LMFDB - Embedded newform 1078.2.c.c.1077.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(1077,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1078.1077");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 $ x^16 - 32x^14 + 512x^12 - 2272x^10 - 1087x^8 + 72448x^6 + 819200x^4 + 1310720*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1077.15
Root			$-3.90726 - 1.61844i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.c.1077.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.84776i q^{3} -1.00000 q^{4} -2.47151i q^{5} -1.84776 q^{6} -1.00000i q^{8} -0.414214 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.84776i q^{3} -1.00000 q^{4} -2.47151i q^{5} -1.84776 q^{6} -1.00000i q^{8} -0.414214 q^{9} +2.47151 q^{10} +(-1.99049 + 2.65291i) q^{11} -1.84776i q^{12} +1.96452 q^{13} +4.56676 q^{15} +1.00000 q^{16} +5.64974 q^{17} -0.414214i q^{18} +0.906978 q^{19} +2.47151i q^{20} +(-2.65291 - 1.99049i) q^{22} -0.936812 q^{23} +1.84776 q^{24} -1.10838 q^{25} +1.96452i q^{26} +4.77791i q^{27} +7.50358i q^{29} +4.56676i q^{30} +4.71925i q^{31} +1.00000i q^{32} +(-4.90195 - 3.67794i) q^{33} +5.64974i q^{34} +0.414214 q^{36} -9.62995 q^{37} +0.906978i q^{38} +3.62995i q^{39} -2.47151 q^{40} +6.93240 q^{41} +6.80940i q^{43} +(1.99049 - 2.65291i) q^{44} +1.02373i q^{45} -0.936812i q^{46} -4.00225i q^{47} +1.84776i q^{48} -1.10838i q^{50} +10.4394i q^{51} -1.96452 q^{52} +6.56676 q^{53} -4.77791 q^{54} +(6.55672 + 4.91952i) q^{55} +1.67588i q^{57} -7.50358 q^{58} -0.965635i q^{59} -4.56676 q^{60} +11.9003 q^{61} -4.71925 q^{62} -1.00000 q^{64} -4.85533i q^{65} +(3.67794 - 4.90195i) q^{66} +6.72004 q^{67} -5.64974 q^{68} -1.73100i q^{69} -11.5485 q^{71} +0.414214i q^{72} -10.8614 q^{73} -9.62995i q^{74} -2.04803i q^{75} -0.906978 q^{76} -3.62995 q^{78} +8.48528i q^{79} -2.47151i q^{80} -10.0711 q^{81} +6.93240i q^{82} +4.83601 q^{83} -13.9634i q^{85} -6.80940 q^{86} -13.8648 q^{87} +(2.65291 + 1.99049i) q^{88} -12.7340i q^{89} -1.02373 q^{90} +0.936812 q^{92} -8.72004 q^{93} +4.00225 q^{94} -2.24161i q^{95} -1.84776 q^{96} +3.82683i q^{97} +(0.824487 - 1.09887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^9	$ 16 q - 16 q^{4} + 16 q^{9} + 16 q^{11} + 16 q^{16} - 8 q^{22} - 16 q^{23} - 64 q^{25} - 16 q^{36} - 80 q^{37} - 16 q^{44} + 32 q^{53} - 48 q^{58} - 16 q^{64} + 16 q^{67} - 48 q^{71} + 16 q^{78} - 48 q^{81} + 32 q^{86} + 8 q^{88} + 16 q^{92} - 48 q^{93} + 24 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^9 + 16 * q^11 + 16 * q^16 - 8 * q^22 - 16 * q^23 - 64 * q^25 - 16 * q^36 - 80 * q^37 - 16 * q^44 + 32 * q^53 - 48 * q^58 - 16 * q^64 + 16 * q^67 - 48 * q^71 + 16 * q^78 - 48 * q^81 + 32 * q^86 + 8 * q^88 + 16 * q^92 - 48 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.84776i			1.06680i	0.845862	+	0.533402i	$0.179087\pi$
$3$			1.84776i			1.06680i	−0.845862	+	0.533402i	$0.820913\pi$
$4$	−1.00000			−0.500000
$5$		−	2.47151i		−	1.10529i	−0.833415	−	0.552647i	$-0.813618\pi$
$5$		−	2.47151i		−	1.10529i	0.833415	−	0.552647i	$-0.186382\pi$
$6$	−1.84776			−0.754344
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−0.414214			−0.138071
$10$	2.47151			0.781562
$11$	−1.99049	+	2.65291i	−0.600155	+	0.799884i
$11$	−1.99049	+	2.65291i	−0.600155	+	0.799884i
$12$		−	1.84776i		−	0.533402i
$13$	1.96452			0.544859			0.272429	−	0.962176i	$-0.412173\pi$
$13$	1.96452			0.544859			0.272429	+	0.962176i	$0.412173\pi$
$14$		0			0
$15$	4.56676			1.17913
$16$	1.00000			0.250000
$17$	5.64974			1.37026			0.685131	−	0.728419i	$-0.259745\pi$
$17$	5.64974			1.37026			0.685131	+	0.728419i	$0.259745\pi$
$18$		−	0.414214i		−	0.0976311i
$19$	0.906978			0.208075			0.104038	−	0.994573i	$-0.466824\pi$
$19$	0.906978			0.208075			0.104038	+	0.994573i	$0.466824\pi$
$20$			2.47151i			0.552647i
$21$		0			0
$22$	−2.65291	−	1.99049i	−0.565603	−	0.424374i
$23$	−0.936812			−0.195339			−0.0976694	−	0.995219i	$-0.531139\pi$
$23$	−0.936812			−0.195339			−0.0976694	+	0.995219i	$0.531139\pi$
$24$	1.84776			0.377172
$25$	−1.10838			−0.221677
$26$			1.96452i			0.385273i
$27$			4.77791i			0.919509i
$28$		0			0
$29$			7.50358i			1.39338i	0.717373	+	0.696689i	$0.245344\pi$
$29$			7.50358i			1.39338i	−0.717373	+	0.696689i	$0.754656\pi$
$30$			4.56676i			0.833773i
$31$			4.71925i			0.847603i	0.905755	+	0.423801i	$0.139305\pi$
$31$			4.71925i			0.847603i	−0.905755	+	0.423801i	$0.860695\pi$
$32$			1.00000i			0.176777i
$33$	−4.90195	−	3.67794i	−0.853319	−	0.640248i
$34$			5.64974i			0.968922i
$35$		0			0
$36$	0.414214			0.0690356
$37$	−9.62995			−1.58315			−0.791577	−	0.611069i	$-0.790740\pi$
$37$	−9.62995			−1.58315			−0.791577	+	0.611069i	$0.790740\pi$
$38$			0.906978i			0.147131i
$39$			3.62995i			0.581257i
$40$	−2.47151			−0.390781
$41$	6.93240			1.08266			0.541329	−	0.840811i	$-0.317921\pi$
$41$	6.93240			1.08266			0.541329	+	0.840811i	$0.317921\pi$
$42$		0			0
$43$			6.80940i			1.03842i	0.854645	+	0.519212i	$0.173775\pi$
$43$			6.80940i			1.03842i	−0.854645	+	0.519212i	$0.826225\pi$
$44$	1.99049	−	2.65291i	0.300077	−	0.399942i
$45$			1.02373i			0.152609i
$46$		−	0.936812i		−	0.138125i
$47$		−	4.00225i		−	0.583788i	−0.956451	−	0.291894i	$-0.905715\pi$
$47$		−	4.00225i		−	0.583788i	0.956451	−	0.291894i	$-0.0942854\pi$
$48$			1.84776i			0.266701i
$49$		0			0
$50$		−	1.10838i		−	0.156749i
$51$			10.4394i			1.46180i
$52$	−1.96452			−0.272429
$53$	6.56676			0.902014			0.451007	−	0.892520i	$-0.351065\pi$
$53$	6.56676			0.902014			0.451007	+	0.892520i	$0.351065\pi$
$54$	−4.77791			−0.650191
$55$	6.55672	+	4.91952i	0.884108	+	0.663348i
$56$		0			0
$57$			1.67588i			0.221975i
$58$	−7.50358			−0.985268
$59$		−	0.965635i		−	0.125715i	−0.998023	−	0.0628575i	$-0.979979\pi$
$59$		−	0.965635i		−	0.125715i	0.998023	−	0.0628575i	$-0.0200214\pi$
$60$	−4.56676			−0.589567
$61$	11.9003			1.52368			0.761838	−	0.647768i	$-0.224297\pi$
$61$	11.9003			1.52368			0.761838	+	0.647768i	$0.224297\pi$
$62$	−4.71925			−0.599346
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	4.85533i		−	0.602230i
$66$	3.67794	−	4.90195i	0.452724	−	0.603388i
$67$	6.72004			0.820984			0.410492	−	0.911864i	$-0.365357\pi$
$67$	6.72004			0.820984			0.410492	+	0.911864i	$0.365357\pi$
$68$	−5.64974			−0.685131
$69$		−	1.73100i		−	0.208388i
$70$		0			0
$71$	−11.5485			−1.37055			−0.685276	−	0.728284i	$-0.740318\pi$
