LMFDB - Embedded newform 416.2.z.a.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(81,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("416.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.z (of order $6$, degree $2$, not 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	416.113
Dual form			416.2.z.a.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.609172 - 0.351705i) q^{3} +2.24007i q^{5} +(-0.471952 - 0.817445i) q^{7} +(-1.25261 - 2.16958i) q^{9} +(4.82849 + 2.78773i) q^{11} +(-0.108823 + 3.60391i) q^{13} +(0.787845 - 1.36459i) q^{15} +(3.03119 + 5.25017i) q^{17} +(-1.43961 + 0.831159i) q^{19} +0.663952i q^{21} +(-1.07746 + 1.86621i) q^{23} -0.0179136 q^{25} +3.87243i q^{27} +(-1.68452 - 0.972558i) q^{29} +1.91161 q^{31} +(-1.96092 - 3.39641i) q^{33} +(1.83113 - 1.05721i) q^{35} +(4.54154 + 2.62206i) q^{37} +(1.33381 - 2.15712i) q^{39} +(-0.332039 + 0.575109i) q^{41} +(-6.97919 + 4.02944i) q^{43} +(4.86001 - 2.80593i) q^{45} +10.5778 q^{47} +(3.05452 - 5.29059i) q^{49} -4.26434i q^{51} -10.3882i q^{53} +(-6.24471 + 10.8162i) q^{55} +1.16929 q^{57} +(-0.411368 + 0.237503i) q^{59} +(-3.06666 + 1.77054i) q^{61} +(-1.18234 + 2.04787i) q^{63} +(-8.07301 - 0.243772i) q^{65} +(-3.91067 - 2.25783i) q^{67} +(1.31271 - 0.757894i) q^{69} +(-5.81695 - 10.0753i) q^{71} -1.91680 q^{73} +(0.0109124 + 0.00630029i) q^{75} -5.26270i q^{77} -13.6120 q^{79} +(-2.39587 + 4.14976i) q^{81} -11.5623i q^{83} +(-11.7607 + 6.79007i) q^{85} +(0.684108 + 1.18491i) q^{87} +(-0.373638 + 0.647161i) q^{89} +(2.99736 - 1.61192i) q^{91} +(-1.16450 - 0.672324i) q^{93} +(-1.86185 - 3.22483i) q^{95} +(0.640742 + 1.10980i) q^{97} -13.9677i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) $ 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.609172	−	0.351705i	−0.351705	−	0.203057i	0.313731	−	0.949512i	$-0.398421\pi$
$3$	−0.609172	−	0.351705i	−0.351705	−	0.203057i	−0.665436	+	0.746455i	$0.731754\pi$
$4$		0			0
$5$			2.24007i			1.00179i	0.865508	+	0.500895i	$0.166996\pi$
$5$			2.24007i			1.00179i	−0.865508	+	0.500895i	$0.833004\pi$
$6$		0			0
$7$	−0.471952	−	0.817445i	−0.178381	−	0.308965i	0.762945	−	0.646463i	$-0.223753\pi$
$7$	−0.471952	−	0.817445i	−0.178381	−	0.308965i	−0.941326	+	0.337498i	$0.890419\pi$
$8$		0			0
$9$	−1.25261	−	2.16958i	−0.417536	−	0.723193i
$10$		0			0
$11$	4.82849	+	2.78773i	1.45584	+	0.840532i	0.998803	−	0.0489128i	$-0.0155756\pi$
$11$	4.82849	+	2.78773i	1.45584	+	0.840532i	0.457042	+	0.889445i	$0.348909\pi$
$12$		0			0
$13$	−0.108823	+	3.60391i	−0.0301821	+	0.999544i
$13$	−0.108823	+	3.60391i	−0.0301821	+	0.999544i
$14$		0			0
$15$	0.787845	−	1.36459i	0.203421	−	0.352335i
$16$		0			0
$17$	3.03119	+	5.25017i	0.735170	+	1.27335i	0.954649	+	0.297735i	$0.0962312\pi$
$17$	3.03119	+	5.25017i	0.735170	+	1.27335i	−0.219478	+	0.975617i	$0.570435\pi$
$18$		0			0
$19$	−1.43961	+	0.831159i	−0.330269	+	0.190681i	−0.655961	−	0.754795i	$-0.727736\pi$
$19$	−1.43961	+	0.831159i	−0.330269	+	0.190681i	0.325692	+	0.945476i	$0.394403\pi$
$20$		0			0
$21$			0.663952i			0.144886i
$22$		0			0
$23$	−1.07746	+	1.86621i	−0.224665	+	0.389131i	−0.956219	−	0.292652i	$-0.905462\pi$
$23$	−1.07746	+	1.86621i	−0.224665	+	0.389131i	0.731554	+	0.681784i	$0.238795\pi$
$24$		0			0
$25$	−0.0179136			−0.00358271
$26$		0			0
$27$			3.87243i			0.745249i
$28$		0			0
$29$	−1.68452	−	0.972558i	−0.312807	−	0.180599i	0.335375	−	0.942085i	$-0.391137\pi$
$29$	−1.68452	−	0.972558i	−0.312807	−	0.180599i	−0.648182	+	0.761485i	$0.724470\pi$
$30$		0			0
$31$	1.91161			0.343335			0.171668	−	0.985155i	$-0.445084\pi$
$31$	1.91161			0.343335			0.171668	+	0.985155i	$0.445084\pi$
$32$		0			0
$33$	−1.96092	−	3.39641i	−0.341352	−	0.591239i
$34$		0			0
$35$	1.83113	−	1.05721i	0.309518	−	0.178700i
$36$		0			0
$37$	4.54154	+	2.62206i	0.746624	+	0.431064i	0.824473	−	0.565902i	$-0.191472\pi$
$37$	4.54154	+	2.62206i	0.746624	+	0.431064i	−0.0778488	+	0.996965i	$0.524805\pi$
$38$		0			0
$39$	1.33381	−	2.15712i	0.213580	−	0.345416i
$40$		0			0
$41$	−0.332039	+	0.575109i	−0.0518558	+	0.0898169i	−0.890788	−	0.454419i	$-0.849847\pi$
$41$	−0.332039	+	0.575109i	−0.0518558	+	0.0898169i	0.838932	+	0.544236i	$0.183180\pi$
$42$		0			0
$43$	−6.97919	+	4.02944i	−1.06432	+	0.614483i	−0.926623	−	0.375992i	$-0.877302\pi$
$43$	−6.97919	+	4.02944i	−1.06432	+	0.614483i	−0.137693	+	0.990475i	$0.543969\pi$
$44$		0			0
$45$	4.86001	−	2.80593i	0.724487	−	0.418283i
$46$		0			0
$47$	10.5778			1.54293			0.771466	−	0.636270i	$-0.219524\pi$
$47$	10.5778			1.54293			0.771466	+	0.636270i	$0.219524\pi$
$48$		0			0
$49$	3.05452	−	5.29059i	0.436360	−	0.755798i
$50$		0			0
$51$		−	4.26434i		−	0.597127i
$52$		0			0
$53$		−	10.3882i		−	1.42693i	−0.700691	−	0.713465i	$-0.747125\pi$
$53$		−	10.3882i		−	1.42693i	0.700691	−	0.713465i	$-0.252875\pi$
$54$		0			0
$55$	−6.24471	+	10.8162i	−0.842037	+	1.45845i
$56$		0			0
$57$	1.16929			0.154877
$58$		0			0
$59$	−0.411368	+	0.237503i	−0.0535555	+	0.0309203i	−0.526539	−	0.850151i	$-0.676510\pi$
$59$	−0.411368	+	0.237503i	−0.0535555	+	0.0309203i	0.472983	+	0.881071i	$0.343177\pi$
$60$		0			0
$61$	−3.06666	+	1.77054i	−0.392646	+	0.226694i	−0.683306	−	0.730132i	$-0.739459\pi$
$61$	−3.06666	+	1.77054i	−0.392646	+	0.226694i	0.290660	+	0.956826i	$0.406125\pi$
$62$		0			0
$63$	−1.18234	+	2.04787i	−0.148961	+	0.258008i
$64$		0			0
$65$	−8.07301	−	0.243772i	−1.00133	−	0.0302362i
$66$		0			0
$67$	−3.91067	−	2.25783i	−0.477764	−	0.275837i	0.241720	−	0.970346i	$-0.422288\pi$
$67$	−3.91067	−	2.25783i	−0.477764	−	0.275837i	−0.719484	+	0.694509i	$0.755622\pi$
$68$		0			0
$69$	1.31271	−	0.757894i	0.158032	−	0.0912397i
$70$		0			0
$71$	−5.81695	−	10.0753i	−0.690345	−	1.19571i	−0.971725	−	0.236117i	$-0.924125\pi$
$71$	−5.81695	−	10.0753i	−0.690345	−	1.19571i	0.281379	−	0.959597i	$-0.409208\pi$
$72$		0			0
$73$	−1.91680			−0.224345			−0.112172	−	0.993689i	$-0.535781\pi$
$73$	−1.91680			−0.224345			−0.112172	+	0.993689i	$0.535781\pi$
$74$		0			0
$75$	0.0109124	+	0.00630029i	0.00126006	+	0.000727495i
$76$		0			0
$77$		−	5.26270i		−	0.599741i
$78$		0			0
$79$	−13.6120			−1.53147			−0.765737	−	0.643154i	$-0.777626\pi$
$79$	−13.6120			−1.53147			−0.765737	+	0.643154i	$0.777626\pi$
$80$		0			0
$81$	−2.39587	+	4.14976i	−0.266207	+	0.461085i
$82$		0			0
$83$		−	11.5623i		−	1.26913i	−0.772871	−	0.634564i	$-0.781180\pi$
