LMFDB - Embedded newform 7650.2.a.ch.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7650,2,Mod(1,7650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7650, 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("7650.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7650.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:	$61.0855575463$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2550)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{7} +1.00000 q^{8} +5.00000 q^{11} +4.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{19} +5.00000 q^{22} +4.00000 q^{23} +4.00000 q^{26} +3.00000 q^{28} +4.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} -9.00000 q^{37} -1.00000 q^{38} +10.0000 q^{41} +11.0000 q^{43} +5.00000 q^{44} +4.00000 q^{46} -9.00000 q^{47} +2.00000 q^{49} +4.00000 q^{52} -3.00000 q^{53} +3.00000 q^{56} +4.00000 q^{58} +8.00000 q^{59} -14.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -7.00000 q^{67} +1.00000 q^{68} -14.0000 q^{71} +2.00000 q^{73} -9.00000 q^{74} -1.00000 q^{76} +15.0000 q^{77} -5.00000 q^{79} +10.0000 q^{82} -8.00000 q^{83} +11.0000 q^{86} +5.00000 q^{88} +2.00000 q^{89} +12.0000 q^{91} +4.00000 q^{92} -9.00000 q^{94} -14.0000 q^{97} +2.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	0	0
$22$	5.00000	1.06600
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	0	0
$26$	4.00000	0.784465
$27$	0	0
$28$	3.00000	0.566947
$29$	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
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	0	0
$36$	0	0
$37$	−9.00000	−1.47959	−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000	−1.47959	−0.739795	+	0.672832i	$0.765078\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	11.0000	1.67748	0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000	1.67748	0.838742	+	0.544529i	$0.183292\pi$
$44$	5.00000	0.753778
$45$	0	0
$46$	4.00000	0.589768
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	0	0
$52$	4.00000	0.554700
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	0	0
$55$	0	0
$56$	3.00000	0.400892
$57$	0	0
$58$	4.00000	0.525226
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−1.00000	−0.127000
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	0	0
$71$	−14.0000	−1.66149	−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000	−1.66149	−0.830747	+	0.556650i	$0.812086\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−9.00000	−1.04623
$75$	0	0
$76$	−1.00000	−0.114708
$77$	15.0000	1.70941
$78$	0	0
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	0	0
$82$	10.0000	1.10432
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	0	0
$86$	11.0000	1.18616
$87$	0	0
$88$	5.00000	0.533002
$89$	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
$91$	12.0000	1.25794
$92$	4.00000	0.417029
$93$	0	0
$94$	−9.00000	−0.928279
$95$	0	0
$96$	0	0
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	2.00000	0.202031
$99$	0	0
$100$	0	0
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−3.00000	−0.291386
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	0	0
$111$	0	0
$112$	3.00000	0.283473
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	0	0
$115$	0	0
$116$	4.00000	0.371391
$117$	0	0
$118$	8.00000	0.736460
$119$	3.00000	0.275010
$120$	0	0
$121$	14.0000	1.27273
$122$	−14.0000	−1.26750
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	−3.00000	−0.260133
$134$	−7.00000	−0.604708
$135$	0	0
$136$	1.00000	0.0857493
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	−14.0000	−1.17485
$143$	20.0000	1.67248
$144$	0	0
$145$	0	0
$146$	2.00000	0.165521
$147$	0	0
$148$	−9.00000	−0.739795
