LMFDB - Embedded newform 245.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,10,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.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:	$126.183779860$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+28.0000 q^{2} +116.000 q^{3} +272.000 q^{4} -625.000 q^{5} +3248.00 q^{6} -6720.00 q^{8} -6227.00 q^{9} +O(q^{10})$

\(q+28.0000 q^{2} +116.000 q^{3} +272.000 q^{4} -625.000 q^{5} +3248.00 q^{6} -6720.00 q^{8} -6227.00 q^{9} -17500.0 q^{10} -25548.0 q^{11} +31552.0 q^{12} +42306.0 q^{13} -72500.0 q^{15} -327424. q^{16} +526342. q^{17} -174356. q^{18} +350060. q^{19} -170000. q^{20} -715344. q^{22} -621976. q^{23} -779520. q^{24} +390625. q^{25} +1.18457e6 q^{26} -3.00556e6 q^{27} +6.72043e6 q^{29} -2.03000e6 q^{30} +6.41221e6 q^{31} -5.72723e6 q^{32} -2.96357e6 q^{33} +1.47376e7 q^{34} -1.69374e6 q^{36} -2.31768e6 q^{37} +9.80168e6 q^{38} +4.90750e6 q^{39} +4.20000e6 q^{40} +1.02247e7 q^{41} +3.01140e7 q^{43} -6.94906e6 q^{44} +3.89188e6 q^{45} -1.74153e7 q^{46} +2.36449e7 q^{47} -3.79812e7 q^{48} +1.09375e7 q^{50} +6.10557e7 q^{51} +1.15072e7 q^{52} +5.72927e7 q^{53} -8.41557e7 q^{54} +1.59675e7 q^{55} +4.06070e7 q^{57} +1.88172e8 q^{58} -8.49348e7 q^{59} -1.97200e7 q^{60} -1.46778e7 q^{61} +1.79542e8 q^{62} +7.27859e6 q^{64} -2.64412e7 q^{65} -8.29799e7 q^{66} -2.44558e8 q^{67} +1.43165e8 q^{68} -7.21492e7 q^{69} +6.19020e7 q^{71} +4.18454e7 q^{72} +2.83764e8 q^{73} -6.48951e7 q^{74} +4.53125e7 q^{75} +9.52163e7 q^{76} +1.37410e8 q^{78} +2.76107e8 q^{79} +2.04640e8 q^{80} -2.26079e8 q^{81} +2.86291e8 q^{82} +7.29960e7 q^{83} -3.28964e8 q^{85} +8.43192e8 q^{86} +7.79570e8 q^{87} +1.71683e8 q^{88} +8.96368e8 q^{89} +1.08973e8 q^{90} -1.69177e8 q^{92} +7.43816e8 q^{93} +6.62058e8 q^{94} -2.18788e8 q^{95} -6.64359e8 q^{96} -1.20581e9 q^{97} +1.59087e8 q^{99} +O(q^{100})\)

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 $

$2$	28.0000	1.23744	0.618718	−	0.785613i	$-0.287652\pi$
$2$	28.0000	1.23744	0.618718	+	0.785613i	$0.287652\pi$
$3$	116.000	0.826823	0.413411	−	0.910544i	$-0.364337\pi$
$3$	116.000	0.826823	0.413411	+	0.910544i	$0.364337\pi$
$4$	272.000	0.531250
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	3248.00	1.02314
$7$	0	0
$7$	0	0
$8$	−6720.00	−0.580049
$9$	−6227.00	−0.316364
$10$	−17500.0	−0.553399
$11$	−25548.0	−0.526126	−0.263063	−	0.964779i	$-0.584733\pi$
$11$	−25548.0	−0.526126	−0.263063	+	0.964779i	$0.584733\pi$
$12$	31552.0	0.439250
$13$	42306.0	0.410825	0.205413	−	0.978675i	$-0.434146\pi$
$13$	42306.0	0.410825	0.205413	+	0.978675i	$0.434146\pi$
$14$	0	0
$15$	−72500.0	−0.369766
$16$	−327424.	−1.24902
$17$	526342.	1.52844	0.764219	−	0.644957i	$-0.223125\pi$
$17$	526342.	1.52844	0.764219	+	0.644957i	$0.223125\pi$
$18$	−174356.	−0.391481
$19$	350060.	0.616242	0.308121	−	0.951347i	$-0.400300\pi$
$19$	350060.	0.616242	0.308121	+	0.951347i	$0.400300\pi$
$20$	−170000.	−0.237582
$21$	0	0
$22$	−715344.	−0.651048
$23$	−621976.	−0.463445	−0.231723	−	0.972782i	$-0.574436\pi$
$23$	−621976.	−0.463445	−0.231723	+	0.972782i	$0.574436\pi$
$24$	−779520.	−0.479597
$25$	390625.	0.200000
$26$	1.18457e6	0.508370
$27$	−3.00556e6	−1.08840
$28$	0	0
$29$	6.72043e6	1.76444	0.882218	−	0.470841i	$-0.156049\pi$
$29$	6.72043e6	1.76444	0.882218	+	0.470841i	$0.156049\pi$
$30$	−2.03000e6	−0.457562
$31$	6.41221e6	1.24704	0.623519	−	0.781808i	$-0.285702\pi$
$31$	6.41221e6	1.24704	0.623519	+	0.781808i	$0.285702\pi$
$32$	−5.72723e6	−0.965539
$33$	−2.96357e6	−0.435013
$34$	1.47376e7	1.89135
$35$	0	0
$36$	−1.69374e6	−0.168069
$37$	−2.31768e6	−0.203304	−0.101652	−	0.994820i	$-0.532413\pi$
$37$	−2.31768e6	−0.203304	−0.101652	+	0.994820i	$0.532413\pi$
$38$	9.80168e6	0.762561
$39$	4.90750e6	0.339679
$40$	4.20000e6	0.259406
$41$	1.02247e7	0.565096	0.282548	−	0.959253i	$-0.408820\pi$
$41$	1.02247e7	0.565096	0.282548	+	0.959253i	$0.408820\pi$
$42$	0	0
$43$	3.01140e7	1.34326	0.671631	−	0.740886i	$-0.265594\pi$
$43$	3.01140e7	1.34326	0.671631	+	0.740886i	$0.265594\pi$
$44$	−6.94906e6	−0.279504
$45$	3.89188e6	0.141482
$46$	−1.74153e7	−0.573484
$47$	2.36449e7	0.706801	0.353401	−	0.935472i	$-0.385025\pi$
$47$	2.36449e7	0.706801	0.353401	+	0.935472i	$0.385025\pi$
$48$	−3.79812e7	−1.03272
$49$	0	0
$50$	1.09375e7	0.247487
$51$	6.10557e7	1.26375
$52$	1.15072e7	0.218251
$53$	5.72927e7	0.997373	0.498686	−	0.866782i	$-0.333816\pi$
$53$	5.72927e7	0.997373	0.498686	+	0.866782i	$0.333816\pi$
$54$	−8.41557e7	−1.34683
$55$	1.59675e7	0.235291
$56$	0	0
$57$	4.06070e7	0.509523
$58$	1.88172e8	2.18338
$59$	−8.49348e7	−0.912539	−0.456270	−	0.889842i	$-0.650815\pi$
$59$	−8.49348e7	−0.912539	−0.456270	+	0.889842i	$0.650815\pi$
$60$	−1.97200e7	−0.196438
$61$	−1.46778e7	−0.135730	−0.0678652	−	0.997694i	$-0.521619\pi$
$61$	−1.46778e7	−0.135730	−0.0678652	+	0.997694i	$0.521619\pi$
$62$	1.79542e8	1.54313
$63$	0	0
$64$	7.27859e6	0.0542297
$65$	−2.64412e7	−0.183727
$66$	−8.29799e7	−0.538301
$67$	−2.44558e8	−1.48267	−0.741336	−	0.671134i	$-0.765807\pi$
$67$	−2.44558e8	−1.48267	−0.741336	+	0.671134i	$0.765807\pi$
$68$	1.43165e8	0.811983
$69$	−7.21492e7	−0.383187
$70$	0	0
$71$	6.19020e7	0.289096	0.144548	−	0.989498i	$-0.453827\pi$
$71$	6.19020e7	0.289096	0.144548	+	0.989498i	$0.453827\pi$
$72$	4.18454e7	0.183507
$73$	2.83764e8	1.16951	0.584755	−	0.811210i	$-0.301191\pi$
$73$	2.83764e8	1.16951	0.584755	+	0.811210i	$0.301191\pi$
$74$	−6.48951e7	−0.251576
