LMFDB - Embedded newform 702.2.w.d.157.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(79,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("702.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.w (of order $9$, degree $6$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			157.6
Character	$\chi$	$=$	702.157
Dual form			702.2.w.d.313.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.147653 - 1.72575i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.992799 - 0.361349i) q^{5} +(1.22240 + 1.22709i) q^{6} +(0.163744 + 0.928638i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.95640 + 0.509623i) q^{9} +(-0.528257 + 0.914969i) q^{10} +(-5.67516 - 2.06559i) q^{11} +(-1.72517 - 0.154263i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-0.722353 - 0.606126i) q^{14} +(-0.770187 - 1.65996i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.24698 - 3.89189i) q^{17} +(1.93715 - 2.29073i) q^{18} +(-2.23673 - 3.87413i) q^{19} +(-0.183462 - 1.04046i) q^{20} +(1.57842 - 0.419697i) q^{21} +(5.67516 - 2.06559i) q^{22} +(0.706638 - 4.00754i) q^{23} +(1.42071 - 0.990744i) q^{24} +(-2.97515 + 2.49644i) q^{25} -1.00000 q^{26} +(1.31600 + 5.02674i) q^{27} +0.942964 q^{28} +(-3.81360 + 3.19999i) q^{29} +(1.65700 + 0.776540i) q^{30} +(-0.895825 + 5.08048i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-2.72673 + 10.0989i) q^{33} +(0.780369 + 4.42569i) q^{34} +(0.498128 + 0.862783i) q^{35} +(-0.0114923 + 2.99998i) q^{36} +(-0.109691 + 0.189991i) q^{37} +(4.20368 + 1.53001i) q^{38} +(0.996179 - 1.41691i) q^{39} +(0.809337 + 0.679115i) q^{40} +(-7.79711 - 6.54255i) q^{41} +(-0.939361 + 1.33609i) q^{42} +(-7.11137 - 2.58833i) q^{43} +(-3.01969 + 5.23026i) q^{44} +(-2.75096 + 1.57425i) q^{45} +(2.03468 + 3.52417i) q^{46} +(-1.87828 - 10.6523i) q^{47} +(-0.451491 + 1.67217i) q^{48} +(5.74229 - 2.09002i) q^{49} +(0.674411 - 3.82477i) q^{50} +(-7.04818 - 3.30307i) q^{51} +(0.766044 - 0.642788i) q^{52} +4.28078 q^{53} +(-4.23924 - 3.00480i) q^{54} -6.38070 q^{55} +(-0.722353 + 0.606126i) q^{56} +(-6.35551 + 4.43206i) q^{57} +(0.864473 - 4.90267i) q^{58} +(-6.68285 + 2.43236i) q^{59} +(-1.76849 + 0.470236i) q^{60} +(0.672600 + 3.81450i) q^{61} +(-2.57943 - 4.46770i) q^{62} +(-0.957348 - 2.66198i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.992799 + 0.361349i) q^{65} +(-4.40264 - 9.48890i) q^{66} +(0.975443 + 0.818494i) q^{67} +(-3.44258 - 2.88866i) q^{68} +(-7.02034 - 0.627752i) q^{69} +(-0.936174 - 0.340739i) q^{70} +(-2.60038 + 4.50399i) q^{71} +(-1.91955 - 2.30550i) q^{72} +(5.52605 + 9.57140i) q^{73} +(-0.0380954 - 0.216050i) q^{74} +(4.74752 + 4.76574i) q^{75} +(-4.20368 + 1.53001i) q^{76} +(0.988913 - 5.60840i) q^{77} +(0.147653 + 1.72575i) q^{78} +(11.7663 - 9.87308i) q^{79} -1.05651 q^{80} +(8.48057 - 3.01330i) q^{81} +10.1784 q^{82} +(-8.14121 + 6.83129i) q^{83} +(-0.139231 - 1.62732i) q^{84} +(0.824471 - 4.67581i) q^{85} +(7.11137 - 2.58833i) q^{86} +(6.08546 + 6.10882i) q^{87} +(-1.04873 - 5.94763i) q^{88} +(-7.83691 - 13.5739i) q^{89} +(1.09545 - 2.97422i) q^{90} +(-0.471482 + 0.816631i) q^{91} +(-3.82395 - 1.39180i) q^{92} +(8.89988 + 0.795819i) q^{93} +(8.28598 + 6.95276i) q^{94} +(-3.62054 - 3.03799i) q^{95} +(-0.728988 - 1.57117i) q^{96} +(-16.1566 - 5.88052i) q^{97} +(-3.05541 + 5.29212i) q^{98} +(17.8307 + 3.21451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) $ 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.147653	−	1.72575i	−0.0852475	−	0.996360i
$3$	−0.147653	−	1.72575i	−0.0852475	−	0.996360i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.992799	−	0.361349i	0.443993	−	0.161600i	−0.110342	−	0.993894i	$-0.535195\pi$
$5$	0.992799	−	0.361349i	0.443993	−	0.161600i	0.554335	+	0.832293i	$0.312972\pi$
$6$	1.22240	+	1.22709i	0.499041	+	0.500957i
$7$	0.163744	+	0.928638i	0.0618894	+	0.350992i	0.999989	+	0.00462747i	$0.00147298\pi$
$7$	0.163744	+	0.928638i	0.0618894	+	0.350992i	−0.938100	+	0.346365i	$0.887416\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.95640	+	0.509623i	−0.985466	+	0.169874i
$10$	−0.528257	+	0.914969i	−0.167050	+	0.289338i
$11$	−5.67516	−	2.06559i	−1.71113	−	0.622799i	−0.714113	−	0.700030i	$-0.753170\pi$
$11$	−5.67516	−	2.06559i	−1.71113	−	0.622799i	−0.997013	+	0.0772314i	$0.975392\pi$
$12$	−1.72517	−	0.154263i	−0.498013	−	0.0445318i
$13$	0.766044	+	0.642788i	0.212463	+	0.178277i
$13$	0.766044	+	0.642788i	0.212463	+	0.178277i
$14$	−0.722353	−	0.606126i	−0.193057	−	0.161994i
$15$	−0.770187	−	1.65996i	−0.198861	−	0.428601i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.24698	−	3.89189i	0.544973	−	0.943921i	−0.453635	−	0.891187i	$-0.649873\pi$
$17$	2.24698	−	3.89189i	0.544973	−	0.943921i	0.998609	−	0.0527339i	$-0.0167935\pi$
$18$	1.93715	−	2.29073i	0.456591	−	0.539930i
$19$	−2.23673	−	3.87413i	−0.513141	−	0.888787i	−0.999884	−	0.0152415i	$-0.995148\pi$
$19$	−2.23673	−	3.87413i	−0.513141	−	0.888787i	0.486742	−	0.873546i	$-0.338185\pi$
$20$	−0.183462	−	1.04046i	−0.0410233	−	0.232655i
$21$	1.57842	−	0.419697i	0.344439	−	0.0915854i
$22$	5.67516	−	2.06559i	1.20995	−	0.440385i
$23$	0.706638	−	4.00754i	0.147344	−	0.835630i	−0.818111	−	0.575061i	$-0.804978\pi$
$23$	0.706638	−	4.00754i	0.147344	−	0.835630i	0.965455	−	0.260570i	$-0.0839104\pi$
$24$	1.42071	−	0.990744i	0.290002	−	0.202235i
$25$	−2.97515	+	2.49644i	−0.595029	+	0.499289i
$26$	−1.00000			−0.196116
$27$	1.31600	+	5.02674i	0.253264	+	0.967397i
$28$	0.942964			0.178203
$29$	−3.81360	+	3.19999i	−0.708168	+	0.594224i	−0.924084	−	0.382188i	$-0.875171\pi$
$29$	−3.81360	+	3.19999i	−0.708168	+	0.594224i	0.215916	+	0.976412i	$0.430726\pi$
$30$	1.65700	+	0.776540i	0.302526	+	0.141776i
$31$	−0.895825	+	5.08048i	−0.160895	+	0.912481i	0.792302	+	0.610130i	$0.208883\pi$
$31$	−0.895825	+	5.08048i	−0.160895	+	0.912481i	−0.953197	+	0.302351i	$0.902228\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−2.72673	+	10.0989i	−0.474663	+	1.75799i
$34$	0.780369	+	4.42569i	0.133832	+	0.759000i
$35$	0.498128	+	0.862783i	0.0841990	+	0.145837i
$36$	−0.0114923	+	2.99998i	−0.00191538	+	0.499996i
$37$	−0.109691	+	0.189991i	−0.0180332	+	0.0312344i	−0.874901	−	0.484302i	$-0.839074\pi$
$37$	−0.109691	+	0.189991i	−0.0180332	+	0.0312344i	0.856868	+	0.515536i	$0.172407\pi$
$38$	4.20368	+	1.53001i	0.681927	+	0.248201i
$39$	0.996179	−	1.41691i	0.159516	−	0.226887i
$40$	0.809337	+	0.679115i	0.127967	+	0.107377i
$41$	−7.79711	−	6.54255i	−1.21770	−	1.02177i	−0.998942	−	0.0459968i	$-0.985354\pi$
$41$	−7.79711	−	6.54255i	−1.21770	−	1.02177i	−0.218762	−	0.975778i	$-0.570202\pi$
$42$	−0.939361	+	1.33609i	−0.144947	+	0.206164i
$43$	−7.11137	−	2.58833i	−1.08447	−	0.394716i	−0.262903	−	0.964822i	$-0.584680\pi$
$43$	−7.11137	−	2.58833i	−1.08447	−	0.394716i	−0.821571	+	0.570106i	$0.806902\pi$
$44$	−3.01969	+	5.23026i	−0.455236	+	0.788491i
$45$	−2.75096	+	1.57425i	−0.410088	+	0.234675i
$46$	2.03468	+	3.52417i	0.299998	+	0.519611i
$47$	−1.87828	−	10.6523i	−0.273975	−	1.55379i	−0.742198	−	0.670180i	$-0.766217\pi$
$47$	−1.87828	−	10.6523i	−0.273975	−	1.55379i	0.468223	−	0.883610i	$-0.344894\pi$
$48$	−0.451491	+	1.67217i	−0.0651672	+	0.241357i
$49$	5.74229	−	2.09002i	0.820327	−	0.298575i
$50$	0.674411	−	3.82477i	0.0953761	−	0.540905i
$51$	−7.04818	−	3.30307i	−0.986943	−	0.462522i
$52$	0.766044	−	0.642788i	0.106231	−	0.0891386i
$53$	4.28078			0.588010			0.294005	−	0.955804i	$-0.405012\pi$
$53$	4.28078			0.588010			0.294005	+	0.955804i	$0.405012\pi$
$54$	−4.23924	−	3.00480i	−0.576888	−	0.408901i
$55$	−6.38070			−0.860373
$56$	−0.722353	+	0.606126i	−0.0965284	+	0.0809970i
$57$	−6.35551	+	4.43206i	−0.841808	+	0.587040i
$58$	0.864473	−	4.90267i	0.113511	−	0.643752i
$59$	−6.68285	+	2.43236i	−0.870033	+	0.316666i	−0.738180	−	0.674603i	$-0.764315\pi$
$59$	−6.68285	+	2.43236i	−0.870033	+	0.316666i	−0.131852	+	0.991269i	$0.542092\pi$
$60$	−1.76849	+	0.470236i	−0.228311	+	0.0607072i
$61$	0.672600	+	3.81450i	0.0861175	+	0.488397i	0.997110	+	0.0759735i	$0.0242064\pi$
$61$	0.672600	+	3.81450i	0.0861175	+	0.488397i	−0.910992	+	0.412423i	$0.864682\pi$
$62$	−2.57943	−	4.46770i	−0.327587	−	0.567398i
$63$	−0.957348	−	2.66198i	−0.120615	−	0.335378i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.992799	+	0.361349i	0.123142	+	0.0448199i
$66$	−4.40264	−	9.48890i	−0.541927	−	1.16800i
$67$	0.975443	+	0.818494i	0.119169	+	0.0999949i	0.700425	−	0.713726i	$-0.252994\pi$
$67$	0.975443	+	0.818494i	0.119169	+	0.0999949i	−0.581256	+	0.813721i	$0.697438\pi$
$68$	−3.44258	−	2.88866i	−0.417474	−	0.350302i
$69$	−7.02034	−	0.627752i	−0.845149	−	0.0755724i
$70$	−0.936174	−	0.340739i	−0.111894	−	0.0407262i
$71$	−2.60038	+	4.50399i	−0.308608	+	0.534525i	−0.978058	−	0.208332i	$-0.933197\pi$
$71$	−2.60038	+	4.50399i	−0.308608	+	0.534525i	0.669450	+	0.742857i	$0.266530\pi$
$72$	−1.91955	−	2.30550i	−0.226221	−	0.271706i
$73$	5.52605	+	9.57140i	0.646776	+	1.12025i	0.983888	+	0.178784i	$0.0572163\pi$
$73$	5.52605	+	9.57140i	0.646776	+	1.12025i	−0.337113	+	0.941464i	$0.609450\pi$
$74$	−0.0380954	−	0.216050i	−0.00442850	−	0.0251153i
$75$	4.74752	+	4.76574i	0.548196	+	0.550300i
$76$	−4.20368	+	1.53001i	−0.482195	+	0.175505i
