LMFDB - Embedded newform 234.2.z.a.137.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.2
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.958654 + 1.44256i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.32591 + 0.891175i) q^{5} +(1.29935 - 1.14529i) q^{6} +(-0.0201488 + 0.0201488i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16197 - 2.76583i) q^{9} +(-2.98193 - 1.72162i) q^{10} +(-1.12616 + 4.20290i) q^{11} +(-1.55150 + 0.769968i) q^{12} +(1.39839 - 3.32333i) q^{13} +(0.0246771 - 0.0142473i) q^{14} +(-4.47397 + 3.94350i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.35521 + 5.81139i) q^{17} +(0.406522 + 2.97233i) q^{18} +(-0.521462 + 1.94612i) q^{19} +(2.43473 + 2.43473i) q^{20} +(-0.00975013 - 0.0483815i) q^{21} +(2.17558 - 3.76822i) q^{22} +0.528142 q^{23} +(1.69792 - 0.342174i) q^{24} +(5.93735 + 3.42793i) q^{25} +(-2.21088 + 2.84816i) q^{26} +(5.10381 + 0.975270i) q^{27} +(-0.0275237 + 0.00737496i) q^{28} +(-7.19404 + 4.15348i) q^{29} +(5.34218 - 2.65118i) q^{30} +(-0.373424 + 1.39364i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.98334 - 5.65369i) q^{33} +(-1.73678 - 6.48176i) q^{34} +(-0.0849690 + 0.0490569i) q^{35} +(0.376625 - 2.97627i) q^{36} +(-2.09857 - 7.83198i) q^{37} +(1.00739 - 1.74484i) q^{38} +(3.45354 + 5.20318i) q^{39} +(-1.72162 - 2.98193i) q^{40} +(3.55302 - 3.55302i) q^{41} +(-0.00310415 + 0.0492564i) q^{42} -8.76179i q^{43} +(-3.07674 + 3.07674i) q^{44} +(-1.39975 - 10.2344i) q^{45} +(-0.510146 - 0.136693i) q^{46} +(-0.775777 + 0.207869i) q^{47} +(-1.72862 - 0.108938i) q^{48} +6.99919i q^{49} +(-4.84783 - 4.84783i) q^{50} +(-11.5998 - 0.731018i) q^{51} +(2.87270 - 2.17889i) q^{52} -5.06566i q^{53} +(-4.67748 - 2.26300i) q^{54} +(-7.49104 + 12.9749i) q^{55} +0.0284946 q^{56} +(-2.30750 - 2.61790i) q^{57} +(8.02391 - 2.15000i) q^{58} +(13.8214 - 3.70343i) q^{59} +(-5.84632 + 1.17819i) q^{60} -0.0214935 q^{61} +(0.721399 - 1.24950i) q^{62} +(0.0791403 + 0.0323159i) q^{63} +1.00000i q^{64} +(7.61257 - 9.80688i) q^{65} +(3.35025 + 6.75082i) q^{66} +(-0.668189 - 0.668189i) q^{67} +6.71041i q^{68} +(-0.506305 + 0.761877i) q^{69} +(0.0947706 - 0.0253937i) q^{70} +(-9.32969 - 2.49988i) q^{71} +(-1.13411 + 2.77737i) q^{72} +(6.53713 - 6.53713i) q^{73} +8.10826i q^{74} +(-10.6369 + 5.27880i) q^{75} +(-1.42466 + 1.42466i) q^{76} +(-0.0619924 - 0.107374i) q^{77} +(-1.98918 - 5.91973i) q^{78} +(1.40950 - 2.44132i) q^{79} +(0.891175 + 3.32591i) q^{80} +(-6.29967 + 6.42761i) q^{81} +(-4.35155 + 2.51237i) q^{82} +(-3.80210 - 14.1896i) q^{83} +(0.0157469 - 0.0467747i) q^{84} +(5.98015 + 22.3182i) q^{85} +(-2.26772 + 8.46324i) q^{86} +(0.904943 - 14.3596i) q^{87} +(3.76822 - 2.17558i) q^{88} +(10.8696 - 2.91249i) q^{89} +(-1.29681 + 10.2480i) q^{90} +(0.0387852 + 0.0951367i) q^{91} +(0.457384 + 0.264071i) q^{92} +(-1.65242 - 1.87470i) q^{93} +0.803143 q^{94} +(-3.46867 + 6.00791i) q^{95} +(1.64153 + 0.552626i) q^{96} +(0.333814 + 0.333814i) q^{97} +(1.81152 - 6.76070i) q^{98} +(12.9331 - 1.76884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.958654	+	1.44256i	−0.553479	+	0.832863i
$3$	−0.958654	+	1.44256i	−0.553479	+	0.832863i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	3.32591	+	0.891175i	1.48739	+	0.398545i	0.908855	−	0.417111i	$-0.136957\pi$
$5$	3.32591	+	0.891175i	1.48739	+	0.398545i	0.578536	+	0.815657i	$0.303624\pi$
$6$	1.29935	−	1.14529i	0.530458	−	0.467562i
$7$	−0.0201488	+	0.0201488i	−0.00761551	+	0.00761551i	−0.710904	−	0.703289i	$-0.751714\pi$
$7$	−0.0201488	+	0.0201488i	−0.00761551	+	0.00761551i	0.703289	+	0.710904i	$0.251714\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.16197	−	2.76583i	−0.387322	−	0.921945i
$10$	−2.98193	−	1.72162i	−0.942969	−	0.544423i
$11$	−1.12616	+	4.20290i	−0.339551	+	1.26722i	0.559299	+	0.828966i	$0.311070\pi$
$11$	−1.12616	+	4.20290i	−0.339551	+	1.26722i	−0.898850	+	0.438256i	$0.855596\pi$
$12$	−1.55150	+	0.769968i	−0.447879	+	0.222271i
$13$	1.39839	−	3.32333i	0.387843	−	0.921726i
$13$	1.39839	−	3.32333i	0.387843	−	0.921726i
$14$	0.0246771	−	0.0142473i	0.00659523	−	0.00380776i
$15$	−4.47397	+	3.94350i	−1.15517	+	1.01821i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.35521	+	5.81139i	0.813757	+	1.40947i	0.910217	+	0.414131i	$0.135915\pi$
$17$	3.35521	+	5.81139i	0.813757	+	1.40947i	−0.0964602	+	0.995337i	$0.530752\pi$
$18$	0.406522	+	2.97233i	0.0958182	+	0.700585i
$19$	−0.521462	+	1.94612i	−0.119632	+	0.446471i	−0.999592	−	0.0285767i	$-0.990903\pi$
$19$	−0.521462	+	1.94612i	−0.119632	+	0.446471i	0.879960	+	0.475048i	$0.157569\pi$
$20$	2.43473	+	2.43473i	0.544423	+	0.544423i
$21$	−0.00975013	−	0.0483815i	−0.00212765	−	0.0105577i
$22$	2.17558	−	3.76822i	0.463835	−	0.803387i
$23$	0.528142			0.110125			0.0550626	−	0.998483i	$-0.482464\pi$
$23$	0.528142			0.110125			0.0550626	+	0.998483i	$0.482464\pi$
$24$	1.69792	−	0.342174i	0.346586	−	0.0698460i
$25$	5.93735	+	3.42793i	1.18747	+	0.685587i
$26$	−2.21088	+	2.84816i	−0.433589	+	0.558570i
$27$	5.10381	+	0.975270i	0.982228	+	0.187691i
$28$	−0.0275237	+	0.00737496i	−0.00520149	+	0.00139374i
$29$	−7.19404	+	4.15348i	−1.33590	+	0.771282i	−0.986197	−	0.165578i	$-0.947051\pi$
$29$	−7.19404	+	4.15348i	−1.33590	+	0.771282i	−0.349703	+	0.936861i	$0.613718\pi$
$30$	5.34218	−	2.65118i	0.975343	−	0.484037i
$31$	−0.373424	+	1.39364i	−0.0670689	+	0.250305i	−0.991318	−	0.131485i	$-0.958025\pi$
$31$	−0.373424	+	1.39364i	−0.0670689	+	0.250305i	0.924249	+	0.381790i	$0.124692\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−4.98334	−	5.65369i	−0.867488	−	0.984180i
$34$	−1.73678	−	6.48176i	−0.297856	−	1.11161i
$35$	−0.0849690	+	0.0490569i	−0.0143624	+	0.00829212i
$36$	0.376625	−	2.97627i	0.0627708	−	0.496044i
$37$	−2.09857	−	7.83198i	−0.345003	−	1.28757i	−0.892608	−	0.450833i	$-0.851127\pi$
$37$	−2.09857	−	7.83198i	−0.345003	−	1.28757i	0.547605	−	0.836737i	$-0.315540\pi$
$38$	1.00739	−	1.74484i	0.163420	−	0.283051i
$39$	3.45354	+	5.20318i	0.553009	+	0.833176i
$40$	−1.72162	−	2.98193i	−0.272212	−	0.471484i
$41$	3.55302	−	3.55302i	0.554889	−	0.554889i	−0.372959	−	0.927848i	$-0.621657\pi$
$41$	3.55302	−	3.55302i	0.554889	−	0.554889i	0.927848	+	0.372959i	$0.121657\pi$
$42$	−0.00310415	+	0.0492564i	−0.000478980	+	0.00760043i
$43$		−	8.76179i		−	1.33616i	−0.744089	−	0.668080i	$-0.767116\pi$
$43$		−	8.76179i		−	1.33616i	0.744089	−	0.668080i	$-0.232884\pi$
$44$	−3.07674	+	3.07674i	−0.463835	+	0.463835i
$45$	−1.39975	−	10.2344i	−0.208663	−	1.52566i
$46$	−0.510146	−	0.136693i	−0.0752169	−	0.0201543i
$47$	−0.775777	+	0.207869i	−0.113159	+	0.0303208i	−0.314954	−	0.949107i	$-0.601989\pi$
$47$	−0.775777	+	0.207869i	−0.113159	+	0.0303208i	0.201795	+	0.979428i	$0.435322\pi$
$48$	−1.72862	−	0.108938i	−0.249505	−	0.0157238i
$49$			6.99919i			0.999884i
$50$	−4.84783	−	4.84783i	−0.685587	−	0.685587i
$51$	−11.5998	−	0.731018i	−1.62429	−	0.102363i
$52$	2.87270	−	2.17889i	0.398372	−	0.302158i
$53$		−	5.06566i		−	0.695822i	−0.937527	−	0.347911i	$-0.886891\pi$
$53$		−	5.06566i		−	0.695822i	0.937527	−	0.347911i	$-0.113109\pi$
$54$	−4.67748	−	2.26300i	−0.636525	−	0.307955i
$55$	−7.49104	+	12.9749i	−1.01009	+	1.74953i
$56$	0.0284946			0.00380776
$57$	−2.30750	−	2.61790i	−0.305636	−	0.346749i
$58$	8.02391	−	2.15000i	1.05359	−	0.282309i
$59$	13.8214	−	3.70343i	1.79939	−	0.482145i	0.805508	−	0.592585i	$-0.201893\pi$
$59$	13.8214	−	3.70343i	1.79939	−	0.482145i	0.993883	+	0.110440i	$0.0352259\pi$
$60$	−5.84632	+	1.17819i	−0.754757	+	0.152103i
$61$	−0.0214935			−0.00275196			−0.00137598	−	0.999999i	$-0.500438\pi$
$61$	−0.0214935			−0.00275196			−0.00137598	+	0.999999i	$0.500438\pi$
$62$	0.721399	−	1.24950i	0.0916178	−	0.158687i
$63$	0.0791403	+	0.0323159i	0.00997074	+	0.00407143i
$64$			1.00000i			0.125000i
$65$	7.61257	−	9.80688i	0.944223	−	1.21639i
$66$	3.35025	+	6.75082i	0.412388	+	0.830969i
$67$	−0.668189	−	0.668189i	−0.0816322	−	0.0816322i	0.665112	−	0.746744i	$-0.268384\pi$
$67$	−0.668189	−	0.668189i	−0.0816322	−	0.0816322i	−0.746744	+	0.665112i	$0.768384\pi$
$68$			6.71041i			0.813757i
$69$	−0.506305	+	0.761877i	−0.0609520	+	0.0917192i
$70$	0.0947706	−	0.0253937i	0.0113273	−	0.00303513i
$71$	−9.32969	−	2.49988i	−1.10723	−	0.296682i	−0.341525	−	0.939873i	$-0.610943\pi$
$71$	−9.32969	−	2.49988i	−1.10723	−	0.296682i	−0.765706	+	0.643191i	$0.777610\pi$
$72$	−1.13411	+	2.77737i	−0.133656	+	0.327317i
$73$	6.53713	−	6.53713i	0.765113	−	0.765113i	−0.212129	−	0.977242i	$-0.568040\pi$
$73$	6.53713	−	6.53713i	0.765113	−	0.765113i	0.977242	+	0.212129i	$0.0680396\pi$
$74$			8.10826i			0.942566i
$75$	−10.6369	+	5.27880i	−1.22824	+	0.609543i
$76$	−1.42466	+	1.42466i	−0.163420	+	0.163420i
$77$	−0.0619924	−	0.107374i	−0.00706469	−	0.0122364i
$78$	−1.98918	−	5.91973i	−0.225230	−	0.670277i
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	−0.775776	−	0.631008i	$-0.782641\pi$
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	0.934357	+	0.356338i	$0.115975\pi$
$80$	0.891175	+	3.32591i	0.0996364	+	0.371848i
$81$	−6.29967	+	6.42761i	−0.699963	+	0.714179i
$82$	−4.35155	+	2.51237i	−0.480548	+	0.277444i
$83$	−3.80210	−	14.1896i	−0.417335	−	1.55752i	−0.780112	−	0.625640i	$-0.784838\pi$
