LMFDB - Embedded newform 230.4.a.a.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)

$f(q)$

$=$

$q-2.00000 q^{2} -5.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +10.0000 q^{6} +12.0000 q^{7} -8.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -5.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +10.0000 q^{6} +12.0000 q^{7} -8.00000 q^{8} -2.00000 q^{9} +10.0000 q^{10} +22.0000 q^{11} -20.0000 q^{12} +19.0000 q^{13} -24.0000 q^{14} +25.0000 q^{15} +16.0000 q^{16} +96.0000 q^{17} +4.00000 q^{18} -98.0000 q^{19} -20.0000 q^{20} -60.0000 q^{21} -44.0000 q^{22} +23.0000 q^{23} +40.0000 q^{24} +25.0000 q^{25} -38.0000 q^{26} +145.000 q^{27} +48.0000 q^{28} -227.000 q^{29} -50.0000 q^{30} -285.000 q^{31} -32.0000 q^{32} -110.000 q^{33} -192.000 q^{34} -60.0000 q^{35} -8.00000 q^{36} -398.000 q^{37} +196.000 q^{38} -95.0000 q^{39} +40.0000 q^{40} +271.000 q^{41} +120.000 q^{42} -100.000 q^{43} +88.0000 q^{44} +10.0000 q^{45} -46.0000 q^{46} -285.000 q^{47} -80.0000 q^{48} -199.000 q^{49} -50.0000 q^{50} -480.000 q^{51} +76.0000 q^{52} +18.0000 q^{53} -290.000 q^{54} -110.000 q^{55} -96.0000 q^{56} +490.000 q^{57} +454.000 q^{58} -352.000 q^{59} +100.000 q^{60} -478.000 q^{61} +570.000 q^{62} -24.0000 q^{63} +64.0000 q^{64} -95.0000 q^{65} +220.000 q^{66} +330.000 q^{67} +384.000 q^{68} -115.000 q^{69} +120.000 q^{70} +835.000 q^{71} +16.0000 q^{72} -1127.00 q^{73} +796.000 q^{74} -125.000 q^{75} -392.000 q^{76} +264.000 q^{77} +190.000 q^{78} +322.000 q^{79} -80.0000 q^{80} -671.000 q^{81} -542.000 q^{82} +572.000 q^{83} -240.000 q^{84} -480.000 q^{85} +200.000 q^{86} +1135.00 q^{87} -176.000 q^{88} -504.000 q^{89} -20.0000 q^{90} +228.000 q^{91} +92.0000 q^{92} +1425.00 q^{93} +570.000 q^{94} +490.000 q^{95} +160.000 q^{96} +1712.00 q^{97} +398.000 q^{98} -44.0000 q^{99} +O(q^{100})\)

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
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	10.0000	0.680414
$7$	12.0000	0.647939	0.323970	−	0.946068i	$-0.394982\pi$
$7$	12.0000	0.647939	0.323970	+	0.946068i	$0.394982\pi$
$8$	−8.00000	−0.353553
$9$	−2.00000	−0.0740741
$10$	10.0000	0.316228
$11$	22.0000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	22.0000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−20.0000	−0.481125
$13$	19.0000	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$13$	19.0000	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$14$	−24.0000	−0.458162
$15$	25.0000	0.430331
$16$	16.0000	0.250000
$17$	96.0000	1.36961	0.684806	−	0.728725i	$-0.259887\pi$
$17$	96.0000	1.36961	0.684806	+	0.728725i	$0.259887\pi$
$18$	4.00000	0.0523783
$19$	−98.0000	−1.18330	−0.591651	−	0.806194i	$-0.701524\pi$
$19$	−98.0000	−1.18330	−0.591651	+	0.806194i	$0.701524\pi$
$20$	−20.0000	−0.223607
$21$	−60.0000	−0.623480
$22$	−44.0000	−0.426401
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	40.0000	0.340207
$25$	25.0000	0.200000
$26$	−38.0000	−0.286631
$27$	145.000	1.03353
$28$	48.0000	0.323970
$29$	−227.000	−1.45355	−0.726773	−	0.686878i	$-0.758981\pi$
$29$	−227.000	−1.45355	−0.726773	+	0.686878i	$0.758981\pi$
$30$	−50.0000	−0.304290
$31$	−285.000	−1.65121	−0.825605	−	0.564248i	$-0.809166\pi$
$31$	−285.000	−1.65121	−0.825605	+	0.564248i	$0.809166\pi$
$32$	−32.0000	−0.176777
$33$	−110.000	−0.580259
$34$	−192.000	−0.968463
$35$	−60.0000	−0.289767
$36$	−8.00000	−0.0370370
$37$	−398.000	−1.76840	−0.884200	−	0.467109i	$-0.845296\pi$
$37$	−398.000	−1.76840	−0.884200	+	0.467109i	$0.845296\pi$
$38$	196.000	0.836721
$39$	−95.0000	−0.390056
$40$	40.0000	0.158114
$41$	271.000	1.03227	0.516135	−	0.856507i	$-0.327370\pi$
$41$	271.000	1.03227	0.516135	+	0.856507i	$0.327370\pi$
$42$	120.000	0.440867
$43$	−100.000	−0.354648	−0.177324	−	0.984153i	$-0.556744\pi$
$43$	−100.000	−0.354648	−0.177324	+	0.984153i	$0.556744\pi$
$44$	88.0000	0.301511
$45$	10.0000	0.0331269
$46$	−46.0000	−0.147442
$47$	−285.000	−0.884500	−0.442250	−	0.896892i	$-0.645820\pi$
$47$	−285.000	−0.884500	−0.442250	+	0.896892i	$0.645820\pi$
$48$	−80.0000	−0.240563
$49$	−199.000	−0.580175
$50$	−50.0000	−0.141421
$51$	−480.000	−1.31791
$52$	76.0000	0.202679
$53$	18.0000	0.0466508	0.0233254	−	0.999728i	$-0.492575\pi$
$53$	18.0000	0.0466508	0.0233254	+	0.999728i	$0.492575\pi$
$54$	−290.000	−0.730815
$55$	−110.000	−0.269680
$56$	−96.0000	−0.229081
$57$	490.000	1.13863
$58$	454.000	1.02781
$59$	−352.000	−0.776720	−0.388360	−	0.921508i	$-0.626958\pi$
$59$	−352.000	−0.776720	−0.388360	+	0.921508i	$0.626958\pi$
$60$	100.000	0.215166
$61$	−478.000	−1.00331	−0.501653	−	0.865069i	$-0.667274\pi$
$61$	−478.000	−1.00331	−0.501653	+	0.865069i	$0.667274\pi$
$62$	570.000	1.16758
$63$	−24.0000	−0.0479955
$64$	64.0000	0.125000
$65$	−95.0000	−0.181282
$66$	220.000	0.410305
$67$	330.000	0.601730	0.300865	−	0.953667i	$-0.402725\pi$
$67$	330.000	0.601730	0.300865	+	0.953667i	$0.402725\pi$
$68$	384.000	0.684806
$69$	−115.000	−0.200643
$70$	120.000	0.204896
$71$	835.000	1.39572	0.697861	−	0.716233i	$-0.254135\pi$
$71$	835.000	1.39572	0.697861	+	0.716233i	$0.254135\pi$
$72$	16.0000	0.0261891
$73$	−1127.00	−1.80692	−0.903461	−	0.428669i	$-0.858983\pi$
$73$	−1127.00	−1.80692	−0.903461	+	0.428669i	$0.858983\pi$
$74$	796.000	1.25045
$75$	−125.000	−0.192450
$76$	−392.000	−0.591651
$77$	264.000	0.390722
