LMFDB - Embedded newform 5850.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5850,2,Mod(1,5850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5850, 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("5850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5850.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:	$46.7124851824$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{7} -1.00000 q^{8} +2.00000 q^{11} -1.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} -3.00000 q^{19} -2.00000 q^{22} +6.00000 q^{23} +1.00000 q^{26} +2.00000 q^{28} +1.00000 q^{29} -1.00000 q^{32} -4.00000 q^{34} +1.00000 q^{37} +3.00000 q^{38} +5.00000 q^{41} -4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} +3.00000 q^{47} -3.00000 q^{49} -1.00000 q^{52} +7.00000 q^{53} -2.00000 q^{56} -1.00000 q^{58} +2.00000 q^{59} -10.0000 q^{61} +1.00000 q^{64} +9.00000 q^{67} +4.00000 q^{68} -1.00000 q^{71} +4.00000 q^{73} -1.00000 q^{74} -3.00000 q^{76} +4.00000 q^{77} -1.00000 q^{79} -5.00000 q^{82} +4.00000 q^{86} -2.00000 q^{88} -10.0000 q^{89} -2.00000 q^{91} +6.00000 q^{92} -3.00000 q^{94} +14.0000 q^{97} +3.00000 q^{98} +O(q^{100})$

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
$5$	0	0
$5$	0	0
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	0	0
$21$	0	0
$22$	−2.00000	−0.426401
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	2.00000	0.377964
$29$	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
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.00000	−0.685994
$35$	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	$0.473806\pi$
$38$	3.00000	0.486664
$39$	0	0
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−6.00000	−0.884652
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	0	0
$51$	0	0
$52$	−1.00000	−0.138675
$53$	7.00000	0.961524	0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000	0.961524	0.480762	+	0.876851i	$0.340360\pi$
$54$	0	0
$55$	0	0
$56$	−2.00000	−0.267261
$57$	0	0
$58$	−1.00000	−0.131306
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	9.00000	1.09952	0.549762	−	0.835321i	$-0.314718\pi$
$67$	9.00000	1.09952	0.549762	+	0.835321i	$0.314718\pi$
$68$	4.00000	0.485071
$69$	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	$0.518899\pi$
$72$	0	0
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	−3.00000	−0.344124
$77$	4.00000	0.455842
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	0	0
$82$	−5.00000	−0.552158
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	4.00000	0.431331
$87$	0	0
$88$	−2.00000	−0.213201
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	6.00000	0.625543
$93$	0	0
$94$	−3.00000	−0.309426
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	0	0
$101$	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
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−7.00000	−0.679900
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	3.00000	0.287348	0.143674	−	0.989625i	$-0.454108\pi$
$109$	3.00000	0.287348	0.143674	+	0.989625i	$0.454108\pi$
$110$	0	0
$111$	0	0
$112$	2.00000	0.188982
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	0	0
$116$	1.00000	0.0928477
$117$	0	0
$118$	−2.00000	−0.184115
$119$	8.00000	0.733359
$120$	0	0
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	0	0
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−11.0000	−0.976092	−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000	−0.976092	−0.488046	+	0.872818i	$0.662290\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−7.00000	−0.611593	−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000	−0.611593	−0.305796	+	0.952097i	$0.598923\pi$
$132$	0	0
$133$	−6.00000	−0.520266
$134$	−9.00000	−0.777482
$135$	0	0
$136$	−4.00000	−0.342997
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	0	0