$77$	0.988913	−	5.60840i	0.112697	−	0.639137i
$78$	0.147653	+	1.72575i	0.0167184	+	0.195402i
$79$	11.7663	−	9.87308i	1.32381	−	1.11081i	0.338327	−	0.941028i	$-0.390139\pi$
$79$	11.7663	−	9.87308i	1.32381	−	1.11081i	0.985482	−	0.169780i	$-0.0543056\pi$
$80$	−1.05651			−0.118122
$81$	8.48057	−	3.01330i	0.942285	−	0.334811i
$82$	10.1784			1.12402
$83$	−8.14121	+	6.83129i	−0.893614	+	0.749831i	−0.968932	−	0.247328i	$-0.920447\pi$
$83$	−8.14121	+	6.83129i	−0.893614	+	0.749831i	0.0753178	+	0.997160i	$0.476003\pi$
$84$	−0.139231	−	1.62732i	−0.0151914	−	0.177555i
$85$	0.824471	−	4.67581i	0.0894264	−	0.507163i
$86$	7.11137	−	2.58833i	0.766839	−	0.279106i
$87$	6.08546	+	6.10882i	0.652430	+	0.654934i
$88$	−1.04873	−	5.94763i	−0.111795	−	0.634020i
$89$	−7.83691	−	13.5739i	−0.830710	−	1.43883i	−0.897476	−	0.441064i	$-0.854601\pi$
$89$	−7.83691	−	13.5739i	−0.830710	−	1.43883i	0.0667654	−	0.997769i	$-0.478732\pi$
$90$	1.09545	−	2.97422i	0.115471	−	0.313511i
$91$	−0.471482	+	0.816631i	−0.0494248	+	0.0856062i
$92$	−3.82395	−	1.39180i	−0.398675	−	0.145106i
$93$	8.89988	+	0.795819i	0.922875	+	0.0825226i
$94$	8.28598	+	6.95276i	0.854634	+	0.717123i
$95$	−3.62054	−	3.03799i	−0.371460	−	0.311692i
$96$	−0.728988	−	1.57117i	−0.0744021	−	0.160357i
$97$	−16.1566	−	5.88052i	−1.64045	−	0.597077i	−0.653336	−	0.757068i	$-0.726631\pi$
$97$	−16.1566	−	5.88052i	−1.64045	−	0.597077i	−0.987118	+	0.159991i	$0.948853\pi$
$98$	−3.05541	+	5.29212i	−0.308643	+	0.534585i
$99$	17.8307	+	3.21451i	1.79205	+	0.323071i
$100$	1.94189	+	3.36345i	0.194189	+	0.336345i
$101$	0.195410	+	1.10823i	0.0194440	+	0.110273i	0.992985	−	0.118240i	$-0.0377251\pi$
$101$	0.195410	+	1.10823i	0.0194440	+	0.110273i	−0.973541	+	0.228512i	$0.926614\pi$
$102$	7.52239	−	2.00018i	0.744828	−	0.198048i
$103$	6.92927	−	2.52205i	0.682761	−	0.248505i	0.0227287	−	0.999742i	$-0.492765\pi$
$103$	6.92927	−	2.52205i	0.682761	−	0.248505i	0.660033	+	0.751237i	$0.270542\pi$
$104$	−0.173648	+	0.984808i	−0.0170276	+	0.0965683i
$105$	1.41539	−	0.987034i	0.138128	−	0.0963247i
$106$	−3.27927	+	2.75163i	−0.318510	+	0.267262i
$107$	−7.73587			−0.747855			−0.373928	−	0.927458i	$-0.621989\pi$
$107$	−7.73587			−0.747855			−0.373928	+	0.927458i	$0.621989\pi$
$108$	5.17890	−	0.423123i	0.498340	−	0.0407150i
$109$	13.7473			1.31675			0.658377	−	0.752688i	$-0.271243\pi$
$109$	13.7473			1.31675			0.658377	+	0.752688i	$0.271243\pi$
$110$	4.88790	−	4.10143i	0.466043	−	0.391056i
$111$	0.344073	+	0.161247i	0.0326579	+	0.0153049i
$112$	0.163744	−	0.928638i	0.0154724	−	0.0877481i
$113$	4.68906	−	1.70668i	0.441110	−	0.160551i	−0.111911	−	0.993718i	$-0.535697\pi$
$113$	4.68906	−	1.70668i	0.441110	−	0.160551i	0.553021	+	0.833167i	$0.313475\pi$
$114$	2.01973	−	7.48039i	0.189165	−	0.700603i
$115$	−0.746573	−	4.23403i	−0.0696183	−	0.394825i
$116$	2.48915	+	4.31134i	0.231112	+	0.400298i
$117$	−2.59231	−	1.50994i	−0.239659	−	0.139594i
$118$	3.55587	−	6.15895i	0.327344	−	0.566977i
$119$	3.98209	+	1.44936i	0.365037	+	0.132863i
$120$	1.05248	−	1.49698i	0.0960777	−	0.136655i
$121$	19.5143	+	16.3745i	1.77403	+	1.48859i
$122$	−2.96716	−	2.48974i	−0.268634	−	0.225410i
$123$	−10.1395	+	14.4219i	−0.914249	+	1.30038i
$124$	4.84774	+	1.76443i	0.435339	+	0.158451i
$125$	−4.69292	+	8.12838i	−0.419748	+	0.727024i
$126$	2.44446	+	1.42382i	0.217770	+	0.126844i
$127$	−3.62693	−	6.28203i	−0.321838	−	0.557440i	0.659029	−	0.752117i	$-0.270967\pi$
$127$	−3.62693	−	6.28203i	−0.321838	−	0.557440i	−0.980867	+	0.194677i	$0.937634\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−3.41678	+	12.6546i	−0.300831	+	1.11417i
$130$	−0.992799	+	0.361349i	−0.0870742	+	0.0316924i
$131$	1.40969	−	7.99478i	0.123166	−	0.698507i	−0.859215	−	0.511615i	$-0.829047\pi$
$131$	1.40969	−	7.99478i	0.123166	−	0.698507i	0.982380	−	0.186892i	$-0.0598414\pi$
$132$	9.47196	+	4.43896i	0.824429	+	0.386362i
$133$	3.23142	−	2.71148i	0.280199	−	0.235115i
$134$	−1.27335			−0.110001
$135$	3.12293	+	4.51501i	0.268779	+	0.388590i
$136$	4.49396			0.385354
$137$	6.55060	−	5.49661i	0.559656	−	0.469607i	−0.318539	−	0.947910i	$-0.603192\pi$
$137$	6.55060	−	5.49661i	0.559656	−	0.469607i	0.878195	+	0.478303i	$0.158748\pi$
$138$	5.78140	−	4.03170i	0.492145	−	0.343201i
$139$	−0.147405	+	0.835973i	−0.0125027	+	0.0709063i	−0.990421	−	0.138082i	$-0.955906\pi$
$139$	−0.147405	+	0.835973i	−0.0125027	+	0.0709063i	0.977918	+	0.208989i	$0.0670172\pi$
$140$	0.936174	−	0.340739i	0.0791211	−	0.0287977i
$141$	−18.1057	+	4.81427i	−1.52478	+	0.405435i
$142$	−0.903103	−	5.12175i	−0.0757867	−	0.429808i
$143$	−3.01969	−	5.23026i	−0.252519	−	0.437376i
$144$	2.95241	+	0.532258i	0.246034	+	0.0443549i
$145$	−2.62983	+	4.55499i	−0.218395	+	0.378271i
$146$	−10.3856	−	3.78004i	−0.859517	−	0.312839i
$147$	−4.45471	−	9.60114i	−0.367419	−	0.791888i
$148$	0.168057	+	0.141017i	0.0138142	+	0.0115915i
$149$	16.2858	+	13.6654i	1.33419	+	1.11952i	0.983079	+	0.183180i	$0.0586391\pi$
$149$	16.2858	+	13.6654i	1.33419	+	1.11952i	0.351107	+	0.936335i	$0.385805\pi$
$150$	−6.70017	−	0.599122i	−0.547066	−	0.0489181i
$151$	−11.2469	−	4.09354i	−0.915261	−	0.333128i	−0.158910	−	0.987293i	$-0.550798\pi$
$151$	−11.2469	−	4.09354i	−0.915261	−	0.333128i	−0.756352	+	0.654165i	$0.773020\pi$
$152$	2.23673	−	3.87413i	0.181423	−	0.314234i
$153$	−4.65958	+	12.6511i	−0.376704	+	1.02278i
$154$	2.84746	+	4.93195i	0.229455	+	0.397428i
$155$	0.946453	+	5.36760i	0.0760209	+	0.431136i
$156$	−1.22240	−	1.22709i	−0.0978701	−	0.0982457i
$157$	−0.593026	+	0.215844i	−0.0473286	+	0.0172262i	−0.365576	−	0.930781i	$-0.619128\pi$
$157$	−0.593026	+	0.215844i	−0.0473286	+	0.0172262i	0.318247	+	0.948008i	$0.396906\pi$
$158$	−2.66720	+	15.1264i	−0.212191	+	1.20339i
$159$	−0.632069	−	7.38753i	−0.0501264	−	0.585869i
$160$	0.809337	−	0.679115i	0.0639837	−	0.0536887i
$161$	3.83727			0.302419
$162$	−4.55958	+	7.75952i	−0.358235	+	0.609646i
$163$	−4.24591			−0.332565			−0.166283	−	0.986078i	$-0.553176\pi$
$163$	−4.24591			−0.332565			−0.166283	+	0.986078i	$0.553176\pi$
$164$	−7.79711	+	6.54255i	−0.608852	+	0.510887i
$165$	0.942129	+	11.0115i	0.0733446	+	0.857241i
$166$	1.84546	−	10.4661i	0.143236	−	0.812330i
$167$	12.7050	−	4.62424i	0.983143	−	0.357835i	0.200082	−	0.979779i	$-0.435879\pi$
$167$	12.7050	−	4.62424i	0.983143	−	0.357835i	0.783061	+	0.621944i	$0.213657\pi$
$168$	1.15268	+	1.15710i	0.0889309	+	0.0892722i
$169$	0.173648	+	0.984808i	0.0133576	+	0.0757544i
$170$	2.37397	+	4.11184i	0.182075	+	0.315363i
$171$	8.58701	+	10.3136i	0.656665	+	0.788700i
$172$	−3.78388	+	6.55387i	−0.288518	+	0.499728i
$173$	14.3388	+	5.21891i	1.09016	+	0.396786i	0.823680	−	0.567054i	$-0.191917\pi$
$173$	14.3388	+	5.21891i	1.09016	+	0.396786i	0.266480	+	0.963840i	$0.414139\pi$
$174$	−8.58841	−	0.767967i	−0.651085	−	0.0582194i
$175$	−2.80546	−	2.35406i	−0.212073	−	0.177950i
$176$	4.62644	+	3.88204i	0.348731	+	0.292620i
$177$	5.18437	+	11.1738i	0.389681	+	0.839871i
$178$	14.7286	+	5.36076i	1.10395	+	0.401806i
$179$	8.06946	−	13.9767i	0.603139	−	1.04467i	−0.389203	−	0.921152i	$-0.627250\pi$
$179$	8.06946	−	13.9767i	0.603139	−	1.04467i	0.992343	−	0.123516i	$-0.0394171\pi$
$180$	1.07263	+	2.98253i	0.0799492	+	0.222305i
$181$	−1.26590	−	2.19260i	−0.0940935	−	0.162975i	0.815136	−	0.579269i	$-0.196662\pi$
$181$	−1.26590	−	2.19260i	−0.0940935	−	0.162975i	−0.909230	+	0.416294i	$0.863329\pi$
$182$	−0.163744	−	0.928638i	−0.0121375	−	0.0688353i
$183$	6.48355	−	1.72396i	0.479278	−	0.127439i
$184$	3.82395	−	1.39180i	0.281905	−	0.102605i
$185$	−0.0402484	+	0.228260i	−0.00295912	+	0.0167820i
$186$	−7.32925	+	5.11110i	−0.537407	+	0.374764i
$187$	−20.7910	+	17.4458i	−1.52039	+	1.27576i
$188$	−10.8166			−0.788880
$189$	−4.45254	+	2.04519i	−0.323875	+	0.148766i
$190$	4.72628			0.342880
$191$	18.2839	−	15.3420i	1.32298	−	1.11011i	0.337312	−	0.941393i	$-0.390482\pi$
$191$	18.2839	−	15.3420i	1.32298	−	1.11011i	0.985665	−	0.168717i	$-0.0539622\pi$
$192$	1.56837	+	0.735002i	0.113187	+	0.0530442i
$193$	3.07617	−	17.4459i	0.221428	−	1.25578i	−0.647970	−	0.761666i	$-0.724382\pi$
$193$	3.07617	−	17.4459i	0.221428	−	1.25578i	0.869397	−	0.494114i	$-0.164507\pi$
$194$	16.1566	−	5.88052i	1.15998	−	0.422197i
$195$	0.477007	−	1.76667i	0.0341592	−	0.126514i
$196$	−1.06113	−	6.01798i	−0.0757952	−	0.429856i
$197$	6.00516	+	10.4012i	0.427850	+	0.741058i	0.996682	−	0.0813957i	$-0.0259378\pi$
$197$	6.00516	+	10.4012i	0.427850	+	0.741058i	−0.568832	+	0.822454i	$0.692604\pi$
$198$	−15.7254	+	8.99890i	−1.11755	+	0.639524i
$199$	6.05953	−	10.4954i	0.429549	−	0.744000i	−0.567285	−	0.823522i	$-0.692006\pi$
$199$	6.05953	−	10.4954i	0.429549	−	0.744000i	0.996833	+	0.0795220i	$0.0253394\pi$
$200$	−3.64956	−	1.32833i	−0.258063	−	0.0939271i
$201$	1.26848	−	1.80422i	0.0894720	−	0.127260i
$202$	−0.862046	−	0.723343i	−0.0606534	−	0.0508942i
$203$	−3.59609	−	3.01748i	−0.252396	−	0.211785i
$204$	−4.47679	+	6.36753i	−0.313438	+	0.445816i
$205$	−10.1051	−	3.67796i	−0.705772	−	0.256880i
$206$	−3.68699	+	6.38605i	−0.256885	+	0.444937i
$207$	−0.0467663	+	12.2080i	−0.00325048	+	0.848515i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	4.69145	+	26.6065i	0.324514	+	1.84041i