$78$	190.000	0.275811
$79$	322.000	0.458580	0.229290	−	0.973358i	$-0.426360\pi$
$79$	322.000	0.458580	0.229290	+	0.973358i	$0.426360\pi$
$80$	−80.0000	−0.111803
$81$	−671.000	−0.920439
$82$	−542.000	−0.729925
$83$	572.000	0.756448	0.378224	−	0.925714i	$-0.376535\pi$
$83$	572.000	0.756448	0.378224	+	0.925714i	$0.376535\pi$
$84$	−240.000	−0.311740
$85$	−480.000	−0.612510
$86$	200.000	0.250774
$87$	1135.00	1.39868
$88$	−176.000	−0.213201
$89$	−504.000	−0.600268	−0.300134	−	0.953897i	$-0.597031\pi$
$89$	−504.000	−0.600268	−0.300134	+	0.953897i	$0.597031\pi$
$90$	−20.0000	−0.0234243
$91$	228.000	0.262647
$92$	92.0000	0.104257
$93$	1425.00	1.58888
$94$	570.000	0.625436
$95$	490.000	0.529189
$96$	160.000	0.170103
$97$	1712.00	1.79203	0.896017	−	0.444020i	$-0.146448\pi$
$97$	1712.00	1.79203	0.896017	+	0.444020i	$0.146448\pi$
$98$	398.000	0.410246
$99$	−44.0000	−0.0446683
$100$	100.000	0.100000
$101$	−1710.00	−1.68467	−0.842333	−	0.538957i	$-0.818819\pi$
$101$	−1710.00	−1.68467	−0.842333	+	0.538957i	$0.818819\pi$
$102$	960.000	0.931904
$103$	36.0000	0.0344387	0.0172193	−	0.999852i	$-0.494519\pi$
$103$	36.0000	0.0344387	0.0172193	+	0.999852i	$0.494519\pi$
$104$	−152.000	−0.143316
$105$	300.000	0.278829
$106$	−36.0000	−0.0329871
$107$	690.000	0.623410	0.311705	−	0.950179i	$-0.399100\pi$
$107$	690.000	0.623410	0.311705	+	0.950179i	$0.399100\pi$
$108$	580.000	0.516764
$109$	380.000	0.333921	0.166961	−	0.985964i	$-0.446605\pi$
$109$	380.000	0.333921	0.166961	+	0.985964i	$0.446605\pi$
$110$	220.000	0.190693
$111$	1990.00	1.70164
$112$	192.000	0.161985
$113$	−2172.00	−1.80818	−0.904091	−	0.427340i	$-0.859451\pi$
$113$	−2172.00	−1.80818	−0.904091	+	0.427340i	$0.859451\pi$
$114$	−980.000	−0.805135
$115$	−115.000	−0.0932505
$116$	−908.000	−0.726773
$117$	−38.0000	−0.0300265
$118$	704.000	0.549224
$119$	1152.00	0.887426
$120$	−200.000	−0.152145
$121$	−847.000	−0.636364
$122$	956.000	0.709444
$123$	−1355.00	−0.993303
$124$	−1140.00	−0.825605
$125$	−125.000	−0.0894427
$126$	48.0000	0.0339379
$127$	−43.0000	−0.0300444	−0.0150222	−	0.999887i	$-0.504782\pi$
$127$	−43.0000	−0.0300444	−0.0150222	+	0.999887i	$0.504782\pi$
$128$	−128.000	−0.0883883
$129$	500.000	0.341260
$130$	190.000	0.128185
$131$	1187.00	0.791669	0.395835	−	0.918322i	$-0.370455\pi$
$131$	1187.00	0.791669	0.395835	+	0.918322i	$0.370455\pi$
$132$	−440.000	−0.290129
$133$	−1176.00	−0.766708
$134$	−660.000	−0.425487
$135$	−725.000	−0.462208
$136$	−768.000	−0.484231
$137$	212.000	0.132207	0.0661036	−	0.997813i	$-0.478943\pi$
$137$	212.000	0.132207	0.0661036	+	0.997813i	$0.478943\pi$
$138$	230.000	0.141876
$139$	−1091.00	−0.665737	−0.332868	−	0.942973i	$-0.608016\pi$
$139$	−1091.00	−0.665737	−0.332868	+	0.942973i	$0.608016\pi$
$140$	−240.000	−0.144884
$141$	1425.00	0.851111
$142$	−1670.00	−0.986925
$143$	418.000	0.244440
$144$	−32.0000	−0.0185185
$145$	1135.00	0.650046
$146$	2254.00	1.27769
$147$	995.000	0.558274
$148$	−1592.00	−0.884200
$149$	−1186.00	−0.652087	−0.326043	−	0.945355i	$-0.605716\pi$
$149$	−1186.00	−0.652087	−0.326043	+	0.945355i	$0.605716\pi$
$150$	250.000	0.136083
$151$	587.000	0.316354	0.158177	−	0.987411i	$-0.449438\pi$
$151$	587.000	0.316354	0.158177	+	0.987411i	$0.449438\pi$
$152$	784.000	0.418361
$153$	−192.000	−0.101453
$154$	−528.000	−0.276282
$155$	1425.00	0.738444
$156$	−380.000	−0.195028
$157$	644.000	0.327368	0.163684	−	0.986513i	$-0.447662\pi$
$157$	644.000	0.327368	0.163684	+	0.986513i	$0.447662\pi$
$158$	−644.000	−0.324265
$159$	−90.0000	−0.0448897
$160$	160.000	0.0790569
$161$	276.000	0.135105
$162$	1342.00	0.650849
$163$	−2779.00	−1.33539	−0.667693	−	0.744436i	$-0.732718\pi$
$163$	−2779.00	−1.33539	−0.667693	+	0.744436i	$0.732718\pi$
$164$	1084.00	0.516135
$165$	550.000	0.259500
$166$	−1144.00	−0.534889
$167$	−568.000	−0.263193	−0.131596	−	0.991303i	$-0.542010\pi$
$167$	−568.000	−0.263193	−0.131596	+	0.991303i	$0.542010\pi$
$168$	480.000	0.220433
$169$	−1836.00	−0.835685
$170$	960.000	0.433110
$171$	196.000	0.0876520
$172$	−400.000	−0.177324
$173$	−2578.00	−1.13296	−0.566479	−	0.824076i	$-0.691695\pi$
$173$	−2578.00	−1.13296	−0.566479	+	0.824076i	$0.691695\pi$
$174$	−2270.00	−0.989013
$175$	300.000	0.129588
$176$	352.000	0.150756
$177$	1760.00	0.747399
$178$	1008.00	0.424454
$179$	4141.00	1.72912	0.864561	−	0.502528i	$-0.167597\pi$
$179$	4141.00	1.72912	0.864561	+	0.502528i	$0.167597\pi$
$180$	40.0000	0.0165635
$181$	−1454.00	−0.597099	−0.298550	−	0.954394i	$-0.596503\pi$
$181$	−1454.00	−0.597099	−0.298550	+	0.954394i	$0.596503\pi$
$182$	−456.000	−0.185720
$183$	2390.00	0.965431
$184$	−184.000	−0.0737210
$185$	1990.00	0.790852
$186$	−2850.00	−1.12351
$187$	2112.00	0.825908
$188$	−1140.00	−0.442250
$189$	1740.00	0.669663
$190$	−980.000	−0.374193
$191$	−3390.00	−1.28425	−0.642125	−	0.766600i	$-0.721947\pi$
$191$	−3390.00	−1.28425	−0.642125	+	0.766600i	$0.721947\pi$
$192$	−320.000	−0.120281
$193$	−2587.00	−0.964851	−0.482426	−	0.875937i	$-0.660244\pi$
$193$	−2587.00	−0.964851	−0.482426	+	0.875937i	$0.660244\pi$
$194$	−3424.00	−1.26716
$195$	475.000	0.174438
$196$	−796.000	−0.290087
$197$	1641.00	0.593484	0.296742	−	0.954958i	$-0.404100\pi$
$197$	1641.00	0.593484	0.296742	+	0.954958i	$0.404100\pi$
$198$	88.0000	0.0315853
$199$	−406.000	−0.144626	−0.0723130	−	0.997382i	$-0.523038\pi$
