LMFDB - Embedded newform 400.3.bg.e.353.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] 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("400.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			353.2
Character	$\chi$	$=$	400.353
Dual form			400.3.bg.e.17.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.466746 - 2.94692i) q^{3} +(4.43224 + 2.31415i) q^{5} +(-6.13972 + 6.13972i) q^{7} +(0.0930182 - 0.0302234i) q^{9} +(4.35777 - 13.4118i) q^{11} +(7.93733 - 15.5779i) q^{13} +(4.75089 - 14.1416i) q^{15} +(-3.91601 + 24.7247i) q^{17} +(6.17152 + 8.49436i) q^{19} +(20.9590 + 15.2276i) q^{21} +(33.2719 - 16.9529i) q^{23} +(14.2894 + 20.5137i) q^{25} +(-12.3234 - 24.1861i) q^{27} +(28.6915 - 39.4904i) q^{29} +(3.88447 - 2.82223i) q^{31} +(-41.5576 - 6.58207i) q^{33} +(-41.4209 + 13.0044i) q^{35} +(-14.4927 - 7.38441i) q^{37} +(-49.6115 - 16.1198i) q^{39} +(-22.5225 - 69.3173i) q^{41} +(-2.30703 - 2.30703i) q^{43} +(0.482220 + 0.0813007i) q^{45} +(10.5071 - 1.66416i) q^{47} -26.3924i q^{49} +74.6896 q^{51} +(3.89089 + 24.5661i) q^{53} +(50.3516 - 49.3599i) q^{55} +(22.1517 - 22.1517i) q^{57} +(-4.38302 + 1.42413i) q^{59} +(16.1478 - 49.6979i) q^{61} +(-0.385542 + 0.756669i) q^{63} +(71.2297 - 50.6767i) q^{65} +(-17.6552 + 111.471i) q^{67} +(-65.4882 - 90.1368i) q^{69} +(12.7289 + 9.24807i) q^{71} +(-33.9690 + 17.3081i) q^{73} +(53.7828 - 51.6845i) q^{75} +(55.5894 + 109.100i) q^{77} +(-29.4277 + 40.5038i) q^{79} +(-64.8105 + 47.0876i) q^{81} +(125.051 + 19.8061i) q^{83} +(-74.5734 + 100.524i) q^{85} +(-129.767 - 66.1195i) q^{87} +(-49.1581 - 15.9724i) q^{89} +(46.9109 + 144.377i) q^{91} +(-10.1300 - 10.1300i) q^{93} +(7.69637 + 51.9308i) q^{95} +(-5.71423 + 0.905044i) q^{97} -1.37925i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) $ 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.466746	−	2.94692i	−0.155582	−	0.982307i	−0.934702	−	0.355432i	$-0.884334\pi$
$3$	−0.466746	−	2.94692i	−0.155582	−	0.982307i	0.779120	−	0.626875i	$-0.215666\pi$
$4$		0			0
$5$	4.43224	+	2.31415i	0.886447	+	0.462830i
$5$	4.43224	+	2.31415i	0.886447	+	0.462830i
$6$		0			0
$7$	−6.13972	+	6.13972i	−0.877103	+	0.877103i	−0.993234	−	0.116131i	$-0.962951\pi$
$7$	−6.13972	+	6.13972i	−0.877103	+	0.877103i	0.116131	+	0.993234i	$0.462951\pi$
$8$		0			0
$9$	0.0930182	−	0.0302234i	0.0103354	−	0.00335816i
$10$		0			0
$11$	4.35777	−	13.4118i	0.396161	−	1.21926i	−0.531893	−	0.846811i	$-0.678519\pi$
$11$	4.35777	−	13.4118i	0.396161	−	1.21926i	0.928054	−	0.372446i	$-0.121481\pi$
$12$		0			0
$13$	7.93733	−	15.5779i	0.610564	−	1.19830i	−0.354197	−	0.935171i	$-0.615246\pi$
$13$	7.93733	−	15.5779i	0.610564	−	1.19830i	0.964761	−	0.263128i	$-0.0847543\pi$
$14$		0			0
$15$	4.75089	−	14.1416i	0.316726	−	0.942771i
$16$		0			0
$17$	−3.91601	+	24.7247i	−0.230354	+	1.45440i	0.553188	+	0.833056i	$0.313411\pi$
$17$	−3.91601	+	24.7247i	−0.230354	+	1.45440i	−0.783542	+	0.621339i	$0.786589\pi$
$18$		0			0
$19$	6.17152	+	8.49436i	0.324817	+	0.447072i	0.939930	−	0.341367i	$-0.110890\pi$
$19$	6.17152	+	8.49436i	0.324817	+	0.447072i	−0.615114	+	0.788439i	$0.710890\pi$
$20$		0			0
$21$	20.9590	+	15.2276i	0.998046	+	0.725123i
$22$		0			0
$23$	33.2719	−	16.9529i	1.44660	−	0.737081i	0.458187	−	0.888856i	$-0.348499\pi$
$23$	33.2719	−	16.9529i	1.44660	−	0.737081i	0.988415	+	0.151775i	$0.0484989\pi$
$24$		0			0
$25$	14.2894	+	20.5137i	0.571577	+	0.820549i
$26$		0			0
$27$	−12.3234	−	24.1861i	−0.456424	−	0.895782i
$28$		0			0
$29$	28.6915	−	39.4904i	0.989361	−	1.36174i	0.0577298	−	0.998332i	$-0.481614\pi$
$29$	28.6915	−	39.4904i	0.989361	−	1.36174i	0.931631	−	0.363406i	$-0.118386\pi$
$30$		0			0
$31$	3.88447	−	2.82223i	0.125306	−	0.0910398i	−0.523367	−	0.852107i	$-0.675324\pi$
$31$	3.88447	−	2.82223i	0.125306	−	0.0910398i	0.648673	+	0.761067i	$0.275324\pi$
$32$		0			0
$33$	−41.5576	−	6.58207i	−1.25932	−	0.199457i
$34$		0			0
$35$	−41.4209	+	13.0044i	−1.18346	+	0.371556i
$36$		0			0
$37$	−14.4927	−	7.38441i	−0.391695	−	0.199579i	0.247040	−	0.969005i	$-0.420542\pi$
$37$	−14.4927	−	7.38441i	−0.391695	−	0.199579i	−0.638735	+	0.769427i	$0.720542\pi$
$38$		0			0
$39$	−49.6115	−	16.1198i	−1.27209	−	0.413327i
$40$		0			0
$41$	−22.5225	−	69.3173i	−0.549330	−	1.69066i	−0.710465	−	0.703732i	$-0.751515\pi$
$41$	−22.5225	−	69.3173i	−0.549330	−	1.69066i	0.161135	−	0.986932i	$-0.448485\pi$
$42$		0			0
$43$	−2.30703	−	2.30703i	−0.0536518	−	0.0536518i	0.679772	−	0.733424i	$-0.262079\pi$
$43$	−2.30703	−	2.30703i	−0.0536518	−	0.0536518i	−0.733424	+	0.679772i	$0.762079\pi$
$44$		0			0
$45$	0.482220	+	0.0813007i	0.0107160	+	0.00180668i
$46$		0			0
$47$	10.5071	−	1.66416i	0.223555	−	0.0354076i	−0.0436522	−	0.999047i	$-0.513899\pi$
$47$	10.5071	−	1.66416i	0.223555	−	0.0354076i	0.267207	+	0.963639i	$0.413899\pi$
$48$		0			0
$49$		−	26.3924i		−	0.538620i
$50$		0			0
$51$	74.6896			1.46450
$52$		0			0
$53$	3.89089	+	24.5661i	0.0734131	+	0.463512i	0.996820	+	0.0796891i	$0.0253927\pi$
$53$	3.89089	+	24.5661i	0.0734131	+	0.463512i	−0.923407	+	0.383823i	$0.874607\pi$
$54$		0			0
$55$	50.3516	−	49.3599i	0.915484	−	0.897452i
$56$		0			0
$57$	22.1517	−	22.1517i	0.388626	−	0.388626i
$58$		0			0
$59$	−4.38302	+	1.42413i	−0.0742884	+	0.0241378i	−0.345925	−	0.938262i	$-0.612435\pi$
$59$	−4.38302	+	1.42413i	−0.0742884	+	0.0241378i	0.271637	+	0.962400i	$0.412435\pi$
$60$		0			0
$61$	16.1478	−	49.6979i	0.264719	−	0.814720i	−0.727039	−	0.686596i	$-0.759104\pi$
$61$	16.1478	−	49.6979i	0.264719	−	0.814720i	0.991758	−	0.128125i	$-0.0408958\pi$
$62$		0			0
$63$	−0.385542	+	0.756669i	−0.00611972	+	0.0120106i
$64$		0			0
$65$	71.2297	−	50.6767i	1.09584	−	0.779641i
$66$		0			0
$67$	−17.6552	+	111.471i	−0.263511	+	1.66374i	0.400711	+	0.916205i	$0.368763\pi$
$67$	−17.6552	+	111.471i	−0.263511	+	1.66374i	−0.664221	+	0.747536i	$0.731237\pi$
$68$		0			0
$69$	−65.4882	−	90.1368i	−0.949105	−	1.30633i
$70$		0			0
$71$	12.7289	+	9.24807i	0.179280	+	0.130254i	0.673806	−	0.738908i	$-0.264658\pi$
$71$	12.7289	+	9.24807i	0.179280	+	0.130254i	−0.494526	+	0.869163i	$0.664658\pi$
$72$		0			0
$73$	−33.9690	+	17.3081i	−0.465329	+	0.237097i	−0.670904	−	0.741545i	$-0.734094\pi$
$73$	−33.9690	+	17.3081i	−0.465329	+	0.237097i	0.205575	+	0.978641i	$0.434094\pi$
$74$		0			0
$75$	53.7828	−	51.6845i	0.717104	−	0.689126i
$76$		0			0
$77$	55.5894	+	109.100i	0.721941	+	1.41689i
$78$		0			0
$79$	−29.4277	+	40.5038i	−0.372503	+	0.512706i	−0.953579	−	0.301143i	$-0.902632\pi$
$79$	−29.4277	+	40.5038i	−0.372503	+	0.512706i	0.581076	+	0.813849i	$0.302632\pi$
$80$		0			0
$81$	−64.8105	+	47.0876i	−0.800130	+	0.581328i
$82$		0			0
$83$	125.051	+	19.8061i	1.50664	+	0.238628i	0.854491	−	0.519467i	$-0.173869\pi$
$83$	125.051	+	19.8061i	1.50664	+	0.238628i	0.652145	+	0.758094i	$0.273869\pi$
