LMFDB - Embedded newform 273.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,4,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	273.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:	$16.1075214316$
Analytic rank:	$1$
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	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} +7.00000 q^{7} +15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -3.00000 q^{6} +7.00000 q^{7} +15.0000 q^{8} +9.00000 q^{9} +5.00000 q^{10} -1.00000 q^{11} -21.0000 q^{12} +13.0000 q^{13} -7.00000 q^{14} -15.0000 q^{15} +41.0000 q^{16} +19.0000 q^{17} -9.00000 q^{18} -117.000 q^{19} +35.0000 q^{20} +21.0000 q^{21} +1.00000 q^{22} -141.000 q^{23} +45.0000 q^{24} -100.000 q^{25} -13.0000 q^{26} +27.0000 q^{27} -49.0000 q^{28} -131.000 q^{29} +15.0000 q^{30} -128.000 q^{31} -161.000 q^{32} -3.00000 q^{33} -19.0000 q^{34} -35.0000 q^{35} -63.0000 q^{36} +55.0000 q^{37} +117.000 q^{38} +39.0000 q^{39} -75.0000 q^{40} -21.0000 q^{42} -201.000 q^{43} +7.00000 q^{44} -45.0000 q^{45} +141.000 q^{46} -96.0000 q^{47} +123.000 q^{48} +49.0000 q^{49} +100.000 q^{50} +57.0000 q^{51} -91.0000 q^{52} +510.000 q^{53} -27.0000 q^{54} +5.00000 q^{55} +105.000 q^{56} -351.000 q^{57} +131.000 q^{58} -156.000 q^{59} +105.000 q^{60} -845.000 q^{61} +128.000 q^{62} +63.0000 q^{63} -167.000 q^{64} -65.0000 q^{65} +3.00000 q^{66} -470.000 q^{67} -133.000 q^{68} -423.000 q^{69} +35.0000 q^{70} +324.000 q^{71} +135.000 q^{72} -373.000 q^{73} -55.0000 q^{74} -300.000 q^{75} +819.000 q^{76} -7.00000 q^{77} -39.0000 q^{78} -526.000 q^{79} -205.000 q^{80} +81.0000 q^{81} +266.000 q^{83} -147.000 q^{84} -95.0000 q^{85} +201.000 q^{86} -393.000 q^{87} -15.0000 q^{88} -250.000 q^{89} +45.0000 q^{90} +91.0000 q^{91} +987.000 q^{92} -384.000 q^{93} +96.0000 q^{94} +585.000 q^{95} -483.000 q^{96} +322.000 q^{97} -49.0000 q^{98} -9.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.00000	−0.875000
$5$	−5.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−5.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−3.00000	−0.204124
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	15.0000	0.662913
$9$	9.00000	0.333333
$10$	5.00000	0.158114
$11$	−1.00000	−0.0274101	−0.0137051	−	0.999906i	$-0.504363\pi$
$11$	−1.00000	−0.0274101	−0.0137051	+	0.999906i	$0.504363\pi$
$12$	−21.0000	−0.505181
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−7.00000	−0.133631
$15$	−15.0000	−0.258199
$16$	41.0000	0.640625
$17$	19.0000	0.271069	0.135535	−	0.990773i	$-0.456725\pi$
$17$	19.0000	0.271069	0.135535	+	0.990773i	$0.456725\pi$
$18$	−9.00000	−0.117851
$19$	−117.000	−1.41272	−0.706359	−	0.707854i	$-0.749664\pi$
$19$	−117.000	−1.41272	−0.706359	+	0.707854i	$0.749664\pi$
$20$	35.0000	0.391312
$21$	21.0000	0.218218
$22$	1.00000	0.00969094
$23$	−141.000	−1.27828	−0.639142	−	0.769089i	$-0.720710\pi$
$23$	−141.000	−1.27828	−0.639142	+	0.769089i	$0.720710\pi$
$24$	45.0000	0.382733
$25$	−100.000	−0.800000
$26$	−13.0000	−0.0980581
$27$	27.0000	0.192450
$28$	−49.0000	−0.330719
$29$	−131.000	−0.838831	−0.419415	−	0.907794i	$-0.637765\pi$
$29$	−131.000	−0.838831	−0.419415	+	0.907794i	$0.637765\pi$
$30$	15.0000	0.0912871
$31$	−128.000	−0.741596	−0.370798	−	0.928714i	$-0.620916\pi$
$31$	−128.000	−0.741596	−0.370798	+	0.928714i	$0.620916\pi$
$32$	−161.000	−0.889408
$33$	−3.00000	−0.0158252
$34$	−19.0000	−0.0958374
$35$	−35.0000	−0.169031
$36$	−63.0000	−0.291667
$37$	55.0000	0.244377	0.122188	−	0.992507i	$-0.461009\pi$
$37$	55.0000	0.244377	0.122188	+	0.992507i	$0.461009\pi$
$38$	117.000	0.499471
$39$	39.0000	0.160128
$40$	−75.0000	−0.296464
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−21.0000	−0.0771517
$43$	−201.000	−0.712842	−0.356421	−	0.934325i	$-0.616003\pi$
$43$	−201.000	−0.712842	−0.356421	+	0.934325i	$0.616003\pi$
$44$	7.00000	0.0239839
$45$	−45.0000	−0.149071
$46$	141.000	0.451942
$47$	−96.0000	−0.297937	−0.148969	−	0.988842i	$-0.547595\pi$
$47$	−96.0000	−0.297937	−0.148969	+	0.988842i	$0.547595\pi$
$48$	123.000	0.369865
$49$	49.0000	0.142857
$50$	100.000	0.282843
$51$	57.0000	0.156502
$52$	−91.0000	−0.242681
$53$	510.000	1.32177	0.660886	−	0.750487i	$-0.270181\pi$
$53$	510.000	1.32177	0.660886	+	0.750487i	$0.270181\pi$
$54$	−27.0000	−0.0680414
$55$	5.00000	0.0122582
$56$	105.000	0.250557
$57$	−351.000	−0.815633
$58$	131.000	0.296571
$59$	−156.000	−0.344228	−0.172114	−	0.985077i	$-0.555060\pi$
$59$	−156.000	−0.344228	−0.172114	+	0.985077i	$0.555060\pi$
$60$	105.000	0.225924
$61$	−845.000	−1.77363	−0.886813	−	0.462129i	$-0.847086\pi$
$61$	−845.000	−1.77363	−0.886813	+	0.462129i	$0.847086\pi$
$62$	128.000	0.262194
$63$	63.0000	0.125988
$64$	−167.000	−0.326172
$65$	−65.0000	−0.124035
$66$	3.00000	0.00559507
$67$	−470.000	−0.857010	−0.428505	−	0.903540i	$-0.640959\pi$
$67$	−470.000	−0.857010	−0.428505	+	0.903540i	$0.640959\pi$
$68$	−133.000	−0.237186
$69$	−423.000	−0.738018
$70$	35.0000	0.0597614
$71$	324.000	0.541574	0.270787	−	0.962639i	$-0.412716\pi$
$71$	324.000	0.541574	0.270787	+	0.962639i	$0.412716\pi$
$72$	135.000	0.220971
$73$	−373.000	−0.598032	−0.299016	−	0.954248i	$-0.596658\pi$
$73$	−373.000	−0.598032	−0.299016	+	0.954248i	$0.596658\pi$
$74$	−55.0000	−0.0864003
$75$	−300.000	−0.461880
$76$	819.000	1.23613
