LMFDB - Embedded newform 8034.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
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	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.00000 q^{12} +1.00000 q^{13} +2.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +2.00000 q^{20} -8.00000 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.00000 q^{29} +2.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} +4.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +10.0000 q^{41} -4.00000 q^{43} +2.00000 q^{45} -8.00000 q^{46} +4.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} +1.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +4.00000 q^{57} -2.00000 q^{58} +12.0000 q^{59} +2.00000 q^{60} +14.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} +16.0000 q^{67} +2.00000 q^{68} -8.00000 q^{69} -4.00000 q^{71} +1.00000 q^{72} +6.00000 q^{73} +10.0000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +1.00000 q^{78} -8.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} +12.0000 q^{83} +4.00000 q^{85} -4.00000 q^{86} -2.00000 q^{87} -2.00000 q^{89} +2.00000 q^{90} -8.00000 q^{92} -4.00000 q^{93} +4.00000 q^{94} +8.00000 q^{95} +1.00000 q^{96} -14.0000 q^{97} -7.00000 q^{98} +O(q^{100})\)

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
$2$	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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	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
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	2.00000	0.516398
$16$	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	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	1.00000	0.204124
$25$	−1.00000	−0.200000
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−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
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	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
$39$	1.00000	0.160128
$40$	2.00000	0.316228
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	2.00000	0.298142
$46$	−8.00000	−1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	−1.00000	−0.141421
$51$	2.00000	0.280056
$52$	1.00000	0.138675
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0	0
$57$	4.00000	0.529813
$58$	−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
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	2.00000	0.242536
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	1.00000	0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	10.0000	1.16248
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	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	$0.648589\pi$
$80$	2.00000	0.223607
$81$	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
$85$	4.00000	0.433861
$86$	−4.00000	−0.431331
$87$	−2.00000	−0.214423
$88$	0	0
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	2.00000	0.210819
$91$	0	0
$92$	−8.00000	−0.834058
$93$	−4.00000	−0.414781
$94$	4.00000	0.412568
$95$	8.00000	0.820783
$96$	1.00000	0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−7.00000	−0.707107
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	2.00000	0.198030
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	0	0
$106$	6.00000	0.582772
$107$	−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
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	0	0
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	4.00000	0.374634
$115$	−16.0000	−1.49201
$116$	−2.00000	−0.185695
$117$	1.00000	0.0924500
$118$	12.0000	1.10469
$119$	0	0
$120$	2.00000	0.182574
$121$	−11.0000	−1.00000
$122$	14.0000	1.26750
$123$	10.0000	0.901670
$124$	−4.00000	−0.359211
$125$	−12.0000	−1.07331
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	2.00000	0.175412
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	0	0
$134$	16.0000	1.38219
$135$	2.00000	0.172133
$136$	2.00000	0.171499
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	−8.00000	−0.681005
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	−4.00000	−0.335673
$143$	0	0
$144$	1.00000	0.0833333
$145$	−4.00000	−0.332182
$146$	6.00000	0.496564
$147$	−7.00000	−0.577350
$148$	10.0000	0.821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	−1.00000	−0.0816497
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	4.00000	0.324443
