LMFDB - Embedded newform 1710.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,4,Mod(1,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1710.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1710.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:	$100.893266110$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -20.0000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -20.0000 q^{7} -8.00000 q^{8} +10.0000 q^{10} +44.0000 q^{11} +42.0000 q^{13} +40.0000 q^{14} +16.0000 q^{16} +86.0000 q^{17} +19.0000 q^{19} -20.0000 q^{20} -88.0000 q^{22} +164.000 q^{23} +25.0000 q^{25} -84.0000 q^{26} -80.0000 q^{28} +162.000 q^{29} -312.000 q^{31} -32.0000 q^{32} -172.000 q^{34} +100.000 q^{35} +226.000 q^{37} -38.0000 q^{38} +40.0000 q^{40} -34.0000 q^{41} -432.000 q^{43} +176.000 q^{44} -328.000 q^{46} -580.000 q^{47} +57.0000 q^{49} -50.0000 q^{50} +168.000 q^{52} -506.000 q^{53} -220.000 q^{55} +160.000 q^{56} -324.000 q^{58} -364.000 q^{59} +518.000 q^{61} +624.000 q^{62} +64.0000 q^{64} -210.000 q^{65} +924.000 q^{67} +344.000 q^{68} -200.000 q^{70} -320.000 q^{71} -542.000 q^{73} -452.000 q^{74} +76.0000 q^{76} -880.000 q^{77} -1208.00 q^{79} -80.0000 q^{80} +68.0000 q^{82} +1120.00 q^{83} -430.000 q^{85} +864.000 q^{86} -352.000 q^{88} +1022.00 q^{89} -840.000 q^{91} +656.000 q^{92} +1160.00 q^{94} -95.0000 q^{95} +1166.00 q^{97} -114.000 q^{98} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	−20.0000	−1.07990	−0.539949	−	0.841698i	$-0.681557\pi$
$7$	−20.0000	−1.07990	−0.539949	+	0.841698i	$0.681557\pi$
$8$	−8.00000	−0.353553
$9$	0	0
$10$	10.0000	0.316228
$11$	44.0000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	44.0000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	42.0000	0.896054	0.448027	−	0.894020i	$-0.352127\pi$
$13$	42.0000	0.896054	0.448027	+	0.894020i	$0.352127\pi$
$14$	40.0000	0.763604
$15$	0	0
$16$	16.0000	0.250000
$17$	86.0000	1.22694	0.613472	−	0.789716i	$-0.289772\pi$
$17$	86.0000	1.22694	0.613472	+	0.789716i	$0.289772\pi$
$18$	0	0
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−88.0000	−0.852803
$23$	164.000	1.48680	0.743399	−	0.668848i	$-0.233212\pi$
$23$	164.000	1.48680	0.743399	+	0.668848i	$0.233212\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−84.0000	−0.633606
$27$	0	0
$28$	−80.0000	−0.539949
$29$	162.000	1.03733	0.518666	−	0.854977i	$-0.326429\pi$
$29$	162.000	1.03733	0.518666	+	0.854977i	$0.326429\pi$
$30$	0	0
$31$	−312.000	−1.80764	−0.903820	−	0.427912i	$-0.859249\pi$
$31$	−312.000	−1.80764	−0.903820	+	0.427912i	$0.859249\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−172.000	−0.867581
$35$	100.000	0.482945
$36$	0	0
$37$	226.000	1.00417	0.502083	−	0.864819i	$-0.332567\pi$
$37$	226.000	1.00417	0.502083	+	0.864819i	$0.332567\pi$
$38$	−38.0000	−0.162221
$39$	0	0
$40$	40.0000	0.158114
$41$	−34.0000	−0.129510	−0.0647550	−	0.997901i	$-0.520627\pi$
$41$	−34.0000	−0.129510	−0.0647550	+	0.997901i	$0.520627\pi$
$42$	0	0
$43$	−432.000	−1.53208	−0.766039	−	0.642794i	$-0.777775\pi$
$43$	−432.000	−1.53208	−0.766039	+	0.642794i	$0.777775\pi$
$44$	176.000	0.603023
$45$	0	0
$46$	−328.000	−1.05133
$47$	−580.000	−1.80004	−0.900018	−	0.435853i	$-0.856447\pi$
$47$	−580.000	−1.80004	−0.900018	+	0.435853i	$0.856447\pi$
$48$	0	0
$49$	57.0000	0.166181
$50$	−50.0000	−0.141421
$51$	0	0
$52$	168.000	0.448027
$53$	−506.000	−1.31140	−0.655702	−	0.755020i	$-0.727627\pi$
$53$	−506.000	−1.31140	−0.655702	+	0.755020i	$0.727627\pi$
$54$	0	0
$55$	−220.000	−0.539360
$56$	160.000	0.381802
$57$	0	0
$58$	−324.000	−0.733505
$59$	−364.000	−0.803199	−0.401600	−	0.915815i	$-0.631546\pi$
$59$	−364.000	−0.803199	−0.401600	+	0.915815i	$0.631546\pi$
$60$	0	0
$61$	518.000	1.08726	0.543632	−	0.839324i	$-0.317049\pi$
$61$	518.000	1.08726	0.543632	+	0.839324i	$0.317049\pi$
$62$	624.000	1.27819
$63$	0	0
$64$	64.0000	0.125000
$65$	−210.000	−0.400728
$66$	0	0
$67$	924.000	1.68484	0.842422	−	0.538818i	$-0.181129\pi$
$67$	924.000	1.68484	0.842422	+	0.538818i	$0.181129\pi$
$68$	344.000	0.613472
$69$	0	0
$70$	−200.000	−0.341494
$71$	−320.000	−0.534888	−0.267444	−	0.963573i	$-0.586179\pi$
$71$	−320.000	−0.534888	−0.267444	+	0.963573i	$0.586179\pi$
$72$	0	0
$73$	−542.000	−0.868990	−0.434495	−	0.900674i	$-0.643073\pi$
$73$	−542.000	−0.868990	−0.434495	+	0.900674i	$0.643073\pi$
$74$	−452.000	−0.710053
$75$	0	0
$76$	76.0000	0.114708
$77$	−880.000	−1.30241
$78$	0	0
$79$	−1208.00	−1.72039	−0.860194	−	0.509967i	$-0.829657\pi$
$79$	−1208.00	−1.72039	−0.860194	+	0.509967i	$0.829657\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	68.0000	0.0915774
$83$	1120.00	1.48116	0.740578	−	0.671970i	$-0.234552\pi$
