LMFDB - Embedded newform 1216.2.m.a.303.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(303,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1216.303");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.m (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			303.2
Character	$\chi$	$=$	1216.303
Dual form			1216.2.m.a.911.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19409 - 2.19409i) q^{3} +(-1.29836 + 1.29836i) q^{5} +4.71096 q^{7} +6.62806i q^{9} +(-1.58474 - 1.58474i) q^{11} +(1.15106 - 1.15106i) q^{13} +5.69744 q^{15} -4.49586 q^{17} +(-3.77529 + 2.17881i) q^{19} +(-10.3363 - 10.3363i) q^{21} +1.10072 q^{23} +1.62852i q^{25} +(7.96029 - 7.96029i) q^{27} +(-3.39896 + 3.39896i) q^{29} -10.6386 q^{31} +6.95410i q^{33} +(-6.11653 + 6.11653i) q^{35} +(4.15324 + 4.15324i) q^{37} -5.05107 q^{39} -3.12271 q^{41} +(-2.25762 - 2.25762i) q^{43} +(-8.60561 - 8.60561i) q^{45} -3.92587i q^{47} +15.1932 q^{49} +(9.86431 + 9.86431i) q^{51} +(1.36482 + 1.36482i) q^{53} +4.11512 q^{55} +(13.0638 + 3.50281i) q^{57} +(-1.17894 + 1.17894i) q^{59} +(6.25950 + 6.25950i) q^{61} +31.2246i q^{63} +2.98899i q^{65} +(5.98603 + 5.98603i) q^{67} +(-2.41507 - 2.41507i) q^{69} +2.56883i q^{71} +7.75197i q^{73} +(3.57312 - 3.57312i) q^{75} +(-7.46563 - 7.46563i) q^{77} -3.39244 q^{79} -15.0470 q^{81} +(-8.05613 + 8.05613i) q^{83} +(5.83724 - 5.83724i) q^{85} +14.9152 q^{87} +0.722185 q^{89} +(5.42261 - 5.42261i) q^{91} +(23.3421 + 23.3421i) q^{93} +(2.07280 - 7.73056i) q^{95} -10.8873i q^{97} +(10.5037 - 10.5037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.19409	−	2.19409i	−1.26676	−	1.26676i	−0.947753	−	0.319005i	$-0.896651\pi$
$3$	−2.19409	−	2.19409i	−1.26676	−	1.26676i	−0.319005	−	0.947753i	$-0.603349\pi$
$4$		0			0
$5$	−1.29836	+	1.29836i	−0.580644	+	0.580644i	−0.935080	−	0.354436i	$-0.884673\pi$
$5$	−1.29836	+	1.29836i	−0.580644	+	0.580644i	0.354436	+	0.935080i	$0.384673\pi$
$6$		0			0
$7$	4.71096			1.78058			0.890289	−	0.455397i	$-0.150503\pi$
$7$	4.71096			1.78058			0.890289	+	0.455397i	$0.150503\pi$
$8$		0			0
$9$			6.62806i			2.20935i
$10$		0			0
$11$	−1.58474	−	1.58474i	−0.477816	−	0.477816i	0.426617	−	0.904433i	$-0.359705\pi$
$11$	−1.58474	−	1.58474i	−0.477816	−	0.477816i	−0.904433	+	0.426617i	$0.859705\pi$
$12$		0			0
$13$	1.15106	−	1.15106i	0.319247	−	0.319247i	−0.529231	−	0.848478i	$-0.677519\pi$
$13$	1.15106	−	1.15106i	0.319247	−	0.319247i	0.848478	+	0.529231i	$0.177519\pi$
$14$		0			0
$15$	5.69744			1.47107
$16$		0			0
$17$	−4.49586			−1.09041			−0.545203	−	0.838304i	$-0.683547\pi$
$17$	−4.49586			−1.09041			−0.545203	+	0.838304i	$0.683547\pi$
$18$		0			0
$19$	−3.77529	+	2.17881i	−0.866110	+	0.499853i
$19$	−3.77529	+	2.17881i	−0.866110	+	0.499853i
$20$		0			0
$21$	−10.3363	−	10.3363i	−2.25556	−	2.25556i
$22$		0			0
$23$	1.10072			0.229515			0.114758	−	0.993394i	$-0.463391\pi$
$23$	1.10072			0.229515			0.114758	+	0.993394i	$0.463391\pi$
$24$		0			0
$25$			1.62852i			0.325704i
$26$		0			0
$27$	7.96029	−	7.96029i	1.53196	−	1.53196i
$28$		0			0
$29$	−3.39896	+	3.39896i	−0.631171	+	0.631171i	−0.948362	−	0.317191i	$-0.897260\pi$
$29$	−3.39896	+	3.39896i	−0.631171	+	0.631171i	0.317191	+	0.948362i	$0.397260\pi$
$30$		0			0
$31$	−10.6386			−1.91075			−0.955377	−	0.295388i	$-0.904551\pi$
$31$	−10.6386			−1.91075			−0.955377	+	0.295388i	$0.904551\pi$
$32$		0			0
$33$			6.95410i			1.21055i
$34$		0			0
$35$	−6.11653	+	6.11653i	−1.03388	+	1.03388i
$36$		0			0
$37$	4.15324	+	4.15324i	0.682788	+	0.682788i	0.960628	−	0.277839i	$-0.0896183\pi$
$37$	4.15324	+	4.15324i	0.682788	+	0.682788i	−0.277839	+	0.960628i	$0.589618\pi$
$38$		0			0
$39$	−5.05107			−0.808818
$40$		0			0
$41$	−3.12271			−0.487686			−0.243843	−	0.969815i	$-0.578408\pi$
$41$	−3.12271			−0.487686			−0.243843	+	0.969815i	$0.578408\pi$
$42$		0			0
$43$	−2.25762	−	2.25762i	−0.344284	−	0.344284i	0.513691	−	0.857975i	$-0.328278\pi$
$43$	−2.25762	−	2.25762i	−0.344284	−	0.344284i	−0.857975	+	0.513691i	$0.828278\pi$
$44$		0			0
$45$	−8.60561	−	8.60561i	−1.28285	−	1.28285i
$46$		0			0
$47$		−	3.92587i		−	0.572647i	−0.958133	−	0.286323i	$-0.907567\pi$
$47$		−	3.92587i		−	0.572647i	0.958133	−	0.286323i	$-0.0924332\pi$
$48$		0			0
$49$	15.1932			2.17046
$50$		0			0
$51$	9.86431	+	9.86431i	1.38128	+	1.38128i
$52$		0			0
$53$	1.36482	+	1.36482i	0.187472	+	0.187472i	0.794602	−	0.607130i	$-0.207679\pi$
$53$	1.36482	+	1.36482i	0.187472	+	0.187472i	−0.607130	+	0.794602i	$0.707679\pi$
$54$		0			0
$55$	4.11512			0.554882
$56$		0			0
$57$	13.0638	+	3.50281i	1.73035	+	0.463958i
$58$		0			0
$59$	−1.17894	+	1.17894i	−0.153485	+	0.153485i	−0.779672	−	0.626188i	$-0.784614\pi$
$59$	−1.17894	+	1.17894i	−0.153485	+	0.153485i	0.626188	+	0.779672i	$0.284614\pi$
$60$		0			0
$61$	6.25950	+	6.25950i	0.801447	+	0.801447i	0.983322	−	0.181875i	$-0.0582165\pi$
$61$	6.25950	+	6.25950i	0.801447	+	0.801447i	−0.181875	+	0.983322i	$0.558216\pi$
$62$		0			0
$63$			31.2246i			3.93392i
$64$		0			0
$65$			2.98899i			0.370738i
$66$		0			0
$67$	5.98603	+	5.98603i	0.731310	+	0.731310i	0.970879	−	0.239569i	$-0.0770062\pi$
$67$	5.98603	+	5.98603i	0.731310	+	0.731310i	−0.239569	+	0.970879i	$0.577006\pi$
$68$		0			0
$69$	−2.41507	−	2.41507i	−0.290740	−	0.290740i
$70$		0			0
$71$			2.56883i			0.304864i	0.988314	+	0.152432i	$0.0487105\pi$
$71$			2.56883i			0.304864i	−0.988314	+	0.152432i	$0.951289\pi$
$72$		0			0
$73$			7.75197i			0.907300i	0.891180	+	0.453650i	$0.149878\pi$
$73$			7.75197i			0.907300i	−0.891180	+	0.453650i	$0.850122\pi$
$74$		0			0
$75$	3.57312	−	3.57312i	0.412589	−	0.412589i
$76$		0			0
$77$	−7.46563	−	7.46563i	−0.850788	−	0.850788i
$78$		0			0
$79$	−3.39244			−0.381679			−0.190840	−	0.981621i	$-0.561121\pi$
$79$	−3.39244			−0.381679			−0.190840	+	0.981621i	$0.561121\pi$
$80$		0			0
$81$	−15.0470			−1.67189
$82$		0			0
$83$	−8.05613	+	8.05613i	−0.884275	+	0.884275i	−0.993966	−	0.109690i	$-0.965014\pi$
$83$	−8.05613	+	8.05613i	−0.884275	+	0.884275i	0.109690	+	0.993966i	$0.465014\pi$
