LMFDB - Embedded newform 7350.2.a.bp.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:	$0$
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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -4.00000 q^{22} -2.00000 q^{23} -1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} +4.00000 q^{29} +1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +3.00000 q^{37} -1.00000 q^{38} +1.00000 q^{39} -12.0000 q^{41} +8.00000 q^{43} -4.00000 q^{44} -2.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} +2.00000 q^{51} -1.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +1.00000 q^{57} +4.00000 q^{58} -6.00000 q^{59} +13.0000 q^{61} +1.00000 q^{64} +4.00000 q^{66} +3.00000 q^{67} -2.00000 q^{68} +2.00000 q^{69} +16.0000 q^{71} +1.00000 q^{72} +11.0000 q^{73} +3.00000 q^{74} -1.00000 q^{76} +1.00000 q^{78} +13.0000 q^{79} +1.00000 q^{81} -12.0000 q^{82} +6.00000 q^{83} +8.00000 q^{86} -4.00000 q^{87} -4.00000 q^{88} +2.00000 q^{89} -2.00000 q^{92} +6.00000 q^{94} -1.00000 q^{96} -17.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	−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
$22$	−4.00000	−0.852803
$23$	−2.00000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	4.00000	0.696311
$34$	−2.00000	−0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−1.00000	−0.162221
$39$	1.00000	0.160128
$40$	0	0
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	−2.00000	−0.294884
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	0	0
$51$	2.00000	0.280056
$52$	−1.00000	−0.138675
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	1.00000	0.132453
$58$	4.00000	0.525226
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−2.00000	−0.242536
$69$	2.00000	0.240772
$70$	0	0
$71$	16.0000	1.89885	0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000	1.89885	0.949425	+	0.313993i	$0.101667\pi$
$72$	1.00000	0.117851
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	1.00000	0.113228
$79$	13.0000	1.46261	0.731307	−	0.682048i	$-0.238911\pi$
$79$	13.0000	1.46261	0.731307	+	0.682048i	$0.238911\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−12.0000	−1.32518
$83$	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
$86$	8.00000	0.862662
$87$	−4.00000	−0.428845
$88$	−4.00000	−0.426401
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	0	0
$92$	−2.00000	−0.208514
$93$	0	0
$94$	6.00000	0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	2.00000	0.198030
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	2.00000	0.194257
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−1.00000	−0.0962250
$109$	−19.0000	−1.81987	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−19.0000	−1.81987	−0.909935	+	0.414751i	$0.863869\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	0	0
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	4.00000	0.371391
$117$	−1.00000	−0.0924500
$118$	−6.00000	−0.552345
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	13.0000	1.17696
$123$	12.0000	1.08200
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−1.00000	−0.0887357	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000	−0.0887357	−0.0443678	+	0.999015i	$0.514127\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	0	0
$131$	−2.00000	−0.174741	−0.0873704	−	0.996176i	$-0.527846\pi$
$131$	−2.00000	−0.174741	−0.0873704	+	0.996176i	$0.527846\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	3.00000	0.259161
$135$	0	0
$136$	−2.00000	−0.171499
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	2.00000	0.170251
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	16.0000	1.34269
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	0	0
$146$	11.0000	0.910366
