LMFDB - Embedded newform 9450.2.a.dc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, 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("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.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:	$75.4586299101$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -5.00000 q^{11} +1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{19} -5.00000 q^{22} -1.00000 q^{23} +1.00000 q^{28} -4.00000 q^{29} -9.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} -5.00000 q^{37} -1.00000 q^{38} +9.00000 q^{41} +10.0000 q^{43} -5.00000 q^{44} -1.00000 q^{46} +6.00000 q^{47} +1.00000 q^{49} +12.0000 q^{53} +1.00000 q^{56} -4.00000 q^{58} +14.0000 q^{59} -9.00000 q^{62} +1.00000 q^{64} +8.00000 q^{67} +2.00000 q^{68} +13.0000 q^{71} +2.00000 q^{73} -5.00000 q^{74} -1.00000 q^{76} -5.00000 q^{77} +6.00000 q^{79} +9.00000 q^{82} -4.00000 q^{83} +10.0000 q^{86} -5.00000 q^{88} +9.00000 q^{89} -1.00000 q^{92} +6.00000 q^{94} -16.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	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
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	1.00000	0.188982
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	0	0
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0	0
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	0	0
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	−1.00000	−0.147442
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−4.00000	−0.525226
$59$	14.0000	1.82264	0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000	1.82264	0.911322	+	0.411693i	$0.135063\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−9.00000	−1.14300
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	0	0
$71$	13.0000	1.54282	0.771408	−	0.636341i	$-0.219553\pi$
$71$	13.0000	1.54282	0.771408	+	0.636341i	$0.219553\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−5.00000	−0.569803
$78$	0	0
$79$	6.00000	0.675053	0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000	0.675053	0.337526	+	0.941316i	$0.390410\pi$
$80$	0	0
$81$	0	0
$82$	9.00000	0.993884
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	10.0000	1.07833
$87$	0	0
$88$	−5.00000	−0.533002
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	0	0
$92$	−1.00000	−0.104257
$93$	0	0
$94$	6.00000	0.618853
$95$	0	0
$96$	0	0
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	0	0
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	1.00000	0.0985329	0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000	0.0985329	0.0492665	+	0.998786i	$0.484312\pi$
$104$	0	0
$105$	0	0
$106$	12.0000	1.16554
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	0	0
$116$	−4.00000	−0.371391
$117$	0	0
$118$	14.0000	1.28880
$119$	2.00000	0.183340
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	0	0
$124$	−9.00000	−0.808224
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−22.0000	−1.92215	−0.961074	−	0.276289i	$-0.910895\pi$
$131$	−22.0000	−1.92215	−0.961074	+	0.276289i	$0.910895\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	8.00000	0.691095
$135$	0	0
$136$	2.00000	0.171499
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	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
$142$	13.0000	1.09094
$143$	0	0
$144$	0	0
$145$	0	0
$146$	2.00000	0.165521
$147$	0	0
$148$	−5.00000	−0.410997
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	−5.00000	−0.402911
$155$	0	0
$156$	0	0
$157$	−8.00000	−0.638470	−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000	−0.638470	−0.319235	+	0.947676i	$0.603426\pi$
$158$	6.00000	0.477334
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	9.00000	0.702782
$165$	0	0
$166$	−4.00000	−0.310460
$167$	10.0000	0.773823	0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000	0.773823	0.386912	+	0.922117i	$0.373542\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	10.0000	0.762493
$173$	7.00000	0.532200	0.266100	−	0.963945i	$-0.414265\pi$
$173$	7.00000	0.532200	0.266100	+	0.963945i	$0.414265\pi$
$174$	0	0
$175$	0	0
$176$	−5.00000	−0.376889
