LMFDB - Embedded newform 1050.4.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,4,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1050.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1050.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:	$61.9520055060$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +28.0000 q^{11} -12.0000 q^{12} +86.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} +66.0000 q^{17} +18.0000 q^{18} -48.0000 q^{19} -21.0000 q^{21} +56.0000 q^{22} -140.000 q^{23} -24.0000 q^{24} +172.000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -34.0000 q^{29} -284.000 q^{31} +32.0000 q^{32} -84.0000 q^{33} +132.000 q^{34} +36.0000 q^{36} +346.000 q^{37} -96.0000 q^{38} -258.000 q^{39} -274.000 q^{41} -42.0000 q^{42} +4.00000 q^{43} +112.000 q^{44} -280.000 q^{46} +448.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -198.000 q^{51} +344.000 q^{52} +94.0000 q^{53} -54.0000 q^{54} +56.0000 q^{56} +144.000 q^{57} -68.0000 q^{58} +308.000 q^{59} +510.000 q^{61} -568.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} -168.000 q^{66} +156.000 q^{67} +264.000 q^{68} +420.000 q^{69} +336.000 q^{71} +72.0000 q^{72} +1170.00 q^{73} +692.000 q^{74} -192.000 q^{76} +196.000 q^{77} -516.000 q^{78} +16.0000 q^{79} +81.0000 q^{81} -548.000 q^{82} -772.000 q^{83} -84.0000 q^{84} +8.00000 q^{86} +102.000 q^{87} +224.000 q^{88} +1630.00 q^{89} +602.000 q^{91} -560.000 q^{92} +852.000 q^{93} +896.000 q^{94} -96.0000 q^{96} -110.000 q^{97} +98.0000 q^{98} +252.000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	28.0000	0.767483	0.383742	−	0.923440i	$-0.374635\pi$
$11$	28.0000	0.767483	0.383742	+	0.923440i	$0.374635\pi$
$12$	−12.0000	−0.288675
$13$	86.0000	1.83478	0.917389	−	0.397992i	$-0.130293\pi$
$13$	86.0000	1.83478	0.917389	+	0.397992i	$0.130293\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	66.0000	0.941609	0.470804	−	0.882238i	$-0.343964\pi$
$17$	66.0000	0.941609	0.470804	+	0.882238i	$0.343964\pi$
$18$	18.0000	0.235702
$19$	−48.0000	−0.579577	−0.289788	−	0.957091i	$-0.593585\pi$
$19$	−48.0000	−0.579577	−0.289788	+	0.957091i	$0.593585\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	56.0000	0.542693
$23$	−140.000	−1.26922	−0.634609	−	0.772833i	$-0.718839\pi$
$23$	−140.000	−1.26922	−0.634609	+	0.772833i	$0.718839\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	172.000	1.29738
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−34.0000	−0.217712	−0.108856	−	0.994058i	$-0.534719\pi$
$29$	−34.0000	−0.217712	−0.108856	+	0.994058i	$0.534719\pi$
$30$	0	0
$31$	−284.000	−1.64542	−0.822708	−	0.568464i	$-0.807538\pi$
$31$	−284.000	−1.64542	−0.822708	+	0.568464i	$0.807538\pi$
$32$	32.0000	0.176777
$33$	−84.0000	−0.443107
$34$	132.000	0.665818
$35$	0	0
$36$	36.0000	0.166667
$37$	346.000	1.53735	0.768676	−	0.639638i	$-0.220916\pi$
$37$	346.000	1.53735	0.768676	+	0.639638i	$0.220916\pi$
$38$	−96.0000	−0.409823
$39$	−258.000	−1.05931
$40$	0	0
$41$	−274.000	−1.04370	−0.521849	−	0.853038i	$-0.674758\pi$
$41$	−274.000	−1.04370	−0.521849	+	0.853038i	$0.674758\pi$
$42$	−42.0000	−0.154303
$43$	4.00000	0.0141859	0.00709296	−	0.999975i	$-0.497742\pi$
$43$	4.00000	0.0141859	0.00709296	+	0.999975i	$0.497742\pi$
$44$	112.000	0.383742
$45$	0	0
$46$	−280.000	−0.897473
$47$	448.000	1.39037	0.695186	−	0.718830i	$-0.255322\pi$
$47$	448.000	1.39037	0.695186	+	0.718830i	$0.255322\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	0	0
$51$	−198.000	−0.543638
$52$	344.000	0.917389
$53$	94.0000	0.243621	0.121810	−	0.992553i	$-0.461130\pi$
$53$	94.0000	0.243621	0.121810	+	0.992553i	$0.461130\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	56.0000	0.133631
$57$	144.000	0.334619
$58$	−68.0000	−0.153945
$59$	308.000	0.679630	0.339815	−	0.940492i	$-0.389635\pi$
$59$	308.000	0.679630	0.339815	+	0.940492i	$0.389635\pi$
$60$	0	0
$61$	510.000	1.07047	0.535236	−	0.844702i	$-0.320223\pi$
$61$	510.000	1.07047	0.535236	+	0.844702i	$0.320223\pi$
$62$	−568.000	−1.16349
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	0	0
$66$	−168.000	−0.313324
$67$	156.000	0.284454	0.142227	−	0.989834i	$-0.454574\pi$
$67$	156.000	0.284454	0.142227	+	0.989834i	$0.454574\pi$
$68$	264.000	0.470804
$69$	420.000	0.732783
$70$	0	0
$71$	336.000	0.561632	0.280816	−	0.959762i	$-0.409395\pi$
$71$	336.000	0.561632	0.280816	+	0.959762i	$0.409395\pi$
$72$	72.0000	0.117851
$73$	1170.00	1.87586	0.937932	−	0.346818i	$-0.112738\pi$
$73$	1170.00	1.87586	0.937932	+	0.346818i	$0.112738\pi$
$74$	692.000	1.08707
$75$	0	0
$76$	−192.000	−0.289788
$77$	196.000	0.290081
$78$	−516.000	−0.749045
$79$	16.0000	0.0227866	0.0113933	−	0.999935i	$-0.496373\pi$
$79$	16.0000	0.0227866	0.0113933	+	0.999935i	$0.496373\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−548.000	−0.738006
$83$	−772.000	−1.02094	−0.510470	−	0.859896i	$-0.670529\pi$
$83$	−772.000	−1.02094	−0.510470	+	0.859896i	$0.670529\pi$