$83$		−	11.5623i		−	1.26913i	0.772871	−	0.634564i	$-0.218820\pi$
$84$		0			0
$85$	−11.7607	+	6.79007i	−1.27563	+	0.736486i
$86$		0			0
$87$	0.684108	+	1.18491i	0.0733440	+	0.127036i
$88$		0			0
$89$	−0.373638	+	0.647161i	−0.0396056	+	0.0685989i	−0.885149	−	0.465308i	$-0.845943\pi$
$89$	−0.373638	+	0.647161i	−0.0396056	+	0.0685989i	0.845543	+	0.533907i	$0.179277\pi$
$90$		0			0
$91$	2.99736	−	1.61192i	0.314208	−	0.168975i
$92$		0			0
$93$	−1.16450	−	0.672324i	−0.120753	−	0.0697167i
$94$		0			0
$95$	−1.86185	−	3.22483i	−0.191022	−	0.330860i
$96$		0			0
$97$	0.640742	+	1.10980i	0.0650575	+	0.112683i	0.896719	−	0.442599i	$-0.145944\pi$
$97$	0.640742	+	1.10980i	0.0650575	+	0.112683i	−0.831662	+	0.555282i	$0.812610\pi$
$98$		0			0
$99$		−	13.9677i		−	1.40381i
$100$		0			0
$101$	−8.45583	−	4.88197i	−0.841386	−	0.485775i	0.0163490	−	0.999866i	$-0.494796\pi$
$101$	−8.45583	−	4.88197i	−0.841386	−	0.485775i	−0.857735	+	0.514092i	$0.828129\pi$
$102$		0			0
$103$	15.0755			1.48544			0.742719	−	0.669604i	$-0.233536\pi$
$103$	15.0755			1.48544			0.742719	+	0.669604i	$0.233536\pi$
$104$		0			0
$105$	−1.48730			−0.145146
$106$		0			0
$107$	13.6044	+	7.85448i	1.31518	+	0.759321i	0.982949	−	0.183876i	$-0.0588646\pi$
$107$	13.6044	+	7.85448i	1.31518	+	0.759321i	0.332233	+	0.943197i	$0.392198\pi$
$108$		0			0
$109$		−	9.69920i		−	0.929015i	−0.885569	−	0.464508i	$-0.846231\pi$
$109$		−	9.69920i		−	0.929015i	0.885569	−	0.464508i	$-0.153769\pi$
$110$		0			0
$111$	−1.84438	−	3.19457i	−0.175061	−	0.303215i
$112$		0			0
$113$	3.78116	+	6.54916i	0.355701	+	0.616093i	0.987238	−	0.159253i	$-0.0509087\pi$
$113$	3.78116	+	6.54916i	0.355701	+	0.616093i	−0.631536	+	0.775346i	$0.717575\pi$
$114$		0			0
$115$	−4.18044	−	2.41358i	−0.389828	−	0.225067i
$116$		0			0
$117$	7.95528	−	4.27818i	0.735465	−	0.395518i
$118$		0			0
$119$	2.86115	−	4.95566i	0.262281	−	0.454284i
$120$		0			0
$121$	10.0429	+	17.3948i	0.912989	+	1.58134i
$122$		0			0
$123$	0.404538	−	0.233560i	0.0364759	−	0.0210594i
$124$		0			0
$125$			11.1602i			0.998201i
$126$		0			0
$127$	1.53962	−	2.66670i	0.136619	−	0.236632i	−0.789596	−	0.613628i	$-0.789710\pi$
$127$	1.53962	−	2.66670i	0.136619	−	0.236632i	0.926215	+	0.376996i	$0.123043\pi$
$128$		0			0
$129$	5.66870			0.499101
$130$		0			0
$131$		−	11.9145i		−	1.04098i	−0.853869	−	0.520488i	$-0.825750\pi$
$131$		−	11.9145i		−	1.04098i	0.853869	−	0.520488i	$-0.174250\pi$
$132$		0			0
$133$	1.35885	+	0.784534i	0.117828	+	0.0680278i
$134$		0			0
$135$	−8.67451			−0.746583
$136$		0			0
$137$	−10.2342	−	17.7261i	−0.874365	−	1.51444i	−0.857437	−	0.514588i	$-0.827945\pi$
$137$	−10.2342	−	17.7261i	−0.874365	−	1.51444i	−0.0169276	−	0.999857i	$-0.505388\pi$
$138$		0			0
$139$	−7.01589	+	4.05062i	−0.595080	+	0.343570i	−0.767104	−	0.641523i	$-0.778303\pi$
$139$	−7.01589	+	4.05062i	−0.595080	+	0.343570i	0.172024	+	0.985093i	$0.444969\pi$
$140$		0			0
$141$	−6.44370	−	3.72027i	−0.542658	−	0.313304i
$142$		0			0
$143$	−10.5722	+	17.0981i	−0.884090	+	1.42981i
$144$		0			0
$145$	2.17860	−	3.77344i	0.180923	−	0.313367i
$146$		0			0
$147$	−3.72146	+	2.14858i	−0.306941	+	0.177212i
$148$		0			0
$149$	−3.13501	+	1.81000i	−0.256830	+	0.148281i	−0.622888	−	0.782311i	$-0.714041\pi$
$149$	−3.13501	+	1.81000i	−0.256830	+	0.148281i	0.366058	+	0.930592i	$0.380707\pi$
$150$		0			0
$151$	16.0939			1.30970			0.654850	−	0.755759i	$-0.272732\pi$
$151$	16.0939			1.30970			0.654850	+	0.755759i	$0.272732\pi$
$152$		0			0
$153$	7.59377	−	13.1528i	0.613920	−	1.06334i
$154$		0			0
$155$			4.28214i			0.343950i
$156$		0			0
$157$			15.4274i			1.23124i	0.788042	+	0.615621i	$0.211095\pi$
$157$			15.4274i			1.23124i	−0.788042	+	0.615621i	$0.788905\pi$
$158$		0			0
$159$	−3.65359	+	6.32820i	−0.289748	+	0.501859i
$160$		0			0
$161$	2.03403			0.160304
$162$		0			0
$163$	−4.33867	+	2.50493i	−0.339831	+	0.196201i	−0.660197	−	0.751092i	$-0.729527\pi$
$163$	−4.33867	+	2.50493i	−0.339831	+	0.196201i	0.320366	+	0.947294i	$0.396194\pi$
$164$		0			0
$165$	7.60820	−	4.39260i	0.592298	−	0.341963i
$166$		0			0
$167$	0.532199	−	0.921796i	0.0411828	−	0.0713308i	−0.844699	−	0.535241i	$-0.820221\pi$
$167$	0.532199	−	0.921796i	0.0411828	−	0.0713308i	0.885882	+	0.463910i	$0.153554\pi$
$168$		0			0
$169$	−12.9763	−	0.784378i	−0.998178	−	0.0603368i
$170$		0			0
$171$	3.60653	+	2.08223i	0.275798	+	0.159232i
$172$		0			0
$173$	18.9047	−	10.9146i	1.43730	−	0.829825i	0.439638	−	0.898175i	$-0.355107\pi$
$173$	18.9047	−	10.9146i	1.43730	−	0.829825i	0.997661	+	0.0683503i	$0.0217736\pi$
$174$		0			0
$175$	0.00845434	+	0.0146433i	0.000639088	+	0.00110693i
$176$		0			0
$177$	0.334125			0.0251144
$178$		0			0
$179$	2.82862	+	1.63310i	0.211421	+	0.122064i	0.601972	−	0.798517i	$-0.294382\pi$
$179$	2.82862	+	1.63310i	0.211421	+	0.122064i	−0.390551	+	0.920581i	$0.627715\pi$
$180$		0			0
$181$			13.1229i			0.975420i	0.873006	+	0.487710i	$0.162168\pi$
$181$			13.1229i			0.975420i	−0.873006	+	0.487710i	$0.837832\pi$
$182$		0			0
$183$	2.49083			0.184128
$184$		0			0
$185$	−5.87359	+	10.1734i	−0.431835	+	0.747960i
$186$		0			0
$187$			33.8005i			2.47174i
$188$		0			0
$189$	3.16550	−	1.82760i	0.230256	−	0.132938i
$190$		0			0
$191$	−4.02136	−	6.96520i	−0.290975	−	0.503984i	0.683065	−	0.730357i	$-0.260646\pi$
$191$	−4.02136	−	6.96520i	−0.290975	−	0.503984i	−0.974041	+	0.226373i	$0.927313\pi$
$192$		0			0
$193$	0.417932	−	0.723880i	0.0300834	−	0.0521060i	−0.850592	−	0.525827i	$-0.823756\pi$
$193$	0.417932	−	0.723880i	0.0300834	−	0.0521060i	0.880675	+	0.473721i	$0.157089\pi$
$194$		0			0
$195$	4.83211	+	2.98782i	0.346035	+	0.213962i
$196$		0			0
$197$	6.06608	+	3.50225i	0.432190	+	0.249525i	0.700279	−	0.713869i	$-0.253059\pi$
$197$	6.06608	+	3.50225i	0.432190	+	0.249525i	−0.268089	+	0.963394i	$0.586392\pi$
$198$		0			0
$199$	7.51756	+	13.0208i	0.532906	+	0.923019i	0.999262	+	0.0384223i	$0.0122332\pi$
$199$	7.51756	+	13.0208i	0.532906	+	0.923019i	−0.466356	+	0.884597i	$0.654433\pi$
$200$		0			0
$201$	1.58818	+	2.75081i	0.112022	+	0.194027i
$202$		0			0
$203$			1.83600i			0.128862i
$204$		0			0
$205$	−1.28828	−	0.743791i	−0.0899777	−	0.0519486i
$206$		0			0
$207$	5.39851			0.375223
$208$		0			0
$209$	−9.26819			−0.641094
$210$		0			0
$211$	−5.82236	−	3.36154i	−0.400828	−	0.231418i	0.286013	−	0.958226i	$-0.407670\pi$
$211$	−5.82236	−	3.36154i	−0.400828	−	0.231418i	−0.686841	+	0.726808i	$0.741003\pi$
$212$		0			0
