LMFDB - Embedded newform 207.4.o.a.11.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(5,207)] 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("207.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 4, names="a")

Level:	$N$	$=$	$207 = 3^{2} \cdot 23$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	207.o (of order $66$ , degree $20$ , 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	207.11
Dual form			207.4.o.a.113.20

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77962 + 0.132410i) q^{2} +(1.13894 + 5.06979i) q^{3} +(-0.254996 + 0.0243491i) q^{4} +(-5.51997 - 5.26328i) q^{5} +(-3.83713 - 13.9413i) q^{6} +(-2.92152 - 15.1583i) q^{7} +(22.7412 - 3.26969i) q^{8} +(-24.4056 + 11.5484i) q^{9} +(16.0403 + 13.8990i) q^{10} +(16.7412 - 8.63070i) q^{11} +(-0.413871 - 1.26504i) q^{12} +(69.6570 + 13.4253i) q^{13} +(10.1278 + 41.7475i) q^{14} +(20.3968 - 33.9797i) q^{15} +(-60.7668 + 11.7118i) q^{16} +(39.2300 + 85.9018i) q^{17} +(66.3093 - 35.3318i) q^{18} +(-54.9456 - 25.0928i) q^{19} +(1.53572 + 1.20771i) q^{20} +(73.5219 - 32.0759i) q^{21} +(-45.3915 + 26.2068i) q^{22} +(-77.8435 + 78.1498i) q^{23} +(42.4776 + 111.569i) q^{24} +(-3.17980 - 66.7522i) q^{25} +(-195.398 - 28.0940i) q^{26} +(-86.3448 - 110.578i) q^{27} +(1.11407 + 3.79416i) q^{28} +(-8.09197 + 84.7430i) q^{29} +(-52.1962 + 97.1515i) q^{30} +(-48.5608 + 38.1886i) q^{31} +(-11.2611 + 2.73192i) q^{32} +(62.8232 + 75.0447i) q^{33} +(-120.419 - 233.580i) q^{34} +(-63.6556 + 99.0500i) q^{35} +(5.94213 - 3.53905i) q^{36} +(-61.8341 + 210.588i) q^{37} +(156.051 + 62.4733i) q^{38} +(11.2720 + 368.437i) q^{39} +(-142.740 - 101.645i) q^{40} +(-182.364 + 191.258i) q^{41} +(-200.116 + 98.8941i) q^{42} +(192.738 - 245.087i) q^{43} +(-4.05879 + 2.60842i) q^{44} +(195.501 + 64.7066i) q^{45} +(206.028 - 227.534i) q^{46} +(516.671 + 298.300i) q^{47} +(-128.587 - 294.736i) q^{48} +(97.1919 - 38.9098i) q^{49} +(17.6773 + 185.125i) q^{50} +(-390.823 + 296.726i) q^{51} +(-18.0891 - 1.72730i) q^{52} +(475.006 + 548.186i) q^{53} +(254.648 + 295.933i) q^{54} +(-137.837 - 40.4725i) q^{55} +(-116.002 - 335.165i) q^{56} +(64.6354 - 307.142i) q^{57} +(11.2718 - 236.625i) q^{58} +(-158.942 + 824.668i) q^{59} +(-4.37372 + 9.16131i) q^{60} +(-132.240 + 330.318i) q^{61} +(129.924 - 112.580i) q^{62} +(246.356 + 336.208i) q^{63} +(505.967 - 148.565i) q^{64} +(-313.843 - 440.731i) q^{65} +(-184.562 - 200.278i) q^{66} +(-271.348 + 526.342i) q^{67} +(-12.0951 - 20.9494i) q^{68} +(-484.863 - 305.642i) q^{69} +(163.823 - 283.750i) q^{70} +(-250.919 - 390.438i) q^{71} +(-517.253 + 342.424i) q^{72} +(76.5970 - 167.724i) q^{73} +(143.992 - 593.542i) q^{74} +(334.798 - 92.1479i) q^{75} +(14.6219 + 5.06068i) q^{76} +(-179.736 - 228.553i) q^{77} +(-80.1167 - 1022.62i) q^{78} +(494.277 - 171.071i) q^{79} +(397.073 + 255.184i) q^{80} +(462.268 - 563.693i) q^{81} +(481.579 - 555.772i) q^{82} +(334.928 - 319.353i) q^{83} +(-17.9667 + 9.96942i) q^{84} +(235.577 - 680.654i) q^{85} +(-503.288 + 706.770i) q^{86} +(-438.846 + 55.4929i) q^{87} +(352.496 - 251.011i) q^{88} +(-0.458025 + 3.18564i) q^{89} +(-551.987 - 153.974i) q^{90} -1095.10i q^{91} +(17.9469 - 21.8233i) q^{92} +(-248.916 - 202.698i) q^{93} +(-1475.65 - 760.750i) q^{94} +(171.228 + 427.706i) q^{95} +(-26.6761 - 53.9801i) q^{96} +(-2.23136 - 0.541323i) q^{97} +(-265.005 + 121.024i) q^{98} +(-308.909 + 403.972i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100})$ 1400 * q - 27 * q^2 - 22 * q^3 - 281 * q^4 - 33 * q^5 + 29 * q^6 - 11 * q^7 - 22 * q^9 - 44 * q^10 - 33 * q^11 + 86 * q^12 - 9 * q^13 - 33 * q^14 + 726 * q^15 + 999 * q^16 + 51 * q^18 - 44 * q^19 - 33 * q^20 + 638 * q^21 + 252 * q^23 - 2564 * q^24 + 1397 * q^25 - 178 * q^27 - 44 * q^28 - 135 * q^29 - 1518 * q^30 - 45 * q^31 - 339 * q^32 + 1914 * q^33 - 11 * q^34 - 2137 * q^36 - 44 * q^37 - 33 * q^38 + 374 * q^39 + 979 * q^40 + 441 * q^41 - 22 * q^42 - 11 * q^43 + 516 * q^46 - 1992 * q^47 - 20 * q^48 - 4633 * q^49 - 6231 * q^50 - 22 * q^51 + 178 * q^52 + 2640 * q^54 + 256 * q^55 + 17391 * q^56 + 2090 * q^57 + 320 * q^58 - 2061 * q^59 + 418 * q^60 - 11 * q^61 - 2112 * q^63 + 8546 * q^64 - 12969 * q^65 - 5775 * q^66 - 11 * q^67 - 519 * q^69 - 1582 * q^70 - 4156 * q^72 - 36 * q^73 - 10065 * q^74 - 7876 * q^75 - 11 * q^76 + 1317 * q^77 - 10053 * q^78 - 11 * q^79 + 12442 * q^81 + 698 * q^82 + 14025 * q^83 + 16720 * q^84 + 241 * q^85 - 33 * q^86 + 11672 * q^87 - 1419 * q^88 - 37136 * q^90 + 3141 * q^92 + 1138 * q^93 + 396 * q^94 + 5883 * q^95 + 9218 * q^96 + 6325 * q^97 - 9262 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$ .

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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

)

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

$2$	−2.77962	+	0.132410i	−0.982746	+	0.0468139i	−0.532799	−	0.846242i	$-0.678860\pi$
$2$	−2.77962	+	0.132410i	−0.982746	+	0.0468139i	−0.449946	+	0.893056i	$0.648557\pi$
$3$	1.13894	+	5.06979i	0.219190	+	0.975682i
$3$	1.13894	+	5.06979i	0.219190	+	0.975682i
$4$	−0.254996	+	0.0243491i	−0.0318744	+	0.00304364i
$5$	−5.51997	−	5.26328i	−0.493721	−	0.470762i	0.401834	−	0.915712i	$-0.368373\pi$
$5$	−5.51997	−	5.26328i	−0.493721	−	0.470762i	−0.895555	+	0.444950i	$0.853221\pi$
$6$	−3.83713	−	13.9413i	−0.261084	−	0.948586i
$7$	−2.92152	−	15.1583i	−0.157747	−	0.818470i	−0.971460	−	0.237203i	$-0.923769\pi$
$7$	−2.92152	−	15.1583i	−0.157747	−	0.818470i	0.813713	−	0.581267i	$-0.197443\pi$
$8$	22.7412	−	3.26969i	1.00503	−	0.144501i
$9$	−24.4056	+	11.5484i	−0.903911	+	0.427720i
$10$	16.0403	+	13.8990i	0.507240	+	0.439526i
$11$	16.7412	−	8.63070i	0.458879	−	0.236569i	−0.213257	−	0.976996i	$-0.568407\pi$
$11$	16.7412	−	8.63070i	0.458879	−	0.236569i	0.672136	+	0.740428i	$0.265377\pi$
$12$	−0.413871	−	1.26504i	−0.00995619	−	0.0304322i
$13$	69.6570	+	13.4253i	1.48611	+	0.286423i	0.866772	−	0.498705i	$-0.166191\pi$
$13$	69.6570	+	13.4253i	1.48611	+	0.286423i	0.619333	+	0.785128i	$0.287403\pi$
$14$	10.1278	+	41.7475i	0.193341	+	0.796963i
$15$	20.3968	−	33.9797i	0.351095	−	0.584901i
$16$	−60.7668	+	11.7118i	−0.949481	+	0.182997i
$17$	39.2300	+	85.9018i	0.559687	+	1.22554i	0.952109	+	0.305758i	$0.0989100\pi$
$17$	39.2300	+	85.9018i	0.559687	+	1.22554i	−0.392422	+	0.919785i	$0.628363\pi$
$18$	66.3093	−	35.3318i	0.868292	−	0.462655i
$19$	−54.9456	−	25.0928i	−0.663442	−	0.302984i	0.0550865	−	0.998482i	$-0.482457\pi$
$19$	−54.9456	−	25.0928i	−0.663442	−	0.302984i	−0.718528	+	0.695498i	$0.755184\pi$
$20$	1.53572	+	1.20771i	0.0171699	+	0.0135026i
$21$	73.5219	−	32.0759i	0.763990	−	0.333312i
$22$	−45.3915	+	26.2068i	−0.439887	+	0.253969i
$23$	−77.8435	+	78.1498i	−0.705717	+	0.708494i
$23$	−77.8435	+	78.1498i	−0.705717	+	0.708494i
$24$	42.4776	+	111.569i	0.361279	+	0.948914i
$25$	−3.17980	−	66.7522i	−0.0254384	−	0.534017i
$26$	−195.398	−	28.0940i	−1.47387	−	0.211911i
$27$	−86.3448	−	110.578i	−0.615447	−	0.788178i
$28$	1.11407	+	3.79416i	0.00751924	+	0.0256082i
$29$	−8.09197	+	84.7430i	−0.0518152	+	0.542634i	0.931877	+	0.362774i	$0.118170\pi$
$29$	−8.09197	+	84.7430i	−0.0518152	+	0.542634i	−0.983692	+	0.179860i	$0.942436\pi$
$30$	−52.1962	+	97.1515i	−0.317656	+	0.591245i
$31$	−48.5608	+	38.1886i	−0.281348	+	0.221254i	−0.748853	−	0.662736i	$-0.769395\pi$
$31$	−48.5608	+	38.1886i	−0.281348	+	0.221254i	0.467506	+	0.883990i	$0.345153\pi$
$32$	−11.2611	+	2.73192i	−0.0622095	+	0.0150919i
$33$	62.8232	+	75.0447i	0.331397	+	0.395867i
$34$	−120.419	−	233.580i	−0.607403	−	1.17820i
$35$	−63.6556	+	99.0500i	−0.307422	+	0.478357i
$36$	5.94213	−	3.53905i	0.0275099	−	0.0163845i
$37$	−61.8341	+	210.588i	−0.274742	+	0.935686i	0.700334	+	0.713815i	$0.253034\pi$
$37$	−61.8341	+	210.588i	−0.274742	+	0.935686i	−0.975076	+	0.221871i	$0.928784\pi$
$38$	156.051	+	62.4733i	0.666178	+	0.266698i
$39$	11.2720	+	368.437i	0.0462813	+	1.51275i
$40$	−142.740	−	101.645i	−0.564229	−	0.401786i
$41$	−182.364	+	191.258i	−0.694646	+	0.728524i	−0.972706	−	0.232040i	$-0.925460\pi$
$41$	−182.364	+	191.258i	−0.694646	+	0.728524i	0.278060	+	0.960564i	$0.410309\pi$
$42$	−200.116	+	98.8941i	−0.735205	+	0.363326i
$43$	192.738	−	245.087i	0.683543	−	0.869195i	−0.313213	−	0.949683i	$-0.601405\pi$
$43$	192.738	−	245.087i	0.683543	−	0.869195i	0.996756	+	0.0804878i	$0.0256478\pi$
$44$	−4.05879	+	2.60842i	−0.0139065	+	0.00893716i
$45$	195.501	+	64.7066i	0.647634	+	0.214353i
$46$	206.028	−	227.534i	0.660373	−	0.729307i
$47$	516.671	+	298.300i	1.60349	+	0.925778i	0.990781	+	0.135472i	$0.0432552\pi$
$47$	516.671	+	298.300i	1.60349	+	0.925778i	0.612713	+	0.790305i	$0.290078\pi$
$48$	−128.587	−	294.736i	−0.386664	−	0.886281i
$49$	97.1919	−	38.9098i	0.283358	−	0.113440i
$50$	17.6773	+	185.125i	0.0499989	+	0.523612i
$51$	−390.823	+	296.726i	−1.07306	+	0.814704i
$52$	−18.0891	−	1.72730i	−0.0482406	−	0.00460641i
$53$	475.006	+	548.186i	1.23108	+	1.42074i	0.873478	+	0.486864i	$0.161859\pi$
$53$	475.006	+	548.186i	1.23108	+	1.42074i	0.357600	+	0.933875i	$0.383595\pi$
$54$	254.648	+	295.933i	0.641725	+	0.745768i
$55$	−137.837	−	40.4725i	−0.337926	−	0.0992239i
$56$	−116.002	−	335.165i	−0.276810	−	0.799791i
