LMFDB - Embedded newform 36.4.e.a.25.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [36,4,Mod(13,36)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(36, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("36.13"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$36 = 2^{2} \cdot 3^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	36.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6831243.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} + 13x^{4} + 49x^{2} + 48$ x^6 + 13x^4 + 49x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{2}\cdot 3^{3}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Root			$2.13353i$ of defining polynomial
Character	$\chi$	$=$	36.25
Dual form			36.4.e.a.13.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.51979 - 4.54430i) q^{3} +(-6.37096 - 11.0348i) q^{5} +(7.02674 - 12.1707i) q^{7} +(-14.3013 + 22.9014i) q^{9} +(21.2745 - 36.8486i) q^{11} +(36.2316 + 62.7550i) q^{13} +(-34.0920 + 56.7570i) q^{15} -59.6114 q^{17} +105.570 q^{19} +(-73.0131 - 1.26403i) q^{21} +(0.112590 + 0.195011i) q^{23} +(-18.6781 + 32.3515i) q^{25} +(140.107 + 7.28259i) q^{27} +(112.855 - 195.470i) q^{29} +(-100.597 - 174.239i) q^{31} +(-221.058 - 3.82705i) q^{33} -179.068 q^{35} -152.926 q^{37} +(193.881 - 322.777i) q^{39} +(244.824 + 424.047i) q^{41} +(3.79372 - 6.57091i) q^{43} +(343.825 + 11.9085i) q^{45} +(-186.696 + 323.366i) q^{47} +(72.7498 + 126.006i) q^{49} +(150.208 + 270.892i) q^{51} -43.6780 q^{53} -542.157 q^{55} +(-266.015 - 479.743i) q^{57} +(335.949 + 581.881i) q^{59} +(-37.0177 + 64.1165i) q^{61} +(178.234 + 334.978i) q^{63} +(461.660 - 799.619i) q^{65} +(-210.436 - 364.485i) q^{67} +(0.602487 - 1.00303i) q^{69} -730.840 q^{71} +473.927 q^{73} +(194.080 + 3.35999i) q^{75} +(-298.982 - 517.851i) q^{77} +(264.811 - 458.666i) q^{79} +(-319.946 - 655.038i) q^{81} +(-13.0767 + 22.6495i) q^{83} +(379.781 + 657.801i) q^{85} +(-1172.65 - 20.3013i) q^{87} +415.949 q^{89} +1018.36 q^{91} +(-538.311 + 896.189i) q^{93} +(-672.583 - 1164.95i) q^{95} +(-463.743 + 803.226i) q^{97} +(539.630 + 1014.20i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 3 q^{3} + 6 q^{5} - 6 q^{7} + 39 q^{9} + 51 q^{11} + 12 q^{13} - 180 q^{15} - 222 q^{17} + 30 q^{19} - 120 q^{21} + 210 q^{23} - 3 q^{25} + 648 q^{27} + 456 q^{29} + 48 q^{31} - 603 q^{33} - 1104 q^{35}+ \cdots - 1854 q^{99}+O(q^{100})$ 6 * q - 3 * q^3 + 6 * q^5 - 6 * q^7 + 39 * q^9 + 51 * q^11 + 12 * q^13 - 180 * q^15 - 222 * q^17 + 30 * q^19 - 120 * q^21 + 210 * q^23 - 3 * q^25 + 648 * q^27 + 456 * q^29 + 48 * q^31 - 603 * q^33 - 1104 * q^35 - 96 * q^37 - 36 * q^39 + 897 * q^41 + 129 * q^43 + 1494 * q^45 + 522 * q^47 - 225 * q^49 - 1647 * q^51 - 2208 * q^53 - 216 * q^55 - 645 * q^57 + 453 * q^59 - 402 * q^61 + 1896 * q^63 + 1110 * q^65 - 213 * q^67 - 198 * q^69 + 120 * q^71 + 750 * q^73 + 921 * q^75 + 1128 * q^77 + 552 * q^79 - 549 * q^81 - 612 * q^83 + 1188 * q^85 - 1386 * q^87 - 924 * q^89 - 264 * q^91 - 1998 * q^93 - 2184 * q^95 + 93 * q^97 - 1854 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$ .

$n$	$19$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−2.51979	−	4.54430i	−0.484934	−	0.874551i
$3$	−2.51979	−	4.54430i	−0.484934	−	0.874551i
$4$		0			0
$5$	−6.37096	−	11.0348i	−0.569836	−	0.986984i	−0.996582	−	0.0826127i	$-0.973674\pi$
$5$	−6.37096	−	11.0348i	−0.569836	−	0.986984i	0.426746	−	0.904371i	$-0.359660\pi$
$6$		0			0
$7$	7.02674	−	12.1707i	0.379408	−	0.657155i	−0.611568	−	0.791192i	$-0.709461\pi$
$7$	7.02674	−	12.1707i	0.379408	−	0.657155i	0.990976	+	0.134037i	$0.0427942\pi$
$8$		0			0
$9$	−14.3013	+	22.9014i	−0.529677	+	0.848199i
$10$		0			0
$11$	21.2745	−	36.8486i	0.583138	−	1.01002i	−0.411967	−	0.911199i	$-0.635158\pi$
$11$	21.2745	−	36.8486i	0.583138	−	1.01002i	0.995105	−	0.0988256i	$-0.0315086\pi$
$12$		0			0
$13$	36.2316	+	62.7550i	0.772988	+	1.33885i	0.935918	+	0.352217i	$0.114572\pi$
$13$	36.2316	+	62.7550i	0.772988	+	1.33885i	−0.162930	+	0.986638i	$0.552095\pi$
$14$		0			0
$15$	−34.0920	+	56.7570i	−0.586835	+	0.976972i
$16$		0			0
$17$	−59.6114			−0.850464			−0.425232	−	0.905084i	$-0.639807\pi$
$17$	−59.6114			−0.850464			−0.425232	+	0.905084i	$0.639807\pi$
$18$		0			0
$19$	105.570			1.27471			0.637354	−	0.770571i	$-0.280029\pi$
$19$	105.570			1.27471			0.637354	+	0.770571i	$0.280029\pi$
$20$		0			0
$21$	−73.0131	−	1.26403i	−0.758703	−	0.0131350i
$22$		0			0
$23$	0.112590	+	0.195011i	0.00102072	+	0.00176794i	0.866535	−	0.499116i	$-0.166342\pi$
$23$	0.112590	+	0.195011i	0.00102072	+	0.00176794i	−0.865515	+	0.500884i	$0.833008\pi$
$24$		0			0
$25$	−18.6781	+	32.3515i	−0.149425	+	0.258812i
$26$		0			0
$27$	140.107	+	7.28259i	0.998652	+	0.0519087i
$28$		0			0
$29$	112.855	−	195.470i	0.722642	−	1.25165i	−0.237296	−	0.971437i	$-0.576261\pi$
$29$	112.855	−	195.470i	0.722642	−	1.25165i	0.959937	−	0.280214i	$-0.0904056\pi$
$30$		0			0
$31$	−100.597	−	174.239i	−0.582831	−	1.00949i	−0.995142	−	0.0984492i	$-0.968612\pi$
$31$	−100.597	−	174.239i	−0.582831	−	1.00949i	0.412312	−	0.911043i	$-0.364722\pi$
$32$		0			0
$33$	−221.058	−	3.82705i	−1.16610	−	0.0201880i
$34$		0			0
$35$	−179.068			−0.864802
$36$		0			0
$37$	−152.926			−0.679485			−0.339743	−	0.940518i	$-0.610340\pi$
$37$	−152.926			−0.679485			−0.339743	+	0.940518i	$0.610340\pi$
$38$		0			0
$39$	193.881	−	322.777i	0.796047	−	1.32527i
$40$		0			0
$41$	244.824	+	424.047i	0.932563	+	1.61525i	0.778923	+	0.627119i	$0.215766\pi$
$41$	244.824	+	424.047i	0.932563	+	1.61525i	0.153639	+	0.988127i	$0.450901\pi$
$42$		0			0
$43$	3.79372	−	6.57091i	0.0134543	−	0.0233036i	−0.859220	−	0.511607i	$-0.829051\pi$
$43$	3.79372	−	6.57091i	0.0134543	−	0.0233036i	0.872674	+	0.488303i	$0.162384\pi$
$44$		0			0
$45$	343.825	+	11.9085i	1.13899	+	0.0394491i
$46$		0			0
$47$	−186.696	+	323.366i	−0.579412	+	1.00357i	0.416135	+	0.909303i	$0.363384\pi$
$47$	−186.696	+	323.366i	−0.579412	+	1.00357i	−0.995547	+	0.0942681i	$0.969949\pi$
$48$		0			0
$49$	72.7498	+	126.006i	0.212098	+	0.367365i
$50$		0			0
$51$	150.208	+	270.892i	0.412419	+	0.743773i
$52$		0			0
$53$	−43.6780			−0.113201			−0.0566003	−	0.998397i	$-0.518026\pi$
$53$	−43.6780			−0.113201			−0.0566003	+	0.998397i	$0.518026\pi$
$54$		0			0
$55$	−542.157			−1.32917
$56$		0			0
$57$	−266.015	−	479.743i	−0.618150	−	1.11480i
$58$		0			0
$59$	335.949	+	581.881i	0.741303	+	1.28397i	0.951902	+	0.306402i	$0.0991251\pi$