$147$	0	0
$148$	3.00000	0.246598
$149$	−16.0000	−1.31077	−0.655386	−	0.755295i	$-0.727494\pi$
$149$	−16.0000	−1.31077	−0.655386	+	0.755295i	$0.727494\pi$
$150$	0	0
$151$	19.0000	1.54620	0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000	1.54620	0.773099	+	0.634285i	$0.218706\pi$
$152$	−1.00000	−0.0811107
$153$	−2.00000	−0.161690
$154$	0	0
$155$	0	0
$156$	1.00000	0.0800641
$157$	21.0000	1.67598	0.837991	−	0.545684i	$-0.183730\pi$
$157$	21.0000	1.67598	0.837991	+	0.545684i	$0.183730\pi$
$158$	13.0000	1.03422
$159$	−2.00000	−0.158610
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	23.0000	1.80150	0.900750	−	0.434339i	$-0.143018\pi$
$163$	23.0000	1.80150	0.900750	+	0.434339i	$0.143018\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	6.00000	0.465690
$167$	−10.0000	−0.773823	−0.386912	−	0.922117i	$-0.626458\pi$
$167$	−10.0000	−0.773823	−0.386912	+	0.922117i	$0.626458\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	8.00000	0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	−4.00000	−0.301511
$177$	6.00000	0.450988
$178$	2.00000	0.149906
$179$	−8.00000	−0.597948	−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000	−0.597948	−0.298974	+	0.954261i	$0.596644\pi$
$180$	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
$183$	−13.0000	−0.960988
$184$	−2.00000	−0.147442
$185$	0	0
$186$	0	0
$187$	8.00000	0.585018
$188$	6.00000	0.437595
$189$	0	0
$190$	0	0
$191$	20.0000	1.44715	0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000	1.44715	0.723575	+	0.690246i	$0.242498\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−17.0000	−1.22053
$195$	0	0
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	−4.00000	−0.284268
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	0	0
$201$	−3.00000	−0.211604
$202$	−12.0000	−0.844317
$203$	0	0
$204$	2.00000	0.140028
$205$	0	0
$206$	−7.00000	−0.487713
$207$	−2.00000	−0.139010
$208$	−1.00000	−0.0693375
$209$	4.00000	0.276686
$210$	0	0
$211$	3.00000	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$211$	3.00000	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$212$	2.00000	0.137361
$213$	−16.0000	−1.09630
$214$	6.00000	0.410152
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−19.0000	−1.28684
$219$	−11.0000	−0.743311
$220$	0	0
$221$	2.00000	0.134535
$222$	−3.00000	−0.201347
$223$	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
$226$	18.0000	1.19734
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	1.00000	0.0662266
$229$	7.00000	0.462573	0.231287	−	0.972886i	$-0.425707\pi$
$229$	7.00000	0.462573	0.231287	+	0.972886i	$0.425707\pi$
$230$	0	0
$231$	0	0
$232$	4.00000	0.262613
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	−1.00000	−0.0653720
$235$	0	0
$236$	−6.00000	−0.390567
$237$	−13.0000	−0.844441
$238$	0	0
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−13.0000	−0.837404	−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000	−0.837404	−0.418702	+	0.908124i	$0.637515\pi$
$242$	5.00000	0.321412
$243$	−1.00000	−0.0641500
$244$	13.0000	0.832240
$245$	0	0
$246$	12.0000	0.765092
$247$	1.00000	0.0636285
$248$	0	0
$249$	−6.00000	−0.380235
$250$	0	0
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−1.00000	−0.0627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	8.00000	0.499026	0.249513	−	0.968371i	$-0.419729\pi$
$257$	8.00000	0.499026	0.249513	+	0.968371i	$0.419729\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	0	0
$261$	4.00000	0.247594
$262$	−2.00000	−0.123560
$263$	32.0000	1.97320	0.986602	−	0.163144i	$-0.0521635\pi$
$263$	32.0000	1.97320	0.986602	+	0.163144i	$0.0521635\pi$
$264$	4.00000	0.246183
$265$	0	0
$266$	0	0
$267$	−2.00000	−0.122398
$268$	3.00000	0.183254
