LMFDB - Embedded newform 7350.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7350,2,Mod(1,7350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7350, 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("7350.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7350.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:	$58.6900454856$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1050)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +6.00000 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -6.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} +3.00000 q^{29} -5.00000 q^{31} -1.00000 q^{32} -6.00000 q^{33} +3.00000 q^{34} +1.00000 q^{36} -10.0000 q^{37} -4.00000 q^{38} -1.00000 q^{39} -9.00000 q^{41} -1.00000 q^{43} +6.00000 q^{44} +3.00000 q^{46} -1.00000 q^{48} +3.00000 q^{51} +1.00000 q^{52} +9.00000 q^{53} +1.00000 q^{54} -4.00000 q^{57} -3.00000 q^{58} -9.00000 q^{59} -11.0000 q^{61} +5.00000 q^{62} +1.00000 q^{64} +6.00000 q^{66} -4.00000 q^{67} -3.00000 q^{68} +3.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} +10.0000 q^{73} +10.0000 q^{74} +4.00000 q^{76} +1.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} -9.00000 q^{83} +1.00000 q^{86} -3.00000 q^{87} -6.00000 q^{88} +6.00000 q^{89} -3.00000 q^{92} +5.00000 q^{93} +1.00000 q^{96} -14.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	0	0
$22$	−6.00000	−1.27920
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	−1.00000	−0.176777
$33$	−6.00000	−1.04447
$34$	3.00000	0.514496
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−4.00000	−0.648886
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	3.00000	0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	0	0
$51$	3.00000	0.420084
$52$	1.00000	0.138675
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	−3.00000	−0.393919
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	5.00000	0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	−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
$69$	3.00000	0.361158
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	4.00000	0.458831
$77$	0	0
$78$	1.00000	0.113228
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.00000	0.993884
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	0.107833
$87$	−3.00000	−0.321634
$88$	−6.00000	−0.639602
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	5.00000	0.518476
$94$	0	0
$95$	0	0
$96$	1.00000	0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	0	0
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	−3.00000	−0.297044
$103$	−17.0000	−1.67506	−0.837530	−	0.546392i	$-0.816001\pi$
$103$	−17.0000	−1.67506	−0.837530	+	0.546392i	$0.816001\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−9.00000	−0.874157
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	−1.00000	−0.0962250
$109$	8.00000	0.766261	0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000	0.766261	0.383131	+	0.923694i	$0.374846\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	3.00000	0.278543
$117$	1.00000	0.0924500
$118$	9.00000	0.828517
$119$	0	0
$120$	0	0
$121$	25.0000	2.27273
$122$	11.0000	0.995893
$123$	9.00000	0.811503
$124$	−5.00000	−0.449013
$125$	0	0
$126$	0	0
$127$	−10.0000	−0.887357	−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000	−0.887357	−0.443678	+	0.896186i	$0.646327\pi$
$128$	−1.00000	−0.0883883
$129$	1.00000	0.0880451
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−6.00000	−0.522233
$133$	0	0
$134$	4.00000	0.345547
$135$	0	0
$136$	3.00000	0.257248
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	−3.00000	−0.255377
$139$	16.0000	1.35710	0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000	1.35710	0.678551	+	0.734553i	$0.262608\pi$
$140$	0	0
$141$	0	0
$142$	12.0000	1.00702
$143$	6.00000	0.501745
$144$	1.00000	0.0833333
$145$	0	0
$146$	−10.0000	−0.827606
$147$	0	0
$148$	−10.0000	−0.821995
