LMFDB - Embedded newform 5950.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5950,2,Mod(1,5950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5950 = 2 \cdot 5^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5950.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:	$47.5109892027$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -2.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} +1.00000 q^{19} -1.00000 q^{21} -2.00000 q^{22} +1.00000 q^{24} +5.00000 q^{26} -5.00000 q^{27} -1.00000 q^{28} +1.00000 q^{29} +7.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} +1.00000 q^{34} -2.00000 q^{36} -8.00000 q^{37} +1.00000 q^{38} +5.00000 q^{39} +12.0000 q^{41} -1.00000 q^{42} +4.00000 q^{43} -2.00000 q^{44} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{51} +5.00000 q^{52} +3.00000 q^{53} -5.00000 q^{54} -1.00000 q^{56} +1.00000 q^{57} +1.00000 q^{58} +5.00000 q^{59} +11.0000 q^{61} +7.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -2.00000 q^{67} +1.00000 q^{68} -1.00000 q^{71} -2.00000 q^{72} +1.00000 q^{73} -8.00000 q^{74} +1.00000 q^{76} +2.00000 q^{77} +5.00000 q^{78} +1.00000 q^{81} +12.0000 q^{82} +12.0000 q^{83} -1.00000 q^{84} +4.00000 q^{86} +1.00000 q^{87} -2.00000 q^{88} -13.0000 q^{89} -5.00000 q^{91} +7.00000 q^{93} +1.00000 q^{94} +1.00000 q^{96} -5.00000 q^{97} +1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000	0.288675
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.00000	−0.471405
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−2.00000	−0.426401
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	5.00000	0.980581
$27$	−5.00000	−0.962250
$28$	−1.00000	−0.188982
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	1.00000	0.176777
$33$	−2.00000	−0.348155
$34$	1.00000	0.171499
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	1.00000	0.162221
$39$	5.00000	0.800641
$40$	0	0
$41$	12.0000	1.87409	0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000	1.87409	0.937043	+	0.349215i	$0.113552\pi$
$42$	−1.00000	−0.154303
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	0	0
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	0	0
$51$	1.00000	0.140028
$52$	5.00000	0.693375
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−1.00000	−0.133631
$57$	1.00000	0.132453
$58$	1.00000	0.131306
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	7.00000	0.889001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−2.00000	−0.235702
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	1.00000	0.114708
$77$	2.00000	0.227921
$78$	5.00000	0.566139
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	4.00000	0.431331
$87$	1.00000	0.107211
$88$	−2.00000	−0.213201
$89$	−13.0000	−1.37800	−0.688999	−	0.724763i	$-0.741949\pi$
$89$	−13.0000	−1.37800	−0.688999	+	0.724763i	$0.741949\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	0	0
$93$	7.00000	0.725866
$94$	1.00000	0.103142
$95$	0	0
$96$	1.00000	0.102062
$97$	−5.00000	−0.507673	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000	−0.507673	−0.253837	+	0.967247i	$0.581693\pi$
$98$	1.00000	0.101015
$99$	4.00000	0.402015
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	1.00000	0.0990148
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	3.00000	0.291386
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−5.00000	−0.481125
$109$	−5.00000	−0.478913	−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000	−0.478913	−0.239457	+	0.970907i	$0.576969\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	−1.00000	−0.0944911
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	1.00000	0.0928477
$117$	−10.0000	−0.924500
$118$	5.00000	0.460287
$119$	−1.00000	−0.0916698
$120$	0	0
$121$	−7.00000	−0.636364
$122$	11.0000	0.995893
$123$	12.0000	1.08200
$124$	7.00000	0.628619