$59$	335.949	+	581.881i	0.741303	+	1.28397i	−0.210599	+	0.977572i	$0.567542\pi$
$60$		0			0
$61$	−37.0177	+	64.1165i	−0.0776988	+	0.134578i	−0.902257	−	0.431199i	$-0.858091\pi$
$61$	−37.0177	+	64.1165i	−0.0776988	+	0.134578i	0.824558	+	0.565778i	$0.191424\pi$
$62$		0			0
$63$	178.234	+	334.978i	0.356434	+	0.669894i
$64$		0			0
$65$	461.660	−	799.619i	0.880952	−	1.52585i
$66$		0			0
$67$	−210.436	−	364.485i	−0.383713	−	0.664611i	0.607876	−	0.794032i	$-0.292022\pi$
$67$	−210.436	−	364.485i	−0.383713	−	0.664611i	−0.991590	+	0.129421i	$0.958688\pi$
$68$		0			0
$69$	0.602487	−	1.00303i	0.00105117	−	0.00175001i
$70$		0			0
$71$	−730.840			−1.22162			−0.610808	−	0.791778i	$-0.709155\pi$
$71$	−730.840			−1.22162			−0.610808	+	0.791778i	$0.709155\pi$
$72$		0			0
$73$	473.927			0.759849			0.379925	−	0.925017i	$-0.375950\pi$
$73$	473.927			0.759849			0.379925	+	0.925017i	$0.375950\pi$
$74$		0			0
$75$	194.080	+	3.35999i	0.298805	+	0.00517304i
$76$		0			0
$77$	−298.982	−	517.851i	−0.442495	−	0.766424i
$78$		0			0
$79$	264.811	−	458.666i	0.377134	−	0.653215i	−0.613510	−	0.789687i	$-0.710243\pi$
$79$	264.811	−	458.666i	0.377134	−	0.653215i	0.990644	+	0.136472i	$0.0435764\pi$
$80$		0			0
$81$	−319.946	−	655.038i	−0.438884	−	0.898544i
$82$		0			0
$83$	−13.0767	+	22.6495i	−0.0172934	+	0.0299531i	−0.874543	−	0.484949i	$-0.838838\pi$
$83$	−13.0767	+	22.6495i	−0.0172934	+	0.0299531i	0.857249	+	0.514902i	$0.172172\pi$
$84$		0			0
$85$	379.781	+	657.801i	0.484624	+	0.839394i
$86$		0			0
$87$	−1172.65	−	20.3013i	−1.44507	−	0.0250176i
$88$		0			0
$89$	415.949			0.495399			0.247700	−	0.968837i	$-0.420325\pi$
$89$	415.949			0.495399			0.247700	+	0.968837i	$0.420325\pi$
$90$		0			0
$91$	1018.36			1.17311
$92$		0			0
$93$	−538.311	+	896.189i	−0.600217	+	0.999252i
$94$		0			0
$95$	−672.583	−	1164.95i	−0.726374	−	1.25812i
$96$		0			0
$97$	−463.743	+	803.226i	−0.485422	+	0.840776i	−0.999860	−	0.0167522i	$-0.994667\pi$
$97$	−463.743	+	803.226i	−0.485422	+	0.840776i	0.514438	+	0.857528i	$0.328001\pi$
$98$		0			0
$99$	539.630	+	1014.20i	0.547827	+	1.02960i
$100$		0			0
$101$	45.0590	−	78.0445i	0.0443915	−	0.0768883i	−0.842976	−	0.537951i	$-0.819198\pi$
$101$	45.0590	−	78.0445i	0.0443915	−	0.0768883i	0.887367	+	0.461063i	$0.152532\pi$
$102$		0			0
$103$	162.826	+	282.023i	0.155765	+	0.269792i	0.933337	−	0.359001i	$-0.116883\pi$
$103$	162.826	+	282.023i	0.155765	+	0.269792i	−0.777573	+	0.628793i	$0.783549\pi$
$104$		0			0
$105$	451.215	+	813.740i	0.419372	+	0.756313i
$106$		0			0
$107$	1073.49			0.969888			0.484944	−	0.874545i	$-0.338840\pi$
$107$	1073.49			0.969888			0.484944	+	0.874545i	$0.338840\pi$
$108$		0			0
$109$	601.488			0.528552			0.264276	−	0.964447i	$-0.414867\pi$
$109$	601.488			0.528552			0.264276	+	0.964447i	$0.414867\pi$
$110$		0			0
$111$	385.343	+	694.944i	0.329506	+	0.594244i
$112$		0			0
$113$	210.019	+	363.764i	0.174840	+	0.302832i	0.940106	−	0.340882i	$-0.110726\pi$
$113$	210.019	+	363.764i	0.174840	+	0.302832i	−0.765266	+	0.643715i	$0.777392\pi$
$114$		0			0
$115$	1.43461	−	2.48482i	0.00116329	−	0.00201487i
$116$		0			0
$117$	−1955.34	−	67.7234i	−1.54505	−	0.0535131i
$118$		0			0
$119$	−418.874	+	725.511i	−0.322673	+	0.558886i
$120$		0			0
$121$	−239.713	−	415.194i	−0.180100	−	0.311942i
$122$		0			0
$123$	1310.09	−	2181.06i	0.960383	−	1.59886i
$124$		0			0
$125$	−1116.75			−0.799080
$126$		0			0
$127$	−980.264			−0.684916			−0.342458	−	0.939533i	$-0.611259\pi$
$127$	−980.264			−0.684916			−0.342458	+	0.939533i	$0.611259\pi$
$128$		0			0
$129$	−39.4195	−	0.682447i	−0.0269046	−	0.000465784i
$130$		0			0
$131$	−677.695	−	1173.80i	−0.451988	−	0.782866i	0.546521	−	0.837445i	$-0.315952\pi$
$131$	−677.695	−	1173.80i	−0.451988	−	0.782866i	−0.998509	+	0.0545787i	$0.982618\pi$
$132$		0			0
$133$	741.815	−	1284.86i	0.483635	−	0.837681i
$134$		0			0
$135$	−812.253	−	1592.45i	−0.517834	−	1.01523i
$136$		0			0
$137$	−453.261	+	785.071i	−0.282662	+	0.489585i	−0.972040	−	0.234817i	$-0.924551\pi$
$137$	−453.261	+	785.071i	−0.282662	+	0.489585i	0.689378	+	0.724402i	$0.257884\pi$
$138$		0			0
$139$	409.209	+	708.771i	0.249703	+	0.432498i	0.963443	−	0.267912i	$-0.0863338\pi$
$139$	409.209	+	708.771i	0.249703	+	0.432498i	−0.713741	+	0.700410i	$0.753000\pi$
$140$		0			0
$141$	1939.91	+	33.5845i	1.15865	+	0.0200590i
$142$		0			0
$143$	3083.25			1.80303
$144$		0			0
$145$	−2875.97			−1.64715
$146$		0			0
$147$	389.296	−	648.106i	0.218426	−	0.363639i
$148$		0			0
$149$	579.748	+	1004.15i	0.318757	+	0.552103i	0.980229	−	0.197867i	$-0.0634013\pi$
$149$	579.748	+	1004.15i	0.318757	+	0.552103i	−0.661472	+	0.749970i	$0.730068\pi$
$150$		0			0
$151$	318.987	−	552.501i	0.171912	−	0.297761i	−0.767176	−	0.641437i	$-0.778339\pi$
$151$	318.987	−	552.501i	0.171912	−	0.297761i	0.939088	+	0.343676i	$0.111672\pi$
$152$		0			0
$153$	852.519	−	1365.18i	0.450471	−	0.721363i
$154$		0			0
$155$	−1281.80	+	2220.14i	−0.664235	+	1.15049i
$156$		0			0
$157$	−1645.86	−	2850.71i	−0.836649	−	1.44912i	−0.892680	−	0.450690i	$-0.851178\pi$
$157$	−1645.86	−	2850.71i	−0.836649	−	1.44912i	0.0560311	−	0.998429i	$-0.482155\pi$
$158$		0			0
$159$	110.059	+	198.486i	0.0548949	+	0.0989997i
$160$		0			0
$161$	3.16456			0.00154908
$162$		0			0
$163$	−1197.14			−0.575258			−0.287629	−	0.957742i	$-0.592867\pi$
$163$	−1197.14			−0.575258			−0.287629	+	0.957742i	$0.592867\pi$
$164$		0			0
$165$	1366.12	+	2463.72i	0.644561	+	1.16243i
$166$		0			0
$167$	−419.419	−	726.455i	−0.194345	−	0.336615i	0.752341	−	0.658774i	$-0.228925\pi$
$167$	−419.419	−	726.455i	−0.194345	−	0.336615i	−0.946686	+	0.322159i	$0.895591\pi$
$168$		0			0
$169$	−1526.96	+	2644.77i	−0.695021	+	1.20381i
$170$		0			0
$171$	−1509.79	+	2417.70i	−0.675184	+	1.08121i
$172$		0			0
$173$	−1153.59	+	1998.08i	−0.506970	+	0.878098i	0.492997	+	0.870031i	$0.335901\pi$
$173$	−1153.59	+	1998.08i	−0.506970	+	0.878098i	−0.999967	+	0.00806725i	$0.997432\pi$
$174$		0			0
$175$	262.493	+	454.651i	0.113386	+	0.196391i
$176$		0			0
$177$	1797.72	−	2992.87i	0.763417	−	1.27095i
$178$		0			0
$179$	3114.47			1.30048			0.650241	−	0.759728i	$-0.274668\pi$
$179$	3114.47			1.30048			0.650241	+	0.759728i	$0.274668\pi$
$180$		0			0
$181$	3902.75			1.60270			0.801350	−	0.598195i	$-0.204115\pi$
$181$	3902.75			1.60270			0.801350	+	0.598195i	$0.204115\pi$
$182$		0			0
$183$	384.641	+	6.65907i	0.155374	+	0.00268990i
$184$		0			0
