LMFDB - Embedded newform 1088.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1088,4,Mod(1,1088)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1088, 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("1088.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1088.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:	$64.1940780862$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 544)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1088.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{3} -8.00000 q^{5} -14.0000 q^{7} -11.0000 q^{9} +O(q^{10})$

$q-4.00000 q^{3} -8.00000 q^{5} -14.0000 q^{7} -11.0000 q^{9} -8.00000 q^{11} +46.0000 q^{13} +32.0000 q^{15} -17.0000 q^{17} +116.000 q^{19} +56.0000 q^{21} +94.0000 q^{23} -61.0000 q^{25} +152.000 q^{27} +112.000 q^{29} -50.0000 q^{31} +32.0000 q^{33} +112.000 q^{35} +20.0000 q^{37} -184.000 q^{39} +62.0000 q^{41} +68.0000 q^{43} +88.0000 q^{45} +60.0000 q^{47} -147.000 q^{49} +68.0000 q^{51} -162.000 q^{53} +64.0000 q^{55} -464.000 q^{57} -724.000 q^{59} +388.000 q^{61} +154.000 q^{63} -368.000 q^{65} +172.000 q^{67} -376.000 q^{69} +1090.00 q^{71} -1062.00 q^{73} +244.000 q^{75} +112.000 q^{77} -114.000 q^{79} -311.000 q^{81} -68.0000 q^{83} +136.000 q^{85} -448.000 q^{87} -666.000 q^{89} -644.000 q^{91} +200.000 q^{93} -928.000 q^{95} -1322.00 q^{97} +88.0000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	0	0
$5$	−8.00000	−0.715542	−0.357771	−	0.933809i	$-0.616463\pi$
$5$	−8.00000	−0.715542	−0.357771	+	0.933809i	$0.616463\pi$
$6$	0	0
$7$	−14.0000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−14.0000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	0	0
$9$	−11.0000	−0.407407
$10$	0	0
$11$	−8.00000	−0.219281	−0.109640	−	0.993971i	$-0.534970\pi$
$11$	−8.00000	−0.219281	−0.109640	+	0.993971i	$0.534970\pi$
$12$	0	0
$13$	46.0000	0.981393	0.490696	−	0.871331i	$-0.336742\pi$
$13$	46.0000	0.981393	0.490696	+	0.871331i	$0.336742\pi$
$14$	0	0
$15$	32.0000	0.550824
$16$	0	0
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	0	0
$19$	116.000	1.40064	0.700322	−	0.713827i	$-0.253040\pi$
$19$	116.000	1.40064	0.700322	+	0.713827i	$0.253040\pi$
$20$	0	0
$21$	56.0000	0.581914
$22$	0	0
$23$	94.0000	0.852189	0.426095	−	0.904679i	$-0.359889\pi$
$23$	94.0000	0.852189	0.426095	+	0.904679i	$0.359889\pi$
$24$	0	0
$25$	−61.0000	−0.488000
$26$	0	0
$27$	152.000	1.08342
$28$	0	0
$29$	112.000	0.717168	0.358584	−	0.933497i	$-0.383260\pi$
$29$	112.000	0.717168	0.358584	+	0.933497i	$0.383260\pi$
$30$	0	0
$31$	−50.0000	−0.289686	−0.144843	−	0.989455i	$-0.546268\pi$
$31$	−50.0000	−0.289686	−0.144843	+	0.989455i	$0.546268\pi$
$32$	0	0
$33$	32.0000	0.168803
$34$	0	0
$35$	112.000	0.540899
$36$	0	0
$37$	20.0000	0.0888643	0.0444322	−	0.999012i	$-0.485852\pi$
$37$	20.0000	0.0888643	0.0444322	+	0.999012i	$0.485852\pi$
$38$	0	0
$39$	−184.000	−0.755476
$40$	0	0
$41$	62.0000	0.236165	0.118083	−	0.993004i	$-0.462325\pi$
$41$	62.0000	0.236165	0.118083	+	0.993004i	$0.462325\pi$
$42$	0	0
$43$	68.0000	0.241161	0.120580	−	0.992704i	$-0.461524\pi$
$43$	68.0000	0.241161	0.120580	+	0.992704i	$0.461524\pi$
$44$	0	0
$45$	88.0000	0.291517
$46$	0	0
$47$	60.0000	0.186211	0.0931053	−	0.995656i	$-0.470321\pi$
$47$	60.0000	0.186211	0.0931053	+	0.995656i	$0.470321\pi$
$48$	0	0
$49$	−147.000	−0.428571
$50$	0	0
$51$	68.0000	0.186704
$52$	0	0
$53$	−162.000	−0.419857	−0.209928	−	0.977717i	$-0.567323\pi$
$53$	−162.000	−0.419857	−0.209928	+	0.977717i	$0.567323\pi$
$54$	0	0
$55$	64.0000	0.156905
$56$	0	0
$57$	−464.000	−1.07822
$58$	0	0
$59$	−724.000	−1.59757	−0.798786	−	0.601615i	$-0.794524\pi$
$59$	−724.000	−1.59757	−0.798786	+	0.601615i	$0.794524\pi$
$60$	0	0
$61$	388.000	0.814399	0.407199	−	0.913339i	$-0.366505\pi$
$61$	388.000	0.814399	0.407199	+	0.913339i	$0.366505\pi$
$62$	0	0
$63$	154.000	0.307971
$64$	0	0
$65$	−368.000	−0.702227
$66$	0	0
$67$	172.000	0.313629	0.156815	−	0.987628i	$-0.449878\pi$
$67$	172.000	0.313629	0.156815	+	0.987628i	$0.449878\pi$
$68$	0	0
$69$	−376.000	−0.656016
$70$	0	0
$71$	1090.00	1.82196	0.910980	−	0.412450i	$-0.135327\pi$
$71$	1090.00	1.82196	0.910980	+	0.412450i	$0.135327\pi$
$72$	0	0
$73$	−1062.00	−1.70271	−0.851354	−	0.524591i	$-0.824218\pi$
$73$	−1062.00	−1.70271	−0.851354	+	0.524591i	$0.824218\pi$
$74$	0	0
$75$	244.000	0.375663
$76$	0	0
$77$	112.000	0.165761
$78$	0	0