$77$	−7.00000	−0.0103601
$78$	−39.0000	−0.0566139
$79$	−526.000	−0.749109	−0.374555	−	0.927205i	$-0.622204\pi$
$79$	−526.000	−0.749109	−0.374555	+	0.927205i	$0.622204\pi$
$80$	−205.000	−0.286496
$81$	81.0000	0.111111
$82$	0	0
$83$	266.000	0.351775	0.175887	−	0.984410i	$-0.443721\pi$
$83$	266.000	0.351775	0.175887	+	0.984410i	$0.443721\pi$
$84$	−147.000	−0.190941
$85$	−95.0000	−0.121226
$86$	201.000	0.252028
$87$	−393.000	−0.484299
$88$	−15.0000	−0.0181705
$89$	−250.000	−0.297752	−0.148876	−	0.988856i	$-0.547566\pi$
$89$	−250.000	−0.297752	−0.148876	+	0.988856i	$0.547566\pi$
$90$	45.0000	0.0527046
$91$	91.0000	0.104828
$92$	987.000	1.11850
$93$	−384.000	−0.428161
$94$	96.0000	0.105337
$95$	585.000	0.631787
$96$	−483.000	−0.513500
$97$	322.000	0.337053	0.168527	−	0.985697i	$-0.446099\pi$
$97$	322.000	0.337053	0.168527	+	0.985697i	$0.446099\pi$
$98$	−49.0000	−0.0505076
$99$	−9.00000	−0.00913671
$100$	700.000	0.700000
$101$	852.000	0.839378	0.419689	−	0.907668i	$-0.362139\pi$
$101$	852.000	0.839378	0.419689	+	0.907668i	$0.362139\pi$
$102$	−57.0000	−0.0553318
$103$	−201.000	−0.192283	−0.0961414	−	0.995368i	$-0.530650\pi$
$103$	−201.000	−0.192283	−0.0961414	+	0.995368i	$0.530650\pi$
$104$	195.000	0.183859
$105$	−105.000	−0.0975900
$106$	−510.000	−0.467317
$107$	1686.00	1.52329	0.761644	−	0.647996i	$-0.224393\pi$
$107$	1686.00	1.52329	0.761644	+	0.647996i	$0.224393\pi$
$108$	−189.000	−0.168394
$109$	−827.000	−0.726718	−0.363359	−	0.931649i	$-0.618370\pi$
$109$	−827.000	−0.726718	−0.363359	+	0.931649i	$0.618370\pi$
$110$	−5.00000	−0.00433392
$111$	165.000	0.141091
$112$	287.000	0.242133
$113$	−138.000	−0.114884	−0.0574422	−	0.998349i	$-0.518295\pi$
$113$	−138.000	−0.114884	−0.0574422	+	0.998349i	$0.518295\pi$
$114$	351.000	0.288370
$115$	705.000	0.571666
$116$	917.000	0.733977
$117$	117.000	0.0924500
$118$	156.000	0.121703
$119$	133.000	0.102455
$120$	−225.000	−0.171163
$121$	−1330.00	−0.999249
$122$	845.000	0.627071
$123$	0	0
$124$	896.000	0.648897
$125$	1125.00	0.804984
$126$	−63.0000	−0.0445435
$127$	1514.00	1.05784	0.528920	−	0.848671i	$-0.322597\pi$
$127$	1514.00	1.05784	0.528920	+	0.848671i	$0.322597\pi$
$128$	1455.00	1.00473
$129$	−603.000	−0.411560
$130$	65.0000	0.0438529
$131$	359.000	0.239435	0.119717	−	0.992808i	$-0.461801\pi$
$131$	359.000	0.239435	0.119717	+	0.992808i	$0.461801\pi$
$132$	21.0000	0.0138471
$133$	−819.000	−0.533957
$134$	470.000	0.302999
$135$	−135.000	−0.0860663
$136$	285.000	0.179695
$137$	2757.00	1.71932	0.859658	−	0.510869i	$-0.170676\pi$
$137$	2757.00	1.71932	0.859658	+	0.510869i	$0.170676\pi$
$138$	423.000	0.260929
$139$	−168.000	−0.102515	−0.0512575	−	0.998685i	$-0.516323\pi$
$139$	−168.000	−0.102515	−0.0512575	+	0.998685i	$0.516323\pi$
$140$	245.000	0.147902
$141$	−288.000	−0.172014
$142$	−324.000	−0.191475
$143$	−13.0000	−0.00760220
$144$	369.000	0.213542
$145$	655.000	0.375136
$146$	373.000	0.211436
$147$	147.000	0.0824786
$148$	−385.000	−0.213830
$149$	−1464.00	−0.804937	−0.402468	−	0.915434i	$-0.631848\pi$
$149$	−1464.00	−0.804937	−0.402468	+	0.915434i	$0.631848\pi$
$150$	300.000	0.163299
$151$	895.000	0.482345	0.241172	−	0.970482i	$-0.422468\pi$
$151$	895.000	0.482345	0.241172	+	0.970482i	$0.422468\pi$
$152$	−1755.00	−0.936509
$153$	171.000	0.0903564
$154$	7.00000	0.00366283
$155$	640.000	0.331652
$156$	−273.000	−0.140112
$157$	−2193.00	−1.11478	−0.557390	−	0.830251i	$-0.688197\pi$
$157$	−2193.00	−1.11478	−0.557390	+	0.830251i	$0.688197\pi$
$158$	526.000	0.264850
$159$	1530.00	0.763125
$160$	805.000	0.397755
$161$	−987.000	−0.483146
$162$	−81.0000	−0.0392837
$163$	146.000	0.0701571	0.0350785	−	0.999385i	$-0.488832\pi$
$163$	146.000	0.0701571	0.0350785	+	0.999385i	$0.488832\pi$
$164$	0	0
$165$	15.0000	0.00707726
$166$	−266.000	−0.124371
$167$	1715.00	0.794675	0.397337	−	0.917673i	$-0.369934\pi$
$167$	1715.00	0.794675	0.397337	+	0.917673i	$0.369934\pi$
$168$	315.000	0.144659
$169$	169.000	0.0769231
$170$	95.0000	0.0428598
$171$	−1053.00	−0.470906
$172$	1407.00	0.623737
$173$	−2994.00	−1.31578	−0.657889	−	0.753115i	$-0.728550\pi$
$173$	−2994.00	−1.31578	−0.657889	+	0.753115i	$0.728550\pi$
$174$	393.000	0.171226
$175$	−700.000	−0.302372
$176$	−41.0000	−0.0175596
$177$	−468.000	−0.198740
$178$	250.000	0.105271
$179$	−1660.00	−0.693152	−0.346576	−	0.938022i	$-0.612656\pi$
$179$	−1660.00	−0.693152	−0.346576	+	0.938022i	$0.612656\pi$
$180$	315.000	0.130437
$181$	4130.00	1.69602	0.848012	−	0.529976i	$-0.177799\pi$
$181$	4130.00	1.69602	0.848012	+	0.529976i	$0.177799\pi$
$182$	−91.0000	−0.0370625
$183$	−2535.00	−1.02400
$184$	−2115.00	−0.847391
$185$	−275.000	−0.109289
$186$	384.000	0.151378
$187$	−19.0000	−0.00743004
$188$	672.000	0.260695
$189$	189.000	0.0727393
$190$	−585.000	−0.223370
$191$	−4397.00	−1.66574	−0.832868	−	0.553471i	$-0.813303\pi$
$191$	−4397.00	−1.66574	−0.832868	+	0.553471i	$0.813303\pi$
$192$	−501.000	−0.188315
$193$	552.000	0.205875	0.102937	−	0.994688i	$-0.467176\pi$
$193$	552.000	0.205875	0.102937	+	0.994688i	$0.467176\pi$
$194$	−322.000	−0.119166
$195$	−195.000	−0.0716115
$196$	−343.000	−0.125000
$197$	1668.00	0.603249	0.301625	−	0.953427i	$-0.402471\pi$
$197$	1668.00	0.603249	0.301625	+	0.953427i	$0.402471\pi$
$198$	9.00000	0.00323031
$199$	−3523.00	−1.25497	−0.627485	−	0.778629i	$-0.715915\pi$