$71$	−11.5485			−1.37055			−0.685276	+	0.728284i	$0.740318\pi$
$72$			0.414214i			0.0488155i
$73$	−10.8614			−1.27123			−0.635617	−	0.772004i	$-0.719254\pi$
$73$	−10.8614			−1.27123			−0.635617	+	0.772004i	$0.719254\pi$
$74$		−	9.62995i		−	1.11946i
$75$		−	2.04803i		−	0.236486i
$76$	−0.906978			−0.104038
$77$		0			0
$78$	−3.62995			−0.411011
$79$			8.48528i			0.954669i	0.878722	+	0.477334i	$0.158397\pi$
$79$			8.48528i			0.954669i	−0.878722	+	0.477334i	$0.841603\pi$
$80$		−	2.47151i		−	0.276324i
$81$	−10.0711			−1.11901
$82$			6.93240i			0.765555i
$83$	4.83601			0.530821			0.265411	−	0.964135i	$-0.414493\pi$
$83$	4.83601			0.530821			0.265411	+	0.964135i	$0.414493\pi$
$84$		0			0
$85$		−	13.9634i		−	1.51454i
$86$	−6.80940			−0.734277
$87$	−13.8648			−1.48646
$88$	2.65291	+	1.99049i	0.282802	+	0.212187i
$89$		−	12.7340i		−	1.34981i	−0.737906	−	0.674903i	$-0.764185\pi$
$89$		−	12.7340i		−	1.34981i	0.737906	−	0.674903i	$-0.235815\pi$
$90$	−1.02373			−0.107911
$91$		0			0
$92$	0.936812			0.0976694
$93$	−8.72004			−0.904226
$94$	4.00225			0.412800
$95$		−	2.24161i		−	0.229984i
$96$	−1.84776			−0.188586
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$	0.824487	−	1.09887i	0.0828641	−	0.110441i
$100$	1.10838			0.110838
$101$	15.8293			1.57508			0.787538	−	0.616266i	$-0.211355\pi$
$101$	15.8293			1.57508			0.787538	+	0.616266i	$0.211355\pi$
$102$	−10.4394			−1.03365
$103$			0.790221i			0.0778628i	0.999242	+	0.0389314i	$0.0123954\pi$
$103$			0.790221i			0.0778628i	−0.999242	+	0.0389314i	$0.987605\pi$
$104$		−	1.96452i		−	0.192637i
$105$		0			0
$106$			6.56676i			0.637820i
$107$			16.6117i			1.60591i	0.596040	+	0.802955i	$0.296740\pi$
$107$			16.6117i			1.60591i	−0.596040	+	0.802955i	$0.703260\pi$
$108$		−	4.77791i		−	0.459755i
$109$			6.00000i			0.574696i	0.957826	+	0.287348i	$0.0927736\pi$
$109$			6.00000i			0.574696i	−0.957826	+	0.287348i	$0.907226\pi$
$110$	−4.91952	+	6.55672i	−0.469058	+	0.625158i
$111$		−	17.7938i		−	1.68892i
$112$		0			0
$113$	−5.76421			−0.542251			−0.271126	−	0.962544i	$-0.587396\pi$
$113$	−5.76421			−0.542251			−0.271126	+	0.962544i	$0.587396\pi$
$114$	−1.67588			−0.156960
$115$			2.31534i			0.215907i
$116$		−	7.50358i		−	0.696689i
$117$	−0.813729			−0.0752293
$118$	0.965635			0.0888940
$119$		0			0
$120$		−	4.56676i		−	0.416887i
$121$	−3.07591	−	10.5612i	−0.279628	−	0.960108i
$122$			11.9003i			1.07740i
$123$			12.8094i			1.15499i
$124$		−	4.71925i		−	0.423801i
$125$		−	9.61818i		−	0.860277i
$126$		0			0
$127$		−	18.6371i		−	1.65378i	−0.562367	−	0.826888i	$-0.690109\pi$
$127$		−	18.6371i		−	1.65378i	0.562367	−	0.826888i	$-0.309891\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.5821			−1.10780
$130$	4.85533			0.425841
$131$	−19.9835			−1.74596			−0.872982	−	0.487753i	$-0.837817\pi$
$131$	−19.9835			−1.74596			−0.872982	+	0.487753i	$0.837817\pi$
$132$	4.90195	+	3.67794i	0.426660	+	0.320124i
$133$		0			0
$134$			6.72004i			0.580523i
$135$	11.8087			1.01633
$136$		−	5.64974i		−	0.484461i
$137$	16.4394			1.40451			0.702254	−	0.711926i	$-0.252177\pi$
$137$	16.4394			1.40451			0.702254	+	0.711926i	$0.252177\pi$
$138$	1.73100			0.147353
$139$	−10.7109			−0.908484			−0.454242	−	0.890878i	$-0.650090\pi$
$139$	−10.7109			−0.908484			−0.454242	+	0.890878i	$0.650090\pi$
$140$		0			0
$141$	7.39519			0.622787
$142$		−	11.5485i		−	0.969126i
$143$	−3.91035	+	5.21169i	−0.327000	+	0.435824i
$144$	−0.414214			−0.0345178
$145$	18.5452			1.54009
$146$		−	10.8614i		−	0.898898i
$147$		0			0
$148$	9.62995			0.791577
$149$		−	14.7635i		−	1.20947i	−0.796426	−	0.604736i	$-0.793279\pi$
$149$		−	14.7635i		−	1.20947i	0.796426	−	0.604736i	$-0.206721\pi$
$150$	2.04803			0.167221
$151$		−	10.4964i		−	0.854187i	−0.904207	−	0.427093i	$-0.859538\pi$
$151$		−	10.4964i		−	0.854187i	0.904207	−	0.427093i	$-0.140462\pi$
$152$		−	0.906978i		−	0.0735656i
$153$	−2.34020			−0.189194
$154$		0			0
$155$	11.6637			0.936851
$156$		−	3.62995i		−	0.290629i
$157$			4.61571i			0.368374i	0.982891	+	0.184187i	$0.0589651\pi$
$157$			4.61571i			0.368374i	−0.982891	+	0.184187i	$0.941035\pi$
$158$	−8.48528			−0.675053
$159$			12.1338i			0.962273i
$160$	2.47151			0.195390
$161$		0			0
$162$		−	10.0711i		−	0.791258i
$163$	14.5746			1.14157			0.570787	−	0.821098i	$-0.306638\pi$
$163$	14.5746			1.14157			0.570787	+	0.821098i	$0.306638\pi$
$164$	−6.93240			−0.541329
$165$	−9.09009	+	12.1152i	−0.707663	+	0.943170i
$166$			4.83601i			0.375347i
$167$	−7.37045			−0.570342			−0.285171	−	0.958477i	$-0.592050\pi$
$167$	−7.37045			−0.570342			−0.285171	+	0.958477i	$0.592050\pi$
$168$		0			0
$169$	−9.14068			−0.703129
$170$	13.9634			1.07094
$171$	−0.375683			−0.0287292
$172$		−	6.80940i		−	0.519212i
$173$	11.1489			0.847637			0.423818	−	0.905747i	$-0.360690\pi$
$173$	11.1489			0.847637			0.423818	+	0.905747i	$0.360690\pi$
$174$		−	13.8648i		−	1.05109i
$175$		0			0
$176$	−1.99049	+	2.65291i	−0.150039	+	0.199971i
$177$	1.78426			0.134113
$178$	12.7340			0.954457
$179$	15.8087			1.18160			0.590798	−	0.806820i	$-0.298813\pi$
$179$	15.8087			1.18160			0.590798	+	0.806820i	$0.298813\pi$
$180$		−	1.02373i		−	0.0763047i
$181$			16.6528i			1.23779i	0.785473	+	0.618896i	$0.212420\pi$
$181$			16.6528i			1.23779i	−0.785473	+	0.618896i	$0.787580\pi$
$182$		0			0
$183$			21.9889i			1.62546i
$184$			0.936812i			0.0690627i
$185$			23.8006i			1.74985i
$186$		−	8.72004i		−	0.639385i
$187$	−11.2457	+	14.9883i	−0.822370	+	1.09605i
$188$			4.00225i			0.291894i
$189$		0			0
$190$	2.24161			0.162623
$191$	26.3568			1.90711			0.953557	−	0.301212i	$-0.0973913\pi$
$191$	26.3568			1.90711			0.953557	+	0.301212i	$0.0973913\pi$
$192$		−	1.84776i		−	0.133351i
$193$		−	0.694171i		−	0.0499675i	−0.999688	−	0.0249838i	$-0.992047\pi$
$193$		−	0.694171i		−	0.0499675i	0.999688	−	0.0249838i	$-0.00795341\pi$
$194$	−3.82683			−0.274751
$195$	8.97148			0.642461
$196$		0			0
$197$		−	9.74519i		−	0.694316i	−0.937807	−	0.347158i	$-0.887147\pi$
$197$		−	9.74519i		−	0.694316i	0.937807	−	0.347158i	$-0.112853\pi$
$198$	1.09887	+	0.824487i	0.0780935	+	0.0585938i
$199$		−	7.03460i		−	0.498669i	−0.968417	−	0.249335i	$-0.919788\pi$
$199$		−	7.03460i		−	0.498669i	0.968417	−	0.249335i	$-0.0802119\pi$
$200$			1.10838i			0.0783746i
$201$			12.4170i			0.875829i
$202$			15.8293i			1.11375i
$203$		0			0
$204$		−	10.4394i		−	0.730901i
