LMFDB - Embedded newform 1170.4.a.d.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)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -28.0000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -28.0000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +36.0000 q^{11} +13.0000 q^{13} +56.0000 q^{14} +16.0000 q^{16} -42.0000 q^{17} -112.000 q^{19} +20.0000 q^{20} -72.0000 q^{22} +168.000 q^{23} +25.0000 q^{25} -26.0000 q^{26} -112.000 q^{28} +210.000 q^{29} -76.0000 q^{31} -32.0000 q^{32} +84.0000 q^{34} -140.000 q^{35} +278.000 q^{37} +224.000 q^{38} -40.0000 q^{40} -150.000 q^{41} -460.000 q^{43} +144.000 q^{44} -336.000 q^{46} +264.000 q^{47} +441.000 q^{49} -50.0000 q^{50} +52.0000 q^{52} -582.000 q^{53} +180.000 q^{55} +224.000 q^{56} -420.000 q^{58} +204.000 q^{59} +614.000 q^{61} +152.000 q^{62} +64.0000 q^{64} +65.0000 q^{65} -304.000 q^{67} -168.000 q^{68} +280.000 q^{70} -1080.00 q^{71} -934.000 q^{73} -556.000 q^{74} -448.000 q^{76} -1008.00 q^{77} +128.000 q^{79} +80.0000 q^{80} +300.000 q^{82} -348.000 q^{83} -210.000 q^{85} +920.000 q^{86} -288.000 q^{88} +834.000 q^{89} -364.000 q^{91} +672.000 q^{92} -528.000 q^{94} -560.000 q^{95} -1582.00 q^{97} -882.000 q^{98} +O(q^{100})\)

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
$7$	−28.0000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−28.0000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−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
$14$	56.0000	1.06904
$15$	0	0
$16$	16.0000	0.250000
$17$	−42.0000	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$18$	0	0
$19$	−112.000	−1.35235	−0.676173	−	0.736743i	$-0.736363\pi$
$19$	−112.000	−1.35235	−0.676173	+	0.736743i	$0.736363\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−72.0000	−0.697748
$23$	168.000	1.52306	0.761531	−	0.648129i	$-0.224448\pi$
$23$	168.000	1.52306	0.761531	+	0.648129i	$0.224448\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−26.0000	−0.196116
$27$	0	0
$28$	−112.000	−0.755929
$29$	210.000	1.34469	0.672345	−	0.740238i	$-0.265287\pi$
$29$	210.000	1.34469	0.672345	+	0.740238i	$0.265287\pi$
$30$	0	0
$31$	−76.0000	−0.440323	−0.220161	−	0.975463i	$-0.570658\pi$
$31$	−76.0000	−0.440323	−0.220161	+	0.975463i	$0.570658\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	84.0000	0.423702
$35$	−140.000	−0.676123
$36$	0	0
$37$	278.000	1.23521	0.617607	−	0.786487i	$-0.288102\pi$
$37$	278.000	1.23521	0.617607	+	0.786487i	$0.288102\pi$
$38$	224.000	0.956253
$39$	0	0
$40$	−40.0000	−0.158114
$41$	−150.000	−0.571367	−0.285684	−	0.958324i	$-0.592221\pi$
$41$	−150.000	−0.571367	−0.285684	+	0.958324i	$0.592221\pi$
$42$	0	0
$43$	−460.000	−1.63138	−0.815690	−	0.578489i	$-0.803642\pi$
$43$	−460.000	−1.63138	−0.815690	+	0.578489i	$0.803642\pi$
$44$	144.000	0.493382
$45$	0	0
$46$	−336.000	−1.07697
$47$	264.000	0.819327	0.409663	−	0.912237i	$-0.365646\pi$
$47$	264.000	0.819327	0.409663	+	0.912237i	$0.365646\pi$
$48$	0	0
$49$	441.000	1.28571
$50$	−50.0000	−0.141421
$51$	0	0
$52$	52.0000	0.138675
$53$	−582.000	−1.50837	−0.754187	−	0.656659i	$-0.771969\pi$
$53$	−582.000	−1.50837	−0.754187	+	0.656659i	$0.771969\pi$
$54$	0	0
$55$	180.000	0.441294
$56$	224.000	0.534522
$57$	0	0
$58$	−420.000	−0.950840
$59$	204.000	0.450145	0.225072	−	0.974342i	$-0.427738\pi$
$59$	204.000	0.450145	0.225072	+	0.974342i	$0.427738\pi$
$60$	0	0
$61$	614.000	1.28876	0.644382	−	0.764703i	$-0.277115\pi$
$61$	614.000	1.28876	0.644382	+	0.764703i	$0.277115\pi$
$62$	152.000	0.311355
$63$	0	0
$64$	64.0000	0.125000
$65$	65.0000	0.124035
$66$	0	0
$67$	−304.000	−0.554321	−0.277161	−	0.960824i	$-0.589393\pi$
$67$	−304.000	−0.554321	−0.277161	+	0.960824i	$0.589393\pi$
$68$	−168.000	−0.299603
$69$	0	0
$70$	280.000	0.478091
$71$	−1080.00	−1.80525	−0.902623	−	0.430433i	$-0.858361\pi$
$71$	−1080.00	−1.80525	−0.902623	+	0.430433i	$0.858361\pi$
$72$	0	0
$73$	−934.000	−1.49749	−0.748743	−	0.662861i	$-0.769342\pi$
$73$	−934.000	−1.49749	−0.748743	+	0.662861i	$0.769342\pi$
$74$	−556.000	−0.873428
$75$	0	0
$76$	−448.000	−0.676173
$77$	−1008.00	−1.49185
$78$	0	0
$79$	128.000	0.182293	0.0911464	−	0.995838i	$-0.470947\pi$
$79$	128.000	0.182293	0.0911464	+	0.995838i	$0.470947\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	300.000	0.404018
$83$	−348.000	−0.460216	−0.230108	−	0.973165i	$-0.573908\pi$
$83$	−348.000	−0.460216	−0.230108	+	0.973165i	$0.573908\pi$
$84$	0	0
$85$	−210.000	−0.267973
$86$	920.000	1.15356
$87$	0	0
$88$	−288.000	−0.348874
$89$	834.000	0.993301	0.496651	−	0.867951i	$-0.334563\pi$
$89$	834.000	0.993301	0.496651	+	0.867951i	$0.334563\pi$
