LMFDB - Embedded newform 2450.4.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, 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("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2450.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:	$144.554679514$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} -14.0000 q^{6} -8.00000 q^{8} +22.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} -14.0000 q^{6} -8.00000 q^{8} +22.0000 q^{9} -33.0000 q^{11} +28.0000 q^{12} -43.0000 q^{13} +16.0000 q^{16} +111.000 q^{17} -44.0000 q^{18} +70.0000 q^{19} +66.0000 q^{22} -42.0000 q^{23} -56.0000 q^{24} +86.0000 q^{26} -35.0000 q^{27} -225.000 q^{29} +88.0000 q^{31} -32.0000 q^{32} -231.000 q^{33} -222.000 q^{34} +88.0000 q^{36} +34.0000 q^{37} -140.000 q^{38} -301.000 q^{39} -432.000 q^{41} +178.000 q^{43} -132.000 q^{44} +84.0000 q^{46} +411.000 q^{47} +112.000 q^{48} +777.000 q^{51} -172.000 q^{52} +708.000 q^{53} +70.0000 q^{54} +490.000 q^{57} +450.000 q^{58} -480.000 q^{59} -812.000 q^{61} -176.000 q^{62} +64.0000 q^{64} +462.000 q^{66} -596.000 q^{67} +444.000 q^{68} -294.000 q^{69} +432.000 q^{71} -176.000 q^{72} -358.000 q^{73} -68.0000 q^{74} +280.000 q^{76} +602.000 q^{78} +425.000 q^{79} -839.000 q^{81} +864.000 q^{82} +972.000 q^{83} -356.000 q^{86} -1575.00 q^{87} +264.000 q^{88} -960.000 q^{89} -168.000 q^{92} +616.000 q^{93} -822.000 q^{94} -224.000 q^{96} -709.000 q^{97} -726.000 q^{99} +O(q^{100})\)

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
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−14.0000	−0.952579
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	22.0000	0.814815
$10$	0	0
$11$	−33.0000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−33.0000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	28.0000	0.673575
$13$	−43.0000	−0.917389	−0.458694	−	0.888594i	$-0.651683\pi$
$13$	−43.0000	−0.917389	−0.458694	+	0.888594i	$0.651683\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	0.250000
$17$	111.000	1.58361	0.791807	−	0.610771i	$-0.209140\pi$
$17$	111.000	1.58361	0.791807	+	0.610771i	$0.209140\pi$
$18$	−44.0000	−0.576161
$19$	70.0000	0.845216	0.422608	−	0.906313i	$-0.361115\pi$
$19$	70.0000	0.845216	0.422608	+	0.906313i	$0.361115\pi$
$20$	0	0
$21$	0	0
$22$	66.0000	0.639602
$23$	−42.0000	−0.380765	−0.190383	−	0.981710i	$-0.560973\pi$
$23$	−42.0000	−0.380765	−0.190383	+	0.981710i	$0.560973\pi$
$24$	−56.0000	−0.476290
$25$	0	0
$26$	86.0000	0.648692
$27$	−35.0000	−0.249472
$28$	0	0
$29$	−225.000	−1.44074	−0.720370	−	0.693590i	$-0.756028\pi$
$29$	−225.000	−1.44074	−0.720370	+	0.693590i	$0.756028\pi$
$30$	0	0
$31$	88.0000	0.509847	0.254924	−	0.966961i	$-0.417950\pi$
$31$	88.0000	0.509847	0.254924	+	0.966961i	$0.417950\pi$
$32$	−32.0000	−0.176777
$33$	−231.000	−1.21854
$34$	−222.000	−1.11978
$35$	0	0
$36$	88.0000	0.407407
$37$	34.0000	0.151069	0.0755347	−	0.997143i	$-0.475934\pi$
$37$	34.0000	0.151069	0.0755347	+	0.997143i	$0.475934\pi$
$38$	−140.000	−0.597658
$39$	−301.000	−1.23586
$40$	0	0
$41$	−432.000	−1.64554	−0.822769	−	0.568376i	$-0.807572\pi$
$41$	−432.000	−1.64554	−0.822769	+	0.568376i	$0.807572\pi$
$42$	0	0
$43$	178.000	0.631273	0.315637	−	0.948880i	$-0.397782\pi$
$43$	178.000	0.631273	0.315637	+	0.948880i	$0.397782\pi$
$44$	−132.000	−0.452267
$45$	0	0
$46$	84.0000	0.269242
$47$	411.000	1.27554	0.637771	−	0.770226i	$-0.279856\pi$
$47$	411.000	1.27554	0.637771	+	0.770226i	$0.279856\pi$
$48$	112.000	0.336788
$49$	0	0
$50$	0	0
$51$	777.000	2.13337
$52$	−172.000	−0.458694
$53$	708.000	1.83493	0.917465	−	0.397817i	$-0.130232\pi$
$53$	708.000	1.83493	0.917465	+	0.397817i	$0.130232\pi$
$54$	70.0000	0.176404
$55$	0	0
$56$	0	0
$57$	490.000	1.13863
$58$	450.000	1.01876
$59$	−480.000	−1.05916	−0.529582	−	0.848259i	$-0.677651\pi$
$59$	−480.000	−1.05916	−0.529582	+	0.848259i	$0.677651\pi$
$60$	0	0
$61$	−812.000	−1.70436	−0.852180	−	0.523249i	$-0.824720\pi$
$61$	−812.000	−1.70436	−0.852180	+	0.523249i	$0.824720\pi$
$62$	−176.000	−0.360516
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	462.000	0.861640
$67$	−596.000	−1.08676	−0.543381	−	0.839487i	$-0.682856\pi$
$67$	−596.000	−1.08676	−0.543381	+	0.839487i	$0.682856\pi$
$68$	444.000	0.791807
$69$	−294.000	−0.512948
$70$	0	0
$71$	432.000	0.722098	0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000	0.722098	0.361049	+	0.932547i	$0.382419\pi$
$72$	−176.000	−0.288081
$73$	−358.000	−0.573983	−0.286991	−	0.957933i	$-0.592655\pi$
$73$	−358.000	−0.573983	−0.286991	+	0.957933i	$0.592655\pi$
$74$	−68.0000	−0.106822
$75$	0	0
$76$	280.000	0.422608
$77$	0	0
$78$	602.000	0.873886
$79$	425.000	0.605269	0.302634	−	0.953107i	$-0.402134\pi$
$79$	425.000	0.605269	0.302634	+	0.953107i	$0.402134\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	864.000	1.16357
