LMFDB - Embedded newform 1850.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,4,Mod(1,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1850.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:	$109.153533511$
Analytic rank:	$0$
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	$\chi$	$=$	1850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -20.0000 q^{6} -32.0000 q^{7} -8.00000 q^{8} +73.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -20.0000 q^{6} -32.0000 q^{7} -8.00000 q^{8} +73.0000 q^{9} +52.0000 q^{11} +40.0000 q^{12} +62.0000 q^{13} +64.0000 q^{14} +16.0000 q^{16} +16.0000 q^{17} -146.000 q^{18} -85.0000 q^{19} -320.000 q^{21} -104.000 q^{22} +189.000 q^{23} -80.0000 q^{24} -124.000 q^{26} +460.000 q^{27} -128.000 q^{28} +98.0000 q^{29} -92.0000 q^{31} -32.0000 q^{32} +520.000 q^{33} -32.0000 q^{34} +292.000 q^{36} +37.0000 q^{37} +170.000 q^{38} +620.000 q^{39} -249.000 q^{41} +640.000 q^{42} -433.000 q^{43} +208.000 q^{44} -378.000 q^{46} +422.000 q^{47} +160.000 q^{48} +681.000 q^{49} +160.000 q^{51} +248.000 q^{52} -63.0000 q^{53} -920.000 q^{54} +256.000 q^{56} -850.000 q^{57} -196.000 q^{58} +37.0000 q^{59} -590.000 q^{61} +184.000 q^{62} -2336.00 q^{63} +64.0000 q^{64} -1040.00 q^{66} -222.000 q^{67} +64.0000 q^{68} +1890.00 q^{69} -154.000 q^{71} -584.000 q^{72} +259.000 q^{73} -74.0000 q^{74} -340.000 q^{76} -1664.00 q^{77} -1240.00 q^{78} -1207.00 q^{79} +2629.00 q^{81} +498.000 q^{82} +64.0000 q^{83} -1280.00 q^{84} +866.000 q^{86} +980.000 q^{87} -416.000 q^{88} +630.000 q^{89} -1984.00 q^{91} +756.000 q^{92} -920.000 q^{93} -844.000 q^{94} -320.000 q^{96} +672.000 q^{97} -1362.00 q^{98} +3796.00 q^{99} +O(q^{100})\)

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
$3$	10.0000	1.92450	0.962250	−	0.272166i	$-0.0877398\pi$
$3$	10.0000	1.92450	0.962250	+	0.272166i	$0.0877398\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−20.0000	−1.36083
$7$	−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
$9$	73.0000	2.70370
$10$	0	0
$11$	52.0000	1.42533	0.712663	−	0.701506i	$-0.247489\pi$
$11$	52.0000	1.42533	0.712663	+	0.701506i	$0.247489\pi$
$12$	40.0000	0.962250
$13$	62.0000	1.32275	0.661373	−	0.750057i	$-0.269974\pi$
$13$	62.0000	1.32275	0.661373	+	0.750057i	$0.269974\pi$
$14$	64.0000	1.22177
$15$	0	0
$16$	16.0000	0.250000
$17$	16.0000	0.228269	0.114134	−	0.993465i	$-0.463591\pi$
$17$	16.0000	0.228269	0.114134	+	0.993465i	$0.463591\pi$
$18$	−146.000	−1.91181
$19$	−85.0000	−1.02633	−0.513167	−	0.858289i	$-0.671528\pi$
$19$	−85.0000	−1.02633	−0.513167	+	0.858289i	$0.671528\pi$
$20$	0	0
$21$	−320.000	−3.32522
$22$	−104.000	−1.00786
$23$	189.000	1.71344	0.856722	−	0.515778i	$-0.172497\pi$
$23$	189.000	1.71344	0.856722	+	0.515778i	$0.172497\pi$
$24$	−80.0000	−0.680414
$25$	0	0
$26$	−124.000	−0.935323
$27$	460.000	3.27878
$28$	−128.000	−0.863919
$29$	98.0000	0.627522	0.313761	−	0.949502i	$-0.398411\pi$
$29$	98.0000	0.627522	0.313761	+	0.949502i	$0.398411\pi$
$30$	0	0
$31$	−92.0000	−0.533022	−0.266511	−	0.963832i	$-0.585871\pi$
$31$	−92.0000	−0.533022	−0.266511	+	0.963832i	$0.585871\pi$
$32$	−32.0000	−0.176777
$33$	520.000	2.74304
$34$	−32.0000	−0.161410
$35$	0	0
$36$	292.000	1.35185
$37$	37.0000	0.164399
$37$	37.0000	0.164399
$38$	170.000	0.725727
$39$	620.000	2.54563
$40$	0	0
$41$	−249.000	−0.948470	−0.474235	−	0.880398i	$-0.657275\pi$
$41$	−249.000	−0.948470	−0.474235	+	0.880398i	$0.657275\pi$
$42$	640.000	2.35129
$43$	−433.000	−1.53563	−0.767813	−	0.640675i	$-0.778655\pi$
$43$	−433.000	−1.53563	−0.767813	+	0.640675i	$0.778655\pi$
$44$	208.000	0.712663
$45$	0	0
$46$	−378.000	−1.21159
$47$	422.000	1.30968	0.654841	−	0.755767i	$-0.272736\pi$
$47$	422.000	1.30968	0.654841	+	0.755767i	$0.272736\pi$
$48$	160.000	0.481125
$49$	681.000	1.98542
$50$	0	0
$51$	160.000	0.439304
$52$	248.000	0.661373
$53$	−63.0000	−0.163278	−0.0816388	−	0.996662i	$-0.526015\pi$
$53$	−63.0000	−0.163278	−0.0816388	+	0.996662i	$0.526015\pi$
$54$	−920.000	−2.31845
$55$	0	0
$56$	256.000	0.610883
$57$	−850.000	−1.97518
$58$	−196.000	−0.443725
$59$	37.0000	0.0816439	0.0408219	−	0.999166i	$-0.487002\pi$
$59$	37.0000	0.0816439	0.0408219	+	0.999166i	$0.487002\pi$
$60$	0	0
$61$	−590.000	−1.23839	−0.619195	−	0.785237i	$-0.712541\pi$
$61$	−590.000	−1.23839	−0.619195	+	0.785237i	$0.712541\pi$
$62$	184.000	0.376904
$63$	−2336.00	−4.67156
$64$	64.0000	0.125000
$65$	0	0
$66$	−1040.00	−1.93962
$67$	−222.000	−0.404800	−0.202400	−	0.979303i	$-0.564874\pi$
$67$	−222.000	−0.404800	−0.202400	+	0.979303i	$0.564874\pi$
$68$	64.0000	0.114134
$69$	1890.00	3.29753
$70$	0	0
$71$	−154.000	−0.257415	−0.128707	−	0.991683i	$-0.541083\pi$
$71$	−154.000	−0.257415	−0.128707	+	0.991683i	$0.541083\pi$
$72$	−584.000	−0.955904
$73$	259.000	0.415256	0.207628	−	0.978208i	$-0.433426\pi$
$73$	259.000	0.415256	0.207628	+	0.978208i	$0.433426\pi$
$74$	−74.0000	−0.116248
