LMFDB - Embedded newform 1400.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,4,Mod(1,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1400.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1400.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:	$82.6026740080$
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	$\chi$	$=$	1400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{3} +7.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+5.00000 q^{3} +7.00000 q^{7} -2.00000 q^{9} +11.0000 q^{11} -46.0000 q^{13} +127.000 q^{17} +117.000 q^{19} +35.0000 q^{21} +80.0000 q^{23} -145.000 q^{27} +34.0000 q^{29} -292.000 q^{31} +55.0000 q^{33} -376.000 q^{37} -230.000 q^{39} +507.000 q^{41} +32.0000 q^{43} -134.000 q^{47} +49.0000 q^{49} +635.000 q^{51} +612.000 q^{53} +585.000 q^{57} +780.000 q^{59} -426.000 q^{61} -14.0000 q^{63} -207.000 q^{67} +400.000 q^{69} +702.000 q^{71} +1185.00 q^{73} +77.0000 q^{77} +54.0000 q^{79} -671.000 q^{81} -309.000 q^{83} +170.000 q^{87} -339.000 q^{89} -322.000 q^{91} -1460.00 q^{93} +182.000 q^{97} -22.0000 q^{99} +O(q^{100})$

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
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	0	0
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	11.0000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	11.0000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−46.0000	−0.981393	−0.490696	−	0.871331i	$-0.663258\pi$
$13$	−46.0000	−0.981393	−0.490696	+	0.871331i	$0.663258\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	127.000	1.81188	0.905942	−	0.423402i	$-0.139164\pi$
$17$	127.000	1.81188	0.905942	+	0.423402i	$0.139164\pi$
$18$	0	0
$19$	117.000	1.41272	0.706359	−	0.707854i	$-0.250336\pi$
$19$	117.000	1.41272	0.706359	+	0.707854i	$0.250336\pi$
$20$	0	0
$21$	35.0000	0.363696
$22$	0	0
$23$	80.0000	0.725268	0.362634	−	0.931932i	$-0.381878\pi$
$23$	80.0000	0.725268	0.362634	+	0.931932i	$0.381878\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−145.000	−1.03353
$28$	0	0
$29$	34.0000	0.217712	0.108856	−	0.994058i	$-0.465281\pi$
$29$	34.0000	0.217712	0.108856	+	0.994058i	$0.465281\pi$
$30$	0	0
$31$	−292.000	−1.69177	−0.845883	−	0.533368i	$-0.820926\pi$
$31$	−292.000	−1.69177	−0.845883	+	0.533368i	$0.820926\pi$
$32$	0	0
$33$	55.0000	0.290129
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−376.000	−1.67065	−0.835325	−	0.549757i	$-0.814720\pi$
$37$	−376.000	−1.67065	−0.835325	+	0.549757i	$0.814720\pi$
$38$	0	0
$39$	−230.000	−0.944346
$40$	0	0
$41$	507.000	1.93122	0.965611	−	0.259991i	$-0.0837197\pi$
$41$	507.000	1.93122	0.965611	+	0.259991i	$0.0837197\pi$
$42$	0	0
$43$	32.0000	0.113487	0.0567437	−	0.998389i	$-0.481928\pi$
$43$	32.0000	0.113487	0.0567437	+	0.998389i	$0.481928\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−134.000	−0.415870	−0.207935	−	0.978143i	$-0.566674\pi$
$47$	−134.000	−0.415870	−0.207935	+	0.978143i	$0.566674\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	635.000	1.74349
$52$	0	0
$53$	612.000	1.58613	0.793063	−	0.609140i	$-0.208485\pi$
$53$	612.000	1.58613	0.793063	+	0.609140i	$0.208485\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	585.000	1.35939
$58$	0	0
$59$	780.000	1.72114	0.860571	−	0.509331i	$-0.170107\pi$
$59$	780.000	1.72114	0.860571	+	0.509331i	$0.170107\pi$
$60$	0	0
$61$	−426.000	−0.894159	−0.447080	−	0.894494i	$-0.647536\pi$
$61$	−426.000	−0.894159	−0.447080	+	0.894494i	$0.647536\pi$
$62$	0	0
$63$	−14.0000	−0.0279974
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−207.000	−0.377449	−0.188724	−	0.982030i	$-0.560435\pi$
$67$	−207.000	−0.377449	−0.188724	+	0.982030i	$0.560435\pi$
$68$	0	0
$69$	400.000	0.697889
$70$	0	0
$71$	702.000	1.17341	0.586705	−	0.809801i	$-0.300425\pi$
$71$	702.000	1.17341	0.586705	+	0.809801i	$0.300425\pi$
$72$	0	0
$73$	1185.00	1.89991	0.949957	−	0.312380i	$-0.101126\pi$
$73$	1185.00	1.89991	0.949957	+	0.312380i	$0.101126\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	77.0000	0.113961
$78$	0	0
$79$	54.0000	0.0769047	0.0384524	−	0.999260i	$-0.487757\pi$
$79$	54.0000	0.0769047	0.0384524	+	0.999260i	$0.487757\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	0	0
$83$	−309.000	−0.408640	−0.204320	−	0.978904i	$-0.565498\pi$
