LMFDB - Embedded newform 140.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,4,Mod(1,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, 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("140.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	140.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:	$8.26026740080$
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	$\chi$	$=$	140.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{3} +5.00000 q^{5} -7.00000 q^{7} -11.0000 q^{9} +O(q^{10})$

$q-4.00000 q^{3} +5.00000 q^{5} -7.00000 q^{7} -11.0000 q^{9} +68.0000 q^{11} +22.0000 q^{13} -20.0000 q^{15} -30.0000 q^{17} +108.000 q^{19} +28.0000 q^{21} +184.000 q^{23} +25.0000 q^{25} +152.000 q^{27} +166.000 q^{29} -32.0000 q^{31} -272.000 q^{33} -35.0000 q^{35} -370.000 q^{37} -88.0000 q^{39} +154.000 q^{41} +212.000 q^{43} -55.0000 q^{45} -512.000 q^{47} +49.0000 q^{49} +120.000 q^{51} -98.0000 q^{53} +340.000 q^{55} -432.000 q^{57} -860.000 q^{59} +390.000 q^{61} +77.0000 q^{63} +110.000 q^{65} +60.0000 q^{67} -736.000 q^{69} +840.000 q^{71} -630.000 q^{73} -100.000 q^{75} -476.000 q^{77} +1312.00 q^{79} -311.000 q^{81} -436.000 q^{83} -150.000 q^{85} -664.000 q^{87} -598.000 q^{89} -154.000 q^{91} +128.000 q^{93} +540.000 q^{95} +914.000 q^{97} -748.000 q^{99} +O(q^{100})$

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
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	0	0
$9$	−11.0000	−0.407407
$10$	0	0
$11$	68.0000	1.86389	0.931944	−	0.362602i	$-0.118111\pi$
$11$	68.0000	1.86389	0.931944	+	0.362602i	$0.118111\pi$
$12$	0	0
$13$	22.0000	0.469362	0.234681	−	0.972072i	$-0.424595\pi$
$13$	22.0000	0.469362	0.234681	+	0.972072i	$0.424595\pi$
$14$	0	0
$15$	−20.0000	−0.344265
$16$	0	0
$17$	−30.0000	−0.428004	−0.214002	−	0.976833i	$-0.568650\pi$
$17$	−30.0000	−0.428004	−0.214002	+	0.976833i	$0.568650\pi$
$18$	0	0
$19$	108.000	1.30405	0.652024	−	0.758199i	$-0.273920\pi$
$19$	108.000	1.30405	0.652024	+	0.758199i	$0.273920\pi$
$20$	0	0
$21$	28.0000	0.290957
$22$	0	0
$23$	184.000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	184.000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	152.000	1.08342
$28$	0	0
$29$	166.000	1.06295	0.531473	−	0.847075i	$-0.321639\pi$
$29$	166.000	1.06295	0.531473	+	0.847075i	$0.321639\pi$
$30$	0	0
$31$	−32.0000	−0.185399	−0.0926995	−	0.995694i	$-0.529550\pi$
$31$	−32.0000	−0.185399	−0.0926995	+	0.995694i	$0.529550\pi$
$32$	0	0
$33$	−272.000	−1.43482
$34$	0	0
$35$	−35.0000	−0.169031
$36$	0	0
$37$	−370.000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−370.000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0	0
$39$	−88.0000	−0.361315
$40$	0	0
$41$	154.000	0.586604	0.293302	−	0.956020i	$-0.405246\pi$
$41$	154.000	0.586604	0.293302	+	0.956020i	$0.405246\pi$
$42$	0	0
$43$	212.000	0.751853	0.375927	−	0.926649i	$-0.377324\pi$
$43$	212.000	0.751853	0.375927	+	0.926649i	$0.377324\pi$
$44$	0	0
$45$	−55.0000	−0.182198
$46$	0	0
$47$	−512.000	−1.58900	−0.794499	−	0.607266i	$-0.792266\pi$
$47$	−512.000	−1.58900	−0.794499	+	0.607266i	$0.792266\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	0	0
$51$	120.000	0.329478
$52$	0	0
$53$	−98.0000	−0.253987	−0.126994	−	0.991904i	$-0.540533\pi$
$53$	−98.0000	−0.253987	−0.126994	+	0.991904i	$0.540533\pi$
$54$	0	0
$55$	340.000	0.833556
$56$	0	0
$57$	−432.000	−1.00386
$58$	0	0
$59$	−860.000	−1.89767	−0.948834	−	0.315774i	$-0.897736\pi$
$59$	−860.000	−1.89767	−0.948834	+	0.315774i	$0.897736\pi$
$60$	0	0
$61$	390.000	0.818596	0.409298	−	0.912401i	$-0.365774\pi$
$61$	390.000	0.818596	0.409298	+	0.912401i	$0.365774\pi$
$62$	0	0
$63$	77.0000	0.153986
$64$	0	0
$65$	110.000	0.209905
$66$	0	0
$67$	60.0000	0.109405	0.0547027	−	0.998503i	$-0.482579\pi$
$67$	60.0000	0.109405	0.0547027	+	0.998503i	$0.482579\pi$
$68$	0	0
$69$	−736.000	−1.28412
$70$	0	0
$71$	840.000	1.40408	0.702040	−	0.712138i	$-0.252273\pi$
$71$	840.000	1.40408	0.702040	+	0.712138i	$0.252273\pi$
$72$	0	0
$73$	−630.000	−1.01008	−0.505041	−	0.863096i	$-0.668522\pi$
$73$	−630.000	−1.01008	−0.505041	+	0.863096i	$0.668522\pi$
$74$	0	0
$75$	−100.000	−0.153960
$76$	0	0
$77$	−476.000	−0.704484
$78$	0	0
$79$	1312.00	1.86850	0.934250	−	0.356618i	$-0.116070\pi$
$79$	1312.00	1.86850	0.934250	+	0.356618i	$0.116070\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	0	0
$83$	−436.000	−0.576593	−0.288296	−	0.957541i	$-0.593089\pi$
$83$	−436.000	−0.576593	−0.288296	+	0.957541i	$0.593089\pi$