$83$	972.000	1.28543	0.642716	−	0.766105i	$-0.277808\pi$
$83$	972.000	1.28543	0.642716	+	0.766105i	$0.277808\pi$
$84$	0	0
$85$	0	0
$86$	−356.000	−0.446378
$87$	−1575.00	−1.94089
$88$	264.000	0.319801
$89$	−960.000	−1.14337	−0.571684	−	0.820474i	$-0.693710\pi$
$89$	−960.000	−1.14337	−0.571684	+	0.820474i	$0.693710\pi$
$90$	0	0
$91$	0	0
$92$	−168.000	−0.190383
$93$	616.000	0.686841
$94$	−822.000	−0.901945
$95$	0	0
$96$	−224.000	−0.238145
$97$	−709.000	−0.742145	−0.371072	−	0.928604i	$-0.621010\pi$
$97$	−709.000	−0.742145	−0.371072	+	0.928604i	$0.621010\pi$
$98$	0	0
$99$	−726.000	−0.737028
$100$	0	0
$101$	438.000	0.431511	0.215756	−	0.976447i	$-0.430779\pi$
$101$	438.000	0.431511	0.215756	+	0.976447i	$0.430779\pi$
$102$	−1554.00	−1.50852
$103$	−1033.00	−0.988199	−0.494100	−	0.869405i	$-0.664502\pi$
$103$	−1033.00	−0.988199	−0.494100	+	0.869405i	$0.664502\pi$
$104$	344.000	0.324346
$105$	0	0
$106$	−1416.00	−1.29749
$107$	−906.000	−0.818564	−0.409282	−	0.912408i	$-0.634221\pi$
$107$	−906.000	−0.818564	−0.409282	+	0.912408i	$0.634221\pi$
$108$	−140.000	−0.124736
$109$	−1915.00	−1.68279	−0.841393	−	0.540423i	$-0.818264\pi$
$109$	−1915.00	−1.68279	−0.841393	+	0.540423i	$0.818264\pi$
$110$	0	0
$111$	238.000	0.203513
$112$	0	0
$113$	558.000	0.464533	0.232266	−	0.972652i	$-0.425386\pi$
$113$	558.000	0.464533	0.232266	+	0.972652i	$0.425386\pi$
$114$	−980.000	−0.805135
$115$	0	0
$116$	−900.000	−0.720370
$117$	−946.000	−0.747502
$118$	960.000	0.748942
$119$	0	0
$120$	0	0
$121$	−242.000	−0.181818
$122$	1624.00	1.20516
$123$	−3024.00	−2.21679
$124$	352.000	0.254924
$125$	0	0
$126$	0	0
$127$	1744.00	1.21854	0.609272	−	0.792962i	$-0.291462\pi$
$127$	1744.00	1.21854	0.609272	+	0.792962i	$0.291462\pi$
$128$	−128.000	−0.0883883
$129$	1246.00	0.850420
$130$	0	0
$131$	318.000	0.212090	0.106045	−	0.994361i	$-0.466181\pi$
$131$	318.000	0.212090	0.106045	+	0.994361i	$0.466181\pi$
$132$	−924.000	−0.609272
$133$	0	0
$134$	1192.00	0.768456
$135$	0	0
$136$	−888.000	−0.559892
$137$	−2496.00	−1.55655	−0.778276	−	0.627922i	$-0.783906\pi$
$137$	−2496.00	−1.55655	−0.778276	+	0.627922i	$0.783906\pi$
$138$	588.000	0.362709
$139$	−1370.00	−0.835985	−0.417992	−	0.908451i	$-0.637266\pi$
$139$	−1370.00	−0.835985	−0.417992	+	0.908451i	$0.637266\pi$
$140$	0	0
$141$	2877.00	1.71835
$142$	−864.000	−0.510600
$143$	1419.00	0.829809
$144$	352.000	0.203704
$145$	0	0
$146$	716.000	0.405867
$147$	0	0
$148$	136.000	0.0755347
$149$	2490.00	1.36905	0.684526	−	0.728988i	$-0.260009\pi$
$149$	2490.00	1.36905	0.684526	+	0.728988i	$0.260009\pi$
$150$	0	0
$151$	137.000	0.0738338	0.0369169	−	0.999318i	$-0.488246\pi$
$151$	137.000	0.0738338	0.0369169	+	0.999318i	$0.488246\pi$
$152$	−560.000	−0.298829
$153$	2442.00	1.29035
$154$	0	0
$155$	0	0
$156$	−1204.00	−0.617930
$157$	−3274.00	−1.66429	−0.832145	−	0.554558i	$-0.812888\pi$
$157$	−3274.00	−1.66429	−0.832145	+	0.554558i	$0.812888\pi$
$158$	−850.000	−0.427990
$159$	4956.00	2.47193
$160$	0	0
$161$	0	0
$162$	1678.00	0.813803
$163$	−902.000	−0.433436	−0.216718	−	0.976234i	$-0.569535\pi$
$163$	−902.000	−0.433436	−0.216718	+	0.976234i	$0.569535\pi$
$164$	−1728.00	−0.822769
$165$	0	0
$166$	−1944.00	−0.908938
$167$	−3969.00	−1.83910	−0.919552	−	0.392968i	$-0.871448\pi$
$167$	−3969.00	−1.83910	−0.919552	+	0.392968i	$0.871448\pi$
$168$	0	0
$169$	−348.000	−0.158398
$170$	0	0
$171$	1540.00	0.688694
$172$	712.000	0.315637
$173$	−1713.00	−0.752815	−0.376407	−	0.926454i	$-0.622841\pi$
$173$	−1713.00	−0.752815	−0.376407	+	0.926454i	$0.622841\pi$
$174$	3150.00	1.37242
$175$	0	0
$176$	−528.000	−0.226134
$177$	−3360.00	−1.42685
$178$	1920.00	0.808484
$179$	−3660.00	−1.52828	−0.764138	−	0.645053i	$-0.776835\pi$
$179$	−3660.00	−1.52828	−0.764138	+	0.645053i	$0.776835\pi$
$180$	0	0
$181$	1708.00	0.701407	0.350703	−	0.936487i	$-0.385943\pi$
$181$	1708.00	0.701407	0.350703	+	0.936487i	$0.385943\pi$
$182$	0	0
$183$	−5684.00	−2.29603
$184$	336.000	0.134621
$185$	0	0
$186$	−1232.00	−0.485670
$187$	−3663.00	−1.43243
$188$	1644.00	0.637771
$189$	0	0
$190$	0	0
$191$	−2073.00	−0.785325	−0.392662	−	0.919683i	$-0.628446\pi$
$191$	−2073.00	−0.785325	−0.392662	+	0.919683i	$0.628446\pi$
$192$	448.000	0.168394
$193$	3688.00	1.37548	0.687741	−	0.725956i	$-0.258602\pi$
$193$	3688.00	1.37548	0.687741	+	0.725956i	$0.258602\pi$
$194$	1418.00	0.524776
$195$	0	0
$196$	0	0
$197$	−3276.00	−1.18480	−0.592399	−	0.805644i	$-0.701819\pi$
$197$	−3276.00	−1.18480	−0.592399	+	0.805644i	$0.701819\pi$
$198$	1452.00	0.521157
$199$	−2360.00	−0.840683	−0.420342	−	0.907366i	$-0.638090\pi$
$199$	−2360.00	−0.840683	−0.420342	+	0.907366i	$0.638090\pi$
$200$	0	0
$201$	−4172.00	−1.46403
$202$	−876.000	−0.305124
$203$	0	0
$204$	3108.00	1.06668
$205$	0	0
$206$	2066.00	0.698762
