LMFDB - Embedded newform 637.2.w.b.92.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(92,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.w (of order $7$, degree $6$, 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:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			92.7
Character	$\chi$	$=$	637.92
Dual form			637.2.w.b.547.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12298 + 1.40817i) q^{2} +(-2.74049 - 1.31975i) q^{3} +(-0.276823 - 1.21284i) q^{4} +(-2.53396 - 1.22029i) q^{5} +(4.93595 - 2.37703i) q^{6} +(-1.05285 - 2.42724i) q^{7} +(-1.22675 - 0.590772i) q^{8} +(3.89808 + 4.88803i) q^{9} +O(q^{10})$	\(q+(-1.12298 + 1.40817i) q^{2} +(-2.74049 - 1.31975i) q^{3} +(-0.276823 - 1.21284i) q^{4} +(-2.53396 - 1.22029i) q^{5} +(4.93595 - 2.37703i) q^{6} +(-1.05285 - 2.42724i) q^{7} +(-1.22675 - 0.590772i) q^{8} +(3.89808 + 4.88803i) q^{9} +(4.56397 - 2.19789i) q^{10} +(3.17207 - 3.97765i) q^{11} +(-0.842016 + 3.68912i) q^{12} +(0.623490 - 0.781831i) q^{13} +(4.60030 + 1.24316i) q^{14} +(5.33382 + 6.68840i) q^{15} +(4.45119 - 2.14358i) q^{16} +(1.01853 - 4.46247i) q^{17} -11.2607 q^{18} -6.08955 q^{19} +(-0.778561 + 3.41110i) q^{20} +(-0.318042 + 8.04133i) q^{21} +(2.03904 + 8.93364i) q^{22} +(-1.71384 - 7.50884i) q^{23} +(2.58223 + 3.23801i) q^{24} +(1.81441 + 2.27520i) q^{25} +(0.400787 + 1.75596i) q^{26} +(-2.20112 - 9.64374i) q^{27} +(-2.65241 + 1.94885i) q^{28} +(-0.224524 + 0.983705i) q^{29} -15.4082 q^{30} -3.95981 q^{31} +(-1.37410 + 6.02033i) q^{32} +(-13.9425 + 6.71437i) q^{33} +(5.14014 + 6.44553i) q^{34} +(-0.294074 + 7.43533i) q^{35} +(4.84933 - 6.08087i) q^{36} +(-1.78303 + 7.81196i) q^{37} +(6.83844 - 8.57513i) q^{38} +(-2.74049 + 1.31975i) q^{39} +(2.38763 + 2.99399i) q^{40} +(-1.56938 - 0.755772i) q^{41} +(-10.9664 - 9.47811i) q^{42} +(1.64536 - 0.792362i) q^{43} +(-5.70236 - 2.74611i) q^{44} +(-3.91275 - 17.1429i) q^{45} +(12.4984 + 6.01889i) q^{46} +(5.86258 - 7.35144i) q^{47} -15.0274 q^{48} +(-4.78303 + 5.11103i) q^{49} -5.24141 q^{50} +(-8.68062 + 10.8852i) q^{51} +(-1.12083 - 0.539765i) q^{52} +(-1.60188 - 7.01827i) q^{53} +(16.0519 + 7.73017i) q^{54} +(-12.8918 + 6.20837i) q^{55} +(-0.142368 + 3.59962i) q^{56} +(16.6884 + 8.03669i) q^{57} +(-1.13309 - 1.42085i) q^{58} +(-4.78645 + 2.30503i) q^{59} +(6.63544 - 8.32058i) q^{60} +(0.909421 - 3.98443i) q^{61} +(4.44678 - 5.57609i) q^{62} +(7.76038 - 14.6079i) q^{63} +(-0.773936 - 0.970485i) q^{64} +(-2.53396 + 1.22029i) q^{65} +(6.20219 - 27.1736i) q^{66} -8.62043 q^{67} -5.69422 q^{68} +(-5.21303 + 22.8398i) q^{69} +(-10.1400 - 8.76383i) q^{70} +(1.07385 + 4.70483i) q^{71} +(-1.89425 - 8.29927i) q^{72} +(0.202349 + 0.253737i) q^{73} +(-8.99828 - 11.2835i) q^{74} +(-1.96968 - 8.62972i) q^{75} +(1.68573 + 7.38565i) q^{76} +(-12.9944 - 3.51153i) q^{77} +(1.21908 - 5.34113i) q^{78} +12.6847 q^{79} -13.8949 q^{80} +(-2.52156 + 11.0477i) q^{81} +(2.82663 - 1.36123i) q^{82} +(-4.50824 - 5.65316i) q^{83} +(9.84090 - 1.84029i) q^{84} +(-8.02644 + 10.0648i) q^{85} +(-0.731920 + 3.20675i) q^{86} +(1.91355 - 2.39952i) q^{87} +(-6.24122 + 3.00561i) q^{88} +(6.12777 + 7.68398i) q^{89} +(28.5341 + 13.7413i) q^{90} +(-2.55413 - 0.690214i) q^{91} +(-8.63260 + 4.15724i) q^{92} +(10.8518 + 5.22596i) q^{93} +(3.76854 + 16.5110i) q^{94} +(15.4307 + 7.43103i) q^{95} +(11.7111 - 14.6852i) q^{96} +4.58831 q^{97} +(-1.82597 - 12.4749i) q^{98} +31.8079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) $ 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−1.12298	+	1.40817i	−0.794066	+	0.995728i	0.205787	+	0.978597i	$0.434025\pi$
$2$	−1.12298	+	1.40817i	−0.794066	+	0.995728i	−0.999853	+	0.0171310i	$0.994547\pi$
$3$	−2.74049	−	1.31975i	−1.58222	−	0.761958i	−0.583482	−	0.812126i	$-0.698310\pi$
$3$	−2.74049	−	1.31975i	−1.58222	−	0.761958i	−0.998741	+	0.0501676i	$0.984024\pi$
$4$	−0.276823	−	1.21284i	−0.138411	−	0.606420i
$5$	−2.53396	−	1.22029i	−1.13322	−	0.545731i	−0.229270	−	0.973363i	$-0.573634\pi$
$5$	−2.53396	−	1.22029i	−1.13322	−	0.545731i	−0.903953	+	0.427632i	$0.859348\pi$
$6$	4.93595	−	2.37703i	2.01509	−	0.970418i
$7$	−1.05285	−	2.42724i	−0.397939	−	0.917412i
$7$	−1.05285	−	2.42724i	−0.397939	−	0.917412i
$8$	−1.22675	−	0.590772i	−0.433722	−	0.208869i
$9$	3.89808	+	4.88803i	1.29936	+	1.62934i
$10$	4.56397	−	2.19789i	1.44325	−	0.695035i
$11$	3.17207	−	3.97765i	0.956415	−	1.19931i	−0.0234663	−	0.999725i	$-0.507470\pi$
$11$	3.17207	−	3.97765i	0.956415	−	1.19931i	0.979881	−	0.199582i	$-0.0639583\pi$
$12$	−0.842016	+	3.68912i	−0.243069	+	1.06496i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$14$	4.60030	+	1.24316i	1.22948	+	0.332248i
$15$	5.33382	+	6.68840i	1.37719	+	1.72694i
$16$	4.45119	−	2.14358i	1.11280	−	0.535895i
$17$	1.01853	−	4.46247i	0.247030	−	1.08231i	−0.687433	−	0.726248i	$-0.741263\pi$
$17$	1.01853	−	4.46247i	0.247030	−	1.08231i	0.934463	−	0.356061i	$-0.115880\pi$
$18$	−11.2607			−2.65416
$19$	−6.08955			−1.39704			−0.698519	−	0.715591i	$-0.746157\pi$
$19$	−6.08955			−1.39704			−0.698519	+	0.715591i	$0.746157\pi$
$20$	−0.778561	+	3.41110i	−0.174092	+	0.762745i
$21$	−0.318042	+	8.04133i	−0.0694024	+	1.75476i
$22$	2.03904	+	8.93364i	0.434726	+	1.90466i
$23$	−1.71384	−	7.50884i	−0.357361	−	1.56570i	−0.759739	−	0.650228i	$-0.774673\pi$
$23$	−1.71384	−	7.50884i	−0.357361	−	1.56570i	0.402378	−	0.915474i	$-0.368184\pi$
$24$	2.58223	+	3.23801i	0.527095	+	0.660956i
$25$	1.81441	+	2.27520i	0.362882	+	0.455039i
$26$	0.400787	+	1.75596i	0.0786008	+	0.344372i
$27$	−2.20112	−	9.64374i	−0.423606	−	1.85594i
$28$	−2.65241	+	1.94885i	−0.501258	+	0.368298i
$29$	−0.224524	+	0.983705i	−0.0416931	+	0.182669i	−0.991487	−	0.130208i	$-0.958436\pi$
$29$	−0.224524	+	0.983705i	−0.0416931	+	0.182669i	0.949794	+	0.312877i	$0.101293\pi$
$30$	−15.4082			−2.81314
$31$	−3.95981			−0.711203			−0.355601	−	0.934638i	$-0.615724\pi$
$31$	−3.95981			−0.711203			−0.355601	+	0.934638i	$0.615724\pi$
$32$	−1.37410	+	6.02033i	−0.242909	+	1.06425i
$33$	−13.9425	+	6.71437i	−2.42708	+	1.16882i
$34$	5.14014	+	6.44553i	0.881526	+	1.10540i
$35$	−0.294074	+	7.43533i	−0.0497075	+	1.25680i
$36$	4.84933	−	6.08087i	0.808221	−	1.01348i
$37$	−1.78303	+	7.81196i	−0.293128	+	1.28428i	0.587017	+	0.809574i	$0.300302\pi$
$37$	−1.78303	+	7.81196i	−0.293128	+	1.28428i	−0.880145	+	0.474704i	$0.842555\pi$
$38$	6.83844	−	8.57513i	1.10934	−	1.39107i
$39$	−2.74049	+	1.31975i	−0.438830	+	0.211329i
$40$	2.38763	+	2.99399i	0.377517	+	0.473391i
$41$	−1.56938	−	0.755772i	−0.245095	−	0.118032i	0.307304	−	0.951611i	$-0.400573\pi$
$41$	−1.56938	−	0.755772i	−0.245095	−	0.118032i	−0.552399	+	0.833580i	$0.686288\pi$
$42$	−10.9664	−	9.47811i	−1.69216	−	1.46250i
$43$	1.64536	−	0.792362i	0.250915	−	0.120834i	−0.304199	−	0.952608i	$-0.598389\pi$
$43$	1.64536	−	0.792362i	0.250915	−	0.120834i	0.555114	+	0.831774i	$0.312675\pi$
$44$	−5.70236	−	2.74611i	−0.859662	−	0.413992i
$45$	−3.91275	−	17.1429i	−0.583279	−	2.55551i
$46$	12.4984	+	6.01889i	1.84278	+	0.887437i
$47$	5.86258	−	7.35144i	0.855145	−	1.07232i	−0.141457	−	0.989944i	$-0.545179\pi$
$47$	5.86258	−	7.35144i	0.855145	−	1.07232i	0.996602	−	0.0823733i	$-0.0262500\pi$
$48$	−15.0274			−2.16902
$49$	−4.78303	+	5.11103i	−0.683290	+	0.730147i
$50$	−5.24141			−0.741247
$51$	−8.68062	+	10.8852i	−1.21553	+	1.52423i
$52$	−1.12083	−	0.539765i	−0.155432	−	0.0748519i
$53$	−1.60188	−	7.01827i	−0.220034	−	0.964034i	−0.957451	−	0.288596i	$-0.906812\pi$
$53$	−1.60188	−	7.01827i	−0.220034	−	0.964034i	0.737417	−	0.675438i	$-0.236045\pi$
$54$	16.0519	+	7.73017i	2.18438	+	1.05194i
$55$	−12.8918	+	6.20837i	−1.73833	+	0.837136i
$56$	−0.142368	+	3.59962i	−0.0190247	+	0.481019i
$57$	16.6884	+	8.03669i	2.21043	+	1.06449i
$58$	−1.13309	−	1.42085i	−0.148782	−	0.186567i
$59$	−4.78645	+	2.30503i	−0.623142	+	0.300090i	−0.718685	−	0.695336i	$-0.755256\pi$
$59$	−4.78645	+	2.30503i	−0.623142	+	0.300090i	0.0955426	+	0.995425i	$0.469541\pi$
$60$	6.63544	−	8.32058i	0.856631	−	1.07418i
$61$	0.909421	−	3.98443i	0.116439	−	0.510154i	−0.882748	−	0.469847i	$-0.844309\pi$
$61$	0.909421	−	3.98443i	0.116439	−	0.510154i	0.999187	−	0.0403074i	$-0.0128337\pi$
$62$	4.44678	−	5.57609i	0.564742	−	0.708164i
$63$	7.76038	−	14.6079i	0.977715	−	1.84043i
$64$	−0.773936	−	0.970485i	−0.0967420	−	0.121311i
$65$	−2.53396	+	1.22029i	−0.314299	+	0.151359i
$66$	6.20219	−	27.1736i	0.763437	−	3.34484i
$67$	−8.62043			−1.05315			−0.526577	−	0.850128i	$-0.676525\pi$
$67$	−8.62043			−1.05315			−0.526577	+	0.850128i	$0.676525\pi$
$68$	−5.69422			−0.690525
$69$	−5.21303	+	22.8398i	−0.627574	+	2.74958i
$70$	−10.1400	−	8.76383i	−1.21196	−	1.04748i
$71$	1.07385	+	4.70483i	0.127442	+	0.558360i	0.997821	+	0.0659779i	$0.0210167\pi$
$71$	1.07385	+	4.70483i	0.127442	+	0.558360i	−0.870379	+	0.492382i	$0.836126\pi$
$72$	−1.89425	−	8.29927i	−0.223240	−	0.978079i
$73$	0.202349	+	0.253737i	0.0236831	+	0.0296977i	0.793532	−	0.608528i	$-0.208240\pi$
$73$	0.202349	+	0.253737i	0.0236831	+	0.0296977i	−0.769849	+	0.638226i	$0.779668\pi$
$74$	−8.99828	−	11.2835i	−1.04603	−	1.31168i
$75$	−1.96968	−	8.62972i	−0.227439	−	0.996474i
$76$	1.68573	+	7.38565i	0.193366	+	0.847192i
$77$	−12.9944	−	3.51153i	−1.48085	−	0.400176i
$78$	1.21908	−	5.34113i	0.138034	−	0.604764i