$84$		0			0
$85$	−74.5734	+	100.524i	−0.877334	+	1.18263i
$86$		0			0
$87$	−129.767	−	66.1195i	−1.49157	−	0.759994i
$88$		0			0
$89$	−49.1581	−	15.9724i	−0.552339	−	0.179466i	0.0195324	−	0.999809i	$-0.493782\pi$
$89$	−49.1581	−	15.9724i	−0.552339	−	0.179466i	−0.571871	+	0.820344i	$0.693782\pi$
$90$		0			0
$91$	46.9109	+	144.377i	0.515504	+	1.58656i
$92$		0			0
$93$	−10.1300	−	10.1300i	−0.108924	−	0.108924i
$94$		0			0
$95$	7.69637	+	51.9308i	0.0810145	+	0.546640i
$96$		0			0
$97$	−5.71423	+	0.905044i	−0.0589095	+	0.00933035i	−0.185820	−	0.982584i	$-0.559494\pi$
$97$	−5.71423	+	0.905044i	−0.0589095	+	0.00933035i	0.126910	+	0.991914i	$0.459494\pi$
$98$		0			0
$99$		−	1.37925i		−	0.0139318i
$100$		0			0
$101$	81.8916			0.810808			0.405404	−	0.914138i	$-0.367131\pi$
$101$	81.8916			0.810808			0.405404	+	0.914138i	$0.367131\pi$
$102$		0			0
$103$	−5.41538	−	34.1913i	−0.0525765	−	0.331955i	−0.999931	−	0.0117676i	$-0.996254\pi$
$103$	−5.41538	−	34.1913i	−0.0525765	−	0.331955i	0.947354	−	0.320187i	$-0.103746\pi$
$104$		0			0
$105$	57.6562	+	115.994i	0.549106	+	1.10471i
$106$		0			0
$107$	−120.310	+	120.310i	−1.12439	+	1.12439i	−0.133316	+	0.991074i	$0.542563\pi$
$107$	−120.310	+	120.310i	−1.12439	+	1.12439i	−0.991074	+	0.133316i	$0.957437\pi$
$108$		0			0
$109$	80.2078	−	26.0611i	0.735852	−	0.239093i	0.0829694	−	0.996552i	$-0.473560\pi$
$109$	80.2078	−	26.0611i	0.735852	−	0.239093i	0.652882	+	0.757459i	$0.273560\pi$
$110$		0			0
$111$	−14.9969	+	46.1556i	−0.135107	+	0.415816i
$112$		0			0
$113$	−57.4231	+	112.699i	−0.508169	+	0.997337i	0.484307	+	0.874898i	$0.339072\pi$
$113$	−57.4231	+	112.699i	−0.508169	+	0.997337i	−0.992476	+	0.122439i	$0.960928\pi$
$114$		0			0
$115$	186.700	+	1.85703i	1.62348	+	0.0161481i
$116$		0			0
$117$	0.267499	−	1.68892i	0.00228631	−	0.0144352i
$118$		0			0
$119$	−127.760	−	175.846i	−1.07361	−	1.47770i
$120$		0			0
$121$	−62.9960	−	45.7693i	−0.520628	−	0.378258i
$122$		0			0
$123$	−193.760	+	98.7257i	−1.57529	+	0.802648i
$124$		0			0
$125$	15.8622	+	123.989i	0.126898	+	0.991916i
$126$		0			0
$127$	−24.2709	−	47.6343i	−0.191109	−	0.375073i	0.775492	−	0.631357i	$-0.217502\pi$
$127$	−24.2709	−	47.6343i	−0.191109	−	0.375073i	−0.966602	+	0.256284i	$0.917502\pi$
$128$		0			0
$129$	−5.72183	+	7.87542i	−0.0443553	+	0.0610498i
$130$		0			0
$131$	−115.313	+	83.7799i	−0.880253	+	0.639541i	−0.933318	−	0.359050i	$-0.883101\pi$
$131$	−115.313	+	83.7799i	−0.880253	+	0.639541i	0.0530653	+	0.998591i	$0.483101\pi$
$132$		0			0
$133$	−90.0444	−	14.2616i	−0.677026	−	0.107230i
$134$		0			0
$135$	1.34992	−	135.717i	0.00999942	−	1.00531i
$136$		0			0
$137$	161.652	+	82.3656i	1.17994	+	0.601209i	0.930182	−	0.367099i	$-0.119649\pi$
$137$	161.652	+	82.3656i	1.17994	+	0.601209i	0.249757	+	0.968308i	$0.419649\pi$
$138$		0			0
$139$	19.6792	+	6.39416i	0.141577	+	0.0460012i	0.378948	−	0.925418i	$-0.376286\pi$
$139$	19.6792	+	6.39416i	0.141577	+	0.0460012i	−0.237371	+	0.971419i	$0.576286\pi$
$140$		0			0
$141$	−9.80827	−	30.1868i	−0.0695622	−	0.214090i
$142$		0			0
$143$	−174.339	−	174.339i	−1.21915	−	1.21915i
$144$		0			0
$145$	218.554	−	108.634i	1.50727	−	0.749203i
$146$		0			0
$147$	−77.7762	+	12.3185i	−0.529090	+	0.0837996i
$148$		0			0
$149$		−	21.8722i		−	0.146793i	−0.997303	−	0.0733967i	$-0.976616\pi$
$149$		−	21.8722i		−	0.146793i	0.997303	−	0.0733967i	$-0.0233839\pi$
$150$		0			0
$151$	221.086			1.46414			0.732072	−	0.681227i	$-0.238553\pi$
$151$	221.086			1.46414			0.732072	+	0.681227i	$0.238553\pi$
$152$		0			0
$153$	0.383006	+	2.41820i	0.00250331	+	0.0158053i
$154$		0			0
$155$	23.7480	−	3.51955i	0.153213	−	0.0227068i
$156$		0			0
$157$	−99.1212	+	99.1212i	−0.631345	+	0.631345i	−0.948405	−	0.317060i	$-0.897304\pi$
$157$	−99.1212	+	99.1212i	−0.631345	+	0.631345i	0.317060	+	0.948405i	$0.397304\pi$
$158$		0			0
$159$	70.5784	−	22.9323i	0.443889	−	0.144228i
$160$		0			0
$161$	−100.194	+	308.366i	−0.622324	+	1.91532i
$162$		0			0
$163$	95.1327	−	186.708i	0.583636	−	1.14545i	−0.390735	−	0.920503i	$-0.627779\pi$
$163$	95.1327	−	186.708i	0.583636	−	1.14545i	0.974371	−	0.224947i	$-0.0722209\pi$
$164$		0			0
$165$	−168.961	−	125.344i	−1.02401	−	0.759659i
$166$		0			0
$167$	−11.3886	+	71.9048i	−0.0681952	+	0.430568i	0.929843	+	0.367957i	$0.119943\pi$
$167$	−11.3886	+	71.9048i	−0.0681952	+	0.430568i	−0.998038	+	0.0626106i	$0.980057\pi$
$168$		0			0
$169$	−80.3337	−	110.570i	−0.475347	−	0.654260i
$170$		0			0
$171$	0.830792	+	0.603606i	0.00485843	+	0.00352986i
$172$		0			0
$173$	−240.785	+	122.686i	−1.39182	+	0.709168i	−0.979420	−	0.201835i	$-0.935310\pi$
$173$	−240.785	+	122.686i	−1.39182	+	0.709168i	−0.412401	+	0.911002i	$0.635310\pi$
$174$		0			0
$175$	−213.682	−	38.2155i	−1.22104	−	0.218374i
$176$		0			0
$177$	6.24255	+	12.2517i	0.0352686	+	0.0692186i
$178$		0			0
$179$	−37.1114	+	51.0794i	−0.207326	+	0.285360i	−0.899999	−	0.435892i	$-0.856433\pi$
$179$	−37.1114	+	51.0794i	−0.207326	+	0.285360i	0.692673	+	0.721252i	$0.256433\pi$
$180$		0			0
$181$	36.6294	−	26.6128i	0.202373	−	0.147032i	−0.481983	−	0.876180i	$-0.660083\pi$
$181$	36.6294	−	26.6128i	0.202373	−	0.147032i	0.684356	+	0.729148i	$0.260083\pi$
$182$		0			0
$183$	−153.993	−	24.3901i	−0.841491	−	0.133279i
$184$		0			0
$185$	−47.1465	−	66.2678i	−0.254846	−	0.358204i
$186$		0			0
$187$	314.539	+	160.265i	1.68203	+	0.857035i
$188$		0			0
$189$	224.158	+	72.8335i	1.18602	+	0.385362i
$190$		0			0
$191$	76.5083	+	235.468i	0.400567	+	1.23282i	0.924540	+	0.381084i	$0.124449\pi$
$191$	76.5083	+	235.468i	0.400567	+	1.23282i	−0.523973	+	0.851735i	$0.675551\pi$
$192$		0			0
$193$	−120.538	−	120.538i	−0.624552	−	0.624552i	0.322140	−	0.946692i	$-0.395598\pi$
$193$	−120.538	−	120.538i	−0.624552	−	0.624552i	−0.946692	+	0.322140i	$0.895598\pi$
$194$		0			0
$195$	−182.586	−	186.255i	−0.936341	−	0.955155i
$196$		0			0
$197$	−358.089	+	56.7157i	−1.81771	+	0.287897i	−0.970097	−	0.242719i	$-0.921961\pi$
$197$	−358.089	+	56.7157i	−1.81771	+	0.287897i	−0.847613	+	0.530616i	$0.821961\pi$
$198$		0			0
$199$			26.3872i			0.132599i	0.997800	+	0.0662994i	$0.0211192\pi$
$199$			26.3872i			0.132599i	−0.997800	+	0.0662994i	$0.978881\pi$
$200$		0			0
$201$	336.736			1.67530
$202$		0			0
$203$	66.3025	+	418.618i	0.326613	+	2.06216i
$204$		0			0
$205$	60.5854	−	359.351i	0.295538	−	1.75293i
$206$		0			0
$207$	2.58251	−	2.58251i	0.0124759	−	0.0124759i
$208$		0			0
$209$	140.819	−	45.7549i	0.673775	−	0.218923i
$210$		0			0
$211$	3.95255	−	12.1647i	0.0187325	−	0.0576526i	−0.941253	−	0.337701i	$-0.890351\pi$
$211$	3.95255	−	12.1647i	0.0187325	−	0.0576526i	0.959986	+	0.280049i	$0.0903506\pi$
$212$		0			0
$213$	21.3122	−	41.8275i	0.100057	−	0.196373i
$214$		0			0
$215$	−4.88648	−	15.5641i	−0.0227278	−	0.0723911i
$216$		0			0