$75$	4.53125e7	0.165365
$76$	9.52163e7	0.327379
$77$	0	0
$78$	1.37410e8	0.420332
$79$	2.76107e8	0.797547	0.398773	−	0.917049i	$-0.369436\pi$
$79$	2.76107e8	0.797547	0.398773	+	0.917049i	$0.369436\pi$
$80$	2.04640e8	0.558580
$81$	−2.26079e8	−0.583549
$82$	2.86291e8	0.699271
$83$	7.29960e7	0.168829	0.0844146	−	0.996431i	$-0.473098\pi$
$83$	7.29960e7	0.168829	0.0844146	+	0.996431i	$0.473098\pi$
$84$	0	0
$85$	−3.28964e8	−0.683538
$86$	8.43192e8	1.66220
$87$	7.79570e8	1.45888
$88$	1.71683e8	0.305179
$89$	8.96368e8	1.51437	0.757184	−	0.653201i	$-0.226575\pi$
$89$	8.96368e8	1.51437	0.757184	+	0.653201i	$0.226575\pi$
$90$	1.08973e8	0.175076
$91$	0	0
$92$	−1.69177e8	−0.246205
$93$	7.43816e8	1.03108
$94$	6.62058e8	0.874622
$95$	−2.18788e8	−0.275592
$96$	−6.64359e8	−0.798330
$97$	−1.20581e9	−1.38295	−0.691474	−	0.722401i	$-0.743038\pi$
$97$	−1.20581e9	−1.38295	−0.691474	+	0.722401i	$0.743038\pi$
$98$	0	0
$99$	1.59087e8	0.166448
$100$	1.06250e8	0.106250
$101$	1.46021e9	1.39627	0.698136	−	0.715965i	$-0.254013\pi$
$101$	1.46021e9	1.39627	0.698136	+	0.715965i	$0.254013\pi$
$102$	1.70956e9	1.56381
$103$	−1.08009e9	−0.945563	−0.472782	−	0.881180i	$-0.656750\pi$
$103$	−1.08009e9	−0.945563	−0.472782	+	0.881180i	$0.656750\pi$
$104$	−2.84296e8	−0.238298
$105$	0	0
$106$	1.60419e9	1.23419
$107$	3.35949e8	0.247769	0.123884	−	0.992297i	$-0.460465\pi$
$107$	3.35949e8	0.247769	0.123884	+	0.992297i	$0.460465\pi$
$108$	−8.17512e8	−0.578212
$109$	−1.42521e9	−0.967072	−0.483536	−	0.875324i	$-0.660648\pi$
$109$	−1.42521e9	−0.967072	−0.483536	+	0.875324i	$0.660648\pi$
$110$	4.47090e8	0.291157
$111$	−2.68851e8	−0.168096
$112$	0	0
$113$	−2.84178e9	−1.63960	−0.819799	−	0.572651i	$-0.805915\pi$
$113$	−2.84178e9	−1.63960	−0.819799	+	0.572651i	$0.805915\pi$
$114$	1.13699e9	0.630502
$115$	3.88735e8	0.207259
$116$	1.82796e9	0.937357
$117$	−2.63439e8	−0.129970
$118$	−2.37817e9	−1.12921
$119$	0	0
$120$	4.87200e8	0.214482
$121$	−1.70525e9	−0.723191
$122$	−4.10979e8	−0.167958
$123$	1.18606e9	0.467234
$124$	1.74412e9	0.662489
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	3.49339e9	1.19160	0.595800	−	0.803133i	$-0.296835\pi$
$127$	3.49339e9	1.19160	0.595800	+	0.803133i	$0.296835\pi$
$128$	3.13614e9	1.03264
$129$	3.49322e9	1.11064
$130$	−7.40355e8	−0.227350
$131$	1.84697e9	0.547946	0.273973	−	0.961737i	$-0.411662\pi$
$131$	1.84697e9	0.547946	0.273973	+	0.961737i	$0.411662\pi$
$132$	−8.06090e8	−0.231101
$133$	0	0
$134$	−6.84762e9	−1.83471
$135$	1.87848e9	0.486747
$136$	−3.53702e9	−0.886568
$137$	1.17238e9	0.284331	0.142166	−	0.989843i	$-0.454593\pi$
$137$	1.17238e9	0.284331	0.142166	+	0.989843i	$0.454593\pi$
$138$	−2.02018e9	−0.474170
$139$	4.89001e9	1.11108	0.555538	−	0.831491i	$-0.312512\pi$
$139$	4.89001e9	1.11108	0.555538	+	0.831491i	$0.312512\pi$
$140$	0	0
$141$	2.74281e9	0.584399
$142$	1.73325e9	0.357738
$143$	−1.08083e9	−0.216146
$144$	2.03887e9	0.395147
$145$	−4.20027e9	−0.789080
$146$	7.94538e9	1.44720
$147$	0	0
$148$	−6.30410e8	−0.108005
$149$	−8.61488e9	−1.43189	−0.715947	−	0.698155i	$-0.754005\pi$
$149$	−8.61488e9	−1.43189	−0.715947	+	0.698155i	$0.754005\pi$
$150$	1.26875e9	0.204628
$151$	5.48905e9	0.859213	0.429607	−	0.903016i	$-0.358652\pi$
$151$	5.48905e9	0.859213	0.429607	+	0.903016i	$0.358652\pi$
$152$	−2.35240e9	−0.357450
$153$	−3.27753e9	−0.483543
$154$	0	0
$155$	−4.00763e9	−0.557693
$156$	1.33484e9	0.180455
$157$	1.33110e9	0.174849	0.0874246	−	0.996171i	$-0.472136\pi$
$157$	1.33110e9	0.174849	0.0874246	+	0.996171i	$0.472136\pi$
$158$	7.73101e9	0.986914
$159$	6.64595e9	0.824650
$160$	3.57952e9	0.431802
$161$	0	0
$162$	−6.33021e9	−0.722105
$163$	1.41097e9	0.156557	0.0782786	−	0.996932i	$-0.475058\pi$
$163$	1.41097e9	0.156557	0.0782786	+	0.996932i	$0.475058\pi$
$164$	2.78111e9	0.300207
$165$	1.85223e9	0.194544
$166$	2.04389e9	0.208915
$167$	−2.48555e8	−0.0247285	−0.0123642	−	0.999924i	$-0.503936\pi$
$167$	−2.48555e8	−0.0247285	−0.0123642	+	0.999924i	$0.503936\pi$
$168$	0	0
$169$	−8.81470e9	−0.831223
$170$	−9.21098e9	−0.845836
$171$	−2.17982e9	−0.194957
$172$	8.19101e9	0.713607
$173$	−1.66522e10	−1.41340	−0.706699	−	0.707515i	$-0.749816\pi$
$173$	−1.66522e10	−1.41340	−0.706699	+	0.707515i	$0.749816\pi$
$174$	2.18280e10	1.80527
$175$	0	0
$176$	8.36503e9	0.657144
$177$	−9.85243e9	−0.754508
$178$	2.50983e10	1.87394
$179$	2.02956e10	1.47762	0.738811	−	0.673913i	$-0.235388\pi$
$179$	2.02956e10	1.47762	0.738811	+	0.673913i	$0.235388\pi$
$180$	1.05859e9	0.0751626
$181$	1.36159e10	0.942960	0.471480	−	0.881877i	$-0.343720\pi$
$181$	1.36159e10	0.942960	0.471480	+	0.881877i	$0.343720\pi$
$182$	0	0
$183$	−1.70263e9	−0.112225
$184$	4.17968e9	0.268821
$185$	1.44855e9	0.0909203
$186$	2.08269e10	1.27590
$187$	−1.34470e10	−0.804151
$188$	6.43142e9	0.375488
$189$	0	0
$190$	−6.12605e9	−0.341027
$191$	1.82357e9	0.0991453	0.0495726	−	0.998771i	$-0.484214\pi$
$191$	1.82357e9	0.0991453	0.0495726	+	0.998771i	$0.484214\pi$
$192$	8.44317e8	0.0448384
$193$	1.23747e10	0.641989	0.320995	−	0.947081i	$-0.395983\pi$
$193$	1.23747e10	0.641989	0.320995	+	0.947081i	$0.395983\pi$
$194$	−3.37627e10	−1.71131
$195$	−3.06718e9	−0.151909
$196$	0	0
$197$	1.93137e10	0.913626	0.456813	−	0.889563i	$-0.348991\pi$
$197$	1.93137e10	0.913626	0.456813	+	0.889563i	$0.348991\pi$
$198$	4.45445e9	0.205968
$199$	−1.52145e10	−0.687733	−0.343867	−	0.939019i	$-0.611737\pi$
$199$	−1.52145e10	−0.687733	−0.343867	+	0.939019i	$0.611737\pi$
