LMFDB - Embedded newform 1078.2.c.c.1077.4

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			1077.4
Root			$0.424903 + 1.02581i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.c.1077.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +3.89937 q^{10} +(0.214882 + 3.30966i) q^{11} +0.765367i q^{12} -1.81903 q^{13} +2.98445 q^{15} +1.00000 q^{16} -6.07606 q^{17} -2.41421i q^{18} -6.82952 q^{19} -3.89937i q^{20} +(3.30966 - 0.214882i) q^{22} -4.37667 q^{23} +0.765367 q^{24} -10.2051 q^{25} +1.81903i q^{26} -4.14386i q^{27} -9.36112i q^{29} -2.98445i q^{30} +7.88318i q^{31} -1.00000i q^{32} +(2.53310 - 0.164463i) q^{33} +6.07606i q^{34} -2.41421 q^{36} -4.60778 q^{37} +6.82952i q^{38} +1.39222i q^{39} -3.89937 q^{40} +3.58235 q^{41} +3.25819i q^{43} +(-0.214882 - 3.30966i) q^{44} +9.41392i q^{45} +4.37667i q^{46} +0.203854i q^{47} -0.765367i q^{48} +10.2051i q^{50} +4.65041i q^{51} +1.81903 q^{52} +4.98445 q^{53} -4.14386 q^{54} +(-12.9056 + 0.837904i) q^{55} +5.22709i q^{57} -9.36112 q^{58} +5.19752i q^{59} -2.98445 q^{60} +8.98372 q^{61} +7.88318 q^{62} -1.00000 q^{64} -7.09306i q^{65} +(-0.164463 - 2.53310i) q^{66} -8.03353 q^{67} +6.07606 q^{68} +3.34976i q^{69} +8.86195 q^{71} +2.41421i q^{72} +0.0557060 q^{73} +4.60778i q^{74} +7.81064i q^{75} +6.82952 q^{76} +1.39222 q^{78} +8.48528i q^{79} +3.89937i q^{80} +4.07107 q^{81} -3.58235i q^{82} -10.4676 q^{83} -23.6928i q^{85} +3.25819 q^{86} -7.16469 q^{87} +(-3.30966 + 0.214882i) q^{88} -1.68771i q^{89} +9.41392 q^{90} +4.37667 q^{92} +6.03353 q^{93} +0.203854 q^{94} -26.6308i q^{95} -0.765367 q^{96} +9.23880i q^{97} +(0.518771 + 7.99022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	0.765367i		−	0.441885i	−0.975287	−	0.220942i	$-0.929087\pi$
$3$		−	0.765367i		−	0.441885i	0.975287	−	0.220942i	$-0.0709133\pi$
$4$	−1.00000			−0.500000
$5$			3.89937i			1.74385i	0.489638	+	0.871926i	$0.337129\pi$
$5$			3.89937i			1.74385i	−0.489638	+	0.871926i	$0.662871\pi$
$6$	−0.765367			−0.312460
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	2.41421			0.804738
$10$	3.89937			1.23309
$11$	0.214882	+	3.30966i	0.0647893	+	0.997899i
$11$	0.214882	+	3.30966i	0.0647893	+	0.997899i
$12$			0.765367i			0.220942i
$13$	−1.81903			−0.504507			−0.252254	−	0.967661i	$-0.581172\pi$
$13$	−1.81903			−0.504507			−0.252254	+	0.967661i	$0.581172\pi$
$14$		0			0
$15$	2.98445			0.770582
$16$	1.00000			0.250000
$17$	−6.07606			−1.47366			−0.736830	−	0.676078i	$-0.763678\pi$
$17$	−6.07606			−1.47366			−0.736830	+	0.676078i	$0.763678\pi$
$18$		−	2.41421i		−	0.569036i
$19$	−6.82952			−1.56680			−0.783400	−	0.621518i	$-0.786516\pi$
$19$	−6.82952			−1.56680			−0.783400	+	0.621518i	$0.786516\pi$
$20$		−	3.89937i		−	0.871926i
$21$		0			0
$22$	3.30966	−	0.214882i	0.705621	−	0.0458130i
$23$	−4.37667			−0.912599			−0.456300	−	0.889826i	$-0.650825\pi$
$23$	−4.37667			−0.912599			−0.456300	+	0.889826i	$0.650825\pi$
$24$	0.765367			0.156230
$25$	−10.2051			−2.04102
$26$			1.81903i			0.356740i
$27$		−	4.14386i		−	0.797486i
$28$		0			0
$29$		−	9.36112i		−	1.73832i	−0.494534	−	0.869158i	$-0.664661\pi$
$29$		−	9.36112i		−	1.73832i	0.494534	−	0.869158i	$-0.335339\pi$
$30$		−	2.98445i		−	0.544884i
$31$			7.88318i			1.41586i	0.706282	+	0.707931i	$0.250371\pi$
$31$			7.88318i			1.41586i	−0.706282	+	0.707931i	$0.749629\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.53310	−	0.164463i	0.440956	−	0.0286294i
$34$			6.07606i			1.04204i
$35$		0			0
$36$	−2.41421			−0.402369
$37$	−4.60778			−0.757514			−0.378757	−	0.925496i	$-0.623648\pi$
$37$	−4.60778			−0.757514			−0.378757	+	0.925496i	$0.623648\pi$
$38$			6.82952i			1.10789i
$39$			1.39222i			0.222934i
$40$	−3.89937			−0.616545
$41$	3.58235			0.559469			0.279734	−	0.960077i	$-0.409754\pi$
$41$	3.58235			0.559469			0.279734	+	0.960077i	$0.409754\pi$
$42$		0			0
$43$			3.25819i			0.496869i	0.968649	+	0.248435i	$0.0799161\pi$
$43$			3.25819i			0.496869i	−0.968649	+	0.248435i	$0.920084\pi$
$44$	−0.214882	−	3.30966i	−0.0323947	−	0.498949i
$45$			9.41392i			1.40334i
$46$			4.37667i			0.645305i
$47$			0.203854i			0.0297351i	0.999889	+	0.0148675i	$0.00473266\pi$
$47$			0.203854i			0.0297351i	−0.999889	+	0.0148675i	$0.995267\pi$
$48$		−	0.765367i		−	0.110471i
$49$		0			0
$50$			10.2051i			1.44322i
$51$			4.65041i			0.651188i
$52$	1.81903			0.252254
$53$	4.98445			0.684667			0.342333	−	0.939579i	$-0.388783\pi$
$53$	4.98445			0.684667			0.342333	+	0.939579i	$0.388783\pi$
$54$	−4.14386			−0.563908
$55$	−12.9056	+	0.837904i	−1.74019	+	0.112983i
$56$		0			0
$57$			5.22709i			0.692345i
$58$	−9.36112			−1.22918
$59$			5.19752i			0.676659i	0.941028	+	0.338330i	$0.109862\pi$
$59$			5.19752i			0.676659i	−0.941028	+	0.338330i	$0.890138\pi$
$60$	−2.98445			−0.385291
$61$	8.98372			1.15025			0.575124	−	0.818066i	$-0.304954\pi$
$61$	8.98372			1.15025			0.575124	+	0.818066i	$0.304954\pi$
$62$	7.88318			1.00117
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	7.09306i		−	0.879786i
$66$	−0.164463	−	2.53310i	−0.0202441	−	0.311803i
$67$	−8.03353			−0.981451			−0.490726	−	0.871314i	$-0.663268\pi$
$67$	−8.03353			−0.981451			−0.490726	+	0.871314i	$0.663268\pi$
$68$	6.07606			0.736830
$69$			3.34976i			0.403264i
$70$		0			0
$71$	8.86195			1.05172			0.525860	−	0.850571i	$-0.323744\pi$
$71$	8.86195			1.05172			0.525860	+	0.850571i	$0.323744\pi$
$72$			2.41421i			0.284518i
$73$	0.0557060			0.00651989			0.00325995	−	0.999995i	$-0.498962\pi$
$73$	0.0557060			0.00651989			0.00325995	+	0.999995i	$0.498962\pi$
$74$			4.60778i			0.535643i
$75$			7.81064i			0.901896i
$76$	6.82952			0.783400
$77$		0			0
$78$	1.39222			0.157638
$79$			8.48528i			0.954669i	0.878722	+	0.477334i	$0.158397\pi$
$79$			8.48528i			0.954669i	−0.878722	+	0.477334i	$0.841603\pi$
$80$			3.89937i			0.435963i
$81$	4.07107			0.452341
$82$		−	3.58235i		−	0.395604i
$83$	−10.4676			−1.14897			−0.574483	−	0.818517i	$-0.694797\pi$
$83$	−10.4676			−1.14897			−0.574483	+	0.818517i	$0.694797\pi$
$84$		0			0
$85$		−	23.6928i		−	2.56985i
$86$	3.25819			0.351340
$87$	−7.16469			−0.768136
$88$	−3.30966	+	0.214882i	−0.352811	+	0.0229065i
