LMFDB - Embedded newform 3822.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
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	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} +5.00000 q^{19} -1.00000 q^{20} -5.00000 q^{22} +9.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{29} +1.00000 q^{30} -2.00000 q^{31} -1.00000 q^{32} +5.00000 q^{33} -3.00000 q^{34} +1.00000 q^{36} +3.00000 q^{37} -5.00000 q^{38} +1.00000 q^{39} +1.00000 q^{40} -12.0000 q^{41} +7.00000 q^{43} +5.00000 q^{44} -1.00000 q^{45} -9.00000 q^{46} -4.00000 q^{47} +1.00000 q^{48} +4.00000 q^{50} +3.00000 q^{51} +1.00000 q^{52} -10.0000 q^{53} -1.00000 q^{54} -5.00000 q^{55} +5.00000 q^{57} +1.00000 q^{58} +14.0000 q^{59} -1.00000 q^{60} -11.0000 q^{61} +2.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -5.00000 q^{66} +4.00000 q^{67} +3.00000 q^{68} +9.00000 q^{69} -10.0000 q^{71} -1.00000 q^{72} -11.0000 q^{73} -3.00000 q^{74} -4.00000 q^{75} +5.00000 q^{76} -1.00000 q^{78} +4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{82} +6.00000 q^{83} -3.00000 q^{85} -7.00000 q^{86} -1.00000 q^{87} -5.00000 q^{88} +16.0000 q^{89} +1.00000 q^{90} +9.00000 q^{92} -2.00000 q^{93} +4.00000 q^{94} -5.00000 q^{95} -1.00000 q^{96} -14.0000 q^{97} +5.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−1.00000	−0.235702
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−5.00000	−1.06600
$23$	9.00000	1.87663	0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000	1.87663	0.938315	+	0.345782i	$0.112386\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	1.00000	0.182574
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	5.00000	0.870388
$34$	−3.00000	−0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−5.00000	−0.811107
$39$	1.00000	0.160128
$40$	1.00000	0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	5.00000	0.753778
$45$	−1.00000	−0.149071
$46$	−9.00000	−1.32698
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	3.00000	0.420084
$52$	1.00000	0.138675
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−1.00000	−0.136083
$55$	−5.00000	−0.674200
$56$	0	0
$57$	5.00000	0.662266
$58$	1.00000	0.131306
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	−1.00000	−0.129099
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−5.00000	−0.615457
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	3.00000	0.363803
$69$	9.00000	1.08347
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−1.00000	−0.117851
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−3.00000	−0.348743
$75$	−4.00000	−0.461880
$76$	5.00000	0.573539
$77$	0	0
$78$	−1.00000	−0.113228
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	12.0000	1.32518
$83$	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
$85$	−3.00000	−0.325396
$86$	−7.00000	−0.754829
$87$	−1.00000	−0.107211
$88$	−5.00000	−0.533002
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	9.00000	0.938315
$93$	−2.00000	−0.207390
$94$	4.00000	0.412568
$95$	−5.00000	−0.512989
$96$	−1.00000	−0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	−4.00000	−0.400000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	−3.00000	−0.297044
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	10.0000	0.971286
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	1.00000	0.0962250
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	5.00000	0.476731
$111$	3.00000	0.284747
$112$	0	0
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	−5.00000	−0.468293
$115$	−9.00000	−0.839254
$116$	−1.00000	−0.0928477
$117$	1.00000	0.0924500
$118$	−14.0000	−1.28880
$119$	0	0
$120$	1.00000	0.0912871
$121$	14.0000	1.27273
$122$	11.0000	0.995893
$123$	−12.0000	−1.08200
$124$	−2.00000	−0.179605
$125$	9.00000	0.804984
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	7.00000	0.616316
$130$	1.00000	0.0877058
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	5.00000	0.435194
$133$	0	0
$134$	−4.00000	−0.345547