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	10.0000	0.604122
$275$	0	0
$276$	2.00000	0.120386
$277$	1.00000	0.0600842	0.0300421	−	0.999549i	$-0.490436\pi$
$277$	1.00000	0.0600842	0.0300421	+	0.999549i	$0.490436\pi$
$278$	13.0000	0.779688
$279$	0	0
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−6.00000	−0.357295
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	4.00000	0.236525
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	17.0000	0.996558
$292$	11.0000	0.643726
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	0	0
$296$	3.00000	0.174371
$297$	4.00000	0.232104
$298$	−16.0000	−0.926855
$299$	2.00000	0.115663
$300$	0	0
$301$	0	0
$302$	19.0000	1.09333
$303$	12.0000	0.689382
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−2.00000	−0.114332
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	7.00000	0.398216
$310$	0	0
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	1.00000	0.0566139
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	21.0000	1.18510
$315$	0	0
$316$	13.0000	0.731307
$317$	22.0000	1.23564	0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000	1.23564	0.617822	+	0.786318i	$0.288015\pi$
$318$	−2.00000	−0.112154
$319$	−16.0000	−0.895828
$320$	0	0
$321$	−6.00000	−0.334887
$322$	0	0
$323$	2.00000	0.111283
$324$	1.00000	0.0555556
$325$	0	0
$326$	23.0000	1.27385
$327$	19.0000	1.05070
$328$	−12.0000	−0.662589
$329$	0	0
$330$	0	0
$331$	21.0000	1.15426	0.577132	−	0.816651i	$-0.304172\pi$
$331$	21.0000	1.15426	0.577132	+	0.816651i	$0.304172\pi$
$332$	6.00000	0.329293
$333$	3.00000	0.164399
$334$	−10.0000	−0.547176
$335$	0	0
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	−12.0000	−0.652714
$339$	−18.0000	−0.977626
$340$	0	0
$341$	0	0
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	8.00000	0.431331
$345$	0	0
$346$	6.00000	0.322562
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	−4.00000	−0.214423
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−4.00000	−0.213201
$353$	20.0000	1.06449	0.532246	−	0.846590i	$-0.321348\pi$
$353$	20.0000	1.06449	0.532246	+	0.846590i	$0.321348\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	−8.00000	−0.422813
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	18.0000	0.946059
$363$	−5.00000	−0.262432
$364$	0	0
$365$	0	0
$366$	−13.0000	−0.679521
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−2.00000	−0.104257
$369$	−12.0000	−0.624695
$370$	0	0
$371$	0	0
$372$	0	0
$373$	23.0000	1.19089	0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000	1.19089	0.595447	+	0.803394i	$0.296975\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	6.00000	0.309426
$377$	−4.00000	−0.206010
$378$	0	0
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	0	0
$381$	1.00000	0.0512316
$382$	20.0000	1.02329
$383$	14.0000	0.715367	0.357683	−	0.933843i	$-0.383567\pi$
$383$	14.0000	0.715367	0.357683	+	0.933843i	$0.383567\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−10.0000	−0.508987
$387$	8.00000	0.406663
$388$	−17.0000	−0.863044
$389$	−20.0000	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$390$	0	0
$391$	4.00000	0.202289
$392$	0	0
$393$	2.00000	0.100887
$394$	0	0
$395$	0	0
$396$	−4.00000	−0.201008
$397$	18.0000	0.903394	0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000	0.903394	0.451697	+	0.892171i	$0.350819\pi$
$398$	−15.0000	−0.751882
$399$	0	0
$400$	0	0
$401$	4.00000	0.199750	0.0998752	−	0.995000i	$-0.468156\pi$
$401$	4.00000	0.199750	0.0998752	+	0.995000i	$0.468156\pi$
$402$	−3.00000	−0.149626
$403$	0	0
$404$	−12.0000	−0.597022
$405$	0	0
$406$	0	0
$407$	−12.0000	−0.594818
$408$	2.00000	0.0990148
$409$	11.0000	0.543915	0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000	0.543915	0.271957	+	0.962309i	$0.412329\pi$
