LMFDB - Embedded newform 954.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [954,2,Mod(1,954)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(954, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("954.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 954 = 2 \cdot 3^{2} \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	954.a (trivial)

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:	yes
Analytic conductor:	$7.61772835283$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 106)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	954.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{8} +4.00000 q^{10} +4.00000 q^{11} +1.00000 q^{13} +1.00000 q^{16} -5.00000 q^{17} -7.00000 q^{19} +4.00000 q^{20} +4.00000 q^{22} -1.00000 q^{23} +11.0000 q^{25} +1.00000 q^{26} -5.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} -5.00000 q^{34} +1.00000 q^{37} -7.00000 q^{38} +4.00000 q^{40} +10.0000 q^{41} -10.0000 q^{43} +4.00000 q^{44} -1.00000 q^{46} +6.00000 q^{47} -7.00000 q^{49} +11.0000 q^{50} +1.00000 q^{52} +1.00000 q^{53} +16.0000 q^{55} -5.00000 q^{58} +6.00000 q^{59} +4.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +4.00000 q^{65} +4.00000 q^{67} -5.00000 q^{68} -15.0000 q^{71} -8.00000 q^{73} +1.00000 q^{74} -7.00000 q^{76} +1.00000 q^{79} +4.00000 q^{80} +10.0000 q^{82} +3.00000 q^{83} -20.0000 q^{85} -10.0000 q^{86} +4.00000 q^{88} -2.00000 q^{89} -1.00000 q^{92} +6.00000 q^{94} -28.0000 q^{95} +17.0000 q^{97} -7.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	4.00000	1.26491
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	0	0
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	4.00000	0.894427
$21$	0	0
$22$	4.00000	0.852803
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	1.00000	0.196116
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−5.00000	−0.857493
$35$	0	0
$36$	0	0
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	−7.00000	−1.13555
$39$	0	0
$40$	4.00000	0.632456
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−1.00000	−0.147442
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	11.0000	1.55563
$51$	0	0
$52$	1.00000	0.138675
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	0	0
$55$	16.0000	2.15744
$56$	0	0
$57$	0	0
$58$	−5.00000	−0.656532
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−5.00000	−0.606339
$69$	0	0
$70$	0	0
$71$	−15.0000	−1.78017	−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000	−1.78017	−0.890086	+	0.455792i	$0.849356\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−7.00000	−0.802955
$77$	0	0
$78$	0	0
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	10.0000	1.10432
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	0	0
$85$	−20.0000	−2.16930
$86$	−10.0000	−1.07833
$87$	0	0
$88$	4.00000	0.426401
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	0	0
$92$	−1.00000	−0.104257
$93$	0	0
$94$	6.00000	0.618853
$95$	−28.0000	−2.87274
$96$	0	0
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	−7.00000	−0.707107
$99$	0	0
$100$	11.0000	1.10000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	−15.0000	−1.47799	−0.738997	−	0.673709i	$-0.764700\pi$
$103$	−15.0000	−1.47799	−0.738997	+	0.673709i	$0.764700\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	1.00000	0.0971286
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0	0
