LMFDB - Embedded newform 2275.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2275,2,Mod(1,2275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2275, 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("2275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2275 = 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2275.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:	$18.1659664598$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+2.00000 q^{3} -2.00000 q^{4} -1.00000 q^{7} +1.00000 q^{9} -4.00000 q^{12} -1.00000 q^{13} +4.00000 q^{16} +6.00000 q^{17} -7.00000 q^{19} -2.00000 q^{21} -3.00000 q^{23} -4.00000 q^{27} +2.00000 q^{28} -9.00000 q^{29} +5.00000 q^{31} -2.00000 q^{36} -2.00000 q^{37} -2.00000 q^{39} -6.00000 q^{41} +1.00000 q^{43} -3.00000 q^{47} +8.00000 q^{48} +1.00000 q^{49} +12.0000 q^{51} +2.00000 q^{52} +9.00000 q^{53} -14.0000 q^{57} -10.0000 q^{61} -1.00000 q^{63} -8.00000 q^{64} -14.0000 q^{67} -12.0000 q^{68} -6.00000 q^{69} -6.00000 q^{71} -11.0000 q^{73} +14.0000 q^{76} -1.00000 q^{79} -11.0000 q^{81} -3.00000 q^{83} +4.00000 q^{84} -18.0000 q^{87} +15.0000 q^{89} +1.00000 q^{91} +6.00000 q^{92} +10.0000 q^{93} +1.00000 q^{97} +O(q^{100})$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	−2.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−4.00000	−1.15470
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	−7.00000	−1.60591	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000	−1.60591	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−4.00000	−0.769800
$28$	2.00000	0.377964
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	8.00000	1.15470
$49$	1.00000	0.142857
$50$	0	0
$51$	12.0000	1.68034
$52$	2.00000	0.277350
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−14.0000	−1.85435
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−14.0000	−1.71037	−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000	−1.71037	−0.855186	+	0.518321i	$0.826557\pi$
$68$	−12.0000	−1.45521
$69$	−6.00000	−0.722315
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	0	0
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	0	0
$75$	0	0
$76$	14.0000	1.60591
$77$	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
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	4.00000	0.436436
$85$	0	0
$86$	0	0
$87$	−18.0000	−1.92980
$88$	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
$91$	1.00000	0.104828
$92$	6.00000	0.625543
$93$	10.0000	1.03695
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	8.00000	0.769800
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	−4.00000	−0.377964
$113$	−9.00000	−0.846649	−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000	−0.846649	−0.423324	+	0.905978i	$0.639137\pi$
$114$	0	0
$115$	0	0
$116$	18.0000	1.67126
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	−12.0000	−1.08200
$124$	−10.0000	−0.898027
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	0	0
$129$	2.00000	0.176090
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	7.00000	0.606977
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	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
$141$	−6.00000	−0.505291
$142$	0	0
$143$	0	0
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	2.00000	0.164957
$148$	4.00000	0.328798
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	0	0
$153$	6.00000	0.485071
$154$	0	0
$155$	0	0
$156$	4.00000	0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	0	0
$159$	18.0000	1.42749
$160$	0	0
$161$	3.00000	0.236433
$162$	0	0
$163$	16.0000	1.25322	0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000	1.25322	0.626608	+	0.779334i	$0.284443\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	0	0
$167$	15.0000	1.16073	0.580367	−	0.814355i	$-0.302909\pi$
$167$	15.0000	1.16073	0.580367	+	0.814355i	$0.302909\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−7.00000	−0.535303
$172$	−2.00000	−0.152499
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	0	0
