LMFDB - Embedded newform 187.2.e.b.89.1

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			89.1
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71846i q^{2} +(2.10133 - 2.10133i) q^{3} -5.39003 q^{4} +(-0.643884 + 0.643884i) q^{5} +(-5.71237 - 5.71237i) q^{6} +(1.95059 + 1.95059i) q^{7} +9.21565i q^{8} -5.83115i q^{9} +O(q^{10})$	\(q-2.71846i q^{2} +(2.10133 - 2.10133i) q^{3} -5.39003 q^{4} +(-0.643884 + 0.643884i) q^{5} +(-5.71237 - 5.71237i) q^{6} +(1.95059 + 1.95059i) q^{7} +9.21565i q^{8} -5.83115i q^{9} +(1.75037 + 1.75037i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-11.3262 + 11.3262i) q^{12} -0.843133 q^{13} +(5.30259 - 5.30259i) q^{14} +2.70602i q^{15} +14.2723 q^{16} +(4.11906 - 0.182599i) q^{17} -15.8517 q^{18} -2.73890i q^{19} +(3.47055 - 3.47055i) q^{20} +8.19764 q^{21} +(-1.92224 + 1.92224i) q^{22} +(0.144370 + 0.144370i) q^{23} +(19.3651 + 19.3651i) q^{24} +4.17083i q^{25} +2.29202i q^{26} +(-5.94917 - 5.94917i) q^{27} +(-10.5137 - 10.5137i) q^{28} +(3.87516 - 3.87516i) q^{29} +7.35622 q^{30} +(-7.72889 + 7.72889i) q^{31} -20.3674i q^{32} -2.97172 q^{33} +(-0.496387 - 11.1975i) q^{34} -2.51191 q^{35} +31.4300i q^{36} +(-7.21588 + 7.21588i) q^{37} -7.44559 q^{38} +(-1.77170 + 1.77170i) q^{39} +(-5.93381 - 5.93381i) q^{40} +(0.838008 + 0.838008i) q^{41} -22.2850i q^{42} -5.42660i q^{43} +(3.81132 + 3.81132i) q^{44} +(3.75459 + 3.75459i) q^{45} +(0.392465 - 0.392465i) q^{46} +6.16407 q^{47} +(29.9908 - 29.9908i) q^{48} +0.609581i q^{49} +11.3382 q^{50} +(8.27179 - 9.03919i) q^{51} +4.54451 q^{52} +2.19351i q^{53} +(-16.1726 + 16.1726i) q^{54} +0.910590 q^{55} +(-17.9759 + 17.9759i) q^{56} +(-5.75532 - 5.75532i) q^{57} +(-10.5345 - 10.5345i) q^{58} -4.42391i q^{59} -14.5855i q^{60} +(5.39241 + 5.39241i) q^{61} +(21.0107 + 21.0107i) q^{62} +(11.3742 - 11.3742i) q^{63} -26.8234 q^{64} +(0.542880 - 0.542880i) q^{65} +8.07852i q^{66} -2.90082 q^{67} +(-22.2018 + 0.984211i) q^{68} +0.606739 q^{69} +6.82852i q^{70} +(0.772676 - 0.772676i) q^{71} +53.7378 q^{72} +(-4.29910 + 4.29910i) q^{73} +(19.6161 + 19.6161i) q^{74} +(8.76427 + 8.76427i) q^{75} +14.7627i q^{76} -2.75855i q^{77} +(4.81629 + 4.81629i) q^{78} +(-4.55626 - 4.55626i) q^{79} +(-9.18973 + 9.18973i) q^{80} -7.50884 q^{81} +(2.27809 - 2.27809i) q^{82} +1.77634i q^{83} -44.1855 q^{84} +(-2.53463 + 2.76977i) q^{85} -14.7520 q^{86} -16.2860i q^{87} +(6.51645 - 6.51645i) q^{88} -11.4493 q^{89} +(10.2067 - 10.2067i) q^{90} +(-1.64461 - 1.64461i) q^{91} +(-0.778161 - 0.778161i) q^{92} +32.4818i q^{93} -16.7568i q^{94} +(1.76353 + 1.76353i) q^{95} +(-42.7987 - 42.7987i) q^{96} +(6.06718 - 6.06718i) q^{97} +1.65712 q^{98} +(-4.12324 + 4.12324i) 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 $

$2$		−	2.71846i		−	1.92224i	−0.276128	−	0.961121i	$-0.589051\pi$
$2$		−	2.71846i		−	1.92224i	0.276128	−	0.961121i	$-0.410949\pi$
$3$	2.10133	−	2.10133i	1.21320	−	1.21320i	0.243234	−	0.969968i	$-0.421792\pi$
$3$	2.10133	−	2.10133i	1.21320	−	1.21320i	0.969968	−	0.243234i	$-0.0782082\pi$
$4$	−5.39003			−2.69501
$5$	−0.643884	+	0.643884i	−0.287954	+	0.287954i	−0.836271	−	0.548317i	$-0.815269\pi$
$5$	−0.643884	+	0.643884i	−0.287954	+	0.287954i	0.548317	+	0.836271i	$0.315269\pi$
$6$	−5.71237	−	5.71237i	−2.33207	−	2.33207i
$7$	1.95059	+	1.95059i	0.737253	+	0.737253i	0.972045	−	0.234793i	$-0.0754412\pi$
$7$	1.95059	+	1.95059i	0.737253	+	0.737253i	−0.234793	+	0.972045i	$0.575441\pi$
$8$			9.21565i			3.25822i
$9$		−	5.83115i		−	1.94372i
$10$	1.75037	+	1.75037i	0.553517	+	0.553517i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	−11.3262	+	11.3262i	−3.26959	+	3.26959i
$13$	−0.843133			−0.233843			−0.116922	−	0.993141i	$-0.537303\pi$
$13$	−0.843133			−0.233843			−0.116922	+	0.993141i	$0.537303\pi$
$14$	5.30259	−	5.30259i	1.41718	−	1.41718i
$15$			2.70602i			0.698692i
$16$	14.2723			3.56808
$17$	4.11906	−	0.182599i	0.999019	−	0.0442866i
$17$	4.11906	−	0.182599i	0.999019	−	0.0442866i
$18$	−15.8517			−3.73629
$19$		−	2.73890i		−	0.628347i	−0.949366	−	0.314173i	$-0.898273\pi$
$19$		−	2.73890i		−	0.628347i	0.949366	−	0.314173i	$-0.101727\pi$
$20$	3.47055	−	3.47055i	0.776039	−	0.776039i
$21$	8.19764			1.78887
$22$	−1.92224	+	1.92224i	−0.409823	+	0.409823i
$23$	0.144370	+	0.144370i	0.0301033	+	0.0301033i	0.721998	−	0.691895i	$-0.243224\pi$
$23$	0.144370	+	0.144370i	0.0301033	+	0.0301033i	−0.691895	+	0.721998i	$0.743224\pi$
$24$	19.3651	+	19.3651i	3.95288	+	3.95288i
$25$			4.17083i			0.834165i
$26$			2.29202i			0.449503i
$27$	−5.94917	−	5.94917i	−1.14492	−	1.14492i
$28$	−10.5137	−	10.5137i	−1.98691	−	1.98691i
$29$	3.87516	−	3.87516i	0.719599	−	0.719599i	−0.248924	−	0.968523i	$-0.580077\pi$
$29$	3.87516	−	3.87516i	0.719599	−	0.719599i	0.968523	+	0.248924i	$0.0800769\pi$
$30$	7.35622			1.34306
$31$	−7.72889	+	7.72889i	−1.38815	+	1.38815i	−0.558943	+	0.829206i	$0.688793\pi$
$31$	−7.72889	+	7.72889i	−1.38815	+	1.38815i	−0.829206	+	0.558943i	$0.811207\pi$
$32$		−	20.3674i		−	3.60049i
$33$	−2.97172			−0.517311
$34$	−0.496387	−	11.1975i	−0.0851296	−	1.92036i
$35$	−2.51191			−0.424590
$36$			31.4300i			5.23834i
$37$	−7.21588	+	7.21588i	−1.18628	+	1.18628i	−0.208196	+	0.978087i	$0.566759\pi$
$37$	−7.21588	+	7.21588i	−1.18628	+	1.18628i	−0.978087	+	0.208196i	$0.933241\pi$
$38$	−7.44559			−1.20783
$39$	−1.77170	+	1.77170i	−0.283699	+	0.283699i
$40$	−5.93381	−	5.93381i	−0.938218	−	0.938218i
$41$	0.838008	+	0.838008i	0.130875	+	0.130875i	0.769510	−	0.638635i	$-0.220501\pi$
$41$	0.838008	+	0.838008i	0.130875	+	0.130875i	−0.638635	+	0.769510i	$0.720501\pi$
$42$		−	22.2850i		−	3.43864i
$43$		−	5.42660i		−	0.827549i	−0.910379	−	0.413775i	$-0.864210\pi$
$43$		−	5.42660i		−	0.827549i	0.910379	−	0.413775i	$-0.135790\pi$
$44$	3.81132	+	3.81132i	0.574579	+	0.574579i
$45$	3.75459	+	3.75459i	0.559701	+	0.559701i
$46$	0.392465	−	0.392465i	0.0578659	−	0.0578659i
$47$	6.16407			0.899122			0.449561	−	0.893250i	$-0.351580\pi$
$47$	6.16407			0.899122			0.449561	+	0.893250i	$0.351580\pi$
$48$	29.9908	−	29.9908i	4.32880	−	4.32880i
$49$			0.609581i			0.0870830i
$50$	11.3382			1.60347
$51$	8.27179	−	9.03919i	1.15828	−	1.26574i
$52$	4.54451			0.630210
$53$			2.19351i			0.301302i	0.988587	+	0.150651i	$0.0481370\pi$
$53$			2.19351i			0.301302i	−0.988587	+	0.150651i	$0.951863\pi$
$54$	−16.1726	+	16.1726i	−2.20081	+	2.20081i
$55$	0.910590			0.122784
$56$	−17.9759	+	17.9759i	−2.40213	+	2.40213i
$57$	−5.75532	−	5.75532i	−0.762311	−	0.762311i
$58$	−10.5345	−	10.5345i	−1.38324	−	1.38324i
$59$		−	4.42391i		−	0.575944i	−0.957639	−	0.287972i	$-0.907019\pi$
$59$		−	4.42391i		−	0.575944i	0.957639	−	0.287972i	$-0.0929809\pi$
$60$		−	14.5855i		−	1.88298i
$61$	5.39241	+	5.39241i	0.690427	+	0.690427i	0.962326	−	0.271899i	$-0.0876516\pi$
$61$	5.39241	+	5.39241i	0.690427	+	0.690427i	−0.271899	+	0.962326i	$0.587652\pi$
$62$	21.0107	+	21.0107i	2.66836	+	2.66836i
$63$	11.3742	−	11.3742i	1.43301	−	1.43301i
$64$	−26.8234			−3.35293
$65$	0.542880	−	0.542880i	0.0673360	−	0.0673360i
$66$			8.07852i			0.994396i
$67$	−2.90082			−0.354392			−0.177196	−	0.984176i	$-0.556703\pi$
$67$	−2.90082			−0.354392			−0.177196	+	0.984176i	$0.556703\pi$
$68$	−22.2018	+	0.984211i	−2.69237	+	0.119353i
$69$	0.606739			0.0730428
$70$			6.82852i			0.816164i
$71$	0.772676	−	0.772676i	0.0916998	−	0.0916998i	−0.659769	−	0.751469i	$-0.729346\pi$
$71$	0.772676	−	0.772676i	0.0916998	−	0.0916998i	0.751469	+	0.659769i	$0.229346\pi$
$72$	53.7378			6.33306
$73$	−4.29910	+	4.29910i	−0.503172	+	0.503172i	−0.912422	−	0.409250i	$-0.865790\pi$
$73$	−4.29910	+	4.29910i	−0.503172	+	0.503172i	0.409250	+	0.912422i	$0.365790\pi$
$74$	19.6161	+	19.6161i	2.28032	+	2.28032i
$75$	8.76427	+	8.76427i	1.01201	+	1.01201i
$76$			14.7627i			1.69340i
$77$		−	2.75855i		−	0.314366i
$78$	4.81629	+	4.81629i	0.545338	+	0.545338i
