LMFDB - Embedded newform 184.4.j.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [184,4,Mod(11,184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("184.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(184, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 11, 9])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	184.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.8563514411$
Analytic rank:	$0$
Dimension:	$700$
Relative dimension:	$70$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	184.11
Dual form			184.4.j.a.67.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.80324 - 0.376587i) q^{2} +(-1.42464 + 9.90857i) q^{3} +(7.71636 + 2.11133i) q^{4} +(9.08722 - 2.66825i) q^{5} +(7.72505 - 27.2397i) q^{6} +(-2.69152 - 3.10618i) q^{7} +(-20.8358 - 8.82446i) q^{8} +(-70.2439 - 20.6255i) q^{9} +(-26.4785 + 4.05763i) q^{10} +(11.8151 - 18.3847i) q^{11} +(-31.9133 + 73.4503i) q^{12} +(-36.8163 - 31.9015i) q^{13} +(6.37525 + 9.72098i) q^{14} +(13.4925 + 93.8426i) q^{15} +(55.0846 + 32.5836i) q^{16} +(-60.4995 + 27.6292i) q^{17} +(189.144 + 84.2712i) q^{18} +(-74.6133 - 34.0747i) q^{19} +(75.7538 - 1.40305i) q^{20} +(34.6123 - 22.2440i) q^{21} +(-40.0442 + 47.0875i) q^{22} +(-51.2782 - 97.6604i) q^{23} +(117.121 - 193.881i) q^{24} +(-29.6987 + 19.0862i) q^{25} +(91.1913 + 103.292i) q^{26} +(192.162 - 420.775i) q^{27} +(-14.2106 - 29.6511i) q^{28} +(-71.3012 + 32.5622i) q^{29} +(-2.48297 - 268.145i) q^{30} +(163.278 - 23.4759i) q^{31} +(-142.145 - 112.084i) q^{32} +(165.334 + 143.263i) q^{33} +(180.000 - 54.6681i) q^{34} +(-32.7465 - 21.0449i) q^{35} +(-498.480 - 307.462i) q^{36} +(-327.634 - 96.2020i) q^{37} +(196.327 + 123.618i) q^{38} +(368.548 - 319.348i) q^{39} +(-212.885 - 24.5948i) q^{40} +(-66.6636 + 19.5742i) q^{41} +(-105.403 + 49.3207i) q^{42} +(87.0624 + 12.5177i) q^{43} +(129.986 - 116.918i) q^{44} -693.355 q^{45} +(106.968 + 293.077i) q^{46} +498.217i q^{47} +(-401.332 + 499.390i) q^{48} +(46.4099 - 322.788i) q^{49} +(90.4404 - 42.3191i) q^{50} +(-187.576 - 638.825i) q^{51} +(-216.733 - 323.895i) q^{52} +(388.886 + 448.798i) q^{53} +(-697.135 + 1107.17i) q^{54} +(58.3118 - 198.592i) q^{55} +(28.6695 + 88.4709i) q^{56} +(443.929 - 690.767i) q^{57} +(212.137 - 64.4286i) q^{58} +(157.739 - 182.041i) q^{59} +(-94.0195 + 752.611i) q^{60} +(-67.5010 - 469.480i) q^{61} +(-466.549 + 4.32016i) q^{62} +(124.997 + 273.704i) q^{63} +(356.258 + 367.729i) q^{64} +(-419.678 - 191.661i) q^{65} +(-409.521 - 463.863i) q^{66} +(-41.1278 - 63.9961i) q^{67} +(-525.171 + 85.4625i) q^{68} +(1040.73 - 368.963i) q^{69} +(83.8713 + 71.3259i) q^{70} +(320.267 + 498.345i) q^{71} +(1281.58 + 1049.61i) q^{72} +(-324.253 + 710.015i) q^{73} +(882.210 + 393.060i) q^{74} +(-146.807 - 321.463i) q^{75} +(-503.800 - 420.467i) q^{76} +(-88.9070 + 12.7829i) q^{77} +(-1153.39 + 756.422i) q^{78} +(337.803 - 389.845i) q^{79} +(587.507 + 149.115i) q^{80} +(2232.65 + 1434.84i) q^{81} +(194.246 - 29.7667i) q^{82} +(-209.131 + 712.235i) q^{83} +(314.045 - 98.5645i) q^{84} +(-476.051 + 412.500i) q^{85} +(-239.343 - 67.8767i) q^{86} +(-221.066 - 752.882i) q^{87} +(-408.413 + 278.797i) q^{88} +(-1434.56 - 206.259i) q^{89} +(1943.65 + 261.109i) q^{90} +200.221i q^{91} +(-189.488 - 861.848i) q^{92} +1651.30i q^{93} +(187.622 - 1396.63i) q^{94} +(-768.947 - 110.558i) q^{95} +(1313.10 - 1248.77i) q^{96} +(-267.028 - 909.414i) q^{97} +(-251.656 + 887.377i) q^{98} +(-1209.14 + 1047.72i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) $ 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−2.80324	−	0.376587i	−0.991097	−	0.133144i
$2$	−2.80324	−	0.376587i	−0.991097	−	0.133144i
$3$	−1.42464	+	9.90857i	−0.274172	+	1.90691i	0.128760	+	0.991676i	$0.458900\pi$
$3$	−1.42464	+	9.90857i	−0.274172	+	1.90691i	−0.402932	+	0.915230i	$0.632009\pi$
$4$	7.71636	+	2.11133i	0.964546	+	0.263916i
$5$	9.08722	−	2.66825i	0.812786	−	0.238655i	0.151179	−	0.988506i	$-0.451693\pi$
$5$	9.08722	−	2.66825i	0.812786	−	0.238655i	0.661607	+	0.749851i	$0.269875\pi$
$6$	7.72505	−	27.2397i	0.525623	−	1.85342i
$7$	−2.69152	−	3.10618i	−0.145329	−	0.167718i	0.678418	−	0.734676i	$-0.262666\pi$
$7$	−2.69152	−	3.10618i	−0.145329	−	0.167718i	−0.823747	+	0.566958i	$0.808120\pi$
$8$	−20.8358	−	8.82446i	−0.920819	−	0.389990i
$9$	−70.2439	−	20.6255i	−2.60163	−	0.763906i
$10$	−26.4785	+	4.05763i	−0.837325	+	0.128313i
$11$	11.8151	−	18.3847i	0.323855	−	0.503927i	−0.640707	−	0.767785i	$-0.721359\pi$
$11$	11.8151	−	18.3847i	0.323855	−	0.503927i	0.964562	+	0.263858i	$0.0849950\pi$
$12$	−31.9133	+	73.4503i	−0.767715	+	1.76694i
$13$	−36.8163	−	31.9015i	−0.785461	−	0.680606i	0.166766	−	0.985996i	$-0.446667\pi$
$13$	−36.8163	−	31.9015i	−0.785461	−	0.680606i	−0.952227	+	0.305391i	$0.901213\pi$
$14$	6.37525	+	9.72098i	0.121704	+	0.185574i
$15$	13.4925	+	93.8426i	0.232251	+	1.61534i
$16$	55.0846	+	32.5836i	0.860696	+	0.509119i
$17$	−60.4995	+	27.6292i	−0.863135	+	0.394180i	−0.797252	−	0.603647i	$-0.793714\pi$
$17$	−60.4995	+	27.6292i	−0.863135	+	0.394180i	−0.0658829	+	0.997827i	$0.520986\pi$
$18$	189.144	+	84.2712i	2.47675	+	1.10349i
$19$	−74.6133	−	34.0747i	−0.900919	−	0.411436i	−0.0895583	−	0.995982i	$-0.528546\pi$
$19$	−74.6133	−	34.0747i	−0.900919	−	0.411436i	−0.811361	+	0.584546i	$0.801273\pi$
$20$	75.7538	−	1.40305i	0.846954	−	0.0156866i
$21$	34.6123	−	22.2440i	0.359667	−	0.231144i
$22$	−40.0442	+	47.0875i	−0.388066	+	0.456322i
$23$	−51.2782	−	97.6604i	−0.464880	−	0.885374i
$23$	−51.2782	−	97.6604i	−0.464880	−	0.885374i
$24$	117.121	−	193.881i	0.996136	−	1.64899i
$25$	−29.6987	+	19.0862i	−0.237590	+	0.152690i
$26$	91.1913	+	103.292i	0.687849	+	0.779125i
$27$	192.162	−	420.775i	1.36969	−	2.99919i
$28$	−14.2106	−	29.6511i	−0.0959125	−	0.200126i
$29$	−71.3012	+	32.5622i	−0.456562	+	0.208505i	−0.630402	−	0.776269i	$-0.717110\pi$
$29$	−71.3012	+	32.5622i	−0.456562	+	0.208505i	0.173840	+	0.984774i	$0.444383\pi$
$30$	−2.48297	−	268.145i	−0.0151109	−	1.63188i
$31$	163.278	−	23.4759i	0.945988	−	0.136012i	0.347979	−	0.937502i	$-0.386868\pi$
$31$	163.278	−	23.4759i	0.945988	−	0.136012i	0.598008	+	0.801490i	$0.295959\pi$
$32$	−142.145	−	112.084i	−0.785247	−	0.619182i
$33$	165.334	+	143.263i	0.872150	+	0.755723i
$34$	180.000	−	54.6681i	0.907933	−	0.275750i
$35$	−32.7465	−	21.0449i	−0.158148	−	0.101635i
$36$	−498.480	−	307.462i	−2.30778	−	1.42343i
$37$	−327.634	−	96.2020i	−1.45575	−	0.427446i	−0.544310	−	0.838884i	$-0.683209\pi$
$37$	−327.634	−	96.2020i	−1.45575	−	0.427446i	−0.911438	+	0.411438i	$0.865027\pi$
$38$	196.327	+	123.618i	0.838118	+	0.527724i
$39$	368.548	−	319.348i	1.51320	−	1.31120i
$40$	−212.885	−	24.5948i	−0.841502	−	0.0972195i
$41$	−66.6636	+	19.5742i	−0.253930	+	0.0745604i	−0.406220	−	0.913775i	$-0.633153\pi$
$41$	−66.6636	+	19.5742i	−0.253930	+	0.0745604i	0.152290	+	0.988336i	$0.451335\pi$
$42$	−105.403	+	49.3207i	−0.387241	+	0.181199i
$43$	87.0624	+	12.5177i	0.308765	+	0.0443937i	0.294956	−	0.955511i	$-0.404695\pi$
$43$	87.0624	+	12.5177i	0.308765	+	0.0443937i	0.0138093	+	0.999905i	$0.495604\pi$
$44$	129.986	−	116.918i	0.445367	−	0.400591i
$45$	−693.355			−2.29687
$46$	106.968	+	293.077i	0.342859	+	0.939387i
$47$			498.217i			1.54622i	0.634270	+	0.773112i	$0.281301\pi$
$47$			498.217i			1.54622i	−0.634270	+	0.773112i	$0.718699\pi$
$48$	−401.332	+	499.390i	−1.20682	+	1.50168i
$49$	46.4099	−	322.788i	0.135306	−	0.941073i
$50$	90.4404	−	42.3191i	0.255804	−	0.119697i
$51$	−187.576	−	638.825i	−0.515018	−	1.75399i
$52$	−216.733	−	323.895i	−0.577990	−	0.863771i
$53$	388.886	+	448.798i	1.00788	+	1.16315i	0.986563	+	0.163382i	$0.0522404\pi$
$53$	388.886	+	448.798i	1.00788	+	1.16315i	0.0213167	+	0.999773i	$0.493214\pi$
$54$	−697.135	+	1107.17i	−1.75681	+	2.79013i
$55$	58.3118	−	198.592i	0.142959	−	0.486875i
$56$	28.6695	+	88.4709i	0.0684130	+	0.211115i
$57$	443.929	−	690.767i	1.03158	−	1.60516i
$58$	212.137	−	64.4286i	0.480258	−	0.145860i
$59$	157.739	−	182.041i	0.348066	−	0.401690i	−0.554540	−	0.832157i	$-0.687106\pi$
$59$	157.739	−	182.041i	0.348066	−	0.401690i	0.902606	+	0.430467i	$0.141651\pi$
$60$	−94.0195	+	752.611i	−0.202298	+	1.61936i
$61$	−67.5010	−	469.480i	−0.141682	−	0.985422i	−0.929318	−	0.369281i	$-0.879604\pi$
$61$	−67.5010	−	469.480i	−0.141682	−	0.985422i	0.787636	−	0.616141i	$-0.211305\pi$
$62$	−466.549	+	4.32016i	−0.955675	+	0.00884937i
$63$	124.997	+	273.704i	0.249970	+	0.547357i
$64$	356.258	+	367.729i	0.695816	+	0.718220i
$65$	−419.678	−	191.661i	−0.800841	−	0.365732i
$66$	−409.521	−	463.863i	−0.763766	−	0.865115i
$67$	−41.1278	−	63.9961i	−0.0749934	−	0.116692i	0.801731	−	0.597685i	$-0.203913\pi$
$67$	−41.1278	−	63.9961i	−0.0749934	−	0.116692i	−0.876724	+	0.480993i	$0.840276\pi$
$68$	−525.171	+	85.4625i	−0.936563	+	0.152410i
$69$	1040.73	−	368.963i	1.81578	−	0.643738i
$70$	83.8713	+	71.3259i	0.143208	+	0.121787i
$71$	320.267	+	498.345i	0.535334	+	0.832995i	0.998582	−	0.0532331i	$-0.0169526\pi$
$71$	320.267	+	498.345i	0.535334	+	0.832995i	−0.463249	+	0.886228i	$0.653316\pi$
$72$	1281.58	+	1049.61i	2.09771	+	1.71803i
$73$	−324.253	+	710.015i	−0.519876	+	1.13837i	0.449610	+	0.893225i	$0.351563\pi$
$73$	−324.253	+	710.015i	−0.519876	+	1.13837i	−0.969486	+	0.245145i	$0.921164\pi$
$74$	882.210	+	393.060i	1.38588	+	0.617464i
$75$	−146.807	−	321.463i	−0.226024	−	0.494924i
