LMFDB - Embedded newform 187.2.e.b.89.12

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			89.12
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.3

$q$-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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.33488i			1.65101i	0.564397	+	0.825503i	$0.309109\pi$
$2$			2.33488i			1.65101i	−0.564397	+	0.825503i	$0.690891\pi$
$3$	1.01883	−	1.01883i	0.588222	−	0.588222i	−0.348927	−	0.937150i	$-0.613454\pi$
$3$	1.01883	−	1.01883i	0.588222	−	0.588222i	0.937150	+	0.348927i	$0.113454\pi$
$4$	−3.45165			−1.72582
$5$	2.72560	−	2.72560i	1.21893	−	1.21893i	0.250917	−	0.968009i	$-0.419268\pi$
$5$	2.72560	−	2.72560i	1.21893	−	1.21893i	0.968009	−	0.250917i	$-0.0807321\pi$
$6$	2.37884	+	2.37884i	0.971159	+	0.971159i
$7$	0.562655	+	0.562655i	0.212664	+	0.212664i	0.805398	−	0.592734i	$-0.201952\pi$
$7$	0.562655	+	0.562655i	0.212664	+	0.212664i	−0.592734	+	0.805398i	$0.701952\pi$
$8$		−	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	$-0.955686\pi$
$19$		−	1.20976i		−	0.277538i	0.990325	−	0.138769i	$-0.0443145\pi$
$20$	−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	−0.997490	−	0.0708105i	$-0.977441\pi$
$23$	−5.12339	−	5.12339i	−1.06830	−	1.06830i	−0.0708105	−	0.997490i	$-0.522559\pi$
$24$	−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	−0.959207	−	0.282706i	$-0.908768\pi$
$29$	−3.64307	+	3.64307i	−0.676500	+	0.676500i	0.282706	+	0.959207i	$0.408768\pi$
$30$	12.9676			2.36754
$31$	−1.42855	+	1.42855i	−0.256575	+	0.256575i	−0.823660	−	0.567084i	$-0.808071\pi$
$31$	−1.42855	+	1.42855i	−0.256575	+	0.256575i	0.567084	+	0.823660i	$0.308071\pi$
$32$		−	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	−0.993036	−	0.117810i	$-0.962413\pi$
$37$	−5.32379	+	5.32379i	−0.875226	+	0.875226i	0.117810	+	0.993036i	$0.462413\pi$
$38$	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	0.996412	+	0.0846317i	$0.0269714\pi$
$41$	6.92206	+	6.92206i	1.08104	+	1.08104i	0.0846317	+	0.996412i	$0.473029\pi$
$42$			2.67694i			0.413060i
$43$		−	7.46079i		−	1.13776i	−0.822421	−	0.568880i	$-0.807377\pi$
$43$		−	7.46079i		−	1.13776i	0.822421	−	0.568880i	$-0.192623\pi$
$44$	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	$0.149734\pi$
$53$			6.59938i			0.906494i	−0.891385	+	0.453247i	$0.850266\pi$
$54$	−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	$-0.908556\pi$
$59$		−	4.35283i		−	0.566691i	0.959018	−	0.283345i	$-0.0914443\pi$
$60$			19.1699i			2.47483i
$61$	−6.98590	−	6.98590i	−0.894453	−	0.894453i	0.100486	−	0.994938i	$-0.467960\pi$
$61$	−6.98590	−	6.98590i	−0.894453	−	0.894453i	−0.994938	+	0.100486i	$0.967960\pi$
$62$	−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	−0.335713	−	0.941964i	$-0.608977\pi$
$71$	5.10836	−	5.10836i	0.606251	−	0.606251i	0.941964	+	0.335713i	$0.108977\pi$
$72$	3.13171			0.369076
$73$	0.463448	−	0.463448i	0.0542425	−	0.0542425i	−0.679465	−	0.733708i	$-0.737788\pi$
$73$	0.463448	−	0.463448i	0.0542425	−	0.0542425i	0.733708	+	0.679465i	$0.237788\pi$
$74$	−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	0.687866	−	0.725838i	$-0.258548\pi$
$79$	−0.337507	−	0.337507i	−0.0379725	−	0.0379725i	−0.725838	+	0.687866i	$0.758548\pi$
$80$	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	$0.0939853\pi$
