LMFDB - Embedded newform 184.4.j.a.67.30

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			67.30
Character	$\chi$	$=$	184.67
Dual form			184.4.j.a.11.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.821955 - 2.70636i) q^{2} +(-1.42464 - 9.90857i) q^{3} +(-6.64878 + 4.44901i) q^{4} +(-9.08722 - 2.66825i) q^{5} +(-25.6452 + 12.0000i) q^{6} +(2.69152 - 3.10618i) q^{7} +(17.5056 + 14.3371i) q^{8} +(-70.2439 + 20.6255i) q^{9} +(0.248038 + 26.7865i) q^{10} +(11.8151 + 18.3847i) q^{11} +(53.5555 + 59.5417i) q^{12} +(36.8163 - 31.9015i) q^{13} +(-10.6188 - 4.73109i) q^{14} +(-13.4925 + 93.8426i) q^{15} +(24.4126 - 59.1610i) q^{16} +(-60.4995 - 27.6292i) q^{17} +(113.557 + 173.152i) q^{18} +(-74.6133 + 34.0747i) q^{19} +(72.2900 - 22.6885i) 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} +(-116.598 - 73.4165i) q^{26} +(192.162 + 420.775i) q^{27} +(-4.07590 + 32.6269i) q^{28} +(71.3012 + 32.5622i) q^{29} +(265.062 - 40.6187i) q^{30} +(-163.278 - 23.4759i) q^{31} +(-180.177 - 17.4416i) q^{32} +(165.334 - 143.263i) q^{33} +(-25.0468 + 186.444i) q^{34} +(-32.7465 + 21.0449i) q^{35} +(375.273 - 449.650i) q^{36} +(327.634 - 96.2020i) q^{37} +(153.547 + 173.923i) q^{38} +(-368.548 - 319.348i) q^{39} +(-120.822 - 176.994i) q^{40} +(-66.6636 - 19.5742i) q^{41} +(-31.7505 + 111.957i) q^{42} +(87.0624 - 12.5177i) q^{43} +(-160.350 - 69.6703i) q^{44} +693.355 q^{45} +(-306.453 - 58.5049i) q^{46} +498.217i q^{47} +(-620.980 - 157.611i) q^{48} +(46.4099 + 322.788i) q^{49} +(-27.2432 + 96.0634i) q^{50} +(-187.576 + 638.825i) q^{51} +(-102.853 + 375.902i) q^{52} +(-388.886 + 448.798i) q^{53} +(980.822 - 865.917i) q^{54} +(-58.3118 - 198.592i) q^{55} +(91.6505 - 15.7870i) q^{56} +(443.929 + 690.767i) q^{57} +(29.5186 - 219.731i) q^{58} +(157.739 + 182.041i) q^{59} +(-327.798 - 683.968i) q^{60} +(67.5010 - 469.480i) q^{61} +(70.6731 + 461.186i) q^{62} +(-124.997 + 273.704i) q^{63} +(100.894 + 501.961i) q^{64} +(-419.678 + 191.661i) q^{65} +(-523.618 - 329.698i) 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} +(-1525.37 - 646.033i) q^{72} +(-324.253 - 710.015i) q^{73} +(-529.657 - 807.622i) q^{74} +(-146.807 + 321.463i) q^{75} +(344.489 - 558.511i) q^{76} +(88.9070 + 12.7829i) q^{77} +(-561.343 + 1259.91i) q^{78} +(-337.803 - 389.845i) q^{79} +(-379.699 + 472.470i) q^{80} +(2232.65 - 1434.84i) q^{81} +(1.81960 + 196.505i) q^{82} +(-209.131 - 712.235i) q^{83} +(329.093 - 6.09520i) q^{84} +(476.051 + 412.500i) q^{85} +(-105.439 - 225.333i) q^{86} +(221.066 - 752.882i) q^{87} +(-56.7524 + 491.231i) q^{88} +(-1434.56 + 206.259i) q^{89} +(-569.907 - 1876.47i) q^{90} -200.221i q^{91} +(93.5547 + 877.460i) q^{92} +1651.30i q^{93} +(1348.36 - 409.512i) q^{94} +(768.947 - 110.558i) q^{95} +(83.8656 + 1810.15i) q^{96} +(-267.028 + 909.414i) q^{97} +(835.434 - 390.919i) 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 $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.821955	−	2.70636i	−0.290605	−	0.956843i
$2$	−0.821955	−	2.70636i	−0.290605	−	0.956843i
$3$	−1.42464	−	9.90857i	−0.274172	−	1.90691i	−0.402932	−	0.915230i	$-0.632009\pi$
$3$	−1.42464	−	9.90857i	−0.274172	−	1.90691i	0.128760	−	0.991676i	$-0.458900\pi$
$4$	−6.64878	+	4.44901i	−0.831098	+	0.556126i
$5$	−9.08722	−	2.66825i	−0.812786	−	0.238655i	−0.151179	−	0.988506i	$-0.548307\pi$
$5$	−9.08722	−	2.66825i	−0.812786	−	0.238655i	−0.661607	+	0.749851i	$0.730125\pi$
$6$	−25.6452	+	12.0000i	−1.74493	+	0.816495i
$7$	2.69152	−	3.10618i	0.145329	−	0.167718i	−0.678418	−	0.734676i	$-0.737334\pi$
$7$	2.69152	−	3.10618i	0.145329	−	0.167718i	0.823747	+	0.566958i	$0.191880\pi$
$8$	17.5056	+	14.3371i	0.773647	+	0.633617i
$9$	−70.2439	+	20.6255i	−2.60163	+	0.763906i
$10$	0.248038	+	26.7865i	0.00784364	+	0.847063i
$11$	11.8151	+	18.3847i	0.323855	+	0.503927i	0.964562	−	0.263858i	$-0.0849950\pi$
$11$	11.8151	+	18.3847i	0.323855	+	0.503927i	−0.640707	+	0.767785i	$0.721359\pi$
$12$	53.5555	+	59.5417i	1.28834	+	1.43235i
$13$	36.8163	−	31.9015i	0.785461	−	0.680606i	−0.166766	−	0.985996i	$-0.553333\pi$
$13$	36.8163	−	31.9015i	0.785461	−	0.680606i	0.952227	+	0.305391i	$0.0987871\pi$
$14$	−10.6188	−	4.73109i	−0.202713	−	0.0903169i
$15$	−13.4925	+	93.8426i	−0.232251	+	1.61534i
$16$	24.4126	−	59.1610i	0.381447	−	0.924391i
$17$	−60.4995	−	27.6292i	−0.863135	−	0.394180i	−0.0658829	−	0.997827i	$-0.520986\pi$
$17$	−60.4995	−	27.6292i	−0.863135	−	0.394180i	−0.797252	+	0.603647i	$0.793714\pi$
$18$	113.557	+	173.152i	1.48698	+	2.26735i
$19$	−74.6133	+	34.0747i	−0.900919	+	0.411436i	−0.811361	−	0.584546i	$-0.801273\pi$
$19$	−74.6133	+	34.0747i	−0.900919	+	0.411436i	−0.0895583	+	0.995982i	$0.528546\pi$
$20$	72.2900	−	22.6885i	0.808227	−	0.253666i
$21$	−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
$26$	−116.598	−	73.4165i	−0.879492	−	0.553776i
$27$	192.162	+	420.775i	1.36969	+	2.99919i
$28$	−4.07590	+	32.6269i	−0.0275097	+	0.220211i
$29$	71.3012	+	32.5622i	0.456562	+	0.208505i	0.630402	−	0.776269i	$-0.282890\pi$
$29$	71.3012	+	32.5622i	0.456562	+	0.208505i	−0.173840	+	0.984774i	$0.555617\pi$
$30$	265.062	−	40.6187i	1.61312	−	0.247198i
$31$	−163.278	−	23.4759i	−0.945988	−	0.136012i	−0.347979	−	0.937502i	$-0.613132\pi$
$31$	−163.278	−	23.4759i	−0.945988	−	0.136012i	−0.598008	+	0.801490i	$0.704041\pi$
$32$	−180.177	−	17.4416i	−0.995347	−	0.0963522i
$33$	165.334	−	143.263i	0.872150	−	0.755723i
$34$	−25.0468	+	186.444i	−0.126338	+	0.940435i
$35$	−32.7465	+	21.0449i	−0.158148	+	0.101635i
$36$	375.273	−	449.650i	1.73738	−	2.08171i
$37$	327.634	−	96.2020i	1.45575	−	0.427446i	0.544310	−	0.838884i	$-0.316791\pi$
$37$	327.634	−	96.2020i	1.45575	−	0.427446i	0.911438	+	0.411438i	$0.134973\pi$
$38$	153.547	+	173.923i	0.655491	+	0.742473i
$39$	−368.548	−	319.348i	−1.51320	−	1.31120i
$40$	−120.822	−	176.994i	−0.477593	−	0.699630i
$41$	−66.6636	−	19.5742i	−0.253930	−	0.0745604i	0.152290	−	0.988336i	$-0.451335\pi$
$41$	−66.6636	−	19.5742i	−0.253930	−	0.0745604i	−0.406220	+	0.913775i	$0.633153\pi$
$42$	−31.7505	+	111.957i	−0.116648	+	0.411317i
$43$	87.0624	−	12.5177i	0.308765	−	0.0443937i	0.0138093	−	0.999905i	$-0.495604\pi$
$43$	87.0624	−	12.5177i	0.308765	−	0.0443937i	0.294956	+	0.955511i	$0.404695\pi$
$44$	−160.350	−	69.6703i	−0.549402	−	0.238709i
$45$	693.355			2.29687
$46$	−306.453	−	58.5049i	−0.982260	−	0.187523i
$47$			498.217i			1.54622i	0.634270	+	0.773112i	$0.281301\pi$
$47$			498.217i			1.54622i	−0.634270	+	0.773112i	$0.718699\pi$
$48$	−620.980	−	157.611i	−1.86731	−	0.473941i
$49$	46.4099	+	322.788i	0.135306	+	0.941073i
$50$	−27.2432	+	96.0634i	−0.0770553	+	0.271708i
$51$	−187.576	+	638.825i	−0.515018	+	1.75399i
$52$	−102.853	+	375.902i	−0.274292	+	1.00247i
$53$	−388.886	+	448.798i	−1.00788	+	1.16315i	−0.0213167	+	0.999773i	$0.506786\pi$
$53$	−388.886	+	448.798i	−1.00788	+	1.16315i	−0.986563	+	0.163382i	$0.947760\pi$
$54$	980.822	−	865.917i	2.47172	−	2.18215i
$55$	−58.3118	−	198.592i	−0.142959	−	0.486875i
$56$	91.6505	−	15.7870i	0.218702	−	0.0376719i
$57$	443.929	+	690.767i	1.03158	+	1.60516i
$58$	29.5186	−	219.731i	0.0668273	−	0.497451i
$59$	157.739	+	182.041i	0.348066	+	0.401690i	0.902606	−	0.430467i	$-0.141651\pi$
$59$	157.739	+	182.041i	0.348066	+	0.401690i	−0.554540	+	0.832157i	$0.687106\pi$
$60$	−327.798	−	683.968i	−0.705309	−	1.47166i
$61$	67.5010	−	469.480i	0.141682	−	0.985422i	−0.787636	−	0.616141i	$-0.788695\pi$
$61$	67.5010	−	469.480i	0.141682	−	0.985422i	0.929318	−	0.369281i	$-0.120396\pi$
$62$	70.6731	+	461.186i	0.144766	+	0.944688i
$63$	−124.997	+	273.704i	−0.249970	+	0.547357i
$64$	100.894	+	501.961i	0.197059	+	0.980392i
$65$	−419.678	+	191.661i	−0.800841	+	0.365732i
$66$	−523.618	−	329.698i	−0.976559	−	0.614895i
$67$	−41.1278	+	63.9961i	−0.0749934	+	0.116692i	−0.876724	−	0.480993i	$-0.840276\pi$
$67$	−41.1278	+	63.9961i	−0.0749934	+	0.116692i	0.801731	+	0.597685i	$0.203913\pi$
$68$	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	$-0.983047\pi$
$71$	−320.267	+	498.345i	−0.535334	+	0.832995i	0.463249	+	0.886228i	$0.346684\pi$
$72$	−1525.37	−	646.033i	−2.49676	−	1.05744i
$73$	−324.253	−	710.015i	−0.519876	−	1.13837i	−0.969486	−	0.245145i	$-0.921164\pi$
$73$	−324.253	−	710.015i	−0.519876	−	1.13837i	0.449610	−	0.893225i	$-0.351563\pi$
$74$	−529.657	−	807.622i	−0.832046	−	1.26870i
$75$	−146.807	+	321.463i	−0.226024	+	0.494924i
$76$	344.489	−	558.511i	0.519941	−	0.842968i
$77$	88.9070	+	12.7829i	0.131583	+	0.0189188i
$78$	−561.343	+	1259.91i	−0.814866	+	1.82894i
$79$	−337.803	−	389.845i	−0.481086	−	0.555202i	0.462376	−	0.886684i	$-0.346997\pi$
$79$	−337.803	−	389.845i	−0.481086	−	0.555202i	−0.943462	+	0.331482i	$0.892452\pi$