$89$		−	1.68771i		−	0.178897i	−0.995991	−	0.0894484i	$-0.971490\pi$
$89$		−	1.68771i		−	0.178897i	0.995991	−	0.0894484i	$-0.0285104\pi$
$90$	9.41392			0.992314
$91$		0			0
$92$	4.37667			0.456300
$93$	6.03353			0.625648
$94$	0.203854			0.0210259
$95$		−	26.6308i		−	2.73227i
$96$	−0.765367			−0.0781149
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$	0.518771	+	7.99022i	0.0521384	+	0.803047i
$100$	10.2051			1.02051
$101$	5.34567			0.531914			0.265957	−	0.963985i	$-0.414312\pi$
$101$	5.34567			0.531914			0.265957	+	0.963985i	$0.414312\pi$
$102$	4.65041			0.460460
$103$			4.24513i			0.418285i	0.977885	+	0.209143i	$0.0670673\pi$
$103$			4.24513i			0.418285i	−0.977885	+	0.209143i	$0.932933\pi$
$104$		−	1.81903i		−	0.178370i
$105$		0			0
$106$		−	4.98445i		−	0.484133i
$107$			7.23863i			0.699784i	0.936790	+	0.349892i	$0.113782\pi$
$107$			7.23863i			0.699784i	−0.936790	+	0.349892i	$0.886218\pi$
$108$			4.14386i			0.398743i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	0.837904	+	12.9056i	0.0798910	+	1.23050i
$111$			3.52664i			0.334734i
$112$		0			0
$113$	16.8400			1.58417			0.792085	−	0.610411i	$-0.208996\pi$
$113$	16.8400			1.58417			0.792085	+	0.610411i	$0.208996\pi$
$114$	5.22709			0.489562
$115$		−	17.0663i		−	1.59144i
$116$			9.36112i			0.869158i
$117$	−4.39152			−0.405996
$118$	5.19752			0.478470
$119$		0			0
$120$			2.98445i			0.272442i
$121$	−10.9077	+	1.42237i	−0.991605	+	0.129306i
$122$		−	8.98372i		−	0.813348i
$123$		−	2.74181i		−	0.247221i
$124$		−	7.88318i		−	0.707931i
$125$		−	20.2966i		−	1.81538i
$126$		0			0
$127$			17.3300i			1.53779i	0.639375	+	0.768895i	$0.279193\pi$
$127$			17.3300i			1.53779i	−0.639375	+	0.768895i	$0.720807\pi$
$128$			1.00000i			0.0883883i
$129$	2.49371			0.219559
$130$	−7.09306			−0.622102
$131$	−6.35552			−0.555284			−0.277642	−	0.960685i	$-0.589553\pi$
$131$	−6.35552			−0.555284			−0.277642	+	0.960685i	$0.589553\pi$
$132$	−2.53310	+	0.164463i	−0.220478	+	0.0143147i
$133$		0			0
$134$			8.03353i			0.693991i
$135$	16.1584			1.39070
$136$		−	6.07606i		−	0.521018i
$137$	1.34959			0.115303			0.0576515	−	0.998337i	$-0.481639\pi$
$137$	1.34959			0.115303			0.0576515	+	0.998337i	$0.481639\pi$
$138$	3.34976			0.285150
$139$	11.8957			1.00898			0.504491	−	0.863417i	$-0.331680\pi$
$139$	11.8957			1.00898			0.504491	+	0.863417i	$0.331680\pi$
$140$		0			0
$141$	0.156023			0.0131395
$142$		−	8.86195i		−	0.743679i
$143$	−0.390876	−	6.02035i	−0.0326867	−	0.503447i
$144$	2.41421			0.201184
$145$	36.5025			3.03137
$146$		−	0.0557060i		−	0.00461026i
$147$		0			0
$148$	4.60778			0.378757
$149$			6.57668i			0.538782i	0.963031	+	0.269391i	$0.0868225\pi$
$149$			6.57668i			0.538782i	−0.963031	+	0.269391i	$0.913178\pi$
$150$	7.81064			0.637736
$151$			8.63888i			0.703022i	0.936184	+	0.351511i	$0.114332\pi$
$151$			8.63888i			0.703022i	−0.936184	+	0.351511i	$0.885668\pi$
$152$		−	6.82952i		−	0.553947i
$153$	−14.6689			−1.18591
$154$		0			0
$155$	−30.7395			−2.46905
$156$		−	1.39222i		−	0.111467i
$157$			2.44991i			0.195524i	0.995210	+	0.0977619i	$0.0311684\pi$
$157$			2.44991i			0.195524i	−0.995210	+	0.0977619i	$0.968832\pi$
$158$	8.48528			0.675053
$159$		−	3.81493i		−	0.302544i
$160$	3.89937			0.308272
$161$		0			0
$162$		−	4.07107i		−	0.319853i
$163$	2.29005			0.179371			0.0896854	−	0.995970i	$-0.471414\pi$
$163$	2.29005			0.179371			0.0896854	+	0.995970i	$0.471414\pi$
$164$	−3.58235			−0.279734
$165$	0.641304	+	9.87750i	0.0499255	+	0.768963i
$166$			10.4676i			0.812441i
$167$	8.51406			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$167$	8.51406			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$168$		0			0
$169$	−9.69114			−0.745473
$170$	−23.6928			−1.81716
$171$	−16.4879			−1.26086
$172$		−	3.25819i		−	0.248435i
$173$	−23.9921			−1.82409			−0.912044	−	0.410092i	$-0.865497\pi$
$173$	−23.9921			−1.82409			−0.912044	+	0.410092i	$0.865497\pi$
$174$			7.16469i			0.543154i
$175$		0			0
$176$	0.214882	+	3.30966i	0.0161973	+	0.249475i
$177$	3.97801			0.299005
$178$	−1.68771			−0.126499
$179$	20.1584			1.50671			0.753357	−	0.657612i	$-0.228433\pi$
$179$	20.1584			1.50671			0.753357	+	0.657612i	$0.228433\pi$
$180$		−	9.41392i		−	0.701672i
$181$			11.1135i			0.826062i	0.910717	+	0.413031i	$0.135530\pi$
$181$			11.1135i			0.826062i	−0.910717	+	0.413031i	$0.864470\pi$
$182$		0			0
$183$		−	6.87584i		−	0.508277i
$184$		−	4.37667i		−	0.322653i
$185$		−	17.9674i		−	1.32099i
$186$		−	6.03353i		−	0.442400i
$187$	−1.30563	−	20.1097i	−0.0954775	−	1.47056i
$188$		−	0.203854i		−	0.0148675i
$189$		0			0
$190$	−26.6308			−1.93200
$191$	−24.5084			−1.77336			−0.886681	−	0.462382i	$-0.846995\pi$
$191$	−24.5084			−1.77336			−0.886681	+	0.462382i	$0.846995\pi$
$192$			0.765367i			0.0552356i
$193$			12.6193i			0.908358i	0.890910	+	0.454179i	$0.150067\pi$
$193$			12.6193i			0.908358i	−0.890910	+	0.454179i	$0.849933\pi$
$194$	9.23880			0.663307
$195$	−5.42879			−0.388764
$196$		0			0
$197$		−	17.2697i		−	1.23042i	−0.788364	−	0.615209i	$-0.789072\pi$
$197$		−	17.2697i		−	1.23042i	0.788364	−	0.615209i	$-0.210928\pi$
$198$	7.99022	−	0.518771i	0.567840	−	0.0368674i
$199$			9.18309i			0.650972i	0.945547	+	0.325486i	$0.105528\pi$
$199$			9.18309i			0.650972i	−0.945547	+	0.325486i	$0.894472\pi$
$200$		−	10.2051i		−	0.721609i
$201$			6.14859i			0.433688i
$202$		−	5.34567i		−	0.376120i
$203$		0			0
$204$		−	4.65041i		−	0.325594i
$205$			13.9689i			0.975630i
$206$	4.24513			0.295772
$207$	−10.5662			−0.734403
$208$	−1.81903			−0.126127
$209$	−1.46754	−	22.6034i	−0.101512	−	1.56351i
$210$		0			0
$211$		−	2.12250i		−	0.146119i	−0.997328	−	0.0730593i	$-0.976724\pi$
$211$		−	2.12250i		−	0.146119i	0.997328	−	0.0730593i	$-0.0232762\pi$
$212$	−4.98445			−0.342333
$213$		−	6.78265i		−	0.464739i
$214$	7.23863			0.494822
$215$	−12.7049			−0.866467
$216$	4.14386			0.281954
$217$		0			0
$218$	−6.00000			−0.406371
$219$		−	0.0426355i		−	0.00288104i
$220$	12.9056	−	0.837904i	0.870094	−	0.0564915i
$221$	11.0525			0.743472
$222$	3.52664			0.236693
$223$		−	5.77586i		−	0.386780i	−0.981122	−	0.193390i	$-0.938052\pi$
