LMFDB - Embedded newform 798.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.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:	$6.37206208130$
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	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} +2.00000 q^{20} -1.00000 q^{21} +4.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -2.00000 q^{29} +2.00000 q^{30} +1.00000 q^{32} -2.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} +2.00000 q^{39} +2.00000 q^{40} -6.00000 q^{41} -1.00000 q^{42} +4.00000 q^{43} +2.00000 q^{45} +4.00000 q^{46} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} -1.00000 q^{56} +1.00000 q^{57} -2.00000 q^{58} +12.0000 q^{59} +2.00000 q^{60} -10.0000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -8.00000 q^{67} -2.00000 q^{68} +4.00000 q^{69} -2.00000 q^{70} +1.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} -1.00000 q^{75} +1.00000 q^{76} +2.00000 q^{78} -4.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} -1.00000 q^{84} -4.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} +10.0000 q^{89} +2.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} +2.00000 q^{95} +1.00000 q^{96} -2.00000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	−1.00000	−0.218218
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	2.00000	0.365148
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	1.00000	0.162221
$39$	2.00000	0.320256
$40$	2.00000	0.316228
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.00000	−0.154303
$43$	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
$45$	2.00000	0.298142
$46$	4.00000	0.589768
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−2.00000	−0.280056
$52$	2.00000	0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	1.00000	0.132453
$58$	−2.00000	−0.262613
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	2.00000	0.258199
$61$	−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
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−2.00000	−0.242536
$69$	4.00000	0.481543
$70$	−2.00000	−0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	0	0
$78$	2.00000	0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	2.00000	0.223607
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−1.00000	−0.109109
$85$	−4.00000	−0.433861
$86$	4.00000	0.431331
$87$	−2.00000	−0.214423
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	2.00000	0.210819
$91$	−2.00000	−0.209657
$92$	4.00000	0.417029
$93$	0	0
$94$	0	0
$95$	2.00000	0.205196
$96$	1.00000	0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	−2.00000	−0.198030
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	0.196116
$105$	−2.00000	−0.195180
$106$	−10.0000	−0.971286
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	1.00000	0.0962250
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	−1.00000	−0.0944911
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	1.00000	0.0936586
$115$	8.00000	0.746004
$116$	−2.00000	−0.185695
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	2.00000	0.183340
$120$	2.00000	0.182574
$121$	−11.0000	−1.00000
$122$	−10.0000	−0.905357
$123$	−6.00000	−0.541002
$124$	0	0
$125$	−12.0000	−1.07331
$126$	−1.00000	−0.0890871
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	1.00000	0.0883883
$129$	4.00000	0.352180
$130$	4.00000	0.350823
$131$	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
$133$	−1.00000	−0.0867110
$134$	−8.00000	−0.691095
$135$	2.00000	0.172133
$136$	−2.00000	−0.171499
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	4.00000	0.340503
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	−4.00000	−0.332182
$146$	−6.00000	−0.496564
$147$	1.00000	0.0824786
$148$	−2.00000	−0.164399
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−1.00000	−0.0816497