$185$	974.288	+	1687.52i	0.387195	+	0.670641i
$186$		0			0
$187$	−1268.20	+	2196.60i	−0.495938	+	0.858989i
$188$		0			0
$189$	1073.13	−	1654.02i	0.413009	−	0.636574i
$190$		0			0
$191$	−52.8697	+	91.5730i	−0.0200289	+	0.0346911i	−0.875866	−	0.482554i	$-0.839709\pi$
$191$	−52.8697	+	91.5730i	−0.0200289	+	0.0346911i	0.855837	+	0.517245i	$0.173042\pi$
$192$		0			0
$193$	792.685	+	1372.97i	0.295641	+	0.512065i	0.975134	−	0.221617i	$-0.0711334\pi$
$193$	792.685	+	1372.97i	0.295641	+	0.512065i	−0.679493	+	0.733682i	$0.737800\pi$
$194$		0			0
$195$	−4796.99	−	83.0475i	−1.76164	−	0.0304982i
$196$		0			0
$197$	−3905.37			−1.41242			−0.706208	−	0.708005i	$-0.749595\pi$
$197$	−3905.37			−1.41242			−0.706208	+	0.708005i	$0.749595\pi$
$198$		0			0
$199$	1538.77			0.548143			0.274072	−	0.961709i	$-0.411629\pi$
$199$	1538.77			0.548143			0.274072	+	0.961709i	$0.411629\pi$
$200$		0			0
$201$	−1126.07	+	1874.71i	−0.395160	+	0.657869i
$202$		0			0
$203$	−1586.00	−	2747.04i	−0.548353	−	0.949775i
$204$		0			0
$205$	3119.52	−	5403.17i	1.06281	−	1.84085i
$206$		0			0
$207$	−6.07621	−	0.210451i	−0.00204022	−	7.06634e-5i
$208$		0			0
$209$	2245.96	−	3890.11i	0.743331	−	1.28749i
$210$		0			0
$211$	−470.733	−	815.334i	−0.153586	−	0.266019i	0.778957	−	0.627077i	$-0.215749\pi$
$211$	−470.733	−	815.334i	−0.153586	−	0.266019i	−0.932543	+	0.361058i	$0.882416\pi$
$212$		0			0
$213$	1841.57	+	3321.16i	0.592404	+	1.06837i
$214$		0			0
$215$	−96.6784			−0.0306670
$216$		0			0
$217$	−2827.48			−0.884523
$218$		0			0
$219$	−1194.20	−	2153.67i	−0.368477	−	0.664527i
$220$		0			0
$221$	−2159.82	−	3740.91i	−0.657398	−	1.13865i
$222$		0			0
$223$	−1660.78	+	2876.56i	−0.498719	+	0.863807i	−0.999999	−	0.00147850i	$-0.999529\pi$
$223$	−1660.78	+	2876.56i	−0.498719	+	0.863807i	0.501280	+	0.865285i	$0.332863\pi$
$224$		0			0
$225$	−473.772	−	890.423i	−0.140377	−	0.263829i
$226$		0			0
$227$	2105.92	−	3647.56i	0.615749	−	1.06651i	−0.374504	−	0.927225i	$-0.622187\pi$
$227$	2105.92	−	3647.56i	0.615749	−	1.06651i	0.990253	−	0.139283i	$-0.0444797\pi$
$228$		0			0
$229$	177.072	+	306.698i	0.0510973	+	0.0885031i	0.890443	−	0.455095i	$-0.150395\pi$
$229$	177.072	+	306.698i	0.0510973	+	0.0885031i	−0.839345	+	0.543598i	$0.817061\pi$
$230$		0			0
$231$	−1599.90	+	2663.54i	−0.455695	+	0.758649i
$232$		0			0
$233$	868.789			0.244276			0.122138	−	0.992513i	$-0.461025\pi$
$233$	868.789			0.244276			0.122138	+	0.992513i	$0.461025\pi$
$234$		0			0
$235$	4757.72			1.32068
$236$		0			0
$237$	−2751.58	−	47.6365i	−0.754154	−	0.0130562i
$238$		0			0
$239$	602.177	+	1043.00i	0.162977	+	0.282285i	0.935935	−	0.352172i	$-0.114557\pi$
$239$	602.177	+	1043.00i	0.162977	+	0.282285i	−0.772958	+	0.634457i	$0.781224\pi$
$240$		0			0
$241$	2543.70	−	4405.82i	0.679893	−	1.17761i	−0.295120	−	0.955460i	$-0.595360\pi$
$241$	2543.70	−	4405.82i	0.679893	−	1.17761i	0.975013	−	0.222149i	$-0.0713072\pi$
$242$		0			0
$243$	−2170.49	+	3104.49i	−0.572992	+	0.819561i
$244$		0			0
$245$	926.971	−	1605.56i	0.241722	−	0.418676i
$246$		0			0
$247$	3824.98	+	6625.06i	0.985335	+	1.70665i
$248$		0			0
$249$	135.877	+	2.35235i	0.0345816	+	0.000598691i
$250$		0			0
$251$	−5463.91			−1.37402			−0.687010	−	0.726648i	$-0.741077\pi$
$251$	−5463.91			−1.37402			−0.687010	+	0.726648i	$0.741077\pi$
$252$		0			0
$253$	9.58119			0.00238089
$254$		0			0
$255$	2032.27	−	3383.36i	0.499082	−	0.830880i
$256$		0			0
$257$	3701.06	+	6410.43i	0.898311	+	1.55592i	0.829653	+	0.558279i	$0.188538\pi$
$257$	3701.06	+	6410.43i	0.898311	+	1.55592i	0.0686576	+	0.997640i	$0.478128\pi$
$258$		0			0
$259$	−1074.58	+	1861.22i	−0.257803	+	0.446527i
$260$		0			0
$261$	2862.57	+	5380.01i	0.678883	+	1.27592i
$262$		0			0
$263$	100.015	−	173.232i	0.0234495	−	0.0406156i	−0.854063	−	0.520170i	$-0.825868\pi$
$263$	100.015	−	173.232i	0.0234495	−	0.0406156i	0.877512	+	0.479555i	$0.159202\pi$
$264$		0			0
$265$	278.270	+	481.979i	0.0645057	+	0.111727i
$266$		0			0
$267$	−1048.11	−	1890.20i	−0.240236	−	0.433252i
$268$		0			0
$269$	−5493.50			−1.24515			−0.622574	−	0.782561i	$-0.713913\pi$
$269$	−5493.50			−1.24515			−0.622574	+	0.782561i	$0.713913\pi$
$270$		0			0
$271$	−1861.89			−0.417350			−0.208675	−	0.977985i	$-0.566915\pi$
$271$	−1861.89			−0.417350			−0.208675	+	0.977985i	$0.566915\pi$
$272$		0			0
$273$	−2566.06	−	4627.74i	−0.568883	−	1.02595i
$274$		0			0
$275$	794.738	+	1376.53i	0.174271	+	0.301846i
$276$		0			0
$277$	−2819.52	+	4883.55i	−0.611582	+	1.05929i	0.379391	+	0.925236i	$0.376133\pi$
$277$	−2819.52	+	4883.55i	−0.611582	+	1.05929i	−0.990974	+	0.134055i	$0.957200\pi$
$278$		0			0
$279$	5428.98	+	188.034i	1.16496	+	0.0403487i
$280$		0			0
$281$	−1279.02	+	2215.33i	−0.271530	+	0.470303i	−0.969254	−	0.246063i	$-0.920863\pi$
$281$	−1279.02	+	2215.33i	−0.271530	+	0.470303i	0.697724	+	0.716367i	$0.254196\pi$
$282$		0			0
$283$	−3733.97	−	6467.43i	−0.784317	−	1.35848i	−0.929406	−	0.369058i	$-0.879680\pi$
$283$	−3733.97	−	6467.43i	−0.784317	−	1.35848i	0.145089	−	0.989419i	$-0.453653\pi$
$284$		0			0
$285$	−3599.10	+	5991.85i	−0.748043	+	1.24536i
$286$		0			0
$287$	6881.26			1.41529
$288$		0			0
$289$	−1359.48			−0.276712
$290$		0			0
$291$	4818.63	+	83.4221i	0.970699	+	0.0168051i
$292$		0			0
$293$	1780.66	+	3084.19i	0.355041	+	0.614950i	0.987125	−	0.159950i	$-0.0511334\pi$
$293$	1780.66	+	3084.19i	0.355041	+	0.614950i	−0.632084	+	0.774900i	$0.717800\pi$
$294$		0			0
$295$	4280.64	−	7414.28i	0.844842	−	1.46331i
$296$		0			0
$297$	3249.07	−	5007.81i	0.634781	−	0.978393i
$298$		0			0
$299$	−8.15863	+	14.1312i	−0.00157801	+	0.00273320i
$300$		0			0
$301$	−53.3149	−	92.3442i	−0.0102094	−	0.0176832i
$302$		0			0
$303$	−468.197	−	8.10561i	−0.0887696	−	0.00153682i
$304$		0			0
$305$	943.352			0.177102
$306$		0			0
$307$	−6101.93			−1.13438			−0.567192	−	0.823586i	$-0.691970\pi$
$307$	−6101.93			−1.13438			−0.567192	+	0.823586i	$0.691970\pi$
$308$		0			0
$309$	871.310	−	1450.57i	0.160411	−	0.267055i
$310$		0			0
$311$	−185.618	−	321.499i	−0.0338438	−	0.0586191i	0.848607	−	0.529023i	$-0.177442\pi$
$311$	−185.618	−	321.499i	−0.0338438	−	0.0586191i	−0.882451	+	0.470404i	$0.844108\pi$
$312$		0			0
$313$	−4660.55	+	8072.31i	−0.841629	+	1.45774i	0.0468881	+	0.998900i	$0.485070\pi$
$313$	−4660.55	+	8072.31i	−0.841629	+	1.45774i	−0.888517	+	0.458844i	$0.848264\pi$
$314$		0			0
$315$	2560.91	−	4100.91i	0.458066	−	0.733524i
$316$		0			0