$90$	0	0
$91$	−364.000	−0.419314
$92$	672.000	0.761531
$93$	0	0
$94$	−528.000	−0.579352
$95$	−560.000	−0.604787
$96$	0	0
$97$	−1582.00	−1.65596	−0.827978	−	0.560760i	$-0.810509\pi$
$97$	−1582.00	−1.65596	−0.827978	+	0.560760i	$0.810509\pi$
$98$	−882.000	−0.909137
$99$	0	0
$100$	100.000	0.100000
$101$	1050.00	1.03444	0.517222	−	0.855851i	$-0.326966\pi$
$101$	1050.00	1.03444	0.517222	+	0.855851i	$0.326966\pi$
$102$	0	0
$103$	1544.00	1.47704	0.738519	−	0.674233i	$-0.235526\pi$
$103$	1544.00	1.47704	0.738519	+	0.674233i	$0.235526\pi$
$104$	−104.000	−0.0980581
$105$	0	0
$106$	1164.00	1.06658
$107$	−60.0000	−0.0542095	−0.0271048	−	0.999633i	$-0.508629\pi$
$107$	−60.0000	−0.0542095	−0.0271048	+	0.999633i	$0.508629\pi$
$108$	0	0
$109$	1166.00	1.02461	0.512305	−	0.858803i	$-0.328792\pi$
$109$	1166.00	1.02461	0.512305	+	0.858803i	$0.328792\pi$
$110$	−360.000	−0.312042
$111$	0	0
$112$	−448.000	−0.377964
$113$	−1698.00	−1.41358	−0.706789	−	0.707424i	$-0.749857\pi$
$113$	−1698.00	−1.41358	−0.706789	+	0.707424i	$0.749857\pi$
$114$	0	0
$115$	840.000	0.681134
$116$	840.000	0.672345
$117$	0	0
$118$	−408.000	−0.318300
$119$	1176.00	0.905914
$120$	0	0
$121$	−35.0000	−0.0262960
$122$	−1228.00	−0.911294
$123$	0	0
$124$	−304.000	−0.220161
$125$	125.000	0.0894427
$126$	0	0
$127$	−520.000	−0.363327	−0.181664	−	0.983361i	$-0.558148\pi$
$127$	−520.000	−0.363327	−0.181664	+	0.983361i	$0.558148\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−130.000	−0.0877058
$131$	−12.0000	−0.00800340	−0.00400170	−	0.999992i	$-0.501274\pi$
$131$	−12.0000	−0.00800340	−0.00400170	+	0.999992i	$0.501274\pi$
$132$	0	0
$133$	3136.00	2.04455
$134$	608.000	0.391964
$135$	0	0
$136$	336.000	0.211851
$137$	618.000	0.385396	0.192698	−	0.981258i	$-0.438276\pi$
$137$	618.000	0.385396	0.192698	+	0.981258i	$0.438276\pi$
$138$	0	0
$139$	524.000	0.319749	0.159874	−	0.987137i	$-0.448891\pi$
$139$	524.000	0.319749	0.159874	+	0.987137i	$0.448891\pi$
$140$	−560.000	−0.338062
$141$	0	0
$142$	2160.00	1.27650
$143$	468.000	0.273679
$144$	0	0
$145$	1050.00	0.601364
$146$	1868.00	1.05888
$147$	0	0
$148$	1112.00	0.617607
$149$	726.000	0.399169	0.199585	−	0.979881i	$-0.436041\pi$
$149$	726.000	0.399169	0.199585	+	0.979881i	$0.436041\pi$
$150$	0	0
$151$	−2524.00	−1.36027	−0.680133	−	0.733089i	$-0.738078\pi$
$151$	−2524.00	−1.36027	−0.680133	+	0.733089i	$0.738078\pi$
$152$	896.000	0.478126
$153$	0	0
$154$	2016.00	1.05490
$155$	−380.000	−0.196918
$156$	0	0
$157$	−2458.00	−1.24949	−0.624744	−	0.780829i	$-0.714797\pi$
$157$	−2458.00	−1.24949	−0.624744	+	0.780829i	$0.714797\pi$
$158$	−256.000	−0.128900
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−4704.00	−2.30265
$162$	0	0
$163$	−592.000	−0.284473	−0.142236	−	0.989833i	$-0.545429\pi$
$163$	−592.000	−0.284473	−0.142236	+	0.989833i	$0.545429\pi$
$164$	−600.000	−0.285684
$165$	0	0
$166$	696.000	0.325422
$167$	−1968.00	−0.911907	−0.455953	−	0.890004i	$-0.650702\pi$
$167$	−1968.00	−0.911907	−0.455953	+	0.890004i	$0.650702\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	420.000	0.189485
$171$	0	0
$172$	−1840.00	−0.815690
$173$	−2214.00	−0.972990	−0.486495	−	0.873683i	$-0.661725\pi$
$173$	−2214.00	−0.972990	−0.486495	+	0.873683i	$0.661725\pi$
$174$	0	0
$175$	−700.000	−0.302372
$176$	576.000	0.246691
$177$	0	0
$178$	−1668.00	−0.702370
$179$	−3084.00	−1.28776	−0.643880	−	0.765127i	$-0.722676\pi$
$179$	−3084.00	−1.28776	−0.643880	+	0.765127i	$0.722676\pi$
$180$	0	0
$181$	686.000	0.281713	0.140856	−	0.990030i	$-0.455014\pi$
$181$	686.000	0.281713	0.140856	+	0.990030i	$0.455014\pi$
$182$	728.000	0.296500
$183$	0	0
$184$	−1344.00	−0.538484
$185$	1390.00	0.552404
$186$	0	0
$187$	−1512.00	−0.591275
$188$	1056.00	0.409663
$189$	0	0
$190$	1120.00	0.427649
$191$	−4440.00	−1.68203	−0.841013	−	0.541014i	$-0.818040\pi$
$191$	−4440.00	−1.68203	−0.841013	+	0.541014i	$0.818040\pi$
$192$	0	0
$193$	−4726.00	−1.76262	−0.881308	−	0.472542i	$-0.843336\pi$
$193$	−4726.00	−1.76262	−0.881308	+	0.472542i	$0.843336\pi$
$194$	3164.00	1.17094
$195$	0	0
$196$	1764.00	0.642857
$197$	−258.000	−0.0933083	−0.0466542	−	0.998911i	$-0.514856\pi$
$197$	−258.000	−0.0933083	−0.0466542	+	0.998911i	$0.514856\pi$
$198$	0	0
$199$	3008.00	1.07151	0.535757	−	0.844372i	$-0.320026\pi$
$199$	3008.00	1.07151	0.535757	+	0.844372i	$0.320026\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−2100.00	−0.731463
$203$	−5880.00	−2.03298
$204$	0	0
$205$	−750.000	−0.255523
$206$	−3088.00	−1.04442
$207$	0	0
$208$	208.000	0.0693375
$209$	−4032.00	−1.33445
$210$	0	0