$153$	2.00000	0.161690
$154$	0	0
$155$	−8.00000	−0.642575
$156$	1.00000	0.0800641
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−8.00000	−0.636446
$159$	6.00000	0.475831
$160$	2.00000	0.158114
$161$	0	0
$162$	1.00000	0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	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
$169$	1.00000	0.0769231
$170$	4.00000	0.306786
$171$	4.00000	0.305888
$172$	−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
$175$	0	0
$176$	0	0
$177$	12.0000	0.901975
$178$	−2.00000	−0.149906
$179$	−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
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	−8.00000	−0.589768
$185$	20.0000	1.47043
$186$	−4.00000	−0.293294
$187$	0	0
$188$	4.00000	0.291730
$189$	0	0
$190$	8.00000	0.580381
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	1.00000	0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−14.0000	−1.00514
$195$	2.00000	0.143223
$196$	−7.00000	−0.500000
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	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
$201$	16.0000	1.12855
$202$	−2.00000	−0.140720
$203$	0	0
$204$	2.00000	0.140028
$205$	20.0000	1.39686
$206$	−1.00000	−0.0696733
$207$	−8.00000	−0.556038
$208$	1.00000	0.0693375
$209$	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	$0.741699\pi$
$212$	6.00000	0.412082
$213$	−4.00000	−0.274075
$214$	−12.0000	−0.820303
$215$	−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
$221$	2.00000	0.134535
$222$	10.0000	0.671156
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	18.0000	1.19734
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	4.00000	0.264906
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	1.00000	0.0653720
$235$	8.00000	0.521862
$236$	12.0000	0.781133
$237$	−8.00000	−0.519656
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	2.00000	0.129099
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	−11.0000	−0.707107
$243$	1.00000	0.0641500
$244$	14.0000	0.896258
$245$	−14.0000	−0.894427
$246$	10.0000	0.637577
$247$	4.00000	0.254514
$248$	−4.00000	−0.254000
$249$	12.0000	0.760469
$250$	−12.0000	−0.758947
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	0	0
$253$	0	0
$254$	−8.00000	−0.501965
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	2.00000	0.124035
$261$	−2.00000	−0.123797
$262$	−12.0000	−0.741362
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	0	0
$267$	−2.00000	−0.122398
$268$	16.0000	0.977356
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	2.00000	0.121716
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	18.0000	1.08742
$275$	0	0
$276$	−8.00000	−0.481543
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−12.0000	−0.719712
$279$	−4.00000	−0.239474
$280$	0	0
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	4.00000	0.238197
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−4.00000	−0.237356
$285$	8.00000	0.473879
$286$	0	0
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−4.00000	−0.234888
$291$	−14.0000	−0.820695
$292$	6.00000	0.351123
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	−7.00000	−0.408248
$295$	24.0000	1.39733
$296$	10.0000	0.581238
$297$	0	0
$298$	−18.0000	−1.04271
$299$	−8.00000	−0.462652
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	4.00000	0.230174
$303$	−2.00000	−0.114897
$304$	4.00000	0.229416
$305$	28.0000	1.60328
$306$	2.00000	0.114332
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	0	0
$309$	−1.00000	−0.0568880
$310$	−8.00000	−0.454369
$311$	32.0000	1.81455	0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000	1.81455	0.907277	+	0.420534i	$0.138157\pi$
$312$	1.00000	0.0566139
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	−2.00000	−0.112867
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	2.00000	0.111803
$321$	−12.0000	−0.669775
$322$	0	0
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	−1.00000	−0.0554700
$326$	−12.0000	−0.664619
$327$	10.0000	0.553001
$328$	10.0000	0.552158
$329$	0	0
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	12.0000	0.658586
$333$	10.0000	0.547997
$334$	0	0
$335$	32.0000	1.74835
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	1.00000	0.0543928
$339$	18.0000	0.977626
$340$	4.00000	0.216930
$341$	0	0
$342$	4.00000	0.216295
$343$	0	0
