LMFDB - Embedded newform 325.3.bm.a.6.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(6,325)] 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("325.6"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([24, 25])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.bm (of order $60$, degree $16$, 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:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$1088$
Relative dimension:	$68$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			6.16
Character	$\chi$	$=$	325.6
Dual form			325.3.bm.a.271.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96882 + 1.27857i) q^{2} +(-0.268630 - 2.55584i) q^{3} +(0.614567 - 1.38034i) q^{4} +(4.97524 + 0.496976i) q^{5} +(3.79670 + 4.68853i) q^{6} +(2.43747 - 9.09675i) q^{7} +(-0.914064 - 5.77117i) q^{8} +(2.34315 - 0.498053i) q^{9} +(-10.4308 + 5.38271i) q^{10} +(-2.24334 - 3.45444i) q^{11} +(-3.69303 - 1.19994i) q^{12} +(-12.8424 - 2.01836i) q^{13} +(6.83186 + 21.0263i) q^{14} +(-0.0663071 - 12.8494i) q^{15} +(13.2226 + 14.6852i) q^{16} +(-13.4803 - 1.41683i) q^{17} +(-3.97645 + 3.97645i) q^{18} +(9.29776 + 11.4818i) q^{19} +(3.74361 - 6.56210i) q^{20} +(-23.9047 - 3.78613i) q^{21} +(8.83346 + 3.93291i) q^{22} +(-4.24098 + 19.9523i) q^{23} +(-14.5047 + 3.88651i) q^{24} +(24.5060 + 4.94515i) q^{25} +(27.8649 - 12.4460i) q^{26} +(-9.04973 - 27.8522i) q^{27} +(-11.0586 - 8.95510i) q^{28} +(-4.25616 - 40.4947i) q^{29} +(16.5594 + 25.2134i) q^{30} +(-29.5674 + 4.68301i) q^{31} +(-22.2328 - 5.95725i) q^{32} +(-8.22639 + 6.66160i) q^{33} +(28.3517 - 14.4459i) q^{34} +(16.6479 - 44.0472i) q^{35} +(0.752543 - 3.54044i) q^{36} +(3.80887 - 72.6775i) q^{37} +(-32.9858 - 10.7177i) q^{38} +(-1.70877 + 33.3653i) q^{39} +(-1.67956 - 29.1672i) q^{40} +(-64.5681 - 3.38387i) q^{41} +(51.9047 - 23.1095i) q^{42} +(19.8434 - 11.4566i) q^{43} +(-6.14699 + 0.973588i) q^{44} +(11.9053 - 1.31344i) q^{45} +(-17.1605 - 44.7047i) q^{46} +(7.08608 + 1.12233i) q^{47} +(33.9810 - 37.7398i) q^{48} +(-34.3744 - 19.8461i) q^{49} +(-54.5706 + 21.5965i) q^{50} +34.8341i q^{51} +(-10.6785 + 16.4864i) q^{52} +(-6.24347 + 4.53615i) q^{53} +(53.4281 + 43.2653i) q^{54} +(-9.44439 - 18.3016i) q^{55} +(-54.7269 - 5.75203i) q^{56} +(26.8480 - 26.8480i) q^{57} +(60.1547 + 74.2848i) q^{58} +(69.5502 + 45.1664i) q^{59} +(-17.7774 - 7.80532i) q^{60} +(44.4561 - 49.3735i) q^{61} +(52.2252 - 47.0238i) q^{62} +(1.18070 - 22.5291i) q^{63} +(-23.7857 + 7.72845i) q^{64} +(-62.8908 - 16.4242i) q^{65} +(7.67897 - 23.6334i) q^{66} +(-8.92958 + 23.2623i) q^{67} +(-10.2402 + 17.7366i) q^{68} +(52.1341 + 5.47951i) q^{69} +(23.5406 + 108.006i) q^{70} +(45.4459 - 17.4451i) q^{71} +(-5.01614 - 13.0675i) q^{72} +(50.8118 - 99.7238i) q^{73} +(85.4240 + 147.959i) q^{74} +(6.05596 - 63.9620i) q^{75} +(21.5629 - 5.77775i) q^{76} +(-36.8923 + 11.9870i) q^{77} +(-39.2954 - 67.8749i) q^{78} +(-80.0466 + 58.1573i) q^{79} +(58.4874 + 79.6336i) q^{80} +(-49.0593 + 21.8426i) q^{81} +(131.449 - 75.8922i) q^{82} +(45.8804 - 7.26674i) q^{83} +(-19.9172 + 30.6697i) q^{84} +(-66.3634 - 13.7484i) q^{85} +(-24.4200 + 47.9270i) q^{86} +(-102.355 + 21.7562i) q^{87} +(-17.8856 + 16.1043i) q^{88} +(52.2796 + 80.5035i) q^{89} +(-21.7600 + 17.8076i) q^{90} +(-49.6634 + 111.904i) q^{91} +(24.9345 + 18.1160i) q^{92} +(19.9117 + 74.3116i) q^{93} +(-15.3862 + 6.85036i) q^{94} +(40.5524 + 61.7454i) q^{95} +(-9.25342 + 58.4238i) q^{96} +(104.384 - 40.0691i) q^{97} +(93.0515 - 4.87662i) q^{98} +(-6.97699 - 6.97699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1088 q - 16 q^{2} - 6 q^{3} - 18 q^{4} - 6 q^{5} - 28 q^{6} - 32 q^{7} - 44 q^{8} + 378 q^{9} - 54 q^{10} - 12 q^{11} + 44 q^{13} - 24 q^{14} + 54 q^{15} - 382 q^{16} - 66 q^{17} - 500 q^{18} + 48 q^{19}+ \cdots - 792 q^{99}+O(q^{100}) $ 1088 * q - 16 * q^2 - 6 * q^3 - 18 * q^4 - 6 * q^5 - 28 * q^6 - 32 * q^7 - 44 * q^8 + 378 * q^9 - 54 * q^10 - 12 * q^11 + 44 * q^13 - 24 * q^14 + 54 * q^15 - 382 * q^16 - 66 * q^17 - 500 * q^18 + 48 * q^19 - 66 * q^20 + 42 * q^21 + 196 * q^22 - 18 * q^23 - 36 * q^24 - 12 * q^26 - 76 * q^28 + 94 * q^29 - 216 * q^30 - 12 * q^31 - 152 * q^32 - 222 * q^33 + 64 * q^34 - 82 * q^35 - 126 * q^36 - 210 * q^37 - 288 * q^39 - 432 * q^40 - 462 * q^41 + 222 * q^42 - 48 * q^43 + 36 * q^44 - 458 * q^45 - 396 * q^46 - 186 * q^47 - 334 * q^48 - 48 * q^49 + 106 * q^50 - 122 * q^52 + 12 * q^53 - 940 * q^54 + 130 * q^55 + 714 * q^56 - 252 * q^57 - 312 * q^58 - 132 * q^59 + 132 * q^60 + 294 * q^61 + 198 * q^62 + 1192 * q^63 + 338 * q^65 + 384 * q^66 - 236 * q^67 - 236 * q^68 - 648 * q^69 - 1114 * q^70 - 92 * q^71 + 546 * q^72 + 928 * q^73 + 164 * q^74 + 132 * q^75 + 620 * q^76 - 1742 * q^78 + 216 * q^79 - 540 * q^80 + 806 * q^81 + 3132 * q^82 + 874 * q^83 + 496 * q^84 + 514 * q^85 - 276 * q^86 + 74 * q^87 - 2394 * q^88 - 672 * q^89 + 308 * q^91 + 1960 * q^92 + 1008 * q^93 + 474 * q^94 + 2328 * q^95 - 1626 * q^96 + 632 * q^97 + 84 * q^98 - 792 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−1.96882	+	1.27857i	−0.984409	+	0.639283i	−0.933182	−	0.359405i	$-0.882980\pi$
$2$	−1.96882	+	1.27857i	−0.984409	+	0.639283i	−0.0512269	+	0.998687i	$0.516313\pi$
$3$	−0.268630	−	2.55584i	−0.0895433	−	0.851948i	−0.943448	−	0.331519i	$-0.892439\pi$
$3$	−0.268630	−	2.55584i	−0.0895433	−	0.851948i	0.853905	−	0.520429i	$-0.174228\pi$
$4$	0.614567	−	1.38034i	0.153642	−	0.345085i
$5$	4.97524	+	0.496976i	0.995048	+	0.0993951i
$5$	4.97524	+	0.496976i	0.995048	+	0.0993951i
$6$	3.79670	+	4.68853i	0.632783	+	0.781421i
$7$	2.43747	−	9.09675i	0.348210	−	1.29954i	−0.540608	−	0.841275i	$-0.681806\pi$
$7$	2.43747	−	9.09675i	0.348210	−	1.29954i	0.888817	−	0.458261i	$-0.151528\pi$
$8$	−0.914064	−	5.77117i	−0.114258	−	0.721396i
$9$	2.34315	−	0.498053i	0.260350	−	0.0553392i
$10$	−10.4308	+	5.38271i	−1.04308	+	0.538271i
$11$	−2.24334	−	3.45444i	−0.203940	−	0.314040i	0.721870	−	0.692028i	$-0.243283\pi$
$11$	−2.24334	−	3.45444i	−0.203940	−	0.314040i	−0.925810	+	0.377988i	$0.876616\pi$
$12$	−3.69303	−	1.19994i	−0.307752	−	0.0999947i
$13$	−12.8424	−	2.01836i	−0.987874	−	0.155259i
$13$	−12.8424	−	2.01836i	−0.987874	−	0.155259i
$14$	6.83186	+	21.0263i	0.487990	+	1.50188i
$15$	−0.0663071	−	12.8494i	−0.00442047	−	0.856629i
$16$	13.2226	+	14.6852i	0.826412	+	0.917823i
$17$	−13.4803	−	1.41683i	−0.792957	−	0.0833431i	−0.300616	−	0.953745i	$-0.597192\pi$
$17$	−13.4803	−	1.41683i	−0.792957	−	0.0833431i	−0.492341	+	0.870402i	$0.663859\pi$
$18$	−3.97645	+	3.97645i	−0.220914	+	0.220914i
$19$	9.29776	+	11.4818i	0.489356	+	0.604304i	0.960681	−	0.277655i	$-0.0895574\pi$
$19$	9.29776	+	11.4818i	0.489356	+	0.604304i	−0.471325	+	0.881960i	$0.656224\pi$
$20$	3.74361	−	6.56210i	0.187181	−	0.328105i
$21$	−23.9047	−	3.78613i	−1.13832	−	0.180292i
$22$	8.83346	+	3.93291i	0.401521	+	0.178769i
$23$	−4.24098	+	19.9523i	−0.184391	+	0.867489i	0.784525	+	0.620097i	$0.212907\pi$
$23$	−4.24098	+	19.9523i	−0.184391	+	0.867489i	−0.968915	+	0.247392i	$0.920426\pi$
$24$	−14.5047	+	3.88651i	−0.604361	+	0.161938i
$25$	24.5060	+	4.94515i	0.980241	+	0.197806i
$26$	27.8649	−	12.4460i	1.07173	−	0.478693i
$27$	−9.04973	−	27.8522i	−0.335175	−	1.03156i
$28$	−11.0586	−	8.95510i	−0.394951	−	0.319825i
$29$	−4.25616	−	40.4947i	−0.146764	−	1.39637i	−0.781628	−	0.623744i	$-0.785611\pi$
$29$	−4.25616	−	40.4947i	−0.146764	−	1.39637i	0.634864	−	0.772624i	$-0.281056\pi$
$30$	16.5594	+	25.2134i	0.551980	+	0.840447i
$31$	−29.5674	+	4.68301i	−0.953787	+	0.151065i	−0.613884	−	0.789396i	$-0.710394\pi$
$31$	−29.5674	+	4.68301i	−0.953787	+	0.151065i	−0.339902	+	0.940461i	$0.610394\pi$
$32$	−22.2328	−	5.95725i	−0.694774	−	0.186164i
$33$	−8.22639	+	6.66160i	−0.249285	+	0.201867i
$34$	28.3517	−	14.4459i	0.833874	−	0.424880i
$35$	16.6479	−	44.0472i	0.475653	−	1.25849i
$36$	0.752543	−	3.54044i	0.0209040	−	0.0983455i
$37$	3.80887	−	72.6775i	0.102942	−	1.96426i	−0.129315	−	0.991604i	$-0.541278\pi$
$37$	3.80887	−	72.6775i	0.102942	−	1.96426i	0.232257	−	0.972654i	$-0.425389\pi$
$38$	−32.9858	−	10.7177i	−0.868047	−	0.282046i
$39$	−1.70877	+	33.3653i	−0.0438146	+	0.855519i
$40$	−1.67956	−	29.1672i	−0.0419889	−	0.729181i
$41$	−64.5681	−	3.38387i	−1.57483	−	0.0825334i	−0.755227	−	0.655464i	$-0.772473\pi$
$41$	−64.5681	−	3.38387i	−1.57483	−	0.0825334i	−0.819604	+	0.572930i	$0.805807\pi$
$42$	51.9047	−	23.1095i	1.23583	−	0.550225i
$43$	19.8434	−	11.4566i	0.461474	−	0.266432i	−0.251190	−	0.967938i	$-0.580822\pi$
$43$	19.8434	−	11.4566i	0.461474	−	0.266432i	0.712664	+	0.701506i	$0.247489\pi$
$44$	−6.14699	+	0.973588i	−0.139704	+	0.0221270i
$45$	11.9053	−	1.31344i	0.264562	−	0.0291876i
$46$	−17.1605	−	44.7047i	−0.373055	−	0.971842i
$47$	7.08608	+	1.12233i	0.150768	+	0.0238793i	0.231362	−	0.972868i	$-0.425682\pi$
$47$	7.08608	+	1.12233i	0.150768	+	0.0238793i	−0.0805943	+	0.996747i	$0.525682\pi$
$48$	33.9810	−	37.7398i	0.707938	−	0.786245i
$49$	−34.3744	−	19.8461i	−0.701519	−	0.405022i
$50$	−54.5706	+	21.5965i	−1.09141	+	0.431929i
$51$			34.8341i			0.683021i
$52$	−10.6785	+	16.4864i	−0.205356	+	0.317046i
$53$	−6.24347	+	4.53615i	−0.117801	+	0.0855877i	−0.645126	−	0.764076i	$-0.723195\pi$
$53$	−6.24347	+	4.53615i	−0.117801	+	0.0855877i	0.527325	+	0.849664i	$0.323195\pi$
$54$	53.4281	+	43.2653i	0.989410	+	0.801208i
$55$	−9.44439	−	18.3016i	−0.171716	−	0.332756i
$56$	−54.7269	−	5.75203i	−0.977267	−	0.102715i
$57$	26.8480	−	26.8480i	0.471017	−	0.471017i
$58$	60.1547	+	74.2848i	1.03715	+	1.28077i
$59$	69.5502	+	45.1664i	1.17882	+	0.765533i	0.976864	−	0.213862i	$-0.0686044\pi$
$59$	69.5502	+	45.1664i	1.17882	+	0.765533i	0.201953	+	0.979395i	$0.435271\pi$
$60$	−17.7774	−	7.80532i	−0.296289	−	0.130089i
