LMFDB - Embedded newform 1512.2.c.g.757.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.8
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.g.757.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10240 + 0.885841i) q^{2} +(0.430570 - 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(1.25548 + 2.53452i) q^{8} +O(q^{10})$	\(q+(-1.10240 + 0.885841i) q^{2} +(0.430570 - 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(1.25548 + 2.53452i) q^{8} +(-2.64867 - 3.29619i) q^{10} +2.13956i q^{11} -0.665739i q^{13} +(-1.10240 + 0.885841i) q^{14} +(-3.62922 - 1.68190i) q^{16} -7.04931 q^{17} +1.39525i q^{19} +(5.83980 + 1.28741i) q^{20} +(-1.89531 - 2.35865i) q^{22} -0.184371 q^{23} -3.94016 q^{25} +(0.589739 + 0.733911i) q^{26} +(0.430570 - 1.95310i) q^{28} +1.27564i q^{29} -7.62308 q^{31} +(5.49074 - 1.36079i) q^{32} +(7.77116 - 6.24457i) q^{34} +2.99001i q^{35} +6.69127i q^{37} +(-1.23597 - 1.53812i) q^{38} +(-7.57823 + 3.75389i) q^{40} +0.274106 q^{41} -2.63971i q^{43} +(4.17877 + 0.921229i) q^{44} +(0.203250 - 0.163323i) q^{46} +5.77739 q^{47} +1.00000 q^{49} +(4.34363 - 3.49036i) q^{50} +(-1.30026 - 0.286647i) q^{52} -7.48353i q^{53} -6.39730 q^{55} +(1.25548 + 2.53452i) q^{56} +(-1.13001 - 1.40626i) q^{58} +9.03787i q^{59} -9.80298i q^{61} +(8.40369 - 6.75284i) q^{62} +(-4.84755 + 6.36406i) q^{64} +1.99057 q^{65} +10.8191i q^{67} +(-3.03522 + 13.7680i) q^{68} +(-2.64867 - 3.29619i) q^{70} -7.93573 q^{71} -2.80408 q^{73} +(-5.92740 - 7.37645i) q^{74} +(2.72506 + 0.600752i) q^{76} +2.13956i q^{77} +7.98350 q^{79} +(5.02888 - 10.8514i) q^{80} +(-0.302174 + 0.242814i) q^{82} -6.76125i q^{83} -21.0775i q^{85} +(2.33837 + 2.91002i) q^{86} +(-5.42274 + 2.68617i) q^{88} -16.7549 q^{89} -0.665739i q^{91} +(-0.0793844 + 0.360095i) q^{92} +(-6.36899 + 5.11785i) q^{94} -4.17180 q^{95} -0.107694 q^{97} +(-1.10240 + 0.885841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) $ 24 * q + 6 * q^4 + 24 * q^7	$ 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) $ 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−1.10240	+	0.885841i	−0.779514	+	0.626384i
$2$	−1.10240	+	0.885841i	−0.779514	+	0.626384i
$3$		0			0
$3$		0			0
$4$	0.430570	−	1.95310i	0.215285	−	0.976551i
$5$			2.99001i			1.33717i	0.743634	+	0.668587i	$0.233100\pi$
$5$			2.99001i			1.33717i	−0.743634	+	0.668587i	$0.766900\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.25548	+	2.53452i	0.443879	+	0.896087i
$9$		0			0
$10$	−2.64867	−	3.29619i	−0.837585	−	1.04235i
$11$			2.13956i			0.645101i	0.946552	+	0.322550i	$0.104540\pi$
$11$			2.13956i			0.645101i	−0.946552	+	0.322550i	$0.895460\pi$
$12$		0			0
$13$		−	0.665739i		−	0.184643i	−0.995729	−	0.0923214i	$-0.970571\pi$
$13$		−	0.665739i		−	0.184643i	0.995729	−	0.0923214i	$-0.0294287\pi$
$14$	−1.10240	+	0.885841i	−0.294629	+	0.236751i
$15$		0			0
$16$	−3.62922	−	1.68190i	−0.907305	−	0.420474i
$17$	−7.04931			−1.70971			−0.854855	−	0.518867i	$-0.826354\pi$
$17$	−7.04931			−1.70971			−0.854855	+	0.518867i	$0.826354\pi$
$18$		0			0
$19$			1.39525i			0.320092i	0.987110	+	0.160046i	$0.0511642\pi$
$19$			1.39525i			0.320092i	−0.987110	+	0.160046i	$0.948836\pi$
$20$	5.83980	+	1.28741i	1.30582	+	0.287873i
$21$		0			0
$22$	−1.89531	−	2.35865i	−0.404081	−	0.502865i
$23$	−0.184371			−0.0384439			−0.0192220	−	0.999815i	$-0.506119\pi$
$23$	−0.184371			−0.0384439			−0.0192220	+	0.999815i	$0.506119\pi$
$24$		0			0
$25$	−3.94016			−0.788032
$26$	0.589739	+	0.733911i	0.115657	+	0.143932i
$27$		0			0
$28$	0.430570	−	1.95310i	0.0813701	−	0.369102i
$29$			1.27564i			0.236880i	0.992961	+	0.118440i	$0.0377893\pi$
$29$			1.27564i			0.236880i	−0.992961	+	0.118440i	$0.962211\pi$
$30$		0			0
$31$	−7.62308			−1.36915			−0.684573	−	0.728944i	$-0.740011\pi$
$31$	−7.62308			−1.36915			−0.684573	+	0.728944i	$0.740011\pi$
$32$	5.49074	−	1.36079i	0.970635	−	0.240556i
$33$		0			0
$34$	7.77116	−	6.24457i	1.33274	−	1.07094i
$35$			2.99001i			0.505404i
$36$		0			0
$37$			6.69127i			1.10004i	0.835152	+	0.550019i	$0.185379\pi$
$37$			6.69127i			1.10004i	−0.835152	+	0.550019i	$0.814621\pi$
$38$	−1.23597	−	1.53812i	−0.200500	−	0.249516i
$39$		0			0
$40$	−7.57823	+	3.75389i	−1.19822	+	0.593543i
$41$	0.274106			0.0428081			0.0214041	−	0.999771i	$-0.493186\pi$
$41$	0.274106			0.0428081			0.0214041	+	0.999771i	$0.493186\pi$
$42$		0			0
$43$		−	2.63971i		−	0.402553i	−0.979535	−	0.201276i	$-0.935491\pi$
$43$		−	2.63971i		−	0.402553i	0.979535	−	0.201276i	$-0.0645089\pi$
$44$	4.17877	+	0.921229i	0.629974	+	0.138881i
$45$		0			0
$46$	0.203250	−	0.163323i	0.0299676	−	0.0240807i
$47$	5.77739			0.842719			0.421359	−	0.906894i	$-0.361553\pi$
$47$	5.77739			0.842719			0.421359	+	0.906894i	$0.361553\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	4.34363	−	3.49036i	0.614283	−	0.493611i
$51$		0			0
$52$	−1.30026	−	0.286647i	−0.180313	−	0.0397508i
$53$		−	7.48353i		−	1.02794i	−0.857808	−	0.513971i	$-0.828174\pi$
$53$		−	7.48353i		−	1.02794i	0.857808	−	0.513971i	$-0.171826\pi$
$54$		0			0
$55$	−6.39730			−0.862611
$56$	1.25548	+	2.53452i	0.167770	+	0.338689i
$57$		0			0
$58$	−1.13001	−	1.40626i	−0.148378	−	0.184651i
$59$			9.03787i			1.17663i	0.808632	+	0.588315i	$0.200208\pi$
$59$			9.03787i			1.17663i	−0.808632	+	0.588315i	$0.799792\pi$
$60$		0			0
$61$		−	9.80298i		−	1.25514i	−0.778559	−	0.627571i	$-0.784049\pi$
$61$		−	9.80298i		−	1.25514i	0.778559	−	0.627571i	$-0.215951\pi$
$62$	8.40369	−	6.75284i	1.06727	−	0.857612i
$63$		0			0
$64$	−4.84755	+	6.36406i	−0.605943	+	0.795508i
$65$	1.99057			0.246900
$66$		0			0
$67$			10.8191i			1.32177i	0.750488	+	0.660884i	$0.229819\pi$
$67$			10.8191i			1.32177i	−0.750488	+	0.660884i	$0.770181\pi$
$68$	−3.03522	+	13.7680i	−0.368075	+	1.66962i
$69$		0			0
$70$	−2.64867	−	3.29619i	−0.316577	−	0.393970i
$71$	−7.93573			−0.941798			−0.470899	−	0.882187i	$-0.656070\pi$
$71$	−7.93573			−0.941798			−0.470899	+	0.882187i	$0.656070\pi$
$72$		0			0
$73$	−2.80408			−0.328193			−0.164097	−	0.986444i	$-0.552471\pi$
$73$	−2.80408			−0.328193			−0.164097	+	0.986444i	$0.552471\pi$
$74$	−5.92740	−	7.37645i	−0.689047	−	0.857495i
$75$		0			0
$76$	2.72506	+	0.600752i	0.312586	+	0.0689110i
$77$			2.13956i			0.243825i
$78$		0			0
$79$	7.98350			0.898214			0.449107	−	0.893478i	$-0.351742\pi$
$79$	7.98350			0.898214			0.449107	+	0.893478i	$0.351742\pi$
$80$	5.02888	−	10.8514i	0.562246	−	1.21322i
$81$		0			0
$82$	−0.302174	+	0.242814i	−0.0333695	+	0.0268143i
