LMFDB - Embedded newform 187.2.e.b.166.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, 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("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			166.3
Character	$\chi$	$=$	187.166
Dual form			187.2.e.b.89.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33488i q^{2} +(1.01883 + 1.01883i) q^{3} -3.45165 q^{4} +(2.72560 + 2.72560i) q^{5} +(2.37884 - 2.37884i) q^{6} +(0.562655 - 0.562655i) q^{7} +3.38941i q^{8} -0.923968i q^{9} +O(q^{10})$	\(q-2.33488i q^{2} +(1.01883 + 1.01883i) q^{3} -3.45165 q^{4} +(2.72560 + 2.72560i) q^{5} +(2.37884 - 2.37884i) q^{6} +(0.562655 - 0.562655i) q^{7} +3.38941i q^{8} -0.923968i q^{9} +(6.36394 - 6.36394i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-3.51664 - 3.51664i) q^{12} -0.362722 q^{13} +(-1.31373 - 1.31373i) q^{14} +5.55385i q^{15} +1.01057 q^{16} +(-0.951728 - 4.01176i) q^{17} -2.15735 q^{18} +1.20976i q^{19} +(-9.40781 - 9.40781i) q^{20} +1.14650 q^{21} +(1.65101 + 1.65101i) q^{22} +(-5.12339 + 5.12339i) q^{23} +(-3.45324 + 3.45324i) q^{24} +9.85780i q^{25} +0.846911i q^{26} +(3.99786 - 3.99786i) q^{27} +(-1.94209 + 1.94209i) q^{28} +(-3.64307 - 3.64307i) q^{29} +12.9676 q^{30} +(-1.42855 - 1.42855i) q^{31} +4.41927i q^{32} -1.44084 q^{33} +(-9.36696 + 2.22217i) q^{34} +3.06715 q^{35} +3.18921i q^{36} +(-5.32379 - 5.32379i) q^{37} +2.82463 q^{38} +(-0.369552 - 0.369552i) q^{39} +(-9.23819 + 9.23819i) q^{40} +(6.92206 - 6.92206i) q^{41} -2.67694i q^{42} +7.46079i q^{43} +(2.44068 - 2.44068i) q^{44} +(2.51837 - 2.51837i) q^{45} +(11.9625 + 11.9625i) q^{46} +5.49866 q^{47} +(1.02960 + 1.02960i) q^{48} +6.36684i q^{49} +23.0167 q^{50} +(3.11765 - 5.05695i) q^{51} +1.25199 q^{52} -6.59938i q^{53} +(-9.33451 - 9.33451i) q^{54} -3.85458 q^{55} +(1.90707 + 1.90707i) q^{56} +(-1.23254 + 1.23254i) q^{57} +(-8.50611 + 8.50611i) q^{58} +4.35283i q^{59} -19.1699i q^{60} +(-6.98590 + 6.98590i) q^{61} +(-3.33549 + 3.33549i) q^{62} +(-0.519875 - 0.519875i) q^{63} +12.3396 q^{64} +(-0.988635 - 0.988635i) q^{65} +3.36419i q^{66} -12.6034 q^{67} +(3.28503 + 13.8472i) q^{68} -10.4397 q^{69} -7.16141i q^{70} +(5.10836 + 5.10836i) q^{71} +3.13171 q^{72} +(0.463448 + 0.463448i) q^{73} +(-12.4304 + 12.4304i) q^{74} +(-10.0434 + 10.0434i) q^{75} -4.17566i q^{76} +0.795715i q^{77} +(-0.862859 + 0.862859i) q^{78} +(-0.337507 + 0.337507i) q^{79} +(2.75441 + 2.75441i) q^{80} +5.37438 q^{81} +(-16.1622 - 16.1622i) q^{82} -5.30213i q^{83} -3.95732 q^{84} +(8.34042 - 13.5285i) q^{85} +17.4200 q^{86} -7.42334i q^{87} +(-2.39668 - 2.39668i) q^{88} +2.22160 q^{89} +(-5.88007 - 5.88007i) q^{90} +(-0.204087 + 0.204087i) q^{91} +(17.6841 - 17.6841i) q^{92} -2.91090i q^{93} -12.8387i q^{94} +(-3.29732 + 3.29732i) q^{95} +(-4.50249 + 4.50249i) q^{96} +(11.0425 + 11.0425i) q^{97} +14.8658 q^{98} +(0.653344 + 0.653344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	2.33488i		−	1.65101i	−0.564397	−	0.825503i	$-0.690891\pi$
$2$		−	2.33488i		−	1.65101i	0.564397	−	0.825503i	$-0.309109\pi$
$3$	1.01883	+	1.01883i	0.588222	+	0.588222i	0.937150	−	0.348927i	$-0.113454\pi$
$3$	1.01883	+	1.01883i	0.588222	+	0.588222i	−0.348927	+	0.937150i	$0.613454\pi$
$4$	−3.45165			−1.72582
$5$	2.72560	+	2.72560i	1.21893	+	1.21893i	0.968009	+	0.250917i	$0.0807321\pi$
$5$	2.72560	+	2.72560i	1.21893	+	1.21893i	0.250917	+	0.968009i	$0.419268\pi$
$6$	2.37884	−	2.37884i	0.971159	−	0.971159i
$7$	0.562655	−	0.562655i	0.212664	−	0.212664i	−0.592734	−	0.805398i	$-0.701952\pi$
$7$	0.562655	−	0.562655i	0.212664	−	0.212664i	0.805398	+	0.592734i	$0.201952\pi$
$8$			3.38941i			1.19834i
$9$		−	0.923968i		−	0.307989i
$10$	6.36394	−	6.36394i	2.01245	−	2.01245i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−3.51664	−	3.51664i	−1.01517	−	1.01517i
$13$	−0.362722			−0.100601			−0.0503005	−	0.998734i	$-0.516018\pi$
$13$	−0.362722			−0.100601			−0.0503005	+	0.998734i	$0.516018\pi$
$14$	−1.31373	−	1.31373i	−0.351109	−	0.351109i
$15$			5.55385i			1.43400i
$16$	1.01057			0.252643
$17$	−0.951728	−	4.01176i	−0.230828	−	0.972995i
$17$	−0.951728	−	4.01176i	−0.230828	−	0.972995i
$18$	−2.15735			−0.508492
$19$			1.20976i			0.277538i	0.990325	+	0.138769i	$0.0443145\pi$
$19$			1.20976i			0.277538i	−0.990325	+	0.138769i	$0.955686\pi$
$20$	−9.40781	−	9.40781i	−2.10365	−	2.10365i
$21$	1.14650			0.250187
$22$	1.65101	+	1.65101i	0.351996	+	0.351996i
$23$	−5.12339	+	5.12339i	−1.06830	+	1.06830i	−0.0708105	+	0.997490i	$0.522559\pi$
$23$	−5.12339	+	5.12339i	−1.06830	+	1.06830i	−0.997490	+	0.0708105i	$0.977441\pi$
$24$	−3.45324	+	3.45324i	−0.704890	+	0.704890i
$25$			9.85780i			1.97156i
$26$			0.846911i			0.166093i
$27$	3.99786	−	3.99786i	0.769388	−	0.769388i
$28$	−1.94209	+	1.94209i	−0.367020	+	0.367020i
$29$	−3.64307	−	3.64307i	−0.676500	−	0.676500i	0.282706	−	0.959207i	$-0.408768\pi$
$29$	−3.64307	−	3.64307i	−0.676500	−	0.676500i	−0.959207	+	0.282706i	$0.908768\pi$
$30$	12.9676			2.36754
$31$	−1.42855	−	1.42855i	−0.256575	−	0.256575i	0.567084	−	0.823660i	$-0.308071\pi$
$31$	−1.42855	−	1.42855i	−0.256575	−	0.256575i	−0.823660	+	0.567084i	$0.808071\pi$
$32$			4.41927i			0.781224i
$33$	−1.44084			−0.250819
$34$	−9.36696	+	2.22217i	−1.60642	+	0.381098i
$35$	3.06715			0.518442
$36$			3.18921i			0.531535i
$37$	−5.32379	−	5.32379i	−0.875226	−	0.875226i	0.117810	−	0.993036i	$-0.462413\pi$
$37$	−5.32379	−	5.32379i	−0.875226	−	0.875226i	−0.993036	+	0.117810i	$0.962413\pi$
$38$	2.82463			0.458216
$39$	−0.369552	−	0.369552i	−0.0591757	−	0.0591757i
$40$	−9.23819	+	9.23819i	−1.46069	+	1.46069i
$41$	6.92206	−	6.92206i	1.08104	−	1.08104i	0.0846317	−	0.996412i	$-0.473029\pi$
$41$	6.92206	−	6.92206i	1.08104	−	1.08104i	0.996412	−	0.0846317i	$-0.0269714\pi$
$42$		−	2.67694i		−	0.413060i
$43$			7.46079i			1.13776i	0.822421	+	0.568880i	$0.192623\pi$
$43$			7.46079i			1.13776i	−0.822421	+	0.568880i	$0.807377\pi$
$44$	2.44068	−	2.44068i	0.367947	−	0.367947i
$45$	2.51837	−	2.51837i	0.375416	−	0.375416i
$46$	11.9625	+	11.9625i	1.76377	+	1.76377i
$47$	5.49866			0.802062			0.401031	−	0.916065i	$-0.368652\pi$
$47$	5.49866			0.802062			0.401031	+	0.916065i	$0.368652\pi$
$48$	1.02960	+	1.02960i	0.148610	+	0.148610i
$49$			6.36684i			0.909548i
$50$	23.0167			3.25506
$51$	3.11765	−	5.05695i	0.436559	−	0.708115i
$52$	1.25199			0.173620
$53$		−	6.59938i		−	0.906494i	−0.891385	−	0.453247i	$-0.850266\pi$
$53$		−	6.59938i		−	0.906494i	0.891385	−	0.453247i	$-0.149734\pi$
$54$	−9.33451	−	9.33451i	−1.27027	−	1.27027i
$55$	−3.85458			−0.519752
$56$	1.90707	+	1.90707i	0.254843	+	0.254843i
$57$	−1.23254	+	1.23254i	−0.163254	+	0.163254i
$58$	−8.50611	+	8.50611i	−1.11691	+	1.11691i
$59$			4.35283i			0.566691i	0.959018	+	0.283345i	$0.0914443\pi$
$59$			4.35283i			0.566691i	−0.959018	+	0.283345i	$0.908556\pi$
$60$		−	19.1699i		−	2.47483i
$61$	−6.98590	+	6.98590i	−0.894453	+	0.894453i	−0.994938	−	0.100486i	$-0.967960\pi$
$61$	−6.98590	+	6.98590i	−0.894453	+	0.894453i	0.100486	+	0.994938i	$0.467960\pi$
$62$	−3.33549	+	3.33549i	−0.423608	+	0.423608i
$63$	−0.519875	−	0.519875i	−0.0654981	−	0.0654981i
$64$	12.3396			1.54245
$65$	−0.988635	−	0.988635i	−0.122625	−	0.122625i
$66$			3.36419i			0.414104i
$67$	−12.6034			−1.53975			−0.769876	−	0.638193i	$-0.779682\pi$
$67$	−12.6034			−1.53975			−0.769876	+	0.638193i	$0.779682\pi$
$68$	3.28503	+	13.8472i	0.398368	+	1.67922i
$69$	−10.4397			−1.25680
$70$		−	7.16141i		−	0.855952i
$71$	5.10836	+	5.10836i	0.606251	+	0.606251i	0.941964	−	0.335713i	$-0.108977\pi$
$71$	5.10836	+	5.10836i	0.606251	+	0.606251i	−0.335713	+	0.941964i	$0.608977\pi$
$72$	3.13171			0.369076
$73$	0.463448	+	0.463448i	0.0542425	+	0.0542425i	0.733708	−	0.679465i	$-0.237788\pi$
$73$	0.463448	+	0.463448i	0.0542425	+	0.0542425i	−0.679465	+	0.733708i	$0.737788\pi$
$74$	−12.4304	+	12.4304i	−1.44500	+	1.44500i
$75$	−10.0434	+	10.0434i	−1.15971	+	1.15971i
