LMFDB - Embedded newform 375.3.p.a.14.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(14,375)] 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("375.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([25, 43])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.p (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$1960$
Relative dimension:	$98$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			14.8
Character	$\chi$	$=$	375.14
Dual form			375.3.p.a.134.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50136 - 3.19056i) q^{2} +(1.39183 + 2.65759i) q^{3} +(-5.37590 + 6.49835i) q^{4} +(-4.53777 + 2.09968i) q^{5} +(6.38957 - 8.43074i) q^{6} +(5.28133 + 1.71601i) q^{7} +(15.1431 + 3.88808i) q^{8} +(-5.12561 + 7.39785i) q^{9} +(13.5120 + 11.3256i) q^{10} +(-0.493220 + 0.232092i) q^{11} +(-24.7523 - 5.24235i) q^{12} +(0.917502 - 7.26277i) q^{13} +(-2.45417 - 19.4268i) q^{14} +(-11.8959 - 9.13714i) q^{15} +(-4.00877 - 21.0147i) q^{16} +(-19.0368 - 23.0116i) q^{17} +(31.2987 + 5.24671i) q^{18} +(0.722099 + 11.4774i) q^{19} +(10.7501 - 40.7757i) q^{20} +(2.79027 + 16.4240i) q^{21} +(1.48101 + 1.22520i) q^{22} +(-0.912651 - 0.501734i) q^{23} +(10.7437 + 45.6557i) q^{24} +(16.1827 - 19.0557i) q^{25} +(-24.5498 + 7.97673i) q^{26} +(-26.7945 - 3.32523i) q^{27} +(-39.5431 + 25.0948i) q^{28} +(-28.3996 + 18.0229i) q^{29} +(-11.2925 + 51.6728i) q^{30} +(-25.8510 - 31.2485i) q^{31} +(-10.4366 + 7.58266i) q^{32} +(-1.30329 - 0.987746i) q^{33} +(-44.8386 + 95.2869i) q^{34} +(-27.5685 + 3.30226i) q^{35} +(-20.5190 - 73.0781i) q^{36} +(-42.7436 + 8.15379i) q^{37} +(35.5353 - 19.5357i) q^{38} +(20.5785 - 7.67021i) q^{39} +(-76.8794 + 14.1524i) q^{40} +(-15.4467 - 28.0975i) q^{41} +(48.2127 - 33.5610i) q^{42} +(-25.7874 + 35.4933i) q^{43} +(1.14329 - 4.45282i) q^{44} +(7.72571 - 44.3319i) q^{45} +(-0.230592 + 3.66516i) q^{46} +(36.7766 - 9.44263i) q^{47} +(50.2690 - 39.9026i) q^{48} +(-14.6941 - 10.6759i) q^{49} +(-85.0946 - 23.0223i) q^{50} +(34.6593 - 82.6203i) q^{51} +(42.2636 + 45.0062i) q^{52} +(6.22529 + 2.46477i) q^{53} +(29.6189 + 90.4818i) q^{54} +(1.75080 - 2.08878i) q^{55} +(73.3035 + 46.5198i) q^{56} +(-29.4973 + 17.8937i) q^{57} +(100.141 + 63.5517i) q^{58} +(18.9682 - 20.1991i) q^{59} +(123.328 - 28.1834i) q^{60} +(-58.9911 - 32.4306i) q^{61} +(-60.8885 + 129.395i) q^{62} +(-39.7648 + 30.2749i) q^{63} +(-35.1274 - 19.3115i) q^{64} +(11.0861 + 34.8832i) q^{65} +(-1.19476 + 5.64118i) q^{66} +(87.4192 + 55.4779i) q^{67} +251.877 q^{68} +(0.0631490 - 3.12378i) q^{69} +(51.9265 + 83.0012i) q^{70} +(19.3459 + 75.3472i) q^{71} +(-106.381 + 92.0973i) q^{72} +(-66.3188 - 70.6224i) q^{73} +(90.1890 + 124.134i) q^{74} +(73.1660 + 16.4846i) q^{75} +(-78.4663 - 57.0091i) q^{76} +(-3.00313 + 0.379384i) q^{77} +(-55.3681 - 54.1412i) q^{78} +(4.81746 - 76.5714i) q^{79} +(62.3150 + 86.9427i) q^{80} +(-28.4563 - 75.8369i) q^{81} +(-66.4556 + 91.4683i) q^{82} +(8.24173 + 130.999i) q^{83} +(-121.729 - 70.1618i) q^{84} +(134.702 + 64.4499i) q^{85} +(151.960 + 28.9879i) q^{86} +(-87.4250 - 50.3897i) q^{87} +(-8.37125 + 1.59690i) q^{88} +(-62.2317 - 66.2701i) q^{89} +(-153.043 + 41.9089i) q^{90} +(17.3086 - 36.7827i) q^{91} +(8.16676 - 3.23345i) q^{92} +(47.0655 - 112.194i) q^{93} +(-85.3424 - 103.161i) q^{94} +(-27.3757 - 50.5658i) q^{95} +(-34.6777 - 17.1826i) q^{96} +(39.3063 - 24.9446i) q^{97} +(-12.0009 + 62.9107i) q^{98} +(0.811075 - 4.83838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) $ 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{43}{50}\right)$	$-1$

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 $

$2$	−1.50136	−	3.19056i	−0.750682	−	1.59528i	−0.802519	−	0.596626i	$-0.796508\pi$
$2$	−1.50136	−	3.19056i	−0.750682	−	1.59528i	0.0518370	−	0.998656i	$-0.483492\pi$
$3$	1.39183	+	2.65759i	0.463944	+	0.885865i
$3$	1.39183	+	2.65759i	0.463944	+	0.885865i
$4$	−5.37590	+	6.49835i	−1.34397	+	1.62459i
$5$	−4.53777	+	2.09968i	−0.907554	+	0.419936i
$5$	−4.53777	+	2.09968i	−0.907554	+	0.419936i
$6$	6.38957	−	8.43074i	1.06493	−	1.40512i
$7$	5.28133	+	1.71601i	0.754476	+	0.245144i	0.660906	−	0.750469i	$-0.270172\pi$
$7$	5.28133	+	1.71601i	0.754476	+	0.245144i	0.0935698	+	0.995613i	$0.470172\pi$
$8$	15.1431	+	3.88808i	1.89288	+	0.486010i
$9$	−5.12561	+	7.39785i	−0.569512	+	0.821983i
$10$	13.5120	+	11.3256i	1.35120	+	1.13256i
$11$	−0.493220	+	0.232092i	−0.0448382	+	0.0210993i	−0.448068	−	0.894000i	$-0.647888\pi$
$11$	−0.493220	+	0.232092i	−0.0448382	+	0.0210993i	0.403229	+	0.915099i	$0.367888\pi$
$12$	−24.7523	−	5.24235i	−2.06269	−	0.436863i
$13$	0.917502	−	7.26277i	0.0705770	−	0.558675i	−0.916690	−	0.399600i	$-0.869149\pi$
$13$	0.917502	−	7.26277i	0.0705770	−	0.558675i	0.987267	−	0.159075i	$-0.0508510\pi$
$14$	−2.45417	−	19.4268i	−0.175298	−	1.38763i
$15$	−11.8959	−	9.13714i	−0.793061	−	0.609143i
$16$	−4.00877	−	21.0147i	−0.250548	−	1.31342i
$17$	−19.0368	−	23.0116i	−1.11981	−	1.35362i	−0.928170	−	0.372156i	$-0.878619\pi$
$17$	−19.0368	−	23.0116i	−1.11981	−	1.35362i	−0.191642	−	0.981465i	$-0.561381\pi$
$18$	31.2987	+	5.24671i	1.73882	+	0.291484i
$19$	0.722099	+	11.4774i	0.0380052	+	0.604075i	0.970228	+	0.242192i	$0.0778663\pi$
$19$	0.722099	+	11.4774i	0.0380052	+	0.604075i	−0.932223	+	0.361884i	$0.882134\pi$
$20$	10.7501	−	40.7757i	0.537507	−	2.03878i
$21$	2.79027	+	16.4240i	0.132870	+	0.782097i
$22$	1.48101	+	1.22520i	0.0673185	+	0.0556907i
$23$	−0.912651	−	0.501734i	−0.0396805	−	0.0218145i	0.461790	−	0.886989i	$-0.347207\pi$
$23$	−0.912651	−	0.501734i	−0.0396805	−	0.0218145i	−0.501470	+	0.865175i	$0.667207\pi$
$24$	10.7437	+	45.6557i	0.447653	+	1.90232i
$25$	16.1827	−	19.0557i	0.647307	−	0.762229i
$26$	−24.5498	+	7.97673i	−0.944225	+	0.306797i
$27$	−26.7945	−	3.32523i	−0.992387	−	0.123157i
$28$	−39.5431	+	25.0948i	−1.41225	+	0.896244i
$29$	−28.3996	+	18.0229i	−0.979296	+	0.621480i	−0.926169	−	0.377108i	$-0.876919\pi$
$29$	−28.3996	+	18.0229i	−0.979296	+	0.621480i	−0.0531265	+	0.998588i	$0.516919\pi$
$30$	−11.2925	+	51.6728i	−0.376418	+	1.72243i
$31$	−25.8510	−	31.2485i	−0.833903	−	1.00802i	−0.999761	−	0.0218657i	$-0.993039\pi$
$31$	−25.8510	−	31.2485i	−0.833903	−	1.00802i	0.165858	−	0.986150i	$-0.446961\pi$
$32$	−10.4366	+	7.58266i	−0.326145	+	0.236958i
$33$	−1.30329	−	0.987746i	−0.0394935	−	0.0299317i
$34$	−44.8386	+	95.2869i	−1.31878	+	2.80256i
$35$	−27.5685	+	3.30226i	−0.787672	+	0.0943503i
$36$	−20.5190	−	73.0781i	−0.569972	−	2.02995i
$37$	−42.7436	+	8.15379i	−1.15523	+	0.220373i	−0.729178	−	0.684324i	$-0.760097\pi$
$37$	−42.7436	+	8.15379i	−1.15523	+	0.220373i	−0.426056	+	0.904697i	$0.640097\pi$
$38$	35.5353	−	19.5357i	0.935141	−	0.514098i
$39$	20.5785	−	7.67021i	0.527654	−	0.196672i
$40$	−76.8794	+	14.1524i	−1.92199	+	0.353810i
$41$	−15.4467	−	28.0975i	−0.376749	−	0.685305i	0.618163	−	0.786050i	$-0.287877\pi$
$41$	−15.4467	−	28.0975i	−0.376749	−	0.685305i	−0.994912	+	0.100745i	$0.967877\pi$
$42$	48.2127	−	33.5610i	1.14792	−	0.799071i
$43$	−25.7874	+	35.4933i	−0.599707	+	0.825426i	−0.995681	−	0.0928359i	$-0.970407\pi$
$43$	−25.7874	+	35.4933i	−0.599707	+	0.825426i	0.395975	+	0.918261i	$0.370407\pi$
$44$	1.14329	−	4.45282i	0.0259838	−	0.101200i
$45$	7.72571	−	44.3319i	0.171682	−	0.985152i
$46$	−0.230592	+	3.66516i	−0.00501287	+	0.0796773i
$47$	36.7766	−	9.44263i	0.782481	−	0.200907i	0.163742	−	0.986503i	$-0.447644\pi$
$47$	36.7766	−	9.44263i	0.782481	−	0.200907i	0.618739	+	0.785596i	$0.287644\pi$
$48$	50.2690	−	39.9026i	1.04727	−	0.831304i
$49$	−14.6941	−	10.6759i	−0.299879	−	0.217875i
$50$	−85.0946	−	23.0223i	−1.70189	−	0.460445i
$51$	34.6593	−	82.6203i	0.679595	−	1.62001i
$52$	42.2636	+	45.0062i	0.812762	+	0.865503i
$53$	6.22529	+	2.46477i	0.117458	+	0.0465051i	0.426119	−	0.904667i	$-0.359881\pi$
$53$	6.22529	+	2.46477i	0.117458	+	0.0465051i	−0.308660	+	0.951172i	$0.599881\pi$
$54$	29.6189	+	90.4818i	0.548498	+	1.67559i
$55$	1.75080	−	2.08878i	0.0318327	−	0.0379779i
$56$	73.3035	+	46.5198i	1.30899	+	0.830711i
$57$	−29.4973	+	17.8937i	−0.517497	+	0.313925i
$58$	100.141	+	63.5517i	1.72658	+	1.09572i
$59$	18.9682	−	20.1991i	0.321495	−	0.342357i	−0.547838	−	0.836584i	$-0.684549\pi$
$59$	18.9682	−	20.1991i	0.321495	−	0.342357i	0.869333	+	0.494227i	$0.164549\pi$
$60$	123.328	−	28.1834i	2.05546	−	0.469723i
$61$	−58.9911	−	32.4306i	−0.967067	−	0.531649i	−0.0817574	−	0.996652i	$-0.526053\pi$
$61$	−58.9911	−	32.4306i	−0.967067	−	0.531649i	−0.885309	+	0.465003i	$0.846053\pi$
$62$	−60.8885	+	129.395i	−0.982072	+	2.08701i
$63$	−39.7648	+	30.2749i	−0.631187	+	0.480554i
$64$	−35.1274	−	19.3115i	−0.548866	−	0.301741i
$65$	11.0861	+	34.8832i	0.170555	+	0.536665i
$66$	−1.19476	+	5.64118i	−0.0181024	+	0.0854724i
$67$	87.4192	+	55.4779i	1.30476	+	0.828029i	0.992533	−	0.121978i	$-0.0389236\pi$
$67$	87.4192	+	55.4779i	1.30476	+	0.828029i	0.312231	+	0.950006i	$0.398924\pi$
$68$	251.877			3.70407
$69$	0.0631490	−	3.12378i	0.000915202	−	0.0452722i
$70$	51.9265	+	83.0012i	0.741807	+	1.18573i
$71$	19.3459	+	75.3472i	0.272477	+	1.06123i	0.946548	+	0.322562i	$0.104544\pi$
$71$	19.3459	+	75.3472i	0.272477	+	1.06123i	−0.674071	+	0.738666i	$0.735456\pi$
$72$	−106.381	+	92.0973i	−1.47751	+	1.27913i
$73$	−66.3188	−	70.6224i	−0.908477	−	0.967430i	0.0911194	−	0.995840i	$-0.470956\pi$