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	16.0000	1.52554
$111$	0	0
$112$	0	0
$113$	9.00000	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	−5.00000	−0.464238
$117$	0	0
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	4.00000	0.362143
$123$	0	0
$124$	−4.00000	−0.359211
$125$	24.0000	2.14663
$126$	0	0
$127$	−5.00000	−0.443678	−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000	−0.443678	−0.221839	+	0.975083i	$0.571206\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	0	0
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	−5.00000	−0.428746
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	0	0
$142$	−15.0000	−1.25877
$143$	4.00000	0.334497
$144$	0	0
$145$	−20.0000	−1.66091
$146$	−8.00000	−0.662085
$147$	0	0
$148$	1.00000	0.0821995
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	0	0
$151$	−5.00000	−0.406894	−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000	−0.406894	−0.203447	+	0.979086i	$0.565214\pi$
$152$	−7.00000	−0.567775
$153$	0	0
$154$	0	0
$155$	−16.0000	−1.28515
$156$	0	0
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	4.00000	0.316228
$161$	0	0
$162$	0	0
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	3.00000	0.232845
$167$	−19.0000	−1.47026	−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000	−1.47026	−0.735132	+	0.677924i	$0.762880\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	−20.0000	−1.53393
$171$	0	0
$172$	−10.0000	−0.762493
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−2.00000	−0.149906
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	4.00000	0.294086
$186$	0	0
$187$	−20.0000	−1.46254
$188$	6.00000	0.437595
$189$	0	0
$190$	−28.0000	−2.03133
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	0	0
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	17.0000	1.22053
$195$	0	0
$196$	−7.00000	−0.500000
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	14.0000	0.985037
$203$	0	0
$204$	0	0
$205$	40.0000	2.79372
$206$	−15.0000	−1.04510
$207$	0	0
$208$	1.00000	0.0693375
$209$	−28.0000	−1.93680
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	1.00000	0.0686803
$213$	0	0
$214$	−6.00000	−0.410152
$215$	−40.0000	−2.72798
$216$	0	0
$217$	0	0
$218$	16.0000	1.08366
$219$	0	0
$220$	16.0000	1.07872
$221$	−5.00000	−0.336336
$222$	0	0
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	0	0
$225$	0	0
$226$	9.00000	0.598671
$227$	−22.0000	−1.46019	−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000	−1.46019	−0.730096	+	0.683345i	$0.760525\pi$
$228$	0	0
$229$	−15.0000	−0.991228	−0.495614	−	0.868543i	$-0.665057\pi$
$229$	−15.0000	−0.991228	−0.495614	+	0.868543i	$0.665057\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−8.00000	−0.524097	−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000	−0.524097	−0.262049	+	0.965055i	$0.584398\pi$
$234$	0	0
$235$	24.0000	1.56559
$236$	6.00000	0.390567
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	−3.00000	−0.193247	−0.0966235	−	0.995321i	$-0.530804\pi$
$241$	−3.00000	−0.193247	−0.0966235	+	0.995321i	$0.530804\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	4.00000	0.256074
$245$	−28.0000	−1.78885
$246$	0	0
$247$	−7.00000	−0.445399
$248$	−4.00000	−0.254000
$249$	0	0
$250$	24.0000	1.51789
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	−5.00000	−0.313728
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0	0
$259$	0	0
$260$	4.00000	0.248069
$261$	0	0