$199$	−406.000	−0.144626	−0.0723130	+	0.997382i	$0.523038\pi$
$200$	−200.000	−0.0707107
$201$	−1650.00	−0.579015
$202$	3420.00	1.19124
$203$	−2724.00	−0.941809
$204$	−1920.00	−0.658955
$205$	−1355.00	−0.461645
$206$	−72.0000	−0.0243518
$207$	−46.0000	−0.0154455
$208$	304.000	0.101339
$209$	−2156.00	−0.713558
$210$	−600.000	−0.197162
$211$	−5060.00	−1.65092	−0.825462	−	0.564458i	$-0.809085\pi$
$211$	−5060.00	−1.65092	−0.825462	+	0.564458i	$0.809085\pi$
$212$	72.0000	0.0233254
$213$	−4175.00	−1.34303
$214$	−1380.00	−0.440817
$215$	500.000	0.158603
$216$	−1160.00	−0.365407
$217$	−3420.00	−1.06988
$218$	−760.000	−0.236118
$219$	5635.00	1.73871
$220$	−440.000	−0.134840
$221$	1824.00	0.555183
$222$	−3980.00	−1.20324
$223$	3232.00	0.970541	0.485271	−	0.874364i	$-0.338721\pi$
$223$	3232.00	0.970541	0.485271	+	0.874364i	$0.338721\pi$
$224$	−384.000	−0.114541
$225$	−50.0000	−0.0148148
$226$	4344.00	1.27858
$227$	−1472.00	−0.430397	−0.215198	−	0.976570i	$-0.569040\pi$
$227$	−1472.00	−0.430397	−0.215198	+	0.976570i	$0.569040\pi$
$228$	1960.00	0.569317
$229$	−4048.00	−1.16812	−0.584060	−	0.811711i	$-0.698537\pi$
$229$	−4048.00	−1.16812	−0.584060	+	0.811711i	$0.698537\pi$
$230$	230.000	0.0659380
$231$	−1320.00	−0.375972
$232$	1816.00	0.513906
$233$	−2313.00	−0.650342	−0.325171	−	0.945655i	$-0.605422\pi$
$233$	−2313.00	−0.650342	−0.325171	+	0.945655i	$0.605422\pi$
$234$	76.0000	0.0212319
$235$	1425.00	0.395561
$236$	−1408.00	−0.388360
$237$	−1610.00	−0.441269
$238$	−2304.00	−0.627505
$239$	379.000	0.102575	0.0512876	−	0.998684i	$-0.483667\pi$
$239$	379.000	0.102575	0.0512876	+	0.998684i	$0.483667\pi$
$240$	400.000	0.107583
$241$	7242.00	1.93568	0.967839	−	0.251572i	$-0.0809474\pi$
$241$	7242.00	1.93568	0.967839	+	0.251572i	$0.0809474\pi$
$242$	1694.00	0.449977
$243$	−560.000	−0.147835
$244$	−1912.00	−0.501653
$245$	995.000	0.259462
$246$	2710.00	0.702371
$247$	−1862.00	−0.479661
$248$	2280.00	0.583791
$249$	−2860.00	−0.727892
$250$	250.000	0.0632456
$251$	−1516.00	−0.381231	−0.190616	−	0.981665i	$-0.561048\pi$
$251$	−1516.00	−0.381231	−0.190616	+	0.981665i	$0.561048\pi$
$252$	−96.0000	−0.0239977
$253$	506.000	0.125739
$254$	86.0000	0.0212446
$255$	2400.00	0.589388
$256$	256.000	0.0625000
$257$	6379.00	1.54829	0.774146	−	0.633007i	$-0.218180\pi$
$257$	6379.00	1.54829	0.774146	+	0.633007i	$0.218180\pi$
$258$	−1000.00	−0.241307
$259$	−4776.00	−1.14582
$260$	−380.000	−0.0906408
$261$	454.000	0.107670
$262$	−2374.00	−0.559795
$263$	1182.00	0.277130	0.138565	−	0.990353i	$-0.455751\pi$
$263$	1182.00	0.277130	0.138565	+	0.990353i	$0.455751\pi$
$264$	880.000	0.205152
$265$	−90.0000	−0.0208629
$266$	2352.00	0.542144
$267$	2520.00	0.577609
$268$	1320.00	0.300865
$269$	1769.00	0.400958	0.200479	−	0.979698i	$-0.435750\pi$
$269$	1769.00	0.400958	0.200479	+	0.979698i	$0.435750\pi$
$270$	1450.00	0.326830
$271$	2208.00	0.494932	0.247466	−	0.968897i	$-0.420402\pi$
$271$	2208.00	0.494932	0.247466	+	0.968897i	$0.420402\pi$
$272$	1536.00	0.342403
$273$	−1140.00	−0.252732
$274$	−424.000	−0.0934846
$275$	550.000	0.120605
$276$	−460.000	−0.100322
$277$	−5083.00	−1.10256	−0.551278	−	0.834322i	$-0.685860\pi$
$277$	−5083.00	−1.10256	−0.551278	+	0.834322i	$0.685860\pi$
$278$	2182.00	0.470747
$279$	570.000	0.122312
$280$	480.000	0.102448
$281$	6924.00	1.46993	0.734967	−	0.678103i	$-0.237198\pi$
$281$	6924.00	1.46993	0.734967	+	0.678103i	$0.237198\pi$
$282$	−2850.00	−0.601826
$283$	6638.00	1.39430	0.697152	−	0.716923i	$-0.254450\pi$
$283$	6638.00	1.39430	0.697152	+	0.716923i	$0.254450\pi$
$284$	3340.00	0.697861
$285$	−2450.00	−0.509212
$286$	−836.000	−0.172845
$287$	3252.00	0.668848
$288$	64.0000	0.0130946
$289$	4303.00	0.875840
$290$	−2270.00	−0.459652
$291$	−8560.00	−1.72439
$292$	−4508.00	−0.903461
$293$	5272.00	1.05117	0.525586	−	0.850740i	$-0.323846\pi$
$293$	5272.00	1.05117	0.525586	+	0.850740i	$0.323846\pi$
$294$	−1990.00	−0.394759
$295$	1760.00	0.347360
$296$	3184.00	0.625224
$297$	3190.00	0.623241
$298$	2372.00	0.461095
$299$	437.000	0.0845230
$300$	−500.000	−0.0962250
$301$	−1200.00	−0.229790
$302$	−1174.00	−0.223696
$303$	8550.00	1.62107
$304$	−1568.00	−0.295826
$305$	2390.00	0.448692
$306$	384.000	0.0717380
$307$	−2192.00	−0.407505	−0.203753	−	0.979022i	$-0.565314\pi$
$307$	−2192.00	−0.407505	−0.203753	+	0.979022i	$0.565314\pi$
$308$	1056.00	0.195361
$309$	−180.000	−0.0331386
$310$	−2850.00	−0.522158
$311$	8987.00	1.63860	0.819302	−	0.573362i	$-0.194361\pi$
$311$	8987.00	1.63860	0.819302	+	0.573362i	$0.194361\pi$
$312$	760.000	0.137906
$313$	4336.00	0.783020	0.391510	−	0.920174i	$-0.371953\pi$
$313$	4336.00	0.783020	0.391510	+	0.920174i	$0.371953\pi$
$314$	−1288.00	−0.231484
$315$	120.000	0.0214642
$316$	1288.00	0.229290
$317$	4554.00	0.806871	0.403436	−	0.915008i	$-0.367816\pi$
$317$	4554.00	0.806871	0.403436	+	0.915008i	$0.367816\pi$
$318$	180.000	0.0317418
$319$	−4994.00	−0.876521
$320$	−320.000	−0.0559017
$321$	−3450.00	−0.599876
$322$	−552.000	−0.0955334
$323$	−9408.00	−1.62067
$324$	−2684.00	−0.460219
$325$	475.000	0.0810716
$326$	5558.00	0.944261
$327$	−1900.00	−0.321316
$328$	−2168.00	−0.364963
$329$	−3420.00	−0.573102
$330$	−1100.00	−0.183494
$331$	961.000	0.159581	0.0797905	−	0.996812i	$-0.474575\pi$
$331$	961.000	0.159581	0.0797905	+	0.996812i	$0.474575\pi$