$200$	−2.62500e9	−0.116010
$201$	−2.83687e10	−1.22591
$202$	4.08860e10	1.72780
$203$	0	0
$204$	1.66071e10	0.671366
$205$	−6.39042e9	−0.252719
$206$	−3.02424e10	−1.17007
$207$	3.87304e9	0.146618
$208$	−1.38520e10	−0.513130
$209$	−8.94333e9	−0.324221
$210$	0	0
$211$	−3.89626e10	−1.35325	−0.676624	−	0.736329i	$-0.736558\pi$
$211$	−3.89626e10	−1.35325	−0.676624	+	0.736329i	$0.736558\pi$
$212$	1.55836e10	0.529854
$213$	7.18063e9	0.239031
$214$	9.40658e9	0.306598
$215$	−1.88213e10	−0.600725
$216$	2.01974e10	0.631325
$217$	0	0
$218$	−3.99058e10	−1.19669
$219$	3.29166e10	0.966977
$220$	4.34316e9	0.124998
$221$	2.22674e10	0.627921
$222$	−7.52783e9	−0.208009
$223$	−1.08324e9	−0.0293328	−0.0146664	−	0.999892i	$-0.504669\pi$
$223$	−1.08324e9	−0.0293328	−0.0146664	+	0.999892i	$0.504669\pi$
$224$	0	0
$225$	−2.43242e9	−0.0632729
$226$	−7.95698e10	−2.02890
$227$	4.94618e10	1.23639	0.618193	−	0.786027i	$-0.287865\pi$
$227$	4.94618e10	1.23639	0.618193	+	0.786027i	$0.287865\pi$
$228$	1.10451e10	0.270684
$229$	4.32776e10	1.03993	0.519965	−	0.854188i	$-0.325945\pi$
$229$	4.32776e10	1.03993	0.519965	+	0.854188i	$0.325945\pi$
$230$	1.08846e10	0.256470
$231$	0	0
$232$	−4.51613e10	−1.02346
$233$	−7.55367e9	−0.167902	−0.0839511	−	0.996470i	$-0.526754\pi$
$233$	−7.55367e9	−0.167902	−0.0839511	+	0.996470i	$0.526754\pi$
$234$	−7.37630e9	−0.160830
$235$	−1.47781e10	−0.316091
$236$	−2.31023e10	−0.484786
$237$	3.20285e10	0.659430
$238$	0	0
$239$	−2.76516e10	−0.548188	−0.274094	−	0.961703i	$-0.588378\pi$
$239$	−2.76516e10	−0.548188	−0.274094	+	0.961703i	$0.588378\pi$
$240$	2.37382e10	0.461847
$241$	8.26006e10	1.57727	0.788635	−	0.614861i	$-0.210788\pi$
$241$	8.26006e10	1.57727	0.788635	+	0.614861i	$0.210788\pi$
$242$	−4.77469e10	−0.894904
$243$	3.29333e10	0.605908
$244$	−3.99237e9	−0.0721068
$245$	0	0
$246$	3.32098e10	0.578173
$247$	1.48096e10	0.253168
$248$	−4.30900e10	−0.723343
$249$	8.46753e9	0.139592
$250$	−6.83594e9	−0.110680
$251$	−2.01817e10	−0.320942	−0.160471	−	0.987041i	$-0.551301\pi$
$251$	−2.01817e10	−0.320942	−0.160471	+	0.987041i	$0.551301\pi$
$252$	0	0
$253$	1.58902e10	0.243831
$254$	9.78150e10	1.47453
$255$	−3.81598e10	−0.565165
$256$	8.40854e10	1.22360
$257$	−2.82781e10	−0.404344	−0.202172	−	0.979350i	$-0.564800\pi$
$257$	−2.82781e10	−0.404344	−0.202172	+	0.979350i	$0.564800\pi$
$258$	9.78103e10	1.37435
$259$	0	0
$260$	−7.19202e9	−0.0976047
$261$	−4.18481e10	−0.558205
$262$	5.17150e10	0.678049
$263$	1.39139e11	1.79328	0.896642	−	0.442756i	$-0.145999\pi$
$263$	1.39139e11	1.79328	0.896642	+	0.442756i	$0.145999\pi$
$264$	1.99152e10	0.252329
$265$	−3.58079e10	−0.446039
$266$	0	0
$267$	1.03979e11	1.25211
$268$	−6.65197e10	−0.787669
$269$	−5.78883e9	−0.0674071	−0.0337035	−	0.999432i	$-0.510730\pi$
$269$	−5.78883e9	−0.0674071	−0.0337035	+	0.999432i	$0.510730\pi$
$270$	5.25973e10	0.602319
$271$	7.46910e10	0.841214	0.420607	−	0.907243i	$-0.361817\pi$
$271$	7.46910e10	0.841214	0.420607	+	0.907243i	$0.361817\pi$
$272$	−1.72337e11	−1.90906
$273$	0	0
$274$	3.28265e10	0.351842
$275$	−9.97969e9	−0.105225
$276$	−1.96246e10	−0.203568
$277$	2.22355e10	0.226928	0.113464	−	0.993542i	$-0.463805\pi$
$277$	2.22355e10	0.226928	0.113464	+	0.993542i	$0.463805\pi$
$278$	1.36920e11	1.37489
$279$	−3.99288e10	−0.394519
$280$	0	0
$281$	−1.36058e11	−1.30180	−0.650901	−	0.759162i	$-0.725609\pi$
$281$	−1.36058e11	−1.30180	−0.650901	+	0.759162i	$0.725609\pi$
$282$	7.67987e10	0.723157
$283$	1.71084e11	1.58551	0.792757	−	0.609538i	$-0.208645\pi$
$283$	1.71084e11	1.58551	0.792757	+	0.609538i	$0.208645\pi$
$284$	1.68373e10	0.153582
$285$	−2.53793e10	−0.227866
$286$	−3.02633e10	−0.267467
$287$	0	0
$288$	3.56635e10	0.305462
$289$	1.58448e11	1.33612
$290$	−1.17608e11	−0.976437
$291$	−1.39874e11	−1.14345
$292$	7.71837e10	0.621302
$293$	−1.05732e11	−0.838115	−0.419058	−	0.907960i	$-0.637639\pi$
$293$	−1.05732e11	−0.838115	−0.419058	+	0.907960i	$0.637639\pi$
$294$	0	0
$295$	5.30842e10	0.408100
$296$	1.55748e10	0.117926
$297$	7.67860e10	0.572636
$298$	−2.41217e11	−1.77188
$299$	−2.63133e10	−0.190395
$300$	1.23250e10	0.0878499
$301$	0	0
$302$	1.53693e11	1.06322
$303$	1.69385e11	1.15447
$304$	−1.14618e11	−0.769701
$305$	9.17364e9	0.0607005
$306$	−9.17709e10	−0.598354
$307$	−1.74144e11	−1.11889	−0.559443	−	0.828869i	$-0.688985\pi$
$307$	−1.74144e11	−1.11889	−0.559443	+	0.828869i	$0.688985\pi$
$308$	0	0
$309$	−1.25290e11	−0.781813
$310$	−1.12214e11	−0.690110
$311$	1.05907e11	0.641954	0.320977	−	0.947087i	$-0.395989\pi$
$311$	1.05907e11	0.641954	0.320977	+	0.947087i	$0.395989\pi$
$312$	−3.29784e10	−0.197031
$313$	2.43558e11	1.43434	0.717171	−	0.696897i	$-0.245437\pi$
$313$	2.43558e11	1.43434	0.717171	+	0.696897i	$0.245437\pi$
$314$	3.72709e10	0.216365
$315$	0	0
$316$	7.51012e10	0.423697
$317$	1.83776e11	1.02217	0.511083	−	0.859531i	$-0.329245\pi$
$317$	1.83776e11	1.02217	0.511083	+	0.859531i	$0.329245\pi$
$318$	1.86087e11	1.02045
$319$	−1.71694e11	−0.928316
$320$	−4.54912e9	−0.0242523
$321$	3.89701e10	0.204861
$322$	0	0
$323$	1.84251e11	0.941888
$324$	−6.14935e10	−0.310011
$325$	1.65258e10	0.0821650
$326$	3.95071e10	0.193730
$327$	−1.65324e11	−0.799597
$328$	−6.87098e10	−0.327783
$329$	0	0
$330$	5.18624e10	0.240736
$331$	−5.81760e10	−0.266390	−0.133195	−	0.991090i	$-0.542524\pi$
$331$	−5.81760e10	−0.266390	−0.133195	+	0.991090i	$0.542524\pi$
$332$	1.98549e10	0.0896905
$333$	1.44322e10	0.0643182
$334$	−6.95953e9	−0.0305999