$199$	−3523.00	−1.25497	−0.627485	+	0.778629i	$0.715915\pi$
$200$	−1500.00	−0.530330
$201$	−1410.00	−0.494795
$202$	−852.000	−0.296765
$203$	−917.000	−0.317048
$204$	−399.000	−0.136939
$205$	0	0
$206$	201.000	0.0679822
$207$	−1269.00	−0.426095
$208$	533.000	0.177677
$209$	117.000	0.0387228
$210$	105.000	0.0345033
$211$	−4163.00	−1.35826	−0.679130	−	0.734018i	$-0.737643\pi$
$211$	−4163.00	−1.35826	−0.679130	+	0.734018i	$0.737643\pi$
$212$	−3570.00	−1.15655
$213$	972.000	0.312678
$214$	−1686.00	−0.538563
$215$	1005.00	0.318793
$216$	405.000	0.127578
$217$	−896.000	−0.280297
$218$	827.000	0.256934
$219$	−1119.00	−0.345274
$220$	−35.0000	−0.0107259
$221$	247.000	0.0751811
$222$	−165.000	−0.0498832
$223$	2926.00	0.878652	0.439326	−	0.898328i	$-0.355217\pi$
$223$	2926.00	0.878652	0.439326	+	0.898328i	$0.355217\pi$
$224$	−1127.00	−0.336165
$225$	−900.000	−0.266667
$226$	138.000	0.0406178
$227$	6578.00	1.92334	0.961668	−	0.274217i	$-0.0884187\pi$
$227$	6578.00	1.92334	0.961668	+	0.274217i	$0.0884187\pi$
$228$	2457.00	0.713679
$229$	1850.00	0.533849	0.266925	−	0.963717i	$-0.413993\pi$
$229$	1850.00	0.533849	0.266925	+	0.963717i	$0.413993\pi$
$230$	−705.000	−0.202114
$231$	−21.0000	−0.00598138
$232$	−1965.00	−0.556071
$233$	−4012.00	−1.12805	−0.564023	−	0.825759i	$-0.690747\pi$
$233$	−4012.00	−1.12805	−0.564023	+	0.825759i	$0.690747\pi$
$234$	−117.000	−0.0326860
$235$	480.000	0.133241
$236$	1092.00	0.301200
$237$	−1578.00	−0.432498
$238$	−133.000	−0.0362231
$239$	−4968.00	−1.34457	−0.672287	−	0.740291i	$-0.734688\pi$
$239$	−4968.00	−1.34457	−0.672287	+	0.740291i	$0.734688\pi$
$240$	−615.000	−0.165409
$241$	−86.0000	−0.0229865	−0.0114933	−	0.999934i	$-0.503658\pi$
$241$	−86.0000	−0.0229865	−0.0114933	+	0.999934i	$0.503658\pi$
$242$	1330.00	0.353288
$243$	243.000	0.0641500
$244$	5915.00	1.55192
$245$	−245.000	−0.0638877
$246$	0	0
$247$	−1521.00	−0.391817
$248$	−1920.00	−0.491613
$249$	798.000	0.203097
$250$	−1125.00	−0.284605
$251$	−525.000	−0.132023	−0.0660114	−	0.997819i	$-0.521027\pi$
$251$	−525.000	−0.132023	−0.0660114	+	0.997819i	$0.521027\pi$
$252$	−441.000	−0.110240
$253$	141.000	0.0350379
$254$	−1514.00	−0.374003
$255$	−285.000	−0.0699898
$256$	−119.000	−0.0290527
$257$	−782.000	−0.189805	−0.0949024	−	0.995487i	$-0.530254\pi$
$257$	−782.000	−0.189805	−0.0949024	+	0.995487i	$0.530254\pi$
$258$	603.000	0.145508
$259$	385.000	0.0923658
$260$	455.000	0.108530
$261$	−1179.00	−0.279610
$262$	−359.000	−0.0846530
$263$	−2388.00	−0.559887	−0.279944	−	0.960016i	$-0.590316\pi$
$263$	−2388.00	−0.559887	−0.279944	+	0.960016i	$0.590316\pi$
$264$	−45.0000	−0.0104908
$265$	−2550.00	−0.591114
$266$	819.000	0.188782
$267$	−750.000	−0.171907
$268$	3290.00	0.749883
$269$	1622.00	0.367640	0.183820	−	0.982960i	$-0.441154\pi$
$269$	1622.00	0.367640	0.183820	+	0.982960i	$0.441154\pi$
$270$	135.000	0.0304290
$271$	1962.00	0.439790	0.219895	−	0.975524i	$-0.429429\pi$
$271$	1962.00	0.439790	0.219895	+	0.975524i	$0.429429\pi$
$272$	779.000	0.173654
$273$	273.000	0.0605228
$274$	−2757.00	−0.607870
$275$	100.000	0.0219281
$276$	2961.00	0.645765
$277$	3338.00	0.724047	0.362023	−	0.932169i	$-0.382086\pi$
$277$	3338.00	0.724047	0.362023	+	0.932169i	$0.382086\pi$
$278$	168.000	0.0362445
$279$	−1152.00	−0.247199
$280$	−525.000	−0.112053
$281$	4762.00	1.01095	0.505475	−	0.862841i	$-0.331317\pi$
$281$	4762.00	1.01095	0.505475	+	0.862841i	$0.331317\pi$
$282$	288.000	0.0608161
$283$	2616.00	0.549488	0.274744	−	0.961517i	$-0.411407\pi$
$283$	2616.00	0.549488	0.274744	+	0.961517i	$0.411407\pi$
$284$	−2268.00	−0.473877
$285$	1755.00	0.364762
$286$	13.0000	0.00268778
$287$	0	0
$288$	−1449.00	−0.296469
$289$	−4552.00	−0.926521
$290$	−655.000	−0.132631
$291$	966.000	0.194598
$292$	2611.00	0.523278
$293$	5670.00	1.13053	0.565264	−	0.824910i	$-0.308774\pi$
$293$	5670.00	1.13053	0.565264	+	0.824910i	$0.308774\pi$
$294$	−147.000	−0.0291606
$295$	780.000	0.153944
$296$	825.000	0.162001
$297$	−27.0000	−0.00527508
$298$	1464.00	0.284588
$299$	−1833.00	−0.354532
$300$	2100.00	0.404145
$301$	−1407.00	−0.269429
$302$	−895.000	−0.170535
$303$	2556.00	0.484615
$304$	−4797.00	−0.905022
$305$	4225.00	0.793189
$306$	−171.000	−0.0319458
$307$	−2128.00	−0.395607	−0.197804	−	0.980242i	$-0.563381\pi$
$307$	−2128.00	−0.395607	−0.197804	+	0.980242i	$0.563381\pi$
$308$	49.0000	0.00906505
$309$	−603.000	−0.111014
$310$	−640.000	−0.117257
$311$	558.000	0.101740	0.0508702	−	0.998705i	$-0.483801\pi$
$311$	558.000	0.101740	0.0508702	+	0.998705i	$0.483801\pi$
$312$	585.000	0.106151
$313$	−6648.00	−1.20053	−0.600267	−	0.799800i	$-0.704939\pi$
$313$	−6648.00	−1.20053	−0.600267	+	0.799800i	$0.704939\pi$
$314$	2193.00	0.394134
$315$	−315.000	−0.0563436
$316$	3682.00	0.655471
$317$	−11180.0	−1.98086	−0.990428	−	0.138030i	$-0.955923\pi$
$317$	−11180.0	−1.98086	−0.990428	+	0.138030i	$0.955923\pi$
$318$	−1530.00	−0.269805
$319$	131.000	0.0229925
$320$	835.000	0.145868
$321$	5058.00	0.879470
$322$	987.000	0.170818
$323$	−2223.00	−0.382944
$324$	−567.000	−0.0972222
$325$	−1300.00	−0.221880
$326$	−146.000	−0.0248043
$327$	−2481.00	−0.419571
$328$	0	0
$329$	−672.000	−0.112610
$330$	−15.0000	−0.00250219
$331$	−1450.00	−0.240783	−0.120392	−	0.992726i	$-0.538415\pi$