$125$	0	0
$126$	2.00000	0.178174
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	1.00000	0.0883883
$129$	4.00000	0.352180
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−2.00000	−0.174078
$133$	−1.00000	−0.0867110
$134$	−2.00000	−0.172774
$135$	0	0
$136$	1.00000	0.0857493
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−1.00000	−0.0839181
$143$	−10.0000	−0.836242
$144$	−2.00000	−0.166667
$145$	0	0
$146$	1.00000	0.0827606
$147$	1.00000	0.0824786
$148$	−8.00000	−0.657596
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	1.00000	0.0811107
$153$	−2.00000	−0.161690
$154$	2.00000	0.161165
$155$	0	0
$156$	5.00000	0.400320
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	3.00000	0.237915
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	12.0000	0.931381
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	−1.00000	−0.0771517
$169$	12.0000	0.923077
$170$	0	0
$171$	−2.00000	−0.152944
$172$	4.00000	0.304997
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	1.00000	0.0758098
$175$	0	0
$176$	−2.00000	−0.150756
$177$	5.00000	0.375823
$178$	−13.0000	−0.974391
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−5.00000	−0.370625
$183$	11.0000	0.813143
$184$	0	0
$185$	0	0
$186$	7.00000	0.513265
$187$	−2.00000	−0.146254
$188$	1.00000	0.0729325
$189$	5.00000	0.363696
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	1.00000	0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−5.00000	−0.358979
$195$	0	0
$196$	1.00000	0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	4.00000	0.284268
$199$	5.00000	0.354441	0.177220	−	0.984171i	$-0.443289\pi$
$199$	5.00000	0.354441	0.177220	+	0.984171i	$0.443289\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	0	0
$203$	−1.00000	−0.0701862
$204$	1.00000	0.0700140
$205$	0	0
$206$	16.0000	1.11477
$207$	0	0
$208$	5.00000	0.346688
$209$	−2.00000	−0.138343
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	3.00000	0.206041
$213$	−1.00000	−0.0685189
$214$	4.00000	0.273434
$215$	0	0
$216$	−5.00000	−0.340207
$217$	−7.00000	−0.475191
$218$	−5.00000	−0.338643
$219$	1.00000	0.0675737
$220$	0	0
$221$	5.00000	0.336336
$222$	−8.00000	−0.536925
$223$	−21.0000	−1.40626	−0.703132	−	0.711059i	$-0.748216\pi$
$223$	−21.0000	−1.40626	−0.703132	+	0.711059i	$0.748216\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	3.00000	0.199557
$227$	23.0000	1.52656	0.763282	−	0.646066i	$-0.223587\pi$
$227$	23.0000	1.52656	0.763282	+	0.646066i	$0.223587\pi$
$228$	1.00000	0.0662266
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	1.00000	0.0656532
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	−10.0000	−0.653720
$235$	0	0
$236$	5.00000	0.325472
$237$	0	0
$238$	−1.00000	−0.0648204
$239$	2.00000	0.129369	0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000	0.129369	0.0646846	+	0.997906i	$0.479396\pi$
$240$	0	0
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	−7.00000	−0.449977
$243$	16.0000	1.02640
$244$	11.0000	0.704203
$245$	0	0
$246$	12.0000	0.765092
$247$	5.00000	0.318142
$248$	7.00000	0.444500
$249$	12.0000	0.760469
$250$	0	0
$251$	4.00000	0.252478	0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000	0.252478	0.126239	+	0.992000i	$0.459709\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	7.00000	0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	28.0000	1.74659	0.873296	−	0.487190i	$-0.161978\pi$
$257$	28.0000	1.74659	0.873296	+	0.487190i	$0.161978\pi$
$258$	4.00000	0.249029
$259$	8.00000	0.497096
$260$	0	0
$261$	−2.00000	−0.123797
$262$	−6.00000	−0.370681
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	−13.0000	−0.795587
$268$	−2.00000	−0.122169
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	0	0
$271$	−26.0000	−1.57939	−0.789694	−	0.613501i	$-0.789761\pi$
$271$	−26.0000	−1.57939	−0.789694	+	0.613501i	$0.789761\pi$
