LMFDB - Embedded newform 2550.2.a.m.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2550,2,Mod(1,2550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2550.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2550, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,1,1,0,-1,1,-1,1,0,-3,1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$20.3618525154$
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	$\chi$	$=$	2550.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -5.00000 q^{19} +1.00000 q^{21} +3.00000 q^{22} +8.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -4.00000 q^{29} -3.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -7.00000 q^{37} +5.00000 q^{38} -4.00000 q^{39} +2.00000 q^{41} -1.00000 q^{42} -1.00000 q^{43} -3.00000 q^{44} -8.00000 q^{46} -7.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{51} -4.00000 q^{52} +7.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} -5.00000 q^{57} +4.00000 q^{58} -8.00000 q^{59} -2.00000 q^{61} +3.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} -11.0000 q^{67} +1.00000 q^{68} +8.00000 q^{69} -6.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} +7.00000 q^{74} -5.00000 q^{76} -3.00000 q^{77} +4.00000 q^{78} -15.0000 q^{79} +1.00000 q^{81} -2.00000 q^{82} +16.0000 q^{83} +1.00000 q^{84} +1.00000 q^{86} -4.00000 q^{87} +3.00000 q^{88} +2.00000 q^{89} -4.00000 q^{91} +8.00000 q^{92} -3.00000 q^{93} +7.00000 q^{94} -1.00000 q^{96} +10.0000 q^{97} +6.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	3.00000	0.639602
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	−3.00000	−0.522233
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	5.00000	0.811107
$39$	−4.00000	−0.640513
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	−1.00000	−0.154303
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−8.00000	−1.17954
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	0	0
$51$	1.00000	0.140028
$52$	−4.00000	−0.554700
$53$	7.00000	0.961524	0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000	0.961524	0.480762	+	0.876851i	$0.340360\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−5.00000	−0.662266
$58$	4.00000	0.525226
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	3.00000	0.381000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	−11.0000	−1.34386	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−11.0000	−1.34386	−0.671932	+	0.740613i	$0.734535\pi$
$68$	1.00000	0.121268
$69$	8.00000	0.963087
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−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
$76$	−5.00000	−0.573539
$77$	−3.00000	−0.341882
$78$	4.00000	0.452911
$79$	−15.0000	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$79$	−15.0000	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	16.0000	1.75623	0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000	1.75623	0.878114	+	0.478451i	$0.158802\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	1.00000	0.107833
$87$	−4.00000	−0.428845
$88$	3.00000	0.319801
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	8.00000	0.834058
$93$	−3.00000	−0.311086
$94$	7.00000	0.721995
$95$	0	0
$96$	−1.00000	−0.102062
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	6.00000	0.606092
$99$	−3.00000	−0.301511
$100$	0	0
$101$	5.00000	0.497519	0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000	0.497519	0.248759	+	0.968565i	$0.419977\pi$
$102$	−1.00000	−0.0990148
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−7.00000	−0.679900
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	1.00000	0.0962250
$109$	−9.00000	−0.862044	−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000	−0.862044	−0.431022	+	0.902342i	$0.641847\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	1.00000	0.0944911
