LMFDB - Embedded newform 546.2.bw.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.61660 - 0.621783i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.475031 - 0.127284i) q^{5} +(-0.182190 + 1.72244i) q^{6} +(2.42388 - 1.06056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22677 + 2.01034i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.61660 - 0.621783i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.475031 - 0.127284i) q^{5} +(-0.182190 + 1.72244i) q^{6} +(2.42388 - 1.06056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22677 + 2.01034i) q^{9} +0.491788i q^{10} +(-0.594605 - 0.594605i) q^{11} +(1.71091 - 0.269819i) q^{12} +(2.41879 - 2.67385i) q^{13} +(-1.65177 - 2.06680i) q^{14} +(0.688791 + 0.501133i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.07782 - 5.33093i) q^{17} +(1.36551 - 2.67121i) q^{18} +(2.66705 + 2.66705i) q^{19} +(0.475031 - 0.127284i) q^{20} +(-4.57788 + 0.207375i) q^{21} +(-0.420449 + 0.728240i) q^{22} +(0.254056 - 0.440038i) q^{23} +(-0.703440 - 1.58277i) q^{24} +(-4.12067 - 2.37907i) q^{25} +(-3.20877 - 1.64433i) q^{26} +(-2.34980 - 4.63449i) q^{27} +(-1.56886 + 2.13042i) q^{28} +(0.304458 - 0.175779i) q^{29} +(0.305785 - 0.795024i) q^{30} +(-3.36734 + 0.902276i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.591522 + 1.33095i) q^{33} +(-4.35269 + 4.35269i) q^{34} +(-1.28641 + 0.195279i) q^{35} +(-2.93361 - 0.627623i) q^{36} +(-0.419258 - 1.56469i) q^{37} +(1.88589 - 3.26646i) q^{38} +(-5.57276 + 2.81857i) q^{39} +(-0.245894 - 0.425901i) q^{40} +(-12.0866 - 3.23859i) q^{41} +(1.38515 + 4.36822i) q^{42} +(2.11242 + 1.21961i) q^{43} +(0.812246 + 0.217641i) q^{44} +(-0.801901 - 1.23841i) q^{45} +(-0.490799 - 0.131509i) q^{46} +(1.80896 - 6.75114i) q^{47} +(-1.34678 + 1.08912i) q^{48} +(4.75041 - 5.14136i) q^{49} +(-1.23150 + 4.59601i) q^{50} +(1.66091 + 10.5317i) q^{51} +(-0.757812 + 3.52501i) q^{52} +(-2.97884 - 1.71983i) q^{53} +(-3.86840 + 3.46922i) q^{54} +(0.206772 + 0.358140i) q^{55} +(2.46388 + 0.964012i) q^{56} +(-2.65322 - 5.96987i) q^{57} +(-0.248589 - 0.248589i) q^{58} +(3.37628 - 12.6004i) q^{59} +(-0.847077 - 0.0895988i) q^{60} +4.31238 q^{61} +(1.74306 + 3.01908i) q^{62} +(7.52953 + 2.51120i) q^{63} +1.00000i q^{64} +(-1.48934 + 0.962286i) q^{65} +(1.13250 - 0.915842i) q^{66} +(6.86006 + 6.86006i) q^{67} +(5.33093 + 3.07782i) q^{68} +(-0.684315 + 0.553397i) q^{69} +(0.521573 + 1.19204i) q^{70} +(3.60248 + 13.4446i) q^{71} +(0.153038 + 2.99609i) q^{72} +(-3.74709 - 13.9843i) q^{73} +(-1.40286 + 0.809943i) q^{74} +(5.18220 + 6.40816i) q^{75} +(-3.64326 - 0.976208i) q^{76} +(-2.07187 - 0.810637i) q^{77} +(4.16486 + 4.65338i) q^{78} +(-3.93483 - 6.81533i) q^{79} +(-0.347747 + 0.347747i) q^{80} +(0.917034 + 8.95316i) q^{81} +12.5129i q^{82} +(-3.62913 + 3.62913i) q^{83} +(3.86087 - 2.46853i) q^{84} +(0.783515 + 2.92412i) q^{85} +(0.631315 - 2.35610i) q^{86} +(-0.601483 + 0.0948571i) q^{87} -0.840899i q^{88} +(-3.52575 + 0.944722i) q^{89} +(-0.988664 + 1.09510i) q^{90} +(3.02708 - 9.04637i) q^{91} +0.508113i q^{92} +(6.00465 + 0.635137i) q^{93} -6.98930 q^{94} +(-0.927458 - 1.60641i) q^{95} +(1.40058 + 1.01900i) q^{96} +(14.4786 - 3.87952i) q^{97} +(-6.19567 - 3.25786i) q^{98} +(-0.128690 - 2.51941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.61660	−	0.621783i	−0.933343	−	0.358986i
$3$	−1.61660	−	0.621783i	−0.933343	−	0.358986i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.475031	−	0.127284i	−0.212440	−	0.0569232i	0.151029	−	0.988529i	$-0.451741\pi$
$5$	−0.475031	−	0.127284i	−0.212440	−	0.0569232i	−0.363470	+	0.931606i	$0.618408\pi$
$6$	−0.182190	+	1.72244i	−0.0743787	+	0.703184i
$7$	2.42388	−	1.06056i	0.916141	−	0.400855i
$7$	2.42388	−	1.06056i	0.916141	−	0.400855i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.22677	+	2.01034i	0.742258	+	0.670115i
$10$			0.491788i			0.155517i
$11$	−0.594605	−	0.594605i	−0.179280	−	0.179280i	0.611762	−	0.791042i	$-0.290461\pi$
$11$	−0.594605	−	0.594605i	−0.179280	−	0.179280i	−0.791042	+	0.611762i	$0.790461\pi$
$12$	1.71091	−	0.269819i	0.493896	−	0.0778900i
$13$	2.41879	−	2.67385i	0.670852	−	0.741591i
$13$	2.41879	−	2.67385i	0.670852	−	0.741591i
$14$	−1.65177	−	2.06680i	−0.441455	−	0.552375i
$15$	0.688791	+	0.501133i	0.177845	+	0.129392i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.07782	−	5.33093i	−0.746480	−	1.29294i	−0.949500	−	0.313767i	$-0.898409\pi$
$17$	−3.07782	−	5.33093i	−0.746480	−	1.29294i	0.203020	−	0.979175i	$-0.434924\pi$
$18$	1.36551	−	2.67121i	0.321854	−	0.629611i
$19$	2.66705	+	2.66705i	0.611863	+	0.611863i	0.943431	−	0.331568i	$-0.107578\pi$
$19$	2.66705	+	2.66705i	0.611863	+	0.611863i	−0.331568	+	0.943431i	$0.607578\pi$
$20$	0.475031	−	0.127284i	0.106220	−	0.0284616i
$21$	−4.57788	+	0.207375i	−0.998976	+	0.0452530i
$22$	−0.420449	+	0.728240i	−0.0896401	+	0.155261i
$23$	0.254056	−	0.440038i	0.0529744	−	0.0917543i	−0.838322	−	0.545175i	$-0.816463\pi$
$23$	0.254056	−	0.440038i	0.0529744	−	0.0917543i	0.891297	+	0.453421i	$0.149796\pi$
$24$	−0.703440	−	1.58277i	−0.143589	−	0.323082i
$25$	−4.12067	−	2.37907i	−0.824135	−	0.475814i
$26$	−3.20877	−	1.64433i	−0.629291	−	0.322480i
$27$	−2.34980	−	4.63449i	−0.452219	−	0.891907i
$28$	−1.56886	+	2.13042i	−0.296487	+	0.402611i
$29$	0.304458	−	0.175779i	0.0565365	−	0.0326413i	−0.471465	−	0.881885i	$-0.656275\pi$
$29$	0.304458	−	0.175779i	0.0565365	−	0.0326413i	0.528002	+	0.849243i	$0.322941\pi$
$30$	0.305785	−	0.795024i	0.0558285	−	0.145151i
$31$	−3.36734	+	0.902276i	−0.604792	+	0.162054i	−0.548205	−	0.836344i	$-0.684689\pi$
$31$	−3.36734	+	0.902276i	−0.604792	+	0.162054i	−0.0565874	+	0.998398i	$0.518022\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.591522	+	1.33095i	0.102971	+	0.231689i
$34$	−4.35269	+	4.35269i	−0.746480	+	0.746480i
$35$	−1.28641	+	0.195279i	−0.217443	+	0.0330081i
$36$	−2.93361	−	0.627623i	−0.488936	−	0.104604i
$37$	−0.419258	−	1.56469i	−0.0689255	−	0.257234i	0.922862	−	0.385131i	$-0.125844\pi$
$37$	−0.419258	−	1.56469i	−0.0689255	−	0.257234i	−0.991787	+	0.127898i	$0.959177\pi$
$38$	1.88589	−	3.26646i	0.305932	−	0.529889i
$39$	−5.57276	+	2.81857i	−0.892356	+	0.451332i
$40$	−0.245894	−	0.425901i	−0.0388793	−	0.0673409i
$41$	−12.0866	−	3.23859i	−1.88760	−	0.505782i	−0.998879	−	0.0473437i	$-0.984924\pi$
$41$	−12.0866	−	3.23859i	−1.88760	−	0.505782i	−0.888726	−	0.458438i	$-0.848409\pi$
$42$	1.38515	+	4.36822i	0.213734	+	0.674031i
$43$	2.11242	+	1.21961i	0.322141	+	0.185988i	0.652347	−	0.757921i	$-0.273785\pi$
$43$	2.11242	+	1.21961i	0.322141	+	0.185988i	−0.330205	+	0.943909i	$0.607118\pi$
$44$	0.812246	+	0.217641i	0.122451	+	0.0328106i
$45$	−0.801901	−	1.23841i	−0.119540	−	0.184611i
$46$	−0.490799	−	0.131509i	−0.0723644	−	0.0193900i
$47$	1.80896	−	6.75114i	0.263864	−	0.984755i	−0.699077	−	0.715046i	$-0.746406\pi$
$47$	1.80896	−	6.75114i	0.263864	−	0.984755i	0.962942	−	0.269709i	$-0.0869276\pi$
$48$	−1.34678	+	1.08912i	−0.194391	+	0.157201i
$49$	4.75041	−	5.14136i	0.678630	−	0.734480i
$50$	−1.23150	+	4.59601i	−0.174160	+	0.649975i
$51$	1.66091	+	10.5317i	0.232573	+	1.47473i
$52$	−0.757812	+	3.52501i	−0.105090	+	0.488831i
$53$	−2.97884	−	1.71983i	−0.409175	−	0.236237i	0.281260	−	0.959632i	$-0.409248\pi$
$53$	−2.97884	−	1.71983i	−0.409175	−	0.236237i	−0.690435	+	0.723394i	$0.742581\pi$
$54$	−3.86840	+	3.46922i	−0.526422	+	0.472101i
$55$	0.206772	+	0.358140i	0.0278811	+	0.0482916i
$56$	2.46388	+	0.964012i	0.329249	+	0.128822i
$57$	−2.65322	−	5.96987i	−0.351428	−	0.790729i
$58$	−0.248589	−	0.248589i	−0.0326413	−	0.0326413i
$59$	3.37628	−	12.6004i	0.439554	−	1.64044i	−0.290374	−	0.956913i	$-0.593780\pi$
$59$	3.37628	−	12.6004i	0.439554	−	1.64044i	0.729928	−	0.683524i	$-0.239554\pi$
$60$	−0.847077	−	0.0895988i	−0.109357	−	0.0115672i
$61$	4.31238			0.552144			0.276072	−	0.961137i	$-0.410967\pi$
$61$	4.31238			0.552144			0.276072	+	0.961137i	$0.410967\pi$
$62$	1.74306	+	3.01908i	0.221369	+	0.383423i
$63$	7.52953	+	2.51120i	0.948632	+	0.316382i
$64$			1.00000i			0.125000i
$65$	−1.48934	+	0.962286i	−0.184730	+	0.119357i
$66$	1.13250	−	0.915842i	0.139402	−	0.112732i
$67$	6.86006	+	6.86006i	0.838089	+	0.838089i	0.988607	−	0.150518i	$-0.0480941\pi$
$67$	6.86006	+	6.86006i	0.838089	+	0.838089i	−0.150518	+	0.988607i	$0.548094\pi$
$68$	5.33093	+	3.07782i	0.646471	+	0.373240i
$69$	−0.684315	+	0.553397i	−0.0823818	+	0.0666212i
$70$	0.521573	+	1.19204i	0.0623398	+	0.142476i
$71$	3.60248	+	13.4446i	0.427536	+	1.59559i	0.758322	+	0.651880i	$0.226019\pi$
$71$	3.60248	+	13.4446i	0.427536	+	1.59559i	−0.330786	+	0.943706i	$0.607314\pi$
$72$	0.153038	+	2.99609i	0.0180357	+	0.353093i
$73$	−3.74709	−	13.9843i	−0.438564	−	1.63674i	−0.732390	−	0.680885i	$-0.761595\pi$
$73$	−3.74709	−	13.9843i	−0.438564	−	1.63674i	0.293826	−	0.955859i	$-0.405071\pi$
$74$	−1.40286	+	0.809943i	−0.163080	+	0.0941540i
$75$	5.18220	+	6.40816i	0.598389	+	0.739951i
$76$	−3.64326	−	0.976208i	−0.417910	−	0.111979i
$77$	−2.07187	−	0.810637i	−0.236111	−	0.0923806i
$78$	4.16486	+	4.65338i	0.471578	+	0.526891i
$79$	−3.93483	−	6.81533i	−0.442703	−	0.766784i	0.555186	−	0.831726i	$-0.312647\pi$
$79$	−3.93483	−	6.81533i	−0.442703	−	0.766784i	−0.997889	+	0.0649419i	$0.979314\pi$
