LMFDB - Embedded newform 4600.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4600,2,Mod(1,4600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4600.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4600 = 2^{3} \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4600.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:	$36.7311849298$
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	$\chi$	$=$	4600.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+2.00000 q^{3} -1.00000 q^{7} +1.00000 q^{9} -5.00000 q^{11} -1.00000 q^{13} +4.00000 q^{17} +7.00000 q^{19} -2.00000 q^{21} +1.00000 q^{23} -4.00000 q^{27} +5.00000 q^{29} +2.00000 q^{31} -10.0000 q^{33} +2.00000 q^{37} -2.00000 q^{39} +11.0000 q^{41} -1.00000 q^{43} +8.00000 q^{47} -6.00000 q^{49} +8.00000 q^{51} +14.0000 q^{57} -14.0000 q^{59} +10.0000 q^{61} -1.00000 q^{63} +8.00000 q^{67} +2.00000 q^{69} -10.0000 q^{71} -7.00000 q^{73} +5.00000 q^{77} +7.00000 q^{79} -11.0000 q^{81} +15.0000 q^{83} +10.0000 q^{87} +10.0000 q^{89} +1.00000 q^{91} +4.00000 q^{93} +4.00000 q^{97} -5.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	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
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−4.00000	−0.769800
$28$	0	0
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	0	0
$33$	−10.0000	−1.74078
$34$	0	0
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	0	0
$41$	11.0000	1.71791	0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000	1.71791	0.858956	+	0.512050i	$0.171114\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	0	0
$51$	8.00000	1.12022
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	14.0000	1.85435
$58$	0	0
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	0	0
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	0	0
$69$	2.00000	0.240772
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	0	0
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	5.00000	0.569803
$78$	0	0
$79$	7.00000	0.787562	0.393781	−	0.919204i	$-0.371167\pi$
$79$	7.00000	0.787562	0.393781	+	0.919204i	$0.371167\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	15.0000	1.64646	0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000	1.64646	0.823232	+	0.567705i	$0.192169\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	10.0000	1.07211
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	0	0
$93$	4.00000	0.414781
$94$	0	0
$95$	0	0
$96$	0	0
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	0	0
$99$	−5.00000	−0.502519
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	0	0
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	−4.00000	−0.366679
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	22.0000	1.98367
$124$	0	0
$125$	0	0
$126$	0	0
$127$	22.0000	1.95218	0.976092	−	0.217357i	$-0.0697436\pi$
$127$	22.0000	1.95218	0.976092	+	0.217357i	$0.0697436\pi$
$128$	0	0
$129$	−2.00000	−0.176090
$130$	0	0
$131$	2.00000	0.174741	0.0873704	−	0.996176i	$-0.472154\pi$
$131$	2.00000	0.174741	0.0873704	+	0.996176i	$0.472154\pi$
$132$	0	0
$133$	−7.00000	−0.606977
$134$	0	0
$135$	0	0
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	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
$141$	16.0000	1.34744
$142$	0	0
$143$	5.00000	0.418121
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−12.0000	−0.989743
$148$	0	0
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	0	0
$153$	4.00000	0.323381
$154$	0	0
$155$	0	0
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	7.00000	0.535303
$172$	0	0
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−28.0000	−2.10461
$178$	0	0
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	0	0
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	0	0
$183$	20.0000	1.47844
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−20.0000	−1.46254
$188$	0	0
$189$	4.00000	0.290957
$190$	0	0
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	0	0