$76$	−503.800	−	420.467i	−0.760393	−	0.634616i
$77$	−88.9070	+	12.7829i	−0.131583	+	0.0189188i
$78$	−1153.39	+	756.422i	−1.67431	+	1.09805i
$79$	337.803	−	389.845i	0.481086	−	0.555202i	−0.462376	−	0.886684i	$-0.653003\pi$
$79$	337.803	−	389.845i	0.481086	−	0.555202i	0.943462	+	0.331482i	$0.107548\pi$
$80$	587.507	+	149.115i	0.821065	+	0.208394i
$81$	2232.65	+	1434.84i	3.06263	+	1.96823i
$82$	194.246	−	29.7667i	0.261596	−	0.0400875i
$83$	−209.131	+	712.235i	−0.276568	+	0.941903i	0.697678	+	0.716412i	$0.254217\pi$
$83$	−209.131	+	712.235i	−0.276568	+	0.941903i	−0.974245	+	0.225491i	$0.927601\pi$
$84$	314.045	−	98.5645i	0.407918	−	0.128027i
$85$	−476.051	+	412.500i	−0.607470	+	0.526376i
$86$	−239.343	−	67.8767i	−0.300105	−	0.0851085i
$87$	−221.066	−	752.882i	−0.272423	−	0.927787i
$88$	−408.413	+	278.797i	−0.494738	+	0.337726i
$89$	−1434.56	−	206.259i	−1.70858	−	0.245656i	−0.782409	−	0.622766i	$-0.786009\pi$
$89$	−1434.56	−	206.259i	−1.70858	−	0.245656i	−0.926169	+	0.377109i	$0.876918\pi$
$90$	1943.65	+	261.109i	2.27642	+	0.305814i
$91$			200.221i			0.230647i
$92$	−189.488	−	861.848i	−0.214733	−	0.976673i
$93$			1651.30i			1.84120i
$94$	187.622	−	1396.63i	0.205870	−	1.53246i
$95$	−768.947	−	110.558i	−0.830445	−	0.119400i
$96$	1313.10	−	1248.77i	1.39601	−	1.32763i
$97$	−267.028	−	909.414i	−0.279511	−	0.951928i	−0.972873	−	0.231339i	$-0.925689\pi$
$97$	−267.028	−	909.414i	−0.279511	−	0.951928i	0.693362	−	0.720590i	$-0.256129\pi$
$98$	−251.656	+	887.377i	−0.259399	+	0.914679i
$99$	−1209.14	+	1047.72i	−1.22750	+	1.06364i
$100$	−269.463	+	84.5723i	−0.269463	+	0.0845723i
$101$	−100.079	+	340.836i	−0.0985959	+	0.335787i	−0.993988	−	0.109493i	$-0.965077\pi$
$101$	−100.079	+	340.836i	−0.0985959	+	0.335787i	0.895392	+	0.445279i	$0.146896\pi$
$102$	285.248	+	1861.42i	0.276900	+	1.80694i
$103$	134.031	+	86.1363i	0.128218	+	0.0824006i	0.603178	−	0.797607i	$-0.293901\pi$
$103$	134.031	+	86.1363i	0.128218	+	0.0824006i	−0.474960	+	0.880008i	$0.657537\pi$
$104$	485.581	+	989.575i	0.457838	+	0.933036i
$105$	255.177	−	294.490i	0.237169	−	0.273707i
$106$	−921.131	−	1404.54i	−0.844040	−	1.28699i
$107$	−1809.19	+	260.123i	−1.63459	+	0.235019i	−0.897576	−	0.440859i	$-0.854674\pi$
$107$	−1809.19	+	260.123i	−1.63459	+	0.235019i	−0.737014	+	0.675877i	$0.763765\pi$
$108$	2371.18	−	2841.14i	2.11266	−	2.53138i
$109$	−527.760	−	1155.63i	−0.463763	−	1.01550i	−0.986614	−	0.163075i	$-0.947859\pi$
$109$	−527.760	−	1155.63i	−0.463763	−	1.01550i	0.522850	−	0.852425i	$-0.324869\pi$
$110$	−238.249	+	534.742i	−0.206511	+	0.463506i
$111$	1419.98	−	3109.33i	1.21422	−	2.65878i
$112$	−47.0508	−	258.802i	−0.0396953	−	0.218344i
$113$	314.994	+	490.141i	0.262232	+	0.408040i	0.947255	−	0.320481i	$-0.103844\pi$
$113$	314.994	+	490.141i	0.262232	+	0.408040i	−0.685023	+	0.728521i	$0.740208\pi$
$114$	−1504.58	+	1769.21i	−1.23611	+	1.45352i
$115$	−726.558	−	750.638i	−0.589147	−	0.608673i
$116$	−618.935	+	100.721i	−0.495403	+	0.0806183i
$117$	1928.13	+	3000.24i	1.52356	+	2.37070i
$118$	−510.736	+	450.903i	−0.398450	+	0.351771i
$119$	248.657	+	113.558i	0.191549	+	0.0874776i
$120$	546.983	−	2074.35i	0.416104	−	1.57801i
$121$	354.517	+	776.284i	0.266354	+	0.583234i
$122$	12.4219	+	1341.49i	0.00921826	+	0.995512i
$123$	−98.9810	−	688.428i	−0.0725595	−	0.504662i
$124$	1309.48	+	163.586i	0.948344	+	0.118471i
$125$	−994.213	+	1147.38i	−0.711401	+	0.821001i
$126$	−247.323	−	814.332i	−0.174867	−	0.575766i
$127$	−998.819	+	1554.19i	−0.697881	+	1.08592i	0.293632	+	0.955918i	$0.405136\pi$
$127$	−998.819	+	1554.19i	−0.697881	+	1.08592i	−0.991513	+	0.130006i	$0.958500\pi$
$128$	−860.196	−	1165.00i	−0.593995	−	0.804469i
$129$	−248.065	+	844.831i	−0.169309	+	0.576614i
$130$	1104.28	+	695.317i	0.745016	+	0.469103i
$131$	−613.247	−	707.724i	−0.409005	−	0.472016i	0.513451	−	0.858119i	$-0.328367\pi$
$131$	−613.247	−	707.724i	−0.409005	−	0.472016i	−0.922456	+	0.386102i	$0.873821\pi$
$132$	973.303	+	1454.54i	0.641781	+	0.959104i
$133$	94.9810	+	323.475i	0.0619240	+	0.210894i
$134$	91.1912	+	194.885i	0.0587889	+	0.125638i
$135$	623.482	−	4336.41i	0.397487	−	2.76458i
$136$	1504.37	−	41.8000i	0.948517	−	0.0263553i
$137$		−	191.131i		−	0.119193i	−0.998223	−	0.0595965i	$-0.981019\pi$
$137$		−	191.131i		−	0.119193i	0.998223	−	0.0595965i	$-0.0189814\pi$
$138$	−3056.36	+	642.369i	−1.88532	+	0.396247i
$139$	−2183.74			−1.33254			−0.666268	−	0.745713i	$-0.732109\pi$
$139$	−2183.74			−1.33254			−0.666268	+	0.745713i	$0.732109\pi$
$140$	−208.251	−	231.529i	−0.125717	−	0.139770i
$141$	−4936.62	−	709.779i	−2.94850	−	0.423931i
$142$	−710.116	−	1517.59i	−0.419659	−	0.896855i
$143$	−1021.49	+	299.936i	−0.597351	+	0.175398i
$144$	−3197.30	−	3424.94i	−1.85029	−	1.98203i
$145$	−561.045	+	486.149i	−0.321326	+	0.278431i
$146$	1176.34	−	1868.24i	0.666814	−	1.05902i
$147$	3132.25	+	919.712i	1.75744	+	0.516031i
$148$	−2325.03	−	1434.07i	−1.29133	−	0.796487i
$149$	1114.62	+	716.325i	0.612842	+	0.393850i	0.809922	−	0.586538i	$-0.199509\pi$
$149$	1114.62	+	716.325i	0.612842	+	0.393850i	−0.197080	+	0.980387i	$0.563146\pi$
$150$	290.478	+	956.424i	0.158116	+	0.520611i
$151$	−296.269	−	256.718i	−0.159669	−	0.138354i	0.571362	−	0.820698i	$-0.306415\pi$
$151$	−296.269	−	256.718i	−0.159669	−	0.138354i	−0.731031	+	0.682344i	$0.760961\pi$
$152$	1253.93	+	1368.40i	0.669128	+	0.730207i
$153$	4819.59	−	692.952i	2.54667	−	0.366156i
$154$	254.042	−	2.35238i	0.132930	−	0.00123091i
$155$	1421.10	−	648.997i	0.736425	−	0.336314i
$156$	3518.10	−	1686.08i	1.80560	−	0.865350i
$157$	1393.87	−	3052.15i	0.708553	−	1.55152i	−0.120729	−	0.992686i	$-0.538523\pi$
$157$	1393.87	−	3052.15i	0.708553	−	1.55152i	0.829282	−	0.558830i	$-0.188750\pi$
$158$	−1093.75	+	965.619i	−0.550724	+	0.486206i
$159$	−5000.97	+	3213.93i	−2.49436	+	1.60303i
$160$	−1590.77	−	639.253i	−0.786009	−	0.315859i
$161$	−165.335	+	422.134i	−0.0809328	+	0.206639i
$162$	−5718.34	−	4863.00i	−2.77330	−	2.35848i
$163$	561.755	−	361.018i	0.269939	−	0.173479i	−0.398668	−	0.917095i	$-0.630527\pi$
$163$	561.755	−	361.018i	0.269939	−	0.173479i	0.668607	+	0.743616i	$0.266891\pi$
$164$	−555.729	+	10.2928i	−0.264604	+	0.00490079i
$165$	1884.69	+	860.708i	0.889228	+	0.406097i
$166$	854.464	−	1917.81i	0.399514	−	0.896694i
$167$	1807.72	−	825.556i	0.837636	−	0.382536i	0.0500550	−	0.998746i	$-0.484060\pi$
$167$	1807.72	−	825.556i	0.837636	−	0.382536i	0.787581	+	0.616211i	$0.211333\pi$
$168$	−917.464	+	158.035i	−0.421333	+	0.0725755i
$169$	25.0673	+	174.347i	0.0114098	+	0.0793568i
$170$	1489.83	−	977.065i	0.672145	−	0.440809i
$171$	4538.32	+	3932.48i	2.02956	+	1.75862i
$172$	645.376	+	280.409i	0.286102	+	0.124308i
$173$	476.130	−	740.872i	0.209245	−	0.325592i	−0.720729	−	0.693217i	$-0.756193\pi$
$173$	476.130	−	740.872i	0.209245	−	0.325592i	0.929974	+	0.367625i	$0.119829\pi$
$174$	336.177	+	2193.76i	0.146468	+	0.955798i
$175$	139.220	+	40.8787i	0.0601374	+	0.0176579i
$176$	1249.87	−	627.735i	0.535299	−	0.268848i
$177$	1579.04	+	1822.31i	0.670555	+	0.773861i
$178$	3943.76	+	1118.43i	1.66066	+	0.470955i
$179$	670.084	−	196.754i	0.279801	−	0.0821570i	−0.138821	−	0.990317i	$-0.544331\pi$
$179$	670.084	−	196.754i	0.279801	−	0.0821570i	0.418622	+	0.908160i	$0.362513\pi$
$180$	−5350.18	−	1463.90i	−2.21544	−	0.606183i
$181$	329.470	−	2291.51i	0.135300	−	0.941031i	−0.803190	−	0.595723i	$-0.796865\pi$
$181$	329.470	−	2291.51i	0.135300	−	0.941031i	0.938489	−	0.345308i	$-0.112225\pi$
$182$	75.4008	−	561.270i	0.0307092	−	0.228594i
$183$	4748.04			1.91795
$184$	206.620	+	2487.33i	0.0827839	+	0.996568i
$185$	−3233.97			−1.28522
$186$	621.857	−	4628.99i	0.245144	−	1.82481i
$187$	−206.855	+	1438.71i	−0.0808917	+	0.562614i
$188$	−1051.90	+	3844.43i	−0.408074	+	1.49140i
$189$	−1824.21	+	535.637i	−0.702074	+	0.206147i
$190$	2113.91	+	599.496i	0.807154	+	0.228905i
$191$	2525.47	+	2914.55i	0.956737	+	1.10413i	0.994488	+	0.104846i	$0.0334350\pi$
$191$	2525.47	+	2914.55i	0.956737	+	1.10413i	−0.0377517	+	0.999287i	$0.512020\pi$
$192$	−4151.20	+	3006.13i	−1.56035	+	1.12994i
$193$	377.791	+	110.929i	0.140902	+	0.0413724i	0.351423	−	0.936217i	$-0.385698\pi$
$193$	377.791	+	110.929i	0.140902	+	0.0413724i	−0.210521	+	0.977589i	$0.567516\pi$
$194$	406.072	+	2649.87i	0.150280	+	0.980668i
$195$	2496.97	−	3885.37i	0.916984	−	1.42686i
$196$	1039.63	−	2392.76i	0.378873	−	0.871998i
$197$	−3299.07	−	2858.66i	−1.19314	−	1.03387i	−0.998596	−	0.0529721i	$-0.983131\pi$
$197$	−3299.07	−	2858.66i	−1.19314	−	1.03387i	−0.194548	−	0.980893i	$-0.562324\pi$
$198$	3784.06	−	2481.68i	1.35819	−	0.890733i
$199$	−410.009	−	2851.68i	−0.146054	−	1.01583i	−0.922597	−	0.385765i	$-0.873937\pi$
$199$	−410.009	−	2851.68i	−0.146054	−	1.01583i	0.776543	−	0.630065i	$-0.216972\pi$
$200$	787.220	−	135.600i	0.278324	−	0.0479420i
$201$	692.702	−	316.346i	0.243082	−	0.111012i
$202$	408.899	−	917.759i	0.142426	−	0.319670i
$203$	293.053	+	133.833i	0.101322	+	0.0462720i
$204$	−98.6337	−	5325.45i	−0.0338517	−	1.82772i
$205$	−553.558	+	355.750i	−0.188596	+	0.121203i
$206$	−343.283	−	291.935i	−0.116105	−	0.0987384i
$207$	1587.69	+	7917.68i	0.533102	+	2.65854i
$208$	−988.543	−	2956.88i	−0.329534	−	0.985688i
$209$	−1508.02	+	969.147i	−0.499101	+	0.320753i
$210$	−826.224	+	729.431i	−0.271500	+	0.239693i
$211$	1945.05	−	4259.07i	0.634610	−	1.38960i	−0.269791	−	0.962919i	$-0.586955\pi$
