LMFDB - Embedded newform 1020.3.bc.a.701.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

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

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.7
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75507 + 1.18727i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(7.37174 + 7.37174i) q^{7} +(6.18077 - 6.54202i) q^{9} +O(q^{10})$	\(q+(-2.75507 + 1.18727i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(7.37174 + 7.37174i) q^{7} +(6.18077 - 6.54202i) q^{9} +(0.717389 - 0.717389i) q^{11} -24.7701 q^{13} +(6.23338 + 2.47890i) q^{15} +(0.170354 + 16.9991i) q^{17} -13.5866i q^{19} +(-29.0619 - 11.5574i) q^{21} +(12.2457 - 12.2457i) q^{23} +5.00000i q^{25} +(-9.26126 + 25.3620i) q^{27} +(32.9689 + 32.9689i) q^{29} +(-13.7594 + 13.7594i) q^{31} +(-1.12472 + 2.82819i) q^{33} -23.3115i q^{35} +(-8.16355 + 8.16355i) q^{37} +(68.2434 - 29.4089i) q^{39} +(37.4408 - 37.4408i) q^{41} +6.67315i q^{43} +(-20.1165 + 0.571195i) q^{45} +7.72884i q^{47} +59.6851i q^{49} +(-20.6519 - 46.6315i) q^{51} -92.1223 q^{53} -2.26858 q^{55} +(16.1310 + 37.4320i) q^{57} +5.96855 q^{59} +(-42.3071 - 42.3071i) q^{61} +(93.7891 - 2.66308i) q^{63} +(39.1650 + 39.1650i) q^{65} -83.0546 q^{67} +(-19.1987 + 48.2766i) q^{69} +(-61.7504 - 61.7504i) q^{71} +(-27.5746 + 27.5746i) q^{73} +(-5.93636 - 13.7753i) q^{75} +10.5768 q^{77} +(-87.9466 - 87.9466i) q^{79} +(-4.59618 - 80.8695i) q^{81} -121.079 q^{83} +(26.6087 - 27.1474i) q^{85} +(-129.975 - 51.6884i) q^{87} +14.2907i q^{89} +(-182.599 - 182.599i) q^{91} +(21.5719 - 54.2441i) q^{93} +(-21.4823 + 21.4823i) q^{95} +(0.110634 - 0.110634i) q^{97} +(-0.259160 - 9.12719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

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
$3$	−2.75507	+	1.18727i	−0.918355	+	0.395757i
$3$	−2.75507	+	1.18727i	−0.918355	+	0.395757i
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	7.37174	+	7.37174i	1.05311	+	1.05311i	0.998508	+	0.0545971i	$0.0173874\pi$
$7$	7.37174	+	7.37174i	1.05311	+	1.05311i	0.0545971	+	0.998508i	$0.482613\pi$
$8$		0			0
$9$	6.18077	−	6.54202i	0.686752	−	0.726892i
$10$		0			0
$11$	0.717389	−	0.717389i	0.0652172	−	0.0652172i	−0.673746	−	0.738963i	$-0.735316\pi$
$11$	0.717389	−	0.717389i	0.0652172	−	0.0652172i	0.738963	+	0.673746i	$0.235316\pi$
$12$		0			0
$13$	−24.7701			−1.90540			−0.952698	−	0.303920i	$-0.901705\pi$
$13$	−24.7701			−1.90540			−0.952698	+	0.303920i	$0.901705\pi$
$14$		0			0
$15$	6.23338	+	2.47890i	0.415559	+	0.165260i
$16$		0			0
$17$	0.170354	+	16.9991i	0.0100208	+	0.999950i
$17$	0.170354	+	16.9991i	0.0100208	+	0.999950i
$18$		0			0
$19$		−	13.5866i		−	0.715084i	−0.933897	−	0.357542i	$-0.883615\pi$
$19$		−	13.5866i		−	0.715084i	0.933897	−	0.357542i	$-0.116385\pi$
$20$		0			0
$21$	−29.0619	−	11.5574i	−1.38390	−	0.550351i
$22$		0			0
$23$	12.2457	−	12.2457i	0.532421	−	0.532421i	−0.388871	−	0.921292i	$-0.627135\pi$
$23$	12.2457	−	12.2457i	0.532421	−	0.532421i	0.921292	+	0.388871i	$0.127135\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−9.26126	+	25.3620i	−0.343010	+	0.939332i
$28$		0			0
$29$	32.9689	+	32.9689i	1.13686	+	1.13686i	0.989010	+	0.147849i	$0.0472351\pi$
$29$	32.9689	+	32.9689i	1.13686	+	1.13686i	0.147849	+	0.989010i	$0.452765\pi$
$30$		0			0
$31$	−13.7594	+	13.7594i	−0.443851	+	0.443851i	−0.893304	−	0.449453i	$-0.851619\pi$
$31$	−13.7594	+	13.7594i	−0.443851	+	0.443851i	0.449453	+	0.893304i	$0.351619\pi$
$32$		0			0
$33$	−1.12472	+	2.82819i	−0.0340823	+	0.0857027i
$34$		0			0
$35$		−	23.3115i		−	0.666042i
$36$		0			0
$37$	−8.16355	+	8.16355i	−0.220637	+	0.220637i	−0.808766	−	0.588130i	$-0.799864\pi$
$37$	−8.16355	+	8.16355i	−0.220637	+	0.220637i	0.588130	+	0.808766i	$0.299864\pi$
$38$		0			0
$39$	68.2434	−	29.4089i	1.74983	−	0.754074i
$40$		0			0
$41$	37.4408	−	37.4408i	0.913189	−	0.913189i	−0.0833325	−	0.996522i	$-0.526556\pi$
$41$	37.4408	−	37.4408i	0.913189	−	0.913189i	0.996522	+	0.0833325i	$0.0265563\pi$
$42$		0			0
$43$			6.67315i			0.155190i	0.996985	+	0.0775948i	$0.0247240\pi$
$43$			6.67315i			0.155190i	−0.996985	+	0.0775948i	$0.975276\pi$
$44$		0			0
$45$	−20.1165	+	0.571195i	−0.447033	+	0.0126932i
$46$		0			0
$47$			7.72884i			0.164443i	0.996614	+	0.0822217i	$0.0262016\pi$
$47$			7.72884i			0.164443i	−0.996614	+	0.0822217i	$0.973798\pi$
$48$		0			0
$49$			59.6851i			1.21806i
$50$		0			0
$51$	−20.6519	−	46.6315i	−0.404940	−	0.914343i
$52$		0			0
$53$	−92.1223			−1.73816			−0.869079	−	0.494674i	$-0.835287\pi$
$53$	−92.1223			−1.73816			−0.869079	+	0.494674i	$0.835287\pi$
$54$		0			0
$55$	−2.26858			−0.0412469
$56$		0			0
$57$	16.1310	+	37.4320i	0.283000	+	0.656701i
$58$		0			0
$59$	5.96855			0.101162			0.0505810	−	0.998720i	$-0.483893\pi$
$59$	5.96855			0.101162			0.0505810	+	0.998720i	$0.483893\pi$
$60$		0			0
$61$	−42.3071	−	42.3071i	−0.693559	−	0.693559i	0.269454	−	0.963013i	$-0.413157\pi$
$61$	−42.3071	−	42.3071i	−0.693559	−	0.693559i	−0.963013	+	0.269454i	$0.913157\pi$
$62$		0			0
$63$	93.7891	−	2.66308i	1.48872	−	0.0422711i
$64$		0			0
$65$	39.1650	+	39.1650i	0.602539	+	0.602539i
$66$		0			0
$67$	−83.0546			−1.23962			−0.619810	−	0.784752i	$-0.712791\pi$
$67$	−83.0546			−1.23962			−0.619810	+	0.784752i	$0.712791\pi$
$68$		0			0
$69$	−19.1987	+	48.2766i	−0.278242	+	0.699660i
$70$		0			0
$71$	−61.7504	−	61.7504i	−0.869725	−	0.869725i	0.122717	−	0.992442i	$-0.460839\pi$
$71$	−61.7504	−	61.7504i	−0.869725	−	0.869725i	−0.992442	+	0.122717i	$0.960839\pi$
$72$		0			0
$73$	−27.5746	+	27.5746i	−0.377734	+	0.377734i	−0.870284	−	0.492550i	$-0.836065\pi$
$73$	−27.5746	+	27.5746i	−0.377734	+	0.377734i	0.492550	+	0.870284i	$0.336065\pi$
$74$		0			0
$75$	−5.93636	−	13.7753i	−0.0791515	−	0.183671i
$76$		0			0
$77$	10.5768			0.137361
$78$		0			0
$79$	−87.9466	−	87.9466i	−1.11325	−	1.11325i	−0.992708	−	0.120540i	$-0.961537\pi$
$79$	−87.9466	−	87.9466i	−1.11325	−	1.11325i	−0.120540	−	0.992708i	$-0.538463\pi$
$80$		0			0
$81$	−4.59618	−	80.8695i	−0.0567429	−	0.998389i
$82$		0			0
$83$	−121.079			−1.45879			−0.729393	−	0.684095i	$-0.760197\pi$
$83$	−121.079			−1.45879			−0.729393	+	0.684095i	$0.760197\pi$
$84$		0			0