$135$	−1.00000	−0.0860663
$136$	−3.00000	−0.257248
$137$	−1.00000	−0.0854358	−0.0427179	−	0.999087i	$-0.513602\pi$
$137$	−1.00000	−0.0854358	−0.0427179	+	0.999087i	$0.513602\pi$
$138$	−9.00000	−0.766131
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	−4.00000	−0.336861
$142$	10.0000	0.839181
$143$	5.00000	0.418121
$144$	1.00000	0.0833333
$145$	1.00000	0.0830455
$146$	11.0000	0.910366
$147$	0	0
$148$	3.00000	0.246598
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	4.00000	0.326599
$151$	7.00000	0.569652	0.284826	−	0.958579i	$-0.408064\pi$
$151$	7.00000	0.569652	0.284826	+	0.958579i	$0.408064\pi$
$152$	−5.00000	−0.405554
$153$	3.00000	0.242536
$154$	0	0
$155$	2.00000	0.160644
$156$	1.00000	0.0800641
$157$	−7.00000	−0.558661	−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000	−0.558661	−0.279330	+	0.960195i	$0.590112\pi$
$158$	−4.00000	−0.318223
$159$	−10.0000	−0.793052
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	−12.0000	−0.937043
$165$	−5.00000	−0.389249
$166$	−6.00000	−0.465690
$167$	−5.00000	−0.386912	−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000	−0.386912	−0.193456	+	0.981109i	$0.561970\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	3.00000	0.230089
$171$	5.00000	0.382360
$172$	7.00000	0.533745
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	1.00000	0.0758098
$175$	0	0
$176$	5.00000	0.376889
$177$	14.0000	1.05230
$178$	−16.0000	−1.19925
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	−1.00000	−0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−11.0000	−0.813143
$184$	−9.00000	−0.663489
$185$	−3.00000	−0.220564
$186$	2.00000	0.146647
$187$	15.0000	1.09691
$188$	−4.00000	−0.291730
$189$	0	0
$190$	5.00000	0.362738
$191$	21.0000	1.51951	0.759753	−	0.650211i	$-0.225320\pi$
$191$	21.0000	1.51951	0.759753	+	0.650211i	$0.225320\pi$
$192$	1.00000	0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	14.0000	1.00514
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	−5.00000	−0.355335
$199$	19.0000	1.34687	0.673437	−	0.739244i	$-0.264817\pi$
$199$	19.0000	1.34687	0.673437	+	0.739244i	$0.264817\pi$
$200$	4.00000	0.282843
$201$	4.00000	0.282138
$202$	−14.0000	−0.985037
$203$	0	0
$204$	3.00000	0.210042
$205$	12.0000	0.838116
$206$	7.00000	0.487713
$207$	9.00000	0.625543
$208$	1.00000	0.0693375
$209$	25.0000	1.72929
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	−10.0000	−0.686803
$213$	−10.0000	−0.685189
$214$	−16.0000	−1.09374
$215$	−7.00000	−0.477396
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	11.0000	0.745014
$219$	−11.0000	−0.743311
$220$	−5.00000	−0.337100
$221$	3.00000	0.201802
$222$	−3.00000	−0.201347
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−16.0000	−1.06430
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	5.00000	0.331133
$229$	−28.0000	−1.85029	−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000	−1.85029	−0.925146	+	0.379611i	$0.876058\pi$
$230$	9.00000	0.593442
$231$	0	0
$232$	1.00000	0.0656532
$233$	−16.0000	−1.04819	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000	−1.04819	−0.524097	+	0.851658i	$0.675597\pi$
$234$	−1.00000	−0.0653720
$235$	4.00000	0.260931
$236$	14.0000	0.911322
$237$	4.00000	0.259828
$238$	0	0
$239$	−18.0000	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$240$	−1.00000	−0.0645497
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	−14.0000	−0.899954
$243$	1.00000	0.0641500
$244$	−11.0000	−0.704203
$245$	0	0
$246$	12.0000	0.765092
$247$	5.00000	0.318142
$248$	2.00000	0.127000
$249$	6.00000	0.380235
$250$	−9.00000	−0.569210
$251$	−1.00000	−0.0631194	−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000	−0.0631194	−0.0315597	+	0.999502i	$0.510047\pi$
$252$	0	0
$253$	45.0000	2.82913
$254$	4.00000	0.250982
$255$	−3.00000	−0.187867
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	−7.00000	−0.435801
$259$	0	0
$260$	−1.00000	−0.0620174
$261$	−1.00000	−0.0618984
$262$	−3.00000	−0.185341