$211$	−4516.00	−1.47343	−0.736716	−	0.676202i	$-0.763625\pi$
$211$	−4516.00	−1.47343	−0.736716	+	0.676202i	$0.763625\pi$
$212$	−2328.00	−0.754187
$213$	0	0
$214$	120.000	0.0383319
$215$	−2300.00	−0.729575
$216$	0	0
$217$	2128.00	0.665705
$218$	−2332.00	−0.724509
$219$	0	0
$220$	720.000	0.220647
$221$	−546.000	−0.166190
$222$	0	0
$223$	−4516.00	−1.35612	−0.678058	−	0.735009i	$-0.737178\pi$
$223$	−4516.00	−1.35612	−0.678058	+	0.735009i	$0.737178\pi$
$224$	896.000	0.267261
$225$	0	0
$226$	3396.00	0.999551
$227$	−372.000	−0.108769	−0.0543844	−	0.998520i	$-0.517320\pi$
$227$	−372.000	−0.108769	−0.0543844	+	0.998520i	$0.517320\pi$
$228$	0	0
$229$	−4138.00	−1.19409	−0.597045	−	0.802208i	$-0.703659\pi$
$229$	−4138.00	−1.19409	−0.597045	+	0.802208i	$0.703659\pi$
$230$	−1680.00	−0.481634
$231$	0	0
$232$	−1680.00	−0.475420
$233$	1446.00	0.406569	0.203285	−	0.979120i	$-0.434838\pi$
$233$	1446.00	0.406569	0.203285	+	0.979120i	$0.434838\pi$
$234$	0	0
$235$	1320.00	0.366414
$236$	816.000	0.225072
$237$	0	0
$238$	−2352.00	−0.640578
$239$	3456.00	0.935356	0.467678	−	0.883899i	$-0.345091\pi$
$239$	3456.00	0.935356	0.467678	+	0.883899i	$0.345091\pi$
$240$	0	0
$241$	5258.00	1.40538	0.702692	−	0.711494i	$-0.251981\pi$
$241$	5258.00	1.40538	0.702692	+	0.711494i	$0.251981\pi$
$242$	70.0000	0.0185941
$243$	0	0
$244$	2456.00	0.644382
$245$	2205.00	0.574989
$246$	0	0
$247$	−1456.00	−0.375073
$248$	608.000	0.155678
$249$	0	0
$250$	−250.000	−0.0632456
$251$	−7020.00	−1.76533	−0.882666	−	0.470000i	$-0.844254\pi$
$251$	−7020.00	−1.76533	−0.882666	+	0.470000i	$0.844254\pi$
$252$	0	0
$253$	6048.00	1.50290
$254$	1040.00	0.256911
$255$	0	0
$256$	256.000	0.0625000
$257$	5694.00	1.38203	0.691015	−	0.722840i	$-0.257164\pi$
$257$	5694.00	1.38203	0.691015	+	0.722840i	$0.257164\pi$
$258$	0	0
$259$	−7784.00	−1.86747
$260$	260.000	0.0620174
$261$	0	0
$262$	24.0000	0.00565926
$263$	960.000	0.225080	0.112540	−	0.993647i	$-0.464101\pi$
$263$	960.000	0.225080	0.112540	+	0.993647i	$0.464101\pi$
$264$	0	0
$265$	−2910.00	−0.674566
$266$	−6272.00	−1.44572
$267$	0	0
$268$	−1216.00	−0.277161
$269$	2370.00	0.537180	0.268590	−	0.963255i	$-0.413442\pi$
$269$	2370.00	0.537180	0.268590	+	0.963255i	$0.413442\pi$
$270$	0	0
$271$	−508.000	−0.113870	−0.0569351	−	0.998378i	$-0.518133\pi$
$271$	−508.000	−0.113870	−0.0569351	+	0.998378i	$0.518133\pi$
$272$	−672.000	−0.149801
$273$	0	0
$274$	−1236.00	−0.272516
$275$	900.000	0.197353
$276$	0	0
$277$	−4498.00	−0.975663	−0.487831	−	0.872938i	$-0.662212\pi$
$277$	−4498.00	−0.975663	−0.487831	+	0.872938i	$0.662212\pi$
$278$	−1048.00	−0.226097
$279$	0	0
$280$	1120.00	0.239046
$281$	−7062.00	−1.49923	−0.749615	−	0.661874i	$-0.769761\pi$
$281$	−7062.00	−1.49923	−0.749615	+	0.661874i	$0.769761\pi$
$282$	0	0
$283$	−4036.00	−0.847757	−0.423879	−	0.905719i	$-0.639332\pi$
$283$	−4036.00	−0.847757	−0.423879	+	0.905719i	$0.639332\pi$
$284$	−4320.00	−0.902623
$285$	0	0
$286$	−936.000	−0.193520
$287$	4200.00	0.863826
$288$	0	0
$289$	−3149.00	−0.640953
$290$	−2100.00	−0.425228
$291$	0	0
$292$	−3736.00	−0.748743
$293$	−1674.00	−0.333775	−0.166888	−	0.985976i	$-0.553372\pi$
$293$	−1674.00	−0.333775	−0.166888	+	0.985976i	$0.553372\pi$
$294$	0	0
$295$	1020.00	0.201311
$296$	−2224.00	−0.436714
$297$	0	0
$298$	−1452.00	−0.282255
$299$	2184.00	0.422421
$300$	0	0
$301$	12880.0	2.46641
$302$	5048.00	0.961854
$303$	0	0
$304$	−1792.00	−0.338086
$305$	3070.00	0.576353
$306$	0	0
$307$	−8968.00	−1.66720	−0.833601	−	0.552368i	$-0.813724\pi$
$307$	−8968.00	−1.66720	−0.833601	+	0.552368i	$0.813724\pi$
$308$	−4032.00	−0.745924
$309$	0	0
$310$	760.000	0.139242
$311$	−672.000	−0.122526	−0.0612631	−	0.998122i	$-0.519513\pi$
$311$	−672.000	−0.122526	−0.0612631	+	0.998122i	$0.519513\pi$
$312$	0	0
$313$	1946.00	0.351420	0.175710	−	0.984442i	$-0.443778\pi$
$313$	1946.00	0.351420	0.175710	+	0.984442i	$0.443778\pi$
$314$	4916.00	0.883522
$315$	0	0
$316$	512.000	0.0911464
$317$	−474.000	−0.0839826	−0.0419913	−	0.999118i	$-0.513370\pi$
$317$	−474.000	−0.0839826	−0.0419913	+	0.999118i	$0.513370\pi$
$318$	0	0
$319$	7560.00	1.32689
$320$	320.000	0.0559017
$321$	0	0
$322$	9408.00	1.62822
$323$	4704.00	0.810333
$324$	0	0
$325$	325.000	0.0554700
$326$	1184.00	0.201152
$327$	0	0
$328$	1200.00	0.202009
$329$	−7392.00	−1.23871
$330$	0	0
$331$	−6928.00	−1.15045	−0.575223	−	0.817997i	$-0.695085\pi$
$331$	−6928.00	−1.15045	−0.575223	+	0.817997i	$0.695085\pi$
$332$	−1392.00	−0.230108
$333$	0	0
$334$	3936.00	0.644815
$335$	−1520.00	−0.247900
$336$	0	0
$337$	2882.00	0.465853	0.232927	−	0.972494i	$-0.425170\pi$