$139$	22.0000	1.86602	0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000	1.86602	0.933008	+	0.359856i	$0.117174\pi$
$140$	0	0
$141$	0	0
$142$	1.00000	0.0839181
$143$	−2.00000	−0.167248
$144$	0	0
$145$	0	0
$146$	−4.00000	−0.331042
$147$	0	0
$148$	1.00000	0.0821995
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	3.00000	0.243332
$153$	0	0
$154$	−4.00000	−0.322329
$155$	0	0
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	0	0
$167$	1.00000	0.0773823	0.0386912	−	0.999251i	$-0.487681\pi$
$167$	1.00000	0.0773823	0.0386912	+	0.999251i	$0.487681\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−1.00000	−0.0760286	−0.0380143	−	0.999277i	$-0.512103\pi$
$173$	−1.00000	−0.0760286	−0.0380143	+	0.999277i	$0.512103\pi$
$174$	0	0
$175$	0	0
$176$	2.00000	0.150756
$177$	0	0
$178$	10.0000	0.749532
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	−6.00000	−0.442326
$185$	0	0
$186$	0	0
$187$	8.00000	0.585018
$188$	3.00000	0.218797
$189$	0	0
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	−3.00000	−0.214286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	−3.00000	−0.212664	−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000	−0.212664	−0.106332	+	0.994331i	$0.533911\pi$
$200$	0	0
$201$	0	0
$202$	−10.0000	−0.703598
$203$	2.00000	0.140372
$204$	0	0
$205$	0	0
$206$	12.0000	0.836080
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−6.00000	−0.415029
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	7.00000	0.480762
$213$	0	0
$214$	−15.0000	−1.02538
$215$	0	0
$216$	0	0
$217$	0	0
$218$	−3.00000	−0.203186
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	2.00000	0.133038
$227$	10.0000	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$227$	10.0000	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$228$	0	0
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	0	0
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	2.00000	0.130189
$237$	0	0
$238$	−8.00000	−0.518563
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	−10.0000	−0.640184
$245$	0	0
$246$	0	0
$247$	3.00000	0.190885
$248$	0	0
$249$	0	0
$250$	0	0
$251$	15.0000	0.946792	0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000	0.946792	0.473396	+	0.880850i	$0.343028\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	11.0000	0.690201
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	0	0
$262$	7.00000	0.432461
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	6.00000	0.367884
$267$	0	0
$268$	9.00000	0.549762
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−9.00000	−0.543710
$275$	0	0
$276$	0	0
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−22.0000	−1.31947
$279$	0	0
$280$	0	0
$281$	27.0000	1.61068	0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000	1.61068	0.805342	+	0.592810i	$0.201981\pi$
$282$	0	0
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	−1.00000	−0.0593391
$285$	0	0
$286$	2.00000	0.118262
$287$	10.0000	0.590281
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	4.00000	0.234082
$293$	32.0000	1.86946	0.934730	−	0.355359i	$-0.115641\pi$
$293$	32.0000	1.86946	0.934730	+	0.355359i	$0.115641\pi$
$294$	0	0
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	0	0
$298$	14.0000	0.810998
$299$	−6.00000	−0.346989
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−6.00000	−0.345261
$303$	0	0
$304$	−3.00000	−0.172062
$305$	0	0
$306$	0	0
$307$	−3.00000	−0.171219	−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000	−0.171219	−0.0856095	+	0.996329i	$0.527284\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	−9.00000	−0.508710	−0.254355	−	0.967111i	$-0.581863\pi$
$313$	−9.00000	−0.508710	−0.254355	+	0.967111i	$0.581863\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	2.00000	0.111979
$320$	0	0
$321$	0	0
$322$	−12.0000	−0.668734