$84$	−84.0000	−0.109109
$85$	0	0
$86$	8.00000	0.0100310
$87$	102.000	0.125696
$88$	224.000	0.271346
$89$	1630.00	1.94134	0.970672	−	0.240407i	$-0.0772809\pi$
$89$	1630.00	1.94134	0.970672	+	0.240407i	$0.0772809\pi$
$90$	0	0
$91$	602.000	0.693481
$92$	−560.000	−0.634609
$93$	852.000	0.949982
$94$	896.000	0.983142
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−110.000	−0.115142	−0.0575712	−	0.998341i	$-0.518336\pi$
$97$	−110.000	−0.115142	−0.0575712	+	0.998341i	$0.518336\pi$
$98$	98.0000	0.101015
$99$	252.000	0.255828
$100$	0	0
$101$	−870.000	−0.857111	−0.428556	−	0.903515i	$-0.640977\pi$
$101$	−870.000	−0.857111	−0.428556	+	0.903515i	$0.640977\pi$
$102$	−396.000	−0.384410
$103$	−1520.00	−1.45408	−0.727039	−	0.686596i	$-0.759104\pi$
$103$	−1520.00	−1.45408	−0.727039	+	0.686596i	$0.759104\pi$
$104$	688.000	0.648692
$105$	0	0
$106$	188.000	0.172266
$107$	416.000	0.375853	0.187926	−	0.982183i	$-0.439823\pi$
$107$	416.000	0.375853	0.187926	+	0.982183i	$0.439823\pi$
$108$	−108.000	−0.0962250
$109$	1206.00	1.05976	0.529880	−	0.848073i	$-0.322237\pi$
$109$	1206.00	1.05976	0.529880	+	0.848073i	$0.322237\pi$
$110$	0	0
$111$	−1038.00	−0.887591
$112$	112.000	0.0944911
$113$	−822.000	−0.684312	−0.342156	−	0.939643i	$-0.611157\pi$
$113$	−822.000	−0.684312	−0.342156	+	0.939643i	$0.611157\pi$
$114$	288.000	0.236611
$115$	0	0
$116$	−136.000	−0.108856
$117$	774.000	0.611593
$118$	616.000	0.480571
$119$	462.000	0.355895
$120$	0	0
$121$	−547.000	−0.410969
$122$	1020.00	0.756938
$123$	822.000	0.602579
$124$	−1136.00	−0.822708
$125$	0	0
$126$	126.000	0.0890871
$127$	1184.00	0.827268	0.413634	−	0.910443i	$-0.364259\pi$
$127$	1184.00	0.827268	0.413634	+	0.910443i	$0.364259\pi$
$128$	128.000	0.0883883
$129$	−12.0000	−0.00819024
$130$	0	0
$131$	1820.00	1.21385	0.606924	−	0.794760i	$-0.292403\pi$
$131$	1820.00	1.21385	0.606924	+	0.794760i	$0.292403\pi$
$132$	−336.000	−0.221553
$133$	−336.000	−0.219059
$134$	312.000	0.201140
$135$	0	0
$136$	528.000	0.332909
$137$	−1998.00	−1.24599	−0.622995	−	0.782226i	$-0.714084\pi$
$137$	−1998.00	−1.24599	−0.622995	+	0.782226i	$0.714084\pi$
$138$	840.000	0.518156
$139$	1712.00	1.04468	0.522338	−	0.852739i	$-0.325060\pi$
$139$	1712.00	1.04468	0.522338	+	0.852739i	$0.325060\pi$
$140$	0	0
$141$	−1344.00	−0.802732
$142$	672.000	0.397134
$143$	2408.00	1.40816
$144$	144.000	0.0833333
$145$	0	0
$146$	2340.00	1.32644
$147$	−147.000	−0.0824786
$148$	1384.00	0.768676
$149$	−1482.00	−0.814833	−0.407417	−	0.913242i	$-0.633570\pi$
$149$	−1482.00	−0.814833	−0.407417	+	0.913242i	$0.633570\pi$
$150$	0	0
$151$	−2712.00	−1.46159	−0.730793	−	0.682599i	$-0.760849\pi$
$151$	−2712.00	−1.46159	−0.730793	+	0.682599i	$0.760849\pi$
$152$	−384.000	−0.204911
$153$	594.000	0.313870
$154$	392.000	0.205119
$155$	0	0
$156$	−1032.00	−0.529655
$157$	−650.000	−0.330418	−0.165209	−	0.986259i	$-0.552830\pi$
$157$	−650.000	−0.330418	−0.165209	+	0.986259i	$0.552830\pi$
$158$	32.0000	0.0161126
$159$	−282.000	−0.140654
$160$	0	0
$161$	−980.000	−0.479719
$162$	162.000	0.0785674
$163$	1940.00	0.932224	0.466112	−	0.884726i	$-0.345654\pi$
$163$	1940.00	0.932224	0.466112	+	0.884726i	$0.345654\pi$
$164$	−1096.00	−0.521849
$165$	0	0
$166$	−1544.00	−0.721914
$167$	1344.00	0.622766	0.311383	−	0.950285i	$-0.399208\pi$
$167$	1344.00	0.622766	0.311383	+	0.950285i	$0.399208\pi$
$168$	−168.000	−0.0771517
$169$	5199.00	2.36641
$170$	0	0
$171$	−432.000	−0.193192
$172$	16.0000	0.00709296
$173$	3942.00	1.73240	0.866199	−	0.499700i	$-0.166556\pi$
$173$	3942.00	1.73240	0.866199	+	0.499700i	$0.166556\pi$
$174$	204.000	0.0888805
$175$	0	0
$176$	448.000	0.191871
$177$	−924.000	−0.392385
$178$	3260.00	1.37274
$179$	−2228.00	−0.930327	−0.465164	−	0.885225i	$-0.654004\pi$
$179$	−2228.00	−0.930327	−0.465164	+	0.885225i	$0.654004\pi$
$180$	0	0
$181$	2982.00	1.22459	0.612294	−	0.790630i	$-0.290247\pi$
$181$	2982.00	1.22459	0.612294	+	0.790630i	$0.290247\pi$
$182$	1204.00	0.490365
$183$	−1530.00	−0.618037
$184$	−1120.00	−0.448736
$185$	0	0
$186$	1704.00	0.671738
$187$	1848.00	0.722669
$188$	1792.00	0.695186
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−2736.00	−1.03649	−0.518246	−	0.855232i	$-0.673415\pi$
$191$	−2736.00	−1.03649	−0.518246	+	0.855232i	$0.673415\pi$
$192$	−192.000	−0.0721688
$193$	−4210.00	−1.57017	−0.785084	−	0.619389i	$-0.787380\pi$
$193$	−4210.00	−1.57017	−0.785084	+	0.619389i	$0.787380\pi$
$194$	−220.000	−0.0814179
$195$	0	0
$196$	196.000	0.0714286
$197$	−2122.00	−0.767443	−0.383721	−	0.923449i	$-0.625358\pi$
$197$	−2122.00	−0.767443	−0.383721	+	0.923449i	$0.625358\pi$
$198$	504.000	0.180898
$199$	276.000	0.0983172	0.0491586	−	0.998791i	$-0.484346\pi$
$199$	276.000	0.0983172	0.0491586	+	0.998791i	$0.484346\pi$
$200$	0	0
$201$	−468.000	−0.164230
$202$	−1740.00	−0.606069
$203$	−238.000	−0.0822873
$204$	−792.000	−0.271819
$205$	0	0
$206$	−3040.00	−1.02819
$207$	−1260.00	−0.423073
$208$	1376.00	0.458694
