LMFDB - Embedded newform 334.2.c.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [334,2,Mod(3,334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(334, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([94]))

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

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

chi := DirichletCharacter("334.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$334 = 2 \cdot 167$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	334.c (of order $83$ , degree $82$ , 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:	$2.66700342751$
Analytic rank:	$0$
Dimension:	$574$
Relative dimension:	$7$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	334.107
Dual form			334.2.c.b.231.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.862854 - 0.505453i) q^{2} +(-0.996353 - 0.311272i) q^{3} +(0.489034 + 0.872265i) q^{4} +(-0.305954 + 1.77887i) q^{5} +(0.702374 + 0.772192i) q^{6} +(0.166237 + 0.498747i) q^{7} +(0.0189241 - 0.999821i) q^{8} +(-1.57064 - 1.08751i) q^{9} +(1.16313 - 1.38026i) q^{10} +(0.0502570 - 0.884232i) q^{11} +(-0.215739 - 1.02131i) q^{12} +(-4.08265 - 1.10776i) q^{13} +(0.108655 - 0.514371i) q^{14} +(0.858550 - 1.67715i) q^{15} +(-0.521692 + 0.853134i) q^{16} +(-1.27343 - 3.03365i) q^{17} +(0.805545 + 1.73225i) q^{18} +(-1.68359 - 0.822017i) q^{19} +(-1.70127 + 0.603054i) q^{20} +(-0.0103850 - 0.548673i) q^{21} +(-0.490302 + 0.737561i) q^{22} +(-7.95264 + 3.51673i) q^{23} +(-0.330071 + 0.990284i) q^{24} +(1.64192 + 0.582017i) q^{25} +(2.96281 + 3.01942i) q^{26} +(3.15229 + 4.04174i) q^{27} +(-0.353744 + 0.388907i) q^{28} +(-8.07607 - 3.57131i) q^{29} +(-1.58852 + 1.01317i) q^{30} +(1.58478 - 0.630236i) q^{31} +(0.881363 - 0.472440i) q^{32} +(-0.325310 + 0.865364i) q^{33} +(-0.434586 + 3.26126i) q^{34} +(-0.938065 + 0.143120i) q^{35} +(0.180503 - 1.90184i) q^{36} +(-5.84353 + 4.04607i) q^{37} +(1.03720 + 1.56026i) q^{38} +(3.72295 + 2.37453i) q^{39} +(1.77276 + 0.339563i) q^{40} +(-2.49972 + 2.36168i) q^{41} +(-0.268368 + 0.478674i) q^{42} +(2.92596 + 2.37245i) q^{43} +(0.795862 - 0.388582i) q^{44} +(2.41508 - 2.46123i) q^{45} +(8.63951 + 0.985268i) q^{46} +(-4.03924 - 2.16517i) q^{47} +(0.785346 - 0.687635i) q^{48} +(5.37906 - 4.03394i) q^{49} +(-1.12255 - 1.33211i) q^{50} +(0.324494 + 3.41897i) q^{51} +(-1.03030 - 4.10288i) q^{52} +(-2.66403 - 9.13094i) q^{53} +(-0.677049 - 5.08077i) q^{54} +(1.55756 + 0.359935i) q^{55} +(0.501803 - 0.156769i) q^{56} +(1.42158 + 1.34307i) q^{57} +(5.16334 + 7.16359i) q^{58} +(-2.15373 + 5.13076i) q^{59} +(1.88277 - 0.0712980i) q^{60} +(2.77539 - 11.0522i) q^{61} +(-1.68599 - 0.257231i) q^{62} +(0.281295 - 0.964136i) q^{63} +(-0.999284 - 0.0378415i) q^{64} +(3.21966 - 6.92357i) q^{65} +(0.718096 - 0.582254i) q^{66} +(1.70193 + 9.89530i) q^{67} +(2.02340 - 2.59433i) q^{68} +(9.01830 - 1.02847i) q^{69} +(0.881754 + 0.350656i) q^{70} +(4.10747 - 0.786765i) q^{71} +(-1.11704 + 1.54978i) q^{72} +(-1.93473 - 3.16390i) q^{73} +(7.08722 - 0.537537i) q^{74} +(-1.45477 - 1.09098i) q^{75} +(-0.106315 - 1.87053i) q^{76} +(0.449363 - 0.121927i) q^{77} +(-2.01215 - 3.93065i) q^{78} +(15.4875 + 1.17467i) q^{79} +(-1.35800 - 1.18904i) q^{80} +(0.133982 + 0.356409i) q^{81} +(3.35061 - 0.774292i) q^{82} +(-8.07965 + 4.73300i) q^{83} +(0.473509 - 0.277378i) q^{84} +(5.78608 - 1.33710i) q^{85} +(-1.32551 - 3.52601i) q^{86} +(6.93497 + 6.07214i) q^{87} +(-0.883123 - 0.0669813i) q^{88} +(1.50808 + 2.94597i) q^{89} +(-3.32790 + 0.902969i) q^{90} +(-0.126198 - 2.22036i) q^{91} +(-6.95663 - 5.21701i) q^{92} +(-1.77517 + 0.134640i) q^{93} +(2.39089 + 3.90987i) q^{94} +(1.97736 - 2.74338i) q^{95} +(-1.02521 + 0.196373i) q^{96} +(4.64222 + 1.84612i) q^{97} +(-6.68032 + 0.761837i) q^{98} +(-1.04055 + 1.33415i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$574 q + 7 q^{2} + 2 q^{3} - 7 q^{4} - 2 q^{6} + 6 q^{7} + 7 q^{8} - 9 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} - 6 q^{14} - 4 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} - 6 q^{21} + 6 q^{22} + 2 q^{23} - 2 q^{24}+ \cdots - 32 q^{99}+O(q^{100})$ 574 * q + 7 * q^2 + 2 * q^3 - 7 * q^4 - 2 * q^6 + 6 * q^7 + 7 * q^8 - 9 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 - 6 * q^14 - 4 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 - 6 * q^21 + 6 * q^22 + 2 * q^23 - 2 * q^24 - 165 * q^25 - 2 * q^26 - 4 * q^27 + 6 * q^28 - 14 * q^29 + 4 * q^30 + 10 * q^31 + 7 * q^32 - 12 * q^33 + 8 * q^34 - 20 * q^35 - 9 * q^36 + 2 * q^37 - 83 * q^38 - 4 * q^39 - 20 * q^41 + 6 * q^42 - 2 * q^43 - 6 * q^44 + 2 * q^45 - 2 * q^46 + 14 * q^47 + 2 * q^48 - 171 * q^49 - q^50 - 417 * q^51 + 2 * q^52 - 4 * q^53 + 4 * q^54 + 18 * q^55 - 6 * q^56 - 6 * q^57 + 14 * q^58 - 2 * q^59 - 4 * q^60 + 16 * q^61 - 10 * q^62 + 40 * q^63 - 7 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 - 8 * q^68 + 16 * q^69 + 20 * q^70 - 4 * q^71 + 9 * q^72 + 22 * q^73 - 2 * q^74 - 533 * q^75 - 239 * q^77 + 4 * q^78 - 10 * q^79 + 17 * q^81 + 20 * q^82 - 14 * q^83 - 6 * q^84 + 6 * q^85 + 2 * q^86 + 10 * q^87 - 160 * q^88 - 16 * q^89 - 417 * q^90 + 10 * q^91 + 2 * q^92 + 10 * q^93 - 14 * q^94 - 38 * q^95 - 2 * q^96 - 8 * q^97 + 5 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/334\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$e\left(\frac{46}{83}\right)$

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

)

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

$2$	−0.862854	−	0.505453i	−0.610130	−	0.357409i
$2$	−0.862854	−	0.505453i	−0.610130	−	0.357409i
$3$	−0.996353	−	0.311272i	−0.575245	−	0.179713i	−0.00328491	−	0.999995i	$-0.501046\pi$
$3$	−0.996353	−	0.311272i	−0.575245	−	0.179713i	−0.571960	+	0.820282i	$0.693817\pi$
$4$	0.489034	+	0.872265i	0.244517	+	0.436132i
$5$	−0.305954	+	1.77887i	−0.136827	+	0.795534i	0.833279	+	0.552852i	$0.186461\pi$
$5$	−0.305954	+	1.77887i	−0.136827	+	0.795534i	−0.970106	+	0.242681i	$0.921973\pi$
$6$	0.702374	+	0.772192i	0.286743	+	0.315246i
$7$	0.166237	+	0.498747i	0.0628317	+	0.188509i	0.975412	−	0.220389i	$-0.0707326\pi$
$7$	0.166237	+	0.498747i	0.0628317	+	0.188509i	−0.912580	+	0.408897i	$0.865913\pi$
$8$	0.0189241	−	0.999821i	0.00669069	−	0.353490i
$9$	−1.57064	−	1.08751i	−0.523546	−	0.362504i
$10$	1.16313	−	1.38026i	0.367813	−	0.436476i
$11$	0.0502570	−	0.884232i	0.0151530	−	0.266606i	−0.981873	−	0.189540i	$-0.939300\pi$
$11$	0.0502570	−	0.884232i	0.0151530	−	0.266606i	0.997026	−	0.0770658i	$-0.0245552\pi$
$12$	−0.215739	−	1.02131i	−0.0622785	−	0.294826i
$13$	−4.08265	−	1.10776i	−1.13232	−	0.307237i	−0.354090	−	0.935211i	$-0.615209\pi$
$13$	−4.08265	−	1.10776i	−1.13232	−	0.307237i	−0.778234	+	0.627975i	$0.783884\pi$
$14$	0.108655	−	0.514371i	0.0290392	−	0.137471i
$15$	0.858550	−	1.67715i	0.221677	−	0.433037i
$16$	−0.521692	+	0.853134i	−0.130423	+	0.213284i
$17$	−1.27343	−	3.03365i	−0.308852	−	0.735769i	−0.999916	−	0.0129753i	$-0.995870\pi$
$17$	−1.27343	−	3.03365i	−0.308852	−	0.735769i	0.691064	−	0.722794i	$-0.257142\pi$
$18$	0.805545	+	1.73225i	0.189869	+	0.408295i
$19$	−1.68359	−	0.822017i	−0.386241	−	0.188584i	0.235376	−	0.971904i	$-0.424368\pi$
$19$	−1.68359	−	0.822017i	−0.386241	−	0.188584i	−0.621618	+	0.783321i	$0.713524\pi$
$20$	−1.70127	+	0.603054i	−0.380414	+	0.134847i
$21$	−0.0103850	−	0.548673i	−0.00226620	−	0.119730i
$22$	−0.490302	+	0.737561i	−0.104533	+	0.157248i
$23$	−7.95264	+	3.51673i	−1.65824	+	0.733288i	−0.999813	−	0.0193553i	$-0.993839\pi$
$23$	−7.95264	+	3.51673i	−1.65824	+	0.733288i	−0.658428	+	0.752644i	$0.728778\pi$
$24$	−0.330071	+	0.990284i	−0.0673755	+	0.202141i
$25$	1.64192	+	0.582017i	0.328384	+	0.116403i
$26$	2.96281	+	3.01942i	0.581056	+	0.592158i
$27$	3.15229	+	4.04174i	0.606658	+	0.777834i
$28$	−0.353744	+	0.388907i	−0.0668513	+	0.0734965i
$29$	−8.07607	−	3.57131i	−1.49969	−	0.663175i	−0.518299	−	0.855200i	$-0.673434\pi$
$29$	−8.07607	−	3.57131i	−1.49969	−	0.663175i	−0.981390	+	0.192025i	$0.938495\pi$
$30$	−1.58852	+	1.01317i	−0.290023	+	0.184979i
$31$	1.58478	−	0.630236i	0.284635	−	0.113194i	−0.222855	−	0.974852i	$-0.571538\pi$
$31$	1.58478	−	0.630236i	0.284635	−	0.113194i	0.507489	+	0.861658i	$0.330574\pi$
$32$	0.881363	−	0.472440i	0.155804	−	0.0835163i
$33$	−0.325310	+	0.865364i	−0.0566293	+	0.150641i
$34$	−0.434586	+	3.26126i	−0.0745310	+	0.559301i
$35$	−0.938065	+	0.143120i	−0.158562	+	0.0241917i
$36$	0.180503	−	1.90184i	0.0300839	−	0.316974i
$37$	−5.84353	+	4.04607i	−0.960671	+	0.665170i	−0.942338	−	0.334662i	$-0.891378\pi$
$37$	−5.84353	+	4.04607i	−0.960671	+	0.665170i	−0.0183328	+	0.999832i	$0.505836\pi$
$38$	1.03720	+	1.56026i	0.168256	+	0.253107i
$39$	3.72295	+	2.37453i	0.596149	+	0.380230i
$40$	1.77276	+	0.339563i	0.280298	+	0.0536896i
$41$	−2.49972	+	2.36168i	−0.390391	+	0.368832i	−0.856723	−	0.515778i	$-0.827503\pi$
$41$	−2.49972	+	2.36168i	−0.390391	+	0.368832i	0.466332	+	0.884610i	$0.345575\pi$
$42$	−0.268368	+	0.478674i	−0.0414100	+	0.0738610i
$43$	2.92596	+	2.37245i	0.446204	+	0.361795i	0.826374	−	0.563121i	$-0.190400\pi$
$43$	2.92596	+	2.37245i	0.446204	+	0.361795i	−0.380170	+	0.924917i	$0.624135\pi$
$44$	0.795862	−	0.388582i	0.119981	−	0.0585810i
$45$	2.41508	−	2.46123i	0.360020	−	0.366898i
$46$	8.63951	+	0.985268i	1.27383	+	0.145270i