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	15.0000	1.20873
$155$	0	0
$156$	0	0
$157$	−24.0000	−1.91541	−0.957704	−	0.287754i	$-0.907091\pi$
$157$	−24.0000	−1.91541	−0.957704	+	0.287754i	$0.907091\pi$
$158$	−5.00000	−0.397779
$159$	0	0
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−18.0000	−1.40987	−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000	−1.40987	−0.704934	+	0.709273i	$0.749024\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−8.00000	−0.620920
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	0	0
$172$	11.0000	0.838742
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	5.00000	0.376889
$177$	0	0
$178$	2.00000	0.149906
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	12.0000	0.889499
$183$	0	0
$184$	4.00000	0.294884
$185$	0	0
$186$	0	0
$187$	5.00000	0.365636
$188$	−9.00000	−0.656392
$189$	0	0
$190$	0	0
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	0	0
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−1.00000	−0.0708881	−0.0354441	−	0.999372i	$-0.511285\pi$
$199$	−1.00000	−0.0708881	−0.0354441	+	0.999372i	$0.511285\pi$
$200$	0	0
$201$	0	0
$202$	−9.00000	−0.633238
$203$	12.0000	0.842235
$204$	0	0
$205$	0	0
$206$	14.0000	0.975426
$207$	0	0
$208$	4.00000	0.277350
$209$	−5.00000	−0.345857
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−3.00000	−0.206041
$213$	0	0
$214$	15.0000	1.02538
$215$	0	0
$216$	0	0
$217$	−3.00000	−0.203653
$218$	1.00000	0.0677285
$219$	0	0
$220$	0	0
$221$	4.00000	0.269069
$222$	0	0
$223$	6.00000	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$224$	3.00000	0.200446
$225$	0	0
$226$	3.00000	0.199557
$227$	21.0000	1.39382	0.696909	−	0.717159i	$-0.254558\pi$
$227$	21.0000	1.39382	0.696909	+	0.717159i	$0.254558\pi$
$228$	0	0
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	0	0
$231$	0	0
$232$	4.00000	0.262613
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	8.00000	0.520756
$237$	0	0
$238$	3.00000	0.194461
$239$	−5.00000	−0.323423	−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000	−0.323423	−0.161712	+	0.986838i	$0.551701\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	−14.0000	−0.896258
$245$	0	0
$246$	0	0
$247$	−4.00000	−0.254514
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	20.0000	1.25739
$254$	−2.00000	−0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.0000	0.748539	0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000	0.748539	0.374270	+	0.927320i	$0.377893\pi$
$258$	0	0
$259$	−27.0000	−1.67770
$260$	0	0
$261$	0	0
$262$	−4.00000	−0.247121
$263$	7.00000	0.431638	0.215819	−	0.976433i	$-0.430758\pi$
$263$	7.00000	0.431638	0.215819	+	0.976433i	$0.430758\pi$
$264$	0	0
$265$	0	0
$266$	−3.00000	−0.183942
$267$	0	0
$268$	−7.00000	−0.427593
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	0	0
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	−13.0000	−0.781094	−0.390547	−	0.920583i	$-0.627714\pi$
$277$	−13.0000	−0.781094	−0.390547	+	0.920583i	$0.627714\pi$
$278$	8.00000	0.479808
$279$	0	0
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	−14.0000	−0.830747
$285$	0	0
$286$	20.0000	1.18262
$287$	30.0000	1.77084
$288$	0	0
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	0	0
$296$	−9.00000	−0.523114
$297$	0	0
$298$	−14.0000	−0.810998
$299$	16.0000	0.925304
$300$	0	0
$301$	33.0000	1.90209
$302$	−24.0000	−1.38104
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	15.0000	0.854704
$309$	0	0
$310$	0	0
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	0	0
$313$	−16.0000	−0.904373	−0.452187	−	0.891923i	$-0.649356\pi$
$313$	−16.0000	−0.904373	−0.452187	+	0.891923i	$0.649356\pi$
$314$	−24.0000	−1.35440