$177$	0	0
$178$	9.00000	0.674579
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	0	0
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	0	0
$187$	−10.0000	−0.731272
$188$	6.00000	0.437595
$189$	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
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−16.0000	−1.14873
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	−13.0000	−0.921546	−0.460773	−	0.887518i	$-0.652428\pi$
$199$	−13.0000	−0.921546	−0.460773	+	0.887518i	$0.652428\pi$
$200$	0	0
$201$	0	0
$202$	14.0000	0.985037
$203$	−4.00000	−0.280745
$204$	0	0
$205$	0	0
$206$	1.00000	0.0696733
$207$	0	0
$208$	0	0
$209$	5.00000	0.345857
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	12.0000	0.820303
$215$	0	0
$216$	0	0
$217$	−9.00000	−0.610960
$218$	7.00000	0.474100
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−5.00000	−0.334825	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	−5.00000	−0.334825	−0.167412	+	0.985887i	$0.553541\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−2.00000	−0.133038
$227$	6.00000	0.398234	0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000	0.398234	0.199117	+	0.979976i	$0.436193\pi$
$228$	0	0
$229$	28.0000	1.85029	0.925146	−	0.379611i	$-0.123942\pi$
$229$	28.0000	1.85029	0.925146	+	0.379611i	$0.123942\pi$
$230$	0	0
$231$	0	0
$232$	−4.00000	−0.262613
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	0	0
$235$	0	0
$236$	14.0000	0.911322
$237$	0	0
$238$	2.00000	0.129641
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	14.0000	0.899954
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−9.00000	−0.571501
$249$	0	0
$250$	0	0
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	5.00000	0.314347
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	27.0000	1.68421	0.842107	−	0.539311i	$-0.181315\pi$
$257$	27.0000	1.68421	0.842107	+	0.539311i	$0.181315\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	0	0
$262$	−22.0000	−1.35916
$263$	−21.0000	−1.29492	−0.647458	−	0.762101i	$-0.724168\pi$
$263$	−21.0000	−1.29492	−0.647458	+	0.762101i	$0.724168\pi$
$264$	0	0
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	8.00000	0.488678
$269$	−13.0000	−0.792624	−0.396312	−	0.918116i	$-0.629710\pi$
$269$	−13.0000	−0.792624	−0.396312	+	0.918116i	$0.629710\pi$
$270$	0	0
$271$	24.0000	1.45790	0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000	1.45790	0.728948	+	0.684569i	$0.240010\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	16.0000	0.966595
$275$	0	0
$276$	0	0
$277$	19.0000	1.14160	0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000	1.14160	0.570800	+	0.821089i	$0.306633\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	13.0000	0.771408
$285$	0	0
$286$	0	0
$287$	9.00000	0.531253
$288$	0	0
$289$	−13.0000	−0.764706
$290$	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
$296$	−5.00000	−0.290619
$297$	0	0
$298$	−6.00000	−0.347571
$299$	0	0
$300$	0	0
$301$	10.0000	0.576390
$302$	10.0000	0.575435
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	5.00000	0.285365	0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000	0.285365	0.142683	+	0.989769i	$0.454427\pi$
$308$	−5.00000	−0.284901
$309$	0	0
$310$	0	0
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	0	0
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	−8.00000	−0.451466
$315$	0	0
$316$	6.00000	0.337526
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	20.0000	1.11979
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−2.00000	−0.111283
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	9.00000	0.496942
$329$	6.00000	0.330791
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	10.0000	0.547176
$335$	0	0
$336$	0	0
$337$	−27.0000	−1.47078	−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000	−1.47078	−0.735392	+	0.677642i	$0.763002\pi$
$338$	−13.0000	−0.707107
$339$	0	0
$340$	0	0
$341$	45.0000	2.43689
$342$	0	0
$343$	1.00000	0.0539949
$344$	10.0000	0.539164
$345$	0	0
$346$	7.00000	0.376322
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	0	0
$352$	−5.00000	−0.266501
