LMFDB - Embedded newform 230.4.a.b.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)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +3.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +3.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +10.0000 q^{10} -2.00000 q^{11} +16.0000 q^{12} -38.0000 q^{13} -6.00000 q^{14} -20.0000 q^{15} +16.0000 q^{16} -45.0000 q^{17} +22.0000 q^{18} -74.0000 q^{19} -20.0000 q^{20} +12.0000 q^{21} +4.00000 q^{22} +23.0000 q^{23} -32.0000 q^{24} +25.0000 q^{25} +76.0000 q^{26} -152.000 q^{27} +12.0000 q^{28} +283.000 q^{29} +40.0000 q^{30} -303.000 q^{31} -32.0000 q^{32} -8.00000 q^{33} +90.0000 q^{34} -15.0000 q^{35} -44.0000 q^{36} +79.0000 q^{37} +148.000 q^{38} -152.000 q^{39} +40.0000 q^{40} -407.000 q^{41} -24.0000 q^{42} -328.000 q^{43} -8.00000 q^{44} +55.0000 q^{45} -46.0000 q^{46} +360.000 q^{47} +64.0000 q^{48} -334.000 q^{49} -50.0000 q^{50} -180.000 q^{51} -152.000 q^{52} -561.000 q^{53} +304.000 q^{54} +10.0000 q^{55} -24.0000 q^{56} -296.000 q^{57} -566.000 q^{58} +101.000 q^{59} -80.0000 q^{60} -268.000 q^{61} +606.000 q^{62} -33.0000 q^{63} +64.0000 q^{64} +190.000 q^{65} +16.0000 q^{66} -69.0000 q^{67} -180.000 q^{68} +92.0000 q^{69} +30.0000 q^{70} -641.000 q^{71} +88.0000 q^{72} +994.000 q^{73} -158.000 q^{74} +100.000 q^{75} -296.000 q^{76} -6.00000 q^{77} +304.000 q^{78} -884.000 q^{79} -80.0000 q^{80} -311.000 q^{81} +814.000 q^{82} +503.000 q^{83} +48.0000 q^{84} +225.000 q^{85} +656.000 q^{86} +1132.00 q^{87} +16.0000 q^{88} +1608.00 q^{89} -110.000 q^{90} -114.000 q^{91} +92.0000 q^{92} -1212.00 q^{93} -720.000 q^{94} +370.000 q^{95} -128.000 q^{96} +1082.00 q^{97} +668.000 q^{98} +22.0000 q^{99} +O(q^{100})\)

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
$3$	4.00000	0.769800	0.384900	−	0.922958i	$-0.374236\pi$
$3$	4.00000	0.769800	0.384900	+	0.922958i	$0.374236\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−8.00000	−0.544331
$7$	3.00000	0.161985	0.0809924	−	0.996715i	$-0.474191\pi$
$7$	3.00000	0.161985	0.0809924	+	0.996715i	$0.474191\pi$
$8$	−8.00000	−0.353553
$9$	−11.0000	−0.407407
$10$	10.0000	0.316228
$11$	−2.00000	−0.0548202	−0.0274101	−	0.999624i	$-0.508726\pi$
$11$	−2.00000	−0.0548202	−0.0274101	+	0.999624i	$0.508726\pi$
$12$	16.0000	0.384900
$13$	−38.0000	−0.810716	−0.405358	−	0.914158i	$-0.632853\pi$
$13$	−38.0000	−0.810716	−0.405358	+	0.914158i	$0.632853\pi$
$14$	−6.00000	−0.114541
$15$	−20.0000	−0.344265
$16$	16.0000	0.250000
$17$	−45.0000	−0.642006	−0.321003	−	0.947078i	$-0.604020\pi$
$17$	−45.0000	−0.642006	−0.321003	+	0.947078i	$0.604020\pi$
$18$	22.0000	0.288081
$19$	−74.0000	−0.893514	−0.446757	−	0.894655i	$-0.647421\pi$
$19$	−74.0000	−0.893514	−0.446757	+	0.894655i	$0.647421\pi$
$20$	−20.0000	−0.223607
$21$	12.0000	0.124696
$22$	4.00000	0.0387638
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−32.0000	−0.272166
$25$	25.0000	0.200000
$26$	76.0000	0.573263
$27$	−152.000	−1.08342
$28$	12.0000	0.0809924
$29$	283.000	1.81213	0.906065	−	0.423138i	$-0.139072\pi$
$29$	283.000	1.81213	0.906065	+	0.423138i	$0.139072\pi$
$30$	40.0000	0.243432
$31$	−303.000	−1.75550	−0.877748	−	0.479122i	$-0.840955\pi$
$31$	−303.000	−1.75550	−0.877748	+	0.479122i	$0.840955\pi$
$32$	−32.0000	−0.176777
$33$	−8.00000	−0.0422006
$34$	90.0000	0.453967
$35$	−15.0000	−0.0724418
$36$	−44.0000	−0.203704
$37$	79.0000	0.351014	0.175507	−	0.984478i	$-0.443844\pi$
$37$	79.0000	0.351014	0.175507	+	0.984478i	$0.443844\pi$
$38$	148.000	0.631810
$39$	−152.000	−0.624089
$40$	40.0000	0.158114
$41$	−407.000	−1.55031	−0.775155	−	0.631771i	$-0.782328\pi$
$41$	−407.000	−1.55031	−0.775155	+	0.631771i	$0.782328\pi$
$42$	−24.0000	−0.0881733
$43$	−328.000	−1.16324	−0.581622	−	0.813459i	$-0.697582\pi$
$43$	−328.000	−1.16324	−0.581622	+	0.813459i	$0.697582\pi$
$44$	−8.00000	−0.0274101
$45$	55.0000	0.182198
$46$	−46.0000	−0.147442
$47$	360.000	1.11726	0.558632	−	0.829416i	$-0.311326\pi$
$47$	360.000	1.11726	0.558632	+	0.829416i	$0.311326\pi$
$48$	64.0000	0.192450
$49$	−334.000	−0.973761
$50$	−50.0000	−0.141421
$51$	−180.000	−0.494217
$52$	−152.000	−0.405358
$53$	−561.000	−1.45395	−0.726974	−	0.686665i	$-0.759074\pi$
$53$	−561.000	−1.45395	−0.726974	+	0.686665i	$0.759074\pi$
$54$	304.000	0.766096
$55$	10.0000	0.0245164
$56$	−24.0000	−0.0572703
$57$	−296.000	−0.687827
$58$	−566.000	−1.28137
$59$	101.000	0.222866	0.111433	−	0.993772i	$-0.464456\pi$
$59$	101.000	0.222866	0.111433	+	0.993772i	$0.464456\pi$
$60$	−80.0000	−0.172133
$61$	−268.000	−0.562523	−0.281261	−	0.959631i	$-0.590753\pi$
$61$	−268.000	−0.562523	−0.281261	+	0.959631i	$0.590753\pi$
$62$	606.000	1.24132
$63$	−33.0000	−0.0659938
$64$	64.0000	0.125000
$65$	190.000	0.362563
$66$	16.0000	0.0298404
$67$	−69.0000	−0.125816	−0.0629081	−	0.998019i	$-0.520038\pi$
$67$	−69.0000	−0.125816	−0.0629081	+	0.998019i	$0.520038\pi$
$68$	−180.000	−0.321003
$69$	92.0000	0.160514
$70$	30.0000	0.0512241
$71$	−641.000	−1.07145	−0.535723	−	0.844394i	$-0.679961\pi$
$71$	−641.000	−1.07145	−0.535723	+	0.844394i	$0.679961\pi$
$72$	88.0000	0.144040
$73$	994.000	1.59368	0.796842	−	0.604188i	$-0.206502\pi$
$73$	994.000	1.59368	0.796842	+	0.604188i	$0.206502\pi$
$74$	−158.000	−0.248204
$75$	100.000	0.153960
$76$	−296.000	−0.446757
$77$	−6.00000	−0.00888004
$78$	304.000	0.441298