$410$	0	0
$411$	−10.0000	−0.493264
$412$	−7.00000	−0.344865
$413$	0	0
$414$	−2.00000	−0.0982946
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	−13.0000	−0.636613
$418$	4.00000	0.195646
$419$	16.0000	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	3.00000	0.146038
$423$	6.00000	0.291730
$424$	2.00000	0.0971286
$425$	0	0
$426$	−16.0000	−0.775203
$427$	0	0
$428$	6.00000	0.290021
$429$	−4.00000	−0.193122
$430$	0	0
$431$	6.00000	0.289010	0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	−1.00000	−0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	0	0
$435$	0	0
$436$	−19.0000	−0.909935
$437$	2.00000	0.0956730
$438$	−11.0000	−0.525600
$439$	23.0000	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$439$	23.0000	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$440$	0	0
$441$	0	0
$442$	2.00000	0.0951303
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	−3.00000	−0.142374
$445$	0	0
$446$	19.0000	0.899676
$447$	16.0000	0.756774
$448$	0	0
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	0	0
$451$	48.0000	2.26023
$452$	18.0000	0.846649
$453$	−19.0000	−0.892698
$454$	8.00000	0.375459
$455$	0	0
$456$	1.00000	0.0468293
$457$	37.0000	1.73079	0.865393	−	0.501093i	$-0.167069\pi$
$457$	37.0000	1.73079	0.865393	+	0.501093i	$0.167069\pi$
$458$	7.00000	0.327089
$459$	2.00000	0.0933520
$460$	0	0
$461$	−26.0000	−1.21094	−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000	−1.21094	−0.605470	+	0.795868i	$0.707015\pi$
$462$	0	0
$463$	−3.00000	−0.139422	−0.0697109	−	0.997567i	$-0.522208\pi$
$463$	−3.00000	−0.139422	−0.0697109	+	0.997567i	$0.522208\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	−4.00000	−0.185296
$467$	−30.0000	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	0	0
$471$	−21.0000	−0.967629
$472$	−6.00000	−0.276172
$473$	−32.0000	−1.47136
$474$	−13.0000	−0.597110
$475$	0	0
$476$	0	0
$477$	2.00000	0.0915737
$478$	−12.0000	−0.548867
$479$	34.0000	1.55350	0.776750	−	0.629809i	$-0.216867\pi$
$479$	34.0000	1.55350	0.776750	+	0.629809i	$0.216867\pi$
$480$	0	0
$481$	−3.00000	−0.136788
$482$	−13.0000	−0.592134
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	40.0000	1.81257	0.906287	−	0.422664i	$-0.138905\pi$
$487$	40.0000	1.81257	0.906287	+	0.422664i	$0.138905\pi$
$488$	13.0000	0.588482
$489$	−23.0000	−1.04010
$490$	0	0
$491$	18.0000	0.812329	0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000	0.812329	0.406164	+	0.913800i	$0.366866\pi$
$492$	12.0000	0.541002
$493$	−8.00000	−0.360302
$494$	1.00000	0.0449921
$495$	0	0
$496$	0	0
$497$	0	0
$498$	−6.00000	−0.268866
$499$	−27.0000	−1.20869	−0.604343	−	0.796724i	$-0.706564\pi$
$499$	−27.0000	−1.20869	−0.604343	+	0.796724i	$0.706564\pi$
$500$	0	0
$501$	10.0000	0.446767
$502$	−24.0000	−1.07117
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	0	0
$506$	8.00000	0.355643
$507$	12.0000	0.532939
$508$	−1.00000	−0.0443678
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	8.00000	0.352865
$515$	0	0
$516$	−8.00000	−0.352180
$517$	−24.0000	−1.05552
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	4.00000	0.175075
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−2.00000	−0.0873704
$525$	0	0
$526$	32.0000	1.39527
$527$	0	0
$528$	4.00000	0.174078
$529$	−19.0000	−0.826087
$530$	0	0
$531$	−6.00000	−0.260378
$532$	0	0
$533$	12.0000	0.519778
$534$	−2.00000	−0.0865485
$535$	0	0
$536$	3.00000	0.129580
$537$	8.00000	0.345225
$538$	0	0
$539$	0	0
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	20.0000	0.859074
$543$	−18.0000	−0.772454
$544$	−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	$0.582583\pi$
$548$	10.0000	0.427179