$205$		−	17.1335i		−	1.19666i
$206$	−0.790221			−0.0550573
$207$	0.388040			0.0269707
$208$	1.96452			0.136215
$209$	−1.80533	+	2.40614i	−0.124877	+	0.166436i
$210$		0			0
$211$			24.1152i			1.66016i	0.557643	+	0.830081i	$0.311706\pi$
$211$			24.1152i			1.66016i	−0.557643	+	0.830081i	$0.688294\pi$
$212$	−6.56676			−0.451007
$213$		−	21.3388i		−	1.46211i
$214$	−16.6117			−1.13555
$215$	16.8295			1.14777
$216$	4.77791			0.325096
$217$		0			0
$218$	−6.00000			−0.406371
$219$		−	20.0693i		−	1.35616i
$220$	−6.55672	−	4.91952i	−0.442054	−	0.331674i
$221$	11.0990			0.746600
$222$	17.7938			1.19424
$223$			2.90530i			0.194553i	0.995257	+	0.0972765i	$0.0310131\pi$
$223$			2.90530i			0.194553i	−0.995257	+	0.0972765i	$0.968987\pi$
$224$		0			0
$225$	0.459108			0.0306072
$226$		−	5.76421i		−	0.383429i
$227$	14.4270			0.957552			0.478776	−	0.877937i	$-0.341081\pi$
$227$	14.4270			0.957552			0.478776	+	0.877937i	$0.341081\pi$
$228$		−	1.67588i		−	0.110988i
$229$		−	7.09696i		−	0.468980i	−0.972118	−	0.234490i	$-0.924658\pi$
$229$		−	7.09696i		−	0.468980i	0.972118	−	0.234490i	$-0.0753421\pi$
$230$	−2.31534			−0.152669
$231$		0			0
$232$	7.50358			0.492634
$233$			4.16116i			0.272607i	0.990667	+	0.136303i	$0.0435222\pi$
$233$			4.16116i			0.272607i	−0.990667	+	0.136303i	$0.956478\pi$
$234$		−	0.813729i		−	0.0531951i
$235$	−9.89162			−0.645258
$236$			0.965635i			0.0628575i
$237$	−15.6788			−1.01844
$238$		0			0
$239$		−	19.8625i		−	1.28480i	−0.766371	−	0.642399i	$-0.777939\pi$
$239$		−	19.8625i		−	1.28480i	0.766371	−	0.642399i	$-0.222061\pi$
$240$	4.56676			0.294783
$241$	−14.4893			−0.933341			−0.466670	−	0.884431i	$-0.654547\pi$
$241$	−14.4893			−0.933341			−0.466670	+	0.884431i	$0.654547\pi$
$242$	10.5612	−	3.07591i	0.678899	−	0.197727i
$243$		−	4.27518i		−	0.274253i
$244$	−11.9003			−0.761838
$245$		0			0
$246$	−12.8094			−0.816698
$247$	1.78177			0.113371
$248$	4.71925			0.299673
$249$			8.93578i			0.566282i
$250$	9.61818			0.608307
$251$		−	14.6156i		−	0.922529i	−0.887263	−	0.461264i	$-0.847396\pi$
$251$		−	14.6156i		−	0.922529i	0.887263	−	0.461264i	$-0.152604\pi$
$252$		0			0
$253$	1.86471	−	2.48528i	0.117234	−	0.156248i
$254$	18.6371			1.16940
$255$	25.8010			1.61572
$256$	1.00000			0.0625000
$257$			23.1182i			1.44207i	0.692898	+	0.721035i	$0.256334\pi$
$257$			23.1182i			1.44207i	−0.692898	+	0.721035i	$0.743666\pi$
$258$		−	12.5821i		−	0.783330i
$259$		0			0
$260$			4.85533i			0.301115i
$261$		−	3.10808i		−	0.192385i
$262$		−	19.9835i		−	1.23458i
$263$			8.48528i			0.523225i	0.965173	+	0.261612i	$0.0842542\pi$
$263$			8.48528i			0.523225i	−0.965173	+	0.261612i	$0.915746\pi$
$264$	−3.67794	+	4.90195i	−0.226362	+	0.301694i
$265$		−	16.2299i		−	0.996992i
$266$		0			0
$267$	23.5294			1.43998
$268$	−6.72004			−0.410492
$269$		−	30.6005i		−	1.86575i	−0.360203	−	0.932874i	$-0.617293\pi$
$269$		−	30.6005i		−	1.86575i	0.360203	−	0.932874i	$-0.382707\pi$
$270$			11.8087i			0.718653i
$271$	13.2016			0.801942			0.400971	−	0.916091i	$-0.368673\pi$
$271$	13.2016			0.801942			0.400971	+	0.916091i	$0.368673\pi$
$272$	5.64974			0.342566
$273$		0			0
$274$			16.4394i			0.993138i
$275$	2.20623	−	2.94045i	0.133040	−	0.177316i
$276$			1.73100i			0.104194i
$277$		−	3.98886i		−	0.239667i	−0.992794	−	0.119834i	$-0.961764\pi$
$277$		−	3.98886i		−	0.239667i	0.992794	−	0.119834i	$-0.0382361\pi$
$278$		−	10.7109i		−	0.642395i
$279$		−	1.95478i		−	0.117030i
$280$		0			0
$281$			5.94293i			0.354526i	0.984164	+	0.177263i	$0.0567243\pi$
$281$			5.94293i			0.354526i	−0.984164	+	0.177263i	$0.943276\pi$
$282$			7.39519i			0.440377i
$283$	−21.2661			−1.26414			−0.632070	−	0.774911i	$-0.717795\pi$
$283$	−21.2661			−1.26414			−0.632070	+	0.774911i	$0.717795\pi$
$284$	11.5485			0.685276
$285$	4.14195			0.245348
$286$	−5.21169	−	3.91035i	−0.308174	−	0.231224i
$287$		0			0
$288$		−	0.414214i		−	0.0244078i
$289$	14.9195			0.877621
$290$			18.5452i			1.08901i
$291$	−7.07107			−0.414513
$292$	10.8614			0.635617
$293$	−27.7920			−1.62362			−0.811812	−	0.583919i	$-0.801519\pi$
$293$	−27.7920			−1.62362			−0.811812	+	0.583919i	$0.801519\pi$
$294$		0			0
$295$	−2.38658			−0.138952
$296$			9.62995i			0.559730i
$297$	−12.6754	−	9.51038i	−0.735501	−	0.551848i
$298$	14.7635			0.855225
$299$	−1.84038			−0.106432
$300$			2.04803i			0.118243i
$301$		0			0
$302$	10.4964			0.604001
$303$			29.2488i			1.68030i
$304$	0.906978			0.0520188
$305$		−	29.4117i		−	1.68411i
$306$		−	2.34020i		−	0.133780i
$307$	16.2674			0.928427			0.464214	−	0.885723i	$-0.346337\pi$
$307$	16.2674			0.928427			0.464214	+	0.885723i	$0.346337\pi$
$308$		0			0
$309$	−1.46014			−0.0830644
$310$			11.6637i			0.662454i
$311$		−	10.7925i		−	0.611985i	−0.952034	−	0.305993i	$-0.901012\pi$
$311$		−	10.7925i		−	0.611985i	0.952034	−	0.305993i	$-0.0989883\pi$
$312$	3.62995			0.205506
$313$		−	18.3111i		−	1.03501i	−0.855681	−	0.517503i	$-0.826862\pi$
$313$		−	18.3111i		−	1.03501i	0.855681	−	0.517503i	$-0.173138\pi$
$314$	−4.61571			−0.260480
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	−0.358905			−0.0201581			−0.0100791	−	0.999949i	$-0.503208\pi$
$317$	−0.358905			−0.0201581			−0.0100791	+	0.999949i	$0.503208\pi$
$318$	−12.1338			−0.680430
$319$	−19.9063	−	14.9358i	−1.11454	−	0.836243i
$320$			2.47151i			0.138162i
$321$	−30.6943			−1.71319
$322$		0			0
$323$	5.12419			0.285118
$324$	10.0711			0.559504
$325$	−2.17744			−0.120783
$326$			14.5746i			0.807215i
$327$	−11.0866			−0.613088
$328$		−	6.93240i		−	0.382778i
$329$		0			0
$330$	−12.1152	−	9.09009i	−0.666922	−	0.500393i
$331$	−28.9135			−1.58923			−0.794615	−	0.607114i	$-0.792327\pi$
$331$	−28.9135			−1.58923			−0.794615	+	0.607114i	$0.792327\pi$
$332$	−4.83601			−0.265411
$333$	3.98886			0.218588
$334$		−	7.37045i		−	0.403293i
$335$		−	16.6087i		−	0.907429i
$336$		0			0
$337$			7.96341i			0.433795i	0.976194	+	0.216897i	$0.0695937\pi$
$337$			7.96341i			0.433795i	−0.976194	+	0.216897i	$0.930406\pi$
$338$		−	9.14068i		−	0.497187i
$339$		−	10.6509i		−	0.578476i
$340$			13.9634i			0.757272i
$341$	−12.5198	−	9.39362i	−0.677984	−	0.508693i
$342$		−	0.375683i		−	0.0203146i
$343$		0			0
$344$	6.80940			0.367138
$345$	−4.27820			−0.230330
$346$			11.1489i			0.599370i
$347$		−	24.6810i		−	1.32494i	−0.749087	−	0.662472i	$-0.769507\pi$
$347$		−	24.6810i		−	1.32494i	0.749087	−	0.662472i	$-0.230493\pi$