$263$	20.0000	1.23325	0.616626	−	0.787256i	$-0.288499\pi$
$263$	20.0000	1.23325	0.616626	+	0.787256i	$0.288499\pi$
$264$	−5.00000	−0.307729
$265$	10.0000	0.614295
$266$	0	0
$267$	16.0000	0.979184
$268$	4.00000	0.244339
$269$	−16.0000	−0.975537	−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	1.00000	0.0608581
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	1.00000	0.0604122
$275$	−20.0000	−1.20605
$276$	9.00000	0.541736
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−12.0000	−0.719712
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	4.00000	0.238197
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−10.0000	−0.593391
$285$	−5.00000	−0.296174
$286$	−5.00000	−0.295656
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	−1.00000	−0.0587220
$291$	−14.0000	−0.820695
$292$	−11.0000	−0.643726
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	−14.0000	−0.815112
$296$	−3.00000	−0.174371
$297$	5.00000	0.290129
$298$	−20.0000	−1.15857
$299$	9.00000	0.520483
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−7.00000	−0.402805
$303$	14.0000	0.804279
$304$	5.00000	0.286770
$305$	11.0000	0.629858
$306$	−3.00000	−0.171499
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	−7.00000	−0.398216
$310$	−2.00000	−0.113592
$311$	−2.00000	−0.113410	−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000	−0.113410	−0.0567048	+	0.998391i	$0.518059\pi$
$312$	−1.00000	−0.0566139
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	7.00000	0.395033
$315$	0	0
$316$	4.00000	0.225018
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	10.0000	0.560772
$319$	−5.00000	−0.279946
$320$	−1.00000	−0.0559017
$321$	16.0000	0.893033
$322$	0	0
$323$	15.0000	0.834622
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−6.00000	−0.332309
$327$	−11.0000	−0.608301
$328$	12.0000	0.662589
$329$	0	0
$330$	5.00000	0.275241
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	6.00000	0.329293
$333$	3.00000	0.164399
$334$	5.00000	0.273588
$335$	−4.00000	−0.218543
$336$	0	0
$337$	23.0000	1.25289	0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000	1.25289	0.626445	+	0.779466i	$0.284509\pi$
$338$	−1.00000	−0.0543928
$339$	16.0000	0.869001
$340$	−3.00000	−0.162698
$341$	−10.0000	−0.541530
$342$	−5.00000	−0.270369
$343$	0	0
$344$	−7.00000	−0.377415
$345$	−9.00000	−0.484544
$346$	−4.00000	−0.215041
$347$	−6.00000	−0.322097	−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000	−0.322097	−0.161048	+	0.986947i	$0.551488\pi$
$348$	−1.00000	−0.0536056
$349$	−24.0000	−1.28469	−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000	−1.28469	−0.642345	+	0.766415i	$0.722038\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−5.00000	−0.266501
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	−14.0000	−0.744092
$355$	10.0000	0.530745
$356$	16.0000	0.847998
$357$	0	0
$358$	6.00000	0.317110
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	1.00000	0.0527046
$361$	6.00000	0.315789
$362$	2.00000	0.105118
$363$	14.0000	0.734809
$364$	0	0
$365$	11.0000	0.575766
$366$	11.0000	0.574979
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	9.00000	0.469157
$369$	−12.0000	−0.624695
$370$	3.00000	0.155963
$371$	0	0
$372$	−2.00000	−0.103695
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−15.0000	−0.775632
$375$	9.00000	0.464758
$376$	4.00000	0.206284
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	−30.0000	−1.54100	−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000	−1.54100	−0.770498	+	0.637442i	$0.779993\pi$
$380$	−5.00000	−0.256495
$381$	−4.00000	−0.204926
$382$	−21.0000	−1.07445
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	7.00000	0.355830
$388$	−14.0000	−0.710742
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	1.00000	0.0506370
$391$	27.0000	1.36545
$392$	0	0
$393$	3.00000	0.151330
$394$	−18.0000	−0.906827
$395$	−4.00000	−0.201262
$396$	5.00000	0.251259
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	−19.0000	−0.952384
