LMFDB - Embedded newform 1078.2.c.c.1077.1

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			1077.1
Root			$2.98338 - 1.23576i$ of defining polynomial
Character	$\chi$	$=$	1078.1077
Dual form			1078.2.c.c.1077.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.84776i q^{3} -1.00000 q^{4} -3.23688i q^{5} -1.84776 q^{6} +1.00000i q^{8} -0.414214 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.84776i q^{3} -1.00000 q^{4} -3.23688i q^{5} -1.84776 q^{6} +1.00000i q^{8} -0.414214 q^{9} -3.23688 q^{10} +(3.28338 - 0.468406i) q^{11} +1.84776i q^{12} -6.10838 q^{13} -5.98098 q^{15} +1.00000 q^{16} -8.13155 q^{17} +0.414214i q^{18} +6.61537 q^{19} +3.23688i q^{20} +(-0.468406 - 3.28338i) q^{22} -5.30583 q^{23} +1.84776 q^{24} -5.47740 q^{25} +6.10838i q^{26} -4.77791i q^{27} -1.32485i q^{29} +5.98098i q^{30} -2.35476i q^{31} -1.00000i q^{32} +(-0.865501 - 6.06690i) q^{33} +8.13155i q^{34} +0.414214 q^{36} +5.28681 q^{37} -6.61537i q^{38} +11.2868i q^{39} +3.23688 q^{40} +1.22400 q^{41} +3.73834i q^{43} +(-3.28338 + 0.468406i) q^{44} +1.34076i q^{45} +5.30583i q^{46} -1.70615i q^{47} -1.84776i q^{48} +5.47740i q^{50} +15.0251i q^{51} +6.10838 q^{52} -3.98098 q^{53} -4.77791 q^{54} +(-1.51617 - 10.6279i) q^{55} -12.2236i q^{57} -1.32485 q^{58} +9.03853i q^{59} +5.98098 q^{60} +8.55638 q^{61} -2.35476 q^{62} -1.00000 q^{64} +19.7721i q^{65} +(-6.06690 + 0.865501i) q^{66} +2.35103 q^{67} +8.13155 q^{68} +9.80389i q^{69} -7.17945 q^{71} -0.414214i q^{72} +10.9927 q^{73} -5.28681i q^{74} +10.1209i q^{75} -6.61537 q^{76} +11.2868 q^{78} -8.48528i q^{79} -3.23688i q^{80} -10.0711 q^{81} -1.22400i q^{82} -5.60138 q^{83} +26.3209i q^{85} +3.73834 q^{86} -2.44801 q^{87} +(0.468406 + 3.28338i) q^{88} +4.66115i q^{89} +1.34076 q^{90} +5.30583 q^{92} -4.35103 q^{93} -1.70615 q^{94} -21.4132i q^{95} -1.84776 q^{96} -3.82683i q^{97} +(-1.36002 + 0.194020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.820913\pi$
$3$		−	1.84776i		−	1.06680i	0.845862	−	0.533402i	$-0.179087\pi$
$4$	−1.00000			−0.500000
$5$		−	3.23688i		−	1.44758i	−0.690022	−	0.723789i	$-0.742399\pi$
$5$		−	3.23688i		−	1.44758i	0.690022	−	0.723789i	$-0.257601\pi$
$6$	−1.84776			−0.754344
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−0.414214			−0.138071
$10$	−3.23688			−1.02359
$11$	3.28338	−	0.468406i	0.989977	−	0.141230i
$11$	3.28338	−	0.468406i	0.989977	−	0.141230i
$12$			1.84776i			0.533402i
$13$	−6.10838			−1.69416			−0.847079	−	0.531467i	$-0.821641\pi$
$13$	−6.10838			−1.69416			−0.847079	+	0.531467i	$0.821641\pi$
$14$		0			0
$15$	−5.98098			−1.54428
$16$	1.00000			0.250000
$17$	−8.13155			−1.97219			−0.986095	−	0.166182i	$-0.946856\pi$
$17$	−8.13155			−1.97219			−0.986095	+	0.166182i	$0.946856\pi$
$18$			0.414214i			0.0976311i
$19$	6.61537			1.51767			0.758835	−	0.651282i	$-0.225769\pi$
$19$	6.61537			1.51767			0.758835	+	0.651282i	$0.225769\pi$
$20$			3.23688i			0.723789i
$21$		0			0
$22$	−0.468406	−	3.28338i	−0.0998645	−	0.700019i
$23$	−5.30583			−1.10634			−0.553171	−	0.833068i	$-0.686582\pi$
$23$	−5.30583			−1.10634			−0.553171	+	0.833068i	$0.686582\pi$
$24$	1.84776			0.377172
$25$	−5.47740			−1.09548
$26$			6.10838i			1.19795i
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$		−	1.32485i		−	0.246019i	−0.992406	−	0.123009i	$-0.960745\pi$
$29$		−	1.32485i		−	0.246019i	0.992406	−	0.123009i	$-0.0392545\pi$
$30$			5.98098i			1.09197i
$31$		−	2.35476i		−	0.422927i	−0.977386	−	0.211464i	$-0.932177\pi$
$31$		−	2.35476i		−	0.422927i	0.977386	−	0.211464i	$-0.0678230\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.865501	−	6.06690i	−0.150664	−	1.05611i
$34$			8.13155i			1.39455i
$35$		0			0
$36$	0.414214			0.0690356
$37$	5.28681			0.869146			0.434573	−	0.900637i	$-0.356899\pi$
$37$	5.28681			0.869146			0.434573	+	0.900637i	$0.356899\pi$
$38$		−	6.61537i		−	1.07316i
$39$			11.2868i			1.80734i
$40$	3.23688			0.511796
$41$	1.22400			0.191157			0.0955786	−	0.995422i	$-0.469530\pi$
$41$	1.22400			0.191157			0.0955786	+	0.995422i	$0.469530\pi$
$42$		0			0
$43$			3.73834i			0.570091i	0.958514	+	0.285045i	$0.0920087\pi$
$43$			3.73834i			0.570091i	−0.958514	+	0.285045i	$0.907991\pi$
$44$	−3.28338	+	0.468406i	−0.494988	+	0.0706148i
$45$			1.34076i			0.199869i
$46$			5.30583i			0.782302i
$47$		−	1.70615i		−	0.248867i	−0.992228	−	0.124434i	$-0.960289\pi$
$47$		−	1.70615i		−	0.248867i	0.992228	−	0.124434i	$-0.0397114\pi$
$48$		−	1.84776i		−	0.266701i
$49$		0			0
$50$			5.47740i			0.774622i
$51$			15.0251i			2.10394i
$52$	6.10838			0.847079
$53$	−3.98098			−0.546829			−0.273415	−	0.961896i	$-0.588153\pi$
$53$	−3.98098			−0.546829			−0.273415	+	0.961896i	$0.588153\pi$
$54$	−4.77791			−0.650191
$55$	−1.51617	−	10.6279i	−0.204441	−	1.43307i
$56$		0			0
$57$		−	12.2236i		−	1.61906i
$58$	−1.32485			−0.173962
$59$			9.03853i			1.17672i	0.808601	+	0.588358i	$0.200225\pi$
$59$			9.03853i			1.17672i	−0.808601	+	0.588358i	$0.799775\pi$
$60$	5.98098			0.772141
$61$	8.55638			1.09553			0.547766	−	0.836631i	$-0.315478\pi$
$61$	8.55638			1.09553			0.547766	+	0.836631i	$0.315478\pi$
$62$	−2.35476			−0.299055
$63$		0			0
$64$	−1.00000			−0.125000
$65$			19.7721i			2.45243i
$66$	−6.06690	+	0.865501i	−0.746784	+	0.106536i
$67$	2.35103			0.287223			0.143612	−	0.989634i	$-0.454128\pi$
$67$	2.35103			0.287223			0.143612	+	0.989634i	$0.454128\pi$
$68$	8.13155			0.986095
$69$			9.80389i			1.18025i
$70$		0			0
$71$	−7.17945			−0.852044			−0.426022	−	0.904713i	$-0.640085\pi$
$71$	−7.17945			−0.852044			−0.426022	+	0.904713i	$0.640085\pi$
$72$		−	0.414214i		−	0.0488155i
$73$	10.9927			1.28660			0.643302	−	0.765613i	$-0.277564\pi$
$73$	10.9927			1.28660			0.643302	+	0.765613i	$0.277564\pi$
$74$		−	5.28681i		−	0.614579i
$75$			10.1209i			1.16866i
$76$	−6.61537			−0.758835
$77$		0			0
$78$	11.2868			1.27798
$79$		−	8.48528i		−	0.954669i	−0.878722	−	0.477334i	$-0.841603\pi$
$79$		−	8.48528i		−	0.954669i	0.878722	−	0.477334i	$-0.158397\pi$
$80$		−	3.23688i		−	0.361894i
$81$	−10.0711			−1.11901
$82$		−	1.22400i		−	0.135169i
$83$	−5.60138			−0.614831			−0.307415	−	0.951575i	$-0.599464\pi$