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	1.00000	0.0811107
$153$	−2.00000	−0.161690
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−4.00000	−0.318223
$159$	−10.0000	−0.793052
$160$	2.00000	0.158114
$161$	−4.00000	−0.315244
$162$	1.00000	0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	4.00000	0.310460
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	−4.00000	−0.306786
$171$	1.00000	0.0764719
$172$	4.00000	0.304997
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−2.00000	−0.151620
$175$	1.00000	0.0755929
$176$	0	0
$177$	12.0000	0.901975
$178$	10.0000	0.749532
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	2.00000	0.149071
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.00000	−0.148250
$183$	−10.0000	−0.739221
$184$	4.00000	0.294884
$185$	−4.00000	−0.294086
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−1.00000	−0.0727393
$190$	2.00000	0.145095
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−2.00000	−0.143592
$195$	4.00000	0.286446
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	−8.00000	−0.564276
$202$	2.00000	0.140720
$203$	2.00000	0.140372
$204$	−2.00000	−0.140028
$205$	−12.0000	−0.838116
$206$	8.00000	0.557386
$207$	4.00000	0.278019
$208$	2.00000	0.138675
$209$	0	0
$210$	−2.00000	−0.138013
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	−4.00000	−0.273434
$215$	8.00000	0.545595
$216$	1.00000	0.0680414
$217$	0	0
$218$	−10.0000	−0.677285
$219$	−6.00000	−0.405442
$220$	0	0
$221$	−4.00000	−0.269069
$222$	−2.00000	−0.134231
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	−1.00000	−0.0668153
$225$	−1.00000	−0.0666667
$226$	2.00000	0.133038
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	1.00000	0.0662266
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	−2.00000	−0.131306
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	12.0000	0.781133
$237$	−4.00000	−0.259828
$238$	2.00000	0.129641
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	2.00000	0.129099
$241$	6.00000	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$242$	−11.0000	−0.707107
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	2.00000	0.127775
$246$	−6.00000	−0.382546
$247$	2.00000	0.127257
$248$	0	0
$249$	4.00000	0.253490
$250$	−12.0000	−0.758947
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	4.00000	0.250982
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	10.0000	0.623783	0.311891	−	0.950118i	$-0.399037\pi$
$257$	10.0000	0.623783	0.311891	+	0.950118i	$0.399037\pi$
$258$	4.00000	0.249029
$259$	2.00000	0.124274
$260$	4.00000	0.248069
$261$	−2.00000	−0.123797
$262$	12.0000	0.741362
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	−20.0000	−1.22859
$266$	−1.00000	−0.0613139
$267$	10.0000	0.611990
$268$	−8.00000	−0.488678
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	2.00000	0.121716
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	−2.00000	−0.121268
$273$	−2.00000	−0.121046
$274$	2.00000	0.120824
$275$	0	0
$276$	4.00000	0.240772
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	−2.00000	−0.119523
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	0	0
$285$	2.00000	0.118470
$286$	0	0
$287$	6.00000	0.354169
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−4.00000	−0.234888
$291$	−2.00000	−0.117242
$292$	−6.00000	−0.351123
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	1.00000	0.0583212
$295$	24.0000	1.39733
$296$	−2.00000	−0.116248
$297$	0	0
$298$	6.00000	0.347571
$299$	8.00000	0.462652
$300$	−1.00000	−0.0577350
$301$	−4.00000	−0.230556
$302$	−12.0000	−0.690522
$303$	2.00000	0.114897
$304$	1.00000	0.0573539
$305$	−20.0000	−1.14520
$306$	−2.00000	−0.114332
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	2.00000	0.113228
