LMFDB - Embedded newform 1170.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,4,Mod(1,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, 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("1170.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1170.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:	$69.0322347067$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{7} +8.00000 q^{8} +O(q^{10})$

\(q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{7} +8.00000 q^{8} +10.0000 q^{10} +36.0000 q^{11} -13.0000 q^{13} -28.0000 q^{14} +16.0000 q^{16} -68.0000 q^{17} -158.000 q^{19} +20.0000 q^{20} +72.0000 q^{22} -46.0000 q^{23} +25.0000 q^{25} -26.0000 q^{26} -56.0000 q^{28} +8.00000 q^{29} -176.000 q^{31} +32.0000 q^{32} -136.000 q^{34} -70.0000 q^{35} +62.0000 q^{37} -316.000 q^{38} +40.0000 q^{40} -30.0000 q^{41} +252.000 q^{43} +144.000 q^{44} -92.0000 q^{46} +120.000 q^{47} -147.000 q^{49} +50.0000 q^{50} -52.0000 q^{52} -758.000 q^{53} +180.000 q^{55} -112.000 q^{56} +16.0000 q^{58} -252.000 q^{59} +398.000 q^{61} -352.000 q^{62} +64.0000 q^{64} -65.0000 q^{65} +884.000 q^{67} -272.000 q^{68} -140.000 q^{70} +80.0000 q^{71} -660.000 q^{73} +124.000 q^{74} -632.000 q^{76} -504.000 q^{77} +568.000 q^{79} +80.0000 q^{80} -60.0000 q^{82} -1084.00 q^{83} -340.000 q^{85} +504.000 q^{86} +288.000 q^{88} -1250.00 q^{89} +182.000 q^{91} -184.000 q^{92} +240.000 q^{94} -790.000 q^{95} +84.0000 q^{97} -294.000 q^{98} +O(q^{100})\)

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
$7$	−14.0000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−14.0000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	8.00000	0.353553
$9$	0	0
$10$	10.0000	0.316228
$11$	36.0000	0.986764	0.493382	−	0.869813i	$-0.335760\pi$
$11$	36.0000	0.986764	0.493382	+	0.869813i	$0.335760\pi$
$12$	0	0
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−28.0000	−0.534522
$15$	0	0
$16$	16.0000	0.250000
$17$	−68.0000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−68.0000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	−158.000	−1.90777	−0.953886	−	0.300168i	$-0.902957\pi$
$19$	−158.000	−1.90777	−0.953886	+	0.300168i	$0.902957\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	72.0000	0.697748
$23$	−46.0000	−0.417029	−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−46.0000	−0.417029	−0.208514	+	0.978019i	$0.566863\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−26.0000	−0.196116
$27$	0	0
$28$	−56.0000	−0.377964
$29$	8.00000	0.0512263	0.0256132	−	0.999672i	$-0.491846\pi$
$29$	8.00000	0.0512263	0.0256132	+	0.999672i	$0.491846\pi$
$30$	0	0
$31$	−176.000	−1.01969	−0.509847	−	0.860265i	$-0.670298\pi$
$31$	−176.000	−1.01969	−0.509847	+	0.860265i	$0.670298\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−136.000	−0.685994
$35$	−70.0000	−0.338062
$36$	0	0
$37$	62.0000	0.275479	0.137740	−	0.990468i	$-0.456016\pi$
$37$	62.0000	0.275479	0.137740	+	0.990468i	$0.456016\pi$
$38$	−316.000	−1.34900
$39$	0	0
$40$	40.0000	0.158114
$41$	−30.0000	−0.114273	−0.0571367	−	0.998366i	$-0.518197\pi$
$41$	−30.0000	−0.114273	−0.0571367	+	0.998366i	$0.518197\pi$
$42$	0	0
$43$	252.000	0.893713	0.446856	−	0.894606i	$-0.352544\pi$
$43$	252.000	0.893713	0.446856	+	0.894606i	$0.352544\pi$
$44$	144.000	0.493382
$45$	0	0
$46$	−92.0000	−0.294884
$47$	120.000	0.372421	0.186211	−	0.982510i	$-0.440379\pi$
$47$	120.000	0.372421	0.186211	+	0.982510i	$0.440379\pi$
$48$	0	0
$49$	−147.000	−0.428571
$50$	50.0000	0.141421
$51$	0	0
$52$	−52.0000	−0.138675
$53$	−758.000	−1.96452	−0.982258	−	0.187537i	$-0.939950\pi$
$53$	−758.000	−1.96452	−0.982258	+	0.187537i	$0.939950\pi$
$54$	0	0
$55$	180.000	0.441294
$56$	−112.000	−0.267261
$57$	0	0
$58$	16.0000	0.0362225
$59$	−252.000	−0.556061	−0.278031	−	0.960572i	$-0.589682\pi$
$59$	−252.000	−0.556061	−0.278031	+	0.960572i	$0.589682\pi$
$60$	0	0
$61$	398.000	0.835388	0.417694	−	0.908588i	$-0.362838\pi$
$61$	398.000	0.835388	0.417694	+	0.908588i	$0.362838\pi$
$62$	−352.000	−0.721033
$63$	0	0
$64$	64.0000	0.125000
$65$	−65.0000	−0.124035
$66$	0	0
$67$	884.000	1.61191	0.805954	−	0.591979i	$-0.201653\pi$
$67$	884.000	1.61191	0.805954	+	0.591979i	$0.201653\pi$
$68$	−272.000	−0.485071
$69$	0	0
$70$	−140.000	−0.239046
$71$	80.0000	0.133722	0.0668609	−	0.997762i	$-0.478702\pi$
$71$	80.0000	0.133722	0.0668609	+	0.997762i	$0.478702\pi$
$72$	0	0
$73$	−660.000	−1.05818	−0.529090	−	0.848566i	$-0.677467\pi$
$73$	−660.000	−1.05818	−0.529090	+	0.848566i	$0.677467\pi$
$74$	124.000	0.194793
$75$	0	0
$76$	−632.000	−0.953886
$77$	−504.000	−0.745924
$78$	0	0
$79$	568.000	0.808924	0.404462	−	0.914555i	$-0.367459\pi$