$83$	1120.00	1.48116	0.740578	+	0.671970i	$0.234552\pi$
$84$	0	0
$85$	−430.000	−0.548706
$86$	864.000	1.08334
$87$	0	0
$88$	−352.000	−0.426401
$89$	1022.00	1.21721	0.608606	−	0.793473i	$-0.291729\pi$
$89$	1022.00	1.21721	0.608606	+	0.793473i	$0.291729\pi$
$90$	0	0
$91$	−840.000	−0.967648
$92$	656.000	0.743399
$93$	0	0
$94$	1160.00	1.27282
$95$	−95.0000	−0.102598
$96$	0	0
$97$	1166.00	1.22051	0.610254	−	0.792205i	$-0.291067\pi$
$97$	1166.00	1.22051	0.610254	+	0.792205i	$0.291067\pi$
$98$	−114.000	−0.117508
$99$	0	0
$100$	100.000	0.100000
$101$	898.000	0.884696	0.442348	−	0.896843i	$-0.354146\pi$
$101$	898.000	0.884696	0.442348	+	0.896843i	$0.354146\pi$
$102$	0	0
$103$	1152.00	1.10204	0.551019	−	0.834493i	$-0.314239\pi$
$103$	1152.00	1.10204	0.551019	+	0.834493i	$0.314239\pi$
$104$	−336.000	−0.316803
$105$	0	0
$106$	1012.00	0.927303
$107$	1156.00	1.04444	0.522218	−	0.852812i	$-0.325105\pi$
$107$	1156.00	1.04444	0.522218	+	0.852812i	$0.325105\pi$
$108$	0	0
$109$	1046.00	0.919162	0.459581	−	0.888136i	$-0.348000\pi$
$109$	1046.00	0.919162	0.459581	+	0.888136i	$0.348000\pi$
$110$	440.000	0.381385
$111$	0	0
$112$	−320.000	−0.269975
$113$	530.000	0.441223	0.220612	−	0.975362i	$-0.429195\pi$
$113$	530.000	0.441223	0.220612	+	0.975362i	$0.429195\pi$
$114$	0	0
$115$	−820.000	−0.664916
$116$	648.000	0.518666
$117$	0	0
$118$	728.000	0.567948
$119$	−1720.00	−1.32498
$120$	0	0
$121$	605.000	0.454545
$122$	−1036.00	−0.768812
$123$	0	0
$124$	−1248.00	−0.903820
$125$	−125.000	−0.0894427
$126$	0	0
$127$	568.000	0.396865	0.198432	−	0.980115i	$-0.436415\pi$
$127$	568.000	0.396865	0.198432	+	0.980115i	$0.436415\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	420.000	0.283357
$131$	924.000	0.616261	0.308131	−	0.951344i	$-0.400297\pi$
$131$	924.000	0.616261	0.308131	+	0.951344i	$0.400297\pi$
$132$	0	0
$133$	−380.000	−0.247746
$134$	−1848.00	−1.19136
$135$	0	0
$136$	−688.000	−0.433791
$137$	702.000	0.437780	0.218890	−	0.975750i	$-0.429756\pi$
$137$	702.000	0.437780	0.218890	+	0.975750i	$0.429756\pi$
$138$	0	0
$139$	−2116.00	−1.29120	−0.645600	−	0.763676i	$-0.723393\pi$
$139$	−2116.00	−1.29120	−0.645600	+	0.763676i	$0.723393\pi$
$140$	400.000	0.241473
$141$	0	0
$142$	640.000	0.378223
$143$	1848.00	1.08068
$144$	0	0
$145$	−810.000	−0.463909
$146$	1084.00	0.614469
$147$	0	0
$148$	904.000	0.502083
$149$	−1454.00	−0.799438	−0.399719	−	0.916638i	$-0.630892\pi$
$149$	−1454.00	−0.799438	−0.399719	+	0.916638i	$0.630892\pi$
$150$	0	0
$151$	−680.000	−0.366474	−0.183237	−	0.983069i	$-0.558658\pi$
$151$	−680.000	−0.366474	−0.183237	+	0.983069i	$0.558658\pi$
$152$	−152.000	−0.0811107
$153$	0	0
$154$	1760.00	0.920941
$155$	1560.00	0.808401
$156$	0	0
$157$	462.000	0.234851	0.117426	−	0.993082i	$-0.462536\pi$
$157$	462.000	0.234851	0.117426	+	0.993082i	$0.462536\pi$
$158$	2416.00	1.21650
$159$	0	0
$160$	160.000	0.0790569
$161$	−3280.00	−1.60559
$162$	0	0
$163$	4136.00	1.98746	0.993732	−	0.111792i	$-0.0356589\pi$
$163$	4136.00	1.98746	0.993732	+	0.111792i	$0.0356589\pi$
$164$	−136.000	−0.0647550
$165$	0	0
$166$	−2240.00	−1.04734
$167$	1464.00	0.678370	0.339185	−	0.940720i	$-0.389849\pi$
$167$	1464.00	0.678370	0.339185	+	0.940720i	$0.389849\pi$
$168$	0	0
$169$	−433.000	−0.197087
$170$	860.000	0.387994
$171$	0	0
$172$	−1728.00	−0.766039
$173$	1422.00	0.624929	0.312464	−	0.949929i	$-0.398846\pi$
$173$	1422.00	0.624929	0.312464	+	0.949929i	$0.398846\pi$
$174$	0	0
$175$	−500.000	−0.215980
$176$	704.000	0.301511
$177$	0	0
$178$	−2044.00	−0.860698
$179$	3212.00	1.34121	0.670604	−	0.741816i	$-0.266035\pi$
$179$	3212.00	1.34121	0.670604	+	0.741816i	$0.266035\pi$
$180$	0	0
$181$	−3234.00	−1.32807	−0.664037	−	0.747700i	$-0.731158\pi$
$181$	−3234.00	−1.32807	−0.664037	+	0.747700i	$0.731158\pi$
$182$	1680.00	0.684230
$183$	0	0
$184$	−1312.00	−0.525663
$185$	−1130.00	−0.449077
$186$	0	0
$187$	3784.00	1.47975
$188$	−2320.00	−0.900018
$189$	0	0
$190$	190.000	0.0725476
$191$	296.000	0.112135	0.0560676	−	0.998427i	$-0.482144\pi$
$191$	296.000	0.112135	0.0560676	+	0.998427i	$0.482144\pi$
$192$	0	0
$193$	−2770.00	−1.03310	−0.516552	−	0.856256i	$-0.672785\pi$
$193$	−2770.00	−1.03310	−0.516552	+	0.856256i	$0.672785\pi$
$194$	−2332.00	−0.863030
$195$	0	0
$196$	228.000	0.0830904
$197$	1154.00	0.417356	0.208678	−	0.977984i	$-0.433084\pi$
$197$	1154.00	0.417356	0.208678	+	0.977984i	$0.433084\pi$
$198$	0	0
$199$	−2680.00	−0.954674	−0.477337	−	0.878720i	$-0.658398\pi$
$199$	−2680.00	−0.954674	−0.477337	+	0.878720i	$0.658398\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−1796.00	−0.625575
$203$	−3240.00	−1.12021
$204$	0	0
$205$	170.000	0.0579186