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	14.0000	0.790066
$315$	−2.00000	−0.112687
$316$	−4.00000	−0.225018
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−10.0000	−0.560772
$319$	0	0
$320$	2.00000	0.111803
$321$	−4.00000	−0.223258
$322$	−4.00000	−0.222911
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	−20.0000	−1.10770
$327$	−10.0000	−0.553001
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	4.00000	0.219529
$333$	−2.00000	−0.109599
$334$	0	0
$335$	−16.0000	−0.874173
$336$	−1.00000	−0.0545545
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−9.00000	−0.489535
$339$	2.00000	0.108625
$340$	−4.00000	−0.216930
$341$	0	0
$342$	1.00000	0.0540738
$343$	−1.00000	−0.0539949
$344$	4.00000	0.215666
$345$	8.00000	0.430706
$346$	6.00000	0.322562
$347$	24.0000	1.28839	0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000	1.28839	0.644194	+	0.764862i	$0.277193\pi$
$348$	−2.00000	−0.107211
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	1.00000	0.0534522
$351$	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	$0.659008\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	10.0000	0.529999
$357$	2.00000	0.105851
$358$	−12.0000	−0.634220
$359$	28.0000	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$360$	2.00000	0.105409
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	−11.0000	−0.577350
$364$	−2.00000	−0.104828
$365$	−12.0000	−0.628109
$366$	−10.0000	−0.522708
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	4.00000	0.208514
$369$	−6.00000	−0.312348
$370$	−4.00000	−0.207950
$371$	10.0000	0.519174
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	0	0
$375$	−12.0000	−0.619677
$376$	0	0
$377$	−4.00000	−0.206010
$378$	−1.00000	−0.0514344
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	2.00000	0.102598
$381$	4.00000	0.204926
$382$	12.0000	0.613973
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	4.00000	0.203331
$388$	−2.00000	−0.101535
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	4.00000	0.202548
$391$	−8.00000	−0.404577
$392$	1.00000	0.0505076
$393$	12.0000	0.605320
$394$	−10.0000	−0.503793
$395$	−8.00000	−0.402524
$396$	0	0
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	16.0000	0.802008
$399$	−1.00000	−0.0500626
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−8.00000	−0.399004
$403$	0	0
$404$	2.00000	0.0995037
$405$	2.00000	0.0993808
$406$	2.00000	0.0992583
$407$	0	0
$408$	−2.00000	−0.0990148
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	−12.0000	−0.592638
$411$	2.00000	0.0986527
$412$	8.00000	0.394132
$413$	−12.0000	−0.590481
$414$	4.00000	0.196589
$415$	8.00000	0.392705
$416$	2.00000	0.0980581
$417$	−20.0000	−0.979404
$418$	0	0
$419$	28.0000	1.36789	0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000	1.36789	0.683945	+	0.729534i	$0.260263\pi$
$420$	−2.00000	−0.0975900
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−8.00000	−0.389434
$423$	0	0
$424$	−10.0000	−0.485643
$425$	2.00000	0.0970143
$426$	0	0
$427$	10.0000	0.483934
$428$	−4.00000	−0.193347
$429$	0	0
$430$	8.00000	0.385794
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	1.00000	0.0481125
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	−4.00000	−0.191785
$436$	−10.0000	−0.478913
$437$	4.00000	0.191346
$438$	−6.00000	−0.286691
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−4.00000	−0.190261
$443$	32.0000	1.52037	0.760183	−	0.649709i	$-0.225109\pi$
$443$	32.0000	1.52037	0.760183	+	0.649709i	$0.225109\pi$
$444$	−2.00000	−0.0949158
$445$	20.0000	0.948091
$446$	−8.00000	−0.378811
$447$	6.00000	0.283790
$448$	−1.00000	−0.0472456
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	2.00000	0.0940721
$453$	−12.0000	−0.563809
$454$	12.0000	0.563188
$455$	−4.00000	−0.187523
$456$	1.00000	0.0468293