$317$	3191.79	−	5528.33i	0.565516	−	0.979502i	−0.431486	−	0.902120i	$-0.642010\pi$
$317$	3191.79	−	5528.33i	0.565516	−	0.979502i	0.997001	−	0.0773824i	$-0.0246562\pi$
$318$		0			0
$319$	−4801.87	−	8317.08i	−0.842799	−	1.45977i
$320$		0			0
$321$	−2704.97	−	4878.25i	−0.470332	−	0.848216i
$322$		0			0
$323$	−6293.19			−1.08409
$324$		0			0
$325$	−2706.96			−0.462015
$326$		0			0
$327$	−1515.63	−	2733.34i	−0.256313	−	0.462245i
$328$		0			0
$329$	2623.73	+	4544.43i	0.439668	+	0.761527i
$330$		0			0
$331$	1264.71	−	2190.54i	0.210014	−	0.363755i	−0.741704	−	0.670727i	$-0.765982\pi$
$331$	1264.71	−	2190.54i	0.210014	−	0.363755i	0.951719	+	0.306971i	$0.0993156\pi$
$332$		0			0
$333$	2187.05	−	3502.23i	0.359908	−	0.576339i
$334$		0			0
$335$	−2681.35	+	4644.24i	−0.437307	+	0.757438i
$336$		0			0
$337$	−1799.91	−	3117.53i	−0.290941	−	0.503924i	0.683092	−	0.730333i	$-0.260635\pi$
$337$	−1799.91	−	3117.53i	−0.290941	−	0.503924i	−0.974032	+	0.226408i	$0.927302\pi$
$338$		0			0
$339$	1123.85	−	1871.00i	0.180056	−	0.299760i
$340$		0			0
$341$	−8560.62			−1.35948
$342$		0			0
$343$	6865.12			1.08070
$344$		0			0
$345$	−14.9067	−	0.258070i	−0.00232623	−	4.02726e-5i
$346$		0			0
$347$	5686.60	+	9849.48i	0.879748	+	1.52377i	0.851617	+	0.524165i	$0.175622\pi$
$347$	5686.60	+	9849.48i	0.879748	+	1.52377i	0.0281313	+	0.999604i	$0.491044\pi$
$348$		0			0
$349$	894.476	−	1549.28i	0.137193	−	0.237624i	−0.789240	−	0.614084i	$-0.789525\pi$
$349$	894.476	−	1549.28i	0.137193	−	0.237624i	0.926433	+	0.376460i	$0.122859\pi$
$350$		0			0
$351$	4619.28	+	9056.27i	0.702448	+	1.37717i
$352$		0			0
$353$	555.184	−	961.608i	0.0837096	−	0.144989i	−0.821131	−	0.570740i	$-0.806657\pi$
$353$	555.184	−	961.608i	0.0837096	−	0.144989i	0.904841	+	0.425750i	$0.139990\pi$
$354$		0			0
$355$	4656.15	+	8064.69i	0.696121	+	1.20572i
$356$		0			0
$357$	4352.41	+	75.3507i	0.645249	+	0.0111708i
$358$		0			0
$359$	2250.71			0.330886			0.165443	−	0.986219i	$-0.447095\pi$
$359$	2250.71			0.330886			0.165443	+	0.986219i	$0.447095\pi$
$360$		0			0
$361$	4286.07			0.624883
$362$		0			0
$363$	−1282.74	+	2135.53i	−0.185472	+	0.308777i
$364$		0			0
$365$	−3019.37	−	5229.70i	−0.432989	−	0.749959i
$366$		0			0
$367$	−1253.69	+	2171.45i	−0.178316	+	0.308852i	−0.941304	−	0.337560i	$-0.890398\pi$
$367$	−1253.69	+	2171.45i	−0.178316	+	0.308852i	0.762988	+	0.646413i	$0.223732\pi$
$368$		0			0
$369$	−13212.6	−	457.620i	−1.86401	−	0.0645603i
$370$		0			0
$371$	−306.914	+	531.591i	−0.0429493	+	0.0743903i
$372$		0			0
$373$	2482.71	+	4300.17i	0.344637	+	0.596929i	0.985288	−	0.170903i	$-0.0546686\pi$
$373$	2482.71	+	4300.17i	0.344637	+	0.596929i	−0.640651	+	0.767833i	$0.721335\pi$
$374$		0			0
$375$	2813.97	+	5074.84i	0.387501	+	0.698836i
$376$		0			0
$377$	16355.6			2.23437
$378$		0			0
$379$	−13541.7			−1.83534			−0.917668	−	0.397349i	$-0.869930\pi$
$379$	−13541.7			−1.83534			−0.917668	+	0.397349i	$0.869930\pi$
$380$		0			0
$381$	2470.06	+	4454.61i	0.332139	+	0.598994i
$382$		0			0
$383$	−4175.04	−	7231.38i	−0.557009	−	0.964768i	−0.997744	−	0.0671311i	$-0.978615\pi$
$383$	−4175.04	−	7231.38i	−0.557009	−	0.964768i	0.440735	−	0.897637i	$-0.354718\pi$
$384$		0			0
$385$	−3809.60	+	6598.41i	−0.504299	+	0.873471i
$386$		0			0
$387$	96.2278	+	180.854i	0.0126396	+	0.0237553i
$388$		0			0
$389$	1162.31	−	2013.18i	0.151495	−	0.262396i	−0.780283	−	0.625427i	$-0.784925\pi$
$389$	1162.31	−	2013.18i	0.151495	−	0.262396i	0.931777	+	0.363031i	$0.118258\pi$
$390$		0			0
$391$	−6.71164	−	11.6249i	−0.000868087	−	0.00150357i
$392$		0			0
$393$	−3626.45	+	6037.38i	−0.465472	+	0.774925i
$394$		0			0
$395$	−6748.39			−0.859617
$396$		0			0
$397$	13253.5			1.67550			0.837749	−	0.546056i	$-0.183871\pi$
$397$	13253.5			1.67550			0.837749	+	0.546056i	$0.183871\pi$
$398$		0			0
$399$	−7708.01	−	133.444i	−0.967126	−	0.0167433i
$400$		0			0
$401$	−7790.28	−	13493.2i	−0.970144	−	1.68034i	−0.695108	−	0.718906i	$-0.744643\pi$
$401$	−7790.28	−	13493.2i	−0.970144	−	1.68034i	−0.275037	−	0.961434i	$-0.588690\pi$
$402$		0			0
$403$	7289.58	−	12625.9i	0.901042	−	1.56065i
$404$		0			0
$405$	−5189.87	+	7703.77i	−0.636757	+	0.945194i
$406$		0			0
$407$	−3253.44	+	5635.13i	−0.396234	+	0.686297i
$408$		0			0
$409$	6119.59	+	10599.4i	0.739840	+	1.28144i	0.952567	+	0.304328i	$0.0984320\pi$
$409$	6119.59	+	10599.4i	0.739840	+	1.28144i	−0.212728	+	0.977112i	$0.568235\pi$
$410$		0			0
$411$	4709.72	+	81.5366i	0.565239	+	0.00978565i
$412$		0			0
$413$	9442.52			1.12503
$414$		0			0
$415$	333.244			0.0394176
$416$		0			0
$417$	2189.74	−	3645.52i	0.257152	−	0.428110i
$418$		0			0
$419$	−3196.50	−	5536.50i	−0.372695	−	0.645526i	0.617284	−	0.786740i	$-0.288233\pi$
$419$	−3196.50	−	5536.50i	−0.372695	−	0.645526i	−0.989979	+	0.141214i	$0.954900\pi$
$420$		0			0
$421$	7916.31	−	13711.5i	0.916431	−	1.58730i	0.111638	−	0.993749i	$-0.464390\pi$
$421$	7916.31	−	13711.5i	0.916431	−	1.58730i	0.804793	−	0.593556i	$-0.202276\pi$
$422$		0			0
$423$	−4735.55	−	8900.15i	−0.544327	−	1.02303i
$424$		0			0
$425$	1113.43	−	1928.52i	0.127081	−	0.220110i
$426$		0			0
$427$	520.227	+	901.060i	0.0589592	+	0.102120i
$428$		0			0
$429$	−7769.14	−	14011.2i	−0.874353	−	1.57684i
$430$		0			0
$431$	−9339.01			−1.04372			−0.521861	−	0.853030i	$-0.674762\pi$
$431$	−9339.01			−1.04372			−0.521861	+	0.853030i	$0.674762\pi$
$432$		0			0
$433$	−3379.19			−0.375043			−0.187522	−	0.982260i	$-0.560045\pi$
$433$	−3379.19			−0.375043			−0.187522	+	0.982260i	$0.560045\pi$
$434$		0			0
$435$	7246.85	+	13069.3i	0.798758	+	1.44051i
$436$		0			0
$437$	11.8861	+	20.5874i	0.00130112	+	0.00225361i
$438$		0			0
$439$	−7273.52	+	12598.1i	−0.790766	+	1.36965i	0.134728	+	0.990883i	$0.456984\pi$
$439$	−7273.52	+	12598.1i	−0.790766	+	1.36965i	−0.925493	+	0.378764i	$0.876349\pi$
$440$		0			0
$441$	−3926.13	−	135.982i	−0.423943	−	0.0146833i
$442$		0			0
$443$	2951.00	−	5111.28i	0.316492	−	0.548181i	−0.663261	−	0.748388i	$-0.730828\pi$
$443$	2951.00	−	5111.28i	0.316492	−	0.548181i	0.979754	+	0.200207i	$0.0641615\pi$
$444$		0			0
$445$	−2650.00	−	4589.93i	−0.282296	−	0.488951i
$446$		0			0
$447$	3102.33	−	5164.80i	0.328266	−	0.546503i
$448$		0			0
$449$	2448.48			0.257352			0.128676	−	0.991687i	$-0.458927\pi$
$449$	2448.48			0.257352			0.128676	+	0.991687i	$0.458927\pi$
$450$		0			0
$451$	20834.1			2.17525
$452$		0			0
$453$	−3314.51	−	57.3821i	−0.343773	−	0.00595154i
$454$		0			0
$455$	−6487.93	−	11237.4i	−0.668481	−	1.15784i