$76$		−	4.17566i		−	0.478981i
$77$			0.795715i			0.0906801i
$78$	−0.862859	+	0.862859i	−0.0976995	+	0.0976995i
$79$	−0.337507	+	0.337507i	−0.0379725	+	0.0379725i	−0.725838	−	0.687866i	$-0.758548\pi$
$79$	−0.337507	+	0.337507i	−0.0379725	+	0.0379725i	0.687866	+	0.725838i	$0.258548\pi$
$80$	2.75441	+	2.75441i	0.307952	+	0.307952i
$81$	5.37438			0.597153
$82$	−16.1622	−	16.1622i	−1.78481	−	1.78481i
$83$		−	5.30213i		−	0.581984i	−0.956725	−	0.290992i	$-0.906015\pi$
$83$		−	5.30213i		−	0.581984i	0.956725	−	0.290992i	$-0.0939853\pi$
$84$	−3.95732			−0.431779
$85$	8.34042	−	13.5285i	0.904646	−	1.46737i
$86$	17.4200			1.87845
$87$		−	7.42334i		−	0.795865i
$88$	−2.39668	−	2.39668i	−0.255487	−	0.255487i
$89$	2.22160			0.235489			0.117744	−	0.993044i	$-0.462434\pi$
$89$	2.22160			0.235489			0.117744	+	0.993044i	$0.462434\pi$
$90$	−5.88007	−	5.88007i	−0.619814	−	0.619814i
$91$	−0.204087	+	0.204087i	−0.0213942	+	0.0213942i
$92$	17.6841	−	17.6841i	1.84370	−	1.84370i
$93$		−	2.91090i		−	0.301847i
$94$		−	12.8387i		−	1.32421i
$95$	−3.29732	+	3.29732i	−0.338298	+	0.338298i
$96$	−4.50249	+	4.50249i	−0.459534	+	0.459534i
$97$	11.0425	+	11.0425i	1.12120	+	1.12120i	0.991562	+	0.129635i	$0.0413807\pi$
$97$	11.0425	+	11.0425i	1.12120	+	1.12120i	0.129635	+	0.991562i	$0.458619\pi$
$98$	14.8658			1.50167
$99$	0.653344	+	0.653344i	0.0656635	+	0.0656635i
$100$		−	34.0256i		−	3.40256i
$101$	−1.48462			−0.147725			−0.0738626	−	0.997268i	$-0.523533\pi$
$101$	−1.48462			−0.147725			−0.0738626	+	0.997268i	$0.523533\pi$
$102$	−11.8074	−	7.27934i	−1.16910	−	0.720762i
$103$	−4.75146			−0.468175			−0.234088	−	0.972215i	$-0.575210\pi$
$103$	−4.75146			−0.468175			−0.234088	+	0.972215i	$0.575210\pi$
$104$		−	1.22942i		−	0.120554i
$105$	3.12490	+	3.12490i	0.304959	+	0.304959i
$106$	−15.4087			−1.49663
$107$	−10.5200	−	10.5200i	−1.01701	−	1.01701i	−0.999853	−	0.0171538i	$-0.994540\pi$
$107$	−10.5200	−	10.5200i	−1.01701	−	1.01701i	−0.0171538	−	0.999853i	$-0.505460\pi$
$108$	−13.7992	+	13.7992i	−1.32783	+	1.32783i
$109$	7.77811	−	7.77811i	0.745008	−	0.745008i	−0.228529	−	0.973537i	$-0.573392\pi$
$109$	7.77811	−	7.77811i	0.745008	−	0.745008i	0.973537	+	0.228529i	$0.0733916\pi$
$110$			8.99997i			0.858113i
$111$		−	10.8481i		−	1.02965i
$112$	0.568603	−	0.568603i	0.0537279	−	0.0537279i
$113$	12.5599	−	12.5599i	1.18154	−	1.18154i	0.202194	−	0.979345i	$-0.435193\pi$
$113$	12.5599	−	12.5599i	1.18154	−	1.18154i	0.979345	−	0.202194i	$-0.0648073\pi$
$114$	2.87782	+	2.87782i	0.269533	+	0.269533i
$115$	−27.9286			−2.60436
$116$	12.5746	+	12.5746i	1.16752	+	1.16752i
$117$			0.335143i			0.0309840i
$118$	10.1633			0.935610
$119$	−2.79273	−	1.72174i	−0.256009	−	0.157832i
$120$	−18.8243			−1.71842
$121$		−	1.00000i		−	0.0909091i
$122$	16.3112	+	16.3112i	1.47675	+	1.47675i
$123$	14.1048			1.27179
$124$	4.93085	+	4.93085i	0.442804	+	0.442804i
$125$	−13.2404	+	13.2404i	−1.18426	+	1.18426i
$126$	−1.21384	+	1.21384i	−0.108138	+	0.108138i
$127$			6.28949i			0.558102i	0.960276	+	0.279051i	$0.0900198\pi$
$127$			6.28949i			0.558102i	−0.960276	+	0.279051i	$0.909980\pi$
$128$		−	19.9729i		−	1.76537i
$129$	−7.60128	+	7.60128i	−0.669255	+	0.669255i
$130$	−2.30834	+	2.30834i	−0.202455	+	0.202455i
$131$	−11.2324	−	11.2324i	−0.981383	−	0.981383i	0.0184472	−	0.999830i	$-0.494128\pi$
$131$	−11.2324	−	11.2324i	−0.981383	−	0.981383i	−0.999830	+	0.0184472i	$0.994128\pi$
$132$	4.97329			0.432869
$133$	0.680677	+	0.680677i	0.0590222	+	0.0590222i
$134$			29.4274i			2.54214i
$135$	21.7931			1.87565
$136$	13.5975	−	3.22580i	1.16598	−	0.276610i
$137$	16.2532			1.38860			0.694302	−	0.719683i	$-0.255713\pi$
$137$	16.2532			1.38860			0.694302	+	0.719683i	$0.255713\pi$
$138$			24.3755i			2.07498i
$139$	12.5412	+	12.5412i	1.06373	+	1.06373i	0.997826	+	0.0659004i	$0.0209920\pi$
$139$	12.5412	+	12.5412i	1.06373	+	1.06373i	0.0659004	+	0.997826i	$0.479008\pi$
$140$	−10.5867			−0.894740
$141$	5.60220	+	5.60220i	0.471791	+	0.471791i
$142$	11.9274	−	11.9274i	1.00092	−	1.00092i
$143$	0.256483	−	0.256483i	0.0214482	−	0.0214482i
$144$		−	0.933734i		−	0.0778112i
$145$		−	19.8591i		−	1.64921i
$146$	1.08209	−	1.08209i	0.0895547	−	0.0895547i
$147$	−6.48673	+	6.48673i	−0.535017	+	0.535017i
$148$	18.3758	+	18.3758i	1.51049	+	1.51049i
$149$	−13.3403			−1.09288			−0.546442	−	0.837497i	$-0.684018\pi$
$149$	−13.3403			−1.09288			−0.546442	+	0.837497i	$0.684018\pi$
$150$	23.4502	+	23.4502i	1.91470	+	1.91470i
$151$			20.3242i			1.65396i	0.562234	+	0.826978i	$0.309942\pi$
$151$			20.3242i			1.65396i	−0.562234	+	0.826978i	$0.690058\pi$
$152$	−4.10037			−0.332584
$153$	−3.70674	+	0.879366i	−0.299672	+	0.0710925i
$154$	1.85790			0.149713
$155$		−	7.78732i		−	0.625493i
$156$	1.27556	+	1.27556i	0.102127	+	0.102127i
$157$	16.4105			1.30970			0.654850	−	0.755758i	$-0.272732\pi$
$157$	16.4105			1.30970			0.654850	+	0.755758i	$0.272732\pi$
$158$	0.788036	+	0.788036i	0.0626928	+	0.0626928i
$159$	6.72365	−	6.72365i	0.533220	−	0.533220i
$160$	−12.0452	+	12.0452i	−0.952255	+	0.952255i
$161$			5.76540i			0.454377i
$162$		−	12.5485i		−	0.985904i
$163$	16.1715	−	16.1715i	1.26665	−	1.26665i	0.318836	−	0.947810i	$-0.396708\pi$
$163$	16.1715	−	16.1715i	1.26665	−	1.26665i	0.947810	−	0.318836i	$-0.103292\pi$
$164$	−23.8925	+	23.8925i	−1.86569	+	1.86569i
$165$	−3.92717	−	3.92717i	−0.305729	−	0.305729i
$166$	−12.3798			−0.960860
$167$	9.94758	+	9.94758i	0.769767	+	0.769767i	0.978065	−	0.208298i	$-0.0667925\pi$
$167$	9.94758	+	9.94758i	0.769767	+	0.769767i	−0.208298	+	0.978065i	$0.566793\pi$
$168$			3.88597i			0.299809i
$169$	−12.8684			−0.989879
$170$	−31.5873	−	19.4739i	−2.42264	−	1.49358i
$171$	1.11778			0.0854786
$172$		−	25.7520i		−	1.96357i
$173$	−8.62128	−	8.62128i	−0.655464	−	0.655464i	0.298840	−	0.954303i	$-0.403400\pi$
$173$	−8.62128	−	8.62128i	−0.655464	−	0.655464i	−0.954303	+	0.298840i	$0.903400\pi$
$174$	−17.3326			−1.31398
$175$	5.54654	+	5.54654i	0.419279	+	0.419279i
$176$	−0.714581	+	0.714581i	−0.0538636	+	0.0538636i
$177$	−4.43480	+	4.43480i	−0.333340	+	0.333340i
$178$		−	5.18715i		−	0.388794i
$179$			0.109646i			0.00819530i	0.999992	+	0.00409765i	$0.00130433\pi$
$179$			0.109646i			0.00819530i	−0.999992	+	0.00409765i	$0.998696\pi$
$180$	−8.69251	+	8.69251i	−0.647902	+	0.647902i
$181$	−2.31574	+	2.31574i	−0.172127	+	0.172127i	−0.787913	−	0.615786i	$-0.788839\pi$
$181$	−2.31574	+	2.31574i	−0.172127	+	0.172127i	0.615786	+	0.787913i	$0.288839\pi$
$182$	0.476519	+	0.476519i	0.0353219	+	0.0353219i
$183$	−14.2349			−1.05227
$184$	−17.3653	−	17.3653i	−1.28019	−	1.28019i
$185$		−	29.0211i		−	2.13367i
$186$	−6.79660			−0.498351
$187$	3.50972	+	2.16377i	0.256656	+	0.158230i
$188$	−18.9794			−1.38422
$189$		−	4.49883i		−	0.327242i
$190$	7.69883	+	7.69883i	0.558532	+	0.558532i
$191$	3.47299			0.251297			0.125648	−	0.992075i	$-0.459899\pi$
$191$	3.47299			0.251297			0.125648	+	0.992075i	$0.459899\pi$
$192$	12.5720	+	12.5720i	0.907303	+	0.907303i
$193$	7.70961	−	7.70961i	0.554950	−	0.554950i	−0.372916	−	0.927865i	$-0.621642\pi$
$193$	7.70961	−	7.70961i	0.554950	−	0.554950i	0.927865	+	0.372916i	$0.121642\pi$
$194$	25.7829	−	25.7829i	1.85110	−	1.85110i
$195$		−	2.01450i		−	0.144262i
$196$		−	21.9761i		−	1.56972i
$197$	10.1583	−	10.1583i	0.723749	−	0.723749i	−0.245618	−	0.969367i	$-0.578991\pi$
$197$	10.1583	−	10.1583i	0.723749	−	0.723749i	0.969367	+	0.245618i	$0.0789907\pi$
$198$	1.52548	−	1.52548i	0.108411	−	0.108411i
$199$	10.7607	+	10.7607i	0.762807	+	0.762807i	0.976829	−	0.214022i	$-0.0686565\pi$
$199$	10.7607	+	10.7607i	0.762807	+	0.762807i	−0.214022	+	0.976829i	$0.568657\pi$
$200$	−33.4122			−2.36260
$201$	−12.8408	−	12.8408i	−0.905717	−	0.905717i
$202$			3.46640i			0.243895i
$203$	−4.09958			−0.287734
$204$	−10.7610	+	17.4548i	−0.753424	+	1.22208i
$205$	37.7335			2.63542
$206$			11.0941i			0.772961i
$207$	4.73385	+	4.73385i	0.329025	+	0.329025i
