LMFDB - Embedded newform 33.9.b.a.23.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,9,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, 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:	$13.4434941320$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.17
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.43364i q^{2} +(80.9807 - 1.77018i) q^{3} +167.006 q^{4} +654.316i q^{5} +(16.6993 + 763.942i) q^{6} -1003.87 q^{7} +3990.49i q^{8} +(6554.73 - 286.701i) q^{9} +O(q^{10})$	\(q+9.43364i q^{2} +(80.9807 - 1.77018i) q^{3} +167.006 q^{4} +654.316i q^{5} +(16.6993 + 763.942i) q^{6} -1003.87 q^{7} +3990.49i q^{8} +(6554.73 - 286.701i) q^{9} -6172.58 q^{10} -4414.43i q^{11} +(13524.3 - 295.632i) q^{12} +15683.4 q^{13} -9470.12i q^{14} +(1158.26 + 52987.0i) q^{15} +5108.80 q^{16} +28664.7i q^{17} +(2704.63 + 61835.0i) q^{18} -155786. q^{19} +109275. i q^{20} +(-81293.8 + 1777.03i) q^{21} +41644.1 q^{22} +398996. i q^{23} +(7063.89 + 323153. i) q^{24} -37504.8 q^{25} +147951. i q^{26} +(530299. - 34820.3i) q^{27} -167652. q^{28} -841380. i q^{29} +(-499860. + 10926.6i) q^{30} +136484. q^{31} +1.06976e6i q^{32} +(-7814.34 - 357483. i) q^{33} -270413. q^{34} -656847. i q^{35} +(1.09468e6 - 47880.9i) q^{36} +1.28540e6 q^{37} -1.46963e6i q^{38} +(1.27005e6 - 27762.4i) q^{39} -2.61104e6 q^{40} -3.48304e6i q^{41} +(-16763.8 - 766897. i) q^{42} +1.46303e6 q^{43} -737238. i q^{44} +(187593. + 4.28887e6i) q^{45} -3.76399e6 q^{46} -4.25096e6i q^{47} +(413714. - 9043.51i) q^{48} -4.75705e6 q^{49} -353806. i q^{50} +(50741.7 + 2.32129e6i) q^{51} +2.61922e6 q^{52} -1.30571e7i q^{53} +(328482. + 5.00265e6i) q^{54} +2.88843e6 q^{55} -4.00592e6i q^{56} +(-1.26156e7 + 275769. i) q^{57} +7.93727e6 q^{58} +2.01517e6i q^{59} +(193437. + 8.84916e6i) q^{60} +1.44306e7 q^{61} +1.28754e6i q^{62} +(-6.58008e6 + 287810. i) q^{63} -8.78388e6 q^{64} +1.02619e7i q^{65} +(3.37237e6 - 73717.7i) q^{66} +2.96951e7 q^{67} +4.78719e6i q^{68} +(706296. + 3.23110e7i) q^{69} +6.19646e6 q^{70} -1.15263e6i q^{71} +(1.14408e6 + 2.61566e7i) q^{72} -4.15279e7 q^{73} +1.21260e7i q^{74} +(-3.03716e6 + 66390.2i) q^{75} -2.60172e7 q^{76} +4.43150e6i q^{77} +(261901. + 1.19812e7i) q^{78} -1.18060e7 q^{79} +3.34277e6i q^{80} +(4.28823e7 - 3.75850e6i) q^{81} +3.28578e7 q^{82} -8.83815e7i q^{83} +(-1.35766e7 + 296775. i) q^{84} -1.87558e7 q^{85} +1.38017e7i q^{86} +(-1.48940e6 - 6.81355e7i) q^{87} +1.76157e7 q^{88} -6.59288e7i q^{89} +(-4.04596e7 + 1.76969e6i) q^{90} -1.57440e7 q^{91} +6.66350e7i q^{92} +(1.10526e7 - 241602. i) q^{93} +4.01021e7 q^{94} -1.01933e8i q^{95} +(1.89367e6 + 8.66299e7i) q^{96} -9.98285e7 q^{97} -4.48763e7i q^{98} +(-1.26562e6 - 2.89354e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) $ 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$			9.43364i			0.589602i	0.955559	+	0.294801i	$0.0952534\pi$
$2$			9.43364i			0.589602i	−0.955559	+	0.294801i	$0.904747\pi$
$3$	80.9807	−	1.77018i	0.999761	−	0.0218541i
$3$	80.9807	−	1.77018i	0.999761	−	0.0218541i
$4$	167.006			0.652369
$5$			654.316i			1.04691i	0.852055	+	0.523453i	$0.175356\pi$
$5$			654.316i			1.04691i	−0.852055	+	0.523453i	$0.824644\pi$
$6$	16.6993	+	763.942i	0.0128852	+	0.589462i
$7$	−1003.87			−0.418104			−0.209052	−	0.977905i	$-0.567038\pi$
$7$	−1003.87			−0.418104			−0.209052	+	0.977905i	$0.567038\pi$
$8$			3990.49i			0.974241i
$9$	6554.73	−	286.701i	0.999045	−	0.0436977i
$10$	−6172.58			−0.617258
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	13524.3	−	295.632i	0.652213	−	0.0142569i
$13$	15683.4			0.549119			0.274559	−	0.961570i	$-0.411468\pi$
$13$	15683.4			0.549119			0.274559	+	0.961570i	$0.411468\pi$
$14$		−	9470.12i		−	0.246515i
$15$	1158.26	+	52987.0i	0.0228792	+	1.04666i
$16$	5108.80			0.0779541
$17$			28664.7i			0.343204i	0.985166	+	0.171602i	$0.0548942\pi$
$17$			28664.7i			0.343204i	−0.985166	+	0.171602i	$0.945106\pi$
$18$	2704.63	+	61835.0i	0.0257643	+	0.589039i
$19$	−155786.			−1.19540			−0.597699	−	0.801720i	$-0.703918\pi$
$19$	−155786.			−1.19540			−0.597699	+	0.801720i	$0.703918\pi$
$20$			109275.i			0.682969i
$21$	−81293.8	+	1777.03i	−0.418004	+	0.00913728i
$22$	41644.1			0.177772
$23$			398996.i			1.42580i	0.701267	+	0.712898i	$0.252618\pi$
$23$			398996.i			1.42580i	−0.701267	+	0.712898i	$0.747382\pi$
$24$	7063.89	+	323153.i	0.0212911	+	0.974008i
$25$	−37504.8			−0.0960122
$26$			147951.i			0.323762i
$27$	530299.	−	34820.3i	0.997851	−	0.0655205i
$28$	−167652.			−0.272758
$29$		−	841380.i		−	1.18960i	−0.803875	−	0.594799i	$-0.797232\pi$
$29$		−	841380.i		−	1.18960i	0.803875	−	0.594799i	$-0.202768\pi$
$30$	−499860.	+	10926.6i	−0.617111	+	0.0134896i
$31$	136484.			0.147787			0.0738934	−	0.997266i	$-0.476458\pi$
$31$	136484.			0.147787			0.0738934	+	0.997266i	$0.476458\pi$
$32$			1.06976e6i			1.02020i
$33$	−7814.34	−	357483.i	−0.00658926	−	0.301439i
$34$	−270413.			−0.202354
$35$		−	656847.i		−	0.437715i
$36$	1.09468e6	−	47880.9i	0.651746	−	0.0285071i
$37$	1.28540e6			0.685851			0.342925	−	0.939363i	$-0.388582\pi$
$37$	1.28540e6			0.685851			0.342925	+	0.939363i	$0.388582\pi$
$38$		−	1.46963e6i		−	0.704810i
$39$	1.27005e6	−	27762.4i	0.548987	−	0.0120005i
$40$	−2.61104e6			−1.01994
$41$		−	3.48304e6i		−	1.23260i	−0.787510	−	0.616302i	$-0.788630\pi$
$41$		−	3.48304e6i		−	1.23260i	0.787510	−	0.616302i	$-0.211370\pi$
$42$	−16763.8	−	766897.i	−0.00538736	−	0.246456i
$43$	1.46303e6			0.427935			0.213968	−	0.976841i	$-0.431361\pi$
$43$	1.46303e6			0.427935			0.213968	+	0.976841i	$0.431361\pi$
$44$		−	737238.i		−	0.196697i
$45$	187593.	+	4.28887e6i	0.0457474	+	1.04591i
$46$	−3.76399e6			−0.840653
$47$		−	4.25096e6i		−	0.871156i	−0.900151	−	0.435578i	$-0.856544\pi$
$47$		−	4.25096e6i		−	0.871156i	0.900151	−	0.435578i	$-0.143456\pi$
$48$	413714.	−	9043.51i	0.0779355	−	0.00170362i
$49$	−4.75705e6			−0.825189
$50$		−	353806.i		−	0.0566090i
$51$	50741.7	+	2.32129e6i	0.00750040	+	0.343122i
$52$	2.61922e6			0.358228
$53$		−	1.30571e7i		−	1.65480i	−0.561616	−	0.827398i	$-0.689820\pi$
$53$		−	1.30571e7i		−	1.65480i	0.561616	−	0.827398i	$-0.310180\pi$
$54$	328482.	+	5.00265e6i	0.0386311	+	0.588336i
$55$	2.88843e6			0.315654
$56$		−	4.00592e6i		−	0.407334i
$57$	−1.26156e7	+	275769.i	−1.19511	+	0.0261244i
$58$	7.93727e6			0.701390
$59$			2.01517e6i			0.166304i	0.996537	+	0.0831520i	$0.0264987\pi$
$59$			2.01517e6i			0.166304i	−0.996537	+	0.0831520i	$0.973501\pi$
$60$	193437.	+	8.84916e6i	0.0149257	+	0.682806i
$61$	1.44306e7			1.04223			0.521116	−	0.853486i	$-0.325516\pi$
$61$	1.44306e7			1.04223			0.521116	+	0.853486i	$0.325516\pi$
$62$			1.28754e6i			0.0871354i
$63$	−6.58008e6	+	287810.i	−0.417705	+	0.0182702i
$64$	−8.78388e6			−0.523560
$65$			1.02619e7i			0.574875i
$66$	3.37237e6	−	73717.7i	0.177729	−	0.00388504i
$67$	2.96951e7			1.47362			0.736810	−	0.676100i	$-0.236331\pi$
$67$	2.96951e7			1.47362			0.736810	+	0.676100i	$0.236331\pi$
$68$			4.78719e6i			0.223895i
$69$	706296.	+	3.23110e7i	0.0311595	+	1.42546i
$70$	6.19646e6			0.258078
$71$		−	1.15263e6i		−	0.0453584i	−0.999743	−	0.0226792i	$-0.992780\pi$
$71$		−	1.15263e6i		−	0.0453584i	0.999743	−	0.0226792i	$-0.00721964\pi$
$72$	1.14408e6	+	2.61566e7i	0.0425721	+	0.973310i
$73$	−4.15279e7			−1.46234			−0.731171	−	0.682194i	$-0.761026\pi$
$73$	−4.15279e7			−1.46234			−0.731171	+	0.682194i	$0.761026\pi$
$74$			1.21260e7i			0.404379i
$75$	−3.03716e6	+	66390.2i	−0.0959893	+	0.00209826i
$76$	−2.60172e7			−0.779841
$77$			4.43150e6i			0.126063i
$78$	261901.	+	1.19812e7i	0.00707552	+	0.323684i
$79$	−1.18060e7			−0.303106			−0.151553	−	0.988449i	$-0.548427\pi$
$79$	−1.18060e7			−0.303106			−0.151553	+	0.988449i	$0.548427\pi$