$210$	−0.449801	+	1.66591i	−0.0310392	+	0.114959i
$211$	5.99532	−	2.18212i	0.412735	−	0.150223i	−0.127303	−	0.991864i	$-0.540632\pi$
$211$	5.99532	−	2.18212i	0.412735	−	0.150223i	0.540038	+	0.841641i	$0.318410\pi$
$212$	0.743349	−	4.21574i	0.0510534	−	0.289538i
$213$	8.15670	+	3.82257i	0.558888	+	0.261918i
$214$	5.92602	−	4.97252i	0.405095	−	0.339915i
$215$	−7.99545			−0.545285
$216$	−3.69529	+	3.65306i	−0.251432	+	0.248559i
$217$	−4.86461			−0.330231
$218$	−10.5311	+	8.83661i	−0.713253	+	0.598491i
$219$	15.7019	−	10.9498i	1.06103	−	0.739920i
$220$	−1.10800	+	6.28376i	−0.0747011	+	0.423651i
$221$	4.22295	−	1.53703i	0.284066	−	0.103392i
$222$	−0.367222	+	0.0976435i	−0.0246464	+	0.00655340i
$223$	3.81831	+	21.6547i	0.255693	+	1.45011i	0.794288	+	0.607541i	$0.207844\pi$
$223$	3.81831	+	21.6547i	0.255693	+	1.45011i	−0.538595	+	0.842565i	$0.681045\pi$
$224$	0.471482	+	0.816631i	0.0315022	+	0.0545635i
$225$	7.52347	−	8.89668i	0.501564	−	0.593112i
$226$	−2.49500	+	4.32146i	−0.165965	+	0.287459i
$227$	6.71029	+	2.44235i	0.445378	+	0.162104i	0.554966	−	0.831873i	$-0.312731\pi$
$227$	6.71029	+	2.44235i	0.445378	+	0.162104i	−0.109589	+	0.993977i	$0.534953\pi$
$228$	3.26110	+	7.02857i	0.215972	+	0.465479i
$229$	5.33821	+	4.47929i	0.352759	+	0.296000i	0.801897	−	0.597463i	$-0.203824\pi$
$229$	5.33821	+	4.47929i	0.352759	+	0.296000i	−0.449138	+	0.893462i	$0.648269\pi$
$230$	3.29349	+	2.76357i	0.217166	+	0.182224i
$231$	−9.82470	−	0.878515i	−0.646417	−	0.0578020i
$232$	−4.67807	−	1.70268i	−0.307131	−	0.111786i
$233$	−5.73131	+	9.92692i	−0.375471	+	0.650334i	−0.990397	−	0.138250i	$-0.955852\pi$
$233$	−5.73131	+	9.92692i	−0.375471	+	0.650334i	0.614927	+	0.788584i	$0.289186\pi$
$234$	2.95640	−	0.509623i	0.193266	−	0.0333151i
$235$	−5.71394	−	9.89683i	−0.372736	−	0.645598i
$236$	1.23494	+	7.00370i	0.0803878	+	0.455902i
$237$	−18.7757	−	18.8478i	−1.21962	−	1.22430i
$238$	−3.98209	+	1.44936i	−0.258120	+	0.0939481i
$239$	4.17722	−	23.6902i	0.270202	−	1.53239i	−0.483600	−	0.875289i	$-0.660671\pi$
$239$	4.17722	−	23.6902i	0.270202	−	1.53239i	0.753802	−	0.657102i	$-0.228218\pi$
$240$	0.155998	+	1.82328i	0.0100696	+	0.117692i
$241$	17.3282	−	14.5401i	1.11621	−	0.936610i	0.117802	−	0.993037i	$-0.462415\pi$
$241$	17.3282	−	14.5401i	1.11621	−	0.936610i	0.998407	+	0.0564267i	$0.0179707\pi$
$242$	−25.4741			−1.63754
$243$	−6.45236	−	14.1904i	−0.413919	−	0.910314i
$244$	3.87335			0.247966
$245$	4.94571	−	4.14995i	0.315970	−	0.265130i
$246$	−1.50287	−	17.5653i	−0.0958196	−	1.11993i
$247$	0.776809	−	4.40550i	0.0494272	−	0.280315i
$248$	−4.84774	+	1.76443i	−0.307831	+	0.112042i
$249$	12.9911	+	13.0410i	0.823280	+	0.826440i
$250$	−1.62983	−	9.24325i	−0.103080	−	0.584594i
$251$	10.0545	+	17.4149i	0.634634	+	1.09922i	0.986593	+	0.163203i	$0.0521824\pi$
$251$	10.0545	+	17.4149i	0.634634	+	1.09922i	−0.351959	+	0.936016i	$0.614484\pi$
$252$	−2.78778	+	0.480556i	−0.175613	+	0.0302722i
$253$	−12.2882	+	21.2838i	−0.772554	+	1.33810i
$254$	6.81640	+	2.48097i	0.427699	+	0.155670i
$255$	−8.19099	−	0.732431i	−0.512940	−	0.0458666i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−16.3206	−	13.6946i	−1.01805	−	0.854247i	−0.0286701	−	0.999589i	$-0.509127\pi$
$257$	−16.3206	−	13.6946i	−1.01805	−	0.854247i	−0.989381	+	0.145342i	$0.953572\pi$
$258$	−5.51681	−	11.8902i	−0.343461	−	0.740254i
$259$	−0.194394	−	0.0707538i	−0.0120791	−	0.00439643i
$260$	0.528257	−	0.914969i	0.0327611	−	0.0567439i
$261$	9.64373	−	11.4039i	0.596932	−	0.705886i
$262$	4.05905	+	7.03049i	0.250769	+	0.434345i
$263$	−0.281406	−	1.59593i	−0.0173522	−	0.0984095i	0.974902	−	0.222636i	$-0.0714661\pi$
$263$	−0.281406	−	1.59593i	−0.0173522	−	0.0984095i	−0.992254	+	0.124227i	$0.960355\pi$
$264$	−10.1093	+	2.68802i	−0.622181	+	0.165436i
$265$	4.24995	−	1.54686i	0.261072	−	0.0950226i
$266$	−0.732503	+	4.15423i	−0.0449126	+	0.254712i
$267$	−22.2680	+	15.5287i	−1.36278	+	0.950343i
$268$	0.975443	−	0.818494i	0.0595846	−	0.0499975i
$269$	−14.0341			−0.855674			−0.427837	−	0.903856i	$-0.640724\pi$
$269$	−14.0341			−0.855674			−0.427837	+	0.903856i	$0.640724\pi$
$270$	−5.29450	−	1.45131i	−0.322213	−	0.0883242i
$271$	−7.49080			−0.455034			−0.227517	−	0.973774i	$-0.573061\pi$
$271$	−7.49080			−0.455034			−0.227517	+	0.973774i	$0.573061\pi$
$272$	−3.44258	+	2.88866i	−0.208737	+	0.175151i
$273$	1.47891	+	0.693080i	0.0895079	+	0.0419471i
$274$	−1.48490	+	8.42129i	−0.0897061	+	0.508749i
$275$	22.0411	−	8.02229i	1.32913	−	0.483762i
$276$	−1.83728	+	6.80467i	−0.110591	+	0.409593i
$277$	−0.642030	−	3.64113i	−0.0385758	−	0.218774i	0.959426	−	0.281961i	$-0.0909848\pi$
$277$	−0.642030	−	3.64113i	−0.0385758	−	0.218774i	−0.998002	+	0.0631865i	$0.979874\pi$
$278$	−0.424435	−	0.735143i	−0.0254559	−	0.0440909i
$279$	0.0592869	−	15.4764i	0.00354942	−	0.926550i
$280$	−0.498128	+	0.862783i	−0.0297688	+	0.0515611i
$281$	6.40992	+	2.33302i	0.382384	+	0.139176i	0.526058	−	0.850449i	$-0.323670\pi$
$281$	6.40992	+	2.33302i	0.382384	+	0.139176i	−0.143674	+	0.989625i	$0.545892\pi$
$282$	10.7753	−	15.3261i	0.641657	−	0.912655i
$283$	8.78620	+	7.37250i	0.522285	+	0.438250i	0.865428	−	0.501034i	$-0.167047\pi$
$283$	8.78620	+	7.37250i	0.522285	+	0.438250i	−0.343142	+	0.939283i	$0.611491\pi$
$284$	3.98401	+	3.34299i	0.236408	+	0.198370i
$285$	−4.70822	+	6.69670i	−0.278891	+	0.396678i
$286$	5.67516	+	2.06559i	0.335579	+	0.122141i
$287$	4.79894	−	8.31200i	0.283272	−	0.490642i
$288$	−2.60380	+	1.49004i	−0.153431	+	0.0878012i
$289$	−1.59786	−	2.76757i	−0.0939916	−	0.162798i
$290$	−0.913329	−	5.17974i	−0.0536325	−	0.304165i
$291$	−7.76272	+	28.7505i	−0.455059	+	1.68538i
$292$	10.3856	−	3.78004i	0.607770	−	0.221210i
$293$	−0.742844	+	4.21288i	−0.0433974	+	0.246119i	−0.998788	−	0.0492277i	$-0.984324\pi$
$293$	−0.742844	+	4.21288i	−0.0433974	+	0.246119i	0.955390	+	0.295347i	$0.0954351\pi$
$294$	9.58400	+	4.49146i	0.558950	+	0.261947i
$295$	−5.75579	+	4.82969i	−0.335115	+	0.281195i
$296$	−0.219383			−0.0127514
$297$	2.91467	−	31.2459i	0.169127	−	1.81307i
$298$	−21.2596			−1.23154
$299$	3.11731	−	2.61574i	0.180279	−	0.151272i
$300$	5.51773	−	3.84783i	0.318566	−	0.222155i
$301$	1.23918	−	7.02771i	0.0714249	−	0.405071i
$302$	11.2469	−	4.09354i	0.647187	−	0.235557i
$303$	1.88366	−	0.500861i	0.108214	−	0.0287737i
$304$	0.776809	+	4.40550i	0.0445530	+	0.252673i
$305$	2.04612	+	3.54399i	0.117161	+	0.202928i
$306$	−4.56251	−	12.6864i	−0.260822	−	0.725234i
$307$	12.1554	−	21.0537i	0.693744	−	1.20160i	−0.276858	−	0.960911i	$-0.589293\pi$
$307$	12.1554	−	21.0537i	0.693744	−	1.20160i	0.970602	−	0.240689i	$-0.0773734\pi$
$308$	−5.35148	−	1.94778i	−0.304929	−	0.110985i
$309$	−5.37554	−	11.5858i	−0.305804	−	0.659092i
$310$	−4.17525	−	3.50345i	−0.237138	−	0.198983i
$311$	−19.2224	−	16.1295i	−1.09000	−	0.914619i	−0.0932884	−	0.995639i	$-0.529738\pi$
$311$	−19.2224	−	16.1295i	−1.09000	−	0.914619i	−0.996712	+	0.0810198i	$0.974182\pi$
$312$	1.72517	+	0.154263i	0.0976684	+	0.00873341i
$313$	−28.6829	−	10.4397i	−1.62125	−	0.590088i	−0.637632	−	0.770341i	$-0.720086\pi$
$313$	−28.6829	−	10.4397i	−1.62125	−	0.590088i	−0.983620	+	0.180253i	$0.942308\pi$
$314$	0.315542	−	0.546536i	0.0178071	−	0.0308428i
$315$	−1.91236	−	2.29687i	−0.107749	−	0.129414i
$316$	−7.67989	−	13.3020i	−0.432028	−	0.748294i
$317$	4.41663	+	25.0480i	0.248063	+	1.40683i	0.813271	+	0.581886i	$0.197685\pi$
$317$	4.41663	+	25.0480i	0.248063	+	1.40683i	−0.565208	+	0.824949i	$0.691204\pi$
$318$	5.23281	+	5.25289i	0.293441	+	0.294568i
$319$	28.2527	−	10.2831i	1.58185	−	0.575745i
$320$	−0.183462	+	1.04046i	−0.0102558	+	0.0581637i
$321$	1.14222	+	13.3502i	0.0637528	+	0.745133i
$322$	−2.93952	+	2.46655i	−0.163813	+	0.137455i
$323$	−20.1036			−1.11859
$324$	−1.49488	−	8.87498i	−0.0830490	−	0.493055i
$325$	−3.88378			−0.215433
$326$	3.25256	−	2.72922i	0.180142	−	0.151157i
$327$	−2.02983	−	23.7244i	−0.112250	−	1.31196i
$328$	1.76746	−	10.0238i	0.0975917	−	0.553470i
$329$	9.58453	−	3.48848i	0.528412	−	0.192326i
$330$	−7.79974	−	7.82968i	−0.429362	−	0.431010i
$331$	1.58117	+	8.96727i	0.0869090	+	0.492885i	0.996928	+	0.0783196i	$0.0249555\pi$
$331$	1.58117	+	8.96727i	0.0869090	+	0.492885i	−0.910019	+	0.414566i	$0.863933\pi$
$332$	5.31380	+	9.20377i	0.291633	+	0.505122i
$333$	0.227468	−	0.617591i	0.0124651	−	0.0338438i
$334$	−6.76019	+	11.7090i	−0.369901	+	0.640688i
$335$	1.26418	+	0.460124i	0.0690696	+	0.0251393i
$336$	−1.62677	−	0.145464i	−0.0887476	−	0.00793573i
$337$	−5.63851	−	4.73127i	−0.307149	−	0.257729i	0.476163	−	0.879357i	$-0.342027\pi$
$337$	−5.63851	−	4.73127i	−0.307149	−	0.257729i	−0.783313	+	0.621628i	$0.786472\pi$
$338$	−0.766044	−	0.642788i	−0.0416673	−	0.0349630i
$339$	−3.63765	−	7.84013i	−0.197570	−	0.425818i
$340$	−4.46160	−	1.62389i	−0.241964	−	0.0880679i
$341$	15.5781	−	26.9821i	0.843604	−	1.46116i
$342$	−13.2075	−	2.38104i	−0.714179	−	0.128752i
$343$	6.18152	+	10.7067i	0.333771	+	0.578107i
$344$	−1.31413	−	7.45279i	−0.0708530	−	0.401827i
$345$	−7.19662	+	1.91356i	−0.387453	+	0.103023i
$346$	−14.3388	+	5.21891i	−0.770860	+	0.280570i
$347$	1.10453	−	6.26410i	0.0592942	−	0.336274i	−0.940701	−	0.339236i	$-0.889832\pi$