$217$	−6.52185	+	41.1773i	−0.0300546	+	0.189757i
$218$		0			0
$219$	66.8604	+	92.0255i	0.305299	+	0.420208i
$220$		0			0
$221$	354.076	+	257.251i	1.60216	+	1.16403i
$222$		0			0
$223$	−135.696	+	69.1403i	−0.608500	+	0.310046i	−0.730953	−	0.682428i	$-0.760924\pi$
$223$	−135.696	+	69.1403i	−0.608500	+	0.310046i	0.122453	+	0.992474i	$0.460924\pi$
$224$		0			0
$225$	1.94917	+	1.47627i	0.00866298	+	0.00656122i
$226$		0			0
$227$	−103.562	−	203.252i	−0.456221	−	0.895384i	−0.998477	−	0.0551707i	$-0.982430\pi$
$227$	−103.562	−	203.252i	−0.456221	−	0.895384i	0.542256	−	0.840213i	$-0.317570\pi$
$228$		0			0
$229$	−149.797	+	206.178i	−0.654137	+	0.900342i	−0.999270	−	0.0382118i	$-0.987834\pi$
$229$	−149.797	+	206.178i	−0.654137	+	0.900342i	0.345133	+	0.938554i	$0.387834\pi$
$230$		0			0
$231$	295.564	−	214.740i	1.27950	−	0.929610i
$232$		0			0
$233$	−103.867	−	16.4508i	−0.445779	−	0.0706045i	−0.0704904	−	0.997512i	$-0.522456\pi$
$233$	−103.867	−	16.4508i	−0.445779	−	0.0706045i	−0.375289	+	0.926908i	$0.622456\pi$
$234$		0			0
$235$	50.4209	+	16.9390i	0.214557	+	0.0720809i
$236$		0			0
$237$	133.097	+	67.8162i	0.561590	+	0.286144i
$238$		0			0
$239$	208.047	+	67.5984i	0.870488	+	0.282839i	0.710002	−	0.704200i	$-0.248694\pi$
$239$	208.047	+	67.5984i	0.870488	+	0.282839i	0.160486	+	0.987038i	$0.448694\pi$
$240$		0			0
$241$	−44.5491	−	137.108i	−0.184851	−	0.568913i	0.815095	−	0.579328i	$-0.196685\pi$
$241$	−44.5491	−	137.108i	−0.184851	−	0.568913i	−0.999946	+	0.0104148i	$0.996685\pi$
$242$		0			0
$243$	−3.73440	−	3.73440i	−0.0153679	−	0.0153679i
$244$		0			0
$245$	61.0759	−	116.977i	0.249289	−	0.477458i
$246$		0			0
$247$	181.310	−	28.7166i	0.734047	−	0.116262i
$248$		0			0
$249$		−	377.759i		−	1.51710i
$250$		0			0
$251$	−106.447			−0.424091			−0.212046	−	0.977260i	$-0.568013\pi$
$251$	−106.447			−0.424091			−0.212046	+	0.977260i	$0.568013\pi$
$252$		0			0
$253$	−82.3778	−	520.113i	−0.325604	−	2.05578i
$254$		0			0
$255$	331.042	+	172.843i	1.29820	+	0.677815i
$256$		0			0
$257$	233.672	−	233.672i	0.909230	−	0.909230i	−0.0869796	−	0.996210i	$-0.527721\pi$
$257$	233.672	−	233.672i	0.909230	−	0.909230i	0.996210	+	0.0869796i	$0.0277215\pi$
$258$		0			0
$259$	134.320	−	43.6431i	0.518608	−	0.168506i
$260$		0			0
$261$	1.47529	−	4.54048i	0.00565246	−	0.0173965i
$262$		0			0
$263$	10.8040	−	21.2040i	0.0410798	−	0.0806237i	−0.869554	−	0.493837i	$-0.835594\pi$
$263$	10.8040	−	21.2040i	0.0410798	−	0.0806237i	0.910634	+	0.413214i	$0.135594\pi$
$264$		0			0
$265$	−39.6044	+	117.887i	−0.149451	+	0.444857i
$266$		0			0
$267$	−24.1252	+	152.320i	−0.0903564	+	0.570488i
$268$		0			0
$269$	17.9737	+	24.7387i	0.0668167	+	0.0919653i	0.841118	−	0.540852i	$-0.181898\pi$
$269$	17.9737	+	24.7387i	0.0668167	+	0.0919653i	−0.774301	+	0.632818i	$0.781898\pi$
$270$		0			0
$271$	−380.924	−	276.758i	−1.40562	−	1.02125i	−0.993940	−	0.109920i	$-0.964941\pi$
$271$	−380.924	−	276.758i	−1.40562	−	1.02125i	−0.411684	−	0.911326i	$-0.635059\pi$
$272$		0			0
$273$	403.572	−	205.630i	1.47829	−	0.753224i
$274$		0			0
$275$	337.396	−	102.253i	1.22690	−	0.371830i
$276$		0			0
$277$	−75.7229	−	148.615i	−0.273368	−	0.536515i	0.712981	−	0.701183i	$-0.247345\pi$
$277$	−75.7229	−	148.615i	−0.273368	−	0.536515i	−0.986349	+	0.164668i	$0.947345\pi$
$278$		0			0
$279$	0.276029	−	0.379921i	0.000989351	−	0.00136173i
$280$		0			0
$281$	−421.611	+	306.319i	−1.50040	+	1.09010i	−0.530173	+	0.847890i	$0.677873\pi$
$281$	−421.611	+	306.319i	−1.50040	+	1.09010i	−0.970223	+	0.242212i	$0.922127\pi$
$282$		0			0
$283$	−193.661	−	30.6728i	−0.684313	−	0.108385i	−0.195409	−	0.980722i	$-0.562603\pi$
$283$	−193.661	−	30.6728i	−0.684313	−	0.108385i	−0.488904	+	0.872337i	$0.662603\pi$
$284$		0			0
$285$	149.444	−	46.9191i	0.524364	−	0.164629i
$286$		0			0
$287$	563.871	+	287.307i	1.96471	+	1.00107i
$288$		0			0
$289$	−321.121	−	104.339i	−1.11115	−	0.361033i
$290$		0			0
$291$	5.33419	+	16.4169i	0.0183305	+	0.0564156i
$292$		0			0
$293$	79.1398	+	79.1398i	0.270102	+	0.270102i	0.829141	−	0.559039i	$-0.188830\pi$
$293$	79.1398	+	79.1398i	0.270102	+	0.270102i	−0.559039	+	0.829141i	$0.688830\pi$
$294$		0			0
$295$	−22.7222	−	3.83089i	−0.0770244	−	0.0129861i
$296$		0			0
$297$	−378.083	+	59.8824i	−1.27301	+	0.201624i
$298$		0			0
$299$		−	652.866i		−	2.18350i
$300$		0			0
$301$	28.3290			0.0941163
$302$		0			0
$303$	−38.2226	−	241.328i	−0.126147	−	0.796462i
$304$		0			0
$305$	186.580	−	182.904i	0.611736	−	0.599687i
$306$		0			0
$307$	34.2757	−	34.2757i	0.111647	−	0.111647i	−0.649076	−	0.760723i	$-0.724844\pi$
$307$	34.2757	−	34.2757i	0.111647	−	0.111647i	0.760723	+	0.649076i	$0.224844\pi$
$308$		0			0
$309$	−98.2316	+	31.9174i	−0.317902	+	0.103292i
$310$		0			0
$311$	−2.87053	+	8.83457i	−0.00922999	+	0.0284070i	−0.955565	−	0.294779i	$-0.904754\pi$
$311$	−2.87053	+	8.83457i	−0.00922999	+	0.0284070i	0.946335	+	0.323186i	$0.104754\pi$
$312$		0			0
$313$	−176.957	+	347.297i	−0.565357	+	1.10958i	0.414532	+	0.910035i	$0.363945\pi$
$313$	−176.957	+	347.297i	−0.565357	+	1.10958i	−0.979889	+	0.199542i	$0.936055\pi$
$314$		0			0
$315$	−3.45986	+	2.46153i	−0.0109837	+	0.00781439i
$316$		0			0
$317$	1.25470	−	7.92188i	0.00395805	−	0.0249902i	−0.985630	−	0.168917i	$-0.945973\pi$
$317$	1.25470	−	7.92188i	0.00395805	−	0.0249902i	0.989588	+	0.143927i	$0.0459730\pi$
$318$		0			0
$319$	−404.608	−	556.895i	−1.26836	−	1.74575i
$320$		0			0
$321$	410.697	+	298.389i	1.27943	+	0.929561i
$322$		0			0
$323$	−234.188	+	119.325i	−0.725042	+	0.369427i
$324$		0			0
$325$	432.980	−	59.7748i	1.33225	−	0.183922i
$326$		0			0
$327$	−114.237	−	224.202i	−0.349348	−	0.685634i
$328$		0			0
$329$	−54.2930	+	74.7279i	−0.165024	+	0.227137i
$330$		0			0
$331$	82.0000	−	59.5765i	0.247734	−	0.179989i	−0.456988	−	0.889473i	$-0.651072\pi$
$331$	82.0000	−	59.5765i	0.247734	−	0.179989i	0.704722	+	0.709483i	$0.251072\pi$
$332$		0			0
$333$	−1.57127	−	0.248865i	−0.00471853	−	0.000747342i
$334$		0			0
$335$	−336.212	+	453.207i	−1.00362	+	1.35286i
$336$		0			0
$337$	99.1082	+	50.4981i	0.294090	+	0.149846i	0.594810	−	0.803866i	$-0.297227\pi$
$337$	99.1082	+	50.4981i	0.294090	+	0.149846i	−0.300721	+	0.953712i	$0.597227\pi$
$338$		0			0
$339$	358.917	+	116.619i	1.05875	+	0.344010i
$340$		0			0
$341$	−20.9237	−	64.3965i	−0.0613598	−	0.188846i
$342$		0			0
$343$	−138.805	−	138.805i	−0.404678	−	0.404678i
$344$		0			0
$345$	−81.6691	−	551.057i	−0.236722	−	1.59727i
$346$		0			0
$347$	−345.287	+	54.6880i	−0.995062	+	0.157602i	−0.632669	−	0.774423i	$-0.718040\pi$
$347$	−345.287	+	54.6880i	−0.995062	+	0.157602i	−0.362394	+	0.932025i	$0.618040\pi$
$348$		0			0
$349$			197.357i			0.565491i	0.959195	+	0.282746i	$0.0912453\pi$
$349$			197.357i			0.565491i	−0.959195	+	0.282746i	$0.908755\pi$
$350$		0			0
$351$	−474.584			−1.35209