$61$	44.4561	−	49.3735i	0.728788	−	0.809401i	−0.258889	−	0.965907i	$-0.583356\pi$
$61$	44.4561	−	49.3735i	0.728788	−	0.809401i	0.987677	+	0.156506i	$0.0500230\pi$
$62$	52.2252	−	47.0238i	0.842343	−	0.758449i
$63$	1.18070	−	22.5291i	0.0187413	−	0.357604i
$64$	−23.7857	+	7.72845i	−0.371652	+	0.120757i
$65$	−62.8908	−	16.4242i	−0.967550	−	0.252679i
$66$	7.67897	−	23.6334i	0.116348	−	0.358082i
$67$	−8.92958	+	23.2623i	−0.133277	+	0.347199i	−0.983937	−	0.178518i	$-0.942870\pi$
$67$	−8.92958	+	23.2623i	−0.133277	+	0.347199i	0.850659	+	0.525717i	$0.176203\pi$
$68$	−10.2402	+	17.7366i	−0.150592	+	0.260833i
$69$	52.1341	+	5.47951i	0.755566	+	0.0794132i
$70$	23.5406	+	108.006i	0.336294	+	1.54295i
$71$	45.4459	−	17.4451i	0.640084	−	0.245705i	−0.0166106	−	0.999862i	$-0.505288\pi$
$71$	45.4459	−	17.4451i	0.640084	−	0.245705i	0.656694	+	0.754157i	$0.271954\pi$
$72$	−5.01614	−	13.0675i	−0.0696686	−	0.181493i
$73$	50.8118	−	99.7238i	0.696052	−	1.36608i	−0.224118	−	0.974562i	$-0.571950\pi$
$73$	50.8118	−	99.7238i	0.696052	−	1.36608i	0.920171	−	0.391517i	$-0.128050\pi$
$74$	85.4240	+	147.959i	1.15438	+	1.99944i
$75$	6.05596	−	63.9620i	0.0807462	−	0.852827i
$76$	21.5629	−	5.77775i	0.283722	−	0.0760231i
$77$	−36.8923	+	11.9870i	−0.479121	+	0.155676i
$78$	−39.2954	−	67.8749i	−0.503787	−	0.870191i
$79$	−80.0466	+	58.1573i	−1.01325	+	0.736168i	−0.964888	−	0.262662i	$-0.915400\pi$
$79$	−80.0466	+	58.1573i	−1.01325	+	0.736168i	−0.0483603	+	0.998830i	$0.515400\pi$
$80$	58.4874	+	79.6336i	0.731092	+	0.995420i
$81$	−49.0593	+	21.8426i	−0.605670	+	0.269662i
$82$	131.449	−	75.8922i	1.60304	−	0.925515i
$83$	45.8804	−	7.26674i	0.552776	−	0.0875511i	0.126203	−	0.992004i	$-0.459721\pi$
$83$	45.8804	−	7.26674i	0.552776	−	0.0875511i	0.426573	+	0.904453i	$0.359721\pi$
$84$	−19.9172	+	30.6697i	−0.237109	+	0.365116i
$85$	−66.3634	−	13.7484i	−0.780746	−	0.161746i
$86$	−24.4200	+	47.9270i	−0.283954	+	0.557290i
$87$	−102.355	+	21.7562i	−1.17649	+	0.250071i
$88$	−17.8856	+	16.1043i	−0.203246	+	0.183003i
$89$	52.2796	+	80.5035i	0.587411	+	0.904534i	0.999980	−	0.00639296i	$-0.00203496\pi$
$89$	52.2796	+	80.5035i	0.587411	+	0.904534i	−0.412569	+	0.910927i	$0.635368\pi$
$90$	−21.7600	+	17.8076i	−0.241778	+	0.197862i
$91$	−49.6634	+	111.904i	−0.545751	+	1.22972i
$92$	24.9345	+	18.1160i	0.271028	+	0.196913i
$93$	19.9117	+	74.3116i	0.214105	+	0.799050i
$94$	−15.3862	+	6.85036i	−0.163683	+	0.0728762i
$95$	40.5524	+	61.7454i	0.426868	+	0.649951i
$96$	−9.25342	+	58.4238i	−0.0963898	+	0.608581i
$97$	104.384	−	40.0691i	1.07612	−	0.413084i	0.245198	−	0.969473i	$-0.421147\pi$
$97$	104.384	−	40.0691i	1.07612	−	0.413084i	0.830922	+	0.556389i	$0.187814\pi$
$98$	93.0515	−	4.87662i	0.949505	−	0.0497615i
$99$	−6.97699	−	6.97699i	−0.0704746	−	0.0704746i
$100$	21.8866	−	30.7875i	0.218866	−	0.307875i
$101$	−125.351	−	72.3712i	−1.24110	−	0.716547i	−0.271778	−	0.962360i	$-0.587612\pi$
$101$	−125.351	−	72.3712i	−1.24110	−	0.716547i	−0.969317	+	0.245813i	$0.920945\pi$
$102$	−44.5376	−	68.5819i	−0.436643	−	0.672372i
$103$	−31.1111	−	42.8207i	−0.302049	−	0.415735i	0.630832	−	0.775920i	$-0.282714\pi$
$103$	−31.1111	−	42.8207i	−0.302049	−	0.415735i	−0.932881	+	0.360184i	$0.882714\pi$
$104$	0.0904314	+	75.9604i	0.000869533	+	0.730388i
$105$	−117.050	−	30.7169i	−1.11476	−	0.292542i
$106$	6.49250	−	16.9135i	0.0612500	−	0.159562i
$107$	−100.418	+	173.929i	−0.938484	+	1.62550i	−0.170183	+	0.985413i	$0.554436\pi$
$107$	−100.418	+	173.929i	−0.938484	+	1.62550i	−0.768301	+	0.640089i	$0.778898\pi$
$108$	−44.0072	−	4.62534i	−0.407474	−	0.0428273i
$109$	−38.1767	−	74.9260i	−0.350245	−	0.687395i	0.646927	−	0.762552i	$-0.276054\pi$
$109$	−38.1767	−	74.9260i	−0.350245	−	0.687395i	−0.997172	+	0.0751577i	$0.976054\pi$
$110$	41.9940	+	23.9572i	0.381764	+	0.217793i
$111$	−186.776	+	9.78850i	−1.68266	+	0.0881846i
$112$	165.817	−	84.4880i	1.48051	−	0.754357i
$113$	−131.081	+	27.8622i	−1.16001	+	0.246568i	−0.747423	−	0.664349i	$-0.768709\pi$
$113$	−131.081	+	27.8622i	−1.16001	+	0.246568i	−0.412590	+	0.910917i	$0.635376\pi$
$114$	−18.5319	+	87.1857i	−0.162560	+	0.764786i
$115$	−31.0157	+	97.1596i	−0.269702	+	0.844866i
$116$	−58.5121	−	19.0117i	−0.504415	−	0.163894i
$117$	−31.0969	+	1.66684i	−0.265785	+	0.0142465i
$118$	−194.680			−1.64983
$119$	−45.7463	+	119.173i	−0.384423	+	1.00146i
$120$	−74.0957	+	12.1279i	−0.617464	+	0.101066i
$121$	42.3145	−	95.0400i	0.349707	−	0.785455i
$122$	−24.3987	+	154.047i	−0.199989	+	1.26268i
$123$	8.69628	+	165.935i	0.0707015	+	1.34906i
$124$	−11.7070	+	43.6911i	−0.0944112	+	0.352347i
$125$	119.466	+	36.7822i	0.955726	+	0.294257i
$126$	26.4803	+	45.8652i	0.210161	+	0.364010i
$127$	6.02103	−	28.3267i	0.0474097	−	0.223045i	−0.948064	−	0.318078i	$-0.896962\pi$
$127$	6.02103	−	28.3267i	0.0474097	−	0.223045i	0.995474	+	0.0950334i	$0.0302958\pi$
$128$	94.8889	−	117.178i	0.741319	−	0.915453i
$129$	−34.6117	−	47.6390i	−0.268308	−	0.369294i
$130$	144.820	−	48.0737i	1.11400	−	0.369798i
$131$	−37.7369	−	27.4174i	−0.288068	−	0.209293i	0.434361	−	0.900739i	$-0.356974\pi$
$131$	−37.7369	−	27.4174i	−0.288068	−	0.209293i	−0.722429	+	0.691445i	$0.756974\pi$
$132$	4.13961	+	15.4492i	0.0313606	+	0.117040i
$133$	127.110	−	56.5930i	0.955714	−	0.425511i
$134$	−12.1617	−	57.2163i	−0.0907590	−	0.426988i
$135$	−31.1827	−	143.069i	−0.230983	−	1.05977i
$136$	4.14504	+	79.0920i	0.0304782	+	0.581559i
$137$	174.504	+	113.324i	1.27375	+	0.827182i	0.991239	−	0.132082i	$-0.0421664\pi$
$137$	174.504	+	113.324i	1.27375	+	0.827182i	0.282510	+	0.959264i	$0.408833\pi$
$138$	−109.648	+	55.8687i	−0.794554	+	0.404845i
$139$	140.763	−	156.333i	1.01268	−	1.12470i	0.0205122	−	0.999790i	$-0.493470\pi$
$139$	140.763	−	156.333i	1.01268	−	1.12470i	0.992169	−	0.124906i	$-0.0398630\pi$
$140$	−50.5689	−	50.0497i	−0.361206	−	0.357498i
$141$	0.964953	−	18.4124i	0.00684364	−	0.130584i
$142$	−67.1701	+	92.4517i	−0.473029	+	0.651068i
$143$	21.8375	+	48.8911i	0.152710	+	0.341896i
$144$	38.2965	+	27.8241i	0.265948	+	0.193223i
$145$	−1.05057	−	203.586i	−0.00724528	−	1.40404i
$146$	27.4642	+	261.304i	0.188111	+	1.78975i
$147$	−41.4895	+	93.1869i	−0.282241	+	0.633925i
$148$	−97.9790	−	49.9228i	−0.662020	−	0.337316i
$149$	10.5600	+	2.82953i	0.0708723	+	0.0189902i	0.294081	−	0.955781i	$-0.404986\pi$
$149$	10.5600	+	2.82953i	0.0708723	+	0.0189902i	−0.223209	+	0.974771i	$0.571653\pi$
$150$	69.8565	+	133.672i	0.465710	+	0.891150i
$151$	101.233	+	101.233i	0.670417	+	0.670417i	0.957812	−	0.287395i	$-0.0927892\pi$
$151$	101.233	+	101.233i	0.670417	+	0.670417i	−0.287395	+	0.957812i	$0.592789\pi$
$152$	57.7646	−	64.1541i	0.380030	−	0.422066i
$153$	−32.2920	+	3.39403i	−0.211059	+	0.0221832i
$154$	57.3080	−	70.7695i	0.372130	−	0.459542i
$155$	−149.432	+	8.60485i	−0.964079	+	0.0555152i
$156$	45.0053	+	22.8639i	0.288495	+	0.146563i
$157$	−29.7941			−0.189772			−0.0948858	−	0.995488i	$-0.530249\pi$
$157$	−29.7941			−0.189772			−0.0948858	+	0.995488i	$0.530249\pi$
$158$	83.2393	−	216.846i	0.526831	−	1.37244i
$159$	13.2709	+	14.7388i	0.0834646	+	0.0926968i
$160$	−107.653	−	40.6879i	−0.672830	−	0.254299i
$161$	171.163	+	87.2121i	1.06313	+	0.541690i
$162$	68.6616	−	105.730i	0.423837	−	0.652652i
$163$	−44.3714	−	28.8151i	−0.272217	−	0.176780i	0.401310	−	0.915942i	$-0.368555\pi$
$163$	−44.3714	−	28.8151i	−0.272217	−	0.176780i	−0.673527	+	0.739162i	$0.735222\pi$
$164$	−44.3523	+	87.0463i	−0.270441	+	0.530770i
$165$	−44.2389	+	29.0547i	−0.268115	+	0.176089i
$166$	−81.0391	+	72.9679i	−0.488187	+	0.439566i
$167$	−22.1452	−	8.50074i	−0.132606	−	0.0509027i	0.291160	−	0.956674i	$-0.405959\pi$
$167$	−22.1452	−	8.50074i	−0.132606	−	0.0509027i	−0.423766	+	0.905772i	$0.639292\pi$
$168$			141.419i			0.841778i
$169$	160.852	+	51.8410i	0.951790	+	0.306752i
$170$	148.236	−	57.7818i	0.871975	−	0.339893i
$171$	27.5046	+	22.2728i	0.160846	+	0.130250i
$172$	−3.61889	−	34.4314i	−0.0210401	−	0.200183i
$173$	103.144	+	92.8715i	0.596210	+	0.536830i	0.911040	−	0.412318i	$-0.135281\pi$
$173$	103.144	+	92.8715i	0.596210	+	0.536830i	−0.314830	+	0.949148i	$0.601948\pi$
$174$	173.701	−	173.701i	0.998282	−	0.998282i
$175$	104.717	−	210.872i	0.598385	−	1.20498i
$176$	21.0663	−	78.6206i	0.119695	−	0.446708i
$177$	96.7551	−	189.893i	0.546639	−	1.07284i
$178$	−205.858	−	91.6538i	−1.15650	−	0.514909i
$179$	148.685	−	15.6274i	0.830642	−	0.0873040i	0.320344	−	0.947301i	$-0.396202\pi$
$179$	148.685	−	15.6274i	0.830642	−	0.0873040i	0.510298	+	0.859997i	$0.329535\pi$
$180$	5.50359	−	17.2405i	0.0305755	−	0.0957807i
$181$	−167.317	+	230.292i	−0.924402	+	1.27233i	0.0376019	+	0.999293i	$0.488028\pi$
$181$	−167.317	+	230.292i	−0.924402	+	1.27233i	−0.962004	+	0.273037i	$0.911972\pi$
$182$	−45.2986	−	283.817i	−0.248893	−	1.55943i
$183$	−138.133	−	100.360i	−0.754826	−	0.548413i
$184$	119.024	+	6.23780i	0.646872	+	0.0339011i
$185$	55.0690	−	359.695i	0.297670	−	1.94430i
$186$	−134.215	−	120.848i	−0.721585	−	0.649718i
$187$	25.3465	+	49.7453i	0.135543	+	0.266017i
$188$	5.90406	−	9.09146i	0.0314046	−	0.0483588i
$189$	−275.423	+	14.4343i	−1.45727	+	0.0763720i
$190$	−158.786	−	69.7164i	−0.835715	−	0.366929i
$191$	−143.301	+	30.4596i	−0.750267	+	0.159474i	−0.567147	−	0.823616i	$-0.691953\pi$
$191$	−143.301	+	30.4596i	−0.750267	+	0.159474i	−0.183120	+	0.983091i	$0.558620\pi$
$192$	26.1423	+	58.7165i	0.136158	+	0.305815i
$193$	−113.001	+	30.2785i	−0.585497	+	0.156884i	−0.539395	−	0.842053i	$-0.681347\pi$
$193$	−113.001	+	30.2785i	−0.585497	+	0.156884i	−0.0461028	+	0.998937i	$0.514680\pi$
$194$	−154.281	+	212.350i	−0.795264	+	1.09459i
$195$	−25.0833	+	165.151i	−0.128632	+	0.846928i
$196$	−48.5198	+	35.2517i	−0.247550	+	0.179855i