$75$	0	0
$76$	−340.000	−0.513167
$77$	−1664.00	−2.46273
$78$	−1240.00	−1.80003
$79$	−1207.00	−1.71896	−0.859482	−	0.511167i	$-0.829214\pi$
$79$	−1207.00	−1.71896	−0.859482	+	0.511167i	$0.829214\pi$
$80$	0	0
$81$	2629.00	3.60631
$82$	498.000	0.670670
$83$	64.0000	0.0846375	0.0423188	−	0.999104i	$-0.486525\pi$
$83$	64.0000	0.0846375	0.0423188	+	0.999104i	$0.486525\pi$
$84$	−1280.00	−1.66261
$85$	0	0
$86$	866.000	1.08585
$87$	980.000	1.20767
$88$	−416.000	−0.503929
$89$	630.000	0.750336	0.375168	−	0.926957i	$-0.377585\pi$
$89$	630.000	0.750336	0.375168	+	0.926957i	$0.377585\pi$
$90$	0	0
$91$	−1984.00	−2.28549
$92$	756.000	0.856722
$93$	−920.000	−1.02580
$94$	−844.000	−0.926085
$95$	0	0
$96$	−320.000	−0.340207
$97$	672.000	0.703415	0.351708	−	0.936110i	$-0.385601\pi$
$97$	672.000	0.703415	0.351708	+	0.936110i	$0.385601\pi$
$98$	−1362.00	−1.40391
$99$	3796.00	3.85366
$100$	0	0
$101$	819.000	0.806867	0.403433	−	0.915009i	$-0.367817\pi$
$101$	819.000	0.806867	0.403433	+	0.915009i	$0.367817\pi$
$102$	−320.000	−0.310635
$103$	1845.00	1.76498	0.882492	−	0.470328i	$-0.155865\pi$
$103$	1845.00	1.76498	0.882492	+	0.470328i	$0.155865\pi$
$104$	−496.000	−0.467662
$105$	0	0
$106$	126.000	0.115455
$107$	2110.00	1.90637	0.953184	−	0.302391i	$-0.0977847\pi$
$107$	2110.00	1.90637	0.953184	+	0.302391i	$0.0977847\pi$
$108$	1840.00	1.63939
$109$	−904.000	−0.794381	−0.397190	−	0.917736i	$-0.630015\pi$
$109$	−904.000	−0.794381	−0.397190	+	0.917736i	$0.630015\pi$
$110$	0	0
$111$	370.000	0.316386
$112$	−512.000	−0.431959
$113$	558.000	0.464533	0.232266	−	0.972652i	$-0.425386\pi$
$113$	558.000	0.464533	0.232266	+	0.972652i	$0.425386\pi$
$114$	1700.00	1.39666
$115$	0	0
$116$	392.000	0.313761
$117$	4526.00	3.57631
$118$	−74.0000	−0.0577310
$119$	−512.000	−0.394411
$120$	0	0
$121$	1373.00	1.03156
$122$	1180.00	0.875674
$123$	−2490.00	−1.82533
$124$	−368.000	−0.266511
$125$	0	0
$126$	4672.00	3.30329
$127$	−2172.00	−1.51759	−0.758795	−	0.651330i	$-0.774211\pi$
$127$	−2172.00	−1.51759	−0.758795	+	0.651330i	$0.774211\pi$
$128$	−128.000	−0.0883883
$129$	−4330.00	−2.95531
$130$	0	0
$131$	1660.00	1.10714	0.553568	−	0.832804i	$-0.313266\pi$
$131$	1660.00	1.10714	0.553568	+	0.832804i	$0.313266\pi$
$132$	2080.00	1.37152
$133$	2720.00	1.77334
$134$	444.000	0.286237
$135$	0	0
$136$	−128.000	−0.0807052
$137$	2598.00	1.62016	0.810081	−	0.586318i	$-0.199423\pi$
$137$	2598.00	1.62016	0.810081	+	0.586318i	$0.199423\pi$
$138$	−3780.00	−2.33170
$139$	2314.00	1.41202	0.706010	−	0.708201i	$-0.250493\pi$
$139$	2314.00	1.41202	0.706010	+	0.708201i	$0.250493\pi$
$140$	0	0
$141$	4220.00	2.52048
$142$	308.000	0.182020
$143$	3224.00	1.88535
$144$	1168.00	0.675926
$145$	0	0
$146$	−518.000	−0.293630
$147$	6810.00	3.82095
$148$	148.000	0.0821995
$149$	1399.00	0.769198	0.384599	−	0.923084i	$-0.374340\pi$
$149$	1399.00	0.769198	0.384599	+	0.923084i	$0.374340\pi$
$150$	0	0
$151$	976.000	0.525998	0.262999	−	0.964796i	$-0.415288\pi$
$151$	976.000	0.525998	0.262999	+	0.964796i	$0.415288\pi$
$152$	680.000	0.362864
$153$	1168.00	0.617171
$154$	3328.00	1.74141
$155$	0	0
$156$	2480.00	1.27281
$157$	−2765.00	−1.40555	−0.702774	−	0.711413i	$-0.748055\pi$
$157$	−2765.00	−1.40555	−0.702774	+	0.711413i	$0.748055\pi$
$158$	2414.00	1.21549
$159$	−630.000	−0.314228
$160$	0	0
$161$	−6048.00	−2.96055
$162$	−5258.00	−2.55005
$163$	1151.00	0.553088	0.276544	−	0.961001i	$-0.410811\pi$
$163$	1151.00	0.553088	0.276544	+	0.961001i	$0.410811\pi$
$164$	−996.000	−0.474235
$165$	0	0
$166$	−128.000	−0.0598478
$167$	1123.00	0.520361	0.260181	−	0.965560i	$-0.416218\pi$
$167$	1123.00	0.520361	0.260181	+	0.965560i	$0.416218\pi$
$168$	2560.00	1.17564
$169$	1647.00	0.749659
$170$	0	0
$171$	−6205.00	−2.77490
$172$	−1732.00	−0.767813
$173$	2774.00	1.21909	0.609547	−	0.792750i	$-0.291351\pi$
$173$	2774.00	1.21909	0.609547	+	0.792750i	$0.291351\pi$
$174$	−1960.00	−0.853950
$175$	0	0
$176$	832.000	0.356332
$177$	370.000	0.157124
$178$	−1260.00	−0.530567
$179$	2700.00	1.12742	0.563708	−	0.825974i	$-0.309374\pi$
$179$	2700.00	1.12742	0.563708	+	0.825974i	$0.309374\pi$
$180$	0	0
$181$	−4131.00	−1.69644	−0.848218	−	0.529648i	$-0.822324\pi$
$181$	−4131.00	−1.69644	−0.848218	+	0.529648i	$0.822324\pi$
$182$	3968.00	1.61609
$183$	−5900.00	−2.38328
$184$	−1512.00	−0.605794
$185$	0	0
$186$	1840.00	0.725351
$187$	832.000	0.325358
$188$	1688.00	0.654841
$189$	−14720.0	−5.66520
$190$	0	0
$191$	−447.000	−0.169339	−0.0846696	−	0.996409i	$-0.526983\pi$
$191$	−447.000	−0.169339	−0.0846696	+	0.996409i	$0.526983\pi$
$192$	640.000	0.240563
$193$	1932.00	0.720562	0.360281	−	0.932844i	$-0.382681\pi$
$193$	1932.00	0.720562	0.360281	+	0.932844i	$0.382681\pi$
$194$	−1344.00	−0.497390
$195$	0	0
$196$	2724.00	0.992711
$197$	−2469.00	−0.892939	−0.446469	−	0.894799i	$-0.647319\pi$
$197$	−2469.00	−0.892939	−0.446469	+	0.894799i	$0.647319\pi$
$198$	−7592.00	−2.72495
