LMFDB - Embedded newform 230.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.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:	$13.5704393013$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.00000 q^{6} -18.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -32.0000 q^{11} +4.00000 q^{12} -47.0000 q^{13} -36.0000 q^{14} -5.00000 q^{15} +16.0000 q^{16} +20.0000 q^{17} -52.0000 q^{18} +36.0000 q^{19} -20.0000 q^{20} -18.0000 q^{21} -64.0000 q^{22} -23.0000 q^{23} +8.00000 q^{24} +25.0000 q^{25} -94.0000 q^{26} -53.0000 q^{27} -72.0000 q^{28} -27.0000 q^{29} -10.0000 q^{30} -33.0000 q^{31} +32.0000 q^{32} -32.0000 q^{33} +40.0000 q^{34} +90.0000 q^{35} -104.000 q^{36} +56.0000 q^{37} +72.0000 q^{38} -47.0000 q^{39} -40.0000 q^{40} -157.000 q^{41} -36.0000 q^{42} +18.0000 q^{43} -128.000 q^{44} +130.000 q^{45} -46.0000 q^{46} +65.0000 q^{47} +16.0000 q^{48} -19.0000 q^{49} +50.0000 q^{50} +20.0000 q^{51} -188.000 q^{52} -14.0000 q^{53} -106.000 q^{54} +160.000 q^{55} -144.000 q^{56} +36.0000 q^{57} -54.0000 q^{58} -744.000 q^{59} -20.0000 q^{60} +552.000 q^{61} -66.0000 q^{62} +468.000 q^{63} +64.0000 q^{64} +235.000 q^{65} -64.0000 q^{66} -156.000 q^{67} +80.0000 q^{68} -23.0000 q^{69} +180.000 q^{70} +699.000 q^{71} -208.000 q^{72} -609.000 q^{73} +112.000 q^{74} +25.0000 q^{75} +144.000 q^{76} +576.000 q^{77} -94.0000 q^{78} -644.000 q^{79} -80.0000 q^{80} +649.000 q^{81} -314.000 q^{82} +512.000 q^{83} -72.0000 q^{84} -100.000 q^{85} +36.0000 q^{86} -27.0000 q^{87} -256.000 q^{88} -102.000 q^{89} +260.000 q^{90} +846.000 q^{91} -92.0000 q^{92} -33.0000 q^{93} +130.000 q^{94} -180.000 q^{95} +32.0000 q^{96} +578.000 q^{97} -38.0000 q^{98} +832.000 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	1.00000	0.192450	0.0962250	−	0.995360i	$-0.469323\pi$
$3$	1.00000	0.192450	0.0962250	+	0.995360i	$0.469323\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	2.00000	0.136083
$7$	−18.0000	−0.971909	−0.485954	−	0.873984i	$-0.661528\pi$
$7$	−18.0000	−0.971909	−0.485954	+	0.873984i	$0.661528\pi$
$8$	8.00000	0.353553
$9$	−26.0000	−0.962963
$10$	−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	$0.644512\pi$
$12$	4.00000	0.0962250
$13$	−47.0000	−1.00273	−0.501364	−	0.865237i	$-0.667168\pi$
$13$	−47.0000	−1.00273	−0.501364	+	0.865237i	$0.667168\pi$
$14$	−36.0000	−0.687243
$15$	−5.00000	−0.0860663
$16$	16.0000	0.250000
$17$	20.0000	0.285336	0.142668	−	0.989771i	$-0.454432\pi$
$17$	20.0000	0.285336	0.142668	+	0.989771i	$0.454432\pi$
$18$	−52.0000	−0.680918
$19$	36.0000	0.434682	0.217341	−	0.976096i	$-0.430262\pi$
$19$	36.0000	0.434682	0.217341	+	0.976096i	$0.430262\pi$
$20$	−20.0000	−0.223607
$21$	−18.0000	−0.187044
$22$	−64.0000	−0.620220
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	8.00000	0.0680414
$25$	25.0000	0.200000
$26$	−94.0000	−0.709035
$27$	−53.0000	−0.377772
$28$	−72.0000	−0.485954
$29$	−27.0000	−0.172889	−0.0864444	−	0.996257i	$-0.527550\pi$
$29$	−27.0000	−0.172889	−0.0864444	+	0.996257i	$0.527550\pi$
$30$	−10.0000	−0.0608581
$31$	−33.0000	−0.191193	−0.0955964	−	0.995420i	$-0.530476\pi$
$31$	−33.0000	−0.191193	−0.0955964	+	0.995420i	$0.530476\pi$
$32$	32.0000	0.176777
$33$	−32.0000	−0.168803
$34$	40.0000	0.201763
$35$	90.0000	0.434651
$36$	−104.000	−0.481481
$37$	56.0000	0.248820	0.124410	−	0.992231i	$-0.460296\pi$
$37$	56.0000	0.248820	0.124410	+	0.992231i	$0.460296\pi$
$38$	72.0000	0.307367
$39$	−47.0000	−0.192975
$40$	−40.0000	−0.158114
$41$	−157.000	−0.598031	−0.299016	−	0.954248i	$-0.596658\pi$
$41$	−157.000	−0.598031	−0.299016	+	0.954248i	$0.596658\pi$
$42$	−36.0000	−0.132260
$43$	18.0000	0.0638366	0.0319183	−	0.999490i	$-0.489838\pi$
$43$	18.0000	0.0638366	0.0319183	+	0.999490i	$0.489838\pi$
$44$	−128.000	−0.438562
$45$	130.000	0.430650
$46$	−46.0000	−0.147442
$47$	65.0000	0.201728	0.100864	−	0.994900i	$-0.467839\pi$
$47$	65.0000	0.201728	0.100864	+	0.994900i	$0.467839\pi$
$48$	16.0000	0.0481125
$49$	−19.0000	−0.0553936
$50$	50.0000	0.141421
$51$	20.0000	0.0549129
$52$	−188.000	−0.501364
$53$	−14.0000	−0.0362839	−0.0181420	−	0.999835i	$-0.505775\pi$
$53$	−14.0000	−0.0362839	−0.0181420	+	0.999835i	$0.505775\pi$
$54$	−106.000	−0.267125
$55$	160.000	0.392262
$56$	−144.000	−0.343622
$57$	36.0000	0.0836547
$58$	−54.0000	−0.122251
$59$	−744.000	−1.64170	−0.820852	−	0.571141i	$-0.806501\pi$
$59$	−744.000	−1.64170	−0.820852	+	0.571141i	$0.806501\pi$
$60$	−20.0000	−0.0430331
$61$	552.000	1.15863	0.579314	−	0.815104i	$-0.303320\pi$
$61$	552.000	1.15863	0.579314	+	0.815104i	$0.303320\pi$
$62$	−66.0000	−0.135194
$63$	468.000	0.935912
$64$	64.0000	0.125000
$65$	235.000	0.448433
$66$	−64.0000	−0.119361
$67$	−156.000	−0.284454	−0.142227	−	0.989834i	$-0.545426\pi$
$67$	−156.000	−0.284454	−0.142227	+	0.989834i	$0.545426\pi$
$68$	80.0000	0.142668
$69$	−23.0000	−0.0401286
$70$	180.000	0.307344
$71$	699.000	1.16839	0.584197	−	0.811612i	$-0.301409\pi$
$71$	699.000	1.16839	0.584197	+	0.811612i	$0.301409\pi$
$72$	−208.000	−0.340459
$73$	−609.000	−0.976412	−0.488206	−	0.872728i	$-0.662348\pi$
$73$	−609.000	−0.976412	−0.488206	+	0.872728i	$0.662348\pi$
$74$	112.000	0.175942
$75$	25.0000	0.0384900
$76$	144.000	0.217341
$77$	576.000	0.852484
$78$	−94.0000	−0.136454
$79$	−644.000	−0.917160	−0.458580	−	0.888653i	$-0.651642\pi$
$79$	−644.000	−0.917160	−0.458580	+	0.888653i	$0.651642\pi$
