LMFDB - Embedded newform 9450.2.a.bl.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:	yes
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)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} -7.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{19} -6.00000 q^{23} +7.00000 q^{26} +1.00000 q^{28} -3.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -3.00000 q^{34} +2.00000 q^{37} +1.00000 q^{38} +6.00000 q^{41} +2.00000 q^{43} +6.00000 q^{46} -3.00000 q^{47} +1.00000 q^{49} -7.00000 q^{52} -9.00000 q^{53} -1.00000 q^{56} +3.00000 q^{58} +6.00000 q^{59} -7.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +3.00000 q^{68} +12.0000 q^{71} +2.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} -1.00000 q^{79} -6.00000 q^{82} +6.00000 q^{83} -2.00000 q^{86} +15.0000 q^{89} -7.00000 q^{91} -6.00000 q^{92} +3.00000 q^{94} -4.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−7.00000	−1.94145	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000	−1.94145	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	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
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	0	0
$26$	7.00000	1.37281
$27$	0	0
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	0	0
$45$	0	0
$46$	6.00000	0.884652
$47$	−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
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−7.00000	−0.970725
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	0	0
$56$	−1.00000	−0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	3.00000	0.363803
$69$	0	0
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	0	0
$82$	−6.00000	−0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	0	0
$86$	−2.00000	−0.215666
$87$	0	0
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	−7.00000	−0.733799
$92$	−6.00000	−0.625543
$93$	0	0
$94$	3.00000	0.309426
$95$	0	0
$96$	0	0
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	7.00000	0.686406
$105$	0	0
$106$	9.00000	0.874157
$107$	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
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−6.00000	−0.552345
$119$	3.00000	0.275010
$120$	0	0
$121$	−11.0000	−1.00000
$122$	7.00000	0.633750
$123$	0	0
$124$	−4.00000	−0.359211
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	4.00000	0.345547
$135$	0	0
$136$	−3.00000	−0.257248
$137$	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
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	0	0
$144$	0	0
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	2.00000	0.164399
$149$	9.00000	0.737309	0.368654	−	0.929567i	$-0.379819\pi$
$149$	9.00000	0.737309	0.368654	+	0.929567i	$0.379819\pi$
$150$	0	0
$151$	−7.00000	−0.569652	−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000	−0.569652	−0.284826	+	0.958579i	$0.591936\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1.00000	−0.0798087	−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000	−0.0798087	−0.0399043	+	0.999204i	$0.512705\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−6.00000	−0.465690
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	36.0000	2.76923
$170$	0	0
$171$	0	0
$172$	2.00000	0.152499
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	−15.0000	−1.12430
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	0	0
$181$	5.00000	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$182$	7.00000	0.518875
$183$	0	0
$184$	6.00000	0.442326
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−3.00000	−0.218797
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−19.0000	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	1.00000	0.0714286
$197$	3.00000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	0	0
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	0	0
$201$	0	0
$202$	6.00000	0.422159
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	4.00000	0.278693
$207$	0	0
$208$	−7.00000	−0.485363
$209$	0	0
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−9.00000	−0.618123
$213$	0	0
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0	0
$217$	−4.00000	−0.271538
$218$	−14.0000	−0.948200
$219$	0	0
$220$	0	0
$221$	−21.0000	−1.41261
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	5.00000	0.330409	0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000	0.330409	0.165205	+	0.986259i	$0.447172\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	−12.0000	−0.786146	−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000	−0.786146	−0.393073	+	0.919507i	$0.628588\pi$