$84$		0			0
$85$	5.83724	−	5.83724i	0.633138	−	0.633138i
$86$		0			0
$87$	14.9152			1.59908
$88$		0			0
$89$	0.722185			0.0765514			0.0382757	−	0.999267i	$-0.487813\pi$
$89$	0.722185			0.0765514			0.0382757	+	0.999267i	$0.487813\pi$
$90$		0			0
$91$	5.42261	−	5.42261i	0.568444	−	0.568444i
$92$		0			0
$93$	23.3421	+	23.3421i	2.42046	+	2.42046i
$94$		0			0
$95$	2.07280	−	7.73056i	0.212665	−	0.793139i
$96$		0			0
$97$		−	10.8873i		−	1.10544i	−0.833366	−	0.552721i	$-0.813589\pi$
$97$		−	10.8873i		−	1.10544i	0.833366	−	0.552721i	$-0.186411\pi$
$98$		0			0
$99$	10.5037	−	10.5037i	1.05566	−	1.05566i
$100$		0			0
$101$	−8.99362	+	8.99362i	−0.894899	+	0.894899i	−0.994979	−	0.100080i	$-0.968090\pi$
$101$	−8.99362	+	8.99362i	−0.894899	+	0.894899i	0.100080	+	0.994979i	$0.468090\pi$
$102$		0			0
$103$			11.7813i			1.16085i	0.814314	+	0.580424i	$0.197113\pi$
$103$			11.7813i			1.16085i	−0.814314	+	0.580424i	$0.802887\pi$
$104$		0			0
$105$	26.8404			2.61936
$106$		0			0
$107$	−12.1132	+	12.1132i	−1.17103	+	1.17103i	−0.189066	+	0.981964i	$0.560546\pi$
$107$	−12.1132	+	12.1132i	−1.17103	+	1.17103i	−0.981964	+	0.189066i	$0.939454\pi$
$108$		0			0
$109$	0.908423	−	0.908423i	0.0870112	−	0.0870112i	−0.662262	−	0.749273i	$-0.730403\pi$
$109$	0.908423	−	0.908423i	0.0870112	−	0.0870112i	0.749273	+	0.662262i	$0.230403\pi$
$110$		0			0
$111$		−	18.2252i		−	1.72985i
$112$		0			0
$113$			13.4511i			1.26538i	0.774407	+	0.632688i	$0.218048\pi$
$113$			13.4511i			1.26538i	−0.774407	+	0.632688i	$0.781952\pi$
$114$		0			0
$115$	−1.42913	+	1.42913i	−0.133267	+	0.133267i
$116$		0			0
$117$	7.62931	+	7.62931i	0.705330	+	0.705330i
$118$		0			0
$119$	−21.1798			−1.94155
$120$		0			0
$121$		−	5.97723i		−	0.543384i
$122$		0			0
$123$	6.85151	+	6.85151i	0.617780	+	0.617780i
$124$		0			0
$125$	−8.60621	−	8.60621i	−0.769763	−	0.769763i
$126$		0			0
$127$	−0.800848			−0.0710638			−0.0355319	−	0.999369i	$-0.511313\pi$
$127$	−0.800848			−0.0710638			−0.0355319	+	0.999369i	$0.511313\pi$
$128$		0			0
$129$			9.90686i			0.872250i
$130$		0			0
$131$	4.83506	−	4.83506i	0.422441	−	0.422441i	−0.463602	−	0.886043i	$-0.653443\pi$
$131$	4.83506	−	4.83506i	0.422441	−	0.422441i	0.886043	+	0.463602i	$0.153443\pi$
$132$		0			0
$133$	−17.7852	+	10.2643i	−1.54218	+	0.890028i
$134$		0			0
$135$			20.6706i			1.77905i
$136$		0			0
$137$		−	13.8006i		−	1.17907i	−0.807745	−	0.589533i	$-0.799312\pi$
$137$		−	13.8006i		−	1.17907i	0.807745	−	0.589533i	$-0.200688\pi$
$138$		0			0
$139$	8.95077	+	8.95077i	0.759195	+	0.759195i	0.976176	−	0.216981i	$-0.0696210\pi$
$139$	8.95077	+	8.95077i	0.759195	+	0.759195i	−0.216981	+	0.976176i	$0.569621\pi$
$140$		0			0
$141$	−8.61371	+	8.61371i	−0.725405	+	0.725405i
$142$		0			0
$143$	−3.64826			−0.305083
$144$		0			0
$145$		−	8.82614i		−	0.732971i
$146$		0			0
$147$	−33.3352	−	33.3352i	−2.74944	−	2.74944i
$148$		0			0
$149$	0.455069	−	0.455069i	0.0372807	−	0.0372807i	−0.688221	−	0.725501i	$-0.741608\pi$
$149$	0.455069	−	0.455069i	0.0372807	−	0.0372807i	0.725501	+	0.688221i	$0.241608\pi$
$150$		0			0
$151$			17.7082i			1.44108i	0.693415	+	0.720538i	$0.256105\pi$
$151$			17.7082i			1.44108i	−0.693415	+	0.720538i	$0.743895\pi$
$152$		0			0
$153$		−	29.7988i		−	2.40909i
$154$		0			0
$155$	13.8128	−	13.8128i	1.10947	−	1.10947i
$156$		0			0
$157$	0.222635	+	0.222635i	0.0177682	+	0.0177682i	0.715935	−	0.698167i	$-0.246001\pi$
$157$	0.222635	+	0.222635i	0.0177682	+	0.0177682i	−0.698167	+	0.715935i	$0.746001\pi$
$158$		0			0
$159$		−	5.98906i		−	0.474963i
$160$		0			0
$161$	5.18544			0.408670
$162$		0			0
$163$	11.4055	−	11.4055i	0.893350	−	0.893350i	−0.101487	−	0.994837i	$-0.532360\pi$
$163$	11.4055	−	11.4055i	0.893350	−	0.893350i	0.994837	+	0.101487i	$0.0323599\pi$
$164$		0			0
$165$	−9.02893	−	9.02893i	−0.702901	−	0.702901i
$166$		0			0
$167$		−	9.05469i		−	0.700673i	−0.936624	−	0.350336i	$-0.886067\pi$
$167$		−	9.05469i		−	0.700673i	0.936624	−	0.350336i	$-0.113933\pi$
$168$		0			0
$169$			10.3501i			0.796163i
$170$		0			0
$171$	−14.4413	−	25.0228i	−1.10435	−	1.91354i
$172$		0			0
$173$	−9.11174	+	9.11174i	−0.692753	+	0.692753i	−0.962837	−	0.270084i	$-0.912949\pi$
$173$	−9.11174	+	9.11174i	−0.692753	+	0.692753i	0.270084	+	0.962837i	$0.412949\pi$
$174$		0			0
$175$			7.67191i			0.579942i
$176$		0			0
$177$	5.17340			0.388857
$178$		0			0
$179$	−12.4047	−	12.4047i	−0.927171	−	0.927171i	0.0703516	−	0.997522i	$-0.477588\pi$
$179$	−12.4047	−	12.4047i	−0.927171	−	0.927171i	−0.997522	+	0.0703516i	$0.977588\pi$
$180$		0			0
$181$	−7.68767	−	7.68767i	−0.571420	−	0.571420i	0.361105	−	0.932525i	$-0.382400\pi$
$181$	−7.68767	−	7.68767i	−0.571420	−	0.571420i	−0.932525	+	0.361105i	$0.882400\pi$
$182$		0			0
$183$		−	27.4678i		−	2.03048i
$184$		0			0
$185$	−10.7848			−0.792914
$186$		0			0
$187$	7.12474	+	7.12474i	0.521013	+	0.521013i
$188$		0			0
$189$	37.5006	−	37.5006i	2.72777	−	2.72777i
$190$		0			0
$191$			3.08602i			0.223297i	0.993748	+	0.111648i	$0.0356130\pi$
$191$			3.08602i			0.223297i	−0.993748	+	0.111648i	$0.964387\pi$
$192$		0			0
$193$		−	9.54148i		−	0.686810i	−0.939187	−	0.343405i	$-0.888420\pi$
$193$		−	9.54148i		−	0.686810i	0.939187	−	0.343405i	$-0.111580\pi$
$194$		0			0
$195$	6.55810	−	6.55810i	0.469635	−	0.469635i
$196$		0			0
$197$	11.3391	−	11.3391i	0.807875	−	0.807875i	−0.176437	−	0.984312i	$-0.556457\pi$
$197$	11.3391	−	11.3391i	0.807875	−	0.807875i	0.984312	+	0.176437i	$0.0564573\pi$
$198$		0			0
$199$	−15.8997			−1.12710			−0.563549	−	0.826082i	$-0.690565\pi$
$199$	−15.8997			−1.12710			−0.563549	+	0.826082i	$0.690565\pi$
$200$		0			0
$201$		−	26.2678i		−	1.85279i
$202$		0			0
$203$	−16.0124	+	16.0124i	−1.12385	+	1.12385i
$204$		0			0
$205$	4.05441	−	4.05441i	0.283172	−	0.283172i
$206$		0			0
$207$			7.29561i			0.507080i
$208$		0			0
$209$	9.43567	+	2.52999i	0.652679	+	0.175003i
$210$		0			0
$211$	−1.30123	−	1.30123i	−0.0895803	−	0.0895803i	0.660897	−	0.750477i	$-0.270176\pi$