$272$	1.00000	0.0606339
$273$	−5.00000	−0.302614
$274$	12.0000	0.724947
$275$	0	0
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	4.00000	0.239904
$279$	−14.0000	−0.838158
$280$	0	0
$281$	−9.00000	−0.536895	−0.268447	−	0.963294i	$-0.586511\pi$
$281$	−9.00000	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$282$	1.00000	0.0595491
$283$	−5.00000	−0.297219	−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000	−0.297219	−0.148610	+	0.988896i	$0.547480\pi$
$284$	−1.00000	−0.0593391
$285$	0	0
$286$	−10.0000	−0.591312
$287$	−12.0000	−0.708338
$288$	−2.00000	−0.117851
$289$	1.00000	0.0588235
$290$	0	0
$291$	−5.00000	−0.293105
$292$	1.00000	0.0585206
$293$	19.0000	1.10999	0.554996	−	0.831853i	$-0.312720\pi$
$293$	19.0000	1.10999	0.554996	+	0.831853i	$0.312720\pi$
$294$	1.00000	0.0583212
$295$	0	0
$296$	−8.00000	−0.464991
$297$	10.0000	0.580259
$298$	6.00000	0.347571
$299$	0	0
$300$	0	0
$301$	−4.00000	−0.230556
$302$	−12.0000	−0.690522
$303$	0	0
$304$	1.00000	0.0573539
$305$	0	0
$306$	−2.00000	−0.114332
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	2.00000	0.113961
$309$	16.0000	0.910208
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	5.00000	0.283069
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	0	0
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	3.00000	0.168232
$319$	−2.00000	−0.111979
$320$	0	0
$321$	4.00000	0.223258
$322$	0	0
$323$	1.00000	0.0556415
$324$	1.00000	0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−5.00000	−0.276501
$328$	12.0000	0.662589
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	12.0000	0.658586
$333$	16.0000	0.876795
$334$	14.0000	0.766046
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	5.00000	0.272367	0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000	0.272367	0.136184	+	0.990684i	$0.456516\pi$
$338$	12.0000	0.652714
$339$	3.00000	0.162938
$340$	0	0
$341$	−14.0000	−0.758143
$342$	−2.00000	−0.108148
$343$	−1.00000	−0.0539949
$344$	4.00000	0.215666
$345$	0	0
$346$	4.00000	0.215041
$347$	−15.0000	−0.805242	−0.402621	−	0.915367i	$-0.631901\pi$
$347$	−15.0000	−0.805242	−0.402621	+	0.915367i	$0.631901\pi$
$348$	1.00000	0.0536056
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	−25.0000	−1.33440
$352$	−2.00000	−0.106600
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	5.00000	0.265747
$355$	0	0
$356$	−13.0000	−0.688999
$357$	−1.00000	−0.0529256
$358$	20.0000	1.05703
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−10.0000	−0.525588
$363$	−7.00000	−0.367405
$364$	−5.00000	−0.262071
$365$	0	0
$366$	11.0000	0.574979
$367$	−34.0000	−1.77479	−0.887393	−	0.461014i	$-0.847486\pi$
$367$	−34.0000	−1.77479	−0.887393	+	0.461014i	$0.847486\pi$
$368$	0	0
$369$	−24.0000	−1.24939
$370$	0	0
$371$	−3.00000	−0.155752
$372$	7.00000	0.362933
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	1.00000	0.0515711
$377$	5.00000	0.257513
$378$	5.00000	0.257172
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	7.00000	0.358621
$382$	−12.0000	−0.613973
$383$	31.0000	1.58403	0.792013	−	0.610504i	$-0.209033\pi$
$383$	31.0000	1.58403	0.792013	+	0.610504i	$0.209033\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	−8.00000	−0.406663
$388$	−5.00000	−0.253837
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	0	0
$392$	1.00000	0.0505076
$393$	−6.00000	−0.302660
$394$	−18.0000	−0.906827
$395$	0	0
$396$	4.00000	0.201008
$397$	−10.0000	−0.501886	−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000	−0.501886	−0.250943	+	0.968002i	$0.580741\pi$
$398$	5.00000	0.250627
$399$	−1.00000	−0.0500626
$400$	0	0
$401$	−38.0000	−1.89763	−0.948815	−	0.315833i	$-0.897716\pi$
$401$	−38.0000	−1.89763	−0.948815	+	0.315833i	$0.897716\pi$
$402$	−2.00000	−0.0997509
$403$	35.0000	1.74347
$404$	0	0
$405$	0	0
