LMFDB - Embedded newform 230.4.a.d.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)

$f(q)$

$=$

$q+2.00000 q^{2} -1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -32.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -32.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} +10.0000 q^{10} -30.0000 q^{11} -4.00000 q^{12} +19.0000 q^{13} -64.0000 q^{14} -5.00000 q^{15} +16.0000 q^{16} -60.0000 q^{17} -52.0000 q^{18} -58.0000 q^{19} +20.0000 q^{20} +32.0000 q^{21} -60.0000 q^{22} +23.0000 q^{23} -8.00000 q^{24} +25.0000 q^{25} +38.0000 q^{26} +53.0000 q^{27} -128.000 q^{28} +85.0000 q^{29} -10.0000 q^{30} -65.0000 q^{31} +32.0000 q^{32} +30.0000 q^{33} -120.000 q^{34} -160.000 q^{35} -104.000 q^{36} -34.0000 q^{37} -116.000 q^{38} -19.0000 q^{39} +40.0000 q^{40} +143.000 q^{41} +64.0000 q^{42} -332.000 q^{43} -120.000 q^{44} -130.000 q^{45} +46.0000 q^{46} -561.000 q^{47} -16.0000 q^{48} +681.000 q^{49} +50.0000 q^{50} +60.0000 q^{51} +76.0000 q^{52} -422.000 q^{53} +106.000 q^{54} -150.000 q^{55} -256.000 q^{56} +58.0000 q^{57} +170.000 q^{58} +392.000 q^{59} -20.0000 q^{60} -246.000 q^{61} -130.000 q^{62} +832.000 q^{63} +64.0000 q^{64} +95.0000 q^{65} +60.0000 q^{66} +894.000 q^{67} -240.000 q^{68} -23.0000 q^{69} -320.000 q^{70} -737.000 q^{71} -208.000 q^{72} +1041.00 q^{73} -68.0000 q^{74} -25.0000 q^{75} -232.000 q^{76} +960.000 q^{77} -38.0000 q^{78} +1114.00 q^{79} +80.0000 q^{80} +649.000 q^{81} +286.000 q^{82} -936.000 q^{83} +128.000 q^{84} -300.000 q^{85} -664.000 q^{86} -85.0000 q^{87} -240.000 q^{88} +824.000 q^{89} -260.000 q^{90} -608.000 q^{91} +92.0000 q^{92} +65.0000 q^{93} -1122.00 q^{94} -290.000 q^{95} -32.0000 q^{96} -868.000 q^{97} +1362.00 q^{98} +780.000 q^{99} +O(q^{100})\)

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
$3$	−1.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−1.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−2.00000	−0.136083
$7$	−32.0000	−1.72784	−0.863919	−	0.503631i	$-0.831997\pi$
$7$	−32.0000	−1.72784	−0.863919	+	0.503631i	$0.831997\pi$
$8$	8.00000	0.353553
$9$	−26.0000	−0.962963
$10$	10.0000	0.316228
$11$	−30.0000	−0.822304	−0.411152	−	0.911567i	$-0.634873\pi$
$11$	−30.0000	−0.822304	−0.411152	+	0.911567i	$0.634873\pi$
$12$	−4.00000	−0.0962250
$13$	19.0000	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$13$	19.0000	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$14$	−64.0000	−1.22177
$15$	−5.00000	−0.0860663
$16$	16.0000	0.250000
$17$	−60.0000	−0.856008	−0.428004	−	0.903777i	$-0.640783\pi$
$17$	−60.0000	−0.856008	−0.428004	+	0.903777i	$0.640783\pi$
$18$	−52.0000	−0.680918
$19$	−58.0000	−0.700322	−0.350161	−	0.936690i	$-0.613873\pi$
$19$	−58.0000	−0.700322	−0.350161	+	0.936690i	$0.613873\pi$
$20$	20.0000	0.223607
$21$	32.0000	0.332522
$22$	−60.0000	−0.581456
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−8.00000	−0.0680414
$25$	25.0000	0.200000
$26$	38.0000	0.286631
$27$	53.0000	0.377772
$28$	−128.000	−0.863919
$29$	85.0000	0.544279	0.272140	−	0.962258i	$-0.412269\pi$
$29$	85.0000	0.544279	0.272140	+	0.962258i	$0.412269\pi$
$30$	−10.0000	−0.0608581
$31$	−65.0000	−0.376592	−0.188296	−	0.982112i	$-0.560296\pi$
$31$	−65.0000	−0.376592	−0.188296	+	0.982112i	$0.560296\pi$
$32$	32.0000	0.176777
$33$	30.0000	0.158252
$34$	−120.000	−0.605289
$35$	−160.000	−0.772712
$36$	−104.000	−0.481481
$37$	−34.0000	−0.151069	−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000	−0.151069	−0.0755347	+	0.997143i	$0.524066\pi$
$38$	−116.000	−0.495202
$39$	−19.0000	−0.0780112
$40$	40.0000	0.158114
$41$	143.000	0.544704	0.272352	−	0.962198i	$-0.412199\pi$
$41$	143.000	0.544704	0.272352	+	0.962198i	$0.412199\pi$
$42$	64.0000	0.235129
$43$	−332.000	−1.17743	−0.588715	−	0.808340i	$-0.700366\pi$
$43$	−332.000	−1.17743	−0.588715	+	0.808340i	$0.700366\pi$
$44$	−120.000	−0.411152
$45$	−130.000	−0.430650
$46$	46.0000	0.147442
$47$	−561.000	−1.74107	−0.870535	−	0.492107i	$-0.836227\pi$
$47$	−561.000	−1.74107	−0.870535	+	0.492107i	$0.836227\pi$
$48$	−16.0000	−0.0481125
$49$	681.000	1.98542
$50$	50.0000	0.141421
$51$	60.0000	0.164739
$52$	76.0000	0.202679
$53$	−422.000	−1.09370	−0.546851	−	0.837230i	$-0.684173\pi$
$53$	−422.000	−1.09370	−0.546851	+	0.837230i	$0.684173\pi$
$54$	106.000	0.267125
$55$	−150.000	−0.367745
$56$	−256.000	−0.610883
$57$	58.0000	0.134777
$58$	170.000	0.384864
$59$	392.000	0.864984	0.432492	−	0.901638i	$-0.357634\pi$
$59$	392.000	0.864984	0.432492	+	0.901638i	$0.357634\pi$
$60$	−20.0000	−0.0430331
$61$	−246.000	−0.516345	−0.258173	−	0.966099i	$-0.583120\pi$
$61$	−246.000	−0.516345	−0.258173	+	0.966099i	$0.583120\pi$
$62$	−130.000	−0.266291
$63$	832.000	1.66384
$64$	64.0000	0.125000
$65$	95.0000	0.181282
$66$	60.0000	0.111901
$67$	894.000	1.63014	0.815071	−	0.579361i	$-0.196698\pi$
$67$	894.000	1.63014	0.815071	+	0.579361i	$0.196698\pi$
$68$	−240.000	−0.428004
$69$	−23.0000	−0.0401286
$70$	−320.000	−0.546390
$71$	−737.000	−1.23191	−0.615956	−	0.787780i	$-0.711230\pi$
$71$	−737.000	−1.23191	−0.615956	+	0.787780i	$0.711230\pi$
$72$	−208.000	−0.340459
$73$	1041.00	1.66904	0.834519	−	0.550979i	$-0.185745\pi$
$73$	1041.00	1.66904	0.834519	+	0.550979i	$0.185745\pi$
$74$	−68.0000	−0.106822
$75$	−25.0000	−0.0384900
$76$	−232.000	−0.350161