$83$			5.30213i			0.581984i	−0.956725	+	0.290992i	$0.906015\pi$
$84$	−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	0.129635	−	0.991562i	$-0.458619\pi$
$97$	11.0425	−	11.0425i	1.12120	−	1.12120i	0.991562	−	0.129635i	$-0.0413807\pi$
$98$	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	−0.0171538	+	0.999853i	$0.505460\pi$
$107$	−10.5200	+	10.5200i	−1.01701	+	1.01701i	−0.999853	+	0.0171538i	$0.994540\pi$
$108$	−13.7992	−	13.7992i	−1.32783	−	1.32783i
$109$	7.77811	+	7.77811i	0.745008	+	0.745008i	0.973537	−	0.228529i	$-0.0733916\pi$
$109$	7.77811	+	7.77811i	0.745008	+	0.745008i	−0.228529	+	0.973537i	$0.573392\pi$
$110$		−	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	0.979345	+	0.202194i	$0.0648073\pi$
$113$	12.5599	+	12.5599i	1.18154	+	1.18154i	0.202194	+	0.979345i	$0.435193\pi$
$114$	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	$-0.909980\pi$
$127$		−	6.28949i		−	0.558102i	0.960276	−	0.279051i	$-0.0900198\pi$
$128$			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	−0.999830	−	0.0184472i	$-0.994128\pi$
$131$	−11.2324	+	11.2324i	−0.981383	+	0.981383i	0.0184472	+	0.999830i	$0.494128\pi$
$132$	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	0.0659004	−	0.997826i	$-0.479008\pi$
$139$	12.5412	−	12.5412i	1.06373	−	1.06373i	0.997826	−	0.0659004i	$-0.0209920\pi$
$140$	−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	$-0.690058\pi$
$151$		−	20.3242i		−	1.65396i	0.562234	−	0.826978i	$-0.309942\pi$
$152$	−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	0.947810	+	0.318836i	$0.103292\pi$
$163$	16.1715	+	16.1715i	1.26665	+	1.26665i	0.318836	+	0.947810i	$0.396708\pi$
$164$	−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	−0.208298	−	0.978065i	$-0.566793\pi$
$167$	9.94758	−	9.94758i	0.769767	−	0.769767i	0.978065	+	0.208298i	$0.0667925\pi$
$168$		−	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	−0.954303	−	0.298840i	$-0.903400\pi$
$173$	−8.62128	+	8.62128i	−0.655464	+	0.655464i	0.298840	+	0.954303i	$0.403400\pi$
$174$	−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	$-0.998696\pi$
$179$		−	0.109646i		−	0.00819530i	0.999992	−	0.00409765i	$-0.00130433\pi$
$180$	−8.69251	−	8.69251i	−0.647902	−	0.647902i
$181$	−2.31574	−	2.31574i	−0.172127	−	0.172127i	0.615786	−	0.787913i	$-0.288839\pi$
$181$	−2.31574	−	2.31574i	−0.172127	−	0.172127i	−0.787913	+	0.615786i	$0.788839\pi$
$182$	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	0.927865	−	0.372916i	$-0.121642\pi$
$193$	7.70961	+	7.70961i	0.554950	+	0.554950i	−0.372916	+	0.927865i	$0.621642\pi$
$194$	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	0.969367	−	0.245618i	$-0.0789907\pi$
$197$	10.1583	+	10.1583i	0.723749	+	0.723749i	−0.245618	+	0.969367i	$0.578991\pi$
$198$	1.52548	+	1.52548i	0.108411	+	0.108411i
$199$	10.7607	−	10.7607i	0.762807	−	0.762807i	−0.214022	−	0.976829i	$-0.568657\pi$
$199$	10.7607	−	10.7607i	0.762807	−	0.762807i	0.976829	+	0.214022i	$0.0686565\pi$
$200$	−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	0.562907	−	0.826520i	$-0.309683\pi$
$211$	−3.82921	−	3.82921i	−0.263614	−	0.263614i	−0.826520	+	0.562907i	$0.809683\pi$
$212$		−	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	$0.0286035\pi$
$223$			2.68020i			0.179479i	−0.995965	+	0.0897397i	$0.971396\pi$