$79$	12.6847			1.42714			0.713568	−	0.700586i	$-0.247078\pi$
$79$	12.6847			1.42714			0.713568	+	0.700586i	$0.247078\pi$
$80$	−13.8949			−1.55350
$81$	−2.52156	+	11.0477i	−0.280173	+	1.22752i
$82$	2.82663	−	1.36123i	0.312149	−	0.150323i
$83$	−4.50824	−	5.65316i	−0.494844	−	0.620515i	0.470213	−	0.882553i	$-0.344177\pi$
$83$	−4.50824	−	5.65316i	−0.494844	−	0.620515i	−0.965058	+	0.262038i	$0.915605\pi$
$84$	9.84090	−	1.84029i	1.07373	−	0.200792i
$85$	−8.02644	+	10.0648i	−0.870589	+	1.09168i
$86$	−0.731920	+	3.20675i	−0.0789250	+	0.345793i
$87$	1.91355	−	2.39952i	0.205154	−	0.257255i
$88$	−6.24122	+	3.00561i	−0.665316	+	0.320400i
$89$	6.12777	+	7.68398i	0.649542	+	0.814500i	0.992160	−	0.124975i	$-0.0398850\pi$
$89$	6.12777	+	7.68398i	0.649542	+	0.814500i	−0.342618	+	0.939475i	$0.611314\pi$
$90$	28.5341	+	13.7413i	3.00776	+	1.44846i
$91$	−2.55413	−	0.690214i	−0.267746	−	0.0723540i
$92$	−8.63260	+	4.15724i	−0.900010	+	0.433422i
$93$	10.8518	+	5.22596i	1.12528	+	0.541907i
$94$	3.76854	+	16.5110i	0.388695	+	1.70298i
$95$	15.4307	+	7.43103i	1.58316	+	0.762408i
$96$	11.7111	−	14.6852i	1.19525	−	1.49880i
$97$	4.58831			0.465873			0.232936	−	0.972492i	$-0.425167\pi$
$97$	4.58831			0.465873			0.232936	+	0.972492i	$0.425167\pi$
$98$	−1.82597	−	12.4749i	−0.184450	−	1.26016i
$99$	31.8079			3.19681
$100$	2.25718	−	2.83041i	0.225718	−	0.283041i
$101$	−6.02431	−	2.90115i	−0.599441	−	0.288676i	0.109451	−	0.993992i	$-0.465091\pi$
$101$	−6.02431	−	2.90115i	−0.599441	−	0.288676i	−0.708892	+	0.705317i	$0.750805\pi$
$102$	−5.58001	−	24.4476i	−0.552503	−	2.42067i
$103$	9.23015	+	4.44501i	0.909474	+	0.437979i	0.829301	−	0.558802i	$-0.188739\pi$
$103$	9.23015	+	4.44501i	0.909474	+	0.437979i	0.0801722	+	0.996781i	$0.474453\pi$
$104$	−1.22675	+	0.590772i	−0.120293	+	0.0579300i
$105$	10.6187	−	19.9883i	1.03628	−	1.95066i
$106$	11.6818	+	5.62566i	1.13464	+	0.546413i
$107$	3.80884	+	4.77614i	0.368215	+	0.461727i	0.931076	−	0.364824i	$-0.118871\pi$
$107$	3.80884	+	4.77614i	0.368215	+	0.461727i	−0.562862	+	0.826551i	$0.690300\pi$
$108$	−11.0870	+	5.33922i	−1.06685	+	0.513766i
$109$	3.40615	−	4.27118i	0.326250	−	0.409105i	−0.591473	−	0.806324i	$-0.701454\pi$
$109$	3.40615	−	4.27118i	0.326250	−	0.409105i	0.917723	+	0.397220i	$0.130025\pi$
$110$	5.73479	−	25.1257i	0.546790	−	2.39565i
$111$	15.1962	−	19.0555i	1.44236	−	1.80866i
$112$	−9.88941	−	8.54727i	−0.934462	−	0.807641i
$113$	3.57343	+	4.48095i	0.336160	+	0.421532i	0.920967	−	0.389641i	$-0.127401\pi$
$113$	3.57343	+	4.48095i	0.336160	+	0.421532i	−0.584806	+	0.811173i	$0.698830\pi$
$114$	−30.0577	+	14.4750i	−2.81516	+	1.35571i
$115$	−4.82016	+	21.1185i	−0.449483	+	1.96931i
$116$	1.25523			0.116545
$117$	6.25203			0.578000
$118$	2.12920	−	9.32864i	0.196009	−	0.858771i
$119$	−11.9039	+	2.22608i	−1.09123	+	0.204064i
$120$	−2.59195	−	11.3561i	−0.236611	−	1.03666i
$121$	−3.31194	−	14.5106i	−0.301085	−	1.31914i
$122$	4.58950	+	5.75506i	0.415514	+	0.521038i
$123$	3.30343	+	4.14237i	0.297860	+	0.373505i
$124$	1.09617	+	4.80262i	0.0984386	+	0.431288i
$125$	1.30795	+	5.73049i	0.116986	+	0.512551i
$126$	11.8557	+	27.3324i	1.05619	+	2.43496i
$127$	−3.51267	+	15.3900i	−0.311699	+	1.36564i	0.540024	+	0.841649i	$0.318415\pi$
$127$	−3.51267	+	15.3900i	−0.311699	+	1.36564i	−0.851723	+	0.523992i	$0.824442\pi$
$128$	−10.1146			−0.894012
$129$	−5.55480			−0.489073
$130$	1.12721	−	4.93862i	0.0988627	−	0.433146i
$131$	17.2757	−	8.31953i	1.50938	−	0.726880i	0.517697	−	0.855564i	$-0.326790\pi$
$131$	17.2757	−	8.31953i	1.50938	−	0.726880i	0.991686	+	0.128684i	$0.0410753\pi$
$132$	12.0031	+	15.0514i	1.04473	+	1.31005i
$133$	6.41136	+	14.7808i	0.555935	+	1.28166i
$134$	9.68057	−	12.1390i	0.836273	−	1.04865i
$135$	−6.19062	+	27.1229i	−0.532804	+	2.33437i
$136$	−3.88579	+	4.87262i	−0.333203	+	0.417824i
$137$	−7.61374	+	3.66659i	−0.650486	+	0.313258i	−0.729869	−	0.683587i	$-0.760419\pi$
$137$	−7.61374	+	3.66659i	−0.650486	+	0.313258i	0.0793833	+	0.996844i	$0.474705\pi$
$138$	−26.3082	−	32.9894i	−2.23950	−	2.80825i
$139$	−10.2973	−	4.95890i	−0.873403	−	0.420609i	−0.0571921	−	0.998363i	$-0.518215\pi$
$139$	−10.2973	−	4.95890i	−0.873403	−	0.420609i	−0.816210	+	0.577755i	$0.803929\pi$
$140$	9.09927	−	1.70161i	0.769029	−	0.143812i
$141$	−25.7684	+	12.4094i	−2.17009	+	1.04506i
$142$	−7.83111	−	3.77127i	−0.657172	−	0.316478i
$143$	−1.13210	−	4.96005i	−0.0946708	−	0.414780i
$144$	27.8290	+	13.4017i	2.31908	+	1.11681i
$145$	1.76934	−	2.21869i	0.146936	−	0.184252i
$146$	−0.584540			−0.0483768
$147$	19.8531	−	7.69432i	1.63746	−	0.634617i
$148$	9.96825			0.819385
$149$	−4.63005	+	5.80590i	−0.379309	+	0.475638i	−0.934438	−	0.356126i	$-0.884097\pi$
$149$	−4.63005	+	5.80590i	−0.379309	+	0.475638i	0.555129	+	0.831764i	$0.312669\pi$
$150$	14.3640	+	6.91735i	1.17282	+	0.564800i
$151$	−1.00745	−	4.41393i	−0.0819853	−	0.359201i	0.917250	−	0.398313i	$-0.130404\pi$
$151$	−1.00745	−	4.41393i	−0.0819853	−	0.359201i	−0.999235	+	0.0391121i	$0.987547\pi$
$152$	7.47036	+	3.59754i	0.605926	+	0.291799i
$153$	25.7830	−	12.4164i	2.08443	−	1.00381i
$154$	19.5373	−	14.3550i	1.57436	−	1.15676i
$155$	10.0340	+	4.83213i	0.805951	+	0.388126i
$156$	2.35928	+	2.95844i	0.188893	+	0.236865i
$157$	−6.53778	+	3.14843i	−0.521771	+	0.251272i	−0.676182	−	0.736735i	$-0.736367\pi$
$157$	−6.53778	+	3.14843i	−0.521771	+	0.251272i	0.154410	+	0.988007i	$0.450652\pi$
$158$	−14.2446	+	17.8622i	−1.13324	+	1.42104i
$159$	−4.87245	+	21.3476i	−0.386410	+	1.69297i
$160$	10.8285	−	13.5785i	0.856067	−	1.07347i
$161$	−16.4214	+	12.0656i	−1.29419	+	0.950901i
$162$	−12.7254	−	15.9571i	−0.999799	−	1.25371i
$163$	−0.741385	+	0.357032i	−0.0580698	+	0.0279649i	−0.462693	−	0.886518i	$-0.653117\pi$
$163$	−0.741385	+	0.357032i	−0.0580698	+	0.0279649i	0.404624	+	0.914483i	$0.367403\pi$
$164$	−0.482191	+	2.11262i	−0.0376528	+	0.164968i
$165$	43.5234			3.38829
$166$	13.0233			1.01080
$167$	−0.0328428	+	0.143894i	−0.00254145	+	0.0111348i	−0.976183	−	0.216950i	$-0.930389\pi$
$167$	−0.0328428	+	0.143894i	−0.00254145	+	0.0111348i	0.973641	+	0.228085i	$0.0732463\pi$
$168$	5.14075	−	9.67682i	0.396618	−	0.746583i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−5.15949	−	22.6052i	−0.395715	−	1.73374i
$171$	−23.7375	−	29.7659i	−1.81525	−	2.27626i
$172$	−1.41648	−	1.77621i	−0.108006	−	0.135435i
$173$	4.97135	+	21.7809i	0.377965	+	1.65597i	0.703690	+	0.710507i	$0.251534\pi$
$173$	4.97135	+	21.7809i	0.377965	+	1.65597i	−0.325726	+	0.945464i	$0.605609\pi$
$174$	1.23005	+	5.38922i	0.0932502	+	0.408556i
$175$	3.61216	−	6.79944i	0.273054	−	0.513990i
$176$	5.59307	−	24.5049i	0.421594	−	1.84712i
$177$	16.1593			1.21461
$178$	−17.7017			−1.32680
$179$	4.42315	−	19.3791i	0.330602	−	1.44846i	−0.487366	−	0.873198i	$-0.662042\pi$
$179$	4.42315	−	19.3791i	0.330602	−	1.44846i	0.817968	−	0.575263i	$-0.195100\pi$
$180$	−19.7085	+	9.49109i	−1.46898	+	0.707424i
$181$	8.88106	+	11.1365i	0.660124	+	0.827770i	0.993357	−	0.115075i	$-0.0367108\pi$
$181$	8.88106	+	11.1365i	0.660124	+	0.827770i	−0.333233	+	0.942845i	$0.608139\pi$
$182$	3.84018	−	2.82157i	0.284653	−	0.209148i
$183$	−7.75072	+	9.71909i	−0.572949	+	0.718456i
$184$	−2.33355	+	10.2240i	−0.172032	+	0.753721i
$185$	14.0510	−	17.6194i	1.03305	−	1.29540i
$186$	−19.5454	+	9.41258i	−1.43314	+	0.690164i
$187$	−14.5193	−	18.2066i	−1.06176	−	1.33140i
$188$	−10.5390	−	5.07532i	−0.768637	−	0.370156i
$189$	−21.0903	+	15.4960i	−1.53409	+	1.12717i
$190$	−27.7925	+	13.3842i	−2.01628	+	0.970990i
$191$	−13.1500	−	6.33269i	−0.951499	−	0.458218i	−0.107287	−	0.994228i	$-0.534216\pi$
$191$	−13.1500	−	6.33269i	−0.951499	−	0.458218i	−0.844211	+	0.536011i	$0.819931\pi$
$192$	0.840166	+	3.68101i	0.0606338	+	0.265654i
$193$	−6.27660	−	3.02265i	−0.451800	−	0.217575i	0.194124	−	0.980977i	$-0.437813\pi$
$193$	−6.27660	−	3.02265i	−0.451800	−	0.217575i	−0.645924	+	0.763402i	$0.723528\pi$
$194$	−5.15258	+	6.46113i	−0.369934	+	0.463882i
$195$	8.55478			0.612621
$196$	7.52292	+	4.38620i	0.537351	+	0.313300i
$197$	−17.8238			−1.26989			−0.634947	−	0.772556i	$-0.718978\pi$
$197$	−17.8238			−1.26989			−0.634947	+	0.772556i	$0.718978\pi$
$198$	−35.7196	+	44.7909i	−2.53848	+	3.18315i
$199$	20.6839	+	9.96086i	1.46624	+	0.706106i	0.985330	−	0.170661i	$-0.0545902\pi$
$199$	20.6839	+	9.96086i	1.46624	+	0.706106i	0.480915	+	0.876767i	$0.340305\pi$
$200$	−0.881704	−	3.86300i	−0.0623459	−	0.273155i
$201$	23.6242	+	11.3768i	1.66632	+	0.802459i
$202$	10.8505	−	5.22532i	0.763438	−	0.367653i
$203$	2.62408	−	0.490715i	0.184174	−	0.0344415i
$204$	15.6049	+	7.51495i	1.09257	+	0.526152i
$205$	3.05448	+	3.83020i	0.213334	+	0.267512i
$206$	−16.6246	+	8.00598i	−1.15829	+	0.557803i
$207$	30.0228	−	37.6474i	2.08673	−	2.61667i
$208$	1.09935	−	4.81658i	0.0762264	−	0.333970i
$209$	−19.3165	+	24.2221i	−1.33615	+	1.67548i
$210$	16.2225	+	37.3994i	1.11946	+	2.58081i
$211$	−8.16076	−	10.2333i	−0.561810	−	0.704487i	0.417082	−	0.908869i	$-0.363053\pi$
$211$	−8.16076	−	10.2333i	−0.561810	−	0.704487i	−0.978891	+	0.204382i	$0.934481\pi$
$212$	−8.06861	+	3.88564i	−0.554154	+	0.266867i
$213$	3.26633	−	14.3107i	0.223806	−	0.980556i
$214$	−11.0029			−0.752141
$215$	−5.13619			−0.350285
$216$	−2.99703	+	13.1308i	−0.203922	+	0.893440i