$79$	−4.55626	−	4.55626i	−0.512620	−	0.512620i	0.402709	−	0.915328i	$-0.368069\pi$
$79$	−4.55626	−	4.55626i	−0.512620	−	0.512620i	−0.915328	+	0.402709i	$0.868069\pi$
$80$	−9.18973	+	9.18973i	−1.02744	+	1.02744i
$81$	−7.50884			−0.834316
$82$	2.27809	−	2.27809i	0.251573	−	0.251573i
$83$			1.77634i			0.194978i	0.995237	+	0.0974891i	$0.0310811\pi$
$83$			1.77634i			0.194978i	−0.995237	+	0.0974891i	$0.968919\pi$
$84$	−44.1855			−4.82103
$85$	−2.53463	+	2.76977i	−0.274919	+	0.300424i
$86$	−14.7520			−1.59075
$87$		−	16.2860i		−	1.74604i
$88$	6.51645	−	6.51645i	0.694656	−	0.694656i
$89$	−11.4493			−1.21362			−0.606810	−	0.794847i	$-0.707551\pi$
$89$	−11.4493			−1.21362			−0.606810	+	0.794847i	$0.707551\pi$
$90$	10.2067	−	10.2067i	1.07588	−	1.07588i
$91$	−1.64461	−	1.64461i	−0.172401	−	0.172401i
$92$	−0.778161	−	0.778161i	−0.0811288	−	0.0811288i
$93$			32.4818i			3.36821i
$94$		−	16.7568i		−	1.72833i
$95$	1.76353	+	1.76353i	0.180935	+	0.180935i
$96$	−42.7987	−	42.7987i	−4.36812	−	4.36812i
$97$	6.06718	−	6.06718i	0.616029	−	0.616029i	−0.328482	−	0.944510i	$-0.606537\pi$
$97$	6.06718	−	6.06718i	0.616029	−	0.616029i	0.944510	+	0.328482i	$0.106537\pi$
$98$	1.65712			0.167395
$99$	−4.12324	+	4.12324i	−0.414402	+	0.414402i
$100$		−	22.4809i		−	2.24809i
$101$	−0.0133492			−0.00132830			−0.000664149	−	1.00000i	$-0.500211\pi$
$101$	−0.0133492			−0.00132830			−0.000664149		1.00000i	$0.500211\pi$
$102$	−24.5727	−	22.4865i	−2.43306	−	2.22650i
$103$	5.37506			0.529620			0.264810	−	0.964301i	$-0.414691\pi$
$103$	5.37506			0.529620			0.264810	+	0.964301i	$0.414691\pi$
$104$		−	7.77002i		−	0.761913i
$105$	−5.27833	+	5.27833i	−0.515113	+	0.515113i
$106$	5.96298			0.579176
$107$	−4.79366	+	4.79366i	−0.463421	+	0.463421i	−0.899775	−	0.436354i	$-0.856269\pi$
$107$	−4.79366	+	4.79366i	−0.463421	+	0.463421i	0.436354	+	0.899775i	$0.356269\pi$
$108$	32.0662	+	32.0662i	3.08557	+	3.08557i
$109$	−1.81821	−	1.81821i	−0.174153	−	0.174153i	0.614648	−	0.788801i	$-0.289298\pi$
$109$	−1.81821	−	1.81821i	−0.174153	−	0.174153i	−0.788801	+	0.614648i	$0.789298\pi$
$110$		−	2.47540i		−	0.236020i
$111$			30.3258i			2.87840i
$112$	27.8394	+	27.8394i	2.63058	+	2.63058i
$113$	7.79800	+	7.79800i	0.733574	+	0.733574i	0.971326	−	0.237752i	$-0.0764104\pi$
$113$	7.79800	+	7.79800i	0.733574	+	0.733574i	−0.237752	+	0.971326i	$0.576410\pi$
$114$	−15.6456	+	15.6456i	−1.46535	+	1.46535i
$115$	−0.185916			−0.0173367
$116$	−20.8872	+	20.8872i	−1.93933	+	1.93933i
$117$			4.91643i			0.454525i
$118$	−12.0262			−1.10710
$119$	8.39076	+	7.67841i	0.769180	+	0.703879i
$120$	−24.9378			−2.27650
$121$			1.00000i			0.0909091i
$122$	14.6590	−	14.6590i	1.32717	−	1.32717i
$123$	3.52186			0.317555
$124$	41.6589	−	41.6589i	3.74108	−	3.74108i
$125$	−5.90495	−	5.90495i	−0.528155	−	0.528155i
$126$	−30.9202	−	30.9202i	−2.75459	−	2.75459i
$127$			17.1235i			1.51946i	0.650238	+	0.759731i	$0.274669\pi$
$127$			17.1235i			1.51946i	−0.650238	+	0.759731i	$0.725331\pi$
$128$			32.1836i			2.84465i
$129$	−11.4031	−	11.4031i	−1.00398	−	1.00398i
$130$	−1.47580	−	1.47580i	−0.129436	−	0.129436i
$131$	2.80394	−	2.80394i	0.244981	−	0.244981i	−0.573926	−	0.818907i	$-0.694580\pi$
$131$	2.80394	−	2.80394i	0.244981	−	0.244981i	0.818907	+	0.573926i	$0.194580\pi$
$132$	16.0177			1.39416
$133$	5.34246	−	5.34246i	0.463250	−	0.463250i
$134$			7.88577i			0.681227i
$135$	7.66115			0.659367
$136$	1.68276	+	37.9598i	0.144296	+	3.25503i
$137$	−22.9817			−1.96346			−0.981728	−	0.190292i	$-0.939057\pi$
$137$	−22.9817			−1.96346			−0.981728	+	0.190292i	$0.939057\pi$
$138$		−	1.64940i		−	0.140406i
$139$	4.99900	−	4.99900i	0.424010	−	0.424010i	−0.462572	−	0.886582i	$-0.653073\pi$
$139$	4.99900	−	4.99900i	0.424010	−	0.424010i	0.886582	+	0.462572i	$0.153073\pi$
$140$	13.5392			1.14427
$141$	12.9527	−	12.9527i	1.09082	−	1.09082i
$142$	−2.10049	−	2.10049i	−0.176269	−	0.176269i
$143$	0.596185	+	0.596185i	0.0498555	+	0.0498555i
$144$		−	83.2240i		−	6.93534i
$145$			4.99031i			0.414423i
$146$	11.6869	+	11.6869i	0.967218	+	0.967218i
$147$	1.28093	+	1.28093i	0.105649	+	0.105649i
$148$	38.8938	−	38.8938i	3.19705	−	3.19705i
$149$	−2.40714			−0.197201			−0.0986004	−	0.995127i	$-0.531437\pi$
$149$	−2.40714			−0.197201			−0.0986004	+	0.995127i	$0.531437\pi$
$150$	23.8253	−	23.8253i	1.94533	−	1.94533i
$151$			3.67004i			0.298664i	0.988787	+	0.149332i	$0.0477123\pi$
$151$			3.67004i			0.298664i	−0.988787	+	0.149332i	$0.952288\pi$
$152$	25.2407			2.04729
$153$	−1.06476	−	24.0188i	−0.0860807	−	1.94181i
$154$	−7.49900			−0.604287
$155$		−	9.95302i		−	0.799446i
$156$	9.54950	−	9.54950i	0.764572	−	0.764572i
$157$	−17.3725			−1.38647			−0.693237	−	0.720709i	$-0.743816\pi$
$157$	−17.3725			−1.38647			−0.693237	+	0.720709i	$0.743816\pi$
$158$	−12.3860	+	12.3860i	−0.985379	+	0.985379i
$159$	4.60929	+	4.60929i	0.365540	+	0.365540i
$160$	13.1143	+	13.1143i	1.03677	+	1.03677i
$161$			0.563214i			0.0443875i
$162$			20.4125i			1.60376i
$163$	−6.86125	−	6.86125i	−0.537415	−	0.537415i	0.385354	−	0.922769i	$-0.374079\pi$
$163$	−6.86125	−	6.86125i	−0.537415	−	0.537415i	−0.922769	+	0.385354i	$0.874079\pi$
$164$	−4.51688	−	4.51688i	−0.352709	−	0.352709i
$165$	1.91345	−	1.91345i	0.148962	−	0.148962i
$166$	4.82890			0.374795
$167$	14.2932	−	14.2932i	1.10604	−	1.10604i	0.112379	−	0.993665i	$-0.464153\pi$
$167$	14.2932	−	14.2932i	1.10604	−	1.10604i	0.993665	−	0.112379i	$-0.0358470\pi$
$168$			75.5466i			5.82855i
$169$	−12.2891			−0.945317
$170$	7.52951	+	6.89028i	0.577487	+	0.528460i
$171$	−15.9709			−1.22133
$172$			29.2495i			2.23026i
$173$	7.49387	−	7.49387i	0.569748	−	0.569748i	−0.362310	−	0.932058i	$-0.618012\pi$
$173$	7.49387	−	7.49387i	0.569748	−	0.569748i	0.932058	+	0.362310i	$0.118012\pi$
$174$	−44.2727			−3.35631
$175$	−8.13556	+	8.13556i	−0.614990	+	0.614990i
$176$	−10.0921	−	10.0921i	−0.760717	−	0.760717i
$177$	−9.29607	−	9.29607i	−0.698736	−	0.698736i
$178$			31.1244i			2.33287i
$179$		−	5.29354i		−	0.395658i	−0.980237	−	0.197829i	$-0.936611\pi$
$179$		−	5.29354i		−	0.395658i	0.980237	−	0.197829i	$-0.0633890\pi$
$180$	−20.2373	−	20.2373i	−1.50840	−	1.50840i
$181$	−3.58271	−	3.58271i	−0.266301	−	0.266301i	0.561307	−	0.827608i	$-0.310299\pi$
$181$	−3.58271	−	3.58271i	−0.266301	−	0.266301i	−0.827608	+	0.561307i	$0.810299\pi$
$182$	−4.47079	+	4.47079i	−0.331397	+	0.331397i
$183$	22.6624			1.67525
$184$	−1.33047	+	1.33047i	−0.0980834	+	0.0980834i
$185$		−	9.29238i		−	0.683190i
$186$	88.3006			6.47451
$187$	−3.04173	−	2.78350i	−0.222433	−	0.203550i
$188$	−33.2245			−2.42315
$189$		−	23.2087i		−	1.68819i
$190$	4.79410	−	4.79410i	0.347800	−	0.347800i
$191$	5.13610			0.371635			0.185817	−	0.982584i	$-0.440507\pi$
$191$	5.13610			0.371635			0.185817	+	0.982584i	$0.440507\pi$
$192$	−56.3648	+	56.3648i	−4.06778	+	4.06778i
$193$	6.48073	+	6.48073i	0.466493	+	0.466493i	0.900776	−	0.434283i	$-0.142998\pi$
$193$	6.48073	+	6.48073i	0.466493	+	0.466493i	−0.434283	+	0.900776i	$0.642998\pi$
$194$	−16.4934	−	16.4934i	−1.18416	−	1.18416i
$195$		−	2.28154i		−	0.163384i
$196$		−	3.28566i		−	0.234690i
$197$	−3.41112	−	3.41112i	−0.243032	−	0.243032i	0.575071	−	0.818103i	$-0.304974\pi$
$197$	−3.41112	−	3.41112i	−0.243032	−	0.243032i	−0.818103	+	0.575071i	$0.804974\pi$
$198$	11.2089	+	11.2089i	0.796580	+	0.796580i
$199$	−7.42901	+	7.42901i	−0.526628	+	0.526628i	−0.919565	−	0.392937i	$-0.871459\pi$
$199$	−7.42901	+	7.42901i	−0.526628	+	0.526628i	0.392937	+	0.919565i	$0.371459\pi$
$200$	−38.4369			−2.71790
$201$	−6.09557	+	6.09557i	−0.429949	+	0.429949i
$202$			0.0362894i			0.00255331i
$203$	15.1177			1.06105
$204$	−44.5852	+	48.7215i	−3.12159	+	3.41118i
$205$	−1.07916			−0.0753718
$206$		−	14.6119i		−	1.01806i
$207$	0.841846	−	0.841846i	0.0585123	−	0.0585123i
$208$	−12.0335			−0.834371
$209$	−1.93669	+	1.93669i	−0.133964	+	0.133964i
$210$	14.3489	+	14.3489i	0.990171	+	0.990171i