$207$	−924.000	−0.310253
$208$	−688.000	−0.229347
$209$	−2310.00	−0.764527
$210$	0	0
$211$	2657.00	0.866898	0.433449	−	0.901178i	$-0.357296\pi$
$211$	2657.00	0.866898	0.433449	+	0.901178i	$0.357296\pi$
$212$	2832.00	0.917465
$213$	3024.00	0.972775
$214$	1812.00	0.578812
$215$	0	0
$216$	280.000	0.0882018
$217$	0	0
$218$	3830.00	1.18991
$219$	−2506.00	−0.773241
$220$	0	0
$221$	−4773.00	−1.45279
$222$	−476.000	−0.143906
$223$	47.0000	0.0141137	0.00705684	−	0.999975i	$-0.497754\pi$
$223$	47.0000	0.0141137	0.00705684	+	0.999975i	$0.497754\pi$
$224$	0	0
$225$	0	0
$226$	−1116.00	−0.328474
$227$	6051.00	1.76925	0.884623	−	0.466306i	$-0.154416\pi$
$227$	6051.00	1.76925	0.884623	+	0.466306i	$0.154416\pi$
$228$	1960.00	0.569317
$229$	−3080.00	−0.888787	−0.444393	−	0.895832i	$-0.646581\pi$
$229$	−3080.00	−0.888787	−0.444393	+	0.895832i	$0.646581\pi$
$230$	0	0
$231$	0	0
$232$	1800.00	0.509378
$233$	3288.00	0.924481	0.462240	−	0.886755i	$-0.347046\pi$
$233$	3288.00	0.924481	0.462240	+	0.886755i	$0.347046\pi$
$234$	1892.00	0.528564
$235$	0	0
$236$	−1920.00	−0.529582
$237$	2975.00	0.815388
$238$	0	0
$239$	−1755.00	−0.474985	−0.237493	−	0.971389i	$-0.576326\pi$
$239$	−1755.00	−0.474985	−0.237493	+	0.971389i	$0.576326\pi$
$240$	0	0
$241$	−2.00000	−0.000534570 0	−0.000267285	−	1.00000i	$-0.500085\pi$
$241$	−2.00000	−0.000534570 0	−0.000267285		1.00000i	$0.500085\pi$
$242$	484.000	0.128565
$243$	−4928.00	−1.30095
$244$	−3248.00	−0.852180
$245$	0	0
$246$	6048.00	1.56751
$247$	−3010.00	−0.775392
$248$	−704.000	−0.180258
$249$	6804.00	1.73167
$250$	0	0
$251$	5418.00	1.36247	0.681237	−	0.732063i	$-0.261442\pi$
$251$	5418.00	1.36247	0.681237	+	0.732063i	$0.261442\pi$
$252$	0	0
$253$	1386.00	0.344415
$254$	−3488.00	−0.861640
$255$	0	0
$256$	256.000	0.0625000
$257$	−2154.00	−0.522813	−0.261406	−	0.965229i	$-0.584186\pi$
$257$	−2154.00	−0.522813	−0.261406	+	0.965229i	$0.584186\pi$
$258$	−2492.00	−0.601338
$259$	0	0
$260$	0	0
$261$	−4950.00	−1.17394
$262$	−636.000	−0.149970
$263$	−3882.00	−0.910169	−0.455084	−	0.890448i	$-0.650391\pi$
$263$	−3882.00	−0.910169	−0.455084	+	0.890448i	$0.650391\pi$
$264$	1848.00	0.430820
$265$	0	0
$266$	0	0
$267$	−6720.00	−1.54029
$268$	−2384.00	−0.543381
$269$	−570.000	−0.129195	−0.0645976	−	0.997911i	$-0.520576\pi$
$269$	−570.000	−0.129195	−0.0645976	+	0.997911i	$0.520576\pi$
$270$	0	0
$271$	−3332.00	−0.746880	−0.373440	−	0.927654i	$-0.621822\pi$
$271$	−3332.00	−0.746880	−0.373440	+	0.927654i	$0.621822\pi$
$272$	1776.00	0.395904
$273$	0	0
$274$	4992.00	1.10065
$275$	0	0
$276$	−1176.00	−0.256474
$277$	394.000	0.0854627	0.0427313	−	0.999087i	$-0.486394\pi$
$277$	394.000	0.0854627	0.0427313	+	0.999087i	$0.486394\pi$
$278$	2740.00	0.591131
$279$	1936.00	0.415431
$280$	0	0
$281$	3267.00	0.693569	0.346784	−	0.937945i	$-0.387274\pi$
$281$	3267.00	0.693569	0.346784	+	0.937945i	$0.387274\pi$
$282$	−5754.00	−1.21506
$283$	677.000	0.142203	0.0711015	−	0.997469i	$-0.477349\pi$
$283$	677.000	0.142203	0.0711015	+	0.997469i	$0.477349\pi$
$284$	1728.00	0.361049
$285$	0	0
$286$	−2838.00	−0.586764
$287$	0	0
$288$	−704.000	−0.144040
$289$	7408.00	1.50784
$290$	0	0
$291$	−4963.00	−0.999781
$292$	−1432.00	−0.286991
$293$	−8613.00	−1.71733	−0.858664	−	0.512540i	$-0.828705\pi$
$293$	−8613.00	−1.71733	−0.858664	+	0.512540i	$0.828705\pi$
$294$	0	0
$295$	0	0
$296$	−272.000	−0.0534111
$297$	1155.00	0.225656
$298$	−4980.00	−0.968066
$299$	1806.00	0.349310
$300$	0	0
$301$	0	0
$302$	−274.000	−0.0522084
$303$	3066.00	0.581311
$304$	1120.00	0.211304
$305$	0	0
$306$	−4884.00	−0.912417
$307$	−3499.00	−0.650484	−0.325242	−	0.945631i	$-0.605446\pi$
$307$	−3499.00	−0.650484	−0.325242	+	0.945631i	$0.605446\pi$
$308$	0	0
$309$	−7231.00	−1.33125
$310$	0	0
$311$	−5682.00	−1.03600	−0.518001	−	0.855380i	$-0.673324\pi$
$311$	−5682.00	−1.03600	−0.518001	+	0.855380i	$0.673324\pi$
$312$	2408.00	0.436943
$313$	4097.00	0.739860	0.369930	−	0.929060i	$-0.379382\pi$
$313$	4097.00	0.739860	0.369930	+	0.929060i	$0.379382\pi$
$314$	6548.00	1.17683
$315$	0	0
$316$	1700.00	0.302634
$317$	4674.00	0.828132	0.414066	−	0.910247i	$-0.364108\pi$
$317$	4674.00	0.828132	0.414066	+	0.910247i	$0.364108\pi$
$318$	−9912.00	−1.74792
$319$	7425.00	1.30320
$320$	0	0
$321$	−6342.00	−1.10273
$322$	0	0
$323$	7770.00	1.33850
$324$	−3356.00	−0.575446
$325$	0	0
$326$	1804.00	0.306486
$327$	−13405.0	−2.26697
$328$	3456.00	0.581786
$329$	0	0
$330$	0	0
$331$	10172.0	1.68913	0.844567	−	0.535449i	$-0.179858\pi$
$331$	10172.0	1.68913	0.844567	+	0.535449i	$0.179858\pi$
$332$	3888.00	0.642716
$333$	748.000	0.123094
$334$	7938.00	1.30044
$335$	0	0
$336$	0	0
$337$	9394.00	1.51847	0.759234	−	0.650818i	$-0.225574\pi$
$337$	9394.00	1.51847	0.759234	+	0.650818i	$0.225574\pi$
$338$	696.000	0.112004
