LMFDB - Embedded newform 1450.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$1$
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	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -6.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -4.00000 q^{21} +6.00000 q^{22} -2.00000 q^{24} +2.00000 q^{26} -4.00000 q^{27} -2.00000 q^{28} -1.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} -12.0000 q^{33} -6.00000 q^{34} +1.00000 q^{36} +7.00000 q^{37} -2.00000 q^{38} -4.00000 q^{39} -12.0000 q^{41} +4.00000 q^{42} -8.00000 q^{43} -6.00000 q^{44} -9.00000 q^{47} +2.00000 q^{48} -3.00000 q^{49} +12.0000 q^{51} -2.00000 q^{52} +6.00000 q^{53} +4.00000 q^{54} +2.00000 q^{56} +4.00000 q^{57} +1.00000 q^{58} -9.00000 q^{59} -1.00000 q^{61} +7.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +12.0000 q^{66} +1.00000 q^{67} +6.00000 q^{68} -12.0000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -7.00000 q^{74} +2.00000 q^{76} +12.0000 q^{77} +4.00000 q^{78} +8.00000 q^{79} -11.0000 q^{81} +12.0000 q^{82} -4.00000 q^{84} +8.00000 q^{86} -2.00000 q^{87} +6.00000 q^{88} -6.00000 q^{89} +4.00000 q^{91} -14.0000 q^{93} +9.00000 q^{94} -2.00000 q^{96} +4.00000 q^{97} +3.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	6.00000	1.27920
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	2.00000	0.392232
$27$	−4.00000	−0.769800
$28$	−2.00000	−0.377964
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	−12.0000	−2.08893
$34$	−6.00000	−1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	7.00000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	4.00000	0.617213
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	0	0
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	2.00000	0.288675
$49$	−3.00000	−0.428571
$50$	0	0
$51$	12.0000	1.68034
$52$	−2.00000	−0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	2.00000	0.267261
$57$	4.00000	0.529813
$58$	1.00000	0.131306
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	7.00000	0.889001
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	12.0000	1.47710
$67$	1.00000	0.122169	0.0610847	−	0.998133i	$-0.480544\pi$
$67$	1.00000	0.122169	0.0610847	+	0.998133i	$0.480544\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−7.00000	−0.813733
$75$	0	0
$76$	2.00000	0.229416
$77$	12.0000	1.36753
$78$	4.00000	0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	12.0000	1.32518
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	8.00000	0.862662
$87$	−2.00000	−0.214423
$88$	6.00000	0.639602
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	0	0
$93$	−14.0000	−1.45173
$94$	9.00000	0.928279
$95$	0	0
$96$	−2.00000	−0.204124
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	3.00000	0.303046
$99$	−6.00000	−0.603023
$100$	0	0
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	−12.0000	−1.18818
$103$	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
$106$	−6.00000	−0.582772
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.00000	−0.384900
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	14.0000	1.32882
$112$	−2.00000	−0.188982
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	−2.00000	−0.184900
$118$	9.00000	0.828517
$119$	−12.0000	−1.10004
$120$	0	0
$121$	25.0000	2.27273
$122$	1.00000	0.0905357
$123$	−24.0000	−2.16401
$124$	−7.00000	−0.628619
$125$	0	0
$126$	2.00000	0.178174
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	−1.00000	−0.0883883
$129$	−16.0000	−1.40872