$217$	4.16907	+	9.61142i	0.283015	+	0.652466i
$218$	2.18951	+	9.59289i	0.148293	+	0.649712i
$219$	−0.219665	−	0.962415i	−0.0148436	−	0.0650340i
$220$	11.0985	+	13.9171i	0.748261	+	0.938290i
$221$	−2.85386	−	3.57862i	−0.191971	−	0.240724i
$222$	9.76831	+	42.7978i	0.655606	+	2.87240i
$223$	−2.93151	−	12.8438i	−0.196308	−	0.860083i	−0.973111	−	0.230338i	$-0.926017\pi$
$223$	−2.93151	−	12.8438i	−0.196308	−	0.860083i	0.776802	−	0.629745i	$-0.216840\pi$
$224$	16.0595	−	3.00321i	1.07302	−	0.200660i
$225$	−4.04853	+	17.7378i	−0.269902	+	1.18252i
$226$	−10.3228			−0.686665
$227$	−9.59818			−0.637053			−0.318527	−	0.947914i	$-0.603188\pi$
$227$	−9.59818			−0.637053			−0.318527	+	0.947914i	$0.603188\pi$
$228$	5.12750	−	22.4651i	0.339577	−	1.48778i
$229$	14.3777	−	6.92392i	0.950103	−	0.457545i	0.106380	−	0.994325i	$-0.466074\pi$
$229$	14.3777	−	6.92392i	0.950103	−	0.457545i	0.843722	+	0.536780i	$0.180360\pi$
$230$	−24.3256	−	30.5033i	−1.60398	−	2.01133i
$231$	30.9768	+	26.7727i	2.03812	+	1.76152i
$232$	0.856581	−	1.07412i	0.0562373	−	0.0705193i
$233$	2.64718	−	11.5981i	0.173423	−	0.759815i	−0.811150	−	0.584838i	$-0.801158\pi$
$233$	2.64718	−	11.5981i	0.173423	−	0.759815i	0.984573	−	0.174976i	$-0.0559849\pi$
$234$	−7.02090	+	8.80393i	−0.458971	+	0.575531i
$235$	−23.8265	+	11.4742i	−1.55427	+	0.748496i
$236$	4.12063	+	5.16711i	0.268230	+	0.336350i
$237$	−34.7622	−	16.7406i	−2.25805	−	1.08742i
$238$	10.2331	−	19.2625i	0.663313	−	1.24860i
$239$	25.7395	−	12.3955i	1.66495	−	0.801796i	0.666534	−	0.745475i	$-0.267777\pi$
$239$	25.7395	−	12.3955i	1.66495	−	0.801796i	0.998413	−	0.0563216i	$-0.0179372\pi$
$240$	38.0790	+	18.3379i	2.45799	+	1.18370i
$241$	−1.07796	−	4.72287i	−0.0694378	−	0.304227i	0.928269	−	0.371909i	$-0.121297\pi$
$241$	−1.07796	−	4.72287i	−0.0694378	−	0.304227i	−0.997707	+	0.0676824i	$0.978440\pi$
$242$	24.1526	+	11.6313i	1.55259	+	0.747687i
$243$	2.98828	−	3.74718i	0.191698	−	0.240382i
$244$	−5.08423			−0.325484
$245$	18.3570	−	7.11447i	1.17278	−	0.454527i
$246$	−9.54285			−0.608430
$247$	−3.79677	+	4.76100i	−0.241583	+	0.302935i
$248$	4.85770	+	2.33934i	0.308464	+	0.148549i
$249$	4.89404	+	21.4422i	0.310147	+	1.35884i
$250$	−9.53831	−	4.59341i	−0.603256	−	0.290513i
$251$	−18.3833	+	8.85294i	−1.16035	+	0.558793i	−0.912126	−	0.409911i	$-0.865560\pi$
$251$	−18.3833	+	8.85294i	−1.16035	+	0.558793i	−0.248220	+	0.968704i	$0.579845\pi$
$252$	−19.8653	−	5.36829i	−1.25140	−	0.338170i
$253$	−35.3040	−	17.0015i	−2.21954	−	1.06887i
$254$	−17.7271	−	22.2291i	−1.11230	−	1.39478i
$255$	35.2794	−	16.9897i	2.20928	−	1.06394i
$256$	12.9063	−	16.1841i	0.806647	−	1.01150i
$257$	4.17791	−	18.3046i	0.260611	−	1.14181i	−0.659981	−	0.751283i	$-0.729436\pi$
$257$	4.17791	−	18.3046i	0.260611	−	1.14181i	0.920591	−	0.390527i	$-0.127707\pi$
$258$	6.23793	−	7.82212i	0.388357	−	0.486984i
$259$	20.8388	−	3.89695i	1.29486	−	0.242145i
$260$	2.18148	+	2.73549i	0.135290	+	0.169648i
$261$	−5.68360	+	2.73708i	−0.351806	+	0.169421i
$262$	−7.68491	+	33.6698i	−0.474775	+	2.08013i
$263$	32.0072			1.97365			0.986824	−	0.161797i	$-0.0517289\pi$
$263$	32.0072			1.97365			0.986824	+	0.161797i	$0.0517289\pi$
$264$	21.0707			1.29681
$265$	−4.50525	+	19.7388i	−0.276755	+	1.21255i
$266$	−28.0138	−	7.57027i	−1.71763	−	0.464163i
$267$	−6.65216	−	29.1450i	−0.407105	−	1.78364i
$268$	2.38633	+	10.4552i	0.145768	+	0.638653i
$269$	−5.70492	−	7.15374i	−0.347835	−	0.436171i	0.576882	−	0.816828i	$-0.304269\pi$
$269$	−5.70492	−	7.15374i	−0.347835	−	0.436171i	−0.924716	+	0.380657i	$0.875698\pi$
$270$	−31.2418	−	39.1759i	−1.90131	−	2.38417i
$271$	−1.65120	−	7.23436i	−0.100303	−	0.439456i	−0.999996	−	0.00293224i	$-0.999067\pi$
$271$	−1.65120	−	7.23436i	−0.100303	−	0.439456i	0.899693	−	0.436524i	$-0.143791\pi$
$272$	−5.03199	−	22.0466i	−0.305110	−	1.33677i
$273$	6.08867	+	5.26234i	0.368503	+	0.318492i
$274$	3.38690	−	14.8390i	0.204610	−	0.896454i
$275$	14.8054			0.892797
$276$	29.1441			1.75427
$277$	−6.47512	+	28.3694i	−0.389052	+	1.70455i	0.278878	+	0.960326i	$0.410037\pi$
$277$	−6.47512	+	28.3694i	−0.389052	+	1.70455i	−0.667931	+	0.744223i	$0.732820\pi$
$278$	18.5466	−	8.93157i	1.11235	−	0.535680i
$279$	−15.4356	−	19.3557i	−0.924108	−	1.15879i
$280$	4.75334	−	8.94756i	0.284066	−	0.534719i
$281$	−5.95708	+	7.46995i	−0.355370	+	0.445620i	−0.927096	−	0.374825i	$-0.877703\pi$
$281$	−5.95708	+	7.46995i	−0.355370	+	0.445620i	0.571726	+	0.820445i	$0.306274\pi$
$282$	11.4628	−	50.2219i	0.682601	−	2.99067i
$283$	−4.90424	+	6.14972i	−0.291527	+	0.365563i	−0.905929	−	0.423430i	$-0.860826\pi$
$283$	−4.90424	+	6.14972i	−0.291527	+	0.365563i	0.614402	+	0.788993i	$0.289397\pi$
$284$	5.40894	−	2.60481i	0.320962	−	0.154567i
$285$	−32.4806	−	40.7293i	−1.92398	−	2.41260i
$286$	8.25592	+	3.97584i	0.488183	+	0.235097i
$287$	−0.182131	+	4.60497i	−0.0107508	+	0.271823i
$288$	−34.7839	+	16.7511i	−2.04966	+	0.987066i
$289$	−3.55977	−	1.71430i	−0.209398	−	0.100841i
$290$	1.13736	+	4.98308i	0.0667878	+	0.292617i
$291$	−12.5742	−	6.05543i	−0.737114	−	0.354976i
$292$	0.251728	−	0.315657i	0.0147313	−	0.0184724i
$293$	−29.4158			−1.71849			−0.859245	−	0.511565i	$-0.829066\pi$
$293$	−29.4158			−1.71849			−0.859245	+	0.511565i	$0.829066\pi$
$294$	−11.4597	+	36.5972i	−0.668345	+	2.13439i
$295$	14.9415			0.869928
$296$	6.80242	−	8.52997i	0.395383	−	0.495794i
$297$	−45.3415	−	21.8353i	−2.63098	−	1.26701i
$298$	−2.97625	−	13.0398i	−0.172410	−	0.755376i
$299$	−6.93921	−	3.34175i	−0.401305	−	0.193258i
$300$	−9.92122	+	4.77781i	−0.572802	+	0.275847i
$301$	−3.65556	−	3.15945i	−0.210703	−	0.182107i
$302$	7.34693	+	3.53809i	0.422768	+	0.203594i
$303$	12.6808	+	15.9012i	0.728491	+	0.913498i
$304$	−27.1057	+	13.0534i	−1.55462	+	0.748666i
$305$	−7.16661	+	8.98665i	−0.410359	+	0.514574i
$306$	−11.4693	+	50.2503i	−0.655657	+	2.87262i
$307$	6.43011	−	8.06310i	0.366986	−	0.460186i	−0.563714	−	0.825970i	$-0.690628\pi$
$307$	6.43011	−	8.06310i	0.366986	−	0.460186i	0.930700	+	0.365785i	$0.119199\pi$
$308$	−0.661775	+	16.7322i	−0.0377081	+	0.953408i
$309$	−19.4288	−	24.3630i	−1.10527	−	1.38596i
$310$	−18.0725	+	8.70323i	−1.02645	+	0.494311i
$311$	−3.26773	+	14.3168i	−0.185296	+	0.811833i	0.793758	+	0.608233i	$0.208121\pi$
$311$	−3.26773	+	14.3168i	−0.185296	+	0.811833i	−0.979054	+	0.203600i	$0.934736\pi$
$312$	4.14157			0.234470
$313$	−18.3587			−1.03770			−0.518848	−	0.854867i	$-0.673639\pi$
$313$	−18.3587			−1.03770			−0.518848	+	0.854867i	$0.673639\pi$
$314$	2.90826	−	12.7419i	0.164123	−	0.719069i
$315$	−37.4905	+	27.5460i	−2.11235	+	1.55204i
$316$	−3.51140	−	15.3845i	−0.197532	−	0.865444i
$317$	−5.61189	−	24.5873i	−0.315195	−	1.38096i	−0.845872	−	0.533386i	$-0.820919\pi$
$317$	−5.61189	−	24.5873i	−0.315195	−	1.38096i	0.530677	−	0.847574i	$-0.321938\pi$
$318$	−24.5894	−	30.8341i	−1.37891	−	1.72909i
$319$	3.20063	+	4.01346i	0.179201	+	0.224711i
$320$	0.776850	+	3.40360i	0.0434272	+	0.190267i
$321$	−4.13479	−	18.1157i	−0.230781	−	1.01112i
$322$	1.45047	−	36.6735i	0.0808315	−	2.04374i
$323$	−6.20239	+	27.1744i	−0.345110	+	1.51203i
$324$	14.0971			0.783172
$325$	2.91008			0.161422
$326$	0.329797	−	1.44494i	0.0182658	−	0.0800277i
$327$	−14.9714	+	7.20985i	−0.827921	+	0.398706i
$328$	1.47874	+	1.85429i	0.0816500	+	0.102386i
$329$	−24.0161	−	6.48997i	−1.32405	−	0.357804i
$330$	−48.8758	+	61.2884i	−2.69053	+	3.37381i
$331$	2.96484	−	12.9898i	0.162962	−	0.713984i	−0.825735	−	0.564058i	$-0.809239\pi$
$331$	2.96484	−	12.9898i	0.162962	−	0.713984i	0.988697	−	0.149926i	$-0.0479036\pi$
$332$	−5.60840	+	7.03271i	−0.307801	+	0.385970i
$333$	−45.1355	+	21.7361i	−2.47341	+	1.19113i
$334$	−0.165745	−	0.207838i	−0.00906918	−	0.0113724i
$335$	21.8439	+	10.5194i	1.19346	+	0.574739i
$336$	15.8216	+	36.4753i	0.863138	+	1.98989i
$337$	29.5100	−	14.2113i	1.60751	−	0.774136i	0.607711	−	0.794158i	$-0.292088\pi$
$337$	29.5100	−	14.2113i	1.60751	−	0.774136i	0.999800	+	0.0200221i	$0.00637365\pi$
$338$	1.62275	+	0.781476i	0.0882661	+	0.0425067i
$339$	−3.87923	−	16.9960i	−0.210691	−	0.923098i
$340$	14.4289	+	6.94861i	0.782519	+	0.376841i
$341$	−12.5608	+	15.7507i	−0.680205	+	0.852950i
$342$	68.5723			3.70797
$343$	17.4415	+	6.22845i	0.941753	+	0.336305i
$344$	−2.48655			−0.134066
$345$	41.0808	−	51.5137i	2.21172	−	2.77340i
$346$	−36.2540	−	17.4590i	−1.94903	−	0.938601i
$347$	−1.87342	−	8.20801i	−0.100571	−	0.440629i	−0.999994	−	0.00354973i	$-0.998870\pi$
$347$	−1.87342	−	8.20801i	−0.100571	−	0.440629i	0.899423	−	0.437079i	$-0.143987\pi$
$348$	−3.43995	−	1.65659i	−0.184401	−	0.0888026i
$349$	30.3911	−	14.6356i	1.62680	−	0.783425i	0.626808	−	0.779173i	$-0.284361\pi$
$349$	30.3911	−	14.6356i	1.62680	−	0.783425i	0.999991	−	0.00425176i	$-0.00135338\pi$
$350$	5.51840	+	12.7222i	0.294971	+	0.680029i
$351$	−8.91216	−	4.29187i	−0.475696	−	0.229083i
$352$	19.5880	+	24.5626i	1.04405	+	1.30919i
$353$	−2.75133	+	1.32497i	−0.146439	+	0.0705212i	−0.505668	−	0.862728i	$-0.668754\pi$
$353$	−2.75133	+	1.32497i	−0.146439	+	0.0705212i	0.359229	+	0.933249i	$0.383040\pi$
$354$	−18.1465	+	22.7550i	−0.964478	+	1.20942i
$355$	3.02018	−	13.2323i	0.160294	−	0.702296i
$356$	7.62313	−	9.55911i	0.404025	−	0.506632i
$357$	35.5603	+	9.60959i	1.88205	+	0.508593i
$358$	22.3220	+	27.9909i	1.17975	+	1.47936i