$339$	3906.00	0.625796
$340$	0	0
$341$	−2904.00	−0.461174
$342$	−3080.00	−0.486980
$343$	0	0
$344$	−1424.00	−0.223189
$345$	0	0
$346$	3426.00	0.532321
$347$	−4566.00	−0.706385	−0.353193	−	0.935551i	$-0.614904\pi$
$347$	−4566.00	−0.706385	−0.353193	+	0.935551i	$0.614904\pi$
$348$	−6300.00	−0.970447
$349$	6730.00	1.03223	0.516116	−	0.856519i	$-0.327378\pi$
$349$	6730.00	1.03223	0.516116	+	0.856519i	$0.327378\pi$
$350$	0	0
$351$	1505.00	0.228863
$352$	1056.00	0.159901
$353$	3027.00	0.456405	0.228202	−	0.973614i	$-0.426715\pi$
$353$	3027.00	0.456405	0.228202	+	0.973614i	$0.426715\pi$
$354$	6720.00	1.00894
$355$	0	0
$356$	−3840.00	−0.571684
$357$	0	0
$358$	7320.00	1.08065
$359$	2760.00	0.405758	0.202879	−	0.979204i	$-0.434970\pi$
$359$	2760.00	0.405758	0.202879	+	0.979204i	$0.434970\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	−3416.00	−0.495970
$363$	−1694.00	−0.244936
$364$	0	0
$365$	0	0
$366$	11368.0	1.62354
$367$	6131.00	0.872032	0.436016	−	0.899939i	$-0.356389\pi$
$367$	6131.00	0.872032	0.436016	+	0.899939i	$0.356389\pi$
$368$	−672.000	−0.0951914
$369$	−9504.00	−1.34081
$370$	0	0
$371$	0	0
$372$	2464.00	0.343421
$373$	−9632.00	−1.33707	−0.668534	−	0.743682i	$-0.733078\pi$
$373$	−9632.00	−1.33707	−0.668534	+	0.743682i	$0.733078\pi$
$374$	7326.00	1.01288
$375$	0	0
$376$	−3288.00	−0.450972
$377$	9675.00	1.32172
$378$	0	0
$379$	−9700.00	−1.31466	−0.657329	−	0.753604i	$-0.728314\pi$
$379$	−9700.00	−1.31466	−0.657329	+	0.753604i	$0.728314\pi$
$380$	0	0
$381$	12208.0	1.64156
$382$	4146.00	0.555308
$383$	1212.00	0.161698	0.0808490	−	0.996726i	$-0.474237\pi$
$383$	1212.00	0.161698	0.0808490	+	0.996726i	$0.474237\pi$
$384$	−896.000	−0.119072
$385$	0	0
$386$	−7376.00	−0.972613
$387$	3916.00	0.514371
$388$	−2836.00	−0.371072
$389$	4305.00	0.561111	0.280555	−	0.959838i	$-0.409481\pi$
$389$	4305.00	0.561111	0.280555	+	0.959838i	$0.409481\pi$
$390$	0	0
$391$	−4662.00	−0.602986
$392$	0	0
$393$	2226.00	0.285717
$394$	6552.00	0.837779
$395$	0	0
$396$	−2904.00	−0.368514
$397$	−1609.00	−0.203409	−0.101705	−	0.994815i	$-0.532430\pi$
$397$	−1609.00	−0.203409	−0.101705	+	0.994815i	$0.532430\pi$
$398$	4720.00	0.594453
$399$	0	0
$400$	0	0
$401$	−13503.0	−1.68157	−0.840783	−	0.541373i	$-0.817905\pi$
$401$	−13503.0	−1.68157	−0.840783	+	0.541373i	$0.817905\pi$
$402$	8344.00	1.03523
$403$	−3784.00	−0.467728
$404$	1752.00	0.215756
$405$	0	0
$406$	0	0
$407$	−1122.00	−0.136647
$408$	−6216.00	−0.754259
$409$	−470.000	−0.0568215	−0.0284108	−	0.999596i	$-0.509045\pi$
$409$	−470.000	−0.0568215	−0.0284108	+	0.999596i	$0.509045\pi$
$410$	0	0
$411$	−17472.0	−2.09691
$412$	−4132.00	−0.494100
$413$	0	0
$414$	1848.00	0.219382
$415$	0	0
$416$	1376.00	0.162173
$417$	−9590.00	−1.12620
$418$	4620.00	0.540602
$419$	11700.0	1.36416	0.682079	−	0.731278i	$-0.261076\pi$
$419$	11700.0	1.36416	0.682079	+	0.731278i	$0.261076\pi$
$420$	0	0
$421$	−6163.00	−0.713459	−0.356730	−	0.934208i	$-0.616108\pi$
$421$	−6163.00	−0.713459	−0.356730	+	0.934208i	$0.616108\pi$
$422$	−5314.00	−0.612989
$423$	9042.00	1.03933
$424$	−5664.00	−0.648746
$425$	0	0
$426$	−6048.00	−0.687856
$427$	0	0
$428$	−3624.00	−0.409282
$429$	9933.00	1.11788
$430$	0	0
$431$	5187.00	0.579696	0.289848	−	0.957073i	$-0.406395\pi$
$431$	5187.00	0.579696	0.289848	+	0.957073i	$0.406395\pi$
$432$	−560.000	−0.0623681
$433$	2882.00	0.319862	0.159931	−	0.987128i	$-0.448873\pi$
$433$	2882.00	0.319862	0.159931	+	0.987128i	$0.448873\pi$
$434$	0	0
$435$	0	0
$436$	−7660.00	−0.841393
$437$	−2940.00	−0.321829
$438$	5012.00	0.546764
$439$	−9830.00	−1.06870	−0.534351	−	0.845263i	$-0.679444\pi$
$439$	−9830.00	−1.06870	−0.534351	+	0.845263i	$0.679444\pi$
$440$	0	0
$441$	0	0
$442$	9546.00	1.02728
$443$	5178.00	0.555337	0.277668	−	0.960677i	$-0.410438\pi$
$443$	5178.00	0.555337	0.277668	+	0.960677i	$0.410438\pi$
$444$	952.000	0.101757
$445$	0	0
$446$	−94.0000	−0.00997989
$447$	17430.0	1.84432
$448$	0	0
$449$	−4545.00	−0.477710	−0.238855	−	0.971055i	$-0.576772\pi$
$449$	−4545.00	−0.477710	−0.238855	+	0.971055i	$0.576772\pi$
$450$	0	0
$451$	14256.0	1.48845
$452$	2232.00	0.232266
$453$	959.000	0.0994652
$454$	−12102.0	−1.25105
$455$	0	0
$456$	−3920.00	−0.402568
$457$	484.000	0.0495417	0.0247709	−	0.999693i	$-0.492114\pi$
$457$	484.000	0.0495417	0.0247709	+	0.999693i	$0.492114\pi$
$458$	6160.00	0.628467
$459$	−3885.00	−0.395068
$460$	0	0
$461$	1368.00	0.138208	0.0691042	−	0.997609i	$-0.477986\pi$
$461$	1368.00	0.138208	0.0691042	+	0.997609i	$0.477986\pi$
$462$	0	0
$463$	−14852.0	−1.49078	−0.745390	−	0.666629i	$-0.767737\pi$
$463$	−14852.0	−1.49078	−0.745390	+	0.666629i	$0.767737\pi$
$464$	−3600.00	−0.360185
$465$	0	0
$466$	−6576.00	−0.653707
$467$	7521.00	0.745247	0.372624	−	0.927983i	$-0.378458\pi$
$467$	7521.00	0.745247	0.372624	+	0.927983i	$0.378458\pi$