$79$	568.000	0.808924	0.404462	+	0.914555i	$0.367459\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	−60.0000	−0.0808036
$83$	−1084.00	−1.43355	−0.716774	−	0.697306i	$-0.754382\pi$
$83$	−1084.00	−1.43355	−0.716774	+	0.697306i	$0.754382\pi$
$84$	0	0
$85$	−340.000	−0.433861
$86$	504.000	0.631950
$87$	0	0
$88$	288.000	0.348874
$89$	−1250.00	−1.48876	−0.744381	−	0.667756i	$-0.767255\pi$
$89$	−1250.00	−1.48876	−0.744381	+	0.667756i	$0.767255\pi$
$90$	0	0
$91$	182.000	0.209657
$92$	−184.000	−0.208514
$93$	0	0
$94$	240.000	0.263342
$95$	−790.000	−0.853182
$96$	0	0
$97$	84.0000	0.0879269	0.0439634	−	0.999033i	$-0.486001\pi$
$97$	84.0000	0.0879269	0.0439634	+	0.999033i	$0.486001\pi$
$98$	−294.000	−0.303046
$99$	0	0
$100$	100.000	0.100000
$101$	−980.000	−0.965482	−0.482741	−	0.875763i	$-0.660359\pi$
$101$	−980.000	−0.965482	−0.482741	+	0.875763i	$0.660359\pi$
$102$	0	0
$103$	−1708.00	−1.63392	−0.816962	−	0.576691i	$-0.804344\pi$
$103$	−1708.00	−1.63392	−0.816962	+	0.576691i	$0.804344\pi$
$104$	−104.000	−0.0980581
$105$	0	0
$106$	−1516.00	−1.38912
$107$	−1908.00	−1.72386	−0.861931	−	0.507025i	$-0.830745\pi$
$107$	−1908.00	−1.72386	−0.861931	+	0.507025i	$0.830745\pi$
$108$	0	0
$109$	656.000	0.576453	0.288227	−	0.957562i	$-0.406934\pi$
$109$	656.000	0.576453	0.288227	+	0.957562i	$0.406934\pi$
$110$	360.000	0.312042
$111$	0	0
$112$	−224.000	−0.188982
$113$	488.000	0.406258	0.203129	−	0.979152i	$-0.434889\pi$
$113$	488.000	0.406258	0.203129	+	0.979152i	$0.434889\pi$
$114$	0	0
$115$	−230.000	−0.186501
$116$	32.0000	0.0256132
$117$	0	0
$118$	−504.000	−0.393195
$119$	952.000	0.733359
$120$	0	0
$121$	−35.0000	−0.0262960
$122$	796.000	0.590709
$123$	0	0
$124$	−704.000	−0.509847
$125$	125.000	0.0894427
$126$	0	0
$127$	−1740.00	−1.21575	−0.607874	−	0.794033i	$-0.707977\pi$
$127$	−1740.00	−1.21575	−0.607874	+	0.794033i	$0.707977\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	−130.000	−0.0877058
$131$	2486.00	1.65804	0.829018	−	0.559221i	$-0.188900\pi$
$131$	2486.00	1.65804	0.829018	+	0.559221i	$0.188900\pi$
$132$	0	0
$133$	2212.00	1.44214
$134$	1768.00	1.13979
$135$	0	0
$136$	−544.000	−0.342997
$137$	1614.00	1.00652	0.503260	−	0.864135i	$-0.332134\pi$
$137$	1614.00	1.00652	0.503260	+	0.864135i	$0.332134\pi$
$138$	0	0
$139$	376.000	0.229438	0.114719	−	0.993398i	$-0.463403\pi$
$139$	376.000	0.229438	0.114719	+	0.993398i	$0.463403\pi$
$140$	−280.000	−0.169031
$141$	0	0
$142$	160.000	0.0945556
$143$	−468.000	−0.273679
$144$	0	0
$145$	40.0000	0.0229091
$146$	−1320.00	−0.748246
$147$	0	0
$148$	248.000	0.137740
$149$	58.0000	0.0318896	0.0159448	−	0.999873i	$-0.494924\pi$
$149$	58.0000	0.0318896	0.0159448	+	0.999873i	$0.494924\pi$
$150$	0	0
$151$	−224.000	−0.120721	−0.0603605	−	0.998177i	$-0.519225\pi$
$151$	−224.000	−0.120721	−0.0603605	+	0.998177i	$0.519225\pi$
$152$	−1264.00	−0.674500
$153$	0	0
$154$	−1008.00	−0.527448
$155$	−880.000	−0.456021
$156$	0	0
$157$	−1890.00	−0.960754	−0.480377	−	0.877062i	$-0.659500\pi$
$157$	−1890.00	−0.960754	−0.480377	+	0.877062i	$0.659500\pi$
$158$	1136.00	0.571996
$159$	0	0
$160$	160.000	0.0790569
$161$	644.000	0.315244
$162$	0	0
$163$	2056.00	0.987965	0.493983	−	0.869472i	$-0.335541\pi$
$163$	2056.00	0.987965	0.493983	+	0.869472i	$0.335541\pi$
$164$	−120.000	−0.0571367
$165$	0	0
$166$	−2168.00	−1.01367
$167$	−1556.00	−0.720999	−0.360500	−	0.932759i	$-0.617394\pi$
$167$	−1556.00	−0.720999	−0.360500	+	0.932759i	$0.617394\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−680.000	−0.306786
$171$	0	0
$172$	1008.00	0.446856
$173$	−22.0000	−0.00966838	−0.00483419	−	0.999988i	$-0.501539\pi$
$173$	−22.0000	−0.00966838	−0.00483419	+	0.999988i	$0.501539\pi$
$174$	0	0
$175$	−350.000	−0.151186
$176$	576.000	0.246691
$177$	0	0
$178$	−2500.00	−1.05271
$179$	−998.000	−0.416726	−0.208363	−	0.978052i	$-0.566814\pi$
$179$	−998.000	−0.416726	−0.208363	+	0.978052i	$0.566814\pi$
$180$	0	0
$181$	−422.000	−0.173298	−0.0866492	−	0.996239i	$-0.527616\pi$
$181$	−422.000	−0.173298	−0.0866492	+	0.996239i	$0.527616\pi$
$182$	364.000	0.148250
$183$	0	0
$184$	−368.000	−0.147442
$185$	310.000	0.123198
$186$	0	0
$187$	−2448.00	−0.957302
$188$	480.000	0.186211
$189$	0	0
$190$	−1580.00	−0.603291
$191$	4928.00	1.86690	0.933449	−	0.358710i	$-0.116783\pi$
$191$	4928.00	1.86690	0.933449	+	0.358710i	$0.116783\pi$
$192$	0	0
$193$	1416.00	0.528114	0.264057	−	0.964507i	$-0.414939\pi$
$193$	1416.00	0.528114	0.264057	+	0.964507i	$0.414939\pi$
$194$	168.000	0.0621737
$195$	0	0
$196$	−588.000	−0.214286
$197$	−1110.00	−0.401443	−0.200721	−	0.979648i	$-0.564329\pi$
$197$	−1110.00	−0.401443	−0.200721	+	0.979648i	$0.564329\pi$
$198$	0	0
$199$	3856.00	1.37359	0.686795	−	0.726851i	$-0.259017\pi$
