LMFDB - Embedded newform 5025.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5025,2,Mod(1,5025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5025 = 3 \cdot 5^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5025.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:	$40.1248270157$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 201)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +5.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +5.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +5.00000 q^{14} -1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} -2.00000 q^{19} -5.00000 q^{21} -4.00000 q^{22} +3.00000 q^{23} +3.00000 q^{24} +4.00000 q^{26} -1.00000 q^{27} -5.00000 q^{28} +4.00000 q^{29} -7.00000 q^{31} +5.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} -1.00000 q^{36} -5.00000 q^{37} -2.00000 q^{38} -4.00000 q^{39} -3.00000 q^{41} -5.00000 q^{42} -7.00000 q^{43} +4.00000 q^{44} +3.00000 q^{46} -8.00000 q^{47} +1.00000 q^{48} +18.0000 q^{49} +6.00000 q^{51} -4.00000 q^{52} +5.00000 q^{53} -1.00000 q^{54} -15.0000 q^{56} +2.00000 q^{57} +4.00000 q^{58} +3.00000 q^{59} -2.00000 q^{61} -7.00000 q^{62} +5.00000 q^{63} +7.00000 q^{64} +4.00000 q^{66} -1.00000 q^{67} +6.00000 q^{68} -3.00000 q^{69} -12.0000 q^{71} -3.00000 q^{72} +13.0000 q^{73} -5.00000 q^{74} +2.00000 q^{76} -20.0000 q^{77} -4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} -3.00000 q^{82} -1.00000 q^{83} +5.00000 q^{84} -7.00000 q^{86} -4.00000 q^{87} +12.0000 q^{88} +4.00000 q^{89} +20.0000 q^{91} -3.00000 q^{92} +7.00000 q^{93} -8.00000 q^{94} -5.00000 q^{96} +12.0000 q^{97} +18.0000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−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
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	5.00000	1.33631
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	0	0
$21$	−5.00000	−1.09109
$22$	−4.00000	−0.852803
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	3.00000	0.612372
$25$	0	0
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−5.00000	−0.944911
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	5.00000	0.883883
$33$	4.00000	0.696311
$34$	−6.00000	−1.02899
$35$	0	0
$36$	−1.00000	−0.166667
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−5.00000	−0.771517
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	3.00000	0.442326
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000	0.144338
$49$	18.0000	2.57143
$50$	0	0
$51$	6.00000	0.840168
$52$	−4.00000	−0.554700
$53$	5.00000	0.686803	0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000	0.686803	0.343401	+	0.939189i	$0.388421\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−15.0000	−2.00446
$57$	2.00000	0.264906
$58$	4.00000	0.525226
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−7.00000	−0.889001
$63$	5.00000	0.629941
$64$	7.00000	0.875000
$65$	0	0
$66$	4.00000	0.492366
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	6.00000	0.727607
$69$	−3.00000	−0.361158
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−3.00000	−0.353553
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	2.00000	0.229416
$77$	−20.0000	−2.27921
$78$	−4.00000	−0.452911
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−1.00000	−0.109764	−0.0548821	−	0.998493i	$-0.517478\pi$
$83$	−1.00000	−0.109764	−0.0548821	+	0.998493i	$0.517478\pi$
$84$	5.00000	0.545545
$85$	0	0
$86$	−7.00000	−0.754829
$87$	−4.00000	−0.428845
$88$	12.0000	1.27920
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	20.0000	2.09657
$92$	−3.00000	−0.312772
$93$	7.00000	0.725866
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−5.00000	−0.510310
$97$	12.0000	1.21842	0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000	1.21842	0.609208	+	0.793011i	$0.291488\pi$
$98$	18.0000	1.81827