$262$	10.0000	0.617802
$263$	−28.0000	−1.72655	−0.863277	−	0.504730i	$-0.831592\pi$
$263$	−28.0000	−1.72655	−0.863277	+	0.504730i	$0.831592\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	0	0
$267$	0	0
$268$	4.00000	0.244339
$269$	19.0000	1.15845	0.579225	−	0.815168i	$-0.303355\pi$
$269$	19.0000	1.15845	0.579225	+	0.815168i	$0.303355\pi$
$270$	0	0
$271$	30.0000	1.82237	0.911185	−	0.411997i	$-0.135169\pi$
$271$	30.0000	1.82237	0.911185	+	0.411997i	$0.135169\pi$
$272$	−5.00000	−0.303170
$273$	0	0
$274$	−8.00000	−0.483298
$275$	44.0000	2.65330
$276$	0	0
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	−12.0000	−0.719712
$279$	0	0
$280$	0	0
$281$	31.0000	1.84930	0.924652	−	0.380812i	$-0.124356\pi$
$281$	31.0000	1.84930	0.924652	+	0.380812i	$0.124356\pi$
$282$	0	0
$283$	13.0000	0.772770	0.386385	−	0.922338i	$-0.373724\pi$
$283$	13.0000	0.772770	0.386385	+	0.922338i	$0.373724\pi$
$284$	−15.0000	−0.890086
$285$	0	0
$286$	4.00000	0.236525
$287$	0	0
$288$	0	0
$289$	8.00000	0.470588
$290$	−20.0000	−1.17444
$291$	0	0
$292$	−8.00000	−0.468165
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	0	0
$295$	24.0000	1.39733
$296$	1.00000	0.0581238
$297$	0	0
$298$	−15.0000	−0.868927
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	0	0
$302$	−5.00000	−0.287718
$303$	0	0
$304$	−7.00000	−0.401478
$305$	16.0000	0.916157
$306$	0	0
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	0	0
$309$	0	0
$310$	−16.0000	−0.908739
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	1.00000	0.0562544
$317$	17.0000	0.954815	0.477408	−	0.878682i	$-0.341577\pi$
$317$	17.0000	0.954815	0.477408	+	0.878682i	$0.341577\pi$
$318$	0	0
$319$	−20.0000	−1.11979
$320$	4.00000	0.223607
$321$	0	0
$322$	0	0
$323$	35.0000	1.94745
$324$	0	0
$325$	11.0000	0.610170
$326$	2.00000	0.110770
$327$	0	0
$328$	10.0000	0.552158
$329$	0	0
$330$	0	0
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	3.00000	0.164646
$333$	0	0
$334$	−19.0000	−1.03963
$335$	16.0000	0.874173
$336$	0	0
$337$	−10.0000	−0.544735	−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000	−0.544735	−0.272367	+	0.962193i	$0.587807\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	−20.0000	−1.08465
$341$	−16.0000	−0.866449
$342$	0	0
$343$	0	0
$344$	−10.0000	−0.539164
$345$	0	0
$346$	−2.00000	−0.107521
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	0	0
$351$	0	0
$352$	4.00000	0.213201
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	0	0
$355$	−60.0000	−3.18447
$356$	−2.00000	−0.106000
$357$	0	0
$358$	15.0000	0.792775
$359$	−7.00000	−0.369446	−0.184723	−	0.982791i	$-0.559139\pi$
$359$	−7.00000	−0.369446	−0.184723	+	0.982791i	$0.559139\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−2.00000	−0.105118
$363$	0	0
$364$	0	0
$365$	−32.0000	−1.67496
$366$	0	0
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	4.00000	0.207950
$371$	0	0
$372$	0	0
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	−20.0000	−1.03418
$375$	0	0
$376$	6.00000	0.309426
$377$	−5.00000	−0.257513
$378$	0	0
$379$	17.0000	0.873231	0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000	0.873231	0.436616	+	0.899648i	$0.356177\pi$
$380$	−28.0000	−1.43637
$381$	0	0
$382$	−13.0000	−0.665138
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	0	0
$385$	0	0
$386$	−12.0000	−0.610784
$387$	0	0
$388$	17.0000	0.863044
$389$	−20.0000	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$390$	0	0
