LMFDB - Embedded newform 1450.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,4,Mod(1,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1450.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:	$85.5527695083$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} -4.00000 q^{6} +32.0000 q^{7} +8.00000 q^{8} -23.0000 q^{9} +12.0000 q^{11} -8.00000 q^{12} -22.0000 q^{13} +64.0000 q^{14} +16.0000 q^{16} -104.000 q^{17} -46.0000 q^{18} +12.0000 q^{19} -64.0000 q^{21} +24.0000 q^{22} -212.000 q^{23} -16.0000 q^{24} -44.0000 q^{26} +100.000 q^{27} +128.000 q^{28} -29.0000 q^{29} +52.0000 q^{31} +32.0000 q^{32} -24.0000 q^{33} -208.000 q^{34} -92.0000 q^{36} +24.0000 q^{38} +44.0000 q^{39} -354.000 q^{41} -128.000 q^{42} -526.000 q^{43} +48.0000 q^{44} -424.000 q^{46} +58.0000 q^{47} -32.0000 q^{48} +681.000 q^{49} +208.000 q^{51} -88.0000 q^{52} -314.000 q^{53} +200.000 q^{54} +256.000 q^{56} -24.0000 q^{57} -58.0000 q^{58} -692.000 q^{59} +730.000 q^{61} +104.000 q^{62} -736.000 q^{63} +64.0000 q^{64} -48.0000 q^{66} +140.000 q^{67} -416.000 q^{68} +424.000 q^{69} +696.000 q^{71} -184.000 q^{72} +404.000 q^{73} +48.0000 q^{76} +384.000 q^{77} +88.0000 q^{78} +116.000 q^{79} +421.000 q^{81} -708.000 q^{82} +172.000 q^{83} -256.000 q^{84} -1052.00 q^{86} +58.0000 q^{87} +96.0000 q^{88} -42.0000 q^{89} -704.000 q^{91} -848.000 q^{92} -104.000 q^{93} +116.000 q^{94} -64.0000 q^{96} -176.000 q^{97} +1362.00 q^{98} -276.000 q^{99} +O(q^{100})\)

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
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−4.00000	−0.272166
$7$	32.0000	1.72784	0.863919	−	0.503631i	$-0.168003\pi$
$7$	32.0000	1.72784	0.863919	+	0.503631i	$0.168003\pi$
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	0	0
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	−8.00000	−0.192450
$13$	−22.0000	−0.469362	−0.234681	−	0.972072i	$-0.575405\pi$
$13$	−22.0000	−0.469362	−0.234681	+	0.972072i	$0.575405\pi$
$14$	64.0000	1.22177
$15$	0	0
$16$	16.0000	0.250000
$17$	−104.000	−1.48375	−0.741874	−	0.670540i	$-0.766063\pi$
$17$	−104.000	−1.48375	−0.741874	+	0.670540i	$0.766063\pi$
$18$	−46.0000	−0.602350
$19$	12.0000	0.144894	0.0724471	−	0.997372i	$-0.476919\pi$
$19$	12.0000	0.144894	0.0724471	+	0.997372i	$0.476919\pi$
$20$	0	0
$21$	−64.0000	−0.665045
$22$	24.0000	0.232583
$23$	−212.000	−1.92196	−0.960979	−	0.276620i	$-0.910786\pi$
$23$	−212.000	−1.92196	−0.960979	+	0.276620i	$0.910786\pi$
$24$	−16.0000	−0.136083
$25$	0	0
$26$	−44.0000	−0.331889
$27$	100.000	0.712778
$28$	128.000	0.863919
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	0	0
$31$	52.0000	0.301273	0.150637	−	0.988589i	$-0.451868\pi$
$31$	52.0000	0.301273	0.150637	+	0.988589i	$0.451868\pi$
$32$	32.0000	0.176777
$33$	−24.0000	−0.126602
$34$	−208.000	−1.04917
$35$	0	0
$36$	−92.0000	−0.425926
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	24.0000	0.102456
$39$	44.0000	0.180657
$40$	0	0
$41$	−354.000	−1.34843	−0.674214	−	0.738536i	$-0.735517\pi$
$41$	−354.000	−1.34843	−0.674214	+	0.738536i	$0.735517\pi$
$42$	−128.000	−0.470258
$43$	−526.000	−1.86545	−0.932724	−	0.360592i	$-0.882575\pi$
$43$	−526.000	−1.86545	−0.932724	+	0.360592i	$0.882575\pi$
$44$	48.0000	0.164461
$45$	0	0
$46$	−424.000	−1.35903
$47$	58.0000	0.180004	0.0900018	−	0.995942i	$-0.471313\pi$
$47$	58.0000	0.180004	0.0900018	+	0.995942i	$0.471313\pi$
$48$	−32.0000	−0.0962250
$49$	681.000	1.98542
$50$	0	0
$51$	208.000	0.571095
$52$	−88.0000	−0.234681
$53$	−314.000	−0.813797	−0.406898	−	0.913473i	$-0.633390\pi$
$53$	−314.000	−0.813797	−0.406898	+	0.913473i	$0.633390\pi$
$54$	200.000	0.504010
$55$	0	0
$56$	256.000	0.610883
$57$	−24.0000	−0.0557698
$58$	−58.0000	−0.131306
$59$	−692.000	−1.52696	−0.763481	−	0.645831i	$-0.776511\pi$
$59$	−692.000	−1.52696	−0.763481	+	0.645831i	$0.776511\pi$
$60$	0	0
$61$	730.000	1.53224	0.766122	−	0.642695i	$-0.222184\pi$
$61$	730.000	1.53224	0.766122	+	0.642695i	$0.222184\pi$
$62$	104.000	0.213032
$63$	−736.000	−1.47186
$64$	64.0000	0.125000
$65$	0	0
$66$	−48.0000	−0.0895211
$67$	140.000	0.255279	0.127640	−	0.991821i	$-0.459260\pi$
$67$	140.000	0.255279	0.127640	+	0.991821i	$0.459260\pi$
$68$	−416.000	−0.741874
$69$	424.000	0.739762
$70$	0	0
$71$	696.000	1.16338	0.581690	−	0.813410i	$-0.302392\pi$
$71$	696.000	1.16338	0.581690	+	0.813410i	$0.302392\pi$
$72$	−184.000	−0.301175
$73$	404.000	0.647735	0.323867	−	0.946103i	$-0.395017\pi$
$73$	404.000	0.647735	0.323867	+	0.946103i	$0.395017\pi$
$74$	0	0
$75$	0	0
$76$	48.0000	0.0724471
$77$	384.000	0.568323
$78$	88.0000	0.127744
$79$	116.000	0.165203	0.0826014	−	0.996583i	$-0.473677\pi$
$79$	116.000	0.165203	0.0826014	+	0.996583i	$0.473677\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	−708.000	−0.953482
$83$	172.000	0.227463	0.113732	−	0.993512i	$-0.463720\pi$