$57$	64.6354	−	307.142i	0.150196	−	0.713719i
$58$	11.2718	−	236.625i	0.0255184	−	0.535697i
$59$	−158.942	+	824.668i	−0.350720	+	1.81971i	0.193899	+	0.981022i	$0.437887\pi$
$59$	−158.942	+	824.668i	−0.350720	+	1.81971i	−0.544618	+	0.838684i	$0.683325\pi$
$60$	−4.37372	+	9.16131i	−0.00941074	+	0.0197120i
$61$	−132.240	+	330.318i	−0.277566	+	0.693327i	0.722432	+	0.691442i	$0.243024\pi$
$61$	−132.240	+	330.318i	−0.277566	+	0.693327i	−0.999998	+	0.00188497i	$0.999400\pi$
$62$	129.924	−	112.580i	0.266135	−	0.230608i
$63$	246.356	+	336.208i	0.492665	+	0.672353i
$64$	505.967	−	148.565i	0.988216	−	0.290167i
$65$	−313.843	−	440.731i	−0.598884	−	0.841015i
$66$	−184.562	−	200.278i	−0.344211	−	0.373522i
$67$	−271.348	+	526.342i	−0.494783	+	0.959745i	0.500773	+	0.865578i	$0.333049\pi$
$67$	−271.348	+	526.342i	−0.494783	+	0.959745i	−0.995556	+	0.0941668i	$0.969981\pi$
$68$	−12.0951	−	20.9494i	−0.0215698	−	0.0373600i
$69$	−484.863	−	305.642i	−0.845951	−	0.533260i
$70$	163.823	−	283.750i	0.279723	−	0.484495i
$71$	−250.919	−	390.438i	−0.419417	−	0.652626i	0.565680	−	0.824625i	$-0.308614\pi$
$71$	−250.919	−	390.438i	−0.419417	−	0.652626i	−0.985097	+	0.171999i	$0.944977\pi$
$72$	−517.253	+	342.424i	−0.846650	+	0.560486i
$73$	76.5970	−	167.724i	0.122808	−	0.268912i	−0.838236	−	0.545308i	$-0.816413\pi$
$73$	76.5970	−	167.724i	0.122808	−	0.268912i	0.961044	+	0.276396i	$0.0891400\pi$
$74$	143.992	−	593.542i	0.226199	−	0.932403i
$75$	334.798	−	92.1479i	0.515455	−	0.141871i
$76$	14.6219	+	5.06068i	0.0220690	+	0.00763816i
$77$	−179.736	−	228.553i	−0.266011	−	0.338261i
$78$	−80.1167	−	1022.62i	−0.116300	−	1.48448i
$79$	494.277	−	171.071i	0.703930	−	0.243633i	0.0484289	−	0.998827i	$-0.484579\pi$
$79$	494.277	−	171.071i	0.703930	−	0.243633i	0.655501	+	0.755194i	$0.272457\pi$
$80$	397.073	+	255.184i	0.554927	+	0.356630i
$81$	462.268	−	563.693i	0.634112	−	0.773241i
$82$	481.579	−	555.772i	0.648555	−	0.748473i
$83$	334.928	−	319.353i	0.442929	−	0.422332i	−0.435512	−	0.900183i	$-0.643433\pi$
$83$	334.928	−	319.353i	0.442929	−	0.422332i	0.878441	+	0.477851i	$0.158584\pi$
$84$	−17.9667	+	9.96942i	−0.0233373	+	0.0129494i
$85$	235.577	−	680.654i	0.300610	−	0.868556i
$86$	−503.288	+	706.770i	−0.631058	+	0.886197i
$87$	−438.846	+	55.4929i	−0.540795	+	0.0683847i
$88$	352.496	−	251.011i	0.427002	−	0.304067i
$89$	−0.458025	+	3.18564i	−0.000545512	+	0.00379412i	−0.990092	−	0.140418i	$-0.955156\pi$
$89$	−0.458025	+	3.18564i	−0.000545512	+	0.00379412i	0.989547	+	0.144212i	$0.0460646\pi$
$90$	−551.987	−	153.974i	−0.646494	−	0.180336i
$91$		−	1095.10i		−	1.26152i
$92$	17.9469	−	21.8233i	0.0203379	−	0.0247308i
$93$	−248.916	−	202.698i	−0.277542	−	0.226009i
$94$	−1475.65	−	760.750i	−1.61917	−	0.834738i
$95$	171.228	+	427.706i	0.184922	+	0.461912i
$96$	−26.6761	−	53.9801i	−0.0283606	−	0.0573887i
$97$	−2.23136	−	0.541323i	−0.00233568	−	0.000566629i	0.234591	−	0.972094i	$-0.424625\pi$
$97$	−2.23136	−	0.541323i	−0.00233568	−	0.000566629i	−0.236927	+	0.971528i	$0.576140\pi$
$98$	−265.005	+	121.024i	−0.273159	+	0.124747i
$99$	−308.909	+	403.972i	−0.313601	+	0.410109i
$100$	2.43619	+	16.9441i	0.00243619	+	0.0169441i
$101$	−336.071	−	352.461i	−0.331092	−	0.347239i	0.537054	−	0.843548i	$-0.319537\pi$
$101$	−336.071	−	352.461i	−0.331092	−	0.347239i	−0.868146	+	0.496308i	$0.834689\pi$
$102$	1047.05	−	876.534i	1.01641	−	0.850881i
$103$	1934.03	+	92.1290i	1.85015	+	0.0881334i	0.943023	−	0.332727i	$-0.107969\pi$
$103$	1934.03	+	92.1290i	1.85015	+	0.0881334i	0.907125	+	0.420861i	$0.138272\pi$
$104$	1627.98	+	77.5502i	1.53497	+	0.0731194i
$105$	−574.663	−	209.908i	−0.534109	−	0.195095i
$106$	−1392.92	−	1460.86i	−1.27635	−	1.33859i
$107$	137.129	+	953.752i	0.123895	+	0.861707i	0.953077	+	0.302729i	$0.0978976\pi$
$107$	137.129	+	953.752i	0.123895	+	0.861707i	−0.829182	+	0.558979i	$0.811193\pi$
$108$	24.7100	+	26.0946i	0.0220160	+	0.0232496i
$109$	−1103.24	+	503.835i	−0.969464	+	0.442739i	−0.836250	−	0.548348i	$-0.815257\pi$
$109$	−1103.24	+	503.835i	−0.969464	+	0.442739i	−0.133214	+	0.991087i	$0.542530\pi$
$110$	388.494	+	94.2475i	0.336740	+	0.0816922i
$111$	−1138.06	−	73.6385i	−0.973153	−	0.0629681i
$112$	355.063	+	886.904i	0.299556	+	0.748255i
$113$	104.082	+	53.6581i	0.0866480	+	0.0446702i	0.501006	−	0.865444i	$-0.332963\pi$
$113$	104.082	+	53.6581i	0.0866480	+	0.0446702i	−0.414358	+	0.910114i	$0.635994\pi$
$114$	−138.994	+	862.299i	−0.114192	+	0.708436i
$115$	841.018	−	21.6726i	0.681959	−	0.0175737i
$116$		−	21.8061i		−	0.0174539i
$117$	−1855.06	+	476.776i	−1.46582	+	0.376735i
$118$	332.604	−	2313.31i	0.259480	−	1.80473i
$119$	1187.51	−	845.624i	0.914782	−	0.651413i
$120$	352.744	−	839.429i	0.268342	−	0.638576i
$121$	−566.276	+	795.224i	−0.425452	+	0.597463i
$122$	323.839	−	935.671i	0.240320	−	0.694358i
$123$	−1177.34	−	706.716i	−0.863067	−	0.518069i
$124$	11.4529	−	10.9203i	0.00829438	−	0.00790867i
$125$	−958.116	+	1105.73i	−0.685572	+	0.791192i
$126$	−729.294	−	901.913i	−0.515640	−	0.637689i
$127$	−1478.32	−	950.058i	−1.03291	−	0.663811i	−0.0896870	−	0.995970i	$-0.528587\pi$
$127$	−1478.32	−	950.058i	−1.03291	−	0.663811i	−0.943224	+	0.332159i	$0.892223\pi$
$128$	−1299.12	+	449.631i	−0.897088	+	0.310485i
$129$	1462.06	+	698.004i	0.997884	+	0.476401i
$130$	930.724	+	1183.51i	0.627922	+	0.798468i
$131$	2541.81	+	879.728i	1.69526	+	0.586734i	0.992229	−	0.124428i	$-0.0397096\pi$
$131$	2541.81	+	879.728i	1.69526	+	0.586734i	0.703028	+	0.711162i	$0.251831\pi$
$132$	−17.8469	−	17.6064i	−0.0117680	−	0.0116094i
$133$	−219.839	+	906.191i	−0.143327	+	0.590802i
$134$	684.553	−	1498.96i	0.441316	−	0.966348i
$135$	−105.384	+	1064.85i	−0.0671855	+	0.678869i
$136$	1173.01	+	1825.24i	0.739594	+	1.15083i
$137$	−60.3256	+	104.487i	−0.0376202	+	0.0651601i	−0.884222	−	0.467066i	$-0.845311\pi$
$137$	−60.3256	+	104.487i	−0.0376202	+	0.0651601i	0.846602	+	0.532226i	$0.178644\pi$
$138$	1388.21	+	785.369i	0.856319	+	0.484457i
$139$	65.7471	+	113.877i	0.0401194	+	0.0694888i	0.885388	−	0.464853i	$-0.153893\pi$
$139$	65.7471	+	113.877i	0.0401194	+	0.0694888i	−0.845268	+	0.534342i	$0.820560\pi$
$140$	13.8201	−	26.8073i	0.00834295	−	0.0161831i
$141$	−923.861	+	2959.16i	−0.551795	+	1.76742i
$142$	749.159	+	1052.05i	0.442732	+	0.621731i
$143$	1282.01	−	376.433i	0.749701	−	0.220132i
$144$	1347.80	−	987.596i	0.779975	−	0.571525i
$145$	490.693	−	425.188i	0.281034	−	0.243517i
$146$	−190.702	+	476.352i	−0.108100	+	0.270022i
$147$	307.961	+	448.427i	0.172790	+	0.251603i
$148$	10.6398	−	55.2045i	0.00590936	−	0.0306607i
$149$	55.7774	−	1170.91i	0.0306675	−	0.643791i	−0.930245	−	0.366939i	$-0.880406\pi$
$149$	55.7774	−	1170.91i	0.0306675	−	0.643791i	0.960913	−	0.276852i	$-0.0892911\pi$
$150$	−918.411	+	300.467i	−0.499920	+	0.163554i
$151$	−408.243	−	1179.54i	−0.220015	−	0.635693i	−0.999952	−	0.00983371i	$-0.996870\pi$
$151$	−408.243	−	1179.54i	−0.220015	−	0.635693i	0.779936	−	0.625859i	$-0.215251\pi$
$152$	−1331.57	−	390.985i	−0.710559	−	0.208639i
$153$	−1949.46	−	1643.44i	−1.03010	−	0.868394i
$154$	529.863	+	611.494i	0.277257	+	0.319971i
$155$	469.051	+	44.7890i	0.243065	+	0.0232099i
$156$	−11.8454	−	93.6754i	−0.00607945	−	0.0480771i
$157$	308.411	+	3229.83i	0.156776	+	1.64184i	0.641467	+	0.767150i	$0.278326\pi$
$157$	308.411	+	3229.83i	0.156776	+	1.64184i	−0.484691	+	0.874686i	$0.661068\pi$
$158$	−1351.25	+	540.960i	−0.680379	+	0.272383i
$159$	−2238.19	+	3032.54i	−1.11635	+	1.51255i
$160$	76.5399	+	44.1903i	0.0378188	+	0.0218347i
$161$	1412.04	+	951.657i	0.691206	+	0.465845i
$162$	−1210.29	+	1628.06i	−0.586972	+	0.789585i
$163$	886.777	−	569.897i	0.426121	−	0.273852i	−0.309954	−	0.950752i	$-0.600314\pi$
$163$	886.777	−	569.897i	0.426121	−	0.273852i	0.736075	+	0.676900i	$0.236677\pi$
$164$	41.8451	−	53.2103i	0.0199241	−	0.0253356i
$165$	48.1989	−	744.900i	0.0227411	−	0.351457i
$166$	−888.689	+	932.030i	−0.415516	+	0.435781i
$167$	−1219.09	−	868.109i	−0.564885	−	0.402253i	0.261629	−	0.965168i	$-0.415740\pi$
$167$	−1219.09	−	868.109i	−0.564885	−	0.402253i	−0.826514	+	0.562915i	$0.809680\pi$
$168$	1567.10	−	969.839i	0.719668	−	0.445385i
$169$	2632.23	+	1053.79i	1.19810	+	0.479648i
$170$	−564.689	+	1923.15i	−0.254763	+	0.867642i
$171$	1630.76	−	22.1299i	0.729284	−	0.00989657i
$172$	−43.1798	+	67.1891i	−0.0191420	+	0.0297856i
$173$	−768.625	−	1490.93i	−0.337789	−	0.655219i	0.657362	−	0.753575i	$-0.271672\pi$
$173$	−768.625	−	1490.93i	−0.337789	−	0.655219i	−0.995151	+	0.0983554i	$0.968642\pi$
$174$	1212.48	−	212.357i	0.528263	−	0.0925215i
$175$	−1002.56	+	243.218i	−0.433064	+	0.105060i
$176$	−916.229	+	720.531i	−0.392406	+	0.308591i
$177$	−4361.92	+	133.449i	−1.85233	+	0.0566705i
$178$	0.851329	−	8.91552i	0.000358482	−	0.00375419i
$179$	−92.9629	−	316.603i	−0.0388177	−	0.132201i	0.937805	−	0.347164i	$-0.112855\pi$
$179$	−92.9629	−	316.603i	−0.0388177	−	0.132201i	−0.976622	+	0.214963i	$0.931037\pi$
$180$	−51.4274	−	11.7396i	−0.0212954	−	0.00486122i
$181$	2145.39	+	308.461i	0.881026	+	0.126672i	0.567957	−	0.823058i	$-0.307734\pi$
$181$	2145.39	+	308.461i	0.881026	+	0.126672i	0.313069	+	0.949731i	$0.398643\pi$
$182$	145.002	+	3043.97i	0.0590565	+	1.23975i
