LMFDB - Embedded newform 575.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,4,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	575.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:	$33.9260982533$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +5.00000 q^{3} -4.00000 q^{4} +10.0000 q^{6} +8.00000 q^{7} -24.0000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +5.00000 q^{3} -4.00000 q^{4} +10.0000 q^{6} +8.00000 q^{7} -24.0000 q^{8} -2.00000 q^{9} +34.0000 q^{11} -20.0000 q^{12} +57.0000 q^{13} +16.0000 q^{14} -16.0000 q^{16} +80.0000 q^{17} -4.00000 q^{18} -70.0000 q^{19} +40.0000 q^{21} +68.0000 q^{22} -23.0000 q^{23} -120.000 q^{24} +114.000 q^{26} -145.000 q^{27} -32.0000 q^{28} +245.000 q^{29} +103.000 q^{31} +160.000 q^{32} +170.000 q^{33} +160.000 q^{34} +8.00000 q^{36} +298.000 q^{37} -140.000 q^{38} +285.000 q^{39} +95.0000 q^{41} +80.0000 q^{42} -88.0000 q^{43} -136.000 q^{44} -46.0000 q^{46} +357.000 q^{47} -80.0000 q^{48} -279.000 q^{49} +400.000 q^{51} -228.000 q^{52} +414.000 q^{53} -290.000 q^{54} -192.000 q^{56} -350.000 q^{57} +490.000 q^{58} -408.000 q^{59} +822.000 q^{61} +206.000 q^{62} -16.0000 q^{63} +448.000 q^{64} +340.000 q^{66} -926.000 q^{67} -320.000 q^{68} -115.000 q^{69} +335.000 q^{71} +48.0000 q^{72} +899.000 q^{73} +596.000 q^{74} +280.000 q^{76} +272.000 q^{77} +570.000 q^{78} -1322.00 q^{79} -671.000 q^{81} +190.000 q^{82} +36.0000 q^{83} -160.000 q^{84} -176.000 q^{86} +1225.00 q^{87} -816.000 q^{88} -460.000 q^{89} +456.000 q^{91} +92.0000 q^{92} +515.000 q^{93} +714.000 q^{94} +800.000 q^{96} +964.000 q^{97} -558.000 q^{98} -68.0000 q^{99} +O(q^{100})\)

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	2.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	10.0000	0.680414
$7$	8.00000	0.431959	0.215980	−	0.976398i	$-0.430705\pi$
$7$	8.00000	0.431959	0.215980	+	0.976398i	$0.430705\pi$
$8$	−24.0000	−1.06066
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	34.0000	0.931944	0.465972	−	0.884799i	$-0.345705\pi$
$11$	34.0000	0.931944	0.465972	+	0.884799i	$0.345705\pi$
$12$	−20.0000	−0.481125
$13$	57.0000	1.21607	0.608037	−	0.793909i	$-0.291957\pi$
$13$	57.0000	1.21607	0.608037	+	0.793909i	$0.291957\pi$
$14$	16.0000	0.305441
$15$	0	0
$16$	−16.0000	−0.250000
$17$	80.0000	1.14134	0.570672	−	0.821178i	$-0.306683\pi$
$17$	80.0000	1.14134	0.570672	+	0.821178i	$0.306683\pi$
$18$	−4.00000	−0.0523783
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	0	0
$21$	40.0000	0.415653
$22$	68.0000	0.658984
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−120.000	−1.02062
$25$	0	0
$26$	114.000	0.859894
$27$	−145.000	−1.03353
$28$	−32.0000	−0.215980
$29$	245.000	1.56881	0.784403	−	0.620252i	$-0.212970\pi$
$29$	245.000	1.56881	0.784403	+	0.620252i	$0.212970\pi$
$30$	0	0
$31$	103.000	0.596753	0.298377	−	0.954448i	$-0.403555\pi$
$31$	103.000	0.596753	0.298377	+	0.954448i	$0.403555\pi$
$32$	160.000	0.883883
$33$	170.000	0.896764
$34$	160.000	0.807052
$35$	0	0
$36$	8.00000	0.0370370
$37$	298.000	1.32408	0.662039	−	0.749469i	$-0.269691\pi$
$37$	298.000	1.32408	0.662039	+	0.749469i	$0.269691\pi$
$38$	−140.000	−0.597658
$39$	285.000	1.17017
$40$	0	0
$41$	95.0000	0.361866	0.180933	−	0.983495i	$-0.442088\pi$
$41$	95.0000	0.361866	0.180933	+	0.983495i	$0.442088\pi$
$42$	80.0000	0.293911
$43$	−88.0000	−0.312090	−0.156045	−	0.987750i	$-0.549875\pi$
$43$	−88.0000	−0.312090	−0.156045	+	0.987750i	$0.549875\pi$
$44$	−136.000	−0.465972
$45$	0	0
$46$	−46.0000	−0.147442
$47$	357.000	1.10795	0.553977	−	0.832532i	$-0.313110\pi$
$47$	357.000	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$48$	−80.0000	−0.240563
$49$	−279.000	−0.813411
$50$	0	0
$51$	400.000	1.09826
$52$	−228.000	−0.608037
$53$	414.000	1.07297	0.536484	−	0.843911i	$-0.319752\pi$
$53$	414.000	1.07297	0.536484	+	0.843911i	$0.319752\pi$
$54$	−290.000	−0.730815
$55$	0	0
$56$	−192.000	−0.458162
$57$	−350.000	−0.813309
$58$	490.000	1.10931
$59$	−408.000	−0.900289	−0.450145	−	0.892956i	$-0.648628\pi$
$59$	−408.000	−0.900289	−0.450145	+	0.892956i	$0.648628\pi$
$60$	0	0
$61$	822.000	1.72535	0.862675	−	0.505759i	$-0.168788\pi$
$61$	822.000	1.72535	0.862675	+	0.505759i	$0.168788\pi$
$62$	206.000	0.421968
$63$	−16.0000	−0.0319970
$64$	448.000	0.875000
$65$	0	0
$66$	340.000	0.634108
$67$	−926.000	−1.68849	−0.844246	−	0.535957i	$-0.819951\pi$
$67$	−926.000	−1.68849	−0.844246	+	0.535957i	$0.819951\pi$
$68$	−320.000	−0.570672
$69$	−115.000	−0.200643
$70$	0	0
$71$	335.000	0.559960	0.279980	−	0.960006i	$-0.409672\pi$
$71$	335.000	0.559960	0.279980	+	0.960006i	$0.409672\pi$
$72$	48.0000	0.0785674
$73$	899.000	1.44137	0.720685	−	0.693263i	$-0.243827\pi$
$73$	899.000	1.44137	0.720685	+	0.693263i	$0.243827\pi$
$74$	596.000	0.936265
$75$	0	0
$76$	280.000	0.422608
$77$	272.000	0.402562
$78$	570.000	0.827433
$79$	−1322.00	−1.88274	−0.941371	−	0.337373i	$-0.890462\pi$
$79$	−1322.00	−1.88274	−0.941371	+	0.337373i	$0.890462\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	190.000	0.255878