$224$	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	0.944457	−	0.328634i	$-0.106588\pi$
$227$	9.27832	+	9.27832i	0.615824	+	0.615824i	−0.328634	+	0.944457i	$0.606588\pi$
$228$	4.25429	+	4.25429i	0.281747	+	0.281747i
$229$		−	5.54761i		−	0.366596i	−0.983057	−	0.183298i	$-0.941323\pi$
$229$		−	5.54761i		−	0.366596i	0.983057	−	0.183298i	$-0.0586774\pi$
$230$		−	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	−0.542637	−	0.839967i	$-0.682574\pi$
$233$	4.53854	−	4.53854i	0.297330	−	0.297330i	0.839967	+	0.542637i	$0.182574\pi$
$234$	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	−0.837652	−	0.546205i	$-0.816072\pi$
$241$	−4.52448	+	4.52448i	−0.291447	+	0.291447i	0.546205	+	0.837652i	$0.316072\pi$
$242$	−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	$0.0868229\pi$
$257$			8.63738i			0.538785i	−0.963030	+	0.269393i	$0.913177\pi$
$258$	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	$-0.942240\pi$
$263$		−	5.85331i		−	0.360931i	0.983581	−	0.180465i	$-0.0577604\pi$
$264$			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	−0.426369	−	0.904549i	$-0.640207\pi$
$269$	7.84274	−	7.84274i	0.478181	−	0.478181i	0.904549	+	0.426369i	$0.140207\pi$
$270$			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	−0.452654	+	0.891686i	$0.649523\pi$
$277$	−22.3743	+	22.3743i	−1.34434	+	1.34434i	−0.891686	+	0.452654i	$0.850477\pi$
$278$	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	$-0.875071\pi$
$281$		−	12.8229i		−	0.764952i	0.923965	−	0.382476i	$-0.124929\pi$
$282$	13.0804	+	13.0804i	0.778929	+	0.778929i
$283$	−1.64004	−	1.64004i	−0.0974901	−	0.0974901i	0.656680	−	0.754170i	$-0.271960\pi$
$283$	−1.64004	−	1.64004i	−0.0974901	−	0.0974901i	−0.754170	+	0.656680i	$0.771960\pi$
$284$	−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	−0.414984	−	0.909829i	$-0.636213\pi$
$311$	8.72668	−	8.72668i	0.494844	−	0.494844i	0.909829	+	0.414984i	$0.136213\pi$
$312$	1.25257	+	1.25257i	0.0709126	+	0.0709126i
$313$	5.68358	+	5.68358i	0.321255	+	0.321255i	0.849248	−	0.527994i	$-0.177055\pi$
$313$	5.68358	+	5.68358i	0.321255	+	0.321255i	−0.527994	+	0.849248i	$0.677055\pi$
$314$			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	−0.929459	−	0.368926i	$-0.879725\pi$
$317$	−23.1171	−	23.1171i	−1.29838	−	1.29838i	−0.368926	−	0.929459i	$-0.620275\pi$
$318$	−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	$0.173277\pi$
$331$			18.8438i			1.03575i	−0.855456	+	0.517875i	$0.826723\pi$
$332$		−	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	−0.531223	−	0.847232i	$-0.678267\pi$
$337$	5.80117	−	5.80117i	0.316010	−	0.316010i	0.847232	+	0.531223i	$0.178267\pi$
$338$		−	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	0.569877	−	0.821730i	$-0.306991\pi$
$347$	−4.69149	−	4.69149i	−0.251852	−	0.251852i	−0.821730	+	0.569877i	$0.806991\pi$
$348$		−	25.6227i		−	1.37352i
$349$			1.08752i			0.0582135i	0.999576	+	0.0291068i	$0.00926628\pi$
$349$			1.08752i			0.0582135i	−0.999576	+	0.0291068i	$0.990734\pi$
$350$	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	$-0.682224\pi$
$359$		−	31.8528i		−	1.68113i	0.541713	−	0.840564i	$-0.317776\pi$
$360$	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	0.279433	−	0.960165i	$-0.409854\pi$