$47$	−4.03924	−	2.16517i	−0.589184	−	0.315822i	0.150676	−	0.988583i	$-0.451855\pi$
$47$	−4.03924	−	2.16517i	−0.589184	−	0.315822i	−0.739860	+	0.672761i	$0.765108\pi$
$48$	0.785346	−	0.687635i	0.113355	−	0.0992516i
$49$	5.37906	−	4.03394i	0.768438	−	0.576277i
$50$	−1.12255	−	1.33211i	−0.158753	−	0.188389i
$51$	0.324494	+	3.41897i	0.0454382	+	0.478752i
$52$	−1.03030	−	4.10288i	−0.142877	−	0.568968i
$53$	−2.66403	−	9.13094i	−0.365933	−	1.25423i	−0.909795	−	0.415057i	$-0.863762\pi$
$53$	−2.66403	−	9.13094i	−0.365933	−	1.25423i	0.543863	−	0.839174i	$-0.316961\pi$
$54$	−0.677049	−	5.08077i	−0.0921347	−	0.691405i
$55$	1.55756	+	0.359935i	0.210021	+	0.0485336i
$56$	0.501803	−	0.156769i	0.0670563	−	0.0209491i
$57$	1.42158	+	1.34307i	0.188292	+	0.177894i
$58$	5.16334	+	7.16359i	0.677980	+	0.940626i
$59$	−2.15373	+	5.13076i	−0.280391	+	0.667968i	−0.999641	−	0.0267835i	$-0.991474\pi$
$59$	−2.15373	+	5.13076i	−0.280391	+	0.667968i	0.719250	+	0.694751i	$0.244486\pi$
$60$	1.88277	−	0.0712980i	0.243065	−	0.00920454i
$61$	2.77539	−	11.0522i	0.355352	−	1.41509i	−0.485693	−	0.874130i	$-0.661433\pi$
$61$	2.77539	−	11.0522i	0.355352	−	1.41509i	0.841045	−	0.540965i	$-0.181941\pi$
$62$	−1.68599	−	0.257231i	−0.214121	−	0.0326683i
$63$	0.281295	−	0.964136i	0.0354398	−	0.121470i
$64$	−0.999284	−	0.0378415i	−0.124910	−	0.00473018i
$65$	3.21966	−	6.92357i	0.399349	−	0.858764i
$66$	0.718096	−	0.582254i	0.0883916	−	0.0716705i
$67$	1.70193	+	9.89530i	0.207924	+	1.20890i	0.882362	+	0.470572i	$0.155952\pi$
$67$	1.70193	+	9.89530i	0.207924	+	1.20890i	−0.674438	+	0.738332i	$0.735614\pi$
$68$	2.02340	−	2.59433i	0.245373	−	0.314608i
$69$	9.01830	−	1.02847i	1.08568	−	0.123813i
$70$	0.881754	+	0.350656i	0.105390	+	0.0419114i
$71$	4.10747	−	0.786765i	0.487467	−	0.0933718i	0.0614935	−	0.998107i	$-0.480414\pi$
$71$	4.10747	−	0.786765i	0.487467	−	0.0933718i	0.425973	+	0.904736i	$0.359932\pi$
$72$	−1.11704	+	1.54978i	−0.131645	+	0.182643i
$73$	−1.93473	−	3.16390i	−0.226443	−	0.370307i	0.719579	−	0.694411i	$-0.244335\pi$
$73$	−1.93473	−	3.16390i	−0.226443	−	0.370307i	−0.946022	+	0.324104i	$0.894937\pi$
$74$	7.08722	−	0.537537i	0.823872	−	0.0624874i
$75$	−1.45477	−	1.09098i	−0.167982	−	0.125975i
$76$	−0.106315	−	1.87053i	−0.0121952	−	0.214564i
$77$	0.449363	−	0.121927i	0.0512096	−	0.0138948i
$78$	−2.01215	−	3.93065i	−0.227831	−	0.445059i
$79$	15.4875	+	1.17467i	1.74248	+	0.132160i	0.908026	−	0.418913i	$-0.137589\pi$
$79$	15.4875	+	1.17467i	1.74248	+	0.132160i	0.834457	+	0.551074i	$0.185782\pi$
$80$	−1.35800	−	1.18904i	−0.151829	−	0.132939i
$81$	0.133982	+	0.356409i	0.0148869	+	0.0396010i
$82$	3.35061	−	0.774292i	0.370013	−	0.0855063i
$83$	−8.07965	+	4.73300i	−0.886856	+	0.519514i	−0.877029	−	0.480438i	$-0.840478\pi$
$83$	−8.07965	+	4.73300i	−0.886856	+	0.519514i	−0.00982772	+	0.999952i	$0.503128\pi$
$84$	0.473509	−	0.277378i	0.0516641	−	0.0302644i
$85$	5.78608	−	1.33710i	0.627588	−	0.145029i
$86$	−1.32551	−	3.52601i	−0.142934	−	0.380220i
$87$	6.93497	+	6.07214i	0.743507	+	0.651002i
$88$	−0.883123	−	0.0669813i	−0.0941412	−	0.00714023i
$89$	1.50808	+	2.94597i	0.159856	+	0.312272i	0.956273	−	0.292475i	$-0.0944789\pi$
$89$	1.50808	+	2.94597i	0.159856	+	0.312272i	−0.796417	+	0.604747i	$0.793274\pi$
$90$	−3.32790	+	0.902969i	−0.350792	+	0.0951812i
$91$	−0.126198	−	2.22036i	−0.0132292	−	0.232757i
$92$	−6.95663	−	5.21701i	−0.725279	−	0.543911i
$93$	−1.77517	+	0.134640i	−0.184077	+	0.0139615i
$94$	2.39089	+	3.90987i	0.246601	+	0.403272i
$95$	1.97736	−	2.74338i	0.202873	−	0.281465i
$96$	−1.02521	+	0.196373i	−0.104635	+	0.0200422i
$97$	4.64222	+	1.84612i	0.471346	+	0.187445i	0.593122	−	0.805112i	$-0.297895\pi$
$97$	4.64222	+	1.84612i	0.471346	+	0.187445i	−0.121776	+	0.992558i	$0.538859\pi$
$98$	−6.68032	+	0.761837i	−0.674814	+	0.0769572i
$99$	−1.04055	+	1.33415i	−0.104579	+	0.134088i
$100$	0.295282	+	1.71682i	0.0295282	+	0.171682i
$101$	−4.11563	+	3.33707i	−0.409520	+	0.332051i	−0.812294	−	0.583249i	$-0.801781\pi$
$101$	−4.11563	+	3.33707i	−0.409520	+	0.332051i	0.402773	+	0.915300i	$0.368046\pi$
$102$	1.44814	−	3.11409i	0.143387	−	0.308341i
$103$	−7.70443	−	0.291756i	−0.759140	−	0.0287476i	−0.344565	−	0.938762i	$-0.611974\pi$
$103$	−7.70443	−	0.291756i	−0.759140	−	0.0287476i	−0.414576	+	0.910015i	$0.636070\pi$
$104$	−1.18482	+	4.06096i	−0.116181	+	0.398210i
$105$	0.979194	+	0.149395i	0.0955595	+	0.0145795i
$106$	−2.31659	+	9.22521i	−0.225008	+	0.896032i
$107$	14.1411	−	0.535502i	1.36707	−	0.0517689i	0.655930	−	0.754822i	$-0.272277\pi$
$107$	14.1411	−	0.535502i	1.36707	−	0.0517689i	0.711138	+	0.703053i	$0.248180\pi$
$108$	−1.98390	+	4.72618i	−0.190900	+	0.454777i
$109$	−4.25306	−	5.90067i	−0.407369	−	0.565182i	0.556740	−	0.830686i	$-0.312052\pi$
$109$	−4.25306	−	5.90067i	−0.407369	−	0.565182i	−0.964110	+	0.265505i	$0.914461\pi$
$110$	−1.16201	−	1.09784i	−0.110794	−	0.104675i
$111$	7.08165	−	2.21239i	0.672161	−	0.209991i
$112$	−0.512222	−	0.118369i	−0.0484005	−	0.0111848i
$113$	0.555279	+	4.16697i	0.0522363	+	0.391996i	0.997785	+	0.0665161i	$0.0211884\pi$
$113$	0.555279	+	4.16697i	0.0522363	+	0.391996i	−0.945549	+	0.325480i	$0.894474\pi$
$114$	−0.547752	−	1.87742i	−0.0513017	−	0.175836i
$115$	−3.82265	−	15.2227i	−0.356464	−	1.41952i
$116$	−0.834348	−	8.79096i	−0.0774673	−	0.816220i
$117$	5.20767	+	6.17982i	0.481449	+	0.571325i
$118$	4.45171	−	3.33849i	0.409813	−	0.307333i
$119$	1.30133	−	1.13942i	0.119293	−	0.104451i
$120$	−1.66060	−	0.890135i	−0.151591	−	0.0812578i
$121$	10.1498	+	1.15751i	0.922711	+	0.105228i
$122$	−7.98115	+	8.13364i	−0.722579	+	0.736385i
$123$	3.22573	−	1.57497i	0.290854	−	0.142011i
$124$	1.32474	+	1.07414i	0.118965	+	0.0964607i
$125$	−5.95118	+	10.6148i	−0.532290	+	0.949418i
$126$	−0.730042	+	0.689727i	−0.0650373	+	0.0614458i
$127$	−10.9989	−	2.10679i	−0.975998	−	0.186947i	−0.324739	−	0.945804i	$-0.605277\pi$
$127$	−10.9989	−	2.10679i	−0.975998	−	0.186947i	−0.651258	+	0.758856i	$0.725759\pi$
$128$	0.843109	+	0.537743i	0.0745210	+	0.0475302i
$129$	−2.17681	−	3.27457i	−0.191657	−	0.288310i
$130$	−6.27764	+	4.34665i	−0.550585	+	0.381226i
$131$	−0.712142	+	7.50336i	−0.0622201	+	0.655572i	0.908905	+	0.417002i	$0.136919\pi$
$131$	−0.712142	+	7.50336i	−0.0622201	+	0.655572i	−0.971125	+	0.238569i	$0.923322\pi$
$132$	−0.913914	+	0.139436i	−0.0795460	+	0.0121363i
$133$	0.130104	−	0.976334i	0.0112814	−	0.0846589i
$134$	3.53310	−	9.39845i	0.305213	−	0.811902i
$135$	−8.15418	+	4.37091i	−0.701800	+	0.376188i
$136$	−3.05721	+	1.21579i	−0.262153	+	0.104253i
$137$	3.00417	−	1.91609i	0.256664	−	0.163703i	−0.403145	−	0.915136i	$-0.632083\pi$
$137$	3.00417	−	1.91609i	0.256664	−	0.163703i	0.659809	+	0.751433i	$0.270637\pi$
$138$	−8.30132	−	3.67091i	−0.706655	−	0.312489i
$139$	−10.3810	+	11.4129i	−0.880501	+	0.968026i	−0.999691	−	0.0248454i	$-0.992091\pi$
$139$	−10.3810	+	11.4129i	−0.880501	+	0.968026i	0.119190	+	0.992871i	$0.461970\pi$
$140$	−0.583585	−	0.748251i	−0.0493219	−	0.0632387i
$141$	3.35056	+	3.41457i	0.282168	+	0.287559i
$142$	−3.94182	−	1.39727i	−0.330790	−	0.117256i
$143$	−1.18470	+	3.55434i	−0.0990693	+	0.297229i
$144$	1.74718	−	0.772619i	0.145599	−	0.0643849i
$145$	8.82379	−	13.2736i	0.732776	−	1.10231i
$146$	0.0701813	+	3.70790i	0.00580825	+	0.306868i
$147$	−6.61510	+	2.34488i	−0.545604	+	0.193402i
$148$	−6.38693	−	3.11844i	−0.525003	−	0.256334i
$149$	−3.15017	−	6.77414i	−0.258072	−	0.554959i	0.734216	−	0.678916i	$-0.237550\pi$
$149$	−3.15017	−	6.77414i	−0.258072	−	0.554959i	−0.992288	+	0.123957i	$0.960442\pi$
$150$	0.703812	+	1.67667i	0.0574660	+	0.136900i
$151$	3.82762	−	6.25939i	0.311487	−	0.509382i	−0.658486	−	0.752593i	$-0.728803\pi$
$151$	3.82762	−	6.25939i	0.311487	−	0.509382i	0.969974	+	0.243211i	$0.0782006\pi$
$152$	−0.853730	+	1.66773i	−0.0692467	+	0.135271i
$153$	−1.29904	+	6.14964i	−0.105021	+	0.497169i
$154$	−0.449363	−	0.121927i	−0.0362107	−	0.00982514i
$155$	0.636236	+	3.01194i	0.0511037	+	0.241924i
$156$	−0.250572	+	4.40863i	−0.0200618	+	0.352973i
$157$	−4.91746	+	5.83544i	−0.392456	+	0.465719i	−0.924602	−	0.380934i	$-0.875603\pi$
$157$	−4.91746	+	5.83544i	−0.392456	+	0.465719i	0.532146	+	0.846653i	$0.321386\pi$
$158$	−12.7697	−	8.84179i	−1.01591	−	0.703415i
$159$	−0.187891	+	9.92688i	−0.0149007	+	0.787253i
$160$	0.570751	+	1.71237i	0.0451218	+	0.135375i
$161$	−3.07598	−	3.38174i	−0.242421	−	0.266519i
$162$	0.0645407	−	0.375250i	0.00507080	−	0.0294825i
$163$	1.16919	+	2.08543i	0.0915784	+	0.163344i	0.914222	−	0.405214i	$-0.132803\pi$
$163$	1.16919	+	2.08543i	0.0915784	+	0.163344i	−0.822644	+	0.568557i	$0.807502\pi$
$164$	−3.28246	−	1.02548i	−0.256317	−	0.0800763i
$165$	−1.43984	−	0.843446i	−0.112091	−	0.0656622i
$166$	9.36386			0.726777
$167$	−12.0876	−	4.57059i	−0.935365	−	0.353683i
$167$	−12.0876	−	4.57059i	−0.935365	−	0.353683i
$168$	−0.548771			−0.0423386
$169$	4.22382	+	2.47428i	0.324909	+	0.190329i
$170$	−5.66838	−	1.77087i	−0.434745	−	0.135819i
$171$	1.75035	+	3.12201i	0.133853	+	0.238746i
$172$	−0.638513	+	3.71242i	−0.0486862	+	0.283069i
$173$	−13.5963	−	14.9478i	−1.03370	−	1.13646i	−0.990517	−	0.137392i	$-0.956128\pi$
$173$	−13.5963	−	14.9478i	−1.03370	−	1.13646i	−0.0431879	−	0.999067i	$-0.513751\pi$
$174$	−2.91468	−	8.74467i	−0.220962	−	0.662932i
$175$	−0.0173311	+	0.915655i	−0.00131011	+	0.0692170i
$176$	0.728150	+	0.504172i	0.0548864	+	0.0380034i