$315$	0	0
$316$	−5.00000	−0.281272
$317$	−4.00000	−0.224662	−0.112331	−	0.993671i	$-0.535832\pi$
$317$	−4.00000	−0.224662	−0.112331	+	0.993671i	$0.535832\pi$
$318$	0	0
$319$	20.0000	1.11979
$320$	0	0
$321$	0	0
$322$	12.0000	0.668734
$323$	−1.00000	−0.0556415
$324$	0	0
$325$	0	0
$326$	−18.0000	−0.996928
$327$	0	0
$328$	10.0000	0.552158
$329$	−27.0000	−1.48856
$330$	0	0
$331$	5.00000	0.274825	0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000	0.274825	0.137412	+	0.990514i	$0.456121\pi$
$332$	−8.00000	−0.439057
$333$	0	0
$334$	−18.0000	−0.984916
$335$	0	0
$336$	0	0
$337$	24.0000	1.30736	0.653682	−	0.756770i	$-0.273224\pi$
$337$	24.0000	1.30736	0.653682	+	0.756770i	$0.273224\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	0	0
$341$	−5.00000	−0.270765
$342$	0	0
$343$	−15.0000	−0.809924
$344$	11.0000	0.593080
$345$	0	0
$346$	14.0000	0.752645
$347$	−11.0000	−0.590511	−0.295255	−	0.955418i	$-0.595405\pi$
$347$	−11.0000	−0.590511	−0.295255	+	0.955418i	$0.595405\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	0	0
$352$	5.00000	0.266501
$353$	−24.0000	−1.27739	−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000	−1.27739	−0.638696	+	0.769460i	$0.720526\pi$
$354$	0	0
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	12.0000	0.634220
$359$	25.0000	1.31945	0.659725	−	0.751507i	$-0.270673\pi$
$359$	25.0000	1.31945	0.659725	+	0.751507i	$0.270673\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−5.00000	−0.262794
$363$	0	0
$364$	12.0000	0.628971
$365$	0	0
$366$	0	0
$367$	25.0000	1.30499	0.652495	−	0.757793i	$-0.273722\pi$
$367$	25.0000	1.30499	0.652495	+	0.757793i	$0.273722\pi$
$368$	4.00000	0.208514
$369$	0	0
$370$	0	0
$371$	−9.00000	−0.467257
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	5.00000	0.258544
$375$	0	0
$376$	−9.00000	−0.464140
$377$	16.0000	0.824042
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	0	0
$381$	0	0
$382$	9.00000	0.460480
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	0	0
$385$	0	0
$386$	6.00000	0.305392
$387$	0	0
$388$	−14.0000	−0.710742
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	4.00000	0.202289
$392$	2.00000	0.101015
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	15.0000	0.752828	0.376414	−	0.926451i	$-0.377157\pi$
$397$	15.0000	0.752828	0.376414	+	0.926451i	$0.377157\pi$
$398$	−1.00000	−0.0501255
$399$	0	0
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	−9.00000	−0.447767
$405$	0	0
$406$	12.0000	0.595550
$407$	−45.0000	−2.23057
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	0	0
$412$	14.0000	0.689730
$413$	24.0000	1.18096
$414$	0	0
$415$	0	0
$416$	4.00000	0.196116
$417$	0	0
$418$	−5.00000	−0.244558
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	24.0000	1.16969	0.584844	−	0.811146i	$-0.301156\pi$
$421$	24.0000	1.16969	0.584844	+	0.811146i	$0.301156\pi$
$422$	−12.0000	−0.584151
$423$	0	0
$424$	−3.00000	−0.145693
$425$	0	0
$426$	0	0
$427$	−42.0000	−2.03252
$428$	15.0000	0.725052
$429$	0	0
$430$	0	0
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	0	0
$433$	27.0000	1.29754	0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000	1.29754	0.648769	+	0.760986i	$0.275284\pi$
$434$	−3.00000	−0.144005
$435$	0	0
$436$	1.00000	0.0478913
$437$	−4.00000	−0.191346
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	0	0
$442$	4.00000	0.190261
$443$	38.0000	1.80543	0.902717	−	0.430234i	$-0.141569\pi$
$443$	38.0000	1.80543	0.902717	+	0.430234i	$0.141569\pi$
$444$	0	0
$445$	0	0
$446$	6.00000	0.284108
$447$	0	0
$448$	3.00000	0.141737
$449$	41.0000	1.93491	0.967455	−	0.253044i	$-0.0814317\pi$
$449$	41.0000	1.93491	0.967455	+	0.253044i	$0.0814317\pi$
