LMFDB - Embedded newform 287.2.f.a.50.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.5
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55423i q^{2} +(-0.820177 - 0.820177i) q^{3} -0.415620 q^{4} +1.07119i q^{5} +(-1.27474 + 1.27474i) q^{6} +(-0.707107 - 0.707107i) q^{7} -2.46249i q^{8} -1.65462i q^{9} +O(q^{10})$	\(q-1.55423i q^{2} +(-0.820177 - 0.820177i) q^{3} -0.415620 q^{4} +1.07119i q^{5} +(-1.27474 + 1.27474i) q^{6} +(-0.707107 - 0.707107i) q^{7} -2.46249i q^{8} -1.65462i q^{9} +1.66487 q^{10} +(-0.684884 - 0.684884i) q^{11} +(0.340882 + 0.340882i) q^{12} +(-3.90259 - 3.90259i) q^{13} +(-1.09900 + 1.09900i) q^{14} +(0.878565 - 0.878565i) q^{15} -4.65850 q^{16} +(0.0855829 - 0.0855829i) q^{17} -2.57165 q^{18} +(-2.20827 + 2.20827i) q^{19} -0.445207i q^{20} +1.15991i q^{21} +(-1.06447 + 1.06447i) q^{22} +7.33685 q^{23} +(-2.01967 + 2.01967i) q^{24} +3.85255 q^{25} +(-6.06551 + 6.06551i) q^{26} +(-3.81761 + 3.81761i) q^{27} +(0.293887 + 0.293887i) q^{28} +(0.934979 + 0.934979i) q^{29} +(-1.36549 - 1.36549i) q^{30} +10.2030 q^{31} +2.31539i q^{32} +1.12345i q^{33} +(-0.133015 - 0.133015i) q^{34} +(0.757445 - 0.757445i) q^{35} +0.687692i q^{36} -9.35874 q^{37} +(3.43215 + 3.43215i) q^{38} +6.40163i q^{39} +2.63779 q^{40} +(-4.94121 + 4.07240i) q^{41} +1.80276 q^{42} -12.4003i q^{43} +(0.284651 + 0.284651i) q^{44} +1.77241 q^{45} -11.4031i q^{46} +(4.96503 - 4.96503i) q^{47} +(3.82080 + 3.82080i) q^{48} +1.00000i q^{49} -5.98774i q^{50} -0.140386 q^{51} +(1.62199 + 1.62199i) q^{52} +(5.23077 + 5.23077i) q^{53} +(5.93343 + 5.93343i) q^{54} +(0.733640 - 0.733640i) q^{55} +(-1.74124 + 1.74124i) q^{56} +3.62234 q^{57} +(1.45317 - 1.45317i) q^{58} +7.62987 q^{59} +(-0.365149 + 0.365149i) q^{60} -2.05835i q^{61} -15.8578i q^{62} +(-1.16999 + 1.16999i) q^{63} -5.71836 q^{64} +(4.18041 - 4.18041i) q^{65} +1.74610 q^{66} +(5.85604 - 5.85604i) q^{67} +(-0.0355699 + 0.0355699i) q^{68} +(-6.01752 - 6.01752i) q^{69} +(-1.17724 - 1.17724i) q^{70} +(10.4988 + 10.4988i) q^{71} -4.07447 q^{72} +13.7484i q^{73} +14.5456i q^{74} +(-3.15978 - 3.15978i) q^{75} +(0.917800 - 0.917800i) q^{76} +0.968572i q^{77} +9.94959 q^{78} +(-4.42051 - 4.42051i) q^{79} -4.99013i q^{80} +1.29838 q^{81} +(6.32942 + 7.67976i) q^{82} +7.54989 q^{83} -0.482080i q^{84} +(0.0916755 + 0.0916755i) q^{85} -19.2729 q^{86} -1.53370i q^{87} +(-1.68652 + 1.68652i) q^{88} +(-0.00682844 - 0.00682844i) q^{89} -2.75473i q^{90} +5.51910i q^{91} -3.04934 q^{92} +(-8.36828 - 8.36828i) q^{93} +(-7.71678 - 7.71678i) q^{94} +(-2.36547 - 2.36547i) q^{95} +(1.89903 - 1.89903i) q^{96} +(0.412657 - 0.412657i) q^{97} +1.55423 q^{98} +(-1.13322 + 1.13322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.55423i		−	1.09900i	−0.835492	−	0.549502i	$-0.814817\pi$
$2$		−	1.55423i		−	1.09900i	0.835492	−	0.549502i	$-0.185183\pi$
$3$	−0.820177	−	0.820177i	−0.473530	−	0.473530i	0.429525	−	0.903055i	$-0.358681\pi$
$3$	−0.820177	−	0.820177i	−0.473530	−	0.473530i	−0.903055	+	0.429525i	$0.858681\pi$
$4$	−0.415620			−0.207810
$5$			1.07119i			0.479050i	0.970890	+	0.239525i	$0.0769917\pi$
$5$			1.07119i			0.479050i	−0.970890	+	0.239525i	$0.923008\pi$
$6$	−1.27474	+	1.27474i	−0.520411	+	0.520411i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		−	2.46249i		−	0.870620i
$9$		−	1.65462i		−	0.551540i
$10$	1.66487			0.526478
$11$	−0.684884	−	0.684884i	−0.206500	−	0.206500i	0.596278	−	0.802778i	$-0.296646\pi$
$11$	−0.684884	−	0.684884i	−0.206500	−	0.206500i	−0.802778	+	0.596278i	$0.796646\pi$
$12$	0.340882	+	0.340882i	0.0984041	+	0.0984041i
$13$	−3.90259	−	3.90259i	−1.08238	−	1.08238i	−0.996287	−	0.0860977i	$-0.972560\pi$
$13$	−3.90259	−	3.90259i	−1.08238	−	1.08238i	−0.0860977	−	0.996287i	$-0.527440\pi$
$14$	−1.09900	+	1.09900i	−0.293721	+	0.293721i
$15$	0.878565	−	0.878565i	0.226844	−	0.226844i
$16$	−4.65850			−1.16462
$17$	0.0855829	−	0.0855829i	0.0207569	−	0.0207569i	−0.696652	−	0.717409i	$-0.745328\pi$
$17$	0.0855829	−	0.0855829i	0.0207569	−	0.0207569i	0.717409	+	0.696652i	$0.245328\pi$
$18$	−2.57165			−0.606144
$19$	−2.20827	+	2.20827i	−0.506612	+	0.506612i	−0.913485	−	0.406873i	$-0.866619\pi$
$19$	−2.20827	+	2.20827i	−0.506612	+	0.506612i	0.406873	+	0.913485i	$0.366619\pi$
$20$		−	0.445207i		−	0.0995513i
$21$			1.15991i			0.253112i
$22$	−1.06447	+	1.06447i	−0.226945	+	0.226945i
$23$	7.33685			1.52984			0.764920	−	0.644126i	$-0.222779\pi$
$23$	7.33685			1.52984			0.764920	+	0.644126i	$0.222779\pi$
$24$	−2.01967	+	2.01967i	−0.412264	+	0.412264i
$25$	3.85255			0.770511
$26$	−6.06551	+	6.06551i	−1.18954	+	1.18954i
$27$	−3.81761	+	3.81761i	−0.734700	+	0.734700i
$28$	0.293887	+	0.293887i	0.0555395	+	0.0555395i
$29$	0.934979	+	0.934979i	0.173621	+	0.173621i	0.788568	−	0.614947i	$-0.210823\pi$
$29$	0.934979	+	0.934979i	0.173621	+	0.173621i	−0.614947	+	0.788568i	$0.710823\pi$
$30$	−1.36549	−	1.36549i	−0.249303	−	0.249303i
$31$	10.2030			1.83251			0.916257	−	0.400590i	$-0.131195\pi$
$31$	10.2030			1.83251			0.916257	+	0.400590i	$0.131195\pi$
$32$			2.31539i			0.409307i
$33$			1.12345i			0.195568i
$34$	−0.133015	−	0.133015i	−0.0228119	−	0.0228119i
$35$	0.757445	−	0.757445i	0.128032	−	0.128032i
$36$			0.687692i			0.114615i
$37$	−9.35874			−1.53857			−0.769283	−	0.638908i	$-0.779387\pi$
$37$	−9.35874			−1.53857			−0.769283	+	0.638908i	$0.779387\pi$
$38$	3.43215	+	3.43215i	0.556768	+	0.556768i
$39$			6.40163i			1.02508i
$40$	2.63779			0.417071
$41$	−4.94121	+	4.07240i	−0.771688	+	0.636001i
$41$	−4.94121	+	4.07240i	−0.771688	+	0.636001i
$42$	1.80276			0.278171
$43$		−	12.4003i		−	1.89103i	−0.325579	−	0.945515i	$-0.605559\pi$
$43$		−	12.4003i		−	1.89103i	0.325579	−	0.945515i	$-0.394441\pi$
$44$	0.284651	+	0.284651i	0.0429128	+	0.0429128i
$45$	1.77241			0.264215
$46$		−	11.4031i		−	1.68130i
$47$	4.96503	−	4.96503i	0.724224	−	0.724224i	−0.245238	−	0.969463i	$-0.578866\pi$
$47$	4.96503	−	4.96503i	0.724224	−	0.724224i	0.969463	+	0.245238i	$0.0788662\pi$
$48$	3.82080	+	3.82080i	0.551484	+	0.551484i
$49$			1.00000i			0.142857i
$50$		−	5.98774i		−	0.846795i
$51$	−0.140386			−0.0196580
$52$	1.62199	+	1.62199i	0.224930	+	0.224930i
$53$	5.23077	+	5.23077i	0.718501	+	0.718501i	0.968298	−	0.249797i	$-0.0803639\pi$
$53$	5.23077	+	5.23077i	0.718501	+	0.718501i	−0.249797	+	0.968298i	$0.580364\pi$
$54$	5.93343	+	5.93343i	0.807438	+	0.807438i
$55$	0.733640	−	0.733640i	0.0989240	−	0.0989240i
$56$	−1.74124	+	1.74124i	−0.232683	+	0.232683i
$57$	3.62234			0.479791
$58$	1.45317	−	1.45317i	0.190810	−	0.190810i
$59$	7.62987			0.993324			0.496662	−	0.867944i	$-0.334559\pi$
$59$	7.62987			0.993324			0.496662	+	0.867944i	$0.334559\pi$
$60$	−0.365149	+	0.365149i	−0.0471405	+	0.0471405i
$61$		−	2.05835i		−	0.263544i	−0.991280	−	0.131772i	$-0.957933\pi$
$61$		−	2.05835i		−	0.263544i	0.991280	−	0.131772i	$-0.0420667\pi$
$62$		−	15.8578i		−	2.01394i
$63$	−1.16999	+	1.16999i	−0.147405	+	0.147405i
$64$	−5.71836			−0.714795
$65$	4.18041	−	4.18041i	0.518517	−	0.518517i
$66$	1.74610			0.214930
$67$	5.85604	−	5.85604i	0.715429	−	0.715429i	−0.252236	−	0.967666i	$-0.581166\pi$
$67$	5.85604	−	5.85604i	0.715429	−	0.715429i	0.967666	+	0.252236i	$0.0811661\pi$
$68$	−0.0355699	+	0.0355699i	−0.00431349	+	0.00431349i
$69$	−6.01752	−	6.01752i	−0.724424	−	0.724424i
$70$	−1.17724	−	1.17724i	−0.140707	−	0.140707i
$71$	10.4988	+	10.4988i	1.24598	+	1.24598i	0.957479	+	0.288503i	$0.0931576\pi$
$71$	10.4988	+	10.4988i	1.24598	+	1.24598i	0.288503	+	0.957479i	$0.406842\pi$
$72$	−4.07447			−0.480181
$73$			13.7484i			1.60912i	0.593868	+	0.804562i	$0.297600\pi$
$73$			13.7484i			1.60912i	−0.593868	+	0.804562i	$0.702400\pi$
$74$			14.5456i			1.69089i
$75$	−3.15978	−	3.15978i	−0.364860	−	0.364860i
$76$	0.917800	−	0.917800i	0.105279	−	0.105279i
$77$			0.968572i			0.110379i
$78$	9.94959			1.12657
$79$	−4.42051	−	4.42051i	−0.497346	−	0.497346i	0.413265	−	0.910611i	$-0.364388\pi$