$79$	−114.000	−0.162354	−0.0811772	−	0.996700i	$-0.525868\pi$
$79$	−114.000	−0.162354	−0.0811772	+	0.996700i	$0.525868\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	0	0
$83$	−68.0000	−0.0899273	−0.0449637	−	0.998989i	$-0.514317\pi$
$83$	−68.0000	−0.0899273	−0.0449637	+	0.998989i	$0.514317\pi$
$84$	0	0
$85$	136.000	0.173544
$86$	0	0
$87$	−448.000	−0.552076
$88$	0	0
$89$	−666.000	−0.793212	−0.396606	−	0.917989i	$-0.629812\pi$
$89$	−666.000	−0.793212	−0.396606	+	0.917989i	$0.629812\pi$
$90$	0	0
$91$	−644.000	−0.741863
$92$	0	0
$93$	200.000	0.223000
$94$	0	0
$95$	−928.000	−1.00222
$96$	0	0
$97$	−1322.00	−1.38380	−0.691901	−	0.721993i	$-0.743226\pi$
$97$	−1322.00	−1.38380	−0.691901	+	0.721993i	$0.743226\pi$
$98$	0	0
$99$	88.0000	0.0893367
$100$	0	0
$101$	126.000	0.124133	0.0620667	−	0.998072i	$-0.480231\pi$
$101$	126.000	0.124133	0.0620667	+	0.998072i	$0.480231\pi$
$102$	0	0
$103$	1712.00	1.63775	0.818876	−	0.573971i	$-0.194598\pi$
$103$	1712.00	1.63775	0.818876	+	0.573971i	$0.194598\pi$
$104$	0	0
$105$	−448.000	−0.416384
$106$	0	0
$107$	1176.00	1.06251	0.531253	−	0.847213i	$-0.321721\pi$
$107$	1176.00	1.06251	0.531253	+	0.847213i	$0.321721\pi$
$108$	0	0
$109$	−216.000	−0.189808	−0.0949039	−	0.995486i	$-0.530254\pi$
$109$	−216.000	−0.189808	−0.0949039	+	0.995486i	$0.530254\pi$
$110$	0	0
$111$	−80.0000	−0.0684078
$112$	0	0
$113$	−342.000	−0.284714	−0.142357	−	0.989815i	$-0.545468\pi$
$113$	−342.000	−0.284714	−0.142357	+	0.989815i	$0.545468\pi$
$114$	0	0
$115$	−752.000	−0.609777
$116$	0	0
$117$	−506.000	−0.399827
$118$	0	0
$119$	238.000	0.183340
$120$	0	0
$121$	−1267.00	−0.951916
$122$	0	0
$123$	−248.000	−0.181800
$124$	0	0
$125$	1488.00	1.06473
$126$	0	0
$127$	−1420.00	−0.992162	−0.496081	−	0.868276i	$-0.665228\pi$
$127$	−1420.00	−0.992162	−0.496081	+	0.868276i	$0.665228\pi$
$128$	0	0
$129$	−272.000	−0.185645
$130$	0	0
$131$	−1048.00	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−1048.00	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	0	0
$133$	−1624.00	−1.05879
$134$	0	0
$135$	−1216.00	−0.775234
$136$	0	0
$137$	946.000	0.589943	0.294972	−	0.955506i	$-0.404690\pi$
$137$	946.000	0.589943	0.294972	+	0.955506i	$0.404690\pi$
$138$	0	0
$139$	2312.00	1.41080	0.705400	−	0.708809i	$-0.250767\pi$
$139$	2312.00	1.41080	0.705400	+	0.708809i	$0.250767\pi$
$140$	0	0
$141$	−240.000	−0.143345
$142$	0	0
$143$	−368.000	−0.215201
$144$	0	0
$145$	−896.000	−0.513164
$146$	0	0
$147$	588.000	0.329914
$148$	0	0
$149$	−1702.00	−0.935794	−0.467897	−	0.883783i	$-0.654988\pi$
$149$	−1702.00	−0.935794	−0.467897	+	0.883783i	$0.654988\pi$
$150$	0	0
$151$	−1396.00	−0.752350	−0.376175	−	0.926549i	$-0.622761\pi$
$151$	−1396.00	−0.752350	−0.376175	+	0.926549i	$0.622761\pi$
$152$	0	0
$153$	187.000	0.0988108
$154$	0	0
$155$	400.000	0.207282
$156$	0	0
$157$	−2630.00	−1.33692	−0.668461	−	0.743747i	$-0.733047\pi$
$157$	−2630.00	−1.33692	−0.668461	+	0.743747i	$0.733047\pi$
$158$	0	0
$159$	648.000	0.323206
$160$	0	0
$161$	−1316.00	−0.644195
$162$	0	0
$163$	−2004.00	−0.962978	−0.481489	−	0.876452i	$-0.659904\pi$
$163$	−2004.00	−0.962978	−0.481489	+	0.876452i	$0.659904\pi$
$164$	0	0
$165$	−256.000	−0.120785
$166$	0	0
$167$	2238.00	1.03702	0.518508	−	0.855073i	$-0.326488\pi$
$167$	2238.00	1.03702	0.518508	+	0.855073i	$0.326488\pi$
$168$	0	0
$169$	−81.0000	−0.0368685
$170$	0	0
$171$	−1276.00	−0.570633
$172$	0	0
$173$	−456.000	−0.200399	−0.100200	−	0.994967i	$-0.531948\pi$
$173$	−456.000	−0.200399	−0.100200	+	0.994967i	$0.531948\pi$
$174$	0	0
$175$	854.000	0.368893
$176$	0	0
$177$	2896.00	1.22981
$178$	0	0
$179$	−956.000	−0.399189	−0.199594	−	0.979879i	$-0.563962\pi$
$179$	−956.000	−0.399189	−0.199594	+	0.979879i	$0.563962\pi$
$180$	0	0
$181$	−1060.00	−0.435299	−0.217650	−	0.976027i	$-0.569839\pi$
$181$	−1060.00	−0.435299	−0.217650	+	0.976027i	$0.569839\pi$
$182$	0	0
$183$	−1552.00	−0.626924
$184$	0	0
$185$	−160.000	−0.0635861
$186$	0	0
$187$	136.000	0.0531834
$188$	0	0
$189$	−2128.00	−0.818991
$190$	0	0
$191$	−2996.00	−1.13499	−0.567495	−	0.823377i	$-0.692087\pi$
$191$	−2996.00	−1.13499	−0.567495	+	0.823377i	$0.692087\pi$
$192$	0	0
$193$	−3154.00	−1.17632	−0.588160	−	0.808744i	$-0.700148\pi$
$193$	−3154.00	−1.17632	−0.588160	+	0.808744i	$0.700148\pi$
$194$	0	0
$195$	1472.00	0.540575
$196$	0	0
$197$	1476.00	0.533810	0.266905	−	0.963723i	$-0.413999\pi$
$197$	1476.00	0.533810	0.266905	+	0.963723i	$0.413999\pi$