$211$	8.25904	+	8.25904i	0.568576	+	0.568576i	0.931729	−	0.363154i	$-0.118300\pi$
$211$	8.25904	+	8.25904i	0.568576	+	0.568576i	−0.363154	+	0.931729i	$0.618300\pi$
$212$		−	11.8231i		−	0.812014i
$213$		−	3.24729i		−	0.222501i
$214$	13.0314	+	13.0314i	0.890807	+	0.890807i
$215$	3.49411	+	3.49411i	0.238296	+	0.238296i
$216$	54.8254	−	54.8254i	3.73040	−	3.73040i
$217$	−30.1517			−2.04683
$218$	−4.94273	+	4.94273i	−0.334764	+	0.334764i
$219$			18.0676i			1.22090i
$220$	−4.90810			−0.330904
$221$	−3.47292	+	0.153955i	−0.233614	+	0.0103561i
$222$	82.4396			5.53298
$223$		−	20.4232i		−	1.36764i	−0.729650	−	0.683821i	$-0.760317\pi$
$223$		−	20.4232i		−	1.36764i	0.729650	−	0.683821i	$-0.239683\pi$
$224$	39.7285	−	39.7285i	2.65447	−	2.65447i
$225$	24.3207			1.62138
$226$	21.1986	−	21.1986i	1.41011	−	1.41011i
$227$	−11.8500	−	11.8500i	−0.786513	−	0.786513i	0.194408	−	0.980921i	$-0.437721\pi$
$227$	−11.8500	−	11.8500i	−0.786513	−	0.786513i	−0.980921	+	0.194408i	$0.937721\pi$
$228$	31.0213	+	31.0213i	2.05444	+	2.05444i
$229$		−	13.0777i		−	0.864196i	−0.901827	−	0.432098i	$-0.857773\pi$
$229$		−	13.0777i		−	0.864196i	0.901827	−	0.432098i	$-0.142227\pi$
$230$			0.505405i			0.0333254i
$231$	−5.79661	−	5.79661i	−0.381389	−	0.381389i
$232$	35.7121	+	35.7121i	2.34462	+	2.34462i
$233$	8.53700	−	8.53700i	0.559277	−	0.559277i	−0.369824	−	0.929102i	$-0.620582\pi$
$233$	8.53700	−	8.53700i	0.559277	−	0.559277i	0.929102	+	0.369824i	$0.120582\pi$
$234$	13.3651			0.873706
$235$	−3.96895	+	3.96895i	−0.258906	+	0.258906i
$236$			23.8450i			1.55218i
$237$	−19.1484			−1.24382
$238$	20.8735	−	22.8099i	1.35303	−	1.47855i
$239$	6.32485			0.409120			0.204560	−	0.978854i	$-0.434424\pi$
$239$	6.32485			0.409120			0.204560	+	0.978854i	$0.434424\pi$
$240$			38.6212i			2.49299i
$241$	−16.0759	+	16.0759i	−1.03554	+	1.03554i	−0.0361942	+	0.999345i	$0.511523\pi$
$241$	−16.0759	+	16.0759i	−1.03554	+	1.03554i	−0.999345	+	0.0361942i	$0.988477\pi$
$242$	2.71846			0.174749
$243$	2.06897	−	2.06897i	0.132725	−	0.132725i
$244$	−29.0652	−	29.0652i	−1.86071	−	1.86071i
$245$	−0.392500	−	0.392500i	−0.0250759	−	0.0250759i
$246$		−	9.57403i		−	0.610418i
$247$			2.30926i			0.146935i
$248$	−71.2267	−	71.2267i	−4.52290	−	4.52290i
$249$	3.73266	+	3.73266i	0.236548	+	0.236548i
$250$	−16.0524	+	16.0524i	−1.01524	+	1.01524i
$251$	1.95215			0.123219			0.0616093	−	0.998100i	$-0.480377\pi$
$251$	1.95215			0.123219			0.0616093	+	0.998100i	$0.480377\pi$
$252$	−61.3070	+	61.3070i	−3.86198	+	3.86198i
$253$		−	0.204171i		−	0.0128361i
$254$	46.5494			2.92077
$255$	0.494116	+	11.1463i	0.0309427	+	0.698007i
$256$	33.8428			2.11518
$257$			17.7522i			1.10735i	0.832732	+	0.553676i	$0.186775\pi$
$257$			17.7522i			1.10735i	−0.832732	+	0.553676i	$0.813225\pi$
$258$	−30.9988	+	30.9988i	−1.92990	+	1.92990i
$259$	−28.1504			−1.74918
$260$	−2.92614	+	2.92614i	−0.181471	+	0.181471i
$261$	−22.5966	−	22.5966i	−1.39870	−	1.39870i
$262$	−7.62239	−	7.62239i	−0.470913	−	0.470913i
$263$		−	21.7342i		−	1.34019i	−0.742275	−	0.670095i	$-0.766253\pi$
$263$		−	21.7342i		−	1.34019i	0.742275	−	0.670095i	$-0.233747\pi$
$264$		−	27.3864i		−	1.68551i
$265$	−1.41237	−	1.41237i	−0.0867612	−	0.0867612i
$266$	−14.5233	−	14.5233i	−0.890479	−	0.890479i
$267$	−24.0587	+	24.0587i	−1.47237	+	1.47237i
$268$	15.6355			0.955090
$269$	−9.25294	+	9.25294i	−0.564162	+	0.564162i	−0.930487	−	0.366325i	$-0.880616\pi$
$269$	−9.25294	+	9.25294i	−0.564162	+	0.564162i	0.366325	+	0.930487i	$0.380616\pi$
$270$		−	20.8265i		−	1.26746i
$271$	−17.2307			−1.04669			−0.523345	−	0.852121i	$-0.675316\pi$
$271$	−17.2307			−1.04669			−0.523345	+	0.852121i	$0.675316\pi$
$272$	58.7886	−	2.60611i	3.56458	−	0.158018i
$273$	−6.91171			−0.418315
$274$			62.4747i			3.77424i
$275$	2.94922	−	2.94922i	0.177845	−	0.177845i
$276$	−3.27034			−0.196851
$277$	21.9061	−	21.9061i	1.31621	−	1.31621i	0.399456	−	0.916752i	$-0.369199\pi$
$277$	21.9061	−	21.9061i	1.31621	−	1.31621i	0.916752	−	0.399456i	$-0.130801\pi$
$278$	−13.5896	−	13.5896i	−0.815050	−	0.815050i
$279$	45.0683	+	45.0683i	2.69817	+	2.69817i
$280$		−	23.1488i		−	1.38341i
$281$			13.0598i			0.779081i	0.921009	+	0.389541i	$0.127366\pi$
$281$			13.0598i			0.779081i	−0.921009	+	0.389541i	$0.872634\pi$
$282$	−35.2115	−	35.2115i	−2.09681	−	2.09681i
$283$	8.16276	+	8.16276i	0.485226	+	0.485226i	0.906796	−	0.421570i	$-0.138521\pi$
$283$	8.16276	+	8.16276i	0.485226	+	0.485226i	−0.421570	+	0.906796i	$0.638521\pi$
$284$	−4.16474	+	4.16474i	−0.247132	+	0.247132i
$285$	7.41153			0.439021
$286$	1.62071	−	1.62071i	0.0958344	−	0.0958344i
$287$			3.26921i			0.192976i
$288$	−118.766			−6.99833
$289$	16.9333	−	1.50427i	0.996077	−	0.0884864i
$290$	13.5660			0.796621
$291$		−	25.4983i		−	1.49473i
$292$	23.1723	−	23.1723i	1.35605	−	1.35605i
$293$	−17.8267			−1.04145			−0.520724	−	0.853725i	$-0.674338\pi$
$293$	−17.8267			−1.04145			−0.520724	+	0.853725i	$0.674338\pi$
$294$	3.48216	−	3.48216i	0.203083	−	0.203083i
$295$	2.84848	+	2.84848i	0.165845	+	0.165845i
$296$	−66.4990	−	66.4990i	−3.86518	−	3.86518i
$297$			8.41339i			0.488194i
$298$			6.54372i			0.379068i
$299$	−0.121724	−	0.121724i	−0.00703946	−	0.00703946i
$300$	−47.2396	−	47.2396i	−2.72738	−	2.72738i
$301$	10.5851	−	10.5851i	0.610113	−	0.610113i
$302$	9.97686			0.574104
$303$	−0.0280511	+	0.0280511i	−0.00161149	+	0.00161149i
$304$		−	39.0905i		−	2.24199i
$305$	−6.94418			−0.397622
$306$	−65.2943	+	2.89450i	−3.73263	+	0.165468i
$307$	31.6084			1.80399			0.901994	−	0.431749i	$-0.142103\pi$
$307$	31.6084			1.80399			0.901994	+	0.431749i	$0.142103\pi$
$308$			14.8686i			0.847219i
$309$	11.2948	−	11.2948i	0.642536	−	0.642536i
$310$	−27.0569			−1.53673
$311$	−3.96801	+	3.96801i	−0.225005	+	0.225005i	−0.810602	−	0.585597i	$-0.800860\pi$
$311$	−3.96801	+	3.96801i	−0.225005	+	0.225005i	0.585597	+	0.810602i	$0.300860\pi$
$312$	−16.3274	−	16.3274i	−0.924354	−	0.924354i
$313$	5.82119	+	5.82119i	0.329033	+	0.329033i	0.852219	−	0.523186i	$-0.175257\pi$
$313$	5.82119	+	5.82119i	0.329033	+	0.329033i	−0.523186	+	0.852219i	$0.675257\pi$
$314$			47.2264i			2.66514i
$315$			14.6473i			0.825281i
$316$	24.5584	+	24.5584i	1.38152	+	1.38152i
$317$	−2.70395	−	2.70395i	−0.151869	−	0.151869i	0.627083	−	0.778952i	$-0.284249\pi$
$317$	−2.70395	−	2.70395i	−0.151869	−	0.151869i	−0.778952	+	0.627083i	$0.784249\pi$
$318$	12.5302	−	12.5302i	0.702657	−	0.702657i
$319$	−5.48030			−0.306838
$320$	17.2712	−	17.2712i	0.965489	−	0.965489i
$321$			20.1461i			1.12445i
$322$	1.53108			0.0853235
$323$	−0.500119	−	11.2817i	−0.0278274	−	0.627730i
$324$	40.4728			2.24849
$325$		−	3.51656i		−	0.195064i
$326$	−18.6520	+	18.6520i	−1.03304	+	1.03304i
$327$	−7.64130			−0.422565
$328$	−7.72279	+	7.72279i	−0.426419	+	0.426419i
$329$	12.0236	+	12.0236i	0.662880	+	0.662880i
$330$	−5.20163	−	5.20163i	−0.286340	−	0.286340i
$331$		−	29.4113i		−	1.61659i	−0.588778	−	0.808295i	$-0.700391\pi$
$331$		−	29.4113i		−	1.61659i	0.588778	−	0.808295i	$-0.299609\pi$
$332$		−	9.57449i		−	0.525469i
$333$	42.0768	+	42.0768i	2.30580	+	2.30580i
$334$	−38.8556	−	38.8556i	−2.12608	−	2.12608i
$335$	1.86779	−	1.86779i	0.102048	−	0.102048i
$336$	116.999			6.38284
$337$	1.17695	−	1.17695i	0.0641123	−	0.0641123i	−0.674324	−	0.738436i	$-0.735565\pi$
$337$	1.17695	−	1.17695i	0.0641123	−	0.0641123i	0.738436	+	0.674324i	$0.235565\pi$
$338$			33.4075i			1.81713i
$339$	32.7723			1.77995
$340$	13.6617	−	14.9291i	0.740910	−	0.809646i
$341$	10.9303			0.591909
$342$			43.4163i			2.34769i
$343$	12.4651	−	12.4651i	0.673050	−	0.673050i
$344$	50.0097			2.69634
$345$	−0.390670	+	0.390670i	−0.0210330	+	0.0210330i
$346$	−20.3718	−	20.3718i	−1.09519	−	1.09519i
$347$	−7.24449	−	7.24449i	−0.388904	−	0.388904i	0.485392	−	0.874297i	$-0.338677\pi$
$347$	−7.24449	−	7.24449i	−0.388904	−	0.388904i	−0.874297	+	0.485392i	$0.838677\pi$