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−4.00000	−0.324443
$153$	−3.00000	−0.242536
$154$	0	0
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	10.0000	0.795557
$159$	−9.00000	−0.713746
$160$	0	0
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	5.00000	0.391630	0.195815	−	0.980641i	$-0.437265\pi$
$163$	5.00000	0.391630	0.195815	+	0.980641i	$0.437265\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	9.00000	0.698535
$167$	−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
$169$	−12.0000	−0.923077
$170$	0	0
$171$	4.00000	0.305888
$172$	−1.00000	−0.0762493
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	3.00000	0.227429
$175$	0	0
$176$	6.00000	0.452267
$177$	9.00000	0.676481
$178$	−6.00000	−0.449719
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	11.0000	0.813143
$184$	3.00000	0.221163
$185$	0	0
$186$	−5.00000	−0.366618
$187$	−18.0000	−1.31629
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	0	0
$197$	−15.0000	−1.06871	−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000	−1.06871	−0.534353	+	0.845262i	$0.679445\pi$
$198$	−6.00000	−0.426401
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	−12.0000	−0.844317
$203$	0	0
$204$	3.00000	0.210042
$205$	0	0
$206$	17.0000	1.18445
$207$	−3.00000	−0.208514
$208$	1.00000	0.0693375
$209$	24.0000	1.66011
$210$	0	0
$211$	−25.0000	−1.72107	−0.860535	−	0.509390i	$-0.829871\pi$
$211$	−25.0000	−1.72107	−0.860535	+	0.509390i	$0.829871\pi$
$212$	9.00000	0.618123
$213$	12.0000	0.822226
$214$	−18.0000	−1.23045
$215$	0	0
$216$	1.00000	0.0680414
$217$	0	0
$218$	−8.00000	−0.541828
$219$	−10.0000	−0.675737
$220$	0	0
$221$	−3.00000	−0.201802
$222$	−10.0000	−0.671156
$223$	19.0000	1.27233	0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000	1.27233	0.636167	+	0.771551i	$0.280519\pi$
$224$	0	0
$225$	0	0
$226$	6.00000	0.399114
$227$	−3.00000	−0.199117	−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000	−0.199117	−0.0995585	+	0.995032i	$0.531743\pi$
$228$	−4.00000	−0.264906
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	0	0
$231$	0	0
$232$	−3.00000	−0.196960
$233$	12.0000	0.786146	0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000	0.786146	0.393073	+	0.919507i	$0.371412\pi$
$234$	−1.00000	−0.0653720
$235$	0	0
$236$	−9.00000	−0.585850
$237$	10.0000	0.649570
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−25.0000	−1.60706
$243$	−1.00000	−0.0641500
$244$	−11.0000	−0.704203
$245$	0	0
$246$	−9.00000	−0.573819
$247$	4.00000	0.254514
$248$	5.00000	0.317500
$249$	9.00000	0.570352
$250$	0	0
$251$	27.0000	1.70422	0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000	1.70422	0.852112	+	0.523359i	$0.175321\pi$
$252$	0	0
$253$	−18.0000	−1.13165
$254$	10.0000	0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	−15.0000	−0.935674	−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000	−0.935674	−0.467837	+	0.883815i	$0.654967\pi$
$258$	−1.00000	−0.0622573
$259$	0	0
$260$	0	0
$261$	3.00000	0.185695
$262$	0	0
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	6.00000	0.369274
$265$	0	0
$266$	0	0
$267$	−6.00000	−0.367194
$268$	−4.00000	−0.244339
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	0	0
$275$	0	0
$276$	3.00000	0.180579
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−16.0000	−0.959616
$279$	−5.00000	−0.299342
$280$	0	0
$281$	−24.0000	−1.43172	−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000	−1.43172	−0.715860	+	0.698244i	$0.753965\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−6.00000	−0.354787
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	0	0
$291$	14.0000	0.820695
$292$	10.0000	0.585206
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	10.0000	0.581238
$297$	−6.00000	−0.348155
$298$	9.00000	0.521356
$299$	−3.00000	−0.173494
$300$	0	0
$301$	0	0
$302$	−2.00000	−0.115087
$303$	−12.0000	−0.689382
$304$	4.00000	0.229416
$305$	0	0
$306$	3.00000	0.171499
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	0	0
