LMFDB - Embedded newform 325.3.bm.a.71.53

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			71.53
Character	$\chi$	$=$	325.71
Dual form			325.3.bm.a.206.53

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.34433 + 0.122861i) q^{2} +(2.34774 - 1.04528i) q^{3} +(1.50269 + 0.157939i) q^{4} +(-0.496976 - 4.97524i) q^{5} +(5.63230 - 2.16204i) q^{6} +(2.43747 - 9.09675i) q^{7} +(-5.77117 - 0.914064i) q^{8} +(-1.60290 + 1.78020i) q^{9} +(-0.553811 - 11.7247i) q^{10} +(-0.215569 + 4.11331i) q^{11} +(3.69303 - 1.19994i) q^{12} +(11.5761 - 5.91566i) q^{13} +(6.83186 - 21.0263i) q^{14} +(-6.36730 - 11.1611i) q^{15} +(-19.3290 - 4.10851i) q^{16} +(-5.51312 + 12.3827i) q^{17} +(-3.97645 + 3.97645i) q^{18} +(13.7930 - 5.29463i) q^{19} +(0.0389849 - 7.55475i) q^{20} +(-3.78613 - 23.9047i) q^{21} +(-1.01073 + 9.61646i) q^{22} +(15.1587 - 13.6489i) 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} +(5.09950 - 13.2847i) q^{28} +(37.1975 - 16.5614i) q^{29} +(-13.5558 - 26.9476i) q^{30} +(-4.68301 + 29.5674i) q^{31} +(-22.2328 - 5.95725i) q^{32} +(3.79346 + 9.88231i) q^{33} +(-14.4459 + 28.3517i) q^{34} +(-46.4699 - 7.60612i) q^{35} +(-2.68984 + 2.42194i) q^{36} +(39.6373 + 61.0362i) q^{37} +(32.9858 - 10.7177i) q^{38} +(20.9940 - 25.9887i) q^{39} +(-1.67956 + 29.1672i) q^{40} +(54.2256 - 35.2145i) q^{41} +(-5.93897 - 56.5055i) q^{42} +(19.8434 - 11.4566i) q^{43} +(-0.973588 + 6.14699i) q^{44} +(9.65355 + 7.09011i) q^{45} +(37.2138 - 30.1351i) q^{46} +(1.12233 + 7.08608i) q^{47} +(-49.6741 + 10.5586i) q^{48} +(-34.3744 - 19.8461i) q^{49} +(-58.0578 + 8.58221i) q^{50} +34.8341i q^{51} +(18.3296 - 7.06111i) q^{52} +(-6.24347 - 4.53615i) q^{53} +(-24.6375 + 64.1829i) q^{54} +(20.5718 - 0.971704i) q^{55} +(-22.3821 + 50.2709i) q^{56} +(26.8480 - 26.8480i) q^{57} +(89.2379 - 34.2552i) q^{58} +(-82.8155 + 4.34017i) q^{59} +(-7.80532 - 17.7774i) q^{60} +(-64.9867 + 13.8134i) q^{61} +(-14.6112 + 68.7403i) q^{62} +(12.2871 + 18.9204i) q^{63} +(23.7857 + 7.72845i) q^{64} +(-35.1849 - 54.6537i) q^{65} +(7.67897 + 23.6334i) q^{66} +(19.3644 + 15.6810i) q^{67} +(-10.2402 + 17.7366i) q^{68} +(21.3216 - 47.8892i) q^{69} +(-108.006 - 23.5406i) q^{70} +(30.6348 + 37.8308i) q^{71} +(10.8778 - 8.80871i) q^{72} +(-99.7238 + 50.8118i) q^{73} +(85.4240 + 147.959i) q^{74} +(-52.3647 + 37.2256i) q^{75} +(21.5629 - 5.77775i) q^{76} +(36.8923 + 11.9870i) q^{77} +(52.4099 - 58.3466i) q^{78} +(-80.0466 - 58.1573i) q^{79} +(-10.8348 + 98.2084i) q^{80} +(5.61339 + 53.4079i) q^{81} +(131.449 - 75.8922i) q^{82} +(7.26674 - 45.8804i) q^{83} +(-1.91390 - 36.5194i) q^{84} +(64.3467 + 21.2752i) q^{85} +(47.9270 - 24.4200i) q^{86} +(70.0187 - 77.7637i) q^{87} +(5.00391 - 23.5416i) q^{88} +(5.02370 - 95.8579i) q^{89} +(21.7600 + 17.8076i) q^{90} +(-25.5971 - 119.724i) q^{91} +(24.9345 - 18.1160i) q^{92} +(19.9117 + 74.3116i) q^{93} +(1.76050 + 16.7500i) q^{94} +(-33.1968 - 65.9921i) q^{95} +(-58.4238 + 9.25342i) q^{96} +(70.3643 + 86.8927i) q^{97} +(-78.1467 - 50.7490i) 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	2.34433	+	0.122861i	1.17216	+	0.0614305i	0.628457	−	0.777844i	$-0.283687\pi$
$2$	2.34433	+	0.122861i	1.17216	+	0.0614305i	0.543707	+	0.839275i	$0.317020\pi$
$3$	2.34774	−	1.04528i	0.782580	−	0.348427i	0.0237519	−	0.999718i	$-0.492439\pi$
$3$	2.34774	−	1.04528i	0.782580	−	0.348427i	0.758828	+	0.651291i	$0.225772\pi$
$4$	1.50269	+	0.157939i	0.375673	+	0.0394849i
$5$	−0.496976	−	4.97524i	−0.0993951	−	0.995048i
$5$	−0.496976	−	4.97524i	−0.0993951	−	0.995048i
$6$	5.63230	−	2.16204i	0.938717	−	0.360340i
$7$	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	$-0.151528\pi$
$8$	−5.77117	−	0.914064i	−0.721396	−	0.114258i
$9$	−1.60290	+	1.78020i	−0.178100	+	0.197800i
$10$	−0.553811	−	11.7247i	−0.0553811	−	1.17247i
$11$	−0.215569	+	4.11331i	−0.0195972	+	0.373937i	0.971172	+	0.238379i	$0.0766160\pi$
$11$	−0.215569	+	4.11331i	−0.0195972	+	0.373937i	−0.990769	+	0.135558i	$0.956717\pi$
$12$	3.69303	−	1.19994i	0.307752	−	0.0999947i
$13$	11.5761	−	5.91566i	0.890465	−	0.455051i
$13$	11.5761	−	5.91566i	0.890465	−	0.455051i
$14$	6.83186	−	21.0263i	0.487990	−	1.50188i
$15$	−6.36730	−	11.1611i	−0.424486	−	0.744073i
$16$	−19.3290	−	4.10851i	−1.20806	−	0.256782i
$17$	−5.51312	+	12.3827i	−0.324301	+	0.728392i	−0.999961	−	0.00882104i	$-0.997192\pi$
$17$	−5.51312	+	12.3827i	−0.324301	+	0.728392i	0.675660	+	0.737213i	$0.263859\pi$
$18$	−3.97645	+	3.97645i	−0.220914	+	0.220914i
$19$	13.7930	−	5.29463i	0.725947	−	0.278665i	0.0328006	−	0.999462i	$-0.489557\pi$
$19$	13.7930	−	5.29463i	0.725947	−	0.278665i	0.693146	+	0.720797i	$0.256224\pi$
$20$	0.0389849	−	7.55475i	0.00194924	−	0.377738i
$21$	−3.78613	−	23.9047i	−0.180292	−	1.13832i
$22$	−1.01073	+	9.61646i	−0.0459423	+	0.437112i
$23$	15.1587	−	13.6489i	0.659072	−	0.593431i	−0.270210	−	0.962801i	$-0.587093\pi$
$23$	15.1587	−	13.6489i	0.659072	−	0.593431i	0.929282	+	0.369370i	$0.120426\pi$
$24$	−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
$28$	5.09950	−	13.2847i	0.182125	−	0.474452i
$29$	37.1975	−	16.5614i	1.28267	−	0.571082i	0.351680	−	0.936120i	$-0.385611\pi$
$29$	37.1975	−	16.5614i	1.28267	−	0.571082i	0.930993	+	0.365038i	$0.118944\pi$
$30$	−13.5558	−	26.9476i	−0.451859	−	0.898252i
$31$	−4.68301	+	29.5674i	−0.151065	+	0.953787i	0.789396	+	0.613884i	$0.210394\pi$
$31$	−4.68301	+	29.5674i	−0.151065	+	0.953787i	−0.940461	+	0.339902i	$0.889606\pi$
$32$	−22.2328	−	5.95725i	−0.694774	−	0.186164i
$33$	3.79346	+	9.88231i	0.114953	+	0.299464i
$34$	−14.4459	+	28.3517i	−0.424880	+	0.833874i
$35$	−46.4699	−	7.60612i	−1.32771	−	0.217318i
$36$	−2.68984	+	2.42194i	−0.0747177	+	0.0672761i
$37$	39.6373	+	61.0362i	1.07128	+	1.64963i	0.687468	+	0.726215i	$0.258722\pi$
$37$	39.6373	+	61.0362i	1.07128	+	1.64963i	0.383812	+	0.923411i	$0.374611\pi$
$38$	32.9858	−	10.7177i	0.868047	−	0.282046i
$39$	20.9940	−	25.9887i	0.538308	−	0.666376i
$40$	−1.67956	+	29.1672i	−0.0419889	+	0.729181i
$41$	54.2256	−	35.2145i	1.32258	−	0.858891i	0.326314	−	0.945262i	$-0.394193\pi$
$41$	54.2256	−	35.2145i	1.32258	−	0.858891i	0.996263	+	0.0863701i	$0.0275268\pi$
$42$	−5.93897	−	56.5055i	−0.141404	−	1.34537i
$43$	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	$0.247489\pi$
$44$	−0.973588	+	6.14699i	−0.0221270	+	0.139704i
$45$	9.65355	+	7.09011i	0.214523	+	0.157558i
$46$	37.2138	−	30.1351i	0.808996	−	0.655112i
$47$	1.12233	+	7.08608i	0.0238793	+	0.150768i	0.996747	−	0.0805943i	$-0.0256818\pi$
$47$	1.12233	+	7.08608i	0.0238793	+	0.150768i	−0.972868	+	0.231362i	$0.925682\pi$
$48$	−49.6741	+	10.5586i	−1.03488	+	0.219970i
$49$	−34.3744	−	19.8461i	−0.701519	−	0.405022i
$50$	−58.0578	+	8.58221i	−1.16116	+	0.171644i
$51$			34.8341i			0.683021i
$52$	18.3296	−	7.06111i	0.352492	−	0.135791i
$53$	−6.24347	−	4.53615i	−0.117801	−	0.0855877i	0.527325	−	0.849664i	$-0.323195\pi$
$53$	−6.24347	−	4.53615i	−0.117801	−	0.0855877i	−0.645126	+	0.764076i	$0.723195\pi$
$54$	−24.6375	+	64.1829i	−0.456250	+	1.18857i
$55$	20.5718	−	0.971704i	0.374033	−	0.0176673i
$56$	−22.3821	+	50.2709i	−0.399680	+	0.897695i
$57$	26.8480	−	26.8480i	0.471017	−	0.471017i
$58$	89.2379	−	34.2552i	1.53858	−	0.590607i
$59$	−82.8155	+	4.34017i	−1.40365	+	0.0735623i	−0.739058	−	0.673642i	$-0.764729\pi$
$59$	−82.8155	+	4.34017i	−1.40365	+	0.0735623i	−0.664594	+	0.747204i	$0.731396\pi$
$60$	−7.80532	−	17.7774i	−0.130089	−	0.296289i
$61$	−64.9867	+	13.8134i	−1.06536	+	0.226448i	−0.707056	−	0.707158i	$-0.749977\pi$
$61$	−64.9867	+	13.8134i	−1.06536	+	0.226448i	−0.358300	+	0.933606i	$0.616644\pi$
$62$	−14.6112	+	68.7403i	−0.235665	+	1.10871i
$63$	12.2871	+	18.9204i	0.195033	+	0.300324i
$64$	23.7857	+	7.72845i	0.371652	+	0.120757i
$65$	−35.1849	−	54.6537i	−0.541305	−	0.840826i
$66$	7.67897	+	23.6334i	0.116348	+	0.358082i
$67$	19.3644	+	15.6810i	0.289021	+	0.234045i	0.762855	−	0.646570i	$-0.223797\pi$
$67$	19.3644	+	15.6810i	0.289021	+	0.234045i	−0.473834	+	0.880614i	$0.657130\pi$
$68$	−10.2402	+	17.7366i	−0.150592	+	0.260833i
$69$	21.3216	−	47.8892i	0.309009	−	0.694046i
$70$	−108.006	−	23.5406i	−1.54295	−	0.336294i
$71$	30.6348	+	37.8308i	0.431476	+	0.532829i	0.945792	−	0.324772i	$-0.105288\pi$
$71$	30.6348	+	37.8308i	0.431476	+	0.532829i	−0.514316	+	0.857601i	$0.671954\pi$
$72$	10.8778	−	8.80871i	0.151081	−	0.122343i
$73$	−99.7238	+	50.8118i	−1.36608	+	0.696052i	−0.974562	−	0.224118i	$-0.928050\pi$
$73$	−99.7238	+	50.8118i	−1.36608	+	0.696052i	−0.391517	+	0.920171i	$0.628050\pi$
$74$	85.4240	+	147.959i	1.15438	+	1.99944i
$75$	−52.3647	+	37.2256i	−0.698196	+	0.496342i
$76$	21.5629	−	5.77775i	0.283722	−	0.0760231i
$77$	36.8923	+	11.9870i	0.479121	+	0.155676i
$78$	52.4099	−	58.3466i	0.671922	−	0.748034i