$391$	5.00000	0.252861
$392$	−7.00000	−0.353553
$393$	0	0
$394$	2.00000	0.100759
$395$	4.00000	0.201262
$396$	0	0
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	0	0
$399$	0	0
$400$	11.0000	0.550000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	14.0000	0.696526
$405$	0	0
$406$	0	0
$407$	4.00000	0.198273
$408$	0	0
$409$	−21.0000	−1.03838	−0.519192	−	0.854658i	$-0.673767\pi$
$409$	−21.0000	−1.03838	−0.519192	+	0.854658i	$0.673767\pi$
$410$	40.0000	1.97546
$411$	0	0
$412$	−15.0000	−0.738997
$413$	0	0
$414$	0	0
$415$	12.0000	0.589057
$416$	1.00000	0.0490290
$417$	0	0
$418$	−28.0000	−1.36952
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	10.0000	0.486792
$423$	0	0
$424$	1.00000	0.0485643
$425$	−55.0000	−2.66789
$426$	0	0
$427$	0	0
$428$	−6.00000	−0.290021
$429$	0	0
$430$	−40.0000	−1.92897
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	17.0000	0.816968	0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000	0.816968	0.408484	+	0.912766i	$0.366058\pi$
$434$	0	0
$435$	0	0
$436$	16.0000	0.766261
$437$	7.00000	0.334855
$438$	0	0
$439$	2.00000	0.0954548	0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000	0.0954548	0.0477274	+	0.998860i	$0.484802\pi$
$440$	16.0000	0.762770
$441$	0	0
$442$	−5.00000	−0.237826
$443$	19.0000	0.902717	0.451359	−	0.892343i	$-0.350940\pi$
$443$	19.0000	0.902717	0.451359	+	0.892343i	$0.350940\pi$
$444$	0	0
$445$	−8.00000	−0.379236
$446$	−14.0000	−0.662919
$447$	0	0
$448$	0	0
$449$	27.0000	1.27421	0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000	1.27421	0.637104	+	0.770778i	$0.280132\pi$
$450$	0	0
$451$	40.0000	1.88353
$452$	9.00000	0.423324
$453$	0	0
$454$	−22.0000	−1.03251
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−15.0000	−0.700904
$459$	0	0
$460$	−4.00000	−0.186501
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	0	0
$463$	39.0000	1.81248	0.906242	−	0.422760i	$-0.138939\pi$
$463$	39.0000	1.81248	0.906242	+	0.422760i	$0.138939\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−8.00000	−0.370593
$467$	28.0000	1.29569	0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000	1.29569	0.647843	+	0.761774i	$0.275671\pi$
$468$	0	0
$469$	0	0
$470$	24.0000	1.10704
$471$	0	0
$472$	6.00000	0.276172
$473$	−40.0000	−1.83920
$474$	0	0
$475$	−77.0000	−3.53300
$476$	0	0
$477$	0	0
$478$	24.0000	1.09773
$479$	3.00000	0.137073	0.0685367	−	0.997649i	$-0.478167\pi$
$479$	3.00000	0.137073	0.0685367	+	0.997649i	$0.478167\pi$
$480$	0	0
$481$	1.00000	0.0455961
$482$	−3.00000	−0.136646
$483$	0	0
$484$	5.00000	0.227273
$485$	68.0000	3.08772
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	4.00000	0.181071
$489$	0	0
$490$	−28.0000	−1.26491
$491$	−33.0000	−1.48927	−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000	−1.48927	−0.744635	+	0.667472i	$0.767376\pi$
$492$	0	0
$493$	25.0000	1.12594
$494$	−7.00000	−0.314945
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	11.0000	0.492428	0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000	0.492428	0.246214	+	0.969216i	$0.420813\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	4.00000	0.178529
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	56.0000	2.49197
$506$	−4.00000	−0.177822
$507$	0	0
$508$	−5.00000	−0.221839
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.0000	0.529297
$515$	−60.0000	−2.64392
$516$	0	0
$517$	24.0000	1.05552
