LMFDB - Embedded newform 637.2.bl.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30989 - 1.57486i) q^{2} +(0.887307 + 0.823300i) q^{3} +(2.12474 + 5.41374i) q^{4} +(-0.535995 + 0.165332i) q^{5} +(-0.753001 - 3.29911i) q^{6} +(2.63410 - 0.247988i) q^{7} +(2.37377 - 10.4002i) q^{8} +(-0.114700 - 1.53057i) q^{9} +O(q^{10})$	\(q+(-2.30989 - 1.57486i) q^{2} +(0.887307 + 0.823300i) q^{3} +(2.12474 + 5.41374i) q^{4} +(-0.535995 + 0.165332i) q^{5} +(-0.753001 - 3.29911i) q^{6} +(2.63410 - 0.247988i) q^{7} +(2.37377 - 10.4002i) q^{8} +(-0.114700 - 1.53057i) q^{9} +(1.49846 + 0.462215i) q^{10} +(0.286387 - 3.82157i) q^{11} +(-2.57184 + 6.55295i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-6.47504 - 3.57551i) q^{14} +(-0.611710 - 0.294584i) q^{15} +(-13.3354 + 12.3734i) q^{16} +(4.09173 - 0.616729i) q^{17} +(-2.14548 + 3.71609i) q^{18} +(1.37416 + 2.38012i) q^{19} +(-2.03392 - 2.55045i) q^{20} +(2.54143 + 1.94862i) q^{21} +(-6.67994 + 8.37638i) q^{22} +(-4.27868 - 0.644907i) q^{23} +(10.6687 - 7.27380i) q^{24} +(-3.87124 + 2.63937i) q^{25} +(2.76444 + 0.416673i) q^{26} +(3.42241 - 4.29157i) q^{27} +(6.93932 + 13.7334i) q^{28} +(-2.87142 - 3.60064i) q^{29} +(0.949056 + 1.64381i) q^{30} +(4.15469 - 7.19614i) q^{31} +(29.1927 - 4.40009i) q^{32} +(3.40041 - 3.15512i) q^{33} +(-10.4227 - 5.01931i) q^{34} +(-1.37087 + 0.568423i) q^{35} +(8.04241 - 3.87302i) q^{36} +(2.52339 - 6.42948i) q^{37} +(0.574182 - 7.66192i) q^{38} +(-1.15665 - 0.356780i) q^{39} +(0.447156 + 5.96689i) q^{40} +(-1.10008 + 4.81975i) q^{41} +(-2.80162 - 8.50347i) q^{42} +(-0.0580847 - 0.254486i) q^{43} +(21.2975 - 6.56940i) q^{44} +(0.314532 + 0.801414i) q^{45} +(8.86764 + 8.22797i) q^{46} +(-2.06866 - 1.41039i) q^{47} -22.0196 q^{48} +(6.87700 - 1.30645i) q^{49} +13.0988 q^{50} +(4.13837 + 2.82149i) q^{51} +(-4.26326 - 3.95572i) q^{52} +(3.80798 + 9.70257i) q^{53} +(-14.6640 + 4.52325i) q^{54} +(0.478327 + 2.09569i) q^{55} +(3.67363 - 27.9837i) q^{56} +(-0.740249 + 3.24324i) q^{57} +(0.962162 + 12.8392i) q^{58} +(6.82284 + 2.10457i) q^{59} +(0.295079 - 3.93755i) q^{60} +(5.35236 - 13.6376i) q^{61} +(-20.9298 + 10.0792i) q^{62} +(-0.681696 - 4.00324i) q^{63} +(-41.5813 - 20.0245i) q^{64} +(0.411180 - 0.381519i) q^{65} +(-12.8234 + 1.93282i) q^{66} +(-0.00818581 + 0.0141782i) q^{67} +(12.0327 + 20.8412i) q^{68} +(-3.26555 - 4.09487i) q^{69} +(4.06173 + 0.845921i) q^{70} +(6.51391 - 8.16818i) q^{71} +(-16.1904 - 2.44032i) q^{72} +(-4.34693 + 2.96368i) q^{73} +(-15.9543 + 10.8774i) q^{74} +(-5.60797 - 0.845265i) q^{75} +(-9.96562 + 12.4965i) q^{76} +(-0.193330 - 10.1374i) q^{77} +(2.10986 + 2.64568i) q^{78} +(2.98467 + 5.16960i) q^{79} +(5.10196 - 8.83686i) q^{80} +(2.01683 - 0.303988i) q^{81} +(10.1315 - 9.40064i) q^{82} +(-7.99426 - 3.84983i) q^{83} +(-5.14945 + 17.8989i) q^{84} +(-2.09118 + 1.00706i) q^{85} +(-0.266609 + 0.679309i) q^{86} +(0.416583 - 5.55891i) q^{87} +(-39.0651 - 12.0500i) q^{88} +(-0.439579 - 5.86577i) q^{89} +(0.535578 - 2.34652i) q^{90} +(-2.26565 + 1.36632i) q^{91} +(-5.59971 - 24.5339i) q^{92} +(9.61107 - 2.96462i) q^{93} +(2.55721 + 6.51568i) q^{94} +(-1.13005 - 1.04854i) q^{95} +(29.5255 + 20.1301i) q^{96} +13.1301 q^{97} +(-17.9426 - 7.81253i) q^{98} -5.88203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	−2.30989	−	1.57486i	−1.63334	−	1.11359i	−0.902156	−	0.431410i	$-0.858016\pi$
$2$	−2.30989	−	1.57486i	−1.63334	−	1.11359i	−0.731183	−	0.682181i	$-0.761031\pi$
$3$	0.887307	+	0.823300i	0.512287	+	0.475333i	0.893442	−	0.449178i	$-0.148283\pi$
$3$	0.887307	+	0.823300i	0.512287	+	0.475333i	−0.381155	+	0.924511i	$0.624474\pi$
$4$	2.12474	+	5.41374i	1.06237	+	2.70687i
$5$	−0.535995	+	0.165332i	−0.239704	+	0.0739389i	−0.412280	−	0.911057i	$-0.635267\pi$
$5$	−0.535995	+	0.165332i	−0.239704	+	0.0739389i	0.172575	+	0.984996i	$0.444791\pi$
$6$	−0.753001	−	3.29911i	−0.307411	−	1.34686i
$7$	2.63410	−	0.247988i	0.995598	−	0.0937307i
$7$	2.63410	−	0.247988i	0.995598	−	0.0937307i
$8$	2.37377	−	10.4002i	0.839253	−	3.67701i
$9$	−0.114700	−	1.53057i	−0.0382335	−	0.510190i
$10$	1.49846	+	0.462215i	0.473856	+	0.146165i
$11$	0.286387	−	3.82157i	0.0863489	−	1.15225i	−0.770765	−	0.637119i	$-0.780126\pi$
$11$	0.286387	−	3.82157i	0.0863489	−	1.15225i	0.857114	−	0.515127i	$-0.172255\pi$
$12$	−2.57184	+	6.55295i	−0.742427	+	1.89167i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	−6.47504	−	3.57551i	−1.73053	−	0.955595i
$15$	−0.611710	−	0.294584i	−0.157943	−	0.0760613i
$16$	−13.3354	+	12.3734i	−3.33384	+	3.09336i
$17$	4.09173	−	0.616729i	0.992390	−	0.149579i	0.367276	−	0.930112i	$-0.380291\pi$
$17$	4.09173	−	0.616729i	0.992390	−	0.149579i	0.625114	+	0.780533i	$0.285052\pi$
$18$	−2.14548	+	3.71609i	−0.505695	+	0.875890i
$19$	1.37416	+	2.38012i	0.315254	+	0.546037i	0.979492	−	0.201485i	$-0.0645768\pi$
$19$	1.37416	+	2.38012i	0.315254	+	0.546037i	−0.664237	+	0.747522i	$0.731243\pi$
$20$	−2.03392	−	2.55045i	−0.454797	−	0.570298i
$21$	2.54143	+	1.94862i	0.554585	+	0.425223i
$22$	−6.67994	+	8.37638i	−1.42417	+	1.78585i
$23$	−4.27868	−	0.644907i	−0.892166	−	0.134472i	−0.313069	−	0.949731i	$-0.601357\pi$
$23$	−4.27868	−	0.644907i	−0.892166	−	0.134472i	−0.579098	+	0.815258i	$0.696595\pi$
$24$	10.6687	−	7.27380i	2.17774	−	1.48476i
$25$	−3.87124	+	2.63937i	−0.774248	+	0.527873i
$26$	2.76444	+	0.416673i	0.542152	+	0.0817163i
$27$	3.42241	−	4.29157i	0.658644	−	0.825913i
$28$	6.93932	+	13.7334i	1.31141	+	2.59538i
$29$	−2.87142	−	3.60064i	−0.533209	−	0.668622i	0.440146	−	0.897926i	$-0.354927\pi$
$29$	−2.87142	−	3.60064i	−0.533209	−	0.668622i	−0.973355	+	0.229304i	$0.926355\pi$
$30$	0.949056	+	1.64381i	0.173273	+	0.300118i
$31$	4.15469	−	7.19614i	0.746205	−	1.29246i	−0.203425	−	0.979091i	$-0.565207\pi$
$31$	4.15469	−	7.19614i	0.746205	−	1.29246i	0.949630	−	0.313374i	$-0.101459\pi$
$32$	29.1927	−	4.40009i	5.16059	−	0.777833i
$33$	3.40041	−	3.15512i	0.591936	−	0.549236i
$34$	−10.4227	−	5.01931i	−1.78748	−	0.860804i
$35$	−1.37087	+	0.568423i	−0.231719	+	0.0960811i
$36$	8.04241	−	3.87302i	1.34040	−	0.645503i
$37$	2.52339	−	6.42948i	0.414842	−	1.05700i	−0.558878	−	0.829250i	$-0.688768\pi$
$37$	2.52339	−	6.42948i	0.414842	−	1.05700i	0.973720	−	0.227750i	$-0.0731369\pi$
$38$	0.574182	−	7.66192i	0.0931446	−	1.24293i
$39$	−1.15665	−	0.356780i	−0.185213	−	0.0571305i
$40$	0.447156	+	5.96689i	0.0707016	+	0.943448i
$41$	−1.10008	+	4.81975i	−0.171803	+	0.752719i	0.813453	+	0.581631i	$0.197585\pi$
$41$	−1.10008	+	4.81975i	−0.171803	+	0.752719i	−0.985256	+	0.171088i	$0.945272\pi$
$42$	−2.80162	−	8.50347i	−0.432300	−	1.31211i
$43$	−0.0580847	−	0.254486i	−0.00885783	−	0.0388087i	0.970306	−	0.241881i	$-0.0777644\pi$
$43$	−0.0580847	−	0.254486i	−0.00885783	−	0.0388087i	−0.979164	+	0.203073i	$0.934907\pi$
$44$	21.2975	−	6.56940i	3.21072	−	0.990374i
$45$	0.314532	+	0.801414i	0.0468877	+	0.119468i
$46$	8.86764	+	8.22797i	1.30746	+	1.21315i
$47$	−2.06866	−	1.41039i	−0.301745	−	0.205726i	0.402977	−	0.915210i	$-0.367976\pi$
$47$	−2.06866	−	1.41039i	−0.301745	−	0.205726i	−0.704721	+	0.709484i	$0.748928\pi$
$48$	−22.0196			−3.17826
$49$	6.87700	−	1.30645i	0.982429	−	0.186636i
$50$	13.0988			1.85244
$51$	4.13837	+	2.82149i	0.579488	+	0.395088i
$52$	−4.26326	−	3.95572i	−0.591207	−	0.548560i
$53$	3.80798	+	9.70257i	0.523066	+	1.33275i	0.911510	+	0.411278i	$0.134918\pi$
$53$	3.80798	+	9.70257i	0.523066	+	1.33275i	−0.388444	+	0.921473i	$0.626987\pi$
$54$	−14.6640	+	4.52325i	−1.99552	+	0.615536i
$55$	0.478327	+	2.09569i	0.0644976	+	0.282583i
$56$	3.67363	−	27.9837i	0.490910	−	3.73949i
$57$	−0.740249	+	3.24324i	−0.0980484	+	0.429578i
$58$	0.962162	+	12.8392i	0.126338	+	1.68586i
$59$	6.82284	+	2.10457i	0.888258	+	0.273991i	0.705114	−	0.709094i	$-0.250896\pi$
$59$	6.82284	+	2.10457i	0.888258	+	0.273991i	0.183145	+	0.983086i	$0.441372\pi$
$60$	0.295079	−	3.93755i	0.0380945	−	0.508336i
$61$	5.35236	−	13.6376i	0.685300	−	1.74612i	0.0197014	−	0.999806i	$-0.493728\pi$
$61$	5.35236	−	13.6376i	0.685300	−	1.74612i	0.665599	−	0.746310i	$-0.268176\pi$
$62$	−20.9298	+	10.0792i	−2.65808	+	1.28007i
$63$	−0.681696	−	4.00324i	−0.0858857	−	0.504361i
$64$	−41.5813	−	20.0245i	−5.19766	−	2.50306i
$65$	0.411180	−	0.381519i	0.0510005	−	0.0473216i
$66$	−12.8234	+	1.93282i	−1.57846	+	0.237914i
$67$	−0.00818581	+	0.0141782i	−0.00100006	+	0.00173215i	−0.866525	−	0.499134i	$-0.833652\pi$
$67$	−0.00818581	+	0.0141782i	−0.00100006	+	0.00173215i	0.865525	+	0.500866i	$0.166985\pi$
$68$	12.0327	+	20.8412i	1.45917	+	2.52736i
$69$	−3.26555	−	4.09487i	−0.393126	−	0.492964i
$70$	4.06173	+	0.845921i	0.485470	+	0.101107i
$71$	6.51391	−	8.16818i	0.773059	−	0.969385i	−0.226931	−	0.973911i	$-0.572869\pi$
$71$	6.51391	−	8.16818i	0.773059	−	0.969385i	0.999990	+	0.00452569i	$0.00144058\pi$
$72$	−16.1904	−	2.44032i	−1.90806	−	0.287594i
$73$	−4.34693	+	2.96368i	−0.508769	+	0.346873i	−0.790341	−	0.612667i	$-0.790097\pi$
$73$	−4.34693	+	2.96368i	−0.508769	+	0.346873i	0.281572	+	0.959540i	$0.409144\pi$
$74$	−15.9543	+	10.8774i	−1.85464	+	1.26448i
$75$	−5.60797	−	0.845265i	−0.647552	−	0.0976028i
$76$	−9.96562	+	12.4965i	−1.14313	+	1.43345i
$77$	−0.193330	−	10.1374i	−0.0220320	−	1.15527i
$78$	2.10986	+	2.64568i	0.238895	+	0.299565i