$83$	−309.000	−0.408640	−0.204320	+	0.978904i	$0.565498\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	170.000	0.209493
$88$	0	0
$89$	−339.000	−0.403752	−0.201876	−	0.979411i	$-0.564704\pi$
$89$	−339.000	−0.403752	−0.201876	+	0.979411i	$0.564704\pi$
$90$	0	0
$91$	−322.000	−0.370932
$92$	0	0
$93$	−1460.00	−1.62790
$94$	0	0
$95$	0	0
$96$	0	0
$97$	182.000	0.190508	0.0952541	−	0.995453i	$-0.469634\pi$
$97$	182.000	0.190508	0.0952541	+	0.995453i	$0.469634\pi$
$98$	0	0
$99$	−22.0000	−0.0223342
$100$	0	0
$101$	1152.00	1.13493	0.567467	−	0.823396i	$-0.307924\pi$
$101$	1152.00	1.13493	0.567467	+	0.823396i	$0.307924\pi$
$102$	0	0
$103$	1588.00	1.51913	0.759565	−	0.650432i	$-0.225412\pi$
$103$	1588.00	1.51913	0.759565	+	0.650432i	$0.225412\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1661.00	−1.50070	−0.750350	−	0.661041i	$-0.770115\pi$
$107$	−1661.00	−1.50070	−0.750350	+	0.661041i	$0.770115\pi$
$108$	0	0
$109$	70.0000	0.0615118	0.0307559	−	0.999527i	$-0.490209\pi$
$109$	70.0000	0.0615118	0.0307559	+	0.999527i	$0.490209\pi$
$110$	0	0
$111$	−1880.00	−1.60758
$112$	0	0
$113$	1839.00	1.53096	0.765480	−	0.643459i	$-0.222501\pi$
$113$	1839.00	1.53096	0.765480	+	0.643459i	$0.222501\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	92.0000	0.0726958
$118$	0	0
$119$	889.000	0.684828
$120$	0	0
$121$	−1210.00	−0.909091
$122$	0	0
$123$	2535.00	1.85832
$124$	0	0
$125$	0	0
$126$	0	0
$127$	106.000	0.0740628	0.0370314	−	0.999314i	$-0.488210\pi$
$127$	106.000	0.0740628	0.0370314	+	0.999314i	$0.488210\pi$
$128$	0	0
$129$	160.000	0.109203
$130$	0	0
$131$	−1152.00	−0.768326	−0.384163	−	0.923265i	$-0.625510\pi$
$131$	−1152.00	−0.768326	−0.384163	+	0.923265i	$0.625510\pi$
$132$	0	0
$133$	819.000	0.533957
$134$	0	0
$135$	0	0
$136$	0	0
$137$	1557.00	0.970974	0.485487	−	0.874244i	$-0.338642\pi$
$137$	1557.00	0.970974	0.485487	+	0.874244i	$0.338642\pi$
$138$	0	0
$139$	733.000	0.447282	0.223641	−	0.974672i	$-0.428206\pi$
$139$	733.000	0.447282	0.223641	+	0.974672i	$0.428206\pi$
$140$	0	0
$141$	−670.000	−0.400171
$142$	0	0
$143$	−506.000	−0.295901
$144$	0	0
$145$	0	0
$146$	0	0
$147$	245.000	0.137464
$148$	0	0
$149$	44.0000	0.0241921	0.0120960	−	0.999927i	$-0.496150\pi$
$149$	44.0000	0.0241921	0.0120960	+	0.999927i	$0.496150\pi$
$150$	0	0
$151$	2360.00	1.27188	0.635941	−	0.771738i	$-0.280612\pi$
$151$	2360.00	1.27188	0.635941	+	0.771738i	$0.280612\pi$
$152$	0	0
$153$	−254.000	−0.134214
$154$	0	0
$155$	0	0
$156$	0	0
$157$	2324.00	1.18137	0.590686	−	0.806902i	$-0.298857\pi$
$157$	2324.00	1.18137	0.590686	+	0.806902i	$0.298857\pi$
$158$	0	0
$159$	3060.00	1.52625
$160$	0	0
$161$	560.000	0.274125
$162$	0	0
$163$	2261.00	1.08647	0.543237	−	0.839580i	$-0.317199\pi$
$163$	2261.00	1.08647	0.543237	+	0.839580i	$0.317199\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−772.000	−0.357719	−0.178860	−	0.983875i	$-0.557241\pi$
$167$	−772.000	−0.357719	−0.178860	+	0.983875i	$0.557241\pi$
$168$	0	0
$169$	−81.0000	−0.0368685
$170$	0	0
$171$	−234.000	−0.104646
$172$	0	0
$173$	26.0000	0.0114263	0.00571313	−	0.999984i	$-0.498181\pi$
$173$	26.0000	0.0114263	0.00571313	+	0.999984i	$0.498181\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	3900.00	1.65617
$178$	0	0
$179$	2339.00	0.976676	0.488338	−	0.872654i	$-0.337603\pi$
$179$	2339.00	0.976676	0.488338	+	0.872654i	$0.337603\pi$
$180$	0	0
$181$	−2270.00	−0.932198	−0.466099	−	0.884733i	$-0.654341\pi$
$181$	−2270.00	−0.932198	−0.466099	+	0.884733i	$0.654341\pi$
$182$	0	0
$183$	−2130.00	−0.860405
$184$	0	0
$185$	0	0
$186$	0	0
$187$	1397.00	0.546304
$188$	0	0
$189$	−1015.00	−0.390637
$190$	0	0
$191$	−4206.00	−1.59338	−0.796690	−	0.604389i	$-0.793417\pi$
$191$	−4206.00	−1.59338	−0.796690	+	0.604389i	$0.793417\pi$
$192$	0	0
$193$	−2683.00	−1.00066	−0.500328	−	0.865836i	$-0.666787\pi$
$193$	−2683.00	−1.00066	−0.500328	+	0.865836i	$0.666787\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	978.000	0.353704	0.176852	−	0.984237i	$-0.443409\pi$
$197$	978.000	0.353704	0.176852	+	0.984237i	$0.443409\pi$
$198$	0	0
$199$	−2450.00	−0.872743	−0.436372	−	0.899767i	$-0.643737\pi$
$199$	−2450.00	−0.872743	−0.436372	+	0.899767i	$0.643737\pi$
$200$	0	0
$201$	−1035.00	−0.363200
$202$	0	0
$203$	238.000	0.0822873
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−160.000	−0.0537235
$208$	0	0
$209$	1287.00	0.425950