$344$	−4.00000	−0.215666
$345$	−16.0000	−0.861411
$346$	6.00000	0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	−2.00000	−0.107211
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	12.0000	0.637793
$355$	−8.00000	−0.424596
$356$	−2.00000	−0.106000
$357$	0	0
$358$	−12.0000	−0.634220
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	2.00000	0.105409
$361$	−3.00000	−0.157895
$362$	−18.0000	−0.946059
$363$	−11.0000	−0.577350
$364$	0	0
$365$	12.0000	0.628109
$366$	14.0000	0.731792
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−8.00000	−0.417029
$369$	10.0000	0.520579
$370$	20.0000	1.03975
$371$	0	0
$372$	−4.00000	−0.207390
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	0	0
$375$	−12.0000	−0.619677
$376$	4.00000	0.206284
$377$	−2.00000	−0.103005
$378$	0	0
$379$	−32.0000	−1.64373	−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000	−1.64373	−0.821865	+	0.569683i	$0.807066\pi$
$380$	8.00000	0.410391
$381$	−8.00000	−0.409852
$382$	−8.00000	−0.409316
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−4.00000	−0.203331
$388$	−14.0000	−0.710742
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	2.00000	0.101274
$391$	−16.0000	−0.809155
$392$	−7.00000	−0.353553
$393$	−12.0000	−0.605320
$394$	2.00000	0.100759
$395$	−16.0000	−0.805047
$396$	0	0
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	16.0000	0.798007
$403$	−4.00000	−0.199254
$404$	−2.00000	−0.0995037
$405$	2.00000	0.0993808
$406$	0	0
$407$	0	0
$408$	2.00000	0.0990148
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	20.0000	0.987730
$411$	18.0000	0.887875
$412$	−1.00000	−0.0492665
$413$	0	0
$414$	−8.00000	−0.393179
$415$	24.0000	1.17811
$416$	1.00000	0.0490290
$417$	−12.0000	−0.587643
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−20.0000	−0.973585
$423$	4.00000	0.194487
$424$	6.00000	0.291386
$425$	−2.00000	−0.0970143
$426$	−4.00000	−0.193801
$427$	0	0
$428$	−12.0000	−0.580042
$429$	0	0
$430$	−8.00000	−0.385794
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	0	0
$435$	−4.00000	−0.191785
$436$	10.0000	0.478913
$437$	−32.0000	−1.53077
$438$	6.00000	0.286691
$439$	−16.0000	−0.763638	−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000	−0.763638	−0.381819	+	0.924237i	$0.624702\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	2.00000	0.0951303
$443$	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
$445$	−4.00000	−0.189618
$446$	0	0
$447$	−18.0000	−0.851371
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	18.0000	0.846649
$453$	4.00000	0.187936
$454$	−8.00000	−0.375459
$455$	0	0
$456$	4.00000	0.187317
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−10.0000	−0.467269
$459$	2.00000	0.0933520
$460$	−16.0000	−0.746004
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−20.0000	−0.929479	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000	−0.929479	−0.464739	+	0.885448i	$0.653852\pi$
$464$	−2.00000	−0.0928477
$465$	−8.00000	−0.370991
$466$	−22.0000	−1.01913
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	8.00000	0.369012
$471$	−2.00000	−0.0921551
$472$	12.0000	0.552345
$473$	0	0
$474$	−8.00000	−0.367452
$475$	−4.00000	−0.183533
$476$	0	0
$477$	6.00000	0.274721
$478$	−16.0000	−0.731823
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	2.00000	0.0912871
$481$	10.0000	0.455961
$482$	22.0000	1.00207
$483$	0	0
$484$	−11.0000	−0.500000
$485$	−28.0000	−1.27141
$486$	1.00000	0.0453609
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	14.0000	0.633750
$489$	−12.0000	−0.542659
$490$	−14.0000	−0.632456
$491$	−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
$494$	4.00000	0.179969
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	12.0000	0.537733
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	20.0000	0.892644
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	0	0
$505$	−4.00000	−0.177998
$506$	0	0
$507$	1.00000	0.0444116
$508$	−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	$0.771642\pi$
$510$	4.00000	0.177123
$511$	0	0
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−14.0000	−0.617514
$515$	−2.00000	−0.0881305
$516$	−4.00000	−0.176090
$517$	0	0
$518$	0	0
$519$	6.00000	0.263371
$520$	2.00000	0.0877058
$521$	26.0000	1.13908	0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000	1.13908	0.569540	+	0.821963i	$0.307121\pi$