$337$	2882.00	0.465853	0.232927	+	0.972494i	$0.425170\pi$
$338$	−338.000	−0.0543928
$339$	0	0
$340$	−840.000	−0.133986
$341$	−2736.00	−0.434495
$342$	0	0
$343$	−2744.00	−0.431959
$344$	3680.00	0.576780
$345$	0	0
$346$	4428.00	0.688008
$347$	7548.00	1.16772	0.583859	−	0.811855i	$-0.301542\pi$
$347$	7548.00	1.16772	0.583859	+	0.811855i	$0.301542\pi$
$348$	0	0
$349$	−5146.00	−0.789281	−0.394640	−	0.918836i	$-0.629131\pi$
$349$	−5146.00	−0.789281	−0.394640	+	0.918836i	$0.629131\pi$
$350$	1400.00	0.213809
$351$	0	0
$352$	−1152.00	−0.174437
$353$	9138.00	1.37781	0.688905	−	0.724852i	$-0.258092\pi$
$353$	9138.00	1.37781	0.688905	+	0.724852i	$0.258092\pi$
$354$	0	0
$355$	−5400.00	−0.807330
$356$	3336.00	0.496651
$357$	0	0
$358$	6168.00	0.910584
$359$	4320.00	0.635100	0.317550	−	0.948242i	$-0.397140\pi$
$359$	4320.00	0.635100	0.317550	+	0.948242i	$0.397140\pi$
$360$	0	0
$361$	5685.00	0.828838
$362$	−1372.00	−0.199201
$363$	0	0
$364$	−1456.00	−0.209657
$365$	−4670.00	−0.669696
$366$	0	0
$367$	−3976.00	−0.565519	−0.282760	−	0.959191i	$-0.591250\pi$
$367$	−3976.00	−0.565519	−0.282760	+	0.959191i	$0.591250\pi$
$368$	2688.00	0.380765
$369$	0	0
$370$	−2780.00	−0.390609
$371$	16296.0	2.28045
$372$	0	0
$373$	−11314.0	−1.57055	−0.785277	−	0.619144i	$-0.787480\pi$
$373$	−11314.0	−1.57055	−0.785277	+	0.619144i	$0.787480\pi$
$374$	3024.00	0.418094
$375$	0	0
$376$	−2112.00	−0.289676
$377$	2730.00	0.372950
$378$	0	0
$379$	200.000	0.0271064	0.0135532	−	0.999908i	$-0.495686\pi$
$379$	200.000	0.0271064	0.0135532	+	0.999908i	$0.495686\pi$
$380$	−2240.00	−0.302394
$381$	0	0
$382$	8880.00	1.18937
$383$	−3960.00	−0.528320	−0.264160	−	0.964479i	$-0.585095\pi$
$383$	−3960.00	−0.528320	−0.264160	+	0.964479i	$0.585095\pi$
$384$	0	0
$385$	−5040.00	−0.667175
$386$	9452.00	1.24636
$387$	0	0
$388$	−6328.00	−0.827978
$389$	12450.0	1.62273	0.811363	−	0.584543i	$-0.198726\pi$
$389$	12450.0	1.62273	0.811363	+	0.584543i	$0.198726\pi$
$390$	0	0
$391$	−7056.00	−0.912627
$392$	−3528.00	−0.454569
$393$	0	0
$394$	516.000	0.0659789
$395$	640.000	0.0815238
$396$	0	0
$397$	−7570.00	−0.956996	−0.478498	−	0.878089i	$-0.658819\pi$
$397$	−7570.00	−0.956996	−0.478498	+	0.878089i	$0.658819\pi$
$398$	−6016.00	−0.757675
$399$	0	0
$400$	400.000	0.0500000
$401$	8010.00	0.997507	0.498754	−	0.866744i	$-0.333791\pi$
$401$	8010.00	0.997507	0.498754	+	0.866744i	$0.333791\pi$
$402$	0	0
$403$	−988.000	−0.122124
$404$	4200.00	0.517222
$405$	0	0
$406$	11760.0	1.43753
$407$	10008.0	1.21887
$408$	0	0
$409$	−3166.00	−0.382759	−0.191380	−	0.981516i	$-0.561296\pi$
$409$	−3166.00	−0.382759	−0.191380	+	0.981516i	$0.561296\pi$
$410$	1500.00	0.180682
$411$	0	0
$412$	6176.00	0.738519
$413$	−5712.00	−0.680555
$414$	0	0
$415$	−1740.00	−0.205815
$416$	−416.000	−0.0490290
$417$	0	0
$418$	8064.00	0.943596
$419$	1188.00	0.138515	0.0692573	−	0.997599i	$-0.477937\pi$
$419$	1188.00	0.138515	0.0692573	+	0.997599i	$0.477937\pi$
$420$	0	0
$421$	14054.0	1.62696	0.813480	−	0.581593i	$-0.197570\pi$
$421$	14054.0	1.62696	0.813480	+	0.581593i	$0.197570\pi$
$422$	9032.00	1.04187
$423$	0	0
$424$	4656.00	0.533291
$425$	−1050.00	−0.119841
$426$	0	0
$427$	−17192.0	−1.94843
$428$	−240.000	−0.0271048
$429$	0	0
$430$	4600.00	0.515888
$431$	−1704.00	−0.190438	−0.0952190	−	0.995456i	$-0.530355\pi$
$431$	−1704.00	−0.190438	−0.0952190	+	0.995456i	$0.530355\pi$
$432$	0	0
$433$	10418.0	1.15625	0.578126	−	0.815947i	$-0.303784\pi$
$433$	10418.0	1.15625	0.578126	+	0.815947i	$0.303784\pi$
$434$	−4256.00	−0.470725
$435$	0	0
$436$	4664.00	0.512305
$437$	−18816.0	−2.05971
$438$	0	0
$439$	−568.000	−0.0617521	−0.0308760	−	0.999523i	$-0.509830\pi$
$439$	−568.000	−0.0617521	−0.0308760	+	0.999523i	$0.509830\pi$
$440$	−1440.00	−0.156021
$441$	0	0
$442$	1092.00	0.117514
$443$	14580.0	1.56369	0.781847	−	0.623470i	$-0.214278\pi$
$443$	14580.0	1.56369	0.781847	+	0.623470i	$0.214278\pi$
$444$	0	0
$445$	4170.00	0.444218
$446$	9032.00	0.958918
$447$	0	0
$448$	−1792.00	−0.188982
$449$	15978.0	1.67940	0.839698	−	0.543054i	$-0.182732\pi$
$449$	15978.0	1.67940	0.839698	+	0.543054i	$0.182732\pi$
$450$	0	0
$451$	−5400.00	−0.563805
$452$	−6792.00	−0.706789
$453$	0	0
$454$	744.000	0.0769111
$455$	−1820.00	−0.187523
$456$	0	0
$457$	−6982.00	−0.714670	−0.357335	−	0.933976i	$-0.616315\pi$
$457$	−6982.00	−0.714670	−0.357335	+	0.933976i	$0.616315\pi$
$458$	8276.00	0.844350
$459$	0	0
$460$	3360.00	0.340567
$461$	−11946.0	−1.20690	−0.603450	−	0.797401i	$-0.706208\pi$
$461$	−11946.0	−1.20690	−0.603450	+	0.797401i	$0.706208\pi$
$462$	0	0
$463$	−7828.00	−0.785741	−0.392870	−	0.919594i	$-0.628518\pi$