$197$	56.8235	+	46.0148i	0.288444	+	0.233577i	0.762611	−	0.646858i	$-0.223917\pi$
$197$	56.8235	+	46.0148i	0.288444	+	0.233577i	−0.474167	+	0.880435i	$0.657251\pi$
$198$	22.6570	+	4.81588i	0.114429	+	0.0243226i
$199$	341.472	−	197.149i	1.71594	−	0.990698i	0.789930	−	0.613197i	$-0.210117\pi$
$199$	341.472	−	197.149i	1.71594	−	0.990698i	0.926009	−	0.377501i	$-0.123217\pi$
$200$	6.13921	−	145.949i	0.0306960	−	0.729743i
$201$	61.8537	+	16.5736i	0.307730	+	0.0824559i
$202$	339.324	−	17.7832i	1.67982	−	0.0880357i
$203$	−378.744	−	59.9872i	−1.86574	−	0.295503i
$204$	48.0829	+	21.4079i	0.235700	+	0.104941i
$205$	−319.560	−	48.9243i	−1.55883	−	0.238655i
$206$	116.001	+	44.5287i	0.563112	+	0.216159i
$207$			48.8634i			0.236055i
$208$	−140.169	−	215.280i	−0.673891	−	1.03500i
$209$	18.8051	−	57.8762i	0.0899766	−	0.276919i
$210$	269.723	−	89.1798i	1.28440	−	0.424666i
$211$	204.655	+	43.5008i	0.969930	+	0.206165i	0.665523	−	0.746377i	$-0.268208\pi$
$211$	204.655	+	43.5008i	0.969930	+	0.206165i	0.304407	+	0.952542i	$0.401542\pi$
$212$	2.42440	+	11.4059i	0.0114358	+	0.0538014i
$213$	−56.7950	−	111.466i	−0.266643	−	0.523317i
$214$	−24.6749	−	470.824i	−0.115303	−	2.20011i
$215$	104.419	−	47.1376i	0.485671	−	0.219244i
$216$	−152.468	+	77.6863i	−0.705870	+	0.359659i
$217$	−29.4693	+	280.382i	−0.135803	+	1.29208i
$218$	170.961	+	98.7042i	0.784224	+	0.452772i
$219$	−268.528	−	103.078i	−1.22616	−	0.470677i
$220$	−31.0666	+	1.78893i	−0.141212	+	0.00813150i
$221$	170.259	+	45.4035i	0.770402	+	0.205446i
$222$	355.212	−	258.077i	1.60005	−	1.16251i
$223$	196.323	−	127.494i	0.880372	−	0.571720i	−0.0234043	−	0.999726i	$-0.507450\pi$
$223$	196.323	−	127.494i	0.880372	−	0.571720i	0.903776	+	0.428006i	$0.140784\pi$
$224$	−108.383	+	187.725i	−0.483854	+	0.838060i
$225$	59.8843	−	0.618060i	0.266153	−	0.00274693i
$226$	222.452	−	222.452i	0.984300	−	0.984300i
$227$	9.90671	+	189.031i	0.0436419	+	0.832737i	0.929509	+	0.368799i	$0.120231\pi$
$227$	9.90671	+	189.031i	0.0436419	+	0.832737i	−0.885867	+	0.463939i	$0.846436\pi$
$228$	−20.5595	−	53.5592i	−0.0901731	−	0.234909i
$229$	16.2102	+	2.56744i	0.0707868	+	0.0112115i	0.191727	−	0.981448i	$-0.438591\pi$
$229$	16.2102	+	2.56744i	0.0707868	+	0.0112115i	−0.120941	+	0.992660i	$0.538591\pi$
$230$	−63.1606	−	230.945i	−0.274611	−	1.00411i
$231$	40.5474	+	91.0709i	0.175530	+	0.394246i
$232$	−229.811	+	61.5777i	−0.990566	+	0.265421i
$233$	−56.6826	+	78.0169i	−0.243273	+	0.334837i	−0.913141	−	0.407644i	$-0.866351\pi$
$233$	−56.6826	+	78.0169i	−0.243273	+	0.334837i	0.669868	+	0.742480i	$0.266351\pi$
$234$	59.0929	−	43.0411i	0.252534	−	0.183936i
$235$	34.6972	+	9.10545i	0.147648	+	0.0387466i
$236$	105.088	−	68.2452i	0.445290	−	0.289174i
$237$	170.144	+	188.964i	0.717906	+	0.797316i
$238$	−62.3046	−	293.120i	−0.261784	−	1.23160i
$239$	271.709	+	138.443i	1.13686	+	0.579259i	0.918033	−	0.396505i	$-0.129777\pi$
$239$	271.709	+	138.443i	1.13686	+	0.579259i	0.218827	+	0.975764i	$0.429777\pi$
$240$	187.819	−	170.877i	0.782581	−	0.711986i
$241$	94.0936	+	61.1051i	0.390430	+	0.253548i	0.724894	−	0.688860i	$-0.241889\pi$
$241$	94.0936	+	61.1051i	0.390430	+	0.253548i	−0.334464	+	0.942408i	$0.608555\pi$
$242$	38.2052	+	241.218i	0.157873	+	0.996770i
$243$	−62.7799	−	108.738i	−0.258354	−	0.447481i
$244$	−40.8310	−	91.7078i	−0.167340	−	0.375852i
$245$	−161.158	−	115.822i	−0.657788	−	0.472744i
$246$	−229.280	−	315.577i	−0.932032	−	1.28283i
$247$	−96.2308	−	166.219i	−0.389599	−	0.672953i
$248$	54.0529	+	166.358i	0.217955	+	0.670798i
$249$	−30.8975	−	115.311i	−0.124086	−	0.463096i
$250$	−282.235	+	80.3274i	−1.12894	+	0.321309i
$251$	100.171	−	57.8339i	0.399089	−	0.230414i	−0.287002	−	0.957930i	$-0.592659\pi$
$251$	100.171	−	57.8339i	0.399089	−	0.230414i	0.686091	+	0.727516i	$0.259325\pi$
$252$	−30.3722	−	15.4754i	−0.120525	−	0.0614103i
$253$	78.4379	−	30.1095i	0.310031	−	0.119010i
$254$	24.3632	+	63.4684i	0.0959183	+	0.249876i
$255$	−17.3117	+	173.308i	−0.0678889	+	0.679639i
$256$	−26.5422	+	252.532i	−0.103681	+	0.986455i
$257$	−220.824	−	127.493i	−0.859239	−	0.496082i	0.00451820	−	0.999990i	$-0.498562\pi$
$257$	−220.824	−	127.493i	−0.859239	−	0.496082i	−0.863757	+	0.503908i	$0.831895\pi$
$258$	129.054	+	49.5391i	0.500208	+	0.192012i
$259$	−651.846	−	211.798i	−2.51678	−	0.817751i
$260$	−61.3215	+	76.7169i	−0.235852	+	0.295065i
$261$	−30.1413	−	92.7654i	−0.115484	−	0.355423i
$262$	109.352	+	5.73089i	0.417374	+	0.0218736i
$263$	79.9973	+	88.8460i	0.304172	+	0.337817i	0.875781	−	0.482709i	$-0.160347\pi$
$263$	79.9973	+	88.8460i	0.304172	+	0.337817i	−0.571609	+	0.820526i	$0.693680\pi$
$264$	45.9647	+	41.3868i	0.174109	+	0.156768i
$265$	−33.3171	+	19.4656i	−0.125725	+	0.0734550i
$266$	−177.898	+	273.940i	−0.668791	+	1.02985i
$267$	191.710	−	155.244i	0.718017	−	0.581438i
$268$	26.6221	+	26.6221i	0.0993363	+	0.0993363i
$269$	−36.1983	+	344.404i	−0.134566	+	1.28031i	0.693817	+	0.720151i	$0.255927\pi$
$269$	−36.1983	+	344.404i	−0.134566	+	1.28031i	−0.828384	+	0.560161i	$0.810739\pi$
$270$	244.316	+	241.807i	0.904874	+	0.895583i
$271$	−30.5411	+	37.7152i	−0.112698	+	0.139170i	−0.830373	−	0.557207i	$-0.811873\pi$
$271$	−30.5411	+	37.7152i	−0.112698	+	0.139170i	0.717675	+	0.696378i	$0.245206\pi$
$272$	−157.438	−	216.694i	−0.578815	−	0.796670i
$273$	299.350	+	96.8710i	1.09652	+	0.354839i
$274$	−488.458			−1.78269
$275$	−37.8927	−	95.7483i	−0.137792	−	0.348176i
$276$	39.6035	−	68.5953i	0.143491	−	0.248534i
$277$	131.761	+	118.638i	0.475673	+	0.428298i	0.871773	−	0.489910i	$-0.162970\pi$
$277$	131.761	+	118.638i	0.475673	+	0.428298i	−0.396101	+	0.918207i	$0.629637\pi$
$278$	−77.2543	+	487.765i	−0.277893	+	1.75455i
$279$	−66.9485	+	25.6991i	−0.239959	+	0.0921116i
$280$	−269.421	−	55.8157i	−0.962218	−	0.199342i
$281$	−33.3888	−	210.809i	−0.118821	−	0.750208i	−0.973098	−	0.230390i	$-0.926000\pi$
$281$	−33.3888	−	210.809i	−0.118821	−	0.750208i	0.854277	−	0.519818i	$-0.174000\pi$
$282$	21.6416	+	37.4844i	0.0767434	+	0.132924i
$283$	36.6855	+	82.3970i	0.129631	+	0.291155i	0.966687	−	0.255961i	$-0.0823920\pi$
$283$	36.6855	+	82.3970i	0.129631	+	0.291155i	−0.837056	+	0.547117i	$0.815725\pi$
$284$	3.84946	−	73.4520i	0.0135544	−	0.258634i
$285$	146.918	−	120.232i	0.515502	−	0.421868i
$286$	−105.504	−	68.3370i	−0.368897	−	0.238940i
$287$	−188.165	+	579.112i	−0.655626	+	2.01781i
$288$	−55.0618	−	2.88567i	−0.191187	−	0.0100197i
$289$	−102.974	−	21.8879i	−0.356313	−	0.0757366i
$290$	262.366	+	399.480i	0.904711	+	1.37752i
$291$	−130.451	−	256.024i	−0.448285	−	0.879809i
$292$	−106.426	−	131.425i	−0.364471	−	0.450084i
$293$	−88.0612	+	328.649i	−0.300550	+	1.12167i	0.636158	+	0.771558i	$0.280522\pi$
$293$	−88.0612	+	328.649i	−0.300550	+	1.12167i	−0.936709	+	0.350110i	$0.886144\pi$
$294$	−37.4603	−	236.515i	−0.127416	−	0.804473i
$295$	323.582	+	259.279i	1.09689	+	0.878911i
$296$	−422.916	+	44.4503i	−1.42877	+	0.150170i
$297$	−75.9122	+	93.7438i	−0.255597	+	0.315636i
$298$	−24.4084	+	7.93077i	−0.0819073	+	0.0266133i
$299$	94.7351	−	247.674i	0.316840	−	0.828342i
$300$	−84.5675	−	47.6682i	−0.281892	−	0.158894i
$301$	−55.8501	−	208.435i	−0.185548	−	0.692476i
$302$	−328.742	−	69.8763i	−1.08855	−	0.231379i
$303$	−151.297	+	339.818i	−0.499329	+	1.12151i
$304$	−45.6714	+	288.358i	−0.150235	+	0.948547i
$305$	245.717	−	223.551i	0.805630	−	0.732955i
$306$	59.2376	−	47.9696i	0.193587	−	0.156764i
$307$	−44.0117	−	44.0117i	−0.143360	−	0.143360i	0.631784	−	0.775144i	$-0.282323\pi$
$307$	−44.0117	−	44.0117i	−0.143360	−	0.143360i	−0.775144	+	0.631784i	$0.782323\pi$
$308$	−6.12661	+	58.2908i	−0.0198916	+	0.189256i
$309$	−101.086	+	91.0180i	−0.327138	+	0.294557i
$310$	283.203	−	208.000i	0.913557	−	0.670968i
$311$	68.7947	−	22.3527i	0.221205	−	0.0718738i	−0.196318	−	0.980540i	$-0.562898\pi$
$311$	68.7947	−	22.3527i	0.221205	−	0.0718738i	0.417523	+	0.908667i	$0.362898\pi$
$312$	194.119	−	20.6364i	0.622175	−	0.0661422i
$313$	185.713	−	571.565i	0.593331	−	1.82609i	0.0304679	−	0.999536i	$-0.490300\pi$
$313$	185.713	−	571.565i	0.593331	−	1.82609i	0.562863	−	0.826550i	$-0.309700\pi$
$314$	58.6592	−	38.0937i	0.186813	−	0.121318i
$315$	17.0707	−	111.501i	0.0541926	−	0.353971i
$316$	31.0828	+	146.233i	0.0983633	+	0.462763i
$317$	195.459	−	30.9577i	0.616590	−	0.0976583i	0.159676	−	0.987169i	$-0.448955\pi$
$317$	195.459	−	30.9577i	0.616590	−	0.0976583i	0.456913	+	0.889511i	$0.348955\pi$
$318$	−44.9724	−	12.0503i	−0.141423	−	0.0378941i
$319$	−130.339	+	105.546i	−0.408585	+	0.330865i
$320$	−122.181	+	26.6300i	−0.381814	+	0.0832187i
$321$	471.510	+	209.930i	1.46888	+	0.653986i
$322$	−448.496	+	47.1388i	−1.39284	+	0.146394i
$323$	−109.069	−	167.951i	−0.337674	−	0.519972i
$324$			81.1423i			0.250439i
$325$	−304.734	−	112.969i	−0.937644	−	0.347598i
$326$	124.201			0.380986
$327$	−181.244	+	117.701i	−0.554262	+	0.359942i
$328$	39.4904	+	375.726i	0.120398	+	1.14551i
$329$	27.4816	−	61.7247i	0.0835307	−	0.187613i
$330$	49.9500	−	113.766i	0.151364	−	0.344745i
$331$	356.493	+	440.232i	1.07702	+	1.33001i	0.940661	+	0.339347i	$0.110206\pi$
$331$	356.493	+	440.232i	1.07702	+	1.33001i	0.136357	+	0.990660i	$0.456460\pi$
$332$	18.1660	−	67.7964i	0.0547169	−	0.204206i
$333$	−27.2725	−	172.192i	−0.0818993	−	0.517092i
$334$	54.4686	−	11.5777i	0.163080	−	0.0346636i
$335$	−55.9876	+	111.298i	−0.167127	+	0.332233i
$336$	−260.482	−	401.106i	−0.775243	−	1.19377i
$337$	45.1902	+	14.6832i	0.134096	+	0.0435703i	0.375296	−	0.926905i	$-0.377541\pi$
$337$	45.1902	+	14.6832i	0.134096	+	0.0435703i	−0.241200	+	0.970475i	$0.577541\pi$
$338$	−382.971	+	103.595i	−1.13305	+	0.306493i
$339$	106.424	+	327.539i	0.313935	+	0.966192i
$340$	−59.7623	+	83.1548i	−0.175772	+	0.244573i