$211$	−1.30123	−	1.30123i	−0.0895803	−	0.0895803i	−0.750477	+	0.660897i	$0.770176\pi$
$212$		0			0
$213$	5.63624	−	5.63624i	0.386189	−	0.386189i
$214$		0			0
$215$	5.86242			0.399813
$216$		0			0
$217$	−50.1182			−3.40225
$218$		0			0
$219$	17.0085	−	17.0085i	1.14933	−	1.14933i
$220$		0			0
$221$	−5.17501	+	5.17501i	−0.348109	+	0.348109i
$222$		0			0
$223$	−15.1433			−1.01407			−0.507034	−	0.861926i	$-0.669258\pi$
$223$	−15.1433			−1.01407			−0.507034	+	0.861926i	$0.669258\pi$
$224$		0			0
$225$	−10.7939			−0.719596
$226$		0			0
$227$	11.5587	+	11.5587i	0.767176	+	0.767176i	0.977608	−	0.210433i	$-0.0674873\pi$
$227$	11.5587	+	11.5587i	0.767176	+	0.767176i	−0.210433	+	0.977608i	$0.567487\pi$
$228$		0			0
$229$	3.11406	−	3.11406i	0.205783	−	0.205783i	−0.596689	−	0.802472i	$-0.703518\pi$
$229$	3.11406	−	3.11406i	0.205783	−	0.205783i	0.802472	+	0.596689i	$0.203518\pi$
$230$		0			0
$231$			32.7605i			2.15549i
$232$		0			0
$233$			16.4933i			1.08051i	0.841500	+	0.540257i	$0.181673\pi$
$233$			16.4933i			1.08051i	−0.841500	+	0.540257i	$0.818327\pi$
$234$		0			0
$235$	5.09719	+	5.09719i	0.332504	+	0.332504i
$236$		0			0
$237$	7.44331	+	7.44331i	0.483495	+	0.483495i
$238$		0			0
$239$			0.361719i			0.0233977i	0.999932	+	0.0116988i	$0.00372394\pi$
$239$			0.361719i			0.0233977i	−0.999932	+	0.0116988i	$0.996276\pi$
$240$		0			0
$241$			17.9224i			1.15448i	0.816574	+	0.577241i	$0.195871\pi$
$241$			17.9224i			1.15448i	−0.816574	+	0.577241i	$0.804129\pi$
$242$		0			0
$243$	9.13358	+	9.13358i	0.585920	+	0.585920i
$244$		0			0
$245$	−19.7262	+	19.7262i	−1.26026	+	1.26026i
$246$		0			0
$247$	−1.83764	+	6.85353i	−0.116926	+	0.436080i
$248$		0			0
$249$	35.3518			2.24033
$250$		0			0
$251$	13.3647	+	13.3647i	0.843571	+	0.843571i	0.989321	−	0.145750i	$-0.0465595\pi$
$251$	13.3647	+	13.3647i	0.843571	+	0.843571i	−0.145750	+	0.989321i	$0.546560\pi$
$252$		0			0
$253$	−1.74434	−	1.74434i	−0.109666	−	0.109666i
$254$		0			0
$255$	−25.6149			−1.60406
$256$		0			0
$257$		−	3.03209i		−	0.189136i	−0.995518	−	0.0945682i	$-0.969853\pi$
$257$		−	3.03209i		−	0.189136i	0.995518	−	0.0945682i	$-0.0301470\pi$
$258$		0			0
$259$	19.5658	+	19.5658i	1.21576	+	1.21576i
$260$		0			0
$261$	−22.5285	−	22.5285i	−1.39448	−	1.39448i
$262$		0			0
$263$	−8.57603			−0.528821			−0.264410	−	0.964410i	$-0.585177\pi$
$263$	−8.57603			−0.528821			−0.264410	+	0.964410i	$0.585177\pi$
$264$		0			0
$265$	−3.54405			−0.217709
$266$		0			0
$267$	−1.58454	−	1.58454i	−0.0969722	−	0.0969722i
$268$		0			0
$269$	12.8132	−	12.8132i	0.781237	−	0.781237i	−0.198803	−	0.980040i	$-0.563705\pi$
$269$	12.8132	−	12.8132i	0.781237	−	0.781237i	0.980040	+	0.198803i	$0.0637053\pi$
$270$		0			0
$271$		−	19.8803i		−	1.20764i	−0.797119	−	0.603822i	$-0.793644\pi$
$271$		−	19.8803i		−	1.20764i	0.797119	−	0.603822i	$-0.206356\pi$
$272$		0			0
$273$	−23.7954			−1.44016
$274$		0			0
$275$	2.58078	−	2.58078i	0.155627	−	0.155627i
$276$		0			0
$277$	−3.55753	+	3.55753i	−0.213751	+	0.213751i	−0.805859	−	0.592108i	$-0.798296\pi$
$277$	−3.55753	+	3.55753i	−0.213751	+	0.213751i	0.592108	+	0.805859i	$0.298296\pi$
$278$		0			0
$279$		−	70.5135i		−	4.22153i
$280$		0			0
$281$	4.62309			0.275790			0.137895	−	0.990447i	$-0.455966\pi$
$281$	4.62309			0.275790			0.137895	+	0.990447i	$0.455966\pi$
$282$		0			0
$283$	−12.0146	−	12.0146i	−0.714193	−	0.714193i	0.253217	−	0.967410i	$-0.418511\pi$
$283$	−12.0146	−	12.0146i	−0.714193	−	0.714193i	−0.967410	+	0.253217i	$0.918511\pi$
$284$		0			0
$285$	−21.5095	+	12.4136i	−1.27411	+	0.735320i
$286$		0			0
$287$	−14.7110			−0.868362
$288$		0			0
$289$	3.21273			0.188984
$290$		0			0
$291$	−23.8878	+	23.8878i	−1.40033	+	1.40033i
$292$		0			0
$293$	−1.40455	−	1.40455i	−0.0820545	−	0.0820545i	0.664888	−	0.746943i	$-0.268479\pi$
$293$	−1.40455	−	1.40455i	−0.0820545	−	0.0820545i	−0.746943	+	0.664888i	$0.768479\pi$
$294$		0			0
$295$		−	3.06138i		−	0.178240i
$296$		0			0
$297$	−25.2299			−1.46399
$298$		0			0
$299$	1.26699	−	1.26699i	0.0732721	−	0.0732721i
$300$		0			0
$301$	−10.6356	−	10.6356i	−0.613025	−	0.613025i
$302$		0			0
$303$	39.4656			2.26724
$304$		0			0
$305$	−16.2542			−0.930712
$306$		0			0
$307$	1.20707	+	1.20707i	0.0688914	+	0.0688914i	0.740713	−	0.671822i	$-0.234488\pi$
$307$	1.20707	+	1.20707i	0.0688914	+	0.0688914i	−0.671822	+	0.740713i	$0.734488\pi$
$308$		0			0
$309$	25.8493	−	25.8493i	1.47052	−	1.47052i
$310$		0			0
$311$	−19.3907			−1.09954			−0.549772	−	0.835315i	$-0.685286\pi$
$311$	−19.3907			−1.09954			−0.549772	+	0.835315i	$0.685286\pi$
$312$		0			0
$313$			13.7576i			0.777626i	0.921317	+	0.388813i	$0.127115\pi$
$313$			13.7576i			0.777626i	−0.921317	+	0.388813i	$0.872885\pi$
$314$		0			0
$315$	−40.5407	−	40.5407i	−2.28421	−	2.28421i
$316$		0			0
$317$	−13.2954	+	13.2954i	−0.746745	+	0.746745i	−0.973866	−	0.227122i	$-0.927068\pi$
$317$	−13.2954	+	13.2954i	−0.746745	+	0.746745i	0.227122	+	0.973866i	$0.427068\pi$
$318$		0			0
$319$	10.7729			0.603166
$320$		0			0
$321$	53.1550			2.96682
$322$		0			0
$323$	16.9731	−	9.79562i	0.944411	−	0.545043i
$324$		0			0
$325$	1.87453	+	1.87453i	0.103980	+	0.103980i
$326$		0			0
$327$	−3.98632			−0.220444
$328$		0			0
$329$		−	18.4946i		−	1.01964i
$330$		0			0
$331$	11.2930	−	11.2930i	0.620717	−	0.620717i	−0.324998	−	0.945715i	$-0.605364\pi$
$331$	11.2930	−	11.2930i	0.620717	−	0.620717i	0.945715	+	0.324998i	$0.105364\pi$
$332$		0			0
$333$	−27.5279	+	27.5279i	−1.50852	+	1.50852i
$334$		0			0
$335$	−15.5440			−0.849262
$336$		0			0
$337$			24.4258i			1.33056i	0.746596	+	0.665278i	$0.231687\pi$
$337$			24.4258i			1.33056i	−0.746596	+	0.665278i	$0.768313\pi$
$338$		0			0
$339$	29.5130	−	29.5130i	1.60292	−	1.60292i
$340$		0			0
$341$	16.8594	+	16.8594i	0.912989	+	0.912989i
$342$		0			0
$343$	38.5978			2.08409
$344$		0			0
$345$	6.27126			0.337634
$346$		0			0
$347$	6.89538	+	6.89538i	0.370163	+	0.370163i	0.867537	−	0.497373i	$-0.165702\pi$
$347$	6.89538	+	6.89538i	0.370163	+	0.370163i	−0.497373	+	0.867537i	$0.665702\pi$