$83$	−5.60138			−0.614831			−0.307415	+	0.951575i	$0.599464\pi$
$84$		0			0
$85$			26.3209i			2.85490i
$86$	3.73834			0.403115
$87$	−2.44801			−0.262454
$88$	0.468406	+	3.28338i	0.0499322	+	0.350010i
$89$			4.66115i			0.494081i	0.969005	+	0.247041i	$0.0794581\pi$
$89$			4.66115i			0.494081i	−0.969005	+	0.247041i	$0.920542\pi$
$90$	1.34076			0.141329
$91$		0			0
$92$	5.30583			0.553171
$93$	−4.35103			−0.451180
$94$	−1.70615			−0.175976
$95$		−	21.4132i		−	2.19695i
$96$	−1.84776			−0.188586
$97$		−	3.82683i		−	0.388556i	−0.980946	−	0.194278i	$-0.937764\pi$
$97$		−	3.82683i		−	0.388556i	0.980946	−	0.194278i	$-0.0622364\pi$
$98$		0			0
$99$	−1.36002	+	0.194020i	−0.136687	+	0.0194997i
$100$	5.47740			0.547740
$101$	−3.66037			−0.364220			−0.182110	−	0.983278i	$-0.558293\pi$
$101$	−3.66037			−0.364220			−0.182110	+	0.983278i	$0.558293\pi$
$102$	15.0251			1.48771
$103$		−	14.5715i		−	1.43577i	−0.696160	−	0.717887i	$-0.745110\pi$
$103$		−	14.5715i		−	1.43577i	0.696160	−	0.717887i	$-0.254890\pi$
$104$		−	6.10838i		−	0.598975i
$105$		0			0
$106$			3.98098i			0.386667i
$107$		−	7.87362i		−	0.761172i	−0.924746	−	0.380586i	$-0.875722\pi$
$107$		−	7.87362i		−	0.761172i	0.924746	−	0.380586i	$-0.124278\pi$
$108$			4.77791i			0.459755i
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	−10.6279	+	1.51617i	−1.01333	+	0.144562i
$111$		−	9.76874i		−	0.927208i
$112$		0			0
$113$	13.5216			1.27200			0.636001	−	0.771688i	$-0.280587\pi$
$113$	13.5216			1.27200			0.636001	+	0.771688i	$0.280587\pi$
$114$	−12.2236			−1.14485
$115$			17.1743i			1.60152i
$116$			1.32485i			0.123009i
$117$	2.53017			0.233914
$118$	9.03853			0.832064
$119$		0			0
$120$		−	5.98098i		−	0.545986i
$121$	10.5612	−	3.07591i	0.960108	−	0.279628i
$122$		−	8.55638i		−	0.774658i
$123$		−	2.26166i		−	0.203927i
$124$			2.35476i			0.211464i
$125$			1.54529i			0.138215i
$126$		0			0
$127$		−	8.63710i		−	0.766419i	−0.923661	−	0.383209i	$-0.874819\pi$
$127$		−	8.63710i		−	0.766419i	0.923661	−	0.383209i	$-0.125181\pi$
$128$			1.00000i			0.0883883i
$129$	6.90755			0.608175
$130$	19.7721			1.73413
$131$	−6.20218			−0.541887			−0.270944	−	0.962595i	$-0.587336\pi$
$131$	−6.20218			−0.541887			−0.270944	+	0.962595i	$0.587336\pi$
$132$	0.865501	+	6.06690i	0.0753322	+	0.528056i
$133$		0			0
$134$		−	2.35103i		−	0.203098i
$135$	−15.4655			−1.33106
$136$		−	8.13155i		−	0.697275i
$137$	−9.02514			−0.771070			−0.385535	−	0.922693i	$-0.625983\pi$
$137$	−9.02514			−0.771070			−0.385535	+	0.922693i	$0.625983\pi$
$138$	9.80389			0.834563
$139$	−8.34638			−0.707930			−0.353965	−	0.935259i	$-0.615167\pi$
$139$	−8.34638			−0.707930			−0.353965	+	0.935259i	$0.615167\pi$
$140$		0			0
$141$	−3.15255			−0.265493
$142$			7.17945i			0.602486i
$143$	−20.0561	+	2.86120i	−1.67718	+	0.239265i
$144$	−0.414214			−0.0345178
$145$	−4.28839			−0.356131
$146$		−	10.9927i		−	0.909766i
$147$		0			0
$148$	−5.28681			−0.434573
$149$		−	21.2488i		−	1.74077i	−0.492375	−	0.870383i	$-0.663871\pi$
$149$		−	21.2488i		−	1.74077i	0.492375	−	0.870383i	$-0.336129\pi$
$150$	10.1209			0.826370
$151$			16.6751i			1.35700i	0.734598	+	0.678502i	$0.237371\pi$
$151$			16.6751i			1.35700i	−0.734598	+	0.678502i	$0.762629\pi$
$152$			6.61537i			0.536578i
$153$	3.36820			0.272303
$154$		0			0
$155$	−7.62207			−0.612220
$156$		−	11.2868i		−	0.903668i
$157$			12.5095i			0.998365i	0.866497	+	0.499183i	$0.166366\pi$
$157$			12.5095i			0.998365i	−0.866497	+	0.499183i	$0.833634\pi$
$158$	−8.48528			−0.675053
$159$			7.35589i			0.583360i
$160$	−3.23688			−0.255898
$161$		0			0
$162$			10.0711i			0.791258i
$163$	8.39592			0.657619			0.328810	−	0.944396i	$-0.393353\pi$
$163$	8.39592			0.657619			0.328810	+	0.944396i	$0.393353\pi$
$164$	−1.22400			−0.0955786
$165$	−19.6378	+	2.80152i	−1.52880	+	0.218098i
$166$			5.60138i			0.434751i
$167$	4.04635			0.313116			0.156558	−	0.987669i	$-0.449960\pi$
$167$	4.04635			0.313116			0.156558	+	0.987669i	$0.449960\pi$
$168$		0			0
$169$	24.3123			1.87017
$170$	26.3209			2.01872
$171$	−2.74018			−0.209547
$172$		−	3.73834i		−	0.285045i
$173$	3.07603			0.233866			0.116933	−	0.993140i	$-0.462694\pi$
$173$	3.07603			0.233866			0.116933	+	0.993140i	$0.462694\pi$
$174$			2.44801i			0.185583i
$175$		0			0
$176$	3.28338	−	0.468406i	0.247494	−	0.0353074i
$177$	16.7010			1.25533
$178$	4.66115			0.349368
$179$	−11.4655			−0.856974			−0.428487	−	0.903548i	$-0.640953\pi$
$179$	−11.4655			−0.856974			−0.428487	+	0.903548i	$0.640953\pi$
$180$		−	1.34076i		−	0.0999344i
$181$			13.2743i			0.986670i	0.869839	+	0.493335i	$0.164222\pi$
$181$			13.2743i			0.986670i	−0.869839	+	0.493335i	$0.835778\pi$
$182$		0			0
$183$		−	15.8101i		−	1.16872i
$184$		−	5.30583i		−	0.391151i
$185$		−	17.1128i		−	1.25816i
$186$			4.35103i			0.319033i
$187$	−26.6990	+	3.80886i	−1.95242	+	0.278532i
$188$			1.70615i			0.124434i
$189$		0			0
$190$	−21.4132			−1.55348
$191$	−12.2147			−0.883825			−0.441913	−	0.897058i	$-0.645700\pi$
$191$	−12.2147			−0.883825			−0.441913	+	0.897058i	$0.645700\pi$
$192$			1.84776i			0.133351i
$193$			5.06319i			0.364456i	0.983256	+	0.182228i	$0.0583309\pi$
$193$			5.06319i			0.364456i	−0.983256	+	0.182228i	$0.941669\pi$
$194$	−3.82683			−0.274751
$195$	36.5341			2.61626
$196$		0			0
$197$		−	20.0883i		−	1.43123i	−0.698493	−	0.715617i	$-0.746146\pi$
$197$		−	20.0883i		−	1.43123i	0.698493	−	0.715617i	$-0.253854\pi$
$198$	0.194020	+	1.36002i	0.0137884	+	0.0966525i
$199$		−	14.8196i		−	1.05053i	−0.850938	−	0.525266i	$-0.823966\pi$
$199$		−	14.8196i		−	1.05053i	0.850938	−	0.525266i	$-0.176034\pi$
$200$		−	5.47740i		−	0.387311i
$201$		−	4.34413i		−	0.306411i
$202$			3.66037i			0.257543i
$203$		0			0
$204$		−	15.0251i		−	1.05197i
$205$		−	3.96195i		−	0.276715i
$206$	−14.5715			−1.01525
$207$	2.19775			0.152754
$208$	−6.10838			−0.423540
$209$	21.7208	−	3.09868i	1.50246	−	0.214340i
$210$		0			0
$211$		−	9.19848i		−	0.633249i	−0.948551	−	0.316625i	$-0.897450\pi$
$211$		−	9.19848i		−	0.633249i	0.948551	−	0.316625i	$-0.102550\pi$
$212$	3.98098			0.273415
$213$			13.2659i			0.908964i
$214$	−7.87362			−0.538230
$215$	12.1006			0.825251
$216$	4.77791			0.325096
$217$		0			0
