LMFDB - Embedded newform 350.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.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:	$20.6506685020$
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	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -20.0000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +73.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} -20.0000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +73.0000 q^{9} +9.00000 q^{11} +40.0000 q^{12} -52.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +96.0000 q^{17} -146.000 q^{18} -10.0000 q^{19} +70.0000 q^{21} -18.0000 q^{22} +75.0000 q^{23} -80.0000 q^{24} +104.000 q^{26} +460.000 q^{27} +28.0000 q^{28} +189.000 q^{29} -232.000 q^{31} -32.0000 q^{32} +90.0000 q^{33} -192.000 q^{34} +292.000 q^{36} +305.000 q^{37} +20.0000 q^{38} -520.000 q^{39} -438.000 q^{41} -140.000 q^{42} +353.000 q^{43} +36.0000 q^{44} -150.000 q^{46} -486.000 q^{47} +160.000 q^{48} +49.0000 q^{49} +960.000 q^{51} -208.000 q^{52} -354.000 q^{53} -920.000 q^{54} -56.0000 q^{56} -100.000 q^{57} -378.000 q^{58} -672.000 q^{59} +206.000 q^{61} +464.000 q^{62} +511.000 q^{63} +64.0000 q^{64} -180.000 q^{66} +599.000 q^{67} +384.000 q^{68} +750.000 q^{69} -471.000 q^{71} -584.000 q^{72} +614.000 q^{73} -610.000 q^{74} -40.0000 q^{76} +63.0000 q^{77} +1040.00 q^{78} +743.000 q^{79} +2629.00 q^{81} +876.000 q^{82} +996.000 q^{83} +280.000 q^{84} -706.000 q^{86} +1890.00 q^{87} -72.0000 q^{88} +180.000 q^{89} -364.000 q^{91} +300.000 q^{92} -2320.00 q^{93} +972.000 q^{94} -320.000 q^{96} -184.000 q^{97} -98.0000 q^{98} +657.000 q^{99} +O(q^{100})\)

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
$3$	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
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	73.0000	2.70370
$10$	0	0
$11$	9.00000	0.246691	0.123346	−	0.992364i	$-0.460638\pi$
$11$	9.00000	0.246691	0.123346	+	0.992364i	$0.460638\pi$
$12$	40.0000	0.962250
$13$	−52.0000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−52.0000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	96.0000	1.36961	0.684806	−	0.728725i	$-0.259887\pi$
$17$	96.0000	1.36961	0.684806	+	0.728725i	$0.259887\pi$
$18$	−146.000	−1.91181
$19$	−10.0000	−0.120745	−0.0603726	−	0.998176i	$-0.519229\pi$
$19$	−10.0000	−0.120745	−0.0603726	+	0.998176i	$0.519229\pi$
$20$	0	0
$21$	70.0000	0.727393
$22$	−18.0000	−0.174437
$23$	75.0000	0.679938	0.339969	−	0.940437i	$-0.389583\pi$
$23$	75.0000	0.679938	0.339969	+	0.940437i	$0.389583\pi$
$24$	−80.0000	−0.680414
$25$	0	0
$26$	104.000	0.784465
$27$	460.000	3.27878
$28$	28.0000	0.188982
$29$	189.000	1.21022	0.605111	−	0.796141i	$-0.293129\pi$
$29$	189.000	1.21022	0.605111	+	0.796141i	$0.293129\pi$
$30$	0	0
$31$	−232.000	−1.34414	−0.672071	−	0.740486i	$-0.734595\pi$
$31$	−232.000	−1.34414	−0.672071	+	0.740486i	$0.734595\pi$
$32$	−32.0000	−0.176777
$33$	90.0000	0.474757
$34$	−192.000	−0.968463
$35$	0	0
$36$	292.000	1.35185
$37$	305.000	1.35518	0.677590	−	0.735439i	$-0.263024\pi$
$37$	305.000	1.35518	0.677590	+	0.735439i	$0.263024\pi$
$38$	20.0000	0.0853797
$39$	−520.000	−2.13504
$40$	0	0
$41$	−438.000	−1.66839	−0.834196	−	0.551467i	$-0.814068\pi$
$41$	−438.000	−1.66839	−0.834196	+	0.551467i	$0.814068\pi$
$42$	−140.000	−0.514344
$43$	353.000	1.25191	0.625953	−	0.779860i	$-0.284710\pi$
$43$	353.000	1.25191	0.625953	+	0.779860i	$0.284710\pi$
$44$	36.0000	0.123346
$45$	0	0
$46$	−150.000	−0.480789
$47$	−486.000	−1.50831	−0.754153	−	0.656699i	$-0.771952\pi$
$47$	−486.000	−1.50831	−0.754153	+	0.656699i	$0.771952\pi$
$48$	160.000	0.481125
$49$	49.0000	0.142857
$50$	0	0
$51$	960.000	2.63582
$52$	−208.000	−0.554700
$53$	−354.000	−0.917465	−0.458732	−	0.888574i	$-0.651696\pi$
$53$	−354.000	−0.917465	−0.458732	+	0.888574i	$0.651696\pi$
$54$	−920.000	−2.31845
$55$	0	0
$56$	−56.0000	−0.133631
$57$	−100.000	−0.232374
$58$	−378.000	−0.855756
$59$	−672.000	−1.48283	−0.741415	−	0.671047i	$-0.765845\pi$
$59$	−672.000	−1.48283	−0.741415	+	0.671047i	$0.765845\pi$
$60$	0	0
$61$	206.000	0.432387	0.216193	−	0.976351i	$-0.430636\pi$
$61$	206.000	0.432387	0.216193	+	0.976351i	$0.430636\pi$
$62$	464.000	0.950453
$63$	511.000	1.02190
$64$	64.0000	0.125000
$65$	0	0
$66$	−180.000	−0.335704
$67$	599.000	1.09223	0.546116	−	0.837710i	$-0.316106\pi$
$67$	599.000	1.09223	0.546116	+	0.837710i	$0.316106\pi$
$68$	384.000	0.684806
$69$	750.000	1.30854
$70$	0	0
$71$	−471.000	−0.787288	−0.393644	−	0.919263i	$-0.628786\pi$
$71$	−471.000	−0.787288	−0.393644	+	0.919263i	$0.628786\pi$
$72$	−584.000	−0.955904
$73$	614.000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$73$	614.000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$74$	−610.000	−0.958258
$75$	0	0
$76$	−40.0000	−0.0603726
$77$	63.0000	0.0932405
$78$	1040.00	1.50970
$79$	743.000	1.05815	0.529076	−	0.848574i	$-0.322539\pi$
$79$	743.000	1.05815	0.529076	+	0.848574i	$0.322539\pi$