$198$	0	0
$199$	−486.000	−0.173124	−0.0865619	−	0.996246i	$-0.527588\pi$
$199$	−486.000	−0.173124	−0.0865619	+	0.996246i	$0.527588\pi$
$200$	0	0
$201$	−688.000	−0.241432
$202$	0	0
$203$	−1568.00	−0.542128
$204$	0	0
$205$	−496.000	−0.168986
$206$	0	0
$207$	−1034.00	−0.347188
$208$	0	0
$209$	−928.000	−0.307134
$210$	0	0
$211$	920.000	0.300168	0.150084	−	0.988673i	$-0.452046\pi$
$211$	920.000	0.300168	0.150084	+	0.988673i	$0.452046\pi$
$212$	0	0
$213$	−4360.00	−1.40255
$214$	0	0
$215$	−544.000	−0.172560
$216$	0	0
$217$	700.000	0.218982
$218$	0	0
$219$	4248.00	1.31075
$220$	0	0
$221$	−782.000	−0.238023
$222$	0	0
$223$	−1176.00	−0.353143	−0.176571	−	0.984288i	$-0.556501\pi$
$223$	−1176.00	−0.353143	−0.176571	+	0.984288i	$0.556501\pi$
$224$	0	0
$225$	671.000	0.198815
$226$	0	0
$227$	−2156.00	−0.630391	−0.315195	−	0.949027i	$-0.602070\pi$
$227$	−2156.00	−0.630391	−0.315195	+	0.949027i	$0.602070\pi$
$228$	0	0
$229$	−966.000	−0.278756	−0.139378	−	0.990239i	$-0.544510\pi$
$229$	−966.000	−0.278756	−0.139378	+	0.990239i	$0.544510\pi$
$230$	0	0
$231$	−448.000	−0.127603
$232$	0	0
$233$	3546.00	0.997022	0.498511	−	0.866883i	$-0.333880\pi$
$233$	3546.00	0.997022	0.498511	+	0.866883i	$0.333880\pi$
$234$	0	0
$235$	−480.000	−0.133241
$236$	0	0
$237$	456.000	0.124981
$238$	0	0
$239$	2556.00	0.691774	0.345887	−	0.938276i	$-0.387578\pi$
$239$	2556.00	0.691774	0.345887	+	0.938276i	$0.387578\pi$
$240$	0	0
$241$	4390.00	1.17338	0.586690	−	0.809811i	$-0.300431\pi$
$241$	4390.00	1.17338	0.586690	+	0.809811i	$0.300431\pi$
$242$	0	0
$243$	−2860.00	−0.755017
$244$	0	0
$245$	1176.00	0.306661
$246$	0	0
$247$	5336.00	1.37458
$248$	0	0
$249$	272.000	0.0692261
$250$	0	0
$251$	−6988.00	−1.75729	−0.878643	−	0.477480i	$-0.841550\pi$
$251$	−6988.00	−1.75729	−0.878643	+	0.477480i	$0.841550\pi$
$252$	0	0
$253$	−752.000	−0.186869
$254$	0	0
$255$	−544.000	−0.133595
$256$	0	0
$257$	−222.000	−0.0538832	−0.0269416	−	0.999637i	$-0.508577\pi$
$257$	−222.000	−0.0538832	−0.0269416	+	0.999637i	$0.508577\pi$
$258$	0	0
$259$	−280.000	−0.0671751
$260$	0	0
$261$	−1232.00	−0.292180
$262$	0	0
$263$	−3276.00	−0.768087	−0.384043	−	0.923315i	$-0.625469\pi$
$263$	−3276.00	−0.768087	−0.384043	+	0.923315i	$0.625469\pi$
$264$	0	0
$265$	1296.00	0.300425
$266$	0	0
$267$	2664.00	0.610615
$268$	0	0
$269$	−2680.00	−0.607444	−0.303722	−	0.952761i	$-0.598229\pi$
$269$	−2680.00	−0.607444	−0.303722	+	0.952761i	$0.598229\pi$
$270$	0	0
$271$	4828.00	1.08221	0.541107	−	0.840954i	$-0.318005\pi$
$271$	4828.00	1.08221	0.541107	+	0.840954i	$0.318005\pi$
$272$	0	0
$273$	2576.00	0.571086
$274$	0	0
$275$	488.000	0.107009
$276$	0	0
$277$	−3488.00	−0.756583	−0.378292	−	0.925686i	$-0.623488\pi$
$277$	−3488.00	−0.756583	−0.378292	+	0.925686i	$0.623488\pi$
$278$	0	0
$279$	550.000	0.118020
$280$	0	0
$281$	−874.000	−0.185546	−0.0927731	−	0.995687i	$-0.529573\pi$
$281$	−874.000	−0.185546	−0.0927731	+	0.995687i	$0.529573\pi$
$282$	0	0
$283$	992.000	0.208368	0.104184	−	0.994558i	$-0.466777\pi$
$283$	992.000	0.208368	0.104184	+	0.994558i	$0.466777\pi$
$284$	0	0
$285$	3712.00	0.771508
$286$	0	0
$287$	−868.000	−0.178524
$288$	0	0
$289$	289.000	0.0588235
$290$	0	0
$291$	5288.00	1.06525
$292$	0	0
$293$	−5574.00	−1.11139	−0.555694	−	0.831387i	$-0.687547\pi$
$293$	−5574.00	−1.11139	−0.555694	+	0.831387i	$0.687547\pi$
$294$	0	0
$295$	5792.00	1.14313
$296$	0	0
$297$	−1216.00	−0.237574
$298$	0	0
$299$	4324.00	0.836332
$300$	0	0
$301$	−952.000	−0.182300
$302$	0	0
$303$	−504.000	−0.0955579
$304$	0	0
$305$	−3104.00	−0.582736
$306$	0	0
$307$	−4572.00	−0.849960	−0.424980	−	0.905203i	$-0.639719\pi$
$307$	−4572.00	−0.849960	−0.424980	+	0.905203i	$0.639719\pi$
$308$	0	0
$309$	−6848.00	−1.26074
$310$	0	0
$311$	2142.00	0.390552	0.195276	−	0.980748i	$-0.437440\pi$
$311$	2142.00	0.390552	0.195276	+	0.980748i	$0.437440\pi$
$312$	0	0
$313$	3502.00	0.632411	0.316206	−	0.948691i	$-0.397591\pi$
$313$	3502.00	0.632411	0.316206	+	0.948691i	$0.397591\pi$
$314$	0	0
$315$	−1232.00	−0.220366
$316$	0	0
$317$	3500.00	0.620125	0.310062	−	0.950716i	$-0.399650\pi$
$317$	3500.00	0.620125	0.310062	+	0.950716i	$0.399650\pi$
$318$	0	0
$319$	−896.000	−0.157261
$320$	0	0
$321$	−4704.00	−0.817918
$322$	0	0
$323$	−1972.00	−0.339706
$324$	0	0
$325$	−2806.00	−0.478920
$326$	0	0
$327$	864.000	0.146114
$328$	0	0
$329$	−840.000	−0.140762
$330$	0	0
