LMFDB - Embedded newform 153.4.n.a.106.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.n (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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$52$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			106.11
Character	$\chi$	$=$	153.106
Dual form			153.4.n.a.13.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.37852 - 1.95059i) q^{2} +(2.12811 + 4.74037i) q^{3} +(3.60959 + 6.25199i) q^{4} +(-13.0578 - 3.49884i) q^{5} +(2.05666 - 20.1665i) q^{6} +(21.5739 - 5.78071i) q^{7} +3.04612i q^{8} +(-17.9423 + 20.1761i) q^{9} +(37.2914 + 37.2914i) q^{10} +(-19.4446 + 5.21015i) q^{11} +(-21.9552 + 30.4157i) q^{12} +(-3.07305 - 5.32267i) q^{13} +(-84.1636 - 22.5516i) q^{14} +(-11.2027 - 69.3450i) q^{15} +(34.8184 - 60.3073i) q^{16} +(10.6010 + 69.2865i) q^{17} +(99.9736 - 33.1672i) q^{18} -122.675i q^{19} +(-25.2587 - 94.2669i) q^{20} +(73.3143 + 89.9664i) q^{21} +(75.8566 + 20.3257i) q^{22} +(45.8656 - 171.173i) q^{23} +(-14.4397 + 6.48248i) q^{24} +(50.0123 + 28.8746i) q^{25} +23.9770i q^{26} +(-133.825 - 42.1163i) q^{27} +(114.014 + 114.014i) q^{28} +(-61.4145 - 229.202i) q^{29} +(-97.4149 + 256.135i) q^{30} +(-249.580 - 66.8748i) q^{31} +(-214.165 + 123.648i) q^{32} +(-66.0782 - 81.0867i) q^{33} +(99.3339 - 254.764i) q^{34} -301.934 q^{35} +(-190.905 - 39.3478i) q^{36} +(43.0054 - 43.0054i) q^{37} +(-239.288 + 414.459i) q^{38} +(18.6917 - 25.8946i) q^{39} +(10.6579 - 39.7758i) q^{40} +(15.5074 - 57.8746i) q^{41} +(-72.2065 - 446.959i) q^{42} +(165.391 + 95.4883i) q^{43} +(-102.761 - 102.761i) q^{44} +(304.881 - 200.679i) q^{45} +(-488.845 + 488.845i) q^{46} +(-10.7518 + 18.6226i) q^{47} +(359.977 + 36.7119i) q^{48} +(134.970 - 77.9249i) q^{49} +(-112.645 - 195.107i) q^{50} +(-305.884 + 197.702i) q^{51} +(22.1849 - 38.4253i) q^{52} -701.690i q^{53} +(369.980 + 403.329i) q^{54} +272.133 q^{55} +(17.6087 + 65.7167i) q^{56} +(581.524 - 261.065i) q^{57} +(-239.589 + 894.157i) q^{58} +(-7.45908 + 4.30650i) q^{59} +(393.107 - 320.346i) q^{60} +(176.465 - 47.2837i) q^{61} +(712.765 + 712.765i) q^{62} +(-270.453 + 538.996i) q^{63} +407.654 q^{64} +(21.5042 + 80.2547i) q^{65} +(65.0797 + 402.844i) q^{66} +(252.944 + 438.113i) q^{67} +(-394.914 + 316.373i) q^{68} +(909.030 - 146.854i) q^{69} +(1020.09 + 588.950i) q^{70} +(486.393 - 486.393i) q^{71} +(-61.4587 - 54.6544i) q^{72} +(-393.785 + 393.785i) q^{73} +(-229.180 + 61.4087i) q^{74} +(-30.4448 + 298.525i) q^{75} +(766.962 - 442.806i) q^{76} +(-389.376 + 224.807i) q^{77} +(-113.660 + 51.0257i) q^{78} +(-594.846 + 159.389i) q^{79} +(-665.659 + 665.659i) q^{80} +(-85.1477 - 724.010i) q^{81} +(-165.282 + 165.282i) q^{82} +(-623.558 - 360.011i) q^{83} +(-297.834 + 783.102i) q^{84} +(103.997 - 941.823i) q^{85} +(-372.517 - 645.218i) q^{86} +(955.806 - 778.894i) q^{87} +(-15.8707 - 59.2304i) q^{88} +1217.37 q^{89} +(-1421.49 + 83.3004i) q^{90} +(-97.0664 - 97.0664i) q^{91} +(1235.73 - 331.112i) q^{92} +(-214.122 - 1325.42i) q^{93} +(72.6501 - 41.9445i) q^{94} +(-429.219 + 1601.87i) q^{95} +(-1041.91 - 752.087i) q^{96} +(217.519 + 811.791i) q^{97} -607.997 q^{98} +(243.760 - 485.797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) $ 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−3.37852	−	1.95059i	−1.19449	−	0.689637i	−0.235166	−	0.971955i	$-0.575563\pi$
$2$	−3.37852	−	1.95059i	−1.19449	−	0.689637i	−0.959321	+	0.282318i	$0.908897\pi$
$3$	2.12811	+	4.74037i	0.409555	+	0.912285i
$3$	2.12811	+	4.74037i	0.409555	+	0.912285i
$4$	3.60959	+	6.25199i	0.451199	+	0.781499i
$5$	−13.0578	−	3.49884i	−1.16793	−	0.312946i	−0.377801	−	0.925887i	$-0.623320\pi$
$5$	−13.0578	−	3.49884i	−1.16793	−	0.312946i	−0.790128	+	0.612941i	$0.789986\pi$
$6$	2.05666	−	20.1665i	0.139938	−	1.37216i
$7$	21.5739	−	5.78071i	1.16488	−	0.312129i	0.375967	−	0.926633i	$-0.377310\pi$
$7$	21.5739	−	5.78071i	1.16488	−	0.312129i	0.788914	+	0.614504i	$0.210644\pi$
$8$			3.04612i			0.134621i
$9$	−17.9423	+	20.1761i	−0.664530	+	0.747262i
$10$	37.2914	+	37.2914i	1.17926	+	1.17926i
$11$	−19.4446	+	5.21015i	−0.532978	+	0.142811i	−0.515263	−	0.857032i	$-0.672306\pi$
$11$	−19.4446	+	5.21015i	−0.532978	+	0.142811i	−0.0177147	+	0.999843i	$0.505639\pi$
$12$	−21.9552	+	30.4157i	−0.528160	+	0.731689i
$13$	−3.07305	−	5.32267i	−0.0655623	−	0.113557i	0.831381	−	0.555703i	$-0.187551\pi$
$13$	−3.07305	−	5.32267i	−0.0655623	−	0.113557i	−0.896943	+	0.442146i	$0.854217\pi$
$14$	−84.1636	−	22.5516i	−1.60669	−	0.430511i
$15$	−11.2027	−	69.3450i	−0.192835	−	1.19365i
$16$	34.8184	−	60.3073i	0.544038	−	0.942302i
$17$	10.6010	+	69.2865i	0.151242	+	0.988497i
$17$	10.6010	+	69.2865i	0.151242	+	0.988497i
$18$	99.9736	−	33.1672i	1.30911	−	0.434310i
$19$		−	122.675i		−	1.48124i	−0.671925	−	0.740619i	$-0.734532\pi$
$19$		−	122.675i		−	1.48124i	0.671925	−	0.740619i	$-0.265468\pi$
$20$	−25.2587	−	94.2669i	−0.282401	−	1.05394i
$21$	73.3143	+	89.9664i	0.761833	+	0.934870i
$22$	75.8566	+	20.3257i	0.735122	+	0.196975i
$23$	45.8656	−	171.173i	0.415810	−	1.55183i	−0.367397	−	0.930064i	$-0.619751\pi$
$23$	45.8656	−	171.173i	0.415810	−	1.55183i	0.783207	−	0.621761i	$-0.213582\pi$
$24$	−14.4397	+	6.48248i	−0.122813	+	0.0551346i
$25$	50.0123	+	28.8746i	0.400098	+	0.230997i
$26$			23.9770i			0.180857i
$27$	−133.825	−	42.1163i	−0.953878	−	0.300196i
$28$	114.014	+	114.014i	0.769521	+	0.769521i
$29$	−61.4145	−	229.202i	−0.393255	−	1.46765i	−0.824733	−	0.565523i	$-0.808675\pi$
$29$	−61.4145	−	229.202i	−0.393255	−	1.46765i	0.431478	−	0.902123i	$-0.357992\pi$
$30$	−97.4149	+	256.135i	−0.592848	+	1.55879i
$31$	−249.580	−	66.8748i	−1.44600	−	0.387454i	−0.551367	−	0.834263i	$-0.685894\pi$
$31$	−249.580	−	66.8748i	−1.44600	−	0.387454i	−0.894629	+	0.446809i	$0.852560\pi$
$32$	−214.165	+	123.648i	−1.18311	+	0.683067i
$33$	−66.0782	−	81.0867i	−0.348568	−	0.427739i
$34$	99.3339	−	254.764i	0.501048	−	1.28505i
$35$	−301.934			−1.45818
$36$	−190.905	−	39.3478i	−0.883819	−	0.182166i
$37$	43.0054	−	43.0054i	0.191082	−	0.191082i	−0.605081	−	0.796164i	$-0.706859\pi$
$37$	43.0054	−	43.0054i	0.191082	−	0.191082i	0.796164	+	0.605081i	$0.206859\pi$
$38$	−239.288	+	414.459i	−1.02152	+	1.76932i
$39$	18.6917	−	25.8946i	0.0767452	−	0.106319i
$40$	10.6579	−	39.7758i	0.0421290	−	0.157227i
$41$	15.5074	−	57.8746i	0.0590697	−	0.220451i	−0.930081	−	0.367354i	$-0.880264\pi$
$41$	15.5074	−	57.8746i	0.0590697	−	0.220451i	0.989151	+	0.146903i	$0.0469305\pi$
$42$	−72.2065	−	446.959i	−0.265279	−	1.64208i
$43$	165.391	+	95.4883i	0.586554	+	0.338647i	0.763734	−	0.645531i	$-0.223364\pi$
$43$	165.391	+	95.4883i	0.586554	+	0.338647i	−0.177180	+	0.984179i	$0.556697\pi$
$44$	−102.761	−	102.761i	−0.352085	−	0.352085i
$45$	304.881	−	200.679i	1.00998	−	0.664787i
$46$	−488.845	+	488.845i	−1.56688	+	1.56688i
$47$	−10.7518	+	18.6226i	−0.0333682	+	0.0577955i	−0.882227	−	0.470824i	$-0.843957\pi$
$47$	−10.7518	+	18.6226i	−0.0333682	+	0.0577955i	0.848859	+	0.528619i	$0.177290\pi$
$48$	359.977	+	36.7119i	1.08246	+	0.110394i
$49$	134.970	−	77.9249i	0.393498	−	0.227186i
$50$	−112.645	−	195.107i	−0.318608	−	0.551845i
$51$	−305.884	+	197.702i	−0.839850	+	0.542819i
$52$	22.1849	−	38.4253i	0.0591632	−	0.102474i
$53$		−	701.690i		−	1.81858i	−0.416167	−	0.909288i	$-0.636627\pi$
$53$		−	701.690i		−	1.81858i	0.416167	−	0.909288i	$-0.363373\pi$
$54$	369.980	+	403.329i	0.932368	+	1.01641i
$55$	272.133			0.667172
$56$	17.6087	+	65.7167i	0.0420190	+	0.156817i
$57$	581.524	−	261.065i	1.35131	−	0.606648i
$58$	−239.589	+	894.157i	−0.542406	+	2.02429i
$59$	−7.45908	+	4.30650i	−0.0164592	+	0.00950270i	−0.508207	−	0.861235i	$-0.669692\pi$
$59$	−7.45908	+	4.30650i	−0.0164592	+	0.00950270i	0.491748	+	0.870738i	$0.336358\pi$
$60$	393.107	−	320.346i	0.845832	−	0.689275i
$61$	176.465	−	47.2837i	0.370395	−	0.0992469i	−0.0688201	−	0.997629i	$-0.521923\pi$
$61$	176.465	−	47.2837i	0.370395	−	0.0992469i	0.439215	+	0.898382i	$0.355257\pi$
$62$	712.765	+	712.765i	1.46002	+	1.46002i
$63$	−270.453	+	538.996i	−0.540856	+	1.07789i
$64$	407.654			0.796198
$65$	21.5042	+	80.2547i	0.0410349	+	0.153144i
$66$	65.0797	+	402.844i	0.121375	+	0.751314i
$67$	252.944	+	438.113i	0.461225	+	0.798865i	0.999022	−	0.0442088i	$-0.0140767\pi$
$67$	252.944	+	438.113i	0.461225	+	0.798865i	−0.537797	+	0.843074i	$0.680743\pi$
$68$	−394.914	+	316.373i	−0.704269	+	0.564204i
$69$	909.030	−	146.854i	1.58600	−	0.256220i
$70$	1020.09	+	588.950i	1.74177	+	1.00561i
$71$	486.393	−	486.393i	0.813017	−	0.813017i	−0.172068	−	0.985085i	$-0.555045\pi$
$71$	486.393	−	486.393i	0.813017	−	0.813017i	0.985085	+	0.172068i	$0.0550449\pi$
$72$	−61.4587	−	54.6544i	−0.100597	−	0.0894595i
$73$	−393.785	+	393.785i	−0.631357	+	0.631357i	−0.948408	−	0.317051i	$-0.897307\pi$
$73$	−393.785	+	393.785i	−0.631357	+	0.631357i	0.317051	+	0.948408i	$0.397307\pi$
$74$	−229.180	+	61.4087i	−0.360023	+	0.0964677i
$75$	−30.4448	+	298.525i	−0.0468729	+	0.459610i
$76$	766.962	−	442.806i	1.15759	−	0.668333i
