LMFDB - Embedded newform 637.2.bl.a.53.23

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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.23
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48290 + 1.01102i) q^{2} +(1.80645 + 1.67614i) q^{3} +(0.446138 + 1.13674i) q^{4} +(-3.30336 + 1.01895i) q^{5} +(0.984164 + 4.31190i) q^{6} +(-2.12029 + 1.58252i) q^{7} +(0.311049 - 1.36279i) q^{8} +(0.229623 + 3.06411i) q^{9} +O(q^{10})$	\(q+(1.48290 + 1.01102i) q^{2} +(1.80645 + 1.67614i) q^{3} +(0.446138 + 1.13674i) q^{4} +(-3.30336 + 1.01895i) q^{5} +(0.984164 + 4.31190i) q^{6} +(-2.12029 + 1.58252i) q^{7} +(0.311049 - 1.36279i) q^{8} +(0.229623 + 3.06411i) q^{9} +(-5.92872 - 1.82877i) q^{10} +(-0.427557 + 5.70535i) q^{11} +(-1.09941 + 2.80125i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-4.74414 + 0.203050i) q^{14} +(-7.67524 - 3.69620i) q^{15} +(3.62941 - 3.36760i) q^{16} +(2.37654 - 0.358206i) q^{17} +(-2.75737 + 4.77591i) q^{18} +(-2.59991 - 4.50318i) q^{19} +(-2.63203 - 3.30047i) q^{20} +(-6.48272 - 0.695166i) q^{21} +(-6.40226 + 8.02818i) q^{22} +(6.85517 + 1.03325i) q^{23} +(2.84612 - 1.94045i) q^{24} +(5.74270 - 3.91531i) q^{25} +(1.77471 + 0.267495i) q^{26} +(-0.111696 + 0.140062i) q^{27} +(-2.74485 - 1.70420i) q^{28} +(2.83612 + 3.55638i) q^{29} +(-7.64466 - 13.2409i) q^{30} +(-2.85073 + 4.93760i) q^{31} +(6.02230 - 0.907716i) q^{32} +(-10.3353 + 9.58977i) q^{33} +(3.88633 + 1.87156i) q^{34} +(5.39157 - 7.38809i) q^{35} +(-3.38065 + 1.62803i) q^{36} +(-3.54519 + 9.03299i) q^{37} +(0.697413 - 9.30633i) q^{38} +(2.35480 + 0.726361i) q^{39} +(0.361114 + 4.81873i) q^{40} +(1.30265 - 5.70730i) q^{41} +(-8.91038 - 7.58504i) q^{42} +(2.24752 + 9.84703i) q^{43} +(-6.67625 + 2.05935i) q^{44} +(-3.88070 - 9.88785i) q^{45} +(9.12087 + 8.46293i) q^{46} +(-3.94698 - 2.69100i) q^{47} +12.2009 q^{48} +(1.99127 - 6.71080i) q^{49} +12.4743 q^{50} +(4.89351 + 3.33634i) q^{51} +(0.895169 + 0.830596i) q^{52} +(0.0686852 + 0.175007i) q^{53} +(-0.307240 + 0.0947711i) q^{54} +(-4.40109 - 19.2824i) q^{55} +(1.49713 + 3.38176i) q^{56} +(2.85135 - 12.4926i) q^{57} +(0.610093 + 8.14112i) q^{58} +(7.44582 + 2.29673i) q^{59} +(0.777407 - 10.3738i) q^{60} +(-1.88133 + 4.79355i) q^{61} +(-9.21937 + 4.43981i) q^{62} +(-5.33587 - 6.13341i) q^{63} +(0.926629 + 0.446241i) q^{64} +(-2.53411 + 2.35131i) q^{65} +(-25.0217 + 3.77141i) q^{66} +(3.89389 - 6.74442i) q^{67} +(1.46745 + 2.54170i) q^{68} +(10.6516 + 13.3567i) q^{69} +(15.4647 - 5.50479i) q^{70} +(5.18953 - 6.50746i) q^{71} +(4.24716 + 0.640157i) q^{72} +(9.54602 - 6.50837i) q^{73} +(-14.3897 + 9.81074i) q^{74} +(16.9365 + 2.55277i) q^{75} +(3.95903 - 4.96447i) q^{76} +(-8.12227 - 12.7736i) q^{77} +(2.75757 + 3.45788i) q^{78} +(-0.667247 - 1.15570i) q^{79} +(-8.55781 + 14.8226i) q^{80} +(8.67860 - 1.30809i) q^{81} +(7.70192 - 7.14634i) q^{82} +(1.46697 + 0.706457i) q^{83} +(-2.10196 - 7.67931i) q^{84} +(-7.48557 + 3.60486i) q^{85} +(-6.62273 + 16.8744i) q^{86} +(-0.837685 + 11.1781i) q^{87} +(7.64221 + 2.35731i) q^{88} +(-0.659284 - 8.79753i) q^{89} +(4.24217 - 18.5862i) q^{90} +(-1.22369 + 2.34576i) q^{91} +(1.88381 + 8.25352i) q^{92} +(-13.4258 + 4.14131i) q^{93} +(-3.13230 - 7.98097i) q^{94} +(13.1770 + 12.2264i) q^{95} +(12.4004 + 8.45448i) q^{96} -1.28632 q^{97} +(9.73763 - 7.93821i) q^{98} -17.5800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * 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 $

$2$	1.48290	+	1.01102i	1.04857	+	0.714901i	0.959667	−	0.281139i	$-0.0907123\pi$
$2$	1.48290	+	1.01102i	1.04857	+	0.714901i	0.0889004	+	0.996041i	$0.471665\pi$
$3$	1.80645	+	1.67614i	1.04295	+	0.967719i	0.999509	−	0.0313365i	$-0.00997636\pi$
$3$	1.80645	+	1.67614i	1.04295	+	0.967719i	0.0434445	+	0.999056i	$0.486167\pi$
$4$	0.446138	+	1.13674i	0.223069	+	0.568370i
$5$	−3.30336	+	1.01895i	−1.47731	+	0.455688i	−0.925649	−	0.378383i	$-0.876480\pi$
$5$	−3.30336	+	1.01895i	−1.47731	+	0.455688i	−0.551656	+	0.834071i	$0.686004\pi$
$6$	0.984164	+	4.31190i	0.401783	+	1.76033i
$7$	−2.12029	+	1.58252i	−0.801395	+	0.598136i
$7$	−2.12029	+	1.58252i	−0.801395	+	0.598136i
$8$	0.311049	−	1.36279i	0.109972	−	0.481820i
$9$	0.229623	+	3.06411i	0.0765410	+	1.02137i
$10$	−5.92872	−	1.82877i	−1.87483	−	0.578307i
$11$	−0.427557	+	5.70535i	−0.128913	+	1.72023i	0.440143	+	0.897928i	$0.354928\pi$
$11$	−0.427557	+	5.70535i	−0.128913	+	1.72023i	−0.569056	+	0.822299i	$0.692691\pi$
$12$	−1.09941	+	2.80125i	−0.317372	+	0.808652i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	−4.74414	+	0.203050i	−1.26792	+	0.0542674i
$15$	−7.67524	−	3.69620i	−1.98174	−	0.954355i
$16$	3.62941	−	3.36760i	0.907352	−	0.841899i
$17$	2.37654	−	0.358206i	0.576396	−	0.0868778i	0.145627	−	0.989340i	$-0.453480\pi$
$17$	2.37654	−	0.358206i	0.576396	−	0.0868778i	0.430770	+	0.902462i	$0.358242\pi$
$18$	−2.75737	+	4.77591i	−0.649919	+	1.12569i
$19$	−2.59991	−	4.50318i	−0.596461	−	1.03310i	−0.993339	−	0.115230i	$-0.963240\pi$
$19$	−2.59991	−	4.50318i	−0.596461	−	1.03310i	0.396878	−	0.917872i	$-0.370094\pi$
$20$	−2.63203	−	3.30047i	−0.588541	−	0.738007i
$21$	−6.48272	−	0.695166i	−1.41464	−	0.151698i
$22$	−6.40226	+	8.02818i	−1.36497	+	1.71161i
$23$	6.85517	+	1.03325i	1.42940	+	0.215448i	0.817701	−	0.575643i	$-0.195248\pi$
$23$	6.85517	+	1.03325i	1.42940	+	0.215448i	0.611700	+	0.791090i	$0.290486\pi$
$24$	2.84612	−	1.94045i	0.580962	−	0.396093i
$25$	5.74270	−	3.91531i	1.14854	−	0.783062i
$26$	1.77471	+	0.267495i	0.348050	+	0.0524600i
$27$	−0.111696	+	0.140062i	−0.0214959	+	0.0269550i
$28$	−2.74485	−	1.70420i	−0.518729	−	0.322064i
$29$	2.83612	+	3.55638i	0.526654	+	0.660403i	0.972007	−	0.234952i	$-0.0754934\pi$
$29$	2.83612	+	3.55638i	0.526654	+	0.660403i	−0.445353	+	0.895355i	$0.646922\pi$
$30$	−7.64466	−	13.2409i	−1.39572	−	2.41745i
$31$	−2.85073	+	4.93760i	−0.512006	+	0.886820i	0.487898	+	0.872901i	$0.337764\pi$
$31$	−2.85073	+	4.93760i	−0.512006	+	0.886820i	−0.999903	+	0.0139187i	$0.995569\pi$
$32$	6.02230	−	0.907716i	1.06460	−	0.160463i
$33$	−10.3353	+	9.58977i	−1.79915	+	1.66936i
$34$	3.88633	+	1.87156i	0.666500	+	0.320969i
$35$	5.39157	−	7.38809i	0.911342	−	1.24882i
$36$	−3.38065	+	1.62803i	−0.563441	+	0.271339i
$37$	−3.54519	+	9.03299i	−0.582825	+	1.48501i	0.270022	+	0.962854i	$0.412969\pi$
$37$	−3.54519	+	9.03299i	−0.582825	+	1.48501i	−0.852847	+	0.522160i	$0.825126\pi$
$38$	0.697413	−	9.30633i	0.113135	−	1.50969i
$39$	2.35480	+	0.726361i	0.377070	+	0.116311i
$40$	0.361114	+	4.81873i	0.0570971	+	0.761908i
$41$	1.30265	−	5.70730i	0.203440	−	0.891331i	−0.765382	−	0.643576i	$-0.777450\pi$
$41$	1.30265	−	5.70730i	0.203440	−	0.891331i	0.968823	−	0.247755i	$-0.0796928\pi$
$42$	−8.91038	−	7.58504i	−1.37490	−	1.17040i
$43$	2.24752	+	9.84703i	0.342744	+	1.50166i	0.793256	+	0.608888i	$0.208384\pi$
$43$	2.24752	+	9.84703i	0.342744	+	1.50166i	−0.450513	+	0.892770i	$0.648759\pi$
$44$	−6.67625	+	2.05935i	−1.00648	+	0.310459i
$45$	−3.88070	−	9.88785i	−0.578500	−	1.47399i
$46$	9.12087	+	8.46293i	1.34480	+	1.24779i
$47$	−3.94698	−	2.69100i	−0.575726	−	0.392523i	0.240162	−	0.970733i	$-0.422799\pi$
$47$	−3.94698	−	2.69100i	−0.575726	−	0.392523i	−0.815888	+	0.578209i	$0.803752\pi$
$48$	12.2009			1.76105
$49$	1.99127	−	6.71080i	0.284468	−	0.958686i
$50$	12.4743			1.76413
$51$	4.89351	+	3.33634i	0.685228	+	0.467181i
$52$	0.895169	+	0.830596i	0.124138	+	0.115183i
$53$	0.0686852	+	0.175007i	0.00943464	+	0.0240391i	0.935513	−	0.353291i	$-0.114937\pi$
$53$	0.0686852	+	0.175007i	0.00943464	+	0.0240391i	−0.926079	+	0.377330i	$0.876842\pi$
$54$	−0.307240	+	0.0947711i	−0.0418101	+	0.0128967i
$55$	−4.40109	−	19.2824i	−0.593443	−	2.60004i
$56$	1.49713	+	3.38176i	0.200062	+	0.451906i
$57$	2.85135	−	12.4926i	0.377671	−	1.65468i
$58$	0.610093	+	8.14112i	0.0801091	+	1.06898i
$59$	7.44582	+	2.29673i	0.969363	+	0.299009i	0.738707	−	0.674026i	$-0.235437\pi$
$59$	7.44582	+	2.29673i	0.969363	+	0.299009i	0.230656	+	0.973035i	$0.425913\pi$
$60$	0.777407	−	10.3738i	0.100363	−	1.33925i
$61$	−1.88133	+	4.79355i	−0.240880	+	0.613751i	−0.999276	−	0.0380423i	$-0.987888\pi$
$61$	−1.88133	+	4.79355i	−0.240880	+	0.613751i	0.758397	+	0.651793i	$0.225983\pi$
$62$	−9.21937	+	4.43981i	−1.17086	+	0.563857i
$63$	−5.33587	−	6.13341i	−0.672256	−	0.772738i
$64$	0.926629	+	0.446241i	0.115829	+	0.0557801i
$65$	−2.53411	+	2.35131i	−0.314318	+	0.291645i
$66$	−25.0217	+	3.77141i	−3.07996	+	0.464229i
$67$	3.89389	−	6.74442i	0.475715	−	0.823962i	−0.523898	−	0.851781i	$-0.675523\pi$
$67$	3.89389	−	6.74442i	0.475715	−	0.823962i	0.999613	+	0.0278189i	$0.00885619\pi$
$68$	1.46745	+	2.54170i	0.177955	+	0.308227i
$69$	10.6516	+	13.3567i	1.28231	+	1.60796i
$70$	15.4647	−	5.50479i	1.84838	−	0.657948i
$71$	5.18953	−	6.50746i	0.615884	−	0.772294i	−0.371875	−	0.928283i	$-0.621285\pi$
$71$	5.18953	−	6.50746i	0.615884	−	0.772294i	0.987759	+	0.155989i	$0.0498565\pi$
$72$	4.24716	+	0.640157i	0.500533	+	0.0754432i
$73$	9.54602	−	6.50837i	1.11728	−	0.761747i	0.143591	−	0.989637i	$-0.454135\pi$
$73$	9.54602	−	6.50837i	1.11728	−	0.761747i	0.973687	+	0.227890i	$0.0731828\pi$
$74$	−14.3897	+	9.81074i	−1.67277	+	1.14048i
$75$	16.9365	+	2.55277i	1.95566	+	0.294768i
