LMFDB - Embedded newform 400.3.bg.e.17.2

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			17.2
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.e.353.2

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

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	0.779120	+	0.626875i	$0.215666\pi$
$3$	−0.466746	+	2.94692i	−0.155582	+	0.982307i	−0.934702	+	0.355432i	$0.884334\pi$
$4$		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	0.116131	−	0.993234i	$-0.462951\pi$
$7$	−6.13972	−	6.13972i	−0.877103	−	0.877103i	−0.993234	+	0.116131i	$0.962951\pi$
$8$		0			0
$9$	0.0930182	+	0.0302234i	0.0103354	+	0.00335816i
$10$		0			0
$11$	4.35777	+	13.4118i	0.396161	+	1.21926i	0.928054	+	0.372446i	$0.121481\pi$
$11$	4.35777	+	13.4118i	0.396161	+	1.21926i	−0.531893	+	0.846811i	$0.678519\pi$
$12$		0			0
$13$	7.93733	+	15.5779i	0.610564	+	1.19830i	0.964761	+	0.263128i	$0.0847543\pi$
$13$	7.93733	+	15.5779i	0.610564	+	1.19830i	−0.354197	+	0.935171i	$0.615246\pi$
$14$		0			0
$15$	4.75089	+	14.1416i	0.316726	+	0.942771i
$16$		0			0
$17$	−3.91601	−	24.7247i	−0.230354	−	1.45440i	−0.783542	−	0.621339i	$-0.786589\pi$
$17$	−3.91601	−	24.7247i	−0.230354	−	1.45440i	0.553188	−	0.833056i	$-0.313411\pi$
$18$		0			0
$19$	6.17152	−	8.49436i	0.324817	−	0.447072i	−0.615114	−	0.788439i	$-0.710890\pi$
$19$	6.17152	−	8.49436i	0.324817	−	0.447072i	0.939930	+	0.341367i	$0.110890\pi$
$20$		0			0
$21$	20.9590	−	15.2276i	0.998046	−	0.725123i
$22$		0			0
$23$	33.2719	+	16.9529i	1.44660	+	0.737081i	0.988415	−	0.151775i	$-0.0484989\pi$
$23$	33.2719	+	16.9529i	1.44660	+	0.737081i	0.458187	+	0.888856i	$0.348499\pi$
$24$		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	0.931631	+	0.363406i	$0.118386\pi$
$29$	28.6915	+	39.4904i	0.989361	+	1.36174i	0.0577298	+	0.998332i	$0.481614\pi$
$30$		0			0
$31$	3.88447	+	2.82223i	0.125306	+	0.0910398i	0.648673	−	0.761067i	$-0.275324\pi$
$31$	3.88447	+	2.82223i	0.125306	+	0.0910398i	−0.523367	+	0.852107i	$0.675324\pi$
$32$		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	−0.638735	−	0.769427i	$-0.720542\pi$
$37$	−14.4927	+	7.38441i	−0.391695	+	0.199579i	0.247040	+	0.969005i	$0.420542\pi$
$38$		0			0
$39$	−49.6115	+	16.1198i	−1.27209	+	0.413327i
$40$		0			0
$41$	−22.5225	+	69.3173i	−0.549330	+	1.69066i	0.161135	+	0.986932i	$0.448485\pi$
$41$	−22.5225	+	69.3173i	−0.549330	+	1.69066i	−0.710465	+	0.703732i	$0.751515\pi$
$42$		0			0
$43$	−2.30703	+	2.30703i	−0.0536518	+	0.0536518i	−0.733424	−	0.679772i	$-0.762079\pi$
$43$	−2.30703	+	2.30703i	−0.0536518	+	0.0536518i	0.679772	+	0.733424i	$0.262079\pi$
$44$		0			0
$45$	0.482220	−	0.0813007i	0.0107160	−	0.00180668i
$46$		0			0
$47$	10.5071	+	1.66416i	0.223555	+	0.0354076i	0.267207	−	0.963639i	$-0.413899\pi$
$47$	10.5071	+	1.66416i	0.223555	+	0.0354076i	−0.0436522	+	0.999047i	$0.513899\pi$
$48$		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	−0.923407	−	0.383823i	$-0.874607\pi$
$53$	3.89089	−	24.5661i	0.0734131	−	0.463512i	0.996820	−	0.0796891i	$-0.0253927\pi$
$54$		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	0.271637	−	0.962400i	$-0.412435\pi$
$59$	−4.38302	−	1.42413i	−0.0742884	−	0.0241378i	−0.345925	+	0.938262i	$0.612435\pi$
$60$		0			0
$61$	16.1478	+	49.6979i	0.264719	+	0.814720i	0.991758	+	0.128125i	$0.0408958\pi$
$61$	16.1478	+	49.6979i	0.264719	+	0.814720i	−0.727039	+	0.686596i	$0.759104\pi$
$62$		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	−0.664221	−	0.747536i	$-0.731237\pi$
$67$	−17.6552	−	111.471i	−0.263511	−	1.66374i	0.400711	−	0.916205i	$-0.368763\pi$
$68$		0			0
$69$	−65.4882	+	90.1368i	−0.949105	+	1.30633i
$70$		0			0
$71$	12.7289	−	9.24807i	0.179280	−	0.130254i	−0.494526	−	0.869163i	$-0.664658\pi$
$71$	12.7289	−	9.24807i	0.179280	−	0.130254i	0.673806	+	0.738908i	$0.264658\pi$
$72$		0			0
$73$	−33.9690	−	17.3081i	−0.465329	−	0.237097i	0.205575	−	0.978641i	$-0.434094\pi$
$73$	−33.9690	−	17.3081i	−0.465329	−	0.237097i	−0.670904	+	0.741545i	$0.734094\pi$