$177$	3.74293	−	4.44165i	0.281336	−	0.333855i
$178$	0.187801	−	3.30420i	0.0140762	−	0.247661i
$179$	1.70192	+	8.05688i	0.127208	+	0.602199i	0.994530	+	0.104452i	$0.0333090\pi$
$179$	1.70192	+	8.05688i	0.127208	+	0.602199i	−0.867322	+	0.497747i	$0.834161\pi$
$180$	3.32790	+	0.902969i	0.248047	+	0.0673033i
$181$	−3.53644	+	16.7415i	−0.262862	+	1.24439i	0.623659	+	0.781697i	$0.285645\pi$
$181$	−3.53644	+	16.7415i	−0.262862	+	1.24439i	−0.886521	+	0.462689i	$0.846885\pi$
$182$	−1.01340	+	1.97963i	−0.0751180	+	0.146740i
$183$	−6.20552	+	10.1480i	−0.458725	+	0.750164i
$184$	3.36560	+	8.01777i	0.248115	+	0.591078i
$185$	−5.40957	−	11.6328i	−0.397720	−	0.855259i
$186$	1.59977	+	0.781093i	0.117301	+	0.0572725i
$187$	−2.74645	+	0.973545i	−0.200841	+	0.0711927i
$188$	−0.0867283	−	4.58213i	−0.00632531	−	0.334186i
$189$	−1.49178	+	2.24408i	−0.108511	+	0.163233i
$190$	−3.09282	+	1.36767i	−0.224377	+	0.0992214i
$191$	0.774665	−	2.32416i	0.0560528	−	0.168170i	−0.916930	−	0.399048i	$-0.869341\pi$
$191$	0.774665	−	2.32416i	0.0560528	−	0.168170i	0.972983	+	0.230878i	$0.0741598\pi$
$192$	0.983861	+	0.348753i	0.0710040	+	0.0251690i
$193$	5.77747	+	5.88786i	0.415871	+	0.423817i	0.889520	−	0.456897i	$-0.151039\pi$
$193$	5.77747	+	5.88786i	0.415871	+	0.423817i	−0.473648	+	0.880714i	$0.657063\pi$
$194$	−3.07243	−	3.93936i	−0.220588	−	0.282830i
$195$	−5.36303	+	5.89614i	−0.384055	+	0.422231i
$196$	6.14921	+	2.71923i	0.439229	+	0.194231i
$197$	9.75716	−	6.22321i	0.695169	−	0.443385i	−0.142334	−	0.989819i	$-0.545461\pi$
$197$	9.75716	−	6.22321i	0.695169	−	0.443385i	0.837503	+	0.546433i	$0.184015\pi$
$198$	1.57219	−	0.625231i	0.111731	−	0.0444332i
$199$	16.6761	−	8.93894i	1.18214	−	0.633664i	0.240617	−	0.970620i	$-0.422650\pi$
$199$	16.6761	−	8.93894i	1.18214	−	0.633664i	0.941520	+	0.336956i	$0.109397\pi$
$200$	0.612985	−	1.63061i	0.0433446	−	0.115302i
$201$	1.38441	−	10.3890i	0.0976486	−	0.732782i
$202$	5.23792	−	0.799147i	0.368539	−	0.0562278i
$203$	0.438635	−	4.62160i	0.0307861	−	0.324373i
$204$	−2.82356	+	1.95504i	−0.197689	+	0.136880i
$205$	−3.43631	−	5.16924i	−0.240003	−	0.361035i
$206$	6.50033	+	4.14597i	0.452900	+	0.288864i
$207$	16.3152	+	3.12510i	1.13399	+	0.217209i
$208$	3.07495	−	2.90514i	0.213209	−	0.201435i
$209$	−0.811466	+	1.44737i	−0.0561303	+	0.100117i
$210$	−0.769389	−	0.623843i	−0.0530929	−	0.0430492i
$211$	−10.3567	+	5.05671i	−0.712986	+	0.348118i	−0.759239	−	0.650812i	$-0.774429\pi$
$211$	−10.3567	+	5.05671i	−0.712986	+	0.348118i	0.0462527	+	0.998930i	$0.485272\pi$
$212$	6.66180	−	6.78908i	0.457534	−	0.466276i
$213$	−4.33739	−	0.494645i	−0.297193	−	0.0338925i
$214$	−12.4723	−	6.68558i	−0.852592	−	0.457017i
$215$	−5.11549	+	4.47903i	−0.348873	+	0.305467i
$216$	4.10067	−	3.07523i	0.279016	−	0.209243i
$217$	0.577777	+	0.685635i	0.0392221	+	0.0465439i
$218$	0.687255	+	7.24114i	0.0465468	+	0.490432i
$219$	0.942836	+	3.75459i	0.0637110	+	0.253712i
$220$	0.447739	+	1.53462i	0.0301866	+	0.103464i
$221$	1.83842	+	13.7960i	0.123665	+	0.928020i
$222$	−7.22869	−	1.67048i	−0.485158	−	0.112115i
$223$	−22.4250	+	7.00584i	−1.50169	+	0.469145i	−0.934959	−	0.354756i	$-0.884564\pi$
$223$	−22.4250	+	7.00584i	−1.50169	+	0.469145i	−0.566733	+	0.823902i	$0.691793\pi$
$224$	0.382143	+	0.361040i	0.0255330	+	0.0241230i
$225$	−1.94591	−	2.69975i	−0.129727	−	0.179983i
$226$	1.62708	−	3.87616i	0.108232	−	0.257838i
$227$	1.65932	−	0.0628363i	0.110133	−	0.00417059i	0.0172826	−	0.999851i	$-0.494498\pi$
$227$	1.65932	−	0.0628363i	0.110133	−	0.00417059i	0.0928506	+	0.995680i	$0.470402\pi$
$228$	−0.476316	+	1.89680i	−0.0315448	+	0.125619i
$229$	−10.1466	−	1.54806i	−0.670505	−	0.102299i	−0.193366	−	0.981127i	$-0.561940\pi$
$229$	−10.1466	−	1.54806i	−0.670505	−	0.102299i	−0.477139	+	0.878828i	$0.658326\pi$
$230$	−4.39596	+	15.0671i	−0.289861	+	0.993495i
$231$	−0.485676	−	0.0183919i	−0.0319551	−	0.00121010i
$232$	−3.72350	+	8.00704i	−0.244460	+	0.525688i
$233$	−15.0623	+	12.2130i	−0.986767	+	0.800099i	−0.979821	−	0.199877i	$-0.935946\pi$
$233$	−15.0623	+	12.2130i	−0.986767	+	0.800099i	−0.00694571	+	0.999976i	$0.502211\pi$
$234$	−1.36985	−	7.96452i	−0.0895498	−	0.520657i
$235$	5.08737	−	6.52283i	0.331863	−	0.425503i
$236$	−5.52862	+	0.630496i	−0.359883	+	0.0410418i
$237$	−15.0654	−	5.99122i	−0.978603	−	0.389171i
$238$	−1.69879	+	0.325394i	−0.110116	+	0.0210922i
$239$	13.8990	−	19.2834i	0.899053	−	1.24734i	−0.0692593	−	0.997599i	$-0.522064\pi$
$239$	13.8990	−	19.2834i	0.899053	−	1.24734i	0.968312	−	0.249743i	$-0.0803460\pi$
$240$	0.982932	+	1.60741i	0.0634480	+	0.103758i
$241$	4.09285	−	0.310426i	0.263644	−	0.0199963i	0.0568570	−	0.998382i	$-0.481892\pi$
$241$	4.09285	−	0.310426i	0.263644	−	0.0199963i	0.206787	+	0.978386i	$0.433699\pi$
$242$	−8.17275	−	6.12902i	−0.525364	−	0.393988i
$243$	−0.895128	−	15.7491i	−0.0574225	−	1.01030i
$244$	10.9977	−	2.98405i	0.704058	−	0.191034i
$245$	5.53010	+	10.8028i	0.353305	+	0.690168i
$246$	−3.57941	−	0.271484i	−0.228215	−	0.0173092i
$247$	5.96291	+	5.22102i	0.379411	+	0.332205i
$248$	−0.600132	−	1.59642i	−0.0381084	−	0.101373i
$249$	9.52343	−	2.20077i	0.603523	−	0.139468i
$250$	10.5003	−	6.15099i	0.664097	−	0.389023i
$251$	14.6460	−	8.57951i	0.924447	−	0.541534i	0.0354118	−	0.999373i	$-0.488726\pi$
$251$	14.6460	−	8.57951i	0.924447	−	0.541534i	0.889035	+	0.457839i	$0.151376\pi$
$252$	0.978545	−	0.226132i	0.0616425	−	0.0142450i
$253$	2.70993	+	7.20872i	0.170372	+	0.453209i
$254$	8.42559	+	7.37730i	0.528669	+	0.462893i
$255$	−6.18118	−	0.468818i	−0.387080	−	0.0293585i
$256$	−0.455676	−	0.890146i	−0.0284797	−	0.0556341i
$257$	−5.98846	+	1.62486i	−0.373550	+	0.101356i	−0.443689	−	0.896181i	$-0.646330\pi$
$257$	−5.98846	+	1.62486i	−0.373550	+	0.101356i	0.0701390	+	0.997537i	$0.477656\pi$
$258$	0.223127	+	3.92575i	0.0138913	+	0.244407i
$259$	−2.98938	−	2.24184i	−0.185751	−	0.139301i
$260$	7.61371	−	0.577469i	0.472182	−	0.0358131i
$261$	8.80075	+	14.3921i	0.544753	+	0.890846i
$262$	4.40707	−	6.11435i	0.272270	−	0.377746i
$263$	1.79859	−	0.344511i	0.110906	−	0.0212435i	−0.132372	−	0.991200i	$-0.542259\pi$
$263$	1.79859	−	0.344511i	0.110906	−	0.0212435i	0.243278	+	0.969957i	$0.421777\pi$
$264$	0.859053	+	0.341628i	0.0528710	+	0.0210258i
$265$	17.0578	−	1.94531i	1.04785	−	0.119499i
$266$	−0.605751	+	0.776672i	−0.0371410	+	0.0476208i
$267$	−0.585579	−	3.40465i	−0.0358368	−	0.208361i
$268$	−7.79902	+	6.32367i	−0.476401	+	0.386280i
$269$	8.02602	−	17.2592i	0.489355	−	1.05231i	−0.493806	−	0.869572i	$-0.664395\pi$
$269$	8.02602	−	17.2592i	0.489355	−	1.05231i	0.983161	−	0.182741i	$-0.0584968\pi$
$270$	9.24516	+	0.350101i	0.562642	+	0.0213065i
$271$	−1.09561	+	3.75519i	−0.0665535	+	0.228111i	−0.986453	−	0.164042i	$-0.947547\pi$
$271$	−1.09561	+	3.75519i	−0.0665535	+	0.228111i	0.919900	+	0.392153i	$0.128270\pi$
$272$	3.25245	+	0.496225i	0.197209	+	0.0300881i
$273$	−0.565398	+	2.25154i	−0.0342194	+	0.136270i
$274$	−3.56066	+	0.134837i	−0.215107	+	0.00814581i
$275$	0.597156	−	1.42259i	0.0360099	−	0.0857853i
$276$	5.30735	+	7.36339i	0.319465	+	0.443224i
$277$	−4.53670	−	4.28617i	−0.272584	−	0.257531i	0.538280	−	0.842766i	$-0.319074\pi$
$277$	−4.53670	−	4.28617i	−0.272584	−	0.257531i	−0.810864	+	0.585235i	$0.801002\pi$
$278$	14.7259	−	4.60054i	0.883202	−	0.275922i
$279$	−3.17451	−	0.733595i	−0.190053	−	0.0439192i
$280$	0.125343	+	0.940606i	0.00749065	+	0.0562119i
$281$	−4.82903	−	16.5515i	−0.288076	−	0.987377i	−0.967340	−	0.253483i	$-0.918424\pi$
$281$	−4.82903	−	16.5515i	−0.288076	−	0.987377i	0.679264	−	0.733894i	$-0.262299\pi$
$282$	−1.16513	−	4.63983i	−0.0693826	−	0.276298i
$283$	−0.653494	−	6.88543i	−0.0388462	−	0.409296i	−0.993688	−	0.112181i	$-0.964216\pi$
$283$	−0.653494	−	6.88543i	−0.0388462	−	0.409296i	0.954842	−	0.297115i	$-0.0960246\pi$
$284$	2.69496	+	3.19805i	0.159916	+	0.189769i
$285$	−2.82409	+	2.11788i	−0.167284	+	0.125452i
$286$	2.81877	−	2.46807i	0.166678	−	0.145940i
$287$	−1.59343	−	0.854129i	−0.0940570	−	0.0504177i
$288$	−1.89809	−	0.216462i	−0.111846	−	0.0127551i
$289$	4.32510	−	4.40774i	0.254418	−	0.259279i
$290$	−14.3228	+	6.99317i	−0.841065	+	0.410653i
$291$	−4.05065	−	3.28438i	−0.237453	−	0.192534i
$292$	1.81361	−	3.23485i	0.106134	−	0.189305i
$293$	−20.7063	+	19.5629i	−1.20968	+	1.14288i	−0.223936	+	0.974604i	$0.571891\pi$
$293$	−20.7063	+	19.5629i	−1.20968	+	1.14288i	−0.985741	+	0.168271i	$0.946182\pi$
$294$	6.89309	+	1.32034i	0.402013	+	0.0770036i
$295$	−8.46800	−	5.40097i	−0.493026	−	0.314457i
$296$	3.93476	+	5.91906i	0.228704	+	0.344038i
$297$	3.73226	−	2.58423i	0.216568	−	0.149952i
$298$	−0.705877	+	7.43735i	−0.0408904	+	0.430834i
$299$	36.3636	−	5.54797i	2.10296	−	0.320848i
$300$	0.240192	−	1.80247i	0.0138675	−	0.104065i
$301$	−0.696850	+	1.85370i	−0.0401657	+	0.106846i
$302$	−6.46650	+	3.46626i	−0.372105	+	0.199461i
$303$	5.13936	−	2.04382i	0.295248	−	0.117414i
$304$	1.57960	−	1.00749i	0.0905965	−	0.0577833i
$305$	18.8113	+	8.31853i	1.07713	+	0.476318i
$306$	4.22924	−	4.64964i	0.241770	−	0.265802i
$307$	−1.27647	−	1.63664i	−0.0728517	−	0.0934078i	0.750718	−	0.660623i	$-0.229708\pi$
$307$	−1.27647	−	1.63664i	−0.0728517	−	0.0934078i	−0.823570	+	0.567215i	$0.808021\pi$
$308$	0.326106	+	0.332337i	0.0185816	+	0.0189366i
$309$	7.58552	+	2.68887i	0.431525	+	0.152964i
$310$	0.973414	−	2.92045i	0.0552862	−	0.165870i