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	5.00000	0.468293
$115$	0	0
$116$	−4.00000	−0.371391
$117$	−4.00000	−0.369800
$118$	8.00000	0.736460
$119$	1.00000	0.0916698
$120$	0	0
$121$	−2.00000	−0.181818
$122$	2.00000	0.181071
$123$	2.00000	0.180334
$124$	−3.00000	−0.269408
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	−1.00000	−0.0883883
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.00000	−0.261116
$133$	−5.00000	−0.433555
$134$	11.0000	0.950255
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−8.00000	−0.681005
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−7.00000	−0.589506
$142$	6.00000	0.503509
$143$	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	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	5.00000	0.405554
$153$	1.00000	0.0808452
$154$	3.00000	0.241747
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	15.0000	1.19334
$159$	7.00000	0.555136
$160$	0	0
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−16.0000	−1.24184
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	−1.00000	−0.0771517
$169$	3.00000	0.230769
$170$	0	0
$171$	−5.00000	−0.382360
$172$	−1.00000	−0.0762493
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	4.00000	0.303239
$175$	0	0
$176$	−3.00000	−0.226134
$177$	−8.00000	−0.601317
$178$	−2.00000	−0.149906
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−19.0000	−1.41226	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000	−1.41226	−0.706129	+	0.708083i	$0.749560\pi$
$182$	4.00000	0.296500
$183$	−2.00000	−0.147844
$184$	−8.00000	−0.589768
$185$	0	0
$186$	3.00000	0.219971
$187$	−3.00000	−0.219382
$188$	−7.00000	−0.510527
$189$	1.00000	0.0727393
$190$	0	0
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	1.00000	0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−6.00000	−0.428571
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	3.00000	0.213201
$199$	13.0000	0.921546	0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000	0.921546	0.460773	+	0.887518i	$0.347572\pi$
$200$	0	0
$201$	−11.0000	−0.775880
$202$	−5.00000	−0.351799
$203$	−4.00000	−0.280745
$204$	1.00000	0.0700140
$205$	0	0
$206$	−10.0000	−0.696733
$207$	8.00000	0.556038
$208$	−4.00000	−0.277350
$209$	15.0000	1.03757
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	7.00000	0.480762
$213$	−6.00000	−0.411113
$214$	−15.0000	−1.02538
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−3.00000	−0.203653
$218$	9.00000	0.609557
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−4.00000	−0.269069
$222$	7.00000	0.469809
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	9.00000	0.598671
$227$	−27.0000	−1.79205	−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000	−1.79205	−0.896026	+	0.444001i	$0.853559\pi$
$228$	−5.00000	−0.331133
$229$	28.0000	1.85029	0.925146	−	0.379611i	$-0.123942\pi$
$229$	28.0000	1.85029	0.925146	+	0.379611i	$0.123942\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	4.00000	0.262613
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	−8.00000	−0.520756
$237$	−15.0000	−0.974355
$238$	−1.00000	−0.0648204
$239$	−3.00000	−0.194054	−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000	−0.194054	−0.0970269	+	0.995282i	$0.530933\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	2.00000	0.128565
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−2.00000	−0.127515
$247$	20.0000	1.27257
$248$	3.00000	0.190500
$249$	16.0000	1.01396
$250$	0	0
$251$	10.0000	0.631194	0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000	0.631194	0.315597	+	0.948893i	$0.397795\pi$
$252$	1.00000	0.0629941
$253$	−24.0000	−1.50887
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	20.0000	1.24757	0.623783	−	0.781598i	$-0.285595\pi$