$208$	−0.366556			−0.0254161
$209$	−0.855428	−	0.855428i	−0.0591712	−	0.0591712i
$210$	7.29626	−	7.29626i	0.503490	−	0.503490i
$211$	−3.82921	+	3.82921i	−0.263614	+	0.263614i	−0.826520	−	0.562907i	$-0.809683\pi$
$211$	−3.82921	+	3.82921i	−0.263614	+	0.263614i	0.562907	+	0.826520i	$0.309683\pi$
$212$			22.7787i			1.56445i
$213$			10.4091i			0.713221i
$214$	−24.5629	+	24.5629i	−1.67908	+	1.67908i
$215$	−20.3351	+	20.3351i	−1.38684	+	1.38684i
$216$	13.5504	+	13.5504i	0.921988	+	0.921988i
$217$	−1.60756			−0.109129
$218$	−18.1609	−	18.1609i	−1.23001	−	1.23001i
$219$			0.944350i			0.0638133i
$220$	13.3047			0.896999
$221$	0.345213	+	1.45515i	0.0232215	+	0.0978842i
$222$	−25.3289			−1.69997
$223$		−	2.68020i		−	0.179479i	−0.995965	−	0.0897397i	$-0.971396\pi$
$223$		−	2.68020i		−	0.179479i	0.995965	−	0.0897397i	$-0.0286035\pi$
$224$	2.48653	+	2.48653i	0.166138	+	0.166138i
$225$	9.10829			0.607219
$226$	−29.3259	−	29.3259i	−1.95073	−	1.95073i
$227$	9.27832	−	9.27832i	0.615824	−	0.615824i	−0.328634	−	0.944457i	$-0.606588\pi$
$227$	9.27832	−	9.27832i	0.615824	−	0.615824i	0.944457	+	0.328634i	$0.106588\pi$
$228$	4.25429	−	4.25429i	0.281747	−	0.281747i
$229$			5.54761i			0.366596i	0.983057	+	0.183298i	$0.0586774\pi$
$229$			5.54761i			0.366596i	−0.983057	+	0.183298i	$0.941323\pi$
$230$			65.2099i			4.29981i
$231$	−0.810699	+	0.810699i	−0.0533401	+	0.0533401i
$232$	12.3479	−	12.3479i	0.810677	−	0.810677i
$233$	4.53854	+	4.53854i	0.297330	+	0.297330i	0.839967	−	0.542637i	$-0.182574\pi$
$233$	4.53854	+	4.53854i	0.297330	+	0.297330i	−0.542637	+	0.839967i	$0.682574\pi$
$234$	0.782518			0.0511548
$235$	14.9871	+	14.9871i	0.977654	+	0.977654i
$236$		−	15.0244i		−	0.978008i
$237$	−0.687724			−0.0446725
$238$	−4.02006	+	6.52068i	−0.260582	+	0.422673i
$239$	−3.74733			−0.242395			−0.121197	−	0.992628i	$-0.538673\pi$
$239$	−3.74733			−0.242395			−0.121197	+	0.992628i	$0.538673\pi$
$240$			5.61256i			0.362289i
$241$	−4.52448	−	4.52448i	−0.291447	−	0.291447i	0.546205	−	0.837652i	$-0.316072\pi$
$241$	−4.52448	−	4.52448i	−0.291447	−	0.291447i	−0.837652	+	0.546205i	$0.816072\pi$
$242$	−2.33488			−0.150092
$243$	−6.51799	−	6.51799i	−0.418129	−	0.418129i
$244$	24.1129	−	24.1129i	1.54367	−	1.54367i
$245$	−17.3535	+	17.3535i	−1.10867	+	1.10867i
$246$		−	32.9330i		−	2.09973i
$247$		−	0.438806i		−	0.0279205i
$248$	4.84195	−	4.84195i	0.307464	−	0.307464i
$249$	5.40197	−	5.40197i	0.342336	−	0.342336i
$250$	30.9147	+	30.9147i	1.95522	+	1.95522i
$251$	9.90043			0.624909			0.312455	−	0.949933i	$-0.398849\pi$
$251$	9.90043			0.624909			0.312455	+	0.949933i	$0.398849\pi$
$252$	1.79443	+	1.79443i	0.113038	+	0.113038i
$253$		−	7.24557i		−	0.455525i
$254$	14.6852			0.921430
$255$	22.2807	−	5.28575i	1.39527	−	0.331007i
$256$	−21.9550			−1.37219
$257$		−	8.63738i		−	0.538785i	−0.963030	−	0.269393i	$-0.913177\pi$
$257$		−	8.63738i		−	0.538785i	0.963030	−	0.269393i	$-0.0868229\pi$
$258$	17.7480	+	17.7480i	1.10495	+	1.10495i
$259$	−5.99092			−0.372258
$260$	3.41242	+	3.41242i	0.211629	+	0.211629i
$261$	−3.36608	+	3.36608i	−0.208355	+	0.208355i
$262$	−26.2264	+	26.2264i	−1.62027	+	1.62027i
$263$			5.85331i			0.360931i	0.983581	+	0.180465i	$0.0577604\pi$
$263$			5.85331i			0.360931i	−0.983581	+	0.180465i	$0.942240\pi$
$264$		−	4.88362i		−	0.300566i
$265$	17.9873	−	17.9873i	1.10495	−	1.10495i
$266$	1.58930	−	1.58930i	0.0974460	−	0.0974460i
$267$	2.26343	+	2.26343i	0.138520	+	0.138520i
$268$	43.5025			2.65734
$269$	7.84274	+	7.84274i	0.478181	+	0.478181i	0.904549	−	0.426369i	$-0.140207\pi$
$269$	7.84274	+	7.84274i	0.478181	+	0.478181i	−0.426369	+	0.904549i	$0.640207\pi$
$270$		−	50.8843i		−	3.09672i
$271$	−29.8121			−1.81096			−0.905478	−	0.424393i	$-0.860488\pi$
$271$	−29.8121			−1.81096			−0.905478	+	0.424393i	$0.860488\pi$
$272$	−0.961788	−	4.05416i	−0.0583169	−	0.245820i
$273$	−0.415861			−0.0251691
$274$		−	37.9492i		−	2.29260i
$275$	−6.97051	−	6.97051i	−0.420338	−	0.420338i
$276$	36.0343			2.16901
$277$	−22.3743	−	22.3743i	−1.34434	−	1.34434i	−0.891686	−	0.452654i	$-0.850477\pi$
$277$	−22.3743	−	22.3743i	−1.34434	−	1.34434i	−0.452654	−	0.891686i	$-0.649523\pi$
$278$	29.2820	−	29.2820i	1.75622	−	1.75622i
$279$	−1.31994	+	1.31994i	−0.0790225	+	0.0790225i
$280$			10.3958i			0.621270i
$281$			12.8229i			0.764952i	0.923965	+	0.382476i	$0.124929\pi$
$281$			12.8229i			0.764952i	−0.923965	+	0.382476i	$0.875071\pi$
$282$	13.0804	−	13.0804i	0.778929	−	0.778929i
$283$	−1.64004	+	1.64004i	−0.0974901	+	0.0974901i	−0.754170	−	0.656680i	$-0.771960\pi$
$283$	−1.64004	+	1.64004i	−0.0974901	+	0.0974901i	0.656680	+	0.754170i	$0.271960\pi$
$284$	−17.6323	−	17.6323i	−1.04628	−	1.04628i
$285$	−6.71882			−0.397988
$286$	−0.598857	−	0.598857i	−0.0354111	−	0.0354111i
$287$		−	7.78947i		−	0.459798i
$288$	4.08327			0.240609
$289$	−15.1884	+	7.63621i	−0.893437	+	0.449189i
$290$	−46.3685			−2.72285
$291$			22.5009i			1.31903i
$292$	−1.59966	−	1.59966i	−0.0936130	−	0.0936130i
$293$	8.79096			0.513573			0.256787	−	0.966468i	$-0.417336\pi$
$293$	8.79096			0.513573			0.256787	+	0.966468i	$0.417336\pi$
$294$	15.1457	+	15.1457i	0.883316	+	0.883316i
$295$	−11.8641	+	11.8641i	−0.690754	+	0.690754i
$296$	18.0445	−	18.0445i	1.04882	−	1.04882i
$297$			5.65383i			0.328068i
$298$			31.1481i			1.80436i
$299$	1.85837	−	1.85837i	0.107472	−	0.107472i
$300$	34.6664	−	34.6664i	2.00146	−	2.00146i
$301$	4.19785	+	4.19785i	0.241960	+	0.241960i
$302$	47.4544			2.73069
$303$	−1.51258	−	1.51258i	−0.0868952	−	0.0868952i
$304$			1.22255i			0.0701178i
$305$	−38.0815			−2.18054
$306$	2.05321	+	8.65477i	0.117374	+	0.494760i
$307$	−0.762924			−0.0435424			−0.0217712	−	0.999763i	$-0.506931\pi$
$307$	−0.762924			−0.0435424			−0.0217712	+	0.999763i	$0.506931\pi$
$308$		−	2.74653i		−	0.156498i
$309$	−4.84094	−	4.84094i	−0.275391	−	0.275391i
$310$	−18.1824			−1.03269
$311$	8.72668	+	8.72668i	0.494844	+	0.494844i	0.909829	−	0.414984i	$-0.136213\pi$
$311$	8.72668	+	8.72668i	0.494844	+	0.494844i	−0.414984	+	0.909829i	$0.636213\pi$
$312$	1.25257	−	1.25257i	0.0709126	−	0.0709126i
$313$	5.68358	−	5.68358i	0.321255	−	0.321255i	−0.527994	−	0.849248i	$-0.677055\pi$
$313$	5.68358	−	5.68358i	0.321255	−	0.321255i	0.849248	+	0.527994i	$0.177055\pi$
$314$		−	38.3165i		−	2.16233i
$315$		−	2.83394i		−	0.159675i
$316$	1.16495	−	1.16495i	0.0655338	−	0.0655338i
$317$	−23.1171	+	23.1171i	−1.29838	+	1.29838i	−0.368926	+	0.929459i	$0.620275\pi$
$317$	−23.1171	+	23.1171i	−1.29838	+	1.29838i	−0.929459	+	0.368926i	$0.879725\pi$
$318$	−15.6989	−	15.6989i	−0.880350	−	0.880350i
$319$	5.15207			0.288461
$320$	33.6328	+	33.6328i	1.88013	+	1.88013i
$321$		−	21.4362i		−	1.19645i
$322$	13.4615			0.750180
$323$	4.85326	−	1.15136i	0.270042	−	0.0640634i
$324$	−18.5505			−1.03058
$325$		−	3.57564i		−	0.198341i
$326$	−37.7583	−	37.7583i	−2.09124	−	2.09124i
$327$	15.8492			0.876461
$328$	23.4617	+	23.4617i	1.29546	+	1.29546i
$329$	3.09385	−	3.09385i	0.170569	−	0.170569i
$330$	−9.16945	+	9.16945i	−0.504761	+	0.504761i
$331$		−	18.8438i		−	1.03575i	−0.855456	−	0.517875i	$-0.826723\pi$
$331$		−	18.8438i		−	1.03575i	0.855456	−	0.517875i	$-0.173277\pi$
$332$			18.3011i			1.00440i
$333$	−4.91901	+	4.91901i	−0.269560	+	0.269560i
$334$	23.2264	−	23.2264i	1.27089	−	1.27089i
$335$	−34.3519	−	34.3519i	−1.87684	−	1.87684i
$336$	1.15862			0.0632079
$337$	5.80117	+	5.80117i	0.316010	+	0.316010i	0.847232	−	0.531223i	$-0.178267\pi$
$337$	5.80117	+	5.80117i	0.316010	+	0.316010i	−0.531223	+	0.847232i	$0.678267\pi$
$338$			30.0462i			1.63430i
$339$	25.5929			1.39002
$340$	−28.7882	+	46.6955i	−1.56126	+	2.53242i
$341$	2.02028			0.109404
$342$		−	2.60987i		−	0.141126i
$343$	7.52092	+	7.52092i	0.406092	+	0.406092i
$344$	−25.2877			−1.36342
$345$	−28.4545	−	28.4545i	−1.53194	−	1.53194i
$346$	−20.1296	+	20.1296i	−1.08218	+	1.08218i
$347$	−4.69149	+	4.69149i	−0.251852	+	0.251852i	−0.821730	−	0.569877i	$-0.806991\pi$