$77$	−389.376	+	224.807i	−0.576280	+	0.332715i
$78$	−113.660	+	51.0257i	−0.164993	+	0.0740707i
$79$	−594.846	+	159.389i	−0.847158	+	0.226995i	−0.656185	−	0.754600i	$-0.727831\pi$
$79$	−594.846	+	159.389i	−0.847158	+	0.226995i	−0.190973	+	0.981595i	$0.561164\pi$
$80$	−665.659	+	665.659i	−0.930287	+	0.930287i
$81$	−85.1477	−	724.010i	−0.116801	−	0.993155i
$82$	−165.282	+	165.282i	−0.222589	+	0.222589i
$83$	−623.558	−	360.011i	−0.824631	−	0.476101i	0.0273799	−	0.999625i	$-0.491284\pi$
$83$	−623.558	−	360.011i	−0.824631	−	0.476101i	−0.852011	+	0.523524i	$0.824617\pi$
$84$	−297.834	+	783.102i	−0.386862	+	1.01718i
$85$	103.997	−	941.823i	0.132706	−	1.20182i
$86$	−372.517	−	645.218i	−0.467087	−	0.809019i
$87$	955.806	−	778.894i	1.17785	−	0.959842i
$88$	−15.8707	−	59.2304i	−0.0192253	−	0.0717498i
$89$	1217.37			1.44989			0.724947	−	0.688804i	$-0.241864\pi$
$89$	1217.37			1.44989			0.724947	+	0.688804i	$0.241864\pi$
$90$	−1421.49	+	83.3004i	−1.66486	+	0.0975626i
$91$	−97.0664	−	97.0664i	−0.111817	−	0.111817i
$92$	1235.73	−	331.112i	1.40036	−	0.375226i
$93$	−214.122	−	1325.42i	−0.238747	−	1.47785i
$94$	72.6501	−	41.9445i	0.0797158	−	0.0460239i
$95$	−429.219	+	1601.87i	−0.463547	+	1.72998i
$96$	−1041.91	−	752.087i	−1.10770	−	0.799578i
$97$	217.519	+	811.791i	0.227687	+	0.849741i	0.981310	+	0.192434i	$0.0616380\pi$
$97$	217.519	+	811.791i	0.227687	+	0.849741i	−0.753623	+	0.657307i	$0.771695\pi$
$98$	−607.997			−0.626704
$99$	243.760	−	485.797i	0.247462	−	0.493176i
$100$			416.902i			0.416902i
$101$	−813.826	+	1409.59i	−0.801769	+	1.38871i	0.116681	+	0.993169i	$0.462774\pi$
$101$	−813.826	+	1409.59i	−0.801769	+	1.38871i	−0.918451	+	0.395536i	$0.870559\pi$
$102$	1419.07	−	71.2853i	1.37754	−	0.0691990i
$103$	−737.099	−	1276.69i	−0.705131	−	1.22132i	−0.966644	−	0.256123i	$-0.917555\pi$
$103$	−737.099	−	1276.69i	−0.705131	−	1.22132i	0.261513	−	0.965200i	$-0.415779\pi$
$104$	16.2135	−	9.36086i	0.0152871	−	0.00882604i
$105$	−642.549	−	1431.28i	−0.597204	−	1.33027i
$106$	−1368.71	+	2370.67i	−1.25416	+	2.17226i
$107$	882.407	−	882.407i	0.797247	−	0.797247i	−0.185413	−	0.982661i	$-0.559362\pi$
$107$	882.407	−	882.407i	0.797247	−	0.797247i	0.982661	+	0.185413i	$0.0593624\pi$
$108$	−219.743	−	988.698i	−0.195785	−	0.880902i
$109$	785.710	+	785.710i	0.690434	+	0.690434i	0.962327	−	0.271893i	$-0.0876497\pi$
$109$	785.710	+	785.710i	0.690434	+	0.690434i	−0.271893	+	0.962327i	$0.587650\pi$
$110$	−919.408	−	530.820i	−0.796928	−	0.460107i
$111$	295.382	+	112.341i	0.252580	+	0.0960629i
$112$	402.551	−	1502.34i	0.339620	−	1.26748i
$113$	−270.532	+	1009.64i	−0.225217	+	0.840520i	0.757101	+	0.653298i	$0.226615\pi$
$113$	−270.532	+	1009.64i	−0.225217	+	0.840520i	−0.982318	+	0.187222i	$0.940052\pi$
$114$	−2473.92	−	252.301i	−2.03249	−	0.207282i
$115$	−1197.81	+	2074.67i	−0.971274	+	1.68230i
$116$	1211.29	−	1211.29i	0.969528	−	0.969528i
$117$	162.528	+	33.4990i	0.128425	+	0.0264699i
$118$	33.6009			0.0262136
$119$	629.229	+	1433.50i	0.484717	+	1.10427i
$120$	211.233	−	34.1248i	0.160690	−	0.0259596i
$121$	−801.735	+	462.882i	−0.602355	+	0.347770i
$122$	−688.422	−	184.462i	−0.510876	−	0.136889i
$123$	307.349	−	49.6523i	0.225306	−	0.0363984i
$124$	−482.781	−	1801.76i	−0.349637	−	1.30486i
$125$	642.851	+	642.851i	0.459987	+	0.459987i
$126$	1965.09	−	1293.46i	1.38940	−	0.914531i
$127$		−	1087.77i		−	0.760030i	−0.924980	−	0.380015i	$-0.875919\pi$
$127$		−	1087.77i		−	0.760030i	0.924980	−	0.380015i	$-0.124081\pi$
$128$	336.058	+	194.023i	0.232059	+	0.133980i
$129$	−100.681	+	987.223i	−0.0687168	+	0.673799i
$130$	83.8916	−	313.088i	0.0565983	−	0.211228i
$131$	−1613.20	−	432.256i	−1.07592	−	0.288293i	−0.322999	−	0.946399i	$-0.604691\pi$
$131$	−1613.20	−	432.256i	−1.07592	−	0.288293i	−0.752925	+	0.658106i	$0.771358\pi$
$132$	268.438	−	705.810i	0.177004	−	0.465401i
$133$	−709.147	−	2646.57i	−0.462337	−	1.72547i
$134$		−	1973.56i		−	1.27231i
$135$	1600.11	+	1018.18i	1.02012	+	0.649120i
$136$	−211.055	+	32.2918i	−0.133072	+	0.0203603i
$137$	−516.061	+	893.844i	−0.321825	+	0.557418i	−0.980865	−	0.194691i	$-0.937630\pi$
$137$	−516.061	+	893.844i	−0.321825	+	0.557418i	0.659039	+	0.752108i	$0.270963\pi$
$138$	−3357.63	−	1276.99i	−2.07116	−	0.787717i
$139$	−1016.71	−	272.428i	−0.620407	−	0.166238i	−0.0650942	−	0.997879i	$-0.520735\pi$
$139$	−1016.71	−	272.428i	−0.620407	−	0.166238i	−0.555313	+	0.831642i	$0.687401\pi$
$140$	−1089.86	−	1887.69i	−0.657928	−	1.13956i
$141$	−111.159	−	11.3365i	−0.0663921	−	0.00677094i
$142$	−2592.04	+	694.535i	−1.53182	+	0.410451i
$143$	87.4859	+	87.4859i	0.0511604	+	0.0511604i
$144$	592.042	+	1784.55i	0.342617	+	1.03273i
$145$			3207.76i			1.83717i
$146$	2098.52	−	562.298i	1.18956	−	0.318740i
$147$	656.624	+	473.975i	0.368418	+	0.265937i
$148$	424.101	+	113.638i	0.235547	+	0.0631145i
$149$	−151.628	−	262.628i	−0.0833684	−	0.144398i	0.821326	−	0.570459i	$-0.193234\pi$
$149$	−151.628	−	262.628i	−0.0833684	−	0.144398i	−0.904695	+	0.426060i	$0.859901\pi$
$150$	685.158	−	949.187i	0.372953	−	0.516672i
$151$	−667.939	−	385.635i	−0.359974	−	0.207831i	0.309095	−	0.951031i	$-0.399974\pi$
$151$	−667.939	−	385.635i	−0.359974	−	0.207831i	−0.669070	+	0.743200i	$0.733307\pi$
$152$	373.682			0.199405
$153$	−1588.14	−	1029.27i	−0.839171	−	0.543868i
$154$	1754.02			0.917812
$155$	3024.99	+	1746.48i	1.56757	+	0.905037i
$156$	229.362	+	23.3913i	0.117716	+	0.0120051i
$157$	−1311.23	−	2271.11i	−0.666543	−	1.15449i	−0.978864	−	0.204510i	$-0.934440\pi$
$157$	−1311.23	−	2271.11i	−0.666543	−	1.15449i	0.312321	−	0.949976i	$-0.398893\pi$
$158$	2320.60	+	621.803i	1.16846	+	0.313089i
$159$	3326.27	−	1493.27i	1.65906	−	0.744807i
$160$	3229.16	−	865.252i	1.59555	−	0.427526i
$161$		−	3958.00i		−	1.93748i
$162$	−1124.57	+	2612.17i	−0.545400	+	1.26686i
$163$	398.944	+	398.944i	0.191704	+	0.191704i	0.796432	−	0.604728i	$-0.206718\pi$
$163$	398.944	+	398.944i	0.191704	+	0.191704i	−0.604728	+	0.796432i	$0.706718\pi$
$164$	417.807	−	111.951i	0.198934	−	0.0533043i
$165$	579.130	+	1290.01i	0.273244	+	0.608651i
$166$	1404.47	+	2432.61i	0.656674	+	1.13739i
$167$	1212.91	+	324.998i	0.562022	+	0.150593i	0.528635	−	0.848849i	$-0.322704\pi$
$167$	1212.91	+	324.998i	0.562022	+	0.150593i	0.0333866	+	0.999443i	$0.489371\pi$
$168$	−274.048	+	223.324i	−0.125853	+	0.102559i
$169$	1079.61	−	1869.94i	0.491403	−	0.851135i
$170$	−2188.46	+	2979.11i	−0.987339	+	1.34404i
$171$	2475.09	+	2201.07i	1.10687	+	0.984327i
$172$			1378.69i			0.611189i
$173$	−801.663	−	2991.85i	−0.352308	−	1.31483i	−0.883838	−	0.467793i	$-0.845049\pi$
$173$	−801.663	−	2991.85i	−0.352308	−	1.31483i	0.531530	−	0.847040i	$-0.321617\pi$
$174$	−4748.51	+	767.124i	−2.06887	+	0.334227i
$175$	1245.88	+	333.831i	0.538168	+	0.144202i
$176$	−362.819	+	1354.06i	−0.155389	+	0.579920i
$177$	−36.2882	−	26.1941i	−0.0154101	−	0.0111236i
$178$	−4112.90	−	2374.58i	−1.73188	−	0.999901i
$179$			171.162i			0.0714707i	0.999361	+	0.0357354i	$0.0113773\pi$
$179$			171.162i			0.0714707i	−0.999361	+	0.0357354i	$0.988623\pi$
$180$	2355.14	+	1181.74i	0.975231	+	0.489344i
$181$	−381.778	−	381.778i	−0.156781	−	0.156781i	0.624358	−	0.781139i	$-0.285361\pi$
$181$	−381.778	−	381.778i	−0.156781	−	0.156781i	−0.781139	+	0.624358i	$0.785361\pi$
$182$	138.604	+	517.277i	0.0564506	+	0.210677i
$183$	599.680	+	735.887i	0.242238	+	0.297259i
$184$	521.413	+	139.712i	0.208908	+	0.0559767i
$185$	−712.027	+	411.089i	−0.282969	+	0.163372i
$186$	−1861.93	+	4895.62i	−0.733997	+	1.92991i
$187$	−567.124	−	1292.01i	−0.221777	−	0.505248i
$188$	−155.238			−0.0602228
$189$	−3130.60	−	135.008i	−1.20485	−	0.0519599i
$190$	4574.71	−	4574.71i	1.74676	−	1.74676i
$191$	−1169.10	+	2024.93i	−0.442894	+	0.767115i	−0.997903	−	0.0647294i	$-0.979382\pi$
$191$	−1169.10	+	2024.93i	−0.442894	+	0.767115i	0.555009	+	0.831845i	$0.312715\pi$
$192$	867.531	+	1932.43i	0.326087	+	0.726360i
$193$	203.892	−	760.936i	0.0760439	−	0.283800i	−0.917424	−	0.397911i	$-0.869735\pi$
$193$	203.892	−	760.936i	0.0760439	−	0.283800i	0.993468	+	0.114111i	$0.0364020\pi$
$194$	848.579	−	3166.94i	0.314043	−	1.17203i
$195$	−334.674	+	272.729i	−0.122905	+	0.100156i
$196$	974.372	+	562.554i	0.355092	+	0.205012i
$197$	−951.804	−	951.804i	−0.344230	−	0.344230i	0.513725	−	0.857955i	$-0.328265\pi$
$197$	−951.804	−	951.804i	−0.344230	−	0.344230i	−0.857955	+	0.513725i	$0.828265\pi$
$198$	−1771.14	+	1165.80i	−0.635703	+	0.418433i
$199$	1284.44	−	1284.44i	0.457546	−	0.457546i	−0.440303	−	0.897849i	$-0.645129\pi$
$199$	1284.44	−	1284.44i	0.457546	−	0.457546i	0.897849	+	0.440303i	$0.145129\pi$
$200$	−87.9555	+	152.343i	−0.0310970	+	0.0538615i
$201$	−1538.52	+	2131.40i	−0.539896	+	0.747948i
$202$	5499.05	−	3174.88i	1.91541	−	1.10586i
$203$	−2649.90	−	4589.76i	−0.916190	−	1.58689i
$204$	−2340.15	−	1198.76i	−0.803152	−	0.411422i
$205$	−404.988	+	701.459i	−0.137978	+	0.238986i
$206$			5751.11i			1.94514i
$207$	2630.66	+	3996.62i	0.883302	+	1.34195i
$208$	−427.995			−0.142673
$209$	639.154	+	2385.36i	0.211537	+	0.789467i