$359$	6.19226	−	2.98204i	0.326815	−	0.157386i	−0.263280	−	0.964719i	$-0.584804\pi$
$359$	6.19226	−	2.98204i	0.326815	−	0.157386i	0.590095	+	0.807334i	$0.299090\pi$
$360$	−5.32757	+	23.3416i	−0.280787	+	1.23021i
$361$	18.0826			0.951717
$362$	−25.6554			−1.34842
$363$	−10.0740	+	44.1370i	−0.528746	+	2.31659i
$364$	−0.130076	+	3.28883i	−0.00681783	+	0.172381i
$365$	−0.203111	−	0.889886i	−0.0106313	−	0.0465788i
$366$	−4.98225	−	21.8287i	−0.260427	−	1.14100i
$367$	12.7495	+	15.9874i	0.665519	+	0.834534i	0.993932	−	0.110000i	$-0.0350851\pi$
$367$	12.7495	+	15.9874i	0.665519	+	0.834534i	−0.328413	+	0.944534i	$0.606514\pi$
$368$	−23.7245	−	29.7495i	−1.23672	−	1.55080i
$369$	−2.42331	−	10.6172i	−0.126153	−	0.552710i
$370$	9.03216	+	39.5725i	0.469560	+	2.05727i
$371$	−15.3485	+	11.2773i	−0.796856	+	0.585489i
$372$	3.33422	−	14.6082i	0.172871	−	0.757399i
$373$	−7.04532			−0.364793			−0.182396	−	0.983225i	$-0.558385\pi$
$373$	−7.04532			−0.364793			−0.182396	+	0.983225i	$0.558385\pi$
$374$	41.9429			2.16882
$375$	3.97840	−	17.4305i	0.205444	−	0.900108i
$376$	−11.5349	+	5.55494i	−0.594869	+	0.286474i
$377$	0.629103	+	0.788870i	0.0324005	+	0.0406289i
$378$	1.86286	−	47.1005i	0.0958154	−	2.42259i
$379$	4.73848	−	5.94187i	0.243399	−	0.305213i	−0.645093	−	0.764104i	$-0.723182\pi$
$379$	4.73848	−	5.94187i	0.243399	−	0.305213i	0.888493	+	0.458891i	$0.151753\pi$
$380$	4.74109	−	20.7721i	0.243213	−	1.06558i
$381$	29.9374	−	37.5403i	1.53374	−	1.92325i
$382$	23.6847	−	11.4059i	1.21181	−	0.583578i
$383$	0.845365	+	1.06005i	0.0431961	+	0.0541663i	0.802960	−	0.596032i	$-0.203257\pi$
$383$	0.845365	+	1.06005i	0.0431961	+	0.0541663i	−0.759764	+	0.650199i	$0.774686\pi$
$384$	27.7189	+	13.3487i	1.41453	+	0.681200i
$385$	28.6423	+	24.7551i	1.45975	+	1.26164i
$386$	11.3049	−	5.44416i	0.575405	−	0.277100i
$387$	10.2868	+	4.95387i	0.522908	+	0.251819i
$388$	−1.27015	−	5.56489i	−0.0644821	−	0.282515i
$389$	−27.3983	−	13.1943i	−1.38915	−	0.668978i	−0.418219	−	0.908346i	$-0.637345\pi$
$389$	−27.3983	−	13.1943i	−1.38915	−	0.668978i	−0.970929	+	0.239368i	$0.923060\pi$
$390$	−9.60685	+	12.0466i	−0.486462	+	0.610004i
$391$	−35.2536			−1.78285
$392$	8.88704	−	3.44428i	0.448863	−	0.173962i
$393$	−58.3235			−2.94203
$394$	20.0158	−	25.0990i	1.00838	−	1.26447i
$395$	−32.1424	−	15.4790i	−1.61726	−	0.778832i
$396$	−8.80514	−	38.5779i	−0.442475	−	1.93861i
$397$	35.1826	+	16.9430i	1.76576	+	0.850346i	0.969385	+	0.245547i	$0.0789674\pi$
$397$	35.1826	+	16.9430i	1.76576	+	0.850346i	0.796378	+	0.604800i	$0.206747\pi$
$398$	−37.2542	+	17.9407i	−1.86739	+	0.899286i
$399$	1.93673	−	48.9681i	0.0969578	−	2.45147i
$400$	12.9533	+	6.23800i	0.647667	+	0.311900i
$401$	8.52935	+	10.6955i	0.425935	+	0.534106i	0.947776	−	0.318937i	$-0.103326\pi$
$401$	8.52935	+	10.6955i	0.425935	+	0.534106i	−0.521841	+	0.853043i	$0.674754\pi$
$402$	−42.5500	+	20.4910i	−2.12220	+	1.02200i
$403$	−2.46890	+	3.09590i	−0.122985	+	0.154218i
$404$	−1.85097	+	8.10963i	−0.0920892	+	0.403469i
$405$	19.8709	−	24.9174i	0.987395	−	1.23815i
$406$	−2.25578	+	4.24622i	−0.111952	+	0.210736i
$407$	25.4174	+	31.8724i	1.25989	+	1.57985i
$408$	17.0796	−	8.22510i	0.845566	−	0.407203i
$409$	−2.18546	+	9.57512i	−0.108064	+	0.473459i	0.891718	+	0.452591i	$0.149500\pi$
$409$	−2.18546	+	9.57512i	−0.108064	+	0.473459i	−0.999782	+	0.0208682i	$0.993357\pi$
$410$	−8.82369			−0.435771
$411$	25.7044			1.26790
$412$	2.83597	−	12.4252i	0.139718	−	0.612145i
$413$	10.6343	+	9.19103i	0.523278	+	0.452261i
$414$	19.2990	+	84.5545i	0.948494	+	4.15562i
$415$	4.52522	+	19.8263i	0.222134	+	0.973234i
$416$	3.85015	+	4.82793i	0.188769	+	0.236709i
$417$	21.6750	+	27.1796i	1.06143	+	1.33099i
$418$	−12.4169	−	54.4018i	−0.607329	−	2.66088i
$419$	5.04081	+	22.0852i	0.246260	+	1.07893i	0.935201	+	0.354117i	$0.115218\pi$
$419$	5.04081	+	22.0852i	0.246260	+	1.07893i	−0.688942	+	0.724817i	$0.741924\pi$
$420$	−27.1822	−	7.34554i	−1.32635	−	0.358426i
$421$	−3.82952	+	16.7782i	−0.186640	+	0.817721i	0.791732	+	0.610868i	$0.209179\pi$
$421$	−3.82952	+	16.7782i	−0.186640	+	0.817721i	−0.978372	+	0.206853i	$0.933678\pi$
$422$	23.5746			1.14759
$423$	58.7869			2.85832
$424$	−2.18110	+	9.55601i	−0.105923	+	0.464081i
$425$	12.0010	−	5.77939i	0.582135	−	0.280342i
$426$	16.4840	+	20.6702i	0.798651	+	1.00148i
$427$	−10.6287	+	1.98761i	−0.514357	+	0.0961871i
$428$	4.73832	−	5.94166i	0.229035	−	0.287201i
$429$	−3.44352	+	15.0870i	−0.166255	+	0.728410i
$430$	5.76783	−	7.23263i	0.278150	−	0.348789i
$431$	−29.5837	+	14.2468i	−1.42500	+	0.686242i	−0.978060	−	0.208323i	$-0.933199\pi$
$431$	−29.5837	+	14.2468i	−1.42500	+	0.686242i	−0.446937	+	0.894565i	$0.647485\pi$
$432$	−30.4697	−	38.2078i	−1.46598	−	1.83828i
$433$	−17.3368	−	8.34896i	−0.833153	−	0.401225i	−0.0318563	−	0.999492i	$-0.510142\pi$
$433$	−17.3368	−	8.34896i	−0.833153	−	0.401225i	−0.801297	+	0.598267i	$0.795856\pi$
$434$	−18.2163	−	4.92266i	−0.874411	−	0.236295i
$435$	−7.77699	+	3.74520i	−0.372878	+	0.179569i
$436$	−6.12316	−	2.94876i	−0.293246	−	0.141220i
$437$	10.4365	+	45.7255i	0.499247	+	2.18735i
$438$	1.60193	+	0.771447i	0.0765430	+	0.0368611i
$439$	−2.61341	+	3.27711i	−0.124731	+	0.156408i	−0.840276	−	0.542159i	$-0.817607\pi$
$439$	−2.61341	+	3.27711i	−0.124731	+	0.156408i	0.715545	+	0.698567i	$0.246179\pi$
$440$	19.4828			0.928804
$441$	−43.6275	−	3.45642i	−2.07750	−	0.164591i
$442$	8.24414			0.392134
$443$	−6.09157	+	7.63859i	−0.289419	+	0.362920i	−0.905191	−	0.425004i	$-0.860273\pi$
$443$	−6.09157	+	7.63859i	−0.289419	+	0.362920i	0.615772	+	0.787924i	$0.288844\pi$
$444$	−27.3179	−	13.1556i	−1.29645	−	0.624337i
$445$	−6.15084	−	26.9486i	−0.291578	−	1.27749i
$446$	21.3783	+	10.2952i	1.01229	+	0.487493i
$447$	20.3510	−	9.80050i	0.962567	−	0.463548i
$448$	−1.54077	+	2.90030i	−0.0727945	+	0.137026i
$449$	−1.48910	−	0.717112i	−0.0702749	−	0.0338426i	0.398416	−	0.917205i	$-0.369560\pi$
$449$	−1.48910	−	0.717112i	−0.0702749	−	0.0338426i	−0.468691	+	0.883362i	$0.655274\pi$
$450$	−20.4314	−	25.6202i	−0.963146	−	1.20775i
$451$	−7.98436	+	3.84507i	−0.375969	+	0.181057i
$452$	4.44546	−	5.57443i	0.209097	−	0.262199i
$453$	−3.06438	+	13.4259i	−0.143977	+	0.630805i
$454$	10.7786	−	13.5159i	0.505863	−	0.634332i
$455$	5.62982	+	4.86577i	0.263930	+	0.228111i
$456$	−15.7246	−	19.7180i	−0.736372	−	0.923381i
$457$	−12.4699	+	6.00516i	−0.583315	+	0.280910i	−0.702179	−	0.712001i	$-0.747789\pi$
$457$	−12.4699	+	6.00516i	−0.583315	+	0.280910i	0.118863	+	0.992911i	$0.462075\pi$
$458$	−6.39576	+	28.0216i	−0.298854	+	1.30936i
$459$	−45.2768			−2.11334
$460$	26.9477			1.25644
$461$	−5.72917	+	25.1012i	−0.266834	+	1.16908i	0.646839	+	0.762627i	$0.276091\pi$
$461$	−5.72917	+	25.1012i	−0.266834	+	1.16908i	−0.913673	+	0.406450i	$0.866766\pi$
$462$	−72.4869	+	13.5554i	−3.37239	+	0.630653i
$463$	−2.70562	−	11.8541i	−0.125741	−	0.550907i	−0.998076	−	0.0619989i	$-0.980252\pi$
$463$	−2.70562	−	11.8541i	−0.125741	−	0.550907i	0.872335	−	0.488908i	$-0.162605\pi$
$464$	1.10925	+	4.85995i	0.0514957	+	0.225617i
$465$	−21.1209	−	26.4848i	−0.979459	−	1.22820i
$466$	13.3593	+	16.7521i	0.618860	+	0.776025i
$467$	5.30712	+	23.2520i	0.245584	+	1.07597i	0.935844	+	0.352413i	$0.114639\pi$
$467$	5.30712	+	23.2520i	0.245584	+	1.07597i	−0.690260	+	0.723561i	$0.742504\pi$
$468$	−1.73071	−	7.58271i	−0.0800019	−	0.350511i
$469$	9.07599	+	20.9239i	0.419090	+	0.966175i
$470$	10.5990	−	46.4371i	0.488894	−	2.14198i
$471$	22.0719			1.01702
$472$	7.23353			0.332950
$473$	2.06745	−	9.05808i	0.0950613	−	0.416491i
$474$	62.6108	−	30.1518i	2.87581	−	1.38492i
$475$	−11.0489	−	13.8549i	−0.506960	−	0.635707i
$476$	5.99514	+	13.8213i	0.274787	+	0.633496i
$477$	28.0613	−	35.1878i	1.28484	−	1.61114i
$478$	−11.4499	+	50.1654i	−0.523708	+	2.29451i
$479$	20.4241	−	25.6110i	0.933202	−	1.17020i	−0.0519737	−	0.998648i	$-0.516551\pi$
$479$	20.4241	−	25.6110i	0.933202	−	1.17020i	0.985175	−	0.171550i	$-0.0548774\pi$
$480$	−47.5956	+	22.9208i	−2.17243	+	1.04619i
$481$	4.99594	+	6.26471i	0.227795	+	0.285646i
$482$	7.86114	+	3.78573i	0.358065	+	0.172435i
$483$	60.9262	−	11.3935i	2.77224	−	0.518421i
$484$	−16.6822	+	8.03371i	−0.758280	+	0.365168i
$485$	−11.6266	−	5.59908i	−0.527938	−	0.254241i
$486$	1.92090	+	8.41601i	0.0871338	+	0.381758i
$487$	6.40155	+	3.08282i	0.290082	+	0.139696i	0.573266	−	0.819370i	$-0.305676\pi$
$487$	6.40155	+	3.08282i	0.290082	+	0.139696i	−0.283184	+	0.959066i	$0.591391\pi$
$488$	−3.46952	+	4.35065i	−0.157058	+	0.196944i
$489$	2.50295			0.113187
$490$	−10.5961	+	33.8392i	−0.478683	+	1.52870i
$491$	15.8484			0.715227			0.357613	−	0.933870i	$-0.383591\pi$
$491$	15.8484			0.715227			0.357613	+	0.933870i	$0.383591\pi$
$492$	4.10957	−	5.15324i	0.185274	−	0.232326i
$493$	4.16107	+	2.00387i	0.187405	+	0.0902496i
$494$	−2.44061	−	10.6930i	−0.109808	−	0.481102i
$495$	−80.5999	−	38.8149i	−3.62270	−	1.74460i
$496$	−17.6259	+	8.48817i	−0.791425	+	0.381130i
$497$	10.2892	−	7.55995i	0.461532	−	0.339110i
$498$	−35.6902	−	17.1875i	−1.59932	−	0.770190i
$499$	0.820116	+	1.02839i	0.0367134	+	0.0460372i	0.799849	−	0.600201i	$-0.204913\pi$
$499$	0.820116	+	1.02839i	0.0367134	+	0.0460372i	−0.763136	+	0.646238i	$0.776341\pi$
$500$	6.58810	−	3.17266i	0.294629	−	0.141886i
$501$	0.279909	−	0.350995i	0.0125054	−	0.0156813i