$83$	172.000	0.227463	0.113732	+	0.993512i	$0.463720\pi$
$84$	−256.000	−0.332522
$85$	0	0
$86$	−1052.00	−1.31907
$87$	58.0000	0.0714742
$88$	96.0000	0.116291
$89$	−42.0000	−0.0500224	−0.0250112	−	0.999687i	$-0.507962\pi$
$89$	−42.0000	−0.0500224	−0.0250112	+	0.999687i	$0.507962\pi$
$90$	0	0
$91$	−704.000	−0.810981
$92$	−848.000	−0.960979
$93$	−104.000	−0.115960
$94$	116.000	0.127282
$95$	0	0
$96$	−64.0000	−0.0680414
$97$	−176.000	−0.184228	−0.0921139	−	0.995748i	$-0.529362\pi$
$97$	−176.000	−0.184228	−0.0921139	+	0.995748i	$0.529362\pi$
$98$	1362.00	1.40391
$99$	−276.000	−0.280192
$100$	0	0
$101$	−1330.00	−1.31030	−0.655148	−	0.755500i	$-0.727394\pi$
$101$	−1330.00	−1.31030	−0.655148	+	0.755500i	$0.727394\pi$
$102$	416.000	0.403825
$103$	−1052.00	−1.00638	−0.503188	−	0.864177i	$-0.667840\pi$
$103$	−1052.00	−1.00638	−0.503188	+	0.864177i	$0.667840\pi$
$104$	−176.000	−0.165944
$105$	0	0
$106$	−628.000	−0.575441
$107$	−1924.00	−1.73832	−0.869159	−	0.494532i	$-0.835339\pi$
$107$	−1924.00	−1.73832	−0.869159	+	0.494532i	$0.835339\pi$
$108$	400.000	0.356389
$109$	1254.00	1.10194	0.550970	−	0.834525i	$-0.314258\pi$
$109$	1254.00	1.10194	0.550970	+	0.834525i	$0.314258\pi$
$110$	0	0
$111$	0	0
$112$	512.000	0.431959
$113$	−148.000	−0.123209	−0.0616047	−	0.998101i	$-0.519622\pi$
$113$	−148.000	−0.123209	−0.0616047	+	0.998101i	$0.519622\pi$
$114$	−48.0000	−0.0394352
$115$	0	0
$116$	−116.000	−0.0928477
$117$	506.000	0.399827
$118$	−1384.00	−1.07972
$119$	−3328.00	−2.56367
$120$	0	0
$121$	−1187.00	−0.891811
$122$	1460.00	1.08346
$123$	708.000	0.519010
$124$	208.000	0.150637
$125$	0	0
$126$	−1472.00	−1.04076
$127$	650.000	0.454159	0.227079	−	0.973876i	$-0.427082\pi$
$127$	650.000	0.454159	0.227079	+	0.973876i	$0.427082\pi$
$128$	128.000	0.0883883
$129$	1052.00	0.718011
$130$	0	0
$131$	−1072.00	−0.714970	−0.357485	−	0.933919i	$-0.616366\pi$
$131$	−1072.00	−0.714970	−0.357485	+	0.933919i	$0.616366\pi$
$132$	−96.0000	−0.0633010
$133$	384.000	0.250354
$134$	280.000	0.180510
$135$	0	0
$136$	−832.000	−0.524584
$137$	2208.00	1.37695	0.688475	−	0.725260i	$-0.258280\pi$
$137$	2208.00	1.37695	0.688475	+	0.725260i	$0.258280\pi$
$138$	848.000	0.523091
$139$	2908.00	1.77448	0.887242	−	0.461304i	$-0.152618\pi$
$139$	2908.00	1.77448	0.887242	+	0.461304i	$0.152618\pi$
$140$	0	0
$141$	−116.000	−0.0692834
$142$	1392.00	0.822634
$143$	−264.000	−0.154383
$144$	−368.000	−0.212963
$145$	0	0
$146$	808.000	0.458018
$147$	−1362.00	−0.764190
$148$	0	0
$149$	1838.00	1.01057	0.505285	−	0.862953i	$-0.331387\pi$
$149$	1838.00	1.01057	0.505285	+	0.862953i	$0.331387\pi$
$150$	0	0
$151$	−2544.00	−1.37104	−0.685522	−	0.728051i	$-0.740426\pi$
$151$	−2544.00	−1.37104	−0.685522	+	0.728051i	$0.740426\pi$
$152$	96.0000	0.0512278
$153$	2392.00	1.26393
$154$	768.000	0.401865
$155$	0	0
$156$	176.000	0.0903287
$157$	−2956.00	−1.50264	−0.751320	−	0.659938i	$-0.770583\pi$
$157$	−2956.00	−1.50264	−0.751320	+	0.659938i	$0.770583\pi$
$158$	232.000	0.116816
$159$	628.000	0.313230
$160$	0	0
$161$	−6784.00	−3.32083
$162$	842.000	0.408357
$163$	−722.000	−0.346941	−0.173471	−	0.984839i	$-0.555498\pi$
$163$	−722.000	−0.346941	−0.173471	+	0.984839i	$0.555498\pi$
$164$	−1416.00	−0.674214
$165$	0	0
$166$	344.000	0.160841
$167$	−2408.00	−1.11579	−0.557894	−	0.829912i	$-0.688390\pi$
$167$	−2408.00	−1.11579	−0.557894	+	0.829912i	$0.688390\pi$
$168$	−512.000	−0.235129
$169$	−1713.00	−0.779700
$170$	0	0
$171$	−276.000	−0.123428
$172$	−2104.00	−0.932724
$173$	362.000	0.159089	0.0795444	−	0.996831i	$-0.474653\pi$
$173$	362.000	0.159089	0.0795444	+	0.996831i	$0.474653\pi$
$174$	116.000	0.0505399
$175$	0	0
$176$	192.000	0.0822304
$177$	1384.00	0.587728
$178$	−84.0000	−0.0353712
$179$	−2340.00	−0.977094	−0.488547	−	0.872538i	$-0.662473\pi$
$179$	−2340.00	−0.977094	−0.488547	+	0.872538i	$0.662473\pi$
$180$	0	0
$181$	650.000	0.266929	0.133464	−	0.991054i	$-0.457390\pi$
$181$	650.000	0.266929	0.133464	+	0.991054i	$0.457390\pi$
$182$	−1408.00	−0.573450
$183$	−1460.00	−0.589761
$184$	−1696.00	−0.679515
$185$	0	0
$186$	−208.000	−0.0819962
$187$	−1248.00	−0.488036
$188$	232.000	0.0900018
$189$	3200.00	1.23156
$190$	0	0
$191$	−1176.00	−0.445510	−0.222755	−	0.974874i	$-0.571505\pi$
$191$	−1176.00	−0.445510	−0.222755	+	0.974874i	$0.571505\pi$
$192$	−128.000	−0.0481125
$193$	−4740.00	−1.76784	−0.883919	−	0.467640i	$-0.845104\pi$
$193$	−4740.00	−1.76784	−0.883919	+	0.467640i	$0.845104\pi$
$194$	−352.000	−0.130269
$195$	0	0
$196$	2724.00	0.992711
$197$	−4286.00	−1.55008	−0.775038	−	0.631915i	$-0.782269\pi$
$197$	−4286.00	−1.55008	−0.775038	+	0.631915i	$0.782269\pi$
$198$	−552.000	−0.198126
$199$	3736.00	1.33084	0.665422	−	0.746467i	$-0.268252\pi$
$199$	3736.00	1.33084	0.665422	+	0.746467i	$0.268252\pi$
$200$	0	0
$201$	−280.000	−0.0982571
$202$	−2660.00	−0.926520
$203$	−928.000	−0.320851
$204$	832.000	0.285547