$331$	7124.00	1.18299	0.591496	−	0.806308i	$-0.298537\pi$
$331$	7124.00	1.18299	0.591496	+	0.806308i	$0.298537\pi$
$332$	0	0
$333$	−220.000	−0.0362040
$334$	0	0
$335$	−1376.00	−0.224415
$336$	0	0
$337$	−3006.00	−0.485897	−0.242948	−	0.970039i	$-0.578115\pi$
$337$	−3006.00	−0.485897	−0.242948	+	0.970039i	$0.578115\pi$
$338$	0	0
$339$	1368.00	0.219173
$340$	0	0
$341$	400.000	0.0635226
$342$	0	0
$343$	6860.00	1.07990
$344$	0	0
$345$	3008.00	0.469407
$346$	0	0
$347$	7324.00	1.13306	0.566532	−	0.824040i	$-0.308285\pi$
$347$	7324.00	1.13306	0.566532	+	0.824040i	$0.308285\pi$
$348$	0	0
$349$	−6258.00	−0.959837	−0.479918	−	0.877313i	$-0.659334\pi$
$349$	−6258.00	−0.959837	−0.479918	+	0.877313i	$0.659334\pi$
$350$	0	0
$351$	6992.00	1.06326
$352$	0	0
$353$	−90.0000	−0.0135700	−0.00678501	−	0.999977i	$-0.502160\pi$
$353$	−90.0000	−0.0135700	−0.00678501	+	0.999977i	$0.502160\pi$
$354$	0	0
$355$	−8720.00	−1.30369
$356$	0	0
$357$	−952.000	−0.141135
$358$	0	0
$359$	−4152.00	−0.610402	−0.305201	−	0.952288i	$-0.598724\pi$
$359$	−4152.00	−0.610402	−0.305201	+	0.952288i	$0.598724\pi$
$360$	0	0
$361$	6597.00	0.961802
$362$	0	0
$363$	5068.00	0.732785
$364$	0	0
$365$	8496.00	1.21836
$366$	0	0
$367$	−11282.0	−1.60467	−0.802337	−	0.596871i	$-0.796410\pi$
$367$	−11282.0	−1.60467	−0.802337	+	0.596871i	$0.796410\pi$
$368$	0	0
$369$	−682.000	−0.0962155
$370$	0	0
$371$	2268.00	0.317382
$372$	0	0
$373$	2142.00	0.297342	0.148671	−	0.988887i	$-0.452500\pi$
$373$	2142.00	0.297342	0.148671	+	0.988887i	$0.452500\pi$
$374$	0	0
$375$	−5952.00	−0.819627
$376$	0	0
$377$	5152.00	0.703824
$378$	0	0
$379$	7052.00	0.955770	0.477885	−	0.878422i	$-0.341404\pi$
$379$	7052.00	0.955770	0.477885	+	0.878422i	$0.341404\pi$
$380$	0	0
$381$	5680.00	0.763767
$382$	0	0
$383$	−3460.00	−0.461613	−0.230806	−	0.973000i	$-0.574136\pi$
$383$	−3460.00	−0.461613	−0.230806	+	0.973000i	$0.574136\pi$
$384$	0	0
$385$	−896.000	−0.118609
$386$	0	0
$387$	−748.000	−0.0982506
$388$	0	0
$389$	9346.00	1.21815	0.609076	−	0.793112i	$-0.291540\pi$
$389$	9346.00	1.21815	0.609076	+	0.793112i	$0.291540\pi$
$390$	0	0
$391$	−1598.00	−0.206686
$392$	0	0
$393$	4192.00	0.538062
$394$	0	0
$395$	912.000	0.116171
$396$	0	0
$397$	6428.00	0.812625	0.406312	−	0.913734i	$-0.366814\pi$
$397$	6428.00	0.812625	0.406312	+	0.913734i	$0.366814\pi$
$398$	0	0
$399$	6496.00	0.815055
$400$	0	0
$401$	2110.00	0.262764	0.131382	−	0.991332i	$-0.458059\pi$
$401$	2110.00	0.262764	0.131382	+	0.991332i	$0.458059\pi$
$402$	0	0
$403$	−2300.00	−0.284296
$404$	0	0
$405$	2488.00	0.305259
$406$	0	0
$407$	−160.000	−0.0194863
$408$	0	0
$409$	2710.00	0.327631	0.163815	−	0.986491i	$-0.447620\pi$
$409$	2710.00	0.327631	0.163815	+	0.986491i	$0.447620\pi$
$410$	0	0
$411$	−3784.00	−0.454139
$412$	0	0
$413$	10136.0	1.20765
$414$	0	0
$415$	544.000	0.0643468
$416$	0	0
$417$	−9248.00	−1.08603
$418$	0	0
$419$	16228.0	1.89210	0.946050	−	0.324021i	$-0.105035\pi$
$419$	16228.0	1.89210	0.946050	+	0.324021i	$0.105035\pi$
$420$	0	0
$421$	7942.00	0.919405	0.459702	−	0.888073i	$-0.347956\pi$
$421$	7942.00	0.919405	0.459702	+	0.888073i	$0.347956\pi$
$422$	0	0
$423$	−660.000	−0.0758636
$424$	0	0
$425$	1037.00	0.118357
$426$	0	0
$427$	−5432.00	−0.615627
$428$	0	0
$429$	1472.00	0.165662
$430$	0	0
$431$	3894.00	0.435191	0.217596	−	0.976039i	$-0.430179\pi$
$431$	3894.00	0.435191	0.217596	+	0.976039i	$0.430179\pi$
$432$	0	0
$433$	−8402.00	−0.932504	−0.466252	−	0.884652i	$-0.654396\pi$
$433$	−8402.00	−0.932504	−0.466252	+	0.884652i	$0.654396\pi$
$434$	0	0
$435$	3584.00	0.395034
$436$	0	0
$437$	10904.0	1.19361
$438$	0	0
$439$	−17422.0	−1.89409	−0.947046	−	0.321097i	$-0.895948\pi$
$439$	−17422.0	−1.89409	−0.947046	+	0.321097i	$0.895948\pi$
$440$	0	0
$441$	1617.00	0.174603
$442$	0	0
$443$	−18476.0	−1.98154	−0.990769	−	0.135562i	$-0.956716\pi$
$443$	−18476.0	−1.98154	−0.990769	+	0.135562i	$0.956716\pi$
$444$	0	0
$445$	5328.00	0.567576
$446$	0	0
$447$	6808.00	0.720374
$448$	0	0
$449$	−13410.0	−1.40948	−0.704741	−	0.709465i	$-0.748937\pi$
$449$	−13410.0	−1.40948	−0.704741	+	0.709465i	$0.748937\pi$
$450$	0	0
$451$	−496.000	−0.0517865
$452$	0	0
$453$	5584.00	0.579159
$454$	0	0
$455$	5152.00	0.530834
$456$	0	0
$457$	17286.0	1.76938	0.884688	−	0.466183i	$-0.154371\pi$
$457$	17286.0	1.76938	0.884688	+	0.466183i	$0.154371\pi$
$458$	0	0
$459$	−2584.00	−0.262769
$460$	0	0
$461$	9630.00	0.972915	0.486457	−	0.873704i	$-0.338289\pi$