$522$	−2.00000	−0.0875376
$523$	−12.0000	−0.524723	−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000	−0.524723	−0.262362	+	0.964970i	$0.584501\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	0	0
$527$	−8.00000	−0.348485
$528$	0	0
$529$	41.0000	1.78261
$530$	12.0000	0.521247
$531$	12.0000	0.520756
$532$	0	0
$533$	10.0000	0.433148
$534$	−2.00000	−0.0865485
$535$	−24.0000	−1.03761
$536$	16.0000	0.691095
$537$	−12.0000	−0.517838
$538$	−2.00000	−0.0862261
$539$	0	0
$540$	2.00000	0.0860663
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	12.0000	0.515444
$543$	−18.0000	−0.772454
$544$	2.00000	0.0857493
$545$	20.0000	0.856706
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	18.0000	0.768922
$549$	14.0000	0.597505
$550$	0	0
$551$	−8.00000	−0.340811
$552$	−8.00000	−0.340503
$553$	0	0
$554$	−26.0000	−1.10463
$555$	20.0000	0.848953
$556$	−12.0000	−0.508913
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−4.00000	−0.169334
$559$	−4.00000	−0.169182
$560$	0	0
$561$	0	0
$562$	22.0000	0.928014
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	4.00000	0.168430
$565$	36.0000	1.51453
$566$	4.00000	0.168133
$567$	0	0
$568$	−4.00000	−0.167836
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	8.00000	0.335083
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	−8.00000	−0.334205
$574$	0	0
$575$	8.00000	0.333623
$576$	1.00000	0.0416667
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	−13.0000	−0.540729
$579$	22.0000	0.914289
$580$	−4.00000	−0.166091
$581$	0	0
$582$	−14.0000	−0.580319
$583$	0	0
$584$	6.00000	0.248282
$585$	2.00000	0.0826898
$586$	−14.0000	−0.578335
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	−7.00000	−0.288675
$589$	−16.0000	−0.659269
$590$	24.0000	0.988064
$591$	2.00000	0.0822690
$592$	10.0000	0.410997
$593$	22.0000	0.903432	0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000	0.903432	0.451716	+	0.892162i	$0.350812\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	16.0000	0.654836
$598$	−8.00000	−0.327144
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	−1.00000	−0.0408248
$601$	2.00000	0.0815817	0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000	0.0815817	0.0407909	+	0.999168i	$0.487012\pi$
$602$	0	0
$603$	16.0000	0.651570
$604$	4.00000	0.162758
$605$	−22.0000	−0.894427
$606$	−2.00000	−0.0812444
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	28.0000	1.13369
$611$	4.00000	0.161823
$612$	2.00000	0.0808452
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	16.0000	0.645707
$615$	20.0000	0.806478
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−1.00000	−0.0402259
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−8.00000	−0.321288
$621$	−8.00000	−0.321029
$622$	32.0000	1.28308
$623$	0	0
$624$	1.00000	0.0400320
$625$	−19.0000	−0.760000
$626$	26.0000	1.03917
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	20.0000	0.797452
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	−8.00000	−0.318223
$633$	−20.0000	−0.794929
$634$	−18.0000	−0.714871
$635$	−16.0000	−0.634941
$636$	6.00000	0.237915
$637$	−7.00000	−0.277350
$638$	0	0
$639$	−4.00000	−0.158238
$640$	2.00000	0.0790569
$641$	34.0000	1.34292	0.671460	−	0.741041i	$-0.265668\pi$
$641$	34.0000	1.34292	0.671460	+	0.741041i	$0.265668\pi$
$642$	−12.0000	−0.473602
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	0	0
$645$	−8.00000	−0.315000
$646$	8.00000	0.314756
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.00000	−0.0392232
$651$	0	0
$652$	−12.0000	−0.469956
$653$	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
$656$	10.0000	0.390434
$657$	6.00000	0.234082
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	8.00000	0.310929
$663$	2.00000	0.0776736
$664$	12.0000	0.465690
$665$	0	0
$666$	10.0000	0.387492
$667$	16.0000	0.619522
$668$	0	0
$669$	0	0
$670$	32.0000	1.23627
$671$	0	0
$672$	0	0
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	18.0000	0.693334
$675$	−1.00000	−0.0384900
$676$	1.00000	0.0384615
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	18.0000	0.691286
$679$	0	0
$680$	4.00000	0.153393
$681$	−8.00000	−0.306561
$682$	0	0
$683$	−8.00000	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$683$	−8.00000	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$684$	4.00000	0.152944
