LMFDB - Embedded newform 315.10.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,10,Mod(1,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	315.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$162.236288392$
Analytic rank:	$1$
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	$\chi$	$=$	315.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-28.0000 q^{2} +272.000 q^{4} -625.000 q^{5} +2401.00 q^{7} +6720.00 q^{8} +17500.0 q^{10} +25548.0 q^{11} -42306.0 q^{13} -67228.0 q^{14} -327424. q^{16} +526342. q^{17} -350060. q^{19} -170000. q^{20} -715344. q^{22} +621976. q^{23} +390625. q^{25} +1.18457e6 q^{26} +653072. q^{28} -6.72043e6 q^{29} -6.41221e6 q^{31} +5.72723e6 q^{32} -1.47376e7 q^{34} -1.50062e6 q^{35} -2.31768e6 q^{37} +9.80168e6 q^{38} -4.20000e6 q^{40} +1.02247e7 q^{41} +3.01140e7 q^{43} +6.94906e6 q^{44} -1.74153e7 q^{46} +2.36449e7 q^{47} +5.76480e6 q^{49} -1.09375e7 q^{50} -1.15072e7 q^{52} -5.72927e7 q^{53} -1.59675e7 q^{55} +1.61347e7 q^{56} +1.88172e8 q^{58} -8.49348e7 q^{59} +1.46778e7 q^{61} +1.79542e8 q^{62} +7.27859e6 q^{64} +2.64412e7 q^{65} -2.44558e8 q^{67} +1.43165e8 q^{68} +4.20175e7 q^{70} -6.19020e7 q^{71} -2.83764e8 q^{73} +6.48951e7 q^{74} -9.52163e7 q^{76} +6.13407e7 q^{77} +2.76107e8 q^{79} +2.04640e8 q^{80} -2.86291e8 q^{82} +7.29960e7 q^{83} -3.28964e8 q^{85} -8.43192e8 q^{86} +1.71683e8 q^{88} +8.96368e8 q^{89} -1.01577e8 q^{91} +1.69177e8 q^{92} -6.62058e8 q^{94} +2.18788e8 q^{95} +1.20581e9 q^{97} -1.61414e8 q^{98} +O(q^{100})\)

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 $

$2$	−28.0000	−1.23744	−0.618718	−	0.785613i	$-0.712348\pi$
$2$	−28.0000	−1.23744	−0.618718	+	0.785613i	$0.712348\pi$
$3$	0	0
$3$	0	0
$4$	272.000	0.531250
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	0	0
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	6720.00	0.580049
$9$	0	0
$10$	17500.0	0.553399
$11$	25548.0	0.526126	0.263063	−	0.964779i	$-0.415267\pi$
$11$	25548.0	0.526126	0.263063	+	0.964779i	$0.415267\pi$
$12$	0	0
$13$	−42306.0	−0.410825	−0.205413	−	0.978675i	$-0.565854\pi$
$13$	−42306.0	−0.410825	−0.205413	+	0.978675i	$0.565854\pi$
$14$	−67228.0	−0.467707
$15$	0	0
$16$	−327424.	−1.24902
$17$	526342.	1.52844	0.764219	−	0.644957i	$-0.223125\pi$
$17$	526342.	1.52844	0.764219	+	0.644957i	$0.223125\pi$
$18$	0	0
$19$	−350060.	−0.616242	−0.308121	−	0.951347i	$-0.599700\pi$
$19$	−350060.	−0.616242	−0.308121	+	0.951347i	$0.599700\pi$
$20$	−170000.	−0.237582
$21$	0	0
$22$	−715344.	−0.651048
$23$	621976.	0.463445	0.231723	−	0.972782i	$-0.425564\pi$
$23$	621976.	0.463445	0.231723	+	0.972782i	$0.425564\pi$
$24$	0	0
$25$	390625.	0.200000
$26$	1.18457e6	0.508370
$27$	0	0
$28$	653072.	0.200794
$29$	−6.72043e6	−1.76444	−0.882218	−	0.470841i	$-0.843951\pi$
$29$	−6.72043e6	−1.76444	−0.882218	+	0.470841i	$0.843951\pi$
$30$	0	0
$31$	−6.41221e6	−1.24704	−0.623519	−	0.781808i	$-0.714298\pi$
$31$	−6.41221e6	−1.24704	−0.623519	+	0.781808i	$0.714298\pi$
$32$	5.72723e6	0.965539
$33$	0	0
$34$	−1.47376e7	−1.89135
$35$	−1.50062e6	−0.169031
$36$	0	0
$37$	−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
$39$	0	0
$40$	−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
$45$	0	0
$46$	−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	$0.385025\pi$
$48$	0	0
$49$	5.76480e6	0.142857
$50$	−1.09375e7	−0.247487
$51$	0	0
$52$	−1.15072e7	−0.218251
$53$	−5.72927e7	−0.997373	−0.498686	−	0.866782i	$-0.666184\pi$
$53$	−5.72927e7	−0.997373	−0.498686	+	0.866782i	$0.666184\pi$
$54$	0	0
$55$	−1.59675e7	−0.235291
$56$	1.61347e7	0.219238