$502$	8.17763	−	35.8286i	0.364986	−	1.59911i
$503$	−9.68547	+	12.1452i	−0.431854	+	0.541528i	−0.949376	−	0.314142i	$-0.898283\pi$
$503$	−9.68547	+	12.1452i	−0.431854	+	0.541528i	0.517522	+	0.855670i	$0.326855\pi$
$504$	−18.1500	+	13.3357i	−0.808465	+	0.594018i
$505$	11.7251	+	14.7028i	0.521761	+	0.654268i
$506$	63.5867	−	30.6217i	2.82677	−	1.36130i
$507$	−0.676845	+	2.96545i	−0.0300598	+	0.131700i
$508$	19.6380			0.871295
$509$	22.8711			1.01374			0.506872	−	0.862021i	$-0.330802\pi$
$509$	22.8711			1.01374			0.506872	+	0.862021i	$0.330802\pi$
$510$	−15.6937	+	68.7586i	−0.694929	+	3.04468i
$511$	0.402841	−	0.758297i	0.0178206	−	0.0335451i
$512$	3.79494	+	16.6267i	0.167714	+	0.734804i
$513$	13.4038	+	58.7260i	0.591794	+	2.59282i
$514$	21.0843	+	26.4389i	0.929990	+	1.16617i
$515$	−17.9647	−	22.5270i	−0.791617	−	0.992657i
$516$	1.53770	+	6.73709i	0.0676933	+	0.296584i
$517$	−10.6449	−	46.6386i	−0.468164	−	2.05116i
$518$	−17.9140	+	33.7208i	−0.787095	+	1.48161i
$519$	15.1214	−	66.2513i	0.663757	−	2.90811i
$520$	3.82946			0.167933
$521$	36.7196			1.60872			0.804358	−	0.594145i	$-0.202509\pi$
$521$	36.7196			1.60872			0.804358	+	0.594145i	$0.202509\pi$
$522$	2.52829	−	11.0772i	0.110660	−	0.484834i
$523$	−6.56926	+	3.16359i	−0.287254	+	0.138334i	−0.571962	−	0.820280i	$-0.693818\pi$
$523$	−6.56926	+	3.16359i	−0.287254	+	0.138334i	0.284708	+	0.958614i	$0.408103\pi$
$524$	−14.8726	−	18.6496i	−0.649711	−	0.814712i
$525$	−18.8727	+	13.8667i	−0.823671	+	0.605190i
$526$	−35.9434	+	45.0716i	−1.56721	+	1.96522i
$527$	−4.03318	+	17.6705i	−0.175688	+	0.769741i
$528$	−47.6681	+	59.7739i	−2.07449	+	2.60132i
$529$	−32.7232	+	15.7586i	−1.42275	+	0.685158i
$530$	−22.7363	−	28.5104i	−0.987603	−	1.23841i
$531$	−29.9250	−	14.4111i	−1.29863	−	0.625390i
$532$	16.1520	−	11.8676i	0.700277	−	0.514527i
$533$	−1.56938	+	0.755772i	−0.0679772	+	0.0327361i
$534$	48.5114	+	23.3619i	2.09929	+	1.01097i
$535$	−3.82318	−	16.7505i	−0.165291	−	0.724186i
$536$	10.5751	+	5.09271i	0.456775	+	0.219971i
$537$	−37.6972	+	47.2707i	−1.62675	+	2.03988i
$538$	16.4802			0.710512
$539$	5.15779	+	35.2378i	0.222162	+	1.51780i
$540$	34.6095			1.48935
$541$	22.0375	−	27.6342i	0.947468	−	1.18809i	−0.0345695	−	0.999402i	$-0.511006\pi$
$541$	22.0375	−	27.6342i	0.947468	−	1.18809i	0.982038	−	0.188685i	$-0.0604226\pi$
$542$	12.0415	+	5.79887i	0.517226	+	0.249083i
$543$	−9.64107	−	42.2403i	−0.413738	−	1.81270i
$544$	25.4660	+	12.2638i	1.09185	+	0.525805i
$545$	−13.8431	+	6.66651i	−0.592975	+	0.285562i
$546$	−14.2477	+	2.66439i	−0.609747	+	0.114025i
$547$	−14.9863	−	7.21704i	−0.640770	−	0.308579i	0.0851393	−	0.996369i	$-0.472866\pi$
$547$	−14.9863	−	7.21704i	−0.640770	−	0.308579i	−0.725909	+	0.687791i	$0.758581\pi$
$548$	6.55464	+	8.21926i	0.280000	+	0.351110i
$549$	23.0210	−	11.0863i	0.982514	−	0.473154i
$550$	−16.6261	+	20.8485i	−0.708940	+	0.888983i
$551$	1.36725	−	5.99032i	0.0582469	−	0.255196i
$552$	19.8882	−	24.9390i	0.846497	−	1.06147i
$553$	−13.3550	−	30.7888i	−0.567912	−	1.30927i
$554$	−32.6775	−	40.9763i	−1.38833	−	1.74092i
$555$	−61.7599	+	29.7420i	−2.62156	+	1.26248i
$556$	−3.16384	+	13.8617i	−0.134177	+	0.587866i
$557$	−14.6642			−0.621343			−0.310671	−	0.950517i	$-0.600554\pi$
$557$	−14.6642			−0.621343			−0.310671	+	0.950517i	$0.600554\pi$
$558$	44.5900			1.88765
$559$	0.406370	−	1.78042i	0.0171876	−	0.0753038i
$560$	14.6292	+	33.7264i	0.618199	+	1.42520i
$561$	15.7618	+	69.0569i	0.665463	+	2.91559i
$562$	−3.82929	−	16.7772i	−0.161529	−	0.707703i
$563$	−14.4180	−	18.0796i	−0.607646	−	0.761964i	0.378902	−	0.925437i	$-0.376302\pi$
$563$	−14.4180	−	18.0796i	−0.607646	−	0.761964i	−0.986548	+	0.163473i	$0.947730\pi$
$564$	22.1839	+	27.8178i	0.934112	+	1.17134i
$565$	−3.58689	−	15.7152i	−0.150902	−	0.661143i
$566$	−3.15250	−	13.8120i	−0.132510	−	0.580563i
$567$	29.4702	−	5.51106i	1.23763	−	0.231443i
$568$	1.46214	−	6.40605i	0.0613500	−	0.268792i
$569$	−29.8282			−1.25046			−0.625231	−	0.780440i	$-0.714995\pi$
$569$	−29.8282			−1.25046			−0.625231	+	0.780440i	$0.714995\pi$
$570$	93.8289			3.93006
$571$	4.75355	−	20.8266i	0.198930	−	0.871568i	−0.772646	−	0.634837i	$-0.781067\pi$
$571$	4.75355	−	20.8266i	0.198930	−	0.871568i	0.971575	−	0.236730i	$-0.0760758\pi$
$572$	−5.70236	+	2.74611i	−0.238427	+	0.114821i
$573$	27.6798	+	34.7094i	1.15634	+	1.45000i
$574$	−6.28006	−	5.42776i	−0.262125	−	0.226550i
$575$	13.9745	−	17.5234i	0.582776	−	0.730778i
$576$	1.72690	−	7.56605i	0.0719542	−	0.315252i
$577$	−3.43078	+	4.30206i	−0.142825	+	0.179097i	−0.848099	−	0.529838i	$-0.822253\pi$
$577$	−3.43078	+	4.30206i	−0.142825	+	0.179097i	0.705274	+	0.708935i	$0.250824\pi$
$578$	6.41158	−	3.08765i	0.266686	−	0.128429i
$579$	13.2118	+	16.5671i	0.549064	+	0.688505i
$580$	−3.18071	−	1.53175i	−0.132072	−	0.0636024i
$581$	−8.97511	+	16.8945i	−0.372350	+	0.700903i
$582$	22.6477	−	10.9066i	0.938777	−	0.452091i
$583$	−32.9975	−	15.8908i	−1.36662	−	0.658128i
$584$	−0.0983306	−	0.430815i	−0.00406895	−	0.0178272i
$585$	−15.8424	−	7.62930i	−0.655003	−	0.315433i
$586$	33.0333	−	41.4225i	1.36459	−	1.71115i
$587$	14.2785			0.589335			0.294668	−	0.955600i	$-0.404791\pi$
$587$	14.2785			0.589335			0.294668	+	0.955600i	$0.404791\pi$
$588$	−14.8278	−	21.9487i	−0.611488	−	0.905150i
$589$	24.1135			0.993578
$590$	−16.7790	+	21.0402i	−0.690780	+	0.866211i
$591$	48.8460	+	23.5230i	2.00926	+	0.967606i
$592$	8.80897	+	38.5946i	0.362046	+	1.58623i
$593$	27.1902	+	13.0941i	1.11657	+	0.537711i	0.898830	−	0.438296i	$-0.144418\pi$
$593$	27.1902	+	13.0941i	1.11657	+	0.537711i	0.217738	+	0.976007i	$0.430132\pi$
$594$	81.6655	−	39.3280i	3.35078	−	1.61365i
$595$	32.8804	+	8.88540i	1.34797	+	0.364266i
$596$	8.32334	+	4.00831i	0.340937	+	0.164187i
$597$	−43.5383	−	54.5953i	−1.78190	−	2.23444i
$598$	12.4984	−	6.01889i	0.511096	−	0.246131i
$599$	−5.89176	+	7.38803i	−0.240731	+	0.301867i	−0.887490	−	0.460828i	$-0.847553\pi$
$599$	−5.89176	+	7.38803i	−0.240731	+	0.301867i	0.646759	+	0.762695i	$0.276124\pi$
$600$	−2.68189	+	11.7501i	−0.109488	+	0.479698i
$601$	−1.28443	+	1.61063i	−0.0523931	+	0.0656989i	−0.807338	−	0.590090i	$-0.799092\pi$
$601$	−1.28443	+	1.61063i	−0.0523931	+	0.0656989i	0.754945	+	0.655789i	$0.227664\pi$
$602$	8.55417	−	1.59967i	0.348642	−	0.0651976i
$603$	−33.6031	−	42.1369i	−1.36842	−	1.71595i
$604$	−5.07451	+	2.44376i	−0.206479	+	0.0994350i
$605$	−9.31478	+	40.8107i	−0.378700	+	1.65919i
$606$	−36.6318			−1.48807
$607$	18.7711			0.761896			0.380948	−	0.924596i	$-0.375598\pi$
$607$	18.7711			0.761896			0.380948	+	0.924596i	$0.375598\pi$
$608$	8.36766	−	36.6611i	0.339353	−	1.48680i
$609$	−7.83889	−	2.11833i	−0.317648	−	0.0858392i
$610$	−4.60678	−	20.1836i	−0.186523	−	0.817212i
$611$	−2.09233	−	9.16710i	−0.0846466	−	0.370861i
$612$	−22.1965	−	27.8335i	−0.897240	−	1.12510i
$613$	5.94705	+	7.45736i	0.240199	+	0.301200i	0.887289	−	0.461213i	$-0.152586\pi$
$613$	5.94705	+	7.45736i	0.240199	+	0.301200i	−0.647090	+	0.762413i	$0.724014\pi$
$614$	4.13335	+	18.1094i	0.166809	+	0.730836i
$615$	−3.31587	−	14.5278i	−0.133709	−	0.585816i
$616$	13.8664	+	11.9845i	0.558693	+	0.482870i
$617$	3.62786	−	15.8947i	0.146052	−	0.639897i	−0.847907	−	0.530145i	$-0.822137\pi$
$617$	3.62786	−	15.8947i	0.146052	−	0.639897i	0.993959	−	0.109752i	$-0.0350055\pi$
$618$	56.1255			2.25770
$619$	−40.3940			−1.62357			−0.811786	−	0.583955i	$-0.801504\pi$
$619$	−40.3940			−1.62357			−0.811786	+	0.583955i	$0.801504\pi$
$620$	3.08295	−	13.5073i	0.123814	−	0.542466i
$621$	−68.6409	+	33.0557i	−2.75447	+	1.32648i
$622$	−16.4910	−	20.6790i	−0.661228	−	0.829154i
$623$	12.1993	−	22.9636i	0.488754	−	0.920019i
$624$	−9.36945	+	11.7489i	−0.375078	+	0.470333i
$625$	6.91636	−	30.3025i	0.276654	−	1.21210i
$626$	20.6165	−	25.8522i	0.824000	−	1.03326i
$627$	84.9037	−	40.8875i	3.39073	−	1.63289i
$628$	5.62835	+	7.05772i	0.224595	+	0.281634i
$629$	33.0446	+	15.9134i	1.31757	+	0.634510i
$630$	3.31146	−	83.7266i	0.131932	−	3.33575i
$631$	−14.7928	+	7.12383i	−0.588891	+	0.283595i	−0.704505	−	0.709699i	$-0.748831\pi$
$631$	−14.7928	+	7.12383i	−0.588891	+	0.283595i	0.115613	+	0.993294i	$0.463117\pi$
$632$	−15.5609	−	7.49374i	−0.618980	−	0.298085i
$633$	8.85912	+	38.8143i	0.352118	+	1.54273i
$634$	40.9252	+	19.7085i	1.62535	+	0.782725i
$635$	27.6813	−	34.7112i	1.09850	−	1.37747i
$636$	27.2400			1.08014
$637$	1.01379	+	6.92620i	0.0401680	+	0.274426i
$638$	−9.24588			−0.366048
$639$	−18.8114	+	23.5888i	−0.744168	+	0.933158i
$640$	25.6300	+	12.3428i	1.01311	+	0.487890i
$641$	−6.66563	−	29.2040i	−0.263276	−	1.15349i	−0.917673	−	0.397338i	$-0.869934\pi$
$641$	−6.66563	−	29.2040i	−0.263276	−	1.15349i	0.654396	−	0.756152i	$-0.272923\pi$
$642$	30.1533	+	14.5211i	1.19005	+	0.573100i
$643$	20.4337	−	9.84034i	0.805826	−	0.388065i	0.0148324	−	0.999890i	$-0.495279\pi$
$643$	20.4337	−	9.84034i	0.805826	−	0.388065i	0.790993	+	0.611825i	$0.209564\pi$
$644$	19.1794	+	16.5765i	0.755775	+	0.653205i
$645$	14.0757	+	6.77849i	0.554229	+	0.266903i
$646$	−31.3011	−	39.2504i	−1.23153	−	1.54429i
$647$	−17.9746	+	8.65610i	−0.706654	+	0.340306i	−0.752455	−	0.658644i	$-0.771130\pi$
$647$	−17.9746	+	8.65610i	−0.706654	+	0.340306i	0.0458009	+	0.998951i	$0.485416\pi$
$648$	9.61998	−	12.0631i	0.377909	−	0.473882i