$335$	1.52849e11	0.663071
$336$	0	0
$337$	−3.40267e11	−1.43709	−0.718547	−	0.695478i	$-0.755193\pi$
$337$	−3.40267e11	−1.43709	−0.718547	+	0.695478i	$0.755193\pi$
$338$	−2.46812e11	−1.02859
$339$	−3.29646e11	−1.35566
$340$	−8.94781e10	−0.363130
$341$	−1.63819e11	−0.656100
$342$	−6.10351e10	−0.241247
$343$	0	0
$344$	−2.02366e11	−0.779157
$345$	4.50933e10	0.171366
$346$	−4.66262e11	−1.74899
$347$	−5.02625e11	−1.86107	−0.930533	−	0.366208i	$-0.880656\pi$
$347$	−5.02625e11	−1.86107	−0.930533	+	0.366208i	$0.880656\pi$
$348$	2.12043e11	0.775028
$349$	−7.14710e10	−0.257879	−0.128939	−	0.991652i	$-0.541157\pi$
$349$	−7.14710e10	−0.257879	−0.128939	+	0.991652i	$0.541157\pi$
$350$	0	0
$351$	−1.27153e11	−0.447142
$352$	1.46319e11	0.507995
$353$	2.55096e10	0.0874414	0.0437207	−	0.999044i	$-0.486079\pi$
$353$	2.55096e10	0.0874414	0.0437207	+	0.999044i	$0.486079\pi$
$354$	−2.75868e11	−0.933656
$355$	−3.86887e10	−0.129288
$356$	2.43812e11	0.804508
$357$	0	0
$358$	5.68277e11	1.82846
$359$	1.49816e11	0.476029	0.238014	−	0.971262i	$-0.423503\pi$
$359$	1.49816e11	0.476029	0.238014	+	0.971262i	$0.423503\pi$
$360$	−2.61534e10	−0.0820667
$361$	−2.00146e11	−0.620246
$362$	3.81246e11	1.16685
$363$	−1.97809e11	−0.597951
$364$	0	0
$365$	−1.77352e11	−0.523021
$366$	−4.76736e10	−0.138871
$367$	4.59514e11	1.32221	0.661107	−	0.750291i	$-0.270087\pi$
$367$	4.59514e11	1.32221	0.661107	+	0.750291i	$0.270087\pi$
$368$	2.03650e11	0.578854
$369$	−6.36691e10	−0.178776
$370$	4.05594e10	0.112508
$371$	0	0
$372$	2.02318e11	0.547761
$373$	−5.04230e11	−1.34877	−0.674386	−	0.738379i	$-0.735592\pi$
$373$	−5.04230e11	−1.34877	−0.674386	+	0.738379i	$0.735592\pi$
$374$	−3.76516e11	−0.995086
$375$	−2.83203e10	−0.0739533
$376$	−1.58894e11	−0.409979
$377$	2.84315e11	0.724875
$378$	0	0
$379$	−9.63136e10	−0.239779	−0.119889	−	0.992787i	$-0.538254\pi$
$379$	−9.63136e10	−0.239779	−0.119889	+	0.992787i	$0.538254\pi$
$380$	−5.95102e10	−0.146408
$381$	4.05234e11	0.985242
$382$	5.10599e10	0.122686
$383$	−6.10835e11	−1.45054	−0.725269	−	0.688465i	$-0.758285\pi$
$383$	−6.10835e11	−1.45054	−0.725269	+	0.688465i	$0.758285\pi$
$384$	3.63793e11	0.853814
$385$	0	0
$386$	3.46492e11	0.794421
$387$	−1.87520e11	−0.424960
$388$	−3.27980e11	−0.734691
$389$	−6.49908e11	−1.43906	−0.719530	−	0.694461i	$-0.755643\pi$
$389$	−6.49908e11	−1.43906	−0.719530	+	0.694461i	$0.755643\pi$
$390$	−8.58812e10	−0.187978
$391$	−3.27372e11	−0.708347
$392$	0	0
$393$	2.14248e11	0.453054
$394$	5.40785e11	1.13055
$395$	−1.72567e11	−0.356674
$396$	4.32718e10	0.0884253
$397$	3.67168e11	0.741836	0.370918	−	0.928666i	$-0.379043\pi$
$397$	3.67168e11	0.741836	0.370918	+	0.928666i	$0.379043\pi$
$398$	−4.26007e11	−0.851026
$399$	0	0
$400$	−1.27900e11	−0.249805
$401$	−9.73985e11	−1.88106	−0.940530	−	0.339712i	$-0.889670\pi$
$401$	−9.73985e11	−1.88106	−0.940530	+	0.339712i	$0.889670\pi$
$402$	−7.94324e11	−1.51698
$403$	2.71275e11	0.512315
$404$	3.97178e11	0.741770
$405$	1.41299e11	0.260971
$406$	0	0
$407$	5.92121e10	0.106964
$408$	−4.10294e11	−0.733035
$409$	−3.58196e11	−0.632944	−0.316472	−	0.948602i	$-0.602498\pi$
$409$	−3.58196e11	−0.632944	−0.316472	+	0.948602i	$0.602498\pi$
$410$	−1.78932e11	−0.312723
$411$	1.35996e11	0.235091
$412$	−2.93783e11	−0.502330
$413$	0	0
$414$	1.08445e11	0.181430
$415$	−4.56225e10	−0.0755027
$416$	−2.42296e11	−0.396668
$417$	5.67242e11	0.918662
$418$	−2.50413e11	−0.401203
$419$	−4.84712e11	−0.768283	−0.384141	−	0.923274i	$-0.625502\pi$
$419$	−4.84712e11	−0.768283	−0.384141	+	0.923274i	$0.625502\pi$
$420$	0	0
$421$	7.18298e11	1.11438	0.557192	−	0.830384i	$-0.311879\pi$
$421$	7.18298e11	1.11438	0.557192	+	0.830384i	$0.311879\pi$
$422$	−1.09095e12	−1.67456
$423$	−1.47237e11	−0.223607
$424$	−3.85007e11	−0.578525
$425$	2.05602e11	0.305688
$426$	2.01058e11	0.295786
$427$	0	0
$428$	9.13782e10	0.131627
$429$	−1.25377e11	−0.178714
$430$	−5.26995e11	−0.743359
$431$	8.27297e11	1.15482	0.577409	−	0.816455i	$-0.304064\pi$
$431$	8.27297e11	1.15482	0.577409	+	0.816455i	$0.304064\pi$
$432$	9.84092e11	1.35944
$433$	−8.73032e11	−1.19353	−0.596767	−	0.802415i	$-0.703548\pi$
$433$	−8.73032e11	−1.19353	−0.596767	+	0.802415i	$0.703548\pi$
$434$	0	0
$435$	−4.87231e11	−0.652429
$436$	−3.87657e11	−0.513757
$437$	−2.17729e11	−0.285594
$438$	9.21665e11	1.19657
$439$	−7.15061e11	−0.918867	−0.459433	−	0.888212i	$-0.651947\pi$
$439$	−7.15061e11	−0.918867	−0.459433	+	0.888212i	$0.651947\pi$
$440$	−1.07302e11	−0.136480
$441$	0	0
$442$	6.23488e11	0.777012
$443$	5.89691e11	0.727457	0.363729	−	0.931505i	$-0.381504\pi$
$443$	5.89691e11	0.727457	0.363729	+	0.931505i	$0.381504\pi$
$444$	−7.31275e10	−0.0893012
$445$	−5.60230e11	−0.677246
$446$	−3.03308e10	−0.0362975
$447$	−9.99326e11	−1.18392
$448$	0	0
$449$	−1.06477e12	−1.23636	−0.618181	−	0.786036i	$-0.712130\pi$
$449$	−1.06477e12	−1.23636	−0.618181	+	0.786036i	$0.712130\pi$
$450$	−6.81078e10	−0.0782962
$451$	−2.61220e11	−0.297312
$452$	−7.72964e11	−0.871037
$453$	6.36730e11	0.710417
$454$	1.38493e12	1.52995
$455$	0	0
$456$	−2.72879e11	−0.295548
$457$	1.54296e12	1.65475	0.827374	−	0.561651i	$-0.189834\pi$
$457$	1.54296e12	1.65475	0.827374	+	0.561651i	$0.189834\pi$
$458$	1.21177e12	1.28685
$459$	−1.58195e12	−1.66355
$460$	1.05736e11	0.110106
$461$	8.38680e11	0.864852	0.432426	−	0.901669i	$-0.357658\pi$
$461$	8.38680e11	0.864852	0.432426	+	0.901669i	$0.357658\pi$
$462$	0	0
$463$	−8.61819e11	−0.871569	−0.435784	−	0.900051i	$-0.643529\pi$