$76$	3.95903	−	4.96447i	0.454132	−	0.569463i
$77$	−8.12227	−	12.7736i	−0.925618	−	1.45569i
$78$	2.75757	+	3.45788i	0.312233	+	0.391528i
$79$	−0.667247	−	1.15570i	−0.0750711	−	0.130027i	0.826046	−	0.563603i	$-0.190585\pi$
$79$	−0.667247	−	1.15570i	−0.0750711	−	0.130027i	−0.901117	+	0.433576i	$0.857252\pi$
$80$	−8.55781	+	14.8226i	−0.956792	+	1.65721i
$81$	8.67860	−	1.30809i	0.964288	−	0.145343i
$82$	7.70192	−	7.14634i	0.850535	−	0.789181i
$83$	1.46697	+	0.706457i	0.161021	+	0.0775437i	0.512659	−	0.858593i	$-0.328661\pi$
$83$	1.46697	+	0.706457i	0.161021	+	0.0775437i	−0.351637	+	0.936136i	$0.614375\pi$
$84$	−2.10196	−	7.67931i	−0.229343	−	0.837881i
$85$	−7.48557	+	3.60486i	−0.811924	+	0.391002i
$86$	−6.62273	+	16.8744i	−0.714147	+	1.81962i
$87$	−0.837685	+	11.1781i	−0.0898093	+	1.19842i
$88$	7.64221	+	2.35731i	0.814662	+	0.251290i
$89$	−0.659284	−	8.79753i	−0.0698839	−	0.932536i	−0.916423	−	0.400210i	$-0.868937\pi$
$89$	−0.659284	−	8.79753i	−0.0698839	−	0.932536i	0.846539	−	0.532326i	$-0.178682\pi$
$90$	4.24217	−	18.5862i	0.447164	−	1.95915i
$91$	−1.22369	+	2.34576i	−0.128277	+	0.245902i
$92$	1.88381	+	8.25352i	0.196401	+	0.860488i
$93$	−13.4258	+	4.14131i	−1.39219	+	0.429434i
$94$	−3.13230	−	7.98097i	−0.323072	−	0.823174i
$95$	13.1770	+	12.2264i	1.35193	+	1.25441i
$96$	12.4004	+	8.45448i	1.26561	+	0.862881i
$97$	−1.28632			−0.130606			−0.0653031	−	0.997865i	$-0.520801\pi$
$97$	−1.28632			−0.130606			−0.0653031	+	0.997865i	$0.520801\pi$
$98$	9.73763	−	7.93821i	0.983649	−	0.801880i
$99$	−17.5800			−1.76685
$100$	7.01273	+	4.78120i	0.701273	+	0.478120i
$101$	−7.58991	−	7.04241i	−0.755224	−	0.700746i	0.205375	−	0.978683i	$-0.434159\pi$
$101$	−7.58991	−	7.04241i	−0.755224	−	0.700746i	−0.960599	+	0.277938i	$0.910349\pi$
$102$	3.88346	+	9.89489i	0.384520	+	0.979740i
$103$	−5.13208	+	1.58304i	−0.505679	+	0.155981i	−0.537089	−	0.843525i	$-0.680476\pi$
$103$	−5.13208	+	1.58304i	−0.505679	+	0.155981i	0.0314107	+	0.999507i	$0.490000\pi$
$104$	−0.311049	−	1.36279i	−0.0305008	−	0.133633i
$105$	22.1231	−	4.30918i	2.15899	−	0.420533i
$106$	−0.0750830	+	0.328960i	−0.00729270	+	0.0319514i
$107$	−0.721234	−	9.62420i	−0.0697243	−	0.930406i	−0.916906	−	0.399103i	$-0.869322\pi$
$107$	−0.721234	−	9.62420i	−0.0697243	−	0.930406i	0.847182	−	0.531303i	$-0.178298\pi$
$108$	−0.209046	−	0.0644823i	−0.0201155	−	0.00620481i
$109$	1.19652	−	15.9664i	0.114606	−	1.52931i	−0.582792	−	0.812621i	$-0.698040\pi$
$109$	1.19652	−	15.9664i	0.114606	−	1.52931i	0.697398	−	0.716684i	$-0.254341\pi$
$110$	12.9686	−	33.0435i	1.23651	−	3.15057i
$111$	−21.5447	+	10.3754i	−2.04494	+	0.984790i
$112$	−2.36612	+	12.8839i	−0.223577	+	1.21741i
$113$	−11.7311	−	5.64941i	−1.10357	−	0.531452i	−0.208792	−	0.977960i	$-0.566953\pi$
$113$	−11.7311	−	5.64941i	−1.10357	−	0.531452i	−0.894780	+	0.446508i	$0.852667\pi$
$114$	16.8586	−	15.6425i	1.57895	−	1.46505i
$115$	−23.6979	+	3.57188i	−2.20984	+	0.333080i
$116$	−2.77738	+	4.81056i	−0.257873	+	0.446649i
$117$	1.53635	+	2.66103i	0.142035	+	0.246013i
$118$	8.71935	+	10.9337i	0.802681	+	1.00653i
$119$	−4.47210	+	4.52043i	−0.409956	+	0.414387i
$120$	−7.42453	+	9.31007i	−0.677764	+	0.849889i
$121$	−21.4910	−	3.23925i	−1.95373	−	0.294477i
$122$	−7.63621	+	5.20628i	−0.691350	+	0.471354i
$123$	11.9194	−	8.12652i	1.07474	−	0.732743i
$124$	−6.88459	−	1.03768i	−0.618254	−	0.0931868i
$125$	−4.20386	+	5.27147i	−0.376005	+	0.471495i
$126$	−1.71153	−	14.4899i	−0.152475	−	1.29086i
$127$	0.577353	+	0.723978i	0.0512318	+	0.0642427i	0.806787	−	0.590842i	$-0.201204\pi$
$127$	0.577353	+	0.723978i	0.0512318	+	0.0642427i	−0.755555	+	0.655085i	$0.772633\pi$
$128$	−5.16739	−	8.95019i	−0.456737	−	0.791092i
$129$	−12.4450	+	21.5553i	−1.09572	+	1.89784i
$130$	−6.13507	+	0.924713i	−0.538081	+	0.0811027i
$131$	−4.75892	+	4.41563i	−0.415789	+	0.385796i	−0.860141	−	0.510057i	$-0.829624\pi$
$131$	−4.75892	+	4.41563i	−0.415789	+	0.385796i	0.444352	+	0.895852i	$0.353434\pi$
$132$	−15.5120	−	7.47021i	−1.35015	−	0.650198i
$133$	12.6389	+	5.43365i	1.09594	+	0.471157i
$134$	12.5930	−	6.06447i	1.08787	−	0.523891i
$135$	0.226255	−	0.576489i	0.0194729	−	0.0496163i
$136$	0.251059	−	3.35016i	0.0215282	−	0.287273i
$137$	10.6118	+	3.27329i	0.906624	+	0.279656i	0.712790	−	0.701378i	$-0.247431\pi$
$137$	10.6118	+	3.27329i	0.906624	+	0.279656i	0.193834	+	0.981034i	$0.437908\pi$
$138$	2.29133	+	30.5757i	0.195051	+	2.60278i
$139$	−3.50359	+	15.3502i	−0.297171	+	1.30199i	0.577148	+	0.816640i	$0.304166\pi$
$139$	−3.50359	+	15.3502i	−0.297171	+	1.30199i	−0.874319	+	0.485352i	$0.838692\pi$
$140$	10.8037	+	2.83271i	0.913081	+	0.239408i
$141$	−2.61952	−	11.4768i	−0.220603	−	0.966525i
$142$	14.2747	−	4.40317i	1.19791	−	0.369506i
$143$	2.09024	+	5.32585i	0.174795	+	0.445370i
$144$	11.1521	+	10.3476i	0.929339	+	0.862300i
$145$	−12.9925	−	8.85812i	−1.07897	−	0.735627i
$146$	20.7359			1.71611
$147$	14.8454	−	8.78506i	1.22443	−	0.724580i
$148$	−11.8498			−0.974048
$149$	−11.9601	−	8.15428i	−0.979812	−	0.668024i	−0.0362923	−	0.999341i	$-0.511555\pi$
$149$	−11.9601	−	8.15428i	−0.979812	−	0.668024i	−0.943520	+	0.331317i	$0.892507\pi$
$150$	22.5342	+	20.9087i	1.83991	+	1.70719i
$151$	7.52451	+	19.1721i	0.612336	+	1.56021i	0.814071	+	0.580765i	$0.197247\pi$
$151$	7.52451	+	19.1721i	0.612336	+	1.56021i	−0.201735	+	0.979440i	$0.564658\pi$
$152$	−6.94560	+	2.14244i	−0.563363	+	0.173774i
$153$	1.64329	+	7.19973i	0.132852	+	0.582063i
$154$	0.869917	−	27.1538i	0.0700999	−	2.18811i
$155$	4.38579	−	19.2154i	0.352275	−	1.54342i
$156$	0.224883	+	3.00086i	0.0180051	+	0.240261i
$157$	13.3479	+	4.11729i	1.06528	+	0.328596i	0.777358	−	0.629058i	$-0.216559\pi$
$157$	13.3479	+	4.11729i	1.06528	+	0.328596i	0.287922	+	0.957654i	$0.407035\pi$
$158$	0.178985	−	2.38839i	0.0142393	−	0.190010i
$159$	−0.169260	+	0.431267i	−0.0134232	+	0.0342017i
$160$	−18.9689	+	9.13494i	−1.49962	+	0.722180i
$161$	−16.1701	+	8.65763i	−1.27438	+	0.682317i
$162$	14.1920	+	6.83450i	1.11503	+	0.536969i
$163$	7.05669	−	6.54765i	0.552723	−	0.512852i	−0.353623	−	0.935388i	$-0.615051\pi$
$163$	7.05669	−	6.54765i	0.552723	−	0.512852i	0.906346	+	0.422536i	$0.138860\pi$
$164$	7.06889	−	1.06546i	0.551987	−	0.0831987i
$165$	24.3697	−	42.2096i	1.89718	−	3.28601i
$166$	1.46113	+	2.53075i	0.113405	+	0.196424i
$167$	9.87037	+	12.3771i	0.763792	+	0.957765i	0.999903	−	0.0139611i	$-0.00444410\pi$
$167$	9.87037	+	12.3771i	0.763792	+	0.957765i	−0.236110	+	0.971726i	$0.575873\pi$
$168$	−2.96381	+	8.61837i	−0.228663	+	0.664922i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−14.7449	−	2.22244i	−1.13089	−	0.170454i
$171$	13.2012	−	9.00044i	1.00952	−	0.688281i
$172$	−10.1908	+	6.94798i	−0.777042	+	0.529778i
$173$	−4.81436	−	0.725648i	−0.366029	−	0.0551700i	−0.0365472	−	0.999332i	$-0.511636\pi$
$173$	−4.81436	−	0.725648i	−0.366029	−	0.0551700i	−0.329482	+	0.944162i	$0.606874\pi$
$174$	−12.5436	+	15.7291i	−0.950924	+	1.19242i
$175$	−5.98016	+	17.3895i	−0.452058	+	1.31452i
$176$	17.6615	+	22.1469i	1.33129	+	1.66938i
$177$	9.60085	+	16.6292i	0.721644	+	1.24992i
$178$	7.91685	−	13.7124i	0.593393	−	1.02779i
$179$	−8.39761	+	1.26574i	−0.627667	+	0.0946056i	−0.455170	−	0.890404i	$-0.650422\pi$
$179$	−8.39761	+	1.26574i	−0.627667	+	0.0946056i	−0.172497	+	0.985010i	$0.555183\pi$
$180$	9.50860	−	8.82269i	0.708729	−	0.657604i
$181$	−9.35486	−	4.50506i	−0.695341	−	0.334859i	0.0526076	−	0.998615i	$-0.483247\pi$
$181$	−9.35486	−	4.50506i	−0.695341	−	0.334859i	−0.747949	+	0.663757i	$0.768961\pi$
$182$	−4.18622	+	2.24135i	−0.310303	+	0.166140i
$183$	−11.4332	+	5.50593i	−0.845165	+	0.407010i
$184$	3.54039	−	9.02078i	0.261001	−	0.665021i
$185$	2.50685	−	33.4515i	0.184307	−	2.45941i
$186$	−24.0960	−	7.43265i	−1.76681	−	0.544988i
$187$	1.02758	+	13.7122i	0.0751444	+	1.00273i
$188$	1.29808	−	5.68725i	0.0946720	−	0.414785i
$189$	0.0151769	−	0.473734i	0.00110396	−	0.0344591i
$190$	7.17889	+	31.4528i	0.520811	+	2.28182i
$191$	6.06388	−	1.87046i	0.438767	−	0.135342i	−0.0674985	−	0.997719i	$-0.521502\pi$
$191$	6.06388	−	1.87046i	0.438767	−	0.135342i	0.506265	+	0.862378i	$0.331026\pi$
$192$	0.925945	+	2.35927i	0.0668243	+	0.170266i
$193$	3.85959	+	3.58118i	0.277819	+	0.257779i	0.806759	−	0.590881i	$-0.201220\pi$
$193$	3.85959	+	3.58118i	0.277819	+	0.257779i	−0.528939	+	0.848660i	$0.677410\pi$
$194$	−1.90748	−	1.30050i	−0.136949	−	0.0933705i
$195$	−8.51888			−0.610049
$196$	8.51682	−	0.730381i	0.608344	−	0.0521700i
$197$	3.05311			0.217525			0.108763	−	0.994068i	$-0.465311\pi$
$197$	3.05311			0.217525			0.108763	+	0.994068i	$0.465311\pi$
$198$	−26.0693	−	17.7737i	−1.85266	−	1.26312i
$199$	−12.3607	−	11.4691i	−0.876228	−	0.813021i	0.107216	−	0.994236i	$-0.465807\pi$
$199$	−12.3607	−	11.4691i	−0.876228	−	0.813021i	−0.983443	+	0.181215i	$0.941997\pi$
$200$	−3.54949	−	9.04397i	−0.250987	−	0.639505i
$201$	18.3387	−	5.65674i	1.29351	−	0.398996i
$202$	−4.13503	−	18.1167i	−0.290940	−	1.27469i
$203$	−11.6414	−	3.05235i	−0.817068	−	0.214233i
$204$	−1.60937	+	7.05111i	−0.112678	+	0.493677i
$205$	1.51233	+	20.1806i	0.105625	+	1.40947i
$206$	−9.21083	−	2.84117i	−0.641749	−	0.197953i
$207$	−1.59188	+	21.2422i	−0.110644	+	1.47644i
$208$	1.80884	−	4.60884i	0.125420	−	0.319566i
$209$	26.8038	−	12.9080i	1.85406	−	0.892868i
