LMFDB - Embedded newform 490.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.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:	$3.91266969904$
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	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.00000 q^{11} +2.00000 q^{12} +2.00000 q^{13} +2.00000 q^{15} +1.00000 q^{16} +8.00000 q^{17} +1.00000 q^{18} -6.00000 q^{19} +1.00000 q^{20} -4.00000 q^{22} -4.00000 q^{23} +2.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -4.00000 q^{27} -6.00000 q^{29} +2.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -8.00000 q^{33} +8.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -6.00000 q^{38} +4.00000 q^{39} +1.00000 q^{40} +4.00000 q^{41} +4.00000 q^{43} -4.00000 q^{44} +1.00000 q^{45} -4.00000 q^{46} +4.00000 q^{47} +2.00000 q^{48} +1.00000 q^{50} +16.0000 q^{51} +2.00000 q^{52} +10.0000 q^{53} -4.00000 q^{54} -4.00000 q^{55} -12.0000 q^{57} -6.00000 q^{58} -14.0000 q^{59} +2.00000 q^{60} -10.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -8.00000 q^{66} -4.00000 q^{67} +8.00000 q^{68} -8.00000 q^{69} +12.0000 q^{71} +1.00000 q^{72} +4.00000 q^{73} -10.0000 q^{74} +2.00000 q^{75} -6.00000 q^{76} +4.00000 q^{78} +4.00000 q^{79} +1.00000 q^{80} -11.0000 q^{81} +4.00000 q^{82} -2.00000 q^{83} +8.00000 q^{85} +4.00000 q^{86} -12.0000 q^{87} -4.00000 q^{88} +8.00000 q^{89} +1.00000 q^{90} -4.00000 q^{92} +8.00000 q^{93} +4.00000 q^{94} -6.00000 q^{95} +2.00000 q^{96} -4.00000 q^{99} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00000	0.816497
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	2.00000	0.577350
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	8.00000	1.94029	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	8.00000	1.94029	0.970143	+	0.242536i	$0.0779791\pi$
$18$	1.00000	0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	2.00000	0.408248
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−4.00000	−0.769800
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	2.00000	0.365148
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	−8.00000	−1.39262
$34$	8.00000	1.37199
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−6.00000	−0.973329
$39$	4.00000	0.640513
$40$	1.00000	0.158114
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−4.00000	−0.603023
$45$	1.00000	0.149071
$46$	−4.00000	−0.589768
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	2.00000	0.288675
$49$	0	0
$50$	1.00000	0.141421
$51$	16.0000	2.24045
$52$	2.00000	0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−4.00000	−0.544331
$55$	−4.00000	−0.539360
$56$	0	0
$57$	−12.0000	−1.58944
$58$	−6.00000	−0.787839
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	2.00000	0.258199
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−8.00000	−0.984732
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	8.00000	0.970143
$69$	−8.00000	−0.963087
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	1.00000	0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−10.0000	−1.16248
$75$	2.00000	0.230940
$76$	−6.00000	−0.688247
$77$	0	0
$78$	4.00000	0.452911
$79$	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
$81$	−11.0000	−1.22222
$82$	4.00000	0.441726
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	8.00000	0.867722
$86$	4.00000	0.431331
$87$	−12.0000	−1.28654
$88$	−4.00000	−0.426401
$89$	8.00000	0.847998	0.423999	−	0.905663i	$-0.360626\pi$
$89$	8.00000	0.847998	0.423999	+	0.905663i	$0.360626\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−4.00000	−0.417029
$93$	8.00000	0.829561
$94$	4.00000	0.412568
$95$	−6.00000	−0.615587
$96$	2.00000	0.204124
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	16.0000	1.58424
