LMFDB - Embedded newform 1710.4.a.e.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:	$0$
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)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -24.0000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -24.0000 q^{7} -8.00000 q^{8} -10.0000 q^{10} -32.0000 q^{11} +2.00000 q^{13} +48.0000 q^{14} +16.0000 q^{16} -106.000 q^{17} -19.0000 q^{19} +20.0000 q^{20} +64.0000 q^{22} -152.000 q^{23} +25.0000 q^{25} -4.00000 q^{26} -96.0000 q^{28} -90.0000 q^{29} +52.0000 q^{31} -32.0000 q^{32} +212.000 q^{34} -120.000 q^{35} +306.000 q^{37} +38.0000 q^{38} -40.0000 q^{40} -62.0000 q^{41} -268.000 q^{43} -128.000 q^{44} +304.000 q^{46} -456.000 q^{47} +233.000 q^{49} -50.0000 q^{50} +8.00000 q^{52} +318.000 q^{53} -160.000 q^{55} +192.000 q^{56} +180.000 q^{58} -300.000 q^{59} +502.000 q^{61} -104.000 q^{62} +64.0000 q^{64} +10.0000 q^{65} -644.000 q^{67} -424.000 q^{68} +240.000 q^{70} +608.000 q^{71} -198.000 q^{73} -612.000 q^{74} -76.0000 q^{76} +768.000 q^{77} +260.000 q^{79} +80.0000 q^{80} +124.000 q^{82} +1248.00 q^{83} -530.000 q^{85} +536.000 q^{86} +256.000 q^{88} -110.000 q^{89} -48.0000 q^{91} -608.000 q^{92} +912.000 q^{94} -95.0000 q^{95} -574.000 q^{97} -466.000 q^{98} +O(q^{100})\)

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
$7$	−24.0000	−1.29588	−0.647939	−	0.761692i	$-0.724369\pi$
$7$	−24.0000	−1.29588	−0.647939	+	0.761692i	$0.724369\pi$
$8$	−8.00000	−0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	−32.0000	−0.877124	−0.438562	−	0.898701i	$-0.644512\pi$
$11$	−32.0000	−0.877124	−0.438562	+	0.898701i	$0.644512\pi$
$12$	0	0
$13$	2.00000	0.0426692	0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000	0.0426692	0.0213346	+	0.999772i	$0.493208\pi$
$14$	48.0000	0.916324
$15$	0	0
$16$	16.0000	0.250000
$17$	−106.000	−1.51228	−0.756140	−	0.654409i	$-0.772917\pi$
$17$	−106.000	−1.51228	−0.756140	+	0.654409i	$0.772917\pi$
$18$	0	0
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	20.0000	0.223607
$21$	0	0
$22$	64.0000	0.620220
$23$	−152.000	−1.37801	−0.689004	−	0.724757i	$-0.741952\pi$
$23$	−152.000	−1.37801	−0.689004	+	0.724757i	$0.741952\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−4.00000	−0.0301717
$27$	0	0
$28$	−96.0000	−0.647939
$29$	−90.0000	−0.576296	−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000	−0.576296	−0.288148	+	0.957586i	$0.593039\pi$
$30$	0	0
$31$	52.0000	0.301273	0.150637	−	0.988589i	$-0.451868\pi$
$31$	52.0000	0.301273	0.150637	+	0.988589i	$0.451868\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	212.000	1.06934
$35$	−120.000	−0.579534
$36$	0	0
$37$	306.000	1.35962	0.679812	−	0.733386i	$-0.262061\pi$
$37$	306.000	1.35962	0.679812	+	0.733386i	$0.262061\pi$
$38$	38.0000	0.162221
$39$	0	0
$40$	−40.0000	−0.158114
$41$	−62.0000	−0.236165	−0.118083	−	0.993004i	$-0.537675\pi$
$41$	−62.0000	−0.236165	−0.118083	+	0.993004i	$0.537675\pi$
$42$	0	0
$43$	−268.000	−0.950456	−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000	−0.950456	−0.475228	+	0.879863i	$0.657634\pi$
$44$	−128.000	−0.438562
$45$	0	0
$46$	304.000	0.974399
$47$	−456.000	−1.41520	−0.707600	−	0.706613i	$-0.750222\pi$
$47$	−456.000	−1.41520	−0.707600	+	0.706613i	$0.750222\pi$
$48$	0	0
$49$	233.000	0.679300
$50$	−50.0000	−0.141421
$51$	0	0
$52$	8.00000	0.0213346
$53$	318.000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	318.000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	−160.000	−0.392262
$56$	192.000	0.458162
$57$	0	0
$58$	180.000	0.407503
$59$	−300.000	−0.661978	−0.330989	−	0.943635i	$-0.607382\pi$
$59$	−300.000	−0.661978	−0.330989	+	0.943635i	$0.607382\pi$
$60$	0	0
$61$	502.000	1.05368	0.526840	−	0.849964i	$-0.323377\pi$
$61$	502.000	1.05368	0.526840	+	0.849964i	$0.323377\pi$
$62$	−104.000	−0.213032
$63$	0	0
$64$	64.0000	0.125000
$65$	10.0000	0.0190823
$66$	0	0
$67$	−644.000	−1.17429	−0.587143	−	0.809483i	$-0.699747\pi$
$67$	−644.000	−1.17429	−0.587143	+	0.809483i	$0.699747\pi$
$68$	−424.000	−0.756140
$69$	0	0
$70$	240.000	0.409793
$71$	608.000	1.01629	0.508143	−	0.861273i	$-0.330332\pi$
$71$	608.000	1.01629	0.508143	+	0.861273i	$0.330332\pi$
$72$	0	0
$73$	−198.000	−0.317454	−0.158727	−	0.987323i	$-0.550739\pi$
$73$	−198.000	−0.317454	−0.158727	+	0.987323i	$0.550739\pi$
$74$	−612.000	−0.961399
$75$	0	0
$76$	−76.0000	−0.114708
$77$	768.000	1.13665
$78$	0	0
$79$	260.000	0.370282	0.185141	−	0.982712i	$-0.440726\pi$
$79$	260.000	0.370282	0.185141	+	0.982712i	$0.440726\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	124.000	0.166994