$341$	82.5069	+	91.6333i	0.241956	+	0.268719i
$342$	−82.6288	−	8.68464i	−0.241605	−	0.0253937i
$343$	61.9834	−	61.9834i	0.180710	−	0.180710i
$344$	−84.2560	−	104.047i	−0.244930	−	0.302464i
$345$	256.656	+	53.1713i	0.743932	+	0.154120i
$346$	−321.815	−	50.9704i	−0.930100	−	0.147313i
$347$	−64.2768	−	28.6179i	−0.185236	−	0.0824723i	0.312023	−	0.950075i	$-0.398993\pi$
$347$	−64.2768	−	28.6179i	−0.185236	−	0.0824723i	−0.497259	+	0.867602i	$0.665660\pi$
$348$	−32.8729	+	154.655i	−0.0944624	+	0.444411i
$349$	332.000	−	88.9592i	0.951290	−	0.254897i	0.250380	−	0.968148i	$-0.419444\pi$
$349$	332.000	−	88.9592i	0.951290	−	0.254897i	0.700909	+	0.713250i	$0.252778\pi$
$350$	63.4437	+	549.056i	0.181268	+	1.56873i
$351$	60.0041	+	375.954i	0.170952	+	1.07109i
$352$	29.2967	+	90.1660i	0.0832293	+	0.256153i
$353$	48.0392	+	38.9014i	0.136088	+	0.110202i	0.694948	−	0.719060i	$-0.255428\pi$
$353$	48.0392	+	38.9014i	0.136088	+	0.110202i	−0.558859	+	0.829262i	$0.688761\pi$
$354$	52.2969	+	497.571i	0.147731	+	1.40557i
$355$	234.774	−	64.2078i	0.661336	−	0.180867i
$356$	143.252	−	22.6888i	0.402392	−	0.0637326i
$357$	316.877	+	84.9069i	0.887610	+	0.237834i
$358$	−272.753	+	220.871i	−0.761879	+	0.616958i
$359$	339.226	−	172.844i	0.944919	−	0.481460i	0.0875485	−	0.996160i	$-0.472097\pi$
$359$	339.226	−	172.844i	0.944919	−	0.481460i	0.857370	+	0.514700i	$0.172097\pi$
$360$	−18.4623	−	67.5068i	−0.0512841	−	0.187519i
$361$	29.6732	−	139.602i	0.0821973	−	0.386708i
$362$	34.9732	−	667.328i	0.0966109	−	1.84345i
$363$	−254.274	−	82.6187i	−0.700480	−	0.227600i
$364$	123.944	+	137.325i	0.340506	+	0.377266i
$365$	302.361	−	470.898i	0.828387	−	1.29013i
$366$	400.275	+	20.9775i	1.09365	+	0.0573157i
$367$	−308.241	+	137.238i	−0.839893	+	0.373944i	−0.781161	−	0.624329i	$-0.785372\pi$
$367$	−308.241	+	137.238i	−0.839893	+	0.373944i	−0.0587318	+	0.998274i	$0.518706\pi$
$368$	−349.079	+	201.541i	−0.948584	+	0.547665i
$369$	−152.978	+	24.2294i	−0.414575	+	0.0656623i
$370$	351.473	+	778.584i	0.949927	+	2.10428i
$371$	26.0460	+	67.8521i	0.0702048	+	0.182890i
$372$	114.812	+	18.1845i	0.308636	+	0.0488831i
$373$	97.6829	−	108.488i	0.261885	−	0.290852i	−0.597834	−	0.801620i	$-0.703972\pi$
$373$	97.6829	−	108.488i	0.261885	−	0.290852i	0.859719	+	0.510767i	$0.170639\pi$
$374$	−113.505	−	65.5322i	−0.303490	−	0.175220i
$375$	61.9174	−	315.217i	0.165113	−	0.840578i
$376$		−	41.9209i		−	0.111492i
$377$	−27.0737	+	528.638i	−0.0718135	+	1.40222i
$378$	523.803	−	380.565i	1.38572	−	1.00679i
$379$	325.222	+	263.360i	0.858105	+	0.694880i	0.953771	−	0.300533i	$-0.0971647\pi$
$379$	325.222	+	263.360i	0.858105	+	0.694880i	−0.0956658	+	0.995414i	$0.530498\pi$
$380$	110.152	−	18.0295i	0.289873	−	0.0474460i
$381$	−74.0161	−	7.77941i	−0.194268	−	0.0204184i
$382$	243.189	−	243.189i	0.636621	−	0.636621i
$383$	−208.090	−	256.969i	−0.543315	−	0.670938i	0.429354	−	0.903136i	$-0.358741\pi$
$383$	−208.090	−	256.969i	−0.543315	−	0.670938i	−0.972668	+	0.232199i	$0.925408\pi$
$384$	−324.979	−	211.044i	−0.846298	−	0.549593i
$385$	−189.505	+	41.3038i	−0.492222	+	0.107283i
$386$	183.765	−	204.092i	0.476076	−	0.528736i
$387$	40.7901	−	36.7276i	0.105401	−	0.0949033i
$388$	8.84172	−	168.710i	0.0227879	−	0.434820i
$389$	475.687	−	154.560i	1.22285	−	0.397327i	0.374729	−	0.927135i	$-0.377736\pi$
$389$	475.687	−	154.560i	1.22285	−	0.397327i	0.848118	+	0.529808i	$0.177736\pi$
$390$	−161.772	−	357.223i	−0.414800	−	0.915956i
$391$	85.4386	−	262.953i	0.218513	−	0.672514i
$392$	−83.1148	+	216.521i	−0.212027	+	0.552350i
$393$	−59.9374	+	103.815i	−0.152513	+	0.264159i
$394$	−170.708	−	17.9421i	−0.433269	−	0.0455384i
$395$	−427.154	+	249.565i	−1.08140	+	0.631810i
$396$	−13.9184	+	5.34279i	−0.0351476	+	0.0134919i
$397$	223.868	+	583.195i	0.563899	+	1.46901i	0.858211	+	0.513297i	$0.171576\pi$
$397$	223.868	+	583.195i	0.563899	+	1.46901i	−0.294313	+	0.955709i	$0.595091\pi$
$398$	−420.228	+	824.744i	−1.05585	+	2.07222i
$399$	−178.788	−	309.671i	−0.448091	−	0.776117i
$400$	251.413	+	425.263i	0.628532	+	1.06316i
$401$	−198.062	+	53.0705i	−0.493920	+	0.132345i	−0.497177	−	0.867649i	$-0.665630\pi$
$401$	−198.062	+	53.0705i	−0.493920	+	0.132345i	0.00325684	+	0.999995i	$0.498963\pi$
$402$	−142.969	+	46.4535i	−0.355644	+	0.115556i
$403$	389.167	−	0.463306i	0.965675	−	0.00114964i
$404$	−176.933	+	128.550i	−0.437954	+	0.318192i
$405$	−254.937	+	84.2909i	−0.629474	+	0.208126i
$406$	822.376	−	366.145i	2.02556	−	0.901836i
$407$	−259.605	+	149.883i	−0.637850	+	0.368263i
$408$	201.033	−	31.8406i	0.492729	−	0.0780406i
$409$	36.4937	−	56.1954i	0.0892267	−	0.137397i	−0.791239	−	0.611507i	$-0.790563\pi$
$409$	36.4937	−	56.1954i	0.0892267	−	0.137397i	0.880466	+	0.474110i	$0.157230\pi$
$410$	691.708	−	312.255i	1.68709	−	0.761598i
$411$	242.761	−	476.446i	0.590660	−	1.15924i
$412$	−78.2271	+	16.6277i	−0.189872	+	0.0403584i
$413$	580.394	−	522.589i	1.40531	−	1.26535i
$414$	−62.4751	−	96.2032i	−0.150906	−	0.232375i
$415$	231.877	−	13.3523i	0.558740	−	0.0321743i
$416$	273.497	+	121.379i	0.657446	+	0.291776i
$417$	−437.375	−	317.772i	−1.04886	−	0.762042i
$418$	36.9746	+	137.991i	0.0884560	+	0.330122i
$419$	−163.097	+	72.6155i	−0.389253	+	0.173307i	−0.592025	−	0.805919i	$-0.701672\pi$
$419$	−163.097	+	72.6155i	−0.389253	+	0.173307i	0.202772	+	0.979226i	$0.435005\pi$
$420$	−114.335	+	142.691i	−0.272226	+	0.339740i
$421$	13.6170	−	85.9745i	0.0323445	−	0.204215i	−0.966224	−	0.257704i	$-0.917034\pi$
$421$	13.6170	−	85.9745i	0.0323445	−	0.204215i	0.998568	+	0.0534888i	$0.0170341\pi$
$422$	−458.547	+	176.020i	−1.08661	+	0.417109i
$423$	17.1628	−	0.899462i	0.0405739	−	0.00212639i
$424$	31.8858	+	31.8858i	0.0752024	+	0.0752024i
$425$	−323.341	−	101.383i	−0.760803	−	0.238548i
$426$	254.336	+	146.841i	0.597033	+	0.344697i
$427$	−340.778	−	524.752i	−0.798075	−	1.22893i
$428$	178.367	+	245.502i	0.416746	+	0.573602i
$429$	119.092	−	68.9468i	0.277603	−	0.160715i
$430$	−145.314	+	226.312i	−0.337939	+	0.526307i
$431$	155.782	−	405.826i	0.361443	−	0.941591i	−0.625457	−	0.780259i	$-0.715087\pi$
$431$	155.782	−	405.826i	0.361443	−	0.941591i	0.986900	−	0.161333i	$-0.0515792\pi$
$432$	289.354	−	501.175i	0.669800	−	1.16013i
$433$	−398.193	−	41.8517i	−0.919613	−	0.0966553i	−0.367121	−	0.930173i	$-0.619657\pi$
$433$	−398.193	−	41.8517i	−0.919613	−	0.0966553i	−0.552492	+	0.833518i	$0.686323\pi$
$434$	−300.467	−	589.699i	−0.692320	−	1.35875i
$435$	−520.052	+	57.3744i	−1.19552	+	0.131895i
$436$	−126.886	+	6.64979i	−0.291022	+	0.0152518i
$437$	−268.519	+	136.817i	−0.614460	+	0.313083i
$438$	660.475	−	140.388i	1.50793	−	0.320521i
$439$	−76.2641	+	358.794i	−0.173722	+	0.817299i	0.801834	+	0.597547i	$0.203858\pi$
$439$	−76.2641	+	358.794i	−0.173722	+	0.817299i	−0.975556	+	0.219752i	$0.929475\pi$
$440$	−96.9887	+	71.2340i	−0.220429	+	0.161895i
$441$	−90.4290	−	29.3822i	−0.205054	−	0.0666262i
$442$	−393.260	+	128.296i	−0.889728	+	0.290262i
$443$	197.519			0.445868			0.222934	−	0.974834i	$-0.428437\pi$
$443$	197.519			0.445868			0.222934	+	0.974834i	$0.428437\pi$
$444$	−101.275	+	263.830i	−0.228096	+	0.594211i
$445$	220.095	+	426.506i	0.494596	+	0.958440i
$446$	−223.515	+	502.023i	−0.501155	+	1.12561i
$447$	4.39512	−	27.7497i	0.00983249	−	0.0620799i
$448$	12.3269	+	235.211i	0.0275154	+	0.525024i
$449$	17.7342	−	66.1848i	0.0394970	−	0.147405i	−0.943361	−	0.331767i	$-0.892355\pi$
$449$	17.7342	−	66.1848i	0.0394970	−	0.147405i	0.982858	+	0.184362i	$0.0590219\pi$
$450$	−117.111	+	77.7829i	−0.260247	+	0.172851i
$451$	133.159	+	230.638i	0.295252	+	0.511392i
$452$	−42.0990	+	198.060i	−0.0931394	+	0.438186i
$453$	231.542	−	285.930i	0.511129	−	0.631192i
$454$	−261.193	−	359.502i	−0.575316	−	0.791854i
$455$	−302.701	+	532.068i	−0.665276	+	1.16938i
$456$	−179.485	−	130.404i	−0.393608	−	0.285973i
$457$	148.432	+	553.957i	0.324797	+	1.21216i	0.914516	+	0.404551i	$0.132572\pi$
$457$	148.432	+	553.957i	0.324797	+	1.21216i	−0.589719	+	0.807609i	$0.700761\pi$
$458$	−35.1975	+	15.6710i	−0.0768505	+	0.0342161i
$459$	82.5309	+	388.277i	0.179806	+	0.845920i
$460$	115.052	+	102.523i	0.250113	+	0.222877i
$461$	−46.7599	−	892.232i	−0.101431	−	1.93543i	−0.297273	−	0.954793i	$-0.596077\pi$
$461$	−46.7599	−	892.232i	−0.101431	−	1.93543i	0.195841	−	0.980636i	$-0.437256\pi$
$462$	−196.270	−	127.459i	−0.424828	−	0.275886i
$463$	−501.415	+	255.484i	−1.08297	+	0.551801i	−0.902021	−	0.431691i	$-0.857917\pi$
$463$	−501.415	+	255.484i	−1.08297	+	0.551801i	−0.180949	+	0.983492i	$0.557917\pi$
$464$	538.394	−	597.947i	1.16033	−	1.28868i
$465$	62.1346	+	379.614i	0.133623	+	0.816374i
$466$	11.8480	−	226.073i	0.0254249	−	0.485136i
$467$	163.923	−	225.621i	0.351014	−	0.483129i	−0.596604	−	0.802536i	$-0.703484\pi$
$467$	163.923	−	225.621i	0.351014	−	0.483129i	0.947618	+	0.319407i	$0.103484\pi$
$468$	−16.8103	+	43.9487i	−0.0359195	+	0.0939074i
$469$	189.846	+	137.931i	0.404789	+	0.294097i
$470$	−79.9543	+	26.4357i	−0.170116	+	0.0562461i
$471$	8.00360	+	76.1492i	0.0169928	+	0.161676i
$472$	197.090	−	442.671i	0.417563	−	0.937863i
$473$	−84.0916	−	42.8468i	−0.177783	−	0.0905852i
$474$	−576.585	−	154.495i	−1.21642	−	0.325940i
$475$	171.072	+	327.352i	0.360152	+	0.689161i
$476$	136.385	+	136.385i	0.286524	+	0.286524i
$477$	−12.3702	+	13.7385i	−0.0259333	+	0.0288018i
$478$	−711.954	+	74.8294i	−1.48944	+	0.156547i
$479$	5.67793	−	7.01165i	0.0118537	−	0.0146381i	−0.771185	−	0.636612i	$-0.780335\pi$
$479$	5.67793	−	7.01165i	0.0118537	−	0.0146381i	0.783038	+	0.621973i	$0.213669\pi$
$480$	−75.0732	+	286.074i	−0.156402	+	0.595987i
$481$	−195.604	+	925.664i	−0.406662	+	1.92446i
$482$	−263.380			−0.546432
$483$	176.921	−	460.895i	0.366296	−	0.954234i