$80$	−80.0000	−0.111803
$81$	649.000	0.890261
$82$	−314.000	−0.422872
$83$	512.000	0.677100	0.338550	−	0.940948i	$-0.390064\pi$
$83$	512.000	0.677100	0.338550	+	0.940948i	$0.390064\pi$
$84$	−72.0000	−0.0935220
$85$	−100.000	−0.127606
$86$	36.0000	0.0451393
$87$	−27.0000	−0.0332725
$88$	−256.000	−0.310110
$89$	−102.000	−0.121483	−0.0607415	−	0.998154i	$-0.519347\pi$
$89$	−102.000	−0.121483	−0.0607415	+	0.998154i	$0.519347\pi$
$90$	260.000	0.304516
$91$	846.000	0.974559
$92$	−92.0000	−0.104257
$93$	−33.0000	−0.0367951
$94$	130.000	0.142643
$95$	−180.000	−0.194396
$96$	32.0000	0.0340207
$97$	578.000	0.605021	0.302510	−	0.953146i	$-0.402175\pi$
$97$	578.000	0.605021	0.302510	+	0.953146i	$0.402175\pi$
$98$	−38.0000	−0.0391692
$99$	832.000	0.844638
$100$	100.000	0.100000
$101$	−6.00000	−0.00591111	−0.00295556	−	0.999996i	$-0.500941\pi$
$101$	−6.00000	−0.00591111	−0.00295556	+	0.999996i	$0.500941\pi$
$102$	40.0000	0.0388293
$103$	−160.000	−0.153061	−0.0765304	−	0.997067i	$-0.524384\pi$
$103$	−160.000	−0.153061	−0.0765304	+	0.997067i	$0.524384\pi$
$104$	−376.000	−0.354518
$105$	90.0000	0.0836486
$106$	−28.0000	−0.0256566
$107$	380.000	0.343327	0.171663	−	0.985156i	$-0.445086\pi$
$107$	380.000	0.343327	0.171663	+	0.985156i	$0.445086\pi$
$108$	−212.000	−0.188886
$109$	250.000	0.219685	0.109842	−	0.993949i	$-0.464965\pi$
$109$	250.000	0.219685	0.109842	+	0.993949i	$0.464965\pi$
$110$	320.000	0.277371
$111$	56.0000	0.0478854
$112$	−288.000	−0.242977
$113$	−390.000	−0.324674	−0.162337	−	0.986735i	$-0.551903\pi$
$113$	−390.000	−0.324674	−0.162337	+	0.986735i	$0.551903\pi$
$114$	72.0000	0.0591528
$115$	115.000	0.0932505
$116$	−108.000	−0.0864444
$117$	1222.00	0.965589
$118$	−1488.00	−1.16086
$119$	−360.000	−0.277321
$120$	−40.0000	−0.0304290
$121$	−307.000	−0.230654
$122$	1104.00	0.819274
$123$	−157.000	−0.115091
$124$	−132.000	−0.0955964
$125$	−125.000	−0.0894427
$126$	936.000	0.661790
$127$	−769.000	−0.537305	−0.268652	−	0.963237i	$-0.586578\pi$
$127$	−769.000	−0.537305	−0.268652	+	0.963237i	$0.586578\pi$
$128$	128.000	0.0883883
$129$	18.0000	0.0122854
$130$	470.000	0.317090
$131$	−213.000	−0.142060	−0.0710301	−	0.997474i	$-0.522629\pi$
$131$	−213.000	−0.142060	−0.0710301	+	0.997474i	$0.522629\pi$
$132$	−128.000	−0.0844013
$133$	−648.000	−0.422472
$134$	−312.000	−0.201140
$135$	265.000	0.168945
$136$	160.000	0.100882
$137$	2836.00	1.76858	0.884291	−	0.466936i	$-0.154642\pi$
$137$	2836.00	1.76858	0.884291	+	0.466936i	$0.154642\pi$
$138$	−46.0000	−0.0283752
$139$	−1631.00	−0.995249	−0.497625	−	0.867393i	$-0.665794\pi$
$139$	−1631.00	−0.995249	−0.497625	+	0.867393i	$0.665794\pi$
$140$	360.000	0.217325
$141$	65.0000	0.0388226
$142$	1398.00	0.826180
$143$	1504.00	0.879516
$144$	−416.000	−0.240741
$145$	135.000	0.0773182
$146$	−1218.00	−0.690427
$147$	−19.0000	−0.0106605
$148$	224.000	0.124410
$149$	−1966.00	−1.08095	−0.540473	−	0.841361i	$-0.681755\pi$
$149$	−1966.00	−1.08095	−0.540473	+	0.841361i	$0.681755\pi$
$150$	50.0000	0.0272166
$151$	35.0000	0.0188626	0.00943132	−	0.999956i	$-0.496998\pi$
$151$	35.0000	0.0188626	0.00943132	+	0.999956i	$0.496998\pi$
$152$	288.000	0.153683
$153$	−520.000	−0.274768
$154$	1152.00	0.602797
$155$	165.000	0.0855040
$156$	−188.000	−0.0964875
$157$	1702.00	0.865187	0.432594	−	0.901589i	$-0.357599\pi$
$157$	1702.00	0.865187	0.432594	+	0.901589i	$0.357599\pi$
$158$	−1288.00	−0.648530
$159$	−14.0000	−0.00698284
$160$	−160.000	−0.0790569
$161$	414.000	0.202657
$162$	1298.00	0.629509
$163$	−2045.00	−0.982680	−0.491340	−	0.870968i	$-0.663493\pi$
$163$	−2045.00	−0.982680	−0.491340	+	0.870968i	$0.663493\pi$
$164$	−628.000	−0.299016
$165$	160.000	0.0754908
$166$	1024.00	0.478782
$167$	1016.00	0.470781	0.235391	−	0.971901i	$-0.424363\pi$
$167$	1016.00	0.470781	0.235391	+	0.971901i	$0.424363\pi$
$168$	−144.000	−0.0661300
$169$	12.0000	0.00546199
$170$	−200.000	−0.0902312
$171$	−936.000	−0.418583
$172$	72.0000	0.0319183
$173$	598.000	0.262804	0.131402	−	0.991329i	$-0.458052\pi$
$173$	598.000	0.262804	0.131402	+	0.991329i	$0.458052\pi$
$174$	−54.0000	−0.0235272
$175$	−450.000	−0.194382
$176$	−512.000	−0.219281
$177$	−744.000	−0.315946
$178$	−204.000	−0.0859014
$179$	−4607.00	−1.92371	−0.961853	−	0.273567i	$-0.911796\pi$
$179$	−4607.00	−1.92371	−0.961853	+	0.273567i	$0.911796\pi$
$180$	520.000	0.215325
$181$	−1212.00	−0.497720	−0.248860	−	0.968540i	$-0.580056\pi$
$181$	−1212.00	−0.497720	−0.248860	+	0.968540i	$0.580056\pi$
$182$	1692.00	0.689117
$183$	552.000	0.222978
$184$	−184.000	−0.0737210
$185$	−280.000	−0.111276
$186$	−66.0000	−0.0260180
$187$	−640.000	−0.250275
$188$	260.000	0.100864
$189$	954.000	0.367160
$190$	−360.000	−0.137459
$191$	−1058.00	−0.400807	−0.200404	−	0.979713i	$-0.564225\pi$
$191$	−1058.00	−0.400807	−0.200404	+	0.979713i	$0.564225\pi$
$192$	64.0000	0.0240563
$193$	1047.00	0.390491	0.195245	−	0.980754i	$-0.437450\pi$
$193$	1047.00	0.390491	0.195245	+	0.980754i	$0.437450\pi$
$194$	1156.00	0.427814
$195$	235.000	0.0863010
$196$	−76.0000	−0.0276968
$197$	251.000	0.0907767	0.0453883	−	0.998969i	$-0.485547\pi$
$197$	251.000	0.0907767	0.0453883	+	0.998969i	$0.485547\pi$
$198$	1664.00	0.597249
$199$	−3508.00	−1.24963	−0.624813	−	0.780775i	$-0.714825\pi$
$199$	−3508.00	−1.24963	−0.624813	+	0.780775i	$0.714825\pi$
$200$	200.000	0.0707107