$74$		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	0.581076	−	0.813849i	$-0.302632\pi$
$79$	−29.4277	−	40.5038i	−0.372503	−	0.512706i	−0.953579	+	0.301143i	$0.902632\pi$
$80$		0			0
$81$	−64.8105	−	47.0876i	−0.800130	−	0.581328i
$82$		0			0
$83$	125.051	−	19.8061i	1.50664	−	0.238628i	0.652145	−	0.758094i	$-0.273869\pi$
$83$	125.051	−	19.8061i	1.50664	−	0.238628i	0.854491	+	0.519467i	$0.173869\pi$
$84$		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	−0.571871	−	0.820344i	$-0.693782\pi$
$89$	−49.1581	+	15.9724i	−0.552339	+	0.179466i	0.0195324	+	0.999809i	$0.493782\pi$
$90$		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	0.126910	−	0.991914i	$-0.459494\pi$
$97$	−5.71423	−	0.905044i	−0.0589095	−	0.00933035i	−0.185820	+	0.982584i	$0.559494\pi$
$98$		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	0.947354	+	0.320187i	$0.103746\pi$
$103$	−5.41538	+	34.1913i	−0.0525765	+	0.331955i	−0.999931	+	0.0117676i	$0.996254\pi$
$104$		0			0
$105$	57.6562	−	115.994i	0.549106	−	1.10471i
$106$		0			0
$107$	−120.310	−	120.310i	−1.12439	−	1.12439i	−0.991074	−	0.133316i	$-0.957437\pi$
$107$	−120.310	−	120.310i	−1.12439	−	1.12439i	−0.133316	−	0.991074i	$-0.542563\pi$
$108$		0			0
$109$	80.2078	+	26.0611i	0.735852	+	0.239093i	0.652882	−	0.757459i	$-0.273560\pi$
$109$	80.2078	+	26.0611i	0.735852	+	0.239093i	0.0829694	+	0.996552i	$0.473560\pi$
$110$		0			0
$111$	−14.9969	−	46.1556i	−0.135107	−	0.415816i
$112$		0			0
$113$	−57.4231	−	112.699i	−0.508169	−	0.997337i	−0.992476	−	0.122439i	$-0.960928\pi$
$113$	−57.4231	−	112.699i	−0.508169	−	0.997337i	0.484307	−	0.874898i	$-0.339072\pi$
$114$		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	−0.966602	−	0.256284i	$-0.917502\pi$
$127$	−24.2709	+	47.6343i	−0.191109	+	0.375073i	0.775492	+	0.631357i	$0.217502\pi$
$128$		0			0
$129$	−5.72183	−	7.87542i	−0.0443553	−	0.0610498i
$130$		0			0
$131$	−115.313	−	83.7799i	−0.880253	−	0.639541i	0.0530653	−	0.998591i	$-0.483101\pi$
$131$	−115.313	−	83.7799i	−0.880253	−	0.639541i	−0.933318	+	0.359050i	$0.883101\pi$
$132$		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	0.249757	−	0.968308i	$-0.419649\pi$
$137$	161.652	−	82.3656i	1.17994	−	0.601209i	0.930182	+	0.367099i	$0.119649\pi$
$138$		0			0
$139$	19.6792	−	6.39416i	0.141577	−	0.0460012i	−0.237371	−	0.971419i	$-0.576286\pi$
$139$	19.6792	−	6.39416i	0.141577	−	0.0460012i	0.378948	+	0.925418i	$0.376286\pi$
$140$		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	$0.0233839\pi$
$149$			21.8722i			0.146793i	−0.997303	+	0.0733967i	$0.976616\pi$
$150$		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	0.317060	−	0.948405i	$-0.397304\pi$
$157$	−99.1212	−	99.1212i	−0.631345	−	0.631345i	−0.948405	+	0.317060i	$0.897304\pi$
$158$		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	0.974371	+	0.224947i	$0.0722209\pi$
$163$	95.1327	+	186.708i	0.583636	+	1.14545i	−0.390735	+	0.920503i	$0.627779\pi$
$164$		0			0
$165$	−168.961	+	125.344i	−1.02401	+	0.759659i
$166$		0			0
$167$	−11.3886	−	71.9048i	−0.0681952	−	0.430568i	−0.998038	−	0.0626106i	$-0.980057\pi$
$167$	−11.3886	−	71.9048i	−0.0681952	−	0.430568i	0.929843	−	0.367957i	$-0.119943\pi$
$168$		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	−0.412401	−	0.911002i	$-0.635310\pi$
$173$	−240.785	−	122.686i	−1.39182	−	0.709168i	−0.979420	+	0.201835i	$0.935310\pi$
$174$		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	0.692673	−	0.721252i	$-0.256433\pi$
$179$	−37.1114	−	51.0794i	−0.207326	−	0.285360i	−0.899999	+	0.435892i	$0.856433\pi$
$180$		0			0
$181$	36.6294	+	26.6128i	0.202373	+	0.147032i	0.684356	−	0.729148i	$-0.260083\pi$
$181$	36.6294	+	26.6128i	0.202373	+	0.147032i	−0.481983	+	0.876180i	$0.660083\pi$
$182$		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	−0.523973	−	0.851735i	$-0.675551\pi$
$191$	76.5083	−	235.468i	0.400567	−	1.23282i	0.924540	−	0.381084i	$-0.124449\pi$
$192$		0			0
$193$	−120.538	+	120.538i	−0.624552	+	0.624552i	−0.946692	−	0.322140i	$-0.895598\pi$
