LMFDB - Embedded newform 740.2.be.a.51.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(51,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("740.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			51.9
Character	$\chi$	$=$	740.51
Dual form			740.2.be.a.711.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31917 - 0.509705i) q^{2} +(0.769115 + 1.33215i) q^{3} +(1.48040 + 1.34477i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.335590 - 2.14935i) q^{6} +(1.23671 - 0.714015i) q^{7} +(-1.26746 - 2.52855i) q^{8} +(0.316923 - 0.548926i) q^{9} +(-1.14230 - 0.833762i) q^{10} +6.06118 q^{11} +(-0.652832 + 3.00640i) q^{12} +(-0.290020 - 0.0777107i) q^{13} +(-1.99536 + 0.311548i) q^{14} +(0.398123 + 1.48582i) q^{15} +(0.383182 + 3.98160i) q^{16} +(-0.400290 - 1.49390i) q^{17} +(-0.697864 + 0.562588i) q^{18} +(1.28276 - 4.78732i) q^{19} +(1.08191 + 1.68211i) q^{20} +(1.90235 + 1.09832i) q^{21} +(-7.99571 - 3.08941i) q^{22} +(-6.35927 - 6.35927i) q^{23} +(2.39357 - 3.63319i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.342975 + 0.250338i) q^{26} +5.58969 q^{27} +(2.79102 + 0.606063i) q^{28} +(-2.10305 - 2.10305i) q^{29} +(0.232137 - 2.16297i) q^{30} +(-1.19269 + 1.19269i) q^{31} +(1.52396 - 5.44771i) q^{32} +(4.66175 + 8.07439i) q^{33} +(-0.233400 + 2.17473i) q^{34} +(1.37937 - 0.369601i) q^{35} +(1.20735 - 0.386443i) q^{36} +(5.51689 + 2.56202i) q^{37} +(-4.13229 + 5.66144i) q^{38} +(-0.119537 - 0.446118i) q^{39} +(-0.569838 - 2.77043i) q^{40} +(-5.18578 + 2.99401i) q^{41} +(-1.94969 - 2.41850i) q^{42} +(-1.36812 - 1.36812i) q^{43} +(8.97299 + 8.15090i) q^{44} +(0.448196 - 0.448196i) q^{45} +(5.14759 + 11.6303i) q^{46} +0.0202388i q^{47} +(-5.00937 + 3.57277i) q^{48} +(-2.48037 + 4.29612i) q^{49} +(-0.887580 - 1.10100i) q^{50} +(1.68223 - 1.68223i) q^{51} +(-0.324843 - 0.505054i) q^{52} +(-7.05090 + 12.2125i) q^{53} +(-7.37374 - 2.84909i) q^{54} +(5.85465 + 1.56875i) q^{55} +(-3.37290 - 2.22209i) q^{56} +(7.36400 - 1.97318i) q^{57} +(1.70234 + 3.84621i) q^{58} +(12.0314 - 3.22381i) q^{59} +(-1.40870 + 2.73499i) q^{60} +(-2.49245 + 9.30193i) q^{61} +(2.18128 - 0.965437i) q^{62} -0.905150i q^{63} +(-4.78708 + 6.40967i) q^{64} +(-0.260025 - 0.150125i) q^{65} +(-2.03407 - 13.0276i) q^{66} +(0.995335 + 1.72397i) q^{67} +(1.41637 - 2.74987i) q^{68} +(3.58047 - 13.3625i) q^{69} +(-2.00801 - 0.215506i) q^{70} +(13.4758 - 7.78027i) q^{71} +(-1.78967 - 0.105611i) q^{72} -4.59995i q^{73} +(-5.97182 - 6.19172i) q^{74} +1.53823i q^{75} +(8.33684 - 5.36214i) q^{76} +(7.49593 - 4.32778i) q^{77} +(-0.0696992 + 0.649433i) q^{78} +(-4.07787 + 15.2188i) q^{79} +(-0.660390 + 3.94511i) q^{80} +(3.34835 + 5.79952i) q^{81} +(8.36697 - 1.30638i) q^{82} +(-5.18716 - 2.99481i) q^{83} +(1.33925 + 4.18418i) q^{84} -1.54660i q^{85} +(1.10745 + 2.50212i) q^{86} +(1.18408 - 4.41906i) q^{87} +(-7.68232 - 15.3260i) q^{88} +(8.06161 - 2.16010i) q^{89} +(-0.819694 + 0.362798i) q^{90} +(-0.414157 + 0.110973i) q^{91} +(-0.862516 - 17.9661i) q^{92} +(-2.50615 - 0.671522i) q^{93} +(0.0103158 - 0.0266983i) q^{94} +(2.47810 - 4.29219i) q^{95} +(8.42925 - 2.15978i) q^{96} +(-11.4502 + 11.4502i) q^{97} +(5.46177 - 4.40304i) q^{98} +(1.92093 - 3.32714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.31917	−	0.509705i	−0.932792	−	0.360416i
$2$	−1.31917	−	0.509705i	−0.932792	−	0.360416i
$3$	0.769115	+	1.33215i	0.444049	+	0.769115i	0.997985	−	0.0634435i	$-0.0202083\pi$
$3$	0.769115	+	1.33215i	0.444049	+	0.769115i	−0.553936	+	0.832559i	$0.686875\pi$
$4$	1.48040	+	1.34477i	0.740201	+	0.672386i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−0.335590	−	2.14935i	−0.137004	−	0.877467i
$7$	1.23671	−	0.714015i	0.467433	−	0.269872i	−0.247732	−	0.968829i	$-0.579685\pi$
$7$	1.23671	−	0.714015i	0.467433	−	0.269872i	0.715164	+	0.698956i	$0.246352\pi$
$8$	−1.26746	−	2.52855i	−0.448115	−	0.893976i
$9$	0.316923	−	0.548926i	0.105641	−	0.182975i
$10$	−1.14230	−	0.833762i	−0.361226	−	0.263659i
$11$	6.06118			1.82752			0.913758	−	0.406260i	$-0.133167\pi$
$11$	6.06118			1.82752			0.913758	+	0.406260i	$0.133167\pi$
$12$	−0.652832	+	3.00640i	−0.188457	+	0.867872i
$13$	−0.290020	−	0.0777107i	−0.0804371	−	0.0215531i	0.218376	−	0.975865i	$-0.429924\pi$
$13$	−0.290020	−	0.0777107i	−0.0804371	−	0.0215531i	−0.298813	+	0.954312i	$0.596591\pi$
$14$	−1.99536	+	0.311548i	−0.533283	+	0.0832647i
$15$	0.398123	+	1.48582i	0.102795	+	0.383636i
$16$	0.383182	+	3.98160i	0.0957955	+	0.995401i
$17$	−0.400290	−	1.49390i	−0.0970845	−	0.362324i	0.900243	−	0.435388i	$-0.143389\pi$
$17$	−0.400290	−	1.49390i	−0.0970845	−	0.362324i	−0.997327	+	0.0730641i	$0.976722\pi$
$18$	−0.697864	+	0.562588i	−0.164488	+	0.132603i
$19$	1.28276	−	4.78732i	0.294285	−	1.09829i	−0.647499	−	0.762066i	$-0.724185\pi$
$19$	1.28276	−	4.78732i	0.294285	−	1.09829i	0.941784	−	0.336219i	$-0.109148\pi$
$20$	1.08191	+	1.68211i	0.241922	+	0.376130i
$21$	1.90235	+	1.09832i	0.415126	+	0.239673i
$22$	−7.99571	−	3.08941i	−1.70469	−	0.658665i
$23$	−6.35927	−	6.35927i	−1.32600	−	1.32600i	−0.908827	−	0.417174i	$-0.863021\pi$
$23$	−6.35927	−	6.35927i	−1.32600	−	1.32600i	−0.417174	−	0.908827i	$-0.636979\pi$
$24$	2.39357	−	3.63319i	0.488585	−	0.741621i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	0.342975	+	0.250338i	0.0672630	+	0.0490953i
$27$	5.58969			1.07574
$28$	2.79102	+	0.606063i	0.527452	+	0.114535i
$29$	−2.10305	−	2.10305i	−0.390526	−	0.390526i	0.484349	−	0.874875i	$-0.339057\pi$
$29$	−2.10305	−	2.10305i	−0.390526	−	0.390526i	−0.874875	+	0.484349i	$0.839057\pi$
$30$	0.232137	−	2.16297i	0.0423822	−	0.394902i
$31$	−1.19269	+	1.19269i	−0.214213	+	0.214213i	−0.806055	−	0.591841i	$-0.798401\pi$
$31$	−1.19269	+	1.19269i	−0.214213	+	0.214213i	0.591841	+	0.806055i	$0.298401\pi$
$32$	1.52396	−	5.44771i	0.269401	−	0.963028i
$33$	4.66175	+	8.07439i	0.811506	+	1.40557i
$34$	−0.233400	+	2.17473i	−0.0400277	+	0.372964i
$35$	1.37937	−	0.369601i	0.233156	−	0.0624740i
$36$	1.20735	−	0.386443i	0.201226	−	0.0644072i
$37$	5.51689	+	2.56202i	0.906970	+	0.421194i
$37$	5.51689	+	2.56202i	0.906970	+	0.421194i
$38$	−4.13229	+	5.66144i	−0.670346	+	0.918407i
$39$	−0.119537	−	0.446118i	−0.0191412	−	0.0714360i
$40$	−0.569838	−	2.77043i	−0.0900993	−	0.438044i
$41$	−5.18578	+	2.99401i	−0.809883	+	0.467586i	−0.846915	−	0.531728i	$-0.821543\pi$
$41$	−5.18578	+	2.99401i	−0.809883	+	0.467586i	0.0370324	+	0.999314i	$0.488210\pi$
$42$	−1.94969	−	2.41850i	−0.300844	−	0.373183i
$43$	−1.36812	−	1.36812i	−0.208637	−	0.208637i	0.595051	−	0.803688i	$-0.297132\pi$
$43$	−1.36812	−	1.36812i	−0.208637	−	0.208637i	−0.803688	+	0.595051i	$0.797132\pi$
$44$	8.97299	+	8.15090i	1.35273	+	1.22879i
$45$	0.448196	−	0.448196i	0.0668132	−	0.0668132i
$46$	5.14759	+	11.6303i	0.758971	+	1.71479i
$47$			0.0202388i			0.00295213i	0.999999	+	0.00147606i	$0.000469846\pi$
$47$			0.0202388i			0.00295213i	−0.999999	+	0.00147606i	$0.999530\pi$
$48$	−5.00937	+	3.57277i	−0.723040	+	0.515685i
$49$	−2.48037	+	4.29612i	−0.354338	+	0.613731i
$50$	−0.887580	−	1.10100i	−0.125523	−	0.155705i
$51$	1.68223	−	1.68223i	0.235559	−	0.235559i
$52$	−0.324843	−	0.505054i	−0.0450477	−	0.0700383i
$53$	−7.05090	+	12.2125i	−0.968515	+	1.67752i	−0.268657	+	0.963236i	$0.586580\pi$
$53$	−7.05090	+	12.2125i	−0.968515	+	1.67752i	−0.699859	+	0.714282i	$0.746754\pi$
$54$	−7.37374	−	2.84909i	−1.00344	−	0.387712i
$55$	5.85465	+	1.56875i	0.789441	+	0.211530i
$56$	−3.37290	−	2.22209i	−0.450723	−	0.296939i
$57$	7.36400	−	1.97318i	0.975385	−	0.261354i
$58$	1.70234	+	3.84621i	0.223528	+	0.505032i
$59$	12.0314	−	3.22381i	1.56636	−	0.419704i	0.631688	−	0.775223i	$-0.282362\pi$
$59$	12.0314	−	3.22381i	1.56636	−	0.419704i	0.934669	+	0.355519i	$0.115696\pi$
$60$	−1.40870	+	2.73499i	−0.181862	+	0.353086i
$61$	−2.49245	+	9.30193i	−0.319125	+	1.19099i	0.600962	+	0.799277i	$0.294784\pi$
$61$	−2.49245	+	9.30193i	−0.319125	+	1.19099i	−0.920087	+	0.391713i	$0.871883\pi$
$62$	2.18128	−	0.965437i	0.277022	−	0.122611i
$63$		−	0.905150i		−	0.114038i
$64$	−4.78708	+	6.40967i	−0.598385	+	0.801208i
$65$	−0.260025	−	0.150125i	−0.0322521	−	0.0186208i
$66$	−2.03407	−	13.0276i	−0.250377	−	1.60358i
$67$	0.995335	+	1.72397i	0.121599	+	0.210617i	0.920399	−	0.390981i	$-0.127864\pi$
$67$	0.995335	+	1.72397i	0.121599	+	0.210617i	−0.798799	+	0.601598i	$0.794531\pi$
$68$	1.41637	−	2.74987i	0.171760	−	0.333471i
$69$	3.58047	−	13.3625i	0.431038	−	1.60866i
$70$	−2.00801	−	0.215506i	−0.240003	−	0.0257579i
$71$	13.4758	−	7.78027i	1.59929	−	0.923348i	0.607660	−	0.794197i	$-0.292108\pi$
$71$	13.4758	−	7.78027i	1.59929	−	0.923348i	0.991625	−	0.129151i	$-0.0412252\pi$
$72$	−1.78967	−	0.105611i	−0.210915	−	0.0124463i
$73$		−	4.59995i		−	0.538384i	−0.963087	−	0.269192i	$-0.913243\pi$
$73$		−	4.59995i		−	0.538384i	0.963087	−	0.269192i	$-0.0867566\pi$
$74$	−5.97182	−	6.19172i	−0.694210	−	0.719773i
$75$			1.53823i			0.177620i
$76$	8.33684	−	5.36214i	0.956301	−	0.615080i
$77$	7.49593	−	4.32778i	0.854240	−	0.493196i
$78$	−0.0696992	+	0.649433i	−0.00789188	+	0.0735338i
$79$	−4.07787	+	15.2188i	−0.458797	+	1.71225i	0.217883	+	0.975975i	$0.430085\pi$