$210$	37.1629	+	15.9768i	2.56449	+	1.10251i
$211$	2.43688	+	1.17354i	0.167761	+	0.0807897i	0.515880	−	0.856661i	$-0.327465\pi$
$211$	2.43688	+	1.17354i	0.167761	+	0.0807897i	−0.348119	+	0.937451i	$0.613179\pi$
$212$	−0.168295	+	0.156155i	−0.0115585	+	0.0107247i
$213$	20.2820	−	3.05702i	1.38970	−	0.209464i
$214$	8.66077	−	15.0009i	0.592038	−	1.02544i
$215$	−17.4580	−	30.2381i	−1.19062	−	2.06222i
$216$	0.156133	+	0.195785i	0.0106235	+	0.0133215i
$217$	−1.76947	−	14.9805i	−0.120120	−	1.01694i
$218$	17.9167	−	22.4669i	1.21347	−	1.52165i
$219$	28.1533	+	4.24343i	1.90243	+	0.286744i
$220$	19.9556	−	13.6055i	1.34541	−	0.917284i
$221$	1.98577	−	1.35388i	0.133577	−	0.0910716i
$222$	−42.4384	−	6.39656i	−2.84828	−	0.429309i
$223$	−6.01663	+	7.54461i	−0.402903	+	0.505224i	−0.941349	−	0.337436i	$-0.890440\pi$
$223$	−6.01663	+	7.54461i	−0.402903	+	0.505224i	0.538445	+	0.842660i	$0.319012\pi$
$224$	−11.3326	+	11.4550i	−0.757189	+	0.765371i
$225$	13.3156	+	16.6972i	0.887705	+	1.11315i
$226$	−11.6844	−	20.2379i	−0.777234	−	1.34621i
$227$	3.39802	−	5.88555i	0.225535	−	0.390637i	−0.730945	−	0.682436i	$-0.760920\pi$
$227$	3.39802	−	5.88555i	0.225535	−	0.390637i	0.956480	+	0.291799i	$0.0942538\pi$
$228$	15.4729	−	2.33217i	1.02472	−	0.154452i
$229$	−4.61811	+	4.28498i	−0.305173	+	0.283159i	−0.817861	−	0.575416i	$-0.804840\pi$
$229$	−4.61811	+	4.28498i	−0.305173	+	0.283159i	0.512688	+	0.858575i	$0.328650\pi$
$230$	−38.7528	−	18.6624i	−2.55528	−	1.23056i
$231$	6.73789	−	36.6889i	0.443321	−	2.41395i
$232$	5.72877	−	2.75883i	0.376112	−	0.181126i
$233$	0.173880	−	0.443039i	0.0113913	−	0.0290245i	−0.925065	−	0.379809i	$-0.875990\pi$
$233$	0.173880	−	0.443039i	0.0113913	−	0.0290245i	0.936456	+	0.350784i	$0.114085\pi$
$234$	−0.412117	+	5.49933i	−0.0269410	+	0.359502i
$235$	15.7803	+	4.86757i	1.02939	+	0.317525i
$236$	0.711074	+	9.48863i	0.0462870	+	0.617657i
$237$	0.731776	−	3.20612i	0.0475339	−	0.208260i
$238$	−11.2019	+	2.18194i	−0.726112	+	0.141434i
$239$	0.501025	+	2.19513i	0.0324086	+	0.141991i	0.988544	−	0.150934i	$-0.0482283\pi$
$239$	0.501025	+	2.19513i	0.0324086	+	0.141991i	−0.956135	+	0.292926i	$0.905371\pi$
$240$	−40.3039	+	12.4321i	−2.60161	+	0.802489i
$241$	1.77457	+	4.52154i	0.114310	+	0.291258i	0.976567	−	0.215214i	$-0.0690448\pi$
$241$	1.77457	+	4.52154i	0.114310	+	0.291258i	−0.862257	+	0.506471i	$0.830950\pi$
$242$	−28.5940	−	26.5314i	−1.83809	−	1.70550i
$243$	18.3140	+	12.4863i	1.17485	+	0.800996i
$244$	−6.28835			−0.402571
$245$	0.260089	+	24.1972i	0.0166165	+	1.54590i
$246$	25.8914			1.65077
$247$	−4.29630	−	2.92917i	−0.273367	−	0.186378i
$248$	5.84221	+	5.42078i	0.370981	+	0.344220i
$249$	1.46589	+	3.73503i	0.0928971	+	0.236698i
$250$	−11.5635	+	3.56686i	−0.731339	+	0.225588i
$251$	4.15838	+	18.2191i	0.262475	+	1.14998i	0.918557	+	0.395288i	$0.129355\pi$
$251$	4.15838	+	18.2191i	0.262475	+	1.14998i	−0.656082	+	0.754689i	$0.727788\pi$
$252$	4.59157	−	8.80185i	0.289242	−	0.554464i
$253$	−8.82602	+	38.6693i	−0.554887	+	2.43112i
$254$	0.124198	+	1.65730i	0.00779286	+	0.103988i
$255$	−19.5646	−	6.03486i	−1.22518	−	0.377918i
$256$	1.53984	−	20.5478i	0.0962402	−	1.28424i
$257$	8.71864	−	22.2147i	0.543854	−	1.38572i	−0.349743	−	0.936846i	$-0.613731\pi$
$257$	8.71864	−	22.2147i	0.543854	−	1.38572i	0.893597	−	0.448871i	$-0.148174\pi$
$258$	−40.2475	+	19.3822i	−2.50570	+	1.20668i
$259$	−6.77804	−	24.7629i	−0.421167	−	1.53869i
$260$	−3.80340	−	1.83162i	−0.235877	−	0.113592i
$261$	−10.2459	+	9.50678i	−0.634204	+	0.588455i
$262$	−11.5213	+	1.73656i	−0.711789	+	0.107285i
$263$	10.0647	−	17.4325i	0.620613	−	1.07493i	−0.368758	−	0.929525i	$-0.620217\pi$
$263$	10.0647	−	17.4325i	0.620613	−	1.07493i	0.989372	−	0.145409i	$-0.0464497\pi$
$264$	9.85408	+	17.0678i	0.606477	+	1.05045i
$265$	−0.405215	−	0.508124i	−0.0248922	−	0.0312138i
$266$	13.2487	+	20.8358i	0.812331	+	1.27753i
$267$	13.5549	−	16.9973i	0.829548	−	1.04022i
$268$	9.40386	+	1.41740i	0.574432	+	0.0865818i
$269$	−11.6185	+	7.92136i	−0.708392	+	0.482974i	−0.863130	−	0.504982i	$-0.831499\pi$
$269$	−11.6185	+	7.92136i	−0.708392	+	0.482974i	0.154738	+	0.987956i	$0.450547\pi$
$270$	0.918357	−	0.626125i	0.0558894	−	0.0381048i
$271$	−12.9081	−	1.94559i	−0.784114	−	0.118186i	−0.255230	−	0.966880i	$-0.582151\pi$
$271$	−12.9081	−	1.94559i	−0.784114	−	0.118186i	−0.528884	+	0.848694i	$0.677389\pi$
$272$	7.41915	−	9.30332i	0.449852	−	0.564096i
$273$	−6.14235	+	2.18642i	−0.371752	+	0.132328i
$274$	12.4268	+	15.5827i	0.750729	+	0.941385i
$275$	19.8829	+	34.4381i	1.19898	+	2.07670i
$276$	−10.4310	+	18.0671i	−0.627874	+	1.08751i
$277$	−29.6883	+	4.47479i	−1.78380	+	0.268864i	−0.956254	−	0.292539i	$-0.905500\pi$
$277$	−29.6883	+	4.47479i	−1.78380	+	0.268864i	−0.827542	+	0.561403i	$0.810262\pi$
$278$	−20.7149	+	19.2206i	−1.24240	+	1.15278i
$279$	−15.7839	−	7.60114i	−0.944959	−	0.455068i
$280$	−8.39140	−	9.64565i	−0.501482	−	0.576438i
$281$	−5.94884	+	2.86481i	−0.354878	+	0.170900i	−0.602825	−	0.797873i	$-0.705958\pi$
$281$	−5.94884	+	2.86481i	−0.354878	+	0.170900i	0.247947	+	0.968774i	$0.420244\pi$
$282$	7.71888	−	19.6674i	0.459653	−	1.17118i
$283$	0.400159	−	5.33975i	0.0237870	−	0.317415i	−0.972600	−	0.232485i	$-0.925314\pi$
$283$	0.400159	−	5.33975i	0.0237870	−	0.317415i	0.996387	−	0.0849300i	$-0.0270667\pi$
$284$	9.71254	+	2.99592i	0.576333	+	0.177775i
$285$	3.31030	+	44.1728i	0.196085	+	2.61657i
$286$	−2.28494	+	10.0110i	−0.135111	+	0.591961i
$287$	6.26990	+	14.1626i	0.370101	+	0.835993i
$288$	4.16420	+	18.2445i	0.245378	+	1.07507i
$289$	−10.7251	+	3.30825i	−0.630888	+	0.194603i
$290$	−10.3108	−	26.2714i	−0.605468	−	1.54271i
$291$	−2.32367	−	2.15605i	−0.136216	−	0.126390i
$292$	11.6572	+	7.94772i	0.682184	+	0.465105i
$293$	−24.1631			−1.41162			−0.705812	−	0.708399i	$-0.749418\pi$
$293$	−24.1631			−1.41162			−0.705812	+	0.708399i	$0.749418\pi$
$294$	30.8961	+	1.98165i	1.80189	+	0.115572i
$295$	−26.9365			−1.56830
$296$	11.2074	+	7.64105i	0.651415	+	0.444127i
$297$	−0.751348	−	0.697149i	−0.0435976	−	0.0404527i
$298$	−9.49149	−	24.1839i	−0.549827	−	1.40094i
$299$	6.62460	−	2.04342i	0.383111	−	0.118174i
$300$	4.65418	+	20.3913i	0.268709	+	1.17729i
$301$	−20.3485	−	17.3218i	−1.17287	−	0.998414i
$302$	−8.22538	+	36.0378i	−0.473318	+	2.07374i
$303$	−1.90673	−	25.4435i	−0.109539	−	1.46169i
$304$	−24.6011	−	7.58842i	−1.41097	−	0.435226i
$305$	1.33031	−	17.7518i	0.0761734	−	1.01646i
$306$	−4.84226	+	12.3379i	−0.276813	+	0.705309i
$307$	10.5024	−	5.05767i	0.599401	−	0.288656i	−0.109475	−	0.993990i	$-0.534917\pi$
$307$	10.5024	−	5.05767i	0.599401	−	0.288656i	0.708876	+	0.705333i	$0.249203\pi$
$308$	10.8966	−	14.9317i	0.620893	−	0.850813i
$309$	−11.9242	−	5.74240i	−0.678345	−	0.326674i
$310$	25.9309	−	24.0604i	1.47278	−	1.36654i
$311$	32.7721	−	4.93960i	1.85834	−	0.280099i	0.878180	−	0.478330i	$-0.158758\pi$
$311$	32.7721	−	4.93960i	1.85834	−	0.280099i	0.980155	+	0.198231i	$0.0635195\pi$
$312$	1.72234	−	2.98317i	0.0975081	−	0.168889i
$313$	2.41261	+	4.17876i	0.136369	+	0.236198i	0.926120	−	0.377230i	$-0.123123\pi$
$313$	2.41261	+	4.17876i	0.136369	+	0.236198i	−0.789751	+	0.613428i	$0.789790\pi$
$314$	15.6309	+	19.6006i	0.882105	+	1.10612i
$315$	23.8759	+	14.8239i	1.34526	+	0.835230i
$316$	1.01605	−	1.27409i	0.0571574	−	0.0716731i
$317$	27.7392	+	4.18102i	1.55799	+	0.234829i	0.870796	−	0.491644i	$-0.163604\pi$
$317$	27.7392	+	4.18102i	1.55799	+	0.234829i	0.687194	+	0.726473i	$0.258842\pi$
$318$	−0.687016	+	0.468400i	−0.0385260	+	0.0262666i
$319$	−21.5030	+	14.6605i	−1.20393	+	0.820829i
$320$	−3.51568	−	0.529904i	−0.196533	−	0.0296225i
$321$	14.8286	−	18.5945i	0.827653	−	1.03784i
$322$	−32.7317	−	3.50994i	−1.82406	−	0.195601i
$323$	−7.79188	−	9.77071i	−0.433552	−	0.543657i
$324$	5.35881	+	9.28172i	0.297711	+	0.515651i
$325$	3.47521	−	6.01924i	0.192770	−	0.333887i
$326$	17.0842	−	2.57503i	0.946205	−	0.142618i
$327$	28.9234	−	26.8370i	1.59947	−	1.48409i
$328$	−7.37268	−	3.55050i	−0.407088	−	0.196043i
$329$	12.6273	−	0.540451i	0.696166	−	0.0297960i
$330$	78.8126	−	37.9542i	4.33849	−	2.08931i
$331$	4.38808	−	11.1806i	0.241191	−	0.614544i	−0.758103	−	0.652135i	$-0.773873\pi$
$331$	4.38808	−	11.1806i	0.241191	−	0.614544i	0.999293	+	0.0375917i	$0.0119686\pi$
$332$	−0.148586	+	1.98274i	−0.00815473	+	0.108817i
$333$	−28.4921	−	8.78865i	−1.56136	−	0.481615i
$334$	2.12327	+	28.3331i	0.116180	+	1.55032i
$335$	−5.99068	+	26.2469i	−0.327306	+	1.43402i
$336$	−25.8695	+	19.3081i	−1.41129	+	1.05335i
$337$	2.72242	+	11.9277i	0.148300	+	0.649744i	0.993357	+	0.115069i	$0.0367090\pi$
$337$	2.72242	+	11.9277i	0.148300	+	0.649744i	−0.845058	+	0.534675i	$0.820434\pi$
$338$	1.71502	−	0.529014i	0.0932849	−	0.0287746i
$339$	−11.7225	−	29.8684i	−0.636677	−	1.62223i
$340$	−7.43739	−	6.90089i	−0.403349	−	0.374253i
$341$	−26.9519	−	18.3755i	−1.45953	−	0.995088i
$342$	28.6757			1.55061
$343$	6.39788	+	17.3801i	0.345453	+	0.938436i
$344$	14.1185			0.761221
$345$	−48.7960	−	33.2685i	−2.62709	−	1.79112i
$346$	−6.40556	−	5.94349i	−0.344365	−	0.319524i
$347$	1.99861	+	5.09237i	0.107291	+	0.273373i	0.974429	−	0.224695i	$-0.0721385\pi$
$347$	1.99861	+	5.09237i	0.107291	+	0.273373i	−0.867138	+	0.498067i	$0.834043\pi$