$83$	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
$85$	−530.000	−0.676313
$86$	536.000	0.672074
$87$	0	0
$88$	256.000	0.310110
$89$	−110.000	−0.131011	−0.0655055	−	0.997852i	$-0.520866\pi$
$89$	−110.000	−0.131011	−0.0655055	+	0.997852i	$0.520866\pi$
$90$	0	0
$91$	−48.0000	−0.0552941
$92$	−608.000	−0.689004
$93$	0	0
$94$	912.000	1.00070
$95$	−95.0000	−0.102598
$96$	0	0
$97$	−574.000	−0.600834	−0.300417	−	0.953808i	$-0.597126\pi$
$97$	−574.000	−0.600834	−0.300417	+	0.953808i	$0.597126\pi$
$98$	−466.000	−0.480338
$99$	0	0
$100$	100.000	0.100000
$101$	838.000	0.825585	0.412793	−	0.910825i	$-0.364553\pi$
$101$	838.000	0.825585	0.412793	+	0.910825i	$0.364553\pi$
$102$	0	0
$103$	1172.00	1.12117	0.560585	−	0.828097i	$-0.310576\pi$
$103$	1172.00	1.12117	0.560585	+	0.828097i	$0.310576\pi$
$104$	−16.0000	−0.0150859
$105$	0	0
$106$	−636.000	−0.582772
$107$	284.000	0.256592	0.128296	−	0.991736i	$-0.459049\pi$
$107$	284.000	0.256592	0.128296	+	0.991736i	$0.459049\pi$
$108$	0	0
$109$	1650.00	1.44992	0.724960	−	0.688791i	$-0.241858\pi$
$109$	1650.00	1.44992	0.724960	+	0.688791i	$0.241858\pi$
$110$	320.000	0.277371
$111$	0	0
$112$	−384.000	−0.323970
$113$	−62.0000	−0.0516148	−0.0258074	−	0.999667i	$-0.508216\pi$
$113$	−62.0000	−0.0516148	−0.0258074	+	0.999667i	$0.508216\pi$
$114$	0	0
$115$	−760.000	−0.616264
$116$	−360.000	−0.288148
$117$	0	0
$118$	600.000	0.468089
$119$	2544.00	1.95973
$120$	0	0
$121$	−307.000	−0.230654
$122$	−1004.00	−0.745065
$123$	0	0
$124$	208.000	0.150637
$125$	125.000	0.0894427
$126$	0	0
$127$	956.000	0.667963	0.333981	−	0.942580i	$-0.391608\pi$
$127$	956.000	0.667963	0.333981	+	0.942580i	$0.391608\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−20.0000	−0.0134932
$131$	−1392.00	−0.928394	−0.464197	−	0.885732i	$-0.653657\pi$
$131$	−1392.00	−0.928394	−0.464197	+	0.885732i	$0.653657\pi$
$132$	0	0
$133$	456.000	0.297295
$134$	1288.00	0.830345
$135$	0	0
$136$	848.000	0.534672
$137$	−2306.00	−1.43806	−0.719032	−	0.694977i	$-0.755415\pi$
$137$	−2306.00	−1.43806	−0.719032	+	0.694977i	$0.755415\pi$
$138$	0	0
$139$	−1820.00	−1.11058	−0.555289	−	0.831657i	$-0.687392\pi$
$139$	−1820.00	−1.11058	−0.555289	+	0.831657i	$0.687392\pi$
$140$	−480.000	−0.289767
$141$	0	0
$142$	−1216.00	−0.718623
$143$	−64.0000	−0.0374262
$144$	0	0
$145$	−450.000	−0.257727
$146$	396.000	0.224474
$147$	0	0
$148$	1224.00	0.679812
$149$	−1650.00	−0.907203	−0.453602	−	0.891205i	$-0.649861\pi$
$149$	−1650.00	−0.907203	−0.453602	+	0.891205i	$0.649861\pi$
$150$	0	0
$151$	1692.00	0.911874	0.455937	−	0.890012i	$-0.349304\pi$
$151$	1692.00	0.911874	0.455937	+	0.890012i	$0.349304\pi$
$152$	152.000	0.0811107
$153$	0	0
$154$	−1536.00	−0.803730
$155$	260.000	0.134734
$156$	0	0
$157$	−3434.00	−1.74562	−0.872812	−	0.488056i	$-0.837706\pi$
$157$	−3434.00	−1.74562	−0.872812	+	0.488056i	$0.837706\pi$
$158$	−520.000	−0.261829
$159$	0	0
$160$	−160.000	−0.0790569
$161$	3648.00	1.78573
$162$	0	0
$163$	−1588.00	−0.763078	−0.381539	−	0.924353i	$-0.624606\pi$
$163$	−1588.00	−0.763078	−0.381539	+	0.924353i	$0.624606\pi$
$164$	−248.000	−0.118083
$165$	0	0
$166$	−2496.00	−1.16703
$167$	−2496.00	−1.15656	−0.578282	−	0.815837i	$-0.696277\pi$
$167$	−2496.00	−1.15656	−0.578282	+	0.815837i	$0.696277\pi$
$168$	0	0
$169$	−2193.00	−0.998179
$170$	1060.00	0.478225
$171$	0	0
$172$	−1072.00	−0.475228
$173$	3638.00	1.59880	0.799399	−	0.600801i	$-0.205151\pi$
$173$	3638.00	1.59880	0.799399	+	0.600801i	$0.205151\pi$
$174$	0	0
$175$	−600.000	−0.259176
$176$	−512.000	−0.219281
$177$	0	0
$178$	220.000	0.0926387
$179$	3140.00	1.31114	0.655572	−	0.755133i	$-0.272428\pi$
$179$	3140.00	1.31114	0.655572	+	0.755133i	$0.272428\pi$
$180$	0	0
$181$	3882.00	1.59418	0.797091	−	0.603860i	$-0.206371\pi$
$181$	3882.00	1.59418	0.797091	+	0.603860i	$0.206371\pi$
$182$	96.0000	0.0390989
$183$	0	0
$184$	1216.00	0.487200
$185$	1530.00	0.608042
$186$	0	0
$187$	3392.00	1.32646
$188$	−1824.00	−0.707600
$189$	0	0
$190$	190.000	0.0725476
$191$	−5032.00	−1.90630	−0.953149	−	0.302503i	$-0.902178\pi$
$191$	−5032.00	−1.90630	−0.953149	+	0.302503i	$0.902178\pi$
$192$	0	0
$193$	1322.00	0.493055	0.246528	−	0.969136i	$-0.420710\pi$
$193$	1322.00	0.493055	0.246528	+	0.969136i	$0.420710\pi$
$194$	1148.00	0.424854
$195$	0	0
$196$	932.000	0.339650
$197$	−346.000	−0.125134	−0.0625672	−	0.998041i	$-0.519929\pi$
$197$	−346.000	−0.125134	−0.0625672	+	0.998041i	$0.519929\pi$
$198$	0	0
$199$	−3240.00	−1.15416	−0.577079	−	0.816688i	$-0.695808\pi$
$199$	−3240.00	−1.15416	−0.577079	+	0.816688i	$0.695808\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−1676.00	−0.583777
$203$	2160.00	0.746809