$79$	−4.42051	−	4.42051i	−0.497346	−	0.497346i	−0.910611	+	0.413265i	$0.864388\pi$
$80$		−	4.99013i		−	0.557914i
$81$	1.29838			0.144265
$82$	6.32942	+	7.67976i	0.698968	+	0.848088i
$83$	7.54989			0.828708			0.414354	−	0.910116i	$-0.364008\pi$
$83$	7.54989			0.828708			0.414354	+	0.910116i	$0.364008\pi$
$84$		−	0.482080i		−	0.0525992i
$85$	0.0916755	+	0.0916755i	0.00994360	+	0.00994360i
$86$	−19.2729			−2.07825
$87$		−	1.53370i		−	0.164430i
$88$	−1.68652	+	1.68652i	−0.179783	+	0.179783i
$89$	−0.00682844	−	0.00682844i	−0.000723813	−	0.000723813i	0.706745	−	0.707469i	$-0.250163\pi$
$89$	−0.00682844	−	0.00682844i	−0.000723813	−	0.000723813i	−0.707469	+	0.706745i	$0.750163\pi$
$90$		−	2.75473i		−	0.290374i
$91$			5.51910i			0.578559i
$92$	−3.04934			−0.317916
$93$	−8.36828	−	8.36828i	−0.867750	−	0.867750i
$94$	−7.71678	−	7.71678i	−0.795926	−	0.795926i
$95$	−2.36547	−	2.36547i	−0.242692	−	0.242692i
$96$	1.89903	−	1.89903i	0.193819	−	0.193819i
$97$	0.412657	−	0.412657i	0.0418989	−	0.0418989i	−0.685847	−	0.727746i	$-0.740568\pi$
$97$	0.412657	−	0.412657i	0.0418989	−	0.0418989i	0.727746	+	0.685847i	$0.240568\pi$
$98$	1.55423			0.157001
$99$	−1.13322	+	1.13322i	−0.113893	+	0.113893i
$100$	−1.60120			−0.160120
$101$	0.620978	−	0.620978i	0.0617896	−	0.0617896i	−0.675537	−	0.737326i	$-0.736088\pi$
$101$	0.620978	−	0.620978i	0.0617896	−	0.0617896i	0.737326	+	0.675537i	$0.236088\pi$
$102$			0.218192i			0.0216042i
$103$		−	0.942797i		−	0.0928966i	−0.998921	−	0.0464483i	$-0.985210\pi$
$103$		−	0.942797i		−	0.0928966i	0.998921	−	0.0464483i	$-0.0147903\pi$
$104$	−9.61008	+	9.61008i	−0.942346	+	0.942346i
$105$	−1.24248			−0.121253
$106$	8.12980	−	8.12980i	0.789636	−	0.789636i
$107$	15.1814			1.46764			0.733819	−	0.679345i	$-0.237736\pi$
$107$	15.1814			1.46764			0.733819	+	0.679345i	$0.237736\pi$
$108$	1.58667	−	1.58667i	0.152678	−	0.152678i
$109$	1.56479	−	1.56479i	0.149879	−	0.149879i	−0.628185	−	0.778064i	$-0.716202\pi$
$109$	1.56479	−	1.56479i	0.149879	−	0.149879i	0.778064	+	0.628185i	$0.216202\pi$
$110$	−1.14024	−	1.14024i	−0.108718	−	0.108718i
$111$	7.67582	+	7.67582i	0.728557	+	0.728557i
$112$	3.29406	+	3.29406i	0.311259	+	0.311259i
$113$	−5.38415			−0.506499			−0.253249	−	0.967401i	$-0.581499\pi$
$113$	−5.38415			−0.506499			−0.253249	+	0.967401i	$0.581499\pi$
$114$		−	5.62994i		−	0.527292i
$115$			7.85915i			0.732870i
$116$	−0.388596	−	0.388596i	−0.0360802	−	0.0360802i
$117$	−6.45730	+	6.45730i	−0.596978	+	0.596978i
$118$		−	11.8585i		−	1.09167i
$119$	−0.121033			−0.0110950
$120$	−2.16345	−	2.16345i	−0.197495	−	0.197495i
$121$		−	10.0619i		−	0.914715i
$122$	−3.19914			−0.289636
$123$	7.39276	+	0.712585i	0.666582	+	0.0642516i
$124$	−4.24057			−0.380815
$125$			9.48276i			0.848164i
$126$	1.81843	+	1.81843i	0.161999	+	0.161999i
$127$	−9.72852			−0.863267			−0.431633	−	0.902049i	$-0.642063\pi$
$127$	−9.72852			−0.863267			−0.431633	+	0.902049i	$0.642063\pi$
$128$			13.5184i			1.19487i
$129$	−10.1705	+	10.1705i	−0.895458	+	0.895458i
$130$	−6.49731	−	6.49731i	−0.569852	−	0.569852i
$131$			9.94399i			0.868810i	0.900718	+	0.434405i	$0.143041\pi$
$131$			9.94399i			0.868810i	−0.900718	+	0.434405i	$0.856959\pi$
$132$		−	0.466929i		−	0.0406409i
$133$	3.12296			0.270795
$134$	−9.10161	−	9.10161i	−0.786260	−	0.786260i
$135$	−4.08938	−	4.08938i	−0.351958	−	0.351958i
$136$	−0.210747	−	0.210747i	−0.0180714	−	0.0180714i
$137$	4.80323	−	4.80323i	0.410368	−	0.410368i	−0.471499	−	0.881867i	$-0.656287\pi$
$137$	4.80323	−	4.80323i	0.410368	−	0.410368i	0.881867	+	0.471499i	$0.156287\pi$
$138$	−9.35259	+	9.35259i	−0.796145	+	0.796145i
$139$	−9.80489			−0.831640			−0.415820	−	0.909447i	$-0.636505\pi$
$139$	−9.80489			−0.831640			−0.415820	+	0.909447i	$0.636505\pi$
$140$	−0.314809	+	0.314809i	−0.0266062	+	0.0266062i
$141$	−8.14441			−0.685883
$142$	16.3176	−	16.3176i	1.36934	−	1.36934i
$143$			5.34565i			0.447026i
$144$			7.70804i			0.642337i
$145$	−1.00154	+	1.00154i	−0.0831733	+	0.0831733i
$146$	21.3681			1.76843
$147$	0.820177	−	0.820177i	0.0676471	−	0.0676471i
$148$	3.88967			0.319729
$149$	−14.8015	+	14.8015i	−1.21258	+	1.21258i	−0.242408	+	0.970174i	$0.577937\pi$
$149$	−14.8015	+	14.8015i	−1.21258	+	1.21258i	−0.970174	+	0.242408i	$0.922063\pi$
$150$	−4.91101	+	4.91101i	−0.400982	+	0.400982i
$151$	1.13465	+	1.13465i	0.0923363	+	0.0923363i	0.751766	−	0.659430i	$-0.229202\pi$
$151$	1.13465	+	1.13465i	0.0923363	+	0.0923363i	−0.659430	+	0.751766i	$0.729202\pi$
$152$	5.43783	+	5.43783i	0.441066	+	0.441066i
$153$	−0.141607	−	0.141607i	−0.0114483	−	0.0114483i
$154$	1.50538			0.121307
$155$			10.9294i			0.877867i
$156$		−	2.66064i		−	0.213022i
$157$	−9.13366	−	9.13366i	−0.728945	−	0.728945i	0.241464	−	0.970410i	$-0.422372\pi$
$157$	−9.13366	−	9.13366i	−0.728945	−	0.728945i	−0.970410	+	0.241464i	$0.922372\pi$
$158$	−6.87048	+	6.87048i	−0.546586	+	0.546586i
$159$		−	8.58031i		−	0.680463i
$160$	−2.48022			−0.196079
$161$	−5.18794	−	5.18794i	−0.408867	−	0.408867i
$162$		−	2.01798i		−	0.158547i
$163$	1.83914			0.144053			0.0720263	−	0.997403i	$-0.477053\pi$
$163$	1.83914			0.144053			0.0720263	+	0.997403i	$0.477053\pi$
$164$	2.05367	−	1.69257i	0.160364	−	0.132167i
$165$	−1.20343			−0.0936869
$166$		−	11.7342i		−	0.910753i
$167$	−17.8726	−	17.8726i	−1.38302	−	1.38302i	−0.839199	−	0.543825i	$-0.816976\pi$
$167$	−17.8726	−	17.8726i	−1.38302	−	1.38302i	−0.543825	−	0.839199i	$-0.683024\pi$
$168$	2.85625			0.220365
$169$			17.4605i			1.34311i
$170$	0.142484	−	0.142484i	0.0109281	−	0.0109281i
$171$	3.65384	+	3.65384i	0.279416	+	0.279416i
$172$			5.15381i			0.392974i
$173$		−	11.5262i		−	0.876318i	−0.898898	−	0.438159i	$-0.855631\pi$
$173$		−	11.5262i		−	0.876318i	0.898898	−	0.438159i	$-0.144369\pi$
$174$	−2.38371			−0.180709
$175$	−2.72417	−	2.72417i	−0.205928	−	0.205928i
$176$	3.19053	+	3.19053i	0.240495	+	0.240495i
$177$	−6.25784	−	6.25784i	−0.470368	−	0.470368i
$178$	−0.0106129	+	0.0106129i	−0.000795473	+	0.000795473i
$179$	1.13442	−	1.13442i	0.0847906	−	0.0847906i	−0.663439	−	0.748230i	$-0.730904\pi$
$179$	1.13442	−	1.13442i	0.0847906	−	0.0847906i	0.748230	+	0.663439i	$0.230904\pi$
$180$	−0.736648			−0.0549065
$181$	12.6888	−	12.6888i	0.943149	−	0.943149i	−0.0553195	−	0.998469i	$-0.517618\pi$
$181$	12.6888	−	12.6888i	0.943149	−	0.943149i	0.998469	+	0.0553195i	$0.0176177\pi$
$182$	8.57793			0.635838
$183$	−1.68821	+	1.68821i	−0.124796	+	0.124796i
$184$		−	18.0669i		−	1.33191i
$185$		−	10.0250i		−	0.737051i
$186$	−13.0062	+	13.0062i	−0.953661	+	0.953661i
$187$	−0.117229			−0.00857262
$188$	−2.06356	+	2.06356i	−0.150501	+	0.150501i
$189$	5.39892			0.392714
$190$	−3.67648	+	3.67648i	−0.266720	+	0.266720i
$191$	1.14187	−	1.14187i	0.0826225	−	0.0826225i	−0.664588	−	0.747210i	$-0.731393\pi$
$191$	1.14187	−	1.14187i	0.0826225	−	0.0826225i	0.747210	+	0.664588i	$0.231393\pi$
$192$	4.69007	+	4.69007i	0.338476	+	0.338476i
$193$	12.5637	+	12.5637i	0.904356	+	0.904356i	0.995809	−	0.0914531i	$-0.0291512\pi$
$193$	12.5637	+	12.5637i	0.904356	+	0.904356i	−0.0914531	+	0.995809i	$0.529151\pi$
$194$	−0.641362	−	0.641362i	−0.0460471	−	0.0460471i
$195$	−6.85736			−0.491066
$196$		−	0.415620i		−	0.0296871i
$197$		−	3.46159i		−	0.246628i	−0.992368	−	0.123314i	$-0.960648\pi$
$197$		−	3.46159i		−	0.246628i	0.992368	−	0.123314i	$-0.0393523\pi$
$198$	1.76128	+	1.76128i	0.125169	+	0.125169i
$199$	−13.0732	+	13.0732i	−0.926732	+	0.926732i	−0.997493	−	0.0707616i	$-0.977457\pi$
$199$	−13.0732	+	13.0732i	−0.926732	+	0.926732i	0.0707616	+	0.997493i	$0.477457\pi$
$200$		−	9.48686i		−	0.670822i
$201$	−9.60598			−0.677554
$202$	−0.965140	−	0.965140i	−0.0679070	−	0.0679070i
$203$		−	1.32226i		−	0.0928045i
$204$	0.0583473			0.00408513
$205$	−4.36230	−	5.29297i	−0.304677	−	0.369677i
$206$	−1.46532			−0.102094
$207$		−	12.1397i		−	0.843767i
$208$	18.1802	+	18.1802i	1.26057	+	1.26057i