$83$		−	6.76125i		−	0.742143i	−0.928604	−	0.371072i	$-0.878990\pi$
$83$		−	6.76125i		−	0.742143i	0.928604	−	0.371072i	$-0.121010\pi$
$84$		0			0
$85$		−	21.0775i		−	2.28618i
$86$	2.33837	+	2.91002i	0.252153	+	0.313795i
$87$		0			0
$88$	−5.42274	+	2.68617i	−0.578066	+	0.286346i
$89$	−16.7549			−1.77602			−0.888010	−	0.459825i	$-0.847912\pi$
$89$	−16.7549			−1.77602			−0.888010	+	0.459825i	$0.847912\pi$
$90$		0			0
$91$		−	0.665739i		−	0.0697884i
$92$	−0.0793844	+	0.360095i	−0.00827640	+	0.0375425i
$93$		0			0
$94$	−6.36899	+	5.11785i	−0.656911	+	0.527866i
$95$	−4.17180			−0.428018
$96$		0			0
$97$	−0.107694			−0.0109346			−0.00546732	−	0.999985i	$-0.501740\pi$
$97$	−0.107694			−0.0109346			−0.00546732	+	0.999985i	$0.501740\pi$
$98$	−1.10240	+	0.885841i	−0.111359	+	0.0894835i
$99$		0			0
$100$	−1.69652	+	7.69554i	−0.169652	+	0.769554i
$101$		−	14.8524i		−	1.47787i	−0.673775	−	0.738937i	$-0.735328\pi$
$101$		−	14.8524i		−	1.47787i	0.673775	−	0.738937i	$-0.264672\pi$
$102$		0			0
$103$	−16.1461			−1.59092			−0.795459	−	0.606007i	$-0.792770\pi$
$103$	−16.1461			−1.59092			−0.795459	+	0.606007i	$0.792770\pi$
$104$	1.68733	−	0.835821i	0.165456	−	0.0819590i
$105$		0			0
$106$	6.62922	+	8.24984i	0.643887	+	0.801295i
$107$			15.6131i			1.50937i	0.656084	+	0.754687i	$0.272211\pi$
$107$			15.6131i			1.50937i	−0.656084	+	0.754687i	$0.727789\pi$
$108$		0			0
$109$			4.15829i			0.398292i	0.979970	+	0.199146i	$0.0638167\pi$
$109$			4.15829i			0.398292i	−0.979970	+	0.199146i	$0.936183\pi$
$110$	7.05238	−	5.66699i	0.672418	−	0.540326i
$111$		0			0
$112$	−3.62922	−	1.68190i	−0.342929	−	0.158924i
$113$	−18.4682			−1.73734			−0.868672	−	0.495388i	$-0.835026\pi$
$113$	−18.4682			−1.73734			−0.868672	+	0.495388i	$0.835026\pi$
$114$		0			0
$115$		−	0.551270i		−	0.0514062i
$116$	2.49145	+	0.549250i	0.231325	+	0.0509966i
$117$		0			0
$118$	−8.00612	−	9.96334i	−0.737023	−	0.917200i
$119$	−7.04931			−0.646209
$120$		0			0
$121$	6.42230			0.583845
$122$	8.68388	+	10.8068i	0.786202	+	0.978402i
$123$		0			0
$124$	−3.28227	+	14.8887i	−0.294757	+	1.33704i
$125$			3.16893i			0.283437i
$126$		0			0
$127$	−4.37444			−0.388169			−0.194084	−	0.980985i	$-0.562174\pi$
$127$	−4.37444			−0.388169			−0.194084	+	0.980985i	$0.562174\pi$
$128$	−0.293616	−	11.3099i	−0.0259523	−	0.999663i
$129$		0			0
$130$	−2.19440	+	1.76333i	−0.192462	+	0.154654i
$131$			5.76264i			0.503484i	0.967794	+	0.251742i	$0.0810035\pi$
$131$			5.76264i			0.503484i	−0.967794	+	0.251742i	$0.918997\pi$
$132$		0			0
$133$			1.39525i			0.120983i
$134$	−9.58404	−	11.9270i	−0.827935	−	1.03034i
$135$		0			0
$136$	−8.85026	−	17.8666i	−0.758904	−	1.53205i
$137$	10.5191			0.898704			0.449352	−	0.893355i	$-0.351655\pi$
$137$	10.5191			0.898704			0.449352	+	0.893355i	$0.351655\pi$
$138$		0			0
$139$		−	7.27000i		−	0.616633i	−0.951284	−	0.308316i	$-0.900234\pi$
$139$		−	7.27000i		−	0.616633i	0.951284	−	0.308316i	$-0.0997656\pi$
$140$	5.83980	+	1.28741i	0.493553	+	0.108806i
$141$		0			0
$142$	8.74835	−	7.02980i	0.734145	−	0.589928i
$143$	1.42439			0.119113
$144$		0			0
$145$	−3.81416			−0.316749
$146$	3.09122	−	2.48397i	0.255831	−	0.205575i
$147$		0			0
$148$	13.0687	+	2.88106i	1.07424	+	0.236822i
$149$			3.06625i			0.251197i	0.992081	+	0.125599i	$0.0400851\pi$
$149$			3.06625i			0.251197i	−0.992081	+	0.125599i	$0.959915\pi$
$150$		0			0
$151$	−15.8992			−1.29386			−0.646930	−	0.762549i	$-0.723947\pi$
$151$	−15.8992			−1.29386			−0.646930	+	0.762549i	$0.723947\pi$
$152$	−3.53628	+	1.75170i	−0.286830	+	0.142082i
$153$		0			0
$154$	−1.89531	−	2.35865i	−0.152728	−	0.190065i
$155$		−	22.7931i		−	1.83079i
$156$		0			0
$157$		−	18.3211i		−	1.46219i	−0.682278	−	0.731093i	$-0.739011\pi$
$157$		−	18.3211i		−	1.46219i	0.682278	−	0.731093i	$-0.260989\pi$
$158$	−8.80101	+	7.07211i	−0.700171	+	0.562627i
$159$		0			0
$160$	4.06878	+	16.4174i	0.321665	+	1.29791i
$161$	−0.184371			−0.0145304
$162$		0			0
$163$			22.0479i			1.72692i	0.504415	+	0.863462i	$0.331708\pi$
$163$			22.0479i			1.72692i	−0.504415	+	0.863462i	$0.668292\pi$
$164$	0.118022	−	0.535357i	0.00921595	−	0.0418043i
$165$		0			0
$166$	5.98939	+	7.45360i	0.464867	+	0.578511i
$167$	−10.2650			−0.794332			−0.397166	−	0.917747i	$-0.630006\pi$
$167$	−10.2650			−0.794332			−0.397166	+	0.917747i	$0.630006\pi$
$168$		0			0
$169$	12.5568			0.965907
$170$	18.6713	+	23.2358i	1.43203	+	1.78211i
$171$		0			0
$172$	−5.15563	−	1.13658i	−0.393113	−	0.0866636i
$173$			15.5234i			1.18022i	0.807322	+	0.590111i	$0.200916\pi$
$173$			15.5234i			1.18022i	−0.807322	+	0.590111i	$0.799084\pi$
$174$		0			0
$175$	−3.94016			−0.297848
$176$	3.59851	−	7.76492i	0.271248	−	0.585303i
$177$		0			0
$178$	18.4706	−	14.8422i	1.38443	−	1.11247i
$179$		−	17.2028i		−	1.28580i	−0.765952	−	0.642898i	$-0.777732\pi$
$179$		−	17.2028i		−	1.28580i	0.765952	−	0.642898i	$-0.222268\pi$
$180$		0			0
$181$		−	10.5145i		−	0.781538i	−0.920489	−	0.390769i	$-0.872209\pi$
$181$		−	10.5145i		−	0.781538i	0.920489	−	0.390769i	$-0.127791\pi$
$182$	0.589739	+	0.733911i	0.0437144	+	0.0544011i
$183$		0			0
$184$	−0.231473	−	0.467290i	−0.0170644	−	0.0344491i
$185$	−20.0070			−1.47094
$186$		0			0
$187$		−	15.0824i		−	1.10293i
$188$	2.48757	−	11.2838i	0.181425	−	0.822958i
$189$		0			0
$190$	4.59900	−	3.69556i	0.333646	−	0.268104i
$191$	−14.3893			−1.04117			−0.520587	−	0.853808i	$-0.674287\pi$
$191$	−14.3893			−1.04117			−0.520587	+	0.853808i	$0.674287\pi$
$192$		0			0
$193$	11.3579			0.817562			0.408781	−	0.912632i	$-0.365954\pi$
$193$	11.3579			0.817562			0.408781	+	0.912632i	$0.365954\pi$
$194$	0.118721	−	0.0953995i	0.00852370	−	0.00684928i
$195$		0			0
$196$	0.430570	−	1.95310i	0.0307550	−	0.139507i
$197$			6.44465i			0.459163i	0.973289	+	0.229581i	$0.0737357\pi$
$197$			6.44465i			0.459163i	−0.973289	+	0.229581i	$0.926264\pi$
$198$		0			0
$199$	−6.48055			−0.459394			−0.229697	−	0.973262i	$-0.573774\pi$
$199$	−6.48055			−0.459394			−0.229697	+	0.973262i	$0.573774\pi$
$200$	−4.94679	−	9.98641i	−0.349791	−	0.706146i
$201$		0			0
$202$	13.1569	+	16.3733i	0.925717	+	1.15202i
$203$			1.27564i			0.0895321i
$204$		0			0
$205$			0.819579i			0.0572419i
$206$	17.7994	−	14.3028i	1.24014	−	0.996527i
$207$		0			0
$208$	−1.11970	+	2.41611i	−0.0776375	+	0.167527i
$209$	−2.98521			−0.206491
$210$		0			0
$211$			10.3150i			0.710112i	0.934845	+	0.355056i	$0.115538\pi$
$211$			10.3150i			0.710112i	−0.934845	+	0.355056i	$0.884462\pi$