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	0	0
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0	0
$201$	16.0000	1.12855
$202$	0	0
$203$	−5.00000	−0.350931
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1.00000	0.0695048
$208$	0	0
$209$	−35.0000	−2.42100
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	0	0
$213$	−20.0000	−1.37038
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−2.00000	−0.135769
$218$	0	0
$219$	−14.0000	−0.946032
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	20.0000	1.33930	0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000	1.33930	0.669650	+	0.742677i	$0.266444\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	10.0000	0.657952
$232$	0	0
$233$	15.0000	0.982683	0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000	0.982683	0.491341	+	0.870967i	$0.336507\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	14.0000	0.909398
$238$	0	0
$239$	−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
$241$	−16.0000	−1.03065	−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000	−1.03065	−0.515325	+	0.856995i	$0.672329\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−7.00000	−0.445399
$248$	0	0
$249$	30.0000	1.90117
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	0	0
$253$	−5.00000	−0.314347
$254$	0	0
$255$	0	0
$256$	0	0
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	0	0
$261$	5.00000	0.309492
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	20.0000	1.22398
$268$	0	0
$269$	17.0000	1.03651	0.518254	−	0.855227i	$-0.326582\pi$
$269$	17.0000	1.03651	0.518254	+	0.855227i	$0.326582\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	2.00000	0.121046
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1.00000	0.0600842	0.0300421	−	0.999549i	$-0.490436\pi$
$277$	1.00000	0.0600842	0.0300421	+	0.999549i	$0.490436\pi$
$278$	0	0
$279$	2.00000	0.119737
$280$	0	0
$281$	−28.0000	−1.67034	−0.835170	−	0.549992i	$-0.814631\pi$
$281$	−28.0000	−1.67034	−0.835170	+	0.549992i	$0.814631\pi$
$282$	0	0
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−11.0000	−0.649309
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	8.00000	0.468968
$292$	0	0
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	20.0000	1.16052
$298$	0	0
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	1.00000	0.0576390
$302$	0	0
$303$	36.0000	2.06815
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	−22.0000	−1.25154
$310$	0	0
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	5.00000	0.280828	0.140414	−	0.990093i	$-0.455157\pi$
$317$	5.00000	0.280828	0.140414	+	0.990093i	$0.455157\pi$
$318$	0	0
$319$	−25.0000	−1.39973
$320$	0	0
$321$	0	0
$322$	0	0
$323$	28.0000	1.55796
$324$	0	0
$325$	0	0
$326$	0	0
$327$	4.00000	0.221201
$328$	0	0
$329$	−8.00000	−0.441054
$330$	0	0
$331$	−18.0000	−0.989369	−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000	−0.989369	−0.494685	+	0.869072i	$0.664716\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	0	0
$335$	0	0
$336$	0	0
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	0	0
$339$	−8.00000	−0.434500
$340$	0	0
$341$	−10.0000	−0.541530
$342$	0	0
$343$	13.0000	0.701934
$344$	0	0
$345$	0	0
$346$	0	0
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	0	0
$349$	21.0000	1.12410	0.562052	−	0.827102i	$-0.310012\pi$
$349$	21.0000	1.12410	0.562052	+	0.827102i	$0.310012\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	0	0
$353$	−11.0000	−0.585471	−0.292735	−	0.956193i	$-0.594566\pi$
$353$	−11.0000	−0.585471	−0.292735	+	0.956193i	$0.594566\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−8.00000	−0.423405
$358$	0	0
$359$	−33.0000	−1.74167	−0.870837	−	0.491572i	$-0.836422\pi$
$359$	−33.0000	−1.74167	−0.870837	+	0.491572i	$0.836422\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	28.0000	1.46962
$364$	0	0
$365$	0	0
$366$	0	0