$199$	3856.00	1.37359	0.686795	+	0.726851i	$0.259017\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	−1960.00	−0.682699
$203$	−112.000	−0.0387234
$204$	0	0
$205$	−150.000	−0.0511047
$206$	−3416.00	−1.15536
$207$	0	0
$208$	−208.000	−0.0693375
$209$	−5688.00	−1.88252
$210$	0	0
$211$	−3684.00	−1.20198	−0.600988	−	0.799258i	$-0.705226\pi$
$211$	−3684.00	−1.20198	−0.600988	+	0.799258i	$0.705226\pi$
$212$	−3032.00	−0.982258
$213$	0	0
$214$	−3816.00	−1.21896
$215$	1260.00	0.399680
$216$	0	0
$217$	2464.00	0.770817
$218$	1312.00	0.407614
$219$	0	0
$220$	720.000	0.220647
$221$	884.000	0.269069
$222$	0	0
$223$	−4146.00	−1.24501	−0.622504	−	0.782617i	$-0.713884\pi$
$223$	−4146.00	−1.24501	−0.622504	+	0.782617i	$0.713884\pi$
$224$	−448.000	−0.133631
$225$	0	0
$226$	976.000	0.287268
$227$	1356.00	0.396480	0.198240	−	0.980154i	$-0.436478\pi$
$227$	1356.00	0.396480	0.198240	+	0.980154i	$0.436478\pi$
$228$	0	0
$229$	2072.00	0.597911	0.298955	−	0.954267i	$-0.403362\pi$
$229$	2072.00	0.597911	0.298955	+	0.954267i	$0.403362\pi$
$230$	−460.000	−0.131876
$231$	0	0
$232$	64.0000	0.0181112
$233$	1516.00	0.426251	0.213125	−	0.977025i	$-0.431636\pi$
$233$	1516.00	0.426251	0.213125	+	0.977025i	$0.431636\pi$
$234$	0	0
$235$	600.000	0.166552
$236$	−1008.00	−0.278031
$237$	0	0
$238$	1904.00	0.518563
$239$	−3888.00	−1.05228	−0.526138	−	0.850399i	$-0.676360\pi$
$239$	−3888.00	−1.05228	−0.526138	+	0.850399i	$0.676360\pi$
$240$	0	0
$241$	−5662.00	−1.51337	−0.756684	−	0.653781i	$-0.773182\pi$
$241$	−5662.00	−1.51337	−0.756684	+	0.653781i	$0.773182\pi$
$242$	−70.0000	−0.0185941
$243$	0	0
$244$	1592.00	0.417694
$245$	−735.000	−0.191663
$246$	0	0
$247$	2054.00	0.529121
$248$	−1408.00	−0.360516
$249$	0	0
$250$	250.000	0.0632456
$251$	5370.00	1.35040	0.675202	−	0.737633i	$-0.264056\pi$
$251$	5370.00	1.35040	0.675202	+	0.737633i	$0.264056\pi$
$252$	0	0
$253$	−1656.00	−0.411509
$254$	−3480.00	−0.859664
$255$	0	0
$256$	256.000	0.0625000
$257$	−6944.00	−1.68543	−0.842714	−	0.538362i	$-0.819043\pi$
$257$	−6944.00	−1.68543	−0.842714	+	0.538362i	$0.819043\pi$
$258$	0	0
$259$	−868.000	−0.208243
$260$	−260.000	−0.0620174
$261$	0	0
$262$	4972.00	1.17241
$263$	−4266.00	−1.00020	−0.500100	−	0.865967i	$-0.666704\pi$
$263$	−4266.00	−1.00020	−0.500100	+	0.865967i	$0.666704\pi$
$264$	0	0
$265$	−3790.00	−0.878558
$266$	4424.00	1.01975
$267$	0	0
$268$	3536.00	0.805954
$269$	−524.000	−0.118769	−0.0593845	−	0.998235i	$-0.518914\pi$
$269$	−524.000	−0.118769	−0.0593845	+	0.998235i	$0.518914\pi$
$270$	0	0
$271$	3712.00	0.832059	0.416029	−	0.909351i	$-0.363421\pi$
$271$	3712.00	0.832059	0.416029	+	0.909351i	$0.363421\pi$
$272$	−1088.00	−0.242536
$273$	0	0
$274$	3228.00	0.711718
$275$	900.000	0.197353
$276$	0	0
$277$	7854.00	1.70361	0.851807	−	0.523856i	$-0.175507\pi$
$277$	7854.00	1.70361	0.851807	+	0.523856i	$0.175507\pi$
$278$	752.000	0.162237
$279$	0	0
$280$	−560.000	−0.119523
$281$	−2010.00	−0.426714	−0.213357	−	0.976974i	$-0.568440\pi$
$281$	−2010.00	−0.426714	−0.213357	+	0.976974i	$0.568440\pi$
$282$	0	0
$283$	2444.00	0.513359	0.256680	−	0.966497i	$-0.417371\pi$
$283$	2444.00	0.513359	0.256680	+	0.966497i	$0.417371\pi$
$284$	320.000	0.0668609
$285$	0	0
$286$	−936.000	−0.193520
$287$	420.000	0.0863826
$288$	0	0
$289$	−289.000	−0.0588235
$290$	80.0000	0.0161992
$291$	0	0
$292$	−2640.00	−0.529090
$293$	−6702.00	−1.33630	−0.668148	−	0.744028i	$-0.732913\pi$
$293$	−6702.00	−1.33630	−0.668148	+	0.744028i	$0.732913\pi$
$294$	0	0
$295$	−1260.00	−0.248678
$296$	496.000	0.0973967
$297$	0	0
$298$	116.000	0.0225493
$299$	598.000	0.115663
$300$	0	0
$301$	−3528.00	−0.675583
$302$	−448.000	−0.0853626
$303$	0	0
$304$	−2528.00	−0.476943
$305$	1990.00	0.373597
$306$	0	0
$307$	−300.000	−0.0557717	−0.0278858	−	0.999611i	$-0.508877\pi$
$307$	−300.000	−0.0557717	−0.0278858	+	0.999611i	$0.508877\pi$
$308$	−2016.00	−0.372962
$309$	0	0
$310$	−1760.00	−0.322456
$311$	3816.00	0.695773	0.347887	−	0.937537i	$-0.386899\pi$
$311$	3816.00	0.695773	0.347887	+	0.937537i	$0.386899\pi$
$312$	0	0
$313$	2910.00	0.525505	0.262752	−	0.964863i	$-0.415370\pi$
$313$	2910.00	0.525505	0.262752	+	0.964863i	$0.415370\pi$
$314$	−3780.00	−0.679356
$315$	0	0
$316$	2272.00	0.404462
$317$	−26.0000	−0.00460664	−0.00230332	−	0.999997i	$-0.500733\pi$
$317$	−26.0000	−0.00460664	−0.00230332	+	0.999997i	$0.500733\pi$
$318$	0	0
$319$	288.000	0.0505483
$320$	320.000	0.0559017
$321$	0	0
$322$	1288.00	0.222911
$323$	10744.0	1.85081
$324$	0	0
$325$	−325.000	−0.0554700
$326$	4112.00	0.698597
$327$	0	0
$328$	−240.000	−0.0404018
$329$	−1680.00	−0.281524
$330$	0	0
$331$	3250.00	0.539686	0.269843	−	0.962904i	$-0.413028\pi$