$210$	−620.977	+	6088.96i	−0.204055	+	2.00085i
$211$	−32.3091	+	120.579i	−0.0105415	+	0.0393413i	−0.970996	−	0.239095i	$-0.923149\pi$
$211$	−32.3091	+	120.579i	−0.0105415	+	0.0393413i	0.960455	+	0.278436i	$0.0898160\pi$
$212$	4386.96	−	2532.81i	1.42122	−	0.820539i
$213$	3340.78	+	1270.59i	1.07468	+	0.408728i
$214$	−4702.44	+	1260.01i	−1.50211	+	0.402490i
$215$	−1825.55	−	1825.55i	−0.579075	−	0.579075i
$216$	128.291	−	407.648i	0.0404126	−	0.128412i
$217$	−5771.00			−1.80535
$218$	−1121.94	−	4187.13i	−0.348565	−	1.30086i
$219$	−2704.71	−	1028.67i	−0.834554	−	0.317403i
$220$	982.290	+	1701.38i	0.301027	+	0.521394i
$221$	336.212	−	269.346i	0.102335	−	0.0819827i
$222$	−778.821	−	955.716i	−0.235455	−	0.288935i
$223$	−1098.85	−	634.424i	−0.329976	−	0.190512i	0.325854	−	0.945420i	$-0.394348\pi$
$223$	−1098.85	−	634.424i	−0.329976	−	0.190512i	−0.655831	+	0.754908i	$0.727681\pi$
$224$	−3905.61	+	3905.61i	−1.16497	+	1.16497i
$225$	−1479.91	+	490.974i	−0.438492	+	0.145474i
$226$	2883.38	−	2883.38i	0.848672	−	0.848672i
$227$	1443.51	−	386.788i	0.422067	−	0.113093i	−0.0415330	−	0.999137i	$-0.513224\pi$
$227$	1443.51	−	386.788i	0.422067	−	0.113093i	0.463600	+	0.886045i	$0.346557\pi$
$228$	3731.24	+	2693.35i	1.08381	+	0.782330i
$229$	−2927.95	+	1690.45i	−0.844910	+	0.487809i	−0.858930	−	0.512093i	$-0.828870\pi$
$229$	−2927.95	+	1690.45i	−0.844910	+	0.487809i	0.0140203	+	0.999902i	$0.495537\pi$
$230$	8093.66	−	4672.88i	2.32035	−	1.33965i
$231$	−1894.30	−	1367.38i	−0.539550	−	0.389467i
$232$	698.176	−	187.076i	0.197576	−	0.0529402i
$233$	−1466.76	+	1466.76i	−0.412406	+	0.412406i	−0.882576	−	0.470170i	$-0.844193\pi$
$233$	−1466.76	+	1466.76i	−0.412406	+	0.412406i	0.470170	+	0.882576i	$0.344193\pi$
$234$	−483.761	−	430.202i	−0.135147	−	0.120185i
$235$	205.552	−	205.552i	0.0570586	−	0.0570586i
$236$	−53.8485	−	31.0894i	−0.0148527	−	0.00857521i
$237$	−2021.46	−	2480.60i	−0.554042	−	0.679883i
$238$	670.305	−	6070.47i	0.182560	−	1.65332i
$239$	2729.65	+	4727.89i	0.738771	+	1.27959i	0.953049	+	0.302816i	$0.0979266\pi$
$239$	2729.65	+	4727.89i	0.738771	+	1.27959i	−0.214279	+	0.976773i	$0.568740\pi$
$240$	−4572.07	−	1738.88i	−1.22969	−	0.467684i
$241$	1096.37	+	4091.72i	0.293044	+	1.09365i	0.942759	+	0.333476i	$0.108222\pi$
$241$	1096.37	+	4091.72i	0.293044	+	1.09365i	−0.649715	+	0.760178i	$0.725112\pi$
$242$	3611.57			0.959340
$243$	3250.88	−	1944.41i	0.858205	−	0.513307i
$244$	932.585	+	932.585i	0.244683	+	0.244683i
$245$	−2035.06	+	545.293i	−0.530675	+	0.142194i
$246$	−1135.23	−	431.759i	−0.294227	−	0.111902i
$247$	−652.957	+	376.985i	−0.168205	+	0.0971133i
$248$	203.708	−	760.250i	0.0521593	−	0.194661i
$249$	379.589	−	3722.04i	0.0966083	−	0.947288i
$250$	−917.946	−	3425.82i	−0.232224	−	0.866672i
$251$	−5205.73			−1.30910			−0.654548	−	0.756021i	$-0.727141\pi$
$251$	−5205.73			−1.30910			−0.654548	+	0.756021i	$0.727141\pi$
$252$	−4346.02	+	254.681i	−1.08640	+	0.0636642i
$253$			3567.34i			0.886470i
$254$	−2121.79	+	3675.04i	−0.524145	+	0.907845i
$255$	4685.91	−	1511.32i	1.15076	−	0.371147i
$256$	−2387.53	−	4135.33i	−0.582894	−	1.00960i
$257$	−74.0155	+	42.7329i	−0.0179648	+	0.0103720i	−0.508956	−	0.860793i	$-0.669968\pi$
$257$	−74.0155	+	42.7329i	−0.0179648	+	0.0103720i	0.490991	+	0.871165i	$0.336635\pi$
$258$	2265.82	−	3138.96i	0.546758	−	0.757455i
$259$	679.192	−	1176.40i	0.162946	−	0.282230i
$260$	−424.131	+	424.131i	−0.101167	+	0.101167i
$261$	5726.31	+	2873.31i	1.35805	+	0.681430i
$262$	4607.08	+	4607.08i	1.08636	+	1.08636i
$263$	−4340.77	−	2506.14i	−1.01773	−	0.587587i	−0.104285	−	0.994547i	$-0.533255\pi$
$263$	−4340.77	−	2506.14i	−1.01773	−	0.587587i	−0.913446	+	0.406961i	$0.866589\pi$
$264$	247.000	−	201.282i	0.0575825	−	0.0469245i
$265$	−2455.10	+	9162.56i	−0.569116	+	2.12397i
$266$	−2766.51	+	10324.7i	−0.637690	+	2.37989i
$267$	2590.69	+	5770.78i	0.593811	+	1.32272i
$268$	−1826.05	+	3162.81i	−0.416208	+	0.720894i
$269$	3112.91	−	3112.91i	0.705566	−	0.705566i	−0.260034	−	0.965600i	$-0.583734\pi$
$269$	3112.91	−	3112.91i	0.705566	−	0.705566i	0.965600	+	0.260034i	$0.0837336\pi$
$270$	−3419.95	−	6561.11i	−0.770858	−	1.47887i
$271$	7604.48			1.70457			0.852286	−	0.523075i	$-0.175215\pi$
$271$	7604.48			1.70457			0.852286	+	0.523075i	$0.175215\pi$
$272$	4547.59	+	1773.13i	1.01374	+	0.395265i
$273$	253.563	−	666.699i	0.0562137	−	0.147804i
$274$	3487.04	−	2013.25i	0.768832	−	0.443885i
$275$	−1122.91	−	300.882i	−0.246232	−	0.0659777i
$276$	4199.36	+	5153.16i	0.915839	+	1.12386i
$277$	779.136	+	2907.78i	0.169003	+	0.630727i	0.997496	+	0.0707274i	$0.0225320\pi$
$277$	779.136	+	2907.78i	0.169003	+	0.630727i	−0.828493	+	0.560000i	$0.810801\pi$
$278$	2903.59	+	2903.59i	0.626424	+	0.626424i
$279$	5827.31	−	3835.66i	1.25044	−	0.823064i
$280$		−	919.728i		−	0.196301i
$281$	4105.39	+	2370.25i	0.871554	+	0.503192i	0.867864	−	0.496801i	$-0.165492\pi$
$281$	4105.39	+	2370.25i	0.871554	+	0.503192i	0.00368981	+	0.999993i	$0.498825\pi$
$282$	353.440	+	255.126i	0.0746350	+	0.0538742i
$283$	1710.81	−	6384.81i	0.359353	−	1.34112i	−0.515565	−	0.856851i	$-0.672418\pi$
$283$	1710.81	−	6384.81i	0.359353	−	1.34112i	0.874917	−	0.484272i	$-0.160915\pi$
$284$	4796.60	+	1285.25i	1.00220	+	0.268540i
$285$	−8506.88	+	1374.29i	−1.76808	+	0.285635i
$286$	−124.924	−	466.222i	−0.0258283	−	0.0963926i
$287$		−	1338.22i		−	0.275237i
$288$	1347.88	−	6539.55i	0.275780	−	1.33801i
$289$	−4688.24	+	1469.01i	−0.954252	+	0.299004i
$290$	6257.02	−	10837.5i	1.26698	−	2.19448i
$291$	−3385.29	+	2758.70i	−0.681956	+	0.555731i
$292$	−3883.35	−	1040.54i	−0.778273	−	0.208538i
$293$	−2010.72	−	3482.66i	−0.400912	−	0.694401i	0.592924	−	0.805258i	$-0.297973\pi$
$293$	−2010.72	−	3482.66i	−0.400912	−	0.694401i	−0.993836	+	0.110858i	$0.964640\pi$
$294$	−1293.89	−	2882.14i	−0.256670	−	0.571733i
$295$	112.467	−	30.1355i	0.0221970	−	0.00594765i
$296$	131.000	+	131.000i	0.0257236	+	0.0257236i
$297$	2821.61	+	121.683i	0.551267	+	0.0237736i
$298$			1183.06i			0.229976i
$299$	−1052.04	+	281.894i	−0.203482	+	0.0545229i
$300$	−1976.27	+	887.213i	−0.380333	+	0.170744i
$301$	4120.11	+	1103.98i	0.788967	+	0.211403i
$302$	1504.43	+	2605.75i	0.286656	+	0.496503i
$303$	−8413.88	−	858.082i	−1.59526	−	0.162692i
$304$	−7398.19	−	4271.34i	−1.39577	−	0.805850i
$305$	−2469.69			−0.463653
$306$	3357.85	+	6575.22i	0.627306	+	1.22837i
$307$	−4378.89			−0.814061			−0.407030	−	0.913415i	$-0.633436\pi$
$307$	−4378.89			−0.814061			−0.407030	+	0.913415i	$0.633436\pi$
$308$	−2810.98	−	1622.92i	−0.520034	−	0.300242i
$309$	4483.37	−	6211.07i	0.825405	−	1.14348i
$310$	−6813.33	−	11801.0i	−1.24829	−	2.16211i
$311$	6448.73	+	1727.93i	1.17580	+	0.315055i	0.793259	−	0.608884i	$-0.208382\pi$
$311$	6448.73	+	1727.93i	1.17580	+	0.315055i	0.382541	+	0.923939i	$0.375049\pi$
$312$	78.8781	+	56.9371i	0.0143128	+	0.0103315i
$313$	1147.50	−	307.471i	0.207222	−	0.0555250i	−0.153715	−	0.988115i	$-0.549124\pi$
$313$	1147.50	−	307.471i	0.207222	−	0.0555250i	0.360937	+	0.932590i	$0.382457\pi$
$314$			10230.7i			1.83869i
$315$	5417.40	−	6091.85i	0.969003	−	1.08964i
$316$	−3143.65	−	3143.65i	−0.559633	−	0.559633i
$317$	−4876.30	+	1306.60i	−0.863977	+	0.231502i	−0.663481	−	0.748193i	$-0.730922\pi$
$317$	−4876.30	+	1306.60i	−0.863977	+	0.231502i	−0.200495	+	0.979695i	$0.564255\pi$
$318$	−14150.6	−	1443.14i	−2.49537	−	0.254488i
$319$	2388.35	+	4136.75i	0.419192	+	0.726061i
$320$	−5323.08	−	1426.31i	−0.929903	−	0.249167i
$321$	6060.80	+	2305.08i	1.05383	+	0.400801i
$322$	−7720.43	+	13372.2i	−1.33616	+	2.31429i
$323$	8499.71	−	1300.47i	1.46420	−	0.224025i
$324$	4219.16	−	3145.72i	0.723450	−	0.539390i
$325$		−	354.932i		−	0.0605787i
$326$	−569.664	−	2126.01i	−0.0967814	−	0.361193i
$327$	−2052.48	+	5396.64i	−0.347103	+	0.912644i
$328$	176.293	+	47.2375i	0.0296773	+	0.00795200i
$329$	−124.306	+	463.915i	−0.0208304	+	0.0777400i
$330$	559.687	−	5487.98i	0.0933628	−	0.915465i
$331$	4850.31	+	2800.33i	0.805430	+	0.465015i	0.845366	−	0.534187i	$-0.179382\pi$
$331$	4850.31	+	2800.33i	0.805430	+	0.465015i	−0.0399366	+	0.999202i	$0.512716\pi$
$332$		−	5197.97i		−	0.859264i
$333$	96.0642	+	1639.30i	0.0158087	+	0.269768i
$334$	−3463.89	−	3463.89i	−0.567472	−	0.567472i
$335$	−1770.02	−	6605.82i	−0.288677	−	1.07736i
$336$	7978.32	−	1288.90i	1.29540	−	0.209272i
$337$	−6976.54	−	1869.36i	−1.12770	−	0.302168i	−0.353707	−	0.935356i	$-0.615079\pi$
$337$	−6976.54	−	1869.36i	−1.12770	−	0.302168i	−0.773998	+	0.633189i	$0.781746\pi$
$338$	−7294.98	+	4211.76i	−1.17395	+	0.677780i
$339$	−5361.78	+	866.198i	−0.859033	+	0.138777i
$340$	6263.66	−	2749.41i	0.999102	−	0.438552i
$341$	5201.40			0.826016
$342$	−4068.78	−	12264.2i	−0.643316	−	1.93911i
$343$	−2955.70	+	2955.70i	−0.465285	+	0.465285i
$344$	−290.869	+	503.799i	−0.0455889	+	0.0789623i
$345$	−12383.8	−	1262.95i	−1.93252	−	0.197087i
$346$	−3127.43	+	11671.7i	−0.485930	+	1.81351i
$347$	2490.03	−	9292.92i	0.385222	−	1.43767i	−0.452596	−	0.891716i	$-0.649502\pi$
