LMFDB - Embedded newform 780.2.r.a.577.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.5
Character	$\chi$	$=$	780.577
Dual form			780.2.r.a.73.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.17614 + 1.90176i) q^{5} -4.16665i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.17614 + 1.90176i) q^{5} -4.16665i q^{7} -1.00000i q^{9} +(-3.15147 - 3.15147i) q^{11} +(1.82867 - 3.10741i) q^{13} +(-2.17641 - 0.513088i) q^{15} +(-4.18610 + 4.18610i) q^{17} +(-4.37727 - 4.37727i) q^{19} +(2.94627 + 2.94627i) q^{21} +(-1.31199 - 1.31199i) q^{23} +(-2.23337 + 4.47348i) q^{25} +(0.707107 + 0.707107i) q^{27} -3.93181i q^{29} +(3.84918 - 3.84918i) q^{31} +4.45686 q^{33} +(7.92397 - 4.90058i) q^{35} -8.44004i q^{37} +(0.904203 + 3.49033i) q^{39} +(1.55464 - 1.55464i) q^{41} +(8.11673 + 8.11673i) q^{43} +(1.90176 - 1.17614i) q^{45} -1.02013i q^{47} -10.3610 q^{49} -5.92004i q^{51} +(-1.36494 + 1.36494i) q^{53} +(2.28676 - 9.69993i) q^{55} +6.19040 q^{57} +(-1.43740 + 1.43740i) q^{59} +0.293533 q^{61} -4.16665 q^{63} +(8.06031 - 0.177065i) q^{65} -11.8746 q^{67} +1.85543 q^{69} +(11.3963 - 11.3963i) q^{71} +6.46158 q^{73} +(-1.58400 - 4.74246i) q^{75} +(-13.1311 + 13.1311i) q^{77} -8.32607i q^{79} -1.00000 q^{81} +15.1492i q^{83} +(-12.8844 - 3.03750i) q^{85} +(2.78021 + 2.78021i) q^{87} +(6.44206 - 6.44206i) q^{89} +(-12.9475 - 7.61943i) q^{91} +5.44357i q^{93} +(3.17622 - 13.4728i) q^{95} -10.9521 q^{97} +(-3.15147 + 3.15147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.17614	+	1.90176i	0.525987	+	0.850492i
$5$	1.17614	+	1.90176i	0.525987	+	0.850492i
$6$		0			0
$7$		−	4.16665i		−	1.57485i	−0.616413	−	0.787423i	$-0.711415\pi$
$7$		−	4.16665i		−	1.57485i	0.616413	−	0.787423i	$-0.288585\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.15147	−	3.15147i	−0.950205	−	0.950205i	0.0486129	−	0.998818i	$-0.484520\pi$
$11$	−3.15147	−	3.15147i	−0.950205	−	0.950205i	−0.998818	+	0.0486129i	$0.984520\pi$
$12$		0			0
$13$	1.82867	−	3.10741i	0.507182	−	0.861839i
$13$	1.82867	−	3.10741i	0.507182	−	0.861839i
$14$		0			0
$15$	−2.17641	−	0.513088i	−0.561945	−	0.132479i
$16$		0			0
$17$	−4.18610	+	4.18610i	−1.01528	+	1.01528i	−0.0153976	+	0.999881i	$0.504901\pi$
$17$	−4.18610	+	4.18610i	−1.01528	+	1.01528i	−0.999881	+	0.0153976i	$0.995099\pi$
$18$		0			0
$19$	−4.37727	−	4.37727i	−1.00422	−	1.00422i	−0.999991	−	0.00422428i	$-0.998655\pi$
$19$	−4.37727	−	4.37727i	−1.00422	−	1.00422i	−0.00422428	−	0.999991i	$-0.501345\pi$
$20$		0			0
$21$	2.94627	+	2.94627i	0.642928	+	0.642928i
$22$		0			0
$23$	−1.31199	−	1.31199i	−0.273569	−	0.273569i	0.556966	−	0.830535i	$-0.311965\pi$
$23$	−1.31199	−	1.31199i	−0.273569	−	0.273569i	−0.830535	+	0.556966i	$0.811965\pi$
$24$		0			0
$25$	−2.23337	+	4.47348i	−0.446675	+	0.894696i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	3.93181i		−	0.730119i	−0.930984	−	0.365060i	$-0.881049\pi$
$29$		−	3.93181i		−	0.730119i	0.930984	−	0.365060i	$-0.118951\pi$
$30$		0			0
$31$	3.84918	−	3.84918i	0.691334	−	0.691334i	−0.271192	−	0.962525i	$-0.587418\pi$
$31$	3.84918	−	3.84918i	0.691334	−	0.691334i	0.962525	+	0.271192i	$0.0874177\pi$
$32$		0			0
$33$	4.45686			0.775839
$34$		0			0
$35$	7.92397	−	4.90058i	1.33939	−	0.828349i
$36$		0			0
$37$		−	8.44004i		−	1.38753i	−0.720200	−	0.693767i	$-0.755950\pi$
$37$		−	8.44004i		−	1.38753i	0.720200	−	0.693767i	$-0.244050\pi$
$38$		0			0
$39$	0.904203	+	3.49033i	0.144788	+	0.558900i
$40$		0			0
$41$	1.55464	−	1.55464i	0.242794	−	0.242794i	−0.575211	−	0.818005i	$-0.695080\pi$
$41$	1.55464	−	1.55464i	0.242794	−	0.242794i	0.818005	+	0.575211i	$0.195080\pi$
$42$		0			0
$43$	8.11673	+	8.11673i	1.23779	+	1.23779i	0.960903	+	0.276887i	$0.0893026\pi$
$43$	8.11673	+	8.11673i	1.23779	+	1.23779i	0.276887	+	0.960903i	$0.410697\pi$
$44$		0			0
$45$	1.90176	−	1.17614i	0.283497	−	0.175329i
$46$		0			0
$47$		−	1.02013i		−	0.148801i	−0.997228	−	0.0744003i	$-0.976296\pi$
$47$		−	1.02013i		−	0.148801i	0.997228	−	0.0744003i	$-0.0237043\pi$
$48$		0			0
$49$	−10.3610			−1.48014
$50$		0			0
$51$		−	5.92004i		−	0.828972i
$52$		0			0
$53$	−1.36494	+	1.36494i	−0.187489	+	0.187489i	−0.794610	−	0.607121i	$-0.792324\pi$
$53$	−1.36494	+	1.36494i	−0.187489	+	0.187489i	0.607121	+	0.794610i	$0.292324\pi$
$54$		0			0
$55$	2.28676	−	9.69993i	0.308346	−	1.30794i
$56$		0			0
$57$	6.19040			0.819938
$58$		0			0
$59$	−1.43740	+	1.43740i	−0.187134	+	0.187134i	−0.794456	−	0.607322i	$-0.792244\pi$
$59$	−1.43740	+	1.43740i	−0.187134	+	0.187134i	0.607322	+	0.794456i	$0.292244\pi$
$60$		0			0
$61$	0.293533			0.0375831			0.0187915	−	0.999823i	$-0.494018\pi$
$61$	0.293533			0.0375831			0.0187915	+	0.999823i	$0.494018\pi$
$62$		0			0
$63$	−4.16665			−0.524949
$64$		0			0
$65$	8.06031	−	0.177065i	0.999759	−	0.0219623i
$66$		0			0
$67$	−11.8746			−1.45071			−0.725357	−	0.688373i	$-0.758325\pi$
$67$	−11.8746			−1.45071			−0.725357	+	0.688373i	$0.758325\pi$
$68$		0			0
$69$	1.85543			0.223368
$70$		0			0
$71$	11.3963	−	11.3963i	1.35249	−	1.35249i	0.469625	−	0.882866i	$-0.344389\pi$
$71$	11.3963	−	11.3963i	1.35249	−	1.35249i	0.882866	−	0.469625i	$-0.155611\pi$
$72$		0			0
$73$	6.46158			0.756271			0.378135	−	0.925750i	$-0.376565\pi$
$73$	6.46158			0.756271			0.378135	+	0.925750i	$0.376565\pi$
$74$		0			0
$75$	−1.58400	−	4.74246i	−0.182904	−	0.547613i
$76$		0			0
$77$	−13.1311	+	13.1311i	−1.49643	+	1.49643i
$78$		0			0
$79$		−	8.32607i		−	0.936756i	−0.883528	−	0.468378i	$-0.844838\pi$
$79$		−	8.32607i		−	0.936756i	0.883528	−	0.468378i	$-0.155162\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			15.1492i			1.66285i	0.555640	+	0.831423i	$0.312473\pi$
$83$			15.1492i			1.66285i	−0.555640	+	0.831423i	$0.687527\pi$
$84$		0			0
$85$	−12.8844	−	3.03750i	−1.39751	−	0.329463i
$86$		0			0
$87$	2.78021	+	2.78021i	0.298070	+	0.298070i
$88$		0			0
$89$	6.44206	−	6.44206i	0.682857	−	0.682857i	−0.277786	−	0.960643i	$-0.589601\pi$
$89$	6.44206	−	6.44206i	0.682857	−	0.682857i	0.960643	+	0.277786i	$0.0896005\pi$
$90$		0			0
$91$	−12.9475	−	7.61943i	−1.35726	−	0.798733i
$92$		0			0
$93$			5.44357i			0.564472i
$94$		0			0
