LMFDB - Embedded newform 1710.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1710.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1710.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$100.893266110$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -2.00000 q^{7} +8.00000 q^{8} -10.0000 q^{10} +16.0000 q^{11} -10.0000 q^{13} -4.00000 q^{14} +16.0000 q^{16} -36.0000 q^{17} +19.0000 q^{19} -20.0000 q^{20} +32.0000 q^{22} -124.000 q^{23} +25.0000 q^{25} -20.0000 q^{26} -8.00000 q^{28} +174.000 q^{29} -74.0000 q^{31} +32.0000 q^{32} -72.0000 q^{34} +10.0000 q^{35} +94.0000 q^{37} +38.0000 q^{38} -40.0000 q^{40} +240.000 q^{41} -276.000 q^{43} +64.0000 q^{44} -248.000 q^{46} -540.000 q^{47} -339.000 q^{49} +50.0000 q^{50} -40.0000 q^{52} -146.000 q^{53} -80.0000 q^{55} -16.0000 q^{56} +348.000 q^{58} -606.000 q^{59} +450.000 q^{61} -148.000 q^{62} +64.0000 q^{64} +50.0000 q^{65} +180.000 q^{67} -144.000 q^{68} +20.0000 q^{70} +456.000 q^{71} +14.0000 q^{73} +188.000 q^{74} +76.0000 q^{76} -32.0000 q^{77} +550.000 q^{79} -80.0000 q^{80} +480.000 q^{82} -1442.00 q^{83} +180.000 q^{85} -552.000 q^{86} +128.000 q^{88} -212.000 q^{89} +20.0000 q^{91} -496.000 q^{92} -1080.00 q^{94} -95.0000 q^{95} -830.000 q^{97} -678.000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	8.00000	0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	16.0000	0.438562	0.219281	−	0.975662i	$-0.429629\pi$
$11$	16.0000	0.438562	0.219281	+	0.975662i	$0.429629\pi$
$12$	0	0
$13$	−10.0000	−0.213346	−0.106673	−	0.994294i	$-0.534020\pi$
$13$	−10.0000	−0.213346	−0.106673	+	0.994294i	$0.534020\pi$
$14$	−4.00000	−0.0763604
$15$	0	0
$16$	16.0000	0.250000
$17$	−36.0000	−0.513605	−0.256802	−	0.966464i	$-0.582669\pi$
$17$	−36.0000	−0.513605	−0.256802	+	0.966464i	$0.582669\pi$
$18$	0	0
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−20.0000	−0.223607
$21$	0	0
$22$	32.0000	0.310110
$23$	−124.000	−1.12416	−0.562082	−	0.827081i	$-0.690000\pi$
$23$	−124.000	−1.12416	−0.562082	+	0.827081i	$0.690000\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−20.0000	−0.150859
$27$	0	0
$28$	−8.00000	−0.0539949
$29$	174.000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	174.000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−74.0000	−0.428735	−0.214368	−	0.976753i	$-0.568769\pi$
$31$	−74.0000	−0.428735	−0.214368	+	0.976753i	$0.568769\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−72.0000	−0.363173
$35$	10.0000	0.0482945
$36$	0	0
$37$	94.0000	0.417662	0.208831	−	0.977952i	$-0.433034\pi$
$37$	94.0000	0.417662	0.208831	+	0.977952i	$0.433034\pi$
$38$	38.0000	0.162221
$39$	0	0
$40$	−40.0000	−0.158114
$41$	240.000	0.914188	0.457094	−	0.889418i	$-0.348890\pi$
$41$	240.000	0.914188	0.457094	+	0.889418i	$0.348890\pi$
$42$	0	0
$43$	−276.000	−0.978828	−0.489414	−	0.872052i	$-0.662789\pi$
$43$	−276.000	−0.978828	−0.489414	+	0.872052i	$0.662789\pi$
$44$	64.0000	0.219281
$45$	0	0
$46$	−248.000	−0.794904
$47$	−540.000	−1.67590	−0.837948	−	0.545750i	$-0.816245\pi$
$47$	−540.000	−1.67590	−0.837948	+	0.545750i	$0.816245\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	50.0000	0.141421
$51$	0	0
$52$	−40.0000	−0.106673
$53$	−146.000	−0.378389	−0.189195	−	0.981940i	$-0.560588\pi$
$53$	−146.000	−0.378389	−0.189195	+	0.981940i	$0.560588\pi$
$54$	0	0
$55$	−80.0000	−0.196131
$56$	−16.0000	−0.0381802
$57$	0	0
$58$	348.000	0.787839
$59$	−606.000	−1.33719	−0.668597	−	0.743625i	$-0.733105\pi$
$59$	−606.000	−1.33719	−0.668597	+	0.743625i	$0.733105\pi$
$60$	0	0
$61$	450.000	0.944534	0.472267	−	0.881455i	$-0.343436\pi$
$61$	450.000	0.944534	0.472267	+	0.881455i	$0.343436\pi$
$62$	−148.000	−0.303162
$63$	0	0
$64$	64.0000	0.125000
$65$	50.0000	0.0954113
$66$	0	0
$67$	180.000	0.328216	0.164108	−	0.986442i	$-0.447525\pi$
$67$	180.000	0.328216	0.164108	+	0.986442i	$0.447525\pi$
$68$	−144.000	−0.256802
$69$	0	0
$70$	20.0000	0.0341494
$71$	456.000	0.762215	0.381107	−	0.924531i	$-0.375543\pi$
$71$	456.000	0.762215	0.381107	+	0.924531i	$0.375543\pi$
$72$	0	0
$73$	14.0000	0.0224462	0.0112231	−	0.999937i	$-0.496427\pi$
$73$	14.0000	0.0224462	0.0112231	+	0.999937i	$0.496427\pi$
$74$	188.000	0.295332
$75$	0	0
$76$	76.0000	0.114708
$77$	−32.0000	−0.0473602
$78$	0	0
$79$	550.000	0.783289	0.391645	−	0.920117i	$-0.371906\pi$
$79$	550.000	0.783289	0.391645	+	0.920117i	$0.371906\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	480.000	0.646428
$83$	−1442.00	−1.90699	−0.953494	−	0.301411i	$-0.902542\pi$
$83$	−1442.00	−1.90699	−0.953494	+	0.301411i	$0.902542\pi$
$84$	0	0
$85$	180.000	0.229691
$86$	−552.000	−0.692136
$87$	0	0
