41} - 53624 q^{42} + 32068 q^{43} + 3716 q^{44} + 968 q^{45} + 63324 q^{46} + 112368 q^{48} - 4524 q^{50} - 19912 q^{51} + 18468 q^{52} - 49460 q^{53} + 1312 q^{54} + 110044 q^{55} - 80984 q^{56} - 4 q^{57} - 84576 q^{58} - 28964 q^{59} - 46088 q^{60} + 96156 q^{61} + 63480 q^{62} - 158768 q^{63} - 49192 q^{64} - 8 q^{65} - 145012 q^{66} - 61164 q^{67} - 151216 q^{68} - 44644 q^{69} - 56296 q^{70} + 143836 q^{71} + 27092 q^{72} - 4 q^{73} + 213100 q^{74} + 205744 q^{75} + 255996 q^{76} - 14900 q^{77} + 83508 q^{78} - 97096 q^{80} + 435196 q^{82} - 329244 q^{83} + 597472 q^{84} + 12496 q^{85} + 269888 q^{86} - 282188 q^{87} - 199840 q^{88} - 4 q^{89} - 706840 q^{90} + 200108 q^{91} - 650328 q^{92} - 976 q^{93} - 261592 q^{94} + 577592 q^{95} - 501376 q^{96} - 8 q^{97} - 395624 q^{98} + 338544 q^{99}+O(q^{100}) \) 76 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 204 * q^10 - 4 * q^11 - 1588 * q^12 - 4 * q^13 + 2476 * q^14 + 4176 * q^16 - 1624 * q^18 - 4 * q^19 - 7604 * q^20 - 4 * q^21 - 12384 * q^22 + 1668 * q^23 + 21456 * q^24 - 4 * q^25 + 12976 * q^26 - 7468 * q^27 - 2184 * q^28 - 4 * q^29 - 32316 * q^30 + 23056 * q^31 - 18584 * q^32 - 8 * q^33 - 6256 * q^34 - 4780 * q^35 + 65584 * q^36 - 4 * q^37 + 404 * q^38 - 44908 * q^39 - 28952 * q^40 - 4 * q^41 - 53624 * q^42 + 32068 * q^43 + 3716 * q^44 + 968 * q^45 + 63324 * q^46 + 112368 * q^48 - 4524 * q^50 - 19912 * q^51 + 18468 * q^52 - 49460 * q^53 + 1312 * q^54 + 110044 * q^55 - 80984 * q^56 - 4 * q^57 - 84576 * q^58 - 28964 * q^59 - 46088 * q^60 + 96156 * q^61 + 63480 * q^62 - 158768 * q^63 - 49192 * q^64 - 8 * q^65 - 145012 * q^66 - 61164 * q^67 - 151216 * q^68 - 44644 * q^69 - 56296 * q^70 + 143836 * q^71 + 27092 * q^72 - 4 * q^73 + 213100 * q^74 + 205744 * q^75 + 255996 * q^76 - 14900 * q^77 + 83508 * q^78 - 97096 * q^80 + 435196 * q^82 - 329244 * q^83 + 597472 * q^84 + 12496 * q^85 + 269888 * q^86 - 282188 * q^87 - 199840 * q^88 - 4 * q^89 - 706840 * q^90 + 200108 * q^91 - 650328 * q^92 - 976 * q^93 - 261592 * q^94 + 577592 * q^95 - 501376 * q^96 - 8 * q^97 - 395624 * q^98 + 338544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	4.48012	+	3.45378i	0.791980	+	0.610547i
$2$	4.48012	+	3.45378i	0.791980	+	0.610547i
$3$	−4.24511	−	10.2486i	−0.272324	−	0.657448i	0.727258	−	0.686364i	$-0.240794\pi$
$3$	−4.24511	−	10.2486i	−0.272324	−	0.657448i	−0.999582	+	0.0289164i	$0.990794\pi$
$4$	8.14287	+	30.9466i	0.254465	+	0.967082i
$5$	36.3338	+	15.0500i	0.649959	+	0.269222i	0.683206	−	0.730225i	$-0.260585\pi$
$5$	36.3338	+	15.0500i	0.649959	+	0.269222i	−0.0332474	+	0.999447i	$0.510585\pi$
$6$	16.3778	−	60.5765i	0.185728	−	0.686952i
$7$	153.750	+	153.750i	1.18596	+	1.18596i	0.978174	+	0.207788i	$0.0666265\pi$
$7$	153.750	+	153.750i	1.18596	+	1.18596i	0.207788	+	0.978174i	$0.433373\pi$
$8$	−70.4017	+	166.768i	−0.388918	+	0.921272i
$9$	84.8142	−	84.8142i	0.349030	−	0.349030i
$10$	110.801	+	192.914i	0.350382	+	0.610049i
$11$	167.030	−	403.247i	0.416211	−	1.00482i	−0.567225	−	0.823563i	$-0.691983\pi$
$11$	167.030	−	403.247i	0.416211	−	1.00482i	0.983435	−	0.181259i	$-0.0580172\pi$
$12$	282.592	−	214.825i	0.566509	−	0.430657i
$13$	−1073.76	+	444.766i	−1.76217	+	0.729916i	−0.765968	+	0.642879i	$0.777740\pi$
$13$	−1073.76	+	444.766i	−1.76217	+	0.729916i	−0.996205	+	0.0870370i	$0.972260\pi$
$14$	157.800	+	1219.84i	0.215173	+	1.66334i
$15$		−	436.259i		−	0.500629i
$16$	−891.387	+	503.989i	−0.870495	+	0.492177i
$17$		−	1210.04i		−	1.01549i	−0.861506	−	0.507747i	$-0.830478\pi$
$17$		−	1210.04i		−	1.01549i	0.861506	−	0.507747i	$-0.169522\pi$
$18$	672.907	−	87.0482i	0.489523	−	0.0633255i
$19$	781.235	−	323.598i	0.496476	−	0.205647i	−0.120373	−	0.992729i	$-0.538409\pi$
$19$	781.235	−	323.598i	0.496476	−	0.205647i	0.616849	+	0.787082i	$0.288409\pi$
$20$	−169.884	+	1246.96i	−0.0949680	+	0.697071i
$21$	923.038	−	2228.41i	0.456742	−	1.10267i
$22$	2141.04	−	1229.71i	0.943122	−	0.541683i
$23$	−353.658	+	353.658i	−0.139400	+	0.139400i	−0.773363	−	0.633963i	$-0.781427\pi$
$23$	−353.658	+	353.658i	−0.139400	+	0.139400i	0.633963	+	0.773363i	$0.281427\pi$
$24$	2008.00	+	13.5699i	0.711600	+	0.00480895i
$25$	−1116.06	−	1116.06i	−0.357141	−	0.357141i
$26$	−6346.69	−	1715.92i	−1.84125	−	0.497811i
$27$	−3719.68	−	1540.74i	−0.981965	−	0.406743i
$28$	−3506.08	+	6010.02i	−0.845137	+	1.44871i
$29$	−470.174	−	1135.10i	−0.103816	−	0.250634i	0.863433	−	0.504464i	$-0.168310\pi$
$29$	−470.174	−	1135.10i	−0.103816	−	0.250634i	−0.967249	+	0.253830i	$0.918310\pi$
$30$	1506.74	−	1954.49i	0.305658	−	0.396489i
$31$	6693.08			1.25090			0.625448	−	0.780265i	$-0.284916\pi$
$31$	6693.08			1.25090			0.625448	+	0.780265i	$0.284916\pi$
$32$	−5734.18	−	820.724i	−0.989912	−	0.141684i
$33$	−4841.77			−0.773962
$34$	4179.21	−	5421.12i	0.620007	−	0.804251i
$35$	3272.40	+	7900.27i	0.451540	+	1.09011i
$36$	3315.34	+	1934.08i	0.426356	+	0.248725i
$37$	−7625.91	−	3158.75i	−0.915771	−	0.379325i	−0.125508	−	0.992093i	$-0.540056\pi$
$37$	−7625.91	−	3158.75i	−0.915771	−	0.379325i	−0.790263	+	0.612768i	$0.790056\pi$
$38$	4617.66	+	1248.45i	0.518756	+	0.140253i
$39$	9116.44	+	9116.44i	0.959763	+	0.959763i
$40$	−5067.81	+	4999.78i	−0.500807	+	0.494084i
$41$	1105.80	−	1105.80i	0.102735	−	0.102735i	−0.653871	−	0.756606i	$-0.726856\pi$
$41$	1105.80	−	1105.80i	0.102735	−	0.102735i	0.756606	+	0.653871i	$0.226856\pi$
$42$	11831.7	−	6795.57i	1.03496	−	0.594433i
$43$	2796.73	−	6751.90i	0.230664	−	0.556872i	−0.765592	−	0.643326i	$-0.777554\pi$
$43$	2796.73	−	6751.90i	0.230664	−	0.556872i	0.996256	+	0.0864548i	$0.0275538\pi$
$44$	13839.2	+	1885.44i	1.07766	+	0.146818i
$45$	4358.07	−	1805.17i	0.320821	−	0.132889i
$46$	−2805.89	+	362.974i	−0.195513	+	0.0252918i
$47$			21741.1i			1.43561i	0.696244	+	0.717805i	$0.254853\pi$
$47$			21741.1i			1.43561i	−0.696244	+	0.717805i	$0.745147\pi$
$48$	8949.21	+	6995.98i	0.560637	+	0.438274i
$49$			30471.3i			1.81301i
$50$	−1145.46	−	8854.73i	−0.0647971	−	0.500899i
$51$	−12401.2	+	5136.75i	−0.667634	+	0.276543i
$52$	−22507.5	−	29607.6i	−1.15430	−	1.51843i
$53$	2074.15	−	5007.43i	0.101426	−	0.244864i	−0.865018	−	0.501740i	$-0.832693\pi$
$53$	2074.15	−	5007.43i	0.101426	−	0.244864i	0.966444	+	0.256876i	$0.0826933\pi$
$54$	−11343.2	−	19749.6i	−0.529361	−	0.921669i
$55$	12137.7	−	12137.7i	0.541040	−	0.541040i
$56$	−36464.9	+	14816.4i	−1.55384	+	0.631352i
$57$	−6632.85	−	6632.85i	−0.270404	−	0.270404i
$58$	1813.95	−	6709.26i	0.0708036	−	0.261881i
$59$	3873.01	+	1604.25i	0.144850	+	0.0599988i	0.453931	−	0.891037i	$-0.350021\pi$
$59$	3873.01	+	1604.25i	0.144850	+	0.0599988i	−0.309081	+	0.951036i	$0.600021\pi$
$60$	13500.7	−	3552.40i	0.484150	−	0.127393i
$61$	−8145.63	−	19665.3i	−0.280285	−	0.676668i	0.719557	−	0.694433i	$-0.244345\pi$
$61$	−8145.63	−	19665.3i	−0.280285	−	0.676668i	−0.999842	+	0.0177651i	$0.994345\pi$
$62$	29985.8	+	23116.4i	0.990685	+	0.763731i
$63$	26080.4			0.827872
$64$	−22855.2	−	23481.5i	−0.697485	−	0.716599i
$65$	−45707.5			−1.34185
$66$	−21691.7	−	16722.4i	−0.612962	−	0.472540i
$67$	−6148.97	−	14844.9i	−0.167346	−	0.404009i	0.817852	−	0.575429i	$-0.195165\pi$
$67$	−6148.97	−	14844.9i	−0.167346	−	0.404009i	−0.985198	+	0.171419i	$0.945165\pi$
$68$	37446.7	−	9853.20i	0.982066	−	0.258407i
$69$	5125.82	+	2123.18i	0.129611	+	0.0536864i
$70$	−12625.0	+	46696.2i	−0.307955	+	1.13903i
$71$	−31210.6	−	31210.6i	−0.734778	−	0.734778i	0.236784	−	0.971562i	$-0.423907\pi$
$71$	−31210.6	−	31210.6i	−0.734778	−	0.734778i	−0.971562	+	0.236784i	$0.923907\pi$
$72$	8173.24	+	20115.4i	0.185807	+	0.457295i
$73$	−12349.9	+	12349.9i	−0.271242	+	0.271242i	−0.829600	−	0.558358i	$-0.811432\pi$
$73$	−12349.9	+	12349.9i	−0.271242	+	0.271242i	0.558358	+	0.829600i	$0.311432\pi$
$74$	−23255.3	−	40489.7i	−0.493677	−	0.859539i
$75$	−6700.28	+	16175.9i	−0.137543	+	0.332059i
$76$	16375.8	+	21541.6i	0.325213	+	0.427803i
$77$	87680.2	−	36318.3i	1.68529	−	0.698070i
$78$	9356.57	+	72328.9i	0.174133	+	1.34609i
$79$		−	1696.53i		−	0.0305840i	−0.999883	−	0.0152920i	$-0.995132\pi$
$79$		−	1696.53i		−	0.0305840i	0.999883	−	0.0152920i	$-0.00486779\pi$
$80$	−39972.5	+	4896.49i	−0.698291	+	0.0855382i
$81$			15515.4i			0.262754i
$82$	8773.30	−	1134.93i	0.144088	−	0.0186395i
$83$	24602.9	−	10190.8i	0.392004	−	0.162373i	−0.177970	−	0.984036i	$-0.556953\pi$
$83$	24602.9	−	10190.8i	0.392004	−	0.162373i	0.569974	+	0.821662i	$0.306953\pi$
$84$	76478.0	+	10419.2i	1.18260	+	0.161116i
$85$	18211.1	−	43965.4i	0.273393	−	0.660030i
$86$	35849.2	−	20590.0i	0.522677	−	0.300200i
$87$	−9637.25	+	9637.25i	−0.136507	+	0.136507i
$88$	55489.5	+	56244.6i	0.763843	+	0.774237i
$89$	98244.6	+	98244.6i	1.31472	+	1.31472i	0.917893	+	0.396828i	$0.129889\pi$
$89$	98244.6	+	98244.6i	1.31472	+	1.31472i	0.396828	+	0.917893i	$0.370111\pi$
$90$	25759.3	+	6964.42i	0.335219	+	0.0906314i
$91$	−233474.	−	96707.9i	−2.95552	−	1.22422i
$92$	−13824.3	−	8064.73i	−0.170284	−	0.0993392i
$93$	−28412.8	−	68594.6i	−0.340649	−	0.822399i
$94$	−75088.8	+	97402.5i	−0.876507	+	1.13697i
$95$	33255.4			0.378053
$96$	15931.0	+	62251.4i	0.176426	+	0.689399i
$97$	−18431.3			−0.198897			−0.0994484	−	0.995043i	$-0.531708\pi$
$97$	−18431.3			−0.198897			−0.0994484	+	0.995043i	$0.531708\pi$
$98$	−105241.	+	136515.i	−1.10693	+	1.43587i
$99$	−20034.5	−	48367.6i	−0.205443	−	0.495983i
$100$	25450.5	−	43626.4i	0.254505	−	0.436264i
$101$	141764.	+	58720.7i	1.38281	+	0.572780i	0.945232	−	0.326399i	$-0.105835\pi$