$79$	−80.0466	−	58.1573i	−1.01325	−	0.736168i	−0.0483603	−	0.998830i	$-0.515400\pi$
$79$	−80.0466	−	58.1573i	−1.01325	−	0.736168i	−0.964888	+	0.262662i	$0.915400\pi$
$80$	−10.8348	+	98.2084i	−0.135435	+	1.22760i
$81$	5.61339	+	53.4079i	0.0693012	+	0.659357i
$82$	131.449	−	75.8922i	1.60304	−	0.925515i
$83$	7.26674	−	45.8804i	0.0875511	−	0.552776i	−0.904453	−	0.426573i	$-0.859721\pi$
$83$	7.26674	−	45.8804i	0.0875511	−	0.552776i	0.992004	−	0.126203i	$-0.0402791\pi$
$84$	−1.91390	−	36.5194i	−0.0227845	−	0.434754i
$85$	64.3467	+	21.2752i	0.757019	+	0.250297i
$86$	47.9270	−	24.4200i	0.557290	−	0.283954i
$87$	70.0187	−	77.7637i	0.804813	−	0.893836i
$88$	5.00391	−	23.5416i	0.0568626	−	0.267518i
$89$	5.02370	−	95.8579i	0.0564460	−	1.07705i	−0.812758	−	0.582601i	$-0.802035\pi$
$89$	5.02370	−	95.8579i	0.0564460	−	1.07705i	0.869204	−	0.494453i	$-0.164632\pi$
$90$	21.7600	+	17.8076i	0.241778	+	0.197862i
$91$	−25.5971	−	119.724i	−0.281286	−	1.31565i
$92$	24.9345	−	18.1160i	0.271028	−	0.196913i
$93$	19.9117	+	74.3116i	0.214105	+	0.799050i
$94$	1.76050	+	16.7500i	0.0187287	+	0.178191i
$95$	−33.1968	−	65.9921i	−0.349440	−	0.694654i
$96$	−58.4238	+	9.25342i	−0.608581	+	0.0963898i
$97$	70.3643	+	86.8927i	0.725405	+	0.895801i	0.997794	−	0.0663865i	$-0.0211470\pi$
$97$	70.3643	+	86.8927i	0.725405	+	0.895801i	−0.272389	+	0.962187i	$0.587814\pi$
$98$	−78.1467	−	50.7490i	−0.797415	−	0.517847i
$99$	−6.97699	−	6.97699i	−0.0704746	−	0.0704746i
$100$	−37.6061	+	3.56057i	−0.376061	+	0.0356057i
$101$	−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	$0.920945\pi$
$102$	−4.27975	+	81.6625i	−0.0419583	+	0.800613i
$103$	31.1111	−	42.8207i	0.302049	−	0.415735i	−0.630832	−	0.775920i	$-0.717286\pi$
$103$	31.1111	−	42.8207i	0.302049	−	0.415735i	0.932881	+	0.360184i	$0.117286\pi$
$104$	−72.2147	+	23.5591i	−0.694372	+	0.226529i
$105$	−117.050	+	30.7169i	−1.11476	+	0.292542i
$106$	−14.0794	−	11.4013i	−0.132825	−	0.107559i
$107$	−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	$0.778898\pi$
$108$	−17.9979	+	40.4240i	−0.166648	+	0.374297i
$109$	74.9260	+	38.1767i	0.687395	+	0.350245i	0.762552	−	0.646927i	$-0.223946\pi$
$109$	74.9260	+	38.1767i	0.687395	+	0.350245i	−0.0751577	+	0.997172i	$0.523946\pi$
$110$	48.3465	+	0.249483i	0.439514	+	0.00226803i
$111$	156.858	+	101.865i	1.41314	+	0.917702i
$112$	−84.4880	+	165.817i	−0.754357	+	1.48051i
$113$	89.6701	−	99.5887i	0.793541	−	0.881316i	−0.201631	−	0.979461i	$-0.564624\pi$
$113$	89.6701	−	99.5887i	0.793541	−	0.881316i	0.995172	+	0.0981451i	$0.0312909\pi$
$114$	66.2391	−	59.6419i	0.581044	−	0.523175i
$115$	−75.4402	−	68.6348i	−0.656001	−	0.596825i
$116$	58.5121	−	19.0117i	0.504415	−	0.163894i
$117$	−8.02420	+	30.0900i	−0.0685829	+	0.257179i
$118$	−194.680			−1.64983
$119$	99.2041	+	80.3339i	0.833648	+	0.675074i
$120$	26.5448	+	70.2327i	0.221207	+	0.585273i
$121$	103.464	+	10.8745i	0.855077	+	0.0898722i
$122$	−154.047	+	24.3987i	−1.26268	+	0.199989i
$123$	90.4986	−	139.356i	0.735761	−	1.13297i
$124$	−11.7070	+	43.6911i	−0.0944112	+	0.352347i
$125$	36.7822	+	119.466i	0.294257	+	0.955726i
$126$	26.4803	+	45.8652i	0.210161	+	0.364010i
$127$	−21.5211	+	19.3777i	−0.169458	+	0.152581i	−0.749496	−	0.662009i	$-0.769704\pi$
$127$	−21.5211	+	19.3777i	−0.169458	+	0.152581i	0.580038	+	0.814589i	$0.303038\pi$
$128$	140.765	+	54.0347i	1.09973	+	0.422146i
$129$	34.6117	−	47.6390i	0.268308	−	0.369294i
$130$	−75.7700	−	132.449i	−0.582846	−	1.01884i
$131$	−37.7369	+	27.4174i	−0.288068	+	0.209293i	−0.722429	−	0.691445i	$-0.756974\pi$
$131$	−37.7369	+	27.4174i	−0.288068	+	0.209293i	0.434361	+	0.900739i	$0.356974\pi$
$132$	4.13961	+	15.4492i	0.0313606	+	0.117040i
$133$	−14.5440	−	138.377i	−0.109353	−	1.04043i
$134$	43.4700	+	39.1405i	0.324403	+	0.292093i
$135$	143.069	+	31.1827i	1.05977	+	0.230983i
$136$	43.1357	−	66.4232i	0.317174	−	0.488406i
$137$	−207.786	+	10.8896i	−1.51669	+	0.0794863i	−0.792397	−	0.610006i	$-0.791167\pi$
$137$	−207.786	+	10.8896i	−1.51669	+	0.0794863i	−0.724293	+	0.689492i	$0.757834\pi$
$138$	55.8687	−	109.648i	0.404845	−	0.794554i
$139$	−205.769	+	43.7376i	−1.48036	+	0.314659i	−0.876099	−	0.482131i	$-0.839863\pi$
$139$	−205.769	+	43.7376i	−1.48036	+	0.314659i	−0.604256	+	0.796790i	$0.706530\pi$
$140$	−68.6287	−	18.7691i	−0.490205	−	0.134065i
$141$	10.0419	+	15.4631i	0.0712190	+	0.109668i
$142$	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
$145$	−100.883	−	176.836i	−0.695746	−	1.21956i
$146$	−240.028	+	106.867i	−1.64403	+	0.731969i
$147$	−101.447	−	10.6625i	−0.690116	−	0.0725341i
$148$	49.9228	+	97.9790i	0.337316	+	0.662020i
$149$	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	$0.571653\pi$
$150$	−127.334	+	80.8355i	−0.848891	+	0.538903i
$151$	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	$0.592789\pi$
$152$	−84.4413	+	17.9486i	−0.555535	+	0.118083i
$153$	−13.2067	−	29.6627i	−0.0863182	−	0.193874i
$154$	85.0149	+	32.6342i	0.552045	+	0.211910i
$155$	149.432	+	8.60485i	0.964079	+	0.0555152i
$156$	35.6522	−	35.7372i	0.228540	−	0.229085i
$157$	−29.7941			−0.189772			−0.0948858	−	0.995488i	$-0.530249\pi$
$157$	−29.7941			−0.189772			−0.0948858	+	0.995488i	$0.530249\pi$
$158$	−180.510	−	146.174i	−1.14247	−	0.925154i
$159$	−19.3996	−	4.12351i	−0.122010	−	0.0259340i
$160$	−18.5896	+	113.574i	−0.116185	+	0.709837i
$161$	−87.2121	−	171.163i	−0.541690	−	1.06313i
$162$	6.59789	+	125.895i	0.0407277	+	0.777131i
$163$	52.8344	−	2.76893i	0.324137	−	0.0169873i	0.110426	−	0.993884i	$-0.464778\pi$
$163$	52.8344	−	2.76893i	0.324137	−	0.0169873i	0.213711	+	0.976897i	$0.431445\pi$
$164$	87.0463	−	44.3523i	0.530770	−	0.270441i
$165$	47.2816	−	23.7847i	0.286555	−	0.144149i
$166$	22.6725	−	106.666i	0.136582	−	0.642565i
$167$	−14.9279	+	18.4345i	−0.0893888	+	0.110386i	−0.819878	−	0.572538i	$-0.805959\pi$
$167$	−14.9279	+	18.4345i	−0.0893888	+	0.110386i	0.730489	+	0.682924i	$0.239292\pi$
$168$			141.419i			0.841778i
$169$	99.0099	−	136.960i	0.585857	−	0.810414i
$170$	148.236	+	57.7818i	0.871975	+	0.339893i
$171$	−12.6833	+	33.0411i	−0.0741713	+	0.193223i
$172$	31.6280	−	14.0817i	0.183883	−	0.0818702i
$173$	−28.8570	−	135.761i	−0.166803	−	0.784747i	−0.979401	−	0.201923i	$-0.935281\pi$
$173$	−28.8570	−	135.761i	−0.166803	−	0.784747i	0.812598	−	0.582824i	$-0.198052\pi$
$174$	173.701	−	173.701i	0.998282	−	0.998282i
$175$	−14.7479	+	234.979i	−0.0842737	+	1.34274i
$176$	21.0663	−	78.6206i	0.119695	−	0.446708i
$177$	−189.893	+	96.7551i	−1.07284	+	0.546639i
$178$	23.5544	−	224.105i	0.132328	−	1.25902i
$179$	60.8087	+	136.579i	0.339713	+	0.763009i	0.999929	+	0.0119326i	$0.00379835\pi$
$179$	60.8087	+	136.579i	0.339713	+	0.763009i	−0.660215	+	0.751076i	$0.729535\pi$
$180$	13.3865	+	12.1789i	0.0743695	+	0.0676608i
$181$	167.317	+	230.292i	0.924402	+	1.27233i	0.962004	+	0.273037i	$0.0880281\pi$
$181$	167.317	+	230.292i	0.924402	+	1.27233i	−0.0376019	+	0.999293i	$0.511972\pi$
$182$	−45.2986	−	283.817i	−0.248893	−	1.55943i
$183$	−138.133	+	100.360i	−0.754826	+	0.548413i
$184$	−99.9592	+	64.9143i	−0.543257	+	0.352795i
$185$	283.971	−	227.539i	1.53498	−	1.22994i
$186$	37.5496	+	176.657i	0.201880	+	0.949770i
$187$	−49.7453	−	25.3465i	−0.266017	−	0.135543i
$188$	0.567339	+	10.8255i	0.00301776	+	0.0575823i
$189$	231.306	+	150.212i	1.22384	+	0.794773i
$190$	−69.7164	−	158.786i	−0.366929	−	0.835715i
$191$	98.0293	−	108.873i	0.513242	−	0.570013i	−0.429699	−	0.902972i	$-0.641380\pi$
$191$	98.0293	−	108.873i	0.513242	−	0.570013i	0.942941	+	0.332959i	$0.108047\pi$
$192$	63.9211	−	6.71838i	0.332923	−	0.0349916i
$193$	−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
$195$	−139.733	−	91.5346i	−0.716582	−	0.469408i
$196$	−48.5198	−	35.2517i	−0.247550	−	0.179855i
$197$	−26.2032	+	68.2617i	−0.133011	+	0.346506i	−0.983869	−	0.178890i	$-0.942749\pi$
$197$	−26.2032	+	68.2617i	−0.133011	+	0.346506i	0.850858	+	0.525396i	$0.176083\pi$
$198$	−15.4992	−	17.2136i	−0.0782786	−	0.0869371i
$199$	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	$-0.123217\pi$
$200$	145.949	−	6.13921i	0.729743	−	0.0306960i
$201$	61.8537	+	16.5736i	0.307730	+	0.0824559i
$202$	−284.971	−	185.063i	−1.41075	−	0.916152i
$203$	−59.9872	−	378.744i	−0.295503	−	1.86574i
$204$	−5.50167	+	52.3449i	−0.0269690	+	0.256593i
$205$	−202.150	−	252.285i	−0.986096	−	1.23066i
$206$	78.1956	−	96.5636i	0.379590	−	0.468755i
$207$			48.8634i			0.236055i
$208$	−248.058	+	66.7837i	−1.19259	+	0.321075i
$209$	18.8051	+	57.8762i	0.0899766	+	0.276919i
$210$	−278.177	+	57.6297i	−1.32465	+	0.274427i
$211$	−140.000	−	155.486i	−0.663509	−	0.736902i	0.313620	−	0.949549i	$-0.398458\pi$
$211$	−140.000	−	155.486i	−0.663509	−	0.736902i	−0.977129	+	0.212647i	$0.931792\pi$
$212$	−8.66559	−	7.80253i	−0.0408754	−	0.0368044i