$518$	0	0
$519$	0	0
$520$	4.00000	0.175412
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	0	0
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	−28.0000	−1.22086
$527$	20.0000	0.871214
$528$	0	0
$529$	−22.0000	−0.956522
$530$	4.00000	0.173749
$531$	0	0
$532$	0	0
$533$	10.0000	0.433148
$534$	0	0
$535$	−24.0000	−1.03761
$536$	4.00000	0.172774
$537$	0	0
$538$	19.0000	0.819148
$539$	−28.0000	−1.20605
$540$	0	0
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	30.0000	1.28861
$543$	0	0
$544$	−5.00000	−0.214373
$545$	64.0000	2.74146
$546$	0	0
$547$	−14.0000	−0.598597	−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000	−0.598597	−0.299298	+	0.954160i	$0.596753\pi$
$548$	−8.00000	−0.341743
$549$	0	0
$550$	44.0000	1.87617
$551$	35.0000	1.49105
$552$	0	0
$553$	0	0
$554$	−16.0000	−0.679775
$555$	0	0
$556$	−12.0000	−0.508913
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	−10.0000	−0.422955
$560$	0	0
$561$	0	0
$562$	31.0000	1.30766
$563$	−45.0000	−1.89652	−0.948262	−	0.317489i	$-0.897160\pi$
$563$	−45.0000	−1.89652	−0.948262	+	0.317489i	$0.897160\pi$
$564$	0	0
$565$	36.0000	1.51453
$566$	13.0000	0.546431
$567$	0	0
$568$	−15.0000	−0.629386
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	0	0
$575$	−11.0000	−0.458732
$576$	0	0
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	−20.0000	−0.830455
$581$	0	0
$582$	0	0
$583$	4.00000	0.165663
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−10.0000	−0.413096
$587$	−24.0000	−0.990586	−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000	−0.990586	−0.495293	+	0.868726i	$0.664939\pi$
$588$	0	0
$589$	28.0000	1.15372
$590$	24.0000	0.988064
$591$	0	0
$592$	1.00000	0.0410997
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	0	0
$595$	0	0
$596$	−15.0000	−0.614424
$597$	0	0
$598$	−1.00000	−0.0408930
$599$	10.0000	0.408589	0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000	0.408589	0.204294	+	0.978909i	$0.434510\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	0	0
$604$	−5.00000	−0.203447
$605$	20.0000	0.813116
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−7.00000	−0.283887
$609$	0	0
$610$	16.0000	0.647821
$611$	6.00000	0.242734
$612$	0	0
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−16.0000	−0.642575
$621$	0	0
$622$	24.0000	0.962312
$623$	0	0
$624$	0	0
$625$	41.0000	1.64000
$626$	22.0000	0.879297
$627$	0	0
$628$	8.00000	0.319235
$629$	−5.00000	−0.199363
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	1.00000	0.0397779
$633$	0	0
$634$	17.0000	0.675156
$635$	−20.0000	−0.793676
$636$	0	0
$637$	−7.00000	−0.277350
$638$	−20.0000	−0.791808
$639$	0	0
$640$	4.00000	0.158114
$641$	34.0000	1.34292	0.671460	−	0.741041i	$-0.265668\pi$
$641$	34.0000	1.34292	0.671460	+	0.741041i	$0.265668\pi$
$642$	0	0
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	0	0
$645$	0	0
$646$	35.0000	1.37706
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	11.0000	0.431455
$651$	0	0
$652$	2.00000	0.0783260
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	40.0000	1.56293
$656$	10.0000	0.390434
$657$	0	0
$658$	0	0
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	3.00000	0.116686	0.0583432	−	0.998297i	$-0.481418\pi$
$661$	3.00000	0.116686	0.0583432	+	0.998297i	$0.481418\pi$
$662$	−12.0000	−0.466393
$663$	0	0
$664$	3.00000	0.116423
$665$	0	0
$666$	0	0
$667$	5.00000	0.193601
$668$	−19.0000	−0.735132