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	0	0
$356$	9.00000	0.476999
$357$	0	0
$358$	−24.0000	−1.26844
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	18.0000	0.946059
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−35.0000	−1.82699	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−35.0000	−1.82699	−0.913493	+	0.406855i	$0.866625\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	17.0000	0.880227	0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000	0.880227	0.440113	+	0.897942i	$0.354938\pi$
$374$	−10.0000	−0.517088
$375$	0	0
$376$	6.00000	0.309426
$377$	0	0
$378$	0	0
$379$	−14.0000	−0.719132	−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000	−0.719132	−0.359566	+	0.933120i	$0.617075\pi$
$380$	0	0
$381$	0	0
$382$	3.00000	0.153493
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	0	0
$385$	0	0
$386$	10.0000	0.508987
$387$	0	0
$388$	−16.0000	−0.812277
$389$	20.0000	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$389$	20.0000	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$390$	0	0
$391$	−2.00000	−0.101144
$392$	1.00000	0.0505076
$393$	0	0
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	−13.0000	−0.651631
$399$	0	0
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	0	0
$404$	14.0000	0.696526
$405$	0	0
$406$	−4.00000	−0.198517
$407$	25.0000	1.23920
$408$	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
$412$	1.00000	0.0492665
$413$	14.0000	0.688895
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	5.00000	0.244558
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−27.0000	−1.31590	−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000	−1.31590	−0.657950	+	0.753062i	$0.728576\pi$
$422$	−22.0000	−1.07094
$423$	0	0
$424$	12.0000	0.582772
$425$	0	0
$426$	0	0
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	0	0
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	−9.00000	−0.432014
$435$	0	0
$436$	7.00000	0.335239
$437$	1.00000	0.0478365
$438$	0	0
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	11.0000	0.522626	0.261313	−	0.965254i	$-0.415845\pi$
$443$	11.0000	0.522626	0.261313	+	0.965254i	$0.415845\pi$
$444$	0	0
$445$	0	0
$446$	−5.00000	−0.236757
$447$	0	0
$448$	1.00000	0.0472456
$449$	−10.0000	−0.471929	−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000	−0.471929	−0.235965	+	0.971762i	$0.575825\pi$
$450$	0	0
$451$	−45.0000	−2.11897
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	6.00000	0.281594
$455$	0	0
$456$	0	0
$457$	−13.0000	−0.608114	−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000	−0.608114	−0.304057	+	0.952654i	$0.598341\pi$
$458$	28.0000	1.30835
$459$	0	0
$460$	0	0
$461$	−31.0000	−1.44381	−0.721907	−	0.691990i	$-0.756734\pi$
$461$	−31.0000	−1.44381	−0.721907	+	0.691990i	$0.756734\pi$
$462$	0	0
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	−4.00000	−0.185695
$465$	0	0
$466$	14.0000	0.648537
$467$	−26.0000	−1.20314	−0.601568	−	0.798821i	$-0.705457\pi$
$467$	−26.0000	−1.20314	−0.601568	+	0.798821i	$0.705457\pi$
$468$	0	0
$469$	8.00000	0.369406
$470$	0	0
$471$	0	0
$472$	14.0000	0.644402
$473$	−50.0000	−2.29900
$474$	0	0
$475$	0	0
$476$	2.00000	0.0916698
$477$	0	0
$478$	−24.0000	−1.09773
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	0	0
$481$	0	0
$482$	14.0000	0.637683
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−9.00000	−0.406164	−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000	−0.406164	−0.203082	+	0.979162i	$0.565096\pi$
$492$	0	0
$493$	−8.00000	−0.360302
$494$	0	0
$495$	0	0
$496$	−9.00000	−0.404112
$497$	13.0000	0.583130
$498$	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
$502$	24.0000	1.07117
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	0	0
$506$	5.00000	0.222277
$507$	0	0
$508$	0	0
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	27.0000	1.19092
$515$	0	0
$516$	0	0
$517$	−30.0000	−1.31940
$518$	−5.00000	−0.219687
$519$	0	0
$520$	0	0
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	0	0