$213$	111.466	+	56.7950i	0.523317	+	0.266643i
$214$	−256.781	+	395.408i	−1.19991	+	1.84770i
$215$	−66.8609	−	93.0319i	−0.310981	−	0.432707i
$216$	77.6863	−	152.468i	0.359659	−	0.705870i
$217$	257.553	+	114.670i	1.18688	+	0.528432i
$218$	170.961	+	98.7042i	0.784224	+	0.452772i
$219$	−181.013	+	223.532i	−0.826543	+	1.02070i
$220$	31.0666	+	1.78893i	0.141212	+	0.00813150i
$221$	9.43154	+	175.956i	0.0426766	+	0.796182i
$222$	355.212	+	258.077i	1.60005	+	1.16251i
$223$	−233.767	−	12.2512i	−1.04828	−	0.0549382i	−0.479594	−	0.877490i	$-0.659216\pi$
$223$	−233.767	−	12.2512i	−1.04828	−	0.0549382i	−0.568690	+	0.822552i	$0.692550\pi$
$224$	−108.383	+	187.725i	−0.483854	+	0.838060i
$225$	30.4774	−	51.5523i	0.135455	−	0.229121i
$226$	222.452	−	222.452i	0.984300	−	0.984300i
$227$	103.095	−	158.753i	0.454164	−	0.699351i	−0.535214	−	0.844716i	$-0.679769\pi$
$227$	103.095	−	158.753i	0.454164	−	0.699351i	0.989378	+	0.145366i	$0.0464359\pi$
$228$	44.5846	−	36.1039i	0.195547	−	0.158351i
$229$	2.56744	+	16.2102i	0.0112115	+	0.0707868i	0.992660	−	0.120941i	$-0.0385910\pi$
$229$	2.56744	+	16.2102i	0.0112115	+	0.0707868i	−0.981448	+	0.191727i	$0.938591\pi$
$230$	−168.424	−	170.171i	−0.732278	−	0.739875i
$231$	99.1434	−	10.4204i	0.429192	−	0.0451099i
$232$	−229.811	+	61.5777i	−0.990566	+	0.265421i
$233$	56.6826	+	78.0169i	0.243273	+	0.334837i	0.913141	−	0.407644i	$-0.133649\pi$
$233$	56.6826	+	78.0169i	0.243273	+	0.334837i	−0.669868	+	0.742480i	$0.733649\pi$
$234$	−22.5082	+	69.5549i	−0.0961891	+	0.297243i
$235$	34.6972	−	9.10545i	0.147648	−	0.0387466i
$236$	−125.132	−	6.55788i	−0.530219	−	0.0277876i
$237$	−248.719	−	52.8669i	−1.04945	−	0.223067i
$238$	222.697	+	200.517i	0.935702	+	0.842510i
$239$	−138.443	−	271.709i	−0.579259	−	1.13686i	−0.975764	−	0.218827i	$-0.929777\pi$
$239$	−138.443	−	271.709i	−0.579259	−	1.13686i	0.396505	−	0.918033i	$-0.370223\pi$
$240$	77.2182	+	241.893i	0.321742	+	1.00789i
$241$	−112.040	+	5.87177i	−0.464896	+	0.0243642i	−0.283347	−	0.959018i	$-0.591445\pi$
$241$	−112.040	+	5.87177i	−0.464896	+	0.0243642i	−0.181550	+	0.983382i	$0.558111\pi$
$242$	241.218	+	38.2052i	0.996770	+	0.157873i
$243$	−62.7799	−	108.738i	−0.258354	−	0.447481i
$244$	−99.8368	+	10.4933i	−0.409167	+	0.0430052i
$245$	−81.6558	+	180.884i	−0.333289	+	0.738302i
$246$	229.280	−	315.577i	0.932032	−	1.28283i
$247$	128.347	−	142.886i	0.519624	−	0.578484i
$248$	54.0529	−	166.358i	0.217955	−	0.670798i
$249$	−30.8975	−	115.311i	−0.124086	−	0.463096i
$250$	71.5518	+	284.586i	0.286207	+	1.13834i
$251$	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	$0.259325\pi$
$252$	15.4754	+	30.3722i	0.0614103	+	0.120525i
$253$	52.8745	+	65.2945i	0.208990	+	0.258081i
$254$	−52.8334	+	42.7836i	−0.208006	+	0.168440i
$255$	173.308	−	17.3117i	0.679639	−	0.0678889i
$256$	231.971	+	103.280i	0.906135	+	0.403437i
$257$	−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	$0.831895\pi$
$258$	86.9943	−	107.429i	0.337187	−	0.416391i
$259$	651.846	−	211.798i	2.51678	−	0.817751i
$260$	−44.2401	−	87.6848i	−0.170154	−	0.337249i
$261$	−30.1413	+	92.7654i	−0.115484	+	0.355423i
$262$	−91.8361	+	59.6391i	−0.350520	+	0.227630i
$263$	−116.942	−	24.8567i	−0.444645	−	0.0945121i	−0.0198522	−	0.999803i	$-0.506320\pi$
$263$	−116.942	−	24.8567i	−0.444645	−	0.0945121i	−0.424792	+	0.905291i	$0.639653\pi$
$264$	−12.8597	−	60.5000i	−0.0487108	−	0.229167i
$265$	−19.4656	+	33.3171i	−0.0734550	+	0.125725i
$266$	−17.0948	−	326.188i	−0.0642661	−	1.22627i
$267$	−88.4041	−	230.301i	−0.331101	−	0.862549i
$268$	26.6221	+	26.6221i	0.0993363	+	0.0993363i
$269$	316.362	+	140.853i	1.17607	+	0.523618i	0.899306	−	0.437321i	$-0.144073\pi$
$269$	316.362	+	140.853i	1.17607	+	0.523618i	0.276760	+	0.960939i	$0.410739\pi$
$270$	331.569	+	90.6801i	1.22803	+	0.335852i
$271$	−45.3070	−	17.3917i	−0.167184	−	0.0641761i	0.273336	−	0.961919i	$-0.411873\pi$
$271$	−45.3070	−	17.3917i	−0.167184	−	0.0641761i	−0.440521	+	0.897742i	$0.645206\pi$
$272$	157.438	−	216.694i	0.578815	−	0.796670i
$273$	−185.240	−	254.324i	−0.678536	−	0.931590i
$274$	−488.458			−1.78269
$275$	−15.0582	−	101.867i	−0.0547569	−	0.370425i
$276$	39.6035	−	68.5953i	0.143491	−	0.248534i
$277$	−36.8632	−	173.428i	−0.133080	−	0.626093i	−0.993241	−	0.116070i	$-0.962970\pi$
$277$	−36.8632	−	173.428i	−0.133080	−	0.626093i	0.860161	−	0.510023i	$-0.170363\pi$
$278$	−487.765	+	77.2543i	−1.75455	+	0.277893i
$279$	−45.1296	−	55.7304i	−0.161755	−	0.199750i
$280$	261.233	+	86.3727i	0.932976	+	0.308474i
$281$	−210.809	−	33.3888i	−0.750208	−	0.118821i	−0.230390	−	0.973098i	$-0.574000\pi$
$281$	−210.809	−	33.3888i	−0.750208	−	0.118821i	−0.519818	+	0.854277i	$0.674000\pi$
$282$	21.6416	+	37.4844i	0.0767434	+	0.132924i
$283$	89.7007	−	9.42792i	0.316963	−	0.0333142i	0.0552890	−	0.998470i	$-0.482392\pi$
$283$	89.7007	−	9.42792i	0.316963	−	0.0333142i	0.261674	+	0.965156i	$0.415725\pi$
$284$	40.0597	+	61.6866i	0.141055	+	0.217206i
$285$	−146.918	−	120.232i	−0.515502	−	0.421868i
$286$	45.1874	+	117.300i	0.157998	+	0.410139i
$287$	−188.165	−	579.112i	−0.655626	−	2.01781i
$288$	46.2421	−	30.0300i	0.160563	−	0.104271i
$289$	70.4427	+	78.2345i	0.243746	+	0.270708i
$290$	−214.777	−	426.956i	−0.740610	−	1.47226i
$291$	256.024	+	130.451i	0.879809	+	0.448285i
$292$	−157.879	+	60.6043i	−0.540683	+	0.207549i
$293$	−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	$0.886144\pi$
$294$	−236.515	−	37.4603i	−0.804473	−	0.127416i
$295$	62.7507	+	409.870i	0.212714	+	1.38939i
$296$	−172.963	−	388.481i	−0.584334	−	1.31244i
$297$	−112.614	−	43.2284i	−0.379171	−	0.145550i
$298$	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
$302$	224.886	+	249.761i	0.744655	+	0.827023i
$303$	−369.939	−	38.8822i	−1.22092	−	0.128324i
$304$	−288.358	+	45.6714i	−0.948547	+	0.150235i
$305$	101.022	+	316.460i	0.331218	+	1.03757i
$306$	−27.3164	−	71.1617i	−0.0892693	−	0.232555i
$307$	−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	$0.782323\pi$
$308$	53.5446	+	23.8396i	0.173846	+	0.0774013i
$309$	28.2810	−	133.052i	0.0915244	−	0.430589i
$310$	349.261	+	38.5320i	1.12665	+	0.124297i
$311$	−68.7947	−	22.3527i	−0.221205	−	0.0718738i	0.196318	−	0.980540i	$-0.437102\pi$
$311$	−68.7947	−	22.3527i	−0.221205	−	0.0718738i	−0.417523	+	0.908667i	$0.637102\pi$
$312$	−144.915	+	130.795i	−0.464473	+	0.419215i
$313$	185.713	+	571.565i	0.593331	+	1.82609i	0.562863	+	0.826550i	$0.309700\pi$
$313$	185.713	+	571.565i	0.593331	+	1.82609i	0.0304679	+	0.999536i	$0.490300\pi$
$314$	−69.8473	−	3.66054i	−0.222443	−	0.0116578i
$315$	88.0272	−	70.5340i	0.279451	−	0.223918i
$316$	−111.100	−	100.035i	−0.351583	−	0.316567i
$317$	30.9577	−	195.459i	0.0976583	−	0.616590i	−0.889511	−	0.456913i	$-0.848955\pi$
$317$	30.9577	−	195.459i	0.0976583	−	0.616590i	0.987169	−	0.159676i	$-0.0510451\pi$
$318$	−44.9724	−	12.0503i	−0.141423	−	0.0378941i
$319$	60.1034	+	156.575i	0.188412	+	0.490830i
$320$	26.6300	−	122.181i	0.0832187	−	0.381814i
$321$	−53.9504	+	513.304i	−0.168070	+	1.59908i
$322$	−183.425	−	411.978i	−0.569642	−	1.27944i
$323$	−10.4807	+	199.984i	−0.0324480	+	0.619146i
$324$			81.1423i			0.250439i
$325$	−254.429	+	202.215i	−0.782859	+	0.622199i
$326$	124.201			0.380986
$327$	215.812	+	11.3102i	0.659976	+	0.0345879i
$328$	−345.134	+	153.663i	−1.05224	+	0.468486i
$329$	67.1960	+	7.06258i	0.204243	+	0.0214668i
$330$	113.766	−	49.9500i	0.344745	−	0.151364i
$331$	528.848	−	203.006i	1.59773	−	0.613311i	0.613419	−	0.789758i	$-0.289794\pi$
$331$	528.848	−	203.006i	1.59773	−	0.613311i	0.984310	+	0.176447i	$0.0564605\pi$
$332$	18.1660	−	67.7964i	0.0547169	−	0.204206i
$333$	−172.192	−	27.2725i	−0.517092	−	0.0818993i
$334$	−37.2608	+	41.3824i	−0.111559	+	0.123899i
$335$	68.3931	−	104.136i	0.204158	−	0.310853i
$336$	−25.0304	+	477.609i	−0.0744953	+	1.42146i
$337$	−45.1902	+	14.6832i	−0.134096	+	0.0435703i	−0.375296	−	0.926905i	$-0.622459\pi$
$337$	−45.1902	+	14.6832i	−0.134096	+	0.0435703i	0.241200	+	0.970475i	$0.422459\pi$
$338$	248.939	−	308.915i	0.736505	−	0.913949i
$339$	106.424	−	327.539i	0.313935	−	0.966192i
$340$	93.3331	+	42.1330i	0.274509	+	0.123921i
$341$	−120.610	−	25.6365i	−0.353696	−	0.0751803i
$342$	−33.7933	+	75.9010i	−0.0988108	+	0.221933i
$343$	61.9834	−	61.9834i	0.180710	−	0.180710i
$344$	−124.992	+	47.9798i	−0.363348	+	0.139476i
$345$	−248.857	−	82.2806i	−0.721324	−	0.238494i
$346$	−50.9704	−	321.815i	−0.147313	−	0.930100i
$347$	7.35459	−	69.9743i	0.0211948	−	0.201655i	−0.978800	−	0.204817i	$-0.934340\pi$
$347$	7.35459	−	69.9743i	0.0211948	−	0.201655i	0.999995	+	0.00316239i	$0.00100662\pi$
$348$	117.499	−	105.796i	0.337640	−	0.304012i
$349$	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
$353$	−22.1525	+	57.7092i	−0.0627549	+	0.163482i	−0.961372	−	0.275251i	$-0.911239\pi$