$348$	13.8648			0.743231
$349$	11.1489			0.596788			0.298394	−	0.954443i	$-0.403549\pi$
$349$	11.1489			0.596788			0.298394	+	0.954443i	$0.403549\pi$
$350$		0			0
$351$			9.38628i			0.501003i
$352$	−2.65291	−	1.99049i	−0.141401	−	0.106093i
$353$			21.3852i			1.13822i	0.822261	+	0.569111i	$0.192713\pi$
$353$			21.3852i			1.13822i	−0.822261	+	0.569111i	$0.807287\pi$
$354$			1.78426i			0.0948324i
$355$			28.5422i			1.51486i
$356$			12.7340i			0.674903i
$357$		0			0
$358$			15.8087i			0.835514i
$359$			6.24367i			0.329528i	0.986333	+	0.164764i	$0.0526863\pi$
$359$			6.24367i			0.329528i	−0.986333	+	0.164764i	$0.947314\pi$
$360$	1.02373			0.0539556
$361$	−18.1774			−0.956705
$362$	−16.6528			−0.875251
$363$	19.5145	−	5.68354i	1.02425	−	0.298309i
$364$		0			0
$365$			26.8442i			1.40509i
$366$	−21.9889			−1.14938
$367$		−	28.7533i		−	1.50091i	−0.660921	−	0.750456i	$-0.729834\pi$
$367$		−	28.7533i		−	1.50091i	0.660921	−	0.750456i	$-0.270166\pi$
$368$	−0.936812			−0.0488347
$369$	−2.87149			−0.149484
$370$	−23.8006			−1.23733
$371$		0			0
$372$	8.72004			0.452113
$373$		−	12.3589i		−	0.639920i	−0.947431	−	0.319960i	$-0.896331\pi$
$373$		−	12.3589i		−	0.639920i	0.947431	−	0.319960i	$-0.103669\pi$
$374$	−14.9883	−	11.2457i	−0.775025	−	0.581503i
$375$	17.7721			0.917747
$376$	−4.00225			−0.206400
$377$			14.7409i			0.759195i
$378$		0			0
$379$	−23.7822			−1.22161			−0.610805	−	0.791781i	$-0.709154\pi$
$379$	−23.7822			−1.22161			−0.610805	+	0.791781i	$0.709154\pi$
$380$			2.24161i			0.114992i
$381$	34.4369			1.76425
$382$			26.3568i			1.34853i
$383$		−	31.8645i		−	1.62820i	−0.580724	−	0.814100i	$-0.697231\pi$
$383$		−	31.8645i		−	1.62820i	0.580724	−	0.814100i	$-0.302769\pi$
$384$	1.84776			0.0942931
$385$		0			0
$386$	0.694171			0.0353324
$387$		−	2.82055i		−	0.143376i
$388$		−	3.82683i		−	0.194278i
$389$	21.0155			1.06553			0.532763	−	0.846264i	$-0.321154\pi$
$389$	21.0155			1.06553			0.532763	+	0.846264i	$0.321154\pi$
$390$			8.97148i			0.454289i
$391$	−5.29274			−0.267665
$392$		0			0
$393$		−	36.9246i		−	1.86260i
$394$	9.74519			0.490955
$395$	20.9715			1.05519
$396$	−0.824487	+	1.09887i	−0.0414320	+	0.0552205i
$397$		−	8.31805i		−	0.417471i	−0.977972	−	0.208735i	$-0.933065\pi$
$397$		−	8.31805i		−	0.417471i	0.977972	−	0.208735i	$-0.0669347\pi$
$398$	7.03460			0.352612
$399$		0			0
$400$	−1.10838			−0.0554192
$401$	−30.6820			−1.53219			−0.766093	−	0.642730i	$-0.777802\pi$
$401$	−30.6820			−1.53219			−0.766093	+	0.642730i	$0.777802\pi$
$402$	−12.4170			−0.619305
$403$			9.27105i			0.461824i
$404$	−15.8293			−0.787538
$405$			24.8908i			1.23683i
$406$		0			0
$407$	19.1683	−	25.5474i	0.950138	−	1.26634i
$408$	10.4394			0.516825
$409$	−9.57877			−0.473640			−0.236820	−	0.971554i	$-0.576105\pi$
$409$	−9.57877			−0.473640			−0.236820	+	0.971554i	$0.576105\pi$
$410$	17.1335			0.846165
$411$			30.3760i			1.49834i
$412$		−	0.790221i		−	0.0389314i
$413$		0			0
$414$			0.388040i			0.0190711i
$415$		−	11.9523i		−	0.586714i
$416$			1.96452i			0.0963183i
$417$		−	19.7911i		−	0.969175i
$418$	−2.40614	−	1.80533i	−0.117688	−	0.0883016i
$419$		−	10.3074i		−	0.503550i	−0.967786	−	0.251775i	$-0.918986\pi$
$419$		−	10.3074i		−	0.503550i	0.967786	−	0.251775i	$-0.0810143\pi$
$420$		0			0
$421$	−25.8805			−1.26134			−0.630669	−	0.776052i	$-0.717219\pi$
$421$	−25.8805			−1.26134			−0.630669	+	0.776052i	$0.717219\pi$
$422$	−24.1152			−1.17391
$423$			1.65779i			0.0806043i
$424$		−	6.56676i		−	0.318910i
$425$	−6.26208			−0.303756
$426$	21.3388			1.03387
$427$		0			0
$428$		−	16.6117i		−	0.802955i
$429$	−9.62995	−	7.22538i	−0.464938	−	0.348845i
$430$			16.8295i			0.811593i
$431$		−	17.0858i		−	0.822994i	−0.911411	−	0.411497i	$-0.865006\pi$
$431$		−	17.0858i		−	0.822994i	0.911411	−	0.411497i	$-0.134994\pi$
$432$			4.77791i			0.229877i
$433$		−	1.92881i		−	0.0926926i	−0.998925	−	0.0463463i	$-0.985242\pi$
$433$		−	1.92881i		−	0.0926926i	0.998925	−	0.0463463i	$-0.0147578\pi$
$434$		0			0
$435$			34.2671i			1.64298i
$436$		−	6.00000i		−	0.287348i
$437$	−0.849668			−0.0406451
$438$	20.0693			0.958949
$439$	−10.4234			−0.497481			−0.248741	−	0.968570i	$-0.580017\pi$
$439$	−10.4234			−0.497481			−0.248741	+	0.968570i	$0.580017\pi$
$440$	4.91952	−	6.55672i	0.234529	−	0.312579i
$441$		0			0
$442$			11.0990i			0.527926i
$443$	15.9254			0.756637			0.378318	−	0.925675i	$-0.376502\pi$
$443$	15.9254			0.756637			0.378318	+	0.925675i	$0.376502\pi$
$444$			17.7938i			0.844458i
$445$	−31.4724			−1.49193
$446$	−2.90530			−0.137570
$447$	27.2794			1.29027
$448$		0			0
$449$	10.4404			0.492712			0.246356	−	0.969179i	$-0.420767\pi$
$449$	10.4404			0.492712			0.246356	+	0.969179i	$0.420767\pi$
$450$			0.459108i			0.0216426i
$451$	−13.7989	+	18.3911i	−0.649763	+	0.866001i
$452$	5.76421			0.271126
$453$	19.3949			0.911250
$454$			14.4270i			0.677092i
$455$		0			0
$456$	1.67588			0.0784801
$457$			18.0582i			0.844725i	0.906427	+	0.422363i	$0.138799\pi$
$457$			18.0582i			0.844725i	−0.906427	+	0.422363i	$0.861201\pi$
$458$	7.09696			0.331619
$459$			26.9939i			1.25997i
$460$		−	2.31534i		−	0.107953i
$461$	−11.4500			−0.533281			−0.266641	−	0.963796i	$-0.585914\pi$
$461$	−11.4500			−0.533281			−0.266641	+	0.963796i	$0.585914\pi$
$462$		0			0
$463$	−26.6805			−1.23995			−0.619975	−	0.784622i	$-0.712857\pi$
$463$	−26.6805			−1.23995			−0.619975	+	0.784622i	$0.712857\pi$
$464$			7.50358i			0.348345i
$465$			21.5517i			0.999437i
$466$	−4.16116			−0.192762
$467$		−	9.71626i		−	0.449615i	−0.974403	−	0.224807i	$-0.927825\pi$
$467$		−	9.71626i		−	0.449615i	0.974403	−	0.224807i	$-0.0721753\pi$
$468$	0.813729			0.0376146
$469$		0			0
$470$		−	9.89162i		−	0.456266i
$471$	−8.52872			−0.392983
$472$	−0.965635			−0.0444470
$473$	−18.0648	−	13.5540i	−0.830619	−	0.623215i
$474$		−	15.6788i		−	0.720149i
$475$	−1.00528			−0.0461254
$476$		0			0
$477$	−2.72004			−0.124542
$478$	19.8625			0.908489
$479$	19.2084			0.877653			0.438826	−	0.898572i	$-0.355394\pi$
$479$	19.2084			0.877653			0.438826	+	0.898572i	$0.355394\pi$
$480$			4.56676i			0.208443i
$481$	−18.9182			−0.862595
$482$		−	14.4893i		−	0.659972i
$483$		0			0
$484$	3.07591	+	10.5612i	0.139814	+	0.480054i
$485$	9.45808			0.429469
$486$	4.27518			0.193926
$487$	0.362596			0.0164308			0.00821539	−	0.999966i	$-0.497385\pi$