$367$	3.00000	0.156599	0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000	0.156599	0.0782994	+	0.996930i	$0.475051\pi$
$368$	0	0
$369$	11.0000	0.572637
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	44.0000	2.25419
$382$	0	0
$383$	19.0000	0.970855	0.485427	−	0.874277i	$-0.338664\pi$
$383$	19.0000	0.970855	0.485427	+	0.874277i	$0.338664\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−1.00000	−0.0508329
$388$	0	0
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	0	0
$391$	4.00000	0.202289
$392$	0	0
$393$	4.00000	0.201773
$394$	0	0
$395$	0	0
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	−14.0000	−0.700877
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−10.0000	−0.495682
$408$	0	0
$409$	−11.0000	−0.543915	−0.271957	−	0.962309i	$-0.587671\pi$
$409$	−11.0000	−0.543915	−0.271957	+	0.962309i	$0.587671\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	0	0
$413$	14.0000	0.688895
$414$	0	0
$415$	0	0
$416$	0	0
$417$	8.00000	0.391762
$418$	0	0
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	0	0
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	0	0
$423$	8.00000	0.388973
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−10.0000	−0.483934
$428$	0	0
$429$	10.0000	0.482805
$430$	0	0
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	0	0
$433$	10.0000	0.480569	0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000	0.480569	0.240285	+	0.970702i	$0.422759\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	7.00000	0.334855
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	0	0
$443$	−30.0000	−1.42534	−0.712672	−	0.701498i	$-0.752515\pi$
$443$	−30.0000	−1.42534	−0.712672	+	0.701498i	$0.752515\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−4.00000	−0.189194
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	−55.0000	−2.58985
$452$	0	0
$453$	20.0000	0.939682
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	0	0
$459$	−16.0000	−0.746816
$460$	0	0
$461$	21.0000	0.978068	0.489034	−	0.872265i	$-0.337349\pi$
$461$	21.0000	0.978068	0.489034	+	0.872265i	$0.337349\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−27.0000	−1.24941	−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000	−1.24941	−0.624705	+	0.780860i	$0.714781\pi$
$468$	0	0
$469$	−8.00000	−0.369406
$470$	0	0
$471$	8.00000	0.368621
$472$	0	0
$473$	5.00000	0.229900
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−35.0000	−1.59919	−0.799595	−	0.600539i	$-0.794953\pi$
$479$	−35.0000	−1.59919	−0.799595	+	0.600539i	$0.794953\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	0	0
$483$	−2.00000	−0.0910032
$484$	0	0
$485$	0	0
$486$	0	0
$487$	20.0000	0.906287	0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000	0.906287	0.453143	+	0.891438i	$0.350303\pi$
$488$	0	0
$489$	−8.00000	−0.361773
$490$	0	0
$491$	6.00000	0.270776	0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000	0.270776	0.135388	+	0.990793i	$0.456772\pi$
$492$	0	0
$493$	20.0000	0.900755
$494$	0	0
$495$	0	0
$496$	0	0
$497$	10.0000	0.448561
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	44.0000	1.96578
$502$	0	0
$503$	−15.0000	−0.668817	−0.334408	−	0.942428i	$-0.608537\pi$
$503$	−15.0000	−0.668817	−0.334408	+	0.942428i	$0.608537\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−24.0000	−1.06588
$508$	0	0
$509$	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
$511$	7.00000	0.309662
$512$	0	0
$513$	−28.0000	−1.23623
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−40.0000	−1.75920
$518$	0	0
$519$	18.0000	0.790112
$520$	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
$523$	1.00000	0.0437269	0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000	0.0437269	0.0218635	+	0.999761i	$0.493040\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	8.00000	0.348485
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−14.0000	−0.607548
$532$	0	0
$533$	−11.0000	−0.476463
$534$	0	0
$535$	0	0
$536$	0	0
$537$	32.0000	1.38090