$77$	960.000	1.42081
$78$	−38.0000	−0.0551622
$79$	1114.00	1.58652	0.793258	−	0.608885i	$-0.208383\pi$
$79$	1114.00	1.58652	0.793258	+	0.608885i	$0.208383\pi$
$80$	80.0000	0.111803
$81$	649.000	0.890261
$82$	286.000	0.385164
$83$	−936.000	−1.23782	−0.618912	−	0.785461i	$-0.712426\pi$
$83$	−936.000	−1.23782	−0.618912	+	0.785461i	$0.712426\pi$
$84$	128.000	0.166261
$85$	−300.000	−0.382818
$86$	−664.000	−0.832569
$87$	−85.0000	−0.104747
$88$	−240.000	−0.290728
$89$	824.000	0.981391	0.490696	−	0.871331i	$-0.336743\pi$
$89$	824.000	0.981391	0.490696	+	0.871331i	$0.336743\pi$
$90$	−260.000	−0.304516
$91$	−608.000	−0.700393
$92$	92.0000	0.104257
$93$	65.0000	0.0724751
$94$	−1122.00	−1.23112
$95$	−290.000	−0.313193
$96$	−32.0000	−0.0340207
$97$	−868.000	−0.908578	−0.454289	−	0.890854i	$-0.650107\pi$
$97$	−868.000	−0.908578	−0.454289	+	0.890854i	$0.650107\pi$
$98$	1362.00	1.40391
$99$	780.000	0.791848
$100$	100.000	0.100000
$101$	50.0000	0.0492593	0.0246296	−	0.999697i	$-0.492159\pi$
$101$	50.0000	0.0492593	0.0246296	+	0.999697i	$0.492159\pi$
$102$	120.000	0.116488
$103$	440.000	0.420917	0.210459	−	0.977603i	$-0.432504\pi$
$103$	440.000	0.420917	0.210459	+	0.977603i	$0.432504\pi$
$104$	152.000	0.143316
$105$	160.000	0.148709
$106$	−844.000	−0.773363
$107$	−318.000	−0.287310	−0.143655	−	0.989628i	$-0.545886\pi$
$107$	−318.000	−0.287310	−0.143655	+	0.989628i	$0.545886\pi$
$108$	212.000	0.188886
$109$	−828.000	−0.727596	−0.363798	−	0.931478i	$-0.618520\pi$
$109$	−828.000	−0.727596	−0.363798	+	0.931478i	$0.618520\pi$
$110$	−300.000	−0.260035
$111$	34.0000	0.0290733
$112$	−512.000	−0.431959
$113$	208.000	0.173159	0.0865796	−	0.996245i	$-0.472406\pi$
$113$	208.000	0.173159	0.0865796	+	0.996245i	$0.472406\pi$
$114$	116.000	0.0953017
$115$	115.000	0.0932505
$116$	340.000	0.272140
$117$	−494.000	−0.390345
$118$	784.000	0.611636
$119$	1920.00	1.47904
$120$	−40.0000	−0.0304290
$121$	−431.000	−0.323817
$122$	−492.000	−0.365111
$123$	−143.000	−0.104828
$124$	−260.000	−0.188296
$125$	125.000	0.0894427
$126$	1664.00	1.17652
$127$	−495.000	−0.345859	−0.172930	−	0.984934i	$-0.555323\pi$
$127$	−495.000	−0.345859	−0.172930	+	0.984934i	$0.555323\pi$
$128$	128.000	0.0883883
$129$	332.000	0.226597
$130$	190.000	0.128185
$131$	335.000	0.223428	0.111714	−	0.993740i	$-0.464366\pi$
$131$	335.000	0.223428	0.111714	+	0.993740i	$0.464366\pi$
$132$	120.000	0.0791262
$133$	1856.00	1.21004
$134$	1788.00	1.15268
$135$	265.000	0.168945
$136$	−480.000	−0.302645
$137$	−652.000	−0.406599	−0.203300	−	0.979117i	$-0.565167\pi$
$137$	−652.000	−0.406599	−0.203300	+	0.979117i	$0.565167\pi$
$138$	−46.0000	−0.0283752
$139$	−1999.00	−1.21981	−0.609903	−	0.792476i	$-0.708792\pi$
$139$	−1999.00	−1.21981	−0.609903	+	0.792476i	$0.708792\pi$
$140$	−640.000	−0.386356
$141$	561.000	0.335069
$142$	−1474.00	−0.871094
$143$	−570.000	−0.333327
$144$	−416.000	−0.240741
$145$	425.000	0.243409
$146$	2082.00	1.18019
$147$	−681.000	−0.382095
$148$	−136.000	−0.0755347
$149$	1870.00	1.02816	0.514082	−	0.857741i	$-0.328133\pi$
$149$	1870.00	1.02816	0.514082	+	0.857741i	$0.328133\pi$
$150$	−50.0000	−0.0272166
$151$	1463.00	0.788459	0.394229	−	0.919012i	$-0.371012\pi$
$151$	1463.00	0.788459	0.394229	+	0.919012i	$0.371012\pi$
$152$	−464.000	−0.247601
$153$	1560.00	0.824304
$154$	1920.00	1.00466
$155$	−325.000	−0.168417
$156$	−76.0000	−0.0390056
$157$	−3004.00	−1.52704	−0.763520	−	0.645784i	$-0.776531\pi$
$157$	−3004.00	−1.52704	−0.763520	+	0.645784i	$0.776531\pi$
$158$	2228.00	1.12184
$159$	422.000	0.210483
$160$	160.000	0.0790569
$161$	−736.000	−0.360279
$162$	1298.00	0.629509
$163$	−4047.00	−1.94470	−0.972348	−	0.233536i	$-0.924970\pi$
$163$	−4047.00	−1.94470	−0.972348	+	0.233536i	$0.924970\pi$
$164$	572.000	0.272352
$165$	150.000	0.0707726
$166$	−1872.00	−0.875273
$167$	−2112.00	−0.978632	−0.489316	−	0.872107i	$-0.662753\pi$
$167$	−2112.00	−0.978632	−0.489316	+	0.872107i	$0.662753\pi$
$168$	256.000	0.117564
$169$	−1836.00	−0.835685
$170$	−600.000	−0.270694
$171$	1508.00	0.674384
$172$	−1328.00	−0.588715
$173$	342.000	0.150299	0.0751496	−	0.997172i	$-0.476057\pi$
$173$	342.000	0.150299	0.0751496	+	0.997172i	$0.476057\pi$
$174$	−170.000	−0.0740671
$175$	−800.000	−0.345568
$176$	−480.000	−0.205576
$177$	−392.000	−0.166466
$178$	1648.00	0.693948
$179$	1689.00	0.705261	0.352631	−	0.935763i	$-0.385287\pi$
$179$	1689.00	0.705261	0.352631	+	0.935763i	$0.385287\pi$
$180$	−520.000	−0.215325
$181$	−194.000	−0.0796680	−0.0398340	−	0.999206i	$-0.512683\pi$
$181$	−194.000	−0.0796680	−0.0398340	+	0.999206i	$0.512683\pi$
$182$	−1216.00	−0.495252
$183$	246.000	0.0993707
$184$	184.000	0.0737210
$185$	−170.000	−0.0675603
$186$	130.000	0.0512476
$187$	1800.00	0.703899
$188$	−2244.00	−0.870535
$189$	−1696.00	−0.652729
$190$	−580.000	−0.221461
$191$	−298.000	−0.112893	−0.0564464	−	0.998406i	$-0.517977\pi$
$191$	−298.000	−0.112893	−0.0564464	+	0.998406i	$0.517977\pi$
$192$	−64.0000	−0.0240563
$193$	2301.00	0.858184	0.429092	−	0.903261i	$-0.358834\pi$
$193$	2301.00	0.858184	0.429092	+	0.903261i	$0.358834\pi$
$194$	−1736.00	−0.642462
$195$	−95.0000	−0.0348876
$196$	2724.00	0.992711
$197$	−535.000	−0.193488	−0.0967441	−	0.995309i	$-0.530843\pi$
$197$	−535.000	−0.193488	−0.0967441	+	0.995309i	$0.530843\pi$
