LMFDB - Embedded newform 4014.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4014,2,Mod(1,4014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4014, 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("4014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4014 = 2 \cdot 3^{2} \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4014.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:	$32.0519513713$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 446)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} +4.00000 q^{10} +5.00000 q^{11} -6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +4.00000 q^{20} +5.00000 q^{22} +5.00000 q^{23} +11.0000 q^{25} -6.00000 q^{26} -4.00000 q^{28} +3.00000 q^{29} +2.00000 q^{31} +1.00000 q^{32} -1.00000 q^{34} -16.0000 q^{35} +5.00000 q^{37} +4.00000 q^{40} +5.00000 q^{41} -6.00000 q^{43} +5.00000 q^{44} +5.00000 q^{46} +6.00000 q^{47} +9.00000 q^{49} +11.0000 q^{50} -6.00000 q^{52} +1.00000 q^{53} +20.0000 q^{55} -4.00000 q^{56} +3.00000 q^{58} +11.0000 q^{59} +2.00000 q^{62} +1.00000 q^{64} -24.0000 q^{65} +11.0000 q^{67} -1.00000 q^{68} -16.0000 q^{70} +12.0000 q^{71} -5.00000 q^{73} +5.00000 q^{74} -20.0000 q^{77} -8.00000 q^{79} +4.00000 q^{80} +5.00000 q^{82} +6.00000 q^{83} -4.00000 q^{85} -6.00000 q^{86} +5.00000 q^{88} -3.00000 q^{89} +24.0000 q^{91} +5.00000 q^{92} +6.00000 q^{94} -18.0000 q^{97} +9.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	4.00000	1.26491
$11$	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
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	0	0
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	4.00000	0.894427
$21$	0	0
$22$	5.00000	1.06600
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	−6.00000	−1.17670
$27$	0	0
$28$	−4.00000	−0.755929
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−1.00000	−0.171499
$35$	−16.0000	−2.70449
$36$	0	0
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	0	0
$39$	0	0
$40$	4.00000	0.632456
$41$	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
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	5.00000	0.737210
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	11.0000	1.55563
$51$	0	0
$52$	−6.00000	−0.832050
$53$	1.00000	0.137361	0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000	0.137361	0.0686803	+	0.997639i	$0.478121\pi$
$54$	0	0
$55$	20.0000	2.69680
$56$	−4.00000	−0.534522
$57$	0	0
$58$	3.00000	0.393919
$59$	11.0000	1.43208	0.716039	−	0.698060i	$-0.245953\pi$
$59$	11.0000	1.43208	0.716039	+	0.698060i	$0.245953\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−24.0000	−2.97683
$66$	0	0
$67$	11.0000	1.34386	0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000	1.34386	0.671932	+	0.740613i	$0.265465\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	−16.0000	−1.91237
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	5.00000	0.581238
$75$	0	0
$76$	0	0
$77$	−20.0000	−2.27921
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	4.00000	0.447214
$81$	0	0
$82$	5.00000	0.552158
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	−4.00000	−0.433861
$86$	−6.00000	−0.646997
$87$	0	0
$88$	5.00000	0.533002
$89$	−3.00000	−0.317999	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000	−0.317999	−0.159000	+	0.987279i	$0.550827\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	5.00000	0.521286
$93$	0	0
$94$	6.00000	0.618853
$95$	0	0
$96$	0	0