$80$	0	0
$81$	2629.00	3.60631
$82$	876.000	1.17973
$83$	996.000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	996.000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	280.000	0.363696
$85$	0	0
$86$	−706.000	−0.885232
$87$	1890.00	2.32907
$88$	−72.0000	−0.0872185
$89$	180.000	0.214382	0.107191	−	0.994238i	$-0.465814\pi$
$89$	180.000	0.214382	0.107191	+	0.994238i	$0.465814\pi$
$90$	0	0
$91$	−364.000	−0.419314
$92$	300.000	0.339969
$93$	−2320.00	−2.58680
$94$	972.000	1.06653
$95$	0	0
$96$	−320.000	−0.340207
$97$	−184.000	−0.192602	−0.0963009	−	0.995352i	$-0.530701\pi$
$97$	−184.000	−0.192602	−0.0963009	+	0.995352i	$0.530701\pi$
$98$	−98.0000	−0.101015
$99$	657.000	0.666980
$100$	0	0
$101$	−726.000	−0.715245	−0.357622	−	0.933866i	$-0.616412\pi$
$101$	−726.000	−0.715245	−0.357622	+	0.933866i	$0.616412\pi$
$102$	−1920.00	−1.86381
$103$	−1798.00	−1.72002	−0.860011	−	0.510276i	$-0.829543\pi$
$103$	−1798.00	−1.72002	−0.860011	+	0.510276i	$0.829543\pi$
$104$	416.000	0.392232
$105$	0	0
$106$	708.000	0.648746
$107$	876.000	0.791459	0.395730	−	0.918367i	$-0.370492\pi$
$107$	876.000	0.791459	0.395730	+	0.918367i	$0.370492\pi$
$108$	1840.00	1.63939
$109$	−691.000	−0.607209	−0.303605	−	0.952798i	$-0.598190\pi$
$109$	−691.000	−0.607209	−0.303605	+	0.952798i	$0.598190\pi$
$110$	0	0
$111$	3050.00	2.60805
$112$	112.000	0.0944911
$113$	−1521.00	−1.26623	−0.633113	−	0.774059i	$-0.718223\pi$
$113$	−1521.00	−1.26623	−0.633113	+	0.774059i	$0.718223\pi$
$114$	200.000	0.164313
$115$	0	0
$116$	756.000	0.605111
$117$	−3796.00	−2.99949
$118$	1344.00	1.04852
$119$	672.000	0.517665
$120$	0	0
$121$	−1250.00	−0.939144
$122$	−412.000	−0.305744
$123$	−4380.00	−3.21082
$124$	−928.000	−0.672071
$125$	0	0
$126$	−1022.00	−0.722595
$127$	1031.00	0.720366	0.360183	−	0.932882i	$-0.382714\pi$
$127$	1031.00	0.720366	0.360183	+	0.932882i	$0.382714\pi$
$128$	−128.000	−0.0883883
$129$	3530.00	2.40930
$130$	0	0
$131$	−1116.00	−0.744316	−0.372158	−	0.928169i	$-0.621382\pi$
$131$	−1116.00	−0.744316	−0.372158	+	0.928169i	$0.621382\pi$
$132$	360.000	0.237379
$133$	−70.0000	−0.0456374
$134$	−1198.00	−0.772324
$135$	0	0
$136$	−768.000	−0.484231
$137$	−1398.00	−0.871819	−0.435909	−	0.899991i	$-0.643573\pi$
$137$	−1398.00	−0.871819	−0.435909	+	0.899991i	$0.643573\pi$
$138$	−1500.00	−0.925279
$139$	674.000	0.411280	0.205640	−	0.978628i	$-0.434072\pi$
$139$	674.000	0.411280	0.205640	+	0.978628i	$0.434072\pi$
$140$	0	0
$141$	−4860.00	−2.90274
$142$	942.000	0.556696
$143$	−468.000	−0.273679
$144$	1168.00	0.675926
$145$	0	0
$146$	−1228.00	−0.696096
$147$	490.000	0.274929
$148$	1220.00	0.677590
$149$	−1281.00	−0.704320	−0.352160	−	0.935940i	$-0.614553\pi$
$149$	−1281.00	−0.704320	−0.352160	+	0.935940i	$0.614553\pi$
$150$	0	0
$151$	953.000	0.513603	0.256801	−	0.966464i	$-0.417331\pi$
$151$	953.000	0.513603	0.256801	+	0.966464i	$0.417331\pi$
$152$	80.0000	0.0426898
$153$	7008.00	3.70303
$154$	−126.000	−0.0659310
$155$	0	0
$156$	−2080.00	−1.06752
$157$	650.000	0.330418	0.165209	−	0.986259i	$-0.447170\pi$
$157$	650.000	0.330418	0.165209	+	0.986259i	$0.447170\pi$
$158$	−1486.00	−0.748227
$159$	−3540.00	−1.76566
$160$	0	0
$161$	525.000	0.256993
$162$	−5258.00	−2.55005
$163$	932.000	0.447852	0.223926	−	0.974606i	$-0.428113\pi$
$163$	932.000	0.447852	0.223926	+	0.974606i	$0.428113\pi$
$164$	−1752.00	−0.834196
$165$	0	0
$166$	−1992.00	−0.931381
$167$	−180.000	−0.0834061	−0.0417030	−	0.999130i	$-0.513278\pi$
$167$	−180.000	−0.0834061	−0.0417030	+	0.999130i	$0.513278\pi$
$168$	−560.000	−0.257172
$169$	507.000	0.230769
$170$	0	0
$171$	−730.000	−0.326459
$172$	1412.00	0.625953
$173$	−834.000	−0.366519	−0.183260	−	0.983065i	$-0.558665\pi$
$173$	−834.000	−0.366519	−0.183260	+	0.983065i	$0.558665\pi$
$174$	−3780.00	−1.64690
$175$	0	0
$176$	144.000	0.0616728
$177$	−6720.00	−2.85371
$178$	−360.000	−0.151591
$179$	−648.000	−0.270580	−0.135290	−	0.990806i	$-0.543197\pi$
$179$	−648.000	−0.270580	−0.135290	+	0.990806i	$0.543197\pi$
$180$	0	0
$181$	−2914.00	−1.19666	−0.598331	−	0.801249i	$-0.704169\pi$
$181$	−2914.00	−1.19666	−0.598331	+	0.801249i	$0.704169\pi$
$182$	728.000	0.296500
$183$	2060.00	0.832129
$184$	−600.000	−0.240394
$185$	0	0
$186$	4640.00	1.82915
$187$	864.000	0.337871
$188$	−1944.00	−0.754153
$189$	3220.00	1.23926
$190$	0	0
$191$	−876.000	−0.331859	−0.165930	−	0.986138i	$-0.553062\pi$
$191$	−876.000	−0.331859	−0.165930	+	0.986138i	$0.553062\pi$
$192$	640.000	0.240563
$193$	−601.000	−0.224150	−0.112075	−	0.993700i	$-0.535750\pi$
$193$	−601.000	−0.224150	−0.112075	+	0.993700i	$0.535750\pi$
$194$	368.000	0.136190
$195$	0	0
$196$	196.000	0.0714286
$197$	−2013.00	−0.728022	−0.364011	−	0.931395i	$-0.618593\pi$
$197$	−2013.00	−0.728022	−0.364011	+	0.931395i	$0.618593\pi$
$198$	−1314.00	−0.471626
$199$	326.000	0.116128	0.0580641	−	0.998313i	$-0.481507\pi$
$199$	326.000	0.116128	0.0580641	+	0.998313i	$0.481507\pi$