$183$	−1825.26	−	294.213i	−0.737307	−	0.118846i
$184$	−1514.73	+	2031.74i	−0.606887	+	0.814033i
$185$	1449.70	−	836.987i	0.576131	−	0.332630i
$186$	718.733	+	530.466i	0.283334	+	0.209117i
$187$	1398.15	+	1099.52i	0.546754	+	0.429972i
$188$	−139.012	−	63.4848i	−0.0539282	−	0.0246282i
$189$	−1423.92	+	1631.90i	−0.548016	+	0.628058i
$190$	−532.581	−	1166.19i	−0.203355	−	0.445286i
$191$	3572.23	−	688.491i	1.35328	−	0.260824i	0.539497	−	0.841987i	$-0.318614\pi$
$191$	3572.23	−	688.491i	1.35328	−	0.260824i	0.813787	+	0.581163i	$0.197402\pi$
$192$	1329.46	+	2395.94i	0.499717	+	0.900584i
$193$	−419.811	−	1730.48i	−0.156573	−	0.645404i	−0.994955	−	0.100321i	$-0.968013\pi$
$193$	−419.811	−	1730.48i	−0.156573	−	0.645404i	0.838382	−	0.545084i	$-0.183502\pi$
$194$	6.27403	+	1.20922i	0.00232190	+	0.000447510i
$195$	1876.97	−	2093.09i	0.689294	−	0.768663i
$196$	−23.8361	+	12.2884i	−0.00868662	+	0.00447826i
$197$	−2436.95	−	2111.63i	−0.881347	−	0.763691i	0.0913382	−	0.995820i	$-0.470886\pi$
$197$	−2436.95	−	2111.63i	−0.881347	−	0.763691i	−0.972685	+	0.232128i	$0.925431\pi$
$198$	805.160	−	1163.79i	0.288991	−	0.417713i
$199$	−2525.21	+	363.070i	−0.899533	+	0.129333i	−0.576541	−	0.817068i	$-0.695598\pi$
$199$	−2525.21	+	363.070i	−0.899533	+	0.129333i	−0.322992	+	0.946402i	$0.604689\pi$
$200$	−290.571	−	1507.63i	−0.102732	−	0.533026i
$201$	−2977.50	−	776.205i	−1.04486	−	0.272384i
$202$	980.820	+	935.210i	0.341635	+	0.325748i
$203$	1308.20	−	124.918i	0.452303	−	0.0431897i
$204$	92.4333	−	85.1799i	0.0317236	−	0.0292342i
$205$	2013.29	−	95.9047i	0.685923	−	0.0326745i
$206$	−5388.07			−1.82235
$207$	997.310	−	2806.26i	0.334869	−	0.942265i
$208$	−4390.07			−1.46344
$209$	−1136.43	+	54.1346i	−0.376116	+	0.0179166i
$210$	1625.14	+	507.375i	0.534026	+	0.166725i
$211$	2976.39	−	284.210i	0.971104	−	0.0927292i	0.402570	−	0.915389i	$-0.368117\pi$
$211$	2976.39	−	284.210i	0.971104	−	0.0927292i	0.568534	+	0.822660i	$0.307511\pi$
$212$	−134.472	−	128.219i	−0.0435641	−	0.0415383i
$213$	1693.66	−	1716.80i	0.544823	−	0.552267i
$214$	−507.453	−	2632.92i	−0.162097	−	0.841039i
$215$	−2353.87	+	338.435i	−0.746663	+	0.107354i
$216$	−2325.14	−	2232.36i	−0.732434	−	0.703208i
$217$	720.745	+	624.529i	0.225472	+	0.195372i
$218$	2999.89	−	1546.55i	0.932010	−	0.480485i
$219$	937.566	+	197.302i	0.289291	+	0.0608788i
$220$	36.1332	+	6.96411i	0.0110732	+	0.00213418i
$221$	1579.39	+	6510.33i	0.480730	+	1.98159i
$222$	3173.13	+	53.9968i	0.959310	+	0.0163245i
$223$	−4547.49	+	876.457i	−1.36557	+	0.263192i	−0.818795	−	0.574086i	$-0.805358\pi$
$223$	−4547.49	+	876.457i	−1.36557	+	0.263192i	−0.546777	+	0.837278i	$0.684145\pi$
$224$	74.3108	+	162.718i	0.0221656	+	0.0485360i
$225$	848.487	+	1592.41i	0.251404	+	0.471824i
$226$	−296.414	−	135.368i	−0.0872442	−	0.0398431i
$227$	−4196.00	−	3299.77i	−1.22686	−	0.964817i	−0.226906	−	0.973917i	$-0.572861\pi$
$227$	−4196.00	−	3299.77i	−1.22686	−	0.964817i	−0.999959	+	0.00909954i	$0.997103\pi$
$228$	−9.00310	+	79.8937i	−0.00261511	+	0.0232065i
$229$	−921.254	+	531.886i	−0.265844	+	0.153485i	−0.626997	−	0.779021i	$-0.715716\pi$
$229$	−921.254	+	531.886i	−0.265844	+	0.153485i	0.361154	+	0.932506i	$0.382383\pi$
$230$	−2334.84	+	171.601i	−0.669370	+	0.0491957i
$231$	954.009	−	1171.54i	0.271728	−	0.333686i
$232$	93.0621	+	1953.61i	0.0263355	+	0.552849i
$233$	−1419.11	−	204.037i	−0.399007	−	0.0573686i	−0.0601095	−	0.998192i	$-0.519145\pi$
$233$	−1419.11	−	204.037i	−0.399007	−	0.0573686i	−0.338898	+	0.940823i	$0.610054\pi$
$234$	5093.25	−	1570.89i	1.42289	−	0.438855i
$235$	−1281.97	−	4365.99i	−0.355858	−	1.21194i
$236$	20.4495	−	214.157i	0.00564046	−	0.0590696i
$237$	1430.25	+	2311.04i	0.392002	+	0.633410i
$238$	−3188.87	+	2507.75i	−0.868503	+	0.682998i
$239$	1049.80	−	254.679i	0.284126	−	0.0689282i	−0.0911633	−	0.995836i	$-0.529059\pi$
$239$	1049.80	−	254.679i	0.284126	−	0.0689282i	0.375289	+	0.926908i	$0.377543\pi$
$240$	−841.484	+	2303.72i	−0.226323	+	0.619602i
$241$	2008.64	+	3896.21i	0.536878	+	1.04140i	0.988787	+	0.149334i	$0.0477131\pi$
$241$	2008.64	+	3896.21i	0.536878	+	1.04140i	−0.451908	+	0.892064i	$0.649257\pi$
$242$	1468.74	−	2285.40i	0.390141	−	0.607072i
$243$	3384.30	+	1701.59i	0.893429	+	0.449205i
$244$	25.6775	−	87.4497i	0.00673703	−	0.0229442i
$245$	−741.289	−	296.767i	−0.193303	−	0.0773868i
$246$	3366.14	+	1808.51i	0.872428	+	0.468726i
$247$	−3490.47	−	2485.55i	−0.899162	−	0.640291i
$248$	−979.465	+	1027.23i	−0.250791	+	0.263022i
$249$	2000.52	+	1334.29i	0.509148	+	0.339587i
$250$	2516.79	−	3200.36i	0.636704	−	0.809635i
$251$	2801.69	−	1800.54i	0.704547	−	0.452785i	−0.138684	−	0.990337i	$-0.544287\pi$
$251$	2801.69	−	1800.54i	0.704547	−	0.452785i	0.843231	+	0.537552i	$0.180651\pi$
$252$	−71.0060	−	79.7331i	−0.0177498	−	0.0199314i
$253$	−628.707	+	1980.17i	−0.156231	+	0.492063i
$254$	4234.97	+	2445.06i	1.04616	+	0.604003i
$255$	3719.08	+	419.097i	0.913325	+	0.102921i
$256$	−364.892	+	146.081i	−0.0890850	+	0.0356643i
$257$	−465.881	−	4878.93i	−0.113077	−	1.18420i	−0.856778	−	0.515686i	$-0.827537\pi$
$257$	−465.881	−	4878.93i	−0.113077	−	1.18420i	0.743701	−	0.668513i	$-0.233069\pi$
$258$	−4156.39	−	1746.60i	−1.00297	−	0.421467i
$259$	3372.80	+	322.063i	0.809171	+	0.0772665i
$260$	90.7601	+	104.743i	0.0216488	+	0.0249841i
$261$	−781.159	−	2161.65i	−0.185259	−	0.512655i
$262$	−7181.75	−	2108.75i	−1.69347	−	0.497249i
$263$	1288.30	+	3722.29i	0.302053	+	0.872724i	0.989248	+	0.146251i	$0.0467206\pi$
$263$	1288.30	+	3722.29i	0.302053	+	0.872724i	−0.687195	+	0.726473i	$0.741158\pi$
$264$	1674.05	+	1501.19i	0.390267	+	0.349970i
$265$	263.239	−	5526.06i	0.0610212	−	1.28099i
$266$	491.083	−	2547.98i	0.113196	−	0.587318i
$267$	−16.6722	+	1.30617i	−0.00382143	+	0.000299387i
$268$	56.3766	−	140.822i	0.0128498	−	0.0320973i
$269$	−957.962	+	830.078i	−0.217130	+	0.188144i	−0.756634	−	0.653839i	$-0.773157\pi$
$269$	−957.962	+	830.078i	−0.217130	+	0.188144i	0.539504	+	0.841983i	$0.318612\pi$
$270$	151.933	−	2973.83i	0.0342457	−	0.670301i
$271$	−2630.49	+	772.383i	−0.589635	+	0.173132i	−0.562921	−	0.826511i	$-0.690323\pi$
$271$	−2630.49	+	772.383i	−0.589635	+	0.173132i	−0.0267140	+	0.999643i	$0.508504\pi$
$272$	−3389.95	−	4760.52i	−0.755684	−	1.06121i
$273$	5551.94	−	1247.26i	1.23084	−	0.276512i
$274$	153.847	−	298.422i	0.0339207	−	0.0657969i
$275$	−629.352	−	1090.07i	−0.138005	−	0.239031i
$276$	131.080	+	66.1314i	0.0285873	+	0.0144226i
$277$	2657.70	−	4603.27i	0.576482	−	0.998496i	−0.419397	−	0.907803i	$-0.637758\pi$
$277$	2657.70	−	4603.27i	0.576482	−	0.998496i	0.995879	−	0.0906934i	$-0.0289083\pi$
$278$	−197.831	−	307.831i	−0.0426802	−	0.0664117i
$279$	744.137	−	1492.82i	0.159679	−	0.320332i
$280$	−1123.74	+	2460.65i	−0.239844	+	0.525185i
$281$	−681.032	+	2807.25i	−0.144580	+	0.595967i	0.852709	+	0.522386i	$0.174958\pi$
$281$	−681.032	+	2807.25i	−0.144580	+	0.595967i	−0.997289	+	0.0735810i	$0.976557\pi$
$282$	2176.16	−	8347.69i	0.459534	−	1.76276i
$283$	1936.85	+	670.352i	0.406834	+	0.140807i	0.522818	−	0.852444i	$-0.324881\pi$
$283$	1936.85	+	670.352i	0.406834	+	0.140807i	−0.115984	+	0.993251i	$0.537002\pi$
$284$	73.4901	+	93.4503i	0.0153551	+	0.0195255i
$285$	−1973.36	+	1355.22i	−0.410147	+	0.281672i
$286$	−3513.67	+	1216.09i	−0.726460	+	0.251430i
$287$	3431.92	+	2205.56i	0.705854	+	0.453625i
$288$	243.285	−	196.722i	0.0497768	−	0.0402499i
$289$	−2622.79	+	3026.86i	−0.533847	+	0.616092i
$290$	−1307.64	+	1246.84i	−0.264785	+	0.252472i
$291$	0.202996	−	11.9291i	4.08929e−5	−	0.00240308i
$292$	−15.4480	+	44.6339i	−0.00309597	+	0.00894522i
$293$	−18.3159	+	25.7210i	−0.00365196	+	0.00512846i	−0.816398	−	0.577490i	$-0.804032\pi$
$293$	−18.3159	+	25.7210i	−0.00365196	+	0.00512846i	0.812746	+	0.582618i	$0.197972\pi$
$294$	−915.391	−	1205.68i	−0.181587	−	0.239173i
$295$	5217.81	−	3715.59i	1.02981	−	0.733321i
$296$	−717.625	+	4991.19i	−0.140916	+	0.980091i
$297$	−2399.89	−	1106.00i	−0.468874	−	0.216083i
$298$			3262.08i			0.634118i
$299$	−6471.52	+	4398.61i	−1.25170	+	0.850763i
$300$	−83.1283	+	31.6494i	−0.0159980	+	0.00609092i
$301$	−4278.18	−	2205.56i	−0.819237	−	0.422346i
$302$	1290.94	+	3224.62i	0.245978	+	0.614424i
$303$	1404.14	−	2105.24i	0.266223	−	0.399152i
$304$	3632.75	+	881.296i	0.685371	+	0.166269i
$305$	2468.52	−	1127.33i	0.463432	−	0.211642i
$306$	5636.38	+	4310.02i	1.05298	+	0.805187i
$307$	847.584	+	5895.07i	0.157571	+	1.09593i	0.903092	+	0.429446i	$0.141291\pi$
$307$	847.584	+	5895.07i	0.157571	+	1.09593i	−0.745522	+	0.666481i	$0.767800\pi$
$308$	51.3971	+	53.9037i	0.00950851	+	0.00997224i
$309$	1735.67	+	9910.04i	0.319544	+	1.82447i
$310$	−1309.72	−	62.3895i	−0.239958	−	0.0114306i
$311$	−715.791	−	34.0973i	−0.130511	−	0.00621699i	−0.0177750	−	0.999842i	$-0.505658\pi$
$311$	−715.791	−	34.0973i	−0.130511	−	0.00621699i	−0.112736	+	0.993625i	$0.535961\pi$
$312$	1461.01	+	8341.84i	0.265108	+	1.51367i
$313$	5617.92	+	5891.90i	1.01452	+	1.06399i	0.997942	+	0.0641306i	$0.0204274\pi$
$313$	5617.92	+	5891.90i	1.01452	+	1.06399i	0.0165740	+	0.999863i	$0.494724\pi$
$314$	−1284.93	−	8936.87i	−0.230932	−	1.60617i
$315$	409.681	−	3152.50i	0.0732791	−	0.563883i
