LMFDB - Embedded newform 580.2.j.a.17.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [580,2,Mod(17,580)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("580.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(580, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 580 = 2^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	580.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.63132331723$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	580.17
Dual form			580.2.j.a.273.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.59876i q^{3} +(0.354774 + 2.20774i) q^{5} +(2.73334 + 2.73334i) q^{7} +0.443956 q^{9} +(0.540948 - 0.540948i) q^{11} +(-0.465868 - 0.465868i) q^{13} +(-3.52966 + 0.567199i) q^{15} -0.571038 q^{17} +(-1.93408 - 1.93408i) q^{19} +(-4.36997 + 4.36997i) q^{21} +(6.25942 - 6.25942i) q^{23} +(-4.74827 + 1.56650i) q^{25} +5.50607i q^{27} +(-5.26711 - 1.12141i) q^{29} +(-0.949715 + 0.949715i) q^{31} +(0.864848 + 0.864848i) q^{33} +(-5.06480 + 7.00424i) q^{35} +5.25961i q^{37} +(0.744813 - 0.744813i) q^{39} +(-0.530668 - 0.530668i) q^{41} -3.30374i q^{43} +(0.157504 + 0.980141i) q^{45} +4.38753i q^{47} +7.94231i q^{49} -0.912955i q^{51} +(6.54515 - 6.54515i) q^{53} +(1.38619 + 1.00236i) q^{55} +(3.09213 - 3.09213i) q^{57} -8.92693i q^{59} +(-4.64415 + 4.64415i) q^{61} +(1.21348 + 1.21348i) q^{63} +(0.863240 - 1.19380i) q^{65} +(0.0174362 - 0.0174362i) q^{67} +(10.0073 + 10.0073i) q^{69} -11.8667i q^{71} -14.6531 q^{73} +(-2.50446 - 7.59136i) q^{75} +2.95719 q^{77} +(4.36262 + 4.36262i) q^{79} -7.47104 q^{81} +(5.02761 - 5.02761i) q^{83} +(-0.202589 - 1.26071i) q^{85} +(1.79287 - 8.42086i) q^{87} +(11.5796 + 11.5796i) q^{89} -2.54675i q^{91} +(-1.51837 - 1.51837i) q^{93} +(3.58379 - 4.95611i) q^{95} -9.37991i q^{97} +(0.240157 - 0.240157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) $ 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$.

$n$	$117$	$291$	$321$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			1.59876i			0.923046i	0.887128	+	0.461523i	$0.152697\pi$
$3$			1.59876i			0.923046i	−0.887128	+	0.461523i	$0.847303\pi$
$4$		0			0
$5$	0.354774	+	2.20774i	0.158660	+	0.987333i
$5$	0.354774	+	2.20774i	0.158660	+	0.987333i
$6$		0			0
$7$	2.73334	+	2.73334i	1.03311	+	1.03311i	0.999433	+	0.0336728i	$0.0107204\pi$
$7$	2.73334	+	2.73334i	1.03311	+	1.03311i	0.0336728	+	0.999433i	$0.489280\pi$
$8$		0			0
$9$	0.443956			0.147985
$10$		0			0
$11$	0.540948	−	0.540948i	0.163102	−	0.163102i	−0.620837	−	0.783939i	$-0.713207\pi$
$11$	0.540948	−	0.540948i	0.163102	−	0.163102i	0.783939	+	0.620837i	$0.213207\pi$
$12$		0			0
$13$	−0.465868	−	0.465868i	−0.129209	−	0.129209i	0.639545	−	0.768754i	$-0.279123\pi$
$13$	−0.465868	−	0.465868i	−0.129209	−	0.129209i	−0.768754	+	0.639545i	$0.779123\pi$
$14$		0			0
$15$	−3.52966	+	0.567199i	−0.911355	+	0.146450i
$16$		0			0
$17$	−0.571038			−0.138497			−0.0692485	−	0.997599i	$-0.522060\pi$
$17$	−0.571038			−0.138497			−0.0692485	+	0.997599i	$0.522060\pi$
$18$		0			0
$19$	−1.93408	−	1.93408i	−0.443708	−	0.443708i	0.449548	−	0.893256i	$-0.351585\pi$
$19$	−1.93408	−	1.93408i	−0.443708	−	0.443708i	−0.893256	+	0.449548i	$0.851585\pi$
$20$		0			0
$21$	−4.36997	+	4.36997i	−0.953605	+	0.953605i
$22$		0			0
$23$	6.25942	−	6.25942i	1.30518	−	1.30518i	0.380328	−	0.924852i	$-0.375811\pi$
$23$	6.25942	−	6.25942i	1.30518	−	1.30518i	0.924852	−	0.380328i	$-0.124189\pi$
$24$		0			0
$25$	−4.74827	+	1.56650i	−0.949654	+	0.313300i
$26$		0			0
$27$			5.50607i			1.05964i
$28$		0			0
$29$	−5.26711	−	1.12141i	−0.978078	−	0.208240i
$29$	−5.26711	−	1.12141i	−0.978078	−	0.208240i
$30$		0			0
$31$	−0.949715	+	0.949715i	−0.170574	+	0.170574i	−0.787231	−	0.616658i	$-0.788486\pi$
$31$	−0.949715	+	0.949715i	−0.170574	+	0.170574i	0.616658	+	0.787231i	$0.288486\pi$
$32$		0			0
$33$	0.864848	+	0.864848i	0.150551	+	0.150551i
$34$		0			0
$35$	−5.06480	+	7.00424i	−0.856108	+	1.18393i
$36$		0			0
$37$			5.25961i			0.864674i	0.901712	+	0.432337i	$0.142311\pi$
$37$			5.25961i			0.864674i	−0.901712	+	0.432337i	$0.857689\pi$
$38$		0			0
$39$	0.744813	−	0.744813i	0.119265	−	0.119265i
$40$		0			0
$41$	−0.530668	−	0.530668i	−0.0828764	−	0.0828764i	0.664453	−	0.747330i	$-0.268664\pi$
$41$	−0.530668	−	0.530668i	−0.0828764	−	0.0828764i	−0.747330	+	0.664453i	$0.768664\pi$
$42$		0			0
$43$		−	3.30374i		−	0.503816i	−0.967751	−	0.251908i	$-0.918942\pi$
$43$		−	3.30374i		−	0.503816i	0.967751	−	0.251908i	$-0.0810581\pi$
$44$		0			0
$45$	0.157504	+	0.980141i	0.0234793	+	0.146111i
$46$		0			0
$47$			4.38753i			0.639987i	0.947420	+	0.319994i	$0.103681\pi$
$47$			4.38753i			0.639987i	−0.947420	+	0.319994i	$0.896319\pi$
$48$		0			0
$49$			7.94231i			1.13462i
$50$		0			0
$51$		−	0.912955i		−	0.127839i
$52$		0			0
$53$	6.54515	−	6.54515i	0.899046	−	0.899046i	−0.0963061	−	0.995352i	$-0.530703\pi$
$53$	6.54515	−	6.54515i	0.899046	−	0.899046i	0.995352	+	0.0963061i	$0.0307028\pi$
$54$		0			0
$55$	1.38619	+	1.00236i	0.186914	+	0.135158i
$56$		0			0
$57$	3.09213	−	3.09213i	0.409563	−	0.409563i
$58$		0			0
$59$		−	8.92693i		−	1.16219i	−0.813837	−	0.581094i	$-0.802625\pi$
$59$		−	8.92693i		−	1.16219i	0.813837	−	0.581094i	$-0.197375\pi$
$60$		0			0
$61$	−4.64415	+	4.64415i	−0.594623	+	0.594623i	−0.938877	−	0.344254i	$-0.888132\pi$
$61$	−4.64415	+	4.64415i	−0.594623	+	0.594623i	0.344254	+	0.938877i	$0.388132\pi$
$62$		0			0
$63$	1.21348	+	1.21348i	0.152884	+	0.152884i
$64$		0			0
$65$	0.863240	−	1.19380i	0.107072	−	0.148072i
$66$		0			0
$67$	0.0174362	−	0.0174362i	0.00213017	−	0.00213017i	−0.706041	−	0.708171i	$-0.749521\pi$
$67$	0.0174362	−	0.0174362i	0.00213017	−	0.00213017i	0.708171	+	0.706041i	$0.249521\pi$
$68$		0			0
$69$	10.0073	+	10.0073i	1.20474	+	1.20474i
$70$		0			0
$71$		−	11.8667i		−	1.40832i	−0.710040	−	0.704162i	$-0.751323\pi$
$71$		−	11.8667i		−	1.40832i	0.710040	−	0.704162i	$-0.248677\pi$
$72$		0			0
$73$	−14.6531			−1.71502			−0.857509	−	0.514469i	$-0.827989\pi$
$73$	−14.6531			−1.71502			−0.857509	+	0.514469i	$0.827989\pi$
$74$		0			0
$75$	−2.50446	−	7.59136i	−0.289190	−	0.876575i
$76$		0			0
$77$	2.95719			0.337003
$78$		0			0
$79$	4.36262	+	4.36262i	0.490834	+	0.490834i	0.908569	−	0.417735i	$-0.137176\pi$