$210$	0	0
$211$	−3543.00	−1.15597	−0.577986	−	0.816047i	$-0.696161\pi$
$211$	−3543.00	−1.15597	−0.577986	+	0.816047i	$0.696161\pi$
$212$	0	0
$213$	3510.00	1.12911
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−2044.00	−0.639427
$218$	0	0
$219$	5925.00	1.82819
$220$	0	0
$221$	−5842.00	−1.77817
$222$	0	0
$223$	5310.00	1.59455	0.797273	−	0.603618i	$-0.206275\pi$
$223$	5310.00	1.59455	0.797273	+	0.603618i	$0.206275\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	2876.00	0.840911	0.420456	−	0.907313i	$-0.361870\pi$
$227$	2876.00	0.840911	0.420456	+	0.907313i	$0.361870\pi$
$228$	0	0
$229$	−2150.00	−0.620419	−0.310210	−	0.950668i	$-0.600399\pi$
$229$	−2150.00	−0.620419	−0.310210	+	0.950668i	$0.600399\pi$
$230$	0	0
$231$	385.000	0.109659
$232$	0	0
$233$	4086.00	1.14885	0.574427	−	0.818556i	$-0.305225\pi$
$233$	4086.00	1.14885	0.574427	+	0.818556i	$0.305225\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	270.000	0.0740016
$238$	0	0
$239$	52.0000	0.0140736	0.00703682	−	0.999975i	$-0.497760\pi$
$239$	52.0000	0.0140736	0.00703682	+	0.999975i	$0.497760\pi$
$240$	0	0
$241$	−5285.00	−1.41260	−0.706300	−	0.707912i	$-0.749637\pi$
$241$	−5285.00	−1.41260	−0.706300	+	0.707912i	$0.749637\pi$
$242$	0	0
$243$	560.000	0.147835
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−5382.00	−1.38643
$248$	0	0
$249$	−1545.00	−0.393214
$250$	0	0
$251$	−2661.00	−0.669167	−0.334583	−	0.942366i	$-0.608596\pi$
$251$	−2661.00	−0.669167	−0.334583	+	0.942366i	$0.608596\pi$
$252$	0	0
$253$	880.000	0.218676
$254$	0	0
$255$	0	0
$256$	0	0
$257$	6786.00	1.64708	0.823539	−	0.567260i	$-0.191996\pi$
$257$	6786.00	1.64708	0.823539	+	0.567260i	$0.191996\pi$
$258$	0	0
$259$	−2632.00	−0.631446
$260$	0	0
$261$	−68.0000	−0.0161268
$262$	0	0
$263$	−2162.00	−0.506900	−0.253450	−	0.967349i	$-0.581565\pi$
$263$	−2162.00	−0.506900	−0.253450	+	0.967349i	$0.581565\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−1695.00	−0.388511
$268$	0	0
$269$	−4486.00	−1.01679	−0.508395	−	0.861124i	$-0.669761\pi$
$269$	−4486.00	−1.01679	−0.508395	+	0.861124i	$0.669761\pi$
$270$	0	0
$271$	7810.00	1.75064	0.875321	−	0.483543i	$-0.160650\pi$
$271$	7810.00	1.75064	0.875321	+	0.483543i	$0.160650\pi$
$272$	0	0
$273$	−1610.00	−0.356929
$274$	0	0
$275$	0	0
$276$	0	0
$277$	8026.00	1.74092	0.870461	−	0.492237i	$-0.163821\pi$
$277$	8026.00	1.74092	0.870461	+	0.492237i	$0.163821\pi$
$278$	0	0
$279$	584.000	0.125316
$280$	0	0
$281$	−3586.00	−0.761291	−0.380646	−	0.924721i	$-0.624298\pi$
$281$	−3586.00	−0.761291	−0.380646	+	0.924721i	$0.624298\pi$
$282$	0	0
$283$	1747.00	0.366955	0.183478	−	0.983024i	$-0.441264\pi$
$283$	1747.00	0.366955	0.183478	+	0.983024i	$0.441264\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	3549.00	0.729933
$288$	0	0
$289$	11216.0	2.28292
$290$	0	0
$291$	910.000	0.183317
$292$	0	0
$293$	506.000	0.100890	0.0504451	−	0.998727i	$-0.483936\pi$
$293$	506.000	0.100890	0.0504451	+	0.998727i	$0.483936\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1595.00	−0.311620
$298$	0	0
$299$	−3680.00	−0.711772
$300$	0	0
$301$	224.000	0.0428942
$302$	0	0
$303$	5760.00	1.09209
$304$	0	0
$305$	0	0
$306$	0	0
$307$	2661.00	0.494695	0.247347	−	0.968927i	$-0.420441\pi$
$307$	2661.00	0.494695	0.247347	+	0.968927i	$0.420441\pi$
$308$	0	0
$309$	7940.00	1.46178
$310$	0	0
$311$	5838.00	1.06445	0.532223	−	0.846604i	$-0.321357\pi$
$311$	5838.00	1.06445	0.532223	+	0.846604i	$0.321357\pi$
$312$	0	0
$313$	−1818.00	−0.328305	−0.164152	−	0.986435i	$-0.552489\pi$
$313$	−1818.00	−0.328305	−0.164152	+	0.986435i	$0.552489\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−6780.00	−1.20127	−0.600635	−	0.799523i	$-0.705086\pi$
$317$	−6780.00	−1.20127	−0.600635	+	0.799523i	$0.705086\pi$
$318$	0	0
$319$	374.000	0.0656426
$320$	0	0
$321$	−8305.00	−1.44405
$322$	0	0
$323$	14859.0	2.55968
$324$	0	0
$325$	0	0
$326$	0	0
$327$	350.000	0.0591897
$328$	0	0
$329$	−938.000	−0.157184
$330$	0	0
$331$	−929.000	−0.154267	−0.0771336	−	0.997021i	$-0.524577\pi$
$331$	−929.000	−0.154267	−0.0771336	+	0.997021i	$0.524577\pi$
$332$	0	0
$333$	752.000	0.123752
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−8829.00	−1.42714	−0.713570	−	0.700584i	$-0.752923\pi$
$337$	−8829.00	−1.42714	−0.713570	+	0.700584i	$0.752923\pi$
$338$	0	0
