LMFDB - Embedded newform 684.3.s.a.445.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.39
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99483 - 0.176040i) q^{3} +(4.35575 + 7.54438i) q^{5} +(5.71458 + 9.89794i) q^{7} +(8.93802 - 1.05442i) q^{9} +O(q^{10})$	\(q+(2.99483 - 0.176040i) q^{3} +(4.35575 + 7.54438i) q^{5} +(5.71458 + 9.89794i) q^{7} +(8.93802 - 1.05442i) q^{9} +(-8.80974 - 15.2589i) q^{11} +5.93511i q^{13} +(14.3728 + 21.8274i) q^{15} +(10.9206 - 18.9151i) q^{17} +(18.1016 + 5.77343i) q^{19} +(18.8566 + 28.6367i) q^{21} -2.29506 q^{23} +(-25.4451 + 44.0722i) q^{25} +(26.5822 - 4.73126i) q^{27} +(26.5631 + 15.3362i) q^{29} +(-40.6831 - 23.4884i) q^{31} +(-29.0698 - 44.1470i) q^{33} +(-49.7826 + 86.2259i) q^{35} -60.1242i q^{37} +(1.04482 + 17.7746i) q^{39} +(-28.7296 + 16.5870i) q^{41} -79.2625 q^{43} +(46.8867 + 62.8390i) q^{45} +(-4.29799 + 7.44434i) q^{47} +(-40.8129 + 70.6900i) q^{49} +(29.3756 - 58.5700i) q^{51} +(11.3408 - 6.54761i) q^{53} +(76.7460 - 132.928i) q^{55} +(55.2275 + 14.1038i) q^{57} +(-22.8023 + 13.1649i) q^{59} +(-22.2757 + 38.5826i) q^{61} +(61.5136 + 82.4425i) q^{63} +(-44.7767 + 25.8519i) q^{65} +71.3349i q^{67} +(-6.87330 + 0.404022i) q^{69} +(71.0020 + 40.9930i) q^{71} +(0.496052 - 0.859188i) q^{73} +(-68.4453 + 136.468i) q^{75} +(100.688 - 174.397i) q^{77} -73.9507i q^{79} +(78.7764 - 18.8489i) q^{81} +(-7.54810 - 13.0737i) q^{83} +190.270 q^{85} +(82.2517 + 41.2532i) q^{87} +(118.258 - 68.2765i) q^{89} +(-58.7454 + 33.9167i) q^{91} +(-125.974 - 63.1820i) q^{93} +(35.2890 + 161.713i) q^{95} -37.3067i q^{97} +(-94.8309 - 127.095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	2.99483	−	0.176040i	0.998277	−	0.0586800i
$3$	2.99483	−	0.176040i	0.998277	−	0.0586800i
$4$		0			0
$5$	4.35575	+	7.54438i	0.871150	+	1.50888i	0.860808	+	0.508929i	$0.169959\pi$
$5$	4.35575	+	7.54438i	0.871150	+	1.50888i	0.0103415	+	0.999947i	$0.496708\pi$
$6$		0			0
$7$	5.71458	+	9.89794i	0.816369	+	1.41399i	0.908341	+	0.418230i	$0.137350\pi$
$7$	5.71458	+	9.89794i	0.816369	+	1.41399i	−0.0919723	+	0.995762i	$0.529317\pi$
$8$		0			0
$9$	8.93802	−	1.05442i	0.993113	−	0.117158i
$10$		0			0
$11$	−8.80974	−	15.2589i	−0.800885	−	1.38717i	−0.919034	−	0.394178i	$-0.871029\pi$
$11$	−8.80974	−	15.2589i	−0.800885	−	1.38717i	0.118149	−	0.992996i	$-0.462304\pi$
$12$		0			0
$13$			5.93511i			0.456547i	0.973597	+	0.228273i	$0.0733080\pi$
$13$			5.93511i			0.456547i	−0.973597	+	0.228273i	$0.926692\pi$
$14$		0			0
$15$	14.3728	+	21.8274i	0.958190	+	1.45516i
$16$		0			0
$17$	10.9206	−	18.9151i	0.642390	−	1.11265i	−0.342508	−	0.939515i	$-0.611276\pi$
$17$	10.9206	−	18.9151i	0.642390	−	1.11265i	0.984898	−	0.173137i	$-0.0553904\pi$
$18$		0			0
$19$	18.1016	+	5.77343i	0.952715	+	0.303865i
$19$	18.1016	+	5.77343i	0.952715	+	0.303865i
$20$		0			0
$21$	18.8566	+	28.6367i	0.897935	+	1.36365i
$22$		0			0
$23$	−2.29506			−0.0997850			−0.0498925	−	0.998755i	$-0.515888\pi$
$23$	−2.29506			−0.0997850			−0.0498925	+	0.998755i	$0.515888\pi$
$24$		0			0
$25$	−25.4451	+	44.0722i	−1.01780	+	1.76289i
$26$		0			0
$27$	26.5822	−	4.73126i	0.984527	−	0.175232i
$28$		0			0
$29$	26.5631	+	15.3362i	0.915968	+	0.528835i	0.882347	−	0.470600i	$-0.155962\pi$
$29$	26.5631	+	15.3362i	0.915968	+	0.528835i	0.0336218	+	0.999435i	$0.489296\pi$
$30$		0			0
$31$	−40.6831	−	23.4884i	−1.31236	−	0.757691i	−0.329873	−	0.944025i	$-0.607006\pi$
$31$	−40.6831	−	23.4884i	−1.31236	−	0.757691i	−0.982486	+	0.186334i	$0.940339\pi$
$32$		0			0
$33$	−29.0698	−	44.1470i	−0.880904	−	1.33779i
$34$		0			0
$35$	−49.7826	+	86.2259i	−1.42236	+	2.46360i
$36$		0			0
$37$		−	60.1242i		−	1.62498i	−0.582976	−	0.812489i	$-0.698112\pi$
$37$		−	60.1242i		−	1.62498i	0.582976	−	0.812489i	$-0.301888\pi$
$38$		0			0
$39$	1.04482	+	17.7746i	0.0267902	+	0.455760i
$40$		0			0
$41$	−28.7296	+	16.5870i	−0.700721	+	0.404561i	−0.807616	−	0.589709i	$-0.799242\pi$
$41$	−28.7296	+	16.5870i	−0.700721	+	0.404561i	0.106895	+	0.994270i	$0.465909\pi$
$42$		0			0
$43$	−79.2625			−1.84331			−0.921657	−	0.388006i	$-0.873164\pi$
$43$	−79.2625			−1.84331			−0.921657	+	0.388006i	$0.873164\pi$
$44$		0			0
$45$	46.8867	+	62.8390i	1.04193	+	1.39642i
$46$		0			0
$47$	−4.29799	+	7.44434i	−0.0914466	+	0.158390i	−0.908120	−	0.418710i	$-0.862482\pi$
$47$	−4.29799	+	7.44434i	−0.0914466	+	0.158390i	0.816673	+	0.577100i	$0.195816\pi$
$48$		0			0
$49$	−40.8129	+	70.6900i	−0.832916	+	1.44265i
$50$		0			0
$51$	29.3756	−	58.5700i	0.575993	−	1.14843i
$52$		0			0
$53$	11.3408	−	6.54761i	0.213977	−	0.123540i	−0.389181	−	0.921161i	$-0.627242\pi$
$53$	11.3408	−	6.54761i	0.213977	−	0.123540i	0.603158	+	0.797621i	$0.293909\pi$
$54$		0			0
$55$	76.7460	−	132.928i	1.39538	−	2.41687i
$56$		0			0
$57$	55.2275	+	14.1038i	0.968904	+	0.247436i
$58$		0			0
$59$	−22.8023	+	13.1649i	−0.386480	+	0.223134i	−0.680634	−	0.732624i	$-0.738296\pi$
$59$	−22.8023	+	13.1649i	−0.386480	+	0.223134i	0.294154	+	0.955758i	$0.404962\pi$
$60$		0			0
$61$	−22.2757	+	38.5826i	−0.365175	+	0.632502i	−0.988804	−	0.149218i	$-0.952324\pi$
$61$	−22.2757	+	38.5826i	−0.365175	+	0.632502i	0.623629	+	0.781721i	$0.285658\pi$
$62$		0			0
$63$	61.5136	+	82.4425i	0.976407	+	1.30861i
$64$		0			0
$65$	−44.7767	+	25.8519i	−0.688873	+	0.397721i
$66$		0			0
$67$			71.3349i			1.06470i	0.846525	+	0.532350i	$0.178691\pi$
$67$			71.3349i			1.06470i	−0.846525	+	0.532350i	$0.821309\pi$
$68$		0			0
$69$	−6.87330	+	0.404022i	−0.0996131	+	0.00585539i
$70$		0			0
$71$	71.0020	+	40.9930i	1.00003	+	0.577366i	0.908257	−	0.418414i	$-0.137414\pi$
$71$	71.0020	+	40.9930i	1.00003	+	0.577366i	0.0917714	+	0.995780i	$0.470747\pi$
$72$		0			0
$73$	0.496052	−	0.859188i	0.00679524	−	0.0117697i	−0.862608	−	0.505873i	$-0.831170\pi$
$73$	0.496052	−	0.859188i	0.00679524	−	0.0117697i	0.869403	+	0.494104i	$0.164504\pi$
$74$		0			0
$75$	−68.4453	+	136.468i	−0.912604	+	1.81958i
$76$		0			0
$77$	100.688	−	174.397i	1.30764	−	2.26489i
$78$		0			0
$79$		−	73.9507i		−	0.936085i	−0.883706	−	0.468042i	$-0.844959\pi$
$79$		−	73.9507i		−	0.936085i	0.883706	−	0.468042i	$-0.155041\pi$
$80$		0			0
$81$	78.7764	−	18.8489i	0.972548	−	0.232702i
$82$		0			0
$83$	−7.54810	−	13.0737i	−0.0909410	−	0.157514i	0.816966	−	0.576685i	$-0.195654\pi$
$83$	−7.54810	−	13.0737i	−0.0909410	−	0.157514i	−0.907907	+	0.419171i	$0.862321\pi$
$84$		0			0
$85$	190.270			2.23847
$86$		0			0
$87$	82.2517	+	41.2532i	0.945422	+	0.474174i