$85$	26.6087	−	27.1474i	0.313043	−	0.319381i
$86$		0			0
$87$	−129.975	−	51.6884i	−1.49396	−	0.594120i
$88$		0			0
$89$			14.2907i			0.160569i	0.996772	+	0.0802847i	$0.0255830\pi$
$89$			14.2907i			0.160569i	−0.996772	+	0.0802847i	$0.974417\pi$
$90$		0			0
$91$	−182.599	−	182.599i	−2.00658	−	2.00658i
$92$		0			0
$93$	21.5719	−	54.2441i	0.231955	−	0.583270i
$94$		0			0
$95$	−21.4823	+	21.4823i	−0.226130	+	0.226130i
$96$		0			0
$97$	0.110634	−	0.110634i	0.00114055	−	0.00114055i	−0.706536	−	0.707677i	$-0.749743\pi$
$97$	0.110634	−	0.110634i	0.00114055	−	0.00114055i	0.707677	+	0.706536i	$0.249743\pi$
$98$		0			0
$99$	−0.259160	−	9.12719i	−0.00261778	−	0.0921938i
$100$		0			0
$101$			113.407i			1.12284i	0.827531	+	0.561420i	$0.189745\pi$
$101$			113.407i			1.12284i	−0.827531	+	0.561420i	$0.810255\pi$
$102$		0			0
$103$	−80.9991			−0.786399			−0.393200	−	0.919453i	$-0.628632\pi$
$103$	−80.9991			−0.786399			−0.393200	+	0.919453i	$0.628632\pi$
$104$		0			0
$105$	27.6771	+	64.2247i	0.263591	+	0.611663i
$106$		0			0
$107$	65.1487	+	65.1487i	0.608866	+	0.608866i	0.942650	−	0.333783i	$-0.108325\pi$
$107$	65.1487	+	65.1487i	0.608866	+	0.608866i	−0.333783	+	0.942650i	$0.608325\pi$
$108$		0			0
$109$	−122.492	−	122.492i	−1.12378	−	1.12378i	−0.991168	−	0.132610i	$-0.957664\pi$
$109$	−122.492	−	122.492i	−1.12378	−	1.12378i	−0.132610	−	0.991168i	$-0.542336\pi$
$110$		0			0
$111$	12.7988	−	32.1835i	0.115304	−	0.289941i
$112$		0			0
$113$	3.17901	−	3.17901i	0.0281329	−	0.0281329i	−0.692900	−	0.721033i	$-0.743667\pi$
$113$	3.17901	−	3.17901i	0.0281329	−	0.0281329i	0.721033	+	0.692900i	$0.243667\pi$
$114$		0			0
$115$	−38.7242			−0.336732
$116$		0			0
$117$	−153.099	+	162.047i	−1.30853	+	1.38502i
$118$		0			0
$119$	−124.057	+	126.569i	−1.04250	+	1.06361i
$120$		0			0
$121$			119.971i			0.991493i
$122$		0			0
$123$	−58.6994	+	147.604i	−0.477231	+	1.20003i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$		−	133.992i		−	1.05506i	−0.849537	−	0.527528i	$-0.823119\pi$
$127$		−	133.992i		−	1.05506i	0.849537	−	0.527528i	$-0.176881\pi$
$128$		0			0
$129$	−7.92285	−	18.3850i	−0.0614174	−	0.142519i
$130$		0			0
$131$	55.0522	+	55.0522i	0.420246	+	0.420246i	0.885288	−	0.465042i	$-0.153961\pi$
$131$	55.0522	+	55.0522i	0.420246	+	0.420246i	−0.465042	+	0.885288i	$0.653961\pi$
$132$		0			0
$133$	100.157	−	100.157i	0.753059	−	0.753059i
$134$		0			0
$135$	54.7441	−	25.4574i	0.405512	−	0.188574i
$136$		0			0
$137$		−	250.320i		−	1.82715i	−0.406667	−	0.913576i	$-0.633309\pi$
$137$		−	250.320i		−	1.82715i	0.406667	−	0.913576i	$-0.366691\pi$
$138$		0			0
$139$	−76.6078	+	76.6078i	−0.551135	+	0.551135i	−0.926768	−	0.375633i	$-0.877425\pi$
$139$	−76.6078	+	76.6078i	−0.551135	+	0.551135i	0.375633	+	0.926768i	$0.377425\pi$
$140$		0			0
$141$	−9.17624	−	21.2935i	−0.0650797	−	0.151018i
$142$		0			0
$143$	−17.7698	+	17.7698i	−0.124264	+	0.124264i
$144$		0			0
$145$		−	104.257i		−	0.719013i
$146$		0			0
$147$	−70.8624	−	164.436i	−0.482057	−	1.11861i
$148$		0			0
$149$		−	26.9749i		−	0.181040i	−0.995895	−	0.0905198i	$-0.971147\pi$
$149$		−	26.9749i		−	0.181040i	0.995895	−	0.0905198i	$-0.0288528\pi$
$150$		0			0
$151$		−	1.82381i		−	0.0120782i	−0.999982	−	0.00603911i	$-0.998078\pi$
$151$		−	1.82381i		−	0.0120782i	0.999982	−	0.00603911i	$-0.00192232\pi$
$152$		0			0
$153$	112.262	+	103.953i	0.733737	+	0.679434i
$154$		0			0
$155$	43.5110			0.280716
$156$		0			0
$157$	170.241			1.08434			0.542170	−	0.840269i	$-0.317603\pi$
$157$	170.241			1.08434			0.542170	+	0.840269i	$0.317603\pi$
$158$		0			0
$159$	253.803	−	109.374i	1.59625	−	0.687889i
$160$		0			0
$161$	180.544			1.12139
$162$		0			0
$163$	−32.8908	−	32.8908i	−0.201784	−	0.201784i	0.598980	−	0.800764i	$-0.295573\pi$
$163$	−32.8908	−	32.8908i	−0.201784	−	0.201784i	−0.800764	+	0.598980i	$0.795573\pi$
$164$		0			0
$165$	6.25009	−	2.69342i	0.0378793	−	0.0163238i
$166$		0			0
$167$	149.410	+	149.410i	0.894671	+	0.894671i	0.994958	−	0.100288i	$-0.0319763\pi$
$167$	149.410	+	149.410i	0.894671	+	0.894671i	−0.100288	+	0.994958i	$0.531976\pi$
$168$		0			0
$169$	444.560			2.63053
$170$		0			0
$171$	−88.8839	−	83.9757i	−0.519789	−	0.491086i
$172$		0			0
$173$	−148.425	−	148.425i	−0.857949	−	0.857949i	0.133147	−	0.991096i	$-0.457492\pi$
$173$	−148.425	−	148.425i	−0.857949	−	0.857949i	−0.991096	+	0.133147i	$0.957492\pi$
$174$		0			0
$175$	−36.8587	+	36.8587i	−0.210621	+	0.210621i
$176$		0			0
$177$	−16.4438	+	7.08630i	−0.0929026	+	0.0400356i
$178$		0			0
$179$	−267.994			−1.49717			−0.748585	−	0.663038i	$-0.769267\pi$
$179$	−267.994			−1.49717			−0.748585	+	0.663038i	$0.769267\pi$
$180$		0			0
$181$	−106.662	−	106.662i	−0.589295	−	0.589295i	0.348146	−	0.937440i	$-0.386811\pi$
$181$	−106.662	−	106.662i	−0.589295	−	0.589295i	−0.937440	+	0.348146i	$0.886811\pi$
$182$		0			0
$183$	166.789	+	66.3288i	0.911415	+	0.362452i
$184$		0			0
$185$	25.8154			0.139543
$186$		0			0
$187$	12.3172	+	12.0728i	0.0658674	+	0.0645603i
$188$		0			0
$189$	−255.233	+	118.690i	−1.35044	+	0.627990i
$190$		0			0
$191$		−	154.377i		−	0.808257i	−0.914702	−	0.404129i	$-0.867575\pi$
$191$		−	154.377i		−	0.808257i	0.914702	−	0.404129i	$-0.132425\pi$
$192$		0			0
$193$	7.20027	+	7.20027i	0.0373071	+	0.0373071i	0.725514	−	0.688207i	$-0.241602\pi$
$193$	7.20027	+	7.20027i	0.0373071	+	0.0373071i	−0.688207	+	0.725514i	$0.741602\pi$
$194$		0			0
$195$	−154.402	−	61.4027i	−0.791804	−	0.314885i
$196$		0			0
$197$	−53.9476	+	53.9476i	−0.273846	+	0.273846i	−0.830646	−	0.556801i	$-0.812029\pi$
$197$	−53.9476	+	53.9476i	−0.273846	+	0.273846i	0.556801	+	0.830646i	$0.312029\pi$
$198$		0			0
$199$	−175.671	+	175.671i	−0.882766	+	0.882766i	−0.993815	−	0.111049i	$-0.964579\pi$
$199$	−175.671	+	175.671i	−0.882766	+	0.882766i	0.111049	+	0.993815i	$0.464579\pi$
$200$		0			0
$201$	228.821	−	98.6084i	1.13841	−	0.490589i
$202$		0			0
$203$			486.077i			2.39447i
$204$		0			0
$205$	−118.398			−0.577552
$206$		0			0
$207$	−4.42381	−	155.799i	−0.0213711	−	0.752653i
$208$		0			0
$209$	−9.74687	−	9.74687i	−0.0466358	−	0.0466358i
$210$		0			0
$211$	−64.7548	−	64.7548i	−0.306895	−	0.306895i	0.536809	−	0.843704i	$-0.319630\pi$
$211$	−64.7548	−	64.7548i	−0.306895	−	0.306895i	−0.843704	+	0.536809i	$0.819630\pi$