$367$	−13.0410	−	13.0410i	−0.680733	−	0.680733i	−0.960165	+	0.279433i	$0.909854\pi$
$368$	−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	−0.995896	−	0.0905071i	$-0.971151\pi$
$379$	−17.6260	+	17.6260i	−0.905389	+	0.905389i	0.0905071	+	0.995896i	$0.471151\pi$
$380$	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	$0.0248619\pi$
$383$			3.05402i			0.156053i	−0.996951	+	0.0780266i	$0.975138\pi$
$384$	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	$-0.974257\pi$
$389$		−	3.18668i		−	0.161571i	0.996732	−	0.0807855i	$-0.0257429\pi$
$390$	−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	−0.997433	−	0.0716045i	$-0.977188\pi$
$397$	−21.3004	−	21.3004i	−1.06904	−	1.06904i	−0.0716045	−	0.997433i	$-0.522812\pi$
$398$	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	0.454007	−	0.890998i	$-0.349994\pi$
$401$	−8.75075	−	8.75075i	−0.436991	−	0.436991i	−0.890998	+	0.454007i	$0.849994\pi$
$402$	−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	0.425690	−	0.904869i	$-0.360031\pi$
$419$	−9.80854	−	9.80854i	−0.479178	−	0.479178i	−0.904869	+	0.425690i	$0.860031\pi$
$420$	−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	0.976648	−	0.214847i	$-0.0689254\pi$
$431$	15.8154	+	15.8154i	0.761800	+	0.761800i	−0.214847	+	0.976648i	$0.568925\pi$
$432$	4.04012	+	4.04012i	0.194380	+	0.194380i
$433$		−	9.62857i		−	0.462720i	−0.972868	−	0.231360i	$-0.925683\pi$
$433$		−	9.62857i		−	0.462720i	0.972868	−	0.231360i	$-0.0743175\pi$
$434$		−	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	−0.988701	−	0.149902i	$-0.952104\pi$
$439$	−17.5748	+	17.5748i	−0.838799	+	0.838799i	0.149902	+	0.988701i	$0.452104\pi$
$440$			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	0.773813	−	0.633414i	$-0.218347\pi$
$449$	2.97501	+	2.97501i	0.140400	+	0.140400i	−0.633414	+	0.773813i	$0.718347\pi$
$450$			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	$-0.909247\pi$
$457$		−	12.0254i		−	0.562525i	0.959631	−	0.281262i	$-0.0907531\pi$
$458$	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	$-0.832307\pi$
$461$		−	21.5907i		−	1.00558i	0.864408	−	0.502791i	$-0.167693\pi$
$462$	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	$-0.955290\pi$
$467$		−	6.05087i		−	0.280001i	0.990151	−	0.140000i	$-0.0447104\pi$
$468$			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	−0.850644	−	0.525743i	$-0.823787\pi$
$479$	−7.11080	+	7.11080i	−0.324901	+	0.324901i	0.525743	+	0.850644i	$0.323787\pi$
$480$	−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	0.765862	−	0.643004i	$-0.222312\pi$
$487$	2.71124	+	2.71124i	0.122858	+	0.122858i	−0.643004	+	0.765862i	$0.722312\pi$
$488$	−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	$-0.814107\pi$
$491$		−	24.4349i		−	1.10273i	0.834264	−	0.551365i	$-0.185893\pi$
$492$	−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	0.807304	−	0.590136i	$-0.200926\pi$
$499$	4.85116	+	4.85116i	0.217168	+	0.217168i	−0.590136	+	0.807304i	$0.700926\pi$
$500$	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	0.946516	+	0.322657i	$0.104576\pi$
$503$	28.4646	+	28.4646i	1.26917	+	1.26917i	0.322657	+	0.946516i	$0.395424\pi$
$504$	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	0.753030	−	0.657986i	$-0.228591\pi$
$521$	2.16944	+	2.16944i	0.0950448	+	0.0950448i	−0.657986	+	0.753030i	$0.728591\pi$