$218$	−6.00000			−0.406371
$219$		−	20.3119i		−	1.37255i
$220$	1.51617	+	10.6279i	0.102220	+	0.716534i
$221$	49.6706			3.34120
$222$	−9.76874			−0.655635
$223$			10.8760i			0.728310i	0.931338	+	0.364155i	$0.118642\pi$
$223$			10.8760i			0.728310i	−0.931338	+	0.364155i	$0.881358\pi$
$224$		0			0
$225$	2.26881			0.151254
$226$		−	13.5216i		−	0.899441i
$227$	23.4793			1.55837			0.779187	−	0.626791i	$-0.215632\pi$
$227$	23.4793			1.55837			0.779187	+	0.626791i	$0.215632\pi$
$228$			12.2236i			0.809529i
$229$		−	22.8301i		−	1.50866i	−0.656498	−	0.754328i	$-0.727963\pi$
$229$		−	22.8301i		−	1.50866i	0.656498	−	0.754328i	$-0.272037\pi$
$230$	17.1743			1.13244
$231$		0			0
$232$	1.32485			0.0869808
$233$		−	14.7089i		−	0.963612i	−0.876278	−	0.481806i	$-0.839981\pi$
$233$		−	14.7089i		−	0.963612i	0.876278	−	0.481806i	$-0.160019\pi$
$234$		−	2.53017i		−	0.165403i
$235$	−5.52260			−0.360255
$236$		−	9.03853i		−	0.588358i
$237$	−15.6788			−1.01844
$238$		0			0
$239$			22.4218i			1.45035i	0.688567	+	0.725173i	$0.258240\pi$
$239$			22.4218i			1.45035i	−0.688567	+	0.725173i	$0.741760\pi$
$240$	−5.98098			−0.386070
$241$	−15.4687			−0.996430			−0.498215	−	0.867054i	$-0.666011\pi$
$241$	−15.4687			−0.996430			−0.498215	+	0.867054i	$0.666011\pi$
$242$	−3.07591	−	10.5612i	−0.197727	−	0.678899i
$243$			4.27518i			0.274253i
$244$	−8.55638			−0.547766
$245$		0			0
$246$	−2.26166			−0.144198
$247$	−40.4092			−2.57118
$248$	2.35476			0.149527
$249$			10.3500i			0.655904i
$250$	1.54529			0.0977329
$251$		−	4.87408i		−	0.307649i	−0.988098	−	0.153825i	$-0.950841\pi$
$251$		−	4.87408i		−	0.307649i	0.988098	−	0.153825i	$-0.0491590\pi$
$252$		0			0
$253$	−17.4211	+	2.48528i	−1.09525	+	0.156248i
$254$	−8.63710			−0.541940
$255$	48.6346			3.04562
$256$	1.00000			0.0625000
$257$		−	19.7743i		−	1.23348i	−0.787165	−	0.616742i	$-0.788452\pi$
$257$		−	19.7743i		−	1.23348i	0.787165	−	0.616742i	$-0.211548\pi$
$258$		−	6.90755i		−	0.430045i
$259$		0			0
$260$		−	19.7721i		−	1.22621i
$261$			0.548772i			0.0339681i
$262$			6.20218i			0.383172i
$263$		−	8.48528i		−	0.523225i	−0.965173	−	0.261612i	$-0.915746\pi$
$263$		−	8.48528i		−	0.523225i	0.965173	−	0.261612i	$-0.0842542\pi$
$264$	6.06690	−	0.865501i	0.373392	−	0.0532679i
$265$			12.8860i			0.791578i
$266$		0			0
$267$	8.61269			0.527088
$268$	−2.35103			−0.143612
$269$		−	7.39943i		−	0.451151i	−0.974226	−	0.225575i	$-0.927574\pi$
$269$		−	7.39943i		−	0.451151i	0.974226	−	0.225575i	$-0.0724262\pi$
$270$			15.4655i			0.941202i
$271$	−14.3609			−0.872365			−0.436183	−	0.899858i	$-0.643670\pi$
$271$	−14.3609			−0.872365			−0.436183	+	0.899858i	$0.643670\pi$
$272$	−8.13155			−0.493048
$273$		0			0
$274$			9.02514i			0.545229i
$275$	−17.9844	+	2.56565i	−1.08450	+	0.154714i
$276$		−	9.80389i		−	0.590125i
$277$		−	2.18987i		−	0.131576i	−0.997834	−	0.0657882i	$-0.979044\pi$
$277$		−	2.18987i		−	0.131576i	0.997834	−	0.0657882i	$-0.0209562\pi$
$278$			8.34638i			0.500582i
$279$			0.975373i			0.0583940i
$280$		0			0
$281$			25.7003i			1.53315i	0.642154	+	0.766575i	$0.278041\pi$
$281$			25.7003i			1.53315i	−0.642154	+	0.766575i	$0.721959\pi$
$282$			3.15255i			0.187732i
$283$	−15.5577			−0.924811			−0.462406	−	0.886668i	$-0.653014\pi$
$283$	−15.5577			−0.924811			−0.462406	+	0.886668i	$0.653014\pi$
$284$	7.17945			0.426022
$285$	−39.5664			−2.34371
$286$	2.86120	+	20.0561i	0.169186	+	1.18594i
$287$		0			0
$288$			0.414214i			0.0244078i
$289$	49.1221			2.88953
$290$			4.28839i			0.251823i
$291$	−7.07107			−0.414513
$292$	−10.9927			−0.643302
$293$	3.11451			0.181952			0.0909759	−	0.995853i	$-0.471001\pi$
$293$	3.11451			0.181952			0.0909759	+	0.995853i	$0.471001\pi$
$294$		0			0
$295$	29.2566			1.70339
$296$			5.28681i			0.307289i
$297$	−2.23800	−	15.6877i	−0.129862	−	0.910293i
$298$	−21.2488			−1.23091
$299$	32.4100			1.87432
$300$		−	10.1209i		−	0.584332i
$301$		0			0
$302$	16.6751			0.959547
$303$			6.76348i			0.388552i
$304$	6.61537			0.379418
$305$		−	27.6960i		−	1.58587i
$306$		−	3.36820i		−	0.192547i
$307$	−8.93072			−0.509703			−0.254852	−	0.966980i	$-0.582027\pi$
$307$	−8.93072			−0.509703			−0.254852	+	0.966980i	$0.582027\pi$
$308$		0			0
$309$	−26.9246			−1.53169
$310$			7.62207i			0.432905i
$311$		−	19.1346i		−	1.08502i	−0.840048	−	0.542512i	$-0.817473\pi$
$311$		−	19.1346i		−	1.08502i	0.840048	−	0.542512i	$-0.182527\pi$
$312$	−11.2868			−0.638990
$313$		−	1.17856i		−	0.0666161i	−0.999445	−	0.0333080i	$-0.989396\pi$
$313$		−	1.17856i		−	0.0666161i	0.999445	−	0.0333080i	$-0.0106042\pi$
$314$	12.5095			0.705951
$315$		0			0
$316$			8.48528i			0.477334i
$317$	−9.09694			−0.510935			−0.255468	−	0.966818i	$-0.582229\pi$
$317$	−9.09694			−0.510935			−0.255468	+	0.966818i	$0.582229\pi$
$318$	7.35589			0.412498
$319$	−0.620568	−	4.34999i	−0.0347452	−	0.243553i
$320$			3.23688i			0.180947i
$321$	−14.5486			−0.812021
$322$		0			0
$323$	−53.7932			−2.99314
$324$	10.0711			0.559504
$325$	33.4580			1.85592
$326$		−	8.39592i		−	0.465007i
$327$	−11.0866			−0.613088
$328$			1.22400i			0.0675843i
$329$		0			0
$330$	2.80152	+	19.6378i	0.154219	+	1.08103i
$331$	2.72973			0.150039			0.0750197	−	0.997182i	$-0.476098\pi$
$331$	2.72973			0.150039			0.0750197	+	0.997182i	$0.476098\pi$
$332$	5.60138			0.307415
$333$	−2.18987			−0.120004
$334$		−	4.04635i		−	0.221406i
$335$		−	7.60999i		−	0.415778i
$336$		0			0
$337$		−	20.3209i		−	1.10695i	−0.832867	−	0.553474i	$-0.813302\pi$
$337$		−	20.3209i		−	1.10695i	0.832867	−	0.553474i	$-0.186698\pi$
$338$		−	24.3123i		−	1.32241i
$339$		−	24.9846i		−	1.35698i
$340$		−	26.3209i		−	1.42745i
$341$	−1.10298	−	7.73157i	−0.0597298	−	0.418688i
$342$			2.74018i			0.148172i
$343$		0			0
$344$	−3.73834			−0.201558
$345$	31.7340			1.70850
$346$		−	3.07603i		−	0.165368i
$347$		−	24.4383i		−	1.31192i	−0.754797	−	0.655959i	$-0.772264\pi$
$347$		−	24.4383i		−	1.31192i	0.754797	−	0.655959i	$-0.227736\pi$
$348$	2.44801			0.131227
$349$	3.07603			0.164656			0.0823280	−	0.996605i	$-0.473764\pi$
$349$	3.07603			0.164656			0.0823280	+	0.996605i	$0.473764\pi$
$350$		0			0
$351$			29.1853i			1.55779i
$352$	−0.468406	−	3.28338i	−0.0249661	−	0.175005i