$193$	−120.538	+	120.538i	−0.624552	+	0.624552i	0.322140	+	0.946692i	$0.395598\pi$
$194$		0			0
$195$	−182.586	+	186.255i	−0.936341	+	0.955155i
$196$		0			0
$197$	−358.089	−	56.7157i	−1.81771	−	0.287897i	−0.847613	−	0.530616i	$-0.821961\pi$
$197$	−358.089	−	56.7157i	−1.81771	−	0.287897i	−0.970097	+	0.242719i	$0.921961\pi$
$198$		0			0
$199$		−	26.3872i		−	0.132599i	−0.997800	−	0.0662994i	$-0.978881\pi$
$199$		−	26.3872i		−	0.132599i	0.997800	−	0.0662994i	$-0.0211192\pi$
$200$		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	0.959986	−	0.280049i	$-0.0903506\pi$
$211$	3.95255	+	12.1647i	0.0187325	+	0.0576526i	−0.941253	+	0.337701i	$0.890351\pi$
$212$		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	0.122453	−	0.992474i	$-0.460924\pi$
$223$	−135.696	−	69.1403i	−0.608500	−	0.310046i	−0.730953	+	0.682428i	$0.760924\pi$
$224$		0			0
$225$	1.94917	−	1.47627i	0.00866298	−	0.00656122i
$226$		0			0
$227$	−103.562	+	203.252i	−0.456221	+	0.895384i	0.542256	+	0.840213i	$0.317570\pi$
$227$	−103.562	+	203.252i	−0.456221	+	0.895384i	−0.998477	+	0.0551707i	$0.982430\pi$
$228$		0			0
$229$	−149.797	−	206.178i	−0.654137	−	0.900342i	0.345133	−	0.938554i	$-0.387834\pi$
$229$	−149.797	−	206.178i	−0.654137	−	0.900342i	−0.999270	+	0.0382118i	$0.987834\pi$
$230$		0			0
$231$	295.564	+	214.740i	1.27950	+	0.929610i
$232$		0			0
$233$	−103.867	+	16.4508i	−0.445779	+	0.0706045i	−0.375289	−	0.926908i	$-0.622456\pi$
$233$	−103.867	+	16.4508i	−0.445779	+	0.0706045i	−0.0704904	+	0.997512i	$0.522456\pi$
$234$		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	0.160486	−	0.987038i	$-0.448694\pi$
$239$	208.047	−	67.5984i	0.870488	−	0.282839i	0.710002	+	0.704200i	$0.248694\pi$
$240$		0			0
$241$	−44.5491	+	137.108i	−0.184851	+	0.568913i	−0.999946	−	0.0104148i	$-0.996685\pi$
$241$	−44.5491	+	137.108i	−0.184851	+	0.568913i	0.815095	+	0.579328i	$0.196685\pi$
$242$		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	0.996210	−	0.0869796i	$-0.0277215\pi$
$257$	233.672	+	233.672i	0.909230	+	0.909230i	−0.0869796	+	0.996210i	$0.527721\pi$
$258$		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	0.910634	−	0.413214i	$-0.135594\pi$
$263$	10.8040	+	21.2040i	0.0410798	+	0.0806237i	−0.869554	+	0.493837i	$0.835594\pi$
$264$		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	−0.774301	−	0.632818i	$-0.781898\pi$
$269$	17.9737	−	24.7387i	0.0668167	−	0.0919653i	0.841118	+	0.540852i	$0.181898\pi$
$270$		0			0
$271$	−380.924	+	276.758i	−1.40562	+	1.02125i	−0.411684	+	0.911326i	$0.635059\pi$
$271$	−380.924	+	276.758i	−1.40562	+	1.02125i	−0.993940	+	0.109920i	$0.964941\pi$
$272$		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	−0.986349	−	0.164668i	$-0.947345\pi$
$277$	−75.7229	+	148.615i	−0.273368	+	0.536515i	0.712981	+	0.701183i	$0.247345\pi$
$278$		0			0
$279$	0.276029	+	0.379921i	0.000989351	+	0.00136173i
$280$		0			0
$281$	−421.611	−	306.319i	−1.50040	−	1.09010i	−0.970223	−	0.242212i	$-0.922127\pi$
$281$	−421.611	−	306.319i	−1.50040	−	1.09010i	−0.530173	−	0.847890i	$-0.677873\pi$
$282$		0			0
$283$	−193.661	+	30.6728i	−0.684313	+	0.108385i	−0.488904	−	0.872337i	$-0.662603\pi$
$283$	−193.661	+	30.6728i	−0.684313	+	0.108385i	−0.195409	+	0.980722i	$0.562603\pi$
$284$		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	−0.559039	−	0.829141i	$-0.688830\pi$
$293$	79.1398	−	79.1398i	0.270102	−	0.270102i	0.829141	+	0.559039i	$0.188830\pi$
$294$		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	0.760723	−	0.649076i	$-0.224844\pi$
$307$	34.2757	+	34.2757i	0.111647	+	0.111647i	−0.649076	+	0.760723i	$0.724844\pi$
$308$		0			0
$309$	−98.2316	−	31.9174i	−0.317902	−	0.103292i
$310$		0			0
$311$	−2.87053	−	8.83457i	−0.00922999	−	0.0284070i	0.946335	−	0.323186i	$-0.104754\pi$
$311$	−2.87053	−	8.83457i	−0.00922999	−	0.0284070i	−0.955565	+	0.294779i	$0.904754\pi$
$312$		0			0
$313$	−176.957	−	347.297i	−0.565357	−	1.10958i	−0.979889	−	0.199542i	$-0.936055\pi$