$399$	0	0
$400$	−4.00000	−0.200000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	−4.00000	−0.199502
$403$	−2.00000	−0.0996271
$404$	14.0000	0.696526
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	15.0000	0.743522
$408$	−3.00000	−0.148522
$409$	−33.0000	−1.63174	−0.815872	−	0.578232i	$-0.803743\pi$
$409$	−33.0000	−1.63174	−0.815872	+	0.578232i	$0.803743\pi$
$410$	−12.0000	−0.592638
$411$	−1.00000	−0.0493264
$412$	−7.00000	−0.344865
$413$	0	0
$414$	−9.00000	−0.442326
$415$	−6.00000	−0.294528
$416$	−1.00000	−0.0490290
$417$	12.0000	0.587643
$418$	−25.0000	−1.22279
$419$	−31.0000	−1.51445	−0.757225	−	0.653155i	$-0.773445\pi$
$419$	−31.0000	−1.51445	−0.757225	+	0.653155i	$0.773445\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−5.00000	−0.243396
$423$	−4.00000	−0.194487
$424$	10.0000	0.485643
$425$	−12.0000	−0.582086
$426$	10.0000	0.484502
$427$	0	0
$428$	16.0000	0.773389
$429$	5.00000	0.241402
$430$	7.00000	0.337570
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	1.00000	0.0479463
$436$	−11.0000	−0.526804
$437$	45.0000	2.15264
$438$	11.0000	0.525600
$439$	21.0000	1.00228	0.501138	−	0.865368i	$-0.332915\pi$
$439$	21.0000	1.00228	0.501138	+	0.865368i	$0.332915\pi$
$440$	5.00000	0.238366
$441$	0	0
$442$	−3.00000	−0.142695
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	3.00000	0.142374
$445$	−16.0000	−0.758473
$446$	2.00000	0.0947027
$447$	20.0000	0.945968
$448$	0	0
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	4.00000	0.188562
$451$	−60.0000	−2.82529
$452$	16.0000	0.752577
$453$	7.00000	0.328889
$454$	−4.00000	−0.187729
$455$	0	0
$456$	−5.00000	−0.234146
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	28.0000	1.30835
$459$	3.00000	0.140028
$460$	−9.00000	−0.419627
$461$	−3.00000	−0.139724	−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000	−0.139724	−0.0698620	+	0.997557i	$0.522256\pi$
$462$	0	0
$463$	11.0000	0.511213	0.255607	−	0.966781i	$-0.417725\pi$
$463$	11.0000	0.511213	0.255607	+	0.966781i	$0.417725\pi$
$464$	−1.00000	−0.0464238
$465$	2.00000	0.0927478
$466$	16.0000	0.741186
$467$	−5.00000	−0.231372	−0.115686	−	0.993286i	$-0.536907\pi$
$467$	−5.00000	−0.231372	−0.115686	+	0.993286i	$0.536907\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	−4.00000	−0.184506
$471$	−7.00000	−0.322543
$472$	−14.0000	−0.644402
$473$	35.0000	1.60930
$474$	−4.00000	−0.183726
$475$	−20.0000	−0.917663
$476$	0	0
$477$	−10.0000	−0.457869
$478$	18.0000	0.823301
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	1.00000	0.0456435
$481$	3.00000	0.136788
$482$	26.0000	1.18427
$483$	0	0
$484$	14.0000	0.636364
$485$	14.0000	0.635707
$486$	−1.00000	−0.0453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	11.0000	0.497947
$489$	6.00000	0.271329
$490$	0	0
$491$	18.0000	0.812329	0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000	0.812329	0.406164	+	0.913800i	$0.366866\pi$
$492$	−12.0000	−0.541002
$493$	−3.00000	−0.135113
$494$	−5.00000	−0.224961
$495$	−5.00000	−0.224733
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−6.00000	−0.268866
$499$	18.0000	0.805791	0.402895	−	0.915246i	$-0.368004\pi$
$499$	18.0000	0.805791	0.402895	+	0.915246i	$0.368004\pi$
$500$	9.00000	0.402492
$501$	−5.00000	−0.223384
$502$	1.00000	0.0446322
$503$	−32.0000	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$504$	0	0
$505$	−14.0000	−0.622992
$506$	−45.0000	−2.00049
$507$	1.00000	0.0444116
$508$	−4.00000	−0.177471
$509$	−11.0000	−0.487566	−0.243783	−	0.969830i	$-0.578389\pi$
$509$	−11.0000	−0.487566	−0.243783	+	0.969830i	$0.578389\pi$
$510$	3.00000	0.132842
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	14.0000	0.617514
$515$	7.00000	0.308457
$516$	7.00000	0.308158
$517$	−20.0000	−0.879599
$518$	0	0
$519$	4.00000	0.175581
$520$	1.00000	0.0438529
$521$	25.0000	1.09527	0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000	1.09527	0.547635	+	0.836717i	$0.315528\pi$