$463$	−7828.00	−0.785741	−0.392870	+	0.919594i	$0.628518\pi$
$464$	3360.00	0.336173
$465$	0	0
$466$	−2892.00	−0.287488
$467$	−2076.00	−0.205708	−0.102854	−	0.994696i	$-0.532798\pi$
$467$	−2076.00	−0.205708	−0.102854	+	0.994696i	$0.532798\pi$
$468$	0	0
$469$	8512.00	0.838055
$470$	−2640.00	−0.259094
$471$	0	0
$472$	−1632.00	−0.159150
$473$	−16560.0	−1.60979
$474$	0	0
$475$	−2800.00	−0.270469
$476$	4704.00	0.452957
$477$	0	0
$478$	−6912.00	−0.661396
$479$	−17760.0	−1.69410	−0.847051	−	0.531511i	$-0.821624\pi$
$479$	−17760.0	−1.69410	−0.847051	+	0.531511i	$0.821624\pi$
$480$	0	0
$481$	3614.00	0.342587
$482$	−10516.0	−0.993757
$483$	0	0
$484$	−140.000	−0.0131480
$485$	−7910.00	−0.740566
$486$	0	0
$487$	3044.00	0.283238	0.141619	−	0.989921i	$-0.454769\pi$
$487$	3044.00	0.283238	0.141619	+	0.989921i	$0.454769\pi$
$488$	−4912.00	−0.455647
$489$	0	0
$490$	−4410.00	−0.406579
$491$	−2700.00	−0.248166	−0.124083	−	0.992272i	$-0.539599\pi$
$491$	−2700.00	−0.248166	−0.124083	+	0.992272i	$0.539599\pi$
$492$	0	0
$493$	−8820.00	−0.805746
$494$	2912.00	0.265217
$495$	0	0
$496$	−1216.00	−0.110081
$497$	30240.0	2.72927
$498$	0	0
$499$	15608.0	1.40022	0.700110	−	0.714035i	$-0.253134\pi$
$499$	15608.0	1.40022	0.700110	+	0.714035i	$0.253134\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	14040.0	1.24828
$503$	7152.00	0.633980	0.316990	−	0.948429i	$-0.397328\pi$
$503$	7152.00	0.633980	0.316990	+	0.948429i	$0.397328\pi$
$504$	0	0
$505$	5250.00	0.462618
$506$	−12096.0	−1.06271
$507$	0	0
$508$	−2080.00	−0.181664
$509$	−21354.0	−1.85953	−0.929764	−	0.368157i	$-0.879989\pi$
$509$	−21354.0	−1.85953	−0.929764	+	0.368157i	$0.879989\pi$
$510$	0	0
$511$	26152.0	2.26399
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−11388.0	−0.977243
$515$	7720.00	0.660551
$516$	0	0
$517$	9504.00	0.808482
$518$	15568.0	1.32050
$519$	0	0
$520$	−520.000	−0.0438529
$521$	−7746.00	−0.651360	−0.325680	−	0.945480i	$-0.605593\pi$
$521$	−7746.00	−0.651360	−0.325680	+	0.945480i	$0.605593\pi$
$522$	0	0
$523$	−8212.00	−0.686588	−0.343294	−	0.939228i	$-0.611543\pi$
$523$	−8212.00	−0.686588	−0.343294	+	0.939228i	$0.611543\pi$
$524$	−48.0000	−0.00400170
$525$	0	0
$526$	−1920.00	−0.159156
$527$	3192.00	0.263844
$528$	0	0
$529$	16057.0	1.31972
$530$	5820.00	0.476990
$531$	0	0
$532$	12544.0	1.02228
$533$	−1950.00	−0.158469
$534$	0	0
$535$	−300.000	−0.0242432
$536$	2432.00	0.195982
$537$	0	0
$538$	−4740.00	−0.379844
$539$	15876.0	1.26870
$540$	0	0
$541$	9758.00	0.775470	0.387735	−	0.921771i	$-0.373258\pi$
$541$	9758.00	0.775470	0.387735	+	0.921771i	$0.373258\pi$
$542$	1016.00	0.0805183
$543$	0	0
$544$	1344.00	0.105926
$545$	5830.00	0.458220
$546$	0	0
$547$	16292.0	1.27348	0.636742	−	0.771077i	$-0.280282\pi$
$547$	16292.0	1.27348	0.636742	+	0.771077i	$0.280282\pi$
$548$	2472.00	0.192698
$549$	0	0
$550$	−1800.00	−0.139550
$551$	−23520.0	−1.81849
$552$	0	0
$553$	−3584.00	−0.275601
$554$	8996.00	0.689898
$555$	0	0
$556$	2096.00	0.159874
$557$	10686.0	0.812891	0.406446	−	0.913675i	$-0.366768\pi$
$557$	10686.0	0.812891	0.406446	+	0.913675i	$0.366768\pi$
$558$	0	0
$559$	−5980.00	−0.452463
$560$	−2240.00	−0.169031
$561$	0	0
$562$	14124.0	1.06012
$563$	−19572.0	−1.46512	−0.732559	−	0.680704i	$-0.761674\pi$
$563$	−19572.0	−1.46512	−0.732559	+	0.680704i	$0.761674\pi$
$564$	0	0
$565$	−8490.00	−0.632172
$566$	8072.00	0.599455
$567$	0	0
$568$	8640.00	0.638251
$569$	4878.00	0.359396	0.179698	−	0.983722i	$-0.442488\pi$
$569$	4878.00	0.359396	0.179698	+	0.983722i	$0.442488\pi$
$570$	0	0
$571$	5612.00	0.411305	0.205652	−	0.978625i	$-0.434068\pi$
$571$	5612.00	0.411305	0.205652	+	0.978625i	$0.434068\pi$
$572$	1872.00	0.136840
$573$	0	0
$574$	−8400.00	−0.610817
$575$	4200.00	0.304612
$576$	0	0
$577$	26474.0	1.91010	0.955049	−	0.296447i	$-0.0958017\pi$
$577$	26474.0	1.91010	0.955049	+	0.296447i	$0.0958017\pi$
$578$	6298.00	0.453222
$579$	0	0
$580$	4200.00	0.300682
$581$	9744.00	0.695782
$582$	0	0
$583$	−20952.0	−1.48841
$584$	7472.00	0.529441
$585$	0	0
$586$	3348.00	0.236015
$587$	−4884.00	−0.343414	−0.171707	−	0.985148i	$-0.554928\pi$
$587$	−4884.00	−0.343414	−0.171707	+	0.985148i	$0.554928\pi$
$588$	0	0
$589$	8512.00	0.595468
$590$	−2040.00	−0.142348
$591$	0	0
$592$	4448.00	0.308804
$593$	−5862.00	−0.405942	−0.202971	−	0.979185i	$-0.565060\pi$
$593$	−5862.00	−0.405942	−0.202971	+	0.979185i	$0.565060\pi$
$594$	0	0
$595$	5880.00	0.405137
$596$	2904.00	0.199585
$597$	0	0
$598$	−4368.00	−0.298697
$599$	5928.00	0.404360	0.202180	−	0.979348i	$-0.435197\pi$
$599$	5928.00	0.404360	0.202180	+	0.979348i	$0.435197\pi$
$600$	0	0