$79$	4.36262	+	4.36262i	0.490834	+	0.490834i	−0.417735	+	0.908569i	$0.637176\pi$
$80$		0			0
$81$	−7.47104			−0.830115
$82$		0			0
$83$	5.02761	−	5.02761i	0.551852	−	0.551852i	−0.375123	−	0.926975i	$-0.622399\pi$
$83$	5.02761	−	5.02761i	0.551852	−	0.551852i	0.926975	+	0.375123i	$0.122399\pi$
$84$		0			0
$85$	−0.202589	−	1.26071i	−0.0219739	−	0.136743i
$86$		0			0
$87$	1.79287	−	8.42086i	0.192215	−	0.902811i
$88$		0			0
$89$	11.5796	+	11.5796i	1.22744	+	1.22744i	0.964929	+	0.262512i	$0.0845508\pi$
$89$	11.5796	+	11.5796i	1.22744	+	1.22744i	0.262512	+	0.964929i	$0.415449\pi$
$90$		0			0
$91$		−	2.54675i		−	0.266972i
$92$		0			0
$93$	−1.51837	−	1.51837i	−0.157448	−	0.157448i
$94$		0			0
$95$	3.58379	−	4.95611i	0.367689	−	0.508486i
$96$		0			0
$97$		−	9.37991i		−	0.952386i	−0.879341	−	0.476193i	$-0.842016\pi$
$97$		−	9.37991i		−	0.952386i	0.879341	−	0.476193i	$-0.157984\pi$
$98$		0			0
$99$	0.240157	−	0.240157i	0.0241367	−	0.0241367i
$100$		0			0
$101$	−7.61081	+	7.61081i	−0.757304	+	0.757304i	−0.975831	−	0.218527i	$-0.929875\pi$
$101$	−7.61081	+	7.61081i	−0.757304	+	0.757304i	0.218527	+	0.975831i	$0.429875\pi$
$102$		0			0
$103$	13.2004	−	13.2004i	1.30067	−	1.30067i	0.372735	−	0.927938i	$-0.378420\pi$
$103$	13.2004	−	13.2004i	1.30067	−	1.30067i	0.927938	−	0.372735i	$-0.121580\pi$
$104$		0			0
$105$	−11.1981	−	8.09742i	−1.09282	−	0.790227i
$106$		0			0
$107$	−0.546180	−	0.546180i	−0.0528012	−	0.0528012i	0.680213	−	0.733014i	$-0.261887\pi$
$107$	−0.546180	−	0.546180i	−0.0528012	−	0.0528012i	−0.733014	+	0.680213i	$0.761887\pi$
$108$		0			0
$109$	0.885913			0.0848551			0.0424276	−	0.999100i	$-0.486491\pi$
$109$	0.885913			0.0848551			0.0424276	+	0.999100i	$0.486491\pi$
$110$		0			0
$111$	−8.40887			−0.798135
$112$		0			0
$113$	11.0070			1.03545			0.517725	−	0.855547i	$-0.326779\pi$
$113$	11.0070			1.03545			0.517725	+	0.855547i	$0.326779\pi$
$114$		0			0
$115$	16.0399	+	11.5985i	1.49573	+	1.08157i
$116$		0			0
$117$	−0.206825	−	0.206825i	−0.0191210	−	0.0191210i
$118$		0			0
$119$	−1.56084	−	1.56084i	−0.143082	−	0.143082i
$120$		0			0
$121$			10.4147i			0.946795i
$122$		0			0
$123$	0.848412	−	0.848412i	0.0764987	−	0.0764987i
$124$		0			0
$125$	−5.14299	−	9.92722i	−0.460003	−	0.887917i
$126$		0			0
$127$	15.6734			1.39079			0.695393	−	0.718629i	$-0.255230\pi$
$127$	15.6734			1.39079			0.695393	+	0.718629i	$0.255230\pi$
$128$		0			0
$129$	5.28191			0.465046
$130$		0			0
$131$	−6.51257	−	6.51257i	−0.569006	−	0.569006i	0.362844	−	0.931850i	$-0.381806\pi$
$131$	−6.51257	−	6.51257i	−0.569006	−	0.569006i	−0.931850	+	0.362844i	$0.881806\pi$
$132$		0			0
$133$		−	10.5730i		−	0.916794i
$134$		0			0
$135$	−12.1560	+	1.95341i	−1.04622	+	0.168123i
$136$		0			0
$137$	11.5453			0.986377			0.493189	−	0.869922i	$-0.335831\pi$
$137$	11.5453			0.986377			0.493189	+	0.869922i	$0.335831\pi$
$138$		0			0
$139$			8.81876i			0.747998i	0.927429	+	0.373999i	$0.122014\pi$
$139$			8.81876i			0.747998i	−0.927429	+	0.373999i	$0.877986\pi$
$140$		0			0
$141$	−7.01463			−0.590738
$142$		0			0
$143$	−0.504021			−0.0421484
$144$		0			0
$145$	0.607150	−	12.0263i	0.0504211	−	0.998728i
$146$		0			0
$147$	−12.6979			−1.04730
$148$		0			0
$149$	−3.80606			−0.311805			−0.155902	−	0.987772i	$-0.549828\pi$
$149$	−3.80606			−0.311805			−0.155902	+	0.987772i	$0.549828\pi$
$150$		0			0
$151$		−	11.4672i		−	0.933189i	−0.884471	−	0.466594i	$-0.845481\pi$
$151$		−	11.4672i		−	0.933189i	0.884471	−	0.466594i	$-0.154519\pi$
$152$		0			0
$153$	−0.253516			−0.0204955
$154$		0			0
$155$	−2.43366	−	1.75979i	−0.195476	−	0.141350i
$156$		0			0
$157$			0.537589i			0.0429043i	0.999770	+	0.0214521i	$0.00682895\pi$
$157$			0.537589i			0.0429043i	−0.999770	+	0.0214521i	$0.993171\pi$
$158$		0			0
$159$	10.4641	+	10.4641i	0.829861	+	0.829861i
$160$		0			0
$161$	34.2183			2.69678
$162$		0			0
$163$	−13.2459			−1.03750			−0.518749	−	0.854927i	$-0.673602\pi$
$163$	−13.2459			−1.03750			−0.518749	+	0.854927i	$0.673602\pi$
$164$		0			0
$165$	−1.60254	+	2.21619i	−0.124757	+	0.172530i
$166$		0			0
$167$	3.79513	−	3.79513i	0.293676	−	0.293676i	−0.544855	−	0.838530i	$-0.683415\pi$
$167$	3.79513	−	3.79513i	0.293676	−	0.293676i	0.838530	+	0.544855i	$0.183415\pi$
$168$		0			0
$169$		−	12.5659i		−	0.966610i
$170$		0			0
$171$	−0.858645	−	0.858645i	−0.0656622	−	0.0656622i
$172$		0			0
$173$	−1.76397	−	1.76397i	−0.134112	−	0.134112i	0.636864	−	0.770976i	$-0.280231\pi$
$173$	−1.76397	−	1.76397i	−0.134112	−	0.134112i	−0.770976	+	0.636864i	$0.780231\pi$
$174$		0			0
$175$	−17.2604	−	8.69687i	−1.30477	−	0.657422i
$176$		0			0
$177$	14.2720			1.07275
$178$		0			0
$179$	−6.91648			−0.516962			−0.258481	−	0.966016i	$-0.583222\pi$
$179$	−6.91648			−0.516962			−0.258481	+	0.966016i	$0.583222\pi$
$180$		0			0
$181$	−7.06719			−0.525300			−0.262650	−	0.964891i	$-0.584596\pi$
$181$	−7.06719			−0.525300			−0.262650	+	0.964891i	$0.584596\pi$
$182$		0			0
$183$	−7.42490	−	7.42490i	−0.548864	−	0.548864i
$184$		0			0
$185$	−11.6119	+	1.86597i	−0.853722	+	0.137189i
$186$		0			0
$187$	−0.308902	+	0.308902i	−0.0225892	+	0.0225892i
$188$		0			0
$189$	−15.0500	+	15.0500i	−1.09472	+	1.09472i
$190$		0			0
$191$	12.7210	−	12.7210i	0.920461	−	0.920461i	−0.0766013	−	0.997062i	$-0.524407\pi$
$191$	12.7210	−	12.7210i	0.920461	−	0.920461i	0.997062	+	0.0766013i	$0.0244069\pi$
$192$		0			0
$193$			19.9168i			1.43364i	0.697258	+	0.716820i	$0.254403\pi$
$193$			19.9168i			1.43364i	−0.697258	+	0.716820i	$0.745597\pi$
$194$		0			0
$195$	1.90860	+	1.38012i	0.136677	+	0.0988322i
$196$		0			0
$197$	−10.8133	−	10.8133i	−0.770415	−	0.770415i	0.207764	−	0.978179i	$-0.433381\pi$
$197$	−10.8133	−	10.8133i	−0.770415	−	0.770415i	−0.978179	+	0.207764i	$0.933381\pi$
$198$		0			0
$199$			3.67921i			0.260813i	0.991461	+	0.130406i	$0.0416282\pi$
$199$			3.67921i			0.260813i	−0.991461	+	0.130406i	$0.958372\pi$
$200$		0			0
$201$	0.0278763	+	0.0278763i	0.00196624	+	0.00196624i
$202$		0			0
$203$	−11.3316	−	17.4620i	−0.795324	−	1.22559i
$204$		0			0
$205$	0.983312	−	1.35985i	0.0686775	−	0.0949757i
$206$		0			0
$207$	2.77891	−	2.77891i	0.193147	−	0.193147i
$208$		0			0
$209$	−2.09247			−0.144739