$316$	−121.873	+	55.6575i	−0.0216959	+	0.00990817i
$317$	−5807.14	−	1408.80i	−1.02890	−	0.249609i	−0.314435	−	0.949279i	$-0.601815\pi$
$317$	−5807.14	−	1408.80i	−1.02890	−	0.249609i	−0.714466	+	0.699670i	$0.753330\pi$
$318$	5819.78	−	8725.67i	1.02628	−	1.53871i
$319$	595.922	+	1488.54i	0.104593	+	0.261261i
$320$	−3574.86	−	1842.97i	−0.624503	−	0.321953i
$321$	−4679.14	+	1781.49i	−0.813596	+	0.309760i
$322$	−4050.95	−	2458.28i	−0.701088	−	0.425449i
$323$		−	5704.32i		−	0.982653i
$324$	−104.151	+	154.995i	−0.0178585	+	0.0265766i
$325$	674.671	−	4692.44i	0.115151	−	0.800892i
$326$	−2389.45	+	1701.52i	−0.405949	+	0.289075i
$327$	−3810.87	−	5019.38i	−0.644470	−	0.848845i
$328$	−3521.82	+	4945.71i	−0.592866	+	0.832564i
$329$	3012.25	−	8703.34i	0.504775	−	1.45845i
$330$	−35.3428	+	2076.92i	−0.00589562	+	0.346457i
$331$	−3886.40	+	3705.67i	−0.645365	+	0.615354i	−0.940375	−	0.340140i	$-0.889526\pi$
$331$	−3886.40	+	3705.67i	−0.645365	+	0.615354i	0.295010	+	0.955494i	$0.404677\pi$
$332$	−77.6292	+	89.5889i	−0.0128327	+	0.0148097i
$333$	−922.857	−	5853.60i	−0.151869	−	0.963290i
$334$	3503.55	+	2251.60i	0.573970	+	0.368868i
$335$	4268.12	−	1477.21i	0.696096	−	0.240921i
$336$	−4092.02	+	2810.23i	−0.664399	+	0.456282i
$337$	243.500	+	309.636i	0.0393599	+	0.0500502i	0.805335	−	0.592821i	$-0.201986\pi$
$337$	243.500	+	309.636i	0.0393599	+	0.0500502i	−0.765975	+	0.642871i	$0.777743\pi$
$338$	−7456.15	−	2580.60i	−1.19988	−	0.415284i
$339$	−153.492	+	588.789i	−0.0245915	+	0.0943322i
$340$	−43.4977	+	179.300i	−0.00693821	+	0.0285997i
$341$	−483.372	+	1058.44i	−0.0767627	+	0.168087i
$342$	−4529.98	+	277.442i	−0.716238	+	0.0438665i
$343$	−3736.43	−	5814.01i	−0.588188	−	0.915239i
$344$	3581.74	−	6203.76i	0.561380	−	0.972338i
$345$	1067.75	+	4239.10i	0.166625	+	0.661524i
$346$	2333.90	+	4042.44i	0.362634	+	0.628101i
$347$	−746.320	+	1447.66i	−0.115460	+	0.223961i	−0.939483	−	0.342595i	$-0.888694\pi$
$347$	−746.320	+	1447.66i	−0.115460	+	0.223961i	0.824023	+	0.566556i	$0.191724\pi$
$348$	110.553	−	24.8360i	0.0170294	−	0.00382571i
$349$	−2159.43	−	3032.50i	−0.331209	−	0.465117i	0.615069	−	0.788473i	$-0.289128\pi$
$349$	−2159.43	−	3032.50i	−0.331209	−	0.465117i	−0.946277	+	0.323356i	$0.895189\pi$
$350$	2754.53	−	808.803i	0.420674	−	0.123521i
$351$	−4529.97	−	8861.76i	−0.688866	−	1.34759i
$352$	−164.947	+	142.927i	−0.0249764	+	0.0216422i
$353$	−3921.59	+	9795.67i	−0.591290	+	1.47697i	0.266944	+	0.963712i	$0.413986\pi$
$353$	−3921.59	+	9795.67i	−0.591290	+	1.47697i	−0.858234	+	0.513259i	$0.828438\pi$
$354$	12106.8	−	948.501i	1.81772	−	0.142407i
$355$	−669.917	+	3475.86i	−0.100156	+	0.519661i
$356$	0.0392270	−	0.823476i	5.83996e−6	−	0.000122596i
$357$	5639.65	+	5057.32i	0.836084	+	0.749753i
$358$	300.323	+	867.727i	0.0443368	+	0.128103i
$359$	−4229.49	−	1241.89i	−0.621794	−	0.182575i	−0.0443641	−	0.999015i	$-0.514126\pi$
$359$	−4229.49	−	1241.89i	−0.621794	−	0.182575i	−0.577430	+	0.816440i	$0.695944\pi$
$360$	4657.49	+	832.277i	0.681865	+	0.121847i
$361$	−2102.32	−	2426.20i	−0.306505	−	0.353726i
$362$	−6004.22	−	573.334i	−0.871754	−	0.0832424i
$363$	−4676.58	−	1965.19i	−0.676189	−	0.284148i
$364$	26.6648	+	279.246i	0.00383960	+	0.0402101i
$365$	−1305.59	+	522.680i	−0.187227	+	0.0749543i
$366$	5112.49	+	576.119i	0.730148	+	0.0822793i
$367$	1594.25	+	920.440i	0.226755	+	0.130917i	0.609074	−	0.793113i	$-0.291541\pi$
$367$	1594.25	+	920.440i	0.226755	+	0.130917i	−0.382319	+	0.924030i	$0.624874\pi$
$368$	3815.02	−	5660.60i	0.540412	−	0.801846i
$369$	2241.98	−	6773.79i	0.316295	−	0.955635i
$370$	−3918.81	+	2518.46i	−0.550619	+	0.353861i
$371$	6921.82	−	8801.82i	0.968634	−	1.23172i
$372$	68.4081	+	45.6263i	0.00953440	+	0.00635918i
$373$	6341.53	−	6650.81i	0.880300	−	0.923232i	−0.117256	−	0.993102i	$-0.537410\pi$
$373$	6341.53	−	6650.81i	0.880300	−	0.923232i	0.997556	+	0.0698695i	$0.0222583\pi$
$374$	−4031.92	−	2871.12i	−0.557449	−	0.396957i
$375$	−6697.04	−	3598.09i	−0.922223	−	0.495479i
$376$	12725.1	+	5094.35i	1.74533	+	0.698726i
$377$	−1701.36	+	5794.30i	−0.232426	+	0.791570i
$378$	3741.89	−	4724.60i	0.509158	−	0.642876i
$379$	7460.18	−	11608.3i	1.01109	−	1.57329i	0.207387	−	0.978259i	$-0.433504\pi$
$379$	7460.18	−	11608.3i	1.01109	−	1.57329i	0.803704	−	0.595029i	$-0.202860\pi$
$380$	−54.0765	−	104.894i	−0.00730018	−	0.0141604i
$381$	3132.87	−	8576.84i	0.421265	−	1.15329i
$382$	−9838.29	+	2386.74i	−1.31772	+	0.319676i
$383$	471.677	−	370.931i	0.0629284	−	0.0494874i	−0.586199	−	0.810167i	$-0.699376\pi$
$383$	471.677	−	370.931i	0.0629284	−	0.0494874i	0.649128	+	0.760679i	$0.275134\pi$
$384$	−3759.16	−	6074.18i	−0.499568	−	0.807218i
$385$	−210.801	+	2207.61i	−0.0279050	+	0.292234i
$386$	1396.05	+	4754.51i	0.184086	+	0.626938i
$387$	−1873.53	+	8207.32i	−0.246090	+	1.07804i
$388$	0.582169	+	0.0837032i	7.61730e−5	+	1.09520e-5i
$389$	489.648	+	10279.0i	0.0638204	+	1.33976i	0.772855	+	0.634582i	$0.218828\pi$
$389$	489.648	+	10279.0i	0.0638204	+	1.33976i	−0.709035	+	0.705173i	$0.750869\pi$
$390$	−4940.11	+	6066.53i	−0.641417	+	0.787668i
$391$	−9767.01	−	3621.07i	−1.26327	−	0.468352i
$392$	2083.04	−	1202.64i	0.268391	−	0.154956i
$393$	−1565.06	+	13888.4i	−0.200883	+	1.78264i
$394$	7053.40	+	5546.86i	0.901891	+	0.709255i
$395$	−3628.79	−	1657.21i	−0.462238	−	0.211097i
$396$	68.9340	−	110.533i	0.00874764	−	0.0140265i
$397$	−5535.40	−	12120.8i	−0.699783	−	1.53231i	−0.840235	−	0.542223i	$-0.817583\pi$
$397$	−5535.40	−	12120.8i	−0.699783	−	1.53231i	0.140452	−	0.990088i	$-0.455144\pi$
$398$	6971.05	−	1343.56i	0.877958	−	0.169212i
$399$	−4844.58	−	82.4397i	−0.607851	−	0.0103437i
$400$	975.017	+	4019.07i	0.121877	+	0.502384i
$401$	7318.70	+	1410.56i	0.911417	+	0.175661i	0.623344	−	0.781947i	$-0.285773\pi$
$401$	7318.70	+	1410.56i	0.911417	+	0.175661i	0.288073	+	0.957609i	$0.406986\pi$
$402$	8379.10	+	1763.31i	1.03958	+	0.218771i
$403$	−3895.29	+	2008.16i	−0.481484	+	0.248222i
$404$	94.2787	+	81.6929i	0.0116102	+	0.0100603i
$405$	−5518.58	+	678.523i	−0.677087	+	0.0832496i
$406$	−3619.76	+	520.443i	−0.442477	+	0.0636186i
$407$	782.340	+	4059.16i	0.0952805	+	0.494362i
$408$	−7917.59	+	8025.76i	−0.960733	+	0.973859i
$409$	10156.9	+	9684.58i	1.22794	+	1.17083i	0.979338	+	0.202228i	$0.0648182\pi$
$409$	10156.9	+	9684.58i	1.22794	+	1.17083i	0.248598	+	0.968607i	$0.420030\pi$
$410$	−5583.49	+	533.158i	−0.672558	+	0.0642215i
$411$	−598.435	−	186.834i	−0.0718215	−	0.0224229i
$412$	−495.411	+	23.5994i	−0.0592407	+	0.00282198i
$413$	12964.9			1.54470
$414$	−2400.57	+	7932.41i	−0.284980	+	0.941683i
$415$	−3529.64			−0.417502
$416$	−821.093	+	39.1135i	−0.0967726	+	0.00460985i
$417$	−502.452	+	463.024i	−0.0590052	+	0.0543750i
$418$	3151.67	−	300.948i	0.368787	−	0.0352149i
$419$	1664.51	+	1587.11i	0.194073	+	0.185049i	0.780885	−	0.624675i	$-0.214769\pi$
$419$	1664.51	+	1587.11i	0.194073	+	0.185049i	−0.586811	+	0.809724i	$0.699617\pi$
$420$	151.648	+	39.5331i	0.0176182	+	0.00459290i
$421$	38.3605	+	199.033i	0.00444080	+	0.0230411i	0.984082	−	0.177718i	$-0.0568714\pi$
$421$	38.3605	+	199.033i	0.00444080	+	0.0230411i	−0.979641	+	0.200759i	$0.935659\pi$
$422$	−8235.60	+	1184.10i	−0.950007	+	0.136590i
$423$	−16054.6	−	1313.46i	−1.84539	−	0.150975i
$424$	12594.6	+	10913.3i	1.44257	+	1.24999i
$425$	5609.39	−	2891.84i	0.640224	−	0.330058i
$426$	−4480.41	+	4996.30i	−0.509569	+	0.568243i
$427$	5393.40	+	1039.49i	0.611253	+	0.117809i
$428$	−58.1903	−	239.864i	−0.00657181	−	0.0270894i
$429$	3368.58	+	6070.80i	0.379106	+	0.683219i
$430$	6498.06	−	1252.40i	0.728754	−	0.140456i
$431$	2788.77	+	6106.56i	0.311671	+	0.682465i	0.999038	−	0.0438451i	$-0.0139608\pi$
$431$	2788.77	+	6106.56i	0.311671	+	0.682465i	−0.687367	+	0.726310i	$0.741234\pi$
$432$	6541.97	+	5708.24i	0.728590	+	0.635735i
$433$	2793.66	+	1275.82i	0.310057	+	0.141598i	0.564366	−	0.825525i	$-0.309121\pi$
$433$	2793.66	+	1275.82i	0.310057	+	0.141598i	−0.254309	+	0.967123i	$0.581848\pi$
$434$	−2086.09	−	1640.52i	−0.230728	−	0.181446i
$435$	2714.49	+	2003.45i	0.299195	+	0.220823i
$436$	269.054	−	155.339i	0.0295536	−	0.0170628i
$437$	6238.16	−	2340.68i	0.682864	−	0.256224i
$438$	−2632.20	−	424.284i	−0.287150	−	0.0462855i
$439$	−834.420	−	17516.6i	−0.0907168	−	1.90438i	−0.347136	−	0.937815i	$-0.612846\pi$
$439$	−834.420	−	17516.6i	−0.0907168	−	1.90438i	0.256419	−	0.966566i	$-0.417457\pi$
$440$	−3266.90	−	469.710i	−0.353963	−	0.0508921i
$441$	−1922.68	+	2072.03i	−0.207611	+	0.223737i
$442$	−5252.14	−	17887.2i	−0.565201	−	1.92490i
$443$	93.8594	−	982.940i	0.0100664	−	0.105420i	−0.989042	−	0.147632i	$-0.952835\pi$
$443$	93.8594	−	982.940i	0.0100664	−	0.105420i	0.999109	+	0.0422129i	$0.0134408\pi$
$444$	291.994	−	8.93331i	0.0312104	−	0.000954856i
$445$	19.2952	−	15.1739i	0.00205546	−	0.00161643i
$446$	12524.3	−	3038.35i	1.32969	−	0.322579i
$447$	5999.81	−	1050.82i	0.634857	−	0.111191i
$448$	−3730.19	−	7235.55i	−0.393381	−	0.763053i
$449$	1674.37	−	2605.38i	0.175988	−	0.273843i	−0.742042	−	0.670353i	$-0.766143\pi$
$449$	1674.37	−	2605.38i	0.175988	−	0.273843i	0.918030	+	0.396510i	$0.129779\pi$
$450$	−2569.33	−	4313.94i	−0.269154	−	0.451914i
$451$	−1402.31	+	4775.82i	−0.146413	+	0.498636i