$461$	9630.00	0.972915	0.486457	+	0.873704i	$0.338289\pi$
$462$	0	0
$463$	−3944.00	−0.395882	−0.197941	−	0.980214i	$-0.563425\pi$
$463$	−3944.00	−0.395882	−0.197941	+	0.980214i	$0.563425\pi$
$464$	0	0
$465$	−1600.00	−0.159566
$466$	0	0
$467$	−1404.00	−0.139121	−0.0695604	−	0.997578i	$-0.522160\pi$
$467$	−1404.00	−0.139121	−0.0695604	+	0.997578i	$0.522160\pi$
$468$	0	0
$469$	−2408.00	−0.237081
$470$	0	0
$471$	10520.0	1.02916
$472$	0	0
$473$	−544.000	−0.0528819
$474$	0	0
$475$	−7076.00	−0.683514
$476$	0	0
$477$	1782.00	0.171053
$478$	0	0
$479$	−10910.0	−1.04069	−0.520345	−	0.853956i	$-0.674197\pi$
$479$	−10910.0	−1.04069	−0.520345	+	0.853956i	$0.674197\pi$
$480$	0	0
$481$	920.000	0.0872108
$482$	0	0
$483$	5264.00	0.495901
$484$	0	0
$485$	10576.0	0.990168
$486$	0	0
$487$	−9730.00	−0.905356	−0.452678	−	0.891674i	$-0.649531\pi$
$487$	−9730.00	−0.905356	−0.452678	+	0.891674i	$0.649531\pi$
$488$	0	0
$489$	8016.00	0.741301
$490$	0	0
$491$	−19812.0	−1.82098	−0.910492	−	0.413527i	$-0.864297\pi$
$491$	−19812.0	−1.82098	−0.910492	+	0.413527i	$0.864297\pi$
$492$	0	0
$493$	−1904.00	−0.173939
$494$	0	0
$495$	−704.000	−0.0639241
$496$	0	0
$497$	−15260.0	−1.37727
$498$	0	0
$499$	−13952.0	−1.25166	−0.625829	−	0.779960i	$-0.715239\pi$
$499$	−13952.0	−1.25166	−0.625829	+	0.779960i	$0.715239\pi$
$500$	0	0
$501$	−8952.00	−0.798295
$502$	0	0
$503$	−8722.00	−0.773151	−0.386575	−	0.922258i	$-0.626342\pi$
$503$	−8722.00	−0.773151	−0.386575	+	0.922258i	$0.626342\pi$
$504$	0	0
$505$	−1008.00	−0.0888226
$506$	0	0
$507$	324.000	0.0283814
$508$	0	0
$509$	18978.0	1.65262	0.826311	−	0.563213i	$-0.190435\pi$
$509$	18978.0	1.65262	0.826311	+	0.563213i	$0.190435\pi$
$510$	0	0
$511$	14868.0	1.28713
$512$	0	0
$513$	17632.0	1.51749
$514$	0	0
$515$	−13696.0	−1.17188
$516$	0	0
$517$	−480.000	−0.0408324
$518$	0	0
$519$	1824.00	0.154267
$520$	0	0
$521$	14086.0	1.18449	0.592245	−	0.805758i	$-0.298242\pi$
$521$	14086.0	1.18449	0.592245	+	0.805758i	$0.298242\pi$
$522$	0	0
$523$	7308.00	0.611007	0.305503	−	0.952191i	$-0.401175\pi$
$523$	7308.00	0.611007	0.305503	+	0.952191i	$0.401175\pi$
$524$	0	0
$525$	−3416.00	−0.283974
$526$	0	0
$527$	850.000	0.0702592
$528$	0	0
$529$	−3331.00	−0.273773
$530$	0	0
$531$	7964.00	0.650863
$532$	0	0
$533$	2852.00	0.231771
$534$	0	0
$535$	−9408.00	−0.760268
$536$	0	0
$537$	3824.00	0.307296
$538$	0	0
$539$	1176.00	0.0939776
$540$	0	0
$541$	−10204.0	−0.810914	−0.405457	−	0.914114i	$-0.632888\pi$
$541$	−10204.0	−0.810914	−0.405457	+	0.914114i	$0.632888\pi$
$542$	0	0
$543$	4240.00	0.335094
$544$	0	0
$545$	1728.00	0.135815
$546$	0	0
$547$	11032.0	0.862330	0.431165	−	0.902273i	$-0.358103\pi$
$547$	11032.0	0.862330	0.431165	+	0.902273i	$0.358103\pi$
$548$	0	0
$549$	−4268.00	−0.331792
$550$	0	0
$551$	12992.0	1.00450
$552$	0	0
$553$	1596.00	0.122728
$554$	0	0
$555$	640.000	0.0489486
$556$	0	0
$557$	22086.0	1.68010	0.840048	−	0.542512i	$-0.182527\pi$
$557$	22086.0	1.68010	0.840048	+	0.542512i	$0.182527\pi$
$558$	0	0
$559$	3128.00	0.236673
$560$	0	0
$561$	−544.000	−0.0409406
$562$	0	0
$563$	5028.00	0.376385	0.188193	−	0.982132i	$-0.439737\pi$
$563$	5028.00	0.376385	0.188193	+	0.982132i	$0.439737\pi$
$564$	0	0
$565$	2736.00	0.203725
$566$	0	0
$567$	4354.00	0.322488
$568$	0	0
$569$	−17934.0	−1.32132	−0.660661	−	0.750684i	$-0.729724\pi$
$569$	−17934.0	−1.32132	−0.660661	+	0.750684i	$0.729724\pi$
$570$	0	0
$571$	−11588.0	−0.849287	−0.424643	−	0.905361i	$-0.639601\pi$
$571$	−11588.0	−0.849287	−0.424643	+	0.905361i	$0.639601\pi$
$572$	0	0
$573$	11984.0	0.873715
$574$	0	0
$575$	−5734.00	−0.415868
$576$	0	0
$577$	−478.000	−0.0344877	−0.0172438	−	0.999851i	$-0.505489\pi$
$577$	−478.000	−0.0344877	−0.0172438	+	0.999851i	$0.505489\pi$
$578$	0	0
$579$	12616.0	0.905532
$580$	0	0
$581$	952.000	0.0679787
$582$	0	0
$583$	1296.00	0.0920666
$584$	0	0
$585$	4048.00	0.286093
$586$	0	0
$587$	11684.0	0.821551	0.410775	−	0.911737i	$-0.365258\pi$
$587$	11684.0	0.821551	0.410775	+	0.911737i	$0.365258\pi$
$588$	0	0
$589$	−5800.00	−0.405747
$590$	0	0
$591$	−5904.00	−0.410927
$592$	0	0
$593$	−5102.00	−0.353312	−0.176656	−	0.984273i	$-0.556528\pi$
$593$	−5102.00	−0.353312	−0.176656	+	0.984273i	$0.556528\pi$
$594$	0	0
$595$	−1904.00	−0.131187
$596$	0	0
$597$	1944.00	0.133271
$598$	0	0
$599$	21560.0	1.47065	0.735324	−	0.677716i	$-0.237030\pi$
$599$	21560.0	1.47065	0.735324	+	0.677716i	$0.237030\pi$