$200$	0	0
$201$	5990.00	2.10200
$202$	1452.00	0.505754
$203$	1323.00	0.457421
$204$	3840.00	1.31791
$205$	0	0
$206$	3596.00	1.21624
$207$	5475.00	1.83835
$208$	−832.000	−0.277350
$209$	−90.0000	−0.0297867
$210$	0	0
$211$	−5956.00	−1.94326	−0.971630	−	0.236505i	$-0.923998\pi$
$211$	−5956.00	−1.94326	−0.971630	+	0.236505i	$0.923998\pi$
$212$	−1416.00	−0.458732
$213$	−4710.00	−1.51514
$214$	−1752.00	−0.559646
$215$	0	0
$216$	−3680.00	−1.15922
$217$	−1624.00	−0.508038
$218$	1382.00	0.429362
$219$	6140.00	1.89453
$220$	0	0
$221$	−4992.00	−1.51945
$222$	−6100.00	−1.84417
$223$	−3118.00	−0.936308	−0.468154	−	0.883647i	$-0.655081\pi$
$223$	−3118.00	−0.936308	−0.468154	+	0.883647i	$0.655081\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	3042.00	0.895358
$227$	−6.00000	−0.00175433	−0.000877167	−	1.00000i	$-0.500279\pi$
$227$	−6.00000	−0.00175433	−0.000877167		1.00000i	$0.500279\pi$
$228$	−400.000	−0.116187
$229$	−586.000	−0.169100	−0.0845502	−	0.996419i	$-0.526945\pi$
$229$	−586.000	−0.169100	−0.0845502	+	0.996419i	$0.526945\pi$
$230$	0	0
$231$	630.000	0.179441
$232$	−1512.00	−0.427878
$233$	1293.00	0.363550	0.181775	−	0.983340i	$-0.441816\pi$
$233$	1293.00	0.363550	0.181775	+	0.983340i	$0.441816\pi$
$234$	7592.00	2.12096
$235$	0	0
$236$	−2688.00	−0.741415
$237$	7430.00	2.03642
$238$	−1344.00	−0.366044
$239$	−5376.00	−1.45500	−0.727499	−	0.686109i	$-0.759317\pi$
$239$	−5376.00	−1.45500	−0.727499	+	0.686109i	$0.759317\pi$
$240$	0	0
$241$	−670.000	−0.179081	−0.0895404	−	0.995983i	$-0.528540\pi$
$241$	−670.000	−0.179081	−0.0895404	+	0.995983i	$0.528540\pi$
$242$	2500.00	0.664075
$243$	13870.0	3.66157
$244$	824.000	0.216193
$245$	0	0
$246$	8760.00	2.27040
$247$	520.000	0.133955
$248$	1856.00	0.475226
$249$	9960.00	2.53490
$250$	0	0
$251$	1380.00	0.347031	0.173516	−	0.984831i	$-0.444487\pi$
$251$	1380.00	0.347031	0.173516	+	0.984831i	$0.444487\pi$
$252$	2044.00	0.510952
$253$	675.000	0.167735
$254$	−2062.00	−0.509376
$255$	0	0
$256$	256.000	0.0625000
$257$	−3576.00	−0.867956	−0.433978	−	0.900923i	$-0.642890\pi$
$257$	−3576.00	−0.867956	−0.433978	+	0.900923i	$0.642890\pi$
$258$	−7060.00	−1.70363
$259$	2135.00	0.512210
$260$	0	0
$261$	13797.0	3.27208
$262$	2232.00	0.526311
$263$	−5919.00	−1.38776	−0.693881	−	0.720090i	$-0.744100\pi$
$263$	−5919.00	−1.38776	−0.693881	+	0.720090i	$0.744100\pi$
$264$	−720.000	−0.167852
$265$	0	0
$266$	140.000	0.0322705
$267$	1800.00	0.412578
$268$	2396.00	0.546116
$269$	−1764.00	−0.399825	−0.199913	−	0.979814i	$-0.564066\pi$
$269$	−1764.00	−0.399825	−0.199913	+	0.979814i	$0.564066\pi$
$270$	0	0
$271$	−340.000	−0.0762123	−0.0381061	−	0.999274i	$-0.512132\pi$
$271$	−340.000	−0.0762123	−0.0381061	+	0.999274i	$0.512132\pi$
$272$	1536.00	0.342403
$273$	−3640.00	−0.806970
$274$	2796.00	0.616469
$275$	0	0
$276$	3000.00	0.654271
$277$	4706.00	1.02078	0.510390	−	0.859943i	$-0.329501\pi$
$277$	4706.00	1.02078	0.510390	+	0.859943i	$0.329501\pi$
$278$	−1348.00	−0.290819
$279$	−16936.0	−3.63416
$280$	0	0
$281$	6681.00	1.41835	0.709173	−	0.705035i	$-0.249069\pi$
$281$	6681.00	1.41835	0.709173	+	0.705035i	$0.249069\pi$
$282$	9720.00	2.05254
$283$	−226.000	−0.0474710	−0.0237355	−	0.999718i	$-0.507556\pi$
$283$	−226.000	−0.0474710	−0.0237355	+	0.999718i	$0.507556\pi$
$284$	−1884.00	−0.393644
$285$	0	0
$286$	936.000	0.193520
$287$	−3066.00	−0.630593
$288$	−2336.00	−0.477952
$289$	4303.00	0.875840
$290$	0	0
$291$	−1840.00	−0.370662
$292$	2456.00	0.492214
$293$	4320.00	0.861355	0.430678	−	0.902506i	$-0.358275\pi$
$293$	4320.00	0.861355	0.430678	+	0.902506i	$0.358275\pi$
$294$	−980.000	−0.194404
$295$	0	0
$296$	−2440.00	−0.479129
$297$	4140.00	0.808846
$298$	2562.00	0.498029
$299$	−3900.00	−0.754324
$300$	0	0
$301$	2471.00	0.473176
$302$	−1906.00	−0.363172
$303$	−7260.00	−1.37649
$304$	−160.000	−0.0301863
$305$	0	0
$306$	−14016.0	−2.61844
$307$	−6604.00	−1.22772	−0.613860	−	0.789415i	$-0.710384\pi$
$307$	−6604.00	−1.22772	−0.613860	+	0.789415i	$0.710384\pi$
$308$	252.000	0.0466202
$309$	−17980.0	−3.31018
$310$	0	0
$311$	6036.00	1.10055	0.550274	−	0.834984i	$-0.314523\pi$
$311$	6036.00	1.10055	0.550274	+	0.834984i	$0.314523\pi$
$312$	4160.00	0.754851
$313$	9146.00	1.65164	0.825819	−	0.563936i	$-0.190713\pi$
$313$	9146.00	1.65164	0.825819	+	0.563936i	$0.190713\pi$
$314$	−1300.00	−0.233641
$315$	0	0
$316$	2972.00	0.529076
$317$	−4449.00	−0.788267	−0.394134	−	0.919053i	$-0.628955\pi$
$317$	−4449.00	−0.788267	−0.394134	+	0.919053i	$0.628955\pi$
$318$	7080.00	1.24851
$319$	1701.00	0.298551
$320$	0	0
$321$	8760.00	1.52316
$322$	−1050.00	−0.181721
$323$	−960.000	−0.165374
$324$	10516.0	1.80316
$325$	0	0
$326$	−1864.00	−0.316679
$327$	−6910.00	−1.16857
$328$	3504.00	0.589866
$329$	−3402.00	−0.570086
$330$	0	0
$331$	−10081.0	−1.67402	−0.837012	−	0.547185i	$-0.815700\pi$
$331$	−10081.0	−1.67402	−0.837012	+	0.547185i	$0.815700\pi$
$332$	3984.00	0.658586