$88$		0			0
$89$	118.258	−	68.2765i	1.32874	−	0.767151i	0.343639	−	0.939102i	$-0.388340\pi$
$89$	118.258	−	68.2765i	1.32874	−	0.767151i	0.985106	+	0.171951i	$0.0550069\pi$
$90$		0			0
$91$	−58.7454	+	33.9167i	−0.645554	+	0.372711i
$92$		0			0
$93$	−125.974	−	63.1820i	−1.35456	−	0.679376i
$94$		0			0
$95$	35.2890	+	161.713i	0.371463	+	1.70224i
$96$		0			0
$97$		−	37.3067i		−	0.384605i	−0.981336	−	0.192303i	$-0.938404\pi$
$97$		−	37.3067i		−	0.384605i	0.981336	−	0.192303i	$-0.0615955\pi$
$98$		0			0
$99$	−94.8309	−	127.095i	−0.957888	−	1.28379i
$100$		0			0
$101$	76.7027	−	132.853i	0.759433	−	1.31538i	−0.183707	−	0.982981i	$-0.558810\pi$
$101$	76.7027	−	132.853i	0.759433	−	1.31538i	0.943140	−	0.332395i	$-0.107857\pi$
$102$		0			0
$103$	−89.1447	−	51.4677i	−0.865483	−	0.499687i	0.000361688	−	1.00000i	$-0.499885\pi$
$103$	−89.1447	−	51.4677i	−0.865483	−	0.499687i	−0.865845	+	0.500313i	$0.833218\pi$
$104$		0			0
$105$	−133.911	+	266.996i	−1.27534	+	2.54282i
$106$		0			0
$107$			15.8800i			0.148411i	0.997243	+	0.0742055i	$0.0236421\pi$
$107$			15.8800i			0.148411i	−0.997243	+	0.0742055i	$0.976358\pi$
$108$		0			0
$109$	−47.1865	−	27.2431i	−0.432903	−	0.249937i	0.267679	−	0.963508i	$-0.413743\pi$
$109$	−47.1865	−	27.2431i	−0.432903	−	0.249937i	−0.700583	+	0.713571i	$0.747077\pi$
$110$		0			0
$111$	−10.5843	−	180.062i	−0.0953537	−	1.62218i
$112$		0			0
$113$	12.2066	+	7.04749i	0.108023	+	0.0623672i	0.553038	−	0.833156i	$-0.313468\pi$
$113$	12.2066	+	7.04749i	0.108023	+	0.0623672i	−0.445015	+	0.895523i	$0.646802\pi$
$114$		0			0
$115$	−9.99669	−	17.3148i	−0.0869277	−	0.150563i
$116$		0			0
$117$	6.25810	+	53.0481i	0.0534880	+	0.453403i
$118$		0			0
$119$	249.627			2.09771
$120$		0			0
$121$	−94.7229	+	164.065i	−0.782834	+	1.35591i
$122$		0			0
$123$	−83.1202	+	54.7329i	−0.675774	+	0.444983i
$124$		0			0
$125$	−225.543			−1.80434
$126$		0			0
$127$	−4.50411	+	2.60045i	−0.0354655	+	0.0204760i	−0.517628	−	0.855606i	$-0.673185\pi$
$127$	−4.50411	+	2.60045i	−0.0354655	+	0.0204760i	0.482162	+	0.876082i	$0.339852\pi$
$128$		0			0
$129$	−237.378	+	13.9534i	−1.84014	+	0.108166i
$130$		0			0
$131$	−65.5781	−	113.585i	−0.500596	−	0.867058i	−1.00000		0.000688231i	$-0.999781\pi$
$131$	−65.5781	−	113.585i	−0.500596	−	0.867058i	0.499404	−	0.866369i	$-0.333552\pi$
$132$		0			0
$133$	46.2979	+	212.161i	0.348104	+	1.59520i
$134$		0			0
$135$	151.480	+	179.938i	1.12207	+	1.33288i
$136$		0			0
$137$	5.91943	−	10.2528i	0.0432075	−	0.0748376i	−0.843613	−	0.536952i	$-0.819576\pi$
$137$	5.91943	−	10.2528i	0.0432075	−	0.0748376i	0.886820	+	0.462114i	$0.152909\pi$
$138$		0			0
$139$	−9.44174			−0.0679262			−0.0339631	−	0.999423i	$-0.510813\pi$
$139$	−9.44174			−0.0679262			−0.0339631	+	0.999423i	$0.510813\pi$
$140$		0			0
$141$	−11.5613	+	23.0512i	−0.0819947	+	0.163483i
$142$		0			0
$143$	90.5633	−	52.2868i	0.633310	−	0.365642i
$144$		0			0
$145$			267.203i			1.84278i
$146$		0			0
$147$	−109.783	+	218.889i	−0.746826	+	1.48904i
$148$		0			0
$149$	−35.7756	−	61.9651i	−0.240105	−	0.415873i	0.720639	−	0.693310i	$-0.243848\pi$
$149$	−35.7756	−	61.9651i	−0.240105	−	0.415873i	−0.960744	+	0.277437i	$0.910515\pi$
$150$		0			0
$151$	143.786	−	83.0149i	0.952226	−	0.549768i	0.0584542	−	0.998290i	$-0.481383\pi$
$151$	143.786	−	83.0149i	0.952226	−	0.549768i	0.893772	+	0.448522i	$0.148050\pi$
$152$		0			0
$153$	77.6644	−	180.578i	0.507610	−	1.18025i
$154$		0			0
$155$		−	409.239i		−	2.64025i
$156$		0			0
$157$	65.2139	+	112.954i	0.415375	+	0.719451i	0.995468	−	0.0950995i	$-0.0303169\pi$
$157$	65.2139	+	112.954i	0.415375	+	0.719451i	−0.580092	+	0.814551i	$0.696984\pi$
$158$		0			0
$159$	32.8111	−	21.6054i	0.206359	−	0.135883i
$160$		0			0
$161$	−13.1153	−	22.7163i	−0.0814614	−	0.141095i
$162$		0			0
$163$	32.5403			0.199634			0.0998170	−	0.995006i	$-0.468174\pi$
$163$	32.5403			0.199634			0.0998170	+	0.995006i	$0.468174\pi$
$164$		0			0
$165$	206.441	−	411.607i	1.25116	−	2.49459i
$166$		0			0
$167$			83.3650i			0.499192i	0.968350	+	0.249596i	$0.0802978\pi$
$167$			83.3650i			0.499192i	−0.968350	+	0.249596i	$0.919702\pi$
$168$		0			0
$169$	133.774			0.791565
$170$		0			0
$171$	167.880	+	32.5164i	0.981754	+	0.190154i
$172$		0			0
$173$			124.873i			0.721811i	0.932602	+	0.360906i	$0.117532\pi$
$173$			124.873i			0.721811i	−0.932602	+	0.360906i	$0.882468\pi$
$174$		0			0
$175$	−581.632			−3.32361
$176$		0			0
$177$	−65.9716	+	43.4409i	−0.372721	+	0.245429i
$178$		0			0
$179$		−	283.506i		−	1.58383i	−0.610628	−	0.791917i	$-0.709083\pi$
$179$		−	283.506i		−	1.58383i	0.610628	−	0.791917i	$-0.290917\pi$
$180$		0			0
$181$	17.7775	−	10.2638i	0.0982181	−	0.0567062i	−0.450086	−	0.892985i	$-0.648607\pi$
$181$	17.7775	−	10.2638i	0.0982181	−	0.0567062i	0.548304	+	0.836279i	$0.315273\pi$
$182$		0			0
$183$	−59.9199	+	119.470i	−0.327431	+	0.652841i
$184$		0			0
$185$	453.600	−	261.886i	2.45189	−	1.41560i
$186$		0			0
$187$	−384.832			−2.05792
$188$		0			0
$189$	198.736	+	236.072i	1.05151	+	1.24906i
$190$		0			0
$191$	39.5688	+	68.5351i	0.207166	+	0.358823i	0.950821	−	0.309742i	$-0.100243\pi$
$191$	39.5688	+	68.5351i	0.207166	+	0.358823i	−0.743654	+	0.668564i	$0.766909\pi$
$192$		0			0
$193$	−143.392	+	82.7872i	−0.742962	+	0.428949i	−0.823145	−	0.567831i	$-0.807783\pi$
$193$	−143.392	+	82.7872i	−0.742962	+	0.428949i	0.0801836	+	0.996780i	$0.474449\pi$
$194$		0			0
$195$	−129.548	+	85.3044i	−0.664347	+	0.437459i
$196$		0			0
$197$	6.34022			0.0321839			0.0160919	−	0.999871i	$-0.494878\pi$
$197$	6.34022			0.0321839			0.0160919	+	0.999871i	$0.494878\pi$
$198$		0			0
$199$	−166.168	−	287.811i	−0.835013	−	1.44628i	−0.894020	−	0.448027i	$-0.852127\pi$
$199$	−166.168	−	287.811i	−0.835013	−	1.44628i	0.0590072	−	0.998258i	$-0.481207\pi$
$200$		0			0
$201$	12.5578	+	213.636i	0.0624766	+	1.06286i
$202$		0			0
$203$			350.560i			1.72690i
$204$		0			0
$205$	−250.277	−	144.498i	−1.22087	−	0.704867i
$206$		0			0
$207$	−20.5132	+	2.41995i	−0.0990978	+	0.0116906i
$208$		0			0
$209$	−71.3739	−	327.073i	−0.341502	−	1.56494i
$210$		0			0
$211$	188.237	−	108.679i	0.892120	−	0.515066i	0.0174845	−	0.999847i	$-0.494434\pi$
$211$	188.237	−	108.679i	0.892120	−	0.515066i	0.874635	+	0.484782i	$0.161101\pi$
$212$		0			0
$213$	219.855	+	110.268i	1.03218	+	0.517690i
$214$		0			0
$215$	−345.248	−	597.986i	−1.60580	−	2.78133i
$216$		0			0
$217$		−	536.906i		−	2.47422i
$218$		0			0