$353$	−22.1525	+	57.7092i	−0.0627549	+	0.163482i	0.898618	+	0.438733i	$0.144572\pi$
$354$	−457.058	+	203.495i	−1.29112	+	0.574845i
$355$	172.993	−	171.216i	0.487303	−	0.482300i
$356$	22.6888	−	143.252i	0.0637326	−	0.402392i
$357$	316.877	+	84.9069i	0.887610	+	0.237834i
$358$	125.775	+	327.656i	0.351328	+	0.915241i
$359$	−172.844	+	339.226i	−0.481460	+	0.944919i	0.514700	+	0.857370i	$0.327903\pi$
$359$	−172.844	+	339.226i	−0.481460	+	0.944919i	−0.996160	+	0.0875485i	$0.972097\pi$
$360$	−49.2315	−	49.7422i	−0.136754	−	0.138173i
$361$	−106.062	+	95.4985i	−0.293800	+	0.264539i
$362$	363.951	+	560.436i	1.00539	+	1.54817i
$363$	254.274	−	82.6187i	0.700480	−	0.227600i
$364$	−19.5555	−	183.951i	−0.0537238	−	0.505359i
$365$	302.361	+	470.898i	0.828387	+	1.29013i
$366$	−336.160	+	218.305i	−0.918469	+	0.596461i
$367$	35.2691	+	335.563i	0.0961011	+	0.914341i	0.931266	+	0.364341i	$0.118706\pi$
$367$	35.2691	+	335.563i	0.0961011	+	0.914341i	−0.835165	+	0.550000i	$0.814628\pi$
$368$	−349.079	+	201.541i	−0.948584	+	0.547665i
$369$	−24.2294	+	152.978i	−0.0656623	+	0.414575i
$370$	693.676	−	498.537i	1.87480	−	1.34740i
$371$	−56.4825	+	45.7386i	−0.152244	+	0.123285i
$372$	18.1845	+	114.812i	0.0488831	+	0.308636i
$373$	−142.795	+	30.3520i	−0.382828	+	0.0813725i	−0.395306	−	0.918550i	$-0.629361\pi$
$373$	−142.795	+	30.3520i	−0.382828	+	0.0813725i	0.0124780	+	0.999922i	$0.496028\pi$
$374$	−113.505	−	65.5322i	−0.303490	−	0.175220i
$375$	211.230	+	242.027i	0.563281	+	0.645405i
$376$		−	41.9209i		−	0.111492i
$377$	332.628	−	411.763i	0.882304	−	1.09221i
$378$	523.803	+	380.565i	1.38572	+	1.00679i
$379$	−149.971	+	390.687i	−0.395701	+	1.03084i	0.580556	+	0.814220i	$0.302835\pi$
$379$	−149.971	+	390.687i	−0.395701	+	1.03084i	−0.976257	+	0.216616i	$0.930498\pi$
$380$	−39.4619	−	104.409i	−0.103847	−	0.274761i
$381$	−30.2709	+	67.9895i	−0.0794511	+	0.178450i
$382$	243.189	−	243.189i	0.636621	−	0.636621i
$383$	−308.695	+	118.497i	−0.805993	+	0.309392i	−0.726256	−	0.687424i	$-0.758741\pi$
$383$	−308.695	+	118.497i	−0.805993	+	0.309392i	−0.0797370	+	0.996816i	$0.525408\pi$
$384$	386.962	−	20.2798i	1.00771	−	0.0528120i
$385$	41.3038	−	189.505i	0.107283	−	0.492222i
$386$	−268.631	+	57.0994i	−0.695937	+	0.147926i
$387$	−11.4120	+	53.6890i	−0.0294883	+	0.138731i
$388$	92.0122	+	141.686i	0.237145	+	0.365171i
$389$	−475.687	−	154.560i	−1.22285	−	0.397327i	−0.374729	−	0.927135i	$-0.622264\pi$
$389$	−475.687	−	154.560i	−1.22285	−	0.397327i	−0.848118	+	0.529808i	$0.822264\pi$
$390$	−316.335	−	231.755i	−0.811115	−	0.594244i
$391$	85.4386	+	262.953i	0.218513	+	0.672514i
$392$	180.240	+	145.956i	0.459796	+	0.372336i
$393$	−59.9374	+	103.815i	−0.152513	+	0.264159i
$394$	−69.8156	+	156.808i	−0.177197	+	0.397991i
$395$	−249.565	+	427.154i	−0.631810	+	1.08140i
$396$	−9.38233	−	11.5862i	−0.0236928	−	0.0292581i
$397$	−485.473	+	393.128i	−1.22285	+	0.990247i	−0.222972	+	0.974825i	$0.571576\pi$
$397$	−485.473	+	393.128i	−1.22285	+	0.990247i	−0.999881	+	0.0154224i	$0.995091\pi$
$398$	824.744	−	420.228i	2.07222	−	1.05585i
$399$	−178.788	−	309.671i	−0.448091	−	0.776117i
$400$	493.995	+	5.09847i	1.23499	+	0.0127462i
$401$	−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
$403$	120.700	+	369.977i	0.299503	+	0.918056i
$404$	−176.933	−	128.550i	−0.437954	−	0.318192i
$405$	262.927	−	54.4704i	0.649203	−	0.134495i
$406$	−94.0968	−	895.271i	−0.231765	−	2.20510i
$407$	−259.605	+	149.883i	−0.637850	+	0.368263i
$408$	31.8406	−	201.033i	0.0780406	−	0.492729i
$409$	3.50679	+	66.9135i	0.00857406	+	0.163603i	0.999561	+	0.0296413i	$0.00943651\pi$
$409$	3.50679	+	66.9135i	0.00857406	+	0.163603i	−0.990987	+	0.133961i	$0.957230\pi$
$410$	−442.909	−	616.275i	−1.08027	−	1.50311i
$411$	−476.446	+	242.761i	−1.15924	+	0.590660i
$412$	53.5135	−	59.4328i	0.129887	−	0.144254i
$413$	−162.379	+	763.931i	−0.393168	+	1.84971i
$414$	−6.00341	+	114.552i	−0.0145010	+	0.276695i
$415$	−231.877	−	13.3523i	−0.558740	−	0.0321743i
$416$	−292.609	+	62.5601i	−0.703387	+	0.150385i
$417$	−437.375	+	317.772i	−1.04886	+	0.762042i
$418$	36.9746	+	137.991i	0.0884560	+	0.330122i
$419$	18.6617	+	177.554i	0.0445386	+	0.423756i	0.993959	+	0.109749i	$0.0350048\pi$
$419$	18.6617	+	177.554i	0.0445386	+	0.423756i	−0.949421	+	0.314007i	$0.898328\pi$
$420$	−180.741	+	27.6713i	−0.430337	+	0.0658841i
$421$	85.9745	−	13.6170i	0.204215	−	0.0323445i	−0.0534888	−	0.998568i	$-0.517034\pi$
$421$	85.9745	−	13.6170i	0.204215	−	0.0323445i	0.257704	+	0.966224i	$0.417034\pi$
$422$	−309.104	−	381.711i	−0.732473	−	0.904529i
$423$	−14.4137	−	9.36033i	−0.0340748	−	0.0221285i
$424$	31.8858	+	31.8858i	0.0752024	+	0.0752024i
$425$	73.8706	−	330.713i	0.173813	−	0.778149i
$426$	254.336	+	146.841i	0.597033	+	0.344697i
$427$	−32.7464	+	624.838i	−0.0766894	+	1.46332i
$428$	−178.367	+	245.502i	−0.416746	+	0.573602i
$429$	102.374	+	91.9572i	0.238633	+	0.214353i
$430$	−145.314	−	226.312i	−0.337939	−	0.526307i
$431$	−337.824	−	273.564i	−0.783814	−	0.634720i	0.151532	−	0.988452i	$-0.451579\pi$
$431$	−337.824	−	273.564i	−0.783814	−	0.634720i	−0.935347	+	0.353732i	$0.884913\pi$
$432$	289.354	−	501.175i	0.669800	−	1.16013i
$433$	−162.852	+	365.771i	−0.376101	+	0.844736i	0.621993	+	0.783023i	$0.286323\pi$
$433$	−162.852	+	365.771i	−0.376101	+	0.844736i	−0.998094	+	0.0617135i	$0.980343\pi$
$434$	589.699	+	300.467i	1.35875	+	0.692320i
$435$	−421.691	−	309.713i	−0.969404	−	0.711985i
$436$	106.561	+	69.2017i	0.244406	+	0.158719i
$437$	136.817	−	268.519i	0.313083	−	0.614460i
$438$	−451.817	+	501.794i	−1.03155	+	1.14565i
$439$	272.593	−	245.444i	0.620940	−	0.559097i	−0.297468	−	0.954732i	$-0.596142\pi$
$439$	272.593	−	245.444i	0.620940	−	0.559097i	0.918408	+	0.395635i	$0.129475\pi$
$440$	−119.612	−	13.1961i	−0.271845	−	0.0299911i
$441$	90.4290	−	29.3822i	0.205054	−	0.0666262i
$442$	0.492463	+	413.658i	0.00111417	+	0.935878i
$443$	197.519			0.445868			0.222934	−	0.974834i	$-0.428437\pi$
$443$	197.519			0.445868			0.222934	+	0.974834i	$0.428437\pi$
$444$	219.621	+	177.846i	0.494643	+	0.400554i
$445$	−479.413	+	22.6449i	−1.07733	+	0.0508874i
$446$	−546.522	−	57.4418i	−1.22539	−	0.128793i
$447$	27.7497	−	4.39512i	0.0620799	−	0.00983249i
$448$	128.281	−	197.535i	0.286341	−	0.440927i
$449$	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	$0.0590219\pi$
$450$	77.7829	−	117.111i	0.172851	−	0.260247i
$451$	133.159	+	230.638i	0.295252	+	0.511392i
$452$	150.476	−	135.489i	0.332911	−	0.299754i
$453$	343.486	+	131.852i	0.758247	+	0.291064i
$454$	261.193	−	359.502i	0.575316	−	0.791854i
$455$	−582.933	+	186.851i	−1.28117	+	0.410662i
$456$	−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	$0.700761\pi$
$458$	4.02733	+	38.3174i	0.00879329	+	0.0836625i
$459$	−294.993	−	265.612i	−0.642685	−	0.578676i
$460$	−102.523	−	115.052i	−0.222877	−	0.250113i
$461$	−486.611	+	749.316i	−1.05556	+	1.62541i	−0.320714	+	0.947176i	$0.603923\pi$
$461$	−486.611	+	749.316i	−1.05556	+	1.62541i	−0.734842	+	0.678238i	$0.762744\pi$
$462$	233.705	−	12.2480i	0.505855	−	0.0265107i
$463$	255.484	−	501.415i	0.551801	−	1.08297i	−0.431691	−	0.902021i	$-0.642083\pi$
$463$	255.484	−	501.415i	0.551801	−	1.08297i	0.983492	−	0.180949i	$-0.0579170\pi$
$464$	−787.034	+	167.289i	−1.69619	+	0.360537i
$465$	359.822	−	135.997i	0.773812	−	0.292466i
$466$	123.297	+	189.861i	0.264587	+	0.407428i
$467$	−163.923	−	225.621i	−0.351014	−	0.483129i	0.596604	−	0.802536i	$-0.296516\pi$
$467$	−163.923	−	225.621i	−0.351014	−	0.483129i	−0.947618	+	0.319407i	$0.896516\pi$
$468$	−16.8103	+	43.9487i	−0.0359195	+	0.0939074i
$469$	189.846	−	137.931i	0.404789	−	0.294097i
$470$	82.4603	−	17.0832i	0.175447	−	0.0363473i
$471$	−69.9489	+	31.1433i	−0.148511	+	0.0661216i
$472$	481.909	+	50.6507i	1.02099	+	0.107311i
$473$	42.8468	+	84.0916i	0.0905852	+	0.177783i
$474$	−576.585	−	154.495i	−1.21642	−	0.325940i
$475$	−311.829	+	197.959i	−0.656481	+	0.416755i
$476$	136.385	+	136.385i	0.286524	+	0.286524i
$477$	18.0830	−	3.84365i	0.0379098	−	0.00805797i
$478$	−291.173	−	653.985i	−0.609149	−	1.36817i
$479$	8.42306	+	3.23331i	0.0175847	+	0.00675012i	0.367144	−	0.930164i	$-0.380335\pi$
$479$	8.42306	+	3.23331i	0.0175847	+	0.00675012i	−0.349560	+	0.936914i	$0.613669\pi$
$480$	75.0732	+	286.074i	0.156402	+	0.595987i
$481$	819.913	+	472.077i	1.70460	+	0.981448i
$482$	−263.380			−0.546432
$483$	−383.665	−	310.686i	−0.794338	−	0.643243i
$484$	153.758	+	32.6822i	0.317681	+	0.0675252i
$485$	397.343	−	393.263i	0.819263	−	0.810851i
$486$	−133.817	−	262.631i	−0.275344	−	0.540393i
$487$	5.41652	+	103.353i	0.0111222	+	0.212224i	0.998537	+	0.0540726i	$0.0172202\pi$
$487$	5.41652	+	103.353i	0.0111222	+	0.212224i	−0.987415	+	0.158152i	$0.949446\pi$
$488$	387.676	−	20.3172i	0.794418	−	0.0416337i