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	0	0
$183$	−20.0000	−1.47844
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	6.00000	0.437595
$189$	4.00000	0.290957
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	−16.0000	−1.15470
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	0	0
$195$	0	0
$196$	−2.00000	−0.142857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	0	0
$201$	−28.0000	−1.97497
$202$	0	0
$203$	9.00000	0.631676
$204$	−24.0000	−1.68034
$205$	0	0
$206$	0	0
$207$	−3.00000	−0.208514
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	23.0000	1.58339	0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000	1.58339	0.791693	+	0.610920i	$0.209200\pi$
$212$	−18.0000	−1.23625
$213$	−12.0000	−0.822226
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−5.00000	−0.339422
$218$	0	0
$219$	−22.0000	−1.48662
$220$	0	0
$221$	−6.00000	−0.403604
$222$	0	0
$223$	1.00000	0.0669650	0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000	0.0669650	0.0334825	+	0.999439i	$0.489340\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	28.0000	1.85435
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	9.00000	0.589610	0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000	0.589610	0.294805	+	0.955557i	$0.404745\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−2.00000	−0.129914
$238$	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
$241$	−1.00000	−0.0644157	−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000	−0.0644157	−0.0322078	+	0.999481i	$0.510254\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	20.0000	1.28037
$245$	0	0
$246$	0	0
$247$	7.00000	0.445399
$248$	0	0
$249$	−6.00000	−0.380235
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	0	0
$259$	2.00000	0.124274
$260$	0	0
$261$	−9.00000	−0.557086
$262$	0	0
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	30.0000	1.83597
$268$	28.0000	1.71037
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	24.0000	1.45521
$273$	2.00000	0.121046
$274$	0	0
$275$	0	0
$276$	12.0000	0.722315
$277$	19.0000	1.14160	0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000	1.14160	0.570800	+	0.821089i	$0.306633\pi$
$278$	0	0
$279$	5.00000	0.299342
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	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
$286$	0	0
$287$	6.00000	0.354169
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	2.00000	0.117242
$292$	22.0000	1.28745
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	3.00000	0.173494
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	0	0
$303$	0	0
$304$	−28.0000	−1.60591
$305$	0	0
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	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
$313$	−8.00000	−0.452187	−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000	−0.452187	−0.226093	+	0.974106i	$0.572595\pi$
$314$	0	0
$315$	0	0
$316$	2.00000	0.112509
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	24.0000	1.33955
$322$	0	0
$323$	−42.0000	−2.33694
$324$	22.0000	1.22222
$325$	0	0
$326$	0	0
$327$	−32.0000	−1.76960
$328$	0	0
$329$	3.00000	0.165395
$330$	0	0
$331$	26.0000	1.42909	0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000	1.42909	0.714545	+	0.699590i	$0.246634\pi$
$332$	6.00000	0.329293
$333$	−2.00000	−0.109599
$334$	0	0
$335$	0	0
$336$	−8.00000	−0.436436
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	0	0
$339$	−18.0000	−0.977626
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	36.0000	1.92980
$349$	−1.00000	−0.0535288	−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000	−0.0535288	−0.0267644	+	0.999642i	$0.508520\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	0	0
$356$	−30.0000	−1.59000
$357$	−12.0000	−0.635107
$358$	0	0
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	−22.0000	−1.15470
$364$	−2.00000	−0.104828
$365$	0	0
$366$	0	0
$367$	28.0000	1.46159	0.730794	−	0.682598i	$-0.239150\pi$
$367$	28.0000	1.46159	0.730794	+	0.682598i	$0.239150\pi$
$368$	−12.0000	−0.625543