$339$	9195.00	1.47317
$340$	0	0
$341$	−3212.00	−0.510087
$342$	0	0
$343$	343.000	0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−5469.00	−0.846084	−0.423042	−	0.906110i	$-0.639038\pi$
$347$	−5469.00	−0.846084	−0.423042	+	0.906110i	$0.639038\pi$
$348$	0	0
$349$	−4840.00	−0.742347	−0.371174	−	0.928563i	$-0.621045\pi$
$349$	−4840.00	−0.742347	−0.371174	+	0.928563i	$0.621045\pi$
$350$	0	0
$351$	6670.00	1.01430
$352$	0	0
$353$	−7058.00	−1.06419	−0.532096	−	0.846684i	$-0.678595\pi$
$353$	−7058.00	−1.06419	−0.532096	+	0.846684i	$0.678595\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	4445.00	0.658976
$358$	0	0
$359$	−7470.00	−1.09819	−0.549097	−	0.835759i	$-0.685028\pi$
$359$	−7470.00	−1.09819	−0.549097	+	0.835759i	$0.685028\pi$
$360$	0	0
$361$	6830.00	0.995772
$362$	0	0
$363$	−6050.00	−0.874773
$364$	0	0
$365$	0	0
$366$	0	0
$367$	88.0000	0.0125165	0.00625826	−	0.999980i	$-0.498008\pi$
$367$	88.0000	0.0125165	0.00625826	+	0.999980i	$0.498008\pi$
$368$	0	0
$369$	−1014.00	−0.143053
$370$	0	0
$371$	4284.00	0.599499
$372$	0	0
$373$	−7092.00	−0.984477	−0.492238	−	0.870460i	$-0.663821\pi$
$373$	−7092.00	−0.984477	−0.492238	+	0.870460i	$0.663821\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−1564.00	−0.213661
$378$	0	0
$379$	8689.00	1.17764	0.588818	−	0.808266i	$-0.299594\pi$
$379$	8689.00	1.17764	0.588818	+	0.808266i	$0.299594\pi$
$380$	0	0
$381$	530.000	0.0712670
$382$	0	0
$383$	6162.00	0.822098	0.411049	−	0.911613i	$-0.365163\pi$
$383$	6162.00	0.822098	0.411049	+	0.911613i	$0.365163\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−64.0000	−0.00840647
$388$	0	0
$389$	2472.00	0.322199	0.161099	−	0.986938i	$-0.448496\pi$
$389$	2472.00	0.322199	0.161099	+	0.986938i	$0.448496\pi$
$390$	0	0
$391$	10160.0	1.31410
$392$	0	0
$393$	−5760.00	−0.739322
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−3662.00	−0.462948	−0.231474	−	0.972841i	$-0.574355\pi$
$397$	−3662.00	−0.462948	−0.231474	+	0.972841i	$0.574355\pi$
$398$	0	0
$399$	4095.00	0.513801
$400$	0	0
$401$	−7987.00	−0.994643	−0.497321	−	0.867566i	$-0.665683\pi$
$401$	−7987.00	−0.994643	−0.497321	+	0.867566i	$0.665683\pi$
$402$	0	0
$403$	13432.0	1.66029
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−4136.00	−0.503720
$408$	0	0
$409$	−9301.00	−1.12446	−0.562231	−	0.826980i	$-0.690057\pi$
$409$	−9301.00	−1.12446	−0.562231	+	0.826980i	$0.690057\pi$
$410$	0	0
$411$	7785.00	0.934321
$412$	0	0
$413$	5460.00	0.650530
$414$	0	0
$415$	0	0
$416$	0	0
$417$	3665.00	0.430398
$418$	0	0
$419$	4721.00	0.550444	0.275222	−	0.961381i	$-0.411249\pi$
$419$	4721.00	0.550444	0.275222	+	0.961381i	$0.411249\pi$
$420$	0	0
$421$	−5276.00	−0.610776	−0.305388	−	0.952228i	$-0.598786\pi$
$421$	−5276.00	−0.610776	−0.305388	+	0.952228i	$0.598786\pi$
$422$	0	0
$423$	268.000	0.0308052
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−2982.00	−0.337960
$428$	0	0
$429$	−2530.00	−0.284731
$430$	0	0
$431$	−4868.00	−0.544045	−0.272022	−	0.962291i	$-0.587692\pi$
$431$	−4868.00	−0.544045	−0.272022	+	0.962291i	$0.587692\pi$
$432$	0	0
$433$	−1825.00	−0.202549	−0.101275	−	0.994858i	$-0.532292\pi$
$433$	−1825.00	−0.202549	−0.101275	+	0.994858i	$0.532292\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	9360.00	1.02460
$438$	0	0
$439$	−6164.00	−0.670140	−0.335070	−	0.942193i	$-0.608760\pi$
$439$	−6164.00	−0.670140	−0.335070	+	0.942193i	$0.608760\pi$
$440$	0	0
$441$	−98.0000	−0.0105820
$442$	0	0
$443$	−12243.0	−1.31305	−0.656527	−	0.754303i	$-0.727975\pi$
$443$	−12243.0	−1.31305	−0.656527	+	0.754303i	$0.727975\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	220.000	0.0232788
$448$	0	0
$449$	−3959.00	−0.416118	−0.208059	−	0.978116i	$-0.566715\pi$
$449$	−3959.00	−0.416118	−0.208059	+	0.978116i	$0.566715\pi$
$450$	0	0
$451$	5577.00	0.582285
$452$	0	0
$453$	11800.0	1.22387
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−10239.0	−1.04805	−0.524026	−	0.851702i	$-0.675571\pi$
$457$	−10239.0	−1.04805	−0.524026	+	0.851702i	$0.675571\pi$
$458$	0	0
$459$	−18415.0	−1.87263
$460$	0	0
$461$	−9630.00	−0.972915	−0.486457	−	0.873704i	$-0.661711\pi$
$461$	−9630.00	−0.972915	−0.486457	+	0.873704i	$0.661711\pi$
$462$	0	0
$463$	−10312.0	−1.03507	−0.517537	−	0.855661i	$-0.673151\pi$