$83$	36.0000	0.0476086	0.0238043	−	0.999717i	$-0.492422\pi$
$83$	36.0000	0.0476086	0.0238043	+	0.999717i	$0.492422\pi$
$84$	−160.000	−0.207827
$85$	0	0
$86$	−176.000	−0.220681
$87$	1225.00	1.50958
$88$	−816.000	−0.988476
$89$	−460.000	−0.547864	−0.273932	−	0.961749i	$-0.588324\pi$
$89$	−460.000	−0.547864	−0.273932	+	0.961749i	$0.588324\pi$
$90$	0	0
$91$	456.000	0.525294
$92$	92.0000	0.104257
$93$	515.000	0.574226
$94$	714.000	0.783441
$95$	0	0
$96$	800.000	0.850517
$97$	964.000	1.00907	0.504533	−	0.863393i	$-0.331665\pi$
$97$	964.000	1.00907	0.504533	+	0.863393i	$0.331665\pi$
$98$	−558.000	−0.575168
$99$	−68.0000	−0.0690329
$100$	0	0
$101$	−310.000	−0.305407	−0.152704	−	0.988272i	$-0.548798\pi$
$101$	−310.000	−0.305407	−0.152704	+	0.988272i	$0.548798\pi$
$102$	800.000	0.776586
$103$	−1044.00	−0.998722	−0.499361	−	0.866394i	$-0.666432\pi$
$103$	−1044.00	−0.998722	−0.499361	+	0.866394i	$0.666432\pi$
$104$	−1368.00	−1.28984
$105$	0	0
$106$	828.000	0.758703
$107$	−414.000	−0.374046	−0.187023	−	0.982356i	$-0.559884\pi$
$107$	−414.000	−0.374046	−0.187023	+	0.982356i	$0.559884\pi$
$108$	580.000	0.516764
$109$	704.000	0.618633	0.309316	−	0.950959i	$-0.399900\pi$
$109$	704.000	0.618633	0.309316	+	0.950959i	$0.399900\pi$
$110$	0	0
$111$	1490.00	1.27409
$112$	−128.000	−0.107990
$113$	−952.000	−0.792537	−0.396268	−	0.918135i	$-0.629695\pi$
$113$	−952.000	−0.792537	−0.396268	+	0.918135i	$0.629695\pi$
$114$	−700.000	−0.575097
$115$	0	0
$116$	−980.000	−0.784403
$117$	−114.000	−0.0900795
$118$	−816.000	−0.636601
$119$	640.000	0.493014
$120$	0	0
$121$	−175.000	−0.131480
$122$	1644.00	1.22001
$123$	475.000	0.348206
$124$	−412.000	−0.298377
$125$	0	0
$126$	−32.0000	−0.0226253
$127$	−261.000	−0.182362	−0.0911811	−	0.995834i	$-0.529064\pi$
$127$	−261.000	−0.182362	−0.0911811	+	0.995834i	$0.529064\pi$
$128$	−384.000	−0.265165
$129$	−440.000	−0.300309
$130$	0	0
$131$	−1441.00	−0.961074	−0.480537	−	0.876974i	$-0.659558\pi$
$131$	−1441.00	−0.961074	−0.480537	+	0.876974i	$0.659558\pi$
$132$	−680.000	−0.448382
$133$	−560.000	−0.365099
$134$	−1852.00	−1.19394
$135$	0	0
$136$	−1920.00	−1.21058
$137$	−1556.00	−0.970351	−0.485175	−	0.874417i	$-0.661244\pi$
$137$	−1556.00	−0.970351	−0.485175	+	0.874417i	$0.661244\pi$
$138$	−230.000	−0.141876
$139$	25.0000	0.0152552	0.00762760	−	0.999971i	$-0.497572\pi$
$139$	25.0000	0.0152552	0.00762760	+	0.999971i	$0.497572\pi$
$140$	0	0
$141$	1785.00	1.06613
$142$	670.000	0.395952
$143$	1938.00	1.13331
$144$	32.0000	0.0185185
$145$	0	0
$146$	1798.00	1.01920
$147$	−1395.00	−0.782705
$148$	−1192.00	−0.662039
$149$	822.000	0.451952	0.225976	−	0.974133i	$-0.427443\pi$
$149$	822.000	0.451952	0.225976	+	0.974133i	$0.427443\pi$
$150$	0	0
$151$	−1489.00	−0.802471	−0.401235	−	0.915975i	$-0.631419\pi$
$151$	−1489.00	−0.802471	−0.401235	+	0.915975i	$0.631419\pi$
$152$	1680.00	0.896487
$153$	−160.000	−0.0845440
$154$	544.000	0.284654
$155$	0	0
$156$	−1140.00	−0.585084
$157$	632.000	0.321268	0.160634	−	0.987014i	$-0.448646\pi$
$157$	632.000	0.321268	0.160634	+	0.987014i	$0.448646\pi$
$158$	−2644.00	−1.33130
$159$	2070.00	1.03246
$160$	0	0
$161$	−184.000	−0.0900698
$162$	−1342.00	−0.650849
$163$	3043.00	1.46225	0.731123	−	0.682245i	$-0.238996\pi$
$163$	3043.00	1.46225	0.731123	+	0.682245i	$0.238996\pi$
$164$	−380.000	−0.180933
$165$	0	0
$166$	72.0000	0.0336644
$167$	2224.00	1.03053	0.515264	−	0.857031i	$-0.327694\pi$
$167$	2224.00	1.03053	0.515264	+	0.857031i	$0.327694\pi$
$168$	−960.000	−0.440867
$169$	1052.00	0.478835
$170$	0	0
$171$	140.000	0.0626086
$172$	352.000	0.156045
$173$	−3230.00	−1.41949	−0.709747	−	0.704457i	$-0.751191\pi$
$173$	−3230.00	−1.41949	−0.709747	+	0.704457i	$0.751191\pi$
$174$	2450.00	1.06744
$175$	0	0
$176$	−544.000	−0.232986
$177$	−2040.00	−0.866304
$178$	−920.000	−0.387398
$179$	369.000	0.154080	0.0770401	−	0.997028i	$-0.475453\pi$
$179$	369.000	0.154080	0.0770401	+	0.997028i	$0.475453\pi$
$180$	0	0
$181$	−1370.00	−0.562604	−0.281302	−	0.959619i	$-0.590766\pi$
$181$	−1370.00	−0.562604	−0.281302	+	0.959619i	$0.590766\pi$
$182$	912.000	0.371439
$183$	4110.00	1.66022
$184$	552.000	0.221163
$185$	0	0
$186$	1030.00	0.406039
$187$	2720.00	1.06367
$188$	−1428.00	−0.553977
$189$	−1160.00	−0.446442
$190$	0	0
$191$	4410.00	1.67066	0.835331	−	0.549747i	$-0.185276\pi$
$191$	4410.00	1.67066	0.835331	+	0.549747i	$0.185276\pi$
$192$	2240.00	0.841969
$193$	135.000	0.0503498	0.0251749	−	0.999683i	$-0.491986\pi$
$193$	135.000	0.0503498	0.0251749	+	0.999683i	$0.491986\pi$
$194$	1928.00	0.713517
$195$	0	0
$196$	1116.00	0.406706
$197$	−1221.00	−0.441587	−0.220794	−	0.975321i	$-0.570865\pi$
$197$	−1221.00	−0.441587	−0.220794	+	0.975321i	$0.570865\pi$
$198$	−136.000	−0.0488136
$199$	−1098.00	−0.391131	−0.195566	−	0.980691i	$-0.562654\pi$
$199$	−1098.00	−0.391131	−0.195566	+	0.980691i	$0.562654\pi$
$200$	0	0
$201$	−4630.00	−1.62475
$202$	−620.000	−0.215956