$79$	2.98467	+	5.16960i	0.335802	+	0.581626i	0.983639	−	0.180153i	$-0.0576594\pi$
$79$	2.98467	+	5.16960i	0.335802	+	0.581626i	−0.647837	+	0.761779i	$0.724326\pi$
$80$	5.10196	−	8.83686i	0.570417	−	0.987991i
$81$	2.01683	−	0.303988i	0.224092	−	0.0337764i
$82$	10.1315	−	9.40064i	1.11883	−	1.03813i
$83$	−7.99426	−	3.84983i	−0.877484	−	0.422574i	−0.0597793	−	0.998212i	$-0.519040\pi$
$83$	−7.99426	−	3.84983i	−0.877484	−	0.422574i	−0.817705	+	0.575637i	$0.804754\pi$
$84$	−5.14945	+	17.8989i	−0.561851	+	1.95293i
$85$	−2.09118	+	1.00706i	−0.226820	+	0.109231i
$86$	−0.266609	+	0.679309i	−0.0287492	+	0.0732517i
$87$	0.416583	−	5.55891i	0.0446624	−	0.595978i
$88$	−39.0651	−	12.0500i	−4.16435	−	1.28453i
$89$	−0.439579	−	5.86577i	−0.0465953	−	0.621771i	−0.970803	−	0.239880i	$-0.922892\pi$
$89$	−0.439579	−	5.86577i	−0.0465953	−	0.621771i	0.924207	−	0.381891i	$-0.124727\pi$
$90$	0.535578	−	2.34652i	0.0564549	−	0.247345i
$91$	−2.26565	+	1.36632i	−0.237504	+	0.143230i
$92$	−5.59971	−	24.5339i	−0.583810	−	2.55784i
$93$	9.61107	−	2.96462i	0.996622	−	0.307417i
$94$	2.55721	+	6.51568i	0.263757	+	0.672041i
$95$	−1.13005	−	1.04854i	−0.115941	−	0.107578i
$96$	29.5255	+	20.1301i	3.01343	+	2.05452i
$97$	13.1301			1.33316			0.666578	−	0.745436i	$-0.267759\pi$
$97$	13.1301			1.33316			0.666578	+	0.745436i	$0.267759\pi$
$98$	−17.9426	−	7.81253i	−1.81248	−	0.789185i
$99$	−5.88203			−0.591166
$100$	−22.5142	−	15.3499i	−2.25142	−	1.53499i
$101$	9.89295	+	9.17932i	0.984386	+	0.913377i	0.996247	−	0.0865531i	$-0.0275852\pi$
$101$	9.89295	+	9.17932i	0.984386	+	0.913377i	−0.0118615	+	0.999930i	$0.503776\pi$
$102$	−5.11574	−	13.0347i	−0.506533	−	1.29063i
$103$	−7.81184	+	2.40963i	−0.769723	+	0.237428i	−0.654653	−	0.755929i	$-0.727185\pi$
$103$	−7.81184	+	2.40963i	−0.769723	+	0.237428i	−0.115070	+	0.993357i	$0.536709\pi$
$104$	2.37377	+	10.4002i	0.232767	+	1.01982i
$105$	−1.68436	−	0.624268i	−0.164377	−	0.0609223i
$106$	6.48415	−	28.4089i	0.629796	−	2.75932i
$107$	−0.201351	−	2.68684i	−0.0194653	−	0.259746i	−0.998443	−	0.0557795i	$-0.982236\pi$
$107$	−0.201351	−	2.68684i	−0.0194653	−	0.259746i	0.978978	−	0.203967i	$-0.0653834\pi$
$108$	30.5052	+	9.40961i	2.93536	+	0.905440i
$109$	−0.702594	+	9.37546i	−0.0672963	+	0.898006i	0.856752	+	0.515729i	$0.172479\pi$
$109$	−0.702594	+	9.37546i	−0.0672963	+	0.898006i	−0.924048	+	0.382277i	$0.875140\pi$
$110$	2.19553	−	5.59411i	0.209335	−	0.533377i
$111$	7.53241	−	3.62742i	0.714945	−	0.344299i
$112$	−32.0583	+	35.8999i	−3.02922	+	3.39222i
$113$	1.87376	+	0.902354i	0.176268	+	0.0848863i	0.519937	−	0.854205i	$-0.325955\pi$
$113$	1.87376	+	0.902354i	0.176268	+	0.0848863i	−0.343669	+	0.939091i	$0.611670\pi$
$114$	6.81754	−	6.32575i	0.638521	−	0.592461i
$115$	2.39997	−	0.361738i	0.223799	−	0.0337322i
$116$	13.3919	−	23.1955i	1.24341	−	2.15365i
$117$	0.767431	+	1.32923i	0.0709491	+	0.122887i
$118$	−12.4456	−	15.6063i	−1.14571	−	1.43668i
$119$	10.6251	−	2.63923i	0.974001	−	0.241938i
$120$	−4.51578	+	5.66261i	−0.412232	+	0.516923i
$121$	−3.64522	−	0.549428i	−0.331383	−	0.0499480i
$122$	−33.8406	+	23.0722i	−3.06379	+	2.08885i
$123$	−4.94421	+	3.37091i	−0.445804	+	0.303944i
$124$	47.7857	+	7.20253i	4.29128	+	0.646806i
$125$	3.38721	−	4.24743i	0.302962	−	0.379902i
$126$	−4.72988	+	10.3206i	−0.421371	+	0.919433i
$127$	9.73344	+	12.2053i	0.863703	+	1.08305i	0.995777	+	0.0918095i	$0.0292651\pi$
$127$	9.73344	+	12.2053i	0.863703	+	1.08305i	−0.132073	+	0.991240i	$0.542163\pi$
$128$	34.9901	+	60.6046i	3.09271	+	5.35674i
$129$	0.157979	−	0.273628i	0.0139093	−	0.0240916i
$130$	−1.55062	+	0.233718i	−0.135998	+	0.0204984i
$131$	6.52886	−	6.05790i	0.570429	−	0.529281i	−0.341364	−	0.939931i	$-0.610889\pi$
$131$	6.52886	−	6.05790i	0.570429	−	0.529281i	0.911793	+	0.410650i	$0.134698\pi$
$132$	24.3060	+	11.7051i	2.11556	+	1.01880i
$133$	4.20993	+	5.92870i	0.365047	+	0.514084i
$134$	0.0412370	−	0.0198587i	0.00356233	−	0.00171553i
$135$	−1.12486	+	2.86610i	−0.0968125	+	0.246674i
$136$	3.29874	−	44.0186i	0.282864	−	3.77456i
$137$	−5.02780	−	1.55087i	−0.429554	−	0.132500i	0.0724365	−	0.997373i	$-0.476923\pi$
$137$	−5.02780	−	1.55087i	−0.429554	−	0.132500i	−0.501990	+	0.864873i	$0.667399\pi$
$138$	1.09423	+	14.6015i	0.0931469	+	1.24296i
$139$	−3.05123	+	13.3683i	−0.258802	+	1.13388i	0.663733	+	0.747970i	$0.268971\pi$
$139$	−3.05123	+	13.3683i	−0.258802	+	1.13388i	−0.922535	+	0.385914i	$0.873886\pi$
$140$	−5.99003	−	6.21376i	−0.506250	−	0.525159i
$141$	−0.674362	−	2.95457i	−0.0567915	−	0.248820i
$142$	−27.9101	+	8.60914i	−2.34217	+	0.722463i
$143$	1.40009	+	3.56737i	0.117081	+	0.298319i
$144$	20.4680	+	18.9915i	1.70566	+	1.58263i
$145$	2.13437	+	1.45519i	0.177250	+	0.120847i
$146$	14.7083			1.21727
$147$	7.17762	+	4.50262i	0.592000	+	0.371369i
$148$	40.1691			3.30188
$149$	6.15152	+	4.19404i	0.503952	+	0.343589i	0.788461	−	0.615084i	$-0.210878\pi$
$149$	6.15152	+	4.19404i	0.503952	+	0.343589i	−0.284509	+	0.958673i	$0.591830\pi$
$150$	11.6226	+	10.7842i	0.948983	+	0.880527i
$151$	−3.87968	−	9.88526i	−0.315724	−	0.804451i	−0.997350	−	0.0727508i	$-0.976822\pi$
$151$	−3.87968	−	9.88526i	−0.315724	−	0.804451i	0.681626	−	0.731701i	$-0.261273\pi$
$152$	28.0155	−	8.64165i	2.27236	−	0.700930i
$153$	−1.41327	−	6.19194i	−0.114256	−	0.500589i
$154$	−15.5184	+	23.7208i	−1.25051	+	1.91148i
$155$	−1.03714	+	4.54400i	−0.0833049	+	0.364983i
$156$	−0.526067	−	7.01988i	−0.0421191	−	0.562040i
$157$	−13.7543	−	4.24263i	−1.09771	−	0.338598i	−0.307570	−	0.951526i	$-0.599516\pi$
$157$	−13.7543	−	4.24263i	−1.09771	−	0.338598i	−0.790139	+	0.612927i	$0.789992\pi$
$158$	1.24712	−	16.6416i	0.0992155	−	1.32394i
$159$	−4.60929	+	11.7443i	−0.365540	+	0.931381i
$160$	−14.9196	+	7.18492i	−1.17950	+	0.568018i
$161$	−11.4304	−	0.637691i	−0.900843	−	0.0502571i
$162$	−5.13738	−	2.47403i	−0.403631	−	0.194378i
$163$	−4.33500	+	4.02229i	−0.339543	+	0.315050i	−0.831452	−	0.555597i	$-0.812490\pi$
$163$	−4.33500	+	4.02229i	−0.339543	+	0.315050i	0.491909	+	0.870647i	$0.336299\pi$
$164$	−28.4303	+	4.28517i	−2.22003	+	0.334616i
$165$	−1.30096	+	2.25333i	−0.101279	+	0.175421i
$166$	12.4029	+	21.4825i	0.962654	+	1.66737i
$167$	−6.15060	−	7.71261i	−0.475948	−	0.596819i	0.484669	−	0.874698i	$-0.338940\pi$
$167$	−6.15060	−	7.71261i	−0.475948	−	0.596819i	−0.960616	+	0.277878i	$0.910369\pi$
$168$	26.2987	−	21.8057i	2.02899	−	1.68234i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	6.41637	+	0.967112i	0.492113	+	0.0741741i
$171$	3.48532	−	2.37625i	0.266529	−	0.181717i
$172$	1.25430	−	0.855170i	0.0956398	−	0.0652061i
$173$	−21.6217	−	3.25894i	−1.64387	−	0.247773i	−0.739073	−	0.673625i	$-0.764736\pi$
$173$	−21.6217	−	3.25894i	−1.64387	−	0.247773i	−0.904793	+	0.425852i	$0.859974\pi$
$174$	−9.71675	+	12.1844i	−0.736625	+	0.923698i
$175$	−9.54271	+	7.91238i	−0.721361	+	0.598120i
$176$	43.4668	+	54.5056i	3.27643	+	4.10852i
$177$	4.32126	+	7.48465i	0.324806	+	0.562581i
$178$	−8.22237	+	14.2416i	−0.616293	+	1.06745i
$179$	−19.4636	+	2.93366i	−1.45477	+	0.219272i	−0.828350	−	0.560210i	$-0.810720\pi$
$179$	−19.4636	+	2.93366i	−1.45477	+	0.219272i	−0.626424	+	0.779482i	$0.715482\pi$
$180$	−3.67035	+	3.40559i	−0.273572	+	0.253838i
$181$	16.4907	+	7.94151i	1.22575	+	0.590288i	0.930906	−	0.365259i	$-0.119020\pi$
$181$	16.4907	+	7.94151i	1.22575	+	0.590288i	0.294839	+	0.955547i	$0.404734\pi$
$182$	7.38516	+	0.412010i	0.547425	+	0.0305402i
$183$	15.9770	−	7.69413i	1.18106	−	0.568767i
$184$	−16.8637	+	42.9681i	−1.24321	+	3.16765i
$185$	−0.289519	+	3.86337i	−0.0212859	+	0.284040i
$186$	−26.8694	−	8.28811i	−1.97016	−	0.607713i
$187$	−1.18505	−	15.8134i	−0.0866597	−	1.15639i
$188$	3.24012	−	14.1959i	0.236310	−	1.03534i
$189$	7.95074	−	12.1532i	0.578331	−	0.884013i
$190$	0.959006	+	4.20168i	0.0695736	+	0.304822i
$191$	16.4425	−	5.07185i	1.18974	−	0.366986i	0.364195	−	0.931323i	$-0.381344\pi$
$191$	16.4425	−	5.07185i	1.18974	−	0.366986i	0.825545	+	0.564337i	$0.190868\pi$
$192$	−20.4092	−	52.0018i	−1.47291	−	3.75290i
$193$	−3.51743	−	3.26370i	−0.253190	−	0.234926i	0.543358	−	0.839501i	$-0.317153\pi$
$193$	−3.51743	−	3.26370i	−0.253190	−	0.234926i	−0.796548	+	0.604575i	$0.793343\pi$
$194$	−30.3290	−	20.6780i	−2.17749	−	1.48459i
$195$	0.678947			0.0486204
$196$	21.6846	+	34.4545i	1.54890	+	2.46103i
$197$	−5.13831			−0.366090			−0.183045	−	0.983105i	$-0.558595\pi$
$197$	−5.13831			−0.366090			−0.183045	+	0.983105i	$0.558595\pi$
$198$	13.5868	+	9.26335i	0.965575	+	0.658318i
$199$	9.30027	+	8.62939i	0.659279	+	0.611721i	0.937162	−	0.348894i	$-0.113443\pi$
$199$	9.30027	+	8.62939i	0.659279	+	0.611721i	−0.277884	+	0.960615i	$0.589633\pi$
$200$	18.2604	+	46.5267i	1.29120	+	3.28994i
$201$	−0.0189363	+	0.00584106i	−0.00133566	+	0.000411997i
$202$	−8.39553	−	36.7832i	−0.590707	−	2.58806i
$203$	−8.45652	−	8.77239i	−0.593532	−	0.615701i
$204$	−6.48189	+	28.3990i	−0.453823	+	1.98833i
$205$	−0.207226	−	2.76524i	−0.0144733	−	0.193133i
$206$	21.8393	+	6.73654i	1.52162	+	0.469357i
$207$	−0.496310	+	6.62279i	−0.0344959	+	0.460316i
$208$	6.64613	−	16.9341i	0.460826	−	1.17417i
$209$	9.48933	−	4.56982i	0.656390	−	0.316101i
$210$	2.90756	+	4.09462i	0.200640	+	0.282555i
$211$	6.16860	+	2.97064i	0.424664	+	0.204507i	0.633995	−	0.773338i	$-0.281414\pi$