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	10.0000	0.971286
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−4.00000	−0.384900
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−4.00000	−0.381385
$111$	−20.0000	−1.89832
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−12.0000	−1.12390
$115$	−4.00000	−0.373002
$116$	−6.00000	−0.557086
$117$	2.00000	0.184900
$118$	−14.0000	−1.28880
$119$	0	0
$120$	2.00000	0.182574
$121$	5.00000	0.454545
$122$	−10.0000	−0.905357
$123$	8.00000	0.721336
$124$	4.00000	0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	2.00000	0.175412
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	−8.00000	−0.696311
$133$	0	0
$134$	−4.00000	−0.345547
$135$	−4.00000	−0.344265
$136$	8.00000	0.685994
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−8.00000	−0.681005
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	12.0000	1.00702
$143$	−8.00000	−0.668994
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	4.00000	0.331042
$147$	0	0
$148$	−10.0000	−0.821995
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	2.00000	0.163299
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−6.00000	−0.486664
$153$	8.00000	0.646762
$154$	0	0
$155$	4.00000	0.321288
$156$	4.00000	0.320256
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	4.00000	0.318223
$159$	20.0000	1.58610
$160$	1.00000	0.0790569
$161$	0	0
$162$	−11.0000	−0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	4.00000	0.312348
$165$	−8.00000	−0.622799
$166$	−2.00000	−0.155230
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	8.00000	0.613572
$171$	−6.00000	−0.458831
$172$	4.00000	0.304997
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−12.0000	−0.909718
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−28.0000	−2.10461
$178$	8.00000	0.599625
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	1.00000	0.0745356
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	0	0
$183$	−20.0000	−1.47844
$184$	−4.00000	−0.294884
$185$	−10.0000	−0.735215
$186$	8.00000	0.586588
$187$	−32.0000	−2.34007
$188$	4.00000	0.291730
$189$	0	0
$190$	−6.00000	−0.435286
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	2.00000	0.144338
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	0	0
$195$	4.00000	0.286446
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	−4.00000	−0.284268
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	−2.00000	−0.140720
$203$	0	0
$204$	16.0000	1.12022
$205$	4.00000	0.279372
$206$	4.00000	0.278693
$207$	−4.00000	−0.278019
$208$	2.00000	0.138675
$209$	24.0000	1.66011
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	10.0000	0.686803
$213$	24.0000	1.64445
$214$	−12.0000	−0.820303
$215$	4.00000	0.272798
$216$	−4.00000	−0.272166
$217$	0	0
$218$	10.0000	0.677285
$219$	8.00000	0.540590
$220$	−4.00000	−0.269680
$221$	16.0000	1.07628
$222$	−20.0000	−1.34231
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−2.00000	−0.133038
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	−12.0000	−0.794719
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	−6.00000	−0.393919
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	2.00000	0.130744
$235$	4.00000	0.260931
$236$	−14.0000	−0.911322
$237$	8.00000	0.519656
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	2.00000	0.129099
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	5.00000	0.321412
$243$	−10.0000	−0.641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	8.00000	0.510061
$247$	−12.0000	−0.763542
$248$	4.00000	0.254000
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	22.0000	1.38863	0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000	1.38863	0.694314	+	0.719672i	$0.255708\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	−12.0000	−0.752947