$538$	0	0
$539$	30.0000	1.29219
$540$	0	0
$541$	−19.0000	−0.816874	−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000	−0.816874	−0.408437	+	0.912787i	$0.633926\pi$
$542$	0	0
$543$	−24.0000	−1.02994
$544$	0	0
$545$	0	0
$546$	0	0
$547$	32.0000	1.36822	0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000	1.36822	0.684111	+	0.729378i	$0.260191\pi$
$548$	0	0
$549$	10.0000	0.426790
$550$	0	0
$551$	35.0000	1.49105
$552$	0	0
$553$	−7.00000	−0.297670
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	0	0
$559$	1.00000	0.0422955
$560$	0	0
$561$	−40.0000	−1.68880
$562$	0	0
$563$	−33.0000	−1.39078	−0.695392	−	0.718631i	$-0.744769\pi$
$563$	−33.0000	−1.39078	−0.695392	+	0.718631i	$0.744769\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	11.0000	0.461957
$568$	0	0
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	−54.0000	−2.25588
$574$	0	0
$575$	0	0
$576$	0	0
$577$	41.0000	1.70685	0.853426	−	0.521214i	$-0.174521\pi$
$577$	41.0000	1.70685	0.853426	+	0.521214i	$0.174521\pi$
$578$	0	0
$579$	−12.0000	−0.498703
$580$	0	0
$581$	−15.0000	−0.622305
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−2.00000	−0.0825488	−0.0412744	−	0.999148i	$-0.513142\pi$
$587$	−2.00000	−0.0825488	−0.0412744	+	0.999148i	$0.513142\pi$
$588$	0	0
$589$	14.0000	0.576860
$590$	0	0
$591$	42.0000	1.72765
$592$	0	0
$593$	23.0000	0.944497	0.472248	−	0.881466i	$-0.343443\pi$
$593$	23.0000	0.944497	0.472248	+	0.881466i	$0.343443\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−34.0000	−1.39153
$598$	0	0
$599$	14.0000	0.572024	0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000	0.572024	0.286012	+	0.958226i	$0.407670\pi$
$600$	0	0
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−36.0000	−1.46119	−0.730597	−	0.682808i	$-0.760758\pi$
$607$	−36.0000	−1.46119	−0.730597	+	0.682808i	$0.760758\pi$
$608$	0	0
$609$	−10.0000	−0.405220
$610$	0	0
$611$	−8.00000	−0.323645
$612$	0	0
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	0	0
$621$	−4.00000	−0.160514
$622$	0	0
$623$	−10.0000	−0.400642
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−70.0000	−2.79553
$628$	0	0
$629$	8.00000	0.318981
$630$	0	0
$631$	13.0000	0.517522	0.258761	−	0.965941i	$-0.416686\pi$
$631$	13.0000	0.517522	0.258761	+	0.965941i	$0.416686\pi$
$632$	0	0
$633$	4.00000	0.158986
$634$	0	0
$635$	0	0
$636$	0	0
$637$	6.00000	0.237729
$638$	0	0
$639$	−10.0000	−0.395594
$640$	0	0
$641$	24.0000	0.947943	0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000	0.947943	0.473972	+	0.880540i	$0.342820\pi$
$642$	0	0
$643$	−5.00000	−0.197181	−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000	−0.197181	−0.0985904	+	0.995128i	$0.531433\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	0	0
$649$	70.0000	2.74774
$650$	0	0
$651$	−4.00000	−0.156772
$652$	0	0
$653$	−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
$655$	0	0
$656$	0	0
$657$	−7.00000	−0.273096
$658$	0	0
$659$	−3.00000	−0.116863	−0.0584317	−	0.998291i	$-0.518610\pi$
$659$	−3.00000	−0.116863	−0.0584317	+	0.998291i	$0.518610\pi$
$660$	0	0
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	0	0
$663$	−8.00000	−0.310694
$664$	0	0
$665$	0	0
$666$	0	0
$667$	5.00000	0.193601
$668$	0	0
$669$	40.0000	1.54649
$670$	0	0
$671$	−50.0000	−1.93023
$672$	0	0
$673$	23.0000	0.886585	0.443292	−	0.896377i	$-0.353810\pi$
$673$	23.0000	0.886585	0.443292	+	0.896377i	$0.353810\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	0	0
$681$	−24.0000	−0.919682
$682$	0	0
$683$	−6.00000	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−44.0000	−1.67870
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	0	0
$693$	5.00000	0.189934
$694$	0	0
$695$	0	0
$696$	0	0
$697$	44.0000	1.66662
$698$	0	0
$699$	30.0000	1.13470
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	0	0
$703$	14.0000	0.528020
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−18.0000	−0.676960
$708$	0	0