$323$	−12.0000	−0.667698
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	−5.00000	−0.276079
$329$	6.00000	0.330791
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	0	0
$333$	0	0
$334$	−1.00000	−0.0547176
$335$	0	0
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	−1.00000	−0.0543928
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−20.0000	−1.07990
$344$	4.00000	0.215666
$345$	0	0
$346$	1.00000	0.0537603
$347$	33.0000	1.77153	0.885766	−	0.464131i	$-0.153633\pi$
$347$	33.0000	1.77153	0.885766	+	0.464131i	$0.153633\pi$
$348$	0	0
$349$	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
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−25.0000	−1.33062	−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000	−1.33062	−0.665308	+	0.746569i	$0.731700\pi$
$354$	0	0
$355$	0	0
$356$	−10.0000	−0.529999
$357$	0	0
$358$	20.0000	1.05703
$359$	−9.00000	−0.475002	−0.237501	−	0.971387i	$-0.576328\pi$
$359$	−9.00000	−0.475002	−0.237501	+	0.971387i	$0.576328\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−10.0000	−0.525588
$363$	0	0
$364$	−2.00000	−0.104828
$365$	0	0
$366$	0	0
$367$	−3.00000	−0.156599	−0.0782994	−	0.996930i	$-0.524949\pi$
$367$	−3.00000	−0.156599	−0.0782994	+	0.996930i	$0.524949\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	14.0000	0.726844
$372$	0	0
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	−3.00000	−0.154713
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0	0
$382$	6.00000	0.306987
$383$	9.00000	0.459879	0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000	0.459879	0.229939	+	0.973205i	$0.426147\pi$
$384$	0	0
$385$	0	0
$386$	16.0000	0.814379
$387$	0	0
$388$	14.0000	0.710742
$389$	−11.0000	−0.557722	−0.278861	−	0.960331i	$-0.589957\pi$
$389$	−11.0000	−0.557722	−0.278861	+	0.960331i	$0.589957\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	3.00000	0.151523
$393$	0	0
$394$	−18.0000	−0.906827
$395$	0	0
$396$	0	0
$397$	17.0000	0.853206	0.426603	−	0.904439i	$-0.359710\pi$
$397$	17.0000	0.853206	0.426603	+	0.904439i	$0.359710\pi$
$398$	3.00000	0.150376
$399$	0	0
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	0	0
$403$	0	0
$404$	10.0000	0.497519
$405$	0	0
$406$	−2.00000	−0.0992583
$407$	2.00000	0.0991363
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	0	0
$411$	0	0
$412$	−12.0000	−0.591198
$413$	4.00000	0.196827
$414$	0	0
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	6.00000	0.293470
$419$	−1.00000	−0.0488532	−0.0244266	−	0.999702i	$-0.507776\pi$
$419$	−1.00000	−0.0488532	−0.0244266	+	0.999702i	$0.507776\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	−10.0000	−0.486792
$423$	0	0
$424$	−7.00000	−0.339950
$425$	0	0
$426$	0	0
$427$	−20.0000	−0.967868
$428$	15.0000	0.725052
$429$	0	0
$430$	0	0
$431$	33.0000	1.58955	0.794777	−	0.606902i	$-0.207588\pi$
$431$	33.0000	1.58955	0.794777	+	0.606902i	$0.207588\pi$
$432$	0	0
$433$	−29.0000	−1.39365	−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000	−1.39365	−0.696826	+	0.717241i	$0.745405\pi$
$434$	0	0
$435$	0	0
$436$	3.00000	0.143674
$437$	−18.0000	−0.861057
$438$	0	0
$439$	1.00000	0.0477274	0.0238637	−	0.999715i	$-0.492403\pi$
$439$	1.00000	0.0477274	0.0238637	+	0.999715i	$0.492403\pi$
$440$	0	0
$441$	0	0
$442$	4.00000	0.190261
$443$	11.0000	0.522626	0.261313	−	0.965254i	$-0.415845\pi$
$443$	11.0000	0.522626	0.261313	+	0.965254i	$0.415845\pi$
$444$	0	0
$445$	0	0
$446$	−10.0000	−0.473514
$447$	0	0
$448$	2.00000	0.0944911
$449$	3.00000	0.141579	0.0707894	−	0.997491i	$-0.477448\pi$
$449$	3.00000	0.141579	0.0707894	+	0.997491i	$0.477448\pi$
$450$	0	0
$451$	10.0000	0.470882
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	−10.0000	−0.469323
$455$	0	0
$456$	0	0
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	−1.00000	−0.0467269