$73$	−66.3188	−	70.6224i	−0.908477	−	0.967430i	−0.999596	+	0.0284103i	$0.990956\pi$
$74$	90.1890	+	124.134i	1.21877	+	1.67749i
$75$	73.1660	+	16.4846i	0.975546	+	0.219795i
$76$	−78.4663	−	57.0091i	−1.03245	−	0.750119i
$77$	−3.00313	+	0.379384i	−0.0390017	+	0.00492706i
$78$	−55.3681	−	54.1412i	−0.709848	−	0.694118i
$79$	4.81746	−	76.5714i	0.0609806	−	0.969258i	−0.841973	−	0.539520i	$-0.818606\pi$
$79$	4.81746	−	76.5714i	0.0609806	−	0.969258i	0.902953	−	0.429738i	$-0.141394\pi$
$80$	62.3150	+	86.9427i	0.778938	+	1.08678i
$81$	−28.4563	−	75.8369i	−0.351312	−	0.936259i
$82$	−66.4556	+	91.4683i	−0.810435	+	1.11547i
$83$	8.24173	+	130.999i	0.0992980	+	1.57830i	0.660634	+	0.750708i	$0.270288\pi$
$83$	8.24173	+	130.999i	0.0992980	+	1.57830i	−0.561336	+	0.827588i	$0.689712\pi$
$84$	−121.729	−	70.1618i	−1.44916	−	0.835259i
$85$	134.702	+	64.4499i	1.58472	+	0.758234i
$86$	151.960	+	28.9879i	1.76698	+	0.337069i
$87$	−87.4250	−	50.3897i	−1.00489	−	0.579192i
$88$	−8.37125	+	1.59690i	−0.0951279	+	0.0181466i
$89$	−62.2317	−	66.2701i	−0.699233	−	0.744607i	0.277109	−	0.960838i	$-0.410624\pi$
$89$	−62.2317	−	66.2701i	−0.699233	−	0.744607i	−0.976342	+	0.216231i	$0.930624\pi$
$90$	−153.043	+	41.9089i	−1.70047	+	0.465655i
$91$	17.3086	−	36.7827i	0.190205	−	0.404205i
$92$	8.16676	−	3.23345i	0.0887691	−	0.0351462i
$93$	47.0655	−	112.194i	0.506081	−	1.20639i
$94$	−85.3424	−	103.161i	−0.907898	−	1.09746i
$95$	−27.3757	−	50.5658i	−0.288165	−	0.532271i
$96$	−34.6777	−	17.1826i	−0.361226	−	0.178985i
$97$	39.3063	−	24.9446i	0.405220	−	0.257160i	−0.317561	−	0.948238i	$-0.602864\pi$
$97$	39.3063	−	24.9446i	0.405220	−	0.257160i	0.722781	+	0.691078i	$0.242864\pi$
$98$	−12.0009	+	62.9107i	−0.122458	+	0.641946i
$99$	0.811075	−	4.83838i	0.00819267	−	0.0488725i
$100$	36.8343	+	207.602i	0.368343	+	2.07602i
$101$	−5.07727	−	1.64971i	−0.0502700	−	0.0163337i	0.283774	−	0.958891i	$-0.408413\pi$
$101$	−5.07727	−	1.64971i	−0.0502700	−	0.0163337i	−0.334044	+	0.942557i	$0.608413\pi$
$102$	−315.642	+	13.4605i	−3.09453	+	0.131966i
$103$	96.0996	+	79.5005i	0.933006	+	0.771850i	0.973821	−	0.227317i	$-0.0729954\pi$
$103$	96.0996	+	79.5005i	0.933006	+	0.771850i	−0.0408150	+	0.999167i	$0.512995\pi$
$104$	42.1320	−	106.413i	0.405115	−	1.02320i
$105$	−47.1468	−	68.6698i	−0.449017	−	0.653998i
$106$	−1.48244	−	23.5627i	−0.0139853	−	0.222290i
$107$	−15.3203	−	47.1511i	−0.143181	−	0.440664i	0.853592	−	0.520942i	$-0.174419\pi$
$107$	−15.3203	−	47.1511i	−0.143181	−	0.440664i	−0.996773	+	0.0802777i	$0.974419\pi$
$108$	165.653	−	156.244i	1.53382	−	1.44670i
$109$	−24.1544	−	126.622i	−0.221600	−	1.16167i	−0.902961	−	0.429722i	$-0.858611\pi$
$109$	−24.1544	−	126.622i	−0.221600	−	1.16167i	0.681361	−	0.731948i	$-0.261389\pi$
$110$	−9.29299	−	2.45001i	−0.0844817	−	0.0222728i
$111$	−81.1614	−	102.247i	−0.731184	−	0.921140i
$112$	14.8898	−	117.865i	0.132944	−	1.05236i
$113$	−123.648	−	116.114i	−1.09423	−	1.02755i	−0.999486	−	0.0320521i	$-0.989796\pi$
$113$	−123.648	−	116.114i	−1.09423	−	1.02755i	−0.0947471	−	0.995501i	$-0.530204\pi$
$114$	101.377	+	67.2481i	0.889274	+	0.589895i
$115$	5.19488	+	0.360477i	0.0451729	+	0.00313459i
$116$	35.5541	−	281.440i	0.306501	−	2.42620i
$117$	49.0261	+	44.0137i	0.419027	+	0.376185i
$118$	−92.9246	−	30.1930i	−0.787496	−	0.255873i
$119$	−61.0517	−	154.199i	−0.513039	−	1.29579i
$120$	−144.615	−	184.617i	−1.20512	−	1.53847i
$121$	−76.9389	+	93.0032i	−0.635859	+	0.768621i
$122$	−14.9048	+	236.905i	−0.122170	+	1.94184i
$123$	53.1725	−	80.1581i	0.432297	−	0.651692i
$124$	342.036			2.75835
$125$	−33.4223	+	120.449i	−0.267378	+	0.963592i
$126$	156.295	+	81.4185i	1.24044	+	0.646178i
$127$	−73.4900	+	34.5818i	−0.578662	+	0.272297i	−0.692756	−	0.721172i	$-0.743604\pi$
$127$	−73.4900	+	34.5818i	−0.578662	+	0.272297i	0.114094	+	0.993470i	$0.463604\pi$
$128$	−12.1154	+	192.569i	−0.0946519	+	1.50445i
$129$	−130.218	−	19.1317i	−1.00945	−	0.148308i
$130$	94.6529	−	87.7434i	0.728099	−	0.674949i
$131$	3.37959	+	8.53588i	0.0257984	+	0.0651594i	0.942105	−	0.335319i	$-0.108844\pi$
$131$	3.37959	+	8.53588i	0.0257984	+	0.0651594i	−0.916306	+	0.400478i	$0.868844\pi$
$132$	13.4250	−	3.15917i	0.101705	−	0.0239331i
$133$	−15.8817	+	61.8553i	−0.119411	+	0.465077i
$134$	45.7576	−	362.209i	0.341475	−	2.70305i
$135$	128.569	−	41.1707i	0.952363	−	0.304968i
$136$	−198.805	−	422.482i	−1.46180	−	3.10649i
$137$	170.728	+	160.324i	1.24619	+	1.17025i	0.978388	+	0.206777i	$0.0662976\pi$
$137$	170.728	+	160.324i	1.24619	+	1.17025i	0.267803	+	0.963474i	$0.413702\pi$
$138$	−10.0614	+	4.48846i	−0.0729090	+	0.0325251i
$139$	−217.106	+	27.4269i	−1.56192	+	0.197316i	−0.858256	−	0.513221i	$-0.828452\pi$
$139$	−217.106	+	27.4269i	−1.56192	+	0.197316i	−0.703660	+	0.710537i	$0.748452\pi$
$140$	126.746	−	196.902i	0.905331	−	1.40645i
$141$	76.2815	+	84.5947i	0.541004	+	0.599963i
$142$	211.355	−	174.848i	1.48841	−	1.23132i
$143$	1.23310	+	3.79509i	0.00862308	+	0.0265391i
$144$	176.011	+	78.0569i	1.22230	+	0.542062i
$145$	91.0283	−	141.414i	0.627782	−	0.975268i
$146$	−125.756	+	317.624i	−0.861345	+	2.17551i
$147$	7.92044	−	53.9098i	0.0538805	−	0.366734i
$148$	176.799	−	321.597i	1.19459	−	2.17295i
$149$	−170.551	−	55.4155i	−1.14464	−	0.371916i	−0.325519	−	0.945536i	$-0.605539\pi$
$149$	−170.551	−	55.4155i	−1.14464	−	0.371916i	−0.819122	+	0.573619i	$0.805539\pi$
$150$	−57.2536	−	258.190i	−0.381691	−	1.72127i
$151$	47.0155	+	144.699i	0.311361	+	0.958270i	0.977227	+	0.212198i	$0.0680623\pi$
$151$	47.0155	+	144.699i	0.311361	+	0.958270i	−0.665866	+	0.746071i	$0.731938\pi$
$152$	−33.6904	+	176.611i	−0.221647	+	1.16191i
$153$	267.811	−	22.8832i	1.75040	−	0.149563i
$154$	5.71924	+	9.01208i	0.0371379	+	0.0585200i
$155$	182.918	+	87.5195i	1.18011	+	0.564642i
$156$	−60.7843	+	174.961i	−0.389643	+	1.12154i
$157$	−80.9594	−	111.431i	−0.515665	−	0.709752i	0.469197	−	0.883094i	$-0.344544\pi$
$157$	−80.9594	−	111.431i	−0.515665	−	0.709752i	−0.984862	+	0.173341i	$0.944544\pi$
$158$	−251.539	+	99.5912i	−1.59202	+	0.630324i
$159$	2.11421	+	19.9748i	0.0132969	+	0.125628i
$160$	31.4379	−	56.3220i	0.196487	−	0.352012i
$161$	−3.95903	−	4.21594i	−0.0245903	−	0.0261860i
$162$	−199.239	+	204.650i	−1.22987	+	1.26327i
$163$	24.1232	+	43.8799i	0.147995	+	0.269202i	0.939905	−	0.341436i	$-0.110913\pi$
$163$	24.1232	+	43.8799i	0.147995	+	0.269202i	−0.791910	+	0.610638i	$0.790913\pi$
$164$	265.627	+	50.6711i	1.61968	+	0.308970i
$165$	7.98796	+	1.74568i	0.0484119	+	0.0105799i
$166$	405.585	−	222.972i	2.44329	−	1.34321i
$167$	6.27950	+	99.8097i	0.0376018	+	0.597663i	0.971039	+	0.238922i	$0.0767940\pi$
$167$	6.27950	+	99.8097i	0.0376018	+	0.597663i	−0.933437	+	0.358741i	$0.883206\pi$
$168$	−21.6047	+	259.559i	−0.128599	+	1.54499i
$169$	111.784	+	28.7014i	0.661447	+	0.169831i
$170$	3.39515	−	526.537i	0.0199714	−	3.09727i
$171$	−88.6095	−	53.4869i	−0.518184	−	0.312789i
$172$	−92.0173	−	358.384i	−0.534984	−	2.08363i
$173$	46.0021	−	5.81141i	0.265908	−	0.0335920i	0.00875124	−	0.999962i	$-0.497214\pi$
$173$	46.0021	−	5.81141i	0.265908	−	0.0335920i	0.257157	+	0.966370i	$0.417214\pi$
$174$	−29.5145	+	354.588i	−0.169624	+	2.03786i
$175$	118.166	−	72.8700i	0.675234	−	0.416400i
$176$	6.85455	+	9.43447i	0.0389463	+	0.0536050i
$177$	80.0814	+	22.2960i	0.452437	+	0.125966i
$178$	−118.006	+	298.050i	−0.662957	+	1.67444i
$179$	38.8305	+	151.235i	0.216930	+	0.844888i	0.980070	+	0.198654i	$0.0636570\pi$
$179$	38.8305	+	151.235i	0.216930	+	0.844888i	−0.763139	+	0.646234i	$0.776343\pi$
$180$	246.551	+	288.528i	1.36973	+	1.60293i
$181$	−152.615	+	240.483i	−0.843179	+	1.32864i	0.0995346	+	0.995034i	$0.468265\pi$
$181$	−152.615	+	240.483i	−0.843179	+	1.32864i	−0.942714	+	0.333603i	$0.891735\pi$
$182$	−143.344			−0.787604
$183$	4.08176	−	201.912i	0.0223047	−	1.10335i
$184$	−11.8695	−	11.1462i	−0.0645084	−	0.0605774i
$185$	176.840	−	126.748i	0.955894	−	0.685124i
$186$	−428.625	+	18.2787i	−2.30443	+	0.0982724i
$187$	14.7301	+	6.93148i	0.0787708	+	0.0370667i
$188$	−136.346	+	289.750i	−0.725244	+	1.54122i
$189$	−135.804	−	63.5412i	−0.718541	−	0.336197i
$190$	−120.232	+	163.261i	−0.632802	+	0.859271i
$191$	187.427	−	199.589i	0.981292	−	1.04497i	−0.0176896	−	0.999844i	$-0.505631\pi$
$191$	187.427	−	199.589i	0.981292	−	1.04497i	0.998981	−	0.0451260i	$-0.0143689\pi$
$192$	2.43057	−	120.233i	0.0126592	−	0.626212i
$193$			6.42180i			0.0332736i	0.999862	+	0.0166368i	$0.00529590\pi$
$193$			6.42180i			0.0332736i	−0.999862	+	0.0166368i	$0.994704\pi$
$194$	−138.600	−	87.9584i	−0.714435	−	0.453394i
$195$	−77.2755	+	78.0139i	−0.396285	+	0.400071i
$196$	148.369	−	38.0947i	0.756986	−	0.194361i
$197$	−118.160	−	46.7828i	−0.599797	−	0.237476i	0.0485509	−	0.998821i	$-0.484540\pi$
$197$	−118.160	−	46.7828i	−0.599797	−	0.237476i	−0.648348	+	0.761344i	$0.724540\pi$
$198$	−16.6549	+	4.67639i	−0.0841155	+	0.0236181i
$199$	12.1040	−	8.79409i	0.0608243	−	0.0441914i	−0.556958	−	0.830541i	$-0.688031\pi$
$199$	12.1040	−	8.79409i	0.0608243	−	0.0441914i	0.617782	+	0.786349i	$0.288031\pi$
$200$	319.145	−	225.643i	1.59573	−	1.12821i
$201$	−25.7649	+	309.541i	−0.128184	+	1.54000i
$202$	2.35935	+	18.6762i	0.0116799	+	0.0924563i
$203$	−180.915	+	46.4511i	−0.891207	+	0.228823i
$204$	350.570	+	669.387i	1.71848	+	3.28131i
$205$	129.089	+	95.0667i	0.629705	+	0.463740i
$206$	109.371	−	425.971i	0.530926	−	2.06782i