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	14.0000	0.654177
$459$	−2.00000	−0.0933520
$460$	8.00000	0.373002
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	18.0000	0.833834
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	2.00000	0.0924500
$469$	8.00000	0.369406
$470$	0	0
$471$	14.0000	0.645086
$472$	12.0000	0.552345
$473$	0	0
$474$	−4.00000	−0.183726
$475$	−1.00000	−0.0458831
$476$	2.00000	0.0916698
$477$	−10.0000	−0.457869
$478$	12.0000	0.548867
$479$	8.00000	0.365529	0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000	0.365529	0.182765	+	0.983157i	$0.441495\pi$
$480$	2.00000	0.0912871
$481$	−4.00000	−0.182384
$482$	6.00000	0.273293
$483$	−4.00000	−0.182006
$484$	−11.0000	−0.500000
$485$	−4.00000	−0.181631
$486$	1.00000	0.0453609
$487$	12.0000	0.543772	0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000	0.543772	0.271886	+	0.962329i	$0.412353\pi$
$488$	−10.0000	−0.452679
$489$	−20.0000	−0.904431
$490$	2.00000	0.0903508
$491$	−40.0000	−1.80517	−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000	−1.80517	−0.902587	+	0.430507i	$0.858335\pi$
$492$	−6.00000	−0.270501
$493$	4.00000	0.180151
$494$	2.00000	0.0899843
$495$	0	0
$496$	0	0
$497$	0	0
$498$	4.00000	0.179244
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−12.0000	−0.536656
$501$	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	$0.752848\pi$
$504$	−1.00000	−0.0445435
$505$	4.00000	0.177998
$506$	0	0
$507$	−9.00000	−0.399704
$508$	4.00000	0.177471
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	−4.00000	−0.177123
$511$	6.00000	0.265424
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	10.0000	0.441081
$515$	16.0000	0.705044
$516$	4.00000	0.176090
$517$	0	0
$518$	2.00000	0.0878750
$519$	6.00000	0.263371
$520$	4.00000	0.175412
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	−2.00000	−0.0875376
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	12.0000	0.524222
$525$	1.00000	0.0436436
$526$	12.0000	0.523225
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−20.0000	−0.868744
$531$	12.0000	0.520756
$532$	−1.00000	−0.0433555
$533$	−12.0000	−0.519778
$534$	10.0000	0.432742
$535$	−8.00000	−0.345870
$536$	−8.00000	−0.345547
$537$	−12.0000	−0.517838
$538$	6.00000	0.258678
$539$	0	0
$540$	2.00000	0.0860663
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	16.0000	0.687259
$543$	2.00000	0.0858282
$544$	−2.00000	−0.0857493
$545$	−20.0000	−0.856706
$546$	−2.00000	−0.0855921
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	2.00000	0.0854358
$549$	−10.0000	−0.426790
$550$	0	0
$551$	−2.00000	−0.0852029
$552$	4.00000	0.170251
$553$	4.00000	0.170097
$554$	−10.0000	−0.424859
$555$	−4.00000	−0.169791
$556$	−20.0000	−0.848189
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−44.0000	−1.85438	−0.927189	−	0.374593i	$-0.877783\pi$
$563$	−44.0000	−1.85438	−0.927189	+	0.374593i	$0.877783\pi$
$564$	0	0
$565$	4.00000	0.168281
$566$	12.0000	0.504398
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	2.00000	0.0837708
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	6.00000	0.250435
$575$	−4.00000	−0.166812
$576$	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	$0.249724\pi$
$578$	−13.0000	−0.540729
$579$	−14.0000	−0.581820
$580$	−4.00000	−0.166091
$581$	−4.00000	−0.165948
$582$	−2.00000	−0.0829027
$583$	0	0
$584$	−6.00000	−0.248282
$585$	4.00000	0.165380
$586$	−2.00000	−0.0826192
$587$	44.0000	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$588$	1.00000	0.0412393
$589$	0	0
$590$	24.0000	0.988064
$591$	−10.0000	−0.411345
$592$	−2.00000	−0.0821995
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	6.00000	0.245770
$597$	16.0000	0.654836
$598$	8.00000	0.327144
$599$	16.0000	0.653742	0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000	0.653742	0.326871	+	0.945069i	$0.394006\pi$