$347$	2490.03	−	9292.92i	0.385222	−	1.43767i	0.837817	−	0.545951i	$-0.183831\pi$
$348$	8319.71	+	3164.20i	1.28156	+	0.487411i
$349$	−5536.99	−	3196.78i	−0.849251	−	0.490315i	0.0111473	−	0.999938i	$-0.496452\pi$
$349$	−5536.99	−	3196.78i	−0.849251	−	0.490315i	−0.860398	+	0.509623i	$0.829785\pi$
$350$	−3558.04	−	3558.04i	−0.543387	−	0.543387i
$351$	187.080	+	841.733i	0.0284490	+	0.128001i
$352$	3520.12	−	3520.12i	0.533020	−	0.533020i
$353$	3096.05	−	5362.52i	0.466817	−	0.808550i	−0.532465	−	0.846452i	$-0.678734\pi$
$353$	3096.05	−	5362.52i	0.466817	−	0.808550i	0.999281	+	0.0379019i	$0.0120674\pi$
$354$	71.5063	+	159.281i	0.0107359	+	0.0239143i
$355$	−8053.05	+	4649.43i	−1.20398	+	0.695116i
$356$	4394.20	+	7610.97i	0.654191	+	1.13309i
$357$	−5456.25	+	6033.42i	−0.808895	+	0.894461i
$358$	333.867	−	578.275i	0.0492889	−	0.0853708i
$359$			6423.78i			0.944385i	0.881495	+	0.472193i	$0.156537\pi$
$359$			6423.78i			0.944385i	−0.881495	+	0.472193i	$0.843463\pi$
$360$	611.292	+	928.703i	0.0894941	+	0.135964i
$361$	−8190.10			−1.19407
$362$	545.152	+	2034.54i	0.0791507	+	0.295394i
$363$	−3900.41	−	2815.46i	−0.563963	−	0.407089i
$364$	256.489	−	957.228i	0.0369331	−	0.137836i
$365$	6519.78	−	3764.20i	0.934961	−	0.539800i
$366$	−590.618	−	3655.94i	−0.0843500	−	0.522128i
$367$	7546.50	−	2022.08i	1.07336	−	0.287607i	0.321488	−	0.946914i	$-0.395817\pi$
$367$	7546.50	−	2022.08i	1.07336	−	0.287607i	0.751874	+	0.659307i	$0.229150\pi$
$368$	−8726.00	−	8726.00i	−1.23607	−	1.23607i
$369$	889.442	+	1351.28i	0.125481	+	0.190637i
$370$	3207.46			0.450670
$371$	−4056.27	−	15138.2i	−0.567630	−	2.11842i
$372$	7513.62	−	6122.91i	1.04721	−	0.853382i
$373$	6098.99	+	10563.8i	0.846632	+	1.46641i	0.884197	+	0.467115i	$0.154707\pi$
$373$	6098.99	+	10563.8i	0.846632	+	1.46641i	−0.0375648	+	0.999294i	$0.511960\pi$
$374$	−604.145	+	5471.31i	−0.0835284	+	0.756457i
$375$	−1679.30	+	4415.41i	−0.231249	+	0.608029i
$376$	−56.7267	−	32.7512i	−0.00778047	−	0.00449205i
$377$	−1031.24	+	1031.24i	−0.140879	+	0.140879i
$378$	10313.4	+	6562.63i	1.40335	+	0.892977i
$379$	4197.11	−	4197.11i	0.568842	−	0.568842i	−0.362962	−	0.931804i	$-0.618235\pi$
$379$	4197.11	−	4197.11i	0.568842	−	0.568842i	0.931804	+	0.362962i	$0.118235\pi$
$380$	−11564.2	+	3098.61i	−1.56113	+	0.418304i
$381$	5156.43	−	2314.89i	0.693364	−	0.311274i
$382$	7899.62	−	4560.85i	1.05806	−	0.610873i
$383$	−12694.8	+	7329.35i	−1.69367	+	0.977839i	−0.742154	+	0.670230i	$0.766196\pi$
$383$	−12694.8	+	7329.35i	−1.69367	+	0.977839i	−0.951513	+	0.307609i	$0.900471\pi$
$384$	−204.574	+	2005.94i	−0.0271865	+	0.266576i
$385$	5870.98	−	1573.12i	0.777176	−	0.208244i
$386$	−2173.13	+	2173.13i	−0.286552	+	0.286552i
$387$	−4894.07	+	1623.65i	−0.642841	+	0.213268i
$388$	−4290.16	+	4290.16i	−0.561340	+	0.561340i
$389$	−1372.70	−	792.531i	−0.178917	−	0.103298i	0.407867	−	0.913042i	$-0.366273\pi$
$389$	−1372.70	−	792.531i	−0.178917	−	0.103298i	−0.586784	+	0.809744i	$0.699606\pi$
$390$	1662.68	−	268.607i	0.215880	−	0.0348755i
$391$	12346.2	+	1363.27i	1.59686	+	0.176326i
$392$	237.368	+	411.134i	0.0305840	+	0.0529730i
$393$	−1384.01	−	8567.07i	−0.177644	−	1.09962i
$394$	1359.11	+	5072.27i	0.173784	+	0.648571i
$395$	8325.09			1.06046
$396$	3917.07	−	229.544i	0.497071	−	0.0291288i
$397$	−5262.97	−	5262.97i	−0.665342	−	0.665342i	0.291292	−	0.956634i	$-0.405915\pi$
$397$	−5262.97	−	5262.97i	−0.665342	−	0.665342i	−0.956634	+	0.291292i	$0.905915\pi$
$398$	−6844.92	+	1834.09i	−0.862073	+	0.230992i
$399$	11036.6	−	8993.82i	1.38477	−	1.12846i
$400$	3482.70	−	2010.74i	0.435337	−	0.251342i
$401$	−1690.20	+	6307.89i	−0.210485	+	0.785539i	0.777223	+	0.629225i	$0.216628\pi$
$401$	−1690.20	+	6307.89i	−0.210485	+	0.785539i	−0.987707	+	0.156314i	$0.950039\pi$
$402$	9355.42	−	4199.96i	1.16071	−	0.521082i
$403$	411.018	+	1533.94i	0.0508047	+	0.189606i
$404$	−11750.3			−1.44703
$405$	−1421.35	+	9751.93i	−0.174389	+	1.19649i
$406$			20675.5i			2.52735i
$407$	−612.156	+	1060.29i	−0.0745539	+	0.129131i
$408$	−602.223	−	931.759i	−0.0730747	−	0.113061i
$409$	2181.87	+	3779.12i	0.263782	+	0.456883i	0.967244	−	0.253850i	$-0.0816968\pi$
$409$	2181.87	+	3779.12i	0.263782	+	0.456883i	−0.703462	+	0.710733i	$0.748363\pi$
$410$	2736.52	−	1579.93i	0.329627	−	0.190310i
$411$	−5335.39	−	544.125i	−0.640329	−	0.0653034i
$412$	5321.25	−	9216.67i	0.636308	−	1.10212i
$413$	−136.027	+	136.027i	−0.0162069	+	0.0162069i
$414$	−1091.97	−	18634.0i	−0.129631	−	2.21210i
$415$	6882.70	+	6882.70i	0.814117	+	0.814117i
$416$	1316.28	+	759.954i	0.155134	+	0.0895669i
$417$	−872.270	−	5399.36i	−0.102435	−	0.634072i
$418$	2493.45	−	9305.69i	0.291767	−	1.08889i
$419$	−507.773	+	1895.03i	−0.0592036	+	0.220951i	−0.989189	−	0.146645i	$-0.953152\pi$
$419$	−507.773	+	1895.03i	−0.0592036	+	0.220951i	0.929986	+	0.367596i	$0.119819\pi$
$420$	6629.03	−	9183.56i	0.770151	−	1.06693i
$421$	171.085	−	296.328i	0.0198057	−	0.0343044i	−0.855953	−	0.517054i	$-0.827029\pi$
$421$	171.085	−	296.328i	0.0198057	−	0.0343044i	0.875758	+	0.482750i	$0.160362\pi$
$422$	344.358	−	344.358i	0.0397229	−	0.0397229i
$423$	−182.820	−	551.061i	−0.0210142	−	0.0633416i
$424$	2137.43			0.244818
$425$	−1470.44	+	3771.27i	−0.167828	+	0.430432i
$426$	−8808.50	−	10809.2i	−1.00181	−	1.22936i
$427$	3533.71	−	2040.19i	0.400488	−	0.231222i
$428$	8701.93	+	2331.67i	0.982765	+	0.263331i
$429$	−228.536	+	600.896i	−0.0257199	+	0.0676259i
$430$	2606.75	+	9728.53i	0.292346	+	1.09105i
$431$	−908.482	−	908.482i	−0.101531	−	0.101531i	0.654516	−	0.756048i	$-0.272872\pi$
$431$	−908.482	−	908.482i	−0.101531	−	0.101531i	−0.756048	+	0.654516i	$0.772872\pi$
$432$	−7199.51	+	6604.22i	−0.801821	+	0.735522i
$433$			8322.91i			0.923726i	0.886951	+	0.461863i	$0.152819\pi$
$433$			8322.91i			0.923726i	−0.886951	+	0.461863i	$0.847181\pi$
$434$	19497.4	+	11256.8i	2.15647	+	1.24504i
$435$	−15206.0	+	6826.47i	−1.67603	+	0.752423i
$436$	−2076.16	+	7748.34i	−0.228051	+	0.851097i
$437$	−20998.6	−	5626.55i	−2.29862	−	0.615914i
$438$	7131.39	+	8751.16i	0.777970	+	0.954672i
$439$	1344.84	+	5019.03i	0.146209	+	0.545661i	0.999699	+	0.0245504i	$0.00781542\pi$
$439$	1344.84	+	5019.03i	0.146209	+	0.545661i	−0.853489	+	0.521111i	$0.825518\pi$
$440$			828.951i			0.0898152i
$441$	−849.452	+	4121.31i	−0.0917235	+	0.445018i
$442$	−1661.28	+	254.179i	−0.178776	+	0.0273531i
$443$	−1676.40	+	2903.62i	−0.179793	+	0.311411i	−0.941810	−	0.336147i	$-0.890876\pi$
$443$	−1676.40	+	2903.62i	−0.179793	+	0.311411i	0.762016	+	0.647558i	$0.224209\pi$
$444$	363.849	+	2252.23i	0.0388908	+	0.240735i
$445$	−15896.2	−	4259.37i	−1.69337	−	0.453738i
$446$	2475.00	+	4286.83i	0.262768	+	0.455128i
$447$	922.274	−	1277.68i	0.0975885	−	0.135195i
$448$	8794.68	−	2356.53i	0.927476	−	0.248517i
$449$	−9861.48	−	9861.48i	−1.03651	−	1.03651i	−0.999308	−	0.0371995i	$-0.988156\pi$
$449$	−9861.48	−	9861.48i	−1.03651	−	1.03651i	−0.0371995	−	0.999308i	$-0.511844\pi$
$450$	5957.60	+	1227.93i	0.624097	+	0.128634i
$451$			1206.14i			0.125931i
$452$	−7288.76	+	1953.02i	−0.758483	+	0.203235i
$453$	406.606	−	3986.96i	0.0421722	−	0.413518i
$454$	−5631.39	−	1508.93i	−0.582146	−	0.155986i
$455$	927.858	+	1607.10i	0.0956015	+	0.165587i
$456$	795.236	+	1771.39i	0.0816674	+	0.181915i
$457$	−5668.35	−	3272.63i	−0.580207	−	0.334982i	0.181009	−	0.983481i	$-0.442064\pi$
$457$	−5668.35	−	3272.63i	−0.580207	−	0.334982i	−0.761215	+	0.648499i	$0.775397\pi$
$458$	13189.5			1.34564
$459$	1499.42	−	9718.76i	0.152477	−	0.988307i
$460$	−17294.4			−1.75295
$461$	10146.9	+	5858.32i	1.02514	+	0.591864i	0.915588	−	0.402118i	$-0.131726\pi$
$461$	10146.9	+	5858.32i	1.02514	+	0.591864i	0.109550	+	0.993981i	$0.465059\pi$
$462$	3732.75	+	8314.71i	0.375894	+	0.837306i
$463$	4384.39	+	7593.98i	0.440086	+	0.762251i	0.997695	−	0.0678525i	$-0.0216147\pi$
$463$	4384.39	+	7593.98i	0.440086	+	0.762251i	−0.557610	+	0.830103i	$0.688281\pi$
$464$	−15960.9	−	4276.71i	−1.59691	−	0.427891i
$465$	−1841.46	+	18056.3i	−0.183646	+	1.80073i
$466$	7816.52	−	2094.43i	0.777025	−	0.208203i
$467$			15933.5i			1.57883i	0.613861	+	0.789414i	$0.289616\pi$
$467$			15933.5i			1.57883i	−0.613861	+	0.789414i	$0.710384\pi$
$468$	377.224	+	1137.04i	0.0372590	+	0.112307i
$469$	7989.60	+	7989.60i	0.786622	+	0.786622i
$470$	−1095.41	+	293.514i	−0.107505	+	0.0288060i
$471$	7975.48	−	11048.9i	0.780235	−	1.08090i
$472$	−13.1181	−	22.7213i	−0.00127926	−	0.00221574i
$473$	−3713.45	−	995.017i	−0.360983	−	0.0967250i
$474$	1990.91	+	12323.8i	0.192923	+	1.19420i
$475$	3542.18	−	6135.24i	0.342161	−	0.592641i
$476$	−6690.97	+	9108.28i	−0.644286	+	0.877053i
$477$	14157.3	+	12589.9i	1.35895	+	1.20850i
$478$		−	21297.7i		−	2.03793i
$479$	2607.76	+	9732.31i	0.248751	+	0.928352i	0.971461	+	0.237200i	$0.0762297\pi$
$479$	2607.76	+	9732.31i	0.248751	+	0.928352i	−0.722710	+	0.691152i	$0.757104\pi$
$480$	10973.6	+	13466.1i	1.04349	+	1.28050i
$481$	−361.061	−	96.7460i	−0.0342265	−	0.00917097i
$482$	4277.14	−	15962.5i	0.404188	−	1.50845i