$463$	−8.61819e11	−0.871569	−0.435784	+	0.900051i	$0.643529\pi$
$464$	−2.20043e12	−2.20382
$465$	−4.64885e11	−0.461113
$466$	−2.11503e11	−0.207768
$467$	−1.46986e12	−1.43005	−0.715023	−	0.699101i	$-0.753584\pi$
$467$	−1.46986e12	−1.43005	−0.715023	+	0.699101i	$0.753584\pi$
$468$	−7.16555e10	−0.0690468
$469$	0	0
$470$	−4.13786e11	−0.391143
$471$	1.54408e11	0.144569
$472$	5.70762e11	0.529317
$473$	−7.69353e11	−0.706725
$474$	8.96797e11	0.816003
$475$	1.36742e11	0.123248
$476$	0	0
$477$	−3.56761e11	−0.315533
$478$	−7.74245e11	−0.678348
$479$	−2.20227e12	−1.91144	−0.955721	−	0.294275i	$-0.904922\pi$
$479$	−2.20227e12	−1.91144	−0.955721	+	0.294275i	$0.904922\pi$
$480$	4.15224e11	0.357024
$481$	−9.80519e10	−0.0835224
$482$	2.31282e12	1.95177
$483$	0	0
$484$	−4.63827e11	−0.384195
$485$	7.53631e11	0.618473
$486$	9.22132e11	0.749773
$487$	1.30073e12	1.04786	0.523932	−	0.851760i	$-0.324464\pi$
$487$	1.30073e12	1.04786	0.523932	+	0.851760i	$0.324464\pi$
$488$	9.86350e10	0.0787303
$489$	1.63672e11	0.129445
$490$	0	0
$491$	6.88947e11	0.534957	0.267479	−	0.963564i	$-0.413810\pi$
$491$	6.88947e11	0.534957	0.267479	+	0.963564i	$0.413810\pi$
$492$	3.22609e11	0.248218
$493$	3.53724e12	2.69683
$494$	4.14670e11	0.313279
$495$	−9.94296e10	−0.0744376
$496$	−2.09951e12	−1.55758
$497$	0	0
$498$	2.37091e11	0.172736
$499$	1.76710e12	1.27588	0.637939	−	0.770087i	$-0.279787\pi$
$499$	1.76710e12	1.27588	0.637939	+	0.770087i	$0.279787\pi$
$500$	−6.64063e10	−0.0475164
$501$	−2.88323e10	−0.0204461
$502$	−5.65088e11	−0.397145
$503$	−2.63527e12	−1.83556	−0.917780	−	0.397089i	$-0.870020\pi$
$503$	−2.63527e12	−1.83556	−0.917780	+	0.397089i	$0.870020\pi$
$504$	0	0
$505$	−9.12633e11	−0.624432
$506$	4.44927e11	0.301725
$507$	−1.02251e12	−0.687274
$508$	9.50203e11	0.633038
$509$	−2.22151e12	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$509$	−2.22151e12	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$510$	−1.06847e12	−0.699356
$511$	0	0
$512$	7.48685e11	0.481487
$513$	−1.05213e12	−0.670718
$514$	−7.91786e11	−0.500350
$515$	6.75053e11	0.422869
$516$	9.50157e11	0.590027
$517$	−6.04080e11	−0.371867
$518$	0	0
$519$	−1.93166e12	−1.16863
$520$	1.77685e11	0.106570
$521$	1.87441e12	1.11454	0.557269	−	0.830332i	$-0.311849\pi$
$521$	1.87441e12	1.11454	0.557269	+	0.830332i	$0.311849\pi$
$522$	−1.17175e12	−0.690743
$523$	1.58412e12	0.925828	0.462914	−	0.886403i	$-0.346804\pi$
$523$	1.58412e12	0.925828	0.462914	+	0.886403i	$0.346804\pi$
$524$	5.02375e11	0.291096
$525$	0	0
$526$	3.89590e12	2.21908
$527$	3.37501e12	1.90602
$528$	9.70343e11	0.543341
$529$	−1.41430e12	−0.785219
$530$	−1.00262e12	−0.551945
$531$	5.28889e11	0.288695
$532$	0	0
$533$	4.32565e11	0.232156
$534$	2.91140e12	1.54941
$535$	−2.09968e11	−0.110806
$536$	1.64343e12	0.860021
$537$	2.35429e12	1.22173
$538$	−1.62087e11	−0.0834120
$539$	0	0
$540$	5.10945e11	0.258584
$541$	2.79888e12	1.40474	0.702370	−	0.711812i	$-0.252125\pi$
$541$	2.79888e12	1.40474	0.702370	+	0.711812i	$0.252125\pi$
$542$	2.09135e12	1.04095
$543$	1.57945e12	0.779660
$544$	−3.01448e12	−1.47577
$545$	8.90755e11	0.432488
$546$	0	0
$547$	1.16606e12	0.556901	0.278451	−	0.960451i	$-0.410179\pi$
$547$	1.16606e12	0.556901	0.278451	+	0.960451i	$0.410179\pi$
$548$	3.18886e11	0.151051
$549$	9.13988e10	0.0429403
$550$	−2.79431e11	−0.130210
$551$	2.35255e12	1.08732
$552$	4.84843e11	0.222267
$553$	0	0
$554$	6.22594e11	0.280809
$555$	1.68032e11	0.0751750
$556$	1.33008e12	0.590259
$557$	3.29033e12	1.44841	0.724204	−	0.689586i	$-0.242207\pi$
$557$	3.29033e12	1.44841	0.724204	+	0.689586i	$0.242207\pi$
$558$	−1.11801e12	−0.488192
$559$	1.27400e12	0.551845
$560$	0	0
$561$	−1.55985e12	−0.664890
$562$	−3.80962e12	−1.61090
$563$	3.63871e12	1.52637	0.763186	−	0.646179i	$-0.223634\pi$
$563$	3.63871e12	1.52637	0.763186	+	0.646179i	$0.223634\pi$
$564$	7.46044e11	0.310462
$565$	1.77611e12	0.733251
$566$	4.79035e12	1.96197
$567$	0	0
$568$	−4.15981e11	−0.167690
$569$	4.35009e12	1.73978	0.869888	−	0.493250i	$-0.164191\pi$
$569$	4.35009e12	1.73978	0.869888	+	0.493250i	$0.164191\pi$
$570$	−7.10622e11	−0.281969
$571$	−4.91136e12	−1.93348	−0.966739	−	0.255767i	$-0.917672\pi$
$571$	−4.91136e12	−1.93348	−0.966739	+	0.255767i	$0.917672\pi$
$572$	−2.93987e11	−0.114827
$573$	2.11534e11	0.0819756
$574$	0	0
$575$	−2.42959e11	−0.0926890
$576$	−4.53238e10	−0.0171564
$577$	1.68758e12	0.633830	0.316915	−	0.948454i	$-0.397353\pi$
$577$	1.68758e12	0.633830	0.316915	+	0.948454i	$0.397353\pi$
$578$	4.43654e12	1.65337
$579$	1.43547e12	0.530811
$580$	−1.14247e12	−0.419199
$581$	0	0
$582$	−3.91647e12	−1.41495
$583$	−1.46371e12	−0.524744
$584$	−1.90689e12	−0.678373
$585$	1.64650e11	0.0581245
$586$	−2.96051e12	−1.03711
$587$	4.82739e12	1.67819	0.839094	−	0.543987i	$-0.183086\pi$
$587$	4.82739e12	1.67819	0.839094	+	0.543987i	$0.183086\pi$
$588$	0	0
$589$	2.24466e12	0.768478
$590$	1.48636e12	0.504998
$591$	2.24039e12	0.755407
$592$	7.58865e11	0.253932
$593$	1.12076e12	0.372193	0.186096	−	0.982532i	$-0.440416\pi$
$593$	1.12076e12	0.372193	0.186096	+	0.982532i	$0.440416\pi$
$594$	2.15001e12	0.708600
$595$	0	0
$596$	−2.34325e12	−0.760694
$597$	−1.76489e12	−0.568633
$598$	−7.36773e11	−0.235602
$599$	1.35944e12	0.431460	0.215730	−	0.976453i	$-0.430787\pi$
$599$	1.35944e12	0.431460	0.215730	+	0.976453i	$0.430787\pi$
$600$	−3.04500e11	−0.0959194
$601$	−9.50421e11	−0.297153	−0.148577	−	0.988901i	$-0.547469\pi$