$212$	−14.6161	−	3.22218i	−1.00384	−	0.221300i
$213$		0			0
$214$	−13.8307	−	17.2119i	−0.945449	−	1.17658i
$215$	7.89277			0.538283
$216$		0			0
$217$	−7.62308			−0.517489
$218$	−3.68358	−	4.58409i	−0.249484	−	0.310474i
$219$		0			0
$220$	−2.75448	+	12.4946i	−0.185707	+	0.842384i
$221$			4.69300i			0.315686i
$222$		0			0
$223$	23.8589			1.59771			0.798854	−	0.601526i	$-0.205440\pi$
$223$	23.8589			1.59771			0.798854	+	0.601526i	$0.205440\pi$
$224$	5.49074	−	1.36079i	0.366866	−	0.0909217i
$225$		0			0
$226$	20.3594	−	16.3599i	1.35428	−	1.08825i
$227$		−	1.88092i		−	0.124841i	−0.998050	−	0.0624206i	$-0.980118\pi$
$227$		−	1.88092i		−	0.124841i	0.998050	−	0.0624206i	$-0.0198820\pi$
$228$		0			0
$229$		−	18.8128i		−	1.24319i	−0.783340	−	0.621594i	$-0.786485\pi$
$229$		−	18.8128i		−	1.24319i	0.783340	−	0.621594i	$-0.213515\pi$
$230$	0.488338	+	0.607720i	0.0322000	+	0.0400719i
$231$		0			0
$232$	−3.23312	+	1.60153i	−0.212265	+	0.105146i
$233$	−9.18759			−0.601899			−0.300949	−	0.953640i	$-0.597304\pi$
$233$	−9.18759			−0.601899			−0.300949	+	0.953640i	$0.597304\pi$
$234$		0			0
$235$			17.2745i			1.12686i
$236$	17.6519	+	3.89144i	1.14904	+	0.253311i
$237$		0			0
$238$	7.77116	−	6.24457i	0.503729	−	0.404776i
$239$	−29.1200			−1.88362			−0.941808	−	0.336152i	$-0.890874\pi$
$239$	−29.1200			−1.88362			−0.941808	+	0.336152i	$0.890874\pi$
$240$		0			0
$241$	25.4640			1.64028			0.820142	−	0.572160i	$-0.193894\pi$
$241$	25.4640			1.64028			0.820142	+	0.572160i	$0.193894\pi$
$242$	−7.07994	+	5.68914i	−0.455116	+	0.365712i
$243$		0			0
$244$	−19.1462	−	4.22087i	−1.22571	−	0.270213i
$245$			2.99001i			0.191025i
$246$		0			0
$247$	0.928871			0.0591027
$248$	−9.57062	−	19.3208i	−0.607735	−	1.22687i
$249$		0			0
$250$	−2.80717	−	3.49342i	−0.177541	−	0.220943i
$251$			2.72427i			0.171955i	0.996297	+	0.0859773i	$0.0274012\pi$
$251$			2.72427i			0.171955i	−0.996297	+	0.0859773i	$0.972599\pi$
$252$		0			0
$253$		−	0.394471i		−	0.0248002i
$254$	4.82238	−	3.87506i	0.302583	−	0.243143i
$255$		0			0
$256$	10.3425	+	12.2079i	0.646404	+	0.762996i
$257$	17.6181			1.09899			0.549494	−	0.835498i	$-0.314821\pi$
$257$	17.6181			1.09899			0.549494	+	0.835498i	$0.314821\pi$
$258$		0			0
$259$			6.69127i			0.415775i
$260$	0.857079	−	3.88778i	0.0531538	−	0.241110i
$261$		0			0
$262$	−5.10479	−	6.35273i	−0.315375	−	0.392473i
$263$	−5.42576			−0.334567			−0.167283	−	0.985909i	$-0.553499\pi$
$263$	−5.42576			−0.334567			−0.167283	+	0.985909i	$0.553499\pi$
$264$		0			0
$265$	22.3758			1.37454
$266$	−1.23597	−	1.53812i	−0.0757821	−	0.0943082i
$267$		0			0
$268$	21.1309	+	4.65840i	1.29077	+	0.284557i
$269$		−	17.6635i		−	1.07696i	−0.842637	−	0.538482i	$-0.818998\pi$
$269$		−	17.6635i		−	1.07696i	0.842637	−	0.538482i	$-0.181002\pi$
$270$		0			0
$271$	11.5223			0.699929			0.349965	−	0.936763i	$-0.386194\pi$
$271$	11.5223			0.699929			0.349965	+	0.936763i	$0.386194\pi$
$272$	25.5835	+	11.8562i	1.55123	+	0.718888i
$273$		0			0
$274$	−11.5962	+	9.31822i	−0.700553	+	0.562935i
$275$		−	8.43020i		−	0.508360i
$276$		0			0
$277$			7.84872i			0.471584i	0.971804	+	0.235792i	$0.0757684\pi$
$277$			7.84872i			0.471584i	−0.971804	+	0.235792i	$0.924232\pi$
$278$	6.44006	+	8.01444i	0.386249	+	0.480674i
$279$		0			0
$280$	−7.57823	+	3.75389i	−0.452886	+	0.224338i
$281$	31.1308			1.85711			0.928555	−	0.371195i	$-0.121052\pi$
$281$	31.1308			1.85711			0.928555	+	0.371195i	$0.121052\pi$
$282$		0			0
$283$			24.7863i			1.47339i	0.676224	+	0.736696i	$0.263615\pi$
$283$			24.7863i			1.47339i	−0.676224	+	0.736696i	$0.736385\pi$
$284$	−3.41689	+	15.4993i	−0.202755	+	0.919714i
$285$		0			0
$286$	−1.57024	+	1.26178i	−0.0928505	+	0.0746107i
$287$	0.274106			0.0161800
$288$		0			0
$289$	32.6928			1.92311
$290$	4.20473	−	3.37874i	0.246910	−	0.198407i
$291$		0			0
$292$	−1.20735	+	5.47666i	−0.0706551	+	0.320497i
$293$			28.9898i			1.69360i	0.531909	+	0.846802i	$0.321475\pi$
$293$			28.9898i			1.69360i	−0.531909	+	0.846802i	$0.678525\pi$
$294$		0			0
$295$	−27.0233			−1.57336
$296$	−16.9591	+	8.40074i	−0.985729	+	0.488283i
$297$		0			0
$298$	−2.71621	−	3.38023i	−0.157346	−	0.195812i
$299$			0.122743i			0.00709839i
$300$		0			0
$301$		−	2.63971i		−	0.152151i
$302$	17.5273	−	14.0842i	1.00858	−	0.810454i
$303$		0			0
$304$	2.34666	−	5.06366i	0.134590	−	0.290421i
$305$	29.3110			1.67834
$306$		0			0
$307$			18.8831i			1.07772i	0.842397	+	0.538858i	$0.181144\pi$
$307$			18.8831i			1.07772i	−0.842397	+	0.538858i	$0.818856\pi$
$308$	4.17877	+	0.921229i	0.238108	+	0.0524919i
$309$		0			0
$310$	20.1911	+	25.1271i	1.14678	+	1.42712i
$311$	−0.147540			−0.00836624			−0.00418312	−	0.999991i	$-0.501332\pi$
$311$	−0.147540			−0.00836624			−0.00418312	+	0.999991i	$0.501332\pi$
$312$		0			0
$313$	−23.3154			−1.31786			−0.658932	−	0.752202i	$-0.728992\pi$
$313$	−23.3154			−1.31786			−0.658932	+	0.752202i	$0.728992\pi$
$314$	16.2296	+	20.1972i	0.915890	+	1.13979i
$315$		0			0
$316$	3.43746	−	15.5926i	0.193372	−	0.877152i
$317$		−	1.43318i		−	0.0804954i	−0.999190	−	0.0402477i	$-0.987185\pi$
$317$		−	1.43318i		−	0.0804954i	0.999190	−	0.0402477i	$-0.0128147\pi$
$318$		0			0
$319$	−2.72929			−0.152811
$320$	−19.0286	−	14.4942i	−1.06373	−	0.810251i
$321$		0			0
$322$	0.203250	−	0.163323i	0.0113267	−	0.00910164i
$323$		−	9.83554i		−	0.547264i
$324$		0			0
$325$			2.62312i			0.145505i
$326$	−19.5309	−	24.3056i	−1.08172	−	1.34616i
$327$		0			0
$328$	0.344134	+	0.694726i	0.0190016	+	0.0383598i
$329$	5.77739			0.318518
$330$		0			0
$331$			23.3196i			1.28176i	0.767640	+	0.640882i	$0.221431\pi$
$331$			23.3196i			1.28176i	−0.767640	+	0.640882i	$0.778569\pi$
$332$	−13.2054	−	2.91119i	−0.724741	−	0.159772i
$333$		0			0
$334$	11.3162	−	9.09319i	0.619193	−	0.497557i
$335$	−32.3493			−1.76743
$336$		0			0
$337$	0.484629			0.0263994			0.0131997	−	0.999913i	$-0.495798\pi$
$337$	0.484629			0.0263994			0.0131997	+	0.999913i	$0.495798\pi$
$338$	−13.8426	+	11.1233i	−0.752938	+	0.605029i
$339$		0			0
$340$	−41.1666	−	9.07535i	−2.23257	−	0.492180i
$341$		−	16.3100i		−	0.883237i
$342$		0			0
$343$	1.00000			0.0539949
$344$	6.69040	−	3.31410i	0.360722	−	0.178685i
$345$		0			0
$346$	−13.7513	−	17.1130i	−0.739272	−	0.919999i
$347$			10.0395i			0.538947i	0.963008	+	0.269473i	$0.0868496\pi$
$347$			10.0395i			0.538947i	−0.963008	+	0.269473i	$0.913150\pi$
$348$		0			0
$349$			9.55791i			0.511623i	0.966727	+	0.255812i	$0.0823427\pi$
$349$			9.55791i			0.511623i	−0.966727	+	0.255812i	$0.917657\pi$