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	6.00000	0.594089
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−12.0000	−1.17670
$105$	0	0
$106$	5.00000	0.485643
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	1.00000	0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	5.00000	0.474579
$112$	−5.00000	−0.472456
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	2.00000	0.187317
$115$	0	0
$116$	−4.00000	−0.371391
$117$	4.00000	0.369800
$118$	3.00000	0.276172
$119$	−30.0000	−2.75010
$120$	0	0
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	3.00000	0.270501
$124$	7.00000	0.628619
$125$	0	0
$126$	5.00000	0.445435
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	7.00000	0.616316
$130$	0	0
$131$	−21.0000	−1.83478	−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000	−1.83478	−0.917389	+	0.397991i	$0.869707\pi$
$132$	−4.00000	−0.348155
$133$	−10.0000	−0.867110
$134$	−1.00000	−0.0863868
$135$	0	0
$136$	18.0000	1.54349
$137$	−21.0000	−1.79415	−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000	−1.79415	−0.897076	+	0.441877i	$0.854313\pi$
$138$	−3.00000	−0.255377
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	−12.0000	−1.00702
$143$	−16.0000	−1.33799
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	13.0000	1.07589
$147$	−18.0000	−1.48461
$148$	5.00000	0.410997
$149$	−12.0000	−0.983078	−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000	−0.983078	−0.491539	+	0.870855i	$0.663566\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	6.00000	0.486664
$153$	−6.00000	−0.485071
$154$	−20.0000	−1.61165
$155$	0	0
$156$	4.00000	0.320256
$157$	9.00000	0.718278	0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000	0.718278	0.359139	+	0.933284i	$0.383070\pi$
$158$	−8.00000	−0.636446
$159$	−5.00000	−0.396526
$160$	0	0
$161$	15.0000	1.18217
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	−1.00000	−0.0776151
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	15.0000	1.15728
$169$	3.00000	0.230769
$170$	0	0
$171$	−2.00000	−0.152944
$172$	7.00000	0.533745
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	4.00000	0.301511
$177$	−3.00000	−0.225494
$178$	4.00000	0.299813
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	20.0000	1.48250
$183$	2.00000	0.147844
$184$	−9.00000	−0.663489
$185$	0	0
$186$	7.00000	0.513265
$187$	24.0000	1.75505
$188$	8.00000	0.583460
$189$	−5.00000	−0.363696
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	−7.00000	−0.505181
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	−18.0000	−1.28571
$197$	−25.0000	−1.78118	−0.890588	−	0.454811i	$-0.849707\pi$
$197$	−25.0000	−1.78118	−0.890588	+	0.454811i	$0.849707\pi$
$198$	−4.00000	−0.284268
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	0	0
$201$	1.00000	0.0705346
$202$	−10.0000	−0.703598
$203$	20.0000	1.40372
$204$	−6.00000	−0.420084
$205$	0	0
$206$	−8.00000	−0.557386
$207$	3.00000	0.208514
$208$	−4.00000	−0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	6.00000	0.413057	0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$212$	−5.00000	−0.343401
$213$	12.0000	0.822226
$214$	16.0000	1.09374
$215$	0	0
$216$	3.00000	0.204124
$217$	−35.0000	−2.37595
$218$	−10.0000	−0.677285
$219$	−13.0000	−0.878459
$220$	0	0
$221$	−24.0000	−1.61441
$222$	5.00000	0.335578
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	25.0000	1.67038
$225$	0	0
$226$	−6.00000	−0.399114
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	−2.00000	−0.132453
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	20.0000	1.31590
$232$	−12.0000	−0.787839
$233$	−1.00000	−0.0655122	−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000	−0.0655122	−0.0327561	+	0.999463i	$0.510428\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	−3.00000	−0.195283
$237$	8.00000	0.519656
$238$	−30.0000	−1.94461