$331$	3250.00	0.539686	0.269843	+	0.962904i	$0.413028\pi$
$332$	−4336.00	−0.716774
$333$	0	0
$334$	−3112.00	−0.509824
$335$	4420.00	0.720867
$336$	0	0
$337$	758.000	0.122525	0.0612624	−	0.998122i	$-0.480487\pi$
$337$	758.000	0.122525	0.0612624	+	0.998122i	$0.480487\pi$
$338$	338.000	0.0543928
$339$	0	0
$340$	−1360.00	−0.216930
$341$	−6336.00	−1.00620
$342$	0	0
$343$	6860.00	1.07990
$344$	2016.00	0.315975
$345$	0	0
$346$	−44.0000	−0.00683657
$347$	11168.0	1.72775	0.863876	−	0.503705i	$-0.168030\pi$
$347$	11168.0	1.72775	0.863876	+	0.503705i	$0.168030\pi$
$348$	0	0
$349$	12968.0	1.98900	0.994500	−	0.104735i	$-0.0333994\pi$
$349$	12968.0	1.98900	0.994500	+	0.104735i	$0.0333994\pi$
$350$	−700.000	−0.106904
$351$	0	0
$352$	1152.00	0.174437
$353$	−6218.00	−0.937538	−0.468769	−	0.883321i	$-0.655302\pi$
$353$	−6218.00	−0.937538	−0.468769	+	0.883321i	$0.655302\pi$
$354$	0	0
$355$	400.000	0.0598022
$356$	−5000.00	−0.744381
$357$	0	0
$358$	−1996.00	−0.294670
$359$	−7296.00	−1.07261	−0.536307	−	0.844023i	$-0.680181\pi$
$359$	−7296.00	−1.07261	−0.536307	+	0.844023i	$0.680181\pi$
$360$	0	0
$361$	18105.0	2.63960
$362$	−844.000	−0.122540
$363$	0	0
$364$	728.000	0.104828
$365$	−3300.00	−0.473233
$366$	0	0
$367$	4492.00	0.638911	0.319456	−	0.947601i	$-0.396500\pi$
$367$	4492.00	0.638911	0.319456	+	0.947601i	$0.396500\pi$
$368$	−736.000	−0.104257
$369$	0	0
$370$	620.000	0.0871142
$371$	10612.0	1.48503
$372$	0	0
$373$	−10378.0	−1.44062	−0.720312	−	0.693651i	$-0.756001\pi$
$373$	−10378.0	−1.44062	−0.720312	+	0.693651i	$0.756001\pi$
$374$	−4896.00	−0.676915
$375$	0	0
$376$	960.000	0.131671
$377$	−104.000	−0.0142076
$378$	0	0
$379$	614.000	0.0832165	0.0416083	−	0.999134i	$-0.486752\pi$
$379$	614.000	0.0832165	0.0416083	+	0.999134i	$0.486752\pi$
$380$	−3160.00	−0.426591
$381$	0	0
$382$	9856.00	1.32010
$383$	7460.00	0.995269	0.497635	−	0.867387i	$-0.334202\pi$
$383$	7460.00	0.995269	0.497635	+	0.867387i	$0.334202\pi$
$384$	0	0
$385$	−2520.00	−0.333587
$386$	2832.00	0.373433
$387$	0	0
$388$	336.000	0.0439634
$389$	2020.00	0.263286	0.131643	−	0.991297i	$-0.457975\pi$
$389$	2020.00	0.263286	0.131643	+	0.991297i	$0.457975\pi$
$390$	0	0
$391$	3128.00	0.404577
$392$	−1176.00	−0.151523
$393$	0	0
$394$	−2220.00	−0.283863
$395$	2840.00	0.361762
$396$	0	0
$397$	3262.00	0.412381	0.206190	−	0.978512i	$-0.433893\pi$
$397$	3262.00	0.412381	0.206190	+	0.978512i	$0.433893\pi$
$398$	7712.00	0.971275
$399$	0	0
$400$	400.000	0.0500000
$401$	12050.0	1.50062	0.750310	−	0.661087i	$-0.229904\pi$
$401$	12050.0	1.50062	0.750310	+	0.661087i	$0.229904\pi$
$402$	0	0
$403$	2288.00	0.282812
$404$	−3920.00	−0.482741
$405$	0	0
$406$	−224.000	−0.0273816
$407$	2232.00	0.271833
$408$	0	0
$409$	1198.00	0.144834	0.0724172	−	0.997374i	$-0.476929\pi$
$409$	1198.00	0.144834	0.0724172	+	0.997374i	$0.476929\pi$
$410$	−300.000	−0.0361364
$411$	0	0
$412$	−6832.00	−0.816962
$413$	3528.00	0.420343
$414$	0	0
$415$	−5420.00	−0.641102
$416$	−416.000	−0.0490290
$417$	0	0
$418$	−11376.0	−1.33114
$419$	−6906.00	−0.805203	−0.402602	−	0.915375i	$-0.631894\pi$
$419$	−6906.00	−0.805203	−0.402602	+	0.915375i	$0.631894\pi$
$420$	0	0
$421$	2724.00	0.315344	0.157672	−	0.987492i	$-0.449601\pi$
$421$	2724.00	0.315344	0.157672	+	0.987492i	$0.449601\pi$
$422$	−7368.00	−0.849926
$423$	0	0
$424$	−6064.00	−0.694561
$425$	−1700.00	−0.194029
$426$	0	0
$427$	−5572.00	−0.631494
$428$	−7632.00	−0.861931
$429$	0	0
$430$	2520.00	0.282617
$431$	−5136.00	−0.573996	−0.286998	−	0.957931i	$-0.592657\pi$
$431$	−5136.00	−0.573996	−0.286998	+	0.957931i	$0.592657\pi$
$432$	0	0
$433$	−6218.00	−0.690111	−0.345055	−	0.938582i	$-0.612140\pi$
$433$	−6218.00	−0.690111	−0.345055	+	0.938582i	$0.612140\pi$
$434$	4928.00	0.545050
$435$	0	0
$436$	2624.00	0.288227
$437$	7268.00	0.795596
$438$	0	0
$439$	2632.00	0.286147	0.143073	−	0.989712i	$-0.454301\pi$
$439$	2632.00	0.286147	0.143073	+	0.989712i	$0.454301\pi$
$440$	1440.00	0.156021
$441$	0	0
$442$	1768.00	0.190261
$443$	408.000	0.0437577	0.0218789	−	0.999761i	$-0.493035\pi$
$443$	408.000	0.0437577	0.0218789	+	0.999761i	$0.493035\pi$
$444$	0	0
$445$	−6250.00	−0.665794
$446$	−8292.00	−0.880353
$447$	0	0
$448$	−896.000	−0.0944911
$449$	4902.00	0.515233	0.257617	−	0.966247i	$-0.417063\pi$
$449$	4902.00	0.515233	0.257617	+	0.966247i	$0.417063\pi$
$450$	0	0
$451$	−1080.00	−0.112761
$452$	1952.00	0.203129
$453$	0	0
$454$	2712.00	0.280353
$455$	910.000	0.0937614
$456$	0	0
$457$	1788.00	0.183018	0.0915089	−	0.995804i	$-0.470831\pi$
$457$	1788.00	0.183018	0.0915089	+	0.995804i	$0.470831\pi$
$458$	4144.00	0.422787
$459$	0	0
$460$	−920.000	−0.0932505
$461$	6590.00	0.665785	0.332893	−	0.942965i	$-0.391975\pi$