$209$	−1344.00	−0.444815
$210$	0	0
$211$	−988.000	−0.322354	−0.161177	−	0.986926i	$-0.551529\pi$
$211$	−988.000	−0.322354	−0.161177	+	0.986926i	$0.551529\pi$
$212$	376.000	0.121810
$213$	−1008.00	−0.324258
$214$	832.000	0.265768
$215$	0	0
$216$	−216.000	−0.0680414
$217$	−1988.00	−0.621909
$218$	2412.00	0.749364
$219$	−3510.00	−1.08303
$220$	0	0
$221$	5676.00	1.72764
$222$	−2076.00	−0.627622
$223$	5592.00	1.67923	0.839614	−	0.543183i	$-0.182781\pi$
$223$	5592.00	1.67923	0.839614	+	0.543183i	$0.182781\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	−1644.00	−0.483882
$227$	4964.00	1.45142	0.725710	−	0.688001i	$-0.241512\pi$
$227$	4964.00	1.45142	0.725710	+	0.688001i	$0.241512\pi$
$228$	576.000	0.167309
$229$	4094.00	1.18139	0.590697	−	0.806894i	$-0.298853\pi$
$229$	4094.00	1.18139	0.590697	+	0.806894i	$0.298853\pi$
$230$	0	0
$231$	−588.000	−0.167479
$232$	−272.000	−0.0769727
$233$	−2022.00	−0.568522	−0.284261	−	0.958747i	$-0.591748\pi$
$233$	−2022.00	−0.568522	−0.284261	+	0.958747i	$0.591748\pi$
$234$	1548.00	0.432461
$235$	0	0
$236$	1232.00	0.339815
$237$	−48.0000	−0.0131558
$238$	924.000	0.251656
$239$	1872.00	0.506651	0.253326	−	0.967381i	$-0.418476\pi$
$239$	1872.00	0.506651	0.253326	+	0.967381i	$0.418476\pi$
$240$	0	0
$241$	−6350.00	−1.69726	−0.848630	−	0.528988i	$-0.822572\pi$
$241$	−6350.00	−1.69726	−0.848630	+	0.528988i	$0.822572\pi$
$242$	−1094.00	−0.290599
$243$	−243.000	−0.0641500
$244$	2040.00	0.535236
$245$	0	0
$246$	1644.00	0.426088
$247$	−4128.00	−1.06339
$248$	−2272.00	−0.581743
$249$	2316.00	0.589440
$250$	0	0
$251$	500.000	0.125736	0.0628680	−	0.998022i	$-0.479975\pi$
$251$	500.000	0.125736	0.0628680	+	0.998022i	$0.479975\pi$
$252$	252.000	0.0629941
$253$	−3920.00	−0.974104
$254$	2368.00	0.584967
$255$	0	0
$256$	256.000	0.0625000
$257$	5410.00	1.31310	0.656550	−	0.754283i	$-0.272015\pi$
$257$	5410.00	1.31310	0.656550	+	0.754283i	$0.272015\pi$
$258$	−24.0000	−0.00579137
$259$	2422.00	0.581065
$260$	0	0
$261$	−306.000	−0.0725706
$262$	3640.00	0.858320
$263$	−1092.00	−0.256029	−0.128014	−	0.991772i	$-0.540860\pi$
$263$	−1092.00	−0.256029	−0.128014	+	0.991772i	$0.540860\pi$
$264$	−672.000	−0.156662
$265$	0	0
$266$	−672.000	−0.154898
$267$	−4890.00	−1.12084
$268$	624.000	0.142227
$269$	−4694.00	−1.06393	−0.531967	−	0.846765i	$-0.678547\pi$
$269$	−4694.00	−1.06393	−0.531967	+	0.846765i	$0.678547\pi$
$270$	0	0
$271$	1292.00	0.289607	0.144803	−	0.989460i	$-0.453745\pi$
$271$	1292.00	0.289607	0.144803	+	0.989460i	$0.453745\pi$
$272$	1056.00	0.235402
$273$	−1806.00	−0.400381
$274$	−3996.00	−0.881048
$275$	0	0
$276$	1680.00	0.366392
$277$	4234.00	0.918399	0.459199	−	0.888333i	$-0.348136\pi$
$277$	4234.00	0.918399	0.459199	+	0.888333i	$0.348136\pi$
$278$	3424.00	0.738697
$279$	−2556.00	−0.548472
$280$	0	0
$281$	−38.0000	−0.00806722	−0.00403361	−	0.999992i	$-0.501284\pi$
$281$	−38.0000	−0.00806722	−0.00403361	+	0.999992i	$0.501284\pi$
$282$	−2688.00	−0.567617
$283$	−1708.00	−0.358763	−0.179382	−	0.983780i	$-0.557410\pi$
$283$	−1708.00	−0.358763	−0.179382	+	0.983780i	$0.557410\pi$
$284$	1344.00	0.280816
$285$	0	0
$286$	4816.00	0.995720
$287$	−1918.00	−0.394481
$288$	288.000	0.0589256
$289$	−557.000	−0.113373
$290$	0	0
$291$	330.000	0.0664775
$292$	4680.00	0.937932
$293$	1422.00	0.283529	0.141765	−	0.989900i	$-0.454722\pi$
$293$	1422.00	0.283529	0.141765	+	0.989900i	$0.454722\pi$
$294$	−294.000	−0.0583212
$295$	0	0
$296$	2768.00	0.543536
$297$	−756.000	−0.147702
$298$	−2964.00	−0.576174
$299$	−12040.0	−2.32873
$300$	0	0
$301$	28.0000	0.00536177
$302$	−5424.00	−1.03350
$303$	2610.00	0.494853
$304$	−768.000	−0.144894
$305$	0	0
$306$	1188.00	0.221939
$307$	916.000	0.170290	0.0851448	−	0.996369i	$-0.472865\pi$
$307$	916.000	0.170290	0.0851448	+	0.996369i	$0.472865\pi$
$308$	784.000	0.145041
$309$	4560.00	0.839512
$310$	0	0
$311$	−6048.00	−1.10274	−0.551368	−	0.834262i	$-0.685894\pi$
$311$	−6048.00	−1.10274	−0.551368	+	0.834262i	$0.685894\pi$
$312$	−2064.00	−0.374522
$313$	−9390.00	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−9390.00	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	−1300.00	−0.233641
$315$	0	0
$316$	64.0000	0.0113933
$317$	−10074.0	−1.78490	−0.892448	−	0.451150i	$-0.851014\pi$
$317$	−10074.0	−1.78490	−0.892448	+	0.451150i	$0.851014\pi$
$318$	−564.000	−0.0994577
$319$	−952.000	−0.167090
$320$	0	0
$321$	−1248.00	−0.216999
$322$	−1960.00	−0.339213
$323$	−3168.00	−0.545734
$324$	324.000	0.0555556
$325$	0	0
$326$	3880.00	0.659182
$327$	−3618.00	−0.611853
$328$	−2192.00	−0.369003
$329$	3136.00	0.525511
$330$	0	0
$331$	−1540.00	−0.255728	−0.127864	−	0.991792i	$-0.540812\pi$
$331$	−1540.00	−0.255728	−0.127864	+	0.991792i	$0.540812\pi$
$332$	−3088.00	−0.510470
$333$	3114.00	0.512451
$334$	2688.00	0.440362
$335$	0	0
$336$	−336.000	−0.0545545
$337$	6414.00	1.03677	0.518387	−	0.855146i	$-0.326533\pi$
$337$	6414.00	1.03677	0.518387	+	0.855146i	$0.326533\pi$