$210$		0			0
$211$	17.0895	+	17.0895i	1.17649	+	1.17649i	0.980632	+	0.195859i	$0.0627494\pi$
$211$	17.0895	+	17.0895i	1.17649	+	1.17649i	0.195859	+	0.980632i	$0.437251\pi$
$212$		0			0
$213$	18.9721			1.29995
$214$		0			0
$215$	7.29382	−	1.17208i	0.497435	−	0.0799353i
$216$		0			0
$217$	−5.19179			−0.352442
$218$		0			0
$219$		−	23.4269i		−	1.58304i
$220$		0			0
$221$	0.266028	+	0.266028i	0.0178950	+	0.0178950i
$222$		0			0
$223$	−11.7975	+	11.7975i	−0.790021	+	0.790021i	−0.981497	−	0.191476i	$-0.938672\pi$
$223$	−11.7975	+	11.7975i	−0.790021	+	0.790021i	0.191476	+	0.981497i	$0.438672\pi$
$224$		0			0
$225$	−2.10802	+	0.695456i	−0.140535	+	0.0463638i
$226$		0			0
$227$	20.4040	+	20.4040i	1.35426	+	1.35426i	0.880833	+	0.473426i	$0.156983\pi$
$227$	20.4040	+	20.4040i	1.35426	+	1.35426i	0.473426	+	0.880833i	$0.343017\pi$
$228$		0			0
$229$	−1.42489	+	1.42489i	−0.0941594	+	0.0941594i	−0.752617	−	0.658458i	$-0.771209\pi$
$229$	−1.42489	+	1.42489i	−0.0941594	+	0.0941594i	0.658458	+	0.752617i	$0.271209\pi$
$230$		0			0
$231$			4.72785i			0.311070i
$232$		0			0
$233$	−4.38963	+	4.38963i	−0.287574	+	0.287574i	−0.836120	−	0.548546i	$-0.815181\pi$
$233$	−4.38963	+	4.38963i	−0.287574	+	0.287574i	0.548546	+	0.836120i	$0.315181\pi$
$234$		0			0
$235$	−9.68655	+	1.55658i	−0.631881	+	0.101540i
$236$		0			0
$237$	−6.97480	+	6.97480i	−0.453062	+	0.453062i
$238$		0			0
$239$		−	10.4062i		−	0.673124i	−0.941661	−	0.336562i	$-0.890736\pi$
$239$		−	10.4062i		−	0.673124i	0.941661	−	0.336562i	$-0.109264\pi$
$240$		0			0
$241$			24.1496i			1.55561i	0.628506	+	0.777805i	$0.283667\pi$
$241$			24.1496i			1.55561i	−0.628506	+	0.777805i	$0.716333\pi$
$242$		0			0
$243$			4.57379i			0.293409i
$244$		0			0
$245$	−17.5346	+	2.81772i	−1.12024	+	0.180018i
$246$		0			0
$247$			1.80205i			0.114662i
$248$		0			0
$249$	8.03797	+	8.03797i	0.509385	+	0.509385i
$250$		0			0
$251$	−10.3137	+	10.3137i	−0.650994	+	0.650994i	−0.953232	−	0.302239i	$-0.902266\pi$
$251$	−10.3137	+	10.3137i	−0.650994	+	0.650994i	0.302239	+	0.953232i	$0.402266\pi$
$252$		0			0
$253$		−	6.77205i		−	0.425755i
$254$		0			0
$255$	2.01557	−	0.323892i	0.126220	−	0.0202829i
$256$		0			0
$257$	−5.97197	−	5.97197i	−0.372521	−	0.372521i	0.495873	−	0.868395i	$-0.334848\pi$
$257$	−5.97197	−	5.97197i	−0.372521	−	0.372521i	−0.868395	+	0.495873i	$0.834848\pi$
$258$		0			0
$259$	−14.3763	+	14.3763i	−0.893300	+	0.893300i
$260$		0			0
$261$	−2.33836	−	0.497856i	−0.144741	−	0.0308165i
$262$		0			0
$263$		−	3.95032i		−	0.243587i	−0.992555	−	0.121794i	$-0.961135\pi$
$263$		−	3.95032i		−	0.243587i	0.992555	−	0.121794i	$-0.0388646\pi$
$264$		0			0
$265$	16.7721	+	12.1280i	1.03030	+	0.745016i
$266$		0			0
$267$	−18.5131	+	18.5131i	−1.13298	+	1.13298i
$268$		0			0
$269$	9.67629	−	9.67629i	0.589974	−	0.589974i	−0.347650	−	0.937624i	$-0.613020\pi$
$269$	9.67629	−	9.67629i	0.589974	−	0.589974i	0.937624	+	0.347650i	$0.113020\pi$
$270$		0			0
$271$	−9.74383	−	9.74383i	−0.591896	−	0.591896i	0.346248	−	0.938143i	$-0.387456\pi$
$271$	−9.74383	−	9.74383i	−0.591896	−	0.591896i	−0.938143	+	0.346248i	$0.887456\pi$
$272$		0			0
$273$	4.07165			0.246428
$274$		0			0
$275$	−1.72117	+	3.41596i	−0.103791	+	0.205990i
$276$		0			0
$277$	12.5005	+	12.5005i	0.751083	+	0.751083i	0.974681	−	0.223598i	$-0.0717803\pi$
$277$	12.5005	+	12.5005i	0.751083	+	0.751083i	−0.223598	+	0.974681i	$0.571780\pi$
$278$		0			0
$279$	−0.421632	+	0.421632i	−0.0252424	+	0.0252424i
$280$		0			0
$281$	12.1452			0.724520			0.362260	−	0.932077i	$-0.382005\pi$
$281$	12.1452			0.724520			0.362260	+	0.932077i	$0.382005\pi$
$282$		0			0
$283$	17.0171	+	17.0171i	1.01156	+	1.01156i	0.999932	+	0.0116316i	$0.00370253\pi$
$283$	17.0171	+	17.0171i	1.01156	+	1.01156i	0.0116316	+	0.999932i	$0.496297\pi$
$284$		0			0
$285$	7.92364	+	5.72963i	0.469356	+	0.339394i
$286$		0			0
$287$		−	2.90099i		−	0.171240i
$288$		0			0
$289$	−16.6739			−0.980819
$290$		0			0
$291$	14.9963			0.879096
$292$		0			0
$293$		−	7.40058i		−	0.432347i	−0.976355	−	0.216173i	$-0.930642\pi$
$293$		−	7.40058i		−	0.432347i	0.976355	−	0.216173i	$-0.0693576\pi$
$294$		0			0
$295$	19.7084	−	3.16704i	1.14747	−	0.184392i
$296$		0			0
$297$	2.97850	+	2.97850i	0.172830	+	0.172830i
$298$		0			0
$299$	−5.83213			−0.337281
$300$		0			0
$301$	9.03026	−	9.03026i	0.520496	−	0.520496i
$302$		0			0
$303$	−12.1679	−	12.1679i	−0.699027	−	0.699027i
$304$		0			0
$305$	−11.9007	−	8.60548i	−0.681433	−	0.492748i
$306$		0			0
$307$	4.42252			0.252406			0.126203	−	0.992004i	$-0.459721\pi$
$307$	4.42252			0.252406			0.126203	+	0.992004i	$0.459721\pi$
$308$		0			0
$309$	21.1043	+	21.1043i	1.20058	+	1.20058i
$310$		0			0
$311$	−20.5726	+	20.5726i	−1.16656	+	1.16656i	−0.183555	+	0.983009i	$0.558760\pi$
$311$	−20.5726	+	20.5726i	−1.16656	+	1.16656i	−0.983009	+	0.183555i	$0.941240\pi$
$312$		0			0
$313$	9.32856	−	9.32856i	0.527281	−	0.527281i	−0.392479	−	0.919761i	$-0.628383\pi$
$313$	9.32856	−	9.32856i	0.527281	−	0.527281i	0.919761	+	0.392479i	$0.128383\pi$
$314$		0			0
$315$	−2.24855	+	3.10957i	−0.126691	+	0.175205i
$316$		0			0
$317$		−	23.0848i		−	1.29657i	−0.761396	−	0.648287i	$-0.775486\pi$
$317$		−	23.0848i		−	1.29657i	0.761396	−	0.648287i	$-0.224514\pi$
$318$		0			0
$319$	−3.45586	+	2.24261i	−0.193491	+	0.125562i
$320$		0			0
$321$	0.873213	−	0.873213i	0.0487380	−	0.0487380i
$322$		0			0
$323$	1.10443	+	1.10443i	0.0614522	+	0.0614522i
$324$		0			0
$325$	2.94185	+	1.48229i	0.163184	+	0.0822224i
$326$		0			0
$327$			1.41637i			0.0783252i
$328$		0			0
$329$	−11.9926	+	11.9926i	−0.661175	+	0.661175i
$330$		0			0
$331$	−9.25474	−	9.25474i	−0.508687	−	0.508687i	0.405437	−	0.914123i	$-0.367120\pi$
$331$	−9.25474	−	9.25474i	−0.508687	−	0.508687i	−0.914123	+	0.405437i	$0.867120\pi$
$332$		0			0
$333$			2.33503i			0.127959i
$334$		0			0
$335$	0.0446805	+	0.0323087i	0.00244116	+	0.00176522i
$336$		0			0
$337$			15.5360i			0.846300i	0.906060	+	0.423150i	$0.139076\pi$
$337$			15.5360i			0.846300i	−0.906060	+	0.423150i	$0.860924\pi$
$338$		0			0
$339$			17.5976i			0.955768i
$340$		0			0
$341$			1.02749i			0.0556419i
$342$		0			0
$343$	−2.57564	+	2.57564i	−0.139072	+	0.139072i
$344$		0			0
$345$	−18.5433	+	25.6440i	−0.998338	+	1.38063i