$205$	0	0
$206$	−2104.00	−0.711615
$207$	4876.00	1.63722
$208$	−352.000	−0.117340
$209$	144.000	0.0476588
$210$	0	0
$211$	−1828.00	−0.596420	−0.298210	−	0.954500i	$-0.596390\pi$
$211$	−1828.00	−0.596420	−0.298210	+	0.954500i	$0.596390\pi$
$212$	−1256.00	−0.406898
$213$	−1392.00	−0.447785
$214$	−3848.00	−1.22918
$215$	0	0
$216$	800.000	0.252005
$217$	1664.00	0.520552
$218$	2508.00	0.779189
$219$	−808.000	−0.249313
$220$	0	0
$221$	2288.00	0.696414
$222$	0	0
$223$	−3068.00	−0.921294	−0.460647	−	0.887584i	$-0.652383\pi$
$223$	−3068.00	−0.921294	−0.460647	+	0.887584i	$0.652383\pi$
$224$	1024.00	0.305441
$225$	0	0
$226$	−296.000	−0.0871222
$227$	−4584.00	−1.34031	−0.670156	−	0.742220i	$-0.733773\pi$
$227$	−4584.00	−1.34031	−0.670156	+	0.742220i	$0.733773\pi$
$228$	−96.0000	−0.0278849
$229$	−206.000	−0.0594448	−0.0297224	−	0.999558i	$-0.509462\pi$
$229$	−206.000	−0.0594448	−0.0297224	+	0.999558i	$0.509462\pi$
$230$	0	0
$231$	−768.000	−0.218748
$232$	−232.000	−0.0656532
$233$	5822.00	1.63696	0.818480	−	0.574534i	$-0.194817\pi$
$233$	5822.00	1.63696	0.818480	+	0.574534i	$0.194817\pi$
$234$	1012.00	0.282720
$235$	0	0
$236$	−2768.00	−0.763481
$237$	−232.000	−0.0635866
$238$	−6656.00	−1.81279
$239$	216.000	0.0584597	0.0292299	−	0.999573i	$-0.490695\pi$
$239$	216.000	0.0584597	0.0292299	+	0.999573i	$0.490695\pi$
$240$	0	0
$241$	−418.000	−0.111725	−0.0558625	−	0.998438i	$-0.517791\pi$
$241$	−418.000	−0.111725	−0.0558625	+	0.998438i	$0.517791\pi$
$242$	−2374.00	−0.630605
$243$	−3542.00	−0.935059
$244$	2920.00	0.766122
$245$	0	0
$246$	1416.00	0.366995
$247$	−264.000	−0.0680078
$248$	416.000	0.106516
$249$	−344.000	−0.0875507
$250$	0	0
$251$	1716.00	0.431526	0.215763	−	0.976446i	$-0.430776\pi$
$251$	1716.00	0.431526	0.215763	+	0.976446i	$0.430776\pi$
$252$	−2944.00	−0.735931
$253$	−2544.00	−0.632174
$254$	1300.00	0.321139
$255$	0	0
$256$	256.000	0.0625000
$257$	2882.00	0.699511	0.349755	−	0.936841i	$-0.386265\pi$
$257$	2882.00	0.699511	0.349755	+	0.936841i	$0.386265\pi$
$258$	2104.00	0.507711
$259$	0	0
$260$	0	0
$261$	667.000	0.158185
$262$	−2144.00	−0.505560
$263$	−1254.00	−0.294011	−0.147006	−	0.989136i	$-0.546964\pi$
$263$	−1254.00	−0.294011	−0.147006	+	0.989136i	$0.546964\pi$
$264$	−192.000	−0.0447605
$265$	0	0
$266$	768.000	0.177027
$267$	84.0000	0.0192536
$268$	560.000	0.127640
$269$	−4114.00	−0.932472	−0.466236	−	0.884660i	$-0.654390\pi$
$269$	−4114.00	−0.932472	−0.466236	+	0.884660i	$0.654390\pi$
$270$	0	0
$271$	3160.00	0.708326	0.354163	−	0.935184i	$-0.384766\pi$
$271$	3160.00	0.708326	0.354163	+	0.935184i	$0.384766\pi$
$272$	−1664.00	−0.370937
$273$	1408.00	0.312147
$274$	4416.00	0.973651
$275$	0	0
$276$	1696.00	0.369881
$277$	5750.00	1.24723	0.623617	−	0.781730i	$-0.285662\pi$
$277$	5750.00	1.24723	0.623617	+	0.781730i	$0.285662\pi$
$278$	5816.00	1.25475
$279$	−1196.00	−0.256640
$280$	0	0
$281$	170.000	0.0360902	0.0180451	−	0.999837i	$-0.494256\pi$
$281$	170.000	0.0360902	0.0180451	+	0.999837i	$0.494256\pi$
$282$	−232.000	−0.0489908
$283$	1692.00	0.355403	0.177701	−	0.984084i	$-0.443134\pi$
$283$	1692.00	0.355403	0.177701	+	0.984084i	$0.443134\pi$
$284$	2784.00	0.581690
$285$	0	0
$286$	−528.000	−0.109165
$287$	−11328.0	−2.32986
$288$	−736.000	−0.150588
$289$	5903.00	1.20151
$290$	0	0
$291$	352.000	0.0709093
$292$	1616.00	0.323867
$293$	5868.00	1.17001	0.585004	−	0.811031i	$-0.301093\pi$
$293$	5868.00	1.17001	0.585004	+	0.811031i	$0.301093\pi$
$294$	−2724.00	−0.540364
$295$	0	0
$296$	0	0
$297$	1200.00	0.234448
$298$	3676.00	0.714580
$299$	4664.00	0.902094
$300$	0	0
$301$	−16832.0	−3.22319
$302$	−5088.00	−0.969475
$303$	2660.00	0.504333
$304$	192.000	0.0362235
$305$	0	0
$306$	4784.00	0.893736
$307$	−5922.00	−1.10093	−0.550466	−	0.834857i	$-0.685550\pi$
$307$	−5922.00	−1.10093	−0.550466	+	0.834857i	$0.685550\pi$
$308$	1536.00	0.284161
$309$	2104.00	0.387354
$310$	0	0
$311$	9468.00	1.72631	0.863153	−	0.504943i	$-0.168486\pi$
$311$	9468.00	1.72631	0.863153	+	0.504943i	$0.168486\pi$
$312$	352.000	0.0638720
$313$	7290.00	1.31647	0.658235	−	0.752812i	$-0.271303\pi$
$313$	7290.00	1.31647	0.658235	+	0.752812i	$0.271303\pi$
$314$	−5912.00	−1.06253
$315$	0	0
$316$	464.000	0.0826014
$317$	5048.00	0.894397	0.447199	−	0.894435i	$-0.352422\pi$
$317$	5048.00	0.894397	0.447199	+	0.894435i	$0.352422\pi$
$318$	1256.00	0.221487
$319$	−348.000	−0.0610792
$320$	0	0
$321$	3848.00	0.669079
$322$	−13568.0	−2.34818
$323$	−1248.00	−0.214986
$324$	1684.00	0.288752
$325$	0	0
$326$	−1444.00	−0.245324
$327$	−2508.00	−0.424137
$328$	−2832.00	−0.476741
$329$	1856.00	0.311017
$330$	0	0
$331$	4872.00	0.809031	0.404516	−	0.914531i	$-0.367440\pi$
$331$	4872.00	0.809031	0.404516	+	0.914531i	$0.367440\pi$
$332$	688.000	0.113732
$333$	0	0
$334$	−4816.00	−0.788981
$335$	0	0
$336$	−1024.00	−0.166261
$337$	−3240.00	−0.523721	−0.261861	−	0.965106i	$-0.584336\pi$