$79$	−4.07787	+	15.2188i	−0.458797	+	1.71225i	−0.676680	+	0.736277i	$0.736582\pi$
$80$	−0.660390	+	3.94511i	−0.0738338	+	0.441077i
$81$	3.34835	+	5.79952i	0.372039	+	0.644391i
$82$	8.36697	−	1.30638i	0.923977	−	0.144266i
$83$	−5.18716	−	2.99481i	−0.569365	−	0.328723i	0.187531	−	0.982259i	$-0.439951\pi$
$83$	−5.18716	−	2.99481i	−0.569365	−	0.328723i	−0.756895	+	0.653536i	$0.773285\pi$
$84$	1.33925	+	4.18418i	0.146124	+	0.456531i
$85$		−	1.54660i		−	0.167752i
$86$	1.10745	+	2.50212i	0.119419	+	0.269811i
$87$	1.18408	−	4.41906i	0.126947	−	0.473773i
$88$	−7.68232	−	15.3260i	−0.818938	−	1.63375i
$89$	8.06161	−	2.16010i	0.854528	−	0.228970i	0.195143	−	0.980775i	$-0.437483\pi$
$89$	8.06161	−	2.16010i	0.854528	−	0.228970i	0.659386	+	0.751805i	$0.270816\pi$
$90$	−0.819694	+	0.362798i	−0.0864033	+	0.0382423i
$91$	−0.414157	+	0.110973i	−0.0434155	+	0.0116331i
$92$	−0.862516	−	17.9661i	−0.0899236	−	1.87309i
$93$	−2.50615	−	0.671522i	−0.259876	−	0.0696336i
$94$	0.0103158	−	0.0266983i	0.00106399	−	0.00275372i
$95$	2.47810	−	4.29219i	0.254247	−	0.440369i
$96$	8.42925	−	2.15978i	0.860307	−	0.220431i
$97$	−11.4502	+	11.4502i	−1.16259	+	1.16259i	−0.178689	+	0.983906i	$0.557186\pi$
$97$	−11.4502	+	11.4502i	−1.16259	+	1.16259i	−0.983906	+	0.178689i	$0.942814\pi$
$98$	5.46177	−	4.40304i	0.551722	−	0.444775i
$99$	1.92093	−	3.32714i	0.193060	−	0.334390i
$100$	0.609680	+	1.90481i	0.0609680	+	0.190481i
$101$		−	10.6821i		−	1.06291i	−0.847086	−	0.531456i	$-0.821645\pi$
$101$		−	10.6821i		−	1.06291i	0.847086	−	0.531456i	$-0.178355\pi$
$102$	−3.07658	+	1.36170i	−0.304627	+	0.134828i
$103$	−8.61750	+	8.61750i	−0.849108	+	0.849108i	−0.990022	−	0.140914i	$-0.954996\pi$
$103$	−8.61750	+	8.61750i	−0.849108	+	0.849108i	0.140914	+	0.990022i	$0.454996\pi$
$104$	0.171094	+	0.831824i	0.0167772	+	0.0815671i
$105$	1.55326	+	1.55326i	0.151583	+	0.151583i
$106$	15.5261	−	12.5165i	1.50803	−	1.21571i
$107$	−4.30322	+	2.48446i	−0.416008	+	0.240182i	−0.693368	−	0.720584i	$-0.743874\pi$
$107$	−4.30322	+	2.48446i	−0.416008	+	0.240182i	0.277360	+	0.960766i	$0.410540\pi$
$108$	8.27500	+	7.51686i	0.796262	+	0.723310i
$109$	2.64299	+	9.86379i	0.253153	+	0.944780i	0.969109	+	0.246634i	$0.0793246\pi$
$109$	2.64299	+	9.86379i	0.253153	+	0.944780i	−0.715956	+	0.698146i	$0.754009\pi$
$110$	−6.92366	−	5.05359i	−0.660146	−	0.481841i
$111$	0.830129	+	9.31980i	0.0787923	+	0.884596i
$112$	3.31681	+	4.65049i	0.313409	+	0.439430i
$113$	−2.94426	+	0.788913i	−0.276973	+	0.0742147i	−0.394632	−	0.918839i	$-0.629128\pi$
$113$	−2.94426	+	0.788913i	−0.276973	+	0.0742147i	0.117659	+	0.993054i	$0.462461\pi$
$114$	−10.7201	−	1.15051i	−1.00403	−	0.107756i
$115$	−4.49669	−	7.78849i	−0.419318	−	0.726280i
$116$	−0.285239	−	5.94148i	−0.0264838	−	0.551652i
$117$	−0.134571	+	0.134571i	−0.0124411	+	0.0124411i
$118$	−17.5146	−	1.87973i	−1.61235	−	0.173043i
$119$	−1.56171	−	1.56171i	−0.143162	−	0.143162i
$120$	3.25235	−	2.88989i	0.296898	−	0.263810i
$121$	25.7379			2.33981
$122$	8.02919	−	11.0004i	0.726929	−	0.995929i
$123$	−7.97693	−	4.60548i	−0.719255	−	0.415262i
$124$	−3.36955	+	0.161766i	−0.302595	+	0.0145270i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−0.461359	+	1.19404i	−0.0411012	+	0.106374i
$127$	−4.08759	−	2.35997i	−0.362715	−	0.209413i	0.307556	−	0.951530i	$-0.400489\pi$
$127$	−4.08759	−	2.35997i	−0.362715	−	0.209413i	−0.670271	+	0.742117i	$0.733822\pi$
$128$	9.58200	−	6.01542i	0.846937	−	0.531693i
$129$	0.770297	−	2.87479i	0.0678209	−	0.253111i
$130$	0.266497	+	0.330576i	0.0233733	+	0.0289935i
$131$	−1.55125	−	5.78934i	−0.135533	−	0.505817i	−0.999995	−	0.00311844i	$-0.999007\pi$
$131$	−1.55125	−	5.78934i	−0.135533	−	0.505817i	0.864462	−	0.502698i	$-0.167659\pi$
$132$	−3.95694	+	18.2223i	−0.344407	+	1.58605i
$133$	−1.83182	−	6.83643i	−0.158839	−	0.592794i
$134$	−0.434297	−	2.78153i	−0.0375175	−	0.240288i
$135$	5.39923	+	1.44672i	0.464692	+	0.124514i
$136$	−3.27004	+	2.90561i	−0.280404	+	0.249154i
$137$	−7.02841			−0.600478			−0.300239	−	0.953864i	$-0.597066\pi$
$137$	−7.02841			−0.600478			−0.300239	+	0.953864i	$0.597066\pi$
$138$	−11.5342	+	15.8024i	−0.981854	+	1.34519i
$139$	−1.81024	+	3.13543i	−0.153543	+	0.265944i	−0.932527	−	0.361099i	$-0.882402\pi$
$139$	−1.81024	+	3.13543i	−0.153543	+	0.265944i	0.778985	+	0.627043i	$0.215735\pi$
$140$	2.53905	+	1.30778i	0.214589	+	0.110528i
$141$	−0.0269610	+	0.0155659i	−0.00227053	+	0.00131089i
$142$	−21.7425	+	3.39478i	−1.82459	+	0.284884i
$143$	−1.75786	−	0.471018i	−0.147000	−	0.0393885i
$144$	2.30705	+	1.05152i	0.192254	+	0.0876269i
$145$	−1.48708	−	2.57570i	−0.123495	−	0.213900i
$146$	−2.34462	+	6.06811i	−0.194042	+	0.502200i
$147$	−7.63075			−0.629374
$148$	4.72187	+	11.2118i	0.388136	+	0.921602i
$149$	−19.3766			−1.58739			−0.793695	−	0.608316i	$-0.791845\pi$
$149$	−19.3766			−1.58739			−0.793695	+	0.608316i	$0.791845\pi$
$150$	0.784044	−	2.02918i	0.0640169	−	0.165682i
$151$	6.62323	+	11.4718i	0.538991	+	0.933560i	0.998959	+	0.0456241i	$0.0145277\pi$
$151$	6.62323	+	11.4718i	0.538991	+	0.933560i	−0.459968	+	0.887936i	$0.652139\pi$
$152$	−13.7308	+	2.82423i	−1.11371	+	0.229075i
$153$	−0.946902	−	0.253722i	−0.0765525	−	0.0205122i
$154$	−12.0943	+	1.88835i	−0.974584	+	0.152167i
$155$	−1.46074	+	0.843359i	−0.117329	+	0.0677402i
$156$	0.422964	−	0.821184i	0.0338642	−	0.0657473i
$157$	−3.16573	+	5.48320i	−0.252653	+	0.437607i	−0.964255	−	0.264975i	$-0.914636\pi$
$157$	−3.16573	+	5.48320i	−0.252653	+	0.437607i	0.711603	+	0.702582i	$0.247970\pi$
$158$	13.1365	−	17.9977i	1.04508	−	1.43182i
$159$	−21.6918			−1.72027
$160$	2.88200	−	4.86765i	0.227842	−	0.384822i
$161$	−12.4052	−	3.32396i	−0.977667	−	0.261965i
$162$	−1.46099	−	9.35720i	−0.114787	−	0.735171i
$163$	2.33870	+	8.72813i	0.183181	+	0.683640i	0.995013	+	0.0997488i	$0.0318039\pi$
$163$	2.33870	+	8.72813i	0.183181	+	0.683640i	−0.811832	+	0.583891i	$0.801529\pi$
$164$	−11.7033	−	2.54135i	−0.913874	−	0.198446i
$165$	2.41310	+	9.00581i	0.187860	+	0.701101i
$166$	5.31626	+	6.59457i	0.412622	+	0.511838i
$167$	3.76698	−	14.0586i	0.291498	−	1.08788i	−0.652461	−	0.757822i	$-0.726264\pi$
$167$	3.76698	−	14.0586i	0.291498	−	1.08788i	0.943959	−	0.330062i	$-0.107070\pi$
$168$	0.366001	−	6.20225i	0.0282376	−	0.478514i
$169$	−11.1803	−	6.45492i	−0.860020	−	0.496533i
$170$	−0.788309	+	2.04022i	−0.0604606	+	0.156478i
$171$	−2.22135	−	2.22135i	−0.169871	−	0.169871i
$172$	−0.185560	−	3.86519i	−0.0141489	−	0.294718i
$173$	3.38179	+	1.95248i	0.257113	+	0.148444i	0.623017	−	0.782208i	$-0.285907\pi$
$173$	3.38179	+	1.95248i	0.257113	+	0.148444i	−0.365904	+	0.930653i	$0.619240\pi$
$174$	−3.81442	+	5.22594i	−0.289170	+	0.396178i
$175$	1.42803			0.107949
$176$	2.32253	+	24.1332i	0.175068	+	1.81911i
$177$	13.5481	+	13.5481i	1.01834	+	1.01834i
$178$	−11.7356	−	1.25950i	−0.879622	−	0.0944039i
$179$	−6.92691	+	6.92691i	−0.517741	+	0.517741i	−0.916887	−	0.399146i	$-0.869307\pi$
$179$	−6.92691	+	6.92691i	−0.517741	+	0.517741i	0.399146	+	0.916887i	$0.369307\pi$
$180$	1.26623	−	0.0607895i	0.0943794	−	0.00453098i
$181$	−1.57497	−	2.72793i	−0.117067	−	0.202766i	0.801537	−	0.597945i	$-0.204016\pi$
$181$	−1.57497	−	2.72793i	−0.117067	−	0.202766i	−0.918604	+	0.395179i	$0.870683\pi$
$182$	0.602906	+	0.0647059i	0.0446904	+	0.00479632i
$183$	−14.3085	+	3.83396i	−1.05772	+	0.283414i
$184$	−8.01958	+	24.1399i	−0.591211	+	1.77961i
$185$	4.66580	+	3.90260i	0.343037	+	0.286925i
$186$	2.96376	+	2.16325i	0.217313	+	0.158617i
$187$	−2.42623	−	9.05481i	−0.177423	−	0.662153i
$188$	−0.0272165	+	0.0299615i	−0.00198497	+	0.00218517i
$189$	6.91283	−	3.99113i	0.502835	−	0.290312i
$190$	−5.45677	+	4.39902i	−0.395876	+	0.319138i
$191$	8.09483	+	8.09483i	0.585721	+	0.585721i	0.936470	−	0.350749i	$-0.114073\pi$
$191$	8.09483	+	8.09483i	0.585721	+	0.585721i	−0.350749	+	0.936470i	$0.614073\pi$
$192$	−12.2204	−	1.44732i	−0.881934	−	0.104452i
$193$	17.8559	−	17.8559i	1.28530	−	1.28530i	0.347688	−	0.937610i	$-0.386967\pi$
$193$	17.8559	−	17.8559i	1.28530	−	1.28530i	0.937610	−	0.347688i	$-0.113033\pi$
$194$	20.9410	−	9.26853i	1.50348	−	0.665441i
$195$		−	0.461855i		−	0.0330741i
$196$	−9.44923	+	3.02446i	−0.674945	+	0.216033i
$197$	−6.45654	+	11.1831i	−0.460009	+	0.796759i	−0.998961	−	0.0455773i	$-0.985487\pi$
$197$	−6.45654	+	11.1831i	−0.460009	+	0.796759i	0.538952	+	0.842337i	$0.318821\pi$
$198$	−4.22988	+	3.40995i	−0.300605	+	0.242335i
$199$	−13.3338	+	13.3338i	−0.945206	+	0.945206i	−0.998575	−	0.0533693i	$-0.983004\pi$
$199$	−13.3338	+	13.3338i	−0.945206	+	0.945206i	0.0533693	+	0.998575i	$0.483004\pi$
$200$	0.166619	−	2.82352i	0.0117817	−	0.199653i
$201$	−1.53105	+	2.65186i	−0.107992	+	0.187048i
$202$	−5.44474	+	14.0915i	−0.383090	+	0.991476i
$203$	−4.10247	−	1.09925i	−0.287937	−	0.0771525i
$204$	4.75258	−	0.228163i	0.332747	−	0.0159746i
$205$	−5.78399	+	1.54981i	−0.403971	+	0.108244i
$206$	15.7603	−	6.97554i	1.09807	−	0.486009i
$207$	−5.50617	+	1.47537i	−0.382705	+	0.102546i
$208$	0.198283	−	1.18452i	0.0137484	−	0.0821319i
$209$	7.77503	−	29.0168i	0.537810	−	2.00713i
$210$	−1.25730	−	2.84071i	−0.0867622	−	0.196028i
$211$		−	20.6973i		−	1.42486i	−0.701744	−	0.712429i	$-0.747595\pi$