$80$	−379.699	+	472.470i	−0.530645	+	0.660297i
$81$	2232.65	−	1434.84i	3.06263	−	1.96823i
$82$	1.81960	+	196.505i	0.00245050	+	0.264638i
$83$	−209.131	−	712.235i	−0.276568	−	0.941903i	−0.974245	−	0.225491i	$-0.927601\pi$
$83$	−209.131	−	712.235i	−0.276568	−	0.941903i	0.697678	−	0.716412i	$-0.254217\pi$
$84$	329.093	−	6.09520i	0.427464	−	0.00791716i
$85$	476.051	+	412.500i	0.607470	+	0.526376i
$86$	−105.439	−	225.333i	−0.132206	−	0.282539i
$87$	221.066	−	752.882i	0.272423	−	0.927787i
$88$	−56.7524	+	491.231i	−0.0687480	+	0.595062i
$89$	−1434.56	+	206.259i	−1.70858	+	0.245656i	−0.926169	−	0.377109i	$-0.876918\pi$
$89$	−1434.56	+	206.259i	−1.70858	+	0.245656i	−0.782409	+	0.622766i	$0.786009\pi$
$90$	−569.907	−	1876.47i	−0.667483	−	2.19775i
$91$		−	200.221i		−	0.230647i
$92$	93.5547	+	877.460i	0.106019	+	0.994364i
$93$			1651.30i			1.84120i
$94$	1348.36	−	409.512i	1.47949	−	0.449340i
$95$	768.947	−	110.558i	0.830445	−	0.119400i
$96$	83.8656	+	1810.15i	0.0891614	+	1.92445i
$97$	−267.028	+	909.414i	−0.279511	+	0.951928i	0.693362	+	0.720590i	$0.256129\pi$
$97$	−267.028	+	909.414i	−0.279511	+	0.951928i	−0.972873	+	0.231339i	$0.925689\pi$
$98$	835.434	−	390.919i	0.861139	−	0.402947i
$99$	−1209.14	−	1047.72i	−1.22750	−	1.06364i
$100$	282.375	−	5.22993i	0.282375	−	0.00522993i
$101$	100.079	+	340.836i	0.0985959	+	0.335787i	0.993988	−	0.109493i	$-0.0349226\pi$
$101$	100.079	+	340.836i	0.0985959	+	0.335787i	−0.895392	+	0.445279i	$0.853104\pi$
$102$	1883.07	−	17.4369i	1.82796	−	0.0169266i
$103$	−134.031	+	86.1363i	−0.128218	+	0.0824006i	−0.603178	−	0.797607i	$-0.706099\pi$
$103$	−134.031	+	86.1363i	−0.128218	+	0.0824006i	0.474960	+	0.880008i	$0.342463\pi$
$104$	1101.87	−	30.6162i	1.03891	−	0.0288670i
$105$	255.177	+	294.490i	0.237169	+	0.273707i
$106$	1534.26	+	683.574i	1.40585	+	0.626364i
$107$	−1809.19	−	260.123i	−1.63459	−	0.235019i	−0.737014	−	0.675877i	$-0.763765\pi$
$107$	−1809.19	−	260.123i	−1.63459	−	0.235019i	−0.897576	+	0.440859i	$0.854674\pi$
$108$	−3149.67	−	1942.71i	−2.80627	−	1.73090i
$109$	527.760	−	1155.63i	0.463763	−	1.01550i	−0.522850	−	0.852425i	$-0.675131\pi$
$109$	527.760	−	1155.63i	0.463763	−	1.01550i	0.986614	−	0.163075i	$-0.0521414\pi$
$110$	−489.531	+	321.046i	−0.424318	+	0.278278i
$111$	−1419.98	−	3109.33i	−1.21422	−	2.65878i
$112$	−118.058	−	235.063i	−0.0996020	−	0.198316i
$113$	314.994	−	490.141i	0.262232	−	0.408040i	−0.685023	−	0.728521i	$-0.740208\pi$
$113$	314.994	−	490.141i	0.262232	−	0.408040i	0.947255	+	0.320481i	$0.103844\pi$
$114$	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
$118$	363.014	−	576.529i	0.283204	−	0.449778i
$119$	−248.657	+	113.558i	−0.191549	+	0.0874776i
$120$	−1581.63	+	1449.33i	−1.20319	+	1.10254i
$121$	354.517	−	776.284i	0.266354	−	0.583234i
$122$	−1326.06	+	203.209i	−0.984068	+	0.150801i
$123$	−98.9810	+	688.428i	−0.0725595	+	0.504662i
$124$	1190.04	−	570.341i	0.861848	−	0.413049i
$125$	994.213	+	1147.38i	0.711401	+	0.821001i
$126$	843.484	+	113.313i	0.596377	+	0.0801171i
$127$	998.819	+	1554.19i	0.697881	+	1.08592i	0.991513	+	0.130006i	$0.0414995\pi$
$127$	998.819	+	1554.19i	0.697881	+	1.08592i	−0.293632	+	0.955918i	$0.594864\pi$
$128$	1275.56	−	685.645i	0.880815	−	0.473461i
$129$	−248.065	−	844.831i	−0.169309	−	0.576614i
$130$	863.660	+	978.265i	0.582677	+	0.659996i
$131$	−613.247	+	707.724i	−0.409005	+	0.472016i	−0.922456	−	0.386102i	$-0.873821\pi$
$131$	−613.247	+	707.724i	−0.409005	+	0.472016i	0.513451	+	0.858119i	$0.328367\pi$
$132$	−461.892	+	1688.10i	−0.304565	+	1.11311i
$133$	−94.9810	+	323.475i	−0.0619240	+	0.210894i
$134$	207.002	+	58.7048i	0.133449	+	0.0378457i
$135$	−623.482	−	4336.41i	−0.397487	−	2.76458i
$136$	−662.959	−	1351.06i	−0.418002	−	0.851853i
$137$			191.131i			0.119193i	0.998223	+	0.0595965i	$0.0189814\pi$
$137$			191.131i			0.119193i	−0.998223	+	0.0595965i	$0.981019\pi$
$138$	−143.116	+	3119.86i	−0.0882817	+	1.92449i
$139$	−2183.74			−1.33254			−0.666268	−	0.745713i	$-0.732109\pi$
$139$	−2183.74			−1.33254			−0.666268	+	0.745713i	$0.732109\pi$
$140$	124.095	−	285.613i	0.0749141	−	0.172419i
$141$	4936.62	−	709.779i	2.94850	−	0.423931i
$142$	1611.95	+	457.141i	0.952616	+	0.270158i
$143$	1021.49	+	299.936i	0.597351	+	0.175398i
$144$	−494.612	+	4659.22i	−0.286234	+	2.69631i
$145$	−561.045	−	486.149i	−0.321326	−	0.278431i
$146$	−1655.04	+	1461.15i	−0.938163	+	0.828256i
$147$	3132.25	−	919.712i	1.75744	−	0.516031i
$148$	−1750.36	+	2097.27i	−0.972155	+	1.16483i
$149$	−1114.62	+	716.325i	−0.612842	+	0.393850i	−0.809922	−	0.586538i	$-0.800491\pi$
$149$	−1114.62	+	716.325i	−0.612842	+	0.393850i	0.197080	+	0.980387i	$0.436854\pi$
$150$	990.663	+	133.085i	0.539249	+	0.0724424i
$151$	296.269	−	256.718i	0.159669	−	0.138354i	−0.571362	−	0.820698i	$-0.693585\pi$
$151$	296.269	−	256.718i	0.159669	−	0.138354i	0.731031	+	0.682344i	$0.239039\pi$
$152$	−1794.69	−	473.240i	−0.957686	−	0.252532i
$153$	4819.59	+	692.952i	2.54667	+	0.366156i
$154$	−38.4824	−	251.121i	−0.0201364	−	0.131402i
$155$	1421.10	+	648.997i	0.736425	+	0.336314i
$156$	3871.18	+	483.605i	1.98681	+	0.248201i
$157$	−1393.87	−	3052.15i	−0.708553	−	1.55152i	−0.829282	−	0.558830i	$-0.811250\pi$
$157$	−1393.87	−	3052.15i	−0.708553	−	1.55152i	0.120729	−	0.992686i	$-0.461477\pi$
$158$	−777.403	+	1234.65i	−0.391436	+	0.621668i
$159$	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	0.668607	−	0.743616i	$-0.266891\pi$
$163$	561.755	+	361.018i	0.269939	+	0.173479i	−0.398668	+	0.917095i	$0.630527\pi$
$164$	530.318	−	166.443i	0.252505	−	0.0792499i
$165$	−1884.69	+	860.708i	−0.889228	+	0.406097i
$166$	−1755.67	+	1151.41i	−0.820881	+	0.538353i
$167$	−1807.72	−	825.556i	−0.837636	−	0.382536i	−0.0500550	−	0.998746i	$-0.515940\pi$
$167$	−1807.72	−	825.556i	−0.837636	−	0.382536i	−0.787581	+	0.616211i	$0.788667\pi$
$168$	−286.995	−	885.635i	−0.131799	−	0.406715i
$169$	25.0673	−	174.347i	0.0114098	−	0.0793568i
$170$	725.083	−	1627.42i	0.327125	−	0.734221i
$171$	4538.32	−	3932.48i	2.02956	−	1.75862i
$172$	−523.168	+	470.569i	−0.231925	+	0.208608i
$173$	−476.130	−	740.872i	−0.209245	−	0.325592i	0.720729	−	0.693217i	$-0.243807\pi$
$173$	−476.130	−	740.872i	−0.209245	−	0.325592i	−0.929974	+	0.367625i	$0.880171\pi$
$174$	−2219.28	+	20.5501i	−0.966914	+	0.00895344i
$175$	−139.220	+	40.8787i	−0.0601374	+	0.0176579i
$176$	1376.10	−	250.177i	0.589359	−	0.107147i
$177$	1579.04	−	1822.31i	0.670555	−	0.773861i
$178$	1737.36	+	3712.91i	0.731575	+	1.56345i
$179$	670.084	+	196.754i	0.279801	+	0.0821570i	0.418622	−	0.908160i	$-0.362513\pi$
$179$	670.084	+	196.754i	0.279801	+	0.0821570i	−0.138821	+	0.990317i	$0.544331\pi$
$180$	−4609.97	+	3084.75i	−1.90893	+	1.27735i
$181$	−329.470	−	2291.51i	−0.135300	−	0.941031i	−0.938489	−	0.345308i	$-0.887775\pi$
$181$	−329.470	−	2291.51i	−0.135300	−	0.941031i	0.803190	−	0.595723i	$-0.203135\pi$
$182$	−541.872	+	164.573i	−0.220693	+	0.0670272i
$183$	−4748.04			−1.91795
$184$	2297.83	−	974.425i	0.920641	−	0.390411i
$185$	−3233.97			−1.28522
$186$	4469.01	−	1357.29i	1.76174	−	0.535062i
$187$	−206.855	−	1438.71i	−0.0808917	−	0.562614i
$188$	−2216.58	−	3312.54i	−0.859896	−	1.28506i
$189$	1824.21	+	535.637i	0.702074	+	0.206147i
$190$	−931.249	−	1990.18i	−0.355579	−	0.759908i
$191$	−2525.47	+	2914.55i	−0.956737	+	1.10413i	0.0377517	+	0.999287i	$0.487980\pi$
$191$	−2525.47	+	2914.55i	−0.956737	+	1.10413i	−0.994488	+	0.104846i	$0.966565\pi$
$192$	4829.97	−	1714.83i	1.81549	−	0.644568i
$193$	377.791	−	110.929i	0.140902	−	0.0413724i	−0.210521	−	0.977589i	$-0.567516\pi$
$193$	377.791	−	110.929i	0.140902	−	0.0413724i	0.351423	+	0.936217i	$0.385698\pi$
$194$	2680.69	−	24.8227i	0.992073	−	0.00918641i
$195$	2496.97	+	3885.37i	0.916984	+	1.42686i
$196$	−1744.66	−	1939.67i	−0.635808	−	0.706876i
$197$	3299.07	−	2858.66i	1.19314	−	1.03387i	0.194548	−	0.980893i	$-0.437676\pi$
$197$	3299.07	−	2858.66i	1.19314	−	1.03387i	0.998596	−	0.0529721i	$-0.0168694\pi$
$198$	−1841.66	+	4133.54i	−0.661015	+	1.48362i
$199$	410.009	−	2851.68i	0.146054	−	1.01583i	−0.776543	−	0.630065i	$-0.783028\pi$
$199$	410.009	−	2851.68i	0.146054	−	1.01583i	0.922597	−	0.385765i	$-0.126063\pi$
$200$	−246.253	−	759.910i	−0.0870637	−	0.268669i
$201$	692.702	+	316.346i	0.243082	+	0.111012i
$202$	840.166	−	551.000i	0.292643	−	0.191922i
$203$	293.053	−	133.833i	0.101322	−	0.0462720i
$204$	−1594.99	−	5081.94i	−0.547410	−	1.74415i
$205$	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
$210$	587.252	−	932.658i	0.192973	−	0.306474i
$211$	1945.05	+	4259.07i	0.634610	+	1.38960i	0.904401	+	0.426684i	$0.140318\pi$