$649$	−6.01434	+	26.3505i	−0.236083	+	1.03435i
$650$	−3.26797	+	4.09790i	−0.128180	+	0.160733i
$651$	1.25938	−	31.8421i	0.0493592	−	1.24799i
$652$	0.638255	+	0.800347i	0.0249960	+	0.0313440i
$653$	28.0379	−	13.5023i	1.09721	−	0.528387i	0.204428	−	0.978882i	$-0.434466\pi$
$653$	28.0379	−	13.5023i	1.09721	−	0.528387i	0.892779	+	0.450494i	$0.148752\pi$
$654$	6.65988	−	29.1788i	0.260422	−	1.14098i
$655$	−53.9282			−2.10715
$656$	−8.60565			−0.335994
$657$	−0.451506	+	1.97818i	−0.0176149	+	0.0771760i
$658$	36.1086	−	26.5307i	1.40766	−	1.03428i
$659$	−7.23000	−	31.6767i	−0.281641	−	1.23395i	−0.895689	−	0.444681i	$-0.853317\pi$
$659$	−7.23000	−	31.6767i	−0.281641	−	1.23395i	0.614048	−	0.789268i	$-0.289540\pi$
$660$	−12.0483	−	52.7869i	−0.468978	−	2.05473i
$661$	5.25670	+	6.59169i	0.204462	+	0.256387i	0.873481	−	0.486858i	$-0.161857\pi$
$661$	5.25670	+	6.59169i	0.204462	+	0.256387i	−0.669019	+	0.743245i	$0.733286\pi$
$662$	14.9624	+	18.7623i	0.581531	+	0.729217i
$663$	3.09808	+	13.5736i	0.120319	+	0.527154i
$664$	2.19076	+	9.59836i	0.0850181	+	0.372489i
$665$	1.79078	−	45.2778i	0.0694433	−	1.75580i
$666$	20.0781	−	87.9678i	0.778010	−	3.40868i
$667$	7.77129			0.300905
$668$	0.183612			0.00710416
$669$	−8.91681	+	39.0671i	−0.344744	+	1.51042i
$670$	−39.3434	+	18.9468i	−1.51997	+	0.731978i
$671$	−12.9639	−	16.2563i	−0.500467	−	0.627566i
$672$	−47.9745	−	12.9643i	−1.85066	−	0.500110i
$673$	19.4865	−	24.4353i	0.751149	−	0.941911i	−0.248494	−	0.968633i	$-0.579936\pi$
$673$	19.4865	−	24.4353i	0.751149	−	0.941911i	0.999643	+	0.0267227i	$0.00850712\pi$
$674$	−13.1272	+	57.5141i	−0.505641	+	2.21536i
$675$	17.9477	−	22.5057i	0.690806	−	0.866243i
$676$	−1.12083	+	0.539765i	−0.0431090	+	0.0207602i
$677$	9.94285	+	12.4679i	0.382135	+	0.479182i	0.935283	−	0.353901i	$-0.115145\pi$
$677$	9.94285	+	12.4679i	0.382135	+	0.479182i	−0.553148	+	0.833083i	$0.686574\pi$
$678$	28.2896	+	13.6236i	1.08646	+	0.523210i
$679$	−4.83079	−	11.1370i	−0.185389	−	0.427397i
$680$	15.7925	−	7.60525i	0.605613	−	0.291648i
$681$	26.3037	+	12.6672i	1.00796	+	0.485408i
$682$	−8.07423	−	35.3755i	−0.309178	−	1.35460i
$683$	6.69983	+	3.22647i	0.256362	+	0.123457i	0.557651	−	0.830075i	$-0.311703\pi$
$683$	6.69983	+	3.22647i	0.256362	+	0.123457i	−0.301289	+	0.953533i	$0.597417\pi$
$684$	−29.5302	+	37.0297i	−1.12912	+	1.41587i
$685$	23.7673			0.908100
$686$	−28.3572	+	17.5662i	−1.08268	+	0.670682i
$687$	−48.5397			−1.85190
$688$	5.62530	−	7.05391i	0.214463	−	0.268928i
$689$	−6.48586	−	3.12343i	−0.247092	−	0.118993i
$690$	26.4072	+	115.698i	1.00531	+	4.40453i
$691$	−15.1270	−	7.28476i	−0.575457	−	0.277125i	0.123435	−	0.992353i	$-0.460609\pi$
$691$	−15.1270	−	7.28476i	−0.575457	−	0.277125i	−0.698892	+	0.715227i	$0.746323\pi$
$692$	25.0406	−	12.0589i	0.951900	−	0.458411i
$693$	−33.4888	−	77.2054i	−1.27213	−	2.93279i
$694$	13.6621	+	6.57932i	0.518606	+	0.249748i
$695$	20.0416	+	25.1314i	0.760221	+	0.953286i
$696$	−3.76502	+	1.81314i	−0.142713	+	0.0687268i
$697$	−4.97107	+	6.23352i	−0.188293	+	0.236111i
$698$	−13.5192	+	59.2314i	−0.511708	+	2.24194i
$699$	−22.5611	+	28.2908i	−0.853341	+	1.07006i
$700$	−9.24657	−	2.49874i	−0.349487	−	0.0944433i
$701$	9.81838	+	12.3119i	0.370835	+	0.465013i	0.931877	−	0.362775i	$-0.118171\pi$
$701$	9.81838	+	12.3119i	0.370835	+	0.465013i	−0.561042	+	0.827788i	$0.689599\pi$
$702$	16.0519	−	7.73017i	0.605838	−	0.291756i
$703$	10.8578	−	47.5713i	0.409511	−	1.79419i
$704$	−6.31523			−0.238014
$705$	80.4393			3.02952
$706$	1.22390	−	5.36227i	0.0460622	−	0.201812i
$707$	−0.699138	+	17.6769i	−0.0262938	+	0.664810i
$708$	−4.47326	−	19.5986i	−0.168115	−	0.736562i
$709$	0.0358311	+	0.156987i	0.00134567	+	0.00589575i	0.975596	−	0.219572i	$-0.0704661\pi$
$709$	0.0358311	+	0.156987i	0.00134567	+	0.00589575i	−0.974251	+	0.225468i	$0.927609\pi$
$710$	15.2417	+	19.1125i	0.572011	+	0.717279i
$711$	49.4458	+	62.0030i	1.85436	+	2.32529i
$712$	−2.97776	−	13.0464i	−0.111596	−	0.488936i
$713$	6.78650	+	29.7336i	0.254156	+	1.11353i
$714$	−53.4654	+	39.2836i	−2.00089	+	1.47015i
$715$	−3.18401	+	13.9501i	−0.119075	+	0.521703i
$716$	−24.7282			−0.924135
$717$	−86.8977			−3.24525
$718$	−2.75456	+	12.0685i	−0.102799	+	0.450394i
$719$	−21.9173	+	10.5548i	−0.817377	+	0.393628i	−0.795366	−	0.606129i	$-0.792721\pi$
$719$	−21.9173	+	10.5548i	−0.817377	+	0.393628i	−0.0220115	+	0.999758i	$0.507007\pi$
$720$	−54.1636	−	67.9190i	−2.01856	−	2.53119i
$721$	1.07118	−	27.0837i	0.0398930	−	1.00865i
$722$	−20.3064	+	25.4634i	−0.755726	+	0.947651i
$723$	−3.27886	+	14.3656i	−0.121942	+	0.534263i
$724$	11.0483	−	13.8542i	0.410608	−	0.514886i
$725$	−2.64550	+	1.27401i	−0.0982514	+	0.0473154i
$726$	−50.8396	−	63.7508i	−1.88683	−	2.36601i
$727$	−23.2419	−	11.1927i	−0.861994	−	0.415115i	−0.0499788	−	0.998750i	$-0.515915\pi$
$727$	−23.2419	−	11.1927i	−0.861994	−	0.415115i	−0.812016	+	0.583636i	$0.801630\pi$
$728$	2.72553	+	2.35563i	0.101015	+	0.0873055i
$729$	17.4941	−	8.42470i	0.647929	−	0.312026i
$730$	1.48120	+	0.713309i	0.0548217	+	0.0264008i
$731$	−1.86005	−	8.14940i	−0.0687963	−	0.301416i
$732$	13.9333	+	6.70992i	0.514989	+	0.248006i
$733$	0.679102	−	0.851567i	0.0250832	−	0.0314533i	−0.769132	−	0.639090i	$-0.779311\pi$
$733$	0.679102	−	0.851567i	0.0250832	−	0.0314533i	0.794215	+	0.607637i	$0.207882\pi$
$734$	−36.8304			−1.35944
$735$	−59.6964	−	4.72949i	−2.20194	−	0.174450i
$736$	47.5607			1.75311
$737$	−27.3446	+	34.2890i	−1.00725	+	1.26305i
$738$	17.6722	+	8.51048i	0.650523	+	0.313275i
$739$	10.6268	+	46.5589i	0.390912	+	1.71270i	0.661451	+	0.749988i	$0.269941\pi$
$739$	10.6268	+	46.5589i	0.390912	+	1.71270i	−0.270540	+	0.962709i	$0.587202\pi$
$740$	−25.2592	−	12.1642i	−0.928546	−	0.447164i
$741$	16.6884	−	8.03669i	0.613062	−	0.295235i
$742$	1.35571	−	34.2776i	0.0497696	−	1.25837i
$743$	−24.9982	−	12.0385i	−0.917096	−	0.441650i	−0.0850623	−	0.996376i	$-0.527109\pi$
$743$	−24.9982	−	12.0385i	−0.917096	−	0.441650i	−0.832033	+	0.554726i	$0.812823\pi$
$744$	−10.2251	−	12.8219i	−0.374871	−	0.470074i
$745$	18.8173	−	9.06193i	0.689412	−	0.332003i
$746$	7.91175	−	9.92102i	0.289670	−	0.363234i
$747$	10.0594	−	44.0729i	0.368052	−	1.61254i
$748$	−18.0625	+	22.6496i	−0.660429	+	0.828151i
$749$	7.58273	−	14.2735i	0.277067	−	0.521544i
$750$	20.0775	+	25.1764i	0.733127	+	0.919312i
$751$	−25.8562	+	12.4517i	−0.943506	+	0.454368i	−0.841405	−	0.540406i	$-0.818271\pi$
$751$	−25.8562	+	12.4517i	−0.943506	+	0.454368i	−0.102101	+	0.994774i	$0.532557\pi$
$752$	10.3370	−	45.2896i	0.376953	−	1.65154i
$753$	62.0630			2.26170
$754$	−1.81733			−0.0661834
$755$	−2.83345	+	12.4141i	−0.103120	+	0.451797i
$756$	24.6325	+	21.2895i	0.895875	+	0.774291i
$757$	10.5427	+	46.1904i	0.383179	+	1.67882i	0.687449	+	0.726232i	$0.258730\pi$
$757$	10.5427	+	46.1904i	0.383179	+	1.67882i	−0.304270	+	0.952586i	$0.598413\pi$
$758$	3.04595	+	13.3452i	0.110634	+	0.484719i
$759$	74.3125	+	93.1849i	2.69737	+	3.38240i
$760$	−14.5396	−	18.2320i	−0.527406	−	0.661346i
$761$	0.495321	+	2.17014i	0.0179554	+	0.0786677i	0.983112	−	0.183006i	$-0.0585827\pi$
$761$	0.495321	+	2.17014i	0.0179554	+	0.0786677i	−0.965156	+	0.261674i	$0.915726\pi$
$762$	19.2441	+	84.3140i	0.697141	+	3.05437i
$763$	−13.9533	−	3.77066i	−0.505145	−	0.136507i
$764$	−4.04033	+	17.7019i	−0.146174	+	0.640431i
$765$	−80.4849			−2.90994
$766$	−2.44207			−0.0882355
$767$	−1.18215	+	5.17936i	−0.0426851	+	0.187016i
$768$	−56.7286	+	27.3191i	−2.04702	+	0.985792i
$769$	−12.0915	−	15.1622i	−0.436030	−	0.546764i	0.514462	−	0.857513i	$-0.327992\pi$
$769$	−12.0915	−	15.1622i	−0.436030	−	0.546764i	−0.950492	+	0.310749i	$0.899420\pi$
$770$	−67.0242	+	12.5338i	−2.41538	+	0.451687i
$771$	−35.6070	+	44.6498i	−1.28236	+	1.60802i
$772$	−1.92849	+	8.44925i	−0.0694078	+	0.304095i
$773$	26.5064	−	33.2380i	0.953369	−	1.19549i	−0.0272627	−	0.999628i	$-0.508679\pi$
$773$	26.5064	−	33.2380i	0.953369	−	1.19549i	0.980632	−	0.195859i	$-0.0627495\pi$
$774$	−18.5278	+	8.92251i	−0.665968	+	0.320713i
$775$	−7.18471	−	9.00934i	−0.258082	−	0.323625i
$776$	−5.62872	−	2.71065i	−0.202059	−	0.0973066i
$777$	−62.2515	−	16.8225i	−2.23326	−	0.603503i
$778$	49.3476	−	23.7645i	1.76920	−	0.852000i
$779$	9.55679	+	4.60231i	0.342408	+	0.164895i
$780$	−2.36816	−	10.3756i	−0.0847937	−	0.371506i
$781$	22.1205	+	10.6527i	0.791533	+	0.381182i
$782$	39.5891	−	49.6431i	1.41570	−	1.77523i
$783$	9.98080			0.356685
$784$	−10.3343	+	33.0030i	−0.369081	+	1.17868i
$785$	20.4085			0.728410
$786$	65.4961	−	82.1295i	2.33617	−	2.92946i
$787$	−24.8894	−	11.9861i	−0.887213	−	0.427259i	−0.0659592	−	0.997822i	$-0.521011\pi$
$787$	−24.8894	−	11.9861i	−0.887213	−	0.427259i	−0.821254	+	0.570563i	$0.806725\pi$
$788$	4.93404	+	21.6174i	0.175768	+	0.770089i
$789$	−87.7154	−	42.2415i	−3.12275	−	1.50384i
$790$	57.8924	−	27.8795i	2.05972	−	0.991908i
$791$	7.11407	−	13.3913i	0.252947	−	0.476141i
$792$	−39.0203	−	18.7912i	−1.38653	−	0.667716i
$793$	−2.54814	−	3.19527i	−0.0904871	−	0.113467i
$794$	−63.3680	+	30.5164i	−2.24885	+	1.08299i
$795$	38.3969	−	48.1482i	1.36180	−	1.70764i
$796$	6.35514	−	27.8437i	0.225252	−	0.986894i
$797$	−25.1523	+	31.5399i	−0.890939	+	1.11720i	0.101545	+	0.994831i	$0.467621\pi$
$797$	−25.1523	+	31.5399i	−0.890939	+	1.11720i	−0.992484	+	0.122371i	$0.960950\pi$