$101$	141764.	+	58720.7i	1.38281	+	0.572780i	0.437581	+	0.899179i	$0.355835\pi$
$102$	−73300.0	−	19817.8i	−0.697596	−	0.188605i
$103$	89456.9	+	89456.9i	0.830847	+	0.830847i	0.987633	−	0.156786i	$-0.0501133\pi$
$103$	89456.9	+	89456.9i	0.830847	+	0.830847i	−0.156786	+	0.987633i	$0.550113\pi$
$104$	1421.74	−	210381.i	0.0128895	−	1.90732i
$105$	67075.0	−	67075.0i	0.593728	−	0.593728i
$106$	26587.0	−	15270.2i	0.229829	−	0.132002i
$107$	21484.0	−	51866.9i	0.181407	−	0.437956i	−0.806850	−	0.590757i	$-0.798829\pi$
$107$	21484.0	−	51866.9i	0.181407	−	0.437956i	0.988257	+	0.152801i	$0.0488293\pi$
$108$	17391.9	−	127658.i	0.143479	−	1.05314i
$109$	−176093.	+	72940.1i	−1.41963	+	0.588031i	−0.954768	−	0.297351i	$-0.903897\pi$
$109$	−176093.	+	72940.1i	−1.41963	+	0.588031i	−0.464864	+	0.885382i	$0.653897\pi$
$110$	96299.1	−	12457.4i	0.758823	−	0.0981625i
$111$			91564.1i			0.705371i
$112$	−214539.	−	59562.6i	−1.61608	−	0.448672i
$113$			119875.i			0.883148i	0.897225	+	0.441574i	$0.145580\pi$
$113$			119875.i			0.883148i	−0.897225	+	0.441574i	$0.854420\pi$
$114$	−6807.57	−	52624.3i	−0.0490602	−	0.379249i
$115$	−18172.3	+	7527.21i	−0.128134	+	0.0530749i
$116$	31299.0	−	23793.3i	0.215966	−	0.164176i
$117$	−53347.6	+	128792.i	−0.360288	+	0.869813i
$118$	11810.8	+	20563.7i	0.0780862	+	0.135956i
$119$	186044.	−	186044.i	1.20434	−	1.20434i
$120$	72754.1	+	30713.4i	0.461216	+	0.194704i
$121$	−20828.5	−	20828.5i	−0.129329	−	0.129329i
$122$	31426.1	−	116236.i	0.191158	−	0.707035i
$123$	−16027.1	−	6638.66i	−0.0955198	−	0.0395656i
$124$	54500.9	+	207128.i	0.318309	+	1.20972i
$125$	−70785.3	−	170891.i	−0.405198	−	0.978236i
$126$	116843.	+	90075.9i	0.655658	+	0.505455i
$127$	−274914.			−1.51248			−0.756238	−	0.654297i	$-0.772965\pi$
$127$	−274914.			−1.51248			−0.756238	+	0.654297i	$0.772965\pi$
$128$	−21294.1	−	184137.i	−0.114877	−	0.993380i
$129$	−81069.9			−0.428929
$130$	−204775.	−	157863.i	−1.06272	−	0.819262i
$131$	49905.8	+	120483.i	0.254081	+	0.613406i	0.998526	−	0.0542780i	$-0.0172857\pi$
$131$	49905.8	+	120483.i	0.254081	+	0.613406i	−0.744445	+	0.667684i	$0.767286\pi$
$132$	−39425.9	−	149837.i	−0.196946	−	0.748485i
$133$	169868.	+	70361.8i	0.832691	+	0.344912i
$134$	23723.0	−	87744.2i	0.114132	−	0.422140i
$135$	−111962.	−	111962.i	−0.528733	−	0.528733i
$136$	201796.	+	85188.9i	0.935547	+	0.394944i
$137$	−78400.5	+	78400.5i	−0.356876	+	0.356876i	−0.862660	−	0.505784i	$-0.831203\pi$
$137$	−78400.5	+	78400.5i	−0.356876	+	0.356876i	0.505784	+	0.862660i	$0.331203\pi$
$138$	15631.3	+	27215.5i	0.0698709	+	0.121652i
$139$	−86039.4	+	207717.i	−0.377712	+	0.911876i	0.614683	+	0.788775i	$0.289284\pi$
$139$	−86039.4	+	207717.i	−0.377712	+	0.911876i	−0.992394	+	0.123102i	$0.960716\pi$
$140$	−217840.	+	165601.i	−0.939328	+	0.714072i
$141$	222815.	−	92293.2i	0.943838	−	0.390951i
$142$	−32032.7	−	247622.i	−0.133313	−	1.03055i
$143$			507279.i			2.07447i
$144$	−32856.9	+	118348.i	−0.132044	+	0.475613i
$145$		−	48318.7i		−	0.190851i
$146$	−97983.0	+	12675.2i	−0.380425	+	0.0492123i
$147$	312288.	−	129354.i	1.19196	−	0.493726i
$148$	35656.0	−	261717.i	0.133807	−	0.982151i
$149$	−101993.	+	246233.i	−0.376361	+	0.908615i	0.616281	+	0.787526i	$0.288639\pi$
$149$	−101993.	+	246233.i	−0.376361	+	0.908615i	−0.992642	+	0.121089i	$0.961361\pi$
$150$	−85885.9	+	49328.6i	−0.311669	+	0.179007i
$151$	222023.	−	222023.i	0.792421	−	0.792421i	−0.189466	−	0.981887i	$-0.560676\pi$
$151$	222023.	−	222023.i	0.792421	−	0.792421i	0.981887	+	0.189466i	$0.0606757\pi$
$152$	−1034.42	+	153067.i	−0.00363150	+	0.537369i
$153$	−102629.	−	102629.i	−0.354438	−	0.354438i
$154$	518253.	+	140117.i	1.76092	+	0.476092i
$155$	243185.	+	100731.i	0.813032	+	0.336769i
$156$	−207889.	+	356357.i	−0.683944	+	1.17240i
$157$	−37695.9	−	91006.0i	−0.122052	−	0.294660i	0.851031	−	0.525116i	$-0.175978\pi$
$157$	−37695.9	−	91006.0i	−0.122052	−	0.294660i	−0.973083	+	0.230456i	$0.925978\pi$
$158$	5859.45	−	7600.67i	0.0186730	−	0.0242219i
$159$	−60124.1			−0.188606
$160$	−195993.	−	116119.i	−0.605258	−	0.358595i
$161$	−108750.			−0.330647
$162$	−53586.6	+	69510.7i	−0.160424	+	0.208096i
$163$	139069.	+	335742.i	0.409979	+	0.989776i	0.985143	+	0.171738i	$0.0549382\pi$
$163$	139069.	+	335742.i	0.409979	+	0.989776i	−0.575164	+	0.818038i	$0.695062\pi$
$164$	43225.2	+	25216.4i	0.125495	+	0.0732105i
$165$	−175920.	−	72868.5i	−0.503043	−	0.208367i
$166$	145421.	+	39316.6i	0.409596	+	0.110740i
$167$	−158093.	−	158093.i	−0.438652	−	0.438652i	0.452906	−	0.891558i	$-0.350387\pi$
$167$	−158093.	−	158093.i	−0.438652	−	0.438652i	−0.891558	+	0.452906i	$0.850387\pi$
$168$	306644.	+	310817.i	0.838227	+	0.849634i
$169$	692599.	−	692599.i	1.86537	−	1.86537i
$170$	233434.	−	134073.i	0.619501	−	0.355811i
$171$	38814.1	−	93705.6i	0.101508	−	0.245062i
$172$	231722.	+	31569.5i	0.597236	+	0.0813666i
$173$	−518782.	+	214887.i	−1.31786	+	0.545876i	−0.927168	−	0.374645i	$-0.877765\pi$
$173$	−518782.	+	214887.i	−1.31786	+	0.545876i	−0.390693	+	0.920521i	$0.627765\pi$
$174$	−76460.9	+	9891.10i	−0.191455	+	0.0247669i
$175$		−	343190.i		−	0.847110i
$176$	54343.2	+	443630.i	0.132240	+	1.07954i
$177$		−	46503.1i		−	0.111570i
$178$	100832.	+	779462.i	0.238534	+	1.84393i
$179$	349227.	−	144654.i	0.814657	−	0.337442i	0.0638466	−	0.997960i	$-0.479663\pi$
$179$	349227.	−	144654.i	0.814657	−	0.337442i	0.750810	+	0.660518i	$0.229663\pi$
$180$	91351.2	+	120168.i	0.210152	+	0.276445i
$181$	−34503.2	+	83298.0i	−0.0782821	+	0.188990i	−0.958175	−	0.286182i	$-0.907614\pi$
$181$	−34503.2	+	83298.0i	−0.0782821	+	0.188990i	0.879893	+	0.475171i	$0.157614\pi$
$182$	−711981.	−	1.23963e6i	−1.59327	−	2.77404i
$183$	−166963.	+	166963.i	−0.368546	+	0.368546i
$184$	−34080.8	−	83877.0i	−0.0742104	−	0.182641i
$185$	−229539.	−	229539.i	−0.493091	−	0.493091i
$186$	109618.	−	405443.i	0.232326	−	0.859306i
$187$	−487945.	−	202113.i	−1.02039	−	0.422660i
$188$	−672813.	+	177035.i	−1.38835	+	0.365312i
$189$	−335012.	−	808791.i	−0.682191	−	1.64696i
$190$	148988.	+	114857.i	0.299411	+	0.230819i
$191$	−27789.4			−0.0551182			−0.0275591	−	0.999620i	$-0.508773\pi$
$191$	−27789.4			−0.0551182			−0.0275591	+	0.999620i	$0.508773\pi$
$192$	−143630.	+	333915.i	−0.281184	+	0.653707i
$193$	−772672.			−1.49314			−0.746572	−	0.665304i	$-0.768302\pi$
$193$	−772672.			−1.49314			−0.746572	+	0.665304i	$0.768302\pi$
$194$	−82574.5	−	63657.7i	−0.157522	−	0.121436i
$195$	194033.	+	468437.i	0.365417	+	0.882196i
$196$	−942984.	+	248124.i	−1.75333	+	0.461348i
$197$	339710.	+	140712.i	0.623653	+	0.258325i	0.672053	−	0.740503i	$-0.265412\pi$
$197$	339710.	+	140712.i	0.623653	+	0.258325i	−0.0484008	+	0.998828i	$0.515412\pi$
$198$	77293.8	−	285887.i	0.140114	−	0.518241i
$199$	−182519.	−	182519.i	−0.326721	−	0.326721i	0.524618	−	0.851338i	$-0.324208\pi$
$199$	−182519.	−	182519.i	−0.326721	−	0.326721i	−0.851338	+	0.524618i	$0.824208\pi$
$200$	264697.	−	107551.i	0.467922	−	0.190125i
$201$	−126037.	+	126037.i	−0.220043	+	0.220043i
$202$	432312.	+	752698.i	0.745451	+	1.29790i
$203$	102233.	−	246812.i	0.174120	−	0.420364i
$204$	−259947.	−	341948.i	−0.437329	−	0.575287i
$205$	56820.2	−	23535.7i	0.0944318	−	0.0391149i
$206$	91813.2	+	709741.i	0.150743	+	1.16528i
$207$			59990.5i			0.0973097i
$208$	732978.	−	937621.i	1.17472	−	1.50269i
$209$		−	369081.i		−	0.584462i
$210$	532165.	−	68841.7i	0.832719	−	0.107722i
$211$	671828.	−	278280.i	1.03885	−	0.430305i	0.202949	−	0.979189i	$-0.434947\pi$
$211$	671828.	−	278280.i	1.03885	−	0.430305i	0.835898	+	0.548885i	$0.184947\pi$
$212$	171853.	+	23413.0i	0.262613	+	0.0357780i
$213$	−187373.	+	452357.i	−0.282981	+	0.683176i
$214$	275387.	−	158169.i	0.411064	−	0.236095i
$215$	203232.	−	203232.i	0.299844	−	0.299844i
$216$	518818.	−	511853.i	0.756625	−	0.746468i
$217$	1.02906e6	+	1.02906e6i	1.48352	+	1.48352i
$218$	−1.04084e6	−	281405.i	−1.48334	−	0.401043i
$219$	178996.	+	74142.6i	0.252193	+	0.104462i
$220$	474456.	+	276785.i	0.660906	+	0.385554i
$221$	538184.	+	1.29929e6i	0.741225	+	1.78948i
$222$	−316242.	+	410218.i	−0.430662	+	0.558640i
$223$	34047.4			0.0458481			0.0229241	−	0.999737i	$-0.492702\pi$
$223$	34047.4			0.0458481			0.0229241	+	0.999737i	$0.492702\pi$
$224$	−755446.	−	1.00782e6i	−1.00597	−	1.34203i
$225$	−189316.			−0.249305
$226$	−414022.	+	537055.i	−0.539203	+	0.699436i
$227$	296001.	+	714611.i	0.381267	+	0.920460i	0.991721	+	0.128408i	$0.0409869\pi$
$227$	296001.	+	714611.i	0.381267	+	0.920460i	−0.610454	+	0.792051i	$0.709013\pi$
$228$	151254.	−	259275.i	0.192695	−	0.330311i
$229$	147005.	+	60891.4i	0.185244	+	0.0767304i	0.473377	−	0.880860i	$-0.343035\pi$
$229$	147005.	+	60891.4i	0.185244	+	0.0767304i	−0.288134	+	0.957590i	$0.593035\pi$
$230$	−107411.	−	29040.2i	−0.133884	−	0.0361977i
$231$	−744424.	−	744424.i	−0.917889	−	0.917889i
$232$	222400.	+	1502.96i	0.271278	+	0.00183328i
$233$	836736.	−	836736.i	1.00971	−	1.00971i	0.00976194	−	0.999952i	$-0.496893\pi$
$233$	836736.	−	836736.i	1.00971	−	1.00971i	0.999952	−	0.00976194i	$-0.00310737\pi$
$234$	−683824.	+	392755.i	−0.816403	+	0.468901i
$235$	−327202.	+	789936.i	−0.386497	+	0.933087i
$236$	−18108.8	+	132920.i	−0.0211646	+	0.155349i
$237$	−17387.1	+	7201.97i	−0.0201074	+	0.00832876i
$238$	1.47605e6	−	190944.i	1.68912	−	0.218507i
$239$			682598.i			0.772983i	0.922293	+	0.386492i	$0.126313\pi$
$239$			682598.i			0.772983i	−0.922293	+	0.386492i	$0.873687\pi$
$240$	219870.	+	388876.i	0.246398	+	0.435796i