$57$	0	0
$58$	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	$0.650815\pi$
$60$	0	0
$61$	1.46778e7	0.135730	0.0678652	−	0.997694i	$-0.478381\pi$
$61$	1.46778e7	0.135730	0.0678652	+	0.997694i	$0.478381\pi$
$62$	1.79542e8	1.54313
$63$	0	0
$64$	7.27859e6	0.0542297
$65$	2.64412e7	0.183727
$66$	0	0
$67$	−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
$69$	0	0
$70$	4.20175e7	0.209165
$71$	−6.19020e7	−0.289096	−0.144548	−	0.989498i	$-0.546173\pi$
$71$	−6.19020e7	−0.289096	−0.144548	+	0.989498i	$0.546173\pi$
$72$	0	0
$73$	−2.83764e8	−1.16951	−0.584755	−	0.811210i	$-0.698809\pi$
$73$	−2.83764e8	−1.16951	−0.584755	+	0.811210i	$0.698809\pi$
$74$	6.48951e7	0.251576
$75$	0	0
$76$	−9.52163e7	−0.327379
$77$	6.13407e7	0.198857
$78$	0	0
$79$	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
$81$	0	0
$82$	−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
$87$	0	0
$88$	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	$0.226575\pi$
$90$	0	0
$91$	−1.01577e8	−0.155277
$92$	1.69177e8	0.246205
$93$	0	0
$94$	−6.62058e8	−0.874622
$95$	2.18788e8	0.275592
$96$	0	0
$97$	1.20581e9	1.38295	0.691474	−	0.722401i	$-0.256962\pi$
$97$	1.20581e9	1.38295	0.691474	+	0.722401i	$0.256962\pi$
$98$	−1.61414e8	−0.176777
$99$	0	0
$100$	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	$0.254013\pi$
$102$	0	0
$103$	1.08009e9	0.945563	0.472782	−	0.881180i	$-0.343250\pi$
$103$	1.08009e9	0.945563	0.472782	+	0.881180i	$0.343250\pi$
$104$	−2.84296e8	−0.238298
$105$	0	0
$106$	1.60419e9	1.23419
$107$	−3.35949e8	−0.247769	−0.123884	−	0.992297i	$-0.539535\pi$
$107$	−3.35949e8	−0.247769	−0.123884	+	0.992297i	$0.539535\pi$
$108$	0	0
$109$	−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
$111$	0	0
$112$	−7.86145e8	−0.472086
$113$	2.84178e9	1.63960	0.819799	−	0.572651i	$-0.194085\pi$
$113$	2.84178e9	1.63960	0.819799	+	0.572651i	$0.194085\pi$
$114$	0	0
$115$	−3.88735e8	−0.207259
$116$	−1.82796e9	−0.937357
$117$	0	0
$118$	2.37817e9	1.12921
$119$	1.26375e9	0.577695
$120$	0	0
$121$	−1.70525e9	−0.723191
$122$	−4.10979e8	−0.167958
$123$	0	0
$124$	−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
$129$	0	0
$130$	−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	$0.411662\pi$
$132$	0	0
$133$	−8.40494e8	−0.232918
$134$	6.84762e9	1.83471
$135$	0	0
$136$	3.53702e9	0.886568
$137$	−1.17238e9	−0.284331	−0.142166	−	0.989843i	$-0.545407\pi$
$137$	−1.17238e9	−0.284331	−0.142166	+	0.989843i	$0.545407\pi$
$138$	0	0
$139$	−4.89001e9	−1.11108	−0.555538	−	0.831491i	$-0.687488\pi$
$139$	−4.89001e9	−1.11108	−0.555538	+	0.831491i	$0.687488\pi$
$140$	−4.08170e8	−0.0897976
$141$	0	0
$142$	1.73325e9	0.357738
$143$	−1.08083e9	−0.216146
$144$	0	0
$145$	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	$-0.245995\pi$
$149$	8.61488e9	1.43189	0.715947	+	0.698155i	$0.245995\pi$
$150$	0	0
$151$	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
$153$	0	0
$154$	−1.71754e9	−0.246073
$155$	4.00763e9	0.557693
$156$	0	0
$157$	−1.33110e9	−0.174849	−0.0874246	−	0.996171i	$-0.527864\pi$
$157$	−1.33110e9	−0.174849	−0.0874246	+	0.996171i	$0.527864\pi$
$158$	−7.73101e9	−0.986914
$159$	0	0
$160$	−3.57952e9	−0.431802
$161$	1.49336e9	0.175166
$162$	0	0
$163$	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
$165$	0	0
$166$	−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
$171$	0	0
$172$	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	$0.749816\pi$
$174$	0	0
$175$	9.37891e8	0.0755929
$176$	−8.36503e9	−0.657144
$177$	0	0
$178$	−2.50983e10	−1.87394