$338$	10398.0	1.67330
$339$	2466.00	0.395088
$340$	0	0
$341$	−7952.00	−1.26283
$342$	−864.000	−0.136608
$343$	343.000	0.0539949
$344$	32.0000	0.00501548
$345$	0	0
$346$	7884.00	1.22499
$347$	4208.00	0.651001	0.325500	−	0.945542i	$-0.394467\pi$
$347$	4208.00	0.651001	0.325500	+	0.945542i	$0.394467\pi$
$348$	408.000	0.0628480
$349$	6702.00	1.02794	0.513968	−	0.857809i	$-0.328175\pi$
$349$	6702.00	1.02794	0.513968	+	0.857809i	$0.328175\pi$
$350$	0	0
$351$	−2322.00	−0.353103
$352$	896.000	0.135673
$353$	−1950.00	−0.294017	−0.147009	−	0.989135i	$-0.546964\pi$
$353$	−1950.00	−0.294017	−0.147009	+	0.989135i	$0.546964\pi$
$354$	−1848.00	−0.277458
$355$	0	0
$356$	6520.00	0.970672
$357$	−1386.00	−0.205476
$358$	−4456.00	−0.657841
$359$	6056.00	0.890316	0.445158	−	0.895452i	$-0.353148\pi$
$359$	6056.00	0.890316	0.445158	+	0.895452i	$0.353148\pi$
$360$	0	0
$361$	−4555.00	−0.664091
$362$	5964.00	0.865914
$363$	1641.00	0.237273
$364$	2408.00	0.346740
$365$	0	0
$366$	−3060.00	−0.437018
$367$	1736.00	0.246917	0.123458	−	0.992350i	$-0.460601\pi$
$367$	1736.00	0.246917	0.123458	+	0.992350i	$0.460601\pi$
$368$	−2240.00	−0.317305
$369$	−2466.00	−0.347899
$370$	0	0
$371$	658.000	0.0920799
$372$	3408.00	0.474991
$373$	−10062.0	−1.39676	−0.698379	−	0.715728i	$-0.746095\pi$
$373$	−10062.0	−1.39676	−0.698379	+	0.715728i	$0.746095\pi$
$374$	3696.00	0.511004
$375$	0	0
$376$	3584.00	0.491571
$377$	−2924.00	−0.399453
$378$	−378.000	−0.0514344
$379$	−10252.0	−1.38947	−0.694736	−	0.719265i	$-0.744479\pi$
$379$	−10252.0	−1.38947	−0.694736	+	0.719265i	$0.744479\pi$
$380$	0	0
$381$	−3552.00	−0.477623
$382$	−5472.00	−0.732911
$383$	−6160.00	−0.821831	−0.410916	−	0.911673i	$-0.634791\pi$
$383$	−6160.00	−0.821831	−0.410916	+	0.911673i	$0.634791\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−8420.00	−1.11028
$387$	36.0000	0.00472864
$388$	−440.000	−0.0575712
$389$	−9586.00	−1.24943	−0.624717	−	0.780852i	$-0.714785\pi$
$389$	−9586.00	−1.24943	−0.624717	+	0.780852i	$0.714785\pi$
$390$	0	0
$391$	−9240.00	−1.19511
$392$	392.000	0.0505076
$393$	−5460.00	−0.700816
$394$	−4244.00	−0.542664
$395$	0	0
$396$	1008.00	0.127914
$397$	7054.00	0.891764	0.445882	−	0.895092i	$-0.352890\pi$
$397$	7054.00	0.891764	0.445882	+	0.895092i	$0.352890\pi$
$398$	552.000	0.0695208
$399$	1008.00	0.126474
$400$	0	0
$401$	7898.00	0.983559	0.491780	−	0.870720i	$-0.336347\pi$
$401$	7898.00	0.983559	0.491780	+	0.870720i	$0.336347\pi$
$402$	−936.000	−0.116128
$403$	−24424.0	−3.01897
$404$	−3480.00	−0.428556
$405$	0	0
$406$	−476.000	−0.0581859
$407$	9688.00	1.17989
$408$	−1584.00	−0.192205
$409$	8450.00	1.02158	0.510789	−	0.859706i	$-0.329353\pi$
$409$	8450.00	1.02158	0.510789	+	0.859706i	$0.329353\pi$
$410$	0	0
$411$	5994.00	0.719373
$412$	−6080.00	−0.727039
$413$	2156.00	0.256876
$414$	−2520.00	−0.299158
$415$	0	0
$416$	2752.00	0.324346
$417$	−5136.00	−0.603144
$418$	−2688.00	−0.314532
$419$	−9772.00	−1.13936	−0.569682	−	0.821865i	$-0.692934\pi$
$419$	−9772.00	−1.13936	−0.569682	+	0.821865i	$0.692934\pi$
$420$	0	0
$421$	−290.000	−0.0335718	−0.0167859	−	0.999859i	$-0.505343\pi$
$421$	−290.000	−0.0335718	−0.0167859	+	0.999859i	$0.505343\pi$
$422$	−1976.00	−0.227939
$423$	4032.00	0.463458
$424$	752.000	0.0861329
$425$	0	0
$426$	−2016.00	−0.229285
$427$	3570.00	0.404600
$428$	1664.00	0.187926
$429$	−7224.00	−0.813002
$430$	0	0
$431$	−11256.0	−1.25796	−0.628982	−	0.777420i	$-0.716528\pi$
$431$	−11256.0	−1.25796	−0.628982	+	0.777420i	$0.716528\pi$
$432$	−432.000	−0.0481125
$433$	9098.00	1.00975	0.504875	−	0.863192i	$-0.331538\pi$
$433$	9098.00	1.00975	0.504875	+	0.863192i	$0.331538\pi$
$434$	−3976.00	−0.439756
$435$	0	0
$436$	4824.00	0.529880
$437$	6720.00	0.735609
$438$	−7020.00	−0.765819
$439$	−6316.00	−0.686666	−0.343333	−	0.939214i	$-0.611556\pi$
$439$	−6316.00	−0.686666	−0.343333	+	0.939214i	$0.611556\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	11352.0	1.22163
$443$	−4112.00	−0.441009	−0.220505	−	0.975386i	$-0.570770\pi$
$443$	−4112.00	−0.441009	−0.220505	+	0.975386i	$0.570770\pi$
$444$	−4152.00	−0.443795
$445$	0	0
$446$	11184.0	1.18739
$447$	4446.00	0.470444
$448$	448.000	0.0472456
$449$	−2750.00	−0.289043	−0.144522	−	0.989502i	$-0.546164\pi$
$449$	−2750.00	−0.289043	−0.144522	+	0.989502i	$0.546164\pi$
$450$	0	0
$451$	−7672.00	−0.801021
$452$	−3288.00	−0.342156
$453$	8136.00	0.843847
$454$	9928.00	1.02631
$455$	0	0
$456$	1152.00	0.118306
$457$	16734.0	1.71287	0.856437	−	0.516251i	$-0.172673\pi$
$457$	16734.0	1.71287	0.856437	+	0.516251i	$0.172673\pi$
$458$	8188.00	0.835371
$459$	−1782.00	−0.181213
$460$	0	0
$461$	−222.000	−0.0224286	−0.0112143	−	0.999937i	$-0.503570\pi$
$461$	−222.000	−0.0224286	−0.0112143	+	0.999937i	$0.503570\pi$
$462$	−1176.00	−0.118425
$463$	11344.0	1.13866	0.569331	−	0.822108i	$-0.307202\pi$
$463$	11344.0	1.13866	0.569331	+	0.822108i	$0.307202\pi$
$464$	−544.000	−0.0544279
$465$	0	0
$466$	−4044.00	−0.402006