$241$		−	234529.i		−	0.260108i	−0.991507	−	0.130054i	$-0.958485\pi$
$241$		−	234529.i		−	0.260108i	0.991507	−	0.130054i	$-0.0415151\pi$
$242$	−21377.2	−	165251.i	−0.0234645	−	0.181387i
$243$	−744871.	+	308536.i	−0.809218	+	0.335189i
$244$	542246.	−	412212.i	0.583071	−	0.443247i
$245$	−458592.	+	1.10714e6i	−0.488102	+	1.17838i
$246$	−48875.0	−	85096.1i	−0.0514931	−	0.0896545i
$247$	−694933.	+	694933.i	−0.724771	+	0.724771i
$248$	−471204.	+	1.11619e6i	−0.486496	+	1.15242i
$249$	−208884.	−	208884.i	−0.213504	−	0.213504i
$250$	273092.	−	1.01009e6i	0.276350	−	1.02214i
$251$	−654901.	−	271269.i	−0.656132	−	0.271779i	0.0296777	−	0.999560i	$-0.490552\pi$
$251$	−654901.	−	271269.i	−0.656132	−	0.271779i	−0.685810	+	0.727781i	$0.740552\pi$
$252$	212369.	+	807101.i	0.210664	+	0.800620i
$253$	83539.9	+	201683.i	0.0820526	+	0.198093i
$254$	−1.23165e6	−	949493.i	−1.19785	−	0.923437i
$255$	−527891.			−0.508386
$256$	540567.	−	898498.i	0.515525	−	0.856875i
$257$	1.72544e6			1.62954			0.814772	−	0.579781i	$-0.196862\pi$
$257$	1.72544e6			1.62954			0.814772	+	0.579781i	$0.196862\pi$
$258$	−363203.	−	279997.i	−0.339703	−	0.261881i
$259$	−686826.	−	1.65814e6i	−0.636205	−	1.53594i
$260$	−372190.	−	1.41449e6i	−0.341453	−	1.29768i
$261$	−136150.	−	56395.2i	−0.123713	−	0.0512438i
$262$	−192538.	+	712142.i	−0.173286	+	0.640934i
$263$	541401.	+	541401.i	0.482647	+	0.482647i	0.905976	−	0.423329i	$-0.139139\pi$
$263$	541401.	+	541401.i	0.482647	+	0.482647i	−0.423329	+	0.905976i	$0.639139\pi$
$264$	340869.	−	807453.i	0.301008	−	0.713030i
$265$	150723.	−	150723.i	0.131846	−	0.131846i
$266$	518016.	+	901917.i	0.448889	+	0.781560i
$267$	589810.	−	1.42393e6i	0.506330	−	1.22239i
$268$	409330.	−	311170.i	0.348126	−	0.264644i
$269$	212588.	−	88056.9i	0.179126	−	0.0741964i	−0.291318	−	0.956626i	$-0.594094\pi$
$269$	212588.	−	88056.9i	0.179126	−	0.0741964i	0.470444	+	0.882430i	$0.344094\pi$
$270$	−114911.	−	888295.i	−0.0959296	−	0.741562i
$271$		−	1882.43i		−	0.00155702i	−1.00000		0.000778511i	$-0.999752\pi$
$271$		−	1882.43i		−	0.00155702i	1.00000		0.000778511i	$-0.000247808\pi$
$272$	609847.	+	1.07861e6i	0.499802	+	0.883983i
$273$			2.80331e6i			2.27649i
$274$	−622021.	+	80465.6i	−0.500528	+	0.0647491i
$275$	−636466.	+	263633.i	−0.507508	+	0.210217i
$276$	−23966.5	+	175915.i	−0.0189379	+	0.139005i
$277$	713504.	−	1.72255e6i	0.558723	−	1.34888i	−0.352054	−	0.935980i	$-0.614517\pi$
$277$	713504.	−	1.72255e6i	0.558723	−	1.34888i	0.910777	−	0.412898i	$-0.135483\pi$
$278$	−1.10288e6	+	633437.i	−0.855883	+	0.491577i
$279$	567668.	−	567668.i	0.436600	−	0.436600i
$280$	−1.54790e6	−	10460.6i	−1.17990	−	0.00797371i
$281$	−1.68552e6	−	1.68552e6i	−1.27341	−	1.27341i	−0.944286	−	0.329125i	$-0.893246\pi$
$281$	−1.68552e6	−	1.68552e6i	−1.27341	−	1.27341i	−0.329125	−	0.944286i	$-0.606754\pi$
$282$	1.31700e6	+	356070.i	0.986195	+	0.266633i
$283$	27520.3	+	11399.3i	0.0204262	+	0.00846081i	0.392873	−	0.919593i	$-0.371481\pi$
$283$	27520.3	+	11399.3i	0.0204262	+	0.00846081i	−0.372447	+	0.928053i	$0.621481\pi$
$284$	711719.	−	1.22001e6i	0.523616	−	0.897566i
$285$	−141173.	−	340821.i	−0.102953	−	0.248550i
$286$	−1.75203e6	+	2.27267e6i	−1.26656	+	1.64294i
$287$	340034.			0.243679
$288$	−555949.	+	416731.i	−0.394961	+	0.296057i
$289$	−44340.3			−0.0312287
$290$	166882.	−	216473.i	0.116524	−	0.151150i
$291$	78243.0	+	188895.i	0.0541643	+	0.130764i
$292$	−482753.	−	281625.i	−0.331335	−	0.193292i
$293$	−802173.	−	332271.i	−0.545882	−	0.226112i	0.0926612	−	0.995698i	$-0.470463\pi$
$293$	−802173.	−	332271.i	−0.545882	−	0.226112i	−0.638543	+	0.769586i	$0.720463\pi$
$294$	1.84585e6	+	499052.i	1.24545	+	0.336727i
$295$	116577.	+	116577.i	0.0779935	+	0.0779935i
$296$	1.06366e6	−	1.04938e6i	0.705622	−	0.696149i
$297$	−1.24260e6	+	1.24260e6i	−0.817409	+	0.817409i
$298$	−1.30737e6	+	750890.i	−0.852823	+	0.489819i
$299$	222449.	−	537039.i	0.143897	−	0.347398i
$300$	−555149.	−	75632.7i	−0.356128	−	0.0485184i
$301$	1.46811e6	−	608109.i	0.933987	−	0.386870i
$302$	1.76151e6	−	227871.i	1.11139	−	0.143771i
$303$		−	1.70216e6i		−	1.06511i
$304$	−533293.	+	682185.i	−0.330965	+	0.423368i
$305$		−	837106.i		−	0.515266i
$306$	−105332.	−	814244.i	−0.0643067	−	0.497108i
$307$	−1.50228e6	+	622263.i	−0.909712	+	0.376815i	−0.787946	−	0.615744i	$-0.788856\pi$
$307$	−1.50228e6	+	622263.i	−0.909712	+	0.376815i	−0.121765	+	0.992559i	$0.538856\pi$
$308$	1.83790e6	+	2.41767e6i	1.10394	+	1.45218i
$309$	537053.	−	1.29656e6i	0.319979	−	0.772497i
$310$	741596.	+	1.29119e6i	0.438292	+	0.763108i
$311$	1.29445e6	−	1.29445e6i	0.758898	−	0.758898i	−0.217224	−	0.976122i	$-0.569700\pi$
$311$	1.29445e6	−	1.29445e6i	0.758898	−	0.758898i	0.976122	+	0.217224i	$0.0697001\pi$
$312$	−2.16215e6	+	878519.i	−1.25747	+	0.510934i
$313$	1.35809e6	+	1.35809e6i	0.783553	+	0.783553i	0.980428	−	0.196876i	$-0.0630796\pi$
$313$	1.35809e6	+	1.35809e6i	0.783553	+	0.783553i	−0.196876	+	0.980428i	$0.563080\pi$
$314$	145432.	−	537911.i	0.0832408	−	0.307883i
$315$	947601.	+	392509.i	0.538083	+	0.222881i
$316$	52502.0	−	13814.7i	0.0295773	−	0.00778256i
$317$	−270698.	−	653523.i	−0.151299	−	0.365269i	0.829998	−	0.557766i	$-0.188341\pi$
$317$	−270698.	−	653523.i	−0.151299	−	0.365269i	−0.981298	+	0.192497i	$0.938341\pi$
$318$	−269363.	−	207655.i	−0.149372	−	0.115153i
$319$	−536259.			−0.295052
$320$	−477021.	−	1.19714e6i	−0.260413	−	0.653538i
$321$	−622764.			−0.337335
$322$	−487213.	−	375598.i	−0.261866	−	0.201876i
$323$	−391567.	−	945326.i	−0.208833	−	0.504168i
$324$	−480149.	+	126340.i	−0.254105	+	0.0668617i
$325$	1.69477e6	+	701997.i	0.890026	+	0.368661i
$326$	−536533.	+	1.98448e6i	−0.279610	+	1.03419i
$327$	1.49507e6	+	1.49507e6i	0.773199	+	0.773199i
$328$	106562.	+	262263.i	0.0546913	+	0.134602i
$329$	−3.34270e6	+	3.34270e6i	−1.70258	+	1.70258i
$330$	−536471.	−	934048.i	−0.271182	−	0.472155i
$331$	−1.09504e6	+	2.64367e6i	−0.549365	+	1.32628i	0.368587	+	0.929593i	$0.379842\pi$
$331$	−1.09504e6	+	2.64367e6i	−0.549365	+	1.32628i	−0.917952	+	0.396691i	$0.870158\pi$
$332$	515710.	+	678393.i	0.256780	+	0.337782i
$333$	−914692.	+	378878.i	−0.452027	+	0.187236i
$334$	−162257.	−	1.25429e6i	−0.0795860	−	0.615221i
$335$		−	631915.i		−	0.307643i
$336$	300310.	+	2.45158e6i	0.145118	+	1.18467i
$337$		−	3.09000e6i		−	1.48212i	−0.671438	−	0.741061i	$-0.734323\pi$
$337$		−	3.09000e6i		−	1.48212i	0.671438	−	0.741061i	$-0.265677\pi$
$338$	5.49500e6	−	710842.i	2.61623	−	0.338440i
$339$	1.22855e6	−	508883.i	0.580624	−	0.240502i
$340$	1.50887e6	+	205566.i	0.707872	+	0.0964394i
$341$	1.11795e6	−	2.69896e6i	0.520637	−	1.25693i
$342$	497530.	−	285757.i	0.230014	−	0.132109i
$343$	−2.10089e6	+	2.10089e6i	−0.964202	+	0.964202i
$344$	929108.	+	941751.i	0.423321	+	0.429082i
$345$	154287.	+	154287.i	0.0697880	+	0.0697880i
$346$	−3.06637e6	−	829040.i	−1.37700	−	0.372293i
$347$	441114.	+	182716.i	0.196665	+	0.0814614i	0.478842	−	0.877901i	$-0.341057\pi$
$347$	441114.	+	182716.i	0.196665	+	0.0814614i	−0.282177	+	0.959362i	$0.591057\pi$
$348$	−376715.	−	219766.i	−0.166750	−	0.0972773i
$349$	−441534.	−	1.06596e6i	−0.194044	−	0.468464i	0.796672	−	0.604412i	$-0.206592\pi$
$349$	−441534.	−	1.06596e6i	−0.194044	−	0.468464i	−0.990716	+	0.135948i	$0.956592\pi$
$350$	1.18530e6	−	1.53753e6i	0.517201	−	0.670894i
$351$	4.67931e6			2.02728
$352$	−1.28874e6	+	2.17520e6i	−0.554380	+	0.935715i
$353$	−969707.			−0.414194			−0.207097	−	0.978320i	$-0.566402\pi$
$353$	−969707.			−0.414194			−0.207097	+	0.978320i	$0.566402\pi$
$354$	160611.	−	208339.i	0.0681190	−	0.0883615i
$355$	−664282.	−	1.60372e6i	−0.279757	−	0.675394i
$356$	−2.24035e6	+	3.84033e6i	−0.936893	+	1.60599i
$357$	−2.69647e6	−	1.11691e6i	−1.11976	−	0.463819i
$358$	2.06418e6	+	558082.i	0.851216	+	0.230139i
$359$	2.37171e6	+	2.37171e6i	0.971238	+	0.971238i	0.999598	−	0.0283602i	$-0.00902854\pi$
$359$	2.37171e6	+	2.37171e6i	0.971238	+	0.971238i	−0.0283602	+	0.999598i	$0.509029\pi$
$360$	−5770.43	+	853875.i	−0.00234667	+	0.347247i
$361$	−1.24525e6	+	1.24525e6i	−0.502909	+	0.502909i
$362$	−442271.	+	254019.i	−0.177385	+	0.101881i
$363$	−125044.	+	301883.i	−0.0498077	+	0.120246i
$364$	1.09164e6	−	8.01270e6i	0.431843	−	3.16975i
$365$	−634586.	+	262854.i	−0.249321	+	0.103272i
$366$	−1.32466e6	+	171360.i	−0.516895	+	0.0668664i
$367$			1.29331e6i			0.501230i	0.968087	+	0.250615i	$0.0806328\pi$
$367$			1.29331e6i			0.501230i	−0.968087	+	0.250615i	$0.919367\pi$
$368$	137007.	−	493486.i	0.0527378	−	0.189957i
$369$		−	187575.i		−	0.0717149i
$370$	−235585.	−	1.82114e6i	−0.0894630	−	0.691574i
$371$	1.08879e6	−	450994.i	0.410687	−	0.170112i
$372$	1.89141e6	−	1.43784e6i	0.708644	−	0.538707i
$373$	−318774.	+	769588.i	−0.118634	+	0.286409i	−0.972031	−	0.234854i	$-0.924539\pi$
$373$	−318774.	+	769588.i	−0.118634	+	0.286409i	0.853396	+	0.521263i	$0.174539\pi$
$374$	−1.48799e6	−	2.59074e6i	−0.550076	−	0.957735i
$375$	−1.45090e6	+	1.45090e6i	−0.532794	+	0.532794i
$376$	−3.62572e6	−	1.53061e6i	−1.32259	−	0.558335i
$377$	1.00971e6	+	1.00971e6i	0.365883	+	0.365883i
$378$	1.29249e6	−	4.78054e6i	0.465262	−	1.72087i
$379$	1.32087e6	+	547120.i	0.472346	+	0.195652i	0.606142	−	0.795357i	$-0.292716\pi$
$379$	1.32087e6	+	547120.i	0.472346	+	0.195652i	−0.133795	+	0.991009i	$0.542716\pi$
$380$	270794.	+	1.02914e6i	0.0962012	+	0.365609i
$381$	1.16704e6	+	2.81749e6i	0.411883	+	0.994373i
$382$	−124500.	−	95978.3i	−0.0436525	−	0.0336523i
$383$	−1.01931e6			−0.355068			−0.177534	−	0.984115i	$-0.556812\pi$