$450$	0	0
$451$	50.0000	2.35441
$452$	3.00000	0.141108
$453$	0	0
$454$	21.0000	0.985579
$455$	0	0
$456$	0	0
$457$	37.0000	1.73079	0.865393	−	0.501093i	$-0.167069\pi$
$457$	37.0000	1.73079	0.865393	+	0.501093i	$0.167069\pi$
$458$	−12.0000	−0.560723
$459$	0	0
$460$	0	0
$461$	5.00000	0.232873	0.116437	−	0.993198i	$-0.462853\pi$
$461$	5.00000	0.232873	0.116437	+	0.993198i	$0.462853\pi$
$462$	0	0
$463$	36.0000	1.67306	0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000	1.67306	0.836531	+	0.547920i	$0.184580\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	6.00000	0.277945
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	0	0
$469$	−21.0000	−0.969690
$470$	0	0
$471$	0	0
$472$	8.00000	0.368230
$473$	55.0000	2.52890
$474$	0	0
$475$	0	0
$476$	3.00000	0.137505
$477$	0	0
$478$	−5.00000	−0.228695
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	0	0
$481$	−36.0000	−1.64146
$482$	−8.00000	−0.364390
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−14.0000	−0.633750
$489$	0	0
$490$	0	0
$491$	30.0000	1.35388	0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000	1.35388	0.676941	+	0.736038i	$0.263305\pi$
$492$	0	0
$493$	4.00000	0.180151
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	−42.0000	−1.88396
$498$	0	0
$499$	−38.0000	−1.70111	−0.850557	−	0.525883i	$-0.823735\pi$
$499$	−38.0000	−1.70111	−0.850557	+	0.525883i	$0.823735\pi$
$500$	0	0
$501$	0	0
$502$	18.0000	0.803379
$503$	−34.0000	−1.51599	−0.757993	−	0.652263i	$-0.773820\pi$
$503$	−34.0000	−1.51599	−0.757993	+	0.652263i	$0.773820\pi$
$504$	0	0
$505$	0	0
$506$	20.0000	0.889108
$507$	0	0
$508$	−2.00000	−0.0887357
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.0000	0.529297
$515$	0	0
$516$	0	0
$517$	−45.0000	−1.97910
$518$	−27.0000	−1.18631
$519$	0	0
$520$	0	0
$521$	−15.0000	−0.657162	−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000	−0.657162	−0.328581	+	0.944476i	$0.606570\pi$
$522$	0	0
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	7.00000	0.305215
$527$	−1.00000	−0.0435607
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	−3.00000	−0.130066
$533$	40.0000	1.73259
$534$	0	0
$535$	0	0
$536$	−7.00000	−0.302354
$537$	0	0
$538$	−28.0000	−1.20717
$539$	10.0000	0.430730
$540$	0	0
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	4.00000	0.171815
$543$	0	0
$544$	1.00000	0.0428746
$545$	0	0
$546$	0	0
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	0	0
$551$	−4.00000	−0.170406
$552$	0	0
$553$	−15.0000	−0.637865
$554$	−13.0000	−0.552317
$555$	0	0
$556$	8.00000	0.339276
$557$	−9.00000	−0.381342	−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000	−0.381342	−0.190671	+	0.981654i	$0.561066\pi$
$558$	0	0
$559$	44.0000	1.86100
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	−16.0000	−0.674320	−0.337160	−	0.941447i	$-0.609466\pi$
$563$	−16.0000	−0.674320	−0.337160	+	0.941447i	$0.609466\pi$
$564$	0	0
$565$	0	0
$566$	22.0000	0.924729
$567$	0	0
$568$	−14.0000	−0.587427
$569$	−14.0000	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$570$	0	0
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	20.0000	0.836242
$573$	0	0
$574$	30.0000	1.25218
$575$	0	0
$576$	0	0
$577$	−45.0000	−1.87337	−0.936687	−	0.350167i	$-0.886125\pi$
$577$	−45.0000	−1.87337	−0.936687	+	0.350167i	$0.886125\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	0	0
$581$	−24.0000	−0.995688
$582$	0	0
$583$	−15.0000	−0.621237
$584$	2.00000	0.0827606
$585$	0	0
$586$	18.0000	0.743573
$587$	−6.00000	−0.247647	−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000	−0.247647	−0.123823	+	0.992304i	$0.539516\pi$
$588$	0	0