$211$	1945.05	+	4259.07i	0.634610	+	1.38960i	−0.269791	+	0.962919i	$0.586955\pi$
$212$	588.909	−	4714.12i	0.190785	−	1.52720i
$213$	5394.15	+	2463.43i	1.73522	+	0.792447i
$214$	783.088	+	5110.14i	0.250144	+	1.63234i
$215$	−824.556	−	118.553i	−0.261555	−	0.0376059i
$216$	−2668.79	+	10121.0i	−0.840687	+	3.18817i
$217$	−512.387	+	443.986i	−0.160291	+	0.138893i
$218$	−3561.35	−	478.431i	−1.10645	−	0.148640i
$219$	−6573.29	+	4224.40i	−2.02823	+	1.30346i
$220$	1271.24	+	1060.96i	0.389577	+	0.325137i
$221$	−3108.78	+	912.819i	−0.946240	+	0.277841i
$222$	−7247.81	+	6398.72i	−2.19118	+	1.93448i
$223$	561.865	+	486.859i	0.168723	+	0.146200i	0.735130	−	0.677927i	$-0.237121\pi$
$223$	561.865	+	486.859i	0.168723	+	0.146200i	−0.566406	+	0.824126i	$0.691667\pi$
$224$	−539.128	+	512.718i	−0.160812	+	0.152935i
$225$	2479.81	+	728.139i	0.734760	+	0.215745i
$226$	−1585.41	−	449.615i	−0.466637	−	0.132336i
$227$	−3675.59	+	528.471i	−1.07470	+	0.154519i	−0.656869	−	0.754004i	$-0.728120\pi$
$227$	−3675.59	+	528.471i	−1.07470	+	0.154519i	−0.417834	+	0.908523i	$0.637211\pi$
$228$	−6024.82	−	2617.71i	−1.75001	−	0.760361i
$229$	3349.56			0.966573			0.483287	−	0.875462i	$-0.339443\pi$
$229$	3349.56			0.966573			0.483287	+	0.875462i	$0.339443\pi$
$230$	2628.70	+	1349.34i	0.753613	+	0.386838i
$231$		−	899.153i		−	0.256103i
$232$	781.324	+	1592.27i	0.221105	+	0.450595i
$233$	−685.566	−	4768.22i	−0.192759	−	1.34067i	−0.824663	−	0.565624i	$-0.808635\pi$
$233$	−685.566	−	4768.22i	−0.192759	−	1.34067i	0.631904	−	0.775047i	$-0.282274\pi$
$234$	9704.56	+	2752.17i	2.71114	+	0.768868i
$235$	1329.37	−	4527.41i	0.369014	−	1.25675i
$236$	−1858.68	−	508.566i	−0.512667	−	0.140275i
$237$	−3381.56	+	3902.53i	−0.926818	+	1.06961i
$238$	511.714	+	579.617i	0.139368	+	0.157861i
$239$	415.615	+	1415.45i	0.112485	+	0.383088i	0.996422	−	0.0845175i	$-0.0269349\pi$
$239$	415.615	+	1415.45i	0.112485	+	0.383088i	−0.883937	+	0.467606i	$0.845117\pi$
$240$	5222.44	+	3089.17i	1.40461	+	0.830855i
$241$	−2175.11	−	3384.54i	−0.581374	−	0.904636i	0.418620	−	0.908162i	$-0.362514\pi$
$241$	−2175.11	−	3384.54i	−0.581374	−	0.904636i	−0.999994	+	0.00352599i	$0.998878\pi$
$242$	−2392.30	−	321.381i	−0.635467	−	0.0853684i
$243$	−9219.00	−	10639.3i	−2.43374	−	2.80869i
$244$	1639.92	+	3421.78i	0.430267	+	0.897775i
$245$	439.542	−	3057.08i	0.114617	−	0.797182i
$246$	1944.49	−	297.978i	0.503969	−	0.0772292i
$247$	−1659.95	+	3634.78i	−0.427611	+	0.936338i
$248$	−2521.71	−	2751.90i	−0.645681	−	0.704620i
$249$	−6759.29	+	3086.87i	−1.72029	+	0.785631i
$250$	2288.04	−	3633.80i	0.578832	−	0.919286i
$251$	1877.67	−	2921.72i	0.472182	−	0.734730i	−0.520712	−	0.853733i	$-0.674333\pi$
$251$	1877.67	−	2921.72i	0.472182	−	0.734730i	0.992894	+	0.119003i	$0.0379697\pi$
$252$	−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
$256$	−2904.05	−	2888.55i	−0.708997	−	0.705212i
$257$	−1997.53	−	4373.98i	−0.484834	−	1.06164i	−0.981106	−	0.193472i	$-0.938025\pi$
$257$	−1997.53	−	4373.98i	−0.484834	−	1.06164i	0.496271	−	0.868167i	$-0.334702\pi$
$258$	−2082.52	+	1365.77i	−0.502527	+	0.329569i
$259$	583.013	−	1276.62i	0.139871	−	0.306275i
$260$	1937.65	−	3141.46i	0.462184	−	0.749328i
$261$	−5680.08	−	816.673i	−1.34708	−	0.193681i
$262$	2419.42	+	1077.95i	0.570504	+	0.254183i
$263$	−5274.10	−	6086.64i	−1.23656	−	1.42707i	−0.867334	−	0.497726i	$-0.834168\pi$
$263$	−5274.10	−	6086.64i	−1.23656	−	1.42707i	−0.369225	−	0.929340i	$-0.620377\pi$
$264$	4948.25	−	137.491i	1.15358	−	0.0320530i
$265$	4731.40	−	3040.69i	1.09678	−	0.704860i
$266$	953.511	−	8.82934i	0.219788	−	0.00203519i
$267$	4087.46	+	13920.6i	0.936887	+	3.19074i
$268$	−11.2697	−	608.474i	−0.00256868	−	0.138688i
$269$	−5054.03	−	4379.34i	−1.14554	−	0.992613i	−0.999995	−	0.00326131i	$-0.998962\pi$
$269$	−5054.03	−	4379.34i	−1.14554	−	0.992613i	−0.145542	−	0.989352i	$-0.546493\pi$
$270$	−11223.4	+	5251.70i	−2.52976	+	1.18373i
$271$	−1161.06	+	3954.20i	−0.260256	+	0.886349i	0.720885	+	0.693054i	$0.243735\pi$
$271$	−1161.06	+	3954.20i	−0.260256	+	0.886349i	−0.981141	+	0.193295i	$0.938083\pi$
$272$	−3111.52	+	2904.71i	−0.693617	+	0.647515i
$273$	−1983.91	+	285.243i	−0.439823	+	0.0632370i
$274$	517.270	−	157.101i	0.114049	−	0.0346381i
$275$		−	771.509i		−	0.169177i
$276$	8561.09	−	2177.06i	1.86709	−	0.474795i
$277$		−	425.078i		−	0.0922038i	−0.998937	−	0.0461019i	$-0.985320\pi$
$277$		−	425.078i		−	0.0922038i	0.998937	−	0.0461019i	$-0.0146799\pi$
$278$	1794.93	+	5909.99i	0.387241	+	1.27503i
$279$	11953.5	−	1718.65i	2.56501	−	0.368792i
$280$	−874.972	−	101.086i	−0.186748	−	0.0215752i
$281$	−2461.36	+	8382.63i	−0.522536	+	1.77959i	0.0977429	+	0.995212i	$0.468838\pi$
$281$	−2461.36	+	8382.63i	−0.522536	+	1.77959i	−0.620279	+	0.784382i	$0.712980\pi$
$282$	−5978.60	−	12776.9i	−1.26248	−	2.69806i
$283$	−1460.78	−	1265.78i	−0.306836	−	0.265875i	0.487808	−	0.872951i	$-0.337797\pi$
$283$	−1460.78	−	1265.78i	−0.306836	−	0.265875i	−0.794644	+	0.607076i	$0.792342\pi$
$284$	−87.7583	−	4738.26i	−0.0183363	−	0.990014i
$285$	−2190.94	−	7461.66i	−0.455369	−	1.55084i
$286$	−27.8818	−	3011.05i	−0.00576463	−	0.622543i
$287$	−240.228	+	154.385i	−0.0494083	+	0.0317528i
$288$	13016.1	−	2491.07i	2.66313	−	0.509680i
$289$	−320.512	−	369.890i	−0.0652375	−	0.0752881i
$290$	−854.540	+	1917.98i	−0.173036	+	0.388372i
$291$	9391.42	+	1350.28i	1.89187	+	0.272010i
$292$	5314.75	+	3278.13i	1.06515	+	0.656980i
$293$	1354.91	−	2966.84i	0.270153	−	0.591552i	−0.725125	−	0.688617i	$-0.758218\pi$
$293$	1354.91	−	2966.84i	0.270153	−	0.591552i	0.995278	+	0.0970651i	$0.0309455\pi$
$294$	−5063.64	−	7721.04i	−1.00448	−	1.53163i
$295$	−947.681	−	2075.13i	−0.187038	−	0.409556i
$296$	7114.70	+	3013.25i	1.39707	+	0.591694i
$297$	−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
$302$	−938.292	−	590.799i	−0.178784	−	0.112572i
$303$	3234.62	−	1477.20i	0.613281	−	0.280076i
$304$	194.393	+	5246.05i	0.0366750	+	0.989742i
$305$	−1866.08	+	4086.16i	−0.350333	+	0.767123i
$306$	−2086.10	−	13613.1i	−0.389721	−	2.54317i
$307$	77.5718	−	539.524i	0.0144210	−	0.100301i	−0.981340	−	0.192282i	$-0.938411\pi$
$307$	77.5718	−	539.524i	0.0144210	−	0.100301i	0.995761	+	0.0919818i	$0.0293202\pi$
$308$	−647.995	+	310.558i	−0.119880	+	0.0574535i
$309$	1044.43	+	1205.34i	0.192284	+	0.221907i
$310$	588.336	−	4379.47i	0.107791	−	0.802378i
$311$	4955.79	+	7711.37i	0.903593	+	1.40602i	0.913842	+	0.406070i	$0.133101\pi$
$311$	4955.79	+	7711.37i	0.903593	+	1.40602i	−0.0102493	+	0.999947i	$0.503263\pi$
$312$	−1873.12	−	10874.3i	−0.339887	−	1.97319i
$313$	−1740.02	−	5925.98i	−0.314224	−	1.07015i	−0.953556	−	0.301217i	$-0.902607\pi$
$313$	−1740.02	−	5925.98i	−0.314224	−	1.07015i	0.639332	−	0.768931i	$-0.279211\pi$
$314$	−7114.52	+	6281.04i	−1.27865	+	1.12885i
$315$	1866.18	−	2153.69i	0.333801	−	0.385227i
$316$	3980.40	+	1089.11i	0.708592	+	0.193883i
$317$	−261.252	+	889.743i	−0.0462883	+	0.157643i	−0.979394	−	0.201959i	$-0.935269\pi$
$317$	−261.252	+	889.743i	−0.0462883	+	0.157643i	0.933106	+	0.359602i	$0.117088\pi$
$318$	4587.48	−	16176.1i	0.808973	−	2.85256i
$319$	243.787	+	1695.58i	0.0427883	+	0.297599i
$320$	422.509	−	4830.64i	0.0738092	−	0.843877i
$321$			18297.1i			3.18145i
$322$	−1006.55	+	794.430i	−0.174202	+	0.137490i
$323$	5455.53			0.939795
$324$	−8460.81	+	19473.0i	−1.45076	+	3.33900i
$325$	−1702.27	+	244.750i	−0.290539	+	0.0417732i
$326$	515.308	−	1817.05i	0.0875468	−	0.308703i
$327$	−12202.5	−	3582.99i	−2.06361	−	0.605932i
$328$	−886.351	−	1298.42i	−0.149209	−	0.218578i
$329$	1547.55	+	1340.96i	0.259330	+	0.224710i
$330$	3878.51	+	4393.18i	0.646985	+	0.732838i
$331$	−795.607	+	233.611i	−0.132116	+	0.0387929i	−0.347122	−	0.937820i	$-0.612841\pi$
$331$	−795.607	+	233.611i	−0.132116	+	0.0387929i	0.215006	+	0.976613i	$0.431023\pi$
$332$	4559.21	+	3805.07i	0.753672	+	0.629007i
$333$	−21030.1	+	13515.2i	−3.46078	+	2.22411i
$334$	−748.393	+	5570.90i	−0.122605	+	0.912653i
$335$	544.495	−	471.807i	0.0888027	−	0.0769480i
$336$	−2160.95	+	1504.66i	−0.350862	+	0.244304i
$337$	1922.40	+	276.399i	0.310741	+	0.0446779i	0.295921	−	0.955212i	$-0.404373\pi$
$337$	1922.40	+	276.399i	0.310741	+	0.0446779i	0.0148200	+	0.999890i	$0.495282\pi$
$338$	−492.450	+	75.4640i	−0.0792477	+	0.0121441i
$339$	−5305.35	−	2422.87i	−0.849991	−	0.388178i
$340$	−5000.38	−	624.669i	−0.797598	−	0.0996395i
$341$	−1497.56	−	3279.19i	−0.237822	−	0.520757i
$342$	−14373.0	−	9050.02i	−2.27252	−	1.43090i
$343$	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	0.972738	−	0.231906i	$-0.0744962\pi$
$347$	7536.12	+	4843.17i	1.16588	+	0.749265i	0.193141	+	0.981171i	$0.438133\pi$
$348$	1879.76	+	5989.27i	0.289557	+	0.922583i