$452$	−27.8470	−	11.1483i	−0.00289782	−	0.00116011i
$453$	5515.06	−	3413.14i	0.572009	−	0.354003i
$454$	12100.2	+	8616.53i	1.25086	+	0.890735i
$455$	−5763.83	+	6044.93i	−0.593874	+	0.622837i
$456$	465.626	−	7196.12i	0.0478179	−	0.739011i
$457$	−8719.04	+	11087.2i	−0.892471	+	1.13487i	0.0977288	+	0.995213i	$0.468842\pi$
$457$	−8719.04	+	11087.2i	−0.892471	+	1.13487i	−0.990200	+	0.139656i	$0.955400\pi$
$458$	2490.31	−	1600.43i	0.254071	−	0.163282i
$459$	6111.57	−	11755.2i	0.621490	−	1.19539i
$460$	−213.928	+	26.0045i	−0.0216836	+	0.00263579i
$461$	−3103.78	−	1791.97i	−0.313574	−	0.181042i	0.334951	−	0.942236i	$-0.391280\pi$
$461$	−3103.78	−	1791.97i	−0.313574	−	0.181042i	−0.648525	+	0.761194i	$0.724614\pi$
$462$	−2496.66	+	3382.75i	−0.251418	+	0.340649i
$463$	−15943.2	+	6382.71i	−1.60031	+	0.640669i	−0.988621	−	0.150427i	$-0.951935\pi$
$463$	−15943.2	+	6382.71i	−1.60031	+	0.640669i	−0.611692	+	0.791096i	$0.709511\pi$
$464$	−500.773	−	5244.33i	−0.0501030	−	0.524703i
$465$	307.153	+	2429.01i	0.0306320	+	0.242242i
$466$	3971.60	+	379.241i	0.394808	+	0.0376996i
$467$	−1637.67	−	1889.97i	−0.162275	−	0.187275i	0.668789	−	0.743452i	$-0.266813\pi$
$467$	−1637.67	−	1889.97i	−0.162275	−	0.187275i	−0.831064	+	0.556177i	$0.812268\pi$
$468$	461.423	−	166.745i	0.0455754	−	0.0164696i
$469$	8771.19	+	2575.45i	0.863574	+	0.253568i
$470$	4141.50	+	11966.1i	0.406453	+	1.17437i
$471$	−16023.3	+	5242.17i	−1.56755	+	0.512838i
$472$	−918.116	+	19273.6i	−0.0895332	+	1.87953i
$473$	1111.41	−	5766.52i	0.108039	−	0.560560i
$474$	−4281.56	−	6234.45i	−0.414891	−	0.604130i
$475$	−1500.28	+	3747.53i	−0.144922	+	0.361997i
$476$	−282.220	+	244.545i	−0.0271755	+	0.0235477i
$477$	−17923.5	−	7893.25i	−1.72046	−	0.757667i
$478$	−2884.34	+	846.917i	−0.275997	+	0.0810400i
$479$	10104.0	+	14189.1i	0.963808	+	1.35348i	0.935288	+	0.353886i	$0.115140\pi$
$479$	10104.0	+	14189.1i	0.963808	+	1.35348i	0.0285200	+	0.999593i	$0.490921\pi$
$480$	−136.861	+	438.372i	−0.0130142	+	0.0416851i
$481$	−7134.37	+	13838.8i	−0.676298	+	1.31184i
$482$	−6099.15	−	10564.0i	−0.576367	−	0.998297i
$483$	−3216.47	+	8242.63i	−0.303011	+	0.776506i
$484$	125.035	−	216.567i	0.0117426	−	0.0203387i
$485$	9.46792	+	14.7324i	0.000886425	+	0.00137930i
$486$	−9632.40	−	4281.66i	−0.899042	−	0.399629i
$487$	854.190	−	1870.42i	0.0794806	−	0.174038i	−0.865720	−	0.500529i	$-0.833139\pi$
$487$	854.190	−	1870.42i	0.0794806	−	0.174038i	0.945200	+	0.326491i	$0.105866\pi$
$488$	−1927.25	+	7944.21i	−0.178775	+	0.736921i
$489$	3899.25	+	3846.70i	0.360594	+	0.355733i
$490$	2099.80	+	726.748i	0.193590	+	0.0670023i
$491$	−982.625	−	1249.51i	−0.0903162	−	0.114846i	0.738795	−	0.673931i	$-0.235395\pi$
$491$	−982.625	−	1249.51i	−0.0903162	−	0.114846i	−0.829111	+	0.559084i	$0.811153\pi$
$492$	317.425	+	151.542i	0.0290866	+	0.0138863i
$493$	−7597.02	+	2629.35i	−0.694022	+	0.240203i
$494$	10031.3	+	6446.72i	0.913622	+	0.587150i
$495$	3831.39	−	604.041i	0.347895	−	0.0548478i
$496$	2503.62	−	2889.34i	0.226645	−	0.261563i
$497$	−5185.30	+	4944.18i	−0.467993	+	0.446231i
$498$	−5737.37	−	3443.94i	−0.516260	−	0.309893i
$499$	6526.98	−	18858.5i	0.585547	−	1.69183i	−0.128485	−	0.991712i	$-0.541011\pi$
$499$	6526.98	−	18858.5i	0.585547	−	1.69183i	0.714031	−	0.700114i	$-0.246868\pi$
$500$	217.392	−	305.284i	0.0194441	−	0.0273055i
$501$	3012.66	−	7169.25i	0.268654	−	0.639318i
$502$	−7549.24	+	5375.79i	−0.671194	+	0.477955i
$503$	755.929	−	5257.60i	0.0670084	−	0.466054i	−0.928496	−	0.371342i	$-0.878898\pi$
$503$	755.929	−	5257.60i	0.0670084	−	0.466054i	0.995505	−	0.0947120i	$-0.0301930\pi$
$504$	6701.72	+	6840.27i	0.592298	+	0.604543i
$505$			3714.41i			0.327305i
$506$	1485.38	−	5587.37i	0.130500	−	0.490887i
$507$	−2344.51	+	14545.1i	−0.205372	+	1.27410i
$508$	400.098	+	206.265i	0.0349439	+	0.0180148i
$509$	7792.79	+	19465.5i	0.678604	+	1.69507i	0.718182	+	0.695855i	$0.244974\pi$
$509$	7792.79	+	19465.5i	0.678604	+	1.69507i	−0.0395781	+	0.999216i	$0.512601\pi$
$510$	−10393.1	−	672.491i	−0.902385	−	0.0583890i
$511$	−2766.19	−	671.070i	−0.239469	−	0.0580947i
$512$	10998.9	−	5023.04i	0.949391	−	0.433572i
$513$	1969.54	+	8242.43i	0.169508	+	0.709381i
$514$	1940.99	+	13499.9i	0.166563	+	1.15847i
$515$	−10190.9	−	10687.9i	−0.871967	−	0.914493i
$516$	−389.814	−	142.388i	−0.0332570	−	0.0121478i
$517$	11224.2	+	534.677i	0.954820	+	0.0454837i
$518$	−9417.75	−	448.623i	−0.798827	−	0.0380528i
$519$	6683.26	−	5594.85i	0.565246	−	0.473192i
$520$	−8578.22	−	8996.58i	−0.723423	−	0.758704i
$521$	68.6740	+	477.638i	0.00577479	+	0.0401645i	0.992505	−	0.122203i	$-0.0389960\pi$
$521$	68.6740	+	477.638i	0.00577479	+	0.0401645i	−0.986730	+	0.162368i	$0.948087\pi$
$522$	2457.55	+	5905.15i	0.206062	+	0.495137i
$523$	13558.4	−	6191.93i	1.13359	−	0.517694i	0.241884	−	0.970305i	$-0.422235\pi$
$523$	13558.4	−	6191.93i	1.13359	−	0.517694i	0.891708	+	0.452611i	$0.149507\pi$
$524$	−669.570	−	162.436i	−0.0558212	−	0.0135421i
$525$	−2374.92	−	4805.75i	−0.197429	−	0.399505i
$526$	−4073.85	−	10176.0i	−0.337697	−	0.843525i
$527$	−5185.51	−	2673.32i	−0.428623	−	0.220971i
$528$	−4696.48	−	3824.45i	−0.387098	−	0.315223i
$529$	−47.7875	−	12166.9i	−0.00392764	−	0.999992i
$530$			15395.2i			1.26175i
$531$	−5644.55	−	21962.1i	−0.461304	−	1.79486i
$532$	33.9931	−	236.427i	0.00277028	−	0.0192677i
$533$	−15270.6	+	10874.2i	−1.24098	+	0.883700i
$534$	46.1695	−	5.83822i	0.00374148	−	0.000473117i
$535$	4262.92	−	5986.43i	0.344490	−	0.483768i
$536$	−4449.81	+	12856.9i	−0.358586	+	1.03607i
$537$	1499.23	−	831.896i	0.120478	−	0.0668509i
$538$	2552.86	−	2434.15i	0.204576	−	0.195063i
$539$	1291.29	−	1490.23i	0.103191	−	0.119089i
$540$	0.944497	−	274.097i	7.52679e−5	−	0.0218431i
$541$	6447.40	+	4143.49i	0.512376	+	0.329284i	0.771150	−	0.636654i	$-0.219682\pi$
$541$	6447.40	+	4143.49i	0.512376	+	0.329284i	−0.258774	+	0.965938i	$0.583318\pi$
$542$	7209.51	−	2495.24i	0.571356	−	0.197748i
$543$	879.650	+	11228.0i	0.0695200	+	0.887366i
$544$	−676.451	−	860.178i	−0.0533136	−	0.0677938i
$545$	8741.69	+	3025.53i	0.687070	+	0.237797i
$546$	−15267.2	+	4202.05i	−1.19666	+	0.329361i
$547$	808.446	−	3332.46i	0.0631931	−	0.260486i	−0.931448	−	0.363875i	$-0.881454\pi$
$547$	808.446	−	3332.46i	0.0631931	−	0.260486i	0.994641	+	0.103389i	$0.0329687\pi$
$548$	12.8386	−	28.1126i	0.00100080	−	0.00219144i
$549$	−587.272	−	9588.78i	−0.0456542	−	0.745427i
$550$	1893.70	+	2946.65i	0.146814	+	0.228446i
$551$	2571.06	−	4453.21i	0.198786	−	0.344307i
$552$	−12025.7	−	5365.31i	−0.927261	−	0.413701i
$553$	−4037.18	−	6992.60i	−0.310449	−	0.537714i
$554$	−6777.88	+	13147.3i	−0.519792	+	1.00826i
$555$	5894.48	+	6396.41i	0.450823	+	0.489212i
$556$	−19.5380	−	27.4373i	−0.00149028	−	0.00209281i
$557$	2370.77	−	696.120i	0.180346	−	0.0529543i	−0.190313	−	0.981724i	$-0.560950\pi$
$557$	2370.77	−	696.120i	0.180346	−	0.0529543i	0.370659	+	0.928769i	$0.379132\pi$
$558$	−1870.76	+	4248.00i	−0.141927	+	0.322280i
$559$	16715.9	−	14484.4i	1.26477	−	1.09593i
$560$	2708.09	−	6764.48i	0.204353	−	0.510449i
$561$	−3981.91	+	8340.63i	−0.299673	+	0.627703i
$562$	1521.31	−	7893.28i	0.114186	−	0.592452i
$563$	389.189	−	8170.08i	0.0291339	−	0.611595i	−0.936340	−	0.351095i	$-0.885810\pi$
$563$	389.189	−	8170.08i	0.0291339	−	0.611595i	0.965474	−	0.260500i	$-0.0838874\pi$
$564$	163.527	−	777.069i	0.0122088	−	0.0580151i
$565$	−292.113	−	844.004i	−0.0217509	−	0.0628452i
$566$	−5472.49	−	1606.87i	−0.406406	−	0.119332i
$567$	−9895.14	−	5360.34i	−0.732905	−	0.397025i
$568$	−6982.81	−	8058.59i	−0.515831	−	0.595301i
$569$	1901.78	+	181.598i	0.140117	+	0.0133796i	0.164879	−	0.986314i	$-0.447277\pi$
$569$	1901.78	+	181.598i	0.140117	+	0.0133796i	−0.0247617	+	0.999693i	$0.507883\pi$
$570$	5305.76	−	4028.30i	0.389884	−	0.296012i
$571$	−1314.08	−	13761.7i	−0.0963094	−	1.00860i	−0.906436	−	0.422343i	$-0.861208\pi$
$571$	−1314.08	−	13761.7i	−0.0963094	−	1.00860i	0.810127	−	0.586255i	$-0.199398\pi$
$572$	−317.742	+	127.205i	−0.0232263	+	0.00929841i
$573$	7559.08	+	17326.3i	0.551108	+	1.26321i
$574$	−9831.50	−	5676.22i	−0.714911	−	0.412754i
$575$	5464.19	+	4947.72i	0.396300	+	0.358842i
$576$	−10632.7	+	9468.95i	−0.769150	+	0.684964i
$577$	8017.08	−	5152.26i	0.578432	−	0.371736i	−0.218471	−	0.975844i	$-0.570107\pi$
$577$	8017.08	−	5152.26i	0.578432	−	0.371736i	0.796903	+	0.604108i	$0.206470\pi$
$578$	6889.59	−	8760.82i	0.495794	−	0.630454i
$579$	8295.06	−	4099.28i	0.595390	−	0.294232i
$580$	−114.772	+	120.369i	−0.00821661	+	0.00861734i
$581$	−5819.35	−	4143.94i	−0.415537	−	0.295903i
$582$	1.01528	+	33.1853i	7.23102e−5	+	0.00236353i
$583$	12683.4	+	5077.67i	0.901018	+	0.360713i
$584$	1193.50	−	4064.69i	0.0845675	−	0.288010i
$585$	12749.3	+	7131.92i	0.901057	+	0.504049i
$586$	47.5055	−	73.9200i	0.00334887	−	0.00521094i
$587$	1058.56	+	2053.32i	0.0744317	+	0.144377i	0.923115	−	0.384524i	$-0.125634\pi$
$587$	1058.56	+	2053.32i	0.0744317	+	0.144377i	−0.848683	+	0.528901i	$0.822604\pi$
$588$	−89.4474	−	106.848i	−0.00627338	−	0.00749379i
$589$	3626.46	−	879.770i	0.253694	−	0.0615455i
$590$	−14011.6	+	11018.8i	−0.977708	+	0.768878i
$591$	7929.97	−	14759.8i	0.551938	−	1.02731i