$348$		0			0
$349$	5.38977	+	5.38977i	0.288508	+	0.288508i	0.836490	−	0.547982i	$-0.184604\pi$
$349$	5.38977	+	5.38977i	0.288508	+	0.288508i	−0.547982	+	0.836490i	$0.684604\pi$
$350$		0			0
$351$		−	18.3256i		−	0.978146i
$352$		0			0
$353$	−5.34421			−0.284444			−0.142222	−	0.989835i	$-0.545425\pi$
$353$	−5.34421			−0.284444			−0.142222	+	0.989835i	$0.545425\pi$
$354$		0			0
$355$	−3.33527	−	3.33527i	−0.177018	−	0.177018i
$356$		0			0
$357$	46.4704	+	46.4704i	2.45948	+	2.45948i
$358$		0			0
$359$	35.5561			1.87658			0.938290	−	0.345850i	$-0.112409\pi$
$359$	35.5561			1.87658			0.938290	+	0.345850i	$0.112409\pi$
$360$		0			0
$361$	9.50557	−	16.4513i	0.500293	−	0.865856i
$362$		0			0
$363$	−13.1146	+	13.1146i	−0.688336	+	0.688336i
$364$		0			0
$365$	−10.0649	−	10.0649i	−0.526818	−	0.526818i
$366$		0			0
$367$		−	19.0452i		−	0.994150i	−0.867708	−	0.497075i	$-0.834407\pi$
$367$		−	19.0452i		−	0.994150i	0.867708	−	0.497075i	$-0.165593\pi$
$368$		0			0
$369$		−	20.6975i		−	1.07747i
$370$		0			0
$371$	6.42960	+	6.42960i	0.333808	+	0.333808i
$372$		0			0
$373$	−21.0610	−	21.0610i	−1.09050	−	1.09050i	−0.995475	−	0.0950223i	$-0.969708\pi$
$373$	−21.0610	−	21.0610i	−1.09050	−	1.09050i	−0.0950223	−	0.995475i	$-0.530292\pi$
$374$		0			0
$375$			37.7656i			1.95021i
$376$		0			0
$377$			7.82482i			0.402999i
$378$		0			0
$379$	−10.5077	+	10.5077i	−0.539746	+	0.539746i	−0.923454	−	0.383708i	$-0.874647\pi$
$379$	−10.5077	+	10.5077i	−0.539746	+	0.539746i	0.383708	+	0.923454i	$0.374647\pi$
$380$		0			0
$381$	1.75713	+	1.75713i	0.0900207	+	0.0900207i
$382$		0			0
$383$	19.1498			0.978510			0.489255	−	0.872141i	$-0.337269\pi$
$383$	19.1498			0.978510			0.489255	+	0.872141i	$0.337269\pi$
$384$		0			0
$385$	19.3862			0.988010
$386$		0			0
$387$	14.9637	−	14.9637i	0.760646	−	0.760646i
$388$		0			0
$389$	11.4334	−	11.4334i	0.579696	−	0.579696i	−0.355123	−	0.934819i	$-0.615561\pi$
$389$	11.4334	−	11.4334i	0.579696	−	0.579696i	0.934819	+	0.355123i	$0.115561\pi$
$390$		0			0
$391$	−4.94866			−0.250265
$392$		0			0
$393$	−21.2171			−1.07026
$394$		0			0
$395$	4.40461	−	4.40461i	0.221620	−	0.221620i
$396$		0			0
$397$	−17.9868	−	17.9868i	−0.902731	−	0.902731i	0.0929404	−	0.995672i	$-0.470373\pi$
$397$	−17.9868	−	17.9868i	−0.902731	−	0.902731i	−0.995672	+	0.0929404i	$0.970373\pi$
$398$		0			0
$399$	61.5432	+	16.5016i	3.08101	+	0.826114i
$400$		0			0
$401$		−	19.6725i		−	0.982399i	−0.871047	−	0.491199i	$-0.836559\pi$
$401$		−	19.6725i		−	0.982399i	0.871047	−	0.491199i	$-0.163441\pi$
$402$		0			0
$403$	−12.2457	+	12.2457i	−0.610003	+	0.610003i
$404$		0			0
$405$	19.5364	−	19.5364i	0.970772	−	0.970772i
$406$		0			0
$407$		−	13.1636i		−	0.652494i
$408$		0			0
$409$	33.9664			1.67953			0.839764	−	0.542951i	$-0.182693\pi$
$409$	33.9664			1.67953			0.839764	+	0.542951i	$0.182693\pi$
$410$		0			0
$411$	−30.2798	+	30.2798i	−1.49359	+	1.49359i
$412$		0			0
$413$	−5.55394	+	5.55394i	−0.273292	+	0.273292i
$414$		0			0
$415$		−	20.9195i		−	1.02690i
$416$		0			0
$417$		−	39.2776i		−	1.92343i
$418$		0			0
$419$	−20.0037	+	20.0037i	−0.977246	+	0.977246i	−0.999747	−	0.0225008i	$-0.992837\pi$
$419$	−20.0037	+	20.0037i	−0.977246	+	0.977246i	0.0225008	+	0.999747i	$0.492837\pi$
$420$		0			0
$421$	2.63510	+	2.63510i	0.128427	+	0.128427i	0.768399	−	0.639972i	$-0.221054\pi$
$421$	2.63510	+	2.63510i	0.128427	+	0.128427i	−0.639972	+	0.768399i	$0.721054\pi$
$422$		0			0
$423$	26.0209			1.26518
$424$		0			0
$425$		−	7.32160i		−	0.355150i
$426$		0			0
$427$	29.4883	+	29.4883i	1.42704	+	1.42704i
$428$		0			0
$429$	8.00460	+	8.00460i	0.386466	+	0.386466i
$430$		0			0
$431$	−11.8295			−0.569806			−0.284903	−	0.958556i	$-0.591961\pi$
$431$	−11.8295			−0.569806			−0.284903	+	0.958556i	$0.591961\pi$
$432$		0			0
$433$		−	18.1618i		−	0.872798i	−0.899753	−	0.436399i	$-0.856254\pi$
$433$		−	18.1618i		−	0.872798i	0.899753	−	0.436399i	$-0.143746\pi$
$434$		0			0
$435$	−19.3653	+	19.3653i	−0.928497	+	0.928497i
$436$		0			0
$437$	−4.15552	+	2.39825i	−0.198785	+	0.114724i
$438$		0			0
$439$		−	18.0504i		−	0.861498i	−0.902472	−	0.430749i	$-0.858249\pi$
$439$		−	18.0504i		−	0.861498i	0.902472	−	0.430749i	$-0.141751\pi$
$440$		0			0
$441$			100.701i			4.79530i
$442$		0			0
$443$	13.9288	+	13.9288i	0.661778	+	0.661778i	0.955799	−	0.294021i	$-0.0949934\pi$
$443$	13.9288	+	13.9288i	0.661778	+	0.661778i	−0.294021	+	0.955799i	$0.594993\pi$
$444$		0			0
$445$	−0.937656	+	0.937656i	−0.0444492	+	0.0444492i
$446$		0			0
$447$	−1.99692			−0.0944512
$448$		0			0
$449$		−	0.732461i		−	0.0345670i	−0.999851	−	0.0172835i	$-0.994498\pi$
$449$		−	0.732461i		−	0.0345670i	0.999851	−	0.0172835i	$-0.00550178\pi$
$450$		0			0
$451$	4.94867	+	4.94867i	0.233024	+	0.233024i
$452$		0			0
$453$	38.8535	−	38.8535i	1.82550	−	1.82550i
$454$		0			0
$455$			14.0810i			0.660128i
$456$		0			0
$457$		−	7.14164i		−	0.334072i	−0.985951	−	0.167036i	$-0.946580\pi$
$457$		−	7.14164i		−	0.334072i	0.985951	−	0.167036i	$-0.0534196\pi$
$458$		0			0
$459$	−35.7883	+	35.7883i	−1.67046	+	1.67046i
$460$		0			0
$461$	0.374745	+	0.374745i	0.0174536	+	0.0174536i	0.715780	−	0.698326i	$-0.246071\pi$
$461$	0.374745	+	0.374745i	0.0174536	+	0.0174536i	−0.698326	+	0.715780i	$0.746071\pi$
$462$		0			0
$463$			5.93476i			0.275812i	0.990445	+	0.137906i	$0.0440372\pi$
$463$			5.93476i			0.275812i	−0.990445	+	0.137906i	$0.955963\pi$
$464$		0			0
$465$	−60.6129			−2.81086
$466$		0			0
$467$	−24.5127	+	24.5127i	−1.13431	+	1.13431i	−0.144860	+	0.989452i	$0.546273\pi$
$467$	−24.5127	+	24.5127i	−1.13431	+	1.13431i	−0.989452	+	0.144860i	$0.953727\pi$
$468$		0			0
$469$	28.2000	+	28.2000i	1.30215	+	1.30215i
$470$		0			0
$471$		−	0.976962i		−	0.0450160i
$472$		0			0
$473$			7.15547i			0.329009i
$474$		0			0
$475$	−3.54824	−	6.14813i	−0.162804	−	0.282096i
$476$		0			0
$477$	−9.04609	+	9.04609i	−0.414192	+	0.414192i
$478$		0			0
$479$		−	33.6517i		−	1.53759i	−0.639497	−	0.768793i	$-0.720858\pi$