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	11.0000	1.10000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	1.00000	0.0971286
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	20.0000	1.90693
$111$	0	0
$112$	−4.00000	−0.377964
$113$	−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
$115$	20.0000	1.86501
$116$	3.00000	0.278543
$117$	0	0
$118$	11.0000	1.01263
$119$	4.00000	0.366679
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	2.00000	0.179605
$125$	24.0000	2.14663
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−24.0000	−2.10494
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	0	0
$133$	0	0
$134$	11.0000	0.950255
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	−22.0000	−1.87959	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−22.0000	−1.87959	−0.939793	+	0.341743i	$0.888983\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	−16.0000	−1.35225
$141$	0	0
$142$	12.0000	1.00702
$143$	−30.0000	−2.50873
$144$	0	0
$145$	12.0000	0.996546
$146$	−5.00000	−0.413803
$147$	0	0
$148$	5.00000	0.410997
$149$	−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
$151$	−11.0000	−0.895167	−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000	−0.895167	−0.447584	+	0.894242i	$0.647715\pi$
$152$	0	0
$153$	0	0
$154$	−20.0000	−1.61165
$155$	8.00000	0.642575
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	4.00000	0.316228
$161$	−20.0000	−1.57622
$162$	0	0
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	6.00000	0.465690
$167$	11.0000	0.851206	0.425603	−	0.904910i	$-0.360062\pi$
$167$	11.0000	0.851206	0.425603	+	0.904910i	$0.360062\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	−4.00000	−0.306786
$171$	0	0
$172$	−6.00000	−0.457496
$173$	−20.0000	−1.52057	−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000	−1.52057	−0.760286	+	0.649589i	$0.774941\pi$
$174$	0	0
$175$	−44.0000	−3.32609
$176$	5.00000	0.376889
$177$	0	0
$178$	−3.00000	−0.224860
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	24.0000	1.77900
$183$	0	0
$184$	5.00000	0.368605
$185$	20.0000	1.47043
$186$	0	0
$187$	−5.00000	−0.365636
$188$	6.00000	0.437595
$189$	0	0
$190$	0	0
$191$	1.00000	0.0723575	0.0361787	−	0.999345i	$-0.488481\pi$
$191$	1.00000	0.0723575	0.0361787	+	0.999345i	$0.488481\pi$
$192$	0	0
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	9.00000	0.642857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	14.0000	0.985037
$203$	−12.0000	−0.842235
$204$	0	0
$205$	20.0000	1.39686
$206$	−1.00000	−0.0696733
$207$	0	0
$208$	−6.00000	−0.416025
$209$	0	0
$210$	0	0
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	1.00000	0.0686803
$213$	0	0
$214$	4.00000	0.273434
$215$	−24.0000	−1.63679
$216$	0	0
$217$	−8.00000	−0.543075
$218$	−2.00000	−0.135457
$219$	0	0
$220$	20.0000	1.34840
$221$	6.00000	0.403604
$222$	0	0
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	−4.00000	−0.267261
$225$	0	0
$226$	−2.00000	−0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	20.0000	1.31876
$231$	0	0
$232$	3.00000	0.196960
$233$	4.00000	0.262049	0.131024	−	0.991379i	$-0.458173\pi$
$233$	4.00000	0.262049	0.131024	+	0.991379i	$0.458173\pi$
$234$	0	0
$235$	24.0000	1.56559
$236$	11.0000	0.716039
$237$	0	0
$238$	4.00000	0.259281
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	5.00000	0.322078	0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000	0.322078	0.161039	+	0.986948i	$0.448515\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	0	0
$245$	36.0000	2.29996
$246$	0	0