$88$	128.000	0.155055
$89$	−212.000	−0.252494	−0.126247	−	0.991999i	$-0.540293\pi$
$89$	−212.000	−0.252494	−0.126247	+	0.991999i	$0.540293\pi$
$90$	0	0
$91$	20.0000	0.0230392
$92$	−496.000	−0.562082
$93$	0	0
$94$	−1080.00	−1.18504
$95$	−95.0000	−0.102598
$96$	0	0
$97$	−830.000	−0.868801	−0.434401	−	0.900720i	$-0.643040\pi$
$97$	−830.000	−0.868801	−0.434401	+	0.900720i	$0.643040\pi$
$98$	−678.000	−0.698861
$99$	0	0
$100$	100.000	0.100000
$101$	−1378.00	−1.35759	−0.678793	−	0.734330i	$-0.737497\pi$
$101$	−1378.00	−1.35759	−0.678793	+	0.734330i	$0.737497\pi$
$102$	0	0
$103$	1312.00	1.25510	0.627550	−	0.778577i	$-0.284058\pi$
$103$	1312.00	1.25510	0.627550	+	0.778577i	$0.284058\pi$
$104$	−80.0000	−0.0754293
$105$	0	0
$106$	−292.000	−0.267562
$107$	−1112.00	−1.00468	−0.502342	−	0.864669i	$-0.667528\pi$
$107$	−1112.00	−1.00468	−0.502342	+	0.864669i	$0.667528\pi$
$108$	0	0
$109$	904.000	0.794381	0.397190	−	0.917736i	$-0.369985\pi$
$109$	904.000	0.794381	0.397190	+	0.917736i	$0.369985\pi$
$110$	−160.000	−0.138685
$111$	0	0
$112$	−32.0000	−0.0269975
$113$	−918.000	−0.764232	−0.382116	−	0.924114i	$-0.624804\pi$
$113$	−918.000	−0.764232	−0.382116	+	0.924114i	$0.624804\pi$
$114$	0	0
$115$	620.000	0.502742
$116$	696.000	0.557086
$117$	0	0
$118$	−1212.00	−0.945539
$119$	72.0000	0.0554641
$120$	0	0
$121$	−1075.00	−0.807663
$122$	900.000	0.667887
$123$	0	0
$124$	−296.000	−0.214368
$125$	−125.000	−0.0894427
$126$	0	0
$127$	24.0000	0.0167689	0.00838447	−	0.999965i	$-0.497331\pi$
$127$	24.0000	0.0167689	0.00838447	+	0.999965i	$0.497331\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	100.000	0.0674660
$131$	−2080.00	−1.38726	−0.693628	−	0.720334i	$-0.743989\pi$
$131$	−2080.00	−1.38726	−0.693628	+	0.720334i	$0.743989\pi$
$132$	0	0
$133$	−38.0000	−0.0247746
$134$	360.000	0.232084
$135$	0	0
$136$	−288.000	−0.181587
$137$	−2352.00	−1.46675	−0.733376	−	0.679824i	$-0.762056\pi$
$137$	−2352.00	−1.46675	−0.733376	+	0.679824i	$0.762056\pi$
$138$	0	0
$139$	604.000	0.368566	0.184283	−	0.982873i	$-0.441004\pi$
$139$	604.000	0.368566	0.184283	+	0.982873i	$0.441004\pi$
$140$	40.0000	0.0241473
$141$	0	0
$142$	912.000	0.538967
$143$	−160.000	−0.0935655
$144$	0	0
$145$	−870.000	−0.498273
$146$	28.0000	0.0158719
$147$	0	0
$148$	376.000	0.208831
$149$	−770.000	−0.423361	−0.211681	−	0.977339i	$-0.567894\pi$
$149$	−770.000	−0.423361	−0.211681	+	0.977339i	$0.567894\pi$
$150$	0	0
$151$	−550.000	−0.296413	−0.148207	−	0.988956i	$-0.547350\pi$
$151$	−550.000	−0.296413	−0.148207	+	0.988956i	$0.547350\pi$
$152$	152.000	0.0811107
$153$	0	0
$154$	−64.0000	−0.0334887
$155$	370.000	0.191736
$156$	0	0
$157$	−984.000	−0.500202	−0.250101	−	0.968220i	$-0.580464\pi$
$157$	−984.000	−0.500202	−0.250101	+	0.968220i	$0.580464\pi$
$158$	1100.00	0.553869
$159$	0	0
$160$	−160.000	−0.0790569
$161$	248.000	0.121398
$162$	0	0
$163$	400.000	0.192211	0.0961056	−	0.995371i	$-0.469361\pi$
$163$	400.000	0.192211	0.0961056	+	0.995371i	$0.469361\pi$
$164$	960.000	0.457094
$165$	0	0
$166$	−2884.00	−1.34844
$167$	−1144.00	−0.530092	−0.265046	−	0.964236i	$-0.585387\pi$
$167$	−1144.00	−0.530092	−0.265046	+	0.964236i	$0.585387\pi$
$168$	0	0
$169$	−2097.00	−0.954483
$170$	360.000	0.162416
$171$	0	0
$172$	−1104.00	−0.489414
$173$	−1978.00	−0.869275	−0.434637	−	0.900606i	$-0.643123\pi$
$173$	−1978.00	−0.869275	−0.434637	+	0.900606i	$0.643123\pi$
$174$	0	0
$175$	−50.0000	−0.0215980
$176$	256.000	0.109640
$177$	0	0
$178$	−424.000	−0.178540
$179$	2030.00	0.847650	0.423825	−	0.905744i	$-0.360687\pi$
$179$	2030.00	0.847650	0.423825	+	0.905744i	$0.360687\pi$
$180$	0	0
$181$	−808.000	−0.331813	−0.165907	−	0.986141i	$-0.553055\pi$
$181$	−808.000	−0.331813	−0.165907	+	0.986141i	$0.553055\pi$
$182$	40.0000	0.0162912
$183$	0	0
$184$	−992.000	−0.397452
$185$	−470.000	−0.186784
$186$	0	0
$187$	−576.000	−0.225248
$188$	−2160.00	−0.837948
$189$	0	0
$190$	−190.000	−0.0725476
$191$	−768.000	−0.290945	−0.145473	−	0.989362i	$-0.546470\pi$
$191$	−768.000	−0.290945	−0.145473	+	0.989362i	$0.546470\pi$
$192$	0	0
$193$	3022.00	1.12709	0.563545	−	0.826085i	$-0.309437\pi$
$193$	3022.00	1.12709	0.563545	+	0.826085i	$0.309437\pi$
$194$	−1660.00	−0.614335
$195$	0	0
$196$	−1356.00	−0.494169
$197$	1150.00	0.415909	0.207955	−	0.978138i	$-0.433319\pi$
$197$	1150.00	0.415909	0.207955	+	0.978138i	$0.433319\pi$
$198$	0	0
$199$	−1716.00	−0.611276	−0.305638	−	0.952148i	$-0.598870\pi$
$199$	−1716.00	−0.611276	−0.305638	+	0.952148i	$0.598870\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	−2756.00	−0.959958
$203$	−348.000	−0.120319
$204$	0	0
$205$	−1200.00	−0.408837
$206$	2624.00	0.887489
$207$	0	0