$348$			87.7817i			4.70559i
$349$			30.4250i			1.62861i	0.580434	+	0.814307i	$0.302883\pi$
$349$			30.4250i			1.62861i	−0.580434	+	0.814307i	$0.697117\pi$
$350$	22.1162	+	22.1162i	1.18216	+	1.18216i
$351$	5.01594	+	5.01594i	0.267731	+	0.267731i
$352$	−14.4020	+	14.4020i	−0.767627	+	0.767627i
$353$	−31.6388			−1.68396			−0.841981	−	0.539508i	$-0.818610\pi$
$353$	−31.6388			−1.68396			−0.841981	+	0.539508i	$0.818610\pi$
$354$	−25.2710	+	25.2710i	−1.34314	+	1.34314i
$355$			0.995028i			0.0528106i
$356$	61.7119			3.27072
$357$	33.7666	−	1.49688i	1.78712	−	0.0792232i
$358$	−14.3903			−0.760549
$359$		−	31.3154i		−	1.65276i	−0.563110	−	0.826382i	$-0.690395\pi$
$359$		−	31.3154i		−	1.65276i	0.563110	−	0.826382i	$-0.309605\pi$
$360$	−34.6009	+	34.6009i	−1.82363	+	1.82363i
$361$	11.4984			0.605181
$362$	−9.73946	+	9.73946i	−0.511894	+	0.511894i
$363$	2.10133	+	2.10133i	0.110291	+	0.110291i
$364$	8.86446	+	8.86446i	0.464624	+	0.464624i
$365$		−	5.53625i		−	0.289781i
$366$		−	61.6069i		−	3.22024i
$367$	13.2881	+	13.2881i	0.693631	+	0.693631i	0.963029	−	0.269398i	$-0.0868246\pi$
$367$	13.2881	+	13.2881i	0.693631	+	0.693631i	−0.269398	+	0.963029i	$0.586825\pi$
$368$	2.06050	+	2.06050i	0.107411	+	0.107411i
$369$	4.88655	−	4.88655i	0.254383	−	0.254383i
$370$	−25.2610			−1.31326
$371$	−4.27864	+	4.27864i	−0.222136	+	0.222136i
$372$		−	175.078i		−	9.07737i
$373$	−35.4083			−1.83337			−0.916686	−	0.399609i	$-0.869146\pi$
$373$	−35.4083			−1.83337			−0.916686	+	0.399609i	$0.869146\pi$
$374$	−7.56683	+	8.26883i	−0.391271	+	0.427571i
$375$	−24.8165			−1.28152
$376$			56.8059i			2.92954i
$377$	−3.26728	+	3.26728i	−0.168273	+	0.168273i
$378$	−63.0920			−3.24510
$379$	−1.27167	+	1.27167i	−0.0653211	+	0.0653211i	−0.739013	−	0.673692i	$-0.764708\pi$
$379$	−1.27167	+	1.27167i	−0.0653211	+	0.0653211i	0.673692	+	0.739013i	$0.264708\pi$
$380$	−9.50550	−	9.50550i	−0.487622	−	0.487622i
$381$	35.9820	+	35.9820i	1.84341	+	1.84341i
$382$		−	13.9623i		−	0.714372i
$383$			7.13487i			0.364575i	0.983245	+	0.182287i	$0.0583501\pi$
$383$			7.13487i			0.364575i	−0.983245	+	0.182287i	$0.941650\pi$
$384$	67.6282	+	67.6282i	3.45114	+	3.45114i
$385$	1.77619	+	1.77619i	0.0905228	+	0.0905228i
$386$	17.6176	−	17.6176i	0.896712	−	0.896712i
$387$	−31.6433			−1.60852
$388$	−32.7023	+	32.7023i	−1.66021	+	1.66021i
$389$			0.104585i			0.00530269i	0.999996	+	0.00265134i	$0.000843950\pi$
$389$			0.104585i			0.00530269i	−0.999996	+	0.00265134i	$0.999156\pi$
$390$	−6.20227			−0.314064
$391$	0.621033	+	0.568309i	0.0314070	+	0.0287406i
$392$	−5.61769			−0.283736
$393$		−	11.7840i		−	0.594423i
$394$	−9.27299	+	9.27299i	−0.467166	+	0.467166i
$395$	5.86741			0.295222
$396$	22.2244	−	22.2244i	1.11682	−	1.11682i
$397$	9.38954	+	9.38954i	0.471247	+	0.471247i	0.902318	−	0.431071i	$-0.141864\pi$
$397$	9.38954	+	9.38954i	0.471247	+	0.471247i	−0.431071	+	0.902318i	$0.641864\pi$
$398$	20.1955	+	20.1955i	1.01231	+	1.01231i
$399$		−	22.4525i		−	1.12403i
$400$			59.5274i			2.97637i
$401$	17.8571	+	17.8571i	0.891742	+	0.891742i	0.994687	−	0.102945i	$-0.0328267\pi$
$401$	17.8571	+	17.8571i	0.891742	+	0.891742i	−0.102945	+	0.994687i	$0.532827\pi$
$402$	16.5706	+	16.5706i	0.826465	+	0.826465i
$403$	6.51648	−	6.51648i	0.324609	−	0.324609i
$404$	0.0719527			0.00357978
$405$	4.83483	−	4.83483i	0.240244	−	0.240244i
$406$		−	41.0968i		−	2.03960i
$407$	10.2048			0.505833
$408$	83.3020	+	76.2299i	4.12406	+	3.77394i
$409$	−30.1939			−1.49299			−0.746497	−	0.665389i	$-0.768266\pi$
$409$	−30.1939			−1.49299			−0.746497	+	0.665389i	$0.768266\pi$
$410$			2.93365i			0.144883i
$411$	−48.2920	+	48.2920i	−2.38207	+	2.38207i
$412$	−28.9717			−1.42733
$413$	8.62922	−	8.62922i	0.424616	−	0.424616i
$414$	−2.28852	−	2.28852i	−0.112475	−	0.112475i
$415$	−1.14375	−	1.14375i	−0.0561447	−	0.0561447i
$416$			17.1725i			0.841950i
$417$		−	21.0091i		−	1.02882i
$418$	5.26483	+	5.26483i	0.257511	+	0.257511i
$419$	−11.7119	−	11.7119i	−0.572164	−	0.572164i	0.360569	−	0.932733i	$-0.382583\pi$
$419$	−11.7119	−	11.7119i	−0.572164	−	0.572164i	−0.932733	+	0.360569i	$0.882583\pi$
$420$	28.4504	−	28.4504i	1.38824	−	1.38824i
$421$	14.6998			0.716423			0.358211	−	0.933641i	$-0.383387\pi$
$421$	14.6998			0.716423			0.358211	+	0.933641i	$0.383387\pi$
$422$	22.4519	−	22.4519i	1.09294	−	1.09294i
$423$		−	35.9436i		−	1.74764i
$424$	−20.2147			−0.981711
$425$	0.761587	+	17.1799i	0.0369424	+	0.833347i
$426$	−8.82763			−0.427700
$427$			21.0367i			1.01804i
$428$	25.8380	−	25.8380i	1.24893	−	1.24893i
$429$	2.50556			0.120970
$430$	9.49859	−	9.49859i	0.458062	−	0.458062i
$431$	21.3352	+	21.3352i	1.02768	+	1.02768i	0.999606	+	0.0280760i	$0.00893804\pi$
$431$	21.3352	+	21.3352i	1.02768	+	1.02768i	0.0280760	+	0.999606i	$0.491062\pi$
$432$	−84.9084	−	84.9084i	−4.08516	−	4.08516i
$433$		−	9.76430i		−	0.469242i	−0.972087	−	0.234621i	$-0.924615\pi$
$433$		−	9.76430i		−	0.469242i	0.972087	−	0.234621i	$-0.0753849\pi$
$434$			81.9663i			3.93451i
$435$	10.4863	+	10.4863i	0.502778	+	0.502778i
$436$	9.80019	+	9.80019i	0.469344	+	0.469344i
$437$	0.395416	−	0.395416i	0.0189153	−	0.0189153i
$438$	49.1162			2.34686
$439$	1.44773	−	1.44773i	0.0690962	−	0.0690962i	−0.671714	−	0.740810i	$-0.734442\pi$
$439$	1.44773	−	1.44773i	0.0690962	−	0.0690962i	0.740810	+	0.671714i	$0.234442\pi$
$440$			8.39168i			0.400058i
$441$	3.55456			0.169265
$442$	0.418520	+	9.44099i	0.0199070	+	0.449062i
$443$	11.8435			0.562700			0.281350	−	0.959605i	$-0.409218\pi$
$443$	11.8435			0.562700			0.281350	+	0.959605i	$0.409218\pi$
$444$		−	163.457i		−	7.75733i
$445$	7.37201	−	7.37201i	0.349467	−	0.349467i
$446$	−55.5198			−2.62894
$447$	−5.05819	+	5.05819i	−0.239244	+	0.239244i
$448$	−52.3215	−	52.3215i	−2.47196	−	2.47196i
$449$	17.5370	+	17.5370i	0.827620	+	0.827620i	0.987187	−	0.159567i	$-0.0510098\pi$
$449$	17.5370	+	17.5370i	0.827620	+	0.827620i	−0.159567	+	0.987187i	$0.551010\pi$
$450$		−	66.1149i		−	3.11668i
$451$		−	1.18512i		−	0.0558052i
$452$	−42.0314	−	42.0314i	−1.97699	−	1.97699i
$453$	7.71195	+	7.71195i	0.362339	+	0.362339i
$454$	−32.2138	+	32.2138i	−1.51187	+	1.51187i
$455$	2.11787			0.0992873
$456$	53.0390	−	53.0390i	2.48378	−	2.48378i
$457$			23.7217i			1.10965i	0.831966	+	0.554827i	$0.187216\pi$
$457$			23.7217i			1.10965i	−0.831966	+	0.554827i	$0.812784\pi$
$458$	−35.5511			−1.66119
$459$	−25.5913	−	23.4187i	−1.19450	−	1.09309i
$460$	1.00209			0.0467227
$461$			6.83273i			0.318232i	0.987260	+	0.159116i	$0.0508644\pi$
$461$			6.83273i			0.318232i	−0.987260	+	0.159116i	$0.949136\pi$
$462$	−15.7578	+	15.7578i	−0.733121	+	0.733121i
$463$	14.4341			0.670809			0.335404	−	0.942074i	$-0.391127\pi$
$463$	14.4341			0.670809			0.335404	+	0.942074i	$0.391127\pi$
$464$	55.3075	−	55.3075i	2.56759	−	2.56759i
$465$	−20.9145	−	20.9145i	−0.969889	−	0.969889i
$466$	−23.2075	−	23.2075i	−1.07507	−	1.07507i
$467$		−	13.6249i		−	0.630485i	−0.949011	−	0.315242i	$-0.897914\pi$
$467$		−	13.6249i		−	0.630485i	0.949011	−	0.315242i	$-0.102086\pi$
$468$		−	26.4997i		−	1.22495i
$469$	−5.65831	−	5.65831i	−0.261276	−	0.261276i
$470$	10.7894	+	10.7894i	0.497679	+	0.497679i
$471$	−36.5053	+	36.5053i	−1.68207	+	1.68207i
$472$	40.7692			1.87655
$473$	−3.83719	+	3.83719i	−0.176434	+	0.176434i
$474$			52.0541i			2.39093i
$475$	11.4235			0.524145
$476$	−45.2264	−	41.3868i	−2.07295	−	1.89696i
$477$	12.7907			0.585646
$478$		−	17.1938i		−	0.786428i
$479$	20.9979	−	20.9979i	0.959420	−	0.959420i	−0.0397881	−	0.999208i	$-0.512668\pi$
$479$	20.9979	−	20.9979i	0.959420	−	0.959420i	0.999208	+	0.0397881i	$0.0126683\pi$
$480$	55.1148			2.51563
$481$	6.08395	−	6.08395i	0.277404	−	0.277404i
$482$	43.7017	+	43.7017i	1.99056	+	1.99056i
$483$	1.18350	+	1.18350i	0.0538510	+	0.0538510i
$484$		−	5.39003i		−	0.245001i
$485$			7.81313i			0.354776i
$486$	−5.62442	−	5.62442i	−0.255129	−	0.255129i