$592$	1291.09	−	13520.9i	0.0896343	−	0.938693i
$593$	2741.65	+	9337.19i	0.189858	+	0.646598i	0.998314	+	0.0580410i	$0.0184854\pi$
$593$	2741.65	+	9337.19i	0.189858	+	0.646598i	−0.808456	+	0.588557i	$0.799696\pi$
$594$	6817.23	+	2756.50i	0.470899	+	0.190405i
$595$	−11005.8	−	1582.39i	−0.758308	−	0.109028i
$596$	14.2877	+	299.935i	0.000981957	+	0.0206138i
$597$	−4716.76	−	12388.8i	−0.323357	−	0.849310i
$598$	17406.0	−	13083.4i	1.19027	−	0.894681i
$599$	12493.7	−	7213.25i	0.852219	−	0.492029i	−0.00918003	−	0.999958i	$-0.502922\pi$
$599$	12493.7	−	7213.25i	0.852219	−	0.492029i	0.861399	+	0.507929i	$0.169589\pi$
$600$	7312.41	−	3190.24i	0.497546	−	0.217068i
$601$	−8096.36	−	6367.04i	−0.549513	−	0.432142i	0.304410	−	0.952541i	$-0.401541\pi$
$601$	−8096.36	−	6367.04i	−0.549513	−	0.432142i	−0.853923	+	0.520399i	$0.825783\pi$
$602$	12183.8	+	5564.15i	0.824874	+	0.376707i
$603$	543.995	−	15979.3i	0.0367383	−	1.07915i
$604$	132.821	+	290.837i	0.00894769	+	0.0195927i
$605$	7311.31	−	1409.14i	0.491317	−	0.0946937i
$606$	−3624.22	+	6037.70i	−0.242944	+	0.404728i
$607$	−3726.55	−	15361.0i	−0.249186	−	1.02716i	−0.949611	−	0.313432i	$-0.898521\pi$
$607$	−3726.55	−	15361.0i	−0.249186	−	1.02716i	0.700425	−	0.713726i	$-0.252994\pi$
$608$	687.301	+	132.466i	0.0458450	+	0.00883590i
$609$	2123.27	+	6490.02i	0.141280	+	0.431838i
$610$	−6712.28	+	3460.42i	−0.445528	+	0.229686i
$611$	31985.0	+	27715.1i	2.11780	+	1.83508i
$612$	537.121	+	371.602i	0.0354768	+	0.0245443i
$613$	−21970.7	+	3158.91i	−1.44761	+	0.208135i	−0.820881	−	0.571099i	$-0.806517\pi$
$613$	−21970.7	+	3158.91i	−1.44761	+	0.208135i	−0.626733	+	0.779234i	$0.715608\pi$
$614$	−3136.53	−	16273.9i	−0.206156	−	1.06964i
$615$	2779.24	+	10097.7i	0.182227	+	0.662081i
$616$	−4834.72	−	4609.89i	−0.316228	−	0.301523i
$617$	4073.99	−	389.019i	0.265823	−	0.0253830i	0.0387065	−	0.999251i	$-0.487676\pi$
$617$	4073.99	−	389.019i	0.265823	−	0.0253830i	0.227116	+	0.973868i	$0.427070\pi$
$618$	−6136.71	−	27316.4i	−0.399441	−	1.77804i
$619$	3940.74	−	187.721i	0.255883	−	0.0121892i	0.0807517	−	0.996734i	$-0.474268\pi$
$619$	3940.74	−	187.721i	0.255883	−	0.0121892i	0.175132	+	0.984545i	$0.443965\pi$
$620$	−120.697			−0.00781821
$621$	15363.1	+	1859.98i	0.992751	+	0.120190i
$622$	1994.15			0.128550
$623$	49.6269	−	2.36402i	0.00319143	−	0.000152026i
$624$	−5000.04	−	22256.7i	−0.320772	−	1.42786i
$625$	2792.85	−	266.685i	0.178743	−	0.0170679i
$626$	−16395.8	−	15633.4i	−1.04682	−	0.998141i
$627$	−1568.78	−	5699.79i	−0.0999217	−	0.363042i
$628$	−157.287	−	816.082i	−0.00999432	−	0.0518554i
$629$	−20515.6	+	2949.70i	−1.30049	+	0.186983i
$630$	−721.338	+	8817.01i	−0.0456172	+	0.557584i
$631$	1516.59	+	1314.14i	0.0956809	+	0.0829080i	0.701388	−	0.712780i	$-0.252564\pi$
$631$	1516.59	+	1314.14i	0.0956809	+	0.0829080i	−0.605707	+	0.795688i	$0.707110\pi$
$632$	10681.1	−	5506.49i	0.672264	−	0.346576i
$633$	4830.83	+	14766.0i	0.303330	+	0.927163i
$634$	16328.2	+	3147.00i	1.02283	+	0.197135i
$635$	3159.85	+	13025.1i	0.197472	+	0.813993i
$636$	496.888	−	827.781i	0.0309794	−	0.0516095i
$637$	7292.47	−	1405.51i	0.453592	−	0.0874227i
$638$	−1853.54	−	4058.68i	−0.115019	−	0.251857i
$639$	10632.8	+	6631.15i	0.658257	+	0.410523i
$640$	9537.65	+	4355.70i	0.589076	+	0.269022i
$641$	−18600.4	−	14627.5i	−1.14613	−	0.901329i	−0.149957	−	0.988693i	$-0.547913\pi$
$641$	−18600.4	−	14627.5i	−1.14613	−	0.901329i	−0.996177	+	0.0873635i	$0.972156\pi$
$642$	12770.4	−	5571.43i	0.785057	−	0.342503i
$643$	8101.55	−	4677.43i	0.496880	−	0.286874i	−0.230544	−	0.973062i	$-0.574051\pi$
$643$	8101.55	−	4677.43i	0.496880	−	0.286874i	0.727424	+	0.686188i	$0.240717\pi$
$644$	−383.236	−	208.287i	−0.0234497	−	0.0127448i
$645$	−4396.73	−	11548.2i	−0.268404	−	0.704975i
$646$	755.308	+	15855.9i	0.0460018	+	0.965698i
$647$	−1124.55	−	161.686i	−0.0683317	−	0.00982462i	0.108064	−	0.994144i	$-0.465535\pi$
$647$	−1124.55	−	161.686i	−0.0683317	−	0.00982462i	−0.176396	+	0.984319i	$0.556444\pi$
$648$	8669.41	−	14330.5i	0.525566	−	0.868759i
$649$	4456.58	+	15177.7i	0.269547	+	0.917994i
$650$	−1254.01	+	13132.6i	−0.0756711	+	0.792464i
$651$	−2345.35	+	4365.33i	−0.141200	+	0.262812i
$652$	−212.248	+	166.914i	−0.0127489	+	0.0100258i
$653$	−10038.3	+	2435.27i	−0.601576	+	0.145941i	−0.524970	−	0.851121i	$-0.675924\pi$
$653$	−10038.3	+	2435.27i	−0.601576	+	0.145941i	−0.0766060	+	0.997061i	$0.524408\pi$
$654$	11257.4	+	13447.4i	0.673088	+	0.804028i
$655$	−9400.44	−	18234.3i	−0.560772	−	1.08775i
$656$	8841.70	−	13758.0i	0.526235	−	0.818838i
$657$	67.5524	+	4977.98i	0.00401137	+	0.295600i
$658$	−7220.53	+	24590.9i	−0.427790	+	1.45692i
$659$	−26600.3	−	10649.1i	−1.57238	−	0.629486i	−0.588530	−	0.808475i	$-0.700293\pi$
$659$	−26600.3	−	10649.1i	−1.57238	−	0.629486i	−0.983851	+	0.178989i	$0.942717\pi$
$660$	5.84716	+	191.120i	0.000344849	+	0.0112717i
$661$	−21330.0	−	15189.0i	−1.25513	−	0.893775i	−0.257758	−	0.966210i	$-0.582984\pi$
$661$	−21330.0	−	15189.0i	−1.25513	−	0.893775i	−0.997373	+	0.0724349i	$0.976923\pi$
$662$	10312.1	−	10815.0i	0.605422	−	0.634949i
$663$	−31207.2	+	15422.1i	−1.82804	+	0.903385i
$664$	6572.48	−	8357.58i	0.384129	−	0.488460i
$665$	5983.04	−	3845.07i	0.348891	−	0.224218i
$666$	3340.27	+	16148.6i	0.194344	+	0.939559i
$667$	−5992.74	−	7229.07i	−0.347886	−	0.419656i
$668$	332.000	+	191.680i	0.0192297	+	0.0111023i
$669$	−9622.80	−	22056.6i	−0.556112	−	1.27467i
$670$	−11668.2	+	4671.23i	−0.672807	+	0.269351i
$671$	637.028	+	6671.26i	0.0366500	+	0.383817i
$672$	−740.311	+	562.067i	−0.0424972	+	0.0322652i
$673$	7174.66	+	685.097i	0.410940	+	0.0392400i	0.298479	−	0.954416i	$-0.403521\pi$
$673$	7174.66	+	685.097i	0.410940	+	0.0392400i	0.112461	+	0.993656i	$0.464127\pi$
$674$	−717.838	−	828.429i	−0.0410238	−	0.0473440i
$675$	−7106.79	+	6115.32i	−0.405245	+	0.348709i
$676$	−696.866	−	204.618i	−0.0396487	−	0.0116419i
$677$	−9489.49	−	27418.1i	−0.538716	−	1.55652i	−0.805399	−	0.592733i	$-0.798049\pi$
$677$	−9489.49	−	27418.1i	−0.538716	−	1.55652i	0.266683	−	0.963784i	$-0.414072\pi$
$678$	348.688	−	1656.94i	0.0197511	−	0.0938558i
$679$	−1.68655	+	35.4051i	−9.53226e−5	+	0.00200107i
$680$	3131.76	−	16249.1i	0.176614	−	0.916361i
$681$	11950.1	−	25031.1i	0.672438	−	1.40851i
$682$	1203.45	−	3006.06i	0.0675694	−	0.168780i
$683$	−10462.2	+	9065.56i	−0.586128	+	0.507883i	−0.896683	−	0.442673i	$-0.854030\pi$
$683$	−10462.2	+	9065.56i	−0.586128	+	0.507883i	0.310555	+	0.950555i	$0.399485\pi$
$684$	−415.299	+	45.3507i	−0.0232154	+	0.00253513i
$685$	882.940	−	259.255i	0.0492488	−	0.0144607i
$686$	11155.7	+	15666.0i	0.620885	+	0.871911i
$687$	−3745.81	−	4064.78i	−0.208023	−	0.225737i
$688$	−8841.68	+	17150.5i	−0.489950	+	0.950371i
$689$	25727.9	+	44562.1i	1.42258	+	2.46398i
$690$	−3529.24	−	11641.7i	−0.194719	−	0.642309i
$691$	2291.07	−	3968.24i	0.126131	−	0.218465i	−0.796044	−	0.605239i	$-0.793077\pi$
$691$	2291.07	−	3968.24i	0.126131	−	0.218465i	0.922174	+	0.386774i	$0.126411\pi$
$692$	232.299	+	361.464i	0.0127611	+	0.0198566i
$693$	7026.01	+	3502.31i	0.385131	+	0.191980i
$694$	1882.80	−	4122.77i	0.102983	−	0.225502i
$695$	236.446	−	974.644i	0.0129049	−	0.0531948i
$696$	−9798.43	+	2696.86i	−0.533633	+	0.146874i
$697$	−23583.6	−	8162.35i	−1.28162	−	0.443574i
$698$	6403.94	+	8143.28i	0.347268	+	0.441587i
$699$	−581.859	−	7426.96i	−0.0314849	−	0.401879i
$700$	249.726	−	86.4309i	0.0134839	−	0.00466683i
$701$	−12824.5	−	8241.80i	−0.690976	−	0.444063i	0.147457	−	0.989069i	$-0.452891\pi$
$701$	−12824.5	−	8241.80i	−0.690976	−	0.444063i	−0.838433	+	0.545005i	$0.816528\pi$
$702$	13765.0	+	24032.5i	0.740066	+	1.29209i
$703$	8681.75	−	10019.3i	0.465773	−	0.537531i
$704$	7188.28	−	6854.01i	0.384827	−	0.366932i
$705$	20674.6	−	11472.0i	1.10447	−	0.612849i
$706$	9603.51	−	27747.5i	0.511945	−	1.47917i
$707$	−4360.86	+	6123.98i	−0.231976	+	0.325765i
$708$	1109.02	−	140.238i	0.0588695	−	0.00744416i
$709$	−24366.6	+	17351.4i	−1.29070	+	0.919104i	−0.999297	−	0.0374964i	$-0.988062\pi$
$709$	−24366.6	+	17351.4i	−1.29070	+	0.919104i	−0.291404	+	0.956600i	$0.594122\pi$
$710$	1401.88	−	9750.29i	0.0741009	−	0.515383i
$711$	−10087.5	+	9883.21i	−0.532084	+	0.521307i
$712$			73.9427i			0.00389202i
$713$	795.706	−	6767.75i	0.0417944	−	0.355476i
$714$	−16345.7	−	13310.7i	−0.856756	−	0.697677i
$715$	−9057.94	−	4669.69i	−0.473773	−	0.244247i
$716$	31.4141	+	78.4687i	0.00163967	+	0.00409569i
$717$	2486.84	+	5032.22i	0.129530	+	0.262108i
$718$	11920.8	+	2891.96i	0.619612	+	0.150316i
$719$	−29179.9	+	13326.0i	−1.51353	+	0.691205i	−0.987260	−	0.159114i	$-0.949136\pi$
$719$	−29179.9	+	13326.0i	−1.51353	+	0.691205i	−0.526268	+	0.850319i	$0.676409\pi$
$720$	−12637.8	−	1642.34i	−0.654143	−	0.0850088i
$721$	−4253.78	−	29585.7i	−0.219721	−	1.52819i
$722$	6164.91	+	6465.57i	0.317776	+	0.333274i
$723$	−17465.3	+	14620.9i	−0.898396	+	0.752087i
$724$	−554.576	−	26.4177i	−0.0284678	−	0.00135609i
$725$	5682.51	+	270.691i	0.291094	+	0.0138665i
$726$	13259.3	+	4843.26i	0.677824	+	0.247590i
$727$	−8037.88	−	8429.88i	−0.410053	−	0.430051i	0.486027	−	0.873944i	$-0.338446\pi$
$727$	−8037.88	−	8429.88i	−0.410053	−	0.430051i	−0.896080	+	0.443893i	$0.853597\pi$