$209$	3.02482			0.209231
$210$			1.93109i			0.133258i
$211$	−20.1999	+	20.1999i	−1.39062	+	1.39062i	−0.566672	+	0.823944i	$0.691769\pi$
$211$	−20.1999	+	20.1999i	−1.39062	+	1.39062i	−0.823944	+	0.566672i	$0.808231\pi$
$212$	−2.17401	−	2.17401i	−0.149312	−	0.149312i
$213$		−	17.2218i		−	1.18002i
$214$		−	23.5953i		−	1.61294i
$215$	13.2831			0.905898
$216$	9.40082	+	9.40082i	0.639645	+	0.639645i
$217$	−7.21462	−	7.21462i	−0.489760	−	0.489760i
$218$	−2.43203	−	2.43203i	−0.164718	−	0.164718i
$219$	11.2761	−	11.2761i	0.761968	−	0.761968i
$220$	−0.304915	+	0.304915i	−0.0205574	+	0.0205574i
$221$	−0.667990			−0.0449339
$222$	11.9300	−	11.9300i	0.800687	−	0.800687i
$223$	−2.89264			−0.193705			−0.0968527	−	0.995299i	$-0.530878\pi$
$223$	−2.89264			−0.193705			−0.0968527	+	0.995299i	$0.530878\pi$
$224$	1.63723	−	1.63723i	0.109392	−	0.109392i
$225$		−	6.37451i		−	0.424967i
$226$			8.36819i			0.556644i
$227$	−11.5680	+	11.5680i	−0.767797	+	0.767797i	−0.977718	−	0.209921i	$-0.932679\pi$
$227$	−11.5680	+	11.5680i	−0.767797	+	0.767797i	0.209921	+	0.977718i	$0.432679\pi$
$228$	−1.50552			−0.0997053
$229$	11.8482	−	11.8482i	0.782954	−	0.782954i	−0.197374	−	0.980328i	$-0.563241\pi$
$229$	11.8482	−	11.8482i	0.782954	−	0.782954i	0.980328	+	0.197374i	$0.0632413\pi$
$230$	12.2149			0.805427
$231$	0.794401	−	0.794401i	0.0522678	−	0.0522678i
$232$	2.30237	−	2.30237i	0.151158	−	0.151158i
$233$	8.52391	+	8.52391i	0.558420	+	0.558420i	0.928857	−	0.370438i	$-0.120792\pi$
$233$	8.52391	+	8.52391i	0.558420	+	0.558420i	−0.370438	+	0.928857i	$0.620792\pi$
$234$	10.0361	+	10.0361i	0.656081	+	0.656081i
$235$	5.31849	+	5.31849i	0.346940	+	0.346940i
$236$	−3.17112			−0.206423
$237$			7.25121i			0.471016i
$238$			0.188112i			0.0121935i
$239$	8.13510	+	8.13510i	0.526216	+	0.526216i	0.919442	−	0.393226i	$-0.128641\pi$
$239$	8.13510	+	8.13510i	0.526216	+	0.526216i	−0.393226	+	0.919442i	$0.628641\pi$
$240$	−4.09279	+	4.09279i	−0.264189	+	0.264189i
$241$			6.34747i			0.408876i	0.978879	+	0.204438i	$0.0655367\pi$
$241$			6.34747i			0.408876i	−0.978879	+	0.204438i	$0.934463\pi$
$242$	−15.6384			−1.00528
$243$	10.3879	+	10.3879i	0.666386	+	0.666386i
$244$			0.855489i			0.0547671i
$245$	−1.07119			−0.0684357
$246$	1.10752	−	11.4900i	0.0706128	−	0.732577i
$247$	17.2359			1.09670
$248$		−	25.1248i		−	1.59542i
$249$	−6.19224	−	6.19224i	−0.392418	−	0.392418i
$250$	14.7384			0.932135
$251$		−	8.89401i		−	0.561385i	−0.959798	−	0.280693i	$-0.909436\pi$
$251$		−	8.89401i		−	0.561385i	0.959798	−	0.280693i	$-0.0905641\pi$
$252$	0.486272	−	0.486272i	0.0306322	−	0.0306322i
$253$	−5.02489	−	5.02489i	−0.315912	−	0.315912i
$254$			15.1203i			0.948733i
$255$		−	0.150380i		−	0.00941718i
$256$	9.57394			0.598372
$257$	−13.5649	−	13.5649i	−0.846153	−	0.846153i	0.143498	−	0.989651i	$-0.454165\pi$
$257$	−13.5649	−	13.5649i	−0.846153	−	0.846153i	−0.989651	+	0.143498i	$0.954165\pi$
$258$	15.8072	+	15.8072i	0.984112	+	0.984112i
$259$	6.61763	+	6.61763i	0.411199	+	0.411199i
$260$	−1.73746	+	1.73746i	−0.107753	+	0.107753i
$261$	1.54703	−	1.54703i	0.0957590	−	0.0957590i
$262$	15.4552			0.954826
$263$	−4.01028	+	4.01028i	−0.247284	+	0.247284i	−0.819855	−	0.572571i	$-0.805946\pi$
$263$	−4.01028	+	4.01028i	−0.247284	+	0.247284i	0.572571	+	0.819855i	$0.305946\pi$
$264$	2.76649			0.170265
$265$	−5.60314	+	5.60314i	−0.344198	+	0.344198i
$266$		−	4.85379i		−	0.297605i
$267$			0.0112011i			0.000685494i
$268$	−2.43388	+	2.43388i	−0.148673	+	0.148673i
$269$	−23.3980			−1.42660			−0.713302	−	0.700857i	$-0.752801\pi$
$269$	−23.3980			−1.42660			−0.713302	+	0.700857i	$0.752801\pi$
$270$	−6.35583	+	6.35583i	−0.386803	+	0.386803i
$271$	19.9102			1.20946			0.604728	−	0.796432i	$-0.293282\pi$
$271$	19.9102			1.20946			0.604728	+	0.796432i	$0.293282\pi$
$272$	−0.398688	+	0.398688i	−0.0241740	+	0.0241740i
$273$	4.52664	−	4.52664i	0.273965	−	0.273965i
$274$	−7.46531	−	7.46531i	−0.450996	−	0.450996i
$275$	−2.63855	−	2.63855i	−0.159111	−	0.159111i
$276$	2.50100	+	2.50100i	0.150542	+	0.150542i
$277$	−4.68661			−0.281591			−0.140796	−	0.990039i	$-0.544966\pi$
$277$	−4.68661			−0.281591			−0.140796	+	0.990039i	$0.544966\pi$
$278$			15.2390i			0.913976i
$279$		−	16.8821i		−	1.01070i
$280$	−1.86520	−	1.86520i	−0.111467	−	0.111467i
$281$	−5.29470	+	5.29470i	−0.315855	+	0.315855i	−0.847173	−	0.531317i	$-0.821697\pi$
$281$	−5.29470	+	5.29470i	−0.315855	+	0.315855i	0.531317	+	0.847173i	$0.321697\pi$
$282$			12.6583i			0.753789i
$283$	13.4069			0.796957			0.398478	−	0.917178i	$-0.369538\pi$
$283$	13.4069			0.796957			0.398478	+	0.917178i	$0.369538\pi$
$284$	−4.36352	−	4.36352i	−0.258927	−	0.258927i
$285$			3.88021i			0.229844i
$286$	8.30835			0.491283
$287$	6.37358	+	0.614347i	0.376221	+	0.0362638i
$288$	3.83109			0.225749
$289$			16.9854i			0.999138i
$290$	1.55662	+	1.55662i	0.0914078	+	0.0914078i
$291$	−0.676903			−0.0396808
$292$		−	5.71409i		−	0.334392i
$293$	3.85145	−	3.85145i	0.225004	−	0.225004i	−0.585598	−	0.810602i	$-0.699140\pi$
$293$	3.85145	−	3.85145i	0.225004	−	0.225004i	0.810602	+	0.585598i	$0.199140\pi$
$294$	−1.27474	−	1.27474i	−0.0743444	−	0.0743444i
$295$			8.17303i			0.475852i
$296$			23.0458i			1.33951i
$297$	5.22924			0.303432
$298$	23.0048	+	23.0048i	1.33263	+	1.33263i
$299$	−28.6327	−	28.6327i	−1.65587	−	1.65587i
$300$	1.31327	+	1.31327i	0.0758214	+	0.0758214i
$301$	−8.76834	+	8.76834i	−0.505399	+	0.505399i
$302$	1.76350	−	1.76350i	0.101478	−	0.101478i
$303$	−1.01862			−0.0585184
$304$	10.2872	−	10.2872i	0.590013	−	0.590013i
$305$	2.20488			0.126251
$306$	−0.220089	+	0.220089i	−0.0125817	+	0.0125817i
$307$			8.22780i			0.469585i	0.972045	+	0.234793i	$0.0754411\pi$
$307$			8.22780i			0.469585i	−0.972045	+	0.234793i	$0.924559\pi$
$308$		−	0.402558i		−	0.0229379i
$309$	−0.773261	+	0.773261i	−0.0439893	+	0.0439893i
$310$	16.9867			0.964779
$311$	1.64553	−	1.64553i	0.0933093	−	0.0933093i	−0.658911	−	0.752221i	$-0.728983\pi$
$311$	1.64553	−	1.64553i	0.0933093	−	0.0933093i	0.752221	+	0.658911i	$0.228983\pi$
$312$	15.7639			0.892457
$313$	21.2658	−	21.2658i	1.20201	−	1.20201i	0.228462	−	0.973553i	$-0.426630\pi$
$313$	21.2658	−	21.2658i	1.20201	−	1.20201i	0.973553	−	0.228462i	$-0.0733697\pi$
$314$	−14.1958	+	14.1958i	−0.801114	+	0.801114i
$315$	−1.25328	−	1.25328i	−0.0706145	−	0.0706145i
$316$	1.83725	+	1.83725i	0.103353	+	0.103353i
$317$	11.7180	+	11.7180i	0.658151	+	0.658151i	0.954942	−	0.296792i	$-0.0959167\pi$
$317$	11.7180	+	11.7180i	0.658151	+	0.658151i	−0.296792	+	0.954942i	$0.595917\pi$
$318$	−13.3358			−0.747832
$319$		−	1.28070i		−	0.0717057i
$320$		−	6.12544i		−	0.342423i
$321$	−12.4514	−	12.4514i	−0.694970	−	0.694970i
$322$	−8.06323	+	8.06323i	−0.449346	+	0.449346i
$323$			0.377980i			0.0210314i
$324$	−0.539633			−0.0299796
$325$	−15.0349	−	15.0349i	−0.833989	−	0.833989i
$326$		−	2.85844i		−	0.158314i
$327$	−2.56680			−0.141945
$328$	10.0282	+	12.1677i	0.553716	+	0.671847i
$329$	−7.02162			−0.387114
$330$			1.87040i			0.102962i
$331$	−3.83644	−	3.83644i	−0.210870	−	0.210870i	0.593767	−	0.804637i	$-0.297640\pi$
$331$	−3.83644	−	3.83644i	−0.210870	−	0.210870i	−0.804637	+	0.593767i	$0.797640\pi$
$332$	−3.13788			−0.172214
$333$			15.4851i			0.848580i
$334$	−27.7781	+	27.7781i	−1.51995	+	1.51995i
$335$	6.27293	+	6.27293i	0.342727	+	0.342727i
$336$		−	5.40342i		−	0.294781i
$337$			17.1414i			0.933749i	0.884324	+	0.466874i	$0.154620\pi$
$337$			17.1414i			0.933749i	−0.884324	+	0.466874i	$0.845380\pi$
$338$	27.1375			1.47609
$339$	4.41596	+	4.41596i	0.239842	+	0.239842i
$340$	−0.0381021	−	0.0381021i	−0.00206638	−	0.00206638i
$341$	−6.98788	−	6.98788i	−0.378415	−	0.378415i
$342$	5.67890	−	5.67890i	0.307080	−	0.307080i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−30.5356			−1.64637
$345$	6.44590	−	6.44590i	0.347036	−	0.347036i
$346$	−17.9143			−0.963077
$347$	7.36331	−	7.36331i	0.395283	−	0.395283i	−0.481282	−	0.876566i	$-0.659829\pi$