$461$	6590.00	0.665785	0.332893	+	0.942965i	$0.391975\pi$
$462$	0	0
$463$	10406.0	1.04451	0.522255	−	0.852790i	$-0.325091\pi$
$463$	10406.0	1.04451	0.522255	+	0.852790i	$0.325091\pi$
$464$	128.000	0.0128066
$465$	0	0
$466$	3032.00	0.301405
$467$	−7284.00	−0.721763	−0.360882	−	0.932612i	$-0.617524\pi$
$467$	−7284.00	−0.721763	−0.360882	+	0.932612i	$0.617524\pi$
$468$	0	0
$469$	−12376.0	−1.21849
$470$	1200.00	0.117770
$471$	0	0
$472$	−2016.00	−0.196597
$473$	9072.00	0.881884
$474$	0	0
$475$	−3950.00	−0.381555
$476$	3808.00	0.366679
$477$	0	0
$478$	−7776.00	−0.744071
$479$	8384.00	0.799738	0.399869	−	0.916572i	$-0.369056\pi$
$479$	8384.00	0.799738	0.399869	+	0.916572i	$0.369056\pi$
$480$	0	0
$481$	−806.000	−0.0764042
$482$	−11324.0	−1.07011
$483$	0	0
$484$	−140.000	−0.0131480
$485$	420.000	0.0393221
$486$	0	0
$487$	−20294.0	−1.88831	−0.944157	−	0.329496i	$-0.893121\pi$
$487$	−20294.0	−1.88831	−0.944157	+	0.329496i	$0.893121\pi$
$488$	3184.00	0.295354
$489$	0	0
$490$	−1470.00	−0.135526
$491$	19302.0	1.77411	0.887054	−	0.461666i	$-0.152748\pi$
$491$	19302.0	1.77411	0.887054	+	0.461666i	$0.152748\pi$
$492$	0	0
$493$	−544.000	−0.0496968
$494$	4108.00	0.374145
$495$	0	0
$496$	−2816.00	−0.254924
$497$	−1120.00	−0.101084
$498$	0	0
$499$	−5186.00	−0.465245	−0.232622	−	0.972567i	$-0.574731\pi$
$499$	−5186.00	−0.465245	−0.232622	+	0.972567i	$0.574731\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	10740.0	0.954880
$503$	11806.0	1.04653	0.523264	−	0.852171i	$-0.324714\pi$
$503$	11806.0	1.04653	0.523264	+	0.852171i	$0.324714\pi$
$504$	0	0
$505$	−4900.00	−0.431777
$506$	−3312.00	−0.290981
$507$	0	0
$508$	−6960.00	−0.607874
$509$	−3002.00	−0.261417	−0.130709	−	0.991421i	$-0.541725\pi$
$509$	−3002.00	−0.261417	−0.130709	+	0.991421i	$0.541725\pi$
$510$	0	0
$511$	9240.00	0.799909
$512$	512.000	0.0441942
$513$	0	0
$514$	−13888.0	−1.19178
$515$	−8540.00	−0.730713
$516$	0	0
$517$	4320.00	0.367492
$518$	−1736.00	−0.147250
$519$	0	0
$520$	−520.000	−0.0438529
$521$	194.000	0.0163134	0.00815671	−	0.999967i	$-0.497404\pi$
$521$	194.000	0.0163134	0.00815671	+	0.999967i	$0.497404\pi$
$522$	0	0
$523$	10268.0	0.858486	0.429243	−	0.903189i	$-0.358780\pi$
$523$	10268.0	0.858486	0.429243	+	0.903189i	$0.358780\pi$
$524$	9944.00	0.829018
$525$	0	0
$526$	−8532.00	−0.707249
$527$	11968.0	0.989249
$528$	0	0
$529$	−10051.0	−0.826087
$530$	−7580.00	−0.621234
$531$	0	0
$532$	8848.00	0.721070
$533$	390.000	0.0316938
$534$	0	0
$535$	−9540.00	−0.770935
$536$	7072.00	0.569895
$537$	0	0
$538$	−1048.00	−0.0839823
$539$	−5292.00	−0.422899
$540$	0	0
$541$	10900.0	0.866225	0.433112	−	0.901340i	$-0.357415\pi$
$541$	10900.0	0.866225	0.433112	+	0.901340i	$0.357415\pi$
$542$	7424.00	0.588354
$543$	0	0
$544$	−2176.00	−0.171499
$545$	3280.00	0.257798
$546$	0	0
$547$	23556.0	1.84128	0.920642	−	0.390409i	$-0.127666\pi$
$547$	23556.0	1.84128	0.920642	+	0.390409i	$0.127666\pi$
$548$	6456.00	0.503260
$549$	0	0
$550$	1800.00	0.139550
$551$	−1264.00	−0.0977281
$552$	0	0
$553$	−7952.00	−0.611489
$554$	15708.0	1.20464
$555$	0	0
$556$	1504.00	0.114719
$557$	10470.0	0.796460	0.398230	−	0.917286i	$-0.369625\pi$
$557$	10470.0	0.796460	0.398230	+	0.917286i	$0.369625\pi$
$558$	0	0
$559$	−3276.00	−0.247871
$560$	−1120.00	−0.0845154
$561$	0	0
$562$	−4020.00	−0.301732
$563$	−22608.0	−1.69239	−0.846193	−	0.532876i	$-0.821111\pi$
$563$	−22608.0	−1.69239	−0.846193	+	0.532876i	$0.821111\pi$
$564$	0	0
$565$	2440.00	0.181684
$566$	4888.00	0.363000
$567$	0	0
$568$	640.000	0.0472778
$569$	−23550.0	−1.73509	−0.867546	−	0.497357i	$-0.834304\pi$
$569$	−23550.0	−1.73509	−0.867546	+	0.497357i	$0.834304\pi$
$570$	0	0
$571$	26424.0	1.93662	0.968310	−	0.249751i	$-0.0803489\pi$
$571$	26424.0	1.93662	0.968310	+	0.249751i	$0.0803489\pi$
$572$	−1872.00	−0.136840
$573$	0	0
$574$	840.000	0.0610817
$575$	−1150.00	−0.0834058
$576$	0	0
$577$	17912.0	1.29235	0.646175	−	0.763189i	$-0.276367\pi$
$577$	17912.0	1.29235	0.646175	+	0.763189i	$0.276367\pi$
$578$	−578.000	−0.0415945
$579$	0	0
$580$	160.000	0.0114545
$581$	15176.0	1.08366
$582$	0	0
$583$	−27288.0	−1.93851
$584$	−5280.00	−0.374123
$585$	0	0
$586$	−13404.0	−0.944905
$587$	23076.0	1.62257	0.811285	−	0.584651i	$-0.198769\pi$
$587$	23076.0	1.62257	0.811285	+	0.584651i	$0.198769\pi$
$588$	0	0
$589$	27808.0	1.94535
$590$	−2520.00	−0.175842
$591$	0	0
$592$	992.000	0.0688698
$593$	−3382.00	−0.234203	−0.117101	−	0.993120i	$-0.537360\pi$
$593$	−3382.00	−0.234203	−0.117101	+	0.993120i	$0.537360\pi$
$594$	0	0
$595$	4760.00	0.327968
$596$	232.000	0.0159448
$597$	0	0
$598$	1196.00	0.0817861
$599$	8296.00	0.565885	0.282943	−	0.959137i	$-0.408689\pi$
$599$	8296.00	0.565885	0.282943	+	0.959137i	$0.408689\pi$