$484$	−105.182	−	116.817i	−0.217319	−	0.241357i
$485$	539.247	−	147.477i	1.11185	−	0.304077i
$486$	262.631	+	133.817i	0.540393	+	0.275344i
$487$	56.3675	−	86.7983i	0.115744	−	0.178231i	−0.776050	−	0.630671i	$-0.782780\pi$
$487$	56.3675	−	86.7983i	0.115744	−	0.178231i	0.891795	+	0.452440i	$0.149446\pi$
$488$	−325.578	−	211.433i	−0.667169	−	0.433265i
$489$	−61.7275	+	121.147i	−0.126232	+	0.247744i
$490$	465.377	+	21.9819i	0.949749	+	0.0448611i
$491$	−120.923	+	108.880i	−0.246280	+	0.221751i	−0.783020	−	0.621996i	$-0.786322\pi$
$491$	−120.923	+	108.880i	−0.246280	+	0.221751i	0.536741	+	0.843747i	$0.319655\pi$
$492$	234.391	+	89.9743i	0.476405	+	0.182875i
$493$			551.909i			1.11949i
$494$	401.983	+	204.218i	0.813731	+	0.413397i
$495$	−31.2448	−	38.1796i	−0.0631208	−	0.0771305i
$496$	−459.728	−	372.281i	−0.926871	−	0.750566i
$497$	−47.9204	−	455.932i	−0.0964193	−	0.917369i
$498$	208.264	+	187.522i	0.418201	+	0.376550i
$499$	38.8570	−	38.8570i	0.0778698	−	0.0778698i	−0.667099	−	0.744969i	$-0.732464\pi$
$499$	38.8570	−	38.8570i	0.0778698	−	0.0778698i	0.744969	+	0.667099i	$0.232464\pi$
$500$	124.192	−	142.298i	0.248383	−	0.284597i
$501$	−15.7777	+	58.8832i	−0.0314924	+	0.117531i
$502$	−123.275	+	241.940i	−0.245567	+	0.481952i
$503$	−697.667	−	310.621i	−1.38701	−	0.617537i	−0.428748	−	0.903424i	$-0.641045\pi$
$503$	−697.667	−	310.621i	−1.38701	−	0.617537i	−0.958263	+	0.285887i	$0.907712\pi$
$504$	−131.098	+	13.7790i	−0.260116	+	0.0273393i
$505$	−587.683	−	422.360i	−1.16373	−	0.836357i
$506$	−115.933	+	159.568i	−0.229117	+	0.315352i
$507$	89.2878	−	425.040i	0.176110	−	0.838343i
$508$	−35.4002	−	25.7197i	−0.0696854	−	0.0506294i
$509$	746.037	+	39.0981i	1.46569	+	0.0768136i	0.768398	−	0.639972i	$-0.221054\pi$
$509$	746.037	+	39.0981i	1.46569	+	0.0768136i	0.697293	+	0.716786i	$0.254387\pi$
$510$	−187.502	−	363.346i	−0.367651	−	0.712442i
$511$	−783.311	−	705.296i	−1.53290	−	1.38023i
$512$	3.18819	+	6.25718i	0.00622693	+	0.0122210i
$513$	235.651	−	362.870i	0.459358	−	0.707350i
$514$	597.771	−	31.3279i	1.16298	−	0.0609492i
$515$	−133.504	−	228.505i	−0.259232	−	0.443699i
$516$	−87.0293	+	18.4986i	−0.168661	+	0.0358501i
$517$	−12.0195	−	26.9962i	−0.0232485	−	0.0522171i
$518$	1554.16	−	416.436i	3.00031	−	0.803931i
$519$	209.657	−	288.569i	0.403964	−	0.556009i
$520$	−37.3005	+	377.966i	−0.0717318	+	0.726858i
$521$	−680.205	+	494.198i	−1.30557	+	0.948556i	−0.999993	−	0.00361028i	$-0.998851\pi$
$521$	−680.205	+	494.198i	−1.30557	+	0.948556i	−0.305581	+	0.952166i	$0.598851\pi$
$522$	177.949	+	144.101i	0.340899	+	0.276055i
$523$	454.155	+	96.5335i	0.868364	+	0.184577i	0.620489	−	0.784215i	$-0.286934\pi$
$523$	454.155	+	96.5335i	0.868364	+	0.184577i	0.247876	+	0.968792i	$0.420268\pi$
$524$	−61.0372	+	35.2399i	−0.116483	+	0.0672516i
$525$	−567.085	−	210.995i	−1.08016	−	0.401895i
$526$	−271.095	−	72.6398i	−0.515391	−	0.138099i
$527$	405.211	−	21.2362i	0.768902	−	0.0402964i
$528$	−206.601	−	32.7224i	−0.391290	−	0.0619742i
$529$	103.159	+	45.9294i	0.195008	+	0.0868231i
$530$	40.7073	−	80.9223i	0.0768063	−	0.152684i
$531$	185.462	+	71.1922i	0.349269	+	0.134072i
$532$		−	210.235i		−	0.395179i
$533$	822.376	+	173.778i	1.54292	+	0.326038i
$534$	−178.953	+	550.762i	−0.335118	+	1.03139i
$535$	−586.041	+	815.432i	−1.09540	+	1.52417i
$536$	142.413	+	30.2709i	0.265696	+	0.0564755i
$537$	−79.8824	−	375.817i	−0.148757	−	0.699846i
$538$	−369.075	−	724.350i	−0.686013	−	1.34638i
$539$	8.55641	+	163.266i	0.0158746	+	0.302906i
$540$	−216.648	−	44.8827i	−0.401200	−	0.0831161i
$541$	−88.3754	+	45.0295i	−0.163356	+	0.0832339i	−0.533757	−	0.845638i	$-0.679220\pi$
$541$	−88.3754	+	45.0295i	−0.163356	+	0.0832339i	0.370401	+	0.928872i	$0.379220\pi$
$542$	11.9086	−	113.303i	0.0219717	−	0.209046i
$543$	633.536	+	365.772i	1.16673	+	0.673613i
$544$	291.263	+	111.806i	0.535411	+	0.205525i
$545$	−152.702	−	391.748i	−0.280187	−	0.718803i
$546$	−713.222	+	192.018i	−1.30627	+	0.351681i
$547$	−176.474	+	128.216i	−0.322622	+	0.234399i	−0.737294	−	0.675572i	$-0.763897\pi$
$547$	−176.474	+	128.216i	−0.322622	+	0.234399i	0.414671	+	0.909971i	$0.363897\pi$
$548$	263.670	−	171.229i	0.481149	−	0.312462i
$549$	79.5768	−	137.831i	0.144949	−	0.251058i
$550$	197.024	+	140.063i	0.358226	+	0.254660i
$551$	425.378	−	425.378i	0.772011	−	0.772011i
$552$	−16.0307	−	305.883i	−0.0290411	−	0.554137i
$553$	333.931	+	869.921i	0.603854	+	1.57309i
$554$	−411.101	−	65.1120i	−0.742060	−	0.117531i
$555$	−934.118	−	44.1228i	−1.68310	−	0.0795005i
$556$	−129.284	−	290.377i	−0.232526	−	0.522261i
$557$	−238.919	+	64.0181i	−0.428939	+	0.114934i	−0.466828	−	0.884348i	$-0.654603\pi$
$557$	−238.919	+	64.0181i	−0.428939	+	0.114934i	0.0378892	+	0.999282i	$0.487937\pi$
$558$	98.9514	−	136.195i	0.177332	−	0.244077i
$559$	−277.959	+	107.078i	−0.497244	+	0.191554i
$560$	866.968	−	337.941i	1.54816	−	0.603466i
$561$	120.332	−	78.1447i	0.214496	−	0.139295i
$562$	335.269	+	372.354i	0.596564	+	0.662551i
$563$	116.841	+	549.694i	0.207533	+	0.976366i	0.951381	+	0.308017i	$0.0996654\pi$
$563$	116.841	+	549.694i	0.207533	+	0.976366i	−0.743848	+	0.668349i	$0.767001\pi$
$564$	−24.8224	−	12.6476i	−0.0440113	−	0.0224249i
$565$	−666.009	+	73.4770i	−1.17878	+	0.130048i
$566$	−177.577	−	115.320i	−0.313740	−	0.203745i
$567$	79.1163	+	499.521i	0.139535	+	0.880989i
$568$	−142.219	−	246.330i	−0.250385	−	0.433680i
$569$	−270.013	−	606.459i	−0.474539	−	1.06583i	−0.979271	−	0.202556i	$-0.935075\pi$
$569$	−270.013	−	606.459i	−0.474539	−	1.06583i	0.504731	−	0.863276i	$-0.331592\pi$
$570$	−135.530	+	424.560i	−0.237771	+	0.744842i
$571$	316.112	+	435.091i	0.553612	+	0.761981i	0.990497	−	0.137536i	$-0.0439184\pi$
$571$	316.112	+	435.091i	0.553612	+	0.761981i	−0.436885	+	0.899517i	$0.643918\pi$
$572$	80.9069	−	0.0963203i	0.141446	−	0.000168392i
$573$	116.345	+	358.073i	0.203045	+	0.624909i
$574$	−369.970	−	1380.75i	−0.644547	−	2.40548i
$575$	−202.596	+	467.978i	−0.352342	+	0.813875i
$576$	−51.8845	+	29.9555i	−0.0900772	+	0.0520061i
$577$	−377.851	−	192.525i	−0.654855	−	0.333665i	0.0947977	−	0.995497i	$-0.469780\pi$
$577$	−377.851	−	192.525i	−0.654855	−	0.333665i	−0.749653	+	0.661831i	$0.769780\pi$
$578$	230.723	−	88.5662i	0.399175	−	0.153229i
$579$	107.743	+	280.679i	0.186084	+	0.484765i
$580$	−281.664	−	123.667i	−0.485627	−	0.213219i
$581$	45.7282	−	435.075i	0.0787061	−	0.748838i
$582$	584.178	+	337.275i	1.00374	+	0.579511i
$583$	29.6761	+	11.3916i	0.0509024	+	0.0195396i
$584$	−621.968	−	202.090i	−1.06501	−	0.346044i
$585$	−155.543	−	7.16144i	−0.265885	−	0.0122418i
$586$	−246.823	−	759.642i	−0.421199	−	1.29632i
$587$	−1103.31	−	57.8223i	−1.87958	−	0.0985047i	−0.922092	−	0.386970i	$-0.873522\pi$
$587$	−1103.31	−	57.8223i	−1.87958	−	0.0985047i	−0.957490	+	0.288466i	$0.906855\pi$
$588$	103.132	+	114.539i	0.175394	+	0.194795i
$589$	−328.680	−	295.945i	−0.558030	−	0.502453i
$590$	−968.579	−	96.7511i	−1.64166	−	0.163985i
$591$	102.342	−	157.593i	0.173168	−	0.266655i
$592$	1117.65	−	905.051i	1.88791	−	1.52880i
$593$	650.129	+	650.129i	1.09634	+	1.09634i	0.994835	+	0.101505i	$0.0323656\pi$
$593$	650.129	+	650.129i	1.09634	+	1.09634i	0.101505	+	0.994835i	$0.467634\pi$
$594$	29.5998	−	281.623i	0.0498313	−	0.474113i
$595$	−286.825	+	570.181i	−0.482059	+	0.958287i
$596$	10.3955	−	12.8374i	0.0174422	−	0.0215393i
$597$	−595.611	−	819.789i	−0.997674	−	1.37318i
$598$	130.151	+	608.750i	0.217645	+	1.01798i
$599$	1135.67			1.89594			0.947972	−	0.318354i	$-0.103130\pi$
$599$	1135.67			1.89594			0.947972	+	0.318354i	$0.103130\pi$
$600$	−374.671	+	23.5153i	−0.624452	+	0.0391922i
$601$	425.604	−	737.169i	0.708160	−	1.22657i	−0.257378	−	0.966311i	$-0.582859\pi$
$601$	425.604	−	737.169i	0.708160	−	1.22657i	0.965539	−	0.260259i	$-0.0838080\pi$
$602$	376.457	+	338.963i	0.625343	+	0.563062i
$603$	−9.33750	+	58.9546i	−0.0154851	+	0.0977689i
$604$	201.951	−	77.5215i	0.334355	−	0.128347i
$605$	257.758	−	451.818i	0.426046	−	0.746806i
$606$	−136.604	−	862.482i	−0.225419	−	1.42324i
$607$	−374.826	−	649.217i	−0.617505	−	1.06955i	−0.989939	−	0.141492i	$-0.954810\pi$
$607$	−374.826	−	649.217i	−0.617505	−	1.06955i	0.372434	−	0.928059i	$-0.378523\pi$
$608$	−138.315	−	310.661i	−0.227492	−	0.510956i
$609$	−51.5758	+	984.126i	−0.0846894	+	1.61597i
$610$	−197.947	+	754.297i	−0.324503	+	1.23655i
$611$	−88.7368	−	28.7156i	−0.145232	−	0.0469977i
$612$	−15.1607	+	46.6598i	−0.0247724	+	0.0762415i
$613$	117.647	+	6.16559i	0.191919	+	0.0100581i	0.148053	−	0.988979i	$-0.452699\pi$
$613$	117.647	+	6.16559i	0.191919	+	0.0100581i	0.0438659	+	0.999037i	$0.486033\pi$
$614$	142.923	+	30.3792i	0.232773	+	0.0494775i
$615$	−39.1995	+	829.888i	−0.0637390	+	1.34941i
$616$	102.901	+	201.955i	0.167047	+	0.327849i
$617$	423.725	+	523.257i	0.686750	+	0.848066i	0.994645	−	0.103355i	$-0.0329576\pi$
$617$	423.725	+	523.257i	0.686750	+	0.848066i	−0.307894	+	0.951421i	$0.599624\pi$
$618$	82.6469	−	308.443i	0.133733	−	0.499098i
$619$	39.7917	+	251.235i	0.0642838	+	0.405872i	0.998757	+	0.0498392i	$0.0158709\pi$
$619$	39.7917	+	251.235i	0.0642838	+	0.405872i	−0.934473	+	0.356033i	$0.884129\pi$
$620$	−79.9585	+	211.556i	−0.128965	+	0.341219i
$621$	594.094	−	62.4418i	0.956673	−	0.100550i
$622$	−106.865	+	131.967i	−0.171808	+	0.212166i
$623$	859.750	−	279.350i	1.38002	−	0.448395i
$624$	−512.569	+	416.082i	−0.821425	+	0.666797i
$625$	576.091	+	242.372i	0.921746	+	0.387795i
$626$	365.148	+	1362.75i	0.583304	+	2.17692i
$627$	−152.974	−	32.5156i	−0.243978	−	0.0518591i
$628$	−18.3105	+	41.1261i	−0.0291569	+	0.0654874i
$629$	−154.317	+	974.316i	−0.245336	+	1.54899i
$630$	108.952	+	241.351i	0.172940	+	0.383096i
