LMFDB - Embedded newform 2070.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,4,Mod(1,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, 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("2070.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2070.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:	$122.133953712$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +20.0000 q^{7} +8.00000 q^{8} -10.0000 q^{10} -6.00000 q^{11} +47.0000 q^{13} +40.0000 q^{14} +16.0000 q^{16} +132.000 q^{17} +146.000 q^{19} -20.0000 q^{20} -12.0000 q^{22} -23.0000 q^{23} +25.0000 q^{25} +94.0000 q^{26} +80.0000 q^{28} +99.0000 q^{29} -253.000 q^{31} +32.0000 q^{32} +264.000 q^{34} -100.000 q^{35} -118.000 q^{37} +292.000 q^{38} -40.0000 q^{40} -495.000 q^{41} +272.000 q^{43} -24.0000 q^{44} -46.0000 q^{46} -639.000 q^{47} +57.0000 q^{49} +50.0000 q^{50} +188.000 q^{52} +342.000 q^{53} +30.0000 q^{55} +160.000 q^{56} +198.000 q^{58} -240.000 q^{59} -370.000 q^{61} -506.000 q^{62} +64.0000 q^{64} -235.000 q^{65} +698.000 q^{67} +528.000 q^{68} -200.000 q^{70} +357.000 q^{71} -259.000 q^{73} -236.000 q^{74} +584.000 q^{76} -120.000 q^{77} +542.000 q^{79} -80.0000 q^{80} -990.000 q^{82} +1248.00 q^{83} -660.000 q^{85} +544.000 q^{86} -48.0000 q^{88} +828.000 q^{89} +940.000 q^{91} -92.0000 q^{92} -1278.00 q^{94} -730.000 q^{95} +992.000 q^{97} +114.000 q^{98} +O(q^{100})\)

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	20.0000	1.07990	0.539949	−	0.841698i	$-0.318443\pi$
$7$	20.0000	1.07990	0.539949	+	0.841698i	$0.318443\pi$
$8$	8.00000	0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	0	0
$13$	47.0000	1.00273	0.501364	−	0.865237i	$-0.332832\pi$
$13$	47.0000	1.00273	0.501364	+	0.865237i	$0.332832\pi$
$14$	40.0000	0.763604
$15$	0	0
$16$	16.0000	0.250000
$17$	132.000	1.88322	0.941609	−	0.336709i	$-0.109314\pi$
$17$	132.000	1.88322	0.941609	+	0.336709i	$0.109314\pi$
$18$	0	0
$19$	146.000	1.76288	0.881439	−	0.472297i	$-0.156575\pi$
$19$	146.000	1.76288	0.881439	+	0.472297i	$0.156575\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−12.0000	−0.116291
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	0	0
$25$	25.0000	0.200000
$26$	94.0000	0.709035
$27$	0	0
$28$	80.0000	0.539949
$29$	99.0000	0.633925	0.316963	−	0.948438i	$-0.397337\pi$
$29$	99.0000	0.633925	0.316963	+	0.948438i	$0.397337\pi$
$30$	0	0
$31$	−253.000	−1.46581	−0.732906	−	0.680330i	$-0.761836\pi$
$31$	−253.000	−1.46581	−0.732906	+	0.680330i	$0.761836\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	264.000	1.33164
$35$	−100.000	−0.482945
$36$	0	0
$37$	−118.000	−0.524299	−0.262150	−	0.965027i	$-0.584431\pi$
$37$	−118.000	−0.524299	−0.262150	+	0.965027i	$0.584431\pi$
$38$	292.000	1.24654
$39$	0	0
$40$	−40.0000	−0.158114
$41$	−495.000	−1.88551	−0.942756	−	0.333483i	$-0.891776\pi$
$41$	−495.000	−1.88551	−0.942756	+	0.333483i	$0.891776\pi$
$42$	0	0
$43$	272.000	0.964642	0.482321	−	0.875995i	$-0.339794\pi$
$43$	272.000	0.964642	0.482321	+	0.875995i	$0.339794\pi$
$44$	−24.0000	−0.0822304
$45$	0	0
$46$	−46.0000	−0.147442
$47$	−639.000	−1.98314	−0.991572	−	0.129560i	$-0.958644\pi$
$47$	−639.000	−1.98314	−0.991572	+	0.129560i	$0.958644\pi$
$48$	0	0
$49$	57.0000	0.166181
$50$	50.0000	0.141421
$51$	0	0
$52$	188.000	0.501364
$53$	342.000	0.886364	0.443182	−	0.896432i	$-0.353849\pi$
$53$	342.000	0.886364	0.443182	+	0.896432i	$0.353849\pi$
$54$	0	0
$55$	30.0000	0.0735491
$56$	160.000	0.381802
$57$	0	0
$58$	198.000	0.448253
$59$	−240.000	−0.529582	−0.264791	−	0.964306i	$-0.585303\pi$
$59$	−240.000	−0.529582	−0.264791	+	0.964306i	$0.585303\pi$
$60$	0	0
$61$	−370.000	−0.776617	−0.388309	−	0.921529i	$-0.626941\pi$
$61$	−370.000	−0.776617	−0.388309	+	0.921529i	$0.626941\pi$
$62$	−506.000	−1.03648
$63$	0	0
$64$	64.0000	0.125000
$65$	−235.000	−0.448433
$66$	0	0
$67$	698.000	1.27275	0.636375	−	0.771380i	$-0.280433\pi$
$67$	698.000	1.27275	0.636375	+	0.771380i	$0.280433\pi$
$68$	528.000	0.941609
$69$	0	0
$70$	−200.000	−0.341494
$71$	357.000	0.596734	0.298367	−	0.954451i	$-0.403558\pi$
$71$	357.000	0.596734	0.298367	+	0.954451i	$0.403558\pi$
$72$	0	0
$73$	−259.000	−0.415256	−0.207628	−	0.978208i	$-0.566574\pi$
$73$	−259.000	−0.415256	−0.207628	+	0.978208i	$0.566574\pi$
$74$	−236.000	−0.370736
$75$	0	0
$76$	584.000	0.881439
$77$	−120.000	−0.177601
$78$	0	0
$79$	542.000	0.771896	0.385948	−	0.922521i	$-0.373874\pi$
$79$	542.000	0.771896	0.385948	+	0.922521i	$0.373874\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	−990.000	−1.33326
$83$	1248.00	1.65043	0.825216	−	0.564818i	$-0.191054\pi$
$83$	1248.00	1.65043	0.825216	+	0.564818i	$0.191054\pi$
$84$	0	0