$208$	−160.000	−0.0533366
$209$	304.000	0.100613
$210$	0	0
$211$	4840.00	1.57914	0.789572	−	0.613658i	$-0.210303\pi$
$211$	4840.00	1.57914	0.789572	+	0.613658i	$0.210303\pi$
$212$	−584.000	−0.189195
$213$	0	0
$214$	−2224.00	−0.710418
$215$	1380.00	0.437745
$216$	0	0
$217$	148.000	0.0462991
$218$	1808.00	0.561712
$219$	0	0
$220$	−320.000	−0.0980654
$221$	360.000	0.109576
$222$	0	0
$223$	−3332.00	−1.00057	−0.500285	−	0.865861i	$-0.666772\pi$
$223$	−3332.00	−1.00057	−0.500285	+	0.865861i	$0.666772\pi$
$224$	−64.0000	−0.0190901
$225$	0	0
$226$	−1836.00	−0.540393
$227$	3220.00	0.941493	0.470746	−	0.882269i	$-0.343985\pi$
$227$	3220.00	0.941493	0.470746	+	0.882269i	$0.343985\pi$
$228$	0	0
$229$	−3138.00	−0.905523	−0.452762	−	0.891632i	$-0.649561\pi$
$229$	−3138.00	−0.905523	−0.452762	+	0.891632i	$0.649561\pi$
$230$	1240.00	0.355492
$231$	0	0
$232$	1392.00	0.393919
$233$	−2692.00	−0.756905	−0.378452	−	0.925621i	$-0.623544\pi$
$233$	−2692.00	−0.756905	−0.378452	+	0.925621i	$0.623544\pi$
$234$	0	0
$235$	2700.00	0.749483
$236$	−2424.00	−0.668597
$237$	0	0
$238$	144.000	0.0392190
$239$	−4336.00	−1.17353	−0.586763	−	0.809759i	$-0.699598\pi$
$239$	−4336.00	−1.17353	−0.586763	+	0.809759i	$0.699598\pi$
$240$	0	0
$241$	−942.000	−0.251782	−0.125891	−	0.992044i	$-0.540179\pi$
$241$	−942.000	−0.251782	−0.125891	+	0.992044i	$0.540179\pi$
$242$	−2150.00	−0.571104
$243$	0	0
$244$	1800.00	0.472267
$245$	1695.00	0.441998
$246$	0	0
$247$	−190.000	−0.0489450
$248$	−592.000	−0.151581
$249$	0	0
$250$	−250.000	−0.0632456
$251$	2364.00	0.594480	0.297240	−	0.954803i	$-0.403934\pi$
$251$	2364.00	0.594480	0.297240	+	0.954803i	$0.403934\pi$
$252$	0	0
$253$	−1984.00	−0.493016
$254$	48.0000	0.0118574
$255$	0	0
$256$	256.000	0.0625000
$257$	3446.00	0.836403	0.418202	−	0.908354i	$-0.362661\pi$
$257$	3446.00	0.836403	0.418202	+	0.908354i	$0.362661\pi$
$258$	0	0
$259$	−188.000	−0.0451033
$260$	200.000	0.0477057
$261$	0	0
$262$	−4160.00	−0.980938
$263$	−6452.00	−1.51273	−0.756364	−	0.654151i	$-0.773026\pi$
$263$	−6452.00	−1.51273	−0.756364	+	0.654151i	$0.773026\pi$
$264$	0	0
$265$	730.000	0.169221
$266$	−76.0000	−0.0175183
$267$	0	0
$268$	720.000	0.164108
$269$	94.0000	0.0213059	0.0106529	−	0.999943i	$-0.496609\pi$
$269$	94.0000	0.0213059	0.0106529	+	0.999943i	$0.496609\pi$
$270$	0	0
$271$	−1404.00	−0.314712	−0.157356	−	0.987542i	$-0.550297\pi$
$271$	−1404.00	−0.314712	−0.157356	+	0.987542i	$0.550297\pi$
$272$	−576.000	−0.128401
$273$	0	0
$274$	−4704.00	−1.03715
$275$	400.000	0.0877124
$276$	0	0
$277$	256.000	0.0555291	0.0277645	−	0.999614i	$-0.491161\pi$
$277$	256.000	0.0555291	0.0277645	+	0.999614i	$0.491161\pi$
$278$	1208.00	0.260615
$279$	0	0
$280$	80.0000	0.0170747
$281$	3240.00	0.687837	0.343918	−	0.939000i	$-0.388246\pi$
$281$	3240.00	0.687837	0.343918	+	0.939000i	$0.388246\pi$
$282$	0	0
$283$	4924.00	1.03428	0.517140	−	0.855901i	$-0.326997\pi$
$283$	4924.00	1.03428	0.517140	+	0.855901i	$0.326997\pi$
$284$	1824.00	0.381107
$285$	0	0
$286$	−320.000	−0.0661608
$287$	−480.000	−0.0987230
$288$	0	0
$289$	−3617.00	−0.736210
$290$	−1740.00	−0.352332
$291$	0	0
$292$	56.0000	0.0112231
$293$	−1542.00	−0.307456	−0.153728	−	0.988113i	$-0.549128\pi$
$293$	−1542.00	−0.307456	−0.153728	+	0.988113i	$0.549128\pi$
$294$	0	0
$295$	3030.00	0.598012
$296$	752.000	0.147666
$297$	0	0
$298$	−1540.00	−0.299362
$299$	1240.00	0.239836
$300$	0	0
$301$	552.000	0.105703
$302$	−1100.00	−0.209596
$303$	0	0
$304$	304.000	0.0573539
$305$	−2250.00	−0.422409
$306$	0	0
$307$	100.000	0.0185906	0.00929528	−	0.999957i	$-0.497041\pi$
$307$	100.000	0.0185906	0.00929528	+	0.999957i	$0.497041\pi$
$308$	−128.000	−0.0236801
$309$	0	0
$310$	740.000	0.135578
$311$	1736.00	0.316526	0.158263	−	0.987397i	$-0.449411\pi$
$311$	1736.00	0.316526	0.158263	+	0.987397i	$0.449411\pi$
$312$	0	0
$313$	5198.00	0.938685	0.469342	−	0.883016i	$-0.344491\pi$
$313$	5198.00	0.938685	0.469342	+	0.883016i	$0.344491\pi$
$314$	−1968.00	−0.353696
$315$	0	0
$316$	2200.00	0.391645
$317$	9738.00	1.72536	0.862682	−	0.505746i	$-0.168783\pi$
$317$	9738.00	1.72536	0.862682	+	0.505746i	$0.168783\pi$
$318$	0	0
$319$	2784.00	0.488633
$320$	−320.000	−0.0559017
$321$	0	0
$322$	496.000	0.0858416
$323$	−684.000	−0.117829
$324$	0	0
$325$	−250.000	−0.0426692
$326$	800.000	0.135914
$327$	0	0
$328$	1920.00	0.323214
$329$	1080.00	0.180980
$330$	0	0
$331$	−7156.00	−1.18831	−0.594153	−	0.804352i	$-0.702513\pi$
$331$	−7156.00	−1.18831	−0.594153	+	0.804352i	$0.702513\pi$
$332$	−5768.00	−0.953494
$333$	0	0
$334$	−2288.00	−0.374832
$335$	−900.000	−0.146783
$336$	0	0
$337$	−9138.00	−1.47709	−0.738544	−	0.674205i	$-0.764486\pi$