$479$		−	33.6517i		−	1.53759i	0.639497	−	0.768793i	$-0.279142\pi$
$480$		0			0
$481$	9.56127			0.435956
$482$		0			0
$483$	−11.3773	−	11.3773i	−0.517686	−	0.517686i
$484$		0			0
$485$	14.1357	+	14.1357i	0.641869	+	0.641869i
$486$		0			0
$487$		−	9.60432i		−	0.435214i	−0.976037	−	0.217607i	$-0.930175\pi$
$487$		−	9.60432i		−	0.435214i	0.976037	−	0.217607i	$-0.0698250\pi$
$488$		0			0
$489$	−50.0495			−2.26332
$490$		0			0
$491$	−19.4895	−	19.4895i	−0.879547	−	0.879547i	0.113940	−	0.993488i	$-0.463653\pi$
$491$	−19.4895	−	19.4895i	−0.879547	−	0.879547i	−0.993488	+	0.113940i	$0.963653\pi$
$492$		0			0
$493$	15.2812	−	15.2812i	0.688232	−	0.688232i
$494$		0			0
$495$			27.2752i			1.22593i
$496$		0			0
$497$			12.1017i			0.542834i
$498$		0			0
$499$	−13.0861	+	13.0861i	−0.585812	+	0.585812i	−0.936494	−	0.350682i	$-0.885950\pi$
$499$	−13.0861	+	13.0861i	−0.585812	+	0.585812i	0.350682	+	0.936494i	$0.385950\pi$
$500$		0			0
$501$	−19.8668	+	19.8668i	−0.887583	+	0.887583i
$502$		0			0
$503$	−24.5252			−1.09352			−0.546761	−	0.837289i	$-0.684139\pi$
$503$	−24.5252			−1.09352			−0.546761	+	0.837289i	$0.684139\pi$
$504$		0			0
$505$		−	23.3539i		−	1.03924i
$506$		0			0
$507$	22.7091	−	22.7091i	1.00855	−	1.00855i
$508$		0			0
$509$	11.7588	−	11.7588i	0.521198	−	0.521198i	−0.396735	−	0.917933i	$-0.629857\pi$
$509$	11.7588	−	11.7588i	0.521198	−	0.521198i	0.917933	+	0.396735i	$0.129857\pi$
$510$		0			0
$511$			36.5193i			1.61552i
$512$		0			0
$513$	−12.7084	+	47.3963i	−0.561090	+	2.09260i
$514$		0			0
$515$	−15.2964	−	15.2964i	−0.674040	−	0.674040i
$516$		0			0
$517$	−6.22146	+	6.22146i	−0.273620	+	0.273620i
$518$		0			0
$519$	39.9839			1.75510
$520$		0			0
$521$	36.6715			1.60661			0.803304	−	0.595569i	$-0.203073\pi$
$521$	36.6715			1.60661			0.803304	+	0.595569i	$0.203073\pi$
$522$		0			0
$523$	−10.7643	+	10.7643i	−0.470692	+	0.470692i	−0.902138	−	0.431447i	$-0.858003\pi$
$523$	−10.7643	+	10.7643i	−0.470692	+	0.470692i	0.431447	+	0.902138i	$0.358003\pi$
$524$		0			0
$525$	16.8329	−	16.8329i	0.734646	−	0.734646i
$526$		0			0
$527$	47.8298			2.08350
$528$		0			0
$529$	−21.7884			−0.947323
$530$		0			0
$531$	−7.81408	−	7.81408i	−0.339102	−	0.339102i
$532$		0			0
$533$	−3.59444	+	3.59444i	−0.155692	+	0.155692i
$534$		0			0
$535$		−	31.4547i		−	1.35990i
$536$		0			0
$537$			54.4340i			2.34900i
$538$		0			0
$539$	−24.0772	−	24.0772i	−1.03708	−	1.03708i
$540$		0			0
$541$	−23.7352	−	23.7352i	−1.02045	−	1.02045i	−0.999786	−	0.0206679i	$-0.993421\pi$
$541$	−23.7352	−	23.7352i	−1.02045	−	1.02045i	−0.0206679	−	0.999786i	$-0.506579\pi$
$542$		0			0
$543$			33.7349i			1.44770i
$544$		0			0
$545$			2.35892i			0.101045i
$546$		0			0
$547$	31.6591	+	31.6591i	1.35364	+	1.35364i	0.881546	+	0.472098i	$0.156503\pi$
$547$	31.6591	+	31.6591i	1.35364	+	1.35364i	0.472098	+	0.881546i	$0.343497\pi$
$548$		0			0
$549$	−41.4884	+	41.4884i	−1.77068	+	1.77068i
$550$		0			0
$551$	5.42635	−	20.2377i	0.231170	−	0.862156i
$552$		0			0
$553$	−15.9817			−0.679609
$554$		0			0
$555$	23.6628	+	23.6628i	1.00443	+	1.00443i
$556$		0			0
$557$	3.12642	+	3.12642i	0.132471	+	0.132471i	0.770233	−	0.637763i	$-0.220140\pi$
$557$	3.12642	+	3.12642i	0.132471	+	0.132471i	−0.637763	+	0.770233i	$0.720140\pi$
$558$		0			0
$559$	−5.19733			−0.219824
$560$		0			0
$561$		−	31.2647i		−	1.31999i
$562$		0			0
$563$	−27.1285	−	27.1285i	−1.14333	−	1.14333i	−0.987837	−	0.155491i	$-0.950304\pi$
$563$	−27.1285	−	27.1285i	−1.14333	−	1.14333i	−0.155491	−	0.987837i	$-0.549696\pi$
$564$		0			0
$565$	−17.4644	−	17.4644i	−0.734733	−	0.734733i
$566$		0			0
$567$	−70.8858			−2.97693
$568$		0			0
$569$	−7.55363			−0.316665			−0.158332	−	0.987386i	$-0.550612\pi$
$569$	−7.55363			−0.316665			−0.158332	+	0.987386i	$0.550612\pi$
$570$		0			0
$571$	−10.1399	−	10.1399i	−0.424340	−	0.424340i	0.462355	−	0.886695i	$-0.347005\pi$
$571$	−10.1399	−	10.1399i	−0.424340	−	0.424340i	−0.886695	+	0.462355i	$0.847005\pi$
$572$		0			0
$573$	6.77101	−	6.77101i	0.282863	−	0.282863i
$574$		0			0
$575$			1.79254i			0.0747541i
$576$		0			0
$577$	−1.40934			−0.0586717			−0.0293359	−	0.999570i	$-0.509339\pi$
$577$	−1.40934			−0.0586717			−0.0293359	+	0.999570i	$0.509339\pi$
$578$		0			0
$579$	−20.9349	+	20.9349i	−0.870023	+	0.870023i
$580$		0			0
$581$	−37.9522	+	37.9522i	−1.57452	+	1.57452i
$582$		0			0
$583$		−	4.32575i		−	0.179154i
$584$		0			0
$585$	−19.8112			−0.819091
$586$		0			0
$587$	−23.8247	−	23.8247i	−0.983351	−	0.983351i	0.0165127	−	0.999864i	$-0.494744\pi$
$587$	−23.8247	−	23.8247i	−0.983351	−	0.983351i	−0.999864	+	0.0165127i	$0.994744\pi$
$588$		0			0
$589$	40.1639	−	23.1796i	1.65492	−	0.955097i
$590$		0			0
$591$	−49.7578			−2.04676
$592$		0			0
$593$	6.52343			0.267885			0.133943	−	0.990989i	$-0.457236\pi$
$593$	6.52343			0.267885			0.133943	+	0.990989i	$0.457236\pi$
$594$		0			0
$595$	27.4990	−	27.4990i	1.12735	−	1.12735i
$596$		0			0
$597$	34.8853	+	34.8853i	1.42776	+	1.42776i
$598$		0			0
$599$			14.4203i			0.589199i	0.955621	+	0.294600i	$0.0951863\pi$
$599$			14.4203i			0.589199i	−0.955621	+	0.294600i	$0.904814\pi$
$600$		0			0
$601$	−29.9230			−1.22058			−0.610292	−	0.792177i	$-0.708948\pi$
$601$	−29.9230			−1.22058			−0.610292	+	0.792177i	$0.708948\pi$
$602$		0			0
$603$	−39.6758	+	39.6758i	−1.61572	+	1.61572i
$604$		0			0
$605$	7.76059	+	7.76059i	0.315513	+	0.315513i
$606$		0			0
$607$	−23.7445			−0.963760			−0.481880	−	0.876237i	$-0.660046\pi$
$607$	−23.7445			−0.963760			−0.481880	+	0.876237i	$0.660046\pi$
$608$		0			0
$609$	70.2651			2.84729
$610$		0			0
$611$	−4.51892	−	4.51892i	−0.182816	−	0.182816i
$612$		0			0
$613$	13.0596	−	13.0596i	0.527473	−	0.527473i	−0.392345	−	0.919818i	$-0.628336\pi$
$613$	13.0596	−	13.0596i	0.527473	−	0.527473i	0.919818	+	0.392345i	$0.128336\pi$
$614$		0			0
$615$	−17.7915			−0.717421
$616$		0			0
$617$			12.4139i			0.499764i	0.968276	+	0.249882i	$0.0803918\pi$
$617$			12.4139i			0.499764i	−0.968276	+	0.249882i	$0.919608\pi$
$618$		0			0