$80$	−0.347747	+	0.347747i	−0.0388793	+	0.0388793i
$81$	0.917034	+	8.95316i	0.101893	+	0.994795i
$82$			12.5129i			1.38182i
$83$	−3.62913	+	3.62913i	−0.398349	+	0.398349i	−0.877650	−	0.479301i	$-0.840890\pi$
$83$	−3.62913	+	3.62913i	−0.398349	+	0.398349i	0.479301	+	0.877650i	$0.340890\pi$
$84$	3.86087	−	2.46853i	0.421256	−	0.269339i
$85$	0.783515	+	2.92412i	0.0849841	+	0.317165i
$86$	0.631315	−	2.35610i	0.0680764	−	0.254065i
$87$	−0.601483	+	0.0948571i	−0.0644857	+	0.0101697i
$88$		−	0.840899i		−	0.0896401i
$89$	−3.52575	+	0.944722i	−0.373729	+	0.100140i	−0.440794	−	0.897608i	$-0.645303\pi$
$89$	−3.52575	+	0.944722i	−0.373729	+	0.100140i	0.0670653	+	0.997749i	$0.478636\pi$
$90$	−0.988664	+	1.09510i	−0.104214	+	0.115434i
$91$	3.02708	−	9.04637i	0.317325	−	0.948317i
$92$			0.508113i			0.0529744i
$93$	6.00465	+	0.635137i	0.622654	+	0.0658606i
$94$	−6.98930			−0.720891
$95$	−0.927458	−	1.60641i	−0.0951552	−	0.164814i
$96$	1.40058	+	1.01900i	0.142946	+	0.104001i
$97$	14.4786	−	3.87952i	1.47008	−	0.393906i	0.567119	−	0.823636i	$-0.308058\pi$
$97$	14.4786	−	3.87952i	1.47008	−	0.393906i	0.902957	+	0.429730i	$0.141391\pi$
$98$	−6.19567	−	3.25786i	−0.625857	−	0.329094i
$99$	−0.128690	−	2.51941i	−0.0129338	−	0.253210i
$100$	4.75814			0.475814
$101$	17.0073			1.69229			0.846145	−	0.532953i	$-0.178918\pi$
$101$	17.0073			1.69229			0.846145	+	0.532953i	$0.178918\pi$
$102$	9.74297	−	4.33012i	0.964698	−	0.428746i
$103$	−1.43335	+	0.827544i	−0.141232	+	0.0815403i	−0.568951	−	0.822371i	$-0.692651\pi$
$103$	−1.43335	+	0.827544i	−0.141232	+	0.0815403i	0.427719	+	0.903912i	$0.359317\pi$
$104$	3.60104	−	0.180350i	0.353111	−	0.0176848i
$105$	2.20103	+	0.484182i	0.214799	+	0.0472513i
$106$	−0.890251	+	3.32246i	−0.0864689	+	0.322706i
$107$	9.01644	+	5.20564i	0.871652	+	0.503249i	0.867897	−	0.496744i	$-0.165471\pi$
$107$	9.01644	+	5.20564i	0.871652	+	0.503249i	0.00375529	+	0.999993i	$0.498805\pi$
$108$	4.35223	+	2.83868i	0.418793	+	0.273152i
$109$	−6.91363	+	1.85250i	−0.662206	+	0.177438i	−0.574241	−	0.818686i	$-0.694703\pi$
$109$	−6.91363	+	1.85250i	−0.662206	+	0.177438i	−0.0879646	+	0.996124i	$0.528036\pi$
$110$	0.292420	−	0.292420i	0.0278811	−	0.0278811i
$111$	−0.295127	+	2.79016i	−0.0280122	+	0.264830i
$112$	0.293467	−	2.62943i	0.0277300	−	0.248457i
$113$	−4.58734	−	2.64850i	−0.431540	−	0.249150i	0.268462	−	0.963290i	$-0.413485\pi$
$113$	−4.58734	−	2.64850i	−0.431540	−	0.249150i	−0.700003	+	0.714140i	$0.746818\pi$
$114$	−5.07975	+	4.10793i	−0.475762	+	0.384743i
$115$	−0.176695	+	0.176695i	−0.0164769	+	0.0164769i
$116$	−0.175779	+	0.304458i	−0.0163207	+	0.0282682i
$117$	10.7614	−	1.09144i	0.994896	−	0.100904i
$118$	−13.0449			−1.20088
$119$	−13.1141	−	9.65734i	−1.20216	−	0.885287i
$120$	0.132694	+	0.841403i	0.0121132	+	0.0768093i
$121$		−	10.2929i		−	0.935717i
$122$	−1.11613	−	4.16544i	−0.101049	−	0.377122i
$123$	17.5254	+	12.7507i	1.58021	+	1.14969i
$124$	2.46507	−	2.46507i	0.221369	−	0.221369i
$125$	3.39336	+	3.39336i	0.303512	+	0.303512i
$126$	0.476851	−	7.92292i	0.0424813	−	0.705830i
$127$	−1.58318	+	0.914049i	−0.140484	+	0.0811087i	−0.568595	−	0.822618i	$-0.692513\pi$
$127$	−1.58318	+	0.914049i	−0.140484	+	0.0811087i	0.428110	+	0.903726i	$0.359179\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−2.65660	−	3.28508i	−0.233901	−	0.289235i
$130$	1.31497	+	1.18953i	0.115330	+	0.104329i
$131$	−1.11887	+	0.645979i	−0.0977560	+	0.0564394i	−0.548081	−	0.836425i	$-0.684641\pi$
$131$	−1.11887	+	0.645979i	−0.0977560	+	0.0564394i	0.450325	+	0.892865i	$0.351308\pi$
$132$	−1.17775	−	0.856877i	−0.102510	−	0.0745816i
$133$	9.29319	+	3.63604i	0.805822	+	0.315285i
$134$	4.85079	−	8.40182i	0.419045	−	0.725807i
$135$	0.526330	+	2.50062i	0.0452993	+	0.215219i
$136$	1.59319	−	5.94588i	0.136615	−	0.509855i
$137$	−2.35220	+	8.77852i	−0.200962	+	0.750000i	0.789681	+	0.613518i	$0.210246\pi$
$137$	−2.35220	+	8.77852i	−0.200962	+	0.750000i	−0.990643	+	0.136482i	$0.956420\pi$
$138$	0.711654	+	0.517768i	0.0605800	+	0.0440753i
$139$	−5.15074	+	8.92134i	−0.436880	+	0.756698i	−0.997447	−	0.0714109i	$-0.977250\pi$
$139$	−5.15074	+	8.92134i	−0.436880	+	0.756698i	0.560567	+	0.828109i	$0.310583\pi$
$140$	1.01643	−	0.812322i	0.0859037	−	0.0686538i
$141$	−7.12211	+	9.78909i	−0.599790	+	0.824391i
$142$	12.0541	−	6.95946i	1.01156	−	0.584025i
$143$	−3.02811	+	0.151656i	−0.253223	+	0.0126821i
$144$	2.85440	−	0.923270i	0.237866	−	0.0769391i
$145$	−0.167001	+	0.0447478i	−0.0138687	+	0.00371610i
$146$	−12.5380	+	7.23883i	−1.03765	+	0.599090i
$147$	−10.8763	+	5.35779i	−0.897063	+	0.441903i
$148$	1.14543	+	1.14543i	0.0941540	+	0.0941540i
$149$	8.84754	−	8.84754i	0.724818	−	0.724818i	−0.244764	−	0.969583i	$-0.578711\pi$
$149$	8.84754	−	8.84754i	0.724818	−	0.724818i	0.969583	+	0.244764i	$0.0787105\pi$
$150$	4.84856	−	6.66418i	0.395883	−	0.544128i
$151$	3.20885	+	11.9756i	0.261132	+	0.974558i	0.964575	+	0.263807i	$0.0849782\pi$
$151$	3.20885	+	11.9756i	0.261132	+	0.974558i	−0.703443	+	0.710751i	$0.748355\pi$
$152$			3.77178i			0.305932i
$153$	3.86341	−	18.0582i	0.312339	−	1.45992i
$154$	−0.246776	+	2.21108i	−0.0198857	+	0.178174i
$155$	1.71444			0.137707
$156$	3.41687	−	5.22733i	0.273568	−	0.418522i
$157$	4.05883	−	7.03010i	0.323930	−	0.561063i	−0.657365	−	0.753572i	$-0.728329\pi$
$157$	4.05883	−	7.03010i	0.323930	−	0.561063i	0.981295	+	0.192509i	$0.0616625\pi$
$158$	−5.56469	+	5.56469i	−0.442703	+	0.442703i
$159$	3.74622	+	4.63247i	0.297095	+	0.367379i
$160$	0.425901	+	0.245894i	0.0336704	+	0.0194396i
$161$	0.149114	−	1.33604i	0.0117518	−	0.105295i
$162$	8.41074	−	3.20303i	0.660810	−	0.251654i
$163$	−3.28724	+	3.28724i	−0.257477	+	0.257477i	−0.824027	−	0.566550i	$-0.808278\pi$
$163$	−3.28724	+	3.28724i	−0.257477	+	0.257477i	0.566550	+	0.824027i	$0.308278\pi$
$164$	12.0866	−	3.23859i	0.943802	−	0.252891i
$165$	−0.111582	−	0.707535i	−0.00868665	−	0.0550815i
$166$	4.44476	+	2.56618i	0.344980	+	0.199174i
$167$	0.291930	−	1.08950i	0.0225902	−	0.0843078i	−0.953710	−	0.300726i	$-0.902771\pi$
$167$	0.291930	−	1.08950i	0.0225902	−	0.0843078i	0.976301	+	0.216419i	$0.0694376\pi$
$168$	−3.38369	−	3.09041i	−0.261057	−	0.238431i
$169$	−1.29890	−	12.9349i	−0.0999152	−	0.994996i
$170$	2.62169	−	1.51363i	0.201075	−	0.116090i
$171$	0.577226	+	11.3006i	0.0441416	+	0.864179i
$172$	−2.43921			−0.185988
$173$	−1.34937			−0.102591			−0.0512955	−	0.998684i	$-0.516335\pi$
$173$	−1.34937			−0.102591			−0.0512955	+	0.998684i	$0.516335\pi$
$174$	0.247300	+	0.556437i	0.0187478	+	0.0421834i
$175$	−12.5112	−	1.39636i	−0.945757	−	0.105555i
$176$	−0.812246	+	0.217641i	−0.0612253	+	0.0164053i
$177$	−13.2928	+	18.2705i	−0.999149	+	1.37330i
$178$	1.82506	+	3.16110i	0.136794	+	0.236935i
$179$	9.98788			0.746529			0.373265	−	0.927725i	$-0.378238\pi$
$179$	9.98788			0.746529			0.373265	+	0.927725i	$0.378238\pi$
$180$	1.31367	+	0.671543i	0.0979153	+	0.0500539i
$181$			25.1753i			1.87127i	0.352972	+	0.935634i	$0.385171\pi$
$181$			25.1753i			1.87127i	−0.352972	+	0.935634i	$0.614829\pi$
$182$	−9.52159	−	0.582566i	−0.705787	−	0.0431827i
$183$	−6.97139	−	2.68137i	−0.515340	−	0.198212i
$184$	0.490799	−	0.131509i	0.0361822	−	0.00969499i
$185$			0.796641i			0.0585702i
$186$	−0.940624	−	5.96444i	−0.0689699	−	0.437334i
$187$	−1.33972	+	4.99989i	−0.0979697	+	0.365628i
$188$	1.80896	+	6.75114i	0.131932	+	0.492378i
$189$	−10.6108	−	8.74134i	−0.771822	−	0.635839i
$190$	−1.31162	+	1.31162i	−0.0951552	+	0.0951552i
$191$			19.8152i			1.43378i	0.697188	+	0.716889i	$0.254434\pi$
$191$			19.8152i			1.43378i	−0.697188	+	0.716889i	$0.745566\pi$
$192$	0.621783	−	1.61660i	0.0448733	−	0.116668i
$193$	6.88051	−	6.88051i	0.495270	−	0.495270i	−0.414692	−	0.909962i	$-0.636111\pi$
$193$	6.88051	−	6.88051i	0.495270	−	0.495270i	0.909962	+	0.414692i	$0.136111\pi$
$194$	−7.49466	−	12.9811i	−0.538085	−	0.931991i
$195$	3.00599	−	0.629583i	0.215264	−	0.0450854i
$196$	−1.54330	+	6.82775i	−0.110235	+	0.487697i
$197$	2.70220	+	0.724053i	0.192524	+	0.0515866i	0.353793	−	0.935324i	$-0.384892\pi$
$197$	2.70220	+	0.724053i	0.192524	+	0.0515866i	−0.161269	+	0.986911i	$0.551559\pi$
$198$	−2.40026	+	0.776376i	−0.170579	+	0.0551747i
$199$	−9.00851	+	5.20107i	−0.638597	+	0.368694i	−0.784074	−	0.620668i	$-0.786862\pi$
$199$	−9.00851	+	5.20107i	−0.638597	+	0.368694i	0.145477	+	0.989362i	$0.453528\pi$
$200$	−1.23150	−	4.59601i	−0.0870801	−	0.324987i
$201$	−6.82448	−	15.3554i	−0.481362	−	1.08309i
$202$	−4.40181	−	16.4278i	−0.309710	−	1.15585i
$203$	0.551546	−	0.748965i	0.0387109	−	0.0525670i
$204$	−6.70424	−	8.29027i	−0.469391	−	0.580435i
$205$	5.32927	+	3.07686i	0.372213	+	0.214897i
$206$	1.17032	+	1.17032i	0.0815403	+	0.0815403i
$207$	1.45035	−	0.469125i	0.100807	−	0.0326064i
$208$	−1.10622	−	3.43166i	−0.0767027	−	0.237943i
$209$		−	3.17168i		−	0.219390i
$210$	−0.101985	−	2.25135i	−0.00703762	−	0.155358i
$211$	−0.341450	−	0.591409i	−0.0235064	−	0.0407142i	0.854033	−	0.520219i	$-0.174150\pi$
$211$	−0.341450	−	0.591409i	−0.0235064	−	0.0407142i	−0.877539	+	0.479505i	$0.840816\pi$
$212$	3.43967			0.236237
$213$	2.53588	−	23.9745i	0.173756	−	1.64271i
$214$	2.69464	−	10.0565i	0.184202	−	0.687450i