$212$		0			0
$213$	243.441	+	96.8119i	1.14292	+	0.454516i
$214$		0			0
$215$	10.5512	−	10.5512i	0.0490753	−	0.0490753i
$216$		0			0
$217$	−202.861			−0.934843
$218$		0			0
$219$	43.2313	−	108.708i	0.197403	−	0.496385i
$220$		0			0
$221$	−4.21968	−	421.071i	−0.0190936	−	1.90530i
$222$		0			0
$223$			17.4822i			0.0783955i	0.999231	+	0.0391977i	$0.0124802\pi$
$223$			17.4822i			0.0783955i	−0.999231	+	0.0391977i	$0.987520\pi$
$224$		0			0
$225$	32.7101	+	30.9038i	0.145378	+	0.137350i
$226$		0			0
$227$	−173.256	+	173.256i	−0.763241	+	0.763241i	−0.976907	−	0.213665i	$-0.931460\pi$
$227$	−173.256	+	173.256i	−0.763241	+	0.763241i	0.213665	+	0.976907i	$0.431460\pi$
$228$		0			0
$229$			384.695i			1.67989i	0.542669	+	0.839947i	$0.317414\pi$
$229$			384.695i			1.67989i	−0.542669	+	0.839947i	$0.682586\pi$
$230$		0			0
$231$	−29.1398	+	12.5575i	−0.126146	+	0.0543617i
$232$		0			0
$233$	239.515	+	239.515i	1.02796	+	1.02796i	0.999598	+	0.0283638i	$0.00902970\pi$
$233$	239.515	+	239.515i	1.02796	+	1.02796i	0.0283638	+	0.999598i	$0.490970\pi$
$234$		0			0
$235$	12.2204	−	12.2204i	0.0520016	−	0.0520016i
$236$		0			0
$237$	346.715	+	137.882i	1.46293	+	0.581781i
$238$		0			0
$239$		−	243.430i		−	1.01854i	−0.860608	−	0.509268i	$-0.829916\pi$
$239$		−	243.430i		−	1.01854i	0.860608	−	0.509268i	$-0.170084\pi$
$240$		0			0
$241$	−323.707	+	323.707i	−1.34318	+	1.34318i	−0.450307	+	0.892874i	$0.648686\pi$
$241$	−323.707	+	323.707i	−1.34318	+	1.34318i	−0.892874	+	0.450307i	$0.851314\pi$
$242$		0			0
$243$	108.677	+	217.344i	0.447230	+	0.894419i
$244$		0			0
$245$	94.3704	−	94.3704i	0.385185	−	0.385185i
$246$		0			0
$247$			336.542i			1.36252i
$248$		0			0
$249$	333.581	−	143.754i	1.33968	−	0.577325i
$250$		0			0
$251$		−	479.592i		−	1.91073i	−0.295435	−	0.955363i	$-0.595465\pi$
$251$		−	479.592i		−	1.91073i	0.295435	−	0.955363i	$-0.404535\pi$
$252$		0			0
$253$		−	17.5698i		−	0.0694459i
$254$		0			0
$255$	−41.0773	+	106.384i	−0.161087	+	0.417194i
$256$		0			0
$257$	−8.44665			−0.0328664			−0.0164332	−	0.999865i	$-0.505231\pi$
$257$	−8.44665			−0.0328664			−0.0164332	+	0.999865i	$0.505231\pi$
$258$		0			0
$259$	−120.359			−0.464707
$260$		0			0
$261$	419.457	−	11.9102i	1.60711	−	0.0456329i
$262$		0			0
$263$	110.338			0.419537			0.209768	−	0.977751i	$-0.432729\pi$
$263$	110.338			0.419537			0.209768	+	0.977751i	$0.432729\pi$
$264$		0			0
$265$	145.658	+	145.658i	0.549654	+	0.549654i
$266$		0			0
$267$	−16.9669	−	39.3718i	−0.0635466	−	0.147460i
$268$		0			0
$269$	−27.4919	−	27.4919i	−0.102201	−	0.102201i	0.654158	−	0.756358i	$-0.273023\pi$
$269$	−27.4919	−	27.4919i	−0.102201	−	0.102201i	−0.756358	+	0.654158i	$0.773023\pi$
$270$		0			0
$271$	−182.381			−0.672993			−0.336496	−	0.941685i	$-0.609242\pi$
$271$	−182.381			−0.672993			−0.336496	+	0.941685i	$0.609242\pi$
$272$		0			0
$273$	719.867	+	286.277i	2.63688	+	1.04864i
$274$		0			0
$275$	3.58694	+	3.58694i	0.0130434	+	0.0130434i
$276$		0			0
$277$	−143.436	+	143.436i	−0.517821	+	0.517821i	−0.916912	−	0.399090i	$-0.869326\pi$
$277$	−143.436	+	143.436i	−0.517821	+	0.517821i	0.399090	+	0.916912i	$0.369326\pi$
$278$		0			0
$279$	4.97065	+	175.058i	0.0178159	+	0.627447i
$280$		0			0
$281$	99.8901			0.355481			0.177740	−	0.984077i	$-0.443121\pi$
$281$	99.8901			0.355481			0.177740	+	0.984077i	$0.443121\pi$
$282$		0			0
$283$	77.7849	+	77.7849i	0.274858	+	0.274858i	0.831052	−	0.556194i	$-0.187739\pi$
$283$	77.7849	+	77.7849i	0.274858	+	0.274858i	−0.556194	+	0.831052i	$0.687739\pi$
$284$		0			0
$285$	33.6798	−	84.6905i	0.118175	−	0.297160i
$286$		0			0
$287$	552.007			1.92337
$288$		0			0
$289$	−288.942	+	5.79173i	−0.999799	+	0.0200406i
$290$		0			0
$291$	−0.173451	+	0.436155i	−0.000596050	+	0.00149881i
$292$		0			0
$293$			358.350i			1.22304i	0.791231	+	0.611518i	$0.209441\pi$
$293$			358.350i			1.22304i	−0.791231	+	0.611518i	$0.790559\pi$
$294$		0			0
$295$	−9.43711	−	9.43711i	−0.0319902	−	0.0319902i
$296$		0			0
$297$	11.5505	+	24.8383i	0.0388904	+	0.0836307i
$298$		0			0
$299$	−303.327	+	303.327i	−1.01447	+	1.01447i
$300$		0			0
$301$	−49.1927	+	49.1927i	−0.163431	+	0.163431i
$302$		0			0
$303$	−134.645	−	312.443i	−0.444372	−	1.03117i
$304$		0			0
$305$			133.787i			0.438645i
$306$		0			0
$307$	37.9130			0.123495			0.0617476	−	0.998092i	$-0.480333\pi$
$307$	37.9130			0.123495			0.0617476	+	0.998092i	$0.480333\pi$
$308$		0			0
$309$	223.158	−	96.1680i	0.722194	−	0.311223i
$310$		0			0
$311$	−174.026	−	174.026i	−0.559569	−	0.559569i	0.369616	−	0.929185i	$-0.379489\pi$
$311$	−174.026	−	174.026i	−0.559569	−	0.559569i	−0.929185	+	0.369616i	$0.879489\pi$
$312$		0			0
$313$	49.4677	+	49.4677i	0.158044	+	0.158044i	0.781699	−	0.623655i	$-0.214353\pi$
$313$	49.4677	+	49.4677i	0.158044	+	0.158044i	−0.623655	+	0.781699i	$0.714353\pi$
$314$		0			0
$315$	−152.504	−	144.083i	−0.484141	−	0.457406i
$316$		0			0
$317$	265.650	−	265.650i	0.838011	−	0.838011i	−0.150586	−	0.988597i	$-0.548116\pi$
$317$	265.650	−	265.650i	0.838011	−	0.838011i	0.988597	+	0.150586i	$0.0481160\pi$
$318$		0			0
$319$	47.3031			0.148285
$320$		0			0
$321$	−256.838	−	102.140i	−0.800119	−	0.318192i
$322$		0			0
$323$	230.961	−	2.31453i	0.715048	−	0.00716572i
$324$		0			0
$325$		−	123.851i		−	0.381079i
$326$		0			0
$327$	482.904	+	192.042i	1.47677	+	0.587284i
$328$		0			0
$329$	−56.9750	+	56.9750i	−0.173176	+	0.173176i
$330$		0			0
$331$		−	34.6392i		−	0.104650i	−0.998630	−	0.0523250i	$-0.983337\pi$
$331$		−	34.6392i		−	0.104650i	0.998630	−	0.0523250i	$-0.0166632\pi$
$332$		0			0
$333$	2.94913	+	103.863i	0.00885623	+	0.311901i
$334$		0			0
$335$	131.321	+	131.321i	0.392003	+	0.392003i
$336$		0			0
$337$	−353.516	+	353.516i	−1.04901	+	1.04901i	−0.0502746	+	0.998735i	$0.516010\pi$
$337$	−353.516	+	353.516i	−1.04901	+	1.04901i	−0.998735	+	0.0502746i	$0.983990\pi$
$338$		0			0
$339$	−4.98404	+	12.5327i	−0.0147022	+	0.0369698i
$340$		0			0
$341$			19.7416i			0.0578934i
$342$		0			0
$343$	−78.7676	+	78.7676i	−0.229643	+	0.229643i
$344$		0			0
$345$	106.688	−	45.9762i	0.309240	−	0.133264i
$346$		0			0
$347$	40.1184	−	40.1184i	0.115615	−	0.115615i	−0.646932	−	0.762547i	$-0.723948\pi$