$352$		0			0
$353$	73.3022	+	462.812i	0.207655	+	1.31108i	0.842606	+	0.538530i	$0.181020\pi$
$353$	73.3022	+	462.812i	0.207655	+	1.31108i	−0.634951	+	0.772552i	$0.718980\pi$
$354$		0			0
$355$	35.0159	+	70.4461i	0.0986364	+	0.198440i
$356$		0			0
$357$	−458.573	+	458.573i	−1.28452	+	1.28452i
$358$		0			0
$359$	−173.385	+	56.3363i	−0.482967	+	0.156926i	−0.540373	−	0.841425i	$-0.681717\pi$
$359$	−173.385	+	56.3363i	−0.482967	+	0.156926i	0.0574061	+	0.998351i	$0.481717\pi$
$360$		0			0
$361$	77.4886	−	238.485i	0.214650	−	0.660624i
$362$		0			0
$363$	−105.475	+	207.007i	−0.290565	+	0.570267i
$364$		0			0
$365$	−190.612	−	1.89594i	−0.522225	−	0.00519437i
$366$		0			0
$367$	81.0178	−	511.526i	0.220757	−	1.39380i	−0.589518	−	0.807755i	$-0.700682\pi$
$367$	81.0178	−	511.526i	0.220757	−	1.39380i	0.810275	−	0.586050i	$-0.199318\pi$
$368$		0			0
$369$	−4.19001	−	5.76706i	−0.0113550	−	0.0156289i
$370$		0			0
$371$	−174.718	−	126.940i	−0.470939	−	0.342157i
$372$		0			0
$373$	496.143	−	252.798i	1.33014	−	0.677741i	0.362955	−	0.931807i	$-0.381768\pi$
$373$	496.143	−	252.798i	1.33014	−	0.677741i	0.967187	+	0.254065i	$0.0817678\pi$
$374$		0			0
$375$	357.984	−	104.616i	0.954623	−	0.278977i
$376$		0			0
$377$	−387.444	−	760.401i	−1.02770	−	2.01698i
$378$		0			0
$379$	236.906	−	326.073i	0.625081	−	0.860350i	−0.372630	−	0.927980i	$-0.621544\pi$
$379$	236.906	−	326.073i	0.625081	−	0.860350i	0.997710	+	0.0676303i	$0.0215438\pi$
$380$		0			0
$381$	−129.046	+	93.7576i	−0.338704	+	0.246083i
$382$		0			0
$383$	−3.35701	−	0.531698i	−0.00876503	−	0.00138824i	0.152050	−	0.988373i	$-0.451412\pi$
$383$	−3.35701	−	0.531698i	−0.00876503	−	0.00138824i	−0.160815	+	0.986984i	$0.551412\pi$
$384$		0			0
$385$	−6.08932	+	612.201i	−0.0158164	+	1.59013i
$386$		0			0
$387$	−0.284322	−	0.144869i	−0.000734682	−	0.000374339i
$388$		0			0
$389$	705.338	+	229.178i	1.81321	+	0.589147i	0.999974	+	0.00721160i	$0.00229554\pi$
$389$	705.338	+	229.178i	1.81321	+	0.589147i	0.813235	+	0.581936i	$0.197704\pi$
$390$		0			0
$391$	288.862	+	889.025i	0.738777	+	2.27372i
$392$		0			0
$393$	300.715	+	300.715i	0.765178	+	0.765178i
$394$		0			0
$395$	−224.163	+	111.422i	−0.567500	+	0.282081i
$396$		0			0
$397$	657.538	−	104.144i	1.65627	−	0.262327i	0.742881	−	0.669423i	$-0.233459\pi$
$397$	657.538	−	104.144i	1.65627	−	0.262327i	0.913385	+	0.407096i	$0.133459\pi$
$398$		0			0
$399$			272.010i			0.681730i
$400$		0			0
$401$	184.383			0.459808			0.229904	−	0.973213i	$-0.426159\pi$
$401$	184.383			0.459808			0.229904	+	0.973213i	$0.426159\pi$
$402$		0			0
$403$	−13.1321	−	82.9129i	−0.0325859	−	0.205739i
$404$		0			0
$405$	−396.223	+	58.7220i	−0.978329	+	0.144993i
$406$		0			0
$407$	−162.194	+	162.194i	−0.398512	+	0.398512i
$408$		0			0
$409$	−213.899	+	69.5001i	−0.522981	+	0.169927i	−0.558598	−	0.829439i	$-0.688660\pi$
$409$	−213.899	+	69.5001i	−0.522981	+	0.169927i	0.0356168	+	0.999366i	$0.488660\pi$
$410$		0			0
$411$	167.275	−	514.819i	0.406994	−	1.25260i
$412$		0			0
$413$	18.1667	−	35.6542i	0.0439873	−	0.0863299i
$414$		0			0
$415$	508.420	+	377.171i	1.22511	+	0.908847i
$416$		0			0
$417$	9.65789	−	60.9775i	0.0231604	−	0.146229i
$418$		0			0
$419$	−51.9496	−	71.5026i	−0.123985	−	0.170650i	0.742512	−	0.669832i	$-0.233634\pi$
$419$	−51.9496	−	71.5026i	−0.123985	−	0.170650i	−0.866497	+	0.499182i	$0.833634\pi$
$420$		0			0
$421$	−218.306	−	158.608i	−0.518540	−	0.376742i	0.297513	−	0.954718i	$-0.403843\pi$
$421$	−218.306	−	158.608i	−0.518540	−	0.376742i	−0.816054	+	0.577976i	$0.803843\pi$
$422$		0			0
$423$	0.927052	−	0.472356i	0.00219161	−	0.00111668i
$424$		0			0
$425$	−563.153	+	272.970i	−1.32507	+	0.642282i
$426$		0			0
$427$	205.988	+	404.275i	0.482408	+	0.946779i
$428$		0			0
$429$	−432.391	+	595.135i	−1.00790	+	1.38726i
$430$		0			0
$431$	559.142	−	406.241i	1.29731	−	0.942554i	0.297389	−	0.954756i	$-0.403884\pi$
$431$	559.142	−	406.241i	1.29731	−	0.942554i	0.999926	+	0.0122025i	$0.00388428\pi$
$432$		0			0
$433$	180.999	+	28.6674i	0.418011	+	0.0662065i	0.361898	−	0.932218i	$-0.382129\pi$
$433$	180.999	+	28.6674i	0.418011	+	0.0662065i	0.0561139	+	0.998424i	$0.482129\pi$
$434$		0			0
$435$	−422.146	−	593.357i	−0.970451	−	1.36404i
$436$		0			0
$437$	349.341	+	177.998i	0.799408	+	0.407319i
$438$		0			0
$439$	−474.438	−	154.154i	−1.08073	−	0.351149i	−0.286069	−	0.958209i	$-0.592349\pi$
$439$	−474.438	−	154.154i	−1.08073	−	0.351149i	−0.794656	+	0.607060i	$0.792349\pi$
$440$		0			0
$441$	−0.797668	−	2.45497i	−0.00180877	−	0.00556682i
$442$		0			0
$443$	59.9191	+	59.9191i	0.135258	+	0.135258i	0.771494	−	0.636237i	$-0.219510\pi$
$443$	59.9191	+	59.9191i	0.135258	+	0.135258i	−0.636237	+	0.771494i	$0.719510\pi$
$444$		0			0
$445$	−180.918	−	184.553i	−0.406557	−	0.414726i
$446$		0			0
$447$	−64.4557	+	10.2088i	−0.144196	+	0.0228384i
$448$		0			0
$449$			850.267i			1.89369i	0.321691	+	0.946845i	$0.395749\pi$
$449$			850.267i			1.89369i	−0.321691	+	0.946845i	$0.604251\pi$
$450$		0			0
$451$	−1027.82			−2.27898
$452$		0			0
$453$	−103.191	−	651.522i	−0.227795	−	1.43824i
$454$		0			0
$455$	−126.190	+	748.471i	−0.277340	+	1.64499i
$456$		0			0
$457$	−477.329	+	477.329i	−1.04448	+	1.04448i	−0.0455205	+	0.998963i	$0.514495\pi$
$457$	−477.329	+	477.329i	−1.04448	+	1.04448i	−0.998963	+	0.0455205i	$0.985505\pi$
$458$		0			0
$459$	646.254	−	209.981i	1.40796	−	0.457474i
$460$		0			0
$461$	192.848	−	593.524i	0.418324	−	1.28747i	−0.490919	−	0.871205i	$-0.663339\pi$
$461$	192.848	−	593.524i	0.418324	−	1.28747i	0.909243	−	0.416265i	$-0.136661\pi$
$462$		0			0
$463$	−18.0901	+	35.5039i	−0.0390715	+	0.0766822i	−0.909717	−	0.415229i	$-0.863701\pi$
$463$	−18.0901	+	35.5039i	−0.0390715	+	0.0766822i	0.870645	+	0.491911i	$0.163701\pi$
$464$		0			0
$465$	−21.4561	−	68.3407i	−0.0461422	−	0.146969i
$466$		0			0
$467$	−59.9564	+	378.550i	−0.128386	+	0.810599i	0.836507	+	0.547957i	$0.184594\pi$
$467$	−59.9564	+	378.550i	−0.128386	+	0.810599i	−0.964893	+	0.262643i	$0.915406\pi$
$468$		0			0
$469$	−576.000	−	792.797i	−1.22815	−	1.69040i
$470$		0			0
$471$	338.367	+	245.838i	0.718401	+	0.521949i
$472$		0			0
$473$	−40.9949	+	20.8880i	−0.0866701	+	0.0441606i
$474$		0			0
$475$	−86.0636	+	247.980i	−0.181187	+	0.522064i
$476$		0			0
$477$	1.10440	+	2.16750i	0.00231530	+	0.00454403i
$478$		0			0
$479$	−522.277	+	718.853i	−1.09035	+	1.50074i	−0.242759	+	0.970087i	$0.578053\pi$
$479$	−522.277	+	718.853i	−1.09035	+	1.50074i	−0.847590	+	0.530651i	$0.821947\pi$
$480$		0			0
$481$	−230.067	+	167.154i	−0.478310	+	0.347513i
$482$		0			0
$483$	955.495	+	151.335i	1.97825	+	0.313324i
$484$		0			0
$485$	−27.4212	−	9.21221i	−0.0565386	−	0.0189942i
$486$		0			0
$487$	193.896	+	98.7949i	0.398143	+	0.202864i	0.641586	−	0.767051i	$-0.278277\pi$