$211$	6.16860	+	2.97064i	0.424664	+	0.204507i	−0.209330	+	0.977845i	$0.567128\pi$
$212$	−44.4363	+	41.2308i	−3.05190	+	2.83175i
$213$	12.5047	−	1.88478i	0.856808	−	0.129143i
$214$	−3.76628	+	6.52339i	−0.257458	+	0.445930i
$215$	0.0732078	+	0.126800i	0.00499273	+	0.00864766i
$216$	−36.5090	−	45.7808i	−2.48412	−	3.11499i
$217$	9.15934	−	19.9857i	0.621776	−	1.35672i
$218$	16.3879	−	20.5498i	1.10993	−	1.39181i
$219$	−6.29706	−	0.949129i	−0.425516	−	0.0641362i
$220$	−10.3292	+	7.04233i	−0.696394	+	0.474794i
$221$	−3.41893	+	2.33099i	−0.229982	+	0.156799i
$222$	−23.1117	−	3.48353i	−1.55116	−	0.233799i
$223$	−3.14014	+	3.93761i	−0.210279	+	0.263682i	−0.875775	−	0.482720i	$-0.839649\pi$
$223$	−3.14014	+	3.93761i	−0.210279	+	0.263682i	0.665495	+	0.746402i	$0.268220\pi$
$224$	75.8054	−	18.8297i	5.06496	−	1.25811i
$225$	4.48377	+	5.62247i	0.298918	+	0.374831i
$226$	−2.90710	−	5.03524i	−0.193377	−	0.334939i
$227$	−13.7160	+	23.7569i	−0.910365	+	1.57680i	−0.0968149	+	0.995302i	$0.530866\pi$
$227$	−13.7160	+	23.7569i	−0.910365	+	1.57680i	−0.813550	+	0.581495i	$0.802468\pi$
$228$	−19.1309	+	2.88352i	−1.26698	+	0.190966i
$229$	6.04052	−	5.60478i	0.399169	−	0.370375i	−0.454893	−	0.890546i	$-0.650322\pi$
$229$	6.04052	−	5.60478i	0.399169	−	0.370375i	0.854062	+	0.520172i	$0.174132\pi$
$230$	−6.11336	−	2.94404i	−0.403103	−	0.194124i
$231$	8.17460	−	9.15417i	0.537849	−	0.602300i
$232$	−44.2633	+	21.3161i	−2.90603	+	1.39947i
$233$	0.492609	−	1.25515i	0.0322719	−	0.0822274i	−0.913829	−	0.406098i	$-0.866889\pi$
$233$	0.492609	−	1.25515i	0.0322719	−	0.0822274i	0.946101	+	0.323871i	$0.104984\pi$
$234$	0.320664	−	4.27897i	0.0209625	−	0.279725i
$235$	1.34197	+	0.413944i	0.0875406	+	0.0270027i
$236$	3.10316	+	41.4088i	0.201998	+	2.69548i
$237$	−1.60782	+	7.04431i	−0.104439	+	0.457577i
$238$	−28.6992	−	10.6367i	−1.86029	−	0.689473i
$239$	0.841100	+	3.68510i	0.0544063	+	0.238369i	0.994818	−	0.101667i	$-0.0324177\pi$
$239$	0.841100	+	3.68510i	0.0544063	+	0.238369i	−0.940412	+	0.340037i	$0.889561\pi$
$240$	11.8024	−	3.64056i	0.761841	−	0.234997i
$241$	−5.68431	−	14.4834i	−0.366159	−	0.932957i	−0.988637	−	0.150321i	$-0.951969\pi$
$241$	−5.68431	−	14.4834i	−0.366159	−	0.932957i	0.622479	−	0.782637i	$-0.286126\pi$
$242$	7.55478	+	7.00981i	0.485640	+	0.450608i
$243$	−11.5662	−	7.88568i	−0.741970	−	0.505867i
$244$	85.2028			5.45455
$245$	−3.47004	+	1.83724i	−0.221693	+	0.117377i
$246$	16.7293			1.06662
$247$	−2.27077	−	1.54819i	−0.144486	−	0.0985087i
$248$	−64.9787	−	60.2914i	−4.12615	−	3.82851i
$249$	−3.92379	−	9.99766i	−0.248660	−	0.633576i
$250$	−14.5132	+	4.47672i	−0.917894	+	0.283133i
$251$	1.31652	+	5.76803i	0.0830978	+	0.364075i	0.999331	−	0.0365700i	$-0.0116432\pi$
$251$	1.31652	+	5.76803i	0.0830978	+	0.364075i	−0.916233	+	0.400645i	$0.868786\pi$
$252$	20.2241	−	12.1964i	1.27400	−	0.768298i
$253$	−3.68991	+	16.1666i	−0.231983	+	1.01638i
$254$	−3.26151	−	43.5218i	−0.204645	−	2.73080i
$255$	−2.68463	−	0.828099i	−0.168118	−	0.0518576i
$256$	7.72245	−	103.049i	0.482653	−	6.44055i
$257$	−0.366530	+	0.933903i	−0.0228635	+	0.0582553i	−0.941850	−	0.336034i	$-0.890914\pi$
$257$	−0.366530	+	0.933903i	−0.0228635	+	0.0582553i	0.918986	+	0.394290i	$0.129009\pi$
$258$	−0.795839	+	0.383256i	−0.0495468	+	0.0238605i
$259$	5.05242	−	17.5617i	0.313942	−	1.09123i
$260$	2.93909	+	1.41539i	0.182275	+	0.0877789i
$261$	−5.18169	+	4.80790i	−0.320738	+	0.297602i
$262$	−24.6213	+	3.71106i	−1.52111	+	0.229270i
$263$	−3.51020	+	6.07984i	−0.216448	+	0.374899i	−0.953720	−	0.300698i	$-0.902781\pi$
$263$	−3.51020	+	6.07984i	−0.216448	+	0.374899i	0.737272	+	0.675597i	$0.236114\pi$
$264$	−24.7419	−	42.8543i	−1.52276	−	2.63750i
$265$	−3.64521	−	4.57095i	−0.223923	−	0.280791i
$266$	−0.387611	−	20.3247i	−0.0237660	−	1.24619i
$267$	4.43925	−	5.56664i	0.271678	−	0.340673i
$268$	−0.0941500	−	0.0141908i	−0.00575112	−	0.000866843i
$269$	−13.8548	+	9.44605i	−0.844743	+	0.575936i	−0.906524	−	0.422154i	$-0.861274\pi$
$269$	−13.8548	+	9.44605i	−0.844743	+	0.575936i	0.0617814	+	0.998090i	$0.480322\pi$
$270$	7.11199	−	4.84888i	0.432822	−	0.295093i
$271$	15.0012	+	2.26106i	0.911255	+	0.137350i	0.587905	−	0.808930i	$-0.299953\pi$
$271$	15.0012	+	2.26106i	0.911255	+	0.137350i	0.323350	+	0.946279i	$0.395191\pi$
$272$	−46.9337	+	58.8530i	−2.84577	+	3.56849i
$273$	−3.13522	−	0.652960i	−0.189752	−	0.0395189i
$274$	9.17127	+	11.5004i	0.554056	+	0.694765i
$275$	8.97784	+	15.5501i	0.541384	+	0.937705i
$276$	15.2301	−	26.3794i	0.916746	−	1.58785i
$277$	−1.51190	+	0.227882i	−0.0908413	+	0.0136921i	−0.194306	−	0.980941i	$-0.562245\pi$
$277$	−1.51190	+	0.227882i	−0.0908413	+	0.0136921i	0.103464	+	0.994633i	$0.467007\pi$
$278$	28.1011	−	26.0740i	1.68539	−	1.56382i
$279$	−11.4907	−	5.53365i	−0.687933	−	0.331291i
$280$	2.65757	+	15.6065i	0.158820	+	0.932668i
$281$	−27.7122	+	13.3455i	−1.65317	+	0.796126i	−0.653957	+	0.756531i	$0.726892\pi$
$281$	−27.7122	+	13.3455i	−1.65317	+	0.796126i	−0.999216	+	0.0395950i	$0.987393\pi$
$282$	−3.09532	+	7.88676i	−0.184324	+	0.469650i
$283$	−1.90270	+	25.3898i	−0.113104	+	1.50926i	0.595326	+	0.803484i	$0.297023\pi$
$283$	−1.90270	+	25.3898i	−0.113104	+	1.50926i	−0.708430	+	0.705781i	$0.750596\pi$
$284$	58.0608	+	17.9094i	3.44527	+	1.06273i
$285$	−0.139444	−	1.86075i	−0.00825994	−	0.110221i
$286$	2.38404	−	10.4452i	0.140971	−	0.617636i
$287$	−1.70248	+	12.9685i	−0.100494	+	0.765508i
$288$	−10.0831	−	44.1768i	−0.594150	−	2.60314i
$289$	0.117149	−	0.0361357i	0.00689113	−	0.00212563i
$290$	−2.63844	−	6.72264i	−0.154935	−	0.394767i
$291$	11.6504	+	10.8100i	0.682958	+	0.633692i
$292$	−25.2807	−	17.2361i	−1.47944	−	1.00867i
$293$	−27.7468			−1.62098			−0.810491	−	0.585751i	$-0.800800\pi$
$293$	−27.7468			−1.62098			−0.810491	+	0.585751i	$0.800800\pi$
$294$	−9.48853	−	21.7043i	−0.553382	−	1.26582i
$295$	−4.00496			−0.233178
$296$	−60.8777	−	41.5057i	−3.53844	−	2.41247i
$297$	−15.4204	−	14.3080i	−0.894782	−	0.830237i
$298$	−7.60434	−	19.3755i	−0.440507	−	1.12239i
$299$	4.13477	−	1.27541i	0.239120	−	0.0737588i
$300$	−7.33941	−	32.1561i	−0.423741	−	1.85653i
$301$	−0.216110	−	0.655937i	−0.0124564	−	0.0378076i
$302$	−6.60624	+	28.9438i	−0.380146	+	1.66553i
$303$	1.22075	+	16.2897i	0.0701301	+	0.935822i
$304$	−47.7752	−	14.7367i	−2.74009	−	0.845207i
$305$	−0.614101	+	8.19460i	−0.0351633	+	0.469222i
$306$	−6.48692	+	16.5284i	−0.370833	+	0.944866i
$307$	−4.86793	+	2.34427i	−0.277827	+	0.133795i	−0.567609	−	0.823298i	$-0.692132\pi$
$307$	−4.86793	+	2.34427i	−0.277827	+	0.133795i	0.289782	+	0.957093i	$0.406417\pi$
$308$	54.4706	−	22.5860i	3.10375	−	1.28696i
$309$	−8.91535	−	4.29341i	−0.507176	−	0.244243i
$310$	9.55182	−	8.86279i	0.542507	−	0.503373i
$311$	16.3265	−	2.46082i	0.925791	−	0.139540i	0.331192	−	0.943563i	$-0.392549\pi$
$311$	16.3265	−	2.46082i	0.925791	−	0.139540i	0.594598	+	0.804023i	$0.297311\pi$
$312$	−6.45619	+	11.1825i	−0.365510	+	0.633082i
$313$	−3.19240	−	5.52941i	−0.180445	−	0.312540i	0.761587	−	0.648063i	$-0.224421\pi$
$313$	−3.19240	−	5.52941i	−0.180445	−	0.312540i	−0.942032	+	0.335522i	$0.891087\pi$
$314$	25.0893	+	31.4610i	1.41587	+	1.77545i
$315$	1.02725	+	2.03301i	0.0578790	+	0.114547i
$316$	−21.6453	+	27.1423i	−1.21764	+	1.52687i
$317$	5.84157	+	0.880475i	0.328095	+	0.0494524i	0.311025	−	0.950402i	$-0.399328\pi$
$317$	5.84157	+	0.880475i	0.328095	+	0.0494524i	0.0170707	+	0.999854i	$0.494566\pi$
$318$	29.1425	−	19.8690i	1.63423	−	1.11420i
$319$	−14.5824	+	9.94213i	−0.816459	+	0.556652i
$320$	25.5980	+	3.85828i	1.43097	+	0.215685i
$321$	2.03341	−	2.54982i	0.113494	−	0.142317i
$322$	25.3987	+	19.4743i	1.41542	+	1.08526i
$323$	7.09059	+	8.89131i	0.394531	+	0.494726i
$324$	5.93094	+	10.2727i	0.329496	+	0.570705i
$325$	2.34269	−	4.05765i	0.129949	−	0.225078i
$326$	16.3479	−	2.46405i	0.905426	−	0.136471i
$327$	−8.34224	+	7.74046i	−0.461327	+	0.428049i
$328$	47.5148	+	22.8819i	2.62357	+	1.26344i
$329$	−5.79882	−	3.20210i	−0.319699	−	0.176538i
$330$	6.55374	−	3.15611i	0.360771	−	0.173738i
$331$	−11.8907	+	30.2970i	−0.653571	+	1.66527i	0.0894402	+	0.995992i	$0.471492\pi$
$331$	−11.8907	+	30.2970i	−0.653571	+	1.66527i	−0.743011	+	0.669279i	$0.766603\pi$
$332$	3.85630	−	51.4588i	0.211642	−	2.82417i
$333$	−10.1302	−	3.12476i	−0.555132	−	0.171236i
$334$	2.06096	+	27.5016i	0.112771	+	1.50482i
$335$	0.00204343	−	0.00895284i	0.000111644	−	0.000489146i
$336$	−58.0019	+	5.46060i	−3.16427	+	0.297900i
$337$	−3.21571	−	14.0889i	−0.175171	−	0.767473i	−0.983817	−	0.179178i	$-0.942656\pi$
$337$	−3.21571	−	14.0889i	−0.175171	−	0.767473i	0.808646	−	0.588296i	$-0.200201\pi$
$338$	−2.67147	+	0.824038i	−0.145309	+	0.0448218i
$339$	0.919689	+	2.34333i	0.0499507	+	0.127272i
$340$	−9.89517	−	9.18137i	−0.536641	−	0.497930i
$341$	−26.3107	−	17.9383i	−1.42480	−	0.971414i
$342$	−11.7930			−0.637691
$343$	17.7908	−	5.14675i	0.960611	−	0.277898i
$344$	−2.78457			−0.150134
$345$	2.42733	+	1.65493i	0.130683	+	0.0890983i
$346$	44.8113	+	41.5789i	2.40907	+	2.23529i
$347$	8.43904	+	21.5023i	0.453031	+	1.15430i	0.956872	+	0.290509i	$0.0938245\pi$
$347$	8.43904	+	21.5023i	0.453031	+	1.15430i	−0.503841	+	0.863796i	$0.668080\pi$
$348$	30.9796	−	9.55595i	1.66068	−	0.512253i