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	−12.0000	−1.04447
$133$	−4.00000	−0.346844
$134$	−1.00000	−0.0863868
$135$	0	0
$136$	−6.00000	−0.514496
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	0	0
$141$	−18.0000	−1.51587
$142$	12.0000	1.00702
$143$	12.0000	1.00349
$144$	1.00000	0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	−6.00000	−0.494872
$148$	7.00000	0.575396
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−2.00000	−0.162221
$153$	6.00000	0.485071
$154$	−12.0000	−0.966988
$155$	0	0
$156$	−4.00000	−0.320256
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	−8.00000	−0.636446
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	11.0000	0.864242
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	0	0
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	4.00000	0.308607
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	−8.00000	−0.609994
$173$	−24.0000	−1.82469	−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000	−1.82469	−0.912343	+	0.409426i	$0.865729\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−6.00000	−0.452267
$177$	−18.0000	−1.35296
$178$	6.00000	0.449719
$179$	21.0000	1.56961	0.784807	−	0.619740i	$-0.212762\pi$
$179$	21.0000	1.56961	0.784807	+	0.619740i	$0.212762\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−4.00000	−0.296500
$183$	−2.00000	−0.147844
$184$	0	0
$185$	0	0
$186$	14.0000	1.02653
$187$	−36.0000	−2.63258
$188$	−9.00000	−0.656392
$189$	8.00000	0.581914
$190$	0	0
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	2.00000	0.144338
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	6.00000	0.426401
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	2.00000	0.141069
$202$	−3.00000	−0.211079
$203$	2.00000	0.140372
$204$	12.0000	0.840168
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	−2.00000	−0.138675
$209$	−12.0000	−0.830057
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	6.00000	0.412082
$213$	−24.0000	−1.64445
$214$	−3.00000	−0.205076
$215$	0	0
$216$	4.00000	0.272166
$217$	14.0000	0.950382
$218$	4.00000	0.270914
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−14.0000	−0.939618
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	−18.0000	−1.19734
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	4.00000	0.264906
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	24.0000	1.57908
$232$	1.00000	0.0656532
$233$	−15.0000	−0.982683	−0.491341	−	0.870967i	$-0.663493\pi$
$233$	−15.0000	−0.982683	−0.491341	+	0.870967i	$0.663493\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	−9.00000	−0.585850
$237$	16.0000	1.03931
$238$	12.0000	0.777844
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	0	0
$241$	−13.0000	−0.837404	−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000	−0.837404	−0.418702	+	0.908124i	$0.637515\pi$
$242$	−25.0000	−1.60706
$243$	−10.0000	−0.641500
$244$	−1.00000	−0.0640184
$245$	0	0
$246$	24.0000	1.53018
$247$	−4.00000	−0.254514
$248$	7.00000	0.444500
$249$	0	0
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	16.0000	0.996116
$259$	−14.0000	−0.869918
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	18.0000	1.11204
$263$	−27.0000	−1.66489	−0.832446	−	0.554107i	$-0.813060\pi$
$263$	−27.0000	−1.66489	−0.832446	+	0.554107i	$0.813060\pi$
$264$	12.0000	0.738549
$265$	0	0
$266$	4.00000	0.245256
$267$	−12.0000	−0.734388
$268$	1.00000	0.0610847
$269$	15.0000	0.914566	0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000	0.914566	0.457283	+	0.889321i	$0.348823\pi$