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	0	0
$467$	5.00000	0.231372	0.115686	−	0.993286i	$-0.463093\pi$
$467$	5.00000	0.231372	0.115686	+	0.993286i	$0.463093\pi$
$468$	0	0
$469$	18.0000	0.831163
$470$	0	0
$471$	0	0
$472$	−2.00000	−0.0920575
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	8.00000	0.366679
$477$	0	0
$478$	16.0000	0.731823
$479$	−23.0000	−1.05090	−0.525448	−	0.850825i	$-0.676102\pi$
$479$	−23.0000	−1.05090	−0.525448	+	0.850825i	$0.676102\pi$
$480$	0	0
$481$	−1.00000	−0.0455961
$482$	22.0000	1.00207
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−10.0000	−0.453143	−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000	−0.453143	−0.226572	+	0.973995i	$0.572752\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	4.00000	0.180151
$494$	−3.00000	−0.134976
$495$	0	0
$496$	0	0
$497$	−2.00000	−0.0897123
$498$	0	0
$499$	−1.00000	−0.0447661	−0.0223831	−	0.999749i	$-0.507125\pi$
$499$	−1.00000	−0.0447661	−0.0223831	+	0.999749i	$0.507125\pi$
$500$	0	0
$501$	0	0
$502$	−15.0000	−0.669483
$503$	−34.0000	−1.51599	−0.757993	−	0.652263i	$-0.773820\pi$
$503$	−34.0000	−1.51599	−0.757993	+	0.652263i	$0.773820\pi$
$504$	0	0
$505$	0	0
$506$	−12.0000	−0.533465
$507$	0	0
$508$	−11.0000	−0.488046
$509$	12.0000	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$510$	0	0
$511$	8.00000	0.353899
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	6.00000	0.264649
$515$	0	0
$516$	0	0
$517$	6.00000	0.263880
$518$	−2.00000	−0.0878750
$519$	0	0
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	0	0
$523$	12.0000	0.524723	0.262362	−	0.964970i	$-0.415499\pi$
$523$	12.0000	0.524723	0.262362	+	0.964970i	$0.415499\pi$
$524$	−7.00000	−0.305796
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−6.00000	−0.260133
$533$	−5.00000	−0.216574
$534$	0	0
$535$	0	0
$536$	−9.00000	−0.388741
$537$	0	0
$538$	3.00000	0.129339
$539$	−6.00000	−0.258438
$540$	0	0
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	2.00000	0.0859074
$543$	0	0
$544$	−4.00000	−0.171499
$545$	0	0
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	9.00000	0.384461
$549$	0	0
$550$	0	0
$551$	−3.00000	−0.127804
$552$	0	0
$553$	−2.00000	−0.0850487
$554$	−8.00000	−0.339887
$555$	0	0
$556$	22.0000	0.933008
$557$	16.0000	0.677942	0.338971	−	0.940797i	$-0.389921\pi$
$557$	16.0000	0.677942	0.338971	+	0.940797i	$0.389921\pi$
$558$	0	0
$559$	4.00000	0.169182
$560$	0	0
$561$	0	0
$562$	−27.0000	−1.13893
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	0	0
$565$	0	0
$566$	22.0000	0.924729
$567$	0	0
$568$	1.00000	0.0419591
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	22.0000	0.920671	0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000	0.920671	0.460336	+	0.887745i	$0.347729\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	−10.0000	−0.417392
$575$	0	0
$576$	0	0
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	14.0000	0.579821
$584$	−4.00000	−0.165521
$585$	0	0
$586$	−32.0000	−1.32191
$587$	−6.00000	−0.247647	−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000	−0.247647	−0.123823	+	0.992304i	$0.539516\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	1.00000	0.0410997
$593$	17.0000	0.698106	0.349053	−	0.937103i	$-0.386503\pi$
$593$	17.0000	0.698106	0.349053	+	0.937103i	$0.386503\pi$
$594$	0	0
$595$	0	0
$596$	−14.0000	−0.573462
$597$	0	0
$598$	6.00000	0.245358
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	13.0000	0.530281	0.265141	−	0.964210i	$-0.414582\pi$
$601$	13.0000	0.530281	0.265141	+	0.964210i	$0.414582\pi$
$602$	8.00000	0.326056
$603$	0	0
$604$	6.00000	0.244137
$605$	0	0
$606$	0	0
$607$	23.0000	0.933541	0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000	0.933541	0.466771	+	0.884378i	$0.345417\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	0	0