$204$	0	0
$205$	−310.000	−0.105616
$206$	−2344.00	−0.792787
$207$	0	0
$208$	32.0000	0.0106673
$209$	608.000	0.201226
$210$	0	0
$211$	1172.00	0.382388	0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00	0.382388	0.191194	+	0.981552i	$0.438764\pi$
$212$	1272.00	0.412082
$213$	0	0
$214$	−568.000	−0.181438
$215$	−1340.00	−0.425057
$216$	0	0
$217$	−1248.00	−0.390414
$218$	−3300.00	−1.02525
$219$	0	0
$220$	−640.000	−0.196131
$221$	−212.000	−0.0645279
$222$	0	0
$223$	−3948.00	−1.18555	−0.592775	−	0.805368i	$-0.701968\pi$
$223$	−3948.00	−1.18555	−0.592775	+	0.805368i	$0.701968\pi$
$224$	768.000	0.229081
$225$	0	0
$226$	124.000	0.0364972
$227$	1684.00	0.492383	0.246192	−	0.969221i	$-0.420821\pi$
$227$	1684.00	0.492383	0.246192	+	0.969221i	$0.420821\pi$
$228$	0	0
$229$	4430.00	1.27835	0.639176	−	0.769060i	$-0.279276\pi$
$229$	4430.00	1.27835	0.639176	+	0.769060i	$0.279276\pi$
$230$	1520.00	0.435764
$231$	0	0
$232$	720.000	0.203751
$233$	2718.00	0.764215	0.382108	−	0.924118i	$-0.375198\pi$
$233$	2718.00	0.764215	0.382108	+	0.924118i	$0.375198\pi$
$234$	0	0
$235$	−2280.00	−0.632897
$236$	−1200.00	−0.330989
$237$	0	0
$238$	−5088.00	−1.38574
$239$	−720.000	−0.194866	−0.0974329	−	0.995242i	$-0.531063\pi$
$239$	−720.000	−0.194866	−0.0974329	+	0.995242i	$0.531063\pi$
$240$	0	0
$241$	482.000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	482.000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	614.000	0.163097
$243$	0	0
$244$	2008.00	0.526840
$245$	1165.00	0.303792
$246$	0	0
$247$	−38.0000	−0.00978900
$248$	−416.000	−0.106516
$249$	0	0
$250$	−250.000	−0.0632456
$251$	6928.00	1.74220	0.871099	−	0.491108i	$-0.163408\pi$
$251$	6928.00	1.74220	0.871099	+	0.491108i	$0.163408\pi$
$252$	0	0
$253$	4864.00	1.20868
$254$	−1912.00	−0.472321
$255$	0	0
$256$	256.000	0.0625000
$257$	5114.00	1.24126	0.620628	−	0.784106i	$-0.286878\pi$
$257$	5114.00	1.24126	0.620628	+	0.784106i	$0.286878\pi$
$258$	0	0
$259$	−7344.00	−1.76191
$260$	40.0000	0.00954113
$261$	0	0
$262$	2784.00	0.656474
$263$	3368.00	0.789657	0.394828	−	0.918755i	$-0.370804\pi$
$263$	3368.00	0.789657	0.394828	+	0.918755i	$0.370804\pi$
$264$	0	0
$265$	1590.00	0.368577
$266$	−912.000	−0.210219
$267$	0	0
$268$	−2576.00	−0.587143
$269$	6310.00	1.43021	0.715107	−	0.699015i	$-0.246378\pi$
$269$	6310.00	1.43021	0.715107	+	0.699015i	$0.246378\pi$
$270$	0	0
$271$	1952.00	0.437548	0.218774	−	0.975776i	$-0.429794\pi$
$271$	1952.00	0.437548	0.218774	+	0.975776i	$0.429794\pi$
$272$	−1696.00	−0.378070
$273$	0	0
$274$	4612.00	1.01687
$275$	−800.000	−0.175425
$276$	0	0
$277$	3526.00	0.764826	0.382413	−	0.923991i	$-0.375093\pi$
$277$	3526.00	0.764826	0.382413	+	0.923991i	$0.375093\pi$
$278$	3640.00	0.785297
$279$	0	0
$280$	960.000	0.204896
$281$	6138.00	1.30307	0.651534	−	0.758619i	$-0.274126\pi$
$281$	6138.00	1.30307	0.651534	+	0.758619i	$0.274126\pi$
$282$	0	0
$283$	3452.00	0.725089	0.362544	−	0.931967i	$-0.381908\pi$
$283$	3452.00	0.725089	0.362544	+	0.931967i	$0.381908\pi$
$284$	2432.00	0.508143
$285$	0	0
$286$	128.000	0.0264643
$287$	1488.00	0.306041
$288$	0	0
$289$	6323.00	1.28699
$290$	900.000	0.182241
$291$	0	0
$292$	−792.000	−0.158727
$293$	−5762.00	−1.14887	−0.574436	−	0.818549i	$-0.694779\pi$
$293$	−5762.00	−1.14887	−0.574436	+	0.818549i	$0.694779\pi$
$294$	0	0
$295$	−1500.00	−0.296045
$296$	−2448.00	−0.480700
$297$	0	0
$298$	3300.00	0.641489
$299$	−304.000	−0.0587986
$300$	0	0
$301$	6432.00	1.23168
$302$	−3384.00	−0.644792
$303$	0	0
$304$	−304.000	−0.0573539
$305$	2510.00	0.471220
$306$	0	0
$307$	2596.00	0.482611	0.241305	−	0.970449i	$-0.422424\pi$
$307$	2596.00	0.482611	0.241305	+	0.970449i	$0.422424\pi$
$308$	3072.00	0.568323
$309$	0	0
$310$	−520.000	−0.0952710
$311$	−832.000	−0.151699	−0.0758495	−	0.997119i	$-0.524167\pi$
$311$	−832.000	−0.151699	−0.0758495	+	0.997119i	$0.524167\pi$
$312$	0	0
$313$	−8838.00	−1.59602	−0.798008	−	0.602646i	$-0.794113\pi$
$313$	−8838.00	−1.59602	−0.798008	+	0.602646i	$0.794113\pi$
$314$	6868.00	1.23434
$315$	0	0
$316$	1040.00	0.185141
$317$	3334.00	0.590713	0.295357	−	0.955387i	$-0.404562\pi$
$317$	3334.00	0.590713	0.295357	+	0.955387i	$0.404562\pi$
$318$	0	0
$319$	2880.00	0.505483
$320$	320.000	0.0559017
$321$	0	0
$322$	−7296.00	−1.26270
$323$	2014.00	0.346941
$324$	0	0
$325$	50.0000	0.00853385
$326$	3176.00	0.539578
$327$	0	0
$328$	496.000	0.0834970
$329$	10944.0	1.83393
$330$	0	0
$331$	1372.00	0.227831	0.113915	−	0.993490i	$-0.463661\pi$
$331$	1372.00	0.227831	0.113915	+	0.993490i	$0.463661\pi$
$332$	4992.00	0.825216
$333$	0	0
$334$	4992.00	0.817815
$335$	−3220.00	−0.525156
$336$	0	0