$349$	−6.20511	−	27.1864i	−0.332152	−	1.45525i	−0.814955	−	0.579524i	$-0.803239\pi$
$349$	−6.20511	−	27.1864i	−0.332152	−	1.45525i	0.482804	−	0.875729i	$-0.339619\pi$
$350$	34.5035	−	3.24834i	1.84429	−	0.173631i
$351$	−1.22145	+	5.35150i	−0.0651959	+	0.285642i
$352$	−8.45483	−	112.822i	−0.450644	−	6.01343i
$353$	10.5558	+	3.25604i	0.561830	+	0.173302i	0.562646	−	0.826698i	$-0.309783\pi$
$353$	10.5558	+	3.25604i	0.561830	+	0.173302i	−0.000815696		1.00000i	$0.500260\pi$
$354$	1.80560	−	24.0941i	0.0959666	−	1.28059i
$355$	−2.14096	+	5.45507i	−0.113630	+	0.289525i
$356$	30.8218	−	14.8430i	1.63355	−	0.786677i
$357$	11.6006	+	6.40584i	0.613969	+	0.339033i
$358$	49.5788	+	23.8759i	2.62032	+	1.26188i
$359$	18.0361	−	16.7351i	0.951910	−	0.883243i	−0.0413512	−	0.999145i	$-0.513166\pi$
$359$	18.0361	−	16.7351i	0.951910	−	0.883243i	0.993261	+	0.115902i	$0.0369758\pi$
$360$	9.08146	−	1.36881i	0.478635	−	0.0721426i
$361$	5.72336	−	9.91314i	0.301229	−	0.521744i
$362$	−25.5850	−	44.3145i	−1.34472	−	2.32912i
$363$	−2.78208	−	3.48862i	−0.146021	−	0.183105i
$364$	−12.2108	−	9.36255i	−0.640022	−	0.490731i
$365$	1.83994	−	2.30721i	0.0963066	−	0.120765i
$366$	−49.0223	−	7.38893i	−2.56244	−	0.386226i
$367$	3.70359	−	2.52506i	0.193326	−	0.131807i	−0.462789	−	0.886469i	$-0.653151\pi$
$367$	3.70359	−	2.52506i	0.193326	−	0.131807i	0.656115	+	0.754661i	$0.272199\pi$
$368$	65.0375	−	44.3418i	3.39031	−	2.31148i
$369$	7.50315	+	1.13092i	0.390599	+	0.0588733i
$370$	6.75300	−	8.46800i	0.351072	−	0.440230i
$371$	12.4367	+	24.6133i	0.645683	+	1.27786i
$372$	36.4707	+	45.7328i	1.89092	+	2.37114i
$373$	8.54427	+	14.7991i	0.442405	+	0.766269i	0.997867	−	0.0652733i	$-0.0207919\pi$
$373$	8.54427	+	14.7991i	0.442405	+	0.766269i	−0.555462	+	0.831542i	$0.687459\pi$
$374$	−22.1665	+	38.3936i	−1.14620	+	1.98529i
$375$	6.50241	−	0.980081i	0.335783	−	0.0506111i
$376$	−19.5787	+	18.1664i	−1.00970	+	0.936862i
$377$	4.14932	+	1.99821i	0.213701	+	0.102913i
$378$	−37.5048	+	15.5512i	−1.92904	+	0.799868i
$379$	5.59920	−	2.69643i	0.287612	−	0.138507i	−0.284515	−	0.958671i	$-0.591833\pi$
$379$	5.59920	−	2.69643i	0.287612	−	0.138507i	0.572127	+	0.820165i	$0.306118\pi$
$380$	3.27544	−	8.34569i	0.168027	−	0.428125i
$381$	−1.41212	+	18.8434i	−0.0723451	+	0.965378i
$382$	−45.9679	−	14.1792i	−2.35192	−	0.725471i
$383$	1.37852	+	18.3950i	0.0704389	+	0.939942i	0.914732	+	0.404060i	$0.132401\pi$
$383$	1.37852	+	18.3950i	0.0704389	+	0.939942i	−0.844293	+	0.535881i	$0.819979\pi$
$384$	−18.8488	+	82.5822i	−0.961876	+	4.21426i
$385$	1.77967	+	5.40164i	0.0907004	+	0.275293i
$386$	2.98502	+	13.0782i	0.151934	+	0.665665i
$387$	−0.382846	+	0.118092i	−0.0194612	+	0.00600297i
$388$	27.8979	+	71.0827i	1.41630	+	3.60868i
$389$	−5.38579	−	4.99728i	−0.273070	−	0.253372i	0.531735	−	0.846911i	$-0.321540\pi$
$389$	−5.38579	−	4.99728i	−0.273070	−	0.253372i	−0.804806	+	0.593538i	$0.797731\pi$
$390$	−1.56829	−	1.06924i	−0.0794136	−	0.0541433i
$391$	−17.9049			−0.905491
$392$	2.73710	−	74.6231i	0.138244	−	3.76904i
$393$	10.7806			0.543808
$394$	11.8689	+	8.09210i	0.597948	+	0.407674i
$395$	−2.45447	−	2.27742i	−0.123498	−	0.114589i
$396$	−12.4978	−	31.8438i	−0.628036	−	1.60021i
$397$	−9.97146	+	3.07579i	−0.500453	+	0.154369i	−0.534697	−	0.845044i	$-0.679574\pi$
$397$	−9.97146	+	3.07579i	−0.500453	+	0.154369i	0.0342433	+	0.999414i	$0.489098\pi$
$398$	−7.89255	−	34.5795i	−0.395618	−	1.73331i
$399$	−1.14561	+	8.72661i	−0.0573521	+	0.436877i
$400$	18.9664	−	83.0974i	0.948322	−	4.15487i
$401$	2.38026	+	31.7623i	0.118864	+	1.58614i	0.663964	+	0.747765i	$0.268873\pi$
$401$	2.38026	+	31.7623i	0.118864	+	1.58614i	−0.545099	+	0.838371i	$0.683508\pi$
$402$	0.0529395	+	0.0163297i	0.00264038	+	0.000814450i
$403$	−0.620961	+	8.28615i	−0.0309323	+	0.412763i
$404$	−28.6745	+	73.0615i	−1.42661	+	3.63495i
$405$	−1.03075	+	0.496383i	−0.0512183	+	0.0246655i
$406$	5.71839	+	33.5811i	0.283799	+	1.66660i
$407$	−23.8480	−	11.4846i	−1.18210	−	0.569271i
$408$	39.1675	−	36.3421i	1.93908	−	1.79920i
$409$	−15.2734	+	2.30209i	−0.755221	+	0.113831i	−0.515357	−	0.856975i	$-0.672341\pi$
$409$	−15.2734	+	2.30209i	−0.755221	+	0.113831i	−0.239863	+	0.970807i	$0.577103\pi$
$410$	−3.87619	+	6.71375i	−0.191431	+	0.331569i
$411$	−3.18437	−	5.51549i	−0.157073	−	0.272059i
$412$	−29.6432	−	37.1714i	−1.46042	−	1.83131i
$413$	18.4940	+	3.85167i	0.910029	+	0.189528i
$414$	11.5764	−	14.5163i	0.568948	−	0.713438i
$415$	4.92139	+	0.741780i	0.241581	+	0.0364125i
$416$	−24.3926	+	16.6306i	−1.19594	+	0.815381i
$417$	−13.7135	+	9.34970i	−0.671553	+	0.457857i
$418$	−29.1161	−	4.38855i	−1.42412	−	0.214651i
$419$	−17.8388	+	22.3692i	−0.871483	+	1.09281i	0.123458	+	0.992350i	$0.460602\pi$
$419$	−17.8388	+	22.3692i	−0.871483	+	1.09281i	−0.994942	+	0.100456i	$0.967970\pi$
$420$	−0.199198	−	10.4451i	−0.00971988	−	0.509669i
$421$	−8.58819	−	10.7693i	−0.418563	−	0.524861i	0.527190	−	0.849747i	$-0.323245\pi$
$421$	−8.58819	−	10.7693i	−0.418563	−	0.524861i	−0.945753	+	0.324886i	$0.894674\pi$
$422$	−9.57046	−	16.5765i	−0.465883	−	0.806932i
$423$	−1.92142	+	3.32800i	−0.0934227	+	0.161813i
$424$	109.948	−	16.5719i	5.33952	−	0.804804i
$425$	−14.2123	+	13.1871i	−0.689397	+	0.639667i
$426$	−31.8528	−	15.3395i	−1.54327	−	0.743200i
$427$	10.7167	−	37.2502i	0.518618	−	1.80266i
$428$	14.1180	−	6.79888i	0.682420	−	0.328636i
$429$	−1.69471	+	4.31805i	−0.0818213	+	0.208477i
$430$	0.0305892	−	0.408185i	0.00147514	−	0.0196844i
$431$	−18.6864	−	5.76400i	−0.900093	−	0.277642i	−0.190029	−	0.981779i	$-0.560858\pi$
$431$	−18.6864	−	5.76400i	−0.900093	−	0.277642i	−0.710065	+	0.704136i	$0.751334\pi$
$432$	7.46224	+	99.5767i	0.359027	+	4.79089i
$433$	−3.79981	+	16.6480i	−0.182607	+	0.800054i	0.797776	+	0.602954i	$0.206010\pi$
$433$	−3.79981	+	16.6480i	−0.182607	+	0.800054i	−0.980383	+	0.197100i	$0.936848\pi$
$434$	−52.6317	+	31.7401i	−2.52640	+	1.52357i
$435$	0.695782	+	3.04842i	0.0333602	+	0.146161i
$436$	−52.2492	+	16.1167i	−2.50228	+	0.771851i
$437$	−4.34464	−	11.0700i	−0.207833	−	0.529549i
$438$	13.0508	+	12.1093i	0.623590	+	0.578607i
$439$	24.2824	+	16.5555i	1.15894	+	0.790149i	0.981022	−	0.193897i	$-0.0621128\pi$
$439$	24.2824	+	16.5555i	1.15894	+	0.790149i	0.177914	+	0.984046i	$0.443065\pi$
$440$	22.9309			1.09319
$441$	−2.78841	−	10.3759i	−0.132782	−	0.494090i
$442$	11.5683			0.550249
$443$	8.80511	+	6.00322i	0.418343	+	0.285222i	0.754141	−	0.656713i	$-0.228054\pi$
$443$	8.80511	+	6.00322i	0.418343	+	0.285222i	−0.335798	+	0.941934i	$0.609006\pi$
$444$	35.6423	+	33.0712i	1.69151	+	1.56949i
$445$	1.20541	+	3.07135i	0.0571421	+	0.145596i
$446$	13.4546	−	4.15018i	0.637092	−	0.196517i
$447$	2.00534	+	8.78595i	0.0948491	+	0.415561i
$448$	−114.495	−	42.4349i	−5.40939	−	2.00486i
$449$	3.63286	−	15.9166i	0.171445	−	0.751152i	−0.813959	−	0.580922i	$-0.802692\pi$
$449$	3.63286	−	15.9166i	0.171445	−	0.751152i	0.985404	−	0.170229i	$-0.0544509\pi$
$450$	−1.50243	−	20.0486i	−0.0708254	−	0.945099i
$451$	18.1040	+	5.58433i	0.852482	+	0.262956i
$452$	−0.903870	+	12.0613i	−0.0425145	+	0.567316i
$453$	4.69608	−	11.9654i	0.220641	−	0.562184i
$454$	69.0961	−	33.2749i	3.24284	−	1.56167i
$455$	0.988477	−	1.10693i	0.0463405	−	0.0518936i
$456$	31.9731	+	15.3974i	1.49728	+	0.721050i
$457$	3.76409	−	3.49256i	0.176077	−	0.163375i	−0.587211	−	0.809434i	$-0.699774\pi$
$457$	3.76409	−	3.49256i	0.176077	−	0.163375i	0.763288	+	0.646058i	$0.223584\pi$
$458$	−22.7797	+	3.43348i	−1.06442	+	0.160436i
$459$	11.3569	−	19.6707i	0.530093	−	0.918147i
$460$	7.05767	+	12.2242i	0.329066	+	0.569958i
$461$	−4.40851	−	5.52809i	−0.205325	−	0.257469i	0.668498	−	0.743714i	$-0.266938\pi$
$461$	−4.40851	−	5.52809i	−0.205325	−	0.257469i	−0.873822	+	0.486245i	$0.838366\pi$
$462$	−33.2989	+	8.27131i	−1.54921	+	0.384816i
$463$	13.9919	−	17.5453i	0.650259	−	0.815400i	−0.341984	−	0.939706i	$-0.611099\pi$
$463$	13.9919	−	17.5453i	0.650259	−	0.815400i	0.992244	+	0.124306i	$0.0396705\pi$
$464$	82.8437	+	12.4867i	3.84592	+	0.579679i
$465$	−4.66134	+	3.17805i	−0.216164	+	0.147378i
$466$	−3.11455	+	2.12346i	−0.144279	+	0.0983675i
$467$	−13.5802	−	2.04688i	−0.628414	−	0.0947182i	−0.172889	−	0.984941i	$-0.555310\pi$
$467$	−13.5802	−	2.04688i	−0.628414	−	0.0947182i	−0.455525	+	0.890223i	$0.650548\pi$
$468$	−5.56552	+	6.97894i	−0.257266	+	0.322602i
$469$	−0.0180462	+	0.0393769i	−0.000833297	+	0.00181826i
$470$	−2.44791	−	3.06958i	−0.112913	−	0.141589i
$471$	−8.71129	−	15.0884i	−0.401395	−	0.695237i
$472$	38.0837	−	65.9629i	1.75294	−	3.03619i
$473$	−0.989168	+	0.149093i	−0.0454820	+	0.00685531i
$474$	14.8077	−	13.7395i	0.680138	−	0.631076i
$475$	−11.6017	−	5.58709i	−0.532323	−	0.256353i
$476$	36.8636	+	51.9139i	1.68964	+	2.37947i
$477$	14.4137	−	6.94127i	0.659958	−	0.317819i
$478$	3.86066	−	9.83679i	0.176582	−	0.449924i
$479$	−0.963840	+	12.8616i	−0.0440390	+	0.587659i	0.930913	+	0.365242i	$0.119014\pi$
$479$	−0.963840	+	12.8616i	−0.0440390	+	0.587659i	−0.974952	+	0.222417i	$0.928605\pi$
$480$	−19.1537	−	5.90812i	−0.874241	−	0.269668i
$481$	0.516156	+	6.88762i	0.0235347	+	0.314048i
$482$	−9.67913	+	42.4070i	−0.440872	+	1.93159i
$483$	−9.61727	−	9.97649i	−0.437601	−	0.453946i
$484$	−4.77067	−	20.9017i	−0.216848	−	0.950075i