$487$	−11.6881	−	11.6881i	−0.529639	−	0.529639i	0.390826	−	0.920465i	$-0.372189\pi$
$487$	−11.6881	−	11.6881i	−0.529639	−	0.529639i	−0.920465	+	0.390826i	$0.872189\pi$
$488$	−49.6945	+	49.6945i	−2.24957	+	2.24957i
$489$	−28.8355			−1.30398
$490$	−1.06700	+	1.06700i	−0.0482019	+	0.0482019i
$491$		−	29.5800i		−	1.33493i	−0.744642	−	0.667464i	$-0.767380\pi$
$491$		−	29.5800i		−	1.33493i	0.744642	−	0.667464i	$-0.232620\pi$
$492$	−18.9829			−0.855815
$493$	15.2544	−	16.6696i	0.687024	−	0.750762i
$494$	6.27762			0.282444
$495$		−	5.30979i		−	0.238657i
$496$	−110.309	+	110.309i	−4.95303	+	4.95303i
$497$	3.01434			0.135212
$498$	10.1471	−	10.1471i	0.454702	−	0.454702i
$499$	28.3188	+	28.3188i	1.26772	+	1.26772i	0.947262	+	0.320460i	$0.103838\pi$
$499$	28.3188	+	28.3188i	1.26772	+	1.26772i	0.320460	+	0.947262i	$0.396162\pi$
$500$	31.8278	+	31.8278i	1.42338	+	1.42338i
$501$		−	60.0695i		−	2.68371i
$502$		−	5.30684i		−	0.236856i
$503$	−9.37489	−	9.37489i	−0.418005	−	0.418005i	0.466510	−	0.884516i	$-0.345511\pi$
$503$	−9.37489	−	9.37489i	−0.418005	−	0.418005i	−0.884516	+	0.466510i	$0.845511\pi$
$504$	104.820	+	104.820i	4.66907	+	4.66907i
$505$	0.00859537	−	0.00859537i	0.000382489	−	0.000382489i
$506$	−0.555030			−0.0246741
$507$	−25.8235	+	25.8235i	−1.14686	+	1.14686i
$508$		−	92.2959i		−	4.09497i
$509$	12.1006			0.536349			0.268175	−	0.963370i	$-0.413580\pi$
$509$	12.1006			0.536349			0.268175	+	0.963370i	$0.413580\pi$
$510$	30.3007	−	1.34323i	1.34174	−	0.0594794i
$511$	−16.7715			−0.741930
$512$		−	27.6333i		−	1.22123i
$513$	−16.2942	+	16.2942i	−0.719405	+	0.719405i
$514$	48.2586			2.12860
$515$	−3.46092	+	3.46092i	−0.152506	+	0.152506i
$516$	61.4628	+	61.4628i	2.70575	+	2.70575i
$517$	−4.35866	−	4.35866i	−0.191693	−	0.191693i
$518$			76.5257i			3.36235i
$519$		−	31.4941i		−	1.38244i
$520$	5.00300	+	5.00300i	0.219396	+	0.219396i
$521$	−22.7068	−	22.7068i	−0.994804	−	0.994804i	0.00518245	−	0.999987i	$-0.498350\pi$
$521$	−22.7068	−	22.7068i	−0.994804	−	0.994804i	−0.999987	+	0.00518245i	$0.998350\pi$
$522$	−61.4280	+	61.4280i	−2.68863	+	2.68863i
$523$	18.0503			0.789286			0.394643	−	0.918835i	$-0.370868\pi$
$523$	18.0503			0.789286			0.394643	+	0.918835i	$0.370868\pi$
$524$	−15.1133	+	15.1133i	−0.660227	+	0.660227i
$525$			34.1909i			1.49221i
$526$	−59.0836			−2.57617
$527$	−30.4245	+	33.2470i	−1.32531	+	1.44826i
$528$	−42.4134			−1.84581
$529$		−	22.9583i		−	0.998188i
$530$	−3.83947	+	3.83947i	−0.166776	+	0.166776i
$531$	−25.7965			−1.11947
$532$	−28.7960	+	28.7960i	−1.24847	+	1.24847i
$533$	−0.706552	−	0.706552i	−0.0306042	−	0.0306042i
$534$	65.4025	+	65.4025i	2.83024	+	2.83024i
$535$		−	6.17313i		−	0.266888i
$536$		−	26.7330i		−	1.15469i
$537$	−11.1235	−	11.1235i	−0.480012	−	0.480012i
$538$	25.1538	+	25.1538i	1.08446	+	1.08446i
$539$	0.431039	−	0.431039i	0.0185662	−	0.0185662i
$540$	−41.2938			−1.77700
$541$	−1.09798	+	1.09798i	−0.0472058	+	0.0472058i	−0.730316	−	0.683110i	$-0.760627\pi$
$541$	−1.09798	+	1.09798i	−0.0472058	+	0.0472058i	0.683110	+	0.730316i	$0.260627\pi$
$542$			46.8410i			2.01199i
$543$	−15.0569			−0.646153
$544$	−3.71907	−	83.8947i	−0.159454	−	3.59696i
$545$	2.34143			0.100296
$546$			18.7892i			0.804103i
$547$	7.68240	−	7.68240i	0.328476	−	0.328476i	−0.523531	−	0.852007i	$-0.675386\pi$
$547$	7.68240	−	7.68240i	0.328476	−	0.328476i	0.852007	+	0.523531i	$0.175386\pi$
$548$	123.872			5.29154
$549$	31.4439	−	31.4439i	1.34199	−	1.34199i
$550$	−8.01733	−	8.01733i	−0.341860	−	0.341860i
$551$	−10.6137	−	10.6137i	−0.452158	−	0.452158i
$552$			5.59149i			0.237990i
$553$		−	17.7748i		−	0.755860i
$554$	−59.5508	−	59.5508i	−2.53007	−	2.53007i
$555$	−19.5263	−	19.5263i	−0.828847	−	0.828847i
$556$	−26.9448	+	26.9448i	−1.14271	+	1.14271i
$557$	23.7355			1.00571			0.502853	−	0.864372i	$-0.332284\pi$
$557$	23.7355			1.00571			0.502853	+	0.864372i	$0.332284\pi$
$558$	122.516	−	122.516i	5.18653	−	5.18653i
$559$			4.57535i			0.193517i
$560$	−35.8507			−1.51497
$561$	−12.2407	+	0.542633i	−0.516803	+	0.0229100i
$562$	35.5025			1.49758
$563$		−	3.46908i		−	0.146204i	−0.997324	−	0.0731021i	$-0.976710\pi$
$563$		−	3.46908i		−	0.146204i	0.997324	−	0.0731021i	$-0.0232899\pi$
$564$	−69.8155	+	69.8155i	−2.93976	+	2.93976i
$565$	−10.0420			−0.422471
$566$	22.1901	−	22.1901i	0.932721	−	0.932721i
$567$	−14.6466	−	14.6466i	−0.615101	−	0.615101i
$568$	7.12071	+	7.12071i	0.298778	+	0.298778i
$569$		−	28.1793i		−	1.18134i	−0.806914	−	0.590670i	$-0.798864\pi$
$569$		−	28.1793i		−	1.18134i	0.806914	−	0.590670i	$-0.201136\pi$
$570$		−	20.1479i		−	0.843904i
$571$	−13.0436	−	13.0436i	−0.545859	−	0.545859i	0.379381	−	0.925240i	$-0.376137\pi$
$571$	−13.0436	−	13.0436i	−0.545859	−	0.545859i	−0.925240	+	0.379381i	$0.876137\pi$
$572$	−3.21345	−	3.21345i	−0.134361	−	0.134361i
$573$	10.7926	−	10.7926i	0.450868	−	0.450868i
$574$	8.88723			0.370946
$575$	−0.602144	+	0.602144i	−0.0251111	+	0.0251111i
$576$			156.411i			6.51714i
$577$	22.2920			0.928027			0.464014	−	0.885828i	$-0.346409\pi$
$577$	22.2920			0.928027			0.464014	+	0.885828i	$0.346409\pi$
$578$	−4.08929	−	46.0325i	−0.170092	−	1.91470i
$579$	27.2363			1.13190
$580$		−	26.8979i		−	1.11687i
$581$	−3.46490	+	3.46490i	−0.143748	+	0.143748i
$582$	−69.3160			−2.87324
$583$	1.55105	−	1.55105i	0.0642379	−	0.0642379i
$584$	−39.6190	−	39.6190i	−1.63945	−	1.63945i
$585$	−3.16562	−	3.16562i	−0.130882	−	0.130882i
$586$			48.4612i			2.00191i
$587$		−	36.2238i		−	1.49512i	−0.664196	−	0.747559i	$-0.731226\pi$
$587$		−	36.2238i		−	1.49512i	0.664196	−	0.747559i	$-0.268774\pi$
$588$	−6.90424	−	6.90424i	−0.284726	−	0.284726i
$589$	21.1686	+	21.1686i	0.872239	+	0.872239i
$590$	7.74349	−	7.74349i	0.318795	−	0.318795i
$591$	−14.3357			−0.589694
$592$	−102.987	+	102.987i	−4.23275	+	4.23275i
$593$			37.7701i			1.55103i	0.631329	+	0.775515i	$0.282510\pi$
$593$			37.7701i			1.55103i	−0.631329	+	0.775515i	$0.717490\pi$
$594$	22.8715			0.938428
$595$	−10.3467	+	0.458670i	−0.424173	+	0.0188036i
$596$	12.9746			0.531459
$597$			31.2215i			1.27781i
$598$	−0.330901	+	0.330901i	−0.0135315	+	0.0135315i
$599$	−34.1475			−1.39523			−0.697615	−	0.716472i	$-0.745756\pi$
$599$	−34.1475			−1.39523			−0.697615	+	0.716472i	$0.745756\pi$
$600$	−80.7684	+	80.7684i	−3.29736	+	3.29736i
$601$	12.5854	+	12.5854i	0.513370	+	0.513370i	0.915557	−	0.402187i	$-0.131750\pi$
$601$	12.5854	+	12.5854i	0.513370	+	0.513370i	−0.402187	+	0.915557i	$0.631750\pi$
$602$	−28.7751	−	28.7751i	−1.17278	−	1.17278i
$603$			16.9151i			0.688837i
$604$		−	19.7816i		−	0.804902i
$605$	−0.643884	−	0.643884i	−0.0261776	−	0.0261776i
$606$	0.0762558	+	0.0762558i	0.00309768	+	0.00309768i
$607$	17.8398	−	17.8398i	0.724097	−	0.724097i	−0.245340	−	0.969437i	$-0.578900\pi$
$607$	17.8398	−	17.8398i	0.724097	−	0.724097i	0.969437	+	0.245340i	$0.0788997\pi$
$608$	−55.7844			−2.26236
$609$	31.7672	−	31.7672i	1.28727	−	1.28727i
$610$			18.8775i			0.764326i
$611$	−5.19713			−0.210254
$612$	5.73908	+	129.462i	0.231988	+	5.23320i
$613$	43.2978			1.74878			0.874391	−	0.485223i	$-0.161261\pi$
$613$	43.2978			1.74878			0.874391	+	0.485223i	$0.161261\pi$
$614$		−	85.9262i		−	3.46770i
$615$	−2.26767	+	2.26767i	−0.0914412	+	0.0914412i
$616$	25.4218			1.02427
$617$	30.4862	−	30.4862i	1.22733	−	1.22733i	0.262356	−	0.964971i	$-0.415500\pi$
$617$	30.4862	−	30.4862i	1.22733	−	1.22733i	0.964971	−	0.262356i	$-0.0844995\pi$
$618$	−30.7043	−	30.7043i	−1.23511	−	1.23511i
$619$	24.3133	+	24.3133i	0.977235	+	0.977235i	0.999747	−	0.0225116i	$-0.00716627\pi$
$619$	24.3133	+	24.3133i	0.977235	+	0.977235i	−0.0225116	+	0.999747i	$0.507166\pi$
$620$			53.6470i			2.15452i
$621$		−	1.71777i		−	0.0689317i
$622$	10.7869	+	10.7869i	0.432514	+	0.432514i
$623$	−22.3328	−	22.3328i	−0.894745	−	0.894745i
$624$	−25.2863	+	25.2863i	−1.01226	+	1.01226i
$625$	−13.2499			−0.529997