$600$	0	0
$601$	−7358.00	−0.499399	−0.249700	−	0.968323i	$-0.580332\pi$
$601$	−7358.00	−0.499399	−0.249700	+	0.968323i	$0.580332\pi$
$602$	0	0
$603$	−1892.00	−0.127775
$604$	0	0
$605$	10136.0	0.681136
$606$	0	0
$607$	−27818.0	−1.86013	−0.930064	−	0.367397i	$-0.880249\pi$
$607$	−27818.0	−1.86013	−0.930064	+	0.367397i	$0.880249\pi$
$608$	0	0
$609$	6272.00	0.417330
$610$	0	0
$611$	2760.00	0.182746
$612$	0	0
$613$	−29566.0	−1.94806	−0.974029	−	0.226424i	$-0.927297\pi$
$613$	−29566.0	−1.94806	−0.974029	+	0.226424i	$0.927297\pi$
$614$	0	0
$615$	1984.00	0.130086
$616$	0	0
$617$	4410.00	0.287747	0.143874	−	0.989596i	$-0.454044\pi$
$617$	4410.00	0.287747	0.143874	+	0.989596i	$0.454044\pi$
$618$	0	0
$619$	−19780.0	−1.28437	−0.642185	−	0.766549i	$-0.721972\pi$
$619$	−19780.0	−1.28437	−0.642185	+	0.766549i	$0.721972\pi$
$620$	0	0
$621$	14288.0	0.923281
$622$	0	0
$623$	9324.00	0.599612
$624$	0	0
$625$	−4279.00	−0.273856
$626$	0	0
$627$	3712.00	0.236432
$628$	0	0
$629$	−340.000	−0.0215528
$630$	0	0
$631$	−7912.00	−0.499163	−0.249581	−	0.968354i	$-0.580293\pi$
$631$	−7912.00	−0.499163	−0.249581	+	0.968354i	$0.580293\pi$
$632$	0	0
$633$	−3680.00	−0.231069
$634$	0	0
$635$	11360.0	0.709934
$636$	0	0
$637$	−6762.00	−0.420597
$638$	0	0
$639$	−11990.0	−0.742280
$640$	0	0
$641$	−10586.0	−0.652296	−0.326148	−	0.945319i	$-0.605751\pi$
$641$	−10586.0	−0.652296	−0.326148	+	0.945319i	$0.605751\pi$
$642$	0	0
$643$	4612.00	0.282861	0.141430	−	0.989948i	$-0.454830\pi$
$643$	4612.00	0.282861	0.141430	+	0.989948i	$0.454830\pi$
$644$	0	0
$645$	2176.00	0.132837
$646$	0	0
$647$	−2652.00	−0.161145	−0.0805725	−	0.996749i	$-0.525675\pi$
$647$	−2652.00	−0.161145	−0.0805725	+	0.996749i	$0.525675\pi$
$648$	0	0
$649$	5792.00	0.350317
$650$	0	0
$651$	−2800.00	−0.168572
$652$	0	0
$653$	480.000	0.0287655	0.0143827	−	0.999897i	$-0.495422\pi$
$653$	480.000	0.0287655	0.0143827	+	0.999897i	$0.495422\pi$
$654$	0	0
$655$	8384.00	0.500137
$656$	0	0
$657$	11682.0	0.693696
$658$	0	0
$659$	−7908.00	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−7908.00	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−14690.0	−0.864410	−0.432205	−	0.901775i	$-0.642264\pi$
$661$	−14690.0	−0.864410	−0.432205	+	0.901775i	$0.642264\pi$
$662$	0	0
$663$	3128.00	0.183230
$664$	0	0
$665$	12992.0	0.757606
$666$	0	0
$667$	10528.0	0.611163
$668$	0	0
$669$	4704.00	0.271849
$670$	0	0
$671$	−3104.00	−0.178582
$672$	0	0
$673$	11302.0	0.647340	0.323670	−	0.946170i	$-0.395083\pi$
$673$	11302.0	0.647340	0.323670	+	0.946170i	$0.395083\pi$
$674$	0	0
$675$	−9272.00	−0.528710
$676$	0	0
$677$	−14068.0	−0.798637	−0.399318	−	0.916812i	$-0.630753\pi$
$677$	−14068.0	−0.798637	−0.399318	+	0.916812i	$0.630753\pi$
$678$	0	0
$679$	18508.0	1.04606
$680$	0	0
$681$	8624.00	0.485275
$682$	0	0
$683$	15372.0	0.861191	0.430595	−	0.902545i	$-0.358304\pi$
$683$	15372.0	0.861191	0.430595	+	0.902545i	$0.358304\pi$
$684$	0	0
$685$	−7568.00	−0.422129
$686$	0	0
$687$	3864.00	0.214586
$688$	0	0
$689$	−7452.00	−0.412044
$690$	0	0
$691$	15920.0	0.876448	0.438224	−	0.898866i	$-0.355608\pi$
$691$	15920.0	0.876448	0.438224	+	0.898866i	$0.355608\pi$
$692$	0	0
$693$	−1232.00	−0.0675322
$694$	0	0
$695$	−18496.0	−1.00949
$696$	0	0
$697$	−1054.00	−0.0572785
$698$	0	0
$699$	−14184.0	−0.767508
$700$	0	0
$701$	28078.0	1.51283	0.756413	−	0.654094i	$-0.226950\pi$
$701$	28078.0	1.51283	0.756413	+	0.654094i	$0.226950\pi$
$702$	0	0
$703$	2320.00	0.124467
$704$	0	0
$705$	1920.00	0.102569
$706$	0	0
$707$	−1764.00	−0.0938360
$708$	0	0
$709$	−15448.0	−0.818282	−0.409141	−	0.912471i	$-0.634172\pi$
$709$	−15448.0	−0.818282	−0.409141	+	0.912471i	$0.634172\pi$
$710$	0	0
$711$	1254.00	0.0661444
$712$	0	0
$713$	−4700.00	−0.246867
$714$	0	0
$715$	2944.00	0.153985
$716$	0	0
$717$	−10224.0	−0.532528
$718$	0	0
$719$	28434.0	1.47484	0.737420	−	0.675435i	$-0.236044\pi$
$719$	28434.0	1.47484	0.737420	+	0.675435i	$0.236044\pi$
$720$	0	0
$721$	−23968.0	−1.23802
$722$	0	0
$723$	−17560.0	−0.903269
$724$	0	0
$725$	−6832.00	−0.349978
$726$	0	0
$727$	−25156.0	−1.28333	−0.641667	−	0.766983i	$-0.721757\pi$
$727$	−25156.0	−1.28333	−0.641667	+	0.766983i	$0.721757\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	−1156.00	−0.0584900
$732$	0	0
$733$	20902.0	1.05325	0.526626	−	0.850097i	$-0.323457\pi$
$733$	20902.0	1.05325	0.526626	+	0.850097i	$0.323457\pi$
$734$	0	0
$735$	−4704.00	−0.236068