$346$		0			0
$347$	−11.9908	+	11.9908i	−0.643699	+	0.643699i	−0.951463	−	0.307764i	$-0.900419\pi$
$347$	−11.9908	+	11.9908i	−0.643699	+	0.643699i	0.307764	+	0.951463i	$0.400419\pi$
$348$		0			0
$349$			0.282167i			0.0151040i	0.999971	+	0.00755202i	$0.00240391\pi$
$349$			0.282167i			0.0151040i	−0.999971	+	0.00755202i	$0.997596\pi$
$350$		0			0
$351$	2.56510	−	2.56510i	0.136915	−	0.136915i
$352$		0			0
$353$	4.73357	+	4.73357i	0.251942	+	0.251942i	0.821767	−	0.569824i	$-0.192989\pi$
$353$	4.73357	+	4.73357i	0.251942	+	0.251942i	−0.569824	+	0.821767i	$0.692989\pi$
$354$		0			0
$355$	26.1987	−	4.21001i	1.39048	−	0.223444i
$356$		0			0
$357$	2.49542	−	2.49542i	0.132071	−	0.132071i
$358$		0			0
$359$	−18.2309	−	18.2309i	−0.962190	−	0.962190i	0.0371209	−	0.999311i	$-0.488181\pi$
$359$	−18.2309	−	18.2309i	−0.962190	−	0.962190i	−0.999311	+	0.0371209i	$0.988181\pi$
$360$		0			0
$361$		−	11.5187i		−	0.606247i
$362$		0			0
$363$	−16.6507			−0.873936
$364$		0			0
$365$	−5.19854	−	32.3503i	−0.272104	−	1.69329i
$366$		0			0
$367$	−13.2026			−0.689170			−0.344585	−	0.938755i	$-0.611980\pi$
$367$	−13.2026			−0.689170			−0.344585	+	0.938755i	$0.611980\pi$
$368$		0			0
$369$	−0.235593	−	0.235593i	−0.0122645	−	0.0122645i
$370$		0			0
$371$	35.7803			1.85762
$372$		0			0
$373$	−24.9507	+	24.9507i	−1.29190	+	1.29190i	−0.358287	+	0.933611i	$0.616639\pi$
$373$	−24.9507	+	24.9507i	−1.29190	+	1.29190i	−0.933611	+	0.358287i	$0.883361\pi$
$374$		0			0
$375$	15.8713	−	8.22242i	0.819589	−	0.424604i
$376$		0			0
$377$	1.93135	+	2.97621i	0.0994696	+	0.153282i
$378$		0			0
$379$	19.3447	+	19.3447i	0.993673	+	0.993673i	0.999980	−	0.00630710i	$-0.00200762\pi$
$379$	19.3447	+	19.3447i	0.993673	+	0.993673i	−0.00630710	+	0.999980i	$0.502008\pi$
$380$		0			0
$381$			25.0580i			1.28376i
$382$		0			0
$383$	16.6755	+	16.6755i	0.852081	+	0.852081i	0.990389	−	0.138309i	$-0.0441666\pi$
$383$	16.6755	+	16.6755i	0.852081	+	0.852081i	−0.138309	+	0.990389i	$0.544167\pi$
$384$		0			0
$385$	1.04913	+	6.52873i	0.0534688	+	0.332735i
$386$		0			0
$387$		−	1.46672i		−	0.0745574i
$388$		0			0
$389$	16.4901	−	16.4901i	0.836083	−	0.836083i	−0.152258	−	0.988341i	$-0.548654\pi$
$389$	16.4901	−	16.4901i	0.836083	−	0.836083i	0.988341	+	0.152258i	$0.0486543\pi$
$390$		0			0
$391$	−3.57437	+	3.57437i	−0.180764	+	0.180764i
$392$		0			0
$393$	10.4121	−	10.4121i	0.525219	−	0.525219i
$394$		0			0
$395$	−8.08381	+	11.1793i	−0.406741	+	0.562492i
$396$		0			0
$397$	−16.6280	−	16.6280i	−0.834537	−	0.834537i	0.153597	−	0.988134i	$-0.450914\pi$
$397$	−16.6280	−	16.6280i	−0.834537	−	0.834537i	−0.988134	+	0.153597i	$0.950914\pi$
$398$		0			0
$399$	16.9037			0.846243
$400$		0			0
$401$	−12.5399			−0.626213			−0.313107	−	0.949718i	$-0.601370\pi$
$401$	−12.5399			−0.626213			−0.313107	+	0.949718i	$0.601370\pi$
$402$		0			0
$403$	0.884883			0.0440792
$404$		0			0
$405$	−2.65053	−	16.4941i	−0.131706	−	0.819600i
$406$		0			0
$407$	2.84518	+	2.84518i	0.141030	+	0.141030i
$408$		0			0
$409$	−17.2547	−	17.2547i	−0.853190	−	0.853190i	0.137335	−	0.990525i	$-0.456146\pi$
$409$	−17.2547	−	17.2547i	−0.853190	−	0.853190i	−0.990525	+	0.137335i	$0.956146\pi$
$410$		0			0
$411$			18.4581i			0.910472i
$412$		0			0
$413$	24.4003	−	24.4003i	1.20066	−	1.20066i
$414$		0			0
$415$	12.8834	+	9.31602i	0.632419	+	0.457306i
$416$		0			0
$417$	−14.0991			−0.690437
$418$		0			0
$419$	−27.7375			−1.35507			−0.677533	−	0.735493i	$-0.736951\pi$
$419$	−27.7375			−1.35507			−0.677533	+	0.735493i	$0.736951\pi$
$420$		0			0
$421$	−20.6612	−	20.6612i	−1.00697	−	1.00697i	−0.999976	−	0.00699138i	$-0.997775\pi$
$421$	−20.6612	−	20.6612i	−1.00697	−	1.00697i	−0.00699138	−	0.999976i	$-0.502225\pi$
$422$		0			0
$423$			1.94787i			0.0947087i
$424$		0			0
$425$	2.71144	−	0.894530i	0.131524	−	0.0433911i
$426$		0			0
$427$	−25.3881			−1.22862
$428$		0			0
$429$		−	0.805810i		−	0.0389049i
$430$		0			0
$431$	−2.03736			−0.0981361			−0.0490680	−	0.998795i	$-0.515625\pi$
$431$	−2.03736			−0.0981361			−0.0490680	+	0.998795i	$0.515625\pi$
$432$		0			0
$433$	−13.7625			−0.661382			−0.330691	−	0.943739i	$-0.607282\pi$
$433$	−13.7625			−0.661382			−0.330691	+	0.943739i	$0.607282\pi$
$434$		0			0
$435$	19.2272	+	0.970689i	0.921872	+	0.0465410i
$436$		0			0
$437$	−24.2124			−1.15824
$438$		0			0
$439$	18.3739			0.876940			0.438470	−	0.898746i	$-0.355521\pi$
$439$	18.3739			0.876940			0.438470	+	0.898746i	$0.355521\pi$
$440$		0			0
$441$			3.52603i			0.167906i
$442$		0			0
$443$	2.63915			0.125390			0.0626949	−	0.998033i	$-0.480030\pi$
$443$	2.63915			0.125390			0.0626949	+	0.998033i	$0.480030\pi$
$444$		0			0
$445$	−21.4568	+	29.6731i	−1.01715	+	1.40664i
$446$		0			0
$447$		−	6.08499i		−	0.287810i
$448$		0			0
$449$	−18.2010	−	18.2010i	−0.858957	−	0.858957i	0.132258	−	0.991215i	$-0.457777\pi$
$449$	−18.2010	−	18.2010i	−0.858957	−	0.858957i	−0.991215	+	0.132258i	$0.957777\pi$
$450$		0			0
$451$	−0.574128			−0.0270346
$452$		0			0
$453$	18.3334			0.861377
$454$		0			0
$455$	5.62258	−	0.903520i	0.263591	−	0.0423577i
$456$		0			0
$457$	0.291967	−	0.291967i	0.0136576	−	0.0136576i	−0.700245	−	0.713903i	$-0.746926\pi$
$457$	0.291967	−	0.291967i	0.0136576	−	0.0136576i	0.713903	+	0.700245i	$0.246926\pi$
$458$		0			0
$459$		−	3.14418i		−	0.146758i
$460$		0			0
$461$	−28.0406	−	28.0406i	−1.30598	−	1.30598i	−0.924290	−	0.381692i	$-0.875342\pi$
$461$	−28.0406	−	28.0406i	−1.30598	−	1.30598i	−0.381692	−	0.924290i	$-0.624658\pi$
$462$		0			0
$463$	−27.0746	−	27.0746i	−1.25826	−	1.25826i	−0.951923	−	0.306338i	$-0.900896\pi$
$463$	−27.0746	−	27.0746i	−1.25826	−	1.25826i	−0.306338	−	0.951923i	$-0.599104\pi$
$464$		0			0
$465$	2.81349	−	3.89085i	0.130473	−	0.180434i
$466$		0			0
$467$	−2.85538			−0.132131			−0.0660657	−	0.997815i	$-0.521045\pi$
$467$	−2.85538			−0.132131			−0.0660657	+	0.997815i	$0.521045\pi$
$468$		0			0
$469$	0.0953181			0.00440138
$470$		0			0
$471$	−0.859477			−0.0396026
$472$		0			0
$473$	−1.78716	−	1.78716i	−0.0821735	−	0.0821735i
$474$		0			0
$475$	12.2133	+	6.15379i	0.560382	+	0.282355i
$476$		0			0
$477$	2.90576	−	2.90576i	0.133046	−	0.133046i
$478$		0			0
$479$	17.7692	−	17.7692i	0.811897	−	0.811897i	−0.173021	−	0.984918i	$-0.555353\pi$