$589$	1.00000	0.0412043
$590$	0	0
$591$	0	0
$592$	−9.00000	−0.369898
$593$	0	0		−	1.00000i	$-0.5\pi$
$593$	0	0			1.00000i	$0.5\pi$
$594$	0	0
$595$	0	0
$596$	−14.0000	−0.573462
$597$	0	0
$598$	16.0000	0.654289
$599$	−39.0000	−1.59350	−0.796748	−	0.604311i	$-0.793448\pi$
$599$	−39.0000	−1.59350	−0.796748	+	0.604311i	$0.793448\pi$
$600$	0	0
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	33.0000	1.34498
$603$	0	0
$604$	−24.0000	−0.976546
$605$	0	0
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	−36.0000	−1.45640
$612$	0	0
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	15.0000	0.604367
$617$	−19.0000	−0.764911	−0.382456	−	0.923974i	$-0.624922\pi$
$617$	−19.0000	−0.764911	−0.382456	+	0.923974i	$0.624922\pi$
$618$	0	0
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	0	0
$621$	0	0
$622$	−10.0000	−0.400963
$623$	6.00000	0.240385
$624$	0	0
$625$	0	0
$626$	−16.0000	−0.639489
$627$	0	0
$628$	−24.0000	−0.957704
$629$	−9.00000	−0.358854
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	−5.00000	−0.198889
$633$	0	0
$634$	−4.00000	−0.158860
$635$	0	0
$636$	0	0
$637$	8.00000	0.316972
$638$	20.0000	0.791808
$639$	0	0
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	12.0000	0.472866
$645$	0	0
$646$	−1.00000	−0.0393445
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	0	0
$649$	40.0000	1.57014
$650$	0	0
$651$	0	0
$652$	−18.0000	−0.704934
$653$	10.0000	0.391330	0.195665	−	0.980671i	$-0.437313\pi$
$653$	10.0000	0.391330	0.195665	+	0.980671i	$0.437313\pi$
$654$	0	0
$655$	0	0
$656$	10.0000	0.390434
$657$	0	0
$658$	−27.0000	−1.05257
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	5.00000	0.194331
$663$	0	0
$664$	−8.00000	−0.310460
$665$	0	0
$666$	0	0
$667$	16.0000	0.619522
$668$	−18.0000	−0.696441
$669$	0	0
$670$	0	0
$671$	−70.0000	−2.70232
$672$	0	0
$673$	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
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	−42.0000	−1.61181
$680$	0	0
$681$	0	0
$682$	−5.00000	−0.191460
$683$	8.00000	0.306111	0.153056	−	0.988218i	$-0.451089\pi$
$683$	8.00000	0.306111	0.153056	+	0.988218i	$0.451089\pi$
$684$	0	0
$685$	0	0
$686$	−15.0000	−0.572703
$687$	0	0
$688$	11.0000	0.419371
$689$	−12.0000	−0.457164
$690$	0	0
$691$	6.00000	0.228251	0.114125	−	0.993466i	$-0.463593\pi$
$691$	6.00000	0.228251	0.114125	+	0.993466i	$0.463593\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	−11.0000	−0.417554
$695$	0	0
$696$	0	0
$697$	10.0000	0.378777
$698$	−10.0000	−0.378506
$699$	0	0
$700$	0	0
$701$	−22.0000	−0.830929	−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000	−0.830929	−0.415464	+	0.909610i	$0.636381\pi$
$702$	0	0
$703$	9.00000	0.339441
$704$	5.00000	0.188445
$705$	0	0
$706$	−24.0000	−0.903252
$707$	−27.0000	−1.01544
$708$	0	0
$709$	49.0000	1.84023	0.920117	−	0.391644i	$-0.128094\pi$
$709$	49.0000	1.84023	0.920117	+	0.391644i	$0.128094\pi$
$710$	0	0
$711$	0	0
$712$	2.00000	0.0749532
$713$	−4.00000	−0.149801
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	0	0
$718$	25.0000	0.932992
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	42.0000	1.56416
$722$	−18.0000	−0.669891
$723$	0	0
$724$	−5.00000	−0.185824
$725$	0	0
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	12.0000	0.444750
$729$	0	0
$730$	0	0
$731$	11.0000	0.406850
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	25.0000	0.922767
$735$	0	0
$736$	4.00000	0.147442
$737$	−35.0000	−1.28924
$738$	0	0
$739$	−17.0000	−0.625355	−0.312678	−	0.949859i	$-0.601226\pi$
$739$	−17.0000	−0.625355	−0.312678	+	0.949859i	$0.601226\pi$
$740$	0	0
$741$	0	0
$742$	−9.00000	−0.330400