$626$	15.8247	−	15.8247i	0.632481	−	0.632481i
$627$			8.13926i			0.325051i
$628$	93.6381			3.73657
$629$	−28.4050	+	31.0402i	−1.13258	+	1.23766i
$630$	39.8181			1.58639
$631$			21.7202i			0.864669i	0.901713	+	0.432335i	$0.142310\pi$
$631$			21.7202i			0.864669i	−0.901713	+	0.432335i	$0.857690\pi$
$632$	41.9889	−	41.9889i	1.67023	−	1.67023i
$633$	34.7099			1.37959
$634$	−7.35058	+	7.35058i	−0.291929	+	0.291929i
$635$	−11.0255	−	11.0255i	−0.437535	−	0.437535i
$636$	−24.8442	−	24.8442i	−0.985136	−	0.985136i
$637$		−	0.513958i		−	0.0203638i
$638$			14.8980i			0.589817i
$639$	−4.50559	−	4.50559i	−0.178238	−	0.178238i
$640$	−20.7225	−	20.7225i	−0.819128	−	0.819128i
$641$	22.0843	−	22.0843i	0.872279	−	0.872279i	−0.120441	−	0.992720i	$-0.538431\pi$
$641$	22.0843	−	22.0843i	0.872279	−	0.872279i	0.992720	+	0.120441i	$0.0384310\pi$
$642$	54.7664			2.16146
$643$	−4.13507	+	4.13507i	−0.163071	+	0.163071i	−0.783926	−	0.620854i	$-0.786786\pi$
$643$	−4.13507	+	4.13507i	−0.163071	+	0.163071i	0.620854	+	0.783926i	$0.286786\pi$
$644$		−	3.03574i		−	0.119625i
$645$	14.6845			0.578202
$646$	−30.6688	+	1.35955i	−1.20665	+	0.0534909i
$647$	−32.1636			−1.26448			−0.632240	−	0.774773i	$-0.717864\pi$
$647$	−32.1636			−1.26448			−0.632240	+	0.774773i	$0.717864\pi$
$648$		−	69.1988i		−	2.71839i
$649$	−3.12817	+	3.12817i	−0.122792	+	0.122792i
$650$	−9.55963			−0.374960
$651$	−63.3586	+	63.3586i	−2.48322	+	2.48322i
$652$	36.9823	+	36.9823i	1.44834	+	1.44834i
$653$	13.9216	+	13.9216i	0.544795	+	0.544795i	0.924931	−	0.380136i	$-0.124123\pi$
$653$	13.9216	+	13.9216i	0.544795	+	0.544795i	−0.380136	+	0.924931i	$0.624123\pi$
$654$			20.7726i			0.812272i
$655$			3.61082i			0.141087i
$656$	11.9603	+	11.9603i	0.466972	+	0.466972i
$657$	25.0687	+	25.0687i	0.978023	+	0.978023i
$658$	32.6856	−	32.6856i	1.27422	−	1.27422i
$659$	32.5730			1.26887			0.634433	−	0.772978i	$-0.281234\pi$
$659$	32.5730			1.26887			0.634433	+	0.772978i	$0.281234\pi$
$660$	−10.3135	+	10.3135i	−0.401454	+	0.401454i
$661$		−	5.86748i		−	0.228218i	−0.993468	−	0.114109i	$-0.963599\pi$
$661$		−	5.86748i		−	0.228218i	0.993468	−	0.114109i	$-0.0364014\pi$
$662$	−79.9533			−3.10747
$663$	−6.97422	+	7.62124i	−0.270856	+	0.295985i
$664$	−16.3701			−0.635283
$665$			6.87986i			0.266789i
$666$	114.384	−	114.384i	4.43230	−	4.43230i
$667$	1.11892			0.0433247
$668$	−77.0409	+	77.0409i	−2.98080	+	2.98080i
$669$	−42.9159	−	42.9159i	−1.65922	−	1.65922i
$670$	−5.07752	−	5.07752i	−0.196162	−	0.196162i
$671$		−	7.62602i		−	0.294399i
$672$		−	166.965i		−	6.44082i
$673$	−7.02800	−	7.02800i	−0.270910	−	0.270910i	0.558557	−	0.829466i	$-0.311355\pi$
$673$	−7.02800	−	7.02800i	−0.270910	−	0.270910i	−0.829466	+	0.558557i	$0.811355\pi$
$674$	−3.19948	−	3.19948i	−0.123239	−	0.123239i
$675$	24.8129	−	24.8129i	0.955050	−	0.955050i
$676$	66.2387			2.54764
$677$	−19.4242	+	19.4242i	−0.746531	+	0.746531i	−0.973826	−	0.227295i	$-0.927012\pi$
$677$	−19.4242	+	19.4242i	−0.746531	+	0.746531i	0.227295	+	0.973826i	$0.427012\pi$
$678$		−	89.0902i		−	3.42149i
$679$	23.6691			0.908338
$680$	−25.5252	−	23.3582i	−0.978848	−	0.895747i
$681$	−49.8015			−1.90840
$682$		−	29.7136i		−	1.13779i
$683$	15.3700	−	15.3700i	0.588116	−	0.588116i	−0.349005	−	0.937121i	$-0.613480\pi$
$683$	15.3700	−	15.3700i	0.588116	−	0.588116i	0.937121	+	0.349005i	$0.113480\pi$
$684$	86.0837			3.29149
$685$	14.7975	−	14.7975i	0.565385	−	0.565385i
$686$	−33.8858	−	33.8858i	−1.29377	−	1.29377i
$687$	−27.4804	−	27.4804i	−1.04844	−	1.04844i
$688$		−	77.4502i		−	2.95276i
$689$		−	1.84943i		−	0.0704575i
$690$	1.06202	+	1.06202i	0.0404304	+	0.0404304i
$691$	−20.9644	−	20.9644i	−0.797522	−	0.797522i	0.185182	−	0.982704i	$-0.440712\pi$
$691$	−20.9644	−	20.9644i	−0.797522	−	0.797522i	−0.982704	+	0.185182i	$0.940712\pi$
$692$	−40.3921	+	40.3921i	−1.53548	+	1.53548i
$693$	−16.0855			−0.611037
$694$	−19.6939	+	19.6939i	−0.747568	+	0.747568i
$695$			6.43756i			0.244191i
$696$	150.086			5.68898
$697$	3.60482	+	3.29879i	0.136542	+	0.124950i
$698$	82.7092			3.13059
$699$		−	35.8780i		−	1.35703i
$700$	43.8509	−	43.8509i	1.65741	−	1.65741i
$701$	−4.48972			−0.169574			−0.0847872	−	0.996399i	$-0.527021\pi$
$701$	−4.48972			−0.169574			−0.0847872	+	0.996399i	$0.527021\pi$
$702$	13.6356	−	13.6356i	0.514644	−	0.514644i
$703$	19.7636	+	19.7636i	0.745397	+	0.745397i
$704$	18.9670	+	18.9670i	0.714847	+	0.714847i
$705$			16.6801i			0.628210i
$706$			86.0087i			3.23698i
$707$	−0.0260389	−	0.0260389i	−0.000979292	−	0.000979292i
$708$	50.1061	+	50.1061i	1.88310	+	1.88310i
$709$	−25.5526	+	25.5526i	−0.959648	+	0.959648i	−0.999217	−	0.0395688i	$-0.987402\pi$
$709$	−25.5526	+	25.5526i	−0.959648	+	0.959648i	0.0395688	+	0.999217i	$0.487402\pi$
$710$	2.70494			0.101515
$711$	−26.5682	+	26.5682i	−0.996387	+	0.996387i
$712$		−	105.512i		−	3.95425i
$713$	−2.23165			−0.0835758
$714$	−4.06920	−	91.7931i	−0.152286	−	3.43527i
$715$	−0.767749			−0.0287122
$716$			28.5323i			1.06630i
$717$	13.2906	−	13.2906i	0.496346	−	0.496346i
$718$	−85.1297			−3.17701
$719$	−11.7079	+	11.7079i	−0.436631	+	0.436631i	−0.890876	−	0.454246i	$-0.849909\pi$
$719$	−11.7079	+	11.7079i	−0.436631	+	0.436631i	0.454246	+	0.890876i	$0.349909\pi$
$720$	53.5867	+	53.5867i	1.99706	+	1.99706i
$721$	10.4845	+	10.4845i	0.390464	+	0.390464i
$722$		−	31.2580i		−	1.16330i
$723$			67.5614i			2.51264i
$724$	19.3109	+	19.3109i	0.717684	+	0.717684i
$725$	16.1626	+	16.1626i	0.600264	+	0.600264i
$726$	5.71237	−	5.71237i	0.212006	−	0.212006i
$727$	−15.1167			−0.560648			−0.280324	−	0.959905i	$-0.590442\pi$
$727$	−15.1167			−0.560648			−0.280324	+	0.959905i	$0.590442\pi$
$728$	15.1561	−	15.1561i	0.561723	−	0.561723i
$729$		−	31.2217i		−	1.15636i
$730$	−15.0501			−0.557028
$731$	−0.990890	−	22.3525i	−0.0366494	−	0.826737i
$732$	−122.151			−4.51483
$733$			15.3984i			0.568754i	0.958713	+	0.284377i	$0.0917867\pi$
$733$			15.3984i			0.568754i	−0.958713	+	0.284377i	$0.908213\pi$
$734$	36.1231	−	36.1231i	1.33333	−	1.33333i
$735$	−1.64954			−0.0608442
$736$	2.94046	−	2.94046i	0.108387	−	0.108387i
$737$	2.05119	+	2.05119i	0.0755566	+	0.0755566i
$738$	−13.2839	−	13.2839i	−0.488986	−	0.488986i
$739$			51.6085i			1.89845i	0.314598	+	0.949225i	$0.398130\pi$
$739$			51.6085i			1.89845i	−0.314598	+	0.949225i	$0.601870\pi$
$740$			50.0862i			1.84120i
$741$	4.85250	+	4.85250i	0.178261	+	0.178261i
$742$	11.6313	+	11.6313i	0.426999	+	0.426999i
$743$	12.5773	−	12.5773i	0.461416	−	0.461416i	−0.437703	−	0.899119i	$-0.644208\pi$
$743$	12.5773	−	12.5773i	0.461416	−	0.461416i	0.899119	+	0.437703i	$0.144208\pi$
$744$	−299.341			−10.9744
$745$	1.54992	−	1.54992i	0.0567847	−	0.0567847i
$746$			96.2560i			3.52418i
$747$	10.3581			0.378982
$748$	16.3950	+	15.0031i	0.599461	+	0.548569i
$749$	−18.7009			−0.683317
$750$			67.4626i			2.46338i
$751$	4.03454	−	4.03454i	0.147222	−	0.147222i	−0.629654	−	0.776876i	$-0.716803\pi$
$751$	4.03454	−	4.03454i	0.147222	−	0.147222i	0.776876	+	0.629654i	$0.216803\pi$
$752$	87.9756			3.20814
$753$	4.10210	−	4.10210i	0.149489	−	0.149489i
$754$	8.88196	+	8.88196i	0.323462	+	0.323462i
$755$	−2.36308	−	2.36308i	−0.0860013	−	0.0860013i
$756$			125.096i			4.54969i
$757$		−	20.5800i		−	0.747992i	−0.927430	−	0.373996i	$-0.877987\pi$
$757$		−	20.5800i		−	0.747992i	0.927430	−	0.373996i	$-0.122013\pi$
$758$	3.45697	+	3.45697i	0.125563	+	0.125563i
$759$	−0.429029	−	0.429029i	−0.0155728	−	0.0155728i
$760$	−16.2521	+	16.2521i	−0.589526	+	0.589526i
$761$	−34.5162			−1.25121			−0.625605	−	0.780140i	$-0.715148\pi$
$761$	−34.5162			−1.25121			−0.625605	+	0.780140i	$0.715148\pi$
$762$	97.8156	−	97.8156i	3.54348	−	3.54348i
$763$		−	7.09315i		−	0.256789i
$764$	−27.6837			−1.00156
$765$	16.1509	+	14.7798i	0.583939	+	0.534364i
$766$	19.3958			0.700800
$767$			3.72994i			0.134680i
$768$	71.1149	−	71.1149i	2.56614	−	2.56614i