$206$	−2304.00	−0.779259
$207$	0	0
$208$	672.000	0.224014
$209$	836.000	0.276686
$210$	0	0
$211$	−2180.00	−0.711267	−0.355634	−	0.934625i	$-0.615735\pi$
$211$	−2180.00	−0.711267	−0.355634	+	0.934625i	$0.615735\pi$
$212$	−2024.00	−0.655702
$213$	0	0
$214$	−2312.00	−0.738528
$215$	2160.00	0.685166
$216$	0	0
$217$	6240.00	1.95207
$218$	−2092.00	−0.649945
$219$	0	0
$220$	−880.000	−0.269680
$221$	3612.00	1.09941
$222$	0	0
$223$	−4296.00	−1.29005	−0.645026	−	0.764161i	$-0.723153\pi$
$223$	−4296.00	−1.29005	−0.645026	+	0.764161i	$0.723153\pi$
$224$	640.000	0.190901
$225$	0	0
$226$	−1060.00	−0.311992
$227$	−500.000	−0.146195	−0.0730973	−	0.997325i	$-0.523288\pi$
$227$	−500.000	−0.146195	−0.0730973	+	0.997325i	$0.523288\pi$
$228$	0	0
$229$	4366.00	1.25988	0.629942	−	0.776642i	$-0.283079\pi$
$229$	4366.00	1.25988	0.629942	+	0.776642i	$0.283079\pi$
$230$	1640.00	0.470167
$231$	0	0
$232$	−1296.00	−0.366752
$233$	−2970.00	−0.835069	−0.417535	−	0.908661i	$-0.637106\pi$
$233$	−2970.00	−0.835069	−0.417535	+	0.908661i	$0.637106\pi$
$234$	0	0
$235$	2900.00	0.805001
$236$	−1456.00	−0.401600
$237$	0	0
$238$	3440.00	0.936899
$239$	144.000	0.0389732	0.0194866	−	0.999810i	$-0.493797\pi$
$239$	144.000	0.0389732	0.0194866	+	0.999810i	$0.493797\pi$
$240$	0	0
$241$	1738.00	0.464541	0.232271	−	0.972651i	$-0.425385\pi$
$241$	1738.00	0.464541	0.232271	+	0.972651i	$0.425385\pi$
$242$	−1210.00	−0.321412
$243$	0	0
$244$	2072.00	0.543632
$245$	−285.000	−0.0743183
$246$	0	0
$247$	798.000	0.205569
$248$	2496.00	0.639097
$249$	0	0
$250$	250.000	0.0632456
$251$	3012.00	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	3012.00	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	7216.00	1.79315
$254$	−1136.00	−0.280626
$255$	0	0
$256$	256.000	0.0625000
$257$	−1014.00	−0.246115	−0.123058	−	0.992400i	$-0.539270\pi$
$257$	−1014.00	−0.246115	−0.123058	+	0.992400i	$0.539270\pi$
$258$	0	0
$259$	−4520.00	−1.08440
$260$	−840.000	−0.200364
$261$	0	0
$262$	−1848.00	−0.435763
$263$	−4284.00	−1.00442	−0.502211	−	0.864745i	$-0.667480\pi$
$263$	−4284.00	−1.00442	−0.502211	+	0.864745i	$0.667480\pi$
$264$	0	0
$265$	2530.00	0.586478
$266$	760.000	0.175183
$267$	0	0
$268$	3696.00	0.842422
$269$	−38.0000	−0.00861301	−0.00430651	−	0.999991i	$-0.501371\pi$
$269$	−38.0000	−0.00861301	−0.00430651	+	0.999991i	$0.501371\pi$
$270$	0	0
$271$	5888.00	1.31982	0.659909	−	0.751346i	$-0.270595\pi$
$271$	5888.00	1.31982	0.659909	+	0.751346i	$0.270595\pi$
$272$	1376.00	0.306736
$273$	0	0
$274$	−1404.00	−0.309557
$275$	1100.00	0.241209
$276$	0	0
$277$	5254.00	1.13965	0.569824	−	0.821767i	$-0.307012\pi$
$277$	5254.00	1.13965	0.569824	+	0.821767i	$0.307012\pi$
$278$	4232.00	0.913016
$279$	0	0
$280$	−800.000	−0.170747
$281$	2558.00	0.543052	0.271526	−	0.962431i	$-0.412472\pi$
$281$	2558.00	0.543052	0.271526	+	0.962431i	$0.412472\pi$
$282$	0	0
$283$	−6776.00	−1.42329	−0.711646	−	0.702539i	$-0.752050\pi$
$283$	−6776.00	−1.42329	−0.711646	+	0.702539i	$0.752050\pi$
$284$	−1280.00	−0.267444
$285$	0	0
$286$	−3696.00	−0.764158
$287$	680.000	0.139858
$288$	0	0
$289$	2483.00	0.505394
$290$	1620.00	0.328033
$291$	0	0
$292$	−2168.00	−0.434495
$293$	2086.00	0.415923	0.207961	−	0.978137i	$-0.433317\pi$
$293$	2086.00	0.415923	0.207961	+	0.978137i	$0.433317\pi$
$294$	0	0
$295$	1820.00	0.359202
$296$	−1808.00	−0.355027
$297$	0	0
$298$	2908.00	0.565288
$299$	6888.00	1.33225
$300$	0	0
$301$	8640.00	1.65449
$302$	1360.00	0.259136
$303$	0	0
$304$	304.000	0.0573539
$305$	−2590.00	−0.486239
$306$	0	0
$307$	7428.00	1.38091	0.690453	−	0.723377i	$-0.257411\pi$
$307$	7428.00	1.38091	0.690453	+	0.723377i	$0.257411\pi$
$308$	−3520.00	−0.651203
$309$	0	0
$310$	−3120.00	−0.571626
$311$	4040.00	0.736615	0.368308	−	0.929704i	$-0.379937\pi$
$311$	4040.00	0.736615	0.368308	+	0.929704i	$0.379937\pi$
$312$	0	0
$313$	−3318.00	−0.599184	−0.299592	−	0.954067i	$-0.596850\pi$
$313$	−3318.00	−0.599184	−0.299592	+	0.954067i	$0.596850\pi$
$314$	−924.000	−0.166065
$315$	0	0
$316$	−4832.00	−0.860194
$317$	7302.00	1.29376	0.646879	−	0.762593i	$-0.276074\pi$
$317$	7302.00	1.29376	0.646879	+	0.762593i	$0.276074\pi$
$318$	0	0
$319$	7128.00	1.25107
$320$	−320.000	−0.0559017
$321$	0	0
$322$	6560.00	1.13532
$323$	1634.00	0.281480
$324$	0	0
$325$	1050.00	0.179211
$326$	−8272.00	−1.40535
$327$	0	0
$328$	272.000	0.0457887
$329$	11600.0	1.94386
$330$	0	0
$331$	1428.00	0.237130	0.118565	−	0.992946i	$-0.462171\pi$
$331$	1428.00	0.237130	0.118565	+	0.992946i	$0.462171\pi$
$332$	4480.00	0.740578
$333$	0	0
$334$	−2928.00	−0.479680
$335$	−4620.00	−0.753485
$336$	0	0
$337$	6302.00	1.01867	0.509335	−	0.860568i	$-0.329891\pi$