$347$	7.36331	−	7.36331i	0.395283	−	0.395283i	0.876566	+	0.481282i	$0.159829\pi$
$348$			0.637434i			0.0341701i
$349$		−	8.78428i		−	0.470212i	−0.971970	−	0.235106i	$-0.924456\pi$
$349$		−	8.78428i		−	0.470212i	0.971970	−	0.235106i	$-0.0755437\pi$
$350$	−4.23397	+	4.23397i	−0.226315	+	0.226315i
$351$	29.7972			1.59046
$352$	1.58577	−	1.58577i	0.0845221	−	0.0845221i
$353$	36.6452			1.95043			0.975213	−	0.221269i	$-0.0710198\pi$
$353$	36.6452			1.95043			0.975213	+	0.221269i	$0.0710198\pi$
$354$	−9.72611	+	9.72611i	−0.516937	+	0.516937i
$355$	−11.2462	+	11.2462i	−0.596888	+	0.596888i
$356$	0.00283803	+	0.00283803i	0.000150415	+	0.000150415i
$357$	0.0992681	+	0.0992681i	0.00525383	+	0.00525383i
$358$	−1.76315	−	1.76315i	−0.0931852	−	0.0931852i
$359$	−1.36120			−0.0718416			−0.0359208	−	0.999355i	$-0.511436\pi$
$359$	−1.36120			−0.0718416			−0.0359208	+	0.999355i	$0.511436\pi$
$360$		−	4.36453i		−	0.230031i
$361$			9.24710i			0.486689i
$362$	−19.7212	−	19.7212i	−1.03652	−	1.03652i
$363$	−8.25251	+	8.25251i	−0.433145	+	0.433145i
$364$		−	2.29385i		−	0.120230i
$365$	−14.7271			−0.770851
$366$	2.62386	+	2.62386i	0.137151	+	0.137151i
$367$			10.3152i			0.538451i	0.963077	+	0.269226i	$0.0867677\pi$
$367$			10.3152i			0.538451i	−0.963077	+	0.269226i	$0.913232\pi$
$368$	−34.1787			−1.78169
$369$	6.73826	+	8.17582i	0.350780	+	0.425616i
$370$	−15.5811			−0.810022
$371$		−	7.39742i		−	0.384055i
$372$	3.47802	+	3.47802i	0.180327	+	0.180327i
$373$	−7.04049			−0.364543			−0.182271	−	0.983248i	$-0.558345\pi$
$373$	−7.04049			−0.364543			−0.182271	+	0.983248i	$0.558345\pi$
$374$			0.182200i			0.00942134i
$375$	7.77754	−	7.77754i	0.401631	−	0.401631i
$376$	−12.2263	−	12.2263i	−0.630524	−	0.630524i
$377$		−	7.29768i		−	0.375850i
$378$		−	8.39114i		−	0.431594i
$379$	26.8498			1.37918			0.689591	−	0.724199i	$-0.257791\pi$
$379$	26.8498			1.37918			0.689591	+	0.724199i	$0.257791\pi$
$380$	0.983137	+	0.983137i	0.0504339	+	0.0504339i
$381$	7.97911	+	7.97911i	0.408782	+	0.408782i
$382$	−1.77472	−	1.77472i	−0.0908024	−	0.0908024i
$383$	−8.40383	+	8.40383i	−0.429416	+	0.429416i	−0.888429	−	0.459014i	$-0.848203\pi$
$383$	−8.40383	+	8.40383i	−0.429416	+	0.429416i	0.459014	+	0.888429i	$0.348203\pi$
$384$	11.0875	−	11.0875i	0.565806	−	0.565806i
$385$	−1.03752			−0.0528771
$386$	19.5269	−	19.5269i	0.993891	−	0.993891i
$387$	−20.5178			−1.04298
$388$	−0.171508	+	0.171508i	−0.00870701	+	0.00870701i
$389$		−	24.0519i		−	1.21948i	−0.792602	−	0.609739i	$-0.791274\pi$
$389$		−	24.0519i		−	1.21948i	0.792602	−	0.609739i	$-0.208726\pi$
$390$			10.6579i			0.539683i
$391$	0.627909	−	0.627909i	0.0317547	−	0.0317547i
$392$	2.46249			0.124374
$393$	8.15583	−	8.15583i	0.411407	−	0.411407i
$394$	−5.38010			−0.271046
$395$	4.73520	−	4.73520i	0.238254	−	0.238254i
$396$	0.470989	−	0.470989i	0.0236681	−	0.0236681i
$397$	−14.0849	−	14.0849i	−0.706902	−	0.706902i	0.258981	−	0.965883i	$-0.416613\pi$
$397$	−14.0849	−	14.0849i	−0.706902	−	0.706902i	−0.965883	+	0.258981i	$0.916613\pi$
$398$	20.3186	+	20.3186i	1.01848	+	1.01848i
$399$	−2.56138	−	2.56138i	−0.128230	−	0.128230i
$400$	−17.9471			−0.897356
$401$		−	0.658316i		−	0.0328747i	−0.999865	−	0.0164374i	$-0.994768\pi$
$401$		−	0.658316i		−	0.0328747i	0.999865	−	0.0164374i	$-0.00523241\pi$
$402$			14.9299i			0.744634i
$403$	−39.8182	−	39.8182i	−1.98349	−	1.98349i
$404$	−0.258091	+	0.258091i	−0.0128405	+	0.0128405i
$405$			1.39081i			0.0691100i
$406$	−2.05509			−0.101992
$407$	6.40965	+	6.40965i	0.317715	+	0.317715i
$408$			0.345699i			0.0171147i
$409$	−9.17866			−0.453855			−0.226928	−	0.973912i	$-0.572868\pi$
$409$	−9.17866			−0.453855			−0.226928	+	0.973912i	$0.572868\pi$
$410$	−8.22648	+	6.78001i	−0.406277	+	0.334841i
$411$	−7.87900			−0.388642
$412$			0.391845i			0.0193048i
$413$	−5.39513	−	5.39513i	−0.265477	−	0.265477i
$414$	−18.8678			−0.927303
$415$			8.08735i			0.396993i
$416$	9.03603	−	9.03603i	0.443028	−	0.443028i
$417$	8.04175	+	8.04175i	0.393806	+	0.393806i
$418$		−	4.70125i		−	0.229946i
$419$		−	7.83745i		−	0.382885i	−0.981504	−	0.191442i	$-0.938684\pi$
$419$		−	7.83745i		−	0.382885i	0.981504	−	0.191442i	$-0.0613165\pi$
$420$	0.516398			0.0251977
$421$	−2.39621	−	2.39621i	−0.116784	−	0.116784i	0.646300	−	0.763084i	$-0.276316\pi$
$421$	−2.39621	−	2.39621i	−0.116784	−	0.116784i	−0.763084	+	0.646300i	$0.776316\pi$
$422$	31.3951	+	31.3951i	1.52829	+	1.52829i
$423$	−8.21524	−	8.21524i	−0.399438	−	0.399438i
$424$	12.8807	−	12.8807i	0.625542	−	0.625542i
$425$	0.329713	−	0.329713i	0.0159934	−	0.0159934i
$426$	−26.7666			−1.29685
$427$	−1.45547	+	1.45547i	−0.0704352	+	0.0704352i
$428$	−6.30967			−0.304990
$429$	4.38438	−	4.38438i	0.211680	−	0.211680i
$430$		−	20.6449i		−	0.995586i
$431$		−	20.4987i		−	0.987388i	−0.869636	−	0.493694i	$-0.835646\pi$
$431$		−	20.4987i		−	0.987388i	0.869636	−	0.493694i	$-0.164354\pi$
$432$	17.7843	−	17.7843i	0.855650	−	0.855650i
$433$	−22.3271			−1.07297			−0.536486	−	0.843909i	$-0.680248\pi$
$433$	−22.3271			−1.07297			−0.536486	+	0.843909i	$0.680248\pi$
$434$	−11.2132	+	11.2132i	−0.538248	+	0.538248i
$435$	1.64288			0.0787700
$436$	−0.650356	+	0.650356i	−0.0311464	+	0.0311464i
$437$	−16.2017	+	16.2017i	−0.775034	+	0.775034i
$438$	−17.5256	−	17.5256i	−0.837406	−	0.837406i
$439$	−0.387627	−	0.387627i	−0.0185004	−	0.0185004i	0.697796	−	0.716296i	$-0.254164\pi$
$439$	−0.387627	−	0.387627i	−0.0185004	−	0.0185004i	−0.716296	+	0.697796i	$0.754164\pi$
$440$	−1.80658	−	1.80658i	−0.0861253	−	0.0861253i
$441$	1.65462			0.0787914
$442$			1.03821i			0.0493825i
$443$			6.48685i			0.308199i	0.988055	+	0.154100i	$0.0492477\pi$
$443$			6.48685i			0.308199i	−0.988055	+	0.154100i	$0.950752\pi$
$444$	−3.19022	−	3.19022i	−0.151401	−	0.151401i
$445$	0.00731455	−	0.00731455i	0.000346743	−	0.000346743i
$446$			4.49581i			0.212883i
$447$	24.2796			1.14839
$448$	4.04349	+	4.04349i	0.191037	+	0.191037i
$449$		−	13.2298i		−	0.624355i	−0.950024	−	0.312177i	$-0.898942\pi$
$449$		−	13.2298i		−	0.624355i	0.950024	−	0.312177i	$-0.101058\pi$
$450$	−9.90743			−0.467041
$451$	6.17328	+	0.595040i	0.290688	+	0.0280193i
$452$	2.23776			0.105255
$453$		−	1.86122i		−	0.0874479i
$454$	17.9793	+	17.9793i	0.843812	+	0.843812i
$455$	−5.91200			−0.277159
$456$		−	8.91997i		−	0.417716i
$457$	−21.4989	+	21.4989i	−1.00568	+	1.00568i	−0.00569141	+	0.999984i	$0.501812\pi$
$457$	−21.4989	+	21.4989i	−1.00568	+	1.00568i	−0.999984	+	0.00569141i	$0.998188\pi$
$458$	−18.4149	−	18.4149i	−0.860470	−	0.860470i
$459$			0.653445i			0.0305002i
$460$		−	3.26642i		−	0.152298i
$461$	16.5758			0.772013			0.386007	−	0.922496i	$-0.373854\pi$
$461$	16.5758			0.772013			0.386007	+	0.922496i	$0.373854\pi$
$462$	−1.23468	−	1.23468i	−0.0574425	−	0.0574425i
$463$	−3.80578	−	3.80578i	−0.176869	−	0.176869i	0.613120	−	0.789990i	$-0.289914\pi$
$463$	−3.80578	−	3.80578i	−0.176869	−	0.176869i	−0.789990	+	0.613120i	$0.789914\pi$
$464$	−4.35560	−	4.35560i	−0.202204	−	0.202204i
$465$	8.96401	−	8.96401i	0.415696	−	0.415696i
$466$	13.2481	−	13.2481i	0.613706	−	0.613706i
$467$	−18.8479			−0.872178			−0.436089	−	0.899904i	$-0.643637\pi$
$467$	−18.8479			−0.872178			−0.436089	+	0.899904i	$0.643637\pi$
$468$	2.68378	−	2.68378i	0.124058	−	0.124058i
$469$	−8.28169			−0.382413
$470$	8.26613	−	8.26613i	0.381288	−	0.381288i
$471$			14.9824i			0.690354i
$472$		−	18.7884i		−	0.864808i
$473$	−8.49278	+	8.49278i	−0.390498	+	0.390498i
$474$	11.2700			0.517649
$475$	−8.50748	+	8.50748i	−0.390350	+	0.390350i
$476$	0.0503035			0.00230566
$477$	8.65493	−	8.65493i	0.396282	−	0.396282i
$478$	12.6438	−	12.6438i	0.578313	−	0.578313i
$479$	−20.9411	−	20.9411i	−0.956825	−	0.956825i	0.0422811	−	0.999106i	$-0.486537\pi$
$479$	−20.9411	−	20.9411i	−0.956825	−	0.956825i	−0.999106	+	0.0422811i	$0.986537\pi$
$480$	2.03422	+	2.03422i	0.0928491	+	0.0928491i
$481$	36.5233	+	36.5233i	1.66532	+	1.66532i