$257$	20.0000	1.24757	0.623783	+	0.781598i	$0.285595\pi$
$258$	1.00000	0.0622573
$259$	−7.00000	−0.434959
$260$	0	0
$261$	−4.00000	−0.247594
$262$	12.0000	0.741362
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	5.00000	0.306570
$267$	2.00000	0.122398
$268$	−11.0000	−0.671932
$269$	−8.00000	−0.487769	−0.243884	−	0.969804i	$-0.578422\pi$
$269$	−8.00000	−0.487769	−0.243884	+	0.969804i	$0.578422\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	1.00000	0.0606339
$273$	−4.00000	−0.242091
$274$	18.0000	1.08742
$275$	0	0
$276$	8.00000	0.481543
$277$	5.00000	0.300421	0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000	0.300421	0.150210	+	0.988654i	$0.452005\pi$
$278$	0	0
$279$	−3.00000	−0.179605
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	7.00000	0.416844
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	−12.0000	−0.709575
$287$	2.00000	0.118056
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	10.0000	0.586210
$292$	−2.00000	−0.117041
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	7.00000	0.406867
$297$	−3.00000	−0.174078
$298$	18.0000	1.04271
$299$	−32.0000	−1.85061
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	−20.0000	−1.15087
$303$	5.00000	0.287242
$304$	−5.00000	−0.286770
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	−3.00000	−0.170941
$309$	10.0000	0.568880
$310$	0	0
$311$	2.00000	0.113410	0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000	0.113410	0.0567048	+	0.998391i	$0.481941\pi$
$312$	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	$0.572595\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−15.0000	−0.843816
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	−7.00000	−0.392541
$319$	12.0000	0.671871
$320$	0	0
$321$	15.0000	0.837218
$322$	−8.00000	−0.445823
$323$	−5.00000	−0.278207
$324$	1.00000	0.0555556
$325$	0	0
$326$	18.0000	0.996928
$327$	−9.00000	−0.497701
$328$	−2.00000	−0.110432
$329$	−7.00000	−0.385922
$330$	0	0
$331$	17.0000	0.934405	0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000	0.934405	0.467202	+	0.884150i	$0.345262\pi$
$332$	16.0000	0.878114
$333$	−7.00000	−0.383598
$334$	10.0000	0.547176
$335$	0	0
$336$	1.00000	0.0545545
$337$	−24.0000	−1.30736	−0.653682	−	0.756770i	$-0.726776\pi$
$337$	−24.0000	−1.30736	−0.653682	+	0.756770i	$0.726776\pi$
$338$	−3.00000	−0.163178
$339$	−9.00000	−0.488813
$340$	0	0
$341$	9.00000	0.487377
$342$	5.00000	0.270369
$343$	−13.0000	−0.701934
$344$	1.00000	0.0539164
$345$	0	0
$346$	−2.00000	−0.107521
$347$	5.00000	0.268414	0.134207	−	0.990953i	$-0.457151\pi$
$347$	5.00000	0.268414	0.134207	+	0.990953i	$0.457151\pi$
$348$	−4.00000	−0.214423
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	3.00000	0.159901
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	2.00000	0.106000
$357$	1.00000	0.0529256
$358$	0	0
$359$	−25.0000	−1.31945	−0.659725	−	0.751507i	$-0.729327\pi$
$359$	−25.0000	−1.31945	−0.659725	+	0.751507i	$0.729327\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	19.0000	0.998618
$363$	−2.00000	−0.104973
$364$	−4.00000	−0.209657
$365$	0	0
$366$	2.00000	0.104542
$367$	−13.0000	−0.678594	−0.339297	−	0.940679i	$-0.610189\pi$
$367$	−13.0000	−0.678594	−0.339297	+	0.940679i	$0.610189\pi$
$368$	8.00000	0.417029
$369$	2.00000	0.104116
$370$	0	0
$371$	7.00000	0.363422
$372$	−3.00000	−0.155543
$373$	−38.0000	−1.96757	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−38.0000	−1.96757	−0.983783	+	0.179364i	$0.942596\pi$
$374$	3.00000	0.155126
$375$	0	0
$376$	7.00000	0.360997
$377$	16.0000	0.824042
$378$	−1.00000	−0.0514344
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	−15.0000	−0.767467
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−1.00000	−0.0508329
$388$	10.0000	0.507673