$353$			33.7399i			1.79579i	0.440206	+	0.897897i	$0.354905\pi$
$353$			33.7399i			1.79579i	−0.440206	+	0.897897i	$0.645095\pi$
$354$		−	16.7010i		−	0.887649i
$355$			23.2390i			1.23340i
$356$		−	4.66115i		−	0.247041i
$357$		0			0
$358$			11.4655i			0.605972i
$359$		−	29.8985i		−	1.57798i	−0.614406	−	0.788990i	$-0.710604\pi$
$359$		−	29.8985i		−	1.57798i	0.614406	−	0.788990i	$-0.289396\pi$
$360$	−1.34076			−0.0706643
$361$	24.7632			1.30333
$362$	13.2743			0.697681
$363$	−5.68354	−	19.5145i	−0.298309	−	1.02425i
$364$		0			0
$365$		−	35.5822i		−	1.86246i
$366$	−15.8101			−0.826409
$367$			3.55525i			0.185583i	0.995686	+	0.0927914i	$0.0295790\pi$
$367$			3.55525i			0.185583i	−0.995686	+	0.0927914i	$0.970421\pi$
$368$	−5.30583			−0.276585
$369$	−0.506999			−0.0263933
$370$	−17.1128			−0.889650
$371$		0			0
$372$	4.35103			0.225590
$373$			21.0969i			1.09236i	0.837668	+	0.546179i	$0.183918\pi$
$373$			21.0969i			1.09236i	−0.837668	+	0.546179i	$0.816082\pi$
$374$	3.80886	+	26.6990i	0.196952	+	1.38057i
$375$	2.85533			0.147449
$376$	1.70615			0.0879879
$377$			8.09269i			0.416795i
$378$		0			0
$379$	8.61063			0.442298			0.221149	−	0.975240i	$-0.429019\pi$
$379$	8.61063			0.442298			0.221149	+	0.975240i	$0.429019\pi$
$380$			21.4132i			1.09847i
$381$	−15.9593			−0.817619
$382$			12.2147i			0.624959i
$383$			34.2290i			1.74902i	0.485007	+	0.874510i	$0.338817\pi$
$383$			34.2290i			1.74902i	−0.485007	+	0.874510i	$0.661183\pi$
$384$	1.84776			0.0942931
$385$		0			0
$386$	5.06319			0.257709
$387$		−	1.54847i		−	0.0787131i
$388$			3.82683i			0.194278i
$389$	22.8252			1.15728			0.578641	−	0.815582i	$-0.303583\pi$
$389$	22.8252			1.15728			0.578641	+	0.815582i	$0.303583\pi$
$390$		−	36.5341i		−	1.84997i
$391$	43.1446			2.18192
$392$		0			0
$393$			11.4601i			0.578088i
$394$	−20.0883			−1.01204
$395$	−27.4659			−1.38196
$396$	1.36002	−	0.194020i	0.0683436	−	0.00974987i
$397$			12.6414i			0.634451i	0.948350	+	0.317226i	$0.102751\pi$
$397$			12.6414i			0.634451i	−0.948350	+	0.317226i	$0.897249\pi$
$398$	−14.8196			−0.742839
$399$		0			0
$400$	−5.47740			−0.273870
$401$	−5.21750			−0.260549			−0.130275	−	0.991478i	$-0.541586\pi$
$401$	−5.21750			−0.260549			−0.130275	+	0.991478i	$0.541586\pi$
$402$	−4.34413			−0.216665
$403$			14.3837i			0.716505i
$404$	3.66037			0.182110
$405$			32.5989i			1.61985i
$406$		0			0
$407$	17.3586	−	2.47637i	0.860434	−	0.122749i
$408$	−15.0251			−0.743855
$409$	20.3483			1.00616			0.503079	−	0.864240i	$-0.332200\pi$
$409$	20.3483			1.00616			0.503079	+	0.864240i	$0.332200\pi$
$410$	−3.96195			−0.195667
$411$			16.6763i			0.822581i
$412$			14.5715i			0.717887i
$413$		0			0
$414$		−	2.19775i		−	0.108013i
$415$			18.1310i			0.890015i
$416$			6.10838i			0.299488i
$417$			15.4221i			0.755223i
$418$	−3.09868	−	21.7208i	−0.151561	−	1.06240i
$419$			20.3391i			0.993631i	0.867856	+	0.496816i	$0.165497\pi$
$419$			20.3391i			0.993631i	−0.867856	+	0.496816i	$0.834503\pi$
$420$		0			0
$421$	−15.3327			−0.747272			−0.373636	−	0.927575i	$-0.621889\pi$
$421$	−15.3327			−0.747272			−0.373636	+	0.927575i	$0.621889\pi$
$422$	−9.19848			−0.447775
$423$			0.706710i			0.0343614i
$424$		−	3.98098i		−	0.193333i
$425$	44.5398			2.16050
$426$	13.2659			0.642735
$427$		0			0
$428$			7.87362i			0.380586i
$429$	5.28681	+	37.0589i	0.255249	+	1.78922i
$430$		−	12.1006i		−	0.583540i
$431$			2.16904i			0.104479i	0.998635	+	0.0522394i	$0.0166359\pi$
$431$			2.16904i			0.104479i	−0.998635	+	0.0522394i	$0.983364\pi$
$432$		−	4.77791i		−	0.229877i
$433$		−	38.4356i		−	1.84710i	−0.383479	−	0.923550i	$-0.625274\pi$
$433$		−	38.4356i		−	1.84710i	0.383479	−	0.923550i	$-0.374726\pi$
$434$		0			0
$435$			7.92391i			0.379922i
$436$			6.00000i			0.287348i
$437$	−35.1000			−1.67906
$438$	−20.3119			−0.970542
$439$	5.72240			0.273115			0.136558	−	0.990632i	$-0.456396\pi$
$439$	5.72240			0.273115			0.136558	+	0.990632i	$0.456396\pi$
$440$	10.6279	−	1.51617i	0.506666	−	0.0722808i
$441$		0			0
$442$		−	49.6706i		−	2.36259i
$443$	7.18733			0.341480			0.170740	−	0.985316i	$-0.445384\pi$
$443$	7.18733			0.341480			0.170740	+	0.985316i	$0.445384\pi$
$444$			9.76874i			0.463604i
$445$	15.0876			0.715221
$446$	10.8760			0.514993
$447$	−39.2626			−1.85706
$448$		0			0
$449$	8.63068			0.407307			0.203654	−	0.979043i	$-0.434718\pi$
$449$	8.63068			0.407307			0.203654	+	0.979043i	$0.434718\pi$
$450$		−	2.26881i		−	0.106953i
$451$	4.01887	−	0.573330i	0.189241	−	0.0269971i
$452$	−13.5216			−0.636001
$453$	30.8117			1.44766
$454$		−	23.4793i		−	1.10194i
$455$		0			0
$456$	12.2236			0.572423
$457$			28.5018i			1.33326i	0.745389	+	0.666629i	$0.232264\pi$
$457$			28.5018i			1.33326i	−0.745389	+	0.666629i	$0.767736\pi$
$458$	−22.8301			−1.06678
$459$			38.8518i			1.81345i
$460$		−	17.1743i		−	0.800758i
$461$	35.6022			1.65816			0.829080	−	0.559129i	$-0.188865\pi$
$461$	35.6022			1.65816			0.829080	+	0.559129i	$0.188865\pi$
$462$		0			0
$463$	32.2369			1.49818			0.749088	−	0.662471i	$-0.230492\pi$
$463$	32.2369			1.49818			0.749088	+	0.662471i	$0.230492\pi$
$464$		−	1.32485i		−	0.0615047i
$465$			14.0838i			0.653118i
$466$	−14.7089			−0.681377
$467$			25.8620i			1.19675i	0.801215	+	0.598376i	$0.204187\pi$
$467$			25.8620i			1.19675i	−0.801215	+	0.598376i	$0.795813\pi$
$468$	−2.53017			−0.116957
$469$		0			0
$470$			5.52260i			0.254738i
$471$	23.1145			1.06506
$472$	−9.03853			−0.416032
$473$	1.75106	+	12.2744i	0.0805138	+	0.564377i
$474$			15.6788i			0.720149i
$475$	−36.2351			−1.66258
$476$		0			0
$477$	1.64897			0.0755014
$478$	22.4218			1.02555
$479$	12.5206			0.572079			0.286040	−	0.958218i	$-0.407661\pi$
$479$	12.5206			0.572079			0.286040	+	0.958218i	$0.407661\pi$
$480$			5.98098i			0.272993i
$481$	−32.2938			−1.47247
$482$			15.4687i			0.704582i
$483$		0			0
$484$	−10.5612	+	3.07591i	−0.480054	+	0.139814i
$485$	−12.3870			−0.562465
$486$	4.27518			0.193926
$487$	20.7085			0.938390			0.469195	−	0.883094i	$-0.344544\pi$
$487$	20.7085			0.938390			0.469195	+	0.883094i	$0.344544\pi$
$488$			8.55638i			0.387329i
$489$		−	15.5136i		−	0.701551i
$490$		0			0
$491$		−	23.6712i		−	1.06826i	−0.845401	−	0.534132i	$-0.820638\pi$