$333$	22265.0	3.66401
$334$	360.000	0.0589770
$335$	0	0
$336$	1120.00	0.181848
$337$	7778.00	1.25725	0.628627	−	0.777707i	$-0.283617\pi$
$337$	7778.00	1.25725	0.628627	+	0.777707i	$0.283617\pi$
$338$	−1014.00	−0.163178
$339$	−15210.0	−2.43685
$340$	0	0
$341$	−2088.00	−0.331588
$342$	1460.00	0.230841
$343$	343.000	0.0539949
$344$	−2824.00	−0.442616
$345$	0	0
$346$	1668.00	0.259168
$347$	1017.00	0.157336	0.0786678	−	0.996901i	$-0.474933\pi$
$347$	1017.00	0.157336	0.0786678	+	0.996901i	$0.474933\pi$
$348$	7560.00	1.16454
$349$	10370.0	1.59053	0.795263	−	0.606265i	$-0.207333\pi$
$349$	10370.0	1.59053	0.795263	+	0.606265i	$0.207333\pi$
$350$	0	0
$351$	−23920.0	−3.63748
$352$	−288.000	−0.0436092
$353$	−9432.00	−1.42214	−0.711069	−	0.703122i	$-0.751789\pi$
$353$	−9432.00	−1.42214	−0.711069	+	0.703122i	$0.751789\pi$
$354$	13440.0	2.01788
$355$	0	0
$356$	720.000	0.107191
$357$	6720.00	0.996247
$358$	1296.00	0.191329
$359$	7557.00	1.11098	0.555492	−	0.831522i	$-0.312530\pi$
$359$	7557.00	1.11098	0.555492	+	0.831522i	$0.312530\pi$
$360$	0	0
$361$	−6759.00	−0.985421
$362$	5828.00	0.846168
$363$	−12500.0	−1.80738
$364$	−1456.00	−0.209657
$365$	0	0
$366$	−4120.00	−0.588404
$367$	−11662.0	−1.65872	−0.829362	−	0.558712i	$-0.811296\pi$
$367$	−11662.0	−1.65872	−0.829362	+	0.558712i	$0.811296\pi$
$368$	1200.00	0.169985
$369$	−31974.0	−4.51084
$370$	0	0
$371$	−2478.00	−0.346769
$372$	−9280.00	−1.29340
$373$	−2377.00	−0.329964	−0.164982	−	0.986297i	$-0.552757\pi$
$373$	−2377.00	−0.329964	−0.164982	+	0.986297i	$0.552757\pi$
$374$	−1728.00	−0.238911
$375$	0	0
$376$	3888.00	0.533267
$377$	−9828.00	−1.34262
$378$	−6440.00	−0.876291
$379$	4427.00	0.599999	0.300000	−	0.953939i	$-0.403013\pi$
$379$	4427.00	0.599999	0.300000	+	0.953939i	$0.403013\pi$
$380$	0	0
$381$	10310.0	1.38634
$382$	1752.00	0.234660
$383$	4608.00	0.614772	0.307386	−	0.951585i	$-0.400546\pi$
$383$	4608.00	0.614772	0.307386	+	0.951585i	$0.400546\pi$
$384$	−1280.00	−0.170103
$385$	0	0
$386$	1202.00	0.158498
$387$	25769.0	3.38479
$388$	−736.000	−0.0963009
$389$	−699.000	−0.0911072	−0.0455536	−	0.998962i	$-0.514505\pi$
$389$	−699.000	−0.0911072	−0.0455536	+	0.998962i	$0.514505\pi$
$390$	0	0
$391$	7200.00	0.931252
$392$	−392.000	−0.0505076
$393$	−11160.0	−1.43244
$394$	4026.00	0.514789
$395$	0	0
$396$	2628.00	0.333490
$397$	−7630.00	−0.964581	−0.482291	−	0.876011i	$-0.660195\pi$
$397$	−7630.00	−0.964581	−0.482291	+	0.876011i	$0.660195\pi$
$398$	−652.000	−0.0821151
$399$	−700.000	−0.0878292
$400$	0	0
$401$	5601.00	0.697508	0.348754	−	0.937214i	$-0.386605\pi$
$401$	5601.00	0.697508	0.348754	+	0.937214i	$0.386605\pi$
$402$	−11980.0	−1.48634
$403$	12064.0	1.49119
$404$	−2904.00	−0.357622
$405$	0	0
$406$	−2646.00	−0.323445
$407$	2745.00	0.334311
$408$	−7680.00	−0.931904
$409$	4670.00	0.564588	0.282294	−	0.959328i	$-0.408905\pi$
$409$	4670.00	0.564588	0.282294	+	0.959328i	$0.408905\pi$
$410$	0	0
$411$	−13980.0	−1.67782
$412$	−7192.00	−0.860011
$413$	−4704.00	−0.560457
$414$	−10950.0	−1.29991
$415$	0	0
$416$	1664.00	0.196116
$417$	6740.00	0.791509
$418$	180.000	0.0210624
$419$	36.0000	0.00419741	0.00209871	−	0.999998i	$-0.499332\pi$
$419$	36.0000	0.00419741	0.00209871	+	0.999998i	$0.499332\pi$
$420$	0	0
$421$	5495.00	0.636128	0.318064	−	0.948069i	$-0.396967\pi$
$421$	5495.00	0.636128	0.318064	+	0.948069i	$0.396967\pi$
$422$	11912.0	1.37409
$423$	−35478.0	−4.07801
$424$	2832.00	0.324373
$425$	0	0
$426$	9420.00	1.07136
$427$	1442.00	0.163427
$428$	3504.00	0.395730
$429$	−4680.00	−0.526696
$430$	0	0
$431$	2700.00	0.301750	0.150875	−	0.988553i	$-0.451791\pi$
$431$	2700.00	0.301750	0.150875	+	0.988553i	$0.451791\pi$
$432$	7360.00	0.819695
$433$	15104.0	1.67633	0.838166	−	0.545415i	$-0.183628\pi$
$433$	15104.0	1.67633	0.838166	+	0.545415i	$0.183628\pi$
$434$	3248.00	0.359237
$435$	0	0
$436$	−2764.00	−0.303605
$437$	−750.000	−0.0820992
$438$	−12280.0	−1.33964
$439$	14948.0	1.62512	0.812562	−	0.582875i	$-0.198072\pi$
$439$	14948.0	1.62512	0.812562	+	0.582875i	$0.198072\pi$
$440$	0	0
$441$	3577.00	0.386243
$442$	9984.00	1.07441
$443$	4980.00	0.534101	0.267051	−	0.963682i	$-0.413951\pi$
$443$	4980.00	0.534101	0.267051	+	0.963682i	$0.413951\pi$
$444$	12200.0	1.30402
$445$	0	0
$446$	6236.00	0.662070
$447$	−12810.0	−1.35546
$448$	448.000	0.0472456
$449$	12375.0	1.30070	0.650348	−	0.759637i	$-0.274623\pi$
$449$	12375.0	1.30070	0.650348	+	0.759637i	$0.274623\pi$
$450$	0	0
$451$	−3942.00	−0.411578
$452$	−6084.00	−0.633113
$453$	9530.00	0.988429
$454$	12.0000	0.00124050
$455$	0	0
$456$	800.000	0.0821567
$457$	10835.0	1.10906	0.554529	−	0.832164i	$-0.312898\pi$
$457$	10835.0	1.10906	0.554529	+	0.832164i	$0.312898\pi$
$458$	1172.00	0.119572
$459$	44160.0	4.49066
$460$	0	0
$461$	5700.00	0.575869	0.287934	−	0.957650i	$-0.407032\pi$
$461$	5700.00	0.575869	0.287934	+	0.957650i	$0.407032\pi$
$462$	−1260.00	−0.126884
$463$	6128.00	0.615102	0.307551	−	0.951532i	$-0.400491\pi$
