LMFDB - Embedded newform 7650.2.a.bd.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7650,2,Mod(1,7650)] 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("7650.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [1,-1,0,1,0,0,3,-1,0,0,3,0,4,-3,0,1,-1,0,-5,0,0,-3,-4,0,0,-4, 0,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)

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)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{7} -1.00000 q^{8} +3.00000 q^{11} +4.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -5.00000 q^{19} -3.00000 q^{22} -4.00000 q^{23} -4.00000 q^{26} +3.00000 q^{28} +7.00000 q^{31} -1.00000 q^{32} +1.00000 q^{34} +3.00000 q^{37} +5.00000 q^{38} -2.00000 q^{41} -1.00000 q^{43} +3.00000 q^{44} +4.00000 q^{46} -3.00000 q^{47} +2.00000 q^{49} +4.00000 q^{52} +11.0000 q^{53} -3.00000 q^{56} +2.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +13.0000 q^{67} -1.00000 q^{68} -2.00000 q^{71} -6.00000 q^{73} -3.00000 q^{74} -5.00000 q^{76} +9.00000 q^{77} -5.00000 q^{79} +2.00000 q^{82} +16.0000 q^{83} +1.00000 q^{86} -3.00000 q^{88} +10.0000 q^{89} +12.0000 q^{91} -4.00000 q^{92} +3.00000 q^{94} -2.00000 q^{97} -2.00000 q^{98} +O(q^{100})$

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
$3$	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
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	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
$19$	−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
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	0	0
$26$	−4.00000	−0.784465
$27$	0	0
$28$	3.00000	0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	0	0
$36$	0	0
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	5.00000	0.811107
$39$	0	0
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	−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
$46$	4.00000	0.589768
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	0	0
$52$	4.00000	0.554700
$53$	11.0000	1.51097	0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000	1.51097	0.755483	+	0.655168i	$0.227402\pi$
$54$	0	0
$55$	0	0
$56$	−3.00000	−0.400892
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−7.00000	−0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−3.00000	−0.348743
$75$	0	0
$76$	−5.00000	−0.573539
$77$	9.00000	1.02565
$78$	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
$82$	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	$0.158802\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	0.107833
$87$	0	0
$88$	−3.00000	−0.319801
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	12.0000	1.25794
$92$	−4.00000	−0.417029
$93$	0	0
$94$	3.00000	0.309426
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	0	0
$101$	−7.00000	−0.696526	−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000	−0.696526	−0.348263	+	0.937397i	$0.613228\pi$
$102$	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
$106$	−11.0000	−1.06841
$107$	17.0000	1.64345	0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000	1.64345	0.821726	+	0.569883i	$0.193011\pi$
$108$	0	0
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	0	0
$111$	0	0
$112$	3.00000	0.283473
$113$	1.00000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−2.00000	−0.181071
$123$	0	0
$124$	7.00000	0.628619
$125$	0	0
$126$	0	0
$127$	18.0000	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$127$	18.0000	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−15.0000	−1.30066
$134$	−13.0000	−1.12303
$135$	0	0
$136$	1.00000	0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	0	0