$313$	−176.957	−	347.297i	−0.565357	−	1.10958i	0.414532	−	0.910035i	$-0.363945\pi$
$314$		0			0
$315$	−3.45986	−	2.46153i	−0.0109837	−	0.00781439i
$316$		0			0
$317$	1.25470	+	7.92188i	0.00395805	+	0.0249902i	0.989588	−	0.143927i	$-0.0459730\pi$
$317$	1.25470	+	7.92188i	0.00395805	+	0.0249902i	−0.985630	+	0.168917i	$0.945973\pi$
$318$		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	0.704722	−	0.709483i	$-0.251072\pi$
$331$	82.0000	+	59.5765i	0.247734	+	0.179989i	−0.456988	+	0.889473i	$0.651072\pi$
$332$		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	−0.300721	−	0.953712i	$-0.597227\pi$
$337$	99.1082	−	50.4981i	0.294090	−	0.149846i	0.594810	+	0.803866i	$0.297227\pi$
$338$		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	−0.362394	−	0.932025i	$-0.618040\pi$
$347$	−345.287	−	54.6880i	−0.995062	−	0.157602i	−0.632669	+	0.774423i	$0.718040\pi$
$348$		0			0
$349$		−	197.357i		−	0.565491i	−0.959195	−	0.282746i	$-0.908755\pi$
$349$		−	197.357i		−	0.565491i	0.959195	−	0.282746i	$-0.0912453\pi$
$350$		0			0
$351$	−474.584			−1.35209
$352$		0			0
$353$	73.3022	−	462.812i	0.207655	−	1.31108i	−0.634951	−	0.772552i	$-0.718980\pi$
$353$	73.3022	−	462.812i	0.207655	−	1.31108i	0.842606	−	0.538530i	$-0.181020\pi$
$354$		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	0.0574061	−	0.998351i	$-0.481717\pi$
$359$	−173.385	−	56.3363i	−0.482967	−	0.156926i	−0.540373	+	0.841425i	$0.681717\pi$
$360$		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	0.810275	+	0.586050i	$0.199318\pi$
$367$	81.0178	+	511.526i	0.220757	+	1.39380i	−0.589518	+	0.807755i	$0.700682\pi$
$368$		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	0.967187	−	0.254065i	$-0.0817678\pi$
$373$	496.143	+	252.798i	1.33014	+	0.677741i	0.362955	+	0.931807i	$0.381768\pi$
$374$		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	0.997710	−	0.0676303i	$-0.0215438\pi$
$379$	236.906	+	326.073i	0.625081	+	0.860350i	−0.372630	+	0.927980i	$0.621544\pi$
$380$		0			0
$381$	−129.046	−	93.7576i	−0.338704	−	0.246083i
$382$		0			0
$383$	−3.35701	+	0.531698i	−0.00876503	+	0.00138824i	−0.160815	−	0.986984i	$-0.551412\pi$
$383$	−3.35701	+	0.531698i	−0.00876503	+	0.00138824i	0.152050	+	0.988373i	$0.451412\pi$
$384$		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	0.813235	−	0.581936i	$-0.197704\pi$
$389$	705.338	−	229.178i	1.81321	−	0.589147i	0.999974	−	0.00721160i	$-0.00229554\pi$
$390$		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	0.913385	−	0.407096i	$-0.133459\pi$
$397$	657.538	+	104.144i	1.65627	+	0.262327i	0.742881	+	0.669423i	$0.233459\pi$
$398$		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	0.0356168	−	0.999366i	$-0.488660\pi$
$409$	−213.899	−	69.5001i	−0.522981	−	0.169927i	−0.558598	+	0.829439i	$0.688660\pi$
$410$		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	−0.866497	−	0.499182i	$-0.833634\pi$
$419$	−51.9496	+	71.5026i	−0.123985	+	0.170650i	0.742512	+	0.669832i	$0.233634\pi$
$420$		0			0
$421$	−218.306	+	158.608i	−0.518540	+	0.376742i	−0.816054	−	0.577976i	$-0.803843\pi$
$421$	−218.306	+	158.608i	−0.518540	+	0.376742i	0.297513	+	0.954718i	$0.403843\pi$
$422$		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	0.999926	−	0.0122025i	$-0.00388428\pi$
$431$	559.142	+	406.241i	1.29731	+	0.942554i	0.297389	+	0.954756i	$0.403884\pi$
$432$		0			0
$433$	180.999	−	28.6674i	0.418011	−	0.0662065i	0.0561139	−	0.998424i	$-0.482129\pi$
$433$	180.999	−	28.6674i	0.418011	−	0.0662065i	0.361898	+	0.932218i	$0.382129\pi$
$434$		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	−0.794656	−	0.607060i	$-0.792349\pi$
$439$	−474.438	+	154.154i	−1.08073	+	0.351149i	−0.286069	+	0.958209i	$0.592349\pi$
$440$		0			0
$441$	−0.797668	+	2.45497i	−0.00180877	+	0.00556682i
$442$		0			0
$443$	59.9191	−	59.9191i	0.135258	−	0.135258i	−0.636237	−	0.771494i	$-0.719510\pi$
$443$	59.9191	−	59.9191i	0.135258	−	0.135258i	0.771494	+	0.636237i	$0.219510\pi$