$743$	−38.0000	−1.39408	−0.697042	−	0.717030i	$-0.745501\pi$
$743$	−38.0000	−1.39408	−0.697042	+	0.717030i	$0.745501\pi$
$744$	0	0
$745$	0	0
$746$	6.00000	0.219676
$747$	0	0
$748$	5.00000	0.182818
$749$	45.0000	1.64426
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−9.00000	−0.328196
$753$	0	0
$754$	16.0000	0.582686
$755$	0	0
$756$	0	0
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	3.00000	0.108607
$764$	9.00000	0.325609
$765$	0	0
$766$	12.0000	0.433578
$767$	32.0000	1.15545
$768$	0	0
$769$	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
$771$	0	0
$772$	6.00000	0.215945
$773$	−22.0000	−0.791285	−0.395643	−	0.918405i	$-0.629478\pi$
$773$	−22.0000	−0.791285	−0.395643	+	0.918405i	$0.629478\pi$
$774$	0	0
$775$	0	0
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−21.0000	−0.752886
$779$	−10.0000	−0.358287
$780$	0	0
$781$	−70.0000	−2.50480
$782$	4.00000	0.143040
$783$	0	0
$784$	2.00000	0.0714286
$785$	0	0
$786$	0	0
$787$	50.0000	1.78231	0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000	1.78231	0.891154	+	0.453701i	$0.149897\pi$
$788$	12.0000	0.427482
$789$	0	0
$790$	0	0
$791$	9.00000	0.320003
$792$	0	0
$793$	−56.0000	−1.98862
$794$	15.0000	0.532330
$795$	0	0
$796$	−1.00000	−0.0354441
$797$	39.0000	1.38145	0.690725	−	0.723117i	$-0.257291\pi$
$797$	39.0000	1.38145	0.690725	+	0.723117i	$0.257291\pi$
$798$	0	0
$799$	−9.00000	−0.318397
$800$	0	0
$801$	0	0
$802$	30.0000	1.05934
$803$	10.0000	0.352892
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	0	0
$808$	−9.00000	−0.316619
$809$	−39.0000	−1.37117	−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000	−1.37117	−0.685583	+	0.727994i	$0.740453\pi$
$810$	0	0
$811$	−22.0000	−0.772524	−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000	−0.772524	−0.386262	+	0.922389i	$0.626234\pi$
$812$	12.0000	0.421117
$813$	0	0
$814$	−45.0000	−1.57725
$815$	0	0
$816$	0	0
$817$	−11.0000	−0.384841
$818$	−26.0000	−0.909069
$819$	0	0
$820$	0	0
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	24.0000	0.835067
$827$	39.0000	1.35616	0.678081	−	0.734987i	$-0.262812\pi$
$827$	39.0000	1.35616	0.678081	+	0.734987i	$0.262812\pi$
$828$	0	0
$829$	−24.0000	−0.833554	−0.416777	−	0.909009i	$-0.636840\pi$
$829$	−24.0000	−0.833554	−0.416777	+	0.909009i	$0.636840\pi$
$830$	0	0
$831$	0	0
$832$	4.00000	0.138675
$833$	2.00000	0.0692959
$834$	0	0
$835$	0	0
$836$	−5.00000	−0.172929
$837$	0	0
$838$	−28.0000	−0.967244
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	24.0000	0.827095
$843$	0	0
$844$	−12.0000	−0.413057
$845$	0	0
$846$	0	0
$847$	42.0000	1.44314
$848$	−3.00000	−0.103020
$849$	0	0
$850$	0	0
$851$	−36.0000	−1.23406
$852$	0	0
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	−42.0000	−1.43721
$855$	0	0
$856$	15.0000	0.512689
$857$	5.00000	0.170797	0.0853984	−	0.996347i	$-0.472784\pi$
$857$	5.00000	0.170797	0.0853984	+	0.996347i	$0.472784\pi$
$858$	0	0
$859$	−25.0000	−0.852989	−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000	−0.852989	−0.426494	+	0.904490i	$0.640252\pi$
$860$	0	0
$861$	0	0
$862$	−14.0000	−0.476842
$863$	−17.0000	−0.578687	−0.289343	−	0.957225i	$-0.593437\pi$
$863$	−17.0000	−0.578687	−0.289343	+	0.957225i	$0.593437\pi$
$864$	0	0
$865$	0	0
$866$	27.0000	0.917497
$867$	0	0
$868$	−3.00000	−0.101827
$869$	−25.0000	−0.848067
$870$	0	0
$871$	−28.0000	−0.948744
$872$	1.00000	0.0338643
$873$	0	0
$874$	−4.00000	−0.135302
$875$	0	0
$876$	0	0
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	20.0000	0.674967
$879$	0	0
$880$	0	0
$881$	35.0000	1.17918	0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000	1.17918	0.589590	+	0.807703i	$0.299289\pi$
$882$	0	0