$211$	1945.05	−	4259.07i	0.634610	−	1.38960i	0.904401	−	0.426684i	$-0.140318\pi$
$212$	2053.22	+	4284.16i	0.665170	+	1.38791i
$213$	−5394.15	+	2463.43i	−1.73522	+	0.792447i
$214$	5169.57	−	47.8692i	1.65133	−	0.0152910i
$215$	824.556	−	118.553i	0.261555	−	0.0376059i
$216$	−7716.95	+	7071.45i	−2.43089	+	2.22755i
$217$	−512.387	−	443.986i	−0.160291	−	0.138893i
$218$	1044.24	+	3438.27i	0.324427	+	1.06821i
$219$	−6573.29	−	4224.40i	−2.02823	−	1.30346i
$220$	869.248	−	1409.29i	0.266385	−	0.431883i
$221$	3108.78	+	912.819i	0.946240	+	0.277841i
$222$	−5151.50	+	8181.47i	−1.55741	+	2.47344i
$223$	−561.865	+	486.859i	−0.168723	+	0.146200i	−0.735130	−	0.677927i	$-0.762879\pi$
$223$	−561.865	+	486.859i	−0.168723	+	0.146200i	0.566406	+	0.824126i	$0.308333\pi$
$224$	34.4333	+	743.205i	0.0102709	+	0.221685i
$225$	2479.81	−	728.139i	0.734760	−	0.215745i
$226$	−698.426	−	1492.61i	−0.205569	−	0.439322i
$227$	−3675.59	−	528.471i	−1.07470	−	0.154519i	−0.417834	−	0.908523i	$-0.637211\pi$
$227$	−3675.59	−	528.471i	−1.07470	−	0.154519i	−0.656869	+	0.754004i	$0.728120\pi$
$228$	4883.96	−	4392.93i	1.41863	−	1.27600i
$229$	−3349.56			−0.966573			−0.483287	−	0.875462i	$-0.660557\pi$
$229$	−3349.56			−0.966573			−0.483287	+	0.875462i	$0.660557\pi$
$230$	1754.04	+	2377.83i	0.502861	+	0.681695i
$231$		−	899.153i		−	0.256103i
$232$	1772.96	−	49.2630i	0.501726	−	0.0139408i
$233$	−685.566	+	4768.22i	−0.192759	+	1.34067i	0.631904	+	0.775047i	$0.282274\pi$
$233$	−685.566	+	4768.22i	−0.192759	+	1.34067i	−0.824663	+	0.565624i	$0.808635\pi$
$234$	−4275.18	−	9136.51i	−1.19435	−	2.55244i
$235$	1329.37	+	4527.41i	0.369014	+	1.25675i
$236$	1601.52	−	1071.65i	0.441738	−	0.295588i
$237$	3381.56	+	3902.53i	0.926818	+	1.06961i
$238$	−654.282	−	411.972i	−0.178197	−	0.112202i
$239$	−415.615	+	1415.45i	−0.112485	+	0.383088i	−0.996422	−	0.0845175i	$-0.973065\pi$
$239$	−415.615	+	1415.45i	−0.112485	+	0.383088i	0.883937	+	0.467606i	$0.154883\pi$
$240$	−2314.50	+	5608.92i	−0.622501	+	1.50856i
$241$	−2175.11	+	3384.54i	−0.581374	+	0.904636i	−0.999994	−	0.00352599i	$-0.998878\pi$
$241$	−2175.11	+	3384.54i	−0.581374	+	0.904636i	0.418620	+	0.908162i	$0.362514\pi$
$242$	−701.460	−	2309.62i	−0.186329	−	0.613504i
$243$	−9219.00	+	10639.3i	−2.43374	+	2.80869i
$244$	470.365	−	3765.19i	0.123410	−	0.987876i
$245$	−439.542	−	3057.08i	−0.114617	−	0.797182i
$246$	18.2150	+	1967.11i	0.00472093	+	0.509830i
$247$	1659.95	+	3634.78i	0.427611	+	0.936338i
$248$	−3609.19	−	951.704i	−0.924127	−	0.243682i
$249$	−6759.29	−	3086.87i	−1.72029	−	0.785631i
$250$	3219.11	−	2841.99i	0.814378	−	0.718973i
$251$	1877.67	+	2921.72i	0.472182	+	0.734730i	0.992894	−	0.119003i	$-0.0379697\pi$
$251$	1877.67	+	2921.72i	0.472182	+	0.734730i	−0.520712	+	0.853733i	$0.674333\pi$
$252$	386.639	+	2375.91i	0.0966506	+	0.593922i
$253$	−2401.32	−	211.136i	−0.596718	−	0.0524664i
$254$	3385.22	−	3980.64i	0.836251	−	0.983337i
$255$	−3409.09	−	5304.65i	−0.837198	−	1.30271i
$256$	1972.62	+	3589.71i	0.481596	+	0.876393i
$257$	−1997.53	+	4373.98i	−0.484834	+	1.06164i	0.496271	+	0.868167i	$0.334702\pi$
$257$	−1997.53	+	4373.98i	−0.484834	+	1.06164i	−0.981106	+	0.193472i	$0.938025\pi$
$258$	1013.54	−	2274.85i	0.244574	−	0.548938i
$259$	583.013	+	1276.62i	0.139871	+	0.306275i
$260$	−2833.73	−	2365.00i	−0.675925	−	0.564120i
$261$	5680.08	−	816.673i	1.34708	−	0.193681i
$262$	1452.56	+	2214.86i	0.342517	+	0.522270i
$263$	5274.10	−	6086.64i	1.23656	−	1.42707i	0.369225	−	0.929340i	$-0.379623\pi$
$263$	5274.10	−	6086.64i	1.23656	−	1.42707i	0.867334	−	0.497726i	$-0.165832\pi$
$264$	−2180.64	−	4443.97i	−0.508369	−	1.03601i
$265$	4731.40	+	3040.69i	1.09678	+	0.704860i
$266$	−144.438	−	942.549i	−0.0332935	−	0.217261i
$267$	4087.46	−	13920.6i	0.936887	−	3.19074i
$268$	−182.240	−	580.651i	−0.0415376	−	0.132347i
$269$	5054.03	−	4379.34i	1.14554	−	0.992613i	0.145542	−	0.989352i	$-0.453507\pi$
$269$	5054.03	−	4379.34i	1.14554	−	0.992613i	0.999995	−	0.00326131i	$-0.00103811\pi$
$270$	−3380.81	+	11921.2i	−0.762035	+	2.68705i
$271$	1161.06	+	3954.20i	0.260256	+	0.886349i	0.981141	+	0.193295i	$0.0619173\pi$
$271$	1161.06	+	3954.20i	0.260256	+	0.886349i	−0.720885	+	0.693054i	$0.756265\pi$
$272$	−4232.85	−	449.349i	−0.943581	−	0.100168i
$273$	−1983.91	−	285.243i	−0.439823	−	0.0632370i
$274$	−71.9775	+	535.788i	−0.0158698	+	0.118132i
$275$			771.509i			0.169177i
$276$	8809.64	−	649.733i	1.92130	−	0.141700i
$277$		−	425.078i		−	0.0922038i	−0.998937	−	0.0461019i	$-0.985320\pi$
$277$		−	425.078i		−	0.0922038i	0.998937	−	0.0461019i	$-0.0146799\pi$
$278$	6121.56	+	822.368i	1.32067	+	0.177418i
$279$	−11953.5	−	1718.65i	−2.56501	−	0.368792i
$280$	496.589	+	727.457i	0.105989	+	0.155264i
$281$	−2461.36	−	8382.63i	−0.522536	−	1.77959i	−0.620279	−	0.784382i	$-0.712980\pi$
$281$	−2461.36	−	8382.63i	−0.522536	−	1.77959i	0.0977429	−	0.995212i	$-0.468838\pi$
$282$	13571.3	+	3848.75i	2.86581	+	0.812730i
$283$	−1460.78	+	1265.78i	−0.306836	+	0.265875i	−0.794644	−	0.607076i	$-0.792342\pi$
$283$	−1460.78	+	1265.78i	−0.306836	+	0.265875i	0.487808	+	0.872951i	$0.337797\pi$
$284$	1419.12	+	4521.60i	0.296513	+	0.944745i
$285$	2190.94	−	7461.66i	0.455369	−	1.55084i
$286$	2976.44	−	456.115i	0.615386	−	0.0943030i
$287$	240.228	+	154.385i	0.0494083	+	0.0317528i
$288$	7673.03	+	10805.0i	1.56992	+	2.21074i
$289$	−320.512	+	369.890i	−0.0652375	+	0.0752881i
$290$	1755.83	−	1151.51i	0.355537	−	0.233169i
$291$	9391.42	−	1350.28i	1.89187	−	0.272010i
$292$	−4001.13	+	4794.13i	−0.801878	+	0.960806i
$293$	−1354.91	−	2966.84i	−0.270153	−	0.591552i	0.725125	−	0.688617i	$-0.241782\pi$
$293$	−1354.91	−	2966.84i	−0.270153	−	0.591552i	−0.995278	+	0.0970651i	$0.969055\pi$
$294$	−8434.12	−	3757.74i	−1.67309	−	0.745429i
$295$	947.681	−	2075.13i	0.187038	−	0.409556i
$296$	5977.57	+	4895.63i	1.17378	+	0.961327i
$297$	−5465.42	−	8504.36i	−1.06780	−	1.66153i
$298$	−2854.80	−	2427.79i	−0.554947	−	0.471939i
$299$	−1227.64	+	5231.34i	−0.237445	+	1.01183i
$300$	−454.103	−	2790.48i	−0.0873922	−	0.537028i
$301$	−195.448	−	304.123i	−0.0374267	−	0.0582371i
$302$	733.837	+	831.215i	0.139826	+	0.158381i
$303$	−3234.62	−	1477.20i	−0.613281	−	0.280076i
$304$	−2999.76	−	4308.16i	−0.565948	−	0.812796i
$305$	−1866.08	−	4086.16i	−0.350333	−	0.767123i
$306$	−13771.4	+	127.521i	−2.57275	+	0.0238232i
$307$	77.5718	+	539.524i	0.0144210	+	0.100301i	0.995761	−	0.0919818i	$-0.0293202\pi$
$307$	77.5718	+	539.524i	0.0144210	+	0.100301i	−0.981340	+	0.192282i	$0.938411\pi$
$308$	−713.028	−	89.0746i	−0.131911	−	0.0164789i
$309$	−1044.43	+	1205.34i	−0.192284	+	0.221907i
$310$	−4228.11	+	1284.13i	−0.774646	+	0.235269i
$311$	−4955.79	+	7711.37i	−0.903593	+	1.40602i	0.0102493	+	0.999947i	$0.496737\pi$
$311$	−4955.79	+	7711.37i	−0.903593	+	1.40602i	−0.913842	+	0.406070i	$0.866899\pi$
$312$	−10497.1	+	3401.63i	−1.90474	+	0.617242i
$313$	−1740.02	+	5925.98i	−0.314224	+	1.07015i	0.639332	+	0.768931i	$0.279211\pi$
$313$	−1740.02	+	5925.98i	−0.314224	+	1.07015i	−0.953556	+	0.301217i	$0.902607\pi$
$314$	−5056.76	+	8031.01i	−0.908819	+	1.44336i
$315$	1866.18	+	2153.69i	0.333801	+	0.385227i
$316$	3429.70	−	2294.97i	0.610556	−	0.408552i
$317$	261.252	+	889.743i	0.0462883	+	0.157643i	0.979394	−	0.201959i	$-0.0647307\pi$
$317$	261.252	+	889.743i	0.0462883	+	0.157643i	−0.933106	+	0.359602i	$0.882912\pi$
$318$	15229.3	−	7126.13i	2.68558	−	1.25665i
$319$	−243.787	+	1695.58i	−0.0427883	+	0.297599i
$320$	4218.58	+	2391.05i	0.736956	+	0.417699i
$321$		−	18297.1i		−	3.18145i
$322$	622.443	−	1121.08i	0.107725	−	0.194023i
$323$	5455.53			0.939795
$324$	14198.6	+	15785.6i	2.43459	+	2.70672i
$325$	1702.27	+	244.750i	0.290539	+	0.0417732i
$326$	−1710.69	+	800.472i	−0.290633	+	0.135994i
$327$	12202.5	−	3582.99i	2.06361	−	0.605932i
$328$	1561.72	+	180.427i	0.262901	+	0.0303732i
$329$	1547.55	−	1340.96i	0.259330	−	0.224710i
$330$	−4959.11	−	3122.52i	−0.827242	−	0.520877i
$331$	−795.607	−	233.611i	−0.132116	−	0.0387929i	0.215006	−	0.976613i	$-0.431023\pi$
$331$	−795.607	−	233.611i	−0.132116	−	0.0387929i	−0.347122	+	0.937820i	$0.612841\pi$
$332$	−3117.49	+	5054.32i	−0.515346	+	0.835517i
$333$	21030.1	+	13515.2i	3.46078	+	2.22411i
$334$	−5378.36	+	1633.47i	−0.881111	+	0.267604i
$335$	−544.495	−	471.807i	−0.0888027	−	0.0769480i
$336$	2631.39	−	97.5065i	0.427244	−	0.0158316i
$337$	1922.40	−	276.399i	0.310741	−	0.0446779i	0.0148200	−	0.999890i	$-0.495282\pi$
$337$	1922.40	−	276.399i	0.310741	−	0.0446779i	0.295921	+	0.955212i	$0.404373\pi$
$338$	−4.61303	−	498.177i	−0.000742354	−	0.0801694i
$339$	−5305.35	+	2422.87i	−0.849991	+	0.388178i
$340$	−4544.31	+	2177.90i	−0.724852	+	0.347392i
$341$	1497.56	−	3279.19i	0.237822	−	0.520757i
$342$	−11241.1	−	12732.8i	−1.77734	−	2.01319i
$343$	−2313.51	+	1486.80i	−0.364192	+	0.234052i
$344$	−1703.55	−	1029.09i	−0.267004	−	0.161294i
$345$	8472.83	−	6129.77i	1.32221	−	0.956567i
$346$	−1613.71	+	1897.54i	−0.250733	+	0.294834i
$347$	7536.12	−	4843.17i	1.16588	−	0.749265i	0.193141	−	0.981171i	$-0.438133\pi$
$347$	7536.12	−	4843.17i	1.16588	−	0.749265i	0.972738	+	0.231906i	$0.0744962\pi$
$348$	−116.244	−	6276.26i	−0.0179061	−	0.966789i
$349$	5420.89	+	2475.64i	0.831443	+	0.379707i	0.785215	−	0.619223i	$-0.212552\pi$
$349$	5420.89	+	2475.64i	0.831443	+	0.379707i	0.0462285	+	0.998931i	$0.485280\pi$
$350$	−374.873	−	167.021i	−0.0572509	−	0.0255076i
