LMFDB - Embedded newform 7350.2.a.d.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:	yes
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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} +5.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} +4.00000 q^{22} -5.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} -1.00000 q^{27} -3.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -5.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} +6.00000 q^{38} +1.00000 q^{39} +5.00000 q^{41} -1.00000 q^{43} -4.00000 q^{44} +5.00000 q^{46} -8.00000 q^{47} -1.00000 q^{48} -5.00000 q^{51} -1.00000 q^{52} +5.00000 q^{53} +1.00000 q^{54} +6.00000 q^{57} +3.00000 q^{58} -1.00000 q^{59} +1.00000 q^{61} +7.00000 q^{62} +1.00000 q^{64} -4.00000 q^{66} +4.00000 q^{67} +5.00000 q^{68} +5.00000 q^{69} -12.0000 q^{71} -1.00000 q^{72} +4.00000 q^{73} -4.00000 q^{74} -6.00000 q^{76} -1.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} -5.00000 q^{82} +13.0000 q^{83} +1.00000 q^{86} +3.00000 q^{87} +4.00000 q^{88} -2.00000 q^{89} -5.00000 q^{92} +7.00000 q^{93} +8.00000 q^{94} +1.00000 q^{96} +18.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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
$17$	5.00000	1.21268	0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000	1.21268	0.606339	+	0.795206i	$0.292637\pi$
$18$	−1.00000	−0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	4.00000	0.852803
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	−5.00000	−0.857493
$35$	0	0
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	6.00000	0.973329
$39$	1.00000	0.160128
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	5.00000	0.737210
$47$	−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
$49$	0	0
$50$	0	0
$51$	−5.00000	−0.700140
$52$	−1.00000	−0.138675
$53$	5.00000	0.686803	0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000	0.686803	0.343401	+	0.939189i	$0.388421\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0	0
$57$	6.00000	0.794719
$58$	3.00000	0.393919
$59$	−1.00000	−0.130189	−0.0650945	−	0.997879i	$-0.520735\pi$
$59$	−1.00000	−0.130189	−0.0650945	+	0.997879i	$0.520735\pi$
$60$	0	0
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.00000	−0.492366
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	5.00000	0.606339
$69$	5.00000	0.601929
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−6.00000	−0.688247
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.00000	−0.552158
$83$	13.0000	1.42694	0.713468	−	0.700688i	$-0.247124\pi$
$83$	13.0000	1.42694	0.713468	+	0.700688i	$0.247124\pi$
$84$	0	0
$85$	0	0
$86$	1.00000	0.107833
$87$	3.00000	0.321634
$88$	4.00000	0.426401
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	0	0
$92$	−5.00000	−0.521286
$93$	7.00000	0.725866
$94$	8.00000	0.825137
$95$	0	0
$96$	1.00000	0.102062
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	0	0
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−16.0000	−1.59206	−0.796030	−	0.605257i	$-0.793070\pi$
$101$	−16.0000	−1.59206	−0.796030	+	0.605257i	$0.793070\pi$
$102$	5.00000	0.495074
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−5.00000	−0.485643
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	−1.00000	−0.0962250
$109$	16.0000	1.53252	0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000	1.53252	0.766261	+	0.642529i	$0.222115\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	0	0
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	−6.00000	−0.561951
$115$	0	0
$116$	−3.00000	−0.278543
$117$	−1.00000	−0.0924500