$485$	−7.03764	+	2.17082i	−0.319563	+	0.0985721i
$486$	14.2978	+	36.4301i	0.648560	+	1.65250i
$487$	5.94532	+	5.51645i	0.269408	+	0.249974i	0.803294	−	0.595582i	$-0.203079\pi$
$487$	5.94532	+	5.51645i	0.269408	+	0.249974i	−0.533886	+	0.845556i	$0.679269\pi$
$488$	−129.128	−	88.0379i	−5.84534	−	3.98529i
$489$	−7.15803			−0.323697
$490$	10.9088	+	1.22098i	0.492809	+	0.0551583i
$491$	−28.1903			−1.27221			−0.636104	−	0.771603i	$-0.719455\pi$
$491$	−28.1903			−1.27221			−0.636104	+	0.771603i	$0.719455\pi$
$492$	−28.7544	−	19.6044i	−1.29635	−	0.883834i
$493$	−13.9697	−	12.9620i	−0.629162	−	0.583777i
$494$	2.80706	+	7.15228i	0.126296	+	0.321796i
$495$	3.15274	−	0.972490i	0.141705	−	0.0437102i
$496$	33.6365	+	147.371i	1.51032	+	6.61715i
$497$	15.1327	−	23.1312i	0.678794	−	1.03758i
$498$	−6.68135	+	29.2729i	−0.299399	+	1.31175i
$499$	0.636950	+	8.49951i	0.0285138	+	0.380490i	0.993145	+	0.116888i	$0.0372917\pi$
$499$	0.636950	+	8.49951i	0.0285138	+	0.380490i	−0.964631	+	0.263603i	$0.915089\pi$
$500$	30.1914	+	9.31282i	1.35020	+	0.416482i
$501$	0.892324	−	11.9072i	0.0398661	−	0.531976i
$502$	6.04282	−	15.3968i	0.269704	−	0.687195i
$503$	32.8804	−	15.8344i	1.46606	−	0.706019i	0.480764	−	0.876850i	$-0.340359\pi$
$503$	32.8804	−	15.8344i	1.46606	−	0.706019i	0.985300	+	0.170831i	$0.0546452\pi$
$504$	−43.2525	−	2.41301i	−1.92662	−	0.107484i
$505$	−6.82021	−	3.28444i	−0.303495	−	0.146156i
$506$	33.9833	−	31.5319i	1.51074	−	1.40176i
$507$	1.19691	−	0.180405i	0.0531566	−	0.00801207i
$508$	−45.3956	+	78.6275i	−2.01410	+	3.48853i
$509$	−10.7530	−	18.6248i	−0.476620	−	0.825530i	0.523021	−	0.852320i	$-0.324805\pi$
$509$	−10.7530	−	18.6248i	−0.476620	−	0.825530i	−0.999641	+	0.0267899i	$0.991471\pi$
$510$	4.89706	+	6.14072i	0.216846	+	0.271916i
$511$	−10.7153	+	8.88463i	−0.474017	+	0.393033i
$512$	−92.8614	+	116.444i	−4.10393	+	5.14617i
$513$	14.9174	+	2.24844i	0.658620	+	0.0992709i
$514$	2.31741	−	1.57998i	0.102216	−	0.0696900i
$515$	3.78871	−	2.58310i	0.166951	−	0.113825i
$516$	1.81702	+	0.273871i	0.0799896	+	0.0120565i
$517$	−5.98232	+	7.50160i	−0.263102	+	0.329920i
$518$	−39.3277	+	32.6087i	−1.72796	+	1.43275i
$519$	−16.5020	−	20.6928i	−0.724357	−	0.908314i
$520$	−2.99181	−	5.18197i	−0.131200	−	0.227244i
$521$	−6.65238	+	11.5223i	−0.291446	+	0.504799i	−0.974152	−	0.225894i	$-0.927470\pi$
$521$	−6.65238	+	11.5223i	−0.291446	+	0.504799i	0.682706	+	0.730693i	$0.260803\pi$
$522$	19.5409	−	2.94531i	0.855281	−	0.128913i
$523$	−7.15441	+	6.63832i	−0.312840	+	0.290273i	−0.820928	−	0.571032i	$-0.806543\pi$
$523$	−7.15441	+	6.63832i	−0.312840	+	0.290273i	0.508087	+	0.861306i	$0.330353\pi$
$524$	46.6680	+	22.4741i	2.03870	+	0.981787i
$525$	−14.9816	−	0.835807i	−0.653850	−	0.0364776i
$526$	17.6830	−	8.51570i	0.771017	−	0.371302i
$527$	12.5618	−	32.0070i	0.547201	−	1.39425i
$528$	−6.30613	+	84.1494i	−0.274439	+	3.66213i
$529$	−4.08698	−	1.26067i	−0.177695	−	0.0548116i
$530$	1.22145	+	16.2991i	0.0530562	+	0.707986i
$531$	2.43861	−	10.6842i	0.105827	−	0.463657i
$532$	−23.1515	+	35.3884i	−1.00374	+	1.53428i
$533$	−1.10008	−	4.81975i	−0.0476496	−	0.208767i
$534$	−19.0208	+	5.86715i	−0.823113	+	0.253897i
$535$	0.552144	+	1.40684i	0.0238713	+	0.0608230i
$536$	0.128025	+	0.118789i	0.00552982	+	0.00513092i
$537$	−19.6854	−	13.4213i	−0.849489	−	0.579172i
$538$	46.8793			2.02111
$539$	−3.02321	−	26.6551i	−0.130219	−	1.14812i
$540$	−17.9063			−0.770566
$541$	23.7077	+	16.1636i	1.01927	+	0.694929i	0.953030	−	0.302875i	$-0.0979464\pi$
$541$	23.7077	+	16.1636i	1.01927	+	0.694929i	0.0662430	+	0.997804i	$0.478899\pi$
$542$	−31.0902	−	28.8475i	−1.33544	−	1.23910i
$543$	8.09408	+	20.6234i	0.347350	+	0.885034i
$544$	116.735	−	36.0079i	5.00497	−	1.54383i
$545$	−1.17348	−	5.14136i	−0.0502664	−	0.220232i
$546$	6.21370	+	6.44579i	0.265922	+	0.275854i
$547$	−3.14422	+	13.7757i	−0.134437	+	0.589008i	0.862164	+	0.506630i	$0.169109\pi$
$547$	−3.14422	+	13.7757i	−0.134437	+	0.589008i	−0.996601	+	0.0823787i	$0.973748\pi$
$548$	−2.28674	−	30.5144i	−0.0976846	−	1.30351i
$549$	−21.4872	−	6.62793i	−0.917053	−	0.282873i
$550$	3.75131	−	50.0578i	0.159956	−	2.13447i
$551$	4.62416	−	11.7822i	0.196996	−	0.501938i
$552$	−50.3389	+	24.2419i	−2.14257	+	1.03181i
$553$	9.14394	+	12.8771i	0.388840	+	0.547590i
$554$	3.85121	+	1.85464i	0.163622	+	0.0787962i
$555$	−3.43760	+	3.18963i	−0.145918	+	0.135392i
$556$	−78.8555	+	11.8856i	−3.34422	+	0.504060i
$557$	−3.60833	+	6.24981i	−0.152890	+	0.264813i	−0.932289	−	0.361715i	$-0.882191\pi$
$557$	−3.60833	+	6.24981i	−0.152890	+	0.264813i	0.779399	+	0.626528i	$0.215525\pi$
$558$	17.8277	+	30.8784i	0.754705	+	1.30719i
$559$	0.162750	+	0.204082i	0.00688358	+	0.00863173i
$560$	11.2477	−	24.5424i	0.475301	−	1.03711i
$561$	11.9677	−	15.0070i	0.505277	−	0.633597i
$562$	85.0295	+	12.8161i	3.58675	+	0.540616i
$563$	4.49227	−	3.06278i	0.189327	−	0.129081i	−0.464947	−	0.885338i	$-0.653927\pi$
$563$	4.49227	−	3.06278i	0.189327	−	0.129081i	0.654274	+	0.756258i	$0.272974\pi$
$564$	14.5625	−	9.92851i	0.613190	−	0.418066i
$565$	−1.15351	−	0.173864i	−0.0485286	−	0.00731451i
$566$	44.3803	−	55.6511i	1.86544	−	2.33919i
$567$	5.23714	−	1.30088i	0.219939	−	0.0546320i
$568$	−69.4879	−	87.1350i	−2.91565	−	3.65610i
$569$	2.04811	+	3.54744i	0.0858614	+	0.148716i	0.905758	−	0.423795i	$-0.139302\pi$
$569$	2.04811	+	3.54744i	0.0858614	+	0.148716i	−0.819897	+	0.572512i	$0.805969\pi$
$570$	−2.60831	+	4.51773i	−0.109250	+	0.189227i
$571$	18.0030	−	2.71352i	0.753403	−	0.113557i	0.238898	−	0.971045i	$-0.423214\pi$
$571$	18.0030	−	2.71352i	0.753403	−	0.113557i	0.514505	+	0.857487i	$0.327976\pi$
$572$	−16.3380	+	15.1595i	−0.683126	+	0.633849i
$573$	18.7652	+	9.03685i	0.783928	+	0.377520i
$574$	24.3561	−	27.2747i	1.01660	−	1.13843i
$575$	18.2659	−	8.79641i	0.761742	−	0.366836i
$576$	−25.8795	+	65.9399i	−1.07831	+	2.74750i
$577$	2.33094	−	31.1043i	0.0970384	−	1.29489i	−0.709921	−	0.704281i	$-0.751270\pi$
$577$	2.33094	−	31.1043i	0.0970384	−	1.29489i	0.806960	−	0.590606i	$-0.201111\pi$
$578$	−0.327510	−	0.101024i	−0.0136226	−	0.00420202i
$579$	−0.434036	−	5.79180i	−0.0180379	−	0.240699i
$580$	−3.34304	+	14.6468i	−0.138812	+	0.608175i
$581$	−22.0124	−	8.15838i	−0.913229	−	0.338467i
$582$	−9.88695	−	43.3176i	−0.409827	−	1.79557i
$583$	38.1696	−	11.7738i	1.58082	−	0.487619i
$584$	20.5042	+	52.2438i	0.848469	+	2.16186i
$585$	−0.631104	−	0.585579i	−0.0260929	−	0.0242107i
$586$	64.0920	+	43.6972i	2.64761	+	1.80511i
$587$	37.2290			1.53661			0.768303	−	0.640086i	$-0.221101\pi$
$587$	37.2290			1.53661			0.768303	+	0.640086i	$0.221101\pi$
$588$	−9.12545	+	48.4246i	−0.376327	+	1.99700i
$589$	22.8369			0.940978
$590$	9.25102	+	6.30724i	0.380858	+	0.259665i
$591$	−4.55926	−	4.23038i	−0.187543	−	0.174014i
$592$	45.9044	+	116.962i	1.88666	+	4.80713i
$593$	13.1130	−	4.04482i	0.538486	−	0.166101i	−0.0135701	−	0.999908i	$-0.504320\pi$
$593$	13.1130	−	4.04482i	0.538486	−	0.166101i	0.552056	+	0.833807i	$0.313843\pi$
$594$	13.0863	+	57.3349i	0.536938	+	2.35248i
$595$	−5.25865	+	3.17129i	−0.215583	+	0.130010i
$596$	−9.63507	+	42.2140i	−0.394668	+	1.72915i
$597$	1.14761	+	15.3138i	0.0469687	+	0.626753i
$598$	−11.5595	−	3.56562i	−0.472701	−	0.145809i
$599$	−1.34835	+	17.9924i	−0.0550919	+	0.735151i	0.899440	+	0.437043i	$0.143974\pi$
$599$	−1.34835	+	17.9924i	−0.0550919	+	0.735151i	−0.954532	+	0.298107i	$0.903645\pi$
$600$	−22.1029	+	56.3173i	−0.902347	+	2.29914i
$601$	11.4325	−	5.50562i	0.466343	−	0.224579i	−0.185930	−	0.982563i	$-0.559530\pi$
$601$	11.4325	−	5.50562i	0.466343	−	0.224579i	0.652273	+	0.757984i	$0.273815\pi$
$602$	−0.533815	+	1.85549i	−0.0217567	+	0.0756239i
$603$	0.0226397	+	0.0109027i	0.000921960	+	0.000443993i
$604$	45.2730	−	42.0072i	1.84213	−	1.70925i
$605$	2.04466	−	0.308182i	0.0831271	−	0.0125294i
$606$	22.8342	−	39.5500i	0.927577	−	1.60661i
$607$	−0.748555	−	1.29654i	−0.0303829	−	0.0526248i	0.850434	−	0.526082i	$-0.176339\pi$
$607$	−0.748555	−	1.29654i	−0.0303829	−	0.0526248i	−0.880817	+	0.473457i	$0.843006\pi$
$608$	50.5882	+	63.4356i	2.05162	+	2.57265i
$609$	−0.281222	−	14.7461i	−0.0113957	−	0.597540i
$610$	14.3238	−	17.9615i	0.579955	−	0.727240i
$611$	2.47574	+	0.373158i	0.100158	+	0.0150963i
$612$	30.5188	−	20.8073i	1.23365	−	0.841087i
$613$	−28.3086	+	19.3005i	−1.14337	+	0.779539i	−0.978392	−	0.206757i	$-0.933709\pi$
$613$	−28.3086	+	19.3005i	−1.14337	+	0.779539i	−0.164982	+	0.986297i	$0.552757\pi$
$614$	14.9363	+	2.25128i	0.602779	+	0.0908543i
$615$	2.09275	−	2.62423i	0.0843879	−	0.105819i
$616$	−105.890	−	22.0532i	−4.26642	−	0.888549i
$617$	11.1904	+	14.0323i	0.450508	+	0.564919i	0.954279	−	0.298918i	$-0.0966258\pi$
$617$	11.1904	+	14.0323i	0.450508	+	0.564919i	−0.503771	+	0.863837i	$0.668054\pi$
$618$	13.8320	+	23.9577i	0.556404	+	0.963720i
$619$	1.06473	−	1.84416i	0.0427950	−	0.0741231i	−0.843835	−	0.536603i	$-0.819707\pi$
$619$	1.06473	−	1.84416i	0.0427950	−	0.0741231i	0.886630	+	0.462480i	$0.153040\pi$
$620$	−26.8037	+	4.04001i	−1.07646	+	0.162251i
$621$	−17.4111	+	16.1551i	−0.698683	+	0.648283i
$622$	−41.5878	−	20.0277i	−1.66752	−	0.803036i
$623$	−2.61254	−	15.3420i	−0.104669	−	0.614666i
$624$	19.8390	−	9.55395i	0.794195	−	0.382464i
$625$	7.44551	−	18.9708i	0.297820	−	0.758834i