$198$	1560.00	0.559921
$199$	278.000	0.0990296	0.0495148	−	0.998773i	$-0.484232\pi$
$199$	278.000	0.0990296	0.0495148	+	0.998773i	$0.484232\pi$
$200$	200.000	0.0707107
$201$	−894.000	−0.313721
$202$	100.000	0.0348316
$203$	−2720.00	−0.940426
$204$	240.000	0.0823694
$205$	715.000	0.243599
$206$	880.000	0.297634
$207$	−598.000	−0.200792
$208$	304.000	0.101339
$209$	1740.00	0.575877
$210$	320.000	0.105153
$211$	−2444.00	−0.797402	−0.398701	−	0.917081i	$-0.630539\pi$
$211$	−2444.00	−0.797402	−0.398701	+	0.917081i	$0.630539\pi$
$212$	−1688.00	−0.546851
$213$	737.000	0.237082
$214$	−636.000	−0.203159
$215$	−1660.00	−0.526563
$216$	424.000	0.133563
$217$	2080.00	0.650689
$218$	−1656.00	−0.514488
$219$	−1041.00	−0.321207
$220$	−600.000	−0.183873
$221$	−1140.00	−0.346990
$222$	68.0000	0.0205579
$223$	−5368.00	−1.61196	−0.805982	−	0.591940i	$-0.798362\pi$
$223$	−5368.00	−1.61196	−0.805982	+	0.591940i	$0.798362\pi$
$224$	−1024.00	−0.305441
$225$	−650.000	−0.192593
$226$	416.000	0.122442
$227$	−5780.00	−1.69001	−0.845005	−	0.534759i	$-0.820402\pi$
$227$	−5780.00	−1.69001	−0.845005	+	0.534759i	$0.820402\pi$
$228$	232.000	0.0673885
$229$	−1064.00	−0.307035	−0.153518	−	0.988146i	$-0.549060\pi$
$229$	−1064.00	−0.307035	−0.153518	+	0.988146i	$0.549060\pi$
$230$	230.000	0.0659380
$231$	−960.000	−0.273434
$232$	680.000	0.192432
$233$	−2833.00	−0.796549	−0.398275	−	0.917266i	$-0.630391\pi$
$233$	−2833.00	−0.796549	−0.398275	+	0.917266i	$0.630391\pi$
$234$	−988.000	−0.276015
$235$	−2805.00	−0.778630
$236$	1568.00	0.432492
$237$	−1114.00	−0.305325
$238$	3840.00	1.04584
$239$	6831.00	1.84879	0.924395	−	0.381437i	$-0.124571\pi$
$239$	6831.00	1.84879	0.924395	+	0.381437i	$0.124571\pi$
$240$	−80.0000	−0.0215166
$241$	−1794.00	−0.479509	−0.239755	−	0.970834i	$-0.577067\pi$
$241$	−1794.00	−0.479509	−0.239755	+	0.970834i	$0.577067\pi$
$242$	−862.000	−0.228973
$243$	−2080.00	−0.549103
$244$	−984.000	−0.258173
$245$	3405.00	0.887908
$246$	−286.000	−0.0741248
$247$	−1102.00	−0.283881
$248$	−520.000	−0.133145
$249$	936.000	0.238219
$250$	250.000	0.0632456
$251$	−6672.00	−1.67782	−0.838910	−	0.544270i	$-0.816807\pi$
$251$	−6672.00	−1.67782	−0.838910	+	0.544270i	$0.816807\pi$
$252$	3328.00	0.831922
$253$	−690.000	−0.171462
$254$	−990.000	−0.244560
$255$	300.000	0.0736734
$256$	256.000	0.0625000
$257$	291.000	0.0706307	0.0353153	−	0.999376i	$-0.488756\pi$
$257$	291.000	0.0706307	0.0353153	+	0.999376i	$0.488756\pi$
$258$	664.000	0.160228
$259$	1088.00	0.261023
$260$	380.000	0.0906408
$261$	−2210.00	−0.524121
$262$	670.000	0.157988
$263$	−5306.00	−1.24404	−0.622019	−	0.783002i	$-0.713687\pi$
$263$	−5306.00	−1.24404	−0.622019	+	0.783002i	$0.713687\pi$
$264$	240.000	0.0559507
$265$	−2110.00	−0.489118
$266$	3712.00	0.855629
$267$	−824.000	−0.188869
$268$	3576.00	0.815071
$269$	7785.00	1.76453	0.882267	−	0.470749i	$-0.156016\pi$
$269$	7785.00	1.76453	0.882267	+	0.470749i	$0.156016\pi$
$270$	530.000	0.119462
$271$	3440.00	0.771089	0.385544	−	0.922689i	$-0.374014\pi$
$271$	3440.00	0.771089	0.385544	+	0.922689i	$0.374014\pi$
$272$	−960.000	−0.214002
$273$	608.000	0.134791
$274$	−1304.00	−0.287509
$275$	−750.000	−0.164461
$276$	−92.0000	−0.0200643
$277$	−7643.00	−1.65785	−0.828923	−	0.559363i	$-0.811046\pi$
$277$	−7643.00	−1.65785	−0.828923	+	0.559363i	$0.811046\pi$
$278$	−3998.00	−0.862533
$279$	1690.00	0.362644
$280$	−1280.00	−0.273195
$281$	5408.00	1.14809	0.574047	−	0.818823i	$-0.305373\pi$
$281$	5408.00	1.14809	0.574047	+	0.818823i	$0.305373\pi$
$282$	1122.00	0.236930
$283$	4402.00	0.924635	0.462318	−	0.886714i	$-0.347018\pi$
$283$	4402.00	0.924635	0.462318	+	0.886714i	$0.347018\pi$
$284$	−2948.00	−0.615956
$285$	290.000	0.0602741
$286$	−1140.00	−0.235698
$287$	−4576.00	−0.941159
$288$	−832.000	−0.170229
$289$	−1313.00	−0.267250
$290$	850.000	0.172116
$291$	868.000	0.174856
$292$	4164.00	0.834519
$293$	9808.00	1.95560	0.977798	−	0.209551i	$-0.0672002\pi$
$293$	9808.00	1.95560	0.977798	+	0.209551i	$0.0672002\pi$
$294$	−1362.00	−0.270182
$295$	1960.00	0.386833
$296$	−272.000	−0.0534111
$297$	−1590.00	−0.310644
$298$	3740.00	0.727021
$299$	437.000	0.0845230
$300$	−100.000	−0.0192450
$301$	10624.0	2.03441
$302$	2926.00	0.557524
$303$	−50.0000	−0.00947995
$304$	−928.000	−0.175080
$305$	−1230.00	−0.230917
$306$	3120.00	0.582871
$307$	−3288.00	−0.611258	−0.305629	−	0.952151i	$-0.598867\pi$
$307$	−3288.00	−0.611258	−0.305629	+	0.952151i	$0.598867\pi$
$308$	3840.00	0.710404
$309$	−440.000	−0.0810056
$310$	−650.000	−0.119089
$311$	3919.00	0.714553	0.357277	−	0.933999i	$-0.383705\pi$
$311$	3919.00	0.714553	0.357277	+	0.933999i	$0.383705\pi$
$312$	−152.000	−0.0275811
$313$	5112.00	0.923154	0.461577	−	0.887100i	$-0.347284\pi$
$313$	5112.00	0.923154	0.461577	+	0.887100i	$0.347284\pi$
$314$	−6008.00	−1.07978
$315$	4160.00	0.744093
$316$	4456.00	0.793258
$317$	8058.00	1.42770	0.713852	−	0.700296i	$-0.246949\pi$
$317$	8058.00	1.42770	0.713852	+	0.700296i	$0.246949\pi$
$318$	844.000	0.148834
$319$	−2550.00	−0.447563
$320$	320.000	0.0559017
$321$	318.000	0.0552929
$322$	−1472.00	−0.254756
$323$	3480.00	0.599481
$324$	2596.00	0.445130
$325$	475.000	0.0810716
$326$	−8094.00	−1.37511
$327$	828.000	0.140026
$328$	1144.00	0.192582
$329$	17952.0	3.00829
$330$	300.000	0.0500438