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	0	0
$246$	3.00000	0.191273
$247$	−8.00000	−0.509028
$248$	21.0000	1.33350
$249$	1.00000	0.0633724
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	−5.00000	−0.314970
$253$	−12.0000	−0.754434
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	7.00000	0.435801
$259$	−25.0000	−1.55342
$260$	0	0
$261$	4.00000	0.247594
$262$	−21.0000	−1.29738
$263$	−7.00000	−0.431638	−0.215819	−	0.976433i	$-0.569242\pi$
$263$	−7.00000	−0.431638	−0.215819	+	0.976433i	$0.569242\pi$
$264$	−12.0000	−0.738549
$265$	0	0
$266$	−10.0000	−0.613139
$267$	−4.00000	−0.244796
$268$	1.00000	0.0610847
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	6.00000	0.363803
$273$	−20.0000	−1.21046
$274$	−21.0000	−1.26866
$275$	0	0
$276$	3.00000	0.180579
$277$	23.0000	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	13.0000	0.779688
$279$	−7.00000	−0.419079
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	8.00000	0.476393
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	−16.0000	−0.946100
$287$	−15.0000	−0.885422
$288$	5.00000	0.294628
$289$	19.0000	1.11765
$290$	0	0
$291$	−12.0000	−0.703452
$292$	−13.0000	−0.760767
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	−18.0000	−1.04978
$295$	0	0
$296$	15.0000	0.871857
$297$	4.00000	0.232104
$298$	−12.0000	−0.695141
$299$	12.0000	0.693978
$300$	0	0
$301$	−35.0000	−2.01737
$302$	−18.0000	−1.03578
$303$	10.0000	0.574485
$304$	2.00000	0.114708
$305$	0	0
$306$	−6.00000	−0.342997
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	20.0000	1.13961
$309$	8.00000	0.455104
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	12.0000	0.679366
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	9.00000	0.507899
$315$	0	0
$316$	8.00000	0.450035
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−5.00000	−0.280386
$319$	−16.0000	−0.895828
$320$	0	0
$321$	−16.0000	−0.893033
$322$	15.0000	0.835917
$323$	12.0000	0.667698
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	10.0000	0.553001
$328$	9.00000	0.496942
$329$	−40.0000	−2.20527
$330$	0	0
$331$	33.0000	1.81384	0.906922	−	0.421299i	$-0.138426\pi$
$331$	33.0000	1.81384	0.906922	+	0.421299i	$0.138426\pi$
$332$	1.00000	0.0548821
$333$	−5.00000	−0.273998
$334$	−3.00000	−0.164153
$335$	0	0
$336$	5.00000	0.272772
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	3.00000	0.163178
$339$	6.00000	0.325875
$340$	0	0
$341$	28.0000	1.51629
$342$	−2.00000	−0.108148
$343$	55.0000	2.96972
$344$	21.0000	1.13224
$345$	0	0
$346$	−14.0000	−0.752645
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	4.00000	0.214423
$349$	15.0000	0.802932	0.401466	−	0.915874i	$-0.368501\pi$
$349$	15.0000	0.802932	0.401466	+	0.915874i	$0.368501\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	−20.0000	−1.06600
$353$	21.0000	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$354$	−3.00000	−0.159448
$355$	0	0
$356$	−4.00000	−0.212000
$357$	30.0000	1.58777
$358$	−6.00000	−0.317110
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	7.00000	0.367912
$363$	−5.00000	−0.262432
$364$	−20.0000	−1.04828
$365$	0	0
$366$	2.00000	0.104542
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	−3.00000	−0.156386
$369$	−3.00000	−0.156174
$370$	0	0
$371$	25.0000	1.29794
$372$	−7.00000	−0.362933
$373$	18.0000	0.932005	0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000	0.932005	0.466002	+	0.884783i	$0.345694\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	24.0000	1.23771
$377$	16.0000	0.824042
$378$	−5.00000	−0.257172
$379$	9.00000	0.462299	0.231149	−	0.972918i	$-0.425751\pi$
$379$	9.00000	0.462299	0.231149	+	0.972918i	$0.425751\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	24.0000	1.22795
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−13.0000	−0.661683
$387$	−7.00000	−0.355830
$388$	−12.0000	−0.609208