$626$	−1.33392	+	17.7999i	−0.0533141	+	0.711427i
$627$	12.1823	+	3.75773i	0.486513	+	0.150069i
$628$	−6.25570	−	83.4765i	−0.249629	−	3.33107i
$629$	6.35976	−	27.8639i	0.253580	−	1.11101i
$630$	0.828859	−	6.31380i	0.0330225	−	0.251548i
$631$	−6.28035	−	27.5160i	−0.250017	−	1.09539i	−0.931552	−	0.363609i	$-0.881544\pi$
$631$	−6.28035	−	27.5160i	−0.250017	−	1.09539i	0.681535	−	0.731786i	$-0.261313\pi$
$632$	60.8496	−	18.7696i	2.42047	−	0.746615i
$633$	3.02771	+	7.71448i	0.120341	+	0.306623i
$634$	−12.1068	−	11.2334i	−0.480821	−	0.446137i
$635$	−7.23501	−	4.93275i	−0.287113	−	0.195750i
$636$	−73.3740			−2.90947
$637$	−5.62912	+	4.16089i	−0.223034	+	0.164861i
$638$	49.3412			1.95344
$639$	−13.2491	−	9.03311i	−0.524128	−	0.357344i
$640$	−28.7744	−	26.6987i	−1.13741	−	1.05536i
$641$	9.90226	+	25.2306i	0.391116	+	0.996547i	0.981846	+	0.189678i	$0.0607444\pi$
$641$	9.90226	+	25.2306i	0.391116	+	0.996547i	−0.590731	+	0.806869i	$0.701160\pi$
$642$	−8.71256	+	2.68747i	−0.343857	+	0.106066i
$643$	−3.62506	−	15.8824i	−0.142958	−	0.626342i	−0.994739	−	0.102443i	$-0.967334\pi$
$643$	−3.62506	−	15.8824i	−0.142958	−	0.626342i	0.851780	−	0.523899i	$-0.175523\pi$
$644$	−20.8343	−	63.2362i	−0.820988	−	2.49186i
$645$	−0.0394364	+	0.172782i	−0.00155281	+	0.00680329i
$646$	−2.37593	−	31.7046i	−0.0934798	−	1.24740i
$647$	−20.6179	−	6.35977i	−0.810572	−	0.250028i	−0.138355	−	0.990383i	$-0.544182\pi$
$647$	−20.6179	−	6.35977i	−0.810572	−	0.250028i	−0.672217	+	0.740354i	$0.734658\pi$
$648$	1.62596	−	21.6969i	0.0638737	−	0.852335i
$649$	9.99672	−	25.4712i	0.392406	−	0.999833i
$650$	−11.8016	+	5.68334i	−0.462896	+	0.222919i
$651$	24.5814	−	10.1926i	0.963420	−	0.399478i
$652$	−30.9864	−	14.9222i	−1.21352	−	0.584400i
$653$	−21.3508	+	19.8106i	−0.835521	+	0.775251i	−0.976672	−	0.214738i	$-0.931110\pi$
$653$	−21.3508	+	19.8106i	−0.835521	+	0.775251i	0.141150	+	0.989988i	$0.454920\pi$
$654$	31.4598	−	4.74180i	1.23017	−	0.185419i
$655$	−2.49787	+	4.32644i	−0.0975998	+	0.169048i
$656$	−44.9669	−	77.8849i	−1.75566	−	3.04090i
$657$	5.03472	+	6.31334i	0.196423	+	0.246307i
$658$	8.35178	+	16.5288i	0.325586	+	0.644360i
$659$	−13.2576	+	16.6245i	−0.516441	+	0.647597i	−0.969849	−	0.243706i	$-0.921637\pi$
$659$	−13.2576	+	16.6245i	−0.516441	+	0.647597i	0.453408	+	0.891303i	$0.350208\pi$
$660$	−14.9631	−	2.25533i	−0.582439	−	0.0877885i
$661$	34.5383	−	23.5478i	1.34338	−	0.915904i	0.343654	−	0.939096i	$-0.388335\pi$
$661$	34.5383	−	23.5478i	1.34338	−	0.915904i	0.999731	+	0.0231923i	$0.00738299\pi$
$662$	75.1795	−	51.2565i	2.92193	−	1.99214i
$663$	−4.95274	−	0.746506i	−0.192349	−	0.0289919i
$664$	−59.0154	+	74.0030i	−2.29024	+	2.87187i
$665$	−3.23671	−	2.48172i	−0.125514	−	0.0962368i
$666$	18.4786	+	23.1715i	0.716033	+	0.897876i
$667$	9.96379	+	17.2578i	0.385799	+	0.668224i
$668$	28.6857	−	49.6850i	1.10988	−	1.92237i
$669$	−6.02811	+	0.908591i	−0.233060	+	0.0351282i
$670$	−0.0188195	+	0.0174620i	−0.000727062	+	0.000674615i
$671$	−50.5842	−	24.3600i	−1.95278	−	0.940409i
$672$	82.7651	+	45.7029i	3.19273	+	1.76303i
$673$	−9.94542	+	4.78946i	−0.383368	+	0.184620i	−0.615634	−	0.788032i	$-0.711100\pi$
$673$	−9.94542	+	4.78946i	−0.383368	+	0.184620i	0.232266	+	0.972652i	$0.425386\pi$
$674$	−14.7601	+	37.6082i	−0.568538	+	1.44861i
$675$	−1.92195	+	25.6467i	−0.0739761	+	0.987142i
$676$	5.55739	+	1.71423i	0.213746	+	0.0659318i
$677$	−3.35608	−	44.7837i	−0.128985	−	1.72118i	−0.568279	−	0.822836i	$-0.692391\pi$
$677$	−3.35608	−	44.7837i	−0.128985	−	1.72118i	0.439295	−	0.898343i	$-0.355228\pi$
$678$	1.56603	−	6.86121i	0.0601429	−	0.263503i
$679$	34.5859	−	3.25610i	1.32729	−	0.124958i
$680$	5.50960	+	24.1391i	0.211283	+	0.925693i
$681$	−31.7294	+	9.78721i	−1.21587	+	0.375047i
$682$	32.5245	+	82.8711i	1.24543	+	3.17330i
$683$	−3.79601	−	3.52219i	−0.145250	−	0.134773i	0.604201	−	0.796832i	$-0.293492\pi$
$683$	−3.79601	−	3.52219i	−0.145250	−	0.134773i	−0.749452	+	0.662059i	$0.769683\pi$
$684$	20.2698	+	13.8197i	0.775036	+	0.528411i
$685$	2.95128			0.112763
$686$	−49.2001	−	16.1295i	−1.87847	−	0.615826i
$687$	9.97422			0.380540
$688$	3.92344	+	2.67495i	0.149580	+	0.101982i
$689$	−7.64066	−	7.08950i	−0.291086	−	0.270088i
$690$	−3.00060	−	7.64540i	−0.114231	−	0.291055i
$691$	−27.2053	+	8.39172i	−1.03494	+	0.319236i	−0.765265	−	0.643716i	$-0.777392\pi$
$691$	−27.2053	+	8.39172i	−1.03494	+	0.319236i	−0.269673	+	0.962952i	$0.586916\pi$
$692$	−28.2973	−	123.979i	−1.07570	−	4.71296i
$693$	−15.4939	+	1.45867i	−0.588564	+	0.0554104i
$694$	14.3698	−	62.9583i	0.545471	−	2.38986i
$695$	−0.574772	−	7.66980i	−0.0218024	−	0.290932i
$696$	−56.8247	−	17.5281i	−2.15393	−	0.664400i
$697$	−1.52874	+	20.3996i	−0.0579050	+	0.772689i
$698$	−28.4815	+	72.5697i	−1.07804	+	2.74680i
$699$	1.47046	−	0.708135i	0.0556178	−	0.0267841i
$700$	−63.1114	−	34.8500i	−2.38539	−	1.31721i
$701$	−13.5723	−	6.53609i	−0.512620	−	0.246865i	0.159646	−	0.987174i	$-0.448965\pi$
$701$	−13.5723	−	6.53609i	−0.512620	−	0.246865i	−0.672266	+	0.740310i	$0.734679\pi$
$702$	11.2493	−	10.4378i	0.424576	−	0.393949i
$703$	18.7705	−	2.82919i	0.707942	−	0.106705i
$704$	−88.4333	+	153.171i	−3.33295	+	5.77285i
$705$	0.849941	+	1.47214i	0.0320106	+	0.0554440i
$706$	−19.2550	−	24.1450i	−0.724672	−	0.908710i
$707$	28.3354	+	21.7259i	1.06566	+	0.817088i
$708$	−31.3384	+	39.2971i	−1.17777	+	1.47688i
$709$	26.8736	+	4.05054i	1.00926	+	0.152121i	0.632802	−	0.774314i	$-0.281905\pi$
$709$	26.8736	+	4.05054i	1.00926	+	0.152121i	0.376456	+	0.926435i	$0.377143\pi$
$710$	13.5363	−	9.22890i	0.508009	−	0.346355i
$711$	7.57010	−	5.16121i	0.283901	−	0.193560i
$712$	−62.0484	−	9.35229i	−2.32536	−	0.350492i
$713$	−22.4174	+	28.1106i	−0.839540	+	1.05275i
$714$	−16.7078	−	33.0661i	−0.625275	−	1.23747i
$715$	−1.34024	−	1.68061i	−0.0501223	−	0.0628513i
$716$	−57.2370	−	99.1374i	−2.13905	−	3.70494i
$717$	−2.28763	+	3.96229i	−0.0854332	+	0.147975i
$718$	−68.0168	+	10.2519i	−2.53836	+	0.382597i
$719$	−16.9833	+	15.7582i	−0.633370	+	0.587682i	−0.930112	−	0.367276i	$-0.880290\pi$
$719$	−16.9833	+	15.7582i	−0.633370	+	0.587682i	0.296742	+	0.954958i	$0.404100\pi$
$720$	−14.1106	−	6.79533i	−0.525872	−	0.253247i
$721$	−19.9796	+	8.28446i	−0.744080	+	0.308530i
$722$	−28.8321	+	13.8848i	−1.07302	+	0.516739i
$723$	6.88045	−	17.5311i	0.255887	−	0.651989i
$724$	−7.95485	+	106.150i	−0.295640	+	3.94504i
$725$	20.6193	+	6.36023i	0.765783	+	0.236213i
$726$	0.932227	+	12.4397i	0.0345982	+	0.461681i
$727$	−2.56336	+	11.2308i	−0.0950696	+	0.416527i	−0.999958	−	0.00912088i	$-0.997097\pi$
$727$	−2.56336	+	11.2308i	−0.0950696	+	0.416527i	0.904889	+	0.425648i	$0.139954\pi$
$728$	8.83186	+	26.8064i	0.327331	+	0.993512i
$729$	−5.13202	−	22.4849i	−0.190075	−	0.832773i
$730$	−7.88357	+	2.43176i	−0.291784	+	0.0900034i
$731$	−0.394615	−	1.00546i	−0.0145954	−	0.0371884i
$732$	75.6010	+	70.1475i	2.79430	+	2.59273i
$733$	−36.0914	−	24.6067i	−1.33306	−	0.908868i	−0.333637	−	0.942701i	$-0.608276\pi$
$733$	−36.0914	−	24.6067i	−1.33306	−	0.908868i	−0.999427	+	0.0338333i	$0.989228\pi$
$734$	−12.5315			−0.462546
$735$	−4.59159	−	1.22669i	−0.169363	−	0.0452470i
$736$	−127.744			−4.70870
$737$	0.0518388	+	0.0353431i	0.00190950	+	0.00130188i
$738$	−15.5504	−	14.4287i	−0.572419	−	0.531127i
$739$	−6.02651	−	15.3553i	−0.221689	−	0.564853i	0.776151	−	0.630547i	$-0.217169\pi$
$739$	−6.02651	−	15.3553i	−0.221689	−	0.564853i	−0.997840	+	0.0656933i	$0.979074\pi$
$740$	−21.5304	+	6.64126i	−0.791474	+	0.244137i
$741$	−0.740249	−	3.24324i	−0.0271937	−	0.119144i
$742$	10.0348	−	76.4400i	0.368391	−	2.80620i
$743$	−8.91308	+	39.0508i	−0.326989	+	1.43263i	0.497848	+	0.867264i	$0.334124\pi$
$743$	−8.91308	+	39.0508i	−0.326989	+	1.43263i	−0.824838	+	0.565370i	$0.808734\pi$
$744$	−8.01809	−	106.994i	−0.293957	−	3.92259i
$745$	−3.99060	−	1.23094i	−0.146204	−	0.0450980i
$746$	3.57015	−	47.6403i	0.130712	−	1.74424i
$747$	−4.97550	+	12.6774i	−0.182044	+	0.463841i
$748$	83.0919	−	40.0150i	3.03814	−	1.46309i
$749$	−1.19668	−	7.02747i	−0.0437258	−	0.256778i
$750$	−16.5633	−	7.97648i	−0.604808	−	0.291260i
$751$	34.7458	−	32.2394i	1.26789	−	1.17643i	0.292424	−	0.956289i	$-0.405538\pi$
$751$	34.7458	−	32.2394i	1.26789	−	1.17643i	0.975468	−	0.220143i	$-0.0706524\pi$
$752$	45.0376	−	6.78833i	1.64235	−	0.247545i
$753$	−3.58067	+	6.20190i	−0.130487	+	0.226010i
$754$	−6.43758	−	11.1502i	−0.234443	−	0.406067i
$755$	3.71384	+	4.65701i	0.135161	+	0.169486i
$756$	82.6873	+	17.2210i	3.00731	+	0.626320i
$757$	−15.5068	+	19.4449i	−0.563603	+	0.706735i	−0.979219	−	0.202805i	$-0.934994\pi$
$757$	−15.5068	+	19.4449i	−0.563603	+	0.706735i	0.415617	+	0.909540i	$0.363566\pi$
$758$	−17.1800	−	2.58948i	−0.624007	−	0.0940540i
$759$	−16.5840	+	11.3068i	−0.601962	+	0.410411i
$760$	−13.5874	+	9.26376i	−0.492868	+	0.336032i
$761$	26.3930	+	3.97810i	0.956745	+	0.144206i	0.608813	−	0.793314i	$-0.291646\pi$
$761$	26.3930	+	3.97810i	0.956745	+	0.144206i	0.347932	+	0.937520i	$0.386884\pi$
$762$	32.9375	−	41.3024i	1.19320	−	1.49623i
$763$	0.474298	+	24.8702i	0.0171707	+	0.900361i
$764$	62.3937	+	78.2393i	2.25733	+	2.83060i
$765$	1.78123	+	3.08519i	0.0644007	+	0.111545i
$766$	25.7853	−	44.6614i	0.931661	−	1.61368i
$767$	−7.06031	+	1.06417i	−0.254933	+	0.0384250i