$611$	−3.00000	−0.121367
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	3.00000	0.121070
$615$	0	0
$616$	−4.00000	−0.161165
$617$	15.0000	0.603877	0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000	0.603877	0.301939	+	0.953327i	$0.402366\pi$
$618$	0	0
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	0	0
$621$	0	0
$622$	6.00000	0.240578
$623$	−20.0000	−0.801283
$624$	0	0
$625$	0	0
$626$	9.00000	0.359712
$627$	0	0
$628$	10.0000	0.399043
$629$	4.00000	0.159490
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	1.00000	0.0397779
$633$	0	0
$634$	−12.0000	−0.476581
$635$	0	0
$636$	0	0
$637$	3.00000	0.118864
$638$	−2.00000	−0.0791808
$639$	0	0
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	0	0
$643$	23.0000	0.907031	0.453516	−	0.891248i	$-0.350170\pi$
$643$	23.0000	0.907031	0.453516	+	0.891248i	$0.350170\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	12.0000	0.472134
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	0	0
$649$	4.00000	0.157014
$650$	0	0
$651$	0	0
$652$	−4.00000	−0.156652
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	0	0
$656$	5.00000	0.195217
$657$	0	0
$658$	−6.00000	−0.233904
$659$	13.0000	0.506408	0.253204	−	0.967413i	$-0.418516\pi$
$659$	13.0000	0.506408	0.253204	+	0.967413i	$0.418516\pi$
$660$	0	0
$661$	−9.00000	−0.350059	−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000	−0.350059	−0.175030	+	0.984563i	$0.556002\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	6.00000	0.232321
$668$	1.00000	0.0386912
$669$	0	0
$670$	0	0
$671$	−20.0000	−0.772091
$672$	0	0
$673$	−7.00000	−0.269830	−0.134915	−	0.990857i	$-0.543076\pi$
$673$	−7.00000	−0.269830	−0.134915	+	0.990857i	$0.543076\pi$
$674$	−14.0000	−0.539260
$675$	0	0
$676$	1.00000	0.0384615
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	28.0000	1.07454
$680$	0	0
$681$	0	0
$682$	0	0
$683$	8.00000	0.306111	0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000	0.306111	0.153056	+	0.988218i	$0.451089\pi$
$684$	0	0
$685$	0	0
$686$	20.0000	0.763604
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−7.00000	−0.266679
$690$	0	0
$691$	13.0000	0.494543	0.247272	−	0.968946i	$-0.420466\pi$
$691$	13.0000	0.494543	0.247272	+	0.968946i	$0.420466\pi$
$692$	−1.00000	−0.0380143
$693$	0	0
$694$	−33.0000	−1.25266
$695$	0	0
$696$	0	0
$697$	20.0000	0.757554
$698$	−14.0000	−0.529908
$699$	0	0
$700$	0	0
$701$	−38.0000	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$702$	0	0
$703$	−3.00000	−0.113147
$704$	2.00000	0.0753778
$705$	0	0
$706$	25.0000	0.940887
$707$	20.0000	0.752177
$708$	0	0
$709$	−22.0000	−0.826227	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000	−0.826227	−0.413114	+	0.910679i	$0.635559\pi$
$710$	0	0
$711$	0	0
$712$	10.0000	0.374766
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−20.0000	−0.747435
$717$	0	0
$718$	9.00000	0.335877
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	−24.0000	−0.893807
$722$	10.0000	0.372161
$723$	0	0
$724$	10.0000	0.371647
$725$	0	0
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	2.00000	0.0741249
$729$	0	0
$730$	0	0
$731$	−16.0000	−0.591781
$732$	0	0
$733$	−43.0000	−1.58824	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000	−1.58824	−0.794121	+	0.607760i	$0.792068\pi$
$734$	3.00000	0.110732
$735$	0	0
$736$	−6.00000	−0.221163
$737$	18.0000	0.663039
$738$	0	0
$739$	33.0000	1.21392	0.606962	−	0.794731i	$-0.292388\pi$
$739$	33.0000	1.21392	0.606962	+	0.794731i	$0.292388\pi$
$740$	0	0
$741$	0	0
$742$	−14.0000	−0.513956
$743$	15.0000	0.550297	0.275148	−	0.961402i	$-0.411273\pi$
$743$	15.0000	0.550297	0.275148	+	0.961402i	$0.411273\pi$
$744$	0	0
$745$	0	0
$746$	−22.0000	−0.805477
$747$	0	0
$748$	8.00000	0.292509
$749$	30.0000	1.09618
$750$	0	0
$751$	29.0000	1.05823	0.529113	−	0.848552i	$-0.322525\pi$