$234$	0	0
$235$	0	0
$236$	6.00000	0.390567
$237$	0	0
$238$	−3.00000	−0.194461
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	0	0
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	11.0000	0.707107
$243$	0	0
$244$	−7.00000	−0.448129
$245$	0	0
$246$	0	0
$247$	7.00000	0.445399
$248$	4.00000	0.254000
$249$	0	0
$250$	0	0
$251$	30.0000	1.89358	0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000	1.89358	0.946792	+	0.321847i	$0.104304\pi$
$252$	0	0
$253$	0	0
$254$	7.00000	0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	−21.0000	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	0	0
$262$	−18.0000	−1.11204
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	0	0
$266$	1.00000	0.0613139
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	23.0000	1.36721	0.683604	−	0.729853i	$-0.260412\pi$
$283$	23.0000	1.36721	0.683604	+	0.729853i	$0.260412\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	0	0
$287$	6.00000	0.354169
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	0	0
$298$	−9.00000	−0.521356
$299$	42.0000	2.42892
$300$	0	0
$301$	2.00000	0.115278
$302$	7.00000	0.402805
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	20.0000	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$314$	1.00000	0.0564333
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	15.0000	0.842484	0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000	0.842484	0.421242	+	0.906948i	$0.361594\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	6.00000	0.334367
$323$	−3.00000	−0.166924
$324$	0	0
$325$	0	0
$326$	−14.0000	−0.775388
$327$	0	0
$328$	−6.00000	−0.331295
$329$	−3.00000	−0.165395
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−1.00000	−0.0544735	−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000	−0.0544735	−0.0272367	+	0.999629i	$0.508671\pi$
$338$	−36.0000	−1.95814
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	1.00000	0.0539949
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−24.0000	−1.29025
$347$	−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
$349$	35.0000	1.87351	0.936754	−	0.349990i	$-0.113815\pi$
$349$	35.0000	1.87351	0.936754	+	0.349990i	$0.113815\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	0	0
$356$	15.0000	0.794998
$357$	0	0
$358$	−9.00000	−0.475665
$359$	−30.0000	−1.58334	−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000	−1.58334	−0.791670	+	0.610949i	$0.790788\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	−5.00000	−0.262794
$363$	0	0
$364$	−7.00000	−0.366900
$365$	0	0
$366$	0	0
$367$	26.0000	1.35719	0.678594	−	0.734513i	$-0.262589\pi$
$367$	26.0000	1.35719	0.678594	+	0.734513i	$0.262589\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	0	0
$371$	−9.00000	−0.467257
$372$	0	0
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	0	0
$375$	0	0
$376$	3.00000	0.154713
$377$	21.0000	1.08156
$378$	0	0
$379$	14.0000	0.719132	0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000	0.719132	0.359566	+	0.933120i	$0.382925\pi$
$380$	0	0
$381$	0	0
$382$	12.0000	0.613973
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	0	0
$386$	19.0000	0.967075
$387$	0	0
$388$	−4.00000	−0.203069
$389$	27.0000	1.36895	0.684477	−	0.729034i	$-0.260031\pi$
$389$	27.0000	1.36895	0.684477	+	0.729034i	$0.260031\pi$
$390$	0	0
$391$	−18.0000	−0.910299
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−3.00000	−0.151138
$395$	0	0
$396$	0	0
$397$	11.0000	0.552074	0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000	0.552074	0.276037	+	0.961147i	$0.410979\pi$
$398$	10.0000	0.501255
$399$	0	0
$400$	0	0
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	0	0
$403$	28.0000	1.39478
$404$	−6.00000	−0.298511
$405$	0	0
$406$	3.00000	0.148888
$407$	0	0
$408$	0	0
$409$	8.00000	0.395575	0.197787	−	0.980245i	$-0.436624\pi$
$409$	8.00000	0.395575	0.197787	+	0.980245i	$0.436624\pi$
$410$	0	0
$411$	0	0
$412$	−4.00000	−0.197066
$413$	6.00000	0.295241
$414$	0	0
$415$	0	0
$416$	7.00000	0.343203
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−2.00000	−0.0973585
$423$	0	0
$424$	9.00000	0.437079
$425$	0	0
$426$	0	0
$427$	−7.00000	−0.338754
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	32.0000	1.53782	0.768911	−	0.639356i	$-0.220799\pi$