$798$	66.7806	+	57.7174i	2.36401	+	2.04318i
$799$	−26.8344	−	33.6492i	−0.949332	−	1.19042i
$800$	−16.1906	+	7.79699i	−0.572425	+	0.275665i
$801$	−13.6730	+	59.9055i	−0.483113	+	2.11666i
$802$	−24.6393			−0.870045
$803$	1.65114			0.0582676
$804$	7.25854	−	31.8018i	0.255989	−	1.12156i
$805$	56.3347	−	10.5348i	1.98554	−	0.371304i
$806$	−1.58704	−	6.95327i	−0.0559011	−	0.244919i
$807$	6.19312	+	27.1338i	0.218008	+	0.955156i
$808$	5.67640	+	7.11798i	0.199695	+	0.250410i
$809$	−16.8976	−	21.1889i	−0.594088	−	0.744963i	0.390355	−	0.920664i	$-0.372352\pi$
$809$	−16.8976	−	21.1889i	−0.594088	−	0.744963i	−0.984444	+	0.175701i	$0.943781\pi$
$810$	12.7733	+	55.9634i	0.448807	+	1.96635i
$811$	−5.11741	−	22.4208i	−0.179696	−	0.787302i	−0.981769	−	0.190076i	$-0.939127\pi$
$811$	−5.11741	−	22.4208i	−0.179696	−	0.787302i	0.802073	−	0.597226i	$-0.203730\pi$
$812$	−1.32157	−	3.04675i	−0.0463779	−	0.106920i
$813$	−5.02246	+	22.0049i	−0.176146	+	0.771744i
$814$	−73.4249			−2.57354
$815$	2.31433			0.0810673
$816$	−15.3059	+	67.0595i	−0.535813	+	2.34755i
$817$	−10.0195	+	4.82513i	−0.350537	+	0.168810i
$818$	−11.0292	−	13.8302i	−0.385626	−	0.483560i
$819$	−6.58243	−	15.1752i	−0.230009	−	0.530265i
$820$	3.79987	−	4.76488i	0.132697	−	0.166397i
$821$	−2.79108	+	12.2285i	−0.0974095	+	0.426779i	−0.999993	−	0.00373587i	$-0.998811\pi$
$821$	−2.79108	+	12.2285i	−0.0974095	+	0.426779i	0.902584	+	0.430515i	$0.141668\pi$
$822$	−28.8655	+	36.1962i	−1.00680	+	1.26249i
$823$	2.82267	−	1.35933i	0.0983921	−	0.0473832i	−0.384040	−	0.923316i	$-0.625468\pi$
$823$	2.82267	−	1.35933i	0.0983921	−	0.0473832i	0.482433	+	0.875933i	$0.339753\pi$
$824$	−8.69711	−	10.9058i	−0.302978	−	0.379922i
$825$	−40.5739	−	19.5394i	−1.41260	−	0.680274i
$826$	−24.8846	+	4.65354i	−0.865847	+	0.161917i
$827$	−21.1716	+	10.1957i	−0.736209	+	0.354539i	−0.764123	−	0.645071i	$-0.776828\pi$
$827$	−21.1716	+	10.1957i	−0.736209	+	0.354539i	0.0279141	+	0.999610i	$0.491114\pi$
$828$	−53.9712	−	25.9912i	−1.87563	−	0.903256i
$829$	−4.22085	−	18.4928i	−0.146596	−	0.642281i	−0.993816	−	0.111038i	$-0.964582\pi$
$829$	−4.22085	−	18.4928i	−0.146596	−	0.642281i	0.847220	−	0.531243i	$-0.178275\pi$
$830$	−33.0005	−	15.8922i	−1.14547	−	0.551627i
$831$	55.1855	−	69.2004i	1.91436	−	2.40054i
$832$	−1.24130			−0.0430342
$833$	17.9362	+	26.5499i	0.621451	+	0.919898i
$834$	−62.6142			−2.16815
$835$	0.258815	−	0.324544i	0.00895666	−	0.0112313i
$836$	34.7248	+	16.7226i	1.20098	+	0.578362i
$837$	8.71602	+	38.1874i	0.301270	+	1.31995i
$838$	−36.7605	−	17.7029i	−1.26987	−	0.611537i
$839$	13.2830	−	6.39678i	0.458582	−	0.220841i	−0.190307	−	0.981725i	$-0.560948\pi$
$839$	13.2830	−	6.39678i	0.458582	−	0.220841i	0.648889	+	0.760883i	$0.275234\pi$
$840$	−24.8350	+	18.2475i	−0.856890	+	0.629598i
$841$	25.2108	+	12.1409i	0.869339	+	0.418652i
$842$	−19.3262	−	24.2342i	−0.666024	−	0.835167i
$843$	26.1838	−	12.6095i	0.901818	−	0.434293i
$844$	−10.1522	+	12.7305i	−0.349454	+	0.438202i
$845$	−0.625837	+	2.74197i	−0.0215295	+	0.0943267i
$846$	−66.0164	+	82.7820i	−2.26969	+	2.84610i
$847$	−31.7337	+	23.3163i	−1.09038	+	0.801156i
$848$	−22.1745	−	27.8059i	−0.761475	−	0.954859i
$849$	21.5561	−	10.3809i	0.739804	−	0.356271i
$850$	−5.33853	+	23.3896i	−0.183110	+	0.802258i
$851$	61.7146			2.11555
$852$	−18.2608			−0.625606
$853$	−2.17649	+	9.53584i	−0.0745217	+	0.326501i	−0.998424	−	0.0561286i	$-0.982124\pi$
$853$	−2.17649	+	9.53584i	−0.0745217	+	0.326501i	0.923902	+	0.382630i	$0.124981\pi$
$854$	9.13689	−	17.1990i	0.312658	−	0.588539i
$855$	23.8269	+	104.393i	0.814863	+	3.57015i
$856$	−1.85089	−	8.10929i	−0.0632622	−	0.277170i
$857$	4.73938	+	5.94299i	0.161894	+	0.203009i	0.856161	−	0.516709i	$-0.172843\pi$
$857$	4.73938	+	5.94299i	0.161894	+	0.203009i	−0.694267	+	0.719717i	$0.744271\pi$
$858$	−17.3782	−	21.7915i	−0.593280	−	0.743950i
$859$	−7.82316	−	34.2755i	−0.266923	−	1.16946i	−0.913572	−	0.406677i	$-0.866687\pi$
$859$	−7.82316	−	34.2755i	−0.266923	−	1.16946i	0.646649	−	0.762787i	$-0.276170\pi$
$860$	1.42181	+	6.22938i	0.0484835	+	0.212420i
$861$	6.57654	−	12.3795i	0.224128	−	0.421893i
$862$	13.1600	−	57.6578i	0.448232	−	1.96383i
$863$	−37.8793			−1.28943			−0.644714	−	0.764424i	$-0.723023\pi$
$863$	−37.8793			−1.28943			−0.644714	+	0.764424i	$0.723023\pi$
$864$	61.0831			2.07809
$865$	13.9819	−	61.2585i	0.475397	−	2.08285i
$866$	31.2256	−	15.0375i	1.06109	−	0.510994i
$867$	7.49308	+	9.39603i	0.254478	+	0.319106i
$868$	10.5030	−	7.71708i	0.356496	−	0.261935i
$869$	40.2366	−	50.4551i	1.36493	−	1.71157i
$870$	3.45951	−	15.1571i	0.117288	−	0.513874i
$871$	−5.37475	+	6.73972i	−0.182116	+	0.228367i
$872$	−6.70179	+	3.22741i	−0.226951	+	0.109294i
$873$	17.8856	+	22.4278i	0.605336	+	0.759067i
$874$	−76.1093	−	36.6523i	−2.57444	−	1.23978i
$875$	12.5322	−	9.20803i	0.423667	−	0.311288i
$876$	−1.10645	+	0.532837i	−0.0373834	+	0.0180029i
$877$	−9.61446	−	4.63008i	−0.324657	−	0.156347i	0.264455	−	0.964398i	$-0.414808\pi$
$877$	−9.61446	−	4.63008i	−0.324657	−	0.156347i	−0.589112	+	0.808051i	$0.700522\pi$
$878$	−1.67993	−	7.36026i	−0.0566950	−	0.248397i
$879$	80.6137	+	38.8215i	2.71903	+	1.30942i
$880$	−44.0757	+	55.2692i	−1.48579	+	1.86313i
$881$	−3.26993			−0.110167			−0.0550833	−	0.998482i	$-0.517542\pi$
$881$	−3.26993			−0.110167			−0.0550833	+	0.998482i	$0.517542\pi$
$882$	53.8600	−	57.5535i	1.81356	−	1.93793i
$883$	−11.0271			−0.371091			−0.185545	−	0.982636i	$-0.559405\pi$
$883$	−11.0271			−0.371091			−0.185545	+	0.982636i	$0.559405\pi$
$884$	−3.55029	+	4.45192i	−0.119409	+	0.149734i
$885$	−40.9470	−	19.7190i	−1.37642	−	0.662849i
$886$	−3.91573	−	17.1560i	−0.131552	−	0.576366i
$887$	−21.9349	−	10.5633i	−0.736502	−	0.354680i	0.0277360	−	0.999615i	$-0.491170\pi$
$887$	−21.9349	−	10.5633i	−0.736502	−	0.354680i	−0.764238	+	0.644935i	$0.776885\pi$
$888$	−29.8994	+	14.3988i	−1.00336	+	0.483192i
$889$	41.0536	−	7.67720i	1.37689	−	0.257485i
$890$	44.8555	+	21.6013i	1.50356	+	0.724076i
$891$	35.9452	+	45.0739i	1.20421	+	1.51003i
$892$	−14.7659	+	7.11090i	−0.494400	+	0.238091i
$893$	−35.7005	+	44.7670i	−1.19467	+	1.49807i
$894$	−9.05291	+	39.6634i	−0.302775	+	1.32654i
$895$	−34.8563	+	43.7084i	−1.16512	+	1.46101i
$896$	10.6491	+	24.5506i	0.355762	+	0.820177i
$897$	14.6066	+	18.3161i	0.487699	+	0.611556i
$898$	2.68205	−	1.29160i	0.0895010	−	0.0431014i
$899$	0.889073	−	3.89528i	0.0296523	−	0.129915i
$900$	22.6338			0.754461
$901$	−32.9504			−1.09774
$902$	3.55176	−	15.5613i	0.118261	−	0.518134i
$903$	5.84836	+	13.4829i	0.194621	+	0.448682i
$904$	−1.73650	−	7.60809i	−0.0577550	−	0.253041i
$905$	−8.91450	−	39.0570i	−0.296328	−	1.29830i
$906$	−15.4648	−	19.3922i	−0.513783	−	0.644263i
$907$	10.7483	+	13.4780i	0.356892	+	0.447528i	0.927572	−	0.373644i	$-0.121892\pi$
$907$	10.7483	+	13.4780i	0.356892	+	0.447528i	−0.570680	+	0.821172i	$0.693320\pi$
$908$	2.65700	+	11.6411i	0.0881755	+	0.386322i
$909$	−9.30228	−	40.7559i	−0.308537	−	1.35179i
$910$	−13.1740	+	2.46360i	−0.436714	+	0.0816675i
$911$	5.67066	−	24.8448i	0.187877	−	0.823145i	−0.789856	−	0.613293i	$-0.789845\pi$
$911$	5.67066	−	24.8448i	0.187877	−	0.823145i	0.977733	−	0.209852i	$-0.0672982\pi$
$912$	91.5103			3.03021
$913$	−36.7868			−1.21746
$914$	5.54709	−	24.3034i	0.183481	−	0.803884i
$915$	31.5002	−	15.1697i	1.04136	−	0.501494i
$916$	−12.3777	−	15.5211i	−0.408970	−	0.512832i
$917$	−38.3821	−	33.1731i	−1.26749	−	1.09547i
$918$	50.8449	−	63.7575i	1.67813	−	2.10431i
$919$	−2.91411	+	12.7675i	−0.0961275	+	0.421162i	−0.999978	−	0.00668718i	$-0.997871\pi$
$919$	−2.91411	+	12.7675i	−0.0961275	+	0.421162i	0.903850	+	0.427849i	$0.140729\pi$
$920$	18.3894	−	23.0595i	0.606280	−	0.760251i
$921$	−28.2629	+	13.6107i	−0.931296	+	0.448488i
$922$	−28.9130	−	36.2557i	−0.952199	−	1.19402i
$923$	4.34791	+	2.09385i	0.143113	+	0.0689198i
$924$	23.8960	−	44.9812i	0.786120	−	1.47977i
$925$	−21.0089	+	10.1173i	−0.690768	+	0.332656i
$926$	19.7310	+	9.50194i	0.648400	+	0.312253i
$927$	14.2525	+	62.4442i	0.468113	+	2.05094i
$928$	−5.61371	−	2.70342i	−0.184279	−	0.0887442i
$929$	−18.0903	+	22.6845i	−0.593524	+	0.744255i	−0.984353	−	0.176208i	$-0.943617\pi$
$929$	−18.0903	+	22.6845i	−0.593524	+	0.744255i	0.390829	+	0.920463i	$0.372188\pi$
$930$	61.0135			2.00071
$931$	29.1265	−	31.1239i	0.954582	−	1.02004i
$932$	−14.7994			−0.484771
$933$	27.8498	−	34.9226i	0.911762	−	1.14331i
$934$	−38.7026	−	18.6382i	−1.26639	−	0.609860i
$935$	14.5740	+	63.8527i	0.476620	+	2.08821i
$936$	−7.66968	−	3.69352i	−0.250691	−	0.120727i
$937$	27.9010	−	13.4364i	0.911484	−	0.438948i	0.0814611	−	0.996677i	$-0.474041\pi$
$937$	27.9010	−	13.4364i	0.911484	−	0.438948i	0.830023	+	0.557729i	$0.188327\pi$
$938$	−39.6566	−	10.7165i	−1.29483	−	0.349908i
$939$	50.3119	+	24.2289i	1.64187	+	0.790681i
$940$	20.5121	+	25.7214i	0.669031	+	0.838939i
$941$	51.8401	−	24.9649i	1.68994	−	0.813831i	0.694387	−	0.719601i	$-0.255675\pi$
$941$	51.8401	−	24.9649i	1.68994	−	0.813831i	0.995550	−	0.0942297i	$-0.0300388\pi$
$942$	−24.7862	+	31.0810i	−0.807579	+	1.01267i
$943$	−2.98530	+	13.0795i	−0.0972149	+	0.425926i
$944$	−16.3644	+	20.5203i	−0.532615	+	0.667878i
$945$	72.3517	−	13.5301i	2.35360	−	0.440134i
$946$	10.4336	+	13.0834i	0.339227	+	0.425377i