$483$	18762.4	−	8423.06i	1.76753	−	0.793504i
$484$	−5787.87	−	3341.63i	−0.543564	−	0.313827i
$485$		−	11361.3i		−	1.06369i
$486$	−14775.9	+	228.087i	−1.37911	+	0.0212886i
$487$	5599.82	+	5599.82i	0.521051	+	0.521051i	0.917889	−	0.396838i	$-0.129892\pi$
$487$	5599.82	+	5599.82i	0.521051	+	0.521051i	−0.396838	+	0.917889i	$0.629892\pi$
$488$	144.032	+	537.534i	0.0133607	+	0.0498628i
$489$	−1042.15	+	2740.14i	−0.0963753	+	0.253402i
$490$	7939.14	+	2127.29i	0.731946	+	0.196124i
$491$	5337.93	−	3081.86i	0.490626	−	0.283263i	−0.234208	−	0.972187i	$-0.575250\pi$
$491$	5337.93	−	3081.86i	0.490626	−	0.283263i	0.724834	+	0.688923i	$0.241916\pi$
$492$	1419.83	+	1742.32i	0.130103	+	0.159654i
$493$	15229.5	−	6684.95i	1.39129	−	0.610700i
$494$	2941.37			0.267892
$495$	−4882.70	+	5490.58i	−0.443356	+	0.498552i
$496$	−12723.0	+	12723.0i	−1.15178	+	1.15178i
$497$	7681.69	−	13305.1i	0.693302	−	1.20083i
$498$	−8542.62	+	11834.6i	−0.768682	+	1.06490i
$499$	3395.18	−	12671.0i	0.304587	−	1.13674i	−0.628713	−	0.777638i	$-0.716418\pi$
$499$	3395.18	−	12671.0i	0.304587	−	1.13674i	0.933300	−	0.359098i	$-0.116916\pi$
$500$	−1698.67	+	6339.53i	−0.151934	+	0.567025i
$501$	1040.59	+	6441.27i	0.0927946	+	0.574400i
$502$	17587.7	+	10154.2i	1.56370	+	0.902801i
$503$	−3953.49	−	3953.49i	−0.350452	−	0.350452i	0.509826	−	0.860278i	$-0.329710\pi$
$503$	−3953.49	−	3953.49i	−0.350452	−	0.350452i	−0.860278	+	0.509826i	$0.829710\pi$
$504$	−1641.85	−	823.833i	−0.145106	−	0.0728104i
$505$	15558.7	−	15558.7i	1.37100	−	1.37100i
$506$	6958.42	−	12052.3i	0.611343	−	1.05888i
$507$	11161.8	+	1138.32i	0.977735	+	0.0997134i
$508$	6800.71	−	3926.39i	0.593962	−	0.342924i
$509$	2433.77	+	4215.42i	0.211935	+	0.367083i	0.952320	−	0.305101i	$-0.0986901\pi$
$509$	2433.77	+	4215.42i	0.211935	+	0.367083i	−0.740385	+	0.672183i	$0.765357\pi$
$510$	−18779.4	−	4034.26i	−1.63052	−	0.350275i
$511$	−6219.13	+	10771.8i	−0.538391	+	0.932521i
$512$			15524.0i			1.33998i
$513$	−5166.61	+	16417.0i	−0.444662	+	1.41292i
$514$	333.417			0.0286117
$515$	5157.98	+	19249.8i	0.441335	+	1.64709i
$516$	−6535.53	+	2934.01i	−0.557579	+	0.250315i
$517$	112.037	−	418.127i	0.00953069	−	0.0355690i
$518$	−4589.33	+	2649.65i	−0.389273	+	0.224747i
$519$	12476.5	−	10167.2i	1.05521	−	0.859902i
$520$	−244.465	+	65.5043i	−0.0206164	+	0.00552414i
$521$	−7908.13	−	7908.13i	−0.664993	−	0.664993i	0.291560	−	0.956553i	$-0.405826\pi$
$521$	−7908.13	−	7908.13i	−0.664993	−	0.664993i	−0.956553	+	0.291560i	$0.905826\pi$
$522$	−13741.8	−	20877.2i	−1.15223	−	1.75052i
$523$	16001.1			1.33782			0.668910	−	0.743343i	$-0.266761\pi$
$523$	16001.1			1.33782			0.668910	+	0.743343i	$0.266761\pi$
$524$	−3120.53	−	11646.0i	−0.260155	−	0.970911i
$525$	1068.87	+	6616.35i	0.0888561	+	0.550021i
$526$	9776.90	+	16934.1i	0.810443	+	1.40373i
$527$	1987.73	−	18001.5i	0.164302	−	1.48796i
$528$	−7190.86	+	1161.69i	−0.592693	+	0.0957499i
$529$	−16659.5	−	9618.38i	−1.36924	−	0.790530i
$530$	26167.0	−	26167.0i	2.14457	−	2.14457i
$531$	46.9448	−	227.764i	0.00383659	−	0.0186141i
$532$	13986.6	−	13986.6i	1.13984	−	1.13984i
$533$	−355.702	+	95.3102i	−0.0289065	+	0.00774548i
$534$	2503.71	−	24550.0i	0.202896	−	1.98948i
$535$	−14609.7	+	8434.93i	−1.18062	+	0.681633i
$536$	−1334.54	+	770.499i	−0.107544	+	0.0620905i
$537$	−811.373	+	364.252i	−0.0652017	+	0.0292712i
$538$	−16589.0	+	4445.01i	−1.32937	+	0.356205i
$539$	−2218.43	+	2218.43i	−0.177281	+	0.177281i
$540$	−589.918	+	13679.1i	−0.0470111	+	1.09010i
$541$	15769.7	−	15769.7i	1.25322	−	1.25322i	0.298955	−	0.954267i	$-0.403362\pi$
$541$	15769.7	−	15769.7i	1.25322	−	1.25322i	0.954267	−	0.298955i	$-0.0966380\pi$
$542$	−25691.9	−	14833.2i	−2.03609	−	1.17554i
$543$	997.305	−	2622.24i	0.0788185	−	0.207239i
$544$	−10837.5	−	13528.0i	−0.854145	−	1.06619i
$545$	−7510.61	−	13008.8i	−0.590310	−	1.02245i
$546$	−2157.12	+	1757.86i	−0.169078	+	0.137783i
$547$	−1942.24	−	7248.56i	−0.151818	−	0.566592i	−0.999357	−	0.0358590i	$-0.988583\pi$
$547$	−1942.24	−	7248.56i	−0.151818	−	0.566592i	0.847539	−	0.530733i	$-0.178083\pi$
$548$	−7451.07			−0.580829
$549$	−2212.19	+	4408.76i	−0.171975	+	0.342734i
$550$	3206.87	+	3206.87i	0.248620	+	0.248620i
$551$	−28117.3	+	7534.01i	−2.17393	+	0.582504i
$552$	447.335	+	2769.01i	0.0344925	+	0.213509i
$553$	−11911.8	+	6877.27i	−0.915986	+	0.528845i
$554$	3039.55	−	11343.8i	0.233101	−	0.869945i
$555$	−3463.99	−	2500.43i	−0.264933	−	0.191239i
$556$	−1966.70	−	7339.84i	−0.150012	−	0.559854i
$557$	17502.0			1.33139			0.665693	−	0.746226i	$-0.268136\pi$
$557$	17502.0			1.33139			0.665693	+	0.746226i	$0.268136\pi$
$558$	−27169.5	+	1592.15i	−2.06125	+	0.120791i
$559$		−	1173.76i		−	0.0888099i
$560$	−10512.9	+	18208.9i	−0.793304	+	1.37404i
$561$	4917.72	−	5437.92i	0.370100	−	0.409250i
$562$	−9246.75	−	16015.8i	−0.694040	−	1.20211i
$563$	2382.33	−	1375.44i	0.178336	−	0.102963i	−0.408174	−	0.912904i	$-0.633834\pi$
$563$	2382.33	−	1375.44i	0.178336	−	0.102963i	0.586511	+	0.809941i	$0.300501\pi$
$564$	−330.363	−	735.886i	−0.0246645	−	0.0549404i
$565$	7065.12	−	12237.1i	0.526074	−	0.911187i
$566$	−18234.1	+	18234.1i	−1.35413	+	1.35413i
$567$	−6022.26	−	15127.5i	−0.446051	−	1.12045i
$568$	1481.61	+	1481.61i	0.109449	+	0.109449i
$569$	2594.11	+	1497.71i	0.191126	+	0.110347i	0.592510	−	0.805563i	$-0.298137\pi$
$569$	2594.11	+	1497.71i	0.191126	+	0.110347i	−0.401384	+	0.915910i	$0.631471\pi$
$570$	31421.3	+	11950.4i	2.30894	+	0.878150i
$571$	3865.52	−	14426.3i	0.283305	−	1.05731i	−0.666764	−	0.745269i	$-0.732321\pi$
$571$	3865.52	−	14426.3i	0.283305	−	1.05731i	0.950069	−	0.312040i	$-0.101012\pi$
$572$	−231.173	+	862.750i	−0.0168983	+	0.0630653i
$573$	−12086.9	−	1232.67i	−0.881218	−	0.0898702i
$574$	−2610.32	+	4521.21i	−0.189813	+	0.328766i
$575$	7236.39	−	7236.39i	0.524832	−	0.524832i
$576$	−7314.24	+	8224.85i	−0.529097	+	0.594969i
$577$	−23858.6			−1.72140			−0.860700	−	0.509113i	$-0.829974\pi$
$577$	−23858.6			−1.72140			−0.860700	+	0.509113i	$0.829974\pi$
$578$	18704.7	+	4181.76i	1.34605	+	0.300931i
$579$	4041.02	−	652.829i	0.290051	−	0.0468578i
$580$	−20054.9	+	11578.7i	−1.43575	+	0.828930i
$581$	−15533.7	−	4162.24i	−1.10920	−	0.297210i
$582$	16818.3	−	2717.01i	1.19784	−	0.193512i
$583$	3655.91	+	13644.0i	0.259712	+	0.969260i
$584$	−1199.52	−	1199.52i	−0.0849938	−	0.0849938i
$585$	−2005.06	−	1006.08i	−0.141708	−	0.0711051i
$586$			15688.3i			1.10594i
$587$	−13930.6	−	8042.85i	−0.979521	−	0.565527i	−0.0773954	−	0.997000i	$-0.524660\pi$
$587$	−13930.6	−	8042.85i	−0.979521	−	0.565527i	−0.902125	+	0.431474i	$0.857994\pi$
$588$	−593.146	+	5816.06i	−0.0416002	+	0.407909i
$589$	−8203.85	+	30617.2i	−0.573911	+	2.14186i
$590$	−438.755	−	117.564i	−0.0306157	−	0.00820345i
$591$	2486.36	−	6537.45i	0.173055	−	0.455017i
$592$	−1096.16	−	4090.92i	−0.0761011	−	0.284013i
$593$		−	18598.9i		−	1.28797i	−0.765040	−	0.643983i	$-0.777281\pi$
$593$		−	18598.9i		−	1.28797i	0.765040	−	0.643983i	$-0.222719\pi$
$594$	−9295.49	−	5914.90i	−0.642085	−	0.408571i
$595$	−3200.79	−	20920.0i	−0.220537	−	1.44140i
$596$	1094.63	−	1895.96i	0.0752314	−	0.130305i
$597$	8822.16	+	3355.30i	0.604803	+	0.230022i
$598$	4104.21	+	1099.72i	0.280658	+	0.0752021i
$599$	−1209.85	−	2095.52i	−0.0825260	−	0.142939i	0.821808	−	0.569764i	$-0.192965\pi$
$599$	−1209.85	−	2095.52i	−0.0825260	−	0.142939i	−0.904334	+	0.426825i	$0.859632\pi$
$600$	−909.343	−	92.7386i	−0.0618730	−	0.00631006i
$601$	−20803.6	+	5574.32i	−1.41198	+	0.378338i	−0.882630	−	0.470068i	$-0.844229\pi$
$601$	−20803.6	+	5574.32i	−1.41198	+	0.378338i	−0.529346	+	0.848406i	$0.677563\pi$
$602$	−11766.5	−	11766.5i	−0.796619	−	0.796619i
$603$	−13377.8	−	2757.32i	−0.903460	−	0.186214i
$604$		−	5567.94i		−	0.375093i
$605$	12088.5	−	3239.10i	0.812341	−	0.217666i
$606$	26752.7	+	19311.1i	1.79332	+	1.29449i
$607$	4875.96	+	1306.51i	0.326045	+	0.0873634i	0.418129	−	0.908388i	$-0.362686\pi$
$607$	4875.96	+	1306.51i	0.326045	+	0.0873634i	−0.0920839	+	0.995751i	$0.529353\pi$
$608$	15168.5	+	26272.7i	1.01179	+	1.75246i
$609$	16117.9	−	22329.0i	1.07246	−	1.48574i
$610$	8343.91	+	4817.36i	0.553828	+	0.319753i
$611$	132.163			0.00875079
$612$	702.495	−	13644.3i	0.0463998	−	0.901204i
$613$	−19748.5			−1.30120			−0.650599	−	0.759422i	$-0.725482\pi$
$613$	−19748.5			−1.30120			−0.650599	+	0.759422i	$0.725482\pi$
$614$	14794.2	+	8541.42i	0.972385	+	0.561407i
$615$	−4187.04	−	427.011i	−0.274533	−	0.0279980i
$616$	−684.788	−	1186.09i	−0.0447904	−	0.0775792i
$617$	24829.2	+	6652.95i	1.62007	+	0.434097i	0.951023	−	0.309121i	$-0.100035\pi$
$617$	24829.2	+	6652.95i	1.62007	+	0.434097i	0.669049	+	0.743218i	$0.266702\pi$
$618$	−27262.4	+	12239.0i	−1.77452	+	0.796641i
$619$	−11742.4	+	3146.36i	−0.762465	+	0.204302i	−0.619040	−	0.785359i	$-0.712478\pi$
$619$	−11742.4	+	3146.36i	−0.762465	+	0.204302i	−0.143425	+	0.989661i	$0.545812\pi$
$620$			25216.3i			1.63341i
$621$	−13347.1	+	20975.6i	−0.862484	+	1.35543i
$622$	−18416.7	−	18416.7i	−1.18720	−	1.18720i
$623$	26263.4	−	7037.24i	1.68896	−	0.452554i