$223$		−	5.77586i		−	0.386780i	0.981122	−	0.193390i	$-0.0619483\pi$
$224$		0			0
$225$	−24.6373			−1.64249
$226$		−	16.8400i		−	1.12018i
$227$	1.21054			0.0803463			0.0401731	−	0.999193i	$-0.487209\pi$
$227$	1.21054			0.0803463			0.0401731	+	0.999193i	$0.487209\pi$
$228$		−	5.22709i		−	0.346173i
$229$		−	19.4012i		−	1.28207i	−0.767511	−	0.641035i	$-0.778505\pi$
$229$		−	19.4012i		−	1.28207i	0.767511	−	0.641035i	$-0.221495\pi$
$230$	−17.0663			−1.12532
$231$		0			0
$232$	9.36112			0.614588
$233$			19.7124i			1.29140i	0.763591	+	0.645700i	$0.223434\pi$
$233$			19.7124i			1.29140i	−0.763591	+	0.645700i	$0.776566\pi$
$234$			4.39152i			0.287082i
$235$	−0.794901			−0.0518536
$236$		−	5.19752i		−	0.338330i
$237$	6.49435			0.421854
$238$		0			0
$239$			11.6292i			0.752229i	0.926573	+	0.376115i	$0.122740\pi$
$239$			11.6292i			0.752229i	−0.926573	+	0.376115i	$0.877260\pi$
$240$	2.98445			0.192645
$241$	27.3738			1.76330			0.881651	−	0.471903i	$-0.156433\pi$
$241$	27.3738			1.76330			0.881651	+	0.471903i	$0.156433\pi$
$242$	1.42237	+	10.9077i	0.0914334	+	0.701170i
$243$		−	15.5474i		−	0.997369i
$244$	−8.98372			−0.575124
$245$		0			0
$246$	−2.74181			−0.174811
$247$	12.4231			0.790462
$248$	−7.88318			−0.500583
$249$			8.01154i			0.507710i
$250$	−20.2966			−1.28367
$251$			13.5021i			0.852243i	0.904666	+	0.426122i	$0.140120\pi$
$251$			13.5021i			0.852243i	−0.904666	+	0.426122i	$0.859880\pi$
$252$		0			0
$253$	−0.940467	−	14.4853i	−0.0591267	−	0.910682i
$254$	17.3300			1.08738
$255$	−18.1337			−1.13558
$256$	1.00000			0.0625000
$257$		−	2.80639i		−	0.175058i	−0.996162	−	0.0875289i	$-0.972103\pi$
$257$		−	2.80639i		−	0.175058i	0.996162	−	0.0875289i	$-0.0278970\pi$
$258$		−	2.49371i		−	0.155252i
$259$		0			0
$260$			7.09306i			0.439893i
$261$		−	22.5997i		−	1.39889i
$262$			6.35552i			0.392645i
$263$			8.48528i			0.523225i	0.965173	+	0.261612i	$0.0842542\pi$
$263$			8.48528i			0.523225i	−0.965173	+	0.261612i	$0.915746\pi$
$264$	0.164463	+	2.53310i	0.0101220	+	0.155902i
$265$			19.4362i			1.19396i
$266$		0			0
$267$	−1.29172			−0.0790518
$268$	8.03353			0.490726
$269$		−	20.9576i		−	1.27781i	−0.769286	−	0.638905i	$-0.779388\pi$
$269$		−	20.9576i		−	1.27781i	0.769286	−	0.638905i	$-0.220612\pi$
$270$		−	16.1584i		−	0.983372i
$271$	14.6132			0.887688			0.443844	−	0.896104i	$-0.353614\pi$
$271$	14.6132			0.887688			0.443844	+	0.896104i	$0.353614\pi$
$272$	−6.07606			−0.368415
$273$		0			0
$274$		−	1.34959i		−	0.0815315i
$275$	−2.19289	−	33.7754i	−0.132236	−	2.03673i
$276$		−	3.34976i		−	0.201632i
$277$		−	11.1242i		−	0.668386i	−0.942505	−	0.334193i	$-0.891536\pi$
$277$		−	11.1242i		−	0.668386i	0.942505	−	0.334193i	$-0.108464\pi$
$278$		−	11.8957i		−	0.713458i
$279$			19.0317i			1.13940i
$280$		0			0
$281$			7.28929i			0.434843i	0.976078	+	0.217421i	$0.0697646\pi$
$281$			7.28929i			0.434843i	−0.976078	+	0.217421i	$0.930235\pi$
$282$		−	0.156023i		−	0.00929102i
$283$	−16.0139			−0.951929			−0.475965	−	0.879464i	$-0.657901\pi$
$283$	−16.0139			−0.951929			−0.475965	+	0.879464i	$0.657901\pi$
$284$	−8.86195			−0.525860
$285$	−20.3824			−1.20735
$286$	−6.02035	+	0.390876i	−0.355991	+	0.0231130i
$287$		0			0
$288$		−	2.41421i		−	0.142259i
$289$	19.9185			1.17168
$290$		−	36.5025i		−	2.14350i
$291$	7.07107			0.414513
$292$	−0.0557060			−0.00325995
$293$	14.2550			0.832783			0.416392	−	0.909185i	$-0.363295\pi$
$293$	14.2550			0.832783			0.416392	+	0.909185i	$0.363295\pi$
$294$		0			0
$295$	−20.2671			−1.17999
$296$		−	4.60778i		−	0.267822i
$297$	13.7148	−	0.890440i	0.795811	−	0.0516686i
$298$	6.57668			0.380977
$299$	7.96128			0.460413
$300$		−	7.81064i		−	0.450948i
$301$		0			0
$302$	8.63888			0.497112
$303$		−	4.09140i		−	0.235045i
$304$	−6.82952			−0.391700
$305$			35.0309i			2.00586i
$306$			14.6689i			0.838565i
$307$	−6.75074			−0.385285			−0.192643	−	0.981269i	$-0.561706\pi$
$307$	−6.75074			−0.385285			−0.192643	+	0.981269i	$0.561706\pi$
$308$		0			0
$309$	3.24908			0.184834
$310$			30.7395i			1.74588i
$311$		−	17.8705i		−	1.01334i	−0.862139	−	0.506672i	$-0.830876\pi$
$311$		−	17.8705i		−	1.01334i	0.862139	−	0.506672i	$-0.169124\pi$
$312$	−1.39222			−0.0788191
$313$			15.0328i			0.849704i	0.905263	+	0.424852i	$0.139674\pi$
$313$			15.0328i			0.849704i	−0.905263	+	0.424852i	$0.860326\pi$
$314$	2.44991			0.138256
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	9.73194			0.546600			0.273300	−	0.961929i	$-0.411885\pi$
$317$	9.73194			0.546600			0.273300	+	0.961929i	$0.411885\pi$
$318$	−3.81493			−0.213931
$319$	30.9821	−	2.01154i	1.73466	−	0.112624i
$320$		−	3.89937i		−	0.217982i
$321$	5.54020			0.309224
$322$		0			0
$323$	41.4966			2.30893
$324$	−4.07107			−0.226170
$325$	18.5633			1.02971
$326$		−	2.29005i		−	0.126834i
$327$	−4.59220			−0.253949
$328$			3.58235i			0.197802i
$329$		0			0
$330$	9.87750	−	0.641304i	0.543739	−	0.0353026i
$331$	18.2599			1.00365			0.501826	−	0.864968i	$-0.332662\pi$
$331$	18.2599			1.00365			0.501826	+	0.864968i	$0.332662\pi$
$332$	10.4676			0.574483
$333$	−11.1242			−0.609600
$334$		−	8.51406i		−	0.465869i
$335$		−	31.3257i		−	1.71151i
$336$		0			0
$337$			29.6928i			1.61747i	0.588173	+	0.808735i	$0.299847\pi$
$337$			29.6928i			1.61747i	−0.588173	+	0.808735i	$0.700153\pi$
$338$			9.69114i			0.527129i
$339$		−	12.8887i		−	0.700021i
$340$			23.6928i			1.28492i
$341$	−26.0906	+	1.69395i	−1.41289	+	0.0917327i
$342$			16.4879i			0.891565i
$343$		0			0
$344$	−3.25819			−0.175670
$345$	−13.0620			−0.703232
$346$			23.9921i			1.28983i
$347$		−	19.2813i		−	1.03507i	−0.855661	−	0.517536i	$-0.826849\pi$
$347$		−	19.2813i		−	1.03507i	0.855661	−	0.517536i	$-0.173151\pi$
$348$	7.16469			0.384068
$349$	−23.9921			−1.28427			−0.642135	−	0.766592i	$-0.721951\pi$
$349$	−23.9921			−1.28427			−0.642135	+	0.766592i	$0.721951\pi$
$350$		0			0
$351$			7.53779i			0.402337i
$352$	3.30966	−	0.214882i	0.176405	−	0.0114532i
$353$			16.1478i			0.859462i	0.902957	+	0.429731i	$0.141392\pi$
$353$			16.1478i			0.859462i	−0.902957	+	0.429731i	$0.858608\pi$
$354$		−	3.97801i		−	0.211429i
$355$			34.5561i			1.83404i