$337$	−3240.00	−0.523721	−0.261861	+	0.965106i	$0.584336\pi$
$338$	−3426.00	−0.551331
$339$	296.000	0.0474233
$340$	0	0
$341$	624.000	0.0990953
$342$	−552.000	−0.0872770
$343$	10816.0	1.70265
$344$	−4208.00	−0.659535
$345$	0	0
$346$	724.000	0.112493
$347$	6152.00	0.951748	0.475874	−	0.879513i	$-0.342132\pi$
$347$	6152.00	0.951748	0.475874	+	0.879513i	$0.342132\pi$
$348$	232.000	0.0357371
$349$	−6662.00	−1.02180	−0.510901	−	0.859640i	$-0.670688\pi$
$349$	−6662.00	−1.02180	−0.510901	+	0.859640i	$0.670688\pi$
$350$	0	0
$351$	−2200.00	−0.334551
$352$	384.000	0.0581456
$353$	6926.00	1.04429	0.522144	−	0.852857i	$-0.325132\pi$
$353$	6926.00	1.04429	0.522144	+	0.852857i	$0.325132\pi$
$354$	2768.00	0.415586
$355$	0	0
$356$	−168.000	−0.0250112
$357$	6656.00	0.986759
$358$	−4680.00	−0.690910
$359$	3704.00	0.544539	0.272270	−	0.962221i	$-0.412226\pi$
$359$	3704.00	0.544539	0.272270	+	0.962221i	$0.412226\pi$
$360$	0	0
$361$	−6715.00	−0.979006
$362$	1300.00	0.188747
$363$	2374.00	0.343258
$364$	−2816.00	−0.405490
$365$	0	0
$366$	−2920.00	−0.417024
$367$	1430.00	0.203393	0.101697	−	0.994815i	$-0.467573\pi$
$367$	1430.00	0.203393	0.101697	+	0.994815i	$0.467573\pi$
$368$	−3392.00	−0.480490
$369$	8142.00	1.14866
$370$	0	0
$371$	−10048.0	−1.40611
$372$	−416.000	−0.0579801
$373$	−2718.00	−0.377299	−0.188650	−	0.982044i	$-0.560411\pi$
$373$	−2718.00	−0.377299	−0.188650	+	0.982044i	$0.560411\pi$
$374$	−2496.00	−0.345094
$375$	0	0
$376$	464.000	0.0636409
$377$	638.000	0.0871583
$378$	6400.00	0.870848
$379$	8104.00	1.09835	0.549175	−	0.835707i	$-0.314942\pi$
$379$	8104.00	1.09835	0.549175	+	0.835707i	$0.314942\pi$
$380$	0	0
$381$	−1300.00	−0.174806
$382$	−2352.00	−0.315023
$383$	−10884.0	−1.45208	−0.726040	−	0.687653i	$-0.758641\pi$
$383$	−10884.0	−1.45208	−0.726040	+	0.687653i	$0.758641\pi$
$384$	−256.000	−0.0340207
$385$	0	0
$386$	−9480.00	−1.25005
$387$	12098.0	1.58909
$388$	−704.000	−0.0921139
$389$	−5146.00	−0.670726	−0.335363	−	0.942089i	$-0.608859\pi$
$389$	−5146.00	−0.670726	−0.335363	+	0.942089i	$0.608859\pi$
$390$	0	0
$391$	22048.0	2.85170
$392$	5448.00	0.701953
$393$	2144.00	0.275192
$394$	−8572.00	−1.09607
$395$	0	0
$396$	−1104.00	−0.140096
$397$	2818.00	0.356250	0.178125	−	0.984008i	$-0.442997\pi$
$397$	2818.00	0.356250	0.178125	+	0.984008i	$0.442997\pi$
$398$	7472.00	0.941049
$399$	−768.000	−0.0963611
$400$	0	0
$401$	−3594.00	−0.447571	−0.223785	−	0.974638i	$-0.571841\pi$
$401$	−3594.00	−0.447571	−0.223785	+	0.974638i	$0.571841\pi$
$402$	−560.000	−0.0694783
$403$	−1144.00	−0.141406
$404$	−5320.00	−0.655148
$405$	0	0
$406$	−1856.00	−0.226876
$407$	0	0
$408$	1664.00	0.201912
$409$	7242.00	0.875535	0.437768	−	0.899088i	$-0.355769\pi$
$409$	7242.00	0.875535	0.437768	+	0.899088i	$0.355769\pi$
$410$	0	0
$411$	−4416.00	−0.529988
$412$	−4208.00	−0.503188
$413$	−22144.0	−2.63834
$414$	9752.00	1.15769
$415$	0	0
$416$	−704.000	−0.0829722
$417$	−5816.00	−0.682999
$418$	288.000	0.0336999
$419$	156.000	0.0181888	0.00909439	−	0.999959i	$-0.497105\pi$
$419$	156.000	0.0181888	0.00909439	+	0.999959i	$0.497105\pi$
$420$	0	0
$421$	13250.0	1.53388	0.766942	−	0.641716i	$-0.221777\pi$
$421$	13250.0	1.53388	0.766942	+	0.641716i	$0.221777\pi$
$422$	−3656.00	−0.421733
$423$	−1334.00	−0.153336
$424$	−2512.00	−0.287721
$425$	0	0
$426$	−2784.00	−0.316632
$427$	23360.0	2.64747
$428$	−7696.00	−0.869159
$429$	528.000	0.0594221
$430$	0	0
$431$	12880.0	1.43946	0.719731	−	0.694253i	$-0.244265\pi$
$431$	12880.0	1.43946	0.719731	+	0.694253i	$0.244265\pi$
$432$	1600.00	0.178195
$433$	−2144.00	−0.237954	−0.118977	−	0.992897i	$-0.537961\pi$
$433$	−2144.00	−0.237954	−0.118977	+	0.992897i	$0.537961\pi$
$434$	3328.00	0.368086
$435$	0	0
$436$	5016.00	0.550970
$437$	−2544.00	−0.278481
$438$	−1616.00	−0.176291
$439$	−4248.00	−0.461836	−0.230918	−	0.972973i	$-0.574173\pi$
$439$	−4248.00	−0.461836	−0.230918	+	0.972973i	$0.574173\pi$
$440$	0	0
$441$	−15663.0	−1.69129
$442$	4576.00	0.492439
$443$	−16310.0	−1.74924	−0.874618	−	0.484813i	$-0.838888\pi$
$443$	−16310.0	−1.74924	−0.874618	+	0.484813i	$0.838888\pi$
$444$	0	0
$445$	0	0
$446$	−6136.00	−0.651453
$447$	−3676.00	−0.388968
$448$	2048.00	0.215980
$449$	−11262.0	−1.18371	−0.591856	−	0.806044i	$-0.701605\pi$
$449$	−11262.0	−1.18371	−0.591856	+	0.806044i	$0.701605\pi$
$450$	0	0
$451$	−4248.00	−0.443527
$452$	−592.000	−0.0616047
$453$	5088.00	0.527715
$454$	−9168.00	−0.947744
$455$	0	0
$456$	−192.000	−0.0197176
$457$	−12018.0	−1.23015	−0.615075	−	0.788469i	$-0.710874\pi$
$457$	−12018.0	−1.23015	−0.615075	+	0.788469i	$0.710874\pi$
$458$	−412.000	−0.0420338
$459$	−10400.0	−1.05758
$460$	0	0
$461$	−90.0000	−0.00909266	−0.00454633	−	0.999990i	$-0.501447\pi$
$461$	−90.0000	−0.00909266	−0.00454633	+	0.999990i	$0.501447\pi$
$462$	−1536.00	−0.154678
$463$	1600.00	0.160601	0.0803005	−	0.996771i	$-0.474412\pi$