$523$	−11.0000	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$523$	−11.0000	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$524$	−22.0000	−0.961074
$525$	0	0
$526$	−21.0000	−0.915644
$527$	−18.0000	−0.784092
$528$	0	0
$529$	−22.0000	−0.956522
$530$	0	0
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	0	0
$535$	0	0
$536$	8.00000	0.345547
$537$	0	0
$538$	−13.0000	−0.560470
$539$	−5.00000	−0.215365
$540$	0	0
$541$	−3.00000	−0.128980	−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000	−0.128980	−0.0644900	+	0.997918i	$0.520542\pi$
$542$	24.0000	1.03089
$543$	0	0
$544$	2.00000	0.0857493
$545$	0	0
$546$	0	0
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	16.0000	0.683486
$549$	0	0
$550$	0	0
$551$	4.00000	0.170406
$552$	0	0
$553$	6.00000	0.255146
$554$	19.0000	0.807233
$555$	0	0
$556$	−20.0000	−0.848189
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	0	0
$566$	20.0000	0.840663
$567$	0	0
$568$	13.0000	0.545468
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	18.0000	0.753277	0.376638	−	0.926360i	$-0.377080\pi$
$571$	18.0000	0.753277	0.376638	+	0.926360i	$0.377080\pi$
$572$	0	0
$573$	0	0
$574$	9.00000	0.375653
$575$	0	0
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	0	0
$581$	−4.00000	−0.165948
$582$	0	0
$583$	−60.0000	−2.48495
$584$	2.00000	0.0827606
$585$	0	0
$586$	18.0000	0.743573
$587$	14.0000	0.577842	0.288921	−	0.957353i	$-0.406704\pi$
$587$	14.0000	0.577842	0.288921	+	0.957353i	$0.406704\pi$
$588$	0	0
$589$	9.00000	0.370839
$590$	0	0
$591$	0	0
$592$	−5.00000	−0.205499
$593$	9.00000	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	0	0
$599$	27.0000	1.10319	0.551595	−	0.834112i	$-0.314019\pi$
$599$	27.0000	1.10319	0.551595	+	0.834112i	$0.314019\pi$
$600$	0	0
$601$	8.00000	0.326327	0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000	0.326327	0.163163	+	0.986599i	$0.447830\pi$
$602$	10.0000	0.407570
$603$	0	0
$604$	10.0000	0.406894
$605$	0	0
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	15.0000	0.605844	0.302922	−	0.953015i	$-0.402038\pi$
$613$	15.0000	0.605844	0.302922	+	0.953015i	$0.402038\pi$
$614$	5.00000	0.201784
$615$	0	0
$616$	−5.00000	−0.201456
$617$	14.0000	0.563619	0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000	0.563619	0.281809	+	0.959470i	$0.409065\pi$
$618$	0	0
$619$	−11.0000	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$620$	0	0
$621$	0	0
$622$	8.00000	0.320771
$623$	9.00000	0.360577
$624$	0	0
$625$	0	0
$626$	8.00000	0.319744
$627$	0	0
$628$	−8.00000	−0.319235
$629$	−10.0000	−0.398726
$630$	0	0
$631$	38.0000	1.51276	0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000	1.51276	0.756378	+	0.654135i	$0.226967\pi$
$632$	6.00000	0.238667
$633$	0	0
$634$	−18.0000	−0.714871
$635$	0	0
$636$	0	0
$637$	0	0
$638$	20.0000	0.791808
$639$	0	0
$640$	0	0
$641$	22.0000	0.868948	0.434474	−	0.900684i	$-0.356934\pi$
$641$	22.0000	0.868948	0.434474	+	0.900684i	$0.356934\pi$
$642$	0	0
$643$	13.0000	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$643$	13.0000	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	−2.00000	−0.0786889
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	−70.0000	−2.74774
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	0	0
$655$	0	0
$656$	9.00000	0.351391
$657$	0	0
$658$	6.00000	0.233904
$659$	−17.0000	−0.662226	−0.331113	−	0.943591i	$-0.607424\pi$
$659$	−17.0000	−0.662226	−0.331113	+	0.943591i	$0.607424\pi$
$660$	0	0
$661$	28.0000	1.08907	0.544537	−	0.838737i	$-0.316705\pi$
$661$	28.0000	1.08907	0.544537	+	0.838737i	$0.316705\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	0	0
$667$	4.00000	0.154881
$668$	10.0000	0.386912
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	−27.0000	−1.04000
$675$	0	0
$676$	−13.0000	−0.500000
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	−16.0000	−0.614024
$680$	0	0
$681$	0	0
$682$	45.0000	1.72314
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	10.0000	0.381246
$689$	0	0
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	7.00000	0.266100
$693$	0	0
$694$	−3.00000	−0.113878
$695$	0	0
$696$	0	0
$697$	18.0000	0.681799
$698$	−26.0000	−0.984115