$487$	0.362596			0.0164308			0.00821539	+	0.999966i	$0.497385\pi$
$488$		−	11.9003i		−	0.538701i
$489$			26.9304i			1.21784i
$490$		0			0
$491$		−	1.04374i		−	0.0471033i	−0.999723	−	0.0235516i	$-0.992503\pi$
$491$		−	1.04374i		−	0.0471033i	0.999723	−	0.0235516i	$-0.00749741\pi$
$492$		−	12.8094i		−	0.577493i
$493$			42.3932i			1.90930i
$494$			1.78177i			0.0801658i
$495$	−2.71588	−	2.03773i	−0.122070	−	0.0915893i
$496$			4.71925i			0.211901i
$497$		0			0
$498$	−8.93578			−0.400422
$499$	19.6008			0.877453			0.438727	−	0.898621i	$-0.355430\pi$
$499$	19.6008			0.877453			0.438727	+	0.898621i	$0.355430\pi$
$500$			9.61818i			0.430138i
$501$		−	13.6188i		−	0.608443i
$502$	14.6156			0.652326
$503$	36.6503			1.63415			0.817077	−	0.576529i	$-0.195593\pi$
$503$	36.6503			1.63415			0.817077	+	0.576529i	$0.195593\pi$
$504$		0			0
$505$		−	39.1224i		−	1.74092i
$506$	2.48528	+	1.86471i	0.110484	+	0.0828966i
$507$		−	16.8898i		−	0.750101i
$508$			18.6371i			0.826888i
$509$		−	37.0949i		−	1.64420i	−0.569342	−	0.822101i	$-0.692802\pi$
$509$		−	37.0949i		−	1.64420i	0.569342	−	0.822101i	$-0.307198\pi$
$510$			25.8010i			1.14249i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			4.33346i			0.191327i
$514$	−23.1182			−1.01970
$515$	1.95304			0.0860614
$516$	12.5821			0.553898
$517$	10.6176	+	7.96643i	0.466963	+	0.350363i
$518$		0			0
$519$			20.6005i			0.904262i
$520$	−4.85533			−0.212920
$521$			19.4850i			0.853653i	0.904333	+	0.426827i	$0.140369\pi$
$521$			19.4850i			0.853653i	−0.904333	+	0.426827i	$0.859631\pi$
$522$	3.10808			0.136037
$523$	−43.0327			−1.88169			−0.940844	−	0.338841i	$-0.889965\pi$
$523$	−43.0327			−1.88169			−0.940844	+	0.338841i	$0.889965\pi$
$524$	19.9835			0.872982
$525$		0			0
$526$	−8.48528			−0.369976
$527$			26.6625i			1.16144i
$528$	−4.90195	−	3.67794i	−0.213330	−	0.160062i
$529$	−22.1224			−0.961843
$530$	16.2299			0.704980
$531$			0.399979i			0.0173576i
$532$		0			0
$533$	13.6188			0.589896
$534$			23.5294i			1.01822i
$535$	41.0560			1.77500
$536$		−	6.72004i		−	0.290262i
$537$			29.2106i			1.26053i
$538$	30.6005			1.31928
$539$		0			0
$540$	−11.8087			−0.508164
$541$			19.6188i			0.843478i	0.906717	+	0.421739i	$0.138580\pi$
$541$			19.6188i			0.843478i	−0.906717	+	0.421739i	$0.861420\pi$
$542$			13.2016i			0.567059i
$543$	−30.7703			−1.32048
$544$			5.64974i			0.242231i
$545$	14.8291			0.635208
$546$		0			0
$547$		−	42.5800i		−	1.82059i	−0.413959	−	0.910295i	$-0.635854\pi$
$547$		−	42.5800i		−	1.82059i	0.413959	−	0.910295i	$-0.364146\pi$
$548$	−16.4394			−0.702254
$549$	−4.92926			−0.210376
$550$	2.94045	+	2.20623i	0.125381	+	0.0940738i
$551$			6.80558i			0.289927i
$552$	−1.73100			−0.0736764
$553$		0			0
$554$	3.98886			0.169470
$555$	−43.9777			−1.86675
$556$	10.7109			0.454242
$557$			8.86441i			0.375597i	0.982208	+	0.187799i	$0.0601352\pi$
$557$			8.86441i			0.375597i	−0.982208	+	0.187799i	$0.939865\pi$
$558$	1.95478			0.0827524
$559$			13.3772i			0.565795i
$560$		0			0
$561$	−27.6947	−	20.7794i	−1.16927	−	0.877308i
$562$	−5.94293			−0.250687
$563$	16.2674			0.685588			0.342794	−	0.939411i	$-0.388627\pi$
$563$	16.2674			0.685588			0.342794	+	0.939411i	$0.388627\pi$
$564$	−7.39519			−0.311394
$565$			14.2463i			0.599347i
$566$		−	21.2661i		−	0.893882i
$567$		0			0
$568$			11.5485i			0.484563i
$569$		−	43.1112i		−	1.80732i	−0.428254	−	0.903659i	$-0.640871\pi$
$569$		−	43.1112i		−	1.80732i	0.428254	−	0.903659i	$-0.359129\pi$
$570$			4.14195i			0.173487i
$571$			4.79826i			0.200801i	0.994947	+	0.100400i	$0.0320124\pi$
$571$			4.79826i			0.200801i	−0.994947	+	0.100400i	$0.967988\pi$
$572$	3.91035	−	5.21169i	0.163500	−	0.217912i
$573$			48.7011i			2.03452i
$574$		0			0
$575$	1.03835			0.0433021
$576$	0.414214			0.0172589
$577$		−	1.91203i		−	0.0795988i	−0.999208	−	0.0397994i	$-0.987328\pi$
$577$		−	1.91203i		−	0.0795988i	0.999208	−	0.0397994i	$-0.0126719\pi$
$578$			14.9195i			0.620571i
$579$	1.28266			0.0533056
$580$	−18.5452			−0.770047
$581$		0			0
$582$		−	7.07107i		−	0.293105i
$583$	−13.0711	+	17.4211i	−0.541348	+	0.721507i
$584$			10.8614i			0.449449i
$585$			2.01114i			0.0831505i
$586$		−	27.7920i		−	1.14808i
$587$			1.71510i			0.0707896i	0.999373	+	0.0353948i	$0.0112689\pi$
$587$			1.71510i			0.0707896i	−0.999373	+	0.0353948i	$0.988731\pi$
$588$		0			0
$589$			4.28026i			0.176365i
$590$		−	2.38658i		−	0.0982540i
$591$	18.0068			0.740699
$592$	−9.62995			−0.395789
$593$	−14.0391			−0.576517			−0.288258	−	0.957553i	$-0.593076\pi$
$593$	−14.0391			−0.576517			−0.288258	+	0.957553i	$0.593076\pi$
$594$	9.51038	−	12.6754i	0.390215	−	0.520077i
$595$		0			0
$596$			14.7635i			0.604736i
$597$	12.9982			0.531983
$598$		−	1.84038i		−	0.0752588i
$599$	6.07034			0.248027			0.124014	−	0.992281i	$-0.460423\pi$
$599$	6.07034			0.248027			0.124014	+	0.992281i	$0.460423\pi$
$600$	−2.04803			−0.0836104
$601$	−18.3373			−0.747995			−0.373998	−	0.927430i	$-0.622013\pi$
$601$	−18.3373			−0.747995			−0.373998	+	0.927430i	$0.622013\pi$
$602$		0			0
$603$	−2.78353			−0.113354
$604$			10.4964i			0.427093i
$605$	−26.1021	+	7.60216i	−1.06120	+	0.309072i
$606$	−29.2488			−1.18815
$607$	−0.212923			−0.00864229			−0.00432114	−	0.999991i	$-0.501375\pi$
$607$	−0.212923			−0.00864229			−0.00432114	+	0.999991i	$0.501375\pi$
$608$			0.906978i			0.0367828i
$609$		0			0
$610$	29.4117			1.19085
$611$		−	7.86248i		−	0.318082i
$612$	2.34020			0.0945969
$613$			16.8899i			0.682175i	0.940032	+	0.341087i	$0.110795\pi$
$613$			16.8899i			0.682175i	−0.940032	+	0.341087i	$0.889205\pi$
$614$			16.2674i			0.656497i
$615$	31.6586			1.27660
$616$		0			0
$617$	33.0864			1.33201			0.666004	−	0.745948i	$-0.268003\pi$
$617$	33.0864			1.33201			0.666004	+	0.745948i	$0.268003\pi$
$618$		−	1.46014i		−	0.0587354i
$619$		−	14.2494i		−	0.572733i	−0.958120	−	0.286366i	$-0.907553\pi$
$619$		−	14.2494i		−	0.572733i	0.958120	−	0.286366i	$-0.0924475\pi$
$620$	−11.6637			−0.468426
$621$		−	4.47600i		−	0.179616i
$622$	10.7925			0.432739
$623$		0			0
$624$			3.62995i			0.145314i
$625$	−29.3134			−1.17254
$626$	18.3111			0.731860
$627$	−4.44596	−	3.33581i	−0.177554	−	0.133220i
$628$		−	4.61571i		−	0.184187i
$629$	−54.4067			−2.16934
$630$		0			0
$631$	−19.3751			−0.771312			−0.385656	−	0.922643i	$-0.626025\pi$
$631$	−19.3751			−0.771312			−0.385656	+	0.922643i	$0.626025\pi$
$632$	8.48528			0.337526