$522$	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	−0.354050	−	0.935227i	$-0.615196\pi$
$541$	13.5178	−	13.5178i	0.581177	−	0.581177i	0.935227	+	0.354050i	$0.115196\pi$
$542$		−	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	−0.612209	−	0.790696i	$-0.709719\pi$
$547$	4.17448	−	4.17448i	0.178488	−	0.178488i	0.790696	+	0.612209i	$0.209719\pi$
$548$	−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	$0.288723\pi$
$563$			37.3800i			1.57538i	−0.616072	+	0.787690i	$0.711277\pi$
$564$	−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	$0.0283527\pi$
$569$			4.24381i			0.177910i	−0.996036	+	0.0889549i	$0.971647\pi$
$570$		−	15.6876i		−	0.657081i
$571$	−4.47971	−	4.47971i	−0.187470	−	0.187470i	0.607132	−	0.794601i	$-0.292320\pi$
$571$	−4.47971	−	4.47971i	−0.187470	−	0.187470i	−0.794601	+	0.607132i	$0.792320\pi$
$572$	−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	$0.149018\pi$
$587$			21.8654i			0.902481i	−0.892402	+	0.451241i	$0.850982\pi$
$588$	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	$0.324238\pi$
$593$			41.4653i			1.70277i	−0.524537	+	0.851387i	$0.675762\pi$
$594$	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	0.0460047	−	0.998941i	$-0.485351\pi$
$601$	−23.3615	−	23.3615i	−0.952937	−	0.952937i	−0.998941	+	0.0460047i	$0.985351\pi$
$602$	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	−0.744942	−	0.667129i	$-0.767523\pi$
$607$	−1.91710	+	1.91710i	−0.0778125	+	0.0778125i	0.667129	+	0.744942i	$0.267523\pi$
$608$	−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	−0.0490902	+	0.998794i	$0.515632\pi$
$617$	−26.0289	+	26.0289i	−1.04788	+	1.04788i	−0.998794	+	0.0490902i	$0.984368\pi$
$618$	−11.3030	−	11.3030i	−0.454673	−	0.454673i
$619$	27.2879	+	27.2879i	1.09679	+	1.09679i	0.994783	+	0.102012i	$0.0325279\pi$
$619$	27.2879	+	27.2879i	1.09679	+	1.09679i	0.102012	+	0.994783i	$0.467472\pi$
$620$		−	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	$-0.862162\pi$
$631$		−	21.0817i		−	0.839248i	0.907698	−	0.419624i	$-0.137838\pi$
$632$	−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	−0.405210	−	0.914224i	$-0.632802\pi$
$641$	12.8872	−	12.8872i	0.509014	−	0.509014i	0.914224	+	0.405210i	$0.132802\pi$
$642$	−50.0509			−1.97535
$643$	−23.6495	+	23.6495i	−0.932645	+	0.932645i	−0.997871	−	0.0652258i	$-0.979223\pi$
$643$	−23.6495	+	23.6495i	−0.932645	+	0.932645i	0.0652258	+	0.997871i	$0.479223\pi$
$644$			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	0.933609	−	0.358292i	$-0.116641\pi$
$653$	14.7016	+	14.7016i	0.575317	+	0.575317i	−0.358292	+	0.933609i	$0.616641\pi$
$654$			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	$0.0710483\pi$
$661$			11.3821i			0.442712i	−0.975193	+	0.221356i	$0.928952\pi$
$662$	−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	0.817843	−	0.575441i	$-0.195170\pi$
$673$	6.28846	+	6.28846i	0.242402	+	0.242402i	−0.575441	+	0.817843i	$0.695170\pi$
$674$	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	−0.601024	−	0.799231i	$-0.705240\pi$
$677$	5.15721	−	5.15721i	0.198208	−	0.198208i	0.799231	+	0.601024i	$0.205240\pi$
$678$			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	−0.0729210	+	0.997338i	$0.523232\pi$
$683$	−27.9704	+	27.9704i	−1.07026	+	1.07026i	−0.997338	+	0.0729210i	$0.976768\pi$