$522$	1.00000	0.0437688
$523$	38.0000	1.66162	0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000	1.66162	0.830812	+	0.556553i	$0.187876\pi$
$524$	3.00000	0.131056
$525$	0	0
$526$	−20.0000	−0.872041
$527$	−6.00000	−0.261364
$528$	5.00000	0.217597
$529$	58.0000	2.52174
$530$	−10.0000	−0.434372
$531$	14.0000	0.607548
$532$	0	0
$533$	−12.0000	−0.519778
$534$	−16.0000	−0.692388
$535$	−16.0000	−0.691740
$536$	−4.00000	−0.172774
$537$	−6.00000	−0.258919
$538$	16.0000	0.689809
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	25.0000	1.07483	0.537417	−	0.843317i	$-0.319400\pi$
$541$	25.0000	1.07483	0.537417	+	0.843317i	$0.319400\pi$
$542$	−8.00000	−0.343629
$543$	−2.00000	−0.0858282
$544$	−3.00000	−0.128624
$545$	11.0000	0.471188
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−1.00000	−0.0427179
$549$	−11.0000	−0.469469
$550$	20.0000	0.852803
$551$	−5.00000	−0.213007
$552$	−9.00000	−0.383065
$553$	0	0
$554$	−28.0000	−1.18961
$555$	−3.00000	−0.127343
$556$	12.0000	0.508913
$557$	−24.0000	−1.01691	−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000	−1.01691	−0.508456	+	0.861088i	$0.669784\pi$
$558$	2.00000	0.0846668
$559$	7.00000	0.296068
$560$	0	0
$561$	15.0000	0.633300
$562$	6.00000	0.253095
$563$	31.0000	1.30649	0.653247	−	0.757145i	$-0.273406\pi$
$563$	31.0000	1.30649	0.653247	+	0.757145i	$0.273406\pi$
$564$	−4.00000	−0.168430
$565$	−16.0000	−0.673125
$566$	−16.0000	−0.672530
$567$	0	0
$568$	10.0000	0.419591
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	5.00000	0.209427
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	5.00000	0.209061
$573$	21.0000	0.877288
$574$	0	0
$575$	−36.0000	−1.50130
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	8.00000	0.332756
$579$	−10.0000	−0.415586
$580$	1.00000	0.0415227
$581$	0	0
$582$	14.0000	0.580319
$583$	−50.0000	−2.07079
$584$	11.0000	0.455183
$585$	−1.00000	−0.0413449
$586$	18.0000	0.743573
$587$	38.0000	1.56843	0.784214	−	0.620491i	$-0.213066\pi$
$587$	38.0000	1.56843	0.784214	+	0.620491i	$0.213066\pi$
$588$	0	0
$589$	−10.0000	−0.412043
$590$	14.0000	0.576371
$591$	18.0000	0.740421
$592$	3.00000	0.123299
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	20.0000	0.819232
$597$	19.0000	0.777618
$598$	−9.00000	−0.368037
$599$	−9.00000	−0.367730	−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000	−0.367730	−0.183865	+	0.982952i	$0.558861\pi$
$600$	4.00000	0.163299
$601$	20.0000	0.815817	0.407909	−	0.913023i	$-0.366258\pi$
$601$	20.0000	0.815817	0.407909	+	0.913023i	$0.366258\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	7.00000	0.284826
$605$	−14.0000	−0.569181
$606$	−14.0000	−0.568711
$607$	21.0000	0.852364	0.426182	−	0.904638i	$-0.359858\pi$
$607$	21.0000	0.852364	0.426182	+	0.904638i	$0.359858\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	−11.0000	−0.445377
$611$	−4.00000	−0.161823
$612$	3.00000	0.121268
$613$	5.00000	0.201948	0.100974	−	0.994889i	$-0.467804\pi$
$613$	5.00000	0.201948	0.100974	+	0.994889i	$0.467804\pi$
$614$	20.0000	0.807134
$615$	12.0000	0.483887
$616$	0	0
$617$	−23.0000	−0.925945	−0.462973	−	0.886373i	$-0.653217\pi$
$617$	−23.0000	−0.925945	−0.462973	+	0.886373i	$0.653217\pi$
$618$	7.00000	0.281581
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	2.00000	0.0803219
$621$	9.00000	0.361158
$622$	2.00000	0.0801927
$623$	0	0
$624$	1.00000	0.0400320
$625$	11.0000	0.440000
$626$	−6.00000	−0.239808
$627$	25.0000	0.998404
$628$	−7.00000	−0.279330
$629$	9.00000	0.358854
$630$	0	0
$631$	−33.0000	−1.31371	−0.656855	−	0.754017i	$-0.728113\pi$
$631$	−33.0000	−1.31371	−0.656855	+	0.754017i	$0.728113\pi$
$632$	−4.00000	−0.159111
$633$	5.00000	0.198732
$634$	−6.00000	−0.238290
$635$	4.00000	0.158735
$636$	−10.0000	−0.396526
$637$	0	0
$638$	5.00000	0.197952
$639$	−10.0000	−0.395594
$640$	1.00000	0.0395285
$641$	−32.0000	−1.26392	−0.631962	−	0.774999i	$-0.717750\pi$
$641$	−32.0000	−1.26392	−0.631962	+	0.774999i	$0.717750\pi$