$601$	−9.50421e11	−0.297153	−0.148577	+	0.988901i	$0.547469\pi$
$602$	0	0
$603$	1.52286e12	0.469064
$604$	1.49302e12	0.456457
$605$	1.06578e12	0.323421
$606$	4.74277e12	1.42858
$607$	−3.35939e12	−1.00441	−0.502205	−	0.864749i	$-0.667478\pi$
$607$	−3.35939e12	−1.00441	−0.502205	+	0.864749i	$0.667478\pi$
$608$	−2.00487e12	−0.595006
$609$	0	0
$610$	2.56862e11	0.0751131
$611$	1.00032e12	0.290372
$612$	−8.91489e11	−0.256882
$613$	−2.62257e12	−0.750162	−0.375081	−	0.926992i	$-0.622385\pi$
$613$	−2.62257e12	−0.750162	−0.375081	+	0.926992i	$0.622385\pi$
$614$	−4.87603e12	−1.38455
$615$	−7.41289e11	−0.208953
$616$	0	0
$617$	−3.35285e10	−0.00931388	−0.00465694	−	0.999989i	$-0.501482\pi$
$617$	−3.35285e10	−0.00931388	−0.00465694	+	0.999989i	$0.501482\pi$
$618$	−3.50812e12	−0.967444
$619$	−5.51587e12	−1.51010	−0.755051	−	0.655666i	$-0.772388\pi$
$619$	−5.51587e12	−1.51010	−0.755051	+	0.655666i	$0.772388\pi$
$620$	−1.09008e12	−0.296274
$621$	1.86939e12	0.504414
$622$	2.96540e12	0.794377
$623$	0	0
$624$	−1.60683e12	−0.424268
$625$	1.52588e11	0.0400000
$626$	6.81962e12	1.77491
$627$	−1.03743e12	−0.268073
$628$	3.62060e11	0.0928886
$629$	−1.21989e12	−0.310738
$630$	0	0
$631$	2.72456e12	0.684170	0.342085	−	0.939669i	$-0.388867\pi$
$631$	2.72456e12	0.684170	0.342085	+	0.939669i	$0.388867\pi$
$632$	−1.85544e12	−0.462616
$633$	−4.51966e12	−1.11890
$634$	5.14572e12	1.26487
$635$	−2.18337e12	−0.532900
$636$	1.80770e12	0.438096
$637$	0	0
$638$	−4.80742e12	−1.14873
$639$	−3.85463e11	−0.0914596
$640$	−1.96009e12	−0.461813
$641$	3.79136e11	0.0887022	0.0443511	−	0.999016i	$-0.485878\pi$
$641$	3.79136e11	0.0887022	0.0443511	+	0.999016i	$0.485878\pi$
$642$	1.09116e12	0.253502
$643$	5.15446e12	1.18914	0.594571	−	0.804043i	$-0.297322\pi$
$643$	5.15446e12	1.18914	0.594571	+	0.804043i	$0.297322\pi$
$644$	0	0
$645$	−2.18327e12	−0.496693
$646$	5.15904e12	1.16553
$647$	2.68059e12	0.601397	0.300699	−	0.953719i	$-0.402780\pi$
$647$	2.68059e12	0.601397	0.300699	+	0.953719i	$0.402780\pi$
$648$	1.51925e12	0.338487
$649$	2.16991e12	0.480111
$650$	4.62722e11	0.101674
$651$	0	0
$652$	3.83783e11	0.0831710
$653$	−6.44986e12	−1.38816	−0.694082	−	0.719896i	$-0.744190\pi$
$653$	−6.44986e12	−1.38816	−0.694082	+	0.719896i	$0.744190\pi$
$654$	−4.62908e12	−0.989451
$655$	−1.15435e12	−0.245049
$656$	−3.34780e12	−0.705818
$657$	−1.76700e12	−0.369991
$658$	0	0
$659$	−2.79549e12	−0.577396	−0.288698	−	0.957420i	$-0.593222\pi$
$659$	−2.79549e12	−0.577396	−0.288698	+	0.957420i	$0.593222\pi$
$660$	5.03807e11	0.103351
$661$	4.93691e11	0.100589	0.0502943	−	0.998734i	$-0.483984\pi$
$661$	4.93691e11	0.100589	0.0502943	+	0.998734i	$0.483984\pi$
$662$	−1.62893e12	−0.329641
$663$	2.58302e12	0.519179
$664$	−4.90533e11	−0.0979291
$665$	0	0
$666$	4.04102e11	0.0795897
$667$	−4.17995e12	−0.817720
$668$	−6.76068e10	−0.0131370
$669$	−1.25656e11	−0.0242530
$670$	4.27976e12	0.820508
$671$	3.74989e11	0.0714113
$672$	0	0
$673$	2.83805e12	0.533277	0.266638	−	0.963797i	$-0.414087\pi$
$673$	2.83805e12	0.533277	0.266638	+	0.963797i	$0.414087\pi$
$674$	−9.52747e12	−1.77831
$675$	−1.17405e12	−0.217680
$676$	−2.39760e12	−0.441587
$677$	−7.71236e12	−1.41104	−0.705519	−	0.708691i	$-0.749286\pi$
$677$	−7.71236e12	−1.41104	−0.705519	+	0.708691i	$0.749286\pi$
$678$	−9.23010e12	−1.67754
$679$	0	0
$680$	2.21064e12	0.396485
$681$	5.73757e12	1.02227
$682$	−4.58693e12	−0.811882
$683$	1.07677e13	1.89334	0.946670	−	0.322204i	$-0.104424\pi$
$683$	1.07677e13	1.89334	0.946670	+	0.322204i	$0.104424\pi$
$684$	−5.92912e11	−0.103571
$685$	−7.32735e11	−0.127157
$686$	0	0
$687$	5.02021e12	0.859837
$688$	−9.86005e12	−1.67776
$689$	2.42382e12	0.409746
$690$	1.26261e12	0.212055
$691$	−2.02298e12	−0.337552	−0.168776	−	0.985654i	$-0.553981\pi$
$691$	−2.02298e12	−0.337552	−0.168776	+	0.985654i	$0.553981\pi$
$692$	−4.52940e12	−0.750867
$693$	0	0
$694$	−1.40735e13	−2.30295
$695$	−3.05626e12	−0.496888
$696$	−5.23871e12	−0.846219
$697$	5.38168e12	0.863714
$698$	−2.00119e12	−0.319109
$699$	−8.76226e11	−0.138825
$700$	0	0
$701$	8.66031e11	0.135457	0.0677286	−	0.997704i	$-0.478425\pi$
$701$	8.66031e11	0.135457	0.0677286	+	0.997704i	$0.478425\pi$
$702$	−3.56029e12	−0.553310
$703$	−8.11328e11	−0.125285
$704$	−1.85953e11	−0.0285317
$705$	−1.71426e12	−0.261351
$706$	7.14268e11	0.108203
$707$	0	0
$708$	−2.67986e12	−0.400832
$709$	−3.78834e12	−0.563042	−0.281521	−	0.959555i	$-0.590839\pi$
$709$	−3.78834e12	−0.563042	−0.281521	+	0.959555i	$0.590839\pi$
$710$	−1.08328e12	−0.159985
$711$	−1.71932e12	−0.252315
$712$	−6.02360e12	−0.878407
$713$	−3.98824e12	−0.577934
$714$	0	0
$715$	6.75521e11	0.0966633
$716$	5.52040e12	0.784986
$717$	−3.20758e12	−0.453254
$718$	4.19485e12	0.589056
$719$	−8.16972e11	−0.114006	−0.0570029	−	0.998374i	$-0.518154\pi$
$719$	−8.16972e11	−0.114006	−0.0570029	+	0.998374i	$0.518154\pi$
$720$	−1.27429e12	−0.176715
$721$	0	0
$722$	−5.60408e12	−0.767515
$723$	9.58166e12	1.30412
$724$	3.70353e12	0.500947
$725$	2.62517e12	0.352887
$726$	−5.53864e12	−0.739927
$727$	−3.13227e12	−0.415867	−0.207933	−	0.978143i	$-0.566674\pi$
$727$	−3.13227e12	−0.415867	−0.207933	+	0.978143i	$0.566674\pi$
$728$	0	0
$729$	8.27017e12	1.08453
$730$	−4.96587e12	−0.647205
$731$	1.58503e13	2.05309
$732$	−4.63115e11	−0.0596195
$733$	1.33197e13	1.70422	0.852112	−	0.523360i	$-0.175322\pi$
$733$	1.33197e13	1.70422	0.852112	+	0.523360i	$0.175322\pi$
$734$	1.28664e13	1.63616
$735$	0	0
$736$	3.56220e12	0.447474