$347$	1.10453	−	6.26410i	0.0592942	−	0.336274i	0.999996	+	0.00296144i	$0.000942658\pi$
$348$	7.07274	−	4.93222i	0.379139	−	0.264395i
$349$	−1.10743	+	0.929245i	−0.0592794	+	0.0497413i	−0.671946	−	0.740600i	$-0.734541\pi$
$349$	−1.10743	+	0.929245i	−0.0592794	+	0.0497413i	0.612667	+	0.790341i	$0.290097\pi$
$350$	3.66226			0.195756
$351$	−2.22301	+	4.69662i	−0.118656	+	0.250687i
$352$	−6.03938			−0.321900
$353$	−17.9550	+	15.0661i	−0.955650	+	0.801886i	−0.980240	−	0.197812i	$-0.936616\pi$
$353$	−17.9550	+	15.0661i	−0.955650	+	0.801886i	0.0245898	+	0.999698i	$0.492172\pi$
$354$	−11.1538	−	5.22714i	−0.592818	−	0.277819i
$355$	−0.954141	+	5.41120i	−0.0506406	+	0.287197i
$356$	−14.7286	+	5.36076i	−0.780612	+	0.284120i
$357$	1.91326	−	7.08607i	0.101261	−	0.375035i
$358$	2.80249	+	15.8937i	0.148116	+	0.840010i
$359$	9.49801	+	16.4510i	0.501286	+	0.868253i	0.999999	+	0.00148539i	$0.000472815\pi$
$359$	9.49801	+	16.4510i	0.501286	+	0.868253i	−0.498713	+	0.866767i	$0.666194\pi$
$360$	−2.73881	−	1.59528i	−0.144348	−	0.0840784i
$361$	−0.505936	+	0.876308i	−0.0266282	+	0.0461214i
$362$	2.37911	+	0.865926i	0.125043	+	0.0455121i
$363$	25.3768	−	36.0945i	1.33194	−	1.89447i
$364$	0.722353	+	0.606126i	0.0378616	+	0.0317696i
$365$	8.94488	+	7.50565i	0.468196	+	0.392863i
$366$	−3.85855	+	5.48817i	−0.201689	+	0.286871i
$367$	−20.5833	−	7.49170i	−1.07444	−	0.391063i	−0.256603	−	0.966517i	$-0.582603\pi$
$367$	−20.5833	−	7.49170i	−1.07444	−	0.391063i	−0.817835	+	0.575453i	$0.804826\pi$
$368$	−2.03468	+	3.52417i	−0.106065	+	0.183710i
$369$	26.3856	+	15.3688i	1.37358	+	0.800068i
$370$	−0.115891	−	0.200728i	−0.00602487	−	0.0104354i
$371$	0.700952	+	3.97529i	0.0363916	+	0.206387i
$372$	2.32918	−	8.62648i	0.120762	−	0.447262i
$373$	−22.2096	+	8.08362i	−1.14997	+	0.418554i	−0.845503	−	0.533970i	$-0.820700\pi$
$373$	−22.2096	+	8.08362i	−1.14997	+	0.418554i	−0.304464	+	0.952524i	$0.598477\pi$
$374$	4.71295	−	26.7284i	0.243701	−	1.38209i
$375$	14.7204	+	6.89861i	0.760160	+	0.356243i
$376$	8.28598	−	6.95276i	0.427317	−	0.358561i
$377$	−4.97830			−0.256396
$378$	2.09622	−	4.42874i	0.107818	−	0.227790i
$379$	−20.2681			−1.04110			−0.520551	−	0.853831i	$-0.674273\pi$
$379$	−20.2681			−1.04110			−0.520551	+	0.853831i	$0.674273\pi$
$380$	−3.62054	+	3.03799i	−0.185730	+	0.155846i
$381$	−10.3057	+	7.18672i	−0.527975	+	0.368187i
$382$	−4.14462	+	23.5053i	−0.212057	+	1.20264i
$383$	−23.1248	+	8.41674i	−1.18162	+	0.430076i	−0.856775	−	0.515691i	$-0.827535\pi$
$383$	−23.1248	+	8.41674i	−1.18162	+	0.430076i	−0.324848	+	0.945766i	$0.605313\pi$
$384$	−1.67389	+	0.445082i	−0.0854202	+	0.0227130i
$385$	−1.04480	−	5.92536i	−0.0532480	−	0.301984i
$386$	8.85749	+	15.3416i	0.450834	+	0.780868i
$387$	22.3431	+	4.02800i	1.13576	+	0.204755i
$388$	−8.59675	+	14.8900i	−0.436434	+	0.755926i
$389$	−0.149819	−	0.0545297i	−0.00759613	−	0.00276477i	0.338219	−	0.941067i	$-0.390175\pi$
$389$	−0.149819	−	0.0545297i	−0.00759613	−	0.00276477i	−0.345815	+	0.938303i	$0.612398\pi$
$390$	0.770187	+	1.65996i	0.0389999	+	0.0840556i
$391$	−14.0091	−	11.7550i	−0.708471	−	0.594477i
$392$	4.68116	+	3.92796i	0.236434	+	0.198392i
$393$	−14.0051	−	1.25232i	−0.706464	−	0.0631713i
$394$	−11.2860	−	4.10777i	−0.568581	−	0.206947i
$395$	8.11392	−	14.0537i	0.408256	−	0.707119i
$396$	6.26195	−	17.0016i	0.314675	−	0.854364i
$397$	−8.17891	−	14.1663i	−0.410488	−	0.710986i	0.584455	−	0.811426i	$-0.301308\pi$
$397$	−8.17891	−	14.1663i	−0.410488	−	0.710986i	−0.994943	+	0.100440i	$0.967975\pi$
$398$	2.10445	+	11.9349i	0.105487	+	0.598244i
$399$	−5.15646	−	5.17625i	−0.258146	−	0.259136i
$400$	3.64956	−	1.32833i	0.182478	−	0.0664165i
$401$	5.35715	−	30.3819i	0.267524	−	1.51720i	−0.494228	−	0.869332i	$-0.664549\pi$
$401$	5.35715	−	30.3819i	0.267524	−	1.51720i	0.761752	−	0.647869i	$-0.224340\pi$
$402$	0.188014	+	2.19748i	0.00937728	+	0.109600i
$403$	−3.95191	+	3.31605i	−0.196859	+	0.165184i
$404$	1.12532			0.0559868
$405$	7.33065	−	6.05605i	0.364263	−	0.300927i
$406$	4.69436			0.232977
$407$	1.01496	−	0.851653i	0.0503097	−	0.0422149i
$408$	−0.663547	−	7.75544i	−0.0328505	−	0.383951i
$409$	5.10149	−	28.9320i	0.252252	−	1.43059i	−0.550776	−	0.834653i	$-0.685668\pi$
$409$	5.10149	−	28.9320i	0.252252	−	1.43059i	0.803029	−	0.595940i	$-0.203221\pi$
$410$	10.1051	−	3.67796i	0.499056	−	0.181641i
$411$	−10.4530	−	10.4931i	−0.515607	−	0.517586i
$412$	−1.28048	−	7.26195i	−0.0630846	−	0.357771i
$413$	−3.35306	−	5.80767i	−0.164993	−	0.285777i
$414$	−7.81133	−	9.38194i	−0.383906	−	0.461097i
$415$	−5.61411	+	9.72392i	−0.275586	+	0.477328i
$416$	0.939693	+	0.342020i	0.0460722	+	0.0167689i
$417$	1.46444	+	0.130949i	0.0717141	+	0.00641260i
$418$	−20.6962	−	17.3662i	−1.01228	−	0.849407i
$419$	8.94566	+	7.50630i	0.437024	+	0.366707i	0.834594	−	0.550865i	$-0.185702\pi$
$419$	8.94566	+	7.50630i	0.437024	+	0.366707i	−0.397570	+	0.917572i	$0.630147\pi$
$420$	−0.726259	−	1.56529i	−0.0354378	−	0.0763782i
$421$	−23.4373	−	8.53048i	−1.14226	−	0.415750i	−0.299534	−	0.954086i	$-0.596831\pi$
$421$	−23.4373	−	8.53048i	−1.14226	−	0.415750i	−0.842731	+	0.538335i	$0.819053\pi$
$422$	−3.19005	+	5.52532i	−0.155289	+	0.268968i
$423$	10.9816	+	30.5351i	0.533942	+	1.48467i
$424$	2.14039	+	3.70726i	0.103946	+	0.180041i
$425$	3.03078	+	17.1884i	0.147014	+	0.833760i
$426$	−8.70549	+	2.31477i	−0.421783	+	0.112151i
$427$	−3.43216	+	1.24920i	−0.166094	+	0.0604532i
$428$	−1.34332	+	7.61835i	−0.0649318	+	0.368247i
$429$	−8.58023	+	5.98348i	−0.414257	+	0.288885i
$430$	6.12487	−	5.13938i	0.295367	−	0.247843i
$431$	−6.19927			−0.298608			−0.149304	−	0.988791i	$-0.547703\pi$
$431$	−6.19927			−0.298608			−0.149304	+	0.988791i	$0.547703\pi$
$432$	0.482611	−	5.17369i	0.0232196	−	0.248919i
$433$	11.1272			0.534740			0.267370	−	0.963594i	$-0.413845\pi$
$433$	11.1272			0.534740			0.267370	+	0.963594i	$0.413845\pi$
$434$	3.72651	−	3.12691i	0.178878	−	0.150097i
$435$	8.24906	+	3.86585i	0.395512	+	0.185353i
$436$	2.38720	−	13.5385i	0.114326	−	0.648375i
$437$	−17.1063	+	6.22619i	−0.818306	+	0.297839i
$438$	−4.98993	+	18.4810i	−0.238428	+	0.883057i
$439$	−1.50998	−	8.56355i	−0.0720676	−	0.408716i	−0.999405	−	0.0344896i	$-0.989019\pi$
$439$	−1.50998	−	8.56355i	−0.0720676	−	0.408716i	0.927337	−	0.374226i	$-0.122092\pi$
$440$	−3.19035	−	5.52585i	−0.152094	−	0.263434i
$441$	−15.9114	+	9.10534i	−0.757684	+	0.433588i
$442$	−2.24698	+	3.89189i	−0.106878	+	0.185118i
$443$	8.45904	+	3.07884i	0.401901	+	0.146280i	0.535059	−	0.844815i	$-0.320289\pi$
$443$	8.45904	+	3.07884i	0.401901	+	0.146280i	−0.133158	+	0.991095i	$0.542512\pi$
$444$	0.218545	−	0.310845i	0.0103717	−	0.0147521i
$445$	−12.6854	−	10.6443i	−0.601346	−	0.504589i
$446$	−16.8444	−	14.1341i	−0.797604	−	0.669269i
$447$	21.1784	−	30.1229i	1.00170	−	1.42477i
$448$	−0.886097	−	0.322513i	−0.0418641	−	0.0152373i
$449$	1.48396	−	2.57029i	0.0700324	−	0.121300i	−0.828883	−	0.559422i	$-0.811023\pi$
$449$	1.48396	−	2.57029i	0.0700324	−	0.121300i	0.898915	+	0.438123i	$0.144356\pi$
$450$	−0.0446334	+	11.6512i	−0.00210404	+	0.549245i
$451$	30.7356	+	53.2357i	1.44728	+	2.50677i
$452$	−0.866504	−	4.91419i	−0.0407569	−	0.231144i
$453$	−5.40377	+	20.0137i	−0.253891	+	0.940328i
$454$	−6.71029	+	2.44235i	−0.314930	+	0.114625i
$455$	−0.172998	+	0.981120i	−0.00811027	+	0.0459956i
$456$	−7.01603	−	3.28800i	−0.328556	−	0.153975i
$457$	9.94731	−	8.34678i	0.465315	−	0.390446i	−0.379767	−	0.925082i	$-0.623996\pi$
$457$	9.94731	−	8.34678i	0.465315	−	0.390446i	0.845082	+	0.534636i	$0.179551\pi$
$458$	−6.96854			−0.325618
$459$	22.5205	+	6.17327i	1.05117	+	0.288144i
$460$	−4.29934			−0.200458
$461$	−7.84898	+	6.58608i	−0.365563	+	0.306744i	−0.807004	−	0.590547i	$-0.798912\pi$
$461$	−7.84898	+	6.58608i	−0.365563	+	0.306744i	0.441440	+	0.897291i	$0.354468\pi$
$462$	8.09085	−	5.64221i	0.376420	−	0.262499i
$463$	0.0948232	−	0.537769i	0.00440681	−	0.0249923i	−0.982525	−	0.186130i	$-0.940405\pi$
$463$	0.0948232	−	0.537769i	0.00440681	−	0.0249923i	0.986932	+	0.161138i	$0.0515164\pi$
$464$	4.67807	−	1.70268i	0.217174	−	0.0790449i
$465$	9.12337	−	2.42588i	0.423086	−	0.112497i
$466$	−1.99046	−	11.2885i	−0.0922065	−	0.522929i
$467$	−18.2591	−	31.6258i	−0.844932	−	1.46347i	−0.885680	−	0.464296i	$-0.846307\pi$
$467$	−18.2591	−	31.6258i	−0.844932	−	1.46347i	0.0407478	−	0.999169i	$-0.487026\pi$
$468$	−1.93715	+	2.29073i	−0.0895449	+	0.105889i
$469$	−0.600362	+	1.03986i	−0.0277221	+	0.0480161i
$470$	10.7387	+	3.90856i	0.495339	+	0.180289i
$471$	0.460054	+	0.991542i	0.0211981	+	0.0456878i
$472$	−5.44791	−	4.57134i	−0.250760	−	0.210413i
$473$	35.0118	+	29.3784i	1.60984	+	1.35082i
$474$	26.4982	+	2.36944i	1.21710	+	0.108832i
$475$	16.3262	+	5.94223i	0.749095	+	0.272648i
$476$	2.11882	−	3.66991i	0.0971161	−	0.168210i
$477$	−12.6557	+	2.18158i	−0.579464	+	0.0998878i
$478$	12.0278	+	20.8328i	0.550140	+	0.952870i
$479$	0.0727771	+	0.412739i	0.00332527	+	0.0188585i	0.986425	−	0.164211i	$-0.0525078\pi$
$479$	0.0727771	+	0.412739i	0.00332527	+	0.0188585i	−0.983100	+	0.183069i	$0.941397\pi$
$480$	−1.29148	−	1.29644i	−0.0589477	−	0.0591740i
$481$	−0.206152	+	0.0750334i	−0.00939974	+	0.00342123i
$482$	−3.92799	+	22.2767i	−0.178915	+	1.01468i