$642$	−16.0000	−0.631470
$643$	−9.00000	−0.354925	−0.177463	−	0.984128i	$-0.556789\pi$
$643$	−9.00000	−0.354925	−0.177463	+	0.984128i	$0.556789\pi$
$644$	0	0
$645$	−7.00000	−0.275625
$646$	−15.0000	−0.590167
$647$	36.0000	1.41531	0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000	1.41531	0.707653	+	0.706560i	$0.249754\pi$
$648$	−1.00000	−0.0392837
$649$	70.0000	2.74774
$650$	4.00000	0.156893
$651$	0	0
$652$	6.00000	0.234978
$653$	5.00000	0.195665	0.0978326	−	0.995203i	$-0.468809\pi$
$653$	5.00000	0.195665	0.0978326	+	0.995203i	$0.468809\pi$
$654$	11.0000	0.430134
$655$	−3.00000	−0.117220
$656$	−12.0000	−0.468521
$657$	−11.0000	−0.429151
$658$	0	0
$659$	−2.00000	−0.0779089	−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000	−0.0779089	−0.0389545	+	0.999241i	$0.512403\pi$
$660$	−5.00000	−0.194625
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−8.00000	−0.310929
$663$	3.00000	0.116510
$664$	−6.00000	−0.232845
$665$	0	0
$666$	−3.00000	−0.116248
$667$	−9.00000	−0.348481
$668$	−5.00000	−0.193456
$669$	−2.00000	−0.0773245
$670$	4.00000	0.154533
$671$	−55.0000	−2.12325
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	−23.0000	−0.885927
$675$	−4.00000	−0.153960
$676$	1.00000	0.0384615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−16.0000	−0.614476
$679$	0	0
$680$	3.00000	0.115045
$681$	4.00000	0.153280
$682$	10.0000	0.382920
$683$	7.00000	0.267848	0.133924	−	0.990992i	$-0.457242\pi$
$683$	7.00000	0.267848	0.133924	+	0.990992i	$0.457242\pi$
$684$	5.00000	0.191180
$685$	1.00000	0.0382080
$686$	0	0
$687$	−28.0000	−1.06827
$688$	7.00000	0.266872
$689$	−10.0000	−0.380970
$690$	9.00000	0.342624
$691$	4.00000	0.152167	0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000	0.152167	0.0760836	+	0.997101i	$0.475758\pi$
$692$	4.00000	0.152057
$693$	0	0
$694$	6.00000	0.227757
$695$	−12.0000	−0.455186
$696$	1.00000	0.0379049
$697$	−36.0000	−1.36360
$698$	24.0000	0.908413
$699$	−16.0000	−0.605176
$700$	0	0
$701$	−2.00000	−0.0755390	−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000	−0.0755390	−0.0377695	+	0.999286i	$0.512025\pi$
$702$	−1.00000	−0.0377426
$703$	15.0000	0.565736
$704$	5.00000	0.188445
$705$	4.00000	0.150649
$706$	−18.0000	−0.677439
$707$	0	0
$708$	14.0000	0.526152
$709$	−38.0000	−1.42712	−0.713560	−	0.700594i	$-0.752918\pi$
$709$	−38.0000	−1.42712	−0.713560	+	0.700594i	$0.752918\pi$
$710$	−10.0000	−0.375293
$711$	4.00000	0.150012
$712$	−16.0000	−0.599625
$713$	−18.0000	−0.674105
$714$	0	0
$715$	−5.00000	−0.186989
$716$	−6.00000	−0.224231
$717$	−18.0000	−0.672222
$718$	20.0000	0.746393
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−6.00000	−0.223297
$723$	−26.0000	−0.966950
$724$	−2.00000	−0.0743294
$725$	4.00000	0.148556
$726$	−14.0000	−0.519589
$727$	17.0000	0.630495	0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000	0.630495	0.315248	+	0.949009i	$0.397912\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.0000	−0.407128
$731$	21.0000	0.776713
$732$	−11.0000	−0.406572
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	−9.00000	−0.331744
$737$	20.0000	0.736709
$738$	12.0000	0.441726
$739$	−26.0000	−0.956425	−0.478213	−	0.878244i	$-0.658715\pi$
$739$	−26.0000	−0.956425	−0.478213	+	0.878244i	$0.658715\pi$
$740$	−3.00000	−0.110282
$741$	5.00000	0.183680
$742$	0	0
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	2.00000	0.0733236
$745$	−20.0000	−0.732743
$746$	2.00000	0.0732252
$747$	6.00000	0.219529
$748$	15.0000	0.548454
$749$	0	0
$750$	−9.00000	−0.328634
$751$	−54.0000	−1.97049	−0.985244	−	0.171156i	$-0.945250\pi$
$751$	−54.0000	−1.97049	−0.985244	+	0.171156i	$0.945250\pi$
$752$	−4.00000	−0.145865
$753$	−1.00000	−0.0364420
$754$	1.00000	0.0364179
$755$	−7.00000	−0.254756
$756$	0	0
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	30.0000	1.08965
$759$	45.0000	1.63340
$760$	5.00000	0.181369
$761$	−40.0000	−1.45000	−0.724999	−	0.688749i	$-0.758160\pi$