$383$	−1.01931e6			−0.355068			−0.177534	+	0.984115i	$0.556812\pi$
$384$	−1.79675e6	+	999914.i	−0.621811	+	0.346047i
$385$	3.73235e6			1.28331
$386$	−3.46166e6	−	2.66863e6i	−1.18254	−	0.911635i
$387$	−335455.	−	809860.i	−0.113856	−	0.274873i
$388$	−150084.	−	570388.i	−0.0506122	−	0.192349i
$389$	−1.50319e6	−	622641.i	−0.503662	−	0.208624i	0.116361	−	0.993207i	$-0.462877\pi$
$389$	−1.50319e6	−	622641.i	−0.503662	−	0.208624i	−0.620023	+	0.784583i	$0.712877\pi$
$390$	−748587.	+	2.76880e6i	−0.249219	+	0.921786i
$391$	427941.	+	427941.i	0.141560	+	0.141560i
$392$	−5.08164e6	−	2.14523e6i	−1.67028	−	0.705113i
$393$	1.02293e6	−	1.02293e6i	0.334090	−	0.334090i
$394$	1.03595e6	+	1.80369e6i	0.336201	+	0.585358i
$395$	25532.8	−	61641.5i	0.00823389	−	0.0198784i
$396$	1.33368e6	−	1.01385e6i	0.427378	−	0.324890i
$397$	−775555.	+	321245.i	−0.246965	+	0.102296i	−0.502733	−	0.864442i	$-0.667672\pi$
$397$	−775555.	+	321245.i	−0.246965	+	0.102296i	0.255767	+	0.966738i	$0.417672\pi$
$398$	−187327.	−	1.44809e6i	−0.0592779	−	0.458234i
$399$		−	2.03961e6i		−	0.641378i
$400$	1.55733e6	+	432362.i	0.486665	+	0.135113i
$401$		−	753849.i		−	0.234112i	−0.993125	−	0.117056i	$-0.962654\pi$
$401$		−	753849.i		−	0.234112i	0.993125	−	0.117056i	$-0.0373457\pi$
$402$	−999961.	+	129357.i	−0.308616	+	0.0399230i
$403$	−7.18675e6	+	2.97685e6i	−2.20430	+	0.913050i
$404$	−662839.	+	4.86528e6i	−0.202048	+	1.48305i
$405$	−233506.	+	563733.i	−0.0707392	+	0.170779i
$406$	1.31045e6	−	752656.i	0.394552	−	0.226611i
$407$	−2.54751e6	+	2.54751e6i	−0.762308	+	0.762308i
$408$	16420.2	−	2.42976e6i	0.00488346	−	0.722626i
$409$	−4.76071e6	−	4.76071e6i	−1.40722	−	1.40722i	−0.773830	−	0.633393i	$-0.781662\pi$
$409$	−4.76071e6	−	4.76071e6i	−1.40722	−	1.40722i	−0.633393	−	0.773830i	$-0.718338\pi$
$410$	335848.	+	90801.6i	0.0986696	+	0.0266768i
$411$	1.13631e6	+	470676.i	0.331813	+	0.137441i
$412$	−2.03995e6	+	3.49683e6i	−0.592076	+	1.01492i
$413$	348822.	+	842130.i	0.100630	+	0.242943i
$414$	−207194.	+	268764.i	−0.0594122	+	0.0770674i
$415$	1.04729e6			0.298501
$416$	6.52216e6	−	1.66911e6i	1.84781	−	0.472880i
$417$	2.49406e6			0.702371
$418$	1.27472e6	−	1.65353e6i	0.356842	−	0.462882i
$419$	−782314.	−	1.88867e6i	−0.217694	−	0.525559i	0.776873	−	0.629657i	$-0.216805\pi$
$419$	−782314.	−	1.88867e6i	−0.217694	−	0.525559i	−0.994567	+	0.104098i	$0.966805\pi$
$420$	2.62193e6	+	1.52956e6i	0.725266	+	0.423101i
$421$	−693657.	−	287322.i	−0.190739	−	0.0790067i	0.285270	−	0.958447i	$-0.407917\pi$
$421$	−693657.	−	287322.i	−0.190739	−	0.0790067i	−0.476009	+	0.879441i	$0.657917\pi$
$422$	3.97098e6	+	1.07361e6i	1.08547	+	0.293472i
$423$	1.84395e6	+	1.84395e6i	0.501070	+	0.501070i
$424$	689057.	+	698433.i	0.186140	+	0.188673i
$425$	−1.35048e6	+	1.35048e6i	−0.362674	+	0.362674i
$426$	−2.40179e6	+	1.37947e6i	−0.641226	+	0.368289i
$427$	1.77115e6	−	4.27594e6i	0.470095	−	1.13491i
$428$	1.78005e6	+	242511.i	0.469701	+	0.0639914i
$429$	5.19890e6	−	2.15345e6i	1.36385	−	0.564927i
$430$	1.61242e6	−	208585.i	0.420539	−	0.0544016i
$431$		−	2.98530e6i		−	0.774095i	−0.922060	−	0.387048i	$-0.873495\pi$
$431$		−	2.98530e6i		−	0.774095i	0.922060	−	0.387048i	$-0.126505\pi$
$432$	4.09219e6	−	501279.i	1.05499	−	0.129232i
$433$			5.54448e6i			1.42115i	0.703620	+	0.710576i	$0.251566\pi$
$433$			5.54448e6i			1.42115i	−0.703620	+	0.710576i	$0.748434\pi$
$434$	1.05617e6	+	8.16447e6i	0.269159	+	2.08067i
$435$	−495198.	+	205118.i	−0.125475	+	0.0519733i
$436$	−3.69115e6	−	4.85554e6i	−0.929920	−	1.22327i
$437$	−161847.	+	390733.i	−0.0405416	+	0.0978762i
$438$	545852.	+	950380.i	0.135953	+	0.236708i
$439$	3.50256e6	−	3.50256e6i	0.867409	−	0.867409i	−0.124776	−	0.992185i	$-0.539821\pi$
$439$	3.50256e6	−	3.50256e6i	0.867409	−	0.867409i	0.992185	+	0.124776i	$0.0398211\pi$
$440$	1.16967e6	+	2.87869e6i	0.288025	+	0.708865i
$441$	2.58440e6	+	2.58440e6i	0.632795	+	0.632795i
$442$	−2.07633e6	+	7.67975e6i	−0.505524	+	1.86978i
$443$	5.34794e6	+	2.21519e6i	1.29472	+	0.536292i	0.920390	−	0.391001i	$-0.127871\pi$
$443$	5.34794e6	+	2.21519e6i	1.29472	+	0.536292i	0.374334	+	0.927294i	$0.377871\pi$
$444$	−2.83360e6	+	745594.i	−0.682152	+	0.179492i
$445$	2.09102e6	+	5.04818e6i	0.500563	+	1.20847i
$446$	152536.	+	117592.i	0.0363108	+	0.0279924i
$447$	2.95651e6			0.699859
$448$	96295.3	−	7.12428e6i	0.0226678	−	1.67705i
$449$	−2.80020e6			−0.655501			−0.327751	−	0.944764i	$-0.606291\pi$
$449$	−2.80020e6			−0.655501			−0.327751	+	0.944764i	$0.606291\pi$
$450$	−848158.	−	653855.i	−0.197445	−	0.152213i
$451$	−261208.	−	630613.i	−0.0604708	−	0.145989i
$452$	−3.70974e6	+	976129.i	−0.854077	+	0.224730i
$453$	−3.21794e6	−	1.33291e6i	−0.736771	−	0.305180i
$454$	−1.14198e6	+	4.22386e6i	−0.260028	+	0.961767i
$455$	−7.02754e6	−	7.02754e6i	−1.59138	−	1.59138i
$456$	1.57311e6	−	639184.i	0.354281	−	0.143951i
$457$	852617.	−	852617.i	0.190969	−	0.190969i	−0.605146	−	0.796115i	$-0.706885\pi$
$457$	852617.	−	852617.i	0.190969	−	0.190969i	0.796115	+	0.605146i	$0.206885\pi$
$458$	448294.	+	780522.i	0.0998617	+	0.173869i
$459$	−1.86436e6	+	4.50096e6i	−0.413046	+	0.997180i
$460$	−380916.	−	501078.i	−0.0839334	−	0.110411i
$461$	−1.98118e6	+	820632.i	−0.434182	+	0.179844i	−0.589059	−	0.808090i	$-0.700502\pi$
$461$	−1.98118e6	+	820632.i	−0.434182	+	0.179844i	0.154878	+	0.987934i	$0.450502\pi$
$462$	−764032.	−	5.90618e6i	−0.166535	−	1.28736i
$463$			305066.i			0.0661366i	0.999453	+	0.0330683i	$0.0105279\pi$
$463$			305066.i			0.0661366i	−0.999453	+	0.0330683i	$0.989472\pi$
$464$	991186.	+	774852.i	0.213727	+	0.167080i
$465$		−	2.91992e6i		−	0.626236i
$466$	6.63857e6	−	858775.i	1.41615	−	0.183196i
$467$	4.21243e6	−	1.74485e6i	0.893800	−	0.370224i	0.111967	−	0.993712i	$-0.464285\pi$
$467$	4.21243e6	−	1.74485e6i	0.893800	−	0.370224i	0.781833	+	0.623488i	$0.214285\pi$
$468$	−4.42009e6	−	602187.i	−0.932861	−	0.127092i
$469$	1.33701e6	−	3.22782e6i	0.280674	−	0.677606i
$470$	−4.19417e6	+	2.40892e6i	−0.875792	+	0.503012i
$471$	−772660.	+	772660.i	−0.160486	+	0.160486i
$472$	−540205.	+	532952.i	−0.111610	+	0.110112i
$473$	−2.25554e6	−	2.25554e6i	−0.463552	−	0.463552i
$474$	−102770.	−	27785.4i	−0.0210098	−	0.00568030i
$475$	−1.23307e6	−	510752.i	−0.250756	−	0.103867i
$476$	7.27237e6	+	4.24250e6i	1.47115	+	0.858232i
$477$	−248784.	−	600618.i	−0.0500642	−	0.120866i
$478$	−2.35754e6	+	3.05812e6i	−0.471943	+	0.612187i
$479$	−9.25979e6			−1.84401			−0.922003	−	0.387183i	$-0.873448\pi$
$479$	−9.25979e6			−1.84401			−0.922003	+	0.387183i	$0.873448\pi$
$480$	−358048.	+	2.50159e6i	−0.0709314	+	0.495579i
$481$	9.59329e6			1.89062
$482$	810011.	−	1.05072e6i	0.158808	−	0.206001i
$483$	461656.	+	1.11454e6i	0.0900431	+	0.217383i
$484$	474969.	−	814177.i	0.0921620	−	0.157981i
$485$	−669681.	−	277391.i	−0.129275	−	0.0535473i
$486$	−4.40272e6	−	1.19034e6i	−0.845533	−	0.228603i
$487$	−4.24991e6	−	4.24991e6i	−0.812003	−	0.812003i	0.172931	−	0.984934i	$-0.444676\pi$
$487$	−4.24991e6	−	4.24991e6i	−0.812003	−	0.812003i	−0.984934	+	0.172931i	$0.944676\pi$
$488$	3.85301e6	+	26038.4i	0.732404	+	0.00494954i
$489$	2.85052e6	−	2.85052e6i	0.539079	−	0.539079i
$490$	−5.87835e6	+	3.37623e6i	−1.10603	+	0.635247i
$491$	2.58409e6	−	6.23855e6i	0.483732	−	1.16783i	−0.474092	−	0.880475i	$-0.657224\pi$
$491$	2.58409e6	−	6.23855e6i	0.483732	−	1.16783i	0.957824	−	0.287356i	$-0.0927763\pi$
$492$	74937.2	−	550044.i	0.0139568	−	0.102444i
$493$	−1.37352e6	+	568930.i	−0.254517	+	0.105424i
$494$	−5.51352e6	+	713238.i	−1.01651	+	0.131497i
$495$		−	2.05890e6i		−	0.377678i
$496$	−5.96612e6	+	3.37324e6i	−1.08890	+	0.615662i
$497$		−	9.59728e6i		−	1.74284i
$498$	−214386.	−	1.65726e6i	−0.0387367	−	0.299445i
$499$	−1.98552e6	+	822430.i	−0.356963	+	0.147859i	−0.553956	−	0.832546i	$-0.686882\pi$
$499$	−1.98552e6	+	822430.i	−0.356963	+	0.147859i	0.196993	+	0.980405i	$0.436882\pi$
$500$	4.71210e6	−	3.58211e6i	0.842925	−	0.640787i
$501$	−949106.	+	2.29135e6i	−0.168935	+	0.407846i
$502$	−1.99713e6	−	3.47720e6i	−0.353710	−	0.615843i
$503$	−5.94624e6	+	5.94624e6i	−1.04791	+	1.04791i	−0.0491122	+	0.998793i	$0.515639\pi$
$503$	−5.94624e6	+	5.94624e6i	−1.04791	+	1.04791i	−0.998793	+	0.0491122i	$0.984361\pi$
$504$	−1.83611e6	+	4.34938e6i	−0.321974	+	0.762695i
$505$	4.26709e6	+	4.26709e6i	0.744567	+	0.744567i
$506$	−322300.	+	1.19209e6i	−0.0559608	+	0.206982i
$507$	−1.00383e7	−	4.15801e6i	−1.73437	−	0.718398i
$508$	−2.23859e6	−	8.50768e6i	−0.384872	−	1.46269i
$509$	3.90579e6	+	9.42941e6i	0.668212	+	1.61321i	0.784600	+	0.620003i	$0.212868\pi$
$509$	3.90579e6	+	9.42941e6i	0.668212	+	1.61321i	−0.116388	+	0.993204i	$0.537132\pi$
$510$	−2.36501e6	−	1.82322e6i	−0.402632	−	0.310394i
$511$	−3.79761e6			−0.643366
$512$	5.52501e6	−	2.15838e6i	0.931447	−	0.363876i
$513$	−3.40453e6			−0.571167
$514$	7.73016e6	+	5.95927e6i	1.29057	+	0.994914i
$515$	1.90399e6	+	4.59663e6i	0.316334	+	0.763698i
$516$	−660142.	−	2.50884e6i	−0.109147	−	0.414810i
$517$	8.76702e6	+	3.63142e6i	1.44253	+	0.597516i
$518$	2.64980e6	−	9.80082e6i	0.433899	−	1.60486i
$519$	4.40457e6	+	4.40457e6i	0.717770	+	0.717770i
$520$	3.21788e6	−	7.62255e6i	0.521869	−	1.23621i
$521$	3.74918e6	−	3.74918e6i	0.605120	−	0.605120i	−0.336547	−	0.941667i	$-0.609259\pi$
$521$	3.74918e6	−	3.74918e6i	0.605120	−	0.605120i	0.941667	+	0.336547i	$0.109259\pi$
$522$	−415192.	−	722889.i	−0.0666918	−	0.116117i
$523$	724028.	−	1.74796e6i	0.115745	−	0.279432i	−0.855382	−	0.517998i	$-0.826677\pi$