$549$	13.0000	0.554826
$550$	0	0
$551$	−4.00000	−0.170406
$552$	2.00000	0.0851257
$553$	0	0
$554$	1.00000	0.0424859
$555$	0	0
$556$	13.0000	0.551323
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−8.00000	−0.337760
$562$	−18.0000	−0.759284
$563$	28.0000	1.18006	0.590030	−	0.807382i	$-0.299116\pi$
$563$	28.0000	1.18006	0.590030	+	0.807382i	$0.299116\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	−13.0000	−0.546431
$567$	0	0
$568$	16.0000	0.671345
$569$	−40.0000	−1.67689	−0.838444	−	0.544988i	$-0.816534\pi$
$569$	−40.0000	−1.67689	−0.838444	+	0.544988i	$0.816534\pi$
$570$	0	0
$571$	−35.0000	−1.46470	−0.732352	−	0.680926i	$-0.761578\pi$
$571$	−35.0000	−1.46470	−0.732352	+	0.680926i	$0.761578\pi$
$572$	4.00000	0.167248
$573$	−20.0000	−0.835512
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	−13.0000	−0.540729
$579$	10.0000	0.415586
$580$	0	0
$581$	0	0
$582$	17.0000	0.704673
$583$	−8.00000	−0.331326
$584$	11.0000	0.455183
$585$	0	0
$586$	−12.0000	−0.495715
$587$	42.0000	1.73353	0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000	1.73353	0.866763	+	0.498721i	$0.166197\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	3.00000	0.123299
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−16.0000	−0.655386
$597$	15.0000	0.613909
$598$	2.00000	0.0817861
$599$	−6.00000	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$600$	0	0
$601$	29.0000	1.18293	0.591467	−	0.806329i	$-0.298549\pi$
$601$	29.0000	1.18293	0.591467	+	0.806329i	$0.298549\pi$
$602$	0	0
$603$	3.00000	0.122169
$604$	19.0000	0.773099
$605$	0	0
$606$	12.0000	0.487467
$607$	−1.00000	−0.0405887	−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000	−0.0405887	−0.0202944	+	0.999794i	$0.506460\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	0	0
$611$	−6.00000	−0.242734
$612$	−2.00000	−0.0808452
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	0	0
$617$	44.0000	1.77137	0.885687	−	0.464283i	$-0.153688\pi$
$617$	44.0000	1.77137	0.885687	+	0.464283i	$0.153688\pi$
$618$	7.00000	0.281581
$619$	−44.0000	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$619$	−44.0000	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$620$	0	0
$621$	2.00000	0.0802572
$622$	14.0000	0.561349
$623$	0	0
$624$	1.00000	0.0400320
$625$	0	0
$626$	18.0000	0.719425
$627$	−4.00000	−0.159745
$628$	21.0000	0.837991
$629$	−6.00000	−0.239236
$630$	0	0
$631$	17.0000	0.676759	0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000	0.676759	0.338380	+	0.941010i	$0.390121\pi$
$632$	13.0000	0.517112
$633$	−3.00000	−0.119239
$634$	22.0000	0.873732
$635$	0	0
$636$	−2.00000	−0.0793052
$637$	0	0
$638$	−16.0000	−0.633446
$639$	16.0000	0.632950
$640$	0	0
$641$	16.0000	0.631962	0.315981	−	0.948766i	$-0.397666\pi$
$641$	16.0000	0.631962	0.315981	+	0.948766i	$0.397666\pi$
$642$	−6.00000	−0.236801
$643$	−11.0000	−0.433798	−0.216899	−	0.976194i	$-0.569594\pi$
$643$	−11.0000	−0.433798	−0.216899	+	0.976194i	$0.569594\pi$
$644$	0	0
$645$	0	0
$646$	2.00000	0.0786889
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.00000	0.0392837
$649$	24.0000	0.942082
$650$	0	0
$651$	0	0
$652$	23.0000	0.900750
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	19.0000	0.742959
$655$	0	0
$656$	−12.0000	−0.468521
$657$	11.0000	0.429151
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	25.0000	0.972387	0.486194	−	0.873851i	$-0.338385\pi$
$661$	25.0000	0.972387	0.486194	+	0.873851i	$0.338385\pi$
$662$	21.0000	0.816188
$663$	−2.00000	−0.0776736
$664$	6.00000	0.232845
$665$	0	0
$666$	3.00000	0.116248
$667$	−8.00000	−0.309761
$668$	−10.0000	−0.386912
$669$	−19.0000	−0.734582
$670$	0	0
$671$	−52.0000	−2.00744
$672$	0	0