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−9.00000	−0.467257
$372$	−20.0000	−1.03695
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	9.00000	0.463524
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	0	0
$381$	32.0000	1.63941
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1.00000	0.0508329
$388$	−2.00000	−0.101535
$389$	−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
$391$	−18.0000	−0.910299
$392$	0	0
$393$	−24.0000	−1.21064
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−11.0000	−0.552074	−0.276037	−	0.961147i	$-0.589021\pi$
$397$	−11.0000	−0.552074	−0.276037	+	0.961147i	$0.589021\pi$
$398$	0	0
$399$	14.0000	0.700877
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	−5.00000	−0.249068
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	23.0000	1.13728	0.568638	−	0.822588i	$-0.307470\pi$
$409$	23.0000	1.13728	0.568638	+	0.822588i	$0.307470\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	−8.00000	−0.394132
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−8.00000	−0.391762
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	0	0
$423$	−3.00000	−0.145865
$424$	0	0
$425$	0	0
$426$	0	0
$427$	10.0000	0.483934
$428$	−24.0000	−1.16008
$429$	0	0
$430$	0	0
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	−16.0000	−0.769800
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	0	0
$436$	32.0000	1.53252
$437$	21.0000	1.00457
$438$	0	0
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	−39.0000	−1.85295	−0.926473	−	0.376361i	$-0.877175\pi$
$443$	−39.0000	−1.85295	−0.926473	+	0.376361i	$0.877175\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	0	0
$447$	0	0
$448$	8.00000	0.377964
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	0	0
$452$	18.0000	0.846649
$453$	−20.0000	−0.939682
$454$	0	0
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	0	0
$459$	−24.0000	−1.12022
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	−36.0000	−1.67126
$465$	0	0
$466$	0	0
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	2.00000	0.0924500
$469$	14.0000	0.646460
$470$	0	0
$471$	−28.0000	−1.29017
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	12.0000	0.550019
$477$	9.00000	0.412082
$478$	0	0
$479$	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
$481$	2.00000	0.0911922
$482$	0	0
$483$	6.00000	0.273009
$484$	22.0000	1.00000
$485$	0	0
$486$	0	0
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	0	0
$489$	32.0000	1.44709
$490$	0	0
$491$	−24.0000	−1.08310	−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000	−1.08310	−0.541552	+	0.840667i	$0.682163\pi$
$492$	24.0000	1.08200
$493$	−54.0000	−2.43204
$494$	0	0
$495$	0	0
$496$	20.0000	0.898027
$497$	6.00000	0.269137
$498$	0	0
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	0	0
$501$	30.0000	1.34030
$502$	0	0
$503$	6.00000	0.267527	0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000	0.267527	0.133763	+	0.991013i	$0.457294\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	2.00000	0.0888231
$508$	−32.0000	−1.41977
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	11.0000	0.486611
$512$	0	0
$513$	28.0000	1.23623
$514$	0	0
$515$	0	0
$516$	−4.00000	−0.176090
$517$	0	0
$518$	0	0
$519$	−12.0000	−0.526742
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−2.00000	−0.0874539	−0.0437269	−	0.999044i	$-0.513923\pi$
$523$	−2.00000	−0.0874539	−0.0437269	+	0.999044i	$0.513923\pi$
$524$	24.0000	1.04844
$525$	0	0
$526$	0	0
$527$	30.0000	1.30682
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	0	0
$532$	−14.0000	−0.606977
$533$	6.00000	0.259889
$534$	0	0
$535$	0	0
$536$	0	0
$537$	30.0000	1.29460
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	0	0
$543$	−32.0000	−1.37325
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−17.0000	−0.726868	−0.363434	−	0.931620i	$-0.618396\pi$
$547$	−17.0000	−0.726868	−0.363434	+	0.931620i	$0.618396\pi$
$548$	12.0000	0.512615
$549$	−10.0000	−0.426790
$550$	0	0
$551$	63.0000	2.68389
$552$	0	0
$553$	1.00000	0.0425243
