LMFDB - Embedded newform 9075.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9075,2,Mod(1,9075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9075, 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("9075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9075 = 3 \cdot 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9075.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:	$72.4642398343$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +3.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +2.00000 q^{29} -5.00000 q^{32} -2.00000 q^{34} -1.00000 q^{36} +10.0000 q^{37} +4.00000 q^{38} -2.00000 q^{39} -10.0000 q^{41} +4.00000 q^{43} -8.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +2.00000 q^{51} +2.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} -4.00000 q^{57} -2.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} +7.00000 q^{64} -12.0000 q^{67} -2.00000 q^{68} -8.00000 q^{71} +3.00000 q^{72} +10.0000 q^{73} -10.0000 q^{74} +4.00000 q^{76} +2.00000 q^{78} +1.00000 q^{81} +10.0000 q^{82} +12.0000 q^{83} -4.00000 q^{86} +2.00000 q^{87} -6.00000 q^{89} +8.00000 q^{94} -5.00000 q^{96} -2.00000 q^{97} +7.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	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		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	−1.00000	−0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	3.00000	0.612372
$25$	0	0
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	−2.00000	−0.342997
$35$	0	0
$36$	−1.00000	−0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	4.00000	0.648886
$39$	−2.00000	−0.320256
$40$	0	0
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	0	0
$51$	2.00000	0.280056
$52$	2.00000	0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	−2.00000	−0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	0	0
$64$	7.00000	0.875000
$65$	0	0
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	3.00000	0.353553
$73$	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
$78$	2.00000	0.226455
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	2.00000	0.214423
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	8.00000	0.825137
$95$	0	0
$96$	−5.00000	−0.510310
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	0	0
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	−2.00000	−0.198030
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−10.0000	−0.971286
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−1.00000	−0.0962250
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	0	0
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	−2.00000	−0.185695
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	0	0
$120$	0	0
$121$	0	0
$122$	−2.00000	−0.181071
$123$	−10.0000	−0.901670
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	3.00000	0.265165
$129$	4.00000	0.352180
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	6.00000	0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	8.00000	0.671345
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−10.0000	−0.827606
$147$	−7.00000	−0.577350
$148$	−10.0000	−0.821995
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−12.0000	−0.973329
$153$	2.00000	0.161690
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	−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
$159$	10.0000	0.793052
$160$	0	0
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−12.0000	−0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−4.00000	−0.305888
$172$	−4.00000	−0.304997
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	−2.00000	−0.151620
$175$	0	0
$176$	0	0
$177$	−4.00000	−0.300658
$178$	6.00000	0.449719
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	7.00000	0.505181
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	7.00000	0.500000