$768$	91.6924	−	85.0781i	3.30866	−	3.06999i
$769$	−28.1830	−	13.5722i	−1.01631	−	0.489427i	−0.149865	−	0.988706i	$-0.547884\pi$
$769$	−28.1830	−	13.5722i	−1.01631	−	0.489427i	−0.866441	+	0.499279i	$0.833598\pi$
$770$	4.39597	−	15.2799i	0.158420	−	0.550650i
$771$	−1.09411	+	0.526895i	−0.0394033	+	0.0189756i
$772$	10.1952	−	25.9770i	0.366934	−	0.934931i
$773$	0.0565074	−	0.754039i	0.00203243	−	0.0271209i	−0.996095	−	0.0882836i	$-0.971862\pi$
$773$	0.0565074	−	0.754039i	0.00203243	−	0.0271209i	0.998128	+	0.0611627i	$0.0194809\pi$
$774$	1.07031	+	0.330147i	0.0384715	+	0.0118669i
$775$	2.90944	+	38.8237i	0.104510	+	1.39459i
$776$	31.1677	−	136.555i	1.11886	−	4.90202i
$777$	18.9416	−	11.4229i	0.679526	−	0.409796i
$778$	4.57058	+	20.0250i	0.163863	+	0.717932i
$779$	−12.9833	+	4.00481i	−0.465174	+	0.143487i
$780$	1.44258	+	3.67564i	0.0516528	+	0.131609i
$781$	−29.3498	−	27.2326i	−1.05022	−	0.974459i
$782$	41.3584	+	28.1977i	1.47897	+	1.00835i
$783$	−25.2796			−0.903419
$784$	−75.5421	+	102.514i	−2.69793	+	3.66122i
$785$	8.07365			0.288161
$786$	−24.9019	−	16.9779i	−0.888223	−	0.605580i
$787$	12.3277	+	11.4385i	0.439437	+	0.407738i	0.868619	−	0.495480i	$-0.165008\pi$
$787$	12.3277	+	11.4385i	0.439437	+	0.407738i	−0.429183	+	0.903218i	$0.641198\pi$
$788$	−10.9176	−	27.8175i	−0.388922	−	0.990957i
$789$	−8.12015	+	2.50474i	−0.289085	+	0.0891710i
$790$	2.08296	+	9.12602i	0.0741082	+	0.324689i
$791$	5.15944	+	1.91222i	0.183449	+	0.0679909i
$792$	−13.9626	+	61.1740i	−0.496138	+	2.17372i
$793$	1.09482	+	14.6094i	0.0388782	+	0.518794i
$794$	27.8769	+	8.59888i	0.989314	+	0.305163i
$795$	0.528844	−	7.05693i	0.0187562	−	0.250284i
$796$	−26.9567	+	68.6844i	−0.955453	+	2.43446i
$797$	11.0268	−	5.31024i	0.390590	−	0.188098i	−0.228273	−	0.973597i	$-0.573308\pi$
$797$	11.0268	−	5.31024i	0.390590	−	0.188098i	0.618863	+	0.785499i	$0.287594\pi$
$798$	16.3894	−	18.3534i	0.580178	−	0.649702i
$799$	−9.33421	−	4.49512i	−0.330221	−	0.159026i
$800$	−101.398	+	94.0839i	−3.58497	+	3.32637i
$801$	−8.92756	+	1.34561i	−0.315440	+	0.0475449i
$802$	44.5230	−	77.1161i	1.57216	−	2.72306i
$803$	10.0810	+	17.4608i	0.355751	+	0.616179i
$804$	−0.0718566	−	0.0901053i	−0.00253419	−	0.00317777i
$805$	6.23207	−	1.54802i	0.219652	−	0.0545605i
$806$	14.4839	−	18.1622i	0.510172	−	0.639735i
$807$	−20.0704	−	3.02513i	−0.706512	−	0.106490i
$808$	118.950	−	81.0987i	4.18464	−	2.85304i
$809$	40.0768	−	27.3239i	1.40903	−	0.960657i	0.410210	−	0.911991i	$-0.365455\pi$
$809$	40.0768	−	27.3239i	1.40903	−	0.960657i	0.998815	−	0.0486662i	$-0.0154971\pi$
$810$	3.16265	+	0.476693i	0.111124	+	0.0167493i
$811$	−12.4755	+	15.6437i	−0.438073	+	0.549326i	−0.951034	−	0.309086i	$-0.899977\pi$
$811$	−12.4755	+	15.6437i	−0.438073	+	0.549326i	0.512961	+	0.858412i	$0.328548\pi$
$812$	29.5235	−	64.4205i	1.03607	−	2.26071i
$813$	11.4491	+	14.3567i	0.401537	+	0.503512i
$814$	36.9997	+	64.0854i	1.29684	+	2.24619i
$815$	1.65852	−	2.87264i	0.0580954	−	0.100624i
$816$	−90.0983	+	13.5801i	−3.15407	+	0.475400i
$817$	0.525888	−	0.487953i	0.0183985	−	0.0170713i
$818$	38.9053	+	18.7358i	1.36029	+	0.655082i
$819$	2.35113	+	3.31102i	0.0821550	+	0.115696i
$820$	14.5300	−	6.99728i	0.507410	−	0.244356i
$821$	17.2792	−	44.0268i	0.603049	−	1.53654i	−0.224102	−	0.974566i	$-0.571945\pi$
$821$	17.2792	−	44.0268i	0.603049	−	1.53654i	0.827152	−	0.561979i	$-0.189960\pi$
$822$	−1.33056	+	17.7551i	−0.0464086	+	0.619280i
$823$	45.5071	+	14.0371i	1.58628	+	0.489302i	0.957536	−	0.288312i	$-0.0930941\pi$
$823$	45.5071	+	14.0371i	1.58628	+	0.489302i	0.628742	+	0.777614i	$0.283570\pi$
$824$	6.51707	+	86.9642i	0.227033	+	3.02954i
$825$	−4.83628	+	21.1891i	−0.168378	+	0.737711i
$826$	−36.6532	−	38.0223i	−1.27533	−	1.32296i
$827$	8.95760	+	39.2458i	0.311486	+	1.36471i	0.852073	+	0.523423i	$0.175345\pi$
$827$	8.95760	+	39.2458i	0.311486	+	1.36471i	−0.540587	+	0.841288i	$0.681798\pi$
$828$	−36.9086	+	11.3848i	−1.28266	+	0.395649i
$829$	−18.9665	−	48.3258i	−0.658734	−	1.67843i	−0.732166	−	0.681126i	$-0.761491\pi$
$829$	−18.9665	−	48.3258i	−0.658734	−	1.67843i	0.0734328	−	0.997300i	$-0.476605\pi$
$830$	−10.1997	−	9.46390i	−0.354035	−	0.328497i
$831$	−1.52914	−	1.04255i	−0.0530451	−	0.0361656i
$832$	46.1517			1.60002
$833$	27.3331	−	9.58690i	0.947036	−	0.332166i
$834$	46.4011			1.60674
$835$	4.57183	+	3.11702i	0.158215	+	0.107869i
$836$	44.9021	+	41.6631i	1.55297	+	1.44095i
$837$	−16.6637	−	42.4583i	−0.575981	−	1.46758i
$838$	76.4339	−	23.5767i	2.64037	−	0.814445i
$839$	−7.67959	−	33.6465i	−0.265129	−	1.16161i	−0.915605	−	0.402079i	$-0.868288\pi$
$839$	−7.67959	−	33.6465i	−0.265129	−	1.16161i	0.650476	−	0.759527i	$-0.274569\pi$
$840$	−10.4908	+	16.0357i	−0.361966	+	0.553286i
$841$	1.73352	−	7.59503i	0.0597764	−	0.261898i
$842$	2.87775	+	38.4010i	0.0991740	+	1.32338i
$843$	−35.5766	−	10.9739i	−1.22532	−	0.377962i
$844$	−2.97563	+	39.7071i	−0.102425	+	1.36677i
$845$	−0.204925	+	0.522141i	−0.00704964	+	0.0179622i
$846$	9.67939	−	4.66135i	0.332784	−	0.160260i
$847$	−9.73813	−	0.543280i	−0.334606	−	0.0186673i
$848$	−170.835	−	82.2697i	−5.86649	−	2.82515i
$849$	−22.5917	+	20.9620i	−0.775345	+	0.719415i
$850$	53.5966	−	8.07838i	1.83835	−	0.277086i
$851$	−14.9432	+	25.8823i	−0.512246	+	0.887235i
$852$	36.7729	+	63.6926i	1.25982	+	2.18207i
$853$	5.98168	+	7.50079i	0.204809	+	0.256822i	0.873618	−	0.486612i	$-0.161767\pi$
$853$	5.98168	+	7.50079i	0.204809	+	0.256822i	−0.668810	+	0.743434i	$0.733196\pi$
$854$	−83.4181	+	69.1665i	−2.85451	+	2.36683i
$855$	−1.47524	+	1.84990i	−0.0504523	+	0.0632651i
$856$	−28.4215	−	4.28385i	−0.971426	−	0.146419i
$857$	−10.3635	+	7.06569i	−0.354009	+	0.241359i	−0.727246	−	0.686377i	$-0.759200\pi$
$857$	−10.3635	+	7.06569i	−0.354009	+	0.241359i	0.373237	+	0.927736i	$0.378248\pi$
$858$	10.7149	−	7.30529i	0.365801	−	0.249399i
$859$	47.3237	+	7.13290i	1.61466	+	0.243371i	0.893391	−	0.449280i	$-0.148319\pi$
$859$	47.3237	+	7.13290i	1.61466	+	0.243371i	0.721273	+	0.692651i	$0.243558\pi$
$860$	−0.530913	+	0.665744i	−0.0181040	+	0.0227017i
$861$	−12.1876	+	10.1054i	−0.415353	+	0.344392i
$862$	34.0861	+	42.7426i	1.16098	+	1.45582i
$863$	2.77702	+	4.80993i	0.0945307	+	0.163732i	0.909413	−	0.415895i	$-0.136532\pi$
$863$	2.77702	+	4.80993i	0.0945307	+	0.163732i	−0.814882	+	0.579627i	$0.803198\pi$
$864$	81.0262	−	140.341i	2.75657	−	4.77451i
$865$	12.1279	−	1.82799i	0.412362	−	0.0621535i
$866$	34.9954	−	32.4710i	1.18919	−	1.10341i
$867$	0.133698	+	0.0643855i	0.00454061	+	0.00218664i
$868$	127.659	+	7.12194i	4.33301	+	0.241734i
$869$	20.6108	−	9.92562i	0.699172	−	0.336704i
$870$	3.19365	−	8.13728i	0.108275	−	0.275880i
$871$	0.00122345	−	0.0163258i	4.14551e−5	−	0.000553180i
$872$	95.8384	+	29.5622i	3.24550	+	1.00110i
$873$	−1.50602	−	20.0965i	−0.0509712	−	0.680163i
$874$	−7.39797	+	32.4126i	−0.250240	+	1.09637i
$875$	7.86896	−	12.0282i	0.266019	−	0.406626i
$876$	−8.24126	−	36.1073i	−0.278446	−	1.21995i
$877$	−47.7914	+	14.7417i	−1.61380	+	0.497792i	−0.964798	−	0.262993i	$-0.915291\pi$
$877$	−47.7914	+	14.7417i	−1.61380	+	0.497792i	−0.649004	+	0.760785i	$0.724814\pi$
$878$	−30.0172	−	76.4826i	−1.01303	−	2.58116i
$879$	−24.6199	−	22.8439i	−0.830408	−	0.770506i
$880$	−32.3095	−	22.0283i	−1.08915	−	0.742572i
$881$	44.6564			1.50451			0.752256	−	0.658871i	$-0.228966\pi$
$881$	44.6564			1.50451			0.752256	+	0.658871i	$0.228966\pi$
$882$	−9.89961	+	28.3585i	−0.333337	+	0.954881i
$883$	25.0779			0.843937			0.421969	−	0.906610i	$-0.361339\pi$
$883$	25.0779			0.843937			0.421969	+	0.906610i	$0.361339\pi$
$884$	−19.8837	−	13.5565i	−0.668761	−	0.455954i
$885$	−3.55363	−	3.29729i	−0.119454	−	0.110837i
$886$	−10.8846	−	27.7336i	−0.365676	−	0.931727i
$887$	−17.6670	+	5.44953i	−0.593198	+	0.182977i	−0.576796	−	0.816888i	$-0.695697\pi$
$887$	−17.6670	+	5.44953i	−0.593198	+	0.182977i	−0.0164020	+	0.999865i	$0.505221\pi$
$888$	−19.8455	−	86.9489i	−0.665972	−	2.91781i
$889$	28.6657	+	29.7364i	0.961416	+	0.997326i
$890$	2.05255	−	8.99283i	0.0688018	−	0.301440i
$891$	−0.584117	−	7.79449i	−0.0195686	−	0.261125i
$892$	−27.9892	−	8.63352i	−0.937147	−	0.289072i
$893$	0.514217	−	6.86175i	0.0172076	−	0.229620i
$894$	9.20450	−	23.4527i	0.307845	−	0.784375i
$895$	9.94734	−	4.79039i	0.332503	−	0.160125i
$896$	107.197	+	150.962i	3.58119	+	5.04327i
$897$	4.71886	+	2.27248i	0.157558	+	0.0758759i
$898$	−33.4579	+	31.0444i	−1.11650	+	1.03596i
$899$	−37.8406	+	5.70355i	−1.26205	+	0.190224i
$900$	−20.9118	+	36.2202i	−0.697059	+	1.20734i
$901$	21.5651	+	37.3518i	0.718437	+	1.24437i
$902$	−33.0236	−	41.4103i	−1.09957	−	1.37881i
$903$	0.348277	−	0.759941i	0.0115899	−	0.0252893i
$904$	13.8325	−	17.3454i	0.460062	−	0.576899i
$905$	−10.1519	−	1.53016i	−0.337462	−	0.0508641i
$906$	−29.6912	+	20.2431i	−0.986424	+	0.672533i
$907$	−20.5824	+	14.0329i	−0.683428	+	0.465954i	−0.854599	−	0.519288i	$-0.826197\pi$
$907$	−20.5824	+	14.0329i	−0.683428	+	0.465954i	0.171171	+	0.985241i	$0.445245\pi$
$908$	−157.756	−	23.7780i	−5.23533	−	0.789099i
$909$	12.9149	−	16.1947i	0.428359	−	0.537146i
$910$	−4.02653	+	1.00017i	−0.133478	+	0.0331554i
$911$	1.47816	+	1.85356i	0.0489738	+	0.0614112i	0.805715	−	0.592303i	$-0.201781\pi$