$619$	12.2337	+	12.2337i	0.491713	+	0.491713i	0.908845	−	0.417133i	$-0.136965\pi$
$619$	12.2337	+	12.2337i	0.491713	+	0.491713i	−0.417133	+	0.908845i	$0.636965\pi$
$620$		0			0
$621$	8.76202	−	8.76202i	0.351608	−	0.351608i
$622$		0			0
$623$	3.40219			0.136306
$624$		0			0
$625$	14.2053			0.568212
$626$		0			0
$627$	−15.1517	−	26.2537i	−0.605100	−	1.04847i
$628$		0			0
$629$	−18.6724	−	18.6724i	−0.744516	−	0.744516i
$630$		0			0
$631$	11.3028			0.449959			0.224979	−	0.974364i	$-0.427768\pi$
$631$	11.3028			0.449959			0.224979	+	0.974364i	$0.427768\pi$
$632$		0			0
$633$			5.71003i			0.226953i
$634$		0			0
$635$	1.03979	−	1.03979i	0.0412628	−	0.0412628i
$636$		0			0
$637$	17.4883	−	17.4883i	0.692912	−	0.692912i
$638$		0			0
$639$	−17.0264			−0.673552
$640$		0			0
$641$		−	47.3208i		−	1.86906i	−0.355884	−	0.934530i	$-0.615820\pi$
$641$		−	47.3208i		−	1.86906i	0.355884	−	0.934530i	$-0.384180\pi$
$642$		0			0
$643$	14.9315	−	14.9315i	0.588840	−	0.588840i	−0.348477	−	0.937317i	$-0.613301\pi$
$643$	14.9315	−	14.9315i	0.588840	−	0.588840i	0.937317	+	0.348477i	$0.113301\pi$
$644$		0			0
$645$	−12.8627	−	12.8627i	−0.506467	−	0.506467i
$646$		0			0
$647$	−23.3524			−0.918077			−0.459039	−	0.888416i	$-0.651806\pi$
$647$	−23.3524			−0.918077			−0.459039	+	0.888416i	$0.651806\pi$
$648$		0			0
$649$	3.73662			0.146675
$650$		0			0
$651$	109.964	+	109.964i	4.30982	+	4.30982i
$652$		0			0
$653$	−4.45146	−	4.45146i	−0.174199	−	0.174199i	0.614622	−	0.788821i	$-0.289308\pi$
$653$	−4.45146	−	4.45146i	−0.174199	−	0.174199i	−0.788821	+	0.614622i	$0.789308\pi$
$654$		0			0
$655$			12.5553i			0.490576i
$656$		0			0
$657$	−51.3805			−2.00455
$658$		0			0
$659$	26.2089	+	26.2089i	1.02095	+	1.02095i	0.999776	+	0.0211773i	$0.00674146\pi$
$659$	26.2089	+	26.2089i	1.02095	+	1.02095i	0.0211773	+	0.999776i	$0.493259\pi$
$660$		0			0
$661$	−13.2264	−	13.2264i	−0.514445	−	0.514445i	0.401440	−	0.915885i	$-0.368510\pi$
$661$	−13.2264	−	13.2264i	−0.514445	−	0.514445i	−0.915885	+	0.401440i	$0.868510\pi$
$662$		0			0
$663$	22.7089			0.881939
$664$		0			0
$665$	9.76489	−	36.4184i	0.378666	−	1.41225i
$666$		0			0
$667$	−3.74129	+	3.74129i	−0.144863	+	0.144863i
$668$		0			0
$669$	33.2257	+	33.2257i	1.28458	+	1.28458i
$670$		0			0
$671$		−	19.8393i		−	0.765888i
$672$		0			0
$673$			20.5186i			0.790935i	0.918480	+	0.395468i	$0.129417\pi$
$673$			20.5186i			0.790935i	−0.918480	+	0.395468i	$0.870583\pi$
$674$		0			0
$675$	12.9635	+	12.9635i	0.498965	+	0.498965i
$676$		0			0
$677$	28.5420	+	28.5420i	1.09696	+	1.09696i	0.994765	+	0.102193i	$0.0325858\pi$
$677$	28.5420	+	28.5420i	1.09696	+	1.09696i	0.102193	+	0.994765i	$0.467414\pi$
$678$		0			0
$679$		−	51.2899i		−	1.96833i
$680$		0			0
$681$		−	50.7215i		−	1.94365i
$682$		0			0
$683$	0.485516	−	0.485516i	0.0185778	−	0.0185778i	−0.697757	−	0.716335i	$-0.745818\pi$
$683$	0.485516	−	0.485516i	0.0185778	−	0.0185778i	0.716335	+	0.697757i	$0.245818\pi$
$684$		0			0
$685$	17.9182	+	17.9182i	0.684618	+	0.684618i
$686$		0			0
$687$	−13.6651			−0.521355
$688$		0			0
$689$	3.14198			0.119700
$690$		0			0
$691$	3.92483	−	3.92483i	0.149308	−	0.149308i	−0.628501	−	0.777809i	$-0.716331\pi$
$691$	3.92483	−	3.92483i	0.149308	−	0.149308i	0.777809	+	0.628501i	$0.216331\pi$
$692$		0			0
$693$	49.4827	−	49.4827i	1.87969	−	1.87969i
$694$		0			0
$695$	−23.2427			−0.881644
$696$		0			0
$697$	14.0393			0.531775
$698$		0			0
$699$	36.1879	−	36.1879i	1.36875	−	1.36875i
$700$		0			0
$701$	−5.69748	−	5.69748i	−0.215191	−	0.215191i	0.591277	−	0.806468i	$-0.298624\pi$
$701$	−5.69748	−	5.69748i	−0.215191	−	0.215191i	−0.806468	+	0.591277i	$0.798624\pi$
$702$		0			0
$703$	−24.7288	−	6.63054i	−0.932664	−	0.250076i
$704$		0			0
$705$		−	22.3674i		−	0.842405i
$706$		0			0
$707$	−42.3686	+	42.3686i	−1.59344	+	1.59344i
$708$		0			0
$709$	−21.4692	+	21.4692i	−0.806292	+	0.806292i	−0.984071	−	0.177778i	$-0.943109\pi$
$709$	−21.4692	+	21.4692i	−0.806292	+	0.806292i	0.177778	+	0.984071i	$0.443109\pi$
$710$		0			0
$711$		−	22.4853i		−	0.843264i
$712$		0			0
$713$	−11.7101			−0.438547
$714$		0			0
$715$	4.73675	−	4.73675i	0.177144	−	0.177144i
$716$		0			0
$717$	0.793644	−	0.793644i	0.0296392	−	0.0296392i
$718$		0			0
$719$		−	13.1745i		−	0.491327i	−0.969355	−	0.245664i	$-0.920994\pi$
$719$		−	13.1745i		−	0.491327i	0.969355	−	0.245664i	$-0.0790059\pi$
$720$		0			0
$721$			55.5014i			2.06698i
$722$		0			0
$723$	39.3233	−	39.3233i	1.46245	−	1.46245i
$724$		0			0
$725$	−5.53528	−	5.53528i	−0.205575	−	0.205575i
$726$		0			0
$727$	−11.8970			−0.441234			−0.220617	−	0.975360i	$-0.570807\pi$
$727$	−11.8970			−0.441234			−0.220617	+	0.975360i	$0.570807\pi$
$728$		0			0
$729$			5.06117i			0.187451i
$730$		0			0
$731$	10.1500	+	10.1500i	0.375410	+	0.375410i
$732$		0			0
$733$	−4.21189	−	4.21189i	−0.155570	−	0.155570i	0.625031	−	0.780600i	$-0.285086\pi$
$733$	−4.21189	−	4.21189i	−0.155570	−	0.155570i	−0.780600	+	0.625031i	$0.785086\pi$
$734$		0			0
$735$	86.5622			3.19290
$736$		0			0
$737$		−	18.9726i		−	0.698863i
$738$		0			0
$739$	4.42329	−	4.42329i	0.162713	−	0.162713i	−0.621054	−	0.783768i	$-0.713295\pi$
$739$	4.42329	−	4.42329i	0.162713	−	0.162713i	0.783768	+	0.621054i	$0.213295\pi$
$740$		0			0
$741$	19.0692	−	11.0053i	0.700525	−	0.404290i
$742$		0			0
$743$			44.5601i			1.63475i	0.576105	+	0.817376i	$0.304572\pi$
$743$			44.5601i			1.63475i	−0.576105	+	0.817376i	$0.695428\pi$
$744$		0			0
$745$			1.18169i			0.0432936i
$746$		0			0
$747$	−53.3965	−	53.3965i	−1.95368	−	1.95368i
$748$		0			0
$749$	−57.0650	+	57.0650i	−2.08511	+	2.08511i
$750$		0			0
$751$	0.774702			0.0282693			0.0141346	−	0.999900i	$-0.495501\pi$
$751$	0.774702			0.0282693			0.0141346	+	0.999900i	$0.495501\pi$
$752$		0			0
$753$		−	58.6466i		−	2.13720i
$754$		0			0
$755$	−22.9917	−	22.9917i	−0.836753	−	0.836753i
$756$		0			0
$757$	4.08476	−	4.08476i	0.148463	−	0.148463i	−0.628968	−	0.777431i	$-0.716522\pi$
$757$	4.08476	−	4.08476i	0.148463	−	0.148463i	0.777431	+	0.628968i	$0.216522\pi$