$95$	3.17622	−	13.4728i	0.325873	−	1.38228i
$96$		0			0
$97$	−10.9521			−1.11201			−0.556007	−	0.831178i	$-0.687667\pi$
$97$	−10.9521			−1.11201			−0.556007	+	0.831178i	$0.687667\pi$
$98$		0			0
$99$	−3.15147	+	3.15147i	−0.316735	+	0.316735i
$100$		0			0
$101$			8.05908i			0.801908i	0.916098	+	0.400954i	$0.131321\pi$
$101$			8.05908i			0.801908i	−0.916098	+	0.400954i	$0.868679\pi$
$102$		0			0
$103$	4.15942	+	4.15942i	0.409840	+	0.409840i	0.881683	−	0.471843i	$-0.156411\pi$
$103$	4.15942	+	4.15942i	0.409840	+	0.409840i	−0.471843	+	0.881683i	$0.656411\pi$
$104$		0			0
$105$	−2.13786	+	9.06832i	−0.208634	+	0.884978i
$106$		0			0
$107$	1.88527	+	1.88527i	0.182256	+	0.182256i	0.792338	−	0.610082i	$-0.208863\pi$
$107$	1.88527	+	1.88527i	0.182256	+	0.182256i	−0.610082	+	0.792338i	$0.708863\pi$
$108$		0			0
$109$	−3.25319	−	3.25319i	−0.311599	−	0.311599i	0.533930	−	0.845529i	$-0.320715\pi$
$109$	−3.25319	−	3.25319i	−0.311599	−	0.311599i	−0.845529	+	0.533930i	$0.820715\pi$
$110$		0			0
$111$	5.96801	+	5.96801i	0.566458	+	0.566458i
$112$		0			0
$113$	7.79437	−	7.79437i	0.733233	−	0.733233i	−0.238026	−	0.971259i	$-0.576500\pi$
$113$	7.79437	−	7.79437i	0.733233	−	0.733233i	0.971259	+	0.238026i	$0.0765003\pi$
$114$		0			0
$115$	0.952001	−	4.03818i	0.0887746	−	0.376562i
$116$		0			0
$117$	−3.10741	−	1.82867i	−0.287280	−	0.169061i
$118$		0			0
$119$	17.4420	+	17.4420i	1.59891	+	1.59891i
$120$		0			0
$121$			8.86356i			0.805778i
$122$		0			0
$123$			2.19859i			0.198240i
$124$		0			0
$125$	−11.1343	+	1.01412i	−0.995878	+	0.0907052i
$126$		0			0
$127$	−4.51457	+	4.51457i	−0.400604	+	0.400604i	−0.878446	−	0.477842i	$-0.841419\pi$
$127$	−4.51457	+	4.51457i	−0.400604	+	0.400604i	0.477842	+	0.878446i	$0.341419\pi$
$128$		0			0
$129$	−11.4788			−1.01065
$130$		0			0
$131$	6.47998			0.566158			0.283079	−	0.959097i	$-0.408644\pi$
$131$	6.47998			0.566158			0.283079	+	0.959097i	$0.408644\pi$
$132$		0			0
$133$	−18.2386	+	18.2386i	−1.58148	+	1.58148i
$134$		0			0
$135$	−0.513088	+	2.17641i	−0.0441596	+	0.187315i
$136$		0			0
$137$			14.7302i			1.25848i	0.777209	+	0.629242i	$0.216635\pi$
$137$			14.7302i			1.25848i	−0.777209	+	0.629242i	$0.783365\pi$
$138$		0			0
$139$		−	7.19379i		−	0.610169i	−0.952325	−	0.305085i	$-0.901315\pi$
$139$		−	7.19379i		−	0.610169i	0.952325	−	0.305085i	$-0.0986848\pi$
$140$		0			0
$141$	0.721338	+	0.721338i	0.0607476	+	0.0607476i
$142$		0			0
$143$	−15.5559	+	4.02990i	−1.30085	+	0.336997i
$144$		0			0
$145$	7.47736	−	4.62438i	0.620961	−	0.384033i
$146$		0			0
$147$	7.32632	−	7.32632i	0.604265	−	0.604265i
$148$		0			0
$149$	7.19801	+	7.19801i	0.589684	+	0.589684i	0.937546	−	0.347862i	$-0.113092\pi$
$149$	7.19801	+	7.19801i	0.589684	+	0.589684i	−0.347862	+	0.937546i	$0.613092\pi$
$150$		0			0
$151$	6.77767	+	6.77767i	0.551559	+	0.551559i	0.926891	−	0.375332i	$-0.122471\pi$
$151$	6.77767	+	6.77767i	0.551559	+	0.551559i	−0.375332	+	0.926891i	$0.622471\pi$
$152$		0			0
$153$	4.18610	+	4.18610i	0.338426	+	0.338426i
$154$		0			0
$155$	11.8474	+	2.79303i	0.951607	+	0.224341i
$156$		0			0
$157$	11.4226	+	11.4226i	0.911626	+	0.911626i	0.996400	−	0.0847741i	$-0.0270169\pi$
$157$	11.4226	+	11.4226i	0.911626	+	0.911626i	−0.0847741	+	0.996400i	$0.527017\pi$
$158$		0			0
$159$		−	1.93032i		−	0.153084i
$160$		0			0
$161$	−5.46661	+	5.46661i	−0.430829	+	0.430829i
$162$		0			0
$163$	−15.5052			−1.21446			−0.607230	−	0.794526i	$-0.707719\pi$
$163$	−15.5052			−1.21446			−0.607230	+	0.794526i	$0.707719\pi$
$164$		0			0
$165$	5.24190	+	8.47587i	0.408081	+	0.659845i
$166$		0			0
$167$		−	10.8047i		−	0.836092i	−0.908426	−	0.418046i	$-0.862715\pi$
$167$		−	10.8047i		−	0.836092i	0.908426	−	0.418046i	$-0.137285\pi$
$168$		0			0
$169$	−6.31194	−	11.3648i	−0.485534	−	0.874218i
$170$		0			0
$171$	−4.37727	+	4.37727i	−0.334738	+	0.334738i
$172$		0			0
$173$	7.61397	+	7.61397i	0.578879	+	0.578879i	0.934594	−	0.355715i	$-0.115763\pi$
$173$	7.61397	+	7.61397i	0.578879	+	0.578879i	−0.355715	+	0.934594i	$0.615763\pi$
$174$		0			0
$175$	18.6394	+	9.30569i	1.40901	+	0.703444i
$176$		0			0
$177$		−	2.03280i		−	0.152794i
$178$		0			0
$179$	−13.2476			−0.990175			−0.495087	−	0.868843i	$-0.664864\pi$
$179$	−13.2476			−0.990175			−0.495087	+	0.868843i	$0.664864\pi$
$180$		0			0
$181$		−	13.5363i		−	1.00614i	−0.864245	−	0.503072i	$-0.832203\pi$
$181$		−	13.5363i		−	1.00614i	0.864245	−	0.503072i	$-0.167797\pi$
$182$		0			0
$183$	−0.207559	+	0.207559i	−0.0153432	+	0.0153432i
$184$		0			0
$185$	16.0509	−	9.92669i	1.18009	−	0.729825i
$186$		0			0
$187$	26.3848			1.92945
$188$		0			0
$189$	2.94627	−	2.94627i	0.214309	−	0.214309i
$190$		0			0
$191$	−23.5256			−1.70226			−0.851128	−	0.524959i	$-0.824081\pi$
$191$	−23.5256			−1.70226			−0.851128	+	0.524959i	$0.824081\pi$
$192$		0			0
$193$	12.6069			0.907466			0.453733	−	0.891138i	$-0.350092\pi$
$193$	12.6069			0.907466			0.453733	+	0.891138i	$0.350092\pi$
$194$		0			0
$195$	−5.57430	+	5.82471i	−0.399184	+	0.417116i
$196$		0			0
$197$	−13.4136			−0.955681			−0.477841	−	0.878447i	$-0.658580\pi$
$197$	−13.4136			−0.955681			−0.477841	+	0.878447i	$0.658580\pi$
$198$		0			0
$199$	22.5835			1.60091			0.800453	−	0.599396i	$-0.204592\pi$
$199$	22.5835			1.60091			0.800453	+	0.599396i	$0.204592\pi$
$200$		0			0
$201$	8.39661	−	8.39661i	0.592251	−	0.592251i
$202$		0			0
$203$	−16.3825			−1.14983
$204$		0			0
$205$	4.78503	+	1.12807i	0.334201	+	0.0787879i
$206$		0			0
$207$	−1.31199	+	1.31199i	−0.0911896	+	0.0911896i
$208$		0			0
$209$			27.5897i			1.90842i
$210$		0			0
$211$	−12.0590			−0.830175			−0.415088	−	0.909781i	$-0.636249\pi$
$211$	−12.0590			−0.830175			−0.415088	+	0.909781i	$0.636249\pi$
$212$		0			0
$213$			16.1168i			1.10430i
$214$		0			0
$215$	−5.88962	+	24.9825i	−0.401669	+	1.70379i
$216$		0			0
$217$	−16.0382	−	16.0382i	−1.08874	−	1.08874i
$218$		0			0
$219$	−4.56903	+	4.56903i	−0.308746	+	0.308746i
$220$		0			0
$221$	5.35292	+	20.6629i	0.360076	+	1.38994i
$222$		0			0
$223$		−	9.25360i		−	0.619667i	−0.950791	−	0.309834i	$-0.899727\pi$
$223$		−	9.25360i		−	0.619667i	0.950791	−	0.309834i	$-0.100273\pi$
$224$		0			0