$601$	14762.0	1.00192	0.500961	−	0.865470i	$-0.332980\pi$
$601$	14762.0	1.00192	0.500961	+	0.865470i	$0.332980\pi$
$602$	−25760.0	−1.74402
$603$	0	0
$604$	−10096.0	−0.680133
$605$	−175.000	−0.0117599
$606$	0	0
$607$	7784.00	0.520499	0.260249	−	0.965541i	$-0.416195\pi$
$607$	7784.00	0.520499	0.260249	+	0.965541i	$0.416195\pi$
$608$	3584.00	0.239063
$609$	0	0
$610$	−6140.00	−0.407543
$611$	3432.00	0.227240
$612$	0	0
$613$	−21994.0	−1.44915	−0.724575	−	0.689196i	$-0.757964\pi$
$613$	−21994.0	−1.44915	−0.724575	+	0.689196i	$0.757964\pi$
$614$	17936.0	1.17889
$615$	0	0
$616$	8064.00	0.527448
$617$	9546.00	0.622865	0.311432	−	0.950268i	$-0.399191\pi$
$617$	9546.00	0.622865	0.311432	+	0.950268i	$0.399191\pi$
$618$	0	0
$619$	−18568.0	−1.20567	−0.602836	−	0.797865i	$-0.705963\pi$
$619$	−18568.0	−1.20567	−0.602836	+	0.797865i	$0.705963\pi$
$620$	−1520.00	−0.0984591
$621$	0	0
$622$	1344.00	0.0866391
$623$	−23352.0	−1.50173
$624$	0	0
$625$	625.000	0.0400000
$626$	−3892.00	−0.248491
$627$	0	0
$628$	−9832.00	−0.624744
$629$	−11676.0	−0.740147
$630$	0	0
$631$	−3580.00	−0.225860	−0.112930	−	0.993603i	$-0.536024\pi$
$631$	−3580.00	−0.225860	−0.112930	+	0.993603i	$0.536024\pi$
$632$	−1024.00	−0.0644502
$633$	0	0
$634$	948.000	0.0593847
$635$	−2600.00	−0.162485
$636$	0	0
$637$	5733.00	0.356593
$638$	−15120.0	−0.938255
$639$	0	0
$640$	−640.000	−0.0395285
$641$	20718.0	1.27662	0.638309	−	0.769780i	$-0.279634\pi$
$641$	20718.0	1.27662	0.638309	+	0.769780i	$0.279634\pi$
$642$	0	0
$643$	18560.0	1.13831	0.569156	−	0.822229i	$-0.307270\pi$
$643$	18560.0	1.13831	0.569156	+	0.822229i	$0.307270\pi$
$644$	−18816.0	−1.15133
$645$	0	0
$646$	−9408.00	−0.572992
$647$	27072.0	1.64499	0.822496	−	0.568771i	$-0.192581\pi$
$647$	27072.0	1.64499	0.822496	+	0.568771i	$0.192581\pi$
$648$	0	0
$649$	7344.00	0.444187
$650$	−650.000	−0.0392232
$651$	0	0
$652$	−2368.00	−0.142236
$653$	−24150.0	−1.44726	−0.723631	−	0.690187i	$-0.757528\pi$
$653$	−24150.0	−1.44726	−0.723631	+	0.690187i	$0.757528\pi$
$654$	0	0
$655$	−60.0000	−0.00357923
$656$	−2400.00	−0.142842
$657$	0	0
$658$	14784.0	0.875897
$659$	11388.0	0.673162	0.336581	−	0.941655i	$-0.390729\pi$
$659$	11388.0	0.673162	0.336581	+	0.941655i	$0.390729\pi$
$660$	0	0
$661$	1598.00	0.0940318	0.0470159	−	0.998894i	$-0.485029\pi$
$661$	1598.00	0.0940318	0.0470159	+	0.998894i	$0.485029\pi$
$662$	13856.0	0.813488
$663$	0	0
$664$	2784.00	0.162711
$665$	15680.0	0.914352
$666$	0	0
$667$	35280.0	2.04805
$668$	−7872.00	−0.455953
$669$	0	0
$670$	3040.00	0.175292
$671$	22104.0	1.27171
$672$	0	0
$673$	−7918.00	−0.453516	−0.226758	−	0.973951i	$-0.572813\pi$
$673$	−7918.00	−0.453516	−0.226758	+	0.973951i	$0.572813\pi$
$674$	−5764.00	−0.329408
$675$	0	0
$676$	676.000	0.0384615
$677$	1578.00	0.0895827	0.0447913	−	0.998996i	$-0.485738\pi$
$677$	1578.00	0.0895827	0.0447913	+	0.998996i	$0.485738\pi$
$678$	0	0
$679$	44296.0	2.50357
$680$	1680.00	0.0947427
$681$	0	0
$682$	5472.00	0.307234
$683$	8580.00	0.480680	0.240340	−	0.970689i	$-0.422741\pi$
$683$	8580.00	0.480680	0.240340	+	0.970689i	$0.422741\pi$
$684$	0	0
$685$	3090.00	0.172354
$686$	5488.00	0.305441
$687$	0	0
$688$	−7360.00	−0.407845
$689$	−7566.00	−0.418348
$690$	0	0
$691$	14168.0	0.779994	0.389997	−	0.920816i	$-0.372476\pi$
$691$	14168.0	0.779994	0.389997	+	0.920816i	$0.372476\pi$
$692$	−8856.00	−0.486495
$693$	0	0
$694$	−15096.0	−0.825701
$695$	2620.00	0.142996
$696$	0	0
$697$	6300.00	0.342367
$698$	10292.0	0.558106
$699$	0	0
$700$	−2800.00	−0.151186
$701$	−11814.0	−0.636532	−0.318266	−	0.948002i	$-0.603100\pi$
$701$	−11814.0	−0.636532	−0.318266	+	0.948002i	$0.603100\pi$
$702$	0	0
$703$	−31136.0	−1.67044
$704$	2304.00	0.123346
$705$	0	0
$706$	−18276.0	−0.974258
$707$	−29400.0	−1.56393
$708$	0	0
$709$	8198.00	0.434249	0.217124	−	0.976144i	$-0.430332\pi$
$709$	8198.00	0.434249	0.217124	+	0.976144i	$0.430332\pi$
$710$	10800.0	0.570869
$711$	0	0
$712$	−6672.00	−0.351185
$713$	−12768.0	−0.670639
$714$	0	0
$715$	2340.00	0.122393
$716$	−12336.0	−0.643880
$717$	0	0
$718$	−8640.00	−0.449083
$719$	11448.0	0.593795	0.296897	−	0.954909i	$-0.404048\pi$
$719$	11448.0	0.593795	0.296897	+	0.954909i	$0.404048\pi$
$720$	0	0
$721$	−43232.0	−2.23307
$722$	−11370.0	−0.586077
$723$	0	0
$724$	2744.00	0.140856
$725$	5250.00	0.268938
$726$	0	0
$727$	−10864.0	−0.554228	−0.277114	−	0.960837i	$-0.589378\pi$
$727$	−10864.0	−0.554228	−0.277114	+	0.960837i	$0.589378\pi$
$728$	2912.00	0.148250
$729$	0	0
$730$	9340.00	0.473546
$731$	19320.0	0.977532
$732$	0	0
$733$	31286.0	1.57650	0.788250	−	0.615355i	$-0.210987\pi$