$337$	−2854.00	−0.461327	−0.230664	−	0.973034i	$-0.574090\pi$
$337$	−2854.00	−0.461327	−0.230664	+	0.973034i	$0.574090\pi$
$338$	4386.00	0.705819
$339$	0	0
$340$	−2120.00	−0.338156
$341$	−1664.00	−0.264254
$342$	0	0
$343$	2640.00	0.415588
$344$	2144.00	0.336037
$345$	0	0
$346$	−7276.00	−1.13052
$347$	−2136.00	−0.330451	−0.165225	−	0.986256i	$-0.552835\pi$
$347$	−2136.00	−0.330451	−0.165225	+	0.986256i	$0.552835\pi$
$348$	0	0
$349$	4430.00	0.679463	0.339731	−	0.940523i	$-0.389664\pi$
$349$	4430.00	0.679463	0.339731	+	0.940523i	$0.389664\pi$
$350$	1200.00	0.183265
$351$	0	0
$352$	1024.00	0.155055
$353$	2318.00	0.349503	0.174752	−	0.984613i	$-0.444088\pi$
$353$	2318.00	0.349503	0.174752	+	0.984613i	$0.444088\pi$
$354$	0	0
$355$	3040.00	0.454497
$356$	−440.000	−0.0655055
$357$	0	0
$358$	−6280.00	−0.927118
$359$	6720.00	0.987933	0.493967	−	0.869481i	$-0.335546\pi$
$359$	6720.00	0.987933	0.493967	+	0.869481i	$0.335546\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	−7764.00	−1.12726
$363$	0	0
$364$	−192.000	−0.0276471
$365$	−990.000	−0.141970
$366$	0	0
$367$	−3624.00	−0.515453	−0.257727	−	0.966218i	$-0.582973\pi$
$367$	−3624.00	−0.515453	−0.257727	+	0.966218i	$0.582973\pi$
$368$	−2432.00	−0.344502
$369$	0	0
$370$	−3060.00	−0.429951
$371$	−7632.00	−1.06802
$372$	0	0
$373$	−6718.00	−0.932560	−0.466280	−	0.884637i	$-0.654406\pi$
$373$	−6718.00	−0.932560	−0.466280	+	0.884637i	$0.654406\pi$
$374$	−6784.00	−0.937947
$375$	0	0
$376$	3648.00	0.500349
$377$	−180.000	−0.0245901
$378$	0	0
$379$	−1460.00	−0.197876	−0.0989382	−	0.995094i	$-0.531545\pi$
$379$	−1460.00	−0.197876	−0.0989382	+	0.995094i	$0.531545\pi$
$380$	−380.000	−0.0512989
$381$	0	0
$382$	10064.0	1.34796
$383$	13608.0	1.81550	0.907750	−	0.419512i	$-0.137799\pi$
$383$	13608.0	1.81550	0.907750	+	0.419512i	$0.137799\pi$
$384$	0	0
$385$	3840.00	0.508323
$386$	−2644.00	−0.348643
$387$	0	0
$388$	−2296.00	−0.300417
$389$	−1330.00	−0.173351	−0.0866757	−	0.996237i	$-0.527624\pi$
$389$	−1330.00	−0.173351	−0.0866757	+	0.996237i	$0.527624\pi$
$390$	0	0
$391$	16112.0	2.08394
$392$	−1864.00	−0.240169
$393$	0	0
$394$	692.000	0.0884834
$395$	1300.00	0.165595
$396$	0	0
$397$	8886.00	1.12336	0.561682	−	0.827353i	$-0.310154\pi$
$397$	8886.00	1.12336	0.561682	+	0.827353i	$0.310154\pi$
$398$	6480.00	0.816113
$399$	0	0
$400$	400.000	0.0500000
$401$	−7142.00	−0.889413	−0.444706	−	0.895676i	$-0.646692\pi$
$401$	−7142.00	−0.889413	−0.444706	+	0.895676i	$0.646692\pi$
$402$	0	0
$403$	104.000	0.0128551
$404$	3352.00	0.412793
$405$	0	0
$406$	−4320.00	−0.528074
$407$	−9792.00	−1.19256
$408$	0	0
$409$	8490.00	1.02641	0.513207	−	0.858265i	$-0.328457\pi$
$409$	8490.00	1.02641	0.513207	+	0.858265i	$0.328457\pi$
$410$	620.000	0.0746820
$411$	0	0
$412$	4688.00	0.560585
$413$	7200.00	0.857842
$414$	0	0
$415$	6240.00	0.738095
$416$	−64.0000	−0.00754293
$417$	0	0
$418$	−1216.00	−0.142288
$419$	2280.00	0.265836	0.132918	−	0.991127i	$-0.457565\pi$
$419$	2280.00	0.265836	0.132918	+	0.991127i	$0.457565\pi$
$420$	0	0
$421$	8642.00	1.00044	0.500220	−	0.865898i	$-0.333252\pi$
$421$	8642.00	1.00044	0.500220	+	0.865898i	$0.333252\pi$
$422$	−2344.00	−0.270389
$423$	0	0
$424$	−2544.00	−0.291386
$425$	−2650.00	−0.302456
$426$	0	0
$427$	−12048.0	−1.36544
$428$	1136.00	0.128296
$429$	0	0
$430$	2680.00	0.300561
$431$	4208.00	0.470284	0.235142	−	0.971961i	$-0.424445\pi$
$431$	4208.00	0.470284	0.235142	+	0.971961i	$0.424445\pi$
$432$	0	0
$433$	−8198.00	−0.909863	−0.454932	−	0.890526i	$-0.650336\pi$
$433$	−8198.00	−0.909863	−0.454932	+	0.890526i	$0.650336\pi$
$434$	2496.00	0.276064
$435$	0	0
$436$	6600.00	0.724960
$437$	2888.00	0.316137
$438$	0	0
$439$	−6540.00	−0.711019	−0.355509	−	0.934673i	$-0.615693\pi$
$439$	−6540.00	−0.711019	−0.355509	+	0.934673i	$0.615693\pi$
$440$	1280.00	0.138685
$441$	0	0
$442$	424.000	0.0456281
$443$	5128.00	0.549974	0.274987	−	0.961448i	$-0.411326\pi$
$443$	5128.00	0.549974	0.274987	+	0.961448i	$0.411326\pi$
$444$	0	0
$445$	−550.000	−0.0585899
$446$	7896.00	0.838310
$447$	0	0
$448$	−1536.00	−0.161985
$449$	210.000	0.0220724	0.0110362	−	0.999939i	$-0.496487\pi$
$449$	210.000	0.0220724	0.0110362	+	0.999939i	$0.496487\pi$
$450$	0	0
$451$	1984.00	0.207146
$452$	−248.000	−0.0258074
$453$	0	0
$454$	−3368.00	−0.348168
$455$	−240.000	−0.0247283
$456$	0	0
$457$	11226.0	1.14908	0.574541	−	0.818476i	$-0.305181\pi$
$457$	11226.0	1.14908	0.574541	+	0.818476i	$0.305181\pi$
$458$	−8860.00	−0.903931
$459$	0	0
$460$	−3040.00	−0.308132
$461$	−2522.00	−0.254797	−0.127398	−	0.991852i	$-0.540663\pi$
$461$	−2522.00	−0.254797	−0.127398	+	0.991852i	$0.540663\pi$