$225$	4.47348	+	2.23337i	0.298232	+	0.148892i
$226$		0			0
$227$	−16.0754			−1.06696			−0.533481	−	0.845812i	$-0.679116\pi$
$227$	−16.0754			−1.06696			−0.533481	+	0.845812i	$0.679116\pi$
$228$		0			0
$229$	−5.43244	+	5.43244i	−0.358986	+	0.358986i	−0.863439	−	0.504453i	$-0.831694\pi$
$229$	−5.43244	+	5.43244i	−0.358986	+	0.358986i	0.504453	+	0.863439i	$0.331694\pi$
$230$		0			0
$231$		−	18.5702i		−	1.22183i
$232$		0			0
$233$	−1.12524	−	1.12524i	−0.0737170	−	0.0737170i	0.669287	−	0.743004i	$-0.266600\pi$
$233$	−1.12524	−	1.12524i	−0.0737170	−	0.0737170i	−0.743004	+	0.669287i	$0.766600\pi$
$234$		0			0
$235$	1.94003	−	1.19981i	0.126554	−	0.0782672i
$236$		0			0
$237$	5.88742	+	5.88742i	0.382429	+	0.382429i
$238$		0			0
$239$	−12.4781	−	12.4781i	−0.807144	−	0.807144i	0.177057	−	0.984201i	$-0.443342\pi$
$239$	−12.4781	−	12.4781i	−0.807144	−	0.807144i	−0.984201	+	0.177057i	$0.943342\pi$
$240$		0			0
$241$	1.27702	+	1.27702i	0.0822603	+	0.0822603i	0.747040	−	0.664779i	$-0.231474\pi$
$241$	1.27702	+	1.27702i	0.0822603	+	0.0822603i	−0.664779	+	0.747040i	$0.731474\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−12.1860	−	19.7041i	−0.778535	−	1.25885i
$246$		0			0
$247$	−21.6065	+	5.59738i	−1.37479	+	0.356153i
$248$		0			0
$249$	−10.7121	−	10.7121i	−0.678854	−	0.678854i
$250$		0			0
$251$		−	19.6566i		−	1.24072i	−0.784319	−	0.620358i	$-0.786987\pi$
$251$		−	19.6566i		−	1.24072i	0.784319	−	0.620358i	$-0.213013\pi$
$252$		0			0
$253$			8.26940i			0.519893i
$254$		0			0
$255$	11.2585	−	6.96282i	0.705034	−	0.436029i
$256$		0			0
$257$	20.8698	−	20.8698i	1.30182	−	1.30182i	0.374662	−	0.927162i	$-0.377759\pi$
$257$	20.8698	−	20.8698i	1.30182	−	1.30182i	0.927162	−	0.374662i	$-0.122241\pi$
$258$		0			0
$259$	−35.1667			−2.18515
$260$		0			0
$261$	−3.93181			−0.243373
$262$		0			0
$263$	3.80349	−	3.80349i	0.234533	−	0.234533i	−0.580049	−	0.814582i	$-0.696966\pi$
$263$	3.80349	−	3.80349i	0.234533	−	0.234533i	0.814582	+	0.580049i	$0.196966\pi$
$264$		0			0
$265$	−4.20115	−	0.990421i	−0.258074	−	0.0608411i
$266$		0			0
$267$			9.11045i			0.557551i
$268$		0			0
$269$			3.31848i			0.202332i	0.994870	+	0.101166i	$0.0322572\pi$
$269$			3.31848i			0.202332i	−0.994870	+	0.101166i	$0.967743\pi$
$270$		0			0
$271$	5.56659	+	5.56659i	0.338146	+	0.338146i	0.855669	−	0.517523i	$-0.173146\pi$
$271$	5.56659	+	5.56659i	0.338146	+	0.338146i	−0.517523	+	0.855669i	$0.673146\pi$
$272$		0			0
$273$	14.5430	−	3.76750i	0.880182	−	0.228019i
$274$		0			0
$275$	21.1365	−	7.05964i	1.27458	−	0.425712i
$276$		0			0
$277$	−3.00278	+	3.00278i	−0.180419	+	0.180419i	−0.791539	−	0.611119i	$-0.790720\pi$
$277$	−3.00278	+	3.00278i	−0.180419	+	0.180419i	0.611119	+	0.791539i	$0.290720\pi$
$278$		0			0
$279$	−3.84918	−	3.84918i	−0.230445	−	0.230445i
$280$		0			0
$281$	2.34615	+	2.34615i	0.139960	+	0.139960i	0.773615	−	0.633656i	$-0.218446\pi$
$281$	2.34615	+	2.34615i	0.139960	+	0.139960i	−0.633656	+	0.773615i	$0.718446\pi$
$282$		0			0
$283$	16.7918	+	16.7918i	0.998167	+	0.998167i	0.999998	−	0.00183106i	$-0.000582846\pi$
$283$	16.7918	+	16.7918i	0.998167	+	0.998167i	−0.00183106	+	0.999998i	$0.500583\pi$
$284$		0			0
$285$	7.28080	+	11.7726i	0.431277	+	0.697351i
$286$		0			0
$287$	−6.47764	−	6.47764i	−0.382363	−	0.382363i
$288$		0			0
$289$		−	18.0469i		−	1.06158i
$290$		0			0
$291$	7.74428	−	7.74428i	0.453978	−	0.453978i
$292$		0			0
$293$	10.6729			0.623516			0.311758	−	0.950162i	$-0.399082\pi$
$293$	10.6729			0.623516			0.311758	+	0.950162i	$0.399082\pi$
$294$		0			0
$295$	−4.42419	−	1.04300i	−0.257586	−	0.0607260i
$296$		0			0
$297$		−	4.45686i		−	0.258613i
$298$		0			0
$299$	−6.47608	+	1.67769i	−0.374522	+	0.0970233i
$300$		0			0
$301$	33.8196	−	33.8196i	1.94933	−	1.94933i
$302$		0			0
$303$	−5.69863	−	5.69863i	−0.327378	−	0.327378i
$304$		0			0
$305$	0.345237	+	0.558229i	0.0197682	+	0.0319641i
$306$		0			0
$307$			9.95047i			0.567903i	0.958839	+	0.283952i	$0.0916455\pi$
$307$			9.95047i			0.567903i	−0.958839	+	0.283952i	$0.908355\pi$
$308$		0			0
$309$	−5.88231			−0.334633
$310$		0			0
$311$			5.16651i			0.292966i	0.989213	+	0.146483i	$0.0467954\pi$
$311$			5.16651i			0.292966i	−0.989213	+	0.146483i	$0.953205\pi$
$312$		0			0
$313$	2.76718	−	2.76718i	0.156410	−	0.156410i	−0.624564	−	0.780974i	$-0.714723\pi$
$313$	2.76718	−	2.76718i	0.156410	−	0.156410i	0.780974	+	0.624564i	$0.214723\pi$
$314$		0			0
$315$	−4.90058	−	7.92397i	−0.276116	−	0.446465i
$316$		0			0
$317$	29.1994			1.64000			0.820000	−	0.572363i	$-0.193973\pi$
$317$	29.1994			1.64000			0.820000	+	0.572363i	$0.193973\pi$
$318$		0			0
$319$	−12.3910	+	12.3910i	−0.693763	+	0.693763i
$320$		0			0
$321$	−2.66618			−0.148812
$322$		0			0
$323$	36.6474			2.03912
$324$		0			0
$325$	9.81682	+	15.1205i	0.544539	+	0.838735i
$326$		0			0
$327$	4.60071			0.254420
$328$		0			0
$329$	−4.25051			−0.234338
$330$		0			0
$331$	−8.69091	+	8.69091i	−0.477696	+	0.477696i	−0.904394	−	0.426698i	$-0.859677\pi$
$331$	−8.69091	+	8.69091i	−0.477696	+	0.477696i	0.426698	+	0.904394i	$0.359677\pi$
$332$		0			0
$333$	−8.44004			−0.462511
$334$		0			0
$335$	−13.9662	−	22.5826i	−0.763057	−	1.23382i
$336$		0			0
$337$	−7.49283	+	7.49283i	−0.408161	+	0.408161i	−0.881097	−	0.472936i	$-0.843194\pi$
$337$	−7.49283	+	7.49283i	−0.408161	+	0.408161i	0.472936	+	0.881097i	$0.343194\pi$
$338$		0			0
$339$			11.0229i			0.598682i
$340$		0			0
$341$	−24.2612			−1.31382
$342$		0			0
$343$			14.0040i			0.756147i
$344$		0			0
$345$	2.18226	+	3.52859i	0.117489	+	0.189973i
$346$		0			0
$347$	−9.92612	−	9.92612i	−0.532862	−	0.532862i	0.388561	−	0.921423i	$-0.372972\pi$
$347$	−9.92612	−	9.92612i	−0.532862	−	0.532862i	−0.921423	+	0.388561i	$0.872972\pi$
$348$		0			0
$349$	7.52765	−	7.52765i	0.402946	−	0.402946i	−0.476324	−	0.879270i	$-0.658031\pi$
$349$	7.52765	−	7.52765i	0.402946	−	0.402946i	0.879270	+	0.476324i	$0.158031\pi$
$350$		0			0
$351$	3.49033	−	0.904203i	0.186300	−	0.0482628i
$352$		0			0
$353$			7.33990i			0.390664i	0.980737	+	0.195332i	$0.0625784\pi$
$353$			7.33990i			0.390664i	−0.980737	+	0.195332i	$0.937422\pi$
$354$		0			0