$337$	6302.00	1.01867	0.509335	+	0.860568i	$0.329891\pi$
$338$	866.000	0.139362
$339$	0	0
$340$	−1720.00	−0.274353
$341$	−13728.0	−2.18010
$342$	0	0
$343$	5720.00	0.900440
$344$	3456.00	0.541672
$345$	0	0
$346$	−2844.00	−0.441891
$347$	−2608.00	−0.403472	−0.201736	−	0.979440i	$-0.564658\pi$
$347$	−2608.00	−0.403472	−0.201736	+	0.979440i	$0.564658\pi$
$348$	0	0
$349$	−8234.00	−1.26291	−0.631455	−	0.775412i	$-0.717542\pi$
$349$	−8234.00	−1.26291	−0.631455	+	0.775412i	$0.717542\pi$
$350$	1000.00	0.152721
$351$	0	0
$352$	−1408.00	−0.213201
$353$	7254.00	1.09374	0.546872	−	0.837216i	$-0.315819\pi$
$353$	7254.00	1.09374	0.546872	+	0.837216i	$0.315819\pi$
$354$	0	0
$355$	1600.00	0.239209
$356$	4088.00	0.608606
$357$	0	0
$358$	−6424.00	−0.948377
$359$	−6000.00	−0.882083	−0.441042	−	0.897487i	$-0.645391\pi$
$359$	−6000.00	−0.882083	−0.441042	+	0.897487i	$0.645391\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	6468.00	0.939090
$363$	0	0
$364$	−3360.00	−0.483824
$365$	2710.00	0.388624
$366$	0	0
$367$	−10204.0	−1.45135	−0.725674	−	0.688039i	$-0.758472\pi$
$367$	−10204.0	−1.45135	−0.725674	+	0.688039i	$0.758472\pi$
$368$	2624.00	0.371700
$369$	0	0
$370$	2260.00	0.317545
$371$	10120.0	1.41618
$372$	0	0
$373$	−3094.00	−0.429494	−0.214747	−	0.976670i	$-0.568893\pi$
$373$	−3094.00	−0.429494	−0.214747	+	0.976670i	$0.568893\pi$
$374$	−7568.00	−1.04634
$375$	0	0
$376$	4640.00	0.636409
$377$	6804.00	0.929506
$378$	0	0
$379$	2708.00	0.367020	0.183510	−	0.983018i	$-0.441254\pi$
$379$	2708.00	0.367020	0.183510	+	0.983018i	$0.441254\pi$
$380$	−380.000	−0.0512989
$381$	0	0
$382$	−592.000	−0.0792915
$383$	8272.00	1.10360	0.551801	−	0.833976i	$-0.313941\pi$
$383$	8272.00	1.10360	0.551801	+	0.833976i	$0.313941\pi$
$384$	0	0
$385$	4400.00	0.582454
$386$	5540.00	0.730514
$387$	0	0
$388$	4664.00	0.610254
$389$	4066.00	0.529960	0.264980	−	0.964254i	$-0.414635\pi$
$389$	4066.00	0.529960	0.264980	+	0.964254i	$0.414635\pi$
$390$	0	0
$391$	14104.0	1.82422
$392$	−456.000	−0.0587538
$393$	0	0
$394$	−2308.00	−0.295115
$395$	6040.00	0.769381
$396$	0	0
$397$	15438.0	1.95167	0.975833	−	0.218520i	$-0.0701228\pi$
$397$	15438.0	1.95167	0.975833	+	0.218520i	$0.0701228\pi$
$398$	5360.00	0.675057
$399$	0	0
$400$	400.000	0.0500000
$401$	−14514.0	−1.80747	−0.903734	−	0.428095i	$-0.859185\pi$
$401$	−14514.0	−1.80747	−0.903734	+	0.428095i	$0.859185\pi$
$402$	0	0
$403$	−13104.0	−1.61974
$404$	3592.00	0.442348
$405$	0	0
$406$	6480.00	0.792111
$407$	9944.00	1.21107
$408$	0	0
$409$	7818.00	0.945172	0.472586	−	0.881285i	$-0.343321\pi$
$409$	7818.00	0.945172	0.472586	+	0.881285i	$0.343321\pi$
$410$	−340.000	−0.0409546
$411$	0	0
$412$	4608.00	0.551019
$413$	7280.00	0.867374
$414$	0	0
$415$	−5600.00	−0.662393
$416$	−1344.00	−0.158401
$417$	0	0
$418$	−1672.00	−0.195646
$419$	3684.00	0.429535	0.214768	−	0.976665i	$-0.431101\pi$
$419$	3684.00	0.429535	0.214768	+	0.976665i	$0.431101\pi$
$420$	0	0
$421$	−5834.00	−0.675372	−0.337686	−	0.941259i	$-0.609644\pi$
$421$	−5834.00	−0.675372	−0.337686	+	0.941259i	$0.609644\pi$
$422$	4360.00	0.502942
$423$	0	0
$424$	4048.00	0.463652
$425$	2150.00	0.245389
$426$	0	0
$427$	−10360.0	−1.17413
$428$	4624.00	0.522218
$429$	0	0
$430$	−4320.00	−0.484486
$431$	−6944.00	−0.776057	−0.388029	−	0.921647i	$-0.626844\pi$
$431$	−6944.00	−0.776057	−0.388029	+	0.921647i	$0.626844\pi$
$432$	0	0
$433$	−738.000	−0.0819077	−0.0409538	−	0.999161i	$-0.513040\pi$
$433$	−738.000	−0.0819077	−0.0409538	+	0.999161i	$0.513040\pi$
$434$	−12480.0	−1.38032
$435$	0	0
$436$	4184.00	0.459581
$437$	3116.00	0.341095
$438$	0	0
$439$	544.000	0.0591428	0.0295714	−	0.999563i	$-0.490586\pi$
$439$	544.000	0.0591428	0.0295714	+	0.999563i	$0.490586\pi$
$440$	1760.00	0.190693
$441$	0	0
$442$	−7224.00	−0.777400
$443$	792.000	0.0849414	0.0424707	−	0.999098i	$-0.486477\pi$
$443$	792.000	0.0849414	0.0424707	+	0.999098i	$0.486477\pi$
$444$	0	0
$445$	−5110.00	−0.544353
$446$	8592.00	0.912204
$447$	0	0
$448$	−1280.00	−0.134987
$449$	−7362.00	−0.773796	−0.386898	−	0.922123i	$-0.626453\pi$
$449$	−7362.00	−0.773796	−0.386898	+	0.922123i	$0.626453\pi$
$450$	0	0
$451$	−1496.00	−0.156195
$452$	2120.00	0.220612
$453$	0	0
$454$	1000.00	0.103375
$455$	4200.00	0.432745
$456$	0	0
$457$	−14278.0	−1.46148	−0.730740	−	0.682656i	$-0.760825\pi$
$457$	−14278.0	−1.46148	−0.730740	+	0.682656i	$0.760825\pi$
$458$	−8732.00	−0.890872
$459$	0	0
$460$	−3280.00	−0.332458
$461$	1002.00	0.101232	0.0506158	−	0.998718i	$-0.483882\pi$
$461$	1002.00	0.101232	0.0506158	+	0.998718i	$0.483882\pi$
$462$	0	0
$463$	8916.00	0.894950	0.447475	−	0.894297i	$-0.352323\pi$
$463$	8916.00	0.894950	0.447475	+	0.894297i	$0.352323\pi$
$464$	2592.00	0.259333