$211$		−	20.6973i		−	1.42486i	0.701744	−	0.712429i	$-0.252405\pi$
$212$	−26.8612	+	8.59759i	−1.84483	+	0.590485i
$213$	20.7289	+	11.9678i	1.42032	+	0.820023i
$214$	6.94300	−	1.08405i	0.474614	−	0.0741043i
$215$	−0.967410	−	1.67560i	−0.0659768	−	0.114275i
$216$	−7.08472	−	14.1338i	−0.482054	−	0.961683i
$217$	−0.623413	+	2.32661i	−0.0423200	+	0.157940i
$218$	1.54107	−	14.3591i	0.104374	−	0.972523i
$219$	6.12782	−	3.53790i	0.414079	−	0.239069i
$220$	6.55763	+	10.1955i	0.442115	+	0.687384i
$221$			0.464368i			0.0312368i
$222$	3.65527	−	12.7175i	0.245325	−	0.853542i
$223$			13.3438i			0.893569i	0.894642	+	0.446785i	$0.147431\pi$
$223$			13.3438i			0.893569i	−0.894642	+	0.446785i	$0.852569\pi$
$224$	−2.00505	−	7.82537i	−0.133968	−	0.522855i
$225$	0.548926	−	0.316923i	0.0365951	−	0.0211282i
$226$	4.28609	+	0.459997i	0.285106	+	0.0305985i
$227$	−3.24395	+	12.1066i	−0.215309	+	0.803543i	0.770749	+	0.637139i	$0.219882\pi$
$227$	−3.24395	+	12.1066i	−0.215309	+	0.803543i	−0.986058	+	0.166404i	$0.946784\pi$
$228$	13.5552	+	6.98180i	0.897712	+	0.462381i
$229$	−1.20177	−	2.08152i	−0.0794151	−	0.137551i	0.823583	−	0.567196i	$-0.191972\pi$
$229$	−1.20177	−	2.08152i	−0.0794151	−	0.137551i	−0.902998	+	0.429645i	$0.858639\pi$
$230$	1.96205	+	12.5663i	0.129374	+	0.828597i
$231$	11.5305	+	6.65712i	0.758649	+	0.438006i
$232$	−2.65212	+	7.98319i	−0.174120	+	0.524122i
$233$			1.37596i			0.0901421i	0.998984	+	0.0450711i	$0.0143514\pi$
$233$			1.37596i			0.0901421i	−0.998984	+	0.0450711i	$0.985649\pi$
$234$	0.246114	−	0.108930i	0.0160890	−	0.00712101i
$235$	−0.00523818	+	0.0195491i	−0.000341701	+	0.00127525i
$236$	22.1466	+	11.4070i	1.44162	+	0.742530i
$237$	−23.4101	+	6.27271i	−1.52065	+	0.407456i
$238$	1.26415	+	2.85617i	0.0819424	+	0.185138i
$239$	−6.44261	+	1.72629i	−0.416738	+	0.111665i	−0.461094	−	0.887351i	$-0.652543\pi$
$239$	−6.44261	+	1.72629i	−0.416738	+	0.111665i	0.0443562	+	0.999016i	$0.485876\pi$
$240$	−5.76338	+	2.15451i	−0.372025	+	0.139073i
$241$	−21.4693	−	5.75267i	−1.38296	−	0.370562i	−0.510763	−	0.859722i	$-0.670637\pi$
$241$	−21.4693	−	5.75267i	−1.38296	−	0.370562i	−0.872194	+	0.489160i	$0.837304\pi$
$242$	−33.9526	−	13.1187i	−2.18256	−	0.843305i
$243$	3.23400	−	5.60146i	0.207461	−	0.359334i
$244$	−16.1988	+	10.4188i	−1.03702	+	0.666998i
$245$	−3.50777	+	3.50777i	−0.224103	+	0.224103i
$246$	8.17546	+	10.1413i	0.521249	+	0.646584i
$247$	−0.744051	+	1.28873i	−0.0473428	+	0.0820002i
$248$	4.52746	+	1.50408i	0.287494	+	0.0955092i
$249$		−	9.21341i		−	0.583876i
$250$	−0.572376	−	1.29321i	−0.0362002	−	0.0817896i
$251$	−2.67760	+	2.67760i	−0.169008	+	0.169008i	−0.786543	−	0.617535i	$-0.788131\pi$
$251$	−2.67760	+	2.67760i	−0.169008	+	0.169008i	0.617535	+	0.786543i	$0.288131\pi$
$252$	1.21722	−	1.33999i	0.0766777	−	0.0844112i
$253$	−38.5447	−	38.5447i	−2.42329	−	2.42329i
$254$	4.18932	+	5.19665i	0.262861	+	0.326067i
$255$	2.06030	−	1.18951i	0.129021	−	0.0744903i
$256$	−15.7063	+	3.05136i	−0.981646	+	0.190710i
$257$	4.29474	+	16.0282i	0.267899	+	0.999811i	0.960452	+	0.278445i	$0.0898189\pi$
$257$	4.29474	+	16.0282i	0.267899	+	0.999811i	−0.692554	+	0.721366i	$0.743514\pi$
$258$	−2.48144	+	3.39970i	−0.154488	+	0.211656i
$259$	8.65211	−	0.770657i	0.537616	−	0.0478863i
$260$	−0.183057	−	0.571920i	−0.0113527	−	0.0354690i
$261$	−1.82092	+	0.487915i	−0.112712	+	0.0302012i
$262$	−0.904497	+	8.42778i	−0.0558800	+	0.520670i
$263$	−5.76370	−	9.98302i	−0.355405	−	0.615579i	0.631782	−	0.775146i	$-0.282324\pi$
$263$	−5.76370	−	9.98302i	−0.355405	−	0.615579i	−0.987187	+	0.159567i	$0.948990\pi$
$264$	14.5079	−	22.0214i	0.892897	−	1.35532i
$265$	−9.97147	+	9.97147i	−0.612543	+	0.612543i
$266$	−1.06809	+	9.95208i	−0.0654888	+	0.610201i
$267$	9.07788	+	9.07788i	0.555557	+	0.555557i
$268$	−0.844850	+	3.89067i	−0.0516074	+	0.237660i
$269$	−5.76409			−0.351443			−0.175721	−	0.984440i	$-0.556226\pi$
$269$	−5.76409			−0.351443			−0.175721	+	0.984440i	$0.556226\pi$
$270$	−6.38508	−	4.66048i	−0.388584	−	0.283628i
$271$	7.11741	+	4.10924i	0.432352	+	0.249619i	0.700348	−	0.713801i	$-0.253028\pi$
$271$	7.11741	+	4.10924i	0.432352	+	0.249619i	−0.267996	+	0.963420i	$0.586361\pi$
$272$	5.79474	−	2.16623i	0.351358	−	0.131347i
$273$	−0.466367	−	0.466367i	−0.0282258	−	0.0282258i
$274$	9.27164	+	3.58241i	0.560121	+	0.216422i
$275$	5.24914	+	3.03059i	0.316535	+	0.182752i
$276$	23.2701	−	14.9670i	1.40069	−	0.900906i
$277$	7.09464	−	26.4776i	0.426275	−	1.59088i	−0.334846	−	0.942273i	$-0.608684\pi$
$277$	7.09464	−	26.4776i	0.426275	−	1.59088i	0.761122	−	0.648609i	$-0.224649\pi$
$278$	3.98615	−	3.21347i	0.239074	−	0.192731i
$279$	0.276708	+	1.03269i	0.0165661	+	0.0618255i
$280$	−2.68285	−	3.01935i	−0.160331	−	0.180440i
$281$	−0.916893	−	3.42189i	−0.0546973	−	0.204133i	0.933170	−	0.359437i	$-0.117031\pi$
$281$	−0.916893	−	3.42189i	−0.0546973	−	0.204133i	−0.987867	+	0.155304i	$0.950364\pi$
$282$	0.0435001	−	0.00679193i	0.00259039	−	0.000404453i
$283$	17.3834	+	4.65786i	1.03333	+	0.276881i	0.735348	−	0.677690i	$-0.237019\pi$
$283$	17.3834	+	4.65786i	1.03333	+	0.276881i	0.297985	+	0.954570i	$0.403685\pi$
$284$	30.4123	+	6.60396i	1.80464	+	0.391873i
$285$	7.62377			0.451593
$286$	2.07884	+	1.51734i	0.122924	+	0.0897224i
$287$	−4.27554	+	7.40545i	−0.252377	+	0.437130i
$288$	−2.50741	−	2.56305i	−0.147751	−	0.151029i
$289$	12.6509	−	7.30401i	0.744172	−	0.429648i
$290$	0.648861	+	4.15575i	0.0381025	+	0.244034i
$291$	−24.0599	−	6.44684i	−1.41042	−	0.377921i
$292$	6.18589	−	6.80978i	0.362002	−	0.398512i
$293$	−9.93288	−	17.2043i	−0.580285	−	1.00508i	−0.995445	−	0.0953350i	$-0.969608\pi$
$293$	−9.93288	−	17.2043i	−0.580285	−	1.00508i	0.415160	−	0.909748i	$-0.363726\pi$
$294$	10.0662	+	3.88943i	0.587074	+	0.226836i
$295$	12.4558			0.725207
$296$	−0.514245	−	17.1970i	−0.0298899	−	0.999553i
$297$	33.8802			1.96593
$298$	25.5609	+	9.87632i	1.48070	+	0.572120i
$299$	1.35013	+	2.33850i	0.0780803	+	0.135239i
$300$	−2.06857	+	2.27720i	−0.119429	+	0.131474i
$301$	−2.66884	−	0.715112i	−0.153829	−	0.0412184i
$302$	−2.88993	−	18.5091i	−0.166297	−	1.06508i
$303$	14.2302	−	8.21580i	0.817503	−	0.471985i
$304$	19.5527	+	3.27302i	1.12143	+	0.187721i
$305$	−4.81504	+	8.33989i	−0.275708	+	0.477540i
$306$	1.11980	+	0.817342i	0.0640147	+	0.0467243i
$307$	3.47409			0.198277			0.0991383	−	0.995074i	$-0.468391\pi$
$307$	3.47409			0.198277			0.0991383	+	0.995074i	$0.468391\pi$
$308$	16.9169	+	3.67346i	0.963927	+	0.209315i
$309$	−18.1076	−	4.85192i	−1.03011	−	0.276016i
$310$	2.35682	−	0.367985i	0.133859	−	0.0209001i
$311$	−6.94897	−	25.9339i	−0.394040	−	1.47058i	−0.823409	−	0.567448i	$-0.807931\pi$
$311$	−6.94897	−	25.9339i	−0.394040	−	1.47058i	0.429369	−	0.903129i	$-0.358736\pi$
$312$	−0.976521	+	0.867692i	−0.0552846	+	0.0491234i
$313$	3.00244	+	11.2053i	0.169708	+	0.633359i	0.997393	+	0.0721655i	$0.0229910\pi$
$313$	3.00244	+	11.2053i	0.169708	+	0.633359i	−0.827685	+	0.561194i	$0.810342\pi$
$314$	6.97093	−	5.61967i	0.393393	−	0.317136i
$315$	0.234270	−	0.874308i	0.0131996	−	0.0492617i
$316$	−26.5027	+	17.0462i	−1.49090	+	0.958923i
$317$	−0.215175	−	0.124231i	−0.0120854	−	0.00697753i	0.493945	−	0.869493i	$-0.335554\pi$
$317$	−0.215175	−	0.124231i	−0.0120854	−	0.00697753i	−0.506031	+	0.862516i	$0.668888\pi$
$318$	28.6151	+	11.0564i	1.60466	+	0.620013i
$319$	−12.7470	−	12.7470i	−0.713693	−	0.713693i
$320$	−6.28291	+	4.95228i	−0.351225	+	0.276841i
$321$	−6.61934	−	3.82168i	−0.369456	−	0.213305i
$322$	14.6703	+	10.7078i	0.817543	+	0.596725i
$323$	−7.66525			−0.426506
$324$	−2.84211	+	13.0884i	−0.157895	+	0.727132i
$325$	−0.212309	−	0.212309i	−0.0117768	−	0.0117768i
$326$	1.36364	−	12.7059i	0.0755250	−	0.703715i
$327$	−11.1073	+	11.1073i	−0.614232	+	0.614232i
$328$	14.1433	+	9.31769i	0.780932	+	0.514483i
$329$	0.0144508	+	0.0250295i	0.000796697	+	0.00137992i
$330$	1.40702	−	13.1101i	0.0774540	−	0.721689i
$331$	12.9372	−	3.46652i	0.711095	−	0.190537i	0.114900	−	0.993377i	$-0.463345\pi$
$331$	12.9372	−	3.46652i	0.711095	−	0.190537i	0.596195	+	0.802840i	$0.296679\pi$
$332$	−3.65175	−	11.4091i	−0.200416	−	0.626153i
$333$	3.15479	−	2.21640i	0.172881	−	0.121458i
$334$	−12.1350	+	16.6255i	−0.663997	+	0.909709i
$335$	0.515223	+	1.92284i	0.0281496	+	0.105056i
$336$	−3.64413	+	7.99525i	−0.198804	+	0.436176i
$337$	9.99698	−	5.77176i	0.544570	−	0.314408i	−0.202359	−	0.979311i	$-0.564861\pi$
$337$	9.99698	−	5.77176i	0.544570	−	0.314408i	0.746929	+	0.664904i	$0.231527\pi$
$338$	11.4585	+	14.2138i	0.623261	+	0.773126i
$339$	−3.31543	−	3.31543i	−0.180069	−	0.180069i
$340$	2.07982	−	2.28959i	0.112794	−	0.124170i
$341$	−7.22911	+	7.22911i	−0.391478	+	0.391478i
$342$	1.79810	+	4.06256i	0.0972300	+	0.219678i
$343$			17.0803i			0.922249i
$344$	−1.72532	+	5.19341i	−0.0930230	+	0.280010i
$345$	6.91694	−	11.9805i	0.372396	−	0.645008i
$346$	−3.46596	−	4.29936i	−0.186331	−	0.231135i
$347$	9.82604	−	9.82604i	0.527490	−	0.527490i	−0.392333	−	0.919823i	$-0.628332\pi$
$347$	9.82604	−	9.82604i	0.527490	−	0.527490i	0.919823	+	0.392333i	$0.128332\pi$
$348$	7.69554	−	4.94966i	0.412524	−	0.265330i
$349$	12.8046	−	22.1783i	0.685416	−	1.18718i	−0.287890	−	0.957664i	$-0.592954\pi$