$554$	0	0
$555$	0	0
$556$	8.00000	0.339276
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	0	0
$567$	11.0000	0.461957
$568$	0	0
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	0	0
$571$	23.0000	0.962520	0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000	0.962520	0.481260	+	0.876578i	$0.340179\pi$
$572$	0	0
$573$	48.0000	2.00523
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	0	0
$579$	44.0000	1.82858
$580$	0	0
$581$	3.00000	0.124461
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	9.00000	0.371470	0.185735	−	0.982600i	$-0.440533\pi$
$587$	9.00000	0.371470	0.185735	+	0.982600i	$0.440533\pi$
$588$	−4.00000	−0.164957
$589$	−35.0000	−1.44215
$590$	0	0
$591$	−12.0000	−0.493614
$592$	−8.00000	−0.328798
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	4.00000	0.163709
$598$	0	0
$599$	15.0000	0.612883	0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000	0.612883	0.306442	+	0.951889i	$0.400862\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	−14.0000	−0.570124
$604$	20.0000	0.813788
$605$	0	0
$606$	0	0
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	0	0
$609$	18.0000	0.729397
$610$	0	0
$611$	3.00000	0.121367
$612$	−12.0000	−0.485071
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	0	0
$615$	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	$0.618017\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	0	0
$621$	12.0000	0.481543
$622$	0	0
$623$	−15.0000	−0.600962
$624$	−8.00000	−0.320256
$625$	0	0
$626$	0	0
$627$	0	0
$628$	28.0000	1.11732
$629$	−12.0000	−0.478471
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	0	0
$633$	46.0000	1.82834
$634$	0	0
$635$	0	0
$636$	−36.0000	−1.42749
$637$	−1.00000	−0.0396214
$638$	0	0
$639$	−6.00000	−0.237356
$640$	0	0
$641$	−39.0000	−1.54041	−0.770204	−	0.637798i	$-0.779845\pi$
$641$	−39.0000	−1.54041	−0.770204	+	0.637798i	$0.779845\pi$
$642$	0	0
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	0	0
$647$	48.0000	1.88707	0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000	1.88707	0.943537	+	0.331266i	$0.107476\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−10.0000	−0.391931
$652$	−32.0000	−1.25322
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	0	0
$656$	−24.0000	−0.937043
$657$	−11.0000	−0.429151
$658$	0	0
$659$	−3.00000	−0.116863	−0.0584317	−	0.998291i	$-0.518610\pi$
$659$	−3.00000	−0.116863	−0.0584317	+	0.998291i	$0.518610\pi$
$660$	0	0
$661$	−13.0000	−0.505641	−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000	−0.505641	−0.252821	+	0.967513i	$0.581358\pi$
$662$	0	0
$663$	−12.0000	−0.466041
$664$	0	0
$665$	0	0
$666$	0	0
$667$	27.0000	1.04544
$668$	−30.0000	−1.16073
$669$	2.00000	0.0773245
$670$	0	0
$671$	0	0
$672$	0	0
$673$	19.0000	0.732396	0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000	0.732396	0.366198	+	0.930537i	$0.380659\pi$
$674$	0	0
$675$	0	0
$676$	−2.00000	−0.0769231
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	−48.0000	−1.83936
$682$	0	0
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	14.0000	0.535303
$685$	0	0
$686$	0	0
$687$	28.0000	1.06827
$688$	4.00000	0.152499
$689$	−9.00000	−0.342873
$690$	0	0
$691$	−37.0000	−1.40755	−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000	−1.40755	−0.703773	+	0.710425i	$0.748503\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−36.0000	−1.36360
$698$	0	0
$699$	18.0000	0.680823
$700$	0	0
$701$	9.00000	0.339925	0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000	0.339925	0.169963	+	0.985451i	$0.445635\pi$
$702$	0	0
$703$	14.0000	0.528020
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	8.00000	0.300446	0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000	0.300446	0.150223	+	0.988652i	$0.452001\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	0	0
$713$	−15.0000	−0.561754
$714$	0	0
$715$	0	0
$716$	−30.0000	−1.12115
$717$	−24.0000	−0.896296
$718$	0	0
$719$	12.0000	0.447524	0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000	0.447524	0.223762	+	0.974644i	$0.428166\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	0	0