$758$		0			0
$759$			7.65450i			0.277841i
$760$		0			0
$761$			37.8011i			1.37029i	0.728407	+	0.685144i	$0.240261\pi$
$761$			37.8011i			1.37029i	−0.728407	+	0.685144i	$0.759739\pi$
$762$		0			0
$763$	4.27955	−	4.27955i	0.154930	−	0.154930i
$764$		0			0
$765$	38.6896	+	38.6896i	1.39882	+	1.39882i
$766$		0			0
$767$			2.71407i			0.0979992i
$768$		0			0
$769$	−7.74433			−0.279268			−0.139634	−	0.990203i	$-0.544593\pi$
$769$	−7.74433			−0.279268			−0.139634	+	0.990203i	$0.544593\pi$
$770$		0			0
$771$	−6.65267	+	6.65267i	−0.239590	+	0.239590i
$772$		0			0
$773$	−15.8591	−	15.8591i	−0.570411	−	0.570411i	0.361832	−	0.932243i	$-0.382151\pi$
$773$	−15.8591	−	15.8591i	−0.570411	−	0.570411i	−0.932243	+	0.361832i	$0.882151\pi$
$774$		0			0
$775$		−	17.3252i		−	0.622341i
$776$		0			0
$777$		−	85.8580i		−	3.08014i
$778$		0			0
$779$	11.7891	−	6.80380i	0.422390	−	0.243771i
$780$		0			0
$781$	4.07092	−	4.07092i	0.145669	−	0.145669i
$782$		0			0
$783$			54.1134i			1.93385i
$784$		0			0
$785$	−0.578121			−0.0206340
$786$		0			0
$787$	18.0270	+	18.0270i	0.642595	+	0.642595i	0.951193	−	0.308598i	$-0.0998597\pi$
$787$	18.0270	+	18.0270i	0.642595	+	0.642595i	−0.308598	+	0.951193i	$0.599860\pi$
$788$		0			0
$789$	18.8166	+	18.8166i	0.669888	+	0.669888i
$790$		0			0
$791$			63.3678i			2.25310i
$792$		0			0
$793$	14.4102			0.511719
$794$		0			0
$795$	7.77596	+	7.77596i	0.275785	+	0.275785i
$796$		0			0
$797$	−12.7483	+	12.7483i	−0.451570	+	0.451570i	−0.895875	−	0.444306i	$-0.853450\pi$
$797$	−12.7483	+	12.7483i	−0.451570	+	0.451570i	0.444306	+	0.895875i	$0.353450\pi$
$798$		0			0
$799$			17.6501i			0.624417i
$800$		0			0
$801$			4.78668i			0.169129i
$802$		0			0
$803$	12.2848	−	12.2848i	0.433522	−	0.433522i
$804$		0			0
$805$	−6.73256	+	6.73256i	−0.237292	+	0.237292i
$806$		0			0
$807$	−56.2268			−1.97928
$808$		0			0
$809$		−	7.53879i		−	0.265050i	−0.991180	−	0.132525i	$-0.957692\pi$
$809$		−	7.53879i		−	0.265050i	0.991180	−	0.132525i	$-0.0423084\pi$
$810$		0			0
$811$	−38.0934	+	38.0934i	−1.33764	+	1.33764i	−0.439299	+	0.898341i	$0.644773\pi$
$811$	−38.0934	+	38.0934i	−1.33764	+	1.33764i	−0.898341	+	0.439299i	$0.855227\pi$
$812$		0			0
$813$	−43.6192	+	43.6192i	−1.52979	+	1.52979i
$814$		0			0
$815$			29.6170i			1.03744i
$816$		0			0
$817$	13.4421	+	3.60424i	0.470280	+	0.126096i
$818$		0			0
$819$	35.9414	+	35.9414i	1.25589	+	1.25589i
$820$		0			0
$821$	−6.99026	+	6.99026i	−0.243962	+	0.243962i	−0.818487	−	0.574525i	$-0.805187\pi$
$821$	−6.99026	+	6.99026i	−0.243962	+	0.243962i	0.574525	+	0.818487i	$0.305187\pi$
$822$		0			0
$823$	−53.6796			−1.87115			−0.935576	−	0.353126i	$-0.885119\pi$
$823$	−53.6796			−1.87115			−0.935576	+	0.353126i	$0.885119\pi$
$824$		0			0
$825$	−11.3249			−0.394283
$826$		0			0
$827$	15.1806	−	15.1806i	0.527882	−	0.527882i	−0.392058	−	0.919940i	$-0.628237\pi$
$827$	15.1806	−	15.1806i	0.527882	−	0.527882i	0.919940	+	0.392058i	$0.128237\pi$
$828$		0			0
$829$	13.8098	−	13.8098i	0.479635	−	0.479635i	−0.425380	−	0.905015i	$-0.639859\pi$
$829$	13.8098	−	13.8098i	0.479635	−	0.479635i	0.905015	+	0.425380i	$0.139859\pi$
$830$		0			0
$831$	15.6111			0.541542
$832$		0			0
$833$	−68.3064			−2.36668
$834$		0			0
$835$	11.7562	+	11.7562i	0.406842	+	0.406842i
$836$		0			0
$837$	−84.6866	+	84.6866i	−2.92720	+	2.92720i
$838$		0			0
$839$		−	39.1275i		−	1.35083i	−0.737438	−	0.675415i	$-0.763964\pi$
$839$		−	39.1275i		−	1.35083i	0.737438	−	0.675415i	$-0.236036\pi$
$840$		0			0
$841$			5.89418i			0.203247i
$842$		0			0
$843$	−10.1435	−	10.1435i	−0.349360	−	0.349360i
$844$		0			0
$845$	−13.4382	−	13.4382i	−0.462287	−	0.462287i
$846$		0			0
$847$		−	28.1585i		−	0.967538i
$848$		0			0
$849$			52.7222i			1.80942i
$850$		0			0
$851$	4.57154	+	4.57154i	0.156710	+	0.156710i
$852$		0			0
$853$	14.8382	−	14.8382i	0.508050	−	0.508050i	−0.405877	−	0.913928i	$-0.633034\pi$
$853$	14.8382	−	14.8382i	0.508050	−	0.508050i	0.913928	+	0.405877i	$0.133034\pi$
$854$		0			0
$855$	51.2386	+	13.7386i	1.75232	+	0.469852i
$856$		0			0
$857$	−0.927011			−0.0316661			−0.0158330	−	0.999875i	$-0.505040\pi$
$857$	−0.927011			−0.0316661			−0.0158330	+	0.999875i	$0.505040\pi$
$858$		0			0
$859$	24.5697	+	24.5697i	0.838306	+	0.838306i	0.988636	−	0.150330i	$-0.0480335\pi$
$859$	24.5697	+	24.5697i	0.838306	+	0.838306i	−0.150330	+	0.988636i	$0.548033\pi$
$860$		0			0
$861$	32.2772	+	32.2772i	1.10001	+	1.10001i
$862$		0			0
$863$	−13.1563			−0.447844			−0.223922	−	0.974607i	$-0.571886\pi$
$863$	−13.1563			−0.447844			−0.223922	+	0.974607i	$0.571886\pi$
$864$		0			0
$865$		−	23.6606i		−	0.804486i
$866$		0			0
$867$	−7.04901	−	7.04901i	−0.239397	−	0.239397i
$868$		0			0
$869$	5.37612	+	5.37612i	0.182372	+	0.182372i
$870$		0			0
$871$	13.7806			0.466937
$872$		0			0
$873$	72.1620			2.44231
$874$		0			0
$875$	−40.5435	−	40.5435i	−1.37062	−	1.37062i
$876$		0			0
$877$	−2.59841	+	2.59841i	−0.0877419	+	0.0877419i	−0.749615	−	0.661874i	$-0.769762\pi$
$877$	−2.59841	+	2.59841i	−0.0877419	+	0.0877419i	0.661874	+	0.749615i	$0.269762\pi$
$878$		0			0
$879$			6.16341i			0.207887i
$880$		0			0
$881$	39.7570			1.33945			0.669724	−	0.742610i	$-0.266412\pi$
$881$	39.7570			1.33945			0.669724	+	0.742610i	$0.266412\pi$
$882$		0			0
$883$	30.0827	−	30.0827i	1.01236	−	1.01236i	0.0124409	−	0.999923i	$-0.496040\pi$
$883$	30.0827	−	30.0827i	1.01236	−	1.01236i	0.999923	−	0.0124409i	$-0.00396016\pi$
$884$		0			0
$885$	−6.71694	+	6.71694i	−0.225787	+	0.225787i
$886$		0			0
$887$			51.4632i			1.72796i	0.503523	+	0.863982i	$0.332037\pi$
$887$			51.4632i			1.72796i	−0.503523	+	0.863982i	$0.667963\pi$
$888$		0			0
$889$	−3.77277			−0.126535
$890$		0			0
$891$	23.8455	+	23.8455i	0.798854	+	0.798854i
$892$		0			0
$893$	8.55372	+	14.8213i	0.286239	+	0.495975i
$894$		0			0
$895$	32.2115			1.07671
$896$		0			0
$897$	−5.55979			−0.185636
$898$		0			0
$899$	36.1603	−	36.1603i	1.20601	−	1.20601i
$900$		0			0
$901$	−6.13602	−	6.13602i	−0.204420	−	0.204420i
$902$		0			0