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−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
$201$	−12.0000	−0.846415
$202$	6.00000	0.422159
$203$	0	0
$204$	−2.00000	−0.140028
$205$	0	0
$206$	−16.0000	−1.11477
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−10.0000	−0.686803
$213$	−8.00000	−0.548151
$214$	12.0000	0.820303
$215$	0	0
$216$	3.00000	0.204124
$217$	0	0
$218$	14.0000	0.948200
$219$	10.0000	0.675737
$220$	0	0
$221$	−4.00000	−0.269069
$222$	−10.0000	−0.671156
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	0	0
$226$	2.00000	0.133038
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	4.00000	0.264906
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	4.00000	0.260378
$237$	0	0
$238$	0	0
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	10.0000	0.637577
$247$	8.00000	0.509028
$248$	0	0
$249$	12.0000	0.760469
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	0	0
$261$	2.00000	0.123797
$262$	−12.0000	−0.741362
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6.00000	−0.367194
$268$	12.0000	0.733017
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	8.00000	0.476393
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−5.00000	−0.294628
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−2.00000	−0.117242
$292$	−10.0000	−0.585206
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	7.00000	0.408248
$295$	0	0
$296$	30.0000	1.74371
$297$	0	0
$298$	22.0000	1.27443
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	−6.00000	−0.344691
$304$	4.00000	0.229416
$305$	0	0
$306$	−2.00000	−0.114332
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	16.0000	0.910208
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−6.00000	−0.339683
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	0	0
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	−10.0000	−0.560772
$319$	0	0
$320$	0	0
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−8.00000	−0.445132
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−14.0000	−0.774202
$328$	−30.0000	−1.65647
$329$	0	0
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−12.0000	−0.658586
$333$	10.0000	0.547997
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	9.00000	0.489535
$339$	−2.00000	−0.108625
$340$	0	0
$341$	0	0
$342$	4.00000	0.216295
$343$	0	0
$344$	12.0000	0.646997
$345$	0	0
$346$	18.0000	0.967686
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	−2.00000	−0.107211
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	−20.0000	−1.05703
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	0	0
$364$	0	0
$365$	0	0
$366$	−2.00000	−0.104542
$367$	24.0000	1.25279	0.626395	−	0.779506i	$-0.284530\pi$
$367$	24.0000	1.25279	0.626395	+	0.779506i	$0.284530\pi$
$368$	0	0
$369$	−10.0000	−0.520579
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	0	0
$375$	0	0
$376$	−24.0000	−1.23771
$377$	−4.00000	−0.206010
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	−16.0000	−0.818631
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−2.00000	−0.101797
$387$	4.00000	0.203331
$388$	2.00000	0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	0	0
$392$	−21.0000	−1.06066
$393$	12.0000	0.605320
$394$	−6.00000	−0.302276
$395$	0	0
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	12.0000	0.598506
$403$	0	0
$404$	6.00000	0.298511
$405$	0	0
$406$	0	0
$407$	0	0
$408$	6.00000	0.297044
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	−16.0000	−0.788263
$413$	0	0
$414$	0	0
$415$	0	0
$416$	10.0000	0.490290
$417$	4.00000	0.195881
$418$	0	0
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	20.0000	0.973585
$423$	−8.00000	−0.388973
$424$	30.0000	1.45693
$425$	0	0
$426$	8.00000	0.387601
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	0	0
$436$	14.0000	0.670478
$437$	0	0
$438$	−10.0000	−0.477818
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	4.00000	0.190261