$255$	16.0000	1.00196
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	8.00000	0.498058
$259$	0	0
$260$	2.00000	0.124035
$261$	−6.00000	−0.371391
$262$	18.0000	1.11204
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	−8.00000	−0.492366
$265$	10.0000	0.614295
$266$	0	0
$267$	16.0000	0.979184
$268$	−4.00000	−0.244339
$269$	26.0000	1.58525	0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000	1.58525	0.792624	+	0.609711i	$0.208714\pi$
$270$	−4.00000	−0.243432
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	8.00000	0.485071
$273$	0	0
$274$	−2.00000	−0.120824
$275$	−4.00000	−0.241209
$276$	−8.00000	−0.481543
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−10.0000	−0.599760
$279$	4.00000	0.239474
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	8.00000	0.476393
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	12.0000	0.712069
$285$	−12.0000	−0.710819
$286$	−8.00000	−0.473050
$287$	0	0
$288$	1.00000	0.0589256
$289$	47.0000	2.76471
$290$	−6.00000	−0.352332
$291$	0	0
$292$	4.00000	0.234082
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	−14.0000	−0.815112
$296$	−10.0000	−0.581238
$297$	16.0000	0.928414
$298$	−10.0000	−0.579284
$299$	−8.00000	−0.462652
$300$	2.00000	0.115470
$301$	0	0
$302$	0	0
$303$	−4.00000	−0.229794
$304$	−6.00000	−0.344124
$305$	−10.0000	−0.572598
$306$	8.00000	0.457330
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	4.00000	0.227185
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	4.00000	0.226455
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	4.00000	0.225018
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	20.0000	1.12154
$319$	24.0000	1.34374
$320$	1.00000	0.0559017
$321$	−24.0000	−1.33955
$322$	0	0
$323$	−48.0000	−2.67079
$324$	−11.0000	−0.611111
$325$	2.00000	0.110940
$326$	−4.00000	−0.221540
$327$	20.0000	1.10600
$328$	4.00000	0.220863
$329$	0	0
$330$	−8.00000	−0.440386
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−2.00000	−0.109764
$333$	−10.0000	−0.547997
$334$	12.0000	0.656611
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−9.00000	−0.489535
$339$	−4.00000	−0.217250
$340$	8.00000	0.433861
$341$	−16.0000	−0.866449
$342$	−6.00000	−0.324443
$343$	0	0
$344$	4.00000	0.215666
$345$	−8.00000	−0.430706
$346$	18.0000	0.967686
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	−12.0000	−0.643268
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	−8.00000	−0.427008
$352$	−4.00000	−0.213201
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	−28.0000	−1.48818
$355$	12.0000	0.636894
$356$	8.00000	0.423999
$357$	0	0
$358$	4.00000	0.211407
$359$	−8.00000	−0.422224	−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000	−0.422224	−0.211112	+	0.977462i	$0.567708\pi$
$360$	1.00000	0.0527046
$361$	17.0000	0.894737
$362$	26.0000	1.36653
$363$	10.0000	0.524864
$364$	0	0
$365$	4.00000	0.209370
$366$	−20.0000	−1.04542
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−4.00000	−0.208514
$369$	4.00000	0.208232
$370$	−10.0000	−0.519875
$371$	0	0
$372$	8.00000	0.414781
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−32.0000	−1.65468
$375$	2.00000	0.103280
$376$	4.00000	0.206284
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	−6.00000	−0.307794
$381$	−24.0000	−1.22956
$382$	12.0000	0.613973
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	−18.0000	−0.916176
$387$	4.00000	0.203331
$388$	0	0
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	4.00000	0.202548
$391$	−32.0000	−1.61831
$392$	0	0
$393$	36.0000	1.81596
$394$	18.0000	0.906827
$395$	4.00000	0.201262
$396$	−4.00000	−0.201008
$397$	26.0000	1.30490	0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000	1.30490	0.652451	+	0.757831i	$0.273741\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	1.00000	0.0500000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	−8.00000	−0.399004