$348$	−13.0804	+	4.03476i	−0.701181	+	0.216286i
$349$	5.38931	+	23.6121i	0.288483	+	1.26393i	0.886607	+	0.462523i	$0.153056\pi$
$349$	5.38931	+	23.6121i	0.288483	+	1.26393i	−0.598124	+	0.801404i	$0.704087\pi$
$350$	−26.4492	+	19.7408i	−1.41377	+	1.05519i
$351$	−0.0398639	+	0.174655i	−0.00212778	+	0.00932240i
$352$	2.60396	+	34.7474i	0.138792	+	1.85204i
$353$	−19.1405	−	5.90408i	−1.01875	−	0.314242i	−0.259988	−	0.965612i	$-0.583719\pi$
$353$	−19.1405	−	5.90408i	−1.01875	−	0.314242i	−0.758761	+	0.651370i	$0.774195\pi$
$354$	−2.57538	+	34.3660i	−0.136880	+	1.82653i
$355$	−10.5121	+	26.7843i	−0.557923	+	1.42156i
$356$	9.70638	−	4.67434i	0.514437	−	0.247740i
$357$	−15.6555	+	0.670057i	−0.828575	+	0.0354632i
$358$	−13.7325	−	6.61322i	−0.725785	−	0.349520i
$359$	6.33837	−	5.88115i	0.334526	−	0.310395i	−0.494967	−	0.868912i	$-0.664820\pi$
$359$	6.33837	−	5.88115i	0.334526	−	0.310395i	0.829493	+	0.558517i	$0.188629\pi$
$360$	−14.6822	+	2.21298i	−0.773819	+	0.116634i
$361$	−4.01911	+	6.96130i	−0.211532	+	0.366384i
$362$	−9.31758	−	16.1385i	−0.489721	−	0.848222i
$363$	−33.3930	−	41.8735i	−1.75268	−	2.19779i
$364$	−3.21245	−	0.344484i	−0.168378	−	0.0180558i
$365$	−24.9022	+	31.2264i	−1.30344	+	1.63446i
$366$	−22.5209	−	3.39447i	−1.17718	−	0.177432i
$367$	5.29547	−	3.61039i	0.276421	−	0.188461i	−0.417172	−	0.908827i	$-0.636979\pi$
$367$	5.29547	−	3.61039i	0.276421	−	0.188461i	0.693594	+	0.720367i	$0.256026\pi$
$368$	28.3598	−	19.3354i	1.47835	−	1.00792i
$369$	17.7869	+	2.68094i	0.925949	+	0.139564i
$370$	37.5377	−	47.0708i	1.95149	−	2.44709i
$371$	−0.422585	−	0.262370i	−0.0219395	−	0.0136216i
$372$	−10.6973	−	13.4141i	−0.554632	−	0.695486i
$373$	12.0640	+	20.8955i	0.624652	+	1.08193i	0.988608	+	0.150513i	$0.0480926\pi$
$373$	12.0640	+	20.8955i	0.624652	+	1.08193i	−0.363956	+	0.931416i	$0.618574\pi$
$374$	−12.3395	+	21.3726i	−0.638060	+	1.10515i
$375$	−16.4298	+	2.47639i	−0.848430	+	0.127880i
$376$	−4.89498	+	4.54188i	−0.252439	+	0.234230i
$377$	4.09831	+	1.97364i	0.211074	+	0.101648i
$378$	0.501462	−	0.687156i	0.0257924	−	0.0353435i
$379$	9.73394	−	4.68762i	0.499999	−	0.240787i	−0.166847	−	0.985983i	$-0.553358\pi$
$379$	9.73394	−	4.68762i	0.499999	−	0.240787i	0.666845	+	0.745196i	$0.267644\pi$
$380$	−8.01954	+	20.4335i	−0.411394	+	1.04821i
$381$	−0.170529	+	2.27555i	−0.00873647	+	0.116580i
$382$	10.8832	+	3.35702i	0.556833	+	0.171760i
$383$	−0.228726	−	3.05214i	−0.0116874	−	0.155957i	−0.999994	−	0.00347728i	$-0.998893\pi$
$383$	−0.228726	−	3.05214i	−0.0116874	−	0.155957i	0.988307	−	0.152480i	$-0.0487259\pi$
$384$	5.66713	−	24.8293i	0.289199	−	1.26707i
$385$	39.8464	+	33.9196i	2.03076	+	1.72870i
$386$	2.10273	+	9.21266i	0.107026	+	0.468912i
$387$	−29.6562	+	9.14774i	−1.50751	+	0.465006i
$388$	−0.573877	−	1.46221i	−0.0291342	−	0.0742327i
$389$	4.37767	+	4.06188i	0.221957	+	0.205946i	0.783311	−	0.621630i	$-0.213529\pi$
$389$	4.37767	+	4.06188i	0.221957	+	0.205946i	−0.561355	+	0.827575i	$0.689720\pi$
$390$	−12.6326	−	8.61278i	−0.639678	−	0.436125i
$391$	16.6617			0.842619
$392$	−8.52605	−	4.80108i	−0.430630	−	0.242491i
$393$	−15.9980			−0.806991
$394$	4.52746	+	3.08677i	0.228090	+	0.155509i
$395$	3.38176	+	3.13781i	0.170155	+	0.157881i
$396$	−7.84308	−	19.9838i	−0.394130	−	1.00423i
$397$	10.7483	−	3.31542i	0.539444	−	0.166396i	−0.0130477	−	0.999915i	$-0.504153\pi$
$397$	10.7483	−	3.31542i	0.539444	−	0.166396i	0.552492	+	0.833518i	$0.313677\pi$
$398$	−6.73419	−	29.5044i	−0.337555	−	1.47892i
$399$	13.7240	+	31.0002i	0.687062	+	1.55195i
$400$	7.65742	−	33.5494i	0.382871	−	1.67747i
$401$	2.11926	+	28.2796i	0.105831	+	1.41221i	0.757066	+	0.653339i	$0.226632\pi$
$401$	2.11926	+	28.2796i	0.105831	+	1.41221i	−0.651235	+	0.758876i	$0.725749\pi$
$402$	32.9135	+	10.1525i	1.64158	+	0.506359i
$403$	−0.426070	+	5.68551i	−0.0212241	+	0.283215i
$404$	4.61924	−	11.7696i	0.229816	−	0.585562i
$405$	−27.3356	+	13.1641i	−1.35832	+	0.654131i
$406$	−14.1770	−	16.2961i	−0.703595	−	0.808760i
$407$	−50.0206	−	24.0886i	−2.47943	−	1.19403i
$408$	6.06885	−	5.63107i	0.300453	−	0.278780i
$409$	19.7849	−	2.98209i	0.978301	−	0.147455i	0.359621	−	0.933098i	$-0.382906\pi$
$409$	19.7849	−	2.98209i	0.978301	−	0.147455i	0.618680	+	0.785643i	$0.287668\pi$
$410$	−18.1604	+	31.4548i	−0.896879	+	1.55344i
$411$	13.6831	+	23.6998i	0.674937	+	1.16903i
$412$	−4.08911	−	5.12759i	−0.201456	−	0.252618i
$413$	−19.4219	+	6.91341i	−0.955691	+	0.340186i
$414$	−23.8370	+	29.8906i	−1.17152	+	1.46904i
$415$	−5.56578	−	0.838906i	−0.273213	−	0.0411803i
$416$	5.03207	−	3.43080i	0.246717	−	0.168209i
$417$	−32.0582	+	21.8569i	−1.56990	+	1.07034i
$418$	52.7977	+	7.95797i	2.58242	+	0.389237i
$419$	−3.31004	+	4.15066i	−0.161706	+	0.202773i	−0.856083	−	0.516839i	$-0.827109\pi$
$419$	−3.31004	+	4.15066i	−0.161706	+	0.202773i	0.694377	+	0.719612i	$0.255680\pi$
$420$	14.7684	+	23.2257i	0.720622	+	1.13330i
$421$	−11.0672	−	13.8779i	−0.539385	−	0.676367i	0.435214	−	0.900327i	$-0.356673\pi$
$421$	−11.0672	−	13.8779i	−0.539385	−	0.676367i	−0.974598	+	0.223960i	$0.928101\pi$
$422$	2.42717	+	4.20397i	0.118153	+	0.204646i
$423$	7.33920	−	12.7119i	0.356844	−	0.618073i
$424$	0.259863	−	0.0391680i	0.0126201	−	0.00190217i
$425$	12.2453	−	11.3620i	0.593984	−	0.551137i
$426$	33.1669	+	15.9723i	1.60694	+	0.773862i
$427$	−3.59691	−	13.1410i	−0.174067	−	0.635936i
$428$	10.6184	−	5.11357i	0.513262	−	0.247174i
$429$	−5.15095	+	13.1244i	−0.248690	+	0.633652i
$430$	4.68301	−	62.4905i	0.225835	−	3.01356i
$431$	4.36215	+	1.34555i	0.210118	+	0.0648127i	0.398027	−	0.917374i	$-0.369695\pi$
$431$	4.36215	+	1.34555i	0.210118	+	0.0648127i	−0.187910	+	0.982186i	$0.560171\pi$
$432$	0.0662834	+	0.884491i	0.00318906	+	0.0425551i
$433$	5.88947	−	25.8035i	0.283030	−	1.24003i	−0.610856	−	0.791741i	$-0.709175\pi$
$433$	5.88947	−	25.8035i	0.283030	−	1.24003i	0.893886	−	0.448294i	$-0.147968\pi$
$434$	12.5217	−	24.0035i	0.601059	−	1.15221i
$435$	−8.62279	−	37.7789i	−0.413431	−	1.81136i
$436$	18.6835	−	5.76309i	0.894777	−	0.276002i
$437$	−13.1699	−	33.5564i	−0.630003	−	1.60522i
$438$	37.4583	+	34.7562i	1.78983	+	1.66072i
$439$	−10.8632	−	7.40643i	−0.518474	−	0.353490i	0.275637	−	0.961262i	$-0.411111\pi$
$439$	−10.8632	−	7.40643i	−0.518474	−	0.353490i	−0.794112	+	0.607772i	$0.792063\pi$
$440$	−27.6469			−1.31802
$441$	21.0198	+	4.56052i	1.00094	+	0.217167i
$442$	4.31350			0.205172
$443$	−29.9555	−	20.4233i	−1.42323	−	0.970339i	−0.997865	−	0.0653160i	$-0.979194\pi$
$443$	−29.9555	−	20.4233i	−1.42323	−	0.970339i	−0.425362	−	0.905023i	$-0.639853\pi$
$444$	−21.4061	−	19.8619i	−1.01589	−	0.942605i
$445$	11.1421	+	28.3896i	0.528186	+	1.34580i
$446$	−16.5498	+	5.10494i	−0.783657	+	0.241726i
$447$	−7.93765	−	34.7771i	−0.375438	−	1.64490i
$448$	−2.67091	+	0.520246i	−0.126189	+	0.0245793i
$449$	4.21572	−	18.4703i	0.198952	−	0.871667i	−0.772610	−	0.634881i	$-0.781049\pi$
$449$	4.21572	−	18.4703i	0.198952	−	0.871667i	0.971562	−	0.236785i	$-0.0760938\pi$
$450$	2.86439	+	38.2226i	0.135029	+	1.80183i
$451$	32.0052	+	9.87229i	1.50707	+	0.464868i
$452$	1.18822	−	15.8557i	0.0558891	−	0.745788i
$453$	−18.5425	+	47.2456i	−0.871204	+	2.21979i
$454$	10.9893	−	5.29219i	0.515755	−	0.248375i
$455$	1.65206	−	8.99575i	0.0774499	−	0.421727i
$456$	−16.1379	−	7.77160i	−0.755726	−	0.363939i
$457$	−0.660979	+	0.613299i	−0.0309193	+	0.0286889i	−0.695481	−	0.718544i	$-0.744809\pi$
$457$	−0.660979	+	0.613299i	−0.0309193	+	0.0286889i	0.664562	+	0.747233i	$0.268618\pi$
$458$	−11.1804	+	1.68517i	−0.522425	+	0.0787429i
$459$	−0.215279	+	0.372875i	−0.0100484	+	0.0174043i
$460$	−14.6328	−	25.3448i	−0.682259	−	1.18171i
$461$	18.2886	+	22.9332i	0.851785	+	1.06810i	0.996899	+	0.0786895i	$0.0250736\pi$
$461$	18.2886	+	22.9332i	0.851785	+	1.06810i	−0.145114	+	0.989415i	$0.546355\pi$
$462$	47.0849	−	47.5938i	2.19059	−	2.21426i
$463$	6.01225	−	7.53913i	0.279413	−	0.350373i	−0.622245	−	0.782823i	$-0.713779\pi$
$463$	6.01225	−	7.53913i	0.279413	−	0.350373i	0.901658	+	0.432450i	$0.142351\pi$
$464$	22.2699	+	3.35664i	1.03385	+	0.155828i
$465$	40.1304	−	27.3604i	1.86100	−	1.26881i
$466$	0.705770	−	0.481186i	0.0326941	−	0.0222905i
$467$	16.0473	+	2.41874i	0.742581	+	0.111926i	0.509427	−	0.860514i	$-0.329857\pi$
$467$	16.0473	+	2.41874i	0.742581	+	0.111926i	0.233154	+	0.972440i	$0.425095\pi$
$468$	−2.33948	+	2.93362i	−0.108143	+	0.135606i
$469$	2.41698	+	20.4623i	0.111606	+	0.944861i
$470$	18.4793	+	23.1723i	0.852387	+	1.06886i
$471$	17.2112	+	29.8107i	0.793050	+	1.37360i
$472$	5.44598	−	9.43272i	0.250672	−	0.434176i
$473$	−57.1416	+	8.61272i	−2.62738	+	0.396013i
$474$	4.32661	−	4.01451i	0.198728	−	0.184392i
$475$	−32.5619	−	15.6810i	−1.49404	−	0.719493i
$476$	−7.13372	−	3.06688i	−0.326974	−	0.140570i
$477$	−0.520468	+	0.250644i	−0.0238306	+	0.0114762i
$478$	−1.47636	+	3.76170i	−0.0675271	+	0.172056i
$479$	1.36637	−	18.2329i	0.0624308	−	0.833081i	−0.874825	−	0.484439i	$-0.839024\pi$
$479$	1.36637	−	18.2329i	0.0624308	−	0.833081i	0.937256	−	0.348642i	$-0.113357\pi$
$480$	−49.5778	−	15.2927i	−2.26290	−	0.698014i
$481$	0.725164	+	9.67664i	0.0330646	+	0.441217i
$482$	−1.93987	+	8.49911i	−0.0883585	+	0.387124i
$483$	−43.7218	−	11.4637i	−1.98941	−	0.521619i
$484$	−5.90577	−	25.8749i	−0.268444	−	1.17613i