$83$	−3.80210	−	14.1896i	−0.417335	−	1.55752i	0.362777	−	0.931876i	$-0.381829\pi$
$84$	0.0157469	−	0.0467747i	0.00171813	−	0.00510353i
$85$	5.98015	+	22.3182i	0.648638	+	2.42075i
$86$	−2.26772	+	8.46324i	−0.244534	+	0.912615i
$87$	0.904943	−	14.3596i	0.0970201	−	1.53951i
$88$	3.76822	−	2.17558i	0.401693	−	0.231918i
$89$	10.8696	−	2.91249i	1.15217	−	0.308724i	0.368337	−	0.929692i	$-0.379927\pi$
$89$	10.8696	−	2.91249i	1.15217	−	0.308724i	0.783835	+	0.620969i	$0.213261\pi$
$90$	−1.29681	+	10.2480i	−0.136696	+	1.08023i
$91$	0.0387852	+	0.0951367i	0.00406579	+	0.00997303i
$92$	0.457384	+	0.264071i	0.0476856	+	0.0275313i
$93$	−1.65242	−	1.87470i	−0.171348	−	0.194398i
$94$	0.803143			0.0828379
$95$	−3.46867	+	6.00791i	−0.355878	+	0.616399i
$96$	1.64153	+	0.552626i	0.167537	+	0.0564022i
$97$	0.333814	+	0.333814i	0.0338937	+	0.0338937i	0.723851	−	0.689957i	$-0.242371\pi$
$97$	0.333814	+	0.333814i	0.0338937	+	0.0338937i	−0.689957	+	0.723851i	$0.742371\pi$
$98$	1.81152	−	6.76070i	0.182991	−	0.682933i
$99$	12.9331	−	1.76884i	1.29982	−	0.177776i
$100$	3.42793	+	5.93735i	0.342793	+	0.593735i
$101$	−2.74544	−	4.75523i	−0.273181	−	0.473163i	0.696494	−	0.717563i	$-0.254742\pi$
$101$	−2.74544	−	4.75523i	−0.273181	−	0.473163i	−0.969675	+	0.244400i	$0.921409\pi$
$102$	11.0153	+	3.70835i	1.09068	+	0.367181i
$103$	3.62390	−	2.09226i	0.357073	−	0.206156i	−0.310723	−	0.950501i	$-0.600571\pi$
$103$	3.62390	−	2.09226i	0.357073	−	0.206156i	0.667796	+	0.744344i	$0.267238\pi$
$104$	−3.33876	+	1.36114i	−0.327392	+	0.133471i
$105$	0.0106883	−	0.169602i	0.00104307	−	0.0165514i
$106$	−1.31109	+	4.89306i	−0.127344	+	0.475256i
$107$	−2.85234	−	1.64680i	−0.275746	−	0.159202i	0.355750	−	0.934581i	$-0.384226\pi$
$107$	−2.85234	−	1.64680i	−0.275746	−	0.159202i	−0.631496	+	0.775379i	$0.717559\pi$
$108$	3.93239	+	3.39651i	0.378395	+	0.326830i
$109$	−5.40316	−	5.40316i	−0.517529	−	0.517529i	0.399294	−	0.916823i	$-0.369255\pi$
$109$	−5.40316	−	5.40316i	−0.517529	−	0.517529i	−0.916823	+	0.399294i	$0.869255\pi$
$110$	10.5939	−	10.5939i	1.01009	−	1.01009i
$111$	13.3099	+	4.48084i	1.26332	+	0.425302i
$112$	−0.0275237	−	0.00737496i	−0.00260075	−	0.000696868i
$113$	0.503942	+	0.290951i	0.0474068	+	0.0273704i	0.523516	−	0.852016i	$-0.324620\pi$
$113$	0.503942	+	0.290951i	0.0474068	+	0.0273704i	−0.476109	+	0.879386i	$0.657953\pi$
$114$	1.55131	+	3.12592i	0.145294	+	0.292769i
$115$	1.75655	+	0.470666i	0.163799	+	0.0438899i
$116$	−8.30696			−0.771282
$117$	−10.8167	−	0.00610869i	−1.00000	−	0.000564749i
$118$	−14.3089			−1.31725
$119$	−0.184695	−	0.0494890i	−0.0169310	−	0.00453665i
$120$	5.95205	+	0.375099i	0.543345	+	0.0342417i
$121$	−6.86984	−	3.96631i	−0.624531	−	0.360573i
$122$	0.0207611	+	0.00556292i	0.00187962	+	0.000503644i
$123$	1.71933	+	8.53157i	0.155027	+	0.769266i
$124$	−1.02021	+	1.02021i	−0.0916178	+	0.0916178i
$125$	4.51854	+	4.51854i	0.404150	+	0.404150i
$126$	−0.0680796	−	0.0516978i	−0.00606502	−	0.00460561i
$127$	8.56275	+	4.94371i	0.759822	+	0.438683i	0.829232	−	0.558905i	$-0.188778\pi$
$127$	8.56275	+	4.94371i	0.759822	+	0.438683i	−0.0694101	+	0.997588i	$0.522112\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	12.6394	+	8.39952i	1.11284	+	0.739537i
$130$	−9.89139	+	7.50244i	−0.867532	+	0.658008i
$131$	−15.6965	+	9.06236i	−1.37141	+	0.791782i	−0.991105	−	0.133081i	$-0.957513\pi$
$131$	−15.6965	+	9.06236i	−1.37141	+	0.791782i	−0.380301	+	0.924863i	$0.624180\pi$
$132$	−1.48886	−	7.38791i	−0.129588	−	0.643035i
$133$	−0.0287051	−	0.0497187i	−0.00248905	−	0.00431116i
$134$	0.472481	+	0.818361i	0.0408161	+	0.0706956i
$135$	16.1057	+	7.79204i	1.38615	+	0.670632i
$136$	1.73678	−	6.48176i	0.148928	−	0.555806i
$137$	11.8200	+	11.8200i	1.00985	+	1.00985i	0.999951	+	0.00990200i	$0.00315196\pi$
$137$	11.8200	+	11.8200i	1.00985	+	1.00985i	0.00990200	+	0.999951i	$0.496848\pi$
$138$	0.686241	−	0.604875i	0.0584167	−	0.0514904i
$139$	−2.54241	+	4.40359i	−0.215645	+	0.373508i	−0.953472	−	0.301482i	$-0.902519\pi$
$139$	−2.54241	+	4.40359i	−0.215645	+	0.373508i	0.737827	+	0.674990i	$0.235852\pi$
$140$	−0.0981137			−0.00829212
$141$	0.443838	−	1.31838i	0.0373779	−	0.111028i
$142$	8.36477	+	4.82940i	0.701956	+	0.405275i
$143$	12.3928	+	9.61989i	1.03634	+	0.804456i
$144$	1.81430	−	2.38921i	0.151192	−	0.199101i
$145$	−27.6282	+	7.40295i	−2.29440	+	0.614782i
$146$	−8.00631	+	4.62245i	−0.662607	+	0.382557i
$147$	−10.0968	−	6.70980i	−0.832767	−	0.553415i
$148$	2.09857	−	7.83198i	0.172502	−	0.643785i
$149$	−1.36845	−	5.10712i	−0.112108	−	0.418392i	0.886947	−	0.461872i	$-0.152822\pi$
$149$	−1.36845	−	5.10712i	−0.112108	−	0.418392i	−0.999054	+	0.0434804i	$0.986155\pi$
$150$	11.6407	−	2.34590i	0.950457	−	0.191542i
$151$	−2.52008	−	9.40508i	−0.205082	−	0.765375i	−0.989425	−	0.145047i	$-0.953667\pi$
$151$	−2.52008	−	9.40508i	−0.205082	−	0.765375i	0.784343	−	0.620327i	$-0.213000\pi$
$152$	1.74484	−	1.00739i	0.141526	−	0.0817098i
$153$	12.1747	−	16.0326i	0.984266	−	1.29616i
$154$	0.0320896	+	0.119760i	0.00258586	+	0.00965055i
$155$	−2.48395	+	4.30232i	−0.199515	+	0.345571i
$156$	0.389261	+	6.23285i	0.0311659	+	0.499028i
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	0.991651	−	0.128952i	$-0.0411612\pi$
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	−0.607501	+	0.794319i	$0.707828\pi$
$158$	−1.99333	+	1.99333i	−0.158581	+	0.158581i
$159$	7.30753	+	4.85622i	0.579525	+	0.385123i
$160$		−	3.44323i		−	0.272212i
$161$	−0.0106414	+	0.0106414i	−0.000838659	+	0.000838659i
$162$	7.74860	−	4.57812i	0.608788	−	0.359691i
$163$	10.7066	+	2.86883i	0.838607	+	0.224704i	0.652465	−	0.757819i	$-0.273735\pi$
$163$	10.7066	+	2.86883i	0.838607	+	0.224704i	0.186142	+	0.982523i	$0.440402\pi$
$164$	4.85352	−	1.30050i	0.378996	−	0.101552i
$165$	−11.5357	−	23.2447i	−0.898054	−	1.80960i
$166$			14.6902i			1.14018i
$167$	−10.5531	−	10.5531i	−0.816620	−	0.816620i	0.168997	−	0.985617i	$-0.445947\pi$
$167$	−10.5531	−	10.5531i	−0.816620	−	0.816620i	−0.985617	+	0.168997i	$0.945947\pi$
$168$	−0.0273165	+	0.0411053i	−0.00210751	+	0.00317134i
$169$	−9.08903	−	9.29459i	−0.699156	−	0.714969i
$170$		−	23.1055i		−	1.77211i
$171$	5.98857	−	0.819050i	0.457957	−	0.0626343i
$172$	4.38090	−	7.58793i	0.334040	−	0.578574i
$173$	−19.0603			−1.44912			−0.724562	−	0.689210i	$-0.757958\pi$
$173$	−19.0603			−1.44912			−0.724562	+	0.689210i	$0.757958\pi$
$174$	−4.59064	+	13.6361i	−0.348016	+	1.03375i
$175$	−0.188699	+	0.0505617i	−0.0142643	+	0.00382211i
$176$	−4.20290	+	1.12616i	−0.316805	+	0.0848878i
$177$	−7.90750	+	23.4885i	−0.594364	+	1.76550i
$178$	−11.2530			−0.843449
$179$	−12.0533	+	20.8769i	−0.900906	+	1.56041i	−0.0745856	+	0.997215i	$0.523763\pi$
$179$	−12.0533	+	20.8769i	−0.900906	+	1.56041i	−0.826320	+	0.563200i	$0.809570\pi$
$180$	3.90499	−	9.56315i	0.291061	−	0.712795i
$181$			1.16505i			0.0865977i	0.999062	+	0.0432988i	$0.0137868\pi$
$181$			1.16505i			0.0865977i	−0.999062	+	0.0432988i	$0.986213\pi$
$182$	−0.0128404	−	0.101933i	−0.000951797	−	0.00755580i
$183$	0.0206048	−	0.0310057i	0.00152315	−	0.00229201i
$184$	−0.373453	−	0.373453i	−0.0275313	−	0.0275313i
$185$		−	27.9187i		−	2.05262i
$186$	1.11091	+	2.23850i	0.0814558	+	0.164135i
$187$	−28.2032	+	7.55702i	−2.06242	+	0.552624i
$188$	−0.775777	−	0.207869i	−0.0565793	−	0.0151604i
$189$	−0.122486	+	0.0831849i	−0.00890953	+	0.00605081i
$190$	4.90544	−	4.90544i	0.355878	−	0.355878i
$191$		−	11.5646i		−	0.836783i	−0.908267	−	0.418392i	$-0.862594\pi$
$191$		−	11.5646i		−	0.836783i	0.908267	−	0.418392i	$-0.137406\pi$
$192$	−1.44256	−	0.958654i	−0.104108	−	0.0691849i
$193$	−1.01826	+	1.01826i	−0.0732962	+	0.0732962i	−0.742805	−	0.669508i	$-0.766505\pi$
$193$	−1.01826	+	1.01826i	−0.0732962	+	0.0732962i	0.669508	+	0.742805i	$0.266505\pi$
$194$	−0.236042	−	0.408837i	−0.0169468	−	0.0293528i
$195$	6.84921	+	20.3830i	0.490482	+	1.45966i
$196$	−3.49959	+	6.06147i	−0.249971	+	0.432962i
$197$	−1.07594	−	4.01546i	−0.0766575	−	0.286090i	0.916947	−	0.399010i	$-0.130646\pi$
$197$	−1.07594	−	4.01546i	−0.0766575	−	0.286090i	−0.993604	+	0.112920i	$0.963980\pi$
$198$	−12.9502	−	1.63876i	−0.920331	−	0.116461i
$199$	1.78437	−	1.03021i	0.126491	−	0.0730295i	−0.435419	−	0.900228i	$-0.643400\pi$
$199$	1.78437	−	1.03021i	0.126491	−	0.0730295i	0.561910	+	0.827198i	$0.310067\pi$
$200$	−1.77443	−	6.62226i	−0.125471	−	0.468264i
$201$	1.60446	−	0.323341i	0.113170	−	0.0228068i
$202$	1.42114	+	5.30377i	0.0999912	+	0.373172i
$203$	0.0612635	−	0.228638i	0.00429985	−	0.0160473i
$204$	−9.68018	−	6.43296i	−0.677748	−	0.450397i
$205$	14.9834	−	8.65067i	1.04649	−	0.604189i
$206$	−4.04193	+	1.08303i	−0.281615	+	0.0754585i
$207$	−0.613682	−	1.46075i	−0.0426539	−	0.101529i
$208$	3.57728	−	0.450627i	0.248040	−	0.0312453i
$209$	−7.59210	−	4.38330i	−0.525157	−	0.303199i
$210$	−0.0542202	+	0.161056i	−0.00374155	+	0.0111139i
$211$	19.1496			1.31831			0.659157	−	0.752005i	$-0.270913\pi$
$211$	19.1496			1.31831			0.659157	+	0.752005i	$0.270913\pi$
$212$	2.53283	−	4.38699i	0.173956	−	0.301300i
$213$	12.5502	−	11.0621i	0.859924	−	0.757965i
$214$	2.32893	+	2.32893i	0.159202	+	0.159202i