$523$	724028.	−	1.74796e6i	0.115745	−	0.279432i	0.971126	+	0.238566i	$0.0766773\pi$
$524$	−3.32217e6	+	2.52549e6i	−0.528559	+	0.401808i
$525$	−3.51722e6	+	1.45688e6i	−0.556931	+	0.230688i
$526$	555662.	+	4.29542e6i	0.0875681	+	0.676926i
$527$		−	8.09889e6i		−	1.27028i
$528$	4.31590e6	−	2.44020e6i	0.673730	−	0.380926i
$529$			6.18619e6i			0.961135i
$530$	1.19582e6	−	154693.i	0.184917	−	0.0239211i
$531$	464549.	−	192423.i	0.0714983	−	0.0296156i
$532$	−794244.	+	5.82980e6i	−0.121668	+	0.893048i
$533$	−695542.	+	1.67919e6i	−0.106049	+	0.256024i
$534$	7.56034e6	−	4.34229e6i	1.14733	−	0.658970i
$535$	1.56119e6	−	1.56119e6i	0.235815	−	0.235815i
$536$	2.90856e6	+	19655.9i	0.437286	+	0.00295515i
$537$	−2.96501e6	−	2.96501e6i	−0.443701	−	0.443701i
$538$	1.25655e6	+	339727.i	0.187164	+	0.0506027i
$539$	1.22874e7	+	5.08963e6i	1.82175	+	0.754595i
$540$	2.55316e6	−	4.37654e6i	0.376784	−	0.645872i
$541$	−3.33247e6	−	8.04530e6i	−0.489523	−	1.18181i	−0.954961	−	0.296733i	$-0.904103\pi$
$541$	−3.33247e6	−	8.04530e6i	−0.489523	−	1.18181i	0.465437	−	0.885081i	$-0.345897\pi$
$542$	6501.48	−	8433.49i	0.000950635	−	0.00123313i
$543$	1.00016e6			0.145569
$544$	−993109.	+	6.93859e6i	−0.143880	+	1.00525i
$545$	−7.49587e6			−1.08101
$546$	−9.68201e6	+	1.25592e7i	−1.38990	+	1.80293i
$547$	4.63425e6	+	1.11881e7i	0.662234	+	1.59877i	0.794294	+	0.607533i	$0.207841\pi$
$547$	4.63425e6	+	1.11881e7i	0.662234	+	1.59877i	−0.132060	+	0.991242i	$0.542159\pi$
$548$	−3.06464e6	−	1.78783e6i	−0.435941	−	0.254316i
$549$	−2.35876e6	−	977031.i	−0.334005	−	0.138349i
$550$	−3.76197e6	−	1.01710e6i	−0.530284	−	0.143370i
$551$	−734634.	−	734634.i	−0.103084	−	0.103084i
$552$	−714945.	+	705347.i	−0.0998677	+	0.0985270i
$553$	260842.	−	260842.i	0.0362715	−	0.0362715i
$554$	9.14588e6	−	5.25294e6i	1.26605	−	0.727157i
$555$	−1.37804e6	+	3.32687e6i	−0.189901	+	0.458462i
$556$	−7.12876e6	−	971212.i	−0.977973	−	0.133238i
$557$	−6.53714e6	+	2.70777e6i	−0.892791	+	0.369806i	−0.781444	−	0.623975i	$-0.785517\pi$
$557$	−6.53714e6	+	2.70777e6i	−0.892791	+	0.369806i	−0.111347	+	0.993782i	$0.535517\pi$
$558$	4.50381e6	−	582620.i	0.612343	−	0.0792137i
$559$			8.49381e6i			1.14967i
$560$	−6.89862e6	−	5.39295e6i	−0.929592	−	0.726702i
$561$			5.85874e6i			0.785954i
$562$	−1.72992e6	−	1.33728e7i	−0.231039	−	1.78599i
$563$	7.58040e6	−	3.13990e6i	1.00791	−	0.417489i	0.183217	−	0.983072i	$-0.441349\pi$
$563$	7.58040e6	−	3.13990e6i	1.00791	−	0.417489i	0.824691	+	0.565583i	$0.191349\pi$
$564$	4.67052e6	+	6.14385e6i	0.618255	+	0.813286i
$565$	−1.80412e6	+	4.35553e6i	−0.237763	+	0.574010i
$566$	83923.6	+	146119.i	0.0110114	+	0.0191719i
$567$	−2.38549e6	+	2.38549e6i	−0.311617	+	0.311617i
$568$	7.40221e6	−	3.00765e6i	0.962700	−	0.391162i
$569$	209587.	+	209587.i	0.0271383	+	0.0271383i	0.720546	−	0.693407i	$-0.243891\pi$
$569$	209587.	+	209587.i	0.0271383	+	0.0271383i	−0.693407	+	0.720546i	$0.743891\pi$
$570$	544649.	−	2.01450e6i	0.0702150	−	0.259704i
$571$	−600834.	−	248874.i	−0.0771195	−	0.0319440i	0.343790	−	0.939046i	$-0.388289\pi$
$571$	−600834.	−	248874.i	−0.0771195	−	0.0319440i	−0.420910	+	0.907103i	$0.638289\pi$
$572$	−1.56986e7	+	4.13071e6i	−2.00618	+	0.527879i
$573$	117969.	+	284802.i	0.0150100	+	0.0362374i
$574$	1.52339e6	+	1.17440e6i	0.192989	+	0.148777i
$575$	789410.			0.0995711
$576$	−3.93001e6	−	53120.0i	−0.493557	−	0.00667116i
$577$	615628.			0.0769801			0.0384901	−	0.999259i	$-0.487745\pi$
$577$	615628.			0.0769801			0.0384901	+	0.999259i	$0.487745\pi$
$578$	−198650.	−	153141.i	−0.0247325	−	0.0190666i
$579$	3.28007e6	+	7.91880e6i	0.406619	+	0.981664i
$580$	1.49530e6	−	393453.i	0.184569	−	0.0485649i
$581$	5.34954e6	+	2.21585e6i	0.657471	+	0.272333i
$582$	−301864.	+	1.11651e6i	−0.0369406	+	0.136632i
$583$	−1.67279e6	−	1.67279e6i	−0.203830	−	0.203830i
$584$	−1.19012e6	−	2.92903e6i	−0.144397	−	0.355379i
$585$	−3.87664e6	+	3.87664e6i	−0.468345	+	0.468345i
$586$	−2.44624e6	−	4.25914e6i	−0.294276	−	0.512363i
$587$	−2.74190e6	+	6.61952e6i	−0.328440	+	0.792924i	0.670269	+	0.742118i	$0.266179\pi$
$587$	−2.74190e6	+	6.61952e6i	−0.328440	+	0.792924i	−0.998709	+	0.0508053i	$0.983821\pi$
$588$	6.54599e6	+	8.61095e6i	0.780786	+	1.02709i
$589$	5.22887e6	−	2.16587e6i	0.621040	−	0.257243i
$590$	119648.	+	924911.i	0.0141506	+	0.109388i
$591$		−	4.07889e6i		−	0.480367i
$592$	8.38961e6	−	1.02770e6i	0.983870	−	0.120521i
$593$		−	9.07710e6i		−	1.06001i	−0.847994	−	0.530005i	$-0.822190\pi$
$593$		−	9.07710e6i		−	1.06001i	0.847994	−	0.530005i	$-0.177810\pi$
$594$	−9.85864e6	+	1.27533e6i	−1.14644	+	0.148305i
$595$	9.55964e6	−	3.95973e6i	1.10700	−	0.458536i
$596$	−8.45059e6	−	1.15130e6i	−0.974476	−	0.132761i
$597$	−1.09575e6	+	2.64538e6i	−0.125828	+	0.303775i
$598$	2.85141e6	−	1.63771e6i	0.326067	−	0.187277i
$599$	7.51556e6	−	7.51556e6i	0.855843	−	0.855843i	−0.135002	−	0.990845i	$-0.543104\pi$
$599$	7.51556e6	−	7.51556e6i	0.855843	−	0.855843i	0.990845	+	0.135002i	$0.0431042\pi$
$600$	−2.22591e6	−	2.25620e6i	−0.252424	−	0.255859i
$601$	2.99436e6	+	2.99436e6i	0.338157	+	0.338157i	0.855673	−	0.517516i	$-0.173143\pi$
$601$	2.99436e6	+	2.99436e6i	0.338157	+	0.338157i	−0.517516	+	0.855673i	$0.673143\pi$
$602$	8.67755e6	+	2.34611e6i	0.975902	+	0.263850i
$603$	−1.78058e6	−	737541.i	−0.199420	−	0.0826024i
$604$	8.67878e6	+	5.06296e6i	0.967980	+	0.564693i
$605$	−443312.	−	1.07025e6i	−0.0492403	−	0.118877i
$606$	5.87888e6	−	7.62588e6i	0.650299	−	0.843545i
$607$	1.16960e7			1.28844			0.644222	−	0.764839i	$-0.277181\pi$
$607$	1.16960e7			1.28844			0.644222	+	0.764839i	$0.277181\pi$
$608$	−4.74533e6	+	1.21439e6i	−0.520604	+	0.133229i
$609$	−2.96346e6			−0.323784
$610$	2.89118e6	−	3.75033e6i	0.314594	−	0.408080i
$611$	−9.66968e6	−	2.33447e7i	−1.04787	−	2.52979i
$612$	2.34032e6	−	4.01170e6i	0.252578	−	0.432962i
$613$	−9.81462e6	−	4.06535e6i	−1.05493	−	0.436965i	−0.213279	−	0.976991i	$-0.568414\pi$
$613$	−9.81462e6	−	4.06535e6i	−1.05493	−	0.436965i	−0.841648	+	0.540026i	$0.818414\pi$
$614$	−8.87953e6	−	2.40071e6i	−0.950537	−	0.256992i
$615$	−482416.	−	482416.i	−0.0514320	−	0.0514320i
$616$	−116096.	+	1.71791e7i	−0.0123272	+	1.82410i
$617$	4.91011e6	−	4.91011e6i	0.519253	−	0.519253i	−0.398093	−	0.917345i	$-0.630328\pi$
$617$	4.91011e6	−	4.91011e6i	0.519253	−	0.519253i	0.917345	+	0.398093i	$0.130328\pi$
$618$	6.88409e6	−	3.95388e6i	0.725063	−	0.416440i
$619$	−5.20220e6	+	1.25592e7i	−0.545708	+	1.31746i	0.374936	+	0.927051i	$0.377665\pi$
$619$	−5.20220e6	+	1.25592e7i	−0.545708	+	1.31746i	−0.920643	+	0.390404i	$0.872335\pi$
$620$	−1.13705e6	+	8.34599e6i	−0.118795	+	0.871964i
$621$	1.86039e6	−	770599.i	0.193587	−	0.0801862i
$622$	1.02700e7	−	1.32854e6i	1.06438	−	0.137689i
$623$			3.02103e7i			3.11842i
$624$	−1.27209e7	−	3.53170e6i	−1.30784	−	0.363096i
$625$		−	2.34207e6i		−	0.239828i
$626$	1.39386e6	+	1.07749e7i	0.142162	+	1.09895i
$627$	−3.78256e6	+	1.56679e6i	−0.384253	+	0.159163i
$628$	2.50938e6	−	1.90761e6i	0.253902	−	0.193015i
$629$	−3.82222e6	+	9.22765e6i	−0.385202	+	0.929961i
$630$	2.88972e6	+	5.03129e6i	0.290071	+	0.505042i
$631$	1.00316e7	−	1.00316e7i	1.00299	−	1.00299i	0.00299903	−	0.999996i	$-0.499045\pi$
$631$	1.00316e7	−	1.00316e7i	1.00299	−	1.00299i	0.999996	−	0.00299903i	$-0.000954623\pi$
$632$	282928.	+	119439.i	0.0281762	+	0.0118947i
$633$	−5.70396e6	−	5.70396e6i	−0.565806	−	0.565806i
$634$	1.04436e6	−	3.86279e6i	0.103188	−	0.381661i
$635$	−9.98869e6	−	4.13745e6i	−0.983047	−	0.407191i
$636$	−489583.	−	1.86064e6i	−0.0479936	−	0.182398i
$637$	−1.35526e7	−	3.27188e7i	−1.32335	−	3.19484i
$638$	−2.40250e6	−	1.85212e6i	−0.233675	−	0.180143i
$639$	−5.29421e6			−0.512919
$640$	1.99755e6	−	7.01086e6i	0.192774	−	0.676584i
$641$	−4.19301e6			−0.403070			−0.201535	−	0.979481i	$-0.564593\pi$
$641$	−4.19301e6			−0.403070			−0.201535	+	0.979481i	$0.564593\pi$
$642$	−2.79006e6	−	2.15089e6i	−0.267162	−	0.205959i
$643$	−4.38325e6	−	1.05821e7i	−0.418089	−	1.00936i	−0.982901	−	0.184137i	$-0.941051\pi$
$643$	−4.38325e6	−	1.05821e7i	−0.418089	−	1.00936i	0.564812	−	0.825220i	$-0.308949\pi$
$644$	−885538.	−	3.36545e6i	−0.0841381	−	0.319763i
$645$	−2.94558e6	−	1.22010e6i	−0.278786	−	0.115477i
$646$	1.51068e6	−	5.58755e6i	0.142427	−	0.526794i
$647$	7.69098e6	+	7.69098e6i	0.722306	+	0.722306i	0.969074	−	0.246768i	$-0.0793687\pi$
$647$	7.69098e6	+	7.69098e6i	0.722306	+	0.722306i	−0.246768	+	0.969074i	$0.579369\pi$
$648$	−2.58747e6	−	1.09231e6i	−0.242068	−	0.102190i
$649$	1.29382e6	−	1.29382e6i	0.120576	−	0.120576i
$650$	5.16823e6	+	8.99839e6i	0.479798	+	0.835375i
$651$	6.17796e6	−	1.49149e7i	0.571338	−	1.37933i
$652$	−9.25766e6	+	7.03762e6i	−0.852869	+	0.648346i
$653$	2.92800e6	−	1.21282e6i	0.268713	−	0.111305i	−0.244259	−	0.969710i	$-0.578545\pi$
$653$	2.92800e6	−	1.21282e6i	0.268713	−	0.111305i	0.512972	+	0.858406i	$0.328545\pi$
$654$	1.53445e6	+	1.18617e7i	0.140284	+	1.08443i
$655$			5.12869e6i			0.467093i
$656$	−428386.	+	1.54301e6i	−0.0388665	+	0.139994i
$657$			2.09490e6i			0.189343i
$658$	−2.65206e7	+	3.43074e6i	−2.38791	+	0.308904i
$659$	−1.05558e7	+	4.37238e6i	−0.946847	+	0.392197i	−0.802045	−	0.597264i	$-0.796254\pi$
$659$	−1.05558e7	+	4.37238e6i	−0.946847	+	0.392197i	−0.144802	+	0.989461i	$0.546254\pi$
$660$	822539.	−	6.03749e6i	0.0735016	−	0.539507i
$661$	92899.5	−	224279.i	0.00827008	−	0.0199657i	−0.919691	−	0.392644i	$-0.871560\pi$
$661$	92899.5	−	224279.i	0.00827008	−	0.0199657i	0.927961	+	0.372678i	$0.121560\pi$
$662$	−1.40365e7	+	8.06190e6i	−1.24484	+	0.714977i