$669$	0	0
$670$	16.0000	0.618134
$671$	16.0000	0.617673
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	−12.0000	−0.461538
$677$	16.0000	0.614930	0.307465	−	0.951559i	$-0.400519\pi$
$677$	16.0000	0.614930	0.307465	+	0.951559i	$0.400519\pi$
$678$	0	0
$679$	0	0
$680$	−20.0000	−0.766965
$681$	0	0
$682$	−16.0000	−0.612672
$683$	2.00000	0.0765279	0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000	0.0765279	0.0382639	+	0.999268i	$0.487817\pi$
$684$	0	0
$685$	−32.0000	−1.22266
$686$	0	0
$687$	0	0
$688$	−10.0000	−0.381246
$689$	1.00000	0.0380970
$690$	0	0
$691$	43.0000	1.63580	0.817899	−	0.575362i	$-0.195139\pi$
$691$	43.0000	1.63580	0.817899	+	0.575362i	$0.195139\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	18.0000	0.683271
$695$	−48.0000	−1.82074
$696$	0	0
$697$	−50.0000	−1.89389
$698$	20.0000	0.757011
$699$	0	0
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−7.00000	−0.264010
$704$	4.00000	0.150756
$705$	0	0
$706$	−10.0000	−0.376355
$707$	0	0
$708$	0	0
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	−60.0000	−2.25176
$711$	0	0
$712$	−2.00000	−0.0749532
$713$	4.00000	0.149801
$714$	0	0
$715$	16.0000	0.598366
$716$	15.0000	0.560576
$717$	0	0
$718$	−7.00000	−0.261238
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	0	0
$722$	30.0000	1.11648
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	−55.0000	−2.04265
$726$	0	0
$727$	−18.0000	−0.667583	−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000	−0.667583	−0.333792	+	0.942647i	$0.608328\pi$
$728$	0	0
$729$	0	0
$730$	−32.0000	−1.18437
$731$	50.0000	1.84932
$732$	0	0
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	−18.0000	−0.664392
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	16.0000	0.589368
$738$	0	0
$739$	−3.00000	−0.110357	−0.0551784	−	0.998477i	$-0.517573\pi$
$739$	−3.00000	−0.110357	−0.0551784	+	0.998477i	$0.517573\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	0	0
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	0	0
$745$	−60.0000	−2.19823
$746$	2.00000	0.0732252
$747$	0	0
$748$	−20.0000	−0.731272
$749$	0	0
$750$	0	0
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	−5.00000	−0.182089
$755$	−20.0000	−0.727875
$756$	0	0
$757$	33.0000	1.19941	0.599703	−	0.800223i	$-0.295286\pi$
$757$	33.0000	1.19941	0.599703	+	0.800223i	$0.295286\pi$
$758$	17.0000	0.617468
$759$	0	0
$760$	−28.0000	−1.01567
$761$	−40.0000	−1.45000	−0.724999	−	0.688749i	$-0.758160\pi$
$761$	−40.0000	−1.45000	−0.724999	+	0.688749i	$0.758160\pi$
$762$	0	0
$763$	0	0
$764$	−13.0000	−0.470323
$765$	0	0
$766$	32.0000	1.15621
$767$	6.00000	0.216647
$768$	0	0
$769$	30.0000	1.08183	0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000	1.08183	0.540914	+	0.841078i	$0.318079\pi$
$770$	0	0
$771$	0	0
$772$	−12.0000	−0.431889
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	0	0
$775$	−44.0000	−1.58053
$776$	17.0000	0.610264
$777$	0	0
$778$	−20.0000	−0.717035
$779$	−70.0000	−2.50801
$780$	0	0
$781$	−60.0000	−2.14697
$782$	5.00000	0.178800
$783$	0	0
$784$	−7.00000	−0.250000
$785$	32.0000	1.14213
$786$	0	0
$787$	−12.0000	−0.427754	−0.213877	−	0.976861i	$-0.568609\pi$
$787$	−12.0000	−0.427754	−0.213877	+	0.976861i	$0.568609\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	4.00000	0.142314
$791$	0	0
$792$	0	0
$793$	4.00000	0.142044
$794$	18.0000	0.638796
$795$	0	0
$796$	0	0