$199$	709.000	0.252561	0.126281	−	0.991995i	$-0.459696\pi$
$199$	709.000	0.252561	0.126281	+	0.991995i	$0.459696\pi$
$200$	0	0
$201$	−2220.00	−0.779038
$202$	−1638.00	−0.570541
$203$	−3136.00	−1.08426
$204$	640.000	0.219652
$205$	0	0
$206$	−3690.00	−1.24803
$207$	13797.0	4.63265
$208$	992.000	0.330687
$209$	−4420.00	−1.46286
$210$	0	0
$211$	2674.00	0.872444	0.436222	−	0.899839i	$-0.356316\pi$
$211$	2674.00	0.872444	0.436222	+	0.899839i	$0.356316\pi$
$212$	−252.000	−0.0816388
$213$	−1540.00	−0.495395
$214$	−4220.00	−1.34801
$215$	0	0
$216$	−3680.00	−1.15922
$217$	2944.00	0.920976
$218$	1808.00	0.561712
$219$	2590.00	0.799160
$220$	0	0
$221$	992.000	0.301942
$222$	−740.000	−0.223719
$223$	−178.000	−0.0534518	−0.0267259	−	0.999643i	$-0.508508\pi$
$223$	−178.000	−0.0534518	−0.0267259	+	0.999643i	$0.508508\pi$
$224$	1024.00	0.305441
$225$	0	0
$226$	−1116.00	−0.328474
$227$	2481.00	0.725417	0.362709	−	0.931903i	$-0.381852\pi$
$227$	2481.00	0.725417	0.362709	+	0.931903i	$0.381852\pi$
$228$	−3400.00	−0.987590
$229$	−1645.00	−0.474693	−0.237346	−	0.971425i	$-0.576278\pi$
$229$	−1645.00	−0.474693	−0.237346	+	0.971425i	$0.576278\pi$
$230$	0	0
$231$	−16640.0	−4.73953
$232$	−784.000	−0.221863
$233$	−13.0000	−0.00365519	−0.00182759	−	0.999998i	$-0.500582\pi$
$233$	−13.0000	−0.00365519	−0.00182759	+	0.999998i	$0.500582\pi$
$234$	−9052.00	−2.52884
$235$	0	0
$236$	148.000	0.0408219
$237$	−12070.0	−3.30815
$238$	1024.00	0.278891
$239$	−713.000	−0.192971	−0.0964856	−	0.995334i	$-0.530760\pi$
$239$	−713.000	−0.192971	−0.0964856	+	0.995334i	$0.530760\pi$
$240$	0	0
$241$	1906.00	0.509445	0.254723	−	0.967014i	$-0.418016\pi$
$241$	1906.00	0.509445	0.254723	+	0.967014i	$0.418016\pi$
$242$	−2746.00	−0.729420
$243$	13870.0	3.66157
$244$	−2360.00	−0.619195
$245$	0	0
$246$	4980.00	1.29070
$247$	−5270.00	−1.35758
$248$	736.000	0.188452
$249$	640.000	0.162885
$250$	0	0
$251$	3675.00	0.924159	0.462080	−	0.886838i	$-0.347103\pi$
$251$	3675.00	0.924159	0.462080	+	0.886838i	$0.347103\pi$
$252$	−9344.00	−2.33578
$253$	9828.00	2.44222
$254$	4344.00	1.07310
$255$	0	0
$256$	256.000	0.0625000
$257$	−792.000	−0.192232	−0.0961160	−	0.995370i	$-0.530642\pi$
$257$	−792.000	−0.192232	−0.0961160	+	0.995370i	$0.530642\pi$
$258$	8660.00	2.08972
$259$	−1184.00	−0.284055
$260$	0	0
$261$	7154.00	1.69663
$262$	−3320.00	−0.782864
$263$	3182.00	0.746048	0.373024	−	0.927822i	$-0.378321\pi$
$263$	3182.00	0.746048	0.373024	+	0.927822i	$0.378321\pi$
$264$	−4160.00	−0.969812
$265$	0	0
$266$	−5440.00	−1.25394
$267$	6300.00	1.44402
$268$	−888.000	−0.202400
$269$	411.000	0.0931566	0.0465783	−	0.998915i	$-0.485168\pi$
$269$	411.000	0.0931566	0.0465783	+	0.998915i	$0.485168\pi$
$270$	0	0
$271$	5092.00	1.14139	0.570696	−	0.821162i	$-0.306674\pi$
$271$	5092.00	1.14139	0.570696	+	0.821162i	$0.306674\pi$
$272$	256.000	0.0570672
$273$	−19840.0	−4.39843
$274$	−5196.00	−1.14563
$275$	0	0
$276$	7560.00	1.64876
$277$	2770.00	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	2770.00	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	−4628.00	−0.998450
$279$	−6716.00	−1.44113
$280$	0	0
$281$	−7284.00	−1.54636	−0.773180	−	0.634187i	$-0.781335\pi$
$281$	−7284.00	−1.54636	−0.773180	+	0.634187i	$0.781335\pi$
$282$	−8440.00	−1.78225
$283$	2819.00	0.592128	0.296064	−	0.955168i	$-0.404326\pi$
$283$	2819.00	0.592128	0.296064	+	0.955168i	$0.404326\pi$
$284$	−616.000	−0.128707
$285$	0	0
$286$	−6448.00	−1.33314
$287$	7968.00	1.63880
$288$	−2336.00	−0.477952
$289$	−4657.00	−0.947893
$290$	0	0
$291$	6720.00	1.35372
$292$	1036.00	0.207628
$293$	−3155.00	−0.629068	−0.314534	−	0.949246i	$-0.601848\pi$
$293$	−3155.00	−0.629068	−0.314534	+	0.949246i	$0.601848\pi$
$294$	−13620.0	−2.70182
$295$	0	0
$296$	−296.000	−0.0581238
$297$	23920.0	4.67333
$298$	−2798.00	−0.543905
$299$	11718.0	2.26645
$300$	0	0
$301$	13856.0	2.65331
$302$	−1952.00	−0.371937
$303$	8190.00	1.55282
$304$	−1360.00	−0.256583
$305$	0	0
$306$	−2336.00	−0.436406
$307$	−4884.00	−0.907963	−0.453981	−	0.891011i	$-0.649997\pi$
$307$	−4884.00	−0.907963	−0.453981	+	0.891011i	$0.649997\pi$
$308$	−6656.00	−1.23137
$309$	18450.0	3.39671
$310$	0	0
$311$	−6487.00	−1.18278	−0.591389	−	0.806386i	$-0.701420\pi$
$311$	−6487.00	−1.18278	−0.591389	+	0.806386i	$0.701420\pi$
$312$	−4960.00	−0.900015
$313$	−2578.00	−0.465550	−0.232775	−	0.972531i	$-0.574781\pi$
$313$	−2578.00	−0.465550	−0.232775	+	0.972531i	$0.574781\pi$
$314$	5530.00	0.993872
$315$	0	0
$316$	−4828.00	−0.859482
$317$	−2583.00	−0.457652	−0.228826	−	0.973467i	$-0.573489\pi$
$317$	−2583.00	−0.457652	−0.228826	+	0.973467i	$0.573489\pi$
$318$	1260.00	0.222193
$319$	5096.00	0.894424
$320$	0	0
$321$	21100.0	3.66881
$322$	12096.0	2.09343
$323$	−1360.00	−0.234280
$324$	10516.0	1.80316
$325$	0	0
$326$	−2302.00	−0.391092
$327$	−9040.00	−1.52879
$328$	1992.00	0.335335
$329$	−13504.0	−2.26292
$330$	0	0
$331$	−1888.00	−0.313516	−0.156758	−	0.987637i	$-0.550104\pi$