$350$	4.34363	−	3.49036i	0.232177	−	0.186568i
$351$		0			0
$352$	2.91149	+	11.7478i	0.155183	+	0.626157i
$353$	−28.2931			−1.50589			−0.752945	−	0.658083i	$-0.771368\pi$
$353$	−28.2931			−1.50589			−0.752945	+	0.658083i	$0.771368\pi$
$354$		0			0
$355$		−	23.7279i		−	1.25935i
$356$	−7.21417	+	32.7241i	−0.382350	+	1.73437i
$357$		0			0
$358$	15.2389	+	18.9643i	0.805402	+	1.00230i
$359$	25.8316			1.36334			0.681671	−	0.731659i	$-0.261254\pi$
$359$	25.8316			1.36334			0.681671	+	0.731659i	$0.261254\pi$
$360$		0			0
$361$	17.0533			0.897541
$362$	9.31419	+	11.5912i	0.489543	+	0.609220i
$363$		0			0
$364$	−1.30026	−	0.286647i	−0.0681520	−	0.0150244i
$365$		−	8.38424i		−	0.438851i
$366$		0			0
$367$	−1.78123			−0.0929793			−0.0464896	−	0.998919i	$-0.514803\pi$
$367$	−1.78123			−0.0929793			−0.0464896	+	0.998919i	$0.514803\pi$
$368$	0.669121	+	0.310092i	0.0348803	+	0.0161647i
$369$		0			0
$370$	22.0557	−	17.7230i	1.14662	−	0.921375i
$371$		−	7.48353i		−	0.388525i
$372$		0			0
$373$			22.1074i			1.14468i	0.820017	+	0.572340i	$0.193964\pi$
$373$			22.1074i			1.14468i	−0.820017	+	0.572340i	$0.806036\pi$
$374$	13.3606	+	16.6268i	0.690861	+	0.859753i
$375$		0			0
$376$	7.25339	+	14.6429i	0.374065	+	0.755149i
$377$	0.849241			0.0437381
$378$		0			0
$379$			35.4109i			1.81893i	0.415776	+	0.909467i	$0.363510\pi$
$379$			35.4109i			1.81893i	−0.415776	+	0.909467i	$0.636490\pi$
$380$	−1.79625	+	8.14796i	−0.0921459	+	0.417982i
$381$		0			0
$382$	15.8628	−	12.7467i	0.811611	−	0.652176i
$383$	24.1927			1.23619			0.618095	−	0.786104i	$-0.287905\pi$
$383$	24.1927			1.23619			0.618095	+	0.786104i	$0.287905\pi$
$384$		0			0
$385$	−6.39730			−0.326036
$386$	−12.5210	+	10.0613i	−0.637302	+	0.512108i
$387$		0			0
$388$	−0.0463697	+	0.210337i	−0.00235406	+	0.0106782i
$389$			13.0465i			0.661483i	0.943721	+	0.330741i	$0.107299\pi$
$389$			13.0465i			0.661483i	−0.943721	+	0.330741i	$0.892701\pi$
$390$		0			0
$391$	1.29969			0.0657279
$392$	1.25548	+	2.53452i	0.0634113	+	0.128012i
$393$		0			0
$394$	−5.70894	−	7.10458i	−0.287612	−	0.357924i
$395$			23.8707i			1.20107i
$396$		0			0
$397$			36.0707i			1.81034i	0.425053	+	0.905168i	$0.360255\pi$
$397$			36.0707i			1.81034i	−0.425053	+	0.905168i	$0.639745\pi$
$398$	7.14416	−	5.74074i	0.358104	−	0.287757i
$399$		0			0
$400$	14.2997	+	6.62694i	0.714986	+	0.331347i
$401$	15.5149			0.774778			0.387389	−	0.921916i	$-0.373377\pi$
$401$	15.5149			0.774778			0.387389	+	0.921916i	$0.373377\pi$
$402$		0			0
$403$			5.07499i			0.252803i
$404$	−29.0083	−	6.39502i	−1.44322	−	0.318164i
$405$		0			0
$406$	−1.13001	−	1.40626i	−0.0560815	−	0.0697915i
$407$	−14.3163			−0.709635
$408$		0			0
$409$	−28.6937			−1.41881			−0.709406	−	0.704800i	$-0.751037\pi$
$409$	−28.6937			−1.41881			−0.709406	+	0.704800i	$0.751037\pi$
$410$	−0.726017	−	0.903504i	−0.0358554	−	0.0446209i
$411$		0			0
$412$	−6.95201	+	31.5349i	−0.342501	+	1.55361i
$413$			9.03787i			0.444724i
$414$		0			0
$415$	20.2162			0.992374
$416$	−0.905932	−	3.65540i	−0.0444170	−	0.179221i
$417$		0			0
$418$	3.29090	−	2.64442i	0.160963	−	0.129343i
$419$			22.9355i			1.12047i	0.828333	+	0.560236i	$0.189290\pi$
$419$			22.9355i			1.12047i	−0.828333	+	0.560236i	$0.810710\pi$
$420$		0			0
$421$		−	13.1562i		−	0.641193i	−0.947216	−	0.320596i	$-0.896117\pi$
$421$		−	13.1562i		−	0.641193i	0.947216	−	0.320596i	$-0.103883\pi$
$422$	−9.13743	−	11.3712i	−0.444803	−	0.553543i
$423$		0			0
$424$	18.9671	−	9.39541i	0.921125	−	0.456281i
$425$	27.7754			1.34731
$426$		0			0
$427$		−	9.80298i		−	0.474399i
$428$	30.4940	+	6.72253i	1.47398	+	0.324946i
$429$		0			0
$430$	−8.70099	+	6.99174i	−0.419599	+	0.337172i
$431$	39.6373			1.90926			0.954631	−	0.297792i	$-0.0962502\pi$
$431$	39.6373			1.90926			0.954631	+	0.297792i	$0.0962502\pi$
$432$		0			0
$433$	11.5906			0.557010			0.278505	−	0.960435i	$-0.410161\pi$
$433$	11.5906			0.557010			0.278505	+	0.960435i	$0.410161\pi$
$434$	8.40369	−	6.75284i	0.403390	−	0.324147i
$435$		0			0
$436$	8.12156	+	1.79043i	0.388952	+	0.0857462i
$437$		−	0.257243i		−	0.0123056i
$438$		0			0
$439$	−9.88971			−0.472010			−0.236005	−	0.971752i	$-0.575838\pi$
$439$	−9.88971			−0.472010			−0.236005	+	0.971752i	$0.575838\pi$
$440$	−8.03167	−	16.2141i	−0.382895	−	0.772975i
$441$		0			0
$442$	−4.15726	−	5.17357i	−0.197741	−	0.246081i
$443$		−	2.14448i		−	0.101888i	−0.998702	−	0.0509438i	$-0.983777\pi$
$443$		−	2.14448i		−	0.101888i	0.998702	−	0.0509438i	$-0.0162229\pi$
$444$		0			0
$445$		−	50.0974i		−	2.37485i
$446$	−26.3020	+	21.1352i	−1.24544	+	1.00078i
$447$		0			0
$448$	−4.84755	+	6.36406i	−0.229025	+	0.300674i
$449$	−4.65352			−0.219613			−0.109807	−	0.993953i	$-0.535023\pi$
$449$	−4.65352			−0.219613			−0.109807	+	0.993953i	$0.535023\pi$
$450$		0			0
$451$			0.586465i			0.0276156i
$452$	−7.95186	+	36.0703i	−0.374024	+	1.69661i
$453$		0			0
$454$	1.66620	+	2.07353i	0.0781986	+	0.0973155i
$455$	1.99057			0.0933192
$456$		0			0
$457$	19.0517			0.891203			0.445601	−	0.895232i	$-0.352990\pi$
$457$	19.0517			0.891203			0.445601	+	0.895232i	$0.352990\pi$
$458$	16.6652	+	20.7393i	0.778713	+	0.969083i
$459$		0			0
$460$	−1.07669	−	0.237360i	−0.0502008	−	0.0110670i
$461$			26.0354i			1.21259i	0.795240	+	0.606294i	$0.207345\pi$
$461$			26.0354i			1.21259i	−0.795240	+	0.606294i	$0.792655\pi$
$462$		0			0
$463$	29.6096			1.37607			0.688036	−	0.725676i	$-0.258473\pi$
$463$	29.6096			1.37607			0.688036	+	0.725676i	$0.258473\pi$
$464$	2.14548	−	4.62956i	0.0996016	−	0.214922i
$465$		0			0
$466$	10.1284	−	8.13875i	0.469189	−	0.377020i
$467$			25.8983i			1.19843i	0.800588	+	0.599216i	$0.204521\pi$
$467$			25.8983i			1.19843i	−0.800588	+	0.599216i	$0.795479\pi$
$468$		0			0
$469$			10.8191i			0.499581i
$470$	−15.3024	−	19.0434i	−0.705848	−	0.878404i
$471$		0			0
$472$	−22.9066	+	11.3468i	−1.05436	+	0.522281i
$473$	5.64782			0.259687
$474$		0			0
$475$		−	5.49750i		−	0.252243i
$476$	−3.03522	+	13.7680i	−0.139119	+	0.631057i
$477$		0			0
$478$	32.1019	−	25.7957i	1.46830	−	1.17987i
$479$	19.2498			0.879544			0.439772	−	0.898109i	$-0.355059\pi$
$479$	19.2498			0.879544			0.439772	+	0.898109i	$0.355059\pi$
$480$		0			0
$481$	4.45464			0.203114
$482$	−28.0716	+	22.5571i	−1.27862	+	1.02745i
$483$		0			0
$484$	2.76525	−	12.5434i	0.125693	−	0.570155i
$485$		−	0.322005i		−	0.0146215i
$486$		0			0
$487$	2.32047			0.105150			0.0525752	−	0.998617i	$-0.483257\pi$