$465$	0	0
$466$	5940.00	0.590483
$467$	−6344.00	−0.628620	−0.314310	−	0.949320i	$-0.601773\pi$
$467$	−6344.00	−0.628620	−0.314310	+	0.949320i	$0.601773\pi$
$468$	0	0
$469$	−18480.0	−1.81946
$470$	−5800.00	−0.569221
$471$	0	0
$472$	2912.00	0.283974
$473$	−19008.0	−1.84776
$474$	0	0
$475$	475.000	0.0458831
$476$	−6880.00	−0.662488
$477$	0	0
$478$	−288.000	−0.0275582
$479$	1800.00	0.171700	0.0858498	−	0.996308i	$-0.472639\pi$
$479$	1800.00	0.171700	0.0858498	+	0.996308i	$0.472639\pi$
$480$	0	0
$481$	9492.00	0.899788
$482$	−3476.00	−0.328480
$483$	0	0
$484$	2420.00	0.227273
$485$	−5830.00	−0.545828
$486$	0	0
$487$	3704.00	0.344649	0.172325	−	0.985040i	$-0.444872\pi$
$487$	3704.00	0.344649	0.172325	+	0.985040i	$0.444872\pi$
$488$	−4144.00	−0.384406
$489$	0	0
$490$	570.000	0.0525510
$491$	−3468.00	−0.318755	−0.159377	−	0.987218i	$-0.550949\pi$
$491$	−3468.00	−0.318755	−0.159377	+	0.987218i	$0.550949\pi$
$492$	0	0
$493$	13932.0	1.27275
$494$	−1596.00	−0.145359
$495$	0	0
$496$	−4992.00	−0.451910
$497$	6400.00	0.577624
$498$	0	0
$499$	5348.00	0.479778	0.239889	−	0.970800i	$-0.422889\pi$
$499$	5348.00	0.479778	0.239889	+	0.970800i	$0.422889\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	−6024.00	−0.535586
$503$	2228.00	0.197498	0.0987491	−	0.995112i	$-0.468516\pi$
$503$	2228.00	0.197498	0.0987491	+	0.995112i	$0.468516\pi$
$504$	0	0
$505$	−4490.00	−0.395648
$506$	−14432.0	−1.26795
$507$	0	0
$508$	2272.00	0.198432
$509$	18082.0	1.57460	0.787299	−	0.616571i	$-0.211479\pi$
$509$	18082.0	1.57460	0.787299	+	0.616571i	$0.211479\pi$
$510$	0	0
$511$	10840.0	0.938421
$512$	−512.000	−0.0441942
$513$	0	0
$514$	2028.00	0.174030
$515$	−5760.00	−0.492846
$516$	0	0
$517$	−25520.0	−2.17093
$518$	9040.00	0.766785
$519$	0	0
$520$	1680.00	0.141679
$521$	10166.0	0.854857	0.427429	−	0.904049i	$-0.359420\pi$
$521$	10166.0	0.854857	0.427429	+	0.904049i	$0.359420\pi$
$522$	0	0
$523$	6268.00	0.524054	0.262027	−	0.965060i	$-0.415609\pi$
$523$	6268.00	0.524054	0.262027	+	0.965060i	$0.415609\pi$
$524$	3696.00	0.308131
$525$	0	0
$526$	8568.00	0.710233
$527$	−26832.0	−2.21788
$528$	0	0
$529$	14729.0	1.21057
$530$	−5060.00	−0.414703
$531$	0	0
$532$	−1520.00	−0.123873
$533$	−1428.00	−0.116048
$534$	0	0
$535$	−5780.00	−0.467086
$536$	−7392.00	−0.595682
$537$	0	0
$538$	76.0000	0.00609032
$539$	2508.00	0.200422
$540$	0	0
$541$	−1594.00	−0.126675	−0.0633377	−	0.997992i	$-0.520175\pi$
$541$	−1594.00	−0.126675	−0.0633377	+	0.997992i	$0.520175\pi$
$542$	−11776.0	−0.933252
$543$	0	0
$544$	−2752.00	−0.216895
$545$	−5230.00	−0.411062
$546$	0	0
$547$	7940.00	0.620640	0.310320	−	0.950632i	$-0.399564\pi$
$547$	7940.00	0.620640	0.310320	+	0.950632i	$0.399564\pi$
$548$	2808.00	0.218890
$549$	0	0
$550$	−2200.00	−0.170561
$551$	3078.00	0.237980
$552$	0	0
$553$	24160.0	1.85784
$554$	−10508.0	−0.805852
$555$	0	0
$556$	−8464.00	−0.645600
$557$	12626.0	0.960468	0.480234	−	0.877140i	$-0.340552\pi$
$557$	12626.0	0.960468	0.480234	+	0.877140i	$0.340552\pi$
$558$	0	0
$559$	−18144.0	−1.37283
$560$	1600.00	0.120736
$561$	0	0
$562$	−5116.00	−0.383995
$563$	21660.0	1.62142	0.810711	−	0.585447i	$-0.199081\pi$
$563$	21660.0	1.62142	0.810711	+	0.585447i	$0.199081\pi$
$564$	0	0
$565$	−2650.00	−0.197321
$566$	13552.0	1.00642
$567$	0	0
$568$	2560.00	0.189111
$569$	−14346.0	−1.05697	−0.528485	−	0.848943i	$-0.677240\pi$
$569$	−14346.0	−1.05697	−0.528485	+	0.848943i	$0.677240\pi$
$570$	0	0
$571$	−5404.00	−0.396060	−0.198030	−	0.980196i	$-0.563454\pi$
$571$	−5404.00	−0.396060	−0.198030	+	0.980196i	$0.563454\pi$
$572$	7392.00	0.540341
$573$	0	0
$574$	−1360.00	−0.0988943
$575$	4100.00	0.297360
$576$	0	0
$577$	1426.00	0.102886	0.0514429	−	0.998676i	$-0.483618\pi$
$577$	1426.00	0.102886	0.0514429	+	0.998676i	$0.483618\pi$
$578$	−4966.00	−0.357367
$579$	0	0
$580$	−3240.00	−0.231955
$581$	−22400.0	−1.59950
$582$	0	0
$583$	−22264.0	−1.58161
$584$	4336.00	0.307235
$585$	0	0
$586$	−4172.00	−0.294102
$587$	18704.0	1.31516	0.657578	−	0.753386i	$-0.271581\pi$
$587$	18704.0	1.31516	0.657578	+	0.753386i	$0.271581\pi$
$588$	0	0
$589$	−5928.00	−0.414701
$590$	−3640.00	−0.253994
$591$	0	0
$592$	3616.00	0.251042
$593$	14270.0	0.988193	0.494097	−	0.869407i	$-0.335499\pi$
$593$	14270.0	0.988193	0.494097	+	0.869407i	$0.335499\pi$
$594$	0	0
$595$	8600.00	0.592547
$596$	−5816.00	−0.399719
$597$	0	0
$598$	−13776.0	−0.942044
$599$	−15296.0	−1.04337	−0.521684	−	0.853139i	$-0.674696\pi$
$599$	−15296.0	−1.04337	−0.521684	+	0.853139i	$0.674696\pi$
$600$	0	0
$601$	10002.0	0.678852	0.339426	−	0.940633i	$-0.389767\pi$
$601$	10002.0	0.678852	0.339426	+	0.940633i	$0.389767\pi$
$602$	−17280.0	−1.16990
