LMFDB - Embedded newform 3610.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3610,2,Mod(1,3610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3610, 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("3610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3610 = 2 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3610.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:	$28.8259951297$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} +5.00000 q^{11} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{18} -1.00000 q^{20} +5.00000 q^{22} +1.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} +4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{35} -3.00000 q^{36} -11.0000 q^{37} -1.00000 q^{40} -9.00000 q^{41} +6.00000 q^{43} +5.00000 q^{44} +3.00000 q^{45} +1.00000 q^{46} -6.00000 q^{49} +1.00000 q^{50} +2.00000 q^{52} +5.00000 q^{53} -5.00000 q^{55} +1.00000 q^{56} +6.00000 q^{58} +4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} +12.0000 q^{67} -1.00000 q^{70} +6.00000 q^{71} -3.00000 q^{72} +14.0000 q^{73} -11.0000 q^{74} +5.00000 q^{77} +10.0000 q^{79} -1.00000 q^{80} +9.00000 q^{81} -9.00000 q^{82} +14.0000 q^{83} +6.00000 q^{86} +5.00000 q^{88} -7.00000 q^{89} +3.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} -2.00000 q^{97} -6.00000 q^{98} -15.0000 q^{99} +O(q^{100})$

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
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	−1.00000	−0.316228
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−3.00000	−0.707107
$19$	0	0
$19$	0	0
$20$	−1.00000	−0.223607
$21$	0	0
$22$	5.00000	1.06600
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	0	0
$35$	−1.00000	−0.169031
$36$	−3.00000	−0.500000
$37$	−11.0000	−1.80839	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−11.0000	−1.80839	−0.904194	+	0.427121i	$0.859528\pi$
$38$	0	0
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	5.00000	0.753778
$45$	3.00000	0.447214
$46$	1.00000	0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	5.00000	0.686803	0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000	0.686803	0.343401	+	0.939189i	$0.388421\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	1.00000	0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	4.00000	0.508001
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	0	0
$69$	0	0
$70$	−1.00000	−0.119523
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−3.00000	−0.353553
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−11.0000	−1.27872
$75$	0	0
$76$	0	0
$77$	5.00000	0.569803
$78$	0	0
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	−1.00000	−0.111803
$81$	9.00000	1.00000
$82$	−9.00000	−0.993884
$83$	14.0000	1.53670	0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000	1.53670	0.768350	+	0.640030i	$0.221078\pi$
$84$	0	0
$85$	0	0
$86$	6.00000	0.646997
$87$	0	0
$88$	5.00000	0.533002
$89$	−7.00000	−0.741999	−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000	−0.741999	−0.370999	+	0.928633i	$0.620985\pi$
$90$	3.00000	0.316228
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−6.00000	−0.606092
$99$	−15.0000	−1.50756
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	5.00000	0.485643
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	−5.00000	−0.476731
$111$	0	0
$112$	1.00000	0.0944911
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	6.00000	0.557086
$117$	−6.00000	−0.554700
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	4.00000	0.359211