$462$	0	0
$463$	−17128.0	−1.71923	−0.859617	−	0.510938i	$-0.829298\pi$
$463$	−17128.0	−1.71923	−0.859617	+	0.510938i	$0.829298\pi$
$464$	−1440.00	−0.144074
$465$	0	0
$466$	−5436.00	−0.540382
$467$	−4816.00	−0.477212	−0.238606	−	0.971116i	$-0.576690\pi$
$467$	−4816.00	−0.477212	−0.238606	+	0.971116i	$0.576690\pi$
$468$	0	0
$469$	15456.0	1.52173
$470$	4560.00	0.447526
$471$	0	0
$472$	2400.00	0.234044
$473$	8576.00	0.833668
$474$	0	0
$475$	−475.000	−0.0458831
$476$	10176.0	0.979866
$477$	0	0
$478$	1440.00	0.137791
$479$	8360.00	0.797449	0.398725	−	0.917071i	$-0.369453\pi$
$479$	8360.00	0.797449	0.398725	+	0.917071i	$0.369453\pi$
$480$	0	0
$481$	612.000	0.0580141
$482$	−964.000	−0.0910975
$483$	0	0
$484$	−1228.00	−0.115327
$485$	−2870.00	−0.268701
$486$	0	0
$487$	−8084.00	−0.752199	−0.376100	−	0.926579i	$-0.622735\pi$
$487$	−8084.00	−0.752199	−0.376100	+	0.926579i	$0.622735\pi$
$488$	−4016.00	−0.372532
$489$	0	0
$490$	−2330.00	−0.214814
$491$	−12072.0	−1.10958	−0.554788	−	0.831992i	$-0.687201\pi$
$491$	−12072.0	−1.10958	−0.554788	+	0.831992i	$0.687201\pi$
$492$	0	0
$493$	9540.00	0.871521
$494$	76.0000	0.00692187
$495$	0	0
$496$	832.000	0.0753184
$497$	−14592.0	−1.31698
$498$	0	0
$499$	10500.0	0.941973	0.470987	−	0.882140i	$-0.343898\pi$
$499$	10500.0	0.941973	0.470987	+	0.882140i	$0.343898\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	−13856.0	−1.23192
$503$	−11832.0	−1.04883	−0.524416	−	0.851462i	$-0.675716\pi$
$503$	−11832.0	−1.04883	−0.524416	+	0.851462i	$0.675716\pi$
$504$	0	0
$505$	4190.00	0.369213
$506$	−9728.00	−0.854669
$507$	0	0
$508$	3824.00	0.333981
$509$	−4170.00	−0.363128	−0.181564	−	0.983379i	$-0.558116\pi$
$509$	−4170.00	−0.363128	−0.181564	+	0.983379i	$0.558116\pi$
$510$	0	0
$511$	4752.00	0.411382
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−10228.0	−0.877700
$515$	5860.00	0.501403
$516$	0	0
$517$	14592.0	1.24131
$518$	14688.0	1.24586
$519$	0	0
$520$	−80.0000	−0.00674660
$521$	−23262.0	−1.95610	−0.978049	−	0.208377i	$-0.933182\pi$
$521$	−23262.0	−1.95610	−0.978049	+	0.208377i	$0.933182\pi$
$522$	0	0
$523$	3892.00	0.325402	0.162701	−	0.986675i	$-0.447979\pi$
$523$	3892.00	0.325402	0.162701	+	0.986675i	$0.447979\pi$
$524$	−5568.00	−0.464197
$525$	0	0
$526$	−6736.00	−0.558372
$527$	−5512.00	−0.455610
$528$	0	0
$529$	10937.0	0.898907
$530$	−3180.00	−0.260623
$531$	0	0
$532$	1824.00	0.148647
$533$	−124.000	−0.0100770
$534$	0	0
$535$	1420.00	0.114751
$536$	5152.00	0.415173
$537$	0	0
$538$	−12620.0	−1.01131
$539$	−7456.00	−0.595831
$540$	0	0
$541$	11822.0	0.939496	0.469748	−	0.882800i	$-0.344345\pi$
$541$	11822.0	0.939496	0.469748	+	0.882800i	$0.344345\pi$
$542$	−3904.00	−0.309393
$543$	0	0
$544$	3392.00	0.267336
$545$	8250.00	0.648424
$546$	0	0
$547$	3716.00	0.290466	0.145233	−	0.989398i	$-0.453607\pi$
$547$	3716.00	0.290466	0.145233	+	0.989398i	$0.453607\pi$
$548$	−9224.00	−0.719032
$549$	0	0
$550$	1600.00	0.124044
$551$	1710.00	0.132211
$552$	0	0
$553$	−6240.00	−0.479840
$554$	−7052.00	−0.540814
$555$	0	0
$556$	−7280.00	−0.555289
$557$	−13386.0	−1.01828	−0.509141	−	0.860683i	$-0.670037\pi$
$557$	−13386.0	−1.01828	−0.509141	+	0.860683i	$0.670037\pi$
$558$	0	0
$559$	−536.000	−0.0405552
$560$	−1920.00	−0.144884
$561$	0	0
$562$	−12276.0	−0.921409
$563$	16588.0	1.24174	0.620871	−	0.783913i	$-0.286779\pi$
$563$	16588.0	1.24174	0.620871	+	0.783913i	$0.286779\pi$
$564$	0	0
$565$	−310.000	−0.0230828
$566$	−6904.00	−0.512715
$567$	0	0
$568$	−4864.00	−0.359311
$569$	−5030.00	−0.370595	−0.185298	−	0.982682i	$-0.559325\pi$
$569$	−5030.00	−0.370595	−0.185298	+	0.982682i	$0.559325\pi$
$570$	0	0
$571$	−188.000	−0.0137786	−0.00688928	−	0.999976i	$-0.502193\pi$
$571$	−188.000	−0.0137786	−0.00688928	+	0.999976i	$0.502193\pi$
$572$	−256.000	−0.0187131
$573$	0	0
$574$	−2976.00	−0.216404
$575$	−3800.00	−0.275602
$576$	0	0
$577$	−4494.00	−0.324242	−0.162121	−	0.986771i	$-0.551833\pi$
$577$	−4494.00	−0.324242	−0.162121	+	0.986771i	$0.551833\pi$
$578$	−12646.0	−0.910042
$579$	0	0
$580$	−1800.00	−0.128864
$581$	−29952.0	−2.13876
$582$	0	0
$583$	−10176.0	−0.722893
$584$	1584.00	0.112237
$585$	0	0
$586$	11524.0	0.812376
$587$	4064.00	0.285757	0.142878	−	0.989740i	$-0.454364\pi$
$587$	4064.00	0.285757	0.142878	+	0.989740i	$0.454364\pi$
$588$	0	0
$589$	−988.000	−0.0691169
$590$	3000.00	0.209336
$591$	0	0
$592$	4896.00	0.339906
$593$	1798.00	0.124511	0.0622555	−	0.998060i	$-0.480171\pi$
$593$	1798.00	0.124511	0.0622555	+	0.998060i	$0.480171\pi$
$594$	0	0
$595$	12720.0	0.876419
$596$	−6600.00	−0.453602
$597$	0	0
$598$	608.000	0.0415769