$487$	193.896	+	98.7949i	0.398143	+	0.202864i	−0.243443	+	0.969915i	$0.578277\pi$
$488$		0			0
$489$	−594.618	−	193.203i	−1.21599	−	0.395098i
$490$		0			0
$491$	−184.760	−	568.634i	−0.376294	−	1.15811i	−0.942601	−	0.333920i	$-0.891628\pi$
$491$	−184.760	−	568.634i	−0.376294	−	1.15811i	0.566307	−	0.824194i	$-0.308372\pi$
$492$		0			0
$493$	864.033	+	864.033i	1.75260	+	1.75260i
$494$		0			0
$495$	3.19179	−	6.11317i	0.00644807	−	0.0123498i
$496$		0			0
$497$	−134.932	+	21.3712i	−0.271493	+	0.0430003i
$498$		0			0
$499$			748.723i			1.50045i	0.661185	+	0.750223i	$0.270054\pi$
$499$			748.723i			1.50045i	−0.661185	+	0.750223i	$0.729946\pi$
$500$		0			0
$501$	217.213			0.433559
$502$		0			0
$503$	87.1263	+	550.094i	0.173213	+	1.09363i	0.909117	+	0.416540i	$0.136758\pi$
$503$	87.1263	+	550.094i	0.173213	+	1.09363i	−0.735904	+	0.677086i	$0.763242\pi$
$504$		0			0
$505$	362.963	+	189.509i	0.718738	+	0.375266i
$506$		0			0
$507$	−288.345	+	288.345i	−0.568728	+	0.568728i
$508$		0			0
$509$	−155.728	+	50.5990i	−0.305949	+	0.0994087i	−0.457968	−	0.888969i	$-0.651422\pi$
$509$	−155.728	+	50.5990i	−0.305949	+	0.0994087i	0.152019	+	0.988378i	$0.451422\pi$
$510$		0			0
$511$	102.293	−	314.827i	0.200183	−	0.616100i
$512$		0			0
$513$	129.391	−	253.945i	0.252225	−	0.495019i
$514$		0			0
$515$	55.1217	−	164.076i	0.107032	−	0.318594i
$516$		0			0
$517$	23.4680	−	148.171i	0.0453926	−	0.286598i
$518$		0			0
$519$	473.932	+	652.311i	0.913163	+	1.25686i
$520$		0			0
$521$	−675.755	−	490.965i	−1.29703	−	0.942350i	−0.297112	−	0.954843i	$-0.596023\pi$
$521$	−675.755	−	490.965i	−1.29703	−	0.942350i	−0.999922	+	0.0124923i	$0.996023\pi$
$522$		0			0
$523$	334.987	−	170.684i	0.640510	−	0.326356i	−0.103396	−	0.994640i	$-0.532971\pi$
$523$	334.987	−	170.684i	0.640510	−	0.326356i	0.743906	+	0.668284i	$0.232971\pi$
$524$		0			0
$525$	−12.8829	+	647.540i	−0.0245389	+	1.23341i
$526$		0			0
$527$	54.5673	+	107.094i	0.103543	+	0.203215i
$528$		0			0
$529$	508.679	−	700.136i	0.961585	−	1.32351i
$530$		0			0
$531$	−0.364658	+	0.264940i	−0.000686739	+	0.000498945i
$532$		0			0
$533$	−1258.59	−	199.340i	−2.36132	−	0.373997i
$534$		0			0
$535$	−811.656	+	254.826i	−1.51711	+	0.476310i
$536$		0			0
$537$	167.849	+	85.5231i	0.312567	+	0.159261i
$538$		0			0
$539$	−353.970	−	115.012i	−0.656716	−	0.213380i
$540$		0			0
$541$	173.342	+	533.491i	0.320410	+	0.986120i	0.973470	+	0.228814i	$0.0734849\pi$
$541$	173.342	+	533.491i	0.320410	+	0.986120i	−0.653060	+	0.757306i	$0.726515\pi$
$542$		0			0
$543$	−95.5226	−	95.5226i	−0.175916	−	0.175916i
$544$		0			0
$545$	415.809	+	70.1041i	0.762953	+	0.128631i
$546$		0			0
$547$	−251.270	+	39.7972i	−0.459360	+	0.0727554i	−0.381826	−	0.924234i	$-0.624705\pi$
$547$	−251.270	+	39.7972i	−0.459360	+	0.0727554i	−0.0775338	+	0.996990i	$0.524705\pi$
$548$		0			0
$549$		−	5.11086i		−	0.00930939i
$550$		0			0
$551$	512.516			0.930155
$552$		0			0
$553$	−68.0040	−	429.360i	−0.122973	−	0.776420i
$554$		0			0
$555$	−173.281	+	169.867i	−0.312217	+	0.306067i
$556$		0			0
$557$	14.5377	−	14.5377i	0.0260999	−	0.0260999i	−0.693936	−	0.720036i	$-0.744125\pi$
$557$	14.5377	−	14.5377i	0.0260999	−	0.0260999i	0.720036	+	0.693936i	$0.244125\pi$
$558$		0			0
$559$	−54.2502	+	17.6270i	−0.0970487	+	0.0315330i
$560$		0			0
$561$	325.480	−	1001.72i	0.580178	−	1.78560i
$562$		0			0
$563$	118.820	−	233.197i	0.211048	−	0.414205i	−0.761079	−	0.648659i	$-0.775330\pi$
$563$	118.820	−	233.197i	0.211048	−	0.414205i	0.972127	+	0.234454i	$0.0753303\pi$
$564$		0			0
$565$	−515.315	+	366.623i	−0.912062	+	0.648891i
$566$		0			0
$567$	108.814	−	687.023i	0.191911	−	1.21168i
$568$		0			0
$569$	501.574	+	690.358i	0.881501	+	1.21328i	0.976003	+	0.217758i	$0.0698743\pi$
$569$	501.574	+	690.358i	0.881501	+	1.21328i	−0.0945015	+	0.995525i	$0.530126\pi$
$570$		0			0
$571$	−856.531	−	622.306i	−1.50005	−	1.08985i	−0.970360	−	0.241665i	$-0.922307\pi$
$571$	−856.531	−	622.306i	−1.50005	−	1.08985i	−0.529695	−	0.848188i	$-0.677693\pi$
$572$		0			0
$573$	658.197	−	335.368i	1.14869	−	0.585284i
$574$		0			0
$575$	823.201	+	440.283i	1.43165	+	0.765710i
$576$		0			0
$577$	−24.4027	−	47.8930i	−0.0422924	−	0.0830035i	0.868893	−	0.494999i	$-0.164832\pi$
$577$	−24.4027	−	47.8930i	−0.0422924	−	0.0830035i	−0.911186	+	0.411996i	$0.864832\pi$
$578$		0			0
$579$	−298.956	+	411.478i	−0.516332	+	0.710671i
$580$		0			0
$581$	−889.381	+	646.173i	−1.53078	+	1.11217i
$582$		0			0
$583$	346.433	+	54.8695i	0.594224	+	0.0941158i
$584$		0			0
$585$	5.09403	−	6.86666i	0.00870775	−	0.0117379i
$586$		0			0
$587$	−594.923	−	303.128i	−1.01350	−	0.516403i	−0.133333	−	0.991071i	$-0.542568\pi$
$587$	−594.923	−	303.128i	−1.01350	−	0.516403i	−0.880165	+	0.474669i	$0.842568\pi$
$588$		0			0
$589$	47.9462	+	15.5787i	0.0814027	+	0.0264493i
$590$		0			0
$591$	334.273	+	1028.79i	0.565606	+	1.74076i
$592$		0			0
$593$	−252.848	−	252.848i	−0.426388	−	0.426388i	0.461008	−	0.887396i	$-0.347488\pi$
$593$	−252.848	−	252.848i	−0.426388	−	0.426388i	−0.887396	+	0.461008i	$0.847488\pi$
$594$		0			0
$595$	−159.327	−	1075.05i	−0.267776	−	1.80680i
$596$		0			0
$597$	77.7609	−	12.3161i	0.130253	−	0.0206300i
$598$		0			0
$599$			13.3819i			0.0223403i	0.999938	+	0.0111702i	$0.00355565\pi$
$599$			13.3819i			0.0223403i	−0.999938	+	0.0111702i	$0.996444\pi$
$600$		0			0
$601$	535.193			0.890504			0.445252	−	0.895405i	$-0.353114\pi$
$601$	535.193			0.890504			0.445252	+	0.895405i	$0.353114\pi$
$602$		0			0
$603$	1.72677	+	10.9024i	0.00286363	+	0.0180803i
$604$		0			0
$605$	−173.296	−	348.642i	−0.286440	−	0.576268i
$606$		0			0
$607$	542.463	−	542.463i	0.893679	−	0.893679i	−0.101188	−	0.994867i	$-0.532264\pi$
$607$	542.463	−	542.463i	0.893679	−	0.893679i	0.994867	+	0.101188i	$0.0322643\pi$
$608$		0			0
$609$	1202.69	−	390.777i	1.97485	−	0.641669i
$610$		0			0
$611$	57.4740	−	176.887i	0.0940655	−	0.289504i
$612$		0			0
$613$	−323.248	+	634.410i	−0.527321	+	1.03493i	0.461684	+	0.887045i	$0.347246\pi$
$613$	−323.248	+	634.410i	−0.527321	+	1.03493i	−0.989005	+	0.147882i	$0.952754\pi$
$614$		0			0
$615$	−1087.26	−	10.8145i	−1.76790	−	0.0175846i
$616$		0			0
$617$	14.7128	−	92.8930i	0.0238457	−	0.150556i	−0.972893	−	0.231257i	$-0.925716\pi$
$617$	14.7128	−	92.8930i	0.0238457	−	0.150556i	0.996738	+	0.0807015i	$0.0257160\pi$
$618$		0			0
$619$	−70.1520	−	96.5560i	−0.113331	−	0.155987i	0.748583	−	0.663041i	$-0.230734\pi$
$619$	−70.1520	−	96.5560i	−0.113331	−	0.155987i	−0.861914	+	0.507054i	$0.830734\pi$
$620$		0			0
$621$	−820.047	−	595.799i	−1.32053	−	0.959419i
$622$		0			0
$623$	399.884	−	203.751i	0.641868	−	0.327048i
$624$		0			0
$625$	−216.625	+	586.258i	−0.346600	+	0.938013i
$626$		0			0
$627$	−200.563	−	393.626i	−0.319877	−	0.627793i
$628$		0			0
$629$	239.331	−	329.411i	0.380495	−	0.523706i
$630$		0			0