$142$	2.00000	0.167836
$143$	12.0000	1.00349
$144$	0	0
$145$	0	0
$146$	6.00000	0.496564
$147$	0	0
$148$	3.00000	0.246598
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	5.00000	0.405554
$153$	0	0
$154$	−9.00000	−0.725241
$155$	0	0
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	5.00000	0.397779
$159$	0	0
$160$	0	0
$161$	−12.0000	−0.945732
$162$	0	0
$163$	−6.00000	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−16.0000	−1.24184
$167$	−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
$172$	−1.00000	−0.0762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	3.00000	0.226134
$177$	0	0
$178$	−10.0000	−0.749532
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	−12.0000	−0.889499
$183$	0	0
$184$	4.00000	0.294884
$185$	0	0
$186$	0	0
$187$	−3.00000	−0.219382
$188$	−3.00000	−0.218797
$189$	0	0
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	0	0
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	2.00000	0.143592
$195$	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
$199$	−25.0000	−1.77220	−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000	−1.77220	−0.886102	+	0.463491i	$0.846597\pi$
$200$	0	0
$201$	0	0
$202$	7.00000	0.492518
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−14.0000	−0.975426
$207$	0	0
$208$	4.00000	0.277350
$209$	−15.0000	−1.03757
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	11.0000	0.755483
$213$	0	0
$214$	−17.0000	−1.16210
$215$	0	0
$216$	0	0
$217$	21.0000	1.42557
$218$	−5.00000	−0.338643
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	−26.0000	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	−1.00000	−0.0665190
$227$	27.0000	1.79205	0.896026	−	0.444001i	$-0.146441\pi$
$227$	27.0000	1.79205	0.896026	+	0.444001i	$0.146441\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	3.00000	0.194461
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	0	0
$241$	12.0000	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	−20.0000	−1.27257
$248$	−7.00000	−0.444500
$249$	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
$253$	−12.0000	−0.754434
$254$	−18.0000	−1.12942
$255$	0	0
$256$	1.00000	0.0625000
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	0	0
$259$	9.00000	0.559233
$260$	0	0
$261$	0	0
$262$	12.0000	0.741362
$263$	−19.0000	−1.17159	−0.585795	−	0.810459i	$-0.699218\pi$
$263$	−19.0000	−1.17159	−0.585795	+	0.810459i	$0.699218\pi$
$264$	0	0
$265$	0	0
$266$	15.0000	0.919709
$267$	0	0
$268$	13.0000	0.794101
$269$	−20.0000	−1.21942	−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000	−1.21942	−0.609711	+	0.792624i	$0.708714\pi$
$270$	0	0
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−2.00000	−0.120824
$275$	0	0
$276$	0	0
$277$	23.0000	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	23.0000	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	20.0000	1.19952
$279$	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
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−12.0000	−0.709575
$287$	−6.00000	−0.354169
$288$	0	0
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	−6.00000	−0.351123
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	−3.00000	−0.174371
$297$	0	0
$298$	10.0000	0.579284
$299$	−16.0000	−0.925304
$300$	0	0
$301$	−3.00000	−0.172917
$302$	−12.0000	−0.690522
$303$	0	0
$304$	−5.00000	−0.286770
$305$	0	0
$306$	0	0
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	9.00000	0.512823
$309$	0	0