$736$	0	0
$737$	−1376.00	−0.0687729
$738$	0	0
$739$	18172.0	0.904557	0.452279	−	0.891877i	$-0.350611\pi$
$739$	18172.0	0.904557	0.452279	+	0.891877i	$0.350611\pi$
$740$	0	0
$741$	−21344.0	−1.05815
$742$	0	0
$743$	−28522.0	−1.40831	−0.704153	−	0.710049i	$-0.748673\pi$
$743$	−28522.0	−1.40831	−0.704153	+	0.710049i	$0.748673\pi$
$744$	0	0
$745$	13616.0	0.669600
$746$	0	0
$747$	748.000	0.0366371
$748$	0	0
$749$	−16464.0	−0.803180
$750$	0	0
$751$	26978.0	1.31084	0.655420	−	0.755264i	$-0.272492\pi$
$751$	26978.0	1.31084	0.655420	+	0.755264i	$0.272492\pi$
$752$	0	0
$753$	27952.0	1.35276
$754$	0	0
$755$	11168.0	0.538338
$756$	0	0
$757$	−31030.0	−1.48983	−0.744917	−	0.667157i	$-0.767511\pi$
$757$	−31030.0	−1.48983	−0.744917	+	0.667157i	$0.767511\pi$
$758$	0	0
$759$	3008.00	0.143852
$760$	0	0
$761$	−18878.0	−0.899247	−0.449623	−	0.893218i	$-0.648442\pi$
$761$	−18878.0	−0.899247	−0.449623	+	0.893218i	$0.648442\pi$
$762$	0	0
$763$	3024.00	0.143481
$764$	0	0
$765$	−1496.00	−0.0707033
$766$	0	0
$767$	−33304.0	−1.56785
$768$	0	0
$769$	−20070.0	−0.941148	−0.470574	−	0.882361i	$-0.655953\pi$
$769$	−20070.0	−0.941148	−0.470574	+	0.882361i	$0.655953\pi$
$770$	0	0
$771$	888.000	0.0414793
$772$	0	0
$773$	−17358.0	−0.807663	−0.403832	−	0.914833i	$-0.632322\pi$
$773$	−17358.0	−0.807663	−0.403832	+	0.914833i	$0.632322\pi$
$774$	0	0
$775$	3050.00	0.141367
$776$	0	0
$777$	1120.00	0.0517114
$778$	0	0
$779$	7192.00	0.330783
$780$	0	0
$781$	−8720.00	−0.399521
$782$	0	0
$783$	17024.0	0.776996
$784$	0	0
$785$	21040.0	0.956624
$786$	0	0
$787$	4784.00	0.216685	0.108343	−	0.994114i	$-0.465446\pi$
$787$	4784.00	0.216685	0.108343	+	0.994114i	$0.465446\pi$
$788$	0	0
$789$	13104.0	0.591273
$790$	0	0
$791$	4788.00	0.215223
$792$	0	0
$793$	17848.0	0.799245
$794$	0	0
$795$	−5184.00	−0.231267
$796$	0	0
$797$	−43626.0	−1.93891	−0.969456	−	0.245267i	$-0.921124\pi$
$797$	−43626.0	−1.93891	−0.969456	+	0.245267i	$0.921124\pi$
$798$	0	0
$799$	−1020.00	−0.0451627
$800$	0	0
$801$	7326.00	0.323160
$802$	0	0
$803$	8496.00	0.373372
$804$	0	0
$805$	10528.0	0.460948
$806$	0	0
$807$	10720.0	0.467611
$808$	0	0
$809$	28870.0	1.25465	0.627327	−	0.778756i	$-0.284149\pi$
$809$	28870.0	1.25465	0.627327	+	0.778756i	$0.284149\pi$
$810$	0	0
$811$	19124.0	0.828033	0.414016	−	0.910269i	$-0.364126\pi$
$811$	19124.0	0.828033	0.414016	+	0.910269i	$0.364126\pi$
$812$	0	0
$813$	−19312.0	−0.833089
$814$	0	0
$815$	16032.0	0.689051
$816$	0	0
$817$	7888.00	0.337780
$818$	0	0
$819$	7084.00	0.302241
$820$	0	0
$821$	1244.00	0.0528817	0.0264409	−	0.999650i	$-0.491583\pi$
$821$	1244.00	0.0528817	0.0264409	+	0.999650i	$0.491583\pi$
$822$	0	0
$823$	−23258.0	−0.985083	−0.492541	−	0.870289i	$-0.663932\pi$
$823$	−23258.0	−0.985083	−0.492541	+	0.870289i	$0.663932\pi$
$824$	0	0
$825$	−1952.00	−0.0823757
$826$	0	0
$827$	−11800.0	−0.496162	−0.248081	−	0.968739i	$-0.579800\pi$
$827$	−11800.0	−0.496162	−0.248081	+	0.968739i	$0.579800\pi$
$828$	0	0
$829$	39842.0	1.66920	0.834602	−	0.550854i	$-0.185698\pi$
$829$	39842.0	1.66920	0.834602	+	0.550854i	$0.185698\pi$
$830$	0	0
$831$	13952.0	0.582418
$832$	0	0
$833$	2499.00	0.103944
$834$	0	0
$835$	−17904.0	−0.742028
$836$	0	0
$837$	−7600.00	−0.313852
$838$	0	0
$839$	−18582.0	−0.764627	−0.382313	−	0.924033i	$-0.624873\pi$
$839$	−18582.0	−0.764627	−0.382313	+	0.924033i	$0.624873\pi$
$840$	0	0
$841$	−11845.0	−0.485670
$842$	0	0
$843$	3496.00	0.142833
$844$	0	0
$845$	648.000	0.0263809
$846$	0	0
$847$	17738.0	0.719581
$848$	0	0
$849$	−3968.00	−0.160402
$850$	0	0
$851$	1880.00	0.0757292
$852$	0	0
$853$	−45232.0	−1.81561	−0.907804	−	0.419394i	$-0.862243\pi$
$853$	−45232.0	−1.81561	−0.907804	+	0.419394i	$0.862243\pi$
$854$	0	0
$855$	10208.0	0.408311
$856$	0	0
$857$	−32466.0	−1.29407	−0.647035	−	0.762461i	$-0.723991\pi$
$857$	−32466.0	−1.29407	−0.647035	+	0.762461i	$0.723991\pi$
$858$	0	0
$859$	−20420.0	−0.811084	−0.405542	−	0.914076i	$-0.632917\pi$
$859$	−20420.0	−0.811084	−0.405542	+	0.914076i	$0.632917\pi$
$860$	0	0
$861$	3472.00	0.137428
$862$	0	0
$863$	16032.0	0.632370	0.316185	−	0.948697i	$-0.397598\pi$
$863$	16032.0	0.632370	0.316185	+	0.948697i	$0.397598\pi$
$864$	0	0
$865$	3648.00	0.143394
$866$	0	0
$867$	−1156.00	−0.0452824
$868$	0	0
$869$	912.000	0.0356012
$870$	0	0
$871$	7912.00	0.307793
$872$	0	0
$873$	14542.0	0.563771
$874$	0	0
$875$	−20832.0	−0.804857
$876$	0	0