$84$	0	0
$85$	−150.000	−0.191409
$86$	0	0
$87$	−664.000	−0.818256
$88$	0	0
$89$	−598.000	−0.712223	−0.356112	−	0.934443i	$-0.615898\pi$
$89$	−598.000	−0.712223	−0.356112	+	0.934443i	$0.615898\pi$
$90$	0	0
$91$	−154.000	−0.177402
$92$	0	0
$93$	128.000	0.142720
$94$	0	0
$95$	540.000	0.583188
$96$	0	0
$97$	914.000	0.956728	0.478364	−	0.878162i	$-0.341230\pi$
$97$	914.000	0.956728	0.478364	+	0.878162i	$0.341230\pi$
$98$	0	0
$99$	−748.000	−0.759362
$100$	0	0
$101$	318.000	0.313289	0.156644	−	0.987655i	$-0.449932\pi$
$101$	318.000	0.313289	0.156644	+	0.987655i	$0.449932\pi$
$102$	0	0
$103$	−280.000	−0.267857	−0.133928	−	0.990991i	$-0.542759\pi$
$103$	−280.000	−0.267857	−0.133928	+	0.990991i	$0.542759\pi$
$104$	0	0
$105$	140.000	0.130120
$106$	0	0
$107$	884.000	0.798687	0.399343	−	0.916801i	$-0.369238\pi$
$107$	884.000	0.798687	0.399343	+	0.916801i	$0.369238\pi$
$108$	0	0
$109$	−1098.00	−0.964856	−0.482428	−	0.875936i	$-0.660245\pi$
$109$	−1098.00	−0.964856	−0.482428	+	0.875936i	$0.660245\pi$
$110$	0	0
$111$	1480.00	1.26554
$112$	0	0
$113$	1170.00	0.974021	0.487010	−	0.873396i	$-0.338087\pi$
$113$	1170.00	0.974021	0.487010	+	0.873396i	$0.338087\pi$
$114$	0	0
$115$	920.000	0.746004
$116$	0	0
$117$	−242.000	−0.191221
$118$	0	0
$119$	210.000	0.161770
$120$	0	0
$121$	3293.00	2.47408
$122$	0	0
$123$	−616.000	−0.451568
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−176.000	−0.122972	−0.0614861	−	0.998108i	$-0.519584\pi$
$127$	−176.000	−0.122972	−0.0614861	+	0.998108i	$0.519584\pi$
$128$	0	0
$129$	−848.000	−0.578777
$130$	0	0
$131$	−1028.00	−0.685624	−0.342812	−	0.939404i	$-0.611379\pi$
$131$	−1028.00	−0.685624	−0.342812	+	0.939404i	$0.611379\pi$
$132$	0	0
$133$	−756.000	−0.492884
$134$	0	0
$135$	760.000	0.484521
$136$	0	0
$137$	−2598.00	−1.62016	−0.810081	−	0.586318i	$-0.800577\pi$
$137$	−2598.00	−1.62016	−0.810081	+	0.586318i	$0.800577\pi$
$138$	0	0
$139$	2420.00	1.47670	0.738352	−	0.674416i	$-0.235605\pi$
$139$	2420.00	1.47670	0.738352	+	0.674416i	$0.235605\pi$
$140$	0	0
$141$	2048.00	1.22321
$142$	0	0
$143$	1496.00	0.874838
$144$	0	0
$145$	830.000	0.475364
$146$	0	0
$147$	−196.000	−0.109971
$148$	0	0
$149$	−594.000	−0.326593	−0.163297	−	0.986577i	$-0.552213\pi$
$149$	−594.000	−0.326593	−0.163297	+	0.986577i	$0.552213\pi$
$150$	0	0
$151$	1464.00	0.788998	0.394499	−	0.918896i	$-0.370918\pi$
$151$	1464.00	0.788998	0.394499	+	0.918896i	$0.370918\pi$
$152$	0	0
$153$	330.000	0.174372
$154$	0	0
$155$	−160.000	−0.0829130
$156$	0	0
$157$	326.000	0.165717	0.0828587	−	0.996561i	$-0.473595\pi$
$157$	326.000	0.165717	0.0828587	+	0.996561i	$0.473595\pi$
$158$	0	0
$159$	392.000	0.195520
$160$	0	0
$161$	−1288.00	−0.630488
$162$	0	0
$163$	1852.00	0.889938	0.444969	−	0.895546i	$-0.353215\pi$
$163$	1852.00	0.889938	0.444969	+	0.895546i	$0.353215\pi$
$164$	0	0
$165$	−1360.00	−0.641672
$166$	0	0
$167$	−3096.00	−1.43458	−0.717292	−	0.696772i	$-0.754619\pi$
$167$	−3096.00	−1.43458	−0.717292	+	0.696772i	$0.754619\pi$
$168$	0	0
$169$	−1713.00	−0.779700
$170$	0	0
$171$	−1188.00	−0.531279
$172$	0	0
$173$	−3018.00	−1.32633	−0.663163	−	0.748475i	$-0.730786\pi$
$173$	−3018.00	−1.32633	−0.663163	+	0.748475i	$0.730786\pi$
$174$	0	0
$175$	−175.000	−0.0755929
$176$	0	0
$177$	3440.00	1.46083
$178$	0	0
$179$	−484.000	−0.202100	−0.101050	−	0.994881i	$-0.532220\pi$
$179$	−484.000	−0.202100	−0.101050	+	0.994881i	$0.532220\pi$
$180$	0	0
$181$	−1170.00	−0.480472	−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00	−0.480472	−0.240236	+	0.970715i	$0.577225\pi$
$182$	0	0
$183$	−1560.00	−0.630156
$184$	0	0
$185$	−1850.00	−0.735215
$186$	0	0
$187$	−2040.00	−0.797752
$188$	0	0
$189$	−1064.00	−0.409495
$190$	0	0
$191$	−1968.00	−0.745547	−0.372774	−	0.927922i	$-0.621593\pi$
$191$	−1968.00	−0.745547	−0.372774	+	0.927922i	$0.621593\pi$
$192$	0	0
$193$	3106.00	1.15842	0.579209	−	0.815179i	$-0.303361\pi$
$193$	3106.00	1.15842	0.579209	+	0.815179i	$0.303361\pi$
$194$	0	0
$195$	−440.000	−0.161585
$196$	0	0
$197$	110.000	0.0397826	0.0198913	−	0.999802i	$-0.493668\pi$
$197$	110.000	0.0397826	0.0198913	+	0.999802i	$0.493668\pi$
$198$	0	0
$199$	−3048.00	−1.08576	−0.542882	−	0.839809i	$-0.682667\pi$
$199$	−3048.00	−1.08576	−0.542882	+	0.839809i	$0.682667\pi$
$200$	0	0
$201$	−240.000	−0.0842204
$202$	0	0
$203$	−1162.00	−0.401756
$204$	0	0
$205$	770.000	0.262337
$206$	0	0
$207$	−2024.00	−0.679603
$208$	0	0
$209$	7344.00	2.43060
$210$	0	0