$737$	6.24796e12	0.780072
$738$	−1.78273e12	−0.221224
$739$	−1.56702e13	−1.93274	−0.966371	−	0.257154i	$-0.917215\pi$
$739$	−1.56702e13	−1.93274	−0.966371	+	0.257154i	$0.917215\pi$
$740$	3.94006e11	0.0483014
$741$	1.71792e12	0.209325
$742$	0	0
$743$	7.91108e12	0.952327	0.476164	−	0.879357i	$-0.342027\pi$
$743$	7.91108e12	0.952327	0.476164	+	0.879357i	$0.342027\pi$
$744$	−4.99844e12	−0.598076
$745$	5.38430e12	0.640362
$746$	−1.41184e13	−1.66902
$747$	−4.54546e11	−0.0534115
$748$	−3.65758e12	−0.427205
$749$	0	0
$750$	−7.92969e11	−0.0915125
$751$	−4.01514e12	−0.460597	−0.230299	−	0.973120i	$-0.573970\pi$
$751$	−4.01514e12	−0.460597	−0.230299	+	0.973120i	$0.573970\pi$
$752$	−7.74191e12	−0.882811
$753$	−2.34108e12	−0.265362
$754$	7.96081e12	0.896987
$755$	−3.43066e12	−0.384252
$756$	0	0
$757$	2.84075e12	0.314414	0.157207	−	0.987566i	$-0.449751\pi$
$757$	2.84075e12	0.314414	0.157207	+	0.987566i	$0.449751\pi$
$758$	−2.69678e12	−0.296711
$759$	1.84327e12	0.201605
$760$	1.47025e12	0.159857
$761$	7.10439e12	0.767884	0.383942	−	0.923357i	$-0.374566\pi$
$761$	7.10439e12	0.767884	0.383942	+	0.923357i	$0.374566\pi$
$762$	1.13465e13	1.21918
$763$	0	0
$764$	4.96011e11	0.0526709
$765$	2.04846e12	0.216247
$766$	−1.71034e13	−1.79495
$767$	−3.59325e12	−0.374894
$768$	9.75390e12	1.01170
$769$	4.97052e12	0.512546	0.256273	−	0.966604i	$-0.417505\pi$
$769$	4.97052e12	0.512546	0.256273	+	0.966604i	$0.417505\pi$
$770$	0	0
$771$	−3.28026e12	−0.334321
$772$	3.36593e12	0.341057
$773$	−1.11565e13	−1.12388	−0.561939	−	0.827179i	$-0.689944\pi$
$773$	−1.11565e13	−1.12388	−0.561939	+	0.827179i	$0.689944\pi$
$774$	−5.25056e12	−0.525861
$775$	2.50477e12	0.249408
$776$	8.10304e12	0.802177
$777$	0	0
$778$	−1.81974e13	−1.78075
$779$	3.57925e12	0.348236
$780$	−8.34274e11	−0.0807018
$781$	−1.58147e12	−0.152101
$782$	−9.16642e12	−0.876535
$783$	−2.01987e13	−1.92041
$784$	0	0
$785$	−8.31940e11	−0.0781949
$786$	5.99894e12	0.560626
$787$	6.23763e12	0.579607	0.289803	−	0.957086i	$-0.406410\pi$
$787$	6.23763e12	0.579607	0.289803	+	0.957086i	$0.406410\pi$
$788$	5.25334e12	0.485364
$789$	1.61402e13	1.48273
$790$	−4.83188e12	−0.441361
$791$	0	0
$792$	−1.06907e12	−0.0965477
$793$	−6.20960e11	−0.0557615
$794$	1.02807e13	0.917975
$795$	−4.15372e12	−0.368795
$796$	−4.13835e12	−0.365358
$797$	1.83799e12	0.161355	0.0806773	−	0.996740i	$-0.474292\pi$
$797$	1.83799e12	0.161355	0.0806773	+	0.996740i	$0.474292\pi$
$798$	0	0
$799$	1.24453e13	1.08030
$800$	−2.23720e12	−0.193108
$801$	−5.58169e12	−0.479092
$802$	−2.72716e13	−2.32769
$803$	−7.24960e12	−0.615310
$804$	−7.71629e12	−0.651263
$805$	0	0
$806$	7.59570e12	0.633957
$807$	−6.71504e11	−0.0557337
$808$	−9.81263e12	−0.809906
$809$	1.92205e13	1.57760	0.788801	−	0.614649i	$-0.210702\pi$
$809$	1.92205e13	1.57760	0.788801	+	0.614649i	$0.210702\pi$
$810$	3.95638e12	0.322935
$811$	1.70316e13	1.38249	0.691246	−	0.722620i	$-0.257062\pi$
$811$	1.70316e13	1.38249	0.691246	+	0.722620i	$0.257062\pi$
$812$	0	0
$813$	8.66416e12	0.695535
$814$	1.65794e12	0.132361
$815$	−8.81855e11	−0.0700145
$816$	−1.99911e13	−1.57845
$817$	1.05417e13	0.827774
$818$	−1.00295e13	−0.783228
$819$	0	0
$820$	−1.73820e12	−0.134257
$821$	1.33485e13	1.02539	0.512694	−	0.858572i	$-0.328648\pi$
$821$	1.33485e13	1.02539	0.512694	+	0.858572i	$0.328648\pi$
$822$	3.80788e12	0.290911
$823$	−1.72858e13	−1.31338	−0.656689	−	0.754161i	$-0.728044\pi$
$823$	−1.72858e13	−1.31338	−0.656689	+	0.754161i	$0.728044\pi$
$824$	7.25817e12	0.548473
$825$	−1.15764e12	−0.0870026
$826$	0	0
$827$	1.64651e13	1.22402	0.612012	−	0.790849i	$-0.290361\pi$
$827$	1.64651e13	1.22402	0.612012	+	0.790849i	$0.290361\pi$
$828$	1.05347e12	0.0778906
$829$	5.91786e12	0.435181	0.217590	−	0.976040i	$-0.430180\pi$
$829$	5.91786e12	0.435181	0.217590	+	0.976040i	$0.430180\pi$
$830$	−1.27743e12	−0.0934298
$831$	2.57932e12	0.187629
$832$	3.07928e11	0.0222789
$833$	0	0
$834$	1.58828e13	1.13679
$835$	1.55347e11	0.0110589
$836$	−2.43259e12	−0.172242
$837$	−1.92723e13	−1.35728
$838$	−1.35719e13	−0.950701
$839$	−2.40380e13	−1.67483	−0.837414	−	0.546569i	$-0.815934\pi$
$839$	−2.40380e13	−1.67483	−0.837414	+	0.546569i	$0.815934\pi$
$840$	0	0
$841$	3.06570e13	2.11324
$842$	2.01123e13	1.37898
$843$	−1.57827e13	−1.07636
$844$	−1.05978e13	−0.718913
$845$	5.50919e12	0.371734
$846$	−4.12263e12	−0.276699
$847$	0	0
$848$	−1.87590e13	−1.24574
$849$	1.98457e13	1.31094
$850$	5.75687e12	0.378269
$851$	1.44154e12	0.0942203
$852$	1.95313e12	0.126985
$853$	−2.26446e13	−1.46452	−0.732258	−	0.681027i	$-0.761534\pi$
$853$	−2.26446e13	−1.46452	−0.732258	+	0.681027i	$0.761534\pi$
$854$	0	0
$855$	1.36239e12	0.0871874
$856$	−2.25758e12	−0.143718
$857$	1.20223e13	0.761334	0.380667	−	0.924712i	$-0.375694\pi$
$857$	1.20223e13	0.761334	0.380667	+	0.924712i	$0.375694\pi$
$858$	−3.51055e12	−0.221148
$859$	9.44258e12	0.591727	0.295864	−	0.955230i	$-0.404393\pi$
$859$	9.44258e12	0.591727	0.295864	+	0.955230i	$0.404393\pi$
$860$	−5.11938e12	−0.319135
$861$	0	0
$862$	2.31643e13	1.42901
$863$	8.80380e12	0.540283	0.270142	−	0.962821i	$-0.412929\pi$
$863$	8.80380e12	0.540283	0.270142	+	0.962821i	$0.412929\pi$
$864$	1.72135e13	1.05089
$865$	1.04076e13	0.632090
$866$	−2.44449e13	−1.47692
$867$	1.83800e13	1.10474
$868$	0	0
$869$	−7.05399e12	−0.419610
$870$	−1.36425e13	−0.807340
$871$	−1.03463e13	−0.609119
$872$	9.57740e12	0.560949
$873$	7.50858e12	0.437516
$874$	−6.09641e12	−0.353405
$875$	0	0