$331$	−1888.00	−0.313516	−0.156758	+	0.987637i	$0.550104\pi$
$332$	256.000	0.0423188
$333$	2701.00	0.444486
$334$	−2246.00	−0.367951
$335$	0	0
$336$	−5120.00	−0.831306
$337$	−6889.00	−1.11355	−0.556777	−	0.830662i	$-0.687962\pi$
$337$	−6889.00	−1.11355	−0.556777	+	0.830662i	$0.687962\pi$
$338$	−3294.00	−0.530089
$339$	5580.00	0.893994
$340$	0	0
$341$	−4784.00	−0.759731
$342$	12410.0	1.96215
$343$	−10816.0	−1.70265
$344$	3464.00	0.542925
$345$	0	0
$346$	−5548.00	−0.862030
$347$	−4839.00	−0.748620	−0.374310	−	0.927304i	$-0.622120\pi$
$347$	−4839.00	−0.748620	−0.374310	+	0.927304i	$0.622120\pi$
$348$	3920.00	0.603833
$349$	−5419.00	−0.831153	−0.415577	−	0.909558i	$-0.636420\pi$
$349$	−5419.00	−0.831153	−0.415577	+	0.909558i	$0.636420\pi$
$350$	0	0
$351$	28520.0	4.33699
$352$	−1664.00	−0.251964
$353$	−3516.00	−0.530135	−0.265068	−	0.964230i	$-0.585394\pi$
$353$	−3516.00	−0.530135	−0.265068	+	0.964230i	$0.585394\pi$
$354$	−740.000	−0.111103
$355$	0	0
$356$	2520.00	0.375168
$357$	−5120.00	−0.759045
$358$	−5400.00	−0.797204
$359$	−10746.0	−1.57981	−0.789906	−	0.613229i	$-0.789870\pi$
$359$	−10746.0	−1.57981	−0.789906	+	0.613229i	$0.789870\pi$
$360$	0	0
$361$	366.000	0.0533605
$362$	8262.00	1.19956
$363$	13730.0	1.98523
$364$	−7936.00	−1.14275
$365$	0	0
$366$	11800.0	1.68523
$367$	−7826.00	−1.11312	−0.556558	−	0.830808i	$-0.687878\pi$
$367$	−7826.00	−1.11312	−0.556558	+	0.830808i	$0.687878\pi$
$368$	3024.00	0.428361
$369$	−18177.0	−2.56438
$370$	0	0
$371$	2016.00	0.282117
$372$	−3680.00	−0.512901
$373$	11326.0	1.57222	0.786110	−	0.618087i	$-0.212092\pi$
$373$	11326.0	1.57222	0.786110	+	0.618087i	$0.212092\pi$
$374$	−1664.00	−0.230063
$375$	0	0
$376$	−3376.00	−0.463042
$377$	6076.00	0.830053
$378$	29440.0	4.00590
$379$	−8552.00	−1.15907	−0.579534	−	0.814948i	$-0.696765\pi$
$379$	−8552.00	−1.15907	−0.579534	+	0.814948i	$0.696765\pi$
$380$	0	0
$381$	−21720.0	−2.92060
$382$	894.000	0.119741
$383$	4103.00	0.547398	0.273699	−	0.961815i	$-0.411753\pi$
$383$	4103.00	0.547398	0.273699	+	0.961815i	$0.411753\pi$
$384$	−1280.00	−0.170103
$385$	0	0
$386$	−3864.00	−0.509514
$387$	−31609.0	−4.15188
$388$	2688.00	0.351708
$389$	−4488.00	−0.584963	−0.292482	−	0.956271i	$-0.594481\pi$
$389$	−4488.00	−0.584963	−0.292482	+	0.956271i	$0.594481\pi$
$390$	0	0
$391$	3024.00	0.391126
$392$	−5448.00	−0.701953
$393$	16600.0	2.13069
$394$	4938.00	0.631403
$395$	0	0
$396$	15184.0	1.92683
$397$	807.000	0.102021	0.0510103	−	0.998698i	$-0.483756\pi$
$397$	807.000	0.102021	0.0510103	+	0.998698i	$0.483756\pi$
$398$	−1418.00	−0.178588
$399$	27200.0	3.41279
$400$	0	0
$401$	−1770.00	−0.220423	−0.110211	−	0.993908i	$-0.535153\pi$
$401$	−1770.00	−0.220423	−0.110211	+	0.993908i	$0.535153\pi$
$402$	4440.00	0.550863
$403$	−5704.00	−0.705053
$404$	3276.00	0.403433
$405$	0	0
$406$	6272.00	0.766685
$407$	1924.00	0.234322
$408$	−1280.00	−0.155317
$409$	−11656.0	−1.40917	−0.704587	−	0.709618i	$-0.748868\pi$
$409$	−11656.0	−1.40917	−0.704587	+	0.709618i	$0.748868\pi$
$410$	0	0
$411$	25980.0	3.11800
$412$	7380.00	0.882492
$413$	−1184.00	−0.141067
$414$	−27594.0	−3.27578
$415$	0	0
$416$	−1984.00	−0.233831
$417$	23140.0	2.71744
$418$	8840.00	1.03440
$419$	4320.00	0.503689	0.251845	−	0.967768i	$-0.418963\pi$
$419$	4320.00	0.503689	0.251845	+	0.967768i	$0.418963\pi$
$420$	0	0
$421$	−14450.0	−1.67280	−0.836401	−	0.548118i	$-0.815345\pi$
$421$	−14450.0	−1.67280	−0.836401	+	0.548118i	$0.815345\pi$
$422$	−5348.00	−0.616911
$423$	30806.0	3.54099
$424$	504.000	0.0577274
$425$	0	0
$426$	3080.00	0.350297
$427$	18880.0	2.13974
$428$	8440.00	0.953184
$429$	32240.0	3.62835
$430$	0	0
$431$	−967.000	−0.108071	−0.0540357	−	0.998539i	$-0.517208\pi$
$431$	−967.000	−0.108071	−0.0540357	+	0.998539i	$0.517208\pi$
$432$	7360.00	0.819695
$433$	−3462.00	−0.384233	−0.192117	−	0.981372i	$-0.561535\pi$
$433$	−3462.00	−0.384233	−0.192117	+	0.981372i	$0.561535\pi$
$434$	−5888.00	−0.651228
$435$	0	0
$436$	−3616.00	−0.397190
$437$	−16065.0	−1.75857
$438$	−5180.00	−0.565091
$439$	4183.00	0.454769	0.227385	−	0.973805i	$-0.426983\pi$
$439$	4183.00	0.454769	0.227385	+	0.973805i	$0.426983\pi$
$440$	0	0
$441$	49713.0	5.36799
$442$	−1984.00	−0.213505
$443$	16968.0	1.81981	0.909903	−	0.414821i	$-0.136156\pi$
$443$	16968.0	1.81981	0.909903	+	0.414821i	$0.136156\pi$
$444$	1480.00	0.158193
$445$	0	0
$446$	356.000	0.0377962
$447$	13990.0	1.48032
$448$	−2048.00	−0.215980
$449$	−9726.00	−1.02227	−0.511134	−	0.859501i	$-0.670774\pi$
$449$	−9726.00	−1.02227	−0.511134	+	0.859501i	$0.670774\pi$
$450$	0	0
$451$	−12948.0	−1.35188
$452$	2232.00	0.232266
$453$	9760.00	1.01228
$454$	−4962.00	−0.512948
$455$	0	0
$456$	6800.00	0.698332
$457$	8824.00	0.903215	0.451608	−	0.892217i	$-0.350851\pi$
$457$	8824.00	0.903215	0.451608	+	0.892217i	$0.350851\pi$
$458$	3290.00	0.335659
$459$	7360.00	0.748443
$460$	0	0