$403$	8.00000	0.398508
$404$	−2.00000	−0.0995037
$405$	−11.0000	−0.546594
$406$	0	0
$407$	40.0000	1.98273
$408$	16.0000	0.792118
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	4.00000	0.197546
$411$	−4.00000	−0.197305
$412$	4.00000	0.197066
$413$	0	0
$414$	−4.00000	−0.196589
$415$	−2.00000	−0.0981761
$416$	2.00000	0.0980581
$417$	−20.0000	−0.979404
$418$	24.0000	1.17388
$419$	6.00000	0.293119	0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000	0.293119	0.146560	+	0.989202i	$0.453180\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	20.0000	0.973585
$423$	4.00000	0.194487
$424$	10.0000	0.485643
$425$	8.00000	0.388057
$426$	24.0000	1.16280
$427$	0	0
$428$	−12.0000	−0.580042
$429$	−16.0000	−0.772487
$430$	4.00000	0.192897
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−4.00000	−0.192450
$433$	−40.0000	−1.92228	−0.961139	−	0.276066i	$-0.910969\pi$
$433$	−40.0000	−1.92228	−0.961139	+	0.276066i	$0.910969\pi$
$434$	0	0
$435$	−12.0000	−0.575356
$436$	10.0000	0.478913
$437$	24.0000	1.14808
$438$	8.00000	0.382255
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	−4.00000	−0.190693
$441$	0	0
$442$	16.0000	0.761042
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	−20.0000	−0.949158
$445$	8.00000	0.379236
$446$	−8.00000	−0.378811
$447$	−20.0000	−0.945968
$448$	0	0
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	1.00000	0.0471405
$451$	−16.0000	−0.753411
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	−18.0000	−0.844782
$455$	0	0
$456$	−12.0000	−0.561951
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	−14.0000	−0.654177
$459$	−32.0000	−1.49363
$460$	−4.00000	−0.186501
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−6.00000	−0.278543
$465$	8.00000	0.370991
$466$	22.0000	1.01913
$467$	−10.0000	−0.462745	−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000	−0.462745	−0.231372	+	0.972865i	$0.574322\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	4.00000	0.184506
$471$	4.00000	0.184310
$472$	−14.0000	−0.644402
$473$	−16.0000	−0.735681
$474$	8.00000	0.367452
$475$	−6.00000	−0.275299
$476$	0	0
$477$	10.0000	0.457869
$478$	−8.00000	−0.365911
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	2.00000	0.0912871
$481$	−20.0000	−0.911922
$482$	4.00000	0.182195
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	−10.0000	−0.453609
$487$	−44.0000	−1.99383	−0.996915	−	0.0784867i	$-0.974991\pi$
$487$	−44.0000	−1.99383	−0.996915	+	0.0784867i	$0.974991\pi$
$488$	−10.0000	−0.452679
$489$	−8.00000	−0.361773
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	8.00000	0.360668
$493$	−48.0000	−2.16181
$494$	−12.0000	−0.539906
$495$	−4.00000	−0.179787
$496$	4.00000	0.179605
$497$	0	0
$498$	−4.00000	−0.179244
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	1.00000	0.0447214
$501$	24.0000	1.07224
$502$	22.0000	0.981908
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	−2.00000	−0.0889988
$506$	16.0000	0.711287
$507$	−18.0000	−0.799408
$508$	−12.0000	−0.532414
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	16.0000	0.708492
$511$	0	0
$512$	1.00000	0.0441942
$513$	24.0000	1.05963
$514$	12.0000	0.529297
$515$	4.00000	0.176261
$516$	8.00000	0.352180
$517$	−16.0000	−0.703679
$518$	0	0
$519$	36.0000	1.58022
$520$	2.00000	0.0877058
$521$	−12.0000	−0.525730	−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000	−0.525730	−0.262865	+	0.964833i	$0.584667\pi$
$522$	−6.00000	−0.262613
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	0	0
$527$	32.0000	1.39394
$528$	−8.00000	−0.348155
$529$	−7.00000	−0.304348
$530$	10.0000	0.434372
$531$	−14.0000	−0.607548
$532$	0	0