$463$	−10312.0	−1.03507	−0.517537	+	0.855661i	$0.673151\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−2604.00	−0.258027	−0.129014	−	0.991643i	$-0.541181\pi$
$467$	−2604.00	−0.258027	−0.129014	+	0.991643i	$0.541181\pi$
$468$	0	0
$469$	−1449.00	−0.142662
$470$	0	0
$471$	11620.0	1.13678
$472$	0	0
$473$	352.000	0.0342177
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1224.00	−0.117491
$478$	0	0
$479$	4434.00	0.422953	0.211477	−	0.977383i	$-0.432173\pi$
$479$	4434.00	0.422953	0.211477	+	0.977383i	$0.432173\pi$
$480$	0	0
$481$	17296.0	1.63956
$482$	0	0
$483$	2800.00	0.263777
$484$	0	0
$485$	0	0
$486$	0	0
$487$	14422.0	1.34194	0.670968	−	0.741486i	$-0.265879\pi$
$487$	14422.0	1.34194	0.670968	+	0.741486i	$0.265879\pi$
$488$	0	0
$489$	11305.0	1.04546
$490$	0	0
$491$	18908.0	1.73789	0.868947	−	0.494905i	$-0.164797\pi$
$491$	18908.0	1.73789	0.868947	+	0.494905i	$0.164797\pi$
$492$	0	0
$493$	4318.00	0.394468
$494$	0	0
$495$	0	0
$496$	0	0
$497$	4914.00	0.443507
$498$	0	0
$499$	11164.0	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$499$	11164.0	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$500$	0	0
$501$	−3860.00	−0.344216
$502$	0	0
$503$	−21190.0	−1.87836	−0.939180	−	0.343424i	$-0.888413\pi$
$503$	−21190.0	−1.87836	−0.939180	+	0.343424i	$0.888413\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−405.000	−0.0354767
$508$	0	0
$509$	11706.0	1.01937	0.509685	−	0.860361i	$-0.329762\pi$
$509$	11706.0	1.01937	0.509685	+	0.860361i	$0.329762\pi$
$510$	0	0
$511$	8295.00	0.718100
$512$	0	0
$513$	−16965.0	−1.46008
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−1474.00	−0.125390
$518$	0	0
$519$	130.000	0.0109949
$520$	0	0
$521$	−2037.00	−0.171291	−0.0856455	−	0.996326i	$-0.527295\pi$
$521$	−2037.00	−0.171291	−0.0856455	+	0.996326i	$0.527295\pi$
$522$	0	0
$523$	17941.0	1.50001	0.750005	−	0.661432i	$-0.230051\pi$
$523$	17941.0	1.50001	0.750005	+	0.661432i	$0.230051\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−37084.0	−3.06528
$528$	0	0
$529$	−5767.00	−0.473987
$530$	0	0
$531$	−1560.00	−0.127492
$532$	0	0
$533$	−23322.0	−1.89529
$534$	0	0
$535$	0	0
$536$	0	0
$537$	11695.0	0.939807
$538$	0	0
$539$	539.000	0.0430730
$540$	0	0
$541$	−946.000	−0.0751788	−0.0375894	−	0.999293i	$-0.511968\pi$
$541$	−946.000	−0.0751788	−0.0375894	+	0.999293i	$0.511968\pi$
$542$	0	0
$543$	−11350.0	−0.897008
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−1237.00	−0.0966916	−0.0483458	−	0.998831i	$-0.515395\pi$
$547$	−1237.00	−0.0966916	−0.0483458	+	0.998831i	$0.515395\pi$
$548$	0	0
$549$	852.000	0.0662340
$550$	0	0
$551$	3978.00	0.307565
$552$	0	0
$553$	378.000	0.0290673
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−24108.0	−1.83391	−0.916956	−	0.398989i	$-0.869361\pi$
$557$	−24108.0	−1.83391	−0.916956	+	0.398989i	$0.869361\pi$
$558$	0	0
$559$	−1472.00	−0.111376
$560$	0	0
$561$	6985.00	0.525681
$562$	0	0
$563$	23564.0	1.76395	0.881975	−	0.471296i	$-0.156214\pi$
$563$	23564.0	1.76395	0.881975	+	0.471296i	$0.156214\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−4697.00	−0.347893
$568$	0	0
$569$	−2451.00	−0.180582	−0.0902911	−	0.995915i	$-0.528780\pi$
$569$	−2451.00	−0.180582	−0.0902911	+	0.995915i	$0.528780\pi$
$570$	0	0
$571$	−9292.00	−0.681012	−0.340506	−	0.940242i	$-0.610598\pi$
$571$	−9292.00	−0.681012	−0.340506	+	0.940242i	$0.610598\pi$
$572$	0	0
$573$	−21030.0	−1.53323
$574$	0	0
$575$	0	0
$576$	0	0
$577$	17573.0	1.26789	0.633946	−	0.773377i	$-0.281434\pi$
$577$	17573.0	1.26789	0.633946	+	0.773377i	$0.281434\pi$
$578$	0	0
$579$	−13415.0	−0.962881
$580$	0	0
$581$	−2163.00	−0.154452
$582$	0	0
$583$	6732.00	0.478235
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−1837.00	−0.129167	−0.0645836	−	0.997912i	$-0.520572\pi$
$587$	−1837.00	−0.129167	−0.0645836	+	0.997912i	$0.520572\pi$
$588$	0	0
$589$	−34164.0	−2.38999
$590$	0	0
$591$	4890.00	0.340351
$592$	0	0
$593$	−11887.0	−0.823171	−0.411586	−	0.911371i	$-0.635025\pi$
$593$	−11887.0	−0.823171	−0.411586	+	0.911371i	$0.635025\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−12250.0	−0.839798
$598$	0	0
$599$	−14216.0	−0.969700	−0.484850	−	0.874597i	$-0.661126\pi$
$599$	−14216.0	−0.969700	−0.484850	+	0.874597i	$0.661126\pi$
$600$	0	0
$601$	−25299.0	−1.71708	−0.858542	−	0.512743i	$-0.828629\pi$
$601$	−25299.0	−1.71708	−0.858542	+	0.512743i	$0.828629\pi$