$603$	0	0
$604$	−2720.00	−0.183237
$605$	−3025.00	−0.203279
$606$	0	0
$607$	−2992.00	−0.200068	−0.100034	−	0.994984i	$-0.531895\pi$
$607$	−2992.00	−0.200068	−0.100034	+	0.994984i	$0.531895\pi$
$608$	−608.000	−0.0405554
$609$	0	0
$610$	5180.00	0.343823
$611$	−24360.0	−1.61293
$612$	0	0
$613$	−13930.0	−0.917826	−0.458913	−	0.888481i	$-0.651761\pi$
$613$	−13930.0	−0.917826	−0.458913	+	0.888481i	$0.651761\pi$
$614$	−14856.0	−0.976448
$615$	0	0
$616$	7040.00	0.460470
$617$	23022.0	1.50216	0.751078	−	0.660213i	$-0.229534\pi$
$617$	23022.0	1.50216	0.751078	+	0.660213i	$0.229534\pi$
$618$	0	0
$619$	26284.0	1.70669	0.853347	−	0.521344i	$-0.174569\pi$
$619$	26284.0	1.70669	0.853347	+	0.521344i	$0.174569\pi$
$620$	6240.00	0.404201
$621$	0	0
$622$	−8080.00	−0.520866
$623$	−20440.0	−1.31446
$624$	0	0
$625$	625.000	0.0400000
$626$	6636.00	0.423687
$627$	0	0
$628$	1848.00	0.117426
$629$	19436.0	1.23206
$630$	0	0
$631$	8408.00	0.530455	0.265228	−	0.964186i	$-0.414553\pi$
$631$	8408.00	0.530455	0.265228	+	0.964186i	$0.414553\pi$
$632$	9664.00	0.608249
$633$	0	0
$634$	−14604.0	−0.914825
$635$	−2840.00	−0.177483
$636$	0	0
$637$	2394.00	0.148907
$638$	−14256.0	−0.884640
$639$	0	0
$640$	640.000	0.0395285
$641$	16262.0	1.00204	0.501022	−	0.865434i	$-0.332958\pi$
$641$	16262.0	1.00204	0.501022	+	0.865434i	$0.332958\pi$
$642$	0	0
$643$	24448.0	1.49943	0.749716	−	0.661760i	$-0.230190\pi$
$643$	24448.0	1.49943	0.749716	+	0.661760i	$0.230190\pi$
$644$	−13120.0	−0.802796
$645$	0	0
$646$	−3268.00	−0.199037
$647$	−10548.0	−0.640935	−0.320467	−	0.947260i	$-0.603840\pi$
$647$	−10548.0	−0.640935	−0.320467	+	0.947260i	$0.603840\pi$
$648$	0	0
$649$	−16016.0	−0.968695
$650$	−2100.00	−0.126721
$651$	0	0
$652$	16544.0	0.993732
$653$	−7662.00	−0.459169	−0.229584	−	0.973289i	$-0.573737\pi$
$653$	−7662.00	−0.459169	−0.229584	+	0.973289i	$0.573737\pi$
$654$	0	0
$655$	−4620.00	−0.275601
$656$	−544.000	−0.0323775
$657$	0	0
$658$	−23200.0	−1.37451
$659$	−32452.0	−1.91829	−0.959143	−	0.282922i	$-0.908696\pi$
$659$	−32452.0	−1.91829	−0.959143	+	0.282922i	$0.908696\pi$
$660$	0	0
$661$	−17690.0	−1.04094	−0.520470	−	0.853880i	$-0.674243\pi$
$661$	−17690.0	−1.04094	−0.520470	+	0.853880i	$0.674243\pi$
$662$	−2856.00	−0.167676
$663$	0	0
$664$	−8960.00	−0.523668
$665$	1900.00	0.110795
$666$	0	0
$667$	26568.0	1.54230
$668$	5856.00	0.339185
$669$	0	0
$670$	9240.00	0.532795
$671$	22792.0	1.31129
$672$	0	0
$673$	−15802.0	−0.905085	−0.452543	−	0.891743i	$-0.649483\pi$
$673$	−15802.0	−0.905085	−0.452543	+	0.891743i	$0.649483\pi$
$674$	−12604.0	−0.720309
$675$	0	0
$676$	−1732.00	−0.0985435
$677$	10518.0	0.597104	0.298552	−	0.954393i	$-0.403496\pi$
$677$	10518.0	0.597104	0.298552	+	0.954393i	$0.403496\pi$
$678$	0	0
$679$	−23320.0	−1.31803
$680$	3440.00	0.193997
$681$	0	0
$682$	27456.0	1.54156
$683$	7092.00	0.397317	0.198659	−	0.980069i	$-0.436341\pi$
$683$	7092.00	0.397317	0.198659	+	0.980069i	$0.436341\pi$
$684$	0	0
$685$	−3510.00	−0.195781
$686$	−11440.0	−0.636707
$687$	0	0
$688$	−6912.00	−0.383020
$689$	−21252.0	−1.17509
$690$	0	0
$691$	508.000	0.0279670	0.0139835	−	0.999902i	$-0.495549\pi$
$691$	508.000	0.0279670	0.0139835	+	0.999902i	$0.495549\pi$
$692$	5688.00	0.312464
$693$	0	0
$694$	5216.00	0.285298
$695$	10580.0	0.577442
$696$	0	0
$697$	−2924.00	−0.158902
$698$	16468.0	0.893013
$699$	0	0
$700$	−2000.00	−0.107990
$701$	31466.0	1.69537	0.847685	−	0.530500i	$-0.177996\pi$
$701$	31466.0	1.69537	0.847685	+	0.530500i	$0.177996\pi$
$702$	0	0
$703$	4294.00	0.230372
$704$	2816.00	0.150756
$705$	0	0
$706$	−14508.0	−0.773393
$707$	−17960.0	−0.955382
$708$	0	0
$709$	−31282.0	−1.65701	−0.828505	−	0.559982i	$-0.810808\pi$
$709$	−31282.0	−1.65701	−0.828505	+	0.559982i	$0.810808\pi$
$710$	−3200.00	−0.169146
$711$	0	0
$712$	−8176.00	−0.430349
$713$	−51168.0	−2.68760
$714$	0	0
$715$	−9240.00	−0.483296
$716$	12848.0	0.670604
$717$	0	0
$718$	12000.0	0.623727
$719$	−18232.0	−0.945673	−0.472836	−	0.881150i	$-0.656770\pi$
$719$	−18232.0	−0.945673	−0.472836	+	0.881150i	$0.656770\pi$
$720$	0	0
$721$	−23040.0	−1.19009
$722$	−722.000	−0.0372161
$723$	0	0
$724$	−12936.0	−0.664037
$725$	4050.00	0.207467
$726$	0	0
$727$	−8884.00	−0.453218	−0.226609	−	0.973986i	$-0.572764\pi$
$727$	−8884.00	−0.453218	−0.226609	+	0.973986i	$0.572764\pi$
$728$	6720.00	0.342115
$729$	0	0
$730$	−5420.00	−0.274799
$731$	−37152.0	−1.87978
$732$	0	0
$733$	6838.00	0.344567	0.172283	−	0.985047i	$-0.444886\pi$
$733$	6838.00	0.344567	0.172283	+	0.985047i	$0.444886\pi$
$734$	20408.0	1.02626
$735$	0	0
$736$	−5248.00	−0.262831
$737$	40656.0	2.03200
$738$	0	0
$739$	32380.0	1.61180	0.805898	−	0.592054i	$-0.201683\pi$