$463$	1600.00	0.160601	0.0803005	+	0.996771i	$0.474412\pi$
$464$	−464.000	−0.0464238
$465$	0	0
$466$	11644.0	1.15751
$467$	−570.000	−0.0564806	−0.0282403	−	0.999601i	$-0.508990\pi$
$467$	−570.000	−0.0564806	−0.0282403	+	0.999601i	$0.508990\pi$
$468$	2024.00	0.199913
$469$	4480.00	0.441081
$470$	0	0
$471$	5912.00	0.578366
$472$	−5536.00	−0.539862
$473$	−6312.00	−0.613586
$474$	−464.000	−0.0449625
$475$	0	0
$476$	−13312.0	−1.28184
$477$	7222.00	0.693234
$478$	432.000	0.0413373
$479$	−2652.00	−0.252971	−0.126485	−	0.991968i	$-0.540370\pi$
$479$	−2652.00	−0.252971	−0.126485	+	0.991968i	$0.540370\pi$
$480$	0	0
$481$	0	0
$482$	−836.000	−0.0790016
$483$	13568.0	1.27819
$484$	−4748.00	−0.445905
$485$	0	0
$486$	−7084.00	−0.661187
$487$	11328.0	1.05405	0.527023	−	0.849851i	$-0.323308\pi$
$487$	11328.0	1.05405	0.527023	+	0.849851i	$0.323308\pi$
$488$	5840.00	0.541730
$489$	1444.00	0.133538
$490$	0	0
$491$	−4208.00	−0.386771	−0.193385	−	0.981123i	$-0.561947\pi$
$491$	−4208.00	−0.386771	−0.193385	+	0.981123i	$0.561947\pi$
$492$	2832.00	0.259505
$493$	3016.00	0.275525
$494$	−528.000	−0.0480888
$495$	0	0
$496$	832.000	0.0753184
$497$	22272.0	2.01013
$498$	−688.000	−0.0619077
$499$	14244.0	1.27785	0.638927	−	0.769267i	$-0.279379\pi$
$499$	14244.0	1.27785	0.638927	+	0.769267i	$0.279379\pi$
$500$	0	0
$501$	4816.00	0.429467
$502$	3432.00	0.305135
$503$	19318.0	1.71242	0.856210	−	0.516628i	$-0.172813\pi$
$503$	19318.0	1.71242	0.856210	+	0.516628i	$0.172813\pi$
$504$	−5888.00	−0.520382
$505$	0	0
$506$	−5088.00	−0.447014
$507$	3426.00	0.300107
$508$	2600.00	0.227079
$509$	4686.00	0.408061	0.204031	−	0.978964i	$-0.434596\pi$
$509$	4686.00	0.408061	0.204031	+	0.978964i	$0.434596\pi$
$510$	0	0
$511$	12928.0	1.11918
$512$	512.000	0.0441942
$513$	1200.00	0.103277
$514$	5764.00	0.494629
$515$	0	0
$516$	4208.00	0.359006
$517$	696.000	0.0592071
$518$	0	0
$519$	−724.000	−0.0612333
$520$	0	0
$521$	−16662.0	−1.40110	−0.700552	−	0.713601i	$-0.747063\pi$
$521$	−16662.0	−1.40110	−0.700552	+	0.713601i	$0.747063\pi$
$522$	1334.00	0.111854
$523$	−2992.00	−0.250155	−0.125077	−	0.992147i	$-0.539918\pi$
$523$	−2992.00	−0.250155	−0.125077	+	0.992147i	$0.539918\pi$
$524$	−4288.00	−0.357485
$525$	0	0
$526$	−2508.00	−0.207897
$527$	−5408.00	−0.447014
$528$	−384.000	−0.0316505
$529$	32777.0	2.69393
$530$	0	0
$531$	15916.0	1.30074
$532$	1536.00	0.125177
$533$	7788.00	0.632900
$534$	168.000	0.0136144
$535$	0	0
$536$	1120.00	0.0902549
$537$	4680.00	0.376084
$538$	−8228.00	−0.659357
$539$	8172.00	0.653048
$540$	0	0
$541$	15590.0	1.23894	0.619470	−	0.785020i	$-0.287348\pi$
$541$	15590.0	1.23894	0.619470	+	0.785020i	$0.287348\pi$
$542$	6320.00	0.500862
$543$	−1300.00	−0.102741
$544$	−3328.00	−0.262292
$545$	0	0
$546$	2816.00	0.220721
$547$	−1964.00	−0.153518	−0.0767592	−	0.997050i	$-0.524457\pi$
$547$	−1964.00	−0.153518	−0.0767592	+	0.997050i	$0.524457\pi$
$548$	8832.00	0.688475
$549$	−16790.0	−1.30525
$550$	0	0
$551$	−348.000	−0.0269062
$552$	3392.00	0.261545
$553$	3712.00	0.285444
$554$	11500.0	0.881928
$555$	0	0
$556$	11632.0	0.887242
$557$	766.000	0.0582701	0.0291351	−	0.999575i	$-0.490725\pi$
$557$	766.000	0.0582701	0.0291351	+	0.999575i	$0.490725\pi$
$558$	−2392.00	−0.181472
$559$	11572.0	0.875570
$560$	0	0
$561$	2496.00	0.187845
$562$	340.000	0.0255196
$563$	−16794.0	−1.25716	−0.628581	−	0.777744i	$-0.716364\pi$
$563$	−16794.0	−1.25716	−0.628581	+	0.777744i	$0.716364\pi$
$564$	−464.000	−0.0346417
$565$	0	0
$566$	3384.00	0.251308
$567$	13472.0	0.997832
$568$	5568.00	0.411317
$569$	−12342.0	−0.909321	−0.454660	−	0.890665i	$-0.650239\pi$
$569$	−12342.0	−0.909321	−0.454660	+	0.890665i	$0.650239\pi$
$570$	0	0
$571$	−13356.0	−0.978864	−0.489432	−	0.872042i	$-0.662796\pi$
$571$	−13356.0	−0.978864	−0.489432	+	0.872042i	$0.662796\pi$
$572$	−1056.00	−0.0771916
$573$	2352.00	0.171477
$574$	−22656.0	−1.64746
$575$	0	0
$576$	−1472.00	−0.106481
$577$	−14148.0	−1.02078	−0.510389	−	0.859944i	$-0.670499\pi$
$577$	−14148.0	−1.02078	−0.510389	+	0.859944i	$0.670499\pi$
$578$	11806.0	0.849593
$579$	9480.00	0.680441
$580$	0	0
$581$	5504.00	0.393020
$582$	704.000	0.0501404
$583$	−3768.00	−0.267675
$584$	3232.00	0.229009
$585$	0	0
$586$	11736.0	0.827320
$587$	16736.0	1.17678	0.588389	−	0.808578i	$-0.299762\pi$
$587$	16736.0	1.17678	0.588389	+	0.808578i	$0.299762\pi$
$588$	−5448.00	−0.382095
$589$	624.000	0.0436528
$590$	0	0
$591$	8572.00	0.596624
$592$	0	0
$593$	−28666.0	−1.98511	−0.992556	−	0.121788i	$-0.961137\pi$
$593$	−28666.0	−1.98511	−0.992556	+	0.121788i	$0.961137\pi$
$594$	2400.00	0.165780
$595$	0	0
$596$	7352.00	0.505285
$597$	−7472.00	−0.512242
$598$	9328.00	0.637877
$599$	20804.0	1.41908	0.709540	−	0.704666i	$-0.248903\pi$
$599$	20804.0	1.41908	0.709540	+	0.704666i	$0.248903\pi$
$600$	0	0
$601$	4134.00	0.280581	0.140291	−	0.990110i	$-0.455196\pi$