$247$	0	0
$248$	2.00000	0.127000
$249$	0	0
$250$	24.0000	1.51789
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	25.0000	1.57174
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	1.00000	0.0623783	0.0311891	−	0.999514i	$-0.490071\pi$
$257$	1.00000	0.0623783	0.0311891	+	0.999514i	$0.490071\pi$
$258$	0	0
$259$	−20.0000	−1.24274
$260$	−24.0000	−1.48842
$261$	0	0
$262$	−10.0000	−0.617802
$263$	−3.00000	−0.184988	−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000	−0.184988	−0.0924940	+	0.995713i	$0.529484\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	0	0
$267$	0	0
$268$	11.0000	0.671932
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	−9.00000	−0.546711	−0.273356	−	0.961913i	$-0.588134\pi$
$271$	−9.00000	−0.546711	−0.273356	+	0.961913i	$0.588134\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−22.0000	−1.32907
$275$	55.0000	3.31662
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−10.0000	−0.599760
$279$	0	0
$280$	−16.0000	−0.956183
$281$	21.0000	1.25275	0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000	1.25275	0.626377	+	0.779520i	$0.284537\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	−30.0000	−1.77394
$287$	−20.0000	−1.18056
$288$	0	0
$289$	−16.0000	−0.941176
$290$	12.0000	0.704664
$291$	0	0
$292$	−5.00000	−0.292603
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	44.0000	2.56178
$296$	5.00000	0.290619
$297$	0	0
$298$	−2.00000	−0.115857
$299$	−30.0000	−1.73494
$300$	0	0
$301$	24.0000	1.38334
$302$	−11.0000	−0.632979
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	−20.0000	−1.13961
$309$	0	0
$310$	8.00000	0.454369
$311$	9.00000	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$311$	9.00000	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−8.00000	−0.450035
$317$	19.0000	1.06715	0.533573	−	0.845754i	$-0.320849\pi$
$317$	19.0000	1.06715	0.533573	+	0.845754i	$0.320849\pi$
$318$	0	0
$319$	15.0000	0.839839
$320$	4.00000	0.223607
$321$	0	0
$322$	−20.0000	−1.11456
$323$	0	0
$324$	0	0
$325$	−66.0000	−3.66102
$326$	16.0000	0.886158
$327$	0	0
$328$	5.00000	0.276079
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	11.0000	0.601893
$335$	44.0000	2.40398
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	−4.00000	−0.216930
$341$	10.0000	0.541530
$342$	0	0
$343$	−8.00000	−0.431959
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−20.0000	−1.07521
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−1.00000	−0.0535288	−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000	−0.0535288	−0.0267644	+	0.999642i	$0.508520\pi$
$350$	−44.0000	−2.35190
$351$	0	0
$352$	5.00000	0.266501
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	0	0
$355$	48.0000	2.54758
$356$	−3.00000	−0.159000
$357$	0	0
$358$	−24.0000	−1.26844
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−7.00000	−0.367912
$363$	0	0
$364$	24.0000	1.25794
$365$	−20.0000	−1.04685
$366$	0	0
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	5.00000	0.260643
$369$	0	0
$370$	20.0000	1.03975
$371$	−4.00000	−0.207670
$372$	0	0
$373$	24.0000	1.24267	0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000	1.24267	0.621336	+	0.783544i	$0.286590\pi$
$374$	−5.00000	−0.258544
$375$	0	0
$376$	6.00000	0.309426
$377$	−18.0000	−0.927047
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	0	0
$382$	1.00000	0.0511645
$383$	−27.0000	−1.37964	−0.689818	−	0.723983i	$-0.742309\pi$
$383$	−27.0000	−1.37964	−0.689818	+	0.723983i	$0.742309\pi$