$215$	7.80829	−	29.1409i	0.532521	−	1.98739i
$216$	−2.91932	−	4.29856i	−0.198634	−	0.292480i
$217$	−0.0205560	−	0.0356041i	−0.00139543	−	0.00241696i
$218$	3.82061	+	6.61749i	0.258764	+	0.448193i
$219$	3.16337	+	15.6971i	0.213760	+	1.06071i
$220$	−12.9749	+	7.49104i	−0.874765	+	0.505046i
$221$	24.0050	−	3.02389i	1.61475	−	0.203409i
$222$	−11.6967	−	7.77302i	−0.785029	−	0.521691i
$223$	6.83797	−	25.5197i	0.457905	−	1.70892i	−0.221501	−	0.975160i	$-0.571096\pi$
$223$	6.83797	−	25.5197i	0.457905	−	1.70892i	0.679406	−	0.733763i	$-0.262238\pi$
$224$	0.0246771	+	0.0142473i	0.00164881	+	0.000951939i
$225$	2.58209	−	20.4049i	0.172139	−	1.36032i
$226$	−0.411467	−	0.411467i	−0.0273704	−	0.0273704i
$227$	−3.63037	+	3.63037i	−0.240956	+	0.240956i	−0.817246	−	0.576289i	$-0.804500\pi$
$227$	−3.63037	+	3.63037i	−0.240956	+	0.240956i	0.576289	+	0.817246i	$0.304500\pi$
$228$	−0.689403	−	3.42091i	−0.0456569	−	0.226556i
$229$	−7.67020	−	2.05522i	−0.506861	−	0.135813i	−0.00367870	−	0.999993i	$-0.501171\pi$
$229$	−7.67020	−	2.05522i	−0.506861	−	0.135813i	−0.503182	+	0.864180i	$0.667838\pi$
$230$	−1.57488	−	0.909258i	−0.103845	−	0.0599547i
$231$	0.214323	+	0.0135066i	0.0141014	+	0.000888672i
$232$	8.02391	+	2.15000i	0.526795	+	0.141154i
$233$	−0.240333			−0.0157448			−0.00787238	−	0.999969i	$-0.502506\pi$
$233$	−0.240333			−0.0157448			−0.00787238	+	0.999969i	$0.502506\pi$
$234$	10.4465	+	2.80546i	0.682909	+	0.183398i
$235$	−2.76541			−0.180395
$236$	13.8214	+	3.70343i	0.899695	+	0.241073i
$237$	2.17054	+	4.37367i	0.140991	+	0.284100i
$238$	0.165593	+	0.0956054i	0.0107338	+	0.00619718i
$239$	−6.49603	−	1.74060i	−0.420193	−	0.112590i	0.0425261	−	0.999095i	$-0.486459\pi$
$239$	−6.49603	−	1.74060i	−0.420193	−	0.112590i	−0.462719	+	0.886505i	$0.653126\pi$
$240$	−5.65216	−	1.90282i	−0.364845	−	0.122827i
$241$	−18.3499	+	18.3499i	−1.18202	+	1.18202i	−0.202800	+	0.979220i	$0.565004\pi$
$241$	−18.3499	+	18.3499i	−1.18202	+	1.18202i	−0.979220	+	0.202800i	$0.934996\pi$
$242$	5.60920	+	5.60920i	0.360573	+	0.360573i
$243$	−3.23301	−	15.2495i	−0.207398	−	0.978257i
$244$	−0.0186139	−	0.0107467i	−0.00119163	−	0.000687990i
$245$	−6.23750	+	23.2787i	−0.398499	+	1.48722i
$246$	0.547384	−	8.68586i	0.0348999	−	0.553790i
$247$	5.73840	+	4.45442i	0.365125	+	0.283428i
$248$	1.24950	−	0.721399i	0.0793434	−	0.0458089i
$249$	24.1143	+	8.11819i	1.52818	+	0.514469i
$250$	−3.19509	−	5.53406i	−0.202075	−	0.350005i
$251$	10.2804	+	17.8061i	0.648892	+	1.12391i	0.983388	+	0.181517i	$0.0581007\pi$
$251$	10.2804	+	17.8061i	0.648892	+	1.12391i	−0.334496	+	0.942397i	$0.608566\pi$
$252$	0.0523795	+	0.0675565i	0.00329960	+	0.00425566i
$253$	−0.594774	+	2.21973i	−0.0373931	+	0.139553i
$254$	−6.99146	−	6.99146i	−0.438683	−	0.438683i
$255$	−37.9283	−	12.7687i	−2.37516	−	0.799608i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.4381			0.963002			0.481501	−	0.876446i	$-0.340092\pi$
$257$	15.4381			0.963002			0.481501	+	0.876446i	$0.340092\pi$
$258$	−10.0348	−	11.3846i	−0.624738	−	0.708777i
$259$	0.200088	+	0.115521i	0.0124329	+	0.00717813i
$260$	11.4961	−	4.68673i	0.712959	−	0.290658i
$261$	19.8471	+	15.0713i	1.22850	+	0.932891i
$262$	17.5071	−	4.69102i	1.08159	−	0.289812i
$263$	−10.9321	+	6.31167i	−0.674104	+	0.389194i	−0.797630	−	0.603147i	$-0.793913\pi$
$263$	−10.9321	+	6.31167i	−0.674104	+	0.389194i	0.123526	+	0.992341i	$0.460580\pi$
$264$	−0.474007	+	7.52151i	−0.0291731	+	0.462917i
$265$	4.51439	−	16.8479i	0.277317	−	1.03496i
$266$	0.0148589	+	0.0554540i	0.000911055	+	0.00340010i
$267$	−6.21871	+	18.4721i	−0.380579	+	1.13047i
$268$	−0.244574	−	0.912763i	−0.0149397	−	0.0557559i
$269$	−13.5676	+	7.83325i	−0.827230	+	0.477602i	−0.852903	−	0.522069i	$-0.825160\pi$
$269$	−13.5676	+	7.83325i	−0.827230	+	0.477602i	0.0256732	+	0.999670i	$0.491827\pi$
$270$	−13.5401	−	11.6950i	−0.824027	−	0.711734i
$271$	−4.43051	−	16.5349i	−0.269134	−	1.00442i	−0.959671	−	0.281126i	$-0.909292\pi$
$271$	−4.43051	−	16.5349i	−0.269134	−	1.00442i	0.690537	−	0.723297i	$-0.257374\pi$
$272$	−3.35521	+	5.81139i	−0.203439	+	0.352367i
$273$	−0.174422	−	0.0352531i	−0.0105565	−	0.00213362i
$274$	−8.35802	−	14.4765i	−0.504926	−	0.874558i
$275$	−21.0937	+	21.0937i	−1.27200	+	1.27200i
$276$	−0.819411	+	0.406652i	−0.0493228	+	0.0244776i
$277$			19.5532i			1.17484i	0.809284	+	0.587418i	$0.199856\pi$
$277$			19.5532i			1.17484i	−0.809284	+	0.587418i	$0.800144\pi$
$278$	3.59552	−	3.59552i	0.215645	−	0.215645i
$279$	4.28847	−	0.586530i	0.256744	−	0.0351146i
$280$	0.0947706	+	0.0253937i	0.00566363	+	0.00151756i
$281$	29.5609	−	7.92083i	1.76346	−	0.472517i	0.776044	−	0.630679i	$-0.217223\pi$
$281$	29.5609	−	7.92083i	1.76346	−	0.472517i	0.987413	+	0.158162i	$0.0505568\pi$
$282$	−0.769936	+	1.15858i	−0.0458490	+	0.0689926i
$283$		−	23.6188i		−	1.40399i	−0.712182	−	0.701995i	$-0.752293\pi$
$283$		−	23.6188i		−	1.40399i	0.712182	−	0.701995i	$-0.247707\pi$
$284$	−6.82981	−	6.82981i	−0.405275	−	0.405275i
$285$	−5.34153	−	10.7633i	−0.316405	−	0.637561i
$286$	−9.48072	−	12.4996i	−0.560607	−	0.739116i
$287$			0.143178i			0.00845153i
$288$	−2.37085	+	1.83822i	−0.139704	+	0.108318i
$289$	−14.0148	+	24.2744i	−0.824401	+	1.42790i
$290$	28.6028			1.67962
$291$	−0.801559	+	0.161535i	−0.0469882	+	0.00946935i
$292$	8.92988	−	2.39276i	0.522582	−	0.140025i
$293$	−21.3337	+	5.71634i	−1.24633	+	0.333952i	−0.820917	−	0.571048i	$-0.806537\pi$
$293$	−21.3337	+	5.71634i	−1.24633	+	0.333952i	−0.425411	+	0.905000i	$0.639870\pi$
$294$	8.01610	+	9.09440i	0.467508	+	0.530396i
$295$	49.2691			2.86856
$296$	−4.05413	+	7.02196i	−0.235642	+	0.408143i
$297$	−9.84668	+	20.3525i	−0.571363	+	1.18097i
$298$			5.28728i			0.306284i
$299$	0.738546	−	1.75519i	0.0427112	−	0.101505i
$300$	−11.8512	−	0.746864i	−0.684229	−	0.0431202i
$301$	0.176539	+	0.176539i	0.0101755	+	0.0101755i
$302$			9.73686i			0.560293i
$303$	9.49164	+	0.598164i	0.545280	+	0.0343636i
$304$	−1.94612	+	0.521462i	−0.111618	+	0.0299079i
$305$	−0.0714854	−	0.0191545i	−0.00409324	−	0.00109678i
$306$	−15.9094	+	12.3352i	−0.909479	+	0.705158i
$307$	2.99786	−	2.99786i	0.171097	−	0.171097i	−0.616364	−	0.787461i	$-0.711395\pi$
$307$	2.99786	−	2.99786i	0.171097	−	0.171097i	0.787461	+	0.616364i	$0.211395\pi$
$308$		−	0.123985i		−	0.00706469i
$309$	−0.455853	+	7.23345i	−0.0259326	+	0.411497i
$310$	3.51283	−	3.51283i	0.199515	−	0.199515i
$311$	15.1300	+	26.2059i	0.857943	+	1.48600i	0.873888	+	0.486128i	$0.161591\pi$
$311$	15.1300	+	26.2059i	0.857943	+	1.48600i	−0.0159450	+	0.999873i	$0.505076\pi$
$312$	1.23718	−	6.12122i	0.0700417	−	0.346546i
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.191710	+	0.981452i	$0.561403\pi$
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.754107	+	0.656751i	$0.771930\pi$
$314$	−2.49159	−	9.29875i	−0.140609	−	0.524759i
$315$	0.234414	+	0.178008i	0.0132077	+	0.0100296i
$316$	2.44132	−	1.40950i	0.137335	−	0.0792905i
$317$	2.88814	+	10.7787i	0.162214	+	0.605392i	0.998379	+	0.0569135i	$0.0181259\pi$
$317$	2.88814	+	10.7787i	0.162214	+	0.605392i	−0.836165	+	0.548478i	$0.815207\pi$
$318$	−5.80165	−	6.58207i	−0.325340	−	0.369104i
$319$	−9.35500	−	34.9133i	−0.523779	−	1.95477i
$320$	−0.891175	+	3.32591i	−0.0498182	+	0.185924i
$321$	5.11002	−	2.53597i	0.285213	−	0.141544i
$322$	0.0130330	−	0.00752460i	0.000726300	−	0.000419330i
$323$	−13.0593	+	3.49922i	−0.726638	+	0.194702i
$324$	−8.66948	+	2.41664i	−0.481638	+	0.134258i
$325$	19.6949	−	14.9382i	1.09247	−	0.828623i
$326$	−9.59929	−	5.54215i	−0.531655	−	0.306951i
$327$	12.9741	−	2.61463i	0.717472	−	0.144589i
$328$	−5.02473			−0.277444
$329$	0.0114426	−	0.0198192i	0.000630853	−	0.00109267i
$330$	5.12648	+	25.4383i	0.282203	+	1.40033i
$331$	2.92713	+	2.92713i	0.160890	+	0.160890i	0.782961	−	0.622071i	$-0.213709\pi$
$331$	2.92713	+	2.92713i	0.160890	+	0.160890i	−0.622071	+	0.782961i	$0.713709\pi$
$332$	3.80210	−	14.1896i	0.208668	−	0.778758i
$333$	−19.2235	+	14.9048i	−1.05344	+	0.816778i
$334$	7.46214	+	12.9248i	0.408310	+	0.707213i
$335$	−1.62686	−	2.81781i	−0.0888850	−	0.153953i
$336$	0.0370245	−	0.0326346i	0.00201985	−	0.00178036i
$337$	−14.3966	+	8.31187i	−0.784232	+	0.452777i	−0.837928	−	0.545781i	$-0.816233\pi$
$337$	−14.3966	+	8.31187i	−0.784232	+	0.452777i	0.0536959	+	0.998557i	$0.482900\pi$
$338$	6.37371	+	11.3303i	0.346684	+	0.616287i
$339$	−0.902820	+	0.448046i	−0.0490345	+	0.0243345i
$340$	−5.98015	+	22.3182i	−0.324319	+	1.21038i
$341$	−5.43678	−	3.13893i	−0.294418	−	0.169982i
$342$	−5.99650	−	0.758814i	−0.324254	−	0.0410320i
$343$	−0.282066	−	0.282066i	−0.0152301	−	0.0152301i
$344$	−6.19552	+	6.19552i	−0.334040	+	0.334040i
$345$	−2.36289	+	2.08273i	−0.127214	+	0.112130i
$346$	18.4108	+	4.93316i	0.989770	+	0.265208i
$347$	−17.6269	−	10.1769i	−0.946261	−	0.546324i	−0.0543438	−	0.998522i	$-0.517307\pi$
$347$	−17.6269	−	10.1769i	−0.946261	−	0.546324i	−0.891918	+	0.452198i	$0.850640\pi$
$348$	7.96350	−	11.9833i	0.426888	−	0.642372i
$349$	18.8920	+	5.06210i	1.01127	+	0.270968i	0.726158	−	0.687527i	$-0.241304\pi$
$349$	18.8920	+	5.06210i	1.01127	+	0.270968i	0.285108	+	0.958495i	$0.407971\pi$
$350$	0.195355			0.0104422
$351$	10.3782	−	15.5978i	0.553949	−	0.832550i