$406$	−1.00000	−0.0496292
$407$	16.0000	0.793091
$408$	1.00000	0.0495074
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	16.0000	0.788263
$413$	−5.00000	−0.246034
$414$	0	0
$415$	0	0
$416$	5.00000	0.245145
$417$	4.00000	0.195881
$418$	−2.00000	−0.0978232
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	−4.00000	−0.194948	−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000	−0.194948	−0.0974740	+	0.995238i	$0.531076\pi$
$422$	12.0000	0.584151
$423$	−2.00000	−0.0972433
$424$	3.00000	0.145693
$425$	0	0
$426$	−1.00000	−0.0484502
$427$	−11.0000	−0.532327
$428$	4.00000	0.193347
$429$	−10.0000	−0.482805
$430$	0	0
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	−5.00000	−0.240563
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	−5.00000	−0.239457
$437$	0	0
$438$	1.00000	0.0477818
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	5.00000	0.237826
$443$	−2.00000	−0.0950229	−0.0475114	−	0.998871i	$-0.515129\pi$
$443$	−2.00000	−0.0950229	−0.0475114	+	0.998871i	$0.515129\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	−21.0000	−0.994379
$447$	6.00000	0.283790
$448$	−1.00000	−0.0472456
$449$	−34.0000	−1.60456	−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000	−1.60456	−0.802280	+	0.596948i	$0.796380\pi$
$450$	0	0
$451$	−24.0000	−1.13012
$452$	3.00000	0.141108
$453$	−12.0000	−0.563809
$454$	23.0000	1.07944
$455$	0	0
$456$	1.00000	0.0468293
$457$	40.0000	1.87112	0.935561	−	0.353166i	$-0.114895\pi$
$457$	40.0000	1.87112	0.935561	+	0.353166i	$0.114895\pi$
$458$	−14.0000	−0.654177
$459$	−5.00000	−0.233380
$460$	0	0
$461$	20.0000	0.931493	0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000	0.931493	0.465746	+	0.884918i	$0.345786\pi$
$462$	2.00000	0.0930484
$463$	9.00000	0.418265	0.209133	−	0.977887i	$-0.432936\pi$
$463$	9.00000	0.418265	0.209133	+	0.977887i	$0.432936\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−21.0000	−0.972806
$467$	38.0000	1.75843	0.879215	−	0.476425i	$-0.158068\pi$
$467$	38.0000	1.75843	0.879215	+	0.476425i	$0.158068\pi$
$468$	−10.0000	−0.462250
$469$	2.00000	0.0923514
$470$	0	0
$471$	10.0000	0.460776
$472$	5.00000	0.230144
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	−1.00000	−0.0458349
$477$	−6.00000	−0.274721
$478$	2.00000	0.0914779
$479$	−15.0000	−0.685367	−0.342684	−	0.939451i	$-0.611336\pi$
$479$	−15.0000	−0.685367	−0.342684	+	0.939451i	$0.611336\pi$
$480$	0	0
$481$	−40.0000	−1.82384
$482$	4.00000	0.182195
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	16.0000	0.725775
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	11.0000	0.497947
$489$	−4.00000	−0.180886
$490$	0	0
$491$	23.0000	1.03798	0.518988	−	0.854782i	$-0.326309\pi$
$491$	23.0000	1.03798	0.518988	+	0.854782i	$0.326309\pi$
$492$	12.0000	0.541002
$493$	1.00000	0.0450377
$494$	5.00000	0.224961
$495$	0	0
$496$	7.00000	0.314309
$497$	1.00000	0.0448561
$498$	12.0000	0.537733
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	0	0
$501$	14.0000	0.625474
$502$	4.00000	0.178529
$503$	6.00000	0.267527	0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000	0.267527	0.133763	+	0.991013i	$0.457294\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	0	0
$507$	12.0000	0.532939
$508$	7.00000	0.310575
$509$	−40.0000	−1.77297	−0.886484	−	0.462758i	$-0.846860\pi$
$509$	−40.0000	−1.77297	−0.886484	+	0.462758i	$0.846860\pi$
$510$	0	0
$511$	−1.00000	−0.0442374
$512$	1.00000	0.0441942
$513$	−5.00000	−0.220755
$514$	28.0000	1.23503
$515$	0	0
$516$	4.00000	0.176090
$517$	−2.00000	−0.0879599
$518$	8.00000	0.351500
$519$	4.00000	0.175581
$520$	0	0
$521$	4.00000	0.175243	0.0876216	−	0.996154i	$-0.472073\pi$
$521$	4.00000	0.175243	0.0876216	+	0.996154i	$0.472073\pi$
$522$	−2.00000	−0.0875376
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	21.0000	0.915644