$533$	8.00000	0.346518
$534$	16.0000	0.692388
$535$	−12.0000	−0.518805
$536$	−4.00000	−0.172774
$537$	8.00000	0.345225
$538$	26.0000	1.12094
$539$	0	0
$540$	−4.00000	−0.172133
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	16.0000	0.687259
$543$	52.0000	2.23153
$544$	8.00000	0.342997
$545$	10.0000	0.428353
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−2.00000	−0.0854358
$549$	−10.0000	−0.426790
$550$	−4.00000	−0.170561
$551$	36.0000	1.53365
$552$	−8.00000	−0.340503
$553$	0	0
$554$	2.00000	0.0849719
$555$	−20.0000	−0.848953
$556$	−10.0000	−0.424094
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	4.00000	0.169334
$559$	8.00000	0.338364
$560$	0	0
$561$	−64.0000	−2.70208
$562$	−10.0000	−0.421825
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	8.00000	0.336861
$565$	−2.00000	−0.0841406
$566$	−26.0000	−1.09286
$567$	0	0
$568$	12.0000	0.503509
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	−12.0000	−0.502625
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−8.00000	−0.334497
$573$	24.0000	1.00261
$574$	0	0
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−20.0000	−0.832611	−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000	−0.832611	−0.416305	+	0.909225i	$0.636675\pi$
$578$	47.0000	1.95494
$579$	−36.0000	−1.49611
$580$	−6.00000	−0.249136
$581$	0	0
$582$	0	0
$583$	−40.0000	−1.65663
$584$	4.00000	0.165521
$585$	2.00000	0.0826898
$586$	6.00000	0.247858
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	−14.0000	−0.576371
$591$	36.0000	1.48084
$592$	−10.0000	−0.410997
$593$	−20.0000	−0.821302	−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000	−0.821302	−0.410651	+	0.911793i	$0.634698\pi$
$594$	16.0000	0.656488
$595$	0	0
$596$	−10.0000	−0.409616
$597$	8.00000	0.327418
$598$	−8.00000	−0.327144
$599$	−28.0000	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$599$	−28.0000	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$600$	2.00000	0.0816497
$601$	40.0000	1.63163	0.815817	−	0.578310i	$-0.196288\pi$
$601$	40.0000	1.63163	0.815817	+	0.578310i	$0.196288\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	0	0
$605$	5.00000	0.203279
$606$	−4.00000	−0.162489
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	−10.0000	−0.404888
$611$	8.00000	0.323645
$612$	8.00000	0.323381
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−2.00000	−0.0807134
$615$	8.00000	0.322591
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	8.00000	0.321807
$619$	−6.00000	−0.241160	−0.120580	−	0.992704i	$-0.538475\pi$
$619$	−6.00000	−0.241160	−0.120580	+	0.992704i	$0.538475\pi$
$620$	4.00000	0.160644
$621$	16.0000	0.642058
$622$	16.0000	0.641542
$623$	0	0
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	−8.00000	−0.319744
$627$	48.0000	1.91694
$628$	2.00000	0.0798087
$629$	−80.0000	−3.18981
$630$	0	0
$631$	4.00000	0.159237	0.0796187	−	0.996825i	$-0.474630\pi$
$631$	4.00000	0.159237	0.0796187	+	0.996825i	$0.474630\pi$
$632$	4.00000	0.159111
$633$	40.0000	1.58986
$634$	18.0000	0.714871
$635$	−12.0000	−0.476205
$636$	20.0000	0.793052
$637$	0	0
$638$	24.0000	0.950169
$639$	12.0000	0.474713
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−24.0000	−0.947204
$643$	18.0000	0.709851	0.354925	−	0.934895i	$-0.384506\pi$
$643$	18.0000	0.709851	0.354925	+	0.934895i	$0.384506\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−48.0000	−1.88853
$647$	28.0000	1.10079	0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000	1.10079	0.550397	+	0.834903i	$0.314476\pi$
$648$	−11.0000	−0.432121
$649$	56.0000	2.19819
$650$	2.00000	0.0784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	20.0000	0.782062
$655$	18.0000	0.703318
$656$	4.00000	0.156174
$657$	4.00000	0.156055
$658$	0	0