$80$			3.34277e6i			0.0816107i
$81$	4.28823e7	−	3.75850e6i	0.996181	−	0.0873120i
$82$	3.28578e7			0.726746
$83$		−	8.83815e7i		−	1.86230i	−0.364640	−	0.931149i	$-0.618808\pi$
$83$		−	8.83815e7i		−	1.86230i	0.364640	−	0.931149i	$-0.381192\pi$
$84$	−1.35766e7	+	296775.i	−0.272693	+	0.00596088i
$85$	−1.87558e7			−0.359302
$86$			1.38017e7i			0.252312i
$87$	−1.48940e6	−	6.81355e7i	−0.0259976	−	1.18931i
$88$	1.76157e7			0.293745
$89$		−	6.59288e7i		−	1.05079i	−0.850859	−	0.525394i	$-0.823918\pi$
$89$		−	6.59288e7i		−	1.05079i	0.850859	−	0.525394i	$-0.176082\pi$
$90$	−4.04596e7	+	1.76969e6i	−0.616669	+	0.0269728i
$91$	−1.57440e7			−0.229589
$92$			6.66350e7i			0.930146i
$93$	1.10526e7	−	241602.i	0.147751	−	0.00322975i
$94$	4.01021e7			0.513636
$95$		−	1.01933e8i		−	1.25147i
$96$	1.89367e6	+	8.66299e7i	0.0222956	+	1.01996i
$97$	−9.98285e7			−1.12763			−0.563816	−	0.825900i	$-0.690667\pi$
$97$	−9.98285e7			−1.12763			−0.563816	+	0.825900i	$0.690667\pi$
$98$		−	4.48763e7i		−	0.486534i
$99$	−1.26562e6	−	2.89354e7i	−0.0131754	−	0.301223i
$100$	−6.26354e6			−0.0626354
$101$		−	3.17394e7i		−	0.305009i	−0.988303	−	0.152505i	$-0.951266\pi$
$101$		−	3.17394e7i		−	0.305009i	0.988303	−	0.152505i	$-0.0487339\pi$
$102$	−2.18982e7	+	478679.i	−0.202305	+	0.00442226i
$103$	1.23434e8			1.09670			0.548348	−	0.836250i	$-0.315257\pi$
$103$	1.23434e8			1.09670			0.548348	+	0.836250i	$0.315257\pi$
$104$			6.25844e7i			0.534974i
$105$	−1.16274e6	−	5.31919e7i	−0.00956587	−	0.437611i
$106$	1.23176e8			0.975672
$107$			4.42222e7i			0.337369i	0.985670	+	0.168685i	$0.0539520\pi$
$107$			4.42222e7i			0.337369i	−0.985670	+	0.168685i	$0.946048\pi$
$108$	8.85634e7	−	5.81521e6i	0.650967	−	0.0427436i
$109$	−3.68722e7			−0.261212			−0.130606	−	0.991434i	$-0.541692\pi$
$109$	−3.68722e7			−0.261212			−0.130606	+	0.991434i	$0.541692\pi$
$110$			2.72484e7i			0.186110i
$111$	1.04092e8	−	2.27538e6i	0.685687	−	0.0149887i
$112$	−5.12856e6			−0.0325929
$113$			1.09977e8i			0.674509i	0.941413	+	0.337255i	$0.109498\pi$
$113$			1.09977e8i			0.674509i	−0.941413	+	0.337255i	$0.890502\pi$
$114$	−2.60150e6	−	1.19011e8i	−0.0154030	−	0.704642i
$115$	−2.61070e8			−1.49268
$116$		−	1.40516e8i		−	0.776057i
$117$	1.02800e8	−	4.49644e6i	0.548594	−	0.0239952i
$118$	−1.90103e7			−0.0980533
$119$		−	2.87756e7i		−	0.143495i
$120$	−2.11444e8	+	4.62202e6i	−1.01969	+	0.0222898i
$121$	−1.94872e7			−0.0909091
$122$			1.36133e8i			0.614502i
$123$	−6.16562e6	−	2.82059e8i	−0.0269374	−	1.23231i
$124$	2.27937e7			0.0964115
$125$			2.31052e8i			0.946390i
$126$	−2.71509e6	−	6.20741e7i	−0.0107722	−	0.246280i
$127$	−1.84864e8			−0.710622			−0.355311	−	0.934748i	$-0.615625\pi$
$127$	−1.84864e8			−0.710622			−0.355311	+	0.934748i	$0.615625\pi$
$128$			1.90995e8i			0.711511i
$129$	1.18477e8	−	2.58982e6i	0.427833	−	0.00935214i
$130$	−9.68069e7			−0.338948
$131$			4.41299e8i			1.49847i	0.662306	+	0.749234i	$0.269578\pi$
$131$			4.41299e8i			1.49847i	−0.662306	+	0.749234i	$0.730422\pi$
$132$	−1.30504e6	−	5.97020e7i	−0.00429863	−	0.196650i
$133$	1.56388e8			0.499801
$134$			2.80133e8i			0.868850i
$135$	2.27835e7	+	3.46983e8i	0.0685938	+	1.04466i
$136$	−1.14386e8			−0.334363
$137$			6.76817e8i			1.92127i	0.277808	+	0.960637i	$0.410392\pi$
$137$			6.76817e8i			1.92127i	−0.277808	+	0.960637i	$0.589608\pi$
$138$	−3.04810e8	+	6.66294e6i	−0.840453	+	0.0183717i
$139$	5.01294e8			1.34287			0.671434	−	0.741064i	$-0.265679\pi$
$139$	5.01294e8			1.34287			0.671434	+	0.741064i	$0.265679\pi$
$140$		−	1.09698e8i		−	0.285552i
$141$	−7.52498e6	−	3.44246e8i	−0.0190383	−	0.870948i
$142$	1.08735e7			0.0267434
$143$		−	6.92331e7i		−	0.165565i
$144$	3.34868e7	−	1.46470e6i	0.0778797	−	0.00340642i
$145$	5.50529e8			1.24540
$146$		−	3.91760e8i		−	0.862200i
$147$	−3.85229e8	+	8.42084e6i	−0.824992	+	0.0180338i
$148$	2.14669e8			0.447428
$149$		−	7.36083e7i		−	0.149342i	−0.997208	−	0.0746709i	$-0.976209\pi$
$149$		−	7.36083e7i		−	0.149342i	0.997208	−	0.0746709i	$-0.0237906\pi$
$150$	−626302.	−	2.86515e7i	−0.00123714	−	0.0565955i
$151$	−5.08352e8			−0.977815			−0.488908	−	0.872336i	$-0.662604\pi$
$151$	−5.08352e8			−0.977815			−0.488908	+	0.872336i	$0.662604\pi$
$152$		−	6.21661e8i		−	1.16461i
$153$	8.21820e6	+	1.87889e8i	0.0149972	+	0.342876i
$154$	−4.18052e7			−0.0743271
$155$			8.93038e7i			0.154719i
$156$	2.12107e8	−	4.63650e6i	0.358142	−	0.00782875i
$157$	3.24316e8			0.533789			0.266894	−	0.963726i	$-0.414002\pi$
$157$	3.24316e8			0.533789			0.266894	+	0.963726i	$0.414002\pi$
$158$		−	1.11373e8i		−	0.178712i
$159$	−2.31135e7	−	1.05738e9i	−0.0361641	−	1.65440i
$160$	−6.99961e8			−1.06806
$161$		−	4.00540e8i		−	0.596131i
$162$	3.54563e7	+	4.04536e8i	0.0514794	+	0.587351i
$163$	3.36024e8			0.476014			0.238007	−	0.971263i	$-0.423506\pi$
$163$	3.36024e8			0.476014			0.238007	+	0.971263i	$0.423506\pi$
$164$		−	5.81690e8i		−	0.804112i
$165$	2.33907e8	−	5.11305e6i	0.315579	−	0.00689833i
$166$	8.33759e8			1.09802
$167$			4.84943e8i			0.623484i	0.950167	+	0.311742i	$0.100912\pi$
$167$			4.84943e8i			0.623484i	−0.950167	+	0.311742i	$0.899088\pi$
$168$	−7.09121e6	−	3.24402e8i	−0.00890191	−	0.407237i
$169$	−5.69762e8			−0.698469
$170$		−	1.76935e8i		−	0.211845i
$171$	−1.02113e9	+	4.46639e7i	−1.19426	+	0.0522362i
$172$	2.44335e8			0.279172
$173$		−	1.16065e9i		−	1.29574i	−0.761750	−	0.647871i	$-0.775660\pi$
$173$		−	1.16065e9i		−	1.29574i	0.761750	−	0.647871i	$-0.224340\pi$
$174$	6.42766e8	−	1.40504e7i	0.701222	−	0.0153282i
$175$	3.76498e7			0.0401431
$176$		−	2.25524e7i		−	0.0235041i
$177$	3.56721e6	+	1.63189e8i	0.00363442	+	0.166264i
$178$	6.21949e8			0.619547
$179$			1.30016e9i			1.26644i	0.773971	+	0.633222i	$0.218268\pi$
$179$			1.30016e9i			1.26644i	−0.773971	+	0.633222i	$0.781732\pi$
$180$	3.13293e7	+	7.16269e8i	0.0298442	+	0.682317i
$181$	−1.93174e9			−1.79984			−0.899921	−	0.436053i	$-0.856376\pi$
$181$	−1.93174e9			−1.79984			−0.899921	+	0.436053i	$0.856376\pi$
$182$		−	1.48523e8i		−	0.135366i
$183$	1.16860e9	−	2.55447e7i	1.04198	−	0.0227770i
$184$	−1.59219e9			−1.38907
$185$			8.41055e8i			0.718022i
$186$	2.27918e6	+	1.04266e8i	0.00190427	+	0.0871146i
$187$	1.26538e8			0.103480
$188$		−	7.09938e8i		−	0.568315i
$189$	−5.32350e8	+	3.49550e7i	−0.417205	+	0.0273944i
$190$	9.61600e8			0.737870
$191$		−	7.40802e8i		−	0.556633i	−0.960489	−	0.278316i	$-0.910224\pi$
$191$		−	7.40802e8i		−	0.556633i	0.960489	−	0.278316i	$-0.0897764\pi$
$192$	−7.11324e8	+	1.55491e7i	−0.523435	+	0.0114419i
$193$	−1.73481e9			−1.25032			−0.625161	−	0.780496i	$-0.714967\pi$
$193$	−1.73481e9			−1.25032			−0.625161	+	0.780496i	$0.714967\pi$
$194$		−	9.41746e8i		−	0.664855i
$195$	1.81654e7	+	8.31014e8i	0.0125634	+	0.574738i
$196$	−7.94458e8			−0.538328
$197$		−	3.66287e8i		−	0.243196i	−0.992579	−	0.121598i	$-0.961198\pi$
$197$		−	3.66287e8i		−	0.243196i	0.992579	−	0.121598i	$-0.0388019\pi$
$198$	2.72966e8	−	1.19394e7i	0.177602	−	0.00776823i
$199$	2.81373e9			1.79419			0.897097	−	0.441833i	$-0.145672\pi$
$199$	2.81373e9			1.79419			0.897097	+	0.441833i	$0.145672\pi$
$200$		−	1.49662e8i		−	0.0935390i
$201$	2.40473e9	−	5.25657e7i	1.47327	−	0.0322046i
$202$	2.99418e8			0.179834
$203$			8.44634e8i			0.497375i
$204$	8.47420e6	+	3.87670e8i	0.00489303	+	0.223842i
$205$	2.27901e9			1.29042
$206$			1.16443e9i			0.646615i
$207$	1.14393e8	+	2.61532e9i	0.0623041	+	1.42444i
$208$	8.01233e7			0.0428061
$209$			6.87704e8i			0.360426i
$210$	5.01793e8	−	1.09689e7i	0.258016	−	0.00564006i
$211$	−2.34269e9			−1.18191			−0.590957	−	0.806703i	$-0.701250\pi$
$211$	−2.34269e9			−1.18191			−0.590957	+	0.806703i	$0.701250\pi$
$212$		−	2.18063e9i		−	1.07954i
$213$	−2.04037e6	−	9.33410e7i	−0.000991267	−	0.0453476i