$684$	−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	0.832162	−	0.554533i	$-0.187103\pi$
$691$	7.29801	+	7.29801i	0.277629	+	0.277629i	−0.554533	+	0.832162i	$0.687103\pi$
$692$	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	−0.281925	−	0.959436i	$-0.590973\pi$
$709$	18.0401	−	18.0401i	0.677511	−	0.677511i	0.959436	+	0.281925i	$0.0909731\pi$
$710$	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	−0.453049	−	0.891486i	$-0.649664\pi$
$719$	11.7563	−	11.7563i	0.438437	−	0.438437i	0.891486	+	0.453049i	$0.149664\pi$
$720$	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	$-0.665402\pi$
$733$		−	47.0007i		−	1.73601i	0.496555	−	0.868005i	$-0.334598\pi$
$734$	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	$-0.941534\pi$
$739$		−	9.93027i		−	0.365291i	0.983179	−	0.182646i	$-0.0584661\pi$
$740$		−	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	−0.998420	−	0.0561988i	$-0.982102\pi$
$743$	−25.6831	+	25.6831i	−0.942221	+	0.942221i	0.0561988	+	0.998420i	$0.482102\pi$
$744$	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	−0.653761	−	0.756701i	$-0.726810\pi$
$751$	2.82101	−	2.82101i	0.102940	−	0.102940i	0.756701	+	0.653761i	$0.226810\pi$
$752$	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	$0.351905\pi$
$757$			49.1783i			1.78741i	−0.448651	+	0.893707i	$0.648095\pi$
$758$	−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	$0.0333089\pi$
$773$			5.80813i			0.208904i	−0.994530	+	0.104452i	$0.966691\pi$
$774$			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	−0.990049	−	0.140721i	$-0.955058\pi$
$787$	−23.8266	+	23.8266i	−0.849328	+	0.849328i	0.140721	+	0.990049i	$0.455058\pi$
$788$	−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	$-0.726158\pi$
$797$		−	42.8006i		−	1.51608i	0.652211	−	0.758038i	$-0.273842\pi$
$798$	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	0.479198	−	0.877707i	$-0.340927\pi$
$809$	−11.3347	−	11.3347i	−0.398508	−	0.398508i	−0.877707	+	0.479198i	$0.840927\pi$
$810$	34.2022	+	34.2022i	1.20174	+	1.20174i
$811$	−4.37978	+	4.37978i	−0.153795	+	0.153795i	−0.779810	−	0.626016i	$-0.784685\pi$
$811$	−4.37978	+	4.37978i	−0.153795	+	0.153795i	0.626016	+	0.779810i	$0.284685\pi$
$812$	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	−0.845060	−	0.534672i	$-0.820435\pi$
$821$	−8.89357	+	8.89357i	−0.310388	+	0.310388i	0.534672	+	0.845060i	$0.320435\pi$
$822$	38.6638	+	38.6638i	1.34856	+	1.34856i
$823$	−3.34004	−	3.34004i	−0.116426	−	0.116426i	0.646493	−	0.762920i	$-0.276235\pi$
$823$	−3.34004	−	3.34004i	−0.116426	−	0.116426i	−0.762920	+	0.646493i	$0.776235\pi$
$824$			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	−0.988074	−	0.153979i	$-0.950791\pi$
$827$	−32.8427	−	32.8427i	−1.14205	−	1.14205i	−0.153979	−	0.988074i	$-0.549209\pi$
$828$	−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	0.677651	−	0.735384i	$-0.262998\pi$
$839$	−1.67228	−	1.67228i	−0.0577335	−	0.0577335i	−0.735384	+	0.677651i	$0.762998\pi$
$840$	−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	−0.0180881	+	0.999836i	$0.505758\pi$
$853$	−29.7297	+	29.7297i	−1.01792	+	1.01792i	−0.999836	+	0.0180881i	$0.994242\pi$
$854$	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	0.771656	−	0.636040i	$-0.219429\pi$