$769$	16.1800			0.583465			0.291732	−	0.956500i	$-0.405768\pi$
$769$	16.1800			0.583465			0.291732	+	0.956500i	$0.405768\pi$
$770$	4.82849	−	4.82849i	0.174007	−	0.174007i
$771$	37.3032	+	37.3032i	1.34344	+	1.34344i
$772$	−34.9313	−	34.9313i	−1.25720	−	1.25720i
$773$			27.9256i			1.00441i	0.864748	+	0.502206i	$0.167478\pi$
$773$			27.9256i			1.00441i	−0.864748	+	0.502206i	$0.832522\pi$
$774$			86.0211i			3.09196i
$775$	−32.2358	−	32.2358i	−1.15795	−	1.15795i
$776$	55.9130	+	55.9130i	2.00716	+	2.00716i
$777$	−59.1532	+	59.1532i	−2.12211	+	2.12211i
$778$	0.284311			0.0101930
$779$	2.29522	−	2.29522i	0.0822348	−	0.0822348i
$780$			12.2975i			0.440323i
$781$	−1.09273			−0.0391009
$782$	1.54492	−	1.68825i	0.0552464	−	0.0603718i
$783$	−46.1079			−1.64776
$784$			8.70014i			0.310719i
$785$	11.1859	−	11.1859i	0.399241	−	0.399241i
$786$	−32.0343			−1.14262
$787$	15.4260	−	15.4260i	0.549877	−	0.549877i	−0.376528	−	0.926405i	$-0.622882\pi$
$787$	15.4260	−	15.4260i	0.549877	−	0.549877i	0.926405	+	0.376528i	$0.122882\pi$
$788$	18.3860	+	18.3860i	0.654975	+	0.654975i
$789$	−45.6707	−	45.6707i	−1.62592	−	1.62592i
$790$		−	15.9503i		−	0.567487i
$791$			30.4214i			1.08166i
$792$	−37.9984	−	37.9984i	−1.35021	−	1.35021i
$793$	−4.54652	−	4.54652i	−0.161452	−	0.161452i
$794$	25.5251	−	25.5251i	0.905851	−	0.905851i
$795$	−5.93570			−0.210518
$796$	40.0425	−	40.0425i	1.41927	−	1.41927i
$797$			29.5940i			1.04827i	0.851635	+	0.524136i	$0.175612\pi$
$797$			29.5940i			1.04827i	−0.851635	+	0.524136i	$0.824388\pi$
$798$	−61.0363			−2.16066
$799$	25.3902	−	1.12555i	0.898240	−	0.0398191i
$800$	84.9491			3.00340
$801$			66.7624i			2.35893i
$802$	48.5439	−	48.5439i	1.71414	−	1.71414i
$803$	6.07985			0.214553
$804$	32.8553	−	32.8553i	1.15872	−	1.15872i
$805$	−0.362645	−	0.362645i	−0.0127816	−	0.0127816i
$806$	−17.7148	−	17.7148i	−0.623977	−	0.623977i
$807$			38.8869i			1.36888i
$808$		−	0.123022i		−	0.00432790i
$809$	26.9753	+	26.9753i	0.948400	+	0.948400i	0.998733	−	0.0503325i	$-0.0160281\pi$
$809$	26.9753	+	26.9753i	0.948400	+	0.948400i	−0.0503325	+	0.998733i	$0.516028\pi$
$810$	−13.1433	−	13.1433i	−0.461808	−	0.461808i
$811$	4.81956	−	4.81956i	0.169238	−	0.169238i	−0.617407	−	0.786644i	$-0.711817\pi$
$811$	4.81956	−	4.81956i	0.169238	−	0.169238i	0.786644	+	0.617407i	$0.211817\pi$
$812$	−81.4847			−2.85955
$813$	−36.2073	+	36.2073i	−1.26985	+	1.26985i
$814$		−	27.7413i		−	0.972333i
$815$	8.83571			0.309501
$816$	118.058	−	129.010i	4.13285	−	4.51626i
$817$	−14.8629			−0.519988
$818$			82.0810i			2.86989i
$819$	−9.58994	+	9.58994i	−0.335099	+	0.335099i
$820$	5.81670			0.203128
$821$	20.9509	−	20.9509i	0.731191	−	0.731191i	−0.239665	−	0.970856i	$-0.577038\pi$
$821$	20.9509	−	20.9509i	0.731191	−	0.731191i	0.970856	+	0.239665i	$0.0770376\pi$
$822$	131.280	+	131.280i	4.57891	+	4.57891i
$823$	7.93140	+	7.93140i	0.276471	+	0.276471i	0.831699	−	0.555227i	$-0.187369\pi$
$823$	7.93140	+	7.93140i	0.276471	+	0.276471i	−0.555227	+	0.831699i	$0.687369\pi$
$824$			49.5347i			1.72562i
$825$		−	12.3945i		−	0.431523i
$826$	−23.4582	−	23.4582i	−0.816214	−	0.816214i
$827$	−12.2431	−	12.2431i	−0.425733	−	0.425733i	0.461439	−	0.887172i	$-0.347333\pi$
$827$	−12.2431	−	12.2431i	−0.425733	−	0.425733i	−0.887172	+	0.461439i	$0.847333\pi$
$828$	−4.53757	+	4.53757i	−0.157691	+	0.157691i
$829$	26.5358			0.921625			0.460813	−	0.887498i	$-0.347558\pi$
$829$	26.5358			0.921625			0.460813	+	0.887498i	$0.347558\pi$
$830$	−3.10925	+	3.10925i	−0.107924	+	0.107924i
$831$		−	92.0636i		−	3.19365i
$832$	22.6157			0.784060
$833$	0.111309	+	2.51090i	0.00385662	+	0.0869976i
$834$	−57.1123			−1.97764
$835$			18.4064i			0.636980i
$836$	10.4388	−	10.4388i	0.361035	−	0.361035i
$837$	91.9609			3.17863
$838$	−31.8383	+	31.8383i	−1.09984	+	1.09984i
$839$	3.75326	+	3.75326i	0.129577	+	0.129577i	0.768921	−	0.639344i	$-0.220794\pi$
$839$	3.75326	+	3.75326i	0.129577	+	0.129577i	−0.639344	+	0.768921i	$0.720794\pi$
$840$	−48.6433	−	48.6433i	−1.67835	−	1.67835i
$841$		−	1.03373i		−	0.0356458i
$842$		−	39.9607i		−	1.37714i
$843$	27.4429	+	27.4429i	0.945183	+	0.945183i
$844$	−44.5164	−	44.5164i	−1.53232	−	1.53232i
$845$	7.91278	−	7.91278i	0.272208	−	0.272208i
$846$	−97.7113			−3.35938
$847$	−1.95059	+	1.95059i	−0.0670230	+	0.0670230i
$848$			31.3065i			1.07507i
$849$	34.3053			1.17735
$850$	46.7028	−	2.07034i	1.60189	−	0.0710122i
$851$	−2.08352			−0.0714221
$852$			17.5030i			0.599642i
$853$	−33.7813	+	33.7813i	−1.15665	+	1.15665i	−0.171457	+	0.985192i	$0.554847\pi$
$853$	−33.7813	+	33.7813i	−1.15665	+	1.15665i	−0.985192	+	0.171457i	$0.945153\pi$
$854$	57.1875			1.95692
$855$	10.2834	−	10.2834i	0.351686	−	0.351686i
$856$	−44.1767	−	44.1767i	−1.50993	−	1.50993i
$857$	−11.7590	−	11.7590i	−0.401680	−	0.401680i	0.477145	−	0.878825i	$-0.341672\pi$
$857$	−11.7590	−	11.7590i	−0.401680	−	0.401680i	−0.878825	+	0.477145i	$0.841672\pi$
$858$		−	6.81127i		−	0.232533i
$859$			1.30929i			0.0446723i	0.999751	+	0.0223362i	$0.00711041\pi$
$859$			1.30929i			0.0446723i	−0.999751	+	0.0223362i	$0.992890\pi$
$860$	−18.8333	−	18.8333i	−0.642211	−	0.642211i
$861$	6.86969	+	6.86969i	0.234118	+	0.234118i
$862$	57.9990	−	57.9990i	1.97545	−	1.97545i
$863$	−31.2569			−1.06400			−0.531999	−	0.846745i	$-0.678559\pi$
$863$	−31.2569			−1.06400			−0.531999	+	0.846745i	$0.678559\pi$
$864$	−121.169	+	121.169i	−4.12226	+	4.12226i
$865$			9.65037i			0.328122i
$866$	−26.5439			−0.901997
$867$	32.4215	−	38.7434i	1.10109	−	1.31579i
$868$	162.519			5.51624
$869$			6.44353i			0.218582i
$870$	28.5065	−	28.5065i	0.966461	−	0.966461i
$871$	2.44578			0.0828721
$872$	16.7560	−	16.7560i	0.567429	−	0.567429i
$873$	−35.3786	−	35.3786i	−1.19739	−	1.19739i
$874$	−1.07492	−	1.07492i	−0.0363598	−	0.0363598i
$875$		−	23.0362i		−	0.778767i
$876$		−	97.3850i		−	3.29034i
$877$	3.32394	+	3.32394i	0.112241	+	0.112241i	0.760997	−	0.648756i	$-0.224710\pi$
$877$	3.32394	+	3.32394i	0.112241	+	0.112241i	−0.648756	+	0.760997i	$0.724710\pi$
$878$	−3.93558	−	3.93558i	−0.132820	−	0.132820i
$879$	−37.4597	+	37.4597i	−1.26349	+	1.26349i
$880$	12.9962			0.438103
$881$	−8.53425	+	8.53425i	−0.287526	+	0.287526i	−0.836101	−	0.548575i	$-0.815171\pi$
$881$	−8.53425	+	8.53425i	−0.287526	+	0.287526i	0.548575	+	0.836101i	$0.315171\pi$
$882$		−	9.66292i		−	0.325368i
$883$	25.1024			0.844764			0.422382	−	0.906418i	$-0.361194\pi$
$883$	25.1024			0.844764			0.422382	+	0.906418i	$0.361194\pi$
$884$	18.7191	−	0.829821i	0.629592	−	0.0279099i
$885$	11.9712			0.402407
$886$		−	32.1960i		−	1.08164i
$887$	−10.8092	+	10.8092i	−0.362937	+	0.362937i	−0.864893	−	0.501956i	$-0.832614\pi$
$887$	−10.8092	+	10.8092i	−0.362937	+	0.362937i	0.501956	+	0.864893i	$0.332614\pi$
$888$	−279.472			−9.37847
$889$	−33.4008	+	33.4008i	−1.12023	+	1.12023i
$890$	−20.0405	−	20.0405i	−0.671759	−	0.671759i
$891$	5.30955	+	5.30955i	0.177877	+	0.177877i
$892$			110.082i			3.68581i
$893$		−	16.8828i		−	0.564960i
$894$	13.7505	+	13.7505i	0.459885	+	0.459885i
$895$	3.40843	+	3.40843i	0.113931	+	0.113931i
$896$	−62.7768	+	62.7768i	−2.09723	+	2.09723i
$897$	−0.511562			−0.0170806
$898$	47.6735	−	47.6735i	1.59089	−	1.59089i
$899$			59.9013i			1.99782i
$900$	−131.089			−4.36964
$901$	0.400532	+	9.03522i	0.0133437	+	0.301007i
$902$	−3.22171			−0.107271
$903$		−	44.4853i		−	1.48038i
$904$	−71.8637	+	71.8637i	−2.39015	+	2.39015i
$905$	4.61370			0.153365
$906$	20.9646	−	20.9646i	0.696503	−	0.696503i
$907$	27.6295	+	27.6295i	0.917423	+	0.917423i	0.996841	−	0.0794182i	$-0.0253062\pi$
$907$	27.6295	+	27.6295i	0.917423	+	0.917423i	−0.0794182	+	0.996841i	$0.525306\pi$
$908$	63.8718	+	63.8718i	2.11966	+	2.11966i
$909$			0.0778414i			0.00258184i
$910$		−	5.75735i		−	0.190854i
$911$	34.6185	+	34.6185i	1.14696	+	1.14696i	0.987147	+	0.159814i	$0.0510895\pi$
$911$	34.6185	+	34.6185i	1.14696	+	1.14696i	0.159814	+	0.987147i	$0.448911\pi$