$876$	8.95331e12	0.513707
$877$	6.73513e12	0.384457	0.192229	−	0.981350i	$-0.438429\pi$
$877$	6.73513e12	0.384457	0.192229	+	0.981350i	$0.438429\pi$
$878$	−2.00217e13	−1.13704
$879$	−1.22650e13	−0.692973
$880$	−5.22814e12	−0.293884
$881$	7.58474e12	0.424179	0.212089	−	0.977250i	$-0.431973\pi$
$881$	7.58474e12	0.424179	0.212089	+	0.977250i	$0.431973\pi$
$882$	0	0
$883$	−1.78234e13	−0.986662	−0.493331	−	0.869842i	$-0.664221\pi$
$883$	−1.78234e13	−0.986662	−0.493331	+	0.869842i	$0.664221\pi$
$884$	6.05674e12	0.333583
$885$	6.15777e12	0.337426
$886$	1.65113e13	0.900182
$887$	2.45177e13	1.32991	0.664956	−	0.746882i	$-0.268450\pi$
$887$	2.45177e13	1.32991	0.664956	+	0.746882i	$0.268450\pi$
$888$	1.80668e12	0.0975041
$889$	0	0
$890$	−1.56864e13	−0.838049
$891$	5.77586e12	0.307020
$892$	−2.94642e11	−0.0155830
$893$	8.27714e12	0.435561
$894$	−2.79811e13	−1.46503
$895$	−1.26847e13	−0.660812
$896$	0	0
$897$	−3.05234e12	−0.157423
$898$	−2.98134e13	−1.52992
$899$	4.30928e13	2.20032
$900$	−6.61619e11	−0.0336137
$901$	3.01555e13	1.52442
$902$	−7.31416e12	−0.367905
$903$	0	0
$904$	1.90968e13	0.951047
$905$	−8.50995e12	−0.421704
$906$	1.78284e13	0.879096
$907$	−8.14231e12	−0.399498	−0.199749	−	0.979847i	$-0.564013\pi$
$907$	−8.14231e12	−0.399498	−0.199749	+	0.979847i	$0.564013\pi$
$908$	1.34536e13	0.656830
$909$	−9.09275e12	−0.441731
$910$	0	0
$911$	−1.26965e13	−0.610733	−0.305367	−	0.952235i	$-0.598779\pi$
$911$	−1.26965e13	−0.610733	−0.305367	+	0.952235i	$0.598779\pi$
$912$	−1.32957e13	−0.636406
$913$	−1.86490e12	−0.0888254
$914$	4.32029e13	2.04765
$915$	1.06414e12	0.0501886
$916$	1.17715e13	0.552463
$917$	0	0
$918$	−4.42947e13	−2.05854
$919$	−2.53575e13	−1.17270	−0.586350	−	0.810058i	$-0.699436\pi$
$919$	−2.53575e13	−1.17270	−0.586350	+	0.810058i	$0.699436\pi$
$920$	−2.61230e12	−0.120220
$921$	−2.02007e13	−0.925120
$922$	2.34830e13	1.07020
$923$	2.61882e12	0.118768
$924$	0	0
$925$	−9.05345e11	−0.0406608
$926$	−2.41309e13	−1.07851
$927$	6.72569e12	0.299143
$928$	−3.84895e13	−1.70363
$929$	−1.89611e13	−0.835203	−0.417602	−	0.908630i	$-0.637129\pi$
$929$	−1.89611e13	−0.835203	−0.417602	+	0.908630i	$0.637129\pi$
$930$	−1.30168e13	−0.570598
$931$	0	0
$932$	−2.05460e12	−0.0891980
$933$	1.22852e13	0.530782
$934$	−4.11561e13	−1.76959
$935$	8.40437e12	0.359627
$936$	1.77031e12	0.0753891
$937$	−8.65559e12	−0.366833	−0.183416	−	0.983035i	$-0.558716\pi$
$937$	−8.65559e12	−0.366833	−0.183416	+	0.983035i	$0.558716\pi$
$938$	0	0
$939$	2.82527e13	1.18595
$940$	−4.01964e12	−0.167923
$941$	−3.42336e13	−1.42331	−0.711654	−	0.702530i	$-0.752054\pi$
$941$	−3.42336e13	−1.42331	−0.711654	+	0.702530i	$0.752054\pi$
$942$	4.32343e12	0.178895
$943$	−6.35950e12	−0.261891
$944$	2.78097e13	1.13978
$945$	0	0
$946$	−2.15419e13	−0.874527
$947$	2.38597e13	0.964030	0.482015	−	0.876163i	$-0.339905\pi$
$947$	2.38597e13	0.964030	0.482015	+	0.876163i	$0.339905\pi$
$948$	8.71174e12	0.350322
$949$	1.20049e13	0.480464
$950$	3.82878e12	0.152512
$951$	2.13180e13	0.845150
$952$	0	0
$953$	−4.83481e13	−1.89872	−0.949360	−	0.314189i	$-0.898267\pi$
$953$	−4.83481e13	−1.89872	−0.949360	+	0.314189i	$0.898267\pi$
$954$	−9.98932e12	−0.390452
$955$	−1.13973e12	−0.0443391
$956$	−7.52123e12	−0.291225
$957$	−1.99165e13	−0.767553
$958$	−6.16636e13	−2.36529
$959$	0	0
$960$	−5.27698e11	−0.0200523
$961$	1.46768e13	0.555106
$962$	−2.74545e12	−0.103354
$963$	−2.09196e12	−0.0783852
$964$	2.24674e13	0.837925
$965$	−7.73421e12	−0.287106
$966$	0	0
$967$	−2.28025e13	−0.838617	−0.419308	−	0.907844i	$-0.637727\pi$
$967$	−2.28025e13	−0.838617	−0.419308	+	0.907844i	$0.637727\pi$
$968$	1.14593e13	0.419486
$969$	2.13731e13	0.778774
$970$	2.11017e13	0.765322
$971$	−7.62385e12	−0.275225	−0.137612	−	0.990486i	$-0.543943\pi$
$971$	−7.62385e12	−0.275225	−0.137612	+	0.990486i	$0.543943\pi$
$972$	8.95785e12	0.321889
$973$	0	0
$974$	3.64203e13	1.29667
$975$	1.91699e12	0.0679359
$976$	4.80587e12	0.169531
$977$	2.97018e13	1.04293	0.521467	−	0.853272i	$-0.325385\pi$
$977$	2.97018e13	1.04293	0.521467	+	0.853272i	$0.325385\pi$
$978$	4.58282e12	0.160180
$979$	−2.29004e13	−0.796749
$980$	0	0
$981$	8.87477e12	0.305947
$982$	1.92905e13	0.661976
$983$	1.08292e13	0.369917	0.184958	−	0.982746i	$-0.440785\pi$
$983$	1.08292e13	0.369917	0.184958	+	0.982746i	$0.440785\pi$
$984$	−7.97034e12	−0.271019
$985$	−1.20711e13	−0.408586
$986$	9.90428e13	3.33716
$987$	0	0
$988$	4.02822e12	0.134495
$989$	−1.87302e13	−0.622528
$990$	−2.78403e12	−0.0921118
$991$	5.29514e12	0.174400	0.0871999	−	0.996191i	$-0.472208\pi$
$991$	5.29514e12	0.174400	0.0871999	+	0.996191i	$0.472208\pi$
$992$	−3.67242e13	−1.20406
$993$	−6.74842e12	−0.220257
$994$	0	0
$995$	9.50909e12	0.307564
$996$	2.30317e12	0.0741581
$997$	−1.64214e13	−0.526360	−0.263180	−	0.964747i	$-0.584771\pi$
$997$	−1.64214e13	−0.526360	−0.263180	+	0.964747i	$0.584771\pi$
$998$	4.94788e13	1.57882
$999$	6.96593e12	0.221276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.b.1.1		1
7.6	odd	2		35.10.a.a.1.1	✓	1
21.20	even	2		315.10.a.a.1.1		1
35.13	even	4		175.10.b.a.99.1		2
35.27	even	4		175.10.b.a.99.2		2
35.34	odd	2		175.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.a.1.1	✓	1	7.6	odd	2
175.10.a.a.1.1		1	35.34	odd	2
175.10.b.a.99.1		2	35.13	even	4
175.10.b.a.99.2		2	35.27	even	4
245.10.a.b.1.1		1	1.1	even	1	trivial
315.10.a.a.1.1		1	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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