$347$	40.1184	−	40.1184i	0.115615	−	0.115615i	0.762547	+	0.646932i	$0.223948\pi$
$348$		0			0
$349$		−	151.474i		−	0.434022i	−0.976169	−	0.217011i	$-0.930369\pi$
$349$		−	151.474i		−	0.434022i	0.976169	−	0.217011i	$-0.0696307\pi$
$350$		0			0
$351$	229.403	−	628.219i	0.653569	−	1.78980i
$352$		0			0
$353$			604.975i			1.71381i	0.515474	+	0.856905i	$0.327616\pi$
$353$			604.975i			1.71381i	−0.515474	+	0.856905i	$0.672384\pi$
$354$		0			0
$355$			195.272i			0.550062i
$356$		0			0
$357$	191.514	−	495.996i	0.536455	−	1.38934i
$358$		0			0
$359$	109.193			0.304158			0.152079	−	0.988368i	$-0.451403\pi$
$359$	109.193			0.304158			0.152079	+	0.988368i	$0.451403\pi$
$360$		0			0
$361$	176.404			0.488654
$362$		0			0
$363$	−142.438	−	330.527i	−0.392391	−	0.910543i
$364$		0			0
$365$	87.1985			0.238900
$366$		0			0
$367$	22.5521	+	22.5521i	0.0614498	+	0.0614498i	0.737164	−	0.675714i	$-0.236165\pi$
$367$	22.5521	+	22.5521i	0.0614498	+	0.0614498i	−0.675714	+	0.737164i	$0.736165\pi$
$368$		0			0
$369$	−13.5257	−	476.351i	−0.0366549	−	1.29092i
$370$		0			0
$371$	−679.102	−	679.102i	−1.83046	−	1.83046i
$372$		0			0
$373$	616.065			1.65165			0.825824	−	0.563928i	$-0.190710\pi$
$373$	616.065			1.65165			0.825824	+	0.563928i	$0.190710\pi$
$374$		0			0
$375$	−12.3945	+	31.1669i	−0.0330520	+	0.0831118i
$376$		0			0
$377$	−816.645	−	816.645i	−2.16617	−	2.16617i
$378$		0			0
$379$	294.393	−	294.393i	0.776761	−	0.776761i	−0.202517	−	0.979279i	$-0.564912\pi$
$379$	294.393	−	294.393i	0.776761	−	0.776761i	0.979279	+	0.202517i	$0.0649123\pi$
$380$		0			0
$381$	159.085	+	369.157i	0.417547	+	0.968917i
$382$		0			0
$383$	−151.157			−0.394667			−0.197333	−	0.980336i	$-0.563228\pi$
$383$	−151.157			−0.394667			−0.197333	+	0.980336i	$0.563228\pi$
$384$		0			0
$385$	−16.7234	−	16.7234i	−0.0434374	−	0.0434374i
$386$		0			0
$387$	43.6559	+	41.2452i	0.112806	+	0.106577i
$388$		0			0
$389$	401.986			1.03338			0.516691	−	0.856172i	$-0.327163\pi$
$389$	401.986			1.03338			0.516691	+	0.856172i	$0.327163\pi$
$390$		0			0
$391$	210.252	+	206.080i	0.537729	+	0.527058i
$392$		0			0
$393$	−217.034	−	86.3105i	−0.552251	−	0.219620i
$394$		0			0
$395$			278.112i			0.704080i
$396$		0			0
$397$	−23.4521	−	23.4521i	−0.0590733	−	0.0590733i	0.676953	−	0.736026i	$-0.263300\pi$
$397$	−23.4521	−	23.4521i	−0.0590733	−	0.0590733i	−0.736026	+	0.676953i	$0.763300\pi$
$398$		0			0
$399$	−157.025	+	394.852i	−0.393547	+	0.989605i
$400$		0			0
$401$	164.811	−	164.811i	0.411000	−	0.411000i	−0.471087	−	0.882087i	$-0.656138\pi$
$401$	164.811	−	164.811i	0.411000	−	0.411000i	0.882087	+	0.471087i	$0.156138\pi$
$402$		0			0
$403$	340.822	−	340.822i	0.845711	−	0.845711i
$404$		0			0
$405$	−120.599	+	135.133i	−0.297775	+	0.333662i
$406$		0			0
$407$			11.7129i			0.0287786i
$408$		0			0
$409$	−397.969			−0.973029			−0.486515	−	0.873672i	$-0.661732\pi$
$409$	−397.969			−0.973029			−0.486515	+	0.873672i	$0.661732\pi$
$410$		0			0
$411$	297.198	+	689.648i	0.723109	+	1.67798i
$412$		0			0
$413$	43.9986	+	43.9986i	0.106534	+	0.106534i
$414$		0			0
$415$	191.443	+	191.443i	0.461308	+	0.461308i
$416$		0			0
$417$	120.105	−	302.014i	0.288022	−	0.724254i
$418$		0			0
$419$	432.995	−	432.995i	1.03340	−	1.03340i	0.0339791	−	0.999423i	$-0.489182\pi$
$419$	432.995	−	432.995i	1.03340	−	1.03340i	0.999423	−	0.0339791i	$-0.0108180\pi$
$420$		0			0
$421$	543.118			1.29007			0.645033	−	0.764155i	$-0.276844\pi$
$421$	543.118			1.29007			0.645033	+	0.764155i	$0.276844\pi$
$422$		0			0
$423$	50.5623	+	47.7702i	0.119533	+	0.112932i
$424$		0			0
$425$	−84.9957	+	0.851768i	−0.199990	+	0.00200416i
$426$		0			0
$427$		−	623.754i		−	1.46078i
$428$		0			0
$429$	27.8594	−	70.0546i	0.0649403	−	0.163297i
$430$		0			0
$431$	−565.286	+	565.286i	−1.31157	+	1.31157i	−0.391311	+	0.920259i	$0.627978\pi$
$431$	−565.286	+	565.286i	−1.31157	+	1.31157i	−0.920259	+	0.391311i	$0.872022\pi$
$432$		0			0
$433$			502.047i			1.15946i	0.814808	+	0.579731i	$0.196843\pi$
$433$			502.047i			1.15946i	−0.814808	+	0.579731i	$0.803157\pi$
$434$		0			0
$435$	123.781	+	287.235i	0.284555	+	0.660309i
$436$		0			0
$437$	−166.377	−	166.377i	−0.380726	−	0.380726i
$438$		0			0
$439$	307.432	−	307.432i	0.700301	−	0.700301i	−0.264174	−	0.964475i	$-0.585099\pi$
$439$	307.432	−	307.432i	0.700301	−	0.700301i	0.964475	+	0.264174i	$0.0850993\pi$
$440$		0			0
$441$	390.461	+	368.900i	0.885400	+	0.836507i
$442$		0			0
$443$		−	535.492i		−	1.20879i	−0.796686	−	0.604393i	$-0.793416\pi$
$443$		−	535.492i		−	1.20879i	0.796686	−	0.604393i	$-0.206584\pi$
$444$		0			0
$445$	22.5956	−	22.5956i	0.0507765	−	0.0507765i
$446$		0			0
$447$	32.0265	+	74.3176i	0.0716477	+	0.166259i
$448$		0			0
$449$	606.203	−	606.203i	1.35012	−	1.35012i	0.464596	−	0.885523i	$-0.346200\pi$
$449$	606.203	−	606.203i	1.35012	−	1.35012i	0.885523	−	0.464596i	$-0.153800\pi$
$450$		0			0
$451$		−	53.7192i		−	0.119111i
$452$		0			0
$453$	2.16536	+	5.02472i	0.00478005	+	0.0110921i
$454$		0			0
$455$			577.429i			1.26907i
$456$		0			0
$457$			636.344i			1.39244i	0.717829	+	0.696219i	$0.245136\pi$
$457$			636.344i			1.39244i	−0.717829	+	0.696219i	$0.754864\pi$
$458$		0			0
$459$	−432.709	−	153.113i	−0.942722	−	0.333580i
$460$		0			0
$461$	259.703			0.563346			0.281673	−	0.959510i	$-0.409111\pi$
$461$	259.703			0.563346			0.281673	+	0.959510i	$0.409111\pi$
$462$		0			0
$463$	−298.444			−0.644588			−0.322294	−	0.946640i	$-0.604454\pi$
$463$	−298.444			−0.644588			−0.322294	+	0.946640i	$0.604454\pi$
$464$		0			0
$465$	−119.876	+	51.6594i	−0.257797	+	0.111095i
$466$		0			0
$467$	−221.292			−0.473858			−0.236929	−	0.971527i	$-0.576141\pi$
$467$	−221.292			−0.473858			−0.236929	+	0.971527i	$0.576141\pi$
$468$		0			0
$469$	−612.257	−	612.257i	−1.30545	−	1.30545i
$470$		0			0
$471$	−469.026	+	202.123i	−0.995809	+	0.429135i
$472$		0			0
$473$	4.78724	+	4.78724i	0.0101210	+	0.0101210i
$474$		0			0
$475$	67.9330			0.143017
$476$		0			0
$477$	−569.387	+	602.667i	−1.19368	+	1.26345i
$478$		0			0
$479$	446.756	+	446.756i	0.932685	+	0.932685i	0.997873	−	0.0651882i	$-0.0207648\pi$
$479$	446.756	+	446.756i	0.932685	+	0.932685i	−0.0651882	+	0.997873i	$0.520765\pi$
$480$		0			0
$481$	202.212	−	202.212i	0.420400	−	0.420400i
$482$		0			0