$215$	−0.848229	−	0.848229i	−0.0578487	−	0.0578487i
$216$	1.61552	−	4.93863i	0.109922	−	0.336031i
$217$	−7.20512	+	5.75829i	−0.489115	+	0.390898i
$218$	3.57876	+	6.19859i	0.242384	+	0.419822i
$219$	−2.63768	+	24.9369i	−0.178238	+	1.68508i
$220$	−0.358140	−	0.206772i	−0.0241458	−	0.0139406i
$221$	−21.6987	−	4.66481i	−1.45961	−	0.313789i
$222$	2.77147	−	0.437076i	0.186009	−	0.0293346i
$223$	−0.0962454	+	0.359193i	−0.00644507	+	0.0240533i	−0.969073	−	0.246772i	$-0.920630\pi$
$223$	−0.0962454	+	0.359193i	−0.00644507	+	0.0240533i	0.962628	+	0.270826i	$0.0872967\pi$
$224$	−2.61578	+	0.397078i	−0.174774	+	0.0265309i
$225$	−4.39305	−	13.5816i	−0.292870	−	0.905442i
$226$	−1.37096	+	5.11651i	−0.0911952	+	0.340345i
$227$	22.3548	+	5.98995i	1.48374	+	0.397567i	0.907618	−	0.419798i	$-0.137899\pi$
$227$	22.3548	+	5.98995i	1.48374	+	0.397567i	0.576121	+	0.817364i	$0.304566\pi$
$228$	5.28269	+	3.84345i	0.349855	+	0.254539i
$229$	−17.2863	−	4.63184i	−1.14231	−	0.306081i	−0.362430	−	0.932011i	$-0.618053\pi$
$229$	−17.2863	−	4.63184i	−1.14231	−	0.306081i	−0.779879	+	0.625930i	$0.784719\pi$
$230$	0.216406	+	0.124942i	0.0142694	+	0.00823843i
$231$	2.84534	+	2.59873i	0.187210	+	0.170984i
$232$	0.339579	+	0.0909899i	0.0222945	+	0.00597378i
$233$	−2.15549	−	3.73341i	−0.141211	−	0.244584i	0.786742	−	0.617282i	$-0.211766\pi$
$233$	−2.15549	−	3.73341i	−0.141211	−	0.244584i	−0.927953	+	0.372698i	$0.878433\pi$
$234$	−3.83952	−	10.1123i	−0.250997	−	0.661060i
$235$	−1.71863	+	2.97675i	−0.112111	+	0.194182i
$236$	3.37628	+	12.6004i	0.219777	+	0.820219i
$237$	2.12339	+	13.4643i	0.137929	+	0.874597i
$238$	−5.93411	+	15.1667i	−0.384651	+	0.983112i
$239$	15.5141	−	15.5141i	1.00352	−	1.00352i	0.00353113	−	0.999994i	$-0.498876\pi$
$239$	15.5141	−	15.5141i	1.00352	−	1.00352i	0.999994	−	0.00353113i	$-0.00112400\pi$
$240$	0.778390	−	0.345944i	0.0502448	−	0.0223306i
$241$	−15.0290	−	4.02702i	−0.968106	−	0.259403i	−0.260078	−	0.965588i	$-0.583748\pi$
$241$	−15.0290	−	4.02702i	−0.968106	−	0.259403i	−0.708028	+	0.706184i	$0.750415\pi$
$242$	−9.94217	+	2.66400i	−0.639107	+	0.171248i
$243$	4.08444	−	15.0438i	0.262017	−	0.965063i
$244$	−3.73463	+	2.15619i	−0.239085	+	0.138036i
$245$	−2.91101	+	1.83765i	−0.185977	+	0.117403i
$246$	7.78033	−	20.2284i	0.496055	−	1.28971i
$247$	13.5823	−	0.680242i	0.864222	−	0.0432827i
$248$	−3.01908	−	1.74306i	−0.191712	−	0.110685i
$249$	8.12338	−	3.61031i	0.514798	−	0.228794i
$250$	2.39947	−	4.15601i	0.151756	−	0.262849i
$251$	−1.90632	+	3.30185i	−0.120326	+	0.208411i	−0.919896	−	0.392162i	$-0.871727\pi$
$251$	−1.90632	+	3.30185i	−0.120326	+	0.208411i	0.799570	+	0.600573i	$0.205061\pi$
$252$	−7.77637	+	1.59000i	−0.489865	+	0.100161i
$253$	−0.412712	+	0.110586i	−0.0259470	+	0.00695248i
$254$	1.29266	+	1.29266i	0.0811087	+	0.0811087i
$255$	0.551537	−	5.21429i	0.0345386	−	0.326532i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.55019	+	16.5414i	−0.595725	+	1.03183i	0.397720	+	0.917507i	$0.369802\pi$
$257$	−9.55019	+	16.5414i	−0.595725	+	1.03183i	−0.993444	+	0.114318i	$0.963532\pi$
$258$	−2.48556	+	3.41632i	−0.154744	+	0.212691i
$259$	−2.67568	−	3.34798i	−0.166259	−	0.208033i
$260$	0.808663	−	1.57803i	0.0501511	−	0.0978655i
$261$	1.03134	+	0.220646i	0.0638381	+	0.0136576i
$262$	0.913552	+	0.913552i	0.0564394	+	0.0564394i
$263$			29.0178i			1.78932i	0.446752	+	0.894658i	$0.352581\pi$
$263$			29.0178i			1.78932i	−0.446752	+	0.894658i	$0.647419\pi$
$264$	−0.522856	+	1.35939i	−0.0321796	+	0.0836649i
$265$	1.19613	+	1.19613i	0.0734779	+	0.0734779i
$266$	1.10689	−	9.91761i	0.0678678	−	0.608088i
$267$	6.28713	+	0.665015i	0.384766	+	0.0406983i
$268$	−9.37101	−	2.51096i	−0.572426	−	0.153381i
$269$	−9.58734	+	5.53525i	−0.584551	+	0.337490i	−0.762940	−	0.646470i	$-0.776245\pi$
$269$	−9.58734	+	5.53525i	−0.584551	+	0.337490i	0.178389	+	0.983960i	$0.442911\pi$
$270$	2.27919	−	1.15560i	0.138707	−	0.0703278i
$271$	−6.16716	−	23.0162i	−0.374628	−	1.39813i	−0.853887	−	0.520459i	$-0.825761\pi$
$271$	−6.16716	−	23.0162i	−0.374628	−	1.39813i	0.479258	−	0.877674i	$-0.340906\pi$
$272$	−6.15563			−0.373240
$273$	−10.5184	+	12.7421i	−0.636606	+	0.771190i
$274$	9.08819			0.549038
$275$	1.03557	+	3.86478i	0.0624469	+	0.233055i
$276$	0.315936	−	0.821413i	0.0190171	−	0.0494433i
$277$	0.306356	−	0.176875i	0.0184071	−	0.0106274i	−0.490768	−	0.871290i	$-0.663284\pi$
$277$	0.306356	−	0.176875i	0.0184071	−	0.0106274i	0.509175	+	0.860663i	$0.329950\pi$
$278$	9.95046	+	2.66622i	0.596789	+	0.159909i
$279$	−9.31219	−	4.76035i	−0.557506	−	0.284995i
$280$	−1.04771	−	0.771548i	−0.0626129	−	0.0461088i
$281$	14.1463	+	14.1463i	0.843899	+	0.843899i	0.989364	−	0.145464i	$-0.0464675\pi$
$281$	14.1463	+	14.1463i	0.843899	+	0.843899i	−0.145464	+	0.989364i	$0.546468\pi$
$282$	11.2989	+	4.34582i	0.672838	+	0.258790i
$283$			13.3627i			0.794332i	0.917747	+	0.397166i	$0.130006\pi$
$283$			13.3627i			0.794332i	−0.917747	+	0.397166i	$0.869994\pi$
$284$	−9.84216	−	9.84216i	−0.584025	−	0.584025i
$285$	0.500492	+	3.17359i	0.0296466	+	0.187987i
$286$	0.930221	+	2.88568i	0.0550051	+	0.170634i
$287$	−32.7311	+	4.96862i	−1.93206	+	0.293288i
$288$	−1.63058	−	2.51817i	−0.0960830	−	0.148385i
$289$	−10.4459	+	18.0928i	−0.614465	+	1.06428i
$290$	0.0864461	+	0.149729i	0.00507629	+	0.00879239i
$291$	−25.8182	−	2.73090i	−1.51349	−	0.160088i
$292$	10.2373	+	10.2373i	0.599090	+	0.599090i
$293$	26.4779	−	7.09474i	1.54686	−	0.414479i	0.618383	−	0.785877i	$-0.287788\pi$
$293$	26.4779	−	7.09474i	1.54686	−	0.414479i	0.928474	+	0.371398i	$0.121121\pi$
$294$	7.99022	+	9.11901i	0.465999	+	0.531832i
$295$	−3.20767	+	5.55585i	−0.186758	+	0.323474i
$296$	0.809943	−	1.40286i	0.0470770	−	0.0815398i
$297$	−1.35849	+	4.15289i	−0.0788274	+	0.240975i
$298$	−10.8360	−	6.25615i	−0.627711	−	0.362409i
$299$	−0.562085	−	1.74367i	−0.0325062	−	0.100839i
$300$	−7.69200	−	2.95853i	−0.444098	−	0.170811i
$301$	6.41373	+	0.715828i	0.369681	+	0.0412596i
$302$	10.7370	−	6.19901i	0.617845	−	0.356713i
$303$	−27.4939	−	10.5748i	−1.57949	−	0.607509i
$304$	3.64326	−	0.976208i	0.208955	−	0.0559894i
$305$	−2.04852	−	0.548898i	−0.117298	−	0.0314298i
$306$	−18.4429	+	0.942047i	−1.05431	+	0.0538533i
$307$	18.3625	−	18.3625i	1.04801	−	1.04801i	0.0492173	−	0.998788i	$-0.484327\pi$
$307$	18.3625	−	18.3625i	1.04801	−	1.04801i	0.998788	−	0.0492173i	$-0.0156727\pi$
$308$	2.19961	−	0.333903i	0.125334	−	0.0190259i
$309$	2.83170	−	0.446574i	0.161090	−	0.0254047i
$310$	−0.443729	−	1.65602i	−0.0252021	−	0.0940556i
$311$	12.6476	−	21.9063i	0.717181	−	1.24219i	−0.244931	−	0.969541i	$-0.578765\pi$
$311$	12.6476	−	21.9063i	0.717181	−	1.24219i	0.962112	−	0.272654i	$-0.0879014\pi$
$312$	−5.93357	−	1.94751i	−0.335922	−	0.110256i
$313$	3.27023	+	5.66420i	0.184844	+	0.320160i	0.943524	−	0.331304i	$-0.107489\pi$
$313$	3.27023	+	5.66420i	0.184844	+	0.320160i	−0.758680	+	0.651464i	$0.774155\pi$
$314$	−7.84106	−	2.10101i	−0.442497	−	0.118567i
$315$	−3.25713	−	2.15129i	−0.183518	−	0.121211i
$316$	6.81533	+	3.93483i	0.383392	+	0.221352i
$317$	13.4616	+	3.60703i	0.756080	+	0.202591i	0.616213	−	0.787579i	$-0.288666\pi$
$317$	13.4616	+	3.60703i	0.756080	+	0.202591i	0.139867	+	0.990170i	$0.455333\pi$
$318$	3.50503	−	4.81754i	0.196552	−	0.270154i
$319$	−0.285552	−	0.0765133i	−0.0159878	−	0.00428392i
$320$	0.127284	−	0.475031i	0.00711540	−	0.0265550i
$321$	−11.3392	−	14.0217i	−0.632891	−	0.782615i
$322$	−1.32911	+	0.201760i	−0.0740686	+	0.0112437i
$323$	6.00918	−	22.4266i	0.334360	−	1.24785i
$324$	−5.27075	−	7.29515i	−0.292820	−	0.405286i
$325$	−16.3283	+	5.26357i	−0.905732	+	0.291970i
$326$	4.02604	+	2.32443i	0.222981	+	0.128738i
$327$	12.3284	+	1.30403i	0.681763	+	0.0721129i
$328$	−6.25647	−	10.8365i	−0.345456	−	0.598347i
$329$	−2.77530	−	18.2825i	−0.153007	−	1.00795i
$330$	−0.654547	+	0.290904i	−0.0360316	+	0.0160137i
$331$	−1.23950	−	1.23950i	−0.0681293	−	0.0681293i	0.672221	−	0.740350i	$-0.265340\pi$
$331$	−1.23950	−	1.23950i	−0.0681293	−	0.0681293i	−0.740350	+	0.672221i	$0.765340\pi$
$332$	1.32835	−	4.95749i	0.0729029	−	0.272077i
$333$	2.21197	−	4.32706i	0.121215	−	0.237122i
$334$	−1.12793			−0.0617176
$335$	−2.38556	−	4.13192i	−0.130337	−	0.225751i
$336$	−2.10935	+	4.06825i	−0.115074	+	0.221941i
$337$			25.2287i			1.37430i	0.726518	+	0.687148i	$0.241138\pi$
$337$			25.2287i			1.37430i	−0.726518	+	0.687148i	$0.758862\pi$
$338$	−12.1580	+	4.60245i	−0.661309	+	0.250340i
$339$	5.76908	+	7.13388i	0.313334	+	0.387459i
$340$	−2.14060	−	2.14060i	−0.116090	−	0.116090i
$341$	2.53874	+	1.46574i	0.137480	+	0.0793743i
$342$	10.7661	−	3.48237i	0.582167	−	0.188305i
$343$	6.06170	−	17.5002i	0.327301	−	0.944920i
$344$	0.631315	+	2.35610i	0.0340382	+	0.127032i
$345$	0.395509	−	0.175778i	0.0212935	−	0.00946359i
$346$	0.349243	+	1.30339i	0.0187754	+	0.0700709i
$347$	−26.6319	+	15.3760i	−1.42968	+	0.825425i	−0.997095	−	0.0761696i	$-0.975731\pi$
$347$	−26.6319	+	15.3760i	−1.42968	+	0.825425i	−0.432583	+	0.901594i	$0.642398\pi$
$348$	0.473471	−	0.382890i	0.0253807	−	0.0205251i
$349$	−11.1271	−	2.98149i	−0.595619	−	0.159596i	−0.0515991	−	0.998668i	$-0.516432\pi$
$349$	−11.1271	−	2.98149i	−0.595619	−	0.159596i	−0.544020	+	0.839072i	$0.683098\pi$
$350$	1.88936	+	12.4463i	0.100990	+	0.665282i