$631$	−215.487	+	156.560i	−0.341501	+	0.248115i	−0.745295	−	0.666735i	$-0.767691\pi$
$631$	−215.487	+	156.560i	−0.341501	+	0.248115i	0.403794	+	0.914850i	$0.367691\pi$
$632$		0			0
$633$	−37.6932	−	5.97002i	−0.0595469	−	0.00943131i
$634$		0			0
$635$	2.65866	−	267.293i	0.00418686	−	0.420934i
$636$		0			0
$637$	−411.137	−	209.485i	−0.645427	−	0.328862i
$638$		0			0
$639$	1.46352	+	0.475528i	0.00229034	+	0.000744175i
$640$		0			0
$641$	−185.129	−	569.768i	−0.288813	−	0.888874i	−0.985230	−	0.171237i	$-0.945224\pi$
$641$	−185.129	−	569.768i	−0.288813	−	0.888874i	0.696417	−	0.717637i	$-0.254776\pi$
$642$		0			0
$643$	−56.2615	−	56.2615i	−0.0874985	−	0.0874985i	0.662003	−	0.749501i	$-0.269707\pi$
$643$	−56.2615	−	56.2615i	−0.0874985	−	0.0874985i	−0.749501	+	0.662003i	$0.769707\pi$
$644$		0			0
$645$	−43.5854	+	21.6645i	−0.0675743	+	0.0335884i
$646$		0			0
$647$	32.3407	−	5.12227i	0.0499856	−	0.00791695i	−0.131392	−	0.991331i	$-0.541945\pi$
$647$	32.3407	−	5.12227i	0.0499856	−	0.00791695i	0.181377	+	0.983414i	$0.441945\pi$
$648$		0			0
$649$			64.9903i			0.100139i
$650$		0			0
$651$	124.390			0.191076
$652$		0			0
$653$	82.7103	+	522.212i	0.126662	+	0.799712i	0.966461	+	0.256814i	$0.0826729\pi$
$653$	82.7103	+	522.212i	0.126662	+	0.799712i	−0.839799	+	0.542898i	$0.817327\pi$
$654$		0			0
$655$	−704.974	+	104.480i	−1.07630	+	0.159512i
$656$		0			0
$657$	−2.63663	+	2.63663i	−0.00401313	+	0.00401313i
$658$		0			0
$659$	−76.2499	+	24.7751i	−0.115705	+	0.0375950i	−0.366297	−	0.930498i	$-0.619375\pi$
$659$	−76.2499	+	24.7751i	−0.115705	+	0.0375950i	0.250592	+	0.968093i	$0.419375\pi$
$660$		0			0
$661$	−99.9847	+	307.721i	−0.151263	+	0.465539i	−0.997763	−	0.0668493i	$-0.978705\pi$
$661$	−99.9847	+	307.721i	−0.151263	+	0.465539i	0.846500	+	0.532388i	$0.178705\pi$
$662$		0			0
$663$	592.836	−	1163.51i	0.894172	−	1.75491i
$664$		0			0
$665$	−366.094	−	271.587i	−0.550518	−	0.408402i
$666$		0			0
$667$	285.143	−	1800.32i	0.427501	−	2.69913i
$668$		0			0
$669$	267.087	+	367.613i	0.399232	+	0.549496i
$670$		0			0
$671$	−596.172	−	433.144i	−0.888483	−	0.645520i
$672$		0			0
$673$	−253.655	+	129.244i	−0.376902	+	0.192041i	−0.632171	−	0.774829i	$-0.717836\pi$
$673$	−253.655	+	129.244i	−0.376902	+	0.192041i	0.255269	+	0.966870i	$0.417836\pi$
$674$		0			0
$675$	320.052	−	598.405i	0.474152	−	0.886526i
$676$		0			0
$677$	−278.550	−	546.686i	−0.411448	−	0.807513i	0.588551	−	0.808460i	$-0.299699\pi$
$677$	−278.550	−	546.686i	−0.411448	−	0.807513i	−1.00000		0.000947157i	$0.999699\pi$
$678$		0			0
$679$	29.5270	−	40.6405i	0.0434861	−	0.0598534i
$680$		0			0
$681$	−550.631	+	400.057i	−0.808562	+	0.587455i
$682$		0			0
$683$	1165.34	+	184.571i	1.70620	+	0.270236i	0.931936	−	0.362623i	$-0.118119\pi$
$683$	1165.34	+	184.571i	1.70620	+	0.270236i	0.774267	+	0.632859i	$0.218119\pi$
$684$		0			0
$685$	525.872	+	739.150i	0.767696	+	1.07905i
$686$		0			0
$687$	677.509	+	345.208i	0.986184	+	0.502486i
$688$		0			0
$689$	413.572	+	134.378i	0.600250	+	0.195033i
$690$		0			0
$691$	337.184	+	1037.75i	0.487965	+	1.50180i	0.827640	+	0.561260i	$0.189683\pi$
$691$	337.184	+	1037.75i	0.487965	+	1.50180i	−0.339674	+	0.940543i	$0.610317\pi$
$692$		0			0
$693$	8.46822	+	8.46822i	0.0122197	+	0.0122197i
$694$		0			0
$695$	72.4258	+	73.8811i	0.104210	+	0.106304i
$696$		0			0
$697$	1802.05	−	285.416i	2.58544	−	0.409493i
$698$		0			0
$699$			313.765i			0.448877i
$700$		0			0
$701$	217.046			0.309623			0.154812	−	0.987944i	$-0.450523\pi$
$701$	217.046			0.309623			0.154812	+	0.987944i	$0.450523\pi$
$702$		0			0
$703$	−26.7162	−	168.680i	−0.0380031	−	0.239942i
$704$		0			0
$705$	26.3841	−	156.493i	0.0374243	−	0.221975i
$706$		0			0
$707$	−502.792	+	502.792i	−0.711162	+	0.711162i
$708$		0			0
$709$	103.524	−	33.6371i	0.146015	−	0.0474430i	−0.235098	−	0.971972i	$-0.575541\pi$
$709$	103.524	−	33.6371i	0.146015	−	0.0474430i	0.381112	+	0.924529i	$0.375541\pi$
$710$		0			0
$711$	−1.51315	+	4.65700i	−0.00212820	+	0.00654993i
$712$		0			0
$713$	81.3987	−	159.754i	0.114164	−	0.224059i
$714$		0			0
$715$	−369.265	−	1176.16i	−0.516454	−	1.64498i
$716$		0			0
$717$	102.102	−	644.648i	0.142402	−	0.899091i
$718$		0			0
$719$	572.847	+	788.457i	0.796728	+	1.09660i	0.993238	+	0.116100i	$0.0370394\pi$
$719$	572.847	+	788.457i	0.796728	+	1.09660i	−0.196509	+	0.980502i	$0.562961\pi$
$720$		0			0
$721$	243.174	+	176.676i	0.337274	+	0.245044i
$722$		0			0
$723$	−383.253	+	195.277i	−0.530088	+	0.270093i
$724$		0			0
$725$	1220.08	+	24.2737i	1.68287	+	0.0334810i
$726$		0			0
$727$	−535.940	−	1051.84i	−0.737193	−	1.44682i	−0.888758	−	0.458376i	$-0.848431\pi$
$727$	−535.940	−	1051.84i	−0.737193	−	1.44682i	0.151565	−	0.988447i	$-0.451569\pi$
$728$		0			0
$729$	−433.050	+	596.043i	−0.594033	+	0.817617i
$730$		0			0
$731$	66.0749	−	48.0062i	0.0903898	−	0.0656720i
$732$		0			0
$733$	1027.27	+	162.703i	1.40145	+	0.221969i	0.810974	−	0.585083i	$-0.198938\pi$
$733$	1027.27	+	162.703i	1.40145	+	0.221969i	0.590481	+	0.807051i	$0.298938\pi$
$734$		0			0
$735$	−373.229	−	125.387i	−0.507795	−	0.170595i
$736$		0			0
$737$	1418.09	+	722.552i	1.92414	+	0.980396i
$738$		0			0
$739$	878.092	+	285.309i	1.18822	+	0.386075i	0.835413	−	0.549623i	$-0.185228\pi$
$739$	878.092	+	285.309i	1.18822	+	0.386075i	0.352803	+	0.935697i	$0.385228\pi$
$740$		0			0
$741$	−169.251	−	520.902i	−0.228409	−	0.702971i
$742$		0			0
$743$	283.985	+	283.985i	0.382213	+	0.382213i	0.871899	−	0.489686i	$-0.162888\pi$
$743$	283.985	+	283.985i	0.382213	+	0.382213i	−0.489686	+	0.871899i	$0.662888\pi$
$744$		0			0
$745$	50.6156	−	96.9428i	0.0679404	−	0.130125i
$746$		0			0
$747$	12.2306	−	1.93714i	0.0163730	−	0.00259322i
$748$		0			0
$749$		−	1477.34i		−	1.97241i
$750$		0			0
$751$	922.621			1.22852			0.614262	−	0.789102i	$-0.289454\pi$
$751$	922.621			1.22852			0.614262	+	0.789102i	$0.289454\pi$
$752$		0			0
$753$	49.6837	+	313.691i	0.0659810	+	0.416588i
$754$		0			0
$755$	979.904	+	511.626i	1.29789	+	0.677650i
$756$		0			0
$757$	694.630	−	694.630i	0.917609	−	0.917609i	−0.0792459	−	0.996855i	$-0.525251\pi$
$757$	694.630	−	694.630i	0.917609	−	0.917609i	0.996855	+	0.0792459i	$0.0252512\pi$
$758$		0			0
$759$	−1494.28	+	485.522i	−1.96875	+	0.639686i
$760$		0			0
$761$	−240.628	+	740.577i	−0.316200	+	0.973163i	0.659058	+	0.752092i	$0.270955\pi$
$761$	−240.628	+	740.577i	−0.316200	+	0.973163i	−0.975258	+	0.221071i	$0.929045\pi$
$762$		0			0
$763$	−332.446	+	652.462i	−0.435709	+	0.855127i
$764$		0			0
$765$	−3.89852	+	11.6044i	−0.00509610	+	0.0151691i
$766$		0			0
$767$	−12.6045	+	79.5819i	−0.0164336	+	0.103757i
$768$		0			0
$769$	166.219	+	228.781i	0.216149	+	0.297504i	0.903299	−	0.429012i	$-0.141138\pi$
$769$	166.219	+	228.781i	0.216149	+	0.297504i	−0.687149	+	0.726516i	$0.741138\pi$
$770$		0			0