$337$	−9138.00	−1.47709	−0.738544	+	0.674205i	$0.764486\pi$
$338$	−4194.00	−0.674922
$339$	0	0
$340$	720.000	0.114846
$341$	−1184.00	−0.188027
$342$	0	0
$343$	1364.00	0.214720
$344$	−2208.00	−0.346068
$345$	0	0
$346$	−3956.00	−0.614670
$347$	8394.00	1.29860	0.649299	−	0.760533i	$-0.275062\pi$
$347$	8394.00	1.29860	0.649299	+	0.760533i	$0.275062\pi$
$348$	0	0
$349$	9350.00	1.43408	0.717040	−	0.697032i	$-0.245496\pi$
$349$	9350.00	1.43408	0.717040	+	0.697032i	$0.245496\pi$
$350$	−100.000	−0.0152721
$351$	0	0
$352$	512.000	0.0775275
$353$	−1720.00	−0.259338	−0.129669	−	0.991557i	$-0.541391\pi$
$353$	−1720.00	−0.259338	−0.129669	+	0.991557i	$0.541391\pi$
$354$	0	0
$355$	−2280.00	−0.340873
$356$	−848.000	−0.126247
$357$	0	0
$358$	4060.00	0.599379
$359$	−4264.00	−0.626867	−0.313434	−	0.949610i	$-0.601479\pi$
$359$	−4264.00	−0.626867	−0.313434	+	0.949610i	$0.601479\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	−1616.00	−0.234627
$363$	0	0
$364$	80.0000	0.0115196
$365$	−70.0000	−0.0100383
$366$	0	0
$367$	−2686.00	−0.382038	−0.191019	−	0.981586i	$-0.561179\pi$
$367$	−2686.00	−0.382038	−0.191019	+	0.981586i	$0.561179\pi$
$368$	−1984.00	−0.281041
$369$	0	0
$370$	−940.000	−0.132076
$371$	292.000	0.0408622
$372$	0	0
$373$	154.000	0.0213775	0.0106888	−	0.999943i	$-0.496598\pi$
$373$	154.000	0.0213775	0.0106888	+	0.999943i	$0.496598\pi$
$374$	−1152.00	−0.159274
$375$	0	0
$376$	−4320.00	−0.592519
$377$	−1740.00	−0.237704
$378$	0	0
$379$	1272.00	0.172396	0.0861982	−	0.996278i	$-0.472528\pi$
$379$	1272.00	0.172396	0.0861982	+	0.996278i	$0.472528\pi$
$380$	−380.000	−0.0512989
$381$	0	0
$382$	−1536.00	−0.205729
$383$	−14504.0	−1.93504	−0.967519	−	0.252797i	$-0.918649\pi$
$383$	−14504.0	−1.93504	−0.967519	+	0.252797i	$0.918649\pi$
$384$	0	0
$385$	160.000	0.0211801
$386$	6044.00	0.796973
$387$	0	0
$388$	−3320.00	−0.434401
$389$	−5162.00	−0.672812	−0.336406	−	0.941717i	$-0.609211\pi$
$389$	−5162.00	−0.672812	−0.336406	+	0.941717i	$0.609211\pi$
$390$	0	0
$391$	4464.00	0.577376
$392$	−2712.00	−0.349430
$393$	0	0
$394$	2300.00	0.294092
$395$	−2750.00	−0.350298
$396$	0	0
$397$	1100.00	0.139062	0.0695308	−	0.997580i	$-0.477850\pi$
$397$	1100.00	0.139062	0.0695308	+	0.997580i	$0.477850\pi$
$398$	−3432.00	−0.432238
$399$	0	0
$400$	400.000	0.0500000
$401$	5100.00	0.635117	0.317558	−	0.948239i	$-0.397137\pi$
$401$	5100.00	0.635117	0.317558	+	0.948239i	$0.397137\pi$
$402$	0	0
$403$	740.000	0.0914690
$404$	−5512.00	−0.678793
$405$	0	0
$406$	−696.000	−0.0850786
$407$	1504.00	0.183171
$408$	0	0
$409$	−1862.00	−0.225110	−0.112555	−	0.993645i	$-0.535903\pi$
$409$	−1862.00	−0.225110	−0.112555	+	0.993645i	$0.535903\pi$
$410$	−2400.00	−0.289092
$411$	0	0
$412$	5248.00	0.627550
$413$	1212.00	0.144403
$414$	0	0
$415$	7210.00	0.852831
$416$	−320.000	−0.0377146
$417$	0	0
$418$	608.000	0.0711441
$419$	6508.00	0.758799	0.379399	−	0.925233i	$-0.376131\pi$
$419$	6508.00	0.758799	0.379399	+	0.925233i	$0.376131\pi$
$420$	0	0
$421$	11032.0	1.27712	0.638559	−	0.769573i	$-0.279531\pi$
$421$	11032.0	1.27712	0.638559	+	0.769573i	$0.279531\pi$
$422$	9680.00	1.11662
$423$	0	0
$424$	−1168.00	−0.133781
$425$	−900.000	−0.102721
$426$	0	0
$427$	−900.000	−0.102000
$428$	−4448.00	−0.502342
$429$	0	0
$430$	2760.00	0.309533
$431$	4824.00	0.539127	0.269564	−	0.962983i	$-0.413121\pi$
$431$	4824.00	0.539127	0.269564	+	0.962983i	$0.413121\pi$
$432$	0	0
$433$	686.000	0.0761364	0.0380682	−	0.999275i	$-0.487880\pi$
$433$	686.000	0.0761364	0.0380682	+	0.999275i	$0.487880\pi$
$434$	296.000	0.0327384
$435$	0	0
$436$	3616.00	0.397190
$437$	−2356.00	−0.257901
$438$	0	0
$439$	−8242.00	−0.896057	−0.448029	−	0.894019i	$-0.647874\pi$
$439$	−8242.00	−0.896057	−0.448029	+	0.894019i	$0.647874\pi$
$440$	−640.000	−0.0693427
$441$	0	0
$442$	720.000	0.0774817
$443$	−15006.0	−1.60938	−0.804691	−	0.593693i	$-0.797669\pi$
$443$	−15006.0	−1.60938	−0.804691	+	0.593693i	$0.797669\pi$
$444$	0	0
$445$	1060.00	0.112919
$446$	−6664.00	−0.707510
$447$	0	0
$448$	−128.000	−0.0134987
$449$	14992.0	1.57576	0.787880	−	0.615829i	$-0.211179\pi$
$449$	14992.0	1.57576	0.787880	+	0.615829i	$0.211179\pi$
$450$	0	0
$451$	3840.00	0.400928
$452$	−3672.00	−0.382116
$453$	0	0
$454$	6440.00	0.665736
$455$	−100.000	−0.0103035
$456$	0	0
$457$	7354.00	0.752748	0.376374	−	0.926468i	$-0.377171\pi$
$457$	7354.00	0.752748	0.376374	+	0.926468i	$0.377171\pi$
$458$	−6276.00	−0.640302
$459$	0	0
$460$	2480.00	0.251371
$461$	2922.00	0.295208	0.147604	−	0.989047i	$-0.452844\pi$
$461$	2922.00	0.295208	0.147604	+	0.989047i	$0.452844\pi$
$462$	0	0
$463$	12118.0	1.21635	0.608176	−	0.793802i	$-0.291901\pi$