$270$	0	0
$271$	−7.00000	−0.425220	−0.212610	−	0.977137i	$-0.568196\pi$
$271$	−7.00000	−0.425220	−0.212610	+	0.977137i	$0.568196\pi$
$272$	6.00000	0.363803
$273$	8.00000	0.484182
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−5.00000	−0.299880
$279$	−7.00000	−0.419079
$280$	0	0
$281$	−33.0000	−1.96861	−0.984307	−	0.176462i	$-0.943535\pi$
$281$	−33.0000	−1.96861	−0.984307	+	0.176462i	$0.943535\pi$
$282$	18.0000	1.07188
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−12.0000	−0.709575
$287$	24.0000	1.41668
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	8.00000	0.468968
$292$	−2.00000	−0.117041
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	−7.00000	−0.406867
$297$	24.0000	1.39262
$298$	−18.0000	−1.04271
$299$	0	0
$300$	0	0
$301$	16.0000	0.922225
$302$	−20.0000	−1.15087
$303$	6.00000	0.344691
$304$	2.00000	0.114708
$305$	0	0
$306$	−6.00000	−0.342997
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	12.0000	0.683763
$309$	8.00000	0.455104
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	4.00000	0.226455
$313$	25.0000	1.41308	0.706542	−	0.707671i	$-0.250254\pi$
$313$	25.0000	1.41308	0.706542	+	0.707671i	$0.250254\pi$
$314$	−7.00000	−0.395033
$315$	0	0
$316$	8.00000	0.450035
$317$	15.0000	0.842484	0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000	0.842484	0.421242	+	0.906948i	$0.361594\pi$
$318$	−12.0000	−0.672927
$319$	6.00000	0.335936
$320$	0	0
$321$	6.00000	0.334887
$322$	0	0
$323$	12.0000	0.667698
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−8.00000	−0.442401
$328$	12.0000	0.662589
$329$	18.0000	0.992372
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	0	0
$333$	7.00000	0.383598
$334$	12.0000	0.656611
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	9.00000	0.489535
$339$	36.0000	1.95525
$340$	0	0
$341$	42.0000	2.27443
$342$	−2.00000	−0.108148
$343$	20.0000	1.07990
$344$	8.00000	0.431331
$345$	0	0
$346$	24.0000	1.29025
$347$	3.00000	0.161048	0.0805242	−	0.996753i	$-0.474341\pi$
$347$	3.00000	0.161048	0.0805242	+	0.996753i	$0.474341\pi$
$348$	−2.00000	−0.107211
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	0	0
$351$	8.00000	0.427008
$352$	6.00000	0.319801
$353$	33.0000	1.75641	0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000	1.75641	0.878206	+	0.478282i	$0.158740\pi$
$354$	18.0000	0.956689
$355$	0	0
$356$	−6.00000	−0.317999
$357$	−24.0000	−1.27021
$358$	−21.0000	−1.10988
$359$	9.00000	0.475002	0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000	0.475002	0.237501	+	0.971387i	$0.423672\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	−2.00000	−0.105118
$363$	50.0000	2.62432
$364$	4.00000	0.209657
$365$	0	0
$366$	2.00000	0.104542
$367$	19.0000	0.991792	0.495896	−	0.868382i	$-0.334840\pi$
$367$	19.0000	0.991792	0.495896	+	0.868382i	$0.334840\pi$
$368$	0	0
$369$	−12.0000	−0.624695
$370$	0	0
$371$	−12.0000	−0.623009
$372$	−14.0000	−0.725866
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	36.0000	1.86152
$375$	0	0
$376$	9.00000	0.464140
$377$	2.00000	0.103005
$378$	−8.00000	−0.411476
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	0	0
$381$	14.0000	0.717242
$382$	−15.0000	−0.767467
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−10.0000	−0.508987
$387$	−8.00000	−0.406663
$388$	4.00000	0.203069
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	0	0
$392$	3.00000	0.151523
$393$	−36.0000	−1.81596
$394$	18.0000	0.906827