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−10.0000	−0.474579
$445$	0	0
$446$	8.00000	0.378811
$447$	−22.0000	−1.04056
$448$	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
$451$	0	0
$452$	2.00000	0.0940721
$453$	8.00000	0.375873
$454$	20.0000	0.938647
$455$	0	0
$456$	−12.0000	−0.561951
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	−6.00000	−0.280362
$459$	2.00000	0.0933520
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	6.00000	0.277945
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	−14.0000	−0.645086
$472$	−12.0000	−0.552345
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	10.0000	0.457869
$478$	−16.0000	−0.731823
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−14.0000	−0.637683
$483$	0	0
$484$	0	0
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	6.00000	0.271607
$489$	4.00000	0.180886
$490$	0	0
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	10.0000	0.450835
$493$	4.00000	0.180151
$494$	−8.00000	−0.359937
$495$	0	0
$496$	0	0
$497$	0	0
$498$	−12.0000	−0.537733
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−32.0000	−1.42681	−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000	−1.42681	−0.713405	+	0.700752i	$0.752848\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	8.00000	0.354943
$509$	−34.0000	−1.50702	−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000	−1.50702	−0.753512	+	0.657434i	$0.771642\pi$
$510$	0	0
$511$	0	0
$512$	11.0000	0.486136
$513$	−4.00000	−0.176604
$514$	18.0000	0.793946
$515$	0	0
$516$	−4.00000	−0.176090
$517$	0	0
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	−2.00000	−0.0875376
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−4.00000	−0.173585
$532$	0	0
$533$	20.0000	0.866296
$534$	6.00000	0.259645
$535$	0	0
$536$	−36.0000	−1.55496
$537$	20.0000	0.863064
$538$	−14.0000	−0.603583
$539$	0	0
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	16.0000	0.687259
$543$	−10.0000	−0.429141
$544$	−10.0000	−0.428746
$545$	0	0
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−6.00000	−0.256307
$549$	2.00000	0.0853579
$550$	0	0
$551$	−8.00000	−0.340811
$552$	0	0
$553$	0	0
$554$	−6.00000	−0.254916
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	12.0000	0.504398
$567$	0	0
$568$	−24.0000	−1.00702
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	0	0
$573$	16.0000	0.668410
$574$	0	0
$575$	0	0
$576$	7.00000	0.291667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	13.0000	0.540729
$579$	2.00000	0.0831172
$580$	0	0
$581$	0	0
$582$	2.00000	0.0829027
$583$	0	0
$584$	30.0000	1.24141
$585$	0	0
$586$	−6.00000	−0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	7.00000	0.288675
$589$	0	0
$590$	0	0
$591$	6.00000	0.246807
$592$	−10.0000	−0.410997
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	0	0
$596$	22.0000	0.901155
$597$	−8.00000	−0.327418
$598$	0	0
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	0	0
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	0	0
$603$	−12.0000	−0.488678
$604$	−8.00000	−0.325515
$605$	0	0
$606$	6.00000	0.243733
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	20.0000	0.811107
$609$	0	0
$610$	0	0
$611$	16.0000	0.647291
$612$	−2.00000	−0.0808452
$613$	22.0000	0.888572	0.444286	−	0.895885i	$-0.353457\pi$
$613$	22.0000	0.888572	0.444286	+	0.895885i	$0.353457\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	6.00000	0.241551	0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000	0.241551	0.120775	+	0.992680i	$0.461462\pi$
$618$	−16.0000	−0.643614
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	24.0000	0.962312
$623$	0	0
$624$	2.00000	0.0800641
$625$	0	0
$626$	26.0000	1.03917
$627$	0	0
$628$	14.0000	0.558661
$629$	20.0000	0.797452
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	−20.0000	−0.794929
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	−10.0000	−0.396526
$637$	14.0000	0.554700