$118$	1.00000	0.0920575
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	−1.00000	−0.0905357
$123$	−5.00000	−0.450835
$124$	−7.00000	−0.628619
$125$	0	0
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	−1.00000	−0.0883883
$129$	1.00000	0.0880451
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−5.00000	−0.428746
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	−5.00000	−0.425628
$139$	22.0000	1.86602	0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000	1.86602	0.933008	+	0.359856i	$0.117174\pi$
$140$	0	0
$141$	8.00000	0.673722
$142$	12.0000	1.00702
$143$	4.00000	0.334497
$144$	1.00000	0.0833333
$145$	0	0
$146$	−4.00000	−0.331042
$147$	0	0
$148$	4.00000	0.328798
$149$	5.00000	0.409616	0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000	0.409616	0.204808	+	0.978802i	$0.434343\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	6.00000	0.486664
$153$	5.00000	0.404226
$154$	0	0
$155$	0	0
$156$	1.00000	0.0800641
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	8.00000	0.636446
$159$	−5.00000	−0.396526
$160$	0	0
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−23.0000	−1.80150	−0.900750	−	0.434339i	$-0.856982\pi$
$163$	−23.0000	−1.80150	−0.900750	+	0.434339i	$0.856982\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	−13.0000	−1.00900
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−6.00000	−0.458831
$172$	−1.00000	−0.0762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−3.00000	−0.227429
$175$	0	0
$176$	−4.00000	−0.301511
$177$	1.00000	0.0751646
$178$	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
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	−1.00000	−0.0739221
$184$	5.00000	0.368605
$185$	0	0
$186$	−7.00000	−0.513265
$187$	−20.0000	−1.46254
$188$	−8.00000	−0.583460
$189$	0	0
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000	−0.0721688
$193$	−18.0000	−1.29567	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000	−1.29567	−0.647834	+	0.761781i	$0.724325\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	0	0
$197$	21.0000	1.49619	0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000	1.49619	0.748094	+	0.663593i	$0.230969\pi$
$198$	4.00000	0.284268
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	16.0000	1.12576
$203$	0	0
$204$	−5.00000	−0.350070
$205$	0	0
$206$	−7.00000	−0.487713
$207$	−5.00000	−0.347524
$208$	−1.00000	−0.0693375
$209$	24.0000	1.66011
$210$	0	0
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	5.00000	0.343401
$213$	12.0000	0.822226
$214$	6.00000	0.410152
$215$	0	0
$216$	1.00000	0.0680414
$217$	0	0
$218$	−16.0000	−1.08366
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−5.00000	−0.336336
$222$	4.00000	0.268462
$223$	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
$226$	4.00000	0.266076
$227$	15.0000	0.995585	0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000	0.995585	0.497792	+	0.867296i	$0.334144\pi$
$228$	6.00000	0.397360
$229$	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
$232$	3.00000	0.196960
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	−1.00000	−0.0650945
$237$	8.00000	0.519656
$238$	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
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−5.00000	−0.321412
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	0	0
$246$	5.00000	0.318788
$247$	6.00000	0.381771
$248$	7.00000	0.444500
$249$	−13.0000	−0.823842
$250$	0	0
$251$	−25.0000	−1.57799	−0.788993	−	0.614402i	$-0.789397\pi$
$251$	−25.0000	−1.57799	−0.788993	+	0.614402i	$0.789397\pi$
$252$	0	0
$253$	20.0000	1.25739