$601$	4134.00	0.280581	0.140291	+	0.990110i	$0.455196\pi$
$602$	−33664.0	−2.27914
$603$	−3220.00	−0.217460
$604$	−10176.0	−0.685522
$605$	0	0
$606$	5320.00	0.356618
$607$	−23606.0	−1.57848	−0.789241	−	0.614084i	$-0.789526\pi$
$607$	−23606.0	−1.57848	−0.789241	+	0.614084i	$0.789526\pi$
$608$	384.000	0.0256139
$609$	1856.00	0.123496
$610$	0	0
$611$	−1276.00	−0.0844868
$612$	9568.00	0.631966
$613$	2630.00	0.173287	0.0866433	−	0.996239i	$-0.472386\pi$
$613$	2630.00	0.173287	0.0866433	+	0.996239i	$0.472386\pi$
$614$	−11844.0	−0.778477
$615$	0	0
$616$	3072.00	0.200932
$617$	−12288.0	−0.801777	−0.400888	−	0.916127i	$-0.631298\pi$
$617$	−12288.0	−0.801777	−0.400888	+	0.916127i	$0.631298\pi$
$618$	4208.00	0.273901
$619$	−22896.0	−1.48670	−0.743351	−	0.668902i	$-0.766765\pi$
$619$	−22896.0	−1.48670	−0.743351	+	0.668902i	$0.766765\pi$
$620$	0	0
$621$	−21200.0	−1.36993
$622$	18936.0	1.22068
$623$	−1344.00	−0.0864305
$624$	704.000	0.0451644
$625$	0	0
$626$	14580.0	0.930885
$627$	−288.000	−0.0183439
$628$	−11824.0	−0.751320
$629$	0	0
$630$	0	0
$631$	14352.0	0.905458	0.452729	−	0.891648i	$-0.350450\pi$
$631$	14352.0	0.905458	0.452729	+	0.891648i	$0.350450\pi$
$632$	928.000	0.0584080
$633$	3656.00	0.229562
$634$	10096.0	0.632434
$635$	0	0
$636$	2512.00	0.156615
$637$	−14982.0	−0.931881
$638$	−696.000	−0.0431895
$639$	−16008.0	−0.991028
$640$	0	0
$641$	17782.0	1.09570	0.547852	−	0.836575i	$-0.315446\pi$
$641$	17782.0	1.09570	0.547852	+	0.836575i	$0.315446\pi$
$642$	7696.00	0.473110
$643$	3460.00	0.212207	0.106103	−	0.994355i	$-0.466163\pi$
$643$	3460.00	0.212207	0.106103	+	0.994355i	$0.466163\pi$
$644$	−27136.0	−1.66042
$645$	0	0
$646$	−2496.00	−0.152018
$647$	25564.0	1.55336	0.776680	−	0.629895i	$-0.216902\pi$
$647$	25564.0	1.55336	0.776680	+	0.629895i	$0.216902\pi$
$648$	3368.00	0.204178
$649$	−8304.00	−0.502250
$650$	0	0
$651$	−3328.00	−0.200360
$652$	−2888.00	−0.173471
$653$	−4368.00	−0.261766	−0.130883	−	0.991398i	$-0.541781\pi$
$653$	−4368.00	−0.261766	−0.130883	+	0.991398i	$0.541781\pi$
$654$	−5016.00	−0.299910
$655$	0	0
$656$	−5664.00	−0.337107
$657$	−9292.00	−0.551774
$658$	3712.00	0.219922
$659$	32108.0	1.89795	0.948976	−	0.315349i	$-0.102122\pi$
$659$	32108.0	1.89795	0.948976	+	0.315349i	$0.102122\pi$
$660$	0	0
$661$	882.000	0.0518999	0.0259499	−	0.999663i	$-0.491739\pi$
$661$	882.000	0.0518999	0.0259499	+	0.999663i	$0.491739\pi$
$662$	9744.00	0.572071
$663$	−4576.00	−0.268050
$664$	1376.00	0.0804204
$665$	0	0
$666$	0	0
$667$	6148.00	0.356899
$668$	−9632.00	−0.557894
$669$	6136.00	0.354606
$670$	0	0
$671$	8760.00	0.503988
$672$	−2048.00	−0.117564
$673$	−8414.00	−0.481926	−0.240963	−	0.970534i	$-0.577463\pi$
$673$	−8414.00	−0.481926	−0.240963	+	0.970534i	$0.577463\pi$
$674$	−6480.00	−0.370327
$675$	0	0
$676$	−6852.00	−0.389850
$677$	32732.0	1.85819	0.929094	−	0.369844i	$-0.120589\pi$
$677$	32732.0	1.85819	0.929094	+	0.369844i	$0.120589\pi$
$678$	592.000	0.0335334
$679$	−5632.00	−0.318316
$680$	0	0
$681$	9168.00	0.515886
$682$	1248.00	0.0700710
$683$	28344.0	1.58793	0.793963	−	0.607967i	$-0.208015\pi$
$683$	28344.0	1.58793	0.793963	+	0.607967i	$0.208015\pi$
$684$	−1104.00	−0.0617142
$685$	0	0
$686$	21632.0	1.20396
$687$	412.000	0.0228803
$688$	−8416.00	−0.466362
$689$	6908.00	0.381965
$690$	0	0
$691$	−26796.0	−1.47521	−0.737603	−	0.675234i	$-0.764043\pi$
$691$	−26796.0	−1.47521	−0.737603	+	0.675234i	$0.764043\pi$
$692$	1448.00	0.0795444
$693$	−8832.00	−0.484127
$694$	12304.0	0.672988
$695$	0	0
$696$	464.000	0.0252699
$697$	36816.0	2.00073
$698$	−13324.0	−0.722523
$699$	−11644.0	−0.630067
$700$	0	0
$701$	12426.0	0.669506	0.334753	−	0.942306i	$-0.391347\pi$
$701$	12426.0	0.669506	0.334753	+	0.942306i	$0.391347\pi$
$702$	−4400.00	−0.236563
$703$	0	0
$704$	768.000	0.0411152
$705$	0	0
$706$	13852.0	0.738423
$707$	−42560.0	−2.26398
$708$	5536.00	0.293864
$709$	−2994.00	−0.158592	−0.0792962	−	0.996851i	$-0.525267\pi$
$709$	−2994.00	−0.158592	−0.0792962	+	0.996851i	$0.525267\pi$
$710$	0	0
$711$	−2668.00	−0.140728
$712$	−336.000	−0.0176856
$713$	−11024.0	−0.579035
$714$	13312.0	0.697744
$715$	0	0
$716$	−9360.00	−0.488547
$717$	−432.000	−0.0225012
$718$	7408.00	0.385047
$719$	17320.0	0.898369	0.449184	−	0.893439i	$-0.351715\pi$
$719$	17320.0	0.898369	0.449184	+	0.893439i	$0.351715\pi$
$720$	0	0
$721$	−33664.0	−1.73885
$722$	−13430.0	−0.692262
$723$	836.000	0.0430030
$724$	2600.00	0.133464
$725$	0	0
$726$	4748.00	0.242720
$727$	−3562.00	−0.181716	−0.0908578	−	0.995864i	$-0.528961\pi$
$727$	−3562.00	−0.181716	−0.0908578	+	0.995864i	$0.528961\pi$
$728$	−5632.00	−0.286725
$729$	−4283.00	−0.217599
$730$	0	0
$731$	54704.0	2.76785
$732$	−5840.00	−0.294881
$733$	−19556.0	−0.985426	−0.492713	−	0.870192i	$-0.663995\pi$
$733$	−19556.0	−0.985426	−0.492713	+	0.870192i	$0.663995\pi$
$734$	2860.00	0.143821
$735$	0	0