$351$	−18.0756	−	4.92686i	−0.964802	−	0.262976i
$352$	0.420449	+	0.728240i	0.0224100	+	0.0388153i
$353$	−8.39939	+	8.39939i	−0.447055	+	0.447055i	−0.894374	−	0.447320i	$-0.852379\pi$
$353$	−8.39939	+	8.39939i	−0.447055	+	0.447055i	0.447320	+	0.894374i	$0.352379\pi$
$354$	21.0884	+	8.11111i	1.12084	+	0.431101i
$355$		−	6.84516i		−	0.363303i
$356$	2.58103	−	2.58103i	0.136794	−	0.136794i
$357$	15.1954	+	23.7661i	0.804225	+	1.25784i
$358$	−2.58505	−	9.64755i	−0.136624	−	0.509889i
$359$	7.92460	−	29.5750i	0.418244	−	1.56091i	−0.360004	−	0.932951i	$-0.617225\pi$
$359$	7.92460	−	29.5750i	0.418244	−	1.56091i	0.778248	−	0.627957i	$-0.216109\pi$
$360$	0.308657	−	1.44272i	0.0162677	−	0.0760379i
$361$		−	4.77368i		−	0.251247i
$362$	24.3175	−	6.51586i	1.27810	−	0.342466i
$363$	−6.39994	+	16.6395i	−0.335910	+	0.873345i
$364$	1.90165	+	9.34793i	0.0996737	+	0.489964i
$365$			7.11994i			0.372675i
$366$	−0.785672	+	7.42783i	−0.0410677	+	0.388259i
$367$	19.7358			1.03020			0.515100	−	0.857130i	$-0.327755\pi$
$367$	19.7358			1.03020			0.515100	+	0.857130i	$0.327755\pi$
$368$	−0.254056	−	0.440038i	−0.0132436	−	0.0229386i
$369$	−20.4034	−	31.5098i	−1.06216	−	1.64033i
$370$	0.769497	−	0.206186i	0.0400042	−	0.0107191i
$371$	−9.04435	−	1.00943i	−0.469559	−	0.0524069i
$372$	−5.51775	+	2.45228i	−0.286082	+	0.127145i
$373$	20.8743			1.08083			0.540414	−	0.841399i	$-0.318267\pi$
$373$	20.8743			1.08083			0.540414	+	0.841399i	$0.318267\pi$
$374$	5.17626			0.267658
$375$	−3.37577	−	7.59564i	−0.174324	−	0.392237i
$376$	6.05291	−	3.49465i	0.312155	−	0.180223i
$377$	0.266415	−	1.23925i	0.0137211	−	0.0638245i
$378$	−5.69721	+	12.5117i	−0.293033	+	0.643531i
$379$	4.31488	−	16.1033i	0.221640	−	0.827173i	−0.762082	−	0.647480i	$-0.775823\pi$
$379$	4.31488	−	16.1033i	0.221640	−	0.827173i	0.983723	−	0.179693i	$-0.0575105\pi$
$380$	1.60641	+	0.927458i	0.0824068	+	0.0475776i
$381$	3.12770	−	0.493256i	0.160237	−	0.0252702i
$382$	19.1400	−	5.12855i	0.979288	−	0.262399i
$383$	−7.69720	+	7.69720i	−0.393309	+	0.393309i	−0.875865	−	0.482556i	$-0.839708\pi$
$383$	−7.69720	+	7.69720i	−0.393309	+	0.393309i	0.482556	+	0.875865i	$0.339708\pi$
$384$	−1.72244	−	0.182190i	−0.0878980	−	0.00929733i
$385$	0.881021	+	0.648794i	0.0449010	+	0.0330656i
$386$	−8.42687	−	4.86526i	−0.428916	−	0.247635i
$387$	2.25205	+	6.96248i	0.114478	+	0.353923i
$388$	−10.5990	+	10.5990i	−0.538085	+	0.538085i
$389$	8.70908	−	15.0846i	0.441568	−	0.764818i	−0.556238	−	0.831023i	$-0.687756\pi$
$389$	8.70908	−	15.0846i	0.441568	−	0.764818i	0.997806	+	0.0662048i	$0.0210891\pi$
$390$	−1.38614	−	2.74062i	−0.0701899	−	0.138777i
$391$	−3.12775			−0.158177
$392$	6.99454	−	0.276443i	0.353278	−	0.0139625i
$393$	2.21042	−	0.348595i	0.111501	−	0.0175843i
$394$		−	2.79752i		−	0.140937i
$395$	1.00168	+	3.73833i	0.0504002	+	0.188096i
$396$	1.37115	+	2.11753i	0.0689031	+	0.106410i
$397$	−8.56875	+	8.56875i	−0.430053	+	0.430053i	−0.888646	−	0.458593i	$-0.848354\pi$
$397$	−8.56875	+	8.56875i	−0.430053	+	0.430053i	0.458593	+	0.888646i	$0.348354\pi$
$398$	7.35542	+	7.35542i	0.368694	+	0.368694i
$399$	−12.7625	−	11.6564i	−0.638925	−	0.583548i
$400$	−4.12067	+	2.37907i	−0.206034	+	0.118954i
$401$	11.4962	−	3.08039i	0.574091	−	0.153827i	0.0399191	−	0.999203i	$-0.487290\pi$
$401$	11.4962	−	3.08039i	0.574091	−	0.153827i	0.534172	+	0.845376i	$0.320623\pi$
$402$	−13.0659	+	10.5662i	−0.651667	+	0.526995i
$403$	−5.73235	+	11.1862i	−0.285549	+	0.557223i
$404$	−14.7287	+	8.50365i	−0.732783	+	0.423072i
$405$	0.703976	−	4.36975i	0.0349808	−	0.217135i
$406$	−0.866195	−	0.338906i	−0.0429885	−	0.0168196i
$407$	−0.681080	+	1.17967i	−0.0337599	+	0.0584739i
$408$	−6.27260	+	8.62148i	−0.310540	+	0.426827i
$409$	0.618309	−	2.30756i	0.0305734	−	0.114102i	−0.948953	−	0.315418i	$-0.897855\pi$
$409$	0.618309	−	2.30756i	0.0305734	−	0.114102i	0.979526	+	0.201316i	$0.0645219\pi$
$410$	1.59270	−	5.94403i	0.0786578	−	0.293555i
$411$	9.26089	−	12.7288i	0.456806	−	0.627864i
$412$	0.827544	−	1.43335i	0.0407702	−	0.0706160i
$413$	−5.17986	−	34.1227i	−0.254884	−	1.67907i
$414$	−0.828519	−	1.27952i	−0.0407195	−	0.0628848i
$415$	2.18588	−	1.26202i	0.107301	−	0.0619501i
$416$	−3.02842	+	1.95671i	−0.148480	+	0.0959355i
$417$	13.8738	−	11.2196i	0.679403	−	0.549425i
$418$	−3.06361	+	0.820892i	−0.149846	+	0.0401511i
$419$	−28.4494	+	16.4253i	−1.38984	+	0.802427i	−0.993297	−	0.115587i	$-0.963125\pi$
$419$	−28.4494	+	16.4253i	−1.38984	+	0.802427i	−0.396547	+	0.918014i	$0.629792\pi$
$420$	−2.14824	+	0.681202i	−0.104823	+	0.0332392i
$421$	−12.3072	−	12.3072i	−0.599815	−	0.599815i	0.340448	−	0.940263i	$-0.389421\pi$
$421$	−12.3072	−	12.3072i	−0.599815	−	0.599815i	−0.940263	+	0.340448i	$0.889421\pi$
$422$	−0.482883	+	0.482883i	−0.0235064	+	0.0235064i
$423$	17.6003	−	11.3966i	0.855754	−	0.554123i
$424$	−0.890251	−	3.32246i	−0.0432344	−	0.161353i
$425$			29.2894i			1.42074i
$426$	−23.8140	+	3.75559i	−1.15379	+	0.181959i
$427$	10.4527	−	4.57356i	0.505842	−	0.221330i
$428$	−10.4113			−0.503249
$429$	4.98953	+	1.63766i	0.240897	+	0.0790669i
$430$	−0.599789	+	1.03886i	−0.0289244	+	0.0500985i
$431$	8.18787	−	8.18787i	0.394396	−	0.394396i	−0.481855	−	0.876251i	$-0.660037\pi$
$431$	8.18787	−	8.18787i	0.394396	−	0.394396i	0.876251	+	0.481855i	$0.160037\pi$
$432$	−5.18848	−	0.282258i	−0.249631	−	0.0135801i
$433$	34.2585	+	19.7792i	1.64636	+	0.950526i	0.978502	+	0.206236i	$0.0661216\pi$
$433$	34.2585	+	19.7792i	1.64636	+	0.950526i	0.667857	+	0.744290i	$0.267212\pi$
$434$	7.42690	+	5.46926i	0.356503	+	0.262533i
$435$	0.297797	+	0.0314992i	0.0142783	+	0.00151027i
$436$	5.06113	−	5.06113i	0.242384	−	0.242384i
$437$	1.85119	−	0.496024i	0.0885542	−	0.0237280i
$438$	24.7699	−	3.90635i	1.18355	−	0.186653i
$439$	−0.169493	−	0.0978570i	−0.00808948	−	0.00467046i	0.495950	−	0.868351i	$-0.334820\pi$
$439$	−0.169493	−	0.0978570i	−0.00808948	−	0.00467046i	−0.504039	+	0.863681i	$0.668153\pi$
$440$	−0.107033	+	0.399453i	−0.00510260	+	0.0190432i
$441$	20.9140	−	1.89868i	0.995904	−	0.0904133i
$442$	1.11017	+	22.1667i	0.0528054	+	1.05436i
$443$	15.6355	−	9.02714i	0.742863	−	0.428892i	−0.0802461	−	0.996775i	$-0.525571\pi$
$443$	15.6355	−	9.02714i	0.742863	−	0.428892i	0.823110	+	0.567883i	$0.192237\pi$
$444$	−1.13949	−	2.56391i	−0.0540780	−	0.121678i
$445$	1.79509			0.0850954
$446$	0.371864			0.0176083
$447$	−19.8041	+	8.80166i	−0.936704	+	0.416304i
$448$	1.06056	+	2.42388i	0.0501069	+	0.114518i
$449$	−3.41471	+	0.914969i	−0.161150	+	0.0431800i	−0.338492	−	0.940969i	$-0.609917\pi$
$449$	−3.41471	+	0.914969i	−0.161150	+	0.0431800i	0.177342	+	0.984149i	$0.443250\pi$
$450$	−11.9818	+	7.75854i	−0.564829	+	0.365741i
$451$	5.26106	+	9.11242i	0.247733	+	0.429087i
$452$	5.29700			0.249150
$453$	2.25879	−	21.3549i	0.106127	−	1.00334i
$454$		−	23.1434i		−	1.08617i
$455$	−2.58942	+	3.91201i	−0.121394	+	0.183398i
$456$	2.34523	−	6.09745i	0.109825	−	0.285539i
$457$	−1.89312	+	0.507259i	−0.0885563	+	0.0237286i	−0.302825	−	0.953046i	$-0.597930\pi$
$457$	−1.89312	+	0.507259i	−0.0885563	+	0.0237286i	0.214269	+	0.976775i	$0.431263\pi$
$458$			17.8961i			0.836228i
$459$	−17.4739	+	26.7907i	−0.815611	+	1.25048i
$460$	0.0646747	−	0.241369i	0.00301547	−	0.0112539i
$461$	7.40526	+	27.6368i	0.344897	+	1.28717i	0.892732	+	0.450587i	$0.148785\pi$
$461$	7.40526	+	27.6368i	0.344897	+	1.28717i	−0.547835	+	0.836586i	$0.684548\pi$
$462$	1.77375	−	3.42099i	0.0825222	−	0.159159i
$463$	16.0515	−	16.0515i	0.745976	−	0.745976i	−0.227745	−	0.973721i	$-0.573135\pi$
$463$	16.0515	−	16.0515i	0.745976	−	0.745976i	0.973721	+	0.227745i	$0.0731353\pi$
$464$		−	0.351558i		−	0.0163207i
$465$	−2.77155	−	1.06601i	−0.128528	−	0.0494349i
$466$	−3.04832	+	3.04832i	−0.141211	+	0.141211i
$467$	9.98943	+	17.3022i	0.462256	+	0.800650i	0.999073	−	0.0430482i	$-0.0137069\pi$
$467$	9.98943	+	17.3022i	0.462256	+	0.800650i	−0.536817	+	0.843698i	$0.680374\pi$
$468$	−8.77397	+	6.32594i	−0.405577	+	0.292417i
$469$	23.9035	+	9.35245i	1.10376	+	0.431856i
$470$	3.32013	+	0.889627i	0.153146	+	0.0410354i
$471$	−10.9327	+	8.84113i	−0.503752	+	0.407378i
$472$	11.2972	−	6.52247i	0.519998	−	0.300221i
$473$	−0.530872	−	1.98124i	−0.0244095	−	0.0910976i
$474$	12.4559	−	5.53584i	0.572118	−	0.254269i
$475$	−4.64494	−	17.3351i	−0.213124	−	0.795391i
$476$	16.1858	+	1.80647i	0.741874	+	0.0827995i
$477$	−3.17574	−	9.81817i	−0.145407	−	0.449543i
$478$	−19.0008	−	10.9701i	−0.869078	−	0.501762i
$479$	26.0274	+	26.0274i	1.18922	+	1.18922i	0.977283	+	0.211939i	$0.0679779\pi$
$479$	26.0274	+	26.0274i	1.18922	+	1.18922i	0.211939	+	0.977283i	$0.432022\pi$
$480$	−0.535618	−	0.662330i	−0.0244475	−	0.0302311i
$481$	−5.19784	−	2.66363i	−0.237001	−	0.121451i
$482$			15.5592i			0.708703i
$483$	−1.07179	+	2.06713i	−0.0487680	+	0.0940576i
$484$	5.14644	+	8.91390i	0.233929	+	0.405177i
$485$	−7.37157			−0.334726
$486$	−15.5884	−	0.0516358i	−0.707103	−	0.00234225i
$487$	4.79861	−	17.9087i	0.217446	−	0.811519i	−0.767845	−	0.640635i	$-0.778671\pi$
$487$	4.79861	−	17.9087i	0.217446	−	0.811519i	0.985291	−	0.170884i	$-0.0546622\pi$
$488$	3.04932	+	3.04932i	0.138036	+	0.138036i
$489$	7.35810	−	3.27020i	0.332745	−	0.147883i
$490$	2.52846	+	2.33620i	0.114224	+	0.105539i