$638$	0	0
$639$	−8.00000	−0.316475
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	12.0000	0.473602
$643$	36.0000	1.41970	0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000	1.41970	0.709851	+	0.704352i	$0.248762\pi$
$644$	0	0
$645$	0	0
$646$	8.00000	0.314756
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	3.00000	0.117851
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−46.0000	−1.80012	−0.900060	−	0.435767i	$-0.856477\pi$
$653$	−46.0000	−1.80012	−0.900060	+	0.435767i	$0.856477\pi$
$654$	14.0000	0.547443
$655$	0	0
$656$	10.0000	0.390434
$657$	10.0000	0.390137
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	−12.0000	−0.466393
$663$	−4.00000	−0.155347
$664$	36.0000	1.39707
$665$	0	0
$666$	−10.0000	−0.387492
$667$	0	0
$668$	0	0
$669$	−8.00000	−0.309298
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−30.0000	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	9.00000	0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	2.00000	0.0768095
$679$	0	0
$680$	0	0
$681$	−20.0000	−0.766402
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	4.00000	0.152944
$685$	0	0
$686$	0	0
$687$	6.00000	0.228914
$688$	−4.00000	−0.152499
$689$	−20.0000	−0.761939
$690$	0	0
$691$	−44.0000	−1.67384	−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000	−1.67384	−0.836919	+	0.547326i	$0.815646\pi$
$692$	18.0000	0.684257
$693$	0	0
$694$	28.0000	1.06287
$695$	0	0
$696$	6.00000	0.227429
$697$	−20.0000	−0.757554
$698$	−2.00000	−0.0757011
$699$	−6.00000	−0.226941
$700$	0	0
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	2.00000	0.0754851
$703$	−40.0000	−1.50863
$704$	0	0
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	4.00000	0.150329
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	0	0
$712$	−18.0000	−0.674579
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−20.0000	−0.747435
$717$	16.0000	0.597531
$718$	−24.0000	−0.895672
$719$	−48.0000	−1.79010	−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000	−1.79010	−0.895049	+	0.445968i	$0.852860\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	14.0000	0.520666
$724$	10.0000	0.371647
$725$	0	0
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	8.00000	0.295891
$732$	−2.00000	−0.0739221
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−24.0000	−0.885856
$735$	0	0
$736$	0	0
$737$	0	0
$738$	10.0000	0.368105
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	0	0
$741$	8.00000	0.293887
$742$	0	0
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	0	0
$745$	0	0
$746$	26.0000	0.951928
$747$	12.0000	0.439057
$748$	0	0
$749$	0	0
$750$	0	0
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	8.00000	0.291730
$753$	12.0000	0.437304
$754$	4.00000	0.145671
$755$	0	0
$756$	0	0
$757$	26.0000	0.944986	0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000	0.944986	0.472493	+	0.881334i	$0.343354\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	8.00000	0.289809
$763$	0	0
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−24.0000	−0.867155
$767$	8.00000	0.288863
$768$	−17.0000	−0.613435
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	−2.00000	−0.0719816
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	−6.00000	−0.215387
$777$	0	0
$778$	−6.00000	−0.215110
$779$	40.0000	1.43315
$780$	0	0
$781$	0	0
$782$	0	0
$783$	2.00000	0.0714742
$784$	7.00000	0.250000
$785$	0	0
$786$	−12.0000	−0.428026
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−6.00000	−0.213741
$789$	16.0000	0.569615
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−4.00000	−0.142044
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	8.00000	0.283552
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	−16.0000	−0.566039
$800$	0	0
$801$	−6.00000	−0.212000
$802$	−18.0000	−0.635602
$803$	0	0
$804$	12.0000	0.423207
$805$	0	0
$806$	0	0
$807$	14.0000	0.492823
$808$	−18.0000	−0.633238