$487$	2.32047			0.105150			0.0525752	+	0.998617i	$0.483257\pi$
$488$	24.8458	−	12.3074i	1.12472	−	0.557131i
$489$		0			0
$490$	−2.64867	−	3.29619i	−0.119655	−	0.148907i
$491$		−	0.578109i		−	0.0260897i	−0.999915	−	0.0130449i	$-0.995848\pi$
$491$		−	0.578109i		−	0.0260897i	0.999915	−	0.0130449i	$-0.00415242\pi$
$492$		0			0
$493$		−	8.99235i		−	0.404995i
$494$	−1.02399	+	0.822833i	−0.0460714	+	0.0370210i
$495$		0			0
$496$	27.6658	+	12.8212i	1.24223	+	0.575690i
$497$	−7.93573			−0.355966
$498$		0			0
$499$		−	26.3969i		−	1.18169i	−0.806785	−	0.590845i	$-0.798795\pi$
$499$		−	26.3969i		−	1.18169i	0.806785	−	0.590845i	$-0.201205\pi$
$500$	6.18924	+	1.36444i	0.276791	+	0.0610198i
$501$		0			0
$502$	−2.41327	−	3.00324i	−0.107710	−	0.134041i
$503$	−8.40780			−0.374885			−0.187443	−	0.982276i	$-0.560020\pi$
$503$	−8.40780			−0.374885			−0.187443	+	0.982276i	$0.560020\pi$
$504$		0			0
$505$	44.4090			1.97617
$506$	0.349439	+	0.434865i	0.0155345	+	0.0193321i
$507$		0			0
$508$	−1.88350	+	8.54373i	−0.0835669	+	0.379067i
$509$		−	32.9679i		−	1.46128i	−0.682764	−	0.730639i	$-0.739222\pi$
$509$		−	32.9679i		−	1.46128i	0.682764	−	0.730639i	$-0.260778\pi$
$510$		0			0
$511$	−2.80408			−0.124045
$512$	−22.2158	−	4.29624i	−0.981809	−	0.189869i
$513$		0			0
$514$	−19.4222	+	15.6069i	−0.856676	+	0.688389i
$515$		−	48.2769i		−	2.12733i
$516$		0			0
$517$			12.3611i			0.543638i
$518$	−5.92740	−	7.37645i	−0.260435	−	0.324103i
$519$		0			0
$520$	2.49911	+	5.04513i	0.109593	+	0.221243i
$521$	−30.9299			−1.35506			−0.677531	−	0.735494i	$-0.736950\pi$
$521$	−30.9299			−1.35506			−0.677531	+	0.735494i	$0.736950\pi$
$522$		0			0
$523$		−	2.73852i		−	0.119747i	−0.998206	−	0.0598735i	$-0.980930\pi$
$523$		−	2.73852i		−	0.119747i	0.998206	−	0.0598735i	$-0.0190697\pi$
$524$	11.2550	+	2.48122i	0.491678	+	0.108393i
$525$		0			0
$526$	5.98136	−	4.80636i	0.260799	−	0.209567i
$527$	53.7375			2.34084
$528$		0			0
$529$	−22.9660			−0.998522
$530$	−24.6671	+	19.8214i	−1.07147	+	0.860988i
$531$		0			0
$532$	2.72506	+	0.600752i	0.118146	+	0.0260459i
$533$		−	0.182483i		−	0.00790421i
$534$		0			0
$535$	−46.6833			−2.01830
$536$	−27.4213	+	13.5832i	−1.18442	+	0.586705i
$537$		0			0
$538$	15.6471	+	19.4723i	0.674594	+	0.839509i
$539$			2.13956i			0.0921572i
$540$		0			0
$541$		−	32.3372i		−	1.39029i	−0.718872	−	0.695143i	$-0.755341\pi$
$541$		−	32.3372i		−	1.39029i	0.718872	−	0.695143i	$-0.244659\pi$
$542$	−12.7022	+	10.2069i	−0.545605	+	0.438425i
$543$		0			0
$544$	−38.7060	+	9.59265i	−1.65950	+	0.411281i
$545$	−12.4333			−0.532585
$546$		0			0
$547$			20.4045i			0.872434i	0.899842	+	0.436217i	$0.143682\pi$
$547$			20.4045i			0.872434i	−0.899842	+	0.436217i	$0.856318\pi$
$548$	4.52920	−	20.5448i	0.193478	−	0.877631i
$549$		0			0
$550$	7.46782	+	9.29345i	0.318429	+	0.396274i
$551$	−1.77983			−0.0758232
$552$		0			0
$553$	7.98350			0.339493
$554$	−6.95272	−	8.65243i	−0.295393	−	0.367606i
$555$		0			0
$556$	−14.1990	−	3.13024i	−0.602174	−	0.132752i
$557$			4.16560i			0.176502i	0.996098	+	0.0882510i	$0.0281278\pi$
$557$			4.16560i			0.176502i	−0.996098	+	0.0882510i	$0.971872\pi$
$558$		0			0
$559$	−1.75736			−0.0743285
$560$	5.02888	−	10.8514i	0.212509	−	0.458555i
$561$		0			0
$562$	−34.3186	+	27.5770i	−1.44764	+	1.16326i
$563$		−	4.37435i		−	0.184357i	−0.995743	−	0.0921784i	$-0.970617\pi$
$563$		−	4.37435i		−	0.184357i	0.995743	−	0.0921784i	$-0.0293830\pi$
$564$		0			0
$565$		−	55.2202i		−	2.32313i
$566$	−21.9567	−	27.3244i	−0.922910	−	1.14853i
$567$		0			0
$568$	−9.96315	−	20.1132i	−0.418044	−	0.843933i
$569$	−4.59520			−0.192641			−0.0963204	−	0.995350i	$-0.530707\pi$
$569$	−4.59520			−0.192641			−0.0963204	+	0.995350i	$0.530707\pi$
$570$		0			0
$571$		−	30.6111i		−	1.28103i	−0.767944	−	0.640517i	$-0.778720\pi$
$571$		−	30.6111i		−	1.28103i	0.767944	−	0.640517i	$-0.221280\pi$
$572$	0.613298	−	2.78197i	0.0256433	−	0.116320i
$573$		0			0
$574$	−0.302174	+	0.242814i	−0.0126125	+	0.0101349i
$575$	0.726450			0.0302951
$576$		0			0
$577$	−8.32558			−0.346598			−0.173299	−	0.984869i	$-0.555443\pi$
$577$	−8.32558			−0.346598			−0.173299	+	0.984869i	$0.555443\pi$
$578$	−36.0405	+	28.9606i	−1.49909	+	1.20460i
$579$		0			0
$580$	−1.64226	+	7.44945i	−0.0681913	+	0.309322i
$581$		−	6.76125i		−	0.280504i
$582$		0			0
$583$	16.0114			0.663126
$584$	−3.52047	−	7.10700i	−0.145678	−	0.294090i
$585$		0			0
$586$	−25.6804	−	31.9584i	−1.06085	−	1.32019i
$587$			24.4147i			1.00770i	0.863791	+	0.503851i	$0.168084\pi$
$587$			24.4147i			1.00770i	−0.863791	+	0.503851i	$0.831916\pi$
$588$		0			0
$589$		−	10.6361i		−	0.438252i
$590$	29.7905	−	23.9384i	1.22646	−	0.985527i
$591$		0			0
$592$	11.2540	−	24.2841i	0.462537	−	0.998069i
$593$	5.57185			0.228809			0.114404	−	0.993434i	$-0.463504\pi$
$593$	5.57185			0.228809			0.114404	+	0.993434i	$0.463504\pi$
$594$		0			0
$595$		−	21.0775i		−	0.864094i
$596$	5.98870	+	1.32024i	0.245307	+	0.0540790i
$597$		0			0
$598$	−0.108731	−	0.135312i	−0.00444632	−	0.00553330i
$599$	28.6835			1.17198			0.585988	−	0.810319i	$-0.300706\pi$
$599$	28.6835			1.17198			0.585988	+	0.810319i	$0.300706\pi$
$600$		0			0
$601$	−28.9086			−1.17921			−0.589603	−	0.807693i	$-0.700716\pi$
$601$	−28.9086			−1.17921			−0.589603	+	0.807693i	$0.700716\pi$
$602$	2.33837	+	2.91002i	0.0953048	+	0.118604i
$603$		0			0
$604$	−6.84573	+	31.0528i	−0.278549	+	1.26352i
$605$			19.2027i			0.780702i
$606$		0			0
$607$	−10.3353			−0.419498			−0.209749	−	0.977755i	$-0.567265\pi$
$607$	−10.3353			−0.419498			−0.209749	+	0.977755i	$0.567265\pi$
$608$	1.89864	+	7.66094i	0.0770001	+	0.310692i
$609$		0			0
$610$	−32.3124	+	25.9649i	−1.30829	+	1.05129i
$611$		−	3.84624i		−	0.155602i
$612$		0			0
$613$		−	2.77963i		−	0.112268i	−0.998423	−	0.0561341i	$-0.982123\pi$
$613$		−	2.77963i		−	0.112268i	0.998423	−	0.0561341i	$-0.0178774\pi$
$614$	−16.7274	−	20.8167i	−0.675064	−	0.840094i
$615$		0			0
$616$	−5.42274	+	2.68617i	−0.218488	+	0.108229i
$617$	−22.1145			−0.890296			−0.445148	−	0.895457i	$-0.646849\pi$
$617$	−22.1145			−0.890296			−0.445148	+	0.895457i	$0.646849\pi$
$618$		0			0
$619$			8.20284i			0.329700i	0.986319	+	0.164850i	$0.0527140\pi$
$619$			8.20284i			0.329700i	−0.986319	+	0.164850i	$0.947286\pi$
$620$	−44.5173	−	9.81403i	−1.78786	−	0.394141i
$621$		0			0
$622$	0.162648	−	0.130697i	0.00652160	−	0.00524048i
$623$	−16.7549			−0.671272
$624$		0			0
$625$	−29.1759			−1.16704
$626$	25.7029	−	20.6537i	1.02729	−	0.825490i
$627$		0			0