$491$	3.31662	+	5.74455i	0.149677	+	0.259248i	0.931108	−	0.364744i	$-0.118843\pi$
$491$	3.31662	+	5.74455i	0.149677	+	0.259248i	−0.781431	+	0.623991i	$0.785510\pi$
$492$	−21.5528	−	2.27973i	−0.971676	−	0.102778i
$493$	−1.87413	−	1.08203i	−0.0844067	−	0.0487322i
$494$	−4.17243	−	12.9435i	−0.187726	−	0.582353i
$495$	−0.259550	+	1.21318i	−0.0116659	+	0.0545283i
$496$	−0.902276	+	3.36734i	−0.0405134	+	0.151198i
$497$	22.9909	+	28.7676i	1.03128	+	1.29040i
$498$	−5.58978	−	6.91216i	−0.250484	−	0.309741i
$499$	−6.31916	+	23.5834i	−0.282885	+	1.05574i	0.667487	+	0.744622i	$0.267370\pi$
$499$	−6.31916	+	23.5834i	−0.282885	+	1.05574i	−0.950371	+	0.311118i	$0.899297\pi$
$500$	−4.63542	−	1.24206i	−0.207302	−	0.0555465i
$501$	−1.14936	+	1.57976i	−0.0513497	+	0.0705785i
$502$	3.68273	+	0.986785i	0.164368	+	0.0440424i
$503$	26.7672	+	15.4541i	1.19349	+	0.689063i	0.959097	−	0.283079i	$-0.0913558\pi$
$503$	26.7672	+	15.4541i	1.19349	+	0.689063i	0.234395	+	0.972141i	$0.424689\pi$
$504$	3.54849	+	7.09987i	0.158062	+	0.316253i
$505$	−8.07899	−	2.16476i	−0.359511	−	0.0963306i
$506$	0.213636	+	0.370028i	0.00949726	+	0.0164497i
$507$	−5.94293	+	21.7182i	−0.263935	+	0.964541i
$508$	0.914049	−	1.58318i	0.0405544	−	0.0702422i
$509$	1.10063	+	4.10760i	0.0487845	+	0.182066i	0.986019	−	0.166634i	$-0.0532898\pi$
$509$	1.10063	+	4.10760i	0.0487845	+	0.182066i	−0.937234	+	0.348700i	$0.886623\pi$
$510$	−5.17937	+	0.816815i	−0.229346	+	0.0361692i
$511$	−23.9138	−	29.9224i	−1.05788	−	1.32369i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.09338	−	18.6274i	0.269029	−	0.822421i
$514$	18.4496	+	4.94354i	0.813775	+	0.218050i
$515$	0.786218	−	0.210667i	0.0346449	−	0.00928308i
$516$	3.94323	+	1.51666i	0.173591	+	0.0667673i
$517$	−5.08988	+	2.93865i	−0.223853	+	0.129241i
$518$	−2.54138	+	3.45103i	−0.111662	+	0.151630i
$519$	2.18139	+	0.839016i	0.0957525	+	0.0368287i
$520$	−1.73356	−	0.372683i	−0.0760217	−	0.0163432i
$521$	6.48176	+	3.74225i	0.283971	+	0.163951i	0.635220	−	0.772331i	$-0.280910\pi$
$521$	6.48176	+	3.74225i	0.283971	+	0.163951i	−0.351249	+	0.936282i	$0.614243\pi$
$522$	−0.0538018	−	1.05330i	−0.00235484	−	0.0461017i
$523$	3.71365	−	6.43223i	0.162387	−	0.281262i	−0.773338	−	0.633995i	$-0.781414\pi$
$523$	3.71365	−	6.43223i	0.162387	−	0.281262i	0.935724	+	0.352733i	$0.114748\pi$
$524$	0.645979	−	1.11887i	0.0282197	−	0.0488780i
$525$	19.3573	+	10.0366i	0.844823	+	0.438032i
$526$	28.0291	−	7.51037i	1.22213	−	0.327468i
$527$	15.1740	+	15.1740i	0.660991	+	0.660991i
$528$	1.44840	+	0.153203i	0.0630335	+	0.00666731i
$529$	11.3709	+	19.6950i	0.494387	+	0.856304i
$530$	0.845794	−	1.46496i	0.0367390	−	0.0636337i
$531$	32.8494	−	21.2708i	1.42554	−	0.923076i
$532$	−9.86616	+	1.49769i	−0.427752	+	0.0649332i
$533$	−37.8944	+	24.4841i	−1.64139	+	1.06053i
$534$	−0.984873	−	6.24502i	−0.0426196	−	0.270248i
$535$	−3.62049	−	3.62049i	−0.156528	−	0.156528i
$536$			9.70159i			0.419045i
$537$	−16.1464	−	6.21029i	−0.696768	−	0.267994i
$538$	7.82803	+	7.82803i	0.337490	+	0.337490i
$539$	−5.88170	+	0.232460i	−0.253343	+	0.0100128i
$540$	−1.70612	−	1.90243i	−0.0734199	−	0.0818677i
$541$	7.42291	+	1.98896i	0.319136	+	0.0855122i	0.414831	−	0.909899i	$-0.363841\pi$
$541$	7.42291	+	1.98896i	0.319136	+	0.0855122i	−0.0956952	+	0.995411i	$0.530507\pi$
$542$	−20.6357	+	11.9140i	−0.886381	+	0.511752i
$543$	15.6536	−	40.6984i	0.671760	−	1.74653i
$544$	1.59319	+	5.94588i	0.0683077	+	0.254928i
$545$	3.51999			0.150780
$546$	15.0303	+	6.86213i	0.643239	+	0.293672i
$547$	41.0985			1.75724			0.878621	−	0.477519i	$-0.158464\pi$
$547$	41.0985			1.75724			0.878621	+	0.477519i	$0.158464\pi$
$548$	−2.35220	−	8.77852i	−0.100481	−	0.375000i
$549$	9.60270	+	8.66938i	0.409833	+	0.370000i
$550$	3.46507	−	2.00056i	0.147751	−	0.0853041i
$551$	1.28082	+	0.343194i	0.0545646	+	0.0146205i
$552$	−0.875194	−	0.0925729i	−0.0372507	−	0.00394016i
$553$	−16.7657	−	12.3464i	−0.712948	−	0.525023i
$554$	−0.250139	−	0.250139i	−0.0106274	−	0.0106274i
$555$	0.495338	−	1.28785i	0.0210259	−	0.0546661i
$556$		−	10.3015i		−	0.436880i
$557$	−5.28502	−	5.28502i	−0.223934	−	0.223934i	0.586219	−	0.810153i	$-0.300616\pi$
$557$	−5.28502	−	5.28502i	−0.223934	−	0.223934i	−0.810153	+	0.586219i	$0.800616\pi$
$558$	−2.18797	+	10.2270i	−0.0926243	+	0.432942i
$559$	8.37055	−	2.69831i	0.354036	−	0.114126i
$560$	−0.474090	+	1.21171i	−0.0200340	+	0.0512039i
$561$	5.27462	−	7.24979i	0.222695	−	0.306086i
$562$	10.0030	−	17.3256i	0.421950	−	0.730838i
$563$	0.446148	+	0.772752i	0.0188029	+	0.0325676i	0.875274	−	0.483628i	$-0.160681\pi$
$563$	0.446148	+	0.772752i	0.0188029	+	0.0325676i	−0.856471	+	0.516195i	$0.827348\pi$
$564$	1.27338	−	12.0387i	0.0536189	−	0.506919i
$565$	1.84201	+	1.84201i	0.0774941	+	0.0774941i
$566$	12.9074	−	3.45853i	0.542539	−	0.145373i
$567$	11.7182	+	20.7288i	0.492117	+	0.870529i
$568$	−6.95946	+	12.0541i	−0.292012	+	0.505780i
$569$	20.8168	−	36.0557i	0.872684	−	1.51153i	0.0134754	−	0.999909i	$-0.495711\pi$
$569$	20.8168	−	36.0557i	0.872684	−	1.51153i	0.859209	−	0.511625i	$-0.170956\pi$
$570$	2.93591	−	1.30482i	0.122972	−	0.0546530i
$571$	−10.7016	−	6.17860i	−0.447850	−	0.258566i	0.259072	−	0.965858i	$-0.416583\pi$
$571$	−10.7016	−	6.17860i	−0.447850	−	0.258566i	−0.706922	+	0.707292i	$0.749917\pi$
$572$	2.54659	−	1.64539i	0.106478	−	0.0687973i
$573$	12.3207	−	32.0332i	0.514706	−	1.33821i
$574$	13.2708	+	30.3299i	0.553911	+	1.26594i
$575$	−2.09377	+	1.20884i	−0.0873161	+	0.0504120i
$576$	−2.01034	+	2.22677i	−0.0837643	+	0.0927822i
$577$	−28.2814	+	7.57797i	−1.17737	+	0.315475i	−0.793882	−	0.608071i	$-0.791943\pi$
$577$	−28.2814	+	7.57797i	−1.17737	+	0.315475i	−0.383487	+	0.923546i	$0.625277\pi$
$578$	20.1799	+	5.40720i	0.839375	+	0.224910i
$579$	−15.4012	+	6.84483i	−0.640052	+	0.284462i
$580$	0.122253	−	0.122253i	0.00507629	−	0.00507629i
$581$	−4.94767	+	12.6455i	−0.205264	+	0.524624i
$582$	4.04440	+	25.6453i	0.167646	+	1.06303i
$583$	0.748611	+	2.79386i	0.0310043	+	0.115710i
$584$	7.23883	−	12.5380i	0.299545	−	0.518827i
$585$	−5.25095	−	0.851293i	−0.217100	−	0.0351966i
$586$	−13.7060	−	23.7395i	−0.566189	−	0.980668i
$587$	30.0764	+	8.05893i	1.24138	+	0.332628i	0.819002	−	0.573790i	$-0.194528\pi$
$587$	30.0764	+	8.05893i	1.24138	+	0.332628i	0.422382	+	0.906418i	$0.361194\pi$
$588$	6.74027	−	10.0781i	0.277964	−	0.415615i
$589$	−11.3873	−	6.57445i	−0.469205	−	0.270896i
$590$	6.19675	+	1.66041i	0.255116	+	0.0683582i
$591$	−3.91817	−	2.85068i	−0.161172	−	0.117261i
$592$	−1.56469	−	0.419258i	−0.0643084	−	0.0172314i
$593$	8.84257	−	33.0009i	0.363121	−	1.35519i	−0.506830	−	0.862046i	$-0.669183\pi$
$593$	8.84257	−	33.0009i	0.363121	−	1.35519i	0.869950	−	0.493139i	$-0.164151\pi$
$594$	4.36299	+	0.237350i	0.179016	+	0.00973861i
$595$	5.00036	+	6.25675i	0.204995	+	0.256502i
$596$	−3.23842	+	12.0860i	−0.132651	+	0.495060i
$597$	17.7971	−	2.80669i	0.728386	−	0.114870i
$598$	−1.53878	+	0.994227i	−0.0629252	+	0.0406570i
$599$	−9.95367	−	5.74675i	−0.406696	−	0.234806i	0.282673	−	0.959216i	$-0.408779\pi$
$599$	−9.95367	−	5.74675i	−0.406696	−	0.234806i	−0.689369	+	0.724410i	$0.742112\pi$
$600$	−0.866885	+	8.19563i	−0.0353904	+	0.334585i
$601$	15.6529	+	27.1117i	0.638497	+	1.10591i	0.985763	+	0.168143i	$0.0537769\pi$
$601$	15.6529	+	27.1117i	0.638497	+	1.10591i	−0.347266	+	0.937767i	$0.612890\pi$
$602$	−0.968559	−	6.38046i	−0.0394755	−	0.260048i
$603$	1.48471	+	29.0669i	0.0604622	+	1.18369i
$604$	−8.76673	−	8.76673i	−0.356713	−	0.356713i
$605$	−1.31012	+	4.88944i	−0.0532640	+	0.198784i
$606$	−3.09855	+	29.2941i	−0.125870	+	1.18999i
$607$	−39.8318			−1.61672			−0.808361	−	0.588687i	$-0.799645\pi$
$607$	−39.8318			−1.61672			−0.808361	+	0.588687i	$0.799645\pi$
$608$	−1.88589	−	3.26646i	−0.0764829	−	0.132472i
$609$	−1.35732	+	0.867833i	−0.0550014	+	0.0351664i
$610$			2.12078i			0.0858679i
$611$	−13.6760	−	21.1665i	−0.553272	−	0.856305i
$612$	5.68331	+	17.5706i	0.229734	+	0.710250i
$613$	−16.6804	−	16.6804i	−0.673713	−	0.673713i	0.284857	−	0.958570i	$-0.408054\pi$
$613$	−16.6804	−	16.6804i	−0.673713	−	0.673713i	−0.958570	+	0.284857i	$0.908054\pi$
$614$	−22.4894	−	12.9843i	−0.907599	−	0.524003i
$615$	−6.70215	−	8.28769i	−0.270257	−	0.334192i
$616$	−0.891826	−	2.03824i	−0.0359327	−	0.0821230i
$617$	2.52347	+	9.41771i	0.101591	+	0.379143i	0.997936	−	0.0642142i	$-0.0204541\pi$
$617$	2.52347	+	9.41771i	0.101591	+	0.379143i	−0.896345	+	0.443357i	$0.853787\pi$
$618$	−1.16426	−	2.61963i	−0.0468332	−	0.105377i
$619$	−4.07178	−	15.1961i	−0.163659	−	0.610783i	−0.998207	−	0.0598485i	$-0.980938\pi$
$619$	−4.07178	−	15.1961i	−0.163659	−	0.610783i	0.834549	−	0.550934i	$-0.185728\pi$
$620$	−1.48475	+	0.857219i	−0.0596288	+	0.0344267i
$621$	−2.63633	−	0.143419i	−0.105792	−	0.00575520i
$622$	−24.4333	−	6.54689i	−0.979688	−	0.262507i
$623$	−7.54407	+	6.02918i	−0.302247	+	0.241554i
$624$	−0.345429	+	6.23544i	−0.0138282	+	0.249617i
$625$	10.7153	+	18.5595i	0.428613	+	0.742380i
$626$	4.62480	−	4.62480i	0.184844	−	0.184844i
$627$	−1.97210	+	5.12734i	−0.0787580	+	0.204766i
$628$			8.11766i			0.323930i
$629$	−7.05086	+	7.05086i	−0.281136	+	0.281136i
$630$	−1.23498	+	3.70294i	−0.0492028	+	0.147529i