$461$	−11872.0	−1.19942	−0.599712	−	0.800216i	$-0.704718\pi$
$461$	−11872.0	−1.19942	−0.599712	+	0.800216i	$0.704718\pi$
$462$	33280.0	3.35135
$463$	3792.00	0.380625	0.190312	−	0.981724i	$-0.439050\pi$
$463$	3792.00	0.380625	0.190312	+	0.981724i	$0.439050\pi$
$464$	1568.00	0.156881
$465$	0	0
$466$	26.0000	0.00258461
$467$	5644.00	0.559257	0.279629	−	0.960108i	$-0.409789\pi$
$467$	5644.00	0.559257	0.279629	+	0.960108i	$0.409789\pi$
$468$	18104.0	1.78816
$469$	7104.00	0.699429
$470$	0	0
$471$	−27650.0	−2.70498
$472$	−296.000	−0.0288655
$473$	−22516.0	−2.18877
$474$	24140.0	2.33921
$475$	0	0
$476$	−2048.00	−0.197206
$477$	−4599.00	−0.441454
$478$	1426.00	0.136451
$479$	−15824.0	−1.50943	−0.754715	−	0.656053i	$-0.772225\pi$
$479$	−15824.0	−1.50943	−0.754715	+	0.656053i	$0.772225\pi$
$480$	0	0
$481$	2294.00	0.217458
$482$	−3812.00	−0.360232
$483$	−60480.0	−5.69759
$484$	5492.00	0.515778
$485$	0	0
$486$	−27740.0	−2.58912
$487$	1728.00	0.160787	0.0803934	−	0.996763i	$-0.474382\pi$
$487$	1728.00	0.160787	0.0803934	+	0.996763i	$0.474382\pi$
$488$	4720.00	0.437837
$489$	11510.0	1.06442
$490$	0	0
$491$	18794.0	1.72742	0.863708	−	0.503992i	$-0.168136\pi$
$491$	18794.0	1.72742	0.863708	+	0.503992i	$0.168136\pi$
$492$	−9960.00	−0.912666
$493$	1568.00	0.143244
$494$	10540.0	0.959953
$495$	0	0
$496$	−1472.00	−0.133256
$497$	4928.00	0.444771
$498$	−1280.00	−0.115177
$499$	9403.00	0.843559	0.421780	−	0.906698i	$-0.361406\pi$
$499$	9403.00	0.843559	0.421780	+	0.906698i	$0.361406\pi$
$500$	0	0
$501$	11230.0	1.00144
$502$	−7350.00	−0.653479
$503$	−20652.0	−1.83067	−0.915335	−	0.402693i	$-0.868074\pi$
$503$	−20652.0	−1.83067	−0.915335	+	0.402693i	$0.868074\pi$
$504$	18688.0	1.65165
$505$	0	0
$506$	−19656.0	−1.72691
$507$	16470.0	1.44272
$508$	−8688.00	−0.758795
$509$	−2295.00	−0.199851	−0.0999254	−	0.994995i	$-0.531860\pi$
$509$	−2295.00	−0.199851	−0.0999254	+	0.994995i	$0.531860\pi$
$510$	0	0
$511$	−8288.00	−0.717494
$512$	−512.000	−0.0441942
$513$	−39100.0	−3.36512
$514$	1584.00	0.135928
$515$	0	0
$516$	−17320.0	−1.47766
$517$	21944.0	1.86672
$518$	2368.00	0.200857
$519$	27740.0	2.34615
$520$	0	0
$521$	12783.0	1.07492	0.537460	−	0.843289i	$-0.319384\pi$
$521$	12783.0	1.07492	0.537460	+	0.843289i	$0.319384\pi$
$522$	−14308.0	−1.19970
$523$	−6412.00	−0.536094	−0.268047	−	0.963406i	$-0.586378\pi$
$523$	−6412.00	−0.536094	−0.268047	+	0.963406i	$0.586378\pi$
$524$	6640.00	0.553568
$525$	0	0
$526$	−6364.00	−0.527535
$527$	−1472.00	−0.121672
$528$	8320.00	0.685760
$529$	23554.0	1.93589
$530$	0	0
$531$	2701.00	0.220741
$532$	10880.0	0.886669
$533$	−15438.0	−1.25459
$534$	−12600.0	−1.02108
$535$	0	0
$536$	1776.00	0.143119
$537$	27000.0	2.16971
$538$	−822.000	−0.0658716
$539$	35412.0	2.82988
$540$	0	0
$541$	−18454.0	−1.46654	−0.733271	−	0.679936i	$-0.762007\pi$
$541$	−18454.0	−1.46654	−0.733271	+	0.679936i	$0.762007\pi$
$542$	−10184.0	−0.807085
$543$	−41310.0	−3.26479
$544$	−512.000	−0.0403526
$545$	0	0
$546$	39680.0	3.11016
$547$	−11900.0	−0.930178	−0.465089	−	0.885264i	$-0.653978\pi$
$547$	−11900.0	−0.930178	−0.465089	+	0.885264i	$0.653978\pi$
$548$	10392.0	0.810081
$549$	−43070.0	−3.34824
$550$	0	0
$551$	−8330.00	−0.644047
$552$	−15120.0	−1.16585
$553$	38624.0	2.97009
$554$	−5540.00	−0.424859
$555$	0	0
$556$	9256.00	0.706010
$557$	15632.0	1.18914	0.594568	−	0.804045i	$-0.297323\pi$
$557$	15632.0	1.18914	0.594568	+	0.804045i	$0.297323\pi$
$558$	13432.0	1.01904
$559$	−26846.0	−2.03124
$560$	0	0
$561$	8320.00	0.626151
$562$	14568.0	1.09344
$563$	−13973.0	−1.04599	−0.522994	−	0.852336i	$-0.675185\pi$
$563$	−13973.0	−1.04599	−0.522994	+	0.852336i	$0.675185\pi$
$564$	16880.0	1.26024
$565$	0	0
$566$	−5638.00	−0.418698
$567$	−84128.0	−6.23112
$568$	1232.00	0.0910098
$569$	24676.0	1.81805	0.909026	−	0.416739i	$-0.136827\pi$
$569$	24676.0	1.81805	0.909026	+	0.416739i	$0.136827\pi$
$570$	0	0
$571$	−15598.0	−1.14318	−0.571590	−	0.820539i	$-0.693673\pi$
$571$	−15598.0	−1.14318	−0.571590	+	0.820539i	$0.693673\pi$
$572$	12896.0	0.942673
$573$	−4470.00	−0.325893
$574$	−15936.0	−1.15881
$575$	0	0
$576$	4672.00	0.337963
$577$	−5116.00	−0.369119	−0.184560	−	0.982821i	$-0.559086\pi$
$577$	−5116.00	−0.369119	−0.184560	+	0.982821i	$0.559086\pi$
$578$	9314.00	0.670262
$579$	19320.0	1.38672
$580$	0	0
$581$	−2048.00	−0.146240
$582$	−13440.0	−0.957227
$583$	−3276.00	−0.232724
$584$	−2072.00	−0.146815
$585$	0	0
$586$	6310.00	0.444819
$587$	−8645.00	−0.607866	−0.303933	−	0.952693i	$-0.598300\pi$
$587$	−8645.00	−0.607866	−0.303933	+	0.952693i	$0.598300\pi$
$588$	27240.0	1.91047
$589$	7820.00	0.547059
$590$	0	0
$591$	−24690.0	−1.71846
$592$	592.000	0.0410997
$593$	−10417.0	−0.721374	−0.360687	−	0.932687i	$-0.617458\pi$
$593$	−10417.0	−0.721374	−0.360687	+	0.932687i	$0.617458\pi$
$594$	−47840.0	−3.30454
$595$	0	0
$596$	5596.00	0.384599
$597$	7090.00	0.486054
$598$	−23436.0	−1.60262
$599$	−5128.00	−0.349790	−0.174895	−	0.984587i	$-0.555959\pi$