$483$	−497.410	+	214.355i	−1.02983	+	0.443798i
$484$		0			0
$485$	−0.349854			−0.000721349
$486$		0			0
$487$	−489.610	−	489.610i	−1.00536	−	1.00536i	−0.999986	−	0.00537385i	$-0.998289\pi$
$487$	−489.610	−	489.610i	−1.00536	−	1.00536i	−0.00537385	−	0.999986i	$-0.501711\pi$
$488$		0			0
$489$	129.667	+	51.5660i	0.265167	+	0.105452i
$490$		0			0
$491$	−149.440			−0.304359			−0.152180	−	0.988353i	$-0.548629\pi$
$491$	−149.440			−0.304359			−0.152180	+	0.988353i	$0.548629\pi$
$492$		0			0
$493$	−554.827	+	566.060i	−1.12541	+	1.14819i
$494$		0			0
$495$	−14.0216	+	14.8411i	−0.0283264	+	0.0299821i
$496$		0			0
$497$		−	910.416i		−	1.83182i
$498$		0			0
$499$	408.704	+	408.704i	0.819047	+	0.819047i	0.985970	−	0.166923i	$-0.0533831\pi$
$499$	408.704	+	408.704i	0.819047	+	0.819047i	−0.166923	+	0.985970i	$0.553383\pi$
$500$		0			0
$501$	−589.025	−	234.244i	−1.17570	−	0.467553i
$502$		0			0
$503$	122.617	−	122.617i	0.243772	−	0.243772i	−0.574636	−	0.818409i	$-0.694857\pi$
$503$	122.617	−	122.617i	0.243772	−	0.243772i	0.818409	+	0.574636i	$0.194857\pi$
$504$		0			0
$505$	179.312	−	179.312i	0.355073	−	0.355073i
$506$		0			0
$507$	−1224.79	+	527.813i	−2.41576	+	1.04105i
$508$		0			0
$509$			600.158i			1.17909i	0.807734	+	0.589547i	$0.200694\pi$
$509$			600.158i			1.17909i	−0.807734	+	0.589547i	$0.799306\pi$
$510$		0			0
$511$	−406.545			−0.795588
$512$		0			0
$513$	344.583	+	125.829i	0.671701	+	0.245281i
$514$		0			0
$515$	128.071	+	128.071i	0.248681	+	0.248681i
$516$		0			0
$517$	5.54458	+	5.54458i	0.0107245	+	0.0107245i
$518$		0			0
$519$	585.142	+	232.700i	1.12744	+	0.448362i
$520$		0			0
$521$	−391.804	+	391.804i	−0.752023	+	0.752023i	−0.974857	−	0.222834i	$-0.928469\pi$
$521$	−391.804	+	391.804i	−0.752023	+	0.752023i	0.222834	+	0.974857i	$0.428469\pi$
$522$		0			0
$523$	−193.244			−0.369491			−0.184745	−	0.982786i	$-0.559146\pi$
$523$	−193.244			−0.369491			−0.184745	+	0.982786i	$0.559146\pi$
$524$		0			0
$525$	57.7868	−	145.309i	0.110070	−	0.276780i
$526$		0			0
$527$	−236.242	−	231.554i	−0.448276	−	0.439381i
$528$		0			0
$529$			229.087i			0.433057i
$530$		0			0
$531$	36.8903	−	39.0464i	0.0694732	−	0.0735338i
$532$		0			0
$533$	−927.413	+	927.413i	−1.73999	+	1.73999i
$534$		0			0
$535$		−	206.018i		−	0.385081i
$536$		0			0
$537$	738.340	−	318.181i	1.37493	−	0.592516i
$538$		0			0
$539$	42.8174	+	42.8174i	0.0794386	+	0.0794386i
$540$		0			0
$541$	−562.218	+	562.218i	−1.03922	+	1.03922i	−0.0400206	+	0.999199i	$0.512742\pi$
$541$	−562.218	+	562.218i	−1.03922	+	1.03922i	−0.999199	+	0.0400206i	$0.987258\pi$
$542$		0			0
$543$	420.499	+	167.224i	0.774399	+	0.307964i
$544$		0			0
$545$			387.353i			0.710740i
$546$		0			0
$547$	194.304	−	194.304i	0.355218	−	0.355218i	−0.506829	−	0.862047i	$-0.669182\pi$
$547$	194.304	−	194.304i	0.355218	−	0.355218i	0.862047	+	0.506829i	$0.169182\pi$
$548$		0			0
$549$	−538.265	+	15.2837i	−0.980446	+	0.0278391i
$550$		0			0
$551$	447.936	−	447.936i	0.812950	−	0.812950i
$552$		0			0
$553$		−	1296.64i		−	2.34474i
$554$		0			0
$555$	−71.1232	+	30.6499i	−0.128150	+	0.0552251i
$556$		0			0
$557$			496.557i			0.891485i	0.895161	+	0.445742i	$0.147060\pi$
$557$			496.557i			0.891485i	−0.895161	+	0.445742i	$0.852940\pi$
$558$		0			0
$559$		−	165.295i		−	0.295698i
$560$		0			0
$561$	−48.2684	−	18.6374i	−0.0860399	−	0.0332218i
$562$		0			0
$563$	920.984			1.63585			0.817925	−	0.575324i	$-0.195124\pi$
$563$	920.984			1.63585			0.817925	+	0.575324i	$0.195124\pi$
$564$		0			0
$565$	−10.0529			−0.0177928
$566$		0			0
$567$	562.267	−	630.031i	0.991653	−	1.11117i
$568$		0			0
$569$	166.966			0.293438			0.146719	−	0.989178i	$-0.453129\pi$
$569$	166.966			0.293438			0.146719	+	0.989178i	$0.453129\pi$
$570$		0			0
$571$	−360.852	−	360.852i	−0.631965	−	0.631965i	0.316596	−	0.948561i	$-0.397460\pi$
$571$	−360.852	−	360.852i	−0.631965	−	0.631965i	−0.948561	+	0.316596i	$0.897460\pi$
$572$		0			0
$573$	183.288	+	425.319i	0.319874	+	0.742267i
$574$		0			0
$575$	61.2284	+	61.2284i	0.106484	+	0.106484i
$576$		0			0
$577$	−623.011			−1.07974			−0.539871	−	0.841748i	$-0.681527\pi$
$577$	−623.011			−1.07974			−0.539871	+	0.841748i	$0.681527\pi$
$578$		0			0
$579$	−28.3859	−	11.2885i	−0.0490257	−	0.0194966i
$580$		0			0
$581$	−892.564	−	892.564i	−1.53625	−	1.53625i
$582$		0			0
$583$	−66.0875	+	66.0875i	−0.113358	+	0.113358i
$584$		0			0
$585$	498.289	−	14.1486i	0.851775	−	0.0241856i
$586$		0			0
$587$	878.053			1.49583			0.747915	−	0.663794i	$-0.231055\pi$
$587$	878.053			1.49583			0.747915	+	0.663794i	$0.231055\pi$
$588$		0			0
$589$	186.943	+	186.943i	0.317391	+	0.317391i
$590$		0			0
$591$	84.5787	−	212.680i	0.143111	−	0.359864i
$592$		0			0
$593$	−599.403			−1.01080			−0.505399	−	0.862886i	$-0.668655\pi$
$593$	−599.403			−1.01080			−0.505399	+	0.862886i	$0.668655\pi$
$594$		0			0
$595$	396.275	−	3.97119i	0.666009	−	0.00667428i
$596$		0			0
$597$	275.415	−	692.552i	0.461332	−	1.16005i
$598$		0			0
$599$			919.559i			1.53516i	0.640955	+	0.767579i	$0.278539\pi$
$599$			919.559i			1.53516i	−0.640955	+	0.767579i	$0.721461\pi$
$600$		0			0
$601$	260.748	+	260.748i	0.433858	+	0.433858i	0.889938	−	0.456081i	$-0.150747\pi$
$601$	260.748	+	260.748i	0.433858	+	0.433858i	−0.456081	+	0.889938i	$0.650747\pi$
$602$		0			0
$603$	−513.341	+	543.345i	−0.851312	+	0.901070i
$604$		0			0
$605$	189.690	−	189.690i	0.313538	−	0.313538i
$606$		0			0
$607$	3.92954	−	3.92954i	0.00647371	−	0.00647371i	−0.703863	−	0.710336i	$-0.748543\pi$
$607$	3.92954	−	3.92954i	0.00647371	−	0.00647371i	0.710336	+	0.703863i	$0.248543\pi$
$608$		0			0
$609$	−577.105	−	1339.17i	−0.947628	−	2.19897i
$610$		0			0
$611$		−	191.445i		−	0.313330i
$612$		0			0
$613$	629.309			1.02661			0.513303	−	0.858208i	$-0.328422\pi$
$613$	629.309			1.02661			0.513303	+	0.858208i	$0.328422\pi$
$614$		0			0
$615$	326.194	−	140.571i	0.530397	−	0.228570i
$616$		0			0
$617$	−10.2093	−	10.2093i	−0.0165466	−	0.0165466i	0.698785	−	0.715332i	$-0.253724\pi$
$617$	−10.2093	−	10.2093i	−0.0165466	−	0.0165466i	−0.715332	+	0.698785i	$0.753724\pi$
$618$		0			0
$619$	−160.357	−	160.357i	−0.259059	−	0.259059i	0.565612	−	0.824671i	$-0.308640\pi$
$619$	−160.357	−	160.357i	−0.259059	−	0.259059i	−0.824671	+	0.565612i	$0.808640\pi$