$628$	−35.7830	−	7.88853i	−1.42790	−	0.314787i
$629$		−	47.1688i		−	1.88074i
$630$		0			0
$631$	−28.2572			−1.12490			−0.562450	−	0.826831i	$-0.690141\pi$
$631$	−28.2572			−1.12490			−0.562450	+	0.826831i	$0.690141\pi$
$632$	10.0231	+	20.2343i	0.398698	+	0.804878i
$633$		0			0
$634$	1.26957	+	1.57994i	0.0504211	+	0.0627473i
$635$		−	13.0796i		−	0.519049i
$636$		0			0
$637$		−	0.665739i		−	0.0263776i
$638$	3.00877	−	2.41772i	0.119118	−	0.0957185i
$639$		0			0
$640$	33.8167	−	0.877916i	1.33672	−	0.0347027i
$641$	48.7144			1.92410			0.962051	−	0.272870i	$-0.0879730\pi$
$641$	48.7144			1.92410			0.962051	+	0.272870i	$0.0879730\pi$
$642$		0			0
$643$		−	23.8806i		−	0.941757i	−0.882198	−	0.470879i	$-0.843937\pi$
$643$		−	23.8806i		−	0.941757i	0.882198	−	0.470879i	$-0.156063\pi$
$644$	−0.0793844	+	0.360095i	−0.00312819	+	0.0141897i
$645$		0			0
$646$	8.71273	+	10.8427i	0.342798	+	0.426600i
$647$	33.9383			1.33425			0.667127	−	0.744944i	$-0.267524\pi$
$647$	33.9383			1.33425			0.667127	+	0.744944i	$0.267524\pi$
$648$		0			0
$649$	−19.3370			−0.759045
$650$	−2.32367	−	2.89173i	−0.0911418	−	0.113423i
$651$		0			0
$652$	43.0618	+	9.49316i	1.68643	+	0.371781i
$653$		−	35.4564i		−	1.38752i	−0.720208	−	0.693759i	$-0.755953\pi$
$653$		−	35.4564i		−	1.38752i	0.720208	−	0.693759i	$-0.244047\pi$
$654$		0			0
$655$	−17.2304			−0.673246
$656$	−0.994790	−	0.461017i	−0.0388400	−	0.0179997i
$657$		0			0
$658$	−6.36899	+	5.11785i	−0.248289	+	0.199515i
$659$		−	4.40093i		−	0.171436i	−0.996319	−	0.0857179i	$-0.972682\pi$
$659$		−	4.40093i		−	0.171436i	0.996319	−	0.0857179i	$-0.0273184\pi$
$660$		0			0
$661$		−	13.8183i		−	0.537470i	−0.963214	−	0.268735i	$-0.913394\pi$
$661$		−	13.8183i		−	0.537470i	0.963214	−	0.268735i	$-0.0866056\pi$
$662$	−20.6575	−	25.7076i	−0.802876	−	0.999153i
$663$		0			0
$664$	17.1365	−	8.48860i	0.665025	−	0.329422i
$665$	−4.17180			−0.161776
$666$		0			0
$667$		−	0.235190i		−	0.00910658i
$668$	−4.41982	+	20.0487i	−0.171008	+	0.775706i
$669$		0			0
$670$	35.6619	−	28.6564i	1.37774	−	1.10709i
$671$	20.9740			0.809693
$672$		0			0
$673$	28.7125			1.10679			0.553393	−	0.832921i	$-0.313333\pi$
$673$	28.7125			1.10679			0.553393	+	0.832921i	$0.313333\pi$
$674$	−0.534255	+	0.429304i	−0.0205787	+	0.0165362i
$675$		0			0
$676$	5.40658	−	24.5247i	0.207945	−	0.943258i
$677$		−	30.5789i		−	1.17524i	−0.809136	−	0.587621i	$-0.800064\pi$
$677$		−	30.5789i		−	1.17524i	0.809136	−	0.587621i	$-0.199936\pi$
$678$		0			0
$679$	−0.107694			−0.00413290
$680$	53.4213	−	26.4624i	2.04861	−	1.01479i
$681$		0			0
$682$	14.4481	+	17.9802i	0.553246	+	0.688496i
$683$			10.0994i			0.386443i	0.981155	+	0.193221i	$0.0618936\pi$
$683$			10.0994i			0.386443i	−0.981155	+	0.193221i	$0.938106\pi$
$684$		0			0
$685$			31.4521i			1.20172i
$686$	−1.10240	+	0.885841i	−0.0420898	+	0.0338216i
$687$		0			0
$688$	−4.43972	+	9.58010i	−0.169263	+	0.365238i
$689$	−4.98208			−0.189802
$690$		0			0
$691$		−	1.93187i		−	0.0734916i	−0.999325	−	0.0367458i	$-0.988301\pi$
$691$		−	1.93187i		−	0.0734916i	0.999325	−	0.0367458i	$-0.0116992\pi$
$692$	30.3188	+	6.68391i	1.15255	+	0.254084i
$693$		0			0
$694$	−8.89338	−	11.0675i	−0.337588	−	0.420117i
$695$	21.7374			0.824545
$696$		0			0
$697$	−1.93226			−0.0731895
$698$	−8.46679	−	10.5366i	−0.320473	−	0.398818i
$699$		0			0
$700$	−1.69652	+	7.69554i	−0.0641223	+	0.290864i
$701$		−	23.6511i		−	0.893288i	−0.894712	−	0.446644i	$-0.852619\pi$
$701$		−	23.6511i		−	0.893288i	0.894712	−	0.446644i	$-0.147381\pi$
$702$		0			0
$703$	−9.33598			−0.352113
$704$	−13.6163	−	10.3716i	−0.513183	−	0.390894i
$705$		0			0
$706$	31.1903	−	25.0632i	1.17386	−	0.943267i
$707$		−	14.8524i		−	0.558584i
$708$		0			0
$709$			20.8417i			0.782728i	0.920236	+	0.391364i	$0.127997\pi$
$709$			20.8417i			0.782728i	−0.920236	+	0.391364i	$0.872003\pi$
$710$	21.0192	+	26.1577i	0.788836	+	0.981680i
$711$		0			0
$712$	−21.0355	−	42.4656i	−0.788337	−	1.59147i
$713$	1.40547			0.0526354
$714$		0			0
$715$			4.25893i			0.159275i
$716$	−33.5988	−	7.40700i	−1.25565	−	0.276813i
$717$		0			0
$718$	−28.4768	+	22.8827i	−1.06274	+	0.853976i
$719$	−2.81902			−0.105132			−0.0525658	−	0.998617i	$-0.516740\pi$
$719$	−2.81902			−0.105132			−0.0525658	+	0.998617i	$0.516740\pi$
$720$		0			0
$721$	−16.1461			−0.601311
$722$	−18.7995	+	15.1065i	−0.699646	+	0.562206i
$723$		0			0
$724$	−20.5359	−	4.52724i	−0.763212	−	0.168253i
$725$		−	5.02621i		−	0.186669i
$726$		0			0
$727$	−14.6918			−0.544887			−0.272444	−	0.962172i	$-0.587832\pi$
$727$	−14.6918			−0.544887			−0.272444	+	0.962172i	$0.587832\pi$
$728$	1.68733	−	0.835821i	0.0625365	−	0.0309776i
$729$		0			0
$730$	7.42711	+	9.24278i	0.274890	+	0.342091i
$731$			18.6082i			0.688248i
$732$		0			0
$733$			45.7679i			1.69048i	0.534389	+	0.845239i	$0.320542\pi$
$733$			45.7679i			1.69048i	−0.534389	+	0.845239i	$0.679458\pi$
$734$	1.96362	−	1.57788i	0.0724787	−	0.0582408i
$735$		0			0
$736$	−1.01233	+	0.250890i	−0.0373150	+	0.00924792i
$737$	−23.1482			−0.852673
$738$		0			0
$739$		−	37.7771i		−	1.38965i	−0.719178	−	0.694826i	$-0.755481\pi$
$739$		−	37.7771i		−	1.38965i	0.719178	−	0.694826i	$-0.244519\pi$
$740$	−8.61440	+	39.0756i	−0.316672	+	1.43645i
$741$		0			0
$742$	6.62922	+	8.24984i	0.243366	+	0.302861i
$743$	6.38675			0.234307			0.117154	−	0.993114i	$-0.462623\pi$
$743$	6.38675			0.234307			0.117154	+	0.993114i	$0.462623\pi$
$744$		0			0
$745$	−9.16812			−0.335894
$746$	−19.5837	−	24.3712i	−0.717009	−	0.892294i
$747$		0			0
$748$	−29.4575	−	6.49403i	−1.07707	−	0.237445i
$749$			15.6131i			0.570490i
$750$		0			0
$751$	52.5372			1.91711			0.958554	−	0.284910i	$-0.0919639\pi$
$751$	52.5372			1.91711			0.958554	+	0.284910i	$0.0919639\pi$
$752$	−20.9674	−	9.71696i	−0.764603	−	0.354341i
$753$		0			0
$754$	−0.936203	+	0.752292i	−0.0340945	+	0.0273969i
$755$		−	47.5388i		−	1.73012i
$756$		0			0
$757$		−	3.80676i		−	0.138359i	−0.997604	−	0.0691794i	$-0.977962\pi$
$757$		−	3.80676i		−	0.138359i	0.997604	−	0.0691794i	$-0.0220381\pi$
$758$	−31.3684	−	39.0369i	−1.13935	−	1.41788i
$759$		0			0
$760$	−5.23761	−	10.5735i	−0.189988	−	0.383541i
$761$	25.9307			0.939986			0.469993	−	0.882670i	$-0.344256\pi$
$761$	25.9307			0.939986			0.469993	+	0.882670i	$0.344256\pi$
$762$		0			0
$763$			4.15829i			0.150540i
$764$	−6.19561	+	28.1038i	−0.224149	+	1.01676i
$765$		0			0
$766$	−26.6700	+	21.4309i	−0.963627	+	0.774330i
$767$	6.01686			0.217256
$768$		0			0