$599$	−5128.00	−0.349790	−0.174895	+	0.984587i	$0.555959\pi$
$600$	0	0
$601$	−1997.00	−0.135540	−0.0677698	−	0.997701i	$-0.521588\pi$
$601$	−1997.00	−0.135540	−0.0677698	+	0.997701i	$0.521588\pi$
$602$	−27712.0	−1.87617
$603$	−16206.0	−1.09446
$604$	3904.00	0.262999
$605$	0	0
$606$	−16380.0	−1.09801
$607$	4064.00	0.271751	0.135875	−	0.990726i	$-0.456615\pi$
$607$	4064.00	0.271751	0.135875	+	0.990726i	$0.456615\pi$
$608$	2720.00	0.181432
$609$	−31360.0	−2.08665
$610$	0	0
$611$	26164.0	1.73238
$612$	4672.00	0.308586
$613$	−1545.00	−0.101798	−0.0508988	−	0.998704i	$-0.516209\pi$
$613$	−1545.00	−0.101798	−0.0508988	+	0.998704i	$0.516209\pi$
$614$	9768.00	0.642027
$615$	0	0
$616$	13312.0	0.870707
$617$	16834.0	1.09840	0.549199	−	0.835692i	$-0.314933\pi$
$617$	16834.0	1.09840	0.549199	+	0.835692i	$0.314933\pi$
$618$	−36900.0	−2.40184
$619$	6150.00	0.399337	0.199668	−	0.979864i	$-0.436014\pi$
$619$	6150.00	0.399337	0.199668	+	0.979864i	$0.436014\pi$
$620$	0	0
$621$	86940.0	5.61801
$622$	12974.0	0.836350
$623$	−20160.0	−1.29646
$624$	9920.00	0.636407
$625$	0	0
$626$	5156.00	0.329194
$627$	−44200.0	−2.81528
$628$	−11060.0	−0.702774
$629$	592.000	0.0375272
$630$	0	0
$631$	−22128.0	−1.39604	−0.698020	−	0.716078i	$-0.745936\pi$
$631$	−22128.0	−1.39604	−0.698020	+	0.716078i	$0.745936\pi$
$632$	9656.00	0.607745
$633$	26740.0	1.67902
$634$	5166.00	0.323609
$635$	0	0
$636$	−2520.00	−0.157114
$637$	42222.0	2.62621
$638$	−10192.0	−0.632453
$639$	−11242.0	−0.695973
$640$	0	0
$641$	−16085.0	−0.991138	−0.495569	−	0.868569i	$-0.665040\pi$
$641$	−16085.0	−0.991138	−0.495569	+	0.868569i	$0.665040\pi$
$642$	−42200.0	−2.59424
$643$	−21556.0	−1.32206	−0.661031	−	0.750359i	$-0.729881\pi$
$643$	−21556.0	−1.32206	−0.661031	+	0.750359i	$0.729881\pi$
$644$	−24192.0	−1.48028
$645$	0	0
$646$	2720.00	0.165661
$647$	−12229.0	−0.743078	−0.371539	−	0.928417i	$-0.621170\pi$
$647$	−12229.0	−0.743078	−0.371539	+	0.928417i	$0.621170\pi$
$648$	−21032.0	−1.27502
$649$	1924.00	0.116369
$650$	0	0
$651$	29440.0	1.77242
$652$	4604.00	0.276544
$653$	2306.00	0.138194	0.0690971	−	0.997610i	$-0.477988\pi$
$653$	2306.00	0.138194	0.0690971	+	0.997610i	$0.477988\pi$
$654$	18080.0	1.08102
$655$	0	0
$656$	−3984.00	−0.237117
$657$	18907.0	1.12273
$658$	27008.0	1.60012
$659$	14232.0	0.841275	0.420637	−	0.907229i	$-0.361806\pi$
$659$	14232.0	0.841275	0.420637	+	0.907229i	$0.361806\pi$
$660$	0	0
$661$	−21140.0	−1.24395	−0.621975	−	0.783037i	$-0.713669\pi$
$661$	−21140.0	−1.24395	−0.621975	+	0.783037i	$0.713669\pi$
$662$	3776.00	0.221689
$663$	9920.00	0.581087
$664$	−512.000	−0.0299239
$665$	0	0
$666$	−5402.00	−0.314299
$667$	18522.0	1.07522
$668$	4492.00	0.260181
$669$	−1780.00	−0.102868
$670$	0	0
$671$	−30680.0	−1.76511
$672$	10240.0	0.587822
$673$	32675.0	1.87151	0.935757	−	0.352646i	$-0.114718\pi$
$673$	32675.0	1.87151	0.935757	+	0.352646i	$0.114718\pi$
$674$	13778.0	0.787402
$675$	0	0
$676$	6588.00	0.374829
$677$	19849.0	1.12682	0.563411	−	0.826176i	$-0.309489\pi$
$677$	19849.0	1.12682	0.563411	+	0.826176i	$0.309489\pi$
$678$	−11160.0	−0.632149
$679$	−21504.0	−1.21539
$680$	0	0
$681$	24810.0	1.39607
$682$	9568.00	0.537211
$683$	−12024.0	−0.673625	−0.336812	−	0.941572i	$-0.609349\pi$
$683$	−12024.0	−0.673625	−0.336812	+	0.941572i	$0.609349\pi$
$684$	−24820.0	−1.38745
$685$	0	0
$686$	21632.0	1.20396
$687$	−16450.0	−0.913547
$688$	−6928.00	−0.383906
$689$	−3906.00	−0.215975
$690$	0	0
$691$	25514.0	1.40463	0.702314	−	0.711867i	$-0.252150\pi$
$691$	25514.0	1.40463	0.702314	+	0.711867i	$0.252150\pi$
$692$	11096.0	0.609547
$693$	−121472.	−6.65850
$694$	9678.00	0.529354
$695$	0	0
$696$	−7840.00	−0.426975
$697$	−3984.00	−0.216506
$698$	10838.0	0.587714
$699$	−130.000	−0.00703441
$700$	0	0
$701$	25998.0	1.40076	0.700379	−	0.713771i	$-0.253014\pi$
$701$	25998.0	1.40076	0.700379	+	0.713771i	$0.253014\pi$
$702$	−57040.0	−3.06672
$703$	−3145.00	−0.168728
$704$	3328.00	0.178166
$705$	0	0
$706$	7032.00	0.374862
$707$	−26208.0	−1.39413
$708$	1480.00	0.0785619
$709$	−5384.00	−0.285191	−0.142595	−	0.989781i	$-0.545545\pi$
$709$	−5384.00	−0.285191	−0.142595	+	0.989781i	$0.545545\pi$
$710$	0	0
$711$	−88111.0	−4.64757
$712$	−5040.00	−0.265284
$713$	−17388.0	−0.913304
$714$	10240.0	0.536726
$715$	0	0
$716$	10800.0	0.563708
$717$	−7130.00	−0.371373
$718$	21492.0	1.11710
$719$	−24020.0	−1.24589	−0.622945	−	0.782266i	$-0.714064\pi$
$719$	−24020.0	−1.24589	−0.622945	+	0.782266i	$0.714064\pi$
$720$	0	0
$721$	−59040.0	−3.04960
$722$	−732.000	−0.0377316
$723$	19060.0	0.980427
$724$	−16524.0	−0.848218
$725$	0	0
$726$	−27460.0	−1.40377
$727$	4968.00	0.253443	0.126721	−	0.991938i	$-0.459555\pi$
$727$	4968.00	0.253443	0.126721	+	0.991938i	$0.459555\pi$
$728$	15872.0	0.808043
$729$	67717.0	3.44038
$730$	0	0
$731$	−6928.00	−0.350535
$732$	−23600.0	−1.19164
$733$	−28678.0	−1.44508	−0.722542	−	0.691327i	$-0.757026\pi$