$433$	32.0000	1.53782	0.768911	+	0.639356i	$0.220799\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	14.0000	0.670478
$437$	6.00000	0.287019
$438$	0	0
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	0	0
$441$	0	0
$442$	21.0000	0.998868
$443$	−21.0000	−0.997740	−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000	−0.997740	−0.498870	+	0.866677i	$0.666252\pi$
$444$	0	0
$445$	0	0
$446$	−8.00000	−0.378811
$447$	0	0
$448$	1.00000	0.0472456
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	0	0
$454$	−12.0000	−0.563188
$455$	0	0
$456$	0	0
$457$	−37.0000	−1.73079	−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000	−1.73079	−0.865393	+	0.501093i	$0.832931\pi$
$458$	−5.00000	−0.233635
$459$	0	0
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−31.0000	−1.44069	−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000	−1.44069	−0.720346	+	0.693615i	$0.756017\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	12.0000	0.555889
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	−6.00000	−0.276172
$473$	0	0
$474$	0	0
$475$	0	0
$476$	3.00000	0.137505
$477$	0	0
$478$	−30.0000	−1.37217
$479$	9.00000	0.411220	0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000	0.411220	0.205610	+	0.978634i	$0.434082\pi$
$480$	0	0
$481$	−14.0000	−0.638345
$482$	−20.0000	−0.910975
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	7.00000	0.316875
$489$	0	0
$490$	0	0
$491$	−39.0000	−1.76005	−0.880023	−	0.474932i	$-0.842473\pi$
$491$	−39.0000	−1.76005	−0.880023	+	0.474932i	$0.842473\pi$
$492$	0	0
$493$	−9.00000	−0.405340
$494$	−7.00000	−0.314945
$495$	0	0
$496$	−4.00000	−0.179605
$497$	12.0000	0.538274
$498$	0	0
$499$	2.00000	0.0895323	0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000	0.0895323	0.0447661	+	0.998997i	$0.485746\pi$
$500$	0	0
$501$	0	0
$502$	−30.0000	−1.33897
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−7.00000	−0.310575
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	21.0000	0.926270
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	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
$523$	5.00000	0.218635	0.109317	−	0.994007i	$-0.465134\pi$
$523$	5.00000	0.218635	0.109317	+	0.994007i	$0.465134\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	18.0000	0.784837
$527$	−12.0000	−0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	−42.0000	−1.81922
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	0	0
$538$	6.00000	0.258678
$539$	0	0
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	0	0
$551$	3.00000	0.127804
$552$	0	0
$553$	−1.00000	−0.0425243
$554$	10.0000	0.424859
$555$	0	0
$556$	−4.00000	−0.169638
$557$	21.0000	0.889799	0.444899	−	0.895581i	$-0.353239\pi$
$557$	21.0000	0.889799	0.444899	+	0.895581i	$0.353239\pi$
$558$	0	0
$559$	−14.0000	−0.592137
$560$	0	0
$561$	0	0
$562$	−30.0000	−1.26547
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	0	0
$565$	0	0
$566$	−23.0000	−0.966762
$567$	0	0
$568$	−12.0000	−0.503509
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	−22.0000	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$572$	0	0
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	0	0
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	0	0
$581$	6.00000	0.248922
$582$	0	0
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	30.0000	1.23929
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	0	0
$591$	0	0
$592$	2.00000	0.0821995
$593$	21.0000	0.862367	0.431183	−	0.902264i	$-0.358096\pi$
$593$	21.0000	0.862367	0.431183	+	0.902264i	$0.358096\pi$
$594$	0	0
$595$	0	0
$596$	9.00000	0.368654
$597$	0	0
$598$	−42.0000	−1.71751
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	−16.0000	−0.652654	−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000	−0.652654	−0.326327	+	0.945257i	$0.605811\pi$
$602$	−2.00000	−0.0815139
$603$	0	0
$604$	−7.00000	−0.284826
$605$	0	0
$606$	0	0
$607$	−4.00000	−0.162355	−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000	−0.162355	−0.0811775	+	0.996700i	$0.525868\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	21.0000	0.849569
$612$	0	0
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	0	0
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	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
$622$	12.0000	0.481156
$623$	15.0000	0.600962
$624$	0	0
$625$	0	0
$626$	−20.0000	−0.799361
$627$	0	0
$628$	−1.00000	−0.0399043
$629$	6.00000	0.239236
$630$	0	0