$624$	−910.819	−	2028.85i	−0.0584326	−	0.130159i
$625$	−9754.34	−	16895.0i	−0.624278	−	1.08128i
$626$	−4476.60	−	1199.50i	−0.285816	−	0.0765842i
$627$	−9947.29	+	8106.13i	−0.633583	+	0.516312i
$628$	9465.98	−	16395.6i	0.601487	−	1.04181i
$629$	3435.59	+	2523.79i	0.217784	+	0.159985i
$630$	−30185.5	+	10014.3i	−1.90892	+	0.633301i
$631$		−	9324.94i		−	0.588304i	−0.955759	−	0.294152i	$-0.904963\pi$
$631$		−	9324.94i		−	0.588304i	0.955759	−	0.294152i	$-0.0950372\pi$
$632$	−485.517	−	1811.97i	−0.0305583	−	0.114045i
$633$	−640.349	+	103.449i	−0.0402078	+	0.00649560i
$634$	19023.3	+	5097.29i	1.19166	+	0.319305i
$635$	−3805.92	+	14203.9i	−0.237848	+	0.887661i
$636$	21342.4	+	15405.7i	1.33063	+	0.960498i
$637$	−829.537	−	478.933i	−0.0515973	−	0.0297897i
$638$		−	18634.8i		−	1.15636i
$639$	1086.49	+	18540.5i	0.0672627	+	1.14781i
$640$	−3709.34	−	3709.34i	−0.229101	−	0.229101i
$641$	1195.70	+	4462.40i	0.0736774	+	0.274968i	0.992930	−	0.118700i	$-0.0378727\pi$
$641$	1195.70	+	4462.40i	0.0736774	+	0.274968i	−0.919253	+	0.393668i	$0.871206\pi$
$642$	−15980.2	−	19609.9i	−0.982383	−	1.20551i
$643$	8648.00	+	2317.22i	0.530395	+	0.142119i	0.514070	−	0.857748i	$-0.328137\pi$
$643$	8648.00	+	2317.22i	0.530395	+	0.142119i	0.0163241	+	0.999867i	$0.494804\pi$
$644$	24745.4	−	14286.8i	1.51414	−	0.874188i
$645$	4768.81	−	12538.7i	0.291119	−	0.765445i
$646$	−31253.1	−	12185.8i	−1.90346	−	0.742171i
$647$	26695.0			1.62208			0.811042	−	0.584988i	$-0.198901\pi$
$647$	26695.0			1.62208			0.811042	+	0.584988i	$0.198901\pi$
$648$	2205.42	−	259.370i	0.133699	−	0.0157238i
$649$	122.601	−	122.601i	0.00741527	−	0.00741527i
$650$	−692.326	+	1199.14i	−0.0417773	+	0.0723604i
$651$	−12281.3	−	27356.7i	−0.739390	−	1.64699i
$652$	−1054.17	+	3934.22i	−0.0633198	+	0.236313i
$653$	3767.00	−	14058.6i	0.225749	−	0.842506i	−0.756354	−	0.654162i	$-0.773021\pi$
$653$	3767.00	−	14058.6i	0.225749	−	0.842506i	0.982103	−	0.188344i	$-0.0603119\pi$
$654$	17461.0	−	14229.1i	1.04400	−	0.850766i
$655$	19552.5	+	11288.7i	1.16638	+	0.673412i
$656$	−2950.31	−	2950.31i	−0.175595	−	0.175595i
$657$	−879.626	−	15010.5i	−0.0522336	−	0.891345i
$658$	1324.88	−	1324.88i	0.0784940	−	0.0784940i
$659$	5119.03	−	8866.42i	0.302593	−	0.524107i	−0.674129	−	0.738613i	$-0.735481\pi$
$659$	5119.03	−	8866.42i	0.302593	−	0.524107i	0.976723	+	0.214506i	$0.0688142\pi$
$660$	−5974.74	+	8277.14i	−0.352373	+	0.488162i
$661$	12461.4	−	7194.58i	0.733269	−	0.423353i	−0.0863476	−	0.996265i	$-0.527520\pi$
$661$	12461.4	−	7194.58i	0.733269	−	0.423353i	0.819617	+	0.572912i	$0.194186\pi$
$662$	−10924.6	−	18921.9i	−0.641383	−	1.11091i
$663$	1992.30	+	1020.57i	0.116703	+	0.0597825i
$664$	1096.64	−	1899.43i	0.0640930	−	0.111012i
$665$			37039.7i			2.15991i
$666$	2873.04	−	5725.77i	0.167159	−	0.333137i
$667$	−42049.9			−2.44105
$668$	2346.22	+	8756.20i	0.135895	+	0.507167i
$669$	668.924	−	6559.11i	0.0386579	−	0.379058i
$670$	−6905.18	+	25770.5i	−0.398165	+	1.48597i
$671$	−3184.93	+	1838.82i	−0.183238	+	0.105793i
$672$	−26825.6	−	10202.5i	−1.53991	−	0.585668i
$673$	28605.0	−	7664.68i	1.63840	−	0.439007i	0.682065	−	0.731292i	$-0.261082\pi$
$673$	28605.0	−	7664.68i	1.63840	−	0.439007i	0.956331	+	0.292285i	$0.0944154\pi$
$674$	19924.0	+	19924.0i	1.13864	+	1.13864i
$675$	−5476.82	−	5970.49i	−0.312300	−	0.340451i
$676$	15587.8			0.886882
$677$	6472.79	+	24156.8i	0.367459	+	1.37137i	0.864057	+	0.503394i	$0.167916\pi$
$677$	6472.79	+	24156.8i	0.367459	+	1.37137i	−0.496598	+	0.867980i	$0.665418\pi$
$678$	19804.5	+	7532.16i	1.12181	+	0.426653i
$679$	9385.45	+	16256.1i	0.530457	+	0.918779i
$680$	2868.91	+	316.786i	0.161791	+	0.0178650i
$681$	4905.47	+	6019.66i	0.276032	+	0.338728i
$682$	−17573.0	−	10145.8i	−0.986665	−	0.569651i
$683$	13318.9	−	13318.9i	0.746170	−	0.746170i	−0.227587	−	0.973758i	$-0.573084\pi$
$683$	13318.9	−	13318.9i	0.746170	−	0.746170i	0.973758	+	0.227587i	$0.0730837\pi$
$684$	−4826.98	+	23419.2i	−0.269831	+	1.30915i
$685$	9866.06	−	9866.06i	0.550311	−	0.550311i
$686$	15751.2	−	4220.53i	0.876655	−	0.234899i
$687$	−14244.4	−	10282.1i	−0.791058	−	0.571014i
$688$	11517.3	−	6649.51i	0.638216	−	0.368474i
$689$	−3734.86	+	2156.33i	−0.206512	+	0.119230i
$690$	39375.4	+	28422.6i	2.17246	+	1.56816i
$691$	29416.9	−	7882.22i	1.61949	−	0.433942i	0.668641	−	0.743585i	$-0.266876\pi$
$691$	29416.9	−	7882.22i	1.61949	−	0.433942i	0.950853	+	0.309643i	$0.100210\pi$
$692$	15811.3	−	15811.3i	0.868579	−	0.868579i
$693$	2450.60	−	11889.6i	0.134330	−	0.651731i
$694$	−26539.3	+	26539.3i	−1.45161	+	1.45161i
$695$	12322.9	+	7114.64i	0.672568	+	0.388307i
$696$	2372.61	+	2911.50i	0.129215	+	0.158563i
$697$	4174.32	+	460.931i	0.226849	+	0.0250488i
$698$	12471.2	+	21600.8i	0.676279	+	1.17135i
$699$	−10074.4	−	3831.57i	−0.545135	−	0.207329i
$700$	2409.99	+	8994.20i	0.130127	+	0.485641i
$701$	11408.2			0.614665			0.307332	−	0.951602i	$-0.400564\pi$
$701$	11408.2			0.614665			0.307332	+	0.951602i	$0.400564\pi$
$702$	1009.82	−	3208.73i	0.0542925	−	0.172515i
$703$	−5275.68	−	5275.68i	−0.283038	−	0.283038i
$704$	−7926.64	+	2123.94i	−0.424356	+	0.113706i
$705$	1411.83	+	536.957i	0.0754223	+	0.0286851i
$706$	−20920.1	+	12078.3i	−1.11521	+	0.643868i
$707$	−9408.98	+	35114.8i	−0.500511	+	1.86793i
$708$	32.7801	−	321.424i	0.00174004	−	0.0170619i
$709$	−1250.70	−	4667.69i	−0.0662498	−	0.247248i	0.924857	−	0.380314i	$-0.124184\pi$
$709$	−1250.70	−	4667.69i	−0.0662498	−	0.247248i	−0.991107	+	0.133067i	$0.957518\pi$
$710$	36276.5			1.91751
$711$	7457.08	−	14861.5i	0.393336	−	0.783894i
$712$			3708.25i			0.195186i
$713$	−22894.3	+	39654.0i	−1.20252	+	2.08283i
$714$	30202.8	−	9741.13i	1.58307	−	0.510578i
$715$	−836.278	−	1448.48i	−0.0437413	−	0.0757622i
$716$	−1070.10	+	617.825i	−0.0558543	+	0.0322475i
$717$	−16603.0	+	23001.0i	−0.864783	+	1.19803i
$718$	12530.2	−	21702.9i	0.651283	−	1.12806i
$719$	−19486.8	+	19486.8i	−1.01076	+	1.01076i	−0.0108150	+	0.999942i	$0.503443\pi$
$719$	−19486.8	+	19486.8i	−1.01076	+	1.01076i	−0.999942	+	0.0108150i	$0.996557\pi$
$720$	−1486.93	−	25373.9i	−0.0769648	−	1.31337i
$721$	−23282.3	−	23282.3i	−1.20260	−	1.20260i
$722$	27670.4	+	15975.5i	1.42630	+	0.823472i
$723$	−17063.1	+	13904.8i	−0.877707	+	0.715251i
$724$	1008.81	−	3764.93i	0.0517848	−	0.193263i
$725$	3546.64	−	13236.2i	0.181681	−	0.678043i
$726$	7685.81	+	17120.2i	0.392903	+	0.875192i
$727$	−6041.38	+	10464.0i	−0.308201	+	0.533820i	−0.977969	−	0.208751i	$-0.933060\pi$
$727$	−6041.38	+	10464.0i	−0.308201	+	0.533820i	0.669768	+	0.742571i	$0.266394\pi$
$728$	295.676	−	295.676i	0.0150528	−	0.0150528i
$729$	16135.4	+	11272.5i	0.819765	+	0.572700i
$730$	−29369.6			−1.48906
$731$	−4862.75	+	12471.6i	−0.246040	+	0.631024i
$732$	−2436.16	+	6405.44i	−0.123010	+	0.323432i
$733$	23922.9	−	13811.9i	1.20547	−	0.695981i	0.243707	−	0.969849i	$-0.421637\pi$
$733$	23922.9	−	13811.9i	1.20547	−	0.695981i	0.961767	+	0.273868i	$0.0883033\pi$
$734$	−29440.2	−	7888.48i	−1.48046	−	0.396688i
$735$	−6915.73	−	8486.51i	−0.347062	−	0.425891i
$736$	11342.4	+	42330.5i	0.568053	+	2.12000i
$737$	−7201.03	−	7201.03i	−0.359909	−	0.359909i
$738$	−369.201	−	6300.27i	−0.0184153	−	0.314249i
$739$			9839.33i			0.489777i	0.969551	+	0.244889i	$0.0787514\pi$
$739$			9839.33i			0.489777i	−0.969551	+	0.244889i	$0.921249\pi$
$740$	−5140.25	−	2967.72i	−0.255350	−	0.147427i
$741$	−3176.62	−	2293.00i	−0.157484	−	0.113678i
$742$	−15824.2	+	59056.8i	−0.782918	+	2.92189i
$743$	33975.2	+	9103.62i	1.67756	+	0.449501i	0.967134	−	0.254268i	$-0.0818345\pi$
$743$	33975.2	+	9103.62i	1.67756	+	0.449501i	0.710429	+	0.703769i	$0.248501\pi$
$744$	4037.39	−	652.242i	0.198949	−	0.0321402i
$745$	1061.05	+	3959.88i	0.0521795	+	0.194737i
$746$		−	47586.5i		−	2.33547i
$747$	18451.7	−	6121.52i	0.903764	−	0.299832i
$748$	6030.57	−	8209.29i	0.294785	−	0.401285i
$749$	13936.0	−	24137.9i	0.679854	−	1.17754i
$750$	14286.2	−	11641.9i	0.695544	−	0.566804i
$751$	−24598.8	−	6591.22i	−1.19524	−	0.320263i	−0.394283	−	0.918989i	$-0.629007\pi$
$751$	−24598.8	−	6591.22i	−1.19524	−	0.320263i	−0.800953	+	0.598727i	$0.795674\pi$
$752$	748.720	+	1296.82i	0.0363072	+	0.0628859i
$753$	−11078.4	−	24677.1i	−0.536146	−	1.19427i
$754$	5495.57	−	1472.53i	0.265434	−	0.0711227i
$755$	7372.57	+	7372.57i	0.355385	+	0.355385i
$756$	−10456.1	−	20059.8i	−0.503022	−	0.965036i
$757$		−	36754.1i		−	1.76466i	−0.470627	−	0.882332i	$-0.655972\pi$
$757$		−	36754.1i		−	1.76466i	0.470627	−	0.882332i	$-0.344028\pi$
$758$	−22366.8	+	5993.18i	−1.07177	+	0.287179i
$759$	−16910.5	+	7591.70i	−0.808714	+	0.363058i
$760$	−4879.48	−	1307.45i	−0.232891	−	0.0624030i
$761$	−1783.88	−	3089.77i	−0.0849744	−	0.147180i	0.820406	−	0.571782i	$-0.193748\pi$
$761$	−1783.88	−	3089.77i	−0.0849744	−	0.147180i	−0.905380	+	0.424602i	$0.860414\pi$
$762$	−21936.5	−	2237.17i	−1.04288	−	0.106357i
$763$	21492.8	+	12408.9i	1.01978	+	0.588769i
$764$	−16879.8			−0.799333
$765$	17136.4	+	18996.7i	0.809891	+	0.897814i
$766$	57186.2			2.69742