$311$	16.9865	−	7.51159i	0.963218	−	0.425943i	0.137797	−	0.990461i	$-0.455998\pi$
$311$	16.9865	−	7.51159i	0.963218	−	0.425943i	0.825421	+	0.564517i	$0.190938\pi$
$312$	2.44456	−	3.67735i	0.138396	−	0.208189i
$313$	−0.588285	−	31.0809i	−0.0332518	−	1.75680i	−0.494180	−	0.869360i	$-0.664531\pi$
$313$	−0.588285	−	31.0809i	−0.0332518	−	1.75680i	0.460928	−	0.887438i	$-0.347517\pi$
$314$	7.19260	−	2.54959i	0.405902	−	0.143881i
$315$	1.62901	+	0.795368i	0.0917841	+	0.0448139i
$316$	6.54931	+	14.0837i	0.368427	+	0.792269i
$317$	4.58028	+	10.9115i	0.257254	+	0.612849i	0.998280	−	0.0586278i	$-0.0186725\pi$
$317$	4.58028	+	10.9115i	0.257254	+	0.612849i	−0.741026	+	0.671476i	$0.765660\pi$
$318$	5.17970	−	8.47048i	0.290463	−	0.475001i
$319$	−3.56374	+	6.96164i	−0.199531	+	0.389777i
$320$	0.373050	−	1.76602i	0.0208541	−	0.0987233i
$321$	−14.2562	−	3.86817i	−0.795702	−	0.215900i
$322$	0.944809	+	4.47272i	0.0526521	+	0.249255i
$323$	−0.349785	+	6.15420i	−0.0194626	+	0.342429i
$324$	−0.245361	+	0.291164i	−0.0136312	+	0.0161758i
$325$	−6.05865	−	4.19502i	−0.336074	−	0.232698i
$326$	0.0452443	−	2.39040i	0.00250585	−	0.132392i
$327$	2.40083	+	7.20301i	0.132766	+	0.398327i
$328$	2.31395	+	2.54397i	0.127767	+	0.140467i
$329$	0.408397	−	2.37449i	0.0225157	−	0.130910i
$330$	0.816047	+	1.45554i	0.0449219	+	0.0801249i
$331$	−5.68633	−	1.77648i	−0.312549	−	0.0976439i	0.137900	−	0.990446i	$-0.455965\pi$
$331$	−5.68633	−	1.77648i	−0.312549	−	0.0976439i	−0.450449	+	0.892802i	$0.648736\pi$
$332$	−8.07965	−	4.73300i	−0.443428	−	0.259757i
$333$	13.5782			0.744083
$334$	8.11960	+	10.0535i	0.444285	+	0.550101i
$335$	−18.1231			−0.990173
$336$	0.473509	+	0.277378i	0.0258321	+	0.0151322i
$337$	10.2382	+	3.19852i	0.557708	+	0.174234i	0.564043	−	0.825746i	$-0.309245\pi$
$337$	10.2382	+	3.19852i	0.557708	+	0.174234i	−0.00633449	+	0.999980i	$0.502016\pi$
$338$	−2.39391	−	4.26989i	−0.130211	−	0.232251i
$339$	0.743807	−	4.32462i	0.0403981	−	0.234881i
$340$	3.99590	+	4.39310i	0.216708	+	0.238249i
$341$	−0.477628	−	1.43299i	−0.0258650	−	0.0776006i
$342$	0.0677333	−	3.57856i	0.00366260	−	0.193507i
$343$	5.93169	+	4.10711i	0.320281	+	0.221763i
$344$	2.42740	−	2.88054i	0.130877	−	0.155308i
$345$	−0.929682	+	16.3570i	−0.0500524	+	0.880633i
$346$	4.17619	+	19.7700i	0.224513	+	1.06284i
$347$	7.69981	+	2.08921i	0.413348	+	0.112155i	0.462463	−	0.886638i	$-0.346966\pi$
$347$	7.69981	+	2.08921i	0.413348	+	0.112155i	−0.0491158	+	0.998793i	$0.515640\pi$
$348$	−1.90508	+	9.01861i	−0.102123	+	0.483448i
$349$	−6.82565	+	13.3337i	−0.365369	+	0.713734i	−0.998163	−	0.0605860i	$-0.980703\pi$
$349$	−6.82565	+	13.3337i	−0.365369	+	0.713734i	0.632794	+	0.774320i	$0.281908\pi$
$350$	0.477775	−	0.781317i	0.0255382	−	0.0417631i
$351$	−8.39241	−	19.9930i	−0.447954	−	1.06715i
$352$	−0.373452	−	0.803073i	−0.0199050	−	0.0428039i
$353$	−14.6850	−	7.16999i	−0.781602	−	0.381620i	0.00428401	−	0.999991i	$-0.498636\pi$
$353$	−14.6850	−	7.16999i	−0.781602	−	0.381620i	−0.785886	+	0.618371i	$0.787793\pi$
$354$	−5.47465	+	1.94062i	−0.290975	+	0.103143i
$355$	0.142853	+	7.54736i	0.00758183	+	0.400572i
$356$	−1.83217	+	2.75612i	−0.0971046	+	0.146074i
$357$	−1.65126	+	0.730201i	−0.0873939	+	0.0386463i
$358$	2.60387	−	7.81215i	0.137619	−	0.412885i
$359$	23.0493	+	8.17038i	1.21650	+	0.431216i	0.863472	−	0.504398i	$-0.168285\pi$
$359$	23.0493	+	8.17038i	1.21650	+	0.431216i	0.353026	+	0.935614i	$0.385153\pi$
$360$	−2.41508	−	2.46123i	−0.127286	−	0.129718i
$361$	−9.52622	−	12.2142i	−0.501380	−	0.642851i
$362$	11.5135	−	12.6580i	0.605135	−	0.665288i
$363$	−9.75250	−	4.31264i	−0.511874	−	0.226355i
$364$	1.87503	−	1.19591i	0.0982781	−	0.0626827i
$365$	6.22010	−	2.47361i	0.325575	−	0.129475i
$366$	10.4838	−	5.61967i	0.547998	−	0.293745i
$367$	2.39059	−	6.35925i	0.124788	−	0.331950i	−0.858818	−	0.512280i	$-0.828801\pi$
$367$	2.39059	−	6.35925i	0.124788	−	0.331950i	0.983606	+	0.180330i	$0.0577166\pi$
$368$	1.14859	−	8.61932i	0.0598742	−	0.449313i
$369$	6.49452	−	0.990866i	0.338091	−	0.0515824i
$370$	−1.21216	+	12.7717i	−0.0630170	+	0.663968i
$371$	4.11117	−	2.84658i	0.213441	−	0.147787i
$372$	−0.985562	−	1.48258i	−0.0510990	−	0.0768681i
$373$	−30.9072	−	19.7129i	−1.60031	−	1.02070i	−0.969605	−	0.244675i	$-0.921319\pi$
$373$	−30.9072	−	19.7129i	−1.60031	−	1.02070i	−0.630709	−	0.776020i	$-0.717236\pi$
$374$	2.86187	+	0.548176i	0.147984	+	0.0283455i
$375$	9.23358	−	8.72367i	0.476820	−	0.450488i
$376$	−2.24122	+	3.99754i	−0.115582	+	0.206158i
$377$	29.0156	+	23.5267i	1.49438	+	1.21169i
$378$	2.42147	−	1.18229i	0.124547	−	0.0608104i
$379$	−22.2414	+	22.6663i	−1.14246	+	1.16429i	−0.158233	+	0.987402i	$0.550580\pi$
$379$	−22.2414	+	22.6663i	−1.14246	+	1.16429i	−0.984231	+	0.176890i	$0.943396\pi$
$380$	3.35995	+	0.383176i	0.172362	+	0.0196565i
$381$	10.3030	+	5.52277i	0.527841	+	0.282940i
$382$	−1.84318	+	1.61385i	−0.0943052	+	0.0825719i
$383$	12.7904	−	9.59199i	0.653561	−	0.490128i	−0.220853	−	0.975307i	$-0.570884\pi$
$383$	12.7904	−	9.59199i	0.653561	−	0.490128i	0.874415	+	0.485179i	$0.161246\pi$
$384$	−0.672650	−	0.798218i	−0.0343260	−	0.0407339i
$385$	0.0794072	+	0.836660i	0.00404697	+	0.0426402i
$386$	−2.00908	−	8.00060i	−0.102259	−	0.407220i
$387$	−2.01555	−	6.90828i	−0.102456	−	0.351168i
$388$	0.659898	+	4.95206i	0.0335013	+	0.251403i
$389$	−23.7118	−	5.47955i	−1.20223	−	0.277824i	−0.423921	−	0.905699i	$-0.639346\pi$
$389$	−23.7118	−	5.47955i	−1.20223	−	0.277824i	−0.778314	+	0.627875i	$0.783925\pi$
$390$	7.60773	−	2.37674i	0.385233	−	0.120351i
$391$	20.7957	+	19.6473i	1.05168	+	0.993605i
$392$	−3.93143	−	5.45444i	−0.198567	−	0.275491i
$393$	3.04513	−	7.25433i	0.153607	−	0.365932i
$394$	−11.5645	+	0.437933i	−0.582613	+	0.0220627i
$395$	−6.82805	+	27.1909i	−0.343556	+	1.36812i
$396$	−1.67260	−	0.255188i	−0.0840513	−	0.0128237i
$397$	−4.68665	+	16.0635i	−0.235216	+	0.806202i	0.753635	+	0.657294i	$0.228299\pi$
$397$	−4.68665	+	16.0635i	−0.235216	+	0.806202i	−0.988851	+	0.148908i	$0.952424\pi$
$398$	−18.9073	−	0.715991i	−0.947735	−	0.0358894i
$399$	−0.433534	+	0.932275i	−0.0217039	+	0.0466721i
$400$	−1.35311	+	1.09714i	−0.0676557	+	0.0548572i
$401$	2.11489	+	12.2963i	0.105613	+	0.614050i	0.989291	+	0.145955i	$0.0466256\pi$
$401$	2.11489	+	12.2963i	0.105613	+	0.614050i	−0.883678	+	0.468095i	$0.844941\pi$
$402$	−6.44569	+	8.26442i	−0.321482	+	0.412192i
$403$	−7.16825	+	0.817483i	−0.357076	+	0.0407217i
$404$	−4.92349	−	1.95798i	−0.244953	−	0.0974130i
$405$	−0.674996	+	0.129292i	−0.0335408	+	0.00642457i
$406$	−2.71448	+	3.76605i	−0.134717	+	0.186906i
$407$	3.28399	+	5.37038i	0.162781	+	0.266200i
$408$	3.42450	−	0.259735i	0.169538	−	0.0128588i
$409$	−28.6887	−	21.5146i	−1.41856	−	1.06383i	−0.986818	−	0.161833i	$-0.948259\pi$
$409$	−28.6887	−	21.5146i	−1.41856	−	1.06383i	−0.431745	−	0.901996i	$-0.642102\pi$
$410$	0.352229	+	6.19720i	0.0173954	+	0.306058i
$411$	−3.58964	+	0.973988i	−0.177064	+	0.0480433i
$412$	−3.51324	−	6.86298i	−0.173085	−	0.338115i
$413$	−2.91698	−	0.221241i	−0.143535	−	0.0108866i
$414$	−12.4981	−	10.9431i	−0.614246	−	0.537823i
$415$	−5.94737	−	15.8207i	−0.291945	−	0.776608i
$416$	−4.12165	+	0.952470i	−0.202080	+	0.0466987i
$417$	13.8956	−	8.13994i	0.680470	−	0.398614i
$418$	1.43175	−	0.838711i	0.0700294	−	0.0410227i
$419$	−20.3379	+	4.69989i	−0.993573	+	0.229605i	−0.690476	−	0.723355i	$-0.742599\pi$
$419$	−20.3379	+	4.69989i	−0.993573	+	0.229605i	−0.303097	+	0.952960i	$0.598021\pi$
$420$	0.348547	+	0.927175i	0.0170073	+	0.0452415i
$421$	−0.0662433	−	0.0580015i	−0.00322850	−	0.00282682i	0.657137	−	0.753771i	$-0.271767\pi$
$421$	−0.0662433	−	0.0580015i	−0.00322850	−	0.00282682i	−0.660365	+	0.750944i	$0.729599\pi$
$422$	11.4923	+	0.871642i	0.559435	+	0.0424309i
$423$	3.98954	+	7.79342i	0.193978	+	0.378929i
$424$	−9.17972	+	2.49076i	−0.445807	+	0.120962i
$425$	−0.325230	−	5.72217i	−0.0157760	−	0.277566i
$426$	3.49251	+	2.61915i	0.169213	+	0.126898i
$427$	5.97364	−	0.453077i	0.289085	−	0.0219259i
$428$	7.38256	+	12.0729i	0.356849	+	0.583564i
$429$	2.28674	−	3.17262i	0.110405	−	0.153175i
$430$	6.67786	−	1.27911i	0.322035	−	0.0616841i
$431$	−33.4627	−	13.3075i	−1.61184	−	0.640998i	−0.621980	−	0.783033i	$-0.713671\pi$
$431$	−33.4627	−	13.3075i	−1.61184	−	0.640998i	−0.989862	+	0.142035i	$0.954635\pi$
$432$	−5.09267	+	0.580779i	−0.245021	+	0.0279427i
$433$	−12.8137	+	16.4293i	−0.615788	+	0.789540i	−0.990487	−	0.137606i	$-0.956059\pi$
$433$	−12.8137	+	16.4293i	−0.615788	+	0.789540i	0.374699	+	0.927146i	$0.377746\pi$
$434$	−0.151981	−	0.883642i	−0.00729532	−	0.0424162i
$435$	−12.9233	+	10.4786i	−0.619625	+	0.502410i
$436$	3.06706	−	6.59542i	0.146885	−	0.315863i
$437$	16.2798	+	0.616492i	0.778767	+	0.0294908i
$438$	1.08424	−	3.71622i	0.0518070	−	0.177568i
$439$	−34.2799	−	5.23007i	−1.63609	−	0.249618i	−0.733364	−	0.679836i	$-0.762051\pi$
$439$	−34.2799	−	5.23007i	−1.63609	−	0.249618i	−0.902725	+	0.430218i	$0.858437\pi$
$440$	0.389346	−	1.55047i	0.0185613	−	0.0739155i
$441$	−12.8355	+	0.486064i	−0.611216	+	0.0231459i
$442$	5.38695	−	12.8332i	0.256231	−	0.610412i
$443$	−21.3620	−	29.6375i	−1.01494	−	1.40812i	−0.910462	−	0.413592i	$-0.864274\pi$
$443$	−21.3620	−	29.6375i	−1.01494	−	1.40812i	−0.104475	−	0.994527i	$-0.533316\pi$
$444$	5.39296	+	5.09514i	0.255938	+	0.241805i
$445$	−5.70189	+	1.78134i	−0.270296	+	0.0844434i