$213$			8.18342i			0.560718i
$214$		0			0
$215$	−9.02622	−	15.6339i	−0.615583	−	1.06622i
$216$		0			0
$217$	−0.902189	−	1.56264i	−0.0612446	−	0.106079i
$218$		0			0
$219$	1.16766	+	0.674149i	0.0789032	+	0.0455548i
$220$		0			0
$221$	−19.2510	+	10.3528i	−1.29496	+	0.696403i
$222$		0			0
$223$	10.4340	−	18.0723i	0.698715	−	1.21021i	−0.270198	−	0.962805i	$-0.587089\pi$
$223$	10.4340	−	18.0723i	0.698715	−	1.21021i	0.968912	−	0.247404i	$-0.0795776\pi$
$224$		0			0
$225$	0.0224386	+	0.0388649i	0.00149591	+	0.00259099i
$226$		0			0
$227$	−16.7688	+	9.68145i	−1.11298	+	0.642580i	−0.939600	−	0.342274i	$-0.888803\pi$
$227$	−16.7688	+	9.68145i	−1.11298	+	0.642580i	−0.173382	+	0.984855i	$0.555469\pi$
$228$		0			0
$229$		−	17.6044i		−	1.16333i	−0.813428	−	0.581666i	$-0.802401\pi$
$229$		−	17.6044i		−	1.16333i	0.813428	−	0.581666i	$-0.197599\pi$
$230$		0			0
$231$	−1.85092	+	3.20589i	−0.121782	+	0.210932i
$232$		0			0
$233$	15.3281			1.00417			0.502087	−	0.864817i	$-0.332566\pi$
$233$	15.3281			1.00417			0.502087	+	0.864817i	$0.332566\pi$
$234$		0			0
$235$			23.6950i			1.54569i
$236$		0			0
$237$	8.29207	+	4.78743i	0.538628	+	0.310977i
$238$		0			0
$239$	14.0854			0.911111			0.455556	−	0.890207i	$-0.349441\pi$
$239$	14.0854			0.911111			0.455556	+	0.890207i	$0.349441\pi$
$240$		0			0
$241$	−7.24993	−	12.5572i	−0.467009	−	0.808883i	0.532281	−	0.846568i	$-0.321335\pi$
$241$	−7.24993	−	12.5572i	−0.467009	−	0.808883i	−0.999290	+	0.0376849i	$0.988002\pi$
$242$		0			0
$243$	12.9798	−	7.49392i	0.832658	−	0.480735i
$244$		0			0
$245$	11.8513	+	6.84234i	0.757151	+	0.437141i
$246$		0			0
$247$	−2.83876	−	5.27867i	−0.180626	−	0.335874i
$248$		0			0
$249$	−4.06652	+	7.04342i	−0.257705	+	0.446359i
$250$		0			0
$251$	24.8381	−	14.3403i	1.56777	−	0.905151i	0.571340	−	0.820714i	$-0.306424\pi$
$251$	24.8381	−	14.3403i	1.56777	−	0.905151i	0.996429	−	0.0844378i	$-0.0269094\pi$
$252$		0			0
$253$	−10.4050	+	6.00731i	−0.654155	+	0.377677i
$254$		0			0
$255$	9.55241			0.598195
$256$		0			0
$257$	5.81269	−	10.0679i	0.362586	−	0.628017i	−0.625800	−	0.779984i	$-0.715227\pi$
$257$	5.81269	−	10.0679i	0.362586	−	0.628017i	0.988386	+	0.151967i	$0.0485607\pi$
$258$		0			0
$259$		−	4.94994i		−	0.307574i
$260$		0			0
$261$			4.87293i			0.301627i
$262$		0			0
$263$	−8.47469	+	14.6786i	−0.522572	+	0.905121i	0.477083	+	0.878858i	$0.341694\pi$
$263$	−8.47469	+	14.6786i	−0.522572	+	0.905121i	−0.999655	+	0.0262631i	$0.991639\pi$
$264$		0			0
$265$	23.2703			1.42948
$266$		0			0
$267$	0.455220	−	0.262821i	0.0278590	−	0.0160844i
$268$		0			0
$269$	6.45180	−	3.72495i	0.393373	−	0.227114i	−0.290247	−	0.956952i	$-0.593738\pi$
$269$	6.45180	−	3.72495i	0.393373	−	0.227114i	0.683621	+	0.729837i	$0.260404\pi$
$270$		0			0
$271$	−7.61248	+	13.1852i	−0.462425	+	0.800944i	−0.999081	−	0.0428569i	$-0.986354\pi$
$271$	−7.61248	+	13.1852i	−0.462425	+	0.800944i	0.536656	+	0.843801i	$0.319687\pi$
$272$		0			0
$273$	−2.39282	−	0.0722535i	−0.144820	−	0.00437298i
$274$		0			0
$275$	−0.0864954	−	0.0499382i	−0.00521587	−	0.00301138i
$276$		0			0
$277$	−13.9928	+	8.07878i	−0.840749	+	0.485407i	−0.857519	−	0.514453i	$-0.827995\pi$
$277$	−13.9928	+	8.07878i	−0.840749	+	0.485407i	0.0167699	+	0.999859i	$0.494662\pi$
$278$		0			0
$279$	−2.39450	−	4.14739i	−0.143355	−	0.248298i
$280$		0			0
$281$	27.7204			1.65366			0.826831	−	0.562450i	$-0.190141\pi$
$281$	27.7204			1.65366			0.826831	+	0.562450i	$0.190141\pi$
$282$		0			0
$283$	−3.28760	−	1.89810i	−0.195428	−	0.112830i	0.399093	−	0.916910i	$-0.369325\pi$
$283$	−3.28760	−	1.89810i	−0.195428	−	0.112830i	−0.594521	+	0.804080i	$0.702658\pi$
$284$		0			0
$285$			2.61930i			0.155154i
$286$		0			0
$287$	0.626827			0.0370004
$288$		0			0
$289$	−9.87617	+	17.1060i	−0.580951	+	1.00624i
$290$		0			0
$291$		−	0.901409i		−	0.0528415i
$292$		0			0
$293$	4.14791	−	2.39480i	0.242324	−	0.139906i	−0.373921	−	0.927461i	$-0.621987\pi$
$293$	4.14791	−	2.39480i	0.242324	−	0.139906i	0.616244	+	0.787555i	$0.288653\pi$
$294$		0			0
$295$	−0.532024	−	0.921493i	−0.0309756	−	0.0536514i
$296$		0			0
$297$	−10.7953	+	18.6980i	−0.626406	+	1.08497i
$298$		0			0
$299$	−6.60839	−	4.08614i	−0.382173	−	0.236308i
$300$		0			0
$301$	6.58768	+	3.80340i	0.379708	+	0.219224i
$302$		0			0
$303$	3.43403	+	5.94792i	0.197280	+	0.341699i
$304$		0			0
$305$	−3.96613	−	6.86954i	−0.227100	−	0.393349i
$306$		0			0
$307$		−	8.95981i		−	0.511363i	−0.966761	−	0.255682i	$-0.917700\pi$
$307$		−	8.95981i		−	0.511363i	0.966761	−	0.255682i	$-0.0822999\pi$
$308$		0			0
$309$	−9.18359	−	5.30215i	−0.522436	−	0.301629i
$310$		0			0
$311$	−9.35196			−0.530301			−0.265150	−	0.964207i	$-0.585422\pi$
$311$	−9.35196			−0.530301			−0.265150	+	0.964207i	$0.585422\pi$
$312$		0			0
$313$	−11.7834			−0.666039			−0.333019	−	0.942920i	$-0.608067\pi$
$313$	−11.7834			−0.666039			−0.333019	+	0.942920i	$0.608067\pi$
$314$		0			0
$315$	−4.58738	−	2.64853i	−0.258470	−	0.149228i
$316$		0			0
$317$			0.828044i			0.0465076i	0.999730	+	0.0232538i	$0.00740258\pi$
$317$			0.828044i			0.0465076i	−0.999730	+	0.0232538i	$0.992597\pi$
$318$		0			0
$319$	−5.42246	−	9.39197i	−0.303599	−	0.525850i
$320$		0			0
$321$	−5.52492	−	9.56945i	−0.308371	−	0.534114i
$322$		0			0
$323$	−8.72745	−	5.03879i	−0.485608	−	0.280366i
$324$		0			0
$325$	0.00194941	−	0.0645588i	0.000108134	−	0.00358108i
$326$		0			0
$327$	−3.41126	+	5.90848i	−0.188643	+	0.326740i
$328$		0			0
$329$	−4.99222	−	8.64678i	−0.275230	−	0.476712i
$330$		0			0
$331$	12.8419	−	7.41425i	0.705853	−	0.407524i	−0.103671	−	0.994612i	$-0.533059\pi$
$331$	12.8419	−	7.41425i	0.705853	−	0.407524i	0.809524	+	0.587087i	$0.199726\pi$
$332$		0			0
$333$		−	13.1376i		−	0.719937i
$334$		0			0
$335$	5.05769	−	8.76018i	0.276331	−	0.478620i
$336$		0			0
$337$	5.53901			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$337$	5.53901			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$338$		0			0
$339$		−	5.31941i		−	0.288911i
$340$		0			0
$341$	9.23019	+	5.32906i	0.499843	+	0.288585i
$342$		0			0
$343$	−12.3737			−0.668116
$344$		0			0
$345$	1.69774	+	2.94056i	0.0914030	+	0.158315i
$346$		0			0
$347$	−13.9803	+	8.07154i	−0.750503	+	0.433303i	−0.825876	−	0.563852i	$-0.809319\pi$
$347$	−13.9803	+	8.07154i	−0.750503	+	0.433303i	0.0753728	+	0.997155i	$0.475985\pi$
$348$		0			0
$349$	−20.7087	−	11.9562i	−1.10851	−	0.640000i	−0.170068	−	0.985432i	$-0.554399\pi$