$79$	−884.000	−1.25896	−0.629480	−	0.777017i	$-0.716732\pi$
$79$	−884.000	−1.25896	−0.629480	+	0.777017i	$0.716732\pi$
$80$	−80.0000	−0.111803
$81$	−311.000	−0.426612
$82$	814.000	1.09623
$83$	503.000	0.665198	0.332599	−	0.943068i	$-0.392074\pi$
$83$	503.000	0.665198	0.332599	+	0.943068i	$0.392074\pi$
$84$	48.0000	0.0623480
$85$	225.000	0.287114
$86$	656.000	0.822538
$87$	1132.00	1.39498
$88$	16.0000	0.0193819
$89$	1608.00	1.91514	0.957571	−	0.288197i	$-0.0930558\pi$
$89$	1608.00	1.91514	0.957571	+	0.288197i	$0.0930558\pi$
$90$	−110.000	−0.128834
$91$	−114.000	−0.131324
$92$	92.0000	0.104257
$93$	−1212.00	−1.35138
$94$	−720.000	−0.790025
$95$	370.000	0.399592
$96$	−128.000	−0.136083
$97$	1082.00	1.13258	0.566291	−	0.824205i	$-0.308378\pi$
$97$	1082.00	1.13258	0.566291	+	0.824205i	$0.308378\pi$
$98$	668.000	0.688553
$99$	22.0000	0.0223342
$100$	100.000	0.100000
$101$	879.000	0.865978	0.432989	−	0.901399i	$-0.357459\pi$
$101$	879.000	0.865978	0.432989	+	0.901399i	$0.357459\pi$
$102$	360.000	0.349464
$103$	360.000	0.344387	0.172193	−	0.985063i	$-0.444915\pi$
$103$	360.000	0.344387	0.172193	+	0.985063i	$0.444915\pi$
$104$	304.000	0.286631
$105$	−60.0000	−0.0557657
$106$	1122.00	1.02810
$107$	1815.00	1.63984	0.819919	−	0.572480i	$-0.194018\pi$
$107$	1815.00	1.63984	0.819919	+	0.572480i	$0.194018\pi$
$108$	−608.000	−0.541711
$109$	−430.000	−0.377858	−0.188929	−	0.981991i	$-0.560502\pi$
$109$	−430.000	−0.377858	−0.188929	+	0.981991i	$0.560502\pi$
$110$	−20.0000	−0.0173357
$111$	316.000	0.270211
$112$	48.0000	0.0404962
$113$	255.000	0.212287	0.106143	−	0.994351i	$-0.466150\pi$
$113$	255.000	0.212287	0.106143	+	0.994351i	$0.466150\pi$
$114$	592.000	0.486367
$115$	−115.000	−0.0932505
$116$	1132.00	0.906065
$117$	418.000	0.330292
$118$	−202.000	−0.157590
$119$	−135.000	−0.103995
$120$	160.000	0.121716
$121$	−1327.00	−0.996995
$122$	536.000	0.397764
$123$	−1628.00	−1.19343
$124$	−1212.00	−0.877748
$125$	−125.000	−0.0894427
$126$	66.0000	0.0466647
$127$	344.000	0.240355	0.120177	−	0.992752i	$-0.461654\pi$
$127$	344.000	0.240355	0.120177	+	0.992752i	$0.461654\pi$
$128$	−128.000	−0.0883883
$129$	−1312.00	−0.895466
$130$	−380.000	−0.256371
$131$	−1348.00	−0.899048	−0.449524	−	0.893268i	$-0.648406\pi$
$131$	−1348.00	−0.899048	−0.449524	+	0.893268i	$0.648406\pi$
$132$	−32.0000	−0.0211003
$133$	−222.000	−0.144736
$134$	138.000	0.0889656
$135$	760.000	0.484521
$136$	360.000	0.226983
$137$	734.000	0.457736	0.228868	−	0.973457i	$-0.426498\pi$
$137$	734.000	0.457736	0.228868	+	0.973457i	$0.426498\pi$
$138$	−184.000	−0.113501
$139$	2659.00	1.62254	0.811271	−	0.584670i	$-0.198776\pi$
$139$	2659.00	1.62254	0.811271	+	0.584670i	$0.198776\pi$
$140$	−60.0000	−0.0362209
$141$	1440.00	0.860070
$142$	1282.00	0.757627
$143$	76.0000	0.0444436
$144$	−176.000	−0.101852
$145$	−1415.00	−0.810409
$146$	−1988.00	−1.12690
$147$	−1336.00	−0.749602
$148$	316.000	0.175507
$149$	−3196.00	−1.75722	−0.878612	−	0.477535i	$-0.841530\pi$
$149$	−3196.00	−1.75722	−0.878612	+	0.477535i	$0.841530\pi$
$150$	−200.000	−0.108866
$151$	−100.000	−0.0538933	−0.0269466	−	0.999637i	$-0.508578\pi$
$151$	−100.000	−0.0538933	−0.0269466	+	0.999637i	$0.508578\pi$
$152$	592.000	0.315905
$153$	495.000	0.261558
$154$	12.0000	0.00627914
$155$	1515.00	0.785082
$156$	−608.000	−0.312045
$157$	−787.000	−0.400060	−0.200030	−	0.979790i	$-0.564104\pi$
$157$	−787.000	−0.400060	−0.200030	+	0.979790i	$0.564104\pi$
$158$	1768.00	0.890219
$159$	−2244.00	−1.11925
$160$	160.000	0.0790569
$161$	69.0000	0.0337762
$162$	622.000	0.301660
$163$	−70.0000	−0.0336370	−0.0168185	−	0.999859i	$-0.505354\pi$
$163$	−70.0000	−0.0336370	−0.0168185	+	0.999859i	$0.505354\pi$
$164$	−1628.00	−0.775155
$165$	40.0000	0.0188727
$166$	−1006.00	−0.470366
$167$	1784.00	0.826647	0.413324	−	0.910584i	$-0.364368\pi$
$167$	1784.00	0.826647	0.413324	+	0.910584i	$0.364368\pi$
$168$	−96.0000	−0.0440867
$169$	−753.000	−0.342740
$170$	−450.000	−0.203020
$171$	814.000	0.364024
$172$	−1312.00	−0.581622
$173$	−28.0000	−0.0123052	−0.00615260	−	0.999981i	$-0.501958\pi$
$173$	−28.0000	−0.0123052	−0.00615260	+	0.999981i	$0.501958\pi$
$174$	−2264.00	−0.986399
$175$	75.0000	0.0323970
$176$	−32.0000	−0.0137051
$177$	404.000	0.171562
$178$	−3216.00	−1.35421
$179$	−32.0000	−0.0133620	−0.00668098	−	0.999978i	$-0.502127\pi$
$179$	−32.0000	−0.0133620	−0.00668098	+	0.999978i	$0.502127\pi$
$180$	220.000	0.0910991
$181$	−1172.00	−0.481293	−0.240647	−	0.970613i	$-0.577359\pi$
$181$	−1172.00	−0.481293	−0.240647	+	0.970613i	$0.577359\pi$
$182$	228.000	0.0928598
$183$	−1072.00	−0.433030
$184$	−184.000	−0.0737210
$185$	−395.000	−0.156978
$186$	2424.00	0.955572
$187$	90.0000	0.0351949
$188$	1440.00	0.558632
$189$	−456.000	−0.175498
$190$	−740.000	−0.282554
$191$	−648.000	−0.245485	−0.122742	−	0.992439i	$-0.539169\pi$
$191$	−648.000	−0.245485	−0.122742	+	0.992439i	$0.539169\pi$
$192$	256.000	0.0962250
$193$	−772.000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−772.000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−2164.00	−0.800856
$195$	760.000	0.279101
$196$	−1336.00	−0.486880
$197$	−66.0000	−0.0238696	−0.0119348	−	0.999929i	$-0.503799\pi$
$197$	−66.0000	−0.0238696	−0.0119348	+	0.999929i	$0.503799\pi$
$198$	−44.0000	−0.0157926
$199$	−3358.00	−1.19619	−0.598096	−	0.801424i	$-0.704076\pi$