$659$	−4.00000	−0.155818	−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000	−0.155818	−0.0779089	+	0.996960i	$0.524824\pi$
$660$	−8.00000	−0.311400
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	−28.0000	−1.08825
$663$	32.0000	1.24278
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	−10.0000	−0.387492
$667$	24.0000	0.929284
$668$	12.0000	0.464294
$669$	−16.0000	−0.618596
$670$	−4.00000	−0.154533
$671$	40.0000	1.54418
$672$	0	0
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	−14.0000	−0.539260
$675$	−4.00000	−0.153960
$676$	−9.00000	−0.346154
$677$	−46.0000	−1.76792	−0.883962	−	0.467559i	$-0.845134\pi$
$677$	−46.0000	−1.76792	−0.883962	+	0.467559i	$0.845134\pi$
$678$	−4.00000	−0.153619
$679$	0	0
$680$	8.00000	0.306786
$681$	−36.0000	−1.37952
$682$	−16.0000	−0.612672
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−6.00000	−0.229416
$685$	−2.00000	−0.0764161
$686$	0	0
$687$	−28.0000	−1.06827
$688$	4.00000	0.152499
$689$	20.0000	0.761939
$690$	−8.00000	−0.304555
$691$	−46.0000	−1.74992	−0.874961	−	0.484193i	$-0.839113\pi$
$691$	−46.0000	−1.74992	−0.874961	+	0.484193i	$0.839113\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	−4.00000	−0.151838
$695$	−10.0000	−0.379322
$696$	−12.0000	−0.454859
$697$	32.0000	1.21209
$698$	10.0000	0.378506
$699$	44.0000	1.66423
$700$	0	0
$701$	−38.0000	−1.43524	−0.717620	−	0.696435i	$-0.754769\pi$
$701$	−38.0000	−1.43524	−0.717620	+	0.696435i	$0.754769\pi$
$702$	−8.00000	−0.301941
$703$	60.0000	2.26294
$704$	−4.00000	−0.150756
$705$	8.00000	0.301297
$706$	−12.0000	−0.451626
$707$	0	0
$708$	−28.0000	−1.05230
$709$	42.0000	1.57734	0.788672	−	0.614815i	$-0.210769\pi$
$709$	42.0000	1.57734	0.788672	+	0.614815i	$0.210769\pi$
$710$	12.0000	0.450352
$711$	4.00000	0.150012
$712$	8.00000	0.299813
$713$	−16.0000	−0.599205
$714$	0	0
$715$	−8.00000	−0.299183
$716$	4.00000	0.149487
$717$	−16.0000	−0.597531
$718$	−8.00000	−0.298557
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	17.0000	0.632674
$723$	8.00000	0.297523
$724$	26.0000	0.966282
$725$	−6.00000	−0.222834
$726$	10.0000	0.371135
$727$	20.0000	0.741759	0.370879	−	0.928681i	$-0.379056\pi$
$727$	20.0000	0.741759	0.370879	+	0.928681i	$0.379056\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	4.00000	0.148047
$731$	32.0000	1.18356
$732$	−20.0000	−0.739221
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−4.00000	−0.147442
$737$	16.0000	0.589368
$738$	4.00000	0.147242
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	−10.0000	−0.367607
$741$	−24.0000	−0.881662
$742$	0	0
$743$	−12.0000	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$744$	8.00000	0.293294
$745$	−10.0000	−0.366372
$746$	−6.00000	−0.219676
$747$	−2.00000	−0.0731762
$748$	−32.0000	−1.17004
$749$	0	0
$750$	2.00000	0.0730297
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	4.00000	0.145865
$753$	44.0000	1.60345
$754$	−12.0000	−0.437014
$755$	0	0
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−4.00000	−0.145287
$759$	32.0000	1.16153
$760$	−6.00000	−0.217643
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	−24.0000	−0.869428
$763$	0	0
$764$	12.0000	0.434145
$765$	8.00000	0.289241
$766$	20.0000	0.722629
$767$	−28.0000	−1.01102
$768$	2.00000	0.0721688
$769$	28.0000	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$770$	0	0
$771$	24.0000	0.864339
$772$	−18.0000	−0.647834
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	4.00000	0.143777
$775$	4.00000	0.143684
$776$	0	0
$777$	0	0
$778$	18.0000	0.645331
$779$	−24.0000	−0.859889
$780$	4.00000	0.143223
$781$	−48.0000	−1.71758
$782$	−32.0000	−1.14432
$783$	24.0000	0.857690
$784$	0	0
$785$	2.00000	0.0713831
$786$	36.0000	1.28408
$787$	6.00000	0.213877	0.106938	−	0.994266i	$-0.465895\pi$