$600$	0	0
$601$	−20042.0	−1.36028	−0.680142	−	0.733081i	$-0.738082\pi$
$601$	−20042.0	−1.36028	−0.680142	+	0.733081i	$0.738082\pi$
$602$	−7056.00	−0.477709
$603$	0	0
$604$	−896.000	−0.0603605
$605$	−175.000	−0.0117599
$606$	0	0
$607$	−6524.00	−0.436245	−0.218123	−	0.975921i	$-0.569993\pi$
$607$	−6524.00	−0.436245	−0.218123	+	0.975921i	$0.569993\pi$
$608$	−5056.00	−0.337250
$609$	0	0
$610$	3980.00	0.264173
$611$	−1560.00	−0.103291
$612$	0	0
$613$	−1226.00	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−1226.00	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	−600.000	−0.0394365
$615$	0	0
$616$	−4032.00	−0.263724
$617$	−4226.00	−0.275741	−0.137871	−	0.990450i	$-0.544026\pi$
$617$	−4226.00	−0.275741	−0.137871	+	0.990450i	$0.544026\pi$
$618$	0	0
$619$	−14866.0	−0.965291	−0.482645	−	0.875816i	$-0.660324\pi$
$619$	−14866.0	−0.965291	−0.482645	+	0.875816i	$0.660324\pi$
$620$	−3520.00	−0.228011
$621$	0	0
$622$	7632.00	0.491986
$623$	17500.0	1.12540
$624$	0	0
$625$	625.000	0.0400000
$626$	5820.00	0.371588
$627$	0	0
$628$	−7560.00	−0.480377
$629$	−4216.00	−0.267254
$630$	0	0
$631$	11580.0	0.730575	0.365287	−	0.930895i	$-0.380971\pi$
$631$	11580.0	0.730575	0.365287	+	0.930895i	$0.380971\pi$
$632$	4544.00	0.285998
$633$	0	0
$634$	−52.0000	−0.00325739
$635$	−8700.00	−0.543699
$636$	0	0
$637$	1911.00	0.118864
$638$	576.000	0.0357430
$639$	0	0
$640$	640.000	0.0395285
$641$	−12738.0	−0.784900	−0.392450	−	0.919773i	$-0.628372\pi$
$641$	−12738.0	−0.784900	−0.392450	+	0.919773i	$0.628372\pi$
$642$	0	0
$643$	−22220.0	−1.36279	−0.681393	−	0.731918i	$-0.738625\pi$
$643$	−22220.0	−1.36279	−0.681393	+	0.731918i	$0.738625\pi$
$644$	2576.00	0.157622
$645$	0	0
$646$	21488.0	1.30872
$647$	−17994.0	−1.09338	−0.546690	−	0.837335i	$-0.684112\pi$
$647$	−17994.0	−1.09338	−0.546690	+	0.837335i	$0.684112\pi$
$648$	0	0
$649$	−9072.00	−0.548701
$650$	−650.000	−0.0392232
$651$	0	0
$652$	8224.00	0.493983
$653$	−10146.0	−0.608030	−0.304015	−	0.952667i	$-0.598327\pi$
$653$	−10146.0	−0.608030	−0.304015	+	0.952667i	$0.598327\pi$
$654$	0	0
$655$	12430.0	0.741497
$656$	−480.000	−0.0285684
$657$	0	0
$658$	−3360.00	−0.199068
$659$	−8370.00	−0.494763	−0.247382	−	0.968918i	$-0.579570\pi$
$659$	−8370.00	−0.494763	−0.247382	+	0.968918i	$0.579570\pi$
$660$	0	0
$661$	3404.00	0.200303	0.100151	−	0.994972i	$-0.468067\pi$
$661$	3404.00	0.200303	0.100151	+	0.994972i	$0.468067\pi$
$662$	6500.00	0.381616
$663$	0	0
$664$	−8672.00	−0.506836
$665$	11060.0	0.644945
$666$	0	0
$667$	−368.000	−0.0213628
$668$	−6224.00	−0.360500
$669$	0	0
$670$	8840.00	0.509730
$671$	14328.0	0.824331
$672$	0	0
$673$	−5078.00	−0.290851	−0.145425	−	0.989369i	$-0.546455\pi$
$673$	−5078.00	−0.290851	−0.145425	+	0.989369i	$0.546455\pi$
$674$	1516.00	0.0866382
$675$	0	0
$676$	676.000	0.0384615
$677$	1094.00	0.0621061	0.0310531	−	0.999518i	$-0.490114\pi$
$677$	1094.00	0.0621061	0.0310531	+	0.999518i	$0.490114\pi$
$678$	0	0
$679$	−1176.00	−0.0664665
$680$	−2720.00	−0.153393
$681$	0	0
$682$	−12672.0	−0.711490
$683$	−3108.00	−0.174121	−0.0870603	−	0.996203i	$-0.527747\pi$
$683$	−3108.00	−0.174121	−0.0870603	+	0.996203i	$0.527747\pi$
$684$	0	0
$685$	8070.00	0.450130
$686$	13720.0	0.763604
$687$	0	0
$688$	4032.00	0.223428
$689$	9854.00	0.544858
$690$	0	0
$691$	−23638.0	−1.30135	−0.650674	−	0.759357i	$-0.725514\pi$
$691$	−23638.0	−1.30135	−0.650674	+	0.759357i	$0.725514\pi$
$692$	−88.0000	−0.00483419
$693$	0	0
$694$	22336.0	1.22170
$695$	1880.00	0.102608
$696$	0	0
$697$	2040.00	0.110862
$698$	25936.0	1.40644
$699$	0	0
$700$	−1400.00	−0.0755929
$701$	−27060.0	−1.45798	−0.728989	−	0.684526i	$-0.760009\pi$
$701$	−27060.0	−1.45798	−0.728989	+	0.684526i	$0.760009\pi$
$702$	0	0
$703$	−9796.00	−0.525552
$704$	2304.00	0.123346
$705$	0	0
$706$	−12436.0	−0.662939
$707$	13720.0	0.729836
$708$	0	0
$709$	3536.00	0.187302	0.0936511	−	0.995605i	$-0.470146\pi$
$709$	3536.00	0.187302	0.0936511	+	0.995605i	$0.470146\pi$
$710$	800.000	0.0422866
$711$	0	0
$712$	−10000.0	−0.526357
$713$	8096.00	0.425242
$714$	0	0
$715$	−2340.00	−0.122393
$716$	−3992.00	−0.208363
$717$	0	0
$718$	−14592.0	−0.758452
$719$	−17204.0	−0.892352	−0.446176	−	0.894945i	$-0.647214\pi$
$719$	−17204.0	−0.892352	−0.446176	+	0.894945i	$0.647214\pi$
$720$	0	0
$721$	23912.0	1.23513
$722$	36210.0	1.86648
$723$	0	0
$724$	−1688.00	−0.0866492
$725$	200.000	0.0102453
$726$	0	0
$727$	−24224.0	−1.23579	−0.617894	−	0.786261i	$-0.712014\pi$
$727$	−24224.0	−1.23579	−0.617894	+	0.786261i	$0.712014\pi$
$728$	1456.00	0.0741249
$729$	0	0
$730$	−6600.00	−0.334626
$731$	−17136.0	−0.867029
$732$	0	0
$733$	25958.0	1.30802	0.654011	−	0.756485i	$-0.273085\pi$