$211$	−2788.00	−0.909639	−0.454820	−	0.890584i	$-0.650296\pi$
$211$	−2788.00	−0.909639	−0.454820	+	0.890584i	$0.650296\pi$
$212$	0	0
$213$	−3360.00	−1.08086
$214$	0	0
$215$	1060.00	0.336239
$216$	0	0
$217$	224.000	0.0700742
$218$	0	0
$219$	2520.00	0.777561
$220$	0	0
$221$	−660.000	−0.200889
$222$	0	0
$223$	1488.00	0.446833	0.223417	−	0.974723i	$-0.428279\pi$
$223$	1488.00	0.446833	0.223417	+	0.974723i	$0.428279\pi$
$224$	0	0
$225$	−275.000	−0.0814815
$226$	0	0
$227$	−4.00000	−0.00116956	−0.000584778	−	1.00000i	$-0.500186\pi$
$227$	−4.00000	−0.00116956	−0.000584778		1.00000i	$0.500186\pi$
$228$	0	0
$229$	−514.000	−0.148323	−0.0741617	−	0.997246i	$-0.523628\pi$
$229$	−514.000	−0.148323	−0.0741617	+	0.997246i	$0.523628\pi$
$230$	0	0
$231$	1904.00	0.542312
$232$	0	0
$233$	−2598.00	−0.730475	−0.365237	−	0.930914i	$-0.619012\pi$
$233$	−2598.00	−0.730475	−0.365237	+	0.930914i	$0.619012\pi$
$234$	0	0
$235$	−2560.00	−0.710621
$236$	0	0
$237$	−5248.00	−1.43837
$238$	0	0
$239$	−1440.00	−0.389732	−0.194866	−	0.980830i	$-0.562427\pi$
$239$	−1440.00	−0.389732	−0.194866	+	0.980830i	$0.562427\pi$
$240$	0	0
$241$	3442.00	0.919995	0.459997	−	0.887920i	$-0.347850\pi$
$241$	3442.00	0.919995	0.459997	+	0.887920i	$0.347850\pi$
$242$	0	0
$243$	−2860.00	−0.755017
$244$	0	0
$245$	245.000	0.0638877
$246$	0	0
$247$	2376.00	0.612070
$248$	0	0
$249$	1744.00	0.443861
$250$	0	0
$251$	−188.000	−0.0472767	−0.0236384	−	0.999721i	$-0.507525\pi$
$251$	−188.000	−0.0472767	−0.0236384	+	0.999721i	$0.507525\pi$
$252$	0	0
$253$	12512.0	3.10918
$254$	0	0
$255$	600.000	0.147347
$256$	0	0
$257$	5458.00	1.32475	0.662375	−	0.749173i	$-0.269549\pi$
$257$	5458.00	1.32475	0.662375	+	0.749173i	$0.269549\pi$
$258$	0	0
$259$	2590.00	0.621370
$260$	0	0
$261$	−1826.00	−0.433052
$262$	0	0
$263$	−2808.00	−0.658360	−0.329180	−	0.944267i	$-0.606772\pi$
$263$	−2808.00	−0.658360	−0.329180	+	0.944267i	$0.606772\pi$
$264$	0	0
$265$	−490.000	−0.113587
$266$	0	0
$267$	2392.00	0.548270
$268$	0	0
$269$	−3082.00	−0.698561	−0.349280	−	0.937018i	$-0.613574\pi$
$269$	−3082.00	−0.698561	−0.349280	+	0.937018i	$0.613574\pi$
$270$	0	0
$271$	−5680.00	−1.27319	−0.636597	−	0.771197i	$-0.719658\pi$
$271$	−5680.00	−1.27319	−0.636597	+	0.771197i	$0.719658\pi$
$272$	0	0
$273$	616.000	0.136564
$274$	0	0
$275$	1700.00	0.372778
$276$	0	0
$277$	2558.00	0.554857	0.277428	−	0.960746i	$-0.410518\pi$
$277$	2558.00	0.554857	0.277428	+	0.960746i	$0.410518\pi$
$278$	0	0
$279$	352.000	0.0755329
$280$	0	0
$281$	1610.00	0.341796	0.170898	−	0.985289i	$-0.445333\pi$
$281$	1610.00	0.341796	0.170898	+	0.985289i	$0.445333\pi$
$282$	0	0
$283$	−1724.00	−0.362124	−0.181062	−	0.983472i	$-0.557954\pi$
$283$	−1724.00	−0.362124	−0.181062	+	0.983472i	$0.557954\pi$
$284$	0	0
$285$	−2160.00	−0.448938
$286$	0	0
$287$	−1078.00	−0.221715
$288$	0	0
$289$	−4013.00	−0.816813
$290$	0	0
$291$	−3656.00	−0.736490
$292$	0	0
$293$	2430.00	0.484512	0.242256	−	0.970212i	$-0.422113\pi$
$293$	2430.00	0.484512	0.242256	+	0.970212i	$0.422113\pi$
$294$	0	0
$295$	−4300.00	−0.848663
$296$	0	0
$297$	10336.0	2.01938
$298$	0	0
$299$	4048.00	0.782949
$300$	0	0
$301$	−1484.00	−0.284174
$302$	0	0
$303$	−1272.00	−0.241170
$304$	0	0
$305$	1950.00	0.366087
$306$	0	0
$307$	8588.00	1.59656	0.798279	−	0.602288i	$-0.205744\pi$
$307$	8588.00	1.59656	0.798279	+	0.602288i	$0.205744\pi$
$308$	0	0
$309$	1120.00	0.206196
$310$	0	0
$311$	−10488.0	−1.91228	−0.956141	−	0.292906i	$-0.905378\pi$
$311$	−10488.0	−1.91228	−0.956141	+	0.292906i	$0.905378\pi$
$312$	0	0
$313$	7866.00	1.42049	0.710244	−	0.703956i	$-0.248585\pi$
$313$	7866.00	1.42049	0.710244	+	0.703956i	$0.248585\pi$
$314$	0	0
$315$	385.000	0.0688644
$316$	0	0
$317$	1014.00	0.179659	0.0898295	−	0.995957i	$-0.471368\pi$
$317$	1014.00	0.179659	0.0898295	+	0.995957i	$0.471368\pi$
$318$	0	0
$319$	11288.0	1.98121
$320$	0	0
$321$	−3536.00	−0.614830
$322$	0	0
$323$	−3240.00	−0.558138
$324$	0	0
$325$	550.000	0.0938723
$326$	0	0
$327$	4392.00	0.742747
$328$	0	0
$329$	3584.00	0.600585
$330$	0	0
$331$	−2620.00	−0.435070	−0.217535	−	0.976053i	$-0.569802\pi$
$331$	−2620.00	−0.435070	−0.217535	+	0.976053i	$0.569802\pi$
$332$	0	0
$333$	4070.00	0.669774
$334$	0	0
$335$	300.000	0.0489276
$336$	0	0
$337$	786.000	0.127051	0.0635254	−	0.997980i	$-0.479766\pi$
$337$	786.000	0.127051	0.0635254	+	0.997980i	$0.479766\pi$
$338$	0	0
$339$	−4680.00	−0.749802
$340$	0	0
$341$	−2176.00	−0.345563
$342$	0	0
$343$	−343.000	−0.0539949