$602$	0	0
$603$	414.000	0.0279592
$604$	0	0
$605$	0	0
$606$	0	0
$607$	10556.0	0.705856	0.352928	−	0.935650i	$-0.385186\pi$
$607$	10556.0	0.705856	0.352928	+	0.935650i	$0.385186\pi$
$608$	0	0
$609$	1190.00	0.0791810
$610$	0	0
$611$	6164.00	0.408132
$612$	0	0
$613$	−24086.0	−1.58699	−0.793495	−	0.608577i	$-0.791741\pi$
$613$	−24086.0	−1.58699	−0.793495	+	0.608577i	$0.791741\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−4834.00	−0.315412	−0.157706	−	0.987486i	$-0.550410\pi$
$617$	−4834.00	−0.315412	−0.157706	+	0.987486i	$0.550410\pi$
$618$	0	0
$619$	−25628.0	−1.66410	−0.832049	−	0.554703i	$-0.812832\pi$
$619$	−25628.0	−1.66410	−0.832049	+	0.554703i	$0.812832\pi$
$620$	0	0
$621$	−11600.0	−0.749584
$622$	0	0
$623$	−2373.00	−0.152604
$624$	0	0
$625$	0	0
$626$	0	0
$627$	6435.00	0.409871
$628$	0	0
$629$	−47752.0	−3.02702
$630$	0	0
$631$	−6976.00	−0.440111	−0.220056	−	0.975487i	$-0.570624\pi$
$631$	−6976.00	−0.440111	−0.220056	+	0.975487i	$0.570624\pi$
$632$	0	0
$633$	−17715.0	−1.11233
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−2254.00	−0.140199
$638$	0	0
$639$	−1404.00	−0.0869192
$640$	0	0
$641$	14690.0	0.905180	0.452590	−	0.891719i	$-0.350500\pi$
$641$	14690.0	0.905180	0.452590	+	0.891719i	$0.350500\pi$
$642$	0	0
$643$	−1528.00	−0.0937145	−0.0468573	−	0.998902i	$-0.514921\pi$
$643$	−1528.00	−0.0937145	−0.0468573	+	0.998902i	$0.514921\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	24984.0	1.51812	0.759059	−	0.651022i	$-0.225659\pi$
$647$	24984.0	1.51812	0.759059	+	0.651022i	$0.225659\pi$
$648$	0	0
$649$	8580.00	0.518944
$650$	0	0
$651$	−10220.0	−0.615289
$652$	0	0
$653$	11188.0	0.670475	0.335238	−	0.942134i	$-0.391183\pi$
$653$	11188.0	0.670475	0.335238	+	0.942134i	$0.391183\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−2370.00	−0.140734
$658$	0	0
$659$	21497.0	1.27072	0.635360	−	0.772216i	$-0.280852\pi$
$659$	21497.0	1.27072	0.635360	+	0.772216i	$0.280852\pi$
$660$	0	0
$661$	−1258.00	−0.0740250	−0.0370125	−	0.999315i	$-0.511784\pi$
$661$	−1258.00	−0.0740250	−0.0370125	+	0.999315i	$0.511784\pi$
$662$	0	0
$663$	−29210.0	−1.71104
$664$	0	0
$665$	0	0
$666$	0	0
$667$	2720.00	0.157899
$668$	0	0
$669$	26550.0	1.53435
$670$	0	0
$671$	−4686.00	−0.269599
$672$	0	0
$673$	22562.0	1.29228	0.646138	−	0.763221i	$-0.276383\pi$
$673$	22562.0	1.29228	0.646138	+	0.763221i	$0.276383\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−21888.0	−1.24258	−0.621288	−	0.783582i	$-0.713390\pi$
$677$	−21888.0	−1.24258	−0.621288	+	0.783582i	$0.713390\pi$
$678$	0	0
$679$	1274.00	0.0720054
$680$	0	0
$681$	14380.0	0.809167
$682$	0	0
$683$	−7453.00	−0.417542	−0.208771	−	0.977965i	$-0.566946\pi$
$683$	−7453.00	−0.417542	−0.208771	+	0.977965i	$0.566946\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−10750.0	−0.596999
$688$	0	0
$689$	−28152.0	−1.55661
$690$	0	0
$691$	−4743.00	−0.261118	−0.130559	−	0.991441i	$-0.541677\pi$
$691$	−4743.00	−0.261118	−0.130559	+	0.991441i	$0.541677\pi$
$692$	0	0
$693$	−154.000	−0.00844152
$694$	0	0
$695$	0	0
$696$	0	0
$697$	64389.0	3.49915
$698$	0	0
$699$	20430.0	1.10548
$700$	0	0
$701$	19488.0	1.05000	0.525001	−	0.851102i	$-0.324065\pi$
$701$	19488.0	1.05000	0.525001	+	0.851102i	$0.324065\pi$
$702$	0	0
$703$	−43992.0	−2.36016
$704$	0	0
$705$	0	0
$706$	0	0
$707$	8064.00	0.428965
$708$	0	0
$709$	980.000	0.0519107	0.0259553	−	0.999663i	$-0.491737\pi$
$709$	980.000	0.0519107	0.0259553	+	0.999663i	$0.491737\pi$
$710$	0	0
$711$	−108.000	−0.00569665
$712$	0	0
$713$	−23360.0	−1.22698
$714$	0	0
$715$	0	0
$716$	0	0
$717$	260.000	0.0135424
$718$	0	0
$719$	−14448.0	−0.749401	−0.374701	−	0.927146i	$-0.622255\pi$
$719$	−14448.0	−0.749401	−0.374701	+	0.927146i	$0.622255\pi$
$720$	0	0
$721$	11116.0	0.574177
$722$	0	0
$723$	−26425.0	−1.35928
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−25922.0	−1.32241	−0.661206	−	0.750204i	$-0.729955\pi$
$727$	−25922.0	−1.32241	−0.661206	+	0.750204i	$0.729955\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	0	0
$731$	4064.00	0.205626
$732$	0	0
$733$	−31768.0	−1.60079	−0.800394	−	0.599474i	$-0.795376\pi$
$733$	−31768.0	−1.60079	−0.800394	+	0.599474i	$0.795376\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−2277.00	−0.113805
$738$	0	0
$739$	−19972.0	−0.994157	−0.497078	−	0.867706i	$-0.665594\pi$