$482$	9.86540			0.449357
$483$			8.51006i			0.387221i
$484$			4.18191i			0.190087i
$485$	0.442033	+	0.442033i	0.0200717	+	0.0200717i
$486$	16.1452	−	16.1452i	0.732361	−	0.732361i
$487$			5.42767i			0.245951i	0.992410	+	0.122976i	$0.0392437\pi$
$487$			5.42767i			0.245951i	−0.992410	+	0.122976i	$0.960756\pi$
$488$	−5.06865			−0.229447
$489$	−1.50842	−	1.50842i	−0.0682132	−	0.0682132i
$490$			1.66487i			0.0752112i
$491$	41.2594			1.86201			0.931006	−	0.365003i	$-0.118932\pi$
$491$	41.2594			1.86201			0.931006	+	0.365003i	$0.118932\pi$
$492$	−3.07257	−	0.296164i	−0.138522	−	0.0133521i
$493$	0.160036			0.00720768
$494$		−	26.7886i		−	1.20527i
$495$	−1.21389	−	1.21389i	−0.0545605	−	0.0545605i
$496$	−47.5307			−2.13419
$497$		−	14.8476i		−	0.666005i
$498$	−9.62415	+	9.62415i	−0.431268	+	0.431268i
$499$	11.7588	+	11.7588i	0.526396	+	0.526396i	0.919496	−	0.393100i	$-0.128597\pi$
$499$	11.7588	+	11.7588i	0.526396	+	0.526396i	−0.393100	+	0.919496i	$0.628597\pi$
$500$		−	3.94122i		−	0.176257i
$501$			29.3174i			1.30981i
$502$	−13.8233			−0.616964
$503$	22.5182	+	22.5182i	1.00404	+	1.00404i	0.999992	+	0.00404349i	$0.00128709\pi$
$503$	22.5182	+	22.5182i	1.00404	+	1.00404i	0.00404349	+	0.999992i	$0.498713\pi$
$504$	2.88109	+	2.88109i	0.128334	+	0.128334i
$505$	0.665185	+	0.665185i	0.0296003	+	0.0296003i
$506$	−7.80982	+	7.80982i	−0.347189	+	0.347189i
$507$	14.3207	−	14.3207i	0.636003	−	0.636003i
$508$	4.04336			0.179395
$509$	−8.32932	+	8.32932i	−0.369191	+	0.369191i	−0.867182	−	0.497991i	$-0.834071\pi$
$509$	−8.32932	+	8.32932i	−0.369191	+	0.369191i	0.497991	+	0.867182i	$0.334071\pi$
$510$	−0.233725			−0.0103495
$511$	9.72156	−	9.72156i	0.430057	−	0.430057i
$512$			12.1567i			0.537257i
$513$		−	16.8606i		−	0.744415i
$514$	−21.0829	+	21.0829i	−0.929925	+	0.929925i
$515$	1.00991			0.0445021
$516$	4.22704	−	4.22704i	0.186085	−	0.186085i
$517$	−6.80094			−0.299105
$518$	10.2853	−	10.2853i	0.451910	−	0.451910i
$519$	−9.45350	+	9.45350i	−0.414962	+	0.414962i
$520$	−10.2942	−	10.2942i	−0.451431	−	0.451431i
$521$	9.16005	+	9.16005i	0.401309	+	0.401309i	0.878694	−	0.477385i	$-0.158415\pi$
$521$	9.16005	+	9.16005i	0.401309	+	0.401309i	−0.477385	+	0.878694i	$0.658415\pi$
$522$	−2.40444	−	2.40444i	−0.105240	−	0.105240i
$523$	−24.2547			−1.06058			−0.530291	−	0.847816i	$-0.677917\pi$
$523$	−24.2547			−1.06058			−0.530291	+	0.847816i	$0.677917\pi$
$524$		−	4.13292i		−	0.180547i
$525$			4.46860i			0.195026i
$526$	6.23288	+	6.23288i	0.271766	+	0.271766i
$527$	0.873203	−	0.873203i	0.0380373	−	0.0380373i
$528$		−	5.23360i		−	0.227763i
$529$	30.8294			1.34041
$530$	8.70855	+	8.70855i	0.378275	+	0.378275i
$531$		−	12.6245i		−	0.547858i
$532$	−1.29796			−0.0562739
$533$	35.1764	+	3.39064i	1.52366	+	0.146865i
$534$	0.0174090			0.000753360
$535$			16.2621i			0.703073i
$536$	−14.4204	−	14.4204i	−0.622867	−	0.622867i
$537$	−1.86085			−0.0803017
$538$			36.3658i			1.56784i
$539$	0.684884	−	0.684884i	0.0295000	−	0.0295000i
$540$	1.69963	+	1.69963i	0.0731403	+	0.0731403i
$541$			11.5197i			0.495271i	0.968853	+	0.247635i	$0.0796535\pi$
$541$			11.5197i			0.495271i	−0.968853	+	0.247635i	$0.920347\pi$
$542$		−	30.9449i		−	1.32920i
$543$	−20.8141			−0.893218
$544$	0.198158	+	0.198158i	0.00849595	+	0.00849595i
$545$	1.67618	+	1.67618i	0.0717998	+	0.0717998i
$546$	−7.03542	−	7.03542i	−0.301088	−	0.301088i
$547$	−8.62263	+	8.62263i	−0.368677	+	0.368677i	−0.866995	−	0.498317i	$-0.833951\pi$
$547$	−8.62263	+	8.62263i	−0.368677	+	0.368677i	0.498317	+	0.866995i	$0.333951\pi$
$548$	−1.99632	+	1.99632i	−0.0852784	+	0.0852784i
$549$	−3.40578			−0.145355
$550$	−4.10091	+	4.10091i	−0.174863	+	0.174863i
$551$	−4.12937			−0.175917
$552$	−14.8181	+	14.8181i	−0.630698	+	0.630698i
$553$			6.25155i			0.265843i
$554$			7.28406i			0.309470i
$555$	−8.22226	+	8.22226i	−0.349015	+	0.349015i
$556$	4.07510			0.172823
$557$	−7.09399	+	7.09399i	−0.300582	+	0.300582i	−0.841242	−	0.540659i	$-0.818175\pi$
$557$	−7.09399	+	7.09399i	−0.300582	+	0.300582i	0.540659	+	0.841242i	$0.318175\pi$
$558$	−26.2386			−1.11077
$559$	−48.3934	+	48.3934i	−2.04682	+	2.04682i
$560$	−3.52856	+	3.52856i	−0.149109	+	0.149109i
$561$	0.0961484	+	0.0961484i	0.00405939	+	0.00405939i
$562$	8.22917	+	8.22917i	0.347126	+	0.347126i
$563$	−0.378533	−	0.378533i	−0.0159532	−	0.0159532i	0.699085	−	0.715038i	$-0.253591\pi$
$563$	−0.378533	−	0.378533i	−0.0159532	−	0.0159532i	−0.715038	+	0.699085i	$0.753591\pi$
$564$	3.38498			0.142533
$565$		−	5.76745i		−	0.242638i
$566$		−	20.8373i		−	0.875859i
$567$	−0.918094	−	0.918094i	−0.0385563	−	0.0385563i
$568$	25.8532	−	25.8532i	1.08478	−	1.08478i
$569$			21.5199i			0.902163i	0.892483	+	0.451081i	$0.148962\pi$
$569$			21.5199i			0.902163i	−0.892483	+	0.451081i	$0.851038\pi$
$570$	6.03073			0.252600
$571$	32.1807	+	32.1807i	1.34672	+	1.34672i	0.889197	+	0.457524i	$0.151264\pi$
$571$	32.1807	+	32.1807i	1.34672	+	1.34672i	0.457524	+	0.889197i	$0.348736\pi$
$572$		−	2.22176i		−	0.0928963i
$573$	−1.87306			−0.0782484
$574$	0.954835	−	9.90599i	0.0398540	−	0.413468i
$575$	28.2656			1.17876
$576$			9.46170i			0.394238i
$577$	10.2355	+	10.2355i	0.426109	+	0.426109i	0.887300	−	0.461192i	$-0.152578\pi$
$577$	10.2355	+	10.2355i	0.426109	+	0.426109i	−0.461192	+	0.887300i	$0.652578\pi$
$578$	26.3991			1.09806
$579$		−	20.6090i		−	0.856479i
$580$	0.416259	−	0.416259i	0.0172842	−	0.0172842i
$581$	−5.33857	−	5.33857i	−0.221481	−	0.221481i
$582$			1.05206i			0.0436093i
$583$		−	7.16494i		−	0.296742i
$584$	33.8552			1.40094
$585$	−6.91699	−	6.91699i	−0.285982	−	0.285982i
$586$	−5.98602	−	5.98602i	−0.247280	−	0.247280i
$587$	20.7899	+	20.7899i	0.858089	+	0.858089i	0.991113	−	0.133023i	$-0.0424686\pi$
$587$	20.7899	+	20.7899i	0.858089	+	0.858089i	−0.133023	+	0.991113i	$0.542469\pi$
$588$	−0.340882	+	0.340882i	−0.0140577	+	0.0140577i
$589$	−22.5310	+	22.5310i	−0.928373	+	0.928373i
$590$	12.7027			0.522964
$591$	−2.83912	+	2.83912i	−0.116786	+	0.116786i
$592$	43.5977			1.79185
$593$	5.14692	−	5.14692i	0.211359	−	0.211359i	−0.593486	−	0.804844i	$-0.702249\pi$
$593$	5.14692	−	5.14692i	0.211359	−	0.211359i	0.804844	+	0.593486i	$0.202249\pi$
$594$		−	8.12743i		−	0.333472i
$595$		−	0.129649i		−	0.00531508i
$596$	6.15177	−	6.15177i	0.251986	−	0.251986i
$597$	21.4446			0.877670
$598$	−44.5018	+	44.5018i	−1.81981	+	1.81981i
$599$	5.95549			0.243335			0.121667	−	0.992571i	$-0.461176\pi$
$599$	5.95549			0.243335			0.121667	+	0.992571i	$0.461176\pi$
$600$	−7.78091	+	7.78091i	−0.317654	+	0.317654i
$601$	22.7839	−	22.7839i	0.929373	−	0.929373i	−0.0682927	−	0.997665i	$-0.521755\pi$
$601$	22.7839	−	22.7839i	0.929373	−	0.929373i	0.997665	+	0.0682927i	$0.0217552\pi$
$602$	13.6280	+	13.6280i	0.555435	+	0.555435i
$603$	−9.68951	−	9.68951i	−0.394588	−	0.394588i
$604$	−0.471582	−	0.471582i	−0.0191884	−	0.0191884i
$605$	10.7782			0.438195
$606$			1.58317i			0.0643120i
$607$		−	14.2259i		−	0.577412i	−0.957418	−	0.288706i	$-0.906775\pi$
$607$		−	14.2259i		−	0.577412i	0.957418	−	0.288706i	$-0.0932249\pi$
$608$	−5.11301	−	5.11301i	−0.207360	−	0.207360i
$609$	−1.08449	+	1.08449i	−0.0439457	+	0.0439457i
$610$		−	3.42688i		−	0.138750i
$611$	−38.7530			−1.56778
$612$	0.0588547	+	0.0588547i	0.00237906	+	0.00237906i
$613$			7.46593i			0.301546i	0.988568	+	0.150773i	$0.0481762\pi$
$613$			7.46593i			0.301546i	−0.988568	+	0.150773i	$0.951824\pi$
$614$	12.7879			0.516076
$615$	−0.763313	+	7.91904i	−0.0307798	+	0.319326i
$616$	2.38510			0.0960983
$617$			22.2877i			0.897271i	0.893715	+	0.448635i	$0.148090\pi$
$617$			22.2877i			0.897271i	−0.893715	+	0.448635i	$0.851910\pi$
$618$	1.20182	+	1.20182i	0.0483444	+	0.0483444i
$619$	0.252180			0.0101360			0.00506799	−	0.999987i	$-0.498387\pi$
$619$	0.252180			0.0101360			0.00506799	+	0.999987i	$0.498387\pi$
$620$		−	4.54245i		−	0.182429i
$621$	−28.0093	+	28.0093i	−1.12397	+	1.12397i