$344$	0	0
$345$	−3680.00	−0.574274
$346$	0	0
$347$	4964.00	0.767958	0.383979	−	0.923342i	$-0.374553\pi$
$347$	4964.00	0.767958	0.383979	+	0.923342i	$0.374553\pi$
$348$	0	0
$349$	−10266.0	−1.57457	−0.787287	−	0.616587i	$-0.788515\pi$
$349$	−10266.0	−1.57457	−0.787287	+	0.616587i	$0.788515\pi$
$350$	0	0
$351$	3344.00	0.508517
$352$	0	0
$353$	4722.00	0.711974	0.355987	−	0.934491i	$-0.384145\pi$
$353$	4722.00	0.711974	0.355987	+	0.934491i	$0.384145\pi$
$354$	0	0
$355$	4200.00	0.627924
$356$	0	0
$357$	−840.000	−0.124531
$358$	0	0
$359$	2632.00	0.386941	0.193470	−	0.981106i	$-0.438026\pi$
$359$	2632.00	0.386941	0.193470	+	0.981106i	$0.438026\pi$
$360$	0	0
$361$	4805.00	0.700539
$362$	0	0
$363$	−13172.0	−1.90455
$364$	0	0
$365$	−3150.00	−0.451722
$366$	0	0
$367$	9472.00	1.34723	0.673616	−	0.739081i	$-0.264740\pi$
$367$	9472.00	1.34723	0.673616	+	0.739081i	$0.264740\pi$
$368$	0	0
$369$	−1694.00	−0.238987
$370$	0	0
$371$	686.000	0.0959982
$372$	0	0
$373$	−11586.0	−1.60831	−0.804156	−	0.594418i	$-0.797382\pi$
$373$	−11586.0	−1.60831	−0.804156	+	0.594418i	$0.797382\pi$
$374$	0	0
$375$	−500.000	−0.0688530
$376$	0	0
$377$	3652.00	0.498906
$378$	0	0
$379$	1172.00	0.158843	0.0794216	−	0.996841i	$-0.474693\pi$
$379$	1172.00	0.158843	0.0794216	+	0.996841i	$0.474693\pi$
$380$	0	0
$381$	704.000	0.0946641
$382$	0	0
$383$	−4720.00	−0.629715	−0.314857	−	0.949139i	$-0.601957\pi$
$383$	−4720.00	−0.629715	−0.314857	+	0.949139i	$0.601957\pi$
$384$	0	0
$385$	−2380.00	−0.315055
$386$	0	0
$387$	−2332.00	−0.306311
$388$	0	0
$389$	−7874.00	−1.02629	−0.513146	−	0.858301i	$-0.671520\pi$
$389$	−7874.00	−1.02629	−0.513146	+	0.858301i	$0.671520\pi$
$390$	0	0
$391$	−5520.00	−0.713960
$392$	0	0
$393$	4112.00	0.527794
$394$	0	0
$395$	6560.00	0.835619
$396$	0	0
$397$	−8746.00	−1.10567	−0.552833	−	0.833292i	$-0.686453\pi$
$397$	−8746.00	−1.10567	−0.552833	+	0.833292i	$0.686453\pi$
$398$	0	0
$399$	3024.00	0.379422
$400$	0	0
$401$	−11342.0	−1.41245	−0.706225	−	0.707987i	$-0.749603\pi$
$401$	−11342.0	−1.41245	−0.706225	+	0.707987i	$0.749603\pi$
$402$	0	0
$403$	−704.000	−0.0870192
$404$	0	0
$405$	−1555.00	−0.190787
$406$	0	0
$407$	−25160.0	−3.06421
$408$	0	0
$409$	−12214.0	−1.47663	−0.738317	−	0.674454i	$-0.764379\pi$
$409$	−12214.0	−1.47663	−0.738317	+	0.674454i	$0.764379\pi$
$410$	0	0
$411$	10392.0	1.24720
$412$	0	0
$413$	6020.00	0.717251
$414$	0	0
$415$	−2180.00	−0.257860
$416$	0	0
$417$	−9680.00	−1.13677
$418$	0	0
$419$	9628.00	1.12257	0.561287	−	0.827621i	$-0.310306\pi$
$419$	9628.00	1.12257	0.561287	+	0.827621i	$0.310306\pi$
$420$	0	0
$421$	−9218.00	−1.06712	−0.533560	−	0.845762i	$-0.679146\pi$
$421$	−9218.00	−1.06712	−0.533560	+	0.845762i	$0.679146\pi$
$422$	0	0
$423$	5632.00	0.647369
$424$	0	0
$425$	−750.000	−0.0856008
$426$	0	0
$427$	−2730.00	−0.309400
$428$	0	0
$429$	−5984.00	−0.673450
$430$	0	0
$431$	−6912.00	−0.772481	−0.386241	−	0.922398i	$-0.626227\pi$
$431$	−6912.00	−0.772481	−0.386241	+	0.922398i	$0.626227\pi$
$432$	0	0
$433$	994.000	0.110320	0.0551600	−	0.998478i	$-0.482433\pi$
$433$	994.000	0.110320	0.0551600	+	0.998478i	$0.482433\pi$
$434$	0	0
$435$	−3320.00	−0.365935
$436$	0	0
$437$	19872.0	2.17530
$438$	0	0
$439$	13544.0	1.47248	0.736241	−	0.676719i	$-0.236599\pi$
$439$	13544.0	1.47248	0.736241	+	0.676719i	$0.236599\pi$
$440$	0	0
$441$	−539.000	−0.0582011
$442$	0	0
$443$	−5276.00	−0.565847	−0.282924	−	0.959142i	$-0.591304\pi$
$443$	−5276.00	−0.565847	−0.282924	+	0.959142i	$0.591304\pi$
$444$	0	0
$445$	−2990.00	−0.318516
$446$	0	0
$447$	2376.00	0.251412
$448$	0	0
$449$	9794.00	1.02942	0.514708	−	0.857366i	$-0.327900\pi$
$449$	9794.00	1.02942	0.514708	+	0.857366i	$0.327900\pi$
$450$	0	0
$451$	10472.0	1.09336
$452$	0	0
$453$	−5856.00	−0.607371
$454$	0	0
$455$	−770.000	−0.0793366
$456$	0	0
$457$	−7686.00	−0.786731	−0.393365	−	0.919382i	$-0.628689\pi$
$457$	−7686.00	−0.786731	−0.393365	+	0.919382i	$0.628689\pi$
$458$	0	0
$459$	−4560.00	−0.463709
$460$	0	0
$461$	−3402.00	−0.343703	−0.171851	−	0.985123i	$-0.554975\pi$
$461$	−3402.00	−0.343703	−0.171851	+	0.985123i	$0.554975\pi$
$462$	0	0
$463$	−7552.00	−0.758037	−0.379019	−	0.925389i	$-0.623738\pi$
$463$	−7552.00	−0.758037	−0.379019	+	0.925389i	$0.623738\pi$
$464$	0	0
$465$	640.000	0.0638264
$466$	0	0
$467$	18156.0	1.79906	0.899528	−	0.436862i	$-0.143910\pi$
$467$	18156.0	1.79906	0.899528	+	0.436862i	$0.143910\pi$
$468$	0	0
$469$	−420.000	−0.0413514
$470$	0	0
$471$	−1304.00	−0.127569