$468$	−3784.00	−0.373751
$469$	0	0
$470$	0	0
$471$	−22918.0	−2.24205
$472$	3840.00	0.374471
$473$	−5874.00	−0.571008
$474$	−5950.00	−0.576567
$475$	0	0
$476$	0	0
$477$	15576.0	1.49513
$478$	3510.00	0.335865
$479$	−8850.00	−0.844190	−0.422095	−	0.906552i	$-0.638705\pi$
$479$	−8850.00	−0.844190	−0.422095	+	0.906552i	$0.638705\pi$
$480$	0	0
$481$	−1462.00	−0.138589
$482$	4.00000	0.000377998 0
$483$	0	0
$484$	−968.000	−0.0909091
$485$	0	0
$486$	9856.00	0.919912
$487$	14614.0	1.35980	0.679901	−	0.733304i	$-0.262023\pi$
$487$	14614.0	1.35980	0.679901	+	0.733304i	$0.262023\pi$
$488$	6496.00	0.602582
$489$	−6314.00	−0.583904
$490$	0	0
$491$	15237.0	1.40048	0.700241	−	0.713907i	$-0.253076\pi$
$491$	15237.0	1.40048	0.700241	+	0.713907i	$0.253076\pi$
$492$	−12096.0	−1.10839
$493$	−24975.0	−2.28158
$494$	6020.00	0.548285
$495$	0	0
$496$	1408.00	0.127462
$497$	0	0
$498$	−13608.0	−1.22448
$499$	−9565.00	−0.858093	−0.429046	−	0.903282i	$-0.641150\pi$
$499$	−9565.00	−0.858093	−0.429046	+	0.903282i	$0.641150\pi$
$500$	0	0
$501$	−27783.0	−2.47755
$502$	−10836.0	−0.963415
$503$	−7263.00	−0.643819	−0.321910	−	0.946770i	$-0.604325\pi$
$503$	−7263.00	−0.643819	−0.321910	+	0.946770i	$0.604325\pi$
$504$	0	0
$505$	0	0
$506$	−2772.00	−0.243538
$507$	−2436.00	−0.213386
$508$	6976.00	0.609272
$509$	7230.00	0.629596	0.314798	−	0.949159i	$-0.398063\pi$
$509$	7230.00	0.629596	0.314798	+	0.949159i	$0.398063\pi$
$510$	0	0
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−2450.00	−0.210858
$514$	4308.00	0.369684
$515$	0	0
$516$	4984.00	0.425210
$517$	−13563.0	−1.15377
$518$	0	0
$519$	−11991.0	−1.01416
$520$	0	0
$521$	−4962.00	−0.417254	−0.208627	−	0.977995i	$-0.566899\pi$
$521$	−4962.00	−0.417254	−0.208627	+	0.977995i	$0.566899\pi$
$522$	9900.00	0.830098
$523$	13772.0	1.15145	0.575724	−	0.817644i	$-0.304720\pi$
$523$	13772.0	1.15145	0.575724	+	0.817644i	$0.304720\pi$
$524$	1272.00	0.106045
$525$	0	0
$526$	7764.00	0.643586
$527$	9768.00	0.807402
$528$	−3696.00	−0.304636
$529$	−10403.0	−0.855018
$530$	0	0
$531$	−10560.0	−0.863023
$532$	0	0
$533$	18576.0	1.50960
$534$	13440.0	1.08915
$535$	0	0
$536$	4768.00	0.384228
$537$	−25620.0	−2.05882
$538$	1140.00	0.0913548
$539$	0	0
$540$	0	0
$541$	−3193.00	−0.253748	−0.126874	−	0.991919i	$-0.540494\pi$
$541$	−3193.00	−0.253748	−0.126874	+	0.991919i	$0.540494\pi$
$542$	6664.00	0.528124
$543$	11956.0	0.944901
$544$	−3552.00	−0.279946
$545$	0	0
$546$	0	0
$547$	−22916.0	−1.79126	−0.895628	−	0.444803i	$-0.853274\pi$
$547$	−22916.0	−1.79126	−0.895628	+	0.444803i	$0.853274\pi$
$548$	−9984.00	−0.778276
$549$	−17864.0	−1.38874
$550$	0	0
$551$	−15750.0	−1.21774
$552$	2352.00	0.181355
$553$	0	0
$554$	−788.000	−0.0604312
$555$	0	0
$556$	−5480.00	−0.417992
$557$	−15096.0	−1.14836	−0.574181	−	0.818728i	$-0.694680\pi$
$557$	−15096.0	−1.14836	−0.574181	+	0.818728i	$0.694680\pi$
$558$	−3872.00	−0.293754
$559$	−7654.00	−0.579123
$560$	0	0
$561$	−25641.0	−1.92970
$562$	−6534.00	−0.490427
$563$	7932.00	0.593773	0.296886	−	0.954913i	$-0.404052\pi$
$563$	7932.00	0.593773	0.296886	+	0.954913i	$0.404052\pi$
$564$	11508.0	0.859174
$565$	0	0
$566$	−1354.00	−0.100553
$567$	0	0
$568$	−3456.00	−0.255300
$569$	−12990.0	−0.957063	−0.478532	−	0.878070i	$-0.658831\pi$
$569$	−12990.0	−0.957063	−0.478532	+	0.878070i	$0.658831\pi$
$570$	0	0
$571$	20252.0	1.48427	0.742136	−	0.670249i	$-0.233813\pi$
$571$	20252.0	1.48427	0.742136	+	0.670249i	$0.233813\pi$
$572$	5676.00	0.414905
$573$	−14511.0	−1.05795
$574$	0	0
$575$	0	0
$576$	1408.00	0.101852
$577$	−24379.0	−1.75894	−0.879472	−	0.475950i	$-0.842104\pi$
$577$	−24379.0	−1.75894	−0.879472	+	0.475950i	$0.842104\pi$
$578$	−14816.0	−1.06620
$579$	25816.0	1.85298
$580$	0	0
$581$	0	0
$582$	9926.00	0.706952
$583$	−23364.0	−1.65976
$584$	2864.00	0.202933
$585$	0	0
$586$	17226.0	1.21433
$587$	−2304.00	−0.162004	−0.0810019	−	0.996714i	$-0.525812\pi$
$587$	−2304.00	−0.162004	−0.0810019	+	0.996714i	$0.525812\pi$
$588$	0	0
$589$	6160.00	0.430931
$590$	0	0
$591$	−22932.0	−1.59610
$592$	544.000	0.0377673
$593$	6837.00	0.473460	0.236730	−	0.971575i	$-0.423924\pi$
$593$	6837.00	0.473460	0.236730	+	0.971575i	$0.423924\pi$
$594$	−2310.00	−0.159563
$595$	0	0
$596$	9960.00	0.684526
$597$	−16520.0	−1.13253
$598$	−3612.00	−0.246999
$599$	−8925.00	−0.608791	−0.304395	−	0.952546i	$-0.598454\pi$
$599$	−8925.00	−0.608791	−0.304395	+	0.952546i	$0.598454\pi$
$600$	0	0
$601$	−20342.0	−1.38064	−0.690322	−	0.723502i	$-0.742531\pi$
$601$	−20342.0	−1.38064	−0.690322	+	0.723502i	$0.742531\pi$
$602$	0	0
$603$	−13112.0	−0.885509
$604$	548.000	0.0369169
$605$	0	0
$606$	−6132.00	−0.411049
$607$	−27439.0	−1.83479	−0.917393	−	0.397983i	$-0.869710\pi$
$607$	−27439.0	−1.83479	−0.917393	+	0.397983i	$0.869710\pi$