$309$	17.0000	0.967096
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	1.00000	0.0566139
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−27.0000	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	9.00000	0.504695
$319$	18.0000	1.00781
$320$	0	0
$321$	−18.0000	−1.00466
$322$	0	0
$323$	−12.0000	−0.667698
$324$	1.00000	0.0555556
$325$	0	0
$326$	−5.00000	−0.276924
$327$	−8.00000	−0.442401
$328$	9.00000	0.496942
$329$	0	0
$330$	0	0
$331$	−19.0000	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$332$	−9.00000	−0.493939
$333$	−10.0000	−0.547997
$334$	18.0000	0.984916
$335$	0	0
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	12.0000	0.652714
$339$	6.00000	0.325875
$340$	0	0
$341$	−30.0000	−1.62459
$342$	−4.00000	−0.216295
$343$	0	0
$344$	1.00000	0.0539164
$345$	0	0
$346$	−12.0000	−0.645124
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	−3.00000	−0.160817
$349$	−17.0000	−0.909989	−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000	−0.909989	−0.454995	+	0.890494i	$0.650359\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−6.00000	−0.319801
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	−9.00000	−0.478345
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	−18.0000	−0.951330
$359$	−3.00000	−0.158334	−0.0791670	−	0.996861i	$-0.525226\pi$
$359$	−3.00000	−0.158334	−0.0791670	+	0.996861i	$0.525226\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	2.00000	0.105118
$363$	−25.0000	−1.31216
$364$	0	0
$365$	0	0
$366$	−11.0000	−0.574979
$367$	37.0000	1.93138	0.965692	−	0.259690i	$-0.0836203\pi$
$367$	37.0000	1.93138	0.965692	+	0.259690i	$0.0836203\pi$
$368$	−3.00000	−0.156386
$369$	−9.00000	−0.468521
$370$	0	0
$371$	0	0
$372$	5.00000	0.259238
$373$	8.00000	0.414224	0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000	0.414224	0.207112	+	0.978317i	$0.433593\pi$
$374$	18.0000	0.930758
$375$	0	0
$376$	0	0
$377$	3.00000	0.154508
$378$	0	0
$379$	35.0000	1.79783	0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000	1.79783	0.898915	+	0.438124i	$0.144357\pi$
$380$	0	0
$381$	10.0000	0.512316
$382$	15.0000	0.767467
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−1.00000	−0.0508329
$388$	−14.0000	−0.710742
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	9.00000	0.455150
$392$	0	0
$393$	0	0
$394$	15.0000	0.755689
$395$	0	0
$396$	6.00000	0.301511
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	0	0
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	−4.00000	−0.199502
$403$	−5.00000	−0.249068
$404$	12.0000	0.597022
$405$	0	0
$406$	0	0
$407$	−60.0000	−2.97409
$408$	−3.00000	−0.148522
$409$	−38.0000	−1.87898	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−38.0000	−1.87898	−0.939490	+	0.342578i	$0.888700\pi$
$410$	0	0
$411$	0	0
$412$	−17.0000	−0.837530
$413$	0	0
$414$	3.00000	0.147442
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−16.0000	−0.783523
$418$	−24.0000	−1.17388
$419$	21.0000	1.02592	0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000	1.02592	0.512959	+	0.858413i	$0.328549\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	25.0000	1.21698
$423$	0	0
$424$	−9.00000	−0.437079
$425$	0	0
$426$	−12.0000	−0.581402
$427$	0	0
$428$	18.0000	0.870063
$429$	−6.00000	−0.289683
$430$	0	0
$431$	−15.0000	−0.722525	−0.361262	−	0.932464i	$-0.617654\pi$
$431$	−15.0000	−0.722525	−0.361262	+	0.932464i	$0.617654\pi$
$432$	−1.00000	−0.0481125
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	0	0
$435$	0	0
$436$	8.00000	0.383131
$437$	−12.0000	−0.574038
$438$	10.0000	0.477818
$439$	−41.0000	−1.95682	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−41.0000	−1.95682	−0.978412	+	0.206666i	$0.933739\pi$
$440$	0	0
$441$	0	0
$442$	3.00000	0.142695
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	10.0000	0.474579
$445$	0	0
$446$	−19.0000	−0.899676
$447$	9.00000	0.425685
$448$	0	0