$736$	−6784.00	−0.339758
$737$	1680.00	0.0839669
$738$	16284.0	0.812225
$739$	−5900.00	−0.293687	−0.146844	−	0.989160i	$-0.546911\pi$
$739$	−5900.00	−0.293687	−0.146844	+	0.989160i	$0.546911\pi$
$740$	0	0
$741$	528.000	0.0261762
$742$	−20096.0	−0.994269
$743$	−34554.0	−1.70614	−0.853071	−	0.521795i	$-0.825263\pi$
$743$	−34554.0	−1.70614	−0.853071	+	0.521795i	$0.825263\pi$
$744$	−832.000	−0.0409981
$745$	0	0
$746$	−5436.00	−0.266791
$747$	−3956.00	−0.193765
$748$	−4992.00	−0.244018
$749$	−61568.0	−3.00353
$750$	0	0
$751$	−10484.0	−0.509410	−0.254705	−	0.967019i	$-0.581978\pi$
$751$	−10484.0	−0.509410	−0.254705	+	0.967019i	$0.581978\pi$
$752$	928.000	0.0450009
$753$	−3432.00	−0.166094
$754$	1276.00	0.0616302
$755$	0	0
$756$	12800.0	0.615782
$757$	33384.0	1.60286	0.801428	−	0.598091i	$-0.204074\pi$
$757$	33384.0	1.60286	0.801428	+	0.598091i	$0.204074\pi$
$758$	16208.0	0.776650
$759$	5088.00	0.243324
$760$	0	0
$761$	−13434.0	−0.639924	−0.319962	−	0.947430i	$-0.603670\pi$
$761$	−13434.0	−0.639924	−0.319962	+	0.947430i	$0.603670\pi$
$762$	−2600.00	−0.123606
$763$	40128.0	1.90397
$764$	−4704.00	−0.222755
$765$	0	0
$766$	−21768.0	−1.02678
$767$	15224.0	0.716697
$768$	−512.000	−0.0240563
$769$	−26018.0	−1.22007	−0.610035	−	0.792375i	$-0.708844\pi$
$769$	−26018.0	−1.22007	−0.610035	+	0.792375i	$0.708844\pi$
$770$	0	0
$771$	−5764.00	−0.269242
$772$	−18960.0	−0.883919
$773$	6648.00	0.309330	0.154665	−	0.987967i	$-0.450570\pi$
$773$	6648.00	0.309330	0.154665	+	0.987967i	$0.450570\pi$
$774$	24196.0	1.12365
$775$	0	0
$776$	−1408.00	−0.0651343
$777$	0	0
$778$	−10292.0	−0.474275
$779$	−4248.00	−0.195379
$780$	0	0
$781$	8352.00	0.382661
$782$	44096.0	2.01646
$783$	−2900.00	−0.132360
$784$	10896.0	0.496356
$785$	0	0
$786$	4288.00	0.194590
$787$	14032.0	0.635561	0.317781	−	0.948164i	$-0.397062\pi$
$787$	14032.0	0.635561	0.317781	+	0.948164i	$0.397062\pi$
$788$	−17144.0	−0.775038
$789$	2508.00	0.113165
$790$	0	0
$791$	−4736.00	−0.212886
$792$	−2208.00	−0.0990630
$793$	−16060.0	−0.719177
$794$	5636.00	0.251907
$795$	0	0
$796$	14944.0	0.665422
$797$	39096.0	1.73758	0.868790	−	0.495181i	$-0.164898\pi$
$797$	39096.0	1.73758	0.868790	+	0.495181i	$0.164898\pi$
$798$	−1536.00	−0.0681376
$799$	−6032.00	−0.267080
$800$	0	0
$801$	966.000	0.0426117
$802$	−7188.00	−0.316480
$803$	4848.00	0.213054
$804$	−1120.00	−0.0491286
$805$	0	0
$806$	−2288.00	−0.0999893
$807$	8228.00	0.358909
$808$	−10640.0	−0.463260
$809$	−30354.0	−1.31915	−0.659573	−	0.751640i	$-0.729263\pi$
$809$	−30354.0	−1.31915	−0.659573	+	0.751640i	$0.729263\pi$
$810$	0	0
$811$	−21396.0	−0.926406	−0.463203	−	0.886252i	$-0.653300\pi$
$811$	−21396.0	−0.926406	−0.463203	+	0.886252i	$0.653300\pi$
$812$	−3712.00	−0.160426
$813$	−6320.00	−0.272635
$814$	0	0
$815$	0	0
$816$	3328.00	0.142774
$817$	−6312.00	−0.270292
$818$	14484.0	0.619097
$819$	16192.0	0.690835
$820$	0	0
$821$	12942.0	0.550157	0.275079	−	0.961422i	$-0.411296\pi$
$821$	12942.0	0.550157	0.275079	+	0.961422i	$0.411296\pi$
$822$	−8832.00	−0.374758
$823$	26066.0	1.10401	0.552007	−	0.833839i	$-0.313862\pi$
$823$	26066.0	1.10401	0.552007	+	0.833839i	$0.313862\pi$
$824$	−8416.00	−0.355807
$825$	0	0
$826$	−44288.0	−1.86559
$827$	5670.00	0.238410	0.119205	−	0.992870i	$-0.461965\pi$
$827$	5670.00	0.238410	0.119205	+	0.992870i	$0.461965\pi$
$828$	19504.0	0.818612
$829$	−39850.0	−1.66954	−0.834769	−	0.550600i	$-0.814399\pi$
$829$	−39850.0	−1.66954	−0.834769	+	0.550600i	$0.814399\pi$
$830$	0	0
$831$	−11500.0	−0.480061
$832$	−1408.00	−0.0586702
$833$	−70824.0	−2.94587
$834$	−11632.0	−0.482953
$835$	0	0
$836$	576.000	0.0238294
$837$	5200.00	0.214741
$838$	312.000	0.0128614
$839$	−19868.0	−0.817544	−0.408772	−	0.912637i	$-0.634043\pi$
$839$	−19868.0	−0.817544	−0.408772	+	0.912637i	$0.634043\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	26500.0	1.08462
$843$	−340.000	−0.0138911
$844$	−7312.00	−0.298210
$845$	0	0
$846$	−2668.00	−0.108425
$847$	−37984.0	−1.54090
$848$	−5024.00	−0.203449
$849$	−3384.00	−0.136795
$850$	0	0
$851$	0	0
$852$	−5568.00	−0.223893
$853$	32196.0	1.29234	0.646172	−	0.763192i	$-0.276369\pi$
$853$	32196.0	1.29234	0.646172	+	0.763192i	$0.276369\pi$
$854$	46720.0	1.87204
$855$	0	0
$856$	−15392.0	−0.614588
$857$	−35166.0	−1.40169	−0.700845	−	0.713314i	$-0.747193\pi$
$857$	−35166.0	−1.40169	−0.700845	+	0.713314i	$0.747193\pi$
$858$	1056.00	0.0420178
$859$	−33416.0	−1.32729	−0.663643	−	0.748049i	$-0.730991\pi$
$859$	−33416.0	−1.32729	−0.663643	+	0.748049i	$0.730991\pi$
$860$	0	0
$861$	22656.0	0.896765
$862$	25760.0	1.01785
$863$	27852.0	1.09860	0.549301	−	0.835625i	$-0.314894\pi$
$863$	27852.0	1.09860	0.549301	+	0.835625i	$0.314894\pi$
$864$	3200.00	0.126003
$865$	0	0
$866$	−4288.00	−0.168259
$867$	−11806.0	−0.462460
$868$	6656.00	0.260276
$869$	1392.00	0.0543387
$870$	0	0
$871$	−3080.00	−0.119818