$214$	−4.17177e8			−0.198914
$215$			9.57281e8i			0.448008i
$216$	1.38950e8	+	2.11615e9i	0.0638328	+	0.972147i
$217$	−1.37012e8			−0.0617902
$218$		−	3.47839e8i		−	0.154011i
$219$	−3.36296e9	+	7.35120e7i	−1.46199	+	0.0319582i
$220$	4.82387e8			0.205923
$221$			4.49559e8i			0.188459i
$222$	2.14651e7	+	9.81968e8i	0.00883735	+	0.404283i
$223$	7.59300e8			0.307039			0.153520	−	0.988146i	$-0.450939\pi$
$223$	7.59300e8			0.307039			0.153520	+	0.988146i	$0.450939\pi$
$224$		−	1.07390e9i		−	0.426551i
$225$	−2.45834e8	+	1.07526e7i	−0.0959205	+	0.00419552i
$226$	−1.03748e9			−0.397692
$227$			4.54793e9i			1.71282i	0.516300	+	0.856408i	$0.327309\pi$
$227$			4.54793e9i			1.71282i	−0.516300	+	0.856408i	$0.672691\pi$
$228$	−2.10689e9	+	4.60552e7i	−0.779655	+	0.0170427i
$229$	−1.86293e9			−0.677413			−0.338707	−	0.940892i	$-0.609989\pi$
$229$	−1.86293e9			−0.677413			−0.338707	+	0.940892i	$0.609989\pi$
$230$		−	2.46284e9i		−	0.880085i
$231$	7.84456e6	+	3.58866e8i	0.00275499	+	0.126033i
$232$	3.35752e9			1.15895
$233$		−	4.67187e9i		−	1.58514i	−0.609783	−	0.792568i	$-0.708744\pi$
$233$		−	4.67187e9i		−	1.58514i	0.609783	−	0.792568i	$-0.291256\pi$
$234$	4.24178e7	+	9.69781e8i	0.0141477	+	0.323452i
$235$	2.78147e9			0.912019
$236$			3.36546e8i			0.108492i
$237$	−9.56057e8	+	2.08987e7i	−0.303033	+	0.00662410i
$238$	2.71458e8			0.0846049
$239$		−	1.52975e9i		−	0.468844i	−0.972135	−	0.234422i	$-0.924680\pi$
$239$		−	1.52975e9i		−	0.468844i	0.972135	−	0.234422i	$-0.0753197\pi$
$240$	5.91731e6	+	2.70700e8i	0.00178353	+	0.0815912i
$241$	−3.94692e9			−1.17001			−0.585006	−	0.811029i	$-0.698908\pi$
$241$	−3.94692e9			−1.17001			−0.585006	+	0.811029i	$0.698908\pi$
$242$		−	1.83835e8i		−	0.0536002i
$243$	3.46599e9	−	3.80275e8i	0.994035	−	0.109062i
$244$	2.41000e9			0.679920
$245$		−	3.11262e9i		−	0.863895i
$246$	2.66084e9	−	5.81642e7i	0.726572	−	0.0158824i
$247$	−2.44324e9			−0.656416
$248$			5.44639e8i			0.143980i
$249$	−1.56451e8	−	7.15719e9i	−0.0406988	−	1.86185i
$250$	−2.17966e9			−0.557994
$251$			6.72012e8i			0.169310i	0.996410	+	0.0846549i	$0.0269788\pi$
$251$			6.72012e8i			0.169310i	−0.996410	+	0.0846549i	$0.973021\pi$
$252$	−1.09892e9	+	4.80661e7i	−0.272497	+	0.0119189i
$253$	1.76134e9			0.429894
$254$		−	1.74394e9i		−	0.418984i
$255$	−1.51886e9	+	3.32011e7i	−0.359216	+	0.00785222i
$256$	−4.05045e9			−0.943068
$257$		−	2.66110e9i		−	0.609998i	−0.952353	−	0.304999i	$-0.901344\pi$
$257$		−	2.66110e9i		−	0.609998i	0.952353	−	0.304999i	$-0.0986560\pi$
$258$	2.44314e7	+	1.11767e9i	0.00551404	+	0.252251i
$259$	−1.29037e9			−0.286757
$260$			1.71380e9i			0.375031i
$261$	−2.41224e8	−	5.51502e9i	−0.0519827	−	1.18846i
$262$	−4.16305e9			−0.883500
$263$			6.79769e9i			1.42082i	0.703789	+	0.710409i	$0.251490\pi$
$263$			6.79769e9i			1.42082i	−0.703789	+	0.710409i	$0.748510\pi$
$264$	1.42653e9	−	3.11830e7i	0.293674	−	0.00641952i
$265$	8.54350e9			1.73242
$266$			1.47531e9i			0.294684i
$267$	−1.16706e8	−	5.33896e9i	−0.0229640	−	1.05054i
$268$	4.95927e9			0.961344
$269$		−	7.24354e9i		−	1.38338i	−0.722194	−	0.691690i	$-0.756866\pi$
$269$		−	7.24354e9i		−	1.38338i	0.722194	−	0.691690i	$-0.243134\pi$
$270$	−3.27332e9	+	2.14931e8i	−0.615932	+	0.0404431i
$271$	9.63308e9			1.78603			0.893013	−	0.450030i	$-0.148587\pi$
$271$	9.63308e9			1.78603			0.893013	+	0.450030i	$0.148587\pi$
$272$			1.46442e8i			0.0267541i
$273$	−1.27496e9	+	2.78698e7i	−0.229534	+	0.00501745i
$274$	−6.38485e9			−1.13279
$275$			1.65562e8i			0.0289488i
$276$	1.17956e8	+	5.39614e9i	0.0203275	+	0.929923i
$277$	−2.47506e9			−0.420404			−0.210202	−	0.977658i	$-0.567412\pi$
$277$	−2.47506e9			−0.420404			−0.210202	+	0.977658i	$0.567412\pi$
$278$			4.72903e9i			0.791758i
$279$	8.94617e8	−	3.91301e7i	0.147646	−	0.00645795i
$280$	2.62114e9			0.426440
$281$			6.69017e9i			1.07303i	0.843891	+	0.536515i	$0.180260\pi$
$281$			6.69017e9i			1.07303i	−0.843891	+	0.536515i	$0.819740\pi$
$282$	3.24749e9	−	7.09879e7i	0.513513	−	0.0112250i
$283$	7.61999e8			0.118798			0.0593989	−	0.998234i	$-0.481082\pi$
$283$	7.61999e8			0.118798			0.0593989	+	0.998234i	$0.481082\pi$
$284$		−	1.92497e8i		−	0.0295904i
$285$	−1.80440e8	−	8.25460e9i	−0.0273498	−	1.25117i
$286$	6.53120e8			0.0976178
$287$			3.49651e9i			0.515356i
$288$	3.06701e8	+	7.01199e9i	0.0445806	+	1.01923i
$289$	6.15409e9			0.882211
$290$			5.19349e9i			0.734289i
$291$	−8.08417e9	+	1.76714e8i	−1.12736	+	0.0246434i
$292$	−6.93543e9			−0.953986
$293$			3.45422e9i			0.468683i	0.972154	+	0.234341i	$0.0752934\pi$
$293$			3.45422e9i			0.468683i	−0.972154	+	0.234341i	$0.924707\pi$
$294$	−7.94392e7	−	3.63411e9i	−0.0106328	−	0.486417i
$295$	−1.31856e9			−0.174105
$296$			5.12936e9i			0.668184i
$297$	−1.53712e8	−	2.34097e9i	−0.0197552	−	0.300863i
$298$	6.94394e8			0.0880523
$299$			6.25761e9i			0.782932i
$300$	−5.07225e8	+	1.10876e7i	−0.0626204	+	0.00136884i
$301$	−1.46868e9			−0.178921
$302$		−	4.79561e9i		−	0.576522i
$303$	−5.61845e7	−	2.57028e9i	−0.00666571	−	0.304937i
$304$	−7.95878e8			−0.0931863
$305$			9.44216e9i			1.09112i
$306$	−1.77248e9	+	7.75275e7i	−0.202160	+	0.00884240i
$307$	−7.57987e9			−0.853313			−0.426657	−	0.904414i	$-0.640309\pi$
$307$	−7.57987e9			−0.853313			−0.426657	+	0.904414i	$0.640309\pi$
$308$			7.40089e8i			0.0822396i
$309$	9.99578e9	−	2.18501e8i	1.09643	−	0.0239673i
$310$	−8.42460e8			−0.0912226
$311$			4.30352e9i			0.460026i	0.973188	+	0.230013i	$0.0738769\pi$
$311$			4.30352e9i			0.460026i	−0.973188	+	0.230013i	$0.926123\pi$
$312$	1.10786e8	+	5.06812e9i	0.0116914	+	0.534846i
$313$	−1.37328e10			−1.43081			−0.715407	−	0.698708i	$-0.753758\pi$
$313$	−1.37328e10			−1.43081			−0.715407	+	0.698708i	$0.753758\pi$
$314$			3.05948e9i			0.314723i
$315$	−1.88319e8	−	4.30546e9i	−0.0191272	−	0.437297i
$316$	−1.97168e9			−0.197737
$317$		−	1.29241e10i		−	1.27986i	−0.768432	−	0.639931i	$-0.778963\pi$
$317$		−	1.29241e10i		−	1.27986i	0.768432	−	0.639931i	$-0.221037\pi$
$318$	9.97490e9	−	2.18044e8i	0.975439	−	0.0213224i
$319$	−3.71421e9			−0.358677
$320$		−	5.74743e9i		−	0.548118i
$321$	7.82814e7	+	3.58115e9i	0.00737290	+	0.337289i
$322$	3.77855e9			0.351480
$323$		−	4.46555e9i		−	0.410265i
$324$	7.16162e9	−	6.27693e8i	0.649878	−	0.0569596i
$325$	−5.88201e8			−0.0527221
$326$			3.16993e9i			0.280659i
$327$	−2.98594e9	+	6.52705e7i	−0.261150	+	0.00570855i
$328$	1.38990e10			1.20085
$329$			4.26740e9i			0.364234i
$330$	4.82347e7	+	2.20660e9i	0.00406727	+	0.186066i
$331$	−1.16501e10			−0.970551			−0.485275	−	0.874361i	$-0.661281\pi$
$331$	−1.16501e10			−0.970551			−0.485275	+	0.874361i	$0.661281\pi$
$332$		−	1.47603e10i		−	1.21490i
$333$	8.42542e9	−	3.68524e8i	0.685196	−	0.0299701i
$334$	−4.57478e9			−0.367608
$335$			1.94300e10i			1.54274i
$336$	−4.15314e8	+	9.07848e6i	−0.0325851	+	0.000712289i
$337$	1.16754e10			0.905218			0.452609	−	0.891709i	$-0.350493\pi$
$337$	1.16754e10			0.905218			0.452609	+	0.891709i	$0.350493\pi$
$338$		−	5.37493e9i		−	0.411819i
$339$	1.94679e8	+	8.90601e9i	0.0147408	+	0.674348i
$340$	−3.13234e9			−0.234397
$341$		−	6.02499e8i		−	0.0445594i
$342$	−4.21343e8	−	9.63300e9i	−0.0307986	−	0.704137i
$343$	1.05625e10			0.763119
$344$			5.83819e9i			0.416912i
$345$	−2.11416e10	+	4.62141e8i	−1.49232	+	0.0326211i
$346$	1.09492e10			0.763972
$347$		−	1.30223e10i		−	0.898195i	−0.893483	−	0.449097i	$-0.851746\pi$
$347$		−	1.30223e10i		−	0.898195i	0.893483	−	0.449097i	$-0.148254\pi$
$348$	−2.48739e8	−	1.13791e10i	−0.0169600	−	0.775871i
$349$	−1.26647e9			−0.0853676			−0.0426838	−	0.999089i	$-0.513591\pi$
$349$	−1.26647e9			−0.0853676			−0.0426838	+	0.999089i	$0.513591\pi$
$350$			3.55175e8i			0.0236685i
$351$	8.31688e9	−	5.46100e8i	0.547939	−	0.0359785i