$485$	4.24918	−	1.31070i	0.192945	−	0.0595157i
$486$	14.5339	+	37.0318i	0.659271	+	1.67980i
$487$	−23.6312	−	21.9265i	−1.07083	−	0.993587i	−0.0708394	−	0.997488i	$-0.522568\pi$
$487$	−23.6312	−	21.9265i	−1.07083	−	0.993587i	−0.999992	+	0.00390101i	$0.998758\pi$
$488$	5.94743	+	4.05489i	0.269227	+	0.183556i
$489$	23.7223			1.07276
$490$	−24.0782	+	36.1449i	−1.08774	+	1.63286i
$491$	28.4565			1.28423			0.642113	−	0.766610i	$-0.278058\pi$
$491$	28.4565			1.28423			0.642113	+	0.766610i	$0.278058\pi$
$492$	14.5554	+	9.92373i	0.656210	+	0.447396i
$493$	8.01407	+	7.43597i	0.360936	+	0.334899i
$494$	−3.40952	−	8.68731i	−0.153402	−	0.390861i
$495$	58.0728	−	17.9131i	2.61018	−	0.805134i
$496$	6.28141	+	27.5207i	0.282044	+	1.23571i
$497$	−0.705136	+	22.0102i	−0.0316297	+	0.987294i
$498$	−1.60243	+	7.02072i	−0.0718067	+	0.314606i
$499$	0.648614	+	8.65516i	0.0290360	+	0.387458i	0.992723	+	0.120423i	$0.0384250\pi$
$499$	0.648614	+	8.65516i	0.0290360	+	0.387458i	−0.963687	+	0.267035i	$0.913956\pi$
$500$	−7.86780	−	2.42689i	−0.351859	−	0.108534i
$501$	−2.91535	+	38.9026i	−0.130248	+	1.73804i
$502$	−12.2534	+	31.2212i	−0.546898	+	1.39347i
$503$	1.83704	−	0.884670i	0.0819094	−	0.0394455i	−0.392481	−	0.919760i	$-0.628383\pi$
$503$	1.83704	−	0.884670i	0.0819094	−	0.0394455i	0.474390	+	0.880315i	$0.342669\pi$
$504$	−10.0183	+	5.36389i	−0.446250	+	0.238927i
$505$	32.2480	+	15.5298i	1.43502	+	0.691069i
$506$	−52.1837	+	48.4194i	−2.31985	+	2.15250i
$507$	2.43676	−	0.367283i	0.108220	−	0.0163116i
$508$	−0.565396	+	0.979295i	−0.0250854	+	0.0434492i
$509$	−2.69900	−	4.67481i	−0.119631	−	0.207207i	0.799990	−	0.600013i	$-0.204838\pi$
$509$	−2.69900	−	4.67481i	−0.119631	−	0.207207i	−0.919622	+	0.392806i	$0.871505\pi$
$510$	−22.9109	−	28.7293i	−1.01451	−	1.27215i
$511$	−9.94074	+	28.9064i	−0.439752	+	1.27874i
$512$	10.1704	−	12.7533i	0.449474	−	0.563623i
$513$	0.921127	+	0.138838i	0.0406688	+	0.00612983i
$514$	35.3885	−	24.1274i	1.56092	−	1.06422i
$515$	15.3400	−	10.4587i	0.675963	−	0.460864i
$516$	−30.0549	−	4.53005i	−1.32310	−	0.199425i
$517$	17.0407	−	21.3683i	0.749448	−	0.939778i
$518$	14.9847	−	43.5736i	0.658390	−	1.91451i
$519$	−7.48060	−	9.38038i	−0.328362	−	0.411753i
$520$	2.41612	+	4.18485i	0.105954	+	0.183518i
$521$	−13.6579	+	23.6562i	−0.598365	+	1.03640i	0.394698	+	0.918811i	$0.370849\pi$
$521$	−13.6579	+	23.6562i	−0.598365	+	1.03640i	−0.993063	+	0.117587i	$0.962484\pi$
$522$	−24.8052	+	3.73878i	−1.08569	+	0.163642i
$523$	−18.8300	+	17.4717i	−0.823378	+	0.763984i	−0.974466	−	0.224537i	$-0.927913\pi$
$523$	−18.8300	+	17.4717i	−0.823378	+	0.763984i	0.151087	+	0.988520i	$0.451723\pi$
$524$	−7.14256	−	3.43968i	−0.312024	−	0.150263i
$525$	−39.9501	+	21.3897i	−1.74357	+	0.933523i
$526$	32.5495	−	15.6750i	1.41923	−	0.683463i
$527$	−5.00619	+	12.7556i	−0.218073	+	0.555642i
$528$	−5.21657	+	69.6103i	−0.227022	+	3.02940i
$529$	23.9475	+	7.38683i	1.04120	+	0.321167i
$530$	−0.0871681	−	1.16318i	−0.00378634	−	0.0505252i
$531$	−5.32770	+	23.3422i	−0.231202	+	1.01296i
$532$	−0.537940	+	16.7914i	−0.0233226	+	0.727998i
$533$	−1.30265	−	5.70730i	−0.0564242	−	0.247211i
$534$	37.2853	−	11.5010i	1.61349	−	0.497696i
$535$	12.1891	+	31.0573i	0.526980	+	1.34272i
$536$	−7.98005	−	7.40441i	−0.344686	−	0.319822i
$537$	−17.2914	−	11.7891i	−0.746179	−	0.508736i
$538$	−25.2377			−1.08808
$539$	37.4360	+	14.2301i	1.61248	+	0.612936i
$540$	0.756259			0.0325442
$541$	−17.0034	−	11.5927i	−0.731033	−	0.498410i	0.139683	−	0.990196i	$-0.455392\pi$
$541$	−17.0034	−	11.5927i	−0.731033	−	0.498410i	−0.870716	+	0.491787i	$0.836344\pi$
$542$	−17.1744	−	15.9355i	−0.737705	−	0.684490i
$543$	−9.34795	−	23.8182i	−0.401159	−	1.02214i
$544$	13.9871	−	4.31445i	0.599693	−	0.184981i
$545$	12.3165	+	53.9619i	0.527579	+	2.31148i
$546$	−11.3190	−	2.96781i	−0.484408	−	0.127011i
$547$	−4.42897	+	19.4046i	−0.189369	+	0.829681i	0.787581	+	0.616212i	$0.211333\pi$
$547$	−4.42897	+	19.4046i	−0.189369	+	0.829681i	−0.976950	+	0.213469i	$0.931524\pi$
$548$	1.01342	+	13.5232i	0.0432912	+	0.577680i
$549$	−15.1199	−	4.66388i	−0.645303	−	0.199050i
$550$	−5.33347	+	71.1703i	−0.227420	+	3.03471i
$551$	8.64136	−	22.0178i	0.368134	−	0.937991i
$552$	21.5156	−	10.3614i	0.915765	−	0.441009i
$553$	3.24368	+	1.39450i	0.137935	+	0.0593002i
$554$	−48.5488	−	23.3799i	−2.06264	−	0.993316i
$555$	60.5979	−	56.2267i	2.57224	−	2.38669i
$556$	−19.0123	+	2.86565i	−0.806303	+	0.121531i
$557$	15.6641	−	27.1309i	0.663707	−	1.14957i	−0.315927	−	0.948784i	$-0.602315\pi$
$557$	15.6641	−	27.1309i	0.663707	−	1.14957i	0.979634	−	0.200791i	$-0.0643512\pi$
$558$	−15.7210	−	27.2296i	−0.665524	−	1.15272i
$559$	6.29741	+	7.89670i	0.266352	+	0.333995i
$560$	−5.31192	−	44.9710i	−0.224469	−	1.90037i
$561$	−21.1272	+	26.4927i	−0.891991	+	1.11852i
$562$	−11.7179	−	1.76619i	−0.494290	−	0.0745023i
$563$	−16.5781	+	11.3027i	−0.698682	+	0.476354i	−0.859832	−	0.510576i	$-0.829432\pi$
$563$	−16.5781	+	11.3027i	−0.698682	+	0.476354i	0.161150	+	0.986930i	$0.448480\pi$
$564$	11.8775	−	8.09796i	0.500134	−	0.340986i
$565$	44.5086	+	6.70859i	1.87249	+	0.282232i
$566$	5.99201	−	7.51374i	0.251863	−	0.315826i
$567$	−16.3311	+	16.5076i	−0.685841	+	0.693252i
$568$	−7.25413	−	9.09639i	−0.304376	−	0.381676i
$569$	−14.7739	−	25.5892i	−0.619356	−	1.07276i	−0.989603	−	0.143823i	$-0.954060\pi$
$569$	−14.7739	−	25.5892i	−0.619356	−	1.07276i	0.370247	−	0.928933i	$-0.379273\pi$
$570$	−39.7509	+	68.8506i	−1.66498	+	2.88383i
$571$	29.1346	−	4.39133i	1.21924	−	0.183771i	0.492273	−	0.870441i	$-0.336166\pi$
$571$	29.1346	−	4.39133i	1.21924	−	0.183771i	0.726970	+	0.686669i	$0.240928\pi$
$572$	−5.12157	+	4.75212i	−0.214144	+	0.198696i
$573$	14.0892	+	6.78502i	0.588586	+	0.283448i
$574$	−5.02111	+	27.3407i	−0.209577	+	1.14118i
$575$	43.4127	−	20.9064i	1.81043	−	0.871859i
$576$	−1.15455	+	2.94176i	−0.0481064	+	0.122573i
$577$	2.25713	−	30.1193i	0.0939655	−	1.25388i	−0.728491	−	0.685055i	$-0.759778\pi$
$577$	2.25713	−	30.1193i	0.0939655	−	1.25388i	0.822457	−	0.568827i	$-0.192603\pi$
$578$	−19.2489	−	5.93751i	−0.800650	−	0.246968i
$579$	0.969601	+	12.9384i	0.0402952	+	0.537702i
$580$	4.27295	−	18.7210i	0.177424	−	0.777347i
$581$	−4.22839	+	0.823617i	−0.175423	+	0.0341694i
$582$	−1.26595	−	5.54650i	−0.0524754	−	0.229910i
$583$	−1.02784	+	0.317048i	−0.0425689	+	0.0131308i
$584$	−5.90028	−	15.0337i	−0.244155	−	0.622097i
$585$	−7.78657	−	7.22488i	−0.321935	−	0.298712i
$586$	−35.8314	−	24.4294i	−1.48018	−	1.00917i
$587$	22.7501			0.938996			0.469498	−	0.882934i	$-0.344435\pi$
$587$	22.7501			0.938996			0.469498	+	0.882934i	$0.344435\pi$
$588$	16.6094	+	12.9560i	0.684961	+	0.534296i
$589$	29.6466			1.22157
$590$	−39.9440	−	27.2334i	−1.64447	−	1.12118i
$591$	5.51529	+	5.11744i	0.226869	+	0.210503i
$592$	17.5525	+	44.7232i	0.721405	+	1.83811i
$593$	3.50151	−	1.08007i	0.143790	−	0.0443532i	−0.222025	−	0.975041i	$-0.571267\pi$
$593$	3.50151	−	1.08007i	0.143790	−	0.0443532i	0.365815	+	0.930688i	$0.380790\pi$
$594$	−0.409339	−	1.79343i	−0.0167954	−	0.0735854i
$595$	10.1668	−	19.4894i	0.416800	−	0.798988i
$596$	3.93343	−	17.2335i	0.161120	−	0.705911i
$597$	−3.10524	−	41.4366i	−0.127089	−	1.69589i
$598$	11.8896	+	3.66744i	0.486200	+	0.149973i
$599$	3.30358	−	44.0832i	0.134981	−	1.80119i	−0.360696	−	0.932683i	$-0.617461\pi$
$599$	3.30358	−	44.0832i	0.134981	−	1.80119i	0.495677	−	0.868507i	$-0.334920\pi$
$600$	8.74696	−	22.2869i	0.357093	−	0.909859i
$601$	−31.5667	+	15.2017i	−1.28763	+	0.620092i	−0.947341	−	0.320228i	$-0.896241\pi$
$601$	−31.5667	+	15.2017i	−1.28763	+	0.620092i	−0.340293	+	0.940319i	$0.610526\pi$
$602$	−12.6620	−	46.2593i	−0.516064	−	1.88539i
$603$	21.5597	+	10.3826i	0.877980	+	0.422813i
$604$	−18.4368	+	17.1068i	−0.750181	+	0.696067i
$605$	74.2931	−	11.1979i	3.02045	−	0.455259i
$606$	22.8965	−	39.6579i	0.930106	−	1.61099i
$607$	−13.1322	−	22.7457i	−0.533020	−	0.923217i	−0.999256	−	0.0385574i	$-0.987724\pi$
$607$	−13.1322	−	22.7457i	−0.533020	−	0.923217i	0.466237	−	0.884660i	$-0.345610\pi$
$608$	−19.7451	−	24.7596i	−0.800769	−	1.00413i
$609$	−15.9135	−	25.0266i	−0.644846	−	1.01413i
$610$	19.9202	−	24.9791i	0.806544	−	1.01137i
$611$	−4.72369	−	0.711981i	−0.191100	−	0.0288037i
$612$	−7.45109	+	5.08006i	−0.301192	+	0.205349i
$613$	−26.0376	+	17.7521i	−1.05165	+	0.717001i	−0.960343	−	0.278822i	$-0.910056\pi$
$613$	−26.0376	+	17.7521i	−1.05165	+	0.717001i	−0.0913048	+	0.995823i	$0.529104\pi$
$614$	20.6873	+	3.11811i	0.834873	+	0.125837i
$615$	−31.0935	+	38.9901i	−1.25381	+	1.57223i
$616$	−19.9342	+	7.09575i	−0.803172	+	0.285896i
$617$	6.34971	+	7.96229i	0.255630	+	0.320550i	0.893042	−	0.449973i	$-0.148567\pi$
$617$	6.34971	+	7.96229i	0.255630	+	0.320550i	−0.637412	+	0.770523i	$0.719995\pi$
$618$	−11.8767	−	20.5711i	−0.477751	−	0.827489i
$619$	−1.43080	+	2.47823i	−0.0575089	+	0.0996083i	−0.893347	−	0.449368i	$-0.851649\pi$
$619$	−1.43080	+	2.47823i	−0.0575089	+	0.0996083i	0.835838	+	0.548977i	$0.184982\pi$
$620$	23.7996	−	3.58721i	0.955815	−	0.144066i
$621$	−0.910415	+	0.844741i	−0.0365337	+	0.0338983i
$622$	53.5917	+	25.8084i	2.14883	+	1.03482i
$623$	15.3201	+	17.6100i	0.613788	+	0.705530i
$624$	10.9926	−	5.29377i	0.440057	−	0.211920i