$733$	−28678.0	−1.44508	−0.722542	+	0.691327i	$0.757026\pi$
$734$	15652.0	0.787092
$735$	0	0
$736$	−6048.00	−0.302897
$737$	−11544.0	−0.576972
$738$	36354.0	1.81329
$739$	27130.0	1.35046	0.675232	−	0.737605i	$-0.264043\pi$
$739$	27130.0	1.35046	0.675232	+	0.737605i	$0.264043\pi$
$740$	0	0
$741$	−52700.0	−2.61266
$742$	−4032.00	−0.199487
$743$	30414.0	1.50172	0.750862	−	0.660459i	$-0.229638\pi$
$743$	30414.0	1.50172	0.750862	+	0.660459i	$0.229638\pi$
$744$	7360.00	0.362676
$745$	0	0
$746$	−22652.0	−1.11173
$747$	4672.00	0.228835
$748$	3328.00	0.162679
$749$	−67520.0	−3.29389
$750$	0	0
$751$	39498.0	1.91918	0.959589	−	0.281406i	$-0.0908007\pi$
$751$	39498.0	1.91918	0.959589	+	0.281406i	$0.0908007\pi$
$752$	6752.00	0.327420
$753$	36750.0	1.77855
$754$	−12152.0	−0.586936
$755$	0	0
$756$	−58880.0	−2.83260
$757$	−6984.00	−0.335321	−0.167660	−	0.985845i	$-0.553621\pi$
$757$	−6984.00	−0.335321	−0.167660	+	0.985845i	$0.553621\pi$
$758$	17104.0	0.819585
$759$	98280.0	4.70005
$760$	0	0
$761$	9637.00	0.459055	0.229528	−	0.973302i	$-0.426282\pi$
$761$	9637.00	0.459055	0.229528	+	0.973302i	$0.426282\pi$
$762$	43440.0	2.06518
$763$	28928.0	1.37256
$764$	−1788.00	−0.0846696
$765$	0	0
$766$	−8206.00	−0.387069
$767$	2294.00	0.107994
$768$	2560.00	0.120281
$769$	−406.000	−0.0190387	−0.00951933	−	0.999955i	$-0.503030\pi$
$769$	−406.000	−0.0190387	−0.00951933	+	0.999955i	$0.503030\pi$
$770$	0	0
$771$	−7920.00	−0.369950
$772$	7728.00	0.360281
$773$	14418.0	0.670866	0.335433	−	0.942064i	$-0.391117\pi$
$773$	14418.0	0.670866	0.335433	+	0.942064i	$0.391117\pi$
$774$	63218.0	2.93582
$775$	0	0
$776$	−5376.00	−0.248695
$777$	−11840.0	−0.546664
$778$	8976.00	0.413631
$779$	21165.0	0.973446
$780$	0	0
$781$	−8008.00	−0.366900
$782$	−6048.00	−0.276568
$783$	45080.0	2.05751
$784$	10896.0	0.496356
$785$	0	0
$786$	−33200.0	−1.50662
$787$	3676.00	0.166500	0.0832498	−	0.996529i	$-0.473470\pi$
$787$	3676.00	0.166500	0.0832498	+	0.996529i	$0.473470\pi$
$788$	−9876.00	−0.446469
$789$	31820.0	1.43577
$790$	0	0
$791$	−17856.0	−0.802638
$792$	−30368.0	−1.36247
$793$	−36580.0	−1.63808
$794$	−1614.00	−0.0721394
$795$	0	0
$796$	2836.00	0.126281
$797$	−20904.0	−0.929056	−0.464528	−	0.885558i	$-0.653776\pi$
$797$	−20904.0	−0.929056	−0.464528	+	0.885558i	$0.653776\pi$
$798$	−54400.0	−2.41321
$799$	6752.00	0.298959
$800$	0	0
$801$	45990.0	2.02869
$802$	3540.00	0.155863
$803$	13468.0	0.591875
$804$	−8880.00	−0.389519
$805$	0	0
$806$	11408.0	0.498548
$807$	4110.00	0.179280
$808$	−6552.00	−0.285270
$809$	−13688.0	−0.594863	−0.297432	−	0.954743i	$-0.596130\pi$
$809$	−13688.0	−0.594863	−0.297432	+	0.954743i	$0.596130\pi$
$810$	0	0
$811$	−32260.0	−1.39680	−0.698398	−	0.715709i	$-0.746103\pi$
$811$	−32260.0	−1.39680	−0.698398	+	0.715709i	$0.746103\pi$
$812$	−12544.0	−0.542128
$813$	50920.0	2.19661
$814$	−3848.00	−0.165691
$815$	0	0
$816$	2560.00	0.109826
$817$	36805.0	1.57606
$818$	23312.0	0.996436
$819$	−144832.	−6.17929
$820$	0	0
$821$	5761.00	0.244897	0.122448	−	0.992475i	$-0.460925\pi$
$821$	5761.00	0.244897	0.122448	+	0.992475i	$0.460925\pi$
$822$	−51960.0	−2.20476
$823$	18730.0	0.793301	0.396651	−	0.917970i	$-0.370172\pi$
$823$	18730.0	0.793301	0.396651	+	0.917970i	$0.370172\pi$
$824$	−14760.0	−0.624016
$825$	0	0
$826$	2368.00	0.0997497
$827$	−17764.0	−0.746934	−0.373467	−	0.927643i	$-0.621831\pi$
$827$	−17764.0	−0.746934	−0.373467	+	0.927643i	$0.621831\pi$
$828$	55188.0	2.31632
$829$	31848.0	1.33429	0.667145	−	0.744928i	$-0.267516\pi$
$829$	31848.0	1.33429	0.667145	+	0.744928i	$0.267516\pi$
$830$	0	0
$831$	27700.0	1.15632
$832$	3968.00	0.165343
$833$	10896.0	0.453210
$834$	−46280.0	−1.92152
$835$	0	0
$836$	−17680.0	−0.731430
$837$	−42320.0	−1.74766
$838$	−8640.00	−0.356162
$839$	45042.0	1.85342	0.926712	−	0.375773i	$-0.122623\pi$
$839$	45042.0	1.85342	0.926712	+	0.375773i	$0.122623\pi$
$840$	0	0
$841$	−14785.0	−0.606216
$842$	28900.0	1.18285
$843$	−72840.0	−2.97597
$844$	10696.0	0.436222
$845$	0	0
$846$	−61612.0	−2.50386
$847$	−43936.0	−1.78236
$848$	−1008.00	−0.0408194
$849$	28190.0	1.13955
$850$	0	0
$851$	6993.00	0.281689
$852$	−6160.00	−0.247697
$853$	26890.0	1.07936	0.539681	−	0.841869i	$-0.318545\pi$
$853$	26890.0	1.07936	0.539681	+	0.841869i	$0.318545\pi$
$854$	−37760.0	−1.51302
$855$	0	0
$856$	−16880.0	−0.674003
$857$	−17366.0	−0.692195	−0.346098	−	0.938199i	$-0.612493\pi$
$857$	−17366.0	−0.692195	−0.346098	+	0.938199i	$0.612493\pi$
$858$	−64480.0	−2.56563
$859$	−30565.0	−1.21404	−0.607022	−	0.794685i	$-0.707636\pi$
$859$	−30565.0	−1.21404	−0.607022	+	0.794685i	$0.707636\pi$
$860$	0	0
$861$	79680.0	3.15388
$862$	1934.00	0.0764180
$863$	−29258.0	−1.15406	−0.577030	−	0.816723i	$-0.695788\pi$
$863$	−29258.0	−1.15406	−0.577030	+	0.816723i	$0.695788\pi$
$864$	−14720.0	−0.579612
$865$	0	0
$866$	6924.00	0.271694
$867$	−46570.0	−1.82422
$868$	11776.0	0.460488
$869$	−62764.0	−2.45008
$870$	0	0