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	4.00000	0.226093	0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000	0.226093	0.113047	+	0.993590i	$0.463939\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	−5.00000	−0.281272
$317$	32.0000	1.79730	0.898650	−	0.438667i	$-0.144549\pi$
$317$	32.0000	1.79730	0.898650	+	0.438667i	$0.144549\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	12.0000	0.668734
$323$	5.00000	0.278207
$324$	0	0
$325$	0	0
$326$	6.00000	0.332309
$327$	0	0
$328$	2.00000	0.110432
$329$	−9.00000	−0.496186
$330$	0	0
$331$	−23.0000	−1.26419	−0.632097	−	0.774889i	$-0.717806\pi$
$331$	−23.0000	−1.26419	−0.632097	+	0.774889i	$0.717806\pi$
$332$	16.0000	0.878114
$333$	0	0
$334$	18.0000	0.984916
$335$	0	0
$336$	0	0
$337$	−12.0000	−0.653682	−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000	−0.653682	−0.326841	+	0.945079i	$0.605984\pi$
$338$	−3.00000	−0.163178
$339$	0	0
$340$	0	0
$341$	21.0000	1.13721
$342$	0	0
$343$	−15.0000	−0.809924
$344$	1.00000	0.0539164
$345$	0	0
$346$	−6.00000	−0.322562
$347$	27.0000	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$347$	27.0000	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$348$	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
$352$	−3.00000	−0.159901
$353$	16.0000	0.851594	0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000	0.851594	0.425797	+	0.904819i	$0.359994\pi$
$354$	0	0
$355$	0	0
$356$	10.0000	0.529999
$357$	0	0
$358$	0	0
$359$	−5.00000	−0.263890	−0.131945	−	0.991257i	$-0.542122\pi$
$359$	−5.00000	−0.263890	−0.131945	+	0.991257i	$0.542122\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−7.00000	−0.367912
$363$	0	0
$364$	12.0000	0.628971
$365$	0	0
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	0	0
$371$	33.0000	1.71327
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	3.00000	0.155126
$375$	0	0
$376$	3.00000	0.154713
$377$	0	0
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	0	0
$382$	−3.00000	−0.153493
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	0	0
$385$	0	0
$386$	6.00000	0.305392
$387$	0	0
$388$	−2.00000	−0.101535
$389$	5.00000	0.253510	0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000	0.253510	0.126755	+	0.991934i	$0.459544\pi$
$390$	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
$397$	3.00000	0.150566	0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000	0.150566	0.0752828	+	0.997162i	$0.476014\pi$
$398$	25.0000	1.25314
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	28.0000	1.39478
$404$	−7.00000	−0.348263
$405$	0	0
$406$	0	0
$407$	9.00000	0.446113
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	0	0
$412$	14.0000	0.689730
$413$	0	0
$414$	0	0
$415$	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
$421$	−28.0000	−1.36464	−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000	−1.36464	−0.682318	+	0.731055i	$0.739028\pi$
$422$	−12.0000	−0.584151
$423$	0	0
$424$	−11.0000	−0.534207
$425$	0	0
$426$	0	0
$427$	6.00000	0.290360
$428$	17.0000	0.821726
$429$	0	0
$430$	0	0
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	0	0
$433$	−21.0000	−1.00920	−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000	−1.00920	−0.504598	+	0.863355i	$0.668359\pi$
$434$	−21.0000	−1.00803
$435$	0	0
$436$	5.00000	0.239457
$437$	20.0000	0.956730
$438$	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
$443$	−14.0000	−0.665160	−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000	−0.665160	−0.332580	+	0.943075i	$0.607919\pi$
$444$	0	0
$445$	0	0
$446$	26.0000	1.23114
$447$	0	0
$448$	3.00000	0.141737
$449$	−5.00000	−0.235965	−0.117982	−	0.993016i	$-0.537643\pi$