$685$	36.0000	1.37549
$686$	0	0
$687$	−10.0000	−0.381524
$688$	−4.00000	−0.152499
$689$	6.00000	0.228582
$690$	−16.0000	−0.609110
$691$	16.0000	0.608669	0.304334	−	0.952565i	$-0.401566\pi$
$691$	16.0000	0.608669	0.304334	+	0.952565i	$0.401566\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	−24.0000	−0.910372
$696$	−2.00000	−0.0758098
$697$	20.0000	0.757554
$698$	18.0000	0.681310
$699$	−22.0000	−0.832116
$700$	0	0
$701$	−34.0000	−1.28416	−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000	−1.28416	−0.642081	+	0.766637i	$0.721929\pi$
$702$	1.00000	0.0377426
$703$	40.0000	1.50863
$704$	0	0
$705$	8.00000	0.301297
$706$	6.00000	0.225813
$707$	0	0
$708$	12.0000	0.450988
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	−8.00000	−0.300235
$711$	−8.00000	−0.300023
$712$	−2.00000	−0.0749532
$713$	32.0000	1.19841
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−16.0000	−0.597531
$718$	−16.0000	−0.597115
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−3.00000	−0.111648
$723$	22.0000	0.818189
$724$	−18.0000	−0.668965
$725$	2.00000	0.0742781
$726$	−11.0000	−0.408248
$727$	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
$730$	12.0000	0.444140
$731$	−8.00000	−0.295891
$732$	14.0000	0.517455
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	8.00000	0.295285
$735$	−14.0000	−0.516398
$736$	−8.00000	−0.294884
$737$	0	0
$738$	10.0000	0.368105
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	20.0000	0.735215
$741$	4.00000	0.146944
$742$	0	0
$743$	36.0000	1.32071	0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000	1.32071	0.660356	+	0.750953i	$0.270405\pi$
$744$	−4.00000	−0.146647
$745$	−36.0000	−1.31894
$746$	−10.0000	−0.366126
$747$	12.0000	0.439057
$748$	0	0
$749$	0	0
$750$	−12.0000	−0.438178
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	4.00000	0.145865
$753$	20.0000	0.728841
$754$	−2.00000	−0.0728357
$755$	8.00000	0.291150
$756$	0	0
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	−32.0000	−1.16229
$759$	0	0
$760$	8.00000	0.290191
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	−8.00000	−0.289809
$763$	0	0
$764$	−8.00000	−0.289430
$765$	4.00000	0.144620
$766$	20.0000	0.722629
$767$	12.0000	0.433295
$768$	1.00000	0.0360844
$769$	6.00000	0.216366	0.108183	−	0.994131i	$-0.465497\pi$
$769$	6.00000	0.216366	0.108183	+	0.994131i	$0.465497\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	22.0000	0.791797
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	−4.00000	−0.143777
$775$	4.00000	0.143684
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−26.0000	−0.932145
$779$	40.0000	1.43315
$780$	2.00000	0.0716115
$781$	0	0
$782$	−16.0000	−0.572159
$783$	−2.00000	−0.0714742
$784$	−7.00000	−0.250000
$785$	−4.00000	−0.142766
$786$	−12.0000	−0.428026
$787$	−44.0000	−1.56843	−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000	−1.56843	−0.784215	+	0.620489i	$0.786934\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	−16.0000	−0.569254
$791$	0	0
$792$	0	0
$793$	14.0000	0.497155
$794$	10.0000	0.354887
$795$	12.0000	0.425596
$796$	16.0000	0.567105
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	−1.00000	−0.0353553
$801$	−2.00000	−0.0706665
$802$	−14.0000	−0.494357
$803$	0	0
$804$	16.0000	0.564276
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−2.00000	−0.0704033
$808$	−2.00000	−0.0703598
$809$	−54.0000	−1.89854	−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000	−1.89854	−0.949269	+	0.314464i	$0.898175\pi$
$810$	2.00000	0.0702728
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	0	0
$813$	12.0000	0.420858
$814$	0	0
$815$	−24.0000	−0.840683
$816$	2.00000	0.0700140
$817$	−16.0000	−0.559769
$818$	−14.0000	−0.489499
$819$	0	0
$820$	20.0000	0.698430
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	18.0000	0.627822
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−1.00000	−0.0348367
$825$	0	0
$826$	0	0
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	−8.00000	−0.278019
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	24.0000	0.833052
$831$	−26.0000	−0.901930
$832$	1.00000	0.0346688
$833$	−14.0000	−0.485071
$834$	−12.0000	−0.415526
$835$	0	0
$836$	0	0
$837$	−4.00000	−0.138260
$838$	12.0000	0.414533
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	22.0000	0.757720