$463$	12118.0	1.21635	0.608176	+	0.793802i	$0.291901\pi$
$464$	2784.00	0.278543
$465$	0	0
$466$	−5384.00	−0.535212
$467$	14294.0	1.41638	0.708188	−	0.706024i	$-0.249513\pi$
$467$	14294.0	1.41638	0.708188	+	0.706024i	$0.249513\pi$
$468$	0	0
$469$	−360.000	−0.0354440
$470$	5400.00	0.529965
$471$	0	0
$472$	−4848.00	−0.472770
$473$	−4416.00	−0.429277
$474$	0	0
$475$	475.000	0.0458831
$476$	288.000	0.0277321
$477$	0	0
$478$	−8672.00	−0.829808
$479$	−11184.0	−1.06683	−0.533413	−	0.845855i	$-0.679091\pi$
$479$	−11184.0	−1.06683	−0.533413	+	0.845855i	$0.679091\pi$
$480$	0	0
$481$	−940.000	−0.0891067
$482$	−1884.00	−0.178037
$483$	0	0
$484$	−4300.00	−0.403832
$485$	4150.00	0.388540
$486$	0	0
$487$	−16376.0	−1.52375	−0.761876	−	0.647723i	$-0.775722\pi$
$487$	−16376.0	−1.52375	−0.761876	+	0.647723i	$0.775722\pi$
$488$	3600.00	0.333943
$489$	0	0
$490$	3390.00	0.312540
$491$	−19584.0	−1.80003	−0.900014	−	0.435861i	$-0.856444\pi$
$491$	−19584.0	−1.80003	−0.900014	+	0.435861i	$0.856444\pi$
$492$	0	0
$493$	−6264.00	−0.572244
$494$	−380.000	−0.0346093
$495$	0	0
$496$	−1184.00	−0.107184
$497$	−912.000	−0.0823115
$498$	0	0
$499$	20724.0	1.85919	0.929593	−	0.368588i	$-0.120159\pi$
$499$	20724.0	1.85919	0.929593	+	0.368588i	$0.120159\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	4728.00	0.420360
$503$	12288.0	1.08925	0.544627	−	0.838678i	$-0.316671\pi$
$503$	12288.0	1.08925	0.544627	+	0.838678i	$0.316671\pi$
$504$	0	0
$505$	6890.00	0.607131
$506$	−3968.00	−0.348615
$507$	0	0
$508$	96.0000	0.00838447
$509$	−50.0000	−0.00435405	−0.00217702	−	0.999998i	$-0.500693\pi$
$509$	−50.0000	−0.00435405	−0.00217702	+	0.999998i	$0.500693\pi$
$510$	0	0
$511$	−28.0000	−0.00242397
$512$	512.000	0.0441942
$513$	0	0
$514$	6892.00	0.591426
$515$	−6560.00	−0.561297
$516$	0	0
$517$	−8640.00	−0.734984
$518$	−376.000	−0.0318928
$519$	0	0
$520$	400.000	0.0337330
$521$	−8484.00	−0.713418	−0.356709	−	0.934216i	$-0.616101\pi$
$521$	−8484.00	−0.713418	−0.356709	+	0.934216i	$0.616101\pi$
$522$	0	0
$523$	5868.00	0.490611	0.245306	−	0.969446i	$-0.421112\pi$
$523$	5868.00	0.490611	0.245306	+	0.969446i	$0.421112\pi$
$524$	−8320.00	−0.693628
$525$	0	0
$526$	−12904.0	−1.06966
$527$	2664.00	0.220200
$528$	0	0
$529$	3209.00	0.263746
$530$	1460.00	0.119657
$531$	0	0
$532$	−152.000	−0.0123873
$533$	−2400.00	−0.195039
$534$	0	0
$535$	5560.00	0.449308
$536$	1440.00	0.116042
$537$	0	0
$538$	188.000	0.0150655
$539$	−5424.00	−0.433448
$540$	0	0
$541$	−4538.00	−0.360636	−0.180318	−	0.983608i	$-0.557713\pi$
$541$	−4538.00	−0.360636	−0.180318	+	0.983608i	$0.557713\pi$
$542$	−2808.00	−0.222535
$543$	0	0
$544$	−1152.00	−0.0907934
$545$	−4520.00	−0.355258
$546$	0	0
$547$	11708.0	0.915170	0.457585	−	0.889166i	$-0.348715\pi$
$547$	11708.0	0.915170	0.457585	+	0.889166i	$0.348715\pi$
$548$	−9408.00	−0.733376
$549$	0	0
$550$	800.000	0.0620220
$551$	3306.00	0.255609
$552$	0	0
$553$	−1100.00	−0.0845873
$554$	512.000	0.0392650
$555$	0	0
$556$	2416.00	0.184283
$557$	20442.0	1.55504	0.777518	−	0.628860i	$-0.216478\pi$
$557$	20442.0	1.55504	0.777518	+	0.628860i	$0.216478\pi$
$558$	0	0
$559$	2760.00	0.208829
$560$	160.000	0.0120736
$561$	0	0
$562$	6480.00	0.486374
$563$	6976.00	0.522208	0.261104	−	0.965311i	$-0.415913\pi$
$563$	6976.00	0.522208	0.261104	+	0.965311i	$0.415913\pi$
$564$	0	0
$565$	4590.00	0.341775
$566$	9848.00	0.731347
$567$	0	0
$568$	3648.00	0.269484
$569$	−1824.00	−0.134387	−0.0671934	−	0.997740i	$-0.521404\pi$
$569$	−1824.00	−0.134387	−0.0671934	+	0.997740i	$0.521404\pi$
$570$	0	0
$571$	−8244.00	−0.604204	−0.302102	−	0.953276i	$-0.597688\pi$
$571$	−8244.00	−0.604204	−0.302102	+	0.953276i	$0.597688\pi$
$572$	−640.000	−0.0467828
$573$	0	0
$574$	−960.000	−0.0698077
$575$	−3100.00	−0.224833
$576$	0	0
$577$	10082.0	0.727416	0.363708	−	0.931513i	$-0.381511\pi$
$577$	10082.0	0.727416	0.363708	+	0.931513i	$0.381511\pi$
$578$	−7234.00	−0.520579
$579$	0	0
$580$	−3480.00	−0.249136
$581$	2884.00	0.205935
$582$	0	0
$583$	−2336.00	−0.165947
$584$	112.000	0.00793595
$585$	0	0
$586$	−3084.00	−0.217404
$587$	−12006.0	−0.844192	−0.422096	−	0.906551i	$-0.638705\pi$
$587$	−12006.0	−0.844192	−0.422096	+	0.906551i	$0.638705\pi$
$588$	0	0
$589$	−1406.00	−0.0983586
$590$	6060.00	0.422858
$591$	0	0
$592$	1504.00	0.104416
$593$	15960.0	1.10523	0.552613	−	0.833438i	$-0.313631\pi$
$593$	15960.0	1.10523	0.552613	+	0.833438i	$0.313631\pi$
$594$	0	0
$595$	−360.000	−0.0248043
$596$	−3080.00	−0.211681
$597$	0	0
$598$	2480.00	0.169590
$599$	−1084.00	−0.0739416	−0.0369708	−	0.999316i	$-0.511771\pi$
$599$	−1084.00	−0.0739416	−0.0369708	+	0.999316i	$0.511771\pi$