$199$	−3358.00	−1.19619	−0.598096	+	0.801424i	$0.704076\pi$
$200$	−200.000	−0.0707107
$201$	−276.000	−0.0968534
$202$	−1758.00	−0.612339
$203$	849.000	0.293538
$204$	−720.000	−0.247108
$205$	2035.00	0.693320
$206$	−720.000	−0.243518
$207$	−253.000	−0.0849503
$208$	−608.000	−0.202679
$209$	148.000	0.0489827
$210$	120.000	0.0394323
$211$	4489.00	1.46462	0.732312	−	0.680970i	$-0.238441\pi$
$211$	4489.00	1.46462	0.732312	+	0.680970i	$0.238441\pi$
$212$	−2244.00	−0.726974
$213$	−2564.00	−0.824800
$214$	−3630.00	−1.15954
$215$	1640.00	0.520219
$216$	1216.00	0.383048
$217$	−909.000	−0.284364
$218$	860.000	0.267186
$219$	3976.00	1.22682
$220$	40.0000	0.0122582
$221$	1710.00	0.520484
$222$	−632.000	−0.191068
$223$	1990.00	0.597580	0.298790	−	0.954319i	$-0.403417\pi$
$223$	1990.00	0.597580	0.298790	+	0.954319i	$0.403417\pi$
$224$	−96.0000	−0.0286351
$225$	−275.000	−0.0814815
$226$	−510.000	−0.150109
$227$	5524.00	1.61516	0.807579	−	0.589760i	$-0.200778\pi$
$227$	5524.00	1.61516	0.807579	+	0.589760i	$0.200778\pi$
$228$	−1184.00	−0.343914
$229$	−1300.00	−0.375137	−0.187569	−	0.982252i	$-0.560061\pi$
$229$	−1300.00	−0.375137	−0.187569	+	0.982252i	$0.560061\pi$
$230$	230.000	0.0659380
$231$	−24.0000	−0.00683586
$232$	−2264.00	−0.640685
$233$	−1212.00	−0.340776	−0.170388	−	0.985377i	$-0.554502\pi$
$233$	−1212.00	−0.340776	−0.170388	+	0.985377i	$0.554502\pi$
$234$	−836.000	−0.233551
$235$	−1800.00	−0.499656
$236$	404.000	0.111433
$237$	−3536.00	−0.969147
$238$	270.000	0.0735357
$239$	2761.00	0.747256	0.373628	−	0.927579i	$-0.378114\pi$
$239$	2761.00	0.747256	0.373628	+	0.927579i	$0.378114\pi$
$240$	−320.000	−0.0860663
$241$	−5742.00	−1.53475	−0.767375	−	0.641199i	$-0.778437\pi$
$241$	−5742.00	−1.53475	−0.767375	+	0.641199i	$0.778437\pi$
$242$	2654.00	0.704982
$243$	2860.00	0.755017
$244$	−1072.00	−0.281261
$245$	1670.00	0.435479
$246$	3256.00	0.843882
$247$	2812.00	0.724386
$248$	2424.00	0.620662
$249$	2012.00	0.512070
$250$	250.000	0.0632456
$251$	−4162.00	−1.04663	−0.523313	−	0.852141i	$-0.675304\pi$
$251$	−4162.00	−1.04663	−0.523313	+	0.852141i	$0.675304\pi$
$252$	−132.000	−0.0329969
$253$	−46.0000	−0.0114308
$254$	−688.000	−0.169957
$255$	900.000	0.221020
$256$	256.000	0.0625000
$257$	2464.00	0.598055	0.299027	−	0.954245i	$-0.403338\pi$
$257$	2464.00	0.598055	0.299027	+	0.954245i	$0.403338\pi$
$258$	2624.00	0.633190
$259$	237.000	0.0568589
$260$	760.000	0.181282
$261$	−3113.00	−0.738275
$262$	2696.00	0.635723
$263$	−4167.00	−0.976989	−0.488495	−	0.872567i	$-0.662454\pi$
$263$	−4167.00	−0.976989	−0.488495	+	0.872567i	$0.662454\pi$
$264$	64.0000	0.0149202
$265$	2805.00	0.650226
$266$	444.000	0.102344
$267$	6432.00	1.47428
$268$	−276.000	−0.0629081
$269$	−1639.00	−0.371493	−0.185746	−	0.982598i	$-0.559470\pi$
$269$	−1639.00	−0.371493	−0.185746	+	0.982598i	$0.559470\pi$
$270$	−1520.00	−0.342608
$271$	2655.00	0.595128	0.297564	−	0.954702i	$-0.403826\pi$
$271$	2655.00	0.595128	0.297564	+	0.954702i	$0.403826\pi$
$272$	−720.000	−0.160502
$273$	−456.000	−0.101093
$274$	−1468.00	−0.323668
$275$	−50.0000	−0.0109640
$276$	368.000	0.0802572
$277$	−826.000	−0.179168	−0.0895840	−	0.995979i	$-0.528554\pi$
$277$	−826.000	−0.179168	−0.0895840	+	0.995979i	$0.528554\pi$
$278$	−5318.00	−1.14731
$279$	3333.00	0.715202
$280$	120.000	0.0256120
$281$	3930.00	0.834321	0.417160	−	0.908833i	$-0.363025\pi$
$281$	3930.00	0.834321	0.417160	+	0.908833i	$0.363025\pi$
$282$	−2880.00	−0.608161
$283$	−7339.00	−1.54155	−0.770774	−	0.637108i	$-0.780130\pi$
$283$	−7339.00	−1.54155	−0.770774	+	0.637108i	$0.780130\pi$
$284$	−2564.00	−0.535723
$285$	1480.00	0.307606
$286$	−152.000	−0.0314264
$287$	−1221.00	−0.251127
$288$	352.000	0.0720201
$289$	−2888.00	−0.587828
$290$	2830.00	0.573046
$291$	4328.00	0.871862
$292$	3976.00	0.796842
$293$	−4763.00	−0.949684	−0.474842	−	0.880071i	$-0.657495\pi$
$293$	−4763.00	−0.949684	−0.474842	+	0.880071i	$0.657495\pi$
$294$	2672.00	0.530048
$295$	−505.000	−0.0996686
$296$	−632.000	−0.124102
$297$	304.000	0.0593935
$298$	6392.00	1.24255
$299$	−874.000	−0.169046
$300$	400.000	0.0769800
$301$	−984.000	−0.188428
$302$	200.000	0.0381083
$303$	3516.00	0.666630
$304$	−1184.00	−0.223378
$305$	1340.00	0.251568
$306$	−990.000	−0.184949
$307$	−4238.00	−0.787868	−0.393934	−	0.919139i	$-0.628886\pi$
$307$	−4238.00	−0.787868	−0.393934	+	0.919139i	$0.628886\pi$
$308$	−24.0000	−0.00444002
$309$	1440.00	0.265109
$310$	−3030.00	−0.555137
$311$	4352.00	0.793503	0.396751	−	0.917926i	$-0.370138\pi$
$311$	4352.00	0.793503	0.396751	+	0.917926i	$0.370138\pi$
$312$	1216.00	0.220649
$313$	−515.000	−0.0930017	−0.0465008	−	0.998918i	$-0.514807\pi$
$313$	−515.000	−0.0930017	−0.0465008	+	0.998918i	$0.514807\pi$
$314$	1574.00	0.282885
$315$	165.000	0.0295133
$316$	−3536.00	−0.629480
$317$	−6816.00	−1.20765	−0.603824	−	0.797117i	$-0.706357\pi$
$317$	−6816.00	−1.20765	−0.603824	+	0.797117i	$0.706357\pi$
$318$	4488.00	0.791429
$319$	−566.000	−0.0993414
$320$	−320.000	−0.0559017
$321$	7260.00	1.26235
$322$	−138.000	−0.0238834
$323$	3330.00	0.573641
$324$	−1244.00	−0.213306
$325$	−950.000	−0.162143
$326$	140.000	0.0237849
$327$	−1720.00	−0.290875
$328$	3256.00	0.548117
$329$	1080.00	0.180980
$330$	−80.0000	−0.0133450
$331$	−8795.00	−1.46047	−0.730237	−	0.683194i	$-0.760590\pi$