$125$	−1.00000	−0.0894427
$126$	−3.00000	−0.267261
$127$	−15.0000	−1.33103	−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000	−1.33103	−0.665517	+	0.746382i	$0.731789\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−2.00000	−0.175412
$131$	1.00000	0.0873704	0.0436852	−	0.999045i	$-0.486090\pi$
$131$	1.00000	0.0873704	0.0436852	+	0.999045i	$0.486090\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	0	0
$137$	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
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	6.00000	0.503509
$143$	10.0000	0.836242
$144$	−3.00000	−0.250000
$145$	−6.00000	−0.498273
$146$	14.0000	1.15865
$147$	0	0
$148$	−11.0000	−0.904194
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	0	0
$154$	5.00000	0.402911
$155$	−4.00000	−0.321288
$156$	0	0
$157$	−21.0000	−1.67598	−0.837991	−	0.545684i	$-0.816270\pi$
$157$	−21.0000	−1.67598	−0.837991	+	0.545684i	$0.816270\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	9.00000	0.707107
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	14.0000	1.08661
$167$	−5.00000	−0.386912	−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000	−0.386912	−0.193456	+	0.981109i	$0.561970\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	6.00000	0.457496
$173$	1.00000	0.0760286	0.0380143	−	0.999277i	$-0.487897\pi$
$173$	1.00000	0.0760286	0.0380143	+	0.999277i	$0.487897\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	5.00000	0.376889
$177$	0	0
$178$	−7.00000	−0.524672
$179$	19.0000	1.42013	0.710063	−	0.704138i	$-0.248666\pi$
$179$	19.0000	1.42013	0.710063	+	0.704138i	$0.248666\pi$
$180$	3.00000	0.223607
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	1.00000	0.0737210
$185$	11.0000	0.808736
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	0	0
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	−6.00000	−0.428571
$197$	23.0000	1.63868	0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000	1.63868	0.819341	+	0.573306i	$0.194340\pi$
$198$	−15.0000	−1.06600
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	10.0000	0.703598
$203$	6.00000	0.421117
$204$	0	0
$205$	9.00000	0.628587
$206$	13.0000	0.905753
$207$	−3.00000	−0.208514
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	5.00000	0.343401
$213$	0	0
$214$	−4.00000	−0.273434
$215$	−6.00000	−0.409197
$216$	0	0
$217$	4.00000	0.271538
$218$	4.00000	0.270914
$219$	0	0
$220$	−5.00000	−0.337100
$221$	0	0
$222$	0	0
$223$	−23.0000	−1.54019	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−23.0000	−1.54019	−0.770097	+	0.637927i	$0.779792\pi$
$224$	1.00000	0.0668153
$225$	−3.00000	−0.200000
$226$	−12.0000	−0.798228
$227$	−10.0000	−0.663723	−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000	−0.663723	−0.331862	+	0.943328i	$0.607677\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	6.00000	0.393919
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	0	0
$245$	6.00000	0.383326
$246$	0	0
$247$	0	0
$248$	4.00000	0.254000
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−3.00000	−0.188982
$253$	5.00000	0.314347
$254$	−15.0000	−0.941184
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	−11.0000	−0.683507
$260$	−2.00000	−0.124035
$261$	−18.0000	−1.11417
$262$	1.00000	0.0617802
$263$	11.0000	0.678289	0.339145	−	0.940734i	$-0.389862\pi$
$263$	11.0000	0.678289	0.339145	+	0.940734i	$0.389862\pi$
$264$	0	0
$265$	−5.00000	−0.307148
$266$	0	0
$267$	0	0
$268$	12.0000	0.733017
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	0	0