$254$	6.00000	0.376473
$255$	0	0
$256$	1.00000	0.0625000
$257$	−27.0000	−1.68421	−0.842107	−	0.539311i	$-0.818685\pi$
$257$	−27.0000	−1.68421	−0.842107	+	0.539311i	$0.818685\pi$
$258$	−1.00000	−0.0622573
$259$	0	0
$260$	0	0
$261$	−3.00000	−0.185695
$262$	12.0000	0.741362
$263$	3.00000	0.184988	0.0924940	−	0.995713i	$-0.470516\pi$
$263$	3.00000	0.184988	0.0924940	+	0.995713i	$0.470516\pi$
$264$	−4.00000	−0.246183
$265$	0	0
$266$	0	0
$267$	2.00000	0.122398
$268$	4.00000	0.244339
$269$	28.0000	1.70719	0.853595	−	0.520937i	$-0.174417\pi$
$269$	28.0000	1.70719	0.853595	+	0.520937i	$0.174417\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	5.00000	0.303170
$273$	0	0
$274$	10.0000	0.604122
$275$	0	0
$276$	5.00000	0.300965
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−22.0000	−1.31947
$279$	−7.00000	−0.419079
$280$	0	0
$281$	−4.00000	−0.238620	−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000	−0.238620	−0.119310	+	0.992857i	$0.538068\pi$
$282$	−8.00000	−0.476393
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−4.00000	−0.236525
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	8.00000	0.470588
$290$	0	0
$291$	−18.0000	−1.05518
$292$	4.00000	0.234082
$293$	−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
$296$	−4.00000	−0.232495
$297$	4.00000	0.232104
$298$	−5.00000	−0.289642
$299$	5.00000	0.289157
$300$	0	0
$301$	0	0
$302$	−12.0000	−0.690522
$303$	16.0000	0.919176
$304$	−6.00000	−0.344124
$305$	0	0
$306$	−5.00000	−0.285831
$307$	−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
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	−1.00000	−0.0566139
$313$	4.00000	0.226093	0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000	0.226093	0.113047	+	0.993590i	$0.463939\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−15.0000	−0.842484	−0.421242	−	0.906948i	$-0.638406\pi$
$317$	−15.0000	−0.842484	−0.421242	+	0.906948i	$0.638406\pi$
$318$	5.00000	0.280386
$319$	12.0000	0.671871
$320$	0	0
$321$	6.00000	0.334887
$322$	0	0
$323$	−30.0000	−1.66924
$324$	1.00000	0.0555556
$325$	0	0
$326$	23.0000	1.27385
$327$	−16.0000	−0.884802
$328$	−5.00000	−0.276079
$329$	0	0
$330$	0	0
$331$	35.0000	1.92377	0.961887	−	0.273447i	$-0.0881639\pi$
$331$	35.0000	1.92377	0.961887	+	0.273447i	$0.0881639\pi$
$332$	13.0000	0.713468
$333$	4.00000	0.219199
$334$	−18.0000	−0.984916
$335$	0	0
$336$	0	0
$337$	−31.0000	−1.68868	−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000	−1.68868	−0.844339	+	0.535810i	$0.820006\pi$
$338$	12.0000	0.652714
$339$	4.00000	0.217250
$340$	0	0
$341$	28.0000	1.51629
$342$	6.00000	0.324443
$343$	0	0
$344$	1.00000	0.0539164
$345$	0	0
$346$	−6.00000	−0.322562
$347$	22.0000	1.18102	0.590511	−	0.807030i	$-0.298926\pi$
$347$	22.0000	1.18102	0.590511	+	0.807030i	$0.298926\pi$
$348$	3.00000	0.160817
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	4.00000	0.213201
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	−1.00000	−0.0531494
$355$	0	0
$356$	−2.00000	−0.106000
$357$	0	0
$358$	8.00000	0.422813
$359$	1.00000	0.0527780	0.0263890	−	0.999652i	$-0.491599\pi$
$359$	1.00000	0.0527780	0.0263890	+	0.999652i	$0.491599\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−10.0000	−0.525588
$363$	−5.00000	−0.262432
$364$	0	0
$365$	0	0
$366$	1.00000	0.0522708
$367$	29.0000	1.51379	0.756894	−	0.653538i	$-0.226716\pi$
$367$	29.0000	1.51379	0.756894	+	0.653538i	$0.226716\pi$
$368$	−5.00000	−0.260643
$369$	5.00000	0.260290
$370$	0	0
$371$	0	0
$372$	7.00000	0.362933
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	20.0000	1.03418
$375$	0	0