$219$	1.33434	−	2.66045i	0.00609288	−	0.0121482i
$220$		0			0
$221$	112.263	+	64.8152i	0.507978	+	0.293281i
$222$		0			0
$223$		−	23.8899i		−	0.107129i	−0.998564	−	0.0535647i	$-0.982942\pi$
$223$		−	23.8899i		−	0.107129i	0.998564	−	0.0535647i	$-0.0170583\pi$
$224$		0			0
$225$	−180.958	+	420.748i	−0.804259	+	1.86999i
$226$		0			0
$227$	−42.7705	+	24.6936i	−0.188416	+	0.108782i	−0.591241	−	0.806495i	$-0.701362\pi$
$227$	−42.7705	+	24.6936i	−0.188416	+	0.108782i	0.402825	+	0.915277i	$0.368028\pi$
$228$		0			0
$229$	−115.476	+	200.010i	−0.504260	+	0.873405i	0.495727	+	0.868478i	$0.334902\pi$
$229$	−115.476	+	200.010i	−0.504260	+	0.873405i	−0.999988	+	0.00492659i	$0.998432\pi$
$230$		0			0
$231$	270.842	−	540.013i	1.17248	−	2.33772i
$232$		0			0
$233$	−172.807	+	299.310i	−0.741661	+	1.28459i	0.210078	+	0.977685i	$0.432628\pi$
$233$	−172.807	+	299.310i	−0.741661	+	1.28459i	−0.951739	+	0.306909i	$0.900705\pi$
$234$		0			0
$235$	−74.8839			−0.318655
$236$		0			0
$237$	−13.0183	−	221.470i	−0.0549295	−	0.934472i
$238$		0			0
$239$	−0.265501	+	0.459860i	−0.00111088	+	0.00192410i	−0.866580	−	0.499038i	$-0.833687\pi$
$239$	−0.265501	+	0.459860i	−0.00111088	+	0.00192410i	0.865469	+	0.500962i	$0.167020\pi$
$240$		0			0
$241$	−191.637	−	110.642i	−0.795174	−	0.459094i	0.0466067	−	0.998913i	$-0.485159\pi$
$241$	−191.637	−	110.642i	−0.795174	−	0.459094i	−0.841781	+	0.539819i	$0.818493\pi$
$242$		0			0
$243$	232.604	−	70.3169i	0.957217	−	0.289370i
$244$		0			0
$245$	−711.082			−2.90238
$246$		0			0
$247$	−34.2659	+	107.435i	−0.138729	+	0.434959i
$248$		0			0
$249$	−24.9068	−	37.8247i	−0.100027	−	0.151907i
$250$		0			0
$251$	−119.585	−	207.127i	−0.476433	−	0.825207i	0.523202	−	0.852209i	$-0.324737\pi$
$251$	−119.585	−	207.127i	−0.476433	−	0.825207i	−0.999635	+	0.0270018i	$0.991404\pi$
$252$		0			0
$253$	20.2188	+	35.0200i	0.0799163	+	0.138419i
$254$		0			0
$255$	569.827	−	33.4952i	2.23462	−	0.131354i
$256$		0			0
$257$		−	36.1932i		−	0.140830i	−0.997518	−	0.0704148i	$-0.977568\pi$
$257$		−	36.1932i		−	0.140830i	0.997518	−	0.0704148i	$-0.0224323\pi$
$258$		0			0
$259$	595.106	−	343.585i	2.29771	−	1.32658i
$260$		0			0
$261$	253.592	+	109.067i	0.971618	+	0.417880i
$262$		0			0
$263$	−384.262			−1.46107			−0.730536	−	0.682874i	$-0.760730\pi$
$263$	−384.262			−1.46107			−0.730536	+	0.682874i	$0.760730\pi$
$264$		0			0
$265$	98.7954	+	57.0395i	0.372813	+	0.215244i
$266$		0			0
$267$	342.144	−	225.295i	1.28144	−	0.843800i
$268$		0			0
$269$	261.191	+	150.799i	0.970970	+	0.560590i	0.899532	−	0.436855i	$-0.143908\pi$
$269$	261.191	+	150.799i	0.970970	+	0.560590i	0.0714384	+	0.997445i	$0.477241\pi$
$270$		0			0
$271$	−164.092	+	284.216i	−0.605505	+	1.04877i	0.386466	+	0.922304i	$0.373696\pi$
$271$	−164.092	+	284.216i	−0.605505	+	1.04877i	−0.991971	+	0.126462i	$0.959638\pi$
$272$		0			0
$273$	−169.962	+	111.916i	−0.622571	+	0.409949i
$274$		0			0
$275$	896.659			3.26058
$276$		0			0
$277$	116.358	+	201.538i	0.420066	+	0.727576i	0.995945	−	0.0899590i	$-0.0286736\pi$
$277$	116.358	+	201.538i	0.420066	+	0.727576i	−0.575880	+	0.817535i	$0.695340\pi$
$278$		0			0
$279$	−388.393	−	167.043i	−1.39209	−	0.598720i
$280$		0			0
$281$	269.298	+	155.479i	0.958355	+	0.553307i	0.895666	−	0.444727i	$-0.146699\pi$
$281$	269.298	+	155.479i	0.958355	+	0.553307i	0.0626887	+	0.998033i	$0.480032\pi$
$282$		0			0
$283$	−147.849	−	256.082i	−0.522435	−	0.904885i	−0.999659	−	0.0261030i	$-0.991690\pi$
$283$	−147.849	−	256.082i	−0.522435	−	0.904885i	0.477224	−	0.878782i	$-0.341643\pi$
$284$		0			0
$285$	134.153	+	478.090i	0.470711	+	1.67751i
$286$		0			0
$287$	−328.355	−	189.576i	−1.14409	−	0.660543i
$288$		0			0
$289$	−94.0204	−	162.848i	−0.325330	−	0.563489i
$290$		0			0
$291$	−6.56747	−	111.727i	−0.0225686	−	0.383943i
$292$		0			0
$293$	369.580	+	213.377i	1.26137	+	0.728250i	0.973339	−	0.229373i	$-0.0736675\pi$
$293$	369.580	+	213.377i	1.26137	+	0.728250i	0.288027	+	0.957622i	$0.407001\pi$
$294$		0			0
$295$	−198.642	−	114.686i	−0.673364	−	0.388767i
$296$		0			0
$297$	−306.376	−	363.935i	−1.03157	−	1.22537i
$298$		0			0
$299$		−	13.6214i		−	0.0455565i
$300$		0			0
$301$	−452.952	−	784.536i	−1.50482	−	2.60643i
$302$		0			0
$303$	206.324	−	411.375i	0.680938	−	1.35767i
$304$		0			0
$305$	−388.109			−1.27249
$306$		0			0
$307$	219.254	+	126.586i	0.714183	+	0.412334i	0.812608	−	0.582811i	$-0.198047\pi$
$307$	219.254	+	126.586i	0.714183	+	0.412334i	−0.0984250	+	0.995144i	$0.531380\pi$
$308$		0			0
$309$	−276.034	−	138.444i	−0.893313	−	0.448039i
$310$		0			0
$311$	90.5142	−	156.775i	0.291042	−	0.504100i	−0.683014	−	0.730405i	$-0.739331\pi$
$311$	90.5142	−	156.775i	0.291042	−	0.504100i	0.974057	+	0.226305i	$0.0726646\pi$
$312$		0			0
$313$	−252.227	+	436.869i	−0.805836	+	1.39575i	0.109890	+	0.993944i	$0.464950\pi$
$313$	−252.227	+	436.869i	−0.805836	+	1.39575i	−0.915725	+	0.401805i	$0.868383\pi$
$314$		0			0
$315$	−354.039	+	823.181i	−1.12393	+	2.61327i
$316$		0			0
$317$	34.6161	+	19.9856i	0.109199	+	0.0630461i	0.553605	−	0.832780i	$-0.313252\pi$
$317$	34.6161	+	19.9856i	0.109199	+	0.0630461i	−0.444406	+	0.895826i	$0.646585\pi$
$318$		0			0
$319$		−	540.432i		−	1.69414i
$320$		0			0
$321$	2.79551	+	47.5579i	0.00870876	+	0.148155i
$322$		0			0
$323$	306.886	−	279.344i	0.950111	−	0.864841i
$324$		0			0
$325$	−261.573	−	151.019i	−0.804841	−	0.464675i
$326$		0			0
$327$	−146.111	−	73.2818i	−0.446824	−	0.224103i
$328$		0			0
$329$	−98.2449			−0.298617
$330$		0			0
$331$	−541.910	+	312.872i	−1.63719	+	0.945232i	−0.655396	+	0.755285i	$0.727498\pi$
$331$	−541.910	+	312.872i	−1.63719	+	0.945232i	−0.981794	+	0.189947i	$0.939168\pi$
$332$		0			0
$333$	−63.3962	−	537.391i	−0.190379	−	1.61379i
$334$		0			0
$335$	−538.177	+	310.717i	−1.60650	+	0.927513i
$336$		0			0
$337$	536.576	−	309.792i	1.59221	−	0.919265i	0.599288	−	0.800534i	$-0.295451\pi$
$337$	536.576	−	309.792i	1.59221	−	0.919265i	0.992926	−	0.118731i	$-0.0378827\pi$
$338$		0			0
$339$	37.7974	+	18.9572i	0.111497	+	0.0559209i
$340$		0			0
$341$			827.707i			2.42729i
$342$		0			0
$343$	−372.885			−1.08713
$344$		0			0
$345$	−32.9865	−	50.0950i	−0.0956130	−	0.145203i
$346$		0			0
$347$	−22.3025	−	38.6290i	−0.0642723	−	0.111323i	0.832099	−	0.554628i	$-0.187139\pi$
$347$	−22.3025	−	38.6290i	−0.0642723	−	0.111323i	−0.896371	+	0.443305i	$0.853806\pi$
$348$		0			0
$349$	50.4508	+	87.3833i	0.144558	+	0.250382i	0.929208	−	0.369557i	$-0.120491\pi$