$456$		0			0
$457$	−2236.87	+	3874.38i	−0.228964	+	0.396577i	−0.957501	−	0.288429i	$-0.906867\pi$
$457$	−2236.87	+	3874.38i	−0.228964	+	0.396577i	0.728537	+	0.685006i	$0.240200\pi$
$458$		0			0
$459$	−8351.97	−	434.125i	−0.849317	−	0.0441464i
$460$		0			0
$461$	−251.107	+	434.929i	−0.0253692	+	0.0439407i	−0.878431	−	0.477869i	$-0.841409\pi$
$461$	−251.107	+	434.929i	−0.0253692	+	0.0439407i	0.853062	+	0.521809i	$0.174743\pi$
$462$		0			0
$463$	−3543.37	−	6137.30i	−0.355668	−	0.616036i	0.631564	−	0.775324i	$-0.282413\pi$
$463$	−3543.37	−	6137.30i	−0.355668	−	0.616036i	−0.987232	+	0.159288i	$0.949080\pi$
$464$		0			0
$465$	13318.8	+	230.581i	1.32827	+	0.0229956i
$466$		0			0
$467$	8057.18			0.798376			0.399188	−	0.916869i	$-0.369292\pi$
$467$	8057.18			0.798376			0.399188	+	0.916869i	$0.369292\pi$
$468$		0			0
$469$	−5914.71			−0.582336
$470$		0			0
$471$	−8807.27	+	14662.5i	−0.861608	+	1.43442i
$472$		0			0
$473$	−161.419	−	279.586i	−0.0156915	−	0.0271784i
$474$		0			0
$475$	−1971.85	+	3415.35i	−0.190473	+	0.329910i
$476$		0			0
$477$	624.651	−	1000.29i	0.0599598	−	0.0960167i
$478$		0			0
$479$	−8580.44	+	14861.8i	−0.818477	+	1.41764i	0.0883271	+	0.996092i	$0.471848\pi$
$479$	−8580.44	+	14861.8i	−0.818477	+	1.41764i	−0.906804	+	0.421552i	$0.861485\pi$
$480$		0			0
$481$	−5540.77	−	9596.90i	−0.525234	−	0.909732i
$482$		0			0
$483$	−7.97404	−	14.3807i	−0.000751203	−	0.00135475i
$484$		0			0
$485$	11817.9			1.10644
$486$		0			0
$487$	−9909.84			−0.922090			−0.461045	−	0.887377i	$-0.652525\pi$
$487$	−9909.84			−0.922090			−0.461045	+	0.887377i	$0.652525\pi$
$488$		0			0
$489$	3016.54	+	5440.15i	0.278963	+	0.503093i
$490$		0			0
$491$	9744.27	+	16877.6i	0.895627	+	1.55127i	0.833026	+	0.553233i	$0.186606\pi$
$491$	9744.27	+	16877.6i	0.895627	+	1.55127i	0.0626007	+	0.998039i	$0.480061\pi$
$492$		0			0
$493$	−6727.43	+	11652.2i	−0.614580	+	1.06448i
$494$		0			0
$495$	7753.54	−	12416.1i	0.704032	−	1.12740i
$496$		0			0
$497$	−5135.43	+	8894.82i	−0.463492	+	0.802791i
$498$		0			0
$499$	462.728	+	801.468i	0.0415121	+	0.0719011i	0.886035	−	0.463618i	$-0.153449\pi$
$499$	462.728	+	801.468i	0.0415121	+	0.0719011i	−0.844523	+	0.535520i	$0.820116\pi$
$500$		0			0
$501$	−2244.38	+	3736.48i	−0.200143	+	0.333201i
$502$		0			0
$503$	8723.45			0.773279			0.386640	−	0.922231i	$-0.373636\pi$
$503$	8723.45			0.773279			0.386640	+	0.922231i	$0.373636\pi$
$504$		0			0
$505$	−1148.28			−0.101183
$506$		0			0
$507$	15866.3	+	274.683i	1.38983	+	0.0240614i
$508$		0			0
$509$	−1524.35	−	2640.25i	−0.132742	−	0.229916i	0.791991	−	0.610533i	$-0.209045\pi$
$509$	−1524.35	−	2640.25i	−0.132742	−	0.229916i	−0.924733	+	0.380617i	$0.875712\pi$
$510$		0			0
$511$	3330.17	−	5768.02i	0.288293	−	0.499339i
$512$		0			0
$513$	14791.1	+	768.824i	1.27299	+	0.0661685i
$514$		0			0
$515$	2074.72	−	3593.52i	0.177520	−	0.307474i
$516$		0			0
$517$	7943.73	+	13758.9i	0.675754	+	1.17044i
$518$		0			0
$519$	11986.7	+	207.518i	1.01379	+	0.0175511i
$520$		0			0
$521$	−15593.0			−1.31121			−0.655607	−	0.755103i	$-0.727587\pi$
$521$	−15593.0			−1.31121			−0.655607	+	0.755103i	$0.727587\pi$
$522$		0			0
$523$	−9052.67			−0.756875			−0.378438	−	0.925627i	$-0.623539\pi$
$523$	−9052.67			−0.756875			−0.378438	+	0.925627i	$0.623539\pi$
$524$		0			0
$525$	1404.64	−	2338.47i	0.116769	−	0.194399i
$526$		0			0
$527$	5996.72	+	10386.6i	0.495676	+	0.858536i
$528$		0			0
$529$	6083.47	−	10536.9i	0.499998	−	0.866022i
$530$		0			0
$531$	−18130.4	−	627.949i	−1.48172	−	0.0513196i
$532$		0			0
$533$	−17740.7	+	30727.9i	−1.44172	+	2.49713i
$534$		0			0
$535$	−6839.14	−	11845.7i	−0.552677	−	0.957264i
$536$		0			0
$537$	−7847.81	−	14153.1i	−0.630648	−	1.13734i
$538$		0			0
$539$	6190.87			0.494730
$540$		0			0
$541$	−11742.8			−0.933200			−0.466600	−	0.884469i	$-0.654521\pi$
$541$	−11742.8			−0.933200			−0.466600	+	0.884469i	$0.654521\pi$
$542$		0			0
$543$	−9834.11	−	17735.2i	−0.777205	−	1.40164i
$544$		0			0
$545$	−3832.05	−	6637.31i	−0.301187	−	0.521672i
$546$		0			0
$547$	−1973.46	+	3418.12i	−0.154257	+	0.267182i	−0.932788	−	0.360424i	$-0.882632\pi$
$547$	−1973.46	+	3418.12i	−0.154257	+	0.267182i	0.778531	+	0.627606i	$0.215965\pi$
$548$		0			0
$549$	−938.956	−	1764.70i	−0.0729939	−	0.137187i
$550$		0			0
$551$	11914.1	−	20635.8i	0.921158	−	1.59549i
$552$		0			0
$553$	−3721.52	−	6445.86i	−0.286175	−	0.495670i
$554$		0			0
$555$	5213.57	−	8679.64i	0.398746	−	0.663839i
$556$		0			0
$557$	3129.69			0.238078			0.119039	−	0.992890i	$-0.462019\pi$
$557$	3129.69			0.238078			0.119039	+	0.992890i	$0.462019\pi$
$558$		0			0
$559$	549.810			0.0416001
$560$		0			0
$561$	13177.6	+	228.136i	0.991726	+	0.0171692i
$562$		0			0
$563$	96.0178	+	166.308i	0.00718769	+	0.0124494i	0.869597	−	0.493762i	$-0.164379\pi$
$563$	96.0178	+	166.308i	0.00718769	+	0.0124494i	−0.862409	+	0.506212i	$0.831045\pi$
$564$		0			0
$565$	2676.05	−	4635.05i	0.199260	−	0.345129i
$566$		0			0
$567$	−10220.4	−	708.824i	−0.756999	−	0.0525006i
$568$		0			0
$569$	−1630.51	+	2824.12i	−0.120131	+	0.208073i	−0.919819	−	0.392343i	$-0.871665\pi$
$569$	−1630.51	+	2824.12i	−0.120131	+	0.208073i	0.799688	+	0.600415i	$0.204998\pi$
$570$		0			0
$571$	4707.22	+	8153.15i	0.344993	+	0.597546i	0.985353	−	0.170530i	$-0.0545479\pi$
$571$	4707.22	+	8153.15i	0.344993	+	0.597546i	−0.640359	+	0.768075i	$0.721215\pi$
$572$		0			0
$573$	549.356	+	9.51067i	0.0400518	+	0.000693392i
$574$		0			0
$575$	−8.41187			−0.000610086
$576$		0			0
$577$	−9739.86			−0.702731			−0.351366	−	0.936238i	$-0.614283\pi$
$577$	−9739.86			−0.702731			−0.351366	+	0.936238i	$0.614283\pi$
$578$		0			0
$579$	4241.79	−	7061.80i	0.304461	−	0.506871i
$580$		0			0
$581$	183.773	+	318.304i	0.0131225	+	0.0227289i
$582$		0			0
$583$	−929.229	+	1609.47i	−0.0660116	+	0.114335i
$584$		0			0
$585$	11710.0	+	22008.2i	0.827608	+	1.55543i
$586$		0			0
$587$	12702.8	−	22002.0i	0.893190	−	1.54705i	0.0571605	−	0.998365i	$-0.481795\pi$
$587$	12702.8	−	22002.0i	0.893190	−	1.54705i	0.836029	−	0.548685i	$-0.184871\pi$
$588$		0			0
$589$	−10620.0	−	18394.5i	−0.742939	−	1.28681i
$590$		0			0
$591$	9840.71	+	17747.1i	0.684929	+	1.23523i
$592$		0			0
$593$	2751.26			0.190524			0.0952620	−	0.995452i	$-0.469631\pi$
$593$	2751.26			0.190524			0.0952620	+	0.995452i	$0.469631\pi$
$594$		0			0
$595$	10674.5			0.735482
$596$		0			0
$597$	−3877.38	−	6992.63i	−0.265814	−	0.479379i