$389$	−16.0000	−0.811232	−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000	−0.811232	−0.405616	+	0.914044i	$0.632943\pi$
$390$	0	0
$391$	−18.0000	−0.910299
$392$	−54.0000	−2.72741
$393$	21.0000	1.05931
$394$	−25.0000	−1.25948
$395$	0	0
$396$	4.00000	0.201008
$397$	−26.0000	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$398$	−20.0000	−1.00251
$399$	10.0000	0.500626
$400$	0	0
$401$	−17.0000	−0.848939	−0.424470	−	0.905442i	$-0.639539\pi$
$401$	−17.0000	−0.848939	−0.424470	+	0.905442i	$0.639539\pi$
$402$	1.00000	0.0498755
$403$	−28.0000	−1.39478
$404$	10.0000	0.497519
$405$	0	0
$406$	20.0000	0.992583
$407$	20.0000	0.991363
$408$	−18.0000	−0.891133
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	21.0000	1.03585
$412$	8.00000	0.394132
$413$	15.0000	0.738102
$414$	3.00000	0.147442
$415$	0	0
$416$	20.0000	0.980581
$417$	−13.0000	−0.636613
$418$	8.00000	0.391293
$419$	33.0000	1.61216	0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000	1.61216	0.806078	+	0.591810i	$0.201586\pi$
$420$	0	0
$421$	3.00000	0.146211	0.0731055	−	0.997324i	$-0.476709\pi$
$421$	3.00000	0.146211	0.0731055	+	0.997324i	$0.476709\pi$
$422$	6.00000	0.292075
$423$	−8.00000	−0.388973
$424$	−15.0000	−0.728464
$425$	0	0
$426$	12.0000	0.581402
$427$	−10.0000	−0.483934
$428$	−16.0000	−0.773389
$429$	16.0000	0.772487
$430$	0	0
$431$	3.00000	0.144505	0.0722525	−	0.997386i	$-0.476981\pi$
$431$	3.00000	0.144505	0.0722525	+	0.997386i	$0.476981\pi$
$432$	1.00000	0.0481125
$433$	−12.0000	−0.576683	−0.288342	−	0.957528i	$-0.593104\pi$
$433$	−12.0000	−0.576683	−0.288342	+	0.957528i	$0.593104\pi$
$434$	−35.0000	−1.68005
$435$	0	0
$436$	10.0000	0.478913
$437$	−6.00000	−0.287019
$438$	−13.0000	−0.621164
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	−24.0000	−1.14156
$443$	22.0000	1.04525	0.522626	−	0.852562i	$-0.324953\pi$
$443$	22.0000	1.04525	0.522626	+	0.852562i	$0.324953\pi$
$444$	−5.00000	−0.237289
$445$	0	0
$446$	−2.00000	−0.0947027
$447$	12.0000	0.567581
$448$	35.0000	1.65359
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	12.0000	0.565058
$452$	6.00000	0.282216
$453$	18.0000	0.845714
$454$	9.00000	0.422391
$455$	0	0
$456$	−6.00000	−0.280976
$457$	34.0000	1.59045	0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000	1.59045	0.795226	+	0.606313i	$0.207352\pi$
$458$	10.0000	0.467269
$459$	6.00000	0.280056
$460$	0	0
$461$	−20.0000	−0.931493	−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000	−0.931493	−0.465746	+	0.884918i	$0.654214\pi$
$462$	20.0000	0.930484
$463$	−13.0000	−0.604161	−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000	−0.604161	−0.302081	+	0.953282i	$0.597681\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	−1.00000	−0.0463241
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	−4.00000	−0.184900
$469$	−5.00000	−0.230879
$470$	0	0
$471$	−9.00000	−0.414698
$472$	−9.00000	−0.414259
$473$	28.0000	1.28744
$474$	8.00000	0.367452
$475$	0	0
$476$	30.0000	1.37505
$477$	5.00000	0.228934
$478$	−14.0000	−0.640345
$479$	13.0000	0.593985	0.296993	−	0.954880i	$-0.404016\pi$
$479$	13.0000	0.593985	0.296993	+	0.954880i	$0.404016\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−25.0000	−1.13872
$483$	−15.0000	−0.682524
$484$	−5.00000	−0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	7.00000	0.317200	0.158600	−	0.987343i	$-0.449302\pi$
$487$	7.00000	0.317200	0.158600	+	0.987343i	$0.449302\pi$
$488$	6.00000	0.271607
$489$	4.00000	0.180886
$490$	0	0
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	−3.00000	−0.135250
$493$	−24.0000	−1.08091
$494$	−8.00000	−0.359937
$495$	0	0
$496$	7.00000	0.314309
$497$	−60.0000	−2.69137
$498$	1.00000	0.0448111
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	3.00000	0.134030
$502$	−8.00000	−0.357057
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	−15.0000	−0.668153