$331$	−2555.00	−0.424276	−0.212138	−	0.977240i	$-0.568043\pi$
$331$	−2555.00	−0.424276	−0.212138	+	0.977240i	$0.568043\pi$
$332$	−3744.00	−0.618912
$333$	884.000	0.145474
$334$	−4224.00	−0.691997
$335$	4470.00	0.729021
$336$	512.000	0.0831306
$337$	−6272.00	−1.01382	−0.506910	−	0.861999i	$-0.669213\pi$
$337$	−6272.00	−1.01382	−0.506910	+	0.861999i	$0.669213\pi$
$338$	−3672.00	−0.590919
$339$	−208.000	−0.0333245
$340$	−1200.00	−0.191409
$341$	1950.00	0.309673
$342$	3016.00	0.476861
$343$	−10816.0	−1.70265
$344$	−2656.00	−0.416285
$345$	−115.000	−0.0179461
$346$	684.000	0.106278
$347$	6844.00	1.05880	0.529402	−	0.848371i	$-0.322416\pi$
$347$	6844.00	1.05880	0.529402	+	0.848371i	$0.322416\pi$
$348$	−340.000	−0.0523733
$349$	4057.00	0.622253	0.311126	−	0.950369i	$-0.399294\pi$
$349$	4057.00	0.622253	0.311126	+	0.950369i	$0.399294\pi$
$350$	−1600.00	−0.244353
$351$	1007.00	0.153133
$352$	−960.000	−0.145364
$353$	−7155.00	−1.07882	−0.539408	−	0.842044i	$-0.681352\pi$
$353$	−7155.00	−1.07882	−0.539408	+	0.842044i	$0.681352\pi$
$354$	−784.000	−0.117709
$355$	−3685.00	−0.550928
$356$	3296.00	0.490696
$357$	−1920.00	−0.284642
$358$	3378.00	0.498695
$359$	−5434.00	−0.798873	−0.399437	−	0.916761i	$-0.630794\pi$
$359$	−5434.00	−0.798873	−0.399437	+	0.916761i	$0.630794\pi$
$360$	−1040.00	−0.152258
$361$	−3495.00	−0.509549
$362$	−388.000	−0.0563338
$363$	431.000	0.0623185
$364$	−2432.00	−0.350196
$365$	5205.00	0.746417
$366$	492.000	0.0702657
$367$	−2944.00	−0.418734	−0.209367	−	0.977837i	$-0.567140\pi$
$367$	−2944.00	−0.418734	−0.209367	+	0.977837i	$0.567140\pi$
$368$	368.000	0.0521286
$369$	−3718.00	−0.524529
$370$	−340.000	−0.0477723
$371$	13504.0	1.88974
$372$	260.000	0.0362376
$373$	−5962.00	−0.827616	−0.413808	−	0.910364i	$-0.635801\pi$
$373$	−5962.00	−0.827616	−0.413808	+	0.910364i	$0.635801\pi$
$374$	3600.00	0.497731
$375$	−125.000	−0.0172133
$376$	−4488.00	−0.615561
$377$	1615.00	0.220628
$378$	−3392.00	−0.461549
$379$	−5856.00	−0.793674	−0.396837	−	0.917889i	$-0.629892\pi$
$379$	−5856.00	−0.793674	−0.396837	+	0.917889i	$0.629892\pi$
$380$	−1160.00	−0.156597
$381$	495.000	0.0665607
$382$	−596.000	−0.0798273
$383$	6456.00	0.861322	0.430661	−	0.902514i	$-0.358281\pi$
$383$	6456.00	0.861322	0.430661	+	0.902514i	$0.358281\pi$
$384$	−128.000	−0.0170103
$385$	4800.00	0.635404
$386$	4602.00	0.606828
$387$	8632.00	1.13382
$388$	−3472.00	−0.454289
$389$	−152.000	−0.0198116	−0.00990579	−	0.999951i	$-0.503153\pi$
$389$	−152.000	−0.0198116	−0.00990579	+	0.999951i	$0.503153\pi$
$390$	−190.000	−0.0246693
$391$	−1380.00	−0.178490
$392$	5448.00	0.701953
$393$	−335.000	−0.0429988
$394$	−1070.00	−0.136817
$395$	5570.00	0.709512
$396$	3120.00	0.395924
$397$	11603.0	1.46685	0.733423	−	0.679773i	$-0.237921\pi$
$397$	11603.0	1.46685	0.733423	+	0.679773i	$0.237921\pi$
$398$	556.000	0.0700245
$399$	−1856.00	−0.232873
$400$	400.000	0.0500000
$401$	602.000	0.0749687	0.0374843	−	0.999297i	$-0.488066\pi$
$401$	602.000	0.0749687	0.0374843	+	0.999297i	$0.488066\pi$
$402$	−1788.00	−0.221834
$403$	−1235.00	−0.152654
$404$	200.000	0.0246296
$405$	3245.00	0.398137
$406$	−5440.00	−0.664982
$407$	1020.00	0.124225
$408$	480.000	0.0582440
$409$	3629.00	0.438735	0.219367	−	0.975642i	$-0.429601\pi$
$409$	3629.00	0.438735	0.219367	+	0.975642i	$0.429601\pi$
$410$	1430.00	0.172250
$411$	652.000	0.0782501
$412$	1760.00	0.210459
$413$	−12544.0	−1.49455
$414$	−1196.00	−0.141981
$415$	−4680.00	−0.553571
$416$	608.000	0.0716578
$417$	1999.00	0.234752
$418$	3480.00	0.407207
$419$	92.0000	0.0107267	0.00536336	−	0.999986i	$-0.498293\pi$
$419$	92.0000	0.0107267	0.00536336	+	0.999986i	$0.498293\pi$
$420$	640.000	0.0743543
$421$	−8280.00	−0.958533	−0.479267	−	0.877669i	$-0.659097\pi$
$421$	−8280.00	−0.958533	−0.479267	+	0.877669i	$0.659097\pi$
$422$	−4888.00	−0.563849
$423$	14586.0	1.67659
$424$	−3376.00	−0.386682
$425$	−1500.00	−0.171202
$426$	1474.00	0.167642
$427$	7872.00	0.892161
$428$	−1272.00	−0.143655
$429$	570.000	0.0641489
$430$	−3320.00	−0.372336
$431$	−15372.0	−1.71797	−0.858983	−	0.512004i	$-0.828903\pi$
$431$	−15372.0	−1.71797	−0.858983	+	0.512004i	$0.828903\pi$
$432$	848.000	0.0944431
$433$	−11342.0	−1.25880	−0.629402	−	0.777080i	$-0.716700\pi$
$433$	−11342.0	−1.25880	−0.629402	+	0.777080i	$0.716700\pi$
$434$	4160.00	0.460107
$435$	−425.000	−0.0468441
$436$	−3312.00	−0.363798
$437$	−1334.00	−0.146027
$438$	−2082.00	−0.227127
$439$	4593.00	0.499344	0.249672	−	0.968330i	$-0.419677\pi$
$439$	4593.00	0.499344	0.249672	+	0.968330i	$0.419677\pi$
$440$	−1200.00	−0.130018
$441$	−17706.0	−1.91189
$442$	−2280.00	−0.245359
$443$	967.000	0.103710	0.0518550	−	0.998655i	$-0.483487\pi$
$443$	967.000	0.103710	0.0518550	+	0.998655i	$0.483487\pi$
$444$	136.000	0.0145367
$445$	4120.00	0.438892
$446$	−10736.0	−1.13983
$447$	−1870.00	−0.197870
$448$	−2048.00	−0.215980
$449$	−11210.0	−1.17825	−0.589123	−	0.808043i	$-0.700527\pi$
$449$	−11210.0	−1.17825	−0.589123	+	0.808043i	$0.700527\pi$
$450$	−1300.00	−0.136184
$451$	−4290.00	−0.447912
$452$	832.000	0.0865796
$453$	−1463.00	−0.151739
$454$	−11560.0	−1.19502
$455$	−3040.00	−0.313225
$456$	464.000	0.0476509
$457$	−72.0000	−0.00736984	−0.00368492	−	0.999993i	$-0.501173\pi$
$457$	−72.0000	−0.00736984	−0.00368492	+	0.999993i	$0.501173\pi$