$751$	29.0000	1.05823	0.529113	+	0.848552i	$0.322525\pi$
$752$	3.00000	0.109399
$753$	0	0
$754$	1.00000	0.0364179
$755$	0	0
$756$	0	0
$757$	48.0000	1.74459	0.872295	−	0.488980i	$-0.162631\pi$
$757$	48.0000	1.74459	0.872295	+	0.488980i	$0.162631\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	0	0
$761$	−31.0000	−1.12375	−0.561875	−	0.827222i	$-0.689920\pi$
$761$	−31.0000	−1.12375	−0.561875	+	0.827222i	$0.689920\pi$
$762$	0	0
$763$	6.00000	0.217215
$764$	−6.00000	−0.217072
$765$	0	0
$766$	−9.00000	−0.325183
$767$	−2.00000	−0.0722158
$768$	0	0
$769$	16.0000	0.576975	0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000	0.576975	0.288487	+	0.957484i	$0.406848\pi$
$770$	0	0
$771$	0	0
$772$	−16.0000	−0.575853
$773$	−26.0000	−0.935155	−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000	−0.935155	−0.467578	+	0.883952i	$0.654873\pi$
$774$	0	0
$775$	0	0
$776$	−14.0000	−0.502571
$777$	0	0
$778$	11.0000	0.394369
$779$	−15.0000	−0.537431
$780$	0	0
$781$	−2.00000	−0.0715656
$782$	−24.0000	−0.858238
$783$	0	0
$784$	−3.00000	−0.107143
$785$	0	0
$786$	0	0
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	0	0
$791$	−4.00000	−0.142224
$792$	0	0
$793$	10.0000	0.355110
$794$	−17.0000	−0.603307
$795$	0	0
$796$	−3.00000	−0.106332
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	0	0
$799$	12.0000	0.424529
$800$	0	0
$801$	0	0
$802$	−6.00000	−0.211867
$803$	8.00000	0.282314
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−10.0000	−0.351799
$809$	−44.0000	−1.54696	−0.773479	−	0.633822i	$-0.781485\pi$
$809$	−44.0000	−1.54696	−0.773479	+	0.633822i	$0.781485\pi$
$810$	0	0
$811$	52.0000	1.82597	0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000	1.82597	0.912983	+	0.407997i	$0.133772\pi$
$812$	2.00000	0.0701862
$813$	0	0
$814$	−2.00000	−0.0701000
$815$	0	0
$816$	0	0
$817$	12.0000	0.419827
$818$	−34.0000	−1.18878
$819$	0	0
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	0	0
$823$	−1.00000	−0.0348578	−0.0174289	−	0.999848i	$-0.505548\pi$
$823$	−1.00000	−0.0348578	−0.0174289	+	0.999848i	$0.505548\pi$
$824$	12.0000	0.418040
$825$	0	0
$826$	−4.00000	−0.139178
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	0	0
$829$	−4.00000	−0.138926	−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000	−0.138926	−0.0694629	+	0.997585i	$0.522129\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−12.0000	−0.415775
$834$	0	0
$835$	0	0
$836$	−6.00000	−0.207514
$837$	0	0
$838$	1.00000	0.0345444
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−10.0000	−0.344623
$843$	0	0
$844$	10.0000	0.344214
$845$	0	0
$846$	0	0
$847$	−14.0000	−0.481046
$848$	7.00000	0.240381
$849$	0	0
$850$	0	0
$851$	6.00000	0.205677
$852$	0	0
$853$	−29.0000	−0.992941	−0.496471	−	0.868054i	$-0.665371\pi$
$853$	−29.0000	−0.992941	−0.496471	+	0.868054i	$0.665371\pi$
$854$	20.0000	0.684386
$855$	0	0
$856$	−15.0000	−0.512689
$857$	26.0000	0.888143	0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000	0.888143	0.444072	+	0.895991i	$0.353534\pi$
$858$	0	0
$859$	18.0000	0.614152	0.307076	−	0.951685i	$-0.400649\pi$
$859$	18.0000	0.614152	0.307076	+	0.951685i	$0.400649\pi$
$860$	0	0
$861$	0	0
$862$	−33.0000	−1.12398
$863$	−45.0000	−1.53182	−0.765909	−	0.642949i	$-0.777711\pi$
$863$	−45.0000	−1.53182	−0.765909	+	0.642949i	$0.777711\pi$
$864$	0	0
$865$	0	0
$866$	29.0000	0.985460
$867$	0	0
$868$	0	0
$869$	−2.00000	−0.0678454
$870$	0	0
$871$	−9.00000	−0.304953
$872$	−3.00000	−0.101593
$873$	0	0
$874$	18.0000	0.608859
$875$	0	0
$876$	0	0
$877$	−5.00000	−0.168838	−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000	−0.168838	−0.0844190	+	0.996430i	$0.526903\pi$
$878$	−1.00000	−0.0337484
$879$	0	0
$880$	0	0
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	0	0