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	6.00000	0.303046
$393$	−12.0000	−0.605320
$394$	0	0
$395$	0	0
$396$	−3.00000	−0.150756
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	−13.0000	−0.651631
$399$	−5.00000	−0.250313
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	11.0000	0.548630
$403$	12.0000	0.597763
$404$	5.00000	0.248759
$405$	0	0
$406$	4.00000	0.198517
$407$	21.0000	1.04093
$408$	−1.00000	−0.0495074
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	0	0
$411$	−18.0000	−0.887875
$412$	10.0000	0.492665
$413$	−8.00000	−0.393654
$414$	−8.00000	−0.393179
$415$	0	0
$416$	4.00000	0.196116
$417$	0	0
$418$	−15.0000	−0.733674
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	0	0
$423$	−7.00000	−0.340352
$424$	−7.00000	−0.339950
$425$	0	0
$426$	6.00000	0.290701
$427$	−2.00000	−0.0967868
$428$	15.0000	0.725052
$429$	12.0000	0.579365
$430$	0	0
$431$	26.0000	1.25238	0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000	1.25238	0.626188	+	0.779672i	$0.284614\pi$
$432$	1.00000	0.0481125
$433$	−5.00000	−0.240285	−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000	−0.240285	−0.120142	+	0.992757i	$0.538335\pi$
$434$	3.00000	0.144005
$435$	0	0
$436$	−9.00000	−0.431022
$437$	−40.0000	−1.91346
$438$	2.00000	0.0955637
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	4.00000	0.190261
$443$	26.0000	1.23530	0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000	1.23530	0.617649	+	0.786454i	$0.288085\pi$
$444$	−7.00000	−0.332205
$445$	0	0
$446$	2.00000	0.0947027
$447$	−18.0000	−0.851371
$448$	1.00000	0.0472456
$449$	13.0000	0.613508	0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000	0.613508	0.306754	+	0.951789i	$0.400757\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	−9.00000	−0.423324
$453$	20.0000	0.939682
$454$	27.0000	1.26717
$455$	0	0
$456$	5.00000	0.234146
$457$	−11.0000	−0.514558	−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000	−0.514558	−0.257279	+	0.966337i	$0.582826\pi$
$458$	−28.0000	−1.30835
$459$	1.00000	0.0466760
$460$	0	0
$461$	−9.00000	−0.419172	−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000	−0.419172	−0.209586	+	0.977790i	$0.567212\pi$
$462$	3.00000	0.139573
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	−22.0000	−1.01913
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	−4.00000	−0.184900
$469$	−11.0000	−0.507933
$470$	0	0
$471$	−4.00000	−0.184310
$472$	8.00000	0.368230
$473$	3.00000	0.137940
$474$	15.0000	0.688973
$475$	0	0
$476$	1.00000	0.0458349
$477$	7.00000	0.320508
$478$	3.00000	0.137217
$479$	−10.0000	−0.456912	−0.228456	−	0.973554i	$-0.573368\pi$
$479$	−10.0000	−0.456912	−0.228456	+	0.973554i	$0.573368\pi$
$480$	0	0
$481$	28.0000	1.27669
$482$	0	0
$483$	8.00000	0.364013
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	−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	$0.138905\pi$
$488$	2.00000	0.0905357
$489$	−18.0000	−0.813988
$490$	0	0
$491$	22.0000	0.992846	0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000	0.992846	0.496423	+	0.868081i	$0.334646\pi$
$492$	2.00000	0.0901670
$493$	−4.00000	−0.180151
$494$	−20.0000	−0.899843
$495$	0	0
$496$	−3.00000	−0.134704
$497$	−6.00000	−0.269137
$498$	−16.0000	−0.716977
$499$	−6.00000	−0.268597	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000	−0.268597	−0.134298	+	0.990941i	$0.542878\pi$
$500$	0	0
$501$	−10.0000	−0.446767
$502$	−10.0000	−0.446322
$503$	2.00000	0.0891756	0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000	0.0891756	0.0445878	+	0.999005i	$0.485803\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	24.0000	1.06693
$507$	3.00000	0.133235
$508$	2.00000	0.0887357
$509$	−29.0000	−1.28540	−0.642701	−	0.766117i	$-0.722186\pi$