$352$	4.35116			0.231918
$353$	−9.77585	−	2.61943i	−0.520316	−	0.139418i	−0.0109033	−	0.999941i	$-0.503471\pi$
$353$	−9.77585	−	2.61943i	−0.520316	−	0.139418i	−0.509413	+	0.860522i	$0.670137\pi$
$354$	13.7173	−	20.6415i	0.729068	−	1.09709i
$355$	−28.8019	−	16.6288i	−1.52864	−	0.882564i
$356$	10.8696	+	2.91249i	0.576086	+	0.154362i
$357$	0.248450	−	0.218992i	0.0131494	−	0.0115903i
$358$	17.0459	−	17.0459i	0.900906	−	0.900906i
$359$	−1.10596	−	1.10596i	−0.0583705	−	0.0583705i	0.677319	−	0.735689i	$-0.263142\pi$
$359$	−1.10596	−	1.10596i	−0.0583705	−	0.0583705i	−0.735689	+	0.677319i	$0.763142\pi$
$360$	−6.24706	+	8.22661i	−0.329249	+	0.433580i
$361$	12.9390	+	7.47034i	0.681001	+	0.393176i
$362$	0.301538	−	1.12535i	0.0158485	−	0.0591473i
$363$	12.3074	−	6.10786i	0.645973	−	0.320579i
$364$	−0.0139794	+	0.101783i	−0.000732718	+	0.00533490i
$365$	27.5676	−	15.9162i	1.44296	−	0.833091i
$366$	−0.0279276	+	0.0246163i	−0.00145980	+	0.00128671i
$367$	3.11681	+	5.39847i	0.162696	+	0.281798i	0.935835	−	0.352439i	$-0.114648\pi$
$367$	3.11681	+	5.39847i	0.162696	+	0.281798i	−0.773139	+	0.634237i	$0.781314\pi$
$368$	0.264071	+	0.457384i	0.0137656	+	0.0238428i
$369$	−13.9556	−	5.69858i	−0.726498	−	0.296656i
$370$	−7.22588	+	26.9673i	−0.375656	+	1.40197i
$371$	0.102067	+	0.102067i	0.00529904	+	0.00529904i
$372$	−0.493689	−	2.44975i	−0.0255966	−	0.127014i
$373$	10.5545	−	18.2810i	0.546493	−	0.946554i	−0.452018	−	0.892009i	$-0.649296\pi$
$373$	10.5545	−	18.2810i	0.546493	−	0.946554i	0.998511	−	0.0545455i	$-0.0173710\pi$
$374$	29.1981			1.50980
$375$	−10.8500	+	2.18655i	−0.560291	+	0.112913i
$376$	0.695542	+	0.401572i	0.0358699	+	0.0207095i
$377$	3.74334	+	29.7163i	0.192792	+	1.53047i
$378$	0.139842	−	0.0486488i	0.00719270	−	0.00250222i
$379$	1.28885	−	0.345346i	0.0662038	−	0.0177393i	−0.225565	−	0.974228i	$-0.572423\pi$
$379$	1.28885	−	0.345346i	0.0662038	−	0.0177393i	0.291769	+	0.956489i	$0.405756\pi$
$380$	−6.00791	+	3.46867i	−0.308199	+	0.177939i
$381$	−15.3403	+	7.61299i	−0.785908	+	0.390025i
$382$	−2.99313	+	11.1705i	−0.153142	+	0.571534i
$383$	6.69236	+	24.9762i	0.341963	+	1.27622i	0.896120	+	0.443812i	$0.146374\pi$
$383$	6.69236	+	24.9762i	0.341963	+	1.27622i	−0.554156	+	0.832413i	$0.686959\pi$
$384$	1.14529	+	1.29935i	0.0584453	+	0.0663072i
$385$	−0.110492	−	0.412362i	−0.00563120	−	0.0210159i
$386$	1.24711	−	0.720021i	0.0634764	−	0.0366481i
$387$	−24.2337	+	10.1809i	−1.23187	+	0.517524i
$388$	0.122184	+	0.455998i	0.00620297	+	0.0231498i
$389$	7.30331	−	12.6497i	0.370292	−	0.641365i	−0.619318	−	0.785140i	$-0.712591\pi$
$389$	7.30331	−	12.6497i	0.370292	−	0.641365i	0.989610	+	0.143775i	$0.0459242\pi$
$390$	−1.34032	−	21.4612i	−0.0678697	−	1.08673i
$391$	1.77202	+	3.06924i	0.0896151	+	0.155218i
$392$	4.94917	−	4.94917i	0.249971	−	0.249971i
$393$	1.97447	−	31.3308i	0.0995988	−	1.58043i
$394$			4.15711i			0.209432i
$395$	6.86351	−	6.86351i	0.345341	−	0.345341i
$396$	12.0848	+	4.93468i	0.607284	+	0.247977i
$397$	2.88194	+	0.772213i	0.144640	+	0.0387563i	0.330413	−	0.943837i	$-0.392812\pi$
$397$	2.88194	+	0.772213i	0.144640	+	0.0387563i	−0.185772	+	0.982593i	$0.559479\pi$
$398$	−1.99021	+	0.533275i	−0.0997601	+	0.0267307i
$399$	0.0992406	+	0.00625415i	0.00496824	+	0.000313099i
$400$			6.85587i			0.342793i
$401$	−7.83107	−	7.83107i	−0.391065	−	0.391065i	0.484002	−	0.875067i	$-0.339183\pi$
$401$	−7.83107	−	7.83107i	−0.391065	−	0.391065i	−0.875067	+	0.484002i	$0.839183\pi$
$402$	−1.63348	−	0.102942i	−0.0814706	−	0.00513429i
$403$	4.10932	+	3.18985i	0.204700	+	0.158898i
$404$		−	5.49087i		−	0.273181i
$405$	−26.6803	+	15.7635i	−1.32575	+	0.783296i
$406$	−0.118352	+	0.204992i	−0.00587371	+	0.0101736i
$407$	35.2804			1.74878
$408$	7.68536	+	8.71918i	0.380482	+	0.431664i
$409$	−14.1786	+	3.79916i	−0.701089	+	0.187856i	−0.591718	−	0.806145i	$-0.701550\pi$
$409$	−14.1786	+	3.79916i	−0.701089	+	0.187856i	−0.109371	+	0.994001i	$0.534884\pi$
$410$	−16.7118	+	4.47792i	−0.825337	+	0.221148i
$411$	−28.3824	+	5.71980i	−1.40000	+	0.282137i
$412$	4.18452			0.206156
$413$	−0.203864	+	0.353103i	−0.0100315	+	0.0173751i
$414$	0.214701	+	1.56981i	0.0105520	+	0.0771520i
$415$		−	50.5818i		−	2.48296i
$416$	−3.57202	−	0.490596i	−0.175133	−	0.0240535i
$417$	−3.91515	−	7.88911i	−0.191726	−	0.386331i
$418$	6.19893	+	6.19893i	0.303199	+	0.303199i
$419$		−	28.1641i		−	1.37591i	−0.725755	−	0.687953i	$-0.758509\pi$
$419$		−	28.1641i		−	1.37591i	0.725755	−	0.687953i	$-0.241491\pi$
$420$	0.0940571	−	0.141535i	0.00458952	−	0.00690620i
$421$	7.03106	−	1.88397i	0.342673	−	0.0918189i	−0.0833784	−	0.996518i	$-0.526571\pi$
$421$	7.03106	−	1.88397i	0.342673	−	0.0918189i	0.426051	+	0.904699i	$0.359904\pi$
$422$	−18.4971	−	4.95629i	−0.900425	−	0.241268i
$423$	1.47636	+	1.90413i	0.0717829	+	0.0925821i
$424$	−3.58197	+	3.58197i	−0.173956	+	0.173956i
$425$			46.0057i			2.23160i
$426$	−14.9856	+	7.43697i	−0.726056	+	0.360322i
$427$	0.000433067	0	0.000433067i	2.09576e−5	0	2.09576e-5i
$428$	−1.64680	−	2.85234i	−0.0796011	−	0.137873i
$429$	−25.7577	+	8.65524i	−1.24359	+	0.417879i
$430$	−15.0845	+	26.1270i	−0.727437	+	1.25996i
$431$	−4.90556	−	18.3078i	−0.236292	−	0.881855i	−0.977562	−	0.210648i	$-0.932443\pi$
$431$	−4.90556	−	18.3078i	−0.236292	−	0.881855i	0.741270	−	0.671207i	$-0.234224\pi$
$432$	1.70729	+	4.90766i	0.0821423	+	0.236120i
$433$	27.2951	−	15.7588i	1.31172	−	0.757322i	0.329339	−	0.944212i	$-0.393174\pi$
$433$	27.2951	−	15.7588i	1.31172	−	0.757322i	0.982381	+	0.186890i	$0.0598407\pi$
$434$	0.0106406	+	0.0397112i	0.000510764	+	0.00190620i
$435$	15.8067	−	46.9522i	0.757872	−	2.25119i
$436$	−1.97769	−	7.38085i	−0.0947143	−	0.353479i
$437$	−0.275406	+	1.02783i	−0.0131744	+	0.0491677i
$438$	1.00712	−	15.9809i	0.0481220	−	0.763598i
$439$	11.1606	−	6.44360i	0.532668	−	0.307536i	−0.209434	−	0.977823i	$-0.567162\pi$
$439$	11.1606	−	6.44360i	0.532668	−	0.307536i	0.742102	+	0.670287i	$0.233829\pi$
$440$	14.4716	−	3.87765i	0.689905	−	0.184860i
$441$	19.3586	−	8.13282i	0.921838	−	0.387277i
$442$	−23.9697	−	3.29210i	−1.14012	−	0.156589i
$443$	−10.9018	−	6.29415i	−0.517959	−	0.299044i	0.218140	−	0.975917i	$-0.430001\pi$
$443$	−10.9018	−	6.29415i	−0.517959	−	0.299044i	−0.736099	+	0.676874i	$0.763334\pi$
$444$	9.28631	+	10.5355i	0.440709	+	0.499992i
$445$	38.7467			1.83677
$446$	−13.2099	+	22.8803i	−0.625509	+	1.08341i
$447$	8.67920	+	2.92189i	0.410512	+	0.138201i
$448$	−0.0201488	−	0.0201488i	−0.000951939	−	0.000951939i
$449$	−1.16977	+	4.36565i	−0.0552050	+	0.206028i	−0.988020	−	0.154329i	$-0.950678\pi$
$449$	−1.16977	+	4.36565i	−0.0552050	+	0.206028i	0.932814	+	0.360357i	$0.117345\pi$
$450$	−7.77528	+	19.0413i	−0.366530	+	0.897615i
$451$	10.9317	+	18.9343i	0.514754	+	0.891581i
$452$	0.290951	+	0.503942i	0.0136852	+	0.0237034i
$453$	15.9833	+	5.38084i	0.750961	+	0.252814i
$454$	4.44628	−	2.56706i	0.208674	−	0.120478i
$455$	0.0442127	+	0.350980i	0.00207272	+	0.0164542i
$456$	−0.219485	+	3.48278i	−0.0102783	+	0.163096i
$457$	2.63241	−	9.82430i	0.123139	−	0.459562i	−0.876627	−	0.481170i	$-0.840212\pi$
$457$	2.63241	−	9.82430i	0.123139	−	0.459562i	0.999767	+	0.0216084i	$0.00687869\pi$
$458$	6.87691	+	3.97039i	0.321337	+	0.185524i
$459$	11.4567	+	32.9324i	0.534751	+	1.53715i
$460$	1.28588	+	1.28588i	0.0599547	+	0.0599547i
$461$	−19.2384	+	19.2384i	−0.896021	+	0.896021i	−0.995081	−	0.0990604i	$-0.968416\pi$
$461$	−19.2384	+	19.2384i	−0.896021	+	0.896021i	0.0990604	+	0.995081i	$0.468416\pi$
$462$	−0.203524	−	0.0685172i	−0.00946880	−	0.00318771i
$463$	11.4472	+	3.06727i	0.531996	+	0.142548i	0.514810	−	0.857304i	$-0.327862\pi$
$463$	11.4472	+	3.06727i	0.531996	+	0.142548i	0.0171864	+	0.999852i	$0.494529\pi$
$464$	−7.19404	−	4.15348i	−0.333975	−	0.192821i
$465$	−3.82512	−	7.70769i	−0.177386	−	0.357435i
$466$	0.232144	+	0.0622029i	0.0107539	+	0.00288149i
$467$	−0.615879			−0.0284995			−0.0142497	−	0.999898i	$-0.504536\pi$
$467$	−0.615879			−0.0284995			−0.0142497	+	0.999898i	$0.504536\pi$
$468$	−9.36444	−	5.41362i	−0.432871	−	0.250245i
$469$	0.0269263			0.00124334
$470$	2.67118	+	0.715741i	0.123212	+	0.0330147i
$471$	−16.6410	−	1.04872i	−0.766779	−	0.0483225i
$472$	−12.3919	−	7.15447i	−0.570384	−	0.329311i
$473$	36.8249	+	9.86721i	1.69321	+	0.453695i
$474$	−0.964588	−	4.78642i	−0.0443050	−	0.219847i
$475$	−9.76728	+	9.76728i	−0.448153	+	0.448153i
$476$	−0.135206	−	0.135206i	−0.00619718	−	0.00619718i
$477$	−14.0108	+	5.88613i	−0.641510	+	0.269507i
$478$	5.82418	+	3.36259i	0.266392	+	0.153801i
$479$	5.18682	−	19.3575i	0.236992	−	0.884466i	−0.740249	−	0.672333i	$-0.765292\pi$
$479$	5.18682	−	19.3575i	0.236992	−	0.884466i	0.977241	−	0.212133i	$-0.0680410\pi$
$480$	4.96708	+	3.30087i	0.226715	+	0.150663i
$481$	−28.9629	−	3.97788i	−1.32059	−	0.181376i
$482$	22.4739	−	12.9753i	1.02366	−	0.591010i
$483$	−0.00514945	−	0.0255523i	−0.000234308	−	0.00116267i
$484$	−3.96631	−	6.86984i	−0.180287	−	0.312266i
$485$	0.812748	+	1.40772i	0.0369050	+	0.0639213i
$486$	−0.824012	+	15.5667i	−0.0373779	+	0.706118i
$487$	−5.47316	+	20.4261i	−0.248012	+	0.925595i	0.723833	+	0.689975i	$0.242379\pi$
$487$	−5.47316	+	20.4261i	−0.248012	+	0.925595i	−0.971845	+	0.235620i	$0.924288\pi$