$349$	12.8046	−	22.1783i	0.685416	−	1.18718i	0.973306	−	0.229512i	$-0.0737130\pi$
$350$	−1.88381	−	0.727874i	−0.100694	−	0.0389065i
$351$	−1.62112	−	0.434379i	−0.0865292	−	0.0231854i
$352$	9.23701	−	33.0196i	0.492334	−	1.75995i
$353$	−13.6708	+	3.66308i	−0.727622	+	0.194966i	−0.603570	−	0.797310i	$-0.706256\pi$
$353$	−13.6708	+	3.66308i	−0.727622	+	0.194966i	−0.124052	+	0.992276i	$0.539589\pi$
$354$	−10.9667	−	24.7778i	−0.582874	−	1.31693i
$355$	15.0303	−	4.02736i	0.797727	−	0.213750i
$356$	14.8393	+	7.64320i	0.786479	+	0.405089i
$357$	0.879292	−	3.28156i	0.0465371	−	0.173679i
$358$	12.6684	−	5.60707i	0.669547	−	0.296343i
$359$			16.1223i			0.850903i	0.904981	+	0.425451i	$0.139885\pi$
$359$			16.1223i			0.850903i	−0.904981	+	0.425451i	$0.860115\pi$
$360$	−1.70136	−	0.565213i	−0.0896694	−	0.0297894i
$361$	−4.81845	−	2.78193i	−0.253603	−	0.146418i
$362$	0.687212	+	4.40137i	0.0361191	+	0.231331i
$363$	19.7954	+	34.2867i	1.03899	+	1.79959i
$364$	−0.762353	−	0.392662i	−0.0399582	−	0.0205811i
$365$	1.19056	−	4.44321i	0.0623165	−	0.232569i
$366$	20.8295	+	2.23549i	1.08878	+	0.116851i
$367$	15.3021	−	8.83469i	0.798765	−	0.461167i	−0.0442743	−	0.999019i	$-0.514098\pi$
$367$	15.3021	−	8.83469i	0.798765	−	0.461167i	0.843039	+	0.537852i	$0.180764\pi$
$368$	22.8834	−	27.7569i	1.19288	−	1.44693i
$369$			3.79548i			0.197585i
$370$	−4.16580	−	7.52636i	−0.216569	−	0.391277i
$371$			20.1378i			1.04550i
$372$	−2.80707	−	4.36432i	−0.145540	−	0.226280i
$373$	3.84006	−	2.21706i	0.198831	−	0.114795i	−0.397279	−	0.917698i	$-0.630046\pi$
$373$	3.84006	−	2.21706i	0.198831	−	0.114795i	0.596110	+	0.802903i	$0.296712\pi$
$374$	−1.41468	+	13.1815i	−0.0731512	+	0.681597i
$375$	−0.398123	+	1.48582i	−0.0205590	+	0.0767273i
$376$	0.0511746	−	0.0256519i	0.00263913	−	0.00132289i
$377$	0.446497	+	0.773356i	0.0229958	+	0.0398299i
$378$	−11.1535	+	1.74146i	−0.573673	+	0.0895709i
$379$	−10.1597	−	5.86569i	−0.521867	−	0.301300i	0.215831	−	0.976431i	$-0.430754\pi$
$379$	−10.1597	−	5.86569i	−0.521867	−	0.301300i	−0.737698	+	0.675131i	$0.764087\pi$
$380$	9.44059	−	3.02170i	0.484292	−	0.155010i
$381$		−	7.26035i		−	0.371959i
$382$	−6.55246	−	14.8044i	−0.335253	−	0.757459i
$383$	7.74314	−	28.8978i	0.395656	−	1.47661i	−0.425005	−	0.905191i	$-0.639728\pi$
$383$	7.74314	−	28.8978i	0.395656	−	1.47661i	0.820660	−	0.571416i	$-0.193606\pi$
$384$	15.3831	+	8.13808i	0.785015	+	0.415294i
$385$	8.36062	−	2.24022i	0.426097	−	0.114172i
$386$	−32.6562	+	14.4537i	−1.66216	+	0.735674i
$387$	−1.18459	+	0.317410i	−0.0602161	+	0.0161348i
$388$	−32.3489	+	1.55301i	−1.64227	+	0.0788421i
$389$	−20.1883	−	5.40945i	−1.02359	−	0.274270i	−0.292292	−	0.956329i	$-0.594418\pi$
$389$	−20.1883	−	5.40945i	−1.02359	−	0.274270i	−0.731297	+	0.682059i	$0.761085\pi$
$390$	−0.235410	+	0.609264i	−0.0119204	+	0.0308513i
$391$	−6.95458	+	12.0457i	−0.351708	+	0.609176i
$392$	14.0067	+	0.826551i	0.707445	+	0.0417471i
$393$	6.51916	−	6.51916i	0.328848	−	0.328848i
$394$	14.2173	−	11.4614i	0.716257	−	0.577416i
$395$	−7.87785	+	13.6448i	−0.396377	+	0.686546i
$396$	7.31799	−	2.34230i	0.367743	−	0.117705i
$397$			25.0709i			1.25827i	0.777296	+	0.629135i	$0.216591\pi$
$397$			25.0709i			1.25827i	−0.777296	+	0.629135i	$0.783409\pi$
$398$	24.3857	−	10.7932i	1.22235	−	0.541013i
$399$	7.69825	−	7.69825i	0.385395	−	0.385395i
$400$	−1.65896	+	3.63976i	−0.0829478	+	0.181988i
$401$	11.2331	+	11.2331i	0.560953	+	0.560953i	0.929578	−	0.368625i	$-0.120171\pi$
$401$	11.2331	+	11.2331i	0.560953	+	0.560953i	−0.368625	+	0.929578i	$0.620171\pi$
$402$	3.37138	−	2.71787i	0.168149	−	0.135555i
$403$	0.438588	−	0.253219i	0.0218476	−	0.0126137i
$404$	14.3650	−	15.8139i	0.714687	−	0.786769i
$405$	1.73323	+	6.46852i	0.0861251	+	0.321423i
$406$	4.85155	+	3.54115i	0.240778	+	0.175744i
$407$	33.4389	+	15.5289i	1.65750	+	0.769739i
$408$	−6.38574	−	2.12143i	−0.316141	−	0.105026i
$409$	−19.2360	+	5.15427i	−0.951159	+	0.254862i	−0.700854	−	0.713305i	$-0.747197\pi$
$409$	−19.2360	+	5.15427i	−0.951159	+	0.254862i	−0.250305	+	0.968167i	$0.580531\pi$
$410$	8.41999	+	0.903661i	0.415834	+	0.0446286i
$411$	−5.40566	−	9.36288i	−0.266641	−	0.461837i
$412$	−24.3459	+	1.16880i	−1.19944	+	0.0575828i
$413$	12.5775	−	12.5775i	0.618900	−	0.618900i
$414$	8.01557	+	0.860257i	0.393944	+	0.0422793i
$415$	−4.23530	−	4.23530i	−0.207903	−	0.207903i
$416$	−0.865325	+	1.46152i	−0.0424260	+	0.0716568i
$417$	−5.56914			−0.272722
$418$	−25.0466	+	34.3150i	−1.22507	+	1.67840i
$419$	−14.3142	−	8.26433i	−0.699296	−	0.403739i	0.107789	−	0.994174i	$-0.465623\pi$
$419$	−14.3142	−	8.26433i	−0.699296	−	0.403739i	−0.807085	+	0.590435i	$0.798956\pi$
$420$	0.210670	+	4.38823i	0.0102797	+	0.214124i
$421$	0.238605	+	0.238605i	0.0116289	+	0.0116289i	0.712897	−	0.701268i	$-0.247383\pi$
$421$	0.238605	+	0.238605i	0.0116289	+	0.0116289i	−0.701268	+	0.712897i	$0.747383\pi$
$422$	−10.5495	+	27.3031i	−0.513541	+	1.32910i
$423$	0.0111096	+	0.00641412i	0.000540167	+	0.000311865i
$424$	39.8166	+	2.34962i	1.93367	+	0.114108i
$425$	0.400290	−	1.49390i	0.0194169	−	0.0724648i
$426$	−21.2448	−	26.3532i	−1.02932	−	1.27682i
$427$	3.55929	+	13.2834i	0.172246	+	0.642831i
$428$	−9.71153	−	2.10884i	−0.469424	−	0.101934i
$429$	−0.724535	−	2.70400i	−0.0349809	−	0.130550i
$430$	0.422112	+	2.70349i	0.0203561	+	0.130374i
$431$	18.5107	+	4.95992i	0.891629	+	0.238911i	0.675418	−	0.737435i	$-0.263963\pi$
$431$	18.5107	+	4.95992i	0.891629	+	0.238911i	0.216211	+	0.976347i	$0.430630\pi$
$432$	2.14187	+	22.2559i	0.103051	+	1.07079i
$433$	−13.1449			−0.631706			−0.315853	−	0.948808i	$-0.602291\pi$
$433$	−13.1449			−0.631706			−0.315853	+	0.948808i	$0.602291\pi$
$434$	2.00827	−	2.75143i	0.0964000	−	0.132073i
$435$	2.28747	−	3.96202i	0.109676	−	0.189964i
$436$	−9.35184	+	18.1566i	−0.447872	+	0.869543i
$437$	−38.6013	+	22.2865i	−1.84655	+	1.06611i
$438$	−9.88689	+	1.54370i	−0.472414	+	0.0737608i
$439$	−7.77116	−	2.08228i	−0.370897	−	0.0993816i	0.0685557	−	0.997647i	$-0.478161\pi$
$439$	−7.77116	−	2.08228i	−0.370897	−	0.0993816i	−0.439453	+	0.898266i	$0.644828\pi$
$440$	−3.45389	−	16.7921i	−0.164658	−	0.800531i
$441$	1.57217	+	2.72308i	0.0748652	+	0.129670i
$442$	0.236691	−	0.612579i	0.0112582	−	0.0291374i
$443$	20.8390			0.990090			0.495045	−	0.868867i	$-0.335152\pi$
$443$	20.8390			0.990090			0.495045	+	0.868867i	$0.335152\pi$
$444$	−11.3041	+	14.9134i	−0.536467	+	0.707758i
$445$	8.34599			0.395638
$446$	6.80142	−	17.6027i	0.322056	−	0.833514i
$447$	−14.9028	−	25.8124i	−0.704879	−	1.22089i
$448$	−1.34364	+	11.3450i	−0.0634808	+	0.535999i
$449$	14.2384	+	3.81517i	0.671951	+	0.180049i	0.578634	−	0.815588i	$-0.303586\pi$
$449$	14.2384	+	3.81517i	0.671951	+	0.180049i	0.0933177	+	0.995636i	$0.470253\pi$
$450$	−0.885662	+	0.138284i	−0.0417505	+	0.00651876i
$451$	−31.4320	+	18.1473i	−1.48007	+	0.854521i
$452$	−5.41960	−	2.79145i	−0.254917	−	0.131299i
$453$	−10.1881	+	17.6462i	−0.478677	+	0.829093i
$454$	10.4501	−	14.3172i	0.490448	−	0.671938i
$455$	−0.428767			−0.0201009
$456$	−14.3229	−	16.1193i	−0.670729	−	0.754854i
$457$	37.7403	+	10.1125i	1.76542	+	0.473042i	0.987804	−	0.155703i	$-0.0497642\pi$
$457$	37.7403	+	10.1125i	1.76542	+	0.473042i	0.777612	+	0.628745i	$0.216431\pi$
$458$	0.524370	+	3.35842i	0.0245022	+	0.156929i
$459$	−2.23750	−	8.35045i	−0.104437	−	0.389766i
$460$	3.81683	−	17.5771i	0.177961	−	0.819537i
$461$	6.11628	+	22.8263i	0.284863	+	1.06312i	0.948939	+	0.315459i	$0.102159\pi$
$461$	6.11628	+	22.8263i	0.284863	+	1.06312i	−0.664076	+	0.747665i	$0.731175\pi$
$462$	−11.8174	−	14.6590i	−0.549797	−	0.681998i
$463$	7.53727	−	28.1295i	0.350286	−	1.30729i	−0.536027	−	0.844201i	$-0.680075\pi$
$463$	7.53727	−	28.1295i	0.350286	−	1.30729i	0.886313	−	0.463086i	$-0.153258\pi$
$464$	7.56766	−	9.17936i	0.351320	−	0.426141i
$465$	−2.24696	−	1.29728i	−0.104200	−	0.0601599i
$466$	0.701333	−	1.81512i	0.0324886	−	0.0840838i
$467$	−0.364411	−	0.364411i	−0.0168629	−	0.0168629i	0.698625	−	0.715488i	$-0.253796\pi$
$467$	−0.364411	−	0.364411i	−0.0168629	−	0.0168629i	−0.715488	+	0.698625i	$0.753796\pi$
$468$	−0.380188	+	0.0182521i	−0.0175742	+	0.000843703i
$469$	2.46188	+	1.42137i	0.113679	+	0.0656327i
$470$	0.0168743	−	0.0231187i	0.000778354	−	0.00106638i
$471$	−9.73924			−0.448760
$472$	−23.4009	−	26.3359i	−1.07711	−	1.21221i
$473$	−8.29245	−	8.29245i	−0.381287	−	0.381287i
$474$	34.0790	+	3.65747i	1.56530	+	0.167993i
$475$	3.50456	−	3.50456i	0.160800	−	0.160800i
$476$	−0.211817	−	4.41210i	−0.00970860	−	0.202228i
$477$	4.46918	+	7.74085i	0.204630	+	0.354429i
$478$	9.37878	+	1.00656i	0.428976	+	0.0460391i
$479$	−12.4415	+	3.33369i	−0.568466	+	0.152320i	−0.531593	−	0.847000i	$-0.678406\pi$
$479$	−12.4415	+	3.33369i	−0.568466	+	0.152320i	−0.0368732	+	0.999320i	$0.511740\pi$
$480$	8.70102	+	0.0954669i	0.397146	+	0.00435745i
$481$	−1.40091	−	1.17176i	−0.0638761	−	0.0534276i
$482$	25.3894	+	18.5317i	1.15645	+	0.844097i
$483$	−5.11302	−	19.0821i	−0.232651	−	0.868264i
$484$	38.1025	+	34.6116i	1.73193	+	1.57326i
$485$	−14.0236	+	8.09653i	−0.636779	+	0.367645i
$486$	−7.12128	+	5.74087i	−0.323028	+	0.260411i