$733$	31286.0	1.57650	0.788250	+	0.615355i	$0.210987\pi$
$734$	7952.00	0.399882
$735$	0	0
$736$	−5376.00	−0.269242
$737$	−10944.0	−0.546984
$738$	0	0
$739$	19712.0	0.981215	0.490607	−	0.871381i	$-0.336775\pi$
$739$	19712.0	0.981215	0.490607	+	0.871381i	$0.336775\pi$
$740$	5560.00	0.276202
$741$	0	0
$742$	−32592.0	−1.61252
$743$	13608.0	0.671910	0.335955	−	0.941878i	$-0.390941\pi$
$743$	13608.0	0.671910	0.335955	+	0.941878i	$0.390941\pi$
$744$	0	0
$745$	3630.00	0.178514
$746$	22628.0	1.11055
$747$	0	0
$748$	−6048.00	−0.295637
$749$	1680.00	0.0819571
$750$	0	0
$751$	1952.00	0.0948462	0.0474231	−	0.998875i	$-0.484899\pi$
$751$	1952.00	0.0948462	0.0474231	+	0.998875i	$0.484899\pi$
$752$	4224.00	0.204832
$753$	0	0
$754$	−5460.00	−0.263715
$755$	−12620.0	−0.608330
$756$	0	0
$757$	−27634.0	−1.32678	−0.663392	−	0.748272i	$-0.730884\pi$
$757$	−27634.0	−1.32678	−0.663392	+	0.748272i	$0.730884\pi$
$758$	−400.000	−0.0191671
$759$	0	0
$760$	4480.00	0.213825
$761$	5370.00	0.255798	0.127899	−	0.991787i	$-0.459177\pi$
$761$	5370.00	0.255798	0.127899	+	0.991787i	$0.459177\pi$
$762$	0	0
$763$	−32648.0	−1.54907
$764$	−17760.0	−0.841013
$765$	0	0
$766$	7920.00	0.373579
$767$	2652.00	0.124848
$768$	0	0
$769$	−11230.0	−0.526611	−0.263306	−	0.964712i	$-0.584813\pi$
$769$	−11230.0	−0.526611	−0.263306	+	0.964712i	$0.584813\pi$
$770$	10080.0	0.471764
$771$	0	0
$772$	−18904.0	−0.881308
$773$	10374.0	0.482700	0.241350	−	0.970438i	$-0.422410\pi$
$773$	10374.0	0.482700	0.241350	+	0.970438i	$0.422410\pi$
$774$	0	0
$775$	−1900.00	−0.0880645
$776$	12656.0	0.585469
$777$	0	0
$778$	−24900.0	−1.14744
$779$	16800.0	0.772686
$780$	0	0
$781$	−38880.0	−1.78135
$782$	14112.0	0.645325
$783$	0	0
$784$	7056.00	0.321429
$785$	−12290.0	−0.558788
$786$	0	0
$787$	−39544.0	−1.79109	−0.895547	−	0.444966i	$-0.853216\pi$
$787$	−39544.0	−1.79109	−0.895547	+	0.444966i	$0.853216\pi$
$788$	−1032.00	−0.0466542
$789$	0	0
$790$	−1280.00	−0.0576460
$791$	47544.0	2.13713
$792$	0	0
$793$	7982.00	0.357439
$794$	15140.0	0.676698
$795$	0	0
$796$	12032.0	0.535757
$797$	12210.0	0.542660	0.271330	−	0.962486i	$-0.412536\pi$
$797$	12210.0	0.542660	0.271330	+	0.962486i	$0.412536\pi$
$798$	0	0
$799$	−11088.0	−0.490945
$800$	−800.000	−0.0353553
$801$	0	0
$802$	−16020.0	−0.705344
$803$	−33624.0	−1.47767
$804$	0	0
$805$	−23520.0	−1.02978
$806$	1976.00	0.0863544
$807$	0	0
$808$	−8400.00	−0.365731
$809$	−13602.0	−0.591126	−0.295563	−	0.955323i	$-0.595507\pi$
$809$	−13602.0	−0.591126	−0.295563	+	0.955323i	$0.595507\pi$
$810$	0	0
$811$	−24040.0	−1.04089	−0.520443	−	0.853896i	$-0.674233\pi$
$811$	−24040.0	−1.04089	−0.520443	+	0.853896i	$0.674233\pi$
$812$	−23520.0	−1.01649
$813$	0	0
$814$	−20016.0	−0.861868
$815$	−2960.00	−0.127220
$816$	0	0
$817$	51520.0	2.20619
$818$	6332.00	0.270652
$819$	0	0
$820$	−3000.00	−0.127762
$821$	1878.00	0.0798327	0.0399164	−	0.999203i	$-0.487291\pi$
$821$	1878.00	0.0798327	0.0399164	+	0.999203i	$0.487291\pi$
$822$	0	0
$823$	17048.0	0.722061	0.361030	−	0.932554i	$-0.382425\pi$
$823$	17048.0	0.722061	0.361030	+	0.932554i	$0.382425\pi$
$824$	−12352.0	−0.522212
$825$	0	0
$826$	11424.0	0.481225
$827$	−26652.0	−1.12065	−0.560327	−	0.828271i	$-0.689325\pi$
$827$	−26652.0	−1.12065	−0.560327	+	0.828271i	$0.689325\pi$
$828$	0	0
$829$	−8746.00	−0.366419	−0.183209	−	0.983074i	$-0.558649\pi$
$829$	−8746.00	−0.366419	−0.183209	+	0.983074i	$0.558649\pi$
$830$	3480.00	0.145533
$831$	0	0
$832$	832.000	0.0346688
$833$	−18522.0	−0.770407
$834$	0	0
$835$	−9840.00	−0.407817
$836$	−16128.0	−0.667223
$837$	0	0
$838$	−2376.00	−0.0979446
$839$	5400.00	0.222203	0.111102	−	0.993809i	$-0.464562\pi$
$839$	5400.00	0.222203	0.111102	+	0.993809i	$0.464562\pi$
$840$	0	0
$841$	19711.0	0.808192
$842$	−28108.0	−1.15043
$843$	0	0
$844$	−18064.0	−0.736716
$845$	845.000	0.0344010
$846$	0	0
$847$	980.000	0.0397558
$848$	−9312.00	−0.377094
$849$	0	0
$850$	2100.00	0.0847405
$851$	46704.0	1.88131
$852$	0	0
$853$	−11338.0	−0.455106	−0.227553	−	0.973766i	$-0.573073\pi$
$853$	−11338.0	−0.455106	−0.227553	+	0.973766i	$0.573073\pi$
$854$	34384.0	1.37775
$855$	0	0
$856$	480.000	0.0191660
$857$	47430.0	1.89052	0.945261	−	0.326314i	$-0.105807\pi$
$857$	47430.0	1.89052	0.945261	+	0.326314i	$0.105807\pi$
$858$	0	0
$859$	10292.0	0.408799	0.204400	−	0.978888i	$-0.434476\pi$
$859$	10292.0	0.408799	0.204400	+	0.978888i	$0.434476\pi$
$860$	−9200.00	−0.364788
$861$	0	0
$862$	3408.00	0.134660
$863$	−34392.0	−1.35657	−0.678283	−	0.734800i	$-0.737276\pi$
$863$	−34392.0	−1.35657	−0.678283	+	0.734800i	$0.737276\pi$
$864$	0	0
$865$	−11070.0	−0.435134
$866$	−20836.0	−0.817594