$600$	0	0
$601$	11682.0	0.792876	0.396438	−	0.918061i	$-0.370246\pi$
$601$	11682.0	0.792876	0.396438	+	0.918061i	$0.370246\pi$
$602$	1104.00	0.0747437
$603$	0	0
$604$	−2200.00	−0.148207
$605$	5375.00	0.361198
$606$	0	0
$607$	13816.0	0.923845	0.461923	−	0.886920i	$-0.347160\pi$
$607$	13816.0	0.923845	0.461923	+	0.886920i	$0.347160\pi$
$608$	608.000	0.0405554
$609$	0	0
$610$	−4500.00	−0.298688
$611$	5400.00	0.357546
$612$	0	0
$613$	−4124.00	−0.271724	−0.135862	−	0.990728i	$-0.543380\pi$
$613$	−4124.00	−0.271724	−0.135862	+	0.990728i	$0.543380\pi$
$614$	200.000	0.0131455
$615$	0	0
$616$	−256.000	−0.0167444
$617$	14632.0	0.954720	0.477360	−	0.878708i	$-0.341594\pi$
$617$	14632.0	0.954720	0.477360	+	0.878708i	$0.341594\pi$
$618$	0	0
$619$	10980.0	0.712962	0.356481	−	0.934303i	$-0.383976\pi$
$619$	10980.0	0.712962	0.356481	+	0.934303i	$0.383976\pi$
$620$	1480.00	0.0958681
$621$	0	0
$622$	3472.00	0.223818
$623$	424.000	0.0272668
$624$	0	0
$625$	625.000	0.0400000
$626$	10396.0	0.663750
$627$	0	0
$628$	−3936.00	−0.250101
$629$	−3384.00	−0.214513
$630$	0	0
$631$	−15736.0	−0.992774	−0.496387	−	0.868101i	$-0.665340\pi$
$631$	−15736.0	−0.992774	−0.496387	+	0.868101i	$0.665340\pi$
$632$	4400.00	0.276934
$633$	0	0
$634$	19476.0	1.22002
$635$	−120.000	−0.00749930
$636$	0	0
$637$	3390.00	0.210858
$638$	5568.00	0.345516
$639$	0	0
$640$	−640.000	−0.0395285
$641$	23704.0	1.46061	0.730306	−	0.683121i	$-0.239378\pi$
$641$	23704.0	1.46061	0.730306	+	0.683121i	$0.239378\pi$
$642$	0	0
$643$	−22276.0	−1.36622	−0.683110	−	0.730315i	$-0.739373\pi$
$643$	−22276.0	−1.36622	−0.683110	+	0.730315i	$0.739373\pi$
$644$	992.000	0.0606992
$645$	0	0
$646$	−1368.00	−0.0833177
$647$	9216.00	0.559997	0.279999	−	0.960000i	$-0.409666\pi$
$647$	9216.00	0.559997	0.279999	+	0.960000i	$0.409666\pi$
$648$	0	0
$649$	−9696.00	−0.586443
$650$	−500.000	−0.0301717
$651$	0	0
$652$	1600.00	0.0961056
$653$	−13742.0	−0.823531	−0.411766	−	0.911290i	$-0.635088\pi$
$653$	−13742.0	−0.823531	−0.411766	+	0.911290i	$0.635088\pi$
$654$	0	0
$655$	10400.0	0.620399
$656$	3840.00	0.228547
$657$	0	0
$658$	2160.00	0.127972
$659$	30990.0	1.83186	0.915932	−	0.401332i	$-0.131453\pi$
$659$	30990.0	1.83186	0.915932	+	0.401332i	$0.131453\pi$
$660$	0	0
$661$	−528.000	−0.0310693	−0.0155347	−	0.999879i	$-0.504945\pi$
$661$	−528.000	−0.0310693	−0.0155347	+	0.999879i	$0.504945\pi$
$662$	−14312.0	−0.840259
$663$	0	0
$664$	−11536.0	−0.674222
$665$	190.000	0.0110795
$666$	0	0
$667$	−21576.0	−1.25251
$668$	−4576.00	−0.265046
$669$	0	0
$670$	−1800.00	−0.103791
$671$	7200.00	0.414237
$672$	0	0
$673$	−11438.0	−0.655130	−0.327565	−	0.944829i	$-0.606228\pi$
$673$	−11438.0	−0.655130	−0.327565	+	0.944829i	$0.606228\pi$
$674$	−18276.0	−1.04446
$675$	0	0
$676$	−8388.00	−0.477242
$677$	24066.0	1.36622	0.683110	−	0.730315i	$-0.260627\pi$
$677$	24066.0	1.36622	0.683110	+	0.730315i	$0.260627\pi$
$678$	0	0
$679$	1660.00	0.0938217
$680$	1440.00	0.0812081
$681$	0	0
$682$	−2368.00	−0.132955
$683$	−12148.0	−0.680571	−0.340286	−	0.940322i	$-0.610524\pi$
$683$	−12148.0	−0.680571	−0.340286	+	0.940322i	$0.610524\pi$
$684$	0	0
$685$	11760.0	0.655951
$686$	2728.00	0.151830
$687$	0	0
$688$	−4416.00	−0.244707
$689$	1460.00	0.0807280
$690$	0	0
$691$	5820.00	0.320410	0.160205	−	0.987084i	$-0.448784\pi$
$691$	5820.00	0.320410	0.160205	+	0.987084i	$0.448784\pi$
$692$	−7912.00	−0.434637
$693$	0	0
$694$	16788.0	0.918248
$695$	−3020.00	−0.164828
$696$	0	0
$697$	−8640.00	−0.469531
$698$	18700.0	1.01405
$699$	0	0
$700$	−200.000	−0.0107990
$701$	6858.00	0.369505	0.184753	−	0.982785i	$-0.440852\pi$
$701$	6858.00	0.369505	0.184753	+	0.982785i	$0.440852\pi$
$702$	0	0
$703$	1786.00	0.0958183
$704$	1024.00	0.0548202
$705$	0	0
$706$	−3440.00	−0.183380
$707$	2756.00	0.146605
$708$	0	0
$709$	−10330.0	−0.547181	−0.273590	−	0.961846i	$-0.588211\pi$
$709$	−10330.0	−0.547181	−0.273590	+	0.961846i	$0.588211\pi$
$710$	−4560.00	−0.241033
$711$	0	0
$712$	−1696.00	−0.0892701
$713$	9176.00	0.481969
$714$	0	0
$715$	800.000	0.0418438
$716$	8120.00	0.423825
$717$	0	0
$718$	−8528.00	−0.443262
$719$	15024.0	0.779278	0.389639	−	0.920968i	$-0.372600\pi$
$719$	15024.0	0.779278	0.389639	+	0.920968i	$0.372600\pi$
$720$	0	0
$721$	−2624.00	−0.135538
$722$	722.000	0.0372161
$723$	0	0
$724$	−3232.00	−0.165907
$725$	4350.00	0.222834
$726$	0	0
$727$	17306.0	0.882867	0.441433	−	0.897294i	$-0.354470\pi$
$727$	17306.0	0.882867	0.441433	+	0.897294i	$0.354470\pi$
$728$	160.000	0.00814560
$729$	0	0
$730$	−140.000	−0.00709813
$731$	9936.00	0.502731
$732$	0	0
$733$	−7524.00	−0.379134	−0.189567	−	0.981868i	$-0.560708\pi$