$797$	44.0000	1.55856	0.779280	−	0.626676i	$-0.215585\pi$
$797$	44.0000	1.55856	0.779280	+	0.626676i	$0.215585\pi$
$798$	0	0
$799$	−30.0000	−1.06132
$800$	11.0000	0.388909
$801$	0	0
$802$	24.0000	0.847469
$803$	−32.0000	−1.12926
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	0	0
$808$	14.0000	0.492518
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	0	0
$811$	34.0000	1.19390	0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000	1.19390	0.596951	+	0.802278i	$0.296379\pi$
$812$	0	0
$813$	0	0
$814$	4.00000	0.140200
$815$	8.00000	0.280228
$816$	0	0
$817$	70.0000	2.44899
$818$	−21.0000	−0.734248
$819$	0	0
$820$	40.0000	1.39686
$821$	48.0000	1.67521	0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000	1.67521	0.837606	+	0.546275i	$0.183955\pi$
$822$	0	0
$823$	−18.0000	−0.627441	−0.313720	−	0.949515i	$-0.601575\pi$
$823$	−18.0000	−0.627441	−0.313720	+	0.949515i	$0.601575\pi$
$824$	−15.0000	−0.522550
$825$	0	0
$826$	0	0
$827$	−45.0000	−1.56480	−0.782402	−	0.622774i	$-0.786006\pi$
$827$	−45.0000	−1.56480	−0.782402	+	0.622774i	$0.786006\pi$
$828$	0	0
$829$	−38.0000	−1.31979	−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000	−1.31979	−0.659897	+	0.751356i	$0.729400\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	1.00000	0.0346688
$833$	35.0000	1.21268
$834$	0	0
$835$	−76.0000	−2.63009
$836$	−28.0000	−0.968400
$837$	0	0
$838$	−12.0000	−0.414533
$839$	2.00000	0.0690477	0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000	0.0690477	0.0345238	+	0.999404i	$0.489009\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−18.0000	−0.620321
$843$	0	0
$844$	10.0000	0.344214
$845$	−48.0000	−1.65125
$846$	0	0
$847$	0	0
$848$	1.00000	0.0343401
$849$	0	0
$850$	−55.0000	−1.88648
$851$	−1.00000	−0.0342796
$852$	0	0
$853$	8.00000	0.273915	0.136957	−	0.990577i	$-0.456268\pi$
$853$	8.00000	0.273915	0.136957	+	0.990577i	$0.456268\pi$
$854$	0	0
$855$	0	0
$856$	−6.00000	−0.205076
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	0	0
$859$	18.0000	0.614152	0.307076	−	0.951685i	$-0.400649\pi$
$859$	18.0000	0.614152	0.307076	+	0.951685i	$0.400649\pi$
$860$	−40.0000	−1.36399
$861$	0	0
$862$	0	0
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	−8.00000	−0.272008
$866$	17.0000	0.577684
$867$	0	0
$868$	0	0
$869$	4.00000	0.135691
$870$	0	0
$871$	4.00000	0.135535
$872$	16.0000	0.541828
$873$	0	0
$874$	7.00000	0.236779
$875$	0	0
$876$	0	0
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	2.00000	0.0674967
$879$	0	0
$880$	16.0000	0.539360
$881$	4.00000	0.134763	0.0673817	−	0.997727i	$-0.478535\pi$
$881$	4.00000	0.134763	0.0673817	+	0.997727i	$0.478535\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−5.00000	−0.168168
$885$	0	0
$886$	19.0000	0.638317
$887$	9.00000	0.302190	0.151095	−	0.988519i	$-0.451720\pi$
$887$	9.00000	0.302190	0.151095	+	0.988519i	$0.451720\pi$
$888$	0	0
$889$	0	0
$890$	−8.00000	−0.268161
$891$	0	0
$892$	−14.0000	−0.468755
$893$	−42.0000	−1.40548
$894$	0	0
$895$	60.0000	2.00558
$896$	0	0
$897$	0	0
$898$	27.0000	0.901002
$899$	20.0000	0.667037
$900$	0	0
$901$	−5.00000	−0.166574
$902$	40.0000	1.33185
$903$	0	0
$904$	9.00000	0.299336
$905$	−8.00000	−0.265929
$906$	0	0
$907$	−34.0000	−1.12895	−0.564476	−	0.825450i	$-0.690922\pi$
$907$	−34.0000	−1.12895	−0.564476	+	0.825450i	$0.690922\pi$
$908$	−22.0000	−0.730096
$909$	0	0
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	0	0