$331$	−1450.00	−0.240783	−0.120392	+	0.992726i	$0.538415\pi$
$332$	−1862.00	−0.307803
$333$	495.000	0.0814590
$334$	−1715.00	−0.280960
$335$	2350.00	0.383266
$336$	861.000	0.139796
$337$	−8685.00	−1.40386	−0.701932	−	0.712244i	$-0.747679\pi$
$337$	−8685.00	−1.40386	−0.701932	+	0.712244i	$0.747679\pi$
$338$	−169.000	−0.0271964
$339$	−414.000	−0.0663286
$340$	665.000	0.106073
$341$	128.000	0.0203272
$342$	1053.00	0.166490
$343$	343.000	0.0539949
$344$	−3015.00	−0.472552
$345$	2115.00	0.330052
$346$	2994.00	0.465198
$347$	−876.000	−0.135522	−0.0677610	−	0.997702i	$-0.521586\pi$
$347$	−876.000	−0.135522	−0.0677610	+	0.997702i	$0.521586\pi$
$348$	2751.00	0.423762
$349$	3598.00	0.551853	0.275926	−	0.961179i	$-0.411015\pi$
$349$	3598.00	0.551853	0.275926	+	0.961179i	$0.411015\pi$
$350$	700.000	0.106904
$351$	351.000	0.0533761
$352$	161.000	0.0243788
$353$	12038.0	1.81507	0.907533	−	0.419981i	$-0.137963\pi$
$353$	12038.0	1.81507	0.907533	+	0.419981i	$0.137963\pi$
$354$	468.000	0.0702653
$355$	−1620.00	−0.242199
$356$	1750.00	0.260533
$357$	399.000	0.0591522
$358$	1660.00	0.245066
$359$	−7680.00	−1.12907	−0.564533	−	0.825410i	$-0.690944\pi$
$359$	−7680.00	−1.12907	−0.564533	+	0.825410i	$0.690944\pi$
$360$	−675.000	−0.0988212
$361$	6830.00	0.995772
$362$	−4130.00	−0.599635
$363$	−3990.00	−0.576916
$364$	−637.000	−0.0917249
$365$	1865.00	0.267448
$366$	2535.00	0.362040
$367$	8944.00	1.27213	0.636067	−	0.771634i	$-0.280560\pi$
$367$	8944.00	1.27213	0.636067	+	0.771634i	$0.280560\pi$
$368$	−5781.00	−0.818901
$369$	0	0
$370$	275.000	0.0386394
$371$	3570.00	0.499583
$372$	2688.00	0.374641
$373$	8644.00	1.19992	0.599959	−	0.800031i	$-0.295184\pi$
$373$	8644.00	1.19992	0.599959	+	0.800031i	$0.295184\pi$
$374$	19.0000	0.00262692
$375$	3375.00	0.464758
$376$	−1440.00	−0.197506
$377$	−1703.00	−0.232650
$378$	−189.000	−0.0257172
$379$	5700.00	0.772531	0.386266	−	0.922388i	$-0.373765\pi$
$379$	5700.00	0.772531	0.386266	+	0.922388i	$0.373765\pi$
$380$	−4095.00	−0.552813
$381$	4542.00	0.610745
$382$	4397.00	0.588927
$383$	−9917.00	−1.32307	−0.661534	−	0.749915i	$-0.730094\pi$
$383$	−9917.00	−1.32307	−0.661534	+	0.749915i	$0.730094\pi$
$384$	4365.00	0.580079
$385$	35.0000	0.00463316
$386$	−552.000	−0.0727877
$387$	−1809.00	−0.237614
$388$	−2254.00	−0.294921
$389$	−14554.0	−1.89696	−0.948480	−	0.316838i	$-0.897379\pi$
$389$	−14554.0	−1.89696	−0.948480	+	0.316838i	$0.897379\pi$
$390$	195.000	0.0253185
$391$	−2679.00	−0.346503
$392$	735.000	0.0947018
$393$	1077.00	0.138238
$394$	−1668.00	−0.213281
$395$	2630.00	0.335012
$396$	63.0000	0.00799462
$397$	9410.00	1.18961	0.594804	−	0.803871i	$-0.297230\pi$
$397$	9410.00	1.18961	0.594804	+	0.803871i	$0.297230\pi$
$398$	3523.00	0.443699
$399$	−2457.00	−0.308280
$400$	−4100.00	−0.512500
$401$	6194.00	0.771356	0.385678	−	0.922634i	$-0.373968\pi$
$401$	6194.00	0.771356	0.385678	+	0.922634i	$0.373968\pi$
$402$	1410.00	0.174936
$403$	−1664.00	−0.205682
$404$	−5964.00	−0.734456
$405$	−405.000	−0.0496904
$406$	917.000	0.112093
$407$	−55.0000	−0.00669840
$408$	855.000	0.103747
$409$	8881.00	1.07369	0.536843	−	0.843682i	$-0.319617\pi$
$409$	8881.00	1.07369	0.536843	+	0.843682i	$0.319617\pi$
$410$	0	0
$411$	8271.00	0.992648
$412$	1407.00	0.168247
$413$	−1092.00	−0.130106
$414$	1269.00	0.150647
$415$	−1330.00	−0.157318
$416$	−2093.00	−0.246677
$417$	−504.000	−0.0591870
$418$	−117.000	−0.0136906
$419$	4109.00	0.479088	0.239544	−	0.970886i	$-0.423002\pi$
$419$	4109.00	0.479088	0.239544	+	0.970886i	$0.423002\pi$
$420$	735.000	0.0853913
$421$	−5206.00	−0.602672	−0.301336	−	0.953518i	$-0.597433\pi$
$421$	−5206.00	−0.602672	−0.301336	+	0.953518i	$0.597433\pi$
$422$	4163.00	0.480217
$423$	−864.000	−0.0993123
$424$	7650.00	0.876219
$425$	−1900.00	−0.216855
$426$	−972.000	−0.110548
$427$	−5915.00	−0.670367
$428$	−11802.0	−1.33288
$429$	−39.0000	−0.00438913
$430$	−1005.00	−0.112710
$431$	6978.00	0.779857	0.389929	−	0.920845i	$-0.372500\pi$
$431$	6978.00	0.779857	0.389929	+	0.920845i	$0.372500\pi$
$432$	1107.00	0.123288
$433$	7252.00	0.804870	0.402435	−	0.915448i	$-0.368164\pi$
$433$	7252.00	0.804870	0.402435	+	0.915448i	$0.368164\pi$
$434$	896.000	0.0990999
$435$	1965.00	0.216585
$436$	5789.00	0.635878
$437$	16497.0	1.80585
$438$	1119.00	0.122073
$439$	1451.00	0.157750	0.0788752	−	0.996884i	$-0.474867\pi$
$439$	1451.00	0.157750	0.0788752	+	0.996884i	$0.474867\pi$
$440$	75.0000	0.00812610
$441$	441.000	0.0476190
$442$	−247.000	−0.0265805
$443$	12718.0	1.36400	0.681998	−	0.731354i	$-0.261111\pi$
$443$	12718.0	1.36400	0.681998	+	0.731354i	$0.261111\pi$
$444$	−1155.00	−0.123455
$445$	1250.00	0.133159
$446$	−2926.00	−0.310650
$447$	−4392.00	−0.464730
$448$	−1169.00	−0.123281
$449$	233.000	0.0244899	0.0122449	−	0.999925i	$-0.496102\pi$
$449$	233.000	0.0244899	0.0122449	+	0.999925i	$0.496102\pi$
$450$	900.000	0.0942809
$451$	0	0
$452$	966.000	0.100524
$453$	2685.00	0.278482
$454$	−6578.00	−0.680002
$455$	−455.000	−0.0468807
$456$	−5265.00	−0.540693
$457$	14132.0	1.44654	0.723268	−	0.690567i	$-0.242639\pi$
$457$	14132.0	1.44654	0.723268	+	0.690567i	$0.242639\pi$
$458$	−1850.00	−0.188744
$459$	513.000	0.0521673
$460$	−4935.00	−0.500208
$461$	8729.00	0.881887	0.440944	−	0.897535i	$-0.354644\pi$
$461$	8729.00	0.881887	0.440944	+	0.897535i	$0.354644\pi$