$458$	−2128.00	−0.217107
$459$	−3180.00	−0.323376
$460$	460.000	0.0466252
$461$	5137.00	0.518989	0.259495	−	0.965745i	$-0.416444\pi$
$461$	5137.00	0.518989	0.259495	+	0.965745i	$0.416444\pi$
$462$	−1920.00	−0.193347
$463$	−19528.0	−1.96014	−0.980068	−	0.198661i	$-0.936341\pi$
$463$	−19528.0	−1.96014	−0.980068	+	0.198661i	$0.936341\pi$
$464$	1360.00	0.136070
$465$	325.000	0.0324119
$466$	−5666.00	−0.563245
$467$	14874.0	1.47385	0.736924	−	0.675976i	$-0.236278\pi$
$467$	14874.0	1.47385	0.736924	+	0.675976i	$0.236278\pi$
$468$	−1976.00	−0.195172
$469$	−28608.0	−2.81662
$470$	−5610.00	−0.550574
$471$	3004.00	0.293879
$472$	3136.00	0.305818
$473$	9960.00	0.968206
$474$	−2228.00	−0.215898
$475$	−1450.00	−0.140064
$476$	7680.00	0.739521
$477$	10972.0	1.05319
$478$	13662.0	1.30729
$479$	10568.0	1.00807	0.504034	−	0.863684i	$-0.331849\pi$
$479$	10568.0	1.00807	0.504034	+	0.863684i	$0.331849\pi$
$480$	−160.000	−0.0152145
$481$	−646.000	−0.0612371
$482$	−3588.00	−0.339064
$483$	736.000	0.0693357
$484$	−1724.00	−0.161908
$485$	−4340.00	−0.406328
$486$	−4160.00	−0.388275
$487$	−9311.00	−0.866369	−0.433184	−	0.901305i	$-0.642610\pi$
$487$	−9311.00	−0.866369	−0.433184	+	0.901305i	$0.642610\pi$
$488$	−1968.00	−0.182556
$489$	4047.00	0.374257
$490$	6810.00	0.627846
$491$	−16511.0	−1.51758	−0.758789	−	0.651336i	$-0.774209\pi$
$491$	−16511.0	−1.51758	−0.758789	+	0.651336i	$0.774209\pi$
$492$	−572.000	−0.0524141
$493$	−5100.00	−0.465908
$494$	−2204.00	−0.200734
$495$	3900.00	0.354125
$496$	−1040.00	−0.0941479
$497$	23584.0	2.12855
$498$	1872.00	0.168446
$499$	2331.00	0.209118	0.104559	−	0.994519i	$-0.466657\pi$
$499$	2331.00	0.209118	0.104559	+	0.994519i	$0.466657\pi$
$500$	500.000	0.0447214
$501$	2112.00	0.188338
$502$	−13344.0	−1.18640
$503$	17062.0	1.51244	0.756220	−	0.654318i	$-0.227044\pi$
$503$	17062.0	1.51244	0.756220	+	0.654318i	$0.227044\pi$
$504$	6656.00	0.588258
$505$	250.000	0.0220294
$506$	−1380.00	−0.121242
$507$	1836.00	0.160828
$508$	−1980.00	−0.172930
$509$	17169.0	1.49509	0.747547	−	0.664209i	$-0.231232\pi$
$509$	17169.0	1.49509	0.747547	+	0.664209i	$0.231232\pi$
$510$	600.000	0.0520950
$511$	−33312.0	−2.88383
$512$	512.000	0.0441942
$513$	−3074.00	−0.264562
$514$	582.000	0.0499434
$515$	2200.00	0.188240
$516$	1328.00	0.113298
$517$	16830.0	1.43169
$518$	2176.00	0.184571
$519$	−342.000	−0.0289251
$520$	760.000	0.0640927
$521$	−10060.0	−0.845944	−0.422972	−	0.906143i	$-0.639013\pi$
$521$	−10060.0	−0.845944	−0.422972	+	0.906143i	$0.639013\pi$
$522$	−4420.00	−0.370609
$523$	15244.0	1.27452	0.637260	−	0.770649i	$-0.280068\pi$
$523$	15244.0	1.27452	0.637260	+	0.770649i	$0.280068\pi$
$524$	1340.00	0.111714
$525$	800.000	0.0665045
$526$	−10612.0	−0.879668
$527$	3900.00	0.322366
$528$	480.000	0.0395631
$529$	529.000	0.0434783
$530$	−4220.00	−0.345859
$531$	−10192.0	−0.832948
$532$	7424.00	0.605021
$533$	2717.00	0.220800
$534$	−1648.00	−0.133550
$535$	−1590.00	−0.128489
$536$	7152.00	0.576342
$537$	−1689.00	−0.135728
$538$	15570.0	1.24771
$539$	−20430.0	−1.63262
$540$	1060.00	0.0844725
$541$	16389.0	1.30244	0.651218	−	0.758891i	$-0.274258\pi$
$541$	16389.0	1.30244	0.651218	+	0.758891i	$0.274258\pi$
$542$	6880.00	0.545242
$543$	194.000	0.0153321
$544$	−1920.00	−0.151322
$545$	−4140.00	−0.325391
$546$	1216.00	0.0953113
$547$	17913.0	1.40019	0.700096	−	0.714049i	$-0.253141\pi$
$547$	17913.0	1.40019	0.700096	+	0.714049i	$0.253141\pi$
$548$	−2608.00	−0.203300
$549$	6396.00	0.497222
$550$	−1500.00	−0.116291
$551$	−4930.00	−0.381171
$552$	−184.000	−0.0141876
$553$	−35648.0	−2.74124
$554$	−15286.0	−1.17227
$555$	170.000	0.0130020
$556$	−7996.00	−0.609903
$557$	−18224.0	−1.38631	−0.693156	−	0.720788i	$-0.743780\pi$
$557$	−18224.0	−1.38631	−0.693156	+	0.720788i	$0.743780\pi$
$558$	3380.00	0.256428
$559$	−6308.00	−0.477281
$560$	−2560.00	−0.193178
$561$	−1800.00	−0.135465
$562$	10816.0	0.811825
$563$	−4860.00	−0.363809	−0.181905	−	0.983316i	$-0.558226\pi$
$563$	−4860.00	−0.363809	−0.181905	+	0.983316i	$0.558226\pi$
$564$	2244.00	0.167534
$565$	1040.00	0.0774392
$566$	8804.00	0.653816
$567$	−20768.0	−1.53823
$568$	−5896.00	−0.435547
$569$	−12438.0	−0.916394	−0.458197	−	0.888851i	$-0.651505\pi$
$569$	−12438.0	−0.916394	−0.458197	+	0.888851i	$0.651505\pi$
$570$	580.000	0.0426202
$571$	7948.00	0.582510	0.291255	−	0.956645i	$-0.405927\pi$
$571$	7948.00	0.582510	0.291255	+	0.956645i	$0.405927\pi$
$572$	−2280.00	−0.166664
$573$	298.000	0.0217262
$574$	−9152.00	−0.665500
$575$	575.000	0.0417029
$576$	−1664.00	−0.120370
$577$	9061.00	0.653751	0.326876	−	0.945067i	$-0.394004\pi$
$577$	9061.00	0.653751	0.326876	+	0.945067i	$0.394004\pi$
$578$	−2626.00	−0.188974
$579$	−2301.00	−0.165158
$580$	1700.00	0.121705
$581$	29952.0	2.13876
$582$	1736.00	0.123642
$583$	12660.0	0.899354
$584$	8328.00	0.590094
$585$	−2470.00	−0.174567
$586$	19616.0	1.38281
$587$	8559.00	0.601819	0.300909	−	0.953653i	$-0.402710\pi$
$587$	8559.00	0.601819	0.300909	+	0.953653i	$0.402710\pi$
$588$	−2724.00	−0.191047
$589$	3770.00	0.263735
$590$	3920.00	0.273532
$591$	535.000	0.0372368
$592$	−544.000	−0.0377673
$593$	−8850.00	−0.612860	−0.306430	−	0.951893i	$-0.599135\pi$
$593$	−8850.00	−0.612860	−0.306430	+	0.951893i	$0.599135\pi$
$594$	−3180.00	−0.219658