$633$	−44.5591			−1.77107
$634$		−	0.358905i		−	0.0142539i
$635$	−46.0619			−1.82791
$636$		−	12.1338i		−	0.481136i
$637$		0			0
$638$	14.9358	−	19.9063i	0.591313	−	0.788100i
$639$	4.78353			0.189234
$640$	−2.47151			−0.0976952
$641$	−36.5087			−1.44201			−0.721003	−	0.692932i	$-0.756319\pi$
$641$	−36.5087			−1.44201			−0.721003	+	0.692932i	$0.756319\pi$
$642$		−	30.6943i		−	1.21141i
$643$		−	2.49558i		−	0.0984161i	−0.998789	−	0.0492080i	$-0.984330\pi$
$643$		−	2.49558i		−	0.0984161i	0.998789	−	0.0492080i	$-0.0156697\pi$
$644$		0			0
$645$			31.0969i			1.22444i
$646$			5.12419i			0.201609i
$647$		−	4.21517i		−	0.165715i	−0.996561	−	0.0828577i	$-0.973595\pi$
$647$		−	4.21517i		−	0.165715i	0.996561	−	0.0828577i	$-0.0264047\pi$
$648$			10.0711i			0.395629i
$649$	2.56175	+	1.92209i	0.100557	+	0.0754485i
$650$		−	2.17744i		−	0.0854062i
$651$		0			0
$652$	−14.5746			−0.570787
$653$	−10.7972			−0.422528			−0.211264	−	0.977429i	$-0.567758\pi$
$653$	−10.7972			−0.422528			−0.211264	+	0.977429i	$0.567758\pi$
$654$		−	11.0866i		−	0.433519i
$655$			49.3894i			1.92981i
$656$	6.93240			0.270665
$657$	4.49895			0.175521
$658$		0			0
$659$		−	42.1591i		−	1.64229i	−0.570723	−	0.821143i	$-0.693337\pi$
$659$		−	42.1591i		−	1.64229i	0.570723	−	0.821143i	$-0.306663\pi$
$660$	9.09009	−	12.1152i	0.353831	−	0.471585i
$661$		−	8.98122i		−	0.349329i	−0.984628	−	0.174664i	$-0.944116\pi$
$661$		−	8.98122i		−	0.349329i	0.984628	−	0.174664i	$-0.0558841\pi$
$662$		−	28.9135i		−	1.12375i
$663$			20.5083i			0.796476i
$664$		−	4.83601i		−	0.187674i
$665$		0			0
$666$			3.98886i			0.154565i
$667$		−	7.02944i		−	0.272181i
$668$	7.37045			0.285171
$669$	−5.36829			−0.207550
$670$	16.6087			0.641649
$671$	−23.6874	+	31.5704i	−0.914441	+	1.21876i
$672$		0			0
$673$			26.4282i			1.01873i	0.860550	+	0.509366i	$0.170120\pi$
$673$			26.4282i			1.01873i	−0.860550	+	0.509366i	$0.829880\pi$
$674$	−7.96341			−0.306739
$675$		−	5.29576i		−	0.203834i
$676$	9.14068			0.351565
$677$	−11.7138			−0.450197			−0.225099	−	0.974336i	$-0.572270\pi$
$677$	−11.7138			−0.450197			−0.225099	+	0.974336i	$0.572270\pi$
$678$	10.6509			0.409044
$679$		0			0
$680$	−13.9634			−0.535472
$681$			26.6576i			1.02152i
$682$	9.39362	−	12.5198i	0.359700	−	0.479407i
$683$	35.9868			1.37700			0.688498	−	0.725238i	$-0.258270\pi$
$683$	35.9868			1.37700			0.688498	+	0.725238i	$0.258270\pi$
$684$	0.375683			0.0143646
$685$		−	40.6301i		−	1.55240i
$686$		0			0
$687$	13.1135			0.500310
$688$			6.80940i			0.259606i
$689$	12.9005			0.491470
$690$		−	4.27820i		−	0.162868i
$691$		−	5.91057i		−	0.224849i	−0.993660	−	0.112424i	$-0.964138\pi$
$691$		−	5.91057i		−	0.224849i	0.993660	−	0.112424i	$-0.0358616\pi$
$692$	−11.1489			−0.423818
$693$		0			0
$694$	24.6810			0.936877
$695$			26.4721i			1.00414i
$696$			13.8648i			0.525544i
$697$	39.1662			1.48353
$698$			11.1489i			0.421993i
$699$	−7.68882			−0.290818
$700$		0			0
$701$			39.6167i			1.49630i	0.663527	+	0.748152i	$0.269059\pi$
$701$			39.6167i			1.49630i	−0.663527	+	0.748152i	$0.730941\pi$
$702$	−9.38628			−0.354262
$703$	−8.73416			−0.329415
$704$	1.99049	−	2.65291i	0.0750194	−	0.0999855i
$705$		−	18.2773i		−	0.688364i
$706$	−21.3852			−0.804844
$707$		0			0
$708$	−1.78426			−0.0670567
$709$	−20.4023			−0.766226			−0.383113	−	0.923701i	$-0.625148\pi$
$709$	−20.4023			−0.766226			−0.383113	+	0.923701i	$0.625148\pi$
$710$	−28.5422			−1.07117
$711$		−	3.51472i		−	0.131812i
$712$	−12.7340			−0.477229
$713$		−	4.42105i		−	0.165570i
$714$		0			0
$715$	12.8808	+	9.66448i	0.481714	+	0.361431i
$716$	−15.8087			−0.590798
$717$	36.7011			1.37063
$718$	−6.24367			−0.233012
$719$		−	28.7190i		−	1.07104i	−0.844524	−	0.535518i	$-0.820116\pi$
$719$		−	28.7190i		−	1.07104i	0.844524	−	0.535518i	$-0.179884\pi$
$720$			1.02373i			0.0381523i
$721$		0			0
$722$		−	18.1774i		−	0.676492i
$723$		−	26.7728i		−	0.995692i
$724$		−	16.6528i		−	0.618896i
$725$		−	8.31685i		−	0.308880i
$726$	5.68354	+	19.5145i	0.210936	+	0.724252i
$727$		−	9.15820i		−	0.339659i	−0.985473	−	0.169829i	$-0.945678\pi$
$727$		−	9.15820i		−	0.339659i	0.985473	−	0.169829i	$-0.0543217\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	−26.8442			−0.993548
$731$			38.4714i			1.42291i
$732$		−	21.9889i		−	0.812732i
$733$	44.7097			1.65139			0.825695	−	0.564116i	$-0.190783\pi$
$733$	44.7097			1.65139			0.825695	+	0.564116i	$0.190783\pi$
$734$	28.7533			1.06130
$735$		0			0
$736$		−	0.936812i		−	0.0345313i
$737$	−13.3762	+	17.8277i	−0.492717	+	0.656692i
$738$		−	2.87149i		−	0.105701i
$739$			21.7013i			0.798296i	0.916887	+	0.399148i	$0.130694\pi$
$739$			21.7013i			0.798296i	−0.916887	+	0.399148i	$0.869306\pi$
$740$		−	23.8006i		−	0.874926i
$741$			3.29229i			0.120945i
$742$		0			0
$743$			8.20708i			0.301089i	0.988603	+	0.150544i	$0.0481026\pi$
$743$			8.20708i			0.301089i	−0.988603	+	0.150544i	$0.951897\pi$
$744$			8.72004i			0.319692i
$745$	−36.4882			−1.33682
$746$	12.3589			0.452492
$747$	−2.00314			−0.0732911
$748$	11.2457	−	14.9883i	0.411185	−	0.548026i
$749$		0			0
$750$			17.7721i			0.648945i
$751$	−19.4206			−0.708669			−0.354335	−	0.935119i	$-0.615293\pi$
$751$	−19.4206			−0.708669			−0.354335	+	0.935119i	$0.615293\pi$
$752$		−	4.00225i		−	0.145947i
$753$	27.0061			0.984158
$754$	−14.7409			−0.536832
$755$	−25.9421			−0.944128
$756$		0			0
$757$	44.7958			1.62813			0.814065	−	0.580774i	$-0.197250\pi$
$757$	44.7958			1.62813			0.814065	+	0.580774i	$0.197250\pi$
$758$		−	23.7822i		−	0.863808i
$759$	4.59220	+	3.44554i	0.166686	+	0.125065i
$760$	−2.24161			−0.0813117
$761$	3.83578			0.139047			0.0695235	−	0.997580i	$-0.477852\pi$
$761$	3.83578			0.139047			0.0695235	+	0.997580i	$0.477852\pi$
$762$			34.4369i			1.24752i
$763$		0			0
$764$	−26.3568			−0.953557
$765$			5.78383i			0.209115i
$766$	31.8645			1.15131
$767$		−	1.89701i		−	0.0684969i
$768$			1.84776i			0.0666753i
$769$	37.6267			1.35685			0.678427	−	0.734667i	$-0.262662\pi$
$769$	37.6267			1.35685			0.678427	+	0.734667i	$0.262662\pi$
$770$		0			0
$771$	−42.7168			−1.53841
$772$			0.694171i			0.0249838i
$773$		−	28.5737i		−	1.02772i	−0.857873	−	0.513861i	$-0.828215\pi$
$773$		−	28.5737i		−	1.02772i	0.857873	−	0.513861i	$-0.171785\pi$
$774$	2.82055			0.101382
$775$		−	5.23075i		−	0.187894i
$776$	3.82683			0.137375
$777$		0			0
$778$			21.0155i			0.753441i