$491$		−	23.6712i		−	1.06826i	0.845401	−	0.534132i	$-0.179362\pi$
$492$			2.26166i			0.101964i
$493$			10.7731i			0.485196i
$494$			40.4092i			1.81810i
$495$	0.628020	+	4.40223i	0.0282274	+	0.197865i
$496$		−	2.35476i		−	0.105732i
$497$		0			0
$498$	10.3500			0.463794
$499$	11.6124			0.519842			0.259921	−	0.965630i	$-0.416304\pi$
$499$	11.6124			0.519842			0.259921	+	0.965630i	$0.416304\pi$
$500$		−	1.54529i		−	0.0691076i
$501$		−	7.47667i		−	0.334033i
$502$	−4.87408			−0.217541
$503$	−11.7871			−0.525561			−0.262780	−	0.964856i	$-0.584639\pi$
$503$	−11.7871			−0.525561			−0.262780	+	0.964856i	$0.584639\pi$
$504$		0			0
$505$			11.8482i			0.527237i
$506$	2.48528	+	17.4211i	0.110484	+	0.774461i
$507$		−	44.9232i		−	1.99511i
$508$			8.63710i			0.383209i
$509$		−	0.905073i		−	0.0401167i	−0.999799	−	0.0200583i	$-0.993615\pi$
$509$		−	0.905073i		−	0.0401167i	0.999799	−	0.0200583i	$-0.00638519\pi$
$510$		−	48.6346i		−	2.15358i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	31.6077i		−	1.39551i
$514$	−19.7743			−0.872205
$515$	−47.1662			−2.07839
$516$	−6.90755			−0.304088
$517$	−0.799170	−	5.60193i	−0.0351474	−	0.246373i
$518$		0			0
$519$		−	5.68376i		−	0.249489i
$520$	−19.7721			−0.867063
$521$		−	8.06821i		−	0.353475i	−0.984258	−	0.176737i	$-0.943446\pi$
$521$		−	8.06821i		−	0.353475i	0.984258	−	0.176737i	$-0.0565543\pi$
$522$	0.548772			0.0240191
$523$	−17.8346			−0.779852			−0.389926	−	0.920846i	$-0.627499\pi$
$523$	−17.8346			−0.779852			−0.389926	+	0.920846i	$0.627499\pi$
$524$	6.20218			0.270944
$525$		0			0
$526$	−8.48528			−0.369976
$527$			19.1478i			0.834093i
$528$	−0.865501	−	6.06690i	−0.0376661	−	0.264028i
$529$	5.15182			0.223992
$530$	12.8860			0.559730
$531$		−	3.74388i		−	0.162471i
$532$		0			0
$533$	−7.47667			−0.323851
$534$		−	8.61269i		−	0.372707i
$535$	−25.4860			−1.10186
$536$			2.35103i			0.101549i
$537$			21.1855i			0.914223i
$538$	−7.39943			−0.319012
$539$		0			0
$540$	15.4655			0.665530
$541$			1.47667i			0.0634871i	0.999496	+	0.0317436i	$0.0101060\pi$
$541$			1.47667i			0.0634871i	−0.999496	+	0.0317436i	$0.989894\pi$
$542$			14.3609i			0.616855i
$543$	24.5277			1.05258
$544$			8.13155i			0.348637i
$545$	−19.4213			−0.831917
$546$		0			0
$547$		−	16.3374i		−	0.698536i	−0.937023	−	0.349268i	$-0.886430\pi$
$547$		−	16.3374i		−	0.698536i	0.937023	−	0.349268i	$-0.113570\pi$
$548$	9.02514			0.385535
$549$	−3.54417			−0.151261
$550$	2.56565	+	17.9844i	0.109400	+	0.766857i
$551$		−	8.76439i		−	0.373376i
$552$	−9.80389			−0.417281
$553$		0			0
$554$	−2.18987			−0.0930385
$555$	−31.6203			−1.34221
$556$	8.34638			0.353965
$557$			17.3497i			0.735130i	0.929998	+	0.367565i	$0.119808\pi$
$557$			17.3497i			0.735130i	−0.929998	+	0.367565i	$0.880192\pi$
$558$	0.975373			0.0412908
$559$		−	22.8352i		−	0.965824i
$560$		0			0
$561$	7.03786	+	49.3333i	0.297139	+	2.08285i
$562$	25.7003			1.08410
$563$	−8.93072			−0.376385			−0.188192	−	0.982132i	$-0.560263\pi$
$563$	−8.93072			−0.376385			−0.188192	+	0.982132i	$0.560263\pi$
$564$	3.15255			0.132746
$565$		−	43.7677i		−	1.84132i
$566$			15.5577i			0.653940i
$567$		0			0
$568$		−	7.17945i		−	0.301243i
$569$			9.65831i			0.404898i	0.979293	+	0.202449i	$0.0648900\pi$
$569$			9.65831i			0.404898i	−0.979293	+	0.202449i	$0.935110\pi$
$570$			39.5664i			1.65725i
$571$			11.9282i			0.499180i	0.968352	+	0.249590i	$0.0802958\pi$
$571$			11.9282i			0.499180i	−0.968352	+	0.249590i	$0.919704\pi$
$572$	20.0561	−	2.86120i	0.838589	−	0.119633i
$573$			22.5698i			0.942868i
$574$		0			0
$575$	29.0622			1.21198
$576$	0.414214			0.0172589
$577$			37.5475i			1.56312i	0.623828	+	0.781561i	$0.285576\pi$
$577$			37.5475i			1.56312i	−0.623828	+	0.781561i	$0.714424\pi$
$578$		−	49.1221i		−	2.04321i
$579$	9.35555			0.388803
$580$	4.28839			0.178066
$581$		0			0
$582$			7.07107i			0.293105i
$583$	−13.0711	+	1.86471i	−0.541348	+	0.0772285i
$584$			10.9927i			0.454883i
$585$		−	8.18987i		−	0.338609i
$586$		−	3.11451i		−	0.128659i
$587$			29.1914i			1.20486i	0.798173	+	0.602429i	$0.205800\pi$
$587$			29.1914i			1.20486i	−0.798173	+	0.602429i	$0.794200\pi$
$588$		0			0
$589$		−	15.5776i		−	0.641864i
$590$		−	29.2566i		−	1.20448i
$591$	−37.1184			−1.52685
$592$	5.28681			0.217286
$593$	28.6899			1.17815			0.589076	−	0.808078i	$-0.299492\pi$
$593$	28.6899			1.17815			0.589076	+	0.808078i	$0.299492\pi$
$594$	−15.6877	+	2.23800i	−0.643674	+	0.0918263i
$595$		0			0
$596$			21.2488i			0.870383i
$597$	−27.3830			−1.12071
$598$		−	32.4100i		−	1.32534i
$599$	−10.6561			−0.435397			−0.217699	−	0.976016i	$-0.569855\pi$
$599$	−10.6561			−0.435397			−0.217699	+	0.976016i	$0.569855\pi$
$600$	−10.1209			−0.413185
$601$	−43.5354			−1.77585			−0.887923	−	0.459992i	$-0.847852\pi$
$601$	−43.5354			−1.77585			−0.887923	+	0.459992i	$0.847852\pi$
$602$		0			0
$603$	−0.973827			−0.0396573
$604$		−	16.6751i		−	0.678502i
$605$	−9.95636	−	34.1853i	−0.404784	−	1.38983i
$606$	6.76348			0.274748
$607$	27.3497			1.11009			0.555044	−	0.831821i	$-0.312701\pi$
$607$	27.3497			1.11009			0.555044	+	0.831821i	$0.312701\pi$
$608$		−	6.61537i		−	0.268289i
$609$		0			0
$610$	−27.6960			−1.12138
$611$			10.4218i			0.421621i
$612$	−3.36820			−0.136151
$613$			27.8604i			1.12527i	0.826705	+	0.562636i	$0.190213\pi$
$613$			27.8604i			1.12527i	−0.826705	+	0.562636i	$0.809787\pi$
$614$			8.93072i			0.360414i
$615$	−7.32074			−0.295201
$616$		0			0
$617$	32.0263			1.28933			0.644665	−	0.764465i	$-0.276997\pi$
$617$	32.0263			1.28933			0.644665	+	0.764465i	$0.276997\pi$
$618$			26.9246i			1.08307i
$619$		−	20.0009i		−	0.803906i	−0.915660	−	0.401953i	$-0.868332\pi$
$619$		−	20.0009i		−	0.803906i	0.915660	−	0.401953i	$-0.131668\pi$
$620$	7.62207			0.306110
$621$			25.3508i			1.01729i
$622$	−19.1346			−0.767227
$623$		0			0
$624$			11.2868i			0.451834i
$625$	−22.3851			−0.895403
$626$	−1.17856			−0.0471047
$627$	−5.72561	−	40.1348i	−0.228659	−	1.60283i
$628$		−	12.5095i		−	0.499183i
$629$	−42.9899			−1.71412
$630$		0			0
$631$	25.3751			1.01017			0.505084	−	0.863070i	$-0.331461\pi$
$631$	25.3751			1.01017			0.505084	+	0.863070i	$0.331461\pi$