$384$	0	0
$385$	−80.0000	−4.07718
$386$	−4.00000	−0.203595
$387$	0	0
$388$	−18.0000	−0.913812
$389$	3.00000	0.152106	0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000	0.152106	0.0760530	+	0.997104i	$0.475768\pi$
$390$	0	0
$391$	−5.00000	−0.252861
$392$	9.00000	0.454569
$393$	0	0
$394$	−6.00000	−0.302276
$395$	−32.0000	−1.61009
$396$	0	0
$397$	−28.0000	−1.40528	−0.702640	−	0.711546i	$-0.747995\pi$
$397$	−28.0000	−1.40528	−0.702640	+	0.711546i	$0.747995\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	11.0000	0.550000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	−12.0000	−0.597763
$404$	14.0000	0.696526
$405$	0	0
$406$	−12.0000	−0.595550
$407$	25.0000	1.23920
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	20.0000	0.987730
$411$	0	0
$412$	−1.00000	−0.0492665
$413$	−44.0000	−2.16510
$414$	0	0
$415$	24.0000	1.17811
$416$	−6.00000	−0.294174
$417$	0	0
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−2.00000	−0.0973585
$423$	0	0
$424$	1.00000	0.0485643
$425$	−11.0000	−0.533578
$426$	0	0
$427$	0	0
$428$	4.00000	0.193347
$429$	0	0
$430$	−24.0000	−1.15738
$431$	−19.0000	−0.915198	−0.457599	−	0.889159i	$-0.651290\pi$
$431$	−19.0000	−0.915198	−0.457599	+	0.889159i	$0.651290\pi$
$432$	0	0
$433$	−26.0000	−1.24948	−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000	−1.24948	−0.624740	+	0.780833i	$0.714795\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	0	0
$438$	0	0
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	20.0000	0.953463
$441$	0	0
$442$	6.00000	0.285391
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	−12.0000	−0.568855
$446$	1.00000	0.0473514
$447$	0	0
$448$	−4.00000	−0.188982
$449$	38.0000	1.79333	0.896665	−	0.442709i	$-0.145982\pi$
$449$	38.0000	1.79333	0.896665	+	0.442709i	$0.145982\pi$
$450$	0	0
$451$	25.0000	1.17720
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	12.0000	0.563188
$455$	96.0000	4.50055
$456$	0	0
$457$	12.0000	0.561336	0.280668	−	0.959805i	$-0.409444\pi$
$457$	12.0000	0.561336	0.280668	+	0.959805i	$0.409444\pi$
$458$	4.00000	0.186908
$459$	0	0
$460$	20.0000	0.932505
$461$	15.0000	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$462$	0	0
$463$	−12.0000	−0.557687	−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000	−0.557687	−0.278844	+	0.960337i	$0.589951\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	4.00000	0.185296
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	0	0
$469$	−44.0000	−2.03173
$470$	24.0000	1.10704
$471$	0	0
$472$	11.0000	0.506316
$473$	−30.0000	−1.37940
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	0	0
$478$	6.00000	0.274434
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	−30.0000	−1.36788
$482$	5.00000	0.227744
$483$	0	0
$484$	14.0000	0.636364
$485$	−72.0000	−3.26935
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	0	0
$489$	0	0
$490$	36.0000	1.62631
$491$	−21.0000	−0.947717	−0.473858	−	0.880601i	$-0.657139\pi$
$491$	−21.0000	−0.947717	−0.473858	+	0.880601i	$0.657139\pi$
$492$	0	0
$493$	−3.00000	−0.135113
$494$	0	0
$495$	0	0
$496$	2.00000	0.0898027
$497$	−48.0000	−2.15309
$498$	0	0
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	−2.00000	−0.0892644
$503$	−35.0000	−1.56057	−0.780286	−	0.625422i	$-0.784927\pi$
$503$	−35.0000	−1.56057	−0.780286	+	0.625422i	$0.784927\pi$
$504$	0	0
$505$	56.0000	2.49197
$506$	25.0000	1.11139
$507$	0	0
$508$	−2.00000	−0.0887357
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	0	0