$779$	6.28754			0.225274
$780$	−8.97148			−0.321230
$781$	22.9871	−	30.6371i	0.822543	−	1.09628i
$782$		−	5.29274i		−	0.189268i
$783$	−35.8514			−1.28122
$784$		0			0
$785$	11.4078			0.407162
$786$	36.9246			1.31706
$787$	23.2666			0.829364			0.414682	−	0.909966i	$-0.363893\pi$
$787$	23.2666			0.829364			0.414682	+	0.909966i	$0.363893\pi$
$788$			9.74519i			0.347158i
$789$	−15.6788			−0.558178
$790$			20.9715i			0.746132i
$791$		0			0
$792$	−1.09887	−	0.824487i	−0.0390468	−	0.0292969i
$793$	23.3783			0.830188
$794$	8.31805			0.295196
$795$	29.9889			1.06360
$796$			7.03460i			0.249335i
$797$			26.8026i			0.949396i	0.880149	+	0.474698i	$0.157443\pi$
$797$			26.8026i			0.949396i	−0.880149	+	0.474698i	$0.842557\pi$
$798$		0			0
$799$		−	22.6117i		−	0.799943i
$800$		−	1.10838i		−	0.0391873i
$801$			5.27461i			0.186369i
$802$		−	30.6820i		−	1.08342i
$803$	21.6196	−	28.8144i	0.762938	−	1.01684i
$804$		−	12.4170i		−	0.437915i
$805$		0			0
$806$	−9.27105			−0.326559
$807$	56.5424			1.99039
$808$		−	15.8293i		−	0.556873i
$809$		−	1.08760i		−	0.0382380i	−0.999817	−	0.0191190i	$-0.993914\pi$
$809$		−	1.08760i		−	0.0382380i	0.999817	−	0.0191190i	$-0.00608614\pi$
$810$	−24.8908			−0.874573
$811$	−23.7806			−0.835051			−0.417525	−	0.908665i	$-0.637103\pi$
$811$	−23.7806			−0.835051			−0.417525	+	0.908665i	$0.637103\pi$
$812$		0			0
$813$			24.3934i			0.855515i
$814$	25.5474	+	19.1683i	0.895437	+	0.671849i
$815$		−	36.0214i		−	1.26178i
$816$			10.4394i			0.365451i
$817$			6.17598i			0.216070i
$818$		−	9.57877i		−	0.334914i
$819$		0			0
$820$			17.1335i			0.598329i
$821$			43.3894i			1.51430i	0.653240	+	0.757151i	$0.273409\pi$
$821$			43.3894i			1.51430i	−0.653240	+	0.757151i	$0.726591\pi$
$822$	−30.3760			−1.05948
$823$	6.80007			0.237035			0.118518	−	0.992952i	$-0.462186\pi$
$823$	6.80007			0.237035			0.118518	+	0.992952i	$0.462186\pi$
$824$	0.790221			0.0275287
$825$	5.43324	+	4.07658i	0.189161	+	0.141928i
$826$		0			0
$827$			36.3112i			1.26266i	0.775513	+	0.631332i	$0.217491\pi$
$827$			36.3112i			1.26266i	−0.775513	+	0.631332i	$0.782509\pi$
$828$	−0.388040			−0.0134853
$829$		−	34.2337i		−	1.18899i	−0.804101	−	0.594493i	$-0.797353\pi$
$829$		−	34.2337i		−	1.18899i	0.804101	−	0.594493i	$-0.202647\pi$
$830$	11.9523			0.414869
$831$	7.37045			0.255678
$832$	−1.96452			−0.0681073
$833$		0			0
$834$	19.7911			0.685310
$835$			18.2162i			0.630396i
$836$	1.80533	−	2.40614i	0.0624386	−	0.0832179i
$837$	−22.5482			−0.779379
$838$	10.3074			0.356064
$839$		−	17.3286i		−	0.598250i	−0.954214	−	0.299125i	$-0.903305\pi$
$839$		−	17.3286i		−	0.598250i	0.954214	−	0.299125i	$-0.0966947\pi$
$840$		0			0
$841$	−27.3036			−0.941505
$842$		−	25.8805i		−	0.891900i
$843$	−10.9811			−0.378209
$844$		−	24.1152i		−	0.830081i
$845$			22.5913i			0.777165i
$846$	−1.65779			−0.0569958
$847$		0			0
$848$	6.56676			0.225504
$849$		−	39.2947i		−	1.34859i
$850$		−	6.26208i		−	0.214788i
$851$	9.02145			0.309251
$852$			21.3388i			0.731055i
$853$	9.22034			0.315698			0.157849	−	0.987463i	$-0.449544\pi$
$853$	9.22034			0.315698			0.157849	+	0.987463i	$0.449544\pi$
$854$		0			0
$855$			0.928505i			0.0317542i
$856$	16.6117			0.567775
$857$	−8.86098			−0.302685			−0.151343	−	0.988481i	$-0.548360\pi$
$857$	−8.86098			−0.302685			−0.151343	+	0.988481i	$0.548360\pi$
$858$	7.22538	−	9.62995i	0.246670	−	0.328761i
$859$			44.3311i			1.51256i	0.654249	+	0.756279i	$0.272985\pi$
$859$			44.3311i			1.51256i	−0.654249	+	0.756279i	$0.727015\pi$
$860$	−16.8295			−0.573883
$861$		0			0
$862$	17.0858			0.581945
$863$	4.90306			0.166902			0.0834511	−	0.996512i	$-0.473406\pi$
$863$	4.90306			0.166902			0.0834511	+	0.996512i	$0.473406\pi$
$864$	−4.77791			−0.162548
$865$		−	27.5547i		−	0.936888i
$866$	1.92881			0.0655436
$867$			27.5677i			0.936249i
$868$		0			0
$869$	−22.5107	−	16.8899i	−0.763624	−	0.572949i
$870$	−34.2671			−1.16176
$871$	13.2016			0.447320
$872$	6.00000			0.203186
$873$		−	1.58513i		−	0.0536484i
$874$		−	0.849668i		−	0.0287404i
$875$		0			0
$876$			20.0693i			0.678079i
$877$		−	14.7157i		−	0.496915i	−0.968643	−	0.248458i	$-0.920076\pi$
$877$		−	14.7157i		−	0.496915i	0.968643	−	0.248458i	$-0.0799237\pi$
$878$		−	10.4234i		−	0.351772i
$879$		−	51.3529i		−	1.73209i
$880$	6.55672	+	4.91952i	0.221027	+	0.165837i
$881$		−	33.3550i		−	1.12376i	−0.827219	−	0.561880i	$-0.810078\pi$
$881$		−	33.3550i		−	1.12376i	0.827219	−	0.561880i	$-0.189922\pi$
$882$		0			0
$883$	45.3385			1.52576			0.762882	−	0.646538i	$-0.223784\pi$
$883$	45.3385			1.52576			0.762882	+	0.646538i	$0.223784\pi$
$884$	−11.0990			−0.373300
$885$		−	4.40983i		−	0.148235i
$886$			15.9254i			0.535023i
$887$	15.9534			0.535664			0.267832	−	0.963466i	$-0.413693\pi$
$887$	15.9534			0.535664			0.267832	+	0.963466i	$0.413693\pi$
$888$	−17.7938			−0.597122
$889$		0			0
$890$		−	31.4724i		−	1.05496i
$891$	20.0463	−	26.7177i	0.671578	−	0.895076i
$892$		−	2.90530i		−	0.0972765i
$893$		−	3.62995i		−	0.121472i
$894$			27.2794i			0.912358i
$895$		−	39.0714i		−	1.30601i
$896$		0			0
$897$		−	3.40058i		−	0.113542i
$898$			10.4404i			0.348400i
$899$	−35.4113			−1.18103
$900$	−0.459108			−0.0153036
$901$	37.1005			1.23600
$902$	−18.3911	−	13.7989i	−0.612355	−	0.459452i
$903$		0			0
$904$			5.76421i			0.191715i
$905$	41.1576			1.36812
$906$			19.3949i			0.644351i
$907$	−16.1841			−0.537385			−0.268692	−	0.963226i	$-0.586591\pi$
$907$	−16.1841			−0.537385			−0.268692	+	0.963226i	$0.586591\pi$
$908$	−14.4270			−0.478776
$909$	−6.55672			−0.217473
$910$		0			0
$911$	−39.2957			−1.30193			−0.650963	−	0.759110i	$-0.725635\pi$
$911$	−39.2957			−1.30193			−0.650963	+	0.759110i	$0.725635\pi$
$912$			1.67588i			0.0554938i
$913$	−9.62602	+	12.8295i	−0.318575	+	0.424595i
$914$	−18.0582			−0.597311
$915$	54.3458			1.79662
$916$			7.09696i			0.234490i
$917$		0			0
$918$	−26.9939			−0.890933
$919$		−	14.2893i		−	0.471362i	−0.971830	−	0.235681i	$-0.924268\pi$
$919$		−	14.2893i		−	0.471362i	0.971830	−	0.235681i	$-0.0757320\pi$
$920$	2.31534			0.0763346
$921$			30.0582i			0.990450i
$922$		−	11.4500i		−	0.377087i
$923$	−22.6872			−0.746757
$924$		0			0
$925$	10.6737			0.350949
$926$		−	26.6805i		−	0.876777i
$927$		−	0.327320i		−	0.0107506i
$928$	−7.50358			−0.246317
$929$		−	21.2116i		−	0.695930i	−0.937508	−	0.347965i	$-0.886873\pi$
$929$		−	21.2116i		−	0.695930i	0.937508	−	0.347965i	$-0.113127\pi$