$349$	−5420.89	+	2475.64i	−0.831443	+	0.379707i	−0.785215	−	0.619223i	$-0.787448\pi$
$349$	−5420.89	+	2475.64i	−0.831443	+	0.379707i	−0.0462285	+	0.998931i	$0.514720\pi$
$350$	225.065	+	343.179i	0.0343721	+	0.0524105i
$351$	20498.0	+	9361.13i	3.11710	+	1.42353i
$352$	−1808.16	−	3518.58i	−0.273793	−	0.532787i
$353$	211.301	−	1469.63i	0.0318596	−	0.221588i	−0.967671	−	0.252215i	$-0.918841\pi$
$353$	211.301	−	1469.63i	0.0318596	−	0.221588i	0.999531	+	0.0306263i	$0.00975017\pi$
$354$	−6229.74	−	2775.60i	−0.935330	−	0.416728i
$355$	4240.04	−	3674.02i	0.633910	−	0.549286i
$356$	8620.45	−	7753.76i	1.28338	−	1.15435i
$357$	1479.44	+	2302.06i	0.219329	+	0.341283i
$358$	−18.2901	−	1975.21i	−0.00270017	−	0.291601i
$359$	−1776.76	+	521.703i	−0.261208	+	0.0766976i	−0.409714	−	0.912214i	$-0.634372\pi$
$359$	−1776.76	+	521.703i	−0.261208	+	0.0766976i	0.148506	+	0.988911i	$0.452553\pi$
$360$	12137.6	+	9940.72i	1.77697	+	1.45534i
$361$	−85.6349	+	98.8280i	−0.0124850	+	0.0144085i
$362$	−5930.85	+	2775.18i	−0.861101	+	0.402929i
$363$	−8196.92	−	2406.83i	−1.18520	−	0.348006i
$364$	890.788	+	1331.23i	0.128269	+	0.191691i
$365$	1052.06	+	7317.25i	0.150870	+	1.04932i
$366$	3902.67	+	12849.9i	0.557366	+	1.83518i
$367$	−3167.35			−0.450502			−0.225251	−	0.974301i	$-0.572320\pi$
$367$	−3167.35			−0.450502			−0.225251	+	0.974301i	$0.572320\pi$
$368$	−4525.85	−	5417.81i	−0.641104	−	0.767454i
$369$	5086.44			0.717587
$370$	2658.18	+	8752.29i	0.373492	+	1.22976i
$371$	347.354	+	2415.90i	0.0486085	+	0.338079i
$372$	−7346.64	−	10979.1i	−1.02394	−	1.53022i
$373$	7600.44	+	2231.69i	1.05506	+	0.309792i	0.762858	−	0.646565i	$-0.223795\pi$
$373$	7600.44	+	2231.69i	1.05506	+	0.309792i	0.292198	+	0.956358i	$0.405613\pi$
$374$	−3723.64	+	1742.38i	−0.514826	+	0.240899i
$375$	9952.54	−	11485.8i	1.37052	−	1.58167i
$376$	−7143.00	+	8721.61i	−0.979713	+	1.19623i
$377$	3663.82	−	1075.80i	0.500521	−	0.146966i
$378$	−49.7923	−	5377.25i	−0.00677523	−	0.731682i
$379$	1495.66	+	2327.30i	0.202710	+	0.315422i	0.927693	−	0.373344i	$-0.121789\pi$
$379$	1495.66	+	2327.30i	0.202710	+	0.315422i	−0.724983	+	0.688766i	$0.758153\pi$
$380$	−4620.69	+	4156.13i	−0.623780	+	0.561066i
$381$	13976.9	−	12111.0i	1.87942	−	1.62852i
$382$	9963.65	+	4439.21i	1.33451	+	0.594581i
$383$	−975.283	+	6783.24i	−0.130117	+	0.904980i	0.815282	+	0.579064i	$0.196582\pi$
$383$	−975.283	+	6783.24i	−0.130117	+	0.904980i	−0.945399	+	0.325916i	$0.894327\pi$
$384$	−8610.96	−	11662.1i	−1.14434	−	1.54982i
$385$	−773.810	−	353.387i	−0.102434	−	0.0467799i
$386$	−610.742	−	931.260i	−0.0805336	−	0.122798i
$387$	−5857.42	+	2674.99i	−0.769378	+	0.351363i
$388$	−2270.58	−	7234.51i	−0.297091	−	0.946589i
$389$	−6897.25	−	4432.60i	−0.898984	−	0.577742i	0.00750509	−	0.999972i	$-0.497611\pi$
$389$	−6897.25	−	4432.60i	−0.898984	−	0.577742i	−0.906489	+	0.422230i	$0.861247\pi$
$390$	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
$394$	−10448.3	−	6578.80i	−1.33598	−	0.841205i
$395$	2029.48	+	4443.95i	0.258517	+	0.566074i
$396$	12700.6	+	1586.62i	1.61169	+	0.201339i
$397$	5744.87	+	2623.59i	0.726263	+	0.331673i	0.744009	−	0.668169i	$-0.232922\pi$
$397$	5744.87	+	2623.59i	0.726263	+	0.331673i	−0.0177460	+	0.999843i	$0.505649\pi$
$398$	−8054.68	+	1234.32i	−1.01443	+	0.155454i
$399$	3340.49	+	480.290i	0.419132	+	0.0602621i
$400$	−1854.18	+	1291.06i	−0.231773	+	0.161383i
$401$	−5204.04	+	4509.32i	−0.648073	+	0.561558i	−0.915649	−	0.401978i	$-0.868323\pi$
$401$	−5204.04	+	4509.32i	−0.648073	+	0.561558i	0.267576	+	0.963537i	$0.413777\pi$
$402$	286.778	−	2134.72i	0.0355801	−	0.264852i
$403$	−6760.20	+	4344.52i	−0.835607	+	0.537012i
$404$	−2181.78	−	1820.89i	−0.268683	−	0.224240i
$405$	−24117.1	+	7081.43i	−2.95899	+	0.868837i
$406$	−603.076	−	683.102i	−0.0737196	−	0.0835019i
$407$	5639.69	+	4886.82i	0.686852	+	0.595161i
$408$	−12442.6	+	8493.74i	−1.50980	+	1.03064i
$409$	−3674.17	−	1078.83i	−0.444195	−	0.130427i	0.0519834	−	0.998648i	$-0.483446\pi$
$409$	−3674.17	−	1078.83i	−0.444195	−	0.130427i	−0.496179	+	0.868220i	$0.665264\pi$
$410$	507.789	−	1790.54i	0.0611656	−	0.215679i
$411$	1893.84	−	272.293i	0.227290	−	0.0326793i
$412$	507.920	−	1169.01i	0.0607364	−	0.139788i
$413$	990.011			0.117955
$414$	22733.1	−	2211.11i	2.69872	−	0.262489i
$415$			7030.25i			0.831569i
$416$	−7189.86	+	5105.78i	−0.847384	+	0.601758i
$417$	3111.04	+	21637.7i	0.365343	+	2.54102i
$418$	−1383.34	+	4877.85i	−0.161869	+	0.570773i
$419$	1950.53	−	6642.90i	0.227422	−	0.774528i	−0.764158	−	0.645029i	$-0.776845\pi$
$419$	1950.53	−	6642.90i	0.227422	−	0.774528i	0.991580	−	0.129498i	$-0.0413367\pi$
$420$	−3006.80	−	822.714i	−0.349326	−	0.0955817i
$421$	4550.78	−	5251.88i	0.526821	−	0.607983i	−0.428505	−	0.903540i	$-0.640959\pi$
$421$	4550.78	−	5251.88i	0.526821	−	0.607983i	0.955325	+	0.295556i	$0.0955049\pi$
$422$	9927.83	−	8764.77i	1.14521	−	1.01105i
$423$	−10276.0	−	34996.7i	−1.18117	−	4.02269i
$424$	−13242.2	+	2280.99i	−1.51674	+	0.261261i
$425$	1269.42	+	1975.26i	0.144885	+	0.225445i
$426$	2233.17	−	16623.3i	0.253985	−	1.89062i
$427$	−1276.61	−	1473.29i	−0.144683	−	0.166973i
$428$	13186.2	−	6319.62i	1.48920	−	0.713716i
$429$	1516.69	−	10548.8i	0.170691	−	1.18718i
$430$	356.899	+	2328.99i	0.0400261	+	0.261195i
$431$	4692.63	−	10275.4i	0.524446	−	1.14838i	−0.443283	−	0.896382i	$-0.646186\pi$
$431$	4692.63	−	10275.4i	0.524446	−	1.14838i	0.967729	−	0.251995i	$-0.0810866\pi$
$432$	29584.7	−	1096.26i	3.29489	−	0.122093i
$433$	2990.04	−	1365.51i	0.331852	−	0.151552i	−0.242519	−	0.970147i	$-0.577974\pi$
$433$	2990.04	−	1365.51i	0.331852	−	0.151552i	0.574372	+	0.818595i	$0.305246\pi$
$434$	1622.74	+	1021.77i	0.179480	+	0.113010i
$435$	−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	$-0.659709\pi$
$439$	4749.50	−	7390.36i	0.516358	−	0.803469i	0.997312	+	0.0732774i	$0.0233458\pi$
$440$	1826.45	−	4312.50i	0.197892	−	0.467250i
$441$	−9917.67	−	21716.7i	−1.07091	−	2.34496i
$442$	5025.69	+	7663.18i	0.540832	+	0.824661i
$443$	−1867.90	+	4090.13i	−0.200331	+	0.438664i	−0.982959	−	0.183826i	$-0.941152\pi$
$443$	−1867.90	+	4090.13i	−0.200331	+	0.438664i	0.782628	+	0.622490i	$0.213879\pi$
$444$	23274.6	+	14355.7i	2.48776	+	1.53444i
$445$	13586.5	+	1953.45i	1.44733	+	0.208095i
$446$	855.789	−	1920.79i	0.0908582	−	0.203928i
$447$	8685.69	+	10023.8i	0.919058	+	1.06065i
$448$	1830.74	+	1037.64i	0.193068	+	0.109429i
$449$	3308.89	−	2126.50i	0.347787	−	0.223509i	−0.355071	−	0.934839i	$-0.615543\pi$
$449$	3308.89	−	2126.50i	0.347787	−	0.223509i	0.702858	+	0.711330i	$0.251907\pi$
$450$	−67.6871	−	7309.77i	−0.00709067	−	0.765746i
$451$	−427.774	−	1456.86i	−0.0446632	−	0.152109i
$452$	86.3135	+	4660.25i	0.00898196	+	0.484955i
$453$	−2965.79	−	2569.87i	−0.307604	−	0.266541i
$454$	4451.40	+	9513.10i	0.460165	+	0.983419i
$455$	−534.241	+	1819.46i	−0.0550452	+	0.187467i
$456$	−2132.35	+	18457.0i	−0.218984	+	1.89545i
$457$	−18863.1	+	2712.11i	−1.93081	+	0.277608i	−0.996819	−	0.0796962i	$-0.974605\pi$
$457$	−18863.1	+	2712.11i	−1.93081	+	0.277608i	−0.933988	+	0.357304i	$0.883696\pi$
$458$	−2753.19	−	9065.12i	−0.280891	−	0.924859i
$459$		−	30766.0i		−	3.12861i
$460$	1491.13	−	8223.29i	0.151140	−	0.833507i
$461$		−	3125.45i		−	0.315763i	−0.987458	−	0.157882i	$-0.949534\pi$
$461$		−	3125.45i		−	0.315763i	0.987458	−	0.157882i	$-0.0504665\pi$
$462$	−2433.43	+	739.063i	−0.245051	+	0.0744249i
$463$	−15641.8	+	2248.96i	−1.57006	+	0.225741i	−0.871712	−	0.490018i	$-0.836990\pi$
$463$	−15641.8	+	2248.96i	−1.57006	+	0.225741i	−0.698348	+	0.715759i	$0.746081\pi$
$464$	3667.06	−	3423.32i	0.366894	−	0.342508i
$465$	4406.07	−	15005.7i	0.439412	−	1.49650i
$466$	−12341.0	+	5774.65i	−1.22680	+	0.574046i
$467$	10380.6	+	8994.84i	1.02860	+	0.891288i	0.994138	−	0.108118i	$-0.0344823\pi$
$467$	10380.6	+	8994.84i	1.02860	+	0.891288i	0.0344636	+	0.999406i	$0.489028\pi$
$468$	−528.340	−	28526.2i	−0.0521849	−	2.81757i
$469$	88.0871	+	299.997i	0.00867268	+	0.0295364i
$470$	−13345.5	+	123.577i	−1.30975	+	0.0121280i
$471$	−28256.7	+	18159.5i	−2.76433	+	1.77653i
$472$	151.384	+	5448.27i	0.0147628	+	0.531307i
$473$	1258.79	+	1452.72i	0.122366	+	0.141218i
$474$	13341.1	+	5944.02i	1.29278	+	0.575987i
$475$	2866.28	+	412.108i	0.276871	+	0.0398080i
$476$	1148.05	−	1861.30i	0.110548	−	0.179228i
$477$	18060.2	−	39546.3i	1.73358	−	3.79602i
$478$	3489.11	−	2288.24i	0.333867	−	0.218958i
$479$	4524.22	+	9906.66i	0.431559	+	0.944983i	0.993071	+	0.117514i	$0.0374926\pi$
$479$	4524.22	+	9906.66i	0.431559	+	0.944983i	−0.561512	+	0.827469i	$0.689780\pi$
$480$	4067.81	−	16673.0i	0.386811	−	1.58544i
$481$	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