$352$	4.72238e9			0.307603
$353$		−	2.70283e9i		−	0.174068i	−0.996205	−	0.0870341i	$-0.972261\pi$
$353$		−	2.70283e9i		−	0.174068i	0.996205	−	0.0870341i	$-0.0277389\pi$
$354$	−1.53947e9	+	3.36518e7i	−0.0980298	+	0.00214287i
$355$	7.54187e8			0.0474860
$356$		−	1.10105e10i		−	0.685502i
$357$	−5.09380e7	−	2.33026e9i	−0.00313595	−	0.143460i
$358$	−1.22653e10			−0.746698
$359$			1.50990e10i			0.909016i	0.890743	+	0.454508i	$0.150185\pi$
$359$			1.50990e10i			0.909016i	−0.890743	+	0.454508i	$0.849815\pi$
$360$	−1.71147e10	+	7.48588e8i	−1.01896	+	0.0445690i
$361$	7.28559e9			0.428979
$362$		−	1.82233e10i		−	1.06119i
$363$	−1.57808e9	+	3.44958e7i	−0.0908874	+	0.00198674i
$364$	−2.62935e9			−0.149776
$365$		−	2.71724e10i		−	1.53093i
$366$	2.40980e8	+	1.10241e10i	0.0134294	+	0.614356i
$367$	−5.03372e9			−0.277475			−0.138738	−	0.990329i	$-0.544305\pi$
$367$	−5.03372e9			−0.277475			−0.138738	+	0.990329i	$0.544305\pi$
$368$			2.03839e9i			0.111147i
$369$	−9.98591e8	−	2.28304e10i	−0.0538620	−	1.23143i
$370$	−7.93421e9			−0.423347
$371$			1.31076e10i			0.691877i
$372$	1.84585e9	−	4.03491e7i	0.0963885	−	0.00210699i
$373$	2.28499e10			1.18045			0.590226	−	0.807238i	$-0.299038\pi$
$373$	2.28499e10			1.18045			0.590226	+	0.807238i	$0.299038\pi$
$374$			1.19372e9i			0.0610119i
$375$	4.09005e8	+	1.87108e10i	0.0206825	+	0.946164i
$376$	1.69634e10			0.848716
$377$		−	1.31957e10i		−	0.653230i
$378$	−3.29753e8	−	5.02200e9i	−0.0161518	−	0.245985i
$379$	−2.78517e9			−0.134988			−0.0674940	−	0.997720i	$-0.521500\pi$
$379$	−2.78517e9			−0.134988			−0.0674940	+	0.997720i	$0.521500\pi$
$380$		−	1.70235e10i		−	0.816420i
$381$	−1.49704e10	+	3.27244e8i	−0.710452	+	0.0155300i
$382$	6.98846e9			0.328192
$383$		−	1.49315e10i		−	0.693920i	−0.937880	−	0.346960i	$-0.887214\pi$
$383$		−	1.49315e10i		−	0.693920i	0.937880	−	0.346960i	$-0.112786\pi$
$384$	3.38095e8	+	1.54669e10i	0.0155494	+	0.711341i
$385$	−2.89960e9			−0.131976
$386$		−	1.63655e10i		−	0.737193i
$387$	9.58974e9	−	4.19451e8i	0.427526	−	0.0186998i
$388$	−1.66720e10			−0.735632
$389$			1.14426e10i			0.499719i	0.968282	+	0.249859i	$0.0803844\pi$
$389$			1.14426e10i			0.499719i	−0.968282	+	0.249859i	$0.919616\pi$
$390$	−7.83949e9	+	1.71366e8i	−0.338867	+	0.00740740i
$391$	−1.14371e10			−0.489339
$392$		−	1.89830e10i		−	0.803933i
$393$	7.81179e8	+	3.57367e10i	0.0327477	+	1.49811i
$394$	3.45542e9			0.143389
$395$		−	7.72485e9i		−	0.317323i
$396$	−2.11367e8	−	4.83240e9i	−0.00859520	−	0.196509i
$397$	−2.19883e10			−0.885176			−0.442588	−	0.896725i	$-0.645940\pi$
$397$	−2.19883e10			−0.885176			−0.442588	+	0.896725i	$0.645940\pi$
$398$			2.65437e10i			1.05786i
$399$	1.26644e10	−	2.76835e8i	0.499682	−	0.0109227i
$400$	−1.91604e8			−0.00748455
$401$			3.25761e10i			1.25986i	0.776653	+	0.629929i	$0.216916\pi$
$401$			3.25761e10i			1.25986i	−0.776653	+	0.629929i	$0.783084\pi$
$402$	4.95886e8	+	2.26853e10i	0.0189879	+	0.868642i
$403$	2.14053e9			0.0811524
$404$		−	5.30069e9i		−	0.198979i
$405$	2.45925e9	+	2.80586e10i	0.0914075	+	1.04291i
$406$	−7.96797e9			−0.293254
$407$		−	5.67428e9i		−	0.206792i
$408$	−9.26307e9	+	2.02484e8i	−0.334283	+	0.00730720i
$409$	−2.21604e10			−0.791926			−0.395963	−	0.918267i	$-0.629589\pi$
$409$	−2.21604e10			−0.791926			−0.395963	+	0.918267i	$0.629589\pi$
$410$			2.14994e10i			0.760835i
$411$	1.19809e9	+	5.48091e10i	0.0419877	+	1.92081i
$412$	2.06143e10			0.715451
$413$		−	2.02296e9i		−	0.0695324i
$414$	−2.46719e10	+	1.07914e9i	−0.839850	+	0.0367347i
$415$	5.78295e10			1.94965
$416$			1.67774e10i			0.560212i
$417$	4.05951e10	−	8.87381e8i	1.34255	−	0.0293472i
$418$	−6.48755e9			−0.212508
$419$			1.97226e10i			0.639893i	0.947436	+	0.319946i	$0.103665\pi$
$419$			1.97226e10i			0.639893i	−0.947436	+	0.319946i	$0.896335\pi$
$420$	−1.94185e8	−	8.88339e9i	−0.00624048	−	0.285484i
$421$	−2.56754e10			−0.817315			−0.408658	−	0.912688i	$-0.634003\pi$
$421$	−2.56754e10			−0.817315			−0.408658	+	0.912688i	$0.634003\pi$
$422$		−	2.21001e10i		−	0.696859i
$423$	−1.21876e9	−	2.78639e10i	−0.0380676	−	0.870324i
$424$	5.21044e10			1.61217
$425$		−	1.07506e9i		−	0.0329517i
$426$	8.80546e8	−	1.92481e7i	0.0267371	−	0.000584454i
$427$	−1.44864e10			−0.435761
$428$			7.38540e9i			0.220089i
$429$	−1.22555e8	−	5.60654e9i	−0.00361828	−	0.165526i
$430$	−9.03065e9			−0.264147
$431$			2.02786e10i			0.587664i	0.955857	+	0.293832i	$0.0949307\pi$
$431$			2.02786e10i			0.587664i	−0.955857	+	0.293832i	$0.905069\pi$
$432$	2.70919e9	−	1.77890e8i	0.0777866	−	0.00510760i
$433$	−1.50102e10			−0.427007			−0.213504	−	0.976942i	$-0.568488\pi$
$433$	−1.50102e10			−0.427007			−0.213504	+	0.976942i	$0.568488\pi$
$434$		−	1.29252e9i		−	0.0364317i
$435$	4.45822e10	−	9.74536e8i	1.24510	−	0.0272170i
$436$	−6.15790e9			−0.170407
$437$		−	6.21579e10i		−	1.70440i
$438$	−6.93486e8	−	3.17250e10i	−0.0188426	−	0.861995i
$439$	−3.61916e10			−0.974427			−0.487213	−	0.873283i	$-0.661987\pi$
$439$	−3.61916e10			−0.974427			−0.487213	+	0.873283i	$0.661987\pi$
$440$			1.15263e10i			0.307523i
$441$	−3.11812e10	+	1.36385e9i	−0.824401	+	0.0360589i
$442$	−4.24098e9			−0.111116
$443$			1.99664e8i			0.00518423i	0.999997	+	0.00259212i	$0.000825097\pi$
$443$			1.99664e8i			0.00518423i	−0.999997	+	0.00259212i	$0.999175\pi$
$444$	1.73841e10	−	3.80004e8i	0.447321	−	0.00977813i
$445$	4.31383e10			1.10008
$446$			7.16296e9i			0.181031i
$447$	−1.30300e8	−	5.96085e9i	−0.00326373	−	0.149306i
$448$	8.81785e9			0.218902
$449$		−	4.72852e10i		−	1.16343i	−0.813393	−	0.581715i	$-0.802382\pi$
$449$		−	4.72852e10i		−	1.16343i	0.813393	−	0.581715i	$-0.197618\pi$
$450$	−1.01437e8	−	2.31911e9i	−0.00247369	−	0.0565550i
$451$	−1.53756e10			−0.371644
$452$			1.83669e10i			0.440029i
$453$	−4.11667e10	+	8.99875e8i	−0.977582	+	0.0213693i
$454$	−4.29036e10			−1.00988
$455$		−	1.03016e10i		−	0.240358i
$456$	−1.10045e9	−	5.03425e10i	−0.0254514	−	1.16433i
$457$	6.39052e10			1.46511			0.732557	−	0.680706i	$-0.238327\pi$
$457$	6.39052e10			1.46511			0.732557	+	0.680706i	$0.238327\pi$
$458$		−	1.75742e10i		−	0.399405i
$459$	9.98114e8	+	1.52009e10i	0.0224869	+	0.342466i
$460$	−4.36003e10			−0.973775
$461$			5.51990e10i			1.22216i	0.791570	+	0.611079i	$0.209264\pi$
$461$			5.51990e10i			1.22216i	−0.791570	+	0.611079i	$0.790736\pi$
$462$	−3.38541e9	+	7.40027e7i	−0.0743093	+	0.00162435i
$463$	−4.87768e10			−1.06142			−0.530712	−	0.847552i	$-0.678075\pi$
$463$	−4.87768e10			−1.06142			−0.530712	+	0.847552i	$0.678075\pi$
$464$		−	4.29844e9i		−	0.0927341i
$465$	1.58084e8	+	7.23188e9i	0.00338124	+	0.154682i
$466$	4.40727e10			0.934600
$467$			1.40745e10i			0.295914i	0.988994	+	0.147957i	$0.0472697\pi$
$467$			1.40745e10i			0.295914i	−0.988994	+	0.147957i	$0.952730\pi$
$468$	1.71683e10	−	7.50934e8i	0.357886	−	0.0156538i
$469$	−2.98099e10			−0.616126
$470$			2.62394e10i			0.537728i
$471$	2.62633e10	−	5.74098e8i	0.533661	−	0.0116655i
$472$	−8.04150e9			−0.162020
$473$		−	6.45842e9i		−	0.129027i
$474$	−1.97151e8	−	9.01910e9i	−0.00390559	−	0.178669i
$475$	5.84270e9			0.114773
$476$		−	4.80570e9i		−	0.0936115i
$477$	−3.74349e9	−	8.55860e10i	−0.0723108	−	1.65322i
$478$	1.44311e10			0.276431
$479$			3.32933e10i			0.632432i	0.948687	+	0.316216i	$0.102413\pi$
$479$			3.32933e10i			0.632432i	−0.948687	+	0.316216i	$0.897587\pi$
$480$	−5.66833e10	+	1.23906e9i	−1.06780	+	0.0233414i
$481$	2.01593e10			0.376613
$482$		−	3.72339e10i		−	0.689842i
$483$	−7.09028e8	−	3.24360e10i	−0.0130279	−	0.595989i
$484$	−3.25448e9			−0.0593063
$485$		−	6.53194e10i		−	1.18052i
$486$	3.58738e9	+	3.26969e10i	0.0643031	+	0.586085i
$487$	−1.01082e11			−1.79705			−0.898523	−	0.438926i	$-0.855359\pi$