$395$	0	0
$396$	−6.00000	−0.301511
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	−8.00000	−0.401004
$399$	−8.00000	−0.400501
$400$	0	0
$401$	−15.0000	−0.749064	−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000	−0.749064	−0.374532	+	0.927214i	$0.622197\pi$
$402$	−2.00000	−0.0997509
$403$	14.0000	0.697390
$404$	3.00000	0.149256
$405$	0	0
$406$	−2.00000	−0.0992583
$407$	−42.0000	−2.08186
$408$	−12.0000	−0.594089
$409$	−28.0000	−1.38451	−0.692255	−	0.721653i	$-0.743383\pi$
$409$	−28.0000	−1.38451	−0.692255	+	0.721653i	$0.743383\pi$
$410$	0	0
$411$	0	0
$412$	4.00000	0.197066
$413$	18.0000	0.885722
$414$	0	0
$415$	0	0
$416$	2.00000	0.0980581
$417$	10.0000	0.489702
$418$	12.0000	0.586939
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	10.0000	0.486792
$423$	−9.00000	−0.437595
$424$	−6.00000	−0.291386
$425$	0	0
$426$	24.0000	1.16280
$427$	2.00000	0.0967868
$428$	3.00000	0.145010
$429$	24.0000	1.15873
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−4.00000	−0.192450
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	−14.0000	−0.672022
$435$	0	0
$436$	−4.00000	−0.191565
$437$	0	0
$438$	4.00000	0.191127
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	12.0000	0.570782
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	14.0000	0.664411
$445$	0	0
$446$	−16.0000	−0.757622
$447$	36.0000	1.70274
$448$	−2.00000	−0.0944911
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	0	0
$451$	72.0000	3.39035
$452$	18.0000	0.846649
$453$	40.0000	1.87936
$454$	3.00000	0.140797
$455$	0	0
$456$	−4.00000	−0.187317
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−14.0000	−0.654177
$459$	−24.0000	−1.12022
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	−24.0000	−1.11658
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	15.0000	0.694862
$467$	−42.0000	−1.94353	−0.971764	−	0.235954i	$-0.924178\pi$
$467$	−42.0000	−1.94353	−0.971764	+	0.235954i	$0.924178\pi$
$468$	−2.00000	−0.0924500
$469$	−2.00000	−0.0923514
$470$	0	0
$471$	14.0000	0.645086
$472$	9.00000	0.414259
$473$	48.0000	2.20704
$474$	−16.0000	−0.734904
$475$	0	0
$476$	−12.0000	−0.550019
$477$	6.00000	0.274721
$478$	−30.0000	−1.37217
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	−14.0000	−0.638345
$482$	13.0000	0.592134
$483$	0	0
$484$	25.0000	1.13636
$485$	0	0
$486$	10.0000	0.453609
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	1.00000	0.0452679
$489$	8.00000	0.361773
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	−24.0000	−1.08200
$493$	−6.00000	−0.270226
$494$	4.00000	0.179969
$495$	0	0
$496$	−7.00000	−0.314309
$497$	24.0000	1.07655
$498$	0	0
$499$	−13.0000	−0.581960	−0.290980	−	0.956729i	$-0.593981\pi$
$499$	−13.0000	−0.581960	−0.290980	+	0.956729i	$0.593981\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	12.0000	0.535586
$503$	21.0000	0.936344	0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000	0.936344	0.468172	+	0.883637i	$0.344913\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	0	0
$507$	−18.0000	−0.799408
$508$	7.00000	0.310575
$509$	−24.0000	−1.06378	−0.531891	−	0.846813i	$-0.678518\pi$
$509$	−24.0000	−1.06378	−0.531891	+	0.846813i	$0.678518\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−6.00000	−0.264649
$515$	0	0
$516$	−16.0000	−0.704361
$517$	54.0000	2.37492
$518$	14.0000	0.615125
$519$	−48.0000	−2.10697
$520$	0	0
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	1.00000	0.0437688