$347$	−4.69149	+	4.69149i	−0.251852	+	0.251852i	0.569877	+	0.821730i	$0.306991\pi$
$348$			25.6227i			1.37352i
$349$		−	1.08752i		−	0.0582135i	−0.999576	−	0.0291068i	$-0.990734\pi$
$349$		−	1.08752i		−	0.0582135i	0.999576	−	0.0291068i	$-0.00926628\pi$
$350$	12.9505	−	12.9505i	0.692233	−	0.692233i
$351$	−1.45011	+	1.45011i	−0.0774012	+	0.0774012i
$352$	−3.12490	−	3.12490i	−0.166558	−	0.166558i
$353$	11.7299			0.624322			0.312161	−	0.950029i	$-0.398947\pi$
$353$	11.7299			0.624322			0.312161	+	0.950029i	$0.398947\pi$
$354$	10.3547	+	10.3547i	0.550347	+	0.550347i
$355$			27.8467i			1.47795i
$356$	−7.66817			−0.406412
$357$	−1.09116	−	4.59949i	−0.0577501	−	0.243431i
$358$	0.256009			0.0135305
$359$			31.8528i			1.68113i	0.541713	+	0.840564i	$0.317776\pi$
$359$			31.8528i			1.68113i	−0.541713	+	0.840564i	$0.682224\pi$
$360$	8.53579	+	8.53579i	0.449876	+	0.449876i
$361$	17.5365			0.922973
$362$	5.40696	+	5.40696i	0.284183	+	0.284183i
$363$	1.01883	−	1.01883i	0.0534747	−	0.0534747i
$364$	0.704438	−	0.704438i	0.0369226	−	0.0369226i
$365$			2.52635i			0.132235i
$366$			33.2367i			1.73731i
$367$	−13.0410	+	13.0410i	−0.680733	+	0.680733i	−0.960165	−	0.279433i	$-0.909854\pi$
$367$	−13.0410	+	13.0410i	−0.680733	+	0.680733i	0.279433	+	0.960165i	$0.409854\pi$
$368$	−5.17754	+	5.17754i	−0.269898	+	0.269898i
$369$	−6.39576	−	6.39576i	−0.332950	−	0.332950i
$370$	−67.7606			−3.52270
$371$	−3.71317	−	3.71317i	−0.192778	−	0.192778i
$372$			10.0474i			0.520934i
$373$	24.2027			1.25317			0.626585	−	0.779353i	$-0.284452\pi$
$373$	24.2027			1.25317			0.626585	+	0.779353i	$0.284452\pi$
$374$	5.05213	−	8.19475i	0.261240	−	0.423740i
$375$	−26.9795			−1.39321
$376$			18.6372i			0.961142i
$377$	1.32142	+	1.32142i	0.0680566	+	0.0680566i
$378$	−10.5042			−0.540279
$379$	−17.6260	−	17.6260i	−0.905389	−	0.905389i	0.0905071	−	0.995896i	$-0.471151\pi$
$379$	−17.6260	−	17.6260i	−0.905389	−	0.905389i	−0.995896	+	0.0905071i	$0.971151\pi$
$380$	11.3812	−	11.3812i	0.583842	−	0.583842i
$381$	−6.40793	+	6.40793i	−0.328288	+	0.328288i
$382$		−	8.10900i		−	0.414892i
$383$		−	3.05402i		−	0.156053i	−0.996951	−	0.0780266i	$-0.975138\pi$
$383$		−	3.05402i		−	0.156053i	0.996951	−	0.0780266i	$-0.0248619\pi$
$384$	20.3490	−	20.3490i	1.03843	−	1.03843i
$385$	−2.16880	+	2.16880i	−0.110532	+	0.110532i
$386$	−18.0010	−	18.0010i	−0.916226	−	0.916226i
$387$	6.89353			0.350418
$388$	−38.1148	−	38.1148i	−1.93499	−	1.93499i
$389$			3.18668i			0.161571i	0.996732	+	0.0807855i	$0.0257429\pi$
$389$			3.18668i			0.161571i	−0.996732	+	0.0807855i	$0.974257\pi$
$390$	−4.70362			−0.238177
$391$	25.4299	+	15.6777i	1.28604	+	0.792857i
$392$	−21.5799			−1.08995
$393$		−	22.8879i		−	1.15454i
$394$	−23.7184	−	23.7184i	−1.19491	−	1.19491i
$395$	−1.83982			−0.0925712
$396$	−2.25511	−	2.25511i	−0.113324	−	0.113324i
$397$	−21.3004	+	21.3004i	−1.06904	+	1.06904i	−0.0716045	+	0.997433i	$0.522812\pi$
$397$	−21.3004	+	21.3004i	−1.06904	+	1.06904i	−0.997433	+	0.0716045i	$0.977188\pi$
$398$	25.1249	−	25.1249i	1.25940	−	1.25940i
$399$			1.38699i			0.0694363i
$400$			9.96199i			0.498100i
$401$	−8.75075	+	8.75075i	−0.436991	+	0.436991i	−0.890998	−	0.454007i	$-0.849994\pi$
$401$	−8.75075	+	8.75075i	−0.436991	+	0.436991i	0.454007	+	0.890998i	$0.349994\pi$
$402$	−29.9816	+	29.9816i	−1.49534	+	1.49534i
$403$	0.518167	+	0.518167i	0.0258117	+	0.0258117i
$404$	5.12438			0.254948
$405$	14.6484	+	14.6484i	0.727886	+	0.727886i
$406$			9.57201i			0.475051i
$407$	7.52898			0.373198
$408$	17.1401	+	10.5670i	0.848562	+	0.523146i
$409$	−19.9339			−0.985668			−0.492834	−	0.870123i	$-0.664039\pi$
$409$	−19.9339			−0.985668			−0.492834	+	0.870123i	$0.664039\pi$
$410$		−	88.1031i		−	4.35110i
$411$	16.5593	+	16.5593i	0.816808	+	0.816808i
$412$	16.4004			0.807988
$413$	2.44915	+	2.44915i	0.120515	+	0.120515i
$414$	11.0529	−	11.0529i	0.543222	−	0.543222i
$415$	14.4515	−	14.4515i	0.709395	−	0.709395i
$416$		−	1.60297i		−	0.0785920i
$417$			25.5546i			1.25142i
$418$	−1.99732	+	1.99732i	−0.0976920	+	0.0976920i
$419$	−9.80854	+	9.80854i	−0.479178	+	0.479178i	−0.904869	−	0.425690i	$-0.860031\pi$
$419$	−9.80854	+	9.80854i	−0.479178	+	0.479178i	0.425690	+	0.904869i	$0.360031\pi$
$420$	−10.7861	−	10.7861i	−0.526306	−	0.526306i
$421$	−8.85304			−0.431471			−0.215735	−	0.976452i	$-0.569215\pi$
$421$	−8.85304			−0.431471			−0.215735	+	0.976452i	$0.569215\pi$
$422$	8.94073	+	8.94073i	0.435228	+	0.435228i
$423$		−	5.08058i		−	0.247026i
$424$	22.3680			1.08629
$425$	39.5471	−	9.38194i	1.91832	−	0.455091i
$426$	24.3040			1.17753
$427$			7.86131i			0.380435i
$428$	36.3113	+	36.3113i	1.75517	+	1.75517i
$429$	0.522626			0.0252326
$430$	47.4800	+	47.4800i	2.28969	+	2.28969i
$431$	15.8154	−	15.8154i	0.761800	−	0.761800i	−0.214847	−	0.976648i	$-0.568925\pi$
$431$	15.8154	−	15.8154i	0.761800	−	0.761800i	0.976648	+	0.214847i	$0.0689254\pi$
$432$	4.04012	−	4.04012i	0.194380	−	0.194380i
$433$			9.62857i			0.462720i	0.972868	+	0.231360i	$0.0743175\pi$
$433$			9.62857i			0.462720i	−0.972868	+	0.231360i	$0.925683\pi$
$434$			3.75346i			0.180172i
$435$	20.2330	−	20.2330i	0.970100	−	0.970100i
$436$	−26.8473	+	26.8473i	−1.28575	+	1.28575i
$437$	−6.19806	−	6.19806i	−0.296493	−	0.296493i
$438$	2.20494			0.105356
$439$	−17.5748	−	17.5748i	−0.838799	−	0.838799i	0.149902	−	0.988701i	$-0.452104\pi$
$439$	−17.5748	−	17.5748i	−0.838799	−	0.838799i	−0.988701	+	0.149902i	$0.952104\pi$
$440$		−	13.0648i		−	0.622839i
$441$	5.88275			0.280131
$442$	3.39760	−	0.806029i	0.161608	−	0.0383389i
$443$	−26.2840			−1.24879			−0.624395	−	0.781109i	$-0.714654\pi$
$443$	−26.2840			−1.24879			−0.624395	+	0.781109i	$0.714654\pi$
$444$			37.4438i			1.77700i
$445$	6.05518	+	6.05518i	0.287043	+	0.287043i
$446$	−6.25793			−0.296322
$447$	−13.5916	−	13.5916i	−0.642858	−	0.642858i
$448$	6.94294	−	6.94294i	0.328023	−	0.328023i
$449$	2.97501	−	2.97501i	0.140400	−	0.140400i	−0.633414	−	0.773813i	$-0.718347\pi$
$449$	2.97501	−	2.97501i	0.140400	−	0.140400i	0.773813	+	0.633414i	$0.218347\pi$
$450$		−	21.2667i		−	1.00252i
$451$			9.78927i			0.460959i
$452$	−43.3525	+	43.3525i	−2.03913	+	2.03913i
$453$	−20.7069	+	20.7069i	−0.972894	+	0.972894i
$454$	−21.6637	−	21.6637i	−1.01673	−	1.01673i
$455$	−1.11252			−0.0521558
$456$	−4.17758	−	4.17758i	−0.195633	−	0.195633i
$457$			12.0254i			0.562525i	0.959631	+	0.281262i	$0.0907531\pi$
$457$			12.0254i			0.562525i	−0.959631	+	0.281262i	$0.909247\pi$
$458$	12.9530			0.605253
$459$	−19.8433	−	12.2336i	−0.926207	−	0.571014i
$460$	96.3997			4.49466
$461$			21.5907i			1.00558i	0.864408	+	0.502791i	$0.167693\pi$
$461$			21.5907i			1.00558i	−0.864408	+	0.502791i	$0.832307\pi$
$462$	1.89288	+	1.89288i	0.0880648	+	0.0880648i
$463$	−3.16294			−0.146994			−0.0734971	−	0.997295i	$-0.523416\pi$
$463$	−3.16294			−0.146994			−0.0734971	+	0.997295i	$0.523416\pi$
$464$	−3.68157	−	3.68157i	−0.170913	−	0.170913i
$465$	7.93396	−	7.93396i	0.367929	−	0.367929i
$466$	10.5969	−	10.5969i	0.490894	−	0.490894i
$467$			6.05087i			0.280001i	0.990151	+	0.140000i	$0.0447104\pi$
$467$			6.05087i			0.280001i	−0.990151	+	0.140000i	$0.955290\pi$
$468$		−	1.15680i		−	0.0534729i
$469$	−7.09138	+	7.09138i	−0.327449	+	0.327449i
$470$	34.9931	−	34.9931i	1.61411	−	1.61411i
$471$	16.7195	+	16.7195i	0.770395	+	0.770395i
$472$	−14.7536			−0.679088
$473$	−5.27557	−	5.27557i	−0.242571	−	0.242571i
$474$			1.60575i			0.0737546i
$475$	−11.9255			−0.547182
$476$	9.63952	+	5.94285i	0.441827	+	0.272390i
$477$	−6.09761			−0.279190
$478$			8.74955i			0.400195i
$479$	−7.11080	−	7.11080i	−0.324901	−	0.324901i	0.525743	−	0.850644i	$-0.323787\pi$
$479$	−7.11080	−	7.11080i	−0.324901	−	0.324901i	−0.850644	+	0.525743i	$0.823787\pi$
$480$	−24.5440			−1.12027
$481$	1.93106	+	1.93106i	0.0880486	+	0.0880486i
$482$	−10.5641	+	10.5641i	−0.481181	+	0.481181i
$483$	−5.87397	+	5.87397i	−0.267275	+	0.267275i