$867$	0	0
$868$	8512.00	0.332853
$869$	4608.00	0.179880
$870$	0	0
$871$	−3952.00	−0.153741
$872$	−9328.00	−0.362255
$873$	0	0
$874$	37632.0	1.45643
$875$	−3500.00	−0.135225
$876$	0	0
$877$	2606.00	0.100340	0.0501701	−	0.998741i	$-0.484024\pi$
$877$	2606.00	0.100340	0.0501701	+	0.998741i	$0.484024\pi$
$878$	1136.00	0.0436653
$879$	0	0
$880$	2880.00	0.110324
$881$	−1290.00	−0.0493317	−0.0246658	−	0.999696i	$-0.507852\pi$
$881$	−1290.00	−0.0493317	−0.0246658	+	0.999696i	$0.507852\pi$
$882$	0	0
$883$	19460.0	0.741655	0.370827	−	0.928702i	$-0.379074\pi$
$883$	19460.0	0.741655	0.370827	+	0.928702i	$0.379074\pi$
$884$	−2184.00	−0.0830949
$885$	0	0
$886$	−29160.0	−1.10570
$887$	−46728.0	−1.76885	−0.884427	−	0.466679i	$-0.845450\pi$
$887$	−46728.0	−1.76885	−0.884427	+	0.466679i	$0.845450\pi$
$888$	0	0
$889$	14560.0	0.549299
$890$	−8340.00	−0.314109
$891$	0	0
$892$	−18064.0	−0.678058
$893$	−29568.0	−1.10801
$894$	0	0
$895$	−15420.0	−0.575904
$896$	3584.00	0.133631
$897$	0	0
$898$	−31956.0	−1.18751
$899$	−15960.0	−0.592098
$900$	0	0
$901$	24444.0	0.903827
$902$	10800.0	0.398670
$903$	0	0
$904$	13584.0	0.499776
$905$	3430.00	0.125986
$906$	0	0
$907$	32300.0	1.18247	0.591237	−	0.806498i	$-0.298640\pi$
$907$	32300.0	1.18247	0.591237	+	0.806498i	$0.298640\pi$
$908$	−1488.00	−0.0543844
$909$	0	0
$910$	3640.00	0.132599
$911$	−21432.0	−0.779444	−0.389722	−	0.920932i	$-0.627429\pi$
$911$	−21432.0	−0.779444	−0.389722	+	0.920932i	$0.627429\pi$
$912$	0	0
$913$	−12528.0	−0.454125
$914$	13964.0	0.505348
$915$	0	0
$916$	−16552.0	−0.597045
$917$	336.000	0.0121000
$918$	0	0
$919$	−35944.0	−1.29019	−0.645094	−	0.764103i	$-0.723182\pi$
$919$	−35944.0	−1.29019	−0.645094	+	0.764103i	$0.723182\pi$
$920$	−6720.00	−0.240817
$921$	0	0
$922$	23892.0	0.853407
$923$	−14040.0	−0.500685
$924$	0	0
$925$	6950.00	0.247043
$926$	15656.0	0.555603
$927$	0	0
$928$	−6720.00	−0.237710
$929$	−27774.0	−0.980878	−0.490439	−	0.871476i	$-0.663163\pi$
$929$	−27774.0	−0.980878	−0.490439	+	0.871476i	$0.663163\pi$
$930$	0	0
$931$	−49392.0	−1.73873
$932$	5784.00	0.203285
$933$	0	0
$934$	4152.00	0.145458
$935$	−7560.00	−0.264426
$936$	0	0
$937$	16106.0	0.561537	0.280768	−	0.959776i	$-0.409411\pi$
$937$	16106.0	0.561537	0.280768	+	0.959776i	$0.409411\pi$
$938$	−17024.0	−0.592594
$939$	0	0
$940$	5280.00	0.183207
$941$	−38802.0	−1.34422	−0.672109	−	0.740452i	$-0.734611\pi$
$941$	−38802.0	−1.34422	−0.672109	+	0.740452i	$0.734611\pi$
$942$	0	0
$943$	−25200.0	−0.870228
$944$	3264.00	0.112536
$945$	0	0
$946$	33120.0	1.13829
$947$	21636.0	0.742424	0.371212	−	0.928548i	$-0.378942\pi$
$947$	21636.0	0.742424	0.371212	+	0.928548i	$0.378942\pi$
$948$	0	0
$949$	−12142.0	−0.415328
$950$	5600.00	0.191251
$951$	0	0
$952$	−9408.00	−0.320289
$953$	56742.0	1.92870	0.964351	−	0.264625i	$-0.0852482\pi$
$953$	56742.0	1.92870	0.964351	+	0.264625i	$0.0852482\pi$
$954$	0	0
$955$	−22200.0	−0.752225
$956$	13824.0	0.467678
$957$	0	0
$958$	35520.0	1.19791
$959$	−17304.0	−0.582665
$960$	0	0
$961$	−24015.0	−0.806116
$962$	−7228.00	−0.242245
$963$	0	0
$964$	21032.0	0.702692
$965$	−23630.0	−0.788266
$966$	0	0
$967$	−13708.0	−0.455863	−0.227932	−	0.973677i	$-0.573196\pi$
$967$	−13708.0	−0.455863	−0.227932	+	0.973677i	$0.573196\pi$
$968$	280.000	0.00929705
$969$	0	0
$970$	15820.0	0.523659
$971$	−6924.00	−0.228838	−0.114419	−	0.993433i	$-0.536501\pi$
$971$	−6924.00	−0.228838	−0.114419	+	0.993433i	$0.536501\pi$
$972$	0	0
$973$	−14672.0	−0.483415
$974$	−6088.00	−0.200279
$975$	0	0
$976$	9824.00	0.322191
$977$	13914.0	0.455628	0.227814	−	0.973705i	$-0.426842\pi$
$977$	13914.0	0.455628	0.227814	+	0.973705i	$0.426842\pi$
$978$	0	0
$979$	30024.0	0.980154
$980$	8820.00	0.287494
$981$	0	0
$982$	5400.00	0.175480
$983$	−10056.0	−0.326283	−0.163142	−	0.986603i	$-0.552163\pi$
$983$	−10056.0	−0.326283	−0.163142	+	0.986603i	$0.552163\pi$
$984$	0	0
$985$	−1290.00	−0.0417287
$986$	17640.0	0.569749
$987$	0	0
$988$	−5824.00	−0.187537
$989$	−77280.0	−2.48469
$990$	0	0
$991$	−4792.00	−0.153605	−0.0768027	−	0.997046i	$-0.524471\pi$
$991$	−4792.00	−0.153605	−0.0768027	+	0.997046i	$0.524471\pi$
$992$	2432.00	0.0778388
$993$	0	0
$994$	−60480.0	−1.92989
$995$	15040.0	0.479196
$996$	0	0
$997$	−27250.0	−0.865613	−0.432806	−	0.901487i	$-0.642477\pi$
$997$	−27250.0	−0.865613	−0.432806	+	0.901487i	$0.642477\pi$
$998$	−31216.0	−0.990105
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.k.1.1	✓	1	3.2	odd	2
1170.4.a.d.1.1		1	1.1	even	1	trivial
1950.4.a.b.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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