$356$			1.68771i			0.0894484i
$357$		0			0
$358$		−	20.1584i		−	1.06541i
$359$		−	18.1456i		−	0.957686i	−0.877900	−	0.478843i	$-0.841056\pi$
$359$		−	18.1456i		−	0.957686i	0.877900	−	0.478843i	$-0.158944\pi$
$360$	−9.41392			−0.496157
$361$	27.6424			1.45486
$362$	11.1135			0.584114
$363$	1.08864	+	8.34836i	0.0571385	+	0.438175i
$364$		0			0
$365$			0.217218i			0.0113697i
$366$	−6.87584			−0.359406
$367$			4.91547i			0.256585i	0.991736	+	0.128293i	$0.0409497\pi$
$367$			4.91547i			0.256585i	−0.991736	+	0.128293i	$0.959050\pi$
$368$	−4.37667			−0.228150
$369$	8.64855			0.450225
$370$	−17.9674			−0.934083
$371$		0			0
$372$	−6.03353			−0.312824
$373$			2.26806i			0.117436i	0.998275	+	0.0587179i	$0.0187013\pi$
$373$			2.26806i			0.117436i	−0.998275	+	0.0587179i	$0.981299\pi$
$374$	−20.1097	+	1.30563i	−1.03985	+	0.0675128i
$375$	−15.5344			−0.802191
$376$	−0.203854			−0.0105129
$377$			17.0281i			0.876993i
$378$		0			0
$379$	14.7984			0.760143			0.380072	−	0.924957i	$-0.375899\pi$
$379$	14.7984			0.760143			0.380072	+	0.924957i	$0.375899\pi$
$380$			26.6308i			1.36613i
$381$	13.2638			0.679526
$382$			24.5084i			1.25396i
$383$		−	7.27031i		−	0.371495i	−0.982597	−	0.185748i	$-0.940529\pi$
$383$		−	7.27031i		−	0.371495i	0.982597	−	0.185748i	$-0.0594707\pi$
$384$	0.765367			0.0390575
$385$		0			0
$386$	12.6193			0.642306
$387$			7.86597i			0.399850i
$388$		−	9.23880i		−	0.469029i
$389$	−35.1936			−1.78439			−0.892194	−	0.451652i	$-0.850835\pi$
$389$	−35.1936			−1.78439			−0.892194	+	0.451652i	$0.850835\pi$
$390$			5.42879i			0.274898i
$391$	26.5929			1.34486
$392$		0			0
$393$			4.86431i			0.245372i
$394$	−17.2697			−0.870036
$395$	−33.0873			−1.66480
$396$	−0.518771	−	7.99022i	−0.0260692	−	0.401524i
$397$		−	18.8310i		−	0.945101i	−0.881304	−	0.472550i	$-0.843333\pi$
$397$		−	18.8310i		−	0.945101i	0.881304	−	0.472550i	$-0.156667\pi$
$398$	9.18309			0.460307
$399$		0			0
$400$	−10.2051			−0.510255
$401$	−7.10695			−0.354904			−0.177452	−	0.984129i	$-0.556785\pi$
$401$	−7.10695			−0.354904			−0.177452	+	0.984129i	$0.556785\pi$
$402$	6.14859			0.306664
$403$		−	14.3397i		−	0.714312i
$404$	−5.34567			−0.265957
$405$			15.8746i			0.788816i
$406$		0			0
$407$	−0.990128	−	15.2502i	−0.0490788	−	0.755922i
$408$	−4.65041			−0.230230
$409$	9.71411			0.480332			0.240166	−	0.970732i	$-0.422798\pi$
$409$	9.71411			0.480332			0.240166	+	0.970732i	$0.422798\pi$
$410$	13.9689			0.689875
$411$		−	1.03293i		−	0.0509506i
$412$		−	4.24513i		−	0.209143i
$413$		0			0
$414$			10.5662i			0.519301i
$415$		−	40.8170i		−	2.00363i
$416$			1.81903i			0.0891851i
$417$		−	9.10459i		−	0.445854i
$418$	−22.6034	+	1.46754i	−1.10557	+	0.0717798i
$419$		−	23.0474i		−	1.12594i	−0.826478	−	0.562970i	$-0.809659\pi$
$419$		−	23.0474i		−	1.12594i	0.826478	−	0.562970i	$-0.190341\pi$
$420$		0			0
$421$	−1.67074			−0.0814270			−0.0407135	−	0.999171i	$-0.512963\pi$
$421$	−1.67074			−0.0814270			−0.0407135	+	0.999171i	$0.512963\pi$
$422$	−2.12250			−0.103322
$423$			0.492146i			0.0239290i
$424$			4.98445i			0.242066i
$425$	62.0068			3.00777
$426$	−6.78265			−0.328620
$427$		0			0
$428$		−	7.23863i		−	0.349892i
$429$	−4.60778	+	0.299163i	−0.222466	+	0.0144437i
$430$			12.7049i			0.612685i
$431$		−	38.8481i		−	1.87125i	−0.353001	−	0.935623i	$-0.614839\pi$
$431$		−	38.8481i		−	1.87125i	0.353001	−	0.935623i	$-0.385161\pi$
$432$		−	4.14386i		−	0.199372i
$433$		−	31.8479i		−	1.53051i	−0.643726	−	0.765256i	$-0.722612\pi$
$433$		−	31.8479i		−	1.53051i	0.643726	−	0.765256i	$-0.277388\pi$
$434$		0			0
$435$		−	27.9378i		−	1.33951i
$436$			6.00000i			0.287348i
$437$	29.8906			1.42986
$438$	−0.0426355			−0.00203720
$439$	−12.0407			−0.574671			−0.287336	−	0.957830i	$-0.592770\pi$
$439$	−12.0407			−0.574671			−0.287336	+	0.957830i	$0.592770\pi$
$440$	−0.837904	−	12.9056i	−0.0399455	−	0.615249i
$441$		0			0
$442$		−	11.0525i		−	0.525714i
$443$	−30.5523			−1.45159			−0.725793	−	0.687914i	$-0.758527\pi$
$443$	−30.5523			−1.45159			−0.725793	+	0.687914i	$0.758527\pi$
$444$		−	3.52664i		−	0.167367i
$445$	6.58101			0.311970
$446$	−5.77586			−0.273495
$447$	5.03357			0.238080
$448$		0			0
$449$	15.7378			0.742712			0.371356	−	0.928490i	$-0.378893\pi$
$449$	15.7378			0.742712			0.371356	+	0.928490i	$0.378893\pi$
$450$			24.6373i			1.16141i
$451$	0.769781	+	11.8563i	0.0362476	+	0.558293i
$452$	−16.8400			−0.792085
$453$	6.61191			0.310655
$454$		−	1.21054i		−	0.0568134i
$455$		0			0
$456$	−5.22709			−0.244781
$457$			17.1668i			0.803029i	0.915853	+	0.401514i	$0.131516\pi$
$457$			17.1668i			0.803029i	−0.915853	+	0.401514i	$0.868484\pi$
$458$	−19.4012			−0.906561
$459$			25.1783i			1.17522i
$460$			17.0663i			0.795719i
$461$	0.312096			0.0145357			0.00726787	−	0.999974i	$-0.497687\pi$
$461$	0.312096			0.0145357			0.00726787	+	0.999974i	$0.497687\pi$
$462$		0			0
$463$	−31.9402			−1.48439			−0.742194	−	0.670185i	$-0.766215\pi$
$463$	−31.9402			−1.48439			−0.742194	+	0.670185i	$0.766215\pi$
$464$		−	9.36112i		−	0.434579i
$465$			23.5270i			1.09104i
$466$	19.7124			0.913158
$467$		−	18.8521i		−	0.872370i	−0.899857	−	0.436185i	$-0.856329\pi$
$467$		−	18.8521i		−	0.872370i	0.899857	−	0.436185i	$-0.143671\pi$
$468$	4.39152			0.202998
$469$		0			0
$470$			0.794901i			0.0366660i
$471$	1.87508			0.0863990
$472$	−5.19752			−0.239235
$473$	−10.7835	+	0.700126i	−0.495826	+	0.0321918i
$474$		−	6.49435i		−	0.298296i
$475$	69.6960			3.19787
$476$		0			0
$477$	12.0335			0.550977
$478$	11.6292			0.531907
$479$	29.0540			1.32751			0.663755	−	0.747950i	$-0.268962\pi$
$479$	29.0540			1.32751			0.663755	+	0.747950i	$0.268962\pi$
$480$		−	2.98445i		−	0.136221i
$481$	8.38167			0.382171
$482$		−	27.3738i		−	1.24684i
$483$		0			0
$484$	10.9077	−	1.42237i	0.495802	−	0.0646532i
$485$	−36.0255			−1.63583
$486$	−15.5474			−0.705246
$487$	−33.1349			−1.50148			−0.750742	−	0.660595i	$-0.770304\pi$
$487$	−33.1349			−1.50148			−0.750742	+	0.660595i	$0.770304\pi$
$488$			8.98372i			0.406674i
$489$		−	1.75273i		−	0.0792613i
$490$		0			0
$491$			42.4151i			1.91416i	0.289817	+	0.957082i	$0.406406\pi$