$733$	−7524.00	−0.379134	−0.189567	+	0.981868i	$0.560708\pi$
$734$	−5372.00	−0.270142
$735$	0	0
$736$	−3968.00	−0.198726
$737$	2880.00	0.143943
$738$	0	0
$739$	26036.0	1.29601	0.648004	−	0.761637i	$-0.275604\pi$
$739$	26036.0	1.29601	0.648004	+	0.761637i	$0.275604\pi$
$740$	−1880.00	−0.0933921
$741$	0	0
$742$	584.000	0.0288940
$743$	14088.0	0.695610	0.347805	−	0.937567i	$-0.386927\pi$
$743$	14088.0	0.695610	0.347805	+	0.937567i	$0.386927\pi$
$744$	0	0
$745$	3850.00	0.189333
$746$	308.000	0.0151162
$747$	0	0
$748$	−2304.00	−0.112624
$749$	2224.00	0.108496
$750$	0	0
$751$	−4970.00	−0.241489	−0.120744	−	0.992684i	$-0.538528\pi$
$751$	−4970.00	−0.241489	−0.120744	+	0.992684i	$0.538528\pi$
$752$	−8640.00	−0.418974
$753$	0	0
$754$	−3480.00	−0.168082
$755$	2750.00	0.132560
$756$	0	0
$757$	5244.00	0.251779	0.125889	−	0.992044i	$-0.459822\pi$
$757$	5244.00	0.251779	0.125889	+	0.992044i	$0.459822\pi$
$758$	2544.00	0.121903
$759$	0	0
$760$	−760.000	−0.0362738
$761$	11266.0	0.536652	0.268326	−	0.963328i	$-0.413530\pi$
$761$	11266.0	0.536652	0.268326	+	0.963328i	$0.413530\pi$
$762$	0	0
$763$	−1808.00	−0.0857851
$764$	−3072.00	−0.145473
$765$	0	0
$766$	−29008.0	−1.36828
$767$	6060.00	0.285285
$768$	0	0
$769$	−2690.00	−0.126143	−0.0630714	−	0.998009i	$-0.520090\pi$
$769$	−2690.00	−0.126143	−0.0630714	+	0.998009i	$0.520090\pi$
$770$	320.000	0.0149766
$771$	0	0
$772$	12088.0	0.563545
$773$	−25698.0	−1.19572	−0.597861	−	0.801600i	$-0.703982\pi$
$773$	−25698.0	−1.19572	−0.597861	+	0.801600i	$0.703982\pi$
$774$	0	0
$775$	−1850.00	−0.0857470
$776$	−6640.00	−0.307168
$777$	0	0
$778$	−10324.0	−0.475750
$779$	4560.00	0.209729
$780$	0	0
$781$	7296.00	0.334278
$782$	8928.00	0.408267
$783$	0	0
$784$	−5424.00	−0.247085
$785$	4920.00	0.223697
$786$	0	0
$787$	−5772.00	−0.261435	−0.130718	−	0.991420i	$-0.541728\pi$
$787$	−5772.00	−0.261435	−0.130718	+	0.991420i	$0.541728\pi$
$788$	4600.00	0.207955
$789$	0	0
$790$	−5500.00	−0.247698
$791$	1836.00	0.0825293
$792$	0	0
$793$	−4500.00	−0.201513
$794$	2200.00	0.0983313
$795$	0	0
$796$	−6864.00	−0.305638
$797$	−5782.00	−0.256975	−0.128487	−	0.991711i	$-0.541012\pi$
$797$	−5782.00	−0.256975	−0.128487	+	0.991711i	$0.541012\pi$
$798$	0	0
$799$	19440.0	0.860748
$800$	800.000	0.0353553
$801$	0	0
$802$	10200.0	0.449095
$803$	224.000	0.00984407
$804$	0	0
$805$	−1240.00	−0.0542910
$806$	1480.00	0.0646784
$807$	0	0
$808$	−11024.0	−0.479979
$809$	37154.0	1.61467	0.807333	−	0.590096i	$-0.200910\pi$
$809$	37154.0	1.61467	0.807333	+	0.590096i	$0.200910\pi$
$810$	0	0
$811$	−11144.0	−0.482514	−0.241257	−	0.970461i	$-0.577560\pi$
$811$	−11144.0	−0.482514	−0.241257	+	0.970461i	$0.577560\pi$
$812$	−1392.00	−0.0601596
$813$	0	0
$814$	3008.00	0.129521
$815$	−2000.00	−0.0859594
$816$	0	0
$817$	−5244.00	−0.224559
$818$	−3724.00	−0.159177
$819$	0	0
$820$	−4800.00	−0.204419
$821$	−36050.0	−1.53246	−0.766232	−	0.642563i	$-0.777871\pi$
$821$	−36050.0	−1.53246	−0.766232	+	0.642563i	$0.777871\pi$
$822$	0	0
$823$	−39202.0	−1.66038	−0.830192	−	0.557478i	$-0.811769\pi$
$823$	−39202.0	−1.66038	−0.830192	+	0.557478i	$0.811769\pi$
$824$	10496.0	0.443745
$825$	0	0
$826$	2424.00	0.102109
$827$	25464.0	1.07070	0.535351	−	0.844630i	$-0.320179\pi$
$827$	25464.0	1.07070	0.535351	+	0.844630i	$0.320179\pi$
$828$	0	0
$829$	3104.00	0.130044	0.0650219	−	0.997884i	$-0.479288\pi$
$829$	3104.00	0.130044	0.0650219	+	0.997884i	$0.479288\pi$
$830$	14420.0	0.603043
$831$	0	0
$832$	−640.000	−0.0266683
$833$	12204.0	0.507615
$834$	0	0
$835$	5720.00	0.237064
$836$	1216.00	0.0503065
$837$	0	0
$838$	13016.0	0.536552
$839$	−39008.0	−1.60513	−0.802566	−	0.596563i	$-0.796532\pi$
$839$	−39008.0	−1.60513	−0.802566	+	0.596563i	$0.796532\pi$
$840$	0	0
$841$	5887.00	0.241379
$842$	22064.0	0.903059
$843$	0	0
$844$	19360.0	0.789572
$845$	10485.0	0.426858
$846$	0	0
$847$	2150.00	0.0872195
$848$	−2336.00	−0.0945974
$849$	0	0
$850$	−1800.00	−0.0726347
$851$	−11656.0	−0.469521
$852$	0	0
$853$	−7248.00	−0.290934	−0.145467	−	0.989363i	$-0.546468\pi$
$853$	−7248.00	−0.290934	−0.145467	+	0.989363i	$0.546468\pi$
$854$	−1800.00	−0.0721250
$855$	0	0
$856$	−8896.00	−0.355209
$857$	574.000	0.0228792	0.0114396	−	0.999935i	$-0.496359\pi$
$857$	574.000	0.0228792	0.0114396	+	0.999935i	$0.496359\pi$
$858$	0	0
$859$	17156.0	0.681438	0.340719	−	0.940165i	$-0.389330\pi$
$859$	17156.0	0.681438	0.340719	+	0.940165i	$0.389330\pi$
$860$	5520.00	0.218873
$861$	0	0
$862$	9648.00	0.381221
$863$	−28016.0	−1.10507	−0.552535	−	0.833490i	$-0.686340\pi$
$863$	−28016.0	−1.10507	−0.552535	+	0.833490i	$0.686340\pi$
$864$	0	0
$865$	9890.00	0.388752
$866$	1372.00	0.0538366