$203$	1960.00	0.677660
$204$	−1600.00	−0.549129
$205$	0	0
$206$	−2088.00	−0.706203
$207$	46.0000	0.0154455
$208$	−912.000	−0.304018
$209$	−2380.00	−0.787694
$210$	0	0
$211$	−3676.00	−1.19937	−0.599683	−	0.800238i	$-0.704707\pi$
$211$	−3676.00	−1.19937	−0.599683	+	0.800238i	$0.704707\pi$
$212$	−1656.00	−0.536484
$213$	1675.00	0.538822
$214$	−828.000	−0.264490
$215$	0	0
$216$	3480.00	1.09622
$217$	824.000	0.257773
$218$	1408.00	0.437439
$219$	4495.00	1.38696
$220$	0	0
$221$	4560.00	1.38796
$222$	2980.00	0.900921
$223$	−1656.00	−0.497282	−0.248641	−	0.968596i	$-0.579984\pi$
$223$	−1656.00	−0.497282	−0.248641	+	0.968596i	$0.579984\pi$
$224$	1280.00	0.381802
$225$	0	0
$226$	−1904.00	−0.560408
$227$	−2940.00	−0.859624	−0.429812	−	0.902918i	$-0.641420\pi$
$227$	−2940.00	−0.859624	−0.429812	+	0.902918i	$0.641420\pi$
$228$	1400.00	0.406655
$229$	3612.00	1.04230	0.521152	−	0.853464i	$-0.325502\pi$
$229$	3612.00	1.04230	0.521152	+	0.853464i	$0.325502\pi$
$230$	0	0
$231$	1360.00	0.387366
$232$	−5880.00	−1.66397
$233$	4325.00	1.21605	0.608026	−	0.793917i	$-0.291962\pi$
$233$	4325.00	1.21605	0.608026	+	0.793917i	$0.291962\pi$
$234$	−228.000	−0.0636958
$235$	0	0
$236$	1632.00	0.450145
$237$	−6610.00	−1.81167
$238$	1280.00	0.348614
$239$	2735.00	0.740219	0.370110	−	0.928988i	$-0.379320\pi$
$239$	2735.00	0.740219	0.370110	+	0.928988i	$0.379320\pi$
$240$	0	0
$241$	−6710.00	−1.79348	−0.896741	−	0.442556i	$-0.854072\pi$
$241$	−6710.00	−1.79348	−0.896741	+	0.442556i	$0.854072\pi$
$242$	−350.000	−0.0929705
$243$	560.000	0.147835
$244$	−3288.00	−0.862675
$245$	0	0
$246$	950.000	0.246219
$247$	−3990.00	−1.02784
$248$	−2472.00	−0.632952
$249$	180.000	0.0458114
$250$	0	0
$251$	−6948.00	−1.74723	−0.873613	−	0.486621i	$-0.838229\pi$
$251$	−6948.00	−1.74723	−0.873613	+	0.486621i	$0.838229\pi$
$252$	64.0000	0.0159985
$253$	−782.000	−0.194324
$254$	−522.000	−0.128950
$255$	0	0
$256$	−4352.00	−1.06250
$257$	4929.00	1.19635	0.598176	−	0.801365i	$-0.295892\pi$
$257$	4929.00	1.19635	0.598176	+	0.801365i	$0.295892\pi$
$258$	−880.000	−0.212350
$259$	2384.00	0.571948
$260$	0	0
$261$	−490.000	−0.116208
$262$	−2882.00	−0.679582
$263$	−6138.00	−1.43911	−0.719554	−	0.694437i	$-0.755654\pi$
$263$	−6138.00	−1.43911	−0.719554	+	0.694437i	$0.755654\pi$
$264$	−4080.00	−0.951162
$265$	0	0
$266$	−1120.00	−0.258164
$267$	−2300.00	−0.527182
$268$	3704.00	0.844246
$269$	−2063.00	−0.467596	−0.233798	−	0.972285i	$-0.575115\pi$
$269$	−2063.00	−0.467596	−0.233798	+	0.972285i	$0.575115\pi$
$270$	0	0
$271$	−1064.00	−0.238500	−0.119250	−	0.992864i	$-0.538049\pi$
$271$	−1064.00	−0.238500	−0.119250	+	0.992864i	$0.538049\pi$
$272$	−1280.00	−0.285336
$273$	2280.00	0.505465
$274$	−3112.00	−0.686142
$275$	0	0
$276$	460.000	0.100322
$277$	−5729.00	−1.24268	−0.621340	−	0.783541i	$-0.713411\pi$
$277$	−5729.00	−1.24268	−0.621340	+	0.783541i	$0.713411\pi$
$278$	50.0000	0.0107871
$279$	−206.000	−0.0442039
$280$	0	0
$281$	−960.000	−0.203804	−0.101902	−	0.994794i	$-0.532493\pi$
$281$	−960.000	−0.203804	−0.101902	+	0.994794i	$0.532493\pi$
$282$	3570.00	0.753867
$283$	114.000	0.0239456	0.0119728	−	0.999928i	$-0.496189\pi$
$283$	114.000	0.0239456	0.0119728	+	0.999928i	$0.496189\pi$
$284$	−1340.00	−0.279980
$285$	0	0
$286$	3876.00	0.801373
$287$	760.000	0.156311
$288$	−320.000	−0.0654729
$289$	1487.00	0.302666
$290$	0	0
$291$	4820.00	0.970974
$292$	−3596.00	−0.720685
$293$	7048.00	1.40529	0.702643	−	0.711543i	$-0.252003\pi$
$293$	7048.00	1.40529	0.702643	+	0.711543i	$0.252003\pi$
$294$	−2790.00	−0.553456
$295$	0	0
$296$	−7152.00	−1.40440
$297$	−4930.00	−0.963191
$298$	1644.00	0.319578
$299$	−1311.00	−0.253569
$300$	0	0
$301$	−704.000	−0.134810
$302$	−2978.00	−0.567433
$303$	−1550.00	−0.293878
$304$	1120.00	0.211304
$305$	0	0
$306$	−320.000	−0.0597816
$307$	−3872.00	−0.719826	−0.359913	−	0.932986i	$-0.617194\pi$
$307$	−3872.00	−0.719826	−0.359913	+	0.932986i	$0.617194\pi$
$308$	−1088.00	−0.201281
$309$	−5220.00	−0.961021
$310$	0	0
$311$	−4977.00	−0.907459	−0.453730	−	0.891139i	$-0.649907\pi$
$311$	−4977.00	−0.907459	−0.453730	+	0.891139i	$0.649907\pi$
$312$	−6840.00	−1.24115
$313$	2536.00	0.457965	0.228983	−	0.973430i	$-0.426460\pi$
$313$	2536.00	0.457965	0.228983	+	0.973430i	$0.426460\pi$
$314$	1264.00	0.227171
$315$	0	0
$316$	5288.00	0.941371
$317$	−1434.00	−0.254074	−0.127037	−	0.991898i	$-0.540547\pi$
$317$	−1434.00	−0.254074	−0.127037	+	0.991898i	$0.540547\pi$
$318$	4140.00	0.730062
$319$	8330.00	1.46204
$320$	0	0
$321$	−2070.00	−0.359926
$322$	−368.000	−0.0636889
$323$	−5600.00	−0.964682
$324$	2684.00	0.460219
$325$	0	0
$326$	6086.00	1.03396
$327$	3520.00	0.595280
$328$	−2280.00	−0.383817
$329$	2856.00	0.478591
$330$	0	0
$331$	5469.00	0.908167	0.454084	−	0.890959i	$-0.349967\pi$
$331$	5469.00	0.908167	0.454084	+	0.890959i	$0.349967\pi$
$332$	−144.000	−0.0238043
$333$	−596.000	−0.0980799
$334$	4448.00	0.728694
$335$	0	0
$336$	−640.000	−0.103913
$337$	7796.00	1.26016	0.630082	−	0.776529i	$-0.283021\pi$