$699$	0	0
$700$	0	0
$701$	20.0000	0.755390	0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000	0.755390	0.377695	+	0.925930i	$0.376717\pi$
$702$	0	0
$703$	5.00000	0.188579
$704$	−5.00000	−0.188445
$705$	0	0
$706$	−3.00000	−0.112906
$707$	14.0000	0.526524
$708$	0	0
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	0	0
$711$	0	0
$712$	9.00000	0.337289
$713$	9.00000	0.337053
$714$	0	0
$715$	0	0
$716$	−24.0000	−0.896922
$717$	0	0
$718$	−4.00000	−0.149279
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	1.00000	0.0372419
$722$	−18.0000	−0.669891
$723$	0	0
$724$	18.0000	0.668965
$725$	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	$0.297782\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	20.0000	0.739727
$732$	0	0
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	−35.0000	−1.29187
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−40.0000	−1.47342
$738$	0	0
$739$	18.0000	0.662141	0.331070	−	0.943606i	$-0.392590\pi$
$739$	18.0000	0.662141	0.331070	+	0.943606i	$0.392590\pi$
$740$	0	0
$741$	0	0
$742$	12.0000	0.440534
$743$	−21.0000	−0.770415	−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000	−0.770415	−0.385208	+	0.922830i	$0.625870\pi$
$744$	0	0
$745$	0	0
$746$	17.0000	0.622414
$747$	0	0
$748$	−10.0000	−0.365636
$749$	12.0000	0.438470
$750$	0	0
$751$	18.0000	0.656829	0.328415	−	0.944534i	$-0.393486\pi$
$751$	18.0000	0.656829	0.328415	+	0.944534i	$0.393486\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	−14.0000	−0.508503
$759$	0	0
$760$	0	0
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	0	0
$763$	7.00000	0.253417
$764$	3.00000	0.108536
$765$	0	0
$766$	−10.0000	−0.361315
$767$	0	0
$768$	0	0
$769$	40.0000	1.44244	0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000	1.44244	0.721218	+	0.692708i	$0.243582\pi$
$770$	0	0
$771$	0	0
$772$	10.0000	0.359908
$773$	19.0000	0.683383	0.341691	−	0.939812i	$-0.389000\pi$
$773$	19.0000	0.683383	0.341691	+	0.939812i	$0.389000\pi$
$774$	0	0
$775$	0	0
$776$	−16.0000	−0.574367
$777$	0	0
$778$	20.0000	0.717035
$779$	−9.00000	−0.322458
$780$	0	0
$781$	−65.0000	−2.32588
$782$	−2.00000	−0.0715199
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	−2.00000	−0.0711118
$792$	0	0
$793$	0	0
$794$	30.0000	1.06466
$795$	0	0
$796$	−13.0000	−0.460773
$797$	−33.0000	−1.16892	−0.584460	−	0.811423i	$-0.698694\pi$
$797$	−33.0000	−1.16892	−0.584460	+	0.811423i	$0.698694\pi$
$798$	0	0
$799$	12.0000	0.424529
$800$	0	0
$801$	0	0
$802$	12.0000	0.423735
$803$	−10.0000	−0.352892
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	14.0000	0.492518
$809$	20.0000	0.703163	0.351581	−	0.936157i	$-0.385644\pi$
$809$	20.0000	0.703163	0.351581	+	0.936157i	$0.385644\pi$
$810$	0	0
$811$	1.00000	0.0351147	0.0175574	−	0.999846i	$-0.494411\pi$
$811$	1.00000	0.0351147	0.0175574	+	0.999846i	$0.494411\pi$
$812$	−4.00000	−0.140372
$813$	0	0
$814$	25.0000	0.876250
$815$	0	0
$816$	0	0
$817$	−10.0000	−0.349856
$818$	−10.0000	−0.349642
$819$	0	0
$820$	0	0
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	0	0
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	1.00000	0.0348367
$825$	0	0
$826$	14.0000	0.487122
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	0	0
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	2.00000	0.0692959
$834$	0	0
$835$	0	0
$836$	5.00000	0.172929
$837$	0	0
$838$	−6.00000	−0.207267
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	−27.0000	−0.930481
$843$	0	0
$844$	−22.0000	−0.757271
$845$	0	0
$846$	0	0
$847$	14.0000	0.481046
$848$	12.0000	0.412082
$849$	0	0
$850$	0	0
$851$	5.00000	0.171398
$852$	0	0
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	0	0
$855$	0	0
$856$	12.0000	0.410152
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	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
$862$	15.0000	0.510902
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	0	0
$866$	4.00000	0.135926
$867$	0	0
$868$	−9.00000	−0.305480
$869$	−30.0000	−1.01768
$870$	0	0
$871$	0	0
$872$	7.00000	0.237050
$873$	0	0
$874$	1.00000	0.0338255
$875$	0	0
$876$	0	0