$479$	17.7692	−	17.7692i	0.811897	−	0.811897i	0.984918	+	0.173021i	$0.0553529\pi$
$480$		0			0
$481$	2.45028	−	2.45028i	0.111723	−	0.111723i
$482$		0			0
$483$			54.7069i			2.48925i
$484$		0			0
$485$	20.7085	−	3.32775i	0.940322	−	0.151105i
$486$		0			0
$487$	4.90420	+	4.90420i	0.222230	+	0.222230i	0.809437	−	0.587207i	$-0.199772\pi$
$487$	4.90420	+	4.90420i	0.222230	+	0.222230i	−0.587207	+	0.809437i	$0.699772\pi$
$488$		0			0
$489$		−	21.1770i		−	0.957658i
$490$		0			0
$491$	−17.0419	−	17.0419i	−0.769089	−	0.769089i	0.208857	−	0.977946i	$-0.433026\pi$
$491$	−17.0419	−	17.0419i	−0.769089	−	0.769089i	−0.977946	+	0.208857i	$0.933026\pi$
$492$		0			0
$493$	3.00772	+	0.640366i	0.135461	+	0.0288407i
$494$		0			0
$495$	0.615407	+	0.445004i	0.0276605	+	0.0200015i
$496$		0			0
$497$	32.4359	−	32.4359i	1.45495	−	1.45495i
$498$		0			0
$499$	21.0072			0.940411			0.470206	−	0.882557i	$-0.344180\pi$
$499$	21.0072			0.940411			0.470206	+	0.882557i	$0.344180\pi$
$500$		0			0
$501$	6.06751	+	6.06751i	0.271076	+	0.271076i
$502$		0			0
$503$	−14.9510			−0.666630			−0.333315	−	0.942815i	$-0.608167\pi$
$503$	−14.9510			−0.666630			−0.333315	+	0.942815i	$0.608167\pi$
$504$		0			0
$505$	−19.5028	−	14.1026i	−0.867865	−	0.627558i
$506$		0			0
$507$	20.0900			0.892226
$508$		0			0
$509$		−	4.49496i		−	0.199235i	−0.995026	−	0.0996177i	$-0.968238\pi$
$509$		−	4.49496i		−	0.199235i	0.995026	−	0.0996177i	$-0.0317620\pi$
$510$		0			0
$511$	−40.0520	−	40.0520i	−1.77180	−	1.77180i
$512$		0			0
$513$	10.6492	−	10.6492i	0.470172	−	0.470172i
$514$		0			0
$515$	33.8262	+	24.4599i	1.49056	+	1.07783i
$516$		0			0
$517$	2.37343	+	2.37343i	0.104383	+	0.104383i
$518$		0			0
$519$	2.82017	−	2.82017i	0.123792	−	0.123792i
$520$		0			0
$521$		−	1.37733i		−	0.0603420i	−0.999545	−	0.0301710i	$-0.990395\pi$
$521$		−	1.37733i		−	0.0603420i	0.999545	−	0.0301710i	$-0.00960519\pi$
$522$		0			0
$523$	−17.7509	+	17.7509i	−0.776194	+	0.776194i	−0.979181	−	0.202987i	$-0.934935\pi$
$523$	−17.7509	+	17.7509i	−0.776194	+	0.776194i	0.202987	+	0.979181i	$0.434935\pi$
$524$		0			0
$525$	13.9042	−	27.5953i	0.606831	−	1.20436i
$526$		0			0
$527$	0.542323	−	0.542323i	0.0236240	−	0.0236240i
$528$		0			0
$529$		−	55.3607i		−	2.40699i
$530$		0			0
$531$		−	3.96316i		−	0.171987i
$532$		0			0
$533$			0.494442i			0.0214167i
$534$		0			0
$535$	1.01206	−	1.39960i	0.0437550	−	0.0605098i
$536$		0			0
$537$		−	11.0578i		−	0.477180i
$538$		0			0
$539$	4.29638	+	4.29638i	0.185058	+	0.185058i
$540$		0			0
$541$	14.9100	−	14.9100i	0.641033	−	0.641033i	−0.309776	−	0.950809i	$-0.600254\pi$
$541$	14.9100	−	14.9100i	0.641033	−	0.641033i	0.950809	+	0.309776i	$0.100254\pi$
$542$		0			0
$543$		−	11.2988i		−	0.484876i
$544$		0			0
$545$	0.314299	+	1.95587i	0.0134631	+	0.0837803i
$546$		0			0
$547$	19.7749	+	19.7749i	0.845514	+	0.845514i	0.989570	−	0.144056i	$-0.0460144\pi$
$547$	19.7749	+	19.7749i	0.845514	+	0.845514i	−0.144056	+	0.989570i	$0.546014\pi$
$548$		0			0
$549$	−2.06180	+	2.06180i	−0.0879954	+	0.0879954i
$550$		0			0
$551$	8.01811	+	12.3559i	0.341583	+	0.526378i
$552$		0			0
$553$			23.8491i			1.01417i
$554$		0			0
$555$	−2.98324	−	18.5646i	−0.126632	−	0.788025i
$556$		0			0
$557$	22.8441	−	22.8441i	0.967934	−	0.967934i	−0.0315675	−	0.999502i	$-0.510050\pi$
$557$	22.8441	−	22.8441i	0.967934	−	0.967934i	0.999502	+	0.0315675i	$0.0100499\pi$
$558$		0			0
$559$	−1.53911	+	1.53911i	−0.0650974	+	0.0650974i
$560$		0			0
$561$	−0.493861	−	0.493861i	−0.0208508	−	0.0208508i
$562$		0			0
$563$	25.8509			1.08949			0.544743	−	0.838603i	$-0.316627\pi$
$563$	25.8509			1.08949			0.544743	+	0.838603i	$0.316627\pi$
$564$		0			0
$565$	3.90499	+	24.3006i	0.164284	+	1.02233i
$566$		0			0
$567$	−20.4209	−	20.4209i	−0.857597	−	0.857597i
$568$		0			0
$569$	−21.3331	+	21.3331i	−0.894328	+	0.894328i	−0.994927	−	0.100599i	$-0.967924\pi$
$569$	−21.3331	+	21.3331i	−0.894328	+	0.894328i	0.100599	+	0.994927i	$0.467924\pi$
$570$		0			0
$571$	−5.74610			−0.240467			−0.120233	−	0.992746i	$-0.538364\pi$
$571$	−5.74610			−0.240467			−0.120233	+	0.992746i	$0.538364\pi$
$572$		0			0
$573$	20.3379	+	20.3379i	0.849628	+	0.849628i
$574$		0			0
$575$	−19.9161	+	39.5268i	−0.830557	+	1.64838i
$576$		0			0
$577$			22.0139i			0.916451i	0.888836	+	0.458225i	$0.151515\pi$
$577$			22.0139i			0.916451i	−0.888836	+	0.458225i	$0.848485\pi$
$578$		0			0
$579$	−31.8422			−1.32332
$580$		0			0
$581$	27.4844			1.14024
$582$		0			0
$583$		−	7.08118i		−	0.293272i
$584$		0			0
$585$	0.383240	−	0.529992i	0.0158450	−	0.0219125i
$586$		0			0
$587$	2.93256	+	2.93256i	0.121040	+	0.121040i	0.765032	−	0.643992i	$-0.222723\pi$
$587$	2.93256	+	2.93256i	0.121040	+	0.121040i	−0.643992	+	0.765032i	$0.722723\pi$
$588$		0			0
$589$	3.67364			0.151370
$590$		0			0
$591$	17.2879	−	17.2879i	0.711129	−	0.711129i
$592$		0			0
$593$	4.85305	+	4.85305i	0.199291	+	0.199291i	0.799696	−	0.600405i	$-0.204994\pi$
$593$	4.85305	+	4.85305i	0.199291	+	0.199291i	−0.600405	+	0.799696i	$0.704994\pi$
$594$		0			0
$595$	2.89219	−	3.99969i	0.118568	−	0.163971i
$596$		0			0
$597$	−5.88219			−0.240742
$598$		0			0
$599$	28.7709	+	28.7709i	1.17555	+	1.17555i	0.980866	+	0.194682i	$0.0623675\pi$
$599$	28.7709	+	28.7709i	1.17555	+	1.17555i	0.194682	+	0.980866i	$0.437633\pi$
$600$		0			0
$601$	27.0402	−	27.0402i	1.10299	−	1.10299i	0.108944	−	0.994048i	$-0.465253\pi$
$601$	27.0402	−	27.0402i	1.10299	−	1.10299i	0.994048	−	0.108944i	$-0.0347468\pi$
$602$		0			0
$603$	0.00774090	−	0.00774090i	0.000315234	−	0.000315234i
$604$		0			0
$605$	−22.9931	+	3.69488i	−0.934803	+	0.150218i
$606$		0			0
$607$		−	3.90056i		−	0.158319i	−0.996862	−	0.0791595i	$-0.974776\pi$
$607$		−	3.90056i		−	0.158319i	0.996862	−	0.0791595i	$-0.0252236\pi$
$608$		0			0
$609$	27.9176	−	18.1166i	1.13128	−	0.734121i
$610$		0			0
$611$	2.04401	−	2.04401i	0.0826918	−	0.0826918i
$612$		0			0
$613$	22.5823	+	22.5823i	0.912092	+	0.912092i	0.996437	−	0.0843447i	$-0.0268797\pi$
$613$	22.5823	+	22.5823i	0.912092	+	0.912092i	−0.0843447	+	0.996437i	$0.526880\pi$
$614$		0			0
$615$	2.17407	+	1.57208i	0.0876670	+	0.0633925i
$616$		0			0
$617$		−	47.2100i		−	1.90060i	−0.311329	−	0.950302i	$-0.600774\pi$