$349$	50.4508	+	87.3833i	0.144558	+	0.250382i	−0.784650	+	0.619939i	$0.787157\pi$
$350$		0			0
$351$	28.0805	+	157.768i	0.0800015	+	0.449483i
$352$		0			0
$353$	164.970	+	285.737i	0.467338	+	0.809453i	0.999304	−	0.0373126i	$-0.0118797\pi$
$353$	164.970	+	285.737i	0.467338	+	0.809453i	−0.531965	+	0.846766i	$0.678546\pi$
$354$		0			0
$355$			714.221i			2.01189i
$356$		0			0
$357$	747.592	−	43.9444i	2.09409	−	0.123094i
$358$		0			0
$359$	287.109	−	497.288i	0.799747	−	1.38520i	−0.120033	−	0.992770i	$-0.538300\pi$
$359$	287.109	−	497.288i	0.799747	−	1.38520i	0.919781	−	0.392433i	$-0.128366\pi$
$360$		0			0
$361$	294.335	+	209.017i	0.815332	+	0.578993i
$362$		0			0
$363$	−254.797	+	508.022i	−0.701920	+	1.39951i
$364$		0			0
$365$	8.64272			0.0236787
$366$		0			0
$367$	84.9259	−	147.096i	0.231406	−	0.400806i	−0.726816	−	0.686832i	$-0.759001\pi$
$367$	84.9259	−	147.096i	0.231406	−	0.400806i	0.958222	+	0.286026i	$0.0923342\pi$
$368$		0			0
$369$	−239.296	+	178.548i	−0.648498	+	0.483870i
$370$		0			0
$371$	129.616	+	74.8337i	0.349369	+	0.201708i
$372$		0			0
$373$	58.1030	+	33.5458i	0.155772	+	0.0899351i	0.575860	−	0.817548i	$-0.304667\pi$
$373$	58.1030	+	33.5458i	0.155772	+	0.0899351i	−0.420088	+	0.907484i	$0.638001\pi$
$374$		0			0
$375$	−675.462	+	39.7045i	−1.80123	+	0.105879i
$376$		0			0
$377$	−91.0221	+	157.655i	−0.241438	+	0.418183i
$378$		0			0
$379$		−	191.909i		−	0.506357i	−0.967420	−	0.253178i	$-0.918524\pi$
$379$		−	191.909i		−	0.506357i	0.967420	−	0.253178i	$-0.0814759\pi$
$380$		0			0
$381$	−13.0313	+	8.58082i	−0.0342028	+	0.0225218i
$382$		0			0
$383$	544.841	−	314.564i	1.42256	−	0.821316i	0.426044	−	0.904703i	$-0.359907\pi$
$383$	544.841	−	314.564i	1.42256	−	0.821316i	0.996517	+	0.0833866i	$0.0265736\pi$
$384$		0			0
$385$	1754.28			4.55658
$386$		0			0
$387$	−708.450	+	83.5760i	−1.83062	+	0.215959i
$388$		0			0
$389$	143.956	−	249.339i	0.370066	−	0.640973i	−0.619509	−	0.784989i	$-0.712668\pi$
$389$	143.956	−	249.339i	0.370066	−	0.640973i	0.989575	+	0.144016i	$0.0460017\pi$
$390$		0			0
$391$	−25.0635	+	43.4112i	−0.0641009	+	0.111026i
$392$		0			0
$393$	−216.391	−	328.622i	−0.550612	−	0.836188i
$394$		0			0
$395$	557.912	−	322.111i	1.41244	−	0.815470i
$396$		0			0
$397$	−46.2663	+	80.1355i	−0.116540	+	0.201853i	−0.918394	−	0.395667i	$-0.870514\pi$
$397$	−46.2663	+	80.1355i	−0.116540	+	0.201853i	0.801854	+	0.597519i	$0.203847\pi$
$398$		0			0
$399$	176.003	+	627.237i	0.441111	+	1.57202i
$400$		0			0
$401$	−326.231	+	188.349i	−0.813543	+	0.469699i	−0.848185	−	0.529701i	$-0.822304\pi$
$401$	−326.231	+	188.349i	−0.813543	+	0.469699i	0.0346417	+	0.999400i	$0.488971\pi$
$402$		0			0
$403$	139.406	−	241.459i	0.345922	−	0.599154i
$404$		0			0
$405$	485.333	+	512.218i	1.19835	+	1.26474i
$406$		0			0
$407$	−917.430	+	529.678i	−2.25413	+	1.30142i
$408$		0			0
$409$		−	48.7232i		−	0.119128i	−0.998225	−	0.0595638i	$-0.981029\pi$
$409$		−	48.7232i		−	0.119128i	0.998225	−	0.0595638i	$-0.0189710\pi$
$410$		0			0
$411$	15.9228	−	31.7473i	0.0387416	−	0.0772441i
$412$		0			0
$413$	−260.611	−	150.464i	−0.631021	−	0.364320i
$414$		0			0
$415$	65.7553	−	113.891i	0.158446	−	0.274437i
$416$		0			0
$417$	−28.2764	+	1.66212i	−0.0678091	+	0.00398591i
$418$		0			0
$419$	−400.534	+	693.745i	−0.955928	+	1.65572i	−0.223698	+	0.974659i	$0.571813\pi$
$419$	−400.534	+	693.745i	−0.955928	+	1.65572i	−0.732230	+	0.681057i	$0.761521\pi$
$420$		0			0
$421$		−	98.7648i		−	0.234596i	−0.993097	−	0.117298i	$-0.962577\pi$
$421$		−	98.7648i		−	0.234596i	0.993097	−	0.117298i	$-0.0374232\pi$
$422$		0			0
$423$	−30.5661	+	71.0695i	−0.0722602	+	0.168013i
$424$		0			0
$425$	555.753	+	962.593i	1.30765	+	2.26492i
$426$		0			0
$427$	−509.185			−1.19247
$428$		0			0
$429$	262.017	−	172.533i	0.610763	−	0.402174i
$430$		0			0
$431$	533.285	−	307.892i	1.23732	−	0.714368i	0.268775	−	0.963203i	$-0.413381\pi$
$431$	533.285	−	307.892i	1.23732	−	0.714368i	0.968546	+	0.248835i	$0.0800478\pi$
$432$		0			0
$433$	−602.808	+	348.032i	−1.39217	+	0.803768i	−0.993555	−	0.113352i	$-0.963841\pi$
$433$	−602.808	+	348.032i	−1.39217	+	0.803768i	−0.398612	+	0.917120i	$0.630508\pi$
$434$		0			0
$435$	47.0384	+	800.227i	0.108134	+	1.83960i
$436$		0			0
$437$	−41.5441	−	13.2503i	−0.0950667	−	0.0303212i
$438$		0			0
$439$			702.268i			1.59970i	0.600201	+	0.799850i	$0.295087\pi$
$439$			702.268i			1.59970i	−0.600201	+	0.799850i	$0.704913\pi$
$440$		0			0
$441$	−290.249	+	674.862i	−0.658162	+	1.53030i
$442$		0			0
$443$	398.530	−	690.274i	0.899616	−	1.55818i	0.0716305	−	0.997431i	$-0.477180\pi$
$443$	398.530	−	690.274i	0.899616	−	1.55818i	0.827986	−	0.560749i	$-0.189487\pi$
$444$		0			0
$445$	1030.21	+	594.790i	2.31507	+	1.33661i
$446$		0			0
$447$	−118.050	−	179.277i	−0.264094	−	0.401067i
$448$		0			0
$449$		−	437.780i		−	0.975011i	−0.873120	−	0.487506i	$-0.837907\pi$
$449$		−	437.780i		−	0.975011i	0.873120	−	0.487506i	$-0.162093\pi$
$450$		0			0
$451$	506.200	+	292.254i	1.12239	+	0.648014i
$452$		0			0
$453$	416.001	−	273.928i	0.918325	−	0.604697i
$454$		0			0
$455$	−511.760	−	295.465i	−1.12475	−	0.649374i
$456$		0			0
$457$	60.3768	+	104.576i	0.132116	+	0.228831i	0.924492	−	0.381202i	$-0.124490\pi$
$457$	60.3768	+	104.576i	0.132116	+	0.228831i	−0.792376	+	0.610033i	$0.791156\pi$
$458$		0			0
$459$	200.803	−	554.474i	0.437479	−	1.20800i
$460$		0			0
$461$	273.346			0.592942			0.296471	−	0.955042i	$-0.404190\pi$
$461$	273.346			0.592942			0.296471	+	0.955042i	$0.404190\pi$
$462$		0			0
$463$	83.4411	−	144.524i	0.180218	−	0.312147i	−0.761736	−	0.647887i	$-0.775653\pi$
$463$	83.4411	−	144.524i	0.180218	−	0.312147i	0.941955	+	0.335740i	$0.108986\pi$
$464$		0			0
$465$	−72.0424	−	1225.60i	−0.154930	−	2.63570i
$466$		0			0
$467$	−635.245			−1.36027			−0.680134	−	0.733087i	$-0.738079\pi$
$467$	−635.245			−1.36027			−0.680134	+	0.733087i	$0.738079\pi$
$468$		0			0
$469$	−706.068	+	407.649i	−1.50548	+	0.869187i
$470$		0			0
$471$	215.189	+	326.797i	0.456877	+	0.693837i
$472$		0			0
$473$	698.282	+	1209.46i	1.47628	+	2.55700i
$474$		0			0
$475$	−715.045	+	650.871i	−1.50536	+	1.37026i
$476$		0			0
$477$	94.4604	−	70.4807i	0.198030	−	0.147758i
$478$		0			0
$479$	−253.734	+	439.481i	−0.529717	+	0.917497i	0.469682	+	0.882836i	$0.344368\pi$
$479$	−253.734	+	439.481i	−0.529717	+	0.917497i	−0.999399	+	0.0346610i	$0.988965\pi$
$480$		0			0
$481$	356.844			0.741879
$482$		0			0