$505$	0	0
$506$	−12.0000	−0.533465
$507$	−3.00000	−0.133235
$508$	−8.00000	−0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	65.0000	2.87543
$512$	−11.0000	−0.486136
$513$	2.00000	0.0883022
$514$	−8.00000	−0.352865
$515$	0	0
$516$	−7.00000	−0.308158
$517$	32.0000	1.40736
$518$	−25.0000	−1.09844
$519$	14.0000	0.614532
$520$	0	0
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	4.00000	0.175075
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	21.0000	0.917389
$525$	0	0
$526$	−7.00000	−0.305215
$527$	42.0000	1.82955
$528$	−4.00000	−0.174078
$529$	−14.0000	−0.608696
$530$	0	0
$531$	3.00000	0.130189
$532$	10.0000	0.433555
$533$	−12.0000	−0.519778
$534$	−4.00000	−0.173097
$535$	0	0
$536$	3.00000	0.129580
$537$	6.00000	0.258919
$538$	14.0000	0.603583
$539$	−72.0000	−3.10126
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−16.0000	−0.687259
$543$	−7.00000	−0.300399
$544$	−30.0000	−1.28624
$545$	0	0
$546$	−20.0000	−0.855921
$547$	37.0000	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$548$	21.0000	0.897076
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	−8.00000	−0.340811
$552$	9.00000	0.383065
$553$	−40.0000	−1.70097
$554$	23.0000	0.977176
$555$	0	0
$556$	−13.0000	−0.551323
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	−7.00000	−0.296334
$559$	−28.0000	−1.18427
$560$	0	0
$561$	−24.0000	−1.01328
$562$	6.00000	0.253095
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−8.00000	−0.336861
$565$	0	0
$566$	−6.00000	−0.252199
$567$	5.00000	0.209980
$568$	36.0000	1.51053
$569$	12.0000	0.503066	0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000	0.503066	0.251533	+	0.967849i	$0.419065\pi$
$570$	0	0
$571$	22.0000	0.920671	0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000	0.920671	0.460336	+	0.887745i	$0.347729\pi$
$572$	16.0000	0.668994
$573$	−24.0000	−1.00261
$574$	−15.0000	−0.626088
$575$	0	0
$576$	7.00000	0.291667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	19.0000	0.790296
$579$	13.0000	0.540262
$580$	0	0
$581$	−5.00000	−0.207435
$582$	−12.0000	−0.497416
$583$	−20.0000	−0.828315
$584$	−39.0000	−1.61383
$585$	0	0
$586$	−30.0000	−1.23929
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	18.0000	0.742307
$589$	14.0000	0.576860
$590$	0	0
$591$	25.0000	1.02836
$592$	5.00000	0.205499
$593$	45.0000	1.84793	0.923964	−	0.382479i	$-0.124930\pi$
$593$	45.0000	1.84793	0.923964	+	0.382479i	$0.124930\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	12.0000	0.491539
$597$	20.0000	0.818546
$598$	12.0000	0.490716
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	0	0
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	−35.0000	−1.42649
$603$	−1.00000	−0.0407231
$604$	18.0000	0.732410
$605$	0	0
$606$	10.0000	0.406222
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	−10.0000	−0.405554
$609$	−20.0000	−0.810441
$610$	0	0
$611$	−32.0000	−1.29458
$612$	6.00000	0.242536
$613$	15.0000	0.605844	0.302922	−	0.953015i	$-0.402038\pi$
$613$	15.0000	0.605844	0.302922	+	0.953015i	$0.402038\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	60.0000	2.41747
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	8.00000	0.321807
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	−3.00000	−0.120386
$622$	−6.00000	−0.240578
$623$	20.0000	0.801283
$624$	4.00000	0.160128
$625$	0	0
$626$	10.0000	0.399680
$627$	−8.00000	−0.319489
$628$	−9.00000	−0.359139
$629$	30.0000	1.19618
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	24.0000	0.954669
$633$	−6.00000	−0.238479
$634$	−6.00000	−0.238290
$635$	0	0
$636$	5.00000	0.198263
$637$	72.0000	2.85274
$638$	−16.0000	−0.633446
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−7.00000	−0.276483	−0.138242	−	0.990399i	$-0.544145\pi$
$641$	−7.00000	−0.276483	−0.138242	+	0.990399i	$0.544145\pi$