$355$	35.0767	+	8.26933i	1.86168	+	0.438890i
$356$		0			0
$357$	−24.6668			−1.30550
$358$		0			0
$359$	24.1816	−	24.1816i	1.27626	−	1.27626i	0.333509	−	0.942747i	$-0.391767\pi$
$359$	24.1816	−	24.1816i	1.27626	−	1.27626i	0.942747	−	0.333509i	$-0.108233\pi$
$360$		0			0
$361$			19.3210i			1.01690i
$362$		0			0
$363$	−6.26749	−	6.26749i	−0.328958	−	0.328958i
$364$		0			0
$365$	7.59974	+	12.2884i	0.397789	+	0.643203i
$366$		0			0
$367$	17.7690	+	17.7690i	0.927537	+	0.927537i	0.997546	−	0.0700097i	$-0.0223030\pi$
$367$	17.7690	+	17.7690i	0.927537	+	0.927537i	−0.0700097	+	0.997546i	$0.522303\pi$
$368$		0			0
$369$	−1.55464	−	1.55464i	−0.0809313	−	0.0809313i
$370$		0			0
$371$	5.68722	+	5.68722i	0.295266	+	0.295266i
$372$		0			0
$373$	−3.42778	+	3.42778i	−0.177484	+	0.177484i	−0.790258	−	0.612774i	$-0.790054\pi$
$373$	−3.42778	+	3.42778i	−0.177484	+	0.177484i	0.612774	+	0.790258i	$0.290054\pi$
$374$		0			0
$375$	7.15602	−	8.59019i	0.369535	−	0.443596i
$376$		0			0
$377$	−12.2177	−	7.18999i	−0.629245	−	0.370303i
$378$		0			0
$379$	6.32325	+	6.32325i	0.324804	+	0.324804i	0.850606	−	0.525803i	$-0.176235\pi$
$379$	6.32325	+	6.32325i	0.324804	+	0.324804i	−0.525803	+	0.850606i	$0.676235\pi$
$380$		0			0
$381$		−	6.38457i		−	0.327092i
$382$		0			0
$383$		−	24.6950i		−	1.26186i	−0.775841	−	0.630928i	$-0.782674\pi$
$383$		−	24.6950i		−	1.26186i	0.775841	−	0.630928i	$-0.217326\pi$
$384$		0			0
$385$	−40.4162	−	9.52812i	−2.05980	−	0.485598i
$386$		0			0
$387$	8.11673	−	8.11673i	0.412596	−	0.412596i
$388$		0			0
$389$	−27.4062			−1.38955			−0.694775	−	0.719228i	$-0.744496\pi$
$389$	−27.4062			−1.38955			−0.694775	+	0.719228i	$0.744496\pi$
$390$		0			0
$391$	10.9843			0.555498
$392$		0			0
$393$	−4.58204	+	4.58204i	−0.231133	+	0.231133i
$394$		0			0
$395$	15.8342	−	9.79265i	0.796704	−	0.492722i
$396$		0			0
$397$		−	39.1875i		−	1.96676i	−0.181554	−	0.983381i	$-0.558113\pi$
$397$		−	39.1875i		−	1.96676i	0.181554	−	0.983381i	$-0.441887\pi$
$398$		0			0
$399$		−	25.7932i		−	1.29128i
$400$		0			0
$401$	21.9890	+	21.9890i	1.09808	+	1.09808i	0.994636	+	0.103441i	$0.0329854\pi$
$401$	21.9890	+	21.9890i	1.09808	+	1.09808i	0.103441	+	0.994636i	$0.467015\pi$
$402$		0			0
$403$	−4.92209	−	18.9999i	−0.245187	−	0.946450i
$404$		0			0
$405$	−1.17614	−	1.90176i	−0.0584430	−	0.0944992i
$406$		0			0
$407$	−26.5985	+	26.5985i	−1.31844	+	1.31844i
$408$		0			0
$409$	−2.71373	−	2.71373i	−0.134185	−	0.134185i	0.636824	−	0.771009i	$-0.280248\pi$
$409$	−2.71373	−	2.71373i	−0.134185	−	0.134185i	−0.771009	+	0.636824i	$0.780248\pi$
$410$		0			0
$411$	−10.4158	−	10.4158i	−0.513774	−	0.513774i
$412$		0			0
$413$	5.98916	+	5.98916i	0.294707	+	0.294707i
$414$		0			0
$415$	−28.8102	+	17.8177i	−1.41424	+	0.874636i
$416$		0			0
$417$	5.08678	+	5.08678i	0.249101	+	0.249101i
$418$		0			0
$419$		−	34.1751i		−	1.66956i	−0.550583	−	0.834780i	$-0.685595\pi$
$419$		−	34.1751i		−	1.66956i	0.550583	−	0.834780i	$-0.314405\pi$
$420$		0			0
$421$	15.5333	−	15.5333i	0.757049	−	0.757049i	−0.218736	−	0.975784i	$-0.570193\pi$
$421$	15.5333	−	15.5333i	0.757049	−	0.757049i	0.975784	+	0.218736i	$0.0701932\pi$
$422$		0			0
$423$	−1.02013			−0.0496002
$424$		0			0
$425$	−9.37732	−	28.0756i	−0.454867	−	1.36187i
$426$		0			0
$427$		−	1.22305i		−	0.0591875i
$428$		0			0
$429$	8.15012	−	13.8493i	0.393491	−	0.668648i
$430$		0			0
$431$	−26.4717	+	26.4717i	−1.27510	+	1.27510i	−0.331722	+	0.943377i	$0.607629\pi$
$431$	−26.4717	+	26.4717i	−1.27510	+	1.27510i	−0.943377	+	0.331722i	$0.892371\pi$
$432$		0			0
$433$	−26.0961	−	26.0961i	−1.25410	−	1.25410i	−0.953866	−	0.300232i	$-0.902936\pi$
$433$	−26.0961	−	26.0961i	−1.25410	−	1.25410i	−0.300232	−	0.953866i	$-0.597064\pi$
$434$		0			0
$435$	−2.01737	+	8.55722i	−0.0967253	+	0.410287i
$436$		0			0
$437$			11.4859i			0.549444i
$438$		0			0
$439$	−12.5133			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$439$	−12.5133			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$440$		0			0
$441$			10.3610i			0.493380i
$442$		0			0
$443$	−1.48719	+	1.48719i	−0.0706585	+	0.0706585i	−0.741553	−	0.670894i	$-0.765910\pi$
$443$	−1.48719	+	1.48719i	−0.0706585	+	0.0706585i	0.670894	+	0.741553i	$0.265910\pi$
$444$		0			0
$445$	19.8280	+	4.67446i	0.939939	+	0.221591i
$446$		0			0
$447$	−10.1795			−0.481475
$448$		0			0
$449$	11.5904	−	11.5904i	0.546986	−	0.546986i	−0.378582	−	0.925568i	$-0.623588\pi$
$449$	11.5904	−	11.5904i	0.546986	−	0.546986i	0.925568	+	0.378582i	$0.123588\pi$
$450$		0			0
$451$	−9.79880			−0.461408
$452$		0			0
$453$	−9.58507			−0.450346
$454$		0			0
$455$	−0.737770	−	33.5845i	−0.0345872	−	1.57447i
$456$		0			0
$457$	34.6269			1.61978			0.809888	−	0.586584i	$-0.199528\pi$
$457$	34.6269			1.61978			0.809888	+	0.586584i	$0.199528\pi$
$458$		0			0
$459$	−5.92004			−0.276324
$460$		0			0
$461$	−18.8332	+	18.8332i	−0.877149	+	0.877149i	−0.993239	−	0.116090i	$-0.962964\pi$
$461$	−18.8332	+	18.8332i	−0.877149	+	0.877149i	0.116090	+	0.993239i	$0.462964\pi$
$462$		0			0
$463$	13.5047			0.627615			0.313808	−	0.949487i	$-0.398395\pi$
$463$	13.5047			0.627615			0.313808	+	0.949487i	$0.398395\pi$
$464$		0			0
$465$	−10.3524	+	6.40242i	−0.480079	+	0.296905i
$466$		0			0
$467$	−7.20739	+	7.20739i	−0.333518	+	0.333518i	−0.853921	−	0.520403i	$-0.825782\pi$
$467$	−7.20739	+	7.20739i	−0.333518	+	0.333518i	0.520403	+	0.853921i	$0.325782\pi$
$468$		0			0
$469$			49.4773i			2.28465i
$470$		0			0
$471$	−16.1541			−0.744340
$472$		0			0
$473$		−	51.1593i		−	2.35231i
$474$		0			0
$475$	29.3577	−	9.80556i	1.34703	−	0.449910i
$476$		0			0
$477$	1.36494	+	1.36494i	0.0624963	+	0.0624963i
$478$		0			0
$479$	12.3993	−	12.3993i	0.566537	−	0.566537i	−0.364620	−	0.931157i	$-0.618801\pi$
$479$	12.3993	−	12.3993i	0.566537	−	0.566537i	0.931157	+	0.364620i	$0.118801\pi$
$480$		0			0
$481$	−26.2266	−	15.4340i	−1.19583	−	0.703731i
$482$		0			0
$483$		−	7.73095i		−	0.351770i
$484$		0			0
$485$	−12.8812	−	20.8282i	−0.584905	−	0.945760i
$486$		0			0
$487$	32.1455			1.45665			0.728326	−	0.685230i	$-0.240298\pi$
$487$	32.1455			1.45665			0.728326	+	0.685230i	$0.240298\pi$
$488$		0			0