$509$	−29.0000	−1.28540	−0.642701	+	0.766117i	$0.722186\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	−1.00000	−0.0441942
$513$	−5.00000	−0.220755
$514$	−20.0000	−0.882162
$515$	0	0
$516$	−1.00000	−0.0440225
$517$	21.0000	0.923579
$518$	7.00000	0.307562
$519$	2.00000	0.0877903
$520$	0	0
$521$	−11.0000	−0.481919	−0.240959	−	0.970535i	$-0.577462\pi$
$521$	−11.0000	−0.481919	−0.240959	+	0.970535i	$0.577462\pi$
$522$	4.00000	0.175075
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−9.00000	−0.392419
$527$	−3.00000	−0.130682
$528$	−3.00000	−0.130558
$529$	41.0000	1.78261
$530$	0	0
$531$	−8.00000	−0.347170
$532$	−5.00000	−0.216777
$533$	−8.00000	−0.346518
$534$	−2.00000	−0.0865485
$535$	0	0
$536$	11.0000	0.475128
$537$	0	0
$538$	8.00000	0.344904
$539$	18.0000	0.775315
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	20.0000	0.859074
$543$	−19.0000	−0.815368
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	4.00000	0.171184
$547$	−42.0000	−1.79579	−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000	−1.79579	−0.897895	+	0.440209i	$0.854904\pi$
$548$	−18.0000	−0.768922
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	20.0000	0.852029
$552$	−8.00000	−0.340503
$553$	−15.0000	−0.637865
$554$	−5.00000	−0.212430
$555$	0	0
$556$	0	0
$557$	−11.0000	−0.466085	−0.233042	−	0.972467i	$-0.574868\pi$
$557$	−11.0000	−0.466085	−0.233042	+	0.972467i	$0.574868\pi$
$558$	3.00000	0.127000
$559$	4.00000	0.169182
$560$	0	0
$561$	−3.00000	−0.126660
$562$	14.0000	0.590554
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	−7.00000	−0.294753
$565$	0	0
$566$	26.0000	1.09286
$567$	1.00000	0.0419961
$568$	6.00000	0.251754
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	30.0000	1.25546	0.627730	−	0.778431i	$-0.283984\pi$
$571$	30.0000	1.25546	0.627730	+	0.778431i	$0.283984\pi$
$572$	12.0000	0.501745
$573$	15.0000	0.626634
$574$	−2.00000	−0.0834784
$575$	0	0
$576$	1.00000	0.0416667
$577$	11.0000	0.457936	0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000	0.457936	0.228968	+	0.973434i	$0.426465\pi$
$578$	−1.00000	−0.0415945
$579$	14.0000	0.581820
$580$	0	0
$581$	16.0000	0.663792
$582$	−10.0000	−0.414513
$583$	−21.0000	−0.869731
$584$	2.00000	0.0827606
$585$	0	0
$586$	10.0000	0.413096
$587$	22.0000	0.908037	0.454019	−	0.890992i	$-0.349990\pi$
$587$	22.0000	0.908037	0.454019	+	0.890992i	$0.349990\pi$
$588$	−6.00000	−0.247436
$589$	15.0000	0.618064
$590$	0	0
$591$	0	0
$592$	−7.00000	−0.287698
$593$	−12.0000	−0.492781	−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000	−0.492781	−0.246390	+	0.969171i	$0.579245\pi$
$594$	3.00000	0.123091
$595$	0	0
$596$	−18.0000	−0.737309
$597$	13.0000	0.532055
$598$	32.0000	1.30858
$599$	15.0000	0.612883	0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000	0.612883	0.306442	+	0.951889i	$0.400862\pi$
$600$	0	0
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	1.00000	0.0407570
$603$	−11.0000	−0.447955
$604$	20.0000	0.813788
$605$	0	0
$606$	−5.00000	−0.203111
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	5.00000	0.202777
$609$	−4.00000	−0.162088
$610$	0	0
$611$	28.0000	1.13276
$612$	1.00000	0.0404226
$613$	−30.0000	−1.21169	−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000	−1.21169	−0.605844	+	0.795583i	$0.707165\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	3.00000	0.120873
$617$	33.0000	1.32853	0.664265	−	0.747497i	$-0.268745\pi$
$617$	33.0000	1.32853	0.664265	+	0.747497i	$0.268745\pi$
$618$	−10.0000	−0.402259
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	8.00000	0.321029
$622$	−2.00000	−0.0801927
$623$	2.00000	0.0801283
$624$	−4.00000	−0.160128
$625$	0	0
$626$	8.00000	0.319744
$627$	15.0000	0.599042
$628$	−4.00000	−0.159617
$629$	−7.00000	−0.279108
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	15.0000	0.596668