$271$	−6.00000	−0.364474	−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000	−0.364474	−0.182237	+	0.983255i	$0.558334\pi$
$272$	0	0
$273$	0	0
$274$	12.0000	0.724947
$275$	5.00000	0.301511
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	16.0000	0.959616
$279$	−12.0000	−0.718421
$280$	−1.00000	−0.0597614
$281$	−15.0000	−0.894825	−0.447412	−	0.894328i	$-0.647654\pi$
$281$	−15.0000	−0.894825	−0.447412	+	0.894328i	$0.647654\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	10.0000	0.591312
$287$	−9.00000	−0.531253
$288$	−3.00000	−0.176777
$289$	−17.0000	−1.00000
$290$	−6.00000	−0.352332
$291$	0	0
$292$	14.0000	0.819288
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	0	0
$295$	0	0
$296$	−11.0000	−0.639362
$297$	0	0
$298$	−4.00000	−0.231714
$299$	2.00000	0.115663
$300$	0	0
$301$	6.00000	0.345834
$302$	−16.0000	−0.920697
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	5.00000	0.284901
$309$	0	0
$310$	−4.00000	−0.227185
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	0	0
$313$	−28.0000	−1.58265	−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000	−1.58265	−0.791327	+	0.611393i	$0.790609\pi$
$314$	−21.0000	−1.18510
$315$	3.00000	0.169031
$316$	10.0000	0.562544
$317$	−27.0000	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	0	0
$319$	30.0000	1.67968
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	1.00000	0.0557278
$323$	0	0
$324$	9.00000	0.500000
$325$	2.00000	0.110940
$326$	10.0000	0.553849
$327$	0	0
$328$	−9.00000	−0.496942
$329$	0	0
$330$	0	0
$331$	−25.0000	−1.37412	−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000	−1.37412	−0.687062	+	0.726599i	$0.741100\pi$
$332$	14.0000	0.768350
$333$	33.0000	1.80839
$334$	−5.00000	−0.273588
$335$	−12.0000	−0.655630
$336$	0	0
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	0	0
$341$	20.0000	1.08306
$342$	0	0
$343$	−13.0000	−0.701934
$344$	6.00000	0.323498
$345$	0	0
$346$	1.00000	0.0537603
$347$	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
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	5.00000	0.266501
$353$	4.00000	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$354$	0	0
$355$	−6.00000	−0.318447
$356$	−7.00000	−0.370999
$357$	0	0
$358$	19.0000	1.00418
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	3.00000	0.158114
$361$	0	0
$362$	2.00000	0.105118
$363$	0	0
$364$	2.00000	0.104828
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	1.00000	0.0521286
$369$	27.0000	1.40556
$370$	11.0000	0.571863
$371$	5.00000	0.259587
$372$	0	0
$373$	31.0000	1.60512	0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000	1.60512	0.802560	+	0.596572i	$0.203471\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	12.0000	0.618031
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	0	0
$381$	0	0
$382$	−18.0000	−0.920960
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	0	0
$385$	−5.00000	−0.254824
$386$	4.00000	0.203595
$387$	−18.0000	−0.914991
$388$	−2.00000	−0.101535
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	0	0
$391$	0	0
$392$	−6.00000	−0.303046
$393$	0	0
$394$	23.0000	1.15872
$395$	−10.0000	−0.503155
$396$	−15.0000	−0.753778
$397$	29.0000	1.45547	0.727734	−	0.685859i	$-0.240573\pi$
$397$	29.0000	1.45547	0.727734	+	0.685859i	$0.240573\pi$
$398$	24.0000	1.20301
$399$	0	0
$400$	1.00000	0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	8.00000	0.398508
$404$	10.0000	0.497519
$405$	−9.00000	−0.447214
$406$	6.00000	0.297775
$407$	−55.0000	−2.72625
$408$	0	0