$489$	10.9638	−	10.9638i	0.495801	−	0.495801i
$490$		0			0
$491$		−	3.73137i		−	0.168395i	−0.996449	−	0.0841973i	$-0.973167\pi$
$491$		−	3.73137i		−	0.168395i	0.996449	−	0.0841973i	$-0.0268326\pi$
$492$		0			0
$493$	16.4590	+	16.4590i	0.741275	+	0.741275i
$494$		0			0
$495$	−9.69993	−	2.28676i	−0.435979	−	0.102782i
$496$		0			0
$497$	−47.4844	−	47.4844i	−2.12997	−	2.12997i
$498$		0			0
$499$	5.85645	+	5.85645i	0.262171	+	0.262171i	0.825936	−	0.563765i	$-0.190647\pi$
$499$	5.85645	+	5.85645i	0.262171	+	0.262171i	−0.563765	+	0.825936i	$0.690647\pi$
$500$		0			0
$501$	7.64007	+	7.64007i	0.341333	+	0.341333i
$502$		0			0
$503$	−21.0951	+	21.0951i	−0.940586	+	0.940586i	−0.998331	−	0.0577458i	$-0.981609\pi$
$503$	−21.0951	+	21.0951i	−0.940586	+	0.940586i	0.0577458	+	0.998331i	$0.481609\pi$
$504$		0			0
$505$	−15.3264	+	9.47863i	−0.682017	+	0.421793i
$506$		0			0
$507$	12.4994	+	3.57294i	0.555116	+	0.158680i
$508$		0			0
$509$	23.2392	+	23.2392i	1.03006	+	1.03006i	0.999534	+	0.0305246i	$0.00971780\pi$
$509$	23.2392	+	23.2392i	1.03006	+	1.03006i	0.0305246	+	0.999534i	$0.490282\pi$
$510$		0			0
$511$		−	26.9231i		−	1.19101i
$512$		0			0
$513$		−	6.19040i		−	0.273313i
$514$		0			0
$515$	−3.01814	+	12.8023i	−0.132995	+	0.564137i
$516$		0			0
$517$	−3.21490	+	3.21490i	−0.141391	+	0.141391i
$518$		0			0
$519$	−10.7678			−0.472653
$520$		0			0
$521$	21.5024			0.942038			0.471019	−	0.882123i	$-0.343886\pi$
$521$	21.5024			0.942038			0.471019	+	0.882123i	$0.343886\pi$
$522$		0			0
$523$	14.0736	−	14.0736i	0.615395	−	0.615395i	−0.328952	−	0.944347i	$-0.606695\pi$
$523$	14.0736	−	14.0736i	0.615395	−	0.615395i	0.944347	+	0.328952i	$0.106695\pi$
$524$		0			0
$525$	−19.7602	+	6.59995i	−0.862405	+	0.288046i
$526$		0			0
$527$			32.2262i			1.40379i
$528$		0			0
$529$		−	19.5574i		−	0.850320i
$530$		0			0
$531$	1.43740	+	1.43740i	0.0623780	+	0.0623780i
$532$		0			0
$533$	−1.98797	−	7.67381i	−0.0861087	−	0.332390i
$534$		0			0
$535$	−1.36798	+	5.80269i	−0.0591431	+	0.250872i
$536$		0			0
$537$	9.36749	−	9.36749i	0.404237	−	0.404237i
$538$		0			0
$539$	32.6523	+	32.6523i	1.40644	+	1.40644i
$540$		0			0
$541$	11.4516	+	11.4516i	0.492344	+	0.492344i	0.909044	−	0.416700i	$-0.136813\pi$
$541$	11.4516	+	11.4516i	0.492344	+	0.492344i	−0.416700	+	0.909044i	$0.636813\pi$
$542$		0			0
$543$	9.57160	+	9.57160i	0.410756	+	0.410756i
$544$		0			0
$545$	2.36057	−	10.0130i	0.101116	−	0.428910i
$546$		0			0
$547$	16.7429	+	16.7429i	0.715874	+	0.715874i	0.967757	−	0.251884i	$-0.0810501\pi$
$547$	16.7429	+	16.7429i	0.715874	+	0.715874i	−0.251884	+	0.967757i	$0.581050\pi$
$548$		0			0
$549$		−	0.293533i		−	0.0125277i
$550$		0			0
$551$	−17.2106	+	17.2106i	−0.733197	+	0.733197i
$552$		0			0
$553$	−34.6918			−1.47525
$554$		0			0
$555$	−4.33048	+	18.3689i	−0.183819	+	0.779718i
$556$		0			0
$557$		−	38.6119i		−	1.63604i	−0.575189	−	0.818020i	$-0.695072\pi$
$557$		−	38.6119i		−	1.63604i	0.575189	−	0.818020i	$-0.304928\pi$
$558$		0			0
$559$	40.0648	−	10.3792i	1.69456	−	0.438991i
$560$		0			0
$561$	−18.6569	+	18.6569i	−0.787693	+	0.787693i
$562$		0			0
$563$	9.62289	+	9.62289i	0.405556	+	0.405556i	0.880186	−	0.474629i	$-0.157418\pi$
$563$	9.62289	+	9.62289i	0.405556	+	0.405556i	−0.474629	+	0.880186i	$0.657418\pi$
$564$		0			0
$565$	23.9903	+	5.65572i	1.00928	+	0.237938i
$566$		0			0
$567$			4.16665i			0.174983i
$568$		0			0
$569$	23.7899			0.997326			0.498663	−	0.866796i	$-0.333825\pi$
$569$	23.7899			0.997326			0.498663	+	0.866796i	$0.333825\pi$
$570$		0			0
$571$		−	11.2205i		−	0.469562i	−0.972048	−	0.234781i	$-0.924563\pi$
$571$		−	11.2205i		−	0.469562i	0.972048	−	0.234781i	$-0.0754373\pi$
$572$		0			0
$573$	16.6351	−	16.6351i	0.694943	−	0.694943i
$574$		0			0
$575$	8.79933	−	2.93900i	0.366957	−	0.122565i
$576$		0			0
$577$	40.0865			1.66882			0.834411	−	0.551143i	$-0.185808\pi$
$577$	40.0865			1.66882			0.834411	+	0.551143i	$0.185808\pi$
$578$		0			0
$579$	−8.91444	+	8.91444i	−0.370471	+	0.370471i
$580$		0			0
$581$	63.1216			2.61873
$582$		0			0
$583$	8.60314			0.356305
$584$		0			0
$585$	−0.177065	−	8.06031i	−0.00732075	−	0.333253i
$586$		0			0
$587$	11.7208			0.483770			0.241885	−	0.970305i	$-0.422234\pi$
$587$	11.7208			0.483770			0.241885	+	0.970305i	$0.422234\pi$
$588$		0			0
$589$	−33.6979			−1.38850
$590$		0			0
$591$	9.48487	−	9.48487i	0.390155	−	0.390155i
$592$		0			0
$593$	−15.4834			−0.635826			−0.317913	−	0.948120i	$-0.602982\pi$
$593$	−15.4834			−0.635826			−0.317913	+	0.948120i	$0.602982\pi$
$594$		0			0
$595$	−12.6562	+	53.6849i	−0.518854	+	2.20086i
$596$		0			0
$597$	−15.9690	+	15.9690i	−0.653567	+	0.653567i
$598$		0			0
$599$			13.5127i			0.552115i	0.961141	+	0.276058i	$0.0890280\pi$
$599$			13.5127i			0.552115i	−0.961141	+	0.276058i	$0.910972\pi$
$600$		0			0
$601$	27.4625			1.12022			0.560108	−	0.828419i	$-0.310759\pi$
$601$	27.4625			1.12022			0.560108	+	0.828419i	$0.310759\pi$
$602$		0			0
$603$			11.8746i			0.483571i
$604$		0			0
$605$	−16.8564	+	10.4248i	−0.685309	+	0.423829i
$606$		0			0
$607$	9.34983	+	9.34983i	0.379498	+	0.379498i	0.870921	−	0.491423i	$-0.163523\pi$
$607$	9.34983	+	9.34983i	0.379498	+	0.379498i	−0.491423	+	0.870921i	$0.663523\pi$
$608$		0			0
$609$	11.5842	−	11.5842i	0.469414	−	0.469414i
$610$		0			0
$611$	−3.16994	−	1.86547i	−0.128242	−	0.0754689i
$612$		0			0
$613$		−	16.7293i		−	0.675690i	−0.941202	−	0.337845i	$-0.890302\pi$
$613$		−	16.7293i		−	0.675690i	0.941202	−	0.337845i	$-0.109698\pi$
$614$		0			0
$615$	−4.18119	+	2.58586i	−0.168602	+	0.104272i
$616$		0			0
$617$	−33.3846			−1.34401			−0.672007	−	0.740544i	$-0.734568\pi$
$617$	−33.3846			−1.34401			−0.672007	+	0.740544i	$0.734568\pi$
$618$		0			0
$619$	12.9465	−	12.9465i	0.520365	−	0.520365i	−0.397316	−	0.917682i	$-0.630058\pi$
$619$	12.9465	−	12.9465i	0.520365	−	0.520365i	0.917682	+	0.397316i	$0.130058\pi$
$620$		0			0
$621$		−	1.85543i		−	0.0744560i
$622$		0			0
$623$	−26.8418	−	26.8418i	−1.07540	−	1.07540i
$624$		0			0
$625$	−15.0241	−	19.9819i	−0.600963	−	0.799277i
$626$		0			0
$627$	−19.5089	−	19.5089i	−0.779109	−	0.779109i
$628$		0			0
$629$	35.3309	+	35.3309i	1.40873	+	1.40873i