$620$		0			0
$621$	197.164	+	423.985i	0.317494	+	0.682745i
$622$		0			0
$623$	−105.347	+	105.347i	−0.169097	+	0.169097i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	38.4255	+	15.2811i	0.0612846	+	0.0243717i
$628$		0			0
$629$	−140.164	−	137.383i	−0.222836	−	0.218415i
$630$		0			0
$631$			1212.22i			1.92111i	0.278092	+	0.960555i	$0.410298\pi$
$631$			1212.22i			1.92111i	−0.278092	+	0.960555i	$0.589702\pi$
$632$		0			0
$633$	255.285	+	101.522i	0.403294	+	0.160383i
$634$		0			0
$635$	−211.860	+	211.860i	−0.333638	+	0.333638i
$636$		0			0
$637$		−	1478.41i		−	2.32089i
$638$		0			0
$639$	−785.638	+	22.3077i	−1.22948	+	0.0349103i
$640$		0			0
$641$	−3.33846	−	3.33846i	−0.00520821	−	0.00520821i	0.704498	−	0.709706i	$-0.251172\pi$
$641$	−3.33846	−	3.33846i	−0.00520821	−	0.00520821i	−0.709706	+	0.704498i	$0.751172\pi$
$642$		0			0
$643$	−361.642	+	361.642i	−0.562429	+	0.562429i	−0.929997	−	0.367568i	$-0.880191\pi$
$643$	−361.642	+	361.642i	−0.562429	+	0.562429i	0.367568	+	0.929997i	$0.380191\pi$
$644$		0			0
$645$	−16.5421	+	41.5963i	−0.0256466	+	0.0644904i
$646$		0			0
$647$		−	407.426i		−	0.629715i	−0.949139	−	0.314857i	$-0.898043\pi$
$647$		−	407.426i		−	0.629715i	0.949139	−	0.314857i	$-0.101957\pi$
$648$		0			0
$649$	4.28177	−	4.28177i	0.00659749	−	0.00659749i
$650$		0			0
$651$	558.895	−	240.851i	0.858518	−	0.369971i
$652$		0			0
$653$	−107.819	+	107.819i	−0.165113	+	0.165113i	−0.784827	−	0.619714i	$-0.787248\pi$
$653$	−107.819	+	107.819i	−0.165113	+	0.165113i	0.619714	+	0.784827i	$0.287248\pi$
$654$		0			0
$655$		−	174.090i		−	0.265787i
$656$		0			0
$657$	9.96147	+	350.826i	0.0151621	+	0.533982i
$658$		0			0
$659$		−	326.558i		−	0.495536i	−0.968819	−	0.247768i	$-0.920303\pi$
$659$		−	326.558i		−	0.495536i	0.968819	−	0.247768i	$-0.0796970\pi$
$660$		0			0
$661$		−	384.426i		−	0.581583i	−0.956786	−	0.290792i	$-0.906081\pi$
$661$		−	384.426i		−	0.581583i	0.956786	−	0.290792i	$-0.0939186\pi$
$662$		0			0
$663$	511.552	+	1155.07i	0.771571	+	1.74219i
$664$		0			0
$665$	−316.724			−0.476276
$666$		0			0
$667$	807.453			1.21057
$668$		0			0
$669$	−20.7561	−	48.1646i	−0.0310256	−	0.0719949i
$670$		0			0
$671$	−60.7013			−0.0904639
$672$		0			0
$673$	507.240	+	507.240i	0.753700	+	0.753700i	0.975168	−	0.221468i	$-0.0710847\pi$
$673$	507.240	+	507.240i	0.753700	+	0.753700i	−0.221468	+	0.975168i	$0.571085\pi$
$674$		0			0
$675$	−126.810	−	46.3063i	−0.187866	−	0.0686019i
$676$		0			0
$677$	−3.16708	−	3.16708i	−0.00467810	−	0.00467810i	0.704764	−	0.709442i	$-0.251053\pi$
$677$	−3.16708	−	3.16708i	−0.00467810	−	0.00467810i	−0.709442	+	0.704764i	$0.751053\pi$
$678$		0			0
$679$	1.63112			0.00240225
$680$		0			0
$681$	271.629	−	683.033i	0.398868	−	1.00299i
$682$		0			0
$683$	−53.6311	−	53.6311i	−0.0785228	−	0.0785228i	0.666755	−	0.745277i	$-0.267683\pi$
$683$	−53.6311	−	53.6311i	−0.0785228	−	0.0785228i	−0.745277	+	0.666755i	$0.767683\pi$
$684$		0			0
$685$	−395.791	+	395.791i	−0.577796	+	0.577796i
$686$		0			0
$687$	−456.738	−	1059.86i	−0.664830	−	1.54274i
$688$		0			0
$689$	2281.88			3.31188
$690$		0			0
$691$	−613.069	−	613.069i	−0.887219	−	0.887219i	0.107036	−	0.994255i	$-0.465864\pi$
$691$	−613.069	−	613.069i	−0.887219	−	0.887219i	−0.994255	+	0.107036i	$0.965864\pi$
$692$		0			0
$693$	65.3728	−	69.1937i	0.0943330	−	0.0998466i
$694$		0			0
$695$	242.255			0.348569
$696$		0			0
$697$	642.839	+	630.083i	0.922294	+	0.903993i
$698$		0			0
$699$	−944.249	−	375.510i	−1.35086	−	0.537210i
$700$		0			0
$701$		−	101.464i		−	0.144742i	−0.997378	−	0.0723708i	$-0.976944\pi$
$701$		−	101.464i		−	0.144742i	0.997378	−	0.0723708i	$-0.0230565\pi$
$702$		0			0
$703$	110.915	+	110.915i	0.157774	+	0.157774i
$704$		0			0
$705$	−19.1590	+	48.1768i	−0.0271759	+	0.0683359i
$706$		0			0
$707$	−836.005	+	836.005i	−1.18247	+	1.18247i
$708$		0			0
$709$	−557.716	+	557.716i	−0.786624	+	0.786624i	−0.980939	−	0.194315i	$-0.937752\pi$
$709$	−557.716	+	557.716i	−0.786624	+	0.786624i	0.194315	+	0.980939i	$0.437752\pi$
$710$		0			0
$711$	−1118.93	+	31.7712i	−1.57374	+	0.0446852i
$712$		0			0
$713$			336.986i			0.472631i
$714$		0			0
$715$	56.1931			0.0785917
$716$		0			0
$717$	289.018	+	670.666i	0.403093	+	0.935378i
$718$		0			0
$719$	39.7806	+	39.7806i	0.0553277	+	0.0553277i	0.734229	−	0.678902i	$-0.237544\pi$
$719$	39.7806	+	39.7806i	0.0553277	+	0.0553277i	−0.678902	+	0.734229i	$0.737544\pi$
$720$		0			0
$721$	−597.104	−	597.104i	−0.828161	−	0.828161i
$722$		0			0
$723$	507.505	−	1276.16i	0.701943	−	1.76509i
$724$		0			0
$725$	−164.845	+	164.845i	−0.227372	+	0.227372i
$726$		0			0
$727$	−1296.27			−1.78303			−0.891517	−	0.452987i	$-0.850358\pi$
$727$	−1296.27			−1.78303			−0.891517	+	0.452987i	$0.850358\pi$
$728$		0			0
$729$	−557.458	−	469.767i	−0.764689	−	0.644400i
$730$		0			0
$731$	−113.438	+	1.13680i	−0.155182	+	0.00155512i
$732$		0			0
$733$			147.100i			0.200683i	0.994953	+	0.100341i	$0.0319935\pi$
$733$			147.100i			0.200683i	−0.994953	+	0.100341i	$0.968007\pi$
$734$		0			0
$735$	−147.953	+	372.040i	−0.201297	+	0.506177i
$736$		0			0
$737$	−59.5824	+	59.5824i	−0.0808445	+	0.0808445i
$738$		0			0
$739$			688.479i			0.931636i	0.884881	+	0.465818i	$0.154240\pi$
$739$			688.479i			0.931636i	−0.884881	+	0.465818i	$0.845760\pi$
$740$		0			0
$741$	−399.567	−	927.195i	−0.539227	−	1.25128i
$742$		0			0
$743$	−554.375	−	554.375i	−0.746130	−	0.746130i	0.227620	−	0.973750i	$-0.426906\pi$
$743$	−554.375	−	554.375i	−0.746130	−	0.746130i	−0.973750	+	0.227620i	$0.926906\pi$
$744$		0			0
$745$	−42.6510	+	42.6510i	−0.0572497	+	0.0572497i
$746$		0			0
$747$	−748.362	+	792.103i	−1.00182	+	1.06038i
$748$		0			0
$749$			960.518i			1.28240i
$750$		0			0
$751$	72.1409	−	72.1409i	0.0960597	−	0.0960597i	−0.657444	−	0.753504i	$-0.728362\pi$
$751$	72.1409	−	72.1409i	0.0960597	−	0.0960597i	0.753504	+	0.657444i	$0.228362\pi$
$752$		0			0
$753$	569.406	+	1321.31i	0.756184	+	1.75472i
$754$		0			0
$755$	−2.88370	+	2.88370i	−0.00381947	+	0.00381947i
$756$		0			0
$757$		−	936.505i		−	1.23713i	−0.785735	−	0.618563i	$-0.787715\pi$
$757$		−	936.505i		−	1.23713i	0.785735	−	0.618563i	$-0.212285\pi$
$758$		0			0
$759$	20.8601	+	48.4060i	0.0274837	+	0.0637760i