$409$	−11.0000	−0.543915	−0.271957	−	0.962309i	$-0.587671\pi$
$409$	−11.0000	−0.543915	−0.271957	+	0.962309i	$0.587671\pi$
$410$	9.00000	0.444478
$411$	0	0
$412$	13.0000	0.640464
$413$	0	0
$414$	−3.00000	−0.147442
$415$	−14.0000	−0.687233
$416$	2.00000	0.0980581
$417$	0	0
$418$	0	0
$419$	−7.00000	−0.341972	−0.170986	−	0.985273i	$-0.554695\pi$
$419$	−7.00000	−0.341972	−0.170986	+	0.985273i	$0.554695\pi$
$420$	0	0
$421$	−8.00000	−0.389896	−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000	−0.389896	−0.194948	+	0.980814i	$0.562454\pi$
$422$	13.0000	0.632830
$423$	0	0
$424$	5.00000	0.242821
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−4.00000	−0.193347
$429$	0	0
$430$	−6.00000	−0.289346
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	4.00000	0.191565
$437$	0	0
$438$	0	0
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−5.00000	−0.238366
$441$	18.0000	0.857143
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	7.00000	0.331832
$446$	−23.0000	−1.08908
$447$	0	0
$448$	1.00000	0.0472456
$449$	−19.0000	−0.896665	−0.448333	−	0.893867i	$-0.647982\pi$
$449$	−19.0000	−0.896665	−0.448333	+	0.893867i	$0.647982\pi$
$450$	−3.00000	−0.141421
$451$	−45.0000	−2.11897
$452$	−12.0000	−0.564433
$453$	0	0
$454$	−10.0000	−0.469323
$455$	−2.00000	−0.0937614
$456$	0	0
$457$	−32.0000	−1.49690	−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000	−1.49690	−0.748448	+	0.663193i	$0.769201\pi$
$458$	6.00000	0.280362
$459$	0	0
$460$	−1.00000	−0.0466252
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	37.0000	1.71954	0.859768	−	0.510685i	$-0.170608\pi$
$463$	37.0000	1.71954	0.859768	+	0.510685i	$0.170608\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	10.0000	0.463241
$467$	34.0000	1.57333	0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000	1.57333	0.786666	+	0.617379i	$0.211805\pi$
$468$	−6.00000	−0.277350
$469$	12.0000	0.554109
$470$	0	0
$471$	0	0
$472$	0	0
$473$	30.0000	1.37940
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−15.0000	−0.686803
$478$	16.0000	0.731823
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	−22.0000	−1.00311
$482$	−18.0000	−0.819878
$483$	0	0
$484$	14.0000	0.636364
$485$	2.00000	0.0908153
$486$	0	0
$487$	−23.0000	−1.04223	−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000	−1.04223	−0.521115	+	0.853487i	$0.674484\pi$
$488$	0	0
$489$	0	0
$490$	6.00000	0.271052
$491$	27.0000	1.21849	0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000	1.21849	0.609246	+	0.792981i	$0.291472\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	15.0000	0.674200
$496$	4.00000	0.179605
$497$	6.00000	0.269137
$498$	0	0
$499$	−39.0000	−1.74588	−0.872940	−	0.487828i	$-0.837789\pi$
$499$	−39.0000	−1.74588	−0.872940	+	0.487828i	$0.837789\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−33.0000	−1.47140	−0.735699	−	0.677309i	$-0.763146\pi$
$503$	−33.0000	−1.47140	−0.735699	+	0.677309i	$0.763146\pi$
$504$	−3.00000	−0.133631
$505$	−10.0000	−0.444994
$506$	5.00000	0.222277
$507$	0	0
$508$	−15.0000	−0.665517
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	1.00000	0.0441942
$513$	0	0
$514$	−14.0000	−0.617514
$515$	−13.0000	−0.572848
$516$	0	0
$517$	0	0
$518$	−11.0000	−0.483312
$519$	0	0
$520$	−2.00000	−0.0877058
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	−18.0000	−0.787839
$523$	−42.0000	−1.83653	−0.918266	−	0.395964i	$-0.870410\pi$
$523$	−42.0000	−1.83653	−0.918266	+	0.395964i	$0.870410\pi$
$524$	1.00000	0.0436852
$525$	0	0
$526$	11.0000	0.479623