$489$	121.147	−	61.7275i	0.247744	−	0.126232i
$490$	−213.652	+	414.019i	−0.436024	+	0.844938i
$491$	33.8310	−	159.163i	0.0689023	−	0.324160i	−0.930175	−	0.367118i	$-0.880345\pi$
$491$	33.8310	−	159.163i	0.0689023	−	0.324160i	0.999077	+	0.0429575i	$0.0136780\pi$
$492$	158.001	−	195.116i	0.321141	−	0.396576i
$493$			551.909i			1.11949i
$494$	318.443	−	319.202i	0.644621	−	0.646158i
$495$	−31.2448	+	38.1796i	−0.0631208	+	0.0771305i
$496$	211.996	−	552.269i	0.427411	−	1.11344i
$497$	418.809	−	186.466i	0.842674	−	0.375183i
$498$	−58.2666	−	274.123i	−0.117001	−	0.550448i
$499$	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	$0.232464\pi$
$500$	36.4040	+	185.330i	0.0728080	+	0.370660i
$501$	−15.7777	+	58.8832i	−0.0314924	+	0.117531i
$502$	241.940	−	123.275i	0.481952	−	0.245567i
$503$	79.8275	−	759.508i	0.158703	−	1.50996i	−0.568014	−	0.823019i	$-0.692288\pi$
$503$	79.8275	−	759.508i	0.158703	−	1.50996i	0.726717	−	0.686937i	$-0.241045\pi$
$504$	−53.6162	−	120.424i	−0.106381	−	0.238937i
$505$	−297.768	+	659.616i	−0.589640	+	1.30617i
$506$	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
$509$	−626.538	+	406.878i	−1.23092	+	0.799368i	−0.985438	−	0.170033i	$-0.945613\pi$
$509$	−626.538	+	406.878i	−1.23092	+	0.799368i	−0.245481	+	0.969401i	$0.578946\pi$
$510$	408.417	−	19.2915i	0.800818	−	0.0378264i
$511$	219.149	+	1031.01i	0.428863	+	2.01764i
$512$	−6.25718	−	3.18819i	−0.0122210	−	0.00622693i
$513$	22.6444	+	432.080i	0.0441411	+	0.842262i
$514$	−502.021	−	326.016i	−0.976695	−	0.634273i
$515$	−228.505	−	133.504i	−0.443699	−	0.259232i
$516$	59.5349	−	66.1202i	0.115378	−	0.128140i
$517$	−29.3892	+	3.08893i	−0.0568456	+	0.00597471i
$518$	1554.16	−	416.436i	3.00031	−	0.803931i
$519$	−209.657	−	288.569i	−0.403964	−	0.556009i
$520$	153.101	+	347.577i	0.294425	+	0.668417i
$521$	−680.205	−	494.198i	−1.30557	−	0.948556i	−0.305581	−	0.952166i	$-0.598851\pi$
$521$	−680.205	−	494.198i	−1.30557	−	0.948556i	−0.999993	+	0.00361028i	$0.998851\pi$
$522$	−82.0584	+	213.769i	−0.157200	+	0.409520i
$523$	−310.678	−	345.043i	−0.594030	−	0.659737i	0.368906	−	0.929467i	$-0.379732\pi$
$523$	−310.678	−	345.043i	−0.594030	−	0.659737i	−0.962936	+	0.269729i	$0.913066\pi$
$524$	−61.0372	+	35.2399i	−0.116483	+	0.0672516i
$525$	210.995	+	567.085i	0.401895	+	1.08016i
$526$	−271.095	−	72.6398i	−0.515391	−	0.138099i
$527$	−340.305	−	220.997i	−0.645740	−	0.419349i
$528$	−32.7224	−	206.601i	−0.0619742	−	0.391290i
$529$	−11.8035	+	112.303i	−0.0223129	+	0.212293i
$530$	−49.7271	+	75.7147i	−0.0938247	+	0.142858i
$531$	125.019	−	154.385i	0.235440	−	0.290744i
$532$		−	210.235i		−	0.395179i
$533$	419.401	−	728.426i	0.786870	−	1.36665i
$534$	−178.953	−	550.762i	−0.335118	−	1.03139i
$535$	915.242	+	413.164i	1.71073	+	0.772269i
$536$	−97.4219	−	108.198i	−0.181757	−	0.201862i
$537$	285.526	+	257.089i	0.531706	+	0.478750i
$538$	724.350	+	369.075i	1.34638	+	0.686013i
$539$	89.0431	−	137.114i	0.165201	−	0.254387i
$540$	210.064	+	69.4543i	0.389007	+	0.128619i
$541$	45.0295	−	88.3754i	0.0832339	−	0.163356i	−0.845638	−	0.533757i	$-0.820780\pi$
$541$	45.0295	−	88.3754i	0.0832339	−	0.163356i	0.928872	+	0.370401i	$0.120780\pi$
$542$	−104.078	−	46.3384i	−0.192025	−	0.0854951i
$543$	633.536	+	365.772i	1.16673	+	0.673613i
$544$	196.339	−	242.458i	0.360917	−	0.445695i
$545$	152.702	−	391.748i	0.280187	−	0.718803i
$546$	−403.017	−	618.978i	−0.738127	−	1.13366i
$547$	−176.474	−	128.216i	−0.322622	−	0.234399i	0.414671	−	0.909971i	$-0.363897\pi$
$547$	−176.474	−	128.216i	−0.322622	−	0.234399i	−0.737294	+	0.675572i	$0.763897\pi$
$548$	−313.959	−	16.4539i	−0.572918	−	0.0300254i
$549$	79.5768	−	137.831i	0.144949	−	0.251058i
$550$	−22.7858	−	240.659i	−0.0414287	−	0.437563i
$551$	425.378	−	425.378i	0.772011	−	0.772011i
$552$	−166.825	+	256.887i	−0.302219	+	0.465376i
$553$	−724.153	+	586.408i	−1.30950	+	1.06041i
$554$	−65.1120	−	411.101i	−0.117531	−	0.742060i
$555$	428.848	−	831.031i	0.772698	−	1.49735i
$556$	−316.116	+	33.2252i	−0.568554	+	0.0597575i
$557$	−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
$559$	161.935	−	250.009i	0.289686	−	0.447243i
$560$	866.968	+	337.941i	1.54816	+	0.603466i
$561$	−143.283	−	7.50915i	−0.255407	−	0.0133853i
$562$	−490.102	−	104.174i	−0.872068	−	0.185364i
$563$	−417.629	−	376.034i	−0.741792	−	0.667912i	0.208940	−	0.977929i	$-0.432999\pi$
$563$	−417.629	−	376.034i	−0.741792	−	0.667912i	−0.950731	+	0.310016i	$0.899665\pi$
$564$	12.6476	+	24.8224i	0.0224249	+	0.0440113i
$565$	−540.042	−	396.637i	−0.955826	−	0.702013i
$566$	211.446	−	11.0814i	0.373580	−	0.0195785i
$567$	499.521	+	79.1163i	0.880989	+	0.139535i
$568$	−142.219	−	246.330i	−0.250385	−	0.433680i
$569$	−660.215	+	69.3914i	−1.16031	+	0.121953i	−0.665054	−	0.746795i	$-0.731592\pi$
$569$	−660.215	+	69.3914i	−1.16031	+	0.121953i	−0.495254	+	0.868748i	$0.664925\pi$
$570$	−329.652	−	299.915i	−0.578337	−	0.526166i
$571$	−316.112	+	435.091i	−0.553612	+	0.761981i	−0.990497	−	0.137536i	$-0.956082\pi$
$571$	−316.112	+	435.091i	−0.553612	+	0.761981i	0.436885	+	0.899517i	$0.356082\pi$
$572$	25.0932	+	76.9173i	0.0438693	+	0.134471i
$573$	116.345	−	358.073i	0.203045	−	0.624909i
$574$	−369.970	−	1380.75i	−0.644547	−	2.40548i
$575$	−303.983	+	409.443i	−0.528666	+	0.712074i
$576$	−51.8845	+	29.9555i	−0.0900772	+	0.0520061i
$577$	192.525	+	377.851i	0.333665	+	0.654855i	0.995497	−	0.0947977i	$-0.0302204\pi$
$577$	192.525	+	377.851i	0.333665	+	0.654855i	−0.661831	+	0.749653i	$0.730220\pi$
$578$	155.529	+	192.062i	0.269081	+	0.332287i
$579$	−233.647	+	189.204i	−0.403536	+	0.326777i
$580$	−123.667	−	281.664i	−0.213219	−	0.485627i
$581$	−399.650	−	177.936i	−0.687866	−	0.306258i
$582$	584.178	+	337.275i	1.00374	+	0.579511i
$583$	20.0045	−	24.7035i	0.0343130	−	0.0423730i
$584$	621.968	−	202.090i	1.06501	−	0.346044i
$585$	153.693	+	24.9683i	0.262722	+	0.0426809i
$586$	−246.823	+	759.642i	−0.421199	+	1.29632i
$587$	926.588	−	601.733i	1.57851	−	1.02510i	0.605070	−	0.796172i	$-0.293145\pi$
$587$	926.588	−	601.733i	1.57851	−	1.02510i	0.973444	−	0.228927i	$-0.0735216\pi$
$588$	−150.760	−	32.0450i	−0.256394	−	0.0544982i
$589$	91.9557	+	432.617i	0.156122	+	0.734495i
$590$	96.7511	+	968.579i	0.163985	+	1.64166i
$591$	9.83434	+	187.650i	0.0166402	+	0.317513i
$592$	−515.384	−	1342.62i	−0.870580	−	2.26794i
$593$	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	$0.467634\pi$
$594$	−258.693	−	115.177i	−0.435510	−	0.193901i
$595$	350.378	−	533.488i	0.588871	−	0.896618i
$596$	15.4215	+	5.91976i	0.0258750	+	0.00993248i
$597$	595.611	−	819.789i	0.997674	−	1.37318i
$598$	252.520	−	568.990i	0.422274	−	0.951489i
$599$	1135.67			1.89594			0.947972	−	0.318354i	$-0.103130\pi$
$599$	1135.67			1.89594			0.947972	+	0.318354i	$0.103130\pi$
$600$	336.232	−	166.971i	0.560387	−	0.278285i
$601$	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	$-0.0838080\pi$
$602$	−105.322	−	495.503i	−0.174954	−	0.823094i
$603$	−58.9546	+	9.33750i	−0.0977689	+	0.0154851i
$604$	136.134	+	168.111i	0.225387	+	0.278329i
$605$	2.68421	−	520.164i	0.00443671	−	0.859776i
$606$	−862.482	−	136.604i	−1.42324	−	0.225419i
$607$	−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	$-0.378523\pi$
$608$	−338.198	+	35.5460i	−0.556246	+	0.0584639i
$609$	−536.729	−	826.490i	−0.881328	−	1.35713i
$610$	197.947	+	754.297i	0.324503	+	1.23655i
$611$	54.9110	+	75.3896i	0.0898706	+	0.123387i
$612$	−15.1607	−	46.6598i	−0.0247724	−	0.0762415i
$613$	−98.8021	+	64.1628i	−0.161178	+	0.104670i	−0.622708	−	0.782455i	$-0.713967\pi$
$613$	−98.8021	+	64.1628i	−0.161178	+	0.104670i	0.461530	+	0.887125i	$0.347301\pi$
$614$	−97.7705	−	108.585i	−0.159235	−	0.176849i
$615$	−738.304	−	380.996i	−1.20049	−	0.619506i
$616$	−201.955	−	102.901i	−0.327849	−	0.167047i
$617$	628.585	−	241.291i	1.01878	−	0.391072i	0.209066	−	0.977902i	$-0.432958\pi$
$617$	628.585	−	241.291i	1.01878	−	0.391072i	0.809710	+	0.586830i	$0.199624\pi$
$618$	82.6469	−	308.443i	0.133733	−	0.499098i
$619$	251.235	+	39.7917i	0.405872	+	0.0642838i	0.356033	−	0.934473i	$-0.384129\pi$
$619$	251.235	+	39.7917i	0.405872	+	0.0642838i	0.0498392	+	0.998757i	$0.484129\pi$
$620$	223.192	+	36.5317i	0.359987	+	0.0589221i
$621$	242.971	+	545.721i	0.391257	+	0.878778i
$622$	−158.531	−	60.8544i	−0.254873	−	0.0978366i
$623$	−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
$627$	104.646	+	116.222i	0.166900	+	0.185361i
$628$	−44.7715	−	4.70567i	−0.0712921	−	0.00749311i
$629$	−974.316	+	154.317i	−1.54899	+	0.245336i
$630$	215.031	−	154.540i	0.341318	−	0.245301i
$631$	250.330	+	652.133i	0.396720	+	1.03349i	0.975886	+	0.218281i	$0.0700451\pi$
$631$	250.330	+	652.133i	0.396720	+	1.03349i	−0.579166	+	0.815210i	$0.696622\pi$
$632$	408.803	+	408.803i	0.646841	+	0.646841i