$488$	0.0151982	+	0.0151982i	0.000687990	+	0.000687990i
$489$	−14.4024	+	12.6947i	−0.651299	+	0.574076i
$490$	12.0499	−	20.8711i	0.544360	−	0.942859i
$491$	−19.7513			−0.891362			−0.445681	−	0.895192i	$-0.647039\pi$
$491$	−19.7513			−0.891362			−0.445681	+	0.895192i	$0.647039\pi$
$492$	−2.77680	+	8.24823i	−0.125188	+	0.371859i
$493$	−48.2750	−	27.8716i	−2.17420	−	1.25527i
$494$	−4.38998	−	5.78784i	−0.197514	−	0.260407i
$495$	44.5906	+	5.64262i	2.00420	+	0.253617i
$496$	−1.39364	+	0.373424i	−0.0625761	+	0.0167672i
$497$	0.238351	−	0.137612i	0.0106915	−	0.00617275i
$498$	−21.1915	−	14.0828i	−0.949614	−	0.631066i
$499$	−1.37420	+	5.12859i	−0.0615177	+	0.229587i	−0.989839	−	0.142191i	$-0.954585\pi$
$499$	−1.37420	+	5.12859i	−0.0615177	+	0.229587i	0.928321	+	0.371778i	$0.121252\pi$
$500$	1.65390	+	6.17244i	0.0739647	+	0.276040i
$501$	25.3402	−	5.10670i	1.13211	−	0.228151i
$502$	−5.32152	−	19.8602i	−0.237511	−	0.886403i
$503$	−16.2322	+	9.37164i	−0.723756	+	0.417861i	−0.816134	−	0.577863i	$-0.803887\pi$
$503$	−16.2322	+	9.37164i	−0.723756	+	0.417861i	0.0923776	+	0.995724i	$0.470553\pi$
$504$	−0.0331098	−	0.0788114i	−0.00147483	−	0.00351054i
$505$	−4.89333	−	18.2621i	−0.217750	−	0.812654i
$506$	1.14901	−	1.99015i	0.0510799	−	0.0884731i
$507$	22.1213	−	4.20119i	0.982440	−	0.186581i
$508$	4.94371	+	8.56275i	0.219342	+	0.379911i
$509$	−12.0815	+	12.0815i	−0.535502	+	0.535502i	−0.922204	−	0.386703i	$-0.873614\pi$
$509$	−12.0815	+	12.0815i	−0.535502	+	0.535502i	0.386703	+	0.922204i	$0.373614\pi$
$510$	33.3311	+	22.1502i	1.47593	+	0.980827i
$511$			0.263430i			0.0116535i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.55943	+	9.42406i	−0.201304	+	0.416083i
$514$	−14.9121	−	3.99567i	−0.657743	−	0.176242i
$515$	13.9173	−	3.72914i	0.613271	−	0.164325i
$516$	6.74630	+	13.5939i	0.296989	+	0.598439i
$517$		−	3.49461i		−	0.153693i
$518$	−0.163371	−	0.163371i	−0.00717813	−	0.00717813i
$519$	18.2722	−	27.4956i	0.802060	−	1.20692i
$520$	−12.3174	+	1.55161i	−0.540154	+	0.0680427i
$521$			6.18564i			0.270998i	0.990777	+	0.135499i	$0.0432637\pi$
$521$			6.18564i			0.270998i	−0.990777	+	0.135499i	$0.956736\pi$
$522$	−15.2701	−	19.6946i	−0.668352	−	0.862008i
$523$	3.32093	−	5.75201i	0.145214	−	0.251518i	−0.784239	−	0.620459i	$-0.786946\pi$
$523$	3.32093	−	5.75201i	0.145214	−	0.251518i	0.929453	+	0.368941i	$0.120280\pi$
$524$	−18.1247			−0.791782
$525$	0.107959	−	0.320681i	0.00471170	−	0.0139957i
$526$	12.1932	−	3.26716i	0.531649	−	0.142455i
$527$	−9.35188	+	2.50583i	−0.407374	+	0.109156i
$528$	2.40457	−	7.14254i	0.104645	−	0.310839i
$529$	−22.7211			−0.987872
$530$	−8.72113	+	15.1054i	−0.378822	+	0.656139i
$531$	−26.3030	−	33.9244i	−1.14145	−	1.47219i
$532$		−	0.0574102i		−	0.00248905i
$533$	−6.83937	−	16.7764i	−0.296246	−	0.726665i
$534$	10.7877	−	16.2332i	0.466831	−	0.702477i
$535$	−8.01904	−	8.01904i	−0.346693	−	0.346693i
$536$			0.944962i			0.0408161i
$537$	−18.5613	−	37.4014i	−0.800979	−	1.61399i
$538$	15.1327	−	4.05479i	0.652416	−	0.174814i
$539$	−29.4169	−	7.88223i	−1.26708	−	0.339512i
$540$	10.0519	+	14.8009i	0.432565	+	0.636931i
$541$	4.34283	−	4.34283i	0.186713	−	0.186713i	−0.607561	−	0.794273i	$-0.707852\pi$
$541$	4.34283	−	4.34283i	0.186713	−	0.186713i	0.794273	+	0.607561i	$0.207852\pi$
$542$			17.1182i			0.735289i
$543$	−1.68066	−	1.11688i	−0.0721240	−	0.0479300i
$544$	4.74498	−	4.74498i	0.203439	−	0.203439i
$545$	−13.1553	−	22.7856i	−0.563509	−	0.976027i
$546$	0.159355	+	0.0791956i	0.00681975	+	0.00338926i
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	0.265733	+	0.964047i	$0.414386\pi$
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	−0.967755	+	0.251892i	$0.918947\pi$
$548$	4.32643	+	16.1465i	0.184816	+	0.689742i
$549$	0.0249747	+	0.0594474i	0.00106589	+	0.00253715i
$550$	25.8344	−	14.9155i	1.10158	−	0.635999i
$551$	−4.33176	−	16.1664i	−0.184539	−	0.688710i
$552$	0.896740	−	0.180716i	0.0381678	−	0.00769180i
$553$	0.0207900	+	0.0775892i	0.000884079	+	0.00329943i
$554$	5.06073	−	18.8869i	0.215010	−	0.802428i
$555$	40.2744	+	26.7643i	1.70955	+	1.13608i
$556$	−4.40359	+	2.54241i	−0.186754	+	0.107822i
$557$	−7.73861	+	2.07355i	−0.327895	+	0.0878593i	−0.419011	−	0.907981i	$-0.637623\pi$
$557$	−7.73861	+	2.07355i	−0.327895	+	0.0878593i	0.0911160	+	0.995840i	$0.470957\pi$
$558$	−4.29415	−	0.543394i	−0.181786	−	0.0230037i
$559$	−29.1183	−	12.2524i	−1.23157	−	0.518220i
$560$	−0.0849690	−	0.0490569i	−0.00359059	−	0.00207303i
$561$	16.1356	−	47.9294i	0.681247	−	2.02358i
$562$	−30.6037			−1.29094
$563$	7.44232	−	12.8905i	0.313656	−	0.543269i	−0.665495	−	0.746403i	$-0.731779\pi$
$563$	7.44232	−	12.8905i	0.313656	−	0.543269i	0.979151	+	0.203134i	$0.0651127\pi$
$564$	1.04356	−	0.919831i	0.0439420	−	0.0387319i
$565$	1.41678	+	1.41678i	0.0596042	+	0.0596042i
$566$	−6.11299	+	22.8140i	−0.256948	+	0.958943i
$567$	−0.00257777	−	0.256439i	−0.000108256	−	0.0107694i
$568$	4.82940	+	8.36477i	0.202637	+	0.350978i
$569$	−4.45227	−	7.71156i	−0.186649	−	0.323285i	0.757482	−	0.652856i	$-0.226429\pi$
$569$	−4.45227	−	7.71156i	−0.186649	−	0.323285i	−0.944131	+	0.329571i	$0.893096\pi$
$570$	2.37378	+	11.7790i	0.0994266	+	0.493369i
$571$	0.862884	−	0.498186i	0.0361106	−	0.0208484i	−0.481836	−	0.876261i	$-0.660030\pi$
$571$	0.862884	−	0.498186i	0.0361106	−	0.0208484i	0.517947	+	0.855413i	$0.326697\pi$
$572$	5.92254	+	14.5275i	0.247634	+	0.607424i
$573$	16.6826	+	11.0864i	0.696926	+	0.463142i
$574$	0.0370572	−	0.138299i	0.00154674	−	0.00577250i
$575$	3.13576	+	1.81043i	0.130770	+	0.0755003i
$576$	2.76583	−	1.16197i	0.115243	−	0.0484152i
$577$	−15.1503	−	15.1503i	−0.630713	−	0.630713i	0.317534	−	0.948247i	$-0.397145\pi$
$577$	−15.1503	−	15.1503i	−0.630713	−	0.630713i	−0.948247	+	0.317534i	$0.897145\pi$
$578$	19.8199	−	19.8199i	0.824401	−	0.824401i
$579$	−0.492745	−	2.44507i	−0.0204778	−	0.101614i
$580$	−27.6282	−	7.40295i	−1.14720	−	0.307391i
$581$	0.362511	+	0.209296i	0.0150395	+	0.00868306i
$582$	0.816055	+	0.0514279i	0.0338266	+	0.00213175i
$583$	21.2905	+	5.70477i	0.881762	+	0.236267i
$584$	−9.24490			−0.382557
$585$	−35.9698	−	9.65984i	−1.48717	−	0.399385i
$586$	22.0863			0.912375
$587$	−6.18262	−	1.65663i	−0.255184	−	0.0683763i	0.128959	−	0.991650i	$-0.458836\pi$
$587$	−6.18262	−	1.65663i	−0.255184	−	0.0683763i	−0.384143	+	0.923274i	$0.625503\pi$
$588$	−5.38915	−	10.8592i	−0.222245	−	0.447827i
$589$	−2.51746	−	1.45346i	−0.103730	−	0.0598886i
$590$	−47.5903	−	12.7518i	−1.95926	−	0.524982i
$591$	6.82400	+	2.29733i	0.280702	+	0.0944995i
$592$	5.73341	−	5.73341i	0.235642	−	0.235642i
$593$	24.4287	+	24.4287i	1.00317	+	1.00317i	0.999995	+	0.00317304i	$0.00101001\pi$
$593$	24.4287	+	24.4287i	1.00317	+	1.00317i	0.00317304	+	0.999995i	$0.498990\pi$
$594$	14.7788	−	17.1105i	0.606381	−	0.702051i
$595$	−0.570177	−	0.329192i	−0.0233750	−	0.0134955i
$596$	1.36845	−	5.10712i	0.0560538	−	0.209196i
$597$	−0.224457	+	3.56168i	−0.00918643	+	0.145770i
$598$	−1.16766	+	1.50423i	−0.0477490	+	0.0615126i
$599$	36.9806	−	21.3507i	1.51099	−	0.872368i	0.511068	−	0.859540i	$-0.329250\pi$
$599$	36.9806	−	21.3507i	1.51099	−	0.872368i	0.999918	−	0.0128274i	$-0.00408321\pi$
$600$	11.2541	+	3.78873i	0.459446	+	0.154674i
$601$	13.5165	+	23.4112i	0.551349	+	0.954965i	0.998178	+	0.0603449i	$0.0192201\pi$
$601$	13.5165	+	23.4112i	0.551349	+	0.954965i	−0.446829	+	0.894620i	$0.647447\pi$
$602$	−0.124832	−	0.216215i	−0.00508777	−	0.00881228i
$603$	−1.07169	+	2.62451i	−0.0436424	+	0.106878i
$604$	2.52008	−	9.40508i	0.102541	−	0.382687i
$605$	−19.3138	−	19.3138i	−0.785218	−	0.785218i
$606$	−9.01340	−	3.03440i	−0.366144	−	0.123264i
$607$	−23.5378	+	40.7687i	−0.955370	+	1.65475i	−0.221851	+	0.975081i	$0.571210\pi$
$607$	−23.5378	+	40.7687i	−0.955370	+	1.65475i	−0.733519	+	0.679669i	$0.762124\pi$
$608$	2.01477			0.0817098
$609$	0.271094	+	0.307561i	0.0109853	+	0.0124630i
$610$	0.0640921	+	0.0370036i	0.00259501	+	0.00149823i
$611$	−0.394019	+	2.86884i	−0.0159403	+	0.116061i
$612$	18.5599	−	7.79727i	0.750239	−	0.315186i
$613$	22.7568	−	6.09767i	0.919139	−	0.246283i	0.231922	−	0.972734i	$-0.425499\pi$
$613$	22.7568	−	6.09767i	0.919139	−	0.246283i	0.687217	+	0.726452i	$0.258832\pi$
$614$	−3.67161	+	2.11981i	−0.148174	+	0.0855484i
$615$	−1.88477	+	29.9075i	−0.0760013	+	1.20599i
$616$	−0.0320896	+	0.119760i	−0.00129293	+	0.00482527i
$617$	1.25606	+	4.68769i	0.0505672	+	0.188719i	0.986589	−	0.163222i	$-0.0521885\pi$
$617$	1.25606	+	4.68769i	0.0505672	+	0.188719i	−0.936022	+	0.351941i	$0.885522\pi$
$618$	2.31247	−	6.86899i	0.0930214	−	0.276311i
$619$	−6.61442	−	24.6854i	−0.265856	−	0.992188i	−0.961724	−	0.274019i	$-0.911647\pi$
$619$	−6.61442	−	24.6854i	−0.265856	−	0.992188i	0.695868	−	0.718170i	$-0.255020\pi$
$620$	−4.30232	+	2.48395i	−0.172785	+	0.0997577i
$621$	2.69553	+	0.515081i	0.108168	+	0.0206695i
$622$	−7.83186	−	29.2289i	−0.314029	−	1.17197i
$623$	−0.160325	+	0.277691i	−0.00642329	+	0.0111255i
$624$	−2.77932	+	5.59244i	−0.111262	+	0.223877i
$625$	−6.13822	−	10.6317i	−0.245529	−	0.425268i
$626$	23.6643	−	23.6643i	0.945817	−	0.945817i
$627$	13.6014	−	6.75000i	0.543187	−	0.269569i