$483$	−43.2770	−	65.7227i	−0.0896005	−	0.136072i
$484$		0			0
$485$	281.456	−	162.499i	0.580322	−	0.335049i
$486$		0			0
$487$			530.952i			1.09025i	0.838354	+	0.545125i	$0.183518\pi$
$487$			530.952i			1.09025i	−0.838354	+	0.545125i	$0.816482\pi$
$488$		0			0
$489$	97.4528	−	5.72840i	0.199290	−	0.0117145i
$490$		0			0
$491$	−287.209	−	497.460i	−0.584946	−	1.01316i	−0.994882	−	0.101042i	$-0.967782\pi$
$491$	−287.209	−	497.460i	−0.584946	−	1.01316i	0.409936	−	0.912114i	$-0.365551\pi$
$492$		0			0
$493$	580.171	−	334.962i	1.17682	−	0.679436i
$494$		0			0
$495$	545.795	−	1269.04i	1.10262	−	2.56371i
$496$		0			0
$497$			937.032i			1.88538i
$498$		0			0
$499$	−6.43095	−	11.1387i	−0.0128877	−	0.0223221i	0.859510	−	0.511120i	$-0.170769\pi$
$499$	−6.43095	−	11.1387i	−0.0128877	−	0.0223221i	−0.872397	+	0.488797i	$0.837436\pi$
$500$		0			0
$501$	14.6756	+	249.664i	0.0292926	+	0.498332i
$502$		0			0
$503$	−56.4383	−	97.7539i	−0.112203	−	0.194342i	0.804455	−	0.594014i	$-0.202457\pi$
$503$	−56.4383	−	97.7539i	−0.112203	−	0.194342i	−0.916658	+	0.399672i	$0.869124\pi$
$504$		0			0
$505$	1336.39			2.64632
$506$		0			0
$507$	400.632	−	23.5497i	0.790201	−	0.0464490i
$508$		0			0
$509$		−	358.701i		−	0.704717i	−0.935865	−	0.352359i	$-0.885380\pi$
$509$		−	358.701i		−	0.704717i	0.935865	−	0.352359i	$-0.114620\pi$
$510$		0			0
$511$	11.3389			0.0221897
$512$		0			0
$513$	508.496	+	67.8274i	0.991221	+	0.132217i
$514$		0			0
$515$		−	896.722i		−	1.74121i
$516$		0			0
$517$	151.457			0.292953
$518$		0			0
$519$	21.9827	+	373.974i	0.0423559	+	0.720567i
$520$		0			0
$521$			450.771i			0.865203i	0.901585	+	0.432601i	$0.142404\pi$
$521$			450.771i			0.865203i	−0.901585	+	0.432601i	$0.857596\pi$
$522$		0			0
$523$	−81.3912	+	46.9913i	−0.155624	+	0.0898494i	−0.575790	−	0.817598i	$-0.695305\pi$
$523$	−81.3912	+	46.9913i	−0.155624	+	0.0898494i	0.420166	+	0.907447i	$0.361972\pi$
$524$		0			0
$525$	−1741.89	+	102.391i	−3.31789	+	0.195030i
$526$		0			0
$527$	−888.571	+	513.017i	−1.68609	+	0.973467i
$528$		0			0
$529$	−523.733			−0.990043
$530$		0			0
$531$	−189.926	+	141.712i	−0.357677	+	0.266877i
$532$		0			0
$533$	−98.4458	−	170.513i	−0.184701	−	0.319912i
$534$		0			0
$535$	−119.805	+	69.1692i	−0.223934	+	0.129288i
$536$		0			0
$537$	−49.9085	−	849.054i	−0.0929394	−	1.58111i
$538$		0			0
$539$	1438.20			2.66828
$540$		0			0
$541$	−129.257	−	223.879i	−0.238922	−	0.413825i	0.721483	−	0.692432i	$-0.243461\pi$
$541$	−129.257	−	223.879i	−0.238922	−	0.413825i	−0.960405	+	0.278607i	$0.910127\pi$
$542$		0			0
$543$	51.4337	−	33.8680i	0.0947213	−	0.0623720i
$544$		0			0
$545$		−	474.657i		−	0.870930i
$546$		0			0
$547$	301.386	+	174.005i	0.550980	+	0.318109i	0.749517	−	0.661985i	$-0.230286\pi$
$547$	301.386	+	174.005i	0.550980	+	0.318109i	−0.198537	+	0.980093i	$0.563619\pi$
$548$		0			0
$549$	−158.418	+	368.340i	−0.288558	+	0.670930i
$550$		0			0
$551$	392.292	+	430.970i	0.711963	+	0.782159i
$552$		0			0
$553$	731.960	−	422.597i	1.32362	−	0.764190i
$554$		0			0
$555$	1312.35	−	864.156i	2.36460	−	1.55704i
$556$		0			0
$557$	−458.243	−	793.700i	−0.822698	−	1.42496i	−0.903666	−	0.428238i	$-0.859134\pi$
$557$	−458.243	−	793.700i	−0.822698	−	1.42496i	0.0809677	−	0.996717i	$-0.474199\pi$
$558$		0			0
$559$		−	470.432i		−	0.841559i
$560$		0			0
$561$	−1152.51	+	67.7458i	−2.05438	+	0.120759i
$562$		0			0
$563$	−43.8510	−	25.3174i	−0.0778881	−	0.0449687i	0.460550	−	0.887634i	$-0.347652\pi$
$563$	−43.8510	−	25.3174i	−0.0778881	−	0.0449687i	−0.538438	+	0.842665i	$0.680985\pi$
$564$		0			0
$565$			122.788i			0.217325i
$566$		0			0
$567$	636.739	+	672.011i	1.12300	+	1.18520i
$568$		0			0
$569$	−113.450	+	65.5003i	−0.199385	+	0.115115i	−0.596368	−	0.802711i	$-0.703390\pi$
$569$	−113.450	+	65.5003i	−0.199385	+	0.115115i	0.396984	+	0.917826i	$0.370057\pi$
$570$		0			0
$571$	−154.844	+	268.197i	−0.271180	+	0.469697i	−0.969164	−	0.246416i	$-0.920747\pi$
$571$	−154.844	+	268.197i	−0.271180	+	0.469697i	0.697984	+	0.716113i	$0.254080\pi$
$572$		0			0
$573$	130.567	+	198.285i	0.227865	+	0.346048i
$574$		0			0
$575$	58.3979	−	101.148i	0.101562	−	0.175910i
$576$		0			0
$577$	−750.124			−1.30004			−0.650021	−	0.759917i	$-0.725240\pi$
$577$	−750.124			−1.30004			−0.650021	+	0.759917i	$0.725240\pi$
$578$		0			0
$579$	−414.860	+	273.176i	−0.716511	+	0.471807i
$580$		0			0
$581$	86.2685	−	149.421i	0.148483	−	0.257180i
$582$		0			0
$583$	−199.819	−	115.366i	−0.342743	−	0.197883i
$584$		0			0
$585$	−372.957	+	278.278i	−0.637532	+	0.475689i
$586$		0			0
$587$	−471.769			−0.803695			−0.401848	−	0.915707i	$-0.631632\pi$
$587$	−471.769			−0.803695			−0.401848	+	0.915707i	$0.631632\pi$
$588$		0			0
$589$	−600.821	−	660.059i	−1.02007	−	1.12064i
$590$		0			0
$591$	18.9879	−	1.11613i	0.0321284	−	0.00188855i
$592$		0			0
$593$	130.389	+	225.841i	0.219881	+	0.380845i	0.954771	−	0.297341i	$-0.0960998\pi$
$593$	130.389	+	225.841i	0.219881	+	0.380845i	−0.734890	+	0.678186i	$0.762766\pi$
$594$		0			0
$595$	1087.31	+	1883.28i	1.82742	+	3.16518i
$596$		0			0
$597$	−548.310	−	832.692i	−0.918442	−	1.39479i
$598$		0			0
$599$		−	88.7186i		−	0.148111i	−0.997254	−	0.0740556i	$-0.976406\pi$
$599$		−	88.7186i		−	0.148111i	0.997254	−	0.0740556i	$-0.0235942\pi$
$600$		0			0
$601$	−220.073	+	127.059i	−0.366178	+	0.211413i	−0.671787	−	0.740744i	$-0.734473\pi$
$601$	−220.073	+	127.059i	−0.366178	+	0.211413i	0.305609	+	0.952157i	$0.401140\pi$
$602$		0			0
$603$	75.2169	+	637.592i	0.124738	+	1.05737i
$604$		0			0
$605$	−1650.36			−2.72786
$606$		0			0
$607$	206.624	+	119.294i	0.340401	+	0.196531i	0.660449	−	0.750870i	$-0.270366\pi$
$607$	206.624	+	119.294i	0.340401	+	0.196531i	−0.320048	+	0.947401i	$0.603699\pi$
$608$		0			0
$609$	61.7126	+	1049.87i	0.101334	+	1.72392i
$610$		0			0
$611$	−44.1830	−	25.5090i	−0.0723126	−	0.0417497i
$612$		0			0
$613$	83.4196	−	144.487i	0.136084	−	0.235705i	−0.789927	−	0.613201i	$-0.789882\pi$
$613$	83.4196	−	144.487i	0.136084	−	0.235705i	0.926011	+	0.377496i	$0.123215\pi$
$614$		0			0
$615$	−774.976	−	388.688i	−1.26012	−	0.632012i
$616$		0			0
$617$	−504.753			−0.818076			−0.409038	−	0.912517i	$-0.634136\pi$
$617$	−504.753			−0.818076			−0.409038	+	0.912517i	$0.634136\pi$
$618$		0			0
$619$	231.552	+	401.060i	0.374074	+	0.647915i	0.990188	−	0.139742i	$-0.0446273\pi$
$619$	231.552	+	401.060i	0.374074	+	0.647915i	−0.616114	+	0.787657i	$0.711294\pi$
$620$		0			0