$642$	−16.0000	−0.631470
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	−15.0000	−0.591083
$645$	0	0
$646$	12.0000	0.472134
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	−3.00000	−0.117851
$649$	−12.0000	−0.471041
$650$	0	0
$651$	35.0000	1.37176
$652$	4.00000	0.156652
$653$	39.0000	1.52619	0.763094	−	0.646288i	$-0.223679\pi$
$653$	39.0000	1.52619	0.763094	+	0.646288i	$0.223679\pi$
$654$	10.0000	0.391031
$655$	0	0
$656$	3.00000	0.117130
$657$	13.0000	0.507178
$658$	−40.0000	−1.55936
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	33.0000	1.28258
$663$	24.0000	0.932083
$664$	3.00000	0.116423
$665$	0	0
$666$	−5.00000	−0.193746
$667$	12.0000	0.464642
$668$	3.00000	0.116073
$669$	2.00000	0.0773245
$670$	0	0
$671$	8.00000	0.308837
$672$	−25.0000	−0.964396
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−3.00000	−0.115385
$677$	−9.00000	−0.345898	−0.172949	−	0.984931i	$-0.555330\pi$
$677$	−9.00000	−0.345898	−0.172949	+	0.984931i	$0.555330\pi$
$678$	6.00000	0.230429
$679$	60.0000	2.30259
$680$	0	0
$681$	−9.00000	−0.344881
$682$	28.0000	1.07218
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	55.0000	2.09991
$687$	−10.0000	−0.381524
$688$	7.00000	0.266872
$689$	20.0000	0.761939
$690$	0	0
$691$	−6.00000	−0.228251	−0.114125	−	0.993466i	$-0.536407\pi$
$691$	−6.00000	−0.228251	−0.114125	+	0.993466i	$0.536407\pi$
$692$	14.0000	0.532200
$693$	−20.0000	−0.759737
$694$	−24.0000	−0.911028
$695$	0	0
$696$	12.0000	0.454859
$697$	18.0000	0.681799
$698$	15.0000	0.567758
$699$	1.00000	0.0378235
$700$	0	0
$701$	5.00000	0.188847	0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000	0.188847	0.0944237	+	0.995532i	$0.469899\pi$
$702$	−4.00000	−0.150970
$703$	10.0000	0.377157
$704$	−28.0000	−1.05529
$705$	0	0
$706$	21.0000	0.790345
$707$	−50.0000	−1.88044
$708$	3.00000	0.112747
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	−12.0000	−0.449719
$713$	−21.0000	−0.786456
$714$	30.0000	1.12272
$715$	0	0
$716$	6.00000	0.224231
$717$	14.0000	0.522840
$718$	−11.0000	−0.410516
$719$	43.0000	1.60363	0.801815	−	0.597573i	$-0.203868\pi$
$719$	43.0000	1.60363	0.801815	+	0.597573i	$0.203868\pi$
$720$	0	0
$721$	−40.0000	−1.48968
$722$	−15.0000	−0.558242
$723$	25.0000	0.929760
$724$	−7.00000	−0.260153
$725$	0	0
$726$	−5.00000	−0.185567
$727$	−37.0000	−1.37225	−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000	−1.37225	−0.686127	+	0.727482i	$0.740691\pi$
$728$	−60.0000	−2.22375
$729$	1.00000	0.0370370
$730$	0	0
$731$	42.0000	1.55343
$732$	−2.00000	−0.0739221
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	−16.0000	−0.590571
$735$	0	0
$736$	15.0000	0.552907
$737$	4.00000	0.147342
$738$	−3.00000	−0.110432
$739$	−23.0000	−0.846069	−0.423034	−	0.906114i	$-0.639035\pi$
$739$	−23.0000	−0.846069	−0.423034	+	0.906114i	$0.639035\pi$
$740$	0	0
$741$	8.00000	0.293887
$742$	25.0000	0.917779
$743$	3.00000	0.110059	0.0550297	−	0.998485i	$-0.482475\pi$
$743$	3.00000	0.110059	0.0550297	+	0.998485i	$0.482475\pi$
$744$	−21.0000	−0.769897
$745$	0	0
$746$	18.0000	0.659027
$747$	−1.00000	−0.0365881
$748$	−24.0000	−0.877527
$749$	80.0000	2.92314
$750$	0	0
$751$	26.0000	0.948753	0.474377	−	0.880322i	$-0.342673\pi$
$751$	26.0000	0.948753	0.474377	+	0.880322i	$0.342673\pi$
$752$	8.00000	0.291730
$753$	8.00000	0.291536
$754$	16.0000	0.582686
$755$	0	0
$756$	5.00000	0.181848
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	9.00000	0.326895
$759$	12.0000	0.435572
$760$	0	0
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	−8.00000	−0.289809
$763$	−50.0000	−1.81012
$764$	−24.0000	−0.868290
$765$	0	0
$766$	−8.00000	−0.289052
$767$	12.0000	0.433295
$768$	17.0000	0.613435
$769$	−24.0000	−0.865462	−0.432731	−	0.901523i	$-0.642450\pi$
$769$	−24.0000	−0.865462	−0.432731	+	0.901523i	$0.642450\pi$
$770$	0	0
$771$	8.00000	0.288113