$463$	6128.00	0.615102	0.307551	+	0.951532i	$0.400491\pi$
$464$	3024.00	0.302555
$465$	0	0
$466$	−2586.00	−0.257069
$467$	−9810.00	−0.972061	−0.486031	−	0.873942i	$-0.661556\pi$
$467$	−9810.00	−0.972061	−0.486031	+	0.873942i	$0.661556\pi$
$468$	−15184.0	−1.49974
$469$	4193.00	0.412825
$470$	0	0
$471$	6500.00	0.635890
$472$	5376.00	0.524259
$473$	3177.00	0.308834
$474$	−14860.0	−1.43996
$475$	0	0
$476$	2688.00	0.258833
$477$	−25842.0	−2.48055
$478$	10752.0	1.02884
$479$	−204.000	−0.0194593	−0.00972964	−	0.999953i	$-0.503097\pi$
$479$	−204.000	−0.0194593	−0.00972964	+	0.999953i	$0.503097\pi$
$480$	0	0
$481$	−15860.0	−1.50344
$482$	1340.00	0.126629
$483$	5250.00	0.494582
$484$	−5000.00	−0.469572
$485$	0	0
$486$	−27740.0	−2.58912
$487$	15401.0	1.43303	0.716515	−	0.697571i	$-0.245736\pi$
$487$	15401.0	1.43303	0.716515	+	0.697571i	$0.245736\pi$
$488$	−1648.00	−0.152872
$489$	9320.00	0.861892
$490$	0	0
$491$	3897.00	0.358186	0.179093	−	0.983832i	$-0.442684\pi$
$491$	3897.00	0.358186	0.179093	+	0.983832i	$0.442684\pi$
$492$	−17520.0	−1.60541
$493$	18144.0	1.65753
$494$	−1040.00	−0.0947203
$495$	0	0
$496$	−3712.00	−0.336036
$497$	−3297.00	−0.297567
$498$	−19920.0	−1.79244
$499$	8132.00	0.729536	0.364768	−	0.931098i	$-0.381148\pi$
$499$	8132.00	0.729536	0.364768	+	0.931098i	$0.381148\pi$
$500$	0	0
$501$	−1800.00	−0.160515
$502$	−2760.00	−0.245388
$503$	−10998.0	−0.974904	−0.487452	−	0.873150i	$-0.662074\pi$
$503$	−10998.0	−0.974904	−0.487452	+	0.873150i	$0.662074\pi$
$504$	−4088.00	−0.361298
$505$	0	0
$506$	−1350.00	−0.118606
$507$	5070.00	0.444116
$508$	4124.00	0.360183
$509$	5940.00	0.517261	0.258631	−	0.965976i	$-0.416729\pi$
$509$	5940.00	0.517261	0.258631	+	0.965976i	$0.416729\pi$
$510$	0	0
$511$	4298.00	0.372079
$512$	−512.000	−0.0441942
$513$	−4600.00	−0.395897
$514$	7152.00	0.613738
$515$	0	0
$516$	14120.0	1.20465
$517$	−4374.00	−0.372086
$518$	−4270.00	−0.362187
$519$	−8340.00	−0.705367
$520$	0	0
$521$	17022.0	1.43138	0.715688	−	0.698420i	$-0.246113\pi$
$521$	17022.0	1.43138	0.715688	+	0.698420i	$0.246113\pi$
$522$	−27594.0	−2.31371
$523$	−15748.0	−1.31666	−0.658329	−	0.752730i	$-0.728736\pi$
$523$	−15748.0	−1.31666	−0.658329	+	0.752730i	$0.728736\pi$
$524$	−4464.00	−0.372158
$525$	0	0
$526$	11838.0	0.981295
$527$	−22272.0	−1.84096
$528$	1440.00	0.118689
$529$	−6542.00	−0.537684
$530$	0	0
$531$	−49056.0	−4.00913
$532$	−280.000	−0.0228187
$533$	22776.0	1.85092
$534$	−3600.00	−0.291736
$535$	0	0
$536$	−4792.00	−0.386162
$537$	−6480.00	−0.520731
$538$	3528.00	0.282719
$539$	441.000	0.0352416
$540$	0	0
$541$	−3373.00	−0.268053	−0.134026	−	0.990978i	$-0.542791\pi$
$541$	−3373.00	−0.268053	−0.134026	+	0.990978i	$0.542791\pi$
$542$	680.000	0.0538902
$543$	−29140.0	−2.30298
$544$	−3072.00	−0.242116
$545$	0	0
$546$	7280.00	0.570614
$547$	−14389.0	−1.12473	−0.562367	−	0.826888i	$-0.690109\pi$
$547$	−14389.0	−1.12473	−0.562367	+	0.826888i	$0.690109\pi$
$548$	−5592.00	−0.435909
$549$	15038.0	1.16905
$550$	0	0
$551$	−1890.00	−0.146128
$552$	−6000.00	−0.462639
$553$	5201.00	0.399944
$554$	−9412.00	−0.721801
$555$	0	0
$556$	2696.00	0.205640
$557$	−4929.00	−0.374952	−0.187476	−	0.982269i	$-0.560031\pi$
$557$	−4929.00	−0.374952	−0.187476	+	0.982269i	$0.560031\pi$
$558$	33872.0	2.56974
$559$	−18356.0	−1.38887
$560$	0	0
$561$	8640.00	0.650234
$562$	−13362.0	−1.00292
$563$	15678.0	1.17362	0.586811	−	0.809724i	$-0.300383\pi$
$563$	15678.0	1.17362	0.586811	+	0.809724i	$0.300383\pi$
$564$	−19440.0	−1.45137
$565$	0	0
$566$	452.000	0.0335671
$567$	18403.0	1.36306
$568$	3768.00	0.278348
$569$	−14499.0	−1.06824	−0.534121	−	0.845408i	$-0.679357\pi$
$569$	−14499.0	−1.06824	−0.534121	+	0.845408i	$0.679357\pi$
$570$	0	0
$571$	−9457.00	−0.693105	−0.346553	−	0.938031i	$-0.612648\pi$
$571$	−9457.00	−0.693105	−0.346553	+	0.938031i	$0.612648\pi$
$572$	−1872.00	−0.136840
$573$	−8760.00	−0.638664
$574$	6132.00	0.445897
$575$	0	0
$576$	4672.00	0.337963
$577$	10370.0	0.748195	0.374098	−	0.927389i	$-0.377952\pi$
$577$	10370.0	0.748195	0.374098	+	0.927389i	$0.377952\pi$
$578$	−8606.00	−0.619312
$579$	−6010.00	−0.431377
$580$	0	0
$581$	6972.00	0.497844
$582$	3680.00	0.262098
$583$	−3186.00	−0.226330
$584$	−4912.00	−0.348048
$585$	0	0
$586$	−8640.00	−0.609070
$587$	−12126.0	−0.852630	−0.426315	−	0.904575i	$-0.640188\pi$
$587$	−12126.0	−0.852630	−0.426315	+	0.904575i	$0.640188\pi$
$588$	1960.00	0.137464
$589$	2320.00	0.162299
$590$	0	0
$591$	−20130.0	−1.40108
$592$	4880.00	0.338795
$593$	1068.00	0.0739587	0.0369793	−	0.999316i	$-0.488226\pi$
$593$	1068.00	0.0739587	0.0369793	+	0.999316i	$0.488226\pi$
$594$	−8280.00	−0.571940
$595$	0	0
$596$	−5124.00	−0.352160
$597$	3260.00	0.223489
$598$	7800.00	0.533387
$599$	3375.00	0.230215	0.115107	−	0.993353i	$-0.463279\pi$
$599$	3375.00	0.230215	0.115107	+	0.993353i	$0.463279\pi$
$600$	0	0
$601$	−27448.0	−1.86294	−0.931470	−	0.363817i	$-0.881473\pi$