$857$	3.97012	+	3.97012i	0.135617	+	0.135617i	−0.636040	+	0.771656i	$0.719429\pi$
$858$			1.22027i			0.0416592i
$859$			1.07981i			0.0368425i	0.999830	+	0.0184212i	$0.00586399\pi$
$859$			1.07981i			0.0368425i	−0.999830	+	0.0184212i	$0.994136\pi$
$860$	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	0.222654	−	0.974898i	$-0.428528\pi$
$877$	−22.2771	−	22.2771i	−0.752244	−	0.752244i	−0.974898	+	0.222654i	$0.928528\pi$
$878$	−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	−0.363255	−	0.931690i	$-0.618335\pi$
$881$	16.8721	−	16.8721i	0.568434	−	0.568434i	0.931690	+	0.363255i	$0.118335\pi$
$882$			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	−0.957071	−	0.289855i	$-0.906393\pi$
$887$	−19.8714	+	19.8714i	−0.667216	+	0.667216i	0.289855	+	0.957071i	$0.406393\pi$
$888$	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	0.984947	−	0.172856i	$-0.0552995\pi$
$907$	24.4573	+	24.4573i	0.812091	+	0.812091i	−0.172856	+	0.984947i	$0.555300\pi$
$908$	−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	0.993036	−	0.117815i	$-0.0375889\pi$
$911$	26.4166	+	26.4166i	0.875221	+	0.875221i	−0.117815	+	0.993036i	$0.537589\pi$
$912$	−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	0.804009	−	0.594617i	$-0.202696\pi$
$929$	6.38214	+	6.38214i	0.209391	+	0.209391i	−0.594617	+	0.804009i	$0.702696\pi$
$930$	−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	$0.161382\pi$
$937$			29.7260i			0.971106i	−0.874207	+	0.485553i	$0.838618\pi$
$938$	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	0.328865	−	0.944377i	$-0.393334\pi$
$941$	−18.8813	−	18.8813i	−0.615511	−	0.615511i	−0.944377	+	0.328865i	$0.893334\pi$
$942$	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	−0.990756	−	0.135654i	$-0.956686\pi$
$947$	−26.3144	+	26.3144i	−0.855102	+	0.855102i	0.135654	+	0.990756i	$0.456686\pi$
$948$	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	$-0.860666\pi$
$967$		−	26.3628i		−	0.847770i	0.905716	−	0.423885i	$-0.139334\pi$
$968$	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	$-0.998681\pi$
$971$		−	0.258176i		−	0.00828527i	0.999991	−	0.00414264i	$-0.00131865\pi$
$972$	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	$-0.791722\pi$
$977$		−	38.0476i		−	1.21725i	0.793458	−	0.608625i	$-0.208278\pi$
$978$			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	−0.815105	−	0.579313i	$-0.803321\pi$
$983$	−7.39276	+	7.39276i	−0.235792	+	0.235792i	0.579313	+	0.815105i	$0.303321\pi$
$984$		−	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	−0.603618	−	0.797273i	$-0.706275\pi$
$991$	6.09629	−	6.09629i	0.193655	−	0.193655i	0.797273	+	0.603618i	$0.206275\pi$
$992$	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	0.892132	−	0.451774i	$-0.149209\pi$
$997$	13.9045	+	13.9045i	0.440359	+	0.440359i	−0.451774	+	0.892132i	$0.649209\pi$
$998$	−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.89.12	✓	28
17.8	even	8		3179.2.a.be.1.12		14
17.9	even	8		3179.2.a.bd.1.12		14
17.13	even	4	inner	187.2.e.b.166.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.12	✓	28	1.1	even	1	trivial
187.2.e.b.166.3	yes	28	17.13	even	4	inner
3179.2.a.bd.1.12		14	17.9	even	8
3179.2.a.be.1.12		14	17.8	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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