$787$	6.00000	0.213877	0.106938	+	0.994266i	$0.465895\pi$
$788$	18.0000	0.641223
$789$	0	0
$790$	4.00000	0.142314
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−20.0000	−0.710221
$794$	26.0000	0.922705
$795$	20.0000	0.709327
$796$	4.00000	0.141776
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	32.0000	1.13208
$800$	1.00000	0.0353553
$801$	8.00000	0.282666
$802$	−14.0000	−0.494357
$803$	−16.0000	−0.564628
$804$	−8.00000	−0.282138
$805$	0	0
$806$	8.00000	0.281788
$807$	52.0000	1.83049
$808$	−2.00000	−0.0703598
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	−11.0000	−0.386501
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	0	0
$813$	32.0000	1.12229
$814$	40.0000	1.40200
$815$	−4.00000	−0.140114
$816$	16.0000	0.560112
$817$	−24.0000	−0.839654
$818$	−20.0000	−0.699284
$819$	0	0
$820$	4.00000	0.139686
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	−4.00000	−0.139516
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	4.00000	0.139347
$825$	−8.00000	−0.278524
$826$	0	0
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	−4.00000	−0.139010
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	−2.00000	−0.0694210
$831$	4.00000	0.138758
$832$	2.00000	0.0693375
$833$	0	0
$834$	−20.0000	−0.692543
$835$	12.0000	0.415277
$836$	24.0000	0.830057
$837$	−16.0000	−0.553041
$838$	6.00000	0.207267
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−34.0000	−1.17172
$843$	−20.0000	−0.688837
$844$	20.0000	0.688428
$845$	−9.00000	−0.309609
$846$	4.00000	0.137523
$847$	0	0
$848$	10.0000	0.343401
$849$	−52.0000	−1.78464
$850$	8.00000	0.274398
$851$	40.0000	1.37118
$852$	24.0000	0.822226
$853$	50.0000	1.71197	0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000	1.71197	0.855984	+	0.517003i	$0.172952\pi$
$854$	0	0
$855$	−6.00000	−0.205196
$856$	−12.0000	−0.410152
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	−16.0000	−0.546231
$859$	38.0000	1.29654	0.648272	−	0.761409i	$-0.275492\pi$
$859$	38.0000	1.29654	0.648272	+	0.761409i	$0.275492\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	−4.00000	−0.136083
$865$	18.0000	0.612018
$866$	−40.0000	−1.35926
$867$	94.0000	3.19241
$868$	0	0
$869$	−16.0000	−0.542763
$870$	−12.0000	−0.406838
$871$	−8.00000	−0.271070
$872$	10.0000	0.338643
$873$	0	0
$874$	24.0000	0.811812
$875$	0	0
$876$	8.00000	0.270295
$877$	−42.0000	−1.41824	−0.709120	−	0.705088i	$-0.750907\pi$
$877$	−42.0000	−1.41824	−0.709120	+	0.705088i	$0.750907\pi$
$878$	−32.0000	−1.07995
$879$	12.0000	0.404750
$880$	−4.00000	−0.134840
$881$	−40.0000	−1.34763	−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000	−1.34763	−0.673817	+	0.738898i	$0.735346\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	16.0000	0.538138
$885$	−28.0000	−0.941210
$886$	4.00000	0.134383
$887$	4.00000	0.134307	0.0671534	−	0.997743i	$-0.478608\pi$
$887$	4.00000	0.134307	0.0671534	+	0.997743i	$0.478608\pi$
$888$	−20.0000	−0.671156
$889$	0	0
$890$	8.00000	0.268161
$891$	44.0000	1.47406
$892$	−8.00000	−0.267860
$893$	−24.0000	−0.803129
$894$	−20.0000	−0.668900
$895$	4.00000	0.133705
$896$	0	0
$897$	−16.0000	−0.534224
$898$	18.0000	0.600668
$899$	−24.0000	−0.800445
$900$	1.00000	0.0333333
$901$	80.0000	2.66519
$902$	−16.0000	−0.532742
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	26.0000	0.864269
$906$	0	0
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	−18.0000	−0.597351
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	−12.0000	−0.397360
$913$	8.00000	0.264761
$914$	6.00000	0.198462
$915$	−20.0000	−0.661180
$916$	−14.0000	−0.462573
$917$	0	0
$918$	−32.0000	−1.05616
$919$	−4.00000	−0.131948	−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000	−0.131948	−0.0659739	+	0.997821i	$0.521015\pi$
$920$	−4.00000	−0.131876
$921$	−4.00000	−0.131804