$601$	−27448.0	−1.86294	−0.931470	+	0.363817i	$0.881473\pi$
$602$	−4942.00	−0.334586
$603$	43727.0	2.95307
$604$	3812.00	0.256801
$605$	0	0
$606$	14520.0	0.973325
$607$	3884.00	0.259714	0.129857	−	0.991533i	$-0.458548\pi$
$607$	3884.00	0.259714	0.129857	+	0.991533i	$0.458548\pi$
$608$	320.000	0.0213449
$609$	13230.0	0.880306
$610$	0	0
$611$	25272.0	1.67332
$612$	28032.0	1.85151
$613$	−3643.00	−0.240032	−0.120016	−	0.992772i	$-0.538295\pi$
$613$	−3643.00	−0.240032	−0.120016	+	0.992772i	$0.538295\pi$
$614$	13208.0	0.868129
$615$	0	0
$616$	−504.000	−0.0329655
$617$	30369.0	1.98154	0.990770	−	0.135555i	$-0.0432819\pi$
$617$	30369.0	1.98154	0.990770	+	0.135555i	$0.0432819\pi$
$618$	35960.0	2.34065
$619$	−10888.0	−0.706988	−0.353494	−	0.935437i	$-0.615007\pi$
$619$	−10888.0	−0.706988	−0.353494	+	0.935437i	$0.615007\pi$
$620$	0	0
$621$	34500.0	2.22937
$622$	−12072.0	−0.778204
$623$	1260.00	0.0810286
$624$	−8320.00	−0.533761
$625$	0	0
$626$	−18292.0	−1.16788
$627$	−900.000	−0.0573246
$628$	2600.00	0.165209
$629$	29280.0	1.85607
$630$	0	0
$631$	28499.0	1.79798	0.898992	−	0.437966i	$-0.144301\pi$
$631$	28499.0	1.79798	0.898992	+	0.437966i	$0.144301\pi$
$632$	−5944.00	−0.374113
$633$	−59560.0	−3.73981
$634$	8898.00	0.557389
$635$	0	0
$636$	−14160.0	−0.882831
$637$	−2548.00	−0.158486
$638$	−3402.00	−0.211107
$639$	−34383.0	−2.12859
$640$	0	0
$641$	5817.00	0.358436	0.179218	−	0.983809i	$-0.442643\pi$
$641$	5817.00	0.358436	0.179218	+	0.983809i	$0.442643\pi$
$642$	−17520.0	−1.07704
$643$	22376.0	1.37235	0.686177	−	0.727435i	$-0.259288\pi$
$643$	22376.0	1.37235	0.686177	+	0.727435i	$0.259288\pi$
$644$	2100.00	0.128496
$645$	0	0
$646$	1920.00	0.116937
$647$	3018.00	0.183385	0.0916923	−	0.995787i	$-0.470772\pi$
$647$	3018.00	0.183385	0.0916923	+	0.995787i	$0.470772\pi$
$648$	−21032.0	−1.27502
$649$	−6048.00	−0.365801
$650$	0	0
$651$	−16240.0	−0.977720
$652$	3728.00	0.223926
$653$	−29682.0	−1.77878	−0.889392	−	0.457145i	$-0.848872\pi$
$653$	−29682.0	−1.77878	−0.889392	+	0.457145i	$0.848872\pi$
$654$	13820.0	0.826307
$655$	0	0
$656$	−7008.00	−0.417098
$657$	44822.0	2.66160
$658$	6804.00	0.403112
$659$	2052.00	0.121297	0.0606484	−	0.998159i	$-0.480683\pi$
$659$	2052.00	0.121297	0.0606484	+	0.998159i	$0.480683\pi$
$660$	0	0
$661$	14222.0	0.836871	0.418435	−	0.908247i	$-0.362579\pi$
$661$	14222.0	0.836871	0.418435	+	0.908247i	$0.362579\pi$
$662$	20162.0	1.18371
$663$	−49920.0	−2.92418
$664$	−7968.00	−0.465690
$665$	0	0
$666$	−44530.0	−2.59084
$667$	14175.0	0.822876
$668$	−720.000	−0.0417030
$669$	−31180.0	−1.80193
$670$	0	0
$671$	1854.00	0.106666
$672$	−2240.00	−0.128586
$673$	20942.0	1.19949	0.599744	−	0.800192i	$-0.295269\pi$
$673$	20942.0	1.19949	0.599744	+	0.800192i	$0.295269\pi$
$674$	−15556.0	−0.889013
$675$	0	0
$676$	2028.00	0.115385
$677$	13074.0	0.742208	0.371104	−	0.928591i	$-0.378979\pi$
$677$	13074.0	0.742208	0.371104	+	0.928591i	$0.378979\pi$
$678$	30420.0	1.72312
$679$	−1288.00	−0.0727966
$680$	0	0
$681$	−60.0000	−0.00337622
$682$	4176.00	0.234468
$683$	−31383.0	−1.75818	−0.879090	−	0.476656i	$-0.841849\pi$
$683$	−31383.0	−1.75818	−0.879090	+	0.476656i	$0.841849\pi$
$684$	−2920.00	−0.163230
$685$	0	0
$686$	−686.000	−0.0381802
$687$	−5860.00	−0.325434
$688$	5648.00	0.312977
$689$	18408.0	1.01784
$690$	0	0
$691$	−622.000	−0.0342431	−0.0171216	−	0.999853i	$-0.505450\pi$
$691$	−622.000	−0.0342431	−0.0171216	+	0.999853i	$0.505450\pi$
$692$	−3336.00	−0.183260
$693$	4599.00	0.252095
$694$	−2034.00	−0.111253
$695$	0	0
$696$	−15120.0	−0.823451
$697$	−42048.0	−2.28505
$698$	−20740.0	−1.12467
$699$	12930.0	0.699653
$700$	0	0
$701$	7782.00	0.419290	0.209645	−	0.977778i	$-0.432769\pi$
$701$	7782.00	0.419290	0.209645	+	0.977778i	$0.432769\pi$
$702$	47840.0	2.57209
$703$	−3050.00	−0.163631
$704$	576.000	0.0308364
$705$	0	0
$706$	18864.0	1.00560
$707$	−5082.00	−0.270337
$708$	−26880.0	−1.42685
$709$	7502.00	0.397382	0.198691	−	0.980062i	$-0.436331\pi$
$709$	7502.00	0.397382	0.198691	+	0.980062i	$0.436331\pi$
$710$	0	0
$711$	54239.0	2.86093
$712$	−1440.00	−0.0757953
$713$	−17400.0	−0.913934
$714$	−13440.0	−0.704453
$715$	0	0
$716$	−2592.00	−0.135290
$717$	−53760.0	−2.80015
$718$	−15114.0	−0.785584
$719$	−20814.0	−1.07960	−0.539799	−	0.841794i	$-0.681500\pi$
$719$	−20814.0	−1.07960	−0.539799	+	0.841794i	$0.681500\pi$
$720$	0	0
$721$	−12586.0	−0.650107
$722$	13518.0	0.696798
$723$	−6700.00	−0.344641
$724$	−11656.0	−0.598331
$725$	0	0
$726$	25000.0	1.27801
$727$	14360.0	0.732576	0.366288	−	0.930501i	$-0.380628\pi$
$727$	14360.0	0.732576	0.366288	+	0.930501i	$0.380628\pi$
$728$	2912.00	0.148250
$729$	67717.0	3.44038
$730$	0	0
$731$	33888.0	1.71463
$732$	8240.00	0.416064
$733$	−1588.00	−0.0800193	−0.0400096	−	0.999199i	$-0.512739\pi$
$733$	−1588.00	−0.0800193	−0.0400096	+	0.999199i	$0.512739\pi$
$734$	23324.0	1.17289
$735$	0	0
$736$	−2400.00	−0.120197
$737$	5391.00	0.269444
$738$	63948.0	3.18965