$621$	−61.0077	+	10.8585i	−0.0982411	+	0.0174855i
$622$		0			0
$623$	1351.59	+	780.343i	2.16949	+	1.25256i
$624$		0			0
$625$	−346.279	−	599.773i	−0.554046	−	0.959637i
$626$		0			0
$627$	−271.331	−	966.963i	−0.432744	−	1.54221i
$628$		0			0
$629$	−1137.25	−	656.594i	−1.80804	−	1.04387i
$630$		0			0
$631$	215.590	+	373.413i	0.341664	+	0.591780i	0.984742	−	0.174021i	$-0.0556760\pi$
$631$	215.590	+	373.413i	0.341664	+	0.591780i	−0.643078	+	0.765801i	$0.722343\pi$
$632$		0			0
$633$	544.607	−	358.612i	0.860358	−	0.566528i
$634$		0			0
$635$	−39.2376	−	22.6538i	−0.0617915	−	0.0356753i
$636$		0			0
$637$	−419.553	−	242.229i	−0.658638	−	0.380265i
$638$		0			0
$639$	677.841	+	291.530i	1.06078	+	0.456229i
$640$		0			0
$641$		−	237.994i		−	0.371285i	−0.982617	−	0.185643i	$-0.940563\pi$
$641$		−	237.994i		−	0.371285i	0.982617	−	0.185643i	$-0.0594367\pi$
$642$		0			0
$643$	−358.408	−	620.781i	−0.557400	−	0.965445i	−0.997712	−	0.0676004i	$-0.978466\pi$
$643$	−358.408	−	620.781i	−0.557400	−	0.965445i	0.440313	−	0.897845i	$-0.354868\pi$
$644$		0			0
$645$	−1139.23	−	1730.09i	−1.76624	−	2.68231i
$646$		0			0
$647$	−133.501			−0.206338			−0.103169	−	0.994664i	$-0.532898\pi$
$647$	−133.501			−0.206338			−0.103169	+	0.994664i	$0.532898\pi$
$648$		0			0
$649$	401.765	+	231.959i	0.619052	+	0.357410i
$650$		0			0
$651$	−94.5169	−	1607.94i	−0.145187	−	2.46996i
$652$		0			0
$653$	380.011	−	658.198i	0.581946	−	1.00796i	−0.413302	−	0.910594i	$-0.635625\pi$
$653$	380.011	−	658.198i	0.581946	−	1.00796i	0.995249	−	0.0973665i	$-0.0310419\pi$
$654$		0			0
$655$	571.283	−	989.492i	0.872188	−	1.51067i
$656$		0			0
$657$	3.52778	−	8.20249i	0.00536953	−	0.0124848i
$658$		0			0
$659$	541.414	+	312.585i	0.821568	+	0.474333i	0.850957	−	0.525235i	$-0.176023\pi$
$659$	541.414	+	312.585i	0.821568	+	0.474333i	−0.0293886	+	0.999568i	$0.509356\pi$
$660$		0			0
$661$			1061.57i			1.60600i	0.595978	+	0.803001i	$0.296765\pi$
$661$			1061.57i			1.60600i	−0.595978	+	0.803001i	$0.703235\pi$
$662$		0			0
$663$	347.619	+	174.348i	0.524312	+	0.262968i
$664$		0			0
$665$	−1398.96	+	1273.41i	−2.10370	+	1.91490i
$666$		0			0
$667$	−60.9638	−	35.1974i	−0.0913999	−	0.0527698i
$668$		0			0
$669$	−4.20557	−	71.5461i	−0.00628636	−	0.106945i
$670$		0			0
$671$	784.972			1.16985
$672$		0			0
$673$	793.451	−	458.099i	1.17898	−	0.680682i	0.223199	−	0.974773i	$-0.428350\pi$
$673$	793.451	−	458.099i	1.17898	−	0.680682i	0.955778	+	0.294091i	$0.0950168\pi$
$674$		0			0
$675$	−467.871	+	1291.93i	−0.693142	+	1.91396i
$676$		0			0
$677$	−1019.90	+	588.838i	−1.50649	+	0.869775i	−0.506523	+	0.862227i	$0.669069\pi$
$677$	−1019.90	+	588.838i	−1.50649	+	0.869775i	−0.999972	+	0.00754839i	$0.997597\pi$
$678$		0			0
$679$	369.260	−	213.192i	0.543829	−	0.313980i
$680$		0			0
$681$	−123.743	+	81.4823i	−0.181708	+	0.119651i
$682$		0			0
$683$		−	47.7905i		−	0.0699715i	−0.999388	−	0.0349857i	$-0.988861\pi$
$683$		−	47.7905i		−	0.0699715i	0.999388	−	0.0349857i	$-0.0111386\pi$
$684$		0			0
$685$	103.134			0.150561
$686$		0			0
$687$	−310.620	+	619.323i	−0.452140	+	0.901490i
$688$		0			0
$689$	38.8608	+	67.3089i	0.0564018	+	0.0976907i
$690$		0			0
$691$	−644.426	−	1116.18i	−0.932600	−	1.61531i	−0.778859	−	0.627199i	$-0.784201\pi$
$691$	−644.426	−	1116.18i	−0.932600	−	1.61531i	−0.153741	−	0.988111i	$-0.549132\pi$
$692$		0			0
$693$	716.063	−	1664.93i	1.03328	−	2.40249i
$694$		0			0
$695$	−41.1258	−	71.2320i	−0.0591739	−	0.102492i
$696$		0			0
$697$			724.563i			1.03955i
$698$		0			0
$699$	−464.837	+	926.805i	−0.665003	+	1.32590i
$700$		0			0
$701$	−274.690	+	475.778i	−0.391855	+	0.678713i	−0.992694	−	0.120657i	$-0.961500\pi$
$701$	−274.690	+	475.778i	−0.391855	+	0.678713i	0.600839	+	0.799370i	$0.294833\pi$
$702$		0			0
$703$	347.123	−	1088.34i	0.493774	−	1.54814i
$704$		0			0
$705$	−224.265	+	13.1826i	−0.318106	+	0.0186987i
$706$		0			0
$707$	1753.30			2.47991
$708$		0			0
$709$	−58.6616	+	101.605i	−0.0827385	+	0.143307i	−0.904425	−	0.426632i	$-0.859700\pi$
$709$	−58.6616	+	101.605i	−0.0827385	+	0.143307i	0.821687	+	0.569939i	$0.193033\pi$
$710$		0			0
$711$	−77.9751	−	660.973i	−0.109670	−	0.929638i
$712$		0			0
$713$	93.3701	+	53.9072i	0.130954	+	0.0756062i
$714$		0			0
$715$	788.942	+	455.496i	1.10342	+	0.637057i
$716$		0			0
$717$	−0.714175	+	1.42394i	−0.000996060	+	0.00198597i
$718$		0			0
$719$	−696.655	+	1206.64i	−0.968922	+	1.67822i	−0.270234	+	0.962795i	$0.587101\pi$
$719$	−696.655	+	1206.64i	−0.968922	+	1.67822i	−0.698688	+	0.715427i	$0.746232\pi$
$720$		0			0
$721$		−	1176.47i		−	1.63171i
$722$		0			0
$723$	−593.398	−	297.617i	−0.820744	−	0.411642i
$724$		0			0
$725$	−1351.80	+	780.463i	−1.86455	+	1.07650i
$726$		0			0
$727$	−515.159			−0.708610			−0.354305	−	0.935130i	$-0.615282\pi$
$727$	−515.159			−0.708610			−0.354305	+	0.935130i	$0.615282\pi$
$728$		0			0
$729$	684.230	−	251.535i	0.938588	−	0.345041i
$730$		0			0
$731$	−865.597	+	1499.26i	−1.18413	+	2.05097i
$732$		0			0
$733$	636.674	−	1102.75i	0.868586	−	1.50444i	0.00514455	−	0.999987i	$-0.498362\pi$
$733$	636.674	−	1102.75i	0.868586	−	1.50444i	0.863442	−	0.504449i	$-0.168304\pi$
$734$		0			0
$735$	−2129.57	+	125.179i	−2.89738	+	0.170312i
$736$		0			0
$737$	1088.49	−	628.441i	1.47692	−	0.852702i
$738$		0			0
$739$	−308.060	+	533.575i	−0.416860	+	0.722023i	−0.995622	−	0.0934738i	$-0.970203\pi$
$739$	−308.060	+	533.575i	−0.416860	+	0.722023i	0.578762	+	0.815497i	$0.303536\pi$
$740$		0			0
$741$	−83.7079	+	327.782i	−0.112966	+	0.442350i
$742$		0			0
$743$	−161.106	+	93.0143i	−0.216831	+	0.125188i	−0.604482	−	0.796619i	$-0.706620\pi$
$743$	−161.106	+	93.0143i	−0.216831	+	0.125188i	0.387651	+	0.921806i	$0.373287\pi$
$744$		0			0
$745$	311.659	−	539.809i	0.418334	−	0.724576i
$746$		0			0
$747$	−81.2502	−	108.894i	−0.108769	−	0.145775i
$748$		0			0
$749$	−157.179	+	90.7474i	−0.209852	+	0.121158i
$750$		0			0
$751$			204.555i			0.272376i	0.990683	+	0.136188i	$0.0434852\pi$
$751$			204.555i			0.272376i	−0.990683	+	0.136188i	$0.956515\pi$
$752$		0			0
$753$	−394.599	−	599.258i	−0.524036	−	0.795828i
$754$		0			0
$755$	1252.59	+	723.185i	1.65906	+	0.957860i
$756$		0			0
$757$	−193.561	+	335.257i	−0.255695	+	0.442876i	−0.965084	−	0.261941i	$-0.915637\pi$
$757$	−193.561	+	335.257i	−0.255695	+	0.442876i	0.709389	+	0.704817i	$0.248971\pi$
$758$		0			0
$759$	66.7169	+	101.320i	0.0879011	+	0.133491i
$760$		0			0