$922$	−6.00000	−0.197599
$923$	24.0000	0.789970
$924$	0	0
$925$	−10.0000	−0.328798
$926$	16.0000	0.525793
$927$	4.00000	0.131377
$928$	−6.00000	−0.196960
$929$	−12.0000	−0.393707	−0.196854	−	0.980433i	$-0.563072\pi$
$929$	−12.0000	−0.393707	−0.196854	+	0.980433i	$0.563072\pi$
$930$	8.00000	0.262330
$931$	0	0
$932$	22.0000	0.720634
$933$	32.0000	1.04763
$934$	−10.0000	−0.327210
$935$	−32.0000	−1.04651
$936$	2.00000	0.0653720
$937$	12.0000	0.392023	0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000	0.392023	0.196011	+	0.980602i	$0.437201\pi$
$938$	0	0
$939$	−16.0000	−0.522140
$940$	4.00000	0.130466
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	4.00000	0.130327
$943$	−16.0000	−0.521032
$944$	−14.0000	−0.455661
$945$	0	0
$946$	−16.0000	−0.520205
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	8.00000	0.259828
$949$	8.00000	0.259691
$950$	−6.00000	−0.194666
$951$	36.0000	1.16738
$952$	0	0
$953$	2.00000	0.0647864	0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000	0.0647864	0.0323932	+	0.999475i	$0.489687\pi$
$954$	10.0000	0.323762
$955$	12.0000	0.388311
$956$	−8.00000	−0.258738
$957$	48.0000	1.55162
$958$	4.00000	0.129234
$959$	0	0
$960$	2.00000	0.0645497
$961$	−15.0000	−0.483871
$962$	−20.0000	−0.644826
$963$	−12.0000	−0.386695
$964$	4.00000	0.128831
$965$	−18.0000	−0.579441
$966$	0	0
$967$	−52.0000	−1.67221	−0.836104	−	0.548572i	$-0.815172\pi$
$967$	−52.0000	−1.67221	−0.836104	+	0.548572i	$0.815172\pi$
$968$	5.00000	0.160706
$969$	−96.0000	−3.08396
$970$	0	0
$971$	−62.0000	−1.98967	−0.994837	−	0.101482i	$-0.967641\pi$
$971$	−62.0000	−1.98967	−0.994837	+	0.101482i	$0.967641\pi$
$972$	−10.0000	−0.320750
$973$	0	0
$974$	−44.0000	−1.40985
$975$	4.00000	0.128103
$976$	−10.0000	−0.320092
$977$	54.0000	1.72761	0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000	1.72761	0.863807	+	0.503824i	$0.168074\pi$
$978$	−8.00000	−0.255812
$979$	−32.0000	−1.02272
$980$	0	0
$981$	10.0000	0.319275
$982$	−12.0000	−0.382935
$983$	20.0000	0.637901	0.318950	−	0.947771i	$-0.396670\pi$
$983$	20.0000	0.637901	0.318950	+	0.947771i	$0.396670\pi$
$984$	8.00000	0.255031
$985$	18.0000	0.573528
$986$	−48.0000	−1.52863
$987$	0	0
$988$	−12.0000	−0.381771
$989$	−16.0000	−0.508770
$990$	−4.00000	−0.127128
$991$	−36.0000	−1.14358	−0.571789	−	0.820401i	$-0.693750\pi$
$991$	−36.0000	−1.14358	−0.571789	+	0.820401i	$0.693750\pi$
$992$	4.00000	0.127000
$993$	−56.0000	−1.77711
$994$	0	0
$995$	4.00000	0.126809
$996$	−4.00000	−0.126745
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	28.0000	0.886325
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.a.i.1.1	yes	1
3.2	odd	2		4410.2.a.i.1.1		1
4.3	odd	2		3920.2.a.j.1.1		1
5.2	odd	4		2450.2.c.n.99.2		2
5.3	odd	4		2450.2.c.n.99.1		2
5.4	even	2		2450.2.a.d.1.1		1
7.2	even	3		490.2.e.b.361.1		2
7.3	odd	6		490.2.e.e.471.1		2
7.4	even	3		490.2.e.b.471.1		2
7.5	odd	6		490.2.e.e.361.1		2
7.6	odd	2		490.2.a.f.1.1	✓	1
21.20	even	2		4410.2.a.s.1.1		1
28.27	even	2		3920.2.a.bg.1.1		1
35.13	even	4		2450.2.c.b.99.1		2
35.27	even	4		2450.2.c.b.99.2		2
35.34	odd	2		2450.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.a.f.1.1	✓	1	7.6	odd	2
490.2.a.i.1.1	yes	1	1.1	even	1	trivial
490.2.e.b.361.1		2	7.2	even	3
490.2.e.b.471.1		2	7.4	even	3
490.2.e.e.361.1		2	7.5	odd	6
490.2.e.e.471.1		2	7.3	odd	6
2450.2.a.d.1.1		1	5.4	even	2
2450.2.a.n.1.1		1	35.34	odd	2
2450.2.c.b.99.1		2	35.13	even	4
2450.2.c.b.99.2		2	35.27	even	4
2450.2.c.n.99.1		2	5.3	odd	4
2450.2.c.n.99.2		2	5.2	odd	4
3920.2.a.j.1.1		1	4.3	odd	2
3920.2.a.bg.1.1		1	28.27	even	2
4410.2.a.i.1.1		1	3.2	odd	2
4410.2.a.s.1.1		1	21.20	even	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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