$631$	5.18146	+	19.3375i	0.206271	+	0.769813i	0.989058	+	0.147524i	$0.0471304\pi$
$631$	5.18146	+	19.3375i	0.206271	+	0.769813i	−0.782788	+	0.622289i	$0.786203\pi$
$632$	2.03682	−	7.60151i	0.0810203	−	0.302372i
$633$	0.184259	+	1.16838i	0.00732365	+	0.0464388i
$634$		−	13.9365i		−	0.553489i
$635$	0.868403	−	0.232688i	0.0344615	−	0.00923394i
$636$	−5.56056	−	2.13873i	−0.220490	−	0.0848060i
$637$	−2.25695	−	25.1377i	−0.0894235	−	0.995994i
$638$			0.295625i			0.0117039i
$639$	−19.0065	+	37.1804i	−0.751884	+	1.47083i
$640$	−0.491788			−0.0194396
$641$	10.4412	+	18.0847i	0.412403	+	0.714303i	0.995152	−	0.0983489i	$-0.0313561\pi$
$641$	10.4412	+	18.0847i	0.412403	+	0.714303i	−0.582749	+	0.812652i	$0.698023\pi$
$642$	−10.6091	+	14.5819i	−0.418709	+	0.575501i
$643$	−37.0135	+	9.91774i	−1.45967	+	0.391117i	−0.899376	−	0.437176i	$-0.855979\pi$
$643$	−37.0135	+	9.91774i	−1.45967	+	0.391117i	−0.560294	+	0.828294i	$0.689312\pi$
$644$	0.538885	+	1.23160i	0.0212351	+	0.0485320i
$645$	0.843831	+	1.89866i	0.0332258	+	0.0747596i
$646$	−23.2177			−0.913488
$647$	−37.8604			−1.48845			−0.744224	−	0.667931i	$-0.767180\pi$
$647$	−37.8604			−1.48845			−0.744224	+	0.667931i	$0.767180\pi$
$648$	−5.68240	+	6.97928i	−0.223226	+	0.274172i
$649$	−9.49984	+	5.48473i	−0.372901	+	0.215295i
$650$	9.31029	+	14.4096i	0.365180	+	0.565192i
$651$	15.2282	−	4.82882i	0.596839	−	0.189256i
$652$	1.20321	−	4.49046i	0.0471215	−	0.175860i
$653$	−24.0610	−	13.8916i	−0.941580	−	0.543622i	−0.0511249	−	0.998692i	$-0.516281\pi$
$653$	−24.0610	−	13.8916i	−0.941580	−	0.543622i	−0.890455	+	0.455071i	$0.849614\pi$
$654$	−1.93124	−	12.2458i	−0.0755173	−	0.478850i
$655$	0.613720	−	0.164446i	0.0239800	−	0.00642543i
$656$	−8.84798	+	8.84798i	−0.345456	+	0.345456i
$657$	19.7694	−	38.6729i	0.771278	−	1.50877i
$658$	−16.9412	+	7.41259i	−0.660438	+	0.288973i
$659$	−30.0678	−	17.3597i	−1.17128	−	0.676236i	−0.217295	−	0.976106i	$-0.569723\pi$
$659$	−30.0678	−	17.3597i	−1.17128	−	0.676236i	−0.953980	+	0.299870i	$0.903057\pi$
$660$	0.450400	+	0.556952i	0.0175318	+	0.0216793i
$661$	−29.3425	+	29.3425i	−1.14129	+	1.14129i	−0.153075	+	0.988215i	$0.548918\pi$
$661$	−29.3425	+	29.3425i	−1.14129	+	1.14129i	−0.988215	+	0.153075i	$0.951082\pi$
$662$	−0.876461	+	1.51808i	−0.0340646	+	0.0590017i
$663$	32.1775	+	21.0330i	1.24967	+	0.816854i
$664$	−5.13237			−0.199174
$665$	−3.95174	−	2.91011i	−0.153242	−	0.112849i
$666$	−4.75212	−	1.01668i	−0.184141	−	0.0393955i
$667$		−	0.178631i		−	0.00691662i
$668$	0.291930	+	1.08950i	0.0112951	+	0.0421539i
$669$	0.378930	−	0.520826i	0.0146503	−	0.0201363i
$670$	−3.37370	+	3.37370i	−0.130337	+	0.130337i
$671$	−2.56417	−	2.56417i	−0.0989885	−	0.0989885i
$672$	4.47557	+	0.984534i	0.172649	+	0.0379792i
$673$	7.85214	−	4.53343i	0.302678	−	0.174751i	−0.340968	−	0.940075i	$-0.610755\pi$
$673$	7.85214	−	4.53343i	0.302678	−	0.174751i	0.643645	+	0.765324i	$0.277421\pi$
$674$	24.3691	−	6.52967i	0.938661	−	0.251514i
$675$	−1.34302	+	24.6875i	−0.0516930	+	0.950224i
$676$	7.59235	+	10.5525i	0.292014	+	0.405867i
$677$	−6.00334	+	3.46603i	−0.230727	+	0.133210i	−0.610907	−	0.791702i	$-0.709195\pi$
$677$	−6.00334	+	3.46603i	−0.230727	+	0.133210i	0.380180	+	0.924912i	$0.375862\pi$
$678$	5.39765	−	7.41889i	0.207296	−	0.284921i
$679$	30.9799	−	24.7589i	1.18890	−	0.950161i
$680$	−1.51363	+	2.62169i	−0.0580452	+	0.100537i
$681$	−32.4142	−	23.5831i	−1.24212	−	0.903708i
$682$	0.758723	−	2.83159i	0.0290530	−	0.108427i
$683$	4.84776	−	18.0921i	0.185494	−	0.692274i	−0.809030	−	0.587767i	$-0.800007\pi$
$683$	4.84776	−	18.0921i	0.185494	−	0.692274i	0.994524	−	0.104506i	$-0.0333263\pi$
$684$	−6.15019	−	9.49800i	−0.235159	−	0.363165i
$685$	2.23473	−	3.87067i	0.0853848	−	0.147891i
$686$	−18.4727	−	1.32578i	−0.705293	−	0.0506185i
$687$	25.0649	+	18.2361i	0.956287	+	0.695751i
$688$	2.11242	−	1.21961i	0.0805353	−	0.0464971i
$689$	−11.8038	+	3.80504i	−0.449687	+	0.144960i
$690$	−0.272154	−	0.336538i	−0.0103607	−	0.0128118i
$691$	14.3758	−	3.85197i	0.546879	−	0.146536i	0.0252078	−	0.999682i	$-0.491975\pi$
$691$	14.3758	−	3.85197i	0.546879	−	0.146536i	0.521672	+	0.853146i	$0.325309\pi$
$692$	1.16859	−	0.674686i	0.0444232	−	0.0256477i
$693$	−2.98392	−	5.97027i	−0.113350	−	0.226792i
$694$	21.7449	+	21.7449i	0.825425	+	0.825425i
$695$	3.58231	−	3.58231i	0.135885	−	0.135885i
$696$	−0.492387	−	0.358238i	−0.0186639	−	0.0135790i
$697$	19.9355	+	74.4005i	0.755113	+	2.81812i
$698$			11.5196i			0.436023i
$699$	1.16318	+	7.37566i	0.0439956	+	0.278973i
$700$	11.5332	−	5.04631i	0.435913	−	0.190733i
$701$	18.3267			0.692188			0.346094	−	0.938200i	$-0.387508\pi$
$701$	18.3267			0.692188			0.346094	+	0.938200i	$0.387508\pi$
$702$	−0.0806776	+	18.7348i	−0.00304498	+	0.707100i
$703$	3.05493	−	5.29129i	0.115219	−	0.199565i
$704$	0.594605	−	0.594605i	0.0224100	−	0.0224100i
$705$	4.62922	−	3.74359i	0.174346	−	0.140992i
$706$	10.2871	+	5.93927i	0.387161	+	0.223527i
$707$	41.2237	−	18.0373i	1.55038	−	0.678363i
$708$	2.37665	−	22.4691i	0.0893201	−	0.844442i
$709$	20.6654	−	20.6654i	0.776106	−	0.776106i	−0.203060	−	0.979166i	$-0.565089\pi$
$709$	20.6654	−	20.6654i	0.776106	−	0.776106i	0.979166	+	0.203060i	$0.0650886\pi$
$710$	−6.61192	+	1.77166i	−0.248141	+	0.0664892i
$711$	4.93918	−	23.0866i	0.185234	−	0.865813i
$712$	−3.16110	−	1.82506i	−0.118467	−	0.0683971i
$713$	−0.458458	+	1.71099i	−0.0171694	+	0.0640770i
$714$	19.0235	−	20.8287i	0.711935	−	0.779496i
$715$	1.45775	+	0.313389i	0.0545167	+	0.0117201i
$716$	−8.64976	+	4.99394i	−0.323257	+	0.186632i
$717$	−34.7265	+	15.4337i	−1.29688	+	0.576381i
$718$	−30.6183			−1.14266
$719$	−4.66554			−0.173995			−0.0869976	−	0.996209i	$-0.527727\pi$
$719$	−4.66554			−0.173995			−0.0869976	+	0.996209i	$0.527727\pi$
$720$	−1.47344	+	0.0752624i	−0.0549120	+	0.00280487i
$721$	−2.59661	+	3.52603i	−0.0967026	+	0.131316i
$722$	−4.61103	+	1.23552i	−0.171605	+	0.0459813i
$723$	21.7920	+	15.8549i	0.810452	+	0.589649i
$724$	−12.5877	−	21.8025i	−0.467817	−	0.810283i
$725$	−1.67276			−0.0621249
$726$	17.7289	+	1.87526i	0.657981	+	0.0695974i
$727$		−	4.79806i		−	0.177950i	−0.996034	−	0.0889751i	$-0.971641\pi$
$727$		−	4.79806i		−	0.177950i	0.996034	−	0.0889751i	$-0.0283591\pi$
$728$	8.53722	−	4.25628i	0.316410	−	0.157748i
$729$	−15.9569	+	21.7802i	−0.590996	+	0.806674i
$730$	6.87734	−	1.84278i	0.254542	−	0.0682042i
$731$		−	15.0149i		−	0.555346i
$732$	7.37808	−	1.16356i	0.272702	−	0.0430065i
$733$	−0.693601	+	2.58855i	−0.0256187	+	0.0956104i	−0.977551	−	0.210697i	$-0.932427\pi$
$733$	−0.693601	+	2.58855i	−0.0256187	+	0.0956104i	0.951933	+	0.306307i	$0.0990934\pi$
$734$	−5.10800	−	19.0633i	−0.188540	−	0.703640i
$735$	5.84855	−	1.16073i	0.215727	−	0.0428143i
$736$	−0.359290	+	0.359290i	−0.0132436	+	0.0132436i
$737$		−	8.15805i		−	0.300506i
$738$	−25.1553	+	27.8635i	−0.925980	+	1.02567i
$739$	−1.27194	+	1.27194i	−0.0467892	+	0.0467892i	−0.730114	−	0.683325i	$-0.760533\pi$
$739$	−1.27194	+	1.27194i	−0.0467892	+	0.0467892i	0.683325	+	0.730114i	$0.260533\pi$
$740$	−0.398321	−	0.689912i	−0.0146426	−	0.0253617i
$741$	−22.3801	−	7.34557i	−0.822154	−	0.269846i
$742$	1.36582	+	8.99743i	0.0501407	+	0.330306i
$743$	−18.4019	−	4.93077i	−0.675099	−	0.180892i	−0.0950485	−	0.995473i	$-0.530301\pi$
$743$	−18.4019	−	4.93077i	−0.675099	−	0.180892i	−0.580051	+	0.814580i	$0.696967\pi$
$744$	3.79682	+	4.69504i	0.139198	+	0.172129i
$745$	−5.32901	+	3.07670i	−0.195240	+	0.112722i
$746$	−5.40266	−	20.1630i	−0.197805	−	0.738220i
$747$	−15.3771	+	0.785449i	−0.562617	+	0.0287381i
$748$	−1.33972	−	4.99989i	−0.0489849	−	0.182814i
$749$	27.3757	+	3.05537i	1.00029	+	0.111641i
$750$	−6.46311	+	5.22664i	−0.235999	+	0.190850i
$751$	−25.9239	−	14.9671i	−0.945975	−	0.546159i	−0.0541467	−	0.998533i	$-0.517244\pi$
$751$	−25.9239	−	14.9671i	−0.945975	−	0.546159i	−0.891828	+	0.452374i	$0.850577\pi$
$752$	−4.94218	−	4.94218i	−0.180223	−	0.180223i
$753$	5.13479	−	4.15244i	0.187122	−	0.151323i
$754$	−1.26597	+	0.0634036i	−0.0461040	+	0.00230902i
$755$		−	6.09721i		−	0.221900i
$756$	13.5599	+	2.26482i	0.493168	+	0.0823708i
$757$	−22.5268	−	39.0176i	−0.818751	−	1.41812i	−0.906603	−	0.421985i	$-0.861333\pi$
$757$	−22.5268	−	39.0176i	−0.818751	−	1.41812i	0.0878512	−	0.996134i	$-0.472000\pi$
$758$	−16.6714			−0.605533
$759$	0.735950	+	0.0778444i	0.0267133	+	0.00282557i
$760$	0.480088	−	1.79171i	0.0174146	−	0.0649922i
$761$	−35.6791	−	35.6791i	−1.29337	−	1.29337i	−0.932692	−	0.360675i	$-0.882546\pi$
$761$	−35.6791	−	35.6791i	−1.29337	−	1.29337i	−0.360675	−	0.932692i	$-0.617454\pi$
$762$	−1.28596	−	2.89346i	−0.0465853	−	0.104819i
$763$	−14.7931	+	11.8226i	−0.535548	+	0.428007i
$764$	−9.90760	−	17.1605i	−0.358444	−	0.620844i
$765$	−4.13377	+	8.08648i	−0.149457	+	0.292367i
$766$	9.42711	+	5.44274i	0.340615	+	0.196654i
$767$	−25.5251	−	39.5055i	−0.921659	−	1.42646i
$768$	0.269819	+	1.71091i	0.00973626	+	0.0617370i
$769$	−6.26416	+	23.3782i	−0.225891	+	0.843038i	0.756154	+	0.654394i	$0.227076\pi$
$769$	−6.26416	+	23.3782i	−0.225891	+	0.843038i	−0.982045	+	0.188645i	$0.939591\pi$
$770$	0.398662	−	1.01892i	0.0143668	−	0.0367194i
$771$	25.7240	−	20.8027i	0.926427	−	0.749190i
$772$	−2.51844	+	9.39895i	−0.0906407	+	0.338276i