$486$	−21216.2	+	33694.9i	−1.98022	+	3.14493i
$487$	4212.96	−	1923.99i	0.392007	−	0.179024i	−0.209653	−	0.977776i	$-0.567233\pi$
$487$	4212.96	−	1923.99i	0.392007	−	0.179024i	0.601660	+	0.798752i	$0.294506\pi$
$488$	7912.63	−	7250.77i	0.733992	−	0.672596i
$489$	2776.87	−	6080.51i	0.256799	−	0.562311i
$490$	−8634.84	+	1323.22i	−0.796086	+	0.121994i
$491$	279.254	−	1942.26i	0.0256671	−	0.178519i	−0.972955	−	0.230994i	$-0.925802\pi$
$491$	279.254	−	1942.26i	0.0256671	−	0.178519i	0.998622	+	0.0524756i	$0.0167112\pi$
$492$	−2404.72	−	5017.57i	−0.220352	−	0.459776i
$493$	−3414.02	−	3939.99i	−0.311886	−	0.359936i
$494$	11201.4	+	1504.79i	1.02019	+	0.137052i
$495$	8192.09	+	12747.1i	0.743853	+	1.15746i
$496$	−5374.90	+	9086.59i	−0.486573	+	0.822581i
$497$	685.945	+	2336.11i	0.0619091	+	0.210843i
$498$	13910.0	+	15755.8i	1.25165	+	1.41774i
$499$	12945.2	−	14939.5i	1.16133	−	1.34025i	0.231254	−	0.972893i	$-0.425717\pi$
$499$	12945.2	−	14939.5i	1.16133	−	1.34025i	0.930080	−	0.367358i	$-0.119737\pi$
$500$	−11715.0	−	3205.43i	−1.04782	−	0.286703i
$501$	−5604.74	+	19088.0i	−0.499803	+	1.70217i
$502$	−9450.59	−	2680.15i	−0.840240	−	0.238288i
$503$	−740.941	−	5153.36i	−0.0656798	−	0.456813i	−0.995948	−	0.0899326i	$-0.971335\pi$
$503$	−740.941	−	5153.36i	−0.0656798	−	0.456813i	0.930268	−	0.366881i	$-0.119574\pi$
$504$	−6112.27	+	2999.27i	−0.540203	+	0.265076i
$505$		−	3364.29i		−	0.296453i
$506$	−2545.18	−	6325.29i	−0.223611	−	0.555718i
$507$	−1763.24			−0.154454
$508$	−13555.6	−	5889.73i	−1.18392	−	0.514399i
$509$	10052.7	−	1445.36i	0.875397	−	0.125863i	0.310054	−	0.950719i	$-0.399653\pi$
$509$	10052.7	−	1445.36i	0.875397	−	0.125863i	0.565343	+	0.824856i	$0.308744\pi$
$510$	−17158.4	−	4866.05i	−1.48978	−	0.422495i
$511$	−3078.17	−	903.832i	−0.266478	−	0.0782450i
$512$	−5430.45	+	10233.7i	−0.468739	+	0.883337i
$513$	−28675.6	−	24847.6i	−2.46795	−	2.13849i
$514$	−10195.7	+	9001.25i	−0.874927	+	0.772428i
$515$	1447.80	−	425.112i	0.123879	−	0.0363742i
$516$	5407.99	+	4513.45i	0.461383	+	0.385065i
$517$	−9159.59	+	5886.51i	−0.779184	+	0.500751i
$518$	−3934.21	−	528.520i	−0.333705	−	0.0448298i
$519$	−6662.67	+	5773.24i	−0.563504	+	0.488279i
$520$	−10094.6	−	2661.84i	−0.851302	−	0.224479i
$521$	−12166.1	−	1749.22i	−1.02304	−	0.147091i	−0.389684	−	0.920949i	$-0.627416\pi$
$521$	−12166.1	−	1749.22i	−1.02304	−	0.147091i	−0.633360	+	0.773857i	$0.718325\pi$
$522$	2458.56	+	16043.6i	0.206146	+	1.34523i
$523$	−3140.33	−	1434.14i	−0.262557	−	0.119906i	0.279788	−	0.960062i	$-0.409736\pi$
$523$	−3140.33	−	1434.14i	−0.262557	−	0.119906i	−0.542344	+	0.840156i	$0.682463\pi$
$524$	928.669	−	7433.84i	0.0774219	−	0.619750i
$525$	603.387	+	1321.23i	0.0501599	+	0.109835i
$526$	−12137.6	+	19276.6i	−1.00613	+	1.59791i
$527$	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
$532$	−807.638	−	2573.29i	−0.0658187	−	0.209711i
$533$	−3078.75	+	1406.02i	−0.250198	+	0.114262i
$534$	34314.5	−	22504.3i	2.78078	−	1.82370i
$535$	15746.4	+	7191.16i	1.27248	+	0.581123i
$536$	−1637.49	+	530.638i	−0.131956	+	0.0427613i
$537$	994.928	−	6919.88i	0.0799522	−	0.556079i
$538$	−7697.89	+	17277.6i	−0.616877	+	1.38456i
$539$	−5386.03	+	4667.02i	−0.430413	+	0.372955i
$540$	23438.1	+	26058.0i	1.86781	+	2.07659i
$541$	−5166.01	−	8038.47i	−0.410544	−	0.638819i	0.572986	−	0.819565i	$-0.305785\pi$
$541$	−5166.01	−	8038.47i	−0.410544	−	0.638819i	−0.983530	+	0.180747i	$0.942149\pi$
$542$	11655.8	−	107.931i	0.923729	−	0.00855355i
$543$	−22236.2	+	6529.15i	−1.75736	+	0.516008i
$544$	10418.7	+	6033.36i	0.821139	+	0.475511i
$545$	−7879.38	+	9093.29i	−0.619295	+	0.714704i
$546$	2402.65	+	5134.72i	0.188323	+	0.402465i
$547$	14813.5	+	4349.65i	1.15792	+	0.339996i	0.803623	−	0.595138i	$-0.202903\pi$
$547$	14813.5	+	4349.65i	1.15792	+	0.339996i	0.354295	+	0.935134i	$0.384721\pi$
$548$	−850.345	−	1270.79i	−0.0662864	−	0.0990610i
$549$	4941.71	+	34370.3i	0.384166	+	2.67193i
$550$	−2087.98	+	634.145i	−0.161876	+	0.0491637i
$551$	−6429.56			−0.497112
$552$	−12928.7	−	21380.0i	−0.996890	−	1.64854i
$553$	−2120.13			−0.163033
$554$	−1150.41	+	349.395i	−0.0882245	+	0.0267949i
$555$	4607.24	+	32044.0i	0.352372	+	2.45080i
$556$	14519.2	−	9715.48i	1.10747	−	0.741058i
$557$	207.509	+	60.9303i	0.0157854	+	0.00463501i	0.289616	−	0.957143i	$-0.406472\pi$
$557$	207.509	+	60.9303i	0.0157854	+	0.00463501i	−0.273830	+	0.961778i	$0.588291\pi$
$558$	−14476.5	−	30937.8i	−1.09828	−	2.34714i
$559$	2805.98	−	3238.27i	0.212308	−	0.245017i
$560$	445.611	+	2451.08i	0.0336259	+	0.184959i
$561$	−13960.9	+	4099.28i	−1.05067	+	0.308506i
$562$	24709.5	−	228.806i	1.85464	−	0.0171736i
$563$	−4188.77	−	6517.85i	−0.313562	−	0.487913i	0.648323	−	0.761365i	$-0.275471\pi$
$563$	−4188.77	−	6517.85i	−0.313562	−	0.487913i	−0.961885	+	0.273453i	$0.911834\pi$
$564$	−29664.7	+	26682.3i	−2.21473	+	1.99207i
$565$	−4170.24	+	3613.53i	−0.310519	+	0.269066i
$566$	−2224.95	+	4993.82i	−0.165233	+	0.370858i
$567$	1552.36	−	10796.9i	0.114979	−	0.799698i
$568$	−12751.3	+	4132.14i	−0.941959	+	0.305248i
$569$	24234.4	+	11067.5i	1.78552	+	0.815419i	0.972399	+	0.233323i	$0.0749601\pi$
$569$	24234.4	+	11067.5i	1.78552	+	0.815419i	0.813120	+	0.582096i	$0.197767\pi$
$570$	−18393.1	+	12062.6i	−1.35158	+	0.886400i
$571$	−2865.02	+	1308.41i	−0.209978	+	0.0958936i	−0.517628	−	0.855606i	$-0.673185\pi$
$571$	−2865.02	+	1308.41i	−0.209978	+	0.0958936i	0.307650	+	0.951500i	$0.400457\pi$
$572$	−8126.08	+	2550.41i	−0.594001	+	0.186430i
$573$	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	0.995017	−	0.0997061i	$-0.0317903\pi$
$577$	18262.9	+	11736.8i	1.31767	+	0.846813i	0.322649	+	0.946519i	$0.395427\pi$
$578$	−737.610	+	1171.45i	−0.0530805	+	0.0843011i
$579$	−1637.37	−	3585.34i	−0.117525	−	0.257343i
$580$	5893.15	+	736.198i	0.421896	+	0.0527051i
$581$	−2775.21	−	1267.40i	−0.198167	−	0.0905000i
$582$	−4064.97	−	26526.4i	−0.289516	−	1.88927i
$583$	−12845.8	−	1846.94i	−0.912552	−	0.131205i
$584$	4503.32	−	17078.1i	0.319090	−	1.21010i
$585$	25526.7	−	22119.1i	1.80410	−	1.56327i
$586$	−9143.02	−	1228.27i	−0.644530	−	0.0865859i
$587$	−5904.97	+	3794.89i	−0.415203	+	0.266835i	−0.731522	−	0.681818i	$-0.761189\pi$
$587$	−5904.97	+	3794.89i	−0.415203	+	0.266835i	0.316319	+	0.948653i	$0.397553\pi$
$588$	−16733.8	+	20050.4i	−1.17363	+	1.40623i
$589$	12982.7	−	3812.05i	0.908219	−	0.266677i
$590$	−4837.11	+	4270.43i	−0.337526	+	0.297985i
$591$	−33025.3	−	28616.6i	−2.29861	−	1.99176i
$592$	2306.98	−	21731.7i	0.160163	−	1.50873i
$593$	794.572	+	233.307i	0.0550239	+	0.0161565i	0.309129	−	0.951020i	$-0.399963\pi$
$593$	794.572	+	233.307i	0.0550239	+	0.0161565i	−0.254105	+	0.967177i	$0.581781\pi$
$594$	27508.2	+	7801.20i	1.90013	+	0.538867i
$595$	2562.60	−	368.447i	0.176565	−	0.0253863i
$596$	4223.95	−	9721.66i	0.290301	−	0.668145i
$597$	−28840.2			−1.97714
$598$	−13148.8	+	7622.35i	−0.899156	+	0.521239i
$599$			10383.3i			0.708267i	0.935195	+	0.354133i	$0.115224\pi$
$599$			10383.3i			0.708267i	−0.935195	+	0.354133i	$0.884776\pi$
$600$	−7178.80	+	3522.62i	−0.488455	+	0.239684i
$601$	−3753.43	−	26105.7i	−0.254752	−	1.77184i	−0.568845	−	0.822444i	$-0.692610\pi$
$601$	−3753.43	−	26105.7i	−0.254752	−	1.77184i	0.314094	−	0.949392i	$-0.398299\pi$
$602$	−983.717	−	278.978i	−0.0666002	−	0.0188875i
$603$	1569.03	−	5343.61i	0.105963	−	0.360877i
$604$	−827.683	+	3024.97i	−0.0557582	+	0.203782i
$605$	−5292.89	+	6108.32i	−0.355680	+	0.410477i
$606$	−6656.56	−	7539.87i	−0.446212	−	0.505423i
$607$	−6454.78	−	21983.0i	−0.431617	−	1.46995i	−0.832604	−	0.553868i	$-0.813151\pi$
$607$	−6454.78	−	21983.0i	−0.431617	−	1.46995i	0.400988	−	0.916083i	$-0.368667\pi$
$608$	14037.9	−	4838.11i	0.936370	−	0.322716i
$609$	−1743.58	−	2713.07i	−0.116016	−	0.180524i
$610$	12592.5	+	1691.67i	0.835825	+	0.112284i
$611$	15893.9	+	18342.5i	1.05237	+	1.21450i
$612$	−35127.3	+	16835.1i	−2.32016	+	1.11196i
$613$	244.736	−	1702.18i	0.0161253	−	0.112154i	−0.980169	−	0.198163i	$-0.936502\pi$
$613$	244.736	−	1702.18i	0.0161253	−	0.112154i	0.996294	+	0.0860094i	$0.0274115\pi$
$614$	−1523.91	+	233.527i	−0.100163	+	0.0153491i
$615$	2736.36	−	5991.79i	0.179416	−	0.392865i
$616$	1373.10	+	1498.44i	0.0898115	+	0.0980097i
$617$	5875.30	−	2683.16i	0.383356	−	0.175073i	−0.214410	−	0.976744i	$-0.568783\pi$
$617$	5875.30	−	2683.16i	0.383356	−	0.175073i	0.597765	+	0.801671i	$0.296055\pi$
$618$	2403.61	−	3817.35i	0.156452	−	0.248473i
$619$	6438.81	−	10019.0i	0.418090	−	0.650561i	−0.566777	−	0.823871i	$-0.691810\pi$
$619$	6438.81	−	10019.0i	0.418090	−	0.650561i	0.984867	+	0.173310i	$0.0554464\pi$
$620$	−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