$487$	−1.01082e11			−1.79705			−0.898523	+	0.438926i	$0.855359\pi$
$488$			5.75851e10i			1.01538i
$489$	2.72114e10	−	5.94823e8i	0.475900	−	0.0104029i
$490$	2.93633e10			0.509355
$491$			5.12897e10i			0.882478i	0.897390	+	0.441239i	$0.145461\pi$
$491$			5.12897e10i			0.882478i	−0.897390	+	0.441239i	$0.854539\pi$
$492$	−1.02970e9	−	4.71057e10i	−0.0175731	−	0.803920i
$493$	2.41179e10			0.408274
$494$		−	2.30487e10i		−	0.387024i
$495$	1.89329e10	−	8.28116e8i	0.315353	−	0.0137934i
$496$	6.97271e8			0.0115206
$497$			1.15709e9i			0.0189645i
$498$	6.75184e10	−	1.47591e9i	1.09775	−	0.0239961i
$499$	1.03716e11			1.67279			0.836397	−	0.548124i	$-0.184658\pi$
$499$	1.03716e11			1.67279			0.836397	+	0.548124i	$0.184658\pi$
$500$			3.85872e10i			0.617396i
$501$	8.58438e8	+	3.92710e10i	0.0136257	+	0.623335i
$502$	−6.33952e9			−0.0998255
$503$		−	5.73744e10i		−	0.896284i	−0.893962	−	0.448142i	$-0.852086\pi$
$503$		−	5.73744e10i		−	0.896284i	0.893962	−	0.448142i	$-0.147914\pi$
$504$	−1.14850e9	−	2.62578e10i	−0.0177996	−	0.406945i
$505$	2.07676e10			0.319316
$506$			1.66159e10i			0.253467i
$507$	−4.61397e10	+	1.00858e9i	−0.698302	+	0.0152644i
$508$	−3.08735e10			−0.463587
$509$		−	1.24239e11i		−	1.85092i	−0.378848	−	0.925459i	$-0.623680\pi$
$509$		−	1.24239e11i		−	1.85092i	0.378848	−	0.925459i	$-0.376320\pi$
$510$	−3.13208e8	−	1.43283e10i	−0.00462969	−	0.211795i
$511$	4.16885e10			0.611411
$512$			1.06842e10i			0.155475i
$513$	−8.26130e10	+	5.42450e9i	−1.19283	+	0.0783232i
$514$	2.51038e10			0.359656
$515$			8.07650e10i			1.14814i
$516$	1.97864e10	−	4.32517e8i	0.279105	−	0.00610104i
$517$	−1.87656e10			−0.262663
$518$		−	1.21729e10i		−	0.169073i
$519$	−2.05457e9	−	9.39905e10i	−0.0283173	−	1.29543i
$520$	−4.09500e10			−0.560067
$521$			1.99173e10i			0.270321i	0.990824	+	0.135160i	$0.0431550\pi$
$521$			1.99173e10i			0.270321i	−0.990824	+	0.135160i	$0.956845\pi$
$522$	5.20267e10	−	2.27562e9i	0.700720	−	0.0306492i
$523$	9.32432e9			0.124626			0.0623132	−	0.998057i	$-0.480152\pi$
$523$	9.32432e9			0.124626			0.0623132	+	0.998057i	$0.480152\pi$
$524$			7.36997e10i			0.977554i
$525$	3.04891e9	−	6.66470e7i	0.0401335	−	0.000877290i
$526$	−6.41270e10			−0.837718
$527$			3.91228e9i			0.0507209i
$528$	−3.99219e7	−	1.82631e9i	−0.000513660	−	0.0234984i
$529$	−8.08872e10			−1.03290
$530$			8.05963e10i			1.02144i
$531$	5.77750e8	+	1.32089e10i	0.00726711	+	0.166145i
$532$	2.61178e10			0.326055
$533$		−	5.46258e10i		−	0.676845i
$534$	5.03658e10	−	1.10096e9i	0.619399	−	0.0135396i
$535$	−2.89353e10			−0.353194
$536$			1.18498e11i			1.43566i
$537$	2.30152e9	+	1.05288e11i	0.0276770	+	1.26614i
$538$	6.83329e10			0.815645
$539$			2.09997e10i			0.248804i
$540$	3.80499e9	+	5.79484e10i	0.0447485	+	0.681501i
$541$	1.15274e11			1.34568			0.672839	−	0.739789i	$-0.265075\pi$
$541$	1.15274e11			1.34568			0.672839	+	0.739789i	$0.265075\pi$
$542$			9.08750e10i			1.05305i
$543$	−1.56434e11	+	3.41953e9i	−1.79941	+	0.0393339i
$544$	−3.06644e10			−0.350137
$545$		−	2.41261e10i		−	0.273464i
$546$	−2.62914e8	−	1.20275e10i	−0.00295830	−	0.135334i
$547$	2.41200e10			0.269419			0.134710	−	0.990885i	$-0.456990\pi$
$547$	2.41200e10			0.269419			0.134710	+	0.990885i	$0.456990\pi$
$548$			1.13033e11i			1.25338i
$549$	9.45886e10	−	4.13726e9i	1.04124	−	0.0455432i
$550$	−1.56185e9			−0.0170683
$551$			1.31075e11i			1.42204i
$552$	−1.28937e11	+	2.81847e9i	−1.38874	+	0.0303569i
$553$	1.18516e10			0.126730
$554$		−	2.33488e10i		−	0.247871i
$555$	1.48882e9	+	6.81092e10i	0.0156917	+	0.717850i
$556$	8.37193e10			0.876045
$557$		−	1.16076e11i		−	1.20593i	−0.797767	−	0.602966i	$-0.793985\pi$
$557$		−	1.16076e11i		−	1.20593i	0.797767	−	0.602966i	$-0.206015\pi$
$558$	3.69140e8	+	8.43950e9i	0.00380762	+	0.0870522i
$559$	2.29452e10			0.234987
$560$		−	3.35570e9i		−	0.0341217i
$561$	1.02472e10	−	2.23996e8i	0.103455	−	0.00226146i
$562$	−6.31127e10			−0.632662
$563$		−	1.43539e11i		−	1.42869i	−0.699794	−	0.714345i	$-0.746725\pi$
$563$		−	1.43539e11i		−	1.42869i	0.699794	−	0.714345i	$-0.253275\pi$
$564$	−1.25672e9	−	5.74913e10i	−0.0124200	−	0.568179i
$565$	−7.19597e10			−0.706148
$566$			7.18843e9i			0.0700435i
$567$	−4.30482e10	+	3.77303e9i	−0.416507	+	0.0365055i
$568$	4.59957e9			0.0441900
$569$		−	5.95031e9i		−	0.0567663i	−0.999597	−	0.0283832i	$-0.990964\pi$
$569$		−	5.95031e9i		−	0.0567663i	0.999597	−	0.0283832i	$-0.00903585\pi$
$570$	7.78710e10	−	1.70221e9i	0.737694	−	0.0161255i
$571$	−1.46668e10			−0.137972			−0.0689862	−	0.997618i	$-0.521976\pi$
$571$	−1.46668e10			−0.137972			−0.0689862	+	0.997618i	$0.521976\pi$
$572$		−	1.15624e10i		−	0.108010i
$573$	−1.31135e9	−	5.99907e10i	−0.0121647	−	0.556500i
$574$	−3.29848e10			−0.303855
$575$		−	1.49643e10i		−	0.136894i
$576$	−5.75760e10	+	2.51835e9i	−0.523060	+	0.0228784i
$577$	8.14507e9			0.0734838			0.0367419	−	0.999325i	$-0.488302\pi$
$577$	8.14507e9			0.0734838			0.0367419	+	0.999325i	$0.488302\pi$
$578$			5.80555e10i			0.520154i
$579$	−1.40486e11	+	3.07092e9i	−1.25002	+	0.0273246i
$580$	9.19418e10			0.812458
$581$			8.87233e10i			0.778634i
$582$	−1.66706e9	−	7.62632e10i	−0.0145298	−	0.664696i
$583$	−5.76398e10			−0.498940
$584$		−	1.65717e11i		−	1.42467i
$585$	2.94209e9	+	6.72639e10i	0.0251208	+	0.574326i
$586$	−3.25858e10			−0.276337
$587$		−	9.70196e10i		−	0.817160i	−0.912722	−	0.408580i	$-0.866024\pi$
$587$		−	9.70196e10i		−	0.817160i	0.912722	−	0.408580i	$-0.133976\pi$
$588$	−6.43357e10	+	1.40634e9i	−0.538199	+	0.0117647i
$589$	−2.12623e10			−0.176664
$590$		−	1.24388e10i		−	0.102653i
$591$	−6.48395e8	−	2.96622e10i	−0.00531484	−	0.243138i
$592$	6.56683e9			0.0534649
$593$			1.70701e10i			0.138044i	0.997615	+	0.0690219i	$0.0219878\pi$
$593$			1.70701e10i			0.138044i	−0.997615	+	0.0690219i	$0.978012\pi$
$594$	2.20838e10	−	1.45006e9i	0.177390	−	0.0116477i
$595$	1.88283e10			0.150226
$596$		−	1.22931e10i		−	0.0974260i
$597$	2.27857e11	−	4.98081e9i	1.79377	−	0.0392105i
$598$	−5.90320e10			−0.461618
$599$		−	2.38404e11i		−	1.85185i	−0.377708	−	0.925925i	$-0.623288\pi$
$599$		−	2.38404e11i		−	1.85185i	0.377708	−	0.925925i	$-0.376712\pi$
$600$	−2.64930e8	−	1.21198e10i	−0.00204421	−	0.0935167i
$601$	1.82138e11			1.39606			0.698028	−	0.716071i	$-0.254061\pi$
$601$	1.82138e11			1.39606			0.698028	+	0.716071i	$0.254061\pi$
$602$		−	1.38550e10i		−	0.105492i
$603$	1.94643e11	−	8.51361e9i	1.47221	−	0.0643939i
$604$	−8.48981e10			−0.637896
$605$		−	1.27508e10i		−	0.0951733i
$606$	2.42471e10	−	5.30024e8i	0.179791	−	0.00393012i
$607$	2.63810e11			1.94329			0.971643	−	0.236453i	$-0.0759848\pi$
$607$	2.63810e11			1.94329			0.971643	+	0.236453i	$0.0759848\pi$
$608$		−	1.66653e11i		−	1.21955i
$609$	1.49516e9	+	6.83990e10i	0.0108697	+	0.497257i
$610$	−8.90739e10			−0.643326
$611$		−	6.66695e10i		−	0.478368i
$612$	1.37249e9	+	3.13788e10i	0.00978372	+	0.223681i
$613$	−1.61834e11			−1.14612			−0.573058	−	0.819515i	$-0.694243\pi$
$613$	−1.61834e11			−1.14612			−0.573058	+	0.819515i	$0.694243\pi$
$614$		−	7.15058e10i		−	0.503116i
$615$	1.84556e11	−	4.03426e9i	1.29011	−	0.0282010i
$616$	−1.76839e10			−0.122816
$617$			7.79064e10i			0.537567i	0.963201	+	0.268783i	$0.0866216\pi$
$617$			7.79064e10i			0.537567i	−0.963201	+	0.268783i	$0.913378\pi$
$618$	2.06126e9	+	9.42966e10i	0.0141312	+	0.646461i
$619$	−9.39221e10			−0.639743			−0.319871	−	0.947461i	$-0.603640\pi$
$619$	−9.39221e10			−0.639743			−0.319871	+	0.947461i	$0.603640\pi$
$620$			1.49143e10i			0.100934i
$621$	1.38932e10	+	2.11587e11i	0.0934190	+	1.42273i
$622$	−4.05979e10			−0.271232
$623$			6.61838e10i			0.439339i
$624$	6.48843e9	−	1.41833e8i	0.0427958	−	0.000935488i
$625$	−1.65832e11			−1.08679
$626$		−	1.29551e11i		−	0.843611i