$771$	−797.679	−	579.548i	−1.03460	−	0.751683i
$772$		0			0
$773$	−562.929	+	286.826i	−0.728239	+	0.371056i	−0.778470	−	0.627681i	$-0.784004\pi$
$773$	−562.929	+	286.826i	−0.728239	+	0.371056i	0.0502316	+	0.998738i	$0.484004\pi$
$774$		0			0
$775$	113.401	+	39.3569i	0.146324	+	0.0507831i
$776$		0			0
$777$	−191.306	−	375.459i	−0.246211	−	0.483216i
$778$		0			0
$779$	449.808	−	619.107i	0.577417	−	0.794746i
$780$		0			0
$781$	179.503	−	130.417i	0.229837	−	0.166987i
$782$		0			0
$783$	−1308.70	−	207.277i	−1.67139	−	0.264722i
$784$		0			0
$785$	−668.710	+	209.947i	−0.851860	+	0.267449i
$786$		0			0
$787$	779.064	+	396.953i	0.989916	+	0.504388i	0.872457	−	0.488690i	$-0.162525\pi$
$787$	779.064	+	396.953i	0.989916	+	0.504388i	0.117459	+	0.993078i	$0.462525\pi$
$788$		0			0
$789$	−67.5294	−	21.9416i	−0.0855885	−	0.0278094i
$790$		0			0
$791$	−339.380	−	1044.50i	−0.429051	−	1.32048i
$792$		0			0
$793$	−646.018	−	646.018i	−0.814651	−	0.814651i
$794$		0			0
$795$	365.889	+	61.6877i	0.460238	+	0.0775945i
$796$		0			0
$797$	1343.31	−	212.760i	1.68546	−	0.266951i	0.761145	−	0.648582i	$-0.224638\pi$
$797$	1343.31	−	212.760i	1.68546	−	0.266951i	0.924314	+	0.381632i	$0.124638\pi$
$798$		0			0
$799$			266.301i			0.333293i
$800$		0			0
$801$	−5.05534			−0.00631129
$802$		0			0
$803$	84.1039	+	531.011i	0.104737	+	0.661284i
$804$		0			0
$805$	−1157.69	+	1134.89i	−1.43812	+	1.40980i
$806$		0			0
$807$	64.5137	−	64.5137i	0.0799426	−	0.0799426i
$808$		0			0
$809$	−1194.42	+	388.089i	−1.47641	+	0.479715i	−0.933038	−	0.359778i	$-0.882853\pi$
$809$	−1194.42	+	388.089i	−1.47641	+	0.479715i	−0.543372	+	0.839492i	$0.682853\pi$
$810$		0			0
$811$	−247.722	+	762.411i	−0.305453	+	0.940087i	0.674055	+	0.738681i	$0.264551\pi$
$811$	−247.722	+	762.411i	−0.305453	+	0.940087i	−0.979508	+	0.201406i	$0.935449\pi$
$812$		0			0
$813$	−637.788	+	1251.73i	−0.784487	+	1.53964i
$814$		0			0
$815$	853.722	−	607.384i	1.04751	−	0.745257i
$816$		0			0
$817$	5.35887	−	33.8346i	0.00655920	−	0.0414132i
$818$		0			0
$819$	8.72714	+	12.0119i	0.0106558	+	0.0146665i
$820$		0			0
$821$	−650.654	−	472.728i	−0.792514	−	0.575795i	0.116195	−	0.993226i	$-0.462930\pi$
$821$	−650.654	−	472.728i	−0.792514	−	0.575795i	−0.908708	+	0.417432i	$0.862930\pi$
$822$		0			0
$823$	−95.8032	+	48.8142i	−0.116407	+	0.0593125i	−0.511224	−	0.859447i	$-0.670808\pi$
$823$	−95.8032	+	48.8142i	−0.116407	+	0.0593125i	0.394817	+	0.918760i	$0.370808\pi$
$824$		0			0
$825$	−458.811	−	946.554i	−0.556134	−	1.14734i
$826$		0			0
$827$	−298.104	−	585.062i	−0.360464	−	0.707451i	0.637552	−	0.770407i	$-0.279947\pi$
$827$	−298.104	−	585.062i	−0.360464	−	0.707451i	−0.998016	+	0.0629564i	$0.979947\pi$
$828$		0			0
$829$	136.148	−	187.392i	0.164231	−	0.226045i	−0.718968	−	0.695044i	$-0.755385\pi$
$829$	136.148	−	187.392i	0.164231	−	0.226045i	0.883199	+	0.468998i	$0.155385\pi$
$830$		0			0
$831$	−402.612	+	292.515i	−0.484491	+	0.352003i
$832$		0			0
$833$	652.544	+	103.353i	0.783366	+	0.124073i
$834$		0			0
$835$	−216.875	+	292.344i	−0.259731	+	0.350113i
$836$		0			0
$837$	−116.129	−	59.1707i	−0.138744	−	0.0706937i
$838$		0			0
$839$	−20.2925	−	6.59343i	−0.0241865	−	0.00785867i	0.296899	−	0.954909i	$-0.404048\pi$
$839$	−20.2925	−	6.59343i	−0.0241865	−	0.00785867i	−0.321085	+	0.947050i	$0.604048\pi$
$840$		0			0
$841$	−476.409	−	1466.24i	−0.566479	−	1.74344i
$842$		0			0
$843$	1099.48	+	1099.48i	1.30425	+	1.30425i
$844$		0			0
$845$	−100.183	−	675.976i	−0.118559	−	0.799972i
$846$		0			0
$847$	667.788	−	105.767i	0.788416	−	0.124873i
$848$		0			0
$849$			585.019i			0.689068i
$850$		0			0
$851$	−607.387			−0.713733
$852$		0			0
$853$	−25.4120	−	160.445i	−0.0297913	−	0.188095i	0.968305	−	0.249771i	$-0.0803554\pi$
$853$	−25.4120	−	160.445i	−0.0297913	−	0.188095i	−0.998096	+	0.0616761i	$0.980355\pi$
$854$		0			0
$855$	2.28543	+	4.59790i	0.00267302	+	0.00537766i
$856$		0			0
$857$	−96.9589	+	96.9589i	−0.113138	+	0.113138i	−0.761409	−	0.648272i	$-0.775492\pi$
$857$	−96.9589	+	96.9589i	−0.113138	+	0.113138i	0.648272	+	0.761409i	$0.275492\pi$
$858$		0			0
$859$	652.308	−	211.948i	0.759380	−	0.246738i	0.0963676	−	0.995346i	$-0.469278\pi$
$859$	652.308	−	211.948i	0.759380	−	0.246738i	0.663013	+	0.748608i	$0.269278\pi$
$860$		0			0
$861$	583.485	−	1795.78i	0.677683	−	2.08569i
$862$		0			0
$863$	642.072	−	1260.14i	0.744000	−	1.46018i	−0.138743	−	0.990328i	$-0.544306\pi$
$863$	642.072	−	1260.14i	0.744000	−	1.46018i	0.882744	−	0.469855i	$-0.155694\pi$
$864$		0			0
$865$	−1351.13	−	13.4392i	−1.56200	−	0.0155366i
$866$		0			0
$867$	−157.595	+	995.019i	−0.181771	+	1.14766i
$868$		0			0
$869$	414.991	+	571.186i	0.477550	+	0.657291i
$870$		0			0
$871$	1596.34	+	1159.81i	1.83277	+	1.33158i
$872$		0			0
$873$	−0.504173	+	0.256889i	−0.000577518	+	0.000294260i
$874$		0			0
$875$	−858.650	−	663.871i	−0.981315	−	0.758710i
$876$		0			0
$877$	−133.555	−	262.116i	−0.152286	−	0.298878i	0.802242	−	0.596999i	$-0.203640\pi$
$877$	−133.555	−	262.116i	−0.152286	−	0.298878i	−0.954528	+	0.298121i	$0.903640\pi$
$878$		0			0
$879$	196.281	−	270.157i	0.223300	−	0.307346i
$880$		0			0
$881$	−709.759	+	515.670i	−0.805628	+	0.585323i	−0.912560	−	0.408943i	$-0.865897\pi$
$881$	−709.759	+	515.670i	−0.805628	+	0.585323i	0.106932	+	0.994266i	$0.465897\pi$
$882$		0			0
$883$	52.7586	+	8.35615i	0.0597493	+	0.00946336i	0.186238	−	0.982505i	$-0.440371\pi$
$883$	52.7586	+	8.35615i	0.0597493	+	0.00946336i	−0.126488	+	0.991968i	$0.540371\pi$
$884$		0			0
$885$	−0.683815	+	68.7486i	−0.000772673	+	0.0776820i
$886$		0			0
$887$	−623.575	−	317.728i	−0.703016	−	0.358205i	0.0656606	−	0.997842i	$-0.479085\pi$
$887$	−623.575	−	317.728i	−0.703016	−	0.358205i	−0.768677	+	0.639637i	$0.779085\pi$
$888$		0			0
$889$	441.478	+	143.445i	0.496601	+	0.161355i
$890$		0			0
$891$	349.102	+	1074.42i	0.391809	+	1.20586i
$892$		0			0
$893$	78.9805	+	78.9805i	0.0884440	+	0.0884440i
$894$		0			0
$895$	−282.692	+	140.515i	−0.315857	+	0.157000i
$896$		0			0
$897$	−1923.94	+	304.723i	−2.14486	+	0.339713i
$898$		0			0
$899$		−	234.373i		−	0.260705i
$900$		0			0
$901$	−622.628			−0.691041
$902$		0			0
$903$	−13.2225	−	83.4833i	−0.0146428	−	0.0924511i
$904$		0			0
$905$	223.936	−	33.1883i	0.247443	−	0.0366722i
$906$		0			0
$907$	−1045.28	+	1045.28i	−1.15246	+	1.15246i	−0.166402	+	0.986058i	$0.553215\pi$
$907$	−1045.28	+	1045.28i	−1.15246	+	1.15246i	−0.986058	+	0.166402i	$0.946785\pi$
$908$		0			0
$909$	7.61741	−	2.47505i	0.00837999	−	0.00272282i
$910$		0			0
$911$	−3.00555	+	9.25014i	−0.00329918	+	0.0101538i	−0.952693	−	0.303936i	$-0.901699\pi$
$911$	−3.00555	+	9.25014i	−0.00329918	+	0.0101538i	0.949393	+	0.314090i	$0.101699\pi$
$912$		0			0
$913$	810.578	−	1590.85i	0.887818	−	1.74244i
$914$		0			0
$915$	−626.090	−	464.465i	−0.684252	−	0.507612i