$947$	−23.3895	+	11.2638i	−0.760055	+	0.366023i	−0.773425	−	0.633887i	$-0.781458\pi$
$947$	−23.3895	+	11.2638i	−0.760055	+	0.366023i	0.0133702	+	0.999911i	$0.495744\pi$
$948$	−10.6807	+	46.7951i	−0.346893	+	1.51984i
$949$	0.324542			0.0105351
$950$	31.9178			1.03555
$951$	−17.0698	+	74.7875i	−0.553525	+	2.42515i
$952$	15.9182	+	4.30163i	0.515911	+	0.139417i
$953$	5.95563	+	26.0933i	0.192922	+	0.845245i	0.975025	+	0.222096i	$0.0712899\pi$
$953$	5.95563	+	26.0933i	0.192922	+	0.845245i	−0.782103	+	0.623149i	$0.785853\pi$
$954$	18.0382	+	79.0303i	0.584007	+	2.55870i
$955$	25.5938	+	32.0936i	0.828196	+	1.03853i
$956$	−22.1590	−	27.7865i	−0.716673	−	0.898680i
$957$	−3.47452	−	15.2229i	−0.112315	−	0.492086i
$958$	13.1289	+	57.5213i	0.424175	+	1.85843i
$959$	16.9158	+	14.6201i	0.546240	+	0.472107i
$960$	2.36296	−	10.3528i	0.0762641	−	0.334135i
$961$	−15.3199			−0.494191
$962$	−14.4321			−0.465310
$963$	−8.49876	+	37.2355i	−0.273869	+	1.19990i
$964$	−5.42968	+	2.61480i	−0.174878	+	0.0842169i
$965$	12.2162	+	15.3186i	0.393252	+	0.493122i
$966$	−52.3749	+	98.5892i	−1.68513	+	3.17205i
$967$	−29.3175	+	36.7630i	−0.942787	+	1.18222i	0.0403199	+	0.999187i	$0.487162\pi$
$967$	−29.3175	+	36.7630i	−0.942787	+	1.18222i	−0.983107	+	0.183031i	$0.941409\pi$
$968$	−4.50950	+	19.7574i	−0.144941	+	0.635028i
$969$	52.8611	−	66.2857i	1.69814	−	2.12940i
$970$	20.9409	−	10.0846i	0.672373	−	0.323798i
$971$	0.675188	+	0.846659i	0.0216678	+	0.0271706i	0.792547	−	0.609810i	$-0.208754\pi$
$971$	0.675188	+	0.846659i	0.0216678	+	0.0271706i	−0.770880	+	0.636981i	$0.780183\pi$
$972$	−5.37195	−	2.58700i	−0.172305	−	0.0829779i
$973$	−1.19503	+	30.2149i	−0.0383108	+	0.968646i
$974$	−11.5300	+	5.55253i	−0.369443	+	0.177915i
$975$	−7.97506	−	3.84059i	−0.255406	−	0.122997i
$976$	−4.49295	−	19.6849i	−0.143816	−	0.630098i
$977$	18.3367	+	8.83048i	0.586643	+	0.282512i	0.703567	−	0.710629i	$-0.251589\pi$
$977$	18.3367	+	8.83048i	0.586643	+	0.282512i	−0.116925	+	0.993141i	$0.537304\pi$
$978$	−2.81076	+	3.52459i	−0.0898783	+	0.112704i
$979$	50.0019			1.59807
$980$	−13.7103	−	20.2946i	−0.437961	−	0.648288i
$981$	34.1551			1.09049
$982$	−17.7974	+	22.3172i	−0.567938	+	0.712171i
$983$	−6.57545	−	3.16657i	−0.209724	−	0.100998i	0.326073	−	0.945345i	$-0.394275\pi$
$983$	−6.57545	−	3.16657i	−0.209724	−	0.100998i	−0.535797	+	0.844347i	$0.679989\pi$
$984$	−1.60529	−	7.03323i	−0.0511747	−	0.224211i
$985$	45.1649	+	21.7503i	1.43907	+	0.693021i
$986$	−7.49459	+	3.60920i	−0.238676	+	0.114940i
$987$	57.2508	+	49.4810i	1.82231	+	1.57500i
$988$	6.82537	+	3.28692i	0.217144	+	0.104571i
$989$	−8.76961	−	10.9967i	−0.278857	−	0.349676i
$990$	145.170	−	69.9102i	4.61381	−	2.22189i
$991$	−14.4782	+	18.1551i	−0.459914	+	0.576714i	−0.956669	−	0.291177i	$-0.905953\pi$
$991$	−14.4782	+	18.1551i	−0.459914	+	0.576714i	0.496755	+	0.867891i	$0.334525\pi$
$992$	5.44118	−	23.8394i	0.172758	−	0.756901i
$993$	−25.2684	+	31.6856i	−0.801869	+	1.00551i
$994$	−0.908823	+	22.9786i	−0.0288261	+	0.728837i
$995$	−40.2572	−	50.4809i	−1.27624	−	1.60035i
$996$	24.6512	−	11.8714i	0.781102	−	0.376159i
$997$	1.74227	−	7.63340i	0.0551784	−	0.241752i	−0.939816	−	0.341680i	$-0.889004\pi$
$997$	1.74227	−	7.63340i	0.0551784	−	0.241752i	0.994995	+	0.0999279i	$0.0318612\pi$
$998$	−2.36913			−0.0749934
$999$	79.2612			2.50771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.w.b.92.7	✓	174
49.8	even	7	inner	637.2.w.b.547.7	yes	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.w.b.92.7	✓	174	1.1	even	1	trivial
637.2.w.b.547.7	yes	174	49.8	even	7	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.w (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12298 + 1.40817i) q^{2} +(-2.74049 - 1.31975i) q^{3} +(-0.276823 - 1.21284i) q^{4} +(-2.53396 - 1.22029i) q^{5} +(4.93595 - 2.37703i) q^{6} +(-1.05285 - 2.42724i) q^{7} +(-1.22675 - 0.590772i) q^{8} +(3.89808 + 4.88803i) q^{9} +O(q^{10})\)	\(q+(-1.12298 + 1.40817i) q^{2} +(-2.74049 - 1.31975i) q^{3} +(-0.276823 - 1.21284i) q^{4} +(-2.53396 - 1.22029i) q^{5} +(4.93595 - 2.37703i) q^{6} +(-1.05285 - 2.42724i) q^{7} +(-1.22675 - 0.590772i) q^{8} +(3.89808 + 4.88803i) q^{9} +(4.56397 - 2.19789i) q^{10} +(3.17207 - 3.97765i) q^{11} +(-0.842016 + 3.68912i) q^{12} +(0.623490 - 0.781831i) q^{13} +(4.60030 + 1.24316i) q^{14} +(5.33382 + 6.68840i) q^{15} +(4.45119 - 2.14358i) q^{16} +(1.01853 - 4.46247i) q^{17} -11.2607 q^{18} -6.08955 q^{19} +(-0.778561 + 3.41110i) q^{20} +(-0.318042 + 8.04133i) q^{21} +(2.03904 + 8.93364i) q^{22} +(-1.71384 - 7.50884i) q^{23} +(2.58223 + 3.23801i) q^{24} +(1.81441 + 2.27520i) q^{25} +(0.400787 + 1.75596i) q^{26} +(-2.20112 - 9.64374i) q^{27} +(-2.65241 + 1.94885i) q^{28} +(-0.224524 + 0.983705i) q^{29} -15.4082 q^{30} -3.95981 q^{31} +(-1.37410 + 6.02033i) q^{32} +(-13.9425 + 6.71437i) q^{33} +(5.14014 + 6.44553i) q^{34} +(-0.294074 + 7.43533i) q^{35} +(4.84933 - 6.08087i) q^{36} +(-1.78303 + 7.81196i) q^{37} +(6.83844 - 8.57513i) q^{38} +(-2.74049 + 1.31975i) q^{39} +(2.38763 + 2.99399i) q^{40} +(-1.56938 - 0.755772i) q^{41} +(-10.9664 - 9.47811i) q^{42} +(1.64536 - 0.792362i) q^{43} +(-5.70236 - 2.74611i) q^{44} +(-3.91275 - 17.1429i) q^{45} +(12.4984 + 6.01889i) q^{46} +(5.86258 - 7.35144i) q^{47} -15.0274 q^{48} +(-4.78303 + 5.11103i) q^{49} -5.24141 q^{50} +(-8.68062 + 10.8852i) q^{51} +(-1.12083 - 0.539765i) q^{52} +(-1.60188 - 7.01827i) q^{53} +(16.0519 + 7.73017i) q^{54} +(-12.8918 + 6.20837i) q^{55} +(-0.142368 + 3.59962i) q^{56} +(16.6884 + 8.03669i) q^{57} +(-1.13309 - 1.42085i) q^{58} +(-4.78645 + 2.30503i) q^{59} +(6.63544 - 8.32058i) q^{60} +(0.909421 - 3.98443i) q^{61} +(4.44678 - 5.57609i) q^{62} +(7.76038 - 14.6079i) q^{63} +(-0.773936 - 0.970485i) q^{64} +(-2.53396 + 1.22029i) q^{65} +(6.20219 - 27.1736i) q^{66} -8.62043 q^{67} -5.69422 q^{68} +(-5.21303 + 22.8398i) q^{69} +(-10.1400 - 8.76383i) q^{70} +(1.07385 + 4.70483i) q^{71} +(-1.89425 - 8.29927i) q^{72} +(0.202349 + 0.253737i) q^{73} +(-8.99828 - 11.2835i) q^{74} +(-1.96968 - 8.62972i) q^{75} +(1.68573 + 7.38565i) q^{76} +(-12.9944 - 3.51153i) q^{77} +(1.21908 - 5.34113i) q^{78} +12.6847 q^{79} -13.8949 q^{80} +(-2.52156 + 11.0477i) q^{81} +(2.82663 - 1.36123i) q^{82} +(-4.50824 - 5.65316i) q^{83} +(9.84090 - 1.84029i) q^{84} +(-8.02644 + 10.0648i) q^{85} +(-0.731920 + 3.20675i) q^{86} +(1.91355 - 2.39952i) q^{87} +(-6.24122 + 3.00561i) q^{88} +(6.12777 + 7.68398i) q^{89} +(28.5341 + 13.7413i) q^{90} +(-2.55413 - 0.690214i) q^{91} +(-8.63260 + 4.15724i) q^{92} +(10.8518 + 5.22596i) q^{93} +(3.76854 + 16.5110i) q^{94} +(15.4307 + 7.43103i) q^{95} +(11.7111 - 14.6852i) q^{96} +4.58831 q^{97} +(-1.82597 - 12.4749i) q^{98} +31.8079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9}+O(q^{10}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9	\( 174 q - 3 q^{2} - 31 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{7} - 15 q^{8} - 31 q^{9} - 10 q^{10} - 5 q^{11} + 25 q^{12} - 29 q^{13} + 15 q^{14} - 10 q^{15} - 51 q^{16} - 9 q^{17} + 44 q^{18} + 24 q^{19} + 63 q^{20} - 28 q^{21} - 8 q^{22} - 13 q^{23} - 48 q^{24} - 49 q^{25} - 3 q^{26} - 9 q^{27} - 44 q^{28} + 2 q^{29} - 22 q^{30} + 10 q^{31} + 24 q^{32} - 26 q^{33} + 118 q^{34} + 5 q^{35} - 55 q^{36} - 32 q^{37} + 16 q^{38} + 42 q^{40} - 14 q^{41} + 4 q^{42} - 50 q^{43} + 35 q^{44} - q^{45} + 4 q^{46} - 24 q^{47} - 116 q^{48} - 25 q^{49} + 156 q^{50} + 12 q^{51} - 31 q^{52} - 30 q^{53} - 78 q^{54} + 25 q^{55} + 3 q^{56} - 63 q^{57} - 12 q^{58} - 4 q^{59} + 128 q^{60} - 42 q^{61} - 38 q^{62} - 85 q^{63} - 105 q^{64} - 4 q^{65} + 15 q^{66} + 94 q^{67} + 214 q^{68} + 32 q^{69} - 57 q^{70} - 29 q^{71} - 64 q^{72} - 66 q^{73} - 90 q^{74} + 131 q^{75} - 21 q^{76} - 82 q^{77} + 19 q^{78} + 6 q^{79} + 22 q^{80} + 49 q^{81} - 50 q^{82} + 25 q^{83} + 89 q^{84} - 86 q^{85} - 28 q^{86} + 24 q^{87} + 48 q^{88} - 50 q^{89} - 155 q^{90} - 5 q^{91} - 98 q^{92} + 89 q^{93} - 28 q^{94} - 130 q^{95} - 105 q^{96} - 42 q^{97} + 195 q^{98} + 438 q^{99}+O(q^{100}) \) 174 * q - 3 * q^2 - 31 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^7 - 15 * q^8 - 31 * q^9 - 10 * q^10 - 5 * q^11 + 25 * q^12 - 29 * q^13 + 15 * q^14 - 10 * q^15 - 51 * q^16 - 9 * q^17 + 44 * q^18 + 24 * q^19 + 63 * q^20 - 28 * q^21 - 8 * q^22 - 13 * q^23 - 48 * q^24 - 49 * q^25 - 3 * q^26 - 9 * q^27 - 44 * q^28 + 2 * q^29 - 22 * q^30 + 10 * q^31 + 24 * q^32 - 26 * q^33 + 118 * q^34 + 5 * q^35 - 55 * q^36 - 32 * q^37 + 16 * q^38 + 42 * q^40 - 14 * q^41 + 4 * q^42 - 50 * q^43 + 35 * q^44 - q^45 + 4 * q^46 - 24 * q^47 - 116 * q^48 - 25 * q^49 + 156 * q^50 + 12 * q^51 - 31 * q^52 - 30 * q^53 - 78 * q^54 + 25 * q^55 + 3 * q^56 - 63 * q^57 - 12 * q^58 - 4 * q^59 + 128 * q^60 - 42 * q^61 - 38 * q^62 - 85 * q^63 - 105 * q^64 - 4 * q^65 + 15 * q^66 + 94 * q^67 + 214 * q^68 + 32 * q^69 - 57 * q^70 - 29 * q^71 - 64 * q^72 - 66 * q^73 - 90 * q^74 + 131 * q^75 - 21 * q^76 - 82 * q^77 + 19 * q^78 + 6 * q^79 + 22 * q^80 + 49 * q^81 - 50 * q^82 + 25 * q^83 + 89 * q^84 - 86 * q^85 - 28 * q^86 + 24 * q^87 + 48 * q^88 - 50 * q^89 - 155 * q^90 - 5 * q^91 - 98 * q^92 + 89 * q^93 - 28 * q^94 - 130 * q^95 - 105 * q^96 - 42 * q^97 + 195 * q^98 + 438 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more