$773$	−29.4548	−	7.89240i	−1.05942	−	0.283870i	−0.313279	−	0.949661i	$-0.601427\pi$
$773$	−29.4548	−	7.89240i	−1.05942	−	0.283870i	−0.746138	+	0.665791i	$0.768094\pi$
$774$	6.14237	−	3.97734i	0.220783	−	0.142962i
$775$	16.0223	+	4.29316i	0.575538	+	0.154215i
$776$	12.9811	+	7.49466i	0.465995	+	0.269043i
$777$	2.24379	+	7.07602i	0.0804955	+	0.253851i
$778$	−16.8247	−	4.50815i	−0.603193	−	0.161625i
$779$	−23.5980	−	40.8730i	−0.845487	−	1.46443i
$780$	−2.28848	+	2.04823i	−0.0819406	+	0.0733385i
$781$	5.85220	−	10.1363i	0.209408	−	0.362706i
$782$	0.809522	+	3.02118i	0.0289485	+	0.108037i
$783$	−1.53006	−	0.997962i	−0.0546799	−	0.0356642i
$784$	−2.07734	−	6.68466i	−0.0741908	−	0.238738i
$785$	−2.82289	+	2.82289i	−0.100753	+	0.100753i
$786$	−0.908815	−	2.04488i	−0.0324163	−	0.0729383i
$787$	31.8797	+	8.54214i	1.13639	+	0.304494i	0.777498	−	0.628885i	$-0.216489\pi$
$787$	31.8797	+	8.54214i	1.13639	+	0.304494i	0.358890	+	0.933380i	$0.383155\pi$
$788$	−2.70220	+	0.724053i	−0.0962619	+	0.0257933i
$789$	18.0428	−	46.9101i	0.642340	−	1.67005i
$790$	3.35170	−	1.93510i	0.119248	−	0.0688479i
$791$	−13.9281	−	1.55449i	−0.495225	−	0.0552714i
$792$	1.69050	−	1.87249i	0.0600691	−	0.0665360i
$793$	10.4308	−	11.5306i	0.370407	−	0.409465i
$794$	10.4945	+	6.05902i	0.372437	+	0.215027i
$795$	−1.18993	−	2.67740i	−0.0422025	−	0.0949576i
$796$	5.20107	−	9.00851i	0.184347	−	0.319298i
$797$	13.9644	−	24.1870i	0.494643	−	0.856746i	−0.505338	−	0.862921i	$-0.668632\pi$
$797$	13.9644	−	24.1870i	0.494643	−	0.856746i	0.999981	+	0.00617504i	$0.00196559\pi$
$798$	−7.95599	+	15.3445i	−0.281639	+	0.543191i
$799$	−41.5575	+	11.1353i	−1.47020	+	0.393939i
$800$	3.36452	+	3.36452i	0.118954	+	0.118954i
$801$	−9.75026	−	4.98429i	−0.344509	−	0.176111i
$802$	−5.95086	−	10.3072i	−0.210132	−	0.363959i
$803$	−6.08712	+	10.5432i	−0.214810	+	0.372062i
$804$	13.5879	+	9.88594i	0.479208	+	0.348650i
$805$	−0.240891	+	0.615682i	−0.00849029	+	0.0217000i
$806$	12.2887	+	2.64183i	0.432849	+	0.0930545i
$807$	18.9406	−	2.98703i	0.666741	−	0.105149i
$808$	12.0260	+	12.0260i	0.423072	+	0.423072i
$809$		−	18.0298i		−	0.633893i	−0.948443	−	0.316947i	$-0.897342\pi$
$809$		−	18.0298i		−	0.633893i	0.948443	−	0.316947i	$-0.102658\pi$
$810$	−4.40306	+	0.450987i	−0.154708	+	0.0158461i
$811$	−25.2399	−	25.2399i	−0.886292	−	0.886292i	0.107873	−	0.994165i	$-0.465596\pi$
$811$	−25.2399	−	25.2399i	−0.886292	−	0.886292i	−0.994165	+	0.107873i	$0.965596\pi$
$812$	−0.103171	+	0.924396i	−0.00362058	+	0.0324399i
$813$	−4.34123	+	41.0425i	−0.152254	+	1.43942i
$814$	1.31575	+	0.352553i	0.0461169	+	0.0123570i
$815$	1.97996	−	1.14313i	0.0693549	−	0.0400421i
$816$	9.95118	+	3.82747i	0.348361	+	0.133988i
$817$	2.38118	+	8.88669i	0.0833070	+	0.310906i
$818$	−2.38896			−0.0835281
$819$	24.9269	−	14.0587i	0.871018	−	0.491252i
$820$	−6.15372			−0.214897
$821$	−8.28837	−	30.9326i	−0.289266	−	1.07956i	−0.945665	−	0.325142i	$-0.894588\pi$
$821$	−8.28837	−	30.9326i	−0.289266	−	1.07956i	0.656399	−	0.754414i	$-0.272079\pi$
$822$	−14.6919	−	5.65088i	−0.512441	−	0.197097i
$823$	−2.53677	+	1.46461i	−0.0884263	+	0.0510530i	−0.543561	−	0.839370i	$-0.682924\pi$
$823$	−2.53677	+	1.46461i	−0.0884263	+	0.0510530i	0.455135	+	0.890423i	$0.349591\pi$
$824$	−1.59869	−	0.428368i	−0.0556931	−	0.0149229i
$825$	0.728963	−	6.89169i	0.0253792	−	0.239938i
$826$	−31.6194	+	13.8350i	−1.10018	+	0.481380i
$827$	−18.0254	−	18.0254i	−0.626804	−	0.626804i	0.320458	−	0.947263i	$-0.396163\pi$
$827$	−18.0254	−	18.0254i	−0.626804	−	0.626804i	−0.947263	+	0.320458i	$0.896163\pi$
$828$	−1.02148	+	1.13145i	−0.0354989	+	0.0393206i
$829$			16.0375i			0.557007i	0.960435	+	0.278503i	$0.0898384\pi$
$829$			16.0375i			0.557007i	−0.960435	+	0.278503i	$0.910162\pi$
$830$	−1.78476	−	1.78476i	−0.0619501	−	0.0619501i
$831$	−0.605232	+	0.0954483i	−0.0209953	+	0.00331107i
$832$	2.67385	+	2.41879i	0.0926989	+	0.0838565i
$833$	−42.0292	−	9.49997i	−1.45622	−	0.329154i
$834$	−14.4281	−	10.4972i	−0.499604	−	0.363489i
$835$	−0.277351	+	0.480387i	−0.00959814	+	0.0166245i
$836$	1.58584	+	2.74676i	0.0548475	+	0.0949986i
$837$	12.0942	+	13.4857i	0.418035	+	0.466135i
$838$	23.2288	+	23.2288i	0.802427	+	0.802427i
$839$	14.9319	−	4.00098i	0.515505	−	0.138129i	0.00831856	−	0.999965i	$-0.497352\pi$
$839$	14.9319	−	4.00098i	0.515505	−	0.138129i	0.507187	+	0.861836i	$0.330685\pi$
$840$	1.21400	+	1.89873i	0.0418868	+	0.0655125i
$841$	−14.4382	+	25.0077i	−0.497869	+	0.862335i
$842$	−8.70249	+	15.0732i	−0.299908	+	0.519455i
$843$	−14.0730	−	31.6649i	−0.484699	−	1.09060i
$844$	0.591409	+	0.341450i	0.0203571	+	0.0117532i
$845$	−1.02940	+	6.30983i	−0.0354124	+	0.217065i
$846$	−15.5636	−	14.0509i	−0.535087	−	0.483080i
$847$	−10.9163	−	24.9488i	−0.375087	−	0.857249i
$848$	−2.97884	+	1.71983i	−0.102294	+	0.0590593i
$849$	8.30871	−	21.6021i	0.285154	−	0.741384i
$850$	28.2914	−	7.58065i	0.970386	−	0.260014i
$851$	−0.795039	−	0.213030i	−0.0272536	−	0.00730257i
$852$	9.79113	+	22.0305i	0.335438	+	0.754752i
$853$	33.5316	−	33.5316i	1.14810	−	1.14810i	0.161175	−	0.986926i	$-0.448472\pi$
$853$	33.5316	−	33.5316i	1.14810	−	1.14810i	0.986926	−	0.161175i	$-0.0515282\pi$
$854$	−7.12308	−	8.91282i	−0.243747	−	0.304990i
$855$	1.16419	−	5.44161i	0.0398144	−	0.186099i
$856$	2.69464	+	10.0565i	0.0921009	+	0.343725i
$857$	−2.00794	+	3.47786i	−0.0685900	+	0.118801i	−0.898281	−	0.439422i	$-0.855183\pi$
$857$	−2.00794	+	3.47786i	−0.0685900	+	0.118801i	0.829691	+	0.558223i	$0.188517\pi$
$858$	0.290471	−	5.24337i	0.00991651	−	0.179006i
$859$	21.9588	+	38.0338i	0.749226	+	1.29770i	0.948194	+	0.317691i	$0.102907\pi$
$859$	21.9588	+	38.0338i	0.749226	+	1.29770i	−0.198969	+	0.980006i	$0.563759\pi$
$860$	1.15870	+	0.310473i	0.0395114	+	0.0105871i
$861$	56.0025	+	12.3194i	1.90856	+	0.419844i
$862$	−10.0280	−	5.78970i	−0.341557	−	0.197198i
$863$	−10.3031	−	2.76071i	−0.350721	−	0.0939755i	0.0791574	−	0.996862i	$-0.474777\pi$
$863$	−10.3031	−	2.76071i	−0.350721	−	0.0939755i	−0.429879	+	0.902887i	$0.641444\pi$
$864$	1.07024	+	5.08474i	0.0364102	+	0.172986i
$865$	0.640994	+	0.171754i	0.0217944	+	0.00583980i
$866$	10.2384	−	38.2104i	0.347917	−	1.29844i
$867$	28.1366	−	22.7538i	0.955570	−	0.772758i
$868$	3.36067	−	8.58939i	0.114069	−	0.291543i
$869$	−1.71276	+	6.39210i	−0.0581013	+	0.216837i
$870$	−0.0466496	−	0.295802i	−0.00158157	−	0.0100286i
$871$	34.9358	−	1.74968i	1.18375	−	0.0592858i
$872$	−6.19859	−	3.57876i	−0.209911	−	0.121192i
$873$	40.0397	+	20.4681i	1.35514	+	0.692740i
$874$	−0.958244	−	1.65973i	−0.0324131	−	0.0561411i
$875$	11.8240	+	4.62624i	0.399724	+	0.156395i
$876$	−10.1842	−	22.9149i	−0.344091	−	0.774221i
$877$	−2.07659	−	2.07659i	−0.0701214	−	0.0701214i	0.671176	−	0.741298i	$-0.265789\pi$
$877$	−2.07659	−	2.07659i	−0.0701214	−	0.0701214i	−0.741298	+	0.671176i	$0.765789\pi$
$878$	−0.0506545	+	0.189045i	−0.00170951	+	0.00637997i
$879$	−47.2155	−	4.99418i	−1.59254	−	0.168449i
$880$	0.413544			0.0139406
$881$	12.3418	+	21.3767i	0.415806	+	0.720198i	0.995513	−	0.0946276i	$-0.0301660\pi$
$881$	12.3418	+	21.3767i	0.415806	+	0.720198i	−0.579706	+	0.814825i	$0.696833\pi$
$882$	−7.24692	−	19.7099i	−0.244017	−	0.663669i
$883$			10.4655i			0.352193i	0.984373	+	0.176096i	$0.0563470\pi$
$883$			10.4655i			0.352193i	−0.984373	+	0.176096i	$0.943653\pi$
$884$	21.1240	−	6.80950i	0.710478	−	0.229028i
$885$	8.64005	−	6.98710i	0.290432	−	0.234869i
$886$	−12.7663	−	12.7663i	−0.428892	−	0.428892i
$887$	−38.1061	−	22.0006i	−1.27948	−	0.738707i	−0.302725	−	0.953078i	$-0.597896\pi$
$887$	−38.1061	−	22.0006i	−1.27948	−	0.738707i	−0.976752	+	0.214371i	$0.931230\pi$
$888$	−2.18163	+	1.76426i	−0.0732106	+	0.0592045i
$889$	−2.86803	+	3.89461i	−0.0961907	+	0.130621i
$890$	−0.464603	−	1.73392i	−0.0155735	−	0.0581212i
$891$	4.77832	−	5.86887i	0.160080	−	0.196614i
$892$	−0.0962454	−	0.359193i	−0.00322253	−	0.0120267i
$893$	22.8302	−	13.1810i	0.763985	−	0.441087i
$894$	13.6274	+	16.8513i	0.455770	+	0.563592i
$895$	−4.74455	−	1.27130i	−0.158593	−	0.0424948i
$896$	2.06680	−	1.65177i	0.0690468	−	0.0551818i
$897$	−0.175517	+	3.16830i	−0.00586034	+	0.105787i
$898$	1.76758	+	3.06154i	0.0589850	+	0.102165i
$899$	−0.866613	+	0.866613i	−0.0289032	+	0.0289032i
$900$	10.5953	+	9.56551i	0.353177	+	0.318850i
$901$			21.1733i			0.705386i
$902$	7.44026	−	7.44026i	0.247733	−	0.247733i
$903$	−9.92333	−	5.14515i	−0.330228	−	0.171220i
$904$	−1.37096	−	5.11651i	−0.0455976	−	0.170173i
$905$	3.20442	−	11.9591i	0.106519	−	0.397533i
$906$	−21.2119	+	3.34522i	−0.704717	+	0.111138i
$907$			19.9058i			0.660962i	0.943813	+	0.330481i	$0.107211\pi$
$907$			19.9058i			0.660962i	−0.943813	+	0.330481i	$0.892789\pi$
$908$	−22.3548	+	5.98995i	−0.741869	+	0.198783i
$909$	37.8714	+	34.1905i	1.25611	+	1.13403i
$910$	4.44890	+	1.48868i	0.147480	+	0.0493494i
$911$			38.2796i			1.26826i	0.773227	+	0.634129i	$0.218641\pi$
$911$			38.2796i			1.26826i	−0.773227	+	0.634129i	$0.781359\pi$
$912$	−6.49667	−	0.687179i	−0.215126	−	0.0227548i
$913$	4.31580			0.142832
$914$	0.979950	+	1.69732i	0.0324139	+	0.0561424i
$915$	2.97033	+	2.16108i	0.0981961	+	0.0714431i
$916$	17.2863	−	4.63184i	0.571154	−	0.153040i
$917$	−2.02690	+	2.75241i	−0.0669342	+	0.0908925i
$918$	30.4004	+	9.94454i	1.00336	+	0.328219i