$332$	2288.00	0.378224
$333$	796.000	0.130993
$334$	1136.00	0.186105
$335$	−1650.00	−0.269102
$336$	−960.000	−0.155870
$337$	−400.000	−0.0646569	−0.0323285	−	0.999477i	$-0.510292\pi$
$337$	−400.000	−0.0646569	−0.0323285	+	0.999477i	$0.510292\pi$
$338$	3672.00	0.590919
$339$	10860.0	1.73992
$340$	−1920.00	−0.306255
$341$	−6270.00	−0.995717
$342$	−392.000	−0.0619793
$343$	−6504.00	−1.02386
$344$	800.000	0.125387
$345$	575.000	0.0897303
$346$	5156.00	0.801122
$347$	−12684.0	−1.96228	−0.981142	−	0.193287i	$-0.938085\pi$
$347$	−12684.0	−1.96228	−0.981142	+	0.193287i	$0.938085\pi$
$348$	4540.00	0.699338
$349$	−3631.00	−0.556914	−0.278457	−	0.960449i	$-0.589823\pi$
$349$	−3631.00	−0.556914	−0.278457	+	0.960449i	$0.589823\pi$
$350$	−600.000	−0.0916324
$351$	2755.00	0.418949
$352$	−704.000	−0.106600
$353$	−6539.00	−0.985937	−0.492969	−	0.870047i	$-0.664088\pi$
$353$	−6539.00	−0.985937	−0.492969	+	0.870047i	$0.664088\pi$
$354$	−3520.00	−0.528491
$355$	−4175.00	−0.624186
$356$	−2016.00	−0.300134
$357$	−5760.00	−0.853926
$358$	−8282.00	−1.22267
$359$	7262.00	1.06761	0.533807	−	0.845606i	$-0.320761\pi$
$359$	7262.00	1.06761	0.533807	+	0.845606i	$0.320761\pi$
$360$	−80.0000	−0.0117121
$361$	2745.00	0.400204
$362$	2908.00	0.422213
$363$	4235.00	0.612341
$364$	912.000	0.131324
$365$	5635.00	0.808080
$366$	−4780.00	−0.682663
$367$	11884.0	1.69030	0.845150	−	0.534530i	$-0.179511\pi$
$367$	11884.0	1.69030	0.845150	+	0.534530i	$0.179511\pi$
$368$	368.000	0.0521286
$369$	−542.000	−0.0764645
$370$	−3980.00	−0.559217
$371$	216.000	0.0302268
$372$	5700.00	0.794439
$373$	−1902.00	−0.264026	−0.132013	−	0.991248i	$-0.542144\pi$
$373$	−1902.00	−0.264026	−0.132013	+	0.991248i	$0.542144\pi$
$374$	−4224.00	−0.584005
$375$	625.000	0.0860663
$376$	2280.00	0.312718
$377$	−4313.00	−0.589206
$378$	−3480.00	−0.473524
$379$	−2472.00	−0.335035	−0.167517	−	0.985869i	$-0.553575\pi$
$379$	−2472.00	−0.335035	−0.167517	+	0.985869i	$0.553575\pi$
$380$	1960.00	0.264594
$381$	215.000	0.0289102
$382$	6780.00	0.908102
$383$	9088.00	1.21247	0.606234	−	0.795286i	$-0.292680\pi$
$383$	9088.00	1.21247	0.606234	+	0.795286i	$0.292680\pi$
$384$	640.000	0.0850517
$385$	−1320.00	−0.174736
$386$	5174.00	0.682253
$387$	200.000	0.0262702
$388$	6848.00	0.896017
$389$	−4480.00	−0.583920	−0.291960	−	0.956430i	$-0.594307\pi$
$389$	−4480.00	−0.583920	−0.291960	+	0.956430i	$0.594307\pi$
$390$	−950.000	−0.123346
$391$	2208.00	0.285584
$392$	1592.00	0.205123
$393$	−5935.00	−0.761784
$394$	−3282.00	−0.419657
$395$	−1610.00	−0.205083
$396$	−176.000	−0.0223342
$397$	−11237.0	−1.42058	−0.710288	−	0.703911i	$-0.751435\pi$
$397$	−11237.0	−1.42058	−0.710288	+	0.703911i	$0.751435\pi$
$398$	812.000	0.102266
$399$	5880.00	0.737765
$400$	400.000	0.0500000
$401$	−6458.00	−0.804232	−0.402116	−	0.915589i	$-0.631725\pi$
$401$	−6458.00	−0.804232	−0.402116	+	0.915589i	$0.631725\pi$
$402$	3300.00	0.409425
$403$	−5415.00	−0.669331
$404$	−6840.00	−0.842333
$405$	3355.00	0.411633
$406$	5448.00	0.665960
$407$	−8756.00	−1.06639
$408$	3840.00	0.465952
$409$	2261.00	0.273348	0.136674	−	0.990616i	$-0.456359\pi$
$409$	2261.00	0.273348	0.136674	+	0.990616i	$0.456359\pi$
$410$	2710.00	0.326433
$411$	−1060.00	−0.127216
$412$	144.000	0.0172193
$413$	−4224.00	−0.503267
$414$	92.0000	0.0109216
$415$	−2860.00	−0.338294
$416$	−608.000	−0.0716578
$417$	5455.00	0.640606
$418$	4312.00	0.504562
$419$	−612.000	−0.0713560	−0.0356780	−	0.999363i	$-0.511359\pi$
$419$	−612.000	−0.0713560	−0.0356780	+	0.999363i	$0.511359\pi$
$420$	1200.00	0.139414
$421$	−4292.00	−0.496863	−0.248431	−	0.968649i	$-0.579915\pi$
$421$	−4292.00	−0.496863	−0.248431	+	0.968649i	$0.579915\pi$
$422$	10120.0	1.16738
$423$	570.000	0.0655186
$424$	−144.000	−0.0164935
$425$	2400.00	0.273923
$426$	8350.00	0.949669
$427$	−5736.00	−0.650081
$428$	2760.00	0.311705
$429$	−2090.00	−0.235212
$430$	−1000.00	−0.112149
$431$	−5132.00	−0.573549	−0.286775	−	0.957998i	$-0.592583\pi$
$431$	−5132.00	−0.573549	−0.286775	+	0.957998i	$0.592583\pi$
$432$	2320.00	0.258382
$433$	15982.0	1.77378	0.886889	−	0.461983i	$-0.152862\pi$
$433$	15982.0	1.77378	0.886889	+	0.461983i	$0.152862\pi$
$434$	6840.00	0.756522
$435$	−5675.00	−0.625507
$436$	1520.00	0.166961
$437$	−2254.00	−0.246736
$438$	−11270.0	−1.22946
$439$	−3323.00	−0.361271	−0.180636	−	0.983550i	$-0.557815\pi$
$439$	−3323.00	−0.361271	−0.180636	+	0.983550i	$0.557815\pi$
$440$	880.000	0.0953463
$441$	398.000	0.0429759
$442$	−3648.00	−0.392574
$443$	8699.00	0.932962	0.466481	−	0.884531i	$-0.345522\pi$
$443$	8699.00	0.932962	0.466481	+	0.884531i	$0.345522\pi$
$444$	7960.00	0.850822
$445$	2520.00	0.268448
$446$	−6464.00	−0.686276
$447$	5930.00	0.627471
$448$	768.000	0.0809924
$449$	6966.00	0.732173	0.366087	−	0.930581i	$-0.380697\pi$
$449$	6966.00	0.732173	0.366087	+	0.930581i	$0.380697\pi$
$450$	100.000	0.0104757
$451$	5962.00	0.622483
$452$	−8688.00	−0.904091
$453$	−2935.00	−0.304411
$454$	2944.00	0.304336
$455$	−1140.00	−0.117459
$456$	−3920.00	−0.402568
$457$	−9020.00	−0.923277	−0.461639	−	0.887068i	$-0.652738\pi$
$457$	−9020.00	−0.923277	−0.461639	+	0.887068i	$0.652738\pi$
$458$	8096.00	0.825985
$459$	13920.0	1.41553
$460$	−460.000	−0.0466252
$461$	−17847.0	−1.80308	−0.901538	−	0.432701i	$-0.857561\pi$
$461$	−17847.0	−1.80308	−0.901538	+	0.432701i	$0.857561\pi$