$625$	−4.18089	+	10.6527i	−0.167235	+	0.426109i
$626$	−0.647170	+	8.63589i	−0.0258661	+	0.345159i
$627$	70.0554	+	21.6092i	2.79774	+	0.862990i
$628$	1.27472	+	17.0100i	0.0508670	+	0.678773i
$629$	−5.18962	+	22.7372i	−0.206924	+	0.906592i
$630$	20.4183	+	46.1214i	0.813484	+	1.83752i
$631$	3.75039	+	16.4315i	0.149301	+	0.654129i	0.993080	+	0.117439i	$0.0374684\pi$
$631$	3.75039	+	16.4315i	0.149301	+	0.654129i	−0.843780	+	0.536690i	$0.819674\pi$
$632$	−1.78253	+	0.549838i	−0.0709053	+	0.0218714i
$633$	2.43508	+	6.20448i	0.0967857	+	0.246606i
$634$	36.9074	+	34.2450i	1.46578	+	1.36004i
$635$	−2.64490	−	1.80326i	−0.104960	−	0.0715603i
$636$	−0.565752			−0.0224335
$637$	−1.11763	−	6.91020i	−0.0442822	−	0.273792i
$638$	−46.7088			−1.84922
$639$	21.1312	+	14.4070i	0.835937	+	0.569932i
$640$	26.1895	+	24.3003i	1.03523	+	0.960555i
$641$	4.08664	+	10.4126i	0.161413	+	0.411273i	0.988583	−	0.150679i	$-0.0481459\pi$
$641$	4.08664	+	10.4126i	0.161413	+	0.411273i	−0.827170	+	0.561952i	$0.810051\pi$
$642$	40.7888	−	12.5817i	1.60981	−	0.496559i
$643$	−2.54916	−	11.1686i	−0.100529	−	0.440446i	−0.999994	−	0.00345342i	$-0.998901\pi$
$643$	−2.54916	−	11.1686i	−0.100529	−	0.440446i	0.899465	−	0.436993i	$-0.143956\pi$
$644$	−17.0556	−	14.5187i	−0.672083	−	0.572117i
$645$	19.1463	−	83.8856i	0.753887	−	3.30299i
$646$	−1.67615	−	22.3667i	−0.0659474	−	0.880007i
$647$	−17.0859	−	5.27029i	−0.671715	−	0.207197i	−0.0599081	−	0.998204i	$-0.519081\pi$
$647$	−17.0859	−	5.27029i	−0.671715	−	0.207197i	−0.611807	+	0.791007i	$0.709557\pi$
$648$	0.916812	−	12.2340i	0.0360158	−	0.480597i
$649$	−16.2872	+	41.4990i	−0.639327	+	1.62898i
$650$	11.2390	−	5.41240i	0.440829	−	0.212292i
$651$	21.9129	−	30.0274i	0.858835	−	1.17686i
$652$	10.5912	+	5.10047i	0.414785	+	0.199750i
$653$	11.8877	−	11.0302i	0.465201	−	0.431643i	−0.412424	−	0.910992i	$-0.635318\pi$
$653$	11.8877	−	11.0302i	0.465201	−	0.431643i	0.877624	+	0.479349i	$0.159127\pi$
$654$	70.0232	−	10.5543i	2.73812	−	0.412706i
$655$	11.2211	−	19.4355i	0.438445	−	0.759408i
$656$	−14.4920	−	25.1009i	−0.565819	−	0.980027i
$657$	22.1343	+	27.7555i	0.863542	+	1.08285i
$658$	19.2714	+	11.9651i	0.751278	+	0.466447i
$659$	23.2186	−	29.1152i	0.904469	−	1.13417i	−0.0859814	−	0.996297i	$-0.527403\pi$
$659$	23.2186	−	29.1152i	0.904469	−	1.13417i	0.990450	−	0.137871i	$-0.0440260\pi$
$660$	58.8536	+	8.87075i	2.29087	+	0.345293i
$661$	19.2862	−	13.1491i	0.750148	−	0.511442i	−0.126859	−	0.991921i	$-0.540489\pi$
$661$	19.2862	−	13.1491i	0.750148	−	0.511442i	0.877006	+	0.480479i	$0.159537\pi$
$662$	17.8110	−	12.1433i	0.692242	−	0.471963i
$663$	5.85648	+	0.882722i	0.227447	+	0.0342821i
$664$	1.41905	−	1.77944i	0.0550700	−	0.0690556i
$665$	−47.2875	−	5.07082i	−1.83373	−	0.196638i
$666$	−33.3653	−	41.8388i	−1.29288	−	1.62122i
$667$	15.7674	+	27.3100i	0.610517	+	1.05745i
$668$	−9.66595	+	16.7419i	−0.373987	+	0.647764i
$669$	−23.5145	+	3.54425i	−0.909125	+	0.137028i
$670$	−35.4198	+	32.8648i	−1.36839	+	1.26968i
$671$	−26.5445	−	12.7831i	−1.02474	−	0.493488i
$672$	−39.6719	+	1.69796i	−1.53038	+	0.0655004i
$673$	2.87561	−	1.38482i	0.110847	−	0.0533809i	−0.377639	−	0.925953i	$-0.623264\pi$
$673$	2.87561	−	1.38482i	0.110847	−	0.0533809i	0.488485	+	0.872572i	$0.337550\pi$
$674$	−8.02212	+	20.4400i	−0.309001	+	0.787321i
$675$	−0.0930497	+	1.24166i	−0.00358148	+	0.0477916i
$676$	1.16690	+	0.359942i	0.0448808	+	0.0138439i
$677$	−1.67397	−	22.3376i	−0.0643358	−	0.858502i	−0.932256	−	0.361799i	$-0.882163\pi$
$677$	−1.67397	−	22.3376i	−0.0643358	−	0.858502i	0.867920	−	0.496703i	$-0.165456\pi$
$678$	12.8144	−	56.1435i	0.492133	−	2.15618i
$679$	2.72738	−	2.03563i	0.104667	−	0.0781202i
$680$	2.58430	+	11.3226i	0.0991035	+	0.434201i
$681$	16.0033	−	4.93638i	0.613249	−	0.189162i
$682$	−21.3889	−	54.4979i	−0.819022	−	2.08683i
$683$	4.62718	+	4.29339i	0.177054	+	0.164282i	0.763722	−	0.645546i	$-0.223370\pi$
$683$	4.62718	+	4.29339i	0.177054	+	0.164282i	−0.586668	+	0.809828i	$0.699561\pi$
$684$	16.1207	+	10.9909i	0.616392	+	0.420249i
$685$	−38.3897			−1.46680
$686$	−8.08425	+	32.2413i	−0.308658	+	1.23098i
$687$	−15.5246			−0.592300
$688$	41.3180	+	28.1701i	1.57523	+	1.07398i
$689$	0.137816	+	0.127875i	0.00525037	+	0.00487163i
$690$	−38.7242	−	98.6677i	−1.47421	−	3.75621i
$691$	−3.72712	+	1.14966i	−0.141786	+	0.0437353i	−0.364836	−	0.931072i	$-0.618875\pi$
$691$	−3.72712	+	1.14966i	−0.141786	+	0.0437353i	0.223050	+	0.974807i	$0.428399\pi$
$692$	−1.32299	−	5.79641i	−0.0502927	−	0.220347i
$693$	37.2746	−	27.8206i	1.41595	−	1.05682i
$694$	−2.18477	+	9.57210i	−0.0829327	+	0.363352i
$695$	−4.06752	−	54.2773i	−0.154290	−	2.05886i
$696$	14.9729	+	4.61853i	0.567547	+	0.175065i
$697$	1.05142	−	14.0303i	0.0398255	−	0.531435i
$698$	−15.8806	+	40.4631i	−0.601089	+	1.53155i
$699$	1.05670	−	0.508881i	0.0399681	−	0.0192476i
$700$	−22.4354	+	0.960237i	−0.847977	+	0.0362936i
$701$	−12.6451	−	6.08957i	−0.477600	−	0.230000i	0.179566	−	0.983746i	$-0.442531\pi$
$701$	−12.6451	−	6.08957i	−0.477600	−	0.230000i	−0.657166	+	0.753746i	$0.728245\pi$
$702$	−0.235694	+	0.218692i	−0.00889571	+	0.00825401i
$703$	49.8944	−	7.52037i	1.88180	−	0.283636i
$704$	−2.94214	+	5.09594i	−0.110886	+	0.192061i
$705$	20.3475	+	35.2429i	0.766332	+	1.32733i
$706$	−22.4143	−	28.1067i	−0.843574	−	1.05781i
$707$	27.2376	+	2.92079i	1.02437	+	0.109848i
$708$	−14.6197	+	18.3326i	−0.549443	+	0.688980i
$709$	−33.1484	−	4.99632i	−1.24492	−	0.187641i	−0.506651	−	0.862151i	$-0.669117\pi$
$709$	−33.1484	−	4.99632i	−1.24492	−	0.187641i	−0.738265	+	0.674510i	$0.764355\pi$
$710$	−42.6679	+	29.0905i	−1.60130	+	1.09175i
$711$	3.38799	−	2.30989i	0.127059	−	0.0866276i
$712$	−12.1943	−	1.83799i	−0.457000	−	0.0688816i
$713$	−24.6440	+	30.9026i	−0.922924	+	1.15731i
$714$	−23.8929	−	14.8344i	−0.894170	−	0.555164i
$715$	−12.3316	−	15.4633i	−0.461175	−	0.578295i
$716$	−5.18530	−	8.98121i	−0.193784	−	0.335644i
$717$	−2.77427	+	4.80518i	−0.103607	+	0.179453i
$718$	15.3451	−	2.31291i	0.572675	−	0.0863169i
$719$	23.6103	−	21.9071i	0.880514	−	0.816998i	−0.103584	−	0.994621i	$-0.533031\pi$
$719$	23.6103	−	21.9071i	0.880514	−	0.816998i	0.984099	+	0.177623i	$0.0568407\pi$
$720$	−47.3829	−	22.8184i	−1.76586	−	0.850392i
$721$	8.37632	−	11.4781i	0.311950	−	0.427467i
$722$	−12.9980	+	6.25949i	−0.483734	+	0.232954i
$723$	−4.37305	+	11.1424i	−0.162636	+	0.414389i
$724$	0.947531	−	12.6439i	0.0352147	−	0.469908i
$725$	30.2113	+	9.31895i	1.12202	+	0.346097i
$726$	−7.18335	−	95.8552i	−0.266599	−	3.55752i
$727$	5.93208	−	25.9901i	0.220009	−	0.963921i	−0.737461	−	0.675389i	$-0.763976\pi$
$727$	5.93208	−	25.9901i	0.220009	−	0.963921i	0.957470	−	0.288532i	$-0.0931672\pi$
$728$	2.81616	+	2.39728i	0.104374	+	0.0888490i
$729$	6.29563	+	27.5830i	0.233172	+	1.02159i
$730$	−68.4980	+	21.1288i	−2.53522	+	0.782013i
$731$	8.86860	+	22.5968i	0.328017	+	0.835773i
$732$	−11.3596	−	10.5402i	−0.419862	−	0.389575i
$733$	6.65225	+	4.53543i	0.245707	+	0.167520i	0.679911	−	0.733294i	$-0.262018\pi$
$733$	6.65225	+	4.53543i	0.245707	+	0.167520i	−0.434205	+	0.900814i	$0.642971\pi$
$734$	11.5028			0.424577
$735$	−40.0880	+	44.1469i	−1.47867	+	1.62838i
$736$	42.2218			1.55632
$737$	36.8144	+	25.0996i	1.35608	+	0.924556i
$738$	23.6657	+	21.9585i	0.871145	+	0.808305i
$739$	−0.160907	−	0.409984i	−0.00591905	−	0.0150815i	0.927884	−	0.372870i	$-0.121626\pi$
$739$	−0.160907	−	0.409984i	−0.00591905	−	0.0150815i	−0.933803	+	0.357788i	$0.883531\pi$
$740$	39.1441	−	12.0744i	1.43897	−	0.443862i
$741$	−2.85135	−	12.4926i	−0.104747	−	0.458927i
$742$	−0.361387	−	0.816311i	−0.0132669	−	0.0299677i
$743$	−2.71928	+	11.9139i	−0.0997607	+	0.437080i	0.900238	+	0.435398i	$0.143393\pi$
$743$	−2.71928	+	11.9139i	−0.0997607	+	0.437080i	−0.999999	+	0.00168188i	$0.999465\pi$
$744$	1.46767	+	19.5847i	0.0538075	+	0.718011i
$745$	47.8174	+	14.7497i	1.75189	+	0.540387i
$746$	−3.23612	+	43.1830i	−0.118483	+	1.58104i
$747$	−1.82781	+	4.65718i	−0.0668760	+	0.170397i
$748$	−15.1287	+	7.28561i	−0.553161	+	0.266388i
$749$	16.7597	+	19.2647i	0.612386	+	0.703918i
$750$	−26.8674	−	12.9386i	−0.981058	−	0.472453i
$751$	15.9539	−	14.8030i	0.582165	−	0.540171i	−0.333168	−	0.942867i	$-0.608118\pi$
$751$	15.9539	−	14.8030i	0.582165	−	0.540171i	0.915333	+	0.402697i	$0.131927\pi$
$752$	−23.3874	+	3.52508i	−0.852851	+	0.128547i
$753$	−23.0258	+	39.8818i	−0.839106	+	1.45337i
$754$	4.08198	+	7.07019i	0.148657	+	0.257481i
$755$	−44.3916	−	55.6653i	−1.61557	−	2.02587i
$756$	0.545284	−	0.194099i	0.0198318	−	0.00705930i
$757$	−21.2272	+	26.6180i	−0.771514	+	0.967448i	−0.999981	−	0.00610351i	$-0.998057\pi$
$757$	−21.2272	+	26.6180i	−0.771514	+	0.967448i	0.228467	+	0.973552i	$0.426629\pi$
$758$	19.1737	+	2.88997i	0.696421	+	0.104969i
$759$	−80.7589	+	55.0605i	−2.93136	+	1.99857i
$760$	20.7608	−	14.1544i	0.753072	−	0.513436i
$761$	−22.5085	−	3.39261i	−0.815933	−	0.122982i	−0.272200	−	0.962241i	$-0.587751\pi$
$761$	−22.5085	−	3.39261i	−0.815933	−	0.122982i	−0.543732	+	0.839259i	$0.682989\pi$
$762$	−2.55351	+	3.20200i	−0.0925040	+	0.115996i
$763$	22.7302	+	35.7470i	0.822888	+	1.29413i
$764$	4.83155	+	6.05858i	0.174799	+	0.219192i
$765$	−12.7645	−	22.1088i	−0.461503	−	0.799346i
$766$	2.74661	−	4.75726i	0.0992389	−	0.171887i