$916$		0			0
$917$	193.605	−	1222.38i	0.211129	−	1.33302i
$918$		0			0
$919$	−256.360	−	352.849i	−0.278955	−	0.383949i	0.646432	−	0.762972i	$-0.276260\pi$
$919$	−256.360	−	352.849i	−0.278955	−	0.383949i	−0.925388	+	0.379022i	$0.876260\pi$
$920$		0			0
$921$	−117.006	−	85.0098i	−0.127042	−	0.0923016i
$922$		0			0
$923$	245.099	−	124.884i	0.265546	−	0.135302i
$924$		0			0
$925$	−55.6108	−	402.819i	−0.0601198	−	0.435480i
$926$		0			0
$927$	−1.53711	−	3.01675i	−0.00165815	−	0.00325431i
$928$		0			0
$929$	418.877	−	576.535i	0.450891	−	0.620598i	−0.521698	−	0.853130i	$-0.674701\pi$
$929$	418.877	−	576.535i	0.450891	−	0.620598i	0.972589	+	0.232532i	$0.0747012\pi$
$930$		0			0
$931$	224.186	−	162.881i	0.240802	−	0.174953i
$932$		0			0
$933$	27.3746	+	4.33571i	0.0293404	+	0.00464706i
$934$		0			0
$935$	1023.23	+	1438.22i	1.09436	+	1.53821i
$936$		0			0
$937$	746.183	+	380.199i	0.796353	+	0.405762i	0.804313	−	0.594206i	$-0.202534\pi$
$937$	746.183	+	380.199i	0.796353	+	0.405762i	−0.00795957	+	0.999968i	$0.502534\pi$
$938$		0			0
$939$	1106.05	+	359.378i	1.17790	+	0.382724i
$940$		0			0
$941$	411.694	+	1267.06i	0.437507	+	1.34651i	0.890495	+	0.454992i	$0.150358\pi$
$941$	411.694	+	1267.06i	0.437507	+	1.34651i	−0.452988	+	0.891516i	$0.649642\pi$
$942$		0			0
$943$	−1924.49	−	1924.49i	−2.04082	−	2.04082i
$944$		0			0
$945$	824.975	+	841.552i	0.872990	+	0.890531i
$946$		0			0
$947$	230.561	−	36.5172i	0.243464	−	0.0385610i	−0.0335096	−	0.999438i	$-0.510668\pi$
$947$	230.561	−	36.5172i	0.243464	−	0.0385610i	0.276974	+	0.960877i	$0.410668\pi$
$948$		0			0
$949$			666.545i			0.702366i
$950$		0			0
$951$	−23.9308			−0.0251638
$952$		0			0
$953$	−96.4787	−	609.143i	−0.101237	−	0.639184i	−0.985171	−	0.171574i	$-0.945115\pi$
$953$	−96.4787	−	609.143i	−0.101237	−	0.639184i	0.883934	−	0.467611i	$-0.154885\pi$
$954$		0			0
$955$	−205.806	+	1220.70i	−0.215504	+	1.27822i
$956$		0			0
$957$	−1452.28	+	1452.28i	−1.51753	+	1.51753i
$958$		0			0
$959$	−1498.20	+	486.794i	−1.56225	+	0.507606i
$960$		0			0
$961$	−289.841	+	892.040i	−0.301604	+	0.928241i
$962$		0			0
$963$	−7.55482	+	14.8272i	−0.00784509	+	0.0153968i
$964$		0			0
$965$	−255.311	−	813.199i	−0.264571	−	0.842693i
$966$		0			0
$967$	58.9805	−	372.389i	0.0609933	−	0.385097i	−0.938241	−	0.345981i	$-0.887546\pi$
$967$	58.9805	−	372.389i	0.0609933	−	0.385097i	0.999235	−	0.0391153i	$-0.0124540\pi$
$968$		0			0
$969$	460.948	+	634.440i	0.475694	+	0.654737i
$970$		0			0
$971$	−1043.04	−	757.815i	−1.07420	−	0.780448i	−0.0975334	−	0.995232i	$-0.531095\pi$
$971$	−1043.04	−	757.815i	−1.07420	−	0.780448i	−0.976662	+	0.214784i	$0.931095\pi$
$972$		0			0
$973$	−160.083	+	81.5665i	−0.164525	+	0.0838299i
$974$		0			0
$975$	−378.243	−	1248.06i	−0.387942	−	1.28006i
$976$		0			0
$977$	−97.8819	−	192.104i	−0.100186	−	0.196626i	0.835473	−	0.549532i	$-0.185194\pi$
$977$	−97.8819	−	192.104i	−0.100186	−	0.196626i	−0.935659	+	0.352905i	$0.885194\pi$
$978$		0			0
$979$	−428.440	+	589.696i	−0.437630	+	0.602346i
$980$		0			0
$981$	6.67313	−	4.84831i	0.00680238	−	0.00494222i
$982$		0			0
$983$	−85.8033	−	13.5899i	−0.0872872	−	0.0138249i	0.112638	−	0.993636i	$-0.464070\pi$
$983$	−85.8033	−	13.5899i	−0.0872872	−	0.0138249i	−0.199925	+	0.979811i	$0.564070\pi$
$984$		0			0
$985$	−1718.38	−	577.294i	−1.74455	−	0.586085i
$986$		0			0
$987$	245.558	+	125.118i	0.248793	+	0.126766i
$988$		0			0
$989$	−115.870	−	37.6484i	−0.117159	−	0.0380671i
$990$		0			0
$991$	−35.3859	−	108.907i	−0.0357073	−	0.109896i	0.931614	−	0.363449i	$-0.118401\pi$
$991$	−35.3859	−	108.907i	−0.0357073	−	0.109896i	−0.967322	+	0.253553i	$0.918401\pi$
$992$		0			0
$993$	−213.840	−	213.840i	−0.215348	−	0.215348i
$994$		0			0
$995$	−61.0638	+	116.954i	−0.0613707	+	0.117542i
$996$		0			0
$997$	−1339.73	+	212.192i	−1.34376	+	0.212830i	−0.786542	−	0.617537i	$-0.788130\pi$
$997$	−1339.73	+	212.192i	−1.34376	+	0.212830i	−0.557216	+	0.830368i	$0.688130\pi$
$998$		0			0
$999$			441.524i			0.441966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.e.353.2		56
4.3	odd	2		200.3.u.a.153.6	yes	56
25.17	odd	20	inner	400.3.bg.e.17.2		56
100.67	even	20		200.3.u.a.17.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.17.6	✓	56	100.67	even	20
200.3.u.a.153.6	yes	56	4.3	odd	2
400.3.bg.e.17.2		56	25.17	odd	20	inner
400.3.bg.e.353.2		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.466746 - 2.94692i) q^{3} +(4.43224 + 2.31415i) q^{5} +(-6.13972 + 6.13972i) q^{7} +(0.0930182 - 0.0302234i) q^{9} +(4.35777 - 13.4118i) q^{11} +(7.93733 - 15.5779i) q^{13} +(4.75089 - 14.1416i) q^{15} +(-3.91601 + 24.7247i) q^{17} +(6.17152 + 8.49436i) q^{19} +(20.9590 + 15.2276i) q^{21} +(33.2719 - 16.9529i) q^{23} +(14.2894 + 20.5137i) q^{25} +(-12.3234 - 24.1861i) q^{27} +(28.6915 - 39.4904i) q^{29} +(3.88447 - 2.82223i) q^{31} +(-41.5576 - 6.58207i) q^{33} +(-41.4209 + 13.0044i) q^{35} +(-14.4927 - 7.38441i) q^{37} +(-49.6115 - 16.1198i) q^{39} +(-22.5225 - 69.3173i) q^{41} +(-2.30703 - 2.30703i) q^{43} +(0.482220 + 0.0813007i) q^{45} +(10.5071 - 1.66416i) q^{47} -26.3924i q^{49} +74.6896 q^{51} +(3.89089 + 24.5661i) q^{53} +(50.3516 - 49.3599i) q^{55} +(22.1517 - 22.1517i) q^{57} +(-4.38302 + 1.42413i) q^{59} +(16.1478 - 49.6979i) q^{61} +(-0.385542 + 0.756669i) q^{63} +(71.2297 - 50.6767i) q^{65} +(-17.6552 + 111.471i) q^{67} +(-65.4882 - 90.1368i) q^{69} +(12.7289 + 9.24807i) q^{71} +(-33.9690 + 17.3081i) q^{73} +(53.7828 - 51.6845i) q^{75} +(55.5894 + 109.100i) q^{77} +(-29.4277 + 40.5038i) q^{79} +(-64.8105 + 47.0876i) q^{81} +(125.051 + 19.8061i) q^{83} +(-74.5734 + 100.524i) q^{85} +(-129.767 - 66.1195i) q^{87} +(-49.1581 - 15.9724i) q^{89} +(46.9109 + 144.377i) q^{91} +(-10.1300 - 10.1300i) q^{93} +(7.69637 + 51.9308i) q^{95} +(-5.71423 + 0.905044i) q^{97} -1.37925i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 10 q^{5} + 4 q^{7} + 40 q^{9} + 16 q^{11} + 14 q^{13} + 10 q^{15} + 22 q^{17} - 50 q^{19} + 100 q^{21} + 48 q^{23} + 150 q^{25} + 210 q^{27} + 108 q^{31} - 140 q^{33} - 70 q^{35} + 236 q^{37} - 80 q^{39}+ \cdots + 386 q^{97}+O(q^{100}) \) 56 * q - 10 * q^5 + 4 * q^7 + 40 * q^9 + 16 * q^11 + 14 * q^13 + 10 * q^15 + 22 * q^17 - 50 * q^19 + 100 * q^21 + 48 * q^23 + 150 * q^25 + 210 * q^27 + 108 * q^31 - 140 * q^33 - 70 * q^35 + 236 * q^37 - 80 * q^39 + 104 * q^41 - 96 * q^43 + 20 * q^45 - 104 * q^47 + 200 * q^51 + 88 * q^53 + 140 * q^55 - 280 * q^57 - 200 * q^59 + 108 * q^61 + 654 * q^63 - 510 * q^65 + 282 * q^67 + 40 * q^69 - 470 * q^71 + 62 * q^73 - 350 * q^75 - 396 * q^77 + 560 * q^79 - 586 * q^81 + 468 * q^83 + 50 * q^85 + 280 * q^87 + 230 * q^89 + 62 * q^91 - 300 * q^93 + 360 * q^95 + 386 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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