$761$	−40.0000	−1.45000	−0.724999	+	0.688749i	$0.758160\pi$
$762$	4.00000	0.144905
$763$	0	0
$764$	21.0000	0.759753
$765$	−3.00000	−0.108465
$766$	−15.0000	−0.541972
$767$	14.0000	0.505511
$768$	1.00000	0.0360844
$769$	−25.0000	−0.901523	−0.450762	−	0.892644i	$-0.648848\pi$
$769$	−25.0000	−0.901523	−0.450762	+	0.892644i	$0.648848\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	−10.0000	−0.359908
$773$	−51.0000	−1.83434	−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000	−1.83434	−0.917171	+	0.398493i	$0.869533\pi$
$774$	−7.00000	−0.251610
$775$	8.00000	0.287368
$776$	14.0000	0.502571
$777$	0	0
$778$	−6.00000	−0.215110
$779$	−60.0000	−2.14972
$780$	−1.00000	−0.0358057
$781$	−50.0000	−1.78914
$782$	−27.0000	−0.965518
$783$	−1.00000	−0.0357371
$784$	0	0
$785$	7.00000	0.249841
$786$	−3.00000	−0.107006
$787$	−23.0000	−0.819861	−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000	−0.819861	−0.409931	+	0.912117i	$0.634447\pi$
$788$	18.0000	0.641223
$789$	20.0000	0.712019
$790$	4.00000	0.142314
$791$	0	0
$792$	−5.00000	−0.177667
$793$	−11.0000	−0.390621
$794$	−14.0000	−0.496841
$795$	10.0000	0.354663
$796$	19.0000	0.673437
$797$	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
$799$	−12.0000	−0.424529
$800$	4.00000	0.141421
$801$	16.0000	0.565332
$802$	−30.0000	−1.05934
$803$	−55.0000	−1.94091
$804$	4.00000	0.141069
$805$	0	0
$806$	2.00000	0.0704470
$807$	−16.0000	−0.563227
$808$	−14.0000	−0.492518
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	1.00000	0.0351364
$811$	17.0000	0.596951	0.298475	−	0.954417i	$-0.403522\pi$
$811$	17.0000	0.596951	0.298475	+	0.954417i	$0.403522\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	−15.0000	−0.525750
$815$	−6.00000	−0.210171
$816$	3.00000	0.105021
$817$	35.0000	1.22449
$818$	33.0000	1.15382
$819$	0	0
$820$	12.0000	0.419058
$821$	−40.0000	−1.39601	−0.698005	−	0.716093i	$-0.745929\pi$
$821$	−40.0000	−1.39601	−0.698005	+	0.716093i	$0.745929\pi$
$822$	1.00000	0.0348790
$823$	46.0000	1.60346	0.801730	−	0.597687i	$-0.203913\pi$
$823$	46.0000	1.60346	0.801730	+	0.597687i	$0.203913\pi$
$824$	7.00000	0.243857
$825$	−20.0000	−0.696311
$826$	0	0
$827$	−39.0000	−1.35616	−0.678081	−	0.734987i	$-0.737188\pi$
$827$	−39.0000	−1.35616	−0.678081	+	0.734987i	$0.737188\pi$
$828$	9.00000	0.312772
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	6.00000	0.208263
$831$	28.0000	0.971309
$832$	1.00000	0.0346688
$833$	0	0
$834$	−12.0000	−0.415526
$835$	5.00000	0.173032
$836$	25.0000	0.864643
$837$	−2.00000	−0.0691301
$838$	31.0000	1.07088
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	6.00000	0.206774
$843$	−6.00000	−0.206651
$844$	5.00000	0.172107
$845$	−1.00000	−0.0344010
$846$	4.00000	0.137523
$847$	0	0
$848$	−10.0000	−0.343401
$849$	16.0000	0.549119
$850$	12.0000	0.411597
$851$	27.0000	0.925548
$852$	−10.0000	−0.342594
$853$	−40.0000	−1.36957	−0.684787	−	0.728743i	$-0.740105\pi$
$853$	−40.0000	−1.36957	−0.684787	+	0.728743i	$0.740105\pi$
$854$	0	0
$855$	−5.00000	−0.170996
$856$	−16.0000	−0.546869
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	−5.00000	−0.170697
$859$	−24.0000	−0.818869	−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000	−0.818869	−0.409435	+	0.912339i	$0.634274\pi$
$860$	−7.00000	−0.238698
$861$	0	0
$862$	−10.0000	−0.340601
$863$	−42.0000	−1.42970	−0.714848	−	0.699280i	$-0.753504\pi$
$863$	−42.0000	−1.42970	−0.714848	+	0.699280i	$0.753504\pi$
$864$	−1.00000	−0.0340207
$865$	−4.00000	−0.136004
$866$	16.0000	0.543702
$867$	−8.00000	−0.271694
$868$	0	0
$869$	20.0000	0.678454
$870$	−1.00000	−0.0339032
$871$	4.00000	0.135535
$872$	11.0000	0.372507
$873$	−14.0000	−0.473828
$874$	−45.0000	−1.52215
$875$	0	0
$876$	−11.0000	−0.371656
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−21.0000	−0.708716
$879$	−18.0000	−0.607125
$880$	−5.00000	−0.168550
$881$	−37.0000	−1.24656	−0.623281	−	0.781998i	$-0.714201\pi$
$881$	−37.0000	−1.24656	−0.623281	+	0.781998i	$0.714201\pi$