$337$	7796.00	1.26016	0.630082	+	0.776529i	$0.283021\pi$
$338$	2104.00	0.338587
$339$	−4760.00	−0.762619
$340$	0	0
$341$	3502.00	0.556141
$342$	280.000	0.0442710
$343$	−4976.00	−0.783320
$344$	2112.00	0.331022
$345$	0	0
$346$	−6460.00	−1.00373
$347$	10068.0	1.55758	0.778788	−	0.627288i	$-0.215835\pi$
$347$	10068.0	1.55758	0.778788	+	0.627288i	$0.215835\pi$
$348$	−4900.00	−0.754792
$349$	−7495.00	−1.14956	−0.574782	−	0.818306i	$-0.694913\pi$
$349$	−7495.00	−1.14956	−0.574782	+	0.818306i	$0.694913\pi$
$350$	0	0
$351$	−8265.00	−1.25685
$352$	5440.00	0.823730
$353$	−10617.0	−1.60081	−0.800405	−	0.599460i	$-0.795382\pi$
$353$	−10617.0	−1.60081	−0.800405	+	0.599460i	$0.795382\pi$
$354$	−4080.00	−0.612569
$355$	0	0
$356$	1840.00	0.273932
$357$	3200.00	0.474403
$358$	738.000	0.108951
$359$	2522.00	0.370769	0.185384	−	0.982666i	$-0.440647\pi$
$359$	2522.00	0.370769	0.185384	+	0.982666i	$0.440647\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	−2740.00	−0.397821
$363$	−875.000	−0.126517
$364$	−1824.00	−0.262647
$365$	0	0
$366$	8220.00	1.17395
$367$	−7204.00	−1.02465	−0.512324	−	0.858792i	$-0.671215\pi$
$367$	−7204.00	−1.02465	−0.512324	+	0.858792i	$0.671215\pi$
$368$	368.000	0.0521286
$369$	−190.000	−0.0268049
$370$	0	0
$371$	3312.00	0.463478
$372$	−2060.00	−0.287113
$373$	13310.0	1.84763	0.923815	−	0.382840i	$-0.125054\pi$
$373$	13310.0	1.84763	0.923815	+	0.382840i	$0.125054\pi$
$374$	5440.00	0.752128
$375$	0	0
$376$	−8568.00	−1.17516
$377$	13965.0	1.90778
$378$	−2320.00	−0.315682
$379$	12952.0	1.75541	0.877704	−	0.479203i	$-0.159074\pi$
$379$	12952.0	1.75541	0.877704	+	0.479203i	$0.159074\pi$
$380$	0	0
$381$	−1305.00	−0.175478
$382$	8820.00	1.18134
$383$	2812.00	0.375161	0.187580	−	0.982249i	$-0.439936\pi$
$383$	2812.00	0.375161	0.187580	+	0.982249i	$0.439936\pi$
$384$	−1920.00	−0.255155
$385$	0	0
$386$	270.000	0.0356027
$387$	176.000	0.0231178
$388$	−3856.00	−0.504533
$389$	1264.00	0.164749	0.0823745	−	0.996601i	$-0.473750\pi$
$389$	1264.00	0.164749	0.0823745	+	0.996601i	$0.473750\pi$
$390$	0	0
$391$	−1840.00	−0.237987
$392$	6696.00	0.862753
$393$	−7205.00	−0.924794
$394$	−2442.00	−0.312249
$395$	0	0
$396$	272.000	0.0345165
$397$	−7119.00	−0.899981	−0.449990	−	0.893033i	$-0.648573\pi$
$397$	−7119.00	−0.899981	−0.449990	+	0.893033i	$0.648573\pi$
$398$	−2196.00	−0.276572
$399$	−2800.00	−0.351317
$400$	0	0
$401$	4262.00	0.530758	0.265379	−	0.964144i	$-0.414503\pi$
$401$	4262.00	0.530758	0.265379	+	0.964144i	$0.414503\pi$
$402$	−9260.00	−1.14887
$403$	5871.00	0.725696
$404$	1240.00	0.152704
$405$	0	0
$406$	3920.00	0.479178
$407$	10132.0	1.23397
$408$	−9600.00	−1.16488
$409$	229.000	0.0276854	0.0138427	−	0.999904i	$-0.495594\pi$
$409$	229.000	0.0276854	0.0138427	+	0.999904i	$0.495594\pi$
$410$	0	0
$411$	−7780.00	−0.933720
$412$	4176.00	0.499361
$413$	−3264.00	−0.388888
$414$	92.0000	0.0109216
$415$	0	0
$416$	9120.00	1.07487
$417$	125.000	0.0146793
$418$	−4760.00	−0.556984
$419$	15776.0	1.83940	0.919699	−	0.392623i	$-0.128432\pi$
$419$	15776.0	1.83940	0.919699	+	0.392623i	$0.128432\pi$
$420$	0	0
$421$	−8728.00	−1.01040	−0.505198	−	0.863003i	$-0.668581\pi$
$421$	−8728.00	−1.01040	−0.505198	+	0.863003i	$0.668581\pi$
$422$	−7352.00	−0.848080
$423$	−714.000	−0.0820706
$424$	−9936.00	−1.13805
$425$	0	0
$426$	3350.00	0.381005
$427$	6576.00	0.745281
$428$	1656.00	0.187023
$429$	9690.00	1.09053
$430$	0	0
$431$	−2928.00	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$431$	−2928.00	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$432$	2320.00	0.258382
$433$	5314.00	0.589780	0.294890	−	0.955531i	$-0.404717\pi$
$433$	5314.00	0.589780	0.294890	+	0.955531i	$0.404717\pi$
$434$	1648.00	0.182273
$435$	0	0
$436$	−2816.00	−0.309316
$437$	1610.00	0.176240
$438$	8990.00	0.980728
$439$	2585.00	0.281037	0.140519	−	0.990078i	$-0.455123\pi$
$439$	2585.00	0.281037	0.140519	+	0.990078i	$0.455123\pi$
$440$	0	0
$441$	558.000	0.0602527
$442$	9120.00	0.981435
$443$	2997.00	0.321426	0.160713	−	0.987001i	$-0.448621\pi$
$443$	2997.00	0.321426	0.160713	+	0.987001i	$0.448621\pi$
$444$	−5960.00	−0.637047
$445$	0	0
$446$	−3312.00	−0.351632
$447$	4110.00	0.434891
$448$	3584.00	0.377964
$449$	−16562.0	−1.74078	−0.870389	−	0.492365i	$-0.836132\pi$
$449$	−16562.0	−1.74078	−0.870389	+	0.492365i	$0.836132\pi$
$450$	0	0
$451$	3230.00	0.337239
$452$	3808.00	0.396268
$453$	−7445.00	−0.772178
$454$	−5880.00	−0.607846
$455$	0	0
$456$	8400.00	0.862645
$457$	−3924.00	−0.401656	−0.200828	−	0.979626i	$-0.564363\pi$
$457$	−3924.00	−0.401656	−0.200828	+	0.979626i	$0.564363\pi$
$458$	7224.00	0.737020
$459$	−11600.0	−1.17961
$460$	0	0
$461$	−4543.00	−0.458977	−0.229489	−	0.973311i	$-0.573705\pi$
$461$	−4543.00	−0.458977	−0.229489	+	0.973311i	$0.573705\pi$
$462$	2720.00	0.273909
$463$	−9616.00	−0.965213	−0.482606	−	0.875837i	$-0.660310\pi$
$463$	−9616.00	−0.965213	−0.482606	+	0.875837i	$0.660310\pi$
$464$	−3920.00	−0.392201
$465$	0	0
$466$	8650.00	0.859879