$633$	−491.212	−	218.701i	−0.776006	−	0.345500i
$634$	96.5892	−	454.417i	0.152349	−	0.716745i
$635$	107.104	+	97.4426i	0.168668	+	0.153453i
$636$	−28.5004	−	9.26034i	−0.0448119	−	0.0145603i
$637$	−515.323	−	26.3918i	−0.808984	−	0.0414314i
$638$	121.665	+	374.447i	0.190698	+	0.586908i
$639$	−116.451	−	6.10295i	−0.182240	−	0.00955078i
$640$	198.879	−	727.194i	0.310748	−	1.13624i
$641$	487.130	+	438.614i	0.759954	+	0.684265i	0.955026	−	0.296524i	$-0.0958273\pi$
$641$	487.130	+	438.614i	0.759954	+	0.684265i	−0.195072	+	0.980789i	$0.562494\pi$
$642$	−189.543	+	1196.73i	−0.295238	+	1.86406i
$643$	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	$0.577608\pi$
$644$	−104.020	−	270.980i	−0.161521	−	0.420777i
$645$	−254.217	−	148.526i	−0.394134	−	0.230273i
$646$	−49.1405	+	467.541i	−0.0760689	+	0.723747i
$647$	−316.248	−	710.304i	−0.488791	−	1.09784i	−0.974636	−	0.223798i	$-0.928155\pi$
$647$	−316.248	−	710.304i	−0.488791	−	1.09784i	0.485845	−	0.874045i	$-0.338512\pi$
$648$	16.4223	−	313.357i	0.0253431	−	0.483576i
$649$		−	341.581i		−	0.526319i
$650$	−621.310	+	442.798i	−0.955862	+	0.681228i
$651$	724.529			1.11295
$652$	79.8312	+	4.18377i	0.122440	+	0.00641683i
$653$	104.930	−	46.7177i	0.160689	−	0.0715432i	−0.324816	−	0.945777i	$-0.605302\pi$
$653$	104.930	−	46.7177i	0.160689	−	0.0715432i	0.485505	+	0.874234i	$0.338636\pi$
$654$	504.545	+	53.0298i	0.771476	+	0.0810854i
$655$	155.163	+	174.124i	0.236889	+	0.265838i
$656$	−1192.81	+	457.876i	−1.81831	+	0.697982i
$657$	69.3922	−	258.975i	0.105620	−	0.394178i
$658$	156.662	+	24.8128i	0.238088	+	0.0377094i
$659$	646.589	−	718.110i	0.981167	−	1.08970i	−0.0147928	−	0.999891i	$-0.504709\pi$
$659$	646.589	−	718.110i	0.981167	−	1.08970i	0.995959	−	0.0898052i	$-0.0286245\pi$
$660$	74.8063	−	28.2734i	0.113343	−	0.0428385i
$661$	−40.4022	+	770.920i	−0.0611229	+	1.16629i	0.780118	+	0.625633i	$0.215159\pi$
$661$	−40.4022	+	770.920i	−0.0611229	+	1.16629i	−0.841241	+	0.540661i	$0.818174\pi$
$662$	1264.74	−	410.938i	1.91048	−	0.620752i
$663$	206.067	+	403.241i	0.310809	+	0.608206i
$664$	−83.8752	+	258.141i	−0.126318	+	0.388767i
$665$	−681.230	+	141.130i	−1.02441	+	0.212225i
$666$	−400.323	−	85.0913i	−0.601086	−	0.127765i
$667$	337.819	−	758.754i	0.506476	−	1.13756i
$668$	−25.3436	+	25.3436i	−0.0379396	+	0.0379396i
$669$	−561.631	+	215.590i	−0.839508	+	0.322257i
$670$	173.130	−	235.725i	0.258403	−	0.351829i
$671$	−42.8094	−	270.288i	−0.0637994	−	0.402814i
$672$	−58.2300	+	554.022i	−0.0866518	+	0.824437i
$673$	−599.368	+	539.673i	−0.890591	+	0.801892i	−0.980999	−	0.194013i	$-0.937850\pi$
$673$	−599.368	+	539.673i	−0.890591	+	0.801892i	0.0904078	+	0.995905i	$0.471183\pi$
$674$	−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	−0.941853	−	0.336025i	$-0.890917\pi$
$677$	11.9374	−	36.7396i	0.0176328	−	0.0542683i	0.959486	+	0.281757i	$0.0909172\pi$
$678$	289.734	−	754.784i	0.427337	−	1.11325i
$679$	961.952	−	428.289i	1.41672	−	0.630764i
$680$	−351.909	−	181.600i	−0.517513	−	0.267059i
$681$	76.0995	−	480.473i	0.111747	−	0.705541i
$682$	−279.600	−	74.9186i	−0.409971	−	0.109851i
$683$	−250.660	−	652.993i	−0.366999	−	0.956065i	−0.985408	−	0.170209i	$-0.945556\pi$
$683$	−250.660	−	652.993i	−0.366999	−	0.956065i	0.618409	−	0.785856i	$-0.287778\pi$
$684$	−24.2776	+	47.6475i	−0.0354936	+	0.0696601i
$685$	157.443	+	1028.38i	0.229844	+	1.50128i
$686$	152.925	−	137.694i	0.222923	−	0.200720i
$687$	22.9719	+	35.3736i	0.0334380	+	0.0514900i
$688$	−430.623	+	139.918i	−0.625905	+	0.203369i
$689$	−99.1091	−	15.5764i	−0.143845	−	0.0226073i
$690$	−573.293	−	223.467i	−0.830859	−	0.323866i
$691$	−282.174	+	183.246i	−0.408356	+	0.265190i	−0.732430	−	0.680842i	$-0.761614\pi$
$691$	−282.174	+	183.246i	−0.408356	+	0.265190i	0.324074	+	0.946032i	$0.394947\pi$
$692$	−21.9211	−	208.565i	−0.0316779	−	0.301395i
$693$	−80.4741	+	46.4618i	−0.116124	+	0.0670444i
$694$	25.8387	−	163.139i	0.0372315	−	0.235071i
$695$	319.868	+	1002.02i	0.460241	+	1.44175i
$696$	−475.171	+	384.786i	−0.682717	+	0.552854i
$697$	137.098	+	865.600i	0.196697	+	1.24189i
$698$	789.247	−	167.760i	1.13073	−	0.240343i
$699$	214.626	+	123.914i	0.307047	+	0.177274i
$700$	−59.2740	+	350.772i	−0.0846772	+	0.501103i
$701$		−	310.721i		−	0.443253i	−0.975132	−	0.221627i	$-0.928863\pi$
$701$		−	310.721i		−	0.443253i	0.975132	−	0.221627i	$-0.0711366\pi$
$702$	94.4793	+	888.731i	0.134586	+	1.26600i
$703$	869.882	+	632.006i	1.23738	+	0.899013i
$704$	−36.9170	+	96.1720i	−0.0524389	+	0.136608i
$705$	71.9423	−	57.6456i	0.102046	−	0.0817668i
$706$	−59.0229	+	132.568i	−0.0836018	+	0.187773i
$707$	−963.881	+	963.881i	−1.36334	+	1.36334i
$708$	−300.632	+	115.402i	−0.424621	+	0.162997i
$709$	−560.884	+	29.3947i	−0.791092	+	0.0414594i	−0.443602	−	0.896224i	$-0.646299\pi$
$709$	−560.884	+	29.3947i	−0.791092	+	0.0414594i	−0.347491	+	0.937683i	$0.612966\pi$
$710$	426.588	−	380.134i	0.600828	−	0.535400i
$711$	231.839	−	49.2788i	0.326074	−	0.0693092i
$712$	−116.613	+	548.620i	−0.163782	+	0.770534i
$713$	332.575	+	512.120i	0.466444	+	0.718261i
$714$	732.432	+	237.982i	1.02581	+	0.333307i
$715$	232.392	−	132.944i	0.325024	−	0.185936i
$716$	69.8057	+	214.840i	0.0974940	+	0.300056i
$717$	−609.041	−	493.191i	−0.849429	−	0.687854i
$718$	−446.881	+	774.021i	−0.622397	+	1.07802i
$719$	−384.215	+	862.961i	−0.534374	+	1.20022i	0.421603	+	0.906781i	$0.361468\pi$
$719$	−384.215	+	862.961i	−0.534374	+	1.20022i	−0.955977	+	0.293443i	$0.905199\pi$
$720$	−157.464	−	176.707i	−0.218700	−	0.245426i
$721$	−313.697	−	387.384i	−0.435087	−	0.537287i
$722$	−260.377	+	210.849i	−0.360633	+	0.292035i
$723$	−256.903	+	130.899i	−0.355330	+	0.181049i
$724$	215.054	+	372.484i	0.297035	+	0.514480i
$725$	−829.664	+	589.801i	−1.14436	+	0.813519i
$726$	606.253	−	162.445i	0.835060	−	0.223754i
$727$	−973.234	−	316.223i	−1.33870	−	0.434970i	−0.449823	−	0.893118i	$-0.648513\pi$
$727$	−973.234	−	316.223i	−1.33870	−	0.434970i	−0.888876	+	0.458148i	$0.848513\pi$
$728$	38.2900	+	714.343i	0.0525961	+	0.981241i
$729$	−652.066	−	473.753i	−0.894466	−	0.649868i
$730$	650.979	+	1141.09i	0.891752	+	1.56313i
$731$	32.4641	+	308.875i	0.0444106	+	0.422538i
$732$	−223.422	+	128.993i	−0.305222	+	0.176220i
$733$	−0.150175	+	0.948166i	−0.000204877	+	0.00129354i	−0.987791	−	0.155788i	$-0.950208\pi$
$733$	−0.150175	+	0.948166i	−0.000204877	+	0.00129354i	0.987586	+	0.157081i	$0.0502084\pi$
$734$	41.4547	+	791.003i	0.0564778	+	1.07766i
$735$	−2.63187	+	510.022i	−0.00358078	+	0.693908i
$736$	−418.329	+	213.149i	−0.568382	+	0.289605i
$737$	−68.6751	+	76.2714i	−0.0931819	+	0.103489i
$738$	−75.5967	+	355.654i	−0.102435	+	0.481916i
$739$	47.3266	−	903.046i	0.0640414	−	1.22198i	−0.757885	−	0.652389i	$-0.773767\pi$
$739$	47.3266	−	903.046i	0.0640414	−	1.22198i	0.821926	−	0.569594i	$-0.192900\pi$
$740$	462.658	−	297.071i	0.625214	−	0.401447i
$741$	151.970	−	469.617i	0.205088	−	0.633761i
$742$	−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	$0.860322\pi$
$744$	−46.9885	−	447.066i	−0.0631566	−	0.600895i
$745$	8.82957	−	53.9446i	0.0118518	−	0.0724088i
$746$	−338.487	+	53.6111i	−0.453736	+	0.0718647i
$747$	70.0286	+	86.4781i	0.0937464	+	0.115767i
$748$	−70.7487	−	45.9447i	−0.0945838	−	0.0614234i
$749$	1337.42	+	1337.42i	1.78561	+	1.78561i
$750$	465.458	+	593.343i	0.620610	+	0.791123i
$751$	−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	$0.678201\pi$
$752$	7.41980	−	141.578i	0.00986675	−	0.188269i
$753$	174.724	−	240.486i	0.232037	−	0.319371i
$754$	830.380	−	924.441i	1.10130	−	1.22605i
$755$	453.348	−	553.969i	0.600461	−	0.733734i
$756$	323.858	+	262.255i	0.428384	+	0.346898i
$757$	−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	$0.942893\pi$
$758$	−399.581	+	897.473i	−0.527151	+	1.18400i
$759$	192.387	+	98.0259i	0.253474	+	0.129151i
$760$	131.264	+	411.196i	0.172715	+	0.541047i
$761$	218.835	+	142.113i	0.287563	+	0.186745i	0.680357	−	0.732881i	$-0.261825\pi$
$761$	218.835	+	142.113i	0.287563	+	0.186745i	−0.392794	+	0.919626i	$0.628491\pi$
$762$	−79.3182	+	155.671i	−0.104092	+	0.204292i
$763$	529.914	−	588.529i	0.694514	−	0.771335i
$764$	164.503	−	148.119i	0.215318	−	0.193874i
$765$	−141.016	+	80.4481i	−0.184334	+	0.105161i
$766$	−738.242	+	239.869i	−0.963762	+	0.313145i
$767$	−933.001	+	540.150i	−1.21643	+	0.704238i
$768$	652.564			0.849692
$769$	−820.123	−	664.123i	−1.06648	−	0.863619i	−0.0754357	−	0.997151i	$-0.524035\pi$
$769$	−820.123	−	664.123i	−1.06648	−	0.863619i	−0.991044	+	0.133532i	$0.957368\pi$
$770$	120.113	−	439.188i	0.155990	−	0.570374i
$771$	−651.705	−	68.4969i	−0.845272	−	0.0888417i
$772$	−174.588	+	27.6520i	−0.226150	+	0.0358187i
$773$	−52.3783	+	80.6555i	−0.0677598	+	0.104341i	−0.870926	−	0.491414i	$-0.836480\pi$