$331$	−8795.00	−1.46047	−0.730237	+	0.683194i	$0.760590\pi$
$332$	2012.00	0.332599
$333$	−869.000	−0.143006
$334$	−3568.00	−0.584528
$335$	345.000	0.0562668
$336$	192.000	0.0311740
$337$	−10654.0	−1.72214	−0.861069	−	0.508488i	$-0.830204\pi$
$337$	−10654.0	−1.72214	−0.861069	+	0.508488i	$0.830204\pi$
$338$	1506.00	0.242354
$339$	1020.00	0.163418
$340$	900.000	0.143557
$341$	606.000	0.0962368
$342$	−1628.00	−0.257404
$343$	−2031.00	−0.319719
$344$	2624.00	0.411269
$345$	−460.000	−0.0717843
$346$	56.0000	0.00870109
$347$	6624.00	1.02477	0.512385	−	0.858756i	$-0.328762\pi$
$347$	6624.00	1.02477	0.512385	+	0.858756i	$0.328762\pi$
$348$	4528.00	0.697489
$349$	9719.00	1.49068	0.745338	−	0.666686i	$-0.232288\pi$
$349$	9719.00	1.49068	0.745338	+	0.666686i	$0.232288\pi$
$350$	−150.000	−0.0229081
$351$	5776.00	0.878348
$352$	64.0000	0.00969094
$353$	664.000	0.100117	0.0500583	−	0.998746i	$-0.484059\pi$
$353$	664.000	0.100117	0.0500583	+	0.998746i	$0.484059\pi$
$354$	−808.000	−0.121313
$355$	3205.00	0.479165
$356$	6432.00	0.957571
$357$	−540.000	−0.0800555
$358$	64.0000	0.00944834
$359$	5600.00	0.823278	0.411639	−	0.911347i	$-0.364957\pi$
$359$	5600.00	0.823278	0.411639	+	0.911347i	$0.364957\pi$
$360$	−440.000	−0.0644168
$361$	−1383.00	−0.201633
$362$	2344.00	0.340326
$363$	−5308.00	−0.767487
$364$	−456.000	−0.0656618
$365$	−4970.00	−0.712717
$366$	2144.00	0.306199
$367$	5689.00	0.809165	0.404582	−	0.914502i	$-0.367417\pi$
$367$	5689.00	0.809165	0.404582	+	0.914502i	$0.367417\pi$
$368$	368.000	0.0521286
$369$	4477.00	0.631608
$370$	790.000	0.111000
$371$	−1683.00	−0.235518
$372$	−4848.00	−0.675691
$373$	−10626.0	−1.47505	−0.737525	−	0.675320i	$-0.764005\pi$
$373$	−10626.0	−1.47505	−0.737525	+	0.675320i	$0.764005\pi$
$374$	−180.000	−0.0248866
$375$	−500.000	−0.0688530
$376$	−2880.00	−0.395012
$377$	−10754.0	−1.46912
$378$	912.000	0.124096
$379$	5160.00	0.699344	0.349672	−	0.936872i	$-0.386293\pi$
$379$	5160.00	0.699344	0.349672	+	0.936872i	$0.386293\pi$
$380$	1480.00	0.199796
$381$	1376.00	0.185025
$382$	1296.00	0.173584
$383$	−11063.0	−1.47596	−0.737980	−	0.674822i	$-0.764220\pi$
$383$	−11063.0	−1.47596	−0.737980	+	0.674822i	$0.764220\pi$
$384$	−512.000	−0.0680414
$385$	30.0000	0.00397128
$386$	1544.00	0.203595
$387$	3608.00	0.473915
$388$	4328.00	0.566291
$389$	−5374.00	−0.700444	−0.350222	−	0.936667i	$-0.613894\pi$
$389$	−5374.00	−0.700444	−0.350222	+	0.936667i	$0.613894\pi$
$390$	−1520.00	−0.197354
$391$	−1035.00	−0.133868
$392$	2672.00	0.344276
$393$	−5392.00	−0.692088
$394$	132.000	0.0168783
$395$	4420.00	0.563024
$396$	88.0000	0.0111671
$397$	376.000	0.0475338	0.0237669	−	0.999718i	$-0.492434\pi$
$397$	376.000	0.0475338	0.0237669	+	0.999718i	$0.492434\pi$
$398$	6716.00	0.845836
$399$	−888.000	−0.111418
$400$	400.000	0.0500000
$401$	−7790.00	−0.970110	−0.485055	−	0.874484i	$-0.661200\pi$
$401$	−7790.00	−0.970110	−0.485055	+	0.874484i	$0.661200\pi$
$402$	552.000	0.0684857
$403$	11514.0	1.42321
$404$	3516.00	0.432989
$405$	1555.00	0.190787
$406$	−1698.00	−0.207562
$407$	−158.000	−0.0192427
$408$	1440.00	0.174732
$409$	11909.0	1.43976	0.719880	−	0.694098i	$-0.244197\pi$
$409$	11909.0	1.43976	0.719880	+	0.694098i	$0.244197\pi$
$410$	−4070.00	−0.490251
$411$	2936.00	0.352365
$412$	1440.00	0.172193
$413$	303.000	0.0361009
$414$	506.000	0.0600689
$415$	−2515.00	−0.297486
$416$	1216.00	0.143316
$417$	10636.0	1.24903
$418$	−296.000	−0.0346360
$419$	9162.00	1.06824	0.534121	−	0.845408i	$-0.320643\pi$
$419$	9162.00	1.06824	0.534121	+	0.845408i	$0.320643\pi$
$420$	−240.000	−0.0278829
$421$	2086.00	0.241486	0.120743	−	0.992684i	$-0.461472\pi$
$421$	2086.00	0.241486	0.120743	+	0.992684i	$0.461472\pi$
$422$	−8978.00	−1.03565
$423$	−3960.00	−0.455182
$424$	4488.00	0.514048
$425$	−1125.00	−0.128401
$426$	5128.00	0.583222
$427$	−804.000	−0.0911201
$428$	7260.00	0.819919
$429$	304.000	0.0342127
$430$	−3280.00	−0.367850
$431$	−9824.00	−1.09792	−0.548962	−	0.835847i	$-0.684977\pi$
$431$	−9824.00	−1.09792	−0.548962	+	0.835847i	$0.684977\pi$
$432$	−2432.00	−0.270856
$433$	−1793.00	−0.198998	−0.0994989	−	0.995038i	$-0.531724\pi$
$433$	−1793.00	−0.198998	−0.0994989	+	0.995038i	$0.531724\pi$
$434$	1818.00	0.201076
$435$	−5660.00	−0.623853
$436$	−1720.00	−0.188929
$437$	−1702.00	−0.186311
$438$	−7952.00	−0.867491
$439$	−7544.00	−0.820172	−0.410086	−	0.912047i	$-0.634501\pi$
$439$	−7544.00	−0.820172	−0.410086	+	0.912047i	$0.634501\pi$
$440$	−80.0000	−0.00866784
$441$	3674.00	0.396717
$442$	−3420.00	−0.368038
$443$	6548.00	0.702268	0.351134	−	0.936325i	$-0.385796\pi$
$443$	6548.00	0.702268	0.351134	+	0.936325i	$0.385796\pi$
$444$	1264.00	0.135105
$445$	−8040.00	−0.856478
$446$	−3980.00	−0.422553
$447$	−12784.0	−1.35271
$448$	192.000	0.0202481
$449$	14235.0	1.49619	0.748097	−	0.663589i	$-0.230968\pi$
$449$	14235.0	1.49619	0.748097	+	0.663589i	$0.230968\pi$
$450$	550.000	0.0576161
$451$	814.000	0.0849884
$452$	1020.00	0.106143
$453$	−400.000	−0.0414871
$454$	−11048.0	−1.14209
$455$	570.000	0.0587297
$456$	2368.00	0.243184
$457$	−8039.00	−0.822863	−0.411432	−	0.911441i	$-0.634971\pi$
$457$	−8039.00	−0.822863	−0.411432	+	0.911441i	$0.634971\pi$
$458$	2600.00	0.265262
$459$	6840.00	0.695564
$460$	−460.000	−0.0466252
$461$	−9354.00	−0.945031	−0.472515	−	0.881322i	$-0.656654\pi$