$772$	13.0000	0.467880
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	−7.00000	−0.251610
$775$	0	0
$776$	−36.0000	−1.29232
$777$	25.0000	0.896870
$778$	−16.0000	−0.573628
$779$	6.00000	0.214972
$780$	0	0
$781$	48.0000	1.71758
$782$	−18.0000	−0.643679
$783$	−4.00000	−0.142948
$784$	−18.0000	−0.642857
$785$	0	0
$786$	21.0000	0.749045
$787$	−31.0000	−1.10503	−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000	−1.10503	−0.552515	+	0.833503i	$0.686332\pi$
$788$	25.0000	0.890588
$789$	7.00000	0.249207
$790$	0	0
$791$	−30.0000	−1.06668
$792$	12.0000	0.426401
$793$	−8.00000	−0.284088
$794$	−26.0000	−0.922705
$795$	0	0
$796$	20.0000	0.708881
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	10.0000	0.353996
$799$	48.0000	1.69812
$800$	0	0
$801$	4.00000	0.141333
$802$	−17.0000	−0.600291
$803$	−52.0000	−1.83504
$804$	−1.00000	−0.0352673
$805$	0	0
$806$	−28.0000	−0.986258
$807$	−14.0000	−0.492823
$808$	30.0000	1.05540
$809$	39.0000	1.37117	0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000	1.37117	0.685583	+	0.727994i	$0.259547\pi$
$810$	0	0
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	−20.0000	−0.701862
$813$	16.0000	0.561144
$814$	20.0000	0.701000
$815$	0	0
$816$	−6.00000	−0.210042
$817$	14.0000	0.489798
$818$	20.0000	0.699284
$819$	20.0000	0.698857
$820$	0	0
$821$	−28.0000	−0.977207	−0.488603	−	0.872506i	$-0.662493\pi$
$821$	−28.0000	−0.977207	−0.488603	+	0.872506i	$0.662493\pi$
$822$	21.0000	0.732459
$823$	42.0000	1.46403	0.732014	−	0.681290i	$-0.238581\pi$
$823$	42.0000	1.46403	0.732014	+	0.681290i	$0.238581\pi$
$824$	24.0000	0.836080
$825$	0	0
$826$	15.0000	0.521917
$827$	−24.0000	−0.834562	−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000	−0.834562	−0.417281	+	0.908778i	$0.637017\pi$
$828$	−3.00000	−0.104257
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	−23.0000	−0.797861
$832$	28.0000	0.970725
$833$	−108.000	−3.74198
$834$	−13.0000	−0.450153
$835$	0	0
$836$	−8.00000	−0.276686
$837$	7.00000	0.241955
$838$	33.0000	1.13997
$839$	28.0000	0.966667	0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000	0.966667	0.483334	+	0.875436i	$0.339426\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	3.00000	0.103387
$843$	−6.00000	−0.206651
$844$	−6.00000	−0.206529
$845$	0	0
$846$	−8.00000	−0.275046
$847$	25.0000	0.859010
$848$	−5.00000	−0.171701
$849$	6.00000	0.205919
$850$	0	0
$851$	−15.0000	−0.514193
$852$	−12.0000	−0.411113
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	−48.0000	−1.64061
$857$	57.0000	1.94708	0.973541	−	0.228510i	$-0.0733855\pi$
$857$	57.0000	1.94708	0.973541	+	0.228510i	$0.0733855\pi$
$858$	16.0000	0.546231
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	0	0
$861$	15.0000	0.511199
$862$	3.00000	0.102180
$863$	41.0000	1.39566	0.697828	−	0.716265i	$-0.254150\pi$
$863$	41.0000	1.39566	0.697828	+	0.716265i	$0.254150\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−12.0000	−0.407777
$867$	−19.0000	−0.645274
$868$	35.0000	1.18798
$869$	32.0000	1.08553
$870$	0	0
$871$	−4.00000	−0.135535
$872$	30.0000	1.01593
$873$	12.0000	0.406138
$874$	−6.00000	−0.202953
$875$	0	0
$876$	13.0000	0.439229
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	−16.0000	−0.539974
$879$	30.0000	1.01187
$880$	0	0
$881$	36.0000	1.21287	0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000	1.21287	0.606435	+	0.795133i	$0.292599\pi$
$882$	18.0000	0.606092
$883$	35.0000	1.17784	0.588922	−	0.808190i	$-0.299553\pi$
$883$	35.0000	1.17784	0.588922	+	0.808190i	$0.299553\pi$
$884$	24.0000	0.807207
$885$	0	0
$886$	22.0000	0.739104
$887$	−17.0000	−0.570804	−0.285402	−	0.958408i	$-0.592127\pi$
$887$	−17.0000	−0.570804	−0.285402	+	0.958408i	$0.592127\pi$
$888$	−15.0000	−0.503367
$889$	40.0000	1.34156
$890$	0	0
$891$	−4.00000	−0.134005
$892$	2.00000	0.0669650
$893$	16.0000	0.535420