$773$	−52.3783	+	80.6555i	−0.0677598	+	0.104341i	0.803166	+	0.595755i	$0.203147\pi$
$774$	−33.3497	+	124.463i	−0.0430874	+	0.160804i
$775$	−31.4529	−	747.737i	−0.0405844	−	0.964822i
$776$	−326.659	−	565.790i	−0.420952	−	0.729111i
$777$	1308.98	−	1178.61i	1.68465	−	1.51687i
$778$	−1096.18	−	420.783i	−1.40897	−	0.540853i
$779$	561.486	−	772.819i	0.720778	−	0.992065i
$780$	−195.520	−	159.618i	−0.250666	−	0.204638i
$781$	−162.214	+	117.855i	−0.207700	+	0.150903i
$782$	167.989	+	626.945i	0.214820	+	0.801720i
$783$	124.644	+	1185.91i	0.159188	+	1.51457i
$784$	582.887	+	524.833i	0.743478	+	0.669430i
$785$	14.8070	+	148.233i	0.0188624	+	0.188832i
$786$	−153.268	+	236.012i	−0.194997	+	0.300269i
$787$	1212.85	−	63.5628i	1.54111	−	0.0807659i	0.737262	−	0.675607i	$-0.236118\pi$
$787$	1212.85	−	63.5628i	1.54111	−	0.0807659i	0.803844	+	0.594841i	$0.202785\pi$
$788$	−50.1566	+	98.4379i	−0.0636505	+	0.124921i
$789$	−300.531	+	63.8798i	−0.380901	+	0.0809629i
$790$	−637.543	+	970.727i	−0.807017	+	1.22877i
$791$	−687.366	−	1058.45i	−0.868984	−	1.33812i
$792$	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
$795$	−10.8743	+	98.5670i	−0.0136784	+	0.123984i
$796$	544.265	−	242.323i	0.683750	−	0.304425i
$797$	795.448	+	83.6049i	0.998052	+	0.104900i	0.589443	−	0.807810i	$-0.299347\pi$
$797$	795.448	+	83.6049i	0.998052	+	0.104900i	0.408609	+	0.912709i	$0.366014\pi$
$798$	−381.092	−	747.936i	−0.477559	−	0.937263i
$799$	−93.9321	−	25.1690i	−0.117562	−	0.0315007i
$800$	574.296	+	36.0444i	0.717871	+	0.0450554i
$801$	162.594	+	162.594i	0.202989	+	0.202989i
$802$	−470.842	+	100.081i	−0.587085	+	0.124789i
$803$	−187.507	−	421.148i	−0.233508	−	0.524468i
$804$	90.3295	+	34.6742i	0.112350	+	0.0431272i
$805$	−808.237	+	518.965i	−1.00402	+	0.644677i
$806$	237.504	+	882.176i	0.294670	+	1.09451i
$807$	889.967			1.10281
$808$	657.268	+	532.245i	0.813451	+	0.658719i
$809$	99.3539	+	21.1183i	0.122811	+	0.0261042i	0.268907	−	0.963166i	$-0.413338\pi$
$809$	99.3539	+	21.1183i	0.122811	+	0.0261042i	−0.146096	+	0.989270i	$0.546671\pi$
$810$	623.080	−	95.3930i	0.769235	−	0.117769i
$811$	−49.6658	−	97.4747i	−0.0612402	−	0.120191i	0.858357	−	0.513052i	$-0.171485\pi$
$811$	−49.6658	−	97.4747i	−0.0612402	−	0.120191i	−0.919598	+	0.392861i	$0.871485\pi$
$812$	−30.3237	−	578.611i	−0.0373445	−	0.712575i
$813$	−124.548	+	6.52730i	−0.153196	+	0.00802866i
$814$	−627.014	+	319.480i	−0.770288	+	0.392481i
$815$	−40.0335	−	261.488i	−0.0491208	−	0.320844i
$816$	143.116	−	673.309i	0.175387	−	0.825133i
$817$	213.041	−	263.084i	0.260760	−	0.322012i
$818$			157.298i			0.192296i
$819$	254.162	+	146.337i	0.310332	+	0.178678i
$820$	−263.923	−	411.034i	−0.321858	−	0.501261i
$821$	296.036	−	771.201i	0.360580	−	0.939344i	−0.626544	−	0.779386i	$-0.715531\pi$
$821$	296.036	−	771.201i	0.360580	−	0.939344i	0.987124	−	0.159958i	$-0.0511357\pi$
$822$	−1146.77	+	510.576i	−1.39510	+	0.621138i
$823$	14.8169	+	69.7082i	0.0180036	+	0.0847001i	0.986232	−	0.165367i	$-0.0528808\pi$
$823$	14.8169	+	69.7082i	0.0180036	+	0.0847001i	−0.968229	+	0.250067i	$0.919547\pi$
$824$	−218.688	+	218.688i	−0.265398	+	0.265398i
$825$	−141.832	−	223.417i	−0.171918	−	0.270808i
$826$	−474.526	+	1770.96i	−0.574487	+	2.14401i
$827$	−827.720	+	421.744i	−1.00087	+	0.509969i	−0.876055	−	0.482211i	$-0.839834\pi$
$827$	−827.720	+	421.744i	−1.00087	+	0.509969i	−0.124815	+	0.992180i	$0.539834\pi$
$828$	−7.71746	+	73.4267i	−0.00932061	+	0.0886796i
$829$	−290.850	−	653.261i	−0.350845	−	0.788011i	−0.999634	−	0.0270426i	$-0.991391\pi$
$829$	−290.850	−	653.261i	−0.350845	−	0.788011i	0.648789	−	0.760968i	$-0.275276\pi$
$830$	−541.956	−	59.7910i	−0.652959	−	0.0720373i
$831$	−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
$834$	−1064.39	+	691.225i	−1.27625	+	0.828807i
$835$	99.1347	+	65.1086i	0.118724	+	0.0779743i
$836$	19.1174	+	89.9402i	0.0228677	+	0.107584i
$837$	−781.137	−	398.009i	−0.933258	−	0.475519i
$838$	21.9346	+	418.537i	0.0261750	+	0.499448i
$839$	866.501	+	562.713i	1.03278	+	0.670694i	0.945544	−	0.325493i	$-0.105530\pi$
$839$	866.501	+	562.713i	1.03278	+	0.670694i	0.0872346	+	0.996188i	$0.472197\pi$
$840$	703.592	−	70.2816i	0.837609	−	0.0836686i
$841$	546.635	−	607.100i	0.649982	−	0.721878i
$842$	203.225	−	21.3599i	0.241360	−	0.0253680i
$843$	−529.824	+	141.966i	−0.628499	+	0.168406i
$844$	−185.820	−	255.760i	−0.220166	−	0.303033i
$845$	−730.614	−	424.532i	−0.864632	−	0.502405i
$846$	−32.6403	−	23.7146i	−0.0385819	−	0.0280314i
$847$	351.114	−	914.683i	0.414538	−	1.07991i
$848$	102.043	+	113.331i	0.120334	+	0.133645i
$849$	200.739	−	115.897i	0.236442	−	0.136510i
$850$	213.809	−	766.225i	0.251540	−	0.901441i
$851$	1433.93	+	384.220i	1.68499	+	0.451492i
$852$	158.530	+	102.950i	0.186068	+	0.120834i
$853$	−207.429	−	1309.66i	−0.243176	−	1.53535i	−0.743038	−	0.669249i	$-0.766616\pi$
$853$	−207.429	−	1309.66i	−0.243176	−	1.53535i	0.499861	−	0.866105i	$-0.333384\pi$
$854$	−153.536	+	1460.80i	−0.179785	+	1.71054i
$855$	170.691	+	46.6818i	0.199638	+	0.0545986i
$856$	738.510	−	911.984i	0.862745	−	1.06540i
$857$		−	425.282i		−	0.496245i	−0.968729	−	0.248123i	$-0.920186\pi$
$857$		−	425.282i		−	0.496245i	0.968729	−	0.248123i	$-0.0798136\pi$
$858$	228.700	+	228.156i	0.266550	+	0.265916i
$859$	−452.985	−	1394.15i	−0.527340	−	1.62299i	−0.759641	−	0.650343i	$-0.774625\pi$
$859$	−452.985	−	1394.15i	−0.527340	−	1.62299i	0.232301	−	0.972644i	$-0.425375\pi$
$860$	−85.7780	−	150.358i	−0.0997419	−	0.174835i
$861$	−1047.10	−	1162.92i	−1.21614	−	1.35066i
$862$	−758.360	−	682.830i	−0.879768	−	0.792147i
$863$	92.4328	+	47.0969i	0.107106	+	0.0545734i	0.506723	−	0.862109i	$-0.330857\pi$
$863$	92.4328	+	47.0969i	0.107106	+	0.0545734i	−0.399617	+	0.916682i	$0.630857\pi$
$864$	367.123	−	565.320i	0.424911	−	0.654306i
$865$	−661.104	+	211.040i	−0.764282	+	0.243977i
$866$	−426.717	+	837.479i	−0.492744	+	0.967066i
$867$	247.158	+	110.042i	0.285073	+	0.126923i
$868$	368.912	+	212.991i	0.425013	+	0.245382i
$869$	256.474	−	316.719i	0.295137	−	0.364464i
$870$	−950.530	−	777.879i	−1.09256	−	0.894114i
$871$	316.927	+	66.9706i	0.363865	+	0.0768894i
$872$	−397.515	−	288.811i	−0.455866	−	0.331206i
$873$	−267.474	−	14.0177i	−0.306385	−	0.0160569i
$874$	353.735	−	612.687i	0.404731	−	0.701015i
$875$	1176.41	−	43.4045i	1.34446	−	0.0496051i
$876$	−307.312	+	307.312i	−0.350812	+	0.350812i
$877$	141.540	−	217.953i	0.161391	−	0.248521i	−0.748718	−	0.662888i	$-0.769330\pi$
$877$	141.540	−	217.953i	0.161391	−	0.248521i	0.910110	+	0.414367i	$0.135997\pi$
$878$	669.203	−	541.910i	0.762190	−	0.617209i
$879$	136.786	+	863.631i	0.155615	+	0.982515i
$880$	−401.626	−	65.7375i	−0.456393	−	0.0747017i
$881$	1422.88	−	149.551i	1.61507	−	0.169751i	0.746526	−	0.665356i	$-0.231720\pi$
$881$	1422.88	−	149.551i	1.61507	−	0.169751i	0.868548	+	0.495605i	$0.165054\pi$
$882$	215.605	−	57.7712i	0.244450	−	0.0655003i
$883$	820.186	+	1128.89i	0.928863	+	1.27847i	0.960301	+	0.278965i	$0.0899912\pi$
$883$	820.186	+	1128.89i	0.928863	+	1.27847i	−0.0314384	+	0.999506i	$0.510009\pi$
$884$	−13.6177	+	265.898i	−0.0154047	+	0.300789i
$885$	575.752	+	896.676i	0.650567	+	1.01319i
$886$	463.050	+	24.2674i	0.522630	+	0.0273899i
$887$	−835.295	−	177.547i	−0.941708	−	0.200166i	−0.288616	−	0.957445i	$-0.593195\pi$
$887$	−835.295	−	177.547i	−0.941708	−	0.200166i	−0.653092	+	0.757279i	$0.726528\pi$
$888$	−812.144	−	731.258i	−0.914577	−	0.823489i
$889$	123.817	+	243.005i	0.139277	+	0.273347i
$890$	−1126.68	−	5.81403i	−1.26594	−	0.00653262i
$891$	−220.893	+	11.5765i	−0.247916	+	0.0129927i
$892$	−349.346	−	55.3309i	−0.391643	−	0.0620302i
$893$	52.9984	+	91.7960i	0.0593487	+	0.102795i
$894$	65.5945	−	6.89425i	0.0733719	−	0.00771169i
$895$	649.291	−	370.414i	0.725465	−	0.413871i
$896$	834.651	−	1148.80i	0.931530	−	1.28214i
$897$	−36.4759	−	680.499i	−0.0406643	−	0.758639i
$898$	49.7063	−	152.980i	0.0553522	−	0.170357i
$899$	315.481	+	1177.39i	0.350924	+	1.30967i
$900$	53.9404	−	72.6538i	0.0599337	−	0.0807264i
$901$	90.5907	−	52.3025i	0.100545	−	0.0580494i
$902$	283.832	+	557.051i	0.314669	+	0.617573i
$903$	−348.995	−	430.973i	−0.386484	−	0.477268i
$904$	−608.532	+	492.780i	−0.673155	+	0.545110i
$905$	1062.60	−	946.890i	1.17415	−	1.04629i
$906$	789.044	+	351.305i	0.870910	+	0.387754i
$907$	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	$0.648107\pi$
$908$	179.994	−	222.274i	0.198231	−	0.244795i
$909$	329.760	−	107.146i	0.362773	−	0.117872i
$910$	−1389.54	+	366.421i	−1.52697	+	0.402661i
$911$	408.417	−	1256.98i	0.448317	−	1.37978i	−0.430488	−	0.902596i	$-0.641658\pi$
$911$	408.417	−	1256.98i	0.448317	−	1.37978i	0.878805	−	0.477182i	$-0.158342\pi$
$912$	−629.251	+	408.640i	−0.689968	+	0.448070i
$913$	187.154	+	39.7807i	0.204987	+	0.0435714i