$491$			42.4151i			1.91416i	−0.289817	+	0.957082i	$0.593594\pi$
$492$			2.74181i			0.123610i
$493$			56.8787i			2.56169i
$494$		−	12.4231i		−	0.558941i
$495$	−31.1568	+	2.02288i	−1.40040	+	0.0909217i
$496$			7.88318i			0.353965i
$497$		0			0
$498$	8.01154			0.359005
$499$	15.4421			0.691282			0.345641	−	0.938367i	$-0.387662\pi$
$499$	15.4421			0.691282			0.345641	+	0.938367i	$0.387662\pi$
$500$			20.2966i			0.907692i
$501$		−	6.51638i		−	0.291130i
$502$	13.5021			0.602627
$503$	−39.5816			−1.76486			−0.882429	−	0.470446i	$-0.844093\pi$
$503$	−39.5816			−1.76486			−0.882429	+	0.470446i	$0.844093\pi$
$504$		0			0
$505$			20.8447i			0.927579i
$506$	−14.4853	+	0.940467i	−0.643949	+	0.0418089i
$507$			7.41728i			0.329413i
$508$		−	17.3300i		−	0.768895i
$509$		−	5.27888i		−	0.233982i	−0.993133	−	0.116991i	$-0.962675\pi$
$509$		−	5.27888i		−	0.233982i	0.993133	−	0.116991i	$-0.0373249\pi$
$510$			18.1337i			0.802973i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			28.3006i			1.24950i
$514$	−2.80639			−0.123785
$515$	−16.5533			−0.729427
$516$	−2.49371			−0.109780
$517$	−0.674685	+	0.0438044i	−0.0296726	+	0.00192652i
$518$		0			0
$519$			18.3628i			0.806037i
$520$	7.09306			0.311051
$521$			27.3087i			1.19641i	0.801341	+	0.598207i	$0.204120\pi$
$521$			27.3087i			1.19641i	−0.801341	+	0.598207i	$0.795880\pi$
$522$	−22.5997			−0.989164
$523$	8.65289			0.378365			0.189182	−	0.981942i	$-0.439416\pi$
$523$	8.65289			0.378365			0.189182	+	0.981942i	$0.439416\pi$
$524$	6.35552			0.277642
$525$		0			0
$526$	8.48528			0.369976
$527$		−	47.8987i		−	2.08650i
$528$	2.53310	−	0.164463i	0.110239	−	0.00715735i
$529$	−3.84474			−0.167163
$530$	19.4362			0.844256
$531$			12.5479i			0.544533i
$532$		0			0
$533$	−6.51638			−0.282256
$534$			1.29172i			0.0558981i
$535$	−28.2261			−1.22032
$536$		−	8.03353i		−	0.346995i
$537$		−	15.4286i		−	0.665794i
$538$	−20.9576			−0.903548
$539$		0			0
$540$	−16.1584			−0.695349
$541$			0.516382i			0.0222010i	0.999938	+	0.0111005i	$0.00353347\pi$
$541$			0.516382i			0.0222010i	−0.999938	+	0.0111005i	$0.996467\pi$
$542$		−	14.6132i		−	0.627690i
$543$	8.50593			0.365024
$544$			6.07606i			0.260509i
$545$	23.3962			1.00218
$546$		0			0
$547$			28.0407i			1.19894i	0.800399	+	0.599468i	$0.204621\pi$
$547$			28.0407i			1.19894i	−0.800399	+	0.599468i	$0.795379\pi$
$548$	−1.34959			−0.0576515
$549$	21.6886			0.925648
$550$	−33.7754	+	2.19289i	−1.44019	+	0.0935052i
$551$			63.9320i			2.72359i
$552$	−3.34976			−0.142575
$553$		0			0
$554$	−11.1242			−0.472620
$555$	−13.7517			−0.583726
$556$	−11.8957			−0.504491
$557$			28.7453i			1.21798i	0.793179	+	0.608989i	$0.208425\pi$
$557$			28.7453i			1.21798i	−0.793179	+	0.608989i	$0.791575\pi$
$558$	19.0317			0.805675
$559$		−	5.92673i		−	0.250674i
$560$		0			0
$561$	−15.3913	+	0.999289i	−0.649820	+	0.0421900i
$562$	7.28929			0.307480
$563$	−6.75074			−0.284510			−0.142255	−	0.989830i	$-0.545435\pi$
$563$	−6.75074			−0.284510			−0.142255	+	0.989830i	$0.545435\pi$
$564$	−0.156023			−0.00656974
$565$			65.6653i			2.76256i
$566$			16.0139i			0.673115i
$567$		0			0
$568$			8.86195i			0.371839i
$569$			9.72058i			0.407508i	0.979022	+	0.203754i	$0.0653143\pi$
$569$			9.72058i			0.407508i	−0.979022	+	0.203754i	$0.934686\pi$
$570$			20.3824i			0.853723i
$571$			20.3824i			0.852975i	0.904494	+	0.426487i	$0.140249\pi$
$571$			20.3824i			0.852975i	−0.904494	+	0.426487i	$0.859751\pi$
$572$	0.390876	+	6.02035i	0.0163433	+	0.251724i
$573$			18.7579i			0.783622i
$574$		0			0
$575$	44.6644			1.86263
$576$	−2.41421			−0.100592
$577$		−	12.2145i		−	0.508497i	−0.967139	−	0.254248i	$-0.918172\pi$
$577$		−	12.2145i		−	0.508497i	0.967139	−	0.254248i	$-0.0818281\pi$
$578$		−	19.9185i		−	0.828499i
$579$	9.65840			0.401390
$580$	−36.5025			−1.51568
$581$		0			0
$582$		−	7.07107i		−	0.293105i
$583$	1.07107	+	16.4968i	0.0443591	+	0.683228i
$584$			0.0557060i			0.00230513i
$585$		−	17.1242i		−	0.707997i
$586$		−	14.2550i		−	0.588867i
$587$		−	22.5689i		−	0.931519i	−0.884911	−	0.465759i	$-0.845781\pi$
$587$		−	22.5689i		−	0.931519i	0.884911	−	0.465759i	$-0.154219\pi$
$588$		0			0
$589$		−	53.8384i		−	2.21837i
$590$			20.2671i			0.834382i
$591$	−13.2177			−0.543703
$592$	−4.60778			−0.189378
$593$	36.6696			1.50584			0.752920	−	0.658112i	$-0.228645\pi$
$593$	36.6696			1.50584			0.752920	+	0.658112i	$0.228645\pi$
$594$	−0.890440	−	13.7148i	−0.0365352	−	0.562723i
$595$		0			0
$596$		−	6.57668i		−	0.269391i
$597$	7.02843			0.287655
$598$		−	7.96128i		−	0.325561i
$599$	6.34557			0.259273			0.129637	−	0.991562i	$-0.458619\pi$
$599$	6.34557			0.259273			0.129637	+	0.991562i	$0.458619\pi$
$600$	−7.81064			−0.318868
$601$	−1.60141			−0.0653230			−0.0326615	−	0.999466i	$-0.510398\pi$
$601$	−1.60141			−0.0653230			−0.0326615	+	0.999466i	$0.510398\pi$
$602$		0			0
$603$	−19.3946			−0.789811
$604$		−	8.63888i		−	0.351511i
$605$	−5.54635	−	42.5330i	−0.225491	−	1.72921i
$606$	−4.09140			−0.166202
$607$	16.7443			0.679631			0.339815	−	0.940492i	$-0.389635\pi$
$607$	16.7443			0.679631			0.339815	+	0.940492i	$0.389635\pi$
$608$			6.82952i			0.276974i
$609$		0			0
$610$	35.0309			1.41836
$611$		−	0.370815i		−	0.0150016i
$612$	14.6689			0.592955
$613$		−	1.82333i		−	0.0736437i	−0.999322	−	0.0368219i	$-0.988277\pi$
$613$		−	1.82333i		−	0.0736437i	0.999322	−	0.0368219i	$-0.0117234\pi$
$614$			6.75074i			0.272438i
$615$	10.6913			0.431116
$616$		0			0
$617$	46.7616			1.88255			0.941276	−	0.337638i	$-0.109628\pi$
$617$	46.7616			1.88255			0.941276	+	0.337638i	$0.109628\pi$
$618$		−	3.24908i		−	0.130697i
$619$			40.4744i			1.62680i	0.581702	+	0.813402i	$0.302387\pi$
$619$			40.4744i			1.62680i	−0.581702	+	0.813402i	$0.697613\pi$
$620$	30.7395			1.23453
$621$			18.1363i			0.727785i
$622$	−17.8705			−0.716542
$623$		0			0
$624$			1.39222i			0.0557335i
$625$	28.1186			1.12474
$626$	15.0328			0.600832
$627$	−17.2999	+	1.12321i	−0.690890	+	0.0448566i
$628$		−	2.44991i		−	0.0977619i
$629$	27.9971			1.11632
$630$		0			0
$631$	12.6619			0.504064			0.252032	−	0.967719i	$-0.418901\pi$
$631$	12.6619			0.504064			0.252032	+	0.967719i	$0.418901\pi$