$617$		−	47.2100i		−	1.90060i	0.311329	−	0.950302i	$-0.399226\pi$
$618$		0			0
$619$	31.0001	−	31.0001i	1.24600	−	1.24600i	0.288528	−	0.957472i	$-0.406834\pi$
$619$	31.0001	−	31.0001i	1.24600	−	1.24600i	0.957472	−	0.288528i	$-0.0931658\pi$
$620$		0			0
$621$	34.4648	+	34.4648i	1.38303	+	1.38303i
$622$		0			0
$623$			63.3023i			2.53615i
$624$		0			0
$625$	20.0922	−	14.8763i	0.803687	−	0.595053i
$626$		0			0
$627$		−	3.34537i		−	0.133601i
$628$		0			0
$629$		−	3.00344i		−	0.119755i
$630$		0			0
$631$		−	14.3987i		−	0.573204i	−0.958050	−	0.286602i	$-0.907474\pi$
$631$		−	14.3987i		−	0.573204i	0.958050	−	0.286602i	$-0.0925257\pi$
$632$		0			0
$633$	−27.3221	+	27.3221i	−1.08596	+	1.08596i
$634$		0			0
$635$	5.56050	+	34.6028i	0.220662	+	1.37317i
$636$		0			0
$637$	3.70007	−	3.70007i	0.146602	−	0.146602i
$638$		0			0
$639$		−	5.26831i		−	0.208411i
$640$		0			0
$641$	14.5821	−	14.5821i	0.575957	−	0.575957i	−0.357830	−	0.933787i	$-0.616483\pi$
$641$	14.5821	−	14.5821i	0.575957	−	0.575957i	0.933787	+	0.357830i	$0.116483\pi$
$642$		0			0
$643$	−26.7869	−	26.7869i	−1.05637	−	1.05637i	−0.998313	−	0.0580603i	$-0.981508\pi$
$643$	−26.7869	−	26.7869i	−1.05637	−	1.05637i	−0.0580603	−	0.998313i	$-0.518492\pi$
$644$		0			0
$645$	1.87388	+	11.6611i	0.0737840	+	0.459155i
$646$		0			0
$647$	10.2001	−	10.2001i	0.401006	−	0.401006i	−0.477581	−	0.878588i	$-0.658486\pi$
$647$	10.2001	−	10.2001i	0.401006	−	0.401006i	0.878588	+	0.477581i	$0.158486\pi$
$648$		0			0
$649$	−4.82901	−	4.82901i	−0.189555	−	0.189555i
$650$		0			0
$651$		−	8.30044i		−	0.325320i
$652$		0			0
$653$	−26.6561			−1.04313			−0.521567	−	0.853210i	$-0.674652\pi$
$653$	−26.6561			−1.04313			−0.521567	+	0.853210i	$0.674652\pi$
$654$		0			0
$655$	12.0676	−	16.6886i	0.471521	−	0.652077i
$656$		0			0
$657$	−6.50534			−0.253798
$658$		0			0
$659$	−27.1496	−	27.1496i	−1.05760	−	1.05760i	−0.998236	−	0.0593630i	$-0.981093\pi$
$659$	−27.1496	−	27.1496i	−1.05760	−	1.05760i	−0.0593630	−	0.998236i	$-0.518907\pi$
$660$		0			0
$661$	−0.0733619			−0.00285345			−0.00142672	−	0.999999i	$-0.500454\pi$
$661$	−0.0733619			−0.00285345			−0.00142672	+	0.999999i	$0.500454\pi$
$662$		0			0
$663$	−0.425316	+	0.425316i	−0.0165179	+	0.0165179i
$664$		0			0
$665$	23.3424	−	3.75101i	0.905181	−	0.145458i
$666$		0			0
$667$	−39.9884	+	25.9497i	−1.54836	+	1.00478i
$668$		0			0
$669$	−18.8615	−	18.8615i	−0.729226	−	0.729226i
$670$		0			0
$671$			5.02449i			0.193968i
$672$		0			0
$673$	−21.7602	−	21.7602i	−0.838793	−	0.838793i	0.149907	−	0.988700i	$-0.452103\pi$
$673$	−21.7602	−	21.7602i	−0.838793	−	0.838793i	−0.988700	+	0.149907i	$0.952103\pi$
$674$		0			0
$675$	−8.62525	−	26.1443i	−0.331986	−	1.00630i
$676$		0			0
$677$			25.2290i			0.969629i	0.874617	+	0.484814i	$0.161113\pi$
$677$			25.2290i			0.969629i	−0.874617	+	0.484814i	$0.838887\pi$
$678$		0			0
$679$	25.6385	−	25.6385i	0.983915	−	0.983915i
$680$		0			0
$681$	−32.6211	+	32.6211i	−1.25004	+	1.25004i
$682$		0			0
$683$	−12.0876	+	12.0876i	−0.462519	+	0.462519i	−0.899480	−	0.436961i	$-0.856055\pi$
$683$	−12.0876	+	12.0876i	−0.462519	+	0.462519i	0.436961	+	0.899480i	$0.356055\pi$
$684$		0			0
$685$	4.09595	+	25.4890i	0.156498	+	0.973883i
$686$		0			0
$687$	−2.27806	−	2.27806i	−0.0869135	−	0.0869135i
$688$		0			0
$689$	−6.09835			−0.232329
$690$		0			0
$691$	−44.3251			−1.68620			−0.843102	−	0.537753i	$-0.819273\pi$
$691$	−44.3251			−1.68620			−0.843102	+	0.537753i	$0.819273\pi$
$692$		0			0
$693$	1.31286			0.0498715
$694$		0			0
$695$	−19.4696	+	3.12866i	−0.738523	+	0.118677i
$696$		0			0
$697$	0.303031	+	0.303031i	0.0114781	+	0.0114781i
$698$		0			0
$699$	−7.01797	−	7.01797i	−0.265444	−	0.265444i
$700$		0			0
$701$			20.0879i			0.758708i	0.925252	+	0.379354i	$0.123854\pi$
$701$			20.0879i			0.758708i	−0.925252	+	0.379354i	$0.876146\pi$
$702$		0			0
$703$	10.1725	−	10.1725i	0.383663	−	0.383663i
$704$		0			0
$705$	−2.48860	−	15.4865i	−0.0937262	−	0.583255i
$706$		0			0
$707$	−41.6059			−1.56475
$708$		0			0
$709$	−25.2344			−0.947699			−0.473850	−	0.880606i	$-0.657136\pi$
$709$	−25.2344			−0.947699			−0.473850	+	0.880606i	$0.657136\pi$
$710$		0			0
$711$	1.93681	+	1.93681i	0.0726362	+	0.0726362i
$712$		0			0
$713$			11.8893i			0.445259i
$714$		0			0
$715$	−0.178813	−	1.11275i	−0.00668724	−	0.0416145i
$716$		0			0
$717$	16.6371			0.621325
$718$		0			0
$719$			7.05961i			0.263279i	0.991298	+	0.131640i	$0.0420241\pi$
$719$			7.05961i			0.263279i	−0.991298	+	0.131640i	$0.957976\pi$
$720$		0			0
$721$	72.1623			2.68747
$722$		0			0
$723$	−38.6094			−1.43590
$724$		0			0
$725$	26.7664	−	2.92617i	0.994077	−	0.108675i
$726$		0			0
$727$	−3.11412			−0.115496			−0.0577481	−	0.998331i	$-0.518392\pi$
$727$	−3.11412			−0.115496			−0.0577481	+	0.998331i	$0.518392\pi$
$728$		0			0
$729$	−29.7255			−1.10095
$730$		0			0
$731$			1.88656i			0.0697771i
$732$		0			0
$733$	40.0739			1.48016			0.740082	−	0.672517i	$-0.234787\pi$
$733$	40.0739			1.48016			0.740082	+	0.672517i	$0.234787\pi$
$734$		0			0
$735$	−4.50487	−	28.0336i	−0.166165	−	1.03404i
$736$		0			0
$737$		−	0.0188641i		−	0.000694870i
$738$		0			0
$739$	−9.39689	−	9.39689i	−0.345670	−	0.345670i	0.512824	−	0.858494i	$-0.328599\pi$
$739$	−9.39689	−	9.39689i	−0.345670	−	0.345670i	−0.858494	+	0.512824i	$0.828599\pi$
$740$		0			0
$741$	−2.88105			−0.105838
$742$		0			0
$743$	−26.5508			−0.974053			−0.487026	−	0.873387i	$-0.661918\pi$
$743$	−26.5508			−0.974053			−0.487026	+	0.873387i	$0.661918\pi$
$744$		0			0
$745$	−1.35029	−	8.40281i	−0.0494708	−	0.307855i
$746$		0			0
$747$	2.23204	−	2.23204i	0.0816661	−	0.0816661i
$748$		0			0
$749$		−	2.98579i		−	0.109099i
$750$		0			0
$751$	−35.0364	−	35.0364i	−1.27850	−	1.27850i	−0.941509	−	0.336988i	$-0.890592\pi$
$751$	−35.0364	−	35.0364i	−1.27850	−	1.27850i	−0.336988	−	0.941509i	$-0.609408\pi$
$752$		0			0
$753$	−16.4891	−	16.4891i	−0.600897	−	0.600897i
$754$		0			0
$755$	25.3167	−	4.06827i	0.921368	−	0.148059i
$756$		0			0
$757$	−8.86028			−0.322032			−0.161016	−	0.986952i	$-0.551477\pi$
$757$	−8.86028			−0.322032			−0.161016	+	0.986952i	$0.551477\pi$
$758$		0			0
$759$	10.8269			0.392992
$760$		0			0