$349$	−20.7087	−	11.9562i	−1.10851	−	0.640000i	−0.938444	+	0.345432i	$0.887732\pi$
$350$		0			0
$351$	−13.9559	−	0.421410i	−0.744909	−	0.0224932i
$352$		0			0
$353$	−2.77899	+	4.81335i	−0.147911	+	0.256189i	−0.930455	−	0.366406i	$-0.880588\pi$
$353$	−2.77899	+	4.81335i	−0.147911	+	0.256189i	0.782544	+	0.622595i	$0.213921\pi$
$354$		0			0
$355$	22.5693	−	13.0304i	1.19785	−	0.691581i
$356$		0			0
$357$	−3.48586	+	2.01256i	−0.184491	+	0.106516i
$358$		0			0
$359$	8.55135			0.451323			0.225661	−	0.974206i	$-0.427546\pi$
$359$	8.55135			0.451323			0.225661	+	0.974206i	$0.427546\pi$
$360$		0			0
$361$	−8.11835	+	14.0614i	−0.427282	+	0.740073i
$362$		0			0
$363$		−	14.1285i		−	0.741556i
$364$		0			0
$365$		−	4.29377i		−	0.224746i
$366$		0			0
$367$	−1.96700	+	3.40695i	−0.102677	+	0.177841i	−0.912787	−	0.408437i	$-0.866074\pi$
$367$	−1.96700	+	3.40695i	−0.102677	+	0.177841i	0.810110	+	0.586278i	$0.199407\pi$
$368$		0			0
$369$	1.66366			0.0866066
$370$		0			0
$371$	−8.49179	+	4.90274i	−0.440872	+	0.254537i
$372$		0			0
$373$	−6.86329	+	3.96253i	−0.355368	+	0.205172i	−0.667047	−	0.745016i	$-0.732442\pi$
$373$	−6.86329	+	3.96253i	−0.355368	+	0.205172i	0.311679	+	0.950187i	$0.399109\pi$
$374$		0			0
$375$	3.92511	−	6.79849i	0.202692	−	0.351073i
$376$		0			0
$377$	3.68832	−	5.96502i	0.189958	−	0.307214i
$378$		0			0
$379$	−22.8779	−	13.2086i	−1.17516	−	0.678479i	−0.220271	−	0.975439i	$-0.570694\pi$
$379$	−22.8779	−	13.2086i	−1.17516	−	0.678479i	−0.954890	+	0.296959i	$0.904027\pi$
$380$		0			0
$381$	−1.87579	+	1.08299i	−0.0960995	+	0.0554831i
$382$		0			0
$383$	0.947088	+	1.64041i	0.0483940	+	0.0838208i	0.889208	−	0.457504i	$-0.151256\pi$
$383$	0.947088	+	1.64041i	0.0483940	+	0.0838208i	−0.840814	+	0.541325i	$0.817923\pi$
$384$		0			0
$385$	11.7888			0.600814
$386$		0			0
$387$	17.4844	+	10.0946i	0.888780	+	0.513137i
$388$		0			0
$389$		−	25.0808i		−	1.27165i	−0.771835	−	0.635823i	$-0.780661\pi$
$389$		−	25.0808i		−	1.27165i	0.771835	−	0.635823i	$-0.219339\pi$
$390$		0			0
$391$	−13.0639			−0.660669
$392$		0			0
$393$	−4.19040	+	7.25798i	−0.211378	+	0.366117i
$394$		0			0
$395$		−	30.4919i		−	1.53422i
$396$		0			0
$397$	7.99993	−	4.61876i	0.401505	−	0.231809i	−0.285628	−	0.958341i	$-0.592202\pi$
$397$	7.99993	−	4.61876i	0.401505	−	0.231809i	0.687133	+	0.726532i	$0.258869\pi$
$398$		0			0
$399$	−0.551850	−	0.955832i	−0.0276270	−	0.0478515i
$400$		0			0
$401$	−2.21136	+	3.83018i	−0.110430	+	0.191270i	−0.915944	−	0.401307i	$-0.868556\pi$
$401$	−2.21136	+	3.83018i	−0.110430	+	0.191270i	0.805514	+	0.592577i	$0.201889\pi$
$402$		0			0
$403$	−0.208028	+	6.88927i	−0.0103626	+	0.343179i
$404$		0			0
$405$	−9.29576	−	5.36691i	−0.461910	−	0.266684i
$406$		0			0
$407$	14.6192	+	25.3212i	0.724646	+	1.25512i
$408$		0			0
$409$	−13.2341	−	22.9221i	−0.654384	−	1.13343i	−0.982048	−	0.188631i	$-0.939595\pi$
$409$	−13.2341	−	22.9221i	−0.654384	−	1.13343i	0.327664	−	0.944794i	$-0.393738\pi$
$410$		0			0
$411$			14.3977i			0.710184i
$412$		0			0
$413$	0.388292	+	0.224180i	0.0191066	+	0.0110312i
$414$		0			0
$415$	25.9004			1.27140
$416$		0			0
$417$	5.69851			0.279057
$418$		0			0
$419$	−4.30501	−	2.48550i	−0.210314	−	0.121425i	0.391144	−	0.920330i	$-0.372080\pi$
$419$	−4.30501	−	2.48550i	−0.210314	−	0.121425i	−0.601457	+	0.798905i	$0.705413\pi$
$420$		0			0
$421$		−	24.0575i		−	1.17249i	−0.810134	−	0.586244i	$-0.800606\pi$
$421$		−	24.0575i		−	1.17249i	0.810134	−	0.586244i	$-0.199394\pi$
$422$		0			0
$423$	−13.2498	−	22.9494i	−0.644229	−	1.11584i
$424$		0			0
$425$	−0.0542993	−	0.0940492i	−0.00263390	−	0.00456205i
$426$		0			0
$427$	2.89464	+	1.67122i	0.140081	+	0.0808760i
$428$		0			0
$429$	12.4538	−	6.69737i	0.601273	−	0.323352i
$430$		0			0
$431$	5.28961	−	9.16188i	0.254792	−	0.441312i	−0.710047	−	0.704154i	$-0.751326\pi$
$431$	5.28961	−	9.16188i	0.254792	−	0.441312i	0.964839	+	0.262842i	$0.0846598\pi$
$432$		0			0
$433$	6.11293	+	10.5879i	0.293769	+	0.508822i	0.974698	−	0.223527i	$-0.0717572\pi$
$433$	6.11293	+	10.5879i	0.293769	+	0.508822i	−0.680929	+	0.732349i	$0.738424\pi$
$434$		0			0
$435$	−2.65428	+	1.53245i	−0.127263	+	0.0734753i
$436$		0			0
$437$		−	3.58215i		−	0.171357i
$438$		0			0
$439$	6.46417	−	11.1963i	0.308518	−	0.534369i	−0.669520	−	0.742794i	$-0.733500\pi$
$439$	6.46417	−	11.1963i	0.308518	−	0.534369i	0.978038	+	0.208425i	$0.0668336\pi$
$440$		0			0
$441$	−15.3045			−0.728784
$442$		0			0
$443$		−	14.0440i		−	0.667248i	−0.942706	−	0.333624i	$-0.891728\pi$
$443$		−	14.0440i		−	0.667248i	0.942706	−	0.333624i	$-0.108272\pi$
$444$		0			0
$445$	−1.44969	−	0.836976i	−0.0687217	−	0.0396765i
$446$		0			0
$447$	2.54634			0.120438
$448$		0			0
$449$	−0.857113	−	1.48456i	−0.0404497	−	0.0700609i	0.845092	−	0.534621i	$-0.179546\pi$
$449$	−0.857113	−	1.48456i	−0.0404497	−	0.0700609i	−0.885541	+	0.464560i	$0.846212\pi$
$450$		0			0
$451$	−3.20650	+	1.85127i	−0.150988	+	0.0871730i
$452$		0			0
$453$	−9.80393	−	5.66030i	−0.460629	−	0.265944i
$454$		0			0
$455$	3.61080	+	6.71429i	0.169277	+	0.314771i
$456$		0			0
$457$	14.5822	−	25.2571i	0.682126	−	1.18148i	−0.292205	−	0.956356i	$-0.594389\pi$
$457$	14.5822	−	25.2571i	0.682126	−	1.18148i	0.974331	−	0.225121i	$-0.0722778\pi$
$458$		0			0
$459$	−20.3309	+	11.7380i	−0.948964	+	0.547885i
$460$		0			0
$461$	22.4501	−	12.9616i	1.04561	−	0.603681i	0.124190	−	0.992258i	$-0.460367\pi$
$461$	22.4501	−	12.9616i	1.04561	−	0.603681i	0.921416	+	0.388577i	$0.127033\pi$
$462$		0			0
$463$	−36.7003			−1.70561			−0.852803	−	0.522233i	$-0.825099\pi$
$463$	−36.7003			−1.70561			−0.852803	+	0.522233i	$0.825099\pi$
$464$		0			0
$465$	1.50605	−	2.60856i	0.0698415	−	0.120969i
$466$		0			0
$467$			27.9836i			1.29492i	0.762097	+	0.647462i	$0.224170\pi$
$467$			27.9836i			1.29492i	−0.762097	+	0.647462i	$0.775830\pi$
$468$		0			0
$469$			4.26234i			0.196817i
$470$		0			0
$471$	5.42590	−	9.39794i	0.250012	−	0.433034i
$472$		0			0
$473$	−44.9319			−2.06597
$474$		0			0
$475$	0.0257885	−	0.0148890i	0.00118326	−	0.000683155i
$476$		0			0
$477$	−22.5380	+	13.0123i	−1.03195	+	0.595794i
$478$		0			0
$479$	−16.2482	+	28.1426i	−0.742397	+	1.28587i	0.209004	+	0.977915i	$0.432978\pi$
$479$	−16.2482	+	28.1426i	−0.742397	+	1.28587i	−0.951401	+	0.307955i	$0.900355\pi$
$480$		0			0
$481$	−9.94388	+	16.0819i	−0.453402	+	0.733273i
$482$		0			0
$483$	−1.23907	−	0.715379i	−0.0563798	−	0.0325509i