$484$			3.45165i			0.156893i
$485$			60.1950i			2.73331i
$486$	−15.2187	+	15.2187i	−0.690335	+	0.690335i
$487$	2.71124	−	2.71124i	0.122858	−	0.122858i	−0.643004	−	0.765862i	$-0.722312\pi$
$487$	2.71124	−	2.71124i	0.122858	−	0.122858i	0.765862	+	0.643004i	$0.222312\pi$
$488$	−23.6781	−	23.6781i	−1.07186	−	1.07186i
$489$	32.9519			1.49014
$490$	40.5182	+	40.5182i	1.83042	+	1.83042i
$491$			24.4349i			1.10273i	0.834264	+	0.551365i	$0.185893\pi$
$491$			24.4349i			1.10273i	−0.834264	+	0.551365i	$0.814107\pi$
$492$	−48.6848			−2.19488
$493$	−11.1479	+	18.0823i	−0.502076	+	0.814386i
$494$	−1.02456			−0.0460970
$495$			3.56151i			0.160078i
$496$	−1.44365	−	1.44365i	−0.0648219	−	0.0648219i
$497$	5.74850			0.257855
$498$	−12.6129	−	12.6129i	−0.565199	−	0.565199i
$499$	4.85116	−	4.85116i	0.217168	−	0.217168i	−0.590136	−	0.807304i	$-0.700926\pi$
$499$	4.85116	−	4.85116i	0.217168	−	0.217168i	0.807304	+	0.590136i	$0.200926\pi$
$500$	45.7012	−	45.7012i	2.04382	−	2.04382i
$501$			20.2698i			0.905588i
$502$		−	23.1163i		−	1.03173i
$503$	28.4646	−	28.4646i	1.26917	−	1.26917i	0.322657	−	0.946516i	$-0.395424\pi$
$503$	28.4646	−	28.4646i	1.26917	−	1.26917i	0.946516	−	0.322657i	$-0.104576\pi$
$504$	1.76207	−	1.76207i	0.0784890	−	0.0784890i
$505$	−4.04648	−	4.04648i	−0.180066	−	0.180066i
$506$	−16.9175			−0.752074
$507$	−13.1108	−	13.1108i	−0.582269	−	0.582269i
$508$		−	21.7091i		−	0.963185i
$509$	−5.23708			−0.232130			−0.116065	−	0.993242i	$-0.537028\pi$
$509$	−5.23708			−0.232130			−0.116065	+	0.993242i	$0.537028\pi$
$510$	−12.3416	−	52.0227i	−0.546494	−	2.30360i
$511$	0.521523			0.0230708
$512$			11.3165i			0.500122i
$513$	4.83644	+	4.83644i	0.213534	+	0.213534i
$514$	−20.1672			−0.889538
$515$	−12.9506	−	12.9506i	−0.570671	−	0.570671i
$516$	26.2369	−	26.2369i	1.15502	−	1.15502i
$517$	−3.88814	+	3.88814i	−0.171000	+	0.171000i
$518$			13.9881i			0.614600i
$519$		−	17.5672i		−	0.771117i
$520$	3.35090	−	3.35090i	0.146946	−	0.146946i
$521$	2.16944	−	2.16944i	0.0950448	−	0.0950448i	−0.657986	−	0.753030i	$-0.728591\pi$
$521$	2.16944	−	2.16944i	0.0950448	−	0.0950448i	0.753030	+	0.657986i	$0.228591\pi$
$522$	7.85937	+	7.85937i	0.343995	+	0.343995i
$523$	15.8960			0.695084			0.347542	−	0.937664i	$-0.387016\pi$
$523$	15.8960			0.695084			0.347542	+	0.937664i	$0.387016\pi$
$524$	38.7704	+	38.7704i	1.69369	+	1.69369i
$525$			11.3020i			0.493259i
$526$	13.6668			0.595899
$527$	−4.37141	+	7.09060i	−0.190422	+	0.308871i
$528$	−1.45607			−0.0633675
$529$		−	29.4982i		−	1.28253i
$530$	−41.9980	−	41.9980i	−1.82428	−	1.82428i
$531$	4.02188			0.174535
$532$	−2.34946	−	2.34946i	−0.101862	−	0.101862i
$533$	−2.51078	+	2.51078i	−0.108754	+	0.108754i
$534$	5.28483	−	5.28483i	0.228697	−	0.228697i
$535$		−	57.3466i		−	2.47931i
$536$		−	42.7182i		−	1.84515i
$537$	−0.111710	+	0.111710i	−0.00482066	+	0.00482066i
$538$	18.3118	−	18.3118i	0.789479	−	0.789479i
$539$	−4.50203	−	4.50203i	−0.193916	−	0.193916i
$540$	−75.2222			−3.23705
$541$	13.5178	+	13.5178i	0.581177	+	0.581177i	0.935227	−	0.354050i	$-0.115196\pi$
$541$	13.5178	+	13.5178i	0.581177	+	0.581177i	−0.354050	+	0.935227i	$0.615196\pi$
$542$			69.6076i			2.98990i
$543$	−4.71869			−0.202498
$544$	17.7291	−	4.20594i	0.760127	−	0.180328i
$545$	42.4001			1.81622
$546$			0.970984i			0.0415543i
$547$	4.17448	+	4.17448i	0.178488	+	0.178488i	0.790696	−	0.612209i	$-0.209719\pi$
$547$	4.17448	+	4.17448i	0.178488	+	0.178488i	−0.612209	+	0.790696i	$0.709719\pi$
$548$	−56.1003			−2.39649
$549$	6.45474	+	6.45474i	0.275482	+	0.275482i
$550$	−16.2753	+	16.2753i	−0.693981	+	0.693981i
$551$	4.40723	−	4.40723i	0.187754	−	0.187754i
$552$		−	35.3846i		−	1.50607i
$553$			0.379800i			0.0161507i
$554$	−52.2412	+	52.2412i	−2.21952	+	2.21952i
$555$	29.5675	−	29.5675i	1.25507	−	1.25507i
$556$	−43.2876	−	43.2876i	−1.83580	−	1.83580i
$557$	−7.01099			−0.297065			−0.148533	−	0.988908i	$-0.547455\pi$
$557$	−7.01099			−0.297065			−0.148533	+	0.988908i	$0.547455\pi$
$558$	3.08189	+	3.08189i	0.130467	+	0.130467i
$559$		−	2.70619i		−	0.114460i
$560$	3.09957			0.130981
$561$	1.37129	+	5.78032i	0.0578960	+	0.244045i
$562$	29.9400			1.26294
$563$		−	37.3800i		−	1.57538i	−0.616072	−	0.787690i	$-0.711277\pi$
$563$		−	37.3800i		−	1.57538i	0.616072	−	0.787690i	$-0.288723\pi$
$564$	−19.3368	−	19.3368i	−0.814227	−	0.814227i
$565$	68.4668			2.88042
$566$	3.82928	+	3.82928i	0.160957	+	0.160957i
$567$	3.02392	−	3.02392i	0.126993	−	0.126993i
$568$	−17.3144	+	17.3144i	−0.726494	+	0.726494i
$569$		−	4.24381i		−	0.177910i	−0.996036	−	0.0889549i	$-0.971647\pi$
$569$		−	4.24381i		−	0.177910i	0.996036	−	0.0889549i	$-0.0283527\pi$
$570$			15.6876i			0.657081i
$571$	−4.47971	+	4.47971i	−0.187470	+	0.187470i	−0.794601	−	0.607132i	$-0.792320\pi$
$571$	−4.47971	+	4.47971i	−0.187470	+	0.187470i	0.607132	+	0.794601i	$0.292320\pi$
$572$	−0.885289	+	0.885289i	−0.0370158	+	0.0370158i
$573$	3.53839	+	3.53839i	0.147818	+	0.147818i
$574$	−18.1874			−0.759129
$575$	−50.5053	−	50.5053i	−2.10622	−	2.10622i
$576$		−	11.4014i		−	0.475058i
$577$	−25.4210			−1.05829			−0.529144	−	0.848532i	$-0.677487\pi$
$577$	−25.4210			−1.05829			−0.529144	+	0.848532i	$0.677487\pi$
$578$	17.8296	+	35.4631i	0.741613	+	1.47507i
$579$	15.7096			0.652867
$580$			68.5465i			2.84624i
$581$	−2.98327	−	2.98327i	−0.123767	−	0.123767i
$582$	52.5368			2.17772
$583$	4.66646	+	4.66646i	0.193265	+	0.193265i
$584$	−1.57082	+	1.57082i	−0.0650009	+	0.0650009i
$585$	−0.913467	+	0.913467i	−0.0377672	+	0.0377672i
$586$		−	20.5258i		−	0.847913i
$587$		−	21.8654i		−	0.902481i	−0.892402	−	0.451241i	$-0.850982\pi$
$587$		−	21.8654i		−	0.902481i	0.892402	−	0.451241i	$-0.149018\pi$
$588$	22.3899	−	22.3899i	0.923344	−	0.923344i
$589$	1.72820	−	1.72820i	0.0712093	−	0.0712093i
$590$	27.7012	+	27.7012i	1.14044	+	1.14044i
$591$	20.6992			0.851451
$592$	−5.38006	−	5.38006i	−0.221119	−	0.221119i
$593$		−	41.4653i		−	1.70277i	−0.524537	−	0.851387i	$-0.675762\pi$
$593$		−	41.4653i		−	1.70277i	0.524537	−	0.851387i	$-0.324238\pi$
$594$	13.2010			0.541643
$595$	−2.91909	−	12.3047i	−0.119671	−	0.504442i
$596$	46.0462			1.88612
$597$			21.9267i			0.897400i
$598$	−4.33905	−	4.33905i	−0.177437	−	0.177437i
$599$	−26.9148			−1.09971			−0.549855	−	0.835260i	$-0.685317\pi$
$599$	−26.9148			−1.09971			−0.549855	+	0.835260i	$0.685317\pi$
$600$	−34.0413	−	34.0413i	−1.38973	−	1.38973i
$601$	−23.3615	+	23.3615i	−0.952937	+	0.952937i	−0.998941	−	0.0460047i	$-0.985351\pi$
$601$	−23.3615	+	23.3615i	−0.952937	+	0.952937i	0.0460047	+	0.998941i	$0.485351\pi$
$602$	9.80146	−	9.80146i	0.399478	−	0.399478i
$603$			11.6452i			0.474227i
$604$		−	70.1518i		−	2.85444i
$605$	2.72560	−	2.72560i	0.110811	−	0.110811i
$606$	−3.53168	+	3.53168i	−0.143465	+	0.143465i
$607$	−1.91710	−	1.91710i	−0.0778125	−	0.0778125i	0.667129	−	0.744942i	$-0.267523\pi$
$607$	−1.91710	−	1.91710i	−0.0778125	−	0.0778125i	−0.744942	+	0.667129i	$0.767523\pi$
$608$	−5.34625			−0.216819
$609$	−4.17678	−	4.17678i	−0.169252	−	0.169252i
$610$			88.9157i			3.60009i
$611$	−1.99448			−0.0806882
$612$	12.7943	−	3.03526i	0.517181	−	0.122693i
$613$	2.69483			0.108843			0.0544216	−	0.998518i	$-0.482668\pi$
$613$	2.69483			0.108843			0.0544216	+	0.998518i	$0.482668\pi$
$614$			1.78133i			0.0718888i
$615$	38.4441	+	38.4441i	1.55022	+	1.55022i
$616$	−2.69701			−0.108666
$617$	−26.0289	−	26.0289i	−1.04788	−	1.04788i	−0.998794	−	0.0490902i	$-0.984368\pi$
$617$	−26.0289	−	26.0289i	−1.04788	−	1.04788i	−0.0490902	−	0.998794i	$-0.515632\pi$
$618$	−11.3030	+	11.3030i	−0.454673	+	0.454673i
$619$	27.2879	−	27.2879i	1.09679	−	1.09679i	0.102012	−	0.994783i	$-0.467472\pi$
$619$	27.2879	−	27.2879i	1.09679	−	1.09679i	0.994783	−	0.102012i	$-0.0325279\pi$
$620$			26.8791i			1.07949i
$621$			40.9652i			1.64388i
$622$	20.3757	−	20.3757i	0.816992	−	0.816992i
$623$	1.24999	−	1.24999i	0.0500799	−	0.0500799i
$624$	−0.373459	−	0.373459i	−0.0149503	−	0.0149503i