$487$	−9.88956	−	9.88956i	−0.448139	−	0.448139i	0.446597	−	0.894735i	$-0.352636\pi$
$487$	−9.88956	−	9.88956i	−0.448139	−	0.448139i	−0.894735	+	0.446597i	$0.852636\pi$
$488$	26.6794	−	5.48758i	1.20772	−	0.248411i
$489$	−9.82843	+	9.82843i	−0.444457	+	0.444457i
$490$	6.41525	−	2.83940i	0.289812	−	0.128271i
$491$			6.25626i			0.282341i	0.989985	+	0.141171i	$0.0450866\pi$
$491$			6.25626i			0.282341i	−0.989985	+	0.141171i	$0.954913\pi$
$492$	−5.61574	−	17.5451i	−0.253177	−	0.790994i
$493$	−2.29992	+	3.98358i	−0.103583	+	0.179411i
$494$	1.63840	−	1.32081i	0.0737152	−	0.0594260i
$495$	2.71660	−	2.71660i	0.122102	−	0.122102i
$496$	−5.20583	−	4.29180i	−0.233749	−	0.192707i
$497$	11.1105	−	19.2439i	0.498372	−	0.863206i
$498$	−4.69612	+	12.1540i	−0.210438	+	0.544635i
$499$	−18.9038	−	5.06526i	−0.846250	−	0.226752i	−0.190460	−	0.981695i	$-0.560998\pi$
$499$	−18.9038	−	5.06526i	−0.846250	−	0.226752i	−0.655790	+	0.754943i	$0.727664\pi$
$500$	0.0959058	+	1.99770i	0.00428904	+	0.0893398i
$501$	21.6253	−	5.79449i	0.966148	−	0.258879i
$502$	4.89698	−	2.16741i	0.218563	−	0.0967364i
$503$	−17.3683	+	4.65381i	−0.774412	+	0.207503i	−0.624320	−	0.781169i	$-0.714624\pi$
$503$	−17.3683	+	4.65381i	−0.774412	+	0.207503i	−0.150092	+	0.988672i	$0.547957\pi$
$504$	−2.28871	+	1.14724i	−0.101947	+	0.0511023i
$505$	2.76474	−	10.3182i	0.123029	−	0.459152i
$506$	31.2005	+	70.4934i	1.38703	+	3.13381i
$507$		−	19.8583i		−	0.881939i
$508$	−2.87765	−	8.99057i	−0.127675	−	0.398892i
$509$	−34.5804	−	19.9650i	−1.53275	−	0.884933i	−0.999234	−	0.0391435i	$-0.987537\pi$
$509$	−34.5804	−	19.9650i	−1.53275	−	0.884933i	−0.533516	−	0.845790i	$-0.679130\pi$
$510$	−3.32418	+	0.519024i	−0.147197	+	0.0229828i
$511$	−3.28444	−	5.68881i	−0.145295	−	0.251658i
$512$	22.2746	+	3.98035i	0.984407	+	0.175908i
$513$	7.17022	−	26.7596i	0.316573	−	1.18147i
$514$	2.50416	−	23.3329i	0.110454	−	1.02917i
$515$	−10.5542	+	6.09349i	−0.465075	+	0.268511i
$516$	5.00628	−	3.21997i	0.220389	−	0.141751i
$517$			0.122671i			0.00539506i
$518$	−11.8064	−	3.39340i	−0.518743	−	0.149097i
$519$			6.00673i			0.263666i
$520$	−0.0500274	+	0.847763i	−0.00219385	+	0.0371769i
$521$	35.0371	−	20.2287i	1.53500	−	0.886234i	0.535882	−	0.844293i	$-0.319979\pi$
$521$	35.0371	−	20.2287i	1.53500	−	0.886234i	0.999120	−	0.0419414i	$-0.0133543\pi$
$522$	2.65079	+	0.284492i	0.116022	+	0.0124519i
$523$	2.91153	−	10.8660i	0.127312	−	0.475136i	−0.872599	−	0.488437i	$-0.837567\pi$
$523$	2.91153	−	10.8660i	0.127312	−	0.475136i	0.999912	+	0.0133008i	$0.00423390\pi$
$524$	5.48886	−	10.6566i	0.239782	−	0.465537i
$525$	1.09832	+	1.90235i	0.0479346	+	0.0830252i
$526$	2.51489	+	16.1071i	0.109654	+	0.702301i
$527$	2.25918	+	1.30434i	0.0984114	+	0.0568179i
$528$	−30.3627	+	21.6552i	−1.32137	+	0.942422i
$529$			57.8808i			2.51655i
$530$	18.2365	−	8.07153i	0.792145	−	0.350605i
$531$	2.04340	−	7.62606i	0.0886759	−	0.330943i
$532$	6.48161	−	12.5840i	0.281013	−	0.545587i
$533$	1.73665	−	0.465333i	0.0752225	−	0.0201558i
$534$	−7.34820	−	16.6023i	−0.317988	−	0.718451i
$535$	−4.79961	+	1.28605i	−0.207505	+	0.0556009i
$536$	3.09759	−	4.70182i	0.133795	−	0.203087i
$537$	−14.5552	−	3.90007i	−0.628105	−	0.168300i
$538$	7.60380	+	2.93798i	0.327823	+	0.126665i
$539$	−15.0339	+	26.0396i	−0.647558	+	1.12160i
$540$	6.04753	+	9.40245i	0.260244	+	0.404617i
$541$	−4.80172	+	4.80172i	−0.206442	+	0.206442i	−0.802753	−	0.596311i	$-0.796632\pi$
$541$	−4.80172	+	4.80172i	−0.206442	+	0.206442i	0.596311	+	0.802753i	$0.296632\pi$
$542$	−7.29456	−	9.04855i	−0.313328	−	0.388669i
$543$	2.42267	−	4.19619i	0.103967	−	0.180076i
$544$	−8.74836	−	0.0959863i	−0.375083	−	0.00411538i
$545$			10.2117i			0.437423i
$546$	0.377507	+	0.852926i	0.0161558	+	0.0365019i
$547$	2.03444	−	2.03444i	0.0869865	−	0.0869865i	−0.662275	−	0.749261i	$-0.730409\pi$
$547$	2.03444	−	2.03444i	0.0869865	−	0.0869865i	0.749261	+	0.662275i	$0.230409\pi$
$548$	−10.4049	−	9.45160i	−0.444474	−	0.403752i
$549$	4.31616	+	4.31616i	0.184209	+	0.184209i
$550$	−5.37978	−	6.67337i	−0.229395	−	0.284553i
$551$	−12.7657	+	7.37026i	−0.543836	+	0.313984i
$552$	−38.3258	+	7.88307i	−1.63125	+	0.335526i
$553$	5.82333	+	21.7329i	0.247633	+	0.924179i
$554$	−22.8547	+	31.3121i	−0.971005	+	1.33033i
$555$	−1.61030	+	9.21708i	−0.0683533	+	0.391243i
$556$	−6.89632	+	2.20734i	−0.292469	+	0.0936119i
$557$	−11.4854	+	3.07751i	−0.486653	+	0.130398i	−0.493799	−	0.869576i	$-0.664392\pi$
$557$	−11.4854	+	3.07751i	−0.486653	+	0.130398i	0.00714598	+	0.999974i	$0.497725\pi$
$558$	0.161342	−	1.50333i	0.00683016	−	0.0636410i
$559$	0.290466	+	0.503102i	0.0122854	+	0.0212789i
$560$	2.00016	+	5.35049i	0.0845220	+	0.226099i
$561$	10.1963	−	10.1963i	0.430487	−	0.430487i
$562$	−0.534619	+	4.98139i	−0.0225516	+	0.210127i
$563$	26.8094	+	26.8094i	1.12988	+	1.12988i	0.990196	+	0.139688i	$0.0446099\pi$
$563$	26.8094	+	26.8094i	1.12988	+	1.12988i	0.139688	+	0.990196i	$0.455390\pi$
$564$	−0.0608458	−	0.0132125i	−0.00256207	−	0.000556347i
$565$	−3.04812			−0.128236
$566$	−20.5574	−	15.0049i	−0.864093	−	0.630702i
$567$	8.28188	+	4.78155i	0.347806	+	0.200806i
$568$	−36.7528	−	24.2130i	−1.54211	−	1.01596i
$569$	5.38160	+	5.38160i	0.225609	+	0.225609i	0.810855	−	0.585247i	$-0.199002\pi$
$569$	5.38160	+	5.38160i	0.225609	+	0.225609i	−0.585247	+	0.810855i	$0.699002\pi$
$570$	−10.0570	−	3.88587i	−0.421243	−	0.162761i
$571$	−4.75846	−	2.74730i	−0.199135	−	0.114971i	0.397117	−	0.917768i	$-0.370011\pi$
$571$	−4.75846	−	2.74730i	−0.199135	−	0.114971i	−0.596252	+	0.802797i	$0.703344\pi$
$572$	−1.96894	−	3.06122i	−0.0823253	−	0.127996i
$573$	−4.55764	+	17.0094i	−0.190398	+	0.710576i
$574$	9.41474	−	7.58976i	0.392964	−	0.316791i
$575$	−2.32766	−	8.68693i	−0.0970700	−	0.362270i
$576$	2.00130	+	4.65913i	0.0833875	+	0.194130i
$577$	8.31991	+	31.0503i	0.346362	+	1.29264i	0.891013	+	0.453978i	$0.149996\pi$
$577$	8.31991	+	31.0503i	0.346362	+	1.29264i	−0.544651	+	0.838663i	$0.683338\pi$
$578$	−20.4116	+	3.18698i	−0.849009	+	0.132561i
$579$	37.5200	+	10.0535i	1.55928	+	0.417807i
$580$	1.26225	−	5.81285i	0.0524120	−	0.241366i
$581$	−8.55335			−0.354853
$582$	28.4531	+	20.7679i	1.17942	+	0.860858i
$583$	−42.7368	+	74.0223i	−1.76998	+	3.06569i
$584$	−11.6312	+	5.83027i	−0.481302	+	0.241258i
$585$	−0.164816	+	0.0951564i	−0.00681429	+	0.00393423i
$586$	4.33404	+	27.7581i	0.179037	+	1.14668i
$587$	−2.27535	−	0.609679i	−0.0939139	−	0.0251641i	0.211556	−	0.977366i	$-0.432147\pi$
$587$	−2.27535	−	0.609679i	−0.0939139	−	0.0251641i	−0.305470	+	0.952202i	$0.598814\pi$
$588$	−11.2966	−	10.2616i	−0.465863	−	0.423182i
$589$	4.17985	+	7.23971i	0.172228	+	0.298307i
$590$	−16.4313	−	6.34880i	−0.676467	−	0.261376i
$591$	−19.8633			−0.817067
$592$	−8.08700	+	22.9478i	−0.332374	+	0.943148i
$593$	−3.30486			−0.135714			−0.0678571	−	0.997695i	$-0.521616\pi$
$593$	−3.30486			−0.135714			−0.0678571	+	0.997695i	$0.521616\pi$
$594$	−44.6936	−	17.2689i	−1.83380	−	0.708550i
$595$	−1.10430	−	1.91270i	−0.0452717	−	0.0784129i
$596$	−28.6851	−	26.0570i	−1.17499	−	1.06734i
$597$	−28.0177	−	7.50733i	−1.14669	−	0.307255i
$598$	−0.589107	−	3.77304i	−0.0240904	−	0.154291i
$599$	7.18062	−	4.14573i	0.293392	−	0.169390i	−0.346078	−	0.938206i	$-0.612487\pi$
$599$	7.18062	−	4.14573i	0.293392	−	0.169390i	0.639471	+	0.768815i	$0.279154\pi$
$600$	3.88949	−	1.94965i	0.158788	−	0.0795941i
$601$	6.41914	−	11.1183i	0.261842	−	0.453524i	−0.704889	−	0.709317i	$-0.749003\pi$
$601$	6.41914	−	11.1183i	0.261842	−	0.453524i	0.966731	+	0.255793i	$0.0823367\pi$
$602$	3.15614	+	2.30367i	0.128635	+	0.0938906i
$603$	1.26178			0.0513835
$604$	−5.62186	+	25.8896i	−0.228750	+	1.05343i
$605$	24.8609	+	6.66147i	1.01074	+	0.270827i
$606$	−22.9596	+	3.58482i	−0.932671	+	0.145623i
$607$	−9.02759	−	33.6914i	−0.366419	−	1.36749i	−0.865488	−	0.500930i	$-0.832991\pi$
$607$	−9.02759	−	33.6914i	−0.366419	−	1.36749i	0.499069	−	0.866562i	$-0.333675\pi$
$608$	−24.1250	−	14.2838i	−0.978399	−	0.579284i
$609$	−1.69091	−	6.31055i	−0.0685190	−	0.255716i
$610$	10.6027	−	8.54745i	0.429291	−	0.346076i
$611$	0.00157277	−	0.00586965i	6.36274e−5	−	0.000237461i
$612$	−1.06060	−	1.64898i	−0.0428722	−	0.0666560i
$613$	−24.4471	−	14.1145i	−0.987408	−	0.570080i	−0.0829095	−	0.996557i	$-0.526421\pi$
$613$	−24.4471	−	14.1145i	−0.987408	−	0.570080i	−0.904498	+	0.426477i	$0.859755\pi$
$614$	−4.58290	−	1.77076i	−0.184951	−	0.0714620i
$615$	−6.51313	−	6.51313i	−0.262635	−	0.262635i
$616$	−20.4438	−	13.4685i	−0.823703	−	0.542661i
$617$	10.4052	+	6.00745i	0.418898	+	0.241851i	0.694606	−	0.719391i	$-0.255579\pi$
$617$	10.4052	+	6.00745i	0.418898	+	0.241851i	−0.275708	+	0.961241i	$0.588912\pi$
$618$	21.4139	+	15.6300i	0.861395	+	0.628733i
$619$	−39.3054			−1.57982			−0.789910	−	0.613223i	$-0.789873\pi$
$619$	−39.3054			−1.57982			−0.789910	+	0.613223i	$0.789873\pi$
$620$	−3.29661	−	0.715851i	−0.132395	−	0.0287493i
$621$	−35.5464	−	35.5464i	−1.42643	−	1.42643i
$622$	−4.05179	+	37.7531i	−0.162462	+	1.51376i
$623$	8.42753	−	8.42753i	0.337642	−	0.337642i
$624$	1.73046	−	0.646893i	0.0692739	−	0.0258964i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	1.75065	−	16.3120i	0.0699702	−	0.651958i