$446$	22.8907	+	5.28979i	1.08390	+	0.250479i
$447$	1.03008	+	7.72999i	0.0487210	+	0.365616i
$448$	−0.147245	−	0.504680i	−0.00695666	−	0.0238439i
$449$	6.21402	+	24.7456i	0.293258	+	1.16782i	0.921052	+	0.389440i	$0.127331\pi$
$449$	6.21402	+	24.7456i	0.293258	+	1.16782i	−0.627794	+	0.778379i	$0.716042\pi$
$450$	0.314441	+	3.31306i	0.0148229	+	0.156179i
$451$	1.96265	+	2.32903i	0.0924173	+	0.109670i
$452$	−3.36315	+	2.52214i	−0.158189	+	0.118632i
$453$	−5.76203	+	5.04513i	−0.270724	+	0.237041i
$454$	−1.46352	−	0.784493i	−0.0686862	−	0.0368181i
$455$	3.98834	+	0.454838i	0.186976	+	0.0213232i
$456$	1.36973	−	1.39591i	0.0641437	−	0.0653693i
$457$	15.2120	−	7.42729i	0.711585	−	0.347434i	−0.0471009	−	0.998890i	$-0.514998\pi$
$457$	15.2120	−	7.42729i	0.711585	−	0.347434i	0.758686	+	0.651456i	$0.225842\pi$
$458$	7.97254	+	6.46437i	0.372532	+	0.302060i
$459$	8.24704	−	14.7098i	0.384939	−	0.686595i
$460$	11.4088	−	10.7788i	0.531937	−	0.502562i
$461$	−20.3975	−	3.90703i	−0.950004	−	0.181968i	−0.310342	−	0.950625i	$-0.600444\pi$
$461$	−20.3975	−	3.90703i	−0.950004	−	0.181968i	−0.639662	+	0.768656i	$0.720926\pi$
$462$	0.409771	+	0.261356i	0.0190643	+	0.0121594i
$463$	−7.10709	−	10.6912i	−0.330294	−	0.496861i	0.629716	−	0.776826i	$-0.283171\pi$
$463$	−7.10709	−	10.6912i	−0.330294	−	0.496861i	−0.960010	+	0.279964i	$0.909677\pi$
$464$	7.26002	−	5.02685i	0.337038	−	0.233366i
$465$	0.303616	−	3.19899i	0.0140798	−	0.148350i
$466$	19.1697	−	2.92471i	0.888019	−	0.135485i
$467$	0.982994	−	7.37666i	0.0454875	−	0.341351i	−0.953690	−	0.300792i	$-0.902749\pi$
$467$	0.982994	−	7.37666i	0.0454875	−	0.341351i	0.999177	−	0.0405587i	$-0.0129138\pi$
$468$	−2.84371	+	7.56461i	−0.131451	+	0.349674i
$469$	−4.65233	+	2.49380i	−0.214825	+	0.115153i
$470$	−7.68664	+	3.05683i	−0.354558	+	0.141001i
$471$	6.71594	−	4.28349i	0.309454	−	0.197373i
$472$	5.08908	+	2.25044i	0.234244	+	0.103585i
$473$	2.24485	−	2.46799i	0.103218	−	0.113478i
$474$	9.97097	+	12.7844i	0.457982	+	0.587207i
$475$	−2.28589	−	2.32956i	−0.104884	−	0.106888i
$476$	1.63028	+	0.577890i	0.0747236	+	0.0264875i
$477$	−5.74579	+	17.2386i	−0.263081	+	0.789300i
$478$	−21.7397	+	9.61348i	−0.994351	+	0.439710i
$479$	−11.2854	+	16.9766i	−0.515642	+	0.775679i	−0.994778	−	0.102061i	$-0.967456\pi$
$479$	−11.2854	+	16.9766i	−0.515642	+	0.775679i	0.479136	+	0.877741i	$0.340950\pi$
$480$	−0.0356554	−	1.88379i	−0.00162744	−	0.0859827i
$481$	28.3392	−	10.0455i	1.29216	−	0.458035i
$482$	−3.68844	−	1.80089i	−0.168004	−	0.0820284i
$483$	2.01212	+	4.32688i	0.0915547	+	0.196880i
$484$	3.95395	+	9.41939i	0.179725	+	0.428154i
$485$	−4.70431	+	7.69307i	−0.213612	+	0.349324i
$486$	−7.18806	+	14.0416i	−0.326057	+	0.636940i
$487$	5.54646	−	26.2569i	0.251334	−	1.18981i	−0.651102	−	0.758990i	$-0.725693\pi$
$487$	5.54646	−	26.2569i	0.251334	−	1.18981i	0.902436	−	0.430824i	$-0.141777\pi$
$488$	−10.9977	−	2.98405i	−0.497844	−	0.135081i
$489$	−0.515794	−	2.44176i	−0.0233250	−	0.110420i
$490$	0.688663	−	12.1165i	0.0311106	−	0.547367i
$491$	9.25902	−	10.9875i	0.417854	−	0.495857i	−0.514457	−	0.857516i	$-0.672006\pi$
$491$	9.25902	−	10.9875i	0.417854	−	0.495857i	0.932310	+	0.361659i	$0.117790\pi$
$492$	2.95129	+	2.04348i	0.133054	+	0.0921270i
$493$	−0.549803	+	29.0478i	−0.0247619	+	1.30825i
$494$	−2.50614	−	7.51895i	−0.112756	−	0.338293i
$495$	−2.05492	−	2.25919i	−0.0923619	−	0.101543i
$496$	−0.289090	+	1.68082i	−0.0129805	+	0.0754710i
$497$	1.07521	+	1.91780i	0.0482298	+	0.0860250i
$498$	−9.32971	−	2.91471i	−0.418075	−	0.130611i
$499$	−12.1193	−	7.09940i	−0.542535	−	0.317813i	0.208557	−	0.978010i	$-0.433123\pi$
$499$	−12.1193	−	7.09940i	−0.542535	−	0.317813i	−0.751092	+	0.660197i	$0.770473\pi$
$500$	−12.1693			−0.544226
$501$	10.6208	+	8.31645i	0.474503	+	0.371552i
$502$	−16.9739			−0.757582
$503$	−0.904366	−	0.529771i	−0.0403237	−	0.0236213i	0.485153	−	0.874429i	$-0.338764\pi$
$503$	−0.904366	−	0.529771i	−0.0403237	−	0.0236213i	−0.525477	+	0.850808i	$0.676113\pi$
$504$	−0.958640	−	0.299490i	−0.0427012	−	0.0133403i
$505$	−4.67701	−	8.34215i	−0.208124	−	0.371221i
$506$	1.30540	−	7.58982i	0.0580322	−	0.337409i
$507$	−3.43824	−	3.78002i	−0.152698	−	0.167877i
$508$	−3.54117	−	10.6243i	−0.157114	−	0.471376i
$509$	−0.599970	+	31.6983i	−0.0265932	+	1.40500i	0.698135	+	0.715966i	$0.254014\pi$
$509$	−0.599970	+	31.6983i	−0.0265932	+	1.40500i	−0.724728	+	0.689035i	$0.758035\pi$
$510$	5.09649	+	3.52882i	0.225676	+	0.156259i
$511$	1.25636	−	1.49090i	0.0555782	−	0.0659534i
$512$	−0.0567453	+	0.998389i	−0.00250781	+	0.0441230i
$513$	−1.98477	−	9.39586i	−0.0876295	−	0.414837i
$514$	5.98846	+	1.62486i	0.264139	+	0.0716697i
$515$	2.87620	−	13.6159i	0.126740	−	0.599988i
$516$	1.79176	−	3.50013i	0.0788777	−	0.154085i
$517$	−2.11751	+	3.46281i	−0.0931280	+	0.152294i
$518$	1.44625	+	3.44537i	0.0635447	+	0.151381i
$519$	8.89385	+	19.1254i	0.390397	+	0.839512i
$520$	−6.86140	−	3.35010i	−0.300893	−	0.146912i
$521$	−13.9940	+	4.96050i	−0.613088	+	0.217324i	−0.622484	−	0.782632i	$-0.713877\pi$
$521$	−13.9940	+	4.96050i	−0.613088	+	0.217324i	0.00939605	+	0.999956i	$0.497009\pi$
$522$	−0.319243	−	16.8666i	−0.0139729	−	0.738232i
$523$	4.24371	−	6.38380i	0.185564	−	0.279144i	−0.728220	−	0.685343i	$-0.759652\pi$
$523$	4.24371	−	6.38380i	0.185564	−	0.279144i	0.913784	+	0.406199i	$0.133146\pi$
$524$	−6.89318	+	3.04822i	−0.301130	+	0.133162i
$525$	0.302286	−	0.906921i	0.0131928	−	0.0395813i
$526$	−1.72606	−	0.611842i	−0.0752597	−	0.0266776i
$527$	−3.93002	−	4.00511i	−0.171194	−	0.174465i
$528$	−0.568560	−	0.728987i	−0.0247434	−	0.0317251i
$529$	35.4011	−	38.9201i	1.53918	−	1.69218i
$530$	−15.7017	−	6.94341i	−0.682036	−	0.301602i
$531$	8.96249	−	5.71636i	0.388939	−	0.248069i
$532$	0.915246	−	0.363976i	0.0396810	−	0.0157803i
$533$	12.8217	−	6.87283i	0.555368	−	0.297695i
$534$	−1.21562	+	3.23370i	−0.0526051	+	0.139936i
$535$	−3.37393	+	25.3189i	−0.145868	+	1.09463i
$536$	9.92574	−	1.51437i	0.428727	−	0.0654107i
$537$	0.812167	−	8.55726i	0.0350476	−	0.369273i
$538$	−15.6490	+	10.8354i	−0.674677	+	0.467147i
$539$	−3.29661	−	4.95908i	−0.141995	−	0.213603i
$540$	−7.80026	−	4.97508i	−0.335670	−	0.214093i
$541$	8.17228	+	1.56536i	0.351354	+	0.0673000i	0.360768	−	0.932656i	$-0.382515\pi$
$541$	8.17228	+	1.56536i	0.351354	+	0.0673000i	−0.00941399	+	0.999956i	$0.502997\pi$
$542$	2.84342	−	2.68640i	0.122135	−	0.115391i
$543$	8.73471	−	15.5796i	0.374842	−	0.668587i
$544$	−2.55557	−	2.07213i	−0.109569	−	0.0888419i
$545$	11.7978	−	5.76029i	0.505360	−	0.246744i
$546$	1.62591	−	1.65697i	0.0695824	−	0.0709119i
$547$	19.7236	+	2.24932i	0.843320	+	0.0961740i	0.524258	−	0.851560i	$-0.324343\pi$
$547$	19.7236	+	2.24932i	0.843320	+	0.0961740i	0.319062	+	0.947734i	$0.396632\pi$
$548$	3.14048	+	1.68340i	0.134155	+	0.0719113i
$549$	−16.3786	+	14.3408i	−0.699021	+	0.612051i
$550$	−1.23431	+	0.925651i	−0.0526312	+	0.0394699i
$551$	10.6611	+	12.6513i	0.454178	+	0.538962i
$552$	−0.857618	−	9.03615i	−0.0365027	−	0.384604i
$553$	1.98874	+	7.91963i	0.0845699	+	0.336777i
$554$	1.74805	+	5.99143i	0.0742676	+	0.254552i
$555$	1.76889	+	13.2742i	0.0750850	+	0.563459i
$556$	−15.0317	−	3.47366i	−0.637485	−	0.147316i
$557$	36.8161	−	11.5018i	1.55995	−	0.487345i	0.608084	−	0.793872i	$-0.291938\pi$
$557$	36.8161	−	11.5018i	1.55995	−	0.487345i	0.951862	+	0.306527i	$0.0991671\pi$
$558$	2.36834	+	2.23755i	0.100260	+	0.0947230i
$559$	−9.31757	−	12.9271i	−0.394091	−	0.546760i
$560$	0.367280	−	0.874960i	0.0155204	−	0.0369738i
$561$	3.03947	−	0.115101i	0.128327	−	0.00485955i
$562$	−4.19924	+	16.7223i	−0.177134	+	0.705389i
$563$	−5.57654	−	0.850810i	−0.235023	−	0.0358574i	0.0322434	−	0.999480i	$-0.489735\pi$
$563$	−5.57654	−	0.850810i	−0.235023	−	0.0358574i	−0.267266	+	0.963623i	$0.586120\pi$
$564$	−1.33988	+	4.59241i	−0.0564190	+	0.193375i
$565$	−7.58238	−	0.287134i	−0.318993	−	0.0120798i
$566$	−2.91639	+	6.27143i	−0.122585	+	0.263608i
$567$	−0.155485	+	0.126072i	−0.00652975	+	0.00529451i
$568$	−0.708893	−	4.12162i	−0.0297445	−	0.172939i
$569$	−13.6922	+	17.5557i	−0.574009	+	0.735973i	−0.984402	−	0.175936i	$-0.943705\pi$
$569$	−13.6922	+	17.5557i	−0.574009	+	0.735973i	0.410393	+	0.911909i	$0.365392\pi$
$570$	3.50726	−	0.399976i	0.146903	−	0.0167531i
$571$	−21.3774	−	8.50137i	−0.894616	−	0.355771i	−0.123409	−	0.992356i	$-0.539383\pi$
$571$	−21.3774	−	8.50137i	−0.894616	−	0.355771i	−0.771207	+	0.636584i	$0.780347\pi$
$572$	−3.67968	+	0.704824i	−0.153855	+	0.0294702i
$573$	−1.49529	+	2.07455i	−0.0624665	+	0.0866657i
$574$	0.943172	+	1.54239i	0.0393673	+	0.0643782i
$575$	−15.1044	+	1.14561i	−0.629897	+	0.0477751i
$576$	1.52836	+	1.14617i	0.0636817	+	0.0477571i
$577$	−2.34430	−	41.2460i	−0.0975943	−	1.71710i	−0.558381	−	0.829584i	$-0.688577\pi$
$577$	−2.34430	−	41.2460i	−0.0975943	−	1.71710i	0.460787	−	0.887511i	$-0.347567\pi$
$578$	−5.95983	+	1.61710i	−0.247896	+	0.0672624i
$579$	−3.92367	−	7.66475i	−0.163062	−	0.318536i
$580$	15.8932	+	1.20544i	0.659930	+	0.0500531i
$581$	−3.70370	−	3.24290i	−0.153656	−	0.134538i
$582$	1.83502	+	4.88136i	0.0760638	+	0.202339i
$583$	−8.20776	+	1.89673i	−0.339931	+	0.0785545i
$584$	−3.19995	+	1.87451i	−0.132415	+	0.0775676i
$585$	−12.5864	+	7.37301i	−0.520383	+	0.304837i
$586$	27.7547	−	6.41382i	1.14653	−	0.264952i