$894$	12.0000	0.401340
$895$	0	0
$896$	−15.0000	−0.501115
$897$	−12.0000	−0.400668
$898$	−12.0000	−0.400445
$899$	−28.0000	−0.933852
$900$	0	0
$901$	−30.0000	−0.999445
$902$	12.0000	0.399556
$903$	35.0000	1.16473
$904$	18.0000	0.598671
$905$	0	0
$906$	18.0000	0.598010
$907$	−20.0000	−0.664089	−0.332045	−	0.943264i	$-0.607738\pi$
$907$	−20.0000	−0.664089	−0.332045	+	0.943264i	$0.607738\pi$
$908$	−9.00000	−0.298675
$909$	−10.0000	−0.331679
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	−2.00000	−0.0662266
$913$	4.00000	0.132381
$914$	34.0000	1.12462
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−105.000	−3.46741
$918$	6.00000	0.198030
$919$	15.0000	0.494804	0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000	0.494804	0.247402	+	0.968913i	$0.420423\pi$
$920$	0	0
$921$	8.00000	0.263609
$922$	−20.0000	−0.658665
$923$	−48.0000	−1.57994
$924$	−20.0000	−0.657952
$925$	0	0
$926$	−13.0000	−0.427207
$927$	−8.00000	−0.262754
$928$	20.0000	0.656532
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	0	0
$931$	−36.0000	−1.17985
$932$	1.00000	0.0327561
$933$	6.00000	0.196431
$934$	12.0000	0.392652
$935$	0	0
$936$	−12.0000	−0.392232
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	−5.00000	−0.163256
$939$	−10.0000	−0.326338
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	−9.00000	−0.293236
$943$	−9.00000	−0.293080
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	28.0000	0.910359
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	−8.00000	−0.259828
$949$	52.0000	1.68799
$950$	0	0
$951$	6.00000	0.194563
$952$	90.0000	2.91692
$953$	40.0000	1.29573	0.647864	−	0.761756i	$-0.275663\pi$
$953$	40.0000	1.29573	0.647864	+	0.761756i	$0.275663\pi$
$954$	5.00000	0.161881
$955$	0	0
$956$	14.0000	0.452792
$957$	16.0000	0.517207
$958$	13.0000	0.420011
$959$	−105.000	−3.39063
$960$	0	0
$961$	18.0000	0.580645
$962$	−20.0000	−0.644826
$963$	16.0000	0.515593
$964$	25.0000	0.805196
$965$	0	0
$966$	−15.0000	−0.482617
$967$	−6.00000	−0.192947	−0.0964735	−	0.995336i	$-0.530756\pi$
$967$	−6.00000	−0.192947	−0.0964735	+	0.995336i	$0.530756\pi$
$968$	−15.0000	−0.482118
$969$	−12.0000	−0.385496
$970$	0	0
$971$	48.0000	1.54039	0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000	1.54039	0.770197	+	0.637806i	$0.220158\pi$
$972$	1.00000	0.0320750
$973$	65.0000	2.08380
$974$	7.00000	0.224294
$975$	0	0
$976$	2.00000	0.0640184
$977$	34.0000	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$978$	4.00000	0.127906
$979$	−16.0000	−0.511362
$980$	0	0
$981$	−10.0000	−0.319275
$982$	−15.0000	−0.478669
$983$	−40.0000	−1.27580	−0.637901	−	0.770118i	$-0.720197\pi$
$983$	−40.0000	−1.27580	−0.637901	+	0.770118i	$0.720197\pi$
$984$	−9.00000	−0.286910
$985$	0	0
$986$	−24.0000	−0.764316
$987$	40.0000	1.27321
$988$	8.00000	0.254514
$989$	−21.0000	−0.667761
$990$	0	0
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	−35.0000	−1.11125
$993$	−33.0000	−1.04722
$994$	−60.0000	−1.90308
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	−27.0000	−0.855099	−0.427549	−	0.903992i	$-0.640623\pi$
$997$	−27.0000	−0.855099	−0.427549	+	0.903992i	$0.640623\pi$
$998$	0	0
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5025.2.a.h.1.1		1
5.4	even	2		201.2.a.b.1.1	✓	1
15.14	odd	2		603.2.a.e.1.1		1
20.19	odd	2		3216.2.a.d.1.1		1
35.34	odd	2		9849.2.a.e.1.1		1
60.59	even	2		9648.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.a.b.1.1	✓	1	5.4	even	2
603.2.a.e.1.1		1	15.14	odd	2
3216.2.a.d.1.1		1	20.19	odd	2
5025.2.a.h.1.1		1	1.1	even	1	trivial
9648.2.a.n.1.1		1	60.59	even	2
9849.2.a.e.1.1		1	35.34	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5025 = 3 \cdot 5^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5025.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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