$449$	−5.00000	−0.235965	−0.117982	+	0.993016i	$0.537643\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	1.00000	0.0470360
$453$	0	0
$454$	−27.0000	−1.26717
$455$	0	0
$456$	0	0
$457$	13.0000	0.608114	0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000	0.608114	0.304057	+	0.952654i	$0.401659\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	0	0
$465$	0	0
$466$	−26.0000	−1.20443
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	0	0
$469$	39.0000	1.80085
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−3.00000	−0.137940
$474$	0	0
$475$	0	0
$476$	−3.00000	−0.137505
$477$	0	0
$478$	15.0000	0.686084
$479$	10.0000	0.456912	0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000	0.456912	0.228456	+	0.973554i	$0.426632\pi$
$480$	0	0
$481$	12.0000	0.547153
$482$	−12.0000	−0.546585
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	0	0
$491$	−2.00000	−0.0902587	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000	−0.0902587	−0.0451294	+	0.998981i	$0.514370\pi$
$492$	0	0
$493$	0	0
$494$	20.0000	0.899843
$495$	0	0
$496$	7.00000	0.314309
$497$	−6.00000	−0.269137
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	0	0
$501$	0	0
$502$	−18.0000	−0.803379
$503$	−14.0000	−0.624229	−0.312115	−	0.950044i	$-0.601037\pi$
$503$	−14.0000	−0.624229	−0.312115	+	0.950044i	$0.601037\pi$
$504$	0	0
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	18.0000	0.798621
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.00000	0.352865
$515$	0	0
$516$	0	0
$517$	−9.00000	−0.395820
$518$	−9.00000	−0.395437
$519$	0	0
$520$	0	0
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	0	0
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	19.0000	0.828439
$527$	−7.00000	−0.304925
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	0	0
$532$	−15.0000	−0.650332
$533$	−8.00000	−0.346518
$534$	0	0
$535$	0	0
$536$	−13.0000	−0.561514
$537$	0	0
$538$	20.0000	0.862261
$539$	6.00000	0.258438
$540$	0	0
$541$	−13.0000	−0.558914	−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000	−0.558914	−0.279457	+	0.960158i	$0.590154\pi$
$542$	−32.0000	−1.37452
$543$	0	0
$544$	1.00000	0.0428746
$545$	0	0
$546$	0	0
$547$	−2.00000	−0.0855138	−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000	−0.0855138	−0.0427569	+	0.999086i	$0.513614\pi$
$548$	2.00000	0.0854358
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−15.0000	−0.637865
$554$	−23.0000	−0.977176
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−23.0000	−0.974541	−0.487271	−	0.873251i	$-0.662007\pi$
$557$	−23.0000	−0.974541	−0.487271	+	0.873251i	$0.662007\pi$
$558$	0	0
$559$	−4.00000	−0.169182
$560$	0	0
$561$	0	0
$562$	−18.0000	−0.759284
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	0	0
$568$	2.00000	0.0839181
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	0	0
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	12.0000	0.501745
$573$	0	0
$574$	6.00000	0.250435
$575$	0	0
$576$	0	0
$577$	43.0000	1.79011	0.895057	−	0.445952i	$-0.147135\pi$
$577$	43.0000	1.79011	0.895057	+	0.445952i	$0.147135\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	48.0000	1.99138
$582$	0	0
$583$	33.0000	1.36672
$584$	6.00000	0.248282
$585$	0	0
$586$	−6.00000	−0.247858
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	0	0
$589$	−35.0000	−1.44215
$590$	0	0
$591$	0	0
$592$	3.00000	0.123299
$593$	36.0000	1.47834	0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000	1.47834	0.739171	+	0.673517i	$0.235217\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	16.0000	0.654289
$599$	35.0000	1.43006	0.715031	−	0.699093i	$-0.246413\pi$