$523$	−29.0000	−1.26808	−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000	−1.26808	−0.634041	+	0.773300i	$0.718605\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	27.0000	1.17726
$527$	−42.0000	−1.82955
$528$	−12.0000	−0.522233
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−9.00000	−0.390567
$532$	−4.00000	−0.173422
$533$	24.0000	1.03956
$534$	12.0000	0.519291
$535$	0	0
$536$	−1.00000	−0.0431934
$537$	42.0000	1.81243
$538$	−15.0000	−0.646696
$539$	18.0000	0.775315
$540$	0	0
$541$	−13.0000	−0.558914	−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000	−0.558914	−0.279457	+	0.960158i	$0.590154\pi$
$542$	7.00000	0.300676
$543$	4.00000	0.171656
$544$	−6.00000	−0.257248
$545$	0	0
$546$	−8.00000	−0.342368
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	0	0
$549$	−1.00000	−0.0426790
$550$	0	0
$551$	−2.00000	−0.0852029
$552$	0	0
$553$	−16.0000	−0.680389
$554$	26.0000	1.10463
$555$	0	0
$556$	5.00000	0.212047
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	7.00000	0.296334
$559$	16.0000	0.676728
$560$	0	0
$561$	−72.0000	−3.03984
$562$	33.0000	1.39202
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	−18.0000	−0.757937
$565$	0	0
$566$	20.0000	0.840663
$567$	22.0000	0.923913
$568$	12.0000	0.503509
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	29.0000	1.21361	0.606806	−	0.794850i	$-0.292450\pi$
$571$	29.0000	1.21361	0.606806	+	0.794850i	$0.292450\pi$
$572$	12.0000	0.501745
$573$	30.0000	1.25327
$574$	−24.0000	−1.00174
$575$	0	0
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−19.0000	−0.790296
$579$	20.0000	0.831172
$580$	0	0
$581$	0	0
$582$	−8.00000	−0.331611
$583$	−36.0000	−1.49097
$584$	2.00000	0.0827606
$585$	0	0
$586$	9.00000	0.371787
$587$	−15.0000	−0.619116	−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000	−0.619116	−0.309558	+	0.950881i	$0.600181\pi$
$588$	−6.00000	−0.247436
$589$	−14.0000	−0.576860
$590$	0	0
$591$	−36.0000	−1.48084
$592$	7.00000	0.287698
$593$	33.0000	1.35515	0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000	1.35515	0.677574	+	0.735455i	$0.263031\pi$
$594$	−24.0000	−0.984732
$595$	0	0
$596$	18.0000	0.737309
$597$	16.0000	0.654836
$598$	0	0
$599$	−27.0000	−1.10319	−0.551595	−	0.834112i	$-0.685981\pi$
$599$	−27.0000	−1.10319	−0.551595	+	0.834112i	$0.685981\pi$
$600$	0	0
$601$	20.0000	0.815817	0.407909	−	0.913023i	$-0.366258\pi$
$601$	20.0000	0.815817	0.407909	+	0.913023i	$0.366258\pi$
$602$	−16.0000	−0.652111
$603$	1.00000	0.0407231
$604$	20.0000	0.813788
$605$	0	0
$606$	−6.00000	−0.243733
$607$	−41.0000	−1.66414	−0.832069	−	0.554672i	$-0.812844\pi$
$607$	−41.0000	−1.66414	−0.832069	+	0.554672i	$0.812844\pi$
$608$	−2.00000	−0.0811107
$609$	4.00000	0.162088
$610$	0	0
$611$	18.0000	0.728202
$612$	6.00000	0.242536
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	−12.0000	−0.483494
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	−8.00000	−0.321807
$619$	−34.0000	−1.36658	−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000	−1.36658	−0.683288	+	0.730149i	$0.739451\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	12.0000	0.480770
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−25.0000	−0.999201
$627$	−24.0000	−0.958468
$628$	7.00000	0.279330
$629$	42.0000	1.67465
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	−8.00000	−0.318223
$633$	−20.0000	−0.794929
$634$	−15.0000	−0.595726
$635$	0	0
$636$	12.0000	0.475831
$637$	6.00000	0.237729
$638$	−6.00000	−0.237542
$639$	−12.0000	−0.474713