$599$	−12800.0	−0.873112	−0.436556	−	0.899677i	$-0.643802\pi$
$599$	−12800.0	−0.873112	−0.436556	+	0.899677i	$0.643802\pi$
$600$	0	0
$601$	19402.0	1.31685	0.658423	−	0.752648i	$-0.271224\pi$
$601$	19402.0	1.31685	0.658423	+	0.752648i	$0.271224\pi$
$602$	−12864.0	−0.870926
$603$	0	0
$604$	6768.00	0.455937
$605$	−1535.00	−0.103151
$606$	0	0
$607$	−29324.0	−1.96083	−0.980416	−	0.196940i	$-0.936900\pi$
$607$	−29324.0	−1.96083	−0.980416	+	0.196940i	$0.936900\pi$
$608$	608.000	0.0405554
$609$	0	0
$610$	−5020.00	−0.333203
$611$	−912.000	−0.0603855
$612$	0	0
$613$	27742.0	1.82788	0.913939	−	0.405852i	$-0.133025\pi$
$613$	27742.0	1.82788	0.913939	+	0.405852i	$0.133025\pi$
$614$	−5192.00	−0.341257
$615$	0	0
$616$	−6144.00	−0.401865
$617$	−27626.0	−1.80256	−0.901281	−	0.433235i	$-0.857372\pi$
$617$	−27626.0	−1.80256	−0.901281	+	0.433235i	$0.857372\pi$
$618$	0	0
$619$	−9380.00	−0.609070	−0.304535	−	0.952501i	$-0.598501\pi$
$619$	−9380.00	−0.609070	−0.304535	+	0.952501i	$0.598501\pi$
$620$	1040.00	0.0673668
$621$	0	0
$622$	1664.00	0.107267
$623$	2640.00	0.169774
$624$	0	0
$625$	625.000	0.0400000
$626$	17676.0	1.12855
$627$	0	0
$628$	−13736.0	−0.872812
$629$	−32436.0	−2.05613
$630$	0	0
$631$	−14408.0	−0.908991	−0.454496	−	0.890749i	$-0.650180\pi$
$631$	−14408.0	−0.908991	−0.454496	+	0.890749i	$0.650180\pi$
$632$	−2080.00	−0.130914
$633$	0	0
$634$	−6668.00	−0.417697
$635$	4780.00	0.298722
$636$	0	0
$637$	466.000	0.0289852
$638$	−5760.00	−0.357430
$639$	0	0
$640$	−640.000	−0.0395285
$641$	−23382.0	−1.44077	−0.720385	−	0.693574i	$-0.756035\pi$
$641$	−23382.0	−1.44077	−0.720385	+	0.693574i	$0.756035\pi$
$642$	0	0
$643$	−9148.00	−0.561061	−0.280530	−	0.959845i	$-0.590510\pi$
$643$	−9148.00	−0.561061	−0.280530	+	0.959845i	$0.590510\pi$
$644$	14592.0	0.892865
$645$	0	0
$646$	−4028.00	−0.245324
$647$	23304.0	1.41604	0.708018	−	0.706195i	$-0.249590\pi$
$647$	23304.0	1.41604	0.708018	+	0.706195i	$0.249590\pi$
$648$	0	0
$649$	9600.00	0.580636
$650$	−100.000	−0.00603434
$651$	0	0
$652$	−6352.00	−0.381539
$653$	−8682.00	−0.520295	−0.260148	−	0.965569i	$-0.583771\pi$
$653$	−8682.00	−0.520295	−0.260148	+	0.965569i	$0.583771\pi$
$654$	0	0
$655$	−6960.00	−0.415190
$656$	−992.000	−0.0590413
$657$	0	0
$658$	−21888.0	−1.29678
$659$	13500.0	0.798005	0.399003	−	0.916950i	$-0.369356\pi$
$659$	13500.0	0.798005	0.399003	+	0.916950i	$0.369356\pi$
$660$	0	0
$661$	−6038.00	−0.355296	−0.177648	−	0.984094i	$-0.556849\pi$
$661$	−6038.00	−0.355296	−0.177648	+	0.984094i	$0.556849\pi$
$662$	−2744.00	−0.161101
$663$	0	0
$664$	−9984.00	−0.583516
$665$	2280.00	0.132954
$666$	0	0
$667$	13680.0	0.794141
$668$	−9984.00	−0.578282
$669$	0	0
$670$	6440.00	0.371342
$671$	−16064.0	−0.924208
$672$	0	0
$673$	10282.0	0.588918	0.294459	−	0.955664i	$-0.404861\pi$
$673$	10282.0	0.588918	0.294459	+	0.955664i	$0.404861\pi$
$674$	5708.00	0.326208
$675$	0	0
$676$	−8772.00	−0.499090
$677$	30654.0	1.74022	0.870110	−	0.492858i	$-0.164048\pi$
$677$	30654.0	1.74022	0.870110	+	0.492858i	$0.164048\pi$
$678$	0	0
$679$	13776.0	0.778607
$680$	4240.00	0.239113
$681$	0	0
$682$	3328.00	0.186856
$683$	23268.0	1.30355	0.651775	−	0.758412i	$-0.274024\pi$
$683$	23268.0	1.30355	0.651775	+	0.758412i	$0.274024\pi$
$684$	0	0
$685$	−11530.0	−0.643122
$686$	−5280.00	−0.293865
$687$	0	0
$688$	−4288.00	−0.237614
$689$	636.000	0.0351664
$690$	0	0
$691$	−5428.00	−0.298829	−0.149415	−	0.988775i	$-0.547739\pi$
$691$	−5428.00	−0.298829	−0.149415	+	0.988775i	$0.547739\pi$
$692$	14552.0	0.799399
$693$	0	0
$694$	4272.00	0.233664
$695$	−9100.00	−0.496666
$696$	0	0
$697$	6572.00	0.357148
$698$	−8860.00	−0.480453
$699$	0	0
$700$	−2400.00	−0.129588
$701$	34638.0	1.86628	0.933138	−	0.359519i	$-0.117059\pi$
$701$	34638.0	1.86628	0.933138	+	0.359519i	$0.117059\pi$
$702$	0	0
$703$	−5814.00	−0.311919
$704$	−2048.00	−0.109640
$705$	0	0
$706$	−4636.00	−0.247136
$707$	−20112.0	−1.06986
$708$	0	0
$709$	−4450.00	−0.235717	−0.117858	−	0.993030i	$-0.537603\pi$
$709$	−4450.00	−0.235717	−0.117858	+	0.993030i	$0.537603\pi$
$710$	−6080.00	−0.321378
$711$	0	0
$712$	880.000	0.0463194
$713$	−7904.00	−0.415157
$714$	0	0
$715$	−320.000	−0.0167375
$716$	12560.0	0.655572
$717$	0	0
$718$	−13440.0	−0.698574
$719$	10360.0	0.537361	0.268681	−	0.963229i	$-0.413412\pi$
$719$	10360.0	0.537361	0.268681	+	0.963229i	$0.413412\pi$
$720$	0	0
$721$	−28128.0	−1.45290
$722$	−722.000	−0.0372161
$723$	0	0
$724$	15528.0	0.797091
$725$	−2250.00	−0.115259
$726$	0	0
$727$	−9464.00	−0.482807	−0.241403	−	0.970425i	$-0.577608\pi$
$727$	−9464.00	−0.482807	−0.241403	+	0.970425i	$0.577608\pi$
$728$	384.000	0.0195494
$729$	0	0
$730$	1980.00	0.100388