$595$	9600.00	0.661448
$596$	7480.00	0.514082
$597$	−278.000	−0.0190583
$598$	874.000	0.0597668
$599$	−7952.00	−0.542421	−0.271210	−	0.962520i	$-0.587424\pi$
$599$	−7952.00	−0.542421	−0.271210	+	0.962520i	$0.587424\pi$
$600$	−200.000	−0.0136083
$601$	27085.0	1.83830	0.919152	−	0.393904i	$-0.128876\pi$
$601$	27085.0	1.83830	0.919152	+	0.393904i	$0.128876\pi$
$602$	21248.0	1.43854
$603$	−23244.0	−1.56977
$604$	5852.00	0.394229
$605$	−2155.00	−0.144815
$606$	−100.000	−0.00670334
$607$	−5204.00	−0.347980	−0.173990	−	0.984747i	$-0.555666\pi$
$607$	−5204.00	−0.347980	−0.173990	+	0.984747i	$0.555666\pi$
$608$	−1856.00	−0.123801
$609$	2720.00	0.180985
$610$	−2460.00	−0.163283
$611$	−10659.0	−0.705756
$612$	6240.00	0.412152
$613$	−4348.00	−0.286483	−0.143241	−	0.989688i	$-0.545753\pi$
$613$	−4348.00	−0.286483	−0.143241	+	0.989688i	$0.545753\pi$
$614$	−6576.00	−0.432224
$615$	−715.000	−0.0468806
$616$	7680.00	0.502331
$617$	−4066.00	−0.265301	−0.132651	−	0.991163i	$-0.542349\pi$
$617$	−4066.00	−0.265301	−0.132651	+	0.991163i	$0.542349\pi$
$618$	−880.000	−0.0572796
$619$	−6080.00	−0.394791	−0.197396	−	0.980324i	$-0.563248\pi$
$619$	−6080.00	−0.394791	−0.197396	+	0.980324i	$0.563248\pi$
$620$	−1300.00	−0.0842085
$621$	1219.00	0.0787710
$622$	7838.00	0.505266
$623$	−26368.0	−1.69568
$624$	−304.000	−0.0195028
$625$	625.000	0.0400000
$626$	10224.0	0.652769
$627$	−1740.00	−0.110828
$628$	−12016.0	−0.763520
$629$	2040.00	0.129317
$630$	8320.00	0.526154
$631$	21200.0	1.33749	0.668747	−	0.743490i	$-0.266831\pi$
$631$	21200.0	1.33749	0.668747	+	0.743490i	$0.266831\pi$
$632$	8912.00	0.560918
$633$	2444.00	0.153460
$634$	16116.0	1.00954
$635$	−2475.00	−0.154673
$636$	1688.00	0.105241
$637$	12939.0	0.804807
$638$	−5100.00	−0.316475
$639$	19162.0	1.18629
$640$	640.000	0.0395285
$641$	14016.0	0.863649	0.431824	−	0.901958i	$-0.357870\pi$
$641$	14016.0	0.863649	0.431824	+	0.901958i	$0.357870\pi$
$642$	636.000	0.0390980
$643$	23894.0	1.46545	0.732727	−	0.680522i	$-0.238247\pi$
$643$	23894.0	1.46545	0.732727	+	0.680522i	$0.238247\pi$
$644$	−2944.00	−0.180140
$645$	1660.00	0.101337
$646$	6960.00	0.423897
$647$	27111.0	1.64736	0.823681	−	0.567053i	$-0.191917\pi$
$647$	27111.0	1.64736	0.823681	+	0.567053i	$0.191917\pi$
$648$	5192.00	0.314755
$649$	−11760.0	−0.711279
$650$	950.000	0.0573263
$651$	−2080.00	−0.125225
$652$	−16188.0	−0.972348
$653$	7819.00	0.468578	0.234289	−	0.972167i	$-0.424724\pi$
$653$	7819.00	0.468578	0.234289	+	0.972167i	$0.424724\pi$
$654$	1656.00	0.0990133
$655$	1675.00	0.0999201
$656$	2288.00	0.136176
$657$	−27066.0	−1.60722
$658$	35904.0	2.12718
$659$	−8712.00	−0.514979	−0.257490	−	0.966281i	$-0.582895\pi$
$659$	−8712.00	−0.514979	−0.257490	+	0.966281i	$0.582895\pi$
$660$	600.000	0.0353863
$661$	−12746.0	−0.750018	−0.375009	−	0.927021i	$-0.622360\pi$
$661$	−12746.0	−0.750018	−0.375009	+	0.927021i	$0.622360\pi$
$662$	−5110.00	−0.300009
$663$	1140.00	0.0667782
$664$	−7488.00	−0.437637
$665$	9280.00	0.541147
$666$	1768.00	0.102866
$667$	1955.00	0.113490
$668$	−8448.00	−0.489316
$669$	5368.00	0.310223
$670$	8940.00	0.515496
$671$	7380.00	0.424593
$672$	1024.00	0.0587822
$673$	−14937.0	−0.855541	−0.427770	−	0.903887i	$-0.640701\pi$
$673$	−14937.0	−0.855541	−0.427770	+	0.903887i	$0.640701\pi$
$674$	−12544.0	−0.716880
$675$	1325.00	0.0755545
$676$	−7344.00	−0.417843
$677$	8226.00	0.466988	0.233494	−	0.972358i	$-0.424984\pi$
$677$	8226.00	0.466988	0.233494	+	0.972358i	$0.424984\pi$
$678$	−416.000	−0.0235640
$679$	27776.0	1.56987
$680$	−2400.00	−0.135347
$681$	5780.00	0.325242
$682$	3900.00	0.218972
$683$	5797.00	0.324767	0.162384	−	0.986728i	$-0.448082\pi$
$683$	5797.00	0.324767	0.162384	+	0.986728i	$0.448082\pi$
$684$	6032.00	0.337192
$685$	−3260.00	−0.181837
$686$	−21632.0	−1.20396
$687$	1064.00	0.0590890
$688$	−5312.00	−0.294358
$689$	−8018.00	−0.443340
$690$	−230.000	−0.0126898
$691$	16892.0	0.929959	0.464980	−	0.885321i	$-0.346062\pi$
$691$	16892.0	0.929959	0.464980	+	0.885321i	$0.346062\pi$
$692$	1368.00	0.0751496
$693$	−24960.0	−1.36818
$694$	13688.0	0.748688
$695$	−9995.00	−0.545514
$696$	−680.000	−0.0370335
$697$	−8580.00	−0.466271
$698$	8114.00	0.439999
$699$	2833.00	0.153296
$700$	−3200.00	−0.172784
$701$	−19008.0	−1.02414	−0.512070	−	0.858944i	$-0.671121\pi$
$701$	−19008.0	−1.02414	−0.512070	+	0.858944i	$0.671121\pi$
$702$	2014.00	0.108281
$703$	1972.00	0.105797
$704$	−1920.00	−0.102788
$705$	2805.00	0.149847
$706$	−14310.0	−0.762838
$707$	−1600.00	−0.0851120
$708$	−1568.00	−0.0832331
$709$	−29484.0	−1.56177	−0.780885	−	0.624675i	$-0.785232\pi$
$709$	−29484.0	−1.56177	−0.780885	+	0.624675i	$0.785232\pi$
$710$	−7370.00	−0.389565
$711$	−28964.0	−1.52776
$712$	6592.00	0.346974
$713$	−1495.00	−0.0785248
$714$	−3840.00	−0.201272
$715$	−2850.00	−0.149068
$716$	6756.00	0.352631
$717$	−6831.00	−0.355800
$718$	−10868.0	−0.564889
$719$	13760.0	0.713715	0.356858	−	0.934159i	$-0.383848\pi$
$719$	13760.0	0.713715	0.356858	+	0.934159i	$0.383848\pi$
$720$	−2080.00	−0.107663
$721$	−14080.0	−0.727277
$722$	−6990.00	−0.360306
$723$	1794.00	0.0922816
$724$	−776.000	−0.0398340
$725$	2125.00	0.108856
$726$	862.000	0.0440659
$727$	−30554.0	−1.55871	−0.779357	−	0.626580i	$-0.784454\pi$
$727$	−30554.0	−1.55871	−0.779357	+	0.626580i	$0.784454\pi$