$376$	8.00000	0.412568
$377$	3.00000	0.154508
$378$	0	0
$379$	−19.0000	−0.975964	−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000	−0.975964	−0.487982	+	0.872854i	$0.662267\pi$
$380$	0	0
$381$	6.00000	0.307389
$382$	15.0000	0.767467
$383$	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
$386$	18.0000	0.916176
$387$	−1.00000	−0.0508329
$388$	18.0000	0.913812
$389$	−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
$391$	−25.0000	−1.26430
$392$	0	0
$393$	12.0000	0.605320
$394$	−21.0000	−1.05796
$395$	0	0
$396$	−4.00000	−0.201008
$397$	−31.0000	−1.55585	−0.777923	−	0.628360i	$-0.783727\pi$
$397$	−31.0000	−1.55585	−0.777923	+	0.628360i	$0.783727\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	0	0
$401$	−38.0000	−1.89763	−0.948815	−	0.315833i	$-0.897716\pi$
$401$	−38.0000	−1.89763	−0.948815	+	0.315833i	$0.897716\pi$
$402$	4.00000	0.199502
$403$	7.00000	0.348695
$404$	−16.0000	−0.796030
$405$	0	0
$406$	0	0
$407$	−16.0000	−0.793091
$408$	5.00000	0.247537
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	7.00000	0.344865
$413$	0	0
$414$	5.00000	0.245737
$415$	0	0
$416$	1.00000	0.0490290
$417$	−22.0000	−1.07734
$418$	−24.0000	−1.17388
$419$	33.0000	1.61216	0.806078	−	0.591810i	$-0.201586\pi$
$419$	33.0000	1.61216	0.806078	+	0.591810i	$0.201586\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	−17.0000	−0.827547
$423$	−8.00000	−0.388973
$424$	−5.00000	−0.242821
$425$	0	0
$426$	−12.0000	−0.581402
$427$	0	0
$428$	−6.00000	−0.290021
$429$	−4.00000	−0.193122
$430$	0	0
$431$	−15.0000	−0.722525	−0.361262	−	0.932464i	$-0.617654\pi$
$431$	−15.0000	−0.722525	−0.361262	+	0.932464i	$0.617654\pi$
$432$	−1.00000	−0.0481125
$433$	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
$436$	16.0000	0.766261
$437$	30.0000	1.43509
$438$	4.00000	0.191127
$439$	5.00000	0.238637	0.119318	−	0.992856i	$-0.461929\pi$
$439$	5.00000	0.238637	0.119318	+	0.992856i	$0.461929\pi$
$440$	0	0
$441$	0	0
$442$	5.00000	0.237826
$443$	8.00000	0.380091	0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000	0.380091	0.190046	+	0.981775i	$0.439136\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	−19.0000	−0.899676
$447$	−5.00000	−0.236492
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	−20.0000	−0.941763
$452$	−4.00000	−0.188144
$453$	−12.0000	−0.563809
$454$	−15.0000	−0.703985
$455$	0	0
$456$	−6.00000	−0.280976
$457$	33.0000	1.54367	0.771837	−	0.635820i	$-0.219338\pi$
$457$	33.0000	1.54367	0.771837	+	0.635820i	$0.219338\pi$
$458$	−14.0000	−0.654177
$459$	−5.00000	−0.233380
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	0	0
$463$	38.0000	1.76601	0.883005	−	0.469364i	$-0.155517\pi$
$463$	38.0000	1.76601	0.883005	+	0.469364i	$0.155517\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	10.0000	0.463241
$467$	5.00000	0.231372	0.115686	−	0.993286i	$-0.463093\pi$
$467$	5.00000	0.231372	0.115686	+	0.993286i	$0.463093\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	0	0
$471$	−14.0000	−0.645086
$472$	1.00000	0.0460287
$473$	4.00000	0.183920
$474$	−8.00000	−0.367452
$475$	0	0
$476$	0	0
$477$	5.00000	0.228934
$478$	−16.0000	−0.731823
$479$	−34.0000	−1.55350	−0.776750	−	0.629809i	$-0.783133\pi$
$479$	−34.0000	−1.55350	−0.776750	+	0.629809i	$0.783133\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	22.0000	1.00207
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	1.00000	0.0453609
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	−1.00000	−0.0452679
$489$	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	$0.366866\pi$
$492$	−5.00000	−0.225417