$444$		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	$-0.604251\pi$
$449$		−	850.267i		−	1.89369i	0.321691	−	0.946845i	$-0.395749\pi$
$450$		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	−0.998963	−	0.0455205i	$-0.985505\pi$
$457$	−477.329	−	477.329i	−1.04448	−	1.04448i	−0.0455205	−	0.998963i	$-0.514495\pi$
$458$		0			0
$459$	646.254	+	209.981i	1.40796	+	0.457474i
$460$		0			0
$461$	192.848	+	593.524i	0.418324	+	1.28747i	0.909243	+	0.416265i	$0.136661\pi$
$461$	192.848	+	593.524i	0.418324	+	1.28747i	−0.490919	+	0.871205i	$0.663339\pi$
$462$		0			0
$463$	−18.0901	−	35.5039i	−0.0390715	−	0.0766822i	0.870645	−	0.491911i	$-0.163701\pi$
$463$	−18.0901	−	35.5039i	−0.0390715	−	0.0766822i	−0.909717	+	0.415229i	$0.863701\pi$
$464$		0			0
$465$	−21.4561	+	68.3407i	−0.0461422	+	0.146969i
$466$		0			0
$467$	−59.9564	−	378.550i	−0.128386	−	0.810599i	−0.964893	−	0.262643i	$-0.915406\pi$
$467$	−59.9564	−	378.550i	−0.128386	−	0.810599i	0.836507	−	0.547957i	$-0.184594\pi$
$468$		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	−0.847590	−	0.530651i	$-0.821947\pi$
$479$	−522.277	−	718.853i	−1.09035	−	1.50074i	−0.242759	−	0.970087i	$-0.578053\pi$
$480$		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	−0.243443	−	0.969915i	$-0.578277\pi$
$487$	193.896	−	98.7949i	0.398143	−	0.202864i	0.641586	+	0.767051i	$0.278277\pi$
$488$		0			0
$489$	−594.618	+	193.203i	−1.21599	+	0.395098i
$490$		0			0
$491$	−184.760	+	568.634i	−0.376294	+	1.15811i	0.566307	+	0.824194i	$0.308372\pi$
$491$	−184.760	+	568.634i	−0.376294	+	1.15811i	−0.942601	+	0.333920i	$0.891628\pi$
$492$		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	$-0.729946\pi$
$499$		−	748.723i		−	1.50045i	0.661185	−	0.750223i	$-0.270054\pi$
$500$		0			0
$501$	217.213			0.433559
$502$		0			0
$503$	87.1263	−	550.094i	0.173213	−	1.09363i	−0.735904	−	0.677086i	$-0.763242\pi$
$503$	87.1263	−	550.094i	0.173213	−	1.09363i	0.909117	−	0.416540i	$-0.136758\pi$
$504$		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	0.152019	−	0.988378i	$-0.451422\pi$
$509$	−155.728	−	50.5990i	−0.305949	−	0.0994087i	−0.457968	+	0.888969i	$0.651422\pi$
$510$		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	−0.999922	−	0.0124923i	$-0.996023\pi$
$521$	−675.755	+	490.965i	−1.29703	+	0.942350i	−0.297112	+	0.954843i	$0.596023\pi$
$522$		0			0
$523$	334.987	+	170.684i	0.640510	+	0.326356i	0.743906	−	0.668284i	$-0.232971\pi$
$523$	334.987	+	170.684i	0.640510	+	0.326356i	−0.103396	+	0.994640i	$0.532971\pi$
$524$		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	−0.653060	−	0.757306i	$-0.726515\pi$
$541$	173.342	−	533.491i	0.320410	−	0.986120i	0.973470	−	0.228814i	$-0.0734849\pi$
$542$		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	−0.0775338	−	0.996990i	$-0.524705\pi$
$547$	−251.270	−	39.7972i	−0.459360	−	0.0727554i	−0.381826	+	0.924234i	$0.624705\pi$
$548$		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	0.720036	−	0.693936i	$-0.244125\pi$
$557$	14.5377	+	14.5377i	0.0260999	+	0.0260999i	−0.693936	+	0.720036i	$0.744125\pi$
$558$		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	0.972127	−	0.234454i	$-0.0753303\pi$
$563$	118.820	+	233.197i	0.211048	+	0.414205i	−0.761079	+	0.648659i	$0.775330\pi$
$564$		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	−0.0945015	−	0.995525i	$-0.530126\pi$
$569$	501.574	−	690.358i	0.881501	−	1.21328i	0.976003	−	0.217758i	$-0.0698743\pi$
$570$		0			0
$571$	−856.531	+	622.306i	−1.50005	+	1.08985i	−0.529695	+	0.848188i	$0.677693\pi$
$571$	−856.531	+	622.306i	−1.50005	+	1.08985i	−0.970360	+	0.241665i	$0.922307\pi$
$572$		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	−0.911186	−	0.411996i	$-0.864832\pi$
$577$	−24.4027	+	47.8930i	−0.0422924	+	0.0830035i	0.868893	+	0.494999i	$0.164832\pi$
$578$		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	−0.880165	−	0.474669i	$-0.842568\pi$
$587$	−594.923	+	303.128i	−1.01350	+	0.516403i	−0.133333	+	0.991071i	$0.542568\pi$