$527$	0	0
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−5.00000	−0.217186
$531$	0	0
$532$	0	0
$533$	−18.0000	−0.779667
$534$	0	0
$535$	4.00000	0.172935
$536$	12.0000	0.518321
$537$	0	0
$538$	−28.0000	−1.20717
$539$	−30.0000	−1.29219
$540$	0	0
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	−6.00000	−0.257722
$543$	0	0
$544$	0	0
$545$	−4.00000	−0.171341
$546$	0	0
$547$	−22.0000	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	5.00000	0.213201
$551$	0	0
$552$	0	0
$553$	10.0000	0.425243
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	16.0000	0.678551
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	−12.0000	−0.508001
$559$	12.0000	0.507546
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−15.0000	−0.632737
$563$	32.0000	1.34864	0.674320	−	0.738440i	$-0.264437\pi$
$563$	32.0000	1.34864	0.674320	+	0.738440i	$0.264437\pi$
$564$	0	0
$565$	12.0000	0.504844
$566$	−14.0000	−0.588464
$567$	9.00000	0.377964
$568$	6.00000	0.251754
$569$	45.0000	1.88650	0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000	1.88650	0.943249	+	0.332086i	$0.107752\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	10.0000	0.418121
$573$	0	0
$574$	−9.00000	−0.375653
$575$	1.00000	0.0417029
$576$	−3.00000	−0.125000
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	−17.0000	−0.707107
$579$	0	0
$580$	−6.00000	−0.249136
$581$	14.0000	0.580818
$582$	0	0
$583$	25.0000	1.03539
$584$	14.0000	0.579324
$585$	6.00000	0.248069
$586$	−21.0000	−0.867502
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−11.0000	−0.452097
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	0	0
$596$	−4.00000	−0.163846
$597$	0	0
$598$	2.00000	0.0817861
$599$	−44.0000	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$600$	0	0
$601$	21.0000	0.856608	0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000	0.856608	0.428304	+	0.903635i	$0.359111\pi$
$602$	6.00000	0.244542
$603$	−36.0000	−1.46603
$604$	−16.0000	−0.651031
$605$	−14.0000	−0.569181
$606$	0	0
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	25.0000	1.00974	0.504870	−	0.863195i	$-0.331540\pi$
$613$	25.0000	1.00974	0.504870	+	0.863195i	$0.331540\pi$
$614$	−2.00000	−0.0807134
$615$	0	0
$616$	5.00000	0.201456
$617$	20.0000	0.805170	0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000	0.805170	0.402585	+	0.915383i	$0.368112\pi$
$618$	0	0
$619$	−45.0000	−1.80870	−0.904351	−	0.426789i	$-0.859645\pi$
$619$	−45.0000	−1.80870	−0.904351	+	0.426789i	$0.859645\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	4.00000	0.160385
$623$	−7.00000	−0.280449
$624$	0	0
$625$	1.00000	0.0400000
$626$	−28.0000	−1.11911
$627$	0	0
$628$	−21.0000	−0.837991
$629$	0	0
$630$	3.00000	0.119523
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	−27.0000	−1.07231
$635$	15.0000	0.595257
$636$	0	0
$637$	−12.0000	−0.475457
$638$	30.0000	1.18771
$639$	−18.0000	−0.712069
$640$	−1.00000	−0.0395285
$641$	−10.0000	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$641$	−10.0000	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	0	0
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	9.00000	0.353553
$649$	0	0
$650$	2.00000	0.0784465
$651$	0	0
$652$	10.0000	0.391630
$653$	−25.0000	−0.978326	−0.489163	−	0.872192i	$-0.662698\pi$
$653$	−25.0000	−0.978326	−0.489163	+	0.872192i	$0.662698\pi$
$654$	0	0
$655$	−1.00000	−0.0390732
$656$	−9.00000	−0.351391
$657$	−42.0000	−1.63858
$658$	0	0
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	0	0