$600$	−1.00000	−0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−4.00000	−0.163028
$603$	−8.00000	−0.325785
$604$	−12.0000	−0.488273
$605$	−22.0000	−0.894427
$606$	2.00000	0.0812444
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	1.00000	0.0405554
$609$	2.00000	0.0810441
$610$	−20.0000	−0.809776
$611$	0	0
$612$	−2.00000	−0.0808452
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−4.00000	−0.161427
$615$	−12.0000	−0.483887
$616$	0	0
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	8.00000	0.321807
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	0	0
$623$	−10.0000	−0.400642
$624$	2.00000	0.0800641
$625$	−19.0000	−0.760000
$626$	26.0000	1.03917
$627$	0	0
$628$	14.0000	0.558661
$629$	4.00000	0.159490
$630$	−2.00000	−0.0796819
$631$	16.0000	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$632$	−4.00000	−0.159111
$633$	−8.00000	−0.317971
$634$	30.0000	1.19145
$635$	8.00000	0.317470
$636$	−10.0000	−0.396526
$637$	2.00000	0.0792429
$638$	0	0
$639$	0	0
$640$	2.00000	0.0790569
$641$	−46.0000	−1.81689	−0.908445	−	0.418004i	$-0.862730\pi$
$641$	−46.0000	−1.81689	−0.908445	+	0.418004i	$0.862730\pi$
$642$	−4.00000	−0.157867
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	−4.00000	−0.157622
$645$	8.00000	0.315000
$646$	−2.00000	−0.0786889
$647$	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
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−20.0000	−0.783260
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	−10.0000	−0.391031
$655$	24.0000	0.937758
$656$	−6.00000	−0.234261
$657$	−6.00000	−0.234082
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	−8.00000	−0.310929
$663$	−4.00000	−0.155347
$664$	4.00000	0.155230
$665$	−2.00000	−0.0775567
$666$	−2.00000	−0.0774984
$667$	−8.00000	−0.309761
$668$	0	0
$669$	−8.00000	−0.309298
$670$	−16.0000	−0.618134
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	−22.0000	−0.847408
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−10.0000	−0.384331	−0.192166	−	0.981363i	$-0.561551\pi$
$677$	−10.0000	−0.384331	−0.192166	+	0.981363i	$0.561551\pi$
$678$	2.00000	0.0768095
$679$	2.00000	0.0767530
$680$	−4.00000	−0.153393
$681$	12.0000	0.459841
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	1.00000	0.0382360
$685$	4.00000	0.152832
$686$	−1.00000	−0.0381802
$687$	14.0000	0.534133
$688$	4.00000	0.152499
$689$	−20.0000	−0.761939
$690$	8.00000	0.304555
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	24.0000	0.911028
$695$	−40.0000	−1.51729
$696$	−2.00000	−0.0758098
$697$	12.0000	0.454532
$698$	−2.00000	−0.0757011
$699$	18.0000	0.680823
$700$	1.00000	0.0377964
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	2.00000	0.0754851
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−2.00000	−0.0752177
$708$	12.0000	0.450988
$709$	22.0000	0.826227	0.413114	−	0.910679i	$-0.364441\pi$
$709$	22.0000	0.826227	0.413114	+	0.910679i	$0.364441\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	10.0000	0.374766
$713$	0	0
$714$	2.00000	0.0748481
$715$	0	0
$716$	−12.0000	−0.448461
$717$	12.0000	0.448148
$718$	28.0000	1.04495
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	2.00000	0.0745356
$721$	−8.00000	−0.297936
$722$	1.00000	0.0372161
$723$	6.00000	0.223142
$724$	2.00000	0.0743294
$725$	2.00000	0.0742781
$726$	−11.0000	−0.408248
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−12.0000	−0.444140
$731$	−8.00000	−0.295891
$732$	−10.0000	−0.369611
$733$	−50.0000	−1.84679	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000	−1.84679	−0.923396	+	0.383849i	$0.874598\pi$
$734$	32.0000	1.18114
$735$	2.00000	0.0737711
$736$	4.00000	0.147442
$737$	0	0
$738$	−6.00000	−0.220863
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	−4.00000	−0.147043
$741$	2.00000	0.0734718