$588$		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	−0.887396	−	0.461008i	$-0.847488\pi$
$593$	−252.848	+	252.848i	−0.426388	+	0.426388i	0.461008	+	0.887396i	$0.347488\pi$
$594$		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	$-0.996444\pi$
$599$		−	13.3819i		−	0.0223403i	0.999938	−	0.0111702i	$-0.00355565\pi$
$600$		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	0.994867	−	0.101188i	$-0.0322643\pi$
$607$	542.463	+	542.463i	0.893679	+	0.893679i	−0.101188	+	0.994867i	$0.532264\pi$
$608$		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	−0.989005	−	0.147882i	$-0.952754\pi$
$613$	−323.248	−	634.410i	−0.527321	−	1.03493i	0.461684	−	0.887045i	$-0.347246\pi$
$614$		0			0
$615$	−1087.26	+	10.8145i	−1.76790	+	0.0175846i
$616$		0			0
$617$	14.7128	+	92.8930i	0.0238457	+	0.150556i	0.996738	−	0.0807015i	$-0.0257160\pi$
$617$	14.7128	+	92.8930i	0.0238457	+	0.150556i	−0.972893	+	0.231257i	$0.925716\pi$
$618$		0			0
$619$	−70.1520	+	96.5560i	−0.113331	+	0.155987i	−0.861914	−	0.507054i	$-0.830734\pi$
$619$	−70.1520	+	96.5560i	−0.113331	+	0.155987i	0.748583	+	0.663041i	$0.230734\pi$
$620$		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	0.403794	−	0.914850i	$-0.367691\pi$
$631$	−215.487	−	156.560i	−0.341501	−	0.248115i	−0.745295	+	0.666735i	$0.767691\pi$
$632$		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	0.696417	+	0.717637i	$0.254776\pi$
$641$	−185.129	+	569.768i	−0.288813	+	0.888874i	−0.985230	+	0.171237i	$0.945224\pi$
$642$		0			0
$643$	−56.2615	+	56.2615i	−0.0874985	+	0.0874985i	−0.749501	−	0.662003i	$-0.769707\pi$
$643$	−56.2615	+	56.2615i	−0.0874985	+	0.0874985i	0.662003	+	0.749501i	$0.269707\pi$
$644$		0			0
$645$	−43.5854	−	21.6645i	−0.0675743	−	0.0335884i
$646$		0			0
$647$	32.3407	+	5.12227i	0.0499856	+	0.00791695i	0.181377	−	0.983414i	$-0.441945\pi$
$647$	32.3407	+	5.12227i	0.0499856	+	0.00791695i	−0.131392	+	0.991331i	$0.541945\pi$
$648$		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	−0.839799	−	0.542898i	$-0.817327\pi$
$653$	82.7103	−	522.212i	0.126662	−	0.799712i	0.966461	−	0.256814i	$-0.0826729\pi$
$654$		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	0.250592	−	0.968093i	$-0.419375\pi$
$659$	−76.2499	−	24.7751i	−0.115705	−	0.0375950i	−0.366297	+	0.930498i	$0.619375\pi$
$660$		0			0
$661$	−99.9847	−	307.721i	−0.151263	−	0.465539i	0.846500	−	0.532388i	$-0.178705\pi$
$661$	−99.9847	−	307.721i	−0.151263	−	0.465539i	−0.997763	+	0.0668493i	$0.978705\pi$
$662$		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	0.255269	−	0.966870i	$-0.417836\pi$
$673$	−253.655	−	129.244i	−0.376902	−	0.192041i	−0.632171	+	0.774829i	$0.717836\pi$
$674$		0			0
$675$	320.052	+	598.405i	0.474152	+	0.886526i
$676$		0			0
$677$	−278.550	+	546.686i	−0.411448	+	0.807513i	−1.00000		0.000947157i	$-0.999699\pi$
$677$	−278.550	+	546.686i	−0.411448	+	0.807513i	0.588551	+	0.808460i	$0.299699\pi$
$678$		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	0.774267	−	0.632859i	$-0.218119\pi$
$683$	1165.34	−	184.571i	1.70620	−	0.270236i	0.931936	+	0.362623i	$0.118119\pi$
$684$		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	−0.339674	−	0.940543i	$-0.610317\pi$
$691$	337.184	−	1037.75i	0.487965	−	1.50180i	0.827640	−	0.561260i	$-0.189683\pi$
$692$		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	0.381112	−	0.924529i	$-0.375541\pi$
$709$	103.524	+	33.6371i	0.146015	+	0.0474430i	−0.235098	+	0.971972i	$0.575541\pi$
$710$		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	−0.196509	−	0.980502i	$-0.562961\pi$
$719$	572.847	−	788.457i	0.796728	−	1.09660i	0.993238	−	0.116100i	$-0.0370394\pi$
$720$		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	0.151565	+	0.988447i	$0.451569\pi$
$727$	−535.940	+	1051.84i	−0.737193	+	1.44682i	−0.888758	+	0.458376i	$0.848431\pi$
$728$		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	0.590481	−	0.807051i	$-0.298938\pi$
$733$	1027.27	−	162.703i	1.40145	−	0.221969i	0.810974	+	0.585083i	$0.198938\pi$