$883$	32.0000	1.07689	0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000	1.07689	0.538443	+	0.842662i	$0.319013\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−11.0000	−0.369552
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	0	0
$889$	−22.0000	−0.737856
$890$	0	0
$891$	0	0
$892$	10.0000	0.334825
$893$	−9.00000	−0.301174
$894$	0	0
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	0	0
$898$	−3.00000	−0.100111
$899$	0	0
$900$	0	0
$901$	28.0000	0.932815
$902$	−10.0000	−0.332964
$903$	0	0
$904$	2.00000	0.0665190
$905$	0	0
$906$	0	0
$907$	10.0000	0.332045	0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000	0.332045	0.166022	+	0.986122i	$0.446908\pi$
$908$	10.0000	0.331862
$909$	0	0
$910$	0	0
$911$	−40.0000	−1.32526	−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000	−1.32526	−0.662630	+	0.748947i	$0.730560\pi$
$912$	0	0
$913$	0	0
$914$	16.0000	0.529233
$915$	0	0
$916$	1.00000	0.0330409
$917$	−14.0000	−0.462321
$918$	0	0
$919$	−35.0000	−1.15454	−0.577272	−	0.816552i	$-0.695883\pi$
$919$	−35.0000	−1.15454	−0.577272	+	0.816552i	$0.695883\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	1.00000	0.0329154
$924$	0	0
$925$	0	0
$926$	−16.0000	−0.525793
$927$	0	0
$928$	−1.00000	−0.0328266
$929$	21.0000	0.688988	0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000	0.688988	0.344494	+	0.938789i	$0.388051\pi$
$930$	0	0
$931$	9.00000	0.294963
$932$	0	0
$933$	0	0
$934$	−5.00000	−0.163605
$935$	0	0
$936$	0	0
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	−18.0000	−0.587721
$939$	0	0
$940$	0	0
$941$	−32.0000	−1.04317	−0.521585	−	0.853199i	$-0.674659\pi$
$941$	−32.0000	−1.04317	−0.521585	+	0.853199i	$0.674659\pi$
$942$	0	0
$943$	30.0000	0.976934
$944$	2.00000	0.0650945
$945$	0	0
$946$	8.00000	0.260102
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	0	0
$949$	−4.00000	−0.129845
$950$	0	0
$951$	0	0
$952$	−8.00000	−0.259281
$953$	−12.0000	−0.388718	−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000	−0.388718	−0.194359	+	0.980930i	$0.562263\pi$
$954$	0	0
$955$	0	0
$956$	−16.0000	−0.517477
$957$	0	0
$958$	23.0000	0.743096
$959$	18.0000	0.581250
$960$	0	0
$961$	−31.0000	−1.00000
$962$	1.00000	0.0322413
$963$	0	0
$964$	−22.0000	−0.708572
$965$	0	0
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	0	0
$971$	−41.0000	−1.31575	−0.657876	−	0.753126i	$-0.728545\pi$
$971$	−41.0000	−1.31575	−0.657876	+	0.753126i	$0.728545\pi$
$972$	0	0
$973$	44.0000	1.41058
$974$	10.0000	0.320421
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	−20.0000	−0.639203
$980$	0	0
$981$	0	0
$982$	−36.0000	−1.14881
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	0	0
$985$	0	0
$986$	−4.00000	−0.127386
$987$	0	0
$988$	3.00000	0.0954427
$989$	−24.0000	−0.763156
$990$	0	0
$991$	−3.00000	−0.0952981	−0.0476491	−	0.998864i	$-0.515173\pi$
$991$	−3.00000	−0.0952981	−0.0476491	+	0.998864i	$0.515173\pi$
$992$	0	0
$993$	0	0
$994$	2.00000	0.0634361
$995$	0	0
$996$	0	0
$997$	16.0000	0.506725	0.253363	−	0.967371i	$-0.418463\pi$
$997$	16.0000	0.506725	0.253363	+	0.967371i	$0.418463\pi$
$998$	1.00000	0.0316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5850.2.a.u.1.1	yes	1
3.2	odd	2		5850.2.a.bw.1.1	yes	1
5.2	odd	4		5850.2.e.w.5149.1		2
5.3	odd	4		5850.2.e.w.5149.2		2
5.4	even	2		5850.2.a.bl.1.1	yes	1
15.2	even	4		5850.2.e.k.5149.2		2
15.8	even	4		5850.2.e.k.5149.1		2
15.14	odd	2		5850.2.a.f.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5850.2.a.f.1.1	✓	1	15.14	odd	2
5850.2.a.u.1.1	yes	1	1.1	even	1	trivial
5850.2.a.bl.1.1	yes	1	5.4	even	2
5850.2.a.bw.1.1	yes	1	3.2	odd	2
5850.2.e.k.5149.1		2	15.8	even	4
5850.2.e.k.5149.2		2	15.2	even	4
5850.2.e.w.5149.1		2	5.2	odd	4
5850.2.e.w.5149.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5850.a (trivial)

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