$608$	−2240.00	−0.149414
$609$	0	0
$610$	0	0
$611$	−17673.0	−1.17017
$612$	9768.00	0.645176
$613$	−6842.00	−0.450809	−0.225404	−	0.974265i	$-0.572370\pi$
$613$	−6842.00	−0.450809	−0.225404	+	0.974265i	$0.572370\pi$
$614$	6998.00	0.459961
$615$	0	0
$616$	0	0
$617$	10494.0	0.684720	0.342360	−	0.939569i	$-0.388774\pi$
$617$	10494.0	0.684720	0.342360	+	0.939569i	$0.388774\pi$
$618$	14462.0	0.941338
$619$	−22970.0	−1.49151	−0.745753	−	0.666223i	$-0.767910\pi$
$619$	−22970.0	−1.49151	−0.745753	+	0.666223i	$0.767910\pi$
$620$	0	0
$621$	1470.00	0.0949904
$622$	11364.0	0.732564
$623$	0	0
$624$	−4816.00	−0.308965
$625$	0	0
$626$	−8194.00	−0.523160
$627$	−16170.0	−1.02993
$628$	−13096.0	−0.832145
$629$	3774.00	0.239236
$630$	0	0
$631$	6347.00	0.400428	0.200214	−	0.979752i	$-0.435836\pi$
$631$	6347.00	0.400428	0.200214	+	0.979752i	$0.435836\pi$
$632$	−3400.00	−0.213995
$633$	18599.0	1.16784
$634$	−9348.00	−0.585578
$635$	0	0
$636$	19824.0	1.23596
$637$	0	0
$638$	−14850.0	−0.921500
$639$	9504.00	0.588376
$640$	0	0
$641$	13602.0	0.838138	0.419069	−	0.907954i	$-0.362356\pi$
$641$	13602.0	0.838138	0.419069	+	0.907954i	$0.362356\pi$
$642$	12684.0	0.779747
$643$	5807.00	0.356152	0.178076	−	0.984017i	$-0.443013\pi$
$643$	5807.00	0.356152	0.178076	+	0.984017i	$0.443013\pi$
$644$	0	0
$645$	0	0
$646$	−15540.0	−0.946460
$647$	−19104.0	−1.16083	−0.580414	−	0.814322i	$-0.697109\pi$
$647$	−19104.0	−1.16083	−0.580414	+	0.814322i	$0.697109\pi$
$648$	6712.00	0.406902
$649$	15840.0	0.958050
$650$	0	0
$651$	0	0
$652$	−3608.00	−0.216718
$653$	−3822.00	−0.229045	−0.114523	−	0.993421i	$-0.536534\pi$
$653$	−3822.00	−0.229045	−0.114523	+	0.993421i	$0.536534\pi$
$654$	26810.0	1.60299
$655$	0	0
$656$	−6912.00	−0.411385
$657$	−7876.00	−0.467690
$658$	0	0
$659$	30555.0	1.80615	0.903076	−	0.429481i	$-0.141304\pi$
$659$	30555.0	1.80615	0.903076	+	0.429481i	$0.141304\pi$
$660$	0	0
$661$	−18632.0	−1.09637	−0.548185	−	0.836357i	$-0.684681\pi$
$661$	−18632.0	−1.09637	−0.548185	+	0.836357i	$0.684681\pi$
$662$	−20344.0	−1.19440
$663$	−33411.0	−1.95713
$664$	−7776.00	−0.454469
$665$	0	0
$666$	−1496.00	−0.0870403
$667$	9450.00	0.548584
$668$	−15876.0	−0.919552
$669$	329.000	0.0190133
$670$	0	0
$671$	26796.0	1.54165
$672$	0	0
$673$	15568.0	0.891682	0.445841	−	0.895112i	$-0.352905\pi$
$673$	15568.0	0.891682	0.445841	+	0.895112i	$0.352905\pi$
$674$	−18788.0	−1.07372
$675$	0	0
$676$	−1392.00	−0.0791989
$677$	31821.0	1.80647	0.903235	−	0.429146i	$-0.141185\pi$
$677$	31821.0	1.80647	0.903235	+	0.429146i	$0.141185\pi$
$678$	−7812.00	−0.442505
$679$	0	0
$680$	0	0
$681$	42357.0	2.38344
$682$	5808.00	0.326099
$683$	25188.0	1.41112	0.705558	−	0.708652i	$-0.250696\pi$
$683$	25188.0	1.41112	0.705558	+	0.708652i	$0.250696\pi$
$684$	6160.00	0.344347
$685$	0	0
$686$	0	0
$687$	−21560.0	−1.19733
$688$	2848.00	0.157818
$689$	−30444.0	−1.68334
$690$	0	0
$691$	2428.00	0.133669	0.0668346	−	0.997764i	$-0.478710\pi$
$691$	2428.00	0.133669	0.0668346	+	0.997764i	$0.478710\pi$
$692$	−6852.00	−0.376407
$693$	0	0
$694$	9132.00	0.499490
$695$	0	0
$696$	12600.0	0.686209
$697$	−47952.0	−2.60590
$698$	−13460.0	−0.729898
$699$	23016.0	1.24541
$700$	0	0
$701$	11187.0	0.602749	0.301375	−	0.953506i	$-0.402555\pi$
$701$	11187.0	0.602749	0.301375	+	0.953506i	$0.402555\pi$
$702$	−3010.00	−0.161831
$703$	2380.00	0.127686
$704$	−2112.00	−0.113067
$705$	0	0
$706$	−6054.00	−0.322727
$707$	0	0
$708$	−13440.0	−0.713427
$709$	22655.0	1.20004	0.600019	−	0.799986i	$-0.295160\pi$
$709$	22655.0	1.20004	0.600019	+	0.799986i	$0.295160\pi$
$710$	0	0
$711$	9350.00	0.493182
$712$	7680.00	0.404242
$713$	−3696.00	−0.194132
$714$	0	0
$715$	0	0
$716$	−14640.0	−0.764138
$717$	−12285.0	−0.639877
$718$	−5520.00	−0.286914
$719$	9750.00	0.505721	0.252861	−	0.967503i	$-0.418629\pi$
$719$	9750.00	0.505721	0.252861	+	0.967503i	$0.418629\pi$
$720$	0	0
$721$	0	0
$722$	3918.00	0.201957
$723$	−14.0000	−0.000720146 0
$724$	6832.00	0.350703
$725$	0	0
$726$	3388.00	0.173196
$727$	−17584.0	−0.897049	−0.448524	−	0.893771i	$-0.648050\pi$
$727$	−17584.0	−0.897049	−0.448524	+	0.893771i	$0.648050\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	19758.0	0.999694
$732$	−22736.0	−1.14801
$733$	20657.0	1.04091	0.520453	−	0.853890i	$-0.325763\pi$
$733$	20657.0	1.04091	0.520453	+	0.853890i	$0.325763\pi$
$734$	−12262.0	−0.616619
$735$	0	0
$736$	1344.00	0.0673105
$737$	19668.0	0.983012
$738$	19008.0	0.948095
$739$	−15505.0	−0.771801	−0.385900	−	0.922540i	$-0.626109\pi$
$739$	−15505.0	−0.771801	−0.385900	+	0.922540i	$0.626109\pi$
$740$	0	0
$741$	−21070.0	−1.04457
$742$	0	0
$743$	1548.00	0.0764342	0.0382171	−	0.999269i	$-0.487832\pi$
$743$	1548.00	0.0764342	0.0382171	+	0.999269i	$0.487832\pi$
$744$	−4928.00	−0.242835
$745$	0	0
$746$	19264.0	0.945449
$747$	21384.0	1.04739