$85$	−660.000	−0.842201
$86$	544.000	0.682105
$87$	0	0
$88$	−48.0000	−0.0581456
$89$	828.000	0.986155	0.493078	−	0.869985i	$-0.335872\pi$
$89$	828.000	0.986155	0.493078	+	0.869985i	$0.335872\pi$
$90$	0	0
$91$	940.000	1.08284
$92$	−92.0000	−0.104257
$93$	0	0
$94$	−1278.00	−1.40229
$95$	−730.000	−0.788383
$96$	0	0
$97$	992.000	1.03837	0.519187	−	0.854660i	$-0.326235\pi$
$97$	992.000	1.03837	0.519187	+	0.854660i	$0.326235\pi$
$98$	114.000	0.117508
$99$	0	0
$100$	100.000	0.100000
$101$	1542.00	1.51916	0.759578	−	0.650416i	$-0.225406\pi$
$101$	1542.00	1.51916	0.759578	+	0.650416i	$0.225406\pi$
$102$	0	0
$103$	32.0000	0.0306122	0.0153061	−	0.999883i	$-0.495128\pi$
$103$	32.0000	0.0306122	0.0153061	+	0.999883i	$0.495128\pi$
$104$	376.000	0.354518
$105$	0	0
$106$	684.000	0.626754
$107$	834.000	0.753512	0.376756	−	0.926312i	$-0.377039\pi$
$107$	834.000	0.753512	0.376756	+	0.926312i	$0.377039\pi$
$108$	0	0
$109$	−1192.00	−1.04746	−0.523729	−	0.851885i	$-0.675460\pi$
$109$	−1192.00	−1.04746	−0.523729	+	0.851885i	$0.675460\pi$
$110$	60.0000	0.0520071
$111$	0	0
$112$	320.000	0.269975
$113$	132.000	0.109890	0.0549448	−	0.998489i	$-0.482502\pi$
$113$	132.000	0.109890	0.0549448	+	0.998489i	$0.482502\pi$
$114$	0	0
$115$	115.000	0.0932505
$116$	396.000	0.316963
$117$	0	0
$118$	−480.000	−0.374471
$119$	2640.00	2.03368
$120$	0	0
$121$	−1295.00	−0.972953
$122$	−740.000	−0.549151
$123$	0	0
$124$	−1012.00	−0.732906
$125$	−125.000	−0.0894427
$126$	0	0
$127$	89.0000	0.0621848	0.0310924	−	0.999517i	$-0.490101\pi$
$127$	89.0000	0.0621848	0.0310924	+	0.999517i	$0.490101\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	−470.000	−0.317090
$131$	1797.00	1.19851	0.599254	−	0.800559i	$-0.295464\pi$
$131$	1797.00	1.19851	0.599254	+	0.800559i	$0.295464\pi$
$132$	0	0
$133$	2920.00	1.90373
$134$	1396.00	0.899970
$135$	0	0
$136$	1056.00	0.665818
$137$	1836.00	1.14496	0.572482	−	0.819917i	$-0.305981\pi$
$137$	1836.00	1.14496	0.572482	+	0.819917i	$0.305981\pi$
$138$	0	0
$139$	−1027.00	−0.626683	−0.313342	−	0.949640i	$-0.601449\pi$
$139$	−1027.00	−0.626683	−0.313342	+	0.949640i	$0.601449\pi$
$140$	−400.000	−0.241473
$141$	0	0
$142$	714.000	0.421955
$143$	−282.000	−0.164909
$144$	0	0
$145$	−495.000	−0.283500
$146$	−518.000	−0.293630
$147$	0	0
$148$	−472.000	−0.262150
$149$	−2310.00	−1.27008	−0.635042	−	0.772477i	$-0.719017\pi$
$149$	−2310.00	−1.27008	−0.635042	+	0.772477i	$0.719017\pi$
$150$	0	0
$151$	−2149.00	−1.15817	−0.579083	−	0.815268i	$-0.696589\pi$
$151$	−2149.00	−1.15817	−0.579083	+	0.815268i	$0.696589\pi$
$152$	1168.00	0.623272
$153$	0	0
$154$	−240.000	−0.125583
$155$	1265.00	0.655531
$156$	0	0
$157$	1832.00	0.931271	0.465635	−	0.884977i	$-0.345826\pi$
$157$	1832.00	0.931271	0.465635	+	0.884977i	$0.345826\pi$
$158$	1084.00	0.545813
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−460.000	−0.225174
$162$	0	0
$163$	1217.00	0.584802	0.292401	−	0.956296i	$-0.405546\pi$
$163$	1217.00	0.584802	0.292401	+	0.956296i	$0.405546\pi$
$164$	−1980.00	−0.942756
$165$	0	0
$166$	2496.00	1.16703
$167$	−3048.00	−1.41234	−0.706172	−	0.708041i	$-0.749579\pi$
$167$	−3048.00	−1.41234	−0.706172	+	0.708041i	$0.749579\pi$
$168$	0	0
$169$	12.0000	0.00546199
$170$	−1320.00	−0.595526
$171$	0	0
$172$	1088.00	0.482321
$173$	−774.000	−0.340151	−0.170076	−	0.985431i	$-0.554401\pi$
$173$	−774.000	−0.340151	−0.170076	+	0.985431i	$0.554401\pi$
$174$	0	0
$175$	500.000	0.215980
$176$	−96.0000	−0.0411152
$177$	0	0
$178$	1656.00	0.697317
$179$	1875.00	0.782928	0.391464	−	0.920193i	$-0.371969\pi$
$179$	1875.00	0.782928	0.391464	+	0.920193i	$0.371969\pi$
$180$	0	0
$181$	−1606.00	−0.659520	−0.329760	−	0.944065i	$-0.606968\pi$
$181$	−1606.00	−0.659520	−0.329760	+	0.944065i	$0.606968\pi$
$182$	1880.00	0.765686
$183$	0	0
$184$	−184.000	−0.0737210
$185$	590.000	0.234474
$186$	0	0
$187$	−792.000	−0.309715
$188$	−2556.00	−0.991572
$189$	0	0
$190$	−1460.00	−0.557471
$191$	−2982.00	−1.12969	−0.564843	−	0.825199i	$-0.691063\pi$
$191$	−2982.00	−1.12969	−0.564843	+	0.825199i	$0.691063\pi$
$192$	0	0
$193$	1385.00	0.516552	0.258276	−	0.966071i	$-0.416846\pi$
$193$	1385.00	0.516552	0.258276	+	0.966071i	$0.416846\pi$
$194$	1984.00	0.734242
$195$	0	0
$196$	228.000	0.0830904
$197$	−957.000	−0.346109	−0.173054	−	0.984912i	$-0.555364\pi$
$197$	−957.000	−0.346109	−0.173054	+	0.984912i	$0.555364\pi$
$198$	0	0
$199$	−358.000	−0.127527	−0.0637637	−	0.997965i	$-0.520310\pi$
$199$	−358.000	−0.127527	−0.0637637	+	0.997965i	$0.520310\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	3084.00	1.07421
$203$	1980.00	0.684575
$204$	0	0
$205$	2475.00	0.843227
$206$	64.0000	0.0216461
$207$	0	0