$767$	45.8442	+	26.4682i	0.00215820	+	0.00124604i
$768$	14522.1	−	20118.2i	0.682318	−	0.945253i
$769$	−11845.6	−	20517.2i	−0.555479	−	0.962118i	−0.997866	−	0.0652939i	$-0.979202\pi$
$769$	−11845.6	−	20517.2i	−0.555479	−	0.962118i	0.442387	−	0.896824i	$-0.354132\pi$
$770$	−22903.7	−	6137.04i	−1.07194	−	0.287225i
$771$	−360.083	−	259.921i	−0.0168198	−	0.0121411i
$772$	5493.33	−	1471.93i	0.256100	−	0.0686218i
$773$		−	9728.89i		−	0.452683i	−0.974048	−	0.226342i	$-0.927323\pi$
$773$		−	9728.89i		−	0.452683i	0.974048	−	0.226342i	$-0.0726765\pi$
$774$	19701.8	+	4060.77i	0.914942	+	0.188581i
$775$	−10551.1	−	10551.1i	−0.489040	−	0.489040i
$776$	−2472.81	+	662.588i	−0.114393	+	0.0306514i
$777$	7021.95	+	716.127i	0.324210	+	0.0330643i
$778$	3091.80	+	5355.16i	0.142476	+	0.246776i
$779$	−7099.75	−	1902.37i	−0.326540	−	0.0874962i
$780$	−2913.13	−	1107.94i	−0.133727	−	0.0508598i
$781$	−6923.51	+	11991.9i	−0.317212	+	0.549427i
$782$	−39052.6	−	28688.2i	−1.78583	−	1.31188i
$783$	−1434.33	+	33259.6i	−0.0654648	+	1.51801i
$784$		−	10852.9i		−	0.494392i
$785$	9175.54	+	34243.6i	0.417184	+	1.55695i
$786$	−12034.9	+	31643.6i	−0.546146	+	1.43599i
$787$	37430.7	+	10029.5i	1.69538	+	0.454275i	0.971768	−	0.235936i	$-0.0758157\pi$
$787$	37430.7	+	10029.5i	1.69538	+	0.454275i	0.723608	+	0.690211i	$0.242482\pi$
$788$	2515.05	−	9386.30i	0.113699	−	0.424331i
$789$	2642.43	−	25910.2i	0.119231	−	1.16911i
$790$	−28126.5	−	16238.8i	−1.26670	−	0.731331i
$791$			23345.7i			1.04940i
$792$	1479.79	+	742.521i	0.0663917	+	0.0333135i
$793$	−793.962	−	793.962i	−0.0355541	−	0.0355541i
$794$	7515.15	+	28046.9i	0.335898	+	1.25359i
$795$	−48658.7	+	7860.83i	−2.17075	+	0.350686i
$796$	12666.6	+	3394.01i	0.564016	+	0.151128i
$797$	−15598.5	+	9005.78i	−0.693257	+	0.400252i	−0.804831	−	0.593504i	$-0.797744\pi$
$797$	−15598.5	+	9005.78i	−0.693257	+	0.400252i	0.111574	+	0.993756i	$0.464411\pi$
$798$	−54830.6	+	8857.91i	−2.43231	+	0.392941i
$799$	−1404.27	−	547.535i	−0.0621773	−	0.0242433i
$800$	−14281.2			−0.631146
$801$	−21842.4	+	24561.7i	−0.963498	+	1.08345i
$802$	18014.5	−	18014.5i	0.793158	−	0.793158i
$803$	5605.30	−	9708.66i	0.246335	−	0.426664i
$804$	−18879.0	−	1925.35i	−0.828121	−	0.0844552i
$805$	−13848.4	+	51682.9i	−0.606326	+	2.26284i
$806$	1603.46	−	5984.18i	0.0700736	−	0.261518i
$807$	21380.9	+	8131.74i	0.932646	+	0.354710i
$808$	−4293.77	−	2479.01i	−0.186949	−	0.107935i
$809$	−18427.0	−	18427.0i	−0.800814	−	0.800814i	0.182408	−	0.983223i	$-0.441611\pi$
$809$	−18427.0	−	18427.0i	−0.800814	−	0.800814i	−0.983223	+	0.182408i	$0.941611\pi$
$810$	23824.1	−	30174.6i	1.03345	−	1.30892i
$811$	−6143.44	+	6143.44i	−0.265999	+	0.265999i	−0.827486	−	0.561487i	$-0.810230\pi$
$811$	−6143.44	+	6143.44i	−0.265999	+	0.265999i	0.561487	+	0.827486i	$0.310230\pi$
$812$	19130.1	−	33134.3i	0.826767	−	1.43200i
$813$	16183.2	+	36048.1i	0.698116	+	1.55506i
$814$	4136.36	−	2388.13i	0.178107	−	0.102830i
$815$	−3813.51	−	6605.18i	−0.163903	−	0.283889i
$816$	1272.46	+	25330.7i	0.0545894	+	1.08671i
$817$	11714.0	−	20289.3i	0.501617	−	0.868826i
$818$		−	17023.8i		−	0.727655i
$819$	3700.01	−	216.824i	0.157862	−	0.00925085i
$820$	−5847.36			−0.249023
$821$	−10688.7	−	39890.6i	−0.454369	−	1.69573i	−0.689936	−	0.723870i	$-0.742362\pi$
$821$	−10688.7	−	39890.6i	−0.454369	−	1.69573i	0.235567	−	0.971858i	$-0.424305\pi$
$822$	16964.3	+	12245.5i	0.719829	+	0.519599i
$823$	9412.09	−	35126.4i	0.398645	−	1.48776i	−0.416837	−	0.908981i	$-0.636861\pi$
$823$	9412.09	−	35126.4i	0.398645	−	1.48776i	0.815482	−	0.578782i	$-0.196472\pi$
$824$	3888.96	−	2245.29i	0.164415	−	0.0949253i
$825$	−963.376	−	5963.31i	−0.0406551	−	0.251656i
$826$	724.902	−	194.237i	0.0305358	−	0.00818204i
$827$	−3357.58	−	3357.58i	−0.141178	−	0.141178i	0.632985	−	0.774164i	$-0.281829\pi$
$827$	−3357.58	−	3357.58i	−0.141178	−	0.141178i	−0.774164	+	0.632985i	$0.781829\pi$
$828$	−15491.2	+	30873.0i	−0.650191	+	1.29579i
$829$	−16581.2			−0.694680			−0.347340	−	0.937739i	$-0.612915\pi$
$829$	−16581.2			−0.694680			−0.347340	+	0.937739i	$0.612915\pi$
$830$	−9828.01	−	36678.6i	−0.411006	−	1.53390i
$831$	−12125.9	+	9881.47i	−0.506187	+	0.412496i
$832$	−1252.74	−	2169.81i	−0.0522006	−	0.0904140i
$833$	6829.95	+	8525.51i	0.284086	+	0.354612i
$834$	−7584.95	+	19943.3i	−0.314923	+	0.828033i
$835$	−14700.8	−	8487.54i	−0.609274	−	0.351764i
$836$	−12606.1	+	12606.1i	−0.521522	+	0.521522i
$837$	30583.6	+	19460.9i	1.26299	+	0.803666i
$838$	5411.95	−	5411.95i	0.223094	−	0.223094i
$839$	−5240.55	+	1404.20i	−0.215642	+	0.0577811i	−0.365023	−	0.930999i	$-0.618939\pi$
$839$	−5240.55	+	1404.20i	−0.215642	+	0.0577811i	0.149381	+	0.988780i	$0.452272\pi$
$840$	4359.86	−	1957.28i	0.179083	−	0.0803960i
$841$	−27640.3	+	15958.1i	−1.13331	+	0.654317i
$842$	−1156.03	+	667.433i	−0.0473152	+	0.0273174i
$843$	−2499.14	+	24505.2i	−0.102106	+	1.00119i
$844$	−870.484	+	233.245i	−0.0355015	+	0.00951260i
$845$	−20640.1	+	20640.1i	−0.840283	+	0.840283i
$846$	−457.234	+	2218.38i	−0.0185816	+	0.0901528i
$847$	−14620.8	+	14620.8i	−0.593123	+	0.593123i
$848$	−42317.0	−	24431.8i	−1.71365	−	0.989375i
$849$	33907.2	−	5477.72i	1.37066	−	0.221431i
$850$	12324.1	−	9873.09i	0.497310	−	0.398405i
$851$	−5388.88	−	9333.82i	−0.217072	−	0.375980i
$852$	4115.15	+	25472.8i	0.165473	+	1.02428i
$853$	−3397.07	−	12678.0i	−0.136358	−	0.508896i	−0.999989	−	0.00477015i	$-0.998482\pi$
$853$	−3397.07	−	12678.0i	−0.136358	−	0.508896i	0.863630	−	0.504125i	$-0.168185\pi$
$854$	−15918.3			−0.637836
$855$	−24618.2	−	37401.2i	−0.984708	−	1.49601i
$856$	2687.92	+	2687.92i	0.107326	+	0.107326i
$857$	−23157.2	+	6204.94i	−0.923026	+	0.247324i	−0.688878	−	0.724877i	$-0.741897\pi$
$857$	−23157.2	+	6204.94i	−0.923026	+	0.247324i	−0.234148	+	0.972201i	$0.575230\pi$
$858$	1944.21	−	1584.36i	0.0773594	−	0.0630408i
$859$	−3854.52	+	2225.41i	−0.153102	+	0.0883934i	−0.574594	−	0.818439i	$-0.694840\pi$
$859$	−3854.52	+	2225.41i	−0.153102	+	0.0883934i	0.421492	+	0.906832i	$0.361507\pi$
$860$	4823.83	−	18002.8i	0.191269	−	0.713825i
$861$	6343.68	−	2847.89i	0.251094	−	0.112724i
$862$	1297.25	+	4841.40i	0.0512581	+	0.191298i
$863$	−31793.2			−1.25406			−0.627029	−	0.778996i	$-0.715729\pi$
$863$	−31793.2			−1.25406			−0.627029	+	0.778996i	$0.715729\pi$
$864$	33868.4	−	7527.43i	1.33359	−	0.296399i
$865$			41872.0i			1.64588i
$866$	16234.6	−	28119.1i	0.637036	−	1.10338i
$867$	−16940.7	−	19097.8i	−0.663595	−	0.748092i
$868$	−20830.9	−	36080.2i	−0.814571	−	1.41088i
$869$	10736.1	−	6198.48i	0.419099	−	0.241967i
$870$	64689.4	+	6597.29i	2.52089	+	0.257091i
$871$	1554.62	−	2692.68i	0.0604779	−	0.104751i
$872$	−2393.37	+	2393.37i	−0.0929468	+	0.0929468i
$873$	−20281.5	−	10176.7i	−0.786284	−	0.394536i
$874$	59969.0	+	59969.0i	2.32092	+	2.32092i
$875$	17584.9	+	10152.7i	0.679405	+	0.392255i
$876$	−3331.64	−	20622.9i	−0.128500	−	0.795415i
$877$	2631.16	−	9819.61i	0.101309	−	0.378090i	−0.896591	−	0.442859i	$-0.853964\pi$
$877$	2631.16	−	9819.61i	0.101309	−	0.378090i	0.997900	+	0.0647690i	$0.0206310\pi$
$878$	5246.48	−	19580.1i	0.201663	−	0.752616i
$879$	12230.1	−	16943.0i	0.469296	−	0.650142i
$880$	9475.26	−	16411.6i	0.362967	−	0.628677i
$881$	33771.6	−	33771.6i	1.29148	−	1.29148i	0.357611	−	0.933871i	$-0.383591\pi$
$881$	33771.6	−	33771.6i	1.29148	−	1.29148i	0.933871	−	0.357611i	$-0.116409\pi$
$882$	10908.9	−	12267.0i	0.416464	−	0.468312i
$883$	15299.3			0.583085			0.291542	−	0.956558i	$-0.405832\pi$
$883$	15299.3			0.583085			0.291542	+	0.956558i	$0.405832\pi$
$884$	2897.54	+	1129.77i	0.110243	+	0.0429844i
$885$	382.196	+	469.005i	0.0145168	+	0.0178141i
$886$	11327.5	−	6539.95i	0.429521	−	0.247984i
$887$	4684.48	+	1255.20i	0.177327	+	0.0475147i	0.346390	−	0.938091i	$-0.387407\pi$
$887$	4684.48	+	1255.20i	0.177327	+	0.0475147i	−0.169063	+	0.985605i	$0.554074\pi$
$888$	−342.206	+	899.768i	−0.0129321	+	0.0340025i
$889$	−6288.07	−	23467.4i	−0.237227	−	0.885344i
$890$	45397.3	+	45397.3i	1.70980	+	1.70980i
$891$	5427.86	+	13634.4i	0.204086	+	0.512649i
$892$		−	9160.04i		−	0.343835i
$893$	2284.52	+	1318.97i	0.0856088	+	0.0494263i
$894$	−5608.14	+	2517.68i	−0.209803	+	0.0941877i
$895$	598.869	−	2235.01i	0.0223665	−	0.0834728i
$896$	8371.67	+	2243.18i	0.312140	+	0.0836378i
$897$	−3575.15	−	4387.18i	−0.133078	−	0.163304i
$898$	14081.5	+	52552.9i	0.523280	+	1.95291i
$899$			61311.3i			2.27458i
$900$	−8411.44	−	7480.18i	−0.311535	−	0.277044i
$901$	48617.6	−	7438.58i	1.79766	−	0.275045i
$902$	2352.68	−	4074.97i	0.0868468	−	0.150423i
$903$	3534.77	+	21880.3i	0.130265	+	0.806345i
$904$	−3075.48	−	824.072i	−0.113151	−	0.0303188i
$905$	3649.42	+	6320.98i	0.134045	+	0.232173i
$906$	−9150.64	+	12676.9i	−0.335551	+	0.464858i
$907$	21496.4	−	5759.95i	0.786964	−	0.210866i	0.157111	−	0.987581i	$-0.449782\pi$
$907$	21496.4	−	5759.95i	0.786964	−	0.210866i	0.629853	+	0.776714i	$0.283115\pi$
$908$	7628.68	+	7628.68i	0.278818	+	0.278818i
$909$	−13838.0	−	41711.1i	−0.504927	−	1.52197i
$910$		−	7239.48i		−	0.263721i