$748$	−14652.0	−0.716217
$749$	0	0
$750$	0	0
$751$	8417.00	0.408976	0.204488	−	0.978869i	$-0.434447\pi$
$751$	8417.00	0.408976	0.204488	+	0.978869i	$0.434447\pi$
$752$	6576.00	0.318886
$753$	37926.0	1.83546
$754$	−19350.0	−0.934596
$755$	0	0
$756$	0	0
$757$	−4376.00	−0.210104	−0.105052	−	0.994467i	$-0.533501\pi$
$757$	−4376.00	−0.210104	−0.105052	+	0.994467i	$0.533501\pi$
$758$	19400.0	0.929604
$759$	9702.00	0.463979
$760$	0	0
$761$	16878.0	0.803978	0.401989	−	0.915645i	$-0.368319\pi$
$761$	16878.0	0.803978	0.401989	+	0.915645i	$0.368319\pi$
$762$	−24416.0	−1.16076
$763$	0	0
$764$	−8292.00	−0.392662
$765$	0	0
$766$	−2424.00	−0.114338
$767$	20640.0	0.971665
$768$	1792.00	0.0841969
$769$	−830.000	−0.0389214	−0.0194607	−	0.999811i	$-0.506195\pi$
$769$	−830.000	−0.0389214	−0.0194607	+	0.999811i	$0.506195\pi$
$770$	0	0
$771$	−15078.0	−0.704307
$772$	14752.0	0.687741
$773$	−15603.0	−0.726004	−0.363002	−	0.931788i	$-0.618248\pi$
$773$	−15603.0	−0.726004	−0.363002	+	0.931788i	$0.618248\pi$
$774$	−7832.00	−0.363715
$775$	0	0
$776$	5672.00	0.262388
$777$	0	0
$778$	−8610.00	−0.396765
$779$	−30240.0	−1.39083
$780$	0	0
$781$	−14256.0	−0.653162
$782$	9324.00	0.426375
$783$	7875.00	0.359425
$784$	0	0
$785$	0	0
$786$	−4452.00	−0.202033
$787$	−12589.0	−0.570203	−0.285101	−	0.958497i	$-0.592027\pi$
$787$	−12589.0	−0.570203	−0.285101	+	0.958497i	$0.592027\pi$
$788$	−13104.0	−0.592399
$789$	−27174.0	−1.22613
$790$	0	0
$791$	0	0
$792$	5808.00	0.260579
$793$	34916.0	1.56356
$794$	3218.00	0.143832
$795$	0	0
$796$	−9440.00	−0.420342
$797$	−5769.00	−0.256397	−0.128199	−	0.991749i	$-0.540919\pi$
$797$	−5769.00	−0.256397	−0.128199	+	0.991749i	$0.540919\pi$
$798$	0	0
$799$	45621.0	2.01997
$800$	0	0
$801$	−21120.0	−0.931634
$802$	27006.0	1.18905
$803$	11814.0	0.519187
$804$	−16688.0	−0.732015
$805$	0	0
$806$	7568.00	0.330734
$807$	−3990.00	−0.174045
$808$	−3504.00	−0.152562
$809$	3945.00	0.171445	0.0857224	−	0.996319i	$-0.472680\pi$
$809$	3945.00	0.171445	0.0857224	+	0.996319i	$0.472680\pi$
$810$	0	0
$811$	1618.00	0.0700563	0.0350282	−	0.999386i	$-0.488848\pi$
$811$	1618.00	0.0700563	0.0350282	+	0.999386i	$0.488848\pi$
$812$	0	0
$813$	−23324.0	−1.00616
$814$	2244.00	0.0966243
$815$	0	0
$816$	12432.0	0.533342
$817$	12460.0	0.533562
$818$	940.000	0.0401789
$819$	0	0
$820$	0	0
$821$	23217.0	0.986941	0.493471	−	0.869762i	$-0.335728\pi$
$821$	23217.0	0.986941	0.493471	+	0.869762i	$0.335728\pi$
$822$	34944.0	1.48274
$823$	−15032.0	−0.636674	−0.318337	−	0.947978i	$-0.603124\pi$
$823$	−15032.0	−0.636674	−0.318337	+	0.947978i	$0.603124\pi$
$824$	8264.00	0.349381
$825$	0	0
$826$	0	0
$827$	12654.0	0.532071	0.266035	−	0.963963i	$-0.414286\pi$
$827$	12654.0	0.532071	0.266035	+	0.963963i	$0.414286\pi$
$828$	−3696.00	−0.155127
$829$	3400.00	0.142445	0.0712225	−	0.997460i	$-0.477310\pi$
$829$	3400.00	0.142445	0.0712225	+	0.997460i	$0.477310\pi$
$830$	0	0
$831$	2758.00	0.115131
$832$	−2752.00	−0.114674
$833$	0	0
$834$	19180.0	0.796342
$835$	0	0
$836$	−9240.00	−0.382263
$837$	−3080.00	−0.127193
$838$	−23400.0	−0.964606
$839$	−16830.0	−0.692534	−0.346267	−	0.938136i	$-0.612551\pi$
$839$	−16830.0	−0.692534	−0.346267	+	0.938136i	$0.612551\pi$
$840$	0	0
$841$	26236.0	1.07573
$842$	12326.0	0.504492
$843$	22869.0	0.934342
$844$	10628.0	0.433449
$845$	0	0
$846$	−18084.0	−0.734918
$847$	0	0
$848$	11328.0	0.458732
$849$	4739.00	0.191569
$850$	0	0
$851$	−1428.00	−0.0575220
$852$	12096.0	0.486387
$853$	25022.0	1.00438	0.502190	−	0.864757i	$-0.332528\pi$
$853$	25022.0	1.00438	0.502190	+	0.864757i	$0.332528\pi$
$854$	0	0
$855$	0	0
$856$	7248.00	0.289406
$857$	−2094.00	−0.0834652	−0.0417326	−	0.999129i	$-0.513288\pi$
$857$	−2094.00	−0.0834652	−0.0417326	+	0.999129i	$0.513288\pi$
$858$	−19866.0	−0.790459
$859$	4300.00	0.170796	0.0853982	−	0.996347i	$-0.472784\pi$
$859$	4300.00	0.170796	0.0853982	+	0.996347i	$0.472784\pi$
$860$	0	0
$861$	0	0
$862$	−10374.0	−0.409907
$863$	7428.00	0.292992	0.146496	−	0.989211i	$-0.453200\pi$
$863$	7428.00	0.292992	0.146496	+	0.989211i	$0.453200\pi$
$864$	1120.00	0.0441009
$865$	0	0
$866$	−5764.00	−0.226176
$867$	51856.0	2.03128
$868$	0	0
$869$	−14025.0	−0.547486
$870$	0	0
$871$	25628.0	0.996982
$872$	15320.0	0.594955
$873$	−15598.0	−0.604711
$874$	5880.00	0.227567
$875$	0	0
$876$	−10024.0	−0.386621
$877$	−33446.0	−1.28779	−0.643895	−	0.765114i	$-0.722682\pi$
$877$	−33446.0	−1.28779	−0.643895	+	0.765114i	$0.722682\pi$
$878$	19660.0	0.755687
$879$	−60291.0	−2.31350
$880$	0	0
$881$	−20592.0	−0.787471	−0.393736	−	0.919224i	$-0.628817\pi$
$881$	−20592.0	−0.787471	−0.393736	+	0.919224i	$0.628817\pi$
$882$	0	0
$883$	47248.0	1.80070	0.900352	−	0.435162i	$-0.143309\pi$
$883$	47248.0	1.80070	0.900352	+	0.435162i	$0.143309\pi$
$884$	−19092.0	−0.726395
$885$	0	0