$633$	0	0
$634$	0	0
$635$	0	0
$636$	7.00000	0.277568
$637$	24.0000	0.950915
$638$	−12.0000	−0.475085
$639$	−6.00000	−0.237356
$640$	0	0
$641$	−2.00000	−0.0789953	−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000	−0.0789953	−0.0394976	+	0.999220i	$0.512576\pi$
$642$	−15.0000	−0.592003
$643$	32.0000	1.26196	0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	5.00000	0.196722
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	−1.00000	−0.0392837
$649$	24.0000	0.942082
$650$	0	0
$651$	−3.00000	−0.117579
$652$	−18.0000	−0.704934
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	9.00000	0.351928
$655$	0	0
$656$	2.00000	0.0780869
$657$	−2.00000	−0.0780274
$658$	7.00000	0.272888
$659$	−48.0000	−1.86981	−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000	−1.86981	−0.934907	+	0.354892i	$0.884518\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	−17.0000	−0.660724
$663$	−4.00000	−0.155347
$664$	−16.0000	−0.620920
$665$	0	0
$666$	7.00000	0.271244
$667$	−32.0000	−1.23904
$668$	−10.0000	−0.386912
$669$	−2.00000	−0.0773245
$670$	0	0
$671$	6.00000	0.231627
$672$	−1.00000	−0.0385758
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	24.0000	0.924445
$675$	0	0
$676$	3.00000	0.115385
$677$	−26.0000	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$678$	9.00000	0.345643
$679$	10.0000	0.383765
$680$	0	0
$681$	−27.0000	−1.03464
$682$	−9.00000	−0.344628
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	−5.00000	−0.191180
$685$	0	0
$686$	13.0000	0.496342
$687$	28.0000	1.06827
$688$	−1.00000	−0.0381246
$689$	−28.0000	−1.06672
$690$	0	0
$691$	18.0000	0.684752	0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000	0.684752	0.342376	+	0.939563i	$0.388768\pi$
$692$	2.00000	0.0760286
$693$	−3.00000	−0.113961
$694$	−5.00000	−0.189797
$695$	0	0
$696$	4.00000	0.151620
$697$	2.00000	0.0757554
$698$	22.0000	0.832712
$699$	22.0000	0.832116
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	4.00000	0.150970
$703$	35.0000	1.32005
$704$	−3.00000	−0.113067
$705$	0	0
$706$	0	0
$707$	5.00000	0.188044
$708$	−8.00000	−0.300658
$709$	−1.00000	−0.0375558	−0.0187779	−	0.999824i	$-0.505978\pi$
$709$	−1.00000	−0.0375558	−0.0187779	+	0.999824i	$0.505978\pi$
$710$	0	0
$711$	−15.0000	−0.562544
$712$	−2.00000	−0.0749532
$713$	−24.0000	−0.898807
$714$	−1.00000	−0.0374241
$715$	0	0
$716$	0	0
$717$	−3.00000	−0.112037
$718$	25.0000	0.932992
$719$	−10.0000	−0.372937	−0.186469	−	0.982461i	$-0.559704\pi$
$719$	−10.0000	−0.372937	−0.186469	+	0.982461i	$0.559704\pi$
$720$	0	0
$721$	10.0000	0.372419
$722$	−6.00000	−0.223297
$723$	0	0
$724$	−19.0000	−0.706129
$725$	0	0
$726$	2.00000	0.0742270
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.00000	−0.0369863
$732$	−2.00000	−0.0739221
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	13.0000	0.479839
$735$	0	0
$736$	−8.00000	−0.294884
$737$	33.0000	1.21557
$738$	−2.00000	−0.0736210
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	0	0
$741$	20.0000	0.734718
$742$	−7.00000	−0.256978
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	3.00000	0.109985
$745$	0	0
$746$	38.0000	1.39128
$747$	16.0000	0.585409
$748$	−3.00000	−0.109691
$749$	15.0000	0.548088
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−7.00000	−0.255264
$753$	10.0000	0.364420
$754$	−16.0000	−0.582686
$755$	0	0
$756$	1.00000	0.0363696
$757$	50.0000	1.81728	0.908640	−	0.417579i	$-0.137121\pi$
$757$	50.0000	1.81728	0.908640	+	0.417579i	$0.137121\pi$
$758$	−16.0000	−0.581146
$759$	−24.0000	−0.871145
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	−2.00000	−0.0724524
$763$	−9.00000	−0.325822
$764$	15.0000	0.542681
$765$	0	0
$766$	−20.0000	−0.722629
$767$	32.0000	1.15545
$768$	1.00000	0.0360844
$769$	11.0000	0.396670	0.198335	−	0.980134i	$-0.436447\pi$