$624$	−27890.2	+	14007.5i	−1.78926	+	0.898638i
$625$	−4139.96	−	9065.25i	−0.264957	−	0.580176i
$626$	−14607.6	+	9580.02i	−0.932648	+	0.611653i
$627$	−7454.47	+	16323.0i	−0.474806	+	1.03968i
$628$	22846.6	+	14091.7i	1.45172	+	0.895416i
$629$	−22479.7	−	3232.09i	−1.42500	−	0.204884i
$630$	−7362.58	−	3280.33i	−0.465606	−	0.207447i
$631$	2228.94	+	2572.34i	0.140622	+	0.162287i	0.821692	−	0.569932i	$-0.193030\pi$
$631$	2228.94	+	2572.34i	0.140622	+	0.162287i	−0.681070	+	0.732219i	$0.738485\pi$
$632$	−324.193	−	11667.6i	−0.0204046	−	0.734355i
$633$	39430.3	−	25340.3i	2.47585	−	1.59113i
$634$	2622.70	−	24.2857i	0.164292	−	0.00152131i
$635$	−4929.52	−	16788.4i	−0.308066	−	1.04918i
$636$	−47549.2	+	880.669i	−2.96454	+	0.0549069i
$637$	12006.0	+	10403.3i	0.746777	+	0.647086i
$638$	4388.47	−	2053.47i	0.272321	−	0.127426i
$639$	12218.2	−	41611.3i	0.756407	−	2.57609i
$640$	−13420.7	+	2827.10i	−0.828908	+	0.174611i
$641$	2552.21	−	366.953i	0.157264	−	0.0226112i	−0.0632329	−	0.997999i	$-0.520141\pi$
$641$	2552.21	−	366.953i	0.157264	−	0.0226112i	0.220497	+	0.975388i	$0.429232\pi$
$642$	49518.5	−	15039.4i	3.04414	−	0.924543i
$643$			14989.8i			0.919348i	0.888088	+	0.459674i	$0.152034\pi$
$643$			14989.8i			0.919348i	−0.888088	+	0.459674i	$0.847966\pi$
$644$	2977.35	+	2071.10i	0.182180	+	0.126728i
$645$			8339.06i			0.509070i
$646$	−4484.20	−	14764.6i	−0.273109	−	0.899236i
$647$	9912.90	−	1425.26i	0.602344	−	0.0866040i	0.165605	−	0.986192i	$-0.447042\pi$
$647$	9912.90	−	1425.26i	0.602344	−	0.0866040i	0.436739	+	0.899588i	$0.356133\pi$
$648$	59655.5	+	6892.06i	3.61650	+	0.417817i
$649$	−1483.06	+	5050.83i	−0.0896997	+	0.305489i
$650$	2061.57	+	4405.79i	0.124402	+	0.265861i
$651$	5129.23	+	4444.50i	0.308803	+	0.267579i
$652$	−5341.16	+	98.9247i	−0.320822	+	0.00594201i
$653$	−6436.64	−	21921.2i	−0.385735	−	1.31369i	−0.892281	−	0.451480i	$-0.850896\pi$
$653$	−6436.64	−	21921.2i	−0.385735	−	1.31369i	0.506546	−	0.862213i	$-0.330922\pi$
$654$	333.071	+	35969.5i	0.0199145	+	2.15064i
$655$	7461.09	−	4794.95i	0.445082	−	0.286037i
$656$	−2785.46	+	3466.03i	−0.165784	+	0.206289i
$657$	37421.2	+	43186.4i	2.22213	+	2.56448i
$658$	2357.11	−	5290.45i	0.139650	−	0.313440i
$659$	6951.32	+	999.448i	0.410903	+	0.0590789i	0.344667	−	0.938725i	$-0.387992\pi$
$659$	6951.32	+	999.448i	0.410903	+	0.0590789i	0.0662359	+	0.997804i	$0.478901\pi$
$660$	8701.57	−	14107.7i	0.513194	−	0.832030i
$661$	−11710.2	+	25641.8i	−0.689070	+	1.50885i	0.163669	+	0.986515i	$0.447667\pi$
$661$	−11710.2	+	25641.8i	−0.689070	+	1.50885i	−0.852739	+	0.522337i	$0.825060\pi$
$662$	1286.19	+	1961.18i	0.0755123	+	0.115141i
$663$	13473.6	+	29503.1i	0.789249	+	1.72821i
$664$	6550.43	−	15466.5i	0.382840	−	0.903938i
$665$	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
$670$	−1724.43	−	1085.79i	−0.0994337	−	0.0626088i
$671$	9428.79	−	4305.98i	0.542466	−	0.247736i
$672$	5848.37	+	4611.55i	0.335723	+	0.264724i
$673$	6610.73	−	14475.5i	0.378640	−	0.829107i	−0.620356	−	0.784320i	$-0.713012\pi$
$673$	6610.73	−	14475.5i	0.378640	−	0.829107i	0.998997	−	0.0447865i	$-0.0142608\pi$
$674$	−832.089	−	5429.90i	−0.0475532	−	0.310314i
$675$	2324.05	−	16164.1i	0.132522	−	0.921714i
$676$	609.004	+	1270.72i	0.0346498	+	0.0722985i
$677$	−11316.8	−	13060.3i	−0.642451	−	0.741428i	0.337355	−	0.941377i	$-0.390468\pi$
$677$	−11316.8	−	13060.3i	−0.642451	−	0.741428i	−0.979806	+	0.199950i	$0.935922\pi$
$678$	−2196.41	+	16349.7i	−0.124414	+	0.926115i
$679$	2106.09	+	3277.15i	0.119035	+	0.185221i
$680$	2419.50	+	14046.3i	0.136447	+	0.792132i
$681$	10472.8	+	35667.0i	0.589306	+	2.00699i
$682$	−7643.76	+	6748.28i	−0.429171	+	0.378893i
$683$	3265.41	−	3768.48i	0.182939	−	0.211123i	−0.656871	−	0.754003i	$-0.728121\pi$
$683$	3265.41	−	3768.48i	0.182939	−	0.211123i	0.839811	+	0.542880i	$0.182666\pi$
$684$	−12678.7	+	46337.2i	−0.708744	+	2.59027i
$685$	509.985	−	1736.85i	0.0284460	−	0.0968783i
$686$	2122.23	−	7483.28i	0.118115	−	0.416491i
$687$	−4771.91	−	33189.4i	−0.265007	−	1.84316i
$688$	1384.86	−	5456.29i	0.0767402	−	0.302353i
$689$			28929.1i			1.59958i
$690$	9625.08	−	27968.9i	0.531044	−	1.54313i
$691$	−22139.7			−1.21886			−0.609431	−	0.792839i	$-0.708602\pi$
$691$	−22139.7			−1.21886			−0.609431	+	0.792839i	$0.708602\pi$
$692$	6461.83	+	2807.59i	0.354974	+	0.154232i
$693$	−6508.83	+	935.828i	−0.356782	+	0.0512975i
$694$	6913.02	−	24376.3i	0.378119	−	1.33330i
$695$	19844.1	+	5826.76i	1.08307	+	0.318017i
$696$	14664.1	−	10010.2i	0.798620	−	0.545167i
$697$	3492.30	+	3026.09i	0.189785	+	0.164450i
$698$	11155.7	+	12636.0i	0.604942	+	0.685216i
$699$	−46269.6	+	13586.0i	−2.50368	+	0.735148i
$700$	743.773	−	891.184i	0.0401600	−	0.0481194i
$701$	−4350.63	+	2795.98i	−0.234409	+	0.150646i	−0.652573	−	0.757726i	$-0.726310\pi$
$701$	−4350.63	+	2795.98i	−0.234409	+	0.150646i	0.418163	+	0.908372i	$0.362674\pi$
$702$	8486.16	−	63169.5i	0.456253	−	3.39626i
$703$	−21167.8	+	18342.0i	−1.13564	+	0.984042i
$704$	−8036.33	+	7785.65i	−0.430228	+	0.416808i
$705$	−46754.0	−	6722.22i	−2.49767	−	0.359111i
$706$	−4151.04	+	636.114i	−0.221284	+	0.0339100i
$707$	1328.06	+	606.506i	0.0706463	+	0.0322631i
$708$	−2391.22	+	19141.3i	−0.126932	+	1.01607i
$709$	−5128.16	−	11229.1i	−0.271639	−	0.594807i	0.723821	−	0.689988i	$-0.242384\pi$
$709$	−5128.16	−	11229.1i	−0.271639	−	0.594807i	−0.995460	+	0.0951811i	$0.969657\pi$
$710$	−13428.3	−	8455.21i	−0.709798	−	0.446927i
$711$	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
$716$	−5330.60	+	1673.03i	−0.278232	+	0.0873243i
$717$	13433.0	−	6134.66i	0.699673	−	0.319530i
$718$	2872.33	+	4379.73i	0.149296	+	0.227646i
$719$	−4822.29	−	2202.27i	−0.250127	−	0.114229i	0.286407	−	0.958108i	$-0.407539\pi$
$719$	−4822.29	−	2202.27i	−0.250127	−	0.114229i	−0.536533	+	0.843879i	$0.680266\pi$
$720$	16926.6	−	41019.6i	0.876135	−	2.12321i
$721$	−93.1916	+	648.162i	−0.00481364	+	0.0334796i
$722$	337.852	+	150.527i	0.0174149	+	0.00775905i
$723$	−30437.2	+	26374.0i	−1.56566	+	1.35665i
$724$	12385.5	+	13769.9i	0.635780	+	0.706845i
$725$	−1496.06	−	2327.92i	−0.0766379	−	0.119251i
$726$	223.737	+	24162.1i	0.0114375	+	1.23518i
$727$	−1561.25	+	458.424i	−0.0796472	+	0.0233865i	−0.321313	−	0.946973i	$-0.604124\pi$
$727$	−1561.25	+	458.424i	−0.0796472	+	0.0233865i	0.241666	+	0.970359i	$0.422306\pi$
$728$	2870.60	−	3505.00i	0.146142	−	0.178440i
$729$	−45361.1	+	52349.5i	−2.30458	+	2.65963i
$730$	18938.4	−	8861.71i	0.960193	−	0.449297i
$731$	−5613.09	−	1648.15i	−0.284005	−	0.0833914i
$732$	31568.7	−	21124.1i	1.59401	−	1.06662i
$733$	−2366.34	−	16458.2i	−0.119240	−	0.829330i	−0.958396	−	0.285440i	$-0.907860\pi$
$733$	−2366.34	−	16458.2i	−0.119240	−	0.829330i	0.839157	−	0.543890i	$-0.183049\pi$
$734$	2603.42	+	8571.99i	0.130918	+	0.431060i
$735$	−30917.5			−1.55158
$736$	−10942.5	+	16701.8i	−0.548025	+	0.836462i
$737$	−1662.48			−0.0830913
$738$	−4180.82	−	13765.7i	−0.208534	−	0.686618i
$739$	−4200.10	−	29212.3i	−0.209070	−	1.45412i	−0.776199	−	0.630488i	$-0.782855\pi$
$739$	−4200.10	−	29212.3i	−0.209070	−	1.45412i	0.567129	−	0.823629i	$-0.308054\pi$
$740$	21502.0	−	14388.0i	1.06815	−	0.714747i
$741$	38380.3	+	11269.5i	1.90275	+	0.558697i
$742$	6252.79	−	2925.83i	0.309363	−	0.144758i
$743$	1795.86	−	2072.53i	0.0886725	−	0.102333i	−0.709679	−	0.704525i	$-0.751160\pi$
$743$	1795.86	−	2072.53i	0.0886725	−	0.102333i	0.798352	+	0.602191i	$0.205706\pi$
$744$	−23674.9	+	28907.0i	−1.16662	+	1.42444i
$745$	12040.2	−	3535.31i	0.592104	−	0.173857i
$746$	−207.456	−	22403.9i	−0.0101816	−	1.09955i
$747$	29380.4	+	45716.7i	1.43905	+	2.23921i
$748$	7776.17	+	8645.37i	0.380114	+	0.422601i
$749$	−5677.47	+	4919.55i	−0.276970	+	0.239995i
$750$	−39265.4	−	17494.3i	−1.91169	−	0.851736i
$751$	5164.72	−	35921.4i	0.250950	−	1.74539i	−0.341586	−	0.939850i	$-0.610964\pi$
$751$	5164.72	−	35921.4i	0.250950	−	1.74539i	0.592536	−	0.805544i	$-0.298127\pi$
$752$	29475.0	+	12162.8i	1.42931	+	0.589802i
$753$	−31625.1	−	14442.7i	−1.53052	−	0.698965i
$754$	−5922.99	−	9031.37i	−0.286078	−	0.436211i
$755$	−3377.25	+	1542.34i	−0.162795	+	0.0743462i
$756$	−14511.8	+	4554.61i	−0.698136	+	0.219113i
$757$	18856.1	+	12118.1i	0.905334	+	0.581823i	0.908368	−	0.418173i	$-0.137329\pi$
$757$	18856.1	+	12118.1i	0.905334	+	0.581823i	−0.00303362	+	0.999995i	$0.500966\pi$
$758$	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	0.601167	−	0.799123i	$-0.294703\pi$
$761$	2603.00	+	1672.85i	0.123993	+	0.0796854i	−0.477174	+	0.878809i	$0.658339\pi$
$762$	−44265.2	−	27871.8i	−2.10441	−	1.32505i
$763$	−2169.13	−	4749.73i	−0.102920	−	0.225363i