$201$	−156.000	−0.0547432
$202$	−12.0000	−0.00417979
$203$	486.000	0.168032
$204$	80.0000	0.0274565
$205$	785.000	0.267448
$206$	−320.000	−0.108230
$207$	598.000	0.200792
$208$	−752.000	−0.250682
$209$	−1152.00	−0.381270
$210$	180.000	0.0591485
$211$	−3296.00	−1.07538	−0.537692	−	0.843141i	$-0.680704\pi$
$211$	−3296.00	−1.07538	−0.537692	+	0.843141i	$0.680704\pi$
$212$	−56.0000	−0.0181420
$213$	699.000	0.224858
$214$	760.000	0.242769
$215$	−90.0000	−0.0285486
$216$	−424.000	−0.133563
$217$	594.000	0.185822
$218$	500.000	0.155341
$219$	−609.000	−0.187911
$220$	640.000	0.196131
$221$	−940.000	−0.286114
$222$	112.000	0.0338601
$223$	−2720.00	−0.816792	−0.408396	−	0.912805i	$-0.633912\pi$
$223$	−2720.00	−0.816792	−0.408396	+	0.912805i	$0.633912\pi$
$224$	−576.000	−0.171811
$225$	−650.000	−0.192593
$226$	−780.000	−0.229579
$227$	−4134.00	−1.20874	−0.604368	−	0.796705i	$-0.706574\pi$
$227$	−4134.00	−1.20874	−0.604368	+	0.796705i	$0.706574\pi$
$228$	144.000	0.0418273
$229$	−4510.00	−1.30144	−0.650719	−	0.759319i	$-0.725532\pi$
$229$	−4510.00	−1.30144	−0.650719	+	0.759319i	$0.725532\pi$
$230$	230.000	0.0659380
$231$	576.000	0.164061
$232$	−216.000	−0.0611254
$233$	−5003.00	−1.40668	−0.703342	−	0.710852i	$-0.748310\pi$
$233$	−5003.00	−1.40668	−0.703342	+	0.710852i	$0.748310\pi$
$234$	2444.00	0.682775
$235$	−325.000	−0.0902156
$236$	−2976.00	−0.820852
$237$	−644.000	−0.176508
$238$	−720.000	−0.196095
$239$	−6309.00	−1.70751	−0.853756	−	0.520674i	$-0.825681\pi$
$239$	−6309.00	−1.70751	−0.853756	+	0.520674i	$0.825681\pi$
$240$	−80.0000	−0.0215166
$241$	3038.00	0.812012	0.406006	−	0.913871i	$-0.366921\pi$
$241$	3038.00	0.812012	0.406006	+	0.913871i	$0.366921\pi$
$242$	−614.000	−0.163097
$243$	2080.00	0.549103
$244$	2208.00	0.579314
$245$	95.0000	0.0247728
$246$	−314.000	−0.0813817
$247$	−1692.00	−0.435868
$248$	−264.000	−0.0675968
$249$	512.000	0.130308
$250$	−250.000	−0.0632456
$251$	−1332.00	−0.334961	−0.167480	−	0.985875i	$-0.553563\pi$
$251$	−1332.00	−0.334961	−0.167480	+	0.985875i	$0.553563\pi$
$252$	1872.00	0.467956
$253$	736.000	0.182893
$254$	−1538.00	−0.379932
$255$	−100.000	−0.0245578
$256$	256.000	0.0625000
$257$	3301.00	0.801209	0.400605	−	0.916251i	$-0.368800\pi$
$257$	3301.00	0.801209	0.400605	+	0.916251i	$0.368800\pi$
$258$	36.0000	0.00868706
$259$	−1008.00	−0.241830
$260$	940.000	0.224217
$261$	702.000	0.166485
$262$	−426.000	−0.100452
$263$	2072.00	0.485798	0.242899	−	0.970052i	$-0.421902\pi$
$263$	2072.00	0.485798	0.242899	+	0.970052i	$0.421902\pi$
$264$	−256.000	−0.0596807
$265$	70.0000	0.0162267
$266$	−1296.00	−0.298733
$267$	−102.000	−0.0233794
$268$	−624.000	−0.142227
$269$	5721.00	1.29671	0.648356	−	0.761337i	$-0.275457\pi$
$269$	5721.00	1.29671	0.648356	+	0.761337i	$0.275457\pi$
$270$	530.000	0.119462
$271$	−5900.00	−1.32251	−0.661254	−	0.750162i	$-0.729975\pi$
$271$	−5900.00	−1.32251	−0.661254	+	0.750162i	$0.729975\pi$
$272$	320.000	0.0713340
$273$	846.000	0.187554
$274$	5672.00	1.25058
$275$	−800.000	−0.175425
$276$	−92.0000	−0.0200643
$277$	6371.00	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$277$	6371.00	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$278$	−3262.00	−0.703747
$279$	858.000	0.184112
$280$	720.000	0.153672
$281$	3190.00	0.677222	0.338611	−	0.940926i	$-0.390043\pi$
$281$	3190.00	0.677222	0.338611	+	0.940926i	$0.390043\pi$
$282$	130.000	0.0274517
$283$	−4226.00	−0.887667	−0.443833	−	0.896109i	$-0.646382\pi$
$283$	−4226.00	−0.887667	−0.443833	+	0.896109i	$0.646382\pi$
$284$	2796.00	0.584197
$285$	−180.000	−0.0374115
$286$	3008.00	0.621912
$287$	2826.00	0.581232
$288$	−832.000	−0.170229
$289$	−4513.00	−0.918583
$290$	270.000	0.0546722
$291$	578.000	0.116436
$292$	−2436.00	−0.488206
$293$	6048.00	1.20590	0.602949	−	0.797780i	$-0.293992\pi$
$293$	6048.00	1.20590	0.602949	+	0.797780i	$0.293992\pi$
$294$	−38.0000	−0.00753811
$295$	3720.00	0.734192
$296$	448.000	0.0879712
$297$	1696.00	0.331353
$298$	−3932.00	−0.764344
$299$	1081.00	0.209083
$300$	100.000	0.0192450
$301$	−324.000	−0.0620434
$302$	70.0000	0.0133379
$303$	−6.00000	−0.00113759
$304$	576.000	0.108671
$305$	−2760.00	−0.518155
$306$	−1040.00	−0.194290
$307$	8628.00	1.60399	0.801997	−	0.597328i	$-0.203771\pi$
$307$	8628.00	1.60399	0.801997	+	0.597328i	$0.203771\pi$
$308$	2304.00	0.426242
$309$	−160.000	−0.0294566
$310$	330.000	0.0604605
$311$	8247.00	1.50368	0.751840	−	0.659346i	$-0.229167\pi$
$311$	8247.00	1.50368	0.751840	+	0.659346i	$0.229167\pi$
$312$	−376.000	−0.0682269
$313$	2620.00	0.473135	0.236567	−	0.971615i	$-0.423978\pi$
$313$	2620.00	0.473135	0.236567	+	0.971615i	$0.423978\pi$
$314$	3404.00	0.611780
$315$	−2340.00	−0.418553
$316$	−2576.00	−0.458580
$317$	9906.00	1.75513	0.877565	−	0.479457i	$-0.159166\pi$
$317$	9906.00	1.75513	0.877565	+	0.479457i	$0.159166\pi$
$318$	−28.0000	−0.00493762
$319$	864.000	0.151645
$320$	−320.000	−0.0559017
$321$	380.000	0.0660733
$322$	828.000	0.143300
$323$	720.000	0.124031
$324$	2596.00	0.445130
$325$	−1175.00	−0.200545
$326$	−4090.00	−0.694859
$327$	250.000	0.0422784
$328$	−1256.00	−0.211436
$329$	−1170.00	−0.196061
$330$	320.000	0.0533801
$331$	−8115.00	−1.34756	−0.673778	−	0.738934i	$-0.735329\pi$
$331$	−8115.00	−1.34756	−0.673778	+	0.738934i	$0.735329\pi$
$332$	2048.00	0.338550
$333$	−1456.00	−0.239605
$334$	2032.00	0.332892