$625$	−22.8872			−0.915487
$626$	−13.2704	−	13.2704i	−0.530394	−	0.530394i
$627$		−	1.74307i		−	0.0696116i
$628$	−56.6433			−2.26031
$629$	−16.2910	+	26.4246i	−0.649563	+	1.05362i
$630$	−6.61691			−0.263624
$631$			21.0817i			0.839248i	0.907698	+	0.419624i	$0.137838\pi$
$631$			21.0817i			0.839248i	−0.907698	+	0.419624i	$0.862162\pi$
$632$	−1.14395	−	1.14395i	−0.0455039	−	0.0455039i
$633$	−7.80264			−0.310127
$634$	53.9755	+	53.9755i	2.14364	+	2.14364i
$635$	−17.1426	+	17.1426i	−0.680285	+	0.680285i
$636$	−23.2076	+	23.2076i	−0.920243	+	0.920243i
$637$		−	2.30939i		−	0.0915015i
$638$		−	12.0295i		−	0.476251i
$639$	4.71996	−	4.71996i	0.186719	−	0.186719i
$640$	54.4381	−	54.4381i	2.15185	−	2.15185i
$641$	12.8872	+	12.8872i	0.509014	+	0.509014i	0.914224	−	0.405210i	$-0.132802\pi$
$641$	12.8872	+	12.8872i	0.509014	+	0.509014i	−0.405210	+	0.914224i	$0.632802\pi$
$642$	−50.0509			−1.97535
$643$	−23.6495	−	23.6495i	−0.932645	−	0.932645i	0.0652258	−	0.997871i	$-0.479223\pi$
$643$	−23.6495	−	23.6495i	−0.932645	−	0.932645i	−0.997871	+	0.0652258i	$0.979223\pi$
$644$		−	19.9001i		−	0.784175i
$645$	−41.4361			−1.63154
$646$	−2.68828	−	11.3318i	−0.105769	−	0.445842i
$647$	−14.4653			−0.568691			−0.284345	−	0.958722i	$-0.591776\pi$
$647$	−14.4653			−0.568691			−0.284345	+	0.958722i	$0.591776\pi$
$648$			18.2160i			0.715592i
$649$	−3.07792	−	3.07792i	−0.120819	−	0.120819i
$650$	−8.34868			−0.327462
$651$	−1.63784	−	1.63784i	−0.0641918	−	0.0641918i
$652$	−55.8181	+	55.8181i	−2.18601	+	2.18601i
$653$	14.7016	−	14.7016i	0.575317	−	0.575317i	−0.358292	−	0.933609i	$-0.616641\pi$
$653$	14.7016	−	14.7016i	0.575317	−	0.575317i	0.933609	+	0.358292i	$0.116641\pi$
$654$		−	37.0058i		−	1.44704i
$655$		−	61.2303i		−	2.39246i
$656$	6.99523	−	6.99523i	0.273118	−	0.273118i
$657$	0.428211	−	0.428211i	0.0167061	−	0.0167061i
$658$	−7.22376	−	7.22376i	−0.281611	−	0.281611i
$659$	9.46965			0.368885			0.184443	−	0.982843i	$-0.440952\pi$
$659$	9.46965			0.368885			0.184443	+	0.982843i	$0.440952\pi$
$660$	13.5552	+	13.5552i	0.527635	+	0.527635i
$661$		−	11.3821i		−	0.442712i	−0.975193	−	0.221356i	$-0.928952\pi$
$661$		−	11.3821i		−	0.442712i	0.975193	−	0.221356i	$-0.0710483\pi$
$662$	−43.9980			−1.71003
$663$	−1.13084	+	1.83427i	−0.0439183	+	0.0712371i
$664$	17.9711			0.697414
$665$			3.71051i			0.143887i
$666$	11.4853	+	11.4853i	0.445046	+	0.445046i
$667$	37.3297			1.44541
$668$	−34.3355	−	34.3355i	−1.32848	−	1.32848i
$669$	2.73067	−	2.73067i	0.105574	−	0.105574i
$670$	−80.2074	+	80.2074i	−3.09868	+	3.09868i
$671$		−	9.87955i		−	0.381396i
$672$			5.06670i			0.195452i
$673$	6.28846	−	6.28846i	0.242402	−	0.242402i	−0.575441	−	0.817843i	$-0.695170\pi$
$673$	6.28846	−	6.28846i	0.242402	−	0.242402i	0.817843	+	0.575441i	$0.195170\pi$
$674$	13.5450	−	13.5450i	0.521734	−	0.521734i
$675$	39.4101	+	39.4101i	1.51689	+	1.51689i
$676$	44.4173			1.70836
$677$	5.15721	+	5.15721i	0.198208	+	0.198208i	0.799231	−	0.601024i	$-0.205240\pi$
$677$	5.15721	+	5.15721i	0.198208	+	0.198208i	−0.601024	+	0.799231i	$0.705240\pi$
$678$		−	59.7563i		−	2.29493i
$679$	12.4263			0.476876
$680$	45.8536	+	28.2692i	1.75841	+	1.08407i
$681$	18.9061			0.724482
$682$		−	4.71710i		−	0.180627i
$683$	−27.9704	−	27.9704i	−1.07026	−	1.07026i	−0.997338	−	0.0729210i	$-0.976768\pi$
$683$	−27.9704	−	27.9704i	−1.07026	−	1.07026i	−0.0729210	−	0.997338i	$-0.523232\pi$
$684$	−3.85817			−0.147521
$685$	44.2997	+	44.2997i	1.69261	+	1.69261i
$686$	17.5604	−	17.5604i	0.670460	−	0.670460i
$687$	−5.65208	+	5.65208i	−0.215640	+	0.215640i
$688$			7.53965i			0.287446i
$689$			2.39374i			0.0911942i
$690$	−66.4378	+	66.4378i	−2.52924	+	2.52924i
$691$	7.29801	−	7.29801i	0.277629	−	0.277629i	−0.554533	−	0.832162i	$-0.687103\pi$
$691$	7.29801	−	7.29801i	0.277629	−	0.277629i	0.832162	+	0.554533i	$0.187103\pi$
$692$	29.7576	+	29.7576i	1.13121	+	1.13121i
$693$	0.735215			0.0279285
$694$	10.9540	+	10.9540i	0.415810	+	0.415810i
$695$			68.3643i			2.59321i
$696$	25.1608			0.953716
$697$	−34.3576	−	21.1817i	−1.30139	−	0.802315i
$698$	−2.53922			−0.0961109
$699$			9.24801i			0.349792i
$700$	−19.1447	−	19.1447i	−0.723602	−	0.723602i
$701$	27.7211			1.04701			0.523506	−	0.852022i	$-0.324624\pi$
$701$	27.7211			1.04701			0.523506	+	0.852022i	$0.324624\pi$
$702$	3.38583	+	3.38583i	0.127790	+	0.127790i
$703$	6.44050	−	6.44050i	0.242908	−	0.242908i
$704$	−8.72541	+	8.72541i	−0.328851	+	0.328851i
$705$			30.5387i			1.15016i
$706$		−	27.3879i		−	1.03076i
$707$	−0.835329	+	0.835329i	−0.0314158	+	0.0314158i
$708$	15.3074	−	15.3074i	0.575286	−	0.575286i
$709$	18.0401	+	18.0401i	0.677511	+	0.677511i	0.959436	−	0.281925i	$-0.0909731\pi$
$709$	18.0401	+	18.0401i	0.677511	+	0.677511i	−0.281925	+	0.959436i	$0.590973\pi$
$710$	65.0186			2.44011
$711$	0.311845	+	0.311845i	0.0116951	+	0.0116951i
$712$			7.52991i			0.282195i
$713$	14.6380			0.548199
$714$	−10.7392	+	2.54772i	−0.401906	+	0.0953459i
$715$	1.39814			0.0522875
$716$		−	0.378458i		−	0.0141436i
$717$	−3.81790	−	3.81790i	−0.142582	−	0.142582i
$718$	74.3724			2.77555
$719$	11.7563	+	11.7563i	0.438437	+	0.438437i	0.891486	−	0.453049i	$-0.149664\pi$
$719$	11.7563	+	11.7563i	0.438437	+	0.438437i	−0.453049	+	0.891486i	$0.649664\pi$
$720$	2.54499	−	2.54499i	0.0948460	−	0.0948460i
$721$	−2.67343	+	2.67343i	−0.0995639	+	0.0995639i
$722$		−	40.9455i		−	1.52383i
$723$		−	9.21935i		−	0.342871i
$724$	7.99310	−	7.99310i	0.297061	−	0.297061i
$725$	35.9126	−	35.9126i	1.33376	−	1.33376i
$726$	−2.37884	−	2.37884i	−0.0882872	−	0.0882872i
$727$	18.0642			0.669963			0.334982	−	0.942225i	$-0.391270\pi$
$727$	18.0642			0.669963			0.334982	+	0.942225i	$0.391270\pi$
$728$	−0.691737	−	0.691737i	−0.0256375	−	0.0256375i
$729$		−	29.4046i		−	1.08906i
$730$	5.89871			0.218321
$731$	29.9309	−	7.10064i	1.10703	−	0.262627i
$732$	49.1338			1.81604
$733$			47.0007i			1.73601i	0.496555	+	0.868005i	$0.334598\pi$
$733$			47.0007i			1.73601i	−0.496555	+	0.868005i	$0.665402\pi$
$734$	30.4490	+	30.4490i	1.12389	+	1.12389i
$735$	−35.3605			−1.30429
$736$	−22.6417	−	22.6417i	−0.834582	−	0.834582i
$737$	8.91196	−	8.91196i	0.328276	−	0.328276i
$738$	−14.9333	+	14.9333i	−0.549703	+	0.549703i
$739$			9.93027i			0.365291i	0.983179	+	0.182646i	$0.0584661\pi$
$739$			9.93027i			0.365291i	−0.983179	+	0.182646i	$0.941534\pi$
$740$			100.170i			3.68234i
$741$	0.447069	−	0.447069i	0.0164235	−	0.0164235i
$742$	−8.66980	+	8.66980i	−0.318278	+	0.318278i
$743$	−25.6831	−	25.6831i	−0.942221	−	0.942221i	0.0561988	−	0.998420i	$-0.482102\pi$
$743$	−25.6831	−	25.6831i	−0.942221	−	0.942221i	−0.998420	+	0.0561988i	$0.982102\pi$
$744$	9.86626			0.361715
$745$	−36.3605	−	36.3605i	−1.33214	−	1.33214i
$746$		−	56.5104i		−	2.06899i
$747$	−4.89900			−0.179245
$748$	−12.1143	−	7.46857i	−0.442943	−	0.273078i
$749$	−11.8383			−0.432561
$750$			62.9937i			2.30021i
$751$	2.82101	+	2.82101i	0.102940	+	0.102940i	0.756701	−	0.653761i	$-0.226810\pi$
$751$	2.82101	+	2.82101i	0.102940	+	0.102940i	−0.653761	+	0.756701i	$0.726810\pi$
$752$	5.55678			0.202635
$753$	10.0869	+	10.0869i	0.367586	+	0.367586i
$754$	3.08535	−	3.08535i	0.112362	−	0.112362i
$755$	−55.3955	+	55.3955i	−2.01605	+	2.01605i
$756$			15.5284i			0.564762i
$757$		−	49.1783i		−	1.78741i	−0.448651	−	0.893707i	$-0.648095\pi$
$757$		−	49.1783i		−	1.78741i	0.448651	−	0.893707i	$-0.351905\pi$
$758$	−41.1546	+	41.1546i	−1.49480	+	1.49480i
$759$	7.38200	−	7.38200i	0.267950	−	0.267950i
$760$	−11.1760	−	11.1760i	−0.405395	−	0.405395i
$761$	−40.0043			−1.45015			−0.725077	−	0.688667i	$-0.758196\pi$
$761$	−40.0043			−1.45015			−0.725077	+	0.688667i	$0.758196\pi$
$762$	14.9617	+	14.9617i	0.542006	+	0.542006i
$763$		−	8.75279i		−	0.316872i
$764$	−11.9875			−0.433693
$765$	−12.4999	−	7.70628i	−0.451934	−	0.278621i
$766$	−7.13076			−0.257645
$767$		−	1.57887i		−	0.0570097i
$768$	−22.3684	−	22.3684i	−0.807152	−	0.807152i