$351$	−20498.0	+	9361.13i	−3.11710	+	1.42353i
$352$	−3740.10	+	1289.01i	−0.566329	+	0.195183i
$353$	211.301	+	1469.63i	0.0318596	+	0.221588i	0.999531	−	0.0306263i	$-0.00975017\pi$
$353$	211.301	+	1469.63i	0.0318596	+	0.221588i	−0.967671	+	0.252215i	$0.918841\pi$
$354$	−3740.19	−	5703.04i	−0.561550	−	0.856251i
$355$	4240.04	+	3674.02i	0.633910	+	0.549286i
$356$	−10634.1	−	4620.41i	−1.58317	−	0.687868i
$357$	−1479.44	+	2302.06i	−0.219329	+	0.341283i
$358$	−1952.50	+	299.206i	−0.288249	+	0.0441718i
$359$	1776.76	+	521.703i	0.261208	+	0.0766976i	0.409714	−	0.912214i	$-0.365628\pi$
$359$	1776.76	+	521.703i	0.261208	+	0.0766976i	−0.148506	+	0.988911i	$0.547447\pi$
$360$	14446.6	+	6118.49i	2.11501	+	0.895757i
$361$	−85.6349	−	98.8280i	−0.0124850	−	0.0144085i
$362$	−1786.54	+	6299.59i	−0.259388	+	0.914639i
$363$	−8196.92	+	2406.83i	−1.18520	+	0.348006i
$364$	−422.734	+	1544.98i	−0.0608716	+	0.222470i
$365$	−1052.06	+	7317.25i	−0.150870	+	1.04932i
$366$	−13309.9	−	1788.05i	−1.90088	−	0.255363i
$367$	3167.35			0.450502			0.225251	−	0.974301i	$-0.427680\pi$
$367$	3167.35			0.450502			0.225251	+	0.974301i	$0.427680\pi$
$368$	357.489	−	7050.41i	0.0506397	−	0.998717i
$369$	5086.44			0.717587
$370$	9065.61	+	1217.87i	1.27378	+	0.171119i
$371$	347.354	−	2415.90i	0.0486085	−	0.338079i
$372$	−3486.44	+	12742.0i	−0.485923	+	1.77592i
$373$	−7600.44	+	2231.69i	−1.05506	+	0.309792i	−0.762858	−	0.646565i	$-0.776205\pi$
$373$	−7600.44	+	2231.69i	−1.05506	+	0.309792i	−0.292198	+	0.956358i	$0.594387\pi$
$374$	1121.67	−	3955.16i	0.155080	−	0.546835i
$375$	−9952.54	−	11485.8i	−1.37052	−	1.58167i
$376$	4396.50	−	10380.7i	0.603011	−	1.42379i
$377$	3663.82	+	1075.80i	0.500521	+	0.146966i
$378$	5315.43	−	814.547i	0.723270	−	0.110835i
$379$	1495.66	−	2327.30i	0.202710	−	0.315422i	−0.724983	−	0.688766i	$-0.758153\pi$
$379$	1495.66	−	2327.30i	0.202710	−	0.315422i	0.927693	+	0.373344i	$0.121789\pi$
$380$	−5700.05	−	2476.61i	−0.769491	−	0.334335i
$381$	−13976.9	−	12111.0i	−1.87942	−	1.62852i
$382$	−5981.94	−	9121.26i	−0.801211	−	1.22169i
$383$	975.283	+	6783.24i	0.130117	+	0.904980i	0.945399	+	0.325916i	$0.105673\pi$
$383$	975.283	+	6783.24i	0.130117	+	0.904980i	−0.815282	+	0.579064i	$0.803418\pi$
$384$	12768.9	−	6863.62i	1.69690	−	0.912129i
$385$	−773.810	+	353.387i	−0.102434	+	0.0467799i
$386$	−1017.27	−	453.234i	−0.134139	−	0.0597642i
$387$	−5857.42	−	2674.99i	−0.769378	−	0.351363i
$388$	−140.412	−	7581.16i	−0.0183720	−	0.991946i
$389$	6897.25	−	4432.60i	0.898984	−	0.577742i	−0.00750509	−	0.999972i	$-0.502389\pi$
$389$	6897.25	−	4432.60i	0.898984	−	0.577742i	0.906489	+	0.422230i	$0.138753\pi$
$390$	−8462.80	+	9951.31i	−1.09880	+	1.29206i
$391$	5800.58	+	4491.63i	0.750251	+	0.580950i
$392$	−3815.42	+	6315.99i	−0.491601	+	0.813790i
$393$	7886.19	−	5068.15i	1.01223	−	0.650520i
$394$	8171.58	+	9255.93i	1.04487	+	1.18352i
$395$	2029.48	−	4443.95i	0.258517	−	0.566074i
$396$	−11542.2	+	5531.72i	−1.46469	+	0.701968i
$397$	−5744.87	+	2623.59i	−0.726263	+	0.331673i	−0.744009	−	0.668169i	$-0.767078\pi$
$397$	−5744.87	+	2623.59i	−0.726263	+	0.331673i	0.0177460	+	0.999843i	$0.494351\pi$
$398$	75.4523	+	8148.36i	0.00950271	+	1.02623i
$399$	−3340.49	+	480.290i	−0.419132	+	0.0602621i
$400$	−2257.84	+	83.6645i	−0.282230	+	0.0104581i
$401$	−5204.04	−	4509.32i	−0.648073	−	0.561558i	0.267576	−	0.963537i	$-0.413777\pi$
$401$	−5204.04	−	4509.32i	−0.648073	−	0.561558i	−0.915649	+	0.401978i	$0.868323\pi$
$402$	−2060.95	+	625.934i	−0.255698	+	0.0776586i
$403$	−6760.20	−	4344.52i	−0.835607	−	0.537012i
$404$	−1491.86	+	2418.72i	−0.183720	+	0.297861i
$405$	24117.1	+	7081.43i	2.95899	+	0.868837i
$406$	−771.099	−	485.526i	−0.0942586	−	0.0593503i
$407$	−5639.69	+	4886.82i	−0.686852	+	0.595161i
$408$	−1729.00	+	14965.7i	−0.209799	+	1.81596i
$409$	−3674.17	+	1078.83i	−0.444195	+	0.130427i	−0.496179	−	0.868220i	$-0.665264\pi$
$409$	−3674.17	+	1078.83i	−0.444195	+	0.130427i	0.0519834	+	0.998648i	$0.483446\pi$
$410$	1685.73	−	788.792i	0.203054	−	0.0950139i
$411$	1893.84	+	272.293i	0.227290	+	0.0326793i
$412$	852.368	+	947.643i	0.101925	+	0.113318i
$413$	−990.011			−0.117955
$414$	−1468.99	−	22793.1i	−0.174388	−	2.70585i
$415$			7030.25i			0.831569i
$416$	1657.60	+	8661.14i	0.195362	+	1.02079i
$417$	3111.04	−	21637.7i	0.365343	−	2.54102i
$418$	4592.32	−	2148.85i	0.537363	−	0.251445i
$419$	1950.53	+	6642.90i	0.227422	+	0.774528i	0.991580	+	0.129498i	$0.0413367\pi$
$419$	1950.53	+	6642.90i	0.227422	+	0.774528i	−0.764158	+	0.645029i	$0.776845\pi$
$420$	2590.80	−	1733.63i	0.300996	−	0.201410i
$421$	−4550.78	−	5251.88i	−0.526821	−	0.607983i	0.428505	−	0.903540i	$-0.359041\pi$
$421$	−4550.78	−	5251.88i	−0.526821	−	0.607983i	−0.955325	+	0.295556i	$0.904495\pi$
$422$	−7056.36	+	11206.7i	−0.813977	+	1.29274i
$423$	10276.0	−	34996.7i	1.18117	−	4.02269i
$424$	−4142.33	−	12782.8i	−0.474456	−	1.46412i
$425$	1269.42	−	1975.26i	0.144885	−	0.225445i
$426$	16048.8	−	4874.22i	1.82528	−	0.554359i
$427$	−1276.61	+	1473.29i	−0.144683	+	0.166973i
$428$	−14509.6	−	1812.60i	−1.63866	−	0.204709i
$429$	−1516.69	−	10548.8i	−0.170691	−	1.18718i
$430$	−2356.08	+	21.8168i	−0.264233	+	0.00244675i
$431$	−4692.63	−	10275.4i	−0.524446	−	1.14838i	−0.967729	−	0.251995i	$-0.918913\pi$
$431$	−4692.63	−	10275.4i	−0.524446	−	1.14838i	0.443283	−	0.896382i	$-0.353814\pi$
$432$	24295.5	−	16916.9i	2.70583	−	1.88406i
$433$	2990.04	+	1365.51i	0.331852	+	0.151552i	0.574372	−	0.818595i	$-0.305246\pi$
$433$	2990.04	+	1365.51i	0.331852	+	0.151552i	−0.242519	+	0.970147i	$0.577974\pi$
$434$	1269.15	+	1437.56i	0.140371	+	0.158998i
$435$	−4017.75	−	6251.74i	−0.442842	−	0.689076i
$436$	−1632.46	−	10031.6i	−0.179314	−	1.10189i
$437$	498.282	+	9034.05i	0.0545448	+	0.988918i
$438$	16835.7	+	14317.4i	1.83662	+	1.56190i
$439$	−4749.50	−	7390.36i	−0.516358	−	0.803469i	0.480954	−	0.876746i	$-0.340291\pi$
$439$	−4749.50	−	7390.36i	−0.516358	−	0.803469i	−0.997312	+	0.0732774i	$0.976654\pi$
$440$	−2967.43	+	3623.24i	−0.321516	+	0.392571i
$441$	−9917.67	+	21716.7i	−1.07091	+	2.34496i
$442$	−8370.91	−	3729.58i	−0.900823	−	0.401353i
$443$	−1867.90	−	4090.13i	−0.200331	−	0.438664i	0.782628	−	0.622490i	$-0.213879\pi$
$443$	−1867.90	−	4090.13i	−0.200331	−	0.438664i	−0.982959	+	0.183826i	$0.941152\pi$
$444$	17521.9	−	20994.7i	1.87287	−	2.24406i
$445$	−13586.5	+	1953.45i	−1.44733	+	0.208095i
$446$	1758.39	−	1153.19i	0.186687	−	0.122433i
$447$	−8685.69	+	10023.8i	−0.919058	+	1.06065i
$448$	183.356	−	2096.35i	0.0193365	−	0.221079i
$449$	3308.89	+	2126.50i	0.347787	+	0.223509i	0.702858	−	0.711330i	$-0.251907\pi$
$449$	3308.89	+	2126.50i	0.347787	+	0.223509i	−0.355071	+	0.934839i	$0.615543\pi$
$450$	−7225.74	+	1107.29i	−0.756943	+	0.115996i
$451$	−427.774	+	1456.86i	−0.0446632	+	0.152109i
$452$	1395.76	+	4447.16i	0.145246	+	0.462781i
$453$	2965.79	−	2569.87i	0.307604	−	0.266541i
$454$	10104.6	+	2865.61i	1.04456	+	0.296233i
$455$	534.241	+	1819.46i	0.0550452	+	0.187467i
$456$	−15345.2	+	10475.2i	−1.57589	+	1.07576i
$457$	−18863.1	−	2712.11i	−1.93081	−	0.277608i	−0.933988	−	0.357304i	$-0.883696\pi$
$457$	−18863.1	−	2712.11i	−1.93081	−	0.277608i	−0.996819	+	0.0796962i	$0.974605\pi$
$458$	9389.64	+	1261.40i	0.957967	+	0.128693i
$459$			30766.0i			3.12861i
$460$	−4021.54	−	7326.20i	−0.407620	−	0.742578i
$461$		−	3125.45i		−	0.315763i	−0.987458	−	0.157882i	$-0.949534\pi$
$461$		−	3125.45i		−	0.315763i	0.987458	−	0.157882i	$-0.0504665\pi$
$462$	−338.609	+	2520.55i	−0.0340985	+	0.253823i
$463$	15641.8	+	2248.96i	1.57006	+	0.225741i	0.871712	−	0.490018i	$-0.163010\pi$
$463$	15641.8	+	2248.96i	1.57006	+	0.225741i	0.698348	+	0.715759i	$0.253919\pi$
$464$	−4988.59	−	529.576i	−0.499115	−	0.0529848i
$465$	4406.07	+	15005.7i	0.439412	+	1.49650i
$466$	3717.46	−	13108.3i	0.369545	−	1.30307i
$467$	10380.6	−	8994.84i	1.02860	−	0.891288i	0.0344636	−	0.999406i	$-0.489028\pi$
$467$	10380.6	−	8994.84i	1.02860	−	0.891288i	0.994138	+	0.108118i	$0.0344823\pi$
$468$	8543.70	+	27221.8i	0.843873	+	2.68874i
$469$	−88.0871	+	299.997i	−0.00867268	+	0.0295364i
$470$	−2021.58	−	13192.1i	−0.198401	−	1.29469i
$471$	28256.7	+	18159.5i	2.76433	+	1.77653i
$472$	−4893.03	+	2401.00i	−0.477161	+	0.234141i
$473$	1258.79	−	1452.72i	0.122366	−	0.141218i
$474$	−8009.70	−	12213.2i	−0.776156	−	1.18348i
$475$	2866.28	−	412.108i	0.276871	−	0.0398080i
$476$	1678.97	+	1401.25i	0.161671	+	0.134929i
$477$	−18060.2	−	39546.3i	−1.73358	−	3.79602i
$478$	1698.11	−	3811.35i	0.162489	−	0.364701i
$479$	−4524.22	+	9906.66i	−0.431559	+	0.944983i	0.561512	+	0.827469i	$0.310220\pi$
$479$	−4524.22	+	9906.66i	−0.431559	+	0.944983i	−0.993071	+	0.117514i	$0.962507\pi$
$480$	8600.35	−	14851.6i	0.817814	−	1.41225i
$481$	8993.27	+	13993.8i	0.852511	+	1.32653i
$482$	7371.94	−	8668.57i	0.696644	−	0.819175i
$483$	−3947.21	−	2239.62i	−0.371851	−	0.210986i
$484$	1096.59	+	6738.59i	0.102986	+	0.632850i
$485$	−4853.09	−	7551.55i	−0.454366	−	0.707007i
$486$	29849.7	−	26352.8i	2.78603	−	2.45964i
$487$	−4212.96	−	1923.99i	−0.392007	−	0.179024i	0.209653	−	0.977776i	$-0.432767\pi$
$487$	−4212.96	−	1923.99i	−0.392007	−	0.179024i	−0.601660	+	0.798752i	$0.705494\pi$
$488$	−2736.47	+	10377.6i	−0.253841	+	0.962650i
$489$	2776.87	+	6080.51i	0.256799	+	0.562311i
$490$	80.8869	+	8735.27i	0.00745734	+	0.805345i