$467$	−17628.0	−1.74674	−0.873369	−	0.487059i	$-0.838070\pi$
$467$	−17628.0	−1.74674	−0.873369	+	0.487059i	$0.838070\pi$
$468$	3096.00	0.305796
$469$	1092.00	0.107514
$470$	0	0
$471$	1950.00	0.190767
$472$	2464.00	0.240286
$473$	112.000	0.0108875
$474$	−96.0000	−0.00930259
$475$	0	0
$476$	1848.00	0.177947
$477$	846.000	0.0812069
$478$	3744.00	0.358256
$479$	−6568.00	−0.626513	−0.313256	−	0.949669i	$-0.601420\pi$
$479$	−6568.00	−0.626513	−0.313256	+	0.949669i	$0.601420\pi$
$480$	0	0
$481$	29756.0	2.82070
$482$	−12700.0	−1.20014
$483$	2940.00	0.276966
$484$	−2188.00	−0.205485
$485$	0	0
$486$	−486.000	−0.0453609
$487$	5152.00	0.479383	0.239691	−	0.970849i	$-0.422954\pi$
$487$	5152.00	0.479383	0.239691	+	0.970849i	$0.422954\pi$
$488$	4080.00	0.378469
$489$	−5820.00	−0.538220
$490$	0	0
$491$	18868.0	1.73422	0.867109	−	0.498119i	$-0.165976\pi$
$491$	18868.0	1.73422	0.867109	+	0.498119i	$0.165976\pi$
$492$	3288.00	0.301290
$493$	−2244.00	−0.204999
$494$	−8256.00	−0.751933
$495$	0	0
$496$	−4544.00	−0.411354
$497$	2352.00	0.212277
$498$	4632.00	0.416797
$499$	4108.00	0.368536	0.184268	−	0.982876i	$-0.441009\pi$
$499$	4108.00	0.368536	0.184268	+	0.982876i	$0.441009\pi$
$500$	0	0
$501$	−4032.00	−0.359554
$502$	1000.00	0.0889087
$503$	−9048.00	−0.802048	−0.401024	−	0.916067i	$-0.631346\pi$
$503$	−9048.00	−0.802048	−0.401024	+	0.916067i	$0.631346\pi$
$504$	504.000	0.0445435
$505$	0	0
$506$	−7840.00	−0.688795
$507$	−15597.0	−1.36625
$508$	4736.00	0.413634
$509$	−7142.00	−0.621932	−0.310966	−	0.950421i	$-0.600653\pi$
$509$	−7142.00	−0.621932	−0.310966	+	0.950421i	$0.600653\pi$
$510$	0	0
$511$	8190.00	0.709010
$512$	512.000	0.0441942
$513$	1296.00	0.111540
$514$	10820.0	0.928501
$515$	0	0
$516$	−48.0000	−0.00409512
$517$	12544.0	1.06709
$518$	4844.00	0.410875
$519$	−11826.0	−1.00020
$520$	0	0
$521$	−1626.00	−0.136730	−0.0683650	−	0.997660i	$-0.521778\pi$
$521$	−1626.00	−0.136730	−0.0683650	+	0.997660i	$0.521778\pi$
$522$	−612.000	−0.0513152
$523$	11044.0	0.923366	0.461683	−	0.887045i	$-0.347246\pi$
$523$	11044.0	0.923366	0.461683	+	0.887045i	$0.347246\pi$
$524$	7280.00	0.606924
$525$	0	0
$526$	−2184.00	−0.181040
$527$	−18744.0	−1.54934
$528$	−1344.00	−0.110777
$529$	7433.00	0.610915
$530$	0	0
$531$	2772.00	0.226543
$532$	−1344.00	−0.109530
$533$	−23564.0	−1.91495
$534$	−9780.00	−0.792551
$535$	0	0
$536$	1248.00	0.100570
$537$	6684.00	0.537125
$538$	−9388.00	−0.752315
$539$	1372.00	0.109640
$540$	0	0
$541$	6518.00	0.517987	0.258993	−	0.965879i	$-0.416609\pi$
$541$	6518.00	0.517987	0.258993	+	0.965879i	$0.416609\pi$
$542$	2584.00	0.204783
$543$	−8946.00	−0.707016
$544$	2112.00	0.166455
$545$	0	0
$546$	−3612.00	−0.283112
$547$	15260.0	1.19282	0.596408	−	0.802681i	$-0.296594\pi$
$547$	15260.0	1.19282	0.596408	+	0.802681i	$0.296594\pi$
$548$	−7992.00	−0.622995
$549$	4590.00	0.356824
$550$	0	0
$551$	1632.00	0.126181
$552$	3360.00	0.259078
$553$	112.000	0.00861252
$554$	8468.00	0.649406
$555$	0	0
$556$	6848.00	0.522338
$557$	4422.00	0.336384	0.168192	−	0.985754i	$-0.446207\pi$
$557$	4422.00	0.336384	0.168192	+	0.985754i	$0.446207\pi$
$558$	−5112.00	−0.387828
$559$	344.000	0.0260280
$560$	0	0
$561$	−5544.00	−0.417233
$562$	−76.0000	−0.00570439
$563$	−23204.0	−1.73700	−0.868501	−	0.495688i	$-0.834916\pi$
$563$	−23204.0	−1.73700	−0.868501	+	0.495688i	$0.834916\pi$
$564$	−5376.00	−0.401366
$565$	0	0
$566$	−3416.00	−0.253684
$567$	567.000	0.0419961
$568$	2688.00	0.198567
$569$	162.000	0.0119357	0.00596783	−	0.999982i	$-0.498100\pi$
$569$	162.000	0.0119357	0.00596783	+	0.999982i	$0.498100\pi$
$570$	0	0
$571$	−2804.00	−0.205506	−0.102753	−	0.994707i	$-0.532765\pi$
$571$	−2804.00	−0.205506	−0.102753	+	0.994707i	$0.532765\pi$
$572$	9632.00	0.704081
$573$	8208.00	0.598419
$574$	−3836.00	−0.278940
$575$	0	0
$576$	576.000	0.0416667
$577$	7946.00	0.573304	0.286652	−	0.958035i	$-0.407458\pi$
$577$	7946.00	0.573304	0.286652	+	0.958035i	$0.407458\pi$
$578$	−1114.00	−0.0801666
$579$	12630.0	0.906537
$580$	0	0
$581$	−5404.00	−0.385879
$582$	660.000	0.0470067
$583$	2632.00	0.186975
$584$	9360.00	0.663218
$585$	0	0
$586$	2844.00	0.200486
$587$	−15132.0	−1.06399	−0.531997	−	0.846746i	$-0.678558\pi$
$587$	−15132.0	−1.06399	−0.531997	+	0.846746i	$0.678558\pi$
$588$	−588.000	−0.0412393
$589$	13632.0	0.953645
$590$	0	0
$591$	6366.00	0.443083
$592$	5536.00	0.384338
$593$	6514.00	0.451093	0.225546	−	0.974232i	$-0.427583\pi$
$593$	6514.00	0.451093	0.225546	+	0.974232i	$0.427583\pi$
$594$	−1512.00	−0.104441
$595$	0	0
$596$	−5928.00	−0.407417
$597$	−828.000	−0.0567635
$598$	−24080.0	−1.64666
$599$	−14264.0	−0.972974	−0.486487	−	0.873688i	$-0.661722\pi$
$599$	−14264.0	−0.972974	−0.486487	+	0.873688i	$0.661722\pi$
$600$	0	0
$601$	−3422.00	−0.232257	−0.116128	−	0.993234i	$-0.537048\pi$
$601$	−3422.00	−0.232257	−0.116128	+	0.993234i	$0.537048\pi$
$602$	56.0000	0.00379134
$603$	1404.00	0.0948181
$604$	−10848.0	−0.730793