$207$	8.38964	−	4.17996i	0.0405297	−	0.0201930i
$208$	−156.303	+	9.83375i	−0.751457	+	0.0472777i
$209$	−3.01997	−	5.49331i	−0.0144496	−	0.0262838i
$210$	−148.311	+	253.523i	−0.706241	+	1.20725i
$211$	−19.5661	+	102.569i	−0.0927303	+	0.486109i	0.905377	+	0.424609i	$0.139588\pi$
$211$	−19.5661	+	102.569i	−0.0927303	+	0.486109i	−0.998107	+	0.0615001i	$0.980412\pi$
$212$	−49.4835	+	27.2038i	−0.233413	+	0.128320i
$213$	−173.316	+	156.284i	−0.813691	+	0.733728i
$214$	−127.437	+	119.671i	−0.595501	+	0.559212i
$215$	42.4926	−	215.206i	0.197640	−	1.00096i
$216$	−392.821	−	154.533i	−1.81862	−	0.715431i
$217$	−82.9050	−	209.394i	−0.382051	−	0.964950i
$218$	−367.731	+	267.172i	−1.68684	+	1.22556i
$219$	95.3809	−	274.543i	0.435529	−	1.25362i
$220$	4.16151	+	22.6064i	0.0189160	+	0.102756i
$221$	−184.594	+	117.147i	−0.835267	+	0.530077i
$222$	−204.371	+	412.460i	−0.920591	+	1.85793i
$223$	−174.397	−	33.2680i	−0.782049	−	0.149184i	−0.219130	−	0.975696i	$-0.570322\pi$
$223$	−174.397	−	33.2680i	−0.782049	−	0.149184i	−0.562919	+	0.826512i	$0.690322\pi$
$224$	−68.1312	+	22.1372i	−0.304157	+	0.0988267i
$225$	58.0253	+	217.389i	0.257890	+	0.966174i
$226$	−184.826	+	568.837i	−0.817815	+	2.51698i
$227$	50.3946	+	27.7046i	0.222002	+	0.122047i	0.588874	−	0.808225i	$-0.299571\pi$
$227$	50.3946	+	27.7046i	0.222002	+	0.122047i	−0.366872	+	0.930271i	$0.619571\pi$
$228$	42.2951	−	287.878i	0.185505	−	1.26262i
$229$	342.468	+	135.592i	1.49549	+	0.592107i	0.966533	−	0.256541i	$-0.0825829\pi$
$229$	342.468	+	135.592i	1.49549	+	0.592107i	0.528958	+	0.848648i	$0.322583\pi$
$230$	−6.64929	−	17.1158i	−0.0289099	−	0.0744165i
$231$	−5.18810	−	7.45306i	−0.0224593	−	0.0322643i
$232$	−500.131	+	162.502i	−2.15574	+	0.700442i
$233$	88.9739	+	107.551i	0.381862	+	0.461592i	0.926066	−	0.377361i	$-0.123168\pi$
$233$	88.9739	+	107.551i	0.381862	+	0.461592i	−0.544204	+	0.838953i	$0.683168\pi$
$234$	66.8223	−	222.502i	0.285565	−	0.950861i
$235$	−147.057	+	120.068i	−0.625775	+	0.510926i
$236$	29.2895	+	231.850i	0.124108	+	0.982415i
$237$	210.201	−	93.7716i	0.886923	−	0.395661i
$238$	−400.321	+	426.298i	−1.68202	+	1.79117i
$239$	292.792	−	137.777i	1.22507	−	0.576474i	0.299155	−	0.954205i	$-0.403295\pi$
$239$	292.792	−	137.777i	1.22507	−	0.576474i	0.925916	+	0.377730i	$0.123295\pi$
$240$	−144.326	+	286.618i	−0.601360	+	1.19424i
$241$	−49.6494	−	6.27217i	−0.206014	−	0.0260256i	0.0216489	−	0.999766i	$-0.493108\pi$
$241$	−49.6494	−	6.27217i	−0.206014	−	0.0260256i	−0.227663	+	0.973740i	$0.573108\pi$
$242$	412.246	+	105.847i	1.70350	+	0.437383i
$243$	161.937	−	181.177i	0.666409	−	0.745586i
$244$	527.875	−	209.001i	2.16342	−	0.856560i
$245$	89.0941	+	17.5917i	0.363650	+	0.0718030i
$246$	−335.581	−	49.3036i	−1.36415	−	0.200421i
$247$	84.0205	+	5.28612i	0.340164	+	0.0214013i
$248$	−269.967	−	573.708i	−1.08857	−	2.31334i
$249$	−336.670	+	204.231i	−1.35209	+	0.820205i
$250$	434.479	−	74.2019i	1.73792	−	0.296808i
$251$		−	300.347i		−	1.19660i	−0.801271	−	0.598301i	$-0.795843\pi$
$251$		−	300.347i		−	1.19660i	0.801271	−	0.598301i	$-0.204157\pi$
$252$	17.0349	−	421.160i	0.0675989	−	1.67127i
$253$	0.566586	+	0.0356466i	0.00223947	+	0.000140896i
$254$	220.671	+	182.555i	0.868782	+	0.718719i
$255$	16.2003	+	447.685i	0.0635307	+	1.75563i
$256$	483.512	−	191.436i	1.88872	−	0.747796i
$257$	−110.922	+	341.384i	−0.431604	+	1.32834i	0.464922	+	0.885351i	$0.346082\pi$
$257$	−110.922	+	341.384i	−0.431604	+	1.32834i	−0.896527	+	0.442990i	$0.853918\pi$
$258$	134.465	+	444.194i	0.521180	+	1.72168i
$259$	−239.735	−	30.2856i	−0.925619	−	0.116933i
$260$	−286.281	−	115.488i	−1.10108	−	0.444183i
$261$	12.2344	−	302.474i	0.0468749	−	1.15890i
$262$	22.1603	−	23.5983i	0.0845811	−	0.0900697i
$263$	−88.0788	−	11.1269i	−0.334900	−	0.0423077i	−0.0439150	−	0.999035i	$-0.513983\pi$
$263$	−88.0788	−	11.1269i	−0.334900	−	0.0423077i	−0.290985	+	0.956728i	$0.593983\pi$
$264$	−15.8953	−	20.0248i	−0.0602095	−	0.0758514i
$265$	−33.4242	+	1.88658i	−0.126129	+	0.00711918i
$266$	221.197	−	42.1957i	0.831569	−	0.158630i
$267$	89.5028	−	257.623i	0.335217	−	0.964882i
$268$	−830.472	+	269.837i	−3.09877	+	1.00685i
$269$	379.844	−	23.8978i	1.41206	−	0.0888393i	0.661651	−	0.749812i	$-0.269856\pi$
$269$	379.844	−	23.8978i	1.41206	−	0.0888393i	0.750410	+	0.660973i	$0.229856\pi$
$270$	−324.387	−	348.395i	−1.20143	−	1.29035i
$271$	121.196	+	47.9850i	0.447219	+	0.177066i	0.580929	−	0.813954i	$-0.302689\pi$
$271$	121.196	+	47.9850i	0.447219	+	0.177066i	−0.133711	+	0.991020i	$0.542689\pi$
$272$	−407.267	+	492.301i	−1.49730	+	1.80993i
$273$	121.844	−	5.19603i	0.446315	−	0.0190331i
$274$	255.200	−	785.424i	0.931386	−	2.86651i
$275$	−3.55895	+	13.1545i	−0.0129416	+	0.0478347i
$276$	19.9600	+	17.2035i	0.0723187	+	0.0623316i
$277$	161.852	+	30.8748i	0.584302	+	0.111462i	0.471053	−	0.882105i	$-0.343874\pi$
$277$	161.852	+	30.8748i	0.584302	+	0.111462i	0.113249	+	0.993567i	$0.463874\pi$
$278$	413.463	+	651.514i	1.48728	+	2.34357i
$279$	363.673	−	31.0741i	1.30349	−	0.111377i
$280$	−430.311	−	57.1822i	−1.53683	−	0.204222i
$281$	−258.660	+	213.982i	−0.920499	+	0.761503i	−0.971461	−	0.237198i	$-0.923771\pi$
$281$	−258.660	+	213.982i	−0.920499	+	0.761503i	0.0509627	+	0.998701i	$0.483771\pi$
$282$	155.378	−	370.388i	0.550987	−	1.31343i
$283$	194.977	+	492.456i	0.688965	+	1.74013i	0.672315	+	0.740265i	$0.265300\pi$
$283$	194.977	+	492.456i	0.688965	+	1.74013i	0.0166492	+	0.999861i	$0.494700\pi$
$284$	−593.634	−	279.343i	−2.09026	−	0.983602i
$285$	96.2809	−	143.132i	0.337828	−	0.502219i
$286$	10.2571	−	9.63210i	0.0358641	−	0.0336787i
$287$	−33.3637	−	174.899i	−0.116250	−	0.609404i
$288$	−2.60123	−	116.074i	−0.00903206	−	0.403036i
$289$	−112.978	+	592.252i	−0.390928	+	2.04932i
$290$	−587.857	−	78.1177i	−2.02709	−	0.269372i
$291$	121.000	+	69.7416i	0.415808	+	0.239662i
$292$	815.452	−	51.3039i	2.79264	−	0.175698i
$293$	−113.385	−	82.3792i	−0.386980	−	0.281158i	0.377237	−	0.926117i	$-0.376874\pi$
$293$	−113.385	−	82.3792i	−0.386980	−	0.281158i	−0.764217	+	0.644959i	$0.776874\pi$
$294$	−183.894	+	55.6677i	−0.625491	+	0.189346i
$295$	−43.6616	+	131.486i	−0.148006	+	0.445715i
$296$	−678.972	−	42.7173i	−2.29382	−	0.144315i
$297$	13.9873	−	4.57870i	0.0470954	−	0.0154165i
$298$	79.2533	+	627.354i	0.265951	+	2.10522i
$299$	−4.48134	+	6.16803i	−0.0149878	+	0.0206289i
$300$	−500.456	+	386.838i	−1.66819	+	1.28946i
$301$	−197.099	+	143.200i	−0.654812	+	0.475749i
$302$	391.083	−	367.251i	1.29498	−	1.21606i
$303$	−2.68246	−	15.7894i	−0.00885300	−	0.0521104i
$304$	238.300	−	61.1851i	0.783882	−	0.201267i
$305$	335.782	+	23.3002i	1.10092	+	0.0763941i
$306$	−475.093	−	820.113i	−1.55259	−	2.68011i
$307$		−	256.831i		−	0.836584i	−0.908313	−	0.418292i	$-0.862629\pi$
$307$		−	256.831i		−	0.836584i	0.908313	−	0.418292i	$-0.137371\pi$
$308$	13.6792	−	21.5549i	0.0444129	−	0.0699835i
$309$	−77.5256	+	366.045i	−0.250892	+	1.18461i
$310$	4.61043	−	715.009i	0.0148723	−	2.30648i
$311$	−119.944	+	218.176i	−0.385670	+	0.701532i	−0.995877	−	0.0907102i	$-0.971086\pi$
$311$	−119.944	+	218.176i	−0.385670	+	0.701532i	0.610207	+	0.792242i	$0.291086\pi$
$312$	341.444	−	36.1396i	1.09437	−	0.115832i
$313$	476.309	+	224.134i	1.52176	+	0.716084i	0.991299	−	0.131628i	$-0.0420206\pi$
$313$	476.309	+	224.134i	1.52176	+	0.716084i	0.530456	+	0.847712i	$0.322021\pi$
$314$	−233.978	+	425.605i	−0.745154	+	1.35543i
$315$	116.876	−	220.874i	0.371035	−	0.701187i
$316$	471.689	+	442.946i	1.49269	+	1.40173i
$317$	−56.6944	+	89.3361i	−0.178847	+	0.281817i	−0.921910	−	0.387404i	$-0.873372\pi$
$317$	−56.6944	+	89.3361i	−0.178847	+	0.281817i	0.743064	+	0.669221i	$0.233372\pi$
$318$	60.5568	−	36.7350i	0.190430	−	0.115519i
$319$	9.82428	−	15.4806i	0.0307971	−	0.0485285i
$320$	199.948	+	13.8746i	0.624837	+	0.0433580i
$321$	103.985	−	106.342i	0.323941	−	0.331282i
$322$	−7.50727	+	18.9612i	−0.0233145	+	0.0588857i
$323$	250.367	−	235.110i	0.775130	−	0.727896i
$324$	645.793	+	222.773i	1.99319	+	0.687571i
$325$	−123.550	−	135.015i	−0.380153	−	0.415430i
$326$	103.784	−	142.846i	0.318355	−	0.438179i
$327$	302.891	−	240.429i	0.926272	−	0.735258i
$328$	−124.666	−	485.540i	−0.380078	−	1.48031i
$329$	210.433	+	13.2393i	0.639614	+	0.0402411i
$330$	−6.42314	−	28.1070i	−0.0194641	−	0.0851727i
$331$	−355.794	−	91.3523i	−1.07491	−	0.275989i	−0.330561	−	0.943785i	$-0.607238\pi$
$331$	−355.794	−	91.3523i	−1.07491	−	0.275989i	−0.744345	+	0.667796i	$0.767238\pi$
$332$	−895.581	−	650.678i	−2.69753	−	1.95987i
$333$	158.767	−	358.004i	0.476777	−	1.07509i
$334$	309.021	−	169.886i	0.925214	−	0.508641i
$335$	−513.174	−	68.1935i	−1.53186	−	0.203563i
$336$	333.960	−	124.477i	0.993930	−	0.370467i
$337$	−160.776	−	292.451i	−0.477081	−	0.867806i	−0.999882	−	0.0153519i	$-0.995113\pi$
$337$	−160.776	−	292.451i	−0.477081	−	0.867806i	0.522802	−	0.852454i	$-0.324887\pi$
$338$	−76.2558	−	399.747i	−0.225609	−	1.18268i
$339$	136.485	−	490.218i	0.402610	−	1.44607i
$340$	−1142.96	+	528.861i	−3.36165	+	1.55547i
$341$	20.0027	+	9.41258i	0.0586591	+	0.0276029i
$342$	−37.6180	+	363.017i	−0.109994	+	1.06145i
$343$	−219.222	−	301.734i	−0.639132	−	0.879690i
$344$	−528.501	+	437.214i	−1.53634	+	1.27097i
$345$	6.27240	+	14.3076i	0.0181809	+	0.0414713i
$346$	−87.6076	−	138.047i	−0.253201	−	0.398981i