$769$	−49.8791			−1.79868			−0.899342	−	0.437245i	$-0.855954\pi$
$769$	−49.8791			−1.79868			−0.899342	+	0.437245i	$0.855954\pi$
$770$	5.06388	+	5.06388i	0.182490	+	0.182490i
$771$	8.80003	−	8.80003i	0.316925	−	0.316925i
$772$	−26.6108	+	26.6108i	−0.957745	+	0.957745i
$773$		−	5.80813i		−	0.208904i	−0.994530	−	0.104452i	$-0.966691\pi$
$773$		−	5.80813i		−	0.208904i	0.994530	−	0.104452i	$-0.0333089\pi$
$774$		−	16.0955i		−	0.578542i
$775$	14.0824	−	14.0824i	0.505854	−	0.505854i
$776$	−37.4276	+	37.4276i	−1.34357	+	1.34357i
$777$	−6.10373	−	6.10373i	−0.218970	−	0.218970i
$778$	7.44050			0.266755
$779$	8.37402	+	8.37402i	0.300030	+	0.300030i
$780$			6.95336i			0.248970i
$781$	−7.22432			−0.258506
$782$	36.6056	−	59.3756i	1.30901	−	2.12327i
$783$	−29.1289			−1.04098
$784$			6.43414i			0.229791i
$785$	44.7285	+	44.7285i	1.59643	+	1.59643i
$786$	−53.4404			−1.90616
$787$	−23.8266	−	23.8266i	−0.849328	−	0.849328i	0.140721	−	0.990049i	$-0.455058\pi$
$787$	−23.8266	−	23.8266i	−0.849328	−	0.849328i	−0.990049	+	0.140721i	$0.955058\pi$
$788$	−35.0629	+	35.0629i	−1.24906	+	1.24906i
$789$	−5.96353	+	5.96353i	−0.212307	+	0.212307i
$790$			4.29574i			0.152836i
$791$		−	14.1338i		−	0.502541i
$792$	−2.21445	+	2.21445i	−0.0786872	+	0.0786872i
$793$	2.53394	−	2.53394i	0.0899828	−	0.0899828i
$794$	49.7339	+	49.7339i	1.76499	+	1.76499i
$795$	36.6519			1.29991
$796$	−37.1422	−	37.1422i	−1.31647	−	1.31647i
$797$			42.8006i			1.51608i	0.652211	+	0.758038i	$0.273842\pi$
$797$			42.8006i			1.51608i	−0.652211	+	0.758038i	$0.726158\pi$
$798$	3.23845			0.114640
$799$	−5.23323	−	22.0593i	−0.185138	−	0.780402i
$800$	−43.5643			−1.54023
$801$		−	2.05268i		−	0.0725280i
$802$	20.4319	+	20.4319i	0.721476	+	0.721476i
$803$	−0.655415			−0.0231291
$804$	44.3217	+	44.3217i	1.56311	+	1.56311i
$805$	−15.7142	+	15.7142i	−0.553852	+	0.553852i
$806$	1.20986	−	1.20986i	0.0426154	−	0.0426154i
$807$			15.9809i			0.562553i
$808$		−	5.03199i		−	0.177025i
$809$	−11.3347	+	11.3347i	−0.398508	+	0.398508i	−0.877707	−	0.479198i	$-0.840927\pi$
$809$	−11.3347	+	11.3347i	−0.398508	+	0.398508i	0.479198	+	0.877707i	$0.340927\pi$
$810$	34.2022	−	34.2022i	1.20174	−	1.20174i
$811$	−4.37978	−	4.37978i	−0.153795	−	0.153795i	0.626016	−	0.779810i	$-0.284685\pi$
$811$	−4.37978	−	4.37978i	−0.153795	−	0.153795i	−0.779810	+	0.626016i	$0.784685\pi$
$812$	14.1503			0.496578
$813$	−30.3735	−	30.3735i	−1.06524	−	1.06524i
$814$		−	17.5792i		−	0.616152i
$815$	88.1538			3.08789
$816$	3.15061	−	5.11041i	0.110293	−	0.178900i
$817$	−9.02575			−0.315771
$818$			46.5432i			1.62734i
$819$	0.188570	+	0.188570i	0.00658918	+	0.00658918i
$820$	−130.243			−4.54828
$821$	−8.89357	−	8.89357i	−0.310388	−	0.310388i	0.534672	−	0.845060i	$-0.320435\pi$
$821$	−8.89357	−	8.89357i	−0.310388	−	0.310388i	−0.845060	+	0.534672i	$0.820435\pi$
$822$	38.6638	−	38.6638i	1.34856	−	1.34856i
$823$	−3.34004	+	3.34004i	−0.116426	+	0.116426i	−0.762920	−	0.646493i	$-0.776235\pi$
$823$	−3.34004	+	3.34004i	−0.116426	+	0.116426i	0.646493	+	0.762920i	$0.276235\pi$
$824$		−	16.1047i		−	0.561033i
$825$		−	14.2035i		−	0.494504i
$826$	5.71845	−	5.71845i	0.198970	−	0.198970i
$827$	−32.8427	+	32.8427i	−1.14205	+	1.14205i	−0.153979	+	0.988074i	$0.549209\pi$
$827$	−32.8427	+	32.8427i	−1.14205	+	1.14205i	−0.988074	+	0.153979i	$0.950791\pi$
$828$	−16.3396	−	16.3396i	−0.567839	−	0.567839i
$829$	−36.1215			−1.25455			−0.627277	−	0.778797i	$-0.715830\pi$
$829$	−36.1215			−1.25455			−0.627277	+	0.778797i	$0.715830\pi$
$830$	−33.7424	−	33.7424i	−1.17122	−	1.17122i
$831$		−	45.5912i		−	1.58154i
$832$	−4.47584			−0.155172
$833$	25.5422	−	6.05950i	0.884986	−	0.209949i
$834$	59.6669			2.06609
$835$			54.2263i			1.87658i
$836$	2.95264	+	2.95264i	0.102119	+	0.102119i
$837$	−11.4223			−0.394812
$838$	22.9017	+	22.9017i	0.791127	+	0.791127i
$839$	−1.67228	+	1.67228i	−0.0577335	+	0.0577335i	−0.735384	−	0.677651i	$-0.762998\pi$
$839$	−1.67228	+	1.67228i	−0.0577335	+	0.0577335i	0.677651	+	0.735384i	$0.262998\pi$
$840$	−10.5916	+	10.5916i	−0.365445	+	0.365445i
$841$		−	2.45614i		−	0.0846946i
$842$			20.6707i			0.712361i
$843$	−13.0644	+	13.0644i	−0.449962	+	0.449962i
$844$	13.2171	−	13.2171i	0.454951	−	0.454951i
$845$	−35.0742	−	35.0742i	−1.20659	−	1.20659i
$846$	−11.8625			−0.407842
$847$	−0.562655	−	0.562655i	−0.0193331	−	0.0193331i
$848$		−	6.66913i		−	0.229019i
$849$	−3.34184			−0.114692
$850$	−21.9057	−	92.3376i	−0.751358	−	3.16715i
$851$	54.5517			1.87001
$852$		−	35.9286i		−	1.23089i
$853$	−29.7297	−	29.7297i	−1.01792	−	1.01792i	−0.999836	−	0.0180881i	$-0.994242\pi$
$853$	−29.7297	−	29.7297i	−1.01792	−	1.01792i	−0.0180881	−	0.999836i	$-0.505758\pi$
$854$	18.3552			0.628101
$855$	3.04661	+	3.04661i	0.104192	+	0.104192i
$856$	35.6566	−	35.6566i	1.21872	−	1.21872i
$857$	3.97012	−	3.97012i	0.135617	−	0.135617i	−0.636040	−	0.771656i	$-0.719429\pi$
$857$	3.97012	−	3.97012i	0.135617	−	0.135617i	0.771656	+	0.636040i	$0.219429\pi$
$858$		−	1.22027i		−	0.0416592i
$859$		−	1.07981i		−	0.0368425i	−0.999830	−	0.0184212i	$-0.994136\pi$
$859$		−	1.07981i		−	0.0368425i	0.999830	−	0.0184212i	$-0.00586399\pi$
$860$	70.1897	−	70.1897i	2.39345	−	2.39345i
$861$	7.93615	−	7.93615i	0.270463	−	0.270463i
$862$	−36.9270	−	36.9270i	−1.25774	−	1.25774i
$863$	−6.91040			−0.235233			−0.117616	−	0.993059i	$-0.537525\pi$
$863$	−6.91040			−0.235233			−0.117616	+	0.993059i	$0.537525\pi$
$864$	17.6676	+	17.6676i	0.601065	+	0.601065i
$865$		−	46.9963i		−	1.59792i
$866$	22.4815			0.763953
$867$	−23.2544	−	7.69444i	−0.789762	−	0.261317i
$868$	5.54874			0.188337
$869$		−	0.477307i		−	0.0161915i
$870$	−47.2417	−	47.2417i	−1.60164	−	1.60164i
$871$	4.57154			0.154901
$872$	26.3632	+	26.3632i	0.892772	+	0.892772i
$873$	10.2029	−	10.2029i	0.345317	−	0.345317i
$874$	−14.4717	+	14.4717i	−0.489513	+	0.489513i
$875$			14.8996i			0.503698i
$876$		−	3.25956i		−	0.110130i
$877$	−22.2771	+	22.2771i	−0.752244	+	0.752244i	−0.974898	−	0.222654i	$-0.928528\pi$
$877$	−22.2771	+	22.2771i	−0.752244	+	0.752244i	0.222654	+	0.974898i	$0.428528\pi$
$878$	−41.0349	+	41.0349i	−1.38486	+	1.38486i
$879$	8.95650	+	8.95650i	0.302095	+	0.302095i
$880$	−3.89532			−0.131311
$881$	16.8721	+	16.8721i	0.568434	+	0.568434i	0.931690	−	0.363255i	$-0.118335\pi$
$881$	16.8721	+	16.8721i	0.568434	+	0.568434i	−0.363255	+	0.931690i	$0.618335\pi$
$882$		−	13.7355i		−	0.462498i
$883$	−9.70160			−0.326485			−0.163242	−	0.986586i	$-0.552195\pi$
$883$	−9.70160			−0.326485			−0.163242	+	0.986586i	$0.552195\pi$
$884$	−1.19155	−	5.02268i	−0.0400762	−	0.168931i
$885$	−24.1750			−0.812634
$886$			61.3698i			2.06176i
$887$	−19.8714	−	19.8714i	−0.667216	−	0.667216i	0.289855	−	0.957071i	$-0.406393\pi$
$887$	−19.8714	−	19.8714i	−0.667216	−	0.667216i	−0.957071	+	0.289855i	$0.906393\pi$
$888$	36.7687			1.23388
$889$	3.53881	+	3.53881i	0.118688	+	0.118688i
$890$	14.1381	−	14.1381i	0.473910	−	0.473910i
$891$	−3.80026	+	3.80026i	−0.127314	+	0.127314i
$892$			9.25110i			0.309750i
$893$			6.65205i			0.222602i
$894$	−31.7346	+	31.7346i	−1.06136	+	1.06136i
$895$	−0.298850	+	0.298850i	−0.00998946	+	0.00998946i
$896$	−11.2378	−	11.2378i	−0.375430	−	0.375430i
$897$	3.78672			0.126435
$898$	−6.94629	−	6.94629i	−0.231801	−	0.231801i
$899$			10.4086i			0.347147i
$900$	−31.4386			−1.04795
$901$	−26.4751	+	6.28081i	−0.882014	+	0.209244i
$902$	22.8567			0.761046
$903$			8.55380i			0.284653i
$904$	42.5708	+	42.5708i	1.41589	+	1.41589i
$905$	−12.6235			−0.419621
$906$	48.3480	+	48.3480i	1.60625	+	1.60625i
$907$	24.4573	−	24.4573i	0.812091	−	0.812091i	−0.172856	−	0.984947i	$-0.555300\pi$
$907$	24.4573	−	24.4573i	0.812091	−	0.812091i	0.984947	+	0.172856i	$0.0552995\pi$
$908$	−32.0255	+	32.0255i	−1.06280	+	1.06280i
$909$			1.37174i			0.0454978i
$910$			2.59760i			0.0861096i
$911$	26.4166	−	26.4166i	0.875221	−	0.875221i	−0.117815	−	0.993036i	$-0.537589\pi$