$631$	−13.0000	−0.517522	−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000	−0.517522	−0.258761	+	0.965941i	$0.583314\pi$
$632$	1.00000	0.0397779
$633$	0	0
$634$	−15.0000	−0.595726
$635$	0	0
$636$	0	0
$637$	−7.00000	−0.277350
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	23.0000	0.907031	0.453516	−	0.891248i	$-0.350170\pi$
$643$	23.0000	0.907031	0.453516	+	0.891248i	$0.350170\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	3.00000	0.118033
$647$	45.0000	1.76913	0.884566	−	0.466415i	$-0.154454\pi$
$647$	45.0000	1.76913	0.884566	+	0.466415i	$0.154454\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	14.0000	0.548282
$653$	−33.0000	−1.29139	−0.645695	−	0.763596i	$-0.723432\pi$
$653$	−33.0000	−1.29139	−0.645695	+	0.763596i	$0.723432\pi$
$654$	0	0
$655$	0	0
$656$	6.00000	0.234261
$657$	0	0
$658$	3.00000	0.116952
$659$	3.00000	0.116863	0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000	0.116863	0.0584317	+	0.998291i	$0.481390\pi$
$660$	0	0
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	−8.00000	−0.310929
$663$	0	0
$664$	−6.00000	−0.232845
$665$	0	0
$666$	0	0
$667$	18.0000	0.696963
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	1.00000	0.0385186
$675$	0	0
$676$	36.0000	1.38462
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	0	0
$681$	0	0
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	2.00000	0.0762493
$689$	63.0000	2.40011
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	24.0000	0.912343
$693$	0	0
$694$	3.00000	0.113878
$695$	0	0
$696$	0	0
$697$	18.0000	0.681799
$698$	−35.0000	−1.32477
$699$	0	0
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	30.0000	1.12906
$707$	−6.00000	−0.225653
$708$	0	0
$709$	−4.00000	−0.150223	−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000	−0.150223	−0.0751116	+	0.997175i	$0.523931\pi$
$710$	0	0
$711$	0	0
$712$	−15.0000	−0.562149
$713$	24.0000	0.898807
$714$	0	0
$715$	0	0
$716$	9.00000	0.336346
$717$	0	0
$718$	30.0000	1.11959
$719$	−21.0000	−0.783168	−0.391584	−	0.920142i	$-0.628073\pi$
$719$	−21.0000	−0.783168	−0.391584	+	0.920142i	$0.628073\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	18.0000	0.669891
$723$	0	0
$724$	5.00000	0.185824
$725$	0	0
$726$	0	0
$727$	14.0000	0.519231	0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000	0.519231	0.259616	+	0.965712i	$0.416404\pi$
$728$	7.00000	0.259437
$729$	0	0
$730$	0	0
$731$	6.00000	0.221918
$732$	0	0
$733$	23.0000	0.849524	0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000	0.849524	0.424762	+	0.905305i	$0.360358\pi$
$734$	−26.0000	−0.959678
$735$	0	0
$736$	6.00000	0.221163
$737$	0	0
$738$	0	0
$739$	2.00000	0.0735712	0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000	0.0735712	0.0367856	+	0.999323i	$0.488288\pi$
$740$	0	0
$741$	0	0
$742$	9.00000	0.330400
$743$	42.0000	1.54083	0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000	1.54083	0.770415	+	0.637542i	$0.220049\pi$
$744$	0	0
$745$	0	0
$746$	−2.00000	−0.0732252
$747$	0	0
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−3.00000	−0.109399
$753$	0	0
$754$	−21.0000	−0.764775
$755$	0	0
$756$	0	0
$757$	−4.00000	−0.145382	−0.0726912	−	0.997354i	$-0.523159\pi$
$757$	−4.00000	−0.145382	−0.0726912	+	0.997354i	$0.523159\pi$
$758$	−14.0000	−0.508503
$759$	0	0
$760$	0	0
$761$	−51.0000	−1.84875	−0.924374	−	0.381487i	$-0.875412\pi$
$761$	−51.0000	−1.84875	−0.924374	+	0.381487i	$0.875412\pi$
$762$	0	0
$763$	14.0000	0.506834
$764$	−12.0000	−0.434145
$765$	0	0
$766$	24.0000	0.867155
$767$	−42.0000	−1.51653
$768$	0	0
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	0	0
$771$	0	0
$772$	−19.0000	−0.683825
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	0	0
$775$	0	0
$776$	4.00000	0.143592
$777$	0	0
$778$	−27.0000	−0.967997
$779$	−6.00000	−0.214972
$780$	0	0
$781$	0	0
$782$	18.0000	0.643679
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	3.00000	0.106871
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	49.0000	1.74004
$794$	−11.0000	−0.390375
$795$	0	0
$796$	−10.0000	−0.354441
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	−9.00000	−0.318397
$800$	0	0
$801$	0	0
$802$	−24.0000	−0.847469
$803$	0	0
$804$	0	0
$805$	0	0
$806$	−28.0000	−0.986258
$807$	0	0
$808$	6.00000	0.211079
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−2.00000	−0.0699711
$818$	−8.00000	−0.279713
$819$	0	0
$820$	0	0