$587$	7.12590	+	18.9557i	0.294117	+	0.782387i	0.997439	+	0.0715155i	$0.0227835\pi$
$587$	7.12590	+	18.9557i	0.294117	+	0.782387i	−0.703322	+	0.710871i	$0.748301\pi$
$588$	−5.28036	−	4.62339i	−0.217759	−	0.190666i
$589$	−3.18618	−	0.241659i	−0.131284	−	0.00995738i
$590$	4.57671	+	8.94042i	0.188420	+	0.368071i
$591$	−11.6587	+	3.16338i	−0.479574	+	0.130124i
$592$	−0.403321	−	7.09612i	−0.0165764	−	0.291649i
$593$	21.2356	+	15.9253i	0.872044	+	0.653975i	0.939051	−	0.343778i	$-0.111707\pi$
$593$	21.2356	+	15.9253i	0.872044	+	0.653975i	−0.0670075	+	0.997752i	$0.521345\pi$
$594$	−4.52661	+	0.343325i	−0.185729	+	0.0140868i
$595$	1.62874	+	2.66351i	0.0667717	+	0.109193i
$596$	4.36830	−	6.06056i	0.178933	−	0.248250i
$597$	−19.3977	+	3.71553i	−0.793896	+	0.152067i
$598$	−34.1807	−	13.5930i	−1.39775	−	0.555859i
$599$	32.9883	−	3.76206i	1.34787	−	0.153714i	0.590677	−	0.806908i	$-0.298861\pi$
$599$	32.9883	−	3.76206i	1.34787	−	0.153714i	0.757190	+	0.653194i	$0.226572\pi$
$600$	−1.11831	+	1.43386i	−0.0456550	+	0.0585371i
$601$	−3.48122	−	20.2404i	−0.142002	−	0.825622i	−0.965906	−	0.258893i	$-0.916642\pi$
$601$	−3.48122	−	20.2404i	−0.142002	−	0.825622i	0.823904	−	0.566729i	$-0.191791\pi$
$602$	1.53824	−	1.24725i	0.0626939	−	0.0508341i
$603$	8.08815	−	17.3928i	0.329375	−	0.708290i
$604$	7.33168	+	0.277640i	0.298322	+	0.0112970i
$605$	−5.16443	+	17.7010i	−0.209964	+	0.719649i
$606$	−5.46757	−	0.834185i	−0.222105	−	0.0338865i
$607$	−5.95792	+	23.7258i	−0.241824	+	0.963000i	0.721014	+	0.692921i	$0.243676\pi$
$607$	−5.95792	+	23.7258i	−0.241824	+	0.963000i	−0.962838	+	0.270079i	$0.912950\pi$
$608$	−1.87221	+	0.0708978i	−0.0759279	+	0.00287528i
$609$	−1.87561	+	4.46821i	−0.0760035	+	0.181061i
$610$	−12.0268	−	16.6859i	−0.486951	−	0.675593i
$611$	14.0923	+	13.3141i	0.570115	+	0.538632i
$612$	−5.99939	+	1.87428i	−0.242511	+	0.0757632i
$613$	19.1768	+	4.43156i	0.774543	+	0.178989i	0.593877	−	0.804556i	$-0.297596\pi$
$613$	19.1768	+	4.43156i	0.774543	+	0.178989i	0.180666	+	0.983545i	$0.442175\pi$
$614$	0.274160	+	2.05737i	0.0110642	+	0.0830288i
$615$	1.81474	+	6.22002i	0.0731775	+	0.250815i
$616$	−0.113401	−	0.451589i	−0.00456906	−	0.0181951i
$617$	0.119907	+	1.26338i	0.00482727	+	0.0508617i	0.997615	−	0.0690235i	$-0.0219883\pi$
$617$	0.119907	+	1.26338i	0.00482727	+	0.0508617i	−0.992788	+	0.119885i	$0.961747\pi$
$618$	−5.18610	−	6.15423i	−0.208616	−	0.247559i
$619$	2.96477	−	2.22338i	0.119164	−	0.0893652i	−0.538718	−	0.842486i	$-0.681091\pi$
$619$	2.96477	−	2.22338i	0.119164	−	0.0893652i	0.657882	+	0.753121i	$0.271453\pi$
$620$	−2.31606	+	2.02790i	−0.0930154	+	0.0814426i
$621$	−39.2827	−	21.0568i	−1.57636	−	0.844981i
$622$	−18.4537	−	2.10449i	−0.739924	−	0.0843825i
$623$	−1.21859	+	1.24188i	−0.0488220	+	0.0497548i
$624$	−3.96803	+	1.93740i	−0.158848	+	0.0775582i
$625$	−10.2960	−	8.34829i	−0.411840	−	0.333932i
$626$	−15.2023	+	27.1156i	−0.607608	+	1.08376i
$627$	1.25903	−	1.18951i	0.0502809	−	0.0475043i
$628$	−7.49486	−	1.43560i	−0.299077	−	0.0572867i
$629$	19.7157	+	12.5749i	0.786117	+	0.501393i
$630$	−1.00357	−	1.50967i	−0.0399833	−	0.0601468i
$631$	−12.4826	+	8.64296i	−0.496924	+	0.344071i	−0.791107	−	0.611678i	$-0.790495\pi$
$631$	−12.4826	+	8.64296i	−0.496924	+	0.344071i	0.294183	+	0.955749i	$0.404952\pi$
$632$	1.46754	−	15.4625i	0.0583758	−	0.615066i
$633$	11.8930	−	1.81451i	0.472703	−	0.0721201i
$634$	1.56312	−	11.7301i	0.0620795	−	0.465862i
$635$	7.11287	−	18.9211i	0.282266	−	0.750860i
$636$	−8.75075	+	4.69069i	−0.346990	+	0.185998i
$637$	−26.4295	+	10.5105i	−1.04717	+	0.416441i
$638$	6.59377	−	4.20557i	0.261050	−	0.166500i
$639$	−7.30697	−	3.23120i	−0.289059	−	0.127824i
$640$	−1.21453	+	1.33525i	−0.0480084	+	0.0527806i
$641$	17.0646	+	21.8796i	0.674012	+	0.864193i	0.996604	−	0.0823448i	$-0.0262409\pi$
$641$	17.0646	+	21.8796i	0.674012	+	0.864193i	−0.322592	+	0.946538i	$0.604554\pi$
$642$	10.3458	+	10.5435i	0.408317	+	0.416118i
$643$	21.1475	+	7.49624i	0.833977	+	0.295623i	0.716617	−	0.697467i	$-0.245689\pi$
$643$	21.1475	+	7.49624i	0.833977	+	0.295623i	0.117360	+	0.993089i	$0.462557\pi$
$644$	1.44552	−	4.33686i	0.0569614	−	0.170896i
$645$	6.49103	−	2.87039i	0.255584	−	0.113021i
$646$	3.41247	−	5.13338i	0.134262	−	0.201970i
$647$	−0.0676790	−	3.57569i	−0.00266074	−	0.140575i	−0.998678	−	0.0514102i	$-0.983628\pi$
$647$	−0.0676790	−	3.57569i	−0.00266074	−	0.140575i	0.996017	−	0.0891648i	$-0.0284198\pi$
$648$	0.358880	−	0.127214i	0.0140982	−	0.00499742i
$649$	4.42854	+	2.16225i	0.173835	+	0.0848757i
$650$	3.10735	+	6.68206i	0.121880	+	0.262092i
$651$	−0.362251	−	0.862980i	−0.0141977	−	0.0338229i
$652$	−1.24727	+	2.03969i	−0.0488470	+	0.0798806i
$653$	−15.5089	+	30.2961i	−0.606912	+	1.18558i	0.360592	+	0.932724i	$0.382575\pi$
$653$	−15.5089	+	30.2961i	−0.606912	+	1.18558i	−0.967504	+	0.252856i	$0.918630\pi$
$654$	1.56922	−	7.42866i	0.0613612	−	0.290483i
$655$	−13.1296	−	3.56249i	−0.513016	−	0.139198i
$656$	−0.710746	−	3.36467i	−0.0277500	−	0.131368i
$657$	−0.402029	+	7.07339i	−0.0156847	+	0.275959i
$658$	−1.55258	+	1.84241i	−0.0605259	+	0.0718247i
$659$	−14.0388	−	9.72051i	−0.546875	−	0.378657i	0.263418	−	0.964682i	$-0.415150\pi$
$659$	−14.0388	−	9.72051i	−0.546875	−	0.378657i	−0.810293	+	0.586025i	$0.800692\pi$
$660$	0.0315785	−	1.66839i	0.00122919	−	0.0649421i
$661$	13.3418	+	40.0284i	0.518938	+	1.55692i	0.801696	+	0.597732i	$0.203931\pi$
$661$	13.3418	+	40.0284i	0.518938	+	1.55692i	−0.282758	+	0.959191i	$0.591249\pi$
$662$	4.00855	+	4.40701i	0.155797	+	0.171283i
$663$	2.46260	−	14.3179i	0.0956393	−	0.556063i
$664$	4.57925	+	8.16777i	0.177709	+	0.316971i
$665$	1.69696	+	0.530150i	0.0658054	+	0.0205583i
$666$	−11.7160	−	6.86316i	−0.453987	−	0.265942i
$667$	76.7854			2.97314
$668$	−1.92447	−	12.7787i	−0.0744602	−	0.494425i
$669$	24.5240			0.948152
$670$	15.6376	+	9.16040i	0.604134	+	0.353897i
$671$	−9.63327	−	3.00954i	−0.371888	−	0.116182i
$672$	−0.268368	−	0.478674i	−0.0103525	−	0.0184652i
$673$	−4.98873	+	29.0053i	−0.192301	+	1.11807i	0.715482	+	0.698632i	$0.246207\pi$
$673$	−4.98873	+	29.0053i	−0.192301	+	1.11807i	−0.907783	+	0.419440i	$0.862226\pi$
$674$	−7.21734	−	7.93477i	−0.278002	−	0.305636i
$675$	2.82344	+	8.47090i	0.108674	+	0.326045i
$676$	−0.0926370	+	4.89430i	−0.00356296	+	0.188242i
$677$	35.3425	+	24.4712i	1.35832	+	0.940505i	0.999976	+	0.00691581i	$0.00220139\pi$
$677$	35.3425	+	24.4712i	1.35832	+	0.940505i	0.358346	+	0.933589i	$0.383341\pi$
$678$	−2.82769	+	3.35555i	−0.108597	+	0.128869i
$679$	−0.149037	+	2.62219i	−0.00571951	+	0.100630i
$680$	−1.22737	−	5.81035i	−0.0470674	−	0.222817i
$681$	−1.67283	−	0.453894i	−0.0641031	−	0.0173933i
$682$	−0.312184	+	1.47788i	−0.0119541	+	0.0565908i
$683$	14.0883	−	27.5210i	0.539074	−	1.05306i	−0.448186	−	0.893941i	$-0.647930\pi$
$683$	14.0883	−	27.5210i	0.539074	−	1.05306i	0.987259	−	0.159120i	$-0.0508655\pi$
$684$	−1.86724	+	3.05354i	−0.0713958	+	0.116755i
$685$	2.48933	+	5.93026i	0.0951125	+	0.226584i
$686$	−3.04223	−	6.54203i	−0.116153	−	0.249776i
$687$	9.62771	+	4.70076i	0.367320	+	0.179345i
$688$	−3.55047	+	1.25855i	−0.135360	+	0.0479816i
$689$	0.761446	+	40.2296i	0.0290088	+	1.53262i
$690$	9.06989	−	13.6438i	0.345285	−	0.519411i
$691$	−32.9071	+	14.5518i	−1.25185	+	0.553577i	−0.920799	−	0.390037i	$-0.872462\pi$
$691$	−32.9071	+	14.5518i	−1.25185	+	0.553577i	−0.331047	+	0.943614i	$0.607402\pi$
$692$	6.38939	−	19.1695i	0.242888	−	0.728716i
$693$	−0.838383	−	0.297185i	−0.0318475	−	0.0112891i
$694$	−5.58782	−	5.69458i	−0.212111	−	0.216163i
$695$	−17.1259	−	21.9582i	−0.649621	−	0.832920i
$696$	6.20229	−	6.81882i	0.235097	−	0.258467i
$697$	10.3477	+	4.57586i	0.391949	+	0.173323i
$698$	12.6291	−	8.05495i	0.478018	−	0.304884i
$699$	18.8090	−	7.47996i	0.711421	−	0.282918i
$700$	−0.807169	+	0.432669i	−0.0305081	+	0.0163534i
$701$	10.1157	−	26.9090i	0.382065	−	1.01634i	−0.595061	−	0.803680i	$-0.702872\pi$
$701$	10.1157	−	26.9090i	0.382065	−	1.01634i	0.977127	−	0.212659i	$-0.0682122\pi$
$702$	−2.86410	+	21.4930i	−0.108099	+	0.811202i
$703$	13.1640	−	2.00843i	0.496491	−	0.0757495i
$704$	−0.0836816	+	0.881697i	−0.00315387	+	0.0332302i
$705$	−7.09919	+	4.91549i	−0.267371	+	0.185128i
$706$	9.04690	+	13.6092i	0.340484	+	0.512190i
$707$	−2.34852	−	1.49791i	−0.0883253	−	0.0563347i
$708$	5.70472	+	1.09271i	0.214396	+	0.0410665i
$709$	30.1934	−	28.5260i	1.13394	−	1.07132i	0.137205	−	0.990543i	$-0.456188\pi$
$709$	30.1934	−	28.5260i	1.13394	−	1.07132i	0.996732	−	0.0807749i	$-0.0257395\pi$
$710$	3.69157	−	6.58447i	0.138542	−	0.247111i
$711$	−23.0478	−	18.6879i	−0.864362	−	0.700850i
$712$	2.97398	−	1.45206i	0.111455	−	0.0544181i
$713$	−10.3868	+	10.5853i	−0.388989	+	0.396422i
$714$	1.79388	+	0.204578i	0.0671342	+	0.00765612i
$715$	−5.96024	−	3.19488i	−0.222900	−	0.119482i
$716$	−6.19543	+	5.42461i	−0.231534	+	0.202727i
$717$	−19.8507	+	14.8867i	−0.741339	+	0.555955i
$718$	−15.7585	−	18.7002i	−0.588101	−	0.697885i
$719$	1.42244	+	14.9873i	0.0530480	+	0.558931i	0.982019	+	0.188780i	$0.0604533\pi$
$719$	1.42244	+	14.9873i	0.0530480	+	0.558931i	−0.928971	+	0.370152i	$0.879306\pi$
$720$	0.839829	+	3.34439i	0.0312986	+	0.124638i
$721$	−1.13525	−	3.89106i	−0.0422790	−	0.144911i
$722$	2.04604	+	15.3541i	0.0761459	+	0.571420i
$723$	−4.17455	−	0.964696i	−0.155253	−	0.0358774i
$724$	−16.3325	+	5.10245i	−0.606991	+	0.189631i