$733$	25958.0	1.30802	0.654011	+	0.756485i	$0.273085\pi$
$734$	8984.00	0.451779
$735$	0	0
$736$	−1472.00	−0.0737210
$737$	31824.0	1.59057
$738$	0	0
$739$	12790.0	0.636655	0.318327	−	0.947981i	$-0.396879\pi$
$739$	12790.0	0.636655	0.318327	+	0.947981i	$0.396879\pi$
$740$	1240.00	0.0615991
$741$	0	0
$742$	21224.0	1.05008
$743$	−5428.00	−0.268013	−0.134007	−	0.990980i	$-0.542784\pi$
$743$	−5428.00	−0.268013	−0.134007	+	0.990980i	$0.542784\pi$
$744$	0	0
$745$	290.000	0.0142614
$746$	−20756.0	−1.01867
$747$	0	0
$748$	−9792.00	−0.478651
$749$	26712.0	1.30312
$750$	0	0
$751$	37720.0	1.83279	0.916393	−	0.400280i	$-0.131087\pi$
$751$	37720.0	1.83279	0.916393	+	0.400280i	$0.131087\pi$
$752$	1920.00	0.0931053
$753$	0	0
$754$	−208.000	−0.0100463
$755$	−1120.00	−0.0539880
$756$	0	0
$757$	10034.0	0.481759	0.240880	−	0.970555i	$-0.422564\pi$
$757$	10034.0	0.481759	0.240880	+	0.970555i	$0.422564\pi$
$758$	1228.00	0.0588430
$759$	0	0
$760$	−6320.00	−0.301645
$761$	2586.00	0.123183	0.0615916	−	0.998101i	$-0.480382\pi$
$761$	2586.00	0.123183	0.0615916	+	0.998101i	$0.480382\pi$
$762$	0	0
$763$	−9184.00	−0.435758
$764$	19712.0	0.933449
$765$	0	0
$766$	14920.0	0.703762
$767$	3276.00	0.154224
$768$	0	0
$769$	2810.00	0.131770	0.0658850	−	0.997827i	$-0.479013\pi$
$769$	2810.00	0.131770	0.0658850	+	0.997827i	$0.479013\pi$
$770$	−5040.00	−0.235882
$771$	0	0
$772$	5664.00	0.264057
$773$	−28958.0	−1.34741	−0.673704	−	0.739001i	$-0.735298\pi$
$773$	−28958.0	−1.34741	−0.673704	+	0.739001i	$0.735298\pi$
$774$	0	0
$775$	−4400.00	−0.203939
$776$	672.000	0.0310868
$777$	0	0
$778$	4040.00	0.186171
$779$	4740.00	0.218008
$780$	0	0
$781$	2880.00	0.131952
$782$	6256.00	0.286079
$783$	0	0
$784$	−2352.00	−0.107143
$785$	−9450.00	−0.429662
$786$	0	0
$787$	35384.0	1.60267	0.801336	−	0.598214i	$-0.204123\pi$
$787$	35384.0	1.60267	0.801336	+	0.598214i	$0.204123\pi$
$788$	−4440.00	−0.200721
$789$	0	0
$790$	5680.00	0.255804
$791$	−6832.00	−0.307102
$792$	0	0
$793$	−5174.00	−0.231695
$794$	6524.00	0.291597
$795$	0	0
$796$	15424.0	0.686795
$797$	−3526.00	−0.156709	−0.0783547	−	0.996926i	$-0.524967\pi$
$797$	−3526.00	−0.156709	−0.0783547	+	0.996926i	$0.524967\pi$
$798$	0	0
$799$	−8160.00	−0.361302
$800$	800.000	0.0353553
$801$	0	0
$802$	24100.0	1.06110
$803$	−23760.0	−1.04417
$804$	0	0
$805$	3220.00	0.140981
$806$	4576.00	0.199979
$807$	0	0
$808$	−7840.00	−0.341349
$809$	−29666.0	−1.28925	−0.644624	−	0.764500i	$-0.722986\pi$
$809$	−29666.0	−1.28925	−0.644624	+	0.764500i	$0.722986\pi$
$810$	0	0
$811$	19666.0	0.851500	0.425750	−	0.904841i	$-0.360010\pi$
$811$	19666.0	0.851500	0.425750	+	0.904841i	$0.360010\pi$
$812$	−448.000	−0.0193617
$813$	0	0
$814$	4464.00	0.192215
$815$	10280.0	0.441832
$816$	0	0
$817$	−39816.0	−1.70500
$818$	2396.00	0.102413
$819$	0	0
$820$	−600.000	−0.0255523
$821$	−19702.0	−0.837521	−0.418760	−	0.908097i	$-0.637535\pi$
$821$	−19702.0	−0.837521	−0.418760	+	0.908097i	$0.637535\pi$
$822$	0	0
$823$	32860.0	1.39177	0.695886	−	0.718153i	$-0.255012\pi$
$823$	32860.0	1.39177	0.695886	+	0.718153i	$0.255012\pi$
$824$	−13664.0	−0.577680
$825$	0	0
$826$	7056.00	0.297227
$827$	−17412.0	−0.732134	−0.366067	−	0.930589i	$-0.619296\pi$
$827$	−17412.0	−0.732134	−0.366067	+	0.930589i	$0.619296\pi$
$828$	0	0
$829$	46910.0	1.96532	0.982661	−	0.185412i	$-0.0593621\pi$
$829$	46910.0	1.96532	0.982661	+	0.185412i	$0.0593621\pi$
$830$	−10840.0	−0.453328
$831$	0	0
$832$	−832.000	−0.0346688
$833$	9996.00	0.415775
$834$	0	0
$835$	−7780.00	−0.322441
$836$	−22752.0	−0.941261
$837$	0	0
$838$	−13812.0	−0.569365
$839$	13720.0	0.564561	0.282281	−	0.959332i	$-0.408909\pi$
$839$	13720.0	0.564561	0.282281	+	0.959332i	$0.408909\pi$
$840$	0	0
$841$	−24325.0	−0.997376
$842$	5448.00	0.222982
$843$	0	0
$844$	−14736.0	−0.600988
$845$	845.000	0.0344010
$846$	0	0
$847$	490.000	0.0198779
$848$	−12128.0	−0.491129
$849$	0	0
$850$	−3400.00	−0.137199
$851$	−2852.00	−0.114883
$852$	0	0
$853$	−10610.0	−0.425885	−0.212942	−	0.977065i	$-0.568305\pi$
$853$	−10610.0	−0.425885	−0.212942	+	0.977065i	$0.568305\pi$
$854$	−11144.0	−0.446534
$855$	0	0
$856$	−15264.0	−0.609478
$857$	−44488.0	−1.77326	−0.886628	−	0.462482i	$-0.846959\pi$
$857$	−44488.0	−1.77326	−0.886628	+	0.462482i	$0.846959\pi$
$858$	0	0
$859$	7764.00	0.308387	0.154193	−	0.988041i	$-0.450722\pi$
$859$	7764.00	0.308387	0.154193	+	0.988041i	$0.450722\pi$
$860$	5040.00	0.199840
$861$	0	0
$862$	−10272.0	−0.405877
$863$	−40572.0	−1.60033	−0.800166	−	0.599778i	$-0.795255\pi$
$863$	−40572.0	−1.60033	−0.800166	+	0.599778i	$0.795255\pi$
$864$	0	0
$865$	−110.000	−0.00432383
$866$	−12436.0	−0.487982
$867$	0	0
$868$	9856.00	0.385408
$869$	20448.0	0.798217
$870$	0	0