$484$		0			0
$485$	−2.48602	+	1.43531i	−0.112885	+	0.0651739i
$486$		0			0
$487$	5.79695	+	10.0406i	0.262685	+	0.454983i	0.966954	−	0.254949i	$-0.0820587\pi$
$487$	5.79695	+	10.0406i	0.262685	+	0.454983i	−0.704270	+	0.709933i	$0.748725\pi$
$488$		0			0
$489$	3.52399			0.159360
$490$		0			0
$491$	−36.2077	−	20.9045i	−1.63403	−	0.943407i	−0.982833	−	0.184498i	$-0.940934\pi$
$491$	−36.2077	−	20.9045i	−1.63403	−	0.943407i	−0.651197	−	0.758909i	$-0.725733\pi$
$492$		0			0
$493$		−	11.7920i		−	0.531085i
$494$		0			0
$495$	31.2887			1.40632
$496$		0			0
$497$	−5.49065	+	9.51008i	−0.246289	+	0.426585i
$498$		0			0
$499$		−	17.9011i		−	0.801363i	−0.916217	−	0.400682i	$-0.868773\pi$
$499$		−	17.9011i		−	0.801363i	0.916217	−	0.400682i	$-0.131227\pi$
$500$		0			0
$501$	−0.648402	+	0.374355i	−0.0289684	+	0.0167249i
$502$		0			0
$503$	7.29456	+	12.6345i	0.325248	+	0.563346i	0.981563	−	0.191141i	$-0.0612188\pi$
$503$	7.29456	+	12.6345i	0.325248	+	0.563346i	−0.656314	+	0.754488i	$0.727886\pi$
$504$		0			0
$505$	10.9360	−	18.9416i	0.486644	−	0.842892i
$506$		0			0
$507$	7.62893	+	5.04166i	0.338813	+	0.223908i
$508$		0			0
$509$	−1.08621	−	0.627122i	−0.0481453	−	0.0277967i	0.475734	−	0.879589i	$-0.342182\pi$
$509$	−1.08621	−	0.627122i	−0.0481453	−	0.0277967i	−0.523879	+	0.851792i	$0.675516\pi$
$510$		0			0
$511$	0.904639	+	1.56688i	0.0400189	+	0.0693147i
$512$		0			0
$513$	−3.21860	−	5.57478i	−0.142105	−	0.246133i
$514$		0			0
$515$			33.7703i			1.48810i
$516$		0			0
$517$	51.0749	+	29.4881i	2.24627	+	1.29688i
$518$		0			0
$519$	−15.3550			−0.674008
$520$		0			0
$521$	8.42526			0.369117			0.184559	−	0.982822i	$-0.440914\pi$
$521$	8.42526			0.369117			0.184559	+	0.982822i	$0.440914\pi$
$522$		0			0
$523$	20.6677	+	11.9325i	0.903736	+	0.521772i	0.878410	−	0.477907i	$-0.158604\pi$
$523$	20.6677	+	11.9325i	0.903736	+	0.521772i	0.0253256	+	0.999679i	$0.491938\pi$
$524$		0			0
$525$		−	0.0118937i		−	0.000519086i
$526$		0			0
$527$	5.79445	+	10.0363i	0.252410	+	0.437187i
$528$		0			0
$529$	9.17818	+	15.8971i	0.399051	+	0.691177i
$530$		0			0
$531$	1.03056	+	0.594997i	0.0447227	+	0.0258207i
$532$		0			0
$533$	−2.03651	−	1.25922i	−0.0882109	−	0.0545431i
$534$		0			0
$535$	−17.5946	+	30.4747i	−0.760680	+	1.31754i
$536$		0			0
$537$	−1.14874	−	1.98968i	−0.0495719	−	0.0858611i
$538$		0			0
$539$	29.4975	−	17.0304i	1.27055	−	0.733550i
$540$		0			0
$541$			19.4928i			0.838059i	0.907973	+	0.419030i	$0.137630\pi$
$541$			19.4928i			0.838059i	−0.907973	+	0.419030i	$0.862370\pi$
$542$		0			0
$543$	4.61541	−	7.99412i	0.198066	−	0.343060i
$544$		0			0
$545$	21.7269			0.930678
$546$		0			0
$547$			2.18538i			0.0934399i	0.998908	+	0.0467200i	$0.0148768\pi$
$547$			2.18538i			0.0934399i	−0.998908	+	0.0467200i	$0.985123\pi$
$548$		0			0
$549$	7.68265	+	4.43558i	0.327887	+	0.189306i
$550$		0			0
$551$	3.23340			0.137747
$552$		0			0
$553$	6.42423	+	11.1271i	0.273186	+	0.473172i
$554$		0			0
$555$	7.15605	−	4.13155i	0.303757	−	0.175374i
$556$		0			0
$557$	29.5902	+	17.0839i	1.25378	+	0.723869i	0.971858	−	0.235568i	$-0.0756951\pi$
$557$	29.5902	+	17.0839i	1.25378	+	0.723869i	0.281921	+	0.959438i	$0.409028\pi$
$558$		0			0
$559$	−13.7622	−	25.5908i	−0.582080	−	1.08238i
$560$		0			0
$561$	11.8878	−	20.5903i	0.501904	−	0.869324i
$562$		0			0
$563$	−20.4379	+	11.7998i	−0.861353	+	0.497302i	−0.864465	−	0.502693i	$-0.832343\pi$
$563$	−20.4379	+	11.7998i	−0.861353	+	0.497302i	0.00311215	+	0.999995i	$0.499009\pi$
$564$		0			0
$565$	−14.6706	+	8.47006i	−0.617195	+	0.356338i
$566$		0			0
$567$	4.52294			0.189946
$568$		0			0
$569$	−1.38906	+	2.40592i	−0.0582323	+	0.100861i	−0.893672	−	0.448721i	$-0.851880\pi$
$569$	−1.38906	+	2.40592i	−0.0582323	+	0.100861i	0.835440	+	0.549582i	$0.185213\pi$
$570$		0			0
$571$		−	19.2497i		−	0.805577i	−0.915293	−	0.402788i	$-0.868041\pi$
$571$		−	19.2497i		−	0.805577i	0.915293	−	0.402788i	$-0.131959\pi$
$572$		0			0
$573$			5.65734i			0.236339i
$574$		0			0
$575$	0.0193011	−	0.0334304i	0.000804910	−	0.00139415i
$576$		0			0
$577$	6.64617			0.276683			0.138342	−	0.990385i	$-0.455823\pi$
$577$	6.64617			0.276683			0.138342	+	0.990385i	$0.455823\pi$
$578$		0			0
$579$	−0.509185	+	0.293978i	−0.0211610	+	0.0122173i
$580$		0			0
$581$	−9.45154	+	5.45685i	−0.392116	+	0.226388i
$582$		0			0
$583$	28.9595	−	50.1594i	1.19938	−	2.07739i
$584$		0			0
$585$	9.58342	+	17.8204i	0.396226	+	0.736782i
$586$		0			0
$587$	23.1016	+	13.3377i	0.953505	+	0.550507i	0.894168	−	0.447731i	$-0.147768\pi$
$587$	23.1016	+	13.3377i	0.953505	+	0.550507i	0.0593374	+	0.998238i	$0.481101\pi$
$588$		0			0
$589$	−2.75197	+	1.58885i	−0.113393	+	0.0654675i
$590$		0			0
$591$	−2.46352	−	4.26694i	−0.101336	−	0.175519i
$592$		0			0
$593$	6.61409			0.271608			0.135804	−	0.990736i	$-0.456638\pi$
$593$	6.61409			0.271608			0.135804	+	0.990736i	$0.456638\pi$
$594$		0			0
$595$	11.1010	+	6.40917i	0.455097	+	0.262751i
$596$		0			0
$597$		−	10.5759i		−	0.432841i
$598$		0			0
$599$	−11.9319			−0.487523			−0.243762	−	0.969835i	$-0.578381\pi$
$599$	−11.9319			−0.487523			−0.243762	+	0.969835i	$0.578381\pi$
$600$		0			0
$601$	6.15610	−	10.6627i	0.251113	−	0.434940i	−0.712720	−	0.701449i	$-0.752537\pi$
$601$	6.15610	−	10.6627i	0.251113	−	0.434940i	0.963832	+	0.266509i	$0.0858702\pi$
$602$		0			0
$603$			11.3127i			0.460688i
$604$		0			0
$605$	−38.9655	+	22.4968i	−1.58417	+	0.914623i
$606$		0			0
$607$	−4.35738	−	7.54720i	−0.176860	−	0.306331i	0.763943	−	0.645284i	$-0.223261\pi$
$607$	−4.35738	−	7.54720i	−0.176860	−	0.306331i	−0.940804	+	0.338952i	$0.889927\pi$
$608$		0			0
$609$	0.645732	−	1.11844i	0.0261664	−	0.0453215i
$610$		0			0
$611$	−1.15111	+	38.1215i	−0.0465690	+	1.54223i
$612$		0			0
$613$	−30.7480	−	17.7523i	−1.24190	−	0.717010i	−0.272418	−	0.962179i	$-0.587823\pi$
$613$	−30.7480	−	17.7523i	−1.24190	−	0.717010i	−0.969480	+	0.245169i	$0.921157\pi$
$614$		0			0
$615$	0.523191	+	0.906193i	0.0210971	+	0.0365412i
$616$		0			0
$617$	12.0318	+	20.8396i	0.484380	+	0.838971i	0.999839	−	0.0179431i	$-0.00571178\pi$
$617$	12.0318	+	20.8396i	0.484380	+	0.838971i	−0.515459	+	0.856914i	$0.672378\pi$
$618$		0			0
$619$		−	21.6806i		−	0.871417i	−0.900088	−	0.435708i	$-0.856498\pi$
$619$		−	21.6806i		−	0.871417i	0.900088	−	0.435708i	$-0.143502\pi$
$620$		0			0
$621$	−7.22675	−	4.17237i	−0.290000	−	0.167431i
$622$		0			0