$764$	3824.44	−	30614.1i	0.181104	−	1.44971i
$765$	−41947.7	−	19156.9i	−1.98251	−	0.905383i
$766$	19159.5	−	2936.05i	0.903737	−	0.138491i
$767$	11614.7	+	1669.95i	0.546785	+	0.0786158i
$768$	−24484.2	+	32890.1i	−1.15039	+	1.54534i
$769$	7623.52	−	6605.82i	0.357492	−	0.309769i	−0.457535	−	0.889192i	$-0.651268\pi$
$769$	7623.52	−	6605.82i	0.357492	−	0.309769i	0.815027	+	0.579423i	$0.196722\pi$
$770$	−320.357	+	2384.68i	−0.0149933	+	0.111607i
$771$	−40494.1	+	26024.0i	−1.89152	+	1.21560i
$772$	−2018.32	+	2418.34i	−0.0940946	+	0.112744i
$773$	18356.6	−	5389.99i	0.854128	−	0.250795i	0.174777	−	0.984608i	$-0.444080\pi$
$773$	18356.6	−	5389.99i	0.854128	−	0.250795i	0.679351	+	0.733813i	$0.262261\pi$
$774$	12054.0	+	13653.6i	0.559785	+	0.634067i
$775$	4401.08	+	3813.56i	0.203989	+	0.176758i
$776$	−17712.9	+	12091.5i	−0.819401	+	0.559353i
$777$	−13480.1	−	3958.10i	−0.622387	−	0.182749i
$778$	−6326.98	+	22309.8i	−0.291559	+	1.02808i
$779$	5640.98	−	811.051i	0.259447	−	0.0373028i
$780$	−33887.9	−	14723.9i	−1.55562	−	0.675897i
$781$	−12945.9			−0.593139
$782$	16923.8	+	12006.6i	0.773905	+	0.549046i
$783$			36259.0i			1.65490i
$784$	20229.5	+	5134.43i	0.921531	+	0.233894i
$785$	4522.51	+	31454.7i	0.205624	+	1.43015i
$786$	7234.15	−	25508.7i	0.328287	−	1.15759i
$787$	2096.50	−	7140.01i	0.0949581	−	0.323398i	−0.898291	−	0.439402i	$-0.855190\pi$
$787$	2096.50	−	7140.01i	0.0949581	−	0.323398i	0.993249	+	0.116004i	$0.0370086\pi$
$788$	−9216.60	+	33684.3i	−0.416659	+	1.52278i
$789$	−52796.2	+	60930.1i	−2.38225	+	2.74926i
$790$	10358.8	−	9145.24i	0.466518	−	0.411864i
$791$	−674.652	−	2297.65i	−0.0303260	−	0.103281i
$792$	−6145.36	−	35676.5i	−0.275715	−	1.60064i
$793$	−12492.0	−	19437.9i	−0.559398	−	0.870440i
$794$	2378.37	−	17704.2i	0.106304	−	0.791306i
$795$	−36869.4	−	42549.5i	−1.64481	−	1.89821i
$796$	9961.09	+	20784.3i	0.443544	+	0.925478i
$797$	−4367.22	+	30374.7i	−0.194096	+	1.34997i	0.626928	+	0.779077i	$0.284312\pi$
$797$	−4367.22	+	30374.7i	−0.194096	+	1.34997i	−0.821025	+	0.570893i	$0.806597\pi$
$798$	−1445.89	−	9435.36i	−0.0641405	−	0.418556i
$799$	13765.4	−	30141.9i	0.609491	−	1.33460i
$800$	5018.13	+	3956.89i	0.221772	+	0.174871i
$801$	96515.1	−	44077.0i	4.25742	−	1.94430i
$802$	16481.3	+	10377.5i	0.725656	+	0.456912i
$803$	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
$808$	−3134.67	+	7401.39i	−0.136482	+	0.322252i
$809$	17932.5	+	39266.6i	0.779322	+	1.70648i	0.704961	+	0.709246i	$0.250965\pi$
$809$	17932.5	+	39266.6i	0.779322	+	1.70648i	0.0743615	+	0.997231i	$0.476308\pi$
$810$	38988.1	+	59449.0i	1.69124	+	2.57880i
$811$	−9456.54	+	20706.9i	−0.409450	+	0.896571i	0.586774	+	0.809751i	$0.300398\pi$
$811$	−9456.54	+	20706.9i	−0.409450	+	0.896571i	−0.996224	+	0.0868200i	$0.972329\pi$
$812$	−1353.02	+	2193.62i	−0.0584750	+	0.0948041i
$813$	40834.6	+	5871.12i	1.76154	+	0.253271i
$814$	8589.93	−	19279.8i	0.369873	−	0.830167i
$815$	−4141.50	−	4779.55i	−0.178001	−	0.205424i
$816$	33214.3	+	26692.6i	1.42492	+	1.14513i
$817$	−6069.48	+	3900.62i	−0.259907	+	0.167032i
$818$	100.287	+	10830.4i	0.00428663	+	0.462928i
$819$	4129.66	+	14064.3i	0.176193	+	0.600058i
$820$	−5263.22	+	97.4813i	−0.224146	+	0.00415146i
$821$	16452.3	+	14256.0i	0.699379	+	0.606015i	0.930231	−	0.366974i	$-0.119606\pi$
$821$	16452.3	+	14256.0i	0.699379	+	0.606015i	−0.230853	+	0.972989i	$0.574152\pi$
$822$	−2293.57	−	4901.60i	−0.0973205	−	0.207984i
$823$	6750.49	−	22990.0i	0.285914	−	0.973734i	−0.683837	−	0.729635i	$-0.739690\pi$
$823$	6750.49	−	22990.0i	0.285914	−	0.973734i	0.969750	−	0.244098i	$-0.0784920\pi$
$824$	−3581.24	−	413.744i	−0.151406	−	0.0174921i
$825$	−7644.55	+	1099.12i	−0.322605	+	0.0463836i
$826$	−813.744	−	2679.33i	−0.0342782	−	0.112864i
$827$		−	16352.0i		−	0.687563i	−0.939050	−	0.343782i	$-0.888292\pi$
$827$		−	16352.0i		−	0.687563i	0.939050	−	0.343782i	$-0.111708\pi$
$828$	−24669.7	−	59706.6i	−1.03542	−	2.50597i
$829$			24111.8i			1.01018i	0.863067	+	0.505089i	$0.168540\pi$
$829$			24111.8i			1.01018i	−0.863067	+	0.505089i	$0.831460\pi$
$830$	19026.4	−	5778.54i	0.795681	−	0.241658i
$831$	−4211.91	+	605.582i	−0.175824	+	0.0252797i
$832$	19727.8	+	15261.6i	0.822042	+	0.635940i
$833$	6110.60	−	20810.8i	0.254165	−	0.865608i
$834$	56002.4	−	26204.8i	2.32519	−	1.08801i
$835$	14224.3	+	12325.4i	0.589524	+	0.510826i
$836$	14338.3	−	265.562i	0.593180	−	0.0109864i
$837$	−21497.7	−	73214.6i	−0.887778	−	3.02349i
$838$	−19581.3	+	181.320i	−0.807191	+	0.00747444i
$839$	38315.2	−	24623.7i	1.57662	−	1.01323i	0.599549	−	0.800338i	$-0.295347\pi$
$839$	38315.2	−	24623.7i	1.57662	−	1.01323i	0.977075	−	0.212896i	$-0.0682895\pi$
$840$	244.896	+	8813.73i	0.0100592	+	0.362027i
$841$	−11947.8	−	13788.5i	−0.489886	−	0.565359i
$842$	−17954.0	−	7999.25i	−0.734841	−	0.327402i
$843$	86566.4	+	12446.4i	3.53678	+	0.508512i
$844$	−31880.8	−	19664.0i	−1.30022	−	0.801972i
$845$	−692.993	+	1517.44i	−0.0282126	+	0.0617770i
$846$	−86267.4	+	56576.2i	−3.50583	+	2.29921i
$847$	−1457.09	−	3190.58i	−0.0591100	−	0.129433i
$848$	17057.7	+	33963.2i	0.690757	+	1.37536i
$849$	−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	$-0.987289\pi$
$853$	−13647.4	+	21235.7i	−0.547805	+	0.852401i	0.451398	+	0.892323i	$0.350925\pi$
$854$	−2937.93	+	4665.94i	−0.117721	+	0.186962i
$855$	−51733.5	+	23625.9i	−2.06930	+	0.945017i
$856$	−27941.6	−	30492.2i	−1.11568	−	1.21753i
$857$	365.330	−	799.962i	0.0145618	−	0.0318859i	−0.902211	−	0.431294i	$-0.858057\pi$
$857$	365.330	−	799.962i	0.0145618	−	0.0318859i	0.916773	+	0.399408i	$0.130784\pi$
$858$	−29795.5	+	4565.93i	−1.18555	+	0.181676i
$859$	−3304.87	+	22985.9i	−0.131270	+	0.913002i	0.812632	+	0.582777i	$0.198034\pi$
$859$	−3304.87	+	22985.9i	−0.131270	+	0.913002i	−0.943902	+	0.330225i	$0.892875\pi$
$860$	6009.73	−	2880.22i	0.238291	−	0.114203i
$861$	1871.97	+	2160.37i	0.0740960	+	0.0855113i
$862$	−31666.2	−	4254.02i	−1.25122	−	0.168089i
$863$	8419.24	+	13100.6i	0.332091	+	0.516743i	0.966640	−	0.256139i	$-0.0824506\pi$
$863$	8419.24	+	13100.6i	0.332091	+	0.516743i	−0.634549	+	0.772882i	$0.718814\pi$
$864$	−27284.1	−	79165.7i	−1.07433	−	3.11721i
$865$	2349.86	+	8002.90i	0.0923673	+	0.314574i
$866$	−6153.23	−	6969.74i	−0.241449	−	0.273489i
$867$	−3208.47	+	3702.77i	−0.125681	+	0.145044i
$868$	1431.45	−	5231.58i	0.0559754	−	0.204575i
$869$	3176.01	−	10816.5i	0.123980	−	0.422237i
$870$	20221.9	+	5734.84i	0.788030	+	0.223482i
$871$	527.398	+	3668.13i	0.0205169	+	0.142698i
$872$	25807.2	−	12663.5i	1.00223	−	0.491790i
$873$		−	69388.4i		−	2.69008i
$874$	24859.0	−	6077.05i	0.962091	−	0.235194i
$875$	6239.93			0.241084
$876$	24910.0	−	57331.8i	0.960765	−	2.21126i
$877$	22108.8	−	3178.77i	0.851268	−	0.122394i	0.297149	−	0.954831i	$-0.403964\pi$
$877$	22108.8	−	3178.77i	0.851268	−	0.122394i	0.554119	+	0.832437i	$0.313055\pi$
$878$	−23904.9	−	6779.31i	−0.918850	−	0.260582i
$879$	−31327.4	−	9198.56i	−1.20210	−	0.352969i
$880$	−13172.4	−	1398.35i	−0.504594	−	0.0535665i
$881$	5006.32	+	4338.00i	0.191450	+	0.165892i	0.745311	−	0.666717i	$-0.232301\pi$
$881$	5006.32	+	4338.00i	0.191450	+	0.165892i	−0.553862	+	0.832609i	$0.686846\pi$
$882$	−50621.3	+	44690.9i	−1.93255	+	1.70615i
$883$	−19071.0	+	5599.74i	−0.726828	+	0.213416i	−0.624157	−	0.781299i	$-0.714557\pi$
$883$	−19071.0	+	5599.74i	−0.726828	+	0.213416i	−0.102672	+	0.994715i	$0.532739\pi$
$884$	16608.4	−	19900.1i	0.631903	−	0.757142i
$885$	−19211.5	+	12346.5i	−0.729703	+	0.468952i
$886$	12604.7	+	1693.31i	0.477950	+	0.0642076i
$887$	2155.90	−	1868.10i	0.0816100	−	0.0707154i	−0.613101	−	0.790005i	$-0.710078\pi$
$887$	2155.90	−	1868.10i	0.0816100	−	0.0707154i	0.694710	+	0.719289i	$0.255532\pi$
$888$	19721.1	−	74789.3i	0.745268	−	2.82631i
$889$	7515.95	+	1080.63i	0.283551	+	0.0407685i
$890$	−5880.78	−	38375.7i	−0.221488	−	1.44535i
$891$	52758.3	+	24093.9i	1.98369	+	0.905921i
$892$	−5901.76	−	737.274i	−0.221531	−	0.0276746i
$893$	−16976.6	−	37173.6i	−0.636172	−	1.39302i
$894$	19988.8	−	31745.7i	0.747793	−	1.18762i
$895$	−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
$900$	−19727.2	+	6191.49i	−0.730639	+	0.229314i
$901$	35927.4	−	16407.5i	1.32843	−	0.606673i
$902$	−3591.19	+	2355.19i	−0.132565	+	0.0869392i
$903$	−3291.87	−	1503.35i	−0.121314	−	0.0554023i
$904$	12541.4	−	4064.11i	0.461416	−	0.149525i
$905$	−3120.36	+	21702.6i	−0.114612	+	0.797147i
$906$	−4517.25	+	10138.8i	−0.165646	+	0.371787i
$907$	−32429.9	+	28100.6i	−1.18723	+	1.02874i	−0.188316	+	0.982109i	$0.560303\pi$
$907$	−32429.9	+	28100.6i	−1.18723	+	1.02874i	−0.998912	+	0.0466303i	$0.985152\pi$
$908$	22087.0	−	19866.4i	0.807252	−	0.726092i
$909$	−14059.8	−	21877.5i	−0.513019	−	0.798273i