$605$	0	0
$606$	5220.00	0.349914
$607$	−19832.0	−1.32612	−0.663061	−	0.748565i	$-0.730743\pi$
$607$	−19832.0	−1.32612	−0.663061	+	0.748565i	$0.730743\pi$
$608$	−1536.00	−0.102456
$609$	714.000	0.0475086
$610$	0	0
$611$	38528.0	2.55102
$612$	2376.00	0.156935
$613$	7706.00	0.507736	0.253868	−	0.967239i	$-0.418297\pi$
$613$	7706.00	0.507736	0.253868	+	0.967239i	$0.418297\pi$
$614$	1832.00	0.120413
$615$	0	0
$616$	1568.00	0.102559
$617$	−86.0000	−0.00561139	−0.00280570	−	0.999996i	$-0.500893\pi$
$617$	−86.0000	−0.00561139	−0.00280570	+	0.999996i	$0.500893\pi$
$618$	9120.00	0.593625
$619$	−9472.00	−0.615043	−0.307522	−	0.951541i	$-0.599500\pi$
$619$	−9472.00	−0.615043	−0.307522	+	0.951541i	$0.599500\pi$
$620$	0	0
$621$	3780.00	0.244261
$622$	−12096.0	−0.779751
$623$	11410.0	0.733759
$624$	−4128.00	−0.264827
$625$	0	0
$626$	−18780.0	−1.19904
$627$	4032.00	0.256814
$628$	−2600.00	−0.165209
$629$	22836.0	1.44758
$630$	0	0
$631$	−27128.0	−1.71149	−0.855744	−	0.517400i	$-0.826900\pi$
$631$	−27128.0	−1.71149	−0.855744	+	0.517400i	$0.826900\pi$
$632$	128.000	0.00805628
$633$	2964.00	0.186111
$634$	−20148.0	−1.26211
$635$	0	0
$636$	−1128.00	−0.0703272
$637$	4214.00	0.262111
$638$	−1904.00	−0.118151
$639$	3024.00	0.187211
$640$	0	0
$641$	930.000	0.0573054	0.0286527	−	0.999589i	$-0.490878\pi$
$641$	930.000	0.0573054	0.0286527	+	0.999589i	$0.490878\pi$
$642$	−2496.00	−0.153441
$643$	1060.00	0.0650114	0.0325057	−	0.999472i	$-0.489651\pi$
$643$	1060.00	0.0650114	0.0325057	+	0.999472i	$0.489651\pi$
$644$	−3920.00	−0.239860
$645$	0	0
$646$	−6336.00	−0.385893
$647$	−27008.0	−1.64110	−0.820552	−	0.571572i	$-0.806334\pi$
$647$	−27008.0	−1.64110	−0.820552	+	0.571572i	$0.806334\pi$
$648$	648.000	0.0392837
$649$	8624.00	0.521605
$650$	0	0
$651$	5964.00	0.359059
$652$	7760.00	0.466112
$653$	−30122.0	−1.80515	−0.902577	−	0.430529i	$-0.858327\pi$
$653$	−30122.0	−1.80515	−0.902577	+	0.430529i	$0.858327\pi$
$654$	−7236.00	−0.432645
$655$	0	0
$656$	−4384.00	−0.260924
$657$	10530.0	0.625288
$658$	6272.00	0.371593
$659$	−7764.00	−0.458942	−0.229471	−	0.973316i	$-0.573700\pi$
$659$	−7764.00	−0.458942	−0.229471	+	0.973316i	$0.573700\pi$
$660$	0	0
$661$	630.000	0.0370713	0.0185357	−	0.999828i	$-0.494100\pi$
$661$	630.000	0.0370713	0.0185357	+	0.999828i	$0.494100\pi$
$662$	−3080.00	−0.180827
$663$	−17028.0	−0.997455
$664$	−6176.00	−0.360957
$665$	0	0
$666$	6228.00	0.362358
$667$	4760.00	0.276324
$668$	5376.00	0.311383
$669$	−16776.0	−0.969503
$670$	0	0
$671$	14280.0	0.821570
$672$	−672.000	−0.0385758
$673$	−26794.0	−1.53467	−0.767335	−	0.641247i	$-0.778418\pi$
$673$	−26794.0	−1.53467	−0.767335	+	0.641247i	$0.778418\pi$
$674$	12828.0	0.733110
$675$	0	0
$676$	20796.0	1.18320
$677$	−24610.0	−1.39710	−0.698552	−	0.715559i	$-0.746172\pi$
$677$	−24610.0	−1.39710	−0.698552	+	0.715559i	$0.746172\pi$
$678$	4932.00	0.279369
$679$	−770.000	−0.0435197
$680$	0	0
$681$	−14892.0	−0.837978
$682$	−15904.0	−0.892955
$683$	−15296.0	−0.856933	−0.428466	−	0.903558i	$-0.640946\pi$
$683$	−15296.0	−0.856933	−0.428466	+	0.903558i	$0.640946\pi$
$684$	−1728.00	−0.0965961
$685$	0	0
$686$	686.000	0.0381802
$687$	−12282.0	−0.682078
$688$	64.0000	0.00354648
$689$	8084.00	0.446990
$690$	0	0
$691$	23376.0	1.28692	0.643462	−	0.765478i	$-0.277497\pi$
$691$	23376.0	1.28692	0.643462	+	0.765478i	$0.277497\pi$
$692$	15768.0	0.866199
$693$	1764.00	0.0966938
$694$	8416.00	0.460327
$695$	0	0
$696$	816.000	0.0444402
$697$	−18084.0	−0.982755
$698$	13404.0	0.726861
$699$	6066.00	0.328236
$700$	0	0
$701$	−21090.0	−1.13632	−0.568159	−	0.822919i	$-0.692344\pi$
$701$	−21090.0	−1.13632	−0.568159	+	0.822919i	$0.692344\pi$
$702$	−4644.00	−0.249682
$703$	−16608.0	−0.891014
$704$	1792.00	0.0959354
$705$	0	0
$706$	−3900.00	−0.207901
$707$	−6090.00	−0.323958
$708$	−3696.00	−0.196192
$709$	−8002.00	−0.423867	−0.211933	−	0.977284i	$-0.567976\pi$
$709$	−8002.00	−0.423867	−0.211933	+	0.977284i	$0.567976\pi$
$710$	0	0
$711$	144.000	0.00759553
$712$	13040.0	0.686369
$713$	39760.0	2.08839
$714$	−2772.00	−0.145293
$715$	0	0
$716$	−8912.00	−0.465164
$717$	−5616.00	−0.292515
$718$	12112.0	0.629549
$719$	−23240.0	−1.20543	−0.602716	−	0.797956i	$-0.705915\pi$
$719$	−23240.0	−1.20543	−0.602716	+	0.797956i	$0.705915\pi$
$720$	0	0
$721$	−10640.0	−0.549590
$722$	−9110.00	−0.469583
$723$	19050.0	0.979913
$724$	11928.0	0.612294
$725$	0	0
$726$	3282.00	0.167777
$727$	37912.0	1.93408	0.967041	−	0.254619i	$-0.0819501\pi$
$727$	37912.0	1.93408	0.967041	+	0.254619i	$0.0819501\pi$
$728$	4816.00	0.245182
$729$	729.000	0.0370370
$730$	0	0
$731$	264.000	0.0133576
$732$	−6120.00	−0.309019
$733$	13270.0	0.668675	0.334337	−	0.942453i	$-0.391487\pi$
$733$	13270.0	0.668675	0.334337	+	0.942453i	$0.391487\pi$
$734$	3472.00	0.174597
$735$	0	0
$736$	−4480.00	−0.224368
$737$	4368.00	0.218314
$738$	−4932.00	−0.246002
$739$	−29020.0	−1.44454	−0.722272	−	0.691609i	$-0.756902\pi$