$630$		0			0
$631$	29.0903	+	29.0903i	1.15807	+	1.15807i	0.984891	+	0.173174i	$0.0554024\pi$
$631$	29.0903	+	29.0903i	1.15807	+	1.15807i	0.173174	+	0.984891i	$0.444598\pi$
$632$		0			0
$633$	8.52700	−	8.52700i	0.338918	−	0.338918i
$634$		0			0
$635$	−13.8954	−	3.27585i	−0.551423	−	0.129998i
$636$		0			0
$637$	−18.9468	+	32.1958i	−0.750700	+	1.27564i
$638$		0			0
$639$	−11.3963	−	11.3963i	−0.450830	−	0.450830i
$640$		0			0
$641$		−	27.5037i		−	1.08633i	−0.839626	−	0.543165i	$-0.817226\pi$
$641$		−	27.5037i		−	1.08633i	0.839626	−	0.543165i	$-0.182774\pi$
$642$		0			0
$643$		−	3.97198i		−	0.156640i	−0.996928	−	0.0783198i	$-0.975044\pi$
$643$		−	3.97198i		−	0.156640i	0.996928	−	0.0783198i	$-0.0249555\pi$
$644$		0			0
$645$	−13.5007	−	21.8299i	−0.531589	−	0.859551i
$646$		0			0
$647$	−24.2989	+	24.2989i	−0.955290	+	0.955290i	−0.999042	−	0.0437527i	$-0.986069\pi$
$647$	−24.2989	+	24.2989i	−0.955290	+	0.955290i	0.0437527	+	0.999042i	$0.486069\pi$
$648$		0			0
$649$	9.05987			0.355631
$650$		0			0
$651$	22.6814			0.888956
$652$		0			0
$653$	−6.39282	+	6.39282i	−0.250170	+	0.250170i	−0.821040	−	0.570870i	$-0.806606\pi$
$653$	−6.39282	+	6.39282i	−0.250170	+	0.250170i	0.570870	+	0.821040i	$0.306606\pi$
$654$		0			0
$655$	7.62138	+	12.3234i	0.297792	+	0.481513i
$656$		0			0
$657$		−	6.46158i		−	0.252090i
$658$		0			0
$659$			11.4763i			0.447052i	0.974698	+	0.223526i	$0.0717567\pi$
$659$			11.4763i			0.447052i	−0.974698	+	0.223526i	$0.928243\pi$
$660$		0			0
$661$	−19.3374	−	19.3374i	−0.752139	−	0.752139i	0.222739	−	0.974878i	$-0.428500\pi$
$661$	−19.3374	−	19.3374i	−0.752139	−	0.752139i	−0.974878	+	0.222739i	$0.928500\pi$
$662$		0			0
$663$	−18.3960	−	10.8258i	−0.714440	−	0.420439i
$664$		0			0
$665$	−56.1365	−	13.2342i	−2.17688	−	0.513200i
$666$		0			0
$667$	−5.15850	+	5.15850i	−0.199738	+	0.199738i
$668$		0			0
$669$	6.54329	+	6.54329i	0.252978	+	0.252978i
$670$		0			0
$671$	−0.925062	−	0.925062i	−0.0357116	−	0.0357116i
$672$		0			0
$673$	6.06351	+	6.06351i	0.233731	+	0.233731i	0.814248	−	0.580517i	$-0.197150\pi$
$673$	6.06351	+	6.06351i	0.233731	+	0.233731i	−0.580517	+	0.814248i	$0.697150\pi$
$674$		0			0
$675$	−4.74246	+	1.58400i	−0.182538	+	0.0609680i
$676$		0			0
$677$	−10.6902	−	10.6902i	−0.410859	−	0.410859i	0.471179	−	0.882038i	$-0.343829\pi$
$677$	−10.6902	−	10.6902i	−0.410859	−	0.410859i	−0.882038	+	0.471179i	$0.843829\pi$
$678$		0			0
$679$			45.6334i			1.75125i
$680$		0			0
$681$	11.3670	−	11.3670i	0.435585	−	0.435585i
$682$		0			0
$683$	−1.96421			−0.0751586			−0.0375793	−	0.999294i	$-0.511965\pi$
$683$	−1.96421			−0.0751586			−0.0375793	+	0.999294i	$0.511965\pi$
$684$		0			0
$685$	−28.0133	+	17.3248i	−1.07033	+	0.661947i
$686$		0			0
$687$		−	7.68263i		−	0.293111i
$688$		0			0
$689$	1.74540	+	6.73744i	0.0664943	+	0.256676i
$690$		0			0
$691$	−29.0749	+	29.0749i	−1.10606	+	1.10606i	−0.112400	+	0.993663i	$0.535854\pi$
$691$	−29.0749	+	29.0749i	−1.10606	+	1.10606i	−0.993663	+	0.112400i	$0.964146\pi$
$692$		0			0
$693$	13.1311	+	13.1311i	0.498809	+	0.498809i
$694$		0			0
$695$	13.6809	−	8.46093i	0.518944	−	0.320941i
$696$		0			0
$697$			13.0158i			0.493007i
$698$		0			0
$699$	1.59133			0.0601897
$700$		0			0
$701$			31.8458i			1.20280i	0.798949	+	0.601399i	$0.205390\pi$
$701$			31.8458i			1.20280i	−0.798949	+	0.601399i	$0.794610\pi$
$702$		0			0
$703$	−36.9443	+	36.9443i	−1.39338	+	1.39338i
$704$		0			0
$705$	−0.523414	+	2.22021i	−0.0197129	+	0.0836178i
$706$		0			0
$707$	33.5794			1.26288
$708$		0			0
$709$	−20.4104	+	20.4104i	−0.766528	+	0.766528i	−0.977493	−	0.210966i	$-0.932339\pi$
$709$	−20.4104	+	20.4104i	−0.766528	+	0.766528i	0.210966	+	0.977493i	$0.432339\pi$
$710$		0			0
$711$	−8.32607			−0.312252
$712$		0			0
$713$	−10.1002			−0.378255
$714$		0			0
$715$	−25.9599	−	24.8438i	−0.970844	−	0.929107i
$716$		0			0
$717$	17.6468			0.659030
$718$		0			0
$719$	31.3675			1.16981			0.584905	−	0.811102i	$-0.301132\pi$
$719$	31.3675			1.16981			0.584905	+	0.811102i	$0.301132\pi$
$720$		0			0
$721$	17.3309	−	17.3309i	0.645435	−	0.645435i
$722$		0			0
$723$	−1.80598			−0.0671652
$724$		0			0
$725$	17.5889	+	8.78121i	0.653235	+	0.326126i
$726$		0			0
$727$	13.3838	−	13.3838i	0.496379	−	0.496379i	−0.413930	−	0.910309i	$-0.635844\pi$
$727$	13.3838	−	13.3838i	0.496379	−	0.496379i	0.910309	+	0.413930i	$0.135844\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−67.9549			−2.51340
$732$		0			0
$733$			23.1954i			0.856740i	0.903603	+	0.428370i	$0.140912\pi$
$733$			23.1954i			0.856740i	−0.903603	+	0.428370i	$0.859088\pi$
$734$		0			0
$735$	22.5497	+	5.31609i	0.831758	+	0.196087i
$736$		0			0
$737$	37.4225	+	37.4225i	1.37847	+	1.37847i
$738$		0			0
$739$	−3.46527	+	3.46527i	−0.127472	+	0.127472i	−0.767965	−	0.640492i	$-0.778730\pi$
$739$	−3.46527	+	3.46527i	−0.127472	+	0.127472i	0.640492	+	0.767965i	$0.278730\pi$
$740$		0			0
$741$	11.3202	−	19.2361i	0.415858	−	0.706655i
$742$		0			0
$743$			1.29558i			0.0475301i	0.999718	+	0.0237650i	$0.00756536\pi$
$743$			1.29558i			0.0475301i	−0.999718	+	0.0237650i	$0.992435\pi$
$744$		0			0
$745$	−5.22299	+	22.1548i	−0.191356	+	0.811688i
$746$		0			0
$747$	15.1492			0.554282
$748$		0			0
$749$	7.85528	−	7.85528i	0.287026	−	0.287026i
$750$		0			0
$751$		−	1.38749i		−	0.0506301i	−0.999680	−	0.0253150i	$-0.991941\pi$
$751$		−	1.38749i		−	0.0506301i	0.999680	−	0.0253150i	$-0.00805889\pi$
$752$		0			0
$753$	13.8993	+	13.8993i	0.506520	+	0.506520i
$754$		0			0
$755$	−4.91798	+	20.8610i	−0.178984	+	0.759210i
$756$		0			0
$757$	−9.11127	−	9.11127i	−0.331155	−	0.331155i	0.521870	−	0.853025i	$-0.325235\pi$
$757$	−9.11127	−	9.11127i	−0.331155	−	0.331155i	−0.853025	+	0.521870i	$0.825235\pi$
$758$		0			0
$759$	−5.84735	−	5.84735i	−0.212245	−	0.212245i
$760$		0			0
$761$	−19.8539	−	19.8539i	−0.719703	−	0.719703i	0.248841	−	0.968544i	$-0.419950\pi$
$761$	−19.8539	−	19.8539i	−0.719703	−	0.719703i	−0.968544	+	0.248841i	$0.919950\pi$
$762$		0			0
$763$	−13.5549	+	13.5549i	−0.490721	+	0.490721i
$764$		0			0
$765$	−3.03750	+	12.8844i	−0.109821	+	0.465837i
$766$		0			0
$767$	1.83806	+	7.09513i	0.0663685	+	0.256190i