$871$	−11492.0	−0.447063
$872$	5248.00	0.203807
$873$	0	0
$874$	14536.0	0.562572
$875$	−1750.00	−0.0676123
$876$	0	0
$877$	−49734.0	−1.91493	−0.957467	−	0.288541i	$-0.906830\pi$
$877$	−49734.0	−1.91493	−0.957467	+	0.288541i	$0.906830\pi$
$878$	5264.00	0.202336
$879$	0	0
$880$	2880.00	0.110324
$881$	27498.0	1.05157	0.525784	−	0.850618i	$-0.323772\pi$
$881$	27498.0	1.05157	0.525784	+	0.850618i	$0.323772\pi$
$882$	0	0
$883$	−31908.0	−1.21607	−0.608035	−	0.793910i	$-0.708042\pi$
$883$	−31908.0	−1.21607	−0.608035	+	0.793910i	$0.708042\pi$
$884$	3536.00	0.134535
$885$	0	0
$886$	816.000	0.0309414
$887$	36842.0	1.39463	0.697313	−	0.716767i	$-0.254379\pi$
$887$	36842.0	1.39463	0.697313	+	0.716767i	$0.254379\pi$
$888$	0	0
$889$	24360.0	0.919019
$890$	−12500.0	−0.470788
$891$	0	0
$892$	−16584.0	−0.622504
$893$	−18960.0	−0.710495
$894$	0	0
$895$	−4990.00	−0.186366
$896$	−1792.00	−0.0668153
$897$	0	0
$898$	9804.00	0.364325
$899$	−1408.00	−0.0522352
$900$	0	0
$901$	51544.0	1.90586
$902$	−2160.00	−0.0797341
$903$	0	0
$904$	3904.00	0.143634
$905$	−2110.00	−0.0775014
$906$	0	0
$907$	10852.0	0.397282	0.198641	−	0.980072i	$-0.436347\pi$
$907$	10852.0	0.397282	0.198641	+	0.980072i	$0.436347\pi$
$908$	5424.00	0.198240
$909$	0	0
$910$	1820.00	0.0662994
$911$	−7484.00	−0.272180	−0.136090	−	0.990696i	$-0.543454\pi$
$911$	−7484.00	−0.272180	−0.136090	+	0.990696i	$0.543454\pi$
$912$	0	0
$913$	−39024.0	−1.41457
$914$	3576.00	0.129413
$915$	0	0
$916$	8288.00	0.298955
$917$	−34804.0	−1.25336
$918$	0	0
$919$	4768.00	0.171145	0.0855723	−	0.996332i	$-0.472728\pi$
$919$	4768.00	0.171145	0.0855723	+	0.996332i	$0.472728\pi$
$920$	−1840.00	−0.0659380
$921$	0	0
$922$	13180.0	0.470781
$923$	−1040.00	−0.0370878
$924$	0	0
$925$	1550.00	0.0550959
$926$	20812.0	0.738580
$927$	0	0
$928$	256.000	0.00905562
$929$	−6994.00	−0.247003	−0.123501	−	0.992344i	$-0.539412\pi$
$929$	−6994.00	−0.247003	−0.123501	+	0.992344i	$0.539412\pi$
$930$	0	0
$931$	23226.0	0.817617
$932$	6064.00	0.213125
$933$	0	0
$934$	−14568.0	−0.510364
$935$	−12240.0	−0.428119
$936$	0	0
$937$	−48270.0	−1.68294	−0.841469	−	0.540306i	$-0.818308\pi$
$937$	−48270.0	−1.68294	−0.841469	+	0.540306i	$0.818308\pi$
$938$	−24752.0	−0.861601
$939$	0	0
$940$	2400.00	0.0832759
$941$	19458.0	0.674084	0.337042	−	0.941490i	$-0.390574\pi$
$941$	19458.0	0.674084	0.337042	+	0.941490i	$0.390574\pi$
$942$	0	0
$943$	1380.00	0.0476553
$944$	−4032.00	−0.139015
$945$	0	0
$946$	18144.0	0.623586
$947$	11548.0	0.396261	0.198131	−	0.980176i	$-0.436513\pi$
$947$	11548.0	0.396261	0.198131	+	0.980176i	$0.436513\pi$
$948$	0	0
$949$	8580.00	0.293486
$950$	−7900.00	−0.269800
$951$	0	0
$952$	7616.00	0.259281
$953$	−35172.0	−1.19552	−0.597761	−	0.801674i	$-0.703943\pi$
$953$	−35172.0	−1.19552	−0.597761	+	0.801674i	$0.703943\pi$
$954$	0	0
$955$	24640.0	0.834902
$956$	−15552.0	−0.526138
$957$	0	0
$958$	16768.0	0.565501
$959$	−22596.0	−0.760858
$960$	0	0
$961$	1185.00	0.0397771
$962$	−1612.00	−0.0540260
$963$	0	0
$964$	−22648.0	−0.756684
$965$	7080.00	0.236180
$966$	0	0
$967$	−56062.0	−1.86436	−0.932178	−	0.362000i	$-0.882094\pi$
$967$	−56062.0	−1.86436	−0.932178	+	0.362000i	$0.882094\pi$
$968$	−280.000	−0.00929705
$969$	0	0
$970$	840.000	0.0278049
$971$	20058.0	0.662916	0.331458	−	0.943470i	$-0.392459\pi$
$971$	20058.0	0.662916	0.331458	+	0.943470i	$0.392459\pi$
$972$	0	0
$973$	−5264.00	−0.173439
$974$	−40588.0	−1.33524
$975$	0	0
$976$	6368.00	0.208847
$977$	−53134.0	−1.73993	−0.869963	−	0.493117i	$-0.835857\pi$
$977$	−53134.0	−1.73993	−0.869963	+	0.493117i	$0.835857\pi$
$978$	0	0
$979$	−45000.0	−1.46906
$980$	−2940.00	−0.0958315
$981$	0	0
$982$	38604.0	1.25448
$983$	−6244.00	−0.202597	−0.101298	−	0.994856i	$-0.532300\pi$
$983$	−6244.00	−0.202597	−0.101298	+	0.994856i	$0.532300\pi$
$984$	0	0
$985$	−5550.00	−0.179531
$986$	−1088.00	−0.0351410
$987$	0	0
$988$	8216.00	0.264561
$989$	−11592.0	−0.372704
$990$	0	0
$991$	55840.0	1.78993	0.894963	−	0.446141i	$-0.147202\pi$
$991$	55840.0	1.78993	0.894963	+	0.446141i	$0.147202\pi$
$992$	−5632.00	−0.180258
$993$	0	0
$994$	−2240.00	−0.0714773
$995$	19280.0	0.614289
$996$	0	0
$997$	−1282.00	−0.0407235	−0.0203618	−	0.999793i	$-0.506482\pi$
$997$	−1282.00	−0.0407235	−0.0203618	+	0.999793i	$0.506482\pi$
$998$	−10372.0	−0.328978
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.4.a.n.1.1		1
3.2	odd	2		390.4.a.a.1.1	✓	1
15.14	odd	2		1950.4.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.a.1.1	✓	1	3.2	odd	2
1170.4.a.n.1.1		1	1.1	even	1	trivial
1950.4.a.q.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1170.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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