$911$	−25307.4	+	6781.10i	−0.920386	+	0.246617i	−0.687750	−	0.725947i	$-0.741402\pi$
$911$	−25307.4	+	6781.10i	−0.920386	+	0.246617i	−0.232636	+	0.972564i	$0.574735\pi$
$912$	4503.62	−	44160.1i	0.163520	−	1.60338i
$913$	14000.5	+	3751.43i	0.507502	+	0.135985i
$914$	12767.1	+	22113.2i	0.462033	+	0.800264i
$915$	−5255.78	−	11707.3i	−0.189892	−	0.422984i
$916$	−21137.4	−	12203.7i	−0.762444	−	0.440198i
$917$	−37301.8			−1.34331
$918$	−24023.1	+	29910.3i	−0.863705	+	1.07537i
$919$	−20334.3			−0.729887			−0.364943	−	0.931030i	$-0.618912\pi$
$919$	−20334.3			−0.729887			−0.364943	+	0.931030i	$0.618912\pi$
$920$	−6319.69	−	3648.68i	−0.226472	−	0.130754i
$921$	−9318.76	−	20757.6i	−0.333403	−	0.742656i
$922$	−22854.3	−	39584.9i	−0.816342	−	1.41395i
$923$	−4083.62	−	1094.20i	−0.145627	−	0.0390207i
$924$	1711.17	−	16778.8i	0.0609237	−	0.597385i
$925$	3392.56	−	909.034i	0.120591	−	0.0323123i
$926$		−	34208.5i		−	1.21400i
$927$	38983.9	+	8035.04i	1.38123	+	0.284688i
$928$	41493.3	+	41493.3i	1.46776	+	1.46776i
$929$	18309.1	−	4905.92i	0.646613	−	0.173259i	0.0794159	−	0.996842i	$-0.474694\pi$
$929$	18309.1	−	4905.92i	0.646613	−	0.173259i	0.567197	+	0.823582i	$0.308028\pi$
$930$	41441.8	−	57411.6i	1.46122	−	2.02430i
$931$	−9559.42	−	16557.4i	−0.336517	−	0.582864i
$932$	−14464.6	−	3875.77i	−0.508372	−	0.136218i
$933$	5532.56	+	34246.6i	0.194135	+	1.20170i
$934$	31079.6	−	53831.5i	1.08882	−	1.88589i
$935$	2884.87	+	18855.2i	0.100904	+	0.659497i
$936$	−102.042	+	495.080i	−0.00356340	+	0.0172887i
$937$			42936.6i			1.49699i	0.663141	+	0.748495i	$0.269223\pi$
$937$			42936.6i			1.49699i	−0.663141	+	0.748495i	$0.730777\pi$
$938$	−11408.6	−	42577.4i	−0.397125	−	1.48209i
$939$	3899.53	+	4785.24i	0.135523	+	0.166305i
$940$	2027.07	+	543.152i	0.0703360	+	0.0188465i
$941$	−8716.45	+	32530.2i	−0.301964	+	1.12695i	0.633563	+	0.773691i	$0.281592\pi$
$941$	−8716.45	+	32530.2i	−0.301964	+	1.12695i	−0.935527	+	0.353254i	$0.885075\pi$
$942$	−48497.1	+	21771.9i	−1.67741	+	0.753045i
$943$	−9195.29	−	5308.90i	−0.317540	−	0.183332i
$944$			599.783i			0.0206793i
$945$	40406.5	+	12716.4i	1.39092	+	0.437739i
$946$	10605.1	+	10605.1i	0.364484	+	0.364484i
$947$	−6727.89	−	25108.8i	−0.230863	−	0.861592i	−0.979970	−	0.199143i	$-0.936184\pi$
$947$	−6727.89	−	25108.8i	−0.230863	−	0.861592i	0.749108	−	0.662448i	$-0.230483\pi$
$948$	8212.04	−	21592.1i	0.281345	−	0.739745i
$949$	3306.11	+	885.869i	0.113088	+	0.0303019i
$950$	−23934.7	+	13818.7i	−0.817414	+	0.471934i
$951$	−16571.1	−	20334.9i	−0.565042	−	0.693381i
$952$	−4366.61	+	1916.71i	−0.148658	+	0.0652530i
$953$	22125.1			0.752049			0.376025	−	0.926610i	$-0.377291\pi$
$953$	22125.1			0.752049			0.376025	+	0.926610i	$0.377291\pi$
$954$	−23273.1	−	70150.5i	−0.789826	−	2.38072i
$955$	22350.8	−	22350.8i	0.757334	−	0.757334i
$956$	−19705.8	+	34131.5i	−0.666665	+	1.15470i
$957$	−14527.1	+	20125.1i	−0.490693	+	0.679784i
$958$	10173.3	−	37967.4i	0.343096	−	1.28045i
$959$	−5966.40	+	22266.9i	−0.200902	+	0.749776i
$960$	−4566.83	−	28268.7i	−0.153535	−	0.950385i
$961$	32018.2	+	18485.7i	1.07476	+	0.620513i
$962$	1031.14	+	1031.14i	0.0345585	+	0.0345585i
$963$	1971.09	+	33635.9i	0.0659581	+	1.12555i
$964$	−21623.9	+	21623.9i	−0.722468	+	0.722468i
$965$	−5324.78	+	9222.79i	−0.177628	+	0.307660i
$966$	−79819.0	−	8140.27i	−2.65852	−	0.271127i
$967$	−19210.5	+	11091.2i	−0.638850	+	0.368840i	−0.784172	−	0.620544i	$-0.786912\pi$
$967$	−19210.5	+	11091.2i	−0.638850	+	0.368840i	0.145321	+	0.989385i	$0.453578\pi$
$968$	−1409.99	−	2442.18i	−0.0468170	−	0.0810895i
$969$	24253.0	+	37524.2i	0.804045	+	1.24402i
$970$	−22161.2	+	38384.4i	−0.733561	+	1.27056i
$971$			32841.6i			1.08542i	0.839922	+	0.542708i	$0.182601\pi$
$971$			32841.6i			1.08542i	−0.839922	+	0.542708i	$0.817399\pi$
$972$	23890.7	+	13305.9i	0.788370	+	0.439083i
$973$	−23509.3			−0.774588
$974$	−7996.14	−	29842.0i	−0.263052	−	0.981725i
$975$	1682.51	−	755.334i	0.0552651	−	0.0248103i
$976$	3292.69	−	12288.5i	0.107988	−	0.403018i
$977$	14533.8	−	8391.12i	0.475925	−	0.274775i	−0.242792	−	0.970078i	$-0.578063\pi$
$977$	14533.8	−	8391.12i	0.475925	−	0.274775i	0.718717	+	0.695303i	$0.244730\pi$
$978$	8865.79	−	7224.81i	0.289874	−	0.236221i
$979$	−23671.2	+	6342.67i	−0.772761	+	0.207061i
$980$	−10754.9	−	10754.9i	−0.350564	−	0.350564i
$981$	−29950.0	+	1755.10i	−0.974750	+	0.0571212i
$982$	−24045.7			−0.781395
$983$	773.141	+	2885.40i	0.0250858	+	0.0936216i	0.977334	−	0.211704i	$-0.0679013\pi$
$983$	773.141	+	2885.40i	0.0250858	+	0.0936216i	−0.952248	+	0.305326i	$0.901235\pi$
$984$	151.247	+	936.221i	0.00489998	+	0.0303309i
$985$	9098.30	+	15758.7i	0.294311	+	0.509761i
$986$	−64492.9	−	7121.34i	−2.08303	−	0.230010i
$987$	−2463.67	+	398.007i	−0.0794523	+	0.0128356i
$988$	−4713.82	−	2721.52i	−0.151788	−	0.0876348i
$989$	23930.7	−	23930.7i	0.769417	−	0.769417i
$990$	27206.2	−	9025.90i	0.873402	−	0.289759i
$991$	4851.50	−	4851.50i	0.155513	−	0.155513i	−0.625062	−	0.780575i	$-0.714926\pi$
$991$	4851.50	−	4851.50i	0.155513	−	0.155513i	0.780575	+	0.625062i	$0.214926\pi$
$992$	61720.3	−	16537.9i	1.97543	−	0.529314i
$993$	−2952.61	+	28951.7i	−0.0943588	+	0.925231i
$994$	−51905.5	+	29967.6i	−1.65628	+	0.956253i
$995$	−21266.1	+	12278.0i	−0.677568	+	0.391194i
$996$	24640.3	−	11061.9i	0.783894	−	0.351916i
$997$	14575.0	−	3905.36i	0.462984	−	0.124056i	−0.0197843	−	0.999804i	$-0.506298\pi$
$997$	14575.0	−	3905.36i	0.462984	−	0.124056i	0.482768	+	0.875748i	$0.339631\pi$
$998$	−36186.5	+	36186.5i	−1.14776	+	1.14776i
$999$	−7566.44	+	3943.98i	−0.239631	+	0.124907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.n.a.106.11	yes	208
9.4	even	3	inner	153.4.n.a.4.42	✓	208
17.13	even	4	inner	153.4.n.a.115.42	yes	208
153.13	even	12	inner	153.4.n.a.13.11	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.n.a.4.42	✓	208	9.4	even	3	inner
153.4.n.a.13.11	yes	208	153.13	even	12	inner
153.4.n.a.106.11	yes	208	1.1	even	1	trivial
153.4.n.a.115.42	yes	208	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.37852 - 1.95059i) q^{2} +(2.12811 + 4.74037i) q^{3} +(3.60959 + 6.25199i) q^{4} +(-13.0578 - 3.49884i) q^{5} +(2.05666 - 20.1665i) q^{6} +(21.5739 - 5.78071i) q^{7} +3.04612i q^{8} +(-17.9423 + 20.1761i) q^{9} +(37.2914 + 37.2914i) q^{10} +(-19.4446 + 5.21015i) q^{11} +(-21.9552 + 30.4157i) q^{12} +(-3.07305 - 5.32267i) q^{13} +(-84.1636 - 22.5516i) q^{14} +(-11.2027 - 69.3450i) q^{15} +(34.8184 - 60.3073i) q^{16} +(10.6010 + 69.2865i) q^{17} +(99.9736 - 33.1672i) q^{18} -122.675i q^{19} +(-25.2587 - 94.2669i) q^{20} +(73.3143 + 89.9664i) q^{21} +(75.8566 + 20.3257i) q^{22} +(45.8656 - 171.173i) q^{23} +(-14.4397 + 6.48248i) q^{24} +(50.0123 + 28.8746i) q^{25} +23.9770i q^{26} +(-133.825 - 42.1163i) q^{27} +(114.014 + 114.014i) q^{28} +(-61.4145 - 229.202i) q^{29} +(-97.4149 + 256.135i) q^{30} +(-249.580 - 66.8748i) q^{31} +(-214.165 + 123.648i) q^{32} +(-66.0782 - 81.0867i) q^{33} +(99.3339 - 254.764i) q^{34} -301.934 q^{35} +(-190.905 - 39.3478i) q^{36} +(43.0054 - 43.0054i) q^{37} +(-239.288 + 414.459i) q^{38} +(18.6917 - 25.8946i) q^{39} +(10.6579 - 39.7758i) q^{40} +(15.5074 - 57.8746i) q^{41} +(-72.2065 - 446.959i) q^{42} +(165.391 + 95.4883i) q^{43} +(-102.761 - 102.761i) q^{44} +(304.881 - 200.679i) q^{45} +(-488.845 + 488.845i) q^{46} +(-10.7518 + 18.6226i) q^{47} +(359.977 + 36.7119i) q^{48} +(134.970 - 77.9249i) q^{49} +(-112.645 - 195.107i) q^{50} +(-305.884 + 197.702i) q^{51} +(22.1849 - 38.4253i) q^{52} -701.690i q^{53} +(369.980 + 403.329i) q^{54} +272.133 q^{55} +(17.6087 + 65.7167i) q^{56} +(581.524 - 261.065i) q^{57} +(-239.589 + 894.157i) q^{58} +(-7.45908 + 4.30650i) q^{59} +(393.107 - 320.346i) q^{60} +(176.465 - 47.2837i) q^{61} +(712.765 + 712.765i) q^{62} +(-270.453 + 538.996i) q^{63} +407.654 q^{64} +(21.5042 + 80.2547i) q^{65} +(65.0797 + 402.844i) q^{66} +(252.944 + 438.113i) q^{67} +(-394.914 + 316.373i) q^{68} +(909.030 - 146.854i) q^{69} +(1020.09 + 588.950i) q^{70} +(486.393 - 486.393i) q^{71} +(-61.4587 - 54.6544i) q^{72} +(-393.785 + 393.785i) q^{73} +(-229.180 + 61.4087i) q^{74} +(-30.4448 + 298.525i) q^{75} +(766.962 - 442.806i) q^{76} +(-389.376 + 224.807i) q^{77} +(-113.660 + 51.0257i) q^{78} +(-594.846 + 159.389i) q^{79} +(-665.659 + 665.659i) q^{80} +(-85.1477 - 724.010i) q^{81} +(-165.282 + 165.282i) q^{82} +(-623.558 - 360.011i) q^{83} +(-297.834 + 783.102i) q^{84} +(103.997 - 941.823i) q^{85} +(-372.517 - 645.218i) q^{86} +(955.806 - 778.894i) q^{87} +(-15.8707 - 59.2304i) q^{88} +1217.37 q^{89} +(-1421.49 + 83.3004i) q^{90} +(-97.0664 - 97.0664i) q^{91} +(1235.73 - 331.112i) q^{92} +(-214.122 - 1325.42i) q^{93} +(72.6501 - 41.9445i) q^{94} +(-429.219 + 1601.87i) q^{95} +(-1041.91 - 752.087i) q^{96} +(217.519 + 811.791i) q^{97} -607.997 q^{98} +(243.760 - 485.797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) \) 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

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