$768$		0			0
$769$	22.6182	+	22.6182i	0.815634	+	0.815634i	0.985472	−	0.169838i	$-0.0543243\pi$
$769$	22.6182	+	22.6182i	0.815634	+	0.815634i	−0.169838	+	0.985472i	$0.554324\pi$
$770$		0			0
$771$			29.5144i			1.06293i
$772$		0			0
$773$			20.5557i			0.739336i	0.929164	+	0.369668i	$0.120529\pi$
$773$			20.5557i			0.739336i	−0.929164	+	0.369668i	$0.879471\pi$
$774$		0			0
$775$	8.62258	+	25.8159i	0.309732	+	0.927335i
$776$		0			0
$777$	24.8666	−	24.8666i	0.892084	−	0.892084i
$778$		0			0
$779$	−13.6102			−0.487634
$780$		0			0
$781$	−71.8302			−2.57029
$782$		0			0
$783$	2.78021	−	2.78021i	0.0993567	−	0.0993567i
$784$		0			0
$785$	−8.28845	+	35.1578i	−0.295827	+	1.25483i
$786$		0			0
$787$		−	13.3191i		−	0.474774i	−0.971415	−	0.237387i	$-0.923709\pi$
$787$		−	13.3191i		−	0.474774i	0.971415	−	0.237387i	$-0.0762909\pi$
$788$		0			0
$789$			5.37895i			0.191496i
$790$		0			0
$791$	−32.4764	−	32.4764i	−1.15473	−	1.15473i
$792$		0			0
$793$	0.536775	−	0.912126i	0.0190614	−	0.0323906i
$794$		0			0
$795$	3.67099	−	2.27033i	0.130197	−	0.0805202i
$796$		0			0
$797$	20.3474	−	20.3474i	0.720743	−	0.720743i	−0.248014	−	0.968757i	$-0.579778\pi$
$797$	20.3474	−	20.3474i	0.720743	−	0.720743i	0.968757	+	0.248014i	$0.0797778\pi$
$798$		0			0
$799$	4.27035	+	4.27035i	0.151074	+	0.151074i
$800$		0			0
$801$	−6.44206	−	6.44206i	−0.227619	−	0.227619i
$802$		0			0
$803$	−20.3635	−	20.3635i	−0.718612	−	0.718612i
$804$		0			0
$805$	−16.8257	−	3.96666i	−0.593027	−	0.139806i
$806$		0			0
$807$	−2.34652	−	2.34652i	−0.0826015	−	0.0826015i
$808$		0			0
$809$			42.5767i			1.49692i	0.663182	+	0.748458i	$0.269205\pi$
$809$			42.5767i			1.49692i	−0.663182	+	0.748458i	$0.730795\pi$
$810$		0			0
$811$	22.7142	−	22.7142i	0.797603	−	0.797603i	−0.185114	−	0.982717i	$-0.559265\pi$
$811$	22.7142	−	22.7142i	0.797603	−	0.797603i	0.982717	+	0.185114i	$0.0592655\pi$
$812$		0			0
$813$	−7.87235			−0.276095
$814$		0			0
$815$	−18.2363	−	29.4871i	−0.638791	−	1.03289i
$816$		0			0
$817$		−	71.0583i		−	2.48601i
$818$		0			0
$819$	−7.61943	+	12.9475i	−0.266244	+	0.452421i
$820$		0			0
$821$	7.60013	−	7.60013i	0.265246	−	0.265246i	−0.561935	−	0.827181i	$-0.689943\pi$
$821$	7.60013	−	7.60013i	0.265246	−	0.265246i	0.827181	+	0.561935i	$0.189943\pi$
$822$		0			0
$823$	25.4074	+	25.4074i	0.885648	+	0.885648i	0.994101	−	0.108454i	$-0.0345900\pi$
$823$	25.4074	+	25.4074i	0.885648	+	0.885648i	−0.108454	+	0.994101i	$0.534590\pi$
$824$		0			0
$825$	−9.95383	+	19.9377i	−0.346548	+	0.694140i
$826$		0			0
$827$			37.7770i			1.31363i	0.754050	+	0.656817i	$0.228098\pi$
$827$			37.7770i			1.31363i	−0.754050	+	0.656817i	$0.771902\pi$
$828$		0			0
$829$	−32.0493			−1.11312			−0.556559	−	0.830808i	$-0.687878\pi$
$829$	−32.0493			−1.11312			−0.556559	+	0.830808i	$0.687878\pi$
$830$		0			0
$831$		−	4.24657i		−	0.147312i
$832$		0			0
$833$	43.3721	−	43.3721i	1.50276	−	1.50276i
$834$		0			0
$835$	20.5479	−	12.7079i	0.711090	−	0.439774i
$836$		0			0
$837$	5.44357			0.188157
$838$		0			0
$839$	−9.17521	+	9.17521i	−0.316763	+	0.316763i	−0.847523	−	0.530759i	$-0.821907\pi$
$839$	−9.17521	+	9.17521i	−0.316763	+	0.316763i	0.530759	+	0.847523i	$0.321907\pi$
$840$		0			0
$841$	13.5408			0.466926
$842$		0			0
$843$	−3.31796			−0.114277
$844$		0			0
$845$	14.1894	−	25.3705i	0.488131	−	0.872770i
$846$		0			0
$847$	36.9314			1.26898
$848$		0			0
$849$	−23.7472			−0.815000
$850$		0			0
$851$	−11.0732	+	11.0732i	−0.379586	+	0.379586i
$852$		0			0
$853$	25.1821			0.862220			0.431110	−	0.902299i	$-0.358122\pi$
$853$	25.1821			0.862220			0.431110	+	0.902299i	$0.358122\pi$
$854$		0			0
$855$	−13.4728	−	3.17622i	−0.460761	−	0.108624i
$856$		0			0
$857$	−7.17990	+	7.17990i	−0.245261	+	0.245261i	−0.819022	−	0.573762i	$-0.805484\pi$
$857$	−7.17990	+	7.17990i	−0.245261	+	0.245261i	0.573762	+	0.819022i	$0.305484\pi$
$858$		0			0
$859$		−	44.4341i		−	1.51607i	−0.652213	−	0.758036i	$-0.726159\pi$
$859$		−	44.4341i		−	1.51607i	0.652213	−	0.758036i	$-0.273841\pi$
$860$		0			0
$861$	9.16076			0.312198
$862$		0			0
$863$		−	21.1546i		−	0.720111i	−0.932931	−	0.360055i	$-0.882758\pi$
$863$		−	21.1546i		−	0.720111i	0.932931	−	0.360055i	$-0.117242\pi$
$864$		0			0
$865$	−5.52482	+	23.4351i	−0.187849	+	0.796816i
$866$		0			0
$867$	12.7611	+	12.7611i	0.433389	+	0.433389i
$868$		0			0
$869$	−26.2394	+	26.2394i	−0.890111	+	0.890111i
$870$		0			0
$871$	−21.7147	+	36.8992i	−0.735775	+	1.25028i
$872$		0			0
$873$			10.9521i			0.370671i
$874$		0			0
$875$	4.22546	+	46.3925i	0.142847	+	1.56835i
$876$		0			0
$877$	38.6352			1.30462			0.652309	−	0.757953i	$-0.273800\pi$
$877$	38.6352			1.30462			0.652309	+	0.757953i	$0.273800\pi$
$878$		0			0
$879$	−7.54686	+	7.54686i	−0.254549	+	0.254549i
$880$		0			0
$881$		−	17.4550i		−	0.588072i	−0.955794	−	0.294036i	$-0.905001\pi$
$881$		−	17.4550i		−	0.588072i	0.955794	−	0.294036i	$-0.0949986\pi$
$882$		0			0
$883$	−22.8569	−	22.8569i	−0.769196	−	0.769196i	0.208769	−	0.977965i	$-0.433054\pi$
$883$	−22.8569	−	22.8569i	−0.769196	−	0.769196i	−0.977965	+	0.208769i	$0.933054\pi$
$884$		0			0
$885$	3.86589	−	2.39086i	0.129950	−	0.0803678i
$886$		0			0
$887$	12.6394	+	12.6394i	0.424390	+	0.424390i	0.886712	−	0.462322i	$-0.152984\pi$
$887$	12.6394	+	12.6394i	0.424390	+	0.424390i	−0.462322	+	0.886712i	$0.652984\pi$
$888$		0			0
$889$	18.8107	+	18.8107i	0.630889	+	0.630889i
$890$		0			0
$891$	3.15147	+	3.15147i	0.105578	+	0.105578i
$892$		0			0
$893$	−4.46537	+	4.46537i	−0.149428	+	0.149428i
$894$		0			0
$895$	−15.5811	−	25.1938i	−0.520819	−	0.842136i
$896$		0			0
$897$	3.39298	−	5.76559i	0.113288	−	0.192507i
$898$		0			0
$899$	−15.1343	−	15.1343i	−0.504756	−	0.504756i
$900$		0			0
$901$		−	11.4275i		−	0.380707i
$902$		0			0
$903$			47.8281i			1.59162i
$904$		0			0
$905$	25.7427	−	15.9206i	0.855718	−	0.529219i
$906$		0			0
$907$	−16.4274	+	16.4274i	−0.545462	+	0.545462i	−0.925125	−	0.379663i	$-0.876040\pi$
$907$	−16.4274	+	16.4274i	−0.545462	+	0.545462i	0.379663	+	0.925125i	$0.376040\pi$
$908$		0			0
$909$	8.05908			0.267303
$910$		0			0
$911$	−2.40393			−0.0796456			−0.0398228	−	0.999207i	$-0.512679\pi$