$623$	0.705358			0.0282596
$624$		0			0
$625$	−25.0892			−1.00357
$626$		0			0
$627$	5.64592	+	3.25967i	0.225476	+	0.130179i
$628$		0			0
$629$			31.7918i			1.26762i
$630$		0			0
$631$	9.48379	+	16.4264i	0.377544	+	0.653925i	0.990704	−	0.136033i	$-0.0434355\pi$
$631$	9.48379	+	16.4264i	0.377544	+	0.653925i	−0.613161	+	0.789958i	$0.710102\pi$
$632$		0			0
$633$	2.36454	+	4.09551i	0.0939821	+	0.162782i
$634$		0			0
$635$	5.97360	+	3.44886i	0.237055	+	0.136864i
$636$		0			0
$637$	18.7344	+	11.5840i	0.742284	+	0.458973i
$638$		0			0
$639$	−14.5727	+	25.2407i	−0.576488	+	0.998506i
$640$		0			0
$641$	−12.4294	−	21.5284i	−0.490934	−	0.850322i	0.509012	−	0.860759i	$-0.330011\pi$
$641$	−12.4294	−	21.5284i	−0.490934	−	0.850322i	−0.999946	+	0.0104375i	$0.996678\pi$
$642$		0			0
$643$	3.25429	−	1.87887i	0.128337	−	0.0740952i	−0.434457	−	0.900692i	$-0.643060\pi$
$643$	3.25429	−	1.87887i	0.128337	−	0.0740952i	0.562794	+	0.826597i	$0.309726\pi$
$644$		0			0
$645$			12.6983i			0.499994i
$646$		0			0
$647$	24.0878	−	41.7213i	0.946989	−	1.64023i	0.195271	−	0.980749i	$-0.437441\pi$
$647$	24.0878	−	41.7213i	0.946989	−	1.64023i	0.751718	−	0.659484i	$-0.229225\pi$
$648$		0			0
$649$	−2.64838			−0.103958
$650$		0			0
$651$			1.26922i			0.0497446i
$652$		0			0
$653$	−21.5793	−	12.4588i	−0.844463	−	0.487551i	0.0143156	−	0.999898i	$-0.495443\pi$
$653$	−21.5793	−	12.4588i	−0.844463	−	0.487551i	−0.858779	+	0.512346i	$0.828776\pi$
$654$		0			0
$655$	26.6894			1.04284
$656$		0			0
$657$	2.40100	+	4.15865i	0.0936719	+	0.162244i
$658$		0			0
$659$	1.75765	−	1.01478i	0.0684684	−	0.0395302i	−0.465375	−	0.885114i	$-0.654081\pi$
$659$	1.75765	−	1.01478i	0.0684684	−	0.0395302i	0.533843	+	0.845583i	$0.320747\pi$
$660$		0			0
$661$	9.61763	+	5.55274i	0.374082	+	0.215977i	0.675240	−	0.737598i	$-0.264040\pi$
$661$	9.61763	+	5.55274i	0.374082	+	0.215977i	−0.301158	+	0.953574i	$0.597373\pi$
$662$		0			0
$663$	15.3683	+	0.464059i	0.596855	+	0.0180226i
$664$		0			0
$665$	−1.75741	+	3.04393i	−0.0681495	+	0.118038i
$666$		0			0
$667$	3.62999	−	2.09578i	0.140554	−	0.0811488i
$668$		0			0
$669$	−12.7122	+	7.33941i	−0.491483	+	0.283758i
$670$		0			0
$671$	−19.7432			−0.762176
$672$		0			0
$673$	−17.0389	+	29.5122i	−0.656800	+	1.13761i	0.324639	+	0.945838i	$0.394757\pi$
$673$	−17.0389	+	29.5122i	−0.656800	+	1.13761i	−0.981439	+	0.191773i	$0.938576\pi$
$674$		0			0
$675$		−	0.0693689i		−	0.00267001i
$676$		0			0
$677$			28.8974i			1.11062i	0.831645	+	0.555308i	$0.187400\pi$
$677$			28.8974i			1.11062i	−0.831645	+	0.555308i	$0.812600\pi$
$678$		0			0
$679$	0.604799	−	1.04754i	0.0232100	−	0.0402010i
$680$		0			0
$681$	13.6201			0.521922
$682$		0			0
$683$	18.5350	−	10.7012i	0.709221	−	0.409469i	−0.101551	−	0.994830i	$-0.532381\pi$
$683$	18.5350	−	10.7012i	0.709221	−	0.409469i	0.810773	+	0.585361i	$0.199047\pi$
$684$		0			0
$685$	39.7078	−	22.9253i	1.51716	−	0.875930i
$686$		0			0
$687$	−6.19156	+	10.7241i	−0.236223	+	0.409150i
$688$		0			0
$689$	37.4381	+	1.13048i	1.42628	+	0.0430678i
$690$		0			0
$691$	42.9878	+	24.8190i	1.63533	+	0.944159i	0.982411	+	0.186733i	$0.0597900\pi$
$691$	42.9878	+	24.8190i	1.63533	+	0.944159i	0.652921	+	0.757426i	$0.273543\pi$
$692$		0			0
$693$	−11.4178	+	6.59210i	−0.433728	+	0.250413i
$694$		0			0
$695$	−9.07368	−	15.7161i	−0.344184	−	0.596145i
$696$		0			0
$697$	−4.02589			−0.152491
$698$		0			0
$699$	−9.33742	−	5.39096i	−0.353174	−	0.203905i
$700$		0			0
$701$			23.3855i			0.883258i	0.897198	+	0.441629i	$0.145599\pi$
$701$			23.3855i			0.883258i	−0.897198	+	0.441629i	$0.854401\pi$
$702$		0			0
$703$	−8.71738			−0.328782
$704$		0			0
$705$	8.33367	−	14.4343i	0.313864	−	0.543629i
$706$		0			0
$707$			9.21623i			0.346612i
$708$		0			0
$709$	41.1118	−	23.7359i	1.54399	−	0.891421i	0.545405	−	0.838172i	$-0.316376\pi$
$709$	41.1118	−	23.7359i	1.54399	−	0.891421i	0.998581	−	0.0532487i	$-0.0169576\pi$
$710$		0			0
$711$	17.0505	+	29.5324i	0.639445	+	1.10755i
$712$		0			0
$713$	−2.05968	+	3.56746i	−0.0771355	+	0.133603i
$714$		0			0
$715$	−38.3009	−	23.6824i	−1.43237	−	0.885672i
$716$		0			0
$717$	−8.58045	−	4.95392i	−0.320443	−	0.185008i
$718$		0			0
$719$	−22.6840	−	39.2899i	−0.845972	−	1.46527i	−0.884774	−	0.466020i	$-0.845688\pi$
$719$	−22.6840	−	39.2899i	−0.845972	−	1.46527i	0.0388023	−	0.999247i	$-0.487646\pi$
$720$		0			0
$721$	−7.11493	−	12.3234i	−0.264974	−	0.458948i
$722$		0			0
$723$			10.1993i			0.379318i
$724$		0			0
$725$	0.0301757	+	0.0174220i	0.00112070	+	0.000647036i
$726$		0			0
$727$	−27.1042			−1.00524			−0.502619	−	0.864508i	$-0.667630\pi$
$727$	−27.1042			−1.00524			−0.502619	+	0.864508i	$0.667630\pi$
$728$		0			0
$729$	3.83260			0.141948
$730$		0			0
$731$	−42.3104	−	24.4279i	−1.56491	−	0.903500i
$732$		0			0
$733$			21.1225i			0.780179i	0.920777	+	0.390090i	$0.127556\pi$
$733$			21.1225i			0.780179i	−0.920777	+	0.390090i	$0.872444\pi$
$734$		0			0
$735$	−4.81298	−	8.33632i	−0.177529	−	0.307490i
$736$		0			0
$737$	−12.5884	−	21.8038i	−0.463701	−	0.803153i
$738$		0			0
$739$	25.6746	+	14.8233i	0.944457	+	0.545283i	0.891355	−	0.453307i	$-0.149756\pi$
$739$	25.6746	+	14.8233i	0.944457	+	0.545283i	0.0531023	+	0.998589i	$0.483089\pi$
$740$		0			0
$741$	−0.127246	+	4.21402i	−0.00467451	+	0.154806i
$742$		0			0
$743$	−5.52318	+	9.56643i	−0.202626	+	0.350958i	−0.949374	−	0.314149i	$-0.898281\pi$
$743$	−5.52318	+	9.56643i	−0.202626	+	0.350958i	0.746748	+	0.665107i	$0.231614\pi$
$744$		0			0
$745$	−4.05452	−	7.02264i	−0.148546	−	0.257290i
$746$		0			0
$747$	−25.0853	+	14.4830i	−0.917824	+	0.529906i
$748$		0			0
$749$		−	14.8277i		−	0.541794i
$750$		0			0
$751$	−18.6034	+	32.2220i	−0.678846	+	1.17580i	0.296483	+	0.955038i	$0.404186\pi$
$751$	−18.6034	+	32.2220i	−0.678846	+	1.17580i	−0.975329	+	0.220758i	$0.929147\pi$
$752$		0			0
$753$	−20.1742			−0.735190
$754$		0			0
$755$			36.0514i			1.31204i
$756$		0			0
$757$	−17.2083	−	9.93522i	−0.625446	−	0.361102i	0.153540	−	0.988142i	$-0.450933\pi$
$757$	−17.2083	−	9.93522i	−0.625446	−	0.361102i	−0.778986	+	0.627041i	$0.784266\pi$
$758$		0			0
$759$	8.45122			0.306760
$760$		0			0
$761$	−4.52926	−	7.84491i	−0.164186	−	0.284378i	0.772180	−	0.635404i	$-0.219166\pi$
$761$	−4.52926	−	7.84491i	−0.164186	−	0.284378i	−0.936366	+	0.351026i	$0.885833\pi$
$762$		0			0
$763$	−7.92857	+	4.57756i	−0.287033	+	0.165719i
$764$		0			0
$765$	29.4632	+	17.0106i	1.06524	+	0.615018i