$761$	70.2455	−	121.669i	0.0923069	−	0.159880i	−0.816175	−	0.577805i	$-0.803909\pi$
$761$	70.2455	−	121.669i	0.0923069	−	0.159880i	0.908481	+	0.417925i	$0.137243\pi$
$762$		0			0
$763$		−	622.732i		−	0.816162i
$764$		0			0
$765$	1700.64	−	200.625i	2.22306	−	0.262254i
$766$		0			0
$767$	−78.1353	−	135.334i	−0.101871	−	0.176446i
$768$		0			0
$769$	605.311			0.787140			0.393570	−	0.919295i	$-0.371240\pi$
$769$	605.311			0.787140			0.393570	+	0.919295i	$0.371240\pi$
$770$		0			0
$771$	−6.37146	−	108.393i	−0.00826389	−	0.140587i
$772$		0			0
$773$	370.599	−	213.965i	0.479429	−	0.276798i	−0.240749	−	0.970587i	$-0.577393\pi$
$773$	370.599	−	213.965i	0.479429	−	0.276798i	0.720179	+	0.693789i	$0.244060\pi$
$774$		0			0
$775$	2070.37	−	1195.33i	2.67145	−	1.54236i
$776$		0			0
$777$	1721.76	−	1133.74i	2.21590	−	1.45912i
$778$		0			0
$779$	−615.815	+	134.383i	−0.790519	+	0.172507i
$780$		0			0
$781$		−	1444.55i		−	1.84962i
$782$		0			0
$783$	778.666	+	281.994i	0.994465	+	0.360145i
$784$		0			0
$785$	−568.111	+	983.997i	−0.723708	+	1.25350i
$786$		0			0
$787$	593.959	+	342.922i	0.754713	+	0.435734i	0.827394	−	0.561622i	$-0.189822\pi$
$787$	593.959	+	342.922i	0.754713	+	0.435734i	−0.0726814	+	0.997355i	$0.523156\pi$
$788$		0			0
$789$	−1150.80	+	67.6455i	−1.45855	+	0.0857357i
$790$		0			0
$791$			161.094i			0.203658i
$792$		0			0
$793$	−228.992	−	132.209i	−0.288767	−	0.166720i
$794$		0			0
$795$	305.917	+	153.432i	0.384801	+	0.192996i
$796$		0			0
$797$	−450.418	−	260.049i	−0.565141	−	0.326284i	0.190065	−	0.981771i	$-0.439130\pi$
$797$	−450.418	−	260.049i	−0.565141	−	0.326284i	−0.755206	+	0.655487i	$0.772463\pi$
$798$		0			0
$799$	93.8736	+	162.594i	0.117489	+	0.203497i
$800$		0			0
$801$	985.003	−	734.950i	1.22972	−	0.917541i
$802$		0			0
$803$	−17.4804			−0.0217688
$804$		0			0
$805$	114.254	−	197.893i	0.141930	−	0.245830i
$806$		0			0
$807$	808.769	+	405.637i	1.00219	+	0.502647i
$808$		0			0
$809$	578.438			0.715004			0.357502	−	0.933912i	$-0.383629\pi$
$809$	578.438			0.715004			0.357502	+	0.933912i	$0.383629\pi$
$810$		0			0
$811$	1268.07	−	732.121i	1.56359	−	0.902739i	0.566701	−	0.823924i	$-0.308220\pi$
$811$	1268.07	−	732.121i	1.56359	−	0.902739i	0.996889	−	0.0788151i	$-0.0251137\pi$
$812$		0			0
$813$	−441.394	+	880.064i	−0.542920	+	1.08249i
$814$		0			0
$815$	141.738	+	245.497i	0.173911	+	0.301223i
$816$		0			0
$817$	−1434.78	−	457.617i	−1.75615	−	0.560118i
$818$		0			0
$819$	−489.305	+	365.090i	−0.597442	+	0.445776i
$820$		0			0
$821$	316.967	−	549.003i	0.386074	−	0.668700i	−0.605843	−	0.795584i	$-0.707164\pi$
$821$	316.967	−	549.003i	0.386074	−	0.668700i	0.991918	+	0.126884i	$0.0404975\pi$
$822$		0			0
$823$	208.065			0.252813			0.126407	−	0.991979i	$-0.459656\pi$
$823$	208.065			0.252813			0.126407	+	0.991979i	$0.459656\pi$
$824$		0			0
$825$	2685.34	−	157.848i	3.25496	−	0.191331i
$826$		0			0
$827$	484.351	−	279.640i	0.585672	−	0.338138i	−0.177712	−	0.984083i	$-0.556870\pi$
$827$	484.351	−	279.640i	0.585672	−	0.338138i	0.763384	+	0.645944i	$0.223536\pi$
$828$		0			0
$829$			168.875i			0.203709i	0.994799	+	0.101854i	$0.0324776\pi$
$829$			168.875i			0.203709i	−0.994799	+	0.101854i	$0.967522\pi$
$830$		0			0
$831$	383.952	+	583.090i	0.462036	+	0.701672i
$832$		0			0
$833$	891.405	+	1543.96i	1.07011	+	1.85349i
$834$		0			0
$835$	−628.937	+	363.117i	−0.753218	+	0.434871i
$836$		0			0
$837$	−1192.58	−	431.892i	−1.42483	−	0.516000i
$838$		0			0
$839$			317.639i			0.378592i	0.981920	+	0.189296i	$0.0606205\pi$
$839$			317.639i			0.378592i	−0.981920	+	0.189296i	$0.939379\pi$
$840$		0			0
$841$	49.8984	+	86.4265i	0.0593322	+	0.102766i
$842$		0			0
$843$	833.872	+	418.227i	0.989172	+	0.496117i
$844$		0			0
$845$	582.688	+	1009.25i	0.689572	+	1.19437i
$846$		0			0
$847$	−2165.21			−2.55632
$848$		0			0
$849$	−487.864	−	740.896i	−0.574634	−	0.872669i
$850$		0			0
$851$			137.988i			0.162148i
$852$		0			0
$853$	−812.672			−0.952722			−0.476361	−	0.879250i	$-0.658045\pi$
$853$	−812.672			−0.952722			−0.476361	+	0.879250i	$0.658045\pi$
$854$		0			0
$855$	485.927	+	1408.18i	0.568336	+	1.64700i
$856$		0			0
$857$		−	468.748i		−	0.546963i	−0.961877	−	0.273482i	$-0.911825\pi$
$857$		−	468.748i		−	0.546963i	0.961877	−	0.273482i	$-0.0881753\pi$
$858$		0			0
$859$	−1260.29			−1.46715			−0.733577	−	0.679606i	$-0.762151\pi$
$859$	−1260.29			−1.46715			−0.733577	+	0.679606i	$0.762151\pi$
$860$		0			0
$861$	−1016.74	−	509.944i	−1.18088	−	0.592269i
$862$		0			0
$863$			575.600i			0.666976i	0.942754	+	0.333488i	$0.108226\pi$
$863$			575.600i			0.666976i	−0.942754	+	0.333488i	$0.891774\pi$
$864$		0			0
$865$	−942.092	+	543.917i	−1.08912	+	0.628806i
$866$		0			0
$867$	−310.243	−	471.151i	−0.357835	−	0.543427i
$868$		0			0
$869$	−1128.41	+	651.486i	−1.29851	+	0.749696i
$870$		0			0
$871$	−423.380			−0.486085
$872$		0			0
$873$	−39.3369	−	333.448i	−0.0450595	−	0.381957i
$874$		0			0
$875$	−1288.88	−	2232.41i	−1.47301	−	2.55132i
$876$		0			0
$877$	−1138.92	+	657.556i	−1.29866	+	0.749779i	−0.980172	−	0.198149i	$-0.936507\pi$
$877$	−1138.92	+	657.556i	−1.29866	+	0.749779i	−0.318484	+	0.947928i	$0.603174\pi$
$878$		0			0
$879$	1144.39	+	573.967i	1.30193	+	0.652978i
$880$		0			0
$881$	−585.318			−0.664379			−0.332189	−	0.943213i	$-0.607787\pi$
$881$	−585.318			−0.664379			−0.332189	+	0.943213i	$0.607787\pi$
$882$		0			0
$883$	−81.8056	−	141.691i	−0.0926451	−	0.160466i	0.815978	−	0.578083i	$-0.196199\pi$
$883$	−81.8056	−	141.691i	−0.0926451	−	0.160466i	−0.908623	+	0.417617i	$0.862866\pi$
$884$		0			0
$885$	−615.090	−	308.497i	−0.695017	−	0.348584i
$886$		0			0
$887$			666.540i			0.751454i	0.926730	+	0.375727i	$0.122607\pi$
$887$			666.540i			0.751454i	−0.926730	+	0.375727i	$0.877393\pi$
$888$		0			0
$889$	−51.4783	−	29.7210i	−0.0579058	−	0.0334319i
$890$		0			0
$891$	−981.612	−	1035.99i	−1.10170	−	1.16273i
$892$		0			0
$893$	−120.780	+	109.940i	−0.135252	+	0.123113i
$894$		0			0
$895$	2138.88	−	1234.88i	2.38981	−	1.37976i
$896$		0			0
$897$	−2.39791	−	40.7938i	−0.00267326	−	0.0454780i
$898$		0			0
$899$	−720.447	−	1247.85i	−0.801387	−	1.38804i
$900$		0			0
$901$		−	286.016i		−	0.317443i
$902$		0			0
$903$	−1494.62	−	2269.81i	−1.65518	−	2.51364i
$904$		0			0
$905$	154.868	+	89.4133i	0.171125	+	0.0987993i
$906$		0			0
$907$			839.238i			0.925290i	0.886543	+	0.462645i	$0.153100\pi$
$907$			839.238i			0.925290i	−0.886543	+	0.462645i	$0.846900\pi$
$908$		0			0