$631$	−542.859	+	439.599i	−0.860315	+	0.696670i	−0.954283	−	0.298906i	$-0.903378\pi$
$631$	−542.859	+	439.599i	−0.860315	+	0.696670i	0.0939673	+	0.995575i	$0.470045\pi$
$632$	408.803	+	408.803i	0.646841	+	0.646841i
$633$	56.2047	−	534.752i	0.0887911	−	0.844791i
$634$	−345.242	+	310.857i	−0.544545	+	0.490311i
$635$	44.0338	−	137.940i	0.0693445	−	0.217228i
$636$	28.5004	−	9.26034i	0.0448119	−	0.0145603i
$637$	401.392	+	324.251i	0.630129	+	0.509028i
$638$	121.665	−	374.447i	0.190698	−	0.586908i
$639$	97.7982	−	63.5109i	0.153049	−	0.0993911i
$640$	530.329	−	535.831i	0.828640	−	0.837236i
$641$	−136.286	−	641.174i	−0.212614	−	1.00027i	−0.946924	−	0.321457i	$-0.895827\pi$
$641$	−136.286	−	641.174i	−0.212614	−	1.00027i	0.734310	−	0.678815i	$-0.237506\pi$
$642$	−1196.73	+	189.543i	−1.86406	+	0.295238i
$643$	22.3410	+	5.98625i	0.0347449	+	0.00930988i	0.276150	−	0.961115i	$-0.410941\pi$
$643$	22.3410	+	5.98625i	0.0347449	+	0.00930988i	−0.241405	+	0.970425i	$0.577608\pi$
$644$	225.574	−	182.666i	0.350270	−	0.283643i
$645$	−148.526	−	254.217i	−0.230273	−	0.394134i
$646$	429.472	+	191.213i	0.664818	+	0.295996i
$647$	−773.265	+	81.2735i	−1.19516	+	0.125616i	−0.681132	−	0.732160i	$-0.738512\pi$
$647$	−773.265	+	81.2735i	−1.19516	+	0.125616i	−0.514023	+	0.857776i	$0.671845\pi$
$648$	170.901	+	263.164i	0.263736	+	0.406117i
$649$		−	341.581i		−	0.526319i
$650$	744.405	−	167.206i	1.14524	−	0.257241i
$651$	724.529			1.11295
$652$	−67.0439	+	43.5388i	−0.102828	+	0.0667774i
$653$	−12.0061	−	114.231i	−0.0183861	−	0.174932i	0.981475	−	0.191590i	$-0.0613642\pi$
$653$	−12.0061	−	114.231i	−0.0183861	−	0.174932i	−0.999861	+	0.0166573i	$0.994698\pi$
$654$	206.347	−	463.464i	0.315516	−	0.708660i
$655$	−174.124	−	155.163i	−0.265838	−	0.236889i
$656$	−804.064	−	992.937i	−1.22571	−	1.51362i
$657$	69.3922	−	258.975i	0.105620	−	0.394178i
$658$	24.8128	+	156.662i	0.0377094	+	0.238088i
$659$	−945.195	+	200.907i	−1.43429	+	0.304867i	−0.858534	−	0.512756i	$-0.828624\pi$
$659$	−945.195	+	200.907i	−1.43429	+	0.304867i	−0.575753	+	0.817623i	$0.695291\pi$
$660$	12.9176	+	78.9208i	0.0195722	+	0.119577i
$661$	−420.449	−	647.435i	−0.636081	−	0.979479i	−0.998866	−	0.0476059i	$-0.984841\pi$
$661$	−420.449	−	647.435i	−0.636081	−	0.979479i	0.362785	−	0.931873i	$-0.381826\pi$
$662$	−1264.74	−	410.938i	−1.91048	−	0.620752i
$663$	70.3077	−	447.352i	0.106045	−	0.674738i
$664$	−83.8752	−	258.141i	−0.126318	−	0.388767i
$665$	660.528	−	218.393i	0.993275	−	0.328411i
$666$	273.853	+	304.144i	0.411190	+	0.456673i
$667$	826.010	+	86.8172i	1.23840	+	0.130161i
$668$	−25.3436	+	25.3436i	−0.0379396	+	0.0379396i
$669$	−378.592	−	467.522i	−0.565907	−	0.698837i
$670$	−32.0723	−	290.709i	−0.0478691	−	0.433894i
$671$	−270.288	−	42.8094i	−0.402814	−	0.0637994i
$672$	508.912	+	226.582i	0.757309	+	0.337176i
$673$	167.687	−	788.904i	0.249163	−	1.17222i	−0.658520	−	0.752564i	$-0.728817\pi$
$673$	167.687	−	788.904i	0.249163	−	1.17222i	0.907683	−	0.419657i	$-0.137850\pi$
$674$	−107.745	+	28.8701i	−0.159859	+	0.0428340i
$675$	−84.0398	−	727.299i	−0.124503	−	1.07748i
$676$	170.413	−	190.171i	0.252090	−	0.281319i
$677$	11.9374	+	36.7396i	0.0176328	+	0.0542683i	0.959486	−	0.281757i	$-0.0909172\pi$
$677$	11.9374	+	36.7396i	0.0176328	+	0.0542683i	−0.941853	+	0.336025i	$0.890917\pi$
$678$	−628.309	−	508.795i	−0.926710	−	0.750435i
$679$	−110.067	−	1047.22i	−0.162102	−	1.54230i
$680$	−18.6842	+	395.562i	−0.0274768	+	0.581708i
$681$	480.473	−	76.0995i	0.705541	−	0.111747i
$682$	−279.600	−	74.9186i	−0.409971	−	0.109851i
$683$	543.575	−	440.178i	0.795863	−	0.644477i	−0.142630	−	0.989776i	$-0.545556\pi$
$683$	543.575	−	440.178i	0.795863	−	0.644477i	0.938493	+	0.345299i	$0.112222\pi$
$684$	47.6475	−	24.2776i	0.0696601	−	0.0354936i
$685$	811.878	+	650.538i	1.18522	+	0.949690i
$686$	−42.7842	+	201.284i	−0.0623677	+	0.293417i
$687$	2.20744	−	42.1204i	0.00321315	−	0.0613106i
$688$	430.623	+	139.918i	0.625905	+	0.203369i
$689$	89.3365	−	45.6533i	0.129661	−	0.0662602i
$690$	−573.293	+	223.467i	−0.830859	+	0.323866i
$691$	335.993	+	17.6086i	0.486242	+	0.0254829i	0.293882	−	0.955842i	$-0.405053\pi$
$691$	335.993	+	17.6086i	0.486242	+	0.0254829i	0.192360	+	0.981325i	$0.438386\pi$
$692$	191.583	−	85.2984i	0.276855	−	0.123264i
$693$	−80.4741	+	46.4618i	−0.116124	+	0.0670444i
$694$	163.139	−	25.8387i	0.235071	−	0.0372315i
$695$	778.021	−	707.837i	1.11946	−	1.01847i
$696$	219.117	+	570.820i	0.314824	+	0.820144i
$697$	865.600	+	137.098i	1.24189	+	0.196697i
$698$	−539.908	+	599.628i	−0.773506	+	0.859066i
$699$	214.626	+	123.914i	0.307047	+	0.177274i
$700$	−226.719	−	274.141i	−0.323884	−	0.391629i
$701$		−	310.721i		−	0.443253i	−0.975132	−	0.221627i	$-0.928863\pi$
$701$		−	310.721i		−	0.443253i	0.975132	−	0.221627i	$-0.0711366\pi$
$702$	−598.818	−	663.465i	−0.853018	−	0.945107i
$703$	869.882	−	632.006i	1.23738	−	0.899013i
$704$	80.0570	+	64.8289i	0.113717	+	0.0920865i
$705$	13.9514	−	91.1266i	0.0197892	−	0.129258i
$706$	−144.318	−	15.1685i	−0.204417	−	0.0214851i
$707$	−963.881	+	963.881i	−1.36334	+	1.36334i
$708$	−202.654	−	250.257i	−0.286234	−	0.353470i
$709$	471.043	+	305.899i	0.664376	+	0.431451i	0.832282	−	0.554352i	$-0.187034\pi$
$709$	471.043	+	305.899i	0.664376	+	0.431451i	−0.167906	+	0.985803i	$0.553701\pi$
$710$	−380.134	+	426.588i	−0.535400	+	0.600828i
$711$	−158.596	+	176.139i	−0.223061	+	0.247734i
$712$	416.813	−	375.300i	0.585411	−	0.527106i
$713$	31.9581	−	609.796i	0.0448220	−	0.855254i
$714$	−732.432	+	237.982i	−1.02581	+	0.333307i
$715$	84.3491	+	254.098i	0.117971	+	0.355381i
$716$	69.8057	−	214.840i	0.0974940	−	0.300056i
$717$	280.849	−	731.637i	0.391700	−	1.02041i
$718$	−446.881	+	774.021i	−0.622397	+	1.07802i
$719$	−939.453	−	98.7405i	−1.30661	−	0.137330i	−0.574494	−	0.818509i	$-0.694801\pi$
$719$	−939.453	−	98.7405i	−1.30661	−	0.137330i	−0.732117	+	0.681179i	$0.761468\pi$
$720$	176.707	+	157.464i	0.245426	+	0.218700i
$721$	−465.362	+	178.636i	−0.645440	+	0.247761i
$722$	120.068	+	312.789i	0.166300	+	0.433226i
$723$	130.899	−	256.903i	0.181049	−	0.355330i
$724$	215.054	+	372.484i	0.297035	+	0.514480i
$725$	95.9504	−	1013.41i	0.132345	−	1.39781i
$726$	606.253	−	162.445i	0.835060	−	0.223754i
$727$	973.234	−	316.223i	1.33870	−	0.434970i	0.449823	−	0.893118i	$-0.351487\pi$
$727$	973.234	−	316.223i	1.33870	−	0.434970i	0.888876	+	0.458148i	$0.151487\pi$
$728$	691.213	+	184.328i	0.949469	+	0.253198i
$729$	−652.066	+	473.753i	−0.894466	+	0.649868i
$730$	6.77910	+	1313.70i	0.00928643	+	1.79959i
$731$	−283.726	+	126.323i	−0.388134	+	0.172808i
$732$	−223.422	+	128.993i	−0.305222	+	0.176220i
$733$	−0.948166	+	0.150175i	−0.00129354	+	0.000204877i	−0.157081	−	0.987586i	$-0.550208\pi$
$733$	−0.948166	+	0.150175i	−0.00129354	+	0.000204877i	0.155788	+	0.987791i	$0.450208\pi$
$734$	431.403	−	664.302i	0.587742	−	0.905043i
$735$	−252.732	+	443.008i	−0.343853	+	0.602732i
$736$	213.149	−	418.329i	0.289605	−	0.568382i
$737$	100.391	−	21.3387i	0.136215	−	0.0289534i
$738$	270.207	−	243.296i	0.366135	−	0.329669i
$739$	492.509	+	758.397i	0.666453	+	1.02625i	0.996606	+	0.0823202i	$0.0262330\pi$
$739$	492.509	+	758.397i	0.666453	+	1.02625i	−0.330153	+	0.943927i	$0.607100\pi$
$740$	−462.658	−	297.071i	−0.625214	−	0.401447i
$741$	−398.980	+	290.603i	−0.538435	+	0.392176i
$742$	−138.033	−	100.287i	−0.186028	−	0.135157i
$743$	67.7244	+	252.751i	0.0911499	+	0.340176i	0.996408	−	0.0846869i	$-0.0269890\pi$
$743$	67.7244	+	252.751i	0.0911499	+	0.340176i	−0.905258	+	0.424863i	$0.860322\pi$
$744$	410.664	−	182.840i	0.551968	−	0.245752i
$745$	51.1322	+	19.3257i	0.0686338	+	0.0259405i
$746$	−53.6111	+	338.487i	−0.0718647	+	0.453736i
$747$	103.886	−	39.8779i	0.139070	−	0.0533841i
$748$	84.2425	−	4.41496i	0.112624	−	0.00590236i
$749$	1337.42	+	1337.42i	1.78561	+	1.78561i
$750$	281.121	+	699.769i	0.374828	+	0.933026i
$751$	−47.1252	−	27.2078i	−0.0627500	−	0.0362287i	0.468297	−	0.883571i	$-0.344868\pi$
$751$	−47.1252	−	27.2078i	−0.0627500	−	0.0362287i	−0.531047	+	0.847343i	$0.678201\pi$
$752$	77.2148	+	118.900i	0.102679	+	0.158112i
$753$	−174.724	−	240.486i	−0.232037	−	0.319371i
$754$	−622.594	−	1075.41i	−0.825722	−	1.42627i
$755$	453.348	+	553.969i	0.600461	+	0.733734i
$756$	−149.342	+	389.049i	−0.197542	+	0.514615i
$757$	−489.411	+	847.684i	−0.646514	+	1.11979i	0.337436	+	0.941348i	$0.390440\pi$
$757$	−489.411	+	847.684i	−0.646514	+	1.11979i	−0.983950	+	0.178446i	$0.942893\pi$
$758$	−977.025	−	102.689i	−1.28895	−	0.135474i
$759$	−98.0259	−	192.387i	−0.129151	−	0.253474i
$760$	319.276	−	290.474i	0.420100	−	0.382203i
$761$	−260.574	+	13.6561i	−0.342409	+	0.0179449i	−0.222766	−	0.974872i	$-0.571509\pi$
$761$	−260.574	+	13.6561i	−0.342409	+	0.0179449i	−0.119644	+	0.992817i	$0.538175\pi$
$762$	155.671	−	79.3182i	0.204292	−	0.104092i
$763$	−774.638	+	164.654i	−1.01525	+	0.215799i
$764$	−46.0235	+	216.524i	−0.0602402	+	0.283408i
$765$	−162.347	+	0.837762i	−0.212219	+	0.00109511i
$766$	738.242	+	239.869i	0.963762	+	0.313145i
$767$	−802.027	−	720.421i	−1.04567	−	0.939271i
$768$	652.564			0.849692
$769$	378.186	−	985.209i	0.491790	−	1.28116i	−0.433246	−	0.901276i	$-0.642632\pi$
$769$	378.186	−	985.209i	0.491790	−	1.28116i	0.925036	−	0.379880i	$-0.124035\pi$
$770$	320.292	−	323.614i	0.415963	−	0.420279i
$771$	−266.532	+	598.641i	−0.345697	+	0.776448i
$772$	−27.6520	+	174.588i	−0.0358187	+	0.226150i
$773$	−5.03319	−	96.0389i	−0.00651124	−	0.124242i	−0.999951	−	0.00988630i	$-0.996853\pi$
$773$	−5.03319	−	96.0389i	−0.00651124	−	0.124242i	0.993440	−	0.114355i	$-0.0364803\pi$
$774$	−33.3497	+	124.463i	−0.0430874	+	0.160804i
$775$	−747.737	−	31.4529i	−0.964822	−	0.0405844i
$776$	−326.659	−	565.790i	−0.420952	−	0.729111i