$766$		0			0
$767$	−0.811174	−	1.50838i	−0.0292898	−	0.0544644i
$768$		0			0
$769$	−5.28678	+	9.15697i	−0.190646	+	0.330209i	−0.945465	−	0.325725i	$-0.894392\pi$
$769$	−5.28678	+	9.15697i	−0.190646	+	0.330209i	0.754818	+	0.655934i	$0.227725\pi$
$770$		0			0
$771$	−7.08185	+	4.08871i	−0.255047	+	0.147251i
$772$		0			0
$773$	22.3264	−	12.8902i	0.803026	−	0.463627i	−0.0415022	−	0.999138i	$-0.513214\pi$
$773$	22.3264	−	12.8902i	0.803026	−	0.463627i	0.844528	+	0.535511i	$0.179881\pi$
$774$		0			0
$775$	−0.0342437			−0.00123007
$776$		0			0
$777$	−1.74092	+	3.01536i	−0.0624552	+	0.108176i
$778$		0			0
$779$		−	1.10391i		−	0.0395517i
$780$		0			0
$781$		−	64.8644i		−	2.32103i
$782$		0			0
$783$	3.76616	−	6.52318i	0.134592	−	0.233119i
$784$		0			0
$785$	−34.5585			−1.23345
$786$		0			0
$787$	12.1719	−	7.02745i	0.433881	−	0.250502i	−0.267117	−	0.963664i	$-0.586071\pi$
$787$	12.1719	−	7.02745i	0.433881	−	0.250502i	0.700999	+	0.713162i	$0.252738\pi$
$788$		0			0
$789$	10.3251	−	5.96119i	0.367583	−	0.212224i
$790$		0			0
$791$	3.56905	−	6.18178i	0.126901	−	0.219799i
$792$		0			0
$793$	−6.04714	−	11.2447i	−0.214740	−	0.399309i
$794$		0			0
$795$	−14.1756	−	8.18429i	−0.502757	−	0.290267i
$796$		0			0
$797$	−19.1331	+	11.0465i	−0.677731	+	0.391288i	−0.798999	−	0.601332i	$-0.794637\pi$
$797$	−19.1331	+	11.0465i	−0.677731	+	0.391288i	0.121269	+	0.992620i	$0.461304\pi$
$798$		0			0
$799$	32.0633	+	55.5353i	1.13432	+	1.96470i
$800$		0			0
$801$	1.87209			0.0661470
$802$		0			0
$803$	−9.25526	−	5.34353i	−0.326611	−	0.188569i
$804$		0			0
$805$			4.55637i			0.160591i
$806$		0			0
$807$	−5.24034			−0.184469
$808$		0			0
$809$	−2.02317	+	3.50424i	−0.0711310	+	0.123202i	−0.899397	−	0.437132i	$-0.855994\pi$
$809$	−2.02317	+	3.50424i	−0.0711310	+	0.123202i	0.828266	+	0.560335i	$0.189328\pi$
$810$		0			0
$811$		−	18.7132i		−	0.657109i	−0.944485	−	0.328555i	$-0.893439\pi$
$811$		−	18.7132i		−	0.657109i	0.944485	−	0.328555i	$-0.106561\pi$
$812$		0			0
$813$	9.27462	−	5.35470i	0.325275	−	0.187798i
$814$		0			0
$815$	−5.61122	−	9.71893i	−0.196553	−	0.340439i
$816$		0			0
$817$	6.69820	−	11.6016i	0.234340	−	0.405889i
$818$		0			0
$819$	−7.25169	−	4.48390i	−0.253394	−	0.156680i
$820$		0			0
$821$	6.46202	+	3.73085i	0.225526	+	0.130208i	0.608506	−	0.793549i	$-0.291769\pi$
$821$	6.46202	+	3.73085i	0.225526	+	0.130208i	−0.382980	+	0.923757i	$0.625102\pi$
$822$		0			0
$823$	9.81336	+	16.9972i	0.342072	+	0.592486i	0.984817	−	0.173594i	$-0.0555380\pi$
$823$	9.81336	+	16.9972i	0.342072	+	0.592486i	−0.642745	+	0.766080i	$0.722205\pi$
$824$		0			0
$825$	0.0351270	+	0.0608418i	0.00122297	+	0.00211824i
$826$		0			0
$827$		−	19.2616i		−	0.669792i	−0.942255	−	0.334896i	$-0.891299\pi$
$827$		−	19.2616i		−	0.669792i	0.942255	−	0.334896i	$-0.108701\pi$
$828$		0			0
$829$	−18.7148	−	10.8050i	−0.649993	−	0.375273i	0.138461	−	0.990368i	$-0.455785\pi$
$829$	−18.7148	−	10.8050i	−0.649993	−	0.375273i	−0.788453	+	0.615094i	$0.789118\pi$
$830$		0			0
$831$	11.3654			0.394261
$832$		0			0
$833$	37.0353			1.28320
$834$		0			0
$835$	2.06489	+	1.19216i	0.0714584	+	0.0412565i
$836$		0			0
$837$			7.40257i			0.255870i
$838$		0			0
$839$	21.0839	+	36.5183i	0.727895	+	1.26075i	0.957771	+	0.287532i	$0.0928347\pi$
$839$	21.0839	+	36.5183i	0.727895	+	1.26075i	−0.229876	+	0.973220i	$0.573832\pi$
$840$		0			0
$841$	−12.6083	−	21.8382i	−0.434768	−	0.753040i
$842$		0			0
$843$	−16.8865	−	9.74942i	−0.581602	−	0.335788i
$844$		0			0
$845$	1.75706	−	29.0679i	0.0604448	−	0.999965i
$846$		0			0
$847$	9.47952	−	16.4190i	0.325720	−	0.564164i
$848$		0			0
$849$	1.33514	+	2.31253i	0.0458220	+	0.0793660i
$850$		0			0
$851$	−9.78661	+	5.65030i	−0.335481	+	0.193690i
$852$		0			0
$853$		−	40.2417i		−	1.37785i	−0.724833	−	0.688924i	$-0.758083\pi$
$853$		−	40.2417i		−	1.37785i	0.724833	−	0.688924i	$-0.241917\pi$
$854$		0			0
$855$	−4.66434	+	8.07888i	−0.159517	+	0.276292i
$856$		0			0
$857$	7.37621			0.251966			0.125983	−	0.992032i	$-0.459791\pi$
$857$	7.37621			0.251966			0.125983	+	0.992032i	$0.459791\pi$
$858$		0			0
$859$		−	31.9493i		−	1.09010i	−0.838405	−	0.545048i	$-0.816511\pi$
$859$		−	31.9493i		−	1.09010i	0.838405	−	0.545048i	$-0.183489\pi$
$860$		0			0
$861$	−0.381845	−	0.220458i	−0.0130132	−	0.00751320i
$862$		0			0
$863$	16.1143			0.548536			0.274268	−	0.961653i	$-0.411564\pi$
$863$	16.1143			0.548536			0.274268	+	0.961653i	$0.411564\pi$
$864$		0			0
$865$	24.4496	+	42.3479i	0.831310	+	1.43987i
$866$		0			0
$867$	12.0326	−	6.94700i	0.408647	−	0.235933i
$868$		0			0
$869$	−65.7256	−	37.9467i	−2.22959	−	1.28725i
$870$		0			0
$871$	8.56257	−	13.8480i	0.290132	−	0.469221i
$872$		0			0
$873$	1.60519	−	2.78028i	0.0543276	−	0.0940982i
$874$		0			0
$875$	9.12287	−	5.26709i	0.308409	−	0.178060i
$876$		0			0
$877$	0.181562	−	0.104825i	0.00613091	−	0.00353968i	−0.496931	−	0.867790i	$-0.665540\pi$
$877$	0.181562	−	0.104825i	0.00613091	−	0.00353968i	0.503062	+	0.864250i	$0.332207\pi$
$878$		0			0
$879$	−3.36906			−0.113635
$880$		0			0
$881$	−20.1008	+	34.8157i	−0.677214	+	1.17297i	0.298602	+	0.954378i	$0.403480\pi$
$881$	−20.1008	+	34.8157i	−0.677214	+	1.17297i	−0.975816	+	0.218592i	$0.929854\pi$
$882$		0			0
$883$		−	4.69019i		−	0.157837i	−0.996881	−	0.0789187i	$-0.974853\pi$
$883$		−	4.69019i		−	0.157837i	0.996881	−	0.0789187i	$-0.0251467\pi$
$884$		0			0
$885$			0.748463i			0.0251593i
$886$		0			0
$887$	11.6991	−	20.2635i	0.392819	−	0.680382i	−0.600002	−	0.799999i	$-0.704833\pi$
$887$	11.6991	−	20.2635i	0.392819	−	0.680382i	0.992820	+	0.119617i	$0.0381667\pi$
$888$		0			0
$889$	−2.90651			−0.0974813
$890$		0			0
$891$	−23.1368	+	13.3581i	−0.775113	+	0.447512i
$892$		0			0
$893$	−15.2279	+	8.79184i	−0.509583	+	0.294208i
$894$		0			0
$895$	−3.65827	+	6.33631i	−0.122282	+	0.211799i
$896$		0			0
$897$	2.58853	+	4.81337i	0.0864284	+	0.160714i
$898$		0			0
$899$	−3.22015	−	1.85915i	−0.107398	−	0.0620062i
$900$		0			0
$901$	54.5398	−	31.4886i	1.81698	−	1.04904i
$902$		0			0
$903$	−2.67535	−	4.63385i	−0.0890302	−	0.154205i
$904$		0			0
$905$	−29.3963			−0.977166
$906$		0			0
$907$	−3.93422	−	2.27142i	−0.130634	−	0.0754213i	0.433259	−	0.901269i	$-0.357363\pi$
$907$	−3.93422	−	2.27142i	−0.130634	−	0.0754213i	−0.563893	+	0.825848i	$0.690697\pi$
$908$		0			0
$909$			24.4608i			0.811313i
$910$		0			0
$911$	29.5451			0.978873			0.489436	−	0.872039i	$-0.337203\pi$