$661$	24.0000	0.933492	0.466746	−	0.884391i	$-0.345426\pi$
$661$	24.0000	0.933492	0.466746	+	0.884391i	$0.345426\pi$
$662$	−25.0000	−0.971653
$663$	0	0
$664$	14.0000	0.543305
$665$	0	0
$666$	33.0000	1.27872
$667$	6.00000	0.232321
$668$	−5.00000	−0.193456
$669$	0	0
$670$	−12.0000	−0.463600
$671$	0	0
$672$	0	0
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	6.00000	0.231111
$675$	0	0
$676$	−9.00000	−0.346154
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	0	0
$682$	20.0000	0.765840
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	−13.0000	−0.496342
$687$	0	0
$688$	6.00000	0.228748
$689$	10.0000	0.380970
$690$	0	0
$691$	−15.0000	−0.570627	−0.285313	−	0.958434i	$-0.592098\pi$
$691$	−15.0000	−0.570627	−0.285313	+	0.958434i	$0.592098\pi$
$692$	1.00000	0.0380143
$693$	−15.0000	−0.569803
$694$	18.0000	0.683271
$695$	−16.0000	−0.606915
$696$	0	0
$697$	0	0
$698$	−28.0000	−1.05982
$699$	0	0
$700$	1.00000	0.0377964
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	0	0
$704$	5.00000	0.188445
$705$	0	0
$706$	4.00000	0.150542
$707$	10.0000	0.376089
$708$	0	0
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	−6.00000	−0.225176
$711$	−30.0000	−1.12509
$712$	−7.00000	−0.262336
$713$	4.00000	0.149801
$714$	0	0
$715$	−10.0000	−0.373979
$716$	19.0000	0.710063
$717$	0	0
$718$	10.0000	0.373197
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	3.00000	0.111803
$721$	13.0000	0.484145
$722$	0	0
$723$	0	0
$724$	2.00000	0.0743294
$725$	6.00000	0.222834
$726$	0	0
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	2.00000	0.0741249
$729$	−27.0000	−1.00000
$730$	−14.0000	−0.518163
$731$	0	0
$732$	0	0
$733$	−15.0000	−0.554038	−0.277019	−	0.960864i	$-0.589346\pi$
$733$	−15.0000	−0.554038	−0.277019	+	0.960864i	$0.589346\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	1.00000	0.0368605
$737$	60.0000	2.21013
$738$	27.0000	0.993884
$739$	−31.0000	−1.14035	−0.570177	−	0.821522i	$-0.693125\pi$
$739$	−31.0000	−1.14035	−0.570177	+	0.821522i	$0.693125\pi$
$740$	11.0000	0.404368
$741$	0	0
$742$	5.00000	0.183556
$743$	−15.0000	−0.550297	−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000	−0.550297	−0.275148	+	0.961402i	$0.588727\pi$
$744$	0	0
$745$	4.00000	0.146549
$746$	31.0000	1.13499
$747$	−42.0000	−1.53670
$748$	0	0
$749$	−4.00000	−0.146157
$750$	0	0
$751$	−20.0000	−0.729810	−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000	−0.729810	−0.364905	+	0.931045i	$0.618899\pi$
$752$	0	0
$753$	0	0
$754$	12.0000	0.437014
$755$	16.0000	0.582300
$756$	0	0
$757$	−15.0000	−0.545184	−0.272592	−	0.962130i	$-0.587881\pi$
$757$	−15.0000	−0.545184	−0.272592	+	0.962130i	$0.587881\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	0	0
$761$	−43.0000	−1.55875	−0.779374	−	0.626559i	$-0.784463\pi$
$761$	−43.0000	−1.55875	−0.779374	+	0.626559i	$0.784463\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	−18.0000	−0.651217
$765$	0	0
$766$	8.00000	0.289052
$767$	0	0
$768$	0	0
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	−5.00000	−0.180187
$771$	0	0
$772$	4.00000	0.143963
$773$	45.0000	1.61854	0.809269	−	0.587439i	$-0.199864\pi$
$773$	45.0000	1.61854	0.809269	+	0.587439i	$0.199864\pi$
$774$	−18.0000	−0.646997
$775$	4.00000	0.143684
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	26.0000	0.932145
$779$	0	0
$780$	0	0
$781$	30.0000	1.07348
$782$	0	0
$783$	0	0
$784$	−6.00000	−0.214286
$785$	21.0000	0.749522
$786$	0	0
$787$	18.0000	0.641631	0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000	0.641631	0.320815	+	0.947142i	$0.396043\pi$