$449$	24.0000	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$450$	0	0
$451$	−54.0000	−2.54276
$452$	−6.00000	−0.282216
$453$	−2.00000	−0.0939682
$454$	3.00000	0.140797
$455$	0	0
$456$	4.00000	0.187317
$457$	−25.0000	−1.16945	−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000	−1.16945	−0.584725	+	0.811231i	$0.698798\pi$
$458$	−22.0000	−1.02799
$459$	3.00000	0.140028
$460$	0	0
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−12.0000	−0.555889
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	0	0
$471$	−10.0000	−0.460776
$472$	9.00000	0.414259
$473$	−6.00000	−0.275880
$474$	−10.0000	−0.459315
$475$	0	0
$476$	0	0
$477$	9.00000	0.412082
$478$	0	0
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	−10.0000	−0.455961
$482$	2.00000	0.0910975
$483$	0	0
$484$	25.0000	1.13636
$485$	0	0
$486$	1.00000	0.0453609
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	11.0000	0.497947
$489$	−5.00000	−0.226108
$490$	0	0
$491$	42.0000	1.89543	0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000	1.89543	0.947717	+	0.319113i	$0.103385\pi$
$492$	9.00000	0.405751
$493$	−9.00000	−0.405340
$494$	−4.00000	−0.179969
$495$	0	0
$496$	−5.00000	−0.224507
$497$	0	0
$498$	−9.00000	−0.403300
$499$	−19.0000	−0.850557	−0.425278	−	0.905063i	$-0.639824\pi$
$499$	−19.0000	−0.850557	−0.425278	+	0.905063i	$0.639824\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	−27.0000	−1.20507
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	0	0
$505$	0	0
$506$	18.0000	0.800198
$507$	12.0000	0.532939
$508$	−10.0000	−0.443678
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	15.0000	0.661622
$515$	0	0
$516$	1.00000	0.0440225
$517$	0	0
$518$	0	0
$519$	−12.0000	−0.526742
$520$	0	0
$521$	21.0000	0.920027	0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000	0.920027	0.460013	+	0.887912i	$0.347845\pi$
$522$	−3.00000	−0.131306
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	0	0
$525$	0	0
$526$	−9.00000	−0.392419
$527$	15.0000	0.653410
$528$	−6.00000	−0.261116
$529$	−14.0000	−0.608696
$530$	0	0
$531$	−9.00000	−0.390567
$532$	0	0
$533$	−9.00000	−0.389833
$534$	6.00000	0.259645
$535$	0	0
$536$	4.00000	0.172774
$537$	−18.0000	−0.776757
$538$	−18.0000	−0.776035
$539$	0	0
$540$	0	0
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	20.0000	0.859074
$543$	2.00000	0.0858282
$544$	3.00000	0.128624
$545$	0	0
$546$	0	0
$547$	17.0000	0.726868	0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000	0.726868	0.363434	+	0.931620i	$0.381604\pi$
$548$	0	0
$549$	−11.0000	−0.469469
$550$	0	0
$551$	12.0000	0.511217
$552$	−3.00000	−0.127688
$553$	0	0
$554$	10.0000	0.424859
$555$	0	0
$556$	16.0000	0.678551
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	5.00000	0.211667
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	18.0000	0.759961
$562$	24.0000	1.01238
$563$	−21.0000	−0.885044	−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000	−0.885044	−0.442522	+	0.896758i	$0.645916\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	12.0000	0.503509
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−13.0000	−0.544033	−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000	−0.544033	−0.272017	+	0.962293i	$0.587691\pi$
$572$	6.00000	0.250873
$573$	15.0000	0.626634
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	8.00000	0.332756
$579$	22.0000	0.914289
$580$	0	0
$581$	0	0
$582$	−14.0000	−0.580319
$583$	54.0000	2.23645
$584$	−10.0000	−0.413803
$585$	0	0
$586$	0	0
$587$	−33.0000	−1.36206	−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000	−1.36206	−0.681028	+	0.732257i	$0.738467\pi$
$588$	0	0
$589$	−20.0000	−0.824086
$590$	0	0
$591$	15.0000	0.617018
$592$	−10.0000	−0.410997
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	6.00000	0.246183
$595$	0	0
$596$	−9.00000	−0.368654
$597$	8.00000	0.327418
$598$	3.00000	0.122679
$599$	9.00000	0.367730	0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000	0.367730	0.183865	+	0.982952i	$0.441139\pi$