$335$	780.000	0.127212
$336$	−288.000	−0.0467610
$337$	−7586.00	−1.22622	−0.613109	−	0.789998i	$-0.710082\pi$
$337$	−7586.00	−1.22622	−0.613109	+	0.789998i	$0.710082\pi$
$338$	24.0000	0.00386221
$339$	−390.000	−0.0624835
$340$	−400.000	−0.0638031
$341$	1056.00	0.167700
$342$	−1872.00	−0.295983
$343$	6516.00	1.02575
$344$	144.000	0.0225697
$345$	115.000	0.0179461
$346$	1196.00	0.185831
$347$	1356.00	0.209781	0.104890	−	0.994484i	$-0.466551\pi$
$347$	1356.00	0.209781	0.104890	+	0.994484i	$0.466551\pi$
$348$	−108.000	−0.0166362
$349$	6649.00	1.01981	0.509904	−	0.860231i	$-0.329681\pi$
$349$	6649.00	1.01981	0.509904	+	0.860231i	$0.329681\pi$
$350$	−900.000	−0.137449
$351$	2491.00	0.378803
$352$	−1024.00	−0.155055
$353$	10691.0	1.61197	0.805984	−	0.591938i	$-0.201637\pi$
$353$	10691.0	1.61197	0.805984	+	0.591938i	$0.201637\pi$
$354$	−1488.00	−0.223408
$355$	−3495.00	−0.522522
$356$	−408.000	−0.0607415
$357$	−360.000	−0.0533704
$358$	−9214.00	−1.36027
$359$	−6420.00	−0.943829	−0.471915	−	0.881644i	$-0.656437\pi$
$359$	−6420.00	−0.943829	−0.471915	+	0.881644i	$0.656437\pi$
$360$	1040.00	0.152258
$361$	−5563.00	−0.811051
$362$	−2424.00	−0.351941
$363$	−307.000	−0.0443893
$364$	3384.00	0.487280
$365$	3045.00	0.436665
$366$	1104.00	0.157669
$367$	−524.000	−0.0745302	−0.0372651	−	0.999305i	$-0.511865\pi$
$367$	−524.000	−0.0745302	−0.0372651	+	0.999305i	$0.511865\pi$
$368$	−368.000	−0.0521286
$369$	4082.00	0.575882
$370$	−560.000	−0.0786838
$371$	252.000	0.0352647
$372$	−132.000	−0.0183975
$373$	5566.00	0.772645	0.386322	−	0.922364i	$-0.373745\pi$
$373$	5566.00	0.772645	0.386322	+	0.922364i	$0.373745\pi$
$374$	−1280.00	−0.176971
$375$	−125.000	−0.0172133
$376$	520.000	0.0713217
$377$	1269.00	0.173360
$378$	1908.00	0.259622
$379$	2240.00	0.303591	0.151796	−	0.988412i	$-0.451494\pi$
$379$	2240.00	0.303591	0.151796	+	0.988412i	$0.451494\pi$
$380$	−720.000	−0.0971979
$381$	−769.000	−0.103404
$382$	−2116.00	−0.283414
$383$	8778.00	1.17111	0.585555	−	0.810633i	$-0.300877\pi$
$383$	8778.00	1.17111	0.585555	+	0.810633i	$0.300877\pi$
$384$	128.000	0.0170103
$385$	−2880.00	−0.381243
$386$	2094.00	0.276119
$387$	−468.000	−0.0614723
$388$	2312.00	0.302510
$389$	4056.00	0.528656	0.264328	−	0.964433i	$-0.414850\pi$
$389$	4056.00	0.528656	0.264328	+	0.964433i	$0.414850\pi$
$390$	470.000	0.0610240
$391$	−460.000	−0.0594967
$392$	−152.000	−0.0195846
$393$	−213.000	−0.0273395
$394$	502.000	0.0641888
$395$	3220.00	0.410167
$396$	3328.00	0.422319
$397$	−9151.00	−1.15687	−0.578433	−	0.815730i	$-0.696335\pi$
$397$	−9151.00	−1.15687	−0.578433	+	0.815730i	$0.696335\pi$
$398$	−7016.00	−0.883619
$399$	−648.000	−0.0813047
$400$	400.000	0.0500000
$401$	15930.0	1.98381	0.991903	−	0.126997i	$-0.0405340\pi$
$401$	15930.0	1.98381	0.991903	+	0.126997i	$0.0405340\pi$
$402$	−312.000	−0.0387093
$403$	1551.00	0.191714
$404$	−24.0000	−0.00295556
$405$	−3245.00	−0.398137
$406$	972.000	0.118817
$407$	−1792.00	−0.218246
$408$	160.000	0.0194147
$409$	−5891.00	−0.712203	−0.356102	−	0.934447i	$-0.615894\pi$
$409$	−5891.00	−0.712203	−0.356102	+	0.934447i	$0.615894\pi$
$410$	1570.00	0.189114
$411$	2836.00	0.340364
$412$	−640.000	−0.0765304
$413$	13392.0	1.59559
$414$	1196.00	0.141981
$415$	−2560.00	−0.302808
$416$	−1504.00	−0.177259
$417$	−1631.00	−0.191536
$418$	−2304.00	−0.269599
$419$	15282.0	1.78180	0.890900	−	0.454199i	$-0.150074\pi$
$419$	15282.0	1.78180	0.890900	+	0.454199i	$0.150074\pi$
$420$	360.000	0.0418243
$421$	−10934.0	−1.26577	−0.632887	−	0.774244i	$-0.718130\pi$
$421$	−10934.0	−1.26577	−0.632887	+	0.774244i	$0.718130\pi$
$422$	−6592.00	−0.760411
$423$	−1690.00	−0.194257
$424$	−112.000	−0.0128283
$425$	500.000	0.0570672
$426$	1398.00	0.158998
$427$	−9936.00	−1.12608
$428$	1520.00	0.171663
$429$	1504.00	0.169263
$430$	−180.000	−0.0201869
$431$	−2794.00	−0.312256	−0.156128	−	0.987737i	$-0.549901\pi$
$431$	−2794.00	−0.312256	−0.156128	+	0.987737i	$0.549901\pi$
$432$	−848.000	−0.0944431
$433$	−15062.0	−1.67167	−0.835835	−	0.548980i	$-0.815016\pi$
$433$	−15062.0	−1.67167	−0.835835	+	0.548980i	$0.815016\pi$
$434$	1188.00	0.131396
$435$	135.000	0.0148799
$436$	1000.00	0.109842
$437$	−828.000	−0.0906376
$438$	−1218.00	−0.132873
$439$	261.000	0.0283755	0.0141878	−	0.999899i	$-0.495484\pi$
$439$	261.000	0.0283755	0.0141878	+	0.999899i	$0.495484\pi$
$440$	1280.00	0.138685
$441$	494.000	0.0533420
$442$	−1880.00	−0.202313
$443$	−7083.00	−0.759647	−0.379823	−	0.925059i	$-0.624015\pi$
$443$	−7083.00	−0.759647	−0.379823	+	0.925059i	$0.624015\pi$
$444$	224.000	0.0239427
$445$	510.000	0.0543288
$446$	−5440.00	−0.577559
$447$	−1966.00	−0.208028
$448$	−1152.00	−0.121489
$449$	−10370.0	−1.08996	−0.544978	−	0.838450i	$-0.683462\pi$
$449$	−10370.0	−1.08996	−0.544978	+	0.838450i	$0.683462\pi$
$450$	−1300.00	−0.136184
$451$	5024.00	0.524547
$452$	−1560.00	−0.162337
$453$	35.0000	0.00363012
$454$	−8268.00	−0.854706
$455$	−4230.00	−0.435836
$456$	288.000	0.0295764
$457$	−10496.0	−1.07436	−0.537180	−	0.843468i	$-0.680510\pi$
$457$	−10496.0	−1.07436	−0.537180	+	0.843468i	$0.680510\pi$
$458$	−9020.00	−0.920255
$459$	−1060.00	−0.107792
$460$	460.000	0.0466252
$461$	18021.0	1.82065	0.910327	−	0.413889i	$-0.135830\pi$
$461$	18021.0	1.82065	0.910327	+	0.413889i	$0.135830\pi$
$462$	1152.00	0.116008
$463$	−17188.0	−1.72526	−0.862629	−	0.505838i	$-0.831183\pi$