$911$	1.47816	+	1.85356i	0.0489738	+	0.0614112i	−0.756741	+	0.653714i	$0.773210\pi$
$912$	−30.2585	−	52.4093i	−1.00196	−	1.73545i
$913$	−17.0018	+	29.4481i	−0.562679	+	0.974589i
$914$	−14.1949	+	2.13954i	−0.469526	+	0.0707696i
$915$	−7.29152	+	6.76554i	−0.241050	+	0.223662i
$916$	43.1774	+	20.7931i	1.42662	+	0.687024i
$917$	15.6954	−	17.5762i	0.518308	−	0.580418i
$918$	−57.2115	+	27.5516i	−1.88826	+	0.909339i
$919$	−8.74913	+	22.2924i	−0.288607	+	0.735359i	0.710879	+	0.703314i	$0.248297\pi$
$919$	−8.74913	+	22.2924i	−0.288607	+	0.735359i	−0.999486	+	0.0320449i	$0.989798\pi$
$920$	1.93485	−	25.8188i	0.0637901	−	0.851220i
$921$	−6.24939	−	1.92768i	−0.205924	−	0.0635192i
$922$	1.47721	+	19.7120i	0.0486494	+	0.649182i
$923$	−2.32479	+	10.1856i	−0.0765213	+	0.335262i
$924$	66.9272	+	24.8050i	2.20174	+	0.816024i
$925$	7.20113	+	31.5502i	0.236772	+	1.03736i
$926$	−59.9511	+	18.4925i	−1.97012	+	0.607700i
$927$	4.58414	+	11.6802i	0.150563	+	0.383628i
$928$	−99.6675	−	92.4779i	−3.27174	−	3.03574i
$929$	32.6189	+	22.2392i	1.07019	+	0.729645i	0.964321	−	0.264735i	$-0.0852846\pi$
$929$	32.6189	+	22.2392i	1.07019	+	0.729645i	0.105871	+	0.994380i	$0.466237\pi$
$930$	15.7721			0.517189
$931$	12.5596	+	14.5728i	0.411625	+	0.477605i
$932$	7.84170			0.256863
$933$	16.5126	+	11.2581i	0.540598	+	0.368574i
$934$	28.1451	+	26.1149i	0.920936	+	0.854504i
$935$	3.24966	+	8.27999i	0.106275	+	0.270785i
$936$	15.6459	−	4.82612i	0.511402	−	0.157747i
$937$	−0.476306	−	2.08683i	−0.0155602	−	0.0681738i	0.966552	−	0.256472i	$-0.0825601\pi$
$937$	−0.476306	−	2.08683i	−0.0155602	−	0.0681738i	−0.982112	+	0.188298i	$0.939703\pi$
$938$	0.103698	−	0.0625361i	0.00338585	−	0.00204188i
$939$	1.71972	−	7.53459i	0.0561209	−	0.245882i
$940$	0.610354	+	8.14461i	0.0199076	+	0.265648i
$941$	−11.4750	−	3.53956i	−0.374073	−	0.115386i	0.102017	−	0.994783i	$-0.467470\pi$
$941$	−11.4750	−	3.53956i	−0.374073	−	0.115386i	−0.476091	+	0.879396i	$0.657947\pi$
$942$	−3.63994	+	48.5716i	−0.118596	+	1.58255i
$943$	7.81517	−	19.9127i	0.254497	−	0.648448i
$944$	−117.026	+	56.3567i	−3.80887	+	1.83425i
$945$	−2.25224	+	7.82855i	−0.0732654	+	0.254663i
$946$	2.51967	+	1.21341i	0.0819215	+	0.0394513i
$947$	25.5649	−	23.7207i	0.830746	−	0.770820i	−0.145068	−	0.989422i	$-0.546340\pi$
$947$	25.5649	−	23.7207i	0.830746	−	0.770820i	0.975814	+	0.218602i	$0.0701496\pi$
$948$	−41.5523	+	6.26299i	−1.34955	+	0.203413i
$949$	2.63055	−	4.55625i	0.0853913	−	0.147902i
$950$	17.9998	+	31.1766i	0.583991	+	1.01150i
$951$	4.45837	+	5.59062i	0.144573	+	0.181288i
$952$	−2.22687	−	116.768i	−0.0721732	−	3.78446i
$953$	−23.6128	+	29.6095i	−0.764893	+	0.959145i	−0.999918	−	0.0128440i	$-0.995912\pi$
$953$	−23.6128	+	29.6095i	−0.764893	+	0.959145i	0.235025	+	0.971989i	$0.424483\pi$
$954$	−44.2256	−	6.66593i	−1.43186	−	0.215818i
$955$	−7.97457	+	5.43697i	−0.258051	+	0.175936i
$956$	−18.1631	+	12.3834i	−0.587436	+	0.400507i
$957$	−21.1244	−	3.18400i	−0.682856	−	0.102924i
$958$	22.4815	−	28.1909i	0.726343	−	0.910805i
$959$	−13.6283	−	2.83832i	−0.440082	−	0.0916541i
$960$	19.5368	+	24.4984i	0.630547	+	0.790681i
$961$	−19.0230	−	32.9487i	−0.613644	−	1.06286i
$962$	9.65475	−	16.7225i	0.311282	−	0.539155i
$963$	−4.08930	+	0.616363i	−0.131776	+	0.0198620i
$964$	66.3317	−	61.5468i	2.13640	−	1.98229i
$965$	2.42492	+	1.16778i	0.0780609	+	0.0375922i
$966$	6.50330	+	38.1904i	0.209240	+	1.22876i
$967$	30.5040	−	14.6899i	0.980942	−	0.472397i	0.126513	−	0.991965i	$-0.459621\pi$
$967$	30.5040	−	14.6899i	0.980942	−	0.472397i	0.854429	+	0.519568i	$0.173907\pi$
$968$	−14.3670	+	36.6066i	−0.461774	+	1.17658i
$969$	−1.02870	+	13.7270i	−0.0330465	+	0.440975i
$970$	19.6749	+	6.06891i	0.631723	+	0.194861i
$971$	−0.0125891	−	0.167990i	−0.000404004	−	0.00539106i	0.996998	−	0.0774254i	$-0.0246699\pi$
$971$	−0.0125891	−	0.167990i	−0.000404004	−	0.00539106i	−0.997402	+	0.0720343i	$0.977051\pi$
$972$	18.1160	−	79.3713i	0.581070	−	2.54583i
$973$	−4.72207	+	35.9701i	−0.151383	+	1.15315i
$974$	−5.04541	−	22.1054i	−0.161665	−	0.708303i
$975$	5.41935	−	1.67165i	0.173558	−	0.0535356i
$976$	97.3680	+	248.090i	3.11667	+	7.94115i
$977$	−11.1561	−	10.3513i	−0.356914	−	0.331168i	0.481253	−	0.876582i	$-0.340182\pi$
$977$	−11.1561	−	10.3513i	−0.356914	−	0.331168i	−0.838167	+	0.545414i	$0.816372\pi$
$978$	16.5343	+	11.2729i	0.528707	+	0.360466i
$979$	−22.5423			−0.720456
$980$	−17.3193	−	14.8822i	−0.553244	−	0.475396i
$981$	14.4304			0.460727
$982$	65.1164	+	44.3956i	2.07795	+	1.41672i
$983$	−5.05435	−	4.68975i	−0.161209	−	0.149580i	0.595444	−	0.803397i	$-0.296976\pi$
$983$	−5.05435	−	4.68975i	−0.161209	−	0.149580i	−0.756653	+	0.653817i	$0.773167\pi$
$984$	23.3215	+	59.4223i	0.743463	+	1.89431i
$985$	2.75411	−	0.849530i	0.0877532	−	0.0270683i
$986$	11.8552	+	51.9409i	0.377546	+	1.65414i
$987$	−2.50904	−	7.61542i	−0.0798635	−	0.242401i
$988$	3.55669	−	15.5829i	0.113153	−	0.495757i
$989$	0.0844061	+	1.12632i	0.00268396	+	0.0358149i
$990$	−8.81401	−	2.71876i	−0.280128	−	0.0864079i
$991$	−3.89806	+	52.0160i	−0.123826	+	1.65234i	0.496529	+	0.868020i	$0.334608\pi$
$991$	−3.89806	+	52.0160i	−0.123826	+	1.65234i	−0.620355	+	0.784322i	$0.713011\pi$
$992$	89.6230	−	228.356i	2.84553	−	7.25030i
$993$	−35.4942	+	17.0931i	−1.12637	+	0.542433i
$994$	−71.3832	+	29.5987i	−2.26414	+	0.938815i
$995$	−6.41161	−	3.08767i	−0.203262	−	0.0978857i
$996$	45.7877	−	42.4848i	1.45084	−	1.34618i
$997$	−1.02402	+	0.154347i	−0.0324311	+	0.00488820i	−0.165238	−	0.986254i	$-0.552839\pi$
$997$	−1.02402	+	0.154347i	−0.0324311	+	0.00488820i	0.132807	+	0.991142i	$0.457601\pi$
$998$	11.9142	−	20.6360i	0.377138	−	0.653222i
$999$	−18.9565	−	32.8336i	−0.599758	−	1.03881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.1	✓	348
49.37	even	21	inner	637.2.bl.b.625.1	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.1	✓	348	1.1	even	1	trivial
637.2.bl.b.625.1	yes	348	49.37	even	21	inner

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30989 - 1.57486i) q^{2} +(0.887307 + 0.823300i) q^{3} +(2.12474 + 5.41374i) q^{4} +(-0.535995 + 0.165332i) q^{5} +(-0.753001 - 3.29911i) q^{6} +(2.63410 - 0.247988i) q^{7} +(2.37377 - 10.4002i) q^{8} +(-0.114700 - 1.53057i) q^{9} +O(q^{10})\)	\(q+(-2.30989 - 1.57486i) q^{2} +(0.887307 + 0.823300i) q^{3} +(2.12474 + 5.41374i) q^{4} +(-0.535995 + 0.165332i) q^{5} +(-0.753001 - 3.29911i) q^{6} +(2.63410 - 0.247988i) q^{7} +(2.37377 - 10.4002i) q^{8} +(-0.114700 - 1.53057i) q^{9} +(1.49846 + 0.462215i) q^{10} +(0.286387 - 3.82157i) q^{11} +(-2.57184 + 6.55295i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-6.47504 - 3.57551i) q^{14} +(-0.611710 - 0.294584i) q^{15} +(-13.3354 + 12.3734i) q^{16} +(4.09173 - 0.616729i) q^{17} +(-2.14548 + 3.71609i) q^{18} +(1.37416 + 2.38012i) q^{19} +(-2.03392 - 2.55045i) q^{20} +(2.54143 + 1.94862i) q^{21} +(-6.67994 + 8.37638i) q^{22} +(-4.27868 - 0.644907i) q^{23} +(10.6687 - 7.27380i) q^{24} +(-3.87124 + 2.63937i) q^{25} +(2.76444 + 0.416673i) q^{26} +(3.42241 - 4.29157i) q^{27} +(6.93932 + 13.7334i) q^{28} +(-2.87142 - 3.60064i) q^{29} +(0.949056 + 1.64381i) q^{30} +(4.15469 - 7.19614i) q^{31} +(29.1927 - 4.40009i) q^{32} +(3.40041 - 3.15512i) q^{33} +(-10.4227 - 5.01931i) q^{34} +(-1.37087 + 0.568423i) q^{35} +(8.04241 - 3.87302i) q^{36} +(2.52339 - 6.42948i) q^{37} +(0.574182 - 7.66192i) q^{38} +(-1.15665 - 0.356780i) q^{39} +(0.447156 + 5.96689i) q^{40} +(-1.10008 + 4.81975i) q^{41} +(-2.80162 - 8.50347i) q^{42} +(-0.0580847 - 0.254486i) q^{43} +(21.2975 - 6.56940i) q^{44} +(0.314532 + 0.801414i) q^{45} +(8.86764 + 8.22797i) q^{46} +(-2.06866 - 1.41039i) q^{47} -22.0196 q^{48} +(6.87700 - 1.30645i) q^{49} +13.0988 q^{50} +(4.13837 + 2.82149i) q^{51} +(-4.26326 - 3.95572i) q^{52} +(3.80798 + 9.70257i) q^{53} +(-14.6640 + 4.52325i) q^{54} +(0.478327 + 2.09569i) q^{55} +(3.67363 - 27.9837i) q^{56} +(-0.740249 + 3.24324i) q^{57} +(0.962162 + 12.8392i) q^{58} +(6.82284 + 2.10457i) q^{59} +(0.295079 - 3.93755i) q^{60} +(5.35236 - 13.6376i) q^{61} +(-20.9298 + 10.0792i) q^{62} +(-0.681696 - 4.00324i) q^{63} +(-41.5813 - 20.0245i) q^{64} +(0.411180 - 0.381519i) q^{65} +(-12.8234 + 1.93282i) q^{66} +(-0.00818581 + 0.0141782i) q^{67} +(12.0327 + 20.8412i) q^{68} +(-3.26555 - 4.09487i) q^{69} +(4.06173 + 0.845921i) q^{70} +(6.51391 - 8.16818i) q^{71} +(-16.1904 - 2.44032i) q^{72} +(-4.34693 + 2.96368i) q^{73} +(-15.9543 + 10.8774i) q^{74} +(-5.60797 - 0.845265i) q^{75} +(-9.96562 + 12.4965i) q^{76} +(-0.193330 - 10.1374i) q^{77} +(2.10986 + 2.64568i) q^{78} +(2.98467 + 5.16960i) q^{79} +(5.10196 - 8.83686i) q^{80} +(2.01683 - 0.303988i) q^{81} +(10.1315 - 9.40064i) q^{82} +(-7.99426 - 3.84983i) q^{83} +(-5.14945 + 17.8989i) q^{84} +(-2.09118 + 1.00706i) q^{85} +(-0.266609 + 0.679309i) q^{86} +(0.416583 - 5.55891i) q^{87} +(-39.0651 - 12.0500i) q^{88} +(-0.439579 - 5.86577i) q^{89} +(0.535578 - 2.34652i) q^{90} +(-2.26565 + 1.36632i) q^{91} +(-5.59971 - 24.5339i) q^{92} +(9.61107 - 2.96462i) q^{93} +(2.55721 + 6.51568i) q^{94} +(-1.13005 - 1.04854i) q^{95} +(29.5255 + 20.1301i) q^{96} +13.1301 q^{97} +(-17.9426 - 7.81253i) q^{98} -5.88203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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