$788$	23.0000	0.819341
$789$	0	0
$790$	−10.0000	−0.355784
$791$	−12.0000	−0.426671
$792$	−15.0000	−0.533002
$793$	0	0
$794$	29.0000	1.02917
$795$	0	0
$796$	24.0000	0.850657
$797$	49.0000	1.73567	0.867835	−	0.496853i	$-0.165511\pi$
$797$	49.0000	1.73567	0.867835	+	0.496853i	$0.165511\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	21.0000	0.741999
$802$	−18.0000	−0.635602
$803$	70.0000	2.47025
$804$	0	0
$805$	−1.00000	−0.0352454
$806$	8.00000	0.281788
$807$	0	0
$808$	10.0000	0.351799
$809$	−2.00000	−0.0703163	−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000	−0.0703163	−0.0351581	+	0.999382i	$0.511193\pi$
$810$	−9.00000	−0.316228
$811$	−5.00000	−0.175574	−0.0877869	−	0.996139i	$-0.527979\pi$
$811$	−5.00000	−0.175574	−0.0877869	+	0.996139i	$0.527979\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	−55.0000	−1.92775
$815$	−10.0000	−0.350285
$816$	0	0
$817$	0	0
$818$	−11.0000	−0.384606
$819$	−6.00000	−0.209657
$820$	9.00000	0.314294
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	−37.0000	−1.28974	−0.644869	−	0.764293i	$-0.723088\pi$
$823$	−37.0000	−1.28974	−0.644869	+	0.764293i	$0.723088\pi$
$824$	13.0000	0.452876
$825$	0	0
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−3.00000	−0.104257
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	−14.0000	−0.485947
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	5.00000	0.173032
$836$	0	0
$837$	0	0
$838$	−7.00000	−0.241811
$839$	26.0000	0.897620	0.448810	−	0.893627i	$-0.351848\pi$
$839$	26.0000	0.897620	0.448810	+	0.893627i	$0.351848\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−8.00000	−0.275698
$843$	0	0
$844$	13.0000	0.447478
$845$	9.00000	0.309609
$846$	0	0
$847$	14.0000	0.481046
$848$	5.00000	0.171701
$849$	0	0
$850$	0	0
$851$	−11.0000	−0.377075
$852$	0	0
$853$	54.0000	1.84892	0.924462	−	0.381273i	$-0.124514\pi$
$853$	54.0000	1.84892	0.924462	+	0.381273i	$0.124514\pi$
$854$	0	0
$855$	0	0
$856$	−4.00000	−0.136717
$857$	−28.0000	−0.956462	−0.478231	−	0.878234i	$-0.658722\pi$
$857$	−28.0000	−0.956462	−0.478231	+	0.878234i	$0.658722\pi$
$858$	0	0
$859$	−49.0000	−1.67186	−0.835929	−	0.548837i	$-0.815071\pi$
$859$	−49.0000	−1.67186	−0.835929	+	0.548837i	$0.815071\pi$
$860$	−6.00000	−0.204598
$861$	0	0
$862$	12.0000	0.408722
$863$	17.0000	0.578687	0.289343	−	0.957225i	$-0.406563\pi$
$863$	17.0000	0.578687	0.289343	+	0.957225i	$0.406563\pi$
$864$	0	0
$865$	−1.00000	−0.0340010
$866$	2.00000	0.0679628
$867$	0	0
$868$	4.00000	0.135769
$869$	50.0000	1.69613
$870$	0	0
$871$	24.0000	0.813209
$872$	4.00000	0.135457
$873$	6.00000	0.203069
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	3.00000	0.101303	0.0506514	−	0.998716i	$-0.483870\pi$
$877$	3.00000	0.101303	0.0506514	+	0.998716i	$0.483870\pi$
$878$	8.00000	0.269987
$879$	0	0
$880$	−5.00000	−0.168550
$881$	−35.0000	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$882$	18.0000	0.606092
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	0	0
$885$	0	0
$886$	36.0000	1.20944
$887$	56.0000	1.88030	0.940148	−	0.340766i	$-0.110687\pi$
$887$	56.0000	1.88030	0.940148	+	0.340766i	$0.110687\pi$
$888$	0	0
$889$	−15.0000	−0.503084
$890$	7.00000	0.234641
$891$	45.0000	1.50756
$892$	−23.0000	−0.770097
$893$	0	0
$894$	0	0
$895$	−19.0000	−0.635100
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.0000	−0.634038
$899$	24.0000	0.800445
$900$	−3.00000	−0.100000
$901$	0	0
$902$	−45.0000	−1.49834
$903$	0	0
$904$	−12.0000	−0.399114