$731$	28408.0	1.43736
$732$	0	0
$733$	−14618.0	−0.736600	−0.368300	−	0.929707i	$-0.620060\pi$
$733$	−14618.0	−0.736600	−0.368300	+	0.929707i	$0.620060\pi$
$734$	7248.00	0.364480
$735$	0	0
$736$	4864.00	0.243600
$737$	20608.0	1.02999
$738$	0	0
$739$	9340.00	0.464922	0.232461	−	0.972606i	$-0.425322\pi$
$739$	9340.00	0.464922	0.232461	+	0.972606i	$0.425322\pi$
$740$	6120.00	0.304021
$741$	0	0
$742$	15264.0	0.755201
$743$	8008.00	0.395404	0.197702	−	0.980262i	$-0.436652\pi$
$743$	8008.00	0.395404	0.197702	+	0.980262i	$0.436652\pi$
$744$	0	0
$745$	−8250.00	−0.405714
$746$	13436.0	0.659419
$747$	0	0
$748$	13568.0	0.663229
$749$	−6816.00	−0.332512
$750$	0	0
$751$	37892.0	1.84114	0.920572	−	0.390574i	$-0.127723\pi$
$751$	37892.0	1.84114	0.920572	+	0.390574i	$0.127723\pi$
$752$	−7296.00	−0.353800
$753$	0	0
$754$	360.000	0.0173878
$755$	8460.00	0.407803
$756$	0	0
$757$	926.000	0.0444598	0.0222299	−	0.999753i	$-0.492923\pi$
$757$	926.000	0.0444598	0.0222299	+	0.999753i	$0.492923\pi$
$758$	2920.00	0.139920
$759$	0	0
$760$	760.000	0.0362738
$761$	10518.0	0.501021	0.250511	−	0.968114i	$-0.419401\pi$
$761$	10518.0	0.501021	0.250511	+	0.968114i	$0.419401\pi$
$762$	0	0
$763$	−39600.0	−1.87892
$764$	−20128.0	−0.953149
$765$	0	0
$766$	−27216.0	−1.28375
$767$	−600.000	−0.0282461
$768$	0	0
$769$	16610.0	0.778897	0.389449	−	0.921048i	$-0.372666\pi$
$769$	16610.0	0.778897	0.389449	+	0.921048i	$0.372666\pi$
$770$	−7680.00	−0.359439
$771$	0	0
$772$	5288.00	0.246528
$773$	−25602.0	−1.19125	−0.595627	−	0.803261i	$-0.703096\pi$
$773$	−25602.0	−1.19125	−0.595627	+	0.803261i	$0.703096\pi$
$774$	0	0
$775$	1300.00	0.0602547
$776$	4592.00	0.212427
$777$	0	0
$778$	2660.00	0.122578
$779$	1178.00	0.0541800
$780$	0	0
$781$	−19456.0	−0.891409
$782$	−32224.0	−1.47357
$783$	0	0
$784$	3728.00	0.169825
$785$	−17170.0	−0.780667
$786$	0	0
$787$	−12124.0	−0.549141	−0.274570	−	0.961567i	$-0.588536\pi$
$787$	−12124.0	−0.549141	−0.274570	+	0.961567i	$0.588536\pi$
$788$	−1384.00	−0.0625672
$789$	0	0
$790$	−2600.00	−0.117093
$791$	1488.00	0.0668865
$792$	0	0
$793$	1004.00	0.0449598
$794$	−17772.0	−0.794338
$795$	0	0
$796$	−12960.0	−0.577079
$797$	28614.0	1.27172	0.635859	−	0.771805i	$-0.280646\pi$
$797$	28614.0	1.27172	0.635859	+	0.771805i	$0.280646\pi$
$798$	0	0
$799$	48336.0	2.14018
$800$	−800.000	−0.0353553
$801$	0	0
$802$	14284.0	0.628910
$803$	6336.00	0.278447
$804$	0	0
$805$	18240.0	0.798603
$806$	−208.000	−0.00908993
$807$	0	0
$808$	−6704.00	−0.291888
$809$	15310.0	0.665353	0.332677	−	0.943041i	$-0.392048\pi$
$809$	15310.0	0.665353	0.332677	+	0.943041i	$0.392048\pi$
$810$	0	0
$811$	−42548.0	−1.84225	−0.921124	−	0.389270i	$-0.872727\pi$
$811$	−42548.0	−1.84225	−0.921124	+	0.389270i	$0.872727\pi$
$812$	8640.00	0.373405
$813$	0	0
$814$	19584.0	0.843266
$815$	−7940.00	−0.341259
$816$	0	0
$817$	5092.00	0.218050
$818$	−16980.0	−0.725785
$819$	0	0
$820$	−1240.00	−0.0528081
$821$	35798.0	1.52175	0.760876	−	0.648897i	$-0.224769\pi$
$821$	35798.0	1.52175	0.760876	+	0.648897i	$0.224769\pi$
$822$	0	0
$823$	−2608.00	−0.110461	−0.0552304	−	0.998474i	$-0.517589\pi$
$823$	−2608.00	−0.110461	−0.0552304	+	0.998474i	$0.517589\pi$
$824$	−9376.00	−0.396394
$825$	0	0
$826$	−14400.0	−0.606586
$827$	8724.00	0.366824	0.183412	−	0.983036i	$-0.441286\pi$
$827$	8724.00	0.366824	0.183412	+	0.983036i	$0.441286\pi$
$828$	0	0
$829$	−41870.0	−1.75417	−0.877084	−	0.480337i	$-0.840514\pi$
$829$	−41870.0	−1.75417	−0.877084	+	0.480337i	$0.840514\pi$
$830$	−12480.0	−0.521912
$831$	0	0
$832$	128.000	0.00533366
$833$	−24698.0	−1.02729
$834$	0	0
$835$	−12480.0	−0.517231
$836$	2432.00	0.100613
$837$	0	0
$838$	−4560.00	−0.187974
$839$	840.000	0.0345650	0.0172825	−	0.999851i	$-0.494499\pi$
$839$	840.000	0.0345650	0.0172825	+	0.999851i	$0.494499\pi$
$840$	0	0
$841$	−16289.0	−0.667883
$842$	−17284.0	−0.707418
$843$	0	0
$844$	4688.00	0.191194
$845$	−10965.0	−0.446399
$846$	0	0
$847$	7368.00	0.298899
$848$	5088.00	0.206041
$849$	0	0
$850$	5300.00	0.213869
$851$	−46512.0	−1.87357
$852$	0	0
$853$	−14458.0	−0.580343	−0.290171	−	0.956975i	$-0.593712\pi$
$853$	−14458.0	−0.580343	−0.290171	+	0.956975i	$0.593712\pi$
$854$	24096.0	0.965513
$855$	0	0
$856$	−2272.00	−0.0907189
$857$	−25846.0	−1.03020	−0.515101	−	0.857130i	$-0.672245\pi$
$857$	−25846.0	−1.03020	−0.515101	+	0.857130i	$0.672245\pi$
$858$	0	0
$859$	13260.0	0.526688	0.263344	−	0.964702i	$-0.415175\pi$
$859$	13260.0	0.526688	0.263344	+	0.964702i	$0.415175\pi$
$860$	−5360.00	−0.212528
$861$	0	0
$862$	−8416.00	−0.332541
$863$	26288.0	1.03691	0.518455	−	0.855105i	$-0.326507\pi$