$912$	−82.1418	−	82.1418i	−2.71999	−	2.71999i
$913$	1.25606	−	1.25606i	0.0415695	−	0.0415695i
$914$	64.4865			2.13302
$915$	−14.5920	+	14.5920i	−0.482396	+	0.482396i
$916$			70.4889i			2.32902i
$917$	10.9387			0.361226
$918$	−63.6627	+	69.5689i	−2.10118	+	2.29612i
$919$	−8.17105			−0.269538			−0.134769	−	0.990877i	$-0.543029\pi$
$919$	−8.17105			−0.269538			−0.134769	+	0.990877i	$0.543029\pi$
$920$		−	1.71333i		−	0.0564870i
$921$	66.4196	−	66.4196i	2.18860	−	2.18860i
$922$	18.5745			0.611719
$923$	−0.651469	+	0.651469i	−0.0214434	+	0.0214434i
$924$	31.2439	+	31.2439i	1.02785	+	1.02785i
$925$	−30.0962	−	30.0962i	−0.989556	−	0.989556i
$926$		−	39.2385i		−	1.28946i
$927$		−	31.3428i		−	1.02943i
$928$	−78.9271	−	78.9271i	−2.59091	−	2.59091i
$929$	−3.38065	−	3.38065i	−0.110915	−	0.110915i	0.649471	−	0.760386i	$-0.274990\pi$
$929$	−3.38065	−	3.38065i	−0.110915	−	0.110915i	−0.760386	+	0.649471i	$0.774990\pi$
$930$	−56.8554	+	56.8554i	−1.86436	+	1.86436i
$931$	1.66958			0.0547183
$932$	−46.0146	+	46.0146i	−1.50726	+	1.50726i
$933$			16.6762i			0.545953i
$934$	−37.0387			−1.21194
$935$	3.75078	−	0.166272i	0.122663	−	0.00543769i
$936$	−45.3081			−1.48094
$937$		−	54.5560i		−	1.78227i	−0.453740	−	0.891134i	$-0.649911\pi$
$937$		−	54.5560i		−	1.78227i	0.453740	−	0.891134i	$-0.350089\pi$
$938$	−15.3819	+	15.3819i	−0.502236	+	0.502236i
$939$	24.4644			0.798367
$940$	21.3927	−	21.3927i	0.697754	−	0.697754i
$941$	−20.3005	−	20.3005i	−0.661778	−	0.661778i	0.294021	−	0.955799i	$-0.405007\pi$
$941$	−20.3005	−	20.3005i	−0.661778	−	0.661778i	−0.955799	+	0.294021i	$0.905007\pi$
$942$	99.2381	+	99.2381i	3.23335	+	3.23335i
$943$			0.241967i			0.00787953i
$944$		−	63.1394i		−	2.05501i
$945$	14.9437	+	14.9437i	0.486120	+	0.486120i
$946$	10.4312	+	10.4312i	0.339149	+	0.339149i
$947$	30.3524	−	30.3524i	0.986321	−	0.986321i	−0.0135870	−	0.999908i	$-0.504325\pi$
$947$	30.3524	−	30.3524i	0.986321	−	0.986321i	0.999908	+	0.0135870i	$0.00432500\pi$
$948$	103.210			3.35212
$949$	3.62472	−	3.62472i	0.117663	−	0.117663i
$950$		−	31.0543i		−	1.00753i
$951$	−11.3638			−0.368495
$952$	−70.7616	+	77.3263i	−2.29340	+	2.50616i
$953$	−14.3583			−0.465111			−0.232555	−	0.972583i	$-0.574709\pi$
$953$	−14.3583			−0.465111			−0.232555	+	0.972583i	$0.574709\pi$
$954$		−	34.7710i		−	1.12575i
$955$	−3.30705	+	3.30705i	−0.107014	+	0.107014i
$956$	−34.0911			−1.10258
$957$	−11.5159	+	11.5159i	−0.372256	+	0.372256i
$958$	−57.0820	−	57.0820i	−1.84424	−	1.84424i
$959$	−44.8277	−	44.8277i	−1.44756	−	1.44756i
$960$		−	72.5848i		−	2.34267i
$961$		−	88.4714i		−	2.85392i
$962$	−16.5390	−	16.5390i	−0.533238	−	0.533238i
$963$	27.9526	+	27.9526i	0.900759	+	0.900759i
$964$	86.6494	−	86.6494i	2.79079	−	2.79079i
$965$	−8.34568			−0.268657
$966$	3.21729	−	3.21729i	0.103515	−	0.103515i
$967$		−	22.6031i		−	0.726867i	−0.931620	−	0.363433i	$-0.881604\pi$
$967$		−	22.6031i		−	0.726867i	0.931620	−	0.363433i	$-0.118396\pi$
$968$	−9.21565			−0.296202
$969$	−24.7574	−	22.6556i	−0.795323	−	0.727803i
$970$	21.2397			0.681965
$971$			31.6940i			1.01711i	0.861030	+	0.508555i	$0.169820\pi$
$971$			31.6940i			1.01711i	−0.861030	+	0.508555i	$0.830180\pi$
$972$	−11.1518	+	11.1518i	−0.357695	+	0.357695i
$973$	19.5020			0.625205
$974$	−31.7737	+	31.7737i	−1.01809	+	1.01809i
$975$	−7.38945	−	7.38945i	−0.236652	−	0.236652i
$976$	76.9622	+	76.9622i	2.46350	+	2.46350i
$977$			3.61138i			0.115538i	0.998330	+	0.0577691i	$0.0183987\pi$
$977$			3.61138i			0.115538i	−0.998330	+	0.0577691i	$0.981601\pi$
$978$			78.3881i			2.50657i
$979$	8.09586	+	8.09586i	0.258745	+	0.258745i
$980$	2.11558	+	2.11558i	0.0675799	+	0.0675799i
$981$	−10.6022	+	10.6022i	−0.338504	+	0.338504i
$982$	−80.4121			−2.56605
$983$	−24.2509	+	24.2509i	−0.773484	+	0.773484i	−0.978714	−	0.205230i	$-0.934206\pi$
$983$	−24.2509	+	24.2509i	−0.773484	+	0.773484i	0.205230	+	0.978714i	$0.434206\pi$
$984$			32.4562i			1.03467i
$985$	4.39273			0.139964
$986$	−45.3157	−	41.4685i	−1.44315	−	1.32063i
$987$	50.5308			1.60841
$988$		−	12.4470i		−	0.395990i
$989$	0.783441	−	0.783441i	0.0249120	−	0.0249120i
$990$	−14.4344			−0.458757
$991$	−30.6946	+	30.6946i	−0.975047	+	0.975047i	−0.999696	−	0.0246489i	$-0.992153\pi$
$991$	−30.6946	+	30.6946i	−0.975047	+	0.975047i	0.0246489	+	0.999696i	$0.492153\pi$
$992$	157.418	+	157.418i	4.99802	+	4.99802i
$993$	−61.8027	−	61.8027i	−1.96125	−	1.96125i
$994$		−	8.19437i		−	0.259910i
$995$		−	9.56684i		−	0.303289i
$996$	−20.1191	−	20.1191i	−0.637499	−	0.637499i
$997$	−13.3304	−	13.3304i	−0.422178	−	0.422178i	0.463775	−	0.885953i	$-0.346495\pi$
$997$	−13.3304	−	13.3304i	−0.422178	−	0.422178i	−0.885953	+	0.463775i	$0.846495\pi$
$998$	76.9834	−	76.9834i	2.43687	−	2.43687i
$999$	85.8569			2.71639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.1	✓	28
17.8	even	8		3179.2.a.be.1.1		14
17.9	even	8		3179.2.a.bd.1.1		14
17.13	even	4	inner	187.2.e.b.166.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.1	✓	28	1.1	even	1	trivial
187.2.e.b.166.14	yes	28	17.13	even	4	inner
3179.2.a.bd.1.1		14	17.9	even	8
3179.2.a.be.1.1		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)

\(f(q)\)	\(=\)	\(q-2.71846i q^{2} +(2.10133 - 2.10133i) q^{3} -5.39003 q^{4} +(-0.643884 + 0.643884i) q^{5} +(-5.71237 - 5.71237i) q^{6} +(1.95059 + 1.95059i) q^{7} +9.21565i q^{8} -5.83115i q^{9} +O(q^{10})\)	\(q-2.71846i q^{2} +(2.10133 - 2.10133i) q^{3} -5.39003 q^{4} +(-0.643884 + 0.643884i) q^{5} +(-5.71237 - 5.71237i) q^{6} +(1.95059 + 1.95059i) q^{7} +9.21565i q^{8} -5.83115i q^{9} +(1.75037 + 1.75037i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-11.3262 + 11.3262i) q^{12} -0.843133 q^{13} +(5.30259 - 5.30259i) q^{14} +2.70602i q^{15} +14.2723 q^{16} +(4.11906 - 0.182599i) q^{17} -15.8517 q^{18} -2.73890i q^{19} +(3.47055 - 3.47055i) q^{20} +8.19764 q^{21} +(-1.92224 + 1.92224i) q^{22} +(0.144370 + 0.144370i) q^{23} +(19.3651 + 19.3651i) q^{24} +4.17083i q^{25} +2.29202i q^{26} +(-5.94917 - 5.94917i) q^{27} +(-10.5137 - 10.5137i) q^{28} +(3.87516 - 3.87516i) q^{29} +7.35622 q^{30} +(-7.72889 + 7.72889i) q^{31} -20.3674i q^{32} -2.97172 q^{33} +(-0.496387 - 11.1975i) q^{34} -2.51191 q^{35} +31.4300i q^{36} +(-7.21588 + 7.21588i) q^{37} -7.44559 q^{38} +(-1.77170 + 1.77170i) q^{39} +(-5.93381 - 5.93381i) q^{40} +(0.838008 + 0.838008i) q^{41} -22.2850i q^{42} -5.42660i q^{43} +(3.81132 + 3.81132i) q^{44} +(3.75459 + 3.75459i) q^{45} +(0.392465 - 0.392465i) q^{46} +6.16407 q^{47} +(29.9908 - 29.9908i) q^{48} +0.609581i q^{49} +11.3382 q^{50} +(8.27179 - 9.03919i) q^{51} +4.54451 q^{52} +2.19351i q^{53} +(-16.1726 + 16.1726i) q^{54} +0.910590 q^{55} +(-17.9759 + 17.9759i) q^{56} +(-5.75532 - 5.75532i) q^{57} +(-10.5345 - 10.5345i) q^{58} -4.42391i q^{59} -14.5855i q^{60} +(5.39241 + 5.39241i) q^{61} +(21.0107 + 21.0107i) q^{62} +(11.3742 - 11.3742i) q^{63} -26.8234 q^{64} +(0.542880 - 0.542880i) q^{65} +8.07852i q^{66} -2.90082 q^{67} +(-22.2018 + 0.984211i) q^{68} +0.606739 q^{69} +6.82852i q^{70} +(0.772676 - 0.772676i) q^{71} +53.7378 q^{72} +(-4.29910 + 4.29910i) q^{73} +(19.6161 + 19.6161i) q^{74} +(8.76427 + 8.76427i) q^{75} +14.7627i q^{76} -2.75855i q^{77} +(4.81629 + 4.81629i) q^{78} +(-4.55626 - 4.55626i) q^{79} +(-9.18973 + 9.18973i) q^{80} -7.50884 q^{81} +(2.27809 - 2.27809i) q^{82} +1.77634i q^{83} -44.1855 q^{84} +(-2.53463 + 2.76977i) q^{85} -14.7520 q^{86} -16.2860i q^{87} +(6.51645 - 6.51645i) q^{88} -11.4493 q^{89} +(10.2067 - 10.2067i) q^{90} +(-1.64461 - 1.64461i) q^{91} +(-0.778161 - 0.778161i) q^{92} +32.4818i q^{93} -16.7568i q^{94} +(1.76353 + 1.76353i) q^{95} +(-42.7987 - 42.7987i) q^{96} +(6.06718 - 6.06718i) q^{97} +1.65712 q^{98} +(-4.12324 + 4.12324i) 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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