$461$	−9354.00	−0.945031	−0.472515	+	0.881322i	$0.656654\pi$
$462$	48.0000	0.00483368
$463$	−2402.00	−0.241102	−0.120551	−	0.992707i	$-0.538466\pi$
$463$	−2402.00	−0.241102	−0.120551	+	0.992707i	$0.538466\pi$
$464$	4528.00	0.453033
$465$	6060.00	0.604356
$466$	2424.00	0.240965
$467$	−14529.0	−1.43966	−0.719831	−	0.694150i	$-0.755781\pi$
$467$	−14529.0	−1.43966	−0.719831	+	0.694150i	$0.755781\pi$
$468$	1672.00	0.165146
$469$	−207.000	−0.0203803
$470$	3600.00	0.353310
$471$	−3148.00	−0.307966
$472$	−808.000	−0.0787949
$473$	656.000	0.0637694
$474$	7072.00	0.685291
$475$	−1850.00	−0.178703
$476$	−540.000	−0.0519976
$477$	6171.00	0.592349
$478$	−5522.00	−0.528390
$479$	1724.00	0.164450	0.0822250	−	0.996614i	$-0.473797\pi$
$479$	1724.00	0.164450	0.0822250	+	0.996614i	$0.473797\pi$
$480$	640.000	0.0608581
$481$	−3002.00	−0.284573
$482$	11484.0	1.08523
$483$	276.000	0.0260009
$484$	−5308.00	−0.498497
$485$	−5410.00	−0.506506
$486$	−5720.00	−0.533878
$487$	−9920.00	−0.923035	−0.461518	−	0.887131i	$-0.652695\pi$
$487$	−9920.00	−0.923035	−0.461518	+	0.887131i	$0.652695\pi$
$488$	2144.00	0.198882
$489$	−280.000	−0.0258937
$490$	−3340.00	−0.307930
$491$	−8665.00	−0.796428	−0.398214	−	0.917293i	$-0.630370\pi$
$491$	−8665.00	−0.796428	−0.398214	+	0.917293i	$0.630370\pi$
$492$	−6512.00	−0.596715
$493$	−12735.0	−1.16340
$494$	−5624.00	−0.512218
$495$	−110.000	−0.00998815
$496$	−4848.00	−0.438874
$497$	−1923.00	−0.173558
$498$	−4024.00	−0.362088
$499$	−12673.0	−1.13692	−0.568458	−	0.822712i	$-0.692460\pi$
$499$	−12673.0	−1.13692	−0.568458	+	0.822712i	$0.692460\pi$
$500$	−500.000	−0.0447214
$501$	7136.00	0.636353
$502$	8324.00	0.740076
$503$	−3667.00	−0.325057	−0.162528	−	0.986704i	$-0.551965\pi$
$503$	−3667.00	−0.325057	−0.162528	+	0.986704i	$0.551965\pi$
$504$	264.000	0.0233323
$505$	−4395.00	−0.387277
$506$	92.0000	0.00808280
$507$	−3012.00	−0.263841
$508$	1376.00	0.120177
$509$	−13246.0	−1.15347	−0.576737	−	0.816930i	$-0.695674\pi$
$509$	−13246.0	−1.15347	−0.576737	+	0.816930i	$0.695674\pi$
$510$	−1800.00	−0.156285
$511$	2982.00	0.258152
$512$	−512.000	−0.0441942
$513$	11248.0	0.968053
$514$	−4928.00	−0.422889
$515$	−1800.00	−0.154015
$516$	−5248.00	−0.447733
$517$	−720.000	−0.0612487
$518$	−474.000	−0.0402053
$519$	−112.000	−0.00947255
$520$	−1520.00	−0.128185
$521$	−4934.00	−0.414899	−0.207450	−	0.978246i	$-0.566516\pi$
$521$	−4934.00	−0.414899	−0.207450	+	0.978246i	$0.566516\pi$
$522$	6226.00	0.522039
$523$	17436.0	1.45779	0.728894	−	0.684627i	$-0.240035\pi$
$523$	17436.0	1.45779	0.728894	+	0.684627i	$0.240035\pi$
$524$	−5392.00	−0.449524
$525$	300.000	0.0249392
$526$	8334.00	0.690836
$527$	13635.0	1.12704
$528$	−128.000	−0.0105502
$529$	529.000	0.0434783
$530$	−5610.00	−0.459779
$531$	−1111.00	−0.0907972
$532$	−888.000	−0.0723678
$533$	15466.0	1.25686
$534$	−12864.0	−1.04247
$535$	−9075.00	−0.733358
$536$	552.000	0.0444828
$537$	−128.000	−0.0102860
$538$	3278.00	0.262685
$539$	668.000	0.0533818
$540$	3040.00	0.242261
$541$	−1714.00	−0.136212	−0.0681059	−	0.997678i	$-0.521696\pi$
$541$	−1714.00	−0.136212	−0.0681059	+	0.997678i	$0.521696\pi$
$542$	−5310.00	−0.420819
$543$	−4688.00	−0.370500
$544$	1440.00	0.113492
$545$	2150.00	0.168983
$546$	912.000	0.0714835
$547$	9616.00	0.751646	0.375823	−	0.926691i	$-0.377360\pi$
$547$	9616.00	0.751646	0.375823	+	0.926691i	$0.377360\pi$
$548$	2936.00	0.228868
$549$	2948.00	0.229176
$550$	100.000	0.00775275
$551$	−20942.0	−1.61916
$552$	−736.000	−0.0567504
$553$	−2652.00	−0.203932
$554$	1652.00	0.126691
$555$	−1580.00	−0.120842
$556$	10636.0	0.811271
$557$	−21385.0	−1.62677	−0.813386	−	0.581725i	$-0.802378\pi$
$557$	−21385.0	−1.62677	−0.813386	+	0.581725i	$0.802378\pi$
$558$	−6666.00	−0.505725
$559$	12464.0	0.943061
$560$	−240.000	−0.0181104
$561$	360.000	0.0270931
$562$	−7860.00	−0.589954
$563$	−5967.00	−0.446677	−0.223338	−	0.974741i	$-0.571696\pi$
$563$	−5967.00	−0.446677	−0.223338	+	0.974741i	$0.571696\pi$
$564$	5760.00	0.430035
$565$	−1275.00	−0.0949374
$566$	14678.0	1.09004
$567$	−933.000	−0.0691046
$568$	5128.00	0.378814
$569$	9714.00	0.715698	0.357849	−	0.933779i	$-0.383510\pi$
$569$	9714.00	0.715698	0.357849	+	0.933779i	$0.383510\pi$
$570$	−2960.00	−0.217510
$571$	4244.00	0.311044	0.155522	−	0.987832i	$-0.450294\pi$
$571$	4244.00	0.311044	0.155522	+	0.987832i	$0.450294\pi$
$572$	304.000	0.0222218
$573$	−2592.00	−0.188974
$574$	2442.00	0.177573
$575$	575.000	0.0417029
$576$	−704.000	−0.0509259
$577$	−15136.0	−1.09206	−0.546031	−	0.837765i	$-0.683862\pi$
$577$	−15136.0	−1.09206	−0.546031	+	0.837765i	$0.683862\pi$
$578$	5776.00	0.415657
$579$	−3088.00	−0.221646
$580$	−5660.00	−0.405205
$581$	1509.00	0.107752
$582$	−8656.00	−0.616500
$583$	1122.00	0.0797058
$584$	−7952.00	−0.563452
$585$	−2090.00	−0.147711
$586$	9526.00	0.671528
$587$	22414.0	1.57602	0.788011	−	0.615661i	$-0.211111\pi$
$587$	22414.0	1.57602	0.788011	+	0.615661i	$0.211111\pi$
$588$	−5344.00	−0.374801
$589$	22422.0	1.56856
$590$	1010.00	0.0704763
$591$	−264.000	−0.0183748
$592$	1264.00	0.0877535
$593$	22560.0	1.56227	0.781137	−	0.624360i	$-0.214640\pi$
$593$	22560.0	1.56227	0.781137	+	0.624360i	$0.214640\pi$
$594$	−608.000	−0.0419975
$595$	675.000	0.0465081
$596$	−12784.0	−0.878612
$597$	−13432.0	−0.920829
$598$	1748.00	0.119534
$599$	−1240.00	−0.0845827	−0.0422913	−	0.999105i	$-0.513466\pi$