$627$	44.6345	−	11.9598i	1.78253	−	0.477628i
$628$	−12.0602	+	3.86016i	−0.481254	+	0.154037i
$629$	1.61906	−	9.26723i	0.0645561	−	0.369509i
$630$	−0.754680	+	1.03395i	−0.0300672	+	0.0411935i
$631$	−9.05474	−	33.7928i	−0.360464	−	1.34527i	−0.873468	−	0.486882i	$-0.838134\pi$
$631$	−9.05474	−	33.7928i	−0.360464	−	1.34527i	0.513004	−	0.858386i	$-0.328533\pi$
$632$	43.6501	−	8.97819i	1.73631	−	0.357133i
$633$	27.5718	−	15.9186i	1.09588	−	0.632707i
$634$	0.220531	+	0.273558i	0.00875839	+	0.0108644i
$635$	−3.33750	−	3.33750i	−0.132445	−	0.132445i
$636$	−32.1126	−	29.1705i	−1.27335	−	1.15669i
$637$	1.05321	−	1.05321i	0.0417297	−	0.0417297i
$638$	10.3182	+	23.3126i	0.408501	+	0.922953i
$639$		−	9.86298i		−	0.390173i
$640$	10.8124	−	3.33045i	0.427398	−	0.131648i
$641$	−3.14294	+	5.44373i	−0.124139	+	0.215015i	−0.921396	−	0.388625i	$-0.872950\pi$
$641$	−3.14294	+	5.44373i	−0.124139	+	0.215015i	0.797257	+	0.603640i	$0.206283\pi$
$642$	6.78409	+	8.41534i	0.267747	+	0.332127i
$643$	−6.30795	+	6.30795i	−0.248761	+	0.248761i	−0.820462	−	0.571701i	$-0.806284\pi$
$643$	−6.30795	+	6.30795i	−0.248761	+	0.248761i	0.571701	+	0.820462i	$0.306284\pi$
$644$	−13.8947	−	21.6030i	−0.547528	−	0.851276i
$645$	1.48810	−	2.57747i	0.0585939	−	0.101488i
$646$	10.1117	+	3.90701i	0.397841	+	0.153719i
$647$	14.6988	+	3.93852i	0.577868	+	0.154839i	0.535903	−	0.844280i	$-0.319971\pi$
$647$	14.6988	+	3.93852i	0.577868	+	0.154839i	0.0419653	+	0.999119i	$0.486638\pi$
$648$	10.4204	−	15.8171i	0.409353	−	0.621355i
$649$	72.9246	−	19.5401i	2.86254	−	0.767016i
$650$	0.171856	+	0.388287i	0.00674077	+	0.0152299i
$651$	−3.57886	+	0.958953i	−0.140267	+	0.0375843i
$652$	−8.27513	+	16.0662i	−0.324079	+	0.629199i
$653$	−1.88032	+	7.01744i	−0.0735825	+	0.274614i	−0.992908	−	0.118884i	$-0.962068\pi$
$653$	−1.88032	+	7.01744i	−0.0735825	+	0.274614i	0.919326	+	0.393498i	$0.128735\pi$
$654$	20.3137	−	8.99090i	0.794330	−	0.351572i
$655$		−	5.99356i		−	0.234188i
$656$	−13.9081	−	19.5005i	−0.543019	−	0.761366i
$657$	−2.52504	−	1.45783i	−0.0985110	−	0.0568754i
$658$	−0.00630534	−	0.0403837i	−0.000245808	−	0.00157432i
$659$	7.27024	+	12.5924i	0.283208	+	0.490531i	0.972173	−	0.234264i	$-0.0752679\pi$
$659$	7.27024	+	12.5924i	0.283208	+	0.490531i	−0.688965	+	0.724795i	$0.741935\pi$
$660$	−8.53839	+	16.5773i	−0.332356	+	0.645270i
$661$	−5.60031	+	20.9006i	−0.217827	+	0.812941i	0.767325	+	0.641258i	$0.221587\pi$
$661$	−5.60031	+	20.9006i	−0.217827	+	0.812941i	−0.985152	+	0.171683i	$0.945080\pi$
$662$	−18.8333	−	2.02125i	−0.731976	−	0.0785581i
$663$	−0.618607	+	0.357153i	−0.0240247	+	0.0138707i
$664$	−0.997982	+	16.9118i	−0.0387292	+	0.656304i
$665$		−	7.07760i		−	0.274457i
$666$	−5.29140	+	1.31579i	−0.205038	+	0.0509858i
$667$			26.7477i			1.03568i
$668$	24.4822	−	15.7466i	0.947245	−	0.609254i
$669$	−17.7760	+	10.2629i	−0.687258	+	0.396789i
$670$	0.300415	−	2.79916i	0.0116060	−	0.108141i
$671$	−15.1072	+	56.3807i	−0.583206	+	2.17655i
$672$	8.88243	−	8.68963i	0.342647	−	0.335210i
$673$	15.3166	+	26.5291i	0.590411	+	1.02262i	0.994177	+	0.107759i	$0.0343675\pi$
$673$	15.3166	+	26.5291i	0.590411	+	1.02262i	−0.403766	+	0.914862i	$0.632299\pi$
$674$	−16.1296	+	2.51841i	−0.621288	+	0.0970053i
$675$	4.84082	+	2.79485i	0.186323	+	0.107574i
$676$	−7.87088	−	24.5908i	−0.302726	−	0.945799i
$677$		−	22.3615i		−	0.859422i	−0.902966	−	0.429711i	$-0.858615\pi$
$677$		−	22.3615i		−	0.859422i	0.902966	−	0.429711i	$-0.141385\pi$
$678$	2.68371	+	6.06349i	0.103067	+	0.232867i
$679$	−5.98498	+	22.3363i	−0.229682	+	0.857187i
$680$	−3.91065	+	1.96026i	−0.149967	+	0.0751724i
$681$	−18.6227	+	4.98995i	−0.713625	+	0.191215i
$682$	13.2211	−	5.85169i	0.506262	−	0.224073i
$683$	−0.546608	+	0.146463i	−0.0209154	+	0.00560426i	−0.269262	−	0.963067i	$-0.586780\pi$
$683$	−0.546608	+	0.146463i	−0.0209154	+	0.00560426i	0.248346	+	0.968671i	$0.420113\pi$
$684$	−0.301284	−	6.27570i	−0.0115199	−	0.239957i
$685$	−6.78892	−	1.81909i	−0.259391	−	0.0695037i
$686$	8.70590	−	22.5317i	0.332393	−	0.860266i
$687$	1.84860	−	3.20186i	0.0705284	−	0.122159i
$688$	4.92309	−	5.97157i	0.187691	−	0.227664i
$689$	2.99394	−	2.99394i	0.114060	−	0.114060i
$690$	−15.2311	+	12.2787i	−0.579839	+	0.467441i
$691$	20.6812	−	35.8209i	0.786750	−	1.36269i	−0.141198	−	0.989981i	$-0.545095\pi$
$691$	20.6812	−	35.8209i	0.786750	−	1.36269i	0.927948	−	0.372710i	$-0.121571\pi$
$692$	2.38078	+	7.43819i	0.0905036	+	0.282758i
$693$		−	5.48628i		−	0.208407i
$694$	−17.9706	+	7.95381i	−0.682154	+	0.301922i
$695$	−2.56007	+	2.56007i	−0.0971089	+	0.0971089i
$696$	−12.6746	+	2.60698i	−0.480428	+	0.0988173i
$697$	6.54857	+	6.54857i	0.248045	+	0.248045i
$698$	−28.1958	+	22.7303i	−1.06723	+	0.860353i
$699$	−1.83298	+	1.05827i	−0.0693297	+	0.0400275i
$700$	2.11406	+	1.92037i	0.0799039	+	0.0725833i
$701$	1.61968	+	6.04471i	0.0611743	+	0.228306i	0.989744	−	0.142852i	$-0.0456274\pi$
$701$	1.61968	+	6.04471i	0.0611743	+	0.228306i	−0.928570	+	0.371158i	$0.878961\pi$
$702$	1.91713	+	1.39931i	0.0723573	+	0.0528136i
$703$	19.3421	−	23.1246i	0.729499	−	0.872162i
$704$	−29.0154	+	38.8502i	−1.09356	+	1.46422i
$705$	−0.0300711	+	0.00805753i	−0.00113254	+	0.000303464i
$706$	19.9011	+	2.13585i	0.748989	+	0.0803840i
$707$	−7.62721	−	13.2107i	−0.286851	−	0.496840i
$708$	1.83755	+	38.2758i	0.0690594	+	1.43849i
$709$	−6.05616	+	6.05616i	−0.227444	+	0.227444i	−0.811624	−	0.584180i	$-0.801416\pi$
$709$	−6.05616	+	6.05616i	−0.227444	+	0.227444i	0.584180	+	0.811624i	$0.301416\pi$
$710$	−21.8803	−	2.34826i	−0.821152	−	0.0881287i
$711$	7.06165	+	7.06165i	0.264832	+	0.264832i
$712$	−15.6797	−	17.6463i	−0.587621	−	0.661323i
$713$	15.1693			0.568094
$714$	−2.83256	+	3.88075i	−0.106006	+	0.145233i
$715$	−1.57606	−	0.909938i	−0.0589412	−	0.0340297i
$716$	−19.5697	+	0.939505i	−0.731354	+	0.0351110i
$717$	−7.25479	−	7.25479i	−0.270935	−	0.270935i
$718$	8.21761	−	21.2680i	0.306679	−	0.793715i
$719$	17.0682	+	9.85432i	0.636536	+	0.367504i	0.783279	−	0.621670i	$-0.213546\pi$
$719$	17.0682	+	9.85432i	0.636536	+	0.367504i	−0.146743	+	0.989175i	$0.546879\pi$
$720$	1.95628	+	1.61280i	0.0729063	+	0.0601055i
$721$	−4.50433	+	16.8104i	−0.167750	+	0.626051i
$722$	4.93838	+	6.12582i	0.183787	+	0.227979i
$723$	−8.84894	−	33.0247i	−0.329096	−	1.22820i
$724$	1.33685	−	6.15642i	0.0496837	−	0.228801i
$725$	−0.769769	−	2.87282i	−0.0285885	−	0.106694i
$726$	−8.63739	−	55.3197i	−0.320564	−	2.05311i
$727$	46.5895	+	12.4836i	1.72791	+	0.462991i	0.979699	−	0.200473i	$-0.0642478\pi$
$727$	46.5895	+	12.4836i	1.72791	+	0.462991i	0.748208	+	0.663464i	$0.230914\pi$
$728$	0.805529	+	0.906562i	0.0298549	+	0.0335994i
$729$	30.0394			1.11257
$730$	−3.83527	+	5.25451i	−0.141950	+	0.194478i
$731$	−1.49620	+	2.59149i	−0.0553388	+	0.0958497i
$732$	−26.3382	−	13.5659i	−0.973487	−	0.501410i
$733$	18.4723	−	10.6650i	0.682290	−	0.393920i	−0.118427	−	0.992963i	$-0.537785\pi$
$733$	18.4723	−	10.6650i	0.682290	−	0.393920i	0.800717	+	0.599042i	$0.204452\pi$
$734$	−24.6891	+	3.85486i	−0.911293	+	0.142286i
$735$	−7.37074	−	1.97498i	−0.271874	−	0.0728483i
$736$	−44.3348	+	24.9522i	−1.63420	+	0.919750i
$737$	6.03291	+	10.4493i	0.222225	+	0.384905i
$738$	1.93457	−	5.00687i	0.0712127	−	0.184306i
$739$	43.6818			1.60686			0.803431	−	0.595398i	$-0.203006\pi$
$739$	43.6818			1.60686			0.803431	+	0.595398i	$0.203006\pi$
$740$	1.65916	+	12.0519i	0.0609919	+	0.443035i
$741$	−2.28904			−0.0840902
$742$	10.2643	−	26.5651i	0.376815	−	0.975235i
$743$	9.45747	+	16.3808i	0.346961	+	0.600954i	0.985708	−	0.168463i	$-0.0538804\pi$
$743$	9.45747	+	16.3808i	0.346961	+	0.600954i	−0.638747	+	0.769417i	$0.720547\pi$
$744$	1.47848	+	7.18805i	0.0542037	+	0.263527i
$745$	−18.7163	−	5.01502i	−0.685713	−	0.183736i
$746$	−6.19572	+	0.967375i	−0.226842	+	0.0354181i
$747$	−3.28786	+	1.89824i	−0.120296	+	0.0694531i
$748$	8.58485	−	16.6675i	0.313893	−	0.609423i
$749$	−3.54789	+	6.14512i	−0.129637	+	0.224538i
$750$	1.28252	−	1.75712i	0.0468310	−	0.0641608i
$751$	−1.82736			−0.0666813			−0.0333407	−	0.999444i	$-0.510615\pi$
$751$	−1.82736			−0.0666813			−0.0333407	+	0.999444i	$0.510615\pi$
$752$	−0.0805827	+	0.00775513i	−0.00293855	+	0.000282800i
$753$	−5.62633	−	1.50757i	−0.205035	−	0.0549390i
$754$	−0.194821	−	1.24777i	−0.00709497	−	0.0454410i
$755$	3.42844	+	12.7951i	0.124774	+	0.465661i
$756$	15.6009	+	3.38770i	0.567400	+	0.123210i
$757$	5.12654	+	19.1325i	0.186327	+	0.695383i	0.994343	+	0.106221i	$0.0338751\pi$
$757$	5.12654	+	19.1325i	0.186327	+	0.695383i	−0.808015	+	0.589161i	$0.799458\pi$
$758$	10.4125	+	12.9162i	0.378200	+	0.469139i
$759$	21.7019	−	80.9926i	0.787729	−	2.93984i
$760$	−13.9939	−	0.825795i	−0.507612	−	0.0299547i
$761$	−31.4341	−	18.1485i	−1.13949	−	0.657882i	−0.193182	−	0.981163i	$-0.561881\pi$
$761$	−31.4341	−	18.1485i	−1.13949	−	0.657882i	−0.946303	+	0.323281i	$0.895214\pi$
$762$	−3.70064	+	9.57762i	−0.134060	+	0.346961i
$763$	10.3115	+	10.3115i	0.373302	+	0.373302i
$764$	1.09791	+	22.8693i	0.0397211	+	0.827382i
$765$	−0.848970	−	0.490153i	−0.0306946	−	0.0177215i
$766$	−24.9438	+	34.1743i	−0.901257	+	1.23477i
$767$	−3.73988			−0.135039
$768$	−16.1448	−	18.5763i	−0.582577	−	0.670315i