$347$	−65.6177	−	103.397i	−0.189100	−	0.297974i	0.736529	−	0.676406i	$-0.236463\pi$
$347$	−65.6177	−	103.397i	−0.189100	−	0.297974i	−0.925629	+	0.378432i	$0.876463\pi$
$348$	797.438	−	297.228i	2.29149	−	0.854104i
$349$	−165.101	−	508.129i	−0.473069	−	1.45596i	−0.848544	−	0.529125i	$-0.822520\pi$
$349$	−165.101	−	508.129i	−0.473069	−	1.45596i	0.375474	−	0.926833i	$-0.377480\pi$
$350$	−409.906	−	267.611i	−1.17116	−	0.764604i
$351$	−48.7344	+	191.551i	−0.138844	+	0.545730i
$352$	3.38769	−	6.16218i	0.00962411	−	0.0175062i
$353$	−66.2543	+	80.0877i	−0.187689	+	0.226877i	−0.855962	−	0.517039i	$-0.827034\pi$
$353$	−66.2543	+	80.0877i	−0.187689	+	0.226877i	0.668272	+	0.743917i	$0.267034\pi$
$354$	−49.0946	−	288.979i	−0.138685	−	0.816326i
$355$	−245.992	−	301.288i	−0.692936	−	0.848699i
$356$	765.197	−	48.1421i	2.14943	−	0.135231i
$357$	324.825	−	376.870i	0.909873	−	1.05566i
$358$	424.226	−	350.950i	1.18499	−	0.980307i
$359$	−497.265	+	94.8583i	−1.38514	+	0.264229i	−0.825450	−	0.564475i	$-0.809079\pi$
$359$	−497.265	+	94.8583i	−1.38514	+	0.264229i	−0.559687	+	0.828704i	$0.689079\pi$
$360$	289.357	−	641.282i	0.803768	−	1.78134i
$361$	226.943	−	28.6696i	0.628652	−	0.0794172i
$362$	996.409	+	125.876i	2.75251	+	0.347723i
$363$	−354.251	−	75.0276i	−0.975897	−	0.206688i
$364$	145.977	+	310.217i	0.401036	+	0.852245i
$365$	449.224	+	181.220i	1.23075	+	0.496492i
$366$	−650.342	+	290.121i	−1.77689	+	0.792680i
$367$	−19.7625	+	76.9699i	−0.0538488	+	0.209727i	−0.989814	−	0.142365i	$-0.954529\pi$
$367$	−19.7625	+	76.9699i	−0.0538488	+	0.209727i	0.935966	+	0.352092i	$0.114529\pi$
$368$	−6.88519	+	21.1904i	−0.0187097	+	0.0575827i
$369$	287.035	+	29.7443i	0.777872	+	0.0806077i
$370$	−669.899	−	373.925i	−1.81054	−	1.01061i
$371$	28.6483	+	23.6999i	0.0772191	+	0.0638812i
$372$	476.056	+	908.992i	1.27972	+	2.44353i
$373$	432.810	−	203.665i	1.16035	−	0.546019i	0.253443	−	0.967350i	$-0.418437\pi$
$373$	432.810	−	203.665i	1.16035	−	0.546019i	0.906907	+	0.421332i	$0.138437\pi$
$374$		−	57.4041i		−	0.153487i
$375$	−366.623	+	78.8218i	−0.977660	+	0.210191i
$376$	593.624			1.57879
$377$	104.840	+	222.796i	0.278089	+	0.590970i
$378$	1.15970	+	528.691i	0.00306799	+	1.39865i
$379$	−386.401	+	467.079i	−1.01953	+	1.23240i	−0.0471741	+	0.998887i	$0.515022\pi$
$379$	−386.401	+	467.079i	−1.01953	+	1.23240i	−0.972354	+	0.233511i	$0.924978\pi$
$380$	475.763	+	93.9399i	1.25201	+	0.247210i
$381$	−194.190	−	147.175i	−0.509685	−	0.386285i
$382$	−918.198	−	298.341i	−2.40366	−	0.780996i
$383$	−523.785	−	134.485i	−1.36759	−	0.351136i	−0.507661	−	0.861557i	$-0.669490\pi$
$383$	−523.785	−	134.485i	−1.36759	−	0.351136i	−0.859925	+	0.510421i	$0.829490\pi$
$384$	−528.634	+	235.826i	−1.37665	+	0.614131i
$385$	12.8309	−	8.02717i	0.0333271	−	0.0208498i
$386$	20.4892	−	9.64147i	0.0530807	−	0.0249779i
$387$	−130.398	−	372.696i	−0.336945	−	0.963039i
$388$	−49.2085	+	389.525i	−0.126826	+	1.00393i
$389$	38.4865	+	304.652i	0.0989371	+	0.783167i	0.961035	+	0.276426i	$0.0891501\pi$
$389$	38.4865	+	304.652i	0.0989371	+	0.783167i	−0.862098	+	0.506741i	$0.830850\pi$
$390$	364.927	+	129.425i	0.935711	+	0.331859i
$391$	5.82828	+	30.5529i	0.0149061	+	0.0781405i
$392$	−181.004	−	218.797i	−0.461746	−	0.558155i
$393$	−17.9811	+	20.8621i	−0.0457534	+	0.0530842i
$394$	28.1376	+	447.235i	0.0714153	+	1.13511i
$395$	138.915	+	357.578i	0.351683	+	0.905262i
$396$	27.0812	+	31.2813i	0.0683869	+	0.0789931i
$397$	−76.6991	−	63.4510i	−0.193197	−	0.159826i	0.535796	−	0.844347i	$-0.320011\pi$
$397$	−76.6991	−	63.4510i	−0.193197	−	0.159826i	−0.728993	+	0.684521i	$0.760011\pi$
$398$	−46.2307	−	25.4155i	−0.116157	−	0.0638581i
$399$	−186.491	+	43.8849i	−0.467396	+	0.109987i
$400$	−465.323	−	263.684i	−1.16331	−	0.659210i
$401$	−507.844	+	165.008i	−1.26644	+	0.411492i	−0.863786	−	0.503859i	$-0.831913\pi$
$401$	−507.844	+	165.008i	−1.26644	+	0.411492i	−0.402657	+	0.915351i	$0.631913\pi$
$402$	1026.29	−	382.529i	2.55296	−	0.951564i
$403$	−250.669	+	159.079i	−0.622007	+	0.394738i
$404$	38.0153	−	24.1252i	0.0940972	−	0.0597159i
$405$	288.361	+	284.381i	0.712003	+	0.702176i
$406$	419.825	+	507.481i	1.03405	+	1.24995i
$407$	19.1896	−	13.9421i	0.0471489	−	0.0342557i
$408$	846.083	−	1116.37i	2.07373	−	2.73619i
$409$	−197.005	+	418.656i	−0.481674	+	1.02361i	0.505331	+	0.862925i	$0.331370\pi$
$409$	−197.005	+	418.656i	−0.481674	+	1.02361i	−0.987006	+	0.160685i	$0.948630\pi$
$410$	109.506	−	554.598i	0.267088	−	1.35268i
$411$	−188.452	+	676.871i	−0.458521	+	1.64689i
$412$	−1033.24	+	197.102i	−2.50787	+	0.478402i
$413$	134.839	−	74.1284i	0.326487	−	0.179488i
$414$	−25.9323	−	20.4920i	−0.0626385	−	0.0494977i
$415$	−312.454	−	577.136i	−0.752902	−	1.39069i
$416$	45.4955	+	82.7560i	0.109364	+	0.198933i
$417$	−375.065	−	538.807i	−0.899437	−	1.29210i
$418$	−12.9927	+	17.8829i	−0.0310829	+	0.0427820i
$419$	79.7297	−	310.527i	0.190286	−	0.741114i	−0.799754	−	0.600327i	$-0.795037\pi$
$419$	79.7297	−	310.527i	0.190286	−	0.741114i	0.990040	−	0.140786i	$-0.0449631\pi$
$420$	699.696	+	62.7854i	1.66594	+	0.149489i
$421$	−7.51370	+	119.427i	−0.0178473	+	0.283674i	0.978973	+	0.203990i	$0.0653911\pi$
$421$	−7.51370	+	119.427i	−0.0178473	+	0.283674i	−0.996820	+	0.0796840i	$0.974609\pi$
$422$	356.629	−	91.5667i	0.845092	−	0.216983i
$423$	−118.647	+	320.467i	−0.280490	+	0.757605i
$424$	84.6868	+	61.5285i	0.199733	+	0.145115i
$425$	−746.569	−	9.62825i	−1.75663	−	0.0226547i
$426$	758.845	+	318.336i	1.78133	+	0.747269i
$427$	−255.900	−	272.506i	−0.599298	−	0.638187i
$428$	388.765	+	153.923i	0.908329	+	0.359633i
$429$	−8.36954	+	8.55921i	−0.0195094	+	0.0199515i
$430$	−750.424	+	187.527i	−1.74517	+	0.436109i
$431$	−617.989	−	392.187i	−1.43385	−	0.909948i	−0.999960	−	0.00898107i	$-0.997141\pi$
$431$	−617.989	−	392.187i	−1.43385	−	0.909948i	−0.433888	−	0.900967i	$-0.642859\pi$
$432$	37.5340	+	576.408i	0.0868843	+	1.33428i
$433$	384.004	+	243.696i	0.886845	+	0.562809i	0.899407	−	0.437112i	$-0.143999\pi$
$433$	384.004	+	243.696i	0.886845	+	0.562809i	−0.0125618	+	0.999921i	$0.503999\pi$
$434$	−543.614	+	578.890i	−1.25257	+	1.33385i
$435$	502.517	+	45.0920i	1.15521	+	0.103660i
$436$	952.686	+	523.743i	2.18506	+	1.20125i
$437$	5.09960	−	10.8372i	0.0116696	−	0.0247991i
$438$	−1019.15	+	107.870i	−2.32682	+	0.246279i
$439$	−18.5522	−	10.1992i	−0.0422601	−	0.0232327i	0.460484	−	0.887668i	$-0.347676\pi$
$439$	−18.5522	−	10.1992i	−0.0422601	−	0.0232327i	−0.502744	+	0.864436i	$0.667676\pi$
$440$	34.6338	−	24.8233i	0.0787132	−	0.0564167i
$441$	154.294	−	53.9841i	0.349874	−	0.122413i
$442$	650.908	+	413.079i	1.47264	+	0.934567i
$443$	600.573			1.35569			0.677847	−	0.735203i	$-0.262913\pi$
$443$	600.573			1.35569			0.677847	+	0.735203i	$0.262913\pi$
$444$	1100.75	+	22.2522i	2.47916	+	0.0501176i
$445$	421.539	+	170.051i	0.947279	+	0.382138i
$446$	155.690	+	606.372i	0.349080	+	1.35958i
$447$	−90.1070	−	530.386i	−0.201582	−	1.18655i
$448$	−152.381	−	162.269i	−0.340136	−	0.362208i
$449$	−413.401	−	568.997i	−0.920714	−	1.26725i	−0.963373	−	0.268164i	$-0.913583\pi$
$449$	−413.401	−	568.997i	−0.920714	−	1.26725i	0.0426591	−	0.999090i	$-0.486417\pi$
$450$	606.477	−	511.514i	1.34773	−	1.13670i
$451$	14.1398	+	10.2732i	0.0313522	+	0.0227787i
$452$	1419.27	−	179.295i	3.13997	−	0.396671i
$453$	−319.113	+	326.344i	−0.704443	+	0.720407i
$454$	12.7328	−	202.382i	0.0280458	−	0.445775i
$455$	−1.31059	+	203.254i	−0.00288043	+	0.446712i
$456$	−516.252	+	156.278i	−1.13213	+	0.342714i
$457$	−69.6561	+	95.8735i	−0.152420	+	0.209789i	−0.878398	−	0.477929i	$-0.841387\pi$
$457$	−69.6561	+	95.8735i	−0.152420	+	0.209789i	0.725978	+	0.687718i	$0.241387\pi$
$458$	−81.5524	−	1296.24i	−0.178062	−	2.83021i
$459$	433.562	+	679.884i	0.944580	+	1.48123i
$460$	−30.2697	+	31.8202i	−0.0658036	+	0.0691744i
$461$	−76.5997	−	14.6122i	−0.166160	−	0.0316967i	0.103630	−	0.994616i	$-0.466954\pi$
$461$	−76.5997	−	14.6122i	−0.166160	−	0.0316967i	−0.269790	+	0.962919i	$0.586954\pi$
$462$	−15.9902	+	27.7427i	−0.0346109	+	0.0600492i
$463$	368.130	−	70.2245i	0.795096	−	0.151673i	0.226199	−	0.974081i	$-0.427370\pi$
$463$	368.130	−	70.2245i	0.795096	−	0.151673i	0.568897	+	0.822408i	$0.307370\pi$
$464$	492.594	+	524.559i	1.06162	+	1.13052i
$465$	21.9992	+	607.933i	0.0473101	+	1.30738i
$466$	209.566	−	445.350i	0.449712	−	0.955687i
$467$	−477.219	+	188.944i	−1.02188	+	0.404592i	−0.818499	−	0.574507i	$-0.805194\pi$
$467$	−477.219	+	188.944i	−1.02188	+	0.404592i	−0.203383	+	0.979099i	$0.565194\pi$
$468$	−549.576	+	81.9756i	−1.17431	+	0.175162i
$469$	366.489	+	443.009i	0.781427	+	0.944583i
$470$	603.870	+	288.930i	1.28483	+	0.614745i
$471$	183.457	−	370.251i	0.389505	−	0.786095i
$472$	365.772	−	232.126i	0.774940	−	0.491792i
$473$	4.48116	−	23.4911i	0.00947391	−	0.0496640i
$474$	−614.772	−	529.873i	−1.29699	−	1.11788i
$475$	230.396	+	171.976i	0.485045	+	0.362054i
$476$	1330.25	+	432.223i	2.79463	+	0.908032i
$477$	−50.1424	+	33.4203i	−0.105120	+	0.0700636i
$478$	−879.175	−	727.317i	−1.83928	−	1.52158i
$479$	246.332	−	622.163i	0.514262	−	1.29888i	−0.408236	−	0.912877i	$-0.633856\pi$
$479$	246.332	−	622.163i	0.514262	−	1.29888i	0.922498	−	0.386002i	$-0.126144\pi$
$480$	193.437	+	5.15840i	0.402994	+	0.0107467i
$481$	20.0017	+	317.918i	0.0415836	+	0.660953i
$482$	54.5301	+	167.826i	0.113133	+	0.348187i
$483$	5.69395	−	16.3894i	0.0117887	−	0.0339325i