$739$	32380.0	1.61180	0.805898	+	0.592054i	$0.201683\pi$
$740$	−4520.00	−0.224539
$741$	0	0
$742$	−20240.0	−1.00139
$743$	4584.00	0.226340	0.113170	−	0.993576i	$-0.463900\pi$
$743$	4584.00	0.226340	0.113170	+	0.993576i	$0.463900\pi$
$744$	0	0
$745$	7270.00	0.357520
$746$	6188.00	0.303698
$747$	0	0
$748$	15136.0	0.739876
$749$	−23120.0	−1.12789
$750$	0	0
$751$	10384.0	0.504551	0.252275	−	0.967655i	$-0.418821\pi$
$751$	10384.0	0.504551	0.252275	+	0.967655i	$0.418821\pi$
$752$	−9280.00	−0.450009
$753$	0	0
$754$	−13608.0	−0.657260
$755$	3400.00	0.163892
$756$	0	0
$757$	−2002.00	−0.0961214	−0.0480607	−	0.998844i	$-0.515304\pi$
$757$	−2002.00	−0.0961214	−0.0480607	+	0.998844i	$0.515304\pi$
$758$	−5416.00	−0.259522
$759$	0	0
$760$	760.000	0.0362738
$761$	2854.00	0.135949	0.0679747	−	0.997687i	$-0.478346\pi$
$761$	2854.00	0.135949	0.0679747	+	0.997687i	$0.478346\pi$
$762$	0	0
$763$	−20920.0	−0.992601
$764$	1184.00	0.0560676
$765$	0	0
$766$	−16544.0	−0.780364
$767$	−15288.0	−0.719710
$768$	0	0
$769$	2322.00	0.108886	0.0544431	−	0.998517i	$-0.482662\pi$
$769$	2322.00	0.108886	0.0544431	+	0.998517i	$0.482662\pi$
$770$	−8800.00	−0.411857
$771$	0	0
$772$	−11080.0	−0.516552
$773$	27678.0	1.28785	0.643925	−	0.765088i	$-0.277305\pi$
$773$	27678.0	1.28785	0.643925	+	0.765088i	$0.277305\pi$
$774$	0	0
$775$	−7800.00	−0.361528
$776$	−9328.00	−0.431515
$777$	0	0
$778$	−8132.00	−0.374738
$779$	−646.000	−0.0297116
$780$	0	0
$781$	−14080.0	−0.645099
$782$	−28208.0	−1.28992
$783$	0	0
$784$	912.000	0.0415452
$785$	−2310.00	−0.105029
$786$	0	0
$787$	12532.0	0.567621	0.283810	−	0.958880i	$-0.408401\pi$
$787$	12532.0	0.567621	0.283810	+	0.958880i	$0.408401\pi$
$788$	4616.00	0.208678
$789$	0	0
$790$	−12080.0	−0.544034
$791$	−10600.0	−0.476476
$792$	0	0
$793$	21756.0	0.974247
$794$	−30876.0	−1.38004
$795$	0	0
$796$	−10720.0	−0.477337
$797$	−4562.00	−0.202753	−0.101377	−	0.994848i	$-0.532325\pi$
$797$	−4562.00	−0.202753	−0.101377	+	0.994848i	$0.532325\pi$
$798$	0	0
$799$	−49880.0	−2.20855
$800$	−800.000	−0.0353553
$801$	0	0
$802$	29028.0	1.27807
$803$	−23848.0	−1.04804
$804$	0	0
$805$	16400.0	0.718042
$806$	26208.0	1.14533
$807$	0	0
$808$	−7184.00	−0.312787
$809$	1350.00	0.0586693	0.0293347	−	0.999570i	$-0.490661\pi$
$809$	1350.00	0.0586693	0.0293347	+	0.999570i	$0.490661\pi$
$810$	0	0
$811$	12892.0	0.558199	0.279099	−	0.960262i	$-0.409964\pi$
$811$	12892.0	0.558199	0.279099	+	0.960262i	$0.409964\pi$
$812$	−12960.0	−0.560107
$813$	0	0
$814$	−19888.0	−0.856356
$815$	−20680.0	−0.888821
$816$	0	0
$817$	−8208.00	−0.351483
$818$	−15636.0	−0.668337
$819$	0	0
$820$	680.000	0.0289593
$821$	32802.0	1.39439	0.697197	−	0.716879i	$-0.254430\pi$
$821$	32802.0	1.39439	0.697197	+	0.716879i	$0.254430\pi$
$822$	0	0
$823$	24916.0	1.05531	0.527653	−	0.849460i	$-0.323072\pi$
$823$	24916.0	1.05531	0.527653	+	0.849460i	$0.323072\pi$
$824$	−9216.00	−0.389629
$825$	0	0
$826$	−14560.0	−0.613326
$827$	1596.00	0.0671081	0.0335540	−	0.999437i	$-0.489317\pi$
$827$	1596.00	0.0671081	0.0335540	+	0.999437i	$0.489317\pi$
$828$	0	0
$829$	25910.0	1.08551	0.542757	−	0.839890i	$-0.317380\pi$
$829$	25910.0	1.08551	0.542757	+	0.839890i	$0.317380\pi$
$830$	11200.0	0.468383
$831$	0	0
$832$	2688.00	0.112007
$833$	4902.00	0.203895
$834$	0	0
$835$	−7320.00	−0.303376
$836$	3344.00	0.138343
$837$	0	0
$838$	−7368.00	−0.303727
$839$	−27504.0	−1.13176	−0.565878	−	0.824489i	$-0.691463\pi$
$839$	−27504.0	−1.13176	−0.565878	+	0.824489i	$0.691463\pi$
$840$	0	0
$841$	1855.00	0.0760589
$842$	11668.0	0.477560
$843$	0	0
$844$	−8720.00	−0.355634
$845$	2165.00	0.0881400
$846$	0	0
$847$	−12100.0	−0.490863
$848$	−8096.00	−0.327851
$849$	0	0
$850$	−4300.00	−0.173516
$851$	37064.0	1.49299
$852$	0	0
$853$	−14514.0	−0.582591	−0.291295	−	0.956633i	$-0.594086\pi$
$853$	−14514.0	−0.582591	−0.291295	+	0.956633i	$0.594086\pi$
$854$	20720.0	0.830239
$855$	0	0
$856$	−9248.00	−0.369264
$857$	−41790.0	−1.66572	−0.832858	−	0.553486i	$-0.813297\pi$
$857$	−41790.0	−1.66572	−0.832858	+	0.553486i	$0.813297\pi$
$858$	0	0
$859$	−6332.00	−0.251508	−0.125754	−	0.992061i	$-0.540135\pi$
$859$	−6332.00	−0.251508	−0.125754	+	0.992061i	$0.540135\pi$
$860$	8640.00	0.342583
$861$	0	0
$862$	13888.0	0.548755
$863$	−3488.00	−0.137582	−0.0687908	−	0.997631i	$-0.521914\pi$
$863$	−3488.00	−0.137582	−0.0687908	+	0.997631i	$0.521914\pi$
$864$	0	0
$865$	−7110.00	−0.279477
$866$	1476.00	0.0579175
$867$	0	0
$868$	24960.0	0.976034
$869$	−53152.0	−2.07487
$870$	0	0
$871$	38808.0	1.50971
$872$	−8368.00	−0.324973
$873$	0	0
$874$	−6232.00	−0.241191
$875$	2500.00	0.0965891
$876$	0	0
$877$	23426.0	0.901984	0.450992	−	0.892528i	$-0.351070\pi$