$761$	−14.8359			−0.537803			−0.268901	−	0.963168i	$-0.586661\pi$
$761$	−14.8359			−0.537803			−0.268901	+	0.963168i	$0.586661\pi$
$762$		0			0
$763$	2.42150	+	2.42150i	0.0876643	+	0.0876643i
$764$		0			0
$765$	−0.0899407	−	0.559698i	−0.00325181	−	0.0202359i
$766$		0			0
$767$	−4.15877	+	4.15877i	−0.150165	+	0.150165i
$768$		0			0
$769$	−18.0413	+	18.0413i	−0.650586	+	0.650586i	−0.953134	−	0.302548i	$-0.902163\pi$
$769$	−18.0413	+	18.0413i	−0.650586	+	0.650586i	0.302548	+	0.953134i	$0.402163\pi$
$770$		0			0
$771$	9.54777	−	9.54777i	0.343854	−	0.343854i
$772$		0			0
$773$			44.2625i			1.59201i	0.605288	+	0.796006i	$0.293058\pi$
$773$			44.2625i			1.59201i	−0.605288	+	0.796006i	$0.706942\pi$
$774$		0			0
$775$	3.02178	−	5.99723i	0.108545	−	0.215427i
$776$		0			0
$777$	−22.9843	−	22.9843i	−0.824557	−	0.824557i
$778$		0			0
$779$			2.05270i			0.0735458i
$780$		0			0
$781$	−6.41930	−	6.41930i	−0.229700	−	0.229700i
$782$		0			0
$783$	6.17455	−	29.0011i	0.220660	−	1.03641i
$784$		0			0
$785$	−1.18686	+	0.190722i	−0.0423608	+	0.00680717i
$786$		0			0
$787$	−32.3949	+	32.3949i	−1.15475	+	1.15475i	−0.169167	+	0.985587i	$0.554108\pi$
$787$	−32.3949	+	32.3949i	−1.15475	+	1.15475i	−0.985587	+	0.169167i	$0.945892\pi$
$788$		0			0
$789$	6.31563			0.224842
$790$		0			0
$791$	30.0858	+	30.0858i	1.06973	+	1.06973i
$792$		0			0
$793$	4.32712			0.153661
$794$		0			0
$795$	−19.3898	+	26.8146i	−0.687684	+	0.951015i
$796$		0			0
$797$	19.5830			0.693664			0.346832	−	0.937927i	$-0.387257\pi$
$797$	19.5830			0.693664			0.346832	+	0.937927i	$0.387257\pi$
$798$		0			0
$799$		−	2.50545i		−	0.0886364i
$800$		0			0
$801$	5.14085	+	5.14085i	0.181643	+	0.181643i
$802$		0			0
$803$	−7.92658	+	7.92658i	−0.279723	+	0.279723i
$804$		0			0
$805$	12.1397	+	75.5452i	0.427870	+	2.66262i
$806$		0			0
$807$	15.4701	+	15.4701i	0.544573	+	0.544573i
$808$		0			0
$809$	−35.9823	+	35.9823i	−1.26507	+	1.26507i	−0.316466	+	0.948604i	$0.602496\pi$
$809$	−35.9823	+	35.9823i	−1.26507	+	1.26507i	−0.948604	+	0.316466i	$0.897504\pi$
$810$		0			0
$811$		−	0.214818i		−	0.00754328i	−0.999993	−	0.00377164i	$-0.998799\pi$
$811$		−	0.214818i		−	0.00754328i	0.999993	−	0.00377164i	$-0.00120055\pi$
$812$		0			0
$813$	15.5781	−	15.5781i	0.546347	−	0.546347i
$814$		0			0
$815$	−4.69929	−	29.2435i	−0.164609	−	1.02436i
$816$		0			0
$817$	−6.38970	+	6.38970i	−0.223547	+	0.223547i
$818$		0			0
$819$		−	1.13065i		−	0.0395080i
$820$		0			0
$821$		−	1.42777i		−	0.0498297i	−0.999690	−	0.0249148i	$-0.992069\pi$
$821$		−	1.42777i		−	0.0498297i	0.999690	−	0.0249148i	$-0.00793146\pi$
$822$		0			0
$823$		−	22.9854i		−	0.801221i	−0.916249	−	0.400610i	$-0.868798\pi$
$823$		−	22.9854i		−	0.801221i	0.916249	−	0.400610i	$-0.131202\pi$
$824$		0			0
$825$	−5.46132	−	2.75175i	−0.190139	−	0.0958037i
$826$		0			0
$827$			27.9527i			0.972011i	0.873956	+	0.486005i	$0.161546\pi$
$827$			27.9527i			0.972011i	−0.873956	+	0.486005i	$0.838454\pi$
$828$		0			0
$829$	−12.6953	−	12.6953i	−0.440927	−	0.440927i	0.451396	−	0.892324i	$-0.350926\pi$
$829$	−12.6953	−	12.6953i	−0.440927	−	0.440927i	−0.892324	+	0.451396i	$0.850926\pi$
$830$		0			0
$831$	−19.9854	+	19.9854i	−0.693285	+	0.693285i
$832$		0			0
$833$		−	4.53536i		−	0.157141i
$834$		0			0
$835$	9.72508	+	7.03226i	0.336550	+	0.243361i
$836$		0			0
$837$	−5.22920	−	5.22920i	−0.180747	−	0.180747i
$838$		0			0
$839$	−32.0270	+	32.0270i	−1.10570	+	1.10570i	−0.111986	+	0.993710i	$0.535721\pi$
$839$	−32.0270	+	32.0270i	−1.10570	+	1.10570i	−0.993710	+	0.111986i	$0.964279\pi$
$840$		0			0
$841$	26.4849	+	11.8132i	0.913272	+	0.407350i
$842$		0			0
$843$			19.4172i			0.668765i
$844$		0			0
$845$	27.7424	−	4.45806i	0.954367	−	0.153362i
$846$		0			0
$847$	−28.4671	+	28.4671i	−0.978140	+	0.978140i
$848$		0			0
$849$	−27.2064	+	27.2064i	−0.933720	+	0.933720i
$850$		0			0
$851$	32.9221	+	32.9221i	1.12856	+	1.12856i
$852$		0			0
$853$	7.89562			0.270341			0.135170	−	0.990822i	$-0.456842\pi$
$853$	7.89562			0.270341			0.135170	+	0.990822i	$0.456842\pi$
$854$		0			0
$855$	1.59104	−	2.20029i	0.0544126	−	0.0752484i
$856$		0			0
$857$	13.1035	+	13.1035i	0.447606	+	0.447606i	0.894558	−	0.446952i	$-0.147491\pi$
$857$	13.1035	+	13.1035i	0.447606	+	0.447606i	−0.446952	+	0.894558i	$0.647491\pi$
$858$		0			0
$859$	17.7813	−	17.7813i	0.606691	−	0.606691i	−0.335389	−	0.942080i	$-0.608868\pi$
$859$	17.7813	−	17.7813i	0.606691	−	0.606691i	0.942080	+	0.335389i	$0.108868\pi$
$860$		0			0
$861$	4.63800			0.158063
$862$		0			0
$863$	19.4883	+	19.4883i	0.663389	+	0.663389i	0.956177	−	0.292788i	$-0.0945830\pi$
$863$	19.4883	+	19.4883i	0.663389	+	0.663389i	−0.292788	+	0.956177i	$0.594583\pi$
$864$		0			0
$865$	3.26858	−	4.52020i	0.111135	−	0.153691i
$866$		0			0
$867$		−	26.6576i		−	0.905341i
$868$		0			0
$869$	4.71991			0.160112
$870$		0			0
$871$	−0.0162459			−0.000550472
$872$		0			0
$873$		−	4.16427i		−	0.140939i
$874$		0			0
$875$	13.0769	−	41.1920i	0.442081	−	1.39254i
$876$		0			0
$877$	6.75233	+	6.75233i	0.228010	+	0.228010i	0.811861	−	0.583851i	$-0.198455\pi$
$877$	6.75233	+	6.75233i	0.228010	+	0.228010i	−0.583851	+	0.811861i	$0.698455\pi$
$878$		0			0
$879$	11.8318			0.399076
$880$		0			0
$881$	−14.2461	+	14.2461i	−0.479964	+	0.479964i	−0.905120	−	0.425156i	$-0.860219\pi$
$881$	−14.2461	+	14.2461i	−0.479964	+	0.479964i	0.425156	+	0.905120i	$0.360219\pi$
$882$		0			0
$883$	27.6509	+	27.6509i	0.930527	+	0.930527i	0.997739	−	0.0672118i	$-0.0214103\pi$
$883$	27.6509	+	27.6509i	0.930527	+	0.930527i	−0.0672118	+	0.997739i	$0.521410\pi$
$884$		0			0
$885$	5.06335	+	31.5090i	0.170203	+	1.05916i
$886$		0			0
$887$	18.5733			0.623631			0.311816	−	0.950143i	$-0.399063\pi$
$887$	18.5733			0.623631			0.311816	+	0.950143i	$0.399063\pi$
$888$		0			0
$889$	42.8407	+	42.8407i	1.43683	+	1.43683i
$890$		0			0
$891$	−4.04144	+	4.04144i	−0.135393	+	0.135393i
$892$		0			0
$893$	8.48582	−	8.48582i	0.283967	−	0.283967i
$894$		0			0
$895$	−2.45378	−	15.2698i	−0.0820210	−	0.510414i
$896$		0			0
$897$		−	9.32419i		−	0.311326i
$898$		0			0
$899$	6.06727	−	3.93723i	0.202355	−	0.131314i
$900$		0			0
$901$	−3.73753	+	3.73753i	−0.124515	+	0.124515i
$902$		0			0
$903$	14.4372	+	14.4372i	0.480442	+	0.480442i
$904$		0			0