$728$	−4864.00	−0.247626
$729$	−15443.0	−0.784586
$730$	10410.0	0.527796
$731$	19920.0	1.00789
$732$	984.000	0.0496854
$733$	37404.0	1.88479	0.942393	−	0.334508i	$-0.108570\pi$
$733$	37404.0	1.88479	0.942393	+	0.334508i	$0.108570\pi$
$734$	−5888.00	−0.296090
$735$	−3405.00	−0.170878
$736$	736.000	0.0368605
$737$	−26820.0	−1.34047
$738$	−7436.00	−0.370898
$739$	6873.00	0.342121	0.171060	−	0.985261i	$-0.445281\pi$
$739$	6873.00	0.342121	0.171060	+	0.985261i	$0.445281\pi$
$740$	−680.000	−0.0337801
$741$	1102.00	0.0546329
$742$	27008.0	1.33625
$743$	25216.0	1.24507	0.622534	−	0.782593i	$-0.286103\pi$
$743$	25216.0	1.24507	0.622534	+	0.782593i	$0.286103\pi$
$744$	520.000	0.0256238
$745$	9350.00	0.459809
$746$	−11924.0	−0.585213
$747$	24336.0	1.19198
$748$	7200.00	0.351949
$749$	10176.0	0.496426
$750$	−250.000	−0.0121716
$751$	−27556.0	−1.33893	−0.669463	−	0.742846i	$-0.733476\pi$
$751$	−27556.0	−1.33893	−0.669463	+	0.742846i	$0.733476\pi$
$752$	−8976.00	−0.435267
$753$	6672.00	0.322897
$754$	3230.00	0.156008
$755$	7315.00	0.352609
$756$	−6784.00	−0.326365
$757$	−30550.0	−1.46679	−0.733394	−	0.679804i	$-0.762065\pi$
$757$	−30550.0	−1.46679	−0.733394	+	0.679804i	$0.762065\pi$
$758$	−11712.0	−0.561212
$759$	690.000	0.0329979
$760$	−2320.00	−0.110731
$761$	10125.0	0.482301	0.241150	−	0.970488i	$-0.422475\pi$
$761$	10125.0	0.482301	0.241150	+	0.970488i	$0.422475\pi$
$762$	990.000	0.0470655
$763$	26496.0	1.25717
$764$	−1192.00	−0.0564464
$765$	7800.00	0.368640
$766$	12912.0	0.609046
$767$	7448.00	0.350628
$768$	−256.000	−0.0120281
$769$	−35210.0	−1.65111	−0.825556	−	0.564320i	$-0.809138\pi$
$769$	−35210.0	−1.65111	−0.825556	+	0.564320i	$0.809138\pi$
$770$	9600.00	0.449299
$771$	−291.000	−0.0135929
$772$	9204.00	0.429092
$773$	15696.0	0.730331	0.365166	−	0.930943i	$-0.381012\pi$
$773$	15696.0	0.730331	0.365166	+	0.930943i	$0.381012\pi$
$774$	17264.0	0.801733
$775$	−1625.00	−0.0753184
$776$	−6944.00	−0.321231
$777$	−1088.00	−0.0502340
$778$	−304.000	−0.0140089
$779$	−8294.00	−0.381468
$780$	−380.000	−0.0174438
$781$	22110.0	1.01301
$782$	−2760.00	−0.126212
$783$	4505.00	0.205614
$784$	10896.0	0.496356
$785$	−15020.0	−0.682913
$786$	−670.000	−0.0304047
$787$	9356.00	0.423768	0.211884	−	0.977295i	$-0.432040\pi$
$787$	9356.00	0.423768	0.211884	+	0.977295i	$0.432040\pi$
$788$	−2140.00	−0.0967441
$789$	5306.00	0.239415
$790$	11140.0	0.501701
$791$	−6656.00	−0.299191
$792$	6240.00	0.279961
$793$	−4674.00	−0.209305
$794$	23206.0	1.03722
$795$	2110.00	0.0941308
$796$	1112.00	0.0495148
$797$	−31110.0	−1.38265	−0.691325	−	0.722544i	$-0.742973\pi$
$797$	−31110.0	−1.38265	−0.691325	+	0.722544i	$0.742973\pi$
$798$	−3712.00	−0.164666
$799$	33660.0	1.49037
$800$	800.000	0.0353553
$801$	−21424.0	−0.945043
$802$	1204.00	0.0530109
$803$	−31230.0	−1.37246
$804$	−3576.00	−0.156860
$805$	−3680.00	−0.161122
$806$	−2470.00	−0.107943
$807$	−7785.00	−0.339585
$808$	400.000	0.0174158
$809$	20890.0	0.907853	0.453927	−	0.891039i	$-0.350023\pi$
$809$	20890.0	0.907853	0.453927	+	0.891039i	$0.350023\pi$
$810$	6490.00	0.281525
$811$	6291.00	0.272388	0.136194	−	0.990682i	$-0.456513\pi$
$811$	6291.00	0.272388	0.136194	+	0.990682i	$0.456513\pi$
$812$	−10880.0	−0.470213
$813$	−3440.00	−0.148396
$814$	2040.00	0.0878402
$815$	−20235.0	−0.869695
$816$	960.000	0.0411847
$817$	19256.0	0.824580
$818$	7258.00	0.310232
$819$	15808.0	0.674452
$820$	2860.00	0.121799
$821$	36210.0	1.53927	0.769633	−	0.638486i	$-0.220439\pi$
$821$	36210.0	1.53927	0.769633	+	0.638486i	$0.220439\pi$
$822$	1304.00	0.0553312
$823$	40867.0	1.73090	0.865452	−	0.500992i	$-0.167031\pi$
$823$	40867.0	1.73090	0.865452	+	0.500992i	$0.167031\pi$
$824$	3520.00	0.148817
$825$	750.000	0.0316505
$826$	−25088.0	−1.05681
$827$	2088.00	0.0877955	0.0438977	−	0.999036i	$-0.486022\pi$
$827$	2088.00	0.0877955	0.0438977	+	0.999036i	$0.486022\pi$
$828$	−2392.00	−0.100396
$829$	−25942.0	−1.08686	−0.543428	−	0.839456i	$-0.682874\pi$
$829$	−25942.0	−1.08686	−0.543428	+	0.839456i	$0.682874\pi$
$830$	−9360.00	−0.391434
$831$	7643.00	0.319053
$832$	1216.00	0.0506697
$833$	−40860.0	−1.69954
$834$	3998.00	0.165995
$835$	−10560.0	−0.437657
$836$	6960.00	0.287939
$837$	−3445.00	−0.142266
$838$	184.000	0.00758493
$839$	19636.0	0.807998	0.403999	−	0.914760i	$-0.367620\pi$
$839$	19636.0	0.807998	0.403999	+	0.914760i	$0.367620\pi$
$840$	1280.00	0.0525764
$841$	−17164.0	−0.703760
$842$	−16560.0	−0.677785
$843$	−5408.00	−0.220951
$844$	−9776.00	−0.398701
$845$	−9180.00	−0.373730
$846$	29172.0	1.18552
$847$	13792.0	0.559503
$848$	−6752.00	−0.273425
$849$	−4402.00	−0.177946
$850$	−3000.00	−0.121058
$851$	−782.000	−0.0315001
$852$	2948.00	0.118541
$853$	−15954.0	−0.640392	−0.320196	−	0.947351i	$-0.603749\pi$
$853$	−15954.0	−0.640392	−0.320196	+	0.947351i	$0.603749\pi$
$854$	15744.0	0.630853
$855$	7540.00	0.301594
$856$	−2544.00	−0.101580
$857$	−36353.0	−1.44900	−0.724501	−	0.689274i	$-0.757930\pi$
$857$	−36353.0	−1.44900	−0.724501	+	0.689274i	$0.757930\pi$
$858$	1140.00	0.0453601
$859$	−34173.0	−1.35735	−0.678677	−	0.734437i	$-0.737447\pi$
$859$	−34173.0	−1.35735	−0.678677	+	0.734437i	$0.737447\pi$
$860$	−6640.00	−0.263282
$861$	4576.00	0.181126
$862$	−30744.0	−1.21479
$863$	9129.00	0.360087	0.180043	−	0.983659i	$-0.442376\pi$