$760$		0			0
$761$			104.084i			0.136773i	0.997659	+	0.0683865i	$0.0217851\pi$
$761$			104.084i			0.136773i	−0.997659	+	0.0683865i	$0.978215\pi$
$762$		0			0
$763$		−	1805.96i		−	2.36691i
$764$		0			0
$765$	−13.1367	−	341.866i	−0.0171722	−	0.446884i
$766$		0			0
$767$	−147.842			−0.192753
$768$		0			0
$769$	−733.630			−0.954006			−0.477003	−	0.878902i	$-0.658277\pi$
$769$	−733.630			−0.954006			−0.477003	+	0.878902i	$0.658277\pi$
$770$		0			0
$771$	23.2711	−	10.0285i	0.0301830	−	0.0130071i
$772$		0			0
$773$	−182.878			−0.236582			−0.118291	−	0.992979i	$-0.537742\pi$
$773$	−182.878			−0.236582			−0.118291	+	0.992979i	$0.537742\pi$
$774$		0			0
$775$	−68.7969	−	68.7969i	−0.0887702	−	0.0887702i
$776$		0			0
$777$	331.597	−	142.899i	0.426766	−	0.183911i
$778$		0			0
$779$	−508.693	−	508.693i	−0.653007	−	0.653007i
$780$		0			0
$781$	−88.5981			−0.113442
$782$		0			0
$783$	−1141.49	+	530.823i	−1.45784	+	0.677935i
$784$		0			0
$785$	−269.175	−	269.175i	−0.342898	−	0.342898i
$786$		0			0
$787$	752.499	−	752.499i	0.956162	−	0.956162i	−0.0429169	−	0.999079i	$-0.513665\pi$
$787$	752.499	−	752.499i	0.956162	−	0.956162i	0.999079	+	0.0429169i	$0.0136651\pi$
$788$		0			0
$789$	−303.989	+	131.001i	−0.385284	+	0.166035i
$790$		0			0
$791$	46.8697			0.0592538
$792$		0			0
$793$	1047.95	+	1047.95i	1.32150	+	1.32150i
$794$		0			0
$795$	−574.234	−	228.362i	−0.722307	−	0.287248i
$796$		0			0
$797$	216.854			0.272087			0.136044	−	0.990703i	$-0.456561\pi$
$797$	216.854			0.272087			0.136044	+	0.990703i	$0.456561\pi$
$798$		0			0
$799$	−131.384	+	1.31664i	−0.164435	+	0.00164785i
$800$		0			0
$801$	93.4900	+	88.3274i	0.116717	+	0.110271i
$802$		0			0
$803$			39.5634i			0.0492695i
$804$		0			0
$805$	−285.465	−	285.465i	−0.354615	−	0.354615i
$806$		0			0
$807$	108.382	+	43.1017i	0.134303	+	0.0534098i
$808$		0			0
$809$	524.211	−	524.211i	0.647974	−	0.647974i	−0.304529	−	0.952503i	$-0.598499\pi$
$809$	524.211	−	524.211i	0.647974	−	0.647974i	0.952503	+	0.304529i	$0.0984991\pi$
$810$		0			0
$811$	41.6787	−	41.6787i	0.0513917	−	0.0513917i	−0.680944	−	0.732336i	$-0.738430\pi$
$811$	41.6787	−	41.6787i	0.0513917	−	0.0513917i	0.732336	+	0.680944i	$0.238430\pi$
$812$		0			0
$813$	502.471	−	216.536i	0.618046	−	0.266342i
$814$		0			0
$815$			104.010i			0.127620i
$816$		0			0
$817$	90.6655			0.110974
$818$		0			0
$819$	−2323.17	+	65.9648i	−2.83659	+	0.0805432i
$820$		0			0
$821$	628.650	+	628.650i	0.765713	+	0.765713i	0.977349	−	0.211636i	$-0.0678790\pi$
$821$	628.650	+	628.650i	0.765713	+	0.765713i	−0.211636	+	0.977349i	$0.567879\pi$
$822$		0			0
$823$	−1043.13	−	1043.13i	−1.26748	−	1.26748i	−0.947387	−	0.320090i	$-0.896287\pi$
$823$	−1043.13	−	1043.13i	−1.26748	−	1.26748i	−0.320090	−	0.947387i	$-0.603713\pi$
$824$		0			0
$825$	−14.1409	−	5.62359i	−0.0171405	−	0.00681647i
$826$		0			0
$827$	−972.435	+	972.435i	−1.17586	+	1.17586i	−0.195069	+	0.980790i	$0.562493\pi$
$827$	−972.435	+	972.435i	−1.17586	+	1.17586i	−0.980790	+	0.195069i	$0.937507\pi$
$828$		0			0
$829$	−405.605			−0.489271			−0.244635	−	0.969615i	$-0.578668\pi$
$829$	−405.605			−0.489271			−0.244635	+	0.969615i	$0.578668\pi$
$830$		0			0
$831$	224.879	−	565.475i	0.270612	−	0.680475i
$832$		0			0
$833$	−1014.60	+	10.1676i	−1.21800	+	0.0122060i
$834$		0			0
$835$		−	472.476i		−	0.565839i
$836$		0			0
$837$	−221.536	−	476.394i	−0.264678	−	0.569168i
$838$		0			0
$839$	−944.331	+	944.331i	−1.12554	+	1.12554i	−0.134650	+	0.990893i	$0.542991\pi$
$839$	−944.331	+	944.331i	−1.12554	+	1.12554i	−0.990893	+	0.134650i	$0.957009\pi$
$840$		0			0
$841$			1332.90i			1.58490i
$842$		0			0
$843$	−275.204	+	118.597i	−0.326458	+	0.140684i
$844$		0			0
$845$	−702.911	−	702.911i	−0.831847	−	0.831847i
$846$		0			0
$847$	−884.393	+	884.393i	−1.04415	+	1.04415i
$848$		0			0
$849$	−306.654	−	121.951i	−0.361195	−	0.143640i
$850$		0			0
$851$			199.936i			0.234943i
$852$		0			0
$853$	−65.1034	+	65.1034i	−0.0763229	+	0.0763229i	−0.744238	−	0.667915i	$-0.767187\pi$
$853$	−65.1034	+	65.1034i	−0.0763229	+	0.0763229i	0.667915	+	0.744238i	$0.267187\pi$
$854$		0			0
$855$	7.76059	+	273.315i	0.00907672	+	0.319667i
$856$		0			0
$857$	642.508	−	642.508i	0.749718	−	0.749718i	−0.224708	−	0.974426i	$-0.572143\pi$
$857$	642.508	−	642.508i	0.749718	−	0.749718i	0.974426	+	0.224708i	$0.0721429\pi$
$858$		0			0
$859$		−	64.9611i		−	0.0756241i	−0.999285	−	0.0378120i	$-0.987961\pi$
$859$		−	64.9611i		−	0.0756241i	0.999285	−	0.0378120i	$-0.0120388\pi$
$860$		0			0
$861$	−1520.82	+	655.383i	−1.76634	+	0.761188i
$862$		0			0
$863$		−	821.697i		−	0.952140i	−0.879407	−	0.476070i	$-0.842061\pi$
$863$		−	821.697i		−	0.952140i	0.879407	−	0.476070i	$-0.157939\pi$
$864$		0			0
$865$			469.362i			0.542615i
$866$		0			0
$867$	789.178	−	359.009i	0.910239	−	0.414082i
$868$		0			0
$869$	−126.184			−0.145206
$870$		0			0
$871$	2057.27			2.36197
$872$		0			0
$873$	−0.0399670	−	1.40757i	−4.57812e−5	−	0.00161234i
$874$		0			0
$875$	116.557			0.133208
$876$		0			0
$877$	−423.666	−	423.666i	−0.483086	−	0.483086i	0.423030	−	0.906116i	$-0.360967\pi$
$877$	−423.666	−	423.666i	−0.483086	−	0.483086i	−0.906116	+	0.423030i	$0.860967\pi$
$878$		0			0
$879$	−425.458	−	987.276i	−0.484025	−	1.12318i
$880$		0			0
$881$	464.095	+	464.095i	0.526782	+	0.526782i	0.919612	−	0.392829i	$-0.128504\pi$
$881$	464.095	+	464.095i	0.526782	+	0.526782i	−0.392829	+	0.919612i	$0.628504\pi$
$882$		0			0
$883$	1502.02			1.70104			0.850522	−	0.525940i	$-0.176286\pi$
$883$	1502.02			1.70104			0.850522	+	0.525940i	$0.176286\pi$
$884$		0			0
$885$	37.2043	+	14.7954i	0.0420387	+	0.0167180i
$886$		0			0
$887$	−201.865	−	201.865i	−0.227582	−	0.227582i	0.584100	−	0.811682i	$-0.301448\pi$
$887$	−201.865	−	201.865i	−0.227582	−	0.227582i	−0.811682	+	0.584100i	$0.801448\pi$
$888$		0			0
$889$	987.756	−	987.756i	1.11109	−	1.11109i
$890$		0			0
$891$	−61.3121	−	54.7176i	−0.0688127	−	0.0614115i
$892$		0			0
$893$	105.009			0.117591
$894$		0			0
$895$	423.735	+	423.735i	0.473447	+	0.473447i
$896$		0			0
$897$	475.554	−	1195.82i	0.530161	−	1.33313i
$898$		0			0
$899$	−907.263			−1.00919
$900$		0			0
$901$	−15.6934	−	1566.00i	−0.0174177	−	1.73807i
$902$		0			0