$600$	0	0
$601$	4.00000	0.163163	0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000	0.163163	0.0815817	+	0.996667i	$0.474003\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	2.00000	0.0813788
$605$	0	0
$606$	12.0000	0.487467
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−3.00000	−0.121268
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−17.0000	−0.683840
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	0	0
$621$	3.00000	0.120386
$622$	−18.0000	−0.721734
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	0	0
$626$	−10.0000	−0.399680
$627$	−24.0000	−0.958468
$628$	10.0000	0.399043
$629$	30.0000	1.19618
$630$	0	0
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	10.0000	0.397779
$633$	25.0000	0.993661
$634$	27.0000	1.07231
$635$	0	0
$636$	−9.00000	−0.356873
$637$	0	0
$638$	−18.0000	−0.712627
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	18.0000	0.710403
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	−1.00000	−0.0392837
$649$	−54.0000	−2.11969
$650$	0	0
$651$	0	0
$652$	5.00000	0.195815
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	8.00000	0.312825
$655$	0	0
$656$	−9.00000	−0.351391
$657$	10.0000	0.390137
$658$	0	0
$659$	42.0000	1.63609	0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000	1.63609	0.818044	+	0.575156i	$0.195059\pi$
$660$	0	0
$661$	−38.0000	−1.47803	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000	−1.47803	−0.739014	+	0.673690i	$0.764708\pi$
$662$	19.0000	0.738456
$663$	3.00000	0.116510
$664$	9.00000	0.349268
$665$	0	0
$666$	10.0000	0.387492
$667$	−9.00000	−0.348481
$668$	−18.0000	−0.696441
$669$	−19.0000	−0.734582
$670$	0	0
$671$	−66.0000	−2.54790
$672$	0	0
$673$	−37.0000	−1.42625	−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000	−1.42625	−0.713123	+	0.701039i	$0.752720\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	−12.0000	−0.461538
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	−6.00000	−0.230429
$679$	0	0
$680$	0	0
$681$	3.00000	0.114960
$682$	30.0000	1.14876
$683$	18.0000	0.688751	0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000	0.688751	0.344375	+	0.938832i	$0.388091\pi$
$684$	4.00000	0.152944
$685$	0	0
$686$	0	0
$687$	−22.0000	−0.839352
$688$	−1.00000	−0.0381246
$689$	9.00000	0.342873
$690$	0	0
$691$	34.0000	1.29342	0.646710	−	0.762736i	$-0.276144\pi$
$691$	34.0000	1.29342	0.646710	+	0.762736i	$0.276144\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	−18.0000	−0.683271
$695$	0	0
$696$	3.00000	0.113715
$697$	27.0000	1.02270
$698$	17.0000	0.643459
$699$	−12.0000	−0.453882
$700$	0	0
$701$	3.00000	0.113308	0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000	0.113308	0.0566542	+	0.998394i	$0.481957\pi$
$702$	1.00000	0.0377426
$703$	−40.0000	−1.50863
$704$	6.00000	0.226134
$705$	0	0
$706$	−30.0000	−1.12906
$707$	0	0
$708$	9.00000	0.338241
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	0	0
$711$	−10.0000	−0.375029
$712$	−6.00000	−0.224860
$713$	15.0000	0.561754
$714$	0	0
$715$	0	0
$716$	18.0000	0.672692
$717$	0	0
$718$	3.00000	0.111959
$719$	−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
$721$	0	0
$722$	3.00000	0.111648
$723$	2.00000	0.0743808
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	25.0000	0.927837
$727$	7.00000	0.259616	0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000	0.259616	0.129808	+	0.991539i	$0.458564\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.00000	0.110959
$732$	11.0000	0.406572
$733$	−29.0000	−1.07114	−0.535570	−	0.844491i	$-0.679903\pi$
$733$	−29.0000	−1.07114	−0.535570	+	0.844491i	$0.679903\pi$
$734$	−37.0000	−1.36569
$735$	0	0
$736$	3.00000	0.110581
$737$	−24.0000	−0.884051
$738$	9.00000	0.331295
$739$	−37.0000	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	−37.0000	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$740$	0	0
$741$	−4.00000	−0.146944
$742$	0	0