$909$	545.488	−	1268.32i	0.600096	−	1.39529i
$910$		0			0
$911$	−10.7166	+	6.18725i	−0.0117636	+	0.00679171i	−0.505870	−	0.862610i	$-0.668829\pi$
$911$	−10.7166	+	6.18725i	−0.0117636	+	0.00679171i	0.494107	+	0.869401i	$0.335495\pi$
$912$		0			0
$913$	−132.994	+	230.352i	−0.145667	+	0.252302i
$914$		0			0
$915$	−1162.32	+	68.3228i	−1.27030	+	0.0746697i
$916$		0			0
$917$	749.502	−	1298.18i	0.817342	−	1.41568i
$918$		0			0
$919$	−106.033			−0.115379			−0.0576895	−	0.998335i	$-0.518373\pi$
$919$	−106.033			−0.115379			−0.0576895	+	0.998335i	$0.518373\pi$
$920$		0			0
$921$	678.913	+	340.507i	0.737148	+	0.369715i
$922$		0			0
$923$	−243.298	+	421.405i	−0.263595	+	0.456560i
$924$		0			0
$925$	2649.81	+	1529.87i	2.86466	+	1.65391i
$926$		0			0
$927$	−851.046	−	366.024i	−0.918065	−	0.394848i
$928$		0			0
$929$	−542.406			−0.583860			−0.291930	−	0.956440i	$-0.594297\pi$
$929$	−542.406			−0.583860			−0.291930	+	0.956440i	$0.594297\pi$
$930$		0			0
$931$	−1146.90	+	1043.97i	−1.23190	+	1.12134i
$932$		0			0
$933$	243.476	−	485.449i	0.260960	−	0.520310i
$934$		0			0
$935$	−1676.23	−	2903.32i	−1.79276	−	3.10515i
$936$		0			0
$937$	123.694	+	214.245i	0.132011	+	0.228650i	0.924452	−	0.381299i	$-0.124523\pi$
$937$	123.694	+	214.245i	0.132011	+	0.228650i	−0.792441	+	0.609949i	$0.791190\pi$
$938$		0			0
$939$	−678.469	+	1352.75i	−0.722545	+	1.44063i
$940$		0			0
$941$		−	1613.33i		−	1.71449i	−0.514913	−	0.857243i	$-0.672176\pi$
$941$		−	1613.33i		−	1.71449i	0.514913	−	0.857243i	$-0.327824\pi$
$942$		0			0
$943$	65.9359	−	38.0681i	0.0699214	−	0.0403692i
$944$		0			0
$945$	−915.375	+	2527.61i	−0.968650	+	2.67472i
$946$		0			0
$947$	−805.635			−0.850723			−0.425361	−	0.905024i	$-0.639853\pi$
$947$	−805.635			−0.850723			−0.425361	+	0.905024i	$0.639853\pi$
$948$		0			0
$949$	5.09938	+	2.94413i	0.00537342	+	0.00310235i
$950$		0			0
$951$	107.188	+	53.7597i	0.112710	+	0.0565296i
$952$		0			0
$953$	−860.305	−	496.697i	−0.902733	−	0.521193i	−0.0246471	−	0.999696i	$-0.507846\pi$
$953$	−860.305	−	496.697i	−0.902733	−	0.521193i	−0.878086	+	0.478503i	$0.841180\pi$
$954$		0			0
$955$	−344.703	+	597.044i	−0.360946	+	0.625177i
$956$		0			0
$957$	−95.1376	−	1618.50i	−0.0994123	−	1.69122i
$958$		0			0
$959$	135.308			0.141093
$960$		0			0
$961$	622.912	+	1078.92i	0.648192	+	1.12270i
$962$		0			0
$963$	16.7442	+	141.936i	0.0173875	+	0.147389i
$964$		0			0
$965$	−1249.16	−	721.200i	−1.29446	−	0.747358i
$966$		0			0
$967$	780.772	+	1352.34i	0.807416	+	1.39849i	0.914648	+	0.404252i	$0.132468\pi$
$967$	780.772	+	1352.34i	0.807416	+	1.39849i	−0.107231	+	0.994234i	$0.534199\pi$
$968$		0			0
$969$	869.895	−	890.611i	0.897725	−	0.919103i
$970$		0			0
$971$	−1167.66	−	674.150i	−1.20254	−	0.694284i	−0.241418	−	0.970421i	$-0.577612\pi$
$971$	−1167.66	−	674.150i	−1.20254	−	0.694284i	−0.961118	+	0.276137i	$0.910946\pi$
$972$		0			0
$973$	−53.9556	−	93.4538i	−0.0554528	−	0.0960471i
$974$		0			0
$975$	−809.954	−	406.230i	−0.830722	−	0.416647i
$976$		0			0
$977$	−861.538	−	497.409i	−0.881820	−	0.509119i	−0.0105621	−	0.999944i	$-0.503362\pi$
$977$	−861.538	−	497.409i	−0.881820	−	0.509119i	−0.871258	+	0.490825i	$0.836695\pi$
$978$		0			0
$979$	−2083.65	−	1203.00i	−2.12834	−	1.22880i
$980$		0			0
$981$	−450.479	−	193.745i	−0.459204	−	0.197498i
$982$		0			0
$983$			1290.14i			1.31245i	0.754566	+	0.656224i	$0.227847\pi$
$983$			1290.14i			1.31245i	−0.754566	+	0.656224i	$0.772153\pi$
$984$		0			0
$985$	27.6164	+	47.8330i	0.0280370	+	0.0485615i
$986$		0			0
$987$	−294.227	+	17.2950i	−0.298102	+	0.0175228i
$988$		0			0
$989$	181.912			0.183935
$990$		0			0
$991$	−738.112	−	426.149i	−0.744815	−	0.430019i	0.0790024	−	0.996874i	$-0.474827\pi$
$991$	−738.112	−	426.149i	−0.744815	−	0.430019i	−0.823817	+	0.566855i	$0.808160\pi$
$992$		0			0
$993$	−1567.85	+	1032.40i	−1.57890	+	1.03967i
$994$		0			0
$995$	1447.57	−	2507.26i	1.45484	−	2.51986i
$996$		0			0
$997$	335.949	−	581.880i	0.336960	−	0.583631i	−0.646900	−	0.762575i	$-0.723935\pi$
$997$	335.949	−	581.880i	0.336960	−	0.583631i	0.983859	+	0.178944i	$0.0572681\pi$
$998$		0			0
$999$	−284.463	−	1598.24i	−0.284748	−	1.59984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.39	✓	80
3.2	odd	2		2052.3.s.a.901.2		80
9.2	odd	6		2052.3.bl.a.1585.39		80
9.7	even	3		684.3.bl.a.673.27	yes	80
19.12	odd	6		684.3.bl.a.373.27	yes	80
57.50	even	6		2052.3.bl.a.145.39		80
171.88	odd	6	inner	684.3.s.a.601.39	yes	80
171.164	even	6		2052.3.s.a.829.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.39	✓	80	1.1	even	1	trivial
684.3.s.a.601.39	yes	80	171.88	odd	6	inner
684.3.bl.a.373.27	yes	80	19.12	odd	6
684.3.bl.a.673.27	yes	80	9.7	even	3
2052.3.s.a.829.2		80	171.164	even	6
2052.3.s.a.901.2		80	3.2	odd	2
2052.3.bl.a.145.39		80	57.50	even	6
2052.3.bl.a.1585.39		80	9.2	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99483 - 0.176040i) q^{3} +(4.35575 + 7.54438i) q^{5} +(5.71458 + 9.89794i) q^{7} +(8.93802 - 1.05442i) q^{9} +O(q^{10})\)	\(q+(2.99483 - 0.176040i) q^{3} +(4.35575 + 7.54438i) q^{5} +(5.71458 + 9.89794i) q^{7} +(8.93802 - 1.05442i) q^{9} +(-8.80974 - 15.2589i) q^{11} +5.93511i q^{13} +(14.3728 + 21.8274i) q^{15} +(10.9206 - 18.9151i) q^{17} +(18.1016 + 5.77343i) q^{19} +(18.8566 + 28.6367i) q^{21} -2.29506 q^{23} +(-25.4451 + 44.0722i) q^{25} +(26.5822 - 4.73126i) q^{27} +(26.5631 + 15.3362i) q^{29} +(-40.6831 - 23.4884i) q^{31} +(-29.0698 - 44.1470i) q^{33} +(-49.7826 + 86.2259i) q^{35} -60.1242i q^{37} +(1.04482 + 17.7746i) q^{39} +(-28.7296 + 16.5870i) q^{41} -79.2625 q^{43} +(46.8867 + 62.8390i) q^{45} +(-4.29799 + 7.44434i) q^{47} +(-40.8129 + 70.6900i) q^{49} +(29.3756 - 58.5700i) q^{51} +(11.3408 - 6.54761i) q^{53} +(76.7460 - 132.928i) q^{55} +(55.2275 + 14.1038i) q^{57} +(-22.8023 + 13.1649i) q^{59} +(-22.2757 + 38.5826i) q^{61} +(61.5136 + 82.4425i) q^{63} +(-44.7767 + 25.8519i) q^{65} +71.3349i q^{67} +(-6.87330 + 0.404022i) q^{69} +(71.0020 + 40.9930i) q^{71} +(0.496052 - 0.859188i) q^{73} +(-68.4453 + 136.468i) q^{75} +(100.688 - 174.397i) q^{77} -73.9507i q^{79} +(78.7764 - 18.8489i) q^{81} +(-7.54810 - 13.0737i) q^{83} +190.270 q^{85} +(82.2517 + 41.2532i) q^{87} +(118.258 - 68.2765i) q^{89} +(-58.7454 + 33.9167i) q^{91} +(-125.974 - 63.1820i) q^{93} +(35.2890 + 161.713i) q^{95} -37.3067i q^{97} +(-94.8309 - 127.095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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