$462$	21.0000	0.00211474
$463$	−12017.0	−1.20621	−0.603107	−	0.797660i	$-0.706071\pi$
$463$	−12017.0	−1.20621	−0.603107	+	0.797660i	$0.706071\pi$
$464$	−5371.00	−0.537376
$465$	1920.00	0.191479
$466$	4012.00	0.398825
$467$	−9357.00	−0.927174	−0.463587	−	0.886051i	$-0.653438\pi$
$467$	−9357.00	−0.927174	−0.463587	+	0.886051i	$0.653438\pi$
$468$	−819.000	−0.0808938
$469$	−3290.00	−0.323919
$470$	−480.000	−0.0471080
$471$	−6579.00	−0.643619
$472$	−2340.00	−0.228193
$473$	201.000	0.0195391
$474$	1578.00	0.152911
$475$	11700.0	1.13017
$476$	−931.000	−0.0896477
$477$	4590.00	0.440590
$478$	4968.00	0.475379
$479$	−13911.0	−1.32695	−0.663476	−	0.748198i	$-0.730919\pi$
$479$	−13911.0	−1.32695	−0.663476	+	0.748198i	$0.730919\pi$
$480$	2415.00	0.229644
$481$	715.000	0.0677779
$482$	86.0000	0.00812696
$483$	−2961.00	−0.278944
$484$	9310.00	0.874343
$485$	−1610.00	−0.150735
$486$	−243.000	−0.0226805
$487$	7776.00	0.723540	0.361770	−	0.932267i	$-0.382172\pi$
$487$	7776.00	0.723540	0.361770	+	0.932267i	$0.382172\pi$
$488$	−12675.0	−1.17576
$489$	438.000	0.0405052
$490$	245.000	0.0225877
$491$	6666.00	0.612693	0.306347	−	0.951920i	$-0.400893\pi$
$491$	6666.00	0.612693	0.306347	+	0.951920i	$0.400893\pi$
$492$	0	0
$493$	−2489.00	−0.227381
$494$	1521.00	0.138528
$495$	45.0000	0.00408606
$496$	−5248.00	−0.475085
$497$	2268.00	0.204696
$498$	−798.000	−0.0718057
$499$	−7596.00	−0.681450	−0.340725	−	0.940163i	$-0.610673\pi$
$499$	−7596.00	−0.681450	−0.340725	+	0.940163i	$0.610673\pi$
$500$	−7875.00	−0.704361
$501$	5145.00	0.458806
$502$	525.000	0.0466771
$503$	−13846.0	−1.22736	−0.613681	−	0.789554i	$-0.710312\pi$
$503$	−13846.0	−1.22736	−0.613681	+	0.789554i	$0.710312\pi$
$504$	945.000	0.0835191
$505$	−4260.00	−0.375381
$506$	−141.000	−0.0123878
$507$	507.000	0.0444116
$508$	−10598.0	−0.925611
$509$	10817.0	0.941955	0.470978	−	0.882145i	$-0.343901\pi$
$509$	10817.0	0.941955	0.470978	+	0.882145i	$0.343901\pi$
$510$	285.000	0.0247451
$511$	−2611.00	−0.226035
$512$	−11521.0	−0.994455
$513$	−3159.00	−0.271878
$514$	782.000	0.0671061
$515$	1005.00	0.0859914
$516$	4221.00	0.360115
$517$	96.0000	0.00816649
$518$	−385.000	−0.0326562
$519$	−8982.00	−0.759665
$520$	−975.000	−0.0822242
$521$	14481.0	1.21770	0.608852	−	0.793284i	$-0.291630\pi$
$521$	14481.0	1.21770	0.608852	+	0.793284i	$0.291630\pi$
$522$	1179.00	0.0988571
$523$	−16588.0	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$523$	−16588.0	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$524$	−2513.00	−0.209506
$525$	−2100.00	−0.174574
$526$	2388.00	0.197950
$527$	−2432.00	−0.201024
$528$	−123.000	−0.0101380
$529$	7714.00	0.634010
$530$	2550.00	0.208990
$531$	−1404.00	−0.114743
$532$	5733.00	0.467213
$533$	0	0
$534$	750.000	0.0607784
$535$	−8430.00	−0.681235
$536$	−7050.00	−0.568122
$537$	−4980.00	−0.400192
$538$	−1622.00	−0.129980
$539$	−49.0000	−0.00391573
$540$	945.000	0.0753080
$541$	10485.0	0.833245	0.416622	−	0.909080i	$-0.363214\pi$
$541$	10485.0	0.833245	0.416622	+	0.909080i	$0.363214\pi$
$542$	−1962.00	−0.155489
$543$	12390.0	0.979200
$544$	−3059.00	−0.241091
$545$	4135.00	0.324998
$546$	−273.000	−0.0213980
$547$	−6620.00	−0.517460	−0.258730	−	0.965950i	$-0.583304\pi$
$547$	−6620.00	−0.517460	−0.258730	+	0.965950i	$0.583304\pi$
$548$	−19299.0	−1.50440
$549$	−7605.00	−0.591209
$550$	−100.000	−0.00775275
$551$	15327.0	1.18503
$552$	−6345.00	−0.489241
$553$	−3682.00	−0.283137
$554$	−3338.00	−0.255989
$555$	−825.000	−0.0630978
$556$	1176.00	0.0897006
$557$	−24648.0	−1.87499	−0.937495	−	0.347999i	$-0.886861\pi$
$557$	−24648.0	−1.87499	−0.937495	+	0.347999i	$0.886861\pi$
$558$	1152.00	0.0873979
$559$	−2613.00	−0.197707
$560$	−1435.00	−0.108285
$561$	−57.0000	−0.00428974
$562$	−4762.00	−0.357425
$563$	−2529.00	−0.189316	−0.0946578	−	0.995510i	$-0.530176\pi$
$563$	−2529.00	−0.189316	−0.0946578	+	0.995510i	$0.530176\pi$
$564$	2016.00	0.150512
$565$	690.000	0.0513779
$566$	−2616.00	−0.194273
$567$	567.000	0.0419961
$568$	4860.00	0.359016
$569$	21650.0	1.59511	0.797553	−	0.603249i	$-0.206127\pi$
$569$	21650.0	1.59511	0.797553	+	0.603249i	$0.206127\pi$
$570$	−1755.00	−0.128963
$571$	−5944.00	−0.435637	−0.217818	−	0.975989i	$-0.569894\pi$
$571$	−5944.00	−0.435637	−0.217818	+	0.975989i	$0.569894\pi$
$572$	91.0000	0.00665193
$573$	−13191.0	−0.961714
$574$	0	0
$575$	14100.0	1.02263
$576$	−1503.00	−0.108724
$577$	−25174.0	−1.81630	−0.908152	−	0.418641i	$-0.862507\pi$
$577$	−25174.0	−1.81630	−0.908152	+	0.418641i	$0.862507\pi$
$578$	4552.00	0.327575
$579$	1656.00	0.118862
$580$	−4585.00	−0.328244
$581$	1862.00	0.132958
$582$	−966.000	−0.0688007
$583$	−510.000	−0.0362299
$584$	−5595.00	−0.396443
$585$	−585.000	−0.0413449
$586$	−5670.00	−0.399702
$587$	10514.0	0.739283	0.369642	−	0.929174i	$-0.379480\pi$
$587$	10514.0	0.739283	0.369642	+	0.929174i	$0.379480\pi$
$588$	−1029.00	−0.0721688
$589$	14976.0	1.04767
$590$	−780.000	−0.0544273
$591$	5004.00	0.348286
$592$	2255.00	0.156554
$593$	20750.0	1.43693	0.718466	−	0.695562i	$-0.244845\pi$
$593$	20750.0	1.43693	0.718466	+	0.695562i	$0.244845\pi$
$594$	27.0000	0.00186502
$595$	−665.000	−0.0458191
$596$	10248.0	0.704320
$597$	−10569.0	−0.724557
$598$	1833.00	0.125346
$599$	−21827.0	−1.48886	−0.744430	−	0.667701i	$-0.767279\pi$
$599$	−21827.0	−1.48886	−0.744430	+	0.667701i	$0.767279\pi$