$632$	8.48528			0.337526
$633$	−16.9966			−0.675553
$634$			9.09694i			0.361286i
$635$	−27.9573			−1.10945
$636$		−	7.35589i		−	0.291680i
$637$		0			0
$638$	−4.34999	+	0.620568i	−0.172218	+	0.0245685i
$639$	2.97383			0.117643
$640$	3.23688			0.127949
$641$	29.3371			1.15875			0.579373	−	0.815063i	$-0.303298\pi$
$641$	29.3371			1.15875			0.579373	+	0.815063i	$0.303298\pi$
$642$			14.5486i			0.574186i
$643$		−	7.53612i		−	0.297196i	−0.988898	−	0.148598i	$-0.952524\pi$
$643$		−	7.53612i		−	0.297196i	0.988898	−	0.148598i	$-0.0474760\pi$
$644$		0			0
$645$		−	22.3589i		−	0.880381i
$646$			53.7932i			2.11647i
$647$		−	29.0558i		−	1.14230i	−0.820845	−	0.571151i	$-0.806497\pi$
$647$		−	29.0558i		−	1.14230i	0.820845	−	0.571151i	$-0.193503\pi$
$648$		−	10.0711i		−	0.395629i
$649$	4.23370	+	29.6769i	0.166187	+	1.16492i
$650$		−	33.4580i		−	1.31233i
$651$		0			0
$652$	−8.39592			−0.328810
$653$	29.5840			1.15771			0.578856	−	0.815430i	$-0.303499\pi$
$653$	29.5840			1.15771			0.578856	+	0.815430i	$0.303499\pi$
$654$			11.0866i			0.433519i
$655$			20.0757i			0.784424i
$656$	1.22400			0.0477893
$657$	−4.55335			−0.177643
$658$		0			0
$659$			5.39725i			0.210247i	0.994459	+	0.105124i	$0.0335238\pi$
$659$			5.39725i			0.210247i	−0.994459	+	0.105124i	$0.966476\pi$
$660$	19.6378	−	2.80152i	0.764402	−	0.109049i
$661$			29.4503i			1.14548i	0.819736	+	0.572742i	$0.194120\pi$
$661$			29.4503i			1.14548i	−0.819736	+	0.572742i	$0.805880\pi$
$662$		−	2.72973i		−	0.106094i
$663$		−	91.7792i		−	3.56441i
$664$		−	5.60138i		−	0.217376i
$665$		0			0
$666$			2.18987i			0.0848556i
$667$			7.02944i			0.272181i
$668$	−4.04635			−0.156558
$669$	20.0962			0.776964
$670$	−7.60999			−0.294000
$671$	28.0939	−	4.00786i	1.08455	−	0.154722i
$672$		0			0
$673$			5.21501i			0.201024i	0.994936	+	0.100512i	$0.0320481\pi$
$673$			5.21501i			0.201024i	−0.994936	+	0.100512i	$0.967952\pi$
$674$	−20.3209			−0.782730
$675$			26.1705i			1.00730i
$676$	−24.3123			−0.935087
$677$	9.73471			0.374135			0.187068	−	0.982347i	$-0.440102\pi$
$677$	9.73471			0.374135			0.187068	+	0.982347i	$0.440102\pi$
$678$	−24.9846			−0.959528
$679$		0			0
$680$	−26.3209			−1.00936
$681$		−	43.3840i		−	1.66248i
$682$	−7.73157	+	1.10298i	−0.296057	+	0.0422354i
$683$	−17.5015			−0.669677			−0.334838	−	0.942276i	$-0.608682\pi$
$683$	−17.5015			−0.669677			−0.334838	+	0.942276i	$0.608682\pi$
$684$	2.74018			0.104773
$685$			29.2133i			1.11618i
$686$		0			0
$687$	−42.1845			−1.60944
$688$			3.73834i			0.142523i
$689$	24.3173			0.926415
$690$		−	31.7340i		−	1.20809i
$691$			46.2750i			1.76038i	0.474617	+	0.880192i	$0.342587\pi$
$691$			46.2750i			1.76038i	−0.474617	+	0.880192i	$0.657413\pi$
$692$	−3.07603			−0.116933
$693$		0			0
$694$	−24.4383			−0.927666
$695$			27.0162i			1.02478i
$696$		−	2.44801i		−	0.0927915i
$697$	−9.95304			−0.376998
$698$		−	3.07603i		−	0.116429i
$699$	−27.1785			−1.02799
$700$		0			0
$701$			28.7883i			1.08732i	0.839306	+	0.543660i	$0.182962\pi$
$701$			28.7883i			1.08732i	−0.839306	+	0.543660i	$0.817038\pi$
$702$	29.1853			1.10153
$703$	34.9742			1.31908
$704$	−3.28338	+	0.468406i	−0.123747	+	0.0176537i
$705$			10.2044i			0.384321i
$706$	33.7399			1.26982
$707$		0			0
$708$	−16.7010			−0.627663
$709$	2.50285			0.0939964			0.0469982	−	0.998895i	$-0.485035\pi$
$709$	2.50285			0.0939964			0.0469982	+	0.998895i	$0.485035\pi$
$710$	23.2390			0.872146
$711$			3.51472i			0.131812i
$712$	−4.66115			−0.174684
$713$			12.4939i			0.467902i
$714$		0			0
$715$	9.26136	+	64.9193i	0.346355	+	2.42784i
$716$	11.4655			0.428487
$717$	41.4301			1.54723
$718$	−29.8985			−1.11580
$719$			2.13580i			0.0796520i	0.999207	+	0.0398260i	$0.0126804\pi$
$719$			2.13580i			0.0796520i	−0.999207	+	0.0398260i	$0.987320\pi$
$720$			1.34076i			0.0499672i
$721$		0			0
$722$		−	24.7632i		−	0.921590i
$723$			28.5825i			1.06300i
$724$		−	13.2743i		−	0.493335i
$725$			7.25675i			0.269509i
$726$	−19.5145	+	5.68354i	−0.724252	+	0.210936i
$727$		−	35.5296i		−	1.31772i	−0.752266	−	0.658859i	$-0.771039\pi$
$727$		−	35.5296i		−	1.31772i	0.752266	−	0.658859i	$-0.228961\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	−35.5822			−1.31696
$731$		−	30.3985i		−	1.12433i
$732$			15.8101i			0.584359i
$733$	−2.34256			−0.0865244			−0.0432622	−	0.999064i	$-0.513775\pi$
$733$	−2.34256			−0.0865244			−0.0432622	+	0.999064i	$0.513775\pi$
$734$	3.55525			0.131227
$735$		0			0
$736$			5.30583i			0.195575i
$737$	7.71931	−	1.10123i	0.284345	−	0.0405645i
$738$			0.506999i			0.0186629i
$739$		−	13.7129i		−	0.504437i	−0.967670	−	0.252218i	$-0.918840\pi$
$739$		−	13.7129i		−	0.504437i	0.967670	−	0.252218i	$-0.0811602\pi$
$740$			17.1128i			0.629078i
$741$			74.6664i			2.74294i
$742$		0			0
$743$		−	44.2193i		−	1.62225i	−0.584873	−	0.811125i	$-0.698856\pi$
$743$		−	44.2193i		−	1.62225i	0.584873	−	0.811125i	$-0.301144\pi$
$744$		−	4.35103i		−	0.159516i
$745$	−68.7797			−2.51989
$746$	21.0969			0.772414
$747$	2.32017			0.0848904
$748$	26.6990	−	3.80886i	0.976211	−	0.139266i
$749$		0			0
$750$		−	2.85533i		−	0.104262i
$751$	9.66328			0.352618			0.176309	−	0.984335i	$-0.443584\pi$
$751$	9.66328			0.352618			0.176309	+	0.984335i	$0.443584\pi$
$752$		−	1.70615i		−	0.0622168i
$753$	−9.00612			−0.328201
$754$	8.09269			0.294718
$755$	53.9755			1.96437
$756$		0			0
$757$	−29.0384			−1.05542			−0.527710	−	0.849425i	$-0.676949\pi$
$757$	−29.0384			−1.05542			−0.527710	+	0.849425i	$0.676949\pi$
$758$		−	8.61063i		−	0.312752i
$759$	4.59220	+	32.1899i	0.166686	+	1.16842i
$760$	21.4132			0.776738
$761$	−21.3623			−0.774383			−0.387191	−	0.921999i	$-0.626555\pi$
$761$	−21.3623			−0.774383			−0.387191	+	0.921999i	$0.626555\pi$
$762$			15.9593i			0.578144i
$763$		0			0
$764$	12.2147			0.441913
$765$		−	10.9025i		−	0.394179i
$766$	34.2290			1.23674
$767$		−	55.2107i		−	1.99354i
$768$		−	1.84776i		−	0.0666753i
$769$	15.7726			0.568773			0.284387	−	0.958710i	$-0.408210\pi$
$769$	15.7726			0.568773			0.284387	+	0.958710i	$0.408210\pi$
$770$		0			0
$771$	−36.5381			−1.31589
$772$		−	5.06319i		−	0.182228i
$773$			6.71948i			0.241683i	0.992672	+	0.120841i	$0.0385592\pi$