$472$	0	0
$473$	14416.0	1.40137
$474$	0	0
$475$	2700.00	0.260809
$476$	0	0
$477$	1078.00	0.103476
$478$	0	0
$479$	7648.00	0.729532	0.364766	−	0.931099i	$-0.381149\pi$
$479$	7648.00	0.729532	0.364766	+	0.931099i	$0.381149\pi$
$480$	0	0
$481$	−8140.00	−0.771626
$482$	0	0
$483$	5152.00	0.485350
$484$	0	0
$485$	4570.00	0.427862
$486$	0	0
$487$	−1048.00	−0.0975142	−0.0487571	−	0.998811i	$-0.515526\pi$
$487$	−1048.00	−0.0975142	−0.0487571	+	0.998811i	$0.515526\pi$
$488$	0	0
$489$	−7408.00	−0.685074
$490$	0	0
$491$	4388.00	0.403315	0.201658	−	0.979456i	$-0.435367\pi$
$491$	4388.00	0.403315	0.201658	+	0.979456i	$0.435367\pi$
$492$	0	0
$493$	−4980.00	−0.454945
$494$	0	0
$495$	−3740.00	−0.339597
$496$	0	0
$497$	−5880.00	−0.530692
$498$	0	0
$499$	−15716.0	−1.40991	−0.704955	−	0.709252i	$-0.749033\pi$
$499$	−15716.0	−1.40991	−0.704955	+	0.709252i	$0.749033\pi$
$500$	0	0
$501$	12384.0	1.10434
$502$	0	0
$503$	1272.00	0.112755	0.0563774	−	0.998410i	$-0.482045\pi$
$503$	1272.00	0.112755	0.0563774	+	0.998410i	$0.482045\pi$
$504$	0	0
$505$	1590.00	0.140107
$506$	0	0
$507$	6852.00	0.600213
$508$	0	0
$509$	−1786.00	−0.155527	−0.0777633	−	0.996972i	$-0.524778\pi$
$509$	−1786.00	−0.155527	−0.0777633	+	0.996972i	$0.524778\pi$
$510$	0	0
$511$	4410.00	0.381775
$512$	0	0
$513$	16416.0	1.41283
$514$	0	0
$515$	−1400.00	−0.119789
$516$	0	0
$517$	−34816.0	−2.96171
$518$	0	0
$519$	12072.0	1.02101
$520$	0	0
$521$	12762.0	1.07315	0.536577	−	0.843851i	$-0.319717\pi$
$521$	12762.0	1.07315	0.536577	+	0.843851i	$0.319717\pi$
$522$	0	0
$523$	16340.0	1.36615	0.683077	−	0.730347i	$-0.260641\pi$
$523$	16340.0	1.36615	0.683077	+	0.730347i	$0.260641\pi$
$524$	0	0
$525$	700.000	0.0581914
$526$	0	0
$527$	960.000	0.0793515
$528$	0	0
$529$	21689.0	1.78261
$530$	0	0
$531$	9460.00	0.773124
$532$	0	0
$533$	3388.00	0.275329
$534$	0	0
$535$	4420.00	0.357184
$536$	0	0
$537$	1936.00	0.155576
$538$	0	0
$539$	3332.00	0.266270
$540$	0	0
$541$	10310.0	0.819337	0.409669	−	0.912234i	$-0.365644\pi$
$541$	10310.0	0.819337	0.409669	+	0.912234i	$0.365644\pi$
$542$	0	0
$543$	4680.00	0.369867
$544$	0	0
$545$	−5490.00	−0.431497
$546$	0	0
$547$	−23204.0	−1.81377	−0.906884	−	0.421380i	$-0.861546\pi$
$547$	−23204.0	−1.81377	−0.906884	+	0.421380i	$0.861546\pi$
$548$	0	0
$549$	−4290.00	−0.333502
$550$	0	0
$551$	17928.0	1.38613
$552$	0	0
$553$	−9184.00	−0.706227
$554$	0	0
$555$	7400.00	0.565968
$556$	0	0
$557$	−14490.0	−1.10226	−0.551132	−	0.834418i	$-0.685804\pi$
$557$	−14490.0	−1.10226	−0.551132	+	0.834418i	$0.685804\pi$
$558$	0	0
$559$	4664.00	0.352891
$560$	0	0
$561$	8160.00	0.614110
$562$	0	0
$563$	−26132.0	−1.95619	−0.978093	−	0.208169i	$-0.933249\pi$
$563$	−26132.0	−1.95619	−0.978093	+	0.208169i	$0.933249\pi$
$564$	0	0
$565$	5850.00	0.435595
$566$	0	0
$567$	2177.00	0.161244
$568$	0	0
$569$	−18198.0	−1.34077	−0.670387	−	0.742012i	$-0.733872\pi$
$569$	−18198.0	−1.34077	−0.670387	+	0.742012i	$0.733872\pi$
$570$	0	0
$571$	4660.00	0.341532	0.170766	−	0.985312i	$-0.445376\pi$
$571$	4660.00	0.341532	0.170766	+	0.985312i	$0.445376\pi$
$572$	0	0
$573$	7872.00	0.573922
$574$	0	0
$575$	4600.00	0.333623
$576$	0	0
$577$	14386.0	1.03795	0.518975	−	0.854789i	$-0.326314\pi$
$577$	14386.0	1.03795	0.518975	+	0.854789i	$0.326314\pi$
$578$	0	0
$579$	−12424.0	−0.891751
$580$	0	0
$581$	3052.00	0.217932
$582$	0	0
$583$	−6664.00	−0.473404
$584$	0	0
$585$	−1210.00	−0.0855168
$586$	0	0
$587$	−20556.0	−1.44538	−0.722689	−	0.691173i	$-0.757094\pi$
$587$	−20556.0	−1.44538	−0.722689	+	0.691173i	$0.757094\pi$
$588$	0	0
$589$	−3456.00	−0.241769
$590$	0	0
$591$	−440.000	−0.0306247
$592$	0	0
$593$	−16286.0	−1.12780	−0.563900	−	0.825843i	$-0.690700\pi$
$593$	−16286.0	−1.12780	−0.563900	+	0.825843i	$0.690700\pi$
$594$	0	0
$595$	1050.00	0.0723459
$596$	0	0
$597$	12192.0	0.835821
$598$	0	0
$599$	22616.0	1.54268	0.771339	−	0.636424i	$-0.219587\pi$
$599$	22616.0	1.54268	0.771339	+	0.636424i	$0.219587\pi$
$600$	0	0
$601$	4138.00	0.280853	0.140426	−	0.990091i	$-0.455153\pi$
$601$	4138.00	0.280853	0.140426	+	0.990091i	$0.455153\pi$
$602$	0	0
$603$	−660.000	−0.0445726
$604$	0	0
$605$	16465.0	1.10644
$606$	0	0
$607$	12560.0	0.839859	0.419930	−	0.907557i	$-0.362055\pi$
$607$	12560.0	0.839859	0.419930	+	0.907557i	$0.362055\pi$
$608$	0	0
$609$	4648.00	0.309272
$610$	0	0
$611$	−11264.0	−0.745815
$612$	0	0
$613$	−12914.0	−0.850883	−0.425442	−	0.904986i	$-0.639881\pi$
$613$	−12914.0	−0.850883	−0.425442	+	0.904986i	$0.639881\pi$