$527$	7.00000	0.304925
$528$	−2.00000	−0.0870388
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−10.0000	−0.433963
$532$	−1.00000	−0.0433555
$533$	60.0000	2.59889
$534$	−13.0000	−0.562565
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	20.0000	0.863064
$538$	−21.0000	−0.905374
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	−26.0000	−1.11680
$543$	−10.0000	−0.429141
$544$	1.00000	0.0428746
$545$	0	0
$546$	−5.00000	−0.213980
$547$	9.00000	0.384812	0.192406	−	0.981315i	$-0.438371\pi$
$547$	9.00000	0.384812	0.192406	+	0.981315i	$0.438371\pi$
$548$	12.0000	0.512615
$549$	−22.0000	−0.938937
$550$	0	0
$551$	1.00000	0.0426014
$552$	0	0
$553$	0	0
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	4.00000	0.169638
$557$	9.00000	0.381342	0.190671	−	0.981654i	$-0.438934\pi$
$557$	9.00000	0.381342	0.190671	+	0.981654i	$0.438934\pi$
$558$	−14.0000	−0.592667
$559$	20.0000	0.845910
$560$	0	0
$561$	−2.00000	−0.0844401
$562$	−9.00000	−0.379642
$563$	−40.0000	−1.68580	−0.842900	−	0.538071i	$-0.819153\pi$
$563$	−40.0000	−1.68580	−0.842900	+	0.538071i	$0.819153\pi$
$564$	1.00000	0.0421076
$565$	0	0
$566$	−5.00000	−0.210166
$567$	−1.00000	−0.0419961
$568$	−1.00000	−0.0419591
$569$	3.00000	0.125767	0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000	0.125767	0.0628833	+	0.998021i	$0.479970\pi$
$570$	0	0
$571$	26.0000	1.08807	0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000	1.08807	0.544033	+	0.839064i	$0.316897\pi$
$572$	−10.0000	−0.418121
$573$	−12.0000	−0.501307
$574$	−12.0000	−0.500870
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	1.00000	0.0415945
$579$	10.0000	0.415586
$580$	0	0
$581$	−12.0000	−0.497844
$582$	−5.00000	−0.207257
$583$	−6.00000	−0.248495
$584$	1.00000	0.0413803
$585$	0	0
$586$	19.0000	0.784883
$587$	−48.0000	−1.98117	−0.990586	−	0.136892i	$-0.956289\pi$
$587$	−48.0000	−1.98117	−0.990586	+	0.136892i	$0.956289\pi$
$588$	1.00000	0.0412393
$589$	7.00000	0.288430
$590$	0	0
$591$	−18.0000	−0.740421
$592$	−8.00000	−0.328798
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	10.0000	0.410305
$595$	0	0
$596$	6.00000	0.245770
$597$	5.00000	0.204636
$598$	0	0
$599$	−40.0000	−1.63436	−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000	−1.63436	−0.817178	+	0.576386i	$0.804463\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	−4.00000	−0.163028
$603$	4.00000	0.162893
$604$	−12.0000	−0.488273
$605$	0	0
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	1.00000	0.0405554
$609$	−1.00000	−0.0405220
$610$	0	0
$611$	5.00000	0.202278
$612$	−2.00000	−0.0808452
$613$	29.0000	1.17130	0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000	1.17130	0.585649	+	0.810564i	$0.300840\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	2.00000	0.0805823
$617$	27.0000	1.08698	0.543490	−	0.839416i	$-0.317103\pi$
$617$	27.0000	1.08698	0.543490	+	0.839416i	$0.317103\pi$
$618$	16.0000	0.643614
$619$	−42.0000	−1.68812	−0.844061	−	0.536247i	$-0.819842\pi$
$619$	−42.0000	−1.68812	−0.844061	+	0.536247i	$0.819842\pi$
$620$	0	0
$621$	0	0
$622$	12.0000	0.481156
$623$	13.0000	0.520834
$624$	5.00000	0.200160
$625$	0	0
$626$	−22.0000	−0.879297
$627$	−2.00000	−0.0798723
$628$	10.0000	0.399043
$629$	−8.00000	−0.318981
$630$	0	0
$631$	34.0000	1.35352	0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000	1.35352	0.676759	+	0.736204i	$0.263384\pi$
$632$	0	0
$633$	12.0000	0.476957
$634$	−12.0000	−0.476581
$635$	0	0
$636$	3.00000	0.118958
$637$	5.00000	0.198107
$638$	−2.00000	−0.0791808
$639$	2.00000	0.0791188
$640$	0	0
$641$	38.0000	1.50091	0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000	1.50091	0.750455	+	0.660922i	$0.229834\pi$
$642$	4.00000	0.157867
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	0	0
$645$	0	0
$646$	1.00000	0.0393445