$769$	−42.2680			−1.52422			−0.762112	−	0.647445i	$-0.775838\pi$
$769$	−42.2680			−1.52422			−0.762112	+	0.647445i	$0.775838\pi$
$770$	7.05238	−	5.66699i	0.254150	−	0.204224i
$771$		0			0
$772$	4.89039	−	22.1832i	0.176009	−	0.798392i
$773$		−	13.4481i		−	0.483696i	−0.970314	−	0.241848i	$-0.922246\pi$
$773$		−	13.4481i		−	0.483696i	0.970314	−	0.241848i	$-0.0777536\pi$
$774$		0			0
$775$	30.0362			1.07893
$776$	−0.135207	−	0.272951i	−0.00485365	−	0.00979838i
$777$		0			0
$778$	−11.5571	−	14.3824i	−0.414343	−	0.515635i
$779$			0.382445i			0.0137025i
$780$		0			0
$781$		−	16.9790i		−	0.607555i
$782$	−1.43277	+	1.15132i	−0.0512359	+	0.0411710i
$783$		0			0
$784$	−3.62922	−	1.68190i	−0.129615	−	0.0600677i
$785$	54.7804			1.95520
$786$		0			0
$787$			1.40104i			0.0499418i	0.999688	+	0.0249709i	$0.00794932\pi$
$787$			1.40104i			0.0499418i	−0.999688	+	0.0249709i	$0.992051\pi$
$788$	12.5871	+	2.77487i	0.448396	+	0.0988508i
$789$		0			0
$790$	−21.1457	−	26.3151i	−0.752330	−	0.936249i
$791$	−18.4682			−0.656654
$792$		0			0
$793$	−6.52623			−0.231753
$794$	−31.9529	−	39.7643i	−1.13397	−	1.41118i
$795$		0			0
$796$	−2.79033	+	12.6572i	−0.0989007	+	0.448622i
$797$		−	19.3605i		−	0.685783i	−0.939375	−	0.342891i	$-0.888594\pi$
$797$		−	19.3605i		−	0.685783i	0.939375	−	0.342891i	$-0.111406\pi$
$798$		0			0
$799$	−40.7266			−1.44080
$800$	−21.6344	+	5.36174i	−0.764892	+	0.189566i
$801$		0			0
$802$	−17.1036	+	13.7438i	−0.603950	+	0.485309i
$803$		−	5.99950i		−	0.211718i
$804$		0			0
$805$		−	0.551270i		−	0.0194297i
$806$	−4.49563	−	5.59466i	−0.158352	−	0.197064i
$807$		0			0
$808$	37.6438	−	18.6469i	1.32430	−	0.655996i
$809$	14.4386			0.507633			0.253816	−	0.967252i	$-0.418314\pi$
$809$	14.4386			0.507633			0.253816	+	0.967252i	$0.418314\pi$
$810$		0			0
$811$			42.1307i			1.47941i	0.672932	+	0.739705i	$0.265035\pi$
$811$			42.1307i			1.47941i	−0.672932	+	0.739705i	$0.734965\pi$
$812$	2.49145	+	0.549250i	0.0874326	+	0.0192749i
$813$		0			0
$814$	15.7823	−	12.6820i	0.553171	−	0.444504i
$815$	−65.9234			−2.30920
$816$		0			0
$817$	3.68305			0.128854
$818$	31.6319	−	25.4181i	1.10598	−	0.888722i
$819$		0			0
$820$	1.60072	+	0.352886i	0.0558996	+	0.0123233i
$821$		−	7.21315i		−	0.251741i	−0.992047	−	0.125870i	$-0.959828\pi$
$821$		−	7.21315i		−	0.251741i	0.992047	−	0.125870i	$-0.0401723\pi$
$822$		0			0
$823$	−6.47104			−0.225566			−0.112783	−	0.993620i	$-0.535977\pi$
$823$	−6.47104			−0.225566			−0.112783	+	0.993620i	$0.535977\pi$
$824$	−20.2710	−	40.9225i	−0.706175	−	1.42560i
$825$		0			0
$826$	−8.00612	−	9.96334i	−0.278568	−	0.346669i
$827$			55.8363i			1.94162i	0.239850	+	0.970810i	$0.422902\pi$
$827$			55.8363i			1.94162i	−0.239850	+	0.970810i	$0.577098\pi$
$828$		0			0
$829$		−	14.1807i		−	0.492517i	−0.969204	−	0.246258i	$-0.920799\pi$
$829$		−	14.1807i		−	0.492517i	0.969204	−	0.246258i	$-0.0792011\pi$
$830$	−22.2863	+	17.9083i	−0.773570	+	0.621608i
$831$		0			0
$832$	4.23681	+	3.22720i	0.146885	+	0.111883i
$833$	−7.04931			−0.244244
$834$		0			0
$835$		−	30.6925i		−	1.06216i
$836$	−1.28534	+	5.83042i	−0.0444545	+	0.201649i
$837$		0			0
$838$	−20.3172	−	25.2841i	−0.701847	−	0.873425i
$839$	−31.4229			−1.08484			−0.542420	−	0.840108i	$-0.682492\pi$
$839$	−31.4229			−1.08484			−0.542420	+	0.840108i	$0.682492\pi$
$840$		0			0
$841$	27.3728			0.943888
$842$	11.6543	+	14.5034i	0.401633	+	0.499819i
$843$		0			0
$844$	20.1462	+	4.44132i	0.693461	+	0.152877i
$845$			37.5449i			1.29159i
$846$		0			0
$847$	6.42230			0.220673
$848$	−12.5865	+	27.1594i	−0.432222	+	0.932656i
$849$		0			0
$850$	−30.6196	+	24.6046i	−1.05024	+	0.843932i
$851$		−	1.23367i		−	0.0422898i
$852$		0			0
$853$			23.3929i			0.800957i	0.916306	+	0.400479i	$0.131156\pi$
$853$			23.3929i			0.800957i	−0.916306	+	0.400479i	$0.868844\pi$
$854$	8.68388	+	10.8068i	0.297156	+	0.369801i
$855$		0			0
$856$	−39.5716	+	19.6019i	−1.35253	+	0.669979i
$857$	24.0033			0.819936			0.409968	−	0.912100i	$-0.365540\pi$
$857$	24.0033			0.819936			0.409968	+	0.912100i	$0.365540\pi$
$858$		0			0
$859$			41.5626i			1.41810i	0.705160	+	0.709048i	$0.250875\pi$
$859$			41.5626i			1.41810i	−0.705160	+	0.709048i	$0.749125\pi$
$860$	3.39839	−	15.4154i	0.115884	−	0.525661i
$861$		0			0
$862$	−43.6961	+	35.1124i	−1.48830	+	1.19593i
$863$	−3.43323			−0.116868			−0.0584342	−	0.998291i	$-0.518611\pi$
$863$	−3.43323			−0.116868			−0.0584342	+	0.998291i	$0.518611\pi$
$864$		0			0
$865$	−46.4151			−1.57816
$866$	−12.7775	+	10.2675i	−0.434197	+	0.348902i
$867$		0			0
$868$	−3.28227	+	14.8887i	−0.111408	+	0.505354i
$869$			17.0812i			0.579438i
$870$		0			0
$871$	7.20273			0.244055
$872$	−10.5392	+	5.22064i	−0.356904	+	0.176793i
$873$		0			0
$874$	0.227876	+	0.283584i	0.00770802	+	0.00959238i
$875$			3.16893i			0.107129i
$876$		0			0
$877$			47.9141i			1.61794i	0.587847	+	0.808972i	$0.299976\pi$
$877$			47.9141i			1.61794i	−0.587847	+	0.808972i	$0.700024\pi$
$878$	10.9024	−	8.76072i	0.367939	−	0.295660i
$879$		0			0
$880$	23.2172	+	10.7596i	0.782651	+	0.362705i
$881$	−25.7071			−0.866095			−0.433047	−	0.901371i	$-0.642562\pi$
$881$	−25.7071			−0.866095			−0.433047	+	0.901371i	$0.642562\pi$
$882$		0			0
$883$			41.7112i			1.40369i	0.712328	+	0.701847i	$0.247641\pi$
$883$			41.7112i			1.40369i	−0.712328	+	0.701847i	$0.752359\pi$
$884$	9.16592	+	2.02067i	0.308283	+	0.0679624i
$885$		0			0
$886$	1.89967	+	2.36408i	0.0638208	+	0.0794228i
$887$	32.6475			1.09620			0.548099	−	0.836414i	$-0.315352\pi$
$887$	32.6475			1.09620			0.548099	+	0.836414i	$0.315352\pi$
$888$		0			0
$889$	−4.37444			−0.146714
$890$	44.3784	+	55.2274i	1.48757	+	1.85123i
$891$		0			0
$892$	10.2729	−	46.5988i	0.343962	−	1.56024i
$893$			8.06089i			0.269747i
$894$		0			0
$895$	51.4365			1.71933
$896$	−0.293616	−	11.3099i	−0.00980903	−	0.377837i
$897$		0			0
$898$	5.13004	−	4.12228i	0.171192	−	0.137562i
$899$		−	9.72428i		−	0.324323i
$900$		0			0
$901$			52.7537i			1.75748i
$902$	−0.519515	−	0.646519i	−0.0172980	−	0.0215267i
$903$		0			0
$904$	−23.1865	−	46.8080i	−0.771170	−	1.55681i
$905$	31.4385			1.04505
$906$		0			0
$907$			22.4610i			0.745804i	0.927871	+	0.372902i	$0.121637\pi$
$907$			22.4610i			0.745804i	−0.927871	+	0.372902i	$0.878363\pi$
$908$	−3.67363	−	0.809869i	−0.121914	−	0.0268764i
$909$		0			0
$910$	−2.19440	+	1.76333i	−0.0727437	+	0.0584537i
$911$	20.7360			0.687015			0.343507	−	0.939150i	$-0.388385\pi$
$911$	20.7360			0.687015			0.343507	+	0.939150i	$0.388385\pi$