$739$	−29020.0	−1.44454	−0.722272	+	0.691609i	$0.756902\pi$
$740$	0	0
$741$	12384.0	0.613951
$742$	1316.00	0.0651104
$743$	−13052.0	−0.644457	−0.322228	−	0.946662i	$-0.604432\pi$
$743$	−13052.0	−0.644457	−0.322228	+	0.946662i	$0.604432\pi$
$744$	6816.00	0.335869
$745$	0	0
$746$	−20124.0	−0.987657
$747$	−6948.00	−0.340313
$748$	7392.00	0.361335
$749$	2912.00	0.142059
$750$	0	0
$751$	20024.0	0.972951	0.486475	−	0.873694i	$-0.338282\pi$
$751$	20024.0	0.972951	0.486475	+	0.873694i	$0.338282\pi$
$752$	7168.00	0.347593
$753$	−1500.00	−0.0725937
$754$	−5848.00	−0.282456
$755$	0	0
$756$	−756.000	−0.0363696
$757$	11842.0	0.568566	0.284283	−	0.958740i	$-0.408244\pi$
$757$	11842.0	0.568566	0.284283	+	0.958740i	$0.408244\pi$
$758$	−20504.0	−0.982505
$759$	11760.0	0.562399
$760$	0	0
$761$	−15954.0	−0.759963	−0.379982	−	0.924994i	$-0.624070\pi$
$761$	−15954.0	−0.759963	−0.379982	+	0.924994i	$0.624070\pi$
$762$	−7104.00	−0.337731
$763$	8442.00	0.400552
$764$	−10944.0	−0.518246
$765$	0	0
$766$	−12320.0	−0.581122
$767$	26488.0	1.24697
$768$	−768.000	−0.0360844
$769$	−9158.00	−0.429449	−0.214724	−	0.976675i	$-0.568885\pi$
$769$	−9158.00	−0.429449	−0.214724	+	0.976675i	$0.568885\pi$
$770$	0	0
$771$	−16230.0	−0.758118
$772$	−16840.0	−0.785084
$773$	39774.0	1.85067	0.925337	−	0.379145i	$-0.123782\pi$
$773$	39774.0	1.85067	0.925337	+	0.379145i	$0.123782\pi$
$774$	72.0000	0.00334365
$775$	0	0
$776$	−880.000	−0.0407090
$777$	−7266.00	−0.335478
$778$	−19172.0	−0.883483
$779$	13152.0	0.604903
$780$	0	0
$781$	9408.00	0.431043
$782$	−18480.0	−0.845068
$783$	918.000	0.0418987
$784$	784.000	0.0357143
$785$	0	0
$786$	−10920.0	−0.495552
$787$	−17908.0	−0.811120	−0.405560	−	0.914068i	$-0.632923\pi$
$787$	−17908.0	−0.811120	−0.405560	+	0.914068i	$0.632923\pi$
$788$	−8488.00	−0.383721
$789$	3276.00	0.147818
$790$	0	0
$791$	−5754.00	−0.258646
$792$	2016.00	0.0904488
$793$	43860.0	1.96408
$794$	14108.0	0.630572
$795$	0	0
$796$	1104.00	0.0491586
$797$	−1290.00	−0.0573327	−0.0286663	−	0.999589i	$-0.509126\pi$
$797$	−1290.00	−0.0573327	−0.0286663	+	0.999589i	$0.509126\pi$
$798$	2016.00	0.0894306
$799$	29568.0	1.30919
$800$	0	0
$801$	14670.0	0.647115
$802$	15796.0	0.695481
$803$	32760.0	1.43970
$804$	−1872.00	−0.0821149
$805$	0	0
$806$	−48848.0	−2.13474
$807$	14082.0	0.614263
$808$	−6960.00	−0.303035
$809$	−34446.0	−1.49698	−0.748490	−	0.663146i	$-0.769221\pi$
$809$	−34446.0	−1.49698	−0.748490	+	0.663146i	$0.769221\pi$
$810$	0	0
$811$	−33456.0	−1.44858	−0.724290	−	0.689495i	$-0.757833\pi$
$811$	−33456.0	−1.44858	−0.724290	+	0.689495i	$0.757833\pi$
$812$	−952.000	−0.0411437
$813$	−3876.00	−0.167204
$814$	19376.0	0.834310
$815$	0	0
$816$	−3168.00	−0.135910
$817$	−192.000	−0.00822182
$818$	16900.0	0.722365
$819$	5418.00	0.231160
$820$	0	0
$821$	−21426.0	−0.910807	−0.455404	−	0.890285i	$-0.650505\pi$
$821$	−21426.0	−0.910807	−0.455404	+	0.890285i	$0.650505\pi$
$822$	11988.0	0.508673
$823$	30888.0	1.30825	0.654124	−	0.756387i	$-0.273037\pi$
$823$	30888.0	1.30825	0.654124	+	0.756387i	$0.273037\pi$
$824$	−12160.0	−0.514094
$825$	0	0
$826$	4312.00	0.181639
$827$	−11632.0	−0.489098	−0.244549	−	0.969637i	$-0.578640\pi$
$827$	−11632.0	−0.489098	−0.244549	+	0.969637i	$0.578640\pi$
$828$	−5040.00	−0.211536
$829$	4174.00	0.174872	0.0874361	−	0.996170i	$-0.472133\pi$
$829$	4174.00	0.174872	0.0874361	+	0.996170i	$0.472133\pi$
$830$	0	0
$831$	−12702.0	−0.530238
$832$	5504.00	0.229347
$833$	3234.00	0.134516
$834$	−10272.0	−0.426487
$835$	0	0
$836$	−5376.00	−0.222408
$837$	7668.00	0.316661
$838$	−19544.0	−0.805652
$839$	−20744.0	−0.853590	−0.426795	−	0.904348i	$-0.640357\pi$
$839$	−20744.0	−0.853590	−0.426795	+	0.904348i	$0.640357\pi$
$840$	0	0
$841$	−23233.0	−0.952602
$842$	−580.000	−0.0237389
$843$	114.000	0.00465761
$844$	−3952.00	−0.161177
$845$	0	0
$846$	8064.00	0.327714
$847$	−3829.00	−0.155332
$848$	1504.00	0.0609052
$849$	5124.00	0.207132
$850$	0	0
$851$	−48440.0	−1.95124
$852$	−4032.00	−0.162129
$853$	27590.0	1.10746	0.553730	−	0.832696i	$-0.313204\pi$
$853$	27590.0	1.10746	0.553730	+	0.832696i	$0.313204\pi$
$854$	7140.00	0.286096
$855$	0	0
$856$	3328.00	0.132884
$857$	32170.0	1.28227	0.641136	−	0.767428i	$-0.278464\pi$
$857$	32170.0	1.28227	0.641136	+	0.767428i	$0.278464\pi$
$858$	−14448.0	−0.574879
$859$	46656.0	1.85318	0.926590	−	0.376072i	$-0.122726\pi$
$859$	46656.0	1.85318	0.926590	+	0.376072i	$0.122726\pi$
$860$	0	0
$861$	5754.00	0.227754
$862$	−22512.0	−0.889515
$863$	28204.0	1.11249	0.556243	−	0.831020i	$-0.312242\pi$
$863$	28204.0	1.11249	0.556243	+	0.831020i	$0.312242\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	18196.0	0.714001
$867$	1671.00	0.0654558
$868$	−7952.00	−0.310954
$869$	448.000	0.0174883
$870$	0	0
$871$	13416.0	0.521910
$872$	9648.00	0.374682
$873$	−990.000	−0.0383808
$874$	13440.0	0.520154
$875$	0	0
$876$	−14040.0	−0.541516
$877$	2194.00	0.0844768	0.0422384	−	0.999108i	$-0.486551\pi$
$877$	2194.00	0.0844768	0.0422384	+	0.999108i	$0.486551\pi$