$640$	0	0
$641$	36.0000	1.42191	0.710957	−	0.703235i	$-0.248262\pi$
$641$	36.0000	1.42191	0.710957	+	0.703235i	$0.248262\pi$
$642$	−6.00000	−0.236801
$643$	−23.0000	−0.907031	−0.453516	−	0.891248i	$-0.649830\pi$
$643$	−23.0000	−0.907031	−0.453516	+	0.891248i	$0.649830\pi$
$644$	0	0
$645$	0	0
$646$	−12.0000	−0.472134
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	11.0000	0.432121
$649$	54.0000	2.11969
$650$	0	0
$651$	28.0000	1.09741
$652$	4.00000	0.156652
$653$	−39.0000	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$654$	8.00000	0.312825
$655$	0	0
$656$	−12.0000	−0.468521
$657$	−2.00000	−0.0780274
$658$	−18.0000	−0.701713
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	−8.00000	−0.310929
$663$	−24.0000	−0.932083
$664$	0	0
$665$	0	0
$666$	−7.00000	−0.271244
$667$	0	0
$668$	−12.0000	−0.464294
$669$	32.0000	1.23719
$670$	0	0
$671$	6.00000	0.231627
$672$	4.00000	0.154303
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−33.0000	−1.26829	−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000	−1.26829	−0.634147	+	0.773213i	$0.718648\pi$
$678$	−36.0000	−1.38257
$679$	−8.00000	−0.307012
$680$	0	0
$681$	−6.00000	−0.229920
$682$	−42.0000	−1.60826
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−20.0000	−0.763604
$687$	28.0000	1.06827
$688$	−8.00000	−0.304997
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−1.00000	−0.0380418	−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000	−0.0380418	−0.0190209	+	0.999819i	$0.506055\pi$
$692$	−24.0000	−0.912343
$693$	12.0000	0.455842
$694$	−3.00000	−0.113878
$695$	0	0
$696$	2.00000	0.0758098
$697$	−72.0000	−2.72719
$698$	−26.0000	−0.984115
$699$	−30.0000	−1.13470
$700$	0	0
$701$	36.0000	1.35970	0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000	1.35970	0.679851	+	0.733351i	$0.262045\pi$
$702$	−8.00000	−0.301941
$703$	14.0000	0.528020
$704$	−6.00000	−0.226134
$705$	0	0
$706$	−33.0000	−1.24197
$707$	−6.00000	−0.225653
$708$	−18.0000	−0.676481
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	6.00000	0.224860
$713$	0	0
$714$	24.0000	0.898177
$715$	0	0
$716$	21.0000	0.784807
$717$	60.0000	2.24074
$718$	−9.00000	−0.335877
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	15.0000	0.558242
$723$	−26.0000	−0.966950
$724$	2.00000	0.0743294
$725$	0	0
$726$	−50.0000	−1.85567
$727$	52.0000	1.92857	0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000	1.92857	0.964287	+	0.264861i	$0.0853260\pi$
$728$	−4.00000	−0.148250
$729$	13.0000	0.481481
$730$	0	0
$731$	−48.0000	−1.77534
$732$	−2.00000	−0.0739221
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−19.0000	−0.701303
$735$	0	0
$736$	0	0
$737$	−6.00000	−0.221013
$738$	12.0000	0.441726
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	12.0000	0.440534
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	14.0000	0.513265
$745$	0	0
$746$	−4.00000	−0.146450
$747$	0	0
$748$	−36.0000	−1.31629
$749$	−6.00000	−0.219235
$750$	0	0
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	−9.00000	−0.328196
$753$	−24.0000	−0.874609
$754$	−2.00000	−0.0728357
$755$	0	0
$756$	8.00000	0.290957
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−2.00000	−0.0726433
$759$	0	0
$760$	0	0
$761$	−21.0000	−0.761249	−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000	−0.761249	−0.380625	+	0.924730i	$0.624291\pi$
$762$	−14.0000	−0.507166
$763$	8.00000	0.289619
$764$	15.0000	0.542681
$765$	0	0
$766$	−6.00000	−0.216789
$767$	18.0000	0.649942