$600$	−4500.00	−0.306186
$601$	6748.00	0.457998	0.228999	−	0.973427i	$-0.426455\pi$
$601$	6748.00	0.457998	0.228999	+	0.973427i	$0.426455\pi$
$602$	1407.00	0.0952575
$603$	−4230.00	−0.285670
$604$	−6265.00	−0.422052
$605$	6650.00	0.446878
$606$	−2556.00	−0.171337
$607$	−24421.0	−1.63298	−0.816489	−	0.577361i	$-0.804083\pi$
$607$	−24421.0	−1.63298	−0.816489	+	0.577361i	$0.804083\pi$
$608$	18837.0	1.25648
$609$	−2751.00	−0.183048
$610$	−4225.00	−0.280435
$611$	−1248.00	−0.0826329
$612$	−1197.00	−0.0790619
$613$	−21155.0	−1.39387	−0.696935	−	0.717134i	$-0.745453\pi$
$613$	−21155.0	−1.39387	−0.696935	+	0.717134i	$0.745453\pi$
$614$	2128.00	0.139868
$615$	0	0
$616$	−105.000	−0.00686781
$617$	4559.00	0.297469	0.148735	−	0.988877i	$-0.452480\pi$
$617$	4559.00	0.297469	0.148735	+	0.988877i	$0.452480\pi$
$618$	603.000	0.0392495
$619$	24939.0	1.61936	0.809679	−	0.586873i	$-0.199641\pi$
$619$	24939.0	1.61936	0.809679	+	0.586873i	$0.199641\pi$
$620$	−4480.00	−0.290195
$621$	−3807.00	−0.246006
$622$	−558.000	−0.0359707
$623$	−1750.00	−0.112540
$624$	1599.00	0.102582
$625$	6875.00	0.440000
$626$	6648.00	0.424453
$627$	351.000	0.0223566
$628$	15351.0	0.975432
$629$	1045.00	0.0662431
$630$	315.000	0.0199205
$631$	8507.00	0.536701	0.268350	−	0.963321i	$-0.413521\pi$
$631$	8507.00	0.536701	0.268350	+	0.963321i	$0.413521\pi$
$632$	−7890.00	−0.496594
$633$	−12489.0	−0.784191
$634$	11180.0	0.700338
$635$	−7570.00	−0.473081
$636$	−10710.0	−0.667734
$637$	637.000	0.0396214
$638$	−131.000	−0.00812906
$639$	2916.00	0.180525
$640$	−7275.00	−0.449328
$641$	−25166.0	−1.55070	−0.775349	−	0.631533i	$-0.782426\pi$
$641$	−25166.0	−1.55070	−0.775349	+	0.631533i	$0.782426\pi$
$642$	−5058.00	−0.310940
$643$	−22099.0	−1.35536	−0.677682	−	0.735355i	$-0.737016\pi$
$643$	−22099.0	−1.35536	−0.677682	+	0.735355i	$0.737016\pi$
$644$	6909.00	0.422753
$645$	3015.00	0.184055
$646$	2223.00	0.135391
$647$	−3964.00	−0.240867	−0.120433	−	0.992721i	$-0.538428\pi$
$647$	−3964.00	−0.240867	−0.120433	+	0.992721i	$0.538428\pi$
$648$	1215.00	0.0736570
$649$	156.000	0.00943534
$650$	1300.00	0.0784465
$651$	−2688.00	−0.161830
$652$	−1022.00	−0.0613874
$653$	10275.0	0.615761	0.307880	−	0.951425i	$-0.400380\pi$
$653$	10275.0	0.615761	0.307880	+	0.951425i	$0.400380\pi$
$654$	2481.00	0.148341
$655$	−1795.00	−0.107079
$656$	0	0
$657$	−3357.00	−0.199344
$658$	672.000	0.0398135
$659$	−1258.00	−0.0743622	−0.0371811	−	0.999309i	$-0.511838\pi$
$659$	−1258.00	−0.0743622	−0.0371811	+	0.999309i	$0.511838\pi$
$660$	−105.000	−0.00619261
$661$	−13890.0	−0.817335	−0.408667	−	0.912683i	$-0.634006\pi$
$661$	−13890.0	−0.817335	−0.408667	+	0.912683i	$0.634006\pi$
$662$	1450.00	0.0851297
$663$	741.000	0.0434058
$664$	3990.00	0.233196
$665$	4095.00	0.238793
$666$	−495.000	−0.0288001
$667$	18471.0	1.07226
$668$	−12005.0	−0.695340
$669$	8778.00	0.507290
$670$	−2350.00	−0.135505
$671$	845.000	0.0486153
$672$	−3381.00	−0.194085
$673$	−929.000	−0.0532100	−0.0266050	−	0.999646i	$-0.508470\pi$
$673$	−929.000	−0.0532100	−0.0266050	+	0.999646i	$0.508470\pi$
$674$	8685.00	0.496341
$675$	−2700.00	−0.153960
$676$	−1183.00	−0.0673077
$677$	26546.0	1.50701	0.753505	−	0.657442i	$-0.228362\pi$
$677$	26546.0	1.50701	0.753505	+	0.657442i	$0.228362\pi$
$678$	414.000	0.0234507
$679$	2254.00	0.127394
$680$	−1425.00	−0.0803621
$681$	19734.0	1.11044
$682$	−128.000	−0.00718676
$683$	−8331.00	−0.466730	−0.233365	−	0.972389i	$-0.574974\pi$
$683$	−8331.00	−0.466730	−0.233365	+	0.972389i	$0.574974\pi$
$684$	7371.00	0.412043
$685$	−13785.0	−0.768902
$686$	−343.000	−0.0190901
$687$	5550.00	0.308218
$688$	−8241.00	−0.456665
$689$	6630.00	0.366593
$690$	−2115.00	−0.116691
$691$	26028.0	1.43293	0.716463	−	0.697625i	$-0.245760\pi$
$691$	26028.0	1.43293	0.716463	+	0.697625i	$0.245760\pi$
$692$	20958.0	1.15131
$693$	−63.0000	−0.00345335
$694$	876.000	0.0479143
$695$	840.000	0.0458461
$696$	−5895.00	−0.321048
$697$	0	0
$698$	−3598.00	−0.195109
$699$	−12036.0	−0.651278
$700$	4900.00	0.264575
$701$	1570.00	0.0845907	0.0422954	−	0.999105i	$-0.486533\pi$
$701$	1570.00	0.0845907	0.0422954	+	0.999105i	$0.486533\pi$
$702$	−351.000	−0.0188713
$703$	−6435.00	−0.345236
$704$	167.000	0.00894041
$705$	1440.00	0.0769270
$706$	−12038.0	−0.641723
$707$	5964.00	0.317255
$708$	3276.00	0.173898
$709$	−12398.0	−0.656723	−0.328362	−	0.944552i	$-0.606496\pi$
$709$	−12398.0	−0.656723	−0.328362	+	0.944552i	$0.606496\pi$
$710$	1620.00	0.0856303
$711$	−4734.00	−0.249703
$712$	−3750.00	−0.197384
$713$	18048.0	0.947970
$714$	−399.000	−0.0209134
$715$	65.0000	0.00339981
$716$	11620.0	0.606508
$717$	−14904.0	−0.776290
$718$	7680.00	0.399185
$719$	−7194.00	−0.373145	−0.186572	−	0.982441i	$-0.559738\pi$
$719$	−7194.00	−0.373145	−0.186572	+	0.982441i	$0.559738\pi$
$720$	−1845.00	−0.0954987
$721$	−1407.00	−0.0726760
$722$	−6830.00	−0.352059
$723$	−258.000	−0.0132713
$724$	−28910.0	−1.48402
$725$	13100.0	0.671065
$726$	3990.00	0.203971
$727$	−33061.0	−1.68661	−0.843304	−	0.537436i	$-0.819393\pi$
$727$	−33061.0	−1.68661	−0.843304	+	0.537436i	$0.819393\pi$
$728$	1365.00	0.0694921
$729$	729.000	0.0370370
$730$	−1865.00	−0.0945572
$731$	−3819.00	−0.193230
$732$	17745.0	0.896003
$733$	1248.00	0.0628867	0.0314433	−	0.999506i	$-0.489990\pi$