$467$	−7826.00	−0.775469	−0.387735	−	0.921771i	$-0.626742\pi$
$467$	−7826.00	−0.775469	−0.387735	+	0.921771i	$0.626742\pi$
$468$	456.000	0.0450398
$469$	−7408.00	−0.729360
$470$	0	0
$471$	3160.00	0.309140
$472$	9792.00	0.954901
$473$	−2992.00	−0.290851
$474$	−13220.0	−1.28104
$475$	0	0
$476$	−2560.00	−0.246507
$477$	−828.000	−0.0794791
$478$	5470.00	0.523414
$479$	11404.0	1.08781	0.543906	−	0.839146i	$-0.316945\pi$
$479$	11404.0	1.08781	0.543906	+	0.839146i	$0.316945\pi$
$480$	0	0
$481$	16986.0	1.61018
$482$	−13420.0	−1.26818
$483$	−920.000	−0.0866697
$484$	700.000	0.0657400
$485$	0	0
$486$	1120.00	0.104535
$487$	9267.00	0.862275	0.431137	−	0.902286i	$-0.358112\pi$
$487$	9267.00	0.862275	0.431137	+	0.902286i	$0.358112\pi$
$488$	−19728.0	−1.83001
$489$	15215.0	1.40705
$490$	0	0
$491$	−18191.0	−1.67199	−0.835996	−	0.548735i	$-0.815110\pi$
$491$	−18191.0	−1.67199	−0.835996	+	0.548735i	$0.815110\pi$
$492$	−1900.00	−0.174103
$493$	19600.0	1.79055
$494$	−7980.00	−0.726796
$495$	0	0
$496$	−1648.00	−0.149188
$497$	2680.00	0.241880
$498$	360.000	0.0323935
$499$	19315.0	1.73278	0.866391	−	0.499366i	$-0.166434\pi$
$499$	19315.0	1.73278	0.866391	+	0.499366i	$0.166434\pi$
$500$	0	0
$501$	11120.0	0.991627
$502$	−13896.0	−1.23548
$503$	−8422.00	−0.746557	−0.373279	−	0.927719i	$-0.621766\pi$
$503$	−8422.00	−0.746557	−0.373279	+	0.927719i	$0.621766\pi$
$504$	384.000	0.0339379
$505$	0	0
$506$	−1564.00	−0.137408
$507$	5260.00	0.460759
$508$	1044.00	0.0911811
$509$	−863.000	−0.0751509	−0.0375754	−	0.999294i	$-0.511963\pi$
$509$	−863.000	−0.0751509	−0.0375754	+	0.999294i	$0.511963\pi$
$510$	0	0
$511$	7192.00	0.622613
$512$	−5632.00	−0.486136
$513$	10150.0	0.873554
$514$	9858.00	0.845949
$515$	0	0
$516$	1760.00	0.150154
$517$	12138.0	1.03255
$518$	4768.00	0.404428
$519$	−16150.0	−1.36591
$520$	0	0
$521$	19260.0	1.61957	0.809785	−	0.586727i	$-0.199584\pi$
$521$	19260.0	1.61957	0.809785	+	0.586727i	$0.199584\pi$
$522$	−980.000	−0.0821713
$523$	11740.0	0.981557	0.490779	−	0.871284i	$-0.336712\pi$
$523$	11740.0	0.981557	0.490779	+	0.871284i	$0.336712\pi$
$524$	5764.00	0.480537
$525$	0	0
$526$	−12276.0	−1.01760
$527$	8240.00	0.681101
$528$	−2720.00	−0.224191
$529$	529.000	0.0434783
$530$	0	0
$531$	816.000	0.0666881
$532$	2240.00	0.182549
$533$	5415.00	0.440056
$534$	−4600.00	−0.372774
$535$	0	0
$536$	22224.0	1.79092
$537$	1845.00	0.148264
$538$	−4126.00	−0.330640
$539$	−9486.00	−0.758054
$540$	0	0
$541$	17741.0	1.40988	0.704940	−	0.709267i	$-0.250974\pi$
$541$	17741.0	1.40988	0.704940	+	0.709267i	$0.250974\pi$
$542$	−2128.00	−0.168645
$543$	−6850.00	−0.541366
$544$	12800.0	1.00882
$545$	0	0
$546$	4560.00	0.357418
$547$	6571.00	0.513630	0.256815	−	0.966461i	$-0.417327\pi$
$547$	6571.00	0.513630	0.256815	+	0.966461i	$0.417327\pi$
$548$	6224.00	0.485175
$549$	−1644.00	−0.127804
$550$	0	0
$551$	−17150.0	−1.32598
$552$	2760.00	0.212814
$553$	−10576.0	−0.813268
$554$	−11458.0	−0.878707
$555$	0	0
$556$	−100.000	−0.00762760
$557$	1372.00	0.104369	0.0521845	−	0.998637i	$-0.483382\pi$
$557$	1372.00	0.104369	0.0521845	+	0.998637i	$0.483382\pi$
$558$	−412.000	−0.0312569
$559$	−5016.00	−0.379524
$560$	0	0
$561$	13600.0	1.02352
$562$	−1920.00	−0.144111
$563$	−4332.00	−0.324284	−0.162142	−	0.986767i	$-0.551840\pi$
$563$	−4332.00	−0.324284	−0.162142	+	0.986767i	$0.551840\pi$
$564$	−7140.00	−0.533064
$565$	0	0
$566$	228.000	0.0169321
$567$	−5368.00	−0.397592
$568$	−8040.00	−0.593928
$569$	−3546.00	−0.261258	−0.130629	−	0.991431i	$-0.541700\pi$
$569$	−3546.00	−0.261258	−0.130629	+	0.991431i	$0.541700\pi$
$570$	0	0
$571$	−6160.00	−0.451468	−0.225734	−	0.974189i	$-0.572478\pi$
$571$	−6160.00	−0.451468	−0.225734	+	0.974189i	$0.572478\pi$
$572$	−7752.00	−0.566656
$573$	22050.0	1.60760
$574$	1520.00	0.110529
$575$	0	0
$576$	−896.000	−0.0648148
$577$	−2953.00	−0.213059	−0.106529	−	0.994310i	$-0.533974\pi$
$577$	−2953.00	−0.213059	−0.106529	+	0.994310i	$0.533974\pi$
$578$	2974.00	0.214017
$579$	675.000	0.0484491
$580$	0	0
$581$	288.000	0.0205650
$582$	9640.00	0.686582
$583$	14076.0	0.999946
$584$	−21576.0	−1.52880
$585$	0	0
$586$	14096.0	0.993687
$587$	2949.00	0.207356	0.103678	−	0.994611i	$-0.466939\pi$
$587$	2949.00	0.207356	0.103678	+	0.994611i	$0.466939\pi$
$588$	5580.00	0.391353
$589$	−7210.00	−0.504385
$590$	0	0
$591$	−6105.00	−0.424917
$592$	−4768.00	−0.331020
$593$	−16390.0	−1.13500	−0.567501	−	0.823372i	$-0.692090\pi$
$593$	−16390.0	−1.13500	−0.567501	+	0.823372i	$0.692090\pi$
$594$	−9860.00	−0.681079
$595$	0	0
$596$	−3288.00	−0.225976
$597$	−5490.00	−0.376366
$598$	−2622.00	−0.179300
$599$	−12920.0	−0.881297	−0.440648	−	0.897680i	$-0.645251\pi$
$599$	−12920.0	−0.881297	−0.440648	+	0.897680i	$0.645251\pi$
$600$	0	0
$601$	−13835.0	−0.939004	−0.469502	−	0.882931i	$-0.655567\pi$
$601$	−13835.0	−0.939004	−0.469502	+	0.882931i	$0.655567\pi$
$602$	−1408.00	−0.0953252
$603$	1852.00	0.125073
$604$	5956.00	0.401235
$605$	0	0
$606$	−3100.00	−0.207803