$208$	752.000	0.250682
$209$	−876.000	−0.289924
$210$	0	0
$211$	−5380.00	−1.75533	−0.877665	−	0.479275i	$-0.840900\pi$
$211$	−5380.00	−1.75533	−0.877665	+	0.479275i	$0.840900\pi$
$212$	1368.00	0.443182
$213$	0	0
$214$	1668.00	0.532814
$215$	−1360.00	−0.431401
$216$	0	0
$217$	−5060.00	−1.58293
$218$	−2384.00	−0.740664
$219$	0	0
$220$	120.000	0.0367745
$221$	6204.00	1.88835
$222$	0	0
$223$	1040.00	0.312303	0.156151	−	0.987733i	$-0.450091\pi$
$223$	1040.00	0.312303	0.156151	+	0.987733i	$0.450091\pi$
$224$	640.000	0.190901
$225$	0	0
$226$	264.000	0.0777036
$227$	3744.00	1.09470	0.547352	−	0.836902i	$-0.315636\pi$
$227$	3744.00	1.09470	0.547352	+	0.836902i	$0.315636\pi$
$228$	0	0
$229$	2804.00	0.809142	0.404571	−	0.914507i	$-0.367421\pi$
$229$	2804.00	0.809142	0.404571	+	0.914507i	$0.367421\pi$
$230$	230.000	0.0659380
$231$	0	0
$232$	792.000	0.224126
$233$	4869.00	1.36901	0.684504	−	0.729009i	$-0.260019\pi$
$233$	4869.00	1.36901	0.684504	+	0.729009i	$0.260019\pi$
$234$	0	0
$235$	3195.00	0.886889
$236$	−960.000	−0.264791
$237$	0	0
$238$	5280.00	1.43803
$239$	2877.00	0.778651	0.389326	−	0.921100i	$-0.372708\pi$
$239$	2877.00	0.778651	0.389326	+	0.921100i	$0.372708\pi$
$240$	0	0
$241$	1622.00	0.433536	0.216768	−	0.976223i	$-0.430448\pi$
$241$	1622.00	0.433536	0.216768	+	0.976223i	$0.430448\pi$
$242$	−2590.00	−0.687981
$243$	0	0
$244$	−1480.00	−0.388309
$245$	−285.000	−0.0743183
$246$	0	0
$247$	6862.00	1.76769
$248$	−2024.00	−0.518242
$249$	0	0
$250$	−250.000	−0.0632456
$251$	4752.00	1.19499	0.597497	−	0.801871i	$-0.296162\pi$
$251$	4752.00	1.19499	0.597497	+	0.801871i	$0.296162\pi$
$252$	0	0
$253$	138.000	0.0342924
$254$	178.000	0.0439713
$255$	0	0
$256$	256.000	0.0625000
$257$	5073.00	1.23130	0.615652	−	0.788018i	$-0.288893\pi$
$257$	5073.00	1.23130	0.615652	+	0.788018i	$0.288893\pi$
$258$	0	0
$259$	−2360.00	−0.566190
$260$	−940.000	−0.224217
$261$	0	0
$262$	3594.00	0.847474
$263$	−1314.00	−0.308079	−0.154039	−	0.988065i	$-0.549228\pi$
$263$	−1314.00	−0.308079	−0.154039	+	0.988065i	$0.549228\pi$
$264$	0	0
$265$	−1710.00	−0.396394
$266$	5840.00	1.34614
$267$	0	0
$268$	2792.00	0.636375
$269$	−5265.00	−1.19336	−0.596678	−	0.802481i	$-0.703513\pi$
$269$	−5265.00	−1.19336	−0.596678	+	0.802481i	$0.703513\pi$
$270$	0	0
$271$	−2488.00	−0.557695	−0.278847	−	0.960335i	$-0.589952\pi$
$271$	−2488.00	−0.557695	−0.278847	+	0.960335i	$0.589952\pi$
$272$	2112.00	0.470804
$273$	0	0
$274$	3672.00	0.809612
$275$	−150.000	−0.0328921
$276$	0	0
$277$	5465.00	1.18542	0.592708	−	0.805418i	$-0.298059\pi$
$277$	5465.00	1.18542	0.592708	+	0.805418i	$0.298059\pi$
$278$	−2054.00	−0.443132
$279$	0	0
$280$	−800.000	−0.170747
$281$	−8940.00	−1.89792	−0.948960	−	0.315396i	$-0.897863\pi$
$281$	−8940.00	−1.89792	−0.948960	+	0.315396i	$0.897863\pi$
$282$	0	0
$283$	842.000	0.176861	0.0884306	−	0.996082i	$-0.471815\pi$
$283$	842.000	0.176861	0.0884306	+	0.996082i	$0.471815\pi$
$284$	1428.00	0.298367
$285$	0	0
$286$	−564.000	−0.116608
$287$	−9900.00	−2.03616
$288$	0	0
$289$	12511.0	2.54651
$290$	−990.000	−0.200465
$291$	0	0
$292$	−1036.00	−0.207628
$293$	4032.00	0.803932	0.401966	−	0.915655i	$-0.368327\pi$
$293$	4032.00	0.803932	0.401966	+	0.915655i	$0.368327\pi$
$294$	0	0
$295$	1200.00	0.236836
$296$	−944.000	−0.185368
$297$	0	0
$298$	−4620.00	−0.898085
$299$	−1081.00	−0.209083
$300$	0	0
$301$	5440.00	1.04172
$302$	−4298.00	−0.818947
$303$	0	0
$304$	2336.00	0.440720
$305$	1850.00	0.347314
$306$	0	0
$307$	−1096.00	−0.203753	−0.101876	−	0.994797i	$-0.532485\pi$
$307$	−1096.00	−0.203753	−0.101876	+	0.994797i	$0.532485\pi$
$308$	−480.000	−0.0888004
$309$	0	0
$310$	2530.00	0.463530
$311$	4653.00	0.848384	0.424192	−	0.905572i	$-0.360558\pi$
$311$	4653.00	0.848384	0.424192	+	0.905572i	$0.360558\pi$
$312$	0	0
$313$	3440.00	0.621215	0.310608	−	0.950538i	$-0.399468\pi$
$313$	3440.00	0.621215	0.310608	+	0.950538i	$0.399468\pi$
$314$	3664.00	0.658508
$315$	0	0
$316$	2168.00	0.385948
$317$	−3066.00	−0.543229	−0.271615	−	0.962406i	$-0.587558\pi$
$317$	−3066.00	−0.543229	−0.271615	+	0.962406i	$0.587558\pi$
$318$	0	0
$319$	−594.000	−0.104256
$320$	−320.000	−0.0559017
$321$	0	0
$322$	−920.000	−0.159222
$323$	19272.0	3.31988
$324$	0	0
$325$	1175.00	0.200545
$326$	2434.00	0.413518
$327$	0	0
$328$	−3960.00	−0.666629
$329$	−12780.0	−2.14159
$330$	0	0
$331$	1505.00	0.249916	0.124958	−	0.992162i	$-0.460120\pi$
$331$	1505.00	0.249916	0.124958	+	0.992162i	$0.460120\pi$
$332$	4992.00	0.825216
$333$	0	0
$334$	−6096.00	−0.998677
$335$	−3490.00	−0.569191
$336$	0	0
$337$	−3268.00	−0.528247	−0.264124	−	0.964489i	$-0.585083\pi$
$337$	−3268.00	−0.528247	−0.264124	+	0.964489i	$0.585083\pi$