$769$	11.0000	0.396670	0.198335	+	0.980134i	$0.436447\pi$
$770$	0	0
$771$	20.0000	0.720282
$772$	14.0000	0.503871
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	−10.0000	−0.358979
$777$	−7.00000	−0.251124
$778$	−9.00000	−0.322666
$779$	−10.0000	−0.358287
$780$	0	0
$781$	18.0000	0.644091
$782$	−8.00000	−0.286079
$783$	−4.00000	−0.142948
$784$	−6.00000	−0.214286
$785$	0	0
$786$	12.0000	0.428026
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	0	0
$789$	9.00000	0.320408
$790$	0	0
$791$	−9.00000	−0.320003
$792$	3.00000	0.106600
$793$	8.00000	0.284088
$794$	−25.0000	−0.887217
$795$	0	0
$796$	13.0000	0.460773
$797$	−51.0000	−1.80651	−0.903256	−	0.429101i	$-0.858830\pi$
$797$	−51.0000	−1.80651	−0.903256	+	0.429101i	$0.858830\pi$
$798$	5.00000	0.176998
$799$	−7.00000	−0.247642
$800$	0	0
$801$	2.00000	0.0706665
$802$	−30.0000	−1.05934
$803$	6.00000	0.211735
$804$	−11.0000	−0.387940
$805$	0	0
$806$	−12.0000	−0.422682
$807$	−8.00000	−0.281613
$808$	−5.00000	−0.175899
$809$	5.00000	0.175791	0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000	0.175791	0.0878953	+	0.996130i	$0.471986\pi$
$810$	0	0
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−4.00000	−0.140372
$813$	−20.0000	−0.701431
$814$	−21.0000	−0.736050
$815$	0	0
$816$	1.00000	0.0350070
$817$	5.00000	0.174928
$818$	2.00000	0.0699284
$819$	−4.00000	−0.139771
$820$	0	0
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	18.0000	0.627822
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	−10.0000	−0.348367
$825$	0	0
$826$	8.00000	0.278356
$827$	47.0000	1.63435	0.817175	−	0.576390i	$-0.195539\pi$
$827$	47.0000	1.63435	0.817175	+	0.576390i	$0.195539\pi$
$828$	8.00000	0.278019
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	0	0
$831$	5.00000	0.173448
$832$	−4.00000	−0.138675
$833$	−6.00000	−0.207888
$834$	0	0
$835$	0	0
$836$	15.0000	0.518786
$837$	−3.00000	−0.103695
$838$	−20.0000	−0.690889
$839$	−34.0000	−1.17381	−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000	−1.17381	−0.586905	+	0.809656i	$0.699654\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	−20.0000	−0.689246
$843$	−14.0000	−0.482186
$844$	0	0
$845$	0	0
$846$	7.00000	0.240665
$847$	−2.00000	−0.0687208
$848$	7.00000	0.240381
$849$	−26.0000	−0.892318
$850$	0	0
$851$	−56.0000	−1.91966
$852$	−6.00000	−0.205557
$853$	−9.00000	−0.308154	−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000	−0.308154	−0.154077	+	0.988059i	$0.549240\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	−15.0000	−0.512689
$857$	41.0000	1.40053	0.700267	−	0.713881i	$-0.253064\pi$
$857$	41.0000	1.40053	0.700267	+	0.713881i	$0.253064\pi$
$858$	−12.0000	−0.409673
$859$	−45.0000	−1.53538	−0.767690	−	0.640821i	$-0.778594\pi$
$859$	−45.0000	−1.53538	−0.767690	+	0.640821i	$0.778594\pi$
$860$	0	0
$861$	2.00000	0.0681598
$862$	−26.0000	−0.885564
$863$	1.00000	0.0340404	0.0170202	−	0.999855i	$-0.494582\pi$
$863$	1.00000	0.0340404	0.0170202	+	0.999855i	$0.494582\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	5.00000	0.169907
$867$	1.00000	0.0339618
$868$	−3.00000	−0.101827
$869$	45.0000	1.52652
$870$	0	0
$871$	44.0000	1.49088
$872$	9.00000	0.304778
$873$	10.0000	0.338449
$874$	40.0000	1.35302
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	12.0000	0.404980
$879$	−10.0000	−0.337292
$880$	0	0
$881$	−57.0000	−1.92038	−0.960189	−	0.279350i	$-0.909881\pi$
$881$	−57.0000	−1.92038	−0.960189	+	0.279350i	$0.909881\pi$
$882$	6.00000	0.202031
$883$	56.0000	1.88455	0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000	1.88455	0.942275	+	0.334840i	$0.108682\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−26.0000	−0.873487
$887$	28.0000	0.940148	0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$888$	7.00000	0.234905