$607$	−6004.00	−0.401474	−0.200737	−	0.979645i	$-0.564334\pi$
$607$	−6004.00	−0.401474	−0.200737	+	0.979645i	$0.564334\pi$
$608$	−11200.0	−0.747072
$609$	9800.00	0.652079
$610$	0	0
$611$	20349.0	1.34735
$612$	640.000	0.0422720
$613$	16416.0	1.08162	0.540812	−	0.841143i	$-0.318117\pi$
$613$	16416.0	1.08162	0.540812	+	0.841143i	$0.318117\pi$
$614$	−7744.00	−0.508994
$615$	0	0
$616$	−6528.00	−0.426982
$617$	−3786.00	−0.247032	−0.123516	−	0.992343i	$-0.539417\pi$
$617$	−3786.00	−0.247032	−0.123516	+	0.992343i	$0.539417\pi$
$618$	−10440.0	−0.679544
$619$	15824.0	1.02750	0.513748	−	0.857941i	$-0.328257\pi$
$619$	15824.0	1.02750	0.513748	+	0.857941i	$0.328257\pi$
$620$	0	0
$621$	3335.00	0.215506
$622$	−9954.00	−0.641670
$623$	−3680.00	−0.236655
$624$	−4560.00	−0.292542
$625$	0	0
$626$	5072.00	0.323830
$627$	−11900.0	−0.757959
$628$	−2528.00	−0.160634
$629$	23840.0	1.51123
$630$	0	0
$631$	17852.0	1.12627	0.563135	−	0.826365i	$-0.309595\pi$
$631$	17852.0	1.12627	0.563135	+	0.826365i	$0.309595\pi$
$632$	31728.0	1.99695
$633$	−18380.0	−1.15409
$634$	−2868.00	−0.179657
$635$	0	0
$636$	−8280.00	−0.516232
$637$	−15903.0	−0.989168
$638$	16660.0	1.03382
$639$	−670.000	−0.0414785
$640$	0	0
$641$	10324.0	0.636152	0.318076	−	0.948065i	$-0.396963\pi$
$641$	10324.0	0.636152	0.318076	+	0.948065i	$0.396963\pi$
$642$	−4140.00	−0.254506
$643$	14702.0	0.901696	0.450848	−	0.892601i	$-0.351122\pi$
$643$	14702.0	0.901696	0.450848	+	0.892601i	$0.351122\pi$
$644$	736.000	0.0450349
$645$	0	0
$646$	−11200.0	−0.682133
$647$	−11939.0	−0.725457	−0.362728	−	0.931895i	$-0.618155\pi$
$647$	−11939.0	−0.725457	−0.362728	+	0.931895i	$0.618155\pi$
$648$	16104.0	0.976273
$649$	−13872.0	−0.839019
$650$	0	0
$651$	4120.00	0.248042
$652$	−12172.0	−0.731123
$653$	−6159.00	−0.369097	−0.184548	−	0.982823i	$-0.559082\pi$
$653$	−6159.00	−0.369097	−0.184548	+	0.982823i	$0.559082\pi$
$654$	7040.00	0.420926
$655$	0	0
$656$	−1520.00	−0.0904665
$657$	−1798.00	−0.106768
$658$	5712.00	0.338415
$659$	−21692.0	−1.28225	−0.641123	−	0.767438i	$-0.721531\pi$
$659$	−21692.0	−1.28225	−0.641123	+	0.767438i	$0.721531\pi$
$660$	0	0
$661$	16502.0	0.971034	0.485517	−	0.874227i	$-0.338631\pi$
$661$	16502.0	0.971034	0.485517	+	0.874227i	$0.338631\pi$
$662$	10938.0	0.642171
$663$	22800.0	1.33556
$664$	−864.000	−0.0504965
$665$	0	0
$666$	−1192.00	−0.0693529
$667$	−5635.00	−0.327119
$668$	−8896.00	−0.515264
$669$	−8280.00	−0.478510
$670$	0	0
$671$	27948.0	1.60793
$672$	6400.00	0.367389
$673$	27733.0	1.58845	0.794226	−	0.607622i	$-0.207876\pi$
$673$	27733.0	1.58845	0.794226	+	0.607622i	$0.207876\pi$
$674$	15592.0	0.891070
$675$	0	0
$676$	−4208.00	−0.239417
$677$	8814.00	0.500369	0.250184	−	0.968198i	$-0.419509\pi$
$677$	8814.00	0.500369	0.250184	+	0.968198i	$0.419509\pi$
$678$	−9520.00	−0.539253
$679$	7712.00	0.435875
$680$	0	0
$681$	−14700.0	−0.827174
$682$	7004.00	0.393251
$683$	22999.0	1.28848	0.644240	−	0.764823i	$-0.277174\pi$
$683$	22999.0	1.28848	0.644240	+	0.764823i	$0.277174\pi$
$684$	−560.000	−0.0313043
$685$	0	0
$686$	−9952.00	−0.553891
$687$	18060.0	1.00296
$688$	1408.00	0.0780225
$689$	23598.0	1.30481
$690$	0	0
$691$	−12140.0	−0.668346	−0.334173	−	0.942512i	$-0.608457\pi$
$691$	−12140.0	−0.668346	−0.334173	+	0.942512i	$0.608457\pi$
$692$	12920.0	0.709747
$693$	−544.000	−0.0298194
$694$	20136.0	1.10137
$695$	0	0
$696$	−29400.0	−1.60116
$697$	7600.00	0.413014
$698$	−14990.0	−0.812865
$699$	21625.0	1.17015
$700$	0	0
$701$	−20024.0	−1.07888	−0.539441	−	0.842024i	$-0.681364\pi$
$701$	−20024.0	−1.07888	−0.539441	+	0.842024i	$0.681364\pi$
$702$	−16530.0	−0.888725
$703$	−20860.0	−1.11913
$704$	15232.0	0.815451
$705$	0	0
$706$	−21234.0	−1.13194
$707$	−2480.00	−0.131924
$708$	8160.00	0.433152
$709$	−4956.00	−0.262520	−0.131260	−	0.991348i	$-0.541902\pi$
$709$	−4956.00	−0.262520	−0.131260	+	0.991348i	$0.541902\pi$
$710$	0	0
$711$	2644.00	0.139462
$712$	11040.0	0.581098
$713$	−2369.00	−0.124432
$714$	6400.00	0.335454
$715$	0	0
$716$	−1476.00	−0.0770401
$717$	13675.0	0.712276
$718$	5044.00	0.262173
$719$	2760.00	0.143158	0.0715790	−	0.997435i	$-0.477196\pi$
$719$	2760.00	0.143158	0.0715790	+	0.997435i	$0.477196\pi$
$720$	0	0
$721$	−8352.00	−0.431407
$722$	−3918.00	−0.201957
$723$	−33550.0	−1.72578
$724$	5480.00	0.281302
$725$	0	0
$726$	−1750.00	−0.0894609
$727$	−7746.00	−0.395163	−0.197581	−	0.980287i	$-0.563309\pi$
$727$	−7746.00	−0.395163	−0.197581	+	0.980287i	$0.563309\pi$
$728$	−10944.0	−0.557159
$729$	20917.0	1.06269
$730$	0	0
$731$	−7040.00	−0.356202
$732$	−16440.0	−0.830109
$733$	11976.0	0.603470	0.301735	−	0.953392i	$-0.402434\pi$
$733$	11976.0	0.603470	0.301735	+	0.953392i	$0.402434\pi$
$734$	−14408.0	−0.724535
$735$	0	0
$736$	−3680.00	−0.184302
$737$	−31484.0	−1.57358
$738$	−380.000	−0.0189539
$739$	15057.0	0.749500	0.374750	−	0.927126i	$-0.377728\pi$
$739$	15057.0	0.749500	0.374750	+	0.927126i	$0.377728\pi$
$740$	0	0
$741$	−19950.0	−0.989044
$742$	6624.00	0.327729