$483$	−0.566584	−	6.62215i	−0.0257805	−	0.301318i
$484$	19.5143	−	16.3745i	0.887015	−	0.744294i
$485$	−18.1652			−0.824839
$486$	14.0642	+	6.72296i	0.637965	+	0.304960i
$487$	−42.0986			−1.90767			−0.953834	−	0.300334i	$-0.902902\pi$
$487$	−42.0986			−1.90767			−0.953834	+	0.300334i	$0.902902\pi$
$488$	−2.96716	+	2.48974i	−0.134317	+	0.112705i
$489$	0.626921	+	7.32736i	0.0283504	+	0.331355i
$490$	−1.12110	+	6.35809i	−0.0506462	+	0.287229i
$491$	−24.4011	+	8.88127i	−1.10121	+	0.400806i	−0.827761	−	0.561081i	$-0.810385\pi$
$491$	−24.4011	+	8.88127i	−1.10121	+	0.400806i	−0.273445	+	0.961888i	$0.588163\pi$
$492$	12.4420	+	12.4898i	0.560931	+	0.563084i
$493$	3.88491	+	22.0324i	0.174968	+	0.992291i
$494$	2.23673	+	3.87413i	0.100635	+	0.174305i
$495$	18.8639	−	3.25175i	0.847868	−	0.146155i
$496$	2.57943	−	4.46770i	0.115820	−	0.200606i
$497$	−4.60838	−	1.67731i	−0.206714	−	0.0752377i
$498$	−18.3344	−	1.63944i	−0.821583	−	0.0734652i
$499$	23.5418	+	19.7539i	1.05388	+	0.884306i	0.993496	−	0.113869i	$-0.0363245\pi$
$499$	23.5418	+	19.7539i	1.05388	+	0.884306i	0.0603793	+	0.998176i	$0.480769\pi$
$500$	7.18997	+	6.03310i	0.321545	+	0.269809i
$501$	−9.85620	−	21.2428i	−0.440343	−	0.949060i
$502$	−18.8963	−	6.87768i	−0.843382	−	0.306966i
$503$	−0.553021	+	0.957860i	−0.0246580	+	0.0427089i	−0.878091	−	0.478494i	$-0.841183\pi$
$503$	−0.553021	+	0.957860i	−0.0246580	+	0.0427089i	0.853433	+	0.521202i	$0.174516\pi$
$504$	1.82667	−	2.16008i	0.0813661	−	0.0962174i
$505$	0.594460	+	1.02963i	0.0264531	+	0.0458181i
$506$	−4.26766	−	24.2031i	−0.189720	−	1.07596i
$507$	1.67389	−	0.445082i	0.0743400	−	0.0197668i
$508$	−6.81640	+	2.48097i	−0.302429	+	0.110075i
$509$	−7.56918	+	42.9270i	−0.335498	+	1.90270i	0.0867623	+	0.996229i	$0.472348\pi$
$509$	−7.56918	+	42.9270i	−0.335498	+	1.90270i	−0.422260	+	0.906475i	$0.638763\pi$
$510$	6.74546	−	4.70399i	0.298694	−	0.208296i
$511$	−7.98352	+	6.69897i	−0.353170	+	0.296345i
$512$	−1.00000			−0.0441942
$513$	16.5307	−	16.3418i	0.729849	−	0.721510i
$514$	21.3050			0.939725
$515$	5.96803	−	5.00778i	0.262983	−	0.220669i
$516$	11.8690	+	5.56232i	0.522504	+	0.244867i
$517$	−11.3436	+	64.3330i	−0.498893	+	2.82936i
$518$	0.194394	−	0.0707538i	0.00854120	−	0.00310874i
$519$	6.88933	−	25.5158i	0.302408	−	1.12002i
$520$	0.183462	+	1.04046i	0.00804533	+	0.0456274i
$521$	13.0657	+	22.6304i	0.572419	+	0.991458i	0.996317	+	0.0857482i	$0.0273281\pi$
$521$	13.0657	+	22.6304i	0.572419	+	0.991458i	−0.423898	+	0.905710i	$0.639339\pi$
$522$	−0.0572120	+	14.9348i	−0.00250410	+	0.653678i
$523$	8.72776	−	15.1169i	0.381638	−	0.661017i	−0.609658	−	0.792664i	$-0.708693\pi$
$523$	8.72776	−	15.1169i	0.381638	−	0.661017i	0.991297	+	0.131647i	$0.0420266\pi$
$524$	−7.62853	−	2.77656i	−0.333254	−	0.121294i
$525$	−3.64827	+	5.18909i	−0.159224	+	0.226470i
$526$	1.24142	+	1.04167i	0.0541283	+	0.0454190i
$527$	17.7597	+	14.9022i	0.773627	+	0.649150i
$528$	6.01631	−	8.55725i	0.261826	−	0.372406i
$529$	6.05187	+	2.20270i	0.263125	+	0.0957696i
$530$	−2.26135	+	3.91678i	−0.0982268	+	0.170134i
$531$	18.5176	−	10.5967i	0.803594	−	0.459860i
$532$	−2.10916	−	3.65317i	−0.0914436	−	0.158385i
$533$	−1.76746	−	10.0238i	−0.0765572	−	0.434178i
$534$	7.07659	−	26.2093i	0.306234	−	1.13419i
$535$	−7.68017	+	2.79535i	−0.332043	+	0.120854i
$536$	−0.221115	+	1.25401i	−0.00955071	+	0.0541648i
$537$	−25.3117	−	11.8621i	−1.09228	−	0.511889i
$538$	10.7507	−	9.02094i	0.463497	−	0.388920i
$539$	−36.9056			−1.58964
$540$	4.98871	−	2.29147i	0.214680	−	0.0986090i
$541$	−30.3642			−1.30546			−0.652729	−	0.757591i	$-0.726376\pi$
$541$	−30.3642			−1.30546			−0.652729	+	0.757591i	$0.726376\pi$
$542$	5.73829	−	4.81500i	0.246481	−	0.206822i
$543$	−3.59696	+	2.50836i	−0.154360	+	0.107644i
$544$	0.780369	−	4.42569i	0.0334580	−	0.189750i
$545$	13.6483	−	4.96758i	0.584630	−	0.212788i
$546$	−1.57842	+	0.419697i	−0.0675500	+	0.0179614i
$547$	2.91602	+	16.5376i	0.124680	+	0.707095i	0.981497	+	0.191475i	$0.0613272\pi$
$547$	2.91602	+	16.5376i	0.124680	+	0.707095i	−0.856817	+	0.515620i	$0.827562\pi$
$548$	−4.27560	−	7.40556i	−0.182645	−	0.316350i
$549$	−3.93243	−	10.9344i	−0.167832	−	0.466669i
$550$	−11.7278	+	20.3132i	−0.500075	+	0.866156i
$551$	20.9272	+	7.61688i	0.891528	+	0.324490i
$552$	−2.96652	−	6.39367i	−0.126263	−	0.272132i
$553$	11.0952	+	9.30996i	0.471815	+	0.395900i
$554$	2.83230	+	2.37658i	0.120333	+	0.100971i
$555$	0.399861	+	0.0357552i	0.0169732	+	0.00151772i
$556$	0.797677	+	0.290331i	0.0338290	+	0.0123128i
$557$	5.48725	−	9.50420i	0.232502	−	0.402706i	−0.726042	−	0.687651i	$-0.758642\pi$
$557$	5.48725	−	9.50420i	0.232502	−	0.402706i	0.958544	+	0.284945i	$0.0919753\pi$
$558$	9.90265	+	11.8938i	0.419213	+	0.503503i
$559$	−3.78388	−	6.55387i	−0.160041	−	0.277199i
$560$	−0.172998	−	0.981120i	−0.00731050	−	0.0414599i
$561$	33.1768	+	33.3041i	1.40073	+	1.40610i
$562$	−6.40992	+	2.33302i	−0.270386	+	0.0984125i
$563$	0.484875	−	2.74986i	0.0204351	−	0.115893i	−0.972884	−	0.231294i	$-0.925704\pi$
$563$	0.484875	−	2.74986i	0.0204351	−	0.115893i	0.993319	+	0.115401i	$0.0368152\pi$
$564$	1.59710	+	18.6667i	0.0672500	+	0.786008i
$565$	4.03859	−	3.38878i	0.169905	−	0.142567i
$566$	−11.4696			−0.482102
$567$	4.18691	+	7.38197i	0.175833	+	0.310014i
$568$	−5.20076			−0.218219
$569$	−9.30978	+	7.81183i	−0.390286	+	0.327489i	−0.816725	−	0.577028i	$-0.804213\pi$
$569$	−9.30978	+	7.81183i	−0.390286	+	0.327489i	0.426438	+	0.904517i	$0.359768\pi$
$570$	−0.697849	−	8.15636i	−0.0292297	−	0.341632i
$571$	−0.913391	+	5.18010i	−0.0382242	+	0.216780i	−0.997937	−	0.0642030i	$-0.979549\pi$
$571$	−0.913391	+	5.18010i	−0.0382242	+	0.216780i	0.959713	+	0.280983i	$0.0906606\pi$
$572$	−5.67516	+	2.06559i	−0.237291	+	0.0863667i
$573$	−29.1761	−	29.2881i	−1.21885	−	1.22353i
$574$	1.66665	+	9.45206i	0.0695647	+	0.394521i
$575$	7.90225	+	13.6871i	0.329547	+	0.570792i
$576$	1.03685	−	2.81513i	0.0432022	−	0.117297i
$577$	−3.27442	+	5.67147i	−0.136316	+	0.236106i	−0.926099	−	0.377280i	$-0.876860\pi$
$577$	−3.27442	+	5.67147i	−0.136316	+	0.236106i	0.789783	+	0.613386i	$0.210193\pi$
$578$	3.00299	+	1.09300i	0.124908	+	0.0454628i
$579$	−30.5613	−	2.73276i	−1.27008	−	0.113570i
$580$	4.02913	+	3.38084i	0.167300	+	0.140382i
$581$	−7.67687	−	6.44166i	−0.318490	−	0.267245i
$582$	−12.5339	−	27.0139i	−0.519545	−	1.11976i
$583$	−24.2941	−	8.84233i	−1.00616	−	0.366212i
$584$	−5.52605	+	9.57140i	−0.228670	+	0.396068i
$585$	−3.11926	−	0.562339i	−0.128966	−	0.0232498i
$586$	−2.13893	−	3.70474i	−0.0883585	−	0.153041i
$587$	3.83698	+	21.7606i	0.158369	+	0.898157i	0.955640	+	0.294536i	$0.0951650\pi$
$587$	3.83698	+	21.7606i	0.158369	+	0.898157i	−0.797271	+	0.603621i	$0.793724\pi$
$588$	−10.2288	+	2.71982i	−0.421830	+	0.112163i
$589$	21.6862	−	7.89312i	0.893563	−	0.325230i
$590$	1.30473	−	7.39951i	0.0537150	−	0.304633i
$591$	17.0632	−	11.8992i	0.701887	−	0.489466i
$592$	0.168057	−	0.141017i	0.00690710	−	0.00579575i
$593$	11.6498			0.478399			0.239200	−	0.970970i	$-0.423115\pi$
$593$	11.6498			0.478399			0.239200	+	0.970970i	$0.423115\pi$
$594$	17.8517	+	25.8093i	0.732465	+	1.05897i
$595$	4.47714			0.183545
$596$	16.2858	−	13.6654i	0.667093	−	0.559758i
$597$	−19.0071	−	8.90753i	−0.777909	−	0.364561i
$598$	−0.706638	+	4.00754i	−0.0288966	+	0.163881i
$599$	−40.7962	+	14.8486i	−1.66689	+	0.606697i	−0.991422	−	0.130697i	$-0.958278\pi$
$599$	−40.7962	+	14.8486i	−1.66689	+	0.606697i	−0.675463	+	0.737394i	$0.736056\pi$
$600$	−1.75349	+	6.49434i	−0.0715860	+	0.265130i
$601$	0.843575	+	4.78415i	0.0344101	+	0.195150i	0.997167	−	0.0752189i	$-0.0239656\pi$
$601$	0.843575	+	4.78415i	0.0344101	+	0.195150i	−0.962757	+	0.270369i	$0.912854\pi$
$602$	3.56806	+	6.18007i	0.145423	+	0.251881i
$603$	−3.30092	−	1.92268i	−0.134424	−	0.0782978i
$604$	−5.98436	+	10.3652i	−0.243500	+	0.421755i
$605$	25.2907	+	9.20507i	1.02821	+	0.374239i
$606$	−1.12102	+	1.59448i	−0.0455384	+	0.0647712i
$607$	29.9042	+	25.0926i	1.21377	+	1.01848i	0.999127	+	0.0417863i	$0.0133049\pi$
$607$	29.9042	+	25.0926i	1.21377	+	1.01848i	0.214648	+	0.976691i	$0.431140\pi$
$608$	−3.42687	−	2.87549i	−0.138978	−	0.116616i
$609$	−4.67643	+	6.65148i	−0.189498	+	0.269531i
$610$	−3.84545	−	1.39963i	−0.155698	−	0.0566694i
$611$	5.40829	−	9.36743i	0.218796	−	0.378966i
$612$	11.6498	+	6.78562i	0.470913	+	0.274293i
$613$	−18.1246	−	31.3927i	−0.732045	−	1.26794i	−0.956008	−	0.293341i	$-0.905233\pi$
$613$	−18.1246	−	31.3927i	−0.732045	−	1.26794i	0.223963	−	0.974598i	$-0.428101\pi$
$614$	4.22152	+	23.9414i	0.170367	+	0.966197i
$615$	−4.85517	+	17.9819i	−0.195779	+	0.725101i
$616$	5.35148	−	1.94778i	0.215617	−	0.0784782i
$617$	−4.68550	+	26.5728i	−0.188631	+	1.06978i	0.732569	+	0.680693i	$0.238321\pi$
$617$	−4.68550	+	26.5728i	−0.188631	+	1.06978i	−0.921200	+	0.389088i	$0.872790\pi$
$618$	11.5651	+	5.41989i	0.465216	+	0.218020i
$619$	8.61308	−	7.22723i	0.346189	−	0.290487i	−0.453069	−	0.891476i	$-0.649671\pi$
$619$	8.61308	−	7.22723i	0.346189	−	0.290487i	0.799257	+	0.600989i	$0.205226\pi$
$620$	5.45040			0.218893
$621$	21.0748	−	1.72184i	0.845703	−	0.0690951i
$622$	25.0930			1.00614
$623$	11.3220	−	9.50030i	0.453607	−	0.380621i