$777$	−366.216	+	1722.91i	−0.471320	+	2.21739i
$778$	−738.926	+	912.498i	−0.949777	+	1.17288i
$779$	−561.486	−	772.819i	−0.720778	−	0.992065i
$780$	212.549	+	136.120i	0.272499	+	0.174513i
$781$	−162.214	−	117.855i	−0.207700	−	0.150903i
$782$	167.989	+	626.945i	0.214820	+	0.801720i
$783$	−1089.35	+	485.009i	−1.39125	+	0.619425i
$784$	−163.076	−	767.211i	−0.208005	−	0.978586i
$785$	−148.233	−	14.8070i	−0.188832	−	0.0188624i
$786$	−14.7279	−	281.026i	−0.0187378	−	0.357539i
$787$	−1018.58	−	661.472i	−1.29425	−	0.840498i	−0.300685	−	0.953724i	$-0.597215\pi$
$787$	−1018.58	−	661.472i	−1.29425	−	0.840498i	−0.993569	+	0.113225i	$0.963882\pi$
$788$	98.4379	−	50.1566i	0.124921	−	0.0636505i
$789$	205.587	−	228.327i	0.260566	−	0.289388i
$790$	521.903	−	1037.49i	0.660636	−	1.31328i
$791$	−66.0510	+	1260.33i	−0.0835032	+	1.59334i
$792$	−33.8880	+	46.6428i	−0.0427879	+	0.0588924i
$793$	−670.574	+	544.343i	−0.845617	+	0.686436i
$794$	−1186.41	−	861.976i	−1.49422	−	1.08561i
$795$	58.7009	+	79.9243i	0.0738377	+	0.100534i
$796$	−62.2752	−	592.509i	−0.0782352	−	0.744358i
$797$	325.320	−	730.680i	0.408180	−	0.916788i	−0.586125	−	0.810221i	$-0.699347\pi$
$797$	325.320	−	730.680i	0.408180	−	0.916788i	0.994305	−	0.106568i	$-0.0339861\pi$
$798$	747.936	+	381.092i	0.937263	+	0.477559i
$799$	−93.9321	−	25.1690i	−0.117562	−	0.0315007i
$800$	−515.378	−	255.933i	−0.644222	−	0.319916i
$801$	162.594	+	162.594i	0.202989	+	0.202989i
$802$	322.094	−	357.721i	0.401613	−	0.446036i
$803$	−458.478	+	48.1880i	−0.570957	+	0.0600100i
$804$	60.8905	−	75.1935i	0.0757344	−	0.0935243i
$805$	808.237	+	518.965i	1.00402	+	0.644677i
$806$	−765.606	+	498.487i	−0.949884	+	0.618471i
$807$	889.967			1.10281
$808$	−303.088	+	789.572i	−0.375109	+	0.977193i
$809$	−67.9659	−	75.4838i	−0.0840123	−	0.0933051i	0.699673	−	0.714463i	$-0.253329\pi$
$809$	−67.9659	−	75.4838i	−0.0840123	−	0.0933051i	−0.783685	+	0.621158i	$0.786662\pi$
$810$	394.153	−	491.907i	0.486608	−	0.607292i
$811$	97.4747	+	49.6658i	0.120191	+	0.0612402i	0.513052	−	0.858357i	$-0.328515\pi$
$811$	97.4747	+	49.6658i	0.120191	+	0.0612402i	−0.392861	+	0.919598i	$0.628515\pi$
$812$	−315.567	+	485.930i	−0.388629	+	0.598436i
$813$	104.598	+	67.9269i	0.128657	+	0.0835510i
$814$	319.480	−	627.014i	0.392481	−	0.770288i
$815$	−206.438	−	165.414i	−0.253298	−	0.202962i
$816$	−511.544	+	460.597i	−0.626892	+	0.564457i
$817$	316.041	+	121.317i	0.386831	+	0.148490i
$818$			157.298i			0.192296i
$819$	−60.6348	+	286.943i	−0.0740351	+	0.350358i
$820$	−263.923	+	411.034i	−0.321858	+	0.501261i
$821$	−641.976	−	519.862i	−0.781944	−	0.633206i	0.152909	−	0.988240i	$-0.451136\pi$
$821$	−641.976	−	519.862i	−0.781944	−	0.633206i	−0.934853	+	0.355035i	$0.884469\pi$
$822$	131.214	+	1248.42i	0.159628	+	1.51876i
$823$	−52.9606	−	47.6859i	−0.0643507	−	0.0579416i	0.636328	−	0.771419i	$-0.280453\pi$
$823$	−52.9606	−	47.6859i	−0.0643507	−	0.0579416i	−0.700678	+	0.713477i	$0.747119\pi$
$824$	−218.688	+	218.688i	−0.265398	+	0.265398i
$825$	−234.539	+	122.569i	−0.284289	+	0.148568i
$826$	−474.526	+	1770.96i	−0.574487	+	2.14401i
$827$	421.744	−	827.720i	0.509969	−	1.00087i	−0.482211	−	0.876055i	$-0.660166\pi$
$827$	421.744	−	827.720i	0.509969	−	1.00087i	0.992180	−	0.124815i	$-0.0398338\pi$
$828$	67.4482	+	30.0299i	0.0814591	+	0.0362679i
$829$	−711.166	+	74.7465i	−0.857860	+	0.0901647i	−0.523237	−	0.852187i	$-0.675276\pi$
$829$	−711.166	+	74.7465i	−0.857860	+	0.0901647i	−0.334623	+	0.942352i	$0.608609\pi$
$830$	−439.452	+	322.759i	−0.529460	+	0.388866i
$831$	267.826	−	368.631i	0.322294	−	0.443600i
$832$	321.064	−	51.2434i	0.385894	−	0.0615906i
$833$	435.258	+	316.233i	0.522519	+	0.379632i
$834$	1267.40	+	66.4218i	1.51967	+	0.0796424i
$835$	−105.953	−	53.2989i	−0.126890	−	0.0638310i
$836$	−68.3318	−	61.5262i	−0.0817366	−	0.0735960i
$837$	398.009	+	781.137i	0.475519	+	0.933258i
$838$	228.265	−	351.497i	0.272392	−	0.419447i
$839$	−1031.77	+	54.0727i	−1.22976	+	0.0644490i	−0.656119	−	0.754658i	$-0.727803\pi$
$839$	−1031.77	+	54.0727i	−1.22976	+	0.0644490i	−0.573641	+	0.819107i	$0.694470\pi$
$840$	−70.2816	+	703.592i	−0.0836686	+	0.837609i
$841$	−799.081	+	169.850i	−0.950156	+	0.201962i
$842$	83.1146	+	186.678i	0.0987109	+	0.221708i
$843$	−529.824	+	141.966i	−0.628499	+	0.168406i
$844$	185.820	−	255.760i	0.220166	−	0.303033i
$845$	774.516	+	337.861i	0.916587	+	0.399836i
$846$	−32.6403	+	23.7146i	−0.0385819	+	0.0280314i
$847$	−761.415	−	616.582i	−0.898955	−	0.727960i
$848$	−149.169	−	31.7069i	−0.175907	−	0.0373902i
$849$	200.739	−	115.897i	0.236442	−	0.136510i
$850$	766.225	−	213.809i	0.901441	−	0.251540i
$851$	1433.93	+	384.220i	1.68499	+	0.451492i
$852$	−188.766	+	9.89281i	−0.221556	+	0.0116113i
$853$	−1309.66	−	207.429i	−1.53535	−	0.243176i	−0.669249	−	0.743038i	$-0.733384\pi$
$853$	−1309.66	−	207.429i	−1.53535	−	0.243176i	−0.866105	+	0.499861i	$0.833384\pi$
$854$	1341.86	+	597.434i	1.57126	+	0.699572i
$855$	125.773	+	124.482i	0.147103	+	0.145593i
$856$	1095.56	+	420.546i	1.27986	+	0.491292i
$857$		−	425.282i		−	0.496245i	−0.968729	−	0.248123i	$-0.920186\pi$
$857$		−	425.282i		−	0.496245i	0.968729	−	0.248123i	$-0.0798136\pi$
$858$	−146.317	+	288.010i	−0.170533	+	0.335676i
$859$	−452.985	+	1394.15i	−0.527340	+	1.62299i	0.232301	+	0.972644i	$0.425375\pi$
$859$	−452.985	+	1394.15i	−0.527340	+	1.62299i	−0.759641	+	0.650343i	$0.774625\pi$
$860$	−0.893266	−	173.103i	−0.00103868	−	0.201283i
$861$	1530.67	+	325.353i	1.77778	+	0.377878i
$862$	212.168	+	998.174i	0.246135	+	1.15797i
$863$	−47.0969	−	92.4328i	−0.0545734	−	0.107106i	0.862109	−	0.506723i	$-0.169143\pi$
$863$	−47.0969	−	92.4328i	−0.0545734	−	0.107106i	−0.916682	+	0.399617i	$0.869143\pi$
$864$	35.2780	+	673.143i	0.0408310	+	0.779101i
$865$	467.013	+	513.318i	0.539899	+	0.593432i
$866$	837.479	−	426.717i	0.967066	−	0.492744i
$867$	−28.2800	+	269.066i	−0.0326182	+	0.310342i
$868$	368.912	+	212.991i	0.425013	+	0.245382i
$869$	380.473	+	146.050i	0.437828	+	0.168067i
$870$	950.530	−	777.879i	1.09256	−	0.894114i
$871$	161.629	−	280.720i	0.185567	−	0.322297i
$872$	−397.515	+	288.811i	−0.455866	+	0.331206i
$873$	224.630	−	145.877i	0.257308	−	0.167098i
$874$	353.735	−	612.687i	0.404731	−	0.701015i
$875$	625.792	−	997.095i	0.715191	−	1.13954i
$876$	−307.312	+	307.312i	−0.350812	+	0.350812i
$877$	13.6010	+	259.523i	0.0155086	+	0.295921i	0.995362	+	0.0962021i	$0.0306695\pi$
$877$	13.6010	+	259.523i	0.0155086	+	0.295921i	−0.979853	+	0.199719i	$0.935997\pi$
$878$	−308.592	−	803.909i	−0.351471	−	0.915614i
$879$	863.631	+	136.786i	0.982515	+	0.155615i
$880$	143.882	−	380.687i	0.163503	−	0.432599i
$881$	581.925	+	1307.03i	0.660528	+	1.48357i	0.863481	+	0.504382i	$0.168280\pi$
$881$	581.925	+	1307.03i	0.660528	+	1.48357i	−0.202952	+	0.979189i	$0.565054\pi$
$882$	215.605	−	57.7712i	0.244450	−	0.0655003i
$883$	−820.186	+	1128.89i	−0.928863	+	1.27847i	0.0314384	+	0.999506i	$0.489991\pi$
$883$	−820.186	+	1128.89i	−0.928863	+	1.27847i	−0.960301	+	0.278965i	$0.910009\pi$
$884$	167.308	−	207.112i	0.189262	−	0.234289i
$885$	575.752	−	896.676i	0.650567	−	1.01319i
$886$	−388.880	+	252.541i	−0.438916	+	0.285036i
$887$	571.408	+	634.613i	0.644203	+	0.715460i	0.973480	−	0.228773i	$-0.0734715\pi$
$887$	571.408	+	634.613i	0.644203	+	0.715460i	−0.329277	+	0.944234i	$0.606805\pi$
$888$	227.216	+	1068.97i	0.255874	+	1.20379i
$889$	−243.005	−	123.817i	−0.273347	−	0.139277i
$890$	−978.643	−	558.306i	−1.09960	−	0.627310i
$891$	185.511	+	120.472i	0.208205	+	0.135210i
$892$	−55.3309	−	349.346i	−0.0620302	−	0.391643i
$893$	52.9984	+	91.7960i	0.0593487	+	0.102795i
$894$	26.8266	+	60.2536i	0.0300074	+	0.0673977i
$895$	747.510	−	3.85738i	0.835206	−	0.00430992i
$896$	−834.651	−	1148.80i	−0.931530	−	1.28214i
$897$	−658.465	−	175.595i	−0.734075	−	0.195758i
$898$	49.7063	+	152.980i	0.0553522	+	0.170357i
$899$	315.481	+	1177.39i	0.350924	+	1.30967i
$900$	35.9498	−	83.0406i	0.0399442	−	0.0922673i
$901$	90.5907	−	52.3025i	0.100545	−	0.0580494i
$902$	−557.051	−	283.832i	−0.617573	−	0.314669i
$903$	−517.725	+	198.736i	−0.573339	+	0.220084i
$904$	280.614	+	731.026i	0.310414	+	0.808657i
$905$	−946.890	+	1062.60i	−1.04629	+	1.17415i
$906$	−90.2830	+	858.985i	−0.0996501	+	0.948107i
$907$	91.5482	+	52.8554i	0.100935	+	0.0582750i	0.549618	−	0.835416i	$-0.314773\pi$
$907$	91.5482	+	52.8554i	0.100935	+	0.0582750i	−0.448683	+	0.893691i	$0.648107\pi$
$908$	267.016	+	102.498i	0.294070	+	0.112883i
$909$	−329.760	−	107.146i	−0.362773	−	0.117872i
$910$	−84.3213	−	1434.57i	−0.0926608	−	1.57645i
$911$	408.417	+	1256.98i	0.448317	+	1.37978i	0.878805	+	0.477182i	$0.158342\pi$
$911$	408.417	+	1256.98i	0.448317	+	1.37978i	−0.430488	+	0.902596i	$0.641658\pi$
$912$	749.267	+	39.2674i	0.821565	+	0.0430564i
$913$	−128.028	−	142.189i	−0.140228	−	0.155739i
$914$	−1000.51	−	900.860i	−1.09465	−	0.985623i
$915$	−637.369	−	567.962i	−0.696578	−	0.620723i
$916$	13.5062	−	20.7977i	0.0147448	−	0.0227049i
$917$	−341.392	+	276.454i	−0.372292	+	0.301476i
$918$	−658.926	−	658.926i	−0.717784	−	0.717784i
$919$	−78.4356	+	746.265i	−0.0853489	+	0.812041i	0.865192	+	0.501441i	$0.167197\pi$
$919$	−78.4356	+	746.265i	−0.0853489	+	0.812041i	−0.950541	+	0.310600i	$0.899470\pi$
$920$	589.075	+	90.1868i	0.640299	+	0.0980291i
$921$	−100.664	+	124.310i	−0.109299	+	0.134973i
$922$	1232.84	+	1696.86i	1.33714	+	1.84041i
$923$	−618.843	+	132.309i	−0.670470	+	0.143347i
$924$	150.628			0.163017
$925$	452.741	−	1762.20i	0.489450	−	1.90508i
$926$	660.543	−	1144.09i	0.713329	−	1.23552i
$927$	−94.2251	−	84.8406i	−0.101645	−	0.0915217i
$928$	−146.611	+	925.664i	−0.157986	+	0.997483i
$929$	985.742	−	378.391i	1.06108	−	0.407310i	0.235663	−	0.971835i	$-0.424274\pi$