$911$	−2.40393			−0.0796456			−0.0398228	+	0.999207i	$0.512679\pi$
$912$		0			0
$913$	47.7424	−	47.7424i	1.58004	−	1.58004i
$914$		0			0
$915$	−0.638847	−	0.150608i	−0.0211196	−	0.00497896i
$916$		0			0
$917$		−	26.9998i		−	0.891612i
$918$		0			0
$919$			7.76783i			0.256237i	0.991759	+	0.128118i	$0.0408938\pi$
$919$			7.76783i			0.256237i	−0.991759	+	0.128118i	$0.959106\pi$
$920$		0			0
$921$	−7.03604	−	7.03604i	−0.231845	−	0.231845i
$922$		0			0
$923$	−14.5729	−	56.2530i	−0.479671	−	1.85159i
$924$		0			0
$925$	37.7563	+	18.8498i	1.24142	+	0.619776i
$926$		0			0
$927$	4.15942	−	4.15942i	0.136613	−	0.136613i
$928$		0			0
$929$	17.0133	+	17.0133i	0.558189	+	0.558189i	0.928792	−	0.370602i	$-0.120849\pi$
$929$	17.0133	+	17.0133i	0.558189	+	0.558189i	−0.370602	+	0.928792i	$0.620849\pi$
$930$		0			0
$931$	45.3528	+	45.3528i	1.48638	+	1.48638i
$932$		0			0
$933$	−3.65328	−	3.65328i	−0.119603	−	0.119603i
$934$		0			0
$935$	31.0323	+	50.1775i	1.01486	+	1.64098i
$936$		0			0
$937$	6.62978	+	6.62978i	0.216586	+	0.216586i	0.807058	−	0.590472i	$-0.201059\pi$
$937$	6.62978	+	6.62978i	0.216586	+	0.216586i	−0.590472	+	0.807058i	$0.701059\pi$
$938$		0			0
$939$			3.91338i			0.127708i
$940$		0			0
$941$	−23.5888	+	23.5888i	−0.768973	+	0.768973i	−0.977926	−	0.208953i	$-0.932994\pi$
$941$	−23.5888	+	23.5888i	−0.768973	+	0.768973i	0.208953	+	0.977926i	$0.432994\pi$
$942$		0			0
$943$	−4.07934			−0.132842
$944$		0			0
$945$	9.06832	+	2.13786i	0.294993	+	0.0695445i
$946$		0			0
$947$			6.31026i			0.205056i	0.994730	+	0.102528i	$0.0326931\pi$
$947$			6.31026i			0.205056i	−0.994730	+	0.102528i	$0.967307\pi$
$948$		0			0
$949$	11.8161	−	20.0787i	0.383567	−	0.651784i
$950$		0			0
$951$	−20.6471	+	20.6471i	−0.669527	+	0.669527i
$952$		0			0
$953$	−4.37109	−	4.37109i	−0.141594	−	0.141594i	0.632757	−	0.774350i	$-0.281923\pi$
$953$	−4.37109	−	4.37109i	−0.141594	−	0.141594i	−0.774350	+	0.632757i	$0.781923\pi$
$954$		0			0
$955$	−27.6695	−	44.7401i	−0.895365	−	1.44776i
$956$		0			0
$957$		−	17.5235i		−	0.566455i
$958$		0			0
$959$	61.3755			1.98192
$960$		0			0
$961$			1.36757i			0.0441152i
$962$		0			0
$963$	1.88527	−	1.88527i	0.0607521	−	0.0607521i
$964$		0			0
$965$	14.8275	+	23.9753i	0.477315	+	0.771793i
$966$		0			0
$967$	−39.7361			−1.27783			−0.638914	−	0.769278i	$-0.720616\pi$
$967$	−39.7361			−1.27783			−0.638914	+	0.769278i	$0.720616\pi$
$968$		0			0
$969$	−25.9136	+	25.9136i	−0.832466	+	0.832466i
$970$		0			0
$971$	31.5420			1.01223			0.506115	−	0.862466i	$-0.331081\pi$
$971$	31.5420			1.01223			0.506115	+	0.862466i	$0.331081\pi$
$972$		0			0
$973$	−29.9740			−0.960923
$974$		0			0
$975$	−17.6334	−	3.75028i	−0.564719	−	0.120105i
$976$		0			0
$977$	−39.9665			−1.27864			−0.639322	−	0.768940i	$-0.720785\pi$
$977$	−39.9665			−1.27864			−0.639322	+	0.768940i	$0.720785\pi$
$978$		0			0
$979$	−40.6040			−1.29771
$980$		0			0
$981$	−3.25319	+	3.25319i	−0.103866	+	0.103866i
$982$		0			0
$983$	−23.4700			−0.748577			−0.374289	−	0.927312i	$-0.622113\pi$
$983$	−23.4700			−0.748577			−0.374289	+	0.927312i	$0.622113\pi$
$984$		0			0
$985$	−15.7763	−	25.5095i	−0.502676	−	0.812800i
$986$		0			0
$987$	3.00556	−	3.00556i	0.0956681	−	0.0956681i
$988$		0			0
$989$		−	21.2981i		−	0.677241i
$990$		0			0
$991$	33.6588			1.06921			0.534604	−	0.845103i	$-0.320461\pi$
$991$	33.6588			1.06921			0.534604	+	0.845103i	$0.320461\pi$
$992$		0			0
$993$		−	12.2908i		−	0.390037i
$994$		0			0
$995$	26.5615	+	42.9485i	0.842056	+	1.36156i
$996$		0			0
$997$	−16.7331	−	16.7331i	−0.529943	−	0.529943i	0.390613	−	0.920555i	$-0.372263\pi$
$997$	−16.7331	−	16.7331i	−0.529943	−	0.529943i	−0.920555	+	0.390613i	$0.872263\pi$
$998$		0			0
$999$	5.96801	−	5.96801i	0.188819	−	0.188819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.577.5	yes	28
3.2	odd	2		2340.2.u.i.577.6		28
5.2	odd	4		3900.2.bm.b.2293.14		28
5.3	odd	4		780.2.bm.a.733.2	yes	28
5.4	even	2		3900.2.r.b.1357.14		28
13.8	odd	4		780.2.bm.a.697.2	yes	28
15.8	even	4		2340.2.bp.i.1513.13		28
39.8	even	4		2340.2.bp.i.1477.13		28
65.8	even	4	inner	780.2.r.a.73.5	✓	28
65.34	odd	4		3900.2.bm.b.2257.14		28
65.47	even	4		3900.2.r.b.3193.14		28
195.8	odd	4		2340.2.u.i.73.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.5	✓	28	65.8	even	4	inner
780.2.r.a.577.5	yes	28	1.1	even	1	trivial
780.2.bm.a.697.2	yes	28	13.8	odd	4
780.2.bm.a.733.2	yes	28	5.3	odd	4
2340.2.u.i.73.6		28	195.8	odd	4
2340.2.u.i.577.6		28	3.2	odd	2
2340.2.bp.i.1477.13		28	39.8	even	4
2340.2.bp.i.1513.13		28	15.8	even	4
3900.2.r.b.1357.14		28	5.4	even	2
3900.2.r.b.3193.14		28	65.47	even	4
3900.2.bm.b.2257.14		28	65.34	odd	4
3900.2.bm.b.2293.14		28	5.2	odd	4

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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.17614 + 1.90176i) q^{5} -4.16665i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.17614 + 1.90176i) q^{5} -4.16665i q^{7} -1.00000i q^{9} +(-3.15147 - 3.15147i) q^{11} +(1.82867 - 3.10741i) q^{13} +(-2.17641 - 0.513088i) q^{15} +(-4.18610 + 4.18610i) q^{17} +(-4.37727 - 4.37727i) q^{19} +(2.94627 + 2.94627i) q^{21} +(-1.31199 - 1.31199i) q^{23} +(-2.23337 + 4.47348i) q^{25} +(0.707107 + 0.707107i) q^{27} -3.93181i q^{29} +(3.84918 - 3.84918i) q^{31} +4.45686 q^{33} +(7.92397 - 4.90058i) q^{35} -8.44004i q^{37} +(0.904203 + 3.49033i) q^{39} +(1.55464 - 1.55464i) q^{41} +(8.11673 + 8.11673i) q^{43} +(1.90176 - 1.17614i) q^{45} -1.02013i q^{47} -10.3610 q^{49} -5.92004i q^{51} +(-1.36494 + 1.36494i) q^{53} +(2.28676 - 9.69993i) q^{55} +6.19040 q^{57} +(-1.43740 + 1.43740i) q^{59} +0.293533 q^{61} -4.16665 q^{63} +(8.06031 - 0.177065i) q^{65} -11.8746 q^{67} +1.85543 q^{69} +(11.3963 - 11.3963i) q^{71} +6.46158 q^{73} +(-1.58400 - 4.74246i) q^{75} +(-13.1311 + 13.1311i) q^{77} -8.32607i q^{79} -1.00000 q^{81} +15.1492i q^{83} +(-12.8844 - 3.03750i) q^{85} +(2.78021 + 2.78021i) q^{87} +(6.44206 - 6.44206i) q^{89} +(-12.9475 - 7.61943i) q^{91} +5.44357i q^{93} +(3.17622 - 13.4728i) q^{95} -10.9521 q^{97} +(-3.15147 + 3.15147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more