$739$	−19972.0	−0.994157	−0.497078	+	0.867706i	$0.665594\pi$
$740$	0	0
$741$	−26910.0	−1.33409
$742$	0	0
$743$	18664.0	0.921556	0.460778	−	0.887516i	$-0.347571\pi$
$743$	18664.0	0.921556	0.460778	+	0.887516i	$0.347571\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	618.000	0.0302697
$748$	0	0
$749$	−11627.0	−0.567211
$750$	0	0
$751$	−358.000	−0.0173949	−0.00869747	−	0.999962i	$-0.502769\pi$
$751$	−358.000	−0.0173949	−0.00869747	+	0.999962i	$0.502769\pi$
$752$	0	0
$753$	−13305.0	−0.643906
$754$	0	0
$755$	0	0
$756$	0	0
$757$	774.000	0.0371618	0.0185809	−	0.999827i	$-0.494085\pi$
$757$	774.000	0.0371618	0.0185809	+	0.999827i	$0.494085\pi$
$758$	0	0
$759$	4400.00	0.210421
$760$	0	0
$761$	−2885.00	−0.137426	−0.0687130	−	0.997636i	$-0.521889\pi$
$761$	−2885.00	−0.137426	−0.0687130	+	0.997636i	$0.521889\pi$
$762$	0	0
$763$	490.000	0.0232493
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−35880.0	−1.68912
$768$	0	0
$769$	−6173.00	−0.289472	−0.144736	−	0.989470i	$-0.546233\pi$
$769$	−6173.00	−0.289472	−0.144736	+	0.989470i	$0.546233\pi$
$770$	0	0
$771$	33930.0	1.58490
$772$	0	0
$773$	17780.0	0.827299	0.413650	−	0.910436i	$-0.364254\pi$
$773$	17780.0	0.827299	0.413650	+	0.910436i	$0.364254\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−13160.0	−0.607609
$778$	0	0
$779$	59319.0	2.72827
$780$	0	0
$781$	7722.00	0.353796
$782$	0	0
$783$	−4930.00	−0.225011
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−17460.0	−0.790828	−0.395414	−	0.918503i	$-0.629399\pi$
$787$	−17460.0	−0.790828	−0.395414	+	0.918503i	$0.629399\pi$
$788$	0	0
$789$	−10810.0	−0.487765
$790$	0	0
$791$	12873.0	0.578649
$792$	0	0
$793$	19596.0	0.877521
$794$	0	0
$795$	0	0
$796$	0	0
$797$	26530.0	1.17910	0.589549	−	0.807733i	$-0.299306\pi$
$797$	26530.0	1.17910	0.589549	+	0.807733i	$0.299306\pi$
$798$	0	0
$799$	−17018.0	−0.753509
$800$	0	0
$801$	678.000	0.0299076
$802$	0	0
$803$	13035.0	0.572846
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−22430.0	−0.978406
$808$	0	0
$809$	12854.0	0.558619	0.279309	−	0.960201i	$-0.409894\pi$
$809$	12854.0	0.558619	0.279309	+	0.960201i	$0.409894\pi$
$810$	0	0
$811$	−42324.0	−1.83255	−0.916274	−	0.400552i	$-0.868818\pi$
$811$	−42324.0	−1.83255	−0.916274	+	0.400552i	$0.868818\pi$
$812$	0	0
$813$	39050.0	1.68456
$814$	0	0
$815$	0	0
$816$	0	0
$817$	3744.00	0.160326
$818$	0	0
$819$	644.000	0.0274764
$820$	0	0
$821$	−3240.00	−0.137731	−0.0688653	−	0.997626i	$-0.521938\pi$
$821$	−3240.00	−0.137731	−0.0688653	+	0.997626i	$0.521938\pi$
$822$	0	0
$823$	9618.00	0.407366	0.203683	−	0.979037i	$-0.434709\pi$
$823$	9618.00	0.407366	0.203683	+	0.979037i	$0.434709\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	4721.00	0.198507	0.0992535	−	0.995062i	$-0.468355\pi$
$827$	4721.00	0.198507	0.0992535	+	0.995062i	$0.468355\pi$
$828$	0	0
$829$	−26996.0	−1.13101	−0.565507	−	0.824744i	$-0.691319\pi$
$829$	−26996.0	−1.13101	−0.565507	+	0.824744i	$0.691319\pi$
$830$	0	0
$831$	40130.0	1.67520
$832$	0	0
$833$	6223.00	0.258841
$834$	0	0
$835$	0	0
$836$	0	0
$837$	42340.0	1.74849
$838$	0	0
$839$	−12262.0	−0.504566	−0.252283	−	0.967653i	$-0.581181\pi$
$839$	−12262.0	−0.504566	−0.252283	+	0.967653i	$0.581181\pi$
$840$	0	0
$841$	−23233.0	−0.952602
$842$	0	0
$843$	−17930.0	−0.732553
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−8470.00	−0.343604
$848$	0	0
$849$	8735.00	0.353103
$850$	0	0
$851$	−30080.0	−1.21167
$852$	0	0
$853$	22982.0	0.922496	0.461248	−	0.887271i	$-0.347402\pi$
$853$	22982.0	0.922496	0.461248	+	0.887271i	$0.347402\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−22381.0	−0.892089	−0.446045	−	0.895011i	$-0.647168\pi$
$857$	−22381.0	−0.892089	−0.446045	+	0.895011i	$0.647168\pi$
$858$	0	0
$859$	−18555.0	−0.737006	−0.368503	−	0.929626i	$-0.620130\pi$
$859$	−18555.0	−0.737006	−0.368503	+	0.929626i	$0.620130\pi$
$860$	0	0
$861$	17745.0	0.702379
$862$	0	0
$863$	6452.00	0.254494	0.127247	−	0.991871i	$-0.459386\pi$
$863$	6452.00	0.254494	0.127247	+	0.991871i	$0.459386\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	56080.0	2.19674
$868$	0	0
$869$	594.000	0.0231877
$870$	0	0
$871$	9522.00	0.370426
$872$	0	0
$873$	−364.000	−0.0141117
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−3632.00	−0.139845	−0.0699224	−	0.997552i	$-0.522275\pi$