$599$	35.0000	1.43006	0.715031	+	0.699093i	$0.246413\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	3.00000	0.122271
$603$	0	0
$604$	12.0000	0.488273
$605$	0	0
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	5.00000	0.202777
$609$	0	0
$610$	0	0
$611$	−12.0000	−0.485468
$612$	0	0
$613$	−46.0000	−1.85792	−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000	−1.85792	−0.928961	+	0.370177i	$0.879297\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	−9.00000	−0.362620
$617$	−33.0000	−1.32853	−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000	−1.32853	−0.664265	+	0.747497i	$0.731255\pi$
$618$	0	0
$619$	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
$621$	0	0
$622$	−18.0000	−0.721734
$623$	30.0000	1.20192
$624$	0	0
$625$	0	0
$626$	−4.00000	−0.159872
$627$	0	0
$628$	−12.0000	−0.478852
$629$	−3.00000	−0.119618
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	5.00000	0.198889
$633$	0	0
$634$	−32.0000	−1.27088
$635$	0	0
$636$	0	0
$637$	8.00000	0.316972
$638$	0	0
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	−12.0000	−0.472866
$645$	0	0
$646$	−5.00000	−0.196722
$647$	−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
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−6.00000	−0.234978
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	0	0
$656$	−2.00000	−0.0780869
$657$	0	0
$658$	9.00000	0.350857
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	23.0000	0.893920
$663$	0	0
$664$	−16.0000	−0.620920
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−18.0000	−0.696441
$669$	0	0
$670$	0	0
$671$	6.00000	0.231627
$672$	0	0
$673$	44.0000	1.69608	0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000	1.69608	0.848038	+	0.529936i	$0.177784\pi$
$674$	12.0000	0.462223
$675$	0	0
$676$	3.00000	0.115385
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	0	0
$679$	−6.00000	−0.230259
$680$	0	0
$681$	0	0
$682$	−21.0000	−0.804132
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	0	0
$685$	0	0
$686$	15.0000	0.572703
$687$	0	0
$688$	−1.00000	−0.0381246
$689$	44.0000	1.67627
$690$	0	0
$691$	42.0000	1.59776	0.798878	−	0.601494i	$-0.205427\pi$
$691$	42.0000	1.59776	0.798878	+	0.601494i	$0.205427\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−27.0000	−1.02491
$695$	0	0
$696$	0	0
$697$	2.00000	0.0757554
$698$	10.0000	0.378506
$699$	0	0
$700$	0	0
$701$	38.0000	1.43524	0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000	1.43524	0.717620	+	0.696435i	$0.245231\pi$
$702$	0	0
$703$	−15.0000	−0.565736
$704$	3.00000	0.113067
$705$	0	0
$706$	−16.0000	−0.602168
$707$	−21.0000	−0.789786
$708$	0	0
$709$	5.00000	0.187779	0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000	0.187779	0.0938895	+	0.995583i	$0.470070\pi$
$710$	0	0
$711$	0	0
$712$	−10.0000	−0.374766
$713$	−28.0000	−1.04861
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	5.00000	0.186598
$719$	−30.0000	−1.11881	−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000	−1.11881	−0.559406	+	0.828894i	$0.688971\pi$
$720$	0	0
$721$	42.0000	1.56416
$722$	−6.00000	−0.223297
$723$	0	0
$724$	7.00000	0.260153
$725$	0	0
$726$	0	0
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−12.0000	−0.444750
$729$	0	0
$730$	0	0
$731$	1.00000	0.0369863
$732$	0	0
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	7.00000	0.258375
$735$	0	0
$736$	4.00000	0.147442
$737$	39.0000	1.43658
$738$	0	0
$739$	35.0000	1.28750	0.643748	−	0.765238i	$-0.277379\pi$
$739$	35.0000	1.28750	0.643748	+	0.765238i	$0.277379\pi$
$740$	0	0
$741$	0	0
$742$	−33.0000	−1.21147