$632$	−8.48528			−0.337526
$633$	−1.62449			−0.0645676
$634$		−	9.73194i		−	0.386505i
$635$	−67.5762			−2.68168
$636$			3.81493i			0.151272i
$637$		0			0
$638$	−2.01154	−	30.9821i	−0.0796374	−	1.22659i
$639$	21.3946			0.846359
$640$	−3.89937			−0.154136
$641$	−1.30695			−0.0516215			−0.0258107	−	0.999667i	$-0.508217\pi$
$641$	−1.30695			−0.0516215			−0.0258107	+	0.999667i	$0.508217\pi$
$642$		−	5.54020i		−	0.218654i
$643$			39.1745i			1.54489i	0.635081	+	0.772446i	$0.280967\pi$
$643$			39.1745i			1.54489i	−0.635081	+	0.772446i	$0.719033\pi$
$644$		0			0
$645$			9.72391i			0.382878i
$646$		−	41.4966i		−	1.63266i
$647$		−	16.5405i		−	0.650273i	−0.945667	−	0.325136i	$-0.894590\pi$
$647$		−	16.5405i		−	0.650273i	0.945667	−	0.325136i	$-0.105410\pi$
$648$			4.07107i			0.159927i
$649$	−17.2020	+	1.11685i	−0.675238	+	0.0438403i
$650$		−	18.5633i		−	0.728114i
$651$		0			0
$652$	−2.29005			−0.0896854
$653$	34.7706			1.36068			0.680339	−	0.732898i	$-0.261833\pi$
$653$	34.7706			1.36068			0.680339	+	0.732898i	$0.261833\pi$
$654$			4.59220i			0.179569i
$655$		−	24.7825i		−	0.968334i
$656$	3.58235			0.139867
$657$	0.134486			0.00524680
$658$		0			0
$659$		−	22.4888i		−	0.876039i	−0.898966	−	0.438019i	$-0.855680\pi$
$659$		−	22.4888i		−	0.876039i	0.898966	−	0.438019i	$-0.144320\pi$
$660$	−0.641304	−	9.87750i	−0.0249627	−	0.384481i
$661$		−	26.2795i		−	1.02215i	−0.859535	−	0.511077i	$-0.829247\pi$
$661$		−	26.2795i		−	1.02215i	0.859535	−	0.511077i	$-0.170753\pi$
$662$		−	18.2599i		−	0.709689i
$663$		−	8.45922i		−	0.328529i
$664$		−	10.4676i		−	0.406221i
$665$		0			0
$666$			11.1242i			0.431052i
$667$			40.9706i			1.58639i
$668$	−8.51406			−0.329419
$669$	−4.42065			−0.170912
$670$	−31.3257			−1.21022
$671$	1.93044	+	29.7330i	0.0745237	+	1.14783i
$672$		0			0
$673$			3.77457i			0.145499i	0.997350	+	0.0727495i	$0.0231774\pi$
$673$			3.77457i			0.145499i	−0.997350	+	0.0727495i	$0.976823\pi$
$674$	29.6928			1.14372
$675$			42.2885i			1.62769i
$676$	9.69114			0.372736
$677$	−31.4258			−1.20779			−0.603896	−	0.797063i	$-0.706386\pi$
$677$	−31.4258			−1.20779			−0.603896	+	0.797063i	$0.706386\pi$
$678$	−12.8887			−0.494989
$679$		0			0
$680$	23.6928			0.908578
$681$		−	0.926506i		−	0.0355038i
$682$	1.69395	+	26.0906i	0.0648648	+	0.999062i
$683$	−19.9006			−0.761474			−0.380737	−	0.924683i	$-0.624330\pi$
$683$	−19.9006			−0.761474			−0.380737	+	0.924683i	$0.624330\pi$
$684$	16.4879			0.630432
$685$			5.26254i			0.201071i
$686$		0			0
$687$	−14.8491			−0.566527
$688$			3.25819i			0.124217i
$689$	−9.06684			−0.345419
$690$			13.0620i			0.497260i
$691$			28.6007i			1.08802i	0.839078	+	0.544011i	$0.183095\pi$
$691$			28.6007i			1.08802i	−0.839078	+	0.544011i	$0.816905\pi$
$692$	23.9921			0.912044
$693$		0			0
$694$	−19.2813			−0.731907
$695$			46.3859i			1.75952i
$696$		−	7.16469i		−	0.271577i
$697$	−21.7665			−0.824467
$698$			23.9921i			0.908116i
$699$	15.0872			0.570650
$700$		0			0
$701$			21.2928i			0.804218i	0.915592	+	0.402109i	$0.131723\pi$
$701$			21.2928i			0.804218i	−0.915592	+	0.402109i	$0.868277\pi$
$702$	7.53779			0.284496
$703$	31.4689			1.18687
$704$	−0.214882	−	3.30966i	−0.00809866	−	0.124737i
$705$			0.608391i			0.0229133i
$706$	16.1478			0.607731
$707$		0			0
$708$	−3.97801			−0.149503
$709$	−16.8783			−0.633877			−0.316938	−	0.948446i	$-0.602655\pi$
$709$	−16.8783			−0.633877			−0.316938	+	0.948446i	$0.602655\pi$
$710$	34.5561			1.29687
$711$			20.4853i			0.768258i
$712$	1.68771			0.0632496
$713$		−	34.5021i		−	1.29211i
$714$		0			0
$715$	23.4756	−	1.52417i	0.877937	−	0.0570007i
$716$	−20.1584			−0.753357
$717$	8.90059			0.332399
$718$	−18.1456			−0.677187
$719$		−	36.1474i		−	1.34807i	−0.738699	−	0.674036i	$-0.764559\pi$
$719$		−	36.1474i		−	1.34807i	0.738699	−	0.674036i	$-0.235441\pi$
$720$			9.41392i			0.350836i
$721$		0			0
$722$		−	27.6424i		−	1.02874i
$723$		−	20.9510i		−	0.779176i
$724$		−	11.1135i		−	0.413031i
$725$			95.5312i			3.54794i
$726$	8.34836	−	1.08864i	0.309837	−	0.0404030i
$727$		−	8.74172i		−	0.324212i	−0.986773	−	0.162106i	$-0.948171\pi$
$727$		−	8.74172i		−	0.324212i	0.986773	−	0.162106i	$-0.0518287\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$	0.217218			0.00803961
$731$		−	19.7970i		−	0.732217i
$732$			6.87584i			0.254138i
$733$	13.4645			0.497323			0.248661	−	0.968590i	$-0.420009\pi$
$733$	13.4645			0.497323			0.248661	+	0.968590i	$0.420009\pi$
$734$	4.91547			0.181433
$735$		0			0
$736$			4.37667i			0.161326i
$737$	−1.72626	−	26.5882i	−0.0635876	−	0.979389i
$738$		−	8.64855i		−	0.318357i
$739$		−	37.3416i		−	1.37363i	−0.726832	−	0.686816i	$-0.759008\pi$
$739$		−	37.3416i		−	1.37363i	0.726832	−	0.686816i	$-0.240992\pi$
$740$			17.9674i			0.660496i
$741$		−	9.50821i		−	0.349293i
$742$		0			0
$743$			17.5472i			0.643746i	0.946783	+	0.321873i	$0.104312\pi$
$743$			17.5472i			0.643746i	−0.946783	+	0.321873i	$0.895688\pi$
$744$			6.03353i			0.221200i
$745$	−25.6449			−0.939557
$746$	2.26806			0.0830397
$747$	−25.2710			−0.924616
$748$	1.30563	+	20.1097i	0.0477387	+	0.735282i
$749$		0			0
$750$			15.5344i			0.567235i
$751$	−34.7247			−1.26712			−0.633561	−	0.773693i	$-0.718407\pi$
$751$	−34.7247			−1.26712			−0.633561	+	0.773693i	$0.718407\pi$
$752$			0.203854i			0.00743377i
$753$	10.3340			0.376593
$754$	17.0281			0.620128
$755$	−33.6862			−1.22597
$756$		0			0
$757$	28.0627			1.01996			0.509978	−	0.860187i	$-0.329653\pi$
$757$	28.0627			1.01996			0.509978	+	0.860187i	$0.329653\pi$
$758$		−	14.7984i		−	0.537502i
$759$	−11.0866	+	0.719803i	−0.402416	+	0.0261272i
$760$	26.6308			0.966002
$761$	7.58299			0.274883			0.137442	−	0.990510i	$-0.456112\pi$
$761$	7.58299			0.274883			0.137442	+	0.990510i	$0.456112\pi$
$762$		−	13.2638i		−	0.480498i
$763$		0			0
$764$	24.5084			0.886681
$765$		−	57.1995i		−	2.06805i
$766$	−7.27031			−0.262687
$767$		−	9.45442i		−	0.341379i
$768$		−	0.765367i		−	0.0276178i
$769$	−1.95786			−0.0706022			−0.0353011	−	0.999377i	$-0.511239\pi$
$769$	−1.95786			−0.0706022			−0.0353011	+	0.999377i	$0.511239\pi$
$770$		0			0
$771$	−2.14792			−0.0773554
$772$		−	12.6193i		−	0.454179i