$484$	−190.751	−	999.951i	−0.394113	−	2.06601i
$485$	−125.987	+	195.723i	−0.259768	+	0.403553i
$486$	−821.185	−	244.658i	−1.68968	−	0.503412i
$487$	−53.8751	+	426.465i	−0.110626	+	0.875698i	0.834956	+	0.550316i	$0.185493\pi$
$487$	−53.8751	+	426.465i	−0.110626	+	0.875698i	−0.945583	+	0.325382i	$0.894507\pi$
$488$	−767.213	−	720.461i	−1.57216	−	1.47635i
$489$	−83.0395	+	125.183i	−0.169815	+	0.255998i
$490$	−77.6353	−	310.672i	−0.158439	−	0.634025i
$491$	−40.1553	+	317.862i	−0.0817827	+	0.647377i	0.896935	+	0.442163i	$0.145789\pi$
$491$	−40.1553	+	317.862i	−0.0817827	+	0.647377i	−0.978717	+	0.205213i	$0.934211\pi$
$492$	235.045	+	776.455i	0.477734	+	1.57816i
$493$	955.373	+	310.420i	1.93788	+	0.629654i
$494$	−109.280	−	276.009i	−0.221214	−	0.558723i
$495$	6.47858	+	23.6584i	0.0130880	+	0.0477948i
$496$	−553.047	+	668.519i	−1.11501	+	1.34782i
$497$	−27.1245	+	431.131i	−0.0545764	+	0.867467i
$498$	1157.08	+	767.541i	2.32345	+	1.54125i
$499$	−51.9240			−0.104056			−0.0520280	−	0.998646i	$-0.516569\pi$
$499$	−51.9240			−0.104056			−0.0520280	+	0.998646i	$0.516569\pi$
$500$	−603.044	−	864.711i	−1.20609	−	1.72942i
$501$	−256.514	+	155.607i	−0.512003	+	0.310592i
$502$	−958.276	+	450.931i	−1.90892	+	0.898268i
$503$	−51.2303	+	814.283i	−0.101850	+	1.61885i	0.532930	+	0.846159i	$0.321091\pi$
$503$	−51.2303	+	814.283i	−0.101850	+	1.61885i	−0.634779	+	0.772693i	$0.718909\pi$
$504$	−719.872	+	303.846i	−1.42832	+	0.602869i
$505$	26.5033	−	3.17467i	0.0524819	−	0.00628647i
$506$	−0.736920	−	1.86125i	−0.00145636	−	0.00367836i
$507$	79.3086	+	337.025i	0.156427	+	0.664744i
$508$	170.351	−	663.472i	0.335336	−	1.30605i
$509$	74.9985	−	593.674i	0.147345	−	1.16635i	−0.728946	−	0.684571i	$-0.759989\pi$
$509$	74.9985	−	593.674i	0.147345	−	1.16635i	0.876291	−	0.481783i	$-0.160011\pi$
$510$	1404.05	−	723.827i	2.75303	−	1.41927i
$511$	−229.063	−	486.784i	−0.448264	−	0.952610i
$512$	−774.097	−	726.925i	−1.51191	−	1.41978i
$513$	18.8169	−	309.933i	0.0366801	−	0.604157i
$514$	1255.74	−	158.637i	2.44308	−	0.308632i
$515$	−603.003	−	158.976i	−1.17088	−	0.308692i
$516$	824.366	−	743.355i	1.59761	−	1.44061i
$517$	−15.9474	+	13.1928i	−0.0308460	+	0.0255181i
$518$	263.302	+	810.360i	0.508305	+	1.56440i
$519$	79.4715	+	114.166i	0.153124	+	0.219974i
$520$	32.2487	+	571.343i	0.0620167	+	1.09874i
$521$	−235.318	+	594.345i	−0.451666	+	1.14078i	0.508429	+	0.861104i	$0.330226\pi$
$521$	−235.318	+	594.345i	−0.451666	+	1.14078i	−0.960095	+	0.279674i	$0.909774\pi$
$522$	−983.431	+	415.090i	−1.88397	+	0.795191i
$523$	231.518	−	421.130i	0.442674	−	0.805221i	−0.557006	−	0.830508i	$-0.688050\pi$
$523$	231.518	−	421.130i	0.442674	−	0.805221i	0.999680	+	0.0252875i	$0.00805011\pi$
$524$	−73.6374	−	23.9263i	−0.140529	−	0.0456608i
$525$	358.126	+	212.614i	0.682145	+	0.404979i
$526$	96.7372	+	297.726i	0.183911	+	0.566020i
$527$	−226.956	+	1189.74i	−0.430656	+	2.25758i
$528$	−15.5326	+	31.3478i	−0.0294178	+	0.0593708i
$529$	−282.871	−	445.734i	−0.534728	−	0.842597i
$530$	56.2011	+	103.809i	0.106040	+	0.195867i
$531$	52.2061	+	243.856i	0.0983165	+	0.459240i
$532$	−316.578	−	435.733i	−0.595072	−	0.819046i
$533$	−218.238	+	86.4066i	−0.409452	+	0.162114i
$534$	−956.340	+	101.222i	−1.79090	+	0.189555i
$535$	168.522	+	181.793i	0.314995	+	0.339800i
$536$	1108.09	+	1180.00i	2.06734	+	2.20149i
$537$	−347.875	+	313.689i	−0.647813	+	0.584151i
$538$	−646.532	−	1176.04i	−1.20173	−	2.18594i
$539$	9.72519	+	1.85518i	0.0180430	+	0.00344189i
$540$	−423.632	+	1056.81i	−0.784505	+	1.95706i
$541$	−184.379	+	101.363i	−0.340811	+	0.187362i	−0.642963	−	0.765897i	$-0.722295\pi$
$541$	−184.379	+	101.363i	−0.340811	+	0.187362i	0.302152	+	0.953260i	$0.402295\pi$
$542$	−28.8607	−	458.727i	−0.0532485	−	0.846360i
$543$	−851.522	−	70.8773i	−1.56818	−	0.130529i
$544$	373.169	+	95.8135i	0.685973	+	0.176128i
$545$	375.473	+	523.865i	0.688942	+	0.961220i
$546$	−199.511	−	380.950i	−0.365404	−	0.697711i
$547$	−112.230	−	437.107i	−0.205174	−	0.799099i	−0.984921	−	0.173005i	$-0.944652\pi$
$547$	−112.230	−	437.107i	−0.205174	−	0.799099i	0.779747	−	0.626094i	$-0.215348\pi$
$548$	−1959.66	+	247.563i	−3.57602	+	0.451757i
$549$	542.282	−	270.180i	0.987763	−	0.492131i
$550$	47.3137	−	8.39472i	0.0860248	−	0.0152631i
$551$	−227.364	−	312.940i	−0.412639	−	0.567949i
$552$	13.1018	−	47.0581i	0.0237351	−	0.0852502i
$553$	156.840	−	396.132i	0.283616	−	0.716333i
$554$	−144.490	−	562.752i	−0.260813	−	1.01580i
$555$	582.977	+	293.558i	1.05041	+	0.528933i
$556$	988.912	−	1558.28i	1.77862	−	2.80266i
$557$	−459.893			−0.825660			−0.412830	−	0.910808i	$-0.635460\pi$
$557$	−459.893			−0.825660			−0.412830	+	0.910808i	$0.635460\pi$
$558$	−645.151	−	1113.67i	−1.15618	−	1.99582i
$559$	234.120	+	219.853i	0.418819	+	0.393297i
$560$	179.912	+	566.106i	0.321271	+	1.01090i
$561$	2.08082	+	48.7942i	0.00370913	+	0.0869771i
$562$	1071.07	+	504.006i	1.90581	+	0.896808i
$563$	−13.0375	+	27.7060i	−0.0231571	+	0.0492114i	−0.916071	−	0.401016i	$-0.868657\pi$
$563$	−13.0375	+	27.7060i	−0.0231571	+	0.0492114i	0.892914	+	0.450228i	$0.148657\pi$
$564$	−959.807	+	40.9309i	−1.70179	+	0.0725725i
$565$	804.889	+	267.274i	1.42458	+	0.473052i
$566$	1278.48	−	1361.44i	2.25880	−	2.40537i
$567$	−20.1501	−	449.351i	−0.0355381	−	0.792506i
$568$			1216.21i			2.14121i
$569$	−637.892	−	404.818i	−1.12108	−	0.711456i	−0.159828	−	0.987145i	$-0.551094\pi$
$569$	−637.892	−	404.818i	−1.12108	−	0.711456i	−0.961247	+	0.275689i	$0.911094\pi$
$570$	−601.226	−	92.2963i	−1.05478	−	0.161923i
$571$	−966.270	+	248.096i	−1.69224	+	0.434494i	−0.967160	−	0.254169i	$-0.918198\pi$
$571$	−966.270	+	248.096i	−1.69224	+	0.434494i	−0.725082	+	0.688663i	$0.758198\pi$
$572$	−31.2908	−	12.3889i	−0.0547043	−	0.0216589i
$573$	791.293	+	220.310i	1.38097	+	0.384484i
$574$	−507.935	+	369.036i	−0.884904	+	0.642920i
$575$	−24.3300	+	9.27183i	−0.0423131	+	0.0161249i
$576$	322.912	−	160.884i	0.560612	−	0.279313i
$577$	−108.602	−	859.670i	−0.188218	−	1.48990i	−0.749353	−	0.662171i	$-0.769635\pi$
$577$	−108.602	−	859.670i	−0.188218	−	1.48990i	0.561135	−	0.827724i	$-0.310365\pi$
$578$	2059.24	−	528.723i	3.56270	−	0.914746i
$579$	−17.0665	+	8.93807i	−0.0294759	+	0.0154371i
$580$	429.597	+	1351.76i	0.740685	+	2.33062i
$581$	−181.267	+	705.990i	−0.311992	+	1.21513i
$582$	40.8495	−	490.767i	0.0701881	−	0.843242i
$583$	−3.64249	+	0.229166i	−0.00624784	+	0.000393081i
$584$	−729.685	−	1327.29i	−1.24946	−	2.27276i
$585$	−314.884	−	96.7846i	−0.538263	−	0.165444i
$586$	−92.6034	+	485.444i	−0.158026	+	0.828403i
$587$	−343.775	+	188.992i	−0.585648	+	0.321962i	−0.746885	−	0.664953i	$-0.768451\pi$
$587$	−343.775	+	188.992i	−0.585648	+	0.321962i	0.161238	+	0.986916i	$0.448451\pi$
$588$	307.745	+	341.284i	0.523376	+	0.580414i
$589$	339.985	−	319.267i	0.577225	−	0.542050i
$590$	485.066	−	58.1030i	0.822145	−	0.0984796i
$591$	−40.1290	−	379.135i	−0.0679002	−	0.641514i
$592$	342.699	+	865.558i	0.578883	+	1.46209i
$593$	−128.530	+	93.3825i	−0.216745	+	0.157475i	−0.690860	−	0.722988i	$-0.742768\pi$
$593$	−128.530	+	93.3825i	−0.216745	+	0.157475i	0.474115	+	0.880463i	$0.342768\pi$
$594$	−35.6087	−	37.7531i	−0.0599473	−	0.0635575i
$595$	600.807	+	571.530i	1.00976	+	0.960555i
$596$	1276.98	−	810.394i	2.14258	−	1.35972i
$597$	40.2179	+	19.9277i	0.0673667	+	0.0333797i
$598$	26.4076	+	5.03752i	0.0441599	+	0.00842395i
$599$	699.320	−	227.223i	1.16748	−	0.379337i	0.339777	−	0.940506i	$-0.389648\pi$
$599$	699.320	−	227.223i	1.16748	−	0.379337i	0.827701	+	0.561169i	$0.189648\pi$
$600$	1043.86	+	534.103i	1.73977	+	0.890171i
$601$	197.586	−	608.107i	0.328762	−	1.01183i	−0.640952	−	0.767581i	$-0.721460\pi$
$601$	197.586	−	608.107i	0.328762	−	1.01183i	0.969714	−	0.244244i	$-0.0785398\pi$
$602$	752.807	+	413.859i	1.25051	+	0.687474i
$603$	−858.494	+	362.356i	−1.42370	+	0.600922i
$604$	−1193.05	−	472.363i	−1.97525	−	0.782058i
$605$	153.854	−	583.574i	0.254304	−	0.964585i
$606$	−46.3498	+	32.2643i	−0.0764849	+	0.0532414i
$607$	463.503	−	150.601i	0.763597	−	0.248108i	0.0987754	−	0.995110i	$-0.468507\pi$
$607$	463.503	−	150.601i	0.763597	−	0.248108i	0.664822	+	0.747002i	$0.268507\pi$
$608$	−94.5658	−	114.310i	−0.155536	−	0.188010i
$609$	−375.251	−	416.147i	−0.616176	−	0.683328i
$610$	−429.790	−	1106.31i	−0.704574	−	1.81363i
$611$	−34.8371	−	275.764i	−0.0570165	−	0.451332i
$612$	−1291.02	+	1863.35i	−2.10952	+	3.04469i
$613$	−368.348	+	392.251i	−0.600895	+	0.639888i	−0.955452	−	0.295146i	$-0.904632\pi$
$613$	−368.348	+	392.251i	−0.600895	+	0.639888i	0.354557	+	0.935034i	$0.384632\pi$
$614$	−819.436	+	385.597i	−1.33459	+	0.628009i
$615$	−72.9779	+	475.384i	−0.118663	+	0.772982i
$616$	−46.9517	−	5.93137i	−0.0762202	−	0.00962886i
$617$	−1156.09	−	296.833i	−1.87373	−	0.481091i	−0.873740	−	0.486393i	$-0.838312\pi$
$617$	−1156.09	−	296.833i	−1.87373	−	0.481091i	−0.999986	+	0.00530185i	$0.998312\pi$
$618$	1284.28	−	302.217i	2.07813	−	0.489024i
$619$	−591.184	+	234.066i	−0.955063	+	0.378136i	−0.793394	−	0.608709i	$-0.791688\pi$
$619$	−591.184	+	234.066i	−0.955063	+	0.378136i	−0.161670	+	0.986845i	$0.551688\pi$
$620$	−1552.08	+	718.166i	−2.50335	+	1.15833i
$621$	22.7856	+	16.4785i	0.0366918	+	0.0265354i
$622$	876.185	+	55.1249i	1.40866	+	0.0886252i
$623$	−214.946	−	456.784i	−0.345018	−	0.733201i