$673$	−9.00000	−0.346925	−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000	−0.346925	−0.173462	+	0.984841i	$0.555495\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	−12.0000	−0.461538
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	−18.0000	−0.691286
$679$	0	0
$680$	0	0
$681$	−8.00000	−0.306561
$682$	0	0
$683$	48.0000	1.83667	0.918334	−	0.395805i	$-0.129534\pi$
$683$	48.0000	1.83667	0.918334	+	0.395805i	$0.129534\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	0	0
$687$	−7.00000	−0.267067
$688$	8.00000	0.304997
$689$	−2.00000	−0.0761939
$690$	0	0
$691$	39.0000	1.48363	0.741815	−	0.670605i	$-0.233965\pi$
$691$	39.0000	1.48363	0.741815	+	0.670605i	$0.233965\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−22.0000	−0.835109
$695$	0	0
$696$	−4.00000	−0.151620
$697$	24.0000	0.909065
$698$	−2.00000	−0.0757011
$699$	4.00000	0.151294
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	1.00000	0.0377426
$703$	−3.00000	−0.113147
$704$	−4.00000	−0.150756
$705$	0	0
$706$	20.0000	0.752710
$707$	0	0
$708$	6.00000	0.225494
$709$	−11.0000	−0.413114	−0.206557	−	0.978435i	$-0.566226\pi$
$709$	−11.0000	−0.413114	−0.206557	+	0.978435i	$0.566226\pi$
$710$	0	0
$711$	13.0000	0.487538
$712$	2.00000	0.0749532
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−8.00000	−0.298974
$717$	12.0000	0.448148
$718$	−6.00000	−0.223918
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	0	0
$722$	−18.0000	−0.669891
$723$	13.0000	0.483475
$724$	18.0000	0.668965
$725$	0	0
$726$	−5.00000	−0.185567
$727$	1.00000	0.0370879	0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000	0.0370879	0.0185440	+	0.999828i	$0.494097\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−16.0000	−0.591781
$732$	−13.0000	−0.480494
$733$	35.0000	1.29275	0.646377	−	0.763018i	$-0.276283\pi$
$733$	35.0000	1.29275	0.646377	+	0.763018i	$0.276283\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	−12.0000	−0.442026
$738$	−12.0000	−0.441726
$739$	−1.00000	−0.0367856	−0.0183928	−	0.999831i	$-0.505855\pi$
$739$	−1.00000	−0.0367856	−0.0183928	+	0.999831i	$0.505855\pi$
$740$	0	0
$741$	−1.00000	−0.0367359
$742$	0	0
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	0	0
$745$	0	0
$746$	23.0000	0.842090
$747$	6.00000	0.219529
$748$	8.00000	0.292509
$749$	0	0
$750$	0	0
$751$	19.0000	0.693320	0.346660	−	0.937991i	$-0.387316\pi$
$751$	19.0000	0.693320	0.346660	+	0.937991i	$0.387316\pi$
$752$	6.00000	0.218797
$753$	24.0000	0.874609
$754$	−4.00000	−0.145671
$755$	0	0
$756$	0	0
$757$	1.00000	0.0363456	0.0181728	−	0.999835i	$-0.494215\pi$
$757$	1.00000	0.0363456	0.0181728	+	0.999835i	$0.494215\pi$
$758$	−5.00000	−0.181608
$759$	−8.00000	−0.290382
$760$	0	0
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	1.00000	0.0362262
$763$	0	0
$764$	20.0000	0.723575
$765$	0	0
$766$	14.0000	0.505841
$767$	6.00000	0.216647
$768$	−1.00000	−0.0360844
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	0	0
$771$	−8.00000	−0.288113
$772$	−10.0000	−0.359908
$773$	32.0000	1.15096	0.575480	−	0.817816i	$-0.304815\pi$
$773$	32.0000	1.15096	0.575480	+	0.817816i	$0.304815\pi$
$774$	8.00000	0.287554
$775$	0	0
$776$	−17.0000	−0.610264
$777$	0	0
$778$	−20.0000	−0.717035
$779$	12.0000	0.429945
$780$	0	0
$781$	−64.0000	−2.29010
$782$	4.00000	0.143040
$783$	−4.00000	−0.142948
$784$	0	0
$785$	0	0
$786$	2.00000	0.0713376
$787$	−23.0000	−0.819861	−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000	−0.819861	−0.409931	+	0.912117i	$0.634447\pi$
$788$	0	0
$789$	−32.0000	−1.13923
$790$	0	0
$791$	0	0
$792$	−4.00000	−0.142134
$793$	−13.0000	−0.461644
$794$	18.0000	0.638796
$795$	0	0
$796$	−15.0000	−0.531661
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	0	0