$663$	1.10313e7	−	1.10313e7i	0.974634	−	0.974634i
$664$	−32576.1	+	4.82043e6i	−0.00286734	+	0.424292i
$665$	5.11303e6	+	5.11303e6i	0.448357	+	0.448357i
$666$	−5.40649e6	−	1.46172e6i	−0.472313	−	0.127697i
$667$	567719.	+	235157.i	0.0494104	+	0.0204665i
$668$	3.60510e6	−	6.17976e6i	0.312591	−	0.535834i
$669$	−144535.	−	348938.i	−0.0124855	−	0.0301427i
$670$	2.18249e6	−	2.83105e6i	0.187830	−	0.243647i
$671$	−9.29053e6			−0.796589
$672$	−7.12178e6	+	1.20206e7i	−0.608366	+	1.02684i
$673$	−1.35339e7			−1.15182			−0.575911	−	0.817512i	$-0.695353\pi$
$673$	−1.35339e7			−1.15182			−0.575911	+	0.817512i	$0.695353\pi$
$674$	1.06722e7	−	1.38436e7i	0.904905	−	1.17381i
$675$	2.43183e6	+	5.87097e6i	0.205435	+	0.495964i
$676$	2.70733e7	+	1.57938e7i	2.27864	+	1.32929i
$677$	2.14118e7	+	8.86908e6i	1.79549	+	0.743715i	0.988124	+	0.153662i	$0.0491066\pi$
$677$	2.14118e7	+	8.86908e6i	1.79549	+	0.743715i	0.807364	+	0.590054i	$0.200893\pi$
$678$	7.26163e6	+	1.96329e6i	0.606680	+	0.164025i
$679$	−2.83382e6	−	2.83382e6i	−0.235884	−	0.235884i
$680$	6.04993e6	+	6.13226e6i	0.501739	+	0.508567i
$681$	6.06720e6	−	6.06720e6i	0.501326	−	0.501326i
$682$	1.43301e7	−	8.23052e6i	1.17975	−	0.677589i
$683$	4.73216e6	−	1.14244e7i	0.388157	−	0.937094i	−0.602173	−	0.798365i	$-0.705698\pi$
$683$	4.73216e6	−	1.14244e7i	0.388157	−	0.937094i	0.990330	−	0.138729i	$-0.0443016\pi$
$684$	3.21593e6	+	438134.i	0.262825	+	0.0358069i
$685$	−4.02851e6	+	1.66866e6i	−0.328034	+	0.135876i
$686$	−1.66682e7	+	2.15623e6i	−1.35232	+	0.174938i
$687$		−	1.76508e6i		−	0.142683i
$688$	909914.	+	7.42808e6i	0.0732874	+	0.598281i
$689$			6.29929e6i			0.505526i
$690$	158351.	+	1.22409e6i	0.0126618	+	0.0978795i
$691$	1.25495e7	−	5.19819e6i	0.999846	−	0.414150i	0.178105	−	0.984011i	$-0.443003\pi$
$691$	1.25495e7	−	5.19819e6i	0.999846	−	0.414150i	0.821741	+	0.569862i	$0.193003\pi$
$692$	−1.08744e7	−	1.43048e7i	−0.863256	−	1.13557i
$693$	4.35622e6	−	1.05168e7i	0.344569	−	0.831864i
$694$	1.34518e6	+	2.34210e6i	0.106019	+	0.184589i
$695$	−6.25228e6	+	6.25228e6i	−0.490994	+	0.490994i
$696$	−928707.	−	2.28567e6i	−0.0726701	−	0.178850i
$697$	−1.33806e6	−	1.33806e6i	−0.104327	−	0.104327i
$698$	1.70345e6	−	6.30057e6i	0.132340	−	0.489487i
$699$	−1.21274e7	−	5.02333e6i	−0.938803	−	0.388865i
$700$	1.06206e7	−	2.79455e6i	0.819225	−	0.215560i
$701$	−2.66180e6	−	6.42616e6i	−0.204588	−	0.493920i	0.787967	−	0.615718i	$-0.211134\pi$
$701$	−2.66180e6	−	6.42616e6i	−0.204588	−	0.493920i	−0.992555	+	0.121798i	$0.961134\pi$
$702$	2.09638e7	+	1.61613e7i	1.60557	+	1.23775i
$703$	−6.97979e6			−0.532665
$704$	−1.32864e7	+	5.29416e6i	−1.01036	+	0.402592i
$705$	9.48474e6			0.718708
$706$	−4.34440e6	−	3.34915e6i	−0.328033	−	0.252885i
$707$	1.27680e7	+	3.08246e7i	0.960669	+	2.31926i
$708$	1.43911e6	−	378669.i	0.107898	−	0.0283907i
$709$	7.36712e6	+	3.05156e6i	0.550405	+	0.227985i	0.640514	−	0.767947i	$-0.278722\pi$
$709$	7.36712e6	+	3.05156e6i	0.550405	+	0.227985i	−0.0901090	+	0.995932i	$0.528722\pi$
$710$	2.56282e6	−	9.47913e6i	0.190798	−	0.705704i
$711$	−143890.	−	143890.i	−0.0106747	−	0.0106747i
$712$	−2.33006e7	+	9.46748e6i	−1.72253	+	0.699897i
$713$	−2.36706e6	+	2.36706e6i	−0.174376	+	0.174376i
$714$	−8.22291e6	−	1.43169e7i	−0.603643	−	1.05100i
$715$	−7.63453e6	+	1.84314e7i	−0.558492	+	1.34832i
$716$	7.32027e6	+	9.62948e6i	0.533636	+	0.701973i
$717$	6.99567e6	−	2.89770e6i	0.508196	−	0.210502i
$718$	2.43418e6	+	1.88169e7i	0.176215	+	1.36219i
$719$		−	1.14926e7i		−	0.829083i	−0.910030	−	0.414541i	$-0.863942\pi$
$719$		−	1.14926e7i		−	0.829083i	0.910030	−	0.414541i	$-0.136058\pi$
$720$	−2.97494e6	+	3.80553e6i	−0.213869	+	0.273580i
$721$			2.75080e7i			1.97070i
$722$	−9.87971e6	+	1.27805e6i	−0.705344	+	0.0912444i
$723$	−2.40360e6	+	995602.i	−0.171008	+	0.0708337i
$724$	−2.85875e6	−	389472.i	−0.202689	−	0.0276140i
$725$	−742101.	+	1.79159e6i	−0.0524346	+	0.126588i
$726$	−1.60285e6	+	920596.i	−0.112863	+	0.0648228i
$727$	3.13309e6	−	3.13309e6i	0.219855	−	0.219855i	−0.588582	−	0.808437i	$-0.700314\pi$
$727$	3.13309e6	−	3.13309e6i	0.219855	−	0.219855i	0.808437	+	0.588582i	$0.200314\pi$
$728$	3.25647e7	−	3.21276e7i	2.27729	−	2.24672i
$729$	8.99008e6	+	8.99008e6i	0.626534	+	0.626534i
$730$	−3.75086e6	−	1.01410e6i	−0.260509	−	0.0704326i
$731$	−8.17007e6	−	3.38416e6i	−0.565500	−	0.234238i
$732$	−6.52648e6	−	3.80737e6i	−0.450196	−	0.262632i
$733$	6.17317e6	+	1.49034e7i	0.424374	+	1.02453i	0.981042	+	0.193794i	$0.0620793\pi$
$733$	6.17317e6	+	1.49034e7i	0.424374	+	1.02453i	−0.556669	+	0.830735i	$0.687921\pi$
$734$	−4.46680e6	+	5.79417e6i	−0.306024	+	0.396964i
$735$	1.32934e7			0.907647
$736$	2.31820e6	−	1.73768e6i	0.157745	−	0.118243i
$737$	−7.01324e6			−0.475609
$738$	647843.	−	840358.i	0.0437853	−	0.0567968i
$739$	−517626.	−	1.24966e6i	−0.0348662	−	0.0841745i	0.905487	−	0.424373i	$-0.139506\pi$
$739$	−517626.	−	1.24966e6i	−0.0348662	−	0.0841745i	−0.940354	+	0.340199i	$0.889506\pi$
$740$	5.23435e6	−	8.97257e6i	0.351385	−	0.602334i
$741$	1.00722e7	+	4.17202e6i	0.673871	+	0.279127i
$742$	6.43556e6	+	1.73995e6i	0.429118	+	0.116018i
$743$	3.31354e6	+	3.31354e6i	0.220202	+	0.220202i	0.808583	−	0.588382i	$-0.200235\pi$
$743$	3.31354e6	+	3.31354e6i	0.220202	+	0.220202i	−0.588382	+	0.808583i	$0.700235\pi$
$744$	1.34397e7	+	90824.7i	0.890138	+	0.00601550i
$745$	−7.41158e6	+	7.41158e6i	−0.489238	+	0.489238i
$746$	−4.08613e6	+	2.34687e6i	−0.268822	+	0.154398i
$747$	1.22234e6	−	2.95100e6i	0.0801479	−	0.193494i
$748$	2.28145e6	−	1.67460e7i	0.149093	−	1.09435i
$749$	1.12777e7	−	4.67138e6i	0.734541	−	0.304257i
$750$	−1.15113e7	+	1.48912e6i	−0.747257	+	0.0966663i
$751$			1.28398e6i			0.0830726i	0.999137	+	0.0415363i	$0.0132252\pi$
$751$			1.28398e6i			0.0830726i	−0.999137	+	0.0415363i	$0.986775\pi$
$752$	−1.09573e7	−	1.93797e7i	−0.706573	−	1.24969i
$753$			7.86338e6i			0.505385i
$754$	1.03630e6	+	8.01091e6i	0.0663833	+	0.513161i
$755$	1.14084e7	−	4.72551e6i	0.728378	−	0.301704i
$756$	2.23014e7	−	1.69534e7i	1.41915	−	1.07883i
$757$	6.38627e6	−	1.54178e7i	0.405049	−	0.977875i	−0.581372	−	0.813638i	$-0.697484\pi$
$757$	6.38627e6	−	1.54178e7i	0.405049	−	0.977875i	0.986421	−	0.164237i	$-0.0525163\pi$
$758$	4.02800e6	+	7.01314e6i	0.254634	+	0.443342i
$759$	1.71233e6	−	1.71233e6i	0.107891	−	0.107891i
$760$	−2.34124e6	+	5.54594e6i	−0.147032	+	0.348290i
$761$	−1.74566e6	−	1.74566e6i	−0.109269	−	0.109269i	0.650358	−	0.759627i	$-0.274619\pi$
$761$	−1.74566e6	−	1.74566e6i	−0.109269	−	0.109269i	−0.759627	+	0.650358i	$0.774619\pi$
$762$	−4.50249e6	+	1.66534e7i	−0.280909	+	1.03900i
$763$	−3.82889e7	−	1.58598e7i	−2.38101	−	0.986247i
$764$	−226285.	−	859987.i	−0.0140256	−	0.0533039i
$765$	−2.18433e6	−	5.27344e6i	−0.134948	−	0.325792i
$766$	−4.56665e6	−	3.52048e6i	−0.281207	−	0.216786i
$767$	−4.87219e6			−0.299045
$768$	−1.15031e7	−	1.72583e6i	−0.703740	−	0.105583i
$769$	−3.03701e7			−1.85195			−0.925977	−	0.377579i	$-0.876757\pi$
$769$	−3.03701e7			−1.85195			−0.925977	+	0.377579i	$0.876757\pi$
$770$	1.67213e7	+	1.28907e7i	1.01635	+	0.783519i
$771$	−7.32466e6	−	1.76833e7i	−0.443764	−	1.07134i
$772$	−6.29177e6	−	2.39116e7i	−0.379953	−	1.44399i
$773$	721854.	+	299002.i	0.0434511	+	0.0179980i	0.404303	−	0.914625i	$-0.367514\pi$
$773$	721854.	+	299002.i	0.0434511	+	0.0179980i	−0.360852	+	0.932623i	$0.617514\pi$
$774$	1.29420e6	−	4.78685e6i	0.0776512	−	0.287209i
$775$	−7.46990e6	−	7.46990e6i	−0.446746	−	0.446746i
$776$	1.29760e6	−	3.07376e6i	0.0773545	−	0.183238i
$777$	−1.40780e7	+	1.40780e7i	−0.836543	+	0.836543i
$778$	−4.58399e6	−	7.98118e6i	−0.271516	−	0.472735i
$779$	506055.	−	1.22173e6i	0.0298782	−	0.0721323i
$780$	−1.29166e7	+	9.81909e6i	−0.760170	+	0.577876i
$781$	−1.77987e7	+	7.37246e6i	−1.04414	+	0.432499i
$782$	439213.	+	3.39523e6i	0.0256837	+	0.198542i
$783$			4.94663e6i			0.288340i
$784$	−1.53572e7	−	2.71617e7i	−0.892322	−	1.57822i
$785$		−	3.87392e6i		−	0.224376i
$786$	8.11580e6	−	1.04987e6i	0.468570	−	0.0606150i
$787$	−4.73096e6	+	1.95963e6i	−0.272278	+	0.112781i	−0.514645	−	0.857403i	$-0.672076\pi$
$787$	−4.73096e6	+	1.95963e6i	−0.272278	+	0.112781i	0.242367	+	0.970185i	$0.422076\pi$
$788$	−1.58836e6	+	1.16587e7i	−0.0911242	+	0.668858i
$789$	3.25029e6	−	7.84690e6i	0.185879	−	0.448751i
$790$	327286.	−	187977.i	0.0186578	−	0.0107161i
$791$	−1.84309e7	+	1.84309e7i	−1.04738	+	1.04738i
$792$	9.47663e6	+	64042.5i	0.536835	+	0.00362790i
$793$	1.74929e7	+	1.74929e7i	0.987822	+	0.987822i
$794$	−4.58408e6	−	1.23938e6i	−0.258048	−	0.0697673i
$795$	−2.18454e6	−	904865.i	−0.122586	−	0.0507769i
$796$	4.16213e6	−	7.13459e6i	0.232827	−	0.399104i
$797$	5.37524e6	+	1.29770e7i	0.299745	+	0.723648i	0.999953	+	0.00970933i	$0.00309062\pi$
$797$	5.37524e6	+	1.29770e7i	0.299745	+	0.723648i	−0.700208	+	0.713939i	$0.746909\pi$
$798$	7.04434e6	−	9.13767e6i	0.391591	−	0.507959i
$799$	2.63076e7			1.45785
$800$	5.48373e6	+	7.31569e6i	0.302936	+	0.404139i
$801$	1.66651e7			0.917753
$802$	2.60363e6	−	3.37733e6i	0.142936	−	0.185412i
$803$	2.91726e6	+	7.04288e6i	0.159656	+	0.385444i
$804$	−4.92671e6	−	2.87411e6i	−0.268792	−	0.156806i
$805$	−3.95130e6	−	1.63668e6i	−0.214907	−	0.0890175i
$806$	−4.24789e7	−	1.14848e7i	−2.30322	−	0.622710i
$807$	−1.80492e6	−	1.80492e6i	−0.0975604	−	0.0975604i
$808$	−1.97732e7	+	1.95077e7i	−1.06549	+	1.05118i
$809$	2.19033e7	−	2.19033e7i	1.17663	−	1.17663i	0.196027	−	0.980599i	$-0.437196\pi$
$809$	2.19033e7	−	2.19033e7i	1.17663	−	1.17663i	0.980599	−	0.196027i	$-0.0628039\pi$