$709$	26.0000	0.976450	0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000	0.976450	0.488225	+	0.872718i	$0.337644\pi$
$710$	0	0
$711$	7.00000	0.262521
$712$	0	0
$713$	2.00000	0.0749006
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−32.0000	−1.19506
$718$	0	0
$719$	38.0000	1.41716	0.708580	−	0.705630i	$-0.249336\pi$
$719$	38.0000	1.41716	0.708580	+	0.705630i	$0.249336\pi$
$720$	0	0
$721$	11.0000	0.409661
$722$	0	0
$723$	−32.0000	−1.19009
$724$	0	0
$725$	0	0
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−4.00000	−0.147945
$732$	0	0
$733$	38.0000	1.40356	0.701781	−	0.712393i	$-0.252388\pi$
$733$	38.0000	1.40356	0.701781	+	0.712393i	$0.252388\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−22.0000	−0.809283	−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000	−0.809283	−0.404642	+	0.914475i	$0.632604\pi$
$740$	0	0
$741$	−14.0000	−0.514303
$742$	0	0
$743$	39.0000	1.43077	0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000	1.43077	0.715386	+	0.698730i	$0.246251\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	15.0000	0.548821
$748$	0	0
$749$	0	0
$750$	0	0
$751$	41.0000	1.49611	0.748056	−	0.663636i	$-0.230988\pi$
$751$	41.0000	1.49611	0.748056	+	0.663636i	$0.230988\pi$
$752$	0	0
$753$	−8.00000	−0.291536
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	0	0
$759$	−10.0000	−0.362977
$760$	0	0
$761$	−23.0000	−0.833749	−0.416875	−	0.908964i	$-0.636875\pi$
$761$	−23.0000	−0.833749	−0.416875	+	0.908964i	$0.636875\pi$
$762$	0	0
$763$	−2.00000	−0.0724049
$764$	0	0
$765$	0	0
$766$	0	0
$767$	14.0000	0.505511
$768$	0	0
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	0	0
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−4.00000	−0.143499
$778$	0	0
$779$	77.0000	2.75881
$780$	0	0
$781$	50.0000	1.78914
$782$	0	0
$783$	−20.0000	−0.714742
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−47.0000	−1.67537	−0.837685	−	0.546154i	$-0.816091\pi$
$787$	−47.0000	−1.67537	−0.837685	+	0.546154i	$0.816091\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	4.00000	0.142224
$792$	0	0
$793$	−10.0000	−0.355110
$794$	0	0
$795$	0	0
$796$	0	0
$797$	54.0000	1.91278	0.956389	−	0.292096i	$-0.0943526\pi$
$797$	54.0000	1.91278	0.956389	+	0.292096i	$0.0943526\pi$
$798$	0	0
$799$	32.0000	1.13208
$800$	0	0
$801$	10.0000	0.353333
$802$	0	0
$803$	35.0000	1.23512
$804$	0	0
$805$	0	0
$806$	0	0
$807$	34.0000	1.19686
$808$	0	0
$809$	17.0000	0.597688	0.298844	−	0.954302i	$-0.403399\pi$
$809$	17.0000	0.597688	0.298844	+	0.954302i	$0.403399\pi$
$810$	0	0
$811$	−56.0000	−1.96643	−0.983213	−	0.182462i	$-0.941593\pi$
$811$	−56.0000	−1.96643	−0.983213	+	0.182462i	$0.941593\pi$
$812$	0	0
$813$	16.0000	0.561144
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−7.00000	−0.244899
$818$	0	0
$819$	1.00000	0.0349428
$820$	0	0
$821$	31.0000	1.08191	0.540954	−	0.841052i	$-0.318063\pi$
$821$	31.0000	1.08191	0.540954	+	0.841052i	$0.318063\pi$
$822$	0	0
$823$	−36.0000	−1.25488	−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000	−1.25488	−0.627441	+	0.778664i	$0.715897\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	41.0000	1.42571	0.712855	−	0.701312i	$-0.247402\pi$
$827$	41.0000	1.42571	0.712855	+	0.701312i	$0.247402\pi$
$828$	0	0
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	0	0
$831$	2.00000	0.0693792
$832$	0	0
$833$	−24.0000	−0.831551
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−8.00000	−0.276520
$838$	0	0
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	−56.0000	−1.92874
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−14.0000	−0.481046
$848$	0	0
$849$	−56.0000	−1.92192
$850$	0	0
$851$	2.00000	0.0685591
$852$	0	0
$853$	7.00000	0.239675	0.119838	−	0.992793i	$-0.461763\pi$
$853$	7.00000	0.239675	0.119838	+	0.992793i	$0.461763\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	58.0000	1.98124	0.990621	−	0.136637i	$-0.0436295\pi$
$857$	58.0000	1.98124	0.990621	+	0.136637i	$0.0436295\pi$