$491$	279.254	+	1942.26i	0.0256671	+	0.178519i	0.998622	−	0.0524756i	$-0.0167112\pi$
$491$	279.254	+	1942.26i	0.0256671	+	0.178519i	−0.972955	+	0.230994i	$0.925802\pi$
$492$	689.725	−	5521.14i	0.0632017	−	0.505919i
$493$	3414.02	−	3939.99i	0.311886	−	0.359936i
$494$	−3284.43	−	10814.3i	−0.299137	−	0.984935i
$495$	−8192.09	+	12747.1i	−0.743853	+	1.15746i
$496$	9759.03	+	4027.03i	0.883455	+	0.364555i
$497$	685.945	−	2336.11i	0.0619091	−	0.210843i
$498$	17785.5	+	11198.7i	1.60037	+	1.00768i
$499$	12945.2	+	14939.5i	1.16133	+	1.34025i	0.930080	+	0.367358i	$0.119737\pi$
$499$	12945.2	+	14939.5i	1.16133	+	1.34025i	0.231254	+	0.972893i	$0.425717\pi$
$500$	−10094.2	+	6754.51i	−0.902854	+	0.604142i
$501$	5604.74	+	19088.0i	0.499803	+	1.70217i
$502$	−4163.30	−	8897.40i	−0.370154	−	0.791057i
$503$	740.941	−	5153.36i	0.0656798	−	0.456813i	−0.930268	−	0.366881i	$-0.880426\pi$
$503$	740.941	−	5153.36i	0.0656798	−	0.456813i	0.995948	−	0.0899326i	$-0.0286652\pi$
$504$	−189.106	−	6805.86i	−0.0167132	−	0.601502i
$505$			3364.29i			0.296453i
$506$	6651.97	+	1496.17i	0.584419	+	0.131448i
$507$	−1763.24			−0.154454
$508$	−10988.7	+	9883.88i	−0.959731	+	0.863241i
$509$	−10052.7	−	1445.36i	−0.875397	−	0.125863i	−0.310054	−	0.950719i	$-0.600347\pi$
$509$	−10052.7	−	1445.36i	−0.875397	−	0.125863i	−0.565343	+	0.824856i	$0.691256\pi$
$510$	7558.85	+	16154.0i	0.656297	+	1.40257i
$511$	3078.17	−	903.832i	0.266478	−	0.0782450i
$512$	−4177.90	−	10805.7i	−0.360623	−	0.932712i
$513$	−28675.6	+	24847.6i	−2.46795	+	2.13849i
$514$	7246.75	−	11509.1i	0.621868	−	0.987635i
$515$	1447.80	+	425.112i	0.123879	+	0.0363742i
$516$	−3697.88	+	5995.28i	−0.315484	+	0.511487i
$517$	9159.59	+	5886.51i	0.779184	+	0.500751i
$518$	−1153.57	−	3798.23i	−0.0978474	−	0.322172i
$519$	6662.67	+	5773.24i	0.563504	+	0.488279i
$520$	7053.02	+	7696.83i	0.594798	+	0.649093i
$521$	−12166.1	+	1749.22i	−1.02304	+	0.147091i	−0.633360	−	0.773857i	$-0.718325\pi$
$521$	−12166.1	+	1749.22i	−1.02304	+	0.147091i	−0.389684	+	0.920949i	$0.627416\pi$
$522$	−16230.2	+	150.289i	−1.36088	+	0.0126015i
$523$	−3140.33	+	1434.14i	−0.262557	+	0.119906i	−0.542344	−	0.840156i	$-0.682463\pi$
$523$	−3140.33	+	1434.14i	−0.262557	+	0.119906i	0.279788	+	0.960062i	$0.409736\pi$
$524$	−3237.79	−	6755.82i	−0.269931	−	0.563224i
$525$	−603.387	+	1321.23i	−0.0501599	+	0.109835i
$526$	−17076.8	+	15076.2i	−1.41555	+	1.24972i
$527$	−9229.63	+	5931.52i	−0.762901	+	0.490287i
$528$	4439.34	+	13278.7i	0.365904	+	1.09448i
$529$	−6908.09	+	10015.7i	−0.567773	+	0.823185i
$530$	−12118.2	−	10305.6i	−0.993171	−	0.844614i
$531$	−14834.9	+	9533.81i	−1.21239	+	0.779157i
$532$	49.9441	+	2696.59i	0.00407021	+	0.219759i
$533$	3078.75	+	1406.02i	0.250198	+	0.114262i
$534$	−16700.5	+	37483.6i	−1.35337	+	3.03760i
$535$	−15746.4	+	7191.16i	−1.27248	+	0.581123i
$536$	292.198	+	1696.34i	0.0235467	+	0.136699i
$537$	994.928	+	6919.88i	0.0799522	+	0.556079i
$538$	−15816.9	+	10373.1i	−1.26750	+	0.831255i
$539$	−5386.03	−	4667.02i	−0.430413	−	0.372955i
$540$	13966.6	−	32145.0i	1.11301	−	2.56166i
$541$	5166.01	−	8038.47i	0.410544	−	0.638819i	−0.572986	−	0.819565i	$-0.694215\pi$
$541$	5166.01	−	8038.47i	0.410544	−	0.638819i	0.983530	+	0.180747i	$0.0578514\pi$
$542$	−1765.63	−	11521.8i	−0.139927	−	0.913109i
$543$	22236.2	+	6529.15i	1.75736	+	0.516008i
$544$	11696.5	+	2853.67i	0.921844	+	0.224908i
$545$	−7879.38	−	9093.29i	−0.619295	−	0.714704i
$546$	5453.96	+	1546.72i	0.427487	+	0.121234i
$547$	14813.5	−	4349.65i	1.15792	−	0.339996i	0.354295	−	0.935134i	$-0.384721\pi$
$547$	14813.5	−	4349.65i	1.15792	−	0.339996i	0.803623	+	0.595138i	$0.202903\pi$
$548$	403.541	−	1474.84i	0.0314570	−	0.114967i
$549$	−4941.71	+	34370.3i	−0.384166	+	2.67193i
$550$	290.540	−	2162.73i	0.0225249	−	0.167671i
$551$	6429.56			0.497112
$552$	−24940.3	−	1496.23i	−1.92306	−	0.115369i
$553$	−2120.13			−0.163033
$554$	−160.079	+	1191.60i	−0.0122763	+	0.0913829i
$555$	4607.24	−	32044.0i	0.352372	−	2.45080i
$556$	−16850.5	−	4610.60i	−1.28529	−	0.351678i
$557$	−207.509	+	60.9303i	−0.0157854	+	0.00463501i	−0.289616	−	0.957143i	$-0.593528\pi$
$557$	−207.509	+	60.9303i	−0.0157854	+	0.00463501i	0.273830	+	0.961778i	$0.411709\pi$
$558$	32861.3	+	9319.33i	2.49307	+	0.707023i
$559$	−2805.98	−	3238.27i	−0.212308	−	0.245017i
$560$	−1118.11	−	2226.25i	−0.0843727	−	0.167993i
$561$	−13960.9	−	4099.28i	−1.05067	−	0.308506i
$562$	3743.01	+	24425.5i	0.280942	+	1.83332i
$563$	−4188.77	+	6517.85i	−0.313562	+	0.487913i	−0.961885	−	0.273453i	$-0.911834\pi$
$563$	−4188.77	+	6517.85i	−0.313562	+	0.487913i	0.648323	+	0.761365i	$0.275471\pi$
$564$	−36594.2	−	15899.8i	−2.73208	−	1.18706i
$565$	4170.24	+	3613.53i	0.310519	+	0.269066i
$566$	4571.61	−	2998.17i	0.339504	−	0.222654i
$567$	−1552.36	−	10796.9i	−0.114979	−	0.799698i
$568$	−2275.38	−	13209.6i	−0.168086	−	0.975813i
$569$	24234.4	−	11067.5i	1.78552	−	0.815419i	0.813120	−	0.582096i	$-0.197767\pi$
$569$	24234.4	−	11067.5i	1.78552	−	0.815419i	0.972399	−	0.233323i	$-0.0749601\pi$
$570$	−8951.71	+	20091.8i	−0.657800	+	1.47641i
$571$	−2865.02	−	1308.41i	−0.209978	−	0.0958936i	0.307650	−	0.951500i	$-0.400457\pi$
$571$	−2865.02	−	1308.41i	−0.209978	−	0.0958936i	−0.517628	+	0.855606i	$0.673185\pi$
$572$	−8515.45	+	157.716i	−0.622463	+	0.0115288i
$573$	−32476.9	+	20871.6i	−2.36779	+	1.52168i
$574$	−615.278	−	523.246i	−0.0447408	−	0.0380485i
$575$	3386.86	+	1921.68i	0.245638	+	0.139373i
$576$	−17440.4	−	33178.7i	−1.26160	−	2.40008i
$577$	18262.9	−	11736.8i	1.31767	−	0.846813i	0.322649	−	0.946519i	$-0.395427\pi$
$577$	18262.9	−	11736.8i	1.31767	−	0.846813i	0.995017	+	0.0997061i	$0.0317903\pi$
$578$	1037.77	−	916.192i	0.0746808	−	0.0659318i
$579$	−1637.37	+	3585.34i	−0.117525	+	0.257343i
$580$	−5355.65	+	2566.75i	−0.383416	+	0.183756i
$581$	2775.21	−	1267.40i	0.198167	−	0.0905000i
$582$	−26834.9	+	248.486i	−1.91124	+	0.0176978i
$583$	12845.8	−	1846.94i	0.912552	−	0.131205i
$584$	13021.6	−	11932.3i	0.922664	−	0.845486i
$585$	25526.7	+	22119.1i	1.80410	+	1.56327i
$586$	2680.87	+	8827.02i	0.188986	+	0.622254i
$587$	−5904.97	−	3794.89i	−0.415203	−	0.266835i	0.316319	−	0.948653i	$-0.397553\pi$
$587$	−5904.97	−	3794.89i	−0.415203	−	0.266835i	−0.731522	+	0.681818i	$0.761189\pi$
$588$	22227.8	+	13710.1i	1.55894	+	0.961553i
$589$	−12982.7	−	3812.05i	−0.908219	−	0.266677i
$590$	−3438.05	+	5460.22i	−0.239902	+	0.381006i
$591$	33025.3	−	28616.6i	2.29861	−	1.99176i
$592$	−14913.0	−	15974.7i	−1.03534	−	1.10905i
$593$	794.572	−	233.307i	0.0550239	−	0.0161565i	−0.254105	−	0.967177i	$-0.581781\pi$
$593$	794.572	−	233.307i	0.0550239	−	0.0161565i	0.309129	+	0.951020i	$0.399963\pi$
$594$	12118.3	+	25898.0i	0.837069	+	1.78890i
$595$	2562.60	+	368.447i	0.176565	+	0.0253863i
$596$	7088.44	+	7880.76i	0.487171	+	0.541625i
$597$	28840.2			1.97714
$598$	5411.42	−	14202.4i	0.370049	−	0.971204i
$599$			10383.3i			0.708267i	0.935195	+	0.354133i	$0.115224\pi$
$599$			10383.3i			0.708267i	−0.935195	+	0.354133i	$0.884776\pi$
$600$	222.103	+	7993.41i	0.0151122	+	0.543883i
$601$	−3753.43	+	26105.7i	−0.254752	+	1.77184i	0.314094	+	0.949392i	$0.398299\pi$
$601$	−3753.43	+	26105.7i	−0.254752	+	1.77184i	−0.568845	+	0.822444i	$0.692610\pi$
$602$	433.360	+	926.136i	0.0293396	+	0.0627018i
$603$	1569.03	+	5343.61i	0.105963	+	0.360877i
$604$	−1744.10	−	2606.45i	−0.117494	−	0.175588i
$605$	5292.89	+	6108.32i	0.355680	+	0.410477i
$606$	8511.15	+	5359.08i	0.570531	+	0.359237i
$607$	6454.78	−	21983.0i	0.431617	−	1.46995i	−0.400988	−	0.916083i	$-0.631333\pi$
$607$	6454.78	−	21983.0i	0.431617	−	1.46995i	0.832604	−	0.553868i	$-0.186849\pi$
$608$	6786.67	+	13206.5i	0.452691	+	0.880912i
$609$	−1743.58	+	2713.07i	−0.116016	+	0.180524i
$610$	3692.30	+	12157.2i	0.245077	+	0.806938i
$611$	15893.9	−	18342.5i	1.05237	−	1.21450i
$612$	38652.7	+	4828.67i	2.55301	+	0.318934i
$613$	−244.736	−	1702.18i	−0.0161253	−	0.112154i	0.980169	−	0.198163i	$-0.0634976\pi$
$613$	−244.736	−	1702.18i	−0.0161253	−	0.112154i	−0.996294	+	0.0860094i	$0.972589\pi$
$614$	−14.2752	−	1541.63i	−0.000938274	−	0.101328i
$615$	−2736.36	−	5991.79i	−0.179416	−	0.392865i
$616$	1965.25	+	518.215i	0.128542	+	0.0338952i
$617$	5875.30	+	2683.16i	0.383356	+	0.175073i	0.597765	−	0.801671i	$-0.296055\pi$
$617$	5875.30	+	2683.16i	0.383356	+	0.175073i	−0.214410	+	0.976744i	$0.568783\pi$
$618$	3381.72	−	2985.54i	0.220118	−	0.194330i
$619$	6438.81	+	10019.0i	0.418090	+	0.650561i	0.984867	−	0.173310i	$-0.0554464\pi$
$619$	6438.81	+	10019.0i	0.418090	+	0.650561i	−0.566777	+	0.823871i	$0.691810\pi$
$620$	12336.0	−	2007.47i	0.799074	−	0.130036i
$621$	−50946.8	+	2810.02i	−3.29215	+	0.181582i
$622$	16796.3	−	19750.6i	1.08275	−	1.27319i
$623$	3220.48	+	5011.17i	0.207104	+	0.322260i
$624$	30706.8	−	5582.56i	1.96996	−	0.358143i
$625$	−4139.96	+	9065.25i	−0.264957	+	0.580176i
$626$	7109.36	−	15956.7i	0.453909	−	1.01878i
$627$	−7454.47	−	16323.0i	−0.474806	−	1.03968i
$628$	17199.7	−	20608.6i	1.09290	−	1.30951i
$629$	22479.7	−	3232.09i	1.42500	−	0.204884i
$630$	−4420.31	−	6740.10i	−0.279539	−	0.426241i
$631$	−2228.94	+	2572.34i	−0.140622	+	0.162287i	−0.821692	−	0.569932i	$-0.806970\pi$
$631$	−2228.94	+	2572.34i	−0.140622	+	0.162287i	0.681070	+	0.732219i	$0.261515\pi$
$632$	−10478.5	+	5141.79i	−0.659516	+	0.323623i
$633$	39430.3	+	25340.3i	2.47585	+	1.59113i
$634$	−397.288	−	2592.55i	−0.0248870	−	0.162403i