$462$	2640.00	0.265853
$463$	−11360.0	−1.14027	−0.570134	−	0.821552i	$-0.693109\pi$
$463$	−11360.0	−1.14027	−0.570134	+	0.821552i	$0.693109\pi$
$464$	−3632.00	−0.363387
$465$	−7125.00	−0.710568
$466$	4626.00	0.459861
$467$	−534.000	−0.0529134	−0.0264567	−	0.999650i	$-0.508422\pi$
$467$	−534.000	−0.0529134	−0.0264567	+	0.999650i	$0.508422\pi$
$468$	−152.000	−0.0150133
$469$	3960.00	0.389884
$470$	−2850.00	−0.279704
$471$	−3220.00	−0.315010
$472$	2816.00	0.274612
$473$	−2200.00	−0.213861
$474$	3220.00	0.312024
$475$	−2450.00	−0.236660
$476$	4608.00	0.443713
$477$	−36.0000	−0.00345561
$478$	−758.000	−0.0725316
$479$	3428.00	0.326992	0.163496	−	0.986544i	$-0.447723\pi$
$479$	3428.00	0.326992	0.163496	+	0.986544i	$0.447723\pi$
$480$	−800.000	−0.0760726
$481$	−7562.00	−0.716835
$482$	−14484.0	−1.36873
$483$	−1380.00	−0.130005
$484$	−3388.00	−0.318182
$485$	−8560.00	−0.801422
$486$	1120.00	0.104535
$487$	6949.00	0.646590	0.323295	−	0.946298i	$-0.395209\pi$
$487$	6949.00	0.646590	0.323295	+	0.946298i	$0.395209\pi$
$488$	3824.00	0.354722
$489$	13895.0	1.28498
$490$	−1990.00	−0.183467
$491$	−9571.00	−0.879701	−0.439850	−	0.898071i	$-0.644969\pi$
$491$	−9571.00	−0.879701	−0.439850	+	0.898071i	$0.644969\pi$
$492$	−5420.00	−0.496651
$493$	−21792.0	−1.99080
$494$	3724.00	0.339171
$495$	220.000	0.0199763
$496$	−4560.00	−0.412803
$497$	10020.0	0.904343
$498$	5720.00	0.514697
$499$	10679.0	0.958031	0.479016	−	0.877806i	$-0.340994\pi$
$499$	10679.0	0.958031	0.479016	+	0.877806i	$0.340994\pi$
$500$	−500.000	−0.0447214
$501$	2840.00	0.253257
$502$	3032.00	0.269571
$503$	−9514.00	−0.843356	−0.421678	−	0.906746i	$-0.638559\pi$
$503$	−9514.00	−0.843356	−0.421678	+	0.906746i	$0.638559\pi$
$504$	192.000	0.0169690
$505$	8550.00	0.753406
$506$	−1012.00	−0.0889108
$507$	9180.00	0.804138
$508$	−172.000	−0.0150222
$509$	6977.00	0.607564	0.303782	−	0.952742i	$-0.401751\pi$
$509$	6977.00	0.607564	0.303782	+	0.952742i	$0.401751\pi$
$510$	−4800.00	−0.416760
$511$	−13524.0	−1.17078
$512$	−512.000	−0.0441942
$513$	−14210.0	−1.22298
$514$	−12758.0	−1.09481
$515$	−180.000	−0.0154015
$516$	2000.00	0.170630
$517$	−6270.00	−0.533374
$518$	9552.00	0.810214
$519$	12890.0	1.09019
$520$	760.000	0.0640927
$521$	−13172.0	−1.10763	−0.553816	−	0.832639i	$-0.686829\pi$
$521$	−13172.0	−1.10763	−0.553816	+	0.832639i	$0.686829\pi$
$522$	−908.000	−0.0761343
$523$	−1512.00	−0.126415	−0.0632076	−	0.998000i	$-0.520133\pi$
$523$	−1512.00	−0.126415	−0.0632076	+	0.998000i	$0.520133\pi$
$524$	4748.00	0.395835
$525$	−1500.00	−0.124696
$526$	−2364.00	−0.195961
$527$	−27360.0	−2.26152
$528$	−1760.00	−0.145065
$529$	529.000	0.0434783
$530$	180.000	0.0147523
$531$	704.000	0.0575348
$532$	−4704.00	−0.383354
$533$	5149.00	0.418439
$534$	−5040.00	−0.408431
$535$	−3450.00	−0.278797
$536$	−2640.00	−0.212744
$537$	−20705.0	−1.66385
$538$	−3538.00	−0.283520
$539$	−4378.00	−0.349859
$540$	−2900.00	−0.231104
$541$	10589.0	0.841510	0.420755	−	0.907174i	$-0.361765\pi$
$541$	10589.0	0.841510	0.420755	+	0.907174i	$0.361765\pi$
$542$	−4416.00	−0.349969
$543$	7270.00	0.574559
$544$	−3072.00	−0.242116
$545$	−1900.00	−0.149334
$546$	2280.00	0.178709
$547$	−3227.00	−0.252242	−0.126121	−	0.992015i	$-0.540253\pi$
$547$	−3227.00	−0.252242	−0.126121	+	0.992015i	$0.540253\pi$
$548$	848.000	0.0661036
$549$	956.000	0.0743189
$550$	−1100.00	−0.0852803
$551$	22246.0	1.71998
$552$	920.000	0.0709380
$553$	3864.00	0.297132
$554$	10166.0	0.779624
$555$	−9950.00	−0.760998
$556$	−4364.00	−0.332868
$557$	−1888.00	−0.143621	−0.0718107	−	0.997418i	$-0.522878\pi$
$557$	−1888.00	−0.143621	−0.0718107	+	0.997418i	$0.522878\pi$
$558$	−1140.00	−0.0864875
$559$	−1900.00	−0.143759
$560$	−960.000	−0.0724418
$561$	−10560.0	−0.794730
$562$	−13848.0	−1.03940
$563$	14388.0	1.07705	0.538527	−	0.842608i	$-0.318981\pi$
$563$	14388.0	1.07705	0.538527	+	0.842608i	$0.318981\pi$
$564$	5700.00	0.425555
$565$	10860.0	0.808644
$566$	−13276.0	−0.985922
$567$	−8052.00	−0.596388
$568$	−6680.00	−0.493462
$569$	−18234.0	−1.34343	−0.671713	−	0.740812i	$-0.734441\pi$
$569$	−18234.0	−1.34343	−0.671713	+	0.740812i	$0.734441\pi$
$570$	4900.00	0.360067
$571$	2024.00	0.148339	0.0741697	−	0.997246i	$-0.476369\pi$
$571$	2024.00	0.148339	0.0741697	+	0.997246i	$0.476369\pi$
$572$	1672.00	0.122220
$573$	16950.0	1.23577
$574$	−6504.00	−0.472947
$575$	575.000	0.0417029
$576$	−128.000	−0.00925926
$577$	7085.00	0.511183	0.255591	−	0.966785i	$-0.417730\pi$
$577$	7085.00	0.511183	0.255591	+	0.966785i	$0.417730\pi$
$578$	−8606.00	−0.619312
$579$	12935.0	0.928429
$580$	4540.00	0.325023
$581$	6864.00	0.490132
$582$	17120.0	1.21932
$583$	396.000	0.0281315
$584$	9016.00	0.638844
$585$	190.000	0.0134283
$586$	−10544.0	−0.743291
$587$	−1421.00	−0.0999164	−0.0499582	−	0.998751i	$-0.515909\pi$
$587$	−1421.00	−0.0999164	−0.0499582	+	0.998751i	$0.515909\pi$
$588$	3980.00	0.279137
$589$	27930.0	1.95388
$590$	−3520.00	−0.245621
$591$	−8205.00	−0.571081
$592$	−6368.00	−0.442100
$593$	−8202.00	−0.567986	−0.283993	−	0.958826i	$-0.591659\pi$
$593$	−8202.00	−0.567986	−0.283993	+	0.958826i	$0.591659\pi$
$594$	−6380.00	−0.440698
$595$	−5760.00	−0.396869
$596$	−4744.00	−0.326043
$597$	2030.00	0.139166
$598$	−874.000	−0.0597668
$599$	16304.0	1.11213	0.556063	−	0.831140i	$-0.312311\pi$