$883$	48.0000	1.61533	0.807664	−	0.589643i	$-0.200731\pi$
$883$	48.0000	1.61533	0.807664	+	0.589643i	$0.200731\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	38.0000	1.27663
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	0	0
$889$	−6.00000	−0.201234
$890$	0	0
$891$	0	0
$892$	6.00000	0.200895
$893$	9.00000	0.301174
$894$	0	0
$895$	0	0
$896$	3.00000	0.100223
$897$	0	0
$898$	41.0000	1.36819
$899$	−4.00000	−0.133407
$900$	0	0
$901$	−3.00000	−0.0999445
$902$	50.0000	1.66482
$903$	0	0
$904$	3.00000	0.0997785
$905$	0	0
$906$	0	0
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	21.0000	0.696909
$909$	0	0
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	−40.0000	−1.32381
$914$	37.0000	1.22385
$915$	0	0
$916$	−12.0000	−0.396491
$917$	−12.0000	−0.396275
$918$	0	0
$919$	−14.0000	−0.461817	−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000	−0.461817	−0.230909	+	0.972975i	$0.574170\pi$
$920$	0	0
$921$	0	0
$922$	5.00000	0.164666
$923$	−56.0000	−1.84326
$924$	0	0
$925$	0	0
$926$	36.0000	1.18303
$927$	0	0
$928$	4.00000	0.131306
$929$	−1.00000	−0.0328089	−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000	−0.0328089	−0.0164045	+	0.999865i	$0.505222\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	6.00000	0.196537
$933$	0	0
$934$	6.00000	0.196326
$935$	0	0
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−21.0000	−0.685674
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	40.0000	1.30258
$944$	8.00000	0.260378
$945$	0	0
$946$	55.0000	1.78820
$947$	29.0000	0.942373	0.471187	−	0.882034i	$-0.343826\pi$
$947$	29.0000	0.942373	0.471187	+	0.882034i	$0.343826\pi$
$948$	0	0
$949$	8.00000	0.259691
$950$	0	0
$951$	0	0
$952$	3.00000	0.0972306
$953$	−12.0000	−0.388718	−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000	−0.388718	−0.194359	+	0.980930i	$0.562263\pi$
$954$	0	0
$955$	0	0
$956$	−5.00000	−0.161712
$957$	0	0
$958$	−30.0000	−0.969256
$959$	18.0000	0.581250
$960$	0	0
$961$	−30.0000	−0.967742
$962$	−36.0000	−1.16069
$963$	0	0
$964$	−8.00000	−0.257663
$965$	0	0
$966$	0	0
$967$	−24.0000	−0.771788	−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000	−0.771788	−0.385894	+	0.922543i	$0.626107\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	0	0
$971$	10.0000	0.320915	0.160458	−	0.987043i	$-0.448703\pi$
$971$	10.0000	0.320915	0.160458	+	0.987043i	$0.448703\pi$
$972$	0	0
$973$	24.0000	0.769405
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−14.0000	−0.448129
$977$	48.0000	1.53566	0.767828	−	0.640656i	$-0.221338\pi$
$977$	48.0000	1.53566	0.767828	+	0.640656i	$0.221338\pi$
$978$	0	0
$979$	10.0000	0.319601
$980$	0	0
$981$	0	0
$982$	30.0000	0.957338
$983$	28.0000	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$984$	0	0
$985$	0	0
$986$	4.00000	0.127386
$987$	0	0
$988$	−4.00000	−0.127257
$989$	44.0000	1.39912
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	−42.0000	−1.33216
$995$	0	0
$996$	0	0
$997$	−25.0000	−0.791758	−0.395879	−	0.918303i	$-0.629560\pi$
$997$	−25.0000	−0.791758	−0.395879	+	0.918303i	$0.629560\pi$
$998$	−38.0000	−1.20287
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7650.2.a.ch.1.1		1
3.2	odd	2		2550.2.a.f.1.1	✓	1
5.4	even	2		7650.2.a.f.1.1		1
15.2	even	4		2550.2.d.l.2449.1		2
15.8	even	4		2550.2.d.l.2449.2		2
15.14	odd	2		2550.2.a.bb.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.f.1.1	✓	1	3.2	odd	2
2550.2.a.bb.1.1	yes	1	15.14	odd	2
2550.2.d.l.2449.1		2	15.2	even	4
2550.2.d.l.2449.2		2	15.8	even	4
7650.2.a.f.1.1		1	5.4	even	2
7650.2.a.ch.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7650.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more