$627$	1.21736e9	+	5.56907e10i	0.00787679	+	0.360340i
$628$	5.41628e10			0.348227
$629$			3.68455e10i			0.235387i
$630$	4.06161e10	−	1.77653e9i	0.257832	−	0.0112774i
$631$	−1.25718e11			−0.793012			−0.396506	−	0.918032i	$-0.629777\pi$
$631$	−1.25718e11			−0.793012			−0.396506	+	0.918032i	$0.629777\pi$
$632$		−	4.71117e10i		−	0.295298i
$633$	−1.89713e11	+	4.14699e9i	−1.18163	+	0.0258296i
$634$	1.21921e11			0.754610
$635$		−	1.20960e11i		−	0.743954i
$636$	−3.86010e9	−	1.76588e11i	−0.0235923	−	1.07928i
$637$	−7.46066e10			−0.453127
$638$		−	3.50385e10i		−	0.211477i
$639$	−3.30461e8	−	7.55521e9i	−0.00198206	−	0.0453151i
$640$	−1.24971e11			−0.744885
$641$			2.55401e11i			1.51283i	0.654092	+	0.756415i	$0.273051\pi$
$641$			2.55401e11i			1.51283i	−0.654092	+	0.756415i	$0.726949\pi$
$642$	−3.37832e10	+	7.38479e8i	−0.198866	+	0.00434708i
$643$	1.62943e11			0.953219			0.476610	−	0.879115i	$-0.341866\pi$
$643$	1.62943e11			0.953219			0.476610	+	0.879115i	$0.341866\pi$
$644$		−	6.68927e10i		−	0.388897i
$645$	1.69456e9	+	7.75213e10i	0.00979081	+	0.447901i
$646$	4.21264e10			0.241893
$647$		−	2.50710e11i		−	1.43072i	−0.698755	−	0.715361i	$-0.746262\pi$
$647$		−	2.50710e11i		−	1.43072i	0.698755	−	0.715361i	$-0.253738\pi$
$648$	1.49982e10	+	1.71122e11i	0.0850629	+	0.970520i
$649$	8.89580e9			0.0501425
$650$		−	5.54888e9i		−	0.0310851i
$651$	−1.10953e10	+	2.42536e8i	−0.0617755	+	0.00135037i
$652$	5.61182e10			0.310537
$653$		−	3.60027e10i		−	0.198008i	−0.995087	−	0.0990038i	$-0.968434\pi$
$653$		−	3.60027e10i		−	0.198008i	0.995087	−	0.0990038i	$-0.0315656\pi$
$654$	−6.15738e8	−	2.81682e10i	−0.00336578	−	0.153974i
$655$	−2.88749e11			−1.56875
$656$		−	1.77942e10i		−	0.0960865i
$657$	−2.72205e11	+	1.19061e10i	−1.46095	+	0.0639011i
$658$	−4.02572e10			−0.214753
$659$			1.05976e11i			0.561910i	0.959721	+	0.280955i	$0.0906512\pi$
$659$			1.05976e11i			0.561910i	−0.959721	+	0.280955i	$0.909349\pi$
$660$	3.90640e10	−	8.53912e8i	0.205874	−	0.00450026i
$661$	−5.55412e10			−0.290944			−0.145472	−	0.989362i	$-0.546470\pi$
$661$	−5.55412e10			−0.290944			−0.145472	+	0.989362i	$0.546470\pi$
$662$		−	1.09903e11i		−	0.572239i
$663$	7.95802e8	+	3.64056e10i	0.00411861	+	0.188414i
$664$	3.52686e11			1.81433
$665$			1.02327e11i			0.523245i
$666$	3.47652e9	+	7.94824e10i	0.0176705	+	0.403993i
$667$	3.35708e11			1.69612
$668$			8.09887e10i			0.406741i
$669$	6.14886e10	−	1.34410e9i	0.306966	−	0.00671006i
$670$	−1.83295e11			−0.909604
$671$		−	6.37027e10i		−	0.314245i
$672$	−1.90099e9	−	8.69649e10i	−0.00932188	−	0.426449i
$673$	3.64622e11			1.77739			0.888696	−	0.458498i	$-0.151612\pi$
$673$	3.64622e11			1.77739			0.888696	+	0.458498i	$0.151612\pi$
$674$			1.10142e11i			0.533719i
$675$	−1.98887e10	+	1.30593e9i	−0.0958059	+	0.00629077i
$676$	−9.51540e10			−0.455659
$677$			3.08651e11i			1.46931i	0.678441	+	0.734655i	$0.262656\pi$
$677$			3.08651e11i			1.46931i	−0.678441	+	0.734655i	$0.737344\pi$
$678$	−8.40161e10	+	1.83653e9i	−0.397597	+	0.00869121i
$679$	1.00215e11			0.471467
$680$		−	7.48448e10i		−	0.350047i
$681$	8.05067e9	+	3.68295e11i	0.0374320	+	1.71241i
$682$	5.68376e9			0.0262723
$683$			1.10656e11i			0.508502i	0.967138	+	0.254251i	$0.0818289\pi$
$683$			1.10656e11i			0.508502i	−0.967138	+	0.254251i	$0.918171\pi$
$684$	−1.70536e11	+	7.45915e9i	−0.779096	+	0.0340773i
$685$	−4.42853e11			−2.01139
$686$			9.96432e10i			0.449937i
$687$	−1.50861e11	+	3.29772e9i	−0.677252	+	0.0148043i
$688$	7.47431e9			0.0333593
$689$		−	2.04780e11i		−	0.908679i
$690$	−4.35967e9	−	1.99442e11i	−0.0192335	−	0.879875i
$691$	6.52617e10			0.286251			0.143125	−	0.989705i	$-0.454285\pi$
$691$	6.52617e10			0.286251			0.143125	+	0.989705i	$0.454285\pi$
$692$		−	1.93837e11i		−	0.845302i
$693$	1.27052e9	+	2.90473e10i	0.00550867	+	0.125943i
$694$	1.22848e11			0.529578
$695$			3.28005e11i			1.40586i
$696$	2.71894e11	−	5.94342e9i	1.15868	−	0.0253279i
$697$	9.98404e10			0.423034
$698$		−	1.19474e10i		−	0.0503329i
$699$	−8.27005e9	−	3.78331e11i	−0.0346417	−	1.58476i
$700$	6.28776e9			0.0261881
$701$			3.10663e11i			1.28652i	0.765646	+	0.643262i	$0.222419\pi$
$701$			3.10663e11i			1.28652i	−0.765646	+	0.643262i	$0.777581\pi$
$702$	5.15171e9	+	7.84584e10i	0.0212130	+	0.323066i
$703$	−2.00246e11			−0.819866
$704$			3.87758e10i			0.157859i
$705$	2.25246e11	−	4.92372e9i	0.911801	−	0.0199313i
$706$	2.54975e10			0.102631
$707$			3.18622e10i			0.127526i
$708$	5.95747e8	+	2.72537e10i	0.00237099	+	0.108466i
$709$	−1.69788e11			−0.671927			−0.335964	−	0.941875i	$-0.609062\pi$
$709$	−1.69788e11			−0.671927			−0.335964	+	0.941875i	$0.609062\pi$
$710$			7.11473e9i			0.0279979i
$711$	−7.73851e10	+	3.38479e9i	−0.302816	+	0.0132450i
$712$	2.63088e11			1.02372
$713$			5.44567e10i			0.210714i
$714$	2.19829e10	−	4.80530e8i	0.0845847	−	0.00184896i
$715$	4.53004e10			0.173331
$716$			2.17136e11i			0.826188i
$717$	−2.70793e9	−	1.23880e11i	−0.0102462	−	0.468732i
$718$	−1.42439e11			−0.535958
$719$			1.37855e11i			0.515829i	0.966168	+	0.257914i	$0.0830353\pi$
$719$			1.37855e11i			0.515829i	−0.966168	+	0.257914i	$0.916965\pi$
$720$	9.58376e8	+	2.19110e10i	0.00356620	+	0.0815327i
$721$	−1.23912e11			−0.458533
$722$			6.87296e10i			0.252927i
$723$	−3.19625e11	+	6.98677e9i	−1.16973	+	0.0255696i
$724$	−3.22613e11			−1.17416
$725$			3.15558e10i			0.114216i
$726$	−3.25421e8	−	1.48871e10i	−0.00117138	−	0.0535874i
$727$	3.86044e11			1.38197			0.690985	−	0.722869i	$-0.257177\pi$
$727$	3.86044e11			1.38197			0.690985	+	0.722869i	$0.257177\pi$
$728$		−	6.28264e10i		−	0.223675i
$729$	2.80005e11	−	3.69303e10i	0.991414	−	0.130759i
$730$	2.56335e11			0.902643
$731$			4.19372e10i			0.146869i
$732$	1.95163e11	−	4.26614e9i	0.679757	−	0.0148590i
$733$	5.36395e11			1.85810			0.929049	−	0.369956i	$-0.120627\pi$
$733$	5.36395e11			1.85810			0.929049	+	0.369956i	$0.120627\pi$
$734$		−	4.74863e10i		−	0.163600i
$735$	−5.50990e9	−	2.52062e11i	−0.0188797	−	0.863689i
$736$	−4.26830e11			−1.45460
$737$		−	1.31087e11i		−	0.444313i
$738$	2.15374e11	−	9.42035e9i	0.726052	−	0.0317572i
$739$	−2.66131e11			−0.892314			−0.446157	−	0.894955i	$-0.647208\pi$
$739$	−2.66131e11			−0.892314			−0.446157	+	0.894955i	$0.647208\pi$
$740$			1.40462e11i			0.468415i
$741$	−1.97855e11	+	4.32499e9i	−0.656259	+	0.0143454i
$742$	−1.23653e11			−0.407932
$743$		−	4.53817e11i		−	1.48911i	−0.667563	−	0.744553i	$-0.732663\pi$
$743$		−	4.53817e11i		−	1.48911i	0.667563	−	0.744553i	$-0.267337\pi$
$744$	9.64109e8	+	4.41052e10i	0.00314655	+	0.143945i
$745$	4.81631e10			0.156347
$746$			2.15558e11i			0.695998i
$747$	−2.53391e10	−	5.79317e11i	−0.0813782	−	1.86052i
$748$	2.11327e10			0.0675070
$749$		−	4.43933e10i		−	0.141055i
$750$	−1.76511e11	+	3.85840e9i	−0.557861	+	0.0121945i
$751$	1.24898e11			0.392640			0.196320	−	0.980540i	$-0.437101\pi$
$751$	1.24898e11			0.392640			0.196320	+	0.980540i	$0.437101\pi$
$752$		−	2.17173e10i		−	0.0679102i
$753$	1.18958e9	+	5.44200e10i	0.00370011	+	0.169269i
$754$	1.24483e11			0.385146
$755$		−	3.32623e11i		−	1.02368i
$756$	−8.89059e10	+	5.83770e9i	−0.272172	+	0.0178712i
$757$	−1.51106e11			−0.460148			−0.230074	−	0.973173i	$-0.573897\pi$
$757$	−1.51106e11			−0.460148			−0.230074	+	0.973173i	$0.573897\pi$
$758$		−	2.62743e10i		−	0.0795892i
$759$	1.42635e11	−	3.11789e9i	0.429791	−	0.00939494i
$760$	4.06763e11			1.21923
$761$		−	1.81909e11i		−	0.542395i	−0.962524	−	0.271197i	$-0.912580\pi$
$761$		−	1.81909e11i		−	0.542395i	0.962524	−	0.271197i	$-0.0874196\pi$
$762$	−3.08710e9	−	1.41226e11i	−0.00915652	−	0.418884i
$763$	3.70148e10			0.109214
$764$		−	1.23719e11i		−	0.363130i
$765$	−1.22939e11	+	5.37730e9i	−0.358959	+	0.0157007i
$766$	1.40859e11			0.409137
$767$			3.16046e10i			0.0913206i