$773$			9.44572i			0.339739i	0.985467	+	0.169869i	$0.0543346\pi$
$773$			9.44572i			0.339739i	−0.985467	+	0.169869i	$0.945665\pi$
$774$	7.86597			0.282736
$775$		−	80.4487i		−	2.88980i
$776$	−9.23880			−0.331653
$777$		0			0
$778$			35.1936i			1.26175i
$779$	−24.4657			−0.876575
$780$	5.42879			0.194382
$781$	1.90427	+	29.3300i	0.0681402	+	1.04951i
$782$		−	26.5929i		−	0.950961i
$783$	−38.7912			−1.38628
$784$		0			0
$785$	−9.55310			−0.340965
$786$	4.86431			0.173504
$787$	−20.0872			−0.716031			−0.358016	−	0.933716i	$-0.616547\pi$
$787$	−20.0872			−0.716031			−0.358016	+	0.933716i	$0.616547\pi$
$788$			17.2697i			0.615209i
$789$	6.49435			0.231205
$790$			33.0873i			1.17719i
$791$		0			0
$792$	−7.99022	+	0.518771i	−0.283920	+	0.0184337i
$793$	−16.3416			−0.580308
$794$	−18.8310			−0.668287
$795$	14.8758			0.527592
$796$		−	9.18309i		−	0.325486i
$797$		−	36.2219i		−	1.28304i	−0.767105	−	0.641522i	$-0.778303\pi$
$797$		−	36.2219i		−	1.28304i	0.767105	−	0.641522i	$-0.221697\pi$
$798$		0			0
$799$		−	1.23863i		−	0.0438194i
$800$			10.2051i			0.360805i
$801$		−	4.07449i		−	0.143965i
$802$			7.10695i			0.250955i
$803$	0.0119702	+	0.184368i	0.000422419	+	0.00650619i
$804$		−	6.14859i		−	0.216844i
$805$		0			0
$806$	−14.3397			−0.505095
$807$	−16.0403			−0.564645
$808$			5.34567i			0.188060i
$809$		−	0.196232i		−	0.00689915i	−0.999994	−	0.00344958i	$-0.998902\pi$
$809$		−	0.196232i		−	0.00689915i	0.999994	−	0.00344958i	$-0.00109804\pi$
$810$	15.8746			0.557777
$811$	13.1515			0.461811			0.230905	−	0.972976i	$-0.425831\pi$
$811$	13.1515			0.461811			0.230905	+	0.972976i	$0.425831\pi$
$812$		0			0
$813$		−	11.1845i		−	0.392256i
$814$	−15.2502	+	0.990128i	−0.534518	+	0.0347040i
$815$			8.92977i			0.312796i
$816$			4.65041i			0.162797i
$817$		−	22.2519i		−	0.778495i
$818$		−	9.71411i		−	0.339646i
$819$		0			0
$820$		−	13.9689i		−	0.487815i
$821$		−	18.7825i		−	0.655515i	−0.944762	−	0.327758i	$-0.893707\pi$
$821$		−	18.7825i		−	0.655515i	0.944762	−	0.327758i	$-0.106293\pi$
$822$	−1.03293			−0.0360275
$823$	36.2695			1.26427			0.632137	−	0.774856i	$-0.282178\pi$
$823$	36.2695			1.26427			0.632137	+	0.774856i	$0.282178\pi$
$824$	−4.24513			−0.147886
$825$	−25.8506	+	1.67837i	−0.900001	+	0.0584332i
$826$		0			0
$827$			26.5489i			0.923196i	0.887089	+	0.461598i	$0.152724\pi$
$827$			26.5489i			0.923196i	−0.887089	+	0.461598i	$0.847276\pi$
$828$	10.5662			0.367202
$829$			9.15743i			0.318051i	0.987275	+	0.159025i	$0.0508352\pi$
$829$			9.15743i			0.318051i	−0.987275	+	0.159025i	$0.949165\pi$
$830$	−40.8170			−1.41678
$831$	−8.51406			−0.295350
$832$	1.81903			0.0630634
$833$		0			0
$834$	−9.10459			−0.315266
$835$			33.1995i			1.14892i
$836$	1.46754	+	22.6034i	0.0507560	+	0.781754i
$837$	32.6668			1.12913
$838$	−23.0474			−0.796159
$839$		−	42.3516i		−	1.46214i	−0.682302	−	0.731070i	$-0.739021\pi$
$839$		−	42.3516i		−	1.46214i	0.682302	−	0.731070i	$-0.260979\pi$
$840$		0			0
$841$	−58.6306			−2.02175
$842$			1.67074i			0.0575775i
$843$	5.57898			0.192150
$844$			2.12250i			0.0730593i
$845$		−	37.7894i		−	1.29999i
$846$	0.492146			0.0169203
$847$		0			0
$848$	4.98445			0.171167
$849$			12.2565i			0.420643i
$850$		−	62.0068i		−	2.12681i
$851$	20.1667			0.691307
$852$			6.78265i			0.232370i
$853$	−56.4552			−1.93299			−0.966495	−	0.256686i	$-0.917369\pi$
$853$	−56.4552			−1.93299			−0.966495	+	0.256686i	$0.917369\pi$
$854$		0			0
$855$		−	64.2926i		−	2.19876i
$856$	−7.23863			−0.247411
$857$	−36.0454			−1.23129			−0.615644	−	0.788024i	$-0.711104\pi$
$857$	−36.0454			−1.23129			−0.615644	+	0.788024i	$0.711104\pi$
$858$	0.299163	+	4.60778i	0.0102133	+	0.157307i
$859$			0.0845360i			0.00288433i	0.999999	+	0.00144217i	$0.000459056\pi$
$859$			0.0845360i			0.00288433i	−0.999999	+	0.00144217i	$0.999541\pi$
$860$	12.7049			0.433233
$861$		0			0
$862$	−38.8481			−1.32317
$863$	45.7239			1.55646			0.778230	−	0.627979i	$-0.216118\pi$
$863$	45.7239			1.55646			0.778230	+	0.627979i	$0.216118\pi$
$864$	−4.14386			−0.140977
$865$		−	93.5543i		−	3.18094i
$866$	−31.8479			−1.08224
$867$		−	15.2449i		−	0.517745i
$868$		0			0
$869$	−28.0834	+	1.82333i	−0.952663	+	0.0618523i
$870$	−27.9378			−0.947180
$871$	14.6132			0.495149
$872$	6.00000			0.203186
$873$			22.3044i			0.754890i
$874$		−	29.8906i		−	1.01106i
$875$		0			0
$876$			0.0426355i			0.00144052i
$877$		−	46.2403i		−	1.56142i	−0.624891	−	0.780712i	$-0.714857\pi$
$877$		−	46.2403i		−	1.56142i	0.624891	−	0.780712i	$-0.285143\pi$
$878$			12.0407i			0.406354i
$879$		−	10.9103i		−	0.367994i
$880$	−12.9056	+	0.837904i	−0.435047	+	0.0282457i
$881$			37.2892i			1.25630i	0.778091	+	0.628152i	$0.216188\pi$
$881$			37.2892i			1.25630i	−0.778091	+	0.628152i	$0.783812\pi$
$882$		0			0
$883$	−24.3548			−0.819603			−0.409801	−	0.912175i	$-0.634402\pi$
$883$	−24.3548			−0.819603			−0.409801	+	0.912175i	$0.634402\pi$
$884$	−11.0525			−0.371736
$885$			15.5117i			0.521421i
$886$			30.5523i			1.02643i
$887$	11.4879			0.385727			0.192863	−	0.981226i	$-0.438223\pi$
$887$	11.4879			0.385727			0.192863	+	0.981226i	$0.438223\pi$
$888$	−3.52664			−0.118346
$889$		0			0
$890$		−	6.58101i		−	0.220596i
$891$	0.874799	+	13.4738i	0.0293069	+	0.451390i
$892$			5.77586i			0.193390i
$893$		−	1.39222i		−	0.0465889i
$894$		−	5.03357i		−	0.168348i
$895$			78.6053i			2.62748i
$896$		0			0
$897$		−	6.09330i		−	0.203449i
$898$		−	15.7378i		−	0.525177i
$899$	73.7954			2.46122
$900$	24.6373			0.821243
$901$	−30.2858			−1.00897
$902$	11.8563	−	0.769781i	0.394773	−	0.0256309i
$903$		0			0
$904$			16.8400i			0.560089i
$905$	−43.3358			−1.44053
$906$		−	6.61191i		−	0.219666i
$907$	−23.3013			−0.773709			−0.386854	−	0.922141i	$-0.626438\pi$
$907$	−23.3013			−0.773709			−0.386854	+	0.922141i	$0.626438\pi$
$908$	−1.21054			−0.0401731
$909$	12.9056			0.428051
$910$		0			0
$911$	−32.6447			−1.08157			−0.540784	−	0.841161i	$-0.681872\pi$
$911$	−32.6447			−1.08157			−0.540784	+	0.841161i	$0.681872\pi$
$912$			5.22709i			0.173086i
$913$	−2.24929	−	34.6441i	−0.0744407	−	1.14655i
$914$	17.1668			0.567827
$915$	26.8115			0.886359
$916$			19.4012i			0.641035i