$599$	−1240.00	−0.0845827	−0.0422913	+	0.999105i	$0.513466\pi$
$600$	−800.000	−0.0544331
$601$	27931.0	1.89572	0.947861	−	0.318683i	$-0.103241\pi$
$601$	27931.0	1.89572	0.947861	+	0.318683i	$0.103241\pi$
$602$	1968.00	0.133239
$603$	759.000	0.0512585
$604$	−400.000	−0.0269466
$605$	6635.00	0.445870
$606$	−7032.00	−0.471379
$607$	8660.00	0.579075	0.289538	−	0.957167i	$-0.406498\pi$
$607$	8660.00	0.579075	0.289538	+	0.957167i	$0.406498\pi$
$608$	2368.00	0.157952
$609$	3396.00	0.225965
$610$	−2680.00	−0.177885
$611$	−13680.0	−0.905783
$612$	1980.00	0.130779
$613$	22326.0	1.47103	0.735513	−	0.677511i	$-0.236941\pi$
$613$	22326.0	1.47103	0.735513	+	0.677511i	$0.236941\pi$
$614$	8476.00	0.557107
$615$	8140.00	0.533718
$616$	48.0000	0.00313957
$617$	−7035.00	−0.459025	−0.229513	−	0.973306i	$-0.573713\pi$
$617$	−7035.00	−0.459025	−0.229513	+	0.973306i	$0.573713\pi$
$618$	−2880.00	−0.187461
$619$	−15808.0	−1.02646	−0.513229	−	0.858252i	$-0.671551\pi$
$619$	−15808.0	−1.02646	−0.513229	+	0.858252i	$0.671551\pi$
$620$	6060.00	0.392541
$621$	−3496.00	−0.225909
$622$	−8704.00	−0.561091
$623$	4824.00	0.310224
$624$	−2432.00	−0.156022
$625$	625.000	0.0400000
$626$	1030.00	0.0657621
$627$	592.000	0.0377069
$628$	−3148.00	−0.200030
$629$	−3555.00	−0.225353
$630$	−330.000	−0.0208691
$631$	−9740.00	−0.614490	−0.307245	−	0.951630i	$-0.599407\pi$
$631$	−9740.00	−0.614490	−0.307245	+	0.951630i	$0.599407\pi$
$632$	7072.00	0.445109
$633$	17956.0	1.12747
$634$	13632.0	0.853937
$635$	−1720.00	−0.107490
$636$	−8976.00	−0.559625
$637$	12692.0	0.789443
$638$	1132.00	0.0702450
$639$	7051.00	0.436515
$640$	640.000	0.0395285
$641$	−18730.0	−1.15412	−0.577060	−	0.816702i	$-0.695800\pi$
$641$	−18730.0	−1.15412	−0.577060	+	0.816702i	$0.695800\pi$
$642$	−14520.0	−0.892615
$643$	18191.0	1.11568	0.557841	−	0.829948i	$-0.311630\pi$
$643$	18191.0	1.11568	0.557841	+	0.829948i	$0.311630\pi$
$644$	276.000	0.0168881
$645$	6560.00	0.400465
$646$	−6660.00	−0.405626
$647$	2126.00	0.129183	0.0645917	−	0.997912i	$-0.479425\pi$
$647$	2126.00	0.129183	0.0645917	+	0.997912i	$0.479425\pi$
$648$	2488.00	0.150830
$649$	−202.000	−0.0122176
$650$	1900.00	0.114653
$651$	−3636.00	−0.218903
$652$	−280.000	−0.0168185
$653$	−27478.0	−1.64670	−0.823352	−	0.567532i	$-0.807898\pi$
$653$	−27478.0	−1.64670	−0.823352	+	0.567532i	$0.807898\pi$
$654$	3440.00	0.205680
$655$	6740.00	0.402067
$656$	−6512.00	−0.387578
$657$	−10934.0	−0.649278
$658$	−2160.00	−0.127972
$659$	−25430.0	−1.50321	−0.751603	−	0.659616i	$-0.770719\pi$
$659$	−25430.0	−1.50321	−0.751603	+	0.659616i	$0.770719\pi$
$660$	160.000	0.00943635
$661$	33610.0	1.97773	0.988863	−	0.148826i	$-0.0475493\pi$
$661$	33610.0	1.97773	0.988863	+	0.148826i	$0.0475493\pi$
$662$	17590.0	1.03271
$663$	6840.00	0.400669
$664$	−4024.00	−0.235183
$665$	1110.00	0.0647278
$666$	1738.00	0.101120
$667$	6509.00	0.377855
$668$	7136.00	0.413324
$669$	7960.00	0.460017
$670$	−690.000	−0.0397866
$671$	536.000	0.0308376
$672$	−384.000	−0.0220433
$673$	20732.0	1.18746	0.593729	−	0.804665i	$-0.297655\pi$
$673$	20732.0	1.18746	0.593729	+	0.804665i	$0.297655\pi$
$674$	21308.0	1.21774
$675$	−3800.00	−0.216685
$676$	−3012.00	−0.171370
$677$	−24271.0	−1.37786	−0.688929	−	0.724829i	$-0.741919\pi$
$677$	−24271.0	−1.37786	−0.688929	+	0.724829i	$0.741919\pi$
$678$	−2040.00	−0.115554
$679$	3246.00	0.183461
$680$	−1800.00	−0.101510
$681$	22096.0	1.24335
$682$	−1212.00	−0.0680497
$683$	−14280.0	−0.800013	−0.400007	−	0.916512i	$-0.630992\pi$
$683$	−14280.0	−0.800013	−0.400007	+	0.916512i	$0.630992\pi$
$684$	3256.00	0.182012
$685$	−3670.00	−0.204706
$686$	4062.00	0.226076
$687$	−5200.00	−0.288781
$688$	−5248.00	−0.290811
$689$	21318.0	1.17874
$690$	920.000	0.0507591
$691$	−4756.00	−0.261833	−0.130917	−	0.991393i	$-0.541792\pi$
$691$	−4756.00	−0.261833	−0.130917	+	0.991393i	$0.541792\pi$
$692$	−112.000	−0.00615260
$693$	66.0000	0.00361780
$694$	−13248.0	−0.724621
$695$	−13295.0	−0.725623
$696$	−9056.00	−0.493199
$697$	18315.0	0.995309
$698$	−19438.0	−1.05407
$699$	−4848.00	−0.262329
$700$	300.000	0.0161985
$701$	5632.00	0.303449	0.151724	−	0.988423i	$-0.451517\pi$
$701$	5632.00	0.303449	0.151724	+	0.988423i	$0.451517\pi$
$702$	−11552.0	−0.621086
$703$	−5846.00	−0.313636
$704$	−128.000	−0.00685253
$705$	−7200.00	−0.384635
$706$	−1328.00	−0.0707931
$707$	2637.00	0.140275
$708$	1616.00	0.0857811
$709$	−8536.00	−0.452153	−0.226076	−	0.974110i	$-0.572590\pi$
$709$	−8536.00	−0.452153	−0.226076	+	0.974110i	$0.572590\pi$
$710$	−6410.00	−0.338821
$711$	9724.00	0.512909
$712$	−12864.0	−0.677105
$713$	−6969.00	−0.366046
$714$	1080.00	0.0566078
$715$	−380.000	−0.0198758
$716$	−128.000	−0.00668098
$717$	11044.0	0.575238
$718$	−11200.0	−0.582145
$719$	32137.0	1.66691	0.833455	−	0.552588i	$-0.186360\pi$
$719$	32137.0	1.66691	0.833455	+	0.552588i	$0.186360\pi$
$720$	880.000	0.0455495
$721$	1080.00	0.0557854
$722$	2766.00	0.142576
$723$	−22968.0	−1.18145
$724$	−4688.00	−0.240647
$725$	7075.00	0.362426
$726$	10616.0	0.542695
$727$	20329.0	1.03709	0.518543	−	0.855052i	$-0.326475\pi$
$727$	20329.0	1.03709	0.518543	+	0.855052i	$0.326475\pi$
$728$	912.000	0.0464299
$729$	19837.0	1.00782
$730$	9940.00	0.503967
$731$	14760.0	0.746810
$732$	−4288.00	−0.216515
$733$	12879.0	0.648972	0.324486	−	0.945890i	$-0.394809\pi$