$624$	−243.682	−	401.703i	−0.390515	−	0.643755i
$625$	−101.242	−	616.746i	−0.161987	−	0.986793i
$626$		−	1856.20i		−	2.96518i
$627$	10.3957	−	15.6716i	0.0165800	−	0.0249946i
$628$	1159.35	+	72.9400i	1.84610	+	0.116146i
$629$	1001.33	+	828.376i	1.59195	+	1.31697i
$630$	−880.185	−	41.2876i	−1.39712	−	0.0655359i
$631$	−56.8343	+	22.5023i	−0.0900703	+	0.0356613i	−0.412728	−	0.910855i	$-0.635424\pi$
$631$	−56.8343	+	22.5023i	−0.0900703	+	0.0356613i	0.322657	+	0.946516i	$0.395424\pi$
$632$	370.667	−	1140.79i	0.586498	−	1.80505i
$633$	−299.820	+	90.7601i	−0.473649	+	0.143381i
$634$	370.151	+	46.7610i	0.583835	+	0.0737555i
$635$	260.870	−	311.230i	0.410819	−	0.490126i
$636$	−141.169	−	93.6439i	−0.221964	−	0.147239i
$637$	−91.0182	+	96.9245i	−0.142886	+	0.152158i
$638$	−64.1416	−	8.10297i	−0.100535	−	0.0127006i
$639$	−656.567	−	243.083i	−1.02749	−	0.380411i
$640$	−349.357	−	899.274i	−0.545871	−	1.40512i
$641$	222.547	−	42.4530i	0.347186	−	0.0662294i	−0.0108388	−	0.999941i	$-0.503450\pi$
$641$	222.547	−	42.4530i	0.347186	−	0.0662294i	0.358025	+	0.933712i	$0.383450\pi$
$642$	−495.409	−	172.114i	−0.771665	−	0.268090i
$643$	−758.868	+	246.571i	−1.18020	+	0.383470i	−0.832440	−	0.554115i	$-0.813057\pi$
$643$	−758.868	+	246.571i	−1.18020	+	0.383470i	−0.347758	+	0.937584i	$0.613057\pi$
$644$	48.6800	−	3.06269i	0.0755901	−	0.00475572i
$645$	631.072	−	186.602i	0.978406	−	0.289305i
$646$	−1126.03	−	445.826i	−1.74308	−	0.690133i
$647$	513.198	−	620.350i	0.793197	−	0.958810i	−0.206611	−	0.978423i	$-0.566243\pi$
$647$	513.198	−	620.350i	0.793197	−	0.958810i	0.999808	+	0.0196130i	$0.00624341\pi$
$648$	−136.055	−	1259.04i	−0.209961	−	1.94297i
$649$	−4.66745	+	14.3649i	−0.00719176	+	0.0221340i
$650$	−245.280	+	596.900i	−0.377354	+	0.918308i
$651$	441.095	−	511.769i	0.677565	−	0.786128i
$652$	−414.831	−	79.1332i	−0.636243	−	0.121370i
$653$	−15.6533	−	24.6657i	−0.0239714	−	0.0377729i	0.832131	−	0.554579i	$-0.187121\pi$
$653$	−15.6533	−	24.6657i	−0.0239714	−	0.0377729i	−0.856102	+	0.516806i	$0.827121\pi$
$654$	−1221.85	−	605.421i	−1.86828	−	0.925720i
$655$	−33.2584	−	31.6378i	−0.0507762	−	0.0483019i
$656$	−528.538	+	437.245i	−0.805698	+	0.666531i
$657$	862.378	−	128.634i	1.31260	−	0.195790i
$658$	−273.696	−	691.277i	−0.415951	−	1.05057i
$659$	−112.983	−	53.1660i	−0.171447	−	0.0806768i	0.338141	−	0.941096i	$-0.390202\pi$
$659$	−112.983	−	53.1660i	−0.171447	−	0.0806768i	−0.509588	+	0.860419i	$0.670202\pi$
$660$	−54.2865	+	42.5239i	−0.0822523	+	0.0644302i
$661$	567.860	−	533.256i	0.859092	−	0.806741i	−0.123533	−	0.992340i	$-0.539423\pi$
$661$	567.860	−	533.256i	0.859092	−	0.806741i	0.982626	+	0.185599i	$0.0594226\pi$
$662$	242.711	+	1272.34i	0.366633	+	1.92196i
$663$	−568.253	−	327.527i	−0.857093	−	0.494008i
$664$	−384.528	+	2015.76i	−0.579108	+	3.03579i
$665$	−57.8087	−	314.031i	−0.0869304	−	0.472228i
$666$	−1380.60	+	30.9393i	−2.07297	+	0.0464555i
$667$	34.9616	−	2.19960i	0.0524162	−	0.00329775i
$668$	−682.356	−	495.761i	−1.02149	−	0.742157i
$669$	−154.318	−	509.780i	−0.230670	−	0.762002i
$670$	552.886	+	1739.70i	0.825203	+	2.59656i
$671$	36.6225	+	2.30409i	0.0545789	+	0.00343382i
$672$	−153.659	−	150.254i	−0.228659	−	0.223592i
$673$	−20.6180	−	163.208i	−0.0306360	−	0.242509i	0.969359	−	0.245648i	$-0.0790007\pi$
$673$	−20.6180	−	163.208i	−0.0306360	−	0.242509i	−0.999995	+	0.00313929i	$0.999001\pi$
$674$	−691.699	+	952.042i	−1.02626	+	1.41252i
$675$	−496.971	+	456.777i	−0.736253	+	0.676706i
$676$	−787.454	+	572.119i	−1.16487	+	0.846329i
$677$	580.875	−	545.478i	0.858014	−	0.805728i	−0.124442	−	0.992227i	$-0.539714\pi$
$677$	580.875	−	545.478i	0.858014	−	0.805728i	0.982455	+	0.186498i	$0.0597139\pi$
$678$	−1768.98	+	300.532i	−2.60912	+	0.443262i
$679$	250.395	−	64.2904i	0.368770	−	0.0946840i
$680$	1789.21	+	1499.70i	2.63119	+	2.20544i
$681$	−3.48695	+	172.488i	−0.00512033	+	0.253287i
$682$		−	77.9517i		−	0.114299i
$683$	402.703	−	634.558i	0.589608	−	0.929074i	−0.410245	−	0.911975i	$-0.634557\pi$
$683$	402.703	−	634.558i	0.589608	−	0.929074i	0.999854	−	0.0170990i	$-0.00544306\pi$
$684$	823.932	−	288.275i	1.20458	−	0.421455i
$685$	−1111.35	−	369.040i	−1.62242	−	0.538745i
$686$	−633.568	+	1152.46i	−0.923568	+	1.67996i
$687$	116.307	+	1098.86i	0.169298	+	1.59951i
$688$	849.257	+	399.630i	1.23438	+	0.580857i
$689$	23.6128	−	42.9515i	0.0342711	−	0.0623388i
$690$	36.2322	−	41.4934i	0.0525104	−	0.0601354i
$691$	330.153	+	310.035i	0.477790	+	0.448675i	0.885639	−	0.464375i	$-0.153721\pi$
$691$	330.153	+	310.035i	0.477790	+	0.448675i	−0.407848	+	0.913050i	$0.633721\pi$
$692$	−209.538	+	330.179i	−0.302800	+	0.477137i
$693$	12.5863	−	24.1613i	0.0181620	−	0.0348648i
$694$	−231.378	+	364.594i	−0.333398	+	0.525352i
$695$	927.591	−	580.311i	1.33466	−	0.834980i
$696$	−1127.96	−	1102.97i	−1.62064	−	1.58473i
$697$	−352.511	+	890.340i	−0.505754	+	1.27739i
$698$	−1373.34	+	1289.65i	−1.96754	+	1.84764i
$699$	−161.990	+	386.150i	−0.231746	+	0.552431i
$700$	−161.713	+	1159.62i	−0.231019	+	1.65661i
$701$	−657.403	+	904.837i	−0.937807	+	1.29078i	0.0189284	+	0.999821i	$0.493975\pi$
$701$	−657.403	+	904.837i	−0.937807	+	1.29078i	−0.956735	+	0.290960i	$0.906025\pi$
$702$	684.324	−	132.098i	0.974821	−	0.188174i
$703$	−124.450	−	484.699i	−0.177027	−	0.689473i
$704$	21.8076	+	1.37202i	0.0309767	+	0.00194889i
$705$	−523.770	−	223.704i	−0.742936	−	0.317311i
$706$	354.997	+	91.1476i	0.502828	+	0.129104i
$707$	−23.9838	−	17.4253i	−0.0339234	−	0.0246468i
$708$	−575.397	+	400.536i	−0.812708	+	0.565728i
$709$	774.759	−	425.927i	1.09275	−	0.600744i	0.169727	−	0.985491i	$-0.445711\pi$
$709$	774.759	−	425.927i	1.09275	−	0.600744i	0.923022	+	0.384747i	$0.125711\pi$
$710$	−591.954	+	1237.20i	−0.833739	+	1.74253i
$711$	541.771	+	428.114i	0.761985	+	0.602129i
$712$	−684.716	−	1245.49i	−0.961679	−	1.74929i
$713$	7.91450	+	41.4893i	0.0111003	+	0.0581897i
$714$	−1690.11	−	470.554i	−2.36710	−	0.659040i
$715$	−13.5640	−	14.6321i	−0.0189706	−	0.0204645i
$716$	−1191.53	−	560.689i	−1.66414	−	0.783086i
$717$	773.673	+	586.359i	1.07904	+	0.817795i
$718$	1049.23	+	1444.14i	1.46132	+	2.01133i
$719$	−191.421	+	158.357i	−0.266233	+	0.220247i	−0.760956	−	0.648804i	$-0.775270\pi$
$719$	−191.421	+	158.357i	−0.266233	+	0.220247i	0.494723	+	0.869051i	$0.335270\pi$
$720$	−962.591	+	15.3626i	−1.33693	+	0.0213370i
$721$	371.110	+	584.776i	0.514716	+	0.811063i
$722$	−432.197	−	681.034i	−0.598611	−	0.943260i
$723$	−52.4347	−	140.678i	−0.0725238	−	0.194575i
$724$	−742.299	−	2284.56i	−1.02528	−	3.15547i
$725$	−116.141	+	832.834i	−0.160195	+	1.14874i
$726$	292.479	+	1242.90i	0.402864	+	1.71199i
$727$	247.985	−	451.084i	0.341108	−	0.620473i	−0.648999	−	0.760789i	$-0.724812\pi$
$727$	247.985	−	451.084i	0.341108	−	0.620473i	0.990107	+	0.140317i	$0.0448120\pi$
$728$	405.119	−	489.705i	0.556482	−	0.672672i
$729$	706.886	+	178.196i	0.969665	+	0.244438i
$730$	−96.2565	−	1705.35i	−0.131858	−	2.33610i
$731$	1307.67	−	82.2714i	1.78887	−	0.112546i
$732$	1290.15	+	1111.98i	1.76250	+	1.51910i
$733$	773.417	−	639.826i	1.05514	−	0.872887i	0.0629986	−	0.998014i	$-0.479934\pi$
$733$	773.417	−	639.826i	1.05514	−	0.872887i	0.992141	+	0.125126i	$0.0399336\pi$
$734$	275.248	−	52.5063i	0.374997	−	0.0715345i
$735$	77.2523	+	261.261i	0.105105	+	0.355457i
$736$	13.3295	−	1.68391i	0.0181107	−	0.00228792i
$737$	−55.9929	−	7.07355i	−0.0759741	−	0.00959776i
$738$	−336.043	−	960.460i	−0.455343	−	1.30144i
$739$	193.523	+	411.258i	0.261872	+	0.556506i	0.991916	−	0.126894i	$-0.0405008\pi$
$739$	193.523	+	411.258i	0.261872	+	0.556506i	−0.730045	+	0.683399i	$0.760501\pi$
$740$	−127.024	+	1830.55i	−0.171654	+	2.47372i
$741$	102.894	+	230.650i	0.138858	+	0.311268i
$742$	32.6045	−	126.986i	0.0439414	−	0.171141i
$743$	−18.2571	+	56.1896i	−0.0245722	+	0.0756254i	−0.962591	−	0.270960i	$-0.912659\pi$
$743$	−18.2571	+	56.1896i	−0.0245722	+	0.0756254i	0.938018	+	0.346585i	$0.112659\pi$
$744$	1148.94	−	1515.97i	1.54427	−	2.03759i
$745$	890.278	−	106.641i	1.19500	−	0.143142i
$746$	−1299.61	−	1075.13i	−1.74211	−	1.44120i
$747$	−1011.35	−	610.477i	−1.35388	−	0.817238i
$748$	−124.231	+	58.4586i	−0.166084	+	0.0781532i
$749$		−	275.310i		−	0.367571i
$750$	801.920	+	1051.39i	1.06923	+	1.40186i
$751$	411.430			0.547843			0.273921	−	0.961752i	$-0.411679\pi$
$751$	411.430			0.547843			0.273921	+	0.961752i	$0.411679\pi$
$752$	−345.863	−	734.996i	−0.459924	−	0.977388i
$753$	798.201	−	418.033i	1.06003	−	0.555156i
$754$	553.441	−	668.996i	0.734007	−	0.887262i
$755$	−517.166	−	557.892i	−0.684989	−	0.738930i
$756$	1142.98	−	540.912i	1.51188	−	0.715492i
$757$	391.266	+	127.130i	0.516864	+	0.167939i	0.555822	−	0.831302i	$-0.312404\pi$
$757$	391.266	+	127.130i	0.516864	+	0.167939i	−0.0389577	+	0.999241i	$0.512404\pi$
$758$	2070.37	+	531.582i	2.73136	+	0.701295i
$759$	0.693859	+	1.55537i	0.000914175	+	0.00204924i
$760$	−217.948	−	872.159i	−0.286773	−	1.14758i
$761$	−1071.57	+	504.240i	−1.40810	+	0.662602i	−0.971497	−	0.237052i	$-0.923819\pi$
$761$	−1071.57	+	504.240i	−1.40810	+	0.662602i	−0.436604	+	0.899654i	$0.643819\pi$
$762$	−178.020	+	840.538i	−0.233622	+	1.10307i
$763$	89.7169	−	710.182i	0.117584	−	0.930776i
$764$	289.412	+	2290.93i	0.378812	+	2.99861i
$765$	−1167.22	+	666.157i	−1.52578	+	0.870793i
$766$	357.309	+	1873.08i	0.466461	+	2.44528i