$338$	24.0000	0.00386221
$339$	0	0
$340$	−2640.00	−0.421100
$341$	1518.00	0.241068
$342$	0	0
$343$	−5720.00	−0.900440
$344$	2176.00	0.341052
$345$	0	0
$346$	−1548.00	−0.240523
$347$	−4164.00	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−4164.00	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−2911.00	−0.446482	−0.223241	−	0.974763i	$-0.571664\pi$
$349$	−2911.00	−0.446482	−0.223241	+	0.974763i	$0.571664\pi$
$350$	1000.00	0.152721
$351$	0	0
$352$	−192.000	−0.0290728
$353$	−9753.00	−1.47054	−0.735269	−	0.677776i	$-0.762944\pi$
$353$	−9753.00	−1.47054	−0.735269	+	0.677776i	$0.762944\pi$
$354$	0	0
$355$	−1785.00	−0.266868
$356$	3312.00	0.493078
$357$	0	0
$358$	3750.00	0.553614
$359$	−3858.00	−0.567180	−0.283590	−	0.958946i	$-0.591525\pi$
$359$	−3858.00	−0.567180	−0.283590	+	0.958946i	$0.591525\pi$
$360$	0	0
$361$	14457.0	2.10774
$362$	−3212.00	−0.466351
$363$	0	0
$364$	3760.00	0.541422
$365$	1295.00	0.185708
$366$	0	0
$367$	7856.00	1.11738	0.558692	−	0.829375i	$-0.311303\pi$
$367$	7856.00	1.11738	0.558692	+	0.829375i	$0.311303\pi$
$368$	−368.000	−0.0521286
$369$	0	0
$370$	1180.00	0.165798
$371$	6840.00	0.957184
$372$	0	0
$373$	−34.0000	−0.00471971	−0.00235986	−	0.999997i	$-0.500751\pi$
$373$	−34.0000	−0.00471971	−0.00235986	+	0.999997i	$0.500751\pi$
$374$	−1584.00	−0.219002
$375$	0	0
$376$	−5112.00	−0.701147
$377$	4653.00	0.635654
$378$	0	0
$379$	−6064.00	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−6064.00	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	−2920.00	−0.394192
$381$	0	0
$382$	−5964.00	−0.798808
$383$	−11868.0	−1.58336	−0.791679	−	0.610937i	$-0.790793\pi$
$383$	−11868.0	−1.58336	−0.791679	+	0.610937i	$0.790793\pi$
$384$	0	0
$385$	600.000	0.0794255
$386$	2770.00	0.365257
$387$	0	0
$388$	3968.00	0.519187
$389$	−8616.00	−1.12300	−0.561502	−	0.827475i	$-0.689776\pi$
$389$	−8616.00	−1.12300	−0.561502	+	0.827475i	$0.689776\pi$
$390$	0	0
$391$	−3036.00	−0.392678
$392$	456.000	0.0587538
$393$	0	0
$394$	−1914.00	−0.244736
$395$	−2710.00	−0.345202
$396$	0	0
$397$	3119.00	0.394303	0.197151	−	0.980373i	$-0.436831\pi$
$397$	3119.00	0.394303	0.197151	+	0.980373i	$0.436831\pi$
$398$	−716.000	−0.0901755
$399$	0	0
$400$	400.000	0.0500000
$401$	−7986.00	−0.994518	−0.497259	−	0.867602i	$-0.665660\pi$
$401$	−7986.00	−0.994518	−0.497259	+	0.867602i	$0.665660\pi$
$402$	0	0
$403$	−11891.0	−1.46981
$404$	6168.00	0.759578
$405$	0	0
$406$	3960.00	0.484068
$407$	708.000	0.0862267
$408$	0	0
$409$	−3475.00	−0.420117	−0.210058	−	0.977689i	$-0.567365\pi$
$409$	−3475.00	−0.420117	−0.210058	+	0.977689i	$0.567365\pi$
$410$	4950.00	0.596251
$411$	0	0
$412$	128.000	0.0153061
$413$	−4800.00	−0.571895
$414$	0	0
$415$	−6240.00	−0.738095
$416$	1504.00	0.177259
$417$	0	0
$418$	−1752.00	−0.205007
$419$	−10992.0	−1.28161	−0.640805	−	0.767704i	$-0.721399\pi$
$419$	−10992.0	−1.28161	−0.640805	+	0.767704i	$0.721399\pi$
$420$	0	0
$421$	2012.00	0.232919	0.116459	−	0.993195i	$-0.462845\pi$
$421$	2012.00	0.232919	0.116459	+	0.993195i	$0.462845\pi$
$422$	−10760.0	−1.24121
$423$	0	0
$424$	2736.00	0.313377
$425$	3300.00	0.376644
$426$	0	0
$427$	−7400.00	−0.838668
$428$	3336.00	0.376756
$429$	0	0
$430$	−2720.00	−0.305047
$431$	9792.00	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$432$	0	0
$433$	5786.00	0.642165	0.321082	−	0.947051i	$-0.395953\pi$
$433$	5786.00	0.642165	0.321082	+	0.947051i	$0.395953\pi$
$434$	−10120.0	−1.11930
$435$	0	0
$436$	−4768.00	−0.523729
$437$	−3358.00	−0.367586
$438$	0	0
$439$	2549.00	0.277123	0.138562	−	0.990354i	$-0.455752\pi$
$439$	2549.00	0.277123	0.138562	+	0.990354i	$0.455752\pi$
$440$	240.000	0.0260035
$441$	0	0
$442$	12408.0	1.33527
$443$	−1311.00	−0.140604	−0.0703019	−	0.997526i	$-0.522396\pi$
$443$	−1311.00	−0.140604	−0.0703019	+	0.997526i	$0.522396\pi$
$444$	0	0
$445$	−4140.00	−0.441022
$446$	2080.00	0.220832
$447$	0	0
$448$	1280.00	0.134987
$449$	14610.0	1.53561	0.767805	−	0.640684i	$-0.221349\pi$
$449$	14610.0	1.53561	0.767805	+	0.640684i	$0.221349\pi$
$450$	0	0
$451$	2970.00	0.310093
$452$	528.000	0.0549448
$453$	0	0
$454$	7488.00	0.774073
$455$	−4700.00	−0.484262
$456$	0	0
$457$	80.0000	0.00818871	0.00409436	−	0.999992i	$-0.498697\pi$
$457$	80.0000	0.00818871	0.00409436	+	0.999992i	$0.498697\pi$
$458$	5608.00	0.572150
$459$	0	0
$460$	460.000	0.0466252
$461$	2343.00	0.236712	0.118356	−	0.992971i	$-0.462238\pi$
$461$	2343.00	0.236712	0.118356	+	0.992971i	$0.462238\pi$
$462$	0	0
$463$	−3400.00	−0.341277	−0.170639	−	0.985334i	$-0.554583\pi$
$463$	−3400.00	−0.341277	−0.170639	+	0.985334i	$0.554583\pi$
$464$	1584.00	0.158481
$465$	0	0
$466$	9738.00	0.968035