$769$	−29.1507	−	29.1507i	−1.05120	−	1.05120i	−0.998616	−	0.0525854i	$-0.983254\pi$
$769$	−29.1507	−	29.1507i	−1.05120	−	1.05120i	−0.0525854	−	0.998616i	$-0.516746\pi$
$770$	−12.1709	−	1.30622i	−0.438609	−	0.0470730i
$771$	−18.0488	+	18.0488i	−0.650010	+	0.650010i
$772$	50.4461	−	2.42182i	1.81560	−	0.0871633i
$773$	−3.46793	−	6.00663i	−0.124733	−	0.216043i	0.796896	−	0.604117i	$-0.206474\pi$
$773$	−3.46793	−	6.00663i	−0.124733	−	0.216043i	−0.921628	+	0.388074i	$0.873141\pi$
$774$	1.72446	+	0.185074i	0.0619843	+	0.00665236i
$775$	−1.62924	+	0.436555i	−0.0585242	+	0.0156815i
$776$	43.4651	+	14.4397i	1.56031	+	0.518355i
$777$	7.68110	+	10.9332i	0.275558	+	0.392225i
$778$	23.8746	+	17.4261i	0.855945	+	0.624754i
$779$	7.68118	+	28.6666i	0.275207	+	1.02709i
$780$	0.621090	−	0.683732i	0.0222386	−	0.0244815i
$781$	81.6794	−	47.1576i	2.92272	−	1.68743i
$782$	15.3140	−	12.3455i	0.547627	−	0.441473i
$783$	−11.7554	−	11.7554i	−0.420104	−	0.420104i
$784$	−18.0559	−	8.22964i	−0.644853	−	0.293916i
$785$	−4.47701	+	4.47701i	−0.159791	+	0.159791i
$786$	−11.9227	+	5.27701i	−0.425269	+	0.188225i
$787$		−	14.0785i		−	0.501846i	−0.968007	−	0.250923i	$-0.919266\pi$
$787$		−	14.0785i		−	0.501846i	0.968007	−	0.250923i	$-0.0807340\pi$
$788$	−24.5969	+	7.87285i	−0.876229	+	0.280459i
$789$	8.86590	−	15.3562i	0.315634	−	0.546695i
$790$	17.3470	−	13.9844i	0.617180	−	0.497544i
$791$	−3.07790	+	3.07790i	−0.109438	+	0.109438i
$792$	−10.8475	−	0.640125i	−0.385450	−	0.0227458i
$793$	1.44572	−	2.50406i	0.0513390	−	0.0889217i
$794$	12.7787	−	33.0726i	0.453500	−	1.17370i
$795$	−20.9527	−	5.61426i	−0.743115	−	0.199117i
$796$	−37.6702	+	1.80848i	−1.33518	+	0.0640997i
$797$	11.4635	−	3.07165i	0.406060	−	0.108803i	−0.0500072	−	0.998749i	$-0.515924\pi$
$797$	11.4635	−	3.07165i	0.406060	−	0.108803i	0.456067	+	0.889945i	$0.349258\pi$
$798$	−14.0791	+	6.23145i	−0.498395	+	0.220591i
$799$	0.0302347	−	0.00810136i	0.00106963	−	0.000286606i
$800$	4.04364	−	3.95587i	0.142964	−	0.139861i
$801$	1.36917	−	5.10981i	0.0483772	−	0.180546i
$802$	−9.09274	−	20.5438i	−0.321076	−	0.725428i
$803$		−	27.8812i		−	0.983905i
$804$	−5.83273	+	1.86691i	−0.205704	+	0.0658408i
$805$	−11.1222	−	6.42140i	−0.392006	−	0.226325i
$806$	−0.707638	+	0.110488i	−0.0249255	+	0.00389176i
$807$	−4.43325	−	7.67861i	−0.156058	−	0.270300i
$808$	−27.0103	+	13.5392i	−0.950218	+	0.476307i
$809$	−0.128056	+	0.477912i	−0.00450222	+	0.0168025i	−0.968140	−	0.250408i	$-0.919435\pi$
$809$	−0.128056	+	0.477912i	−0.00450222	+	0.0168025i	0.963638	+	0.267211i	$0.0861019\pi$
$810$	1.01061	−	9.41649i	0.0355092	−	0.330862i
$811$	−0.189805	+	0.109584i	−0.00666497	+	0.00384802i	−0.503329	−	0.864095i	$-0.667892\pi$
$811$	−0.189805	+	0.109584i	−0.00666497	+	0.00384802i	0.496664	+	0.867943i	$0.334558\pi$
$812$	−4.59506	−	7.14422i	−0.161255	−	0.250713i
$813$			12.6419i			0.443372i
$814$	−36.1963	−	37.5291i	−1.26868	−	1.31540i
$815$			9.03603i			0.316518i
$816$	7.34256	+	6.05336i	0.257041	+	0.211910i
$817$	−8.30462	+	4.79467i	−0.290542	+	0.167744i
$818$	28.0026	+	3.00534i	0.979089	+	0.105079i
$819$	−0.0703398	+	0.262512i	−0.00245787	+	0.00917291i
$820$	−10.6468	−	5.48379i	−0.371801	−	0.191502i
$821$	12.3269	+	21.3509i	0.430213	+	0.745151i	0.996891	−	0.0787880i	$-0.0251050\pi$
$821$	12.3269	+	21.3509i	0.430213	+	0.745151i	−0.566678	+	0.823939i	$0.691772\pi$
$822$	2.35866	+	15.1065i	0.0822679	+	0.526899i
$823$	−6.09383	−	3.51828i	−0.212418	−	0.122639i	0.390017	−	0.920808i	$-0.372469\pi$
$823$	−6.09383	−	3.51828i	−0.212418	−	0.122639i	−0.602434	+	0.798168i	$0.705803\pi$
$824$	32.7121	+	10.8674i	1.13958	+	0.378583i
$825$			9.32350i			0.324603i
$826$	−23.0027	+	10.1810i	−0.800366	+	0.354243i
$827$	−2.47629	+	9.24162i	−0.0861089	+	0.321363i	−0.995522	−	0.0945315i	$-0.969865\pi$
$827$	−2.47629	+	9.24162i	−0.0861089	+	0.321363i	0.909413	+	0.415894i	$0.136531\pi$
$828$	−10.1354	−	5.22039i	−0.352229	−	0.181421i
$829$	9.58206	−	2.56750i	0.332799	−	0.0891731i	−0.0885504	−	0.996072i	$-0.528223\pi$
$829$	9.58206	−	2.56750i	0.332799	−	0.0891731i	0.421349	+	0.906899i	$0.361557\pi$
$830$	3.42831	+	7.74581i	0.118998	+	0.268861i
$831$	40.7286	−	10.9132i	1.41286	−	0.378574i
$832$	1.88645	−	1.48693i	0.0654009	−	0.0515499i
$833$	7.41084	+	1.98573i	0.256770	+	0.0688014i
$834$	7.34662	+	2.83862i	0.254393	+	0.0982932i
$835$	7.27725	−	12.6046i	0.251840	−	0.436199i
$836$	50.5311	−	32.5009i	1.74766	−	1.12407i
$837$	−6.66677	+	6.66677i	−0.230437	+	0.230437i
$838$	14.6705	+	18.1981i	0.506784	+	0.628642i
$839$	−14.1738	+	24.5497i	−0.489333	+	0.847549i	−0.999925	−	0.0122740i	$-0.996093\pi$
$839$	−14.1738	+	24.5497i	−0.489333	+	0.847549i	0.510592	+	0.859823i	$0.329426\pi$
$840$	1.95879	−	5.89618i	0.0675847	−	0.203438i
$841$		−	20.1544i		−	0.694978i
$842$	−0.193142	−	0.436379i	−0.00665611	−	0.0150386i
$843$	3.85327	−	3.85327i	0.132714	−	0.132714i
$844$	27.8331	−	30.6403i	0.958054	−	1.05468i
$845$	−9.12864	−	9.12864i	−0.314035	−	0.314035i
$846$	−0.0113861	−	0.0141239i	−0.000391462	−	0.000485590i
$847$	31.8304	−	18.3773i	1.09370	−	0.631451i
$848$	−51.3272	−	23.3943i	−1.76258	−	0.803362i
$849$	7.16486	+	26.7396i	0.245897	+	0.917701i
$850$	−1.28950	+	1.76668i	−0.0442294	+	0.0605965i
$851$	−18.7908	−	51.3760i	−0.644139	−	1.76115i
$852$	14.5931	+	45.5929i	0.499952	+	1.56199i
$853$	−19.8920	+	5.33005i	−0.681090	+	0.182498i	−0.582745	−	0.812655i	$-0.698021\pi$
$853$	−19.8920	+	5.33005i	−0.681090	+	0.182498i	−0.0983447	+	0.995152i	$0.531355\pi$
$854$	2.07534	−	19.3373i	0.0710166	−	0.661707i
$855$	−1.57073	−	2.72059i	−0.0537179	−	0.0930421i
$856$	11.7362	+	7.73192i	0.401136	+	0.264271i
$857$	19.0789	−	19.0789i	0.651721	−	0.651721i	−0.301686	−	0.953407i	$-0.597549\pi$
$857$	19.0789	−	19.0789i	0.651721	−	0.651721i	0.953407	+	0.301686i	$0.0975495\pi$
$858$	−0.422460	+	3.93633i	−0.0144225	+	0.134384i
$859$	−34.3307	−	34.3307i	−1.17135	−	1.17135i	−0.981888	−	0.189461i	$-0.939326\pi$
$859$	−34.3307	−	34.3307i	−1.17135	−	1.17135i	−0.189461	−	0.981888i	$-0.560674\pi$
$860$	0.821147	−	3.78151i	0.0280009	−	0.128949i
$861$	−13.1535			−0.448271
$862$	−21.8906	−	15.9780i	−0.745597	−	0.544211i
$863$	27.2530	+	15.7345i	0.927701	+	0.535609i	0.886084	−	0.463525i	$-0.153416\pi$
$863$	27.2530	+	15.7345i	0.927701	+	0.535609i	0.0416174	+	0.999134i	$0.486749\pi$
$864$	8.51848	−	30.4510i	0.289805	−	1.03597i
$865$	2.76122	+	2.76122i	0.0938844	+	0.0938844i
$866$	17.3404	+	6.70004i	0.589250	+	0.227677i
$867$	19.4600	+	11.2353i	0.660898	+	0.381569i
$868$	−4.05166	+	2.60597i	−0.137522	+	0.0884524i
$869$	−24.7167	+	92.2441i	−0.838458	+	3.12917i
$870$	−5.03702	+	4.06063i	−0.170771	+	0.137668i
$871$	−0.154696	−	0.577334i	−0.00524168	−	0.0195622i
$872$	21.5911	−	19.1849i	0.731169	−	0.649683i
$873$	2.65649	+	9.91417i	0.0899087	+	0.335544i
$874$	62.2810	−	9.72430i	2.10669	−	0.328929i
$875$	1.37937	+	0.369601i	0.0466313	+	0.0124948i
$876$	13.8293	+	3.00300i	0.467249	+	0.101462i
$877$	18.7830			0.634255			0.317128	−	0.948383i	$-0.397282\pi$
$877$	18.7830			0.634255			0.317128	+	0.948383i	$0.397282\pi$
$878$	9.19011	+	6.70786i	0.310151	+	0.226379i
$879$	15.2791	−	26.4641i	0.515350	−	0.892613i
$880$	−4.00274	+	23.9120i	−0.134932	+	0.806074i
$881$	−37.9602	+	21.9164i	−1.27891	+	0.738381i	−0.976649	−	0.214843i	$-0.931076\pi$
$881$	−37.9602	+	21.9164i	−1.27891	+	0.738381i	−0.302264	+	0.953224i	$0.597743\pi$
$882$	−0.685988	−	4.39353i	−0.0230984	−	0.147938i
$883$	−37.1771	−	9.96158i	−1.25111	−	0.335234i	−0.428345	−	0.903615i	$-0.640903\pi$
$883$	−37.1771	−	9.96158i	−1.25111	−	0.335234i	−0.822765	+	0.568382i	$0.807570\pi$
$884$	−0.624469	+	0.687452i	−0.0210032	+	0.0231215i
$885$	9.57998	+	16.5930i	0.322027	+	0.557768i
$886$	−27.4901	−	10.6217i	−0.923547	−	0.356844i
$887$	22.4703			0.754480			0.377240	−	0.926115i	$-0.376873\pi$
$887$	22.4703			0.754480			0.377240	+	0.926115i	$0.376873\pi$
$888$	22.5134	−	13.9115i	0.755499	−	0.466839i
$889$	−6.74021			−0.226059
$890$	−11.0098	−	4.25399i	−0.369048	−	0.142594i
$891$	20.2950	+	35.1519i	0.679907	+	1.17763i
$892$	−17.9444	+	19.7542i	−0.600823	+	0.661421i
$893$	0.0968894	+	0.0259614i	0.00324228	+	0.000868766i
$894$	6.50258	+	41.6469i	0.217479	+	1.39288i
$895$	−8.48369	+	4.89806i	−0.283579	+	0.163724i
$896$	7.55505	−	14.2810i	0.252397	−	0.477096i
$897$	−2.07682	+	3.59715i	−0.0693429	+	0.120106i
$898$	−16.8382	−	12.2902i	−0.561898	−	0.410130i
$899$	5.01657			0.167312
$900$	1.23882	+	0.269007i	0.0412940	+	0.00896690i
$901$	21.0667	+	5.64480i	0.701833	+	0.188056i
$902$	50.7137	−	7.91823i	1.68858	−	0.263648i
$903$	−1.10001	−	4.10529i	−0.0366060	−	0.136615i
$904$	5.72654	+	6.44478i	0.190462	+	0.214350i
$905$	−0.815266	−	3.04261i	−0.0271004	−	0.101140i
$906$	22.4341	−	18.0854i	0.745324	−	0.600848i
$907$	0.646067	−	2.41116i	0.0214523	−	0.0800611i	−0.954370	−	0.298627i	$-0.903471\pi$
$907$	0.646067	−	2.41116i	0.0214523	−	0.0800611i	0.975822	+	0.218566i	$0.0701379\pi$
$908$	−21.0830	+	13.5603i	−0.699662	+	0.450013i
$909$	−5.86371	−	3.38541i	−0.194487	−	0.112287i
$910$	0.565616	+	0.218545i	0.0187500	+	0.00724469i
$911$	−0.857094	−	0.857094i	−0.0283968	−	0.0283968i	0.692766	−	0.721163i	$-0.256392\pi$