$742$	10.0000	0.367112
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	12.0000	0.439646
$746$	6.00000	0.219676
$747$	4.00000	0.146352
$748$	0	0
$749$	4.00000	0.146157
$750$	−12.0000	−0.438178
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	0	0
$753$	−12.0000	−0.437304
$754$	−4.00000	−0.145671
$755$	−24.0000	−0.873449
$756$	−1.00000	−0.0363696
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	8.00000	0.290573
$759$	0	0
$760$	2.00000	0.0725476
$761$	−50.0000	−1.81250	−0.906249	−	0.422744i	$-0.861067\pi$
$761$	−50.0000	−1.81250	−0.906249	+	0.422744i	$0.861067\pi$
$762$	4.00000	0.144905
$763$	10.0000	0.362024
$764$	12.0000	0.434145
$765$	−4.00000	−0.144620
$766$	0	0
$767$	24.0000	0.866590
$768$	1.00000	0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	10.0000	0.360141
$772$	−14.0000	−0.503871
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	4.00000	0.143777
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	2.00000	0.0717496
$778$	−18.0000	−0.645331
$779$	−6.00000	−0.214972
$780$	4.00000	0.143223
$781$	0	0
$782$	−8.00000	−0.286079
$783$	−2.00000	−0.0714742
$784$	1.00000	0.0357143
$785$	28.0000	0.999363
$786$	12.0000	0.428026
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−10.0000	−0.356235
$789$	12.0000	0.427211
$790$	−8.00000	−0.284627
$791$	−2.00000	−0.0711118
$792$	0	0
$793$	−20.0000	−0.710221
$794$	30.0000	1.06466
$795$	−20.0000	−0.709327
$796$	16.0000	0.567105
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	−1.00000	−0.0353996
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	18.0000	0.635602
$803$	0	0
$804$	−8.00000	−0.282138
$805$	−8.00000	−0.281963
$806$	0	0
$807$	6.00000	0.211210
$808$	2.00000	0.0703598
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	2.00000	0.0702728
$811$	−44.0000	−1.54505	−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000	−1.54505	−0.772524	+	0.634985i	$0.781006\pi$
$812$	2.00000	0.0701862
$813$	16.0000	0.561144
$814$	0	0
$815$	−40.0000	−1.40114
$816$	−2.00000	−0.0700140
$817$	4.00000	0.139942
$818$	22.0000	0.769212
$819$	−2.00000	−0.0698857
$820$	−12.0000	−0.419058
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	2.00000	0.0697580
$823$	−8.00000	−0.278862	−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000	−0.278862	−0.139431	+	0.990232i	$0.544527\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−12.0000	−0.417533
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	4.00000	0.139010
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	8.00000	0.277684
$831$	−10.0000	−0.346896
$832$	2.00000	0.0693375
$833$	−2.00000	−0.0692959
$834$	−20.0000	−0.692543
$835$	0	0
$836$	0	0
$837$	0	0
$838$	28.0000	0.967244
$839$	16.0000	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$840$	−2.00000	−0.0690066
$841$	−25.0000	−0.862069
$842$	−10.0000	−0.344623
$843$	−6.00000	−0.206651
$844$	−8.00000	−0.275371
$845$	−18.0000	−0.619219
$846$	0	0
$847$	11.0000	0.377964
$848$	−10.0000	−0.343401
$849$	12.0000	0.411839
$850$	2.00000	0.0685994
$851$	−8.00000	−0.274236
$852$	0	0
$853$	30.0000	1.02718	0.513590	−	0.858036i	$-0.328315\pi$
$853$	30.0000	1.02718	0.513590	+	0.858036i	$0.328315\pi$
$854$	10.0000	0.342193
$855$	2.00000	0.0683986
$856$	−4.00000	−0.136717
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	0	0
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	8.00000	0.272798
$861$	6.00000	0.204479
$862$	24.0000	0.817443
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	1.00000	0.0340207
$865$	12.0000	0.408012
$866$	−2.00000	−0.0679628
$867$	−13.0000	−0.441503
$868$	0	0
$869$	0	0
$870$	−4.00000	−0.135613
$871$	−16.0000	−0.542139
$872$	−10.0000	−0.338643
$873$	−2.00000	−0.0676897
$874$	4.00000	0.135302
$875$	12.0000	0.405674
$876$	−6.00000	−0.202721