$599$	16304.0	1.11213	0.556063	+	0.831140i	$0.312311\pi$
$600$	1000.00	0.0680414
$601$	18829.0	1.27795	0.638977	−	0.769225i	$-0.279358\pi$
$601$	18829.0	1.27795	0.638977	+	0.769225i	$0.279358\pi$
$602$	2400.00	0.162486
$603$	−660.000	−0.0445726
$604$	2348.00	0.158177
$605$	4235.00	0.284590
$606$	−17100.0	−1.14627
$607$	−6556.00	−0.438385	−0.219193	−	0.975682i	$-0.570342\pi$
$607$	−6556.00	−0.438385	−0.219193	+	0.975682i	$0.570342\pi$
$608$	3136.00	0.209180
$609$	13620.0	0.906257
$610$	−4780.00	−0.317273
$611$	−5415.00	−0.358539
$612$	−768.000	−0.0507264
$613$	−8208.00	−0.540812	−0.270406	−	0.962746i	$-0.587158\pi$
$613$	−8208.00	−0.540812	−0.270406	+	0.962746i	$0.587158\pi$
$614$	4384.00	0.288150
$615$	6775.00	0.444218
$616$	−2112.00	−0.138141
$617$	−5874.00	−0.383271	−0.191636	−	0.981466i	$-0.561379\pi$
$617$	−5874.00	−0.383271	−0.191636	+	0.981466i	$0.561379\pi$
$618$	360.000	0.0234326
$619$	23864.0	1.54956	0.774778	−	0.632233i	$-0.217862\pi$
$619$	23864.0	1.54956	0.774778	+	0.632233i	$0.217862\pi$
$620$	5700.00	0.369222
$621$	3335.00	0.215506
$622$	−17974.0	−1.15867
$623$	−6048.00	−0.388937
$624$	−1520.00	−0.0975139
$625$	625.000	0.0400000
$626$	−8672.00	−0.553679
$627$	10780.0	0.686622
$628$	2576.00	0.163684
$629$	−38208.0	−2.42202
$630$	−240.000	−0.0151775
$631$	−23120.0	−1.45863	−0.729313	−	0.684180i	$-0.760160\pi$
$631$	−23120.0	−1.45863	−0.729313	+	0.684180i	$0.760160\pi$
$632$	−2576.00	−0.162133
$633$	25300.0	1.58860
$634$	−9108.00	−0.570544
$635$	215.000	0.0134362
$636$	−360.000	−0.0224449
$637$	−3781.00	−0.235178
$638$	9988.00	0.619794
$639$	−1670.00	−0.103387
$640$	640.000	0.0395285
$641$	17264.0	1.06379	0.531893	−	0.846811i	$-0.321481\pi$
$641$	17264.0	1.06379	0.531893	+	0.846811i	$0.321481\pi$
$642$	6900.00	0.424176
$643$	1130.00	0.0693046	0.0346523	−	0.999399i	$-0.488968\pi$
$643$	1130.00	0.0693046	0.0346523	+	0.999399i	$0.488968\pi$
$644$	1104.00	0.0675523
$645$	−2500.00	−0.152616
$646$	18816.0	1.14598
$647$	17075.0	1.03754	0.518769	−	0.854914i	$-0.326390\pi$
$647$	17075.0	1.03754	0.518769	+	0.854914i	$0.326390\pi$
$648$	5368.00	0.325424
$649$	−7744.00	−0.468380
$650$	−950.000	−0.0573263
$651$	17100.0	1.02950
$652$	−11116.0	−0.667693
$653$	6059.00	0.363104	0.181552	−	0.983381i	$-0.441888\pi$
$653$	6059.00	0.363104	0.181552	+	0.983381i	$0.441888\pi$
$654$	3800.00	0.227205
$655$	−5935.00	−0.354045
$656$	4336.00	0.258068
$657$	2254.00	0.133846
$658$	6840.00	0.405245
$659$	−980.000	−0.0579293	−0.0289646	−	0.999580i	$-0.509221\pi$
$659$	−980.000	−0.0579293	−0.0289646	+	0.999580i	$0.509221\pi$
$660$	2200.00	0.129750
$661$	31126.0	1.83156	0.915780	−	0.401680i	$-0.131574\pi$
$661$	31126.0	1.83156	0.915780	+	0.401680i	$0.131574\pi$
$662$	−1922.00	−0.112841
$663$	−9120.00	−0.534225
$664$	−4576.00	−0.267445
$665$	5880.00	0.342882
$666$	−1592.00	−0.0926257
$667$	−5221.00	−0.303085
$668$	−2272.00	−0.131596
$669$	−16160.0	−0.933904
$670$	3300.00	0.190284
$671$	−10516.0	−0.605016
$672$	1920.00	0.110217
$673$	23399.0	1.34022	0.670108	−	0.742264i	$-0.266248\pi$
$673$	23399.0	1.34022	0.670108	+	0.742264i	$0.266248\pi$
$674$	800.000	0.0457194
$675$	3625.00	0.206706
$676$	−7344.00	−0.417843
$677$	7106.00	0.403406	0.201703	−	0.979447i	$-0.435352\pi$
$677$	7106.00	0.403406	0.201703	+	0.979447i	$0.435352\pi$
$678$	−21720.0	−1.23031
$679$	20544.0	1.16113
$680$	3840.00	0.216555
$681$	7360.00	0.414150
$682$	12540.0	0.704078
$683$	4281.00	0.239836	0.119918	−	0.992784i	$-0.461737\pi$
$683$	4281.00	0.239836	0.119918	+	0.992784i	$0.461737\pi$
$684$	784.000	0.0438260
$685$	−1060.00	−0.0591248
$686$	13008.0	0.723976
$687$	20240.0	1.12402
$688$	−1600.00	−0.0886620
$689$	342.000	0.0189103
$690$	−1150.00	−0.0634489
$691$	29036.0	1.59853	0.799263	−	0.600981i	$-0.205223\pi$
$691$	29036.0	1.59853	0.799263	+	0.600981i	$0.205223\pi$
$692$	−10312.0	−0.566479
$693$	−528.000	−0.0289424
$694$	25368.0	1.38754
$695$	5455.00	0.297727
$696$	−9080.00	−0.494506
$697$	26016.0	1.41381
$698$	7262.00	0.393798
$699$	11565.0	0.625792
$700$	1200.00	0.0647939
$701$	5740.00	0.309268	0.154634	−	0.987972i	$-0.450580\pi$
$701$	5740.00	0.309268	0.154634	+	0.987972i	$0.450580\pi$
$702$	−5510.00	−0.296242
$703$	39004.0	2.09255
$704$	1408.00	0.0753778
$705$	−7125.00	−0.380628
$706$	13078.0	0.697163
$707$	−20520.0	−1.09156
$708$	7040.00	0.373700
$709$	−13432.0	−0.711494	−0.355747	−	0.934582i	$-0.615774\pi$
$709$	−13432.0	−0.711494	−0.355747	+	0.934582i	$0.615774\pi$
$710$	8350.00	0.441366
$711$	−644.000	−0.0339689
$712$	4032.00	0.212227
$713$	−6555.00	−0.344301
$714$	11520.0	0.603817
$715$	−2090.00	−0.109317
$716$	16564.0	0.864561
$717$	−1895.00	−0.0987030
$718$	−14524.0	−0.754918
$719$	−2768.00	−0.143573	−0.0717865	−	0.997420i	$-0.522870\pi$
$719$	−2768.00	−0.143573	−0.0717865	+	0.997420i	$0.522870\pi$
$720$	160.000	0.00828173
$721$	432.000	0.0223142
$722$	−5490.00	−0.282987
$723$	−36210.0	−1.86261
$724$	−5816.00	−0.298550
$725$	−5675.00	−0.290709
$726$	−8470.00	−0.432991
$727$	22378.0	1.14161	0.570807	−	0.821084i	$-0.306630\pi$
$727$	22378.0	1.14161	0.570807	+	0.821084i	$0.306630\pi$
$728$	−1824.00	−0.0928598
$729$	20917.0	1.06269
$730$	−11270.0	−0.571399
$731$	−9600.00	−0.485730
$732$	9560.00	0.482716
$733$	13368.0	0.673613	0.336807	−	0.941574i	$-0.390653\pi$
$733$	13368.0	0.673613	0.336807	+	0.941574i	$0.390653\pi$