$622$	−2.55752	−	2.55752i	−0.102547	−	0.102547i
$623$			0.00965687i			0.000386894i
$624$		−	29.8220i		−	1.19384i
$625$	9.10495			0.364198
$626$	−33.0519	−	33.0519i	−1.32102	−	1.32102i
$627$	−2.48089	−	2.48089i	−0.0990770	−	0.0990770i
$628$	3.79613	+	3.79613i	0.151482	+	0.151482i
$629$	−0.800948	+	0.800948i	−0.0319359	+	0.0319359i
$630$	−1.94788	+	1.94788i	−0.0776056	+	0.0776056i
$631$	22.7000			0.903672			0.451836	−	0.892101i	$-0.350769\pi$
$631$	22.7000			0.903672			0.451836	+	0.892101i	$0.350769\pi$
$632$	−10.8854	+	10.8854i	−0.433000	+	0.433000i
$633$	33.1349			1.31699
$634$	18.2125	−	18.2125i	0.723310	−	0.723310i
$635$		−	10.4211i		−	0.413548i
$636$			3.56615i			0.141407i
$637$	3.90259	−	3.90259i	0.154626	−	0.154626i
$638$	−1.99050			−0.0788048
$639$	17.3716	−	17.3716i	0.687208	−	0.687208i
$640$	−14.4808			−0.572402
$641$	−16.2623	+	16.2623i	−0.642322	+	0.642322i	−0.951126	−	0.308804i	$-0.900071\pi$
$641$	−16.2623	+	16.2623i	−0.642322	+	0.642322i	0.308804	+	0.951126i	$0.400071\pi$
$642$	−19.3523	+	19.3523i	−0.763775	+	0.763775i
$643$	−0.251318	−	0.251318i	−0.00991101	−	0.00991101i	0.702134	−	0.712045i	$-0.252231\pi$
$643$	−0.251318	−	0.251318i	−0.00991101	−	0.00991101i	−0.712045	+	0.702134i	$0.752231\pi$
$644$	2.15621	+	2.15621i	0.0849665	+	0.0849665i
$645$	−10.8945	−	10.8945i	−0.428970	−	0.428970i
$646$	0.587467			0.0231136
$647$		−	26.7768i		−	1.05271i	−0.850266	−	0.526353i	$-0.823559\pi$
$647$		−	26.7768i		−	1.05271i	0.850266	−	0.526353i	$-0.176441\pi$
$648$		−	3.19725i		−	0.125600i
$649$	−5.22558	−	5.22558i	−0.205122	−	0.205122i
$650$	−23.3677	+	23.3677i	−0.916557	+	0.916557i
$651$			11.8345i			0.463832i
$652$	−0.764383			−0.0299355
$653$	−16.6619	−	16.6619i	−0.652032	−	0.652032i	0.301450	−	0.953482i	$-0.402529\pi$
$653$	−16.6619	−	16.6619i	−0.652032	−	0.652032i	−0.953482	+	0.301450i	$0.902529\pi$
$654$			3.98940i			0.155998i
$655$	−10.6519			−0.416204
$656$	23.0186	−	18.9713i	0.898727	−	0.740703i
$657$	22.7483			0.887496
$658$			10.9132i			0.425440i
$659$	23.2110	+	23.2110i	0.904174	+	0.904174i	0.995794	−	0.0916200i	$-0.0292045\pi$
$659$	23.2110	+	23.2110i	0.904174	+	0.904174i	−0.0916200	+	0.995794i	$0.529205\pi$
$660$	0.500169			0.0194691
$661$			2.42954i			0.0944981i	0.998883	+	0.0472491i	$0.0150454\pi$
$661$			2.42954i			0.0944981i	−0.998883	+	0.0472491i	$0.984955\pi$
$662$	−5.96270	+	5.96270i	−0.231747	+	0.231747i
$663$	0.547871	+	0.547871i	0.0212775	+	0.0212775i
$664$		−	18.5915i		−	0.721490i
$665$			3.34528i			0.129725i
$666$	24.0674			0.932593
$667$	6.85980	+	6.85980i	0.265613	+	0.265613i
$668$	7.42820	+	7.42820i	0.287406	+	0.287406i
$669$	2.37248	+	2.37248i	0.0917252	+	0.0917252i
$670$	9.74955	−	9.74955i	0.376658	−	0.376658i
$671$	−1.40973	+	1.40973i	−0.0544220	+	0.0544220i
$672$	−2.68564			−0.103601
$673$	26.6138	−	26.6138i	1.02589	−	1.02589i	0.0262314	−	0.999656i	$-0.491649\pi$
$673$	26.6138	−	26.6138i	1.02589	−	1.02589i	0.999656	−	0.0262314i	$-0.00835066\pi$
$674$	26.6415			1.02619
$675$	−14.7076	+	14.7076i	−0.566094	+	0.566094i
$676$		−	7.25691i		−	0.279112i
$677$			28.6422i			1.10081i	0.834898	+	0.550404i	$0.185526\pi$
$677$			28.6422i			1.10081i	−0.834898	+	0.550404i	$0.814474\pi$
$678$	6.86340	−	6.86340i	0.263587	−	0.263587i
$679$	−0.583585			−0.0223959
$680$	0.225750	−	0.225750i	0.00865710	−	0.00865710i
$681$	18.9757			0.727149
$682$	−10.8607	+	10.8607i	−0.415880	+	0.415880i
$683$	−3.31825	+	3.31825i	−0.126969	+	0.126969i	−0.767736	−	0.640766i	$-0.778617\pi$
$683$	−3.31825	+	3.31825i	−0.126969	+	0.126969i	0.640766	+	0.767736i	$0.278617\pi$
$684$	−1.51861	−	1.51861i	−0.0580655	−	0.0580655i
$685$	5.14517	+	5.14517i	0.196587	+	0.196587i
$686$	−1.09900	−	1.09900i	−0.0419602	−	0.0419602i
$687$	−19.4353			−0.741504
$688$			57.7668i			2.20234i
$689$		−	40.8271i		−	1.55539i
$690$	−10.0184	−	10.0184i	−0.381393	−	0.381393i
$691$	12.3235	−	12.3235i	0.468808	−	0.468808i	−0.432720	−	0.901528i	$-0.642446\pi$
$691$	12.3235	−	12.3235i	0.468808	−	0.468808i	0.901528	+	0.432720i	$0.142446\pi$
$692$			4.79050i			0.182107i
$693$	1.60262			0.0608784
$694$	−11.4442	−	11.4442i	−0.434418	−	0.434418i
$695$		−	10.5029i		−	0.398397i
$696$	−3.77671			−0.143156
$697$	−0.0743560	+	0.771411i	−0.00281643	+	0.0292193i
$698$	−13.6528			−0.516764
$699$		−	13.9822i		−	0.528857i
$700$	1.13222	+	1.13222i	0.0427938	+	0.0427938i
$701$	27.5540			1.04070			0.520351	−	0.853953i	$-0.325801\pi$
$701$	27.5540			1.04070			0.520351	+	0.853953i	$0.325801\pi$
$702$		−	46.3115i		−	1.74792i
$703$	20.6666	−	20.6666i	0.779456	−	0.779456i
$704$	3.91641	+	3.91641i	0.147605	+	0.147605i
$705$		−	8.72421i		−	0.328573i
$706$		−	56.9549i		−	2.14353i
$707$	−0.878195			−0.0330279
$708$	2.60088	+	2.60088i	0.0977472	+	0.0977472i
$709$	−14.7787	−	14.7787i	−0.555026	−	0.555026i	0.372861	−	0.927887i	$-0.378377\pi$
$709$	−14.7787	−	14.7787i	−0.555026	−	0.555026i	−0.927887	+	0.372861i	$0.878377\pi$
$710$	17.4792	+	17.4792i	0.655982	+	0.655982i
$711$	−7.31426	+	7.31426i	−0.274306	+	0.274306i
$712$	−0.0168149	+	0.0168149i	−0.000630166	+	0.000630166i
$713$	74.8580			2.80345
$714$	0.154285	−	0.154285i	0.00577397	−	0.00577397i
$715$	−5.72620			−0.214148
$716$	−0.471488	+	0.471488i	−0.0176203	+	0.0176203i
$717$		−	13.3444i		−	0.498357i
$718$			2.11562i			0.0789542i
$719$	21.9763	−	21.9763i	0.819577	−	0.819577i	−0.166470	−	0.986047i	$-0.553237\pi$
$719$	21.9763	−	21.9763i	0.819577	−	0.819577i	0.986047	+	0.166470i	$0.0532369\pi$
$720$	−8.25677			−0.307712
$721$	−0.666658	+	0.666658i	−0.0248277	+	0.0248277i
$722$	14.3721			0.534873
$723$	5.20605	−	5.20605i	0.193615	−	0.193615i
$724$	−5.27370	+	5.27370i	−0.195996	+	0.195996i
$725$	3.60206	+	3.60206i	0.133777	+	0.133777i
$726$	12.8263	+	12.8263i	0.476028	+	0.476028i
$727$	2.36558	+	2.36558i	0.0877346	+	0.0877346i	0.749612	−	0.661877i	$-0.230240\pi$
$727$	2.36558	+	2.36558i	0.0877346	+	0.0877346i	−0.661877	+	0.749612i	$0.730240\pi$
$728$	13.5907			0.503705
$729$		−	20.9350i		−	0.775372i
$730$			22.8892i			0.847169i
$731$	−1.06125	−	1.06125i	−0.0392519	−	0.0392519i
$732$	0.701653	−	0.701653i	0.0259338	−	0.0259338i
$733$			10.3921i			0.383840i	0.981411	+	0.191920i	$0.0614714\pi$
$733$			10.3921i			0.383840i	−0.981411	+	0.191920i	$0.938529\pi$
$734$	16.0322			0.591760
$735$	0.878565	+	0.878565i	0.0324063	+	0.0324063i
$736$			16.9877i			0.626174i
$737$	−8.02142			−0.295473
$738$	12.7071	−	10.4728i	0.467754	−	0.385508i
$739$	27.9021			1.02639			0.513197	−	0.858271i	$-0.328461\pi$
$739$	27.9021			1.02639			0.513197	+	0.858271i	$0.328461\pi$
$740$			4.16658i			0.153166i
$741$	−14.1365	−	14.1365i	−0.519318	−	0.519318i
$742$	−11.4973			−0.422078
$743$		−	24.6632i		−	0.904805i	−0.891814	−	0.452403i	$-0.850567\pi$
$743$		−	24.6632i		−	0.904805i	0.891814	−	0.452403i	$-0.149433\pi$
$744$	−20.6068	+	20.6068i	−0.755481	+	0.755481i
$745$	−15.8552	−	15.8552i	−0.580888	−	0.580888i
$746$			10.9425i			0.400634i
$747$		−	12.4922i		−	0.457065i
$748$	0.0487226			0.00178147
$749$	−10.7348	−	10.7348i	−0.392243	−	0.392243i
$750$	−12.0881	−	12.0881i	−0.441394	−	0.441394i
$751$	−34.9794	−	34.9794i	−1.27642	−	1.27642i	−0.942658	−	0.333759i	$-0.891683\pi$
$751$	−34.9794	−	34.9794i	−1.27642	−	1.27642i	−0.333759	−	0.942658i	$-0.608317\pi$
$752$	−23.1296	+	23.1296i	−0.843450	+	0.843450i
$753$	−7.29467	+	7.29467i	−0.265832	+	0.265832i
$754$	−11.3423			−0.413060
$755$	−1.21542	+	1.21542i	−0.0442337	+	0.0442337i
$756$	−2.24390			−0.0816097
$757$	−10.6596	+	10.6596i	−0.387430	+	0.387430i	−0.873770	−	0.486340i	$-0.838332\pi$
$757$	−10.6596	+	10.6596i	−0.387430	+	0.387430i	0.486340	+	0.873770i	$0.338332\pi$
$758$		−	41.7307i		−	1.51573i
$759$			8.24261i			0.299188i
$760$	−5.82494	+	5.82494i	−0.211293	+	0.211293i
$761$	4.90518			0.177813			0.0889063	−	0.996040i	$-0.471663\pi$
$761$	4.90518			0.177813			0.0889063	+	0.996040i	$0.471663\pi$
$762$	12.4013	−	12.4013i	0.449253	−	0.449253i