$878$	−12632.0	−0.485546
$879$	−4266.00	−0.163696
$880$	0	0
$881$	50174.0	1.91873	0.959367	−	0.282161i	$-0.0910511\pi$
$881$	50174.0	1.91873	0.959367	+	0.282161i	$0.0910511\pi$
$882$	882.000	0.0336718
$883$	4596.00	0.175162	0.0875808	−	0.996157i	$-0.472086\pi$
$883$	4596.00	0.175162	0.0875808	+	0.996157i	$0.472086\pi$
$884$	22704.0	0.863821
$885$	0	0
$886$	−8224.00	−0.311841
$887$	−39928.0	−1.51144	−0.755722	−	0.654892i	$-0.772714\pi$
$887$	−39928.0	−1.51144	−0.755722	+	0.654892i	$0.772714\pi$
$888$	−8304.00	−0.313811
$889$	8288.00	0.312678
$890$	0	0
$891$	2268.00	0.0852759
$892$	22368.0	0.839614
$893$	−21504.0	−0.805827
$894$	8892.00	0.332654
$895$	0	0
$896$	896.000	0.0334077
$897$	36120.0	1.34449
$898$	−5500.00	−0.204385
$899$	9656.00	0.358227
$900$	0	0
$901$	6204.00	0.229395
$902$	−15344.0	−0.566407
$903$	−84.0000	−0.00309562
$904$	−6576.00	−0.241941
$905$	0	0
$906$	16272.0	0.596690
$907$	−39908.0	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−39908.0	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	19856.0	0.725710
$909$	−7830.00	−0.285704
$910$	0	0
$911$	−30064.0	−1.09338	−0.546688	−	0.837337i	$-0.684111\pi$
$911$	−30064.0	−1.09338	−0.546688	+	0.837337i	$0.684111\pi$
$912$	2304.00	0.0836547
$913$	−21616.0	−0.783554
$914$	33468.0	1.21118
$915$	0	0
$916$	16376.0	0.590697
$917$	12740.0	0.458792
$918$	−3564.00	−0.128137
$919$	−2496.00	−0.0895924	−0.0447962	−	0.998996i	$-0.514264\pi$
$919$	−2496.00	−0.0895924	−0.0447962	+	0.998996i	$0.514264\pi$
$920$	0	0
$921$	−2748.00	−0.0983167
$922$	−444.000	−0.0158594
$923$	28896.0	1.03047
$924$	−2352.00	−0.0837393
$925$	0	0
$926$	22688.0	0.805155
$927$	−13680.0	−0.484693
$928$	−1088.00	−0.0384864
$929$	−5322.00	−0.187954	−0.0939769	−	0.995574i	$-0.529958\pi$
$929$	−5322.00	−0.187954	−0.0939769	+	0.995574i	$0.529958\pi$
$930$	0	0
$931$	−2352.00	−0.0827967
$932$	−8088.00	−0.284261
$933$	18144.0	0.636664
$934$	−35256.0	−1.23513
$935$	0	0
$936$	6192.00	0.216231
$937$	1818.00	0.0633847	0.0316924	−	0.999498i	$-0.489910\pi$
$937$	1818.00	0.0633847	0.0316924	+	0.999498i	$0.489910\pi$
$938$	2184.00	0.0760236
$939$	28170.0	0.979013
$940$	0	0
$941$	−43206.0	−1.49679	−0.748393	−	0.663256i	$-0.769174\pi$
$941$	−43206.0	−1.49679	−0.748393	+	0.663256i	$0.769174\pi$
$942$	3900.00	0.134893
$943$	38360.0	1.32468
$944$	4928.00	0.169908
$945$	0	0
$946$	224.000	0.00769859
$947$	−43136.0	−1.48018	−0.740091	−	0.672507i	$-0.765217\pi$
$947$	−43136.0	−1.48018	−0.740091	+	0.672507i	$0.765217\pi$
$948$	−192.000	−0.00657792
$949$	100620.	3.44179
$950$	0	0
$951$	30222.0	1.03051
$952$	3696.00	0.125828
$953$	−4094.00	−0.139158	−0.0695790	−	0.997576i	$-0.522166\pi$
$953$	−4094.00	−0.139158	−0.0695790	+	0.997576i	$0.522166\pi$
$954$	1692.00	0.0574219
$955$	0	0
$956$	7488.00	0.253326
$957$	2856.00	0.0964696
$958$	−13136.0	−0.443011
$959$	−13986.0	−0.470940
$960$	0	0
$961$	50865.0	1.70739
$962$	59512.0	1.99454
$963$	3744.00	0.125284
$964$	−25400.0	−0.848630
$965$	0	0
$966$	5880.00	0.195845
$967$	42032.0	1.39778	0.698892	−	0.715227i	$-0.253677\pi$
$967$	42032.0	1.39778	0.698892	+	0.715227i	$0.253677\pi$
$968$	−4376.00	−0.145300
$969$	9504.00	0.315080
$970$	0	0
$971$	5244.00	0.173314	0.0866570	−	0.996238i	$-0.472382\pi$
$971$	5244.00	0.173314	0.0866570	+	0.996238i	$0.472382\pi$
$972$	−972.000	−0.0320750
$973$	11984.0	0.394850
$974$	10304.0	0.338975
$975$	0	0
$976$	8160.00	0.267618
$977$	28434.0	0.931100	0.465550	−	0.885022i	$-0.345857\pi$
$977$	28434.0	0.931100	0.465550	+	0.885022i	$0.345857\pi$
$978$	−11640.0	−0.380579
$979$	45640.0	1.48995
$980$	0	0
$981$	10854.0	0.353253
$982$	37736.0	1.22628
$983$	−3344.00	−0.108502	−0.0542508	−	0.998527i	$-0.517277\pi$
$983$	−3344.00	−0.108502	−0.0542508	+	0.998527i	$0.517277\pi$
$984$	6576.00	0.213044
$985$	0	0
$986$	−4488.00	−0.144956
$987$	−9408.00	−0.303404
$988$	−16512.0	−0.531697
$989$	−560.000	−0.0180050
$990$	0	0
$991$	26200.0	0.839829	0.419914	−	0.907564i	$-0.362060\pi$
$991$	26200.0	0.839829	0.419914	+	0.907564i	$0.362060\pi$
$992$	−9088.00	−0.290871
$993$	4620.00	0.147645
$994$	4704.00	0.150102
$995$	0	0
$996$	9264.00	0.294720
$997$	−56666.0	−1.80003	−0.900015	−	0.435859i	$-0.856445\pi$
$997$	−56666.0	−1.80003	−0.900015	+	0.435859i	$0.856445\pi$
$998$	8216.00	0.260594
$999$	−9342.00	−0.295864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.4.a.q.1.1		1
5.2	odd	4		1050.4.g.i.799.2		2
5.3	odd	4		1050.4.g.i.799.1		2
5.4	even	2		210.4.a.d.1.1	✓	1
15.14	odd	2		630.4.a.t.1.1		1
20.19	odd	2		1680.4.a.d.1.1		1
35.34	odd	2		1470.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.d.1.1	✓	1	5.4	even	2
630.4.a.t.1.1		1	15.14	odd	2
1050.4.a.q.1.1		1	1.1	even	1	trivial
1050.4.g.i.799.1		2	5.3	odd	4
1050.4.g.i.799.2		2	5.2	odd	4
1470.4.a.h.1.1		1	35.34	odd	2
1680.4.a.d.1.1		1	20.19	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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