$810$	−2.99314e6	+	1.71911e6i	−0.160293	+	0.0920644i
$811$	8.54849e6	−	2.06379e7i	0.456391	−	1.10183i	−0.513457	−	0.858116i	$-0.671635\pi$
$811$	8.54849e6	−	2.06379e7i	0.456391	−	1.10183i	0.969848	−	0.243711i	$-0.0783647\pi$
$812$	8.47045e6	+	1.15400e6i	0.450834	+	0.0614210i
$813$	−19292.2	+	7991.10i	−0.00102366	+	0.000424014i
$814$	−2.02117e7	+	2.61462e6i	−1.06916	+	0.138308i
$815$			1.42918e7i			0.753689i
$816$	8.46542e6	−	1.08289e7i	0.445065	−	0.569324i
$817$		−	6.17984e6i		−	0.323908i
$818$	−4.88610e6	−	3.77709e7i	−0.255317	−	1.97367i
$819$	−2.80041e7	+	1.15997e7i	−1.45885	+	0.604277i
$820$	1.19103e6	+	1.56675e6i	0.0618569	+	0.0813699i
$821$	−9.56706e6	+	2.30969e7i	−0.495360	+	1.19590i	0.456598	+	0.889673i	$0.349068\pi$
$821$	−9.56706e6	+	2.30969e7i	−0.495360	+	1.19590i	−0.951957	+	0.306231i	$0.900932\pi$
$822$	3.46520e6	+	6.03326e6i	0.178875	+	0.311438i
$823$	1.44872e7	−	1.44872e7i	0.745563	−	0.745563i	−0.228079	−	0.973643i	$-0.573245\pi$
$823$	1.44872e7	−	1.44872e7i	0.745563	−	0.745563i	0.973643	+	0.228079i	$0.0732446\pi$
$824$	−2.12165e7	+	8.62064e6i	−1.08857	+	0.442305i
$825$	5.40373e6	+	5.40373e6i	0.276413	+	0.276413i
$826$	−1.34577e6	+	4.97759e6i	−0.0686309	+	0.253845i
$827$	3.35155e7	+	1.38826e7i	1.70405	+	0.705839i	0.999991	−	0.00430634i	$-0.00137076\pi$
$827$	3.35155e7	+	1.38826e7i	1.70405	+	0.705839i	0.704055	+	0.710145i	$0.251371\pi$
$828$	−1.85650e6	+	488495.i	−0.0941065	+	0.0247619i
$829$	−3.48966e6	−	8.42478e6i	−0.176358	−	0.425767i	0.810839	−	0.585269i	$-0.199011\pi$
$829$	−3.48966e6	−	8.42478e6i	−0.176358	−	0.425767i	−0.987198	+	0.159502i	$0.949011\pi$
$830$	4.69197e6	+	3.61710e6i	0.236407	+	0.182249i
$831$	−2.06826e7			−1.03897
$832$	3.49848e7	+	1.50483e7i	1.75215	+	0.753665i
$833$	3.68715e7			1.84110
$834$	1.11737e7	+	8.61392e6i	0.556264	+	0.428830i
$835$	−3.36482e6	−	8.12339e6i	−0.167011	−	0.403200i
$836$	1.14218e7	−	3.00538e6i	0.565223	−	0.148725i
$837$	−2.48961e7	−	1.03123e7i	−1.22834	−	0.508794i
$838$	3.01819e6	−	1.11634e7i	0.148469	−	0.549144i
$839$	−5.50321e6	−	5.50321e6i	−0.269905	−	0.269905i	0.559157	−	0.829062i	$-0.311125\pi$
$839$	−5.50321e6	−	5.50321e6i	−0.269905	−	0.269905i	−0.829062	+	0.559157i	$0.811125\pi$
$840$	6.46377e6	+	1.59082e7i	0.316073	+	0.777896i
$841$	1.34362e7	−	1.34362e7i	0.655067	−	0.655067i
$842$	−2.11532e6	−	3.68297e6i	−0.102824	−	0.179027i
$843$	−1.01190e7	+	2.44295e7i	−0.490421	+	1.18398i
$844$	1.40824e7	+	1.85248e7i	0.680490	+	0.895153i
$845$	3.55883e7	−	1.47412e7i	1.71461	−	0.710215i
$846$	1.89252e6	+	1.46297e7i	0.0909107	+	0.702765i
$847$		−	6.40479e6i		−	0.306758i
$848$	674822.	+	5.50891e6i	0.0322255	+	0.263073i
$849$		−	330436.i		−	0.0157332i
$850$	−1.07146e7	+	1.38605e6i	−0.508660	+	0.0658011i
$851$	3.81408e6	−	1.57984e6i	0.180537	−	0.0747809i
$852$	−1.55247e7	−	2.11506e6i	−0.732696	−	0.0998214i
$853$	−558547.	+	1.34845e6i	−0.0262837	+	0.0634546i	−0.936476	−	0.350730i	$-0.885933\pi$
$853$	−558547.	+	1.34845e6i	−0.0262837	+	0.0634546i	0.910193	+	0.414185i	$0.135933\pi$
$854$	2.27031e7	−	1.30395e7i	1.06522	−	0.611811i
$855$	2.82053e6	−	2.82053e6i	0.131952	−	0.131952i
$856$	7.13723e6	+	7.23435e6i	0.332924	+	0.337455i
$857$	−1.84308e7	−	1.84308e7i	−0.857220	−	0.857220i	0.133790	−	0.991010i	$-0.457285\pi$
$857$	−1.84308e7	−	1.84308e7i	−0.857220	−	0.857220i	−0.991010	+	0.133790i	$0.957285\pi$
$858$	3.07292e7	+	8.30810e6i	1.42506	+	0.385286i
$859$	9.39546e6	+	3.89173e6i	0.434445	+	0.179953i	0.589178	−	0.808003i	$-0.299452\pi$
$859$	9.39546e6	+	3.89173e6i	0.434445	+	0.179953i	−0.154733	+	0.987956i	$0.549452\pi$
$860$	7.94423e6	+	4.63445e6i	0.366273	+	0.213674i
$861$	−1.44348e6	−	3.48487e6i	−0.0663596	−	0.160206i
$862$	1.03105e7	−	1.33745e7i	0.472621	−	0.613068i
$863$	−6.93839e6			−0.317126			−0.158563	−	0.987349i	$-0.550686\pi$
$863$	−6.93839e6			−0.317126			−0.158563	+	0.987349i	$0.550686\pi$
$864$	2.00648e7	+	1.18877e7i	0.914430	+	0.541769i
$865$	−2.20834e7			−1.00352
$866$	−1.91494e7	+	2.48399e7i	−0.867680	+	1.12552i
$867$	188229.	+	454426.i	0.00850432	+	0.0205312i
$868$	−2.34665e7	+	4.02255e7i	−1.05718	+	1.81218i
$869$	−684122.	−	283372.i	−0.0307315	−	0.0127294i
$870$	−2.92698e6	−	791352.i	−0.131106	−	0.0354464i
$871$	1.32050e7	+	1.32050e7i	0.589786	+	0.589786i
$872$	233161.	−	3.45018e7i	0.0103840	−	1.53656i
$873$	−1.56324e6	+	1.56324e6i	−0.0694208	+	0.0694208i
$874$	−2.07460e6	+	1.19155e6i	−0.0918662	+	0.0527634i
$875$	1.53912e7	−	3.71578e7i	0.679600	−	1.64070i
$876$	−836922.	+	6.14306e6i	−0.0368489	+	0.270473i
$877$	−3.47850e7	+	1.44084e7i	−1.52719	+	0.632582i	−0.979016	−	0.203783i	$-0.934676\pi$
$877$	−3.47850e7	+	1.44084e7i	−1.52719	+	0.632582i	−0.548172	+	0.836365i	$0.684676\pi$
$878$	2.77889e7	−	3.59482e6i	1.21657	−	0.157377i
$879$			9.63167e6i			0.420464i
$880$	−4.70212e6	+	1.69366e7i	−0.204686	+	0.737260i
$881$		−	5.00415e6i		−	0.217215i	−0.994085	−	0.108608i	$-0.965361\pi$
$881$		−	5.00415e6i		−	0.217215i	0.994085	−	0.108608i	$-0.0346392\pi$
$882$	2.65247e6	+	2.05043e7i	0.114810	+	0.887512i
$883$	1.38054e7	−	5.71839e6i	0.595865	−	0.246815i	−0.0643065	−	0.997930i	$-0.520484\pi$
$883$	1.38054e7	−	5.71839e6i	0.595865	−	0.246815i	0.660172	+	0.751115i	$0.270484\pi$
$884$	−3.58263e7	+	2.72350e7i	−1.54195	+	1.17218i
$885$	699870.	−	1.68964e6i	0.0300372	−	0.0725162i
$886$	1.63086e7	+	2.83949e7i	0.697964	+	1.21522i
$887$	−2.53398e6	+	2.53398e6i	−0.108142	+	0.108142i	−0.759107	−	0.650965i	$-0.774364\pi$
$887$	−2.53398e6	+	2.53398e6i	−0.108142	+	0.108142i	0.650965	+	0.759107i	$0.274364\pi$
$888$	−1.52700e7	−	6.44626e6i	−0.649839	−	0.274332i
$889$	−4.22682e7	−	4.22682e7i	−1.79374	−	1.79374i
$890$	−8.06724e6	+	2.98383e7i	−0.341389	+	1.26270i
$891$	6.25652e6	+	2.59154e6i	0.264021	+	0.109361i
$892$	277243.	+	1.05365e6i	0.0116667	+	0.0443389i
$893$	7.03537e6	+	1.69849e7i	0.295229	+	0.712745i
$894$	1.32455e7	+	1.02111e7i	0.554274	+	0.427297i
$895$	1.48658e7			0.620340
$896$	2.50371e7	−	3.15850e7i	1.04187	−	1.31435i
$897$	−6.44821e6			−0.267583
$898$	−1.25452e7	−	9.67127e6i	−0.519144	−	0.400214i
$899$	−3.14691e6	−	7.59732e6i	−0.129863	−	0.313517i
$900$	−1.54158e6	−	5.85870e6i	−0.0634394	−	0.241099i
$901$	−6.05919e6	−	2.50980e6i	−0.248658	−	0.102998i
$902$	1.00775e6	−	3.72737e6i	0.0412417	−	0.152541i
$903$	−1.24645e7	−	1.24645e7i	−0.508694	−	0.508694i
$904$	−1.99914e7	−	8.43942e6i	−0.813620	−	0.343472i
$905$	−2.50726e6	+	2.50726e6i	−0.101760	+	0.101760i
$906$	−9.81315e6	−	1.70856e7i	−0.397181	−	0.691530i
$907$	−1.31083e7	+	3.16463e7i	−0.529089	+	1.27733i	0.403031	+	0.915186i	$0.367957\pi$
$907$	−1.31083e7	+	3.16463e7i	−0.529089	+	1.27733i	−0.932120	+	0.362148i	$0.882043\pi$
$908$	−1.97045e7	+	1.49792e7i	−0.793141	+	0.602941i
$909$	1.70040e7	−	7.04328e6i	0.682560	−	0.282726i
$910$	−7.21264e6	−	5.57557e7i	−0.288729	−	2.23196i
$911$		−	4.50643e7i		−	1.79902i	−0.436898	−	0.899511i	$-0.643923\pi$
$911$		−	4.50643e7i		−	1.79902i	0.436898	−	0.899511i	$-0.356077\pi$
$912$	9.25533e6	+	2.56956e6i	0.368472	+	0.102299i
$913$		−	1.16232e7i		−	0.461476i
$914$	6.76457e6	−	875075.i	0.267840	−	0.0346481i
$915$	−8.57916e6	+	3.55361e6i	−0.338760	+	0.140319i
$916$	−687342.	+	5.04514e6i	−0.0270666	+	0.198671i
$917$	−1.08513e7	+	2.61973e7i	−0.426146	+	1.02881i
$918$	−2.38979e7	+	1.37258e7i	−0.935949	+	0.537563i
$919$	−2.10669e7	+	2.10669e7i	−0.822833	+	0.822833i	−0.986513	−	0.163681i	$-0.947663\pi$
$919$	−2.10669e7	+	2.10669e7i	−0.822833	+	0.822833i	0.163681	+	0.986513i	$0.447663\pi$
$920$	24061.5	−	3.56049e6i	0.000937246	−	0.138688i
$921$	1.27546e7	+	1.27546e7i	0.495472	+	0.495472i
$922$	−1.17102e7	−	3.16603e6i	−0.453666	−	0.122656i
$923$	4.73941e7	+	1.96313e7i	1.83113	+	0.758480i
$924$	1.69757e7	−	2.90992e7i	0.654104	−	1.12124i
$925$	4.98563e6	+	1.20364e7i	0.191587	+	0.462531i
$926$	−1.05363e6	+	1.36673e6i	−0.0403795	+	0.0523788i
$927$	1.51744e7			0.579980
$928$	1.76446e6	+	6.89476e6i	0.0672577	+	0.262814i
$929$	7.36154e6			0.279852			0.139926	−	0.990162i	$-0.455313\pi$
$929$	7.36154e6			0.279852			0.139926	+	0.990162i	$0.455313\pi$
$930$	1.00847e7	−	1.30816e7i	0.382346	−	0.495966i
$931$	9.86046e6	+	2.38053e7i	0.372840	+	0.900116i
$932$	3.27076e7	+	1.90807e7i	1.23341	+	0.719540i
$933$	−1.87613e7	−	7.77120e6i	−0.705602	−	0.292270i
$934$	2.48985e7	+	6.73168e6i	0.933911	+	0.252497i
$935$	−1.46871e7	−	1.46871e7i	−0.549423	−	0.549423i
$936$	−1.77227e7	−	1.79639e7i	−0.661212	−	0.670210i
$937$	9.21981e6	−	9.21981e6i	0.343062	−	0.343062i	−0.514455	−	0.857517i	$-0.672006\pi$
$937$	9.21981e6	−	9.21981e6i	0.343062	−	0.343062i	0.857517	+	0.514455i	$0.172006\pi$
$938$	1.71381e7	−	9.84328e6i	0.635998	−	0.365286i
$939$	8.15329e6	−	1.96838e7i	0.301765	−	0.728525i
$940$	−2.71102e7	−	3.69346e6i	−1.00072	−	0.136337i
$941$	−2.56811e6	+	1.06375e6i	−0.0945453	+	0.0391619i	−0.429455	−	0.903088i	$-0.641294\pi$
$941$	−2.56811e6	+	1.06375e6i	−0.0945453	+	0.0391619i	0.334910	+	0.942250i	$0.391294\pi$
$942$	−6.13020e6	+	793012.i	−0.225086	+	0.0291174i
$943$			782151.i			0.0286425i
$944$	−4.26088e6	+	521942.i	−0.155621	+	0.0190631i
$945$		−	3.44284e7i		−	1.25411i
$946$	−2.31496e6	−	1.78952e7i	−0.0841037	−	0.650144i
$947$	3.44613e6	−	1.42744e6i	0.124870	−	0.0517227i	−0.319374	−	0.947629i	$-0.603473\pi$
$947$	3.44613e6	−	1.42744e6i	0.124870	−	0.0517227i	0.444243	+	0.895906i	$0.353473\pi$
$948$	−364457.	−	479427.i	−0.0131712	−	0.0173261i
$949$	7.76803e6	−	1.87537e7i	0.279992	−	0.675960i