$733$	12879.0	0.648972	0.324486	+	0.945890i	$0.394809\pi$
$734$	−11378.0	−0.572166
$735$	6680.00	0.335232
$736$	−736.000	−0.0368605
$737$	138.000	0.00689728
$738$	−8954.00	−0.446614
$739$	16689.0	0.830737	0.415369	−	0.909653i	$-0.363653\pi$
$739$	16689.0	0.830737	0.415369	+	0.909653i	$0.363653\pi$
$740$	−1580.00	−0.0784891
$741$	11248.0	0.557632
$742$	3366.00	0.166536
$743$	32328.0	1.59623	0.798115	−	0.602505i	$-0.205831\pi$
$743$	32328.0	1.59623	0.798115	+	0.602505i	$0.205831\pi$
$744$	9696.00	0.477786
$745$	15980.0	0.785855
$746$	21252.0	1.04302
$747$	−5533.00	−0.271007
$748$	360.000	0.0175975
$749$	5445.00	0.265629
$750$	1000.00	0.0486864
$751$	−13966.0	−0.678597	−0.339299	−	0.940679i	$-0.610190\pi$
$751$	−13966.0	−0.678597	−0.339299	+	0.940679i	$0.610190\pi$
$752$	5760.00	0.279316
$753$	−16648.0	−0.805693
$754$	21508.0	1.03883
$755$	500.000	0.0241018
$756$	−1824.00	−0.0877490
$757$	−14103.0	−0.677123	−0.338562	−	0.940944i	$-0.609940\pi$
$757$	−14103.0	−0.677123	−0.338562	+	0.940944i	$0.609940\pi$
$758$	−10320.0	−0.494511
$759$	−184.000	−0.00879944
$760$	−2960.00	−0.141277
$761$	28805.0	1.37212	0.686058	−	0.727547i	$-0.259340\pi$
$761$	28805.0	1.37212	0.686058	+	0.727547i	$0.259340\pi$
$762$	−2752.00	−0.130833
$763$	−1290.00	−0.0612073
$764$	−2592.00	−0.122742
$765$	−2475.00	−0.116972
$766$	22126.0	1.04366
$767$	−3838.00	−0.180681
$768$	1024.00	0.0481125
$769$	−26264.0	−1.23160	−0.615802	−	0.787901i	$-0.711168\pi$
$769$	−26264.0	−1.23160	−0.615802	+	0.787901i	$0.711168\pi$
$770$	−60.0000	−0.00280812
$771$	9856.00	0.460383
$772$	−3088.00	−0.143963
$773$	29622.0	1.37830	0.689152	−	0.724617i	$-0.257983\pi$
$773$	29622.0	1.37830	0.689152	+	0.724617i	$0.257983\pi$
$774$	−7216.00	−0.335108
$775$	−7575.00	−0.351099
$776$	−8656.00	−0.400428
$777$	948.000	0.0437700
$778$	10748.0	0.495289
$779$	30118.0	1.38522
$780$	3040.00	0.139551
$781$	1282.00	0.0587370
$782$	2070.00	0.0946586
$783$	−43016.0	−1.96330
$784$	−5344.00	−0.243440
$785$	3935.00	0.178912
$786$	10784.0	0.489380
$787$	−8129.00	−0.368193	−0.184096	−	0.982908i	$-0.558936\pi$
$787$	−8129.00	−0.368193	−0.184096	+	0.982908i	$0.558936\pi$
$788$	−264.000	−0.0119348
$789$	−16668.0	−0.752087
$790$	−8840.00	−0.398118
$791$	765.000	0.0343872
$792$	−176.000	−0.00789632
$793$	10184.0	0.456046
$794$	−752.000	−0.0336114
$795$	11220.0	0.500544
$796$	−13432.0	−0.598096
$797$	−35431.0	−1.57469	−0.787347	−	0.616511i	$-0.788546\pi$
$797$	−35431.0	−1.57469	−0.787347	+	0.616511i	$0.788546\pi$
$798$	1776.00	0.0787841
$799$	−16200.0	−0.717290
$800$	−800.000	−0.0353553
$801$	−17688.0	−0.780243
$802$	15580.0	0.685971
$803$	−1988.00	−0.0873661
$804$	−1104.00	−0.0484267
$805$	−345.000	−0.0151052
$806$	−23028.0	−1.00636
$807$	−6556.00	−0.285975
$808$	−7032.00	−0.306169
$809$	−36025.0	−1.56560	−0.782801	−	0.622272i	$-0.786210\pi$
$809$	−36025.0	−1.56560	−0.782801	+	0.622272i	$0.786210\pi$
$810$	−3110.00	−0.134906
$811$	−35351.0	−1.53063	−0.765315	−	0.643656i	$-0.777417\pi$
$811$	−35351.0	−1.53063	−0.765315	+	0.643656i	$0.777417\pi$
$812$	3396.00	0.146769
$813$	10620.0	0.458130
$814$	316.000	0.0136066
$815$	350.000	0.0150429
$816$	−2880.00	−0.123554
$817$	24272.0	1.03938
$818$	−23818.0	−1.01806
$819$	1254.00	0.0535022
$820$	8140.00	0.346660
$821$	−33534.0	−1.42551	−0.712756	−	0.701412i	$-0.752553\pi$
$821$	−33534.0	−1.42551	−0.712756	+	0.701412i	$0.752553\pi$
$822$	−5872.00	−0.249160
$823$	452.000	0.0191443	0.00957213	−	0.999954i	$-0.496953\pi$
$823$	452.000	0.0191443	0.00957213	+	0.999954i	$0.496953\pi$
$824$	−2880.00	−0.121759
$825$	−200.000	−0.00844013
$826$	−606.000	−0.0255272
$827$	−2379.00	−0.100031	−0.0500157	−	0.998748i	$-0.515927\pi$
$827$	−2379.00	−0.100031	−0.0500157	+	0.998748i	$0.515927\pi$
$828$	−1012.00	−0.0424752
$829$	−599.000	−0.0250955	−0.0125477	−	0.999921i	$-0.503994\pi$
$829$	−599.000	−0.0250955	−0.0125477	+	0.999921i	$0.503994\pi$
$830$	5030.00	0.210354
$831$	−3304.00	−0.137924
$832$	−2432.00	−0.101339
$833$	15030.0	0.625160
$834$	−21272.0	−0.883200
$835$	−8920.00	−0.369688
$836$	592.000	0.0244913
$837$	46056.0	1.90195
$838$	−18324.0	−0.755360
$839$	−16746.0	−0.689078	−0.344539	−	0.938772i	$-0.611965\pi$
$839$	−16746.0	−0.689078	−0.344539	+	0.938772i	$0.611965\pi$
$840$	480.000	0.0197162
$841$	55700.0	2.28382
$842$	−4172.00	−0.170756
$843$	15720.0	0.642260
$844$	17956.0	0.732312
$845$	3765.00	0.153278
$846$	7920.00	0.321862
$847$	−3981.00	−0.161498
$848$	−8976.00	−0.363487
$849$	−29356.0	−1.18668
$850$	2250.00	0.0907934
$851$	1817.00	0.0731915
$852$	−10256.0	−0.412400
$853$	−41754.0	−1.67600	−0.838001	−	0.545669i	$-0.816276\pi$
$853$	−41754.0	−1.67600	−0.838001	+	0.545669i	$0.816276\pi$
$854$	1608.00	0.0644316
$855$	−4070.00	−0.162797
$856$	−14520.0	−0.579770
$857$	−8802.00	−0.350841	−0.175420	−	0.984494i	$-0.556128\pi$
$857$	−8802.00	−0.350841	−0.175420	+	0.984494i	$0.556128\pi$
$858$	−608.000	−0.0241920
$859$	7901.00	0.313828	0.156914	−	0.987612i	$-0.449845\pi$
$859$	7901.00	0.313828	0.156914	+	0.987612i	$0.449845\pi$
$860$	6560.00	0.260109
$861$	−4884.00	−0.193317
$862$	19648.0	0.776350
$863$	−43358.0	−1.71022	−0.855112	−	0.518443i	$-0.826512\pi$
$863$	−43358.0	−1.71022	−0.855112	+	0.518443i	$0.826512\pi$
$864$	4864.00	0.191524
$865$	140.000	0.00550306
$866$	3586.00	0.140713
$867$	−11552.0	−0.452510