$872$	10032.0	0.389594
$873$	4048.00	0.156935
$874$	−5088.00	−0.196916
$875$	0	0
$876$	−3232.00	−0.124657
$877$	30686.0	1.18152	0.590760	−	0.806848i	$-0.298828\pi$
$877$	30686.0	1.18152	0.590760	+	0.806848i	$0.298828\pi$
$878$	−8496.00	−0.326567
$879$	−11736.0	−0.450336
$880$	0	0
$881$	20622.0	0.788618	0.394309	−	0.918978i	$-0.370984\pi$
$881$	20622.0	0.788618	0.394309	+	0.918978i	$0.370984\pi$
$882$	−31326.0	−1.19592
$883$	−23584.0	−0.898828	−0.449414	−	0.893324i	$-0.648367\pi$
$883$	−23584.0	−0.898828	−0.449414	+	0.893324i	$0.648367\pi$
$884$	9152.00	0.348207
$885$	0	0
$886$	−32620.0	−1.23690
$887$	45682.0	1.72926	0.864629	−	0.502411i	$-0.167554\pi$
$887$	45682.0	1.72926	0.864629	+	0.502411i	$0.167554\pi$
$888$	0	0
$889$	20800.0	0.784713
$890$	0	0
$891$	5052.00	0.189953
$892$	−12272.0	−0.460647
$893$	696.000	0.0260815
$894$	−7352.00	−0.275042
$895$	0	0
$896$	4096.00	0.152721
$897$	−9328.00	−0.347216
$898$	−22524.0	−0.837011
$899$	−1508.00	−0.0559451
$900$	0	0
$901$	32656.0	1.20747
$902$	−8496.00	−0.313621
$903$	33664.0	1.24061
$904$	−1184.00	−0.0435611
$905$	0	0
$906$	10176.0	0.373151
$907$	47118.0	1.72495	0.862474	−	0.506102i	$-0.168914\pi$
$907$	47118.0	1.72495	0.862474	+	0.506102i	$0.168914\pi$
$908$	−18336.0	−0.670156
$909$	30590.0	1.11618
$910$	0	0
$911$	−8148.00	−0.296329	−0.148164	−	0.988963i	$-0.547336\pi$
$911$	−8148.00	−0.296329	−0.148164	+	0.988963i	$0.547336\pi$
$912$	−384.000	−0.0139424
$913$	2064.00	0.0748176
$914$	−24036.0	−0.869847
$915$	0	0
$916$	−824.000	−0.0297224
$917$	−34304.0	−1.23535
$918$	−20800.0	−0.747824
$919$	−24736.0	−0.887884	−0.443942	−	0.896056i	$-0.646420\pi$
$919$	−24736.0	−0.887884	−0.443942	+	0.896056i	$0.646420\pi$
$920$	0	0
$921$	11844.0	0.423749
$922$	−180.000	−0.00642948
$923$	−15312.0	−0.546046
$924$	−3072.00	−0.109374
$925$	0	0
$926$	3200.00	0.113562
$927$	24196.0	0.857283
$928$	−928.000	−0.0328266
$929$	−27230.0	−0.961666	−0.480833	−	0.876812i	$-0.659666\pi$
$929$	−27230.0	−0.961666	−0.480833	+	0.876812i	$0.659666\pi$
$930$	0	0
$931$	8172.00	0.287676
$932$	23288.0	0.818480
$933$	−18936.0	−0.664455
$934$	−1140.00	−0.0399378
$935$	0	0
$936$	4048.00	0.141360
$937$	−33250.0	−1.15926	−0.579632	−	0.814878i	$-0.696804\pi$
$937$	−33250.0	−1.15926	−0.579632	+	0.814878i	$0.696804\pi$
$938$	8960.00	0.311892
$939$	−14580.0	−0.506710
$940$	0	0
$941$	26870.0	0.930858	0.465429	−	0.885085i	$-0.345900\pi$
$941$	26870.0	0.930858	0.465429	+	0.885085i	$0.345900\pi$
$942$	11824.0	0.408967
$943$	75048.0	2.59162
$944$	−11072.0	−0.381740
$945$	0	0
$946$	−12624.0	−0.433871
$947$	38414.0	1.31815	0.659075	−	0.752078i	$-0.270948\pi$
$947$	38414.0	1.31815	0.659075	+	0.752078i	$0.270948\pi$
$948$	−928.000	−0.0317933
$949$	−8888.00	−0.304022
$950$	0	0
$951$	−10096.0	−0.344254
$952$	−26624.0	−0.906396
$953$	−18602.0	−0.632296	−0.316148	−	0.948710i	$-0.602390\pi$
$953$	−18602.0	−0.632296	−0.316148	+	0.948710i	$0.602390\pi$
$954$	14444.0	0.490191
$955$	0	0
$956$	864.000	0.0292299
$957$	696.000	0.0235094
$958$	−5304.00	−0.178877
$959$	70656.0	2.37915
$960$	0	0
$961$	−27087.0	−0.909234
$962$	0	0
$963$	44252.0	1.48079
$964$	−1672.00	−0.0558625
$965$	0	0
$966$	27136.0	0.903816
$967$	−20794.0	−0.691510	−0.345755	−	0.938325i	$-0.612377\pi$
$967$	−20794.0	−0.691510	−0.345755	+	0.938325i	$0.612377\pi$
$968$	−9496.00	−0.315303
$969$	2496.00	0.0827483
$970$	0	0
$971$	−6720.00	−0.222096	−0.111048	−	0.993815i	$-0.535421\pi$
$971$	−6720.00	−0.222096	−0.111048	+	0.993815i	$0.535421\pi$
$972$	−14168.0	−0.467530
$973$	93056.0	3.06602
$974$	22656.0	0.745323
$975$	0	0
$976$	11680.0	0.383061
$977$	45274.0	1.48254	0.741271	−	0.671206i	$-0.234223\pi$
$977$	45274.0	1.48254	0.741271	+	0.671206i	$0.234223\pi$
$978$	2888.00	0.0944254
$979$	−504.000	−0.0164534
$980$	0	0
$981$	−28842.0	−0.938689
$982$	−8416.00	−0.273488
$983$	6542.00	0.212266	0.106133	−	0.994352i	$-0.466153\pi$
$983$	6542.00	0.212266	0.106133	+	0.994352i	$0.466153\pi$
$984$	5664.00	0.183498
$985$	0	0
$986$	6032.00	0.194826
$987$	−3712.00	−0.119710
$988$	−1056.00	−0.0340039
$989$	111512.	3.58531
$990$	0	0
$991$	48432.0	1.55247	0.776233	−	0.630447i	$-0.217128\pi$
$991$	48432.0	1.55247	0.776233	+	0.630447i	$0.217128\pi$
$992$	1664.00	0.0532581
$993$	−9744.00	−0.311396
$994$	44544.0	1.42138
$995$	0	0
$996$	−1376.00	−0.0437753
$997$	1256.00	0.0398976	0.0199488	−	0.999801i	$-0.493650\pi$
$997$	1256.00	0.0398976	0.0199488	+	0.999801i	$0.493650\pi$
$998$	28488.0	0.903579
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.4.a.f.1.1		1
5.4	even	2		290.4.a.a.1.1	✓	1
20.19	odd	2		2320.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.4.a.a.1.1	✓	1	5.4	even	2
1450.4.a.f.1.1		1	1.1	even	1	trivial
2320.4.a.b.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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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