$743$	−18532.0	−0.915038	−0.457519	−	0.889200i	$-0.651262\pi$
$743$	−18532.0	−0.915038	−0.457519	+	0.889200i	$0.651262\pi$
$744$	−12360.0	−0.609059
$745$	0	0
$746$	26620.0	1.30647
$747$	−72.0000	−0.00352656
$748$	−10880.0	−0.531834
$749$	−3312.00	−0.161573
$750$	0	0
$751$	−192.000	−0.00932913	−0.00466457	−	0.999989i	$-0.501485\pi$
$751$	−192.000	−0.00932913	−0.00466457	+	0.999989i	$0.501485\pi$
$752$	−5712.00	−0.276988
$753$	−34740.0	−1.68127
$754$	27930.0	1.34901
$755$	0	0
$756$	4640.00	0.223221
$757$	9830.00	0.471965	0.235982	−	0.971757i	$-0.424169\pi$
$757$	9830.00	0.471965	0.235982	+	0.971757i	$0.424169\pi$
$758$	25904.0	1.24126
$759$	−3910.00	−0.186988
$760$	0	0
$761$	−30219.0	−1.43947	−0.719736	−	0.694248i	$-0.755737\pi$
$761$	−30219.0	−1.43947	−0.719736	+	0.694248i	$0.755737\pi$
$762$	−2610.00	−0.124082
$763$	5632.00	0.267224
$764$	−17640.0	−0.835331
$765$	0	0
$766$	5624.00	0.265279
$767$	−23256.0	−1.09482
$768$	−21760.0	−1.02239
$769$	1122.00	0.0526142	0.0263071	−	0.999654i	$-0.491625\pi$
$769$	1122.00	0.0526142	0.0263071	+	0.999654i	$0.491625\pi$
$770$	0	0
$771$	24645.0	1.15119
$772$	−540.000	−0.0251749
$773$	−19300.0	−0.898024	−0.449012	−	0.893526i	$-0.648224\pi$
$773$	−19300.0	−0.898024	−0.449012	+	0.893526i	$0.648224\pi$
$774$	352.000	0.0163467
$775$	0	0
$776$	−23136.0	−1.07028
$777$	11920.0	0.550357
$778$	2528.00	0.116495
$779$	−6650.00	−0.305855
$780$	0	0
$781$	11390.0	0.521852
$782$	−3680.00	−0.168282
$783$	−35525.0	−1.62140
$784$	4464.00	0.203353
$785$	0	0
$786$	−14410.0	−0.653928
$787$	19396.0	0.878517	0.439258	−	0.898361i	$-0.355241\pi$
$787$	19396.0	0.878517	0.439258	+	0.898361i	$0.355241\pi$
$788$	4884.00	0.220794
$789$	−30690.0	−1.38478
$790$	0	0
$791$	−7616.00	−0.342344
$792$	1632.00	0.0732204
$793$	46854.0	2.09815
$794$	−14238.0	−0.636383
$795$	0	0
$796$	4392.00	0.195566
$797$	39034.0	1.73482	0.867412	−	0.497590i	$-0.165782\pi$
$797$	39034.0	1.73482	0.867412	+	0.497590i	$0.165782\pi$
$798$	−5600.00	−0.248418
$799$	28560.0	1.26456
$800$	0	0
$801$	920.000	0.0405825
$802$	8524.00	0.375303
$803$	30566.0	1.34328
$804$	18520.0	0.812376
$805$	0	0
$806$	11742.0	0.513144
$807$	−10315.0	−0.449944
$808$	7440.00	0.323934
$809$	−10310.0	−0.448060	−0.224030	−	0.974582i	$-0.571921\pi$
$809$	−10310.0	−0.448060	−0.224030	+	0.974582i	$0.571921\pi$
$810$	0	0
$811$	−40693.0	−1.76193	−0.880965	−	0.473182i	$-0.843105\pi$
$811$	−40693.0	−1.76193	−0.880965	+	0.473182i	$0.843105\pi$
$812$	−7840.00	−0.338830
$813$	−5320.00	−0.229496
$814$	20264.0	0.872546
$815$	0	0
$816$	−6400.00	−0.274565
$817$	6160.00	0.263784
$818$	458.000	0.0195765
$819$	−912.000	−0.0389107
$820$	0	0
$821$	−13934.0	−0.592326	−0.296163	−	0.955137i	$-0.595707\pi$
$821$	−13934.0	−0.592326	−0.296163	+	0.955137i	$0.595707\pi$
$822$	−15560.0	−0.660240
$823$	−6175.00	−0.261539	−0.130770	−	0.991413i	$-0.541745\pi$
$823$	−6175.00	−0.261539	−0.130770	+	0.991413i	$0.541745\pi$
$824$	25056.0	1.05930
$825$	0	0
$826$	−6528.00	−0.274986
$827$	−28664.0	−1.20525	−0.602627	−	0.798023i	$-0.705879\pi$
$827$	−28664.0	−1.20525	−0.602627	+	0.798023i	$0.705879\pi$
$828$	−184.000	−0.00772276
$829$	−39590.0	−1.65865	−0.829323	−	0.558770i	$-0.811274\pi$
$829$	−39590.0	−1.65865	−0.829323	+	0.558770i	$0.811274\pi$
$830$	0	0
$831$	−28645.0	−1.19577
$832$	25536.0	1.06406
$833$	−22320.0	−0.928382
$834$	250.000	0.0103798
$835$	0	0
$836$	9520.00	0.393847
$837$	−14935.0	−0.616761
$838$	31552.0	1.30065
$839$	−14316.0	−0.589086	−0.294543	−	0.955638i	$-0.595167\pi$
$839$	−14316.0	−0.589086	−0.294543	+	0.955638i	$0.595167\pi$
$840$	0	0
$841$	35636.0	1.46115
$842$	−17456.0	−0.714458
$843$	−4800.00	−0.196110
$844$	14704.0	0.599683
$845$	0	0
$846$	−1428.00	−0.0580327
$847$	−1400.00	−0.0567941
$848$	−6624.00	−0.268242
$849$	570.000	0.0230416
$850$	0	0
$851$	−6854.00	−0.276089
$852$	−6700.00	−0.269411
$853$	−28366.0	−1.13861	−0.569304	−	0.822127i	$-0.692787\pi$
$853$	−28366.0	−1.13861	−0.569304	+	0.822127i	$0.692787\pi$
$854$	13152.0	0.526993
$855$	0	0
$856$	9936.00	0.396735
$857$	−19283.0	−0.768605	−0.384303	−	0.923207i	$-0.625558\pi$
$857$	−19283.0	−0.768605	−0.384303	+	0.923207i	$0.625558\pi$
$858$	19380.0	0.771122
$859$	−26101.0	−1.03673	−0.518367	−	0.855158i	$-0.673460\pi$
$859$	−26101.0	−1.03673	−0.518367	+	0.855158i	$0.673460\pi$
$860$	0	0
$861$	3800.00	0.150411
$862$	−5856.00	−0.231388
$863$	−973.000	−0.0383793	−0.0191896	−	0.999816i	$-0.506109\pi$
$863$	−973.000	−0.0383793	−0.0191896	+	0.999816i	$0.506109\pi$
$864$	−23200.0	−0.913519
$865$	0	0
$866$	10628.0	0.417037
$867$	7435.00	0.291241
$868$	−3296.00	−0.128887
$869$	−44948.0	−1.75461
$870$	0	0
$871$	−52782.0	−2.05333
$872$	−16896.0	−0.656159
$873$	−1928.00	−0.0747456
$874$	3220.00	0.124620
$875$	0	0
$876$	−17980.0	−0.693479
$877$	−5694.00	−0.219239	−0.109620	−	0.993974i	$-0.534963\pi$
$877$	−5694.00	−0.219239	−0.109620	+	0.993974i	$0.534963\pi$
$878$	5170.00	0.198723
$879$	35240.0	1.35224
$880$	0	0
$881$	45960.0	1.75758	0.878792	−	0.477205i	$-0.158350\pi$