$768$	−3.28008e11	+	7.17003e9i	−0.942843	+	0.0206099i
$769$	−4.38439e11			−1.25373			−0.626864	−	0.779128i	$-0.715662\pi$
$769$	−4.38439e11			−1.25373			−0.626864	+	0.779128i	$0.715662\pi$
$770$		−	2.73538e10i		−	0.0778135i
$771$	−4.71062e9	−	2.15497e11i	−0.0133309	−	0.609852i
$772$	−2.89724e11			−0.815671
$773$		−	1.20107e11i		−	0.336396i	−0.985753	−	0.168198i	$-0.946205\pi$
$773$		−	1.20107e11i		−	0.336396i	0.985753	−	0.168198i	$-0.0537948\pi$
$774$	3.95695e9	+	9.04662e10i	0.0110255	+	0.252071i
$775$	−5.11881e9			−0.0141893
$776$		−	3.98364e11i		−	1.09859i
$777$	−1.04495e11	+	2.28418e9i	−0.286688	+	0.00626681i
$778$	−1.07945e11			−0.294635
$779$			5.42608e11i			1.47345i
$780$	3.03374e9	+	1.38785e11i	0.00819596	+	0.374941i
$781$	−5.08822e9			−0.0136761
$782$		−	1.07894e11i		−	0.288515i
$783$	−2.92971e10	−	4.46183e11i	−0.0779431	−	1.18704i
$784$	−2.43028e10			−0.0643269
$785$			2.12205e11i			0.558827i
$786$	−3.37127e11	+	7.36936e9i	−0.883289	+	0.0193081i
$787$	−7.26524e11			−1.89387			−0.946937	−	0.321418i	$-0.895840\pi$
$787$	−7.26524e11			−1.89387			−0.946937	+	0.321418i	$0.895840\pi$
$788$		−	6.11723e10i		−	0.158654i
$789$	1.20332e10	+	5.50482e11i	0.0310507	+	1.42048i
$790$	7.28735e10			0.187095
$791$		−	1.10402e11i		−	0.282015i
$792$	1.15466e11	−	5.05045e9i	0.293464	−	0.0128360i
$793$	2.26320e11			0.572309
$794$		−	2.07430e11i		−	0.521902i
$795$	6.91858e11	−	1.51235e10i	1.73200	−	0.0378604i
$796$	4.69910e11			1.17048
$797$			1.76890e11i			0.438400i	0.975680	+	0.219200i	$0.0703447\pi$
$797$			1.76890e11i			0.438400i	−0.975680	+	0.219200i	$0.929655\pi$
$798$	2.61156e9	+	1.19471e11i	0.00644005	+	0.294613i
$799$	1.21853e11			0.298984
$800$		−	4.01211e10i		−	0.0979519i
$801$	−1.89019e10	−	4.32146e11i	−0.0459171	−	1.04978i
$802$	−3.07311e11			−0.742815
$803$			1.83322e11i			0.440913i
$804$	4.01605e11	−	8.77881e9i	0.961114	−	0.0210093i
$805$	2.62080e11			0.624093
$806$			2.01930e10i			0.0478477i
$807$	−1.28224e10	−	5.86586e11i	−0.0302325	−	1.38305i
$808$	1.26656e11			0.297153
$809$			5.66801e11i			1.32323i	0.749842	+	0.661617i	$0.230129\pi$
$809$			5.66801e11i			1.32323i	−0.749842	+	0.661617i	$0.769871\pi$
$810$	−2.64695e11	+	2.31996e10i	−0.614901	+	0.0538941i
$811$	−1.10981e11			−0.256545			−0.128273	−	0.991739i	$-0.540943\pi$
$811$	−1.10981e11			−0.256545			−0.128273	+	0.991739i	$0.540943\pi$
$812$			1.41059e11i			0.324472i
$813$	7.80093e11	−	1.70523e10i	1.78560	−	0.0390320i
$814$	5.35291e10			0.121925
$815$			2.19866e11i			0.498342i
$816$	2.59230e8	+	1.18590e10i	0.000584688	+	0.0267478i
$817$	−2.27918e11			−0.511553
$818$		−	2.09053e11i		−	0.466921i
$819$	−1.03198e11	+	4.51383e9i	−0.229369	+	0.0100325i
$820$	3.80610e11			0.841830
$821$			1.68985e11i			0.371943i	0.982555	+	0.185971i	$0.0595432\pi$
$821$			1.68985e11i			0.371943i	−0.982555	+	0.185971i	$0.940457\pi$
$822$	−5.17049e11	+	1.13023e10i	−1.13252	+	0.0247560i
$823$	3.90269e11			0.850677			0.425339	−	0.905034i	$-0.360155\pi$
$823$	3.90269e11			0.850677			0.425339	+	0.905034i	$0.360155\pi$
$824$			4.92563e11i			1.06845i
$825$	2.93075e8	+	1.34073e10i	0.000632649	+	0.0289419i
$826$	1.90839e10			0.0409964
$827$			6.26831e11i			1.34007i	0.742328	+	0.670037i	$0.233722\pi$
$827$			6.26831e11i			1.34007i	−0.742328	+	0.670037i	$0.766278\pi$
$828$	1.91043e10	+	4.36774e11i	0.0406453	+	0.929257i
$829$	2.19781e11			0.465341			0.232671	−	0.972556i	$-0.425254\pi$
$829$	2.19781e11			0.465341			0.232671	+	0.972556i	$0.425254\pi$
$830$			5.45542e11i			1.14952i
$831$	−2.00432e11	+	4.38130e9i	−0.420303	+	0.00918754i
$832$	−1.37761e11			−0.287496
$833$		−	1.36359e11i		−	0.283208i
$834$	8.37124e9	+	3.82960e11i	0.0173032	+	0.791569i
$835$	−3.17306e11			−0.652729
$836$			1.14851e11i			0.235131i
$837$	7.23774e10	−	4.75242e9i	0.147469	−	0.00968307i
$838$	−1.86055e11			−0.377282
$839$		−	9.65408e10i		−	0.194833i	−0.995244	−	0.0974166i	$-0.968942\pi$
$839$		−	9.65408e10i		−	0.194833i	0.995244	−	0.0974166i	$-0.0310579\pi$
$840$	2.12262e11	−	4.63989e9i	0.426338	−	0.00931947i
$841$	−2.07674e11			−0.415143
$842$		−	2.42213e11i		−	0.481891i
$843$	1.18428e10	+	5.41775e11i	0.0234501	+	1.07277i
$844$	−3.91245e11			−0.771043
$845$		−	3.72805e11i		−	0.731231i
$846$	2.62858e11	−	1.14973e10i	0.513145	−	0.0224447i
$847$	1.95625e10			0.0380094
$848$		−	6.67063e10i		−	0.128998i
$849$	6.17072e10	−	1.34888e9i	0.118770	−	0.00259622i
$850$	1.01418e10			0.0194284
$851$			5.12868e11i			0.977884i
$852$	−3.40755e8	−	1.55886e10i	−0.000646672	−	0.0295834i
$853$	−5.28926e11			−0.999076			−0.499538	−	0.866292i	$-0.666497\pi$
$853$	−5.28926e11			−0.999076			−0.499538	+	0.866292i	$0.666497\pi$
$854$		−	1.36659e11i		−	0.256926i
$855$	−2.92243e10	−	6.68144e11i	−0.0546864	−	1.25027i
$856$	−1.76468e11			−0.328679
$857$		−	5.60134e11i		−	1.03841i	−0.854650	−	0.519205i	$-0.826228\pi$
$857$		−	5.60134e11i		−	1.03841i	0.854650	−	0.519205i	$-0.173772\pi$
$858$	5.28901e10	−	1.15614e9i	0.0975945	−	0.00213335i
$859$	−6.65910e11			−1.22305			−0.611523	−	0.791227i	$-0.709443\pi$
$859$	−6.65910e11			−1.22305			−0.611523	+	0.791227i	$0.709443\pi$
$860$			1.59872e11i			0.292266i
$861$	6.18946e9	+	2.83150e11i	0.0112626	+	0.515233i
$862$	−1.91301e11			−0.346488
$863$		−	7.17319e11i		−	1.29321i	−0.762825	−	0.646605i	$-0.776188\pi$
$863$		−	7.17319e11i		−	1.29321i	0.762825	−	0.646605i	$-0.223812\pi$
$864$	3.72494e10	+	5.67293e11i	0.0668442	+	1.01801i
$865$	7.59435e11			1.35652
$866$		−	1.41601e11i		−	0.251765i
$867$	4.98362e11	−	1.08939e10i	0.882001	−	0.0192799i
$868$	−2.28819e10			−0.0403100
$869$			5.21167e10i			0.0913898i
$870$	9.19342e9	+	4.20572e11i	0.0160472	+	0.734114i
$871$	4.65719e11			0.809192
$872$		−	1.47138e11i		−	0.254483i
$873$	−6.54349e11	+	2.86209e10i	−1.12655	+	0.0492750i
$874$	5.86375e11			1.00492
$875$		−	2.31946e11i		−	0.395689i
$876$	−5.61636e11	+	1.22770e10i	−0.953759	+	0.0208485i
$877$	3.53642e11			0.597813			0.298907	−	0.954282i	$-0.403378\pi$
$877$	3.53642e11			0.597813			0.298907	+	0.954282i	$0.403378\pi$
$878$		−	3.41418e11i		−	0.574524i
$879$	6.11459e9	+	2.79725e11i	0.0102426	+	0.468571i
$880$	1.47564e10			0.0246065
$881$		−	1.08549e12i		−	1.80187i	−0.433956	−	0.900934i	$-0.642883\pi$
$881$		−	1.08549e12i		−	1.80187i	0.433956	−	0.900934i	$-0.357117\pi$
$882$	−1.28661e10	−	2.94152e11i	−0.0212604	−	0.486069i
$883$	1.71060e11			0.281388			0.140694	−	0.990053i	$-0.455067\pi$
$883$	1.71060e11			0.281388			0.140694	+	0.990053i	$0.455067\pi$
$884$			7.50793e10i			0.122945i
$885$	−1.06778e11	+	2.33408e9i	−0.174063	+	0.00380490i
$886$	−1.88356e9			−0.00305664
$887$			7.24330e11i			1.17015i	0.810978	+	0.585076i	$0.198935\pi$
$887$			7.24330e11i			1.17015i	−0.810978	+	0.585076i	$0.801065\pi$
$888$	9.07989e9	+	4.15379e11i	0.0146026	+	0.668024i
$889$	1.85579e11			0.297114
$890$			4.06951e11i			0.648608i
$891$	−1.65916e10	−	1.89301e11i	−0.0263256	−	0.300360i
$892$	1.26808e11			0.200303
$893$			6.62239e11i			1.04138i
$894$	5.62325e10	−	1.22920e9i	0.0880313	−	0.00192430i
$895$	−8.50718e11			−1.32585
$896$		−	1.91733e11i		−	0.297485i
$897$	1.10771e10	+	5.06745e11i	0.0171103	+	0.782745i
$898$	4.46072e11			0.685961
$899$		−	1.14835e11i		−	0.175807i
$900$	−4.10558e10	+	1.79576e9i	−0.0625755	+	0.00273702i
$901$	3.74279e11			0.567932
$902$		−	1.45048e11i		−	0.219122i
$903$	−1.18935e11	+	2.59984e9i	−0.178879	+	0.00391016i
$904$	−4.38862e11			−0.657135
$905$		−	1.26397e12i		−	1.88426i
$906$	−8.48910e9	−	3.88352e11i	−0.0125994	−	0.576385i
$907$	−6.42137e11			−0.948852			−0.474426	−	0.880295i	$-0.657344\pi$
$907$	−6.42137e11			−0.948852			−0.474426	+	0.880295i	$0.657344\pi$
$908$			7.59534e11i			1.11739i
$909$	−9.09972e9	−	2.08043e11i	−0.0133282	−	0.304718i