$467$	1374.00	0.136148	0.0680740	−	0.997680i	$-0.478315\pi$
$467$	1374.00	0.136148	0.0680740	+	0.997680i	$0.478315\pi$
$468$	0	0
$469$	13960.0	1.37444
$470$	6390.00	0.627125
$471$	0	0
$472$	−1920.00	−0.187236
$473$	−1632.00	−0.158646
$474$	0	0
$475$	3650.00	0.352576
$476$	10560.0	1.01684
$477$	0	0
$478$	5754.00	0.550590
$479$	−4536.00	−0.432683	−0.216341	−	0.976318i	$-0.569412\pi$
$479$	−4536.00	−0.432683	−0.216341	+	0.976318i	$0.569412\pi$
$480$	0	0
$481$	−5546.00	−0.525729
$482$	3244.00	0.306556
$483$	0	0
$484$	−5180.00	−0.486476
$485$	−4960.00	−0.464375
$486$	0	0
$487$	−11455.0	−1.06586	−0.532932	−	0.846158i	$-0.678910\pi$
$487$	−11455.0	−1.06586	−0.532932	+	0.846158i	$0.678910\pi$
$488$	−2960.00	−0.274576
$489$	0	0
$490$	−570.000	−0.0525510
$491$	10395.0	0.955437	0.477719	−	0.878513i	$-0.341464\pi$
$491$	10395.0	0.955437	0.477719	+	0.878513i	$0.341464\pi$
$492$	0	0
$493$	13068.0	1.19382
$494$	13724.0	1.24994
$495$	0	0
$496$	−4048.00	−0.366453
$497$	7140.00	0.644412
$498$	0	0
$499$	−5497.00	−0.493145	−0.246573	−	0.969124i	$-0.579304\pi$
$499$	−5497.00	−0.493145	−0.246573	+	0.969124i	$0.579304\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	9504.00	0.844989
$503$	−7158.00	−0.634512	−0.317256	−	0.948340i	$-0.602761\pi$
$503$	−7158.00	−0.634512	−0.317256	+	0.948340i	$0.602761\pi$
$504$	0	0
$505$	−7710.00	−0.679387
$506$	276.000	0.0242484
$507$	0	0
$508$	356.000	0.0310924
$509$	−12801.0	−1.11472	−0.557362	−	0.830270i	$-0.688186\pi$
$509$	−12801.0	−1.11472	−0.557362	+	0.830270i	$0.688186\pi$
$510$	0	0
$511$	−5180.00	−0.448434
$512$	512.000	0.0441942
$513$	0	0
$514$	10146.0	0.870663
$515$	−160.000	−0.0136902
$516$	0	0
$517$	3834.00	0.326149
$518$	−4720.00	−0.400357
$519$	0	0
$520$	−1880.00	−0.158545
$521$	−16788.0	−1.41170	−0.705850	−	0.708361i	$-0.749435\pi$
$521$	−16788.0	−1.41170	−0.705850	+	0.708361i	$0.749435\pi$
$522$	0	0
$523$	19040.0	1.59189	0.795947	−	0.605366i	$-0.206973\pi$
$523$	19040.0	1.59189	0.795947	+	0.605366i	$0.206973\pi$
$524$	7188.00	0.599254
$525$	0	0
$526$	−2628.00	−0.217845
$527$	−33396.0	−2.76044
$528$	0	0
$529$	529.000	0.0434783
$530$	−3420.00	−0.280293
$531$	0	0
$532$	11680.0	0.951865
$533$	−23265.0	−1.89065
$534$	0	0
$535$	−4170.00	−0.336981
$536$	5584.00	0.449985
$537$	0	0
$538$	−10530.0	−0.843830
$539$	−342.000	−0.0273302
$540$	0	0
$541$	−13339.0	−1.06005	−0.530026	−	0.847981i	$-0.677818\pi$
$541$	−13339.0	−1.06005	−0.530026	+	0.847981i	$0.677818\pi$
$542$	−4976.00	−0.394350
$543$	0	0
$544$	4224.00	0.332909
$545$	5960.00	0.468437
$546$	0	0
$547$	−22975.0	−1.79587	−0.897934	−	0.440130i	$-0.854932\pi$
$547$	−22975.0	−1.79587	−0.897934	+	0.440130i	$0.854932\pi$
$548$	7344.00	0.572482
$549$	0	0
$550$	−300.000	−0.0232583
$551$	14454.0	1.11753
$552$	0	0
$553$	10840.0	0.833569
$554$	10930.0	0.838215
$555$	0	0
$556$	−4108.00	−0.313342
$557$	17964.0	1.36653	0.683267	−	0.730169i	$-0.260559\pi$
$557$	17964.0	1.36653	0.683267	+	0.730169i	$0.260559\pi$
$558$	0	0
$559$	12784.0	0.967273
$560$	−1600.00	−0.120736
$561$	0	0
$562$	−17880.0	−1.34203
$563$	−12636.0	−0.945904	−0.472952	−	0.881088i	$-0.656812\pi$
$563$	−12636.0	−0.945904	−0.472952	+	0.881088i	$0.656812\pi$
$564$	0	0
$565$	−660.000	−0.0491441
$566$	1684.00	0.125060
$567$	0	0
$568$	2856.00	0.210977
$569$	10302.0	0.759020	0.379510	−	0.925188i	$-0.376093\pi$
$569$	10302.0	0.759020	0.379510	+	0.925188i	$0.376093\pi$
$570$	0	0
$571$	12380.0	0.907333	0.453666	−	0.891172i	$-0.350116\pi$
$571$	12380.0	0.907333	0.453666	+	0.891172i	$0.350116\pi$
$572$	−1128.00	−0.0824546
$573$	0	0
$574$	−19800.0	−1.43978
$575$	−575.000	−0.0417029
$576$	0	0
$577$	1913.00	0.138023	0.0690115	−	0.997616i	$-0.478015\pi$
$577$	1913.00	0.138023	0.0690115	+	0.997616i	$0.478015\pi$
$578$	25022.0	1.80065
$579$	0	0
$580$	−1980.00	−0.141750
$581$	24960.0	1.78230
$582$	0	0
$583$	−2052.00	−0.145772
$584$	−2072.00	−0.146815
$585$	0	0
$586$	8064.00	0.568465
$587$	−16767.0	−1.17896	−0.589479	−	0.807784i	$-0.700667\pi$
$587$	−16767.0	−1.17896	−0.589479	+	0.807784i	$0.700667\pi$
$588$	0	0
$589$	−36938.0	−2.58405
$590$	2400.00	0.167469
$591$	0	0
$592$	−1888.00	−0.131075
$593$	16722.0	1.15799	0.578997	−	0.815330i	$-0.303444\pi$
$593$	16722.0	1.15799	0.578997	+	0.815330i	$0.303444\pi$
$594$	0	0
$595$	−13200.0	−0.909491
$596$	−9240.00	−0.635042
$597$	0	0
$598$	−2162.00	−0.147844
$599$	4200.00	0.286490	0.143245	−	0.989687i	$-0.454246\pi$
$599$	4200.00	0.286490	0.143245	+	0.989687i	$0.454246\pi$
$600$	0	0
$601$	−19915.0	−1.35166	−0.675832	−	0.737056i	$-0.736215\pi$
$601$	−19915.0	−1.35166	−0.675832	+	0.737056i	$0.736215\pi$
$602$	10880.0	0.736604
$603$	0	0
$604$	−8596.00	−0.579083
$605$	6475.00	0.435118