$739$	2957.00	0.147192	0.0735961	−	0.997288i	$-0.476552\pi$
$739$	2957.00	0.147192	0.0735961	+	0.997288i	$0.476552\pi$
$740$	0	0
$741$	5200.00	0.257796
$742$	4956.00	0.245203
$743$	−12384.0	−0.611474	−0.305737	−	0.952116i	$-0.598903\pi$
$743$	−12384.0	−0.611474	−0.305737	+	0.952116i	$0.598903\pi$
$744$	18560.0	0.914573
$745$	0	0
$746$	4754.00	0.233319
$747$	72708.0	3.56124
$748$	3456.00	0.168936
$749$	6132.00	0.299143
$750$	0	0
$751$	−20236.0	−0.983252	−0.491626	−	0.870806i	$-0.663597\pi$
$751$	−20236.0	−0.983252	−0.491626	+	0.870806i	$0.663597\pi$
$752$	−7776.00	−0.377077
$753$	13800.0	0.667862
$754$	19656.0	0.949376
$755$	0	0
$756$	12880.0	0.619631
$757$	37601.0	1.80533	0.902663	−	0.430348i	$-0.141609\pi$
$757$	37601.0	1.80533	0.902663	+	0.430348i	$0.141609\pi$
$758$	−8854.00	−0.424264
$759$	6750.00	0.322806
$760$	0	0
$761$	−13392.0	−0.637923	−0.318962	−	0.947768i	$-0.603334\pi$
$761$	−13392.0	−0.637923	−0.318962	+	0.947768i	$0.603334\pi$
$762$	−20620.0	−0.980294
$763$	−4837.00	−0.229503
$764$	−3504.00	−0.165930
$765$	0	0
$766$	−9216.00	−0.434710
$767$	34944.0	1.64505
$768$	2560.00	0.120281
$769$	22430.0	1.05182	0.525908	−	0.850541i	$-0.323726\pi$
$769$	22430.0	1.05182	0.525908	+	0.850541i	$0.323726\pi$
$770$	0	0
$771$	−35760.0	−1.67038
$772$	−2404.00	−0.112075
$773$	34704.0	1.61477	0.807384	−	0.590026i	$-0.200882\pi$
$773$	34704.0	1.61477	0.807384	+	0.590026i	$0.200882\pi$
$774$	−51538.0	−2.39340
$775$	0	0
$776$	1472.00	0.0680950
$777$	21350.0	0.985749
$778$	1398.00	0.0644225
$779$	4380.00	0.201450
$780$	0	0
$781$	−4239.00	−0.194217
$782$	−14400.0	−0.658495
$783$	86940.0	3.96805
$784$	784.000	0.0357143
$785$	0	0
$786$	22320.0	1.01289
$787$	37646.0	1.70513	0.852564	−	0.522624i	$-0.175047\pi$
$787$	37646.0	1.70513	0.852564	+	0.522624i	$0.175047\pi$
$788$	−8052.00	−0.364011
$789$	−59190.0	−2.67075
$790$	0	0
$791$	−10647.0	−0.478589
$792$	−5256.00	−0.235813
$793$	−10712.0	−0.479690
$794$	15260.0	0.682062
$795$	0	0
$796$	1304.00	0.0580641
$797$	−8988.00	−0.399462	−0.199731	−	0.979851i	$-0.564007\pi$
$797$	−8988.00	−0.399462	−0.199731	+	0.979851i	$0.564007\pi$
$798$	1400.00	0.0621046
$799$	−46656.0	−2.06580
$800$	0	0
$801$	13140.0	0.579624
$802$	−11202.0	−0.493212
$803$	5526.00	0.242850
$804$	23960.0	1.05100
$805$	0	0
$806$	−24128.0	−1.05443
$807$	−17640.0	−0.769464
$808$	5808.00	0.252877
$809$	−28029.0	−1.21811	−0.609053	−	0.793130i	$-0.708450\pi$
$809$	−28029.0	−1.21811	−0.609053	+	0.793130i	$0.708450\pi$
$810$	0	0
$811$	8078.00	0.349762	0.174881	−	0.984590i	$-0.444046\pi$
$811$	8078.00	0.349762	0.174881	+	0.984590i	$0.444046\pi$
$812$	5292.00	0.228710
$813$	−3400.00	−0.146671
$814$	−5490.00	−0.236394
$815$	0	0
$816$	15360.0	0.658955
$817$	−3530.00	−0.151162
$818$	−9340.00	−0.399224
$819$	−26572.0	−1.13370
$820$	0	0
$821$	−35574.0	−1.51223	−0.756115	−	0.654439i	$-0.772905\pi$
$821$	−35574.0	−1.51223	−0.756115	+	0.654439i	$0.772905\pi$
$822$	27960.0	1.18640
$823$	6599.00	0.279498	0.139749	−	0.990187i	$-0.455370\pi$
$823$	6599.00	0.279498	0.139749	+	0.990187i	$0.455370\pi$
$824$	14384.0	0.608119
$825$	0	0
$826$	9408.00	0.396303
$827$	−663.000	−0.0278776	−0.0139388	−	0.999903i	$-0.504437\pi$
$827$	−663.000	−0.0278776	−0.0139388	+	0.999903i	$0.504437\pi$
$828$	21900.0	0.919176
$829$	−22564.0	−0.945332	−0.472666	−	0.881242i	$-0.656708\pi$
$829$	−22564.0	−0.945332	−0.472666	+	0.881242i	$0.656708\pi$
$830$	0	0
$831$	47060.0	1.96449
$832$	−3328.00	−0.138675
$833$	4704.00	0.195659
$834$	−13480.0	−0.559681
$835$	0	0
$836$	−360.000	−0.0148934
$837$	−106720.	−4.40715
$838$	−72.0000	−0.00296802
$839$	−294.000	−0.0120977	−0.00604887	−	0.999982i	$-0.501925\pi$
$839$	−294.000	−0.0120977	−0.00604887	+	0.999982i	$0.501925\pi$
$840$	0	0
$841$	11332.0	0.464636
$842$	−10990.0	−0.449810
$843$	66810.0	2.72961
$844$	−23824.0	−0.971630
$845$	0	0
$846$	70956.0	2.88359
$847$	−8750.00	−0.354963
$848$	−5664.00	−0.229366
$849$	−2260.00	−0.0913581
$850$	0	0
$851$	22875.0	0.921439
$852$	−18840.0	−0.757568
$853$	−28852.0	−1.15812	−0.579058	−	0.815286i	$-0.696580\pi$
$853$	−28852.0	−1.15812	−0.579058	+	0.815286i	$0.696580\pi$
$854$	−2884.00	−0.115560
$855$	0	0
$856$	−7008.00	−0.279823
$857$	−7422.00	−0.295835	−0.147918	−	0.989000i	$-0.547257\pi$
$857$	−7422.00	−0.295835	−0.147918	+	0.989000i	$0.547257\pi$
$858$	9360.00	0.372430
$859$	8138.00	0.323242	0.161621	−	0.986853i	$-0.448328\pi$
$859$	8138.00	0.323242	0.161621	+	0.986853i	$0.448328\pi$
$860$	0	0
$861$	−30660.0	−1.21358
$862$	−5400.00	−0.213370
$863$	−32199.0	−1.27007	−0.635033	−	0.772485i	$-0.719013\pi$
$863$	−32199.0	−1.27007	−0.635033	+	0.772485i	$0.719013\pi$
$864$	−14720.0	−0.579612
$865$	0	0
$866$	−30208.0	−1.18535
$867$	43030.0	1.68555
$868$	−6496.00	−0.254019
$869$	6687.00	0.261037
$870$	0	0
$871$	−31148.0	−1.21172
$872$	5528.00	0.214681
$873$	−13432.0	−0.520738
$874$	1500.00	0.0580529
$875$	0	0
$876$	24560.0	0.947267