$801$	2.00000	0.0706665
$802$	4.00000	0.141245
$803$	−44.0000	−1.55273
$804$	−3.00000	−0.105802
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−12.0000	−0.422159
$809$	14.0000	0.492214	0.246107	−	0.969243i	$-0.420849\pi$
$809$	14.0000	0.492214	0.246107	+	0.969243i	$0.420849\pi$
$810$	0	0
$811$	5.00000	0.175574	0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000	0.175574	0.0877869	+	0.996139i	$0.472021\pi$
$812$	0	0
$813$	−20.0000	−0.701431
$814$	−12.0000	−0.420600
$815$	0	0
$816$	2.00000	0.0700140
$817$	−8.00000	−0.279885
$818$	11.0000	0.384606
$819$	0	0
$820$	0	0
$821$	−44.0000	−1.53561	−0.767805	−	0.640683i	$-0.778651\pi$
$821$	−44.0000	−1.53561	−0.767805	+	0.640683i	$0.778651\pi$
$822$	−10.0000	−0.348790
$823$	9.00000	0.313720	0.156860	−	0.987621i	$-0.449863\pi$
$823$	9.00000	0.313720	0.156860	+	0.987621i	$0.449863\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	0	0
$827$	40.0000	1.39094	0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000	1.39094	0.695468	+	0.718557i	$0.255197\pi$
$828$	−2.00000	−0.0695048
$829$	3.00000	0.104194	0.0520972	−	0.998642i	$-0.483409\pi$
$829$	3.00000	0.104194	0.0520972	+	0.998642i	$0.483409\pi$
$830$	0	0
$831$	−1.00000	−0.0346896
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−13.0000	−0.450153
$835$	0	0
$836$	4.00000	0.138343
$837$	0	0
$838$	16.0000	0.552711
$839$	−50.0000	−1.72619	−0.863096	−	0.505040i	$-0.831478\pi$
$839$	−50.0000	−1.72619	−0.863096	+	0.505040i	$0.831478\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	1.00000	0.0344623
$843$	18.0000	0.619953
$844$	3.00000	0.103264
$845$	0	0
$846$	6.00000	0.206284
$847$	0	0
$848$	2.00000	0.0686803
$849$	13.0000	0.446159
$850$	0	0
$851$	−6.00000	−0.205677
$852$	−16.0000	−0.548151
$853$	38.0000	1.30110	0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000	1.30110	0.650548	+	0.759465i	$0.274539\pi$
$854$	0	0
$855$	0	0
$856$	6.00000	0.205076
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	−4.00000	−0.136558
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	0	0
$862$	6.00000	0.204361
$863$	−34.0000	−1.15737	−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000	−1.15737	−0.578687	+	0.815550i	$0.696435\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	2.00000	0.0679628
$867$	13.0000	0.441503
$868$	0	0
$869$	−52.0000	−1.76398
$870$	0	0
$871$	−3.00000	−0.101651
$872$	−19.0000	−0.643421
$873$	−17.0000	−0.575363
$874$	2.00000	0.0676510
$875$	0	0
$876$	−11.0000	−0.371656
$877$	−13.0000	−0.438979	−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000	−0.438979	−0.219489	+	0.975615i	$0.570439\pi$
$878$	23.0000	0.776212
$879$	12.0000	0.404750
$880$	0	0
$881$	40.0000	1.34763	0.673817	−	0.738898i	$-0.264654\pi$
$881$	40.0000	1.34763	0.673817	+	0.738898i	$0.264654\pi$
$882$	0	0
$883$	−1.00000	−0.0336527	−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000	−0.0336527	−0.0168263	+	0.999858i	$0.505356\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	6.00000	0.201574
$887$	46.0000	1.54453	0.772264	−	0.635301i	$-0.219124\pi$
$887$	46.0000	1.54453	0.772264	+	0.635301i	$0.219124\pi$
$888$	−3.00000	−0.100673
$889$	0	0
$890$	0	0
$891$	−4.00000	−0.134005
$892$	19.0000	0.636167
$893$	−6.00000	−0.200782
$894$	16.0000	0.535120
$895$	0	0
$896$	0	0
$897$	−2.00000	−0.0667781
$898$	2.00000	0.0667409
$899$	0	0
$900$	0	0
$901$	−4.00000	−0.133259
$902$	48.0000	1.59823
$903$	0	0
$904$	18.0000	0.598671
$905$	0	0
$906$	−19.0000	−0.631233
$907$	−47.0000	−1.56061	−0.780305	−	0.625400i	$-0.784936\pi$
$907$	−47.0000	−1.56061	−0.780305	+	0.625400i	$0.784936\pi$
$908$	8.00000	0.265489
$909$	−12.0000	−0.398015
$910$	0	0
$911$	−46.0000	−1.52405	−0.762024	−	0.647549i	$-0.775794\pi$