$598$		0			0
$599$	−1658.11	−	2871.93i	−0.113103	−	0.195900i	0.803917	−	0.594742i	$-0.202746\pi$
$599$	−1658.11	−	2871.93i	−0.113103	−	0.195900i	−0.917020	+	0.398842i	$0.869412\pi$
$600$		0			0
$601$	3959.84	−	6858.65i	0.268761	−	0.465508i	−0.699781	−	0.714357i	$-0.746719\pi$
$601$	3959.84	−	6858.65i	0.268761	−	0.465508i	0.968542	+	0.248850i	$0.0800525\pi$
$602$		0			0
$603$	11356.7	+	393.342i	0.766967	+	0.0265640i
$604$		0			0
$605$	−3054.40	+	5290.37i	−0.205254	+	0.355511i
$606$		0			0
$607$	4737.24	+	8205.13i	0.316768	+	0.548659i	0.979812	−	0.199922i	$-0.0640688\pi$
$607$	4737.24	+	8205.13i	0.316768	+	0.548659i	−0.663043	+	0.748581i	$0.730736\pi$
$608$		0			0
$609$	−8486.96	+	14129.2i	−0.564711	+	0.940141i
$610$		0			0
$611$	−27057.2			−1.79151
$612$		0			0
$613$	−3165.90			−0.208596			−0.104298	−	0.994546i	$-0.533260\pi$
$613$	−3165.90			−0.208596			−0.104298	+	0.994546i	$0.533260\pi$
$614$		0			0
$615$	−32414.2	−	561.168i	−2.12531	−	0.0367942i
$616$		0			0
$617$	315.172	+	545.894i	0.0205646	+	0.0356189i	0.876125	−	0.482085i	$-0.160120\pi$
$617$	315.172	+	545.894i	0.0205646	+	0.0356189i	−0.855560	+	0.517704i	$0.826787\pi$
$618$		0			0
$619$	−586.272	+	1015.45i	−0.0380683	+	0.0659362i	−0.884432	−	0.466669i	$-0.845454\pi$
$619$	−586.272	+	1015.45i	−0.0380683	+	0.0659362i	0.846364	+	0.532606i	$0.178787\pi$
$620$		0			0
$621$	14.3544	+	28.1424i	0.000927574	+	0.00181854i
$622$		0			0
$623$	2922.77	−	5062.39i	0.187959	−	0.325554i
$624$		0			0
$625$	9449.52	+	16367.1i	0.604769	+	1.04749i
$626$		0			0
$627$	−23337.2	−	404.023i	−1.48644	−	0.0257338i
$628$		0			0
$629$	9116.16			0.577878
$630$		0			0
$631$	17925.9			1.13093			0.565465	−	0.824772i	$-0.308697\pi$
$631$	17925.9			1.13093			0.565465	+	0.824772i	$0.308697\pi$
$632$		0			0
$633$	−2518.97	+	4193.63i	−0.158168	+	0.263320i
$634$		0			0
$635$	6245.22	+	10817.0i	0.390290	+	0.676001i
$636$		0			0
$637$	−5271.68	+	9130.82i	−0.327899	+	0.567938i
$638$		0			0
$639$	10452.0	−	16737.3i	0.647063	−	1.03617i
$640$		0			0
$641$	3348.43	−	5799.65i	0.206326	−	0.357367i	−0.744228	−	0.667925i	$-0.767183\pi$
$641$	3348.43	−	5799.65i	0.206326	−	0.357367i	0.950554	+	0.310558i	$0.100516\pi$
$642$		0			0
$643$	14845.5	+	25713.2i	0.910498	+	1.57703i	0.813362	+	0.581758i	$0.197635\pi$
$643$	14845.5	+	25713.2i	0.910498	+	1.57703i	0.0971358	+	0.995271i	$0.469032\pi$
$644$		0			0
$645$	243.609	+	439.335i	0.0148715	+	0.0268199i
$646$		0			0
$647$	−12607.6			−0.766084			−0.383042	−	0.923731i	$-0.625124\pi$
$647$	−12607.6			−0.766084			−0.383042	+	0.923731i	$0.625124\pi$
$648$		0			0
$649$	28588.7			1.72913
$650$		0			0
$651$	7124.65	+	12848.9i	0.428936	+	0.773560i
$652$		0			0
$653$	469.730	+	813.596i	0.0281500	+	0.0487573i	0.879757	−	0.475423i	$-0.157705\pi$
$653$	469.730	+	813.596i	0.0281500	+	0.0487573i	−0.851607	+	0.524180i	$0.824372\pi$
$654$		0			0
$655$	−8635.12	+	14956.5i	−0.515118	+	0.892210i
$656$		0			0
$657$	−6777.77	+	10853.6i	−0.402475	+	0.644504i
$658$		0			0
$659$	6941.60	−	12023.2i	0.410328	−	0.710709i	−0.584597	−	0.811324i	$-0.698747\pi$
$659$	6941.60	−	12023.2i	0.410328	−	0.710709i	0.994926	+	0.100614i	$0.0320808\pi$
$660$		0			0
$661$	−4072.30	−	7053.42i	−0.239628	−	0.415047i	0.720980	−	0.692956i	$-0.243692\pi$
$661$	−4072.30	−	7053.42i	−0.239628	−	0.415047i	−0.960608	+	0.277909i	$0.910359\pi$
$662$		0			0
$663$	−11557.5	+	19241.2i	−0.677009	+	1.12710i
$664$		0			0
$665$	−18904.3			−1.10237
$666$		0			0
$667$	50.8252			0.00295047
$668$		0			0
$669$	17256.8	+	298.757i	0.997289	+	0.0172655i
$670$		0			0
$671$	1575.07	+	2728.10i	0.0906182	+	0.156955i
$672$		0			0
$673$	14461.2	−	25047.6i	0.828290	−	1.43464i	−0.0710895	−	0.997470i	$-0.522648\pi$
$673$	14461.2	−	25047.6i	0.828290	−	1.43464i	0.899379	−	0.437170i	$-0.144019\pi$
$674$		0			0
$675$	−2852.54	+	4396.64i	−0.162658	+	0.250706i
$676$		0			0
$677$	13590.4	−	23539.3i	0.771524	−	1.33632i	−0.165203	−	0.986260i	$-0.552828\pi$
$677$	13590.4	−	23539.3i	0.771524	−	1.33632i	0.936727	−	0.350060i	$-0.113839\pi$
$678$		0			0
$679$	6517.20	+	11288.1i	0.368346	+	0.637995i
$680$		0			0
$681$	−21882.1	−	378.832i	−1.23131	−	0.0213170i
$682$		0			0
$683$	−7985.87			−0.447395			−0.223697	−	0.974659i	$-0.571813\pi$
$683$	−7985.87			−0.447395			−0.223697	+	0.974659i	$0.571813\pi$
$684$		0			0
$685$	11550.8			0.644283
$686$		0			0
$687$	947.543	−	1577.49i	0.0526216	−	0.0876053i
$688$		0			0
$689$	−1582.52	−	2741.01i	−0.0875027	−	0.151559i
$690$		0			0
$691$	−4625.03	+	8010.78i	−0.254623	+	0.441020i	−0.964793	−	0.263010i	$-0.915285\pi$
$691$	−4625.03	+	8010.78i	−0.254623	+	0.441020i	0.710170	+	0.704030i	$0.248618\pi$
$692$		0			0
$693$	16135.3	+	558.850i	0.884459	+	0.0306334i
$694$		0			0
$695$	5214.11	−	9031.10i	0.284579	−	0.492905i
$696$		0			0
$697$	−14594.3	−	25278.0i	−0.793111	−	1.37371i
$698$		0			0
$699$	−2189.17	−	3948.03i	−0.118458	−	0.213631i
$700$		0			0
$701$	−10267.4			−0.553201			−0.276601	−	0.960985i	$-0.589208\pi$
$701$	−10267.4			−0.553201			−0.276601	+	0.960985i	$0.589208\pi$
$702$		0			0
$703$	−16144.5			−0.866146
$704$		0			0
$705$	−11988.5	−	21620.5i	−0.640442	−	1.15500i
$706$		0			0
$707$	−633.236	−	1096.80i	−0.0336850	−	0.0583441i
$708$		0			0
$709$	−6979.33	+	12088.6i	−0.369696	+	0.640332i	−0.989518	−	0.144410i	$-0.953871\pi$
$709$	−6979.33	+	12088.6i	−0.369696	+	0.640332i	0.619822	+	0.784742i	$0.287205\pi$
$710$		0			0
$711$	6716.95	+	12624.0i	0.354297	+	0.665877i
$712$		0			0
$713$	22.6524	−	39.2351i	0.00118982	−	0.00206082i
$714$		0			0
$715$	−19643.2	−	34023.0i	−1.02743	−	1.77957i
$716$		0			0
$717$	3222.35	−	5364.62i	0.167839	−	0.279422i
$718$		0			0
$719$	26373.7			1.36798			0.683988	−	0.729493i	$-0.260244\pi$
$719$	26373.7			1.36798			0.683988	+	0.729493i	$0.260244\pi$
$720$		0			0
$721$	4576.55			0.236394
$722$		0			0
$723$	−26431.0	−	457.584i	−1.35958	−	0.0235376i
$724$		0			0
$725$	4215.83	+	7302.04i	0.215962	+	0.374056i
$726$		0			0
$727$	4396.92	−	7615.69i	0.224309	−	0.388515i	−0.731803	−	0.681516i	$-0.761321\pi$
$727$	4396.92	−	7615.69i	0.224309	−	0.388515i	0.956112	+	0.293002i	$0.0946541\pi$
$728$		0			0
$729$	19576.9	+	2040.68i	0.994611	+	0.103677i
$730$		0			0
$731$	−226.149	+	391.701i	−0.0114424	+	0.0198189i
$732$		0			0
$733$	5337.00	+	9243.95i	0.268931	+	0.465802i	0.968586	−	0.248678i	$-0.0799963\pi$
$733$	5337.00	+	9243.95i	0.268931	+	0.465802i	−0.699655	+	0.714481i	$0.746663\pi$