$734$		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	0.352803	−	0.935697i	$-0.385228\pi$
$739$	878.092	−	285.309i	1.18822	−	0.386075i	0.835413	+	0.549623i	$0.185228\pi$
$740$		0			0
$741$	−169.251	+	520.902i	−0.228409	+	0.702971i
$742$		0			0
$743$	283.985	−	283.985i	0.382213	−	0.382213i	−0.489686	−	0.871899i	$-0.662888\pi$
$743$	283.985	−	283.985i	0.382213	−	0.382213i	0.871899	+	0.489686i	$0.162888\pi$
$744$		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	0.996855	−	0.0792459i	$-0.0252512\pi$
$757$	694.630	+	694.630i	0.917609	+	0.917609i	−0.0792459	+	0.996855i	$0.525251\pi$
$758$		0			0
$759$	−1494.28	−	485.522i	−1.96875	−	0.639686i
$760$		0			0
$761$	−240.628	−	740.577i	−0.316200	−	0.973163i	−0.975258	−	0.221071i	$-0.929045\pi$
$761$	−240.628	−	740.577i	−0.316200	−	0.973163i	0.659058	−	0.752092i	$-0.270955\pi$
$762$		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	−0.687149	−	0.726516i	$-0.741138\pi$
$769$	166.219	−	228.781i	0.216149	−	0.297504i	0.903299	+	0.429012i	$0.141138\pi$
$770$		0			0
$771$	−797.679	+	579.548i	−1.03460	+	0.751683i
$772$		0			0
$773$	−562.929	−	286.826i	−0.728239	−	0.371056i	0.0502316	−	0.998738i	$-0.484004\pi$
$773$	−562.929	−	286.826i	−0.728239	−	0.371056i	−0.778470	+	0.627681i	$0.784004\pi$
$774$		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	0.117459	−	0.993078i	$-0.462525\pi$
$787$	779.064	−	396.953i	0.989916	−	0.504388i	0.872457	+	0.488690i	$0.162525\pi$
$788$		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	0.924314	−	0.381632i	$-0.124638\pi$
$797$	1343.31	+	212.760i	1.68546	+	0.266951i	0.761145	+	0.648582i	$0.224638\pi$
$798$		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	−0.543372	−	0.839492i	$-0.682853\pi$
$809$	−1194.42	−	388.089i	−1.47641	−	0.479715i	−0.933038	+	0.359778i	$0.882853\pi$
$810$		0			0
$811$	−247.722	−	762.411i	−0.305453	−	0.940087i	−0.979508	−	0.201406i	$-0.935449\pi$
$811$	−247.722	−	762.411i	−0.305453	−	0.940087i	0.674055	−	0.738681i	$-0.264551\pi$
$812$		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	−0.908708	−	0.417432i	$-0.862930\pi$
$821$	−650.654	+	472.728i	−0.792514	+	0.575795i	0.116195	+	0.993226i	$0.462930\pi$
$822$		0			0
$823$	−95.8032	−	48.8142i	−0.116407	−	0.0593125i	0.394817	−	0.918760i	$-0.370808\pi$
$823$	−95.8032	−	48.8142i	−0.116407	−	0.0593125i	−0.511224	+	0.859447i	$0.670808\pi$
$824$		0			0
$825$	−458.811	+	946.554i	−0.556134	+	1.14734i
$826$		0			0
$827$	−298.104	+	585.062i	−0.360464	+	0.707451i	−0.998016	−	0.0629564i	$-0.979947\pi$
$827$	−298.104	+	585.062i	−0.360464	+	0.707451i	0.637552	+	0.770407i	$0.279947\pi$
$828$		0			0
$829$	136.148	+	187.392i	0.164231	+	0.226045i	0.883199	−	0.468998i	$-0.155385\pi$
$829$	136.148	+	187.392i	0.164231	+	0.226045i	−0.718968	+	0.695044i	$0.755385\pi$
$830$		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	−0.321085	−	0.947050i	$-0.604048\pi$
$839$	−20.2925	+	6.59343i	−0.0241865	+	0.00785867i	0.296899	+	0.954909i	$0.404048\pi$
$840$		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	−0.998096	−	0.0616761i	$-0.980355\pi$
$853$	−25.4120	+	160.445i	−0.0297913	+	0.188095i	0.968305	+	0.249771i	$0.0803554\pi$
$854$		0			0
$855$	2.28543	−	4.59790i	0.00267302	−	0.00537766i
$856$		0			0
$857$	−96.9589	−	96.9589i	−0.113138	−	0.113138i	0.648272	−	0.761409i	$-0.275492\pi$
$857$	−96.9589	−	96.9589i	−0.113138	−	0.113138i	−0.761409	+	0.648272i	$0.775492\pi$
$858$		0			0
$859$	652.308	+	211.948i	0.759380	+	0.246738i	0.663013	−	0.748608i	$-0.269278\pi$
$859$	652.308	+	211.948i	0.759380	+	0.246738i	0.0963676	+	0.995346i	$0.469278\pi$
$860$		0			0
$861$	583.485	+	1795.78i	0.677683	+	2.08569i
$862$		0			0
$863$	642.072	+	1260.14i	0.744000	+	1.46018i	0.882744	+	0.469855i	$0.155694\pi$
$863$	642.072	+	1260.14i	0.744000	+	1.46018i	−0.138743	+	0.990328i	$0.544306\pi$
$864$		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	−0.954528	−	0.298121i	$-0.903640\pi$
$877$	−133.555	+	262.116i	−0.152286	+	0.298878i	0.802242	+	0.596999i	$0.203640\pi$