$463$	−17188.0	−1.72526	−0.862629	+	0.505838i	$0.831183\pi$
$464$	−432.000	−0.0432222
$465$	165.000	0.0164553
$466$	−10006.0	−0.994676
$467$	−15246.0	−1.51071	−0.755354	−	0.655317i	$-0.772535\pi$
$467$	−15246.0	−1.51071	−0.755354	+	0.655317i	$0.772535\pi$
$468$	4888.00	0.482795
$469$	2808.00	0.276464
$470$	−650.000	−0.0637921
$471$	1702.00	0.166505
$472$	−5952.00	−0.580430
$473$	−576.000	−0.0559926
$474$	−1288.00	−0.124810
$475$	900.000	0.0869365
$476$	−1440.00	−0.138660
$477$	364.000	0.0349401
$478$	−12618.0	−1.20739
$479$	−8556.00	−0.816145	−0.408073	−	0.912949i	$-0.633799\pi$
$479$	−8556.00	−0.816145	−0.408073	+	0.912949i	$0.633799\pi$
$480$	−160.000	−0.0152145
$481$	−2632.00	−0.249499
$482$	6076.00	0.574179
$483$	414.000	0.0390014
$484$	−1228.00	−0.115327
$485$	−2890.00	−0.270573
$486$	4160.00	0.388275
$487$	−1805.00	−0.167951	−0.0839757	−	0.996468i	$-0.526762\pi$
$487$	−1805.00	−0.167951	−0.0839757	+	0.996468i	$0.526762\pi$
$488$	4416.00	0.409637
$489$	−2045.00	−0.189117
$490$	190.000	0.0175170
$491$	5245.00	0.482085	0.241042	−	0.970515i	$-0.422511\pi$
$491$	5245.00	0.482085	0.241042	+	0.970515i	$0.422511\pi$
$492$	−628.000	−0.0575456
$493$	−540.000	−0.0493314
$494$	−3384.00	−0.308205
$495$	−4160.00	−0.377734
$496$	−528.000	−0.0477982
$497$	−12582.0	−1.13557
$498$	1024.00	0.0921416
$499$	9027.00	0.809828	0.404914	−	0.914355i	$-0.367302\pi$
$499$	9027.00	0.809828	0.404914	+	0.914355i	$0.367302\pi$
$500$	−500.000	−0.0447214
$501$	1016.00	0.0906019
$502$	−2664.00	−0.236853
$503$	3522.00	0.312203	0.156102	−	0.987741i	$-0.450107\pi$
$503$	3522.00	0.312203	0.156102	+	0.987741i	$0.450107\pi$
$504$	3744.00	0.330895
$505$	30.0000	0.00264353
$506$	1472.00	0.129325
$507$	12.0000	0.00105116
$508$	−3076.00	−0.268652
$509$	3949.00	0.343883	0.171941	−	0.985107i	$-0.444996\pi$
$509$	3949.00	0.343883	0.171941	+	0.985107i	$0.444996\pi$
$510$	−200.000	−0.0173650
$511$	10962.0	0.948983
$512$	512.000	0.0441942
$513$	−1908.00	−0.164211
$514$	6602.00	0.566540
$515$	800.000	0.0684509
$516$	72.0000	0.00614268
$517$	−2080.00	−0.176941
$518$	−2016.00	−0.171000
$519$	598.000	0.0505767
$520$	1880.00	0.158545
$521$	3236.00	0.272115	0.136057	−	0.990701i	$-0.456557\pi$
$521$	3236.00	0.272115	0.136057	+	0.990701i	$0.456557\pi$
$522$	1404.00	0.117723
$523$	12394.0	1.03624	0.518118	−	0.855309i	$-0.326633\pi$
$523$	12394.0	1.03624	0.518118	+	0.855309i	$0.326633\pi$
$524$	−852.000	−0.0710301
$525$	−450.000	−0.0374088
$526$	4144.00	0.343511
$527$	−660.000	−0.0545542
$528$	−512.000	−0.0422006
$529$	529.000	0.0434783
$530$	140.000	0.0114740
$531$	19344.0	1.58090
$532$	−2592.00	−0.211236
$533$	7379.00	0.599662
$534$	−204.000	−0.0165317
$535$	−1900.00	−0.153540
$536$	−1248.00	−0.100570
$537$	−4607.00	−0.370217
$538$	11442.0	0.916914
$539$	608.000	0.0485870
$540$	1060.00	0.0844725
$541$	−7159.00	−0.568927	−0.284463	−	0.958687i	$-0.591815\pi$
$541$	−7159.00	−0.568927	−0.284463	+	0.958687i	$0.591815\pi$
$542$	−11800.0	−0.935154
$543$	−1212.00	−0.0957862
$544$	640.000	0.0504408
$545$	−1250.00	−0.0982461
$546$	1692.00	0.132621
$547$	−19761.0	−1.54464	−0.772321	−	0.635232i	$-0.780904\pi$
$547$	−19761.0	−1.54464	−0.772321	+	0.635232i	$0.780904\pi$
$548$	11344.0	0.884291
$549$	−14352.0	−1.11572
$550$	−1600.00	−0.124044
$551$	−972.000	−0.0751517
$552$	−184.000	−0.0141876
$553$	11592.0	0.891396
$554$	12742.0	0.977176
$555$	−280.000	−0.0214150
$556$	−6524.00	−0.497625
$557$	18010.0	1.37003	0.685016	−	0.728528i	$-0.259795\pi$
$557$	18010.0	1.37003	0.685016	+	0.728528i	$0.259795\pi$
$558$	1716.00	0.130187
$559$	−846.000	−0.0640107
$560$	1440.00	0.108663
$561$	−640.000	−0.0481655
$562$	6380.00	0.478868
$563$	−2648.00	−0.198224	−0.0991118	−	0.995076i	$-0.531600\pi$
$563$	−2648.00	−0.198224	−0.0991118	+	0.995076i	$0.531600\pi$
$564$	260.000	0.0194113
$565$	1950.00	0.145198
$566$	−8452.00	−0.627675
$567$	−11682.0	−0.865252
$568$	5592.00	0.413090
$569$	−1566.00	−0.115378	−0.0576890	−	0.998335i	$-0.518373\pi$
$569$	−1566.00	−0.115378	−0.0576890	+	0.998335i	$0.518373\pi$
$570$	−360.000	−0.0264539
$571$	2864.00	0.209903	0.104952	−	0.994477i	$-0.466531\pi$
$571$	2864.00	0.209903	0.104952	+	0.994477i	$0.466531\pi$
$572$	6016.00	0.439758
$573$	−1058.00	−0.0771354
$574$	5652.00	0.410993
$575$	−575.000	−0.0417029
$576$	−1664.00	−0.120370
$577$	−929.000	−0.0670273	−0.0335137	−	0.999438i	$-0.510670\pi$
$577$	−929.000	−0.0670273	−0.0335137	+	0.999438i	$0.510670\pi$
$578$	−9026.00	−0.649537
$579$	1047.00	0.0751500
$580$	540.000	0.0386591
$581$	−9216.00	−0.658079
$582$	1156.00	0.0823329
$583$	448.000	0.0318255
$584$	−4872.00	−0.345214
$585$	−6110.00	−0.431825
$586$	12096.0	0.852698
$587$	−19499.0	−1.37106	−0.685528	−	0.728046i	$-0.740429\pi$
$587$	−19499.0	−1.37106	−0.685528	+	0.728046i	$0.740429\pi$
$588$	−76.0000	−0.00533025
$589$	−1188.00	−0.0831081
$590$	7440.00	0.519152
$591$	251.000	0.0174700
$592$	896.000	0.0622050
$593$	6570.00	0.454971	0.227485	−	0.973782i	$-0.426950\pi$
$593$	6570.00	0.454971	0.227485	+	0.973782i	$0.426950\pi$
$594$	3392.00	0.234302
$595$	1800.00	0.124022
$596$	−7864.00	−0.540473
$597$	−3508.00	−0.240491
$598$	2162.00	0.147844
$599$	1880.00	0.128238	0.0641191	−	0.997942i	$-0.479576\pi$
$599$	1880.00	0.128238	0.0641191	+	0.997942i	$0.479576\pi$
$600$	200.000	0.0136083