$844$	−20.0000	−0.688428
$845$	2.00000	0.0688021
$846$	4.00000	0.137523
$847$	0	0
$848$	6.00000	0.206041
$849$	4.00000	0.137280
$850$	−2.00000	−0.0685994
$851$	−80.0000	−2.74236
$852$	−4.00000	−0.137038
$853$	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
$855$	8.00000	0.273594
$856$	−12.0000	−0.410152
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−24.0000	−0.817443
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	1.00000	0.0340207
$865$	12.0000	0.408012
$866$	−38.0000	−1.29129
$867$	−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
$873$	−14.0000	−0.473828
$874$	−32.0000	−1.08242
$875$	0	0
$876$	6.00000	0.202721
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	−16.0000	−0.539974
$879$	−14.0000	−0.472208
$880$	0	0
$881$	50.0000	1.68454	0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000	1.68454	0.842271	+	0.539054i	$0.181218\pi$
$882$	−7.00000	−0.235702
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	2.00000	0.0672673
$885$	24.0000	0.806751
$886$	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	$0.201714\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	−4.00000	−0.134080
$891$	0	0
$892$	0	0
$893$	16.0000	0.535420
$894$	−18.0000	−0.602010
$895$	−24.0000	−0.802232
$896$	0	0
$897$	−8.00000	−0.267112
$898$	30.0000	1.00111
$899$	8.00000	0.266815
$900$	−1.00000	−0.0333333
$901$	12.0000	0.399778
$902$	0	0
$903$	0	0
$904$	18.0000	0.598671
$905$	−36.0000	−1.19668
$906$	4.00000	0.132891
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−8.00000	−0.265489
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	−40.0000	−1.32526	−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000	−1.32526	−0.662630	+	0.748947i	$0.730560\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−10.0000	−0.330771
$915$	28.0000	0.925651
$916$	−10.0000	−0.330409
$917$	0	0
$918$	2.00000	0.0660098
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	−16.0000	−0.527504
$921$	16.0000	0.527218
$922$	6.00000	0.197599
$923$	−4.00000	−0.131662
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−20.0000	−0.657241
$927$	−1.00000	−0.0328443
$928$	−2.00000	−0.0656532
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	−8.00000	−0.262330
$931$	−28.0000	−0.917663
$932$	−22.0000	−0.720634
$933$	32.0000	1.04763
$934$	12.0000	0.392652
$935$	0	0
$936$	1.00000	0.0326860
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	26.0000	0.848478
$940$	8.00000	0.260931
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	−2.00000	−0.0651635
$943$	−80.0000	−2.60516
$944$	12.0000	0.390567
$945$	0	0
$946$	0	0
$947$	8.00000	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$947$	8.00000	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$948$	−8.00000	−0.259828
$949$	6.00000	0.194768
$950$	−4.00000	−0.129777
$951$	−18.0000	−0.583690
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	6.00000	0.194257
$955$	−16.0000	−0.517748
$956$	−16.0000	−0.517477
$957$	0	0
$958$	36.0000	1.16311
$959$	0	0
$960$	2.00000	0.0645497
$961$	−15.0000	−0.483871
$962$	10.0000	0.322413
$963$	−12.0000	−0.386695
$964$	22.0000	0.708572
$965$	44.0000	1.41641
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	−11.0000	−0.353553
$969$	8.00000	0.256997
$970$	−28.0000	−0.899026
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−20.0000	−0.640841
$975$	−1.00000	−0.0320256
$976$	14.0000	0.448129
$977$	34.0000	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$978$	−12.0000	−0.383718
$979$	0	0
$980$	−14.0000	−0.447214
$981$	10.0000	0.319275
$982$	−28.0000	−0.893516
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	10.0000	0.318788
$985$	4.00000	0.127451
$986$	−4.00000	−0.127386
$987$	0	0
$988$	4.00000	0.127257
$989$	32.0000	1.01754
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−4.00000	−0.127000
$993$	8.00000	0.253872
$994$	0	0
$995$	32.0000	1.01447
$996$	12.0000	0.380235
$997$	−34.0000	−1.07679	−0.538395	−	0.842692i	$-0.680969\pi$
$997$	−34.0000	−1.07679	−0.538395	+	0.842692i	$0.680969\pi$
$998$	−40.0000	−1.26618
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.j.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.j.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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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