$624$	−1.42071	+	0.990744i	−0.0568740	+	0.0396615i
$625$	1.65011	−	9.35824i	0.0660044	−	0.374329i
$626$	28.6829	−	10.4397i	1.14640	−	0.417255i
$627$	45.2234	−	12.0248i	1.80605	−	0.480223i
$628$	0.109587	+	0.621497i	0.00437299	+	0.0248004i
$629$	0.492949	+	0.853813i	0.0196552	+	0.0340438i
$630$	2.94135	+	0.530265i	0.117186	+	0.0211263i
$631$	−9.21442	+	15.9598i	−0.366820	+	0.635352i	−0.989067	−	0.147470i	$-0.952887\pi$
$631$	−9.21442	+	15.9598i	−0.366820	+	0.635352i	0.622246	+	0.782822i	$0.286220\pi$
$632$	14.4335	+	5.25336i	0.574133	+	0.208967i
$633$	−4.65101	−	10.0242i	−0.184861	−	0.398427i
$634$	−19.4839	−	16.3489i	−0.773803	−	0.649298i
$635$	−5.87082	−	4.92620i	−0.232976	−	0.195490i
$636$	−7.38506	−	0.660365i	−0.292837	−	0.0261852i
$637$	5.74229	+	2.09002i	0.227518	+	0.0828097i
$638$	−15.0329	+	26.0378i	−0.595160	+	1.03085i
$639$	5.39242	−	14.6408i	0.213321	−	0.579181i
$640$	−0.528257	−	0.914969i	−0.0208812	−	0.0361673i
$641$	6.65029	+	37.7157i	0.262671	+	1.48968i	0.775587	+	0.631241i	$0.217454\pi$
$641$	6.65029	+	37.7157i	0.262671	+	1.48968i	−0.512916	+	0.858439i	$0.671435\pi$
$642$	−9.45631	−	9.49260i	−0.373211	−	0.374643i
$643$	12.7143	−	4.62764i	0.501404	−	0.182496i	−0.0789211	−	0.996881i	$-0.525148\pi$
$643$	12.7143	−	4.62764i	0.501404	−	0.182496i	0.580326	+	0.814385i	$0.302925\pi$
$644$	0.666334	−	3.77897i	0.0262572	−	0.148912i
$645$	1.18055	+	13.7981i	0.0464842	+	0.543300i
$646$	15.4002	−	12.9223i	0.605914	−	0.508422i
$647$	22.4717			0.883455			0.441727	−	0.897149i	$-0.354366\pi$
$647$	22.4717			0.883455			0.441727	+	0.897149i	$0.354366\pi$
$648$	6.84988	+	5.83774i	0.269089	+	0.229328i
$649$	42.9505			1.68596
$650$	2.97515	−	2.49644i	0.116695	−	0.0979186i
$651$	0.718275	+	8.39509i	0.0281514	+	0.329029i
$652$	−0.737294	+	4.18140i	−0.0288747	+	0.163756i
$653$	21.8773	−	7.96270i	0.856126	−	0.311604i	0.123591	−	0.992333i	$-0.460559\pi$
$653$	21.8773	−	7.96270i	0.856126	−	0.311604i	0.732535	+	0.680729i	$0.238337\pi$
$654$	16.8047	+	16.8692i	0.657115	+	0.659637i
$655$	−1.48936	−	8.44660i	−0.0581942	−	0.330036i
$656$	5.08920	+	8.81476i	0.198700	+	0.344158i
$657$	−21.2150	−	25.4807i	−0.827677	−	0.994096i
$658$	−5.09982	+	8.83315i	−0.198812	+	0.344352i
$659$	−14.0119	−	5.09993i	−0.545828	−	0.198665i	0.0543641	−	0.998521i	$-0.482687\pi$
$659$	−14.0119	−	5.09993i	−0.545828	−	0.198665i	−0.600192	+	0.799856i	$0.704909\pi$
$660$	11.0078	+	0.984304i	0.428477	+	0.0383140i
$661$	−31.8036	−	26.6864i	−1.23702	−	1.03798i	−0.997751	−	0.0670251i	$-0.978649\pi$
$661$	−31.8036	−	26.6864i	−1.23702	−	1.03798i	−0.239265	−	0.970954i	$-0.576906\pi$
$662$	−6.97529	−	5.85297i	−0.271103	−	0.227482i
$663$	−3.27605	−	7.06078i	−0.127231	−	0.274218i
$664$	−9.98667	−	3.63485i	−0.387558	−	0.141060i
$665$	2.22836	−	3.85963i	0.0864120	−	0.149670i
$666$	0.222729	+	0.619315i	0.00863058	+	0.0239980i
$667$	10.1293	+	17.5444i	0.392207	+	0.679322i
$668$	−2.34779	−	13.3150i	−0.0908387	−	0.515172i
$669$	36.8067	−	9.78681i	1.42303	−	0.378380i
$670$	−1.26418	+	0.460124i	−0.0488396	+	0.0177761i
$671$	4.06209	−	23.0372i	0.156815	−	0.889343i
$672$	1.33968	−	0.934236i	0.0516793	−	0.0360389i
$673$	8.97139	−	7.52789i	0.345822	−	0.290179i	−0.453288	−	0.891364i	$-0.649749\pi$
$673$	8.97139	−	7.52789i	0.345822	−	0.290179i	0.799110	+	0.601185i	$0.205305\pi$
$674$	7.36056			0.283518
$675$	−16.4643	−	11.6700i	−0.633710	−	0.449177i
$676$	1.00000			0.0384615
$677$	5.43432	−	4.55994i	0.208858	−	0.175253i	−0.532358	−	0.846519i	$-0.678694\pi$
$677$	5.43432	−	4.55994i	0.208858	−	0.175253i	0.741216	+	0.671267i	$0.234249\pi$
$678$	7.82614	+	3.66766i	0.300561	+	0.140855i
$679$	2.81533	−	15.9665i	0.108043	−	0.612740i
$680$	4.46160	−	1.62389i	0.171095	−	0.0622734i
$681$	3.22407	−	11.9409i	0.123547	−	0.457575i
$682$	5.41023	+	30.6830i	0.207168	+	1.17491i
$683$	−17.5761	−	30.4427i	−0.672531	−	1.16486i	−0.977184	−	0.212394i	$-0.931874\pi$
$683$	−17.5761	−	30.4427i	−0.672531	−	1.16486i	0.304654	−	0.952463i	$-0.401459\pi$
$684$	11.6480	−	6.66562i	0.445373	−	0.254866i
$685$	4.51724	−	7.82408i	0.172595	−	0.298943i
$686$	−11.6175	−	4.22841i	−0.443556	−	0.161441i
$687$	6.94191	−	9.87377i	0.264850	−	0.376708i
$688$	5.79724	+	4.86446i	0.221018	+	0.185456i
$689$	3.27927	+	2.75163i	0.124930	+	0.104829i
$690$	4.28292	−	6.09177i	0.163048	−	0.231910i
$691$	−1.83561	−	0.668107i	−0.0698299	−	0.0254160i	0.306869	−	0.951752i	$-0.400719\pi$
$691$	−1.83561	−	0.668107i	−0.0698299	−	0.0254160i	−0.376699	+	0.926336i	$0.622941\pi$
$692$	7.62953	−	13.2147i	0.290031	−	0.502349i
$693$	−0.0654476	+	17.0846i	−0.00248615	+	0.648992i
$694$	3.18037	+	5.50855i	0.120725	+	0.209102i
$695$	0.155735	+	0.883218i	0.00590737	+	0.0335024i
$696$	−2.24766	+	8.32457i	−0.0851974	+	0.315542i
$697$	−42.9828	+	15.6445i	−1.62809	+	0.592577i
$698$	0.251034	−	1.42369i	0.00950178	−	0.0538873i
$699$	17.9776	+	8.42505i	0.679975	+	0.318665i
$700$	−2.80546	+	2.35406i	−0.106036	+	0.0889750i
$701$	11.2600			0.425284			0.212642	−	0.977130i	$-0.431793\pi$
$701$	11.2600			0.425284			0.212642	+	0.977130i	$0.431793\pi$
$702$	−1.31600	−	5.02674i	−0.0496692	−	0.189722i
$703$	0.981401			0.0370142
$704$	4.62644	−	3.88204i	0.174365	−	0.146310i
$705$	−16.2357	+	11.3221i	−0.611473	+	0.426415i
$706$	4.07008	−	23.0826i	0.153179	−	0.868723i
$707$	−0.997144	+	0.362931i	−0.0375014	+	0.0136494i
$708$	11.9043	−	3.16531i	0.447389	−	0.118960i
$709$	−1.85073	−	10.4960i	−0.0695057	−	0.394186i	−0.999637	−	0.0269581i	$-0.991418\pi$
$709$	−1.85073	−	10.4960i	−0.0695057	−	0.394186i	0.930131	−	0.367228i	$-0.119693\pi$
$710$	−2.74734	−	4.75853i	−0.103106	−	0.178585i
$711$	−29.7542	+	35.1851i	−1.11587	+	1.31954i
$712$	7.83691	−	13.5739i	0.293700	−	0.508704i
$713$	19.7272	+	7.18012i	0.738790	+	0.268897i
$714$	3.08920	+	6.65807i	0.115610	+	0.249172i
$715$	−4.88790	−	4.10143i	−0.182797	−	0.153385i
$716$	−12.3631	−	10.3739i	−0.462032	−	0.387691i
$717$	−41.5000	−	3.71089i	−1.54985	−	0.138586i
$718$	−17.8504	−	6.49702i	−0.666172	−	0.242467i
$719$	13.8580	−	24.0028i	0.516817	−	0.895154i	−0.482992	−	0.875625i	$-0.660450\pi$
$719$	13.8580	−	24.0028i	0.516817	−	0.895154i	0.999809	−	0.0195290i	$-0.00621666\pi$
$720$	3.12348	−	0.538424i	0.116405	−	0.0200659i
$721$	3.47670	+	6.02182i	0.129479	+	0.224264i
$722$	−0.175710	−	0.996500i	−0.00653924	−	0.0370859i
$723$	−27.6511	−	27.7572i	−1.02835	−	1.03230i
$724$	−2.37911	+	0.865926i	−0.0884190	+	0.0321819i
$725$	3.35742	−	19.0409i	0.124691	−	0.707161i
$726$	3.76133	+	43.9619i	0.139596	+	1.63158i
$727$	−19.1756	+	16.0902i	−0.711183	+	0.596753i	−0.924931	−	0.380136i	$-0.875877\pi$
$727$	−19.1756	+	16.0902i	−0.711183	+	0.596753i	0.213748	+	0.976889i	$0.431433\pi$
$728$	−0.942964			−0.0349486
$729$	−23.5363	+	13.2304i	−0.871714	+	0.490015i
$730$	−11.6767			−0.432175
$731$	−26.0526	+	21.8607i	−0.963590	+	0.808548i
$732$	−0.571911	−	6.68441i	−0.0211384	−	0.247063i
$733$	4.53128	−	25.6982i	0.167367	−	0.949183i	−0.779224	−	0.626745i	$-0.784387\pi$
$733$	4.53128	−	25.6982i	0.167367	−	0.949183i	0.946591	−	0.322438i	$-0.104502\pi$
$734$	20.5833	−	7.49170i	0.759742	−	0.276524i
$735$	−7.89200	−	7.92229i	−0.291101	−	0.292218i
$736$	−0.706638	−	4.00754i	−0.0260470	−	0.147720i
$737$	−3.84512	−	6.65995i	−0.141637	−	0.245322i
$738$	−30.0914	+	5.18715i	−1.10768	+	0.190942i
$739$	−2.07244	+	3.58958i	−0.0762361	+	0.132045i	−0.901623	−	0.432523i	$-0.857624\pi$
$739$	−2.07244	+	3.58958i	−0.0762361	+	0.132045i	0.825387	+	0.564567i	$0.190957\pi$
$740$	0.217803	+	0.0792739i	0.00800660	+	0.00291416i
$741$	−7.71747	−	0.690089i	−0.283508	−	0.0253511i
$742$	−3.09223	−	2.59469i	−0.113519	−	0.0952540i
$743$	−3.42001	−	2.86973i	−0.125468	−	0.105280i	0.577895	−	0.816111i	$-0.303874\pi$
$743$	−3.42001	−	2.86973i	−0.125468	−	0.105280i	−0.703363	+	0.710831i	$0.748319\pi$
$744$	3.76074	+	8.10544i	0.137876	+	0.297160i
$745$	21.1065	+	7.68215i	0.773284	+	0.281452i
$746$	11.8175	−	20.4684i	0.432668	−	0.749403i
$747$	20.5873	−	24.3449i	0.753249	−	0.890735i
$748$	13.5704	+	23.5046i	0.496182	+	0.859413i
$749$	−1.26670	−	7.18383i	−0.0462843	−	0.262491i
$750$	−15.7108	+	4.17747i	−0.573679	+	0.152540i
$751$	8.02534	−	2.92099i	0.292849	−	0.106588i	−0.191418	−	0.981509i	$-0.561309\pi$
$751$	8.02534	−	2.92099i	0.292849	−	0.106588i	0.484267	+	0.874920i	$0.339086\pi$
$752$	−1.87828	+	10.6523i	−0.0684938	+	0.388448i
$753$	28.5691	−	19.9229i	1.04112	−	0.726029i
$754$	3.81360	−	3.19999i	0.138883	−	0.116537i
$755$	−12.6451			−0.460203
$756$	1.24094	+	4.74004i	0.0451326	+	0.172394i
$757$	36.3144			1.31987			0.659935	−	0.751323i	$-0.270584\pi$
$757$	36.3144			1.31987			0.659935	+	0.751323i	$0.270584\pi$
$758$	15.5263	−	13.0281i	0.563939	−	0.473201i
$759$	38.5449	+	18.0637i	1.39909	+	0.655672i
$760$	0.820710	−	4.65448i	0.0297703	−	0.168836i
$761$	−17.8889	+	6.51102i	−0.648471	+	0.236024i	−0.645251	−	0.763971i	$-0.723247\pi$
$761$	−17.8889	+	6.51102i	−0.648471	+	0.236024i	−0.00322002	+	0.999995i	$0.501025\pi$
$762$	3.27506	−	12.1297i	0.118643	−	0.439413i
$763$	2.25104	+	12.7663i	0.0814932	+	0.462171i
$764$	−11.9340	−	20.6702i	−0.431756	−	0.747823i
$765$	−0.0545646	+	14.2437i	−0.00197279	+	0.514983i