$903$			46.6708i			1.55311i
$904$		0			0
$905$	19.9627			0.663584
$906$		0			0
$907$	39.2649	−	39.2649i	1.30377	−	1.30377i	0.377939	−	0.925831i	$-0.376633\pi$
$907$	39.2649	−	39.2649i	1.30377	−	1.30377i	0.925831	−	0.377939i	$-0.123367\pi$
$908$		0			0
$909$	−59.6103	−	59.6103i	−1.97715	−	1.97715i
$910$		0			0
$911$	50.2183			1.66381			0.831903	−	0.554921i	$-0.187251\pi$
$911$	50.2183			1.66381			0.831903	+	0.554921i	$0.187251\pi$
$912$		0			0
$913$	25.5337			0.845042
$914$		0			0
$915$	35.6631	+	35.6631i	1.17899	+	1.17899i
$916$		0			0
$917$	22.7778	−	22.7778i	0.752189	−	0.752189i
$918$		0			0
$919$	−17.5959			−0.580434			−0.290217	−	0.956961i	$-0.593728\pi$
$919$	−17.5959			−0.580434			−0.290217	+	0.956961i	$0.593728\pi$
$920$		0			0
$921$		−	5.29686i		−	0.174537i
$922$		0			0
$923$	2.95688	+	2.95688i	0.0973270	+	0.0973270i
$924$		0			0
$925$	−6.76364	+	6.76364i	−0.222387	+	0.222387i
$926$		0			0
$927$	−78.0874			−2.56473
$928$		0			0
$929$	−33.6911			−1.10537			−0.552685	−	0.833390i	$-0.686397\pi$
$929$	−33.6911			−1.10537			−0.552685	+	0.833390i	$0.686397\pi$
$930$		0			0
$931$	−57.3586	+	33.1031i	−1.87985	+	1.08491i
$932$		0			0
$933$	42.5449	+	42.5449i	1.39286	+	1.39286i
$934$		0			0
$935$	−18.5010			−0.605046
$936$		0			0
$937$			39.7834i			1.29967i	0.760077	+	0.649833i	$0.225161\pi$
$937$			39.7834i			1.29967i	−0.760077	+	0.649833i	$0.774839\pi$
$938$		0			0
$939$	30.1854	−	30.1854i	0.985064	−	0.985064i
$940$		0			0
$941$	24.1141	−	24.1141i	0.786099	−	0.786099i	−0.194754	−	0.980852i	$-0.562391\pi$
$941$	24.1141	−	24.1141i	0.786099	−	0.786099i	0.980852	+	0.194754i	$0.0623907\pi$
$942$		0			0
$943$	−3.43722			−0.111931
$944$		0			0
$945$			97.3786i			3.16773i
$946$		0			0
$947$	−36.4084	+	36.4084i	−1.18311	+	1.18311i	−0.204182	+	0.978933i	$0.565453\pi$
$947$	−36.4084	+	36.4084i	−1.18311	+	1.18311i	−0.978933	+	0.204182i	$0.934547\pi$
$948$		0			0
$949$	8.92300	+	8.92300i	0.289653	+	0.289653i
$950$		0			0
$951$	58.3426			1.89189
$952$		0			0
$953$	7.29438			0.236288			0.118144	−	0.992996i	$-0.462306\pi$
$953$	7.29438			0.236288			0.118144	+	0.992996i	$0.462306\pi$
$954$		0			0
$955$	−4.00677	−	4.00677i	−0.129656	−	0.129656i
$956$		0			0
$957$	−23.6367	−	23.6367i	−0.764066	−	0.764066i
$958$		0			0
$959$		−	65.0142i		−	2.09942i
$960$		0			0
$961$	82.1805			2.65098
$962$		0			0
$963$	−80.2872	−	80.2872i	−2.58722	−	2.58722i
$964$		0			0
$965$	12.3883	+	12.3883i	0.398793	+	0.398793i
$966$		0			0
$967$	33.4855			1.07682			0.538410	−	0.842683i	$-0.319025\pi$
$967$	33.4855			1.07682			0.538410	+	0.842683i	$0.319025\pi$
$968$		0			0
$969$	−58.7331	−	15.7481i	−1.88678	−	0.505903i
$970$		0			0
$971$	20.2658	−	20.2658i	0.650360	−	0.650360i	−0.302719	−	0.953080i	$-0.597895\pi$
$971$	20.2658	−	20.2658i	0.650360	−	0.650360i	0.953080	+	0.302719i	$0.0978945\pi$
$972$		0			0
$973$	42.1668	+	42.1668i	1.35180	+	1.35180i
$974$		0			0
$975$		−	8.22577i		−	0.263435i
$976$		0			0
$977$			4.46381i			0.142810i	0.997447	+	0.0714050i	$0.0227483\pi$
$977$			4.46381i			0.142810i	−0.997447	+	0.0714050i	$0.977252\pi$
$978$		0			0
$979$	−1.14447	−	1.14447i	−0.0365775	−	0.0365775i
$980$		0			0
$981$	6.02108	+	6.02108i	0.192238	+	0.192238i
$982$		0			0
$983$		−	2.33954i		−	0.0746198i	−0.999304	−	0.0373099i	$-0.988121\pi$
$983$		−	2.33954i		−	0.0746198i	0.999304	−	0.0373099i	$-0.0118789\pi$
$984$		0			0
$985$			29.4444i			0.938176i
$986$		0			0
$987$	−40.5789	+	40.5789i	−1.29164	+	1.29164i
$988$		0			0
$989$	−2.48500	−	2.48500i	−0.0790185	−	0.0790185i
$990$		0			0
$991$	50.7347			1.61164			0.805820	−	0.592160i	$-0.201725\pi$
$991$	50.7347			1.61164			0.805820	+	0.592160i	$0.201725\pi$
$992$		0			0
$993$	−49.5555			−1.57260
$994$		0			0
$995$	20.6435	−	20.6435i	0.654444	−	0.654444i
$996$		0			0
$997$	4.14003	−	4.14003i	0.131116	−	0.131116i	−0.638503	−	0.769619i	$-0.720446\pi$
$997$	4.14003	−	4.14003i	0.131116	−	0.131116i	0.769619	+	0.638503i	$0.220446\pi$
$998$		0			0
$999$	66.1219			2.09201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.m.a.303.2		76
4.3	odd	2		304.2.m.a.227.6	yes	76
16.5	even	4		304.2.m.a.75.33	yes	76
16.11	odd	4	inner	1216.2.m.a.911.37		76
19.18	odd	2	inner	1216.2.m.a.303.37		76
76.75	even	2		304.2.m.a.227.33	yes	76
304.37	odd	4		304.2.m.a.75.6	✓	76
304.75	even	4	inner	1216.2.m.a.911.2		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.6	✓	76	304.37	odd	4
304.2.m.a.75.33	yes	76	16.5	even	4
304.2.m.a.227.6	yes	76	4.3	odd	2
304.2.m.a.227.33	yes	76	76.75	even	2
1216.2.m.a.303.2		76	1.1	even	1	trivial
1216.2.m.a.303.37		76	19.18	odd	2	inner
1216.2.m.a.911.2		76	304.75	even	4	inner
1216.2.m.a.911.37		76	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.19409 - 2.19409i) q^{3} +(-1.29836 + 1.29836i) q^{5} +4.71096 q^{7} +6.62806i q^{9} +(-1.58474 - 1.58474i) q^{11} +(1.15106 - 1.15106i) q^{13} +5.69744 q^{15} -4.49586 q^{17} +(-3.77529 + 2.17881i) q^{19} +(-10.3363 - 10.3363i) q^{21} +1.10072 q^{23} +1.62852i q^{25} +(7.96029 - 7.96029i) q^{27} +(-3.39896 + 3.39896i) q^{29} -10.6386 q^{31} +6.95410i q^{33} +(-6.11653 + 6.11653i) q^{35} +(4.15324 + 4.15324i) q^{37} -5.05107 q^{39} -3.12271 q^{41} +(-2.25762 - 2.25762i) q^{43} +(-8.60561 - 8.60561i) q^{45} -3.92587i q^{47} +15.1932 q^{49} +(9.86431 + 9.86431i) q^{51} +(1.36482 + 1.36482i) q^{53} +4.11512 q^{55} +(13.0638 + 3.50281i) q^{57} +(-1.17894 + 1.17894i) q^{59} +(6.25950 + 6.25950i) q^{61} +31.2246i q^{63} +2.98899i q^{65} +(5.98603 + 5.98603i) q^{67} +(-2.41507 - 2.41507i) q^{69} +2.56883i q^{71} +7.75197i q^{73} +(3.57312 - 3.57312i) q^{75} +(-7.46563 - 7.46563i) q^{77} -3.39244 q^{79} -15.0470 q^{81} +(-8.05613 + 8.05613i) q^{83} +(5.83724 - 5.83724i) q^{85} +14.9152 q^{87} +0.722185 q^{89} +(5.42261 - 5.42261i) q^{91} +(23.3421 + 23.3421i) q^{93} +(2.07280 - 7.73056i) q^{95} -10.8873i q^{97} +(10.5037 - 10.5037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Introduction

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