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	1.00000	0.0392837
$649$	−10.0000	−0.392534
$650$	0	0
$651$	−7.00000	−0.274352
$652$	−4.00000	−0.156652
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	−5.00000	−0.195515
$655$	0	0
$656$	12.0000	0.468521
$657$	−2.00000	−0.0780274
$658$	−1.00000	−0.0389841
$659$	31.0000	1.20759	0.603794	−	0.797140i	$-0.293655\pi$
$659$	31.0000	1.20759	0.603794	+	0.797140i	$0.293655\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	−5.00000	−0.194331
$663$	5.00000	0.194184
$664$	12.0000	0.465690
$665$	0	0
$666$	16.0000	0.619987
$667$	0	0
$668$	14.0000	0.541676
$669$	−21.0000	−0.811907
$670$	0	0
$671$	−22.0000	−0.849301
$672$	−1.00000	−0.0385758
$673$	−35.0000	−1.34915	−0.674575	−	0.738206i	$-0.735673\pi$
$673$	−35.0000	−1.34915	−0.674575	+	0.738206i	$0.735673\pi$
$674$	5.00000	0.192593
$675$	0	0
$676$	12.0000	0.461538
$677$	48.0000	1.84479	0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000	1.84479	0.922395	+	0.386248i	$0.126229\pi$
$678$	3.00000	0.115214
$679$	5.00000	0.191882
$680$	0	0
$681$	23.0000	0.881362
$682$	−14.0000	−0.536088
$683$	−15.0000	−0.573959	−0.286980	−	0.957937i	$-0.592651\pi$
$683$	−15.0000	−0.573959	−0.286980	+	0.957937i	$0.592651\pi$
$684$	−2.00000	−0.0764719
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−14.0000	−0.534133
$688$	4.00000	0.152499
$689$	15.0000	0.571454
$690$	0	0
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	4.00000	0.152057
$693$	−4.00000	−0.151947
$694$	−15.0000	−0.569392
$695$	0	0
$696$	1.00000	0.0379049
$697$	12.0000	0.454532
$698$	14.0000	0.529908
$699$	−21.0000	−0.794293
$700$	0	0
$701$	−24.0000	−0.906467	−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000	−0.906467	−0.453234	+	0.891392i	$0.649730\pi$
$702$	−25.0000	−0.943564
$703$	−8.00000	−0.301726
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	0	0
$707$	0	0
$708$	5.00000	0.187912
$709$	−27.0000	−1.01401	−0.507003	−	0.861944i	$-0.669247\pi$
$709$	−27.0000	−1.01401	−0.507003	+	0.861944i	$0.669247\pi$
$710$	0	0
$711$	0	0
$712$	−13.0000	−0.487196
$713$	0	0
$714$	−1.00000	−0.0374241
$715$	0	0
$716$	20.0000	0.747435
$717$	2.00000	0.0746914
$718$	20.0000	0.746393
$719$	31.0000	1.15610	0.578052	−	0.816000i	$-0.303813\pi$
$719$	31.0000	1.15610	0.578052	+	0.816000i	$0.303813\pi$
$720$	0	0
$721$	−16.0000	−0.595871
$722$	−18.0000	−0.669891
$723$	4.00000	0.148762
$724$	−10.0000	−0.371647
$725$	0	0
$726$	−7.00000	−0.259794
$727$	−23.0000	−0.853023	−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000	−0.853023	−0.426511	+	0.904482i	$0.640258\pi$
$728$	−5.00000	−0.185312
$729$	13.0000	0.481481
$730$	0	0
$731$	4.00000	0.147945
$732$	11.0000	0.406572
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−34.0000	−1.25496
$735$	0	0
$736$	0	0
$737$	4.00000	0.147342
$738$	−24.0000	−0.883452
$739$	35.0000	1.28750	0.643748	−	0.765238i	$-0.277379\pi$
$739$	35.0000	1.28750	0.643748	+	0.765238i	$0.277379\pi$
$740$	0	0
$741$	5.00000	0.183680
$742$	−3.00000	−0.110133
$743$	12.0000	0.440237	0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000	0.440237	0.220119	+	0.975473i	$0.429356\pi$
$744$	7.00000	0.256632
$745$	0	0
$746$	−26.0000	−0.951928
$747$	−24.0000	−0.878114
$748$	−2.00000	−0.0731272
$749$	−4.00000	−0.146157
$750$	0	0
$751$	5.00000	0.182453	0.0912263	−	0.995830i	$-0.470921\pi$
$751$	5.00000	0.182453	0.0912263	+	0.995830i	$0.470921\pi$
$752$	1.00000	0.0364662
$753$	4.00000	0.145768
$754$	5.00000	0.182089
$755$	0	0
$756$	5.00000	0.181848
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	0	0
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	7.00000	0.253583
$763$	5.00000	0.181012
$764$	−12.0000	−0.434145
$765$	0	0
$766$	31.0000	1.12008
$767$	25.0000	0.902698
$768$	1.00000	0.0360844
$769$	41.0000	1.47850	0.739249	−	0.673432i	$-0.235181\pi$