$917$		0			0
$918$	25.1783			0.831009
$919$			38.1861i			1.25964i	0.776740	+	0.629822i	$0.216872\pi$
$919$			38.1861i			1.25964i	−0.776740	+	0.629822i	$0.783128\pi$
$920$	17.0663			0.562658
$921$			5.16679i			0.170252i
$922$		−	0.312096i		−	0.0102783i
$923$	−16.1201			−0.530600
$924$		0			0
$925$	47.0228			1.54610
$926$			31.9402i			1.04962i
$927$			10.2487i			0.336610i
$928$	−9.36112			−0.307294
$929$			8.14309i			0.267166i	0.991038	+	0.133583i	$0.0426483\pi$
$929$			8.14309i			0.267166i	−0.991038	+	0.133583i	$0.957352\pi$
$930$	23.5270			0.771479
$931$		0			0
$932$		−	19.7124i		−	0.645700i
$933$	−13.6775			−0.447781
$934$	−18.8521			−0.616859
$935$	78.4151	−	5.09115i	2.56445	−	0.166499i
$936$		−	4.39152i		−	0.143541i
$937$	29.3997			0.960445			0.480222	−	0.877147i	$-0.340556\pi$
$937$	29.3997			0.960445			0.480222	+	0.877147i	$0.340556\pi$
$938$		0			0
$939$	11.5056			0.375471
$940$	0.794901			0.0259268
$941$	25.1038			0.818362			0.409181	−	0.912453i	$-0.365814\pi$
$941$	25.1038			0.818362			0.409181	+	0.912453i	$0.365814\pi$
$942$		−	1.87508i		−	0.0610933i
$943$	−15.6788			−0.510571
$944$			5.19752i			0.169165i
$945$		0			0
$946$	0.700126	+	10.7835i	0.0227631	+	0.350602i
$947$	58.1180			1.88858			0.944290	−	0.329114i	$-0.106750\pi$
$947$	58.1180			1.88858			0.944290	+	0.329114i	$0.106750\pi$
$948$	−6.49435			−0.210927
$949$	−0.101331			−0.00328933
$950$		−	69.6960i		−	2.26124i
$951$		−	7.44850i		−	0.241534i
$952$		0			0
$953$		−	56.3237i		−	1.82450i	−0.409632	−	0.912251i	$-0.634343\pi$
$953$		−	56.3237i		−	1.82450i	0.409632	−	0.912251i	$-0.365657\pi$
$954$		−	12.0335i		−	0.389600i
$955$		−	95.5672i		−	3.09248i
$956$		−	11.6292i		−	0.376115i
$957$	−1.53956	−	23.7127i	−0.0497670	−	0.766522i
$958$		−	29.0540i		−	0.938692i
$959$		0			0
$960$	−2.98445			−0.0963227
$961$	−31.1446			−1.00466
$962$		−	8.38167i		−	0.270236i
$963$			17.4756i			0.563143i
$964$	−27.3738			−0.881651
$965$	−49.2074			−1.58404
$966$		0			0
$967$			28.3825i			0.912721i	0.889795	+	0.456360i	$0.150847\pi$
$967$			28.3825i			0.912721i	−0.889795	+	0.456360i	$0.849153\pi$
$968$	−1.42237	−	10.9077i	−0.0457167	−	0.350585i
$969$		−	31.7601i		−	1.02028i
$970$			36.0255i			1.15671i
$971$			44.1406i			1.41654i	0.705942	+	0.708270i	$0.250524\pi$
$971$			44.1406i			1.41654i	−0.705942	+	0.708270i	$0.749476\pi$
$972$			15.5474i			0.498684i
$973$		0			0
$974$			33.1349i			1.06171i
$975$		−	14.2078i		−	0.455013i
$976$	8.98372			0.287562
$977$	−9.66406			−0.309181			−0.154590	−	0.987979i	$-0.549406\pi$
$977$	−9.66406			−0.309181			−0.154590	+	0.987979i	$0.549406\pi$
$978$	−1.75273			−0.0560462
$979$	5.58574	−	0.362658i	0.178521	−	0.0115906i
$980$		0			0
$981$		−	14.4853i		−	0.462479i
$982$	42.4151			1.35352
$983$		−	26.6997i		−	0.851588i	−0.904820	−	0.425794i	$-0.859995\pi$
$983$		−	26.6997i		−	0.851588i	0.904820	−	0.425794i	$-0.140005\pi$
$984$	2.74181			0.0874057
$985$	67.3411			2.14567
$986$	56.8787			1.81139
$987$		0			0
$988$	−12.4231			−0.395231
$989$		−	14.2600i		−	0.453443i
$990$	2.02288	+	31.1568i	0.0642913	+	0.990229i
$991$	−36.4437			−1.15767			−0.578837	−	0.815444i	$-0.696493\pi$
$991$	−36.4437			−1.15767			−0.578837	+	0.815444i	$0.696493\pi$
$992$	7.88318			0.250291
$993$		−	13.9755i		−	0.443499i
$994$		0			0
$995$	−35.8083			−1.13520
$996$		−	8.01154i		−	0.253855i
$997$	−29.0257			−0.919253			−0.459627	−	0.888112i	$-0.652017\pi$
$997$	−29.0257			−0.919253			−0.459627	+	0.888112i	$0.652017\pi$
$998$		−	15.4421i		−	0.488810i
$999$			19.0940i			0.604107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.c.1077.4	✓	16
7.2	even	3		1078.2.i.d.1011.2		32
7.3	odd	6		1078.2.i.d.901.12		32
7.4	even	3		1078.2.i.d.901.11		32
7.5	odd	6		1078.2.i.d.1011.1		32
7.6	odd	2	inner	1078.2.c.c.1077.5	yes	16
11.10	odd	2	inner	1078.2.c.c.1077.12	yes	16
77.10	even	6		1078.2.i.d.901.2		32
77.32	odd	6		1078.2.i.d.901.1		32
77.54	even	6		1078.2.i.d.1011.11		32
77.65	odd	6		1078.2.i.d.1011.12		32
77.76	even	2	inner	1078.2.c.c.1077.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.4	✓	16	1.1	even	1	trivial
1078.2.c.c.1077.5	yes	16	7.6	odd	2	inner
1078.2.c.c.1077.12	yes	16	11.10	odd	2	inner
1078.2.c.c.1077.13	yes	16	77.76	even	2	inner
1078.2.i.d.901.1		32	77.32	odd	6
1078.2.i.d.901.2		32	77.10	even	6
1078.2.i.d.901.11		32	7.4	even	3
1078.2.i.d.901.12		32	7.3	odd	6
1078.2.i.d.1011.1		32	7.5	odd	6
1078.2.i.d.1011.2		32	7.2	even	3
1078.2.i.d.1011.11		32	77.54	even	6
1078.2.i.d.1011.12		32	77.65	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +3.89937 q^{10} +(0.214882 + 3.30966i) q^{11} +0.765367i q^{12} -1.81903 q^{13} +2.98445 q^{15} +1.00000 q^{16} -6.07606 q^{17} -2.41421i q^{18} -6.82952 q^{19} -3.89937i q^{20} +(3.30966 - 0.214882i) q^{22} -4.37667 q^{23} +0.765367 q^{24} -10.2051 q^{25} +1.81903i q^{26} -4.14386i q^{27} -9.36112i q^{29} -2.98445i q^{30} +7.88318i q^{31} -1.00000i q^{32} +(2.53310 - 0.164463i) q^{33} +6.07606i q^{34} -2.41421 q^{36} -4.60778 q^{37} +6.82952i q^{38} +1.39222i q^{39} -3.89937 q^{40} +3.58235 q^{41} +3.25819i q^{43} +(-0.214882 - 3.30966i) q^{44} +9.41392i q^{45} +4.37667i q^{46} +0.203854i q^{47} -0.765367i q^{48} +10.2051i q^{50} +4.65041i q^{51} +1.81903 q^{52} +4.98445 q^{53} -4.14386 q^{54} +(-12.9056 + 0.837904i) q^{55} +5.22709i q^{57} -9.36112 q^{58} +5.19752i q^{59} -2.98445 q^{60} +8.98372 q^{61} +7.88318 q^{62} -1.00000 q^{64} -7.09306i q^{65} +(-0.164463 - 2.53310i) q^{66} -8.03353 q^{67} +6.07606 q^{68} +3.34976i q^{69} +8.86195 q^{71} +2.41421i q^{72} +0.0557060 q^{73} +4.60778i q^{74} +7.81064i q^{75} +6.82952 q^{76} +1.39222 q^{78} +8.48528i q^{79} +3.89937i q^{80} +4.07107 q^{81} -3.58235i q^{82} -10.4676 q^{83} -23.6928i q^{85} +3.25819 q^{86} -7.16469 q^{87} +(-3.30966 + 0.214882i) q^{88} -1.68771i q^{89} +9.41392 q^{90} +4.37667 q^{92} +6.03353 q^{93} +0.203854 q^{94} -26.6308i q^{95} -0.765367 q^{96} +9.23880i q^{97} +(0.518771 + 7.99022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) \) 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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