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	24.0000	0.809961
$879$	0	0
$880$	0	0
$881$	15.0000	0.505363	0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000	0.505363	0.252681	+	0.967550i	$0.418688\pi$
$882$	0	0
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	0	0
$885$	0	0
$886$	11.0000	0.369552
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	0	0
$892$	−5.00000	−0.167412
$893$	−6.00000	−0.200782
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−10.0000	−0.333704
$899$	36.0000	1.20067
$900$	0	0
$901$	24.0000	0.799556
$902$	−45.0000	−1.49834
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	0	0
$906$	0	0
$907$	−30.0000	−0.996134	−0.498067	−	0.867139i	$-0.665957\pi$
$907$	−30.0000	−0.996134	−0.498067	+	0.867139i	$0.665957\pi$
$908$	6.00000	0.199117
$909$	0	0
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	0	0
$913$	20.0000	0.661903
$914$	−13.0000	−0.430002
$915$	0	0
$916$	28.0000	0.925146
$917$	−22.0000	−0.726504
$918$	0	0
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	0	0
$922$	−31.0000	−1.02093
$923$	0	0
$924$	0	0
$925$	0	0
$926$	14.0000	0.460069
$927$	0	0
$928$	−4.00000	−0.131306
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	14.0000	0.458585
$933$	0	0
$934$	−26.0000	−0.850746
$935$	0	0
$936$	0	0
$937$	28.0000	0.914720	0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000	0.914720	0.457360	+	0.889282i	$0.348795\pi$
$938$	8.00000	0.261209
$939$	0	0
$940$	0	0
$941$	−13.0000	−0.423788	−0.211894	−	0.977293i	$-0.567963\pi$
$941$	−13.0000	−0.423788	−0.211894	+	0.977293i	$0.567963\pi$
$942$	0	0
$943$	−9.00000	−0.293080
$944$	14.0000	0.455661
$945$	0	0
$946$	−50.0000	−1.62564
$947$	−17.0000	−0.552426	−0.276213	−	0.961096i	$-0.589079\pi$
$947$	−17.0000	−0.552426	−0.276213	+	0.961096i	$0.589079\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	2.00000	0.0648204
$953$	44.0000	1.42530	0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000	1.42530	0.712650	+	0.701520i	$0.247495\pi$
$954$	0	0
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	−32.0000	−1.03387
$959$	16.0000	0.516667
$960$	0	0
$961$	50.0000	1.61290
$962$	0	0
$963$	0	0
$964$	14.0000	0.450910
$965$	0	0
$966$	0	0
$967$	−2.00000	−0.0643157	−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000	−0.0643157	−0.0321578	+	0.999483i	$0.510238\pi$
$968$	14.0000	0.449977
$969$	0	0
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	−20.0000	−0.641171
$974$	−26.0000	−0.833094
$975$	0	0
$976$	0	0
$977$	60.0000	1.91957	0.959785	−	0.280736i	$-0.0905785\pi$
$977$	60.0000	1.91957	0.959785	+	0.280736i	$0.0905785\pi$
$978$	0	0
$979$	−45.0000	−1.43821
$980$	0	0
$981$	0	0
$982$	−9.00000	−0.287202
$983$	−30.0000	−0.956851	−0.478426	−	0.878128i	$-0.658792\pi$
$983$	−30.0000	−0.956851	−0.478426	+	0.878128i	$0.658792\pi$
$984$	0	0
$985$	0	0
$986$	−8.00000	−0.254772
$987$	0	0
$988$	0	0
$989$	−10.0000	−0.317982
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−9.00000	−0.285750
$993$	0	0
$994$	13.0000	0.412335
$995$	0	0
$996$	0	0
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	10.0000	0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.dc.1.1		1
3.2	odd	2		9450.2.a.bx.1.1		1
5.4	even	2		378.2.a.c.1.1	✓	1
15.14	odd	2		378.2.a.f.1.1	yes	1
20.19	odd	2		3024.2.a.m.1.1		1
35.34	odd	2		2646.2.a.i.1.1		1
45.4	even	6		1134.2.f.n.379.1		2
45.14	odd	6		1134.2.f.c.379.1		2
45.29	odd	6		1134.2.f.c.757.1		2
45.34	even	6		1134.2.f.n.757.1		2
60.59	even	2		3024.2.a.t.1.1		1
105.104	even	2		2646.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.a.c.1.1	✓	1	5.4	even	2
378.2.a.f.1.1	yes	1	15.14	odd	2
1134.2.f.c.379.1		2	45.14	odd	6
1134.2.f.c.757.1		2	45.29	odd	6
1134.2.f.n.379.1		2	45.4	even	6
1134.2.f.n.757.1		2	45.34	even	6
2646.2.a.i.1.1		1	35.34	odd	2
2646.2.a.v.1.1		1	105.104	even	2
3024.2.a.m.1.1		1	20.19	odd	2
3024.2.a.t.1.1		1	60.59	even	2
9450.2.a.bx.1.1		1	3.2	odd	2
9450.2.a.dc.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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

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