$493$	−15.0000	−0.675566
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−7.00000	−0.314309
$497$	0	0
$498$	13.0000	0.582544
$499$	43.0000	1.92494	0.962472	−	0.271380i	$-0.0874801\pi$
$499$	43.0000	1.92494	0.962472	+	0.271380i	$0.0874801\pi$
$500$	0	0
$501$	−18.0000	−0.804181
$502$	25.0000	1.11580
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	0	0
$506$	−20.0000	−0.889108
$507$	12.0000	0.532939
$508$	−6.00000	−0.266207
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	6.00000	0.264906
$514$	27.0000	1.19092
$515$	0	0
$516$	1.00000	0.0440225
$517$	32.0000	1.40736
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	27.0000	1.18289	0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000	1.18289	0.591446	+	0.806345i	$0.298557\pi$
$522$	3.00000	0.131306
$523$	−16.0000	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−3.00000	−0.130806
$527$	−35.0000	−1.52462
$528$	4.00000	0.174078
$529$	2.00000	0.0869565
$530$	0	0
$531$	−1.00000	−0.0433963
$532$	0	0
$533$	−5.00000	−0.216574
$534$	−2.00000	−0.0865485
$535$	0	0
$536$	−4.00000	−0.172774
$537$	8.00000	0.345225
$538$	−28.0000	−1.20717
$539$	0	0
$540$	0	0
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−8.00000	−0.343629
$543$	−10.0000	−0.429141
$544$	−5.00000	−0.214373
$545$	0	0
$546$	0	0
$547$	5.00000	0.213785	0.106892	−	0.994271i	$-0.465910\pi$
$547$	5.00000	0.213785	0.106892	+	0.994271i	$0.465910\pi$
$548$	−10.0000	−0.427179
$549$	1.00000	0.0426790
$550$	0	0
$551$	18.0000	0.766826
$552$	−5.00000	−0.212814
$553$	0	0
$554$	8.00000	0.339887
$555$	0	0
$556$	22.0000	0.933008
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	7.00000	0.296334
$559$	1.00000	0.0422955
$560$	0	0
$561$	20.0000	0.844401
$562$	4.00000	0.168730
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	−22.0000	−0.924729
$567$	0	0
$568$	12.0000	0.503509
$569$	16.0000	0.670755	0.335377	−	0.942084i	$-0.391136\pi$
$569$	16.0000	0.670755	0.335377	+	0.942084i	$0.391136\pi$
$570$	0	0
$571$	21.0000	0.878823	0.439411	−	0.898286i	$-0.355187\pi$
$571$	21.0000	0.878823	0.439411	+	0.898286i	$0.355187\pi$
$572$	4.00000	0.167248
$573$	15.0000	0.626634
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	−8.00000	−0.332756
$579$	18.0000	0.748054
$580$	0	0
$581$	0	0
$582$	18.0000	0.746124
$583$	−20.0000	−0.828315
$584$	−4.00000	−0.165521
$585$	0	0
$586$	12.0000	0.495715
$587$	−7.00000	−0.288921	−0.144460	−	0.989511i	$-0.546145\pi$
$587$	−7.00000	−0.288921	−0.144460	+	0.989511i	$0.546145\pi$
$588$	0	0
$589$	42.0000	1.73058
$590$	0	0
$591$	−21.0000	−0.863825
$592$	4.00000	0.164399
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	5.00000	0.204808
$597$	−8.00000	−0.327418
$598$	−5.00000	−0.204465
$599$	29.0000	1.18491	0.592454	−	0.805604i	$-0.298159\pi$
$599$	29.0000	1.18491	0.592454	+	0.805604i	$0.298159\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	0	0
$603$	4.00000	0.162893
$604$	12.0000	0.488273
$605$	0	0
$606$	−16.0000	−0.649956
$607$	20.0000	0.811775	0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000	0.811775	0.405887	+	0.913923i	$0.366962\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	0	0
$611$	8.00000	0.323645
$612$	5.00000	0.202113
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	7.00000	0.281581
$619$	30.0000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$620$	0	0
$621$	5.00000	0.200643
$622$	28.0000	1.12270
$623$	0	0
$624$	1.00000	0.0400320
$625$	0	0
$626$	−4.00000	−0.159872
$627$	−24.0000	−0.958468
$628$	14.0000	0.558661
$629$	20.0000	0.797452
$630$	0	0
$631$	10.0000	0.398094	0.199047	−	0.979990i	$-0.436215\pi$