$821$	27.0000	0.942306	0.471153	−	0.882051i	$-0.343838\pi$
$821$	27.0000	0.942306	0.471153	+	0.882051i	$0.343838\pi$
$822$	0	0
$823$	20.0000	0.697156	0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000	0.697156	0.348578	+	0.937280i	$0.386665\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	−6.00000	−0.208767
$827$	33.0000	1.14752	0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000	1.14752	0.573761	+	0.819023i	$0.305484\pi$
$828$	0	0
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	0	0
$831$	0	0
$832$	−7.00000	−0.242681
$833$	3.00000	0.103944
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−27.0000	−0.932144	−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	10.0000	0.344623
$843$	0	0
$844$	2.00000	0.0688428
$845$	0	0
$846$	0	0
$847$	−11.0000	−0.377964
$848$	−9.00000	−0.309061
$849$	0	0
$850$	0	0
$851$	−12.0000	−0.411355
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	7.00000	0.239535
$855$	0	0
$856$	−12.0000	−0.410152
$857$	−27.0000	−0.922302	−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000	−0.922302	−0.461151	+	0.887322i	$0.652563\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	0	0
$865$	0	0
$866$	−32.0000	−1.08740
$867$	0	0
$868$	−4.00000	−0.135769
$869$	0	0
$870$	0	0
$871$	28.0000	0.948744
$872$	−14.0000	−0.474100
$873$	0	0
$874$	−6.00000	−0.202953
$875$	0	0
$876$	0	0
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	22.0000	0.742464
$879$	0	0
$880$	0	0
$881$	45.0000	1.51609	0.758044	−	0.652203i	$-0.226155\pi$
$881$	45.0000	1.51609	0.758044	+	0.652203i	$0.226155\pi$
$882$	0	0
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	−21.0000	−0.706306
$885$	0	0
$886$	21.0000	0.705509
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	−7.00000	−0.234772
$890$	0	0
$891$	0	0
$892$	8.00000	0.267860
$893$	3.00000	0.100391
$894$	0	0
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	12.0000	0.400445
$899$	12.0000	0.400222
$900$	0	0
$901$	−27.0000	−0.899500
$902$	0	0
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	0	0
$913$	0	0
$914$	37.0000	1.22385
$915$	0	0
$916$	5.00000	0.165205
$917$	18.0000	0.594412
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	0	0
$921$	0	0
$922$	6.00000	0.197599
$923$	−84.0000	−2.76489
$924$	0	0
$925$	0	0
$926$	31.0000	1.01872
$927$	0	0
$928$	3.00000	0.0984798
$929$	9.00000	0.295280	0.147640	−	0.989041i	$-0.452832\pi$
$929$	9.00000	0.295280	0.147640	+	0.989041i	$0.452832\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	−12.0000	−0.393073
$933$	0	0
$934$	−12.0000	−0.392652
$935$	0	0
$936$	0	0
$937$	−16.0000	−0.522697	−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000	−0.522697	−0.261349	+	0.965244i	$0.584167\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−36.0000	−1.17232
$944$	6.00000	0.195283
$945$	0	0
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	0	0
$949$	−14.0000	−0.454459
$950$	0	0
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	0	0
$955$	0	0
$956$	30.0000	0.970269
$957$	0	0
$958$	−9.00000	−0.290777
$959$	6.00000	0.193750
$960$	0	0
$961$	−15.0000	−0.483871
$962$	14.0000	0.451378
$963$	0	0
$964$	20.0000	0.644157
$965$	0	0
$966$	0	0
$967$	59.0000	1.89731	0.948656	−	0.316310i	$-0.102444\pi$
$967$	59.0000	1.89731	0.948656	+	0.316310i	$0.102444\pi$
$968$	11.0000	0.353553
$969$	0	0
$970$	0	0
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−7.00000	−0.224065
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	39.0000	1.24454
$983$	57.0000	1.81802	0.909009	−	0.416777i	$-0.136840\pi$
$983$	57.0000	1.81802	0.909009	+	0.416777i	$0.136840\pi$
$984$	0	0
$985$	0	0
$986$	9.00000	0.286618
$987$	0	0
$988$	7.00000	0.222700
$989$	−12.0000	−0.381578
$990$	0	0
$991$	−49.0000	−1.55654	−0.778268	−	0.627932i	$-0.783902\pi$
$991$	−49.0000	−1.55654	−0.778268	+	0.627932i	$0.783902\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	−12.0000	−0.380617
$995$	0	0
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−2.00000	−0.0633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.bl.1.1	yes	1
3.2	odd	2		9450.2.a.dl.1.1	yes	1
5.4	even	2		9450.2.a.co.1.1	yes	1
15.14	odd	2		9450.2.a.p.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9450.2.a.p.1.1	✓	1	15.14	odd	2
9450.2.a.bl.1.1	yes	1	1.1	even	1	trivial
9450.2.a.co.1.1	yes	1	5.4	even	2
9450.2.a.dl.1.1	yes	1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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