$910$	5363.23	−	49.6625i	0.195373	−	0.00180912i
$911$	−7043.39	+	2068.13i	−0.256156	+	0.0752141i	−0.407289	−	0.913299i	$-0.633526\pi$
$911$	−7043.39	+	2068.13i	−0.256156	+	0.0752141i	0.151133	+	0.988513i	$0.451708\pi$
$912$	51703.9	−	9399.88i	1.87729	−	0.341295i
$913$	10623.3	−	12260.0i	0.385083	−	0.444410i
$914$	22844.6	+	48821.2i	0.826729	+	1.76681i
$915$	43146.5	+	12668.9i	1.55888	+	0.457729i
$916$	−22270.5	+	14902.2i	−0.803317	+	0.537537i
$917$	547.754	+	3809.71i	0.0197257	+	0.137195i
$918$	−83263.8	+	25288.2i	−2.99359	+	0.909190i
$919$	−5958.22			−0.213867			−0.106933	−	0.994266i	$-0.534103\pi$
$919$	−5958.22			−0.213867			−0.106933	+	0.994266i	$0.534103\pi$
$920$	−23480.8	+	2723.64i	−0.841457	+	0.0976042i
$921$	−5456.42			−0.195217
$922$	−8458.61	+	2568.98i	−0.302136	+	0.0917624i
$923$	4106.91	+	28564.2i	0.146458	+	1.01864i
$924$	4000.34	+	5978.27i	0.142426	+	0.212847i
$925$	−11566.4	−	3396.21i	−0.411137	−	0.120721i
$926$	18943.4	+	40483.9i	0.672265	+	1.43670i
$927$	7638.24	−	8815.00i	0.270629	−	0.312322i
$928$	−12278.9	−	7110.56i	−0.434348	−	0.251525i
$929$	−2121.14	+	622.823i	−0.0749110	+	0.0219959i	−0.318973	−	0.947764i	$-0.603338\pi$
$929$	−2121.14	+	622.823i	−0.0749110	+	0.0219959i	0.244062	+	0.969760i	$0.421520\pi$
$930$	−44232.4	+	409.584i	−1.55961	+	0.0144417i
$931$	−14461.7	−	22502.9i	−0.509091	−	0.792161i
$932$	25772.0	+	28652.8i	0.905785	+	1.00703i
$933$	69348.4	−	60090.7i	2.43340	−	2.10856i
$934$	15810.9	−	35487.0i	0.553907	−	1.24322i
$935$	−1959.10	+	13625.8i	−0.0685233	+	0.476590i
$936$	−76767.9	+	24877.1i	−2.68081	+	0.868733i
$937$	15956.8	+	7287.22i	0.556335	+	0.254069i	0.673682	−	0.739021i	$-0.264712\pi$
$937$	15956.8	+	7287.22i	0.556335	+	0.254069i	−0.117347	+	0.993091i	$0.537439\pi$
$938$	739.497	−	484.980i	0.0257414	−	0.0168818i
$939$	−56239.1	+	25683.5i	−1.95452	+	0.892599i
$940$	11303.8	+	36016.1i	0.392224	+	1.24970i
$941$	−23108.8	−	14851.1i	−0.800557	−	0.514487i	0.0752403	−	0.997165i	$-0.476028\pi$
$941$	−23108.8	−	14851.1i	−0.800557	−	0.514487i	−0.875798	+	0.482678i	$0.839664\pi$
$942$	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
$946$	2896.92	−	4600.81i	0.0995633	−	0.158124i
$947$	−1898.25	−	4156.59i	−0.0651371	−	0.142630i	0.874264	−	0.485452i	$-0.161345\pi$
$947$	−1898.25	−	4156.59i	−0.0651371	−	0.142630i	−0.939401	+	0.342821i	$0.888617\pi$
$948$	5120.86	−	40991.7i	0.175441	−	1.40437i
$949$	−34588.3	−	15795.9i	−1.18312	−	0.540314i
$950$	−1240.63	−	8095.91i	−0.0423700	−	0.276491i
$951$	9188.27	+	1321.07i	0.313302	+	0.0450460i
$952$	−5980.99	−	1577.12i	−0.203619	−	0.0536921i
$953$	−24778.5	+	21470.7i	−0.842241	+	0.729806i	−0.964893	−	0.262644i	$-0.915406\pi$
$953$	−24778.5	+	21470.7i	−0.842241	+	0.729806i	0.122652	+	0.992450i	$0.460860\pi$
$954$	−121871.	−	16372.1i	−4.13598	−	0.555626i
$955$	30726.3	−	19746.6i	1.04113	−	0.669093i
$956$	−9060.70	−	7561.97i	−0.306531	−	0.255828i
$957$	16453.5	−	4831.17i	0.555763	−	0.163187i
$958$	23092.3	−	20387.0i	0.778787	−	0.687551i
$959$	593.688	+	514.434i	0.0199908	+	0.0173221i
$960$	−48466.6	+	2695.45i	−1.62943	+	0.0906200i
$961$	−2475.62	−	726.908i	−0.0830997	−	0.0244003i
$962$	−45264.3	−	12836.8i	−1.51703	−	0.430222i
$963$	132450.	−	19043.4i	4.43212	−	0.637243i
$964$	29519.7	+	12826.0i	0.986270	+	0.428523i
$965$	−3729.06			−0.124396
$966$	9305.64	+	8841.71i	0.309942	+	0.294490i
$967$			25822.1i			0.858722i	0.903133	+	0.429361i	$0.141261\pi$
$967$			25822.1i			0.858722i	−0.903133	+	0.429361i	$0.858739\pi$
$968$	17335.7	−	8506.59i	0.575611	−	0.282450i
$969$	−7772.15	−	54056.5i	−0.257665	−	1.79210i
$970$	−24426.2	−	6927.17i	−0.808535	−	0.229297i
$971$	12648.6	−	43077.3i	0.418037	−	1.42370i	−0.434327	−	0.900755i	$-0.643014\pi$
$971$	12648.6	−	43077.3i	0.418037	−	1.42370i	0.852364	−	0.522948i	$-0.175168\pi$
$972$	108629.	+	29722.9i	3.58466	+	0.980825i
$973$	−5877.58	+	6783.09i	−0.193655	+	0.223490i
$974$	−8669.89	−	9820.36i	−0.285217	−	0.323064i
$975$	4850.24	+	16518.4i	0.159315	+	0.542577i
$976$	−26127.0	−	15454.6i	−0.856871	−	0.506856i
$977$	−19429.3	−	30232.7i	−0.636233	−	0.989998i	−0.998325	−	0.0578558i	$-0.981574\pi$
$977$	−19429.3	−	30232.7i	−0.636233	−	0.989998i	0.362092	−	0.932142i	$-0.382063\pi$
$978$	−18738.5	−	2517.32i	−0.612670	−	0.0823059i
$979$	−20741.6	−	23937.1i	−0.677124	−	0.781442i
$980$	10678.6	+	22281.4i	0.348076	+	0.726278i
$981$	−13236.4	+	92061.4i	−0.430792	+	2.99622i
$982$	−5485.98	+	840.683i	−0.178274	+	0.0273190i
$983$	−10087.9	+	22089.3i	−0.327317	+	0.716724i	−0.999725	−	0.0234566i	$-0.992533\pi$
$983$	−10087.9	+	22089.3i	−0.327317	+	0.716724i	0.672408	+	0.740181i	$0.265260\pi$
$984$	−11602.8	+	10632.3i	−0.375898	+	0.344455i
$985$	−37607.0	+	17174.6i	−1.21651	+	0.555560i
$986$	−7856.87	+	12478.1i	−0.253766	+	0.403025i
$987$	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	$-0.753227\pi$
$991$	6835.82	−	10636.7i	0.219119	−	0.340956i	0.933359	+	0.358946i	$0.116864\pi$
$992$	29009.5	+	7077.65i	0.928481	+	0.226528i
$993$	3448.21	+	7550.52i	0.110197	+	0.241298i
$994$	5758.55	−	3776.59i	0.183753	−	0.120509i
$995$	−11334.8	+	24819.8i	−0.361144	+	0.790795i
$996$	31207.6	−	50596.1i	0.992821	−	1.60964i
$997$	16909.1	+	2431.17i	0.537129	+	0.0772275i	0.405541	−	0.914077i	$-0.367083\pi$
$997$	16909.1	+	2431.17i	0.537129	+	0.0772275i	0.131588	+	0.991304i	$0.457992\pi$
$998$	−51072.1	−	22754.7i	−1.61990	−	0.721731i
$999$	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.67.30	yes	700
8.3	odd	2	inner	184.4.j.a.67.5	yes	700
23.11	odd	22	inner	184.4.j.a.11.5	✓	700
184.11	even	22	inner	184.4.j.a.11.30	yes	700

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.4.j.a.11.5	✓	700	23.11	odd	22	inner
184.4.j.a.11.30	yes	700	184.11	even	22	inner
184.4.j.a.67.5	yes	700	8.3	odd	2	inner
184.4.j.a.67.30	yes	700	1.1	even	1	trivial

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+(-0.821955 - 2.70636i) q^{2} +(-1.42464 - 9.90857i) q^{3} +(-6.64878 + 4.44901i) q^{4} +(-9.08722 - 2.66825i) q^{5} +(-25.6452 + 12.0000i) q^{6} +(2.69152 - 3.10618i) q^{7} +(17.5056 + 14.3371i) q^{8} +(-70.2439 + 20.6255i) q^{9} +(0.248038 + 26.7865i) q^{10} +(11.8151 + 18.3847i) q^{11} +(53.5555 + 59.5417i) q^{12} +(36.8163 - 31.9015i) q^{13} +(-10.6188 - 4.73109i) q^{14} +(-13.4925 + 93.8426i) q^{15} +(24.4126 - 59.1610i) q^{16} +(-60.4995 - 27.6292i) q^{17} +(113.557 + 173.152i) q^{18} +(-74.6133 + 34.0747i) q^{19} +(72.2900 - 22.6885i) 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} +(-116.598 - 73.4165i) q^{26} +(192.162 + 420.775i) q^{27} +(-4.07590 + 32.6269i) q^{28} +(71.3012 + 32.5622i) q^{29} +(265.062 - 40.6187i) q^{30} +(-163.278 - 23.4759i) q^{31} +(-180.177 - 17.4416i) q^{32} +(165.334 - 143.263i) q^{33} +(-25.0468 + 186.444i) q^{34} +(-32.7465 + 21.0449i) q^{35} +(375.273 - 449.650i) q^{36} +(327.634 - 96.2020i) q^{37} +(153.547 + 173.923i) q^{38} +(-368.548 - 319.348i) q^{39} +(-120.822 - 176.994i) q^{40} +(-66.6636 - 19.5742i) q^{41} +(-31.7505 + 111.957i) q^{42} +(87.0624 - 12.5177i) q^{43} +(-160.350 - 69.6703i) q^{44} +693.355 q^{45} +(-306.453 - 58.5049i) q^{46} +498.217i q^{47} +(-620.980 - 157.611i) q^{48} +(46.4099 + 322.788i) q^{49} +(-27.2432 + 96.0634i) q^{50} +(-187.576 + 638.825i) q^{51} +(-102.853 + 375.902i) q^{52} +(-388.886 + 448.798i) q^{53} +(980.822 - 865.917i) q^{54} +(-58.3118 - 198.592i) q^{55} +(91.6505 - 15.7870i) q^{56} +(443.929 + 690.767i) q^{57} +(29.5186 - 219.731i) q^{58} +(157.739 + 182.041i) q^{59} +(-327.798 - 683.968i) q^{60} +(67.5010 - 469.480i) q^{61} +(70.6731 + 461.186i) q^{62} +(-124.997 + 273.704i) q^{63} +(100.894 + 501.961i) q^{64} +(-419.678 + 191.661i) q^{65} +(-523.618 - 329.698i) 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} +(-1525.37 - 646.033i) q^{72} +(-324.253 - 710.015i) q^{73} +(-529.657 - 807.622i) q^{74} +(-146.807 + 321.463i) q^{75} +(344.489 - 558.511i) q^{76} +(88.9070 + 12.7829i) q^{77} +(-561.343 + 1259.91i) q^{78} +(-337.803 - 389.845i) q^{79} +(-379.699 + 472.470i) q^{80} +(2232.65 - 1434.84i) q^{81} +(1.81960 + 196.505i) q^{82} +(-209.131 - 712.235i) q^{83} +(329.093 - 6.09520i) q^{84} +(476.051 + 412.500i) q^{85} +(-105.439 - 225.333i) q^{86} +(221.066 - 752.882i) q^{87} +(-56.7524 + 491.231i) q^{88} +(-1434.56 + 206.259i) q^{89} +(-569.907 - 1876.47i) q^{90} -200.221i q^{91} +(93.5547 + 877.460i) q^{92} +1651.30i q^{93} +(1348.36 - 409.512i) q^{94} +(768.947 - 110.558i) q^{95} +(83.8656 + 1810.15i) q^{96} +(-267.028 + 909.414i) q^{97} +(835.434 - 390.919i) 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

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