$882$	0	0
$883$	19.0000	0.639401	0.319700	−	0.947519i	$-0.396418\pi$
$883$	19.0000	0.639401	0.319700	+	0.947519i	$0.396418\pi$
$884$	3.00000	0.100901
$885$	−14.0000	−0.470605
$886$	−6.00000	−0.201574
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−3.00000	−0.100673
$889$	0	0
$890$	16.0000	0.536321
$891$	5.00000	0.167506
$892$	−2.00000	−0.0669650
$893$	−20.0000	−0.669274
$894$	−20.0000	−0.668900
$895$	6.00000	0.200558
$896$	0	0
$897$	9.00000	0.300501
$898$	9.00000	0.300334
$899$	2.00000	0.0667037
$900$	−4.00000	−0.133333
$901$	−30.0000	−0.999445
$902$	60.0000	1.99778
$903$	0	0
$904$	−16.0000	−0.532152
$905$	2.00000	0.0664822
$906$	−7.00000	−0.232559
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	4.00000	0.132745
$909$	14.0000	0.464351
$910$	0	0
$911$	−41.0000	−1.35839	−0.679195	−	0.733958i	$-0.737671\pi$
$911$	−41.0000	−1.35839	−0.679195	+	0.733958i	$0.737671\pi$
$912$	5.00000	0.165567
$913$	30.0000	0.992855
$914$	−26.0000	−0.860004
$915$	11.0000	0.363649
$916$	−28.0000	−0.925146
$917$	0	0
$918$	−3.00000	−0.0990148
$919$	18.0000	0.593765	0.296883	−	0.954914i	$-0.404053\pi$
$919$	18.0000	0.593765	0.296883	+	0.954914i	$0.404053\pi$
$920$	9.00000	0.296721
$921$	−20.0000	−0.659022
$922$	3.00000	0.0987997
$923$	−10.0000	−0.329154
$924$	0	0
$925$	−12.0000	−0.394558
$926$	−11.0000	−0.361482
$927$	−7.00000	−0.229910
$928$	1.00000	0.0328266
$929$	−24.0000	−0.787414	−0.393707	−	0.919236i	$-0.628808\pi$
$929$	−24.0000	−0.787414	−0.393707	+	0.919236i	$0.628808\pi$
$930$	−2.00000	−0.0655826
$931$	0	0
$932$	−16.0000	−0.524097
$933$	−2.00000	−0.0654771
$934$	5.00000	0.163605
$935$	−15.0000	−0.490552
$936$	−1.00000	−0.0326860
$937$	−12.0000	−0.392023	−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000	−0.392023	−0.196011	+	0.980602i	$0.562799\pi$
$938$	0	0
$939$	6.00000	0.195803
$940$	4.00000	0.130466
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	7.00000	0.228072
$943$	−108.000	−3.51696
$944$	14.0000	0.455661
$945$	0	0
$946$	−35.0000	−1.13795
$947$	29.0000	0.942373	0.471187	−	0.882034i	$-0.343826\pi$
$947$	29.0000	0.942373	0.471187	+	0.882034i	$0.343826\pi$
$948$	4.00000	0.129914
$949$	−11.0000	−0.357075
$950$	20.0000	0.648886
$951$	6.00000	0.194563
$952$	0	0
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	10.0000	0.323762
$955$	−21.0000	−0.679544
$956$	−18.0000	−0.582162
$957$	−5.00000	−0.161627
$958$	3.00000	0.0969256
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	−3.00000	−0.0967239
$963$	16.0000	0.515593
$964$	−26.0000	−0.837404
$965$	10.0000	0.321911
$966$	0	0
$967$	1.00000	0.0321578	0.0160789	−	0.999871i	$-0.494882\pi$
$967$	1.00000	0.0321578	0.0160789	+	0.999871i	$0.494882\pi$
$968$	−14.0000	−0.449977
$969$	15.0000	0.481869
$970$	−14.0000	−0.449513
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−40.0000	−1.28168
$975$	−4.00000	−0.128103
$976$	−11.0000	−0.352101
$977$	29.0000	0.927792	0.463896	−	0.885890i	$-0.346451\pi$
$977$	29.0000	0.927792	0.463896	+	0.885890i	$0.346451\pi$
$978$	−6.00000	−0.191859
$979$	80.0000	2.55681
$980$	0	0
$981$	−11.0000	−0.351203
$982$	−18.0000	−0.574403
$983$	−7.00000	−0.223265	−0.111633	−	0.993750i	$-0.535608\pi$
$983$	−7.00000	−0.223265	−0.111633	+	0.993750i	$0.535608\pi$
$984$	12.0000	0.382546
$985$	−18.0000	−0.573528
$986$	3.00000	0.0955395
$987$	0	0
$988$	5.00000	0.159071
$989$	63.0000	2.00328
$990$	5.00000	0.158910
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	2.00000	0.0635001
$993$	8.00000	0.253872
$994$	0	0
$995$	−19.0000	−0.602340
$996$	6.00000	0.190117
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	−18.0000	−0.569780
$999$	3.00000	0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.m.1.1	yes	1
7.6	odd	2		3822.2.a.g.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.g.1.1	✓	1	7.6	odd	2
3822.2.a.m.1.1	yes	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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