$734$		0			0
$735$	−9631.92	−	166.752i	−0.483372	−	0.00836834i
$736$		0			0
$737$	−17907.7			−0.895031
$738$		0			0
$739$	−12678.1			−0.631084			−0.315542	−	0.948912i	$-0.602186\pi$
$739$	−12678.1			−0.631084			−0.315542	+	0.948912i	$0.602186\pi$
$740$		0			0
$741$	20468.1	−	34075.6i	1.01473	−	1.68934i
$742$		0			0
$743$	−11055.6	−	19148.9i	−0.545884	−	0.945499i	−0.998551	−	0.0538194i	$-0.982860\pi$
$743$	−11055.6	−	19148.9i	−0.545884	−	0.945499i	0.452666	−	0.891680i	$-0.350473\pi$
$744$		0			0
$745$	7387.10	−	12794.8i	0.363278	−	0.629216i
$746$		0			0
$747$	−331.691	−	623.391i	−0.0162462	−	0.0305337i
$748$		0			0
$749$	7543.12	−	13065.1i	0.367984	−	0.637366i
$750$		0			0
$751$	11075.5	+	19183.4i	0.538151	+	0.932105i	0.999004	+	0.0446283i	$0.0142104\pi$
$751$	11075.5	+	19183.4i	0.538151	+	0.932105i	−0.460853	+	0.887477i	$0.652456\pi$
$752$		0			0
$753$	13767.9	+	24829.6i	0.666309	+	1.20165i
$754$		0			0
$755$	−8129.00			−0.391847
$756$		0			0
$757$	−25282.2			−1.21387			−0.606933	−	0.794753i	$-0.707601\pi$
$757$	−25282.2			−1.21387			−0.606933	+	0.794753i	$0.707601\pi$
$758$		0			0
$759$	−24.1426	−	43.5398i	−0.00115457	−	0.00208221i
$760$		0			0
$761$	5064.47	+	8771.91i	0.241244	+	0.417847i	0.961069	−	0.276309i	$-0.0891112\pi$
$761$	5064.47	+	8771.91i	0.241244	+	0.417847i	−0.719825	+	0.694156i	$0.755778\pi$
$762$		0			0
$763$	4226.50	−	7320.52i	0.200537	−	0.347340i
$764$		0			0
$765$	−20495.9	−	709.879i	−0.968668	−	0.0335500i
$766$		0			0
$767$	−24344.0	+	42165.0i	−1.14604	+	1.98499i
$768$		0			0
$769$	12617.2	+	21853.7i	0.591663	+	1.02479i	0.994009	+	0.109303i	$0.0348618\pi$
$769$	12617.2	+	21853.7i	0.591663	+	1.02479i	−0.402345	+	0.915488i	$0.631805\pi$
$770$		0			0
$771$	19805.0	−	32971.7i	0.925109	−	1.54014i
$772$		0			0
$773$	30384.6			1.41379			0.706895	−	0.707319i	$-0.250096\pi$
$773$	30384.6			1.41379			0.706895	+	0.707319i	$0.250096\pi$
$774$		0			0
$775$	7515.85			0.348358
$776$		0			0
$777$	11165.6	+	193.304i	0.515528	+	0.00892503i
$778$		0			0
$779$	25846.1	+	44766.8i	1.18875	+	2.05897i
$780$		0			0
$781$	−15548.3	+	26930.4i	−0.712371	+	1.23386i
$782$		0			0
$783$	17235.3	−	26564.9i	0.786639	−	1.21245i
$784$		0			0
$785$	−20971.4	+	36323.5i	−0.953505	+	1.65152i
$786$		0			0
$787$	−15072.3	−	26106.0i	−0.682682	−	1.18244i	−0.974159	−	0.225862i	$-0.927480\pi$
$787$	−15072.3	−	26106.0i	−0.682682	−	1.18244i	0.291478	−	0.956578i	$-0.405853\pi$
$788$		0			0
$789$	−1039.23	−	17.9916i	−0.0468919	−	0.000811811i
$790$		0			0
$791$	5903.01			0.265344
$792$		0			0
$793$	−5364.84			−0.240241
$794$		0			0
$795$	1489.07	−	2479.03i	0.0664300	−	0.110594i
$796$		0			0
$797$	8064.02	+	13967.3i	0.358397	+	0.620761i	0.987693	−	0.156404i	$-0.0499902\pi$
$797$	8064.02	+	13967.3i	0.358397	+	0.620761i	−0.629296	+	0.777165i	$0.716657\pi$
$798$		0			0
$799$	11129.2	−	19276.3i	0.492769	−	0.853501i
$800$		0			0
$801$	−5948.61	+	9525.82i	−0.262402	+	0.420197i
$802$		0			0
$803$	10082.6	−	17463.6i	0.443097	−	0.767466i
$804$		0			0
$805$	−20.1613	−	34.9203i	−0.000882722	−	0.00152892i
$806$		0			0
$807$	13842.5	+	24964.1i	0.603815	+	1.08895i
$808$		0			0
$809$	−23446.4			−1.01895			−0.509475	−	0.860485i	$-0.670160\pi$
$809$	−23446.4			−1.01895			−0.509475	+	0.860485i	$0.670160\pi$
$810$		0			0
$811$	−37762.1			−1.63503			−0.817513	−	0.575910i	$-0.804648\pi$
$811$	−37762.1			−1.63503			−0.817513	+	0.575910i	$0.804648\pi$
$812$		0			0
$813$	4691.58	+	8460.99i	0.202387	+	0.364994i
$814$		0			0
$815$	7626.92	+	13210.2i	0.327803	+	0.567771i
$816$		0			0
$817$	400.503	−	693.692i	0.0171504	−	0.0297053i
$818$		0			0
$819$	−14563.9	+	23321.9i	−0.621371	+	0.995033i
$820$		0			0
$821$	5942.36	−	10292.5i	0.252606	−	0.437527i	−0.711636	−	0.702548i	$-0.752046\pi$
$821$	5942.36	−	10292.5i	0.252606	−	0.437527i	0.964243	+	0.265021i	$0.0853789\pi$
$822$		0			0
$823$	4532.02	+	7849.70i	0.191952	+	0.332471i	0.945897	−	0.324467i	$-0.105185\pi$
$823$	4532.02	+	7849.70i	0.191952	+	0.332471i	−0.753945	+	0.656937i	$0.771852\pi$
$824$		0			0
$825$	4252.77	−	7080.09i	0.179470	−	0.298784i
$826$		0			0
$827$	−36451.4			−1.53270			−0.766348	−	0.642426i	$-0.777928\pi$
$827$	−36451.4			−1.53270			−0.766348	+	0.642426i	$0.777928\pi$
$828$		0			0
$829$	−15293.4			−0.640725			−0.320362	−	0.947295i	$-0.603805\pi$
$829$	−15293.4			−0.640725			−0.320362	+	0.947295i	$0.603805\pi$
$830$		0			0
$831$	29296.9	+	507.199i	1.22298	+	0.0211727i
$832$		0			0
$833$	−4336.71	−	7511.41i	−0.180382	−	0.312431i
$834$		0			0
$835$	−5344.20	+	9256.42i	−0.221489	+	0.383631i
$836$		0			0
$837$	−12825.4	−	25144.7i	−0.529643	−	1.03839i
$838$		0			0
$839$	176.769	−	306.174i	0.00727385	−	0.0125987i	−0.862366	−	0.506286i	$-0.831018\pi$
$839$	176.769	−	306.174i	0.00727385	−	0.0125987i	0.869639	+	0.493687i	$0.164351\pi$
$840$		0			0
$841$	−13277.9	−	22998.0i	−0.544422	−	0.942966i
$842$		0			0
$843$	13290.0	+	230.081i	0.542978	+	0.00940026i
$844$		0			0
$845$	38912.8			1.58419
$846$		0			0
$847$	−6737.59			−0.273325
$848$		0			0
$849$	−19981.1	+	33264.9i	−0.807714	+	1.34470i
$850$		0			0
$851$	−17.2180	−	29.8224i	−0.000693566	−	0.00120129i
$852$		0			0
$853$	−12846.3	+	22250.5i	−0.515651	+	0.893134i	0.484184	+	0.874966i	$0.339117\pi$
$853$	−12846.3	+	22250.5i	−0.515651	+	0.893134i	−0.999835	+	0.0181675i	$0.994217\pi$
$854$		0			0
$855$	36297.7	+	1257.18i	1.45188	+	0.0502861i
$856$		0			0
$857$	6508.98	−	11273.9i	0.259443	−	0.449368i	−0.706650	−	0.707563i	$-0.749794\pi$
$857$	6508.98	−	11273.9i	0.259443	−	0.449368i	0.966093	+	0.258195i	$0.0831278\pi$
$858$		0			0
$859$	1066.04	+	1846.43i	0.0423431	+	0.0733404i	0.886420	−	0.462881i	$-0.153184\pi$
$859$	1066.04	+	1846.43i	0.0423431	+	0.0733404i	−0.844077	+	0.536222i	$0.819851\pi$
$860$		0			0
$861$	−17339.3	−	31270.5i	−0.686322	−	1.23774i
$862$		0			0
$863$	39300.5			1.55018			0.775090	−	0.631851i	$-0.217705\pi$
$863$	39300.5			1.55018			0.775090	+	0.631851i	$0.217705\pi$
$864$		0			0
$865$	29397.9			1.15556
$866$		0			0
$867$	3425.62	+	6177.90i	0.134187	+	0.241998i
$868$		0			0
$869$	−11267.5	−	19515.8i	−0.439842	−	0.761828i
$870$		0			0
$871$	15248.8	−	26411.8i	0.593212	−	1.02747i
$872$		0			0
$873$	−11762.9	−	22107.5i	−0.456028	−	0.857074i
$874$		0			0
$875$	−7847.11	+	13591.6i	−0.303178	+	0.525119i
$876$		0			0
$877$	5304.23	+	9187.20i	0.204232	+	0.353740i	0.949888	−	0.312591i	$-0.101197\pi$
$877$	5304.23	+	9187.20i	0.204232	+	0.353740i	−0.745656	+	0.666331i	$0.767864\pi$