$614$	0	0
$615$	−3080.00	−0.201947
$616$	0	0
$617$	10138.0	0.661492	0.330746	−	0.943720i	$-0.392700\pi$
$617$	10138.0	0.661492	0.330746	+	0.943720i	$0.392700\pi$
$618$	0	0
$619$	−23788.0	−1.54462	−0.772311	−	0.635245i	$-0.780899\pi$
$619$	−23788.0	−1.54462	−0.772311	+	0.635245i	$0.780899\pi$
$620$	0	0
$621$	27968.0	1.80727
$622$	0	0
$623$	4186.00	0.269195
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−29376.0	−1.87108
$628$	0	0
$629$	11100.0	0.703634
$630$	0	0
$631$	−10280.0	−0.648558	−0.324279	−	0.945961i	$-0.605122\pi$
$631$	−10280.0	−0.648558	−0.324279	+	0.945961i	$0.605122\pi$
$632$	0	0
$633$	11152.0	0.700240
$634$	0	0
$635$	−880.000	−0.0549949
$636$	0	0
$637$	1078.00	0.0670517
$638$	0	0
$639$	−9240.00	−0.572032
$640$	0	0
$641$	5634.00	0.347160	0.173580	−	0.984820i	$-0.444466\pi$
$641$	5634.00	0.347160	0.173580	+	0.984820i	$0.444466\pi$
$642$	0	0
$643$	22940.0	1.40694	0.703472	−	0.710723i	$-0.251632\pi$
$643$	22940.0	1.40694	0.703472	+	0.710723i	$0.251632\pi$
$644$	0	0
$645$	−4240.00	−0.258837
$646$	0	0
$647$	−1592.00	−0.0967357	−0.0483678	−	0.998830i	$-0.515402\pi$
$647$	−1592.00	−0.0967357	−0.0483678	+	0.998830i	$0.515402\pi$
$648$	0	0
$649$	−58480.0	−3.53704
$650$	0	0
$651$	−896.000	−0.0539432
$652$	0	0
$653$	−17498.0	−1.04862	−0.524311	−	0.851527i	$-0.675677\pi$
$653$	−17498.0	−1.04862	−0.524311	+	0.851527i	$0.675677\pi$
$654$	0	0
$655$	−5140.00	−0.306620
$656$	0	0
$657$	6930.00	0.411515
$658$	0	0
$659$	16956.0	1.00229	0.501147	−	0.865362i	$-0.332912\pi$
$659$	16956.0	1.00229	0.501147	+	0.865362i	$0.332912\pi$
$660$	0	0
$661$	−31602.0	−1.85957	−0.929785	−	0.368104i	$-0.880007\pi$
$661$	−31602.0	−1.85957	−0.929785	+	0.368104i	$0.880007\pi$
$662$	0	0
$663$	2640.00	0.154644
$664$	0	0
$665$	−3780.00	−0.220424
$666$	0	0
$667$	30544.0	1.77312
$668$	0	0
$669$	−5952.00	−0.343973
$670$	0	0
$671$	26520.0	1.52577
$672$	0	0
$673$	−5342.00	−0.305972	−0.152986	−	0.988228i	$-0.548889\pi$
$673$	−5342.00	−0.305972	−0.152986	+	0.988228i	$0.548889\pi$
$674$	0	0
$675$	3800.00	0.216685
$676$	0	0
$677$	−24418.0	−1.38620	−0.693102	−	0.720840i	$-0.743756\pi$
$677$	−24418.0	−1.38620	−0.693102	+	0.720840i	$0.743756\pi$
$678$	0	0
$679$	−6398.00	−0.361609
$680$	0	0
$681$	16.0000	0.000900325 0
$682$	0	0
$683$	1300.00	0.0728303	0.0364152	−	0.999337i	$-0.488406\pi$
$683$	1300.00	0.0728303	0.0364152	+	0.999337i	$0.488406\pi$
$684$	0	0
$685$	−12990.0	−0.724558
$686$	0	0
$687$	2056.00	0.114179
$688$	0	0
$689$	−2156.00	−0.119212
$690$	0	0
$691$	−15540.0	−0.855527	−0.427764	−	0.903891i	$-0.640698\pi$
$691$	−15540.0	−0.855527	−0.427764	+	0.903891i	$0.640698\pi$
$692$	0	0
$693$	5236.00	0.287012
$694$	0	0
$695$	12100.0	0.660402
$696$	0	0
$697$	−4620.00	−0.251069
$698$	0	0
$699$	10392.0	0.562320
$700$	0	0
$701$	25350.0	1.36584	0.682922	−	0.730492i	$-0.260709\pi$
$701$	25350.0	1.36584	0.682922	+	0.730492i	$0.260709\pi$
$702$	0	0
$703$	−39960.0	−2.14384
$704$	0	0
$705$	10240.0	0.547036
$706$	0	0
$707$	−2226.00	−0.118412
$708$	0	0
$709$	−21730.0	−1.15104	−0.575520	−	0.817788i	$-0.695200\pi$
$709$	−21730.0	−1.15104	−0.575520	+	0.817788i	$0.695200\pi$
$710$	0	0
$711$	−14432.0	−0.761241
$712$	0	0
$713$	−5888.00	−0.309267
$714$	0	0
$715$	7480.00	0.391239
$716$	0	0
$717$	5760.00	0.300016
$718$	0	0
$719$	−2512.00	−0.130295	−0.0651473	−	0.997876i	$-0.520752\pi$
$719$	−2512.00	−0.130295	−0.0651473	+	0.997876i	$0.520752\pi$
$720$	0	0
$721$	1960.00	0.101240
$722$	0	0
$723$	−13768.0	−0.708212
$724$	0	0
$725$	4150.00	0.212589
$726$	0	0
$727$	−34696.0	−1.77002	−0.885009	−	0.465573i	$-0.845848\pi$
$727$	−34696.0	−1.77002	−0.885009	+	0.465573i	$0.845848\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	−6360.00	−0.321796
$732$	0	0
$733$	36902.0	1.85949	0.929745	−	0.368204i	$-0.120027\pi$
$733$	36902.0	1.85949	0.929745	+	0.368204i	$0.120027\pi$
$734$	0	0
$735$	−980.000	−0.0491807
$736$	0	0
$737$	4080.00	0.203920
$738$	0	0
$739$	−1300.00	−0.0647108	−0.0323554	−	0.999476i	$-0.510301\pi$
$739$	−1300.00	−0.0647108	−0.0323554	+	0.999476i	$0.510301\pi$
$740$	0	0
$741$	−9504.00	−0.471172
$742$	0	0
$743$	−22520.0	−1.11195	−0.555975	−	0.831199i	$-0.687655\pi$
$743$	−22520.0	−1.11195	−0.555975	+	0.831199i	$0.687655\pi$
$744$	0	0
$745$	−2970.00	−0.146057
$746$	0	0
$747$	4796.00	0.234908
$748$	0	0
$749$	−6188.00	−0.301875
$750$	0	0
$751$	36128.0	1.75543	0.877716	−	0.479181i	$-0.159066\pi$
$751$	36128.0	1.75543	0.877716	+	0.479181i	$0.159066\pi$