$601$	3701.00	0.251193	0.125596	−	0.992081i	$-0.459916\pi$
$601$	3701.00	0.251193	0.125596	+	0.992081i	$0.459916\pi$
$602$	−648.000	−0.0438713
$603$	4056.00	0.273919
$604$	140.000	0.00943132
$605$	1535.00	0.103151
$606$	−12.0000	−0.000804400 0
$607$	−3080.00	−0.205953	−0.102976	−	0.994684i	$-0.532837\pi$
$607$	−3080.00	−0.205953	−0.102976	+	0.994684i	$0.532837\pi$
$608$	1152.00	0.0768417
$609$	486.000	0.0323378
$610$	−5520.00	−0.366391
$611$	−3055.00	−0.202278
$612$	−2080.00	−0.137384
$613$	24004.0	1.58159	0.790793	−	0.612083i	$-0.209668\pi$
$613$	24004.0	1.58159	0.790793	+	0.612083i	$0.209668\pi$
$614$	17256.0	1.13419
$615$	785.000	0.0514703
$616$	4608.00	0.301399
$617$	780.000	0.0508940	0.0254470	−	0.999676i	$-0.491899\pi$
$617$	780.000	0.0508940	0.0254470	+	0.999676i	$0.491899\pi$
$618$	−320.000	−0.0208289
$619$	21892.0	1.42151	0.710754	−	0.703440i	$-0.248354\pi$
$619$	21892.0	1.42151	0.710754	+	0.703440i	$0.248354\pi$
$620$	660.000	0.0427520
$621$	1219.00	0.0787710
$622$	16494.0	1.06326
$623$	1836.00	0.118070
$624$	−752.000	−0.0482437
$625$	625.000	0.0400000
$626$	5240.00	0.334557
$627$	−1152.00	−0.0733755
$628$	6808.00	0.432594
$629$	1120.00	0.0709973
$630$	−4680.00	−0.295961
$631$	8050.00	0.507869	0.253935	−	0.967221i	$-0.418275\pi$
$631$	8050.00	0.507869	0.253935	+	0.967221i	$0.418275\pi$
$632$	−5152.00	−0.324265
$633$	−3296.00	−0.206958
$634$	19812.0	1.24106
$635$	3845.00	0.240290
$636$	−56.0000	−0.00349142
$637$	893.000	0.0555447
$638$	1728.00	0.107229
$639$	−18174.0	−1.12512
$640$	−640.000	−0.0395285
$641$	−25890.0	−1.59531	−0.797655	−	0.603114i	$-0.793926\pi$
$641$	−25890.0	−1.59531	−0.797655	+	0.603114i	$0.793926\pi$
$642$	760.000	0.0467209
$643$	4774.00	0.292797	0.146398	−	0.989226i	$-0.453232\pi$
$643$	4774.00	0.292797	0.146398	+	0.989226i	$0.453232\pi$
$644$	1656.00	0.101328
$645$	−90.0000	−0.00549418
$646$	1440.00	0.0877029
$647$	3349.00	0.203497	0.101749	−	0.994810i	$-0.467556\pi$
$647$	3349.00	0.203497	0.101749	+	0.994810i	$0.467556\pi$
$648$	5192.00	0.314755
$649$	23808.0	1.43998
$650$	−2350.00	−0.141807
$651$	594.000	0.0357614
$652$	−8180.00	−0.491340
$653$	24813.0	1.48699	0.743497	−	0.668739i	$-0.233166\pi$
$653$	24813.0	1.48699	0.743497	+	0.668739i	$0.233166\pi$
$654$	500.000	0.0298953
$655$	1065.00	0.0635313
$656$	−2512.00	−0.149508
$657$	15834.0	0.940248
$658$	−2340.00	−0.138636
$659$	18180.0	1.07465	0.537323	−	0.843376i	$-0.319435\pi$
$659$	18180.0	1.07465	0.537323	+	0.843376i	$0.319435\pi$
$660$	640.000	0.0377454
$661$	−29250.0	−1.72117	−0.860585	−	0.509307i	$-0.829902\pi$
$661$	−29250.0	−1.72117	−0.860585	+	0.509307i	$0.829902\pi$
$662$	−16230.0	−0.952865
$663$	−940.000	−0.0550627
$664$	4096.00	0.239391
$665$	3240.00	0.188935
$666$	−2912.00	−0.169426
$667$	621.000	0.0360498
$668$	4064.00	0.235391
$669$	−2720.00	−0.157192
$670$	1560.00	0.0899523
$671$	−17664.0	−1.01626
$672$	−576.000	−0.0330650
$673$	−23027.0	−1.31891	−0.659454	−	0.751745i	$-0.729213\pi$
$673$	−23027.0	−1.31891	−0.659454	+	0.751745i	$0.729213\pi$
$674$	−15172.0	−0.867068
$675$	−1325.00	−0.0755545
$676$	48.0000	0.00273100
$677$	20106.0	1.14141	0.570706	−	0.821154i	$-0.306669\pi$
$677$	20106.0	1.14141	0.570706	+	0.821154i	$0.306669\pi$
$678$	−780.000	−0.0441825
$679$	−10404.0	−0.588025
$680$	−800.000	−0.0451156
$681$	−4134.00	−0.232621
$682$	2112.00	0.118582
$683$	−18745.0	−1.05016	−0.525079	−	0.851054i	$-0.675964\pi$
$683$	−18745.0	−1.05016	−0.525079	+	0.851054i	$0.675964\pi$
$684$	−3744.00	−0.209292
$685$	−14180.0	−0.790934
$686$	13032.0	0.725312
$687$	−4510.00	−0.250462
$688$	288.000	0.0159592
$689$	658.000	0.0363829
$690$	230.000	0.0126898
$691$	24424.0	1.34462	0.672310	−	0.740270i	$-0.265302\pi$
$691$	24424.0	1.34462	0.672310	+	0.740270i	$0.265302\pi$
$692$	2392.00	0.131402
$693$	−14976.0	−0.820911
$694$	2712.00	0.148337
$695$	8155.00	0.445089
$696$	−216.000	−0.0117636
$697$	−3140.00	−0.170640
$698$	13298.0	0.721113
$699$	−5003.00	−0.270717
$700$	−1800.00	−0.0971909
$701$	−27278.0	−1.46972	−0.734862	−	0.678217i	$-0.762753\pi$
$701$	−27278.0	−1.46972	−0.734862	+	0.678217i	$0.762753\pi$
$702$	4982.00	0.267854
$703$	2016.00	0.108158
$704$	−2048.00	−0.109640
$705$	−325.000	−0.0173620
$706$	21382.0	1.13983
$707$	108.000	0.00574506
$708$	−2976.00	−0.157973
$709$	12214.0	0.646977	0.323488	−	0.946232i	$-0.395144\pi$
$709$	12214.0	0.646977	0.323488	+	0.946232i	$0.395144\pi$
$710$	−6990.00	−0.369479
$711$	16744.0	0.883191
$712$	−816.000	−0.0429507
$713$	759.000	0.0398664
$714$	−720.000	−0.0377385
$715$	−7520.00	−0.393332
$716$	−18428.0	−0.961853
$717$	−6309.00	−0.328611
$718$	−12840.0	−0.667388
$719$	12932.0	0.670768	0.335384	−	0.942082i	$-0.391134\pi$
$719$	12932.0	0.670768	0.335384	+	0.942082i	$0.391134\pi$
$720$	2080.00	0.107663
$721$	2880.00	0.148761
$722$	−11126.0	−0.573500
$723$	3038.00	0.156272
$724$	−4848.00	−0.248860
$725$	−675.000	−0.0345778
$726$	−614.000	−0.0313880
$727$	10046.0	0.512497	0.256249	−	0.966611i	$-0.417513\pi$
$727$	10046.0	0.512497	0.256249	+	0.966611i	$0.417513\pi$
$728$	6768.00	0.344559
$729$	−15443.0	−0.784586
$730$	6090.00	0.308769
$731$	360.000	0.0182149
$732$	2208.00	0.111489
$733$	−5924.00	−0.298510	−0.149255	−	0.988799i	$-0.547688\pi$
$733$	−5924.00	−0.298510	−0.149255	+	0.988799i	$0.547688\pi$
$734$	−1048.00	−0.0527008
$735$	95.0000	0.00476752
$736$	−736.000	−0.0368605