$628$			9.62677i			0.384150i
$629$	38.4735	−	38.4735i	1.53404	−	1.53404i
$630$	−0.180355	−	0.232613i	−0.00718551	−	0.00926753i
$631$	18.8379	+	5.04759i	0.749924	+	0.200942i	0.613484	−	0.789707i	$-0.289767\pi$
$631$	18.8379	+	5.04759i	0.749924	+	0.200942i	0.136440	+	0.990648i	$0.456434\pi$
$632$	−2.72294	+	0.729610i	−0.108313	+	0.0290223i
$633$	−18.3579	+	27.6245i	−0.729659	+	1.09798i
$634$		−	11.1589i		−	0.443177i
$635$	24.0732	+	24.0732i	0.955317	+	0.955317i
$636$	3.90040	+	7.85937i	0.154661	+	0.311644i
$637$	23.2606	+	9.78757i	0.921619	+	0.387798i
$638$			36.1449i			1.43099i
$639$	3.92652	+	28.7092i	0.155331	+	1.13572i
$640$	1.72162	−	2.98193i	0.0680529	−	0.117871i
$641$	−22.8781			−0.903629			−0.451814	−	0.892112i	$-0.649223\pi$
$641$	−22.8781			−0.903629			−0.451814	+	0.892112i	$0.649223\pi$
$642$	−5.59225	+	1.12699i	−0.220709	+	0.0444786i
$643$	−12.7791	+	3.42415i	−0.503959	+	0.135035i	−0.501837	−	0.864962i	$-0.667342\pi$
$643$	−12.7791	+	3.42415i	−0.503959	+	0.135035i	−0.00212223	+	0.999998i	$0.500676\pi$
$644$	−0.0145364	+	0.00389502i	−0.000572815	+	0.000153485i
$645$	34.5521	+	39.2000i	1.36049	+	1.54350i
$646$	13.5200			0.531936
$647$	5.87399	−	10.1741i	0.230930	−	0.399983i	−0.727152	−	0.686477i	$-0.759156\pi$
$647$	5.87399	−	10.1741i	0.230930	−	0.399983i	0.958082	+	0.286493i	$0.0924897\pi$
$648$	8.99955	−	0.0904650i	0.353536	−	0.00355380i
$649$			62.2606i			2.44394i
$650$	−22.8901	+	9.33179i	−0.897822	+	0.366023i
$651$	0.0710671	+	0.00447866i	0.00278534	+	0.000175533i
$652$	7.83779	+	7.83779i	0.306951	+	0.306951i
$653$			9.22206i			0.360887i	0.983585	+	0.180444i	$0.0577533\pi$
$653$			9.22206i			0.360887i	−0.983585	+	0.180444i	$0.942247\pi$
$654$	−13.2088	−	0.832419i	−0.516504	−	0.0325501i
$655$	−60.2811	+	16.1523i	−2.35538	+	0.631122i
$656$	4.85352	+	1.30050i	0.189498	+	0.0507759i
$657$	−25.6765	−	10.4847i	−1.00174	−	0.409047i
$658$	−0.0161823	+	0.0161823i	−0.000630853	+	0.000630853i
$659$			4.26895i			0.166295i	0.996537	+	0.0831474i	$0.0264972\pi$
$659$			4.26895i			0.166295i	−0.996537	+	0.0831474i	$0.973503\pi$
$660$	1.63212	−	25.8983i	0.0635300	−	1.00809i
$661$	−31.5763	+	31.5763i	−1.22818	+	1.22818i	−0.263522	+	0.964654i	$0.584884\pi$
$661$	−31.5763	+	31.5763i	−1.22818	+	1.22818i	−0.964654	+	0.263522i	$0.915116\pi$
$662$	−2.06979	−	3.58499i	−0.0804448	−	0.139335i
$663$	−18.6504	+	37.5276i	−0.724320	+	1.45745i
$664$	−7.34510	+	12.7221i	−0.285045	+	0.493713i
$665$	−0.0511626	−	0.190941i	−0.00198400	−	0.00740438i
$666$	22.4261	−	9.42152i	0.868994	−	0.365077i
$667$	−3.79947	+	2.19363i	−0.147116	+	0.0849375i
$668$	−3.86269	−	14.4157i	−0.149452	−	0.557762i
$669$	30.2584	+	34.3287i	1.16986	+	1.32722i
$670$	0.842126	+	3.14286i	0.0325342	+	0.121419i
$671$	0.0242052	−	0.0903350i	0.000934431	−	0.00348734i
$672$	−0.0442094	+	0.0219400i	−0.00170541	+	0.000846352i
$673$	−4.88433	+	2.81997i	−0.188277	+	0.108702i	−0.591176	−	0.806543i	$-0.701336\pi$
$673$	−4.88433	+	2.81997i	−0.188277	+	0.108702i	0.402899	+	0.915245i	$0.368003\pi$
$674$	16.0573	−	4.30254i	0.618504	−	0.165728i
$675$	26.9599	+	23.2860i	1.03769	+	0.896280i
$676$	−3.22404	−	12.5939i	−0.124001	−	0.484380i
$677$	−21.2676	−	12.2789i	−0.817381	−	0.471915i	0.0321318	−	0.999484i	$-0.489770\pi$
$677$	−21.2676	−	12.2789i	−0.817381	−	0.471915i	−0.849512	+	0.527569i	$0.823104\pi$
$678$	0.988020	−	0.199112i	0.0379447	−	0.00764684i
$679$	−0.0134519			−0.000516235
$680$	11.5528	−	20.0100i	0.443028	−	0.767347i
$681$	−1.75676	−	8.71731i	−0.0673194	−	0.334048i
$682$	4.43911	+	4.43911i	0.169982	+	0.169982i
$683$	7.16139	−	26.7267i	0.274023	−	1.02267i	−0.682470	−	0.730913i	$-0.739094\pi$
$683$	7.16139	−	26.7267i	0.274023	−	1.02267i	0.956493	−	0.291755i	$-0.0942391\pi$
$684$	5.59578	+	2.28497i	0.213960	+	0.0873679i
$685$	28.7786	+	49.8460i	1.09957	+	1.90452i
$686$	0.199451	+	0.345459i	0.00761507	+	0.0131897i
$687$	10.3179	−	9.09449i	0.393651	−	0.346976i
$688$	7.58793	−	4.38090i	0.289287	−	0.167020i
$689$	−16.8349	−	7.08375i	−0.641357	−	0.269870i
$690$	2.82143	−	1.40020i	0.107410	−	0.0533046i
$691$	−2.04478	+	7.63123i	−0.0777871	+	0.290306i	−0.993851	−	0.110727i	$-0.964682\pi$
$691$	−2.04478	+	7.63123i	−0.0777871	+	0.290306i	0.916064	+	0.401033i	$0.131349\pi$
$692$	−16.5067	−	9.53013i	−0.627489	−	0.362281i
$693$	−0.224946	+	0.296226i	−0.00854497	+	0.0112527i
$694$	14.3923	+	14.3923i	0.546324	+	0.546324i
$695$	−12.3802	+	12.3802i	−0.469608	+	0.469608i
$696$	−10.7937	+	9.51387i	−0.409133	+	0.360622i
$697$	32.5691	+	8.72687i	1.23364	+	0.330554i
$698$	−16.9381	−	9.77922i	−0.641117	−	0.370149i
$699$	0.230397	−	0.346696i	0.00871440	−	0.0131132i
$700$	−0.188699	−	0.0505617i	−0.00713215	−	0.00191105i
$701$	39.9569			1.50915			0.754575	−	0.656214i	$-0.227843\pi$
$701$	39.9569			1.50915			0.754575	+	0.656214i	$0.227843\pi$
$702$	−14.0616	+	12.3803i	−0.530722	+	0.467263i
$703$	16.3363			0.616136
$704$	−4.20290	−	1.12616i	−0.158403	−	0.0424439i
$705$	2.65107	−	3.98927i	0.0998451	−	0.150245i
$706$	8.76479	+	5.06035i	0.329867	+	0.190449i
$707$	0.151129	+	0.0404949i	0.00568380	+	0.00152297i
$708$	−18.5923	+	16.3879i	−0.698743	+	0.615894i
$709$	−35.9885	+	35.9885i	−1.35158	+	1.35158i	−0.467680	+	0.883898i	$0.654910\pi$
$709$	−35.9885	+	35.9885i	−1.35158	+	1.35158i	−0.883898	+	0.467680i	$0.845090\pi$
$710$	23.5166	+	23.5166i	0.882564	+	0.882564i
$711$	−8.39008	−	1.06170i	−0.314653	−	0.0398170i
$712$	−9.74539	−	5.62650i	−0.365224	−	0.210862i
$713$	−0.197221	+	0.736038i	−0.00738597	+	0.0275648i
$714$	−0.296663	+	0.147226i	−0.0111023	+	0.00550980i
$715$	32.6444	+	43.0390i	1.22083	+	1.60957i
$716$	−20.8769	+	12.0533i	−0.780207	+	0.450453i
$717$	8.73837	−	7.70228i	0.326340	−	0.287647i
$718$	0.782034	+	1.35452i	0.0291853	+	0.0505504i
$719$	−0.750575	−	1.30003i	−0.0279917	−	0.0484831i	0.851690	−	0.524046i	$-0.175578\pi$
$719$	−0.750575	−	1.30003i	−0.0279917	−	0.0484831i	−0.879682	+	0.475563i	$0.842245\pi$
$720$	8.16340	−	6.32943i	0.304232	−	0.235884i
$721$	−0.0308606	+	0.115173i	−0.00114931	+	0.00428928i
$722$	−10.5647	−	10.5647i	−0.393176	−	0.393176i
$723$	−8.87965	−	44.0620i	−0.330238	−	1.63868i
$724$	−0.582526	+	1.00897i	−0.0216494	+	0.0374979i
$725$	−56.9514			−2.11512
$726$	−13.4689	+	2.71434i	−0.499878	+	0.100738i
$727$	41.9032	+	24.1928i	1.55410	+	0.897261i	0.997801	+	0.0662809i	$0.0211133\pi$
$727$	41.9032	+	24.1928i	1.55410	+	0.897261i	0.556301	+	0.830981i	$0.312220\pi$
$728$	0.0398465	−	0.0946971i	0.00147681	−	0.00350971i
$729$	25.0977	+	9.95518i	0.929544	+	0.368710i
$730$	−30.7477	+	8.23882i	−1.13802	+	0.304932i
$731$	50.9182	−	29.3976i	1.88328	−	1.08731i
$732$	0.0333471	−	0.0165493i	0.00123255	−	0.000611680i
$733$	−6.15729	+	22.9793i	−0.227425	+	0.848761i	0.753994	+	0.656882i	$0.228125\pi$
$733$	−6.15729	+	22.9793i	−0.227425	+	0.848761i	−0.981419	+	0.191879i	$0.938542\pi$
$734$	−1.61338	−	6.02121i	−0.0595509	−	0.222247i
$735$	−27.6013	−	31.3142i	−1.01809	−	1.15504i
$736$	−0.136693	−	0.510146i	−0.00503857	−	0.0188042i
$737$	3.56082	−	2.05584i	0.131164	−	0.0757279i
$738$	12.0051	+	9.11637i	0.441915	+	0.335578i
$739$	12.0076	+	44.8128i	0.441705	+	1.64847i	0.724491	+	0.689284i	$0.242075\pi$
$739$	12.0076	+	44.8128i	0.441705	+	1.64847i	−0.282786	+	0.959183i	$0.591259\pi$
$740$	13.9593	−	24.1783i	0.513155	−	0.888811i
$741$	−11.9269	+	4.00774i	−0.438146	+	0.147228i
$742$	−0.0721721	−	0.125006i	−0.00264952	−	0.00458911i
$743$	−25.5083	+	25.5083i	−0.935809	+	0.935809i	−0.998061	−	0.0622513i	$-0.980172\pi$
$743$	−25.5083	+	25.5083i	−0.935809	+	0.935809i	0.0622513	+	0.998061i	$0.480172\pi$
$744$	−0.157176	+	2.49405i	−0.00576233	+	0.0914364i
$745$		−	18.2053i		−	0.666992i
$746$	−14.9264	+	14.9264i	−0.546493	+	0.546493i
$747$	−34.8283	+	27.0039i	−1.27430	+	0.988020i
$748$	−28.2032	−	7.55702i	−1.03121	−	0.276312i
$749$	0.0906521	−	0.0242902i	0.00331236	−	0.000887543i
$750$	11.0462	+	0.696133i	0.403350	+	0.0254192i
$751$		−	17.5054i		−	0.638780i	−0.947623	−	0.319390i	$-0.896522\pi$
$751$		−	17.5054i		−	0.638780i	0.947623	−	0.319390i	$-0.103478\pi$
$752$	−0.567908	−	0.567908i	−0.0207095	−	0.0207095i
$753$	−35.5418	−	2.23985i	−1.29521	−	0.0816246i
$754$	4.07537	−	29.6726i	0.148416	−	1.08061i
$755$		−	33.5263i		−	1.22015i
$756$	−0.147668	+	0.0107973i	−0.00537064	+	0.000392694i
$757$	0.816598	−	1.41439i	0.0296798	−	0.0514068i	−0.850804	−	0.525483i	$-0.823885\pi$
$757$	0.816598	−	1.41439i	0.0296798	−	0.0514068i	0.880484	+	0.474076i	$0.157218\pi$
$758$	−1.33432			−0.0484645
$759$	−2.63191	−	2.98595i	−0.0955322	−	0.108383i
$760$	6.70095	−	1.79552i	0.243069	−	0.0651302i
$761$	17.1049	−	4.58324i	0.620051	−	0.166142i	0.0649002	−	0.997892i	$-0.479327\pi$
$761$	17.1049	−	4.58324i	0.620051	−	0.166142i	0.555151	+	0.831750i	$0.312660\pi$
$762$	16.7880	−	3.38322i	0.608165	−	0.122561i
$763$	0.217734			0.00788249
$764$	5.78229	−	10.0152i	0.209196	−	0.362338i
$765$	54.7798	−	42.4731i	1.98057	−	1.53562i
$766$		−	25.8573i		−	0.934261i
$767$	7.01992	−	51.1118i	0.253475	−	1.84554i
$768$	−0.769968	−	1.55150i	−0.0277838	−	0.0559849i
$769$	14.4842	+	14.4842i	0.522312	+	0.522312i	0.918269	−	0.395957i	$-0.129587\pi$
$769$	14.4842	+	14.4842i	0.522312	+	0.522312i	−0.395957	+	0.918269i	$0.629587\pi$