$635$	−4929.52	+	16788.4i	−0.308066	+	1.04918i
$636$	−45375.0	+	14241.2i	−2.82899	+	0.887891i
$637$	−12006.0	+	10403.3i	−0.746777	+	0.647086i
$638$	1321.93	−	4661.32i	0.0820308	−	0.289253i
$639$	−12218.2	−	41611.3i	−0.756407	−	2.57609i
$640$	−10925.3	−	8291.35i	−0.674781	−	0.512101i
$641$	2552.21	+	366.953i	0.157264	+	0.0226112i	0.220497	−	0.975388i	$-0.429232\pi$
$641$	2552.21	+	366.953i	0.157264	+	0.0226112i	−0.0632329	+	0.997999i	$0.520141\pi$
$642$	−6890.44	+	51291.2i	−0.423589	+	3.15312i
$643$		−	14989.8i		−	0.919348i	−0.888088	−	0.459674i	$-0.847966\pi$
$643$		−	14989.8i		−	0.919348i	0.888088	−	0.459674i	$-0.152034\pi$
$644$	−2167.05	+	2908.27i	−0.132599	+	0.177953i
$645$			8339.06i			0.509070i
$646$	−15293.2	−	2054.48i	−0.931427	−	0.125128i
$647$	−9912.90	−	1425.26i	−0.602344	−	0.0866040i	−0.165605	−	0.986192i	$-0.552958\pi$
$647$	−9912.90	−	1425.26i	−0.602344	−	0.0866040i	−0.436739	+	0.899588i	$0.643867\pi$
$648$	−33857.4	−	49597.9i	−2.05254	−	3.00678i
$649$	−1483.06	−	5050.83i	−0.0896997	−	0.305489i
$650$	−4679.72	−	1327.15i	−0.282390	−	0.0800846i
$651$	5129.23	−	4444.50i	0.308803	−	0.267579i
$652$	5096.93	−	1599.70i	0.306152	−	0.0960873i
$653$	6436.64	−	21921.2i	0.385735	−	1.31369i	−0.506546	−	0.862213i	$-0.669078\pi$
$653$	6436.64	−	21921.2i	0.385735	−	1.31369i	0.892281	−	0.451480i	$-0.149104\pi$
$654$	−35556.0	+	5448.68i	−2.12592	+	0.325780i
$655$	−7461.09	−	4794.95i	−0.445082	−	0.286037i
$656$	−4309.94	−	1093.90i	−0.256516	−	0.0651064i
$657$	37421.2	−	43186.4i	2.22213	−	2.56448i
$658$	−4843.16	+	3176.26i	−0.286939	+	0.188182i
$659$	6951.32	−	999.448i	0.410903	−	0.0590789i	0.0662359	−	0.997804i	$-0.478901\pi$
$659$	6951.32	−	999.448i	0.410903	−	0.0590789i	0.344667	+	0.938725i	$0.387992\pi$
$660$	12725.7	+	10620.7i	0.750526	+	0.626381i
$661$	11710.2	+	25641.8i	0.689070	+	1.50885i	0.852739	+	0.522337i	$0.174940\pi$
$661$	11710.2	+	25641.8i	0.689070	+	1.50885i	−0.163669	+	0.986515i	$0.552333\pi$
$662$	2142.31	+	954.485i	0.125775	+	0.0560379i
$663$	−13473.6	+	29503.1i	−0.789249	+	1.72821i
$664$	10642.5	−	12994.5i	0.622001	−	0.759464i
$665$	1726.23	+	2686.06i	0.100662	+	0.156633i
$666$	−53862.8	−	45806.1i	−3.13384	−	2.66509i
$667$	6836.23	+	5293.57i	0.396851	+	0.307298i
$668$	15692.0	−	2553.61i	0.908896	−	0.147907i
$669$	−4023.62	−	6260.88i	−0.232530	−	0.361823i
$670$	1348.68	+	1527.64i	0.0777670	+	0.0880864i
$671$	−9428.79	−	4305.98i	−0.542466	−	0.247736i
$672$	−7413.15	−	717.612i	−0.425548	−	0.0411942i
$673$	6610.73	+	14475.5i	0.378640	+	0.829107i	0.998997	+	0.0447865i	$0.0142608\pi$
$673$	6610.73	+	14475.5i	0.378640	+	0.829107i	−0.620356	+	0.784320i	$0.713012\pi$
$674$	−5493.05	+	50.8646i	−0.313923	+	0.00290687i
$675$	2324.05	+	16164.1i	0.132522	+	0.921714i
$676$	−174.675	+	1398.25i	−0.00993829	+	0.0795545i
$677$	11316.8	−	13060.3i	0.642451	−	0.741428i	−0.337355	−	0.941377i	$-0.609532\pi$
$677$	11316.8	−	13060.3i	0.642451	−	0.741428i	0.979806	+	0.199950i	$0.0640778\pi$
$678$	15784.6	−	4793.98i	0.894107	−	0.271551i
$679$	−2106.09	+	3277.15i	−0.119035	+	0.185221i
$680$	13559.0	−	4393.87i	0.764651	−	0.247790i
$681$	10472.8	−	35667.0i	0.589306	−	2.00699i
$682$	−5432.92	+	8628.42i	−0.305040	+	0.484457i
$683$	3265.41	+	3768.48i	0.182939	+	0.211123i	0.839811	−	0.542880i	$-0.182666\pi$
$683$	3265.41	+	3768.48i	0.182939	+	0.211123i	−0.656871	+	0.754003i	$0.728121\pi$
$684$	26716.6	+	39926.3i	1.49347	+	2.23190i
$685$	−509.985	−	1736.85i	−0.0284460	−	0.0968783i
$686$	7045.25	−	3296.64i	0.392112	−	0.183478i
$687$	4771.91	−	33189.4i	0.265007	−	1.84316i
$688$	4387.92	+	3526.34i	0.243151	+	0.195408i
$689$		−	28929.1i		−	1.59958i
$690$	−26059.8	+	13992.5i	−1.43780	+	0.772007i
$691$	−22139.7			−1.21886			−0.609431	−	0.792839i	$-0.708602\pi$
$691$	−22139.7			−1.21886			−0.609431	+	0.792839i	$0.708602\pi$
$692$	5238.21	−	4711.57i	0.287756	−	0.258825i
$693$	6508.83	+	935.828i	0.356782	+	0.0512975i
$694$	−22949.5	+	10738.6i	−1.25526	+	0.587365i
$695$	−19844.1	+	5826.76i	−1.08307	+	0.318017i
$696$	−2037.70	+	17637.7i	−0.110975	+	0.960566i
$697$	3492.30	−	3026.09i	0.189785	−	0.164450i
$698$	−14263.8	−	8981.26i	−0.773485	−	0.487028i
$699$	−46269.6	−	13586.0i	−2.50368	−	0.735148i
$700$	987.963	+	609.374i	0.0533450	+	0.0329031i
$701$	4350.63	+	2795.98i	0.234409	+	0.150646i	0.652573	−	0.757726i	$-0.273690\pi$
$701$	4350.63	+	2795.98i	0.234409	+	0.150646i	−0.418163	+	0.908372i	$0.637326\pi$
$702$	60986.2	−	18522.3i	3.27889	−	0.995837i
$703$	21167.8	+	18342.0i	1.13564	+	0.984042i
$704$	10969.8	−	2204.94i	0.587274	−	0.118042i
$705$	−46754.0	+	6722.22i	−2.49767	+	0.359111i
$706$	−38.8849	−	4199.32i	−0.00207288	−	0.223857i
$707$	1328.06	−	606.506i	0.0706463	−	0.0322631i
$708$	8336.97	+	17395.5i	0.442546	+	0.923395i
$709$	5128.16	−	11229.1i	0.271639	−	0.594807i	−0.723821	−	0.689988i	$-0.757616\pi$
$709$	5128.16	−	11229.1i	0.271639	−	0.594807i	0.995460	+	0.0951811i	$0.0303430\pi$
$710$	−10502.3	−	11895.9i	−0.555132	−	0.628797i
$711$	−31769.3	+	20416.9i	−1.67573	+	1.07692i
$712$	28070.1	+	16956.8i	1.47749	+	0.892533i
$713$	−10665.3	−	14742.0i	−0.560193	−	0.774323i
$714$	5014.17	−	5896.09i	0.262816	−	0.309042i
$715$	−8482.19	+	5451.17i	−0.443659	+	0.285122i
$716$	5586.02	−	103.460i	0.291564	−	0.00540011i
$717$	−13433.0	−	6134.66i	−0.699673	−	0.319530i
$718$	−4784.22	−	2131.57i	−0.248671	−	0.110793i
$719$	4822.29	−	2202.27i	0.250127	−	0.114229i	−0.286407	−	0.958108i	$-0.592461\pi$
$719$	4822.29	−	2202.27i	0.250127	−	0.114229i	0.536533	+	0.843879i	$0.319734\pi$
$720$	−38193.2	−	22592.0i	−1.97691	−	1.16938i
$721$	−93.1916	−	648.162i	−0.00481364	−	0.0334796i
$722$	202.838	+	309.288i	0.0104555	+	0.0159425i
$723$	−30437.2	−	26374.0i	−1.56566	−	1.35665i
$724$	7380.44	−	16986.5i	0.378856	−	0.871960i
$725$	1496.06	−	2327.92i	0.0766379	−	0.119251i
$726$	23884.4	−	3660.09i	1.22098	−	0.187106i
$727$	1561.25	+	458.424i	0.0796472	+	0.0233865i	0.321313	−	0.946973i	$-0.395876\pi$
$727$	1561.25	+	458.424i	0.0796472	+	0.0233865i	−0.241666	+	0.970359i	$0.577694\pi$
$728$	1766.85	−	4171.77i	0.0899501	−	0.212385i
$729$	−45361.1	−	52349.5i	−2.30458	−	2.65963i
$730$	5704.77	−	20115.9i	0.289237	−	1.01989i
$731$	−5613.09	+	1648.15i	−0.284005	+	0.0833914i
$732$	36637.6	+	10024.7i	1.84995	+	0.506179i
$733$	2366.34	−	16458.2i	0.119240	−	0.829330i	−0.839157	−	0.543890i	$-0.816951\pi$
$733$	2366.34	−	16458.2i	0.119240	−	0.829330i	0.958396	−	0.285440i	$-0.0921399\pi$
$734$	−8878.86	−	1192.78i	−0.446491	−	0.0599815i
$735$	30917.5			1.55158
$736$	−3657.22	+	19629.4i	−0.183162	+	0.983083i
$737$	−1662.48			−0.0830913
$738$	−14258.5	−	1915.49i	−0.711198	−	0.0955421i
$739$	−4200.10	+	29212.3i	−0.209070	+	1.45412i	0.567129	+	0.823629i	$0.308054\pi$
$739$	−4200.10	+	29212.3i	−0.209070	+	1.45412i	−0.776199	+	0.630488i	$0.782855\pi$
$740$	−24954.5	−	6827.98i	−1.23966	−	0.339191i
$741$	−38380.3	+	11269.5i	−1.90275	+	0.558697i
$742$	−1883.52	+	6641.56i	−0.0931888	+	0.328597i
$743$	−1795.86	−	2072.53i	−0.0886725	−	0.102333i	0.709679	−	0.704525i	$-0.248840\pi$
$743$	−1795.86	−	2072.53i	−0.0886725	−	0.102333i	−0.798352	+	0.602191i	$0.794294\pi$
$744$	14571.8	−	34406.0i	0.718049	−	1.69541i
$745$	12040.2	+	3535.31i	0.592104	+	0.173857i
$746$	22146.3	−	3393.75i	1.08691	−	0.166560i
$747$	29380.4	−	45716.7i	1.43905	−	2.23921i
$748$	−4633.76	+	10664.9i	−0.226507	+	0.521319i
$749$	5677.47	+	4919.55i	0.276970	+	0.239995i
$750$	23574.0	+	35945.6i	1.14773	+	1.75006i
$751$	−5164.72	−	35921.4i	−0.250950	−	1.74539i	−0.592536	−	0.805544i	$-0.701873\pi$
$751$	−5164.72	−	35921.4i	−0.250950	−	1.74539i	0.341586	−	0.939850i	$-0.389036\pi$
$752$	−16233.7	+	27444.1i	−0.787211	+	1.33083i
$753$	−31625.1	+	14442.7i	−1.53052	+	0.698965i
$754$	−9865.46	−	4395.47i	−0.476497	−	0.212299i
$755$	−3377.25	−	1542.34i	−0.162795	−	0.0743462i
$756$	−15207.2	+	281.656i	−0.731588	+	0.0135499i
$757$	−18856.1	+	12118.1i	−0.905334	+	0.581823i	−0.908368	−	0.418173i	$-0.862671\pi$
$757$	−18856.1	+	12118.1i	−0.905334	+	0.581823i	0.00303362	+	0.999995i	$0.499034\pi$
$758$	−5069.14	+	5960.73i	−0.242901	+	0.285625i
$759$	5513.06	−	23492.8i	0.263652	−	1.12350i
$760$	15046.0	+	9089.10i	0.718125	+	0.433811i
$761$	2603.00	−	1672.85i	0.123993	−	0.0796854i	−0.477174	−	0.878809i	$-0.658339\pi$
$761$	2603.00	−	1672.85i	0.123993	−	0.0796854i	0.601167	+	0.799123i	$0.294703\pi$
$762$	34619.8	+	39213.7i	1.64586	+	1.86426i
$763$	−2169.13	+	4749.73i	−0.102920	+	0.225363i
$764$	13333.9	+	27821.8i	0.631418	+	1.31749i
$765$	41947.7	−	19156.9i	1.98251	−	0.905383i
$766$	−179.477	−	19382.4i	−0.00846576	−	0.914247i
$767$	−11614.7	+	1669.95i	−0.546785	+	0.0786158i
$768$	−38379.1	+	14431.8i	−1.80324	+	0.678077i
$769$	7623.52	+	6605.82i	0.357492	+	0.309769i	0.815027	−	0.579423i	$-0.196722\pi$
$769$	7623.52	+	6605.82i	0.357492	+	0.309769i	−0.457535	+	0.889192i	$0.651268\pi$
$770$	2302.26	−	699.224i	0.107750	−	0.0327250i
$771$	−40494.1	−	26024.0i	−1.89152	−	1.21560i
$772$	2680.96	+	1653.61i	0.124987	+	0.0770918i
$773$	−18356.6	−	5389.99i	−0.854128	−	0.250795i	−0.174777	−	0.984608i	$-0.555920\pi$
$773$	−18356.6	−	5389.99i	−0.854128	−	0.250795i	−0.679351	+	0.733813i	$0.737739\pi$
$774$	15412.4	+	9704.49i	0.715747	+	0.450673i
$775$	−4401.08	+	3813.56i	−0.203989	+	0.176758i
$776$	−2461.35	+	21304.7i	−0.113863	+	0.985560i
$777$	−13480.1	+	3958.10i	−0.622387	+	0.182749i