$871$	−13764.0	−0.535448
$872$	7232.00	0.280856
$873$	49056.0	1.90183
$874$	32130.0	1.24349
$875$	0	0
$876$	10360.0	0.399580
$877$	−31193.0	−1.20104	−0.600520	−	0.799609i	$-0.705040\pi$
$877$	−31193.0	−1.20104	−0.600520	+	0.799609i	$0.705040\pi$
$878$	−8366.00	−0.321570
$879$	−31550.0	−1.21064
$880$	0	0
$881$	−5791.00	−0.221457	−0.110729	−	0.993851i	$-0.535318\pi$
$881$	−5791.00	−0.221457	−0.110729	+	0.993851i	$0.535318\pi$
$882$	−99426.0	−3.79575
$883$	8168.00	0.311297	0.155648	−	0.987813i	$-0.450253\pi$
$883$	8168.00	0.311297	0.155648	+	0.987813i	$0.450253\pi$
$884$	3968.00	0.150971
$885$	0	0
$886$	−33936.0	−1.28680
$887$	−13534.0	−0.512319	−0.256160	−	0.966634i	$-0.582457\pi$
$887$	−13534.0	−0.512319	−0.256160	+	0.966634i	$0.582457\pi$
$888$	−2960.00	−0.111859
$889$	69504.0	2.62215
$890$	0	0
$891$	136708.	5.14017
$892$	−712.000	−0.0267259
$893$	−35870.0	−1.34417
$894$	−27980.0	−1.04675
$895$	0	0
$896$	4096.00	0.152721
$897$	117180.	4.36179
$898$	19452.0	0.722853
$899$	−9016.00	−0.334483
$900$	0	0
$901$	−1008.00	−0.0372712
$902$	25896.0	0.955923
$903$	138560.	5.10630
$904$	−4464.00	−0.164237
$905$	0	0
$906$	−19520.0	−0.715793
$907$	−24131.0	−0.883414	−0.441707	−	0.897159i	$-0.645627\pi$
$907$	−24131.0	−0.883414	−0.441707	+	0.897159i	$0.645627\pi$
$908$	9924.00	0.362709
$909$	59787.0	2.18153
$910$	0	0
$911$	−17239.0	−0.626952	−0.313476	−	0.949596i	$-0.601494\pi$
$911$	−17239.0	−0.626952	−0.313476	+	0.949596i	$0.601494\pi$
$912$	−13600.0	−0.493795
$913$	3328.00	0.120636
$914$	−17648.0	−0.638670
$915$	0	0
$916$	−6580.00	−0.237346
$917$	−53120.0	−1.91295
$918$	−14720.0	−0.529229
$919$	−26304.0	−0.944166	−0.472083	−	0.881554i	$-0.656498\pi$
$919$	−26304.0	−0.944166	−0.472083	+	0.881554i	$0.656498\pi$
$920$	0	0
$921$	−48840.0	−1.74738
$922$	23744.0	0.848120
$923$	−9548.00	−0.340494
$924$	−66560.0	−2.36977
$925$	0	0
$926$	−7584.00	−0.269142
$927$	134685.	4.77199
$928$	−3136.00	−0.110931
$929$	24290.0	0.857835	0.428918	−	0.903344i	$-0.358895\pi$
$929$	24290.0	0.857835	0.428918	+	0.903344i	$0.358895\pi$
$930$	0	0
$931$	−57885.0	−2.03771
$932$	−52.0000	−0.00182759
$933$	−64870.0	−2.27626
$934$	−11288.0	−0.395455
$935$	0	0
$936$	−36208.0	−1.26442
$937$	51734.0	1.80371	0.901855	−	0.432039i	$-0.142206\pi$
$937$	51734.0	1.80371	0.901855	+	0.432039i	$0.142206\pi$
$938$	−14208.0	−0.494571
$939$	−25780.0	−0.895952
$940$	0	0
$941$	−37954.0	−1.31484	−0.657420	−	0.753524i	$-0.728352\pi$
$941$	−37954.0	−1.31484	−0.657420	+	0.753524i	$0.728352\pi$
$942$	55300.0	1.91271
$943$	−47061.0	−1.62515
$944$	592.000	0.0204110
$945$	0	0
$946$	45032.0	1.54769
$947$	−7689.00	−0.263843	−0.131921	−	0.991260i	$-0.542115\pi$
$947$	−7689.00	−0.263843	−0.131921	+	0.991260i	$0.542115\pi$
$948$	−48280.0	−1.65407
$949$	16058.0	0.549278
$950$	0	0
$951$	−25830.0	−0.880752
$952$	4096.00	0.139446
$953$	−45903.0	−1.56028	−0.780139	−	0.625607i	$-0.784851\pi$
$953$	−45903.0	−1.56028	−0.780139	+	0.625607i	$0.784851\pi$
$954$	9198.00	0.312155
$955$	0	0
$956$	−2852.00	−0.0964856
$957$	50960.0	1.72132
$958$	31648.0	1.06733
$959$	−83136.0	−2.79938
$960$	0	0
$961$	−21327.0	−0.715887
$962$	−4588.00	−0.153766
$963$	154030.	5.15425
$964$	7624.00	0.254723
$965$	0	0
$966$	120960.	4.02880
$967$	15023.0	0.499594	0.249797	−	0.968298i	$-0.419636\pi$
$967$	15023.0	0.499594	0.249797	+	0.968298i	$0.419636\pi$
$968$	−10984.0	−0.364710
$969$	−13600.0	−0.450872
$970$	0	0
$971$	11484.0	0.379546	0.189773	−	0.981828i	$-0.439225\pi$
$971$	11484.0	0.379546	0.189773	+	0.981828i	$0.439225\pi$
$972$	55480.0	1.83078
$973$	−74048.0	−2.43974
$974$	−3456.00	−0.113693
$975$	0	0
$976$	−9440.00	−0.309597
$977$	−51346.0	−1.68138	−0.840688	−	0.541520i	$-0.817849\pi$
$977$	−51346.0	−1.68138	−0.840688	+	0.541520i	$0.817849\pi$
$978$	−23020.0	−0.752657
$979$	32760.0	1.06947
$980$	0	0
$981$	−65992.0	−2.14777
$982$	−37588.0	−1.22147
$983$	4678.00	0.151785	0.0758927	−	0.997116i	$-0.475819\pi$
$983$	4678.00	0.151785	0.0758927	+	0.997116i	$0.475819\pi$
$984$	19920.0	0.645352
$985$	0	0
$986$	−3136.00	−0.101289
$987$	−135040.	−4.35499
$988$	−21080.0	−0.678790
$989$	−81837.0	−2.63121
$990$	0	0
$991$	57685.0	1.84907	0.924533	−	0.381102i	$-0.124455\pi$
$991$	57685.0	1.84907	0.924533	+	0.381102i	$0.124455\pi$
$992$	2944.00	0.0942259
$993$	−18880.0	−0.603362
$994$	−9856.00	−0.314500
$995$	0	0
$996$	2560.00	0.0814425
$997$	228.000	0.00724256	0.00362128	−	0.999993i	$-0.498847\pi$
$997$	228.000	0.00724256	0.00362128	+	0.999993i	$0.498847\pi$
$998$	−18806.0	−0.596487
$999$	17020.0	0.539028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.4.a.e.1.1	✓	1
5.4	even	2		1850.4.a.f.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.4.a.e.1.1	✓	1	1.1	even	1	trivial
1850.4.a.f.1.1	yes	1	5.4	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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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