$606$	0	0
$607$	24044.0	1.60777	0.803885	−	0.594785i	$-0.202763\pi$
$607$	24044.0	1.60777	0.803885	+	0.594785i	$0.202763\pi$
$608$	4672.00	0.311636
$609$	0	0
$610$	3700.00	0.245588
$611$	−30033.0	−1.98855
$612$	0	0
$613$	3452.00	0.227447	0.113723	−	0.993512i	$-0.463722\pi$
$613$	3452.00	0.227447	0.113723	+	0.993512i	$0.463722\pi$
$614$	−2192.00	−0.144075
$615$	0	0
$616$	−960.000	−0.0627914
$617$	16374.0	1.06838	0.534192	−	0.845363i	$-0.320616\pi$
$617$	16374.0	1.06838	0.534192	+	0.845363i	$0.320616\pi$
$618$	0	0
$619$	−12760.0	−0.828542	−0.414271	−	0.910154i	$-0.635963\pi$
$619$	−12760.0	−0.828542	−0.414271	+	0.910154i	$0.635963\pi$
$620$	5060.00	0.327765
$621$	0	0
$622$	9306.00	0.599898
$623$	16560.0	1.06495
$624$	0	0
$625$	625.000	0.0400000
$626$	6880.00	0.439265
$627$	0	0
$628$	7328.00	0.465635
$629$	−15576.0	−0.987370
$630$	0	0
$631$	29420.0	1.85609	0.928044	−	0.372470i	$-0.121489\pi$
$631$	29420.0	1.85609	0.928044	+	0.372470i	$0.121489\pi$
$632$	4336.00	0.272906
$633$	0	0
$634$	−6132.00	−0.384121
$635$	−445.000	−0.0278099
$636$	0	0
$637$	2679.00	0.166634
$638$	−1188.00	−0.0737200
$639$	0	0
$640$	−640.000	−0.0395285
$641$	13692.0	0.843684	0.421842	−	0.906669i	$-0.361384\pi$
$641$	13692.0	0.843684	0.421842	+	0.906669i	$0.361384\pi$
$642$	0	0
$643$	27398.0	1.68036	0.840180	−	0.542307i	$-0.182449\pi$
$643$	27398.0	1.68036	0.840180	+	0.542307i	$0.182449\pi$
$644$	−1840.00	−0.112587
$645$	0	0
$646$	38544.0	2.34751
$647$	6417.00	0.389920	0.194960	−	0.980811i	$-0.437542\pi$
$647$	6417.00	0.389920	0.194960	+	0.980811i	$0.437542\pi$
$648$	0	0
$649$	1440.00	0.0870954
$650$	2350.00	0.141807
$651$	0	0
$652$	4868.00	0.292401
$653$	−14583.0	−0.873931	−0.436965	−	0.899478i	$-0.643947\pi$
$653$	−14583.0	−0.873931	−0.436965	+	0.899478i	$0.643947\pi$
$654$	0	0
$655$	−8985.00	−0.535989
$656$	−7920.00	−0.471378
$657$	0	0
$658$	−25560.0	−1.51434
$659$	9624.00	0.568889	0.284444	−	0.958693i	$-0.408191\pi$
$659$	9624.00	0.568889	0.284444	+	0.958693i	$0.408191\pi$
$660$	0	0
$661$	−24586.0	−1.44672	−0.723362	−	0.690469i	$-0.757404\pi$
$661$	−24586.0	−1.44672	−0.723362	+	0.690469i	$0.757404\pi$
$662$	3010.00	0.176717
$663$	0	0
$664$	9984.00	0.583516
$665$	−14600.0	−0.851374
$666$	0	0
$667$	−2277.00	−0.132183
$668$	−12192.0	−0.706172
$669$	0	0
$670$	−6980.00	−0.402479
$671$	2220.00	0.127723
$672$	0	0
$673$	14339.0	0.821289	0.410645	−	0.911795i	$-0.365304\pi$
$673$	14339.0	0.821289	0.410645	+	0.911795i	$0.365304\pi$
$674$	−6536.00	−0.373527
$675$	0	0
$676$	48.0000	0.00273100
$677$	−14658.0	−0.832131	−0.416066	−	0.909335i	$-0.636591\pi$
$677$	−14658.0	−0.832131	−0.416066	+	0.909335i	$0.636591\pi$
$678$	0	0
$679$	19840.0	1.12134
$680$	−5280.00	−0.297763
$681$	0	0
$682$	3036.00	0.170461
$683$	−16797.0	−0.941024	−0.470512	−	0.882394i	$-0.655931\pi$
$683$	−16797.0	−0.941024	−0.470512	+	0.882394i	$0.655931\pi$
$684$	0	0
$685$	−9180.00	−0.512043
$686$	−11440.0	−0.636707
$687$	0	0
$688$	4352.00	0.241161
$689$	16074.0	0.888782
$690$	0	0
$691$	8132.00	0.447693	0.223846	−	0.974624i	$-0.428139\pi$
$691$	8132.00	0.447693	0.223846	+	0.974624i	$0.428139\pi$
$692$	−3096.00	−0.170076
$693$	0	0
$694$	−8328.00	−0.455514
$695$	5135.00	0.280261
$696$	0	0
$697$	−65340.0	−3.55083
$698$	−5822.00	−0.315711
$699$	0	0
$700$	2000.00	0.107990
$701$	−19668.0	−1.05970	−0.529850	−	0.848091i	$-0.677752\pi$
$701$	−19668.0	−1.05970	−0.529850	+	0.848091i	$0.677752\pi$
$702$	0	0
$703$	−17228.0	−0.924276
$704$	−384.000	−0.0205576
$705$	0	0
$706$	−19506.0	−1.03983
$707$	30840.0	1.64053
$708$	0	0
$709$	18200.0	0.964055	0.482028	−	0.876156i	$-0.339900\pi$
$709$	18200.0	0.964055	0.482028	+	0.876156i	$0.339900\pi$
$710$	−3570.00	−0.188704
$711$	0	0
$712$	6624.00	0.348659
$713$	5819.00	0.305643
$714$	0	0
$715$	1410.00	0.0737497
$716$	7500.00	0.391464
$717$	0	0
$718$	−7716.00	−0.401056
$719$	11880.0	0.616202	0.308101	−	0.951354i	$-0.400307\pi$
$719$	11880.0	0.616202	0.308101	+	0.951354i	$0.400307\pi$
$720$	0	0
$721$	640.000	0.0330580
$722$	28914.0	1.49040
$723$	0	0
$724$	−6424.00	−0.329760
$725$	2475.00	0.126785
$726$	0	0
$727$	−2554.00	−0.130292	−0.0651462	−	0.997876i	$-0.520751\pi$
$727$	−2554.00	−0.130292	−0.0651462	+	0.997876i	$0.520751\pi$
$728$	7520.00	0.382843
$729$	0	0
$730$	2590.00	0.131315
$731$	35904.0	1.81663
$732$	0	0
$733$	6308.00	0.317860	0.158930	−	0.987290i	$-0.449196\pi$
$733$	6308.00	0.317860	0.158930	+	0.987290i	$0.449196\pi$
$734$	15712.0	0.790110
$735$	0	0
$736$	−736.000	−0.0368605
$737$	−4188.00	−0.209317
$738$	0	0
$739$	9557.00	0.475724	0.237862	−	0.971299i	$-0.423553\pi$
$739$	9557.00	0.475724	0.237862	+	0.971299i	$0.423553\pi$