$734$	−23768.0	−1.19522
$735$	−4975.00	−0.249668
$736$	−736.000	−0.0368605
$737$	7260.00	0.362857
$738$	1084.00	0.0540686
$739$	−25803.0	−1.28441	−0.642205	−	0.766533i	$-0.721980\pi$
$739$	−25803.0	−1.28441	−0.642205	+	0.766533i	$0.721980\pi$
$740$	7960.00	0.395426
$741$	9310.00	0.461554
$742$	−432.000	−0.0213736
$743$	−16812.0	−0.830111	−0.415055	−	0.909796i	$-0.636238\pi$
$743$	−16812.0	−0.830111	−0.415055	+	0.909796i	$0.636238\pi$
$744$	−11400.0	−0.561753
$745$	5930.00	0.291622
$746$	3804.00	0.186695
$747$	−1144.00	−0.0560332
$748$	8448.00	0.412954
$749$	8280.00	0.403931
$750$	−1250.00	−0.0608581
$751$	−18052.0	−0.877133	−0.438566	−	0.898699i	$-0.644514\pi$
$751$	−18052.0	−0.877133	−0.438566	+	0.898699i	$0.644514\pi$
$752$	−4560.00	−0.221125
$753$	7580.00	0.366840
$754$	8626.00	0.416632
$755$	−2935.00	−0.141478
$756$	6960.00	0.334832
$757$	−20946.0	−1.00567	−0.502837	−	0.864381i	$-0.667710\pi$
$757$	−20946.0	−1.00567	−0.502837	+	0.864381i	$0.667710\pi$
$758$	4944.00	0.236905
$759$	−2530.00	−0.120992
$760$	−3920.00	−0.187097
$761$	19805.0	0.943404	0.471702	−	0.881758i	$-0.343640\pi$
$761$	19805.0	0.943404	0.471702	+	0.881758i	$0.343640\pi$
$762$	−430.000	−0.0204426
$763$	4560.00	0.216361
$764$	−13560.0	−0.642125
$765$	960.000	0.0453711
$766$	−18176.0	−0.857344
$767$	−6688.00	−0.314850
$768$	−1280.00	−0.0601407
$769$	14098.0	0.661101	0.330551	−	0.943788i	$-0.392766\pi$
$769$	14098.0	0.661101	0.330551	+	0.943788i	$0.392766\pi$
$770$	2640.00	0.123557
$771$	−31895.0	−1.48984
$772$	−10348.0	−0.482426
$773$	6480.00	0.301513	0.150756	−	0.988571i	$-0.451829\pi$
$773$	6480.00	0.301513	0.150756	+	0.988571i	$0.451829\pi$
$774$	−400.000	−0.0185758
$775$	−7125.00	−0.330242
$776$	−13696.0	−0.633580
$777$	23880.0	1.10256
$778$	8960.00	0.412894
$779$	−26558.0	−1.22149
$780$	1900.00	0.0872191
$781$	18370.0	0.841652
$782$	−4416.00	−0.201938
$783$	−32915.0	−1.50228
$784$	−3184.00	−0.145044
$785$	−3220.00	−0.146403
$786$	11870.0	0.538663
$787$	196.000	0.00887757	0.00443878	−	0.999990i	$-0.498587\pi$
$787$	196.000	0.00887757	0.00443878	+	0.999990i	$0.498587\pi$
$788$	6564.00	0.296742
$789$	−5910.00	−0.266669
$790$	3220.00	0.145016
$791$	−26064.0	−1.17159
$792$	352.000	0.0157926
$793$	−9082.00	−0.406698
$794$	22474.0	1.00450
$795$	450.000	0.0200753
$796$	−1624.00	−0.0723130
$797$	10826.0	0.481150	0.240575	−	0.970631i	$-0.422664\pi$
$797$	10826.0	0.481150	0.240575	+	0.970631i	$0.422664\pi$
$798$	−11760.0	−0.521679
$799$	−27360.0	−1.21142
$800$	−800.000	−0.0353553
$801$	1008.00	0.0444643
$802$	12916.0	0.568678
$803$	−24794.0	−1.08962
$804$	−6600.00	−0.289508
$805$	−1380.00	−0.0604206
$806$	10830.0	0.473288
$807$	−8845.00	−0.385822
$808$	13680.0	0.595620
$809$	−14110.0	−0.613203	−0.306601	−	0.951838i	$-0.599192\pi$
$809$	−14110.0	−0.613203	−0.306601	+	0.951838i	$0.599192\pi$
$810$	−6710.00	−0.291068
$811$	33775.0	1.46239	0.731196	−	0.682167i	$-0.238962\pi$
$811$	33775.0	1.46239	0.731196	+	0.682167i	$0.238962\pi$
$812$	−10896.0	−0.470905
$813$	−11040.0	−0.476248
$814$	17512.0	0.754048
$815$	13895.0	0.597203
$816$	−7680.00	−0.329478
$817$	9800.00	0.419656
$818$	−4522.00	−0.193286
$819$	−456.000	−0.0194553
$820$	−5420.00	−0.230823
$821$	−2310.00	−0.0981968	−0.0490984	−	0.998794i	$-0.515635\pi$
$821$	−2310.00	−0.0981968	−0.0490984	+	0.998794i	$0.515635\pi$
$822$	2120.00	0.0899556
$823$	16967.0	0.718630	0.359315	−	0.933216i	$-0.383010\pi$
$823$	16967.0	0.718630	0.359315	+	0.933216i	$0.383010\pi$
$824$	−288.000	−0.0121759
$825$	−2750.00	−0.116052
$826$	8448.00	0.355864
$827$	−21888.0	−0.920339	−0.460169	−	0.887831i	$-0.652211\pi$
$827$	−21888.0	−0.920339	−0.460169	+	0.887831i	$0.652211\pi$
$828$	−184.000	−0.00772276
$829$	−45830.0	−1.92007	−0.960037	−	0.279872i	$-0.909708\pi$
$829$	−45830.0	−1.92007	−0.960037	+	0.279872i	$0.909708\pi$
$830$	5720.00	0.239210
$831$	25415.0	1.06093
$832$	1216.00	0.0506697
$833$	−19104.0	−0.794615
$834$	−10910.0	−0.452977
$835$	2840.00	0.117703
$836$	−8624.00	−0.356779
$837$	−41325.0	−1.70657
$838$	1224.00	0.0504563
$839$	−35304.0	−1.45272	−0.726358	−	0.687316i	$-0.758789\pi$
$839$	−35304.0	−1.45272	−0.726358	+	0.687316i	$0.758789\pi$
$840$	−2400.00	−0.0985808
$841$	27140.0	1.11280
$842$	8584.00	0.351335
$843$	−34620.0	−1.41444
$844$	−20240.0	−0.825462
$845$	9180.00	0.373730
$846$	−1140.00	−0.0463286
$847$	−10164.0	−0.412325
$848$	288.000	0.0116627
$849$	−33190.0	−1.34167
$850$	−4800.00	−0.193693
$851$	−9154.00	−0.368737
$852$	−16700.0	−0.671517
$853$	−15522.0	−0.623052	−0.311526	−	0.950238i	$-0.600840\pi$
$853$	−15522.0	−0.623052	−0.311526	+	0.950238i	$0.600840\pi$
$854$	11472.0	0.459677
$855$	−980.000	−0.0391992
$856$	−5520.00	−0.220409
$857$	39399.0	1.57041	0.785207	−	0.619234i	$-0.212557\pi$
$857$	39399.0	1.57041	0.785207	+	0.619234i	$0.212557\pi$
$858$	4180.00	0.166320
$859$	−40825.0	−1.62157	−0.810786	−	0.585342i	$-0.800960\pi$
$859$	−40825.0	−1.62157	−0.810786	+	0.585342i	$0.800960\pi$
$860$	2000.00	0.0793017
$861$	−16260.0	−0.643600
$862$	10264.0	0.405561
$863$	48061.0	1.89573	0.947865	−	0.318671i	$-0.103237\pi$
$863$	48061.0	1.89573	0.947865	+	0.318671i	$0.103237\pi$
$864$	−4640.00	−0.182704
$865$	12890.0	0.506674
$866$	−31964.0	−1.25425
$867$	−21515.0	−0.842777
$868$	−13680.0	−0.534942
$869$	7084.00	0.276534
$870$	11350.0	0.442300