$778$	−21003.9	+	9828.24i	−0.967902	+	0.452904i
$779$	5640.98	+	811.051i	0.259447	+	0.0373028i
$780$	27470.8	−	24709.0i	1.26104	−	1.13426i
$781$	12945.9			0.593139
$782$	−14569.0	−	14775.6i	−0.666222	−	0.675669i
$783$			36259.0i			1.65490i
$784$	13074.1	−	16268.4i	0.595575	−	0.741091i
$785$	4522.51	−	31454.7i	0.205624	−	1.43015i
$786$	−24015.5	+	11237.4i	−1.08983	+	0.509956i
$787$	2096.50	+	7140.01i	0.0949581	+	0.323398i	0.993249	−	0.116004i	$-0.0370086\pi$
$787$	2096.50	+	7140.01i	0.0949581	+	0.323398i	−0.898291	+	0.439402i	$0.855190\pi$
$788$	−19421.3	−	29023.9i	−0.877988	−	1.31210i
$789$	52796.2	+	60930.1i	2.38225	+	2.74926i
$790$	−7362.67	+	11693.2i	−0.331585	+	0.526614i
$791$	674.652	−	2297.65i	0.0303260	−	0.103281i
$792$	34438.8	−	11160.1i	1.54511	−	0.500704i
$793$	−12492.0	+	19437.9i	−0.559398	+	0.870440i
$794$	17092.3	−	5191.13i	0.763957	−	0.232023i
$795$	−36869.4	+	42549.5i	−1.64481	+	1.89821i
$796$	2857.05	−	22870.3i	0.127218	−	1.01836i
$797$	4367.22	+	30374.7i	0.194096	+	1.34997i	0.821025	+	0.570893i	$0.193403\pi$
$797$	4367.22	+	30374.7i	0.194096	+	1.34997i	−0.626928	+	0.779077i	$0.715688\pi$
$798$	9545.09	−	88.3858i	0.423424	−	0.00392083i
$799$	−13765.4	−	30141.9i	−0.609491	−	1.33460i
$800$	6360.78	+	615.740i	0.281109	+	0.0272121i
$801$	96515.1	+	44077.0i	4.25742	+	1.94430i
$802$	12890.0	+	14600.5i	0.567535	+	0.642845i
$803$	9222.34	+	14350.2i	0.405292	+	0.630646i
$804$	6013.05	−	978.521i	0.263761	−	0.0429226i
$805$	−376.071	+	4277.18i	−0.0164656	+	0.187268i
$806$	17314.4	+	14724.6i	0.756668	+	0.643487i
$807$	36192.8	+	56317.2i	1.57875	+	2.45658i
$808$	5092.91	−	6218.44i	0.221742	−	0.270748i
$809$	17932.5	−	39266.6i	0.779322	−	1.70648i	0.0743615	−	0.997231i	$-0.476308\pi$
$809$	17932.5	−	39266.6i	0.779322	−	1.70648i	0.704961	−	0.709246i	$-0.250965\pi$
$810$	−64939.4	−	28933.2i	−2.81696	−	1.25507i
$811$	−9456.54	−	20706.9i	−0.409450	−	0.896571i	−0.996224	−	0.0868200i	$-0.972329\pi$
$811$	−9456.54	−	20706.9i	−0.409450	−	0.896571i	0.586774	−	0.809751i	$-0.300398\pi$
$812$	1978.74	+	1651.43i	0.0855173	+	0.0713718i
$813$	−40834.6	+	5871.12i	−1.76154	+	0.253271i
$814$	17649.7	−	11575.1i	0.759979	−	0.498412i
$815$	4141.50	−	4779.55i	0.178001	−	0.205424i
$816$	10482.7	−	41301.3i	0.449715	−	1.77186i
$817$	−6069.48	−	3900.62i	−0.259907	−	0.167032i
$818$	10705.9	−	1640.59i	0.457606	−	0.0701245i
$819$	4129.66	−	14064.3i	0.176193	−	0.600058i
$820$	−5022.56	+	1576.35i	−0.213897	+	0.0671325i
$821$	−16452.3	+	14256.0i	−0.699379	+	0.606015i	−0.930231	−	0.366974i	$-0.880394\pi$
$821$	−16452.3	+	14256.0i	−0.699379	+	0.606015i	0.230853	+	0.972989i	$0.425848\pi$
$822$	−5206.35	−	1476.50i	−0.220915	−	0.0626506i
$823$	−6750.49	−	22990.0i	−0.285914	−	0.973734i	−0.969750	−	0.244098i	$-0.921508\pi$
$823$	−6750.49	−	22990.0i	−0.285914	−	0.973734i	0.683837	−	0.729635i	$-0.260310\pi$
$824$	−2032.53	−	2977.46i	−0.0859301	−	0.125880i
$825$	−7644.55	−	1099.12i	−0.322605	−	0.0463836i
$826$	2775.24	+	372.825i	0.116904	+	0.0157049i
$827$			16352.0i			0.687563i	0.939050	+	0.343782i	$0.111708\pi$
$827$			16352.0i			0.687563i	−0.939050	+	0.343782i	$0.888292\pi$
$828$	−4465.66	+	64447.9i	−0.187430	+	2.70497i
$829$			24111.8i			1.01018i	0.863067	+	0.505089i	$0.168540\pi$
$829$			24111.8i			1.01018i	−0.863067	+	0.505089i	$0.831460\pi$
$830$	2647.50	−	19707.5i	0.110718	−	0.824166i
$831$	4211.91	+	605.582i	0.175824	+	0.0252797i
$832$	−1385.00	−	24903.5i	−0.0577117	−	1.03771i
$833$	6110.60	+	20810.8i	0.254165	+	0.865608i
$834$	−16869.5	+	59484.3i	−0.700411	+	2.46975i
$835$	14224.3	−	12325.4i	0.589524	−	0.510826i
$836$	−13682.6	+	4294.36i	−0.566057	+	0.177660i
$837$	21497.7	−	73214.6i	0.887778	−	3.02349i
$838$	−2966.19	−	19356.2i	−0.122274	−	0.797912i
$839$	−38315.2	−	24623.7i	−1.57662	−	1.01323i	−0.977075	−	0.212896i	$-0.931710\pi$
$839$	−38315.2	−	24623.7i	−1.57662	−	1.01323i	−0.599549	−	0.800338i	$-0.704653\pi$
$840$	−7915.52	+	3884.12i	−0.325133	+	0.159542i
$841$	−11947.8	+	13788.5i	−0.489886	+	0.565359i
$842$	10779.2	+	16436.1i	0.441181	+	0.672713i
$843$	86566.4	−	12446.4i	3.53678	−	0.508512i
$844$	24001.0	−	28757.9i	0.978849	−	1.17285i
$845$	692.993	+	1517.44i	0.0282126	+	0.0617770i
$846$	−41985.4	+	94234.6i	−1.70625	+	3.82961i
$847$	1457.09	−	3190.58i	0.0591100	−	0.129433i
$848$	6798.16	+	37393.2i	0.275294	+	1.51425i
$849$	−10460.9	−	16277.5i	−0.422872	−	0.658002i
$850$	−4302.35	+	5059.08i	−0.173611	+	0.204147i
$851$	7405.35	+	36929.9i	0.298299	+	1.48759i
$852$	−46824.3	+	7619.86i	−1.88284	+	0.306399i
$853$	13647.4	+	21235.7i	0.547805	+	0.852401i	0.999203	−	0.0399219i	$-0.0127109\pi$
$853$	13647.4	+	21235.7i	0.547805	+	0.852401i	−0.451398	+	0.892323i	$0.649075\pi$
$854$	4133.47	−	3649.23i	0.165626	−	0.146222i
$855$	51733.5	+	23625.9i	2.06930	+	0.945017i
$856$	39991.3	+	10545.3i	1.59682	+	0.421064i
$857$	365.330	+	799.962i	0.0145618	+	0.0318859i	0.916773	−	0.399408i	$-0.130784\pi$
$857$	365.330	+	799.962i	0.0145618	+	0.0318859i	−0.902211	+	0.431294i	$0.858057\pi$
$858$	279.110	+	30142.0i	0.0111056	+	1.19934i
$859$	−3304.87	−	22985.9i	−0.131270	−	0.913002i	−0.943902	−	0.330225i	$-0.892875\pi$
$859$	−3304.87	−	22985.9i	−0.131270	−	0.913002i	0.812632	−	0.582777i	$-0.198034\pi$
$860$	6612.88	+	826.110i	0.262206	+	0.0327559i
$861$	−1871.97	+	2160.37i	−0.0740960	+	0.0855113i
$862$	9285.01	+	30571.8i	0.366878	+	1.20798i
$863$	−8419.24	+	13100.6i	−0.332091	+	0.516743i	−0.966640	−	0.256139i	$-0.917549\pi$
$863$	−8419.24	+	13100.6i	−0.332091	+	0.516743i	0.634549	+	0.772882i	$0.281186\pi$
$864$	−74477.0	+	38272.9i	−2.93259	+	1.50702i
$865$	2349.86	−	8002.90i	0.0923673	−	0.314574i
$866$	−7867.58	−	4953.86i	−0.308720	−	0.194387i
$867$	−3208.47	−	3702.77i	−0.125681	−	0.145044i
$868$	−3016.36	−	4507.78i	−0.117952	−	0.176272i
$869$	−3176.01	−	10816.5i	−0.123980	−	0.422237i
$870$	8908.42	+	19038.2i	0.347154	+	0.741903i
$871$	−527.398	+	3668.13i	−0.0205169	+	0.142698i
$872$	798.443	+	28735.7i	0.0310077	+	1.11595i
$873$			69388.4i			2.69008i
$874$	2005.30	−	25512.3i	0.0776090	−	0.987376i
$875$	6239.93			0.241084
$876$	−41802.8	−	46475.4i	−1.61231	−	1.79253i
$877$	−22108.8	−	3178.77i	−0.851268	−	0.122394i	−0.297149	−	0.954831i	$-0.596036\pi$
$877$	−22108.8	−	3178.77i	−0.851268	−	0.122394i	−0.554119	+	0.832437i	$0.686945\pi$
$878$	10530.9	+	22505.6i	0.404784	+	0.865065i
$879$	31327.4	−	9198.56i	1.20210	−	0.352969i
$880$	9682.91	−	9039.33i	0.370921	−	0.346268i
$881$	5006.32	−	4338.00i	0.191450	−	0.165892i	−0.553862	−	0.832609i	$-0.686846\pi$
$881$	5006.32	−	4338.00i	0.191450	−	0.165892i	0.745311	+	0.666717i	$0.232301\pi$
$882$	35979.9	−	57142.3i	1.37359	−	2.18150i
$883$	−19071.0	−	5599.74i	−0.726828	−	0.213416i	−0.102672	−	0.994715i	$-0.532739\pi$
$883$	−19071.0	−	5599.74i	−0.726828	−	0.213416i	−0.624157	+	0.781299i	$0.714557\pi$
$884$	22061.2	+	13607.3i	0.839365	+	0.517719i
$885$	19211.5	+	12346.5i	0.729703	+	0.468952i
$886$	3695.90	+	12169.1i	0.140142	+	0.461431i
$887$	−2155.90	−	1868.10i	−0.0816100	−	0.0707154i	0.613101	−	0.790005i	$-0.289922\pi$
$887$	−2155.90	−	1868.10i	−0.0816100	−	0.0707154i	−0.694710	+	0.719289i	$0.744468\pi$
$888$	−57024.6	+	52254.7i	−2.15498	+	1.97472i
$889$	7515.95	−	1080.63i	0.283551	−	0.0407685i
$890$	38822.0	−	359.485i	1.46215	−	0.0135393i
$891$	52758.3	−	24093.9i	1.98369	−	0.905921i
$892$	−5363.48	+	2570.50i	−0.201326	+	0.0964873i
$893$	16976.6	−	37173.6i	0.636172	−	1.39302i
$894$	28123.0	−	24828.3i	1.05209	−	0.928840i
$895$	5564.21	−	3575.90i	0.207811	−	0.133552i
$896$	−1303.45	+	5807.54i	−0.0485996	+	0.216536i
$897$	−50086.1	−	19616.9i	−1.86436	−	0.730200i
$898$	−8474.82	−	7207.17i	−0.314932	−	0.267825i
$899$	−10877.5	+	6990.54i	−0.403543	+	0.259341i
$900$	20672.5	−	382.880i	0.765648	−	0.0141807i
$901$	−35927.4	−	16407.5i	−1.32843	−	0.606673i
$902$	1747.79	−	3922.85i	0.0645178	−	0.144808i
$903$	3291.87	−	1503.35i	0.121314	−	0.0554023i
$904$	−2237.92	−	12992.1i	−0.0823364	−	0.477999i
$905$	−3120.36	−	21702.6i	−0.114612	−	0.797147i
$906$	−9281.61	+	6087.10i	−0.340354	+	0.223212i
$907$	−32429.9	−	28100.6i	−1.18723	−	1.02874i	−0.998912	−	0.0466303i	$-0.985152\pi$
$907$	−32429.9	−	28100.6i	−1.18723	−	1.02874i	−0.188316	−	0.982109i	$-0.560303\pi$
$908$	−27246.4	−	11838.3i	−0.995820	−	0.432672i
$909$	14059.8	−	21877.5i	0.513019	−	0.798273i
$910$	−812.424	−	5301.57i	−0.0295952	−	0.193127i
$911$	7043.39	+	2068.13i	0.256156	+	0.0752141i	0.407289	−	0.913299i	$-0.366474\pi$
$911$	7043.39	+	2068.13i	0.256156	+	0.0752141i	−0.151133	+	0.988513i	$0.548292\pi$
$912$	46961.3	−	23585.8i	1.70509	−	0.856364i
$913$	10623.3	+	12260.0i	0.385083	+	0.444410i
$914$	51856.6	+	14706.3i	1.87666	+	0.532211i
$915$	43146.5	−	12668.9i	1.55888	−	0.457729i
$916$	−25846.4	−	7072.03i	−0.932304	−	0.255094i
$917$	−547.754	+	3809.71i	−0.0197257	+	0.137195i
$918$	11586.1	−	86244.6i	0.416555	−	3.10076i
$919$	5958.22			0.213867			0.106933	−	0.994266i	$-0.465897\pi$
$919$	5958.22			0.213867			0.106933	+	0.994266i	$0.465897\pi$
$920$	8514.42	+	22051.6i	0.305122	+	0.790239i
$921$	−5456.42			−0.195217
$922$	−1177.01	+	8761.42i	−0.0420419	+	0.312952i
$923$	4106.91	−	28564.2i	0.146458	−	1.01864i
$924$	1898.41	−	6938.19i	0.0675899	−	0.247023i
$925$	11566.4	−	3396.21i	0.411137	−	0.120721i
$926$	−43001.0	−	12194.9i	−1.52603	−	0.432774i
$927$	−7638.24	−	8815.00i	−0.270629	−	0.312322i