$911$	26.4166	−	26.4166i	0.875221	−	0.875221i	0.993036	+	0.117815i	$0.0375889\pi$
$912$	−1.24557	+	1.24557i	−0.0412448	+	0.0412448i
$913$	3.74917	+	3.74917i	0.124079	+	0.124079i
$914$	28.0778			0.928732
$915$	−38.7986	−	38.7986i	−1.28264	−	1.28264i
$916$		−	19.1484i		−	0.632680i
$917$	−12.6400			−0.417409
$918$	−28.5639	+	46.3317i	−0.942749	+	1.52917i
$919$	17.7249			0.584690			0.292345	−	0.956313i	$-0.405564\pi$
$919$	17.7249			0.584690			0.292345	+	0.956313i	$0.405564\pi$
$920$		−	94.6617i		−	3.12090i
$921$	−0.777291	−	0.777291i	−0.0256126	−	0.0256126i
$922$	50.4117			1.66022
$923$	−1.85292	−	1.85292i	−0.0609895	−	0.0609895i
$924$	2.79824	−	2.79824i	0.0920555	−	0.0920555i
$925$	52.4808	−	52.4808i	1.72556	−	1.72556i
$926$			7.38507i			0.242688i
$927$			4.39020i			0.144193i
$928$	16.0997	−	16.0997i	0.528499	−	0.528499i
$929$	6.38214	−	6.38214i	0.209391	−	0.209391i	−0.594617	−	0.804009i	$-0.702696\pi$
$929$	6.38214	−	6.38214i	0.209391	−	0.209391i	0.804009	+	0.594617i	$0.202696\pi$
$930$	−18.5248	−	18.5248i	−0.607453	−	0.607453i
$931$	−7.70233			−0.252434
$932$	−15.6654	−	15.6654i	−0.513139	−	0.513139i
$933$			17.7820i			0.582157i
$934$	14.1280			0.462283
$935$	3.66851	+	15.4637i	0.119973	+	0.505716i
$936$	−1.13594			−0.0371294
$937$		−	29.7260i		−	0.971106i	−0.874207	−	0.485553i	$-0.838618\pi$
$937$		−	29.7260i		−	0.971106i	0.874207	−	0.485553i	$-0.161382\pi$
$938$	16.5575	+	16.5575i	0.540621	+	0.540621i
$939$	11.5812			0.377938
$940$	−51.7303	−	51.7303i	−1.68726	−	1.68726i
$941$	−18.8813	+	18.8813i	−0.615511	+	0.615511i	−0.944377	−	0.328865i	$-0.893334\pi$
$941$	−18.8813	+	18.8813i	−0.615511	+	0.615511i	0.328865	+	0.944377i	$0.393334\pi$
$942$	39.0380	−	39.0380i	1.27193	−	1.27193i
$943$			70.9288i			2.30976i
$944$			4.39884i			0.143170i
$945$	12.2620	−	12.2620i	0.398884	−	0.398884i
$946$	−12.3178	+	12.3178i	−0.400487	+	0.400487i
$947$	−26.3144	−	26.3144i	−0.855102	−	0.855102i	0.135654	−	0.990756i	$-0.456686\pi$
$947$	−26.3144	−	26.3144i	−0.855102	−	0.855102i	−0.990756	+	0.135654i	$0.956686\pi$
$948$	2.37378			0.0770968
$949$	−0.168103	−	0.168103i	−0.00545685	−	0.00545685i
$950$			27.8447i			0.903401i
$951$	−47.1048			−1.52748
$952$	5.83570	−	9.46573i	0.189136	−	0.306786i
$953$	25.8190			0.836361			0.418180	−	0.908364i	$-0.362668\pi$
$953$	25.8190			0.836361			0.418180	+	0.908364i	$0.362668\pi$
$954$			14.2372i			0.460945i
$955$	9.46598	+	9.46598i	0.306312	+	0.306312i
$956$	12.9345			0.418330
$957$	5.24909	+	5.24909i	0.169679	+	0.169679i
$958$	−16.6028	+	16.6028i	−0.536413	+	0.536413i
$959$	9.14495	−	9.14495i	0.295306	−	0.295306i
$960$			68.5323i			2.21187i
$961$		−	26.9185i		−	0.868338i
$962$	4.50878	−	4.50878i	0.145369	−	0.145369i
$963$	−9.72014	+	9.72014i	−0.313227	+	0.313227i
$964$	15.6169	+	15.6169i	0.502986	+	0.502986i
$965$	42.0266			1.35288
$966$	13.7150	+	13.7150i	0.441273	+	0.441273i
$967$			26.3628i			0.847770i	0.905716	+	0.423885i	$0.139334\pi$
$967$			26.3628i			0.847770i	−0.905716	+	0.423885i	$0.860666\pi$
$968$	3.38941			0.108940
$969$	6.11769	+	3.77161i	0.196529	+	0.121161i
$970$	140.548			4.51272
$971$			0.258176i			0.00828527i	0.999991	+	0.00414264i	$0.00131865\pi$
$971$			0.258176i			0.00828527i	−0.999991	+	0.00414264i	$0.998681\pi$
$972$	22.4978	+	22.4978i	0.721617	+	0.721617i
$973$	14.1127			0.452432
$974$	−6.33041	−	6.33041i	−0.202840	−	0.202840i
$975$	3.64297	−	3.64297i	0.116668	−	0.116668i
$976$	−7.05974	+	7.05974i	−0.225977	+	0.225977i
$977$			38.0476i			1.21725i	0.793458	+	0.608625i	$0.208278\pi$
$977$			38.0476i			1.21725i	−0.793458	+	0.608625i	$0.791722\pi$
$978$		−	76.9387i		−	2.46023i
$979$	−1.57091	+	1.57091i	−0.0502064	+	0.0502064i
$980$	59.8980	−	59.8980i	1.91337	−	1.91337i
$981$	−7.18672	−	7.18672i	−0.229454	−	0.229454i
$982$	57.0524			1.82061
$983$	−7.39276	−	7.39276i	−0.235792	−	0.235792i	0.579313	−	0.815105i	$-0.303321\pi$
$983$	−7.39276	−	7.39276i	−0.235792	−	0.235792i	−0.815105	+	0.579313i	$0.803321\pi$
$984$			47.8071i			1.52403i
$985$	55.3750			1.76439
$986$	42.2200	+	26.0290i	1.34456	+	0.828931i
$987$	6.30422			0.200665
$988$			1.51460i			0.0481859i
$989$	−38.2245	−	38.2245i	−1.21547	−	1.21547i
$990$	8.31568			0.264290
$991$	6.09629	+	6.09629i	0.193655	+	0.193655i	0.797273	−	0.603618i	$-0.206275\pi$
$991$	6.09629	+	6.09629i	0.193655	+	0.193655i	−0.603618	+	0.797273i	$0.706275\pi$
$992$	6.31316	−	6.31316i	0.200443	−	0.200443i
$993$	19.1987	−	19.1987i	0.609251	−	0.609251i
$994$		−	13.4220i		−	0.425721i
$995$			58.6588i			1.85961i
$996$	−18.6457	+	18.6457i	−0.590811	+	0.590811i
$997$	13.9045	−	13.9045i	0.440359	−	0.440359i	−0.451774	−	0.892132i	$-0.649209\pi$
$997$	13.9045	−	13.9045i	0.440359	−	0.440359i	0.892132	+	0.451774i	$0.149209\pi$
$998$	−11.3269	−	11.3269i	−0.358546	−	0.358546i
$999$	−42.5675			−1.34678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.166.3	yes	28
17.2	even	8		3179.2.a.bd.1.12		14
17.4	even	4	inner	187.2.e.b.89.12	✓	28
17.15	even	8		3179.2.a.be.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.12	✓	28	17.4	even	4	inner
187.2.e.b.166.3	yes	28	1.1	even	1	trivial
3179.2.a.bd.1.12		14	17.2	even	8
3179.2.a.be.1.12		14	17.15	even	8

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.33488i q^{2} +(1.01883 + 1.01883i) q^{3} -3.45165 q^{4} +(2.72560 + 2.72560i) q^{5} +(2.37884 - 2.37884i) q^{6} +(0.562655 - 0.562655i) q^{7} +3.38941i q^{8} -0.923968i q^{9} +O(q^{10})\)	\(q-2.33488i q^{2} +(1.01883 + 1.01883i) q^{3} -3.45165 q^{4} +(2.72560 + 2.72560i) q^{5} +(2.37884 - 2.37884i) q^{6} +(0.562655 - 0.562655i) q^{7} +3.38941i q^{8} -0.923968i q^{9} +(6.36394 - 6.36394i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-3.51664 - 3.51664i) q^{12} -0.362722 q^{13} +(-1.31373 - 1.31373i) q^{14} +5.55385i q^{15} +1.01057 q^{16} +(-0.951728 - 4.01176i) q^{17} -2.15735 q^{18} +1.20976i q^{19} +(-9.40781 - 9.40781i) q^{20} +1.14650 q^{21} +(1.65101 + 1.65101i) q^{22} +(-5.12339 + 5.12339i) q^{23} +(-3.45324 + 3.45324i) q^{24} +9.85780i q^{25} +0.846911i q^{26} +(3.99786 - 3.99786i) q^{27} +(-1.94209 + 1.94209i) q^{28} +(-3.64307 - 3.64307i) q^{29} +12.9676 q^{30} +(-1.42855 - 1.42855i) q^{31} +4.41927i q^{32} -1.44084 q^{33} +(-9.36696 + 2.22217i) q^{34} +3.06715 q^{35} +3.18921i q^{36} +(-5.32379 - 5.32379i) q^{37} +2.82463 q^{38} +(-0.369552 - 0.369552i) q^{39} +(-9.23819 + 9.23819i) q^{40} +(6.92206 - 6.92206i) q^{41} -2.67694i q^{42} +7.46079i q^{43} +(2.44068 - 2.44068i) q^{44} +(2.51837 - 2.51837i) q^{45} +(11.9625 + 11.9625i) q^{46} +5.49866 q^{47} +(1.02960 + 1.02960i) q^{48} +6.36684i q^{49} +23.0167 q^{50} +(3.11765 - 5.05695i) q^{51} +1.25199 q^{52} -6.59938i q^{53} +(-9.33451 - 9.33451i) q^{54} -3.85458 q^{55} +(1.90707 + 1.90707i) q^{56} +(-1.23254 + 1.23254i) q^{57} +(-8.50611 + 8.50611i) q^{58} +4.35283i q^{59} -19.1699i q^{60} +(-6.98590 + 6.98590i) q^{61} +(-3.33549 + 3.33549i) q^{62} +(-0.519875 - 0.519875i) q^{63} +12.3396 q^{64} +(-0.988635 - 0.988635i) q^{65} +3.36419i q^{66} -12.6034 q^{67} +(3.28503 + 13.8472i) q^{68} -10.4397 q^{69} -7.16141i q^{70} +(5.10836 + 5.10836i) q^{71} +3.13171 q^{72} +(0.463448 + 0.463448i) q^{73} +(-12.4304 + 12.4304i) q^{74} +(-10.0434 + 10.0434i) q^{75} -4.17566i q^{76} +0.795715i q^{77} +(-0.862859 + 0.862859i) q^{78} +(-0.337507 + 0.337507i) q^{79} +(2.75441 + 2.75441i) q^{80} +5.37438 q^{81} +(-16.1622 - 16.1622i) q^{82} -5.30213i q^{83} -3.95732 q^{84} +(8.34042 - 13.5285i) q^{85} +17.4200 q^{86} -7.42334i q^{87} +(-2.39668 - 2.39668i) q^{88} +2.22160 q^{89} +(-5.88007 - 5.88007i) q^{90} +(-0.204087 + 0.204087i) q^{91} +(17.6841 - 17.6841i) q^{92} -2.91090i q^{93} -12.8387i q^{94} +(-3.29732 + 3.29732i) q^{95} +(-4.50249 + 4.50249i) q^{96} +(11.0425 + 11.0425i) q^{97} +14.8658 q^{98} +(0.653344 + 0.653344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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