$871$	6270.00	0.243916
$872$	−3040.00	−0.118059
$873$	−3424.00	−0.132743
$874$	4508.00	0.174468
$875$	−1500.00	−0.0579534
$876$	22540.0	0.869356
$877$	16006.0	0.616288	0.308144	−	0.951340i	$-0.400292\pi$
$877$	16006.0	0.616288	0.308144	+	0.951340i	$0.400292\pi$
$878$	6646.00	0.255457
$879$	−26360.0	−1.01149
$880$	−1760.00	−0.0674200
$881$	−9632.00	−0.368343	−0.184172	−	0.982894i	$-0.558960\pi$
$881$	−9632.00	−0.368343	−0.184172	+	0.982894i	$0.558960\pi$
$882$	−796.000	−0.0303886
$883$	49052.0	1.86946	0.934729	−	0.355362i	$-0.115642\pi$
$883$	49052.0	1.86946	0.934729	+	0.355362i	$0.115642\pi$
$884$	7296.00	0.277592
$885$	−8800.00	−0.334247
$886$	−17398.0	−0.659703
$887$	27963.0	1.05852	0.529259	−	0.848460i	$-0.322470\pi$
$887$	27963.0	1.05852	0.529259	+	0.848460i	$0.322470\pi$
$888$	−15920.0	−0.601622
$889$	−516.000	−0.0194669
$890$	−5040.00	−0.189822
$891$	−14762.0	−0.555046
$892$	12928.0	0.485271
$893$	27930.0	1.04663
$894$	−11860.0	−0.443689
$895$	−20705.0	−0.773287
$896$	−1536.00	−0.0572703
$897$	−2185.00	−0.0813322
$898$	−13932.0	−0.517725
$899$	64695.0	2.40011
$900$	−200.000	−0.00740741
$901$	1728.00	0.0638935
$902$	−11924.0	−0.440162
$903$	6000.00	0.221116
$904$	17376.0	0.639289
$905$	7270.00	0.267031
$906$	5870.00	0.215251
$907$	−17110.0	−0.626382	−0.313191	−	0.949690i	$-0.601398\pi$
$907$	−17110.0	−0.626382	−0.313191	+	0.949690i	$0.601398\pi$
$908$	−5888.00	−0.215198
$909$	3420.00	0.124790
$910$	2280.00	0.0830563
$911$	−4390.00	−0.159657	−0.0798283	−	0.996809i	$-0.525437\pi$
$911$	−4390.00	−0.159657	−0.0798283	+	0.996809i	$0.525437\pi$
$912$	7840.00	0.284658
$913$	12584.0	0.456155
$914$	18040.0	0.652856
$915$	−11950.0	−0.431754
$916$	−16192.0	−0.584060
$917$	14244.0	0.512953
$918$	−27840.0	−1.00093
$919$	−47576.0	−1.70771	−0.853856	−	0.520509i	$-0.825742\pi$
$919$	−47576.0	−1.70771	−0.853856	+	0.520509i	$0.825742\pi$
$920$	920.000	0.0329690
$921$	10960.0	0.392122
$922$	35694.0	1.27497
$923$	15865.0	0.565767
$924$	−5280.00	−0.187986
$925$	−9950.00	−0.353680
$926$	22720.0	0.806291
$927$	−72.0000	−0.00255101
$928$	7264.00	0.256953
$929$	1143.00	0.0403666	0.0201833	−	0.999796i	$-0.493575\pi$
$929$	1143.00	0.0403666	0.0201833	+	0.999796i	$0.493575\pi$
$930$	14250.0	0.502447
$931$	19502.0	0.686522
$932$	−9252.00	−0.325171
$933$	−44935.0	−1.57675
$934$	1068.00	0.0374154
$935$	−10560.0	−0.369357
$936$	304.000	0.0106160
$937$	−50494.0	−1.76048	−0.880239	−	0.474531i	$-0.842618\pi$
$937$	−50494.0	−1.76048	−0.880239	+	0.474531i	$0.842618\pi$
$938$	−7920.00	−0.275690
$939$	−21680.0	−0.753461
$940$	5700.00	0.197780
$941$	−16444.0	−0.569670	−0.284835	−	0.958577i	$-0.591939\pi$
$941$	−16444.0	−0.569670	−0.284835	+	0.958577i	$0.591939\pi$
$942$	6440.00	0.222746
$943$	6233.00	0.215243
$944$	−5632.00	−0.194180
$945$	−8700.00	−0.299483
$946$	4400.00	0.151222
$947$	−4949.00	−0.169821	−0.0849107	−	0.996389i	$-0.527061\pi$
$947$	−4949.00	−0.169821	−0.0849107	+	0.996389i	$0.527061\pi$
$948$	−6440.00	−0.220634
$949$	−21413.0	−0.732450
$950$	4900.00	0.167344
$951$	−22770.0	−0.776412
$952$	−9216.00	−0.313752
$953$	4718.00	0.160368	0.0801842	−	0.996780i	$-0.474449\pi$
$953$	4718.00	0.160368	0.0801842	+	0.996780i	$0.474449\pi$
$954$	72.0000	0.00244349
$955$	16950.0	0.574334
$956$	1516.00	0.0512876
$957$	24970.0	0.843433
$958$	−6856.00	−0.231218
$959$	2544.00	0.0856622
$960$	1600.00	0.0537914
$961$	51434.0	1.72649
$962$	15124.0	0.506879
$963$	−1380.00	−0.0461785
$964$	28968.0	0.967839
$965$	12935.0	0.431495
$966$	2760.00	0.0919271
$967$	47793.0	1.58937	0.794684	−	0.607023i	$-0.207636\pi$
$967$	47793.0	1.58937	0.794684	+	0.607023i	$0.207636\pi$
$968$	6776.00	0.224989
$969$	47040.0	1.55949
$970$	17120.0	0.566691
$971$	−17858.0	−0.590206	−0.295103	−	0.955465i	$-0.595354\pi$
$971$	−17858.0	−0.590206	−0.295103	+	0.955465i	$0.595354\pi$
$972$	−2240.00	−0.0739177
$973$	−13092.0	−0.431357
$974$	−13898.0	−0.457208
$975$	−2375.00	−0.0780112
$976$	−7648.00	−0.250826
$977$	−41238.0	−1.35038	−0.675190	−	0.737644i	$-0.735938\pi$
$977$	−41238.0	−1.35038	−0.675190	+	0.737644i	$0.735938\pi$
$978$	−27790.0	−0.908616
$979$	−11088.0	−0.361976
$980$	3980.00	0.129731
$981$	−760.000	−0.0247349
$982$	19142.0	0.622043
$983$	−19158.0	−0.621613	−0.310806	−	0.950473i	$-0.600599\pi$
$983$	−19158.0	−0.621613	−0.310806	+	0.950473i	$0.600599\pi$
$984$	10840.0	0.351186
$985$	−8205.00	−0.265414
$986$	43584.0	1.40771
$987$	17100.0	0.551468
$988$	−7448.00	−0.239830
$989$	−2300.00	−0.0739492
$990$	−440.000	−0.0141254
$991$	−48816.0	−1.56477	−0.782387	−	0.622792i	$-0.785998\pi$
$991$	−48816.0	−1.56477	−0.782387	+	0.622792i	$0.785998\pi$
$992$	9120.00	0.291895
$993$	−4805.00	−0.153557
$994$	−20040.0	−0.639467
$995$	2030.00	0.0646787
$996$	−11440.0	−0.363946
$997$	31550.0	1.00221	0.501103	−	0.865388i	$-0.332928\pi$
$997$	31550.0	1.00221	0.501103	+	0.865388i	$0.332928\pi$
$998$	−21358.0	−0.677431
$999$	−57710.0	−1.82769

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.a.1.1	✓	1	1.1	even	1	trivial
1150.4.a.i.1.1		1	5.4	even	2
1150.4.b.h.599.1		2	5.2	odd	4
1150.4.b.h.599.2		2	5.3	odd	4
1840.4.a.g.1.1		1	4.3	odd	2
2070.4.a.o.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 $\F_{q}$

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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