$740$	2360.00	0.117237
$741$	0	0
$742$	13680.0	0.676831
$743$	−19128.0	−0.944466	−0.472233	−	0.881474i	$-0.656552\pi$
$743$	−19128.0	−0.944466	−0.472233	+	0.881474i	$0.656552\pi$
$744$	0	0
$745$	11550.0	0.567999
$746$	−68.0000	−0.00333734
$747$	0	0
$748$	−3168.00	−0.154858
$749$	16680.0	0.813717
$750$	0	0
$751$	−18448.0	−0.896374	−0.448187	−	0.893940i	$-0.647930\pi$
$751$	−18448.0	−0.896374	−0.448187	+	0.893940i	$0.647930\pi$
$752$	−10224.0	−0.495786
$753$	0	0
$754$	9306.00	0.449476
$755$	10745.0	0.517948
$756$	0	0
$757$	−5602.00	−0.268967	−0.134484	−	0.990916i	$-0.542938\pi$
$757$	−5602.00	−0.268967	−0.134484	+	0.990916i	$0.542938\pi$
$758$	−12128.0	−0.581146
$759$	0	0
$760$	−5840.00	−0.278736
$761$	−4005.00	−0.190777	−0.0953884	−	0.995440i	$-0.530409\pi$
$761$	−4005.00	−0.190777	−0.0953884	+	0.995440i	$0.530409\pi$
$762$	0	0
$763$	−23840.0	−1.13115
$764$	−11928.0	−0.564843
$765$	0	0
$766$	−23736.0	−1.11960
$767$	−11280.0	−0.531026
$768$	0	0
$769$	41726.0	1.95667	0.978334	−	0.207032i	$-0.0663803\pi$
$769$	41726.0	1.95667	0.978334	+	0.207032i	$0.0663803\pi$
$770$	1200.00	0.0561623
$771$	0	0
$772$	5540.00	0.258276
$773$	−34116.0	−1.58741	−0.793705	−	0.608303i	$-0.791850\pi$
$773$	−34116.0	−1.58741	−0.793705	+	0.608303i	$0.791850\pi$
$774$	0	0
$775$	−6325.00	−0.293162
$776$	7936.00	0.367121
$777$	0	0
$778$	−17232.0	−0.794084
$779$	−72270.0	−3.32393
$780$	0	0
$781$	−2142.00	−0.0981393
$782$	−6072.00	−0.277665
$783$	0	0
$784$	912.000	0.0415452
$785$	−9160.00	−0.416477
$786$	0	0
$787$	1652.00	0.0748252	0.0374126	−	0.999300i	$-0.488088\pi$
$787$	1652.00	0.0748252	0.0374126	+	0.999300i	$0.488088\pi$
$788$	−3828.00	−0.173054
$789$	0	0
$790$	−5420.00	−0.244095
$791$	2640.00	0.118670
$792$	0	0
$793$	−17390.0	−0.778735
$794$	6238.00	0.278814
$795$	0	0
$796$	−1432.00	−0.0637637
$797$	−12486.0	−0.554927	−0.277463	−	0.960736i	$-0.589494\pi$
$797$	−12486.0	−0.554927	−0.277463	+	0.960736i	$0.589494\pi$
$798$	0	0
$799$	−84348.0	−3.73469
$800$	800.000	0.0353553
$801$	0	0
$802$	−15972.0	−0.703231
$803$	1554.00	0.0682932
$804$	0	0
$805$	2300.00	0.100701
$806$	−23782.0	−1.03931
$807$	0	0
$808$	12336.0	0.537103
$809$	−5490.00	−0.238589	−0.119294	−	0.992859i	$-0.538063\pi$
$809$	−5490.00	−0.238589	−0.119294	+	0.992859i	$0.538063\pi$
$810$	0	0
$811$	−14785.0	−0.640162	−0.320081	−	0.947390i	$-0.603710\pi$
$811$	−14785.0	−0.640162	−0.320081	+	0.947390i	$0.603710\pi$
$812$	7920.00	0.342288
$813$	0	0
$814$	1416.00	0.0609715
$815$	−6085.00	−0.261532
$816$	0	0
$817$	39712.0	1.70055
$818$	−6950.00	−0.297067
$819$	0	0
$820$	9900.00	0.421613
$821$	12486.0	0.530773	0.265386	−	0.964142i	$-0.414500\pi$
$821$	12486.0	0.530773	0.265386	+	0.964142i	$0.414500\pi$
$822$	0	0
$823$	−39805.0	−1.68592	−0.842962	−	0.537973i	$-0.819190\pi$
$823$	−39805.0	−1.68592	−0.842962	+	0.537973i	$0.819190\pi$
$824$	256.000	0.0108230
$825$	0	0
$826$	−9600.00	−0.404391
$827$	−15024.0	−0.631724	−0.315862	−	0.948805i	$-0.602294\pi$
$827$	−15024.0	−0.631724	−0.315862	+	0.948805i	$0.602294\pi$
$828$	0	0
$829$	14618.0	0.612430	0.306215	−	0.951962i	$-0.400937\pi$
$829$	14618.0	0.612430	0.306215	+	0.951962i	$0.400937\pi$
$830$	−12480.0	−0.521912
$831$	0	0
$832$	3008.00	0.125341
$833$	7524.00	0.312955
$834$	0	0
$835$	15240.0	0.631619
$836$	−3504.00	−0.144962
$837$	0	0
$838$	−21984.0	−0.906235
$839$	10152.0	0.417743	0.208871	−	0.977943i	$-0.433021\pi$
$839$	10152.0	0.417743	0.208871	+	0.977943i	$0.433021\pi$
$840$	0	0
$841$	−14588.0	−0.598139
$842$	4024.00	0.164699
$843$	0	0
$844$	−21520.0	−0.877665
$845$	−60.0000	−0.00244268
$846$	0	0
$847$	−25900.0	−1.05069
$848$	5472.00	0.221591
$849$	0	0
$850$	6600.00	0.266327
$851$	2714.00	0.109324
$852$	0	0
$853$	−22306.0	−0.895361	−0.447680	−	0.894194i	$-0.647750\pi$
$853$	−22306.0	−0.895361	−0.447680	+	0.894194i	$0.647750\pi$
$854$	−14800.0	−0.593028
$855$	0	0
$856$	6672.00	0.266407
$857$	−1731.00	−0.0689963	−0.0344982	−	0.999405i	$-0.510983\pi$
$857$	−1731.00	−0.0689963	−0.0344982	+	0.999405i	$0.510983\pi$
$858$	0	0
$859$	−12649.0	−0.502419	−0.251210	−	0.967933i	$-0.580828\pi$
$859$	−12649.0	−0.502419	−0.251210	+	0.967933i	$0.580828\pi$
$860$	−5440.00	−0.215701
$861$	0	0
$862$	19584.0	0.773821
$863$	16143.0	0.636749	0.318374	−	0.947965i	$-0.396863\pi$
$863$	16143.0	0.636749	0.318374	+	0.947965i	$0.396863\pi$
$864$	0	0
$865$	3870.00	0.152120
$866$	11572.0	0.454079
$867$	0	0
$868$	−20240.0	−0.791464
$869$	−3252.00	−0.126947
$870$	0	0
$871$	32806.0	1.27622
$872$	−9536.00	−0.370332
$873$	0	0
$874$	−6716.00	−0.259922
$875$	−2500.00	−0.0965891
$876$	0	0
$877$	4094.00	0.157633	0.0788167	−	0.996889i	$-0.474886\pi$
$877$	4094.00	0.157633	0.0788167	+	0.996889i	$0.474886\pi$