$878$		0			0
$879$	196.281	+	270.157i	0.223300	+	0.307346i
$880$		0			0
$881$	−709.759	−	515.670i	−0.805628	−	0.585323i	0.106932	−	0.994266i	$-0.465897\pi$
$881$	−709.759	−	515.670i	−0.805628	−	0.585323i	−0.912560	+	0.408943i	$0.865897\pi$
$882$		0			0
$883$	52.7586	−	8.35615i	0.0597493	−	0.00946336i	−0.126488	−	0.991968i	$-0.540371\pi$
$883$	52.7586	−	8.35615i	0.0597493	−	0.00946336i	0.186238	+	0.982505i	$0.440371\pi$
$884$		0			0
$885$	−0.683815	−	68.7486i	−0.000772673	−	0.0776820i
$886$		0			0
$887$	−623.575	+	317.728i	−0.703016	+	0.358205i	−0.768677	−	0.639637i	$-0.779085\pi$
$887$	−623.575	+	317.728i	−0.703016	+	0.358205i	0.0656606	+	0.997842i	$0.479085\pi$
$888$		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	−0.986058	−	0.166402i	$-0.946785\pi$
$907$	−1045.28	−	1045.28i	−1.15246	−	1.15246i	−0.166402	−	0.986058i	$-0.553215\pi$
$908$		0			0
$909$	7.61741	+	2.47505i	0.00837999	+	0.00272282i
$910$		0			0
$911$	−3.00555	−	9.25014i	−0.00329918	−	0.0101538i	0.949393	−	0.314090i	$-0.101699\pi$
$911$	−3.00555	−	9.25014i	−0.00329918	−	0.0101538i	−0.952693	+	0.303936i	$0.901699\pi$
$912$		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	−0.925388	−	0.379022i	$-0.876260\pi$
$919$	−256.360	+	352.849i	−0.278955	+	0.383949i	0.646432	+	0.762972i	$0.276260\pi$
$920$		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	0.972589	−	0.232532i	$-0.0747012\pi$
$929$	418.877	+	576.535i	0.450891	+	0.620598i	−0.521698	+	0.853130i	$0.674701\pi$
$930$		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	−0.00795957	−	0.999968i	$-0.502534\pi$
$937$	746.183	−	380.199i	0.796353	−	0.405762i	0.804313	+	0.594206i	$0.202534\pi$
$938$		0			0
$939$	1106.05	−	359.378i	1.17790	−	0.382724i
$940$		0			0
$941$	411.694	−	1267.06i	0.437507	−	1.34651i	−0.452988	−	0.891516i	$-0.649642\pi$
$941$	411.694	−	1267.06i	0.437507	−	1.34651i	0.890495	−	0.454992i	$-0.150358\pi$
$942$		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	0.276974	−	0.960877i	$-0.410668\pi$
$947$	230.561	+	36.5172i	0.243464	+	0.0385610i	−0.0335096	+	0.999438i	$0.510668\pi$
$948$		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	0.883934	+	0.467611i	$0.154885\pi$
$953$	−96.4787	+	609.143i	−0.101237	+	0.639184i	−0.985171	+	0.171574i	$0.945115\pi$
$954$		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	0.999235	+	0.0391153i	$0.0124540\pi$
$967$	58.9805	+	372.389i	0.0609933	+	0.385097i	−0.938241	+	0.345981i	$0.887546\pi$
$968$		0			0
$969$	460.948	−	634.440i	0.475694	−	0.654737i
$970$		0			0
$971$	−1043.04	+	757.815i	−1.07420	+	0.780448i	−0.976662	−	0.214784i	$-0.931095\pi$
$971$	−1043.04	+	757.815i	−1.07420	+	0.780448i	−0.0975334	+	0.995232i	$0.531095\pi$
$972$		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	−0.935659	−	0.352905i	$-0.885194\pi$
$977$	−97.8819	+	192.104i	−0.100186	+	0.196626i	0.835473	+	0.549532i	$0.185194\pi$
$978$		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	−0.199925	−	0.979811i	$-0.564070\pi$
$983$	−85.8033	+	13.5899i	−0.0872872	+	0.0138249i	0.112638	+	0.993636i	$0.464070\pi$
$984$		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	−0.967322	−	0.253553i	$-0.918401\pi$
$991$	−35.3859	+	108.907i	−0.0357073	+	0.109896i	0.931614	+	0.363449i	$0.118401\pi$
$992$		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	−0.557216	−	0.830368i	$-0.688130\pi$
$997$	−1339.73	−	212.192i	−1.34376	−	0.212830i	−0.786542	+	0.617537i	$0.788130\pi$
$998$		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.17.2		56
4.3	odd	2		200.3.u.a.17.6	✓	56
25.3	odd	20	inner	400.3.bg.e.353.2		56
100.3	even	20		200.3.u.a.153.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.a.17.6	✓	56	4.3	odd	2
200.3.u.a.153.6	yes	56	100.3	even	20
400.3.bg.e.17.2		56	1.1	even	1	trivial
400.3.bg.e.353.2		56	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
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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