$867$	0	0
$868$	592.000	0.0231495
$869$	8800.00	0.343521
$870$	0	0
$871$	−1800.00	−0.0700237
$872$	7232.00	0.280856
$873$	0	0
$874$	−4712.00	−0.182364
$875$	250.000	0.00965891
$876$	0	0
$877$	36666.0	1.41177	0.705885	−	0.708326i	$-0.250549\pi$
$877$	36666.0	1.41177	0.705885	+	0.708326i	$0.250549\pi$
$878$	−16484.0	−0.633608
$879$	0	0
$880$	−1280.00	−0.0490327
$881$	−33322.0	−1.27429	−0.637143	−	0.770745i	$-0.719884\pi$
$881$	−33322.0	−1.27429	−0.637143	+	0.770745i	$0.719884\pi$
$882$	0	0
$883$	708.000	0.0269831	0.0134916	−	0.999909i	$-0.495705\pi$
$883$	708.000	0.0269831	0.0134916	+	0.999909i	$0.495705\pi$
$884$	1440.00	0.0547878
$885$	0	0
$886$	−30012.0	−1.13801
$887$	22864.0	0.865499	0.432750	−	0.901514i	$-0.357543\pi$
$887$	22864.0	0.865499	0.432750	+	0.901514i	$0.357543\pi$
$888$	0	0
$889$	−48.0000	−0.00181088
$890$	2120.00	0.0798456
$891$	0	0
$892$	−13328.0	−0.500285
$893$	−10260.0	−0.384477
$894$	0	0
$895$	−10150.0	−0.379081
$896$	−256.000	−0.00954504
$897$	0	0
$898$	29984.0	1.11423
$899$	−12876.0	−0.477685
$900$	0	0
$901$	5256.00	0.194343
$902$	7680.00	0.283499
$903$	0	0
$904$	−7344.00	−0.270197
$905$	4040.00	0.148391
$906$	0	0
$907$	8516.00	0.311763	0.155882	−	0.987776i	$-0.450178\pi$
$907$	8516.00	0.311763	0.155882	+	0.987776i	$0.450178\pi$
$908$	12880.0	0.470746
$909$	0	0
$910$	−200.000	−0.00728564
$911$	12012.0	0.436855	0.218428	−	0.975853i	$-0.429907\pi$
$911$	12012.0	0.436855	0.218428	+	0.975853i	$0.429907\pi$
$912$	0	0
$913$	−23072.0	−0.836333
$914$	14708.0	0.532273
$915$	0	0
$916$	−12552.0	−0.452762
$917$	4160.00	0.149809
$918$	0	0
$919$	4672.00	0.167699	0.0838493	−	0.996478i	$-0.473279\pi$
$919$	4672.00	0.167699	0.0838493	+	0.996478i	$0.473279\pi$
$920$	4960.00	0.177746
$921$	0	0
$922$	5844.00	0.208744
$923$	−4560.00	−0.162616
$924$	0	0
$925$	2350.00	0.0835325
$926$	24236.0	0.860091
$927$	0	0
$928$	5568.00	0.196960
$929$	−17202.0	−0.607513	−0.303756	−	0.952750i	$-0.598241\pi$
$929$	−17202.0	−0.607513	−0.303756	+	0.952750i	$0.598241\pi$
$930$	0	0
$931$	−6441.00	−0.226740
$932$	−10768.0	−0.378452
$933$	0	0
$934$	28588.0	1.00153
$935$	2880.00	0.100734
$936$	0	0
$937$	−27214.0	−0.948818	−0.474409	−	0.880305i	$-0.657338\pi$
$937$	−27214.0	−0.948818	−0.474409	+	0.880305i	$0.657338\pi$
$938$	−720.000	−0.0250627
$939$	0	0
$940$	10800.0	0.374742
$941$	22314.0	0.773024	0.386512	−	0.922284i	$-0.373680\pi$
$941$	22314.0	0.773024	0.386512	+	0.922284i	$0.373680\pi$
$942$	0	0
$943$	−29760.0	−1.02770
$944$	−9696.00	−0.334299
$945$	0	0
$946$	−8832.00	−0.303544
$947$	−27714.0	−0.950986	−0.475493	−	0.879719i	$-0.657730\pi$
$947$	−27714.0	−0.950986	−0.475493	+	0.879719i	$0.657730\pi$
$948$	0	0
$949$	−140.000	−0.00478882
$950$	950.000	0.0324443
$951$	0	0
$952$	576.000	0.0196095
$953$	25950.0	0.882060	0.441030	−	0.897492i	$-0.354613\pi$
$953$	25950.0	0.882060	0.441030	+	0.897492i	$0.354613\pi$
$954$	0	0
$955$	3840.00	0.130115
$956$	−17344.0	−0.586763
$957$	0	0
$958$	−22368.0	−0.754360
$959$	4704.00	0.158394
$960$	0	0
$961$	−24315.0	−0.816186
$962$	−1880.00	−0.0630079
$963$	0	0
$964$	−3768.00	−0.125891
$965$	−15110.0	−0.504050
$966$	0	0
$967$	27214.0	0.905009	0.452504	−	0.891762i	$-0.350531\pi$
$967$	27214.0	0.905009	0.452504	+	0.891762i	$0.350531\pi$
$968$	−8600.00	−0.285552
$969$	0	0
$970$	8300.00	0.274739
$971$	−16642.0	−0.550018	−0.275009	−	0.961442i	$-0.588681\pi$
$971$	−16642.0	−0.550018	−0.275009	+	0.961442i	$0.588681\pi$
$972$	0	0
$973$	−1208.00	−0.0398013
$974$	−32752.0	−1.07746
$975$	0	0
$976$	7200.00	0.236134
$977$	3974.00	0.130133	0.0650663	−	0.997881i	$-0.479274\pi$
$977$	3974.00	0.130133	0.0650663	+	0.997881i	$0.479274\pi$
$978$	0	0
$979$	−3392.00	−0.110734
$980$	6780.00	0.220999
$981$	0	0
$982$	−39168.0	−1.27281
$983$	−25680.0	−0.833230	−0.416615	−	0.909083i	$-0.636784\pi$
$983$	−25680.0	−0.833230	−0.416615	+	0.909083i	$0.636784\pi$
$984$	0	0
$985$	−5750.00	−0.186000
$986$	−12528.0	−0.404638
$987$	0	0
$988$	−760.000	−0.0244725
$989$	34224.0	1.10036
$990$	0	0
$991$	22170.0	0.710649	0.355325	−	0.934743i	$-0.384370\pi$
$991$	22170.0	0.710649	0.355325	+	0.934743i	$0.384370\pi$
$992$	−2368.00	−0.0757904
$993$	0	0
$994$	−1824.00	−0.0582030
$995$	8580.00	0.273371
$996$	0	0
$997$	1096.00	0.0348151	0.0174076	−	0.999848i	$-0.494459\pi$
$997$	1096.00	0.0348151	0.0174076	+	0.999848i	$0.494459\pi$
$998$	41448.0	1.31464
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.4.a.h.1.1		1
3.2	odd	2		570.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.a.a.1.1	✓	1	3.2	odd	2
1710.4.a.h.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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