$752$	0	0
$753$	752.000	0.0363936
$754$	0	0
$755$	7320.00	0.352850
$756$	0	0
$757$	−33154.0	−1.59181	−0.795907	−	0.605419i	$-0.793005\pi$
$757$	−33154.0	−1.59181	−0.795907	+	0.605419i	$0.793005\pi$
$758$	0	0
$759$	−50048.0	−2.39345
$760$	0	0
$761$	−40278.0	−1.91863	−0.959314	−	0.282340i	$-0.908889\pi$
$761$	−40278.0	−1.91863	−0.959314	+	0.282340i	$0.908889\pi$
$762$	0	0
$763$	7686.00	0.364681
$764$	0	0
$765$	1650.00	0.0779815
$766$	0	0
$767$	−18920.0	−0.890693
$768$	0	0
$769$	5794.00	0.271700	0.135850	−	0.990729i	$-0.456624\pi$
$769$	5794.00	0.271700	0.135850	+	0.990729i	$0.456624\pi$
$770$	0	0
$771$	−21832.0	−1.01979
$772$	0	0
$773$	−354.000	−0.0164715	−0.00823577	−	0.999966i	$-0.502622\pi$
$773$	−354.000	−0.0164715	−0.00823577	+	0.999966i	$0.502622\pi$
$774$	0	0
$775$	−800.000	−0.0370798
$776$	0	0
$777$	−10360.0	−0.478331
$778$	0	0
$779$	16632.0	0.764959
$780$	0	0
$781$	57120.0	2.61705
$782$	0	0
$783$	25232.0	1.15162
$784$	0	0
$785$	1630.00	0.0741111
$786$	0	0
$787$	28204.0	1.27746	0.638732	−	0.769429i	$-0.279459\pi$
$787$	28204.0	1.27746	0.638732	+	0.769429i	$0.279459\pi$
$788$	0	0
$789$	11232.0	0.506806
$790$	0	0
$791$	−8190.00	−0.368145
$792$	0	0
$793$	8580.00	0.384218
$794$	0	0
$795$	1960.00	0.0874390
$796$	0	0
$797$	33414.0	1.48505	0.742525	−	0.669819i	$-0.233628\pi$
$797$	33414.0	1.48505	0.742525	+	0.669819i	$0.233628\pi$
$798$	0	0
$799$	15360.0	0.680097
$800$	0	0
$801$	6578.00	0.290165
$802$	0	0
$803$	−42840.0	−1.88268
$804$	0	0
$805$	−6440.00	−0.281963
$806$	0	0
$807$	12328.0	0.537752
$808$	0	0
$809$	37626.0	1.63518	0.817589	−	0.575802i	$-0.195310\pi$
$809$	37626.0	1.63518	0.817589	+	0.575802i	$0.195310\pi$
$810$	0	0
$811$	23316.0	1.00954	0.504769	−	0.863254i	$-0.331578\pi$
$811$	23316.0	1.00954	0.504769	+	0.863254i	$0.331578\pi$
$812$	0	0
$813$	22720.0	0.980105
$814$	0	0
$815$	9260.00	0.397992
$816$	0	0
$817$	22896.0	0.980452
$818$	0	0
$819$	1694.00	0.0722749
$820$	0	0
$821$	38190.0	1.62344	0.811718	−	0.584050i	$-0.198533\pi$
$821$	38190.0	1.62344	0.811718	+	0.584050i	$0.198533\pi$
$822$	0	0
$823$	35064.0	1.48512	0.742560	−	0.669779i	$-0.233611\pi$
$823$	35064.0	1.48512	0.742560	+	0.669779i	$0.233611\pi$
$824$	0	0
$825$	−6800.00	−0.286964
$826$	0	0
$827$	−12796.0	−0.538042	−0.269021	−	0.963134i	$-0.586700\pi$
$827$	−12796.0	−0.538042	−0.269021	+	0.963134i	$0.586700\pi$
$828$	0	0
$829$	−15674.0	−0.656671	−0.328336	−	0.944561i	$-0.606488\pi$
$829$	−15674.0	−0.656671	−0.328336	+	0.944561i	$0.606488\pi$
$830$	0	0
$831$	−10232.0	−0.427129
$832$	0	0
$833$	−1470.00	−0.0611434
$834$	0	0
$835$	−15480.0	−0.641566
$836$	0	0
$837$	−4864.00	−0.200866
$838$	0	0
$839$	−3784.00	−0.155707	−0.0778535	−	0.996965i	$-0.524807\pi$
$839$	−3784.00	−0.155707	−0.0778535	+	0.996965i	$0.524807\pi$
$840$	0	0
$841$	3167.00	0.129854
$842$	0	0
$843$	−6440.00	−0.263114
$844$	0	0
$845$	−8565.00	−0.348692
$846$	0	0
$847$	−23051.0	−0.935114
$848$	0	0
$849$	6896.00	0.278763
$850$	0	0
$851$	−68080.0	−2.74236
$852$	0	0
$853$	−4178.00	−0.167705	−0.0838523	−	0.996478i	$-0.526722\pi$
$853$	−4178.00	−0.167705	−0.0838523	+	0.996478i	$0.526722\pi$
$854$	0	0
$855$	−5940.00	−0.237595
$856$	0	0
$857$	30874.0	1.23061	0.615307	−	0.788288i	$-0.289032\pi$
$857$	30874.0	1.23061	0.615307	+	0.788288i	$0.289032\pi$
$858$	0	0
$859$	20196.0	0.802187	0.401093	−	0.916037i	$-0.368630\pi$
$859$	20196.0	0.802187	0.401093	+	0.916037i	$0.368630\pi$
$860$	0	0
$861$	4312.00	0.170677
$862$	0	0
$863$	39952.0	1.57588	0.787939	−	0.615754i	$-0.211148\pi$
$863$	39952.0	1.57588	0.787939	+	0.615754i	$0.211148\pi$
$864$	0	0
$865$	−15090.0	−0.593151
$866$	0	0
$867$	16052.0	0.628783
$868$	0	0
$869$	89216.0	3.48268
$870$	0	0
$871$	1320.00	0.0513507
$872$	0	0
$873$	−10054.0	−0.389778
$874$	0	0
$875$	−875.000	−0.0338062
$876$	0	0
$877$	42950.0	1.65373	0.826863	−	0.562403i	$-0.190123\pi$
$877$	42950.0	1.65373	0.826863	+	0.562403i	$0.190123\pi$
$878$	0	0
$879$	−9720.00	−0.372978
$880$	0	0
$881$	−20558.0	−0.786171	−0.393085	−	0.919502i	$-0.628592\pi$
$881$	−20558.0	−0.786171	−0.393085	+	0.919502i	$0.628592\pi$
$882$	0	0
$883$	33228.0	1.26638	0.633189	−	0.773997i	$-0.281746\pi$
$883$	33228.0	1.26638	0.633189	+	0.773997i	$0.281746\pi$
$884$	0	0
$885$	17200.0	0.653301
$886$	0	0
$887$	−1864.00	−0.0705603	−0.0352802	−	0.999377i	$-0.511232\pi$
$887$	−1864.00	−0.0705603	−0.0352802	+	0.999377i	$0.511232\pi$
$888$	0	0
$889$	1232.00	0.0464791
$890$	0	0
$891$	−21148.0	−0.795157