$769$	41.0000	1.47850	0.739249	+	0.673432i	$0.235181\pi$
$770$	0	0
$771$	28.0000	1.00840
$772$	10.0000	0.359908
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−5.00000	−0.179490
$777$	8.00000	0.286998
$778$	−6.00000	−0.215110
$779$	12.0000	0.429945
$780$	0	0
$781$	2.00000	0.0715656
$782$	0	0
$783$	−5.00000	−0.178685
$784$	1.00000	0.0357143
$785$	0	0
$786$	−6.00000	−0.214013
$787$	41.0000	1.46149	0.730746	−	0.682649i	$-0.239172\pi$
$787$	41.0000	1.46149	0.730746	+	0.682649i	$0.239172\pi$
$788$	−18.0000	−0.641223
$789$	21.0000	0.747620
$790$	0	0
$791$	−3.00000	−0.106668
$792$	4.00000	0.142134
$793$	55.0000	1.95311
$794$	−10.0000	−0.354887
$795$	0	0
$796$	5.00000	0.177220
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	−1.00000	−0.0353996
$799$	1.00000	0.0353775
$800$	0	0
$801$	26.0000	0.918665
$802$	−38.0000	−1.34183
$803$	−2.00000	−0.0705785
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	35.0000	1.23282
$807$	−21.0000	−0.739235
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	−32.0000	−1.12367	−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000	−1.12367	−0.561836	+	0.827249i	$0.689905\pi$
$812$	−1.00000	−0.0350931
$813$	−26.0000	−0.911860
$814$	16.0000	0.560800
$815$	0	0
$816$	1.00000	0.0350070
$817$	4.00000	0.139942
$818$	−19.0000	−0.664319
$819$	10.0000	0.349428
$820$	0	0
$821$	−17.0000	−0.593304	−0.296652	−	0.954986i	$-0.595870\pi$
$821$	−17.0000	−0.593304	−0.296652	+	0.954986i	$0.595870\pi$
$822$	12.0000	0.418548
$823$	−22.0000	−0.766872	−0.383436	−	0.923567i	$-0.625259\pi$
$823$	−22.0000	−0.766872	−0.383436	+	0.923567i	$0.625259\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	−5.00000	−0.173972
$827$	−24.0000	−0.834562	−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000	−0.834562	−0.417281	+	0.908778i	$0.637017\pi$
$828$	0	0
$829$	−18.0000	−0.625166	−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000	−0.625166	−0.312583	+	0.949890i	$0.601194\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	5.00000	0.173344
$833$	1.00000	0.0346479
$834$	4.00000	0.138509
$835$	0	0
$836$	−2.00000	−0.0691714
$837$	−35.0000	−1.20978
$838$	−28.0000	−0.967244
$839$	−51.0000	−1.76072	−0.880358	−	0.474310i	$-0.842698\pi$
$839$	−51.0000	−1.76072	−0.880358	+	0.474310i	$0.842698\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−4.00000	−0.137849
$843$	−9.00000	−0.309976
$844$	12.0000	0.413057
$845$	0	0
$846$	−2.00000	−0.0687614
$847$	7.00000	0.240523
$848$	3.00000	0.103020
$849$	−5.00000	−0.171600
$850$	0	0
$851$	0	0
$852$	−1.00000	−0.0342594
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	−11.0000	−0.376412
$855$	0	0
$856$	4.00000	0.136717
$857$	−13.0000	−0.444072	−0.222036	−	0.975039i	$-0.571270\pi$
$857$	−13.0000	−0.444072	−0.222036	+	0.975039i	$0.571270\pi$
$858$	−10.0000	−0.341394
$859$	25.0000	0.852989	0.426494	−	0.904490i	$-0.359748\pi$
$859$	25.0000	0.852989	0.426494	+	0.904490i	$0.359748\pi$
$860$	0	0
$861$	−12.0000	−0.408959
$862$	8.00000	0.272481
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	0	0
$867$	1.00000	0.0339618
$868$	−7.00000	−0.237595
$869$	0	0
$870$	0	0
$871$	−10.0000	−0.338837
$872$	−5.00000	−0.169321
$873$	10.0000	0.338449
$874$	0	0
$875$	0	0
$876$	1.00000	0.0337869
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	−16.0000	−0.539974
$879$	19.0000	0.640854
$880$	0	0
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	−2.00000	−0.0673435
$883$	−46.0000	−1.54802	−0.774012	−	0.633171i	$-0.781753\pi$
$883$	−46.0000	−1.54802	−0.774012	+	0.633171i	$0.781753\pi$
$884$	5.00000	0.168168
$885$	0	0
$886$	−2.00000	−0.0671913
$887$	42.0000	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$888$	−8.00000	−0.268462
$889$	−7.00000	−0.234772
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	−21.0000	−0.703132
$893$	1.00000	0.0334637