$868$	−3636.00	−0.142182
$869$	1768.00	0.0690164
$870$	11320.0	0.441131
$871$	2622.00	0.102001
$872$	3440.00	0.133593
$873$	−11902.0	−0.461422
$874$	3404.00	0.131741
$875$	−375.000	−0.0144884
$876$	15904.0	0.613409
$877$	−5834.00	−0.224630	−0.112315	−	0.993673i	$-0.535827\pi$
$877$	−5834.00	−0.224630	−0.112315	+	0.993673i	$0.535827\pi$
$878$	15088.0	0.579949
$879$	−19052.0	−0.731067
$880$	160.000	0.00612909
$881$	−40940.0	−1.56561	−0.782806	−	0.622266i	$-0.786212\pi$
$881$	−40940.0	−1.56561	−0.782806	+	0.622266i	$0.786212\pi$
$882$	−7348.00	−0.280522
$883$	−22756.0	−0.867271	−0.433636	−	0.901088i	$-0.642769\pi$
$883$	−22756.0	−0.867271	−0.433636	+	0.901088i	$0.642769\pi$
$884$	6840.00	0.260242
$885$	−2020.00	−0.0767249
$886$	−13096.0	−0.496579
$887$	20814.0	0.787898	0.393949	−	0.919132i	$-0.371109\pi$
$887$	20814.0	0.787898	0.393949	+	0.919132i	$0.371109\pi$
$888$	−2528.00	−0.0955339
$889$	1032.00	0.0389338
$890$	16080.0	0.605621
$891$	622.000	0.0233870
$892$	7960.00	0.298790
$893$	−26640.0	−0.998291
$894$	25568.0	0.956512
$895$	160.000	0.00597565
$896$	−384.000	−0.0143176
$897$	−3496.00	−0.130132
$898$	−28470.0	−1.05797
$899$	−85749.0	−3.18119
$900$	−1100.00	−0.0407407
$901$	25245.0	0.933444
$902$	−1628.00	−0.0600959
$903$	−3936.00	−0.145052
$904$	−2040.00	−0.0750546
$905$	5860.00	0.215241
$906$	800.000	0.0293358
$907$	−36661.0	−1.34213	−0.671063	−	0.741400i	$-0.734162\pi$
$907$	−36661.0	−1.34213	−0.671063	+	0.741400i	$0.734162\pi$
$908$	22096.0	0.807579
$909$	−9669.00	−0.352806
$910$	−1140.00	−0.0415282
$911$	22340.0	0.812467	0.406233	−	0.913769i	$-0.366842\pi$
$911$	22340.0	0.812467	0.406233	+	0.913769i	$0.366842\pi$
$912$	−4736.00	−0.171957
$913$	−1006.00	−0.0364663
$914$	16078.0	0.581852
$915$	5360.00	0.193657
$916$	−5200.00	−0.187569
$917$	−4044.00	−0.145632
$918$	−13680.0	−0.491838
$919$	−34112.0	−1.22443	−0.612215	−	0.790691i	$-0.709721\pi$
$919$	−34112.0	−1.22443	−0.612215	+	0.790691i	$0.709721\pi$
$920$	920.000	0.0329690
$921$	−16952.0	−0.606501
$922$	18708.0	0.668238
$923$	24358.0	0.868639
$924$	−96.0000	−0.00341793
$925$	1975.00	0.0702028
$926$	4804.00	0.170485
$927$	−3960.00	−0.140306
$928$	−9056.00	−0.320342
$929$	−14133.0	−0.499127	−0.249563	−	0.968358i	$-0.580287\pi$
$929$	−14133.0	−0.499127	−0.249563	+	0.968358i	$0.580287\pi$
$930$	−12120.0	−0.427345
$931$	24716.0	0.870069
$932$	−4848.00	−0.170388
$933$	17408.0	0.610839
$934$	29058.0	1.01799
$935$	−450.000	−0.0157397
$936$	−3344.00	−0.116776
$937$	22442.0	0.782442	0.391221	−	0.920297i	$-0.372053\pi$
$937$	22442.0	0.782442	0.391221	+	0.920297i	$0.372053\pi$
$938$	414.000	0.0144111
$939$	−2060.00	−0.0715927
$940$	−7200.00	−0.249828
$941$	−36076.0	−1.24978	−0.624891	−	0.780712i	$-0.714856\pi$
$941$	−36076.0	−1.24978	−0.624891	+	0.780712i	$0.714856\pi$
$942$	6296.00	0.217765
$943$	−9361.00	−0.323262
$944$	1616.00	0.0557164
$945$	2280.00	0.0784851
$946$	−1312.00	−0.0450918
$947$	−43316.0	−1.48636	−0.743179	−	0.669093i	$-0.766683\pi$
$947$	−43316.0	−1.48636	−0.743179	+	0.669093i	$0.766683\pi$
$948$	−14144.0	−0.484574
$949$	−37772.0	−1.29202
$950$	3700.00	0.126362
$951$	−27264.0	−0.929649
$952$	1080.00	0.0367679
$953$	−8326.00	−0.283007	−0.141503	−	0.989938i	$-0.545194\pi$
$953$	−8326.00	−0.283007	−0.141503	+	0.989938i	$0.545194\pi$
$954$	−12342.0	−0.418854
$955$	3240.00	0.109784
$956$	11044.0	0.373628
$957$	−2264.00	−0.0764731
$958$	−3448.00	−0.116284
$959$	2202.00	0.0741463
$960$	−1280.00	−0.0430331
$961$	62018.0	2.08177
$962$	6004.00	0.201223
$963$	−19965.0	−0.668082
$964$	−22968.0	−0.767375
$965$	3860.00	0.128765
$966$	−552.000	−0.0183854
$967$	47244.0	1.57111	0.785556	−	0.618791i	$-0.212377\pi$
$967$	47244.0	1.57111	0.785556	+	0.618791i	$0.212377\pi$
$968$	10616.0	0.352491
$969$	13320.0	0.441589
$970$	10820.0	0.358154
$971$	−40460.0	−1.33720	−0.668601	−	0.743621i	$-0.733107\pi$
$971$	−40460.0	−1.33720	−0.668601	+	0.743621i	$0.733107\pi$
$972$	11440.0	0.377508
$973$	7977.00	0.262827
$974$	19840.0	0.652684
$975$	−3800.00	−0.124818
$976$	−4288.00	−0.140631
$977$	42369.0	1.38741	0.693707	−	0.720257i	$-0.255976\pi$
$977$	42369.0	1.38741	0.693707	+	0.720257i	$0.255976\pi$
$978$	560.000	0.0183096
$979$	−3216.00	−0.104989
$980$	6680.00	0.217740
$981$	4730.00	0.153942
$982$	17330.0	0.563159
$983$	56331.0	1.82775	0.913876	−	0.405994i	$-0.133075\pi$
$983$	56331.0	1.82775	0.913876	+	0.405994i	$0.133075\pi$
$984$	13024.0	0.421941
$985$	330.000	0.0106748
$986$	25470.0	0.822647
$987$	4320.00	0.139318
$988$	11248.0	0.362193
$989$	−7544.00	−0.242553
$990$	220.000	0.00706269
$991$	237.000	0.00759693	0.00379846	−	0.999993i	$-0.498791\pi$
$991$	237.000	0.00759693	0.00379846	+	0.999993i	$0.498791\pi$
$992$	9696.00	0.310331
$993$	−35180.0	−1.12427
$994$	3846.00	0.122724
$995$	16790.0	0.534954
$996$	8048.00	0.256035
$997$	−36856.0	−1.17075	−0.585377	−	0.810761i	$-0.699053\pi$
$997$	−36856.0	−1.17075	−0.585377	+	0.810761i	$0.699053\pi$
$998$	25346.0	0.803921
$999$	−12008.0	−0.380297

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.b.1.1	✓	1	1.1	even	1	trivial
1150.4.a.f.1.1		1	5.4	even	2
1150.4.b.c.599.1		2	5.2	odd	4
1150.4.b.c.599.2		2	5.3	odd	4
1840.4.a.b.1.1		1	4.3	odd	2
2070.4.a.n.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

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