$743$	26.0000	0.953847	0.476924	−	0.878945i	$-0.341752\pi$
$743$	26.0000	0.953847	0.476924	+	0.878945i	$0.341752\pi$
$744$	0	0
$745$	0	0
$746$	−14.0000	−0.512576
$747$	0	0
$748$	−3.00000	−0.109691
$749$	51.0000	1.86350
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	−3.00000	−0.109399
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	48.0000	1.74000	0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000	1.74000	0.869999	+	0.493053i	$0.164119\pi$
$762$	0	0
$763$	15.0000	0.543036
$764$	3.00000	0.108536
$765$	0	0
$766$	4.00000	0.144526
$767$	0	0
$768$	0	0
$769$	35.0000	1.26213	0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000	1.26213	0.631066	+	0.775729i	$0.282618\pi$
$770$	0	0
$771$	0	0
$772$	−6.00000	−0.215945
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	0	0
$776$	2.00000	0.0717958
$777$	0	0
$778$	−5.00000	−0.179259
$779$	10.0000	0.358287
$780$	0	0
$781$	−6.00000	−0.214697
$782$	−4.00000	−0.143040
$783$	0	0
$784$	2.00000	0.0714286
$785$	0	0
$786$	0	0
$787$	−42.0000	−1.49714	−0.748569	−	0.663057i	$-0.769259\pi$
$787$	−42.0000	−1.49714	−0.748569	+	0.663057i	$0.769259\pi$
$788$	12.0000	0.427482
$789$	0	0
$790$	0	0
$791$	3.00000	0.106668
$792$	0	0
$793$	8.00000	0.284088
$794$	−3.00000	−0.106466
$795$	0	0
$796$	−25.0000	−0.886102
$797$	17.0000	0.602171	0.301085	−	0.953597i	$-0.402651\pi$
$797$	17.0000	0.602171	0.301085	+	0.953597i	$0.402651\pi$
$798$	0	0
$799$	3.00000	0.106132
$800$	0	0
$801$	0	0
$802$	−18.0000	−0.635602
$803$	−18.0000	−0.635206
$804$	0	0
$805$	0	0
$806$	−28.0000	−0.986258
$807$	0	0
$808$	7.00000	0.246259
$809$	−45.0000	−1.58212	−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000	−1.58212	−0.791058	+	0.611741i	$0.790469\pi$
$810$	0	0
$811$	2.00000	0.0702295	0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000	0.0702295	0.0351147	+	0.999383i	$0.488820\pi$
$812$	0	0
$813$	0	0
$814$	−9.00000	−0.315450
$815$	0	0
$816$	0	0
$817$	5.00000	0.174928
$818$	10.0000	0.349642
$819$	0	0
$820$	0	0
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	0	0
$827$	17.0000	0.591148	0.295574	−	0.955320i	$-0.404489\pi$
$827$	17.0000	0.591148	0.295574	+	0.955320i	$0.404489\pi$
$828$	0	0
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	0	0
$832$	4.00000	0.138675
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	0	0
$836$	−15.0000	−0.518786
$837$	0	0
$838$	−20.0000	−0.690889
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	28.0000	0.964944
$843$	0	0
$844$	12.0000	0.413057
$845$	0	0
$846$	0	0
$847$	−6.00000	−0.206162
$848$	11.0000	0.377742
$849$	0	0
$850$	0	0
$851$	−12.0000	−0.411355
$852$	0	0
$853$	−51.0000	−1.74621	−0.873103	−	0.487535i	$-0.837896\pi$
$853$	−51.0000	−1.74621	−0.873103	+	0.487535i	$0.837896\pi$
$854$	−6.00000	−0.205316
$855$	0	0
$856$	−17.0000	−0.581048
$857$	47.0000	1.60549	0.802745	−	0.596323i	$-0.203372\pi$
$857$	47.0000	1.60549	0.802745	+	0.596323i	$0.203372\pi$
$858$	0	0
$859$	35.0000	1.19418	0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000	1.19418	0.597092	+	0.802173i	$0.296323\pi$
$860$	0	0
$861$	0	0
$862$	2.00000	0.0681203
$863$	−19.0000	−0.646768	−0.323384	−	0.946268i	$-0.604820\pi$
$863$	−19.0000	−0.646768	−0.323384	+	0.946268i	$0.604820\pi$
$864$	0	0
$865$	0	0
$866$	21.0000	0.713609
$867$	0	0
$868$	21.0000	0.712786
$869$	−15.0000	−0.508840
$870$	0	0
$871$	52.0000	1.76195
$872$	−5.00000	−0.169321
$873$	0	0
$874$	−20.0000	−0.676510
$875$	0	0
$876$	0	0
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	−20.0000	−0.674967
$879$	0	0
$880$	0	0