$725$	−11.1817	−	10.5642i	−0.415278	−	0.392345i
$726$	6.23515	+	8.65061i	0.231408	+	0.321054i
$727$	−1.42349	+	3.39114i	−0.0527944	+	0.125770i	−0.946309	−	0.323264i	$-0.895220\pi$
$727$	−1.42349	+	3.39114i	−0.0527944	+	0.125770i	0.893515	+	0.449034i	$0.148232\pi$
$728$	−2.22235	+	0.0841573i	−0.0823658	+	0.00311908i
$729$	−3.73218	+	14.8624i	−0.138229	+	0.550459i
$730$	−6.61733	−	1.00960i	−0.244919	−	0.0373671i
$731$	3.47120	−	11.8975i	0.128387	−	0.440045i
$732$	−11.8865	−	0.450125i	−0.439337	−	0.0166371i
$733$	16.2104	−	34.8589i	0.598745	−	1.28754i	−0.339185	−	0.940720i	$-0.610151\pi$
$733$	16.2104	−	34.8589i	0.598745	−	1.28754i	0.937930	−	0.346825i	$-0.112740\pi$
$734$	−5.27703	+	4.27877i	−0.194779	+	0.157932i
$735$	−2.14731	−	12.4848i	−0.0792047	−	0.460509i
$736$	−5.34773	+	6.85666i	−0.197120	+	0.252740i
$737$	8.83528	−	1.00759i	0.325452	−	0.0371152i
$738$	−6.10466	−	2.42770i	−0.224716	−	0.0893650i
$739$	−3.48820	+	0.668146i	−0.128315	+	0.0245781i	−0.251881	−	0.967758i	$-0.581049\pi$
$739$	−3.48820	+	0.668146i	−0.128315	+	0.0245781i	0.123565	+	0.992336i	$0.460567\pi$
$740$	7.50140	−	10.4074i	0.275757	−	0.382584i
$741$	−4.31600	−	7.05806i	−0.158552	−	0.259284i
$742$	−4.98615	+	0.378179i	−0.183047	+	0.0138834i
$743$	39.4578	+	29.5907i	1.44757	+	1.08558i	0.979398	+	0.201938i	$0.0647240\pi$
$743$	39.4578	+	29.5907i	1.44757	+	1.08558i	0.468167	+	0.883640i	$0.344915\pi$
$744$	0.101022	+	1.77740i	0.00370365	+	0.0651628i
$745$	13.0141	−	3.53115i	0.476800	−	0.129371i
$746$	16.7044	+	32.6315i	0.611593	+	1.19472i
$747$	17.8374	+	1.35289i	0.652636	+	0.0494998i
$748$	−2.19230	−	1.91954i	−0.0801583	−	0.0701852i
$749$	2.61785	+	6.96379i	0.0956541	+	0.254451i
$750$	−12.3766	+	2.86011i	−0.451931	+	0.104437i
$751$	6.54995	−	3.83691i	0.239011	−	0.140011i	−0.381076	−	0.924544i	$-0.624447\pi$
$751$	6.54995	−	3.83691i	0.239011	−	0.140011i	0.620087	+	0.784533i	$0.287097\pi$
$752$	3.95441	−	2.31647i	0.144203	−	0.0844728i
$753$	−17.2631	+	3.98934i	−0.629104	+	0.145379i
$754$	−13.1446	−	34.9662i	−0.478698	−	1.27339i
$755$	9.96355	+	8.72391i	0.362611	+	0.317496i
$756$	−2.68696	−	0.203795i	−0.0977239	−	0.00741196i
$757$	6.07140	+	11.8603i	0.220669	+	0.431068i	0.973992	−	0.226582i	$-0.0727552\pi$
$757$	6.07140	+	11.8603i	0.220669	+	0.431068i	−0.753323	+	0.657650i	$0.771550\pi$
$758$	30.6479	−	8.31577i	1.11318	−	0.302042i
$759$	−0.456170	−	8.02596i	−0.0165579	−	0.291324i
$760$	−2.70547	−	2.02892i	−0.0981376	−	0.0735967i
$761$	34.4749	−	2.61478i	1.24971	−	0.0947857i	0.565919	−	0.824461i	$-0.308522\pi$
$761$	34.4749	−	2.61478i	1.24971	−	0.0947857i	0.683794	+	0.729675i	$0.260329\pi$
$762$	−6.09852	−	9.97305i	−0.220926	−	0.361285i
$763$	2.23592	−	3.10211i	0.0809459	−	0.112304i
$764$	2.40612	−	0.460880i	0.0870504	−	0.0166741i
$765$	−10.5420	−	4.19233i	−0.381145	−	0.151574i
$766$	−15.8846	+	1.81151i	−0.573934	+	0.0654526i
$767$	14.4765	−	18.5613i	0.522718	−	0.670210i
$768$	0.176937	+	1.02874i	0.00638465	+	0.0371214i
$769$	14.5994	−	11.8376i	0.526467	−	0.426874i	−0.329309	−	0.944222i	$-0.606816\pi$
$769$	14.5994	−	11.8376i	0.526467	−	0.426874i	0.855775	+	0.517348i	$0.173081\pi$
$770$	0.354376	−	0.762052i	0.0127708	−	0.0274625i
$771$	6.47239	+	0.245100i	0.233098	+	0.00882708i
$772$	−2.31039	+	7.91884i	−0.0831528	+	0.285005i
$773$	8.16154	+	1.24520i	0.293550	+	0.0447869i	0.295928	−	0.955210i	$-0.404371\pi$
$773$	8.16154	+	1.24520i	0.293550	+	0.0447869i	−0.00237746	+	0.999997i	$0.500757\pi$
$774$	−1.75269	+	6.97960i	−0.0629990	+	0.250877i
$775$	2.96889	−	0.112428i	0.106646	−	0.00403852i
$776$	1.93364	−	4.60646i	0.0694137	−	0.165362i
$777$	2.28066	+	3.16417i	0.0818181	+	0.113514i
$778$	17.6901	+	16.7132i	0.634222	+	0.599199i
$779$	6.14984	−	1.92128i	0.220341	−	0.0688370i
$780$	−7.76570	−	1.79457i	−0.278057	−	0.0642560i
$781$	−0.489254	−	3.67150i	−0.0175069	−	0.131376i
$782$	−8.01284	−	27.4640i	−0.286539	−	0.982109i
$783$	−11.0238	−	43.8992i	−0.393957	−	1.56883i
$784$	0.635282	+	6.69354i	0.0226886	+	0.239055i
$785$	−8.87596	−	10.5329i	−0.316796	−	0.375935i
$786$	−6.29423	+	4.72025i	−0.224508	+	0.168366i
$787$	28.9801	−	25.3744i	1.03303	−	0.904501i	0.0375314	−	0.999295i	$-0.488051\pi$
$787$	28.9801	−	25.3744i	1.03303	−	0.904501i	0.995497	+	0.0947941i	$0.0302193\pi$
$788$	10.1999	+	5.46746i	0.363355	+	0.194770i
$789$	−1.89927	−	0.216597i	−0.0676159	−	0.00771106i
$790$	19.6353	−	20.0105i	0.698593	−	0.711941i
$791$	−1.98596	+	0.969649i	−0.0706124	+	0.0344768i
$792$	1.31422	+	1.06561i	0.0466989	+	0.0378648i
$793$	−23.5742	+	42.0480i	−0.837143	+	1.49317i
$794$	12.1632	−	11.4915i	0.431657	−	0.407819i
$795$	−17.6011	−	3.37140i	−0.624247	−	0.119571i
$796$	15.9523	+	10.1745i	0.565414	+	0.360627i
$797$	−18.2111	−	27.3949i	−0.645070	−	0.970377i	−0.999379	−	0.0352487i	$-0.988778\pi$
$797$	−18.2111	−	27.3949i	−0.645070	−	0.970377i	0.354308	−	0.935129i	$-0.384716\pi$
$798$	0.845299	−	0.585286i	0.0299232	−	0.0207189i
$799$	−1.42468	+	15.0108i	−0.0504014	+	0.531045i
$800$	1.72210	−	0.262739i	0.0608853	−	0.00928924i
$801$	0.835138	−	6.26711i	0.0295081	−	0.221437i
$802$	4.39038	−	11.6789i	0.155030	−	0.412397i
$803$	−2.89486	+	1.55174i	−0.102157	+	0.0547597i
$804$	9.73896	−	3.87300i	0.343467	−	0.136590i
$805$	6.95678	−	4.43710i	0.245194	−	0.156387i
$806$	6.59835	+	2.91785i	0.232417	+	0.102777i
$807$	−13.3691	+	14.6980i	−0.470613	+	0.517394i
$808$	3.25859	+	4.17804i	0.114637	+	0.146983i
$809$	−5.11617	−	5.21392i	−0.179875	−	0.183312i	0.617919	−	0.786242i	$-0.287976\pi$
$809$	−5.11617	−	5.21392i	−0.179875	−	0.183312i	−0.797794	+	0.602930i	$0.794000\pi$
$810$	0.647774	+	0.229619i	0.0227605	+	0.00806798i
$811$	9.81257	−	29.4398i	0.344566	−	1.03377i	−0.623231	−	0.782038i	$-0.714180\pi$
$811$	9.81257	−	29.4398i	0.344566	−	1.03377i	0.967797	−	0.251733i	$-0.0810004\pi$
$812$	4.24576	−	1.87751i	0.148997	−	0.0658878i
$813$	2.26050	−	3.40046i	0.0792791	−	0.119259i
$814$	−0.119125	−	6.29376i	−0.00417534	−	0.220596i
$815$	−4.06743	+	1.44180i	−0.142476	+	0.0505039i
$816$	−3.08613	−	1.50681i	−0.108036	−	0.0527490i
$817$	−2.97591	−	6.39942i	−0.104114	−	0.223887i
$818$	13.8795	+	33.0647i	0.485286	+	1.15608i
$819$	−2.21646	+	3.62463i	−0.0774493	+	0.126655i
$820$	2.82847	−	5.52531i	0.0987745	−	0.192952i
$821$	7.53235	−	35.6581i	0.262881	−	1.24448i	−0.623612	−	0.781734i	$-0.714336\pi$
$821$	7.53235	−	35.6581i	0.262881	−	1.24448i	0.886493	−	0.462742i	$-0.153134\pi$
$822$	3.58964	+	0.973988i	0.125203	+	0.0339717i
$823$	6.79448	+	32.1650i	0.236841	+	1.12120i	0.920300	+	0.391213i	$0.127945\pi$
$823$	6.79448	+	32.1650i	0.236841	+	1.12120i	−0.683459	+	0.729989i	$0.739525\pi$
$824$	−0.437504	+	7.69753i	−0.0152412	+	0.268156i
$825$	−1.03779	+	1.23152i	−0.0361312	+	0.0428761i
$826$	2.40510	+	1.66529i	0.0836841	+	0.0579430i
$827$	−0.529129	+	27.9555i	−0.0183996	+	0.972109i	0.864524	+	0.502592i	$0.167620\pi$
$827$	−0.529129	+	27.9555i	−0.0183996	+	0.972109i	−0.882923	+	0.469517i	$0.844428\pi$
$828$	5.25278	+	15.7595i	0.182547	+	0.547679i
$829$	−25.9039	−	28.4788i	−0.899678	−	0.989109i	0.100305	−	0.994957i	$-0.468018\pi$
$829$	−25.9039	−	28.4788i	−0.899678	−	0.989109i	−0.999983	+	0.00584759i	$0.998139\pi$
$830$	−2.86491	+	16.6571i	−0.0994426	+	0.578175i
$831$	3.18599	+	5.68269i	0.110521	+	0.197130i
$832$	4.03781	+	1.26146i	0.139986	+	0.0437332i
$833$	−19.0874	−	11.1813i	−0.661341	−	0.387408i
$834$	−16.1042			−0.557644
$835$	11.8287	−	20.1038i	0.409350	−	0.695721i
$836$	−1.65932			−0.0573889
$837$	7.54293	+	4.41859i	0.260722	+	0.152729i
$838$	19.9242	+	6.22456i	0.688272	+	0.215024i
$839$	9.85987	+	17.5865i	0.340400	+	0.607155i	0.987933	−	0.154883i	$-0.0495001\pi$
$839$	9.85987	+	17.5865i	0.340400	+	0.607155i	−0.647532	+	0.762038i	$0.724199\pi$
$840$	0.167899	−	0.976191i	0.00579306	−	0.0336818i
$841$	32.9554	+	36.2313i	1.13639	+	1.24935i
$842$	0.0278413	+	0.0835297i	0.000959474	+	0.00287863i
$843$	−0.340586	+	17.9942i	−0.0117304	+	0.619754i
$844$	−9.47558	−	6.56091i	−0.326163	−	0.225836i
$845$	−5.69372	+	6.75660i	−0.195870	+	0.232434i
$846$	0.496817	−	8.74111i	0.0170809	−	0.300526i
$847$	1.10997	+	5.25461i	0.0381392	+	0.180551i
$848$	9.17972	+	2.49076i	0.315233	+	0.0855330i
$849$	−1.49213	+	7.06374i	−0.0512098	+	0.242427i
$850$	−2.61167	+	5.10179i	−0.0895794	+	0.174990i
$851$	32.2426	−	52.7271i	1.10526	−	1.80746i
$852$	−1.68967	−	4.02525i	−0.0578871	−	0.137903i
$853$	−8.90482	−	19.1490i	−0.304895	−	0.655649i	0.692969	−	0.720967i	$-0.256302\pi$
$853$	−8.90482	−	19.1490i	−0.304895	−	0.655649i	−0.997864	+	0.0653183i	$0.979194\pi$
$854$	−5.38339	−	2.62846i	−0.184216	−	0.0899440i
$855$	−6.08918	+	2.15845i	−0.208245	+	0.0738175i
$856$	−0.267799	−	14.1487i	−0.00915318	−	0.483591i
$857$	10.5839	−	15.9213i	0.361538	−	0.543861i	−0.606364	−	0.795187i	$-0.707373\pi$
$857$	10.5839	−	15.9213i	0.361538	−	0.543861i	0.967902	+	0.251326i	$0.0808667\pi$
$858$	−3.57673	+	1.58166i	−0.122108	+	0.0539971i
$859$	−8.47988	+	25.4414i	−0.289330	+	0.868050i	0.698920	+	0.715200i	$0.253664\pi$
$859$	−8.47988	+	25.4414i	−0.289330	+	0.868050i	−0.988249	+	0.152850i	$0.951155\pi$
$860$	−6.40855	−	2.27166i	−0.218530	−	0.0774630i
$861$	1.32175	+	1.34700i	0.0450451	+	0.0459058i
$862$	22.1471	+	28.3962i	0.754334	+	0.967179i
$863$	−15.4046	+	16.9359i	−0.524379	+	0.576505i	−0.943478	−	0.331436i	$-0.892467\pi$