$889$	2.00000	0.0670778
$890$	0	0
$891$	−3.00000	−0.100504
$892$	−2.00000	−0.0669650
$893$	35.0000	1.17123
$894$	18.0000	0.602010
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−32.0000	−1.06845
$898$	−13.0000	−0.433816
$899$	12.0000	0.400222
$900$	0	0
$901$	7.00000	0.233204
$902$	6.00000	0.199778
$903$	−1.00000	−0.0332779
$904$	9.00000	0.299336
$905$	0	0
$906$	−20.0000	−0.664455
$907$	−40.0000	−1.32818	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000	−1.32818	−0.664089	+	0.747653i	$0.731180\pi$
$908$	−27.0000	−0.896026
$909$	5.00000	0.165840
$910$	0	0
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	−5.00000	−0.165567
$913$	−48.0000	−1.58857
$914$	11.0000	0.363848
$915$	0	0
$916$	28.0000	0.925146
$917$	−12.0000	−0.396275
$918$	−1.00000	−0.0330049
$919$	26.0000	0.857661	0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000	0.857661	0.428830	+	0.903385i	$0.358926\pi$
$920$	0	0
$921$	−16.0000	−0.527218
$922$	9.00000	0.296399
$923$	24.0000	0.789970
$924$	−3.00000	−0.0986928
$925$	0	0
$926$	16.0000	0.525793
$927$	10.0000	0.328443
$928$	4.00000	0.131306
$929$	19.0000	0.623370	0.311685	−	0.950186i	$-0.399107\pi$
$929$	19.0000	0.623370	0.311685	+	0.950186i	$0.399107\pi$
$930$	0	0
$931$	30.0000	0.983210
$932$	22.0000	0.720634
$933$	2.00000	0.0654771
$934$	18.0000	0.588978
$935$	0	0
$936$	4.00000	0.130744
$937$	42.0000	1.37208	0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000	1.37208	0.686040	+	0.727564i	$0.259347\pi$
$938$	11.0000	0.359163
$939$	−8.00000	−0.261070
$940$	0	0
$941$	−58.0000	−1.89075	−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−58.0000	−1.89075	−0.945373	+	0.325991i	$0.894302\pi$
$942$	4.00000	0.130327
$943$	16.0000	0.521032
$944$	−8.00000	−0.260378
$945$	0	0
$946$	−3.00000	−0.0975384
$947$	13.0000	0.422443	0.211222	−	0.977438i	$-0.432256\pi$
$947$	13.0000	0.422443	0.211222	+	0.977438i	$0.432256\pi$
$948$	−15.0000	−0.487177
$949$	8.00000	0.259691
$950$	0	0
$951$	0	0
$952$	−1.00000	−0.0324102
$953$	4.00000	0.129573	0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000	0.129573	0.0647864	+	0.997899i	$0.479363\pi$
$954$	−7.00000	−0.226633
$955$	0	0
$956$	−3.00000	−0.0970269
$957$	12.0000	0.387905
$958$	10.0000	0.323085
$959$	−18.0000	−0.581250
$960$	0	0
$961$	−22.0000	−0.709677
$962$	−28.0000	−0.902756
$963$	15.0000	0.483368
$964$	0	0
$965$	0	0
$966$	−8.00000	−0.257396
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	2.00000	0.0642824
$969$	−5.00000	−0.160623
$970$	0	0
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−40.0000	−1.28168
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	18.0000	0.575577
$979$	−6.00000	−0.191761
$980$	0	0
$981$	−9.00000	−0.287348
$982$	−22.0000	−0.702048
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	−2.00000	−0.0637577
$985$	0	0
$986$	4.00000	0.127386
$987$	−7.00000	−0.222812
$988$	20.0000	0.636285
$989$	−8.00000	−0.254385
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	3.00000	0.0952501
$993$	17.0000	0.539479
$994$	6.00000	0.190308
$995$	0	0
$996$	16.0000	0.506979
$997$	25.0000	0.791758	0.395879	−	0.918303i	$-0.370440\pi$
$997$	25.0000	0.791758	0.395879	+	0.918303i	$0.370440\pi$
$998$	6.00000	0.189927
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.a.m.1.1	✓	1
3.2	odd	2		7650.2.a.cc.1.1		1
5.2	odd	4		2550.2.d.d.2449.1		2
5.3	odd	4		2550.2.d.d.2449.2		2
5.4	even	2		2550.2.a.v.1.1	yes	1
15.14	odd	2		7650.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.m.1.1	✓	1	1.1	even	1	trivial
2550.2.a.v.1.1	yes	1	5.4	even	2
2550.2.d.d.2449.1		2	5.2	odd	4
2550.2.d.d.2449.2		2	5.3	odd	4
7650.2.a.o.1.1		1	15.14	odd	2
7650.2.a.cc.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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