$910$	9.71813e10			0.141715
$911$		−	1.53902e11i		−	0.223445i	−0.993739	−	0.111723i	$-0.964363\pi$
$911$		−	1.53902e11i		−	0.223445i	0.993739	−	0.111723i	$-0.0356368\pi$
$912$	−6.44507e10	+	1.40885e9i	−0.0931640	+	0.00203650i
$913$	−3.90154e11			−0.561504
$914$			6.02858e11i			0.863834i
$915$	1.67143e10	+	7.64632e11i	0.0238454	+	1.09086i
$916$	−3.11121e11			−0.441923
$917$		−	4.43005e11i		−	0.626515i
$918$	−1.43399e11	+	9.41584e9i	−0.201919	+	0.0132583i
$919$	−1.90278e11			−0.266763			−0.133382	−	0.991065i	$-0.542584\pi$
$919$	−1.90278e11			−0.266763			−0.133382	+	0.991065i	$0.542584\pi$
$920$		−	1.04180e12i		−	1.45423i
$921$	−6.13823e11	+	1.34178e10i	−0.853109	+	0.0186484i
$922$	−5.20727e11			−0.720587
$923$		−	1.80772e10i		−	0.0249072i
$924$	1.31009e9	+	5.99329e10i	0.00179727	+	0.0822200i
$925$	−4.82084e10			−0.0658501
$926$		−	4.60142e11i		−	0.625818i
$927$	8.09078e11	−	3.53887e10i	1.09565	−	0.0479232i
$928$	9.00075e11			1.21363
$929$		−	8.05848e11i		−	1.08191i	−0.841052	−	0.540954i	$-0.818063\pi$
$929$		−	8.05848e11i		−	1.08191i	0.841052	−	0.540954i	$-0.181937\pi$
$930$	−6.82230e10	+	1.49131e9i	−0.0912008	+	0.00199359i
$931$	7.41080e11			0.986430
$932$		−	7.80232e11i		−	1.03409i
$933$	7.61801e9	+	3.48502e11i	0.0100535	+	0.459916i
$934$	−1.32774e11			−0.174471
$935$			8.27960e10i			0.108334i
$936$	1.79430e10	+	4.10224e11i	0.0233771	+	0.534463i
$937$	1.34399e12			1.74356			0.871779	−	0.489899i	$-0.162967\pi$
$937$	1.34399e12			1.74356			0.871779	+	0.489899i	$0.162967\pi$
$938$		−	2.81216e11i		−	0.363269i
$939$	−1.11209e12	+	2.43096e10i	−1.43047	+	0.0312691i
$940$	4.64524e11			0.594973
$941$		−	1.55227e11i		−	0.197975i	−0.995089	−	0.0989874i	$-0.968440\pi$
$941$		−	1.55227e11i		−	0.197975i	0.995089	−	0.0989874i	$-0.0315604\pi$
$942$	5.41583e9	+	2.47759e11i	0.00687799	+	0.314648i
$943$	1.38972e12			1.75744
$944$			1.02951e10i			0.0129641i
$945$	−2.28716e10	−	3.48325e11i	−0.0286793	−	0.436775i
$946$	6.09264e10			0.0760748
$947$			8.72752e11i			1.08515i	0.840007	+	0.542576i	$0.182551\pi$
$947$			8.72752e11i			1.08515i	−0.840007	+	0.542576i	$0.817449\pi$
$948$	−1.59668e11	+	3.49023e9i	−0.197689	+	0.00432136i
$949$	−6.51298e11			−0.802999
$950$			5.51179e10i			0.0676704i
$951$	−2.28780e10	−	1.04660e12i	−0.0279702	−	1.27956i
$952$	1.14829e11			0.139798
$953$		−	5.23143e11i		−	0.634233i	−0.948387	−	0.317117i	$-0.897285\pi$
$953$		−	5.23143e11i		−	0.634233i	0.948387	−	0.317117i	$-0.102715\pi$
$954$	8.07388e11	−	3.53148e10i	0.974740	−	0.0426347i
$955$	4.84719e11			0.582742
$956$		−	2.55478e11i		−	0.305859i
$957$	−3.00779e11	+	6.57483e9i	−0.358592	+	0.00783857i
$958$	−3.14077e11			−0.372884
$959$		−	6.79435e11i		−	0.803292i
$960$	−1.01740e10	−	4.65431e11i	−0.0119786	−	0.547987i
$961$	−8.34263e11			−0.978159
$962$			1.90176e11i			0.222052i
$963$	1.26786e10	+	2.89865e11i	0.0147423	+	0.337047i
$964$	−6.59162e11			−0.763280
$965$		−	1.13511e12i		−	1.30897i
$966$	3.05989e11	−	6.68871e9i	0.351397	−	0.00768129i
$967$	5.27384e11			0.603145			0.301572	−	0.953443i	$-0.402489\pi$
$967$	5.27384e11			0.603145			0.301572	+	0.953443i	$0.402489\pi$
$968$		−	7.77634e10i		−	0.0885673i
$969$	−7.90483e9	−	3.61623e11i	−0.00896597	−	0.410167i
$970$	6.16200e11			0.696040
$971$			9.85260e11i			1.10834i	0.832403	+	0.554171i	$0.186965\pi$
$971$			9.85260e11i			1.10834i	−0.832403	+	0.554171i	$0.813035\pi$
$972$	5.78842e11	−	6.35084e10i	0.648478	−	0.0711485i
$973$	−5.03233e11			−0.561458
$974$		−	9.53574e11i		−	1.05954i
$975$	−4.76329e10	+	1.04122e9i	−0.0527095	+	0.00115219i
$976$	7.37230e10			0.0812463
$977$			1.10638e12i			1.21430i	0.794588	+	0.607148i	$0.207687\pi$
$977$			1.10638e12i			1.21430i	−0.794588	+	0.607148i	$0.792313\pi$
$978$	5.61135e9	+	2.56703e11i	0.00613355	+	0.280592i
$979$	−2.91038e11			−0.316825
$980$		−	5.19827e11i		−	0.563579i
$981$	−2.41688e11	+	1.05713e10i	−0.260963	+	0.0114144i
$982$	−4.83848e11			−0.520311
$983$		−	1.56145e11i		−	0.167230i	−0.996498	−	0.0836152i	$-0.973353\pi$
$983$		−	1.56145e11i		−	0.167230i	0.996498	−	0.0836152i	$-0.0266466\pi$
$984$	1.12555e12	−	2.46038e10i	1.20057	−	0.0262435i
$985$	2.39668e11			0.254604
$986$			2.27520e11i			0.240719i
$987$	7.55408e9	+	3.45577e11i	0.00796000	+	0.364147i
$988$	−4.08037e11			−0.428225
$989$			5.83742e11i			0.610149i
$990$	7.81215e9	+	1.78606e11i	0.00813261	+	0.185933i
$991$	−1.22532e12			−1.27045			−0.635223	−	0.772329i	$-0.719092\pi$
$991$	−1.22532e12			−1.27045			−0.635223	+	0.772329i	$0.719092\pi$
$992$			1.46005e11i			0.150772i
$993$	−9.43434e11	+	2.06228e10i	−0.970319	+	0.0212105i
$994$	−1.09156e10			−0.0111815
$995$			1.84107e12i			1.87835i
$996$	−2.61284e10	−	1.19530e12i	−0.0265506	−	1.21461i
$997$	−7.31861e11			−0.740710			−0.370355	−	0.928890i	$-0.620764\pi$
$997$	−7.31861e11			−0.740710			−0.370355	+	0.928890i	$0.620764\pi$
$998$			9.78417e11i			0.986284i
$999$	6.81644e11	−	4.47578e10i	0.684377	−	0.0449373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.17	yes	26
3.2	odd	2	inner	33.9.b.a.23.10	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.10	✓	26	3.2	odd	2	inner
33.9.b.a.23.17	yes	26	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9.43364i q^{2} +(80.9807 - 1.77018i) q^{3} +167.006 q^{4} +654.316i q^{5} +(16.6993 + 763.942i) q^{6} -1003.87 q^{7} +3990.49i q^{8} +(6554.73 - 286.701i) q^{9} +O(q^{10})\)	\(q+9.43364i q^{2} +(80.9807 - 1.77018i) q^{3} +167.006 q^{4} +654.316i q^{5} +(16.6993 + 763.942i) q^{6} -1003.87 q^{7} +3990.49i q^{8} +(6554.73 - 286.701i) q^{9} -6172.58 q^{10} -4414.43i q^{11} +(13524.3 - 295.632i) q^{12} +15683.4 q^{13} -9470.12i q^{14} +(1158.26 + 52987.0i) q^{15} +5108.80 q^{16} +28664.7i q^{17} +(2704.63 + 61835.0i) q^{18} -155786. q^{19} +109275. i q^{20} +(-81293.8 + 1777.03i) q^{21} +41644.1 q^{22} +398996. i q^{23} +(7063.89 + 323153. i) q^{24} -37504.8 q^{25} +147951. i q^{26} +(530299. - 34820.3i) q^{27} -167652. q^{28} -841380. i q^{29} +(-499860. + 10926.6i) q^{30} +136484. q^{31} +1.06976e6i q^{32} +(-7814.34 - 357483. i) q^{33} -270413. q^{34} -656847. i q^{35} +(1.09468e6 - 47880.9i) q^{36} +1.28540e6 q^{37} -1.46963e6i q^{38} +(1.27005e6 - 27762.4i) q^{39} -2.61104e6 q^{40} -3.48304e6i q^{41} +(-16763.8 - 766897. i) q^{42} +1.46303e6 q^{43} -737238. i q^{44} +(187593. + 4.28887e6i) q^{45} -3.76399e6 q^{46} -4.25096e6i q^{47} +(413714. - 9043.51i) q^{48} -4.75705e6 q^{49} -353806. i q^{50} +(50741.7 + 2.32129e6i) q^{51} +2.61922e6 q^{52} -1.30571e7i q^{53} +(328482. + 5.00265e6i) q^{54} +2.88843e6 q^{55} -4.00592e6i q^{56} +(-1.26156e7 + 275769. i) q^{57} +7.93727e6 q^{58} +2.01517e6i q^{59} +(193437. + 8.84916e6i) q^{60} +1.44306e7 q^{61} +1.28754e6i q^{62} +(-6.58008e6 + 287810. i) q^{63} -8.78388e6 q^{64} +1.02619e7i q^{65} +(3.37237e6 - 73717.7i) q^{66} +2.96951e7 q^{67} +4.78719e6i q^{68} +(706296. + 3.23110e7i) q^{69} +6.19646e6 q^{70} -1.15263e6i q^{71} +(1.14408e6 + 2.61566e7i) q^{72} -4.15279e7 q^{73} +1.21260e7i q^{74} +(-3.03716e6 + 66390.2i) q^{75} -2.60172e7 q^{76} +4.43150e6i q^{77} +(261901. + 1.19812e7i) q^{78} -1.18060e7 q^{79} +3.34277e6i q^{80} +(4.28823e7 - 3.75850e6i) q^{81} +3.28578e7 q^{82} -8.83815e7i q^{83} +(-1.35766e7 + 296775. i) q^{84} -1.87558e7 q^{85} +1.38017e7i q^{86} +(-1.48940e6 - 6.81355e7i) q^{87} +1.76157e7 q^{88} -6.59288e7i q^{89} +(-4.04596e7 + 1.76969e6i) q^{90} -1.57440e7 q^{91} +6.66350e7i q^{92} +(1.10526e7 - 241602. i) q^{93} +4.01021e7 q^{94} -1.01933e8i q^{95} +(1.89367e6 + 8.66299e7i) q^{96} -9.98285e7 q^{97} -4.48763e7i q^{98} +(-1.26562e6 - 2.89354e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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