$768$	2.00000	0.0721688
$769$	38.0000	1.37032	0.685158	−	0.728395i	$-0.259733\pi$
$769$	38.0000	1.37032	0.685158	+	0.728395i	$0.259733\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	10.0000	0.359908
$773$	39.0000	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$773$	39.0000	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	−4.00000	−0.143592
$777$	−28.0000	−1.00449
$778$	9.00000	0.322666
$779$	−24.0000	−0.859889
$780$	0	0
$781$	72.0000	2.57636
$782$	0	0
$783$	4.00000	0.142948
$784$	−3.00000	−0.107143
$785$	0	0
$786$	36.0000	1.28408
$787$	31.0000	1.10503	0.552515	−	0.833503i	$-0.313668\pi$
$787$	31.0000	1.10503	0.552515	+	0.833503i	$0.313668\pi$
$788$	−18.0000	−0.641223
$789$	−54.0000	−1.92245
$790$	0	0
$791$	−36.0000	−1.28001
$792$	6.00000	0.213201
$793$	2.00000	0.0710221
$794$	−34.0000	−1.20661
$795$	0	0
$796$	8.00000	0.283552
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	8.00000	0.283197
$799$	−54.0000	−1.91038
$800$	0	0
$801$	−6.00000	−0.212000
$802$	15.0000	0.529668
$803$	12.0000	0.423471
$804$	2.00000	0.0705346
$805$	0	0
$806$	−14.0000	−0.493129
$807$	30.0000	1.05605
$808$	−3.00000	−0.105540
$809$	24.0000	0.843795	0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000	0.843795	0.421898	+	0.906644i	$0.361364\pi$
$810$	0	0
$811$	−19.0000	−0.667180	−0.333590	−	0.942718i	$-0.608260\pi$
$811$	−19.0000	−0.667180	−0.333590	+	0.942718i	$0.608260\pi$
$812$	2.00000	0.0701862
$813$	−14.0000	−0.491001
$814$	42.0000	1.47210
$815$	0	0
$816$	12.0000	0.420084
$817$	−16.0000	−0.559769
$818$	28.0000	0.978997
$819$	4.00000	0.139771
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	−18.0000	−0.626300
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	0	0
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	0	0
$831$	−52.0000	−1.80386
$832$	−2.00000	−0.0693375
$833$	−18.0000	−0.623663
$834$	−10.0000	−0.346272
$835$	0	0
$836$	−12.0000	−0.415029
$837$	28.0000	0.967822
$838$	9.00000	0.310900
$839$	−15.0000	−0.517858	−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000	−0.517858	−0.258929	+	0.965896i	$0.583369\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−17.0000	−0.585859
$843$	−66.0000	−2.27316
$844$	−10.0000	−0.344214
$845$	0	0
$846$	9.00000	0.309426
$847$	−50.0000	−1.71802
$848$	6.00000	0.206041
$849$	−40.0000	−1.37280
$850$	0	0
$851$	0	0
$852$	−24.0000	−0.822226
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	−3.00000	−0.102538
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	−24.0000	−0.819346
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	0	0
$861$	48.0000	1.63584
$862$	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
$865$	0	0
$866$	−4.00000	−0.135926
$867$	38.0000	1.29055
$868$	14.0000	0.475191
$869$	−48.0000	−1.62829
$870$	0	0
$871$	−2.00000	−0.0677674
$872$	4.00000	0.135457
$873$	4.00000	0.135379
$874$	0	0
$875$	0	0
$876$	−4.00000	−0.135147
$877$	−8.00000	−0.270141	−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000	−0.270141	−0.135070	+	0.990836i	$0.543126\pi$
$878$	28.0000	0.944954
$879$	−18.0000	−0.607125
$880$	0	0
$881$	−48.0000	−1.61716	−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000	−1.61716	−0.808581	+	0.588386i	$0.799764\pi$
$882$	3.00000	0.101015
$883$	−17.0000	−0.572096	−0.286048	−	0.958215i	$-0.592342\pi$
$883$	−17.0000	−0.572096	−0.286048	+	0.958215i	$0.592342\pi$
$884$	−12.0000	−0.403604
$885$	0	0
$886$	18.0000	0.604722
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−14.0000	−0.469809