$737$	4992.00	0.249502
$738$	8164.00	0.407210
$739$	829.000	0.0412656	0.0206328	−	0.999787i	$-0.493432\pi$
$739$	829.000	0.0412656	0.0206328	+	0.999787i	$0.493432\pi$
$740$	−1120.00	−0.0556379
$741$	−1692.00	−0.0838828
$742$	504.000	0.0249359
$743$	7072.00	0.349188	0.174594	−	0.984641i	$-0.444139\pi$
$743$	7072.00	0.349188	0.174594	+	0.984641i	$0.444139\pi$
$744$	−264.000	−0.0130090
$745$	9830.00	0.483414
$746$	11132.0	0.546342
$747$	−13312.0	−0.652022
$748$	−2560.00	−0.125138
$749$	−6840.00	−0.333682
$750$	−250.000	−0.0121716
$751$	16234.0	0.788798	0.394399	−	0.918939i	$-0.370953\pi$
$751$	16234.0	0.788798	0.394399	+	0.918939i	$0.370953\pi$
$752$	1040.00	0.0504320
$753$	−1332.00	−0.0644632
$754$	2538.00	0.122584
$755$	−175.000	−0.00843563
$756$	3816.00	0.183580
$757$	9128.00	0.438260	0.219130	−	0.975696i	$-0.429678\pi$
$757$	9128.00	0.438260	0.219130	+	0.975696i	$0.429678\pi$
$758$	4480.00	0.214671
$759$	736.000	0.0351978
$760$	−1440.00	−0.0687293
$761$	165.000	0.00785972	0.00392986	−	0.999992i	$-0.498749\pi$
$761$	165.000	0.00785972	0.00392986	+	0.999992i	$0.498749\pi$
$762$	−1538.00	−0.0731179
$763$	−4500.00	−0.213514
$764$	−4232.00	−0.200404
$765$	2600.00	0.122880
$766$	17556.0	0.828099
$767$	34968.0	1.64618
$768$	256.000	0.0120281
$769$	−20834.0	−0.976974	−0.488487	−	0.872571i	$-0.662451\pi$
$769$	−20834.0	−0.976974	−0.488487	+	0.872571i	$0.662451\pi$
$770$	−5760.00	−0.269579
$771$	3301.00	0.154193
$772$	4188.00	0.195245
$773$	−31782.0	−1.47881	−0.739404	−	0.673262i	$-0.764893\pi$
$773$	−31782.0	−1.47881	−0.739404	+	0.673262i	$0.764893\pi$
$774$	−936.000	−0.0434675
$775$	−825.000	−0.0382385
$776$	4624.00	0.213907
$777$	−1008.00	−0.0465403
$778$	8112.00	0.373817
$779$	−5652.00	−0.259954
$780$	940.000	0.0431505
$781$	−22368.0	−1.02483
$782$	−920.000	−0.0420705
$783$	1431.00	0.0653126
$784$	−304.000	−0.0138484
$785$	−8510.00	−0.386923
$786$	−426.000	−0.0193320
$787$	33104.0	1.49940	0.749701	−	0.661776i	$-0.230197\pi$
$787$	33104.0	1.49940	0.749701	+	0.661776i	$0.230197\pi$
$788$	1004.00	0.0453883
$789$	2072.00	0.0934920
$790$	6440.00	0.290032
$791$	7020.00	0.315553
$792$	6656.00	0.298625
$793$	−25944.0	−1.16179
$794$	−18302.0	−0.818027
$795$	70.0000	0.00312282
$796$	−14032.0	−0.624813
$797$	4736.00	0.210486	0.105243	−	0.994447i	$-0.466438\pi$
$797$	4736.00	0.210486	0.105243	+	0.994447i	$0.466438\pi$
$798$	−1296.00	−0.0574911
$799$	1300.00	0.0575603
$800$	800.000	0.0353553
$801$	2652.00	0.116984
$802$	31860.0	1.40276
$803$	19488.0	0.856434
$804$	−624.000	−0.0273716
$805$	−2070.00	−0.0906309
$806$	3102.00	0.135562
$807$	5721.00	0.249552
$808$	−48.0000	−0.00208989
$809$	−7470.00	−0.324637	−0.162318	−	0.986738i	$-0.551897\pi$
$809$	−7470.00	−0.324637	−0.162318	+	0.986738i	$0.551897\pi$
$810$	−6490.00	−0.281525
$811$	19919.0	0.862455	0.431227	−	0.902243i	$-0.358081\pi$
$811$	19919.0	0.862455	0.431227	+	0.902243i	$0.358081\pi$
$812$	1944.00	0.0840160
$813$	−5900.00	−0.254517
$814$	−3584.00	−0.154323
$815$	10225.0	0.439468
$816$	320.000	0.0137282
$817$	648.000	0.0277487
$818$	−11782.0	−0.503604
$819$	−21996.0	−0.938465
$820$	3140.00	0.133724
$821$	−22694.0	−0.964709	−0.482354	−	0.875976i	$-0.660218\pi$
$821$	−22694.0	−0.964709	−0.482354	+	0.875976i	$0.660218\pi$
$822$	5672.00	0.240674
$823$	−31907.0	−1.35141	−0.675704	−	0.737173i	$-0.736160\pi$
$823$	−31907.0	−1.35141	−0.675704	+	0.737173i	$0.736160\pi$
$824$	−1280.00	−0.0541152
$825$	−800.000	−0.0337605
$826$	26784.0	1.12825
$827$	−15236.0	−0.640638	−0.320319	−	0.947310i	$-0.603790\pi$
$827$	−15236.0	−0.640638	−0.320319	+	0.947310i	$0.603790\pi$
$828$	2392.00	0.100396
$829$	27286.0	1.14316	0.571581	−	0.820545i	$-0.306330\pi$
$829$	27286.0	1.14316	0.571581	+	0.820545i	$0.306330\pi$
$830$	−5120.00	−0.214118
$831$	6371.00	0.265954
$832$	−3008.00	−0.125341
$833$	−380.000	−0.0158058
$834$	−3262.00	−0.135436
$835$	−5080.00	−0.210540
$836$	−4608.00	−0.190635
$837$	1749.00	0.0722273
$838$	30564.0	1.25992
$839$	23054.0	0.948644	0.474322	−	0.880351i	$-0.342693\pi$
$839$	23054.0	0.948644	0.474322	+	0.880351i	$0.342693\pi$
$840$	720.000	0.0295742
$841$	−23660.0	−0.970109
$842$	−21868.0	−0.895037
$843$	3190.00	0.130331
$844$	−13184.0	−0.537692
$845$	−60.0000	−0.00244268
$846$	−3380.00	−0.137360
$847$	5526.00	0.224174
$848$	−224.000	−0.00907098
$849$	−4226.00	−0.170832
$850$	1000.00	0.0403526
$851$	−1288.00	−0.0518826
$852$	2796.00	0.112429
$853$	−34506.0	−1.38507	−0.692534	−	0.721385i	$-0.743506\pi$
$853$	−34506.0	−1.38507	−0.692534	+	0.721385i	$0.743506\pi$
$854$	−19872.0	−0.796260
$855$	4680.00	0.187196
$856$	3040.00	0.121384
$857$	−22263.0	−0.887386	−0.443693	−	0.896179i	$-0.646332\pi$
$857$	−22263.0	−0.887386	−0.443693	+	0.896179i	$0.646332\pi$
$858$	3008.00	0.119687
$859$	12851.0	0.510443	0.255221	−	0.966883i	$-0.417852\pi$
$859$	12851.0	0.510443	0.255221	+	0.966883i	$0.417852\pi$
$860$	−360.000	−0.0142743
$861$	2826.00	0.111858
$862$	−5588.00	−0.220798
$863$	15723.0	0.620182	0.310091	−	0.950707i	$-0.399640\pi$
$863$	15723.0	0.620182	0.310091	+	0.950707i	$0.399640\pi$
$864$	−1696.00	−0.0667814
$865$	−2990.00	−0.117530
$866$	−30124.0	−1.18205
$867$	−4513.00	−0.176781
$868$	2376.00	0.0929109
$869$	20608.0	0.804463
$870$	270.000	0.0105217
$871$	7332.00	0.285230
$872$	2000.00	0.0776704
$873$	−15028.0	−0.582613
$874$	−1656.00	−0.0640904