$770$			0.426909i			0.0153847i
$771$	−14.7998	+	22.2704i	−0.533001	+	0.802049i
$772$	−1.39097	+	0.372710i	−0.0500622	+	0.0134141i
$773$	8.74973	+	2.34448i	0.314706	+	0.0843252i	0.412715	−	0.910860i	$-0.364581\pi$
$773$	8.74973	+	2.34448i	0.314706	+	0.0843252i	−0.0980088	+	0.995186i	$0.531247\pi$
$774$	26.0429	−	3.56186i	0.936094	−	0.128029i
$775$	−6.99444	+	6.99444i	−0.251248	+	0.251248i
$776$		−	0.472084i		−	0.0169468i
$777$	−0.358462	+	0.177895i	−0.0128597	+	0.00638194i
$778$	−10.3284	+	10.3284i	−0.370292	+	0.370292i
$779$	5.06185	+	8.76738i	0.181360	+	0.314124i
$780$	−4.25991	+	21.0768i	−0.152529	+	0.754671i
$781$	21.0135	−	36.3965i	0.751923	−	1.30237i
$782$	−0.917267	−	3.42329i	−0.0328014	−	0.122416i
$783$	−40.7678	+	14.1824i	−1.45692	+	0.506839i
$784$	−6.06147	+	3.49959i	−0.216481	+	0.124986i
$785$	8.57914	+	32.0178i	0.306203	+	1.14276i
$786$	−10.0162	+	29.7522i	−0.357266	+	1.06122i
$787$	−4.89695	−	18.2757i	−0.174558	−	0.651458i	−0.996627	−	0.0820699i	$-0.973847\pi$
$787$	−4.89695	−	18.2757i	−0.174558	−	0.651458i	0.822069	−	0.569388i	$-0.192820\pi$
$788$	1.07594	−	4.01546i	0.0383288	−	0.143045i
$789$	1.37516	−	21.8210i	0.0489570	−	0.776847i
$790$	−8.40604	+	4.85323i	−0.299074	+	0.172670i
$791$	−0.0160161	+	0.00429150i	−0.000569467	+	0.000152588i
$792$	−10.3958	−	7.89431i	−0.369400	−	0.280512i
$793$	−0.0300562	+	0.0714299i	−0.00106733	+	0.00253655i
$794$	−2.58388	−	1.49180i	−0.0916983	−	0.0529421i
$795$	19.9764	+	22.6636i	0.708491	+	0.803796i
$796$	2.06042			0.0730295
$797$	16.8536	−	29.1913i	0.596986	−	1.03401i	−0.396277	−	0.918131i	$-0.629698\pi$
$797$	16.8536	−	29.1913i	0.596986	−	1.03401i	0.993263	−	0.115879i	$-0.0369685\pi$
$798$	−0.0942403	−	0.0317264i	−0.00333607	−	0.00112310i
$799$	−3.81090	−	3.81090i	−0.134820	−	0.134820i
$800$	1.77443	−	6.62226i	0.0627355	−	0.234132i
$801$	−20.6855	−	26.6792i	−0.730888	−	0.942663i
$802$	5.53740	+	9.59106i	0.195533	+	0.338672i
$803$	20.1130	+	34.8368i	0.709773	+	1.22936i
$804$	1.55118	+	0.522210i	0.0547058	+	0.0184169i
$805$	−0.0448757	+	0.0259090i	−0.00158166	+	0.000913171i
$806$	−3.14371	−	4.14473i	−0.110732	−	0.145992i
$807$	1.70668	−	27.0814i	0.0600778	−	0.953312i
$808$	−1.42114	+	5.30377i	−0.0499956	+	0.186586i
$809$	−9.20764	−	5.31603i	−0.323723	−	0.186902i	0.329328	−	0.944216i	$-0.393178\pi$
$809$	−9.20764	−	5.31603i	−0.323723	−	0.186902i	−0.653051	+	0.757314i	$0.726511\pi$
$810$	29.8511	−	8.32105i	1.04886	−	0.292372i
$811$	7.65216	+	7.65216i	0.268704	+	0.268704i	0.828578	−	0.559874i	$-0.189151\pi$
$811$	7.65216	+	7.65216i	0.268704	+	0.268704i	−0.559874	+	0.828578i	$0.689151\pi$
$812$	0.167375	−	0.167375i	0.00587371	−	0.00587371i
$813$	28.0999	+	9.45995i	0.985507	+	0.331775i
$814$	−34.0782	−	9.13123i	−1.19444	−	0.320049i
$815$	33.0526	+	19.0829i	1.15778	+	0.668446i
$816$	−5.16680	−	10.4112i	−0.180874	−	0.364465i
$817$	17.0515	+	4.56894i	0.596557	+	0.159847i
$818$	14.6788			0.513233
$819$	0.218065	−	0.217819i	0.00761981	−	0.00761121i
$820$	17.3013			0.604189
$821$	14.8427	+	3.97709i	0.518013	+	0.138801i	0.508347	−	0.861152i	$-0.330257\pi$
$821$	14.8427	+	3.97709i	0.518013	+	0.138801i	0.00966583	+	0.999953i	$0.496923\pi$
$822$	28.8957	+	1.82101i	1.00785	+	0.0635151i
$823$	13.1817	+	7.61045i	0.459485	+	0.265284i	0.711828	−	0.702354i	$-0.247868\pi$
$823$	13.1817	+	7.61045i	0.459485	+	0.265284i	−0.252343	+	0.967638i	$0.581201\pi$
$824$	−4.04193	−	1.08303i	−0.140807	−	0.0377292i
$825$	−10.2074	−	50.6505i	−0.355376	−	1.76342i
$826$	0.288307	−	0.288307i	0.0100315	−	0.0100315i
$827$	16.9790	+	16.9790i	0.590418	+	0.590418i	0.937744	−	0.347326i	$-0.112910\pi$
$827$	16.9790	+	16.9790i	0.590418	+	0.590418i	−0.347326	+	0.937744i	$0.612910\pi$
$828$	0.198911	−	1.57189i	0.00691265	−	0.0546269i
$829$	−14.6492	−	8.45773i	−0.508788	−	0.293749i	0.223547	−	0.974693i	$-0.428236\pi$
$829$	−14.6492	−	8.45773i	−0.508788	−	0.293749i	−0.732335	+	0.680944i	$0.761570\pi$
$830$	−13.0915	+	48.8583i	−0.454414	+	1.69590i
$831$	−28.2066	−	18.7447i	−0.978477	−	0.650247i
$832$	3.32333	+	1.39839i	0.115216	+	0.0484803i
$833$	−40.6750	+	23.4837i	−1.40930	+	0.813662i
$834$	1.73990	+	8.63361i	0.0602477	+	0.298957i
$835$	−25.6939	−	44.5031i	−0.889174	−	1.54009i
$836$	−4.38330	−	7.59210i	−0.151600	−	0.262578i
$837$	−3.26506	+	6.74866i	−0.112857	+	0.233268i
$838$	−7.28940	+	27.2044i	−0.251808	+	0.939761i
$839$	16.7213	+	16.7213i	0.577282	+	0.577282i	0.934154	−	0.356871i	$-0.116156\pi$
$839$	16.7213	+	16.7213i	0.577282	+	0.577282i	−0.356871	+	0.934154i	$0.616156\pi$
$840$	−0.127484	+	0.112369i	−0.00439862	+	0.00387709i
$841$	20.0028	−	34.6459i	0.689752	−	1.19469i
$842$	−7.27909			−0.250854
$843$	−16.9124	+	50.2368i	−0.582495	+	1.73025i
$844$	16.5841	+	9.57481i	0.570847	+	0.329579i
$845$	−21.9462	−	39.0129i	−0.754972	−	1.34208i
$846$	−0.933225	−	2.22136i	−0.0320849	−	0.0763719i
$847$	0.218335	−	0.0585027i	0.00750208	−	0.00201018i
$848$	4.38699	−	2.53283i	0.150650	−	0.0869778i
$849$	34.0715	+	22.6422i	1.16933	+	0.777079i
$850$	11.9071	−	44.4381i	0.408412	−	1.52421i
$851$	−1.10834	−	4.13640i	−0.0379935	−	0.141794i
$852$	16.3998	−	3.30500i	0.561849	−	0.113227i
$853$	−14.8432	−	55.3955i	−0.508221	−	1.89671i	−0.437522	−	0.899208i	$-0.644144\pi$
$853$	−14.8432	−	55.3955i	−0.508221	−	1.89671i	−0.0706986	−	0.997498i	$-0.522523\pi$
$854$	−0.000530397	0	0.000306225i	−1.81498e−5	0	1.04788e-5i
$855$	20.6474	+	2.61277i	0.706125	+	0.0893550i
$856$	0.852446	+	3.18137i	0.0291360	+	0.108737i
$857$	9.63613	−	16.6903i	0.329164	−	0.570129i	−0.653182	−	0.757201i	$-0.726566\pi$
$857$	9.63613	−	16.6903i	0.329164	−	0.570129i	0.982346	+	0.187072i	$0.0598998\pi$
$858$	27.1202	−	1.69374i	0.925867	−	0.0578233i
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	−0.960761	−	0.277378i	$-0.910534\pi$
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	0.240164	−	0.970732i	$-0.422799\pi$
$860$	21.3326	−	21.3326i	0.727437	−	0.727437i
$861$	−0.206543	−	0.137258i	−0.00703897	−	0.00467774i
$862$			18.9536i			0.645563i
$863$	4.51248	−	4.51248i	0.153607	−	0.153607i	−0.626120	−	0.779727i	$-0.715358\pi$
$863$	4.51248	−	4.51248i	0.153607	−	0.153607i	0.779727	+	0.626120i	$0.215358\pi$
$864$	−0.378924	−	5.18232i	−0.0128913	−	0.176306i
$865$	−63.3927	−	16.9860i	−2.15542	−	0.577542i
$866$	−30.4438	+	8.15738i	−1.03452	+	0.277199i
$867$	−21.5819	−	43.4879i	−0.732960	−	1.47693i
$868$		−	0.0411120i		−	0.00139543i
$869$	8.67331	+	8.67331i	0.294222	+	0.294222i
$870$	−27.4202	+	41.2613i	−0.929632	+	1.39889i
$871$	−3.15500	+	1.28623i	−0.106903	+	0.0435821i
$872$			7.64122i			0.258764i
$873$	0.535393	−	1.31115i	0.0181203	−	0.0443758i
$874$	0.532043	−	0.921525i	0.0179966	−	0.0311711i
$875$	−0.182086			−0.00615563
$876$	−5.10897	+	15.1757i	−0.172616	+	0.512740i
$877$	11.6623	−	3.12491i	0.393808	−	0.105521i	−0.0564803	−	0.998404i	$-0.517988\pi$
$877$	11.6623	−	3.12491i	0.393808	−	0.105521i	0.450288	+	0.892883i	$0.351321\pi$
$878$	−12.4481	+	3.33545i	−0.420102	+	0.112566i
$879$	12.2054	−	36.2551i	0.411679	−	1.22286i
$880$	−14.9821			−0.505046
$881$	−23.1313	+	40.0646i	−0.779314	+	1.34981i	0.153023	+	0.988223i	$0.451099\pi$
$881$	−23.1313	+	40.0646i	−0.779314	+	1.34981i	−0.932337	+	0.361589i	$0.882234\pi$
$882$	−20.8039	+	2.84533i	−0.700503	+	0.0958071i
$883$		−	5.00836i		−	0.168545i	−0.996443	−	0.0842723i	$-0.973143\pi$
$883$		−	5.00836i		−	0.168545i	0.996443	−	0.0842723i	$-0.0268566\pi$
$884$	22.3009	+	9.38375i	0.750061	+	0.315610i
$885$	−47.2320	+	71.0736i	−1.58769	+	2.38911i
$886$	8.90127	+	8.90127i	0.299044	+	0.299044i
$887$			21.6986i			0.728567i	0.931288	+	0.364284i	$0.118686\pi$
$887$			21.6986i			0.728567i	−0.931288	+	0.364284i	$0.881314\pi$
$888$	−6.24310	−	12.5800i	−0.209505	−	0.422156i
$889$	−0.272138	+	0.0729193i	−0.00912723	+	0.00244563i
$890$	−37.4265	−	10.0284i	−1.25454	−	0.336153i
$891$	−19.9201	−	33.7154i	−0.667350	−	1.12951i
$892$	18.6817	−	18.6817i	0.625509	−	0.625509i
$893$		−	1.61815i		−	0.0541494i
$894$	−7.62723	−	5.06867i	−0.255093	−	0.169522i
$895$	−58.6932	+	58.6932i	−1.96190	+	1.96190i
$896$	0.0142473	+	0.0246771i	0.000475970	+	0.000824403i
$897$	1.82396	+	2.74802i	0.0609001	+	0.0917536i
$898$	2.25983	−	3.91414i	0.0754115	−	0.130616i
$899$	−3.10202	−	11.5769i	−0.103458	−	0.386111i
$900$	12.4386	−	16.3801i	0.414620	−	0.546003i
$901$	29.4385	−	16.9963i	0.980740	−	0.566230i
$902$	−5.65867	−	21.1185i	−0.188413	−	0.703167i
$903$	−0.423908	+	0.0854286i	−0.0141068	+	0.00284289i
$904$	−0.150607	−	0.562074i	−0.00500912	−	0.0186943i
$905$	−1.03827	+	3.87486i	−0.0345131	+	0.128805i
$906$	−14.0460	−	9.33427i	−0.466647	−	0.310110i
$907$	26.6615	−	15.3930i	0.885282	−	0.511118i	0.0128856	−	0.999917i	$-0.495898\pi$
$907$	26.6615	−	15.3930i	0.885282	−	0.511118i	0.872396	+	0.488799i	$0.162565\pi$
$908$	−4.95918	+	1.32881i	−0.164576	+	0.0440981i
$909$	−9.96208	+	13.1188i	−0.330421	+	0.435124i
$910$	0.0481342	−	0.350464i	0.00159563	−	0.0116178i
$911$	13.1044	+	7.56582i	0.434168	+	0.250667i	0.701120	−	0.713043i	$-0.252684\pi$
$911$	13.1044	+	7.56582i	0.434168	+	0.250667i	−0.266953	+	0.963710i	$0.586017\pi$
$912$	1.11342	−	3.30730i	0.0368689	−	0.109516i