$889$	−14.0000	−0.469545
$890$	0	0
$891$	66.0000	2.21108
$892$	16.0000	0.535720
$893$	−18.0000	−0.602347
$894$	−36.0000	−1.20402
$895$	0	0
$896$	2.00000	0.0668153
$897$	0	0
$898$	−12.0000	−0.400445
$899$	7.00000	0.233463
$900$	0	0
$901$	36.0000	1.19933
$902$	−72.0000	−2.39734
$903$	32.0000	1.06489
$904$	−18.0000	−0.598671
$905$	0	0
$906$	−40.0000	−1.32891
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	−3.00000	−0.0995585
$909$	3.00000	0.0995037
$910$	0	0
$911$	27.0000	0.894550	0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000	0.894550	0.447275	+	0.894397i	$0.352395\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−10.0000	−0.330771
$915$	0	0
$916$	14.0000	0.462573
$917$	36.0000	1.18882
$918$	24.0000	0.792118
$919$	−46.0000	−1.51740	−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000	−1.51740	−0.758700	+	0.651440i	$0.774165\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	30.0000	0.987997
$923$	24.0000	0.789970
$924$	24.0000	0.789542
$925$	0	0
$926$	−4.00000	−0.131448
$927$	4.00000	0.131377
$928$	1.00000	0.0328266
$929$	3.00000	0.0984268	0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000	0.0984268	0.0492134	+	0.998788i	$0.484329\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−15.0000	−0.491341
$933$	0	0
$934$	42.0000	1.37428
$935$	0	0
$936$	2.00000	0.0653720
$937$	−11.0000	−0.359354	−0.179677	−	0.983726i	$-0.557505\pi$
$937$	−11.0000	−0.359354	−0.179677	+	0.983726i	$0.557505\pi$
$938$	2.00000	0.0653023
$939$	50.0000	1.63169
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	−14.0000	−0.456145
$943$	0	0
$944$	−9.00000	−0.292925
$945$	0	0
$946$	−48.0000	−1.56061
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	16.0000	0.519656
$949$	4.00000	0.129845
$950$	0	0
$951$	30.0000	0.972817
$952$	12.0000	0.388922
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	30.0000	0.970269
$957$	12.0000	0.387905
$958$	36.0000	1.16311
$959$	0	0
$960$	0	0
$961$	18.0000	0.580645
$962$	14.0000	0.451378
$963$	3.00000	0.0966736
$964$	−13.0000	−0.418702
$965$	0	0
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	−25.0000	−0.803530
$969$	24.0000	0.770991
$970$	0	0
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	−10.0000	−0.320750
$973$	−10.0000	−0.320585
$974$	38.0000	1.21760
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	57.0000	1.82359	0.911796	−	0.410644i	$-0.134696\pi$
$977$	57.0000	1.82359	0.911796	+	0.410644i	$0.134696\pi$
$978$	−8.00000	−0.255812
$979$	36.0000	1.15056
$980$	0	0
$981$	−4.00000	−0.127710
$982$	30.0000	0.957338
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	24.0000	0.765092
$985$	0	0
$986$	6.00000	0.191079
$987$	36.0000	1.14589
$988$	−4.00000	−0.127257
$989$	0	0
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	7.00000	0.222250
$993$	16.0000	0.507745
$994$	−24.0000	−0.761234
$995$	0	0
$996$	0	0
$997$	1.00000	0.0316703	0.0158352	−	0.999875i	$-0.494959\pi$
$997$	1.00000	0.0316703	0.0158352	+	0.999875i	$0.494959\pi$
$998$	13.0000	0.411508
$999$	−28.0000	−0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.a.d.1.1	✓	1
5.2	odd	4		1450.2.b.a.349.1		2
5.3	odd	4		1450.2.b.a.349.2		2
5.4	even	2		1450.2.a.e.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.d.1.1	✓	1	1.1	even	1	trivial
1450.2.a.e.1.1	yes	1	5.4	even	2
1450.2.b.a.349.1		2	5.2	odd	4
1450.2.b.a.349.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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