$913$	12.0000	0.397142
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	−15.0000	−0.495614
$917$	0	0
$918$	0	0
$919$	9.00000	0.296883	0.148441	−	0.988921i	$-0.452574\pi$
$919$	9.00000	0.296883	0.148441	+	0.988921i	$0.452574\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	−3.00000	−0.0987997
$923$	−15.0000	−0.493731
$924$	0	0
$925$	11.0000	0.361678
$926$	39.0000	1.28162
$927$	0	0
$928$	−5.00000	−0.164133
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	0	0
$931$	49.0000	1.60591
$932$	−8.00000	−0.262049
$933$	0	0
$934$	28.0000	0.916188
$935$	−80.0000	−2.61628
$936$	0	0
$937$	9.00000	0.294017	0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000	0.294017	0.147009	+	0.989135i	$0.453036\pi$
$938$	0	0
$939$	0	0
$940$	24.0000	0.782794
$941$	6.00000	0.195594	0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000	0.195594	0.0977972	+	0.995206i	$0.468820\pi$
$942$	0	0
$943$	−10.0000	−0.325645
$944$	6.00000	0.195283
$945$	0	0
$946$	−40.0000	−1.30051
$947$	−32.0000	−1.03986	−0.519930	−	0.854209i	$-0.674042\pi$
$947$	−32.0000	−1.03986	−0.519930	+	0.854209i	$0.674042\pi$
$948$	0	0
$949$	−8.00000	−0.259691
$950$	−77.0000	−2.49821
$951$	0	0
$952$	0	0
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	0	0
$955$	−52.0000	−1.68268
$956$	24.0000	0.776215
$957$	0	0
$958$	3.00000	0.0969256
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	1.00000	0.0322413
$963$	0	0
$964$	−3.00000	−0.0966235
$965$	−48.0000	−1.54517
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	68.0000	2.18335
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	0	0
$973$	0	0
$974$	−12.0000	−0.384505
$975$	0	0
$976$	4.00000	0.128037
$977$	−28.0000	−0.895799	−0.447900	−	0.894084i	$-0.647828\pi$
$977$	−28.0000	−0.895799	−0.447900	+	0.894084i	$0.647828\pi$
$978$	0	0
$979$	−8.00000	−0.255681
$980$	−28.0000	−0.894427
$981$	0	0
$982$	−33.0000	−1.05307
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	0	0
$985$	8.00000	0.254901
$986$	25.0000	0.796162
$987$	0	0
$988$	−7.00000	−0.222700
$989$	10.0000	0.317982
$990$	0	0
$991$	42.0000	1.33417	0.667087	−	0.744980i	$-0.267541\pi$
$991$	42.0000	1.33417	0.667087	+	0.744980i	$0.267541\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	23.0000	0.728417	0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000	0.728417	0.364209	+	0.931317i	$0.381339\pi$
$998$	11.0000	0.348199
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	954.2.a.m.1.1		1
3.2	odd	2		106.2.a.a.1.1	✓	1
4.3	odd	2		7632.2.a.r.1.1		1
12.11	even	2		848.2.a.d.1.1		1
15.2	even	4		2650.2.b.f.849.1		2
15.8	even	4		2650.2.b.f.849.2		2
15.14	odd	2		2650.2.a.j.1.1		1
21.20	even	2		5194.2.a.j.1.1		1
24.5	odd	2		3392.2.a.n.1.1		1
24.11	even	2		3392.2.a.i.1.1		1
159.158	odd	2		5618.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
106.2.a.a.1.1	✓	1	3.2	odd	2
848.2.a.d.1.1		1	12.11	even	2
954.2.a.m.1.1		1	1.1	even	1	trivial
2650.2.a.j.1.1		1	15.14	odd	2
2650.2.b.f.849.1		2	15.2	even	4
2650.2.b.f.849.2		2	15.8	even	4
3392.2.a.i.1.1		1	24.11	even	2
3392.2.a.n.1.1		1	24.5	odd	2
5194.2.a.j.1.1		1	21.20	even	2
5618.2.a.j.1.1		1	159.158	odd	2
7632.2.a.r.1.1		1	4.3	odd	2

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:	\( N \)	\(=\)	\( 954 = 2 \cdot 3^{2} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	954.a (trivial)

Introduction

L-functions

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