$631$	10.0000	0.398094	0.199047	+	0.979990i	$0.436215\pi$
$632$	8.00000	0.318223
$633$	−17.0000	−0.675689
$634$	15.0000	0.595726
$635$	0	0
$636$	−5.00000	−0.198263
$637$	0	0
$638$	−12.0000	−0.475085
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	−6.00000	−0.236801
$643$	24.0000	0.946468	0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000	0.946468	0.473234	+	0.880937i	$0.343087\pi$
$644$	0	0
$645$	0	0
$646$	30.0000	1.18033
$647$	16.0000	0.629025	0.314512	−	0.949253i	$-0.398159\pi$
$647$	16.0000	0.629025	0.314512	+	0.949253i	$0.398159\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	0	0
$651$	0	0
$652$	−23.0000	−0.900750
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	16.0000	0.625650
$655$	0	0
$656$	5.00000	0.195217
$657$	4.00000	0.156055
$658$	0	0
$659$	14.0000	0.545363	0.272681	−	0.962104i	$-0.412090\pi$
$659$	14.0000	0.545363	0.272681	+	0.962104i	$0.412090\pi$
$660$	0	0
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−35.0000	−1.36031
$663$	5.00000	0.194184
$664$	−13.0000	−0.504498
$665$	0	0
$666$	−4.00000	−0.154997
$667$	15.0000	0.580802
$668$	18.0000	0.696441
$669$	−19.0000	−0.734582
$670$	0	0
$671$	−4.00000	−0.154418
$672$	0	0
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	31.0000	1.19408
$675$	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	$0.487763\pi$
$678$	−4.00000	−0.153619
$679$	0	0
$680$	0	0
$681$	−15.0000	−0.574801
$682$	−28.0000	−1.07218
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	−6.00000	−0.229416
$685$	0	0
$686$	0	0
$687$	−14.0000	−0.534133
$688$	−1.00000	−0.0381246
$689$	−5.00000	−0.190485
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−22.0000	−0.835109
$695$	0	0
$696$	−3.00000	−0.113715
$697$	25.0000	0.946943
$698$	−23.0000	−0.870563
$699$	10.0000	0.378235
$700$	0	0
$701$	−11.0000	−0.415464	−0.207732	−	0.978186i	$-0.566608\pi$
$701$	−11.0000	−0.415464	−0.207732	+	0.978186i	$0.566608\pi$
$702$	−1.00000	−0.0377426
$703$	−24.0000	−0.905177
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−6.00000	−0.225813
$707$	0	0
$708$	1.00000	0.0375823
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	2.00000	0.0749532
$713$	35.0000	1.31076
$714$	0	0
$715$	0	0
$716$	−8.00000	−0.298974
$717$	−16.0000	−0.597531
$718$	−1.00000	−0.0373197
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	0	0
$721$	0	0
$722$	−17.0000	−0.632674
$723$	22.0000	0.818189
$724$	10.0000	0.371647
$725$	0	0
$726$	5.00000	0.185567
$727$	−13.0000	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−5.00000	−0.184932
$732$	−1.00000	−0.0369611
$733$	21.0000	0.775653	0.387826	−	0.921732i	$-0.373226\pi$
$733$	21.0000	0.775653	0.387826	+	0.921732i	$0.373226\pi$
$734$	−29.0000	−1.07041
$735$	0	0
$736$	5.00000	0.184302
$737$	−16.0000	−0.589368
$738$	−5.00000	−0.184053
$739$	−15.0000	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$740$	0	0
$741$	−6.00000	−0.220416
$742$	0	0
$743$	−15.0000	−0.550297	−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000	−0.550297	−0.275148	+	0.961402i	$0.588727\pi$
$744$	−7.00000	−0.256632
$745$	0	0
$746$	−12.0000	−0.439351
$747$	13.0000	0.475645
$748$	−20.0000	−0.731272
$749$	0	0
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	−8.00000	−0.291730
$753$	25.0000	0.911051
$754$	−3.00000	−0.109254
$755$	0	0
$756$	0	0
$757$	20.0000	0.726912	0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000	0.726912	0.363456	+	0.931611i	$0.381597\pi$
$758$	19.0000	0.690111
$759$	−20.0000	−0.725954
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	−6.00000	−0.217357
$763$	0	0
$764$	−15.0000	−0.542681