$723$	−2.00000	−0.0743808
$724$	32.0000	1.18927
$725$	0	0
$726$	0	0
$727$	−26.0000	−0.964287	−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000	−0.964287	−0.482143	+	0.876092i	$0.660142\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	6.00000	0.221918
$732$	40.0000	1.47844
$733$	49.0000	1.80986	0.904928	−	0.425564i	$-0.139924\pi$
$733$	49.0000	1.80986	0.904928	+	0.425564i	$0.139924\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	14.0000	0.514303
$742$	0	0
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−3.00000	−0.109764
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	−12.0000	−0.437595
$753$	24.0000	0.874609
$754$	0	0
$755$	0	0
$756$	−8.00000	−0.290957
$757$	43.0000	1.56286	0.781431	−	0.623992i	$-0.214490\pi$
$757$	43.0000	1.56286	0.781431	+	0.623992i	$0.214490\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	0	0
$763$	16.0000	0.579239
$764$	−48.0000	−1.73658
$765$	0	0
$766$	0	0
$767$	0	0
$768$	32.0000	1.15470
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	0	0
$771$	48.0000	1.72868
$772$	−44.0000	−1.58359
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	4.00000	0.143499
$778$	0	0
$779$	42.0000	1.50481
$780$	0	0
$781$	0	0
$782$	0	0
$783$	36.0000	1.28654
$784$	4.00000	0.142857
$785$	0	0
$786$	0	0
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	12.0000	0.427482
$789$	−18.0000	−0.640817
$790$	0	0
$791$	9.00000	0.320003
$792$	0	0
$793$	10.0000	0.355110
$794$	0	0
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−54.0000	−1.91278	−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000	−1.91278	−0.956389	+	0.292096i	$0.905647\pi$
$798$	0	0
$799$	−18.0000	−0.636794
$800$	0	0
$801$	15.0000	0.529999
$802$	0	0
$803$	0	0
$804$	56.0000	1.97497
$805$	0	0
$806$	0	0
$807$	−48.0000	−1.68968
$808$	0	0
$809$	−3.00000	−0.105474	−0.0527372	−	0.998608i	$-0.516795\pi$
$809$	−3.00000	−0.105474	−0.0527372	+	0.998608i	$0.516795\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	−18.0000	−0.631676
$813$	−32.0000	−1.12229
$814$	0	0
$815$	0	0
$816$	48.0000	1.68034
$817$	−7.00000	−0.244899
$818$	0	0
$819$	1.00000	0.0349428
$820$	0	0
$821$	−54.0000	−1.88461	−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000	−1.88461	−0.942306	+	0.334751i	$0.891348\pi$
$822$	0	0
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	6.00000	0.208514
$829$	20.0000	0.694629	0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000	0.694629	0.347314	+	0.937749i	$0.387094\pi$
$830$	0	0
$831$	38.0000	1.31821
$832$	8.00000	0.277350
$833$	6.00000	0.207888
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−20.0000	−0.691301
$838$	0	0
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	0	0
$843$	24.0000	0.826604
$844$	−46.0000	−1.58339
$845$	0	0
$846$	0	0
$847$	11.0000	0.377964
$848$	36.0000	1.23625
$849$	8.00000	0.274559
$850$	0	0
$851$	6.00000	0.205677
$852$	24.0000	0.822226
$853$	−17.0000	−0.582069	−0.291034	−	0.956713i	$-0.593999\pi$
$853$	−17.0000	−0.582069	−0.291034	+	0.956713i	$0.593999\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	50.0000	1.70598	0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000	1.70598	0.852989	+	0.521929i	$0.174787\pi$
$860$	0	0
$861$	12.0000	0.408959
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	38.0000	1.29055
$868$	10.0000	0.339422
$869$	0	0
$870$	0	0
$871$	14.0000	0.474372
$872$	0	0
$873$	1.00000	0.0338449
$874$	0	0
$875$	0	0
$876$	44.0000	1.48662
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	0	0
$879$	−18.0000	−0.607125
$880$	0	0
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	0	0
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	0	0
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	0	0
$891$	0	0
$892$	−2.00000	−0.0669650
$893$	21.0000	0.702738
$894$	0	0
$895$	0	0
$896$	0	0
$897$	6.00000	0.200334
$898$	0	0
$899$	−45.0000	−1.50083
$900$	0	0
$901$	54.0000	1.79900
$902$	0	0
$903$	−2.00000	−0.0665558
$904$	0	0