$877$	23426.0	0.901984	0.450992	+	0.892528i	$0.351070\pi$
$878$	−1088.00	−0.0418203
$879$	0	0
$880$	−3520.00	−0.134840
$881$	31230.0	1.19429	0.597143	−	0.802135i	$-0.296303\pi$
$881$	31230.0	1.19429	0.597143	+	0.802135i	$0.296303\pi$
$882$	0	0
$883$	24120.0	0.919256	0.459628	−	0.888112i	$-0.347983\pi$
$883$	24120.0	0.919256	0.459628	+	0.888112i	$0.347983\pi$
$884$	14448.0	0.549705
$885$	0	0
$886$	−1584.00	−0.0600627
$887$	33696.0	1.27554	0.637768	−	0.770228i	$-0.279858\pi$
$887$	33696.0	1.27554	0.637768	+	0.770228i	$0.279858\pi$
$888$	0	0
$889$	−11360.0	−0.428574
$890$	10220.0	0.384916
$891$	0	0
$892$	−17184.0	−0.645026
$893$	−11020.0	−0.412957
$894$	0	0
$895$	−16060.0	−0.599806
$896$	2560.00	0.0954504
$897$	0	0
$898$	14724.0	0.547156
$899$	−50544.0	−1.87512
$900$	0	0
$901$	−43516.0	−1.60902
$902$	2992.00	0.110446
$903$	0	0
$904$	−4240.00	−0.155996
$905$	16170.0	0.593933
$906$	0	0
$907$	−7412.00	−0.271347	−0.135673	−	0.990754i	$-0.543320\pi$
$907$	−7412.00	−0.271347	−0.135673	+	0.990754i	$0.543320\pi$
$908$	−2000.00	−0.0730973
$909$	0	0
$910$	−8400.00	−0.305997
$911$	−18288.0	−0.665103	−0.332551	−	0.943085i	$-0.607909\pi$
$911$	−18288.0	−0.665103	−0.332551	+	0.943085i	$0.607909\pi$
$912$	0	0
$913$	49280.0	1.78634
$914$	28556.0	1.03342
$915$	0	0
$916$	17464.0	0.629942
$917$	−18480.0	−0.665500
$918$	0	0
$919$	−34040.0	−1.22185	−0.610923	−	0.791690i	$-0.709201\pi$
$919$	−34040.0	−1.22185	−0.610923	+	0.791690i	$0.709201\pi$
$920$	6560.00	0.235083
$921$	0	0
$922$	−2004.00	−0.0715816
$923$	−13440.0	−0.479288
$924$	0	0
$925$	5650.00	0.200833
$926$	−17832.0	−0.632825
$927$	0	0
$928$	−5184.00	−0.183376
$929$	−41778.0	−1.47545	−0.737724	−	0.675102i	$-0.764100\pi$
$929$	−41778.0	−1.47545	−0.737724	+	0.675102i	$0.764100\pi$
$930$	0	0
$931$	1083.00	0.0381245
$932$	−11880.0	−0.417535
$933$	0	0
$934$	12688.0	0.444501
$935$	−18920.0	−0.661765
$936$	0	0
$937$	14834.0	0.517189	0.258594	−	0.965986i	$-0.416741\pi$
$937$	14834.0	0.517189	0.258594	+	0.965986i	$0.416741\pi$
$938$	36960.0	1.28655
$939$	0	0
$940$	11600.0	0.402500
$941$	18026.0	0.624475	0.312237	−	0.950004i	$-0.398922\pi$
$941$	18026.0	0.624475	0.312237	+	0.950004i	$0.398922\pi$
$942$	0	0
$943$	−5576.00	−0.192555
$944$	−5824.00	−0.200800
$945$	0	0
$946$	38016.0	1.30656
$947$	−57112.0	−1.95976	−0.979879	−	0.199593i	$-0.936038\pi$
$947$	−57112.0	−1.95976	−0.979879	+	0.199593i	$0.936038\pi$
$948$	0	0
$949$	−22764.0	−0.778662
$950$	−950.000	−0.0324443
$951$	0	0
$952$	13760.0	0.468450
$953$	7842.00	0.266555	0.133278	−	0.991079i	$-0.457450\pi$
$953$	7842.00	0.266555	0.133278	+	0.991079i	$0.457450\pi$
$954$	0	0
$955$	−1480.00	−0.0501484
$956$	576.000	0.0194866
$957$	0	0
$958$	−3600.00	−0.121410
$959$	−14040.0	−0.472758
$960$	0	0
$961$	67553.0	2.26756
$962$	−18984.0	−0.636246
$963$	0	0
$964$	6952.00	0.232271
$965$	13850.0	0.462018
$966$	0	0
$967$	−25068.0	−0.833643	−0.416821	−	0.908988i	$-0.636856\pi$
$967$	−25068.0	−0.833643	−0.416821	+	0.908988i	$0.636856\pi$
$968$	−4840.00	−0.160706
$969$	0	0
$970$	11660.0	0.385959
$971$	−11628.0	−0.384305	−0.192153	−	0.981365i	$-0.561547\pi$
$971$	−11628.0	−0.384305	−0.192153	+	0.981365i	$0.561547\pi$
$972$	0	0
$973$	42320.0	1.39436
$974$	−7408.00	−0.243704
$975$	0	0
$976$	8288.00	0.271816
$977$	22554.0	0.738553	0.369277	−	0.929320i	$-0.379606\pi$
$977$	22554.0	0.738553	0.369277	+	0.929320i	$0.379606\pi$
$978$	0	0
$979$	44968.0	1.46801
$980$	−1140.00	−0.0371591
$981$	0	0
$982$	6936.00	0.225394
$983$	38136.0	1.23739	0.618693	−	0.785633i	$-0.287663\pi$
$983$	38136.0	1.23739	0.618693	+	0.785633i	$0.287663\pi$
$984$	0	0
$985$	−5770.00	−0.186647
$986$	−27864.0	−0.899970
$987$	0	0
$988$	3192.00	0.102784
$989$	−70848.0	−2.27789
$990$	0	0
$991$	22720.0	0.728279	0.364140	−	0.931344i	$-0.381363\pi$
$991$	22720.0	0.728279	0.364140	+	0.931344i	$0.381363\pi$
$992$	9984.00	0.319549
$993$	0	0
$994$	−12800.0	−0.408442
$995$	13400.0	0.426943
$996$	0	0
$997$	18230.0	0.579087	0.289544	−	0.957165i	$-0.406496\pi$
$997$	18230.0	0.579087	0.289544	+	0.957165i	$0.406496\pi$
$998$	−10696.0	−0.339254
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.4.a.b.1.1		1
3.2	odd	2		190.4.a.c.1.1	✓	1
12.11	even	2		1520.4.a.g.1.1		1
15.2	even	4		950.4.b.a.799.2		2
15.8	even	4		950.4.b.a.799.1		2
15.14	odd	2		950.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.4.a.c.1.1	✓	1	3.2	odd	2
950.4.a.a.1.1		1	15.14	odd	2
950.4.b.a.799.1		2	15.8	even	4
950.4.b.a.799.2		2	15.2	even	4
1520.4.a.g.1.1		1	12.11	even	2
1710.4.a.b.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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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