$511$	20.0000	0.884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	1.00000	0.0441081
$515$	−4.00000	−0.176261
$516$	0	0
$517$	30.0000	1.31940
$518$	−20.0000	−0.878750
$519$	0	0
$520$	−24.0000	−1.05247
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	−10.0000	−0.436852
$525$	0	0
$526$	−3.00000	−0.130806
$527$	−2.00000	−0.0871214
$528$	0	0
$529$	2.00000	0.0869565
$530$	4.00000	0.173749
$531$	0	0
$532$	0	0
$533$	−30.0000	−1.29944
$534$	0	0
$535$	16.0000	0.691740
$536$	11.0000	0.475128
$537$	0	0
$538$	−24.0000	−1.03471
$539$	45.0000	1.93829
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−9.00000	−0.386583
$543$	0	0
$544$	−1.00000	−0.0428746
$545$	−8.00000	−0.342682
$546$	0	0
$547$	38.0000	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$548$	−22.0000	−0.939793
$549$	0	0
$550$	55.0000	2.34521
$551$	0	0
$552$	0	0
$553$	32.0000	1.36078
$554$	−8.00000	−0.339887
$555$	0	0
$556$	−10.0000	−0.424094
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	0	0
$559$	36.0000	1.52264
$560$	−16.0000	−0.676123
$561$	0	0
$562$	21.0000	0.885832
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	0	0
$565$	−8.00000	−0.336563
$566$	6.00000	0.252199
$567$	0	0
$568$	12.0000	0.503509
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	0	0
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	−30.0000	−1.25436
$573$	0	0
$574$	−20.0000	−0.834784
$575$	55.0000	2.29366
$576$	0	0
$577$	9.00000	0.374675	0.187337	−	0.982296i	$-0.440014\pi$
$577$	9.00000	0.374675	0.187337	+	0.982296i	$0.440014\pi$
$578$	−16.0000	−0.665512
$579$	0	0
$580$	12.0000	0.498273
$581$	−24.0000	−0.995688
$582$	0	0
$583$	5.00000	0.207079
$584$	−5.00000	−0.206901
$585$	0	0
$586$	24.0000	0.991431
$587$	5.00000	0.206372	0.103186	−	0.994662i	$-0.467096\pi$
$587$	5.00000	0.206372	0.103186	+	0.994662i	$0.467096\pi$
$588$	0	0
$589$	0	0
$590$	44.0000	1.81145
$591$	0	0
$592$	5.00000	0.205499
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	0	0
$595$	16.0000	0.655936
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	−30.0000	−1.22679
$599$	20.0000	0.817178	0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000	0.817178	0.408589	+	0.912719i	$0.366021\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	24.0000	0.978167
$603$	0	0
$604$	−11.0000	−0.447584
$605$	56.0000	2.27672
$606$	0	0
$607$	11.0000	0.446476	0.223238	−	0.974764i	$-0.428337\pi$
$607$	11.0000	0.446476	0.223238	+	0.974764i	$0.428337\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−36.0000	−1.45640
$612$	0	0
$613$	−20.0000	−0.807792	−0.403896	−	0.914805i	$-0.632344\pi$
$613$	−20.0000	−0.807792	−0.403896	+	0.914805i	$0.632344\pi$
$614$	−23.0000	−0.928204
$615$	0	0
$616$	−20.0000	−0.805823
$617$	13.0000	0.523360	0.261680	−	0.965155i	$-0.415723\pi$
$617$	13.0000	0.523360	0.261680	+	0.965155i	$0.415723\pi$
$618$	0	0
$619$	7.00000	0.281354	0.140677	−	0.990056i	$-0.455072\pi$
$619$	7.00000	0.281354	0.140677	+	0.990056i	$0.455072\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	9.00000	0.360867
$623$	12.0000	0.480770
$624$	0	0
$625$	41.0000	1.64000
$626$	−26.0000	−1.03917
$627$	0	0
$628$	−14.0000	−0.558661
$629$	−5.00000	−0.199363
$630$	0	0
$631$	21.0000	0.835997	0.417998	−	0.908448i	$-0.362732\pi$
$631$	21.0000	0.835997	0.417998	+	0.908448i	$0.362732\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	19.0000	0.754586
$635$	−8.00000	−0.317470
$636$	0	0
$637$	−54.0000	−2.13956
$638$	15.0000	0.593856
$639$	0	0
$640$	4.00000	0.158114