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	0	0
$811$	−12.0000	−0.421377	−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000	−0.421377	−0.210688	+	0.977553i	$0.567571\pi$
$812$	0	0
$813$	−16.0000	−0.561144
$814$	0	0
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	−16.0000	−0.559769
$818$	26.0000	0.909069
$819$	0	0
$820$	0	0
$821$	−54.0000	−1.88461	−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000	−1.88461	−0.942306	+	0.334751i	$0.891348\pi$
$822$	−6.00000	−0.209274
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	48.0000	1.67216
$825$	0	0
$826$	0	0
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	0	0
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	0	0
$831$	6.00000	0.208138
$832$	−14.0000	−0.485363
$833$	−14.0000	−0.485071
$834$	−4.00000	−0.138509
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−4.00000	−0.138178
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	26.0000	0.896019
$843$	6.00000	0.206651
$844$	20.0000	0.688428
$845$	0	0
$846$	8.00000	0.275046
$847$	0	0
$848$	−10.0000	−0.343401
$849$	−12.0000	−0.411839
$850$	0	0
$851$	0	0
$852$	8.00000	0.274075
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	0	0
$855$	0	0
$856$	−36.0000	−1.23045
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−14.0000	−0.475739
$867$	−13.0000	−0.441503
$868$	0	0
$869$	0	0
$870$	0	0
$871$	24.0000	0.813209
$872$	−42.0000	−1.42230
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	0	0
$876$	−10.0000	−0.337869
$877$	30.0000	1.01303	0.506514	−	0.862232i	$-0.330934\pi$
$877$	30.0000	1.01303	0.506514	+	0.862232i	$0.330934\pi$
$878$	40.0000	1.34993
$879$	6.00000	0.202375
$880$	0	0
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	7.00000	0.235702
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	−12.0000	−0.403148
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	30.0000	1.00673
$889$	0	0
$890$	0	0
$891$	0	0
$892$	8.00000	0.267860
$893$	32.0000	1.07084
$894$	22.0000	0.735790
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−2.00000	−0.0667409
$899$	0	0
$900$	0	0
$901$	20.0000	0.666297
$902$	0	0
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	−8.00000	−0.265782
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	20.0000	0.663723
$909$	−6.00000	−0.199007
$910$	0	0
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−6.00000	−0.198246
$917$	0	0
$918$	−2.00000	−0.0660098
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	28.0000	0.922631
$922$	−18.0000	−0.592798
$923$	16.0000	0.526646
$924$	0	0
$925$	0	0
$926$	24.0000	0.788689
$927$	16.0000	0.525509
$928$	−10.0000	−0.328266
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	0	0
$931$	28.0000	0.917663
$932$	6.00000	0.196537
$933$	−24.0000	−0.785725
$934$	28.0000	0.916188
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−54.0000	−1.76410	−0.882052	−	0.471153i	$-0.843838\pi$
$937$	−54.0000	−1.76410	−0.882052	+	0.471153i	$0.843838\pi$
$938$	0	0
$939$	−26.0000	−0.848478
$940$	0	0
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	14.0000	0.456145
$943$	0	0
$944$	4.00000	0.130189
$945$	0	0
$946$	0	0
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	0	0
$949$	−20.0000	−0.649227
$950$	0	0
$951$	2.00000	0.0648544
$952$	0	0
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	−10.0000	−0.323762
$955$	0	0
$956$	−16.0000	−0.517477
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	20.0000	0.644826
$963$	−12.0000	−0.386695
$964$	−14.0000	−0.450910
$965$	0	0
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	0	0
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	32.0000	1.02535
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	−4.00000	−0.127906
$979$	0	0
$980$	0	0
$981$	−14.0000	−0.446986
$982$	28.0000	0.893516
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−30.0000	−0.956365
$985$	0	0
$986$	−4.00000	−0.127386