$878$		0			0
$879$	9528.59	−	15863.4i	0.365633	−	0.608712i
$880$		0			0
$881$	41310.4			1.57978			0.789888	−	0.613251i	$-0.210139\pi$
$881$	41310.4			1.57978			0.789888	+	0.613251i	$0.210139\pi$
$882$		0			0
$883$	47180.5			1.79813			0.899066	−	0.437814i	$-0.144247\pi$
$883$	47180.5			1.79813			0.899066	+	0.437814i	$0.144247\pi$
$884$		0			0
$885$	−44479.0	−	770.039i	−1.68943	−	0.0292481i
$886$		0			0
$887$	−24888.8	−	43108.7i	−0.942148	−	1.63185i	−0.761363	−	0.648325i	$-0.775470\pi$
$887$	−24888.8	−	43108.7i	−0.942148	−	1.63185i	−0.180785	−	0.983523i	$-0.557864\pi$
$888$		0			0
$889$	−6888.06	+	11930.5i	−0.259863	+	0.450096i
$890$		0			0
$891$	−30944.0	−	2146.07i	−1.16348	−	0.0806916i
$892$		0			0
$893$	−19709.5	+	34137.9i	−0.738582	+	1.27926i
$894$		0			0
$895$	−19842.1	−	34367.6i	−0.741060	−	1.28355i
$896$		0			0
$897$	84.7742	+	1.46765i	0.00315555	+	5.46302e-5i
$898$		0			0
$899$	−45411.4			−1.68471
$900$		0			0
$901$	2603.70			0.0962730
$902$		0			0
$903$	−285.297	+	474.967i	−0.0105139	+	0.0175038i
$904$		0			0
$905$	−24864.2	−	43066.1i	−0.913276	−	1.58184i
$906$		0			0
$907$	−518.253	+	897.641i	−0.0189728	+	0.0328618i	−0.875356	−	0.483479i	$-0.839373\pi$
$907$	−518.253	+	897.641i	−0.0189728	+	0.0328618i	0.856383	+	0.516341i	$0.172706\pi$
$908$		0			0
$909$	1142.92	+	2148.05i	0.0417034	+	0.0783788i
$910$		0			0
$911$	−12390.5	+	21460.9i	−0.450620	+	0.780496i	−0.998425	−	0.0561098i	$-0.982130\pi$
$911$	−12390.5	+	21460.9i	−0.450620	+	0.780496i	0.547805	+	0.836606i	$0.315464\pi$
$912$		0			0
$913$	556.401	+	963.715i	0.0201689	+	0.0349335i
$914$		0			0
$915$	−2377.05	−	4286.87i	−0.0858829	−	0.154885i
$916$		0			0
$917$	−19047.9			−0.685953
$918$		0			0
$919$	25210.4			0.904912			0.452456	−	0.891787i	$-0.350548\pi$
$919$	25210.4			0.904912			0.452456	+	0.891787i	$0.350548\pi$
$920$		0			0
$921$	15375.6	+	27729.0i	0.550102	+	0.992076i
$922$		0			0
$923$	−26479.5	−	45863.9i	−0.944295	−	1.63557i
$924$		0			0
$925$	2856.38	−	4947.40i	0.101532	−	0.175859i
$926$		0			0
$927$	−8787.35	−	304.351i	−0.311342	−	0.0107834i
$928$		0			0
$929$	13939.3	−	24143.5i	0.492285	−	0.852663i	−0.507675	−	0.861548i	$-0.669495\pi$
$929$	13939.3	−	24143.5i	0.492285	−	0.852663i	0.999961	+	0.00888567i	$0.00282843\pi$
$930$		0			0
$931$	7680.21	+	13302.5i	0.270364	+	0.468284i
$932$		0			0
$933$	−993.270	+	1653.61i	−0.0348534	+	0.0580245i
$934$		0			0
$935$	32318.7			1.13041
$936$		0			0
$937$	5091.76			0.177525			0.0887623	−	0.996053i	$-0.471709\pi$
$937$	5091.76			0.177525			0.0887623	+	0.996053i	$0.471709\pi$
$938$		0			0
$939$	48426.6	+	838.381i	1.68301	+	0.0291369i
$940$		0			0
$941$	21549.7	+	37325.2i	0.746547	+	1.29306i	0.949469	+	0.313862i	$0.101623\pi$
$941$	21549.7	+	37325.2i	0.746547	+	1.29306i	−0.202922	+	0.979195i	$0.565044\pi$
$942$		0			0
$943$	−55.1294	+	95.4869i	−0.00190377	+	0.00329743i
$944$		0			0
$945$	−25088.7	−	1304.08i	−0.863636	−	0.0448907i
$946$		0			0
$947$	12342.8	−	21378.4i	0.423536	−	0.733586i	−0.572747	−	0.819732i	$-0.694122\pi$
$947$	12342.8	−	21378.4i	0.423536	−	0.733586i	0.996282	+	0.0861469i	$0.0274554\pi$
$948$		0			0
$949$	17171.2	+	29741.3i	0.587354	+	1.01733i
$950$		0			0
$951$	−33165.0	−	574.167i	−1.13086	−	0.0195779i
$952$		0			0
$953$	9714.42			0.330200			0.165100	−	0.986277i	$-0.447205\pi$
$953$	9714.42			0.330200			0.165100	+	0.986277i	$0.447205\pi$
$954$		0			0
$955$	1347.32			0.0456527
$956$		0			0
$957$	−25695.6	+	42778.4i	−0.867941	+	1.44496i
$958$		0			0
$959$	6369.90	+	11033.0i	0.214489	+	0.371505i
$960$		0			0
$961$	−5344.00	+	9256.07i	−0.179383	+	0.310700i
$962$		0			0
$963$	−15352.3	+	24584.4i	−0.513728	+	0.822658i
$964$		0			0
$965$	10100.3	−	17494.3i	0.336934	−	0.583586i
$966$		0			0
$967$	17184.1	+	29763.7i	0.571461	+	0.989799i	0.996416	+	0.0845849i	$0.0269564\pi$
$967$	17184.1	+	29763.7i	0.571461	+	0.989799i	−0.424955	+	0.905214i	$0.639710\pi$
$968$		0			0
$969$	15857.5	+	28598.1i	0.525714	+	0.948095i
$970$		0			0
$971$	31313.7			1.03492			0.517458	−	0.855708i	$-0.326878\pi$
$971$	31313.7			1.03492			0.517458	+	0.855708i	$0.326878\pi$
$972$		0			0
$973$	11501.6			0.378957
$974$		0			0
$975$	6820.97	+	12301.2i	0.224047	+	0.404056i
$976$		0			0
$977$	−12699.1	−	21995.4i	−0.415844	−	0.720263i	0.579673	−	0.814849i	$-0.303180\pi$
$977$	−12699.1	−	21995.4i	−0.415844	−	0.720263i	−0.995517	+	0.0945867i	$0.969847\pi$
$978$		0			0
$979$	8849.14	−	15327.2i	0.288886	−	0.500366i
$980$		0			0
$981$	−8602.06	+	13774.9i	−0.279962	+	0.448317i
$982$		0			0
$983$	−24447.1	+	42343.7i	−0.793227	+	1.37391i	0.130732	+	0.991418i	$0.458267\pi$
$983$	−24447.1	+	42343.7i	−0.793227	+	1.37391i	−0.923959	+	0.382492i	$0.875066\pi$
$984$		0			0
$985$	24880.9	+	43095.0i	0.804844	+	1.39403i
$986$		0			0
$987$	14040.0	−	23374.0i	0.452784	−	0.753802i
$988$		0			0
$989$	1.70854			5.49325e−5
$990$		0			0
$991$	−46870.9			−1.50242			−0.751212	−	0.660061i	$-0.770530\pi$
$991$	−46870.9			−1.50242			−0.751212	+	0.660061i	$0.770530\pi$
$992$		0			0
$993$	−13141.3	−	227.507i	−0.419966	−	0.00727061i
$994$		0			0
$995$	−9803.43	−	16980.0i	−0.312352	−	0.541009i
$996$		0			0
$997$	15704.1	−	27200.3i	0.498851	−	0.864035i	−0.501148	−	0.865362i	$-0.667089\pi$
$997$	15704.1	−	27200.3i	0.498851	−	0.864035i	0.999999	+	0.00132618i	$0.000422137\pi$
$998$		0			0
$999$	−21426.1	−	1113.70i	−0.678569	−	0.0352712i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.e.a.25.2	yes	6
3.2	odd	2		108.4.e.a.73.3		6
4.3	odd	2		144.4.i.d.97.2		6
9.2	odd	6		324.4.a.d.1.1		3
9.4	even	3	inner	36.4.e.a.13.2	✓	6
9.5	odd	6		108.4.e.a.37.3		6
9.7	even	3		324.4.a.c.1.3		3
12.11	even	2		432.4.i.d.289.3		6
36.7	odd	6		1296.4.a.v.1.3		3
36.11	even	6		1296.4.a.w.1.1		3
36.23	even	6		432.4.i.d.145.3		6
36.31	odd	6		144.4.i.d.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.e.a.13.2	✓	6	9.4	even	3	inner
36.4.e.a.25.2	yes	6	1.1	even	1	trivial
108.4.e.a.37.3		6	9.5	odd	6
108.4.e.a.73.3		6	3.2	odd	2
144.4.i.d.49.2		6	36.31	odd	6
144.4.i.d.97.2		6	4.3	odd	2
324.4.a.c.1.3		3	9.7	even	3
324.4.a.d.1.1		3	9.2	odd	6
432.4.i.d.145.3		6	36.23	even	6
432.4.i.d.289.3		6	12.11	even	2
1296.4.a.v.1.3		3	36.7	odd	6
1296.4.a.w.1.1		3	36.11	even	6

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	36.4.e.a.25.2

Level	$36$
Weight	$4$
Character	36.25
Analytic conductor	$2.124$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$