$905$	0	0
$906$	0	0
$907$	37.0000	1.22856	0.614282	−	0.789086i	$-0.289446\pi$
$907$	37.0000	1.22856	0.614282	+	0.789086i	$0.289446\pi$
$908$	48.0000	1.59294
$909$	0	0
$910$	0	0
$911$	−15.0000	−0.496972	−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000	−0.496972	−0.248486	+	0.968635i	$0.579933\pi$
$912$	−56.0000	−1.85435
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−28.0000	−0.925146
$917$	12.0000	0.396275
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	−22.0000	−0.724925
$922$	0	0
$923$	6.00000	0.197492
$924$	0	0
$925$	0	0
$926$	0	0
$927$	4.00000	0.131377
$928$	0	0
$929$	−3.00000	−0.0984268	−0.0492134	−	0.998788i	$-0.515671\pi$
$929$	−3.00000	−0.0984268	−0.0492134	+	0.998788i	$0.515671\pi$
$930$	0	0
$931$	−7.00000	−0.229416
$932$	−18.0000	−0.589610
$933$	−24.0000	−0.785725
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−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
$939$	−16.0000	−0.522140
$940$	0	0
$941$	15.0000	0.488986	0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000	0.488986	0.244493	+	0.969651i	$0.421378\pi$
$942$	0	0
$943$	18.0000	0.586161
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−54.0000	−1.75476	−0.877382	−	0.479792i	$-0.840712\pi$
$947$	−54.0000	−1.75476	−0.877382	+	0.479792i	$0.840712\pi$
$948$	4.00000	0.129914
$949$	11.0000	0.357075
$950$	0	0
$951$	−24.0000	−0.778253
$952$	0	0
$953$	−21.0000	−0.680257	−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000	−0.680257	−0.340128	+	0.940379i	$0.610471\pi$
$954$	0	0
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	0	0
$959$	6.00000	0.193750
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	12.0000	0.386695
$964$	2.00000	0.0644157
$965$	0	0
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	0	0
$969$	−84.0000	−2.69847
$970$	0	0
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	20.0000	0.641500
$973$	4.00000	0.128234
$974$	0	0
$975$	0	0
$976$	−40.0000	−1.28037
$977$	−48.0000	−1.53566	−0.767828	−	0.640656i	$-0.778662\pi$
$977$	−48.0000	−1.53566	−0.767828	+	0.640656i	$0.778662\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−16.0000	−0.510841
$982$	0	0
$983$	−57.0000	−1.81802	−0.909009	−	0.416777i	$-0.863160\pi$
$983$	−57.0000	−1.81802	−0.909009	+	0.416777i	$0.863160\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	6.00000	0.190982
$988$	−14.0000	−0.445399
$989$	−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	$0.581789\pi$
$992$	0	0
$993$	52.0000	1.65017
$994$	0	0
$995$	0	0
$996$	12.0000	0.380235
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2275.2.a.d.1.1		1
5.4	even	2		91.2.a.b.1.1	✓	1
15.14	odd	2		819.2.a.c.1.1		1
20.19	odd	2		1456.2.a.k.1.1		1
35.4	even	6		637.2.e.c.79.1		2
35.9	even	6		637.2.e.c.508.1		2
35.19	odd	6		637.2.e.b.508.1		2
35.24	odd	6		637.2.e.b.79.1		2
35.34	odd	2		637.2.a.b.1.1		1
40.19	odd	2		5824.2.a.f.1.1		1
40.29	even	2		5824.2.a.bd.1.1		1
65.34	odd	4		1183.2.c.a.337.1		2
65.44	odd	4		1183.2.c.a.337.2		2
65.64	even	2		1183.2.a.a.1.1		1
105.104	even	2		5733.2.a.f.1.1		1
455.454	odd	2		8281.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.b.1.1	✓	1	5.4	even	2
637.2.a.b.1.1		1	35.34	odd	2
637.2.e.b.79.1		2	35.24	odd	6
637.2.e.b.508.1		2	35.19	odd	6
637.2.e.c.79.1		2	35.4	even	6
637.2.e.c.508.1		2	35.9	even	6
819.2.a.c.1.1		1	15.14	odd	2
1183.2.a.a.1.1		1	65.64	even	2
1183.2.c.a.337.1		2	65.34	odd	4
1183.2.c.a.337.2		2	65.44	odd	4
1456.2.a.k.1.1		1	20.19	odd	2
2275.2.a.d.1.1		1	1.1	even	1	trivial
5733.2.a.f.1.1		1	105.104	even	2
5824.2.a.f.1.1		1	40.19	odd	2
5824.2.a.bd.1.1		1	40.29	even	2
8281.2.a.h.1.1		1	455.454	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:	\( N \)	\(=\)	\( 2275 = 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2275.a (trivial)

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L-functions

Modular forms

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Fields

Representations

Groups

Database

Properties

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