$930$	−21.5517			−0.706709
$931$		0			0
$932$		−	4.16116i		−	0.136303i
$933$	19.9419			0.652869
$934$	9.71626			0.317926
$935$	37.0437	+	27.7940i	1.21146	+	0.908961i
$936$			0.813729i			0.0265976i
$937$	50.6154			1.65353			0.826767	−	0.562544i	$-0.190177\pi$
$937$	50.6154			1.65353			0.826767	+	0.562544i	$0.190177\pi$
$938$		0			0
$939$	33.8345			1.10415
$940$	9.89162			0.322629
$941$	34.5874			1.12752			0.563759	−	0.825939i	$-0.309355\pi$
$941$	34.5874			1.12752			0.563759	+	0.825939i	$0.309355\pi$
$942$		−	8.52872i		−	0.277881i
$943$	−6.49435			−0.211485
$944$		−	0.965635i		−	0.0314288i
$945$		0			0
$946$	13.5540	−	18.0648i	0.440680	−	0.587336i
$947$	1.70338			0.0553525			0.0276763	−	0.999617i	$-0.491189\pi$
$947$	1.70338			0.0553525			0.0276763	+	0.999617i	$0.491189\pi$
$948$	15.6788			0.509222
$949$	−21.3375			−0.692643
$950$		−	1.00528i		−	0.0326156i
$951$		−	0.663170i		−	0.0215047i
$952$		0			0
$953$		−	10.2050i		−	0.330573i	−0.986246	−	0.165287i	$-0.947145\pi$
$953$		−	10.2050i		−	0.330573i	0.986246	−	0.165287i	$-0.0528549\pi$
$954$		−	2.72004i		−	0.0880646i
$955$		−	65.1413i		−	2.10792i
$956$			19.8625i			0.642399i
$957$	27.5977	−	36.7821i	0.892108	−	1.18900i
$958$			19.2084i			0.620594i
$959$		0			0
$960$	−4.56676			−0.147392
$961$	8.72865			0.281569
$962$		−	18.9182i		−	0.609947i
$963$		−	6.88077i		−	0.221730i
$964$	14.4893			0.466670
$965$	−1.71565			−0.0552289
$966$		0			0
$967$		−	29.7361i		−	0.956249i	−0.878292	−	0.478124i	$-0.841317\pi$
$967$		−	29.7361i		−	0.956249i	0.878292	−	0.478124i	$-0.158683\pi$
$968$	−10.5612	+	3.07591i	−0.339450	+	0.0988635i
$969$			9.46827i			0.304165i
$970$			9.45808i			0.303681i
$971$			35.6308i			1.14345i	0.820447	+	0.571723i	$0.193725\pi$
$971$			35.6308i			1.14345i	−0.820447	+	0.571723i	$0.806275\pi$
$972$			4.27518i			0.137126i
$973$		0			0
$974$			0.362596i			0.0116183i
$975$		−	4.02338i		−	0.128851i
$976$	11.9003			0.380919
$977$	−27.6432			−0.884385			−0.442193	−	0.896920i	$-0.645799\pi$
$977$	−27.6432			−0.884385			−0.442193	+	0.896920i	$0.645799\pi$
$978$	−26.9304			−0.861140
$979$	33.7823	+	25.3470i	1.07969	+	0.810093i
$980$		0			0
$981$		−	2.48528i		−	0.0793489i
$982$	1.04374			0.0333070
$983$			43.2786i			1.38037i	0.723631	+	0.690187i	$0.242472\pi$
$983$			43.2786i			1.38037i	−0.723631	+	0.690187i	$0.757528\pi$
$984$	12.8094			0.408349
$985$	−24.0854			−0.767424
$986$	−42.3932			−1.35008
$987$		0			0
$988$	−1.78177			−0.0566857
$989$		−	6.37913i		−	0.202845i
$990$	2.03773	−	2.71588i	0.0647634	−	0.0863164i
$991$	−3.49673			−0.111077			−0.0555386	−	0.998457i	$-0.517688\pi$
$991$	−3.49673			−0.111077			−0.0555386	+	0.998457i	$0.517688\pi$
$992$	−4.71925			−0.149836
$993$		−	53.4252i		−	1.69540i
$994$		0			0
$995$	−17.3861			−0.551177
$996$		−	8.93578i		−	0.283141i
$997$	−16.1304			−0.510856			−0.255428	−	0.966828i	$-0.582216\pi$
$997$	−16.1304			−0.510856			−0.255428	+	0.966828i	$0.582216\pi$
$998$			19.6008i			0.620453i
$999$		−	46.0110i		−	1.45573i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.c.1077.15	yes	16
7.2	even	3		1078.2.i.d.1011.9		32
7.3	odd	6		1078.2.i.d.901.5		32
7.4	even	3		1078.2.i.d.901.6		32
7.5	odd	6		1078.2.i.d.1011.10		32
7.6	odd	2	inner	1078.2.c.c.1077.10	yes	16
11.10	odd	2	inner	1078.2.c.c.1077.7	yes	16
77.10	even	6		1078.2.i.d.901.9		32
77.32	odd	6		1078.2.i.d.901.10		32
77.54	even	6		1078.2.i.d.1011.6		32
77.65	odd	6		1078.2.i.d.1011.5		32
77.76	even	2	inner	1078.2.c.c.1077.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.2	✓	16	77.76	even	2	inner
1078.2.c.c.1077.7	yes	16	11.10	odd	2	inner
1078.2.c.c.1077.10	yes	16	7.6	odd	2	inner
1078.2.c.c.1077.15	yes	16	1.1	even	1	trivial
1078.2.i.d.901.5		32	7.3	odd	6
1078.2.i.d.901.6		32	7.4	even	3
1078.2.i.d.901.9		32	77.10	even	6
1078.2.i.d.901.10		32	77.32	odd	6
1078.2.i.d.1011.5		32	77.65	odd	6
1078.2.i.d.1011.6		32	77.54	even	6
1078.2.i.d.1011.9		32	7.2	even	3
1078.2.i.d.1011.10		32	7.5	odd	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.84776i q^{3} -1.00000 q^{4} -2.47151i q^{5} -1.84776 q^{6} -1.00000i q^{8} -0.414214 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.84776i q^{3} -1.00000 q^{4} -2.47151i q^{5} -1.84776 q^{6} -1.00000i q^{8} -0.414214 q^{9} +2.47151 q^{10} +(-1.99049 + 2.65291i) q^{11} -1.84776i q^{12} +1.96452 q^{13} +4.56676 q^{15} +1.00000 q^{16} +5.64974 q^{17} -0.414214i q^{18} +0.906978 q^{19} +2.47151i q^{20} +(-2.65291 - 1.99049i) q^{22} -0.936812 q^{23} +1.84776 q^{24} -1.10838 q^{25} +1.96452i q^{26} +4.77791i q^{27} +7.50358i q^{29} +4.56676i q^{30} +4.71925i q^{31} +1.00000i q^{32} +(-4.90195 - 3.67794i) q^{33} +5.64974i q^{34} +0.414214 q^{36} -9.62995 q^{37} +0.906978i q^{38} +3.62995i q^{39} -2.47151 q^{40} +6.93240 q^{41} +6.80940i q^{43} +(1.99049 - 2.65291i) q^{44} +1.02373i q^{45} -0.936812i q^{46} -4.00225i q^{47} +1.84776i q^{48} -1.10838i q^{50} +10.4394i q^{51} -1.96452 q^{52} +6.56676 q^{53} -4.77791 q^{54} +(6.55672 + 4.91952i) q^{55} +1.67588i q^{57} -7.50358 q^{58} -0.965635i q^{59} -4.56676 q^{60} +11.9003 q^{61} -4.71925 q^{62} -1.00000 q^{64} -4.85533i q^{65} +(3.67794 - 4.90195i) q^{66} +6.72004 q^{67} -5.64974 q^{68} -1.73100i q^{69} -11.5485 q^{71} +0.414214i q^{72} -10.8614 q^{73} -9.62995i q^{74} -2.04803i q^{75} -0.906978 q^{76} -3.62995 q^{78} +8.48528i q^{79} -2.47151i q^{80} -10.0711 q^{81} +6.93240i q^{82} +4.83601 q^{83} -13.9634i q^{85} -6.80940 q^{86} -13.8648 q^{87} +(2.65291 + 1.99049i) q^{88} -12.7340i q^{89} -1.02373 q^{90} +0.936812 q^{92} -8.72004 q^{93} +4.00225 q^{94} -2.24161i q^{95} -1.84776 q^{96} +3.82683i q^{97} +(0.824487 - 1.09887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^9	\( 16 q - 16 q^{4} + 16 q^{9} + 16 q^{11} + 16 q^{16} - 8 q^{22} - 16 q^{23} - 64 q^{25} - 16 q^{36} - 80 q^{37} - 16 q^{44} + 32 q^{53} - 48 q^{58} - 16 q^{64} + 16 q^{67} - 48 q^{71} + 16 q^{78} - 48 q^{81} + 32 q^{86} + 8 q^{88} + 16 q^{92} - 48 q^{93} + 24 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^9 + 16 * q^11 + 16 * q^16 - 8 * q^22 - 16 * q^23 - 64 * q^25 - 16 * q^36 - 80 * q^37 - 16 * q^44 + 32 * q^53 - 48 * q^58 - 16 * q^64 + 16 * q^67 - 48 * q^71 + 16 * q^78 - 48 * q^81 + 32 * q^86 + 8 * q^88 + 16 * q^92 - 48 * q^93 + 24 * q^99

Introduction

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