$912$		0			0
$913$	14.4661			0.478757
$914$	−21.0026	+	16.8768i	−0.694705	+	0.558236i
$915$		0			0
$916$	−36.7434	−	8.10025i	−1.21404	−	0.267640i
$917$			5.76264i			0.190299i
$918$		0			0
$919$	−42.9827			−1.41787			−0.708935	−	0.705274i	$-0.750824\pi$
$919$	−42.9827			−1.41787			−0.708935	+	0.705274i	$0.750824\pi$
$920$	1.39720	−	0.692108i	0.0460644	−	0.0228181i
$921$		0			0
$922$	−23.0632	−	28.7014i	−0.759547	−	0.945230i
$923$			5.28313i			0.173896i
$924$		0			0
$925$		−	26.3647i		−	0.866865i
$926$	−32.6416	+	26.2294i	−1.07267	+	0.861951i
$927$		0			0
$928$	1.73587	+	7.00418i	0.0569829	+	0.229924i
$929$	−3.62200			−0.118834			−0.0594170	−	0.998233i	$-0.518924\pi$
$929$	−3.62200			−0.118834			−0.0594170	+	0.998233i	$0.518924\pi$
$930$		0			0
$931$			1.39525i			0.0457274i
$932$	−3.95590	+	17.9443i	−0.129580	+	0.587785i
$933$		0			0
$934$	−22.9418	−	28.5503i	−0.750679	−	0.934194i
$935$	45.0965			1.47481
$936$		0			0
$937$	21.8189			0.712793			0.356396	−	0.934335i	$-0.384005\pi$
$937$	21.8189			0.712793			0.356396	+	0.934335i	$0.384005\pi$
$938$	−9.58404	−	11.9270i	−0.312930	−	0.389431i
$939$		0			0
$940$	33.7388	+	7.43786i	1.10044	+	0.242596i
$941$			16.8639i			0.549747i	0.961480	+	0.274873i	$0.0886359\pi$
$941$			16.8639i			0.549747i	−0.961480	+	0.274873i	$0.911364\pi$
$942$		0			0
$943$	−0.0505370			−0.00164571
$944$	15.2007	−	32.8004i	0.494742	−	1.06756i
$945$		0			0
$946$	−6.22615	+	5.00307i	−0.202430	+	0.162664i
$947$		−	18.5568i		−	0.603016i	−0.953464	−	0.301508i	$-0.902510\pi$
$947$		−	18.5568i		−	0.603016i	0.953464	−	0.301508i	$-0.0974900\pi$
$948$		0			0
$949$			1.86679i			0.0605985i
$950$	4.86992	+	6.06044i	0.158001	+	0.196627i
$951$		0			0
$952$	−8.85026	−	17.8666i	−0.286839	−	0.579060i
$953$	−36.6643			−1.18767			−0.593836	−	0.804586i	$-0.702387\pi$
$953$	−36.6643			−1.18767			−0.593836	+	0.804586i	$0.702387\pi$
$954$		0			0
$955$		−	43.0242i		−	1.39223i
$956$	−12.5382	+	56.8743i	−0.405514	+	1.83945i
$957$		0			0
$958$	−21.2209	+	17.0522i	−0.685617	+	0.550933i
$959$	10.5191			0.339678
$960$		0			0
$961$	27.1114			0.874562
$962$	−4.91079	+	3.94610i	−0.158330	+	0.127228i
$963$		0			0
$964$	10.9641	−	49.7339i	0.353129	−	1.60182i
$965$			33.9604i			1.09322i
$966$		0			0
$967$	−11.1440			−0.358367			−0.179184	−	0.983816i	$-0.557346\pi$
$967$	−11.1440			−0.358367			−0.179184	+	0.983816i	$0.557346\pi$
$968$	8.06306	+	16.2774i	0.259156	+	0.523176i
$969$		0			0
$970$	0.285245	+	0.354978i	0.00915868	+	0.0113977i
$971$			3.98773i			0.127972i	0.997951	+	0.0639862i	$0.0203814\pi$
$971$			3.98773i			0.127972i	−0.997951	+	0.0639862i	$0.979619\pi$
$972$		0			0
$973$		−	7.27000i		−	0.233065i
$974$	−2.55808	+	2.05556i	−0.0819662	+	0.0658645i
$975$		0			0
$976$	−16.4876	+	35.5772i	−0.527755	+	1.13880i
$977$	32.7959			1.04923			0.524617	−	0.851338i	$-0.324209\pi$
$977$	32.7959			1.04923			0.524617	+	0.851338i	$0.324209\pi$
$978$		0			0
$979$		−	35.8481i		−	1.14571i
$980$	5.83980	+	1.28741i	0.186545	+	0.0411248i
$981$		0			0
$982$	0.512113	+	0.637308i	0.0163422	+	0.0203373i
$983$	−26.0499			−0.830864			−0.415432	−	0.909624i	$-0.636370\pi$
$983$	−26.0499			−0.830864			−0.415432	+	0.909624i	$0.636370\pi$
$984$		0			0
$985$	−19.2696			−0.613980
$986$	7.96580	+	9.91317i	0.253683	+	0.315700i
$987$		0			0
$988$	0.399944	−	1.81418i	0.0127239	−	0.0577168i
$989$			0.486686i			0.0154757i
$990$		0			0
$991$	−17.5053			−0.556075			−0.278037	−	0.960570i	$-0.589684\pi$
$991$	−17.5053			−0.556075			−0.278037	+	0.960570i	$0.589684\pi$
$992$	−41.8564	+	10.3734i	−1.32894	+	0.329357i
$993$		0			0
$994$	8.74835	−	7.02980i	0.277481	−	0.222972i
$995$		−	19.3769i		−	0.614289i
$996$		0			0
$997$		−	29.5008i		−	0.934300i	−0.884178	−	0.467150i	$-0.845281\pi$
$997$		−	29.5008i		−	0.934300i	0.884178	−	0.467150i	$-0.154719\pi$
$998$	23.3835	+	29.1000i	0.740192	+	0.921144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.g.757.8	yes	24
3.2	odd	2	inner	1512.2.c.g.757.17	yes	24
4.3	odd	2		6048.2.c.f.3025.19		24
8.3	odd	2		6048.2.c.f.3025.6		24
8.5	even	2	inner	1512.2.c.g.757.7	✓	24
12.11	even	2		6048.2.c.f.3025.5		24
24.5	odd	2	inner	1512.2.c.g.757.18	yes	24
24.11	even	2		6048.2.c.f.3025.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.g.757.7	✓	24	8.5	even	2	inner
1512.2.c.g.757.8	yes	24	1.1	even	1	trivial
1512.2.c.g.757.17	yes	24	3.2	odd	2	inner
1512.2.c.g.757.18	yes	24	24.5	odd	2	inner
6048.2.c.f.3025.5		24	12.11	even	2
6048.2.c.f.3025.6		24	8.3	odd	2
6048.2.c.f.3025.19		24	4.3	odd	2
6048.2.c.f.3025.20		24	24.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10240 + 0.885841i) q^{2} +(0.430570 - 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(1.25548 + 2.53452i) q^{8} +O(q^{10})\)	\(q+(-1.10240 + 0.885841i) q^{2} +(0.430570 - 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(1.25548 + 2.53452i) q^{8} +(-2.64867 - 3.29619i) q^{10} +2.13956i q^{11} -0.665739i q^{13} +(-1.10240 + 0.885841i) q^{14} +(-3.62922 - 1.68190i) q^{16} -7.04931 q^{17} +1.39525i q^{19} +(5.83980 + 1.28741i) q^{20} +(-1.89531 - 2.35865i) q^{22} -0.184371 q^{23} -3.94016 q^{25} +(0.589739 + 0.733911i) q^{26} +(0.430570 - 1.95310i) q^{28} +1.27564i q^{29} -7.62308 q^{31} +(5.49074 - 1.36079i) q^{32} +(7.77116 - 6.24457i) q^{34} +2.99001i q^{35} +6.69127i q^{37} +(-1.23597 - 1.53812i) q^{38} +(-7.57823 + 3.75389i) q^{40} +0.274106 q^{41} -2.63971i q^{43} +(4.17877 + 0.921229i) q^{44} +(0.203250 - 0.163323i) q^{46} +5.77739 q^{47} +1.00000 q^{49} +(4.34363 - 3.49036i) q^{50} +(-1.30026 - 0.286647i) q^{52} -7.48353i q^{53} -6.39730 q^{55} +(1.25548 + 2.53452i) q^{56} +(-1.13001 - 1.40626i) q^{58} +9.03787i q^{59} -9.80298i q^{61} +(8.40369 - 6.75284i) q^{62} +(-4.84755 + 6.36406i) q^{64} +1.99057 q^{65} +10.8191i q^{67} +(-3.03522 + 13.7680i) q^{68} +(-2.64867 - 3.29619i) q^{70} -7.93573 q^{71} -2.80408 q^{73} +(-5.92740 - 7.37645i) q^{74} +(2.72506 + 0.600752i) q^{76} +2.13956i q^{77} +7.98350 q^{79} +(5.02888 - 10.8514i) q^{80} +(-0.302174 + 0.242814i) q^{82} -6.76125i q^{83} -21.0775i q^{85} +(2.33837 + 2.91002i) q^{86} +(-5.42274 + 2.68617i) q^{88} -16.7549 q^{89} -0.665739i q^{91} +(-0.0793844 + 0.360095i) q^{92} +(-6.36899 + 5.11785i) q^{94} -4.17180 q^{95} -0.107694 q^{97} +(-1.10240 + 0.885841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q + 6 * q^4 + 24 * q^7	\( 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) \) 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more