$773$			6.71948i			0.241683i	−0.992672	+	0.120841i	$0.961441\pi$
$774$	−1.54847			−0.0556586
$775$			12.8980i			0.463308i
$776$	3.82683			0.137375
$777$		0			0
$778$		−	22.8252i		−	0.818322i
$779$	8.09724			0.290114
$780$	−36.5341			−1.30813
$781$	−23.5729	+	3.36290i	−0.843504	+	0.120334i
$782$		−	43.1446i		−	1.54285i
$783$	−6.33002			−0.226217
$784$		0			0
$785$	40.4917			1.44521
$786$	11.4601			0.408770
$787$	47.0796			1.67821			0.839103	−	0.543973i	$-0.183081\pi$
$787$	47.0796			1.67821			0.839103	+	0.543973i	$0.183081\pi$
$788$			20.0883i			0.715617i
$789$	−15.6788			−0.558178
$790$			27.4659i			0.977191i
$791$		0			0
$792$	−0.194020	−	1.36002i	−0.00689420	−	0.0483263i
$793$	−52.2656			−1.85601
$794$	12.6414			0.448625
$795$	23.8101			0.844458
$796$			14.8196i			0.525266i
$797$			0.354303i			0.0125501i	0.999980	+	0.00627504i	$0.00199742\pi$
$797$			0.354303i			0.0125501i	−0.999980	+	0.00627504i	$0.998003\pi$
$798$		0			0
$799$			13.8736i			0.490814i
$800$			5.47740i			0.193655i
$801$		−	1.93071i		−	0.0682184i
$802$			5.21750i			0.184236i
$803$	36.0934	−	5.14907i	1.27371	−	0.181707i
$804$			4.34413i			0.153206i
$805$		0			0
$806$	14.3837			0.506646
$807$	−13.6724			−0.481290
$808$		−	3.66037i		−	0.128771i
$809$		−	45.4724i		−	1.59872i	−0.600850	−	0.799362i	$-0.705171\pi$
$809$		−	45.4724i		−	1.59872i	0.600850	−	0.799362i	$-0.294829\pi$
$810$	32.5989			1.14541
$811$	18.9483			0.665366			0.332683	−	0.943039i	$-0.392046\pi$
$811$	18.9483			0.665366			0.332683	+	0.943039i	$0.392046\pi$
$812$		0			0
$813$			26.5356i			0.930643i
$814$	−2.47637	−	17.3586i	−0.0867968	−	0.608419i
$815$		−	27.1766i		−	0.951955i
$816$			15.0251i			0.525985i
$817$			24.7305i			0.865210i
$818$		−	20.3483i		−	0.711462i
$819$		0			0
$820$			3.96195i			0.138357i
$821$			26.0757i			0.910049i	0.890479	+	0.455025i	$0.150370\pi$
$821$			26.0757i			0.910049i	−0.890479	+	0.455025i	$0.849630\pi$
$822$	16.6763			0.581652
$823$	−41.5696			−1.44903			−0.724513	−	0.689261i	$-0.757935\pi$
$823$	−41.5696			−1.44903			−0.724513	+	0.689261i	$0.757935\pi$
$824$	14.5715			0.507623
$825$	4.74070	+	33.2308i	0.165050	+	1.15695i
$826$		0			0
$827$		−	51.2279i		−	1.78137i	−0.454621	−	0.890685i	$-0.650225\pi$
$827$		−	51.2279i		−	1.78137i	0.454621	−	0.890685i	$-0.349775\pi$
$828$	−2.19775			−0.0763770
$829$			4.30662i			0.149575i	0.997199	+	0.0747875i	$0.0238279\pi$
$829$			4.30662i			0.149575i	−0.997199	+	0.0747875i	$0.976172\pi$
$830$	18.1310			0.629336
$831$	−4.04635			−0.140366
$832$	6.10838			0.211770
$833$		0			0
$834$	15.4221			0.534023
$835$		−	13.0975i		−	0.453259i
$836$	−21.7208	+	3.09868i	−0.751230	+	0.107170i
$837$	−11.2508			−0.388885
$838$	20.3391			0.702603
$839$		−	32.0881i		−	1.10781i	−0.832581	−	0.553903i	$-0.813138\pi$
$839$		−	32.0881i		−	1.10781i	0.832581	−	0.553903i	$-0.186862\pi$
$840$		0			0
$841$	27.2448			0.939475
$842$			15.3327i			0.528401i
$843$	47.4879			1.63557
$844$			9.19848i			0.316625i
$845$		−	78.6959i		−	2.70722i
$846$	0.706710			0.0242972
$847$		0			0
$848$	−3.98098			−0.136707
$849$			28.7469i			0.986593i
$850$		−	44.5398i		−	1.52770i
$851$	−28.0509			−0.961572
$852$		−	13.2659i		−	0.454482i
$853$	46.8146			1.60290			0.801451	−	0.598060i	$-0.204062\pi$
$853$	46.8146			1.60290			0.801451	+	0.598060i	$0.204062\pi$
$854$		0			0
$855$			8.86963i			0.303335i
$856$	7.87362			0.269115
$857$	42.5146			1.45227			0.726135	−	0.687552i	$-0.241315\pi$
$857$	42.5146			1.45227			0.726135	+	0.687552i	$0.241315\pi$
$858$	37.0589	−	5.28681i	1.26517	−	0.180489i
$859$		−	23.4563i		−	0.800320i	−0.916445	−	0.400160i	$-0.868955\pi$
$859$		−	23.4563i		−	0.800320i	0.916445	−	0.400160i	$-0.131045\pi$
$860$	−12.1006			−0.412625
$861$		0			0
$862$	2.16904			0.0738777
$863$	13.6411			0.464348			0.232174	−	0.972674i	$-0.425416\pi$
$863$	13.6411			0.464348			0.232174	+	0.972674i	$0.425416\pi$
$864$	−4.77791			−0.162548
$865$		−	9.95673i		−	0.338539i
$866$	−38.4356			−1.30610
$867$		−	90.7658i		−	3.08257i
$868$		0			0
$869$	−3.97456	−	27.8604i	−0.134828	−	0.945100i
$870$	7.92391			0.268646
$871$	−14.3609			−0.486602
$872$	6.00000			0.203186
$873$			1.58513i			0.0536484i
$874$			35.1000i			1.18728i
$875$		0			0
$876$			20.3119i			0.686277i
$877$		−	15.1178i		−	0.510491i	−0.966876	−	0.255245i	$-0.917844\pi$
$877$		−	15.1178i		−	0.510491i	0.966876	−	0.255245i	$-0.0821563\pi$
$878$		−	5.72240i		−	0.193122i
$879$		−	5.75487i		−	0.194107i
$880$	−1.51617	−	10.6279i	−0.0511102	−	0.358267i
$881$		−	4.23924i		−	0.142824i	−0.997447	−	0.0714118i	$-0.977250\pi$
$881$		−	4.23924i		−	0.142824i	0.997447	−	0.0714118i	$-0.0227504\pi$
$882$		0			0
$883$	12.9457			0.435658			0.217829	−	0.975987i	$-0.430102\pi$
$883$	12.9457			0.435658			0.217829	+	0.975987i	$0.430102\pi$
$884$	−49.6706			−1.67060
$885$		−	54.0592i		−	1.81718i
$886$		−	7.18733i		−	0.241463i
$887$	22.6413			0.760219			0.380109	−	0.924942i	$-0.375886\pi$
$887$	22.6413			0.760219			0.380109	+	0.924942i	$0.375886\pi$
$888$	9.76874			0.327818
$889$		0			0
$890$		−	15.0876i		−	0.505738i
$891$	−33.0672	+	4.71735i	−1.10779	+	0.158037i
$892$		−	10.8760i		−	0.364155i
$893$		−	11.2868i		−	0.377699i
$894$			39.2626i			1.31314i
$895$			37.1126i			1.24054i
$896$		0			0
$897$		−	59.8859i		−	1.99953i
$898$		−	8.63068i		−	0.288010i
$899$	−3.11971			−0.104048
$900$	−2.26881			−0.0756271
$901$	32.3715			1.07845
$902$	−0.573330	−	4.01887i	−0.0190898	−	0.133814i
$903$		0			0
$904$			13.5216i			0.449721i
$905$	42.9673			1.42828
$906$		−	30.8117i		−	1.02365i
$907$	48.9120			1.62410			0.812049	−	0.583590i	$-0.198352\pi$
$907$	48.9120			1.62410			0.812049	+	0.583590i	$0.198352\pi$
$908$	−23.4793			−0.779187
$909$	1.51617			0.0502883
$910$		0			0
$911$	−52.4028			−1.73618			−0.868091	−	0.496406i	$-0.834653\pi$
$911$	−52.4028			−1.73618			−0.868091	+	0.496406i	$0.834653\pi$
$912$		−	12.2236i		−	0.404764i
$913$	−18.3915	+	2.62372i	−0.608668	+	0.0868324i
$914$	28.5018			0.942756
$915$	−51.1755			−1.69181
$916$			22.8301i			0.754328i
$917$		0			0
$918$	38.8518			1.28230
$919$		−	15.5442i		−	0.512755i	−0.966577	−	0.256378i	$-0.917471\pi$
$919$		−	15.5442i		−	0.512755i	0.966577	−	0.256378i	$-0.0825290\pi$