$766$	12.3045	−	21.3119i	0.444578	−	0.770032i
$767$	−6.68285	−	2.43236i	−0.241304	−	0.0878274i
$768$	0.996179	−	1.41691i	0.0359465	−	0.0511282i
$769$	35.4657	+	29.7593i	1.27893	+	1.07315i	0.993391	+	0.114779i	$0.0366160\pi$
$769$	35.4657	+	29.7593i	1.27893	+	1.07315i	0.285536	+	0.958368i	$0.407828\pi$
$770$	4.60911	+	3.86750i	0.166101	+	0.139375i
$771$	−21.2236	+	30.1873i	−0.764351	+	1.08717i
$772$	−16.6466	−	6.05888i	−0.599126	−	0.218064i
$773$	4.03431	−	6.98763i	0.145104	−	0.251328i	−0.784308	−	0.620372i	$-0.786982\pi$
$773$	4.03431	−	6.98763i	0.145104	−	0.251328i	0.929412	+	0.369044i	$0.120315\pi$
$774$	−19.7050	+	11.2762i	−0.708280	+	0.405316i
$775$	−10.0179	−	17.3515i	−0.359854	−	0.623286i
$776$	−2.98562	−	16.9323i	−0.107178	−	0.607834i
$777$	−0.0934001	+	0.345922i	−0.00335071	+	0.0124099i
$778$	0.149819	−	0.0545297i	0.00537128	−	0.00195498i
$779$	−7.90667	+	44.8410i	−0.283286	+	1.60659i
$780$	−1.65700	−	0.776540i	−0.0593302	−	0.0278046i
$781$	24.0610	−	20.1896i	0.860970	−	0.722440i
$782$	18.2876			0.653963
$783$	−21.1042	−	14.9588i	−0.754204	−	0.534584i
$784$	−6.11082			−0.218244
$785$	−0.510761	+	0.428579i	−0.0182298	+	0.0152966i
$786$	11.5335	−	8.04297i	0.411386	−	0.286883i
$787$	−1.98260	+	11.2439i	−0.0706719	+	0.400800i	0.928866	+	0.370415i	$0.120785\pi$
$787$	−1.98260	+	11.2439i	−0.0706719	+	0.400800i	−0.999538	+	0.0303852i	$0.990327\pi$
$788$	11.2860	−	4.10777i	0.402048	−	0.146333i
$789$	−2.71262	+	0.721280i	−0.0965720	+	0.0256782i
$790$	2.81793	+	15.9813i	0.100258	+	0.568589i
$791$	2.35269	+	4.07499i	0.0836522	+	0.144890i
$792$	6.13151	+	17.0491i	0.217874	+	0.605814i
$793$	−1.93667	+	3.35442i	−0.0687733	+	0.119119i
$794$	15.3713	+	5.59471i	0.545508	+	0.198549i
$795$	−3.29700	−	7.10594i	−0.116932	−	0.252022i
$796$	−9.28373	−	7.78998i	−0.329053	−	0.276108i
$797$	−40.0526	−	33.6081i	−1.41874	−	1.19046i	−0.952013	−	0.306056i	$-0.900990\pi$
$797$	−40.0526	−	33.6081i	−1.41874	−	1.19046i	−0.466722	−	0.884404i	$-0.654565\pi$
$798$	7.27730	+	0.650729i	0.257614	+	0.0230356i
$799$	−45.6778	−	16.6254i	−1.61597	−	0.588163i
$800$	−1.94189	+	3.36345i	−0.0686561	+	0.118916i
$801$	30.0866	+	36.1360i	1.06306	+	1.27680i
$802$	15.4253	+	26.7174i	0.544687	+	0.943425i
$803$	−11.5907	−	65.7338i	−0.409025	−	2.31970i
$804$	−1.55654	−	1.56251i	−0.0548949	−	0.0551056i
$805$	3.80963	−	1.38659i	0.134272	−	0.0488710i
$806$	0.895825	−	5.08048i	0.0315541	−	0.178952i
$807$	2.07218	+	24.2193i	0.0729440	+	0.852559i
$808$	−0.862046	+	0.723343i	−0.0303267	+	0.0254471i
$809$	33.0759			1.16289			0.581443	−	0.813587i	$-0.302488\pi$
$809$	33.0759			1.16289			0.581443	+	0.813587i	$0.302488\pi$
$810$	−1.72285	+	9.35125i	−0.0605348	+	0.328569i
$811$	−5.23894			−0.183964			−0.0919820	−	0.995761i	$-0.529320\pi$
$811$	−5.23894			−0.183964			−0.0919820	+	0.995761i	$0.529320\pi$
$812$	−3.59609	+	3.01748i	−0.126198	+	0.105893i
$813$	1.10604	+	12.9272i	0.0387905	+	0.453377i
$814$	−0.230073	+	1.30481i	−0.00806405	+	0.0457335i
$815$	−4.21534	+	1.53426i	−0.147657	+	0.0537427i
$816$	5.49341	+	5.51449i	0.192308	+	0.193046i
$817$	5.87870	+	33.3398i	0.205670	+	1.16641i
$818$	14.6891	+	25.4423i	0.513594	+	0.889570i
$819$	0.977714	−	2.65456i	0.0341641	−	0.0927580i
$820$	−5.37682	+	9.31292i	−0.187767	+	0.325221i
$821$	−4.24352	−	1.54451i	−0.148100	−	0.0539039i	0.266907	−	0.963722i	$-0.413998\pi$
$821$	−4.24352	−	1.54451i	−0.148100	−	0.0539039i	−0.415006	+	0.909818i	$0.636221\pi$
$822$	14.7523	+	1.31913i	0.514544	+	0.0460100i
$823$	−8.58241	−	7.20150i	−0.299164	−	0.251028i	0.480832	−	0.876813i	$-0.340335\pi$
$823$	−8.58241	−	7.20150i	−0.299164	−	0.251028i	−0.779996	+	0.625784i	$0.784779\pi$
$824$	5.64879	+	4.73990i	0.196785	+	0.165122i
$825$	−17.0989	−	36.8528i	−0.595306	−	1.28305i
$826$	6.30169	+	2.29363i	0.219264	+	0.0798055i
$827$	−20.7061	+	35.8641i	−0.720023	+	1.24712i	0.240967	+	0.970533i	$0.422535\pi$
$827$	−20.7061	+	35.8641i	−0.720023	+	1.24712i	−0.960990	+	0.276583i	$0.910798\pi$
$828$	12.0144	+	2.16595i	0.417530	+	0.0752721i
$829$	−0.130998	−	0.226896i	−0.00454976	−	0.00788042i	0.863742	−	0.503935i	$-0.168115\pi$
$829$	−0.130998	−	0.226896i	−0.00454976	−	0.00788042i	−0.868291	+	0.496055i	$0.834782\pi$
$830$	−1.94976	−	11.0576i	−0.0676771	−	0.383816i
$831$	−6.18887	+	1.64560i	−0.214689	+	0.0570854i
$832$	−0.939693	+	0.342020i	−0.0325780	+	0.0118574i
$833$	4.76869	−	27.0446i	0.165225	−	0.937040i
$834$	−1.20600	+	0.841013i	−0.0417604	+	0.0291219i
$835$	10.9426	−	9.18189i	0.378683	−	0.317752i
$836$	27.0170			0.934401
$837$	−26.7172	+	2.18283i	−0.923480	+	0.0754496i
$838$	−11.6777			−0.403400
$839$	23.9977	−	20.1364i	0.828492	−	0.695187i	−0.126452	−	0.991973i	$-0.540359\pi$
$839$	23.9977	−	20.1364i	0.828492	−	0.695187i	0.954944	+	0.296785i	$0.0959146\pi$
$840$	1.56249	+	0.732250i	0.0539112	+	0.0252650i
$841$	−0.732187	+	4.15244i	−0.0252478	+	0.143188i
$842$	23.4373	−	8.53048i	0.807703	−	0.293980i
$843$	3.07976	−	11.4064i	0.106072	−	0.392856i
$844$	−1.10789	−	6.28316i	−0.0381352	−	0.216275i
$845$	0.528257	+	0.914969i	0.0181726	+	0.0314759i
$846$	−28.0399	−	16.3324i	−0.964033	−	0.561520i
$847$	−12.0106	+	20.8030i	−0.412689	+	0.714799i
$848$	−4.02261	−	1.46411i	−0.138137	−	0.0502778i
$849$	11.4257	−	16.2513i	0.392131	−	0.557744i
$850$	−13.3702	−	11.2189i	−0.458594	−	0.384806i
$851$	0.683885	+	0.573848i	0.0234433	+	0.0196713i
$852$	5.18089	−	7.36900i	0.177494	−	0.252458i
$853$	26.2998	+	9.57234i	0.900488	+	0.327751i	0.750448	−	0.660929i	$-0.229838\pi$
$853$	26.2998	+	9.57234i	0.900488	+	0.327751i	0.150039	+	0.988680i	$0.452060\pi$
$854$	1.82621	−	3.16309i	0.0624917	−	0.108239i
$855$	12.2520	+	7.13641i	0.419009	+	0.244060i
$856$	−3.86794	−	6.69946i	−0.132203	−	0.228983i
$857$	2.00764	+	11.3859i	0.0685796	+	0.388934i	0.999706	+	0.0242381i	$0.00771599\pi$
$857$	2.00764	+	11.3859i	0.0685796	+	0.388934i	−0.931127	+	0.364696i	$0.881173\pi$
$858$	2.72673	−	10.0989i	0.0930890	−	0.344770i
$859$	−36.0388	+	13.1170i	−1.22963	+	0.447548i	−0.873470	−	0.486878i	$-0.838136\pi$
$859$	−36.0388	+	13.1170i	−1.22963	+	0.447548i	−0.356158	+	0.934426i	$0.615913\pi$
$860$	−1.38840	+	7.87398i	−0.0473439	+	0.268501i
$861$	−15.0530	−	7.05445i	−0.513004	−	0.240415i
$862$	4.74892	−	3.98482i	0.161749	−	0.135723i
$863$	27.7266			0.943826			0.471913	−	0.881645i	$-0.343564\pi$
$863$	27.7266			0.943826			0.471913	+	0.881645i	$0.343564\pi$
$864$	2.95588	+	4.27349i	0.100561	+	0.145387i
$865$	16.1214			0.548145
$866$	−8.52394	+	7.15244i	−0.289655	+	0.243050i
$867$	−4.54019	+	3.16614i	−0.154193	+	0.107528i
$868$	−0.844731	+	4.79071i	−0.0286720	+	0.162607i
$869$	−87.1693	+	31.7270i	−2.95702	+	1.07627i
$870$	−8.80407	+	2.34098i	−0.298486	+	0.0793666i
$871$	0.221115	+	1.25401i	0.00749219	+	0.0424903i
$872$	6.87366	+	11.9055i	0.232772	+	0.403172i
$873$	50.7622	+	9.15138i	1.71804	+	0.309727i
$874$	9.10208	−	15.7653i	0.307882	−	0.533268i
$875$	−8.31676	−	3.02705i	−0.281158	−	0.102333i
$876$	−8.05686	−	17.3647i	−0.272216	−	0.586700i
$877$	−13.9776	−	11.7286i	−0.471991	−	0.396047i	0.375529	−	0.926810i	$-0.377461\pi$
$877$	−13.9776	−	11.7286i	−0.471991	−	0.396047i	−0.847520	+	0.530763i	$0.821905\pi$
$878$	6.66126	+	5.58946i	0.224807	+	0.188635i
$879$	7.38003	+	0.659916i	0.248922	+	0.0222584i
$880$	5.99589	+	2.18233i	0.202122	+	0.0735662i
$881$	11.8334	−	20.4961i	0.398679	−	0.690532i	−0.594884	−	0.803811i	$-0.702802\pi$
$881$	11.8334	−	20.4961i	0.398679	−	0.690532i	0.993563	+	0.113279i	$0.0361355\pi$
$882$	6.33601	−	17.2027i	0.213345	−	0.579246i
$883$	−16.7180	−	28.9564i	−0.562604	−	0.974459i	−0.997268	−	0.0738663i	$-0.976466\pi$
$883$	−16.7180	−	28.9564i	−0.562604	−	0.974459i	0.434664	−	0.900593i	$-0.356867\pi$
$884$	−0.780369	−	4.42569i	−0.0262466	−	0.148852i
$885$	9.18467	+	9.21992i	0.308739	+	0.309924i
$886$	−8.45904	+	3.07884i	−0.284187	+	0.103436i
$887$	−1.58993	+	9.01693i	−0.0533846	+	0.302759i	−0.999796	−	0.0202050i	$-0.993568\pi$
$887$	−1.58993	+	9.01693i	−0.0533846	+	0.302759i	0.946411	+	0.322964i	$0.104679\pi$
$888$	0.0323925	+	0.378599i	0.00108702	+	0.0127050i
$889$	5.23984	−	4.39675i	0.175739	−	0.147462i
$890$	16.5596			0.555079
$891$	−54.3529	−	0.416434i	−1.82089	−	0.0139511i
$892$	21.9888			0.736238
$893$	−37.0670	+	31.1029i	−1.24040	+	1.04082i
$894$	3.13905	+	36.6887i	0.104985	+	1.22705i
$895$	2.96087	−	16.7920i	0.0989711	−	0.561293i
$896$	0.886097	−	0.322513i	0.0296024	−	0.0107744i
$897$	−4.97438	−	4.99347i	−0.166090	−	0.166727i
$898$	0.515374	+	2.92283i	0.0171982	+	0.0975360i
$899$	−12.8412	−	22.2416i	−0.428277	−	0.741797i
$900$	−7.45508	−	8.95406i	−0.248503	−	0.298469i
$901$	9.61883	−	16.6603i	0.320450	−	0.555035i
$902$	−57.7641	−	21.0244i	−1.92333	−	0.700036i
$903$	−12.3110	−	1.10084i	−0.409685	−	0.0366336i
$904$	3.82256	+	3.20751i	0.127136	+	0.106680i
$905$	−2.04908	−	1.71938i	−0.0681137	−	0.0571542i
$906$	−8.72506	−	18.8049i	−0.289871	−	0.624751i
$907$	27.3310	+	9.94767i	0.907511	+	0.330307i	0.753259	−	0.657725i	$-0.228481\pi$
$907$	27.3310	+	9.94767i	0.907511	+	0.330307i	0.154252	+	0.988031i	$0.450703\pi$
$908$	3.57047	−	6.18424i	0.118490	−	0.205231i
$909$	−1.14249	−	3.17677i	−0.0378939	−	0.105367i