$894$	6.00000	0.200670
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−34.0000	−1.13459
$899$	7.00000	0.233463
$900$	0	0
$901$	3.00000	0.0999445
$902$	−24.0000	−0.799113
$903$	−4.00000	−0.133112
$904$	3.00000	0.0997785
$905$	0	0
$906$	−12.0000	−0.398673
$907$	31.0000	1.02934	0.514669	−	0.857389i	$-0.327915\pi$
$907$	31.0000	1.02934	0.514669	+	0.857389i	$0.327915\pi$
$908$	23.0000	0.763282
$909$	0	0
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	1.00000	0.0331133
$913$	−24.0000	−0.794284
$914$	40.0000	1.32308
$915$	0	0
$916$	−14.0000	−0.462573
$917$	6.00000	0.198137
$918$	−5.00000	−0.165025
$919$	−50.0000	−1.64935	−0.824674	−	0.565608i	$-0.808641\pi$
$919$	−50.0000	−1.64935	−0.824674	+	0.565608i	$0.808641\pi$
$920$	0	0
$921$	−20.0000	−0.659022
$922$	20.0000	0.658665
$923$	−5.00000	−0.164577
$924$	2.00000	0.0657952
$925$	0	0
$926$	9.00000	0.295758
$927$	−32.0000	−1.05102
$928$	1.00000	0.0328266
$929$	−2.00000	−0.0656179	−0.0328089	−	0.999462i	$-0.510445\pi$
$929$	−2.00000	−0.0656179	−0.0328089	+	0.999462i	$0.510445\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	−21.0000	−0.687878
$933$	12.0000	0.392862
$934$	38.0000	1.24340
$935$	0	0
$936$	−10.0000	−0.326860
$937$	−32.0000	−1.04539	−0.522697	−	0.852518i	$-0.675074\pi$
$937$	−32.0000	−1.04539	−0.522697	+	0.852518i	$0.675074\pi$
$938$	2.00000	0.0653023
$939$	−22.0000	−0.717943
$940$	0	0
$941$	21.0000	0.684580	0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000	0.684580	0.342290	+	0.939594i	$0.388797\pi$
$942$	10.0000	0.325818
$943$	0	0
$944$	5.00000	0.162736
$945$	0	0
$946$	−8.00000	−0.260102
$947$	27.0000	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$948$	0	0
$949$	5.00000	0.162307
$950$	0	0
$951$	−12.0000	−0.389127
$952$	−1.00000	−0.0324102
$953$	52.0000	1.68445	0.842223	−	0.539130i	$-0.181247\pi$
$953$	52.0000	1.68445	0.842223	+	0.539130i	$0.181247\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	2.00000	0.0646846
$957$	−2.00000	−0.0646508
$958$	−15.0000	−0.484628
$959$	−12.0000	−0.387500
$960$	0	0
$961$	18.0000	0.580645
$962$	−40.0000	−1.28965
$963$	−8.00000	−0.257796
$964$	4.00000	0.128831
$965$	0	0
$966$	0	0
$967$	24.0000	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$968$	−7.00000	−0.224989
$969$	1.00000	0.0321246
$970$	0	0
$971$	−27.0000	−0.866471	−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000	−0.866471	−0.433236	+	0.901281i	$0.642628\pi$
$972$	16.0000	0.513200
$973$	−4.00000	−0.128234
$974$	−38.0000	−1.21760
$975$	0	0
$976$	11.0000	0.352101
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	−4.00000	−0.127906
$979$	26.0000	0.830964
$980$	0	0
$981$	10.0000	0.319275
$982$	23.0000	0.733959
$983$	−6.00000	−0.191370	−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000	−0.191370	−0.0956851	+	0.995412i	$0.530504\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	1.00000	0.0318465
$987$	−1.00000	−0.0318304
$988$	5.00000	0.159071
$989$	0	0
$990$	0	0
$991$	−29.0000	−0.921215	−0.460608	−	0.887604i	$-0.652368\pi$
$991$	−29.0000	−0.921215	−0.460608	+	0.887604i	$0.652368\pi$
$992$	7.00000	0.222250
$993$	−5.00000	−0.158670
$994$	1.00000	0.0317181
$995$	0	0
$996$	12.0000	0.380235
$997$	−60.0000	−1.90022	−0.950110	−	0.311916i	$-0.899029\pi$
$997$	−60.0000	−1.90022	−0.950110	+	0.311916i	$0.899029\pi$
$998$	16.0000	0.506471
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5950.2.a.p.1.1		1
5.2	odd	4		1190.2.e.b.239.2	yes	2
5.3	odd	4		1190.2.e.b.239.1	✓	2
5.4	even	2		5950.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.e.b.239.1	✓	2	5.3	odd	4
1190.2.e.b.239.2	yes	2	5.2	odd	4
5950.2.a.e.1.1		1	5.4	even	2
5950.2.a.p.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5950 = 2 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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