$875$	2250.00	0.0869302
$876$	−2436.00	−0.0939553
$877$	−886.000	−0.0341141	−0.0170571	−	0.999855i	$-0.505430\pi$
$877$	−886.000	−0.0341141	−0.0170571	+	0.999855i	$0.505430\pi$
$878$	522.000	0.0200645
$879$	6048.00	0.232075
$880$	2560.00	0.0980654
$881$	−37120.0	−1.41953	−0.709764	−	0.704439i	$-0.751199\pi$
$881$	−37120.0	−1.41953	−0.709764	+	0.704439i	$0.751199\pi$
$882$	988.000	0.0377185
$883$	−7524.00	−0.286753	−0.143376	−	0.989668i	$-0.545796\pi$
$883$	−7524.00	−0.286753	−0.143376	+	0.989668i	$0.545796\pi$
$884$	−3760.00	−0.143057
$885$	3720.00	0.141295
$886$	−14166.0	−0.537151
$887$	9221.00	0.349054	0.174527	−	0.984652i	$-0.444160\pi$
$887$	9221.00	0.349054	0.174527	+	0.984652i	$0.444160\pi$
$888$	448.000	0.0169301
$889$	13842.0	0.522211
$890$	1020.00	0.0384163
$891$	−20768.0	−0.780869
$892$	−10880.0	−0.408396
$893$	2340.00	0.0876877
$894$	−3932.00	−0.147098
$895$	23035.0	0.860307
$896$	−2304.00	−0.0859054
$897$	1081.00	0.0402381
$898$	−20740.0	−0.770716
$899$	891.000	0.0330551
$900$	−2600.00	−0.0962963
$901$	−280.000	−0.0103531
$902$	10048.0	0.370911
$903$	−324.000	−0.0119402
$904$	−3120.00	−0.114789
$905$	6060.00	0.222587
$906$	70.0000	0.00256688
$907$	29116.0	1.06591	0.532955	−	0.846143i	$-0.321081\pi$
$907$	29116.0	1.06591	0.532955	+	0.846143i	$0.321081\pi$
$908$	−16536.0	−0.604368
$909$	156.000	0.00569218
$910$	−8460.00	−0.308183
$911$	11440.0	0.416053	0.208026	−	0.978123i	$-0.433296\pi$
$911$	11440.0	0.416053	0.208026	+	0.978123i	$0.433296\pi$
$912$	576.000	0.0209137
$913$	−16384.0	−0.593901
$914$	−20992.0	−0.759687
$915$	−2760.00	−0.0997189
$916$	−18040.0	−0.650719
$917$	3834.00	0.138070
$918$	−2120.00	−0.0762205
$919$	2958.00	0.106176	0.0530878	−	0.998590i	$-0.483094\pi$
$919$	2958.00	0.106176	0.0530878	+	0.998590i	$0.483094\pi$
$920$	920.000	0.0329690
$921$	8628.00	0.308689
$922$	36042.0	1.28740
$923$	−32853.0	−1.17158
$924$	2304.00	0.0820303
$925$	1400.00	0.0497640
$926$	−34376.0	−1.21994
$927$	4160.00	0.147392
$928$	−864.000	−0.0305627
$929$	20907.0	0.738360	0.369180	−	0.929358i	$-0.379639\pi$
$929$	20907.0	0.738360	0.369180	+	0.929358i	$0.379639\pi$
$930$	330.000	0.0116356
$931$	−684.000	−0.0240786
$932$	−20012.0	−0.703342
$933$	8247.00	0.289383
$934$	−30492.0	−1.06823
$935$	3200.00	0.111926
$936$	9776.00	0.341387
$937$	9748.00	0.339865	0.169932	−	0.985456i	$-0.445645\pi$
$937$	9748.00	0.339865	0.169932	+	0.985456i	$0.445645\pi$
$938$	5616.00	0.195489
$939$	2620.00	0.0910548
$940$	−1300.00	−0.0451078
$941$	19624.0	0.679834	0.339917	−	0.940455i	$-0.389601\pi$
$941$	19624.0	0.679834	0.339917	+	0.940455i	$0.389601\pi$
$942$	3404.00	0.117737
$943$	3611.00	0.124698
$944$	−11904.0	−0.410426
$945$	−4770.00	−0.164199
$946$	−1152.00	−0.0395928
$947$	−41859.0	−1.43636	−0.718181	−	0.695856i	$-0.755025\pi$
$947$	−41859.0	−1.43636	−0.718181	+	0.695856i	$0.755025\pi$
$948$	−2576.00	−0.0882538
$949$	28623.0	0.979075
$950$	1800.00	0.0614734
$951$	9906.00	0.337775
$952$	−2880.00	−0.0980476
$953$	29226.0	0.993413	0.496707	−	0.867918i	$-0.334542\pi$
$953$	29226.0	0.993413	0.496707	+	0.867918i	$0.334542\pi$
$954$	728.000	0.0247064
$955$	5290.00	0.179246
$956$	−25236.0	−0.853756
$957$	864.000	0.0291841
$958$	−17112.0	−0.577102
$959$	−51048.0	−1.71890
$960$	−320.000	−0.0107583
$961$	−28702.0	−0.963445
$962$	−5264.00	−0.176422
$963$	−9880.00	−0.330611
$964$	12152.0	0.406006
$965$	−5235.00	−0.174633
$966$	828.000	0.0275781
$967$	−29849.0	−0.992636	−0.496318	−	0.868141i	$-0.665315\pi$
$967$	−29849.0	−0.992636	−0.496318	+	0.868141i	$0.665315\pi$
$968$	−2456.00	−0.0815484
$969$	720.000	0.0238697
$970$	−5780.00	−0.191324
$971$	−9390.00	−0.310339	−0.155170	−	0.987888i	$-0.549592\pi$
$971$	−9390.00	−0.310339	−0.155170	+	0.987888i	$0.549592\pi$
$972$	8320.00	0.274552
$973$	29358.0	0.967291
$974$	−3610.00	−0.118760
$975$	−1175.00	−0.0385950
$976$	8832.00	0.289657
$977$	33536.0	1.09817	0.549085	−	0.835767i	$-0.314976\pi$
$977$	33536.0	1.09817	0.549085	+	0.835767i	$0.314976\pi$
$978$	−4090.00	−0.133726
$979$	3264.00	0.106556
$980$	380.000	0.0123864
$981$	−6500.00	−0.211548
$982$	10490.0	0.340885
$983$	28994.0	0.940758	0.470379	−	0.882465i	$-0.344117\pi$
$983$	28994.0	0.940758	0.470379	+	0.882465i	$0.344117\pi$
$984$	−1256.00	−0.0406909
$985$	−1255.00	−0.0405966
$986$	−1080.00	−0.0348826
$987$	−1170.00	−0.0377320
$988$	−6768.00	−0.217934
$989$	−414.000	−0.0133109
$990$	−8320.00	−0.267098
$991$	11272.0	0.361319	0.180659	−	0.983546i	$-0.442177\pi$
$991$	11272.0	0.361319	0.180659	+	0.983546i	$0.442177\pi$
$992$	−1056.00	−0.0337984
$993$	−8115.00	−0.259337
$994$	−25164.0	−0.802971
$995$	17540.0	0.558850
$996$	2048.00	0.0651540
$997$	61186.0	1.94361	0.971805	−	0.235784i	$-0.0757658\pi$
$997$	61186.0	1.94361	0.971805	+	0.235784i	$0.0757658\pi$
$998$	18054.0	0.572635
$999$	−2968.00	−0.0939974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.e.1.1	✓	1
3.2	odd	2		2070.4.a.e.1.1		1
4.3	odd	2		1840.4.a.d.1.1		1
5.2	odd	4		1150.4.b.f.599.2		2
5.3	odd	4		1150.4.b.f.599.1		2
5.4	even	2		1150.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.e.1.1	✓	1	1.1	even	1	trivial
1150.4.a.b.1.1		1	5.4	even	2
1150.4.b.f.599.1		2	5.3	odd	4
1150.4.b.f.599.2		2	5.2	odd	4
1840.4.a.d.1.1		1	4.3	odd	2
2070.4.a.e.1.1		1	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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