$892$	0	0
$893$	−55296.0	−2.07213
$894$	0	0
$895$	−2420.00	−0.0903818
$896$	0	0
$897$	−16192.0	−0.602715
$898$	0	0
$899$	−5312.00	−0.197069
$900$	0	0
$901$	2940.00	0.108708
$902$	0	0
$903$	5936.00	0.218757
$904$	0	0
$905$	−5850.00	−0.214874
$906$	0	0
$907$	15284.0	0.559534	0.279767	−	0.960068i	$-0.409743\pi$
$907$	15284.0	0.559534	0.279767	+	0.960068i	$0.409743\pi$
$908$	0	0
$909$	−3498.00	−0.127636
$910$	0	0
$911$	−16352.0	−0.594694	−0.297347	−	0.954770i	$-0.596102\pi$
$911$	−16352.0	−0.594694	−0.297347	+	0.954770i	$0.596102\pi$
$912$	0	0
$913$	−29648.0	−1.07470
$914$	0	0
$915$	−7800.00	−0.281814
$916$	0	0
$917$	7196.00	0.259142
$918$	0	0
$919$	14040.0	0.503957	0.251979	−	0.967733i	$-0.418919\pi$
$919$	14040.0	0.503957	0.251979	+	0.967733i	$0.418919\pi$
$920$	0	0
$921$	−34352.0	−1.22903
$922$	0	0
$923$	18480.0	0.659021
$924$	0	0
$925$	−9250.00	−0.328798
$926$	0	0
$927$	3080.00	0.109127
$928$	0	0
$929$	3618.00	0.127775	0.0638874	−	0.997957i	$-0.479650\pi$
$929$	3618.00	0.127775	0.0638874	+	0.997957i	$0.479650\pi$
$930$	0	0
$931$	5292.00	0.186292
$932$	0	0
$933$	41952.0	1.47208
$934$	0	0
$935$	−10200.0	−0.356765
$936$	0	0
$937$	31626.0	1.10264	0.551321	−	0.834293i	$-0.314124\pi$
$937$	31626.0	1.10264	0.551321	+	0.834293i	$0.314124\pi$
$938$	0	0
$939$	−31464.0	−1.09349
$940$	0	0
$941$	−16170.0	−0.560177	−0.280089	−	0.959974i	$-0.590364\pi$
$941$	−16170.0	−0.560177	−0.280089	+	0.959974i	$0.590364\pi$
$942$	0	0
$943$	28336.0	0.978523
$944$	0	0
$945$	−5320.00	−0.183132
$946$	0	0
$947$	10348.0	0.355084	0.177542	−	0.984113i	$-0.443185\pi$
$947$	10348.0	0.355084	0.177542	+	0.984113i	$0.443185\pi$
$948$	0	0
$949$	−13860.0	−0.474093
$950$	0	0
$951$	−4056.00	−0.138302
$952$	0	0
$953$	−30134.0	−1.02428	−0.512139	−	0.858903i	$-0.671147\pi$
$953$	−30134.0	−1.02428	−0.512139	+	0.858903i	$0.671147\pi$
$954$	0	0
$955$	−9840.00	−0.333419
$956$	0	0
$957$	−45152.0	−1.52514
$958$	0	0
$959$	18186.0	0.612363
$960$	0	0
$961$	−28767.0	−0.965627
$962$	0	0
$963$	−9724.00	−0.325391
$964$	0	0
$965$	15530.0	0.518061
$966$	0	0
$967$	−29336.0	−0.975576	−0.487788	−	0.872962i	$-0.662196\pi$
$967$	−29336.0	−0.975576	−0.487788	+	0.872962i	$0.662196\pi$
$968$	0	0
$969$	12960.0	0.429654
$970$	0	0
$971$	16308.0	0.538979	0.269490	−	0.963003i	$-0.413145\pi$
$971$	16308.0	0.538979	0.269490	+	0.963003i	$0.413145\pi$
$972$	0	0
$973$	−16940.0	−0.558141
$974$	0	0
$975$	−2200.00	−0.0722630
$976$	0	0
$977$	−38670.0	−1.26629	−0.633144	−	0.774034i	$-0.718236\pi$
$977$	−38670.0	−1.26629	−0.633144	+	0.774034i	$0.718236\pi$
$978$	0	0
$979$	−40664.0	−1.32750
$980$	0	0
$981$	12078.0	0.393090
$982$	0	0
$983$	−22184.0	−0.719796	−0.359898	−	0.932992i	$-0.617189\pi$
$983$	−22184.0	−0.719796	−0.359898	+	0.932992i	$0.617189\pi$
$984$	0	0
$985$	550.000	0.0177913
$986$	0	0
$987$	−14336.0	−0.462330
$988$	0	0
$989$	39008.0	1.25418
$990$	0	0
$991$	7888.00	0.252846	0.126423	−	0.991976i	$-0.459650\pi$
$991$	7888.00	0.252846	0.126423	+	0.991976i	$0.459650\pi$
$992$	0	0
$993$	10480.0	0.334917
$994$	0	0
$995$	−15240.0	−0.485568
$996$	0	0
$997$	37886.0	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	37886.0	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	0	0
$999$	−56240.0	−1.78114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.4.a.c.1.1	✓	1
3.2	odd	2		1260.4.a.a.1.1		1
4.3	odd	2		560.4.a.m.1.1		1
5.2	odd	4		700.4.e.g.449.2		2
5.3	odd	4		700.4.e.g.449.1		2
5.4	even	2		700.4.a.i.1.1		1
7.2	even	3		980.4.i.m.361.1		2
7.3	odd	6		980.4.i.f.961.1		2
7.4	even	3		980.4.i.m.961.1		2
7.5	odd	6		980.4.i.f.361.1		2
7.6	odd	2		980.4.a.k.1.1		1
8.3	odd	2		2240.4.a.n.1.1		1
8.5	even	2		2240.4.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.4.a.c.1.1	✓	1	1.1	even	1	trivial
560.4.a.m.1.1		1	4.3	odd	2
700.4.a.i.1.1		1	5.4	even	2
700.4.e.g.449.1		2	5.3	odd	4
700.4.e.g.449.2		2	5.2	odd	4
980.4.a.k.1.1		1	7.6	odd	2
980.4.i.f.361.1		2	7.5	odd	6
980.4.i.f.961.1		2	7.3	odd	6
980.4.i.m.361.1		2	7.2	even	3
980.4.i.m.961.1		2	7.4	even	3
1260.4.a.a.1.1		1	3.2	odd	2
2240.4.a.n.1.1		1	8.3	odd	2
2240.4.a.x.1.1		1	8.5	even	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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	140.a (trivial)

Introduction

L-functions

Modular forms

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Fields

Representations

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Database

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