$877$	−4536.00	−0.174652	−0.0873260	−	0.996180i	$-0.527832\pi$
$877$	−4536.00	−0.174652	−0.0873260	+	0.996180i	$0.527832\pi$
$878$	0	0
$879$	22296.0	0.855547
$880$	0	0
$881$	−13062.0	−0.499512	−0.249756	−	0.968309i	$-0.580350\pi$
$881$	−13062.0	−0.499512	−0.249756	+	0.968309i	$0.580350\pi$
$882$	0	0
$883$	6156.00	0.234616	0.117308	−	0.993096i	$-0.462574\pi$
$883$	6156.00	0.234616	0.117308	+	0.993096i	$0.462574\pi$
$884$	0	0
$885$	−23168.0	−0.879982
$886$	0	0
$887$	12210.0	0.462200	0.231100	−	0.972930i	$-0.425767\pi$
$887$	12210.0	0.462200	0.231100	+	0.972930i	$0.425767\pi$
$888$	0	0
$889$	19880.0	0.750004
$890$	0	0
$891$	2488.00	0.0935479
$892$	0	0
$893$	6960.00	0.260815
$894$	0	0
$895$	7648.00	0.285636
$896$	0	0
$897$	−17296.0	−0.643809
$898$	0	0
$899$	−5600.00	−0.207754
$900$	0	0
$901$	2754.00	0.101830
$902$	0	0
$903$	3808.00	0.140335
$904$	0	0
$905$	8480.00	0.311475
$906$	0	0
$907$	−24104.0	−0.882426	−0.441213	−	0.897402i	$-0.645452\pi$
$907$	−24104.0	−0.882426	−0.441213	+	0.897402i	$0.645452\pi$
$908$	0	0
$909$	−1386.00	−0.0505728
$910$	0	0
$911$	−7814.00	−0.284182	−0.142091	−	0.989854i	$-0.545382\pi$
$911$	−7814.00	−0.284182	−0.142091	+	0.989854i	$0.545382\pi$
$912$	0	0
$913$	544.000	0.0197194
$914$	0	0
$915$	12416.0	0.448590
$916$	0	0
$917$	14672.0	0.528367
$918$	0	0
$919$	−34716.0	−1.24611	−0.623055	−	0.782178i	$-0.714109\pi$
$919$	−34716.0	−1.24611	−0.623055	+	0.782178i	$0.714109\pi$
$920$	0	0
$921$	18288.0	0.654300
$922$	0	0
$923$	50140.0	1.78806
$924$	0	0
$925$	−1220.00	−0.0433658
$926$	0	0
$927$	−18832.0	−0.667232
$928$	0	0
$929$	−46434.0	−1.63988	−0.819941	−	0.572448i	$-0.805994\pi$
$929$	−46434.0	−1.63988	−0.819941	+	0.572448i	$0.805994\pi$
$930$	0	0
$931$	−17052.0	−0.600276
$932$	0	0
$933$	−8568.00	−0.300647
$934$	0	0
$935$	−1088.00	−0.0380550
$936$	0	0
$937$	−49274.0	−1.71794	−0.858971	−	0.512024i	$-0.828896\pi$
$937$	−49274.0	−1.71794	−0.858971	+	0.512024i	$0.828896\pi$
$938$	0	0
$939$	−14008.0	−0.486830
$940$	0	0
$941$	16836.0	0.583250	0.291625	−	0.956533i	$-0.405804\pi$
$941$	16836.0	0.583250	0.291625	+	0.956533i	$0.405804\pi$
$942$	0	0
$943$	5828.00	0.201257
$944$	0	0
$945$	17024.0	0.586022
$946$	0	0
$947$	−45264.0	−1.55320	−0.776601	−	0.629993i	$-0.783058\pi$
$947$	−45264.0	−1.55320	−0.776601	+	0.629993i	$0.783058\pi$
$948$	0	0
$949$	−48852.0	−1.67103
$950$	0	0
$951$	−14000.0	−0.477372
$952$	0	0
$953$	−5290.00	−0.179811	−0.0899055	−	0.995950i	$-0.528657\pi$
$953$	−5290.00	−0.179811	−0.0899055	+	0.995950i	$0.528657\pi$
$954$	0	0
$955$	23968.0	0.812132
$956$	0	0
$957$	3584.00	0.121060
$958$	0	0
$959$	−13244.0	−0.445955
$960$	0	0
$961$	−27291.0	−0.916082
$962$	0	0
$963$	−12936.0	−0.432873
$964$	0	0
$965$	25232.0	0.841707
$966$	0	0
$967$	33312.0	1.10780	0.553900	−	0.832584i	$-0.313139\pi$
$967$	33312.0	1.10780	0.553900	+	0.832584i	$0.313139\pi$
$968$	0	0
$969$	7888.00	0.261506
$970$	0	0
$971$	−44628.0	−1.47495	−0.737477	−	0.675372i	$-0.763983\pi$
$971$	−44628.0	−1.47495	−0.737477	+	0.675372i	$0.763983\pi$
$972$	0	0
$973$	−32368.0	−1.06646
$974$	0	0
$975$	11224.0	0.368672
$976$	0	0
$977$	−40294.0	−1.31947	−0.659734	−	0.751500i	$-0.729331\pi$
$977$	−40294.0	−1.31947	−0.659734	+	0.751500i	$0.729331\pi$
$978$	0	0
$979$	5328.00	0.173936
$980$	0	0
$981$	2376.00	0.0773291
$982$	0	0
$983$	33498.0	1.08690	0.543449	−	0.839442i	$-0.317118\pi$
$983$	33498.0	1.08690	0.543449	+	0.839442i	$0.317118\pi$
$984$	0	0
$985$	−11808.0	−0.381964
$986$	0	0
$987$	3360.00	0.108359
$988$	0	0
$989$	6392.00	0.205514
$990$	0	0
$991$	−28206.0	−0.904130	−0.452065	−	0.891985i	$-0.649313\pi$
$991$	−28206.0	−0.904130	−0.452065	+	0.891985i	$0.649313\pi$
$992$	0	0
$993$	−28496.0	−0.910668
$994$	0	0
$995$	3888.00	0.123877
$996$	0	0
$997$	932.000	0.0296056	0.0148028	−	0.999890i	$-0.495288\pi$
$997$	932.000	0.0296056	0.0148028	+	0.999890i	$0.495288\pi$
$998$	0	0
$999$	3040.00	0.0962776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.4.a.c.1.1		1
4.3	odd	2		1088.4.a.j.1.1		1
8.3	odd	2		544.4.a.b.1.1	✓	1
8.5	even	2		544.4.a.c.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.4.a.b.1.1	✓	1	8.3	odd	2
544.4.a.c.1.1	yes	1	8.5	even	2
1088.4.a.c.1.1		1	1.1	even	1	trivial
1088.4.a.j.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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1088.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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