$911$	29.5451			0.978873			0.489436	+	0.872039i	$0.337203\pi$
$912$		0			0
$913$	32.2326	−	55.8285i	1.06674	−	1.84765i
$914$		0			0
$915$			5.57964i			0.184457i
$916$		0			0
$917$	−9.73946	+	5.62308i	−0.321625	+	0.185691i
$918$		0			0
$919$	−15.5647	−	26.9588i	−0.513431	−	0.889288i	−0.999879	−	0.0155787i	$-0.995041\pi$
$919$	−15.5647	−	26.9588i	−0.513431	−	0.889288i	0.486448	−	0.873710i	$-0.338292\pi$
$920$		0			0
$921$	−3.15121	+	5.45806i	−0.103836	+	0.179849i
$922$		0			0
$923$	36.9433	−	19.8673i	1.21600	−	0.653942i
$924$		0			0
$925$	−0.0813551	−	0.0469704i	−0.00267494	−	0.00154438i
$926$		0			0
$927$	−18.8837	−	32.7076i	−0.620223	−	1.07426i
$928$		0			0
$929$	11.9251	+	20.6548i	0.391249	+	0.677663i	0.992615	−	0.121311i	$-0.0387098\pi$
$929$	11.9251	+	20.6548i	0.391249	+	0.677663i	−0.601366	+	0.798974i	$0.705376\pi$
$930$		0			0
$931$			10.1552i			0.332822i
$932$		0			0
$933$	5.69695	+	3.28913i	0.186510	+	0.107681i
$934$		0			0
$935$	−75.7155			−2.47616
$936$		0			0
$937$	−9.97996			−0.326031			−0.163016	−	0.986623i	$-0.552122\pi$
$937$	−9.97996			−0.326031			−0.163016	+	0.986623i	$0.552122\pi$
$938$		0			0
$939$	7.17813	+	4.14430i	0.234249	+	0.135244i
$940$		0			0
$941$		−	12.2242i		−	0.398498i	−0.979949	−	0.199249i	$-0.936150\pi$
$941$		−	12.2242i		−	0.398498i	0.979949	−	0.199249i	$-0.0638502\pi$
$942$		0			0
$943$	−0.715515	−	1.23931i	−0.0233004	−	0.0403575i
$944$		0			0
$945$	4.09395	+	7.09093i	0.133176	+	0.230668i
$946$		0			0
$947$	−2.80497	−	1.61945i	−0.0911494	−	0.0526251i	0.453732	−	0.891138i	$-0.350092\pi$
$947$	−2.80497	−	1.61945i	−0.0911494	−	0.0526251i	−0.544882	+	0.838513i	$0.683426\pi$
$948$		0			0
$949$	0.208593	−	6.90798i	0.00677120	−	0.224242i
$950$		0			0
$951$	0.291228	−	0.504421i	0.00944370	−	0.0163570i
$952$		0			0
$953$	−3.08301	−	5.33994i	−0.0998686	−	0.172977i	0.811762	−	0.583989i	$-0.198509\pi$
$953$	−3.08301	−	5.33994i	−0.0998686	−	0.172977i	−0.911630	+	0.411012i	$0.865176\pi$
$954$		0			0
$955$	15.6025	−	9.00813i	0.504886	−	0.291496i
$956$		0			0
$957$			7.62843i			0.246592i
$958$		0			0
$959$	−9.66009	+	16.7318i	−0.311941	+	0.540297i
$960$		0			0
$961$	−27.3457			−0.882121
$962$		0			0
$963$		−	39.3543i		−	1.26817i
$964$		0			0
$965$	1.62154	+	0.936197i	0.0521993	+	0.0301373i
$966$		0			0
$967$	−44.1828			−1.42082			−0.710411	−	0.703787i	$-0.751491\pi$
$967$	−44.1828			−1.42082			−0.710411	+	0.703787i	$0.751491\pi$
$968$		0			0
$969$	3.54434	+	6.13898i	0.113861	+	0.197212i
$970$		0			0
$971$	33.2299	−	19.1853i	1.06640	−	0.615686i	0.139204	−	0.990264i	$-0.455546\pi$
$971$	33.2299	−	19.1853i	1.06640	−	0.615686i	0.927195	+	0.374578i	$0.122212\pi$
$972$		0			0
$973$	6.62233	+	3.82340i	0.212302	+	0.122573i
$974$		0			0
$975$	−0.0238932	+	0.0386418i	−0.000765195	+	0.00123753i
$976$		0			0
$977$	−9.04005	+	15.6578i	−0.289217	+	0.500938i	−0.973623	−	0.228163i	$-0.926728\pi$
$977$	−9.04005	+	15.6578i	−0.289217	+	0.500938i	0.684406	+	0.729101i	$0.260062\pi$
$978$		0			0
$979$	−3.60822	+	2.08321i	−0.115319	+	0.0665796i
$980$		0			0
$981$	−21.0432	+	12.1493i	−0.671857	+	0.387897i
$982$		0			0
$983$	−18.8329			−0.600677			−0.300339	−	0.953833i	$-0.597100\pi$
$983$	−18.8329			−0.600677			−0.300339	+	0.953833i	$0.597100\pi$
$984$		0			0
$985$	−7.84529	+	13.5884i	−0.249972	+	0.432964i
$986$		0			0
$987$			7.02316i			0.223550i
$988$		0			0
$989$		−	17.3662i		−	0.552212i
$990$		0			0
$991$	24.8600	−	43.0588i	0.789704	−	1.36781i	−0.136444	−	0.990648i	$-0.543567\pi$
$991$	24.8600	−	43.0588i	0.789704	−	1.36781i	0.926148	−	0.377160i	$-0.123099\pi$
$992$		0			0
$993$	−10.4305			−0.331003
$994$		0			0
$995$	−29.1675	+	16.8399i	−0.924671	+	0.533859i
$996$		0			0
$997$	−41.6202	+	24.0294i	−1.31812	+	0.761020i	−0.983427	−	0.181306i	$-0.941968\pi$
$997$	−41.6202	+	24.0294i	−1.31812	+	0.761020i	−0.334698	+	0.942325i	$0.608634\pi$
$998$		0			0
$999$	−10.1537	+	17.5868i	−0.321250	+	0.556421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.z.a.113.5		24
4.3	odd	2		104.2.r.a.61.10	yes	24
8.3	odd	2		104.2.r.a.61.7	yes	24
8.5	even	2	inner	416.2.z.a.113.8		24
12.11	even	2		936.2.be.a.685.3		24
13.3	even	3	inner	416.2.z.a.81.8		24
24.11	even	2		936.2.be.a.685.6		24
52.3	odd	6		104.2.r.a.29.7	✓	24
104.3	odd	6		104.2.r.a.29.10	yes	24
104.29	even	6	inner	416.2.z.a.81.5		24
156.107	even	6		936.2.be.a.757.6		24
312.107	even	6		936.2.be.a.757.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.7	✓	24	52.3	odd	6
104.2.r.a.29.10	yes	24	104.3	odd	6
104.2.r.a.61.7	yes	24	8.3	odd	2
104.2.r.a.61.10	yes	24	4.3	odd	2
416.2.z.a.81.5		24	104.29	even	6	inner
416.2.z.a.81.8		24	13.3	even	3	inner
416.2.z.a.113.5		24	1.1	even	1	trivial
416.2.z.a.113.8		24	8.5	even	2	inner
936.2.be.a.685.3		24	12.11	even	2
936.2.be.a.685.6		24	24.11	even	2
936.2.be.a.757.3		24	312.107	even	6
936.2.be.a.757.6		24	156.107	even	6

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.609172 - 0.351705i) q^{3} +2.24007i q^{5} +(-0.471952 - 0.817445i) q^{7} +(-1.25261 - 2.16958i) q^{9} +(4.82849 + 2.78773i) q^{11} +(-0.108823 + 3.60391i) q^{13} +(0.787845 - 1.36459i) q^{15} +(3.03119 + 5.25017i) q^{17} +(-1.43961 + 0.831159i) q^{19} +0.663952i q^{21} +(-1.07746 + 1.86621i) q^{23} -0.0179136 q^{25} +3.87243i q^{27} +(-1.68452 - 0.972558i) q^{29} +1.91161 q^{31} +(-1.96092 - 3.39641i) q^{33} +(1.83113 - 1.05721i) q^{35} +(4.54154 + 2.62206i) q^{37} +(1.33381 - 2.15712i) q^{39} +(-0.332039 + 0.575109i) q^{41} +(-6.97919 + 4.02944i) q^{43} +(4.86001 - 2.80593i) q^{45} +10.5778 q^{47} +(3.05452 - 5.29059i) q^{49} -4.26434i q^{51} -10.3882i q^{53} +(-6.24471 + 10.8162i) q^{55} +1.16929 q^{57} +(-0.411368 + 0.237503i) q^{59} +(-3.06666 + 1.77054i) q^{61} +(-1.18234 + 2.04787i) q^{63} +(-8.07301 - 0.243772i) q^{65} +(-3.91067 - 2.25783i) q^{67} +(1.31271 - 0.757894i) q^{69} +(-5.81695 - 10.0753i) q^{71} -1.91680 q^{73} +(0.0109124 + 0.00630029i) q^{75} -5.26270i q^{77} -13.6120 q^{79} +(-2.39587 + 4.14976i) q^{81} -11.5623i q^{83} +(-11.7607 + 6.79007i) q^{85} +(0.684108 + 1.18491i) q^{87} +(-0.373638 + 0.647161i) q^{89} +(2.99736 - 1.61192i) q^{91} +(-1.16450 - 0.672324i) q^{93} +(-1.86185 - 3.22483i) q^{95} +(0.640742 + 1.10980i) q^{97} -13.9677i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) \) 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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