$733$	1248.00	0.0628867	0.0314433	+	0.999506i	$0.489990\pi$
$734$	−8944.00	−0.449767
$735$	−735.000	−0.0368856
$736$	22701.0	1.13692
$737$	470.000	0.0234907
$738$	0	0
$739$	−16570.0	−0.824814	−0.412407	−	0.911000i	$-0.635312\pi$
$739$	−16570.0	−0.824814	−0.412407	+	0.911000i	$0.635312\pi$
$740$	1925.00	0.0956276
$741$	−4563.00	−0.226216
$742$	−3570.00	−0.176629
$743$	−8706.00	−0.429868	−0.214934	−	0.976629i	$-0.568954\pi$
$743$	−8706.00	−0.429868	−0.214934	+	0.976629i	$0.568954\pi$
$744$	−5760.00	−0.283833
$745$	7320.00	0.359979
$746$	−8644.00	−0.424235
$747$	2394.00	0.117258
$748$	133.000	0.00650129
$749$	11802.0	0.575749
$750$	−3375.00	−0.164317
$751$	20852.0	1.01318	0.506591	−	0.862186i	$-0.330905\pi$
$751$	20852.0	1.01318	0.506591	+	0.862186i	$0.330905\pi$
$752$	−3936.00	−0.190866
$753$	−1575.00	−0.0762234
$754$	1703.00	0.0822541
$755$	−4475.00	−0.215711
$756$	−1323.00	−0.0636469
$757$	4258.00	0.204438	0.102219	−	0.994762i	$-0.467406\pi$
$757$	4258.00	0.204438	0.102219	+	0.994762i	$0.467406\pi$
$758$	−5700.00	−0.273131
$759$	423.000	0.0202292
$760$	8775.00	0.418819
$761$	27736.0	1.32119	0.660597	−	0.750740i	$-0.270303\pi$
$761$	27736.0	1.32119	0.660597	+	0.750740i	$0.270303\pi$
$762$	−4542.00	−0.215931
$763$	−5789.00	−0.274673
$764$	30779.0	1.45752
$765$	−855.000	−0.0404086
$766$	9917.00	0.467775
$767$	−2028.00	−0.0954718
$768$	−357.000	−0.0167736
$769$	1785.00	0.0837045	0.0418522	−	0.999124i	$-0.486674\pi$
$769$	1785.00	0.0837045	0.0418522	+	0.999124i	$0.486674\pi$
$770$	−35.0000	−0.00163807
$771$	−2346.00	−0.109584
$772$	−3864.00	−0.180140
$773$	34193.0	1.59099	0.795496	−	0.605959i	$-0.207210\pi$
$773$	34193.0	1.59099	0.795496	+	0.605959i	$0.207210\pi$
$774$	1809.00	0.0840093
$775$	12800.0	0.593277
$776$	4830.00	0.223437
$777$	1155.00	0.0533274
$778$	14554.0	0.670676
$779$	0	0
$780$	1365.00	0.0626601
$781$	−324.000	−0.0148446
$782$	2679.00	0.122507
$783$	−3537.00	−0.161433
$784$	2009.00	0.0915179
$785$	10965.0	0.498545
$786$	−1077.00	−0.0488745
$787$	−11069.0	−0.501356	−0.250678	−	0.968071i	$-0.580654\pi$
$787$	−11069.0	−0.501356	−0.250678	+	0.968071i	$0.580654\pi$
$788$	−11676.0	−0.527843
$789$	−7164.00	−0.323251
$790$	−2630.00	−0.118445
$791$	−966.000	−0.0434223
$792$	−135.000	−0.00605684
$793$	−10985.0	−0.491915
$794$	−9410.00	−0.420590
$795$	−7650.00	−0.341280
$796$	24661.0	1.09810
$797$	−9352.00	−0.415640	−0.207820	−	0.978167i	$-0.566637\pi$
$797$	−9352.00	−0.415640	−0.207820	+	0.978167i	$0.566637\pi$
$798$	2457.00	0.108994
$799$	−1824.00	−0.0807616
$800$	16100.0	0.711526
$801$	−2250.00	−0.0992507
$802$	−6194.00	−0.272715
$803$	373.000	0.0163921
$804$	9870.00	0.432945
$805$	4935.00	0.216069
$806$	1664.00	0.0727195
$807$	4866.00	0.212257
$808$	12780.0	0.556434
$809$	−24858.0	−1.08030	−0.540149	−	0.841570i	$-0.681632\pi$
$809$	−24858.0	−1.08030	−0.540149	+	0.841570i	$0.681632\pi$
$810$	405.000	0.0175682
$811$	−4249.00	−0.183974	−0.0919868	−	0.995760i	$-0.529322\pi$
$811$	−4249.00	−0.183974	−0.0919868	+	0.995760i	$0.529322\pi$
$812$	6419.00	0.277417
$813$	5886.00	0.253913
$814$	55.0000	0.00236824
$815$	−730.000	−0.0313752
$816$	2337.00	0.100259
$817$	23517.0	1.00704
$818$	−8881.00	−0.379605
$819$	819.000	0.0349428
$820$	0	0
$821$	14440.0	0.613836	0.306918	−	0.951736i	$-0.400702\pi$
$821$	14440.0	0.613836	0.306918	+	0.951736i	$0.400702\pi$
$822$	−8271.00	−0.350954
$823$	10716.0	0.453872	0.226936	−	0.973910i	$-0.427129\pi$
$823$	10716.0	0.453872	0.226936	+	0.973910i	$0.427129\pi$
$824$	−3015.00	−0.127467
$825$	300.000	0.0126602
$826$	1092.00	0.0459994
$827$	16151.0	0.679112	0.339556	−	0.940586i	$-0.389723\pi$
$827$	16151.0	0.679112	0.339556	+	0.940586i	$0.389723\pi$
$828$	8883.00	0.372833
$829$	9539.00	0.399642	0.199821	−	0.979832i	$-0.435964\pi$
$829$	9539.00	0.399642	0.199821	+	0.979832i	$0.435964\pi$
$830$	1330.00	0.0556205
$831$	10014.0	0.418029
$832$	−2171.00	−0.0904638
$833$	931.000	0.0387242
$834$	504.000	0.0209258
$835$	−8575.00	−0.355389
$836$	−819.000	−0.0338824
$837$	−3456.00	−0.142720
$838$	−4109.00	−0.169383
$839$	−14700.0	−0.604887	−0.302444	−	0.953167i	$-0.597802\pi$
$839$	−14700.0	−0.604887	−0.302444	+	0.953167i	$0.597802\pi$
$840$	−1575.00	−0.0646936
$841$	−7228.00	−0.296363
$842$	5206.00	0.213077
$843$	14286.0	0.583673
$844$	29141.0	1.18848
$845$	−845.000	−0.0344010
$846$	864.000	0.0351122
$847$	−9310.00	−0.377681
$848$	20910.0	0.846760
$849$	7848.00	0.317247
$850$	1900.00	0.0766700
$851$	−7755.00	−0.312383
$852$	−6804.00	−0.273593
$853$	−7980.00	−0.320317	−0.160158	−	0.987091i	$-0.551200\pi$
$853$	−7980.00	−0.320317	−0.160158	+	0.987091i	$0.551200\pi$
$854$	5915.00	0.237011
$855$	5265.00	0.210596
$856$	25290.0	1.00981
$857$	30574.0	1.21866	0.609328	−	0.792918i	$-0.291439\pi$
$857$	30574.0	1.21866	0.609328	+	0.792918i	$0.291439\pi$
$858$	39.0000	0.00155179
$859$	−4604.00	−0.182871	−0.0914357	−	0.995811i	$-0.529146\pi$
$859$	−4604.00	−0.182871	−0.0914357	+	0.995811i	$0.529146\pi$
$860$	−7035.00	−0.278944
$861$	0	0
$862$	−6978.00	−0.275721
$863$	−38074.0	−1.50180	−0.750900	−	0.660416i	$-0.770380\pi$
$863$	−38074.0	−1.50180	−0.750900	+	0.660416i	$0.770380\pi$
$864$	−4347.00	−0.171167
$865$	14970.0	0.588434
$866$	−7252.00	−0.284565
$867$	−13656.0	−0.534927
$868$	6272.00	0.245260
$869$	526.000	0.0205332