$641$	22.0000	0.868948	0.434474	−	0.900684i	$-0.356934\pi$
$641$	22.0000	0.868948	0.434474	+	0.900684i	$0.356934\pi$
$642$	0	0
$643$	−40.0000	−1.57745	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−40.0000	−1.57745	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−20.0000	−0.788110
$645$	0	0
$646$	0	0
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	0	0
$649$	55.0000	2.15894
$650$	−66.0000	−2.58873
$651$	0	0
$652$	16.0000	0.626608
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	0	0
$655$	−40.0000	−1.56293
$656$	5.00000	0.195217
$657$	0	0
$658$	−24.0000	−0.935617
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	−5.00000	−0.194331
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	0	0
$667$	15.0000	0.580802
$668$	11.0000	0.425603
$669$	0	0
$670$	44.0000	1.69987
$671$	0	0
$672$	0	0
$673$	−9.00000	−0.346925	−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000	−0.346925	−0.173462	+	0.984841i	$0.555495\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	23.0000	0.884615
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	0	0
$679$	72.0000	2.76311
$680$	−4.00000	−0.153393
$681$	0	0
$682$	10.0000	0.382920
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	0	0
$685$	−88.0000	−3.36231
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−6.00000	−0.228582
$690$	0	0
$691$	52.0000	1.97817	0.989087	−	0.147335i	$-0.0470696\pi$
$691$	52.0000	1.97817	0.989087	+	0.147335i	$0.0470696\pi$
$692$	−20.0000	−0.760286
$693$	0	0
$694$	12.0000	0.455514
$695$	−40.0000	−1.51729
$696$	0	0
$697$	−5.00000	−0.189389
$698$	−1.00000	−0.0378506
$699$	0	0
$700$	−44.0000	−1.66304
$701$	−23.0000	−0.868698	−0.434349	−	0.900745i	$-0.643022\pi$
$701$	−23.0000	−0.868698	−0.434349	+	0.900745i	$0.643022\pi$
$702$	0	0
$703$	0	0
$704$	5.00000	0.188445
$705$	0	0
$706$	−34.0000	−1.27961
$707$	−56.0000	−2.10610
$708$	0	0
$709$	−8.00000	−0.300446	−0.150223	−	0.988652i	$-0.547999\pi$
$709$	−8.00000	−0.300446	−0.150223	+	0.988652i	$0.547999\pi$
$710$	48.0000	1.80141
$711$	0	0
$712$	−3.00000	−0.112430
$713$	10.0000	0.374503
$714$	0	0
$715$	−120.000	−4.48775
$716$	−24.0000	−0.896922
$717$	0	0
$718$	36.0000	1.34351
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	4.00000	0.148968
$722$	−19.0000	−0.707107
$723$	0	0
$724$	−7.00000	−0.260153
$725$	33.0000	1.22559
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	24.0000	0.889499
$729$	0	0
$730$	−20.0000	−0.740233
$731$	6.00000	0.221918
$732$	0	0
$733$	−11.0000	−0.406294	−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000	−0.406294	−0.203147	+	0.979148i	$0.565117\pi$
$734$	18.0000	0.664392
$735$	0	0
$736$	5.00000	0.184302
$737$	55.0000	2.02595
$738$	0	0
$739$	−36.0000	−1.32428	−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000	−1.32428	−0.662141	+	0.749380i	$0.730352\pi$
$740$	20.0000	0.735215
$741$	0	0
$742$	−4.00000	−0.146845
$743$	38.0000	1.39408	0.697042	−	0.717030i	$-0.254499\pi$
$743$	38.0000	1.39408	0.697042	+	0.717030i	$0.254499\pi$
$744$	0	0
$745$	−8.00000	−0.293097
$746$	24.0000	0.878702
$747$	0	0
$748$	−5.00000	−0.182818
$749$	−16.0000	−0.584627
$750$	0	0
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	−18.0000	−0.655521
$755$	−44.0000	−1.60132
$756$	0	0
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	8.00000	0.290000	0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000	0.290000	0.145000	+	0.989432i	$0.453682\pi$
$762$	0	0
$763$	8.00000	0.289619
$764$	1.00000	0.0361787
$765$	0	0