$881$	−7.00000	−0.235836	−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000	−0.235836	−0.117918	+	0.993023i	$0.537622\pi$
$882$	0	0
$883$	24.0000	0.807664	0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000	0.807664	0.403832	+	0.914833i	$0.367678\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	14.0000	0.470339
$887$	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
$889$	54.0000	1.81110
$890$	0	0
$891$	0	0
$892$	−26.0000	−0.870544
$893$	15.0000	0.501956
$894$	0	0
$895$	0	0
$896$	−3.00000	−0.100223
$897$	0	0
$898$	5.00000	0.166852
$899$	0	0
$900$	0	0
$901$	−11.0000	−0.366463
$902$	6.00000	0.199778
$903$	0	0
$904$	−1.00000	−0.0332595
$905$	0	0
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	27.0000	0.896026
$909$	0	0
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	0	0
$913$	48.0000	1.58857
$914$	−13.0000	−0.430002
$915$	0	0
$916$	0	0
$917$	−36.0000	−1.18882
$918$	0	0
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	0	0
$921$	0	0
$922$	37.0000	1.21853
$923$	−8.00000	−0.263323
$924$	0	0
$925$	0	0
$926$	−24.0000	−0.788689
$927$	0	0
$928$	0	0
$929$	−35.0000	−1.14831	−0.574156	−	0.818746i	$-0.694670\pi$
$929$	−35.0000	−1.14831	−0.574156	+	0.818746i	$0.694670\pi$
$930$	0	0
$931$	−10.0000	−0.327737
$932$	26.0000	0.851658
$933$	0	0
$934$	18.0000	0.588978
$935$	0	0
$936$	0	0
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	−39.0000	−1.27340
$939$	0	0
$940$	0	0
$941$	38.0000	1.23876	0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000	1.23876	0.619382	+	0.785090i	$0.287383\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	0	0
$945$	0	0
$946$	3.00000	0.0975384
$947$	27.0000	0.877382	0.438691	−	0.898638i	$-0.355442\pi$
$947$	27.0000	0.877382	0.438691	+	0.898638i	$0.355442\pi$
$948$	0	0
$949$	−24.0000	−0.779073
$950$	0	0
$951$	0	0
$952$	3.00000	0.0972306
$953$	16.0000	0.518291	0.259145	−	0.965838i	$-0.416559\pi$
$953$	16.0000	0.518291	0.259145	+	0.965838i	$0.416559\pi$
$954$	0	0
$955$	0	0
$956$	−15.0000	−0.485135
$957$	0	0
$958$	−10.0000	−0.323085
$959$	6.00000	0.193750
$960$	0	0
$961$	18.0000	0.580645
$962$	−12.0000	−0.386896
$963$	0	0
$964$	12.0000	0.386494
$965$	0	0
$966$	0	0
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	0	0
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	0	0
$973$	−60.0000	−1.92351
$974$	32.0000	1.02535
$975$	0	0
$976$	2.00000	0.0640184
$977$	−28.0000	−0.895799	−0.447900	−	0.894084i	$-0.647828\pi$
$977$	−28.0000	−0.895799	−0.447900	+	0.894084i	$0.647828\pi$
$978$	0	0
$979$	30.0000	0.958804
$980$	0	0
$981$	0	0
$982$	2.00000	0.0638226
$983$	−44.0000	−1.40338	−0.701691	−	0.712481i	$-0.747571\pi$
$983$	−44.0000	−1.40338	−0.701691	+	0.712481i	$0.747571\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−20.0000	−0.636285
$989$	4.00000	0.127193
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	−7.00000	−0.222250
$993$	0	0
$994$	6.00000	0.190308
$995$	0	0
$996$	0	0
$997$	−37.0000	−1.17180	−0.585901	−	0.810383i	$-0.699259\pi$
$997$	−37.0000	−1.17180	−0.585901	+	0.810383i	$0.699259\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7650.2.a.bd.1.1		1
3.2	odd	2		2550.2.a.bf.1.1	yes	1
5.4	even	2		7650.2.a.bk.1.1		1
15.2	even	4		2550.2.d.o.2449.2		2
15.8	even	4		2550.2.d.o.2449.1		2
15.14	odd	2		2550.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.a.1.1	✓	1	15.14	odd	2
2550.2.a.bf.1.1	yes	1	3.2	odd	2
2550.2.d.o.2449.1		2	15.8	even	4
2550.2.d.o.2449.2		2	15.2	even	4
7650.2.a.bd.1.1		1	1.1	even	1	trivial
7650.2.a.bk.1.1		1	5.4	even	2

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

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