$950$	−3.76025e6	−	6.54696e6i	−0.135179	−	0.235359i
$951$	−5.54855e6	+	5.54855e6i	−0.198943	+	0.198943i
$952$	1.79284e7	+	4.41240e7i	0.641134	+	1.57791i
$953$	2.90587e6	+	2.90587e6i	0.103644	+	0.103644i	0.757027	−	0.653383i	$-0.226651\pi$
$953$	2.90587e6	+	2.90587e6i	0.103644	+	0.103644i	−0.653383	+	0.757027i	$0.726651\pi$
$954$	959819.	−	3.55008e6i	0.0341443	−	0.126290i
$955$	−1.00969e6	−	418229.i	−0.0358246	−	0.0148390i
$956$	−2.11241e7	+	5.55831e6i	−0.747538	+	0.196697i
$957$	2.27648e6	+	5.49590e6i	0.0803496	+	0.193981i
$958$	−4.14849e7	−	3.19812e7i	−1.46042	−	1.12585i
$959$	−2.41082e7			−0.846483
$960$	−1.02440e7	+	9.97079e6i	−0.358751	+	0.349182i
$961$	1.61681e7			0.564743
$962$	4.29791e7	+	3.31331e7i	1.49734	+	1.15431i
$963$	−2.57690e6	−	6.22119e6i	−0.0895431	−	0.216176i
$964$	7.25789e6	−	1.90974e6i	0.251546	−	0.0661884i
$965$	−2.80741e7	−	1.16287e7i	−0.970483	−	0.401987i
$966$	−1.78108e6	+	6.58770e6i	−0.0614104	+	0.227139i
$967$	1.89157e7	+	1.89157e7i	0.650513	+	0.650513i	0.953117	−	0.302603i	$-0.0978557\pi$
$967$	1.89157e7	+	1.89157e7i	0.650513	+	0.650513i	−0.302603	+	0.953117i	$0.597856\pi$
$968$	4.93990e6	−	2.00717e6i	0.169445	−	0.0688488i
$969$	−8.02602e6	+	8.02602e6i	−0.274594	+	0.274594i
$970$	−2.04220e6	−	3.55567e6i	−0.0696898	−	0.121337i
$971$	−1.63321e7	+	3.94292e7i	−0.555897	+	1.34205i	0.357091	+	0.934070i	$0.383769\pi$
$971$	−1.63321e7	+	3.94292e7i	−0.555897	+	1.34205i	−0.912988	+	0.407985i	$0.866231\pi$
$972$	−1.56135e7	−	2.05389e7i	−0.530073	−	0.697287i
$973$	−4.51652e7	+	1.87080e7i	−1.52940	+	0.633499i
$974$	−4.36186e6	−	3.37183e7i	−0.147324	−	1.13886i
$975$		−	2.03491e7i		−	0.685540i
$976$	1.71720e7	+	1.34241e7i	0.577027	+	0.451087i
$977$		−	5.15617e7i		−	1.72819i	−0.503330	−	0.864094i	$-0.667892\pi$
$977$		−	5.15617e7i		−	1.72819i	0.503330	−	0.864094i	$-0.332108\pi$
$978$	2.26157e7	−	2.92561e6i	0.756073	−	0.0978067i
$979$	5.60266e7	−	2.32070e7i	1.86826	−	0.773859i
$980$	−3.79964e7	−	5.17658e6i	−1.26380	−	0.172178i
$981$	−8.74883e6	+	2.11215e7i	−0.290253	+	0.700734i
$982$	3.31236e7	−	1.90246e7i	1.09612	−	0.629558i
$983$	−2.14946e7	+	2.14946e7i	−0.709487	+	0.709487i	−0.966427	−	0.256940i	$-0.917286\pi$
$983$	−2.14946e7	+	2.14946e7i	−0.709487	+	0.709487i	0.256940	+	0.966427i	$0.417286\pi$
$984$	2.23545e6	−	2.20544e6i	0.0736001	−	0.0726120i
$985$	1.02252e7	+	1.02252e7i	0.335802	+	0.335802i
$986$	−8.11848e6	−	2.19495e6i	−0.265939	−	0.0719006i
$987$	4.84480e7	+	2.00678e7i	1.58301	+	0.655704i
$988$	−2.71646e7	−	1.58471e7i	−0.885341	−	0.516484i
$989$	1.39878e6	+	3.37695e6i	0.0454735	+	0.109783i
$990$	7.11097e6	−	9.22410e6i	0.230590	−	0.299113i
$991$	7.90747e6			0.255772			0.127886	−	0.991789i	$-0.459181\pi$
$991$	7.90747e6			0.255772			0.127886	+	0.991789i	$0.459181\pi$
$992$	−3.83793e7	−	5.49317e6i	−1.23828	−	0.177233i
$993$	3.17424e7			1.02157
$994$	3.31469e7	−	4.29969e7i	1.06408	−	1.38029i
$995$	−3.88472e6	−	9.37854e6i	−0.124395	−	0.300315i
$996$	4.76333e6	−	8.16516e6i	0.152147	−	0.260805i
$997$	7.22090e6	+	2.99099e6i	0.230066	+	0.0952966i	0.494739	−	0.869042i	$-0.335264\pi$
$997$	7.22090e6	+	2.99099e6i	0.230066	+	0.0952966i	−0.264672	+	0.964338i	$0.585264\pi$
$998$	−1.17359e7	−	3.17297e6i	−0.372983	−	0.100841i
$999$	2.34991e7	+	2.34991e7i	0.744968	+	0.744968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.6.g.a.5.15	✓	76
4.3	odd	2		128.6.g.a.113.13		76
32.13	even	8	inner	32.6.g.a.13.15	yes	76
32.19	odd	8		128.6.g.a.17.13		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.6.g.a.5.15	✓	76	1.1	even	1	trivial
32.6.g.a.13.15	yes	76	32.13	even	8	inner
128.6.g.a.17.13		76	32.19	odd	8
128.6.g.a.113.13		76	4.3	odd	2

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.48012 + 3.45378i) q^{2} +(-4.24511 - 10.2486i) q^{3} +(8.14287 + 30.9466i) q^{4} +(36.3338 + 15.0500i) q^{5} +(16.3778 - 60.5765i) q^{6} +(153.750 + 153.750i) q^{7} +(-70.4017 + 166.768i) q^{8} +(84.8142 - 84.8142i) q^{9} +O(q^{10})\)	\(q+(4.48012 + 3.45378i) q^{2} +(-4.24511 - 10.2486i) q^{3} +(8.14287 + 30.9466i) q^{4} +(36.3338 + 15.0500i) q^{5} +(16.3778 - 60.5765i) q^{6} +(153.750 + 153.750i) q^{7} +(-70.4017 + 166.768i) q^{8} +(84.8142 - 84.8142i) q^{9} +(110.801 + 192.914i) q^{10} +(167.030 - 403.247i) q^{11} +(282.592 - 214.825i) q^{12} +(-1073.76 + 444.766i) q^{13} +(157.800 + 1219.84i) q^{14} -436.259i q^{15} +(-891.387 + 503.989i) q^{16} -1210.04i q^{17} +(672.907 - 87.0482i) q^{18} +(781.235 - 323.598i) q^{19} +(-169.884 + 1246.96i) q^{20} +(923.038 - 2228.41i) q^{21} +(2141.04 - 1229.71i) q^{22} +(-353.658 + 353.658i) q^{23} +(2008.00 + 13.5699i) q^{24} +(-1116.06 - 1116.06i) q^{25} +(-6346.69 - 1715.92i) q^{26} +(-3719.68 - 1540.74i) q^{27} +(-3506.08 + 6010.02i) q^{28} +(-470.174 - 1135.10i) q^{29} +(1506.74 - 1954.49i) q^{30} +6693.08 q^{31} +(-5734.18 - 820.724i) q^{32} -4841.77 q^{33} +(4179.21 - 5421.12i) q^{34} +(3272.40 + 7900.27i) q^{35} +(3315.34 + 1934.08i) q^{36} +(-7625.91 - 3158.75i) q^{37} +(4617.66 + 1248.45i) q^{38} +(9116.44 + 9116.44i) q^{39} +(-5067.81 + 4999.78i) q^{40} +(1105.80 - 1105.80i) q^{41} +(11831.7 - 6795.57i) q^{42} +(2796.73 - 6751.90i) q^{43} +(13839.2 + 1885.44i) q^{44} +(4358.07 - 1805.17i) q^{45} +(-2805.89 + 362.974i) q^{46} +21741.1i q^{47} +(8949.21 + 6995.98i) q^{48} +30471.3i q^{49} +(-1145.46 - 8854.73i) q^{50} +(-12401.2 + 5136.75i) q^{51} +(-22507.5 - 29607.6i) q^{52} +(2074.15 - 5007.43i) q^{53} +(-11343.2 - 19749.6i) q^{54} +(12137.7 - 12137.7i) q^{55} +(-36464.9 + 14816.4i) q^{56} +(-6632.85 - 6632.85i) q^{57} +(1813.95 - 6709.26i) q^{58} +(3873.01 + 1604.25i) q^{59} +(13500.7 - 3552.40i) q^{60} +(-8145.63 - 19665.3i) q^{61} +(29985.8 + 23116.4i) q^{62} +26080.4 q^{63} +(-22855.2 - 23481.5i) q^{64} -45707.5 q^{65} +(-21691.7 - 16722.4i) q^{66} +(-6148.97 - 14844.9i) q^{67} +(37446.7 - 9853.20i) q^{68} +(5125.82 + 2123.18i) q^{69} +(-12625.0 + 46696.2i) q^{70} +(-31210.6 - 31210.6i) q^{71} +(8173.24 + 20115.4i) q^{72} +(-12349.9 + 12349.9i) q^{73} +(-23255.3 - 40489.7i) q^{74} +(-6700.28 + 16175.9i) q^{75} +(16375.8 + 21541.6i) q^{76} +(87680.2 - 36318.3i) q^{77} +(9356.57 + 72328.9i) q^{78} -1696.53i q^{79} +(-39972.5 + 4896.49i) q^{80} +15515.4i q^{81} +(8773.30 - 1134.93i) q^{82} +(24602.9 - 10190.8i) q^{83} +(76478.0 + 10419.2i) q^{84} +(18211.1 - 43965.4i) q^{85} +(35849.2 - 20590.0i) q^{86} +(-9637.25 + 9637.25i) q^{87} +(55489.5 + 56244.6i) q^{88} +(98244.6 + 98244.6i) q^{89} +(25759.3 + 6964.42i) q^{90} +(-233474. - 96707.9i) q^{91} +(-13824.3 - 8064.73i) q^{92} +(-28412.8 - 68594.6i) q^{93} +(-75088.8 + 97402.5i) q^{94} +33255.4 q^{95} +(15931.0 + 62251.4i) q^{96} -18431.3 q^{97} +(-105241. + 136515. i) q^{98} +(-20034.5 - 48367.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 76 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 76 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} - 4 q^{13} + 2476 q^{14} + 4176 q^{16} - 1624 q^{18} - 4 q^{19} - 7604 q^{20} - 4 q^{21} - 12384 q^{22} + 1668 q^{23} + 21456 q^{24} - 4 q^{25} + 12976 q^{26} - 7468 q^{27} - 2184 q^{28} - 4 q^{29} - 32316 q^{30} + 23056 q^{31} - 18584 q^{32} - 8 q^{33} - 6256 q^{34} - 4780 q^{35} + 65584 q^{36} - 4 q^{37} + 404 q^{38} - 44908 q^{39} - 28952 q^{40} - 4 q^{41} - 53624 q^{42} + 32068 q^{43} + 3716 q^{44} + 968 q^{45} + 63324 q^{46} + 112368 q^{48} - 4524 q^{50} - 19912 q^{51} + 18468 q^{52} - 49460 q^{53} + 1312 q^{54} + 110044 q^{55} - 80984 q^{56} - 4 q^{57} - 84576 q^{58} - 28964 q^{59} - 46088 q^{60} + 96156 q^{61} + 63480 q^{62} - 158768 q^{63} - 49192 q^{64} - 8 q^{65} - 145012 q^{66} - 61164 q^{67} - 151216 q^{68} - 44644 q^{69} - 56296 q^{70} + 143836 q^{71} + 27092 q^{72} - 4 q^{73} + 213100 q^{74} + 205744 q^{75} + 255996 q^{76} - 14900 q^{77} + 83508 q^{78} - 97096 q^{80} + 435196 q^{82} - 329244 q^{83} + 597472 q^{84} + 12496 q^{85} + 269888 q^{86} - 282188 q^{87} - 199840 q^{88} - 4 q^{89} - 706840 q^{90} + 200108 q^{91} - 650328 q^{92} - 976 q^{93} - 261592 q^{94} + 577592 q^{95} - 501376 q^{96} - 8 q^{97} - 395624 q^{98} + 338544 q^{99}+O(q^{100}) \) 76 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 204 * q^10 - 4 * q^11 - 1588 * q^12 - 4 * q^13 + 2476 * q^14 + 4176 * q^16 - 1624 * q^18 - 4 * q^19 - 7604 * q^20 - 4 * q^21 - 12384 * q^22 + 1668 * q^23 + 21456 * q^24 - 4 * q^25 + 12976 * q^26 - 7468 * q^27 - 2184 * q^28 - 4 * q^29 - 32316 * q^30 + 23056 * q^31 - 18584 * q^32 - 8 * q^33 - 6256 * q^34 - 4780 * q^35 + 65584 * q^36 - 4 * q^37 + 404 * q^38 - 44908 * q^39 - 28952 * q^40 - 4 * q^41 - 53624 * q^42 + 32068 * q^43 + 3716 * q^44 + 968 * q^45 + 63324 * q^46 + 112368 * q^48 - 4524 * q^50 - 19912 * q^51 + 18468 * q^52 - 49460 * q^53 + 1312 * q^54 + 110044 * q^55 - 80984 * q^56 - 4 * q^57 - 84576 * q^58 - 28964 * q^59 - 46088 * q^60 + 96156 * q^61 + 63480 * q^62 - 158768 * q^63 - 49192 * q^64 - 8 * q^65 - 145012 * q^66 - 61164 * q^67 - 151216 * q^68 - 44644 * q^69 - 56296 * q^70 + 143836 * q^71 + 27092 * q^72 - 4 * q^73 + 213100 * q^74 + 205744 * q^75 + 255996 * q^76 - 14900 * q^77 + 83508 * q^78 - 97096 * q^80 + 435196 * q^82 - 329244 * q^83 + 597472 * q^84 + 12496 * q^85 + 269888 * q^86 - 282188 * q^87 - 199840 * q^88 - 4 * q^89 - 706840 * q^90 + 200108 * q^91 - 650328 * q^92 - 976 * q^93 - 261592 * q^94 + 577592 * q^95 - 501376 * q^96 - 8 * q^97 - 395624 * q^98 + 338544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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