$878$	5098.00	0.195956
$879$	0	0
$880$	480.000	0.0183873
$881$	−30396.0	−1.16239	−0.581196	−	0.813764i	$-0.697415\pi$
$881$	−30396.0	−1.16239	−0.581196	+	0.813764i	$0.697415\pi$
$882$	0	0
$883$	−21148.0	−0.805987	−0.402994	−	0.915203i	$-0.632030\pi$
$883$	−21148.0	−0.805987	−0.402994	+	0.915203i	$0.632030\pi$
$884$	24816.0	0.944177
$885$	0	0
$886$	−2622.00	−0.0994219
$887$	−5031.00	−0.190445	−0.0952223	−	0.995456i	$-0.530356\pi$
$887$	−5031.00	−0.190445	−0.0952223	+	0.995456i	$0.530356\pi$
$888$	0	0
$889$	1780.00	0.0671533
$890$	−8280.00	−0.311850
$891$	0	0
$892$	4160.00	0.156151
$893$	−93294.0	−3.49604
$894$	0	0
$895$	−9375.00	−0.350136
$896$	2560.00	0.0954504
$897$	0	0
$898$	29220.0	1.08584
$899$	−25047.0	−0.929215
$900$	0	0
$901$	45144.0	1.66922
$902$	5940.00	0.219269
$903$	0	0
$904$	1056.00	0.0388518
$905$	8030.00	0.294946
$906$	0	0
$907$	−538.000	−0.0196957	−0.00984785	−	0.999952i	$-0.503135\pi$
$907$	−538.000	−0.0196957	−0.00984785	+	0.999952i	$0.503135\pi$
$908$	14976.0	0.547352
$909$	0	0
$910$	−9400.00	−0.342425
$911$	−3078.00	−0.111941	−0.0559707	−	0.998432i	$-0.517825\pi$
$911$	−3078.00	−0.111941	−0.0559707	+	0.998432i	$0.517825\pi$
$912$	0	0
$913$	−7488.00	−0.271431
$914$	160.000	0.00579029
$915$	0	0
$916$	11216.0	0.404571
$917$	35940.0	1.29427
$918$	0	0
$919$	20288.0	0.728226	0.364113	−	0.931355i	$-0.381372\pi$
$919$	20288.0	0.728226	0.364113	+	0.931355i	$0.381372\pi$
$920$	920.000	0.0329690
$921$	0	0
$922$	4686.00	0.167381
$923$	16779.0	0.598361
$924$	0	0
$925$	−2950.00	−0.104860
$926$	−6800.00	−0.241320
$927$	0	0
$928$	3168.00	0.112063
$929$	−28911.0	−1.02103	−0.510516	−	0.859868i	$-0.670546\pi$
$929$	−28911.0	−1.02103	−0.510516	+	0.859868i	$0.670546\pi$
$930$	0	0
$931$	8322.00	0.292957
$932$	19476.0	0.684504
$933$	0	0
$934$	2748.00	0.0962712
$935$	3960.00	0.138509
$936$	0	0
$937$	14810.0	0.516352	0.258176	−	0.966098i	$-0.416879\pi$
$937$	14810.0	0.516352	0.258176	+	0.966098i	$0.416879\pi$
$938$	27920.0	0.971877
$939$	0	0
$940$	12780.0	0.443444
$941$	2544.00	0.0881318	0.0440659	−	0.999029i	$-0.485969\pi$
$941$	2544.00	0.0881318	0.0440659	+	0.999029i	$0.485969\pi$
$942$	0	0
$943$	11385.0	0.393157
$944$	−3840.00	−0.132396
$945$	0	0
$946$	−3264.00	−0.112179
$947$	11145.0	0.382433	0.191216	−	0.981548i	$-0.438757\pi$
$947$	11145.0	0.382433	0.191216	+	0.981548i	$0.438757\pi$
$948$	0	0
$949$	−12173.0	−0.416388
$950$	7300.00	0.249309
$951$	0	0
$952$	21120.0	0.719016
$953$	4386.00	0.149083	0.0745417	−	0.997218i	$-0.476251\pi$
$953$	4386.00	0.149083	0.0745417	+	0.997218i	$0.476251\pi$
$954$	0	0
$955$	14910.0	0.505211
$956$	11508.0	0.389326
$957$	0	0
$958$	−9072.00	−0.305953
$959$	36720.0	1.23644
$960$	0	0
$961$	34218.0	1.14860
$962$	−11092.0	−0.371747
$963$	0	0
$964$	6488.00	0.216768
$965$	−6925.00	−0.231009
$966$	0	0
$967$	56381.0	1.87496	0.937482	−	0.348033i	$-0.113150\pi$
$967$	56381.0	1.87496	0.937482	+	0.348033i	$0.113150\pi$
$968$	−10360.0	−0.343991
$969$	0	0
$970$	−9920.00	−0.328363
$971$	−43782.0	−1.44699	−0.723497	−	0.690327i	$-0.757466\pi$
$971$	−43782.0	−1.44699	−0.723497	+	0.690327i	$0.757466\pi$
$972$	0	0
$973$	−20540.0	−0.676755
$974$	−22910.0	−0.753679
$975$	0	0
$976$	−5920.00	−0.194154
$977$	−3714.00	−0.121619	−0.0608093	−	0.998149i	$-0.519368\pi$
$977$	−3714.00	−0.121619	−0.0608093	+	0.998149i	$0.519368\pi$
$978$	0	0
$979$	−4968.00	−0.162184
$980$	−1140.00	−0.0371591
$981$	0	0
$982$	20790.0	0.675596
$983$	4662.00	0.151266	0.0756331	−	0.997136i	$-0.475902\pi$
$983$	4662.00	0.151266	0.0756331	+	0.997136i	$0.475902\pi$
$984$	0	0
$985$	4785.00	0.154785
$986$	26136.0	0.844158
$987$	0	0
$988$	27448.0	0.883843
$989$	−6256.00	−0.201142
$990$	0	0
$991$	51440.0	1.64889	0.824443	−	0.565945i	$-0.191489\pi$
$991$	51440.0	1.64889	0.824443	+	0.565945i	$0.191489\pi$
$992$	−8096.00	−0.259121
$993$	0	0
$994$	14280.0	0.455668
$995$	1790.00	0.0570320
$996$	0	0
$997$	686.000	0.0217912	0.0108956	−	0.999941i	$-0.496532\pi$
$997$	686.000	0.0217912	0.0108956	+	0.999941i	$0.496532\pi$
$998$	−10994.0	−0.348706
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.4.a.j.1.1		1
3.2	odd	2		230.4.a.c.1.1	✓	1
12.11	even	2		1840.4.a.a.1.1		1
15.2	even	4		1150.4.b.b.599.1		2
15.8	even	4		1150.4.b.b.599.2		2
15.14	odd	2		1150.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.c.1.1	✓	1	3.2	odd	2
1150.4.a.e.1.1		1	15.14	odd	2
1150.4.b.b.599.1		2	15.2	even	4
1150.4.b.b.599.2		2	15.8	even	4
1840.4.a.a.1.1		1	12.11	even	2
2070.4.a.j.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2070.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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