$877$	−3632.00	−0.139845	−0.0699224	+	0.997552i	$0.522275\pi$
$878$	0	0
$879$	2530.00	0.0970817
$880$	0	0
$881$	−1542.00	−0.0589686	−0.0294843	−	0.999565i	$-0.509386\pi$
$881$	−1542.00	−0.0589686	−0.0294843	+	0.999565i	$0.509386\pi$
$882$	0	0
$883$	−38145.0	−1.45377	−0.726886	−	0.686758i	$-0.759033\pi$
$883$	−38145.0	−1.45377	−0.726886	+	0.686758i	$0.759033\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−23898.0	−0.904641	−0.452320	−	0.891856i	$-0.649404\pi$
$887$	−23898.0	−0.904641	−0.452320	+	0.891856i	$0.649404\pi$
$888$	0	0
$889$	742.000	0.0279931
$890$	0	0
$891$	−7381.00	−0.277523
$892$	0	0
$893$	−15678.0	−0.587508
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−18400.0	−0.684903
$898$	0	0
$899$	−9928.00	−0.368317
$900$	0	0
$901$	77724.0	2.87388
$902$	0	0
$903$	1120.00	0.0412749
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−43324.0	−1.58605	−0.793026	−	0.609187i	$-0.791496\pi$
$907$	−43324.0	−1.58605	−0.793026	+	0.609187i	$0.791496\pi$
$908$	0	0
$909$	−2304.00	−0.0840691
$910$	0	0
$911$	−21756.0	−0.791228	−0.395614	−	0.918417i	$-0.629468\pi$
$911$	−21756.0	−0.791228	−0.395614	+	0.918417i	$0.629468\pi$
$912$	0	0
$913$	−3399.00	−0.123210
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−8064.00	−0.290400
$918$	0	0
$919$	−19290.0	−0.692403	−0.346202	−	0.938160i	$-0.612529\pi$
$919$	−19290.0	−0.692403	−0.346202	+	0.938160i	$0.612529\pi$
$920$	0	0
$921$	13305.0	0.476020
$922$	0	0
$923$	−32292.0	−1.15158
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−3176.00	−0.112528
$928$	0	0
$929$	34990.0	1.23572	0.617860	−	0.786288i	$-0.288000\pi$
$929$	34990.0	1.23572	0.617860	+	0.786288i	$0.288000\pi$
$930$	0	0
$931$	5733.00	0.201817
$932$	0	0
$933$	29190.0	1.02426
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−14415.0	−0.502580	−0.251290	−	0.967912i	$-0.580855\pi$
$937$	−14415.0	−0.502580	−0.251290	+	0.967912i	$0.580855\pi$
$938$	0	0
$939$	−9090.00	−0.315912
$940$	0	0
$941$	9336.00	0.323427	0.161714	−	0.986838i	$-0.448298\pi$
$941$	9336.00	0.323427	0.161714	+	0.986838i	$0.448298\pi$
$942$	0	0
$943$	40560.0	1.40065
$944$	0	0
$945$	0	0
$946$	0	0
$947$	3636.00	0.124767	0.0623834	−	0.998052i	$-0.480130\pi$
$947$	3636.00	0.124767	0.0623834	+	0.998052i	$0.480130\pi$
$948$	0	0
$949$	−54510.0	−1.86456
$950$	0	0
$951$	−33900.0	−1.15592
$952$	0	0
$953$	−5247.00	−0.178349	−0.0891747	−	0.996016i	$-0.528423\pi$
$953$	−5247.00	−0.178349	−0.0891747	+	0.996016i	$0.528423\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	1870.00	0.0631646
$958$	0	0
$959$	10899.0	0.366994
$960$	0	0
$961$	55473.0	1.86207
$962$	0	0
$963$	3322.00	0.111163
$964$	0	0
$965$	0	0
$966$	0	0
$967$	42182.0	1.40277	0.701387	−	0.712781i	$-0.252565\pi$
$967$	42182.0	1.40277	0.701387	+	0.712781i	$0.252565\pi$
$968$	0	0
$969$	74295.0	2.46305
$970$	0	0
$971$	−23227.0	−0.767652	−0.383826	−	0.923405i	$-0.625394\pi$
$971$	−23227.0	−0.767652	−0.383826	+	0.923405i	$0.625394\pi$
$972$	0	0
$973$	5131.00	0.169057
$974$	0	0
$975$	0	0
$976$	0	0
$977$	11821.0	0.387090	0.193545	−	0.981091i	$-0.438001\pi$
$977$	11821.0	0.387090	0.193545	+	0.981091i	$0.438001\pi$
$978$	0	0
$979$	−3729.00	−0.121736
$980$	0	0
$981$	−140.000	−0.00455643
$982$	0	0
$983$	3420.00	0.110968	0.0554838	−	0.998460i	$-0.482330\pi$
$983$	3420.00	0.110968	0.0554838	+	0.998460i	$0.482330\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−4690.00	−0.151251
$988$	0	0
$989$	2560.00	0.0823087
$990$	0	0
$991$	−4636.00	−0.148605	−0.0743024	−	0.997236i	$-0.523673\pi$
$991$	−4636.00	−0.148605	−0.0743024	+	0.997236i	$0.523673\pi$
$992$	0	0
$993$	−4645.00	−0.148444
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−14722.0	−0.467653	−0.233827	−	0.972278i	$-0.575125\pi$
$997$	−14722.0	−0.467653	−0.233827	+	0.972278i	$0.575125\pi$
$998$	0	0
$999$	54520.0	1.72666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.4.a.h.1.1	yes	1
5.2	odd	4		1400.4.g.d.449.1		2
5.3	odd	4		1400.4.g.d.449.2		2
5.4	even	2		1400.4.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.4.a.c.1.1	✓	1	5.4	even	2
1400.4.a.h.1.1	yes	1	1.1	even	1	trivial
1400.4.g.d.449.1		2	5.2	odd	4
1400.4.g.d.449.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1400.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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