$987$	0	0
$988$	−8.00000	−0.254514
$989$	0	0
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	0	0
$993$	12.0000	0.380808
$994$	0	0
$995$	0	0
$996$	−12.0000	−0.380235
$997$	54.0000	1.71020	0.855099	−	0.518465i	$-0.173497\pi$
$997$	54.0000	1.71020	0.855099	+	0.518465i	$0.173497\pi$
$998$	−4.00000	−0.126618
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9075.2.a.g.1.1		1
5.4	even	2		1815.2.a.d.1.1		1
11.10	odd	2		75.2.a.b.1.1		1
15.14	odd	2		5445.2.a.c.1.1		1
33.32	even	2		225.2.a.b.1.1		1
44.43	even	2		1200.2.a.e.1.1		1
55.32	even	4		75.2.b.b.49.2		2
55.43	even	4		75.2.b.b.49.1		2
55.54	odd	2		15.2.a.a.1.1	✓	1
77.76	even	2		3675.2.a.j.1.1		1
88.21	odd	2		4800.2.a.t.1.1		1
88.43	even	2		4800.2.a.bz.1.1		1
132.131	odd	2		3600.2.a.u.1.1		1
165.32	odd	4		225.2.b.b.199.1		2
165.98	odd	4		225.2.b.b.199.2		2
165.164	even	2		45.2.a.a.1.1		1
220.43	odd	4		1200.2.f.h.49.1		2
220.87	odd	4		1200.2.f.h.49.2		2
220.219	even	2		240.2.a.d.1.1		1
385.54	even	6		735.2.i.d.361.1		2
385.109	odd	6		735.2.i.e.226.1		2
385.164	even	6		735.2.i.d.226.1		2
385.219	odd	6		735.2.i.e.361.1		2
385.384	even	2		735.2.a.c.1.1		1
440.43	odd	4		4800.2.f.c.3649.2		2
440.109	odd	2		960.2.a.l.1.1		1
440.197	even	4		4800.2.f.bf.3649.2		2
440.219	even	2		960.2.a.a.1.1		1
440.307	odd	4		4800.2.f.c.3649.1		2
440.373	even	4		4800.2.f.bf.3649.1		2
495.164	even	6		405.2.e.c.271.1		2
495.274	odd	6		405.2.e.f.136.1		2
495.329	even	6		405.2.e.c.136.1		2
495.439	odd	6		405.2.e.f.271.1		2
660.263	even	4		3600.2.f.e.2449.2		2
660.527	even	4		3600.2.f.e.2449.1		2
660.659	odd	2		720.2.a.c.1.1		1
715.714	odd	2		2535.2.a.j.1.1		1
880.109	odd	4		3840.2.k.m.1921.1		2
880.219	even	4		3840.2.k.r.1921.1		2
880.549	odd	4		3840.2.k.m.1921.2		2
880.659	even	4		3840.2.k.r.1921.2		2
935.934	odd	2		4335.2.a.c.1.1		1
1045.1044	even	2		5415.2.a.j.1.1		1
1155.1154	odd	2		2205.2.a.i.1.1		1
1265.1264	even	2		7935.2.a.d.1.1		1
1320.659	odd	2		2880.2.a.bc.1.1		1
1320.989	even	2		2880.2.a.y.1.1		1
2145.2144	even	2		7605.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.2.a.a.1.1	✓	1	55.54	odd	2
45.2.a.a.1.1		1	165.164	even	2
75.2.a.b.1.1		1	11.10	odd	2
75.2.b.b.49.1		2	55.43	even	4
75.2.b.b.49.2		2	55.32	even	4
225.2.a.b.1.1		1	33.32	even	2
225.2.b.b.199.1		2	165.32	odd	4
225.2.b.b.199.2		2	165.98	odd	4
240.2.a.d.1.1		1	220.219	even	2
405.2.e.c.136.1		2	495.329	even	6
405.2.e.c.271.1		2	495.164	even	6
405.2.e.f.136.1		2	495.274	odd	6
405.2.e.f.271.1		2	495.439	odd	6
720.2.a.c.1.1		1	660.659	odd	2
735.2.a.c.1.1		1	385.384	even	2
735.2.i.d.226.1		2	385.164	even	6
735.2.i.d.361.1		2	385.54	even	6
735.2.i.e.226.1		2	385.109	odd	6
735.2.i.e.361.1		2	385.219	odd	6
960.2.a.a.1.1		1	440.219	even	2
960.2.a.l.1.1		1	440.109	odd	2
1200.2.a.e.1.1		1	44.43	even	2
1200.2.f.h.49.1		2	220.43	odd	4
1200.2.f.h.49.2		2	220.87	odd	4
1815.2.a.d.1.1		1	5.4	even	2
2205.2.a.i.1.1		1	1155.1154	odd	2
2535.2.a.j.1.1		1	715.714	odd	2
2880.2.a.y.1.1		1	1320.989	even	2
2880.2.a.bc.1.1		1	1320.659	odd	2
3600.2.a.u.1.1		1	132.131	odd	2
3600.2.f.e.2449.1		2	660.527	even	4
3600.2.f.e.2449.2		2	660.263	even	4
3675.2.a.j.1.1		1	77.76	even	2
3840.2.k.m.1921.1		2	880.109	odd	4
3840.2.k.m.1921.2		2	880.549	odd	4
3840.2.k.r.1921.1		2	880.219	even	4
3840.2.k.r.1921.2		2	880.659	even	4
4335.2.a.c.1.1		1	935.934	odd	2
4800.2.a.t.1.1		1	88.21	odd	2
4800.2.a.bz.1.1		1	88.43	even	2
4800.2.f.c.3649.1		2	440.307	odd	4
4800.2.f.c.3649.2		2	440.43	odd	4
4800.2.f.bf.3649.1		2	440.373	even	4
4800.2.f.bf.3649.2		2	440.197	even	4
5415.2.a.j.1.1		1	1045.1044	even	2
5445.2.a.c.1.1		1	15.14	odd	2
7605.2.a.g.1.1		1	2145.2144	even	2
7935.2.a.d.1.1		1	1265.1264	even	2
9075.2.a.g.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9075.a (trivial)

Introduction

L-functions

Modular forms

Varieties

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