$919$	−27.3756			−0.903039			−0.451519	−	0.892261i	$-0.649118\pi$
$919$	−27.3756			−0.903039			−0.451519	+	0.892261i	$0.649118\pi$
$920$	−0.249884			−0.00823843
$921$	−41.1023	+	18.2673i	−1.35437	+	0.601929i
$922$	24.7785	−	14.3059i	0.816035	−	0.471138i
$923$	44.6625	+	22.8873i	1.47009	+	0.753345i
$924$	−3.76350	−	0.827893i	−0.123810	−	0.0272357i
$925$	−1.99489	+	7.44502i	−0.0655915	+	0.244791i
$926$	−19.6590	−	11.3501i	−0.646034	−	0.372988i
$927$	−4.85539	−	1.03877i	−0.159472	−	0.0341177i
$928$	−0.339579	+	0.0909899i	−0.0111472	+	0.00298689i
$929$	−9.83220	+	9.83220i	−0.322584	+	0.322584i	−0.849758	−	0.527174i	$-0.823252\pi$
$929$	−9.83220	+	9.83220i	−0.322584	+	0.322584i	0.527174	+	0.849758i	$0.323252\pi$
$930$	−0.312353	+	2.95302i	−0.0102425	+	0.0968333i
$931$	26.3819	−	1.04268i	0.864630	−	0.0341725i
$932$	3.73341	+	2.15549i	0.122292	+	0.0706053i
$933$	−34.0671	+	27.5496i	−1.11531	+	0.901935i
$934$	14.1272	−	14.1272i	0.462256	−	0.462256i
$935$	1.27281	−	2.20458i	0.0416254	−	0.0720974i
$936$	8.38126	+	6.83773i	0.273950	+	0.223498i
$937$	−46.4282			−1.51674			−0.758371	−	0.651823i	$-0.774005\pi$
$937$	−46.4282			−1.51674			−0.758371	+	0.651823i	$0.774005\pi$
$938$	2.84709	−	25.5096i	0.0929608	−	0.832918i
$939$	−1.76474	−	11.1901i	−0.0575901	−	0.365175i
$940$		−	3.43725i		−	0.112111i
$941$	5.07917	+	18.9557i	0.165576	+	0.617939i	0.997966	+	0.0637484i	$0.0203055\pi$
$941$	5.07917	+	18.9557i	0.165576	+	0.617939i	−0.832390	+	0.554191i	$0.813028\pi$
$942$	11.3695	+	8.27191i	0.370437	+	0.269513i
$943$	−4.49577	+	4.49577i	−0.146402	+	0.146402i
$944$	−9.22416	−	9.22416i	−0.300221	−	0.300221i
$945$	3.92782	+	5.50299i	0.127772	+	0.179012i
$946$	−1.77633	+	1.02557i	−0.0577535	+	0.0333440i
$947$	21.9919	−	5.89271i	0.714640	−	0.191487i	0.116861	−	0.993148i	$-0.462717\pi$
$947$	21.9919	−	5.89271i	0.714640	−	0.191487i	0.597779	+	0.801661i	$0.296050\pi$
$948$	−8.57103	−	10.5987i	−0.278374	−	0.344229i
$949$	−46.4554	−	23.8061i	−1.50801	−	0.772777i
$950$	−15.5423	+	8.97333i	−0.504258	+	0.291133i
$951$	−19.5192	−	14.2013i	−0.632955	−	0.460509i
$952$	−2.44427	−	16.1018i	−0.0792192	−	0.521863i
$953$	3.43446	−	5.94865i	0.111253	−	0.192696i	−0.805023	−	0.593244i	$-0.797847\pi$
$953$	3.43446	−	5.94865i	0.111253	−	0.192696i	0.916276	+	0.400548i	$0.131180\pi$
$954$	−8.66168	+	5.60866i	−0.280432	+	0.181587i
$955$	2.52216	−	9.41283i	0.0816152	−	0.304592i
$956$	−5.67856	+	21.1927i	−0.183658	+	0.685420i
$957$	0.414047	+	0.301242i	0.0133842	+	0.00973778i
$958$	18.4041	−	31.8769i	0.594611	−	1.02990i
$959$	3.60873	+	23.7728i	0.116532	+	0.767662i
$960$	−0.501133	+	0.688791i	−0.0161740	+	0.0222306i
$961$	−16.3219	+	9.42345i	−0.526513	+	0.303982i
$962$	−1.22757	+	5.71012i	−0.0395784	+	0.184102i
$963$	9.61243	+	29.7179i	0.309756	+	0.957647i
$964$	15.0290	−	4.02702i	0.484053	−	0.129702i
$965$	−4.14424	+	2.39268i	−0.133408	+	0.0770230i
$966$	2.27409	+	0.500254i	0.0731677	+	0.0160954i
$967$	−28.4048	−	28.4048i	−0.913437	−	0.913437i	0.0831041	−	0.996541i	$-0.473517\pi$
$967$	−28.4048	−	28.4048i	−0.913437	−	0.913437i	−0.996541	+	0.0831041i	$0.973517\pi$
$968$	7.27817	−	7.27817i	0.233929	−	0.233929i
$969$	−23.6589	+	32.5183i	−0.760032	+	1.04464i
$970$	1.90790	+	7.12039i	0.0612591	+	0.228622i
$971$			41.1789i			1.32149i	0.750609	+	0.660746i	$0.229760\pi$
$971$			41.1789i			1.32149i	−0.750609	+	0.660746i	$0.770240\pi$
$972$	3.98469	+	15.0706i	0.127809	+	0.483389i
$973$	−3.02314	+	27.0870i	−0.0969174	+	0.868368i
$974$	−18.5404			−0.594073
$975$	29.6691	+	1.64360i	0.950172	+	0.0526374i
$976$	2.15619	−	3.73463i	0.0690180	−	0.119543i
$977$	27.2184	−	27.2184i	0.870792	−	0.870792i	−0.121766	−	0.992559i	$-0.538856\pi$
$977$	27.2184	−	27.2184i	0.870792	−	0.870792i	0.992559	+	0.121766i	$0.0388559\pi$
$978$	−5.06319	−	6.26099i	−0.161903	−	0.200204i
$979$	2.65817	+	1.53469i	0.0849554	+	0.0490490i
$980$	1.60218	−	3.04696i	0.0511797	−	0.0973315i
$981$	−19.1193	−	9.77368i	−0.610431	−	0.312050i
$982$	4.69040	−	4.69040i	0.149677	−	0.149677i
$983$	−9.57316	+	2.56512i	−0.305336	+	0.0818146i	−0.408234	−	0.912877i	$-0.633855\pi$
$983$	−9.57316	+	2.56512i	−0.305336	+	0.0818146i	0.102898	+	0.994692i	$0.467189\pi$
$984$	3.37623	+	21.4085i	0.107630	+	0.682477i
$985$	−1.19147	−	0.687895i	−0.0379634	−	0.0219182i
$986$	−0.560101	+	2.09032i	−0.0178372	+	0.0665695i
$987$	−6.88120	+	31.2811i	−0.219031	+	0.995687i
$988$	−11.4225	+	7.38027i	−0.363399	+	0.234798i
$989$	1.07335	−	0.619698i	0.0341305	−	0.0197052i
$990$	1.23902	−	0.0632881i	0.0393786	−	0.00201143i
$991$	34.0368			1.08122			0.540608	−	0.841275i	$-0.318194\pi$
$991$	34.0368			1.08122			0.540608	+	0.841275i	$0.318194\pi$
$992$	3.48613			0.110685
$993$	1.23308	+	2.77448i	0.0391305	+	0.0880455i
$994$	21.8369	−	29.6531i	0.692623	−	0.940539i
$995$	4.94134	−	1.32403i	0.156651	−	0.0419745i
$996$	−5.22989	+	7.18831i	−0.165716	+	0.227770i
$997$	14.9433	+	25.8826i	0.473259	+	0.819709i	0.999531	−	0.0306069i	$-0.00974401\pi$
$997$	14.9433	+	25.8826i	0.473259	+	0.819709i	−0.526272	+	0.850316i	$0.676411\pi$
$998$	24.4154			0.772855
$999$	−6.26636	+	5.61975i	−0.198259	+	0.177801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.2	✓	152
3.2	odd	2	inner	546.2.bw.a.11.21	yes	152
7.2	even	3		546.2.ch.a.401.15	yes	152
13.6	odd	12		546.2.ch.a.305.30	yes	152
21.2	odd	6		546.2.ch.a.401.30	yes	152
39.32	even	12		546.2.ch.a.305.15	yes	152
91.58	odd	12	inner	546.2.bw.a.149.21	yes	152
273.149	even	12	inner	546.2.bw.a.149.2	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.2	✓	152	1.1	even	1	trivial
546.2.bw.a.11.21	yes	152	3.2	odd	2	inner
546.2.bw.a.149.2	yes	152	273.149	even	12	inner
546.2.bw.a.149.21	yes	152	91.58	odd	12	inner
546.2.ch.a.305.15	yes	152	39.32	even	12
546.2.ch.a.305.30	yes	152	13.6	odd	12
546.2.ch.a.401.15	yes	152	7.2	even	3
546.2.ch.a.401.30	yes	152	21.2	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.61660 - 0.621783i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.475031 - 0.127284i) q^{5} +(-0.182190 + 1.72244i) q^{6} +(2.42388 - 1.06056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22677 + 2.01034i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.61660 - 0.621783i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.475031 - 0.127284i) q^{5} +(-0.182190 + 1.72244i) q^{6} +(2.42388 - 1.06056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.22677 + 2.01034i) q^{9} +0.491788i q^{10} +(-0.594605 - 0.594605i) q^{11} +(1.71091 - 0.269819i) q^{12} +(2.41879 - 2.67385i) q^{13} +(-1.65177 - 2.06680i) q^{14} +(0.688791 + 0.501133i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.07782 - 5.33093i) q^{17} +(1.36551 - 2.67121i) q^{18} +(2.66705 + 2.66705i) q^{19} +(0.475031 - 0.127284i) q^{20} +(-4.57788 + 0.207375i) q^{21} +(-0.420449 + 0.728240i) q^{22} +(0.254056 - 0.440038i) q^{23} +(-0.703440 - 1.58277i) q^{24} +(-4.12067 - 2.37907i) q^{25} +(-3.20877 - 1.64433i) q^{26} +(-2.34980 - 4.63449i) q^{27} +(-1.56886 + 2.13042i) q^{28} +(0.304458 - 0.175779i) q^{29} +(0.305785 - 0.795024i) q^{30} +(-3.36734 + 0.902276i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.591522 + 1.33095i) q^{33} +(-4.35269 + 4.35269i) q^{34} +(-1.28641 + 0.195279i) q^{35} +(-2.93361 - 0.627623i) q^{36} +(-0.419258 - 1.56469i) q^{37} +(1.88589 - 3.26646i) q^{38} +(-5.57276 + 2.81857i) q^{39} +(-0.245894 - 0.425901i) q^{40} +(-12.0866 - 3.23859i) q^{41} +(1.38515 + 4.36822i) q^{42} +(2.11242 + 1.21961i) q^{43} +(0.812246 + 0.217641i) q^{44} +(-0.801901 - 1.23841i) q^{45} +(-0.490799 - 0.131509i) q^{46} +(1.80896 - 6.75114i) q^{47} +(-1.34678 + 1.08912i) q^{48} +(4.75041 - 5.14136i) q^{49} +(-1.23150 + 4.59601i) q^{50} +(1.66091 + 10.5317i) q^{51} +(-0.757812 + 3.52501i) q^{52} +(-2.97884 - 1.71983i) q^{53} +(-3.86840 + 3.46922i) q^{54} +(0.206772 + 0.358140i) q^{55} +(2.46388 + 0.964012i) q^{56} +(-2.65322 - 5.96987i) q^{57} +(-0.248589 - 0.248589i) q^{58} +(3.37628 - 12.6004i) q^{59} +(-0.847077 - 0.0895988i) q^{60} +4.31238 q^{61} +(1.74306 + 3.01908i) q^{62} +(7.52953 + 2.51120i) q^{63} +1.00000i q^{64} +(-1.48934 + 0.962286i) q^{65} +(1.13250 - 0.915842i) q^{66} +(6.86006 + 6.86006i) q^{67} +(5.33093 + 3.07782i) q^{68} +(-0.684315 + 0.553397i) q^{69} +(0.521573 + 1.19204i) q^{70} +(3.60248 + 13.4446i) q^{71} +(0.153038 + 2.99609i) q^{72} +(-3.74709 - 13.9843i) q^{73} +(-1.40286 + 0.809943i) q^{74} +(5.18220 + 6.40816i) q^{75} +(-3.64326 - 0.976208i) q^{76} +(-2.07187 - 0.810637i) q^{77} +(4.16486 + 4.65338i) q^{78} +(-3.93483 - 6.81533i) q^{79} +(-0.347747 + 0.347747i) q^{80} +(0.917034 + 8.95316i) q^{81} +12.5129i q^{82} +(-3.62913 + 3.62913i) q^{83} +(3.86087 - 2.46853i) q^{84} +(0.783515 + 2.92412i) q^{85} +(0.631315 - 2.35610i) q^{86} +(-0.601483 + 0.0948571i) q^{87} -0.840899i q^{88} +(-3.52575 + 0.944722i) q^{89} +(-0.988664 + 1.09510i) q^{90} +(3.02708 - 9.04637i) q^{91} +0.508113i q^{92} +(6.00465 + 0.635137i) q^{93} -6.98930 q^{94} +(-0.927458 - 1.60641i) q^{95} +(1.40058 + 1.01900i) q^{96} +(14.4786 - 3.87952i) q^{97} +(-6.19567 - 3.25786i) q^{98} +(-0.128690 - 2.51941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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