$881$	45960.0	1.75758	0.878792	+	0.477205i	$0.158350\pi$
$882$	1116.00	0.0426051
$883$	−17188.0	−0.655065	−0.327532	−	0.944840i	$-0.606217\pi$
$883$	−17188.0	−0.655065	−0.327532	+	0.944840i	$0.606217\pi$
$884$	−18240.0	−0.693979
$885$	0	0
$886$	5994.00	0.227283
$887$	−8451.00	−0.319906	−0.159953	−	0.987125i	$-0.551134\pi$
$887$	−8451.00	−0.319906	−0.159953	+	0.987125i	$0.551134\pi$
$888$	−35760.0	−1.35138
$889$	−2088.00	−0.0787731
$890$	0	0
$891$	−22814.0	−0.857798
$892$	6624.00	0.248641
$893$	−24990.0	−0.936460
$894$	8220.00	0.307514
$895$	0	0
$896$	−3072.00	−0.114541
$897$	−6555.00	−0.243997
$898$	−33124.0	−1.23092
$899$	25235.0	0.936190
$900$	0	0
$901$	33120.0	1.22463
$902$	6460.00	0.238464
$903$	−3520.00	−0.129721
$904$	22848.0	0.840612
$905$	0	0
$906$	−14890.0	−0.546012
$907$	−32774.0	−1.19983	−0.599913	−	0.800065i	$-0.704798\pi$
$907$	−32774.0	−1.19983	−0.599913	+	0.800065i	$0.704798\pi$
$908$	11760.0	0.429812
$909$	620.000	0.0226228
$910$	0	0
$911$	−23690.0	−0.861564	−0.430782	−	0.902456i	$-0.641762\pi$
$911$	−23690.0	−0.861564	−0.430782	+	0.902456i	$0.641762\pi$
$912$	5600.00	0.203327
$913$	1224.00	0.0443686
$914$	−7848.00	−0.284014
$915$	0	0
$916$	−14448.0	−0.521152
$917$	−11528.0	−0.415145
$918$	−23200.0	−0.834111
$919$	−30044.0	−1.07841	−0.539206	−	0.842174i	$-0.681275\pi$
$919$	−30044.0	−1.07841	−0.539206	+	0.842174i	$0.681275\pi$
$920$	0	0
$921$	−19360.0	−0.692653
$922$	−9086.00	−0.324546
$923$	19095.0	0.680953
$924$	−5440.00	−0.193683
$925$	0	0
$926$	−19232.0	−0.682508
$927$	2088.00	0.0739794
$928$	39200.0	1.38664
$929$	−39705.0	−1.40224	−0.701119	−	0.713044i	$-0.747316\pi$
$929$	−39705.0	−1.40224	−0.701119	+	0.713044i	$0.747316\pi$
$930$	0	0
$931$	19530.0	0.687508
$932$	−17300.0	−0.608026
$933$	−24885.0	−0.873203
$934$	−15652.0	−0.548339
$935$	0	0
$936$	2736.00	0.0955438
$937$	−17422.0	−0.607419	−0.303710	−	0.952765i	$-0.598225\pi$
$937$	−17422.0	−0.607419	−0.303710	+	0.952765i	$0.598225\pi$
$938$	−14816.0	−0.515735
$939$	12680.0	0.440677
$940$	0	0
$941$	−25292.0	−0.876191	−0.438095	−	0.898928i	$-0.644347\pi$
$941$	−25292.0	−0.876191	−0.438095	+	0.898928i	$0.644347\pi$
$942$	6320.00	0.218595
$943$	−2185.00	−0.0754543
$944$	6528.00	0.225072
$945$	0	0
$946$	−5984.00	−0.205662
$947$	−33211.0	−1.13961	−0.569806	−	0.821779i	$-0.692982\pi$
$947$	−33211.0	−1.13961	−0.569806	+	0.821779i	$0.692982\pi$
$948$	26440.0	0.905835
$949$	51243.0	1.75281
$950$	0	0
$951$	−7170.00	−0.244483
$952$	−15360.0	−0.522921
$953$	14154.0	0.481105	0.240552	−	0.970636i	$-0.422671\pi$
$953$	14154.0	0.481105	0.240552	+	0.970636i	$0.422671\pi$
$954$	−1656.00	−0.0562002
$955$	0	0
$956$	−10940.0	−0.370110
$957$	41650.0	1.40685
$958$	22808.0	0.769199
$959$	−12448.0	−0.419152
$960$	0	0
$961$	−19182.0	−0.643886
$962$	33972.0	1.13857
$963$	828.000	0.0277071
$964$	26840.0	0.896741
$965$	0	0
$966$	−1840.00	−0.0612847
$967$	46343.0	1.54115	0.770574	−	0.637350i	$-0.219970\pi$
$967$	46343.0	1.54115	0.770574	+	0.637350i	$0.219970\pi$
$968$	4200.00	0.139456
$969$	−28000.0	−0.928266
$970$	0	0
$971$	11710.0	0.387015	0.193508	−	0.981099i	$-0.438014\pi$
$971$	11710.0	0.387015	0.193508	+	0.981099i	$0.438014\pi$
$972$	−2240.00	−0.0739177
$973$	200.000	0.00658963
$974$	18534.0	0.609720
$975$	0	0
$976$	−13152.0	−0.431337
$977$	−47854.0	−1.56703	−0.783513	−	0.621375i	$-0.786574\pi$
$977$	−47854.0	−1.56703	−0.783513	+	0.621375i	$0.786574\pi$
$978$	30430.0	0.994933
$979$	−15640.0	−0.510579
$980$	0	0
$981$	−1408.00	−0.0458246
$982$	−36382.0	−1.18228
$983$	22078.0	0.716357	0.358178	−	0.933653i	$-0.383398\pi$
$983$	22078.0	0.716357	0.358178	+	0.933653i	$0.383398\pi$
$984$	−11400.0	−0.369328
$985$	0	0
$986$	39200.0	1.26611
$987$	14280.0	0.460524
$988$	15960.0	0.513922
$989$	2024.00	0.0650753
$990$	0	0
$991$	−4288.00	−0.137450	−0.0687249	−	0.997636i	$-0.521893\pi$
$991$	−4288.00	−0.137450	−0.0687249	+	0.997636i	$0.521893\pi$
$992$	16480.0	0.527460
$993$	27345.0	0.873885
$994$	5360.00	0.171035
$995$	0	0
$996$	−720.000	−0.0229057
$997$	−28966.0	−0.920123	−0.460061	−	0.887887i	$-0.652173\pi$
$997$	−28966.0	−0.920123	−0.460061	+	0.887887i	$0.652173\pi$
$998$	38630.0	1.22526
$999$	−43210.0	−1.36847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.4.a.g.1.1		1
5.2	odd	4		575.4.b.b.24.2		2
5.3	odd	4		575.4.b.b.24.1		2
5.4	even	2		23.4.a.a.1.1	✓	1
15.14	odd	2		207.4.a.a.1.1		1
20.19	odd	2		368.4.a.d.1.1		1
35.34	odd	2		1127.4.a.a.1.1		1
40.19	odd	2		1472.4.a.c.1.1		1
40.29	even	2		1472.4.a.h.1.1		1
115.114	odd	2		529.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.a.a.1.1	✓	1	5.4	even	2
207.4.a.a.1.1		1	15.14	odd	2
368.4.a.d.1.1		1	20.19	odd	2
529.4.a.a.1.1		1	115.114	odd	2
575.4.a.g.1.1		1	1.1	even	1	trivial
575.4.b.b.24.1		2	5.3	odd	4
575.4.b.b.24.2		2	5.2	odd	4
1127.4.a.a.1.1		1	35.34	odd	2
1472.4.a.c.1.1		1	40.19	odd	2
1472.4.a.h.1.1		1	40.29	even	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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