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	−5.00000	−0.183309
$745$	0	0
$746$	−8.00000	−0.292901
$747$	−9.00000	−0.329293
$748$	−18.0000	−0.658145
$749$	0	0
$750$	0	0
$751$	8.00000	0.291924	0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000	0.291924	0.145962	+	0.989290i	$0.453372\pi$
$752$	0	0
$753$	−27.0000	−0.983935
$754$	−3.00000	−0.109254
$755$	0	0
$756$	0	0
$757$	14.0000	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$758$	−35.0000	−1.27126
$759$	18.0000	0.653359
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	−10.0000	−0.362262
$763$	0	0
$764$	−15.0000	−0.542681
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−9.00000	−0.324971
$768$	−1.00000	−0.0360844
$769$	4.00000	0.144244	0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000	0.144244	0.0721218	+	0.997396i	$0.477023\pi$
$770$	0	0
$771$	15.0000	0.540212
$772$	−22.0000	−0.791797
$773$	48.0000	1.72644	0.863220	−	0.504828i	$-0.168444\pi$
$773$	48.0000	1.72644	0.863220	+	0.504828i	$0.168444\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	6.00000	0.215110
$779$	−36.0000	−1.28983
$780$	0	0
$781$	−72.0000	−2.57636
$782$	−9.00000	−0.321839
$783$	−3.00000	−0.107211
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	−15.0000	−0.534353
$789$	−9.00000	−0.320408
$790$	0	0
$791$	0	0
$792$	−6.00000	−0.213201
$793$	−11.0000	−0.390621
$794$	29.0000	1.02917
$795$	0	0
$796$	−8.00000	−0.283552
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	6.00000	0.212000
$802$	12.0000	0.423735
$803$	60.0000	2.11735
$804$	4.00000	0.141069
$805$	0	0
$806$	5.00000	0.176117
$807$	−18.0000	−0.633630
$808$	−12.0000	−0.422159
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	0	0
$811$	34.0000	1.19390	0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000	1.19390	0.596951	+	0.802278i	$0.296379\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	60.0000	2.10300
$815$	0	0
$816$	3.00000	0.105021
$817$	−4.00000	−0.139942
$818$	38.0000	1.32864
$819$	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
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	17.0000	0.592223
$825$	0	0
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−3.00000	−0.104257
$829$	−29.0000	−1.00721	−0.503606	−	0.863934i	$-0.667994\pi$
$829$	−29.0000	−1.00721	−0.503606	+	0.863934i	$0.667994\pi$
$830$	0	0
$831$	10.0000	0.346896
$832$	1.00000	0.0346688
$833$	0	0
$834$	16.0000	0.554035
$835$	0	0
$836$	24.0000	0.830057
$837$	5.00000	0.172825
$838$	−21.0000	−0.725433
$839$	−36.0000	−1.24286	−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000	−1.24286	−0.621429	+	0.783470i	$0.713448\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	34.0000	1.17172
$843$	24.0000	0.826604
$844$	−25.0000	−0.860535
$845$	0	0
$846$	0	0
$847$	0	0
$848$	9.00000	0.309061
$849$	−4.00000	−0.137280
$850$	0	0
$851$	30.0000	1.02839
$852$	12.0000	0.411113
$853$	19.0000	0.650548	0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000	0.650548	0.325274	+	0.945620i	$0.394544\pi$
$854$	0	0
$855$	0	0
$856$	−18.0000	−0.615227
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	6.00000	0.204837
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	0	0
$861$	0	0
$862$	15.0000	0.510902
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	38.0000	1.29129
$867$	8.00000	0.271694
$868$	0	0
$869$	−60.0000	−2.03536
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−8.00000	−0.270914
$873$	−14.0000	−0.473828
$874$	12.0000	0.405906
$875$	0	0
$876$	−10.0000	−0.337869
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	41.0000	1.38368
$879$	0	0
$880$	0	0
$881$	−33.0000	−1.11180	−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000	−1.11180	−0.555899	+	0.831250i	$0.687626\pi$
$882$	0	0
$883$	5.00000	0.168263	0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000	0.168263	0.0841317	+	0.996455i	$0.473188\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	−24.0000	−0.806296