$863$	26288.0	1.03691	0.518455	+	0.855105i	$0.326507\pi$
$864$	0	0
$865$	18190.0	0.715004
$866$	16396.0	0.643370
$867$	0	0
$868$	−4992.00	−0.195207
$869$	−8320.00	−0.324783
$870$	0	0
$871$	−1288.00	−0.0501059
$872$	−13200.0	−0.512624
$873$	0	0
$874$	−5776.00	−0.223542
$875$	−3000.00	−0.115907
$876$	0	0
$877$	−26614.0	−1.02473	−0.512367	−	0.858767i	$-0.671231\pi$
$877$	−26614.0	−1.02473	−0.512367	+	0.858767i	$0.671231\pi$
$878$	13080.0	0.502766
$879$	0	0
$880$	−2560.00	−0.0980654
$881$	−26442.0	−1.01118	−0.505592	−	0.862773i	$-0.668726\pi$
$881$	−26442.0	−1.01118	−0.505592	+	0.862773i	$0.668726\pi$
$882$	0	0
$883$	−39148.0	−1.49200	−0.745999	−	0.665947i	$-0.768028\pi$
$883$	−39148.0	−1.49200	−0.745999	+	0.665947i	$0.768028\pi$
$884$	−848.000	−0.0322639
$885$	0	0
$886$	−10256.0	−0.388891
$887$	−2736.00	−0.103569	−0.0517846	−	0.998658i	$-0.516491\pi$
$887$	−2736.00	−0.103569	−0.0517846	+	0.998658i	$0.516491\pi$
$888$	0	0
$889$	−22944.0	−0.865598
$890$	1100.00	0.0414293
$891$	0	0
$892$	−15792.0	−0.592775
$893$	8664.00	0.324669
$894$	0	0
$895$	15700.0	0.586361
$896$	3072.00	0.114541
$897$	0	0
$898$	−420.000	−0.0156076
$899$	−4680.00	−0.173623
$900$	0	0
$901$	−33708.0	−1.24637
$902$	−3968.00	−0.146474
$903$	0	0
$904$	496.000	0.0182486
$905$	19410.0	0.712939
$906$	0	0
$907$	−7724.00	−0.282769	−0.141384	−	0.989955i	$-0.545155\pi$
$907$	−7724.00	−0.282769	−0.141384	+	0.989955i	$0.545155\pi$
$908$	6736.00	0.246192
$909$	0	0
$910$	480.000	0.0174855
$911$	−44472.0	−1.61737	−0.808684	−	0.588243i	$-0.799820\pi$
$911$	−44472.0	−1.61737	−0.808684	+	0.588243i	$0.799820\pi$
$912$	0	0
$913$	−39936.0	−1.44763
$914$	−22452.0	−0.812523
$915$	0	0
$916$	17720.0	0.639176
$917$	33408.0	1.20309
$918$	0	0
$919$	−45640.0	−1.63822	−0.819110	−	0.573636i	$-0.805532\pi$
$919$	−45640.0	−1.63822	−0.819110	+	0.573636i	$0.805532\pi$
$920$	6080.00	0.217882
$921$	0	0
$922$	5044.00	0.180168
$923$	1216.00	0.0433642
$924$	0	0
$925$	7650.00	0.271925
$926$	34256.0	1.21568
$927$	0	0
$928$	2880.00	0.101876
$929$	150.000	0.00529746	0.00264873	−	0.999996i	$-0.499157\pi$
$929$	150.000	0.00529746	0.00264873	+	0.999996i	$0.499157\pi$
$930$	0	0
$931$	−4427.00	−0.155842
$932$	10872.0	0.382108
$933$	0	0
$934$	9632.00	0.337440
$935$	16960.0	0.593210
$936$	0	0
$937$	−1814.00	−0.0632452	−0.0316226	−	0.999500i	$-0.510067\pi$
$937$	−1814.00	−0.0632452	−0.0316226	+	0.999500i	$0.510067\pi$
$938$	−30912.0	−1.07603
$939$	0	0
$940$	−9120.00	−0.316449
$941$	−44682.0	−1.54792	−0.773959	−	0.633235i	$-0.781727\pi$
$941$	−44682.0	−1.54792	−0.773959	+	0.633235i	$0.781727\pi$
$942$	0	0
$943$	9424.00	0.325438
$944$	−4800.00	−0.165494
$945$	0	0
$946$	−17152.0	−0.589492
$947$	−13976.0	−0.479577	−0.239788	−	0.970825i	$-0.577078\pi$
$947$	−13976.0	−0.479577	−0.239788	+	0.970825i	$0.577078\pi$
$948$	0	0
$949$	−396.000	−0.0135455
$950$	950.000	0.0324443
$951$	0	0
$952$	−20352.0	−0.692870
$953$	3138.00	0.106663	0.0533315	−	0.998577i	$-0.483016\pi$
$953$	3138.00	0.106663	0.0533315	+	0.998577i	$0.483016\pi$
$954$	0	0
$955$	−25160.0	−0.852522
$956$	−2880.00	−0.0974329
$957$	0	0
$958$	−16720.0	−0.563882
$959$	55344.0	1.86356
$960$	0	0
$961$	−27087.0	−0.909234
$962$	−1224.00	−0.0410222
$963$	0	0
$964$	1928.00	0.0644157
$965$	6610.00	0.220501
$966$	0	0
$967$	−50744.0	−1.68750	−0.843752	−	0.536733i	$-0.819658\pi$
$967$	−50744.0	−1.68750	−0.843752	+	0.536733i	$0.819658\pi$
$968$	2456.00	0.0815484
$969$	0	0
$970$	5740.00	0.190000
$971$	22068.0	0.729347	0.364673	−	0.931135i	$-0.381181\pi$
$971$	22068.0	0.729347	0.364673	+	0.931135i	$0.381181\pi$
$972$	0	0
$973$	43680.0	1.43917
$974$	16168.0	0.531885
$975$	0	0
$976$	8032.00	0.263420
$977$	−36766.0	−1.20394	−0.601970	−	0.798519i	$-0.705617\pi$
$977$	−36766.0	−1.20394	−0.601970	+	0.798519i	$0.705617\pi$
$978$	0	0
$979$	3520.00	0.114913
$980$	4660.00	0.151896
$981$	0	0
$982$	24144.0	0.784589
$983$	−19912.0	−0.646077	−0.323039	−	0.946386i	$-0.604704\pi$
$983$	−19912.0	−0.646077	−0.323039	+	0.946386i	$0.604704\pi$
$984$	0	0
$985$	−1730.00	−0.0559618
$986$	−19080.0	−0.616259
$987$	0	0
$988$	−152.000	−0.00489450
$989$	40736.0	1.30974
$990$	0	0
$991$	−47228.0	−1.51387	−0.756936	−	0.653489i	$-0.773304\pi$
$991$	−47228.0	−1.51387	−0.756936	+	0.653489i	$0.773304\pi$
$992$	−1664.00	−0.0532581
$993$	0	0
$994$	29184.0	0.931248
$995$	−16200.0	−0.516155
$996$	0	0
$997$	−13234.0	−0.420386	−0.210193	−	0.977660i	$-0.567409\pi$
$997$	−13234.0	−0.420386	−0.210193	+	0.977660i	$0.567409\pi$
$998$	−21000.0	−0.666076
$999$	0	0

Twists

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

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