$870$	−1965.00	−0.0765744
$871$	−6110.00	−0.237692
$872$	−12405.0	−0.481750
$873$	2898.00	0.112351
$874$	−16497.0	−0.638466
$875$	7875.00	0.304256
$876$	7833.00	0.302115
$877$	314.000	0.0120901	0.00604506	−	0.999982i	$-0.498076\pi$
$877$	314.000	0.0120901	0.00604506	+	0.999982i	$0.498076\pi$
$878$	−1451.00	−0.0557732
$879$	17010.0	0.652711
$880$	205.000	0.00785290
$881$	37331.0	1.42760	0.713799	−	0.700351i	$-0.246973\pi$
$881$	37331.0	1.42760	0.713799	+	0.700351i	$0.246973\pi$
$882$	−441.000	−0.0168359
$883$	20407.0	0.777747	0.388873	−	0.921291i	$-0.372864\pi$
$883$	20407.0	0.777747	0.388873	+	0.921291i	$0.372864\pi$
$884$	−1729.00	−0.0657834
$885$	2340.00	0.0888794
$886$	−12718.0	−0.482246
$887$	−1524.00	−0.0576899	−0.0288449	−	0.999584i	$-0.509183\pi$
$887$	−1524.00	−0.0576899	−0.0288449	+	0.999584i	$0.509183\pi$
$888$	2475.00	0.0935310
$889$	10598.0	0.399826
$890$	−1250.00	−0.0470788
$891$	−81.0000	−0.00304557
$892$	−20482.0	−0.768821
$893$	11232.0	0.420901
$894$	4392.00	0.164307
$895$	8300.00	0.309987
$896$	10185.0	0.379751
$897$	−5499.00	−0.204689
$898$	−233.000	−0.00865848
$899$	16768.0	0.622074
$900$	6300.00	0.233333
$901$	9690.00	0.358292
$902$	0	0
$903$	−4221.00	−0.155555
$904$	−2070.00	−0.0761584
$905$	−20650.0	−0.758485
$906$	−2685.00	−0.0984582
$907$	−41364.0	−1.51430	−0.757149	−	0.653242i	$-0.773409\pi$
$907$	−41364.0	−1.51430	−0.757149	+	0.653242i	$0.773409\pi$
$908$	−46046.0	−1.68292
$909$	7668.00	0.279793
$910$	455.000	0.0165748
$911$	17341.0	0.630662	0.315331	−	0.948982i	$-0.397884\pi$
$911$	17341.0	0.630662	0.315331	+	0.948982i	$0.397884\pi$
$912$	−14391.0	−0.522515
$913$	−266.000	−0.00964219
$914$	−14132.0	−0.511428
$915$	12675.0	0.457948
$916$	−12950.0	−0.467118
$917$	2513.00	0.0904979
$918$	−513.000	−0.0184439
$919$	13278.0	0.476606	0.238303	−	0.971191i	$-0.423409\pi$
$919$	13278.0	0.476606	0.238303	+	0.971191i	$0.423409\pi$
$920$	10575.0	0.378965
$921$	−6384.00	−0.228404
$922$	−8729.00	−0.311794
$923$	4212.00	0.150205
$924$	147.000	0.00523371
$925$	−5500.00	−0.195501
$926$	12017.0	0.426461
$927$	−1809.00	−0.0640942
$928$	21091.0	0.746062
$929$	−43188.0	−1.52524	−0.762622	−	0.646844i	$-0.776088\pi$
$929$	−43188.0	−1.52524	−0.762622	+	0.646844i	$0.776088\pi$
$930$	−1920.00	−0.0676982
$931$	−5733.00	−0.201817
$932$	28084.0	0.987041
$933$	1674.00	0.0587399
$934$	9357.00	0.327806
$935$	95.0000	0.00332282
$936$	1755.00	0.0612863
$937$	−10822.0	−0.377310	−0.188655	−	0.982043i	$-0.560413\pi$
$937$	−10822.0	−0.377310	−0.188655	+	0.982043i	$0.560413\pi$
$938$	3290.00	0.114523
$939$	−19944.0	−0.693129
$940$	−3360.00	−0.116586
$941$	20522.0	0.710944	0.355472	−	0.934687i	$-0.384320\pi$
$941$	20522.0	0.710944	0.355472	+	0.934687i	$0.384320\pi$
$942$	6579.00	0.227554
$943$	0	0
$944$	−6396.00	−0.220521
$945$	−945.000	−0.0325300
$946$	−201.000	−0.00690811
$947$	3723.00	0.127752	0.0638761	−	0.997958i	$-0.479654\pi$
$947$	3723.00	0.127752	0.0638761	+	0.997958i	$0.479654\pi$
$948$	11046.0	0.378436
$949$	−4849.00	−0.165864
$950$	−11700.0	−0.399577
$951$	−33540.0	−1.14365
$952$	1995.00	0.0679184
$953$	−31092.0	−1.05684	−0.528420	−	0.848983i	$-0.677215\pi$
$953$	−31092.0	−1.05684	−0.528420	+	0.848983i	$0.677215\pi$
$954$	−4590.00	−0.155772
$955$	21985.0	0.744940
$956$	34776.0	1.17650
$957$	393.000	0.0132747
$958$	13911.0	0.469148
$959$	19299.0	0.649841
$960$	2505.00	0.0842172
$961$	−13407.0	−0.450035
$962$	−715.000	−0.0239631
$963$	15174.0	0.507763
$964$	602.000	0.0201132
$965$	−2760.00	−0.0920700
$966$	2961.00	0.0986218
$967$	−47227.0	−1.57055	−0.785273	−	0.619150i	$-0.787477\pi$
$967$	−47227.0	−1.57055	−0.785273	+	0.619150i	$0.787477\pi$
$968$	−19950.0	−0.662415
$969$	−6669.00	−0.221093
$970$	1610.00	0.0532928
$971$	−35880.0	−1.18583	−0.592917	−	0.805264i	$-0.702024\pi$
$971$	−35880.0	−1.18583	−0.592917	+	0.805264i	$0.702024\pi$
$972$	−1701.00	−0.0561313
$973$	−1176.00	−0.0387470
$974$	−7776.00	−0.255810
$975$	−3900.00	−0.128103
$976$	−34645.0	−1.13623
$977$	−26349.0	−0.862824	−0.431412	−	0.902155i	$-0.641984\pi$
$977$	−26349.0	−0.862824	−0.431412	+	0.902155i	$0.641984\pi$
$978$	−438.000	−0.0143208
$979$	250.000	0.00816142
$980$	1715.00	0.0559017
$981$	−7443.00	−0.242239
$982$	−6666.00	−0.216620
$983$	−28303.0	−0.918337	−0.459169	−	0.888349i	$-0.651853\pi$
$983$	−28303.0	−0.918337	−0.459169	+	0.888349i	$0.651853\pi$
$984$	0	0
$985$	−8340.00	−0.269781
$986$	2489.00	0.0803914
$987$	−2016.00	−0.0650152
$988$	10647.0	0.342840
$989$	28341.0	0.911215
$990$	−45.0000	−0.00144464
$991$	−4838.00	−0.155080	−0.0775399	−	0.996989i	$-0.524707\pi$
$991$	−4838.00	−0.155080	−0.0775399	+	0.996989i	$0.524707\pi$
$992$	20608.0	0.659581
$993$	−4350.00	−0.139016
$994$	−2268.00	−0.0723708
$995$	17615.0	0.561239
$996$	−5586.00	−0.177710
$997$	−50822.0	−1.61439	−0.807196	−	0.590283i	$-0.799016\pi$
$997$	−50822.0	−1.61439	−0.807196	+	0.590283i	$0.799016\pi$
$998$	7596.00	0.240929
$999$	1485.00	0.0470304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.4.a.b.1.1	✓	1
3.2	odd	2		819.4.a.b.1.1		1
7.6	odd	2		1911.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.a.b.1.1	✓	1	1.1	even	1	trivial
819.4.a.b.1.1		1	3.2	odd	2
1911.4.a.e.1.1		1	7.6	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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