$728$	−3580.64	−	24903.9i	−0.182290	−	1.26786i
$729$	−4772.16	+	19095.7i	−0.242451	+	0.970164i
$730$	3559.84	−	1625.73i	0.180487	−	0.0824258i
$731$	28614.5	+	6941.81i	1.44781	+	0.351234i
$732$	472.597	+	30.5795i	0.0238630	+	0.00154406i
$733$	12478.8	+	31170.4i	0.628804	+	1.57068i	0.809488	+	0.587136i	$0.199745\pi$
$733$	12478.8	+	31170.4i	0.628804	+	1.57068i	−0.180684	+	0.983541i	$0.557831\pi$
$734$	−4553.29	−	2347.38i	−0.228971	−	0.118043i
$735$	660.262	−	4096.18i	0.0331349	−	0.205565i
$736$	663.106	−	1092.72i	0.0332098	−	0.0547257i
$737$			11153.5i			0.557457i
$738$	−5334.94	+	19125.4i	−0.266100	+	0.953953i
$739$	222.533	−	1547.75i	0.0110771	−	0.0770432i	−0.983533	−	0.180729i	$-0.942154\pi$
$739$	222.533	−	1547.75i	0.0110771	−	0.0770432i	0.994610	+	0.103685i	$0.0330635\pi$
$740$	−349.288	+	248.727i	−0.0173515	+	0.0123559i
$741$	8625.78	−	20526.9i	0.427633	−	1.01764i
$742$	−18074.6	+	25382.3i	−0.894259	+	1.25581i
$743$	2458.35	−	7102.93i	0.121384	−	0.350715i	−0.867896	−	0.496745i	$-0.834528\pi$
$743$	2458.35	−	7102.93i	0.121384	−	0.350715i	0.989280	+	0.146030i	$0.0466496\pi$
$744$	−6323.41	−	3795.72i	−0.311596	−	0.187040i
$745$	−6470.72	+	6169.82i	−0.318213	+	0.303416i
$746$	−16746.4	+	19326.4i	−0.821891	+	0.948513i
$747$	−4486.10	+	11661.9i	−0.219729	+	0.571201i
$748$	−383.295	−	246.329i	−0.0187362	−	0.0120410i
$749$	14056.6	−	4865.04i	0.685738	−	0.237336i
$750$	19091.7	+	9114.59i	0.929506	+	0.443757i
$751$	11377.6	+	14467.7i	0.552827	+	0.702976i	0.979503	−	0.201428i	$-0.0645582\pi$
$751$	11377.6	+	14467.7i	0.552827	+	0.702976i	−0.426677	+	0.904404i	$0.640316\pi$
$752$	−34890.1	−	12075.6i	−1.69190	−	0.585573i
$753$	12319.3	+	12153.3i	0.596204	+	0.588168i
$754$	3961.92	−	16331.3i	0.191359	−	0.788792i
$755$	−3954.76	+	8659.72i	−0.190634	+	0.417430i
$756$	323.358	−	450.797i	0.0155561	−	0.0216870i
$757$	17558.1	+	27320.9i	0.843010	+	1.31175i	0.948322	+	0.317310i	$0.102780\pi$
$757$	17558.1	+	27320.9i	0.843010	+	1.31175i	−0.105312	+	0.994439i	$0.533584\pi$
$758$	−19199.4	+	33254.4i	−0.919993	+	1.59348i
$759$	−10755.1	−	932.115i	−0.514342	−	0.0445766i
$760$	5292.38	+	9166.67i	0.252598	+	0.437513i
$761$	−12312.0	+	23882.0i	−0.586479	+	1.13761i	0.389760	+	0.920916i	$0.372558\pi$
$761$	−12312.0	+	23882.0i	−0.586479	+	1.13761i	−0.976239	+	0.216694i	$0.930472\pi$
$762$	−7572.56	+	24255.2i	−0.360006	+	1.15311i
$763$	10860.4	+	15251.3i	0.515299	+	0.723637i
$764$	−894.138	+	262.543i	−0.0423413	+	0.0124325i
$765$	2111.09	+	19332.3i	0.0997734	+	0.913675i
$766$	−1261.97	+	1093.50i	−0.0595259	+	0.0515795i
$767$	−22142.8	+	55310.0i	−1.04241	+	2.60382i
$768$	−1156.19	−	1683.55i	−0.0543235	−	0.0791014i
$769$	−4905.58	+	25452.6i	−0.230039	+	1.19355i	0.664751	+	0.747065i	$0.268538\pi$
$769$	−4905.58	+	25452.6i	−0.230039	+	1.19355i	−0.894789	+	0.446488i	$0.852674\pi$
$770$	293.639	−	6164.24i	0.0137429	−	0.288498i
$771$	24204.5	−	7918.75i	1.13062	−	0.369892i
$772$	149.186	+	431.044i	0.00695507	+	0.0200954i
$773$	6858.62	+	2013.87i	0.319130	+	0.0937050i	0.437374	−	0.899280i	$-0.355908\pi$
$773$	6858.62	+	2013.87i	0.319130	+	0.0937050i	−0.118244	+	0.992985i	$0.537727\pi$
$774$	4120.98	−	23061.3i	0.191377	−	1.07096i
$775$	2703.59	+	3120.10i	0.125311	+	0.144616i
$776$	−52.5138	−	5.01446i	−0.00242930	−	0.000231970i
$777$	2208.63	+	17466.2i	0.101975	+	0.806430i
$778$	−2722.08	−	28506.9i	−0.125438	−	1.31365i
$779$	14819.3	−	5932.76i	0.681588	−	0.272867i
$780$	−427.653	+	579.431i	−0.0196313	+	0.0265987i
$781$	−7570.44	−	4370.80i	−0.346853	−	0.200255i
$782$	27628.1	+	8771.98i	1.26340	+	0.401132i
$783$	10069.4	−	6422.32i	0.459582	−	0.293122i
$784$	−5450.34	+	3502.72i	−0.248284	+	0.159563i
$785$	15297.1	−	19451.8i	0.695510	−	0.884413i
$786$	2511.32	−	38811.7i	0.113964	−	1.76128i
$787$	−2565.33	+	2690.44i	−0.116193	+	0.121860i	−0.779261	−	0.626699i	$-0.784406\pi$
$787$	−2565.33	+	2690.44i	−0.116193	+	0.121860i	0.663068	+	0.748559i	$0.269254\pi$
$788$	672.827	+	479.118i	0.0304169	+	0.0216597i
$789$	−17404.0	+	10770.9i	−0.785294	+	0.486000i
$790$	10306.1	+	4125.94i	0.464145	+	0.185816i
$791$	509.286	−	1734.47i	0.0228927	−	0.0779654i
$792$	−5704.09	+	10196.8i	−0.255917	+	0.457486i
$793$	−13646.0	+	21233.6i	−0.611078	+	0.950855i
$794$	16991.3	+	32958.4i	0.759442	+	1.47311i
$795$	28315.8	−	4959.31i	1.26322	−	0.221244i
$796$	635.076	−	154.068i	0.0282785	−	0.00686028i
$797$	−6610.00	+	5198.16i	−0.293774	+	0.231027i	−0.754157	−	0.656694i	$-0.771954\pi$
$797$	−6610.00	+	5198.16i	−0.293774	+	0.231027i	0.460383	+	0.887720i	$0.347712\pi$
$798$	13477.0	−	412.319i	0.597847	−	0.0182906i
$799$	−5355.50	+	56085.3i	−0.237126	+	2.48330i
$800$	218.170	+	743.018i	0.00964183	+	0.0328370i
$801$	−25.6107	−	83.0369i	−0.00112972	−	0.00366288i
$802$	−20530.0	−	2951.77i	−0.903914	−	0.129963i
$803$	−165.248	−	3468.99i	−0.00726213	−	0.152451i
$804$	778.149	+	125.429i	0.0341333	+	0.00550193i
$805$	−2785.57	−	12685.1i	−0.121961	−	0.555391i
$806$	10561.5	−	6097.71i	0.461556	−	0.266480i
$807$	−5299.39	−	3911.25i	−0.231162	−	0.170610i
$808$	−8795.08	−	6916.53i	−0.382933	−	0.301142i
$809$	−31325.0	−	14305.7i	−1.36135	−	0.621706i	−0.405101	−	0.914272i	$-0.632764\pi$
$809$	−31325.0	−	14305.7i	−1.36135	−	0.621706i	−0.956245	+	0.292566i	$0.905491\pi$
$810$	15249.7	−	2616.75i	0.661507	−	0.113510i
$811$	8713.82	+	19080.6i	0.377292	+	0.826153i	0.999077	+	0.0429653i	$0.0136805\pi$
$811$	8713.82	+	19080.6i	0.377292	+	0.826153i	−0.621785	+	0.783188i	$0.713592\pi$
$812$	−330.543	+	63.7070i	−0.0142855	+	0.00275330i
$813$	−6911.81	−	12456.4i	−0.298164	−	0.537348i
$814$	−2712.08	−	11179.4i	−0.116779	−	0.481372i
$815$	−7894.51	−	1521.54i	−0.339304	−	0.0653955i
$816$	20273.9	−	22608.3i	0.869765	−	0.969914i
$817$	−16740.1	+	8630.10i	−0.716842	+	0.369558i
$818$	−29514.7	−	25574.6i	−1.26156	−	1.09315i
$819$	12646.7	+	26726.6i	0.539575	+	1.14030i
$820$	−511.044	+	73.4771i	−0.0217640	+	0.00312918i
$821$	−5298.24	−	27489.9i	−0.225225	−	1.16858i	−0.901783	−	0.432189i	$-0.857741\pi$
$821$	−5298.24	−	27489.9i	−0.225225	−	1.16858i	0.676558	−	0.736389i	$-0.263471\pi$
$822$	1688.16	+	440.088i	0.0716320	+	0.0186738i
$823$	−13702.4	−	13065.2i	−0.580358	−	0.553370i	0.342003	−	0.939699i	$-0.388895\pi$
$823$	−13702.4	−	13065.2i	−0.580358	−	0.553370i	−0.922361	+	0.386329i	$0.873743\pi$
$824$	44283.3	−	4228.54i	1.87219	−	0.178772i
$825$	4809.63	−	4432.21i	0.202969	−	0.187042i
$826$	−36037.6	+	1716.68i	−1.51805	+	0.0723135i
$827$	−19932.1			−0.838098			−0.419049	−	0.907964i	$-0.637636\pi$
$827$	−19932.1			−0.838098			−0.419049	+	0.907964i	$0.637636\pi$
$828$	−185.980	+	739.869i	−0.00780584	+	0.0310534i
$829$	22699.5			0.951008			0.475504	−	0.879714i	$-0.342266\pi$
$829$	22699.5			0.951008			0.475504	+	0.879714i	$0.342266\pi$
$830$	9811.07	−	467.359i	0.410298	−	0.0195449i
$831$	26364.6	+	8231.11i	1.10057	+	0.343603i
$832$	37238.6	−	3555.86i	1.55170	−	0.148170i
$833$	7155.26	+	6822.53i	0.297617	+	0.283777i
$834$	1335.32	−	1353.56i	0.0554416	−	0.0561991i
$835$	2160.23	+	11208.3i	0.0895303	+	0.464527i
$836$	288.465	−	41.4751i	0.0119340	−	0.00171584i
$837$	8415.80	+	2072.38i	0.347542	+	0.0855819i
$838$	−4836.87	−	4191.17i	−0.199388	−	0.172770i
$839$	22863.3	−	11786.8i	0.940796	−	0.485014i	0.0816029	−	0.996665i	$-0.473996\pi$
$839$	22863.3	−	11786.8i	0.940796	−	0.485014i	0.859194	+	0.511651i	$0.170966\pi$
$840$	−13754.9	−	2894.59i	−0.564985	−	0.118896i
$841$	16832.4	+	3244.17i	0.690162	+	0.133018i
$842$	−132.982	−	548.159i	−0.00544282	−	0.0224356i
$843$	−15007.8	−	255.387i	−0.613165	−	0.0104341i
$844$	−752.045	+	144.945i	−0.0306712	+	0.00591138i
$845$	−8983.46	−	19671.0i	−0.365728	−	0.800833i
$846$	44799.6	+	1525.14i	1.82062	+	0.0619804i
$847$	13708.6	+	6260.51i	0.556120	+	0.253971i
$848$	−35284.9	−	27748.3i	−1.42888	−	1.12368i
$849$	−1192.58	+	10582.9i	−0.0482086	+	0.427804i
$850$	−15209.1	+	8780.96i	−0.613726	+	0.354335i
$851$	−11644.0	−	21225.2i	−0.469038	−	0.854983i
$852$	−390.072	+	479.014i	−0.0156850	+	0.0192615i
$853$	357.223	+	7499.03i	0.0143389	+	0.301010i	0.994633	+	0.103466i	$0.0329934\pi$
$853$	357.223	+	7499.03i	0.0143389	+	0.301010i	−0.980294	+	0.197544i	$0.936704\pi$
$854$	−15129.3	−	2175.26i	−0.606221	−	0.0871615i
$855$	−9118.24	−	8461.01i	−0.364722	−	0.338433i
$856$	6236.94	+	21241.1i	0.249035	+	0.848137i
$857$	1135.26	−	11889.0i	0.0452507	−	0.473887i	−0.944237	−	0.329268i	$-0.893198\pi$
$857$	1135.26	−	11889.0i	0.0452507	−	0.473887i	0.989487	−	0.144619i	$-0.0461957\pi$
$858$	−10167.2	−	16428.5i	−0.404549	−	0.653683i
$859$	32827.2	−	25815.6i	1.30390	−	1.02540i	0.306607	−	0.951836i	$-0.400806\pi$
$859$	32827.2	−	25815.6i	1.30390	−	1.02540i	0.997291	−	0.0735604i	$-0.0234362\pi$
$860$	591.986	−	143.614i	0.0234727	−	0.00569442i
$861$	−7272.98	+	19911.2i	−0.287877	+	0.788119i
$862$	−8560.31	−	16604.7i	−0.338243	−	0.656099i
$863$	608.495	−	946.837i	0.0240017	−	0.0373473i	−0.829045	−	0.559181i	$-0.811116\pi$
$863$	608.495	−	946.837i	0.0240017	−	0.0373473i	0.853047	+	0.521834i	$0.174752\pi$
$864$	1274.43	+	1009.35i	0.0501817	+	0.0397440i
$865$	−3604.37	+	12275.3i	−0.141679	+	0.482514i
$866$	−7934.25	−	3176.40i	−0.311336	−	0.124640i