$767$	−129.298	−	156.294i	−0.168576	−	0.203774i
$768$	1181.73	+	1018.53i	1.53870	+	1.32621i
$769$	36.8251	+	585.318i	0.0478870	+	0.761141i	0.946561	+	0.322525i	$0.104531\pi$
$769$	36.8251	+	585.318i	0.0478870	+	0.761141i	−0.898674	+	0.438617i	$0.855469\pi$
$770$	−44.8751	−	28.8862i	−0.0582793	−	0.0375145i
$771$	−1061.64	+	180.362i	−1.37697	+	0.233933i
$772$	−41.7311	−	34.5230i	−0.0540558	−	0.0447189i
$773$	775.331	+	426.242i	1.00302	+	0.551412i	0.896568	−	0.442906i	$-0.146052\pi$
$773$	775.331	+	426.242i	1.00302	+	0.551412i	0.106447	+	0.994318i	$0.466052\pi$
$774$	−993.335	+	975.595i	−1.28338	+	1.26046i
$775$	−1013.80	−	13.0747i	−1.30813	−	0.0168705i
$776$	692.204	−	224.911i	0.892016	−	0.289834i
$777$	−253.184	−	679.271i	−0.325849	−	0.874223i
$778$	914.229	−	580.188i	1.17510	−	0.745743i
$779$	311.333	−	197.578i	0.399657	−	0.253630i
$780$	−91.5362	−	921.558i	−0.117354	−	1.18148i
$781$	−27.0293	−	32.6728i	−0.0346085	−	0.0418345i
$782$	88.7307	−	64.4666i	0.113466	−	0.0824381i
$783$	820.882	−	388.479i	1.04838	−	0.496142i
$784$	−165.445	+	351.588i	−0.211027	+	0.448454i
$785$	601.345	+	335.660i	0.766045	+	0.427592i
$786$	93.5580	+	26.0481i	0.119030	+	0.0331401i
$787$	522.868	−	99.7425i	0.664382	−	0.126738i	0.155850	−	0.987781i	$-0.450188\pi$
$787$	522.868	−	99.7425i	0.664382	−	0.126738i	0.508532	+	0.861043i	$0.330188\pi$
$788$	939.227	−	516.345i	1.19191	−	0.655260i
$789$	−93.0199	−	249.564i	−0.117896	−	0.316305i
$790$	932.314	−	980.073i	1.18014	−	1.24060i
$791$	−453.776	−	825.416i	−0.573674	−	1.04351i
$792$	31.0941	−	70.1144i	0.0392603	−	0.0885282i
$793$	−289.661	+	398.684i	−0.365272	+	0.502754i
$794$	−87.2911	+	339.977i	−0.109938	+	0.428182i
$795$	−51.5346	−	86.2020i	−0.0648234	−	0.108430i
$796$	−7.92299	+	125.932i	−0.00995351	+	0.158206i
$797$	705.096	−	181.038i	0.884688	−	0.227149i	0.221103	−	0.975250i	$-0.429034\pi$
$797$	705.096	−	181.038i	0.884688	−	0.227149i	0.663585	+	0.748101i	$0.269034\pi$
$798$	420.008	+	529.123i	0.526326	+	0.663062i
$799$	−917.399	−	666.529i	−1.14818	−	0.834204i
$800$	−24.3996	+	321.586i	−0.0304995	+	0.401982i
$801$	809.231	−	120.706i	1.01028	−	0.150695i
$802$	1288.93	+	1372.57i	1.60714	+	1.71143i
$803$	49.1007	+	19.4403i	0.0611465	+	0.0242096i
$804$	−1872.99	−	1831.49i	−2.32959	−	2.27797i
$805$	26.8173	+	10.8183i	0.0333134	+	0.0134388i
$806$	883.898	+	560.939i	1.09665	+	0.695954i
$807$	592.190	+	976.210i	0.733816	+	1.20968i
$808$	−70.4713	−	44.7224i	−0.0872169	−	0.0553495i
$809$	275.468	−	293.344i	0.340504	−	0.362600i	−0.535811	−	0.844338i	$-0.679994\pi$
$809$	275.468	−	293.344i	0.340504	−	0.362600i	0.876316	+	0.481737i	$0.159994\pi$
$810$	474.401	−	1347.00i	0.585681	−	1.66296i
$811$	−195.420	−	107.433i	−0.240961	−	0.132470i	0.356698	−	0.934220i	$-0.383903\pi$
$811$	−195.420	−	107.433i	−0.240961	−	0.132470i	−0.597659	+	0.801750i	$0.703903\pi$
$812$	670.726	−	1425.37i	0.826017	−	1.75538i
$813$	41.1602	+	388.877i	0.0506275	+	0.478324i
$814$	−73.2936	−	40.2935i	−0.0900413	−	0.0495006i
$815$	−201.599	−	148.466i	−0.247361	−	0.182167i
$816$	−1875.18	−	397.150i	−2.29802	−	0.486703i
$817$	−425.993	−	270.343i	−0.521411	−	0.330898i
$818$	1631.53			1.99453
$819$	183.395	+	316.580i	0.223926	+	0.386545i
$820$	−1311.75	+	327.799i	−1.59969	+	0.399755i
$821$	319.459	+	1244.21i	0.389110	+	1.51548i	0.797864	+	0.602838i	$0.205963\pi$
$821$	319.459	+	1244.21i	0.389110	+	1.51548i	−0.408754	+	0.912645i	$0.634037\pi$
$822$	2442.53	−	414.961i	2.97145	−	0.504819i
$823$	819.039	+	872.188i	0.995187	+	1.05977i	0.998212	+	0.0597715i	$0.0190372\pi$
$823$	819.039	+	872.188i	0.995187	+	1.05977i	−0.00302473	+	0.999995i	$0.500963\pi$
$824$	1146.14	+	1577.52i	1.39094	+	1.91447i
$825$	−39.9129	+	8.85067i	−0.0483792	+	0.0107281i
$826$	−438.954	−	318.919i	−0.531421	−	0.386100i
$827$	−73.3510	+	9.26639i	−0.0886953	+	0.0112048i	−0.169556	−	0.985521i	$-0.554233\pi$
$827$	−73.3510	+	9.26639i	−0.0886953	+	0.0112048i	0.0808603	+	0.996725i	$0.474233\pi$
$828$	−17.9391	+	76.9898i	−0.0216655	+	0.0929829i
$829$	53.9853	−	858.072i	0.0651210	−	1.03507i	−0.820795	−	0.571223i	$-0.806469\pi$
$829$	53.9853	−	858.072i	0.0651210	−	1.03507i	0.885916	−	0.463846i	$-0.153531\pi$
$830$	−1372.28	+	1863.40i	−1.65335	+	2.24506i
$831$	143.217	+	473.108i	0.172343	+	0.569324i
$832$	−172.484	+	237.404i	−0.207313	+	0.285341i
$833$	34.0600	+	541.368i	0.0408883	+	0.649901i
$834$	−1155.99	+	2005.61i	−1.38608	+	2.40481i
$835$	−238.063	−	439.728i	−0.285106	−	0.526621i
$836$	51.9325	+	9.90665i	0.0621202	+	0.0118501i
$837$	588.755	+	923.246i	0.703411	+	1.10304i
$838$	−1110.46	+	211.831i	−1.32513	+	0.252782i
$839$	954.524	+	1016.47i	1.13769	+	1.21152i	0.974371	+	0.224947i	$0.0722209\pi$
$839$	954.524	+	1016.47i	1.13769	+	1.21152i	0.163322	+	0.986573i	$0.447779\pi$
$840$	−446.954	−	1223.18i	−0.532088	−	1.45617i
$841$	123.630	−	262.727i	0.147004	−	0.312399i
$842$	392.320	−	155.330i	0.465938	−	0.184478i
$843$	−928.689	−	389.586i	−1.10165	−	0.462143i
$844$	−561.344	−	678.548i	−0.665099	−	0.803967i
$845$	−567.516	+	104.472i	−0.671616	+	0.123635i
$846$	1200.60	−	102.586i	1.41915	−	0.121260i
$847$	−565.934	+	359.153i	−0.668163	+	0.424029i
$848$	26.8406	−	140.703i	0.0316516	−	0.165924i
$849$	−1037.37	+	1203.59i	−1.22188	+	1.41765i
$850$	1090.15	+	2396.43i	1.28253	+	2.81933i
$851$	43.1011	+	14.0044i	0.0506475	+	0.0164564i
$852$	−83.8585	−	1966.44i	−0.0984254	−	2.30802i
$853$	−364.653	−	301.667i	−0.427494	−	0.353654i	0.398659	−	0.917099i	$-0.369476\pi$
$853$	−364.653	−	301.667i	−0.427494	−	0.353654i	−0.826154	+	0.563445i	$0.809476\pi$
$854$	−485.248	+	1225.60i	−0.568206	+	1.43512i
$855$	514.395	+	56.6593i	0.601631	+	0.0662682i
$856$	−48.6694	−	773.579i	−0.0568568	−	0.903713i
$857$	−351.314	−	1081.23i	−0.409935	−	1.26165i	−0.916704	−	0.399568i	$-0.869160\pi$
$857$	−351.314	−	1081.23i	−0.409935	−	1.26165i	0.506769	−	0.862082i	$-0.330840\pi$
$858$	39.8744	+	13.8531i	0.0464737	+	0.0161458i
$859$	−222.984	−	1168.92i	−0.259585	−	1.36079i	−0.838275	−	0.545247i	$-0.816436\pi$
$859$	−222.984	−	1168.92i	−0.259585	−	1.36079i	0.578690	−	0.815548i	$-0.303564\pi$
$860$	1170.04	+	1433.06i	1.36052	+	1.66634i
$861$	418.373	−	332.097i	0.485916	−	0.385711i
$862$	−323.472	+	2560.55i	−0.375258	+	2.97047i
$863$	250.645	+	235.372i	0.290435	+	0.272736i	0.816044	−	0.577990i	$-0.196163\pi$
$863$	250.645	+	235.372i	0.290435	+	0.272736i	−0.525609	+	0.850726i	$0.676163\pi$
$864$	304.858	−	168.469i	0.352845	−	0.194987i
$865$	−196.545	+	122.961i	−0.227219	+	0.142151i
$866$	200.998	−	1591.07i	0.232100	−	1.83726i
$867$	−1731.21	+	524.066i	−1.99679	+	0.604459i
$868$	1806.40	+	586.936i	2.08111	+	0.676194i
$869$	15.3955	+	38.8847i	0.0177164	+	0.0447464i
$870$	−610.592	−	1671.01i	−0.701830	−	1.92070i
$871$	483.131	−	584.005i	0.554685	−	0.670499i
$872$	126.544	−	2011.36i	0.145119	−	2.30661i
$873$	−16.9329	+	418.638i	−0.0193962	+	0.479540i
$874$	−42.2331			−0.0483216
$875$	−383.206	+	578.778i	−0.437949	+	0.661460i
$876$	1271.32	+	2095.73i	1.45127	+	2.39239i
$877$	446.454	−	210.085i	0.509070	−	0.239550i	−0.154051	−	0.988063i	$-0.549232\pi$
$877$	446.454	−	210.085i	0.509070	−	0.239550i	0.663120	+	0.748513i	$0.269232\pi$
$878$	−4.68743	+	74.5046i	−0.00533876	+	0.0848572i
$879$	61.1173	−	415.990i	0.0695305	−	0.473254i
$880$	−50.9137	−	28.4191i	−0.0578565	−	0.0322944i
$881$	−250.586	−	632.908i	−0.284434	−	0.718397i	−0.999807	−	0.0196547i	$-0.993743\pi$
$881$	−250.586	−	632.908i	−0.284434	−	0.718397i	0.715373	−	0.698743i	$-0.246257\pi$
$882$	−403.892	−	411.236i	−0.457927	−	0.466254i
$883$	−291.334	+	1134.67i	−0.329936	+	1.28502i	0.559833	+	0.828605i	$0.310865\pi$
$883$	−291.334	+	1134.67i	−0.329936	+	1.28502i	−0.889769	+	0.456411i	$0.849135\pi$
$884$	231.098	−	1829.33i	0.261423	−	2.06937i
$885$	−410.206	+	66.9712i	−0.463509	+	0.0756737i
$886$	−901.679	−	1916.17i	−1.01770	−	2.16271i
$887$	−485.702	−	456.105i	−0.547579	−	0.514211i	0.360641	−	0.932705i	$-0.382558\pi$
$887$	−485.702	−	456.105i	−0.547579	−	0.514211i	−0.908220	+	0.418494i	$0.862558\pi$
$888$	−831.490	−	1863.89i	−0.936362	−	2.09897i
$889$	−447.468	+	56.5283i	−0.503338	+	0.0635864i
$890$	−90.3244	−	1600.26i	−0.101488	−	1.79804i
$891$	31.6363	+	30.7998i	0.0355065	+	0.0345677i
$892$	1153.73	−	954.446i	1.29342	−	1.07001i
$893$	134.933	+	415.282i	0.151101	+	0.465042i
$894$	−1556.95	+	1083.79i	−1.74155	+	1.21230i
$895$	−493.749	−	604.737i	−0.551675	−	0.675684i
$896$	−394.437	+	996.233i	−0.440219	+	1.11187i
$897$	−22.6294	−	3.32471i	−0.0252279	−	0.00370648i
$898$	−1194.76	+	2173.25i	−1.33046	+	2.42010i
$899$	1297.35	+	421.533i	1.44310	+	0.468891i
$900$	−1724.61	−	791.594i	−1.91623	−	0.879549i
$901$	−61.7916	−	190.175i	−0.0685811	−	0.211071i
$902$	11.5482	−	60.5378i	0.0128029	−	0.0671151i
$903$	−654.897	−	324.497i	−0.725246	−	0.359354i
$904$	−1420.96	−	2239.07i	−1.57185	−	2.47685i
$905$	187.595	−	1411.70i	0.207287	−	1.55989i
$906$	1520.33	+	528.188i	1.67806	+	0.582989i
$907$	−52.7963	−	72.6679i	−0.0582098	−	0.0801190i	0.778920	−	0.627124i	$-0.215768\pi$
$907$	−52.7963	−	72.6679i	−0.0582098	−	0.0801190i	−0.837130	+	0.547005i	$0.815768\pi$
$908$	−450.950	+	178.544i	−0.496641	+	0.196634i
$909$	38.2284	−	29.1051i	0.0420554	−	0.0320188i
$910$	650.462	−	300.977i	0.714793	−	0.330743i
$911$	−644.722	−	686.559i	−0.707708	−	0.753632i	0.270169	−	0.962813i	$-0.412920\pi$