$913$	63.9194			2.11542
$914$	−5.08543	+	8.80823i	−0.168211	+	0.291350i
$915$	0.0961612	−	0.0847596i	0.00317899	−	0.00280207i
$916$	−5.61498	−	5.61498i	−0.185524	−	0.185524i
$917$	0.133669	−	0.498859i	0.00441414	−	0.0164738i
$918$	−2.54274	−	34.7755i	−0.0839228	−	1.14776i
$919$	−26.7304	−	46.2985i	−0.881755	−	1.52724i	−0.849388	−	0.527769i	$-0.823029\pi$
$919$	−26.7304	−	46.2985i	−0.881755	−	1.52724i	−0.0323673	−	0.999476i	$-0.510305\pi$
$920$	−0.909258	−	1.57488i	−0.0299773	−	0.0519223i
$921$	1.45069	+	7.19850i	0.0478017	+	0.237199i
$922$	23.5621	−	13.6036i	0.775977	−	0.448011i
$923$	−21.3544	+	27.5098i	−0.702890	+	0.905497i
$924$	0.178856	+	0.118858i	0.00588392	+	0.00391016i
$925$	14.3875	−	53.6950i	0.473059	−	1.76548i
$926$	−10.2633	−	5.92551i	−0.337272	−	0.194724i
$927$	−9.99769	−	7.59197i	−0.328367	−	0.249353i
$928$	5.87391	+	5.87391i	0.192821	+	0.192821i
$929$	37.9968	−	37.9968i	1.24663	−	1.24663i	0.289436	−	0.957197i	$-0.406532\pi$
$929$	37.9968	−	37.9968i	1.24663	−	1.24663i	0.957197	−	0.289436i	$-0.0934677\pi$
$930$	1.69989	+	8.43507i	0.0557414	+	0.276597i
$931$	−13.6213	−	3.64981i	−0.446419	−	0.119618i
$932$	−0.208135	−	0.120167i	−0.00681769	−	0.00393619i
$933$	−52.3080	−	3.29646i	−1.71249	−	0.107921i
$934$	0.594893	+	0.159401i	0.0194655	+	0.00521576i
$935$	−100.536			−3.28787
$936$	7.64421	+	7.65285i	0.249859	+	0.250141i
$937$	−2.41921			−0.0790323			−0.0395162	−	0.999219i	$-0.512582\pi$
$937$	−2.41921			−0.0790323			−0.0395162	+	0.999219i	$0.512582\pi$
$938$	−0.0260088	−	0.00696905i	−0.000849219	−	0.000227548i
$939$	−25.7681	−	51.9231i	−0.840909	−	1.69445i
$940$	−2.39492	−	1.38271i	−0.0781135	−	0.0450989i
$941$	−0.0432503	−	0.0115889i	−0.00140992	−	0.000377786i	0.258114	−	0.966114i	$-0.416899\pi$
$941$	−0.0432503	−	0.0115889i	−0.00140992	−	0.000377786i	−0.259524	+	0.965737i	$0.583566\pi$
$942$	15.8026	+	5.32001i	0.514876	+	0.173335i
$943$	1.87650	−	1.87650i	0.0611072	−	0.0611072i
$944$	10.1180	+	10.1180i	0.329311	+	0.329311i
$945$	−0.481509	+	0.167509i	−0.0156635	+	0.00544907i
$946$	−33.0163	−	19.0620i	−1.07345	−	0.619759i
$947$	−6.08611	+	22.7137i	−0.197772	+	0.738095i	0.793760	+	0.608231i	$0.208121\pi$
$947$	−6.08611	+	22.7137i	−0.197772	+	0.738095i	−0.991532	+	0.129864i	$0.958546\pi$
$948$	−0.307096	+	4.87298i	−0.00997400	+	0.158267i
$949$	−12.5836	−	30.8665i	−0.408481	−	1.00197i
$950$	11.9624	−	6.90651i	0.388112	−	0.224077i
$951$	−18.3176	−	6.16671i	−0.593990	−	0.199969i
$952$	0.0956054	+	0.165593i	0.00309859	+	0.00536691i
$953$	−13.8021	−	23.9060i	−0.447095	−	0.774392i	0.551100	−	0.834439i	$-0.314208\pi$
$953$	−13.8021	−	23.9060i	−0.447095	−	0.774392i	−0.998196	+	0.0600474i	$0.980875\pi$
$954$	15.0568	−	2.05931i	0.487483	−	0.0666725i
$955$	10.3061	−	38.4627i	0.333496	−	1.24462i
$956$	−4.75542	−	4.75542i	−0.153801	−	0.153801i
$957$	59.3328	+	19.9746i	1.91796	+	0.645688i
$958$	−10.0202	+	17.3554i	−0.323737	+	0.560729i
$959$	−0.476318			−0.0153811
$960$	−3.94350	−	4.47397i	−0.127276	−	0.144397i
$961$	25.0440	+	14.4592i	0.807871	+	0.466425i
$962$	26.9464	+	11.3385i	0.868788	+	0.365567i
$963$	−1.24045	+	9.80263i	−0.0399730	+	0.315885i
$964$	−25.0664	+	6.71652i	−0.807335	+	0.216325i
$965$	−4.29410	+	2.47920i	−0.138232	+	0.0798083i
$966$	−0.00163943	+	0.0260144i	−5.27478e−5	+	0.000836999i
$967$	−8.31034	+	31.0146i	−0.267243	+	0.997363i	0.693621	+	0.720340i	$0.256014\pi$
$967$	−8.31034	+	31.0146i	−0.267243	+	0.997363i	−0.960863	+	0.277023i	$0.910652\pi$
$968$	2.05311	+	7.66231i	0.0659895	+	0.246276i
$969$	7.47148	−	22.1933i	0.240019	−	0.712953i
$970$	−0.420710	−	1.57011i	−0.0135082	−	0.0504132i
$971$	16.6187	−	9.59478i	0.533318	−	0.307911i	−0.209049	−	0.977905i	$-0.567037\pi$
$971$	16.6187	−	9.59478i	0.533318	−	0.307911i	0.742366	+	0.669994i	$0.233703\pi$
$972$	4.82488	−	14.8230i	0.154758	−	0.475447i
$973$	−0.0375004	−	0.139953i	−0.00120221	−	0.00448670i
$974$	10.5733	−	18.3135i	0.338791	−	0.586804i
$975$	2.66872	+	42.7316i	0.0854676	+	1.36851i
$976$	−0.0107467	−	0.0186139i	−0.000343995	−	0.000595817i
$977$	21.6436	−	21.6436i	0.692440	−	0.692440i	−0.270328	−	0.962768i	$-0.587132\pi$
$977$	21.6436	−	21.6436i	0.692440	−	0.692440i	0.962768	+	0.270328i	$0.0871321\pi$
$978$	17.1973	−	8.53456i	0.549909	−	0.272905i
$979$			48.9637i			1.56489i
$980$	−17.0412	+	17.0412i	−0.544360	+	0.544360i
$981$	−8.66595	+	21.2225i	−0.276683	+	0.677583i
$982$	19.0783	+	5.11201i	0.608812	+	0.163131i
$983$	−21.8828	+	5.86347i	−0.697952	+	0.187016i	−0.590313	−	0.807175i	$-0.700996\pi$
$983$	−21.8828	+	5.86347i	−0.697952	+	0.187016i	−0.107639	+	0.994190i	$0.534329\pi$
$984$	4.81698	−	7.24849i	0.153560	−	0.231073i
$985$		−	14.3139i		−	0.456079i
$986$	39.4163	+	39.4163i	1.25527	+	1.25527i
$987$	0.0176209	+	0.0355065i	0.000560880	+	0.00113018i
$988$	2.74239	+	6.72684i	0.0872470	+	0.214009i
$989$		−	4.62747i		−	0.147145i
$990$	−41.6108	−	16.9913i	−1.32248	−	0.540018i
$991$	−18.1139	+	31.3742i	−0.575408	+	0.996636i	0.420589	+	0.907251i	$0.361823\pi$
$991$	−18.1139	+	31.3742i	−0.575408	+	0.996636i	−0.995997	+	0.0893845i	$0.971510\pi$
$992$	1.44280			0.0458089
$993$	−7.02867	+	1.41646i	−0.223048	+	0.0449500i
$994$	−0.265846	+	0.0712333i	−0.00843213	+	0.00225938i
$995$	6.85276	−	1.83619i	0.217247	−	0.0582111i
$996$	16.8245	+	19.0877i	0.533106	+	0.604818i
$997$	−17.7685			−0.562733			−0.281366	−	0.959600i	$-0.590788\pi$
$997$	−17.7685			−0.562733			−0.281366	+	0.959600i	$0.590788\pi$
$998$	2.65476	−	4.59817i	0.0840348	−	0.145553i
$999$	−3.07241	−	42.0196i	−0.0972069	−	1.32944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.137.2	yes	56
3.2	odd	2		702.2.bc.a.683.8		56
9.4	even	3		702.2.bb.a.449.8		56
9.5	odd	6		234.2.y.a.59.3	✓	56
13.2	odd	12		234.2.y.a.119.3	yes	56
39.2	even	12		702.2.bb.a.197.8		56
117.41	even	12	inner	234.2.z.a.41.2	yes	56
117.67	odd	12		702.2.bc.a.665.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.3	✓	56	9.5	odd	6
234.2.y.a.119.3	yes	56	13.2	odd	12
234.2.z.a.41.2	yes	56	117.41	even	12	inner
234.2.z.a.137.2	yes	56	1.1	even	1	trivial
702.2.bb.a.197.8		56	39.2	even	12
702.2.bb.a.449.8		56	9.4	even	3
702.2.bc.a.665.8		56	117.67	odd	12
702.2.bc.a.683.8		56	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.958654 + 1.44256i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.32591 + 0.891175i) q^{5} +(1.29935 - 1.14529i) q^{6} +(-0.0201488 + 0.0201488i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.16197 - 2.76583i) q^{9} +(-2.98193 - 1.72162i) q^{10} +(-1.12616 + 4.20290i) q^{11} +(-1.55150 + 0.769968i) q^{12} +(1.39839 - 3.32333i) q^{13} +(0.0246771 - 0.0142473i) q^{14} +(-4.47397 + 3.94350i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.35521 + 5.81139i) q^{17} +(0.406522 + 2.97233i) q^{18} +(-0.521462 + 1.94612i) q^{19} +(2.43473 + 2.43473i) q^{20} +(-0.00975013 - 0.0483815i) q^{21} +(2.17558 - 3.76822i) q^{22} +0.528142 q^{23} +(1.69792 - 0.342174i) q^{24} +(5.93735 + 3.42793i) q^{25} +(-2.21088 + 2.84816i) q^{26} +(5.10381 + 0.975270i) q^{27} +(-0.0275237 + 0.00737496i) q^{28} +(-7.19404 + 4.15348i) q^{29} +(5.34218 - 2.65118i) q^{30} +(-0.373424 + 1.39364i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.98334 - 5.65369i) q^{33} +(-1.73678 - 6.48176i) q^{34} +(-0.0849690 + 0.0490569i) q^{35} +(0.376625 - 2.97627i) q^{36} +(-2.09857 - 7.83198i) q^{37} +(1.00739 - 1.74484i) q^{38} +(3.45354 + 5.20318i) q^{39} +(-1.72162 - 2.98193i) q^{40} +(3.55302 - 3.55302i) q^{41} +(-0.00310415 + 0.0492564i) q^{42} -8.76179i q^{43} +(-3.07674 + 3.07674i) q^{44} +(-1.39975 - 10.2344i) q^{45} +(-0.510146 - 0.136693i) q^{46} +(-0.775777 + 0.207869i) q^{47} +(-1.72862 - 0.108938i) q^{48} +6.99919i q^{49} +(-4.84783 - 4.84783i) q^{50} +(-11.5998 - 0.731018i) q^{51} +(2.87270 - 2.17889i) q^{52} -5.06566i q^{53} +(-4.67748 - 2.26300i) q^{54} +(-7.49104 + 12.9749i) q^{55} +0.0284946 q^{56} +(-2.30750 - 2.61790i) q^{57} +(8.02391 - 2.15000i) q^{58} +(13.8214 - 3.70343i) q^{59} +(-5.84632 + 1.17819i) q^{60} -0.0214935 q^{61} +(0.721399 - 1.24950i) q^{62} +(0.0791403 + 0.0323159i) q^{63} +1.00000i q^{64} +(7.61257 - 9.80688i) q^{65} +(3.35025 + 6.75082i) q^{66} +(-0.668189 - 0.668189i) q^{67} +6.71041i q^{68} +(-0.506305 + 0.761877i) q^{69} +(0.0947706 - 0.0253937i) q^{70} +(-9.32969 - 2.49988i) q^{71} +(-1.13411 + 2.77737i) q^{72} +(6.53713 - 6.53713i) q^{73} +8.10826i q^{74} +(-10.6369 + 5.27880i) q^{75} +(-1.42466 + 1.42466i) q^{76} +(-0.0619924 - 0.107374i) q^{77} +(-1.98918 - 5.91973i) q^{78} +(1.40950 - 2.44132i) q^{79} +(0.891175 + 3.32591i) q^{80} +(-6.29967 + 6.42761i) q^{81} +(-4.35155 + 2.51237i) q^{82} +(-3.80210 - 14.1896i) q^{83} +(0.0157469 - 0.0467747i) q^{84} +(5.98015 + 22.3182i) q^{85} +(-2.26772 + 8.46324i) q^{86} +(0.904943 - 14.3596i) q^{87} +(3.76822 - 2.17558i) q^{88} +(10.8696 - 2.91249i) q^{89} +(-1.29681 + 10.2480i) q^{90} +(0.0387852 + 0.0951367i) q^{91} +(0.457384 + 0.264071i) q^{92} +(-1.65242 - 1.87470i) q^{93} +0.803143 q^{94} +(-3.46867 + 6.00791i) q^{95} +(1.64153 + 0.552626i) q^{96} +(0.333814 + 0.333814i) q^{97} +(1.81152 - 6.76070i) q^{98} +(12.9331 - 1.76884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more