$903$	77.1240	−	193.934i	0.0854087	−	0.214767i
$904$		0			0
$905$			337.296i			0.372703i
$906$		0			0
$907$	513.861	+	513.861i	0.566550	+	0.566550i	0.931160	−	0.364610i	$-0.118798\pi$
$907$	513.861	+	513.861i	0.566550	+	0.566550i	−0.364610	+	0.931160i	$0.618798\pi$
$908$		0			0
$909$	741.910	+	700.941i	0.816182	+	0.771112i
$910$		0			0
$911$	−573.912	+	573.912i	−0.629981	+	0.629981i	−0.948063	−	0.318082i	$-0.896961\pi$
$911$	−573.912	+	573.912i	−0.629981	+	0.629981i	0.318082	+	0.948063i	$0.396961\pi$
$912$		0			0
$913$	−86.8608	+	86.8608i	−0.0951378	+	0.0951378i
$914$		0			0
$915$	−158.841	−	368.591i	−0.173597	−	0.402832i
$916$		0			0
$917$			811.661i			0.885127i
$918$		0			0
$919$	946.852			1.03031			0.515153	−	0.857098i	$-0.327735\pi$
$919$	946.852			1.03031			0.515153	+	0.857098i	$0.327735\pi$
$920$		0			0
$921$	−104.453	+	45.0131i	−0.113412	+	0.0488741i
$922$		0			0
$923$	1529.57	+	1529.57i	1.65717	+	1.65717i
$924$		0			0
$925$	−40.8178	−	40.8178i	−0.0441273	−	0.0441273i
$926$		0			0
$927$	−500.637	+	529.898i	−0.540061	+	0.571627i
$928$		0			0
$929$	−901.774	+	901.774i	−0.970693	+	0.970693i	−0.999583	−	0.0288896i	$-0.990803\pi$
$929$	−901.774	+	901.774i	−0.970693	+	0.970693i	0.0288896	+	0.999583i	$0.490803\pi$
$930$		0			0
$931$	810.917			0.871018
$932$		0			0
$933$	686.069	+	272.836i	0.735336	+	0.292429i
$934$		0			0
$935$	−0.386461	−	38.5640i	−0.000413327	−	0.0412449i
$936$		0			0
$937$			1146.32i			1.22339i	0.791092	+	0.611697i	$0.209513\pi$
$937$			1146.32i			1.22339i	−0.791092	+	0.611697i	$0.790487\pi$
$938$		0			0
$939$	−195.018	−	77.5552i	−0.207687	−	0.0825934i
$940$		0			0
$941$	1030.88	−	1030.88i	1.09551	−	1.09551i	0.100587	−	0.994928i	$-0.467928\pi$
$941$	1030.88	−	1030.88i	1.09551	−	1.09551i	0.994928	−	0.100587i	$-0.0320720\pi$
$942$		0			0
$943$		−	916.975i		−	0.972401i
$944$		0			0
$945$	591.225	+	215.894i	0.625635	+	0.228459i
$946$		0			0
$947$	−1263.94	−	1263.94i	−1.33468	−	1.33468i	−0.901132	−	0.433545i	$-0.857262\pi$
$947$	−1263.94	−	1263.94i	−1.33468	−	1.33468i	−0.433545	−	0.901132i	$-0.642738\pi$
$948$		0			0
$949$	683.027	−	683.027i	0.719733	−	0.719733i
$950$		0			0
$951$	−416.484	+	1047.28i	−0.437943	+	1.10124i
$952$		0			0
$953$		−	808.646i		−	0.848527i	−0.905539	−	0.424264i	$-0.860533\pi$
$953$		−	808.646i		−	0.848527i	0.905539	−	0.424264i	$-0.139467\pi$
$954$		0			0
$955$	−244.092	+	244.092i	−0.255593	+	0.255593i
$956$		0			0
$957$	−130.323	+	56.1616i	−0.136179	+	0.0586851i
$958$		0			0
$959$	1845.29	−	1845.29i	1.92418	−	1.92418i
$960$		0			0
$961$			582.359i			0.605993i
$962$		0			0
$963$	828.873	−	23.5353i	0.860720	−	0.0244396i
$964$		0			0
$965$		−	22.7693i		−	0.0235951i
$966$		0			0
$967$			541.947i			0.560442i	0.959936	+	0.280221i	$0.0904077\pi$
$967$			541.947i			0.560442i	−0.959936	+	0.280221i	$0.909592\pi$
$968$		0			0
$969$	−633.564	+	280.590i	−0.653832	+	0.289566i
$970$		0			0
$971$	503.661			0.518703			0.259352	−	0.965783i	$-0.416491\pi$
$971$	503.661			0.518703			0.259352	+	0.965783i	$0.416491\pi$
$972$		0			0
$973$	−1129.47			−1.16081
$974$		0			0
$975$	147.044	+	341.217i	0.150815	+	0.349966i
$976$		0			0
$977$	−1756.83			−1.79819			−0.899095	−	0.437753i	$-0.855774\pi$
$977$	−1756.83			−1.79819			−0.899095	+	0.437753i	$0.855774\pi$
$978$		0			0
$979$	10.2520	+	10.2520i	0.0104719	+	0.0104719i
$980$		0			0
$981$	−1558.44	+	44.2508i	−1.58862	+	0.0451079i
$982$		0			0
$983$	−1272.16	−	1272.16i	−1.29416	−	1.29416i	−0.932187	−	0.361976i	$-0.882102\pi$
$983$	−1272.16	−	1272.16i	−1.29416	−	1.29416i	−0.361976	−	0.932187i	$-0.617898\pi$
$984$		0			0
$985$	170.597			0.173195
$986$		0			0
$987$	89.3250	−	224.615i	0.0905016	−	0.227573i
$988$		0			0
$989$	81.7172	+	81.7172i	0.0826261	+	0.0826261i
$990$		0			0
$991$	1178.91	−	1178.91i	1.18961	−	1.18961i	0.212437	−	0.977175i	$-0.431860\pi$
$991$	1178.91	−	1178.91i	1.18961	−	1.18961i	0.977175	−	0.212437i	$-0.0681399\pi$
$992$		0			0
$993$	41.1261	+	95.4332i	0.0414160	+	0.0961059i
$994$		0			0
$995$	555.519			0.558311
$996$		0			0
$997$	−387.226	−	387.226i	−0.388391	−	0.388391i	0.485722	−	0.874113i	$-0.338557\pi$
$997$	−387.226	−	387.226i	−0.388391	−	0.388391i	−0.874113	+	0.485722i	$0.838557\pi$
$998$		0			0
$999$	−131.439	−	282.648i	−0.131570	−	0.282931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.7	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.18	yes	96
17.13	even	4	inner	1020.3.bc.a.761.18	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.7	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.18	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.7	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.18	yes	96	17.13	even	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75507 + 1.18727i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(7.37174 + 7.37174i) q^{7} +(6.18077 - 6.54202i) q^{9} +O(q^{10})\)	\(q+(-2.75507 + 1.18727i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(7.37174 + 7.37174i) q^{7} +(6.18077 - 6.54202i) q^{9} +(0.717389 - 0.717389i) q^{11} -24.7701 q^{13} +(6.23338 + 2.47890i) q^{15} +(0.170354 + 16.9991i) q^{17} -13.5866i q^{19} +(-29.0619 - 11.5574i) q^{21} +(12.2457 - 12.2457i) q^{23} +5.00000i q^{25} +(-9.26126 + 25.3620i) q^{27} +(32.9689 + 32.9689i) q^{29} +(-13.7594 + 13.7594i) q^{31} +(-1.12472 + 2.82819i) q^{33} -23.3115i q^{35} +(-8.16355 + 8.16355i) q^{37} +(68.2434 - 29.4089i) q^{39} +(37.4408 - 37.4408i) q^{41} +6.67315i q^{43} +(-20.1165 + 0.571195i) q^{45} +7.72884i q^{47} +59.6851i q^{49} +(-20.6519 - 46.6315i) q^{51} -92.1223 q^{53} -2.26858 q^{55} +(16.1310 + 37.4320i) q^{57} +5.96855 q^{59} +(-42.3071 - 42.3071i) q^{61} +(93.7891 - 2.66308i) q^{63} +(39.1650 + 39.1650i) q^{65} -83.0546 q^{67} +(-19.1987 + 48.2766i) q^{69} +(-61.7504 - 61.7504i) q^{71} +(-27.5746 + 27.5746i) q^{73} +(-5.93636 - 13.7753i) q^{75} +10.5768 q^{77} +(-87.9466 - 87.9466i) q^{79} +(-4.59618 - 80.8695i) q^{81} -121.079 q^{83} +(26.6087 - 27.1474i) q^{85} +(-129.975 - 51.6884i) q^{87} +14.2907i q^{89} +(-182.599 - 182.599i) q^{91} +(21.5719 - 54.2441i) q^{93} +(-21.4823 + 21.4823i) q^{95} +(0.110634 - 0.110634i) q^{97} +(-0.259160 - 9.12719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more