$763$	−2.21294			−0.0801139
$764$	−0.474582	+	0.474582i	−0.0171698	+	0.0171698i
$765$	0.151688	−	0.151688i	0.00548429	−	0.00548429i
$766$	13.0615	+	13.0615i	0.471930	+	0.471930i
$767$	−29.7763	−	29.7763i	−1.07516	−	1.07516i
$768$	−7.85233	−	7.85233i	−0.283347	−	0.283347i
$769$	−40.2207			−1.45040			−0.725198	−	0.688541i	$-0.758252\pi$
$769$	−40.2207			−1.45040			−0.725198	+	0.688541i	$0.758252\pi$
$770$			1.61255i			0.0581122i
$771$			22.2512i			0.801357i
$772$	−5.22173	−	5.22173i	−0.187934	−	0.187934i
$773$	−25.3116	+	25.3116i	−0.910396	+	0.910396i	−0.996303	−	0.0859073i	$-0.972621\pi$
$773$	−25.3116	+	25.3116i	−0.910396	+	0.910396i	0.0859073	+	0.996303i	$0.472621\pi$
$774$			31.8893i			1.14624i
$775$	39.3077			1.41197
$776$	−1.01616	−	1.01616i	−0.0364781	−	0.0364781i
$777$		−	10.8553i		−	0.389430i
$778$	−37.3821			−1.34021
$779$	1.91858	−	19.9045i	0.0687404	−	0.713152i
$780$	2.85005			0.102048
$781$		−	14.3810i		−	0.514591i
$782$	−0.975913	−	0.975913i	−0.0348986	−	0.0348986i
$783$	−7.13877			−0.255119
$784$		−	4.65850i		−	0.166375i
$785$	9.78387	−	9.78387i	0.349201	−	0.349201i
$786$	−12.6760	−	12.6760i	−0.452138	−	0.452138i
$787$			33.2597i			1.18558i	0.805357	+	0.592790i	$0.201974\pi$
$787$			33.2597i			1.18558i	−0.805357	+	0.592790i	$0.798026\pi$
$788$			1.43871i			0.0512518i
$789$	6.57828			0.234193
$790$	−7.35958	−	7.35958i	−0.261842	−	0.261842i
$791$	3.80717	+	3.80717i	0.135367	+	0.135367i
$792$	2.79054	+	2.79054i	0.0991576	+	0.0991576i
$793$	−8.03289	+	8.03289i	−0.285256	+	0.285256i
$794$	−21.8912	+	21.8912i	−0.776888	+	0.776888i
$795$	9.19114			0.325976
$796$	5.43346	−	5.43346i	0.192584	−	0.192584i
$797$	−48.2876			−1.71044			−0.855218	−	0.518269i	$-0.826577\pi$
$797$	−48.2876			−1.71044			−0.855218	+	0.518269i	$0.826577\pi$
$798$	−3.98097	+	3.98097i	−0.140925	+	0.140925i
$799$		−	0.849844i		−	0.0300653i
$800$			8.92017i			0.315376i
$801$	−0.0112985	+	0.0112985i	−0.000399212	+	0.000399212i
$802$	−1.02317			−0.0361294
$803$	9.41604	−	9.41604i	0.332285	−	0.332285i
$804$	3.99243			0.140802
$805$	5.55726	−	5.55726i	0.195868	−	0.195868i
$806$	−61.8865	+	61.8865i	−2.17986	+	2.17986i
$807$	19.1905	+	19.1905i	0.675539	+	0.675539i
$808$	−1.52915	−	1.52915i	−0.0537953	−	0.0537953i
$809$	12.2234	+	12.2234i	0.429752	+	0.429752i	0.888544	−	0.458792i	$-0.151718\pi$
$809$	12.2234	+	12.2234i	0.429752	+	0.429752i	−0.458792	+	0.888544i	$0.651718\pi$
$810$	2.16164			0.0759521
$811$			22.7759i			0.799769i	0.916565	+	0.399885i	$0.130950\pi$
$811$			22.7759i			0.799769i	−0.916565	+	0.399885i	$0.869050\pi$
$812$			0.549557i			0.0192857i
$813$	−16.3299	−	16.3299i	−0.572713	−	0.572713i
$814$	9.96205	−	9.96205i	0.349170	−	0.349170i
$815$			1.97007i			0.0690084i
$816$	0.653989			0.0228942
$817$	27.3832	+	27.3832i	0.958018	+	0.958018i
$818$			14.2657i			0.498789i
$819$	9.13200			0.319098
$820$	1.81306	+	2.19986i	0.0633148	+	0.0768226i
$821$	43.1522			1.50602			0.753011	−	0.658007i	$-0.228600\pi$
$821$	43.1522			1.50602			0.753011	+	0.658007i	$0.228600\pi$
$822$			12.2458i			0.427120i
$823$	−20.9674	−	20.9674i	−0.730878	−	0.730878i	0.239915	−	0.970794i	$-0.422880\pi$
$823$	−20.9674	−	20.9674i	−0.730878	−	0.730878i	−0.970794	+	0.239915i	$0.922880\pi$
$824$	−2.32163			−0.0808777
$825$			4.32816i			0.150687i
$826$	−8.38526	+	8.38526i	−0.291760	+	0.291760i
$827$	−21.0132	−	21.0132i	−0.730701	−	0.730701i	0.240058	−	0.970759i	$-0.422834\pi$
$827$	−21.0132	−	21.0132i	−0.730701	−	0.730701i	−0.970759	+	0.240058i	$0.922834\pi$
$828$			5.04549i			0.175343i
$829$			17.9222i			0.622464i	0.950334	+	0.311232i	$0.100742\pi$
$829$			17.9222i			0.622464i	−0.950334	+	0.311232i	$0.899258\pi$
$830$	12.5696			0.436296
$831$	3.84385	+	3.84385i	0.133342	+	0.133342i
$832$	22.3164	+	22.3164i	0.773683	+	0.773683i
$833$	0.0855829	+	0.0855829i	0.00296527	+	0.00296527i
$834$	12.4987	−	12.4987i	0.432794	−	0.432794i
$835$	19.1449	−	19.1449i	0.662538	−	0.662538i
$836$	−1.25717			−0.0434802
$837$	−38.9511	+	38.9511i	−1.34635	+	1.34635i
$838$	−12.1812			−0.420792
$839$	12.7683	−	12.7683i	0.440811	−	0.440811i	−0.451474	−	0.892284i	$-0.649102\pi$
$839$	12.7683	−	12.7683i	0.440811	−	0.440811i	0.892284	+	0.451474i	$0.149102\pi$
$840$			3.05958i			0.105566i
$841$		−	27.2516i		−	0.939711i
$842$	−3.72425	+	3.72425i	−0.128346	+	0.128346i
$843$	8.68519			0.299134
$844$	8.39546	−	8.39546i	0.288983	−	0.288983i
$845$	−18.7034			−0.643418
$846$	−12.7683	+	12.7683i	−0.438984	+	0.438984i
$847$	−7.11481	+	7.11481i	−0.244468	+	0.244468i
$848$	−24.3675	−	24.3675i	−0.836785	−	0.836785i
$849$	−10.9960	−	10.9960i	−0.377383	−	0.377383i
$850$	−0.512448	−	0.512448i	−0.0175768	−	0.0175768i
$851$	−68.6637			−2.35376
$852$			7.15772i			0.245219i
$853$		−	40.9621i		−	1.40252i	−0.712907	−	0.701258i	$-0.752622\pi$
$853$		−	40.9621i		−	1.40252i	0.712907	−	0.701258i	$-0.247378\pi$
$854$	2.26213	+	2.26213i	0.0774085	+	0.0774085i
$855$	−3.91396	+	3.91396i	−0.133854	+	0.133854i
$856$		−	37.3839i		−	1.27776i
$857$	22.8235			0.779637			0.389818	−	0.920892i	$-0.372538\pi$
$857$	22.8235			0.779637			0.389818	+	0.920892i	$0.372538\pi$
$858$	−6.81432	−	6.81432i	−0.232637	−	0.232637i
$859$			29.8724i			1.01923i	0.860402	+	0.509616i	$0.170213\pi$
$859$			29.8724i			1.01923i	−0.860402	+	0.509616i	$0.829787\pi$
$860$	−5.52071			−0.188254
$861$	−4.72359	−	5.73134i	−0.160980	−	0.195324i
$862$	−31.8596			−1.08514
$863$			22.9136i			0.779988i	0.920817	+	0.389994i	$0.127523\pi$
$863$			22.9136i			0.779988i	−0.920817	+	0.389994i	$0.872477\pi$
$864$	−8.83927	−	8.83927i	−0.300718	−	0.300718i
$865$	12.3467			0.419800
$866$			34.7014i			1.17920i
$867$	13.9310	−	13.9310i	0.473122	−	0.473122i
$868$	2.99854	+	2.99854i	0.101777	+	0.101777i
$869$			6.05508i			0.205404i
$870$		−	2.55341i		−	0.0865686i
$871$	−45.7075			−1.54874
$872$	−3.85326	−	3.85326i	−0.130488	−	0.130488i
$873$	−0.682789	−	0.682789i	−0.0231089	−	0.0231089i
$874$	25.1812	+	25.1812i	0.851766	+	0.851766i
$875$	6.70532	−	6.70532i	0.226681	−	0.226681i
$876$	−4.68657	+	4.68657i	−0.158344	+	0.158344i
$877$	−58.1006			−1.96192			−0.980958	−	0.194219i	$-0.937783\pi$
$877$	−58.1006			−1.96192			−0.980958	+	0.194219i	$0.937783\pi$
$878$	−0.602460	+	0.602460i	−0.0203320	+	0.0203320i
$879$	−6.31774			−0.213092
$880$	−3.41766	+	3.41766i	−0.115209	+	0.115209i
$881$		−	8.59882i		−	0.289702i	−0.989454	−	0.144851i	$-0.953730\pi$
$881$		−	8.59882i		−	0.289702i	0.989454	−	0.144851i	$-0.0462702\pi$
$882$		−	2.57165i		−	0.0865920i
$883$	−9.41519	+	9.41519i	−0.316846	+	0.316846i	−0.847555	−	0.530708i	$-0.821926\pi$
$883$	−9.41519	+	9.41519i	−0.316846	+	0.316846i	0.530708	+	0.847555i	$0.321926\pi$
$884$	0.277630			0.00933770
$885$	6.70333	−	6.70333i	0.225330	−	0.225330i
$886$	10.0820			0.338712
$887$	−7.82581	+	7.82581i	−0.262765	+	0.262765i	−0.826176	−	0.563412i	$-0.809489\pi$
$887$	−7.82581	+	7.82581i	−0.262765	+	0.262765i	0.563412	+	0.826176i	$0.309489\pi$
$888$	18.9016	−	18.9016i	0.634296	−	0.634296i
$889$	6.87910	+	6.87910i	0.230718	+	0.230718i
$890$	−0.0113685	−	0.0113685i	−0.000381072	−	0.000381072i
$891$	−0.889241	−	0.889241i	−0.0297907	−	0.0297907i
$892$	1.20224			0.0402539
$893$			21.9283i			0.733801i
$894$		−	37.7360i		−	1.26208i
$895$	1.21518	+	1.21518i	0.0406190	+	0.0406190i
$896$	9.55895	−	9.55895i	0.319342	−	0.319342i
$897$			46.9678i			1.56821i
$898$	−20.5622			−0.686168
$899$	9.53960	+	9.53960i	0.318164	+	0.318164i
$900$			2.64937i			0.0883123i
$901$	0.895329			0.0298277
$902$	0.924827	−	9.59467i	0.0307934	−	0.319468i
$903$	14.3832			0.478643
$904$			13.2584i			0.440968i
$905$	13.5921	+	13.5921i	0.451816	+	0.451816i
$906$	−2.89276			−0.0961056
$907$			39.9265i			1.32574i	0.748736	+	0.662869i	$0.230661\pi$
$907$			39.9265i			1.32574i	−0.748736	+	0.662869i	$0.769339\pi$
$908$	4.80790	−	4.80790i	0.159556	−	0.159556i
$909$	−1.02748	−	1.02748i	−0.0340794	−	0.0340794i