$877$	−58.0000	−1.95852	−0.979260	−	0.202606i	$-0.935059\pi$
$877$	−58.0000	−1.95852	−0.979260	+	0.202606i	$0.935059\pi$
$878$	−8.00000	−0.269987
$879$	−2.00000	−0.0674583
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	1.00000	0.0336718
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−4.00000	−0.134535
$885$	24.0000	0.806751
$886$	32.0000	1.07506
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	−2.00000	−0.0671156
$889$	−4.00000	−0.134156
$890$	20.0000	0.670402
$891$	0	0
$892$	−8.00000	−0.267860
$893$	0	0
$894$	6.00000	0.200670
$895$	−24.0000	−0.802232
$896$	−1.00000	−0.0334077
$897$	8.00000	0.267112
$898$	−14.0000	−0.467186
$899$	0	0
$900$	−1.00000	−0.0333333
$901$	20.0000	0.666297
$902$	0	0
$903$	−4.00000	−0.133112
$904$	2.00000	0.0665190
$905$	4.00000	0.132964
$906$	−12.0000	−0.398673
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	12.0000	0.398234
$909$	2.00000	0.0663358
$910$	−4.00000	−0.132599
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	26.0000	0.860004
$915$	−20.0000	−0.661180
$916$	14.0000	0.462573
$917$	−12.0000	−0.396275
$918$	−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	$0.729333\pi$
$920$	8.00000	0.263752
$921$	−4.00000	−0.131804
$922$	10.0000	0.329332
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	16.0000	0.525793
$927$	8.00000	0.262754
$928$	−2.00000	−0.0656532
$929$	−2.00000	−0.0656179	−0.0328089	−	0.999462i	$-0.510445\pi$
$929$	−2.00000	−0.0656179	−0.0328089	+	0.999462i	$0.510445\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	18.0000	0.589610
$933$	0	0
$934$	4.00000	0.130884
$935$	0	0
$936$	2.00000	0.0653720
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	8.00000	0.261209
$939$	26.0000	0.848478
$940$	0	0
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	14.0000	0.456145
$943$	−24.0000	−0.781548
$944$	12.0000	0.390567
$945$	−2.00000	−0.0650600
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	−4.00000	−0.129914
$949$	−12.0000	−0.389536
$950$	−1.00000	−0.0324443
$951$	30.0000	0.972817
$952$	2.00000	0.0648204
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−10.0000	−0.323762
$955$	24.0000	0.776622
$956$	12.0000	0.388108
$957$	0	0
$958$	8.00000	0.258468
$959$	−2.00000	−0.0645834
$960$	2.00000	0.0645497
$961$	−31.0000	−1.00000
$962$	−4.00000	−0.128965
$963$	−4.00000	−0.128898
$964$	6.00000	0.193247
$965$	−28.0000	−0.901352
$966$	−4.00000	−0.128698
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−11.0000	−0.353553
$969$	−2.00000	−0.0642493
$970$	−4.00000	−0.128432
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	1.00000	0.0320750
$973$	20.0000	0.641171
$974$	12.0000	0.384505
$975$	−2.00000	−0.0640513
$976$	−10.0000	−0.320092
$977$	50.0000	1.59964	0.799821	−	0.600239i	$-0.204928\pi$
$977$	50.0000	1.59964	0.799821	+	0.600239i	$0.204928\pi$
$978$	−20.0000	−0.639529
$979$	0	0
$980$	2.00000	0.0638877
$981$	−10.0000	−0.319275
$982$	−40.0000	−1.27645
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	−6.00000	−0.191273
$985$	−20.0000	−0.637253
$986$	4.00000	0.127386
$987$	0	0
$988$	2.00000	0.0636285
$989$	16.0000	0.508770
$990$	0	0
$991$	−36.0000	−1.14358	−0.571789	−	0.820401i	$-0.693750\pi$
$991$	−36.0000	−1.14358	−0.571789	+	0.820401i	$0.693750\pi$
$992$	0	0
$993$	−8.00000	−0.253872
$994$	0	0
$995$	32.0000	1.01447
$996$	4.00000	0.126745
$997$	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
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.a.i.1.1	✓	1
3.2	odd	2		2394.2.a.b.1.1		1
4.3	odd	2		6384.2.a.m.1.1		1
7.6	odd	2		5586.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.i.1.1	✓	1	1.1	even	1	trivial
2394.2.a.b.1.1		1	3.2	odd	2
5586.2.a.t.1.1		1	7.6	odd	2
6384.2.a.m.1.1		1	4.3	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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