$767$	7.70497	−	1.16134i	0.278210	−	0.0419335i
$768$	37.2226	−	34.5375i	1.34315	−	1.24626i
$769$	26.5103	+	12.7667i	0.955986	+	0.460379i	0.845781	−	0.533530i	$-0.179135\pi$
$769$	26.5103	+	12.7667i	0.955986	+	0.460379i	0.110205	+	0.993909i	$0.464849\pi$
$770$	24.7947	+	90.5849i	0.893539	+	3.26445i
$771$	52.9847	−	25.5161i	1.90820	−	0.918940i
$772$	−2.34896	+	5.98505i	−0.0845409	+	0.215407i
$773$	−1.27758	+	17.0482i	−0.0459515	+	0.613181i	0.925928	+	0.377701i	$0.123285\pi$
$773$	−1.27758	+	17.0482i	−0.0459515	+	0.613181i	−0.971879	+	0.235480i	$0.924334\pi$
$774$	−53.2258	−	16.4180i	−1.91316	−	0.590132i
$775$	2.96136	+	39.5167i	0.106375	+	1.41948i
$776$	−0.400108	+	1.75299i	−0.0143631	+	0.0629287i
$777$	29.2619	−	56.0938i	1.04976	−	2.01235i
$778$	2.38498	+	10.4493i	0.0855057	+	0.374625i
$779$	−29.0878	+	8.97241i	−1.04218	+	0.321470i
$780$	−3.80059	−	9.68375i	−0.136083	−	0.346734i
$781$	34.9085	+	32.3904i	1.24912	+	1.15902i
$782$	24.7076	+	16.8454i	0.883543	+	0.602389i
$783$	−0.814898			−0.0291221
$784$	−15.3721	−	31.0620i	−0.549005	−	1.10936i
$785$	−48.2883			−1.72348
$786$	−23.7234	−	16.1743i	−0.846184	−	0.576918i
$787$	−3.51614	−	3.26250i	−0.125337	−	0.116296i	0.615014	−	0.788516i	$-0.289150\pi$
$787$	−3.51614	−	3.26250i	−0.125337	−	0.116296i	−0.740351	+	0.672220i	$0.765341\pi$
$788$	1.36211	+	3.47060i	0.0485231	+	0.123635i
$789$	47.4006	−	14.6211i	1.68751	−	0.520526i
$790$	1.84240	+	8.07209i	0.0655497	+	0.287192i
$791$	33.8137	−	6.58632i	1.20228	−	0.234183i
$792$	−5.46822	+	23.9578i	−0.194305	+	0.851305i
$793$	0.384824	+	5.13512i	0.0136655	+	0.182353i
$794$	19.2907	+	5.95038i	0.684600	+	0.211171i
$795$	0.119686	−	1.59710i	0.00424482	−	0.0566432i
$796$	7.52277	−	19.1677i	0.266638	−	0.679381i
$797$	27.5471	−	13.2660i	0.975769	−	0.469906i	0.123121	−	0.992392i	$-0.460710\pi$
$797$	27.5471	−	13.2660i	0.975769	−	0.469906i	0.852648	+	0.522486i	$0.174995\pi$
$798$	−10.9906	+	59.8455i	−0.389063	+	2.11851i
$799$	−10.3441	−	4.98146i	−0.365948	−	0.176231i
$800$	31.0303	−	28.7919i	1.09709	−	1.01795i
$801$	26.8052	−	4.04023i	0.947114	−	0.142754i
$802$	−25.4487	+	44.0784i	−0.898623	+	1.55646i
$803$	33.0510	+	57.2460i	1.16635	+	2.02017i
$804$	14.6118	+	18.3227i	0.515319	+	0.646190i
$805$	44.5938	−	45.0758i	1.57173	−	1.58871i
$806$	−6.38000	+	8.00027i	−0.224726	+	0.281797i
$807$	−34.2655	−	5.16470i	−1.20620	−	0.181806i
$808$	−11.9582	+	8.15294i	−0.420687	+	0.286820i
$809$	15.2247	−	10.3800i	0.535272	−	0.364942i	−0.265312	−	0.964163i	$-0.585475\pi$
$809$	15.2247	−	10.3800i	0.535272	−	0.364942i	0.800584	+	0.599220i	$0.204523\pi$
$810$	−53.8452	−	8.11585i	−1.89193	−	0.285162i
$811$	2.33738	−	2.93099i	0.0820766	−	0.102921i	−0.739098	−	0.673598i	$-0.764748\pi$
$811$	2.33738	−	2.93099i	0.0820766	−	0.102921i	0.821174	+	0.570677i	$0.193319\pi$
$812$	−1.72395	−	14.5950i	−0.0604987	−	0.512186i
$813$	−20.0568	−	25.1505i	−0.703423	−	0.882065i
$814$	−49.8212	−	86.2929i	−1.74623	−	3.02457i
$815$	−16.6390	+	28.8196i	−0.582840	+	1.00951i
$816$	28.9960	−	4.37044i	1.01506	−	0.152996i
$817$	38.4996	−	35.7224i	1.34693	−	1.24977i
$818$	32.3540	+	15.5808i	1.13123	+	0.544772i
$819$	−7.46864	−	3.21087i	−0.260975	−	0.112197i
$820$	−22.2654	+	10.7224i	−0.777541	+	0.374444i
$821$	7.58434	−	19.3246i	0.264695	−	0.674433i	−0.735299	−	0.677743i	$-0.762958\pi$
$821$	7.58434	−	19.3246i	0.264695	−	0.674433i	0.999995	+	0.00330998i	$0.00105360\pi$
$822$	−3.67042	+	48.9783i	−0.128021	+	1.70832i
$823$	−46.1149	−	14.2246i	−1.60747	−	0.495837i	−0.644306	−	0.764768i	$-0.722854\pi$
$823$	−46.1149	−	14.2246i	−1.60747	−	0.495837i	−0.963160	+	0.268931i	$0.913330\pi$
$824$	0.561025	+	7.48636i	0.0195442	+	0.260800i
$825$	−21.8057	+	95.5371i	−0.759178	+	3.32618i
$826$	−35.7904	−	9.38414i	−1.24531	−	0.326516i
$827$	−8.29515	−	36.3434i	−0.288451	−	1.26378i	−0.886651	−	0.462438i	$-0.846975\pi$
$827$	−8.29515	−	36.3434i	−0.288451	−	1.26378i	0.598201	−	0.801346i	$-0.295883\pi$
$828$	−24.8571	+	7.66739i	−0.863843	+	0.266460i
$829$	19.2747	+	49.1112i	0.669439	+	1.70570i	0.707774	+	0.706439i	$0.249700\pi$
$829$	19.2747	+	49.1112i	0.669439	+	1.70570i	−0.0383345	+	0.999265i	$0.512205\pi$
$830$	−7.40533	−	6.87114i	−0.257043	−	0.238501i
$831$	−61.1307	−	41.6782i	−2.12060	−	1.44580i
$832$	1.02848			0.0356561
$833$	2.32850	−	16.6618i	0.0806776	−	0.577297i
$834$	−69.6369			−2.41133
$835$	−45.2169	−	30.8284i	−1.56480	−	1.06686i
$836$	26.6313	+	24.7102i	0.921063	+	0.854621i
$837$	−0.373158	−	0.950791i	−0.0128982	−	0.0328641i
$838$	−9.10487	+	2.80848i	−0.314523	+	0.0970174i
$839$	1.81783	+	7.96443i	0.0627585	+	0.274963i	0.996565	−	0.0828159i	$-0.0263914\pi$
$839$	1.81783	+	7.96443i	0.0627585	+	0.274963i	−0.933806	+	0.357779i	$0.883534\pi$
$840$	1.00882	−	31.4895i	0.0348076	−	1.08649i
$841$	1.84884	−	8.10032i	0.0637532	−	0.279321i
$842$	−2.38074	−	31.7687i	−0.0820456	−	1.09482i
$843$	−15.5481	−	4.79595i	−0.535505	−	0.165181i
$844$	−0.246825	+	3.29365i	−0.00849608	+	0.113372i
$845$	−1.26296	+	3.21797i	−0.0434472	+	0.110702i
$846$	23.7353	−	11.4303i	0.816036	−	0.392982i
$847$	50.6934	−	27.1418i	1.74185	−	0.932603i
$848$	0.838640	+	0.403868i	0.0287990	+	0.0138689i
$849$	9.67303	−	8.97526i	0.331978	−	0.308030i
$850$	29.6457	−	4.46838i	1.01684	−	0.153264i
$851$	−33.6362	+	58.2596i	−1.15303	+	1.99711i
$852$	12.5236	+	21.6915i	0.429052	+	0.743140i
$853$	30.8632	+	38.7012i	1.05674	+	1.32511i	0.943440	+	0.331544i	$0.107570\pi$
$853$	30.8632	+	38.7012i	1.05674	+	1.32511i	0.113296	+	0.993561i	$0.463859\pi$
$854$	7.95196	−	23.1233i	0.272110	−	0.791262i
$855$	−34.4373	+	43.1831i	−1.17773	+	1.47683i
$856$	−13.3401	−	2.01070i	−0.455956	−	0.0687243i
$857$	−35.7981	+	24.4067i	−1.22284	+	0.833718i	−0.990310	−	0.138871i	$-0.955653\pi$
$857$	−35.7981	+	24.4067i	−1.22284	+	0.833718i	−0.232529	+	0.972589i	$0.574700\pi$
$858$	−20.9074	+	14.2544i	−0.713767	+	0.486638i
$859$	−8.58193	−	1.29352i	−0.292812	−	0.0441343i	0.000993706	−	1.00000i	$-0.499684\pi$
$859$	−8.58193	−	1.29352i	−0.292812	−	0.0441343i	−0.293805	+	0.955865i	$0.594922\pi$
$860$	26.5842	−	33.3356i	0.906515	−	1.13673i
$861$	−12.4123	+	36.0933i	−0.423009	+	1.23006i
$862$	5.10825	+	6.40555i	0.173988	+	0.218174i
$863$	8.03374	+	13.9148i	0.273472	+	0.473667i	0.969748	−	0.244107i	$-0.0784947\pi$
$863$	8.03374	+	13.9148i	0.273472	+	0.473667i	−0.696277	+	0.717773i	$0.745161\pi$
$864$	−0.545531	+	0.944887i	−0.0185593	+	0.0321457i
$865$	16.6429	−	2.50852i	0.565877	−	0.0852922i
$866$	34.8214	−	32.3095i	1.18328	−	1.09792i
$867$	−24.9194	−	12.0006i	−0.846308	−	0.407560i
$868$	16.2395	−	8.69479i	0.551204	−	0.295120i
$869$	6.87898	−	3.31274i	0.233353	−	0.112377i
$870$	25.4086	−	64.7401i	0.861433	−	2.19490i
$871$	0.581982	−	7.76601i	0.0197197	−	0.263141i
$872$	−21.3867	−	6.59694i	−0.724246	−	0.223400i
$873$	−0.295369	−	3.94143i	−0.00999673	−	0.133397i
$874$	14.3967	−	63.0759i	0.486974	−	2.13357i
$875$	0.571207	−	17.8297i	0.0193103	−	0.602756i
$876$	7.73658	+	33.8962i	0.261395	+	1.14525i
$877$	−46.6423	+	14.3872i	−1.57500	+	0.485822i	−0.954456	−	0.298351i	$-0.903563\pi$
$877$	−46.6423	+	14.3872i	−1.57500	+	0.485822i	−0.620541	+	0.784174i	$0.713087\pi$
$878$	−8.62101	−	21.9660i	−0.290945	−	0.741316i
$879$	−43.6494	−	40.5007i	−1.47226	−	1.36606i
$880$	−80.9088	−	55.1627i	−2.72744	−	1.85953i
$881$	−22.8154			−0.768669			−0.384335	−	0.923194i	$-0.625569\pi$
$881$	−22.8154			−0.768669			−0.384335	+	0.923194i	$0.625569\pi$
$882$	26.5595	+	28.0143i	0.894305	+	0.943291i
$883$	−51.7516			−1.74158			−0.870790	−	0.491655i	$-0.836392\pi$
$883$	−51.7516			−1.74158			−0.870790	+	0.491655i	$0.836392\pi$
$884$	2.42493	+	1.65329i	0.0815593	+	0.0556062i
$885$	−48.6593	−	45.1492i	−1.63566	−	1.51768i
$886$	−23.7725	−	60.5713i	−0.798652	−	2.03493i
$887$	−2.62432	+	0.809495i	−0.0881160	+	0.0271802i	−0.338500	−	0.940966i	$-0.609919\pi$
$887$	−2.62432	+	0.809495i	−0.0881160	+	0.0271802i	0.250384	+	0.968147i	$0.419443\pi$
$888$	7.43806	+	32.5883i	0.249605	+	1.09359i
$889$	−2.36987	−	0.621373i	−0.0794827	−	0.0208402i
$890$	−12.1799	+	53.3638i	−0.408272	+	1.78876i
$891$	3.75250	+	50.0737i	0.125714	+	1.67753i
$892$	−11.2605	−	3.47341i	−0.377030	−	0.116298i
$893$	−1.85628	+	24.7704i	−0.0621181	+	0.828908i
$894$	23.3897	−	59.5961i	0.782270	−	1.99319i
$895$	26.4506	−	12.7379i	0.884145	−	0.425782i
$896$	25.1202	+	10.7995i	0.839207	+	0.360786i
$897$	15.3921	+	7.41242i	0.513926	+	0.247494i
$898$	24.9254	−	23.1274i	0.831770	−	0.771770i
$899$	−25.6450	+	3.86536i	−0.855307	+	0.128917i
$900$	−13.0398	+	22.5856i	−0.434660	+	0.752854i
$901$	0.225922	+	0.391309i	0.00752656	+	0.0130364i
$902$	37.4793	+	46.9976i	1.24792	+	1.56485i
$903$	−7.72471	−	65.3979i	−0.257062	−	2.17631i
$904$	−11.3479	+	14.2299i	−0.377427	+	0.473278i
$905$	35.4929	+	5.34969i	1.17982	+	0.177830i
$906$	−75.2630	+	51.3135i	−2.50045	+	1.70478i
$907$	−5.51249	+	3.75835i	−0.183039	+	0.124794i	−0.651373	−	0.758757i	$-0.725807\pi$
$907$	−5.51249	+	3.75835i	−0.183039	+	0.124794i	0.468334	+	0.883551i	$0.344854\pi$
$908$	8.20632	+	1.23690i	0.272336	+	0.0410481i
$909$	19.8359	−	24.8734i	0.657914	−	0.824998i
$910$	11.5448	−	11.6695i	0.382705	−	0.386841i
$911$	5.78735	+	7.25711i	0.191743	+	0.240439i	0.868405	−	0.495855i	$-0.165145\pi$