$910$			9.18858i			0.304599i
$911$			42.7863i			1.41757i	0.705422	+	0.708787i	$0.250757\pi$
$911$			42.7863i			1.41757i	−0.705422	+	0.708787i	$0.749243\pi$
$912$	−16.8747			−0.558777
$913$	−5.17080	−	5.17080i	−0.171128	−	0.171128i
$914$	33.4141	+	33.4141i	1.10524	+	1.10524i
$915$	−1.80839	−	1.80839i	−0.0597835	−	0.0597835i
$916$	−4.92436	+	4.92436i	−0.162706	+	0.162706i
$917$	7.03146	−	7.03146i	0.232199	−	0.232199i
$918$	1.01560			0.0335198
$919$	−10.5024	+	10.5024i	−0.346442	+	0.346442i	−0.858782	−	0.512341i	$-0.828778\pi$
$919$	−10.5024	+	10.5024i	−0.346442	+	0.346442i	0.512341	+	0.858782i	$0.328778\pi$
$920$	19.3531			0.638051
$921$	6.74825	−	6.74825i	0.222362	−	0.222362i
$922$		−	25.7626i		−	0.848446i
$923$		−	81.9453i		−	2.69726i
$924$	−0.330169	+	0.330169i	−0.0108618	+	0.0108618i
$925$	−36.0550			−1.18548
$926$	−5.91504	+	5.91504i	−0.194380	+	0.194380i
$927$	−1.55997			−0.0512361
$928$	−2.16484	+	2.16484i	−0.0710644	+	0.0710644i
$929$	16.5387	−	16.5387i	0.542616	−	0.542616i	−0.381679	−	0.924295i	$-0.624654\pi$
$929$	16.5387	−	16.5387i	0.542616	−	0.542616i	0.924295	+	0.381679i	$0.124654\pi$
$930$	−13.9321	−	13.9321i	−0.456851	−	0.456851i
$931$	−2.20827	−	2.20827i	−0.0723731	−	0.0723731i
$932$	−3.54270	−	3.54270i	−0.116045	−	0.116045i
$933$	−2.69925			−0.0883694
$934$			29.2939i			0.958527i
$935$		−	0.125574i		−	0.00410671i
$936$	15.9010	+	15.9010i	0.519741	+	0.519741i
$937$	20.8250	−	20.8250i	0.680323	−	0.680323i	−0.279750	−	0.960073i	$-0.590251\pi$
$937$	20.8250	−	20.8250i	0.680323	−	0.680323i	0.960073	+	0.279750i	$0.0902514\pi$
$938$			12.8716i			0.420273i
$939$	−34.8835			−1.13838
$940$	−2.21047	−	2.21047i	−0.0720975	−	0.0720975i
$941$			16.8206i			0.548336i	0.961682	+	0.274168i	$0.0884025\pi$
$941$			16.8206i			0.548336i	−0.961682	+	0.274168i	$0.911598\pi$
$942$	23.2861			0.758702
$943$	−36.2530	+	29.8786i	−1.18056	+	0.972980i
$944$	−35.5437			−1.15685
$945$			5.78326i			0.188130i
$946$	13.1997	+	13.1997i	0.429159	+	0.429159i
$947$	−33.4771			−1.08786			−0.543929	−	0.839131i	$-0.683064\pi$
$947$	−33.4771			−1.08786			−0.543929	+	0.839131i	$0.683064\pi$
$948$		−	3.01374i		−	0.0978818i
$949$	53.6543	−	53.6543i	1.74169	−	1.74169i
$950$	13.2225	+	13.2225i	0.428996	+	0.428996i
$951$		−	19.2217i		−	0.623307i
$952$			0.298041i			0.00965956i
$953$	−58.0991			−1.88201			−0.941007	−	0.338386i	$-0.890119\pi$
$953$	−58.0991			−1.88201			−0.941007	+	0.338386i	$0.890119\pi$
$954$	−13.4517	−	13.4517i	−0.435515	−	0.435515i
$955$	1.22315	+	1.22315i	0.0395803	+	0.0395803i
$956$	−3.38111	−	3.38111i	−0.109353	−	0.109353i
$957$	−1.05040	+	1.05040i	−0.0339548	+	0.0339548i
$958$	−32.5473	+	32.5473i	−1.05155	+	1.05155i
$959$	−6.79279			−0.219351
$960$	−5.02395	+	5.02395i	−0.162147	+	0.162147i
$961$	73.1014			2.35811
$962$	56.7655	−	56.7655i	1.83019	−	1.83019i
$963$		−	25.1194i		−	0.809461i
$964$		−	2.63813i		−	0.0849685i
$965$	−13.4581	+	13.4581i	−0.433232	+	0.433232i
$966$	13.2266			0.425557
$967$	−16.6781	+	16.6781i	−0.536332	+	0.536332i	−0.922449	−	0.386118i	$-0.873816\pi$
$967$	−16.6781	+	16.6781i	−0.536332	+	0.536332i	0.386118	+	0.922449i	$0.373816\pi$
$968$	−24.7772			−0.796370
$969$	0.310011	−	0.310011i	0.00995898	−	0.00995898i
$970$	0.687020	−	0.687020i	0.0220589	−	0.0220589i
$971$	−20.9560	−	20.9560i	−0.672509	−	0.672509i	0.285785	−	0.958294i	$-0.407746\pi$
$971$	−20.9560	−	20.9560i	−0.672509	−	0.672509i	−0.958294	+	0.285785i	$0.907746\pi$
$972$	−4.31743	−	4.31743i	−0.138482	−	0.138482i
$973$	6.93310	+	6.93310i	0.222265	+	0.222265i
$974$	8.43583			0.270301
$975$			24.6626i			0.789837i
$976$			9.58880i			0.306930i
$977$	37.7954	+	37.7954i	1.20918	+	1.20918i	0.971292	+	0.237892i	$0.0764563\pi$
$977$	37.7954	+	37.7954i	1.20918	+	1.20918i	0.237892	+	0.971292i	$0.423544\pi$
$978$	−2.34443	+	2.34443i	−0.0749665	+	0.0749665i
$979$			0.00935338i			0.000298935i
$980$	0.445207			0.0142216
$981$	−2.58913	−	2.58913i	−0.0826644	−	0.0826644i
$982$		−	64.1265i		−	2.04636i
$983$	42.5707			1.35780			0.678898	−	0.734233i	$-0.262458\pi$
$983$	42.5707			1.35780			0.678898	+	0.734233i	$0.262458\pi$
$984$	1.75473	−	18.2046i	0.0559388	−	0.580340i
$985$	3.70802			0.118147
$986$		−	0.248733i		−	0.00792127i
$987$	5.75897	+	5.75897i	0.183310	+	0.183310i
$988$	−7.16360			−0.227904
$989$		−	90.9792i		−	2.89297i
$990$	−1.88667	+	1.88667i	−0.0599622	+	0.0599622i
$991$	−40.1859	−	40.1859i	−1.27655	−	1.27655i	−0.942587	−	0.333960i	$-0.891615\pi$
$991$	−40.1859	−	40.1859i	−1.27655	−	1.27655i	−0.333960	−	0.942587i	$-0.608385\pi$
$992$			23.6240i			0.750062i
$993$			6.29313i			0.199706i
$994$	−23.0765			−0.731943
$995$	−14.0038	−	14.0038i	−0.443951	−	0.443951i
$996$	2.57362	+	2.57362i	0.0815482	+	0.0815482i
$997$	12.0700	+	12.0700i	0.382261	+	0.382261i	0.871916	−	0.489655i	$-0.162877\pi$
$997$	12.0700	+	12.0700i	0.382261	+	0.382261i	−0.489655	+	0.871916i	$0.662877\pi$
$998$	18.2758	−	18.2758i	0.578511	−	0.578511i
$999$	35.7280	−	35.7280i	1.13038	−	1.13038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.5	✓	40
41.32	even	4	inner	287.2.f.a.155.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.5	✓	40	1.1	even	1	trivial
287.2.f.a.155.16	yes	40	41.32	even	4	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.55423i q^{2} +(-0.820177 - 0.820177i) q^{3} -0.415620 q^{4} +1.07119i q^{5} +(-1.27474 + 1.27474i) q^{6} +(-0.707107 - 0.707107i) q^{7} -2.46249i q^{8} -1.65462i q^{9} +O(q^{10})\)	\(q-1.55423i q^{2} +(-0.820177 - 0.820177i) q^{3} -0.415620 q^{4} +1.07119i q^{5} +(-1.27474 + 1.27474i) q^{6} +(-0.707107 - 0.707107i) q^{7} -2.46249i q^{8} -1.65462i q^{9} +1.66487 q^{10} +(-0.684884 - 0.684884i) q^{11} +(0.340882 + 0.340882i) q^{12} +(-3.90259 - 3.90259i) q^{13} +(-1.09900 + 1.09900i) q^{14} +(0.878565 - 0.878565i) q^{15} -4.65850 q^{16} +(0.0855829 - 0.0855829i) q^{17} -2.57165 q^{18} +(-2.20827 + 2.20827i) q^{19} -0.445207i q^{20} +1.15991i q^{21} +(-1.06447 + 1.06447i) q^{22} +7.33685 q^{23} +(-2.01967 + 2.01967i) q^{24} +3.85255 q^{25} +(-6.06551 + 6.06551i) q^{26} +(-3.81761 + 3.81761i) q^{27} +(0.293887 + 0.293887i) q^{28} +(0.934979 + 0.934979i) q^{29} +(-1.36549 - 1.36549i) q^{30} +10.2030 q^{31} +2.31539i q^{32} +1.12345i q^{33} +(-0.133015 - 0.133015i) q^{34} +(0.757445 - 0.757445i) q^{35} +0.687692i q^{36} -9.35874 q^{37} +(3.43215 + 3.43215i) q^{38} +6.40163i q^{39} +2.63779 q^{40} +(-4.94121 + 4.07240i) q^{41} +1.80276 q^{42} -12.4003i q^{43} +(0.284651 + 0.284651i) q^{44} +1.77241 q^{45} -11.4031i q^{46} +(4.96503 - 4.96503i) q^{47} +(3.82080 + 3.82080i) q^{48} +1.00000i q^{49} -5.98774i q^{50} -0.140386 q^{51} +(1.62199 + 1.62199i) q^{52} +(5.23077 + 5.23077i) q^{53} +(5.93343 + 5.93343i) q^{54} +(0.733640 - 0.733640i) q^{55} +(-1.74124 + 1.74124i) q^{56} +3.62234 q^{57} +(1.45317 - 1.45317i) q^{58} +7.62987 q^{59} +(-0.365149 + 0.365149i) q^{60} -2.05835i q^{61} -15.8578i q^{62} +(-1.16999 + 1.16999i) q^{63} -5.71836 q^{64} +(4.18041 - 4.18041i) q^{65} +1.74610 q^{66} +(5.85604 - 5.85604i) q^{67} +(-0.0355699 + 0.0355699i) q^{68} +(-6.01752 - 6.01752i) q^{69} +(-1.17724 - 1.17724i) q^{70} +(10.4988 + 10.4988i) q^{71} -4.07447 q^{72} +13.7484i q^{73} +14.5456i q^{74} +(-3.15978 - 3.15978i) q^{75} +(0.917800 - 0.917800i) q^{76} +0.968572i q^{77} +9.94959 q^{78} +(-4.42051 - 4.42051i) q^{79} -4.99013i q^{80} +1.29838 q^{81} +(6.32942 + 7.67976i) q^{82} +7.54989 q^{83} -0.482080i q^{84} +(0.0916755 + 0.0916755i) q^{85} -19.2729 q^{86} -1.53370i q^{87} +(-1.68652 + 1.68652i) q^{88} +(-0.00682844 - 0.00682844i) q^{89} -2.75473i q^{90} +5.51910i q^{91} -3.04934 q^{92} +(-8.36828 - 8.36828i) q^{93} +(-7.71678 - 7.71678i) q^{94} +(-2.36547 - 2.36547i) q^{95} +(1.89903 - 1.89903i) q^{96} +(0.412657 - 0.412657i) q^{97} +1.55423 q^{98} +(-1.13322 + 1.13322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

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