$863$	9129.00	0.360087	0.180043	+	0.983659i	$0.442376\pi$
$864$	1696.00	0.0667814
$865$	1710.00	0.0672159
$866$	−22684.0	−0.890108
$867$	1313.00	0.0514323
$868$	8320.00	0.325345
$869$	−33420.0	−1.30460
$870$	−850.000	−0.0331238
$871$	16986.0	0.660791
$872$	−6624.00	−0.257244
$873$	22568.0	0.874927
$874$	−2668.00	−0.103257
$875$	−4000.00	−0.154542
$876$	−4164.00	−0.160603
$877$	−8106.00	−0.312110	−0.156055	−	0.987748i	$-0.549878\pi$
$877$	−8106.00	−0.312110	−0.156055	+	0.987748i	$0.549878\pi$
$878$	9186.00	0.353089
$879$	−9808.00	−0.376355
$880$	−2400.00	−0.0919363
$881$	14124.0	0.540124	0.270062	−	0.962843i	$-0.412956\pi$
$881$	14124.0	0.540124	0.270062	+	0.962843i	$0.412956\pi$
$882$	−35412.0	−1.35191
$883$	−1700.00	−0.0647900	−0.0323950	−	0.999475i	$-0.510313\pi$
$883$	−1700.00	−0.0647900	−0.0323950	+	0.999475i	$0.510313\pi$
$884$	−4560.00	−0.173495
$885$	−1960.00	−0.0744460
$886$	1934.00	0.0733341
$887$	26711.0	1.01112	0.505562	−	0.862790i	$-0.331285\pi$
$887$	26711.0	1.01112	0.505562	+	0.862790i	$0.331285\pi$
$888$	272.000	0.0102790
$889$	15840.0	0.597589
$890$	8240.00	0.310343
$891$	−19470.0	−0.732065
$892$	−21472.0	−0.805982
$893$	32538.0	1.21931
$894$	−3740.00	−0.139915
$895$	8445.00	0.315402
$896$	−4096.00	−0.152721
$897$	−437.000	−0.0162664
$898$	−22420.0	−0.833146
$899$	−5525.00	−0.204971
$900$	−2600.00	−0.0962963
$901$	25320.0	0.936217
$902$	−8580.00	−0.316721
$903$	−10624.0	−0.391522
$904$	1664.00	0.0612210
$905$	−970.000	−0.0356286
$906$	−2926.00	−0.107296
$907$	−18758.0	−0.686714	−0.343357	−	0.939205i	$-0.611564\pi$
$907$	−18758.0	−0.686714	−0.343357	+	0.939205i	$0.611564\pi$
$908$	−23120.0	−0.845005
$909$	−1300.00	−0.0474348
$910$	−6080.00	−0.221484
$911$	20298.0	0.738203	0.369101	−	0.929389i	$-0.379666\pi$
$911$	20298.0	0.738203	0.369101	+	0.929389i	$0.379666\pi$
$912$	928.000	0.0336942
$913$	28080.0	1.01787
$914$	−144.000	−0.00521127
$915$	1230.00	0.0444399
$916$	−4256.00	−0.153518
$917$	−10720.0	−0.386048
$918$	−6360.00	−0.228662
$919$	39276.0	1.40979	0.704894	−	0.709312i	$-0.250994\pi$
$919$	39276.0	1.40979	0.704894	+	0.709312i	$0.250994\pi$
$920$	920.000	0.0329690
$921$	3288.00	0.117637
$922$	10274.0	0.366981
$923$	−14003.0	−0.499366
$924$	−3840.00	−0.136717
$925$	−850.000	−0.0302139
$926$	−39056.0	−1.38603
$927$	−11440.0	−0.405328
$928$	2720.00	0.0962159
$929$	−51265.0	−1.81050	−0.905248	−	0.424884i	$-0.860315\pi$
$929$	−51265.0	−1.81050	−0.905248	+	0.424884i	$0.860315\pi$
$930$	650.000	0.0229186
$931$	−39498.0	−1.39043
$932$	−11332.0	−0.398275
$933$	−3919.00	−0.137516
$934$	29748.0	1.04217
$935$	9000.00	0.314793
$936$	−3952.00	−0.138008
$937$	12182.0	0.424726	0.212363	−	0.977191i	$-0.431884\pi$
$937$	12182.0	0.424726	0.212363	+	0.977191i	$0.431884\pi$
$938$	−57216.0	−1.99165
$939$	−5112.00	−0.177661
$940$	−11220.0	−0.389315
$941$	33192.0	1.14987	0.574935	−	0.818199i	$-0.305027\pi$
$941$	33192.0	1.14987	0.574935	+	0.818199i	$0.305027\pi$
$942$	6008.00	0.207804
$943$	3289.00	0.113579
$944$	6272.00	0.216246
$945$	−8480.00	−0.291909
$946$	19920.0	0.684625
$947$	18127.0	0.622015	0.311008	−	0.950407i	$-0.399334\pi$
$947$	18127.0	0.622015	0.311008	+	0.950407i	$0.399334\pi$
$948$	−4456.00	−0.152663
$949$	19779.0	0.676558
$950$	−2900.00	−0.0990404
$951$	−8058.00	−0.274762
$952$	15360.0	0.522921
$953$	−31722.0	−1.07825	−0.539127	−	0.842224i	$-0.681246\pi$
$953$	−31722.0	−1.07825	−0.539127	+	0.842224i	$0.681246\pi$
$954$	21944.0	0.744720
$955$	−1490.00	−0.0504872
$956$	27324.0	0.924395
$957$	2550.00	0.0861335
$958$	21136.0	0.712811
$959$	20864.0	0.702538
$960$	−320.000	−0.0107583
$961$	−25566.0	−0.858179
$962$	−1292.00	−0.0433012
$963$	8268.00	0.276669
$964$	−7176.00	−0.239755
$965$	11505.0	0.383792
$966$	1472.00	0.0490278
$967$	−1459.00	−0.0485194	−0.0242597	−	0.999706i	$-0.507723\pi$
$967$	−1459.00	−0.0485194	−0.0242597	+	0.999706i	$0.507723\pi$
$968$	−3448.00	−0.114486
$969$	−3480.00	−0.115370
$970$	−8680.00	−0.287318
$971$	−29626.0	−0.979139	−0.489569	−	0.871964i	$-0.662846\pi$
$971$	−29626.0	−0.979139	−0.489569	+	0.871964i	$0.662846\pi$
$972$	−8320.00	−0.274552
$973$	63968.0	2.10763
$974$	−18622.0	−0.612615
$975$	−475.000	−0.0156022
$976$	−3936.00	−0.129086
$977$	−40202.0	−1.31645	−0.658227	−	0.752819i	$-0.728693\pi$
$977$	−40202.0	−1.31645	−0.658227	+	0.752819i	$0.728693\pi$
$978$	8094.00	0.264640
$979$	−24720.0	−0.807002
$980$	13620.0	0.443954
$981$	21528.0	0.700648
$982$	−33022.0	−1.07309
$983$	−9278.00	−0.301040	−0.150520	−	0.988607i	$-0.548095\pi$
$983$	−9278.00	−0.301040	−0.150520	+	0.988607i	$0.548095\pi$
$984$	−1144.00	−0.0370624
$985$	−2675.00	−0.0865305
$986$	−10200.0	−0.329446
$987$	−17952.0	−0.578945
$988$	−4408.00	−0.141940
$989$	−7636.00	−0.245511
$990$	7800.00	0.250404
$991$	37264.0	1.19448	0.597240	−	0.802062i	$-0.296264\pi$
$991$	37264.0	1.19448	0.597240	+	0.802062i	$0.296264\pi$
$992$	−2080.00	−0.0665726
$993$	2555.00	0.0816520
$994$	47168.0	1.50511
$995$	1390.00	0.0442874
$996$	3744.00	0.119110
$997$	−41930.0	−1.33193	−0.665966	−	0.745982i	$-0.731980\pi$
$997$	−41930.0	−1.33193	−0.665966	+	0.745982i	$0.731980\pi$
$998$	4662.00	0.147869
$999$	−1802.00	−0.0570698

Twists

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

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