$905$	−2.50725	−	15.6026i	−0.0833439	−	0.518646i
$906$		0			0
$907$		−	18.3036i		−	0.607762i	−0.952710	−	0.303881i	$-0.901717\pi$
$907$		−	18.3036i		−	0.607762i	0.952710	−	0.303881i	$-0.0982825\pi$
$908$		0			0
$909$	−3.37887	+	3.37887i	−0.112070	+	0.112070i
$910$		0			0
$911$	23.0249	+	23.0249i	0.762848	+	0.762848i	0.976836	−	0.213988i	$-0.0686455\pi$
$911$	23.0249	+	23.0249i	0.762848	+	0.762848i	−0.213988	+	0.976836i	$0.568645\pi$
$912$		0			0
$913$		−	5.43936i		−	0.180017i
$914$		0			0
$915$	13.7581	−	19.0264i	0.454830	−	0.628995i
$916$		0			0
$917$		−	35.6022i		−	1.17569i
$918$		0			0
$919$			54.0220i			1.78202i	0.453984	+	0.891010i	$0.350002\pi$
$919$			54.0220i			1.78202i	−0.453984	+	0.891010i	$0.649998\pi$
$920$		0			0
$921$			7.07056i			0.232983i
$922$		0			0
$923$	−5.52834	+	5.52834i	−0.181967	+	0.181967i
$924$		0			0
$925$	−8.23917	−	24.9740i	−0.270902	−	0.821142i
$926$		0			0
$927$	5.86039	−	5.86039i	0.192480	−	0.192480i
$928$		0			0
$929$			23.6369i			0.775502i	0.921764	+	0.387751i	$0.126748\pi$
$929$			23.6369i			0.775502i	−0.921764	+	0.387751i	$0.873252\pi$
$930$		0			0
$931$	15.3610	−	15.3610i	0.503437	−	0.503437i
$932$		0			0
$933$	−32.8907	−	32.8907i	−1.07679	−	1.07679i
$934$		0			0
$935$	−0.791567	−	0.572387i	−0.0258870	−	0.0187190i
$936$		0			0
$937$	−41.7796	+	41.7796i	−1.36488	+	1.36488i	−0.497300	+	0.867579i	$0.665675\pi$
$937$	−41.7796	+	41.7796i	−1.36488	+	1.36488i	−0.867579	+	0.497300i	$0.834325\pi$
$938$		0			0
$939$	14.9142	+	14.9142i	0.486705	+	0.486705i
$940$		0			0
$941$			20.1624i			0.657277i	0.944456	+	0.328638i	$0.106590\pi$
$941$			20.1624i			0.657277i	−0.944456	+	0.328638i	$0.893410\pi$
$942$		0			0
$943$	−6.64335			−0.216337
$944$		0			0
$945$	−38.5658	−	27.8872i	−1.25455	−	0.907169i
$946$		0			0
$947$	−41.0806			−1.33494			−0.667470	−	0.744637i	$-0.732623\pi$
$947$	−41.0806			−1.33494			−0.667470	+	0.744637i	$0.732623\pi$
$948$		0			0
$949$	6.82642	+	6.82642i	0.221595	+	0.221595i
$950$		0			0
$951$	36.9072			1.19680
$952$		0			0
$953$	−36.3697	+	36.3697i	−1.17813	+	1.17813i	−0.197911	+	0.980220i	$0.563416\pi$
$953$	−36.3697	+	36.3697i	−1.17813	+	1.17813i	−0.980220	+	0.197911i	$0.936584\pi$
$954$		0			0
$955$	32.5978	+	23.5717i	1.05484	+	0.762762i
$956$		0			0
$957$	−3.58540	−	5.52510i	−0.115900	−	0.178601i
$958$		0			0
$959$	31.5571	+	31.5571i	1.01903	+	1.01903i
$960$		0			0
$961$			29.1961i			0.941809i
$962$		0			0
$963$	−0.242480	−	0.242480i	−0.00781381	−	0.00781381i
$964$		0			0
$965$	−43.9711	+	7.06594i	−1.41548	+	0.227461i
$966$		0			0
$967$			10.0953i			0.324643i	0.986738	+	0.162321i	$0.0518981\pi$
$967$			10.0953i			0.324643i	−0.986738	+	0.162321i	$0.948102\pi$
$968$		0			0
$969$	−1.76572	+	1.76572i	−0.0567232	+	0.0567232i
$970$		0			0
$971$	30.8215	−	30.8215i	0.989109	−	0.989109i	−0.0108325	−	0.999941i	$-0.503448\pi$
$971$	30.8215	−	30.8215i	0.989109	−	0.989109i	0.999941	+	0.0108325i	$0.00344814\pi$
$972$		0			0
$973$	−24.1047	+	24.1047i	−0.772761	+	0.772761i
$974$		0			0
$975$	−2.36982	+	4.70332i	−0.0758951	+	0.150627i
$976$		0			0
$977$	−20.8270	−	20.8270i	−0.666316	−	0.666316i	0.290545	−	0.956861i	$-0.406163\pi$
$977$	−20.8270	−	20.8270i	−0.666316	−	0.666316i	−0.956861	+	0.290545i	$0.906163\pi$
$978$		0			0
$979$	12.5280			0.400396
$980$		0			0
$981$	0.393307			0.0125573
$982$		0			0
$983$	−9.59663			−0.306085			−0.153042	−	0.988220i	$-0.548907\pi$
$983$	−9.59663			−0.306085			−0.153042	+	0.988220i	$0.548907\pi$
$984$		0			0
$985$	20.0367	−	27.7092i	0.638423	−	0.882890i
$986$		0			0
$987$	−19.1734	−	19.1734i	−0.610295	−	0.610295i
$988$		0			0
$989$	−20.6795	−	20.6795i	−0.657571	−	0.657571i
$990$		0			0
$991$		−	2.81868i		−	0.0895384i	−0.998997	−	0.0447692i	$-0.985745\pi$
$991$		−	2.81868i		−	0.0895384i	0.998997	−	0.0447692i	$-0.0142552\pi$
$992$		0			0
$993$	14.7961	−	14.7961i	0.469541	−	0.469541i
$994$		0			0
$995$	−8.12277	+	1.30529i	−0.257509	+	0.0413804i
$996$		0			0
$997$	35.9263			1.13780			0.568898	−	0.822408i	$-0.307370\pi$
$997$	35.9263			1.13780			0.568898	+	0.822408i	$0.307370\pi$
$998$		0			0
$999$	−28.9598			−0.916247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.17.11	✓	30
5.2	odd	4		2900.2.s.d.1293.11		30
5.3	odd	4		580.2.s.a.133.5	yes	30
5.4	even	2		2900.2.j.d.1757.5		30
29.12	odd	4		580.2.s.a.157.5	yes	30
145.12	even	4		2900.2.j.d.2593.11		30
145.99	odd	4		2900.2.s.d.157.11		30
145.128	even	4	inner	580.2.j.a.273.5	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.11	✓	30	1.1	even	1	trivial
580.2.j.a.273.5	yes	30	145.128	even	4	inner
580.2.s.a.133.5	yes	30	5.3	odd	4
580.2.s.a.157.5	yes	30	29.12	odd	4
2900.2.j.d.1757.5		30	5.4	even	2
2900.2.j.d.2593.11		30	145.12	even	4
2900.2.s.d.157.11		30	145.99	odd	4
2900.2.s.d.1293.11		30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.59876i q^{3} +(0.354774 + 2.20774i) q^{5} +(2.73334 + 2.73334i) q^{7} +0.443956 q^{9} +(0.540948 - 0.540948i) q^{11} +(-0.465868 - 0.465868i) q^{13} +(-3.52966 + 0.567199i) q^{15} -0.571038 q^{17} +(-1.93408 - 1.93408i) q^{19} +(-4.36997 + 4.36997i) q^{21} +(6.25942 - 6.25942i) q^{23} +(-4.74827 + 1.56650i) q^{25} +5.50607i q^{27} +(-5.26711 - 1.12141i) q^{29} +(-0.949715 + 0.949715i) q^{31} +(0.864848 + 0.864848i) q^{33} +(-5.06480 + 7.00424i) q^{35} +5.25961i q^{37} +(0.744813 - 0.744813i) q^{39} +(-0.530668 - 0.530668i) q^{41} -3.30374i q^{43} +(0.157504 + 0.980141i) q^{45} +4.38753i q^{47} +7.94231i q^{49} -0.912955i q^{51} +(6.54515 - 6.54515i) q^{53} +(1.38619 + 1.00236i) q^{55} +(3.09213 - 3.09213i) q^{57} -8.92693i q^{59} +(-4.64415 + 4.64415i) q^{61} +(1.21348 + 1.21348i) q^{63} +(0.863240 - 1.19380i) q^{65} +(0.0174362 - 0.0174362i) q^{67} +(10.0073 + 10.0073i) q^{69} -11.8667i q^{71} -14.6531 q^{73} +(-2.50446 - 7.59136i) q^{75} +2.95719 q^{77} +(4.36262 + 4.36262i) q^{79} -7.47104 q^{81} +(5.02761 - 5.02761i) q^{83} +(-0.202589 - 1.26071i) q^{85} +(1.79287 - 8.42086i) q^{87} +(11.5796 + 11.5796i) q^{89} -2.54675i q^{91} +(-1.51837 - 1.51837i) q^{93} +(3.58379 - 4.95611i) q^{95} -9.37991i q^{97} +(0.240157 - 0.240157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Introduction

L-functions

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