$911$	−644.722	−	686.559i	−0.707708	−	0.753632i	−0.977877	+	0.209181i	$0.932920\pi$
$912$	494.279	+	548.146i	0.541972	+	0.601037i
$913$	−34.4687	−	62.6983i	−0.0377532	−	0.0686729i
$914$	410.470	+	78.3013i	0.449091	+	0.0856688i
$915$	405.429	+	924.801i	0.443092	+	1.01071i
$916$	−2722.20	+	1496.54i	−2.97183	+	1.63378i
$917$	3.20111	+	50.8802i	0.00349085	+	0.0554855i
$918$	1518.28	−	2404.06i	1.65390	−	2.61880i
$919$	247.636	+	63.5821i	0.269462	+	0.0691862i	0.381003	−	0.924574i	$-0.375579\pi$
$919$	247.636	+	63.5821i	0.269462	+	0.0691862i	−0.111541	+	0.993760i	$0.535579\pi$
$920$	77.2648	+	25.6568i	0.0839835	+	0.0278879i
$921$	682.553	−	357.466i	0.741100	−	0.388128i
$922$	68.3830	+	266.334i	0.0741681	+	0.288866i
$923$	564.980	−	71.3735i	0.612112	−	0.0773278i
$924$	76.3233	+	6.35285i	0.0826010	+	0.00687538i
$925$	−536.330	+	946.461i	−0.579817	+	1.02320i
$926$	−776.752	−	1069.11i	−0.838825	−	1.15454i
$927$	−1080.70	+	303.442i	−1.16581	+	0.327337i
$928$	159.734	−	403.443i	0.172128	−	0.434745i
$929$	−238.876	−	930.361i	−0.257133	−	1.00147i	−0.957674	−	0.287854i	$-0.907058\pi$
$929$	−238.876	−	930.361i	−0.257133	−	1.00147i	0.700542	−	0.713611i	$-0.252942\pi$
$930$	1906.62	−	982.919i	2.05013	−	1.05690i
$931$	111.921	−	176.359i	0.120216	−	0.189430i
$932$	−1177.22			−1.26311
$933$	−746.765	−	15.0963i	−0.800392	−	0.0161803i
$934$	1319.32	+	1238.92i	1.41255	+	1.32647i
$935$	−81.3958	−	0.524846i	−0.0870544	−	0.000561333i
$936$	571.277	+	857.119i	0.610339	+	0.915726i
$937$	−671.104	−	315.798i	−0.716226	−	0.337031i	0.0328991	−	0.999459i	$-0.489526\pi$
$937$	−671.104	−	315.798i	−0.716226	−	0.337031i	−0.749125	+	0.662428i	$0.769526\pi$
$938$	863.215	−	1834.43i	0.920272	−	1.95568i
$939$	67.2849	+	1577.79i	0.0716559	+	1.68029i
$940$	10.3240	−	1601.10i	0.0109830	−	1.70330i
$941$	698.222	−	743.531i	0.742000	−	0.790150i	−0.241626	−	0.970369i	$-0.577681\pi$
$941$	698.222	−	743.531i	0.742000	−	0.790150i	0.983626	+	0.180220i	$0.0576809\pi$
$942$	−1456.74	−	29.4488i	−1.54644	−	0.0312620i
$943$			33.3934i			0.0354118i
$944$	−500.516	−	317.637i	−0.530208	−	0.336480i
$945$	749.664	+	3.18943i	0.793296	+	0.00337506i
$946$	−81.6775	+	20.9712i	−0.0863399	+	0.0221683i
$947$	115.029	+	45.5431i	0.121466	+	0.0480920i	0.428072	−	0.903745i	$-0.359193\pi$
$947$	115.029	+	45.5431i	0.121466	+	0.0480920i	−0.306605	+	0.951837i	$0.599193\pi$
$948$	−520.658	+	1870.06i	−0.549217	+	1.97264i
$949$	−573.762	+	416.862i	−0.604596	+	0.439265i
$950$	202.790	−	993.292i	0.213463	−	1.04557i
$951$	−316.328	−	26.3299i	−0.332627	−	0.0276865i
$952$	−324.972	−	2572.42i	−0.341357	−	2.70212i
$953$	130.831	−	33.5916i	0.137283	−	0.0352483i	−0.179423	−	0.983772i	$-0.557423\pi$
$953$	130.831	−	33.5916i	0.137283	−	0.0352483i	0.316706	+	0.948524i	$0.397423\pi$
$954$	181.912	+	109.806i	0.190683	+	0.115101i
$955$	−431.425	+	1299.23i	−0.451754	+	1.36045i
$956$	−678.694	+	2643.34i	−0.709931	+	2.76500i
$957$	54.8148	+	4.56257i	0.0572778	+	0.00476758i
$958$	−2354.88	+	148.157i	−2.45812	+	0.154652i
$959$	626.554	+	1139.70i	0.653341	+	1.18842i
$960$	241.421	+	550.691i	0.251480	+	0.573637i
$961$	−128.120	+	671.630i	−0.133320	+	0.698886i
$962$	984.309	−	541.128i	1.02319	−	0.562504i
$963$	427.343	+	128.341i	0.443762	+	0.133272i
$964$	307.669	−	288.920i	0.319159	−	0.299710i
$965$	−13.4837	−	29.1406i	−0.0139728	−	0.0301976i
$966$	−60.8400	+	6.43953i	−0.0629814	+	0.00666618i
$967$	−407.021	−	1028.02i	−0.420911	−	1.06310i	−0.973305	−	0.229517i	$-0.926286\pi$
$967$	−407.021	−	1028.02i	−0.420911	−	1.06310i	0.552394	−	0.833583i	$-0.313714\pi$
$968$	−1526.69	+	1109.21i	−1.57716	+	1.14588i
$969$	973.297	+	338.140i	1.00443	+	0.348958i
$970$	813.621	+	108.119i	0.838784	+	0.111462i
$971$	80.9192	−	51.3529i	0.0833360	−	0.0528866i	−0.493506	−	0.869742i	$-0.664285\pi$
$971$	80.9192	−	51.3529i	0.0833360	−	0.0528866i	0.576842	+	0.816856i	$0.304285\pi$
$972$	306.794	+	2026.32i	0.315632	+	2.08469i
$973$	−1193.68	−	227.706i	−1.22680	−	0.234024i
$974$	1441.55	−	468.388i	1.48003	−	0.480891i
$975$	186.854	−	516.263i	0.191645	−	0.529501i
$976$	−445.038	+	1369.69i	−0.455982	+	1.40337i
$977$	606.706	+	333.540i	0.620989	+	0.341392i	0.760994	−	0.648759i	$-0.224712\pi$
$977$	606.706	+	333.540i	0.620989	+	0.341392i	−0.140005	+	0.990151i	$0.544712\pi$
$978$	524.077	+	76.9975i	0.535866	+	0.0787295i
$979$	46.0747	+	18.2423i	0.0470630	+	0.0186336i
$980$	−593.278	+	484.393i	−0.605386	+	0.494279i
$981$	1060.54	+	470.324i	1.08108	+	0.479434i
$982$	1074.45	−	349.109i	1.09414	−	0.355508i
$983$	−832.358	−	1006.15i	−0.846753	−	1.02355i	−0.999378	−	0.0352643i	$-0.988773\pi$
$983$	−832.358	−	1006.15i	−0.846753	−	1.02355i	0.152625	−	0.988284i	$-0.451227\pi$
$984$	1116.85	−	1007.10i	1.13502	−	1.02348i
$985$	634.412	−	35.8085i	0.644073	−	0.0363538i
$986$	−443.951	−	3514.23i	−0.450254	−	3.56413i
$987$	257.703	+	577.672i	0.261097	+	0.585281i
$988$	−486.037	+	517.577i	−0.491940	+	0.523863i
$989$	41.3431	−	19.4546i	0.0418029	−	0.0196710i
$990$	65.7570	−	56.1903i	0.0664212	−	0.0567579i
$991$	−1141.31	−	144.180i	−1.15167	−	0.145490i	−0.473773	−	0.880647i	$-0.657108\pi$
$991$	−1141.31	−	144.180i	−1.15167	−	0.145490i	−0.677897	+	0.735157i	$0.737108\pi$
$992$	506.744	+	130.110i	0.510831	+	0.131159i
$993$	−252.428	−	1072.70i	−0.254207	−	1.08026i
$994$	1416.28	−	560.743i	1.42482	−	0.564128i
$995$	−36.4605	+	65.3202i	−0.0366437	+	0.0656484i
$996$	482.739	−	3285.72i	0.484678	−	3.29892i
$997$	765.172	+	48.1405i	0.767474	+	0.0482854i	0.441701	−	0.897162i	$-0.354375\pi$
$997$	765.172	+	48.1405i	0.767474	+	0.0482854i	0.325774	+	0.945448i	$0.394375\pi$
$998$	77.9568	+	165.667i	0.0781131	+	0.165999i
$999$	1172.41	−	76.3438i	1.17358	−	0.0764202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.p.a.14.8	✓	1960
3.2	odd	2	inner	375.3.p.a.14.91	yes	1960
125.9	even	50	inner	375.3.p.a.134.91	yes	1960
375.134	odd	50	inner	375.3.p.a.134.8	yes	1960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.p.a.14.8	✓	1960	1.1	even	1	trivial
375.3.p.a.14.91	yes	1960	3.2	odd	2	inner
375.3.p.a.134.8	yes	1960	375.134	odd	50	inner
375.3.p.a.134.91	yes	1960	125.9	even	50	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.p (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50136 - 3.19056i) q^{2} +(1.39183 + 2.65759i) q^{3} +(-5.37590 + 6.49835i) q^{4} +(-4.53777 + 2.09968i) q^{5} +(6.38957 - 8.43074i) q^{6} +(5.28133 + 1.71601i) q^{7} +(15.1431 + 3.88808i) q^{8} +(-5.12561 + 7.39785i) q^{9} +(13.5120 + 11.3256i) q^{10} +(-0.493220 + 0.232092i) q^{11} +(-24.7523 - 5.24235i) q^{12} +(0.917502 - 7.26277i) q^{13} +(-2.45417 - 19.4268i) q^{14} +(-11.8959 - 9.13714i) q^{15} +(-4.00877 - 21.0147i) q^{16} +(-19.0368 - 23.0116i) q^{17} +(31.2987 + 5.24671i) q^{18} +(0.722099 + 11.4774i) q^{19} +(10.7501 - 40.7757i) q^{20} +(2.79027 + 16.4240i) q^{21} +(1.48101 + 1.22520i) q^{22} +(-0.912651 - 0.501734i) q^{23} +(10.7437 + 45.6557i) q^{24} +(16.1827 - 19.0557i) q^{25} +(-24.5498 + 7.97673i) q^{26} +(-26.7945 - 3.32523i) q^{27} +(-39.5431 + 25.0948i) q^{28} +(-28.3996 + 18.0229i) q^{29} +(-11.2925 + 51.6728i) q^{30} +(-25.8510 - 31.2485i) q^{31} +(-10.4366 + 7.58266i) q^{32} +(-1.30329 - 0.987746i) q^{33} +(-44.8386 + 95.2869i) q^{34} +(-27.5685 + 3.30226i) q^{35} +(-20.5190 - 73.0781i) q^{36} +(-42.7436 + 8.15379i) q^{37} +(35.5353 - 19.5357i) q^{38} +(20.5785 - 7.67021i) q^{39} +(-76.8794 + 14.1524i) q^{40} +(-15.4467 - 28.0975i) q^{41} +(48.2127 - 33.5610i) q^{42} +(-25.7874 + 35.4933i) q^{43} +(1.14329 - 4.45282i) q^{44} +(7.72571 - 44.3319i) q^{45} +(-0.230592 + 3.66516i) q^{46} +(36.7766 - 9.44263i) q^{47} +(50.2690 - 39.9026i) q^{48} +(-14.6941 - 10.6759i) q^{49} +(-85.0946 - 23.0223i) q^{50} +(34.6593 - 82.6203i) q^{51} +(42.2636 + 45.0062i) q^{52} +(6.22529 + 2.46477i) q^{53} +(29.6189 + 90.4818i) q^{54} +(1.75080 - 2.08878i) q^{55} +(73.3035 + 46.5198i) q^{56} +(-29.4973 + 17.8937i) q^{57} +(100.141 + 63.5517i) q^{58} +(18.9682 - 20.1991i) q^{59} +(123.328 - 28.1834i) q^{60} +(-58.9911 - 32.4306i) q^{61} +(-60.8885 + 129.395i) q^{62} +(-39.7648 + 30.2749i) q^{63} +(-35.1274 - 19.3115i) q^{64} +(11.0861 + 34.8832i) q^{65} +(-1.19476 + 5.64118i) q^{66} +(87.4192 + 55.4779i) q^{67} +251.877 q^{68} +(0.0631490 - 3.12378i) q^{69} +(51.9265 + 83.0012i) q^{70} +(19.3459 + 75.3472i) q^{71} +(-106.381 + 92.0973i) q^{72} +(-66.3188 - 70.6224i) q^{73} +(90.1890 + 124.134i) q^{74} +(73.1660 + 16.4846i) q^{75} +(-78.4663 - 57.0091i) q^{76} +(-3.00313 + 0.379384i) q^{77} +(-55.3681 - 54.1412i) q^{78} +(4.81746 - 76.5714i) q^{79} +(62.3150 + 86.9427i) q^{80} +(-28.4563 - 75.8369i) q^{81} +(-66.4556 + 91.4683i) q^{82} +(8.24173 + 130.999i) q^{83} +(-121.729 - 70.1618i) q^{84} +(134.702 + 64.4499i) q^{85} +(151.960 + 28.9879i) q^{86} +(-87.4250 - 50.3897i) q^{87} +(-8.37125 + 1.59690i) q^{88} +(-62.2317 - 66.2701i) q^{89} +(-153.043 + 41.9089i) q^{90} +(17.3086 - 36.7827i) q^{91} +(8.16676 - 3.23345i) q^{92} +(47.0655 - 112.194i) q^{93} +(-85.3424 - 103.161i) q^{94} +(-27.3757 - 50.5658i) q^{95} +(-34.6777 - 17.1826i) q^{96} +(39.3063 - 24.9446i) q^{97} +(-12.0009 + 62.9107i) q^{98} +(0.811075 - 4.83838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) \) 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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