$858$	0	0
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	0	0
$861$	−22.0000	−0.749758
$862$	0	0
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−2.00000	−0.0679236
$868$	0	0
$869$	−35.0000	−1.18729
$870$	0	0
$871$	−8.00000	−0.271070
$872$	0	0
$873$	4.00000	0.135379
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	0	0
$879$	24.0000	0.809500
$880$	0	0
$881$	14.0000	0.471672	0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000	0.471672	0.235836	+	0.971793i	$0.424217\pi$
$882$	0	0
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	−22.0000	−0.737856
$890$	0	0
$891$	55.0000	1.84257
$892$	0	0
$893$	56.0000	1.87397
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−2.00000	−0.0667781
$898$	0	0
$899$	10.0000	0.333519
$900$	0	0
$901$	0	0
$902$	0	0
$903$	2.00000	0.0665558
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−7.00000	−0.232431	−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000	−0.232431	−0.116216	+	0.993224i	$0.537076\pi$
$908$	0	0
$909$	18.0000	0.597022
$910$	0	0
$911$	47.0000	1.55718	0.778590	−	0.627533i	$-0.215935\pi$
$911$	47.0000	1.55718	0.778590	+	0.627533i	$0.215935\pi$
$912$	0	0
$913$	−75.0000	−2.48214
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−2.00000	−0.0660458
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	−32.0000	−1.05444
$922$	0	0
$923$	10.0000	0.329154
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−11.0000	−0.361287
$928$	0	0
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	0	0
$931$	−42.0000	−1.37649
$932$	0	0
$933$	4.00000	0.130954
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−48.0000	−1.56809	−0.784046	−	0.620703i	$-0.786847\pi$
$937$	−48.0000	−1.56809	−0.784046	+	0.620703i	$0.786847\pi$
$938$	0	0
$939$	−44.0000	−1.43589
$940$	0	0
$941$	−20.0000	−0.651981	−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000	−0.651981	−0.325991	+	0.945373i	$0.605698\pi$
$942$	0	0
$943$	11.0000	0.358209
$944$	0	0
$945$	0	0
$946$	0	0
$947$	38.0000	1.23483	0.617417	−	0.786636i	$-0.288179\pi$
$947$	38.0000	1.23483	0.617417	+	0.786636i	$0.288179\pi$
$948$	0	0
$949$	7.00000	0.227230
$950$	0	0
$951$	10.0000	0.324272
$952$	0	0
$953$	−38.0000	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−50.0000	−1.61627
$958$	0	0
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	0	0
$969$	56.0000	1.79898
$970$	0	0
$971$	−55.0000	−1.76503	−0.882517	−	0.470281i	$-0.844153\pi$
$971$	−55.0000	−1.76503	−0.882517	+	0.470281i	$0.844153\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	0	0
$975$	0	0
$976$	0	0
$977$	8.00000	0.255943	0.127971	−	0.991778i	$-0.459153\pi$
$977$	8.00000	0.255943	0.127971	+	0.991778i	$0.459153\pi$
$978$	0	0
$979$	−50.0000	−1.59801
$980$	0	0
$981$	2.00000	0.0638551
$982$	0	0
$983$	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
$985$	0	0
$986$	0	0
$987$	−16.0000	−0.509286
$988$	0	0
$989$	−1.00000	−0.0317982
$990$	0	0
$991$	28.0000	0.889449	0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000	0.889449	0.444725	+	0.895667i	$0.353302\pi$
$992$	0	0
$993$	−36.0000	−1.14243
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−23.0000	−0.728417	−0.364209	−	0.931317i	$-0.618661\pi$
$997$	−23.0000	−0.728417	−0.364209	+	0.931317i	$0.618661\pi$
$998$	0	0
$999$	−8.00000	−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4600.2.a.n.1.1	yes	1
4.3	odd	2		9200.2.a.i.1.1		1
5.2	odd	4		4600.2.e.c.4049.1		2
5.3	odd	4		4600.2.e.c.4049.2		2
5.4	even	2		4600.2.a.c.1.1	✓	1
20.19	odd	2		9200.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4600.2.a.c.1.1	✓	1	5.4	even	2
4600.2.a.n.1.1	yes	1	1.1	even	1	trivial
4600.2.e.c.4049.1		2	5.2	odd	4
4600.2.e.c.4049.2		2	5.3	odd	4
9200.2.a.i.1.1		1	4.3	odd	2
9200.2.a.bd.1.1		1	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4600.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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