$911$	5.78735	+	7.25711i	0.191743	+	0.240439i	−0.676662	+	0.736294i	$0.736574\pi$
$912$	−31.7213	−	54.9429i	−1.05040	−	1.81934i
$913$	−4.65780	+	8.06754i	−0.154151	+	0.266997i
$914$	−1.60022	+	0.241195i	−0.0529307	+	0.00797802i
$915$	32.1576	−	29.8379i	1.06310	−	0.986410i
$916$	−6.93122	−	3.33790i	−0.229014	−	0.110287i
$917$	3.10248	−	16.8935i	0.102453	−	0.557873i
$918$	−0.696222	+	0.335283i	−0.0229788	+	0.0110660i
$919$	4.89070	−	12.4613i	0.161329	−	0.411060i	−0.827236	−	0.561855i	$-0.810088\pi$
$919$	4.89070	−	12.4613i	0.161329	−	0.411060i	0.988565	+	0.150794i	$0.0481832\pi$
$920$	−2.50346	+	33.4063i	−0.0825366	+	1.10137i
$921$	27.4493	+	8.46699i	0.904486	+	0.278997i
$922$	3.93416	+	52.4977i	0.129565	+	1.72892i
$923$	1.85212	−	8.11467i	0.0609633	−	0.267098i
$924$	44.7118	−	8.70908i	1.47091	−	0.286508i
$925$	15.0080	+	65.7543i	0.493460	+	2.16199i
$926$	16.5378	−	5.10123i	0.543465	−	0.167637i
$927$	−6.02903	−	15.3617i	−0.198019	−	0.504545i
$928$	20.3081	+	18.8432i	0.666647	+	0.618558i
$929$	8.27231	+	5.63996i	0.271406	+	0.185041i	0.691373	−	0.722498i	$-0.257006\pi$
$929$	8.27231	+	5.63996i	0.271406	+	0.185041i	−0.419967	+	0.907539i	$0.637959\pi$
$930$	87.1713			2.85846
$931$	−35.3971	+	8.48044i	−1.16009	+	0.277935i
$932$	0.581195			0.0190377
$933$	67.4806	+	46.0075i	2.20921	+	1.50622i
$934$	21.3511	+	19.8109i	0.698630	+	0.648234i
$935$	−17.3665	−	44.2491i	−0.567945	−	1.44710i
$936$	4.10432	−	1.26601i	0.134154	−	0.0413810i
$937$	−7.99035	−	35.0080i	−0.261033	−	1.14366i	−0.920133	−	0.391606i	$-0.871920\pi$
$937$	−7.99035	−	35.0080i	−0.261033	−	1.14366i	0.659100	−	0.752055i	$-0.270937\pi$
$938$	−17.1037	+	32.7871i	−0.558456	+	1.07054i
$939$	−2.64593	+	11.5926i	−0.0863468	+	0.378310i
$940$	1.50701	+	20.1097i	0.0491533	+	0.655905i
$941$	−3.10693	−	0.958360i	−0.101283	−	0.0312416i	0.243699	−	0.969851i	$-0.421639\pi$
$941$	−3.10693	−	0.958360i	−0.101283	−	0.0312416i	−0.344982	+	0.938609i	$0.612115\pi$
$942$	−4.61681	+	61.6071i	−0.150424	+	2.00727i
$943$	14.8270	−	37.7785i	0.482833	−	1.23024i
$944$	34.7584	−	16.7388i	1.13129	−	0.544800i
$945$	0.432577	+	1.58038i	0.0140717	+	0.0514097i
$946$	−93.4429	−	44.9997i	−3.03809	−	1.46307i
$947$	6.08952	−	5.65025i	0.197883	−	0.183608i	−0.575007	−	0.818148i	$-0.695001\pi$
$947$	6.08952	−	5.65025i	0.197883	−	0.183608i	0.772890	+	0.634540i	$0.218810\pi$
$948$	3.97100	−	0.598532i	0.128972	−	0.0194394i
$949$	5.77679	−	10.0057i	0.187523	−	0.324799i
$950$	−32.4321	−	56.1741i	−1.05224	−	1.82253i
$951$	43.1015	+	54.0476i	1.39766	+	1.75261i
$952$	4.76936	+	7.50061i	0.154576	+	0.243096i
$953$	−18.4273	+	23.1071i	−0.596920	+	0.748514i	−0.984894	−	0.173156i	$-0.944603\pi$
$953$	−18.4273	+	23.1071i	−0.596920	+	0.748514i	0.387975	+	0.921670i	$0.373175\pi$
$954$	−1.02521	−	0.154525i	−0.0331924	−	0.00500294i
$955$	−18.1252	+	12.3576i	−0.586519	+	0.399882i
$956$	−2.27177	+	1.54887i	−0.0734743	+	0.0500939i
$957$	−63.4170	−	9.55857i	−2.04998	−	0.308985i
$958$	20.4600	−	25.6561i	0.661034	−	0.828910i
$959$	−27.6801	+	9.85296i	−0.893836	+	0.318169i
$960$	−5.46270	−	6.85001i	−0.176308	−	0.221083i
$961$	−0.753280	−	1.30472i	−0.0242993	−	0.0420877i
$962$	−8.70796	+	15.0826i	−0.280756	+	0.486284i
$963$	29.3239	−	4.41987i	0.944951	−	0.142428i
$964$	−4.34811	+	4.03446i	−0.140043	+	0.129941i
$965$	−16.3986	−	7.89717i	−0.527891	−	0.254219i
$966$	−53.2449	−	61.2033i	−1.71313	−	1.96918i
$967$	−25.2075	+	12.1393i	−0.810617	+	0.390373i	−0.792810	−	0.609469i	$-0.791383\pi$
$967$	−25.2075	+	12.1393i	−0.810617	+	0.390373i	−0.0178070	+	0.999841i	$0.505668\pi$
$968$	−11.0992	+	28.2802i	−0.356741	+	0.908961i
$969$	2.30144	−	30.7105i	0.0739328	−	0.986565i
$970$	7.62624	+	2.35238i	0.244864	+	0.0755305i
$971$	1.79566	+	23.9615i	0.0576256	+	0.768960i	0.948916	+	0.315528i	$0.102181\pi$
$971$	1.79566	+	23.9615i	0.0576256	+	0.768960i	−0.891291	+	0.453432i	$0.850199\pi$
$972$	−6.02309	+	26.3889i	−0.193191	+	0.846424i
$973$	−16.8634	−	38.0915i	−0.540616	−	1.22116i
$974$	−12.8744	−	56.4065i	−0.412523	−	1.80738i
$975$	16.3669	−	5.04851i	0.524159	−	0.161682i
$976$	9.31463	+	23.7333i	0.298154	+	0.759684i
$977$	−30.1324	−	27.9588i	−0.964021	−	0.894481i	0.0304456	−	0.999536i	$-0.490307\pi$
$977$	−30.1324	−	27.9588i	−0.964021	−	0.894481i	−0.994466	+	0.105056i	$0.966498\pi$
$978$	35.1778	+	23.9838i	1.12486	+	0.766918i
$979$	50.4748			1.61318
$980$	−27.3899	+	11.0909i	−0.874937	+	0.354286i
$981$	49.1975			1.57076
$982$	42.1982	+	28.7702i	1.34660	+	0.918094i
$983$	7.88099	+	7.31249i	0.251364	+	0.233232i	0.795783	−	0.605581i	$-0.207059\pi$
$983$	7.88099	+	7.31249i	0.251364	+	0.233232i	−0.544419	+	0.838813i	$0.683250\pi$
$984$	−7.36724	−	18.7714i	−0.234859	−	0.598411i
$985$	−10.0855	+	3.11097i	−0.321351	+	0.0991238i
$986$	4.36611	+	19.1292i	0.139045	+	0.609198i
$987$	23.7165	+	20.1888i	0.754903	+	0.642618i
$988$	1.41296	−	6.19059i	0.0449523	−	0.196949i
$989$	5.23268	+	69.8253i	0.166390	+	2.22031i
$990$	104.227	+	32.1497i	3.31254	+	1.02178i
$991$	0.387978	−	5.17721i	0.0123245	−	0.164459i	−0.987645	−	0.156705i	$-0.949913\pi$
$991$	0.387978	−	5.17721i	0.0123245	−	0.164459i	0.999970	−	0.00775411i	$-0.00246824\pi$
$992$	−12.6860	+	32.3234i	−0.402781	+	1.02627i
$993$	26.6671	−	12.8422i	0.846256	−	0.407535i
$994$	−23.2985	+	31.9260i	−0.738984	+	1.01263i
$995$	52.5183	+	25.2915i	1.66494	+	0.801793i
$996$	−3.59177	+	3.33267i	−0.113810	+	0.105600i
$997$	−11.4921	+	1.73216i	−0.363959	+	0.0548579i	−0.328476	−	0.944512i	$-0.606535\pi$
$997$	−11.4921	+	1.73216i	−0.363959	+	0.0548579i	−0.0354828	+	0.999370i	$0.511297\pi$
$998$	−7.78873	+	13.4905i	−0.246548	+	0.427034i
$999$	−0.869199	−	1.50550i	−0.0275002	−	0.0476318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.23	✓	324
49.37	even	21	inner	637.2.bl.a.625.23	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.23	✓	324	1.1	even	1	trivial
637.2.bl.a.625.23	yes	324	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)

\(f(q)\)	\(=\)	\(q+(1.48290 + 1.01102i) q^{2} +(1.80645 + 1.67614i) q^{3} +(0.446138 + 1.13674i) q^{4} +(-3.30336 + 1.01895i) q^{5} +(0.984164 + 4.31190i) q^{6} +(-2.12029 + 1.58252i) q^{7} +(0.311049 - 1.36279i) q^{8} +(0.229623 + 3.06411i) q^{9} +O(q^{10})\)	\(q+(1.48290 + 1.01102i) q^{2} +(1.80645 + 1.67614i) q^{3} +(0.446138 + 1.13674i) q^{4} +(-3.30336 + 1.01895i) q^{5} +(0.984164 + 4.31190i) q^{6} +(-2.12029 + 1.58252i) q^{7} +(0.311049 - 1.36279i) q^{8} +(0.229623 + 3.06411i) q^{9} +(-5.92872 - 1.82877i) q^{10} +(-0.427557 + 5.70535i) q^{11} +(-1.09941 + 2.80125i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-4.74414 + 0.203050i) q^{14} +(-7.67524 - 3.69620i) q^{15} +(3.62941 - 3.36760i) q^{16} +(2.37654 - 0.358206i) q^{17} +(-2.75737 + 4.77591i) q^{18} +(-2.59991 - 4.50318i) q^{19} +(-2.63203 - 3.30047i) q^{20} +(-6.48272 - 0.695166i) q^{21} +(-6.40226 + 8.02818i) q^{22} +(6.85517 + 1.03325i) q^{23} +(2.84612 - 1.94045i) q^{24} +(5.74270 - 3.91531i) q^{25} +(1.77471 + 0.267495i) q^{26} +(-0.111696 + 0.140062i) q^{27} +(-2.74485 - 1.70420i) q^{28} +(2.83612 + 3.55638i) q^{29} +(-7.64466 - 13.2409i) q^{30} +(-2.85073 + 4.93760i) q^{31} +(6.02230 - 0.907716i) q^{32} +(-10.3353 + 9.58977i) q^{33} +(3.88633 + 1.87156i) q^{34} +(5.39157 - 7.38809i) q^{35} +(-3.38065 + 1.62803i) q^{36} +(-3.54519 + 9.03299i) q^{37} +(0.697413 - 9.30633i) q^{38} +(2.35480 + 0.726361i) q^{39} +(0.361114 + 4.81873i) q^{40} +(1.30265 - 5.70730i) q^{41} +(-8.91038 - 7.58504i) q^{42} +(2.24752 + 9.84703i) q^{43} +(-6.67625 + 2.05935i) q^{44} +(-3.88070 - 9.88785i) q^{45} +(9.12087 + 8.46293i) q^{46} +(-3.94698 - 2.69100i) q^{47} +12.2009 q^{48} +(1.99127 - 6.71080i) q^{49} +12.4743 q^{50} +(4.89351 + 3.33634i) q^{51} +(0.895169 + 0.830596i) q^{52} +(0.0686852 + 0.175007i) q^{53} +(-0.307240 + 0.0947711i) q^{54} +(-4.40109 - 19.2824i) q^{55} +(1.49713 + 3.38176i) q^{56} +(2.85135 - 12.4926i) q^{57} +(0.610093 + 8.14112i) q^{58} +(7.44582 + 2.29673i) q^{59} +(0.777407 - 10.3738i) q^{60} +(-1.88133 + 4.79355i) q^{61} +(-9.21937 + 4.43981i) q^{62} +(-5.33587 - 6.13341i) q^{63} +(0.926629 + 0.446241i) q^{64} +(-2.53411 + 2.35131i) q^{65} +(-25.0217 + 3.77141i) q^{66} +(3.89389 - 6.74442i) q^{67} +(1.46745 + 2.54170i) q^{68} +(10.6516 + 13.3567i) q^{69} +(15.4647 - 5.50479i) q^{70} +(5.18953 - 6.50746i) q^{71} +(4.24716 + 0.640157i) q^{72} +(9.54602 - 6.50837i) q^{73} +(-14.3897 + 9.81074i) q^{74} +(16.9365 + 2.55277i) q^{75} +(3.95903 - 4.96447i) q^{76} +(-8.12227 - 12.7736i) q^{77} +(2.75757 + 3.45788i) q^{78} +(-0.667247 - 1.15570i) q^{79} +(-8.55781 + 14.8226i) q^{80} +(8.67860 - 1.30809i) q^{81} +(7.70192 - 7.14634i) q^{82} +(1.46697 + 0.706457i) q^{83} +(-2.10196 - 7.67931i) q^{84} +(-7.48557 + 3.60486i) q^{85} +(-6.62273 + 16.8744i) q^{86} +(-0.837685 + 11.1781i) q^{87} +(7.64221 + 2.35731i) q^{88} +(-0.659284 - 8.79753i) q^{89} +(4.24217 - 18.5862i) q^{90} +(-1.22369 + 2.34576i) q^{91} +(1.88381 + 8.25352i) q^{92} +(-13.4258 + 4.14131i) q^{93} +(-3.13230 - 7.98097i) q^{94} +(13.1770 + 12.2264i) q^{95} +(12.4004 + 8.45448i) q^{96} -1.28632 q^{97} +(9.73763 - 7.93821i) q^{98} -17.5800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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