$766$	−27.0000	−0.975550
$767$	−66.0000	−2.38312
$768$	0	0
$769$	51.0000	1.83911	0.919554	−	0.392965i	$-0.128551\pi$
$769$	51.0000	1.83911	0.919554	+	0.392965i	$0.128551\pi$
$770$	−80.0000	−2.88300
$771$	0	0
$772$	−4.00000	−0.143963
$773$	−16.0000	−0.575480	−0.287740	−	0.957709i	$-0.592904\pi$
$773$	−16.0000	−0.575480	−0.287740	+	0.957709i	$0.592904\pi$
$774$	0	0
$775$	22.0000	0.790263
$776$	−18.0000	−0.646162
$777$	0	0
$778$	3.00000	0.107555
$779$	0	0
$780$	0	0
$781$	60.0000	2.14697
$782$	−5.00000	−0.178800
$783$	0	0
$784$	9.00000	0.321429
$785$	−56.0000	−1.99873
$786$	0	0
$787$	−31.0000	−1.10503	−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000	−1.10503	−0.552515	+	0.833503i	$0.686332\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	−32.0000	−1.13851
$791$	8.00000	0.284447
$792$	0	0
$793$	0	0
$794$	−28.0000	−0.993683
$795$	0	0
$796$	2.00000	0.0708881
$797$	−51.0000	−1.80651	−0.903256	−	0.429101i	$-0.858830\pi$
$797$	−51.0000	−1.80651	−0.903256	+	0.429101i	$0.858830\pi$
$798$	0	0
$799$	−6.00000	−0.212265
$800$	11.0000	0.388909
$801$	0	0
$802$	18.0000	0.635602
$803$	−25.0000	−0.882231
$804$	0	0
$805$	−80.0000	−2.81963
$806$	−12.0000	−0.422682
$807$	0	0
$808$	14.0000	0.492518
$809$	−40.0000	−1.40633	−0.703163	−	0.711029i	$-0.748229\pi$
$809$	−40.0000	−1.40633	−0.703163	+	0.711029i	$0.748229\pi$
$810$	0	0
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	−12.0000	−0.421117
$813$	0	0
$814$	25.0000	0.876250
$815$	64.0000	2.24182
$816$	0	0
$817$	0	0
$818$	−10.0000	−0.349642
$819$	0	0
$820$	20.0000	0.698430
$821$	27.0000	0.942306	0.471153	−	0.882051i	$-0.343838\pi$
$821$	27.0000	0.942306	0.471153	+	0.882051i	$0.343838\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−1.00000	−0.0348367
$825$	0	0
$826$	−44.0000	−1.53096
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	0	0
$829$	−40.0000	−1.38926	−0.694629	−	0.719368i	$-0.744431\pi$
$829$	−40.0000	−1.38926	−0.694629	+	0.719368i	$0.744431\pi$
$830$	24.0000	0.833052
$831$	0	0
$832$	−6.00000	−0.208013
$833$	−9.00000	−0.311832
$834$	0	0
$835$	44.0000	1.52268
$836$	0	0
$837$	0	0
$838$	−36.0000	−1.24360
$839$	27.0000	0.932144	0.466072	−	0.884747i	$-0.345669\pi$
$839$	27.0000	0.932144	0.466072	+	0.884747i	$0.345669\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−22.0000	−0.758170
$843$	0	0
$844$	−2.00000	−0.0688428
$845$	92.0000	3.16490
$846$	0	0
$847$	−56.0000	−1.92418
$848$	1.00000	0.0343401
$849$	0	0
$850$	−11.0000	−0.377297
$851$	25.0000	0.856989
$852$	0	0
$853$	−24.0000	−0.821744	−0.410872	−	0.911693i	$-0.634776\pi$
$853$	−24.0000	−0.821744	−0.410872	+	0.911693i	$0.634776\pi$
$854$	0	0
$855$	0	0
$856$	4.00000	0.136717
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−24.0000	−0.818393
$861$	0	0
$862$	−19.0000	−0.647143
$863$	−9.00000	−0.306364	−0.153182	−	0.988198i	$-0.548952\pi$
$863$	−9.00000	−0.306364	−0.153182	+	0.988198i	$0.548952\pi$
$864$	0	0
$865$	−80.0000	−2.72008
$866$	−26.0000	−0.883516
$867$	0	0
$868$	−8.00000	−0.271538
$869$	−40.0000	−1.35691
$870$	0	0
$871$	−66.0000	−2.23632
$872$	−2.00000	−0.0677285
$873$	0	0
$874$	0	0
$875$	−96.0000	−3.24539
$876$	0	0
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	35.0000	1.18119
$879$	0	0
$880$	20.0000	0.674200
$881$	55.0000	1.85300	0.926499	−	0.376298i	$-0.122803\pi$
$881$	55.0000	1.85300	0.926499	+	0.376298i	$0.122803\pi$
$882$	0	0
$883$	−28.0000	−0.942275	−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000	−0.942275	−0.471138	+	0.882060i	$0.656156\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	24.0000	0.806296