$911$	−0.857094	−	0.857094i	−0.0283968	−	0.0283968i	−0.721163	+	0.692766i	$0.756392\pi$
$912$	10.6782	+	28.5644i	0.353589	+	0.945863i
$913$	−31.4403	−	18.1521i	−1.04052	−	0.600746i
$914$	−44.6313	−	32.5764i	−1.47627	−	1.07753i
$915$	−14.8133			−0.489712
$916$	1.02007	−	4.69760i	0.0337041	−	0.155213i
$917$	−6.05212	−	6.05212i	−0.199859	−	0.199859i
$918$	−1.30463	+	12.1561i	−0.0430593	+	0.401211i
$919$	−9.12268	+	9.12268i	−0.300930	+	0.300930i	−0.841377	−	0.540448i	$-0.818255\pi$
$919$	−9.12268	+	9.12268i	−0.300930	+	0.300930i	0.540448	+	0.841377i	$0.318255\pi$
$920$	−13.9942	+	21.2417i	−0.461374	+	0.700318i
$921$	2.67197	+	4.62800i	0.0880446	+	0.152498i
$922$	3.56626	−	33.2291i	0.117448	−	1.09434i
$923$	−4.51287	+	1.20922i	−0.148543	+	0.0398019i
$924$	8.11743	+	25.3611i	0.267044	+	0.834317i
$925$	3.49675	+	4.97722i	0.114972	+	0.163650i
$926$	−24.2806	+	33.2657i	−0.797911	+	1.09318i
$927$	1.99929	+	7.46145i	0.0656653	+	0.245066i
$928$	−14.6618	+	8.25184i	−0.481296	+	0.270880i
$929$	−48.8596	+	28.2091i	−1.60303	+	0.925511i	−0.612156	+	0.790737i	$0.709698\pi$
$929$	−48.8596	+	28.2091i	−1.60303	+	0.925511i	−0.990876	+	0.134774i	$0.956969\pi$
$930$	2.30288	+	2.85661i	0.0755144	+	0.0936720i
$931$	17.3852	+	17.3852i	0.569776	+	0.569776i
$932$	−1.85035	+	2.03697i	−0.0606103	+	0.0667233i
$933$	29.2032	−	29.2032i	0.956071	−	0.956071i
$934$	0.294977	+	0.666460i	0.00965193	+	0.0218073i
$935$		−	9.37423i		−	0.306570i
$936$	0.510834	+	0.169706i	0.0166971	+	0.00554701i
$937$	21.5268	−	37.2854i	0.703249	−	1.21806i	−0.264071	−	0.964503i	$-0.585065\pi$
$937$	21.5268	−	37.2854i	0.703249	−	1.21806i	0.967320	−	0.253559i	$-0.0816013\pi$
$938$	−2.52315	−	3.12985i	−0.0823839	−	0.102193i
$939$	−12.6178	+	12.6178i	−0.411768	+	0.411768i
$940$	−0.0340437	+	0.0218964i	−0.00111038	+	0.000714183i
$941$	−13.7029	+	23.7341i	−0.446701	+	0.773709i	−0.998169	−	0.0604874i	$-0.980734\pi$
$941$	−13.7029	+	23.7341i	−0.446701	+	0.773709i	0.551468	+	0.834196i	$0.314068\pi$
$942$	12.8477	+	4.96414i	0.418600	+	0.161740i
$943$	52.0175	+	13.9381i	1.69392	+	0.453886i
$944$	17.4461	+	46.6690i	0.567824	+	1.51895i
$945$	7.71026	−	2.06596i	0.250815	−	0.0672056i
$946$	6.71243	+	15.1658i	0.218240	+	0.493084i
$947$	−55.9064	+	14.9801i	−1.81671	+	0.486787i	−0.996373	−	0.0850896i	$-0.972882\pi$
$947$	−55.9064	+	14.9801i	−1.81671	+	0.486787i	−0.820340	+	0.571876i	$0.806216\pi$
$948$	−43.0917	−	22.1951i	−1.39955	−	0.720862i
$949$	−0.357466	+	1.33408i	−0.0116038	+	0.0433061i
$950$	−6.40939	+	2.83681i	−0.207948	+	0.0920382i
$951$		−	0.382193i		−	0.0123935i
$952$	−1.96945	+	5.92826i	−0.0638301	+	0.192136i
$953$	41.6894	+	24.0694i	1.35045	+	0.779684i	0.988313	−	0.152440i	$-0.0487131\pi$
$953$	41.6894	+	24.0694i	1.35045	+	0.779684i	0.362139	+	0.932124i	$0.382046\pi$
$954$	−1.95005	−	12.4894i	−0.0631351	−	0.404360i
$955$	5.72391	+	9.91410i	0.185221	+	0.320813i
$956$	−11.8591	−	6.10823i	−0.383552	−	0.197554i
$957$	7.17694	−	26.7847i	0.231998	−	0.865827i
$958$	18.1116	+	1.94380i	0.585159	+	0.0628012i
$959$	−8.69211	+	5.01839i	−0.280683	+	0.162052i
$960$	−11.4294	−	4.56089i	−0.368884	−	0.147202i
$961$			28.1550i			0.908225i
$962$	1.25078	+	2.25980i	0.0403269	+	0.0728588i
$963$			3.14953i			0.101492i
$964$	−24.0471	−	37.3875i	−0.774506	−	1.20417i
$965$	21.8690	−	12.6261i	0.703987	−	0.406447i
$966$	−2.98129	+	27.7786i	−0.0959213	+	0.893760i
$967$	−1.82739	+	6.81990i	−0.0587648	+	0.219313i	−0.989064	−	0.147489i	$-0.952881\pi$
$967$	−1.82739	+	6.81990i	−0.0587648	+	0.219313i	0.930299	+	0.366802i	$0.119547\pi$
$968$	−32.6218	−	65.0795i	−1.04851	−	2.09174i
$969$	−5.89546	−	10.2112i	−0.189390	−	0.328032i
$970$	22.6263	−	3.53278i	0.726487	−	0.113431i
$971$	21.9832	+	12.6920i	0.705474	+	0.407305i	0.809383	−	0.587281i	$-0.199802\pi$
$971$	21.9832	+	12.6920i	0.705474	+	0.407305i	−0.103909	+	0.994587i	$0.533135\pi$
$972$	12.3203	−	3.94342i	0.395174	−	0.126485i
$973$			5.17016i			0.165748i
$974$	8.00523	+	18.0867i	0.256504	+	0.579537i
$975$	0.119537	−	0.446118i	0.00382825	−	0.0142872i
$976$	−37.9917	−	6.35960i	−1.21608	−	0.203566i
$977$	−3.13218	+	0.839265i	−0.100207	+	0.0268505i	−0.308574	−	0.951200i	$-0.599852\pi$
$977$	−3.13218	+	0.839265i	−0.100207	+	0.0268505i	0.208367	+	0.978051i	$0.433185\pi$
$978$	17.9749	−	7.95574i	0.574775	−	0.254397i
$979$	48.8629	−	13.0928i	1.56166	−	0.418447i
$980$	−9.91005	+	0.475763i	−0.316565	+	0.0151977i
$981$	6.25212	+	1.67525i	0.199615	+	0.0534866i
$982$	3.18885	−	8.25305i	0.101760	−	0.263365i
$983$	19.0570	−	33.0078i	0.607825	−	1.05278i	−0.383773	−	0.923428i	$-0.625375\pi$
$983$	19.0570	−	33.0078i	0.607825	−	1.05278i	0.991598	−	0.129357i	$-0.0412913\pi$
$984$	−1.53472	+	26.0073i	−0.0489251	+	0.829082i
$985$	−9.13092	+	9.13092i	−0.290935	+	0.290935i
$986$	5.06442	−	4.08272i	0.161284	−	0.130020i
$987$	−0.0222286	+	0.0385011i	−0.000707545	+	0.00122550i
$988$	−2.83455	+	0.907267i	−0.0901790	+	0.0288640i
$989$			17.4006i			0.553306i
$990$	−4.96831	+	2.19899i	−0.157903	+	0.0698883i
$991$	10.3917	−	10.3917i	0.330104	−	0.330104i	−0.522522	−	0.852626i	$-0.675009\pi$
$991$	10.3917	−	10.3917i	0.330104	−	0.330104i	0.852626	+	0.522522i	$0.175009\pi$
$992$	4.67981	+	8.31504i	0.148584	+	0.264003i
$993$	14.5681	+	14.5681i	0.462306	+	0.462306i
$994$	−24.4652	+	19.7228i	−0.775990	+	0.625570i
$995$	−16.3305	+	9.42840i	−0.517710	+	0.298900i
$996$	12.3899	−	13.6396i	0.392590	−	0.432186i
$997$	−6.83002	−	25.4900i	−0.216309	−	0.807276i	−0.985702	−	0.168500i	$-0.946108\pi$
$997$	−6.83002	−	25.4900i	−0.216309	−	0.807276i	0.769393	−	0.638776i	$-0.220559\pi$
$998$	22.3555	+	16.3173i	0.707650	+	0.516514i
$999$	30.8377	+	14.3209i	0.975662	+	0.453094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.51.9	✓	304
4.3	odd	2	inner	740.2.be.a.51.22	yes	304
37.8	odd	12	inner	740.2.be.a.711.22	yes	304
148.119	even	12	inner	740.2.be.a.711.9	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.51.9	✓	304	1.1	even	1	trivial
740.2.be.a.51.22	yes	304	4.3	odd	2	inner
740.2.be.a.711.9	yes	304	148.119	even	12	inner
740.2.be.a.711.22	yes	304	37.8	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31917 - 0.509705i) q^{2} +(0.769115 + 1.33215i) q^{3} +(1.48040 + 1.34477i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.335590 - 2.14935i) q^{6} +(1.23671 - 0.714015i) q^{7} +(-1.26746 - 2.52855i) q^{8} +(0.316923 - 0.548926i) q^{9} +(-1.14230 - 0.833762i) q^{10} +6.06118 q^{11} +(-0.652832 + 3.00640i) q^{12} +(-0.290020 - 0.0777107i) q^{13} +(-1.99536 + 0.311548i) q^{14} +(0.398123 + 1.48582i) q^{15} +(0.383182 + 3.98160i) q^{16} +(-0.400290 - 1.49390i) q^{17} +(-0.697864 + 0.562588i) q^{18} +(1.28276 - 4.78732i) q^{19} +(1.08191 + 1.68211i) q^{20} +(1.90235 + 1.09832i) q^{21} +(-7.99571 - 3.08941i) q^{22} +(-6.35927 - 6.35927i) q^{23} +(2.39357 - 3.63319i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.342975 + 0.250338i) q^{26} +5.58969 q^{27} +(2.79102 + 0.606063i) q^{28} +(-2.10305 - 2.10305i) q^{29} +(0.232137 - 2.16297i) q^{30} +(-1.19269 + 1.19269i) q^{31} +(1.52396 - 5.44771i) q^{32} +(4.66175 + 8.07439i) q^{33} +(-0.233400 + 2.17473i) q^{34} +(1.37937 - 0.369601i) q^{35} +(1.20735 - 0.386443i) q^{36} +(5.51689 + 2.56202i) q^{37} +(-4.13229 + 5.66144i) q^{38} +(-0.119537 - 0.446118i) q^{39} +(-0.569838 - 2.77043i) q^{40} +(-5.18578 + 2.99401i) q^{41} +(-1.94969 - 2.41850i) q^{42} +(-1.36812 - 1.36812i) q^{43} +(8.97299 + 8.15090i) q^{44} +(0.448196 - 0.448196i) q^{45} +(5.14759 + 11.6303i) q^{46} +0.0202388i q^{47} +(-5.00937 + 3.57277i) q^{48} +(-2.48037 + 4.29612i) q^{49} +(-0.887580 - 1.10100i) q^{50} +(1.68223 - 1.68223i) q^{51} +(-0.324843 - 0.505054i) q^{52} +(-7.05090 + 12.2125i) q^{53} +(-7.37374 - 2.84909i) q^{54} +(5.85465 + 1.56875i) q^{55} +(-3.37290 - 2.22209i) q^{56} +(7.36400 - 1.97318i) q^{57} +(1.70234 + 3.84621i) q^{58} +(12.0314 - 3.22381i) q^{59} +(-1.40870 + 2.73499i) q^{60} +(-2.49245 + 9.30193i) q^{61} +(2.18128 - 0.965437i) q^{62} -0.905150i q^{63} +(-4.78708 + 6.40967i) q^{64} +(-0.260025 - 0.150125i) q^{65} +(-2.03407 - 13.0276i) q^{66} +(0.995335 + 1.72397i) q^{67} +(1.41637 - 2.74987i) q^{68} +(3.58047 - 13.3625i) q^{69} +(-2.00801 - 0.215506i) q^{70} +(13.4758 - 7.78027i) q^{71} +(-1.78967 - 0.105611i) q^{72} -4.59995i q^{73} +(-5.97182 - 6.19172i) q^{74} +1.53823i q^{75} +(8.33684 - 5.36214i) q^{76} +(7.49593 - 4.32778i) q^{77} +(-0.0696992 + 0.649433i) q^{78} +(-4.07787 + 15.2188i) q^{79} +(-0.660390 + 3.94511i) q^{80} +(3.34835 + 5.79952i) q^{81} +(8.36697 - 1.30638i) q^{82} +(-5.18716 - 2.99481i) q^{83} +(1.33925 + 4.18418i) q^{84} -1.54660i q^{85} +(1.10745 + 2.50212i) q^{86} +(1.18408 - 4.41906i) q^{87} +(-7.68232 - 15.3260i) q^{88} +(8.06161 - 2.16010i) q^{89} +(-0.819694 + 0.362798i) q^{90} +(-0.414157 + 0.110973i) q^{91} +(-0.862516 - 17.9661i) q^{92} +(-2.50615 - 0.671522i) q^{93} +(0.0103158 - 0.0266983i) q^{94} +(2.47810 - 4.29219i) q^{95} +(8.42925 - 2.15978i) q^{96} +(-11.4502 + 11.4502i) q^{97} +(5.46177 - 4.40304i) q^{98} +(1.92093 - 3.32714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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