$765$	0	0
$766$	−14.0000	−0.505841
$767$	1.00000	0.0361079
$768$	−1.00000	−0.0360844
$769$	20.0000	0.721218	0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000	0.721218	0.360609	+	0.932717i	$0.382569\pi$
$770$	0	0
$771$	27.0000	0.972381
$772$	−18.0000	−0.647834
$773$	−24.0000	−0.863220	−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000	−0.863220	−0.431610	+	0.902060i	$0.642054\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	−18.0000	−0.646162
$777$	0	0
$778$	6.00000	0.215110
$779$	−30.0000	−1.07486
$780$	0	0
$781$	48.0000	1.71758
$782$	25.0000	0.893998
$783$	3.00000	0.107211
$784$	0	0
$785$	0	0
$786$	−12.0000	−0.428026
$787$	−30.0000	−1.06938	−0.534692	−	0.845047i	$-0.679572\pi$
$787$	−30.0000	−1.06938	−0.534692	+	0.845047i	$0.679572\pi$
$788$	21.0000	0.748094
$789$	−3.00000	−0.106803
$790$	0	0
$791$	0	0
$792$	4.00000	0.142134
$793$	−1.00000	−0.0355110
$794$	31.0000	1.10015
$795$	0	0
$796$	8.00000	0.283552
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	0	0
$799$	−40.0000	−1.41510
$800$	0	0
$801$	−2.00000	−0.0706665
$802$	38.0000	1.34183
$803$	−16.0000	−0.564628
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−7.00000	−0.246564
$807$	−28.0000	−0.985647
$808$	16.0000	0.562878
$809$	−28.0000	−0.984428	−0.492214	−	0.870474i	$-0.663812\pi$
$809$	−28.0000	−0.984428	−0.492214	+	0.870474i	$0.663812\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	16.0000	0.560800
$815$	0	0
$816$	−5.00000	−0.175035
$817$	6.00000	0.209913
$818$	4.00000	0.139857
$819$	0	0
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	−10.0000	−0.348790
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	0	0
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	−5.00000	−0.173762
$829$	−17.0000	−0.590434	−0.295217	−	0.955430i	$-0.595392\pi$
$829$	−17.0000	−0.590434	−0.295217	+	0.955430i	$0.595392\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	22.0000	0.761798
$835$	0	0
$836$	24.0000	0.830057
$837$	7.00000	0.241955
$838$	−33.0000	−1.13997
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	34.0000	1.17172
$843$	4.00000	0.137767
$844$	17.0000	0.585164
$845$	0	0
$846$	8.00000	0.275046
$847$	0	0
$848$	5.00000	0.171701
$849$	−22.0000	−0.755038
$850$	0	0
$851$	−20.0000	−0.685591
$852$	12.0000	0.411113
$853$	17.0000	0.582069	0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000	0.582069	0.291034	+	0.956713i	$0.406001\pi$
$854$	0	0
$855$	0	0
$856$	6.00000	0.205076
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	4.00000	0.136558
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	0	0
$862$	15.0000	0.510902
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−8.00000	−0.271694
$868$	0	0
$869$	32.0000	1.08553
$870$	0	0
$871$	−4.00000	−0.135535
$872$	−16.0000	−0.541828
$873$	18.0000	0.609208
$874$	−30.0000	−1.01477
$875$	0	0
$876$	−4.00000	−0.135147
$877$	48.0000	1.62084	0.810422	−	0.585846i	$-0.199238\pi$
$877$	48.0000	1.62084	0.810422	+	0.585846i	$0.199238\pi$
$878$	−5.00000	−0.168742
$879$	12.0000	0.404750
$880$	0	0
$881$	37.0000	1.24656	0.623281	−	0.781998i	$-0.285799\pi$
$881$	37.0000	1.24656	0.623281	+	0.781998i	$0.285799\pi$
$882$	0	0
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	−5.00000	−0.168168
$885$	0	0
$886$	−8.00000	−0.268765
$887$	4.00000	0.134307	0.0671534	−	0.997743i	$-0.478608\pi$
$887$	4.00000	0.134307	0.0671534	+	0.997743i	$0.478608\pi$
$888$	4.00000	0.134231
$889$	0	0
$890$	0	0
$891$	−4.00000	−0.134005
$892$	19.0000	0.636167
$893$	48.0000	1.60626
$894$	5.00000	0.167225
$895$	0	0
$896$	0	0
$897$	−5.00000	−0.166945