$914$	279.914	+	1316.89i	0.306252	+	1.44080i
$915$	567.962	+	637.369i	0.620723	+	0.696578i
$916$	1.29785	+	24.7644i	0.00141687	+	0.0270354i
$917$	157.427	+	410.112i	0.171676	+	0.447232i
$918$	−658.926	−	658.926i	−0.717784	−	0.717784i
$919$	685.502	+	305.205i	0.745922	+	0.332106i	0.744258	−	0.667893i	$-0.232803\pi$
$919$	685.502	+	305.205i	0.745922	+	0.332106i	0.00166455	+	0.999999i	$0.499470\pi$
$920$	372.641	+	465.060i	0.405045	+	0.505500i
$921$	−149.333	−	57.3234i	−0.162142	−	0.0622404i
$922$	−1232.84	+	1696.86i	−1.33714	+	1.84041i
$923$	578.424	+	256.706i	0.626679	+	0.278122i
$924$	150.628			0.163017
$925$	−1273.19	−	1299.74i	−1.37642	−	1.40513i
$926$	660.543	−	1144.09i	0.713329	−	1.23552i
$927$	26.3616	+	124.022i	0.0284375	+	0.133788i
$928$	−925.664	+	146.611i	−0.997483	+	0.157986i
$929$	664.482	+	820.567i	0.715266	+	0.883280i	0.997094	−	0.0761849i	$-0.0242739\pi$
$929$	664.482	+	820.567i	0.715266	+	0.883280i	−0.281827	+	0.959465i	$0.590941\pi$
$930$	860.251	−	274.613i	0.925001	−	0.295283i
$931$	−579.204	−	91.7369i	−0.622131	−	0.0985359i
$932$	72.8546	+	126.188i	0.0781702	+	0.135395i
$933$	−184.877	+	19.4314i	−0.198153	+	0.0208267i
$934$	−356.570	−	549.070i	−0.381767	−	0.587869i
$935$	−101.383	+	260.091i	−0.108431	+	0.278172i
$936$	73.8132	−	166.320i	0.0788602	−	0.177692i
$937$	−234.496	−	721.704i	−0.250263	−	0.770229i	−0.994726	−	0.102566i	$-0.967295\pi$
$937$	−234.496	−	721.704i	−0.250263	−	0.770229i	0.744464	−	0.667663i	$-0.232705\pi$
$938$	462.008	−	300.032i	0.492546	−	0.319863i
$939$	1033.45	+	1147.76i	1.10059	+	1.22233i
$940$	53.5774	−	8.20264i	0.0569972	−	0.00872621i
$941$	−294.866	−	150.242i	−0.313354	−	0.159662i	0.290240	−	0.956954i	$-0.406265\pi$
$941$	−294.866	−	150.242i	−0.313354	−	0.159662i	−0.603593	+	0.797292i	$0.706265\pi$
$942$	−167.810	+	64.4160i	−0.178142	+	0.0683822i
$943$	341.348	−	1273.93i	0.361981	−	1.35093i
$944$	1618.57	+	256.357i	1.71459	+	0.271565i
$945$	632.388	−	1225.46i	0.669193	−	1.29678i
$946$	90.1154	+	202.402i	0.0952594	+	0.213956i
$947$	407.695	+	156.499i	0.430512	+	0.165258i	0.563968	−	0.825797i	$-0.309274\pi$
$947$	407.695	+	156.499i	0.430512	+	0.165258i	−0.133456	+	0.991055i	$0.542607\pi$
$948$	−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
$952$	−499.093	−	554.299i	−0.524258	−	0.582247i
$953$	−840.024	−	88.2901i	−0.881453	−	0.0926444i	−0.347022	−	0.937857i	$-0.612807\pi$
$953$	−840.024	−	88.2901i	−0.881453	−	0.0926444i	−0.534430	+	0.845212i	$0.679474\pi$
$954$	42.8646	−	6.78909i	0.0449315	−	0.00711644i
$955$	−590.385	−	433.612i	−0.618205	−	0.454044i
$956$	−165.124	−	430.162i	−0.172723	−	0.449960i
$957$	304.772	+	304.772i	0.318466	+	0.318466i
$958$	19.3492	+	8.61480i	0.0201975	+	0.00899249i
$959$	−407.413	+	1916.73i	−0.424831	+	1.99867i
$960$	−65.1928	−	314.684i	−0.0679092	−	0.327796i
$961$	61.6658	+	20.0364i	0.0641684	+	0.0208496i
$962$	1864.15	+	1207.44i	1.93778	+	1.25513i
$963$	−148.669	−	457.555i	−0.154381	−	0.475135i
$964$	−169.289	−	8.87207i	−0.175611	−	0.00920339i
$965$	206.802	+	547.159i	0.214302	+	0.567005i
$966$	−861.267	−	775.488i	−0.891580	−	0.802783i
$967$	−22.8311	+	144.150i	−0.0236102	+	0.149069i	−0.996677	−	0.0814538i	$-0.974044\pi$
$967$	−22.8311	+	144.150i	−0.0236102	+	0.149069i	0.973067	+	0.230523i	$0.0740437\pi$
$968$	−587.170	−	157.332i	−0.606581	−	0.162533i
$969$	184.434	+	480.466i	0.190334	+	0.495837i
$970$	979.818	−	873.119i	1.01012	−	0.900123i
$971$	82.4215	−	784.189i	0.0848832	−	0.807609i	−0.866412	−	0.499329i	$-0.833580\pi$
$971$	82.4215	−	784.189i	0.0848832	−	0.807609i	0.951296	−	0.308280i	$-0.0997534\pi$
$972$	−77.1649	−	173.315i	−0.0793878	−	0.178308i
$973$	−103.686	+	1978.44i	−0.106563	+	2.03334i
$974$			242.960i			0.249445i
$975$	−385.963	+	740.698i	−0.395859	+	0.759690i
$976$	1312.88			1.34517
$977$	535.601	+	28.0697i	0.548210	+	0.0287305i	0.324431	−	0.945909i	$-0.394827\pi$
$977$	535.601	+	28.0697i	0.548210	+	0.0287305i	0.223779	+	0.974640i	$0.428161\pi$
$978$	291.592	−	129.825i	0.298152	−	0.132746i
$979$	393.210	+	41.3280i	0.401644	+	0.0422145i
$980$	−151.272	+	258.917i	−0.154360	+	0.264201i
$981$	−188.061	+	72.1900i	−0.191704	+	0.0735882i
$982$	98.8660	−	368.973i	0.100678	−	0.375736i
$983$	−727.191	−	115.176i	−0.739767	−	0.117168i	−0.224833	−	0.974397i	$-0.572184\pi$
$983$	−727.191	−	115.176i	−0.739767	−	0.117168i	−0.514934	+	0.857230i	$0.672184\pi$
$984$	−649.663	+	721.524i	−0.660227	+	0.733256i
$985$	352.641	+	96.4429i	0.358011	+	0.0979115i
$986$	−67.8082	+	1293.86i	−0.0687709	+	1.31223i
$987$	165.141	−	53.6576i	0.167316	−	0.0543643i
$988$	215.434	−	194.442i	0.218050	−	0.196804i
$989$	144.429	−	444.507i	0.146035	−	0.449451i
$990$	−77.9389	+	85.6667i	−0.0787261	+	0.0865320i
$991$	1239.27	+	263.416i	1.25053	+	0.265808i	0.785151	−	0.619304i	$-0.212585\pi$
$991$	1239.27	+	263.416i	1.25053	+	0.265808i	0.465377	+	0.885112i	$0.345919\pi$
$992$	280.257	−	629.467i	0.282517	−	0.634543i
$993$	1029.40	−	1029.40i	1.03666	−	1.03666i
$994$	1004.74	−	385.682i	1.01080	−	0.388010i
$995$	−1150.57	−	1600.93i	−1.15635	−	1.60897i
$996$	−28.2173	−	178.157i	−0.0283306	−	0.178873i
$997$	106.872	−	1016.82i	0.107194	−	1.01988i	−0.800238	−	0.599682i	$-0.795294\pi$
$997$	106.872	−	1016.82i	0.107194	−	1.01988i	0.907432	−	0.420199i	$-0.138040\pi$
$998$	95.8676	−	86.3196i	0.0960597	−	0.0864926i
$999$	−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.71.53	yes	1088
13.11	odd	12	inner	325.3.bm.a.271.16	yes	1088
25.6	even	5	inner	325.3.bm.a.6.16	✓	1088
325.206	odd	60	inner	325.3.bm.a.206.53	yes	1088

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.bm.a.6.16	✓	1088	25.6	even	5	inner
325.3.bm.a.71.53	yes	1088	1.1	even	1	trivial
325.3.bm.a.206.53	yes	1088	325.206	odd	60	inner
325.3.bm.a.271.16	yes	1088	13.11	odd	12	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+(2.34433 + 0.122861i) q^{2} +(2.34774 - 1.04528i) q^{3} +(1.50269 + 0.157939i) q^{4} +(-0.496976 - 4.97524i) q^{5} +(5.63230 - 2.16204i) q^{6} +(2.43747 - 9.09675i) q^{7} +(-5.77117 - 0.914064i) q^{8} +(-1.60290 + 1.78020i) q^{9} +(-0.553811 - 11.7247i) q^{10} +(-0.215569 + 4.11331i) q^{11} +(3.69303 - 1.19994i) q^{12} +(11.5761 - 5.91566i) q^{13} +(6.83186 - 21.0263i) q^{14} +(-6.36730 - 11.1611i) q^{15} +(-19.3290 - 4.10851i) q^{16} +(-5.51312 + 12.3827i) q^{17} +(-3.97645 + 3.97645i) q^{18} +(13.7930 - 5.29463i) q^{19} +(0.0389849 - 7.55475i) q^{20} +(-3.78613 - 23.9047i) q^{21} +(-1.01073 + 9.61646i) q^{22} +(15.1587 - 13.6489i) 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} +(5.09950 - 13.2847i) q^{28} +(37.1975 - 16.5614i) q^{29} +(-13.5558 - 26.9476i) q^{30} +(-4.68301 + 29.5674i) q^{31} +(-22.2328 - 5.95725i) q^{32} +(3.79346 + 9.88231i) q^{33} +(-14.4459 + 28.3517i) q^{34} +(-46.4699 - 7.60612i) q^{35} +(-2.68984 + 2.42194i) q^{36} +(39.6373 + 61.0362i) q^{37} +(32.9858 - 10.7177i) q^{38} +(20.9940 - 25.9887i) q^{39} +(-1.67956 + 29.1672i) q^{40} +(54.2256 - 35.2145i) q^{41} +(-5.93897 - 56.5055i) q^{42} +(19.8434 - 11.4566i) q^{43} +(-0.973588 + 6.14699i) q^{44} +(9.65355 + 7.09011i) q^{45} +(37.2138 - 30.1351i) q^{46} +(1.12233 + 7.08608i) q^{47} +(-49.6741 + 10.5586i) q^{48} +(-34.3744 - 19.8461i) q^{49} +(-58.0578 + 8.58221i) q^{50} +34.8341i q^{51} +(18.3296 - 7.06111i) q^{52} +(-6.24347 - 4.53615i) q^{53} +(-24.6375 + 64.1829i) q^{54} +(20.5718 - 0.971704i) q^{55} +(-22.3821 + 50.2709i) q^{56} +(26.8480 - 26.8480i) q^{57} +(89.2379 - 34.2552i) q^{58} +(-82.8155 + 4.34017i) q^{59} +(-7.80532 - 17.7774i) q^{60} +(-64.9867 + 13.8134i) q^{61} +(-14.6112 + 68.7403i) q^{62} +(12.2871 + 18.9204i) q^{63} +(23.7857 + 7.72845i) q^{64} +(-35.1849 - 54.6537i) q^{65} +(7.67897 + 23.6334i) q^{66} +(19.3644 + 15.6810i) q^{67} +(-10.2402 + 17.7366i) q^{68} +(21.3216 - 47.8892i) q^{69} +(-108.006 - 23.5406i) q^{70} +(30.6348 + 37.8308i) q^{71} +(10.8778 - 8.80871i) q^{72} +(-99.7238 + 50.8118i) q^{73} +(85.4240 + 147.959i) q^{74} +(-52.3647 + 37.2256i) q^{75} +(21.5629 - 5.77775i) q^{76} +(36.8923 + 11.9870i) q^{77} +(52.4099 - 58.3466i) q^{78} +(-80.0466 - 58.1573i) q^{79} +(-10.8348 + 98.2084i) q^{80} +(5.61339 + 53.4079i) q^{81} +(131.449 - 75.8922i) q^{82} +(7.26674 - 45.8804i) q^{83} +(-1.91390 - 36.5194i) q^{84} +(64.3467 + 21.2752i) q^{85} +(47.9270 - 24.4200i) q^{86} +(70.0187 - 77.7637i) q^{87} +(5.00391 - 23.5416i) q^{88} +(5.02370 - 95.8579i) q^{89} +(21.7600 + 17.8076i) q^{90} +(-25.5971 - 119.724i) q^{91} +(24.9345 - 18.1160i) q^{92} +(19.9117 + 74.3116i) q^{93} +(1.76050 + 16.7500i) q^{94} +(-33.1968 - 65.9921i) q^{95} +(-58.4238 + 9.25342i) q^{96} +(70.3643 + 86.8927i) q^{97} +(-78.1467 - 50.7490i) 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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