$905$	−2.00000	−0.0664822
$906$	0	0
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	−10.0000	−0.331862
$909$	−30.0000	−0.995037
$910$	−2.00000	−0.0662994
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	0	0
$913$	70.0000	2.31666
$914$	−32.0000	−1.05847
$915$	0	0
$916$	6.00000	0.198246
$917$	1.00000	0.0330229
$918$	0	0
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	−1.00000	−0.0329690
$921$	0	0
$922$	−30.0000	−0.987997
$923$	12.0000	0.394985
$924$	0	0
$925$	−11.0000	−0.361678
$926$	37.0000	1.21590
$927$	−39.0000	−1.28093
$928$	6.00000	0.196960
$929$	−27.0000	−0.885841	−0.442921	−	0.896561i	$-0.646058\pi$
$929$	−27.0000	−0.885841	−0.442921	+	0.896561i	$0.646058\pi$
$930$	0	0
$931$	0	0
$932$	10.0000	0.327561
$933$	0	0
$934$	34.0000	1.11251
$935$	0	0
$936$	−6.00000	−0.196116
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	−9.00000	−0.293080
$944$	0	0
$945$	0	0
$946$	30.0000	0.975384
$947$	−60.0000	−1.94974	−0.974869	−	0.222779i	$-0.928487\pi$
$947$	−60.0000	−1.94974	−0.974869	+	0.222779i	$0.928487\pi$
$948$	0	0
$949$	28.0000	0.908918
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	−15.0000	−0.485643
$955$	18.0000	0.582466
$956$	16.0000	0.517477
$957$	0	0
$958$	−18.0000	−0.581554
$959$	12.0000	0.387500
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−22.0000	−0.709308
$963$	12.0000	0.386695
$964$	−18.0000	−0.579741
$965$	−4.00000	−0.128765
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	2.00000	0.0642161
$971$	−20.0000	−0.641831	−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000	−0.641831	−0.320915	+	0.947108i	$0.603990\pi$
$972$	0	0
$973$	16.0000	0.512936
$974$	−23.0000	−0.736968
$975$	0	0
$976$	0	0
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	−35.0000	−1.11860
$980$	6.00000	0.191663
$981$	−12.0000	−0.383131
$982$	27.0000	0.861605
$983$	21.0000	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$984$	0	0
$985$	−23.0000	−0.732841
$986$	0	0
$987$	0	0
$988$	0	0
$989$	6.00000	0.190789
$990$	15.0000	0.476731
$991$	18.0000	0.571789	0.285894	−	0.958261i	$-0.407709\pi$
$991$	18.0000	0.571789	0.285894	+	0.958261i	$0.407709\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	6.00000	0.190308
$995$	−24.0000	−0.760851
$996$	0	0
$997$	−53.0000	−1.67853	−0.839263	−	0.543725i	$-0.817013\pi$
$997$	−53.0000	−1.67853	−0.839263	+	0.543725i	$0.817013\pi$
$998$	−39.0000	−1.23452
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3610.2.a.g.1.1		1
19.7	even	3		190.2.e.a.11.1	✓	2
19.11	even	3		190.2.e.a.121.1	yes	2
19.18	odd	2		3610.2.a.c.1.1		1
57.11	odd	6		1710.2.l.h.1261.1		2
57.26	odd	6		1710.2.l.h.1531.1		2
76.7	odd	6		1520.2.q.f.961.1		2
76.11	odd	6		1520.2.q.f.881.1		2
95.7	odd	12		950.2.j.d.49.1		4
95.49	even	6		950.2.e.f.501.1		2
95.64	even	6		950.2.e.f.201.1		2
95.68	odd	12		950.2.j.d.349.1		4
95.83	odd	12		950.2.j.d.49.2		4
95.87	odd	12		950.2.j.d.349.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.a.11.1	✓	2	19.7	even	3
190.2.e.a.121.1	yes	2	19.11	even	3
950.2.e.f.201.1		2	95.64	even	6
950.2.e.f.501.1		2	95.49	even	6
950.2.j.d.49.1		4	95.7	odd	12
950.2.j.d.49.2		4	95.83	odd	12
950.2.j.d.349.1		4	95.68	odd	12
950.2.j.d.349.2		4	95.87	odd	12
1520.2.q.f.881.1		2	76.11	odd	6
1520.2.q.f.961.1		2	76.7	odd	6
1710.2.l.h.1261.1		2	57.11	odd	6
1710.2.l.h.1531.1		2	57.26	odd	6
3610.2.a.c.1.1		1	19.18	odd	2
3610.2.a.g.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:	\( N \)	\(=\)	\( 3610 = 2 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more