$898$	−30.0000	−1.00111
$899$	21.0000	0.700389
$900$	0	0
$901$	25.0000	0.832871
$902$	20.0000	0.665927
$903$	0	0
$904$	4.00000	0.133038
$905$	0	0
$906$	12.0000	0.398673
$907$	5.00000	0.166022	0.0830111	−	0.996549i	$-0.473546\pi$
$907$	5.00000	0.166022	0.0830111	+	0.996549i	$0.473546\pi$
$908$	15.0000	0.497792
$909$	−16.0000	−0.530687
$910$	0	0
$911$	−53.0000	−1.75597	−0.877984	−	0.478690i	$-0.841112\pi$
$911$	−53.0000	−1.75597	−0.877984	+	0.478690i	$0.841112\pi$
$912$	6.00000	0.198680
$913$	−52.0000	−1.72095
$914$	−33.0000	−1.09154
$915$	0	0
$916$	14.0000	0.462573
$917$	0	0
$918$	5.00000	0.165025
$919$	2.00000	0.0659739	0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000	0.0659739	0.0329870	+	0.999456i	$0.489498\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	−12.0000	−0.395199
$923$	12.0000	0.394985
$924$	0	0
$925$	0	0
$926$	−38.0000	−1.24876
$927$	7.00000	0.229910
$928$	3.00000	0.0984798
$929$	−27.0000	−0.885841	−0.442921	−	0.896561i	$-0.646058\pi$
$929$	−27.0000	−0.885841	−0.442921	+	0.896561i	$0.646058\pi$
$930$	0	0
$931$	0	0
$932$	−10.0000	−0.327561
$933$	28.0000	0.916679
$934$	−5.00000	−0.163605
$935$	0	0
$936$	1.00000	0.0326860
$937$	−60.0000	−1.96011	−0.980057	−	0.198715i	$-0.936323\pi$
$937$	−60.0000	−1.96011	−0.980057	+	0.198715i	$0.936323\pi$
$938$	0	0
$939$	−4.00000	−0.130535
$940$	0	0
$941$	28.0000	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	14.0000	0.456145
$943$	−25.0000	−0.814112
$944$	−1.00000	−0.0325472
$945$	0	0
$946$	−4.00000	−0.130051
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	8.00000	0.259828
$949$	−4.00000	−0.129845
$950$	0	0
$951$	15.0000	0.486408
$952$	0	0
$953$	4.00000	0.129573	0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000	0.129573	0.0647864	+	0.997899i	$0.479363\pi$
$954$	−5.00000	−0.161881
$955$	0	0
$956$	16.0000	0.517477
$957$	−12.0000	−0.387905
$958$	34.0000	1.09849
$959$	0	0
$960$	0	0
$961$	18.0000	0.580645
$962$	4.00000	0.128965
$963$	−6.00000	−0.193347
$964$	−22.0000	−0.708572
$965$	0	0
$966$	0	0
$967$	−38.0000	−1.22200	−0.610999	−	0.791632i	$-0.709232\pi$
$967$	−38.0000	−1.22200	−0.610999	+	0.791632i	$0.709232\pi$
$968$	−5.00000	−0.160706
$969$	30.0000	0.963739
$970$	0	0
$971$	44.0000	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$971$	44.0000	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	1.00000	0.0320092
$977$	−36.0000	−1.15174	−0.575871	−	0.817541i	$-0.695337\pi$
$977$	−36.0000	−1.15174	−0.575871	+	0.817541i	$0.695337\pi$
$978$	−23.0000	−0.735459
$979$	8.00000	0.255681
$980$	0	0
$981$	16.0000	0.510841
$982$	−18.0000	−0.574403
$983$	−28.0000	−0.893061	−0.446531	−	0.894768i	$-0.647341\pi$
$983$	−28.0000	−0.893061	−0.446531	+	0.894768i	$0.647341\pi$
$984$	5.00000	0.159394
$985$	0	0
$986$	15.0000	0.477697
$987$	0	0
$988$	6.00000	0.190885
$989$	5.00000	0.158991
$990$	0	0
$991$	48.0000	1.52477	0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000	1.52477	0.762385	+	0.647124i	$0.224028\pi$
$992$	7.00000	0.222250
$993$	−35.0000	−1.11069
$994$	0	0
$995$	0	0
$996$	−13.0000	−0.411921
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	−43.0000	−1.36114
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.d.1.1	✓	1
5.4	even	2		7350.2.a.ck.1.1	yes	1
7.6	odd	2		7350.2.a.x.1.1	yes	1
35.34	odd	2		7350.2.a.bq.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7350.2.a.d.1.1	✓	1	1.1	even	1	trivial
7350.2.a.x.1.1	yes	1	7.6	odd	2
7350.2.a.bq.1.1	yes	1	35.34	odd	2
7350.2.a.ck.1.1	yes	1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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