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	−12.0000	−0.402241
$891$	0	0
$892$	1.00000	0.0334825
$893$	0	0
$894$	0	0
$895$	−96.0000	−3.20893
$896$	−4.00000	−0.133631
$897$	0	0
$898$	38.0000	1.26808
$899$	6.00000	0.200111
$900$	0	0
$901$	−1.00000	−0.0333148
$902$	25.0000	0.832409
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	−28.0000	−0.930751
$906$	0	0
$907$	−36.0000	−1.19536	−0.597680	−	0.801735i	$-0.703911\pi$
$907$	−36.0000	−1.19536	−0.597680	+	0.801735i	$0.703911\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	96.0000	3.18237
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	0	0
$913$	30.0000	0.992855
$914$	12.0000	0.396925
$915$	0	0
$916$	4.00000	0.132164
$917$	40.0000	1.32092
$918$	0	0
$919$	−56.0000	−1.84727	−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000	−1.84727	−0.923635	+	0.383274i	$0.874797\pi$
$920$	20.0000	0.659380
$921$	0	0
$922$	15.0000	0.493999
$923$	−72.0000	−2.36991
$924$	0	0
$925$	55.0000	1.80839
$926$	−12.0000	−0.394344
$927$	0	0
$928$	3.00000	0.0984798
$929$	−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
$932$	4.00000	0.131024
$933$	0	0
$934$	21.0000	0.687141
$935$	−20.0000	−0.654070
$936$	0	0
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	−44.0000	−1.43665
$939$	0	0
$940$	24.0000	0.782794
$941$	−3.00000	−0.0977972	−0.0488986	−	0.998804i	$-0.515571\pi$
$941$	−3.00000	−0.0977972	−0.0488986	+	0.998804i	$0.515571\pi$
$942$	0	0
$943$	25.0000	0.814112
$944$	11.0000	0.358020
$945$	0	0
$946$	−30.0000	−0.975384
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	30.0000	0.973841
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	−8.00000	−0.259145	−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000	−0.259145	−0.129573	+	0.991570i	$0.541361\pi$
$954$	0	0
$955$	4.00000	0.129437
$956$	6.00000	0.194054
$957$	0	0
$958$	6.00000	0.193851
$959$	88.0000	2.84167
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−30.0000	−0.967239
$963$	0	0
$964$	5.00000	0.161039
$965$	−16.0000	−0.515058
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	−72.0000	−2.31178
$971$	−39.0000	−1.25157	−0.625785	−	0.779996i	$-0.715221\pi$
$971$	−39.0000	−1.25157	−0.625785	+	0.779996i	$0.715221\pi$
$972$	0	0
$973$	40.0000	1.28234
$974$	28.0000	0.897178
$975$	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
$979$	−15.0000	−0.479402
$980$	36.0000	1.14998
$981$	0	0
$982$	−21.0000	−0.670137
$983$	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
$985$	−24.0000	−0.764704
$986$	−3.00000	−0.0955395
$987$	0	0
$988$	0	0
$989$	−30.0000	−0.953945
$990$	0	0
$991$	−56.0000	−1.77890	−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000	−1.77890	−0.889449	+	0.457034i	$0.848912\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	−48.0000	−1.52247
$995$	8.00000	0.253617
$996$	0	0
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	−40.0000	−1.26618
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4014.2.a.i.1.1		1
3.2	odd	2		446.2.a.a.1.1	✓	1
12.11	even	2		3568.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
446.2.a.a.1.1	✓	1	3.2	odd	2
3568.2.a.h.1.1		1	12.11	even	2
4014.2.a.i.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:	\( N \)	\(=\)	\( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4014.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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