$920$	−17.1743			−0.566221
$921$			16.5018i			0.543753i
$922$		−	35.6022i		−	1.17250i
$923$	43.8548			1.44350
$924$		0			0
$925$	−28.9580			−0.952132
$926$		−	32.2369i		−	1.05937i
$927$			6.03572i			0.198239i
$928$	−1.32485			−0.0434904
$929$		−	27.2257i		−	0.893248i	−0.894722	−	0.446624i	$-0.852626\pi$
$929$		−	27.2257i		−	0.893248i	0.894722	−	0.446624i	$-0.147374\pi$
$930$	14.0838			0.461824
$931$		0			0
$932$			14.7089i			0.481806i
$933$	−35.3561			−1.15751
$934$	25.8620			0.846232
$935$	12.3288	+	86.4214i	0.403196	+	2.82628i
$936$			2.53017i			0.0827013i
$937$	28.7613			0.939590			0.469795	−	0.882776i	$-0.344328\pi$
$937$	28.7613			0.939590			0.469795	+	0.882776i	$0.344328\pi$
$938$		0			0
$939$	−2.17769			−0.0710663
$940$	5.52260			0.180127
$941$	−35.2984			−1.15070			−0.575348	−	0.817909i	$-0.695133\pi$
$941$	−35.2984			−1.15070			−0.575348	+	0.817909i	$0.695133\pi$
$942$		−	23.1145i		−	0.753111i
$943$	−6.49435			−0.211485
$944$			9.03853i			0.294179i
$945$		0			0
$946$	12.2744	−	1.75106i	0.399075	−	0.0569318i
$947$	41.0245			1.33312			0.666559	−	0.745452i	$-0.267766\pi$
$947$	41.0245			1.33312			0.666559	+	0.745452i	$0.267766\pi$
$948$	15.6788			0.509222
$949$	−67.1478			−2.17971
$950$			36.2351i			1.17562i
$951$			16.8090i			0.545068i
$952$		0			0
$953$		−	1.09232i		−	0.0353838i	−0.999843	−	0.0176919i	$-0.994368\pi$
$953$		−	1.09232i		−	0.0353838i	0.999843	−	0.0176919i	$-0.00563181\pi$
$954$		−	1.64897i		−	0.0533875i
$955$			39.5376i			1.27941i
$956$		−	22.4218i		−	0.725173i
$957$	−8.03774	+	1.14666i	−0.259823	+	0.0370663i
$958$		−	12.5206i		−	0.404521i
$959$		0			0
$960$	5.98098			0.193035
$961$	25.4551			0.821133
$962$			32.2938i			1.04119i
$963$			3.26136i			0.105096i
$964$	15.4687			0.498215
$965$	16.3889			0.527579
$966$		0			0
$967$			41.0334i			1.31955i	0.751465	+	0.659773i	$0.229348\pi$
$967$			41.0334i			1.31955i	−0.751465	+	0.659773i	$0.770652\pi$
$968$	3.07591	+	10.5612i	0.0988635	+	0.339450i
$969$			99.3969i			3.19309i
$970$			12.3870i			0.397723i
$971$			8.07758i			0.259222i	0.991565	+	0.129611i	$0.0413728\pi$
$971$			8.07758i			0.259222i	−0.991565	+	0.129611i	$0.958627\pi$
$972$		−	4.27518i		−	0.137126i
$973$		0			0
$974$		−	20.7085i		−	0.663542i
$975$		−	61.8224i		−	1.97990i
$976$	8.55638			0.273883
$977$	35.6432			1.14033			0.570164	−	0.821531i	$-0.306880\pi$
$977$	35.6432			1.14033			0.570164	+	0.821531i	$0.306880\pi$
$978$	−15.5136			−0.496071
$979$	2.18331	+	15.3043i	0.0697789	+	0.489129i
$980$		0			0
$981$			2.48528i			0.0793489i
$982$	−23.6712			−0.755377
$983$			39.0034i			1.24402i	0.783011	+	0.622008i	$0.213683\pi$
$983$			39.0034i			1.24402i	−0.783011	+	0.622008i	$0.786317\pi$
$984$	2.26166			0.0720992
$985$	−65.0235			−2.07182
$986$	10.7731			0.343085
$987$		0			0
$988$	40.4092			1.28559
$989$		−	19.8350i		−	0.630715i
$990$	4.40223	−	0.628020i	0.139912	−	0.0199598i
$991$	−16.6038			−0.527436			−0.263718	−	0.964600i	$-0.584949\pi$
$991$	−16.6038			−0.527436			−0.263718	+	0.964600i	$0.584949\pi$
$992$	−2.35476			−0.0747636
$993$		−	5.04388i		−	0.160063i
$994$		0			0
$995$	−47.9692			−1.52073
$996$		−	10.3500i		−	0.327952i
$997$	42.3386			1.34088			0.670439	−	0.741965i	$-0.266106\pi$
$997$	42.3386			1.34088			0.670439	+	0.741965i	$0.266106\pi$
$998$		−	11.6124i		−	0.367584i
$999$		−	25.2599i		−	0.799187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.c.c.1077.1	✓	16
7.2	even	3		1078.2.i.d.1011.4		32
7.3	odd	6		1078.2.i.d.901.16		32
7.4	even	3		1078.2.i.d.901.15		32
7.5	odd	6		1078.2.i.d.1011.3		32
7.6	odd	2	inner	1078.2.c.c.1077.8	yes	16
11.10	odd	2	inner	1078.2.c.c.1077.9	yes	16
77.10	even	6		1078.2.i.d.901.4		32
77.32	odd	6		1078.2.i.d.901.3		32
77.54	even	6		1078.2.i.d.1011.15		32
77.65	odd	6		1078.2.i.d.1011.16		32
77.76	even	2	inner	1078.2.c.c.1077.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.1	✓	16	1.1	even	1	trivial
1078.2.c.c.1077.8	yes	16	7.6	odd	2	inner
1078.2.c.c.1077.9	yes	16	11.10	odd	2	inner
1078.2.c.c.1077.16	yes	16	77.76	even	2	inner
1078.2.i.d.901.3		32	77.32	odd	6
1078.2.i.d.901.4		32	77.10	even	6
1078.2.i.d.901.15		32	7.4	even	3
1078.2.i.d.901.16		32	7.3	odd	6
1078.2.i.d.1011.3		32	7.5	odd	6
1078.2.i.d.1011.4		32	7.2	even	3
1078.2.i.d.1011.15		32	77.54	even	6
1078.2.i.d.1011.16		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.84776i q^{3} -1.00000 q^{4} -3.23688i q^{5} -1.84776 q^{6} +1.00000i q^{8} -0.414214 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.84776i q^{3} -1.00000 q^{4} -3.23688i q^{5} -1.84776 q^{6} +1.00000i q^{8} -0.414214 q^{9} -3.23688 q^{10} +(3.28338 - 0.468406i) q^{11} +1.84776i q^{12} -6.10838 q^{13} -5.98098 q^{15} +1.00000 q^{16} -8.13155 q^{17} +0.414214i q^{18} +6.61537 q^{19} +3.23688i q^{20} +(-0.468406 - 3.28338i) q^{22} -5.30583 q^{23} +1.84776 q^{24} -5.47740 q^{25} +6.10838i q^{26} -4.77791i q^{27} -1.32485i q^{29} +5.98098i q^{30} -2.35476i q^{31} -1.00000i q^{32} +(-0.865501 - 6.06690i) q^{33} +8.13155i q^{34} +0.414214 q^{36} +5.28681 q^{37} -6.61537i q^{38} +11.2868i q^{39} +3.23688 q^{40} +1.22400 q^{41} +3.73834i q^{43} +(-3.28338 + 0.468406i) q^{44} +1.34076i q^{45} +5.30583i q^{46} -1.70615i q^{47} -1.84776i q^{48} +5.47740i q^{50} +15.0251i q^{51} +6.10838 q^{52} -3.98098 q^{53} -4.77791 q^{54} +(-1.51617 - 10.6279i) q^{55} -12.2236i q^{57} -1.32485 q^{58} +9.03853i q^{59} +5.98098 q^{60} +8.55638 q^{61} -2.35476 q^{62} -1.00000 q^{64} +19.7721i q^{65} +(-6.06690 + 0.865501i) q^{66} +2.35103 q^{67} +8.13155 q^{68} +9.80389i q^{69} -7.17945 q^{71} -0.414214i q^{72} +10.9927 q^{73} -5.28681i q^{74} +10.1209i q^{75} -6.61537 q^{76} +11.2868 q^{78} -8.48528i q^{79} -3.23688i q^{80} -10.0711 q^{81} -1.22400i q^{82} -5.60138 q^{83} +26.3209i q^{85} +3.73834 q^{86} -2.44801 q^{87} +(0.468406 + 3.28338i) q^{88} +4.66115i q^{89} +1.34076 q^{90} +5.30583 q^{92} -4.35103 q^{93} -1.70615 q^{94} -21.4132i q^{95} -1.84776 q^{96} -3.82683i q^{97} +(-1.36002 + 0.194020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) \) 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

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