$863$	−15.4046	+	16.9359i	−0.524379	+	0.576505i	0.419098	+	0.907941i	$0.362346\pi$
$864$	4.68779	+	2.07298i	0.159482	+	0.0705242i
$865$	30.7499	−	19.6126i	1.04553	−	0.666849i
$866$	19.3606	−	7.69933i	0.657899	−	0.261634i
$867$	−5.68133	+	3.04538i	−0.192948	+	0.103427i
$868$	−0.315502	+	0.839274i	−0.0107089	+	0.0284868i
$869$	1.81703	−	13.6355i	0.0616387	−	0.462554i
$870$	16.4474	−	2.50937i	0.557618	−	0.0850756i
$871$	4.01320	−	42.2844i	0.135982	−	1.43275i
$872$	−5.98010	+	4.14063i	−0.202512	+	0.140219i
$873$	−5.28357	−	7.94807i	−0.178822	−	0.269001i
$874$	−13.7355	−	8.76061i	−0.464609	−	0.296332i
$875$	−6.28341	−	1.20356i	−0.212418	−	0.0406876i
$876$	−2.81392	+	2.65853i	−0.0950735	+	0.0898232i
$877$	−10.7646	+	19.2002i	−0.363493	+	0.648344i	−0.991536	−	0.129835i	$-0.958555\pi$
$877$	−10.7646	+	19.2002i	−0.363493	+	0.648344i	0.628042	+	0.778179i	$0.283856\pi$
$878$	26.9350	+	21.8397i	0.909011	+	0.737053i
$879$	26.7202	−	13.0462i	0.901250	−	0.440038i
$880$	−1.11964	+	1.14103i	−0.0377429	+	0.0384641i
$881$	−9.65541	−	1.10112i	−0.325299	−	0.0370978i	−0.0508703	−	0.998705i	$-0.516200\pi$
$881$	−9.65541	−	1.10112i	−0.325299	−	0.0370978i	−0.274429	+	0.961607i	$0.588489\pi$
$882$	11.3209	+	6.06836i	0.381194	+	0.204332i
$883$	−18.2517	+	15.9809i	−0.614220	+	0.537800i	−0.908482	−	0.417925i	$-0.862758\pi$
$883$	−18.2517	+	15.9809i	−0.614220	+	0.537800i	0.294262	+	0.955725i	$0.404926\pi$
$884$	−11.1347	+	8.35030i	−0.374501	+	0.280851i
$885$	6.75594	+	8.01712i	0.227099	+	0.269493i
$886$	3.45190	+	36.3703i	0.115969	+	1.22188i
$887$	−11.5313	−	45.9204i	−0.387184	−	1.54186i	−0.782109	−	0.623142i	$-0.785856\pi$
$887$	−11.5313	−	45.9204i	−0.387184	−	1.54186i	0.394925	−	0.918713i	$-0.370771\pi$
$888$	−2.07798	−	7.12225i	−0.0697324	−	0.239007i
$889$	−0.777677	−	5.83591i	−0.0260825	−	0.195730i
$890$	5.82028	+	1.34501i	0.195096	+	0.0450847i
$891$	0.321882	−	0.100559i	0.0107834	−	0.00336887i
$892$	−17.0775	−	16.1345i	−0.571799	−	0.540222i
$893$	5.02061	+	6.96557i	0.168008	+	0.233094i
$894$	3.01834	−	7.19051i	0.100948	−	0.240487i
$895$	−14.8528	+	0.562456i	−0.496475	+	0.0188008i
$896$	−0.128041	+	0.509891i	−0.00427757	+	0.0170343i
$897$	−37.9579	−	5.79122i	−1.26738	−	0.193363i
$898$	7.14598	−	24.4928i	0.238464	−	0.817335i
$899$	−15.0496	−	0.569906i	−0.501931	−	0.0190074i
$900$	1.40328	−	3.01762i	0.0467759	−	0.100587i
$901$	−24.3077	+	19.7094i	−0.809805	+	0.656614i
$902$	−0.516262	−	3.00163i	−0.0171897	−	0.0999435i
$903$	1.27131	−	1.63003i	0.0423067	−	0.0542441i
$904$	4.17673	−	0.476323i	0.138916	−	0.0158423i
$905$	−28.6989	−	11.4130i	−0.953984	−	0.379381i
$906$	7.52187	−	1.44078i	0.249897	−	0.0478666i
$907$	−24.5111	+	34.0065i	−0.813876	+	1.12917i	0.175599	+	0.984462i	$0.443814\pi$
$907$	−24.5111	+	34.0065i	−0.813876	+	1.12917i	−0.989475	+	0.144706i	$0.953776\pi$
$908$	0.866276	+	1.41664i	0.0287484	+	0.0470129i
$909$	10.0933	−	0.765534i	0.334773	−	0.0253912i
$910$	−3.21145	−	2.40838i	−0.106459	−	0.0798369i
$911$	−0.929060	−	16.3461i	−0.0307811	−	0.541570i	−0.976356	−	0.216167i	$-0.930645\pi$
$911$	−0.929060	−	16.3461i	−0.0307811	−	0.541570i	0.945575	−	0.325403i	$-0.105500\pi$
$912$	−1.88745	+	0.512126i	−0.0624996	+	0.0169582i
$913$	3.77901	+	7.38215i	0.125067	+	0.244313i
$914$	−16.8798	−	1.28027i	−0.558336	−	0.0423475i
$915$	−16.1534	−	14.1436i	−0.534015	−	0.467574i
$916$	−3.61170	−	9.60756i	−0.119334	−	0.317443i
$917$	−3.86066	+	0.892159i	−0.127490	+	0.0294617i
$918$	−14.5511	+	8.52393i	−0.480258	+	0.281332i
$919$	−31.0310	+	18.1777i	−1.02362	+	0.599628i	−0.918742	−	0.394858i	$-0.870794\pi$
$919$	−31.0310	+	18.1777i	−1.02362	+	0.599628i	−0.104876	+	0.994485i	$0.533444\pi$
$920$	−15.2923	+	3.53389i	−0.504171	+	0.116509i
$921$	0.762371	+	2.02800i	0.0251210	+	0.0668247i
$922$	15.6252	+	13.6812i	0.514589	+	0.450565i
$923$	−17.6409	−	1.33799i	−0.580658	−	0.0440405i
$924$	−0.221470	−	0.432632i	−0.00728581	−	0.0142326i
$925$	−11.9495	+	3.24229i	−0.392897	+	0.106606i
$926$	0.728491	+	12.8172i	0.0239397	+	0.421200i
$927$	11.7836	+	8.83691i	0.387024	+	0.290242i
$928$	−8.80518	+	0.667837i	−0.289044	+	0.0219228i
$929$	28.3148	+	46.3038i	0.928978	+	1.51918i	0.852898	+	0.522077i	$0.174843\pi$
$929$	28.3148	+	46.3038i	0.928978	+	1.51918i	0.0760792	+	0.997102i	$0.475760\pi$
$930$	−1.87892	+	2.60680i	−0.0616121	+	0.0854804i
$931$	−12.3721	+	2.36981i	−0.405479	+	0.0776674i
$932$	−18.0190	−	7.16578i	−0.590230	−	0.234723i
$933$	−19.2627	+	2.19676i	−0.630634	+	0.0719188i
$934$	−4.57674	+	5.86812i	−0.149755	+	0.192011i
$935$	−0.891519	−	5.18343i	−0.0291558	−	0.169516i
$936$	6.27727	−	5.08979i	0.205179	−	0.166365i
$937$	−15.6124	+	33.5730i	−0.510035	+	1.09678i	0.467108	+	0.884200i	$0.345296\pi$
$937$	−15.6124	+	33.5730i	−0.510035	+	1.09678i	−0.977143	+	0.212583i	$0.931813\pi$
$938$	5.27478	+	0.199748i	0.172228	+	0.00652202i
$939$	−9.08848	+	31.1507i	−0.296591	+	1.01656i
$940$	8.17753	+	1.24764i	0.266722	+	0.0406936i
$941$	−10.9596	+	43.6437i	−0.357273	+	1.42274i	0.480629	+	0.876924i	$0.340408\pi$
$941$	−10.9596	+	43.6437i	−0.357273	+	1.42274i	−0.837902	+	0.545820i	$0.816218\pi$
$942$	−7.95998	+	0.301433i	−0.259350	+	0.00982123i
$943$	11.5740	−	27.5724i	0.376902	−	0.897882i
$944$	−3.25364	−	4.51409i	−0.105897	−	0.146921i
$945$	−3.53550	−	3.34026i	−0.115010	−	0.108659i
$946$	−3.18443	+	0.994853i	−0.103535	+	0.0323454i
$947$	−32.9302	−	7.60983i	−1.07009	−	0.247286i	−0.346875	−	0.937912i	$-0.612757\pi$
$947$	−32.9302	−	7.60983i	−1.07009	−	0.247286i	−0.723213	+	0.690625i	$0.757335\pi$
$948$	−2.14157	−	16.0709i	−0.0695549	−	0.521960i
$949$	4.39398	+	15.0603i	0.142635	+	0.488879i
$950$	0.794902	+	3.16548i	0.0257900	+	0.102702i
$951$	−1.16714	−	12.2974i	−0.0378471	−	0.398770i
$952$	−1.11459	−	1.32266i	−0.0361242	−	0.0428678i
$953$	17.0221	−	12.7654i	0.551399	−	0.413513i	−0.287515	−	0.957776i	$-0.592829\pi$
$953$	17.0221	−	12.7654i	0.551399	−	0.413513i	0.838915	+	0.544263i	$0.183191\pi$
$954$	13.6711	−	11.9701i	0.442617	−	0.387548i
$955$	3.89736	+	2.08911i	0.126116	+	0.0676021i
$956$	23.6173	+	2.69337i	0.763840	+	0.0871099i
$957$	5.71771	−	5.82696i	0.184827	−	0.188359i
$958$	18.3185	−	8.94407i	0.591844	−	0.288970i
$959$	1.45505	+	1.17980i	0.0469860	+	0.0380976i
$960$	−0.921401	+	1.64346i	−0.0297381	+	0.0530423i
$961$	−20.4193	+	19.2917i	−0.658688	+	0.622314i
$962$	−29.5301	−	5.65634i	−0.952089	−	0.182368i
$963$	−22.7929	−	14.5375i	−0.734490	−	0.468464i
$964$	2.27232	+	3.41824i	0.0731864	+	0.110094i
$965$	−12.2414	+	8.47594i	−0.394063	+	0.272850i
$966$	0.450868	−	4.75050i	0.0145065	−	0.152845i
$967$	44.7858	−	6.83295i	1.44021	−	0.219733i	0.616776	−	0.787139i	$-0.288438\pi$
$967$	44.7858	−	6.83295i	1.44021	−	0.219733i	0.823438	+	0.567406i	$0.192053\pi$
$968$	1.34938	−	10.1261i	0.0433706	−	0.325465i
$969$	2.26414	−	6.02288i	0.0727347	−	0.193483i
$970$	7.94762	−	4.26019i	0.255183	−	0.136786i
$971$	−48.0582	+	19.1118i	−1.54226	+	0.613327i	−0.977313	−	0.211799i	$-0.932068\pi$
$971$	−48.0582	+	19.1118i	−1.54226	+	0.613327i	−0.564948	+	0.825126i	$0.691104\pi$
$972$	13.2996	−	8.48262i	0.426585	−	0.272080i
$973$	−7.41783	−	3.28023i	−0.237805	−	0.105159i
$974$	−18.0574	+	19.8524i	−0.578597	+	0.636112i
$975$	4.73077	+	6.06561i	0.151506	+	0.194255i
$976$	7.98115	+	8.13364i	0.255470	+	0.260352i
$977$	−5.08598	−	1.80285i	−0.162715	−	0.0576782i	0.251500	−	0.967857i	$-0.419076\pi$
$977$	−5.08598	−	1.80285i	−0.162715	−	0.0576782i	−0.414215	+	0.910179i	$0.635944\pi$
$978$	−0.789143	+	2.36760i	−0.0252340	+	0.0757074i
$979$	2.68071	−	1.18543i	0.0856760	−	0.0378866i
$980$	−6.71853	+	10.1067i	−0.214616	+	0.322846i
$981$	0.262961	+	13.8931i	0.00839571	+	0.443572i
$982$	−13.5428	+	4.80057i	−0.432169	+	0.153192i
$983$	−32.9645	−	16.0950i	−1.05140	−	0.513351i	−0.169867	−	0.985467i	$-0.554334\pi$
$983$	−32.9645	−	16.0950i	−1.05140	−	0.513351i	−0.881537	+	0.472116i	$0.843490\pi$
$984$	−1.51365	−	3.25496i	−0.0482533	−	0.103764i
$985$	8.08502	+	19.2607i	0.257610	+	0.613697i
$986$	15.1567	−	24.7861i	0.482688	−	0.789351i
$987$	−1.14602	+	2.23871i	−0.0364782	+	0.0712588i
$988$	−1.63804	+	7.75449i	−0.0521131	+	0.246703i
$989$	−31.6124	−	8.57747i	−1.00521	−	0.272748i
$990$	0.631184	+	2.98802i	0.0200603	+	0.0949654i
$991$	−0.187380	+	3.29680i	−0.00595232	+	0.104726i	−0.999991	−	0.00430396i	$-0.998630\pi$
$991$	−0.187380	+	3.29680i	−0.00595232	+	0.104726i	0.994038	+	0.109030i	$0.0347746\pi$
$992$	1.09902	−	1.30418i	0.0348938	−	0.0414077i
$993$	5.11263	+	3.53999i	0.162244	+	0.112338i
$994$	0.0416074	−	2.19825i	0.00131971	−	0.0697242i
$995$	10.7991	+	32.3995i	0.342353	+	1.02713i
$996$	6.57693	+	7.23070i	0.208398	+	0.229114i
$997$	−3.65481	+	21.2497i	−0.115749	+	0.672983i	0.868431	+	0.495810i	$0.165129\pi$
$997$	−3.65481	+	21.2497i	−0.115749	+	0.672983i	−0.984180	+	0.177173i	$0.943305\pi$
$998$	6.86878	+	12.2515i	0.217428	+	0.387814i
$999$	−34.7737	−	10.8637i	−1.10019	−	0.343712i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	334.2.c.b.107.3	✓	574
167.64	even	83	inner	334.2.c.b.231.3	yes	574

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
334.2.c.b.107.3	✓	574	1.1	even	1	trivial
334.2.c.b.231.3	yes	574	167.64	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	334.2.c.b.107.3

Level	$334$
Weight	$2$
Character	334.107
Analytic conductor	$2.667$
Analytic rank	$0$
Dimension	$574$
Inner twists	$2$