$929$	985.742	−	378.391i	1.06108	−	0.407310i	0.825416	+	0.564525i	$0.190941\pi$
$930$	−607.693	−	667.947i	−0.653433	−	0.718223i
$931$	−91.7369	−	579.204i	−0.0985359	−	0.622131i
$932$	72.8546	+	126.188i	0.0781702	+	0.135395i
$933$	−75.6104	−	169.824i	−0.0810401	−	0.182019i
$934$	−34.2639	+	653.794i	−0.0366851	+	0.699993i
$935$	101.383	+	260.091i	0.108431	+	0.278172i
$936$	38.0442	+	177.942i	0.0406455	+	0.190109i
$937$	−234.496	+	721.704i	−0.250263	+	0.770229i	0.744464	+	0.667663i	$0.232705\pi$
$937$	−234.496	+	721.704i	−0.250263	+	0.770229i	−0.994726	+	0.102566i	$0.967295\pi$
$938$	−550.127	−	28.8309i	−0.586489	−	0.0307366i
$939$	−1510.72	−	321.113i	−1.60886	−	0.341973i
$940$	33.8924	−	42.2980i	0.0360557	−	0.0449979i
$941$	150.242	+	294.866i	0.159662	+	0.313354i	0.956954	−	0.290240i	$-0.0937351\pi$
$941$	150.242	+	294.866i	0.159662	+	0.313354i	−0.797292	+	0.603593i	$0.793735\pi$
$942$	−113.119	−	139.691i	−0.120084	−	0.148292i
$943$	341.348	−	1273.93i	0.361981	−	1.35093i
$944$	256.357	+	1618.57i	0.271565	+	1.71459i
$945$	−1377.47	−	65.0644i	−1.45764	−	0.0688512i
$946$	220.343	−	23.1590i	0.232921	−	0.0244810i
$947$	274.825	−	339.380i	0.290205	−	0.358374i	−0.611104	−	0.791551i	$-0.709274\pi$
$947$	274.825	−	339.380i	0.290205	−	0.358374i	0.901309	+	0.433177i	$0.142607\pi$
$948$	365.399	−	118.725i	0.385442	−	0.125238i
$949$	−853.822	+	1178.13i	−0.899707	+	1.24145i
$950$	−755.350	−	425.769i	−0.795106	−	0.448178i
$951$	−131.629	−	491.247i	−0.138411	−	0.516558i
$952$	729.584	+	155.078i	0.766370	+	0.162897i
$953$	−343.551	+	771.628i	−0.360494	+	0.809683i	0.638697	+	0.769459i	$0.279474\pi$
$953$	−343.551	+	771.628i	−0.360494	+	0.809683i	−0.999191	+	0.0402241i	$0.987193\pi$
$954$	6.78909	−	42.8646i	0.00711644	−	0.0449315i
$955$	−728.095	+	80.3266i	−0.762403	+	0.0841116i
$956$	358.082	−	289.969i	0.374563	−	0.303315i
$957$	304.772	+	304.772i	0.318466	+	0.318466i
$958$	−2.21394	+	21.0643i	−0.00231101	+	0.0219878i
$959$	1456.23	−	1311.19i	1.51848	−	1.36725i
$960$	100.883	+	305.121i	0.105087	+	0.317834i
$961$	−61.6658	+	20.0364i	−0.0641684	+	0.0208496i
$962$	−798.412	−	2072.56i	−0.829950	−	2.15442i
$963$	−148.669	+	457.555i	−0.154381	+	0.475135i
$964$	142.173	−	92.3280i	0.147482	−	0.0957760i
$965$	−577.255	+	94.4842i	−0.598191	+	0.0979111i
$966$	240.959	+	1133.62i	0.249440	+	1.17352i
$967$	−144.150	+	22.8311i	−0.149069	+	0.0236102i	−0.230523	−	0.973067i	$-0.574044\pi$
$967$	−144.150	+	22.8311i	−0.149069	+	0.0236102i	0.0814538	+	0.996677i	$0.474044\pi$
$968$	−587.170	−	157.332i	−0.606581	−	0.162533i
$969$	−399.957	+	323.879i	−0.412752	+	0.334240i
$970$	−873.119	+	979.818i	−0.900123	+	1.01012i
$971$	−720.338	−	320.715i	−0.741852	−	0.330294i	0.000774589	−	1.00000i	$-0.499753\pi$
$971$	−720.338	−	320.715i	−0.741852	−	0.330294i	−0.742626	+	0.669706i	$0.766420\pi$
$972$	−188.678	+	19.8308i	−0.194113	+	0.0204021i
$973$	−1079.02	−	1661.54i	−1.10896	−	1.70765i
$974$			242.960i			0.249445i
$975$	−206.871	+	809.200i	−0.212176	+	0.829949i
$976$	1312.88			1.34517
$977$	−449.809	+	292.110i	−0.460398	+	0.298986i	−0.753920	−	0.656966i	$-0.771839\pi$
$977$	−449.809	+	292.110i	−0.460398	+	0.298986i	0.293522	+	0.955952i	$0.405173\pi$
$978$	−33.3642	−	317.439i	−0.0341147	−	0.324580i
$979$	160.814	−	361.194i	0.164263	−	0.368941i
$980$	−258.917	+	151.272i	−0.264201	+	0.154360i
$981$	−126.771	−	156.549i	−0.129226	−	0.159581i
$982$	98.8660	−	368.973i	0.100678	−	0.375736i
$983$	−115.176	−	727.191i	−0.117168	−	0.739767i	−0.974397	−	0.224833i	$-0.927816\pi$
$983$	−115.176	−	727.191i	−0.117168	−	0.739767i	0.857230	−	0.514934i	$-0.172184\pi$
$984$	949.690	−	201.863i	0.965132	−	0.205145i
$985$	259.842	+	257.174i	0.263799	+	0.261091i
$986$	−705.652	−	1086.61i	−0.715671	−	1.10204i
$987$	−165.141	−	53.6576i	−0.167316	−	0.0543643i
$988$	−288.580	+	30.6783i	−0.292085	+	0.0310510i
$989$	144.429	+	444.507i	0.146035	+	0.449451i
$990$	110.330	+	35.2201i	0.111445	+	0.0355759i
$991$	−847.761	−	941.534i	−0.855461	−	0.950085i	0.143758	−	0.989613i	$-0.454081\pi$
$991$	−847.761	−	941.534i	−0.855461	−	0.950085i	−0.999218	+	0.0395276i	$0.987415\pi$
$992$	685.263	+	72.0240i	0.690789	+	0.0726049i
$993$	1029.40	−	1029.40i	1.03666	−	1.03666i
$994$	677.286	+	836.378i	0.681374	+	0.841427i
$995$	1796.88	−	811.160i	1.80591	−	0.815236i
$996$	−178.157	−	28.2173i	−0.178873	−	0.0283306i
$997$	−934.029	−	415.856i	−0.936839	−	0.417108i	−0.119221	−	0.992868i	$-0.538040\pi$
$997$	−934.029	−	415.856i	−0.936839	−	0.417108i	−0.817619	+	0.575760i	$0.804706\pi$
$998$	−26.8212	+	126.184i	−0.0268749	+	0.126436i
$999$	−2058.70	+	551.627i	−2.06076	+	0.552179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.bm.a.6.16	✓	1088
13.11	odd	12	inner	325.3.bm.a.206.53	yes	1088
25.21	even	5	inner	325.3.bm.a.71.53	yes	1088
325.271	odd	60	inner	325.3.bm.a.271.16	yes	1088

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.bm.a.6.16	✓	1088	1.1	even	1	trivial
325.3.bm.a.71.53	yes	1088	25.21	even	5	inner
325.3.bm.a.206.53	yes	1088	13.11	odd	12	inner
325.3.bm.a.271.16	yes	1088	325.271	odd	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.bm (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96882 + 1.27857i) q^{2} +(-0.268630 - 2.55584i) q^{3} +(0.614567 - 1.38034i) q^{4} +(4.97524 + 0.496976i) q^{5} +(3.79670 + 4.68853i) q^{6} +(2.43747 - 9.09675i) q^{7} +(-0.914064 - 5.77117i) q^{8} +(2.34315 - 0.498053i) q^{9} +(-10.4308 + 5.38271i) q^{10} +(-2.24334 - 3.45444i) q^{11} +(-3.69303 - 1.19994i) q^{12} +(-12.8424 - 2.01836i) q^{13} +(6.83186 + 21.0263i) q^{14} +(-0.0663071 - 12.8494i) q^{15} +(13.2226 + 14.6852i) q^{16} +(-13.4803 - 1.41683i) q^{17} +(-3.97645 + 3.97645i) q^{18} +(9.29776 + 11.4818i) q^{19} +(3.74361 - 6.56210i) q^{20} +(-23.9047 - 3.78613i) q^{21} +(8.83346 + 3.93291i) q^{22} +(-4.24098 + 19.9523i) q^{23} +(-14.5047 + 3.88651i) q^{24} +(24.5060 + 4.94515i) q^{25} +(27.8649 - 12.4460i) q^{26} +(-9.04973 - 27.8522i) q^{27} +(-11.0586 - 8.95510i) q^{28} +(-4.25616 - 40.4947i) q^{29} +(16.5594 + 25.2134i) q^{30} +(-29.5674 + 4.68301i) q^{31} +(-22.2328 - 5.95725i) q^{32} +(-8.22639 + 6.66160i) q^{33} +(28.3517 - 14.4459i) q^{34} +(16.6479 - 44.0472i) q^{35} +(0.752543 - 3.54044i) q^{36} +(3.80887 - 72.6775i) q^{37} +(-32.9858 - 10.7177i) q^{38} +(-1.70877 + 33.3653i) q^{39} +(-1.67956 - 29.1672i) q^{40} +(-64.5681 - 3.38387i) q^{41} +(51.9047 - 23.1095i) q^{42} +(19.8434 - 11.4566i) q^{43} +(-6.14699 + 0.973588i) q^{44} +(11.9053 - 1.31344i) q^{45} +(-17.1605 - 44.7047i) q^{46} +(7.08608 + 1.12233i) q^{47} +(33.9810 - 37.7398i) q^{48} +(-34.3744 - 19.8461i) q^{49} +(-54.5706 + 21.5965i) q^{50} +34.8341i q^{51} +(-10.6785 + 16.4864i) q^{52} +(-6.24347 + 4.53615i) q^{53} +(53.4281 + 43.2653i) q^{54} +(-9.44439 - 18.3016i) q^{55} +(-54.7269 - 5.75203i) q^{56} +(26.8480 - 26.8480i) q^{57} +(60.1547 + 74.2848i) q^{58} +(69.5502 + 45.1664i) q^{59} +(-17.7774 - 7.80532i) q^{60} +(44.4561 - 49.3735i) q^{61} +(52.2252 - 47.0238i) q^{62} +(1.18070 - 22.5291i) q^{63} +(-23.7857 + 7.72845i) q^{64} +(-62.8908 - 16.4242i) q^{65} +(7.67897 - 23.6334i) q^{66} +(-8.92958 + 23.2623i) q^{67} +(-10.2402 + 17.7366i) q^{68} +(52.1341 + 5.47951i) q^{69} +(23.5406 + 108.006i) q^{70} +(45.4459 - 17.4451i) q^{71} +(-5.01614 - 13.0675i) q^{72} +(50.8118 - 99.7238i) q^{73} +(85.4240 + 147.959i) q^{74} +(6.05596 - 63.9620i) q^{75} +(21.5629 - 5.77775i) q^{76} +(-36.8923 + 11.9870i) q^{77} +(-39.2954 - 67.8749i) q^{78} +(-80.0466 + 58.1573i) q^{79} +(58.4874 + 79.6336i) q^{80} +(-49.0593 + 21.8426i) q^{81} +(131.449 - 75.8922i) q^{82} +(45.8804 - 7.26674i) q^{83} +(-19.9172 + 30.6697i) q^{84} +(-66.3634 - 13.7484i) q^{85} +(-24.4200 + 47.9270i) q^{86} +(-102.355 + 21.7562i) q^{87} +(-17.8856 + 16.1043i) q^{88} +(52.2796 + 80.5035i) q^{89} +(-21.7600 + 17.8076i) q^{90} +(-49.6634 + 111.904i) q^{91} +(24.9345 + 18.1160i) q^{92} +(19.9117 + 74.3116i) q^{93} +(-15.3862 + 6.85036i) q^{94} +(40.5524 + 61.7454i) q^{95} +(-9.25342 + 58.4238i) q^{96} +(104.384 - 40.0691i) q^{97} +(93.0515 - 4.87662i) q^{98} +(-6.97699 - 6.97699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1088 q - 16 q^{2} - 6 q^{3} - 18 q^{4} - 6 q^{5} - 28 q^{6} - 32 q^{7} - 44 q^{8} + 378 q^{9} - 54 q^{10} - 12 q^{11} + 44 q^{13} - 24 q^{14} + 54 q^{15} - 382 q^{16} - 66 q^{17} - 500 q^{18} + 48 q^{19}+ \cdots - 792 q^{99}+O(q^{100}) \) 1088 * q - 16 * q^2 - 6 * q^3 - 18 * q^4 - 6 * q^5 - 28 * q^6 - 32 * q^7 - 44 * q^8 + 378 * q^9 - 54 * q^10 - 12 * q^11 + 44 * q^13 - 24 * q^14 + 54 * q^15 - 382 * q^16 - 66 * q^17 - 500 * q^18 + 48 * q^19 - 66 * q^20 + 42 * q^21 + 196 * q^22 - 18 * q^23 - 36 * q^24 - 12 * q^26 - 76 * q^28 + 94 * q^29 - 216 * q^30 - 12 * q^31 - 152 * q^32 - 222 * q^33 + 64 * q^34 - 82 * q^35 - 126 * q^36 - 210 * q^37 - 288 * q^39 - 432 * q^40 - 462 * q^41 + 222 * q^42 - 48 * q^43 + 36 * q^44 - 458 * q^45 - 396 * q^46 - 186 * q^47 - 334 * q^48 - 48 * q^49 + 106 * q^50 - 122 * q^52 + 12 * q^53 - 940 * q^54 + 130 * q^55 + 714 * q^56 - 252 * q^57 - 312 * q^58 - 132 * q^59 + 132 * q^60 + 294 * q^61 + 198 * q^62 + 1192 * q^63 + 338 * q^65 + 384 * q^66 - 236 * q^67 - 236 * q^68 - 648 * q^69 - 1114 * q^70 - 92 * q^71 + 546 * q^72 + 928 * q^73 + 164 * q^74 + 132 * q^75 + 620 * q^76 - 1742 * q^78 + 216 * q^79 - 540 * q^80 + 806 * q^81 + 3132 * q^82 + 874 * q^83 + 496 * q^84 + 514 * q^85 - 276 * q^86 + 74 * q^87 - 2394 * q^88 - 672 * q^89 + 308 * q^91 + 1960 * q^92 + 1008 * q^93 + 474 * q^94 + 2328 * q^95 - 1626 * q^96 + 632 * q^97 + 84 * q^98 - 792 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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