$911$	−46.0000	−1.52405	−0.762024	+	0.647549i	$0.775794\pi$
$912$	1.00000	0.0331133
$913$	−24.0000	−0.794284
$914$	37.0000	1.22385
$915$	0	0
$916$	7.00000	0.231287
$917$	0	0
$918$	2.00000	0.0660098
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	−26.0000	−0.856264
$923$	−16.0000	−0.526646
$924$	0	0
$925$	0	0
$926$	−3.00000	−0.0985861
$927$	−7.00000	−0.229910
$928$	4.00000	0.131306
$929$	20.0000	0.656179	0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000	0.656179	0.328089	+	0.944647i	$0.393595\pi$
$930$	0	0
$931$	0	0
$932$	−4.00000	−0.131024
$933$	−14.0000	−0.458339
$934$	−30.0000	−0.981630
$935$	0	0
$936$	−1.00000	−0.0326860
$937$	−46.0000	−1.50275	−0.751377	−	0.659873i	$-0.770610\pi$
$937$	−46.0000	−1.50275	−0.751377	+	0.659873i	$0.770610\pi$
$938$	0	0
$939$	−18.0000	−0.587408
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	−21.0000	−0.684217
$943$	24.0000	0.781548
$944$	−6.00000	−0.195283
$945$	0	0
$946$	−32.0000	−1.04041
$947$	−38.0000	−1.23483	−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000	−1.23483	−0.617417	+	0.786636i	$0.711821\pi$
$948$	−13.0000	−0.422220
$949$	−11.0000	−0.357075
$950$	0	0
$951$	−22.0000	−0.713399
$952$	0	0
$953$	−4.00000	−0.129573	−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000	−0.129573	−0.0647864	+	0.997899i	$0.520637\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	−12.0000	−0.388108
$957$	16.0000	0.517207
$958$	34.0000	1.09849
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−3.00000	−0.0967239
$963$	6.00000	0.193347
$964$	−13.0000	−0.418702
$965$	0	0
$966$	0	0
$967$	−11.0000	−0.353736	−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000	−0.353736	−0.176868	+	0.984235i	$0.556597\pi$
$968$	5.00000	0.160706
$969$	−2.00000	−0.0642493
$970$	0	0
$971$	−16.0000	−0.513464	−0.256732	−	0.966483i	$-0.582646\pi$
$971$	−16.0000	−0.513464	−0.256732	+	0.966483i	$0.582646\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	40.0000	1.28168
$975$	0	0
$976$	13.0000	0.416120
$977$	−48.0000	−1.53566	−0.767828	−	0.640656i	$-0.778662\pi$
$977$	−48.0000	−1.53566	−0.767828	+	0.640656i	$0.778662\pi$
$978$	−23.0000	−0.735459
$979$	−8.00000	−0.255681
$980$	0	0
$981$	−19.0000	−0.606623
$982$	18.0000	0.574403
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	−8.00000	−0.254772
$987$	0	0
$988$	1.00000	0.0318142
$989$	−16.0000	−0.508770
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	0	0
$993$	−21.0000	−0.666415
$994$	0	0
$995$	0	0
$996$	−6.00000	−0.190117
$997$	−31.0000	−0.981780	−0.490890	−	0.871222i	$-0.663328\pi$
$997$	−31.0000	−0.981780	−0.490890	+	0.871222i	$0.663328\pi$
$998$	−27.0000	−0.854670
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.bp.1.1		1
5.4	even	2		7350.2.a.y.1.1		1
7.3	odd	6		1050.2.i.a.751.1	yes	2
7.5	odd	6		1050.2.i.a.151.1	✓	2
7.6	odd	2		7350.2.a.cl.1.1		1
35.3	even	12		1050.2.o.k.499.2		4
35.12	even	12		1050.2.o.k.949.2		4
35.17	even	12		1050.2.o.k.499.1		4
35.19	odd	6		1050.2.i.t.151.1	yes	2
35.24	odd	6		1050.2.i.t.751.1	yes	2
35.33	even	12		1050.2.o.k.949.1		4
35.34	odd	2		7350.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.a.151.1	✓	2	7.5	odd	6
1050.2.i.a.751.1	yes	2	7.3	odd	6
1050.2.i.t.151.1	yes	2	35.19	odd	6
1050.2.i.t.751.1	yes	2	35.24	odd	6
1050.2.o.k.499.1		4	35.17	even	12
1050.2.o.k.499.2		4	35.3	even	12
1050.2.o.k.949.1		4	35.33	even	12
1050.2.o.k.949.2		4	35.12	even	12
7350.2.a.c.1.1		1	35.34	odd	2
7350.2.a.y.1.1		1	5.4	even	2
7350.2.a.bp.1.1		1	1.1	even	1	trivial
7350.2.a.cl.1.1		1	7.6	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:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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