$928$	13784.8	+	3363.17i	0.487617	+	0.118967i
$929$	−2121.14	−	622.823i	−0.0749110	−	0.0219959i	0.244062	−	0.969760i	$-0.421520\pi$
$929$	−2121.14	−	622.823i	−0.0749110	−	0.0219959i	−0.318973	+	0.947764i	$0.603338\pi$
$930$	−6700.35	−	43723.9i	−0.236251	−	1.54168i
$931$	−14461.7	+	22502.9i	−0.509091	+	0.792161i
$932$	−15357.4	+	35345.9i	−0.539750	+	1.24227i
$933$	−69348.4	−	60090.7i	−2.43340	−	2.10856i
$934$	−32486.7	+	21305.6i	−1.13811	+	0.746401i
$935$	1959.10	+	13625.8i	0.0685233	+	0.476590i
$936$	−13698.7	−	79526.9i	−0.478372	−	2.77716i
$937$	15956.8	−	7287.22i	0.556335	−	0.254069i	−0.117347	−	0.993091i	$-0.537439\pi$
$937$	15956.8	−	7287.22i	0.556335	−	0.254069i	0.673682	+	0.739021i	$0.264712\pi$
$938$	359.905	−	807.793i	0.0125280	−	0.0281187i
$939$	−56239.1	−	25683.5i	−1.95452	−	0.892599i
$940$	699.026	+	37741.9i	0.0242550	+	1.30958i
$941$	23108.8	−	14851.1i	0.800557	−	0.514487i	−0.0752403	−	0.997165i	$-0.523972\pi$
$941$	23108.8	−	14851.1i	0.800557	−	0.514487i	0.875798	+	0.482678i	$0.160336\pi$
$942$	−72371.8	−	61546.5i	−2.50318	−	2.12876i
$943$	5330.02	+	5506.67i	0.184061	+	0.190161i
$944$	14620.5	−	4887.93i	0.504087	−	0.168526i
$945$	−15147.8	+	9734.90i	−0.521437	+	0.335107i
$946$	−4075.77	+	3598.29i	−0.140079	+	0.123669i
$947$	−1898.25	+	4156.59i	−0.0651371	+	0.142630i	−0.939401	−	0.342821i	$-0.888617\pi$
$947$	−1898.25	+	4156.59i	−0.0651371	+	0.142630i	0.874264	+	0.485452i	$0.161345\pi$
$948$	17853.8	+	37252.9i	0.611672	+	1.27629i
$949$	34588.3	−	15795.9i	1.18312	−	0.540314i
$950$	−8190.07	+	75.8385i	−0.279706	+	0.00259003i
$951$	−9188.27	+	1321.07i	−0.313302	+	0.0450460i
$952$	−4178.87	−	4560.33i	−0.142267	−	0.155253i
$953$	−24778.5	−	21470.7i	−0.842241	−	0.729806i	0.122652	−	0.992450i	$-0.460860\pi$
$953$	−24778.5	−	21470.7i	−0.842241	−	0.729806i	−0.964893	+	0.262644i	$0.915406\pi$
$954$	35734.5	+	117659.i	1.21273	+	3.99304i
$955$	30726.3	+	19746.6i	1.04113	+	0.669093i
$956$	−6195.53	+	10044.7i	−0.209600	+	0.339819i
$957$	−16453.5	−	4831.17i	−0.555763	−	0.163187i
$958$	16413.2	−	26067.0i	0.553535	−	0.879110i
$959$	−593.688	+	514.434i	−0.0199908	+	0.0173221i
$960$	−29701.8	+	38393.8i	−0.998564	+	1.29079i
$961$	−2475.62	+	726.908i	−0.0830997	+	0.0244003i
$962$	−19940.4	−	42614.8i	−0.668301	−	1.42823i
$963$	132450.	+	19043.4i	4.43212	+	0.637243i
$964$	−23929.8	+	21523.9i	−0.799510	+	0.719128i
$965$	3729.06			0.124396
$966$	10221.6	+	7764.66i	0.340449	+	0.258617i
$967$			25822.1i			0.858722i	0.903133	+	0.429361i	$0.141261\pi$
$967$			25822.1i			0.858722i	−0.903133	+	0.429361i	$0.858739\pi$
$968$	−536.346	−	19302.9i	−0.0178087	−	0.640928i
$969$	−7772.15	+	54056.5i	−0.257665	+	1.79210i
$970$	10760.6	+	22996.5i	0.356187	+	0.761208i
$971$	12648.6	+	43077.3i	0.418037	+	1.42370i	0.852364	+	0.522948i	$0.175168\pi$
$971$	12648.6	+	43077.3i	0.418037	+	1.42370i	−0.434327	+	0.900755i	$0.643014\pi$
$972$	−93600.2	+	62632.3i	−3.08871	+	2.06680i
$973$	5877.58	+	6783.09i	0.193655	+	0.223490i
$974$	11085.4	+	6979.97i	0.364681	+	0.229623i
$975$	−4850.24	+	16518.4i	−0.159315	+	0.542577i
$976$	11579.1	−	28060.5i	0.379751	−	0.920282i
$977$	−19429.3	+	30232.7i	−0.636233	+	0.989998i	0.362092	+	0.932142i	$0.382063\pi$
$977$	−19429.3	+	30232.7i	−0.636233	+	0.989998i	−0.998325	+	0.0578558i	$0.981574\pi$
$978$	−5494.42	−	18090.9i	−0.179644	−	0.591495i
$979$	−20741.6	+	23937.1i	−0.677124	+	0.781442i
$980$	3062.84	−	24517.5i	0.0998356	−	0.799168i
$981$	13236.4	+	92061.4i	0.430792	+	2.99622i
$982$	−51.3899	−	5549.78i	−0.00166998	−	0.180347i
$983$	10087.9	+	22089.3i	0.327317	+	0.716724i	0.999725	−	0.0234566i	$-0.00746717\pi$
$983$	10087.9	+	22089.3i	0.327317	+	0.716724i	−0.672408	+	0.740181i	$0.734740\pi$
$984$	−4012.66	+	15217.4i	−0.129999	+	0.493000i
$985$	−37607.0	−	17174.6i	−1.21651	−	0.555560i
$986$	−11054.1	+	9759.08i	−0.357032	+	0.315205i
$987$	11082.3	+	17244.4i	0.357401	+	0.556126i
$988$	5134.54	+	31552.0i	0.165336	+	1.01599i
$989$	−3241.92	−	9144.43i	−0.104234	−	0.294010i
$990$	27764.9	−	32648.3i	0.891338	−	1.04811i
$991$	−6835.82	−	10636.7i	−0.219119	−	0.340956i	0.714239	−	0.699901i	$-0.246773\pi$
$991$	−6835.82	−	10636.7i	−0.219119	−	0.340956i	−0.933359	+	0.358946i	$0.883136\pi$
$992$	−25840.4	−	14963.9i	−0.827051	−	0.478935i
$993$	3448.21	−	7550.52i	0.110197	−	0.241298i
$994$	−2802.62	+	6290.38i	−0.0894303	+	0.200723i
$995$	−11334.8	−	24819.8i	−0.361144	−	0.790795i
$996$	−45639.8	−	38090.5i	−1.45196	−	1.21179i
$997$	−16909.1	+	2431.17i	−0.537129	+	0.0772275i	−0.405541	−	0.914077i	$-0.632917\pi$
$997$	−16909.1	+	2431.17i	−0.537129	+	0.0772275i	−0.131588	+	0.991304i	$0.542008\pi$
$998$	−30662.5	−	46754.1i	−0.972549	−	1.48294i
$999$	−103438.	+	119374.i	−3.27591	+	3.78060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.4.j.a.11.5	✓	700
8.3	odd	2	inner	184.4.j.a.11.30	yes	700
23.21	odd	22	inner	184.4.j.a.67.30	yes	700
184.67	even	22	inner	184.4.j.a.67.5	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.j.a.11.5	✓	700	1.1	even	1	trivial
184.4.j.a.11.30	yes	700	8.3	odd	2	inner
184.4.j.a.67.5	yes	700	184.67	even	22	inner
184.4.j.a.67.30	yes	700	23.21	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80324 - 0.376587i) q^{2} +(-1.42464 + 9.90857i) q^{3} +(7.71636 + 2.11133i) q^{4} +(9.08722 - 2.66825i) q^{5} +(7.72505 - 27.2397i) q^{6} +(-2.69152 - 3.10618i) q^{7} +(-20.8358 - 8.82446i) q^{8} +(-70.2439 - 20.6255i) q^{9} +(-26.4785 + 4.05763i) q^{10} +(11.8151 - 18.3847i) q^{11} +(-31.9133 + 73.4503i) q^{12} +(-36.8163 - 31.9015i) q^{13} +(6.37525 + 9.72098i) q^{14} +(13.4925 + 93.8426i) q^{15} +(55.0846 + 32.5836i) q^{16} +(-60.4995 + 27.6292i) q^{17} +(189.144 + 84.2712i) q^{18} +(-74.6133 - 34.0747i) q^{19} +(75.7538 - 1.40305i) q^{20} +(34.6123 - 22.2440i) q^{21} +(-40.0442 + 47.0875i) q^{22} +(-51.2782 - 97.6604i) q^{23} +(117.121 - 193.881i) q^{24} +(-29.6987 + 19.0862i) q^{25} +(91.1913 + 103.292i) q^{26} +(192.162 - 420.775i) q^{27} +(-14.2106 - 29.6511i) q^{28} +(-71.3012 + 32.5622i) q^{29} +(-2.48297 - 268.145i) q^{30} +(163.278 - 23.4759i) q^{31} +(-142.145 - 112.084i) q^{32} +(165.334 + 143.263i) q^{33} +(180.000 - 54.6681i) q^{34} +(-32.7465 - 21.0449i) q^{35} +(-498.480 - 307.462i) q^{36} +(-327.634 - 96.2020i) q^{37} +(196.327 + 123.618i) q^{38} +(368.548 - 319.348i) q^{39} +(-212.885 - 24.5948i) q^{40} +(-66.6636 + 19.5742i) q^{41} +(-105.403 + 49.3207i) q^{42} +(87.0624 + 12.5177i) q^{43} +(129.986 - 116.918i) q^{44} -693.355 q^{45} +(106.968 + 293.077i) q^{46} +498.217i q^{47} +(-401.332 + 499.390i) q^{48} +(46.4099 - 322.788i) q^{49} +(90.4404 - 42.3191i) q^{50} +(-187.576 - 638.825i) q^{51} +(-216.733 - 323.895i) q^{52} +(388.886 + 448.798i) q^{53} +(-697.135 + 1107.17i) q^{54} +(58.3118 - 198.592i) q^{55} +(28.6695 + 88.4709i) q^{56} +(443.929 - 690.767i) q^{57} +(212.137 - 64.4286i) q^{58} +(157.739 - 182.041i) q^{59} +(-94.0195 + 752.611i) q^{60} +(-67.5010 - 469.480i) q^{61} +(-466.549 + 4.32016i) q^{62} +(124.997 + 273.704i) q^{63} +(356.258 + 367.729i) q^{64} +(-419.678 - 191.661i) q^{65} +(-409.521 - 463.863i) q^{66} +(-41.1278 - 63.9961i) q^{67} +(-525.171 + 85.4625i) q^{68} +(1040.73 - 368.963i) q^{69} +(83.8713 + 71.3259i) q^{70} +(320.267 + 498.345i) q^{71} +(1281.58 + 1049.61i) q^{72} +(-324.253 + 710.015i) q^{73} +(882.210 + 393.060i) q^{74} +(-146.807 - 321.463i) q^{75} +(-503.800 - 420.467i) q^{76} +(-88.9070 + 12.7829i) q^{77} +(-1153.39 + 756.422i) q^{78} +(337.803 - 389.845i) q^{79} +(587.507 + 149.115i) q^{80} +(2232.65 + 1434.84i) q^{81} +(194.246 - 29.7667i) q^{82} +(-209.131 + 712.235i) q^{83} +(314.045 - 98.5645i) q^{84} +(-476.051 + 412.500i) q^{85} +(-239.343 - 67.8767i) q^{86} +(-221.066 - 752.882i) q^{87} +(-408.413 + 278.797i) q^{88} +(-1434.56 - 206.259i) q^{89} +(1943.65 + 261.109i) q^{90} +200.221i q^{91} +(-189.488 - 861.848i) q^{92} +1651.30i q^{93} +(187.622 - 1396.63i) q^{94} +(-768.947 - 110.558i) q^{95} +(1313.10 - 1248.77i) q^{96} +(-267.028 - 909.414i) q^{97} +(-251.656 + 887.377i) q^{98} +(-1209.14 + 1047.72i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 700 q - 7 q^{2} - 18 q^{3} - 11 q^{4} + 10 q^{6} - 40 q^{8} - 612 q^{9} - 11 q^{10} - 22 q^{11} + 6 q^{12} - 11 q^{14} - 27 q^{16} - 22 q^{17} + 244 q^{18} - 22 q^{19} - 11 q^{20} - 194 q^{24} - 1568 q^{25}+ \cdots - 22 q^{99}+O(q^{100}) \) 700 * q - 7 * q^2 - 18 * q^3 - 11 * q^4 + 10 * q^6 - 40 * q^8 - 612 * q^9 - 11 * q^10 - 22 * q^11 + 6 * q^12 - 11 * q^14 - 27 * q^16 - 22 * q^17 + 244 * q^18 - 22 * q^19 - 11 * q^20 - 194 * q^24 - 1568 * q^25 + 380 * q^26 + 222 * q^27 - 11 * q^28 - 11 * q^30 - 427 * q^32 - 22 * q^33 + 1903 * q^34 + 482 * q^35 - 1329 * q^36 + 594 * q^38 + 1309 * q^40 - 18 * q^41 - 3641 * q^42 - 22 * q^43 + 3300 * q^44 - 2727 * q^46 + 3204 * q^48 - 2860 * q^49 - 80 * q^50 - 22 * q^51 + 934 * q^52 + 2088 * q^54 - 3586 * q^56 - 22 * q^57 + 6159 * q^58 + 1002 * q^59 - 3641 * q^60 - 618 * q^62 + 1666 * q^64 - 22 * q^65 + 286 * q^66 - 22 * q^67 - 1474 * q^70 + 89 * q^72 - 18 * q^73 + 2354 * q^74 + 590 * q^75 + 8184 * q^76 + 10268 * q^78 + 4048 * q^80 - 5516 * q^81 - 4052 * q^82 - 22 * q^83 - 5401 * q^84 - 6721 * q^86 - 6963 * q^88 - 22 * q^89 - 18700 * q^90 - 4776 * q^92 - 8575 * q^94 - 5643 * q^96 - 22 * q^97 - 3995 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more