$867$	−18332.8	−	9849.58i	−0.718124	−	0.385824i
$868$	−198.994	−	141.703i	−0.00778143	−	0.00554113i
$869$	6798.34	−	7129.89i	0.265383	−	0.278326i
$870$	−7810.54	−	5209.41i	−0.304370	−	0.203006i
$871$	−25967.6	+	33020.5i	−1.01019	+	1.28457i
$872$	−23441.7	+	15065.1i	−0.910362	+	0.585054i
$873$	60.7092	−	12.5574i	0.00235360	−	0.000486832i
$874$	−17029.8	+	7332.20i	−0.659087	+	0.283770i
$875$	19560.0	+	11293.0i	0.755715	+	0.436312i
$876$	−243.879	−	27.4824i	−0.00940630	−	0.00105998i
$877$	29194.3	−	11687.6i	1.12408	−	0.450015i	0.266229	−	0.963910i	$-0.414222\pi$
$877$	29194.3	−	11687.6i	1.12408	−	0.450015i	0.857853	+	0.513895i	$0.171798\pi$
$878$	4638.75	+	48579.2i	0.178303	+	1.86727i
$879$	−151.261	−	63.5628i	−0.00580422	−	0.00243905i
$880$	8849.91	+	845.064i	0.339012	+	0.0323717i
$881$	−16887.6	−	19489.3i	−0.645807	−	0.745301i	0.334583	−	0.942366i	$-0.391404\pi$
$881$	−16887.6	−	19489.3i	−0.645807	−	0.745301i	−0.980390	+	0.197065i	$0.936859\pi$
$882$	5069.97	−	6014.05i	0.193554	−	0.229596i
$883$	33129.6	+	9727.72i	1.26263	+	0.370740i	0.843471	−	0.537175i	$-0.180508\pi$
$883$	33129.6	+	9727.72i	1.26263	+	0.370740i	0.419155	+	0.907915i	$0.362327\pi$
$884$	−561.258	−	1621.65i	−0.0213543	−	0.0616991i
$885$	24780.1	+	22221.4i	0.941212	+	0.844027i
$886$	−130.743	+	2744.63i	−0.00495756	+	0.104072i
$887$	6034.60	−	31310.5i	0.228435	−	1.18524i	−0.668718	−	0.743516i	$-0.733157\pi$
$887$	6034.60	−	31310.5i	0.228435	−	1.18524i	0.897153	−	0.441719i	$-0.145631\pi$
$888$	−26121.6	+	2046.48i	−0.987145	+	0.0773371i
$889$	−10082.3	+	25184.4i	−0.380371	+	0.950121i
$890$	−51.6242	+	44.7326i	−0.00194432	+	0.00168476i
$891$	2873.86	−	13426.6i	0.108056	−	0.504835i
$892$	1138.25	−	334.220i	0.0427258	−	0.0125454i
$893$	−20903.6	−	29355.0i	−0.783329	−	1.10003i
$894$	−16538.1	+	3715.33i	−0.618698	+	0.138992i
$895$	−1153.22	+	2236.93i	−0.0430701	+	0.0835444i
$896$	10611.0	+	18378.9i	0.395636	+	0.685262i
$897$	−29670.7	−	27799.5i	−1.10443	−	1.03478i
$898$	−4309.16	+	7463.68i	−0.160132	+	0.277356i
$899$	−2843.26	−	4424.21i	−0.105482	−	0.164133i
$900$	−255.134	−	385.396i	−0.00944941	−	0.0142739i
$901$	−28455.7	+	62309.2i	−1.05216	+	2.30391i
$902$	3265.52	−	13460.7i	0.120543	−	0.496886i
$903$	6309.11	−	24201.5i	0.232507	−	0.891889i
$904$	2542.40	+	879.932i	0.0935386	+	0.0323740i
$905$	−10219.0	−	12994.5i	−0.375348	−	0.477294i
$906$	−14877.9	+	10217.5i	−0.545567	+	0.374672i
$907$	7999.38	−	2768.61i	0.292850	−	0.101356i	−0.176693	−	0.984266i	$-0.556540\pi$
$907$	7999.38	−	2768.61i	0.292850	−	0.101356i	0.469543	+	0.882910i	$0.344419\pi$
$908$	1150.31	+	739.258i	0.0420422	+	0.0270189i
$909$	12272.4	+	4720.93i	0.447799	+	0.172259i
$910$	15220.9	−	17565.8i	0.554469	−	0.639892i
$911$	4375.94	−	4172.45i	0.159145	−	0.151745i	−0.606323	−	0.795219i	$-0.707356\pi$
$911$	4375.94	−	4172.45i	0.159145	−	0.151745i	0.765468	+	0.643474i	$0.222507\pi$
$912$	−330.486	+	19421.1i	−0.0119994	+	0.705148i
$913$	2850.86	−	8237.03i	0.103340	−	0.298583i
$914$	22767.6	−	31972.6i	0.823944	−	1.15707i
$915$	8526.85	+	11230.9i	0.308075	+	0.405773i
$916$	221.965	−	158.060i	0.00800647	−	0.00570138i
$917$	5909.22	−	41099.6i	0.212802	−	1.48007i
$918$	−15431.4	+	33484.2i	−0.554805	+	1.20386i
$919$			4148.46i			0.148906i	0.997225	+	0.0744532i	$0.0237211\pi$
$919$			4148.46i			0.148906i	−0.997225	+	0.0744532i	$0.976279\pi$
$920$	19054.9	−	3242.73i	0.682849	−	0.116206i
$921$	−28921.5	+	11011.2i	−1.03474	+	0.393955i
$922$	8864.63	+	4570.03i	0.316639	+	0.163239i
$923$	−12236.5	−	30565.4i	−0.436371	−	1.09000i
$924$	−214.742	+	321.966i	−0.00764556	+	0.0114631i
$925$	14253.8	+	3457.93i	0.506661	+	0.122915i
$926$	43471.1	−	19852.6i	1.54271	−	0.704532i
$927$	−48265.0	+	20086.5i	−1.71007	+	0.711680i
$928$	−140.386	−	976.408i	−0.00496596	−	0.0345390i
$929$	18188.9	+	19076.0i	0.642368	+	0.673696i	0.961750	−	0.273930i	$-0.0883237\pi$
$929$	18188.9	+	19076.0i	0.642368	+	0.673696i	−0.319382	+	0.947626i	$0.603475\pi$
$930$	−1175.39	−	6711.05i	−0.0414437	−	0.236628i
$931$	−6316.62	−	300.898i	−0.222362	−	0.0105924i
$932$	366.834	+	17.4744i	0.0128927	+	0.000614157i
$933$	−642.380	−	3667.75i	−0.0225408	−	0.128700i
$934$	4802.36	+	5036.57i	0.168242	+	0.176447i
$935$	−1930.68	−	13428.2i	−0.0675294	−	0.469677i
$936$	−40627.4	+	16907.9i	−1.41875	+	0.590441i
$937$	27294.1	−	12464.8i	0.951612	−	0.434587i	0.121754	−	0.992560i	$-0.461148\pi$
$937$	27294.1	−	12464.8i	0.951612	−	0.434587i	0.829859	+	0.557974i	$0.188421\pi$
$938$	−24721.6	−	5997.41i	−0.860544	−	0.208766i
$939$	−23472.2	+	35192.2i	−0.815748	+	1.22306i
$940$	433.205	+	1082.09i	0.0150315	+	0.0375468i
$941$	−4200.54	−	2165.53i	−0.145519	−	0.0750204i	0.383929	−	0.923363i	$-0.374571\pi$
$941$	−4200.54	−	2165.53i	−0.145519	−	0.0750204i	−0.529448	+	0.848342i	$0.677601\pi$
$942$	43844.6	−	16692.9i	1.51649	−	0.577372i
$943$	−750.920	−	29139.9i	−0.0259314	−	1.00628i
$944$		−	51973.9i		−	1.79196i
$945$	16449.1	−	1513.52i	0.566233	−	0.0521004i
$946$	−2325.75	+	16175.9i	−0.0799329	+	0.555946i
$947$	22910.1	−	16314.2i	0.786145	−	0.559812i	−0.114981	−	0.993368i	$-0.536681\pi$
$947$	22910.1	−	16314.2i	0.786145	−	0.559812i	0.901127	+	0.433556i	$0.142741\pi$
$948$	−420.979	−	554.480i	−0.0144227	−	0.0189965i
$949$	7587.25	−	10654.8i	0.259529	−	0.364457i
$950$	3674.02	−	10615.4i	0.125475	−	0.362535i
$951$	528.298	−	31045.5i	0.0180139	−	1.05859i
$952$	24240.5	−	23113.3i	0.825251	−	0.786876i
$953$	−23418.5	+	27026.4i	−0.796012	+	0.918647i	−0.998155	−	0.0607091i	$-0.980664\pi$
$953$	−23418.5	+	27026.4i	−0.796012	+	0.918647i	0.202144	+	0.979356i	$0.435209\pi$
$954$	50865.8	+	19567.0i	1.72625	+	0.664052i
$955$	−23342.3	−	15001.2i	−0.790931	−	0.508301i
$956$	−261.494	+	90.5039i	−0.00884657	+	0.00306183i
$957$	−6867.87	+	4716.57i	−0.231982	+	0.159315i
$958$	−29964.1	−	38102.5i	−1.01054	−	1.28501i
$959$	1760.09	+	609.172i	0.0592661	+	0.0205122i
$960$	5271.90	−	20222.8i	0.177240	−	0.679885i
$961$	−6123.72	+	25242.3i	−0.205556	+	0.847313i
$962$	17998.5	−	39411.2i	0.603217	−	1.32086i
$963$	−14361.0	−	21693.3i	−0.480559	−	0.725915i
$964$	−607.063	−	944.608i	−0.0202823	−	0.0315599i
$965$	−6790.68	+	11761.8i	−0.226528	+	0.392358i
$966$	7849.18	−	23337.3i	0.261432	−	0.777293i
$967$	−3700.57	−	6409.57i	−0.123063	−	0.213152i	0.797911	−	0.602775i	$-0.205938\pi$
$967$	−3700.57	−	6409.57i	−0.123063	−	0.213152i	−0.920974	+	0.389623i	$0.872605\pi$
$968$	−10277.7	+	19935.9i	−0.341257	+	0.661945i
$969$	28919.7	−	6496.90i	0.958757	−	0.215388i
$970$	−28.2680	−	39.6968i	−0.000935701	−	0.00131401i
$971$	−2650.75	+	778.332i	−0.0876074	+	0.0257238i	−0.325242	−	0.945631i	$-0.605446\pi$
$971$	−2650.75	+	778.332i	−0.0876074	+	0.0257238i	0.237635	+	0.971354i	$0.423628\pi$
$972$	−904.415	−	351.492i	−0.0298448	−	0.0115989i
$973$	1534.10	−	1329.31i	0.0505458	−	0.0437982i
$974$	−2126.67	+	5312.16i	−0.0699618	+	0.174756i
$975$	24558.1	−	1923.99i	0.806656	−	0.0631968i
$976$	4167.14	−	21621.2i	0.136667	−	0.709095i
$977$	262.654	−	5513.78i	0.00860086	−	0.180554i	−0.990479	−	0.137664i	$-0.956040\pi$
$977$	262.654	−	5513.78i	0.00860086	−	0.180554i	0.999080	−	0.0428900i	$-0.0136565\pi$
$978$	−11347.8	−	10176.1i	−0.371025	−	0.332715i
$979$	19.8264	+	57.2845i	0.000647246	+	0.00187009i
$980$	196.251	+	57.6246i	0.00639696	+	0.00187832i
$981$	21106.8	−	25037.1i	0.686941	−	0.814856i
$982$	2896.78	+	3343.06i	0.0941342	+	0.108637i
$983$	21425.7	+	2045.91i	0.695192	+	0.0663828i	0.436669	−	0.899622i	$-0.356158\pi$
$983$	21425.7	+	2045.91i	0.695192	+	0.0663828i	0.258523	+	0.966005i	$0.416764\pi$
$984$	−29084.9	−	12222.0i	−0.942268	−	0.395959i
$985$	2337.79	+	24482.5i	0.0756225	+	0.791955i
$986$	20768.7	−	8314.54i	0.670802	−	0.268549i
$987$	47554.9	+	5358.89i	1.53363	+	0.172822i
$988$	950.575	+	548.815i	0.0306091	+	0.0176722i
$989$	4150.06	+	34140.9i	0.133432	+	1.09769i
$990$	−10569.8	+	2186.32i	−0.339325	+	0.0701877i
$991$	−22175.1	+	14251.1i	−0.710812	+	0.456811i	−0.845430	−	0.534086i	$-0.820656\pi$
$991$	−22175.1	+	14251.1i	−0.710812	+	0.456811i	0.134618	+	0.990898i	$0.457019\pi$
$992$	442.521	−	562.711i	0.0141634	−	0.0180102i
$993$	−23213.4	−	15482.7i	−0.741848	−	0.494792i
$994$	13758.5	−	14429.5i	0.439028	−	0.460440i
$995$	15850.0	+	11286.7i	0.505004	+	0.359611i
$996$	−542.613	−	291.527i	−0.0172624	−	0.00927450i
$997$	−1258.14	−	503.682i	−0.0399655	−	0.0159998i	0.351594	−	0.936153i	$-0.385640\pi$
$997$	−1258.14	−	503.682i	−0.0399655	−	0.0159998i	−0.391559	+	0.920153i	$0.628064\pi$
$998$	−15645.5	+	53283.7i	−0.496242	+	1.69005i
$999$	28625.5	−	11345.6i	0.906577	−	0.359319i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.11.20	✓	1400
9.5	odd	6	inner	207.4.o.a.149.20	yes	1400
23.21	odd	22	inner	207.4.o.a.182.20	yes	1400
207.113	even	66	inner	207.4.o.a.113.20	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.20	✓	1400	1.1	even	1	trivial
207.4.o.a.113.20	yes	1400	207.113	even	66	inner
207.4.o.a.149.20	yes	1400	9.5	odd	6	inner
207.4.o.a.182.20	yes	1400	23.21	odd	22	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	207.4.o.a.11.20

Level	$207$
Weight	$4$
Character	207.11
Analytic conductor	$12.213$
Analytic rank	$0$
Dimension	$1400$
Inner twists	$4$