$886$	−10356.0	−0.392682
$887$	−16824.0	−0.636860	−0.318430	−	0.947946i	$-0.603156\pi$
$887$	−16824.0	−0.636860	−0.318430	+	0.947946i	$0.603156\pi$
$888$	−1904.00	−0.0719528
$889$	0	0
$890$	0	0
$891$	27687.0	1.04102
$892$	188.000	0.00705684
$893$	28770.0	1.07811
$894$	−34860.0	−1.30413
$895$	0	0
$896$	0	0
$897$	12642.0	0.470573
$898$	9090.00	0.337792
$899$	−19800.0	−0.734557
$900$	0	0
$901$	78588.0	2.90582
$902$	−28512.0	−1.05249
$903$	0	0
$904$	−4464.00	−0.164237
$905$	0	0
$906$	−1918.00	−0.0703325
$907$	−8066.00	−0.295289	−0.147645	−	0.989040i	$-0.547169\pi$
$907$	−8066.00	−0.295289	−0.147645	+	0.989040i	$0.547169\pi$
$908$	24204.0	0.884623
$909$	9636.00	0.351602
$910$	0	0
$911$	−21168.0	−0.769843	−0.384922	−	0.922949i	$-0.625772\pi$
$911$	−21168.0	−0.769843	−0.384922	+	0.922949i	$0.625772\pi$
$912$	7840.00	0.284658
$913$	−32076.0	−1.16272
$914$	−968.000	−0.0350313
$915$	0	0
$916$	−12320.0	−0.444393
$917$	0	0
$918$	7770.00	0.279355
$919$	10685.0	0.383532	0.191766	−	0.981441i	$-0.438579\pi$
$919$	10685.0	0.383532	0.191766	+	0.981441i	$0.438579\pi$
$920$	0	0
$921$	−24493.0	−0.876299
$922$	−2736.00	−0.0977282
$923$	−18576.0	−0.662445
$924$	0	0
$925$	0	0
$926$	29704.0	1.05414
$927$	−22726.0	−0.805199
$928$	7200.00	0.254689
$929$	−5820.00	−0.205541	−0.102771	−	0.994705i	$-0.532771\pi$
$929$	−5820.00	−0.205541	−0.102771	+	0.994705i	$0.532771\pi$
$930$	0	0
$931$	0	0
$932$	13152.0	0.462240
$933$	−39774.0	−1.39565
$934$	−15042.0	−0.526969
$935$	0	0
$936$	7568.00	0.264282
$937$	−1429.00	−0.0498222	−0.0249111	−	0.999690i	$-0.507930\pi$
$937$	−1429.00	−0.0498222	−0.0249111	+	0.999690i	$0.507930\pi$
$938$	0	0
$939$	28679.0	0.996703
$940$	0	0
$941$	−16932.0	−0.586575	−0.293288	−	0.956024i	$-0.594749\pi$
$941$	−16932.0	−0.586575	−0.293288	+	0.956024i	$0.594749\pi$
$942$	45836.0	1.58537
$943$	18144.0	0.626564
$944$	−7680.00	−0.264791
$945$	0	0
$946$	11748.0	0.403764
$947$	45804.0	1.57173	0.785866	−	0.618397i	$-0.212218\pi$
$947$	45804.0	1.57173	0.785866	+	0.618397i	$0.212218\pi$
$948$	11900.0	0.407694
$949$	15394.0	0.526565
$950$	0	0
$951$	32718.0	1.11562
$952$	0	0
$953$	41508.0	1.41089	0.705444	−	0.708766i	$-0.250748\pi$
$953$	41508.0	1.41089	0.705444	+	0.708766i	$0.250748\pi$
$954$	−31152.0	−1.05722
$955$	0	0
$956$	−7020.00	−0.237493
$957$	51975.0	1.75560
$958$	17700.0	0.596932
$959$	0	0
$960$	0	0
$961$	−22047.0	−0.740056
$962$	2924.00	0.0979974
$963$	−19932.0	−0.666978
$964$	−8.00000	−0.000267285 0
$965$	0	0
$966$	0	0
$967$	−39566.0	−1.31578	−0.657889	−	0.753115i	$-0.728550\pi$
$967$	−39566.0	−1.31578	−0.657889	+	0.753115i	$0.728550\pi$
$968$	1936.00	0.0642824
$969$	54390.0	1.80316
$970$	0	0
$971$	40188.0	1.32821	0.664106	−	0.747638i	$-0.268812\pi$
$971$	40188.0	1.32821	0.664106	+	0.747638i	$0.268812\pi$
$972$	−19712.0	−0.650476
$973$	0	0
$974$	−29228.0	−0.961525
$975$	0	0
$976$	−12992.0	−0.426090
$977$	17214.0	0.563690	0.281845	−	0.959460i	$-0.409054\pi$
$977$	17214.0	0.563690	0.281845	+	0.959460i	$0.409054\pi$
$978$	12628.0	0.412882
$979$	31680.0	1.03422
$980$	0	0
$981$	−42130.0	−1.37116
$982$	−30474.0	−0.990290
$983$	12657.0	0.410677	0.205339	−	0.978691i	$-0.434170\pi$
$983$	12657.0	0.410677	0.205339	+	0.978691i	$0.434170\pi$
$984$	24192.0	0.783753
$985$	0	0
$986$	49950.0	1.61332
$987$	0	0
$988$	−12040.0	−0.387696
$989$	−7476.00	−0.240367
$990$	0	0
$991$	38072.0	1.22038	0.610190	−	0.792255i	$-0.291093\pi$
$991$	38072.0	1.22038	0.610190	+	0.792255i	$0.291093\pi$
$992$	−2816.00	−0.0901291
$993$	71204.0	2.27552
$994$	0	0
$995$	0	0
$996$	27216.0	0.865835
$997$	−35269.0	−1.12034	−0.560171	−	0.828377i	$-0.689264\pi$
$997$	−35269.0	−1.12034	−0.560171	+	0.828377i	$0.689264\pi$
$998$	19130.0	0.606763
$999$	−1190.00	−0.0376876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.4.a.s.1.1		1
5.4	even	2		490.4.a.i.1.1		1
7.6	odd	2		350.4.a.b.1.1		1
35.4	even	6		490.4.e.h.471.1		2
35.9	even	6		490.4.e.h.361.1		2
35.13	even	4		350.4.c.l.99.2		2
35.19	odd	6		490.4.e.b.361.1		2
35.24	odd	6		490.4.e.b.471.1		2
35.27	even	4		350.4.c.l.99.1		2
35.34	odd	2		70.4.a.f.1.1	✓	1
105.104	even	2		630.4.a.j.1.1		1
140.139	even	2		560.4.a.c.1.1		1
280.69	odd	2		2240.4.a.f.1.1		1
280.139	even	2		2240.4.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.f.1.1	✓	1	35.34	odd	2
350.4.a.b.1.1		1	7.6	odd	2
350.4.c.l.99.1		2	35.27	even	4
350.4.c.l.99.2		2	35.13	even	4
490.4.a.i.1.1		1	5.4	even	2
490.4.e.b.361.1		2	35.19	odd	6
490.4.e.b.471.1		2	35.24	odd	6
490.4.e.h.361.1		2	35.9	even	6
490.4.e.h.471.1		2	35.4	even	6
560.4.a.c.1.1		1	140.139	even	2
630.4.a.j.1.1		1	105.104	even	2
2240.4.a.f.1.1		1	280.69	odd	2
2240.4.a.bh.1.1		1	280.139	even	2
2450.4.a.s.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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