$910$	−0.498128	−	0.862783i	−0.0165128	−	0.0286010i
$911$	9.85747	+	55.9045i	0.326593	+	1.85220i	0.498239	+	0.867040i	$0.333980\pi$
$911$	9.85747	+	55.9045i	0.326593	+	1.85220i	−0.171646	+	0.985159i	$0.554909\pi$
$912$	7.48808	−	1.99106i	0.247955	−	0.0659306i
$913$	60.3133	−	21.9523i	1.99608	−	0.726514i
$914$	−2.25487	+	12.7880i	−0.0745845	+	0.422990i
$915$	5.81391	−	4.05437i	0.192202	−	0.134033i
$916$	5.33821	−	4.47929i	0.176379	−	0.148000i
$917$	7.65509			0.252793
$918$	−21.2198	+	9.74692i	−0.700359	+	0.321696i
$919$	20.3277			0.670550			0.335275	−	0.942120i	$-0.391171\pi$
$919$	20.3277			0.670550			0.335275	+	0.942120i	$0.391171\pi$
$920$	3.29349	−	2.76357i	0.108583	−	0.0911120i
$921$	−38.1282	−	17.8684i	−1.25637	−	0.588785i
$922$	1.77922	−	10.0905i	0.0585955	−	0.332311i
$923$	−4.88712	+	1.77877i	−0.160861	+	0.0585488i
$924$	−2.57121	+	9.52288i	−0.0845866	+	0.313280i
$925$	−0.147954	−	0.839090i	−0.00486470	−	0.0275891i
$926$	0.273033	+	0.472906i	0.00897241	+	0.0155407i
$927$	−19.2004	+	10.9875i	−0.630623	+	0.360877i
$928$	−2.48915	+	4.31134i	−0.0817104	+	0.141527i
$929$	6.19874	+	2.25616i	0.203374	+	0.0740221i	0.441699	−	0.897163i	$-0.354376\pi$
$929$	6.19874	+	2.25616i	0.203374	+	0.0740221i	−0.238325	+	0.971186i	$0.576598\pi$
$930$	−5.42958	+	7.72272i	−0.178043	+	0.253238i
$931$	−20.9410	−	17.5716i	−0.686313	−	0.575885i
$932$	8.78088	+	7.36803i	0.287627	+	0.241348i
$933$	−24.9972	+	35.5545i	−0.818370	+	1.16400i
$934$	34.3160	+	12.4900i	1.12285	+	0.408685i
$935$	−14.3373	+	24.8330i	−0.468880	+	0.812124i
$936$	0.0114923	−	2.99998i	0.000375637	−	0.0980573i
$937$	−18.3372	−	31.7609i	−0.599049	−	1.03758i	−0.992962	−	0.118435i	$-0.962212\pi$
$937$	−18.3372	−	31.7609i	−0.599049	−	1.03758i	0.393913	−	0.919148i	$-0.371121\pi$
$938$	−0.208503	−	1.18248i	−0.00680788	−	0.0386094i
$939$	−13.7812	+	51.0408i	−0.449732	+	1.66565i
$940$	−10.7387	+	3.90856i	−0.350257	+	0.127483i
$941$	0.596058	−	3.38041i	0.0194309	−	0.110198i	−0.973550	−	0.228475i	$-0.926626\pi$
$941$	0.596058	−	3.38041i	0.0194309	−	0.110198i	0.992981	+	0.118277i	$0.0377371\pi$
$942$	−0.989772	−	0.463849i	−0.0322485	−	0.0151130i
$943$	−31.7293	+	26.6240i	−1.03325	+	0.866998i
$944$	7.11174			0.231467
$945$	−3.68145	+	3.63938i	−0.119758	+	0.118389i
$946$	−45.7046			−1.48598
$947$	−29.9115	+	25.0988i	−0.971994	+	0.815600i	−0.982862	−	0.184341i	$-0.940985\pi$
$947$	−29.9115	+	25.0988i	−0.971994	+	0.815600i	0.0108682	+	0.999941i	$0.496540\pi$
$948$	−21.8218	+	15.2176i	−0.708741	+	0.494245i
$949$	−1.91918	+	10.8842i	−0.0622992	+	0.353316i
$950$	−16.3262	+	5.94223i	−0.529690	+	0.192792i
$951$	42.5743	−	11.3204i	1.38057	−	0.367089i
$952$	0.735860	+	4.17327i	0.0238494	+	0.135256i
$953$	−12.6295	−	21.8750i	−0.409111	−	0.708600i	0.585680	−	0.810543i	$-0.300828\pi$
$953$	−12.6295	−	21.8750i	−0.409111	−	0.708600i	−0.994790	+	0.101942i	$0.967494\pi$
$954$	8.29252	−	9.80610i	0.268480	−	0.317484i
$955$	12.6084	−	21.8384i	0.407999	−	0.706675i
$956$	−22.6049	−	8.22752i	−0.731095	−	0.266097i
$957$	−21.9177	−	47.2386i	−0.708498	−	1.52701i
$958$	−0.321054	−	0.269396i	−0.0103728	−	0.00870380i
$959$	6.17698	+	5.18310i	0.199465	+	0.167371i
$960$	1.82266	+	0.162981i	0.0588263	+	0.00526019i
$961$	4.12172	+	1.50018i	0.132959	+	0.0483930i
$962$	0.109691	−	0.189991i	0.00353659	−	0.00612556i
$963$	22.8703	−	3.94238i	0.736986	−	0.127041i
$964$	−11.3102	−	19.5898i	−0.364277	−	0.630946i
$965$	−3.25002	−	18.4318i	−0.104622	−	0.593341i
$966$	4.69066	+	4.70866i	0.150920	+	0.151499i
$967$	22.6528	−	8.24493i	0.728464	−	0.265139i	0.0489492	−	0.998801i	$-0.484413\pi$
$967$	22.6528	−	8.24493i	0.728464	−	0.265139i	0.679514	+	0.733662i	$0.262191\pi$
$968$	−4.42354	+	25.0871i	−0.142178	+	0.806331i
$969$	2.96835	+	34.6937i	0.0953573	+	1.11452i
$970$	13.9153	−	11.6764i	0.446795	−	0.374905i
$971$	15.9939			0.513269			0.256635	−	0.966509i	$-0.417386\pi$
$971$	15.9939			0.513269			0.256635	+	0.966509i	$0.417386\pi$
$972$	−15.0952	+	3.89020i	−0.484180	+	0.124778i
$973$	−0.800454			−0.0256614
$974$	32.2494	−	27.0604i	1.03334	−	0.867072i
$975$	0.573451	+	6.70241i	0.0183651	+	0.214649i
$976$	0.672600	−	3.81450i	0.0215294	−	0.122099i
$977$	−53.7336	+	19.5574i	−1.71909	+	0.625698i	−0.997760	−	0.0668931i	$-0.978691\pi$
$977$	−53.7336	+	19.5574i	−1.71909	+	0.625698i	−0.721331	+	0.692591i	$0.756469\pi$
$978$	−5.19019	−	5.21011i	−0.165964	−	0.166601i
$979$	16.4376	+	93.2220i	0.525347	+	2.97939i
$980$	−3.22808	−	5.59121i	−0.103117	−	0.178605i
$981$	−40.6425	+	7.00595i	−1.29762	+	0.223683i
$982$	12.9836	−	22.4882i	0.414322	−	0.717626i
$983$	−10.4941	−	3.81954i	−0.334710	−	0.121824i	0.169198	−	0.985582i	$-0.445882\pi$
$983$	−10.4941	−	3.81954i	−0.334710	−	0.121824i	−0.503907	+	0.863758i	$0.668105\pi$
$984$	−17.5595	−	1.57015i	−0.559775	−	0.0500545i
$985$	9.72041	+	8.15639i	0.309718	+	0.259884i
$986$	−17.1382	−	14.3806i	−0.545791	−	0.457973i
$987$	−7.43542	−	16.0254i	−0.236672	−	0.510094i
$988$	−4.20368	−	1.53001i	−0.133737	−	0.0486762i
$989$	−15.3980	+	26.6701i	−0.489628	+	0.848060i
$990$	−12.3604	+	14.6165i	−0.392839	+	0.464541i
$991$	23.7202	+	41.0847i	0.753498	+	1.30510i	0.946118	+	0.323824i	$0.104968\pi$
$991$	23.7202	+	41.0847i	0.753498	+	1.30510i	−0.192619	+	0.981274i	$0.561698\pi$
$992$	0.895825	+	5.08048i	0.0284425	+	0.161305i
$993$	15.2418	−	4.05274i	0.483683	−	0.128610i
$994$	4.60838	−	1.67731i	0.146169	−	0.0532011i
$995$	2.22338	−	12.6094i	0.0704860	−	0.399746i
$996$	15.0988	−	10.5292i	0.478423	−	0.333631i
$997$	45.4239	−	38.1151i	1.43859	−	1.20712i	0.498178	−	0.867075i	$-0.334003\pi$
$997$	45.4239	−	38.1151i	1.43859	−	1.20712i	0.940410	−	0.340044i	$-0.110442\pi$
$998$	−30.7316			−0.972792
$999$	−1.09939	−	0.301362i	−0.0347832	−	0.00953468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.w.d.157.6	✓	66
27.16	even	9	inner	702.2.w.d.313.6	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.w.d.157.6	✓	66	1.1	even	1	trivial
702.2.w.d.313.6	yes	66	27.16	even	9	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.147653 - 1.72575i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.992799 - 0.361349i) q^{5} +(1.22240 + 1.22709i) q^{6} +(0.163744 + 0.928638i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.95640 + 0.509623i) q^{9} +(-0.528257 + 0.914969i) q^{10} +(-5.67516 - 2.06559i) q^{11} +(-1.72517 - 0.154263i) q^{12} +(0.766044 + 0.642788i) q^{13} +(-0.722353 - 0.606126i) q^{14} +(-0.770187 - 1.65996i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.24698 - 3.89189i) q^{17} +(1.93715 - 2.29073i) q^{18} +(-2.23673 - 3.87413i) q^{19} +(-0.183462 - 1.04046i) q^{20} +(1.57842 - 0.419697i) q^{21} +(5.67516 - 2.06559i) q^{22} +(0.706638 - 4.00754i) q^{23} +(1.42071 - 0.990744i) q^{24} +(-2.97515 + 2.49644i) q^{25} -1.00000 q^{26} +(1.31600 + 5.02674i) q^{27} +0.942964 q^{28} +(-3.81360 + 3.19999i) q^{29} +(1.65700 + 0.776540i) q^{30} +(-0.895825 + 5.08048i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-2.72673 + 10.0989i) q^{33} +(0.780369 + 4.42569i) q^{34} +(0.498128 + 0.862783i) q^{35} +(-0.0114923 + 2.99998i) q^{36} +(-0.109691 + 0.189991i) q^{37} +(4.20368 + 1.53001i) q^{38} +(0.996179 - 1.41691i) q^{39} +(0.809337 + 0.679115i) q^{40} +(-7.79711 - 6.54255i) q^{41} +(-0.939361 + 1.33609i) q^{42} +(-7.11137 - 2.58833i) q^{43} +(-3.01969 + 5.23026i) q^{44} +(-2.75096 + 1.57425i) q^{45} +(2.03468 + 3.52417i) q^{46} +(-1.87828 - 10.6523i) q^{47} +(-0.451491 + 1.67217i) q^{48} +(5.74229 - 2.09002i) q^{49} +(0.674411 - 3.82477i) q^{50} +(-7.04818 - 3.30307i) q^{51} +(0.766044 - 0.642788i) q^{52} +4.28078 q^{53} +(-4.23924 - 3.00480i) q^{54} -6.38070 q^{55} +(-0.722353 + 0.606126i) q^{56} +(-6.35551 + 4.43206i) q^{57} +(0.864473 - 4.90267i) q^{58} +(-6.68285 + 2.43236i) q^{59} +(-1.76849 + 0.470236i) q^{60} +(0.672600 + 3.81450i) q^{61} +(-2.57943 - 4.46770i) q^{62} +(-0.957348 - 2.66198i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.992799 + 0.361349i) q^{65} +(-4.40264 - 9.48890i) q^{66} +(0.975443 + 0.818494i) q^{67} +(-3.44258 - 2.88866i) q^{68} +(-7.02034 - 0.627752i) q^{69} +(-0.936174 - 0.340739i) q^{70} +(-2.60038 + 4.50399i) q^{71} +(-1.91955 - 2.30550i) q^{72} +(5.52605 + 9.57140i) q^{73} +(-0.0380954 - 0.216050i) q^{74} +(4.74752 + 4.76574i) q^{75} +(-4.20368 + 1.53001i) q^{76} +(0.988913 - 5.60840i) q^{77} +(0.147653 + 1.72575i) q^{78} +(11.7663 - 9.87308i) q^{79} -1.05651 q^{80} +(8.48057 - 3.01330i) q^{81} +10.1784 q^{82} +(-8.14121 + 6.83129i) q^{83} +(-0.139231 - 1.62732i) q^{84} +(0.824471 - 4.67581i) q^{85} +(7.11137 - 2.58833i) q^{86} +(6.08546 + 6.10882i) q^{87} +(-1.04873 - 5.94763i) q^{88} +(-7.83691 - 13.5739i) q^{89} +(1.09545 - 2.97422i) q^{90} +(-0.471482 + 0.816631i) q^{91} +(-3.82395 - 1.39180i) q^{92} +(8.89988 + 0.795819i) q^{93} +(8.28598 + 6.95276i) q^{94} +(-3.62054 - 3.03799i) q^{95} +(-0.728988 - 1.57117i) q^{96} +(-16.1566 - 5.88052i) q^{97} +(-3.05541 + 5.29212i) q^{98} +(17.8307 + 3.21451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) \) 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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Database

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