$877$	−11158.0	−0.429622	−0.214811	−	0.976656i	$-0.568914\pi$
$877$	−11158.0	−0.429622	−0.214811	+	0.976656i	$0.568914\pi$
$878$	−29896.0	−1.14914
$879$	43200.0	1.65768
$880$	0	0
$881$	16272.0	0.622267	0.311134	−	0.950366i	$-0.399291\pi$
$881$	16272.0	0.622267	0.311134	+	0.950366i	$0.399291\pi$
$882$	−7154.00	−0.273115
$883$	9071.00	0.345712	0.172856	−	0.984947i	$-0.444701\pi$
$883$	9071.00	0.345712	0.172856	+	0.984947i	$0.444701\pi$
$884$	−19968.0	−0.759725
$885$	0	0
$886$	−9960.00	−0.377667
$887$	−30138.0	−1.14085	−0.570426	−	0.821349i	$-0.693222\pi$
$887$	−30138.0	−1.14085	−0.570426	+	0.821349i	$0.693222\pi$
$888$	−24400.0	−0.922084
$889$	7217.00	0.272273
$890$	0	0
$891$	23661.0	0.889645
$892$	−12472.0	−0.468154
$893$	4860.00	0.182121
$894$	25620.0	0.958457
$895$	0	0
$896$	−896.000	−0.0334077
$897$	−39000.0	−1.45170
$898$	−24750.0	−0.919731
$899$	−43848.0	−1.62671
$900$	0	0
$901$	−33984.0	−1.25657
$902$	7884.00	0.291029
$903$	24710.0	0.910628
$904$	12168.0	0.447679
$905$	0	0
$906$	−19060.0	−0.698925
$907$	25844.0	0.946126	0.473063	−	0.881029i	$-0.343148\pi$
$907$	25844.0	0.946126	0.473063	+	0.881029i	$0.343148\pi$
$908$	−24.0000	−0.000877167 0
$909$	−52998.0	−1.93381
$910$	0	0
$911$	40815.0	1.48437	0.742185	−	0.670195i	$-0.233790\pi$
$911$	40815.0	1.48437	0.742185	+	0.670195i	$0.233790\pi$
$912$	−1600.00	−0.0580935
$913$	8964.00	0.324934
$914$	−21670.0	−0.784223
$915$	0	0
$916$	−2344.00	−0.0845502
$917$	−7812.00	−0.281325
$918$	−88320.0	−3.17538
$919$	−5389.00	−0.193435	−0.0967175	−	0.995312i	$-0.530834\pi$
$919$	−5389.00	−0.193435	−0.0967175	+	0.995312i	$0.530834\pi$
$920$	0	0
$921$	−66040.0	−2.36275
$922$	−11400.0	−0.407201
$923$	24492.0	0.873417
$924$	2520.00	0.0897207
$925$	0	0
$926$	−12256.0	−0.434943
$927$	−131254.	−4.65043
$928$	−6048.00	−0.213939
$929$	43662.0	1.54198	0.770992	−	0.636844i	$-0.219761\pi$
$929$	43662.0	1.54198	0.770992	+	0.636844i	$0.219761\pi$
$930$	0	0
$931$	−490.000	−0.0172493
$932$	5172.00	0.181775
$933$	60360.0	2.11800
$934$	19620.0	0.687351
$935$	0	0
$936$	30368.0	1.06048
$937$	−11950.0	−0.416638	−0.208319	−	0.978061i	$-0.566799\pi$
$937$	−11950.0	−0.416638	−0.208319	+	0.978061i	$0.566799\pi$
$938$	−8386.00	−0.291911
$939$	91460.0	3.17858
$940$	0	0
$941$	−8448.00	−0.292664	−0.146332	−	0.989236i	$-0.546747\pi$
$941$	−8448.00	−0.292664	−0.146332	+	0.989236i	$0.546747\pi$
$942$	−13000.0	−0.449642
$943$	−32850.0	−1.13440
$944$	−10752.0	−0.370707
$945$	0	0
$946$	−6354.00	−0.218379
$947$	25692.0	0.881603	0.440801	−	0.897605i	$-0.354694\pi$
$947$	25692.0	0.881603	0.440801	+	0.897605i	$0.354694\pi$
$948$	29720.0	1.01821
$949$	−31928.0	−1.09213
$950$	0	0
$951$	−44490.0	−1.51702
$952$	−5376.00	−0.183022
$953$	47547.0	1.61616	0.808079	−	0.589074i	$-0.200507\pi$
$953$	47547.0	1.61616	0.808079	+	0.589074i	$0.200507\pi$
$954$	51684.0	1.75402
$955$	0	0
$956$	−21504.0	−0.727499
$957$	17010.0	0.574561
$958$	408.000	0.0137598
$959$	−9786.00	−0.329517
$960$	0	0
$961$	24033.0	0.806720
$962$	31720.0	1.06309
$963$	63948.0	2.13987
$964$	−2680.00	−0.0895404
$965$	0	0
$966$	−10500.0	−0.349723
$967$	51608.0	1.71624	0.858119	−	0.513452i	$-0.171633\pi$
$967$	51608.0	1.71624	0.858119	+	0.513452i	$0.171633\pi$
$968$	10000.0	0.332037
$969$	−9600.00	−0.318263
$970$	0	0
$971$	−11754.0	−0.388469	−0.194235	−	0.980955i	$-0.562222\pi$
$971$	−11754.0	−0.388469	−0.194235	+	0.980955i	$0.562222\pi$
$972$	55480.0	1.83078
$973$	4718.00	0.155449
$974$	−30802.0	−1.01331
$975$	0	0
$976$	3296.00	0.108097
$977$	12765.0	0.418003	0.209001	−	0.977915i	$-0.432979\pi$
$977$	12765.0	0.418003	0.209001	+	0.977915i	$0.432979\pi$
$978$	−18640.0	−0.609449
$979$	1620.00	0.0528860
$980$	0	0
$981$	−50443.0	−1.64171
$982$	−7794.00	−0.253275
$983$	−32112.0	−1.04193	−0.520963	−	0.853579i	$-0.674427\pi$
$983$	−32112.0	−1.04193	−0.520963	+	0.853579i	$0.674427\pi$
$984$	35040.0	1.13520
$985$	0	0
$986$	−36288.0	−1.17205
$987$	−34020.0	−1.09713
$988$	2080.00	0.0669773
$989$	26475.0	0.851219
$990$	0	0
$991$	−42505.0	−1.36248	−0.681239	−	0.732061i	$-0.738559\pi$
$991$	−42505.0	−1.36248	−0.681239	+	0.732061i	$0.738559\pi$
$992$	7424.00	0.237613
$993$	−100810.	−3.22166
$994$	6594.00	0.210411
$995$	0	0
$996$	39840.0	1.26745
$997$	59654.0	1.89495	0.947473	−	0.319836i	$-0.103628\pi$
$997$	59654.0	1.89495	0.947473	+	0.319836i	$0.103628\pi$
$998$	−16264.0	−0.515860
$999$	140300.	4.44334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.a.j.1.1	✓	1
5.2	odd	4		350.4.c.a.99.1		2
5.3	odd	4		350.4.c.a.99.2		2
5.4	even	2		350.4.a.k.1.1	yes	1
7.6	odd	2		2450.4.a.a.1.1		1
35.34	odd	2		2450.4.a.bp.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.a.j.1.1	✓	1	1.1	even	1	trivial
350.4.a.k.1.1	yes	1	5.4	even	2
350.4.c.a.99.1		2	5.2	odd	4
350.4.c.a.99.2		2	5.3	odd	4
2450.4.a.a.1.1		1	7.6	odd	2
2450.4.a.bp.1.1		1	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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