$887$	−54.0000	−1.81314	−0.906571	−	0.422053i	$-0.861310\pi$
$887$	−54.0000	−1.81314	−0.906571	+	0.422053i	$0.861310\pi$
$888$	−10.0000	−0.335578
$889$	0	0
$890$	0	0
$891$	6.00000	0.201008
$892$	19.0000	0.636167
$893$	0	0
$894$	−9.00000	−0.301005
$895$	0	0
$896$	0	0
$897$	3.00000	0.100167
$898$	−24.0000	−0.800890
$899$	−15.0000	−0.500278
$900$	0	0
$901$	−27.0000	−0.899500
$902$	54.0000	1.79800
$903$	0	0
$904$	6.00000	0.199557
$905$	0	0
$906$	2.00000	0.0664455
$907$	53.0000	1.75984	0.879918	−	0.475125i	$-0.157597\pi$
$907$	53.0000	1.75984	0.879918	+	0.475125i	$0.157597\pi$
$908$	−3.00000	−0.0995585
$909$	12.0000	0.398015
$910$	0	0
$911$	15.0000	0.496972	0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000	0.496972	0.248486	+	0.968635i	$0.420067\pi$
$912$	−4.00000	−0.132453
$913$	−54.0000	−1.78714
$914$	25.0000	0.826927
$915$	0	0
$916$	22.0000	0.726900
$917$	0	0
$918$	−3.00000	−0.0990148
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	2.00000	0.0659022
$922$	12.0000	0.395199
$923$	−12.0000	−0.394985
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	−17.0000	−0.558353
$928$	−3.00000	−0.0984798
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	0	0
$931$	0	0
$932$	12.0000	0.393073
$933$	−18.0000	−0.589294
$934$	−3.00000	−0.0981630
$935$	0	0
$936$	−1.00000	−0.0326860
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	0	0
$939$	−10.0000	−0.326338
$940$	0	0
$941$	−24.0000	−0.782378	−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000	−0.782378	−0.391189	+	0.920310i	$0.627936\pi$
$942$	10.0000	0.325818
$943$	27.0000	0.879241
$944$	−9.00000	−0.292925
$945$	0	0
$946$	6.00000	0.195077
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	10.0000	0.324785
$949$	10.0000	0.324614
$950$	0	0
$951$	27.0000	0.875535
$952$	0	0
$953$	24.0000	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$954$	−9.00000	−0.291386
$955$	0	0
$956$	0	0
$957$	−18.0000	−0.581857
$958$	24.0000	0.775405
$959$	0	0
$960$	0	0
$961$	−6.00000	−0.193548
$962$	10.0000	0.322413
$963$	18.0000	0.580042
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	0	0
$967$	−28.0000	−0.900419	−0.450210	−	0.892923i	$-0.648651\pi$
$967$	−28.0000	−0.900419	−0.450210	+	0.892923i	$0.648651\pi$
$968$	−25.0000	−0.803530
$969$	12.0000	0.385496
$970$	0	0
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−11.0000	−0.352101
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	5.00000	0.159882
$979$	36.0000	1.15056
$980$	0	0
$981$	8.00000	0.255420
$982$	−42.0000	−1.34027
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	−9.00000	−0.286910
$985$	0	0
$986$	9.00000	0.286618
$987$	0	0
$988$	4.00000	0.127257
$989$	3.00000	0.0953945
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	5.00000	0.158750
$993$	19.0000	0.602947
$994$	0	0
$995$	0	0
$996$	9.00000	0.285176
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	19.0000	0.601434
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.r.1.1		1
5.4	even	2		7350.2.a.cz.1.1		1
7.6	odd	2		1050.2.a.j.1.1	✓	1
21.20	even	2		3150.2.a.bg.1.1		1
28.27	even	2		8400.2.a.a.1.1		1
35.13	even	4		1050.2.g.e.799.2		2
35.27	even	4		1050.2.g.e.799.1		2
35.34	odd	2		1050.2.a.l.1.1	yes	1
105.62	odd	4		3150.2.g.a.2899.2		2
105.83	odd	4		3150.2.g.a.2899.1		2
105.104	even	2		3150.2.a.a.1.1		1
140.139	even	2		8400.2.a.ci.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.a.j.1.1	✓	1	7.6	odd	2
1050.2.a.l.1.1	yes	1	35.34	odd	2
1050.2.g.e.799.1		2	35.27	even	4
1050.2.g.e.799.2		2	35.13	even	4
3150.2.a.a.1.1		1	105.104	even	2
3150.2.a.bg.1.1		1	21.20	even	2
3150.2.g.a.2899.1		2	105.83	odd	4
3150.2.g.a.2899.2		2	105.62	odd	4
7350.2.a.r.1.1		1	1.1	even	1	trivial
7350.2.a.cz.1.1		1	5.4	even	2
8400.2.a.a.1.1		1	28.27	even	2
8400.2.a.ci.1.1		1	140.139	even	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:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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