$179$	−2.02956e10	−1.47762	−0.738811	−	0.673913i	$-0.764612\pi$
$179$	−2.02956e10	−1.47762	−0.738811	+	0.673913i	$0.764612\pi$
$180$	0	0
$181$	−1.36159e10	−0.942960	−0.471480	−	0.881877i	$-0.656280\pi$
$181$	−1.36159e10	−0.942960	−0.471480	+	0.881877i	$0.656280\pi$
$182$	2.84415e9	0.192146
$183$	0	0
$184$	4.17968e9	0.268821
$185$	1.44855e9	0.0909203
$186$	0	0
$187$	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	$-0.515786\pi$
$191$	−1.82357e9	−0.0991453	−0.0495726	+	0.998771i	$0.515786\pi$
$192$	0	0
$193$	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
$195$	0	0
$196$	1.56803e9	0.0758929
$197$	−1.93137e10	−0.913626	−0.456813	−	0.889563i	$-0.651009\pi$
$197$	−1.93137e10	−0.913626	−0.456813	+	0.889563i	$0.651009\pi$
$198$	0	0
$199$	1.52145e10	0.687733	0.343867	−	0.939019i	$-0.388263\pi$
$199$	1.52145e10	0.687733	0.343867	+	0.939019i	$0.388263\pi$
$200$	2.62500e9	0.116010
$201$	0	0
$202$	−4.08860e10	−1.72780
$203$	−1.61358e10	−0.666894
$204$	0	0
$205$	−6.39042e9	−0.252719
$206$	−3.02424e10	−1.17007
$207$	0	0
$208$	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
$213$	0	0
$214$	9.40658e9	0.306598
$215$	−1.88213e10	−0.600725
$216$	0	0
$217$	−1.53957e10	−0.471336
$218$	3.99058e10	1.19669
$219$	0	0
$220$	−4.34316e9	−0.124998
$221$	−2.22674e10	−0.627921
$222$	0	0
$223$	1.08324e9	0.0293328	0.0146664	−	0.999892i	$-0.495331\pi$
$223$	1.08324e9	0.0293328	0.0146664	+	0.999892i	$0.495331\pi$
$224$	1.37511e10	0.364939
$225$	0	0
$226$	−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	$0.287865\pi$
$228$	0	0
$229$	−4.32776e10	−1.03993	−0.519965	−	0.854188i	$-0.674055\pi$
$229$	−4.32776e10	−1.03993	−0.519965	+	0.854188i	$0.674055\pi$
$230$	1.08846e10	0.256470
$231$	0	0
$232$	−4.51613e10	−1.02346
$233$	7.55367e9	0.167902	0.0839511	−	0.996470i	$-0.473246\pi$
$233$	7.55367e9	0.167902	0.0839511	+	0.996470i	$0.473246\pi$
$234$	0	0
$235$	−1.47781e10	−0.316091
$236$	−2.31023e10	−0.484786
$237$	0	0
$238$	−3.53849e10	−0.714862
$239$	2.76516e10	0.548188	0.274094	−	0.961703i	$-0.411622\pi$
$239$	2.76516e10	0.548188	0.274094	+	0.961703i	$0.411622\pi$
$240$	0	0
$241$	−8.26006e10	−1.57727	−0.788635	−	0.614861i	$-0.789212\pi$
$241$	−8.26006e10	−1.57727	−0.788635	+	0.614861i	$0.789212\pi$
$242$	4.77469e10	0.894904
$243$	0	0
$244$	3.99237e9	0.0721068
$245$	−3.60300e9	−0.0638877
$246$	0	0
$247$	1.48096e10	0.253168
$248$	−4.30900e10	−0.723343
$249$	0	0
$250$	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
$255$	0	0
$256$	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	$0.564800\pi$
$258$	0	0
$259$	−5.56475e9	−0.0768417
$260$	7.19202e9	0.0976047
$261$	0	0
$262$	−5.17150e10	−0.678049
$263$	−1.39139e11	−1.79328	−0.896642	−	0.442756i	$-0.854001\pi$
$263$	−1.39139e11	−1.79328	−0.896642	+	0.442756i	$0.854001\pi$
$264$	0	0
$265$	3.58079e10	0.446039
$266$	2.35338e10	0.288221
$267$	0	0
$268$	−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	$0.510730\pi$
$270$	0	0
$271$	−7.46910e10	−0.841214	−0.420607	−	0.907243i	$-0.638183\pi$
$271$	−7.46910e10	−0.841214	−0.420607	+	0.907243i	$0.638183\pi$
$272$	−1.72337e11	−1.90906
$273$	0	0
$274$	3.28265e10	0.351842
$275$	9.97969e9	0.105225
$276$	0	0
$277$	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
$279$	0	0
$280$	−1.00842e10	−0.0980461
$281$	1.36058e11	1.30180	0.650901	−	0.759162i	$-0.274391\pi$
$281$	1.36058e11	1.30180	0.650901	+	0.759162i	$0.274391\pi$
$282$	0	0
$283$	−1.71084e11	−1.58551	−0.792757	−	0.609538i	$-0.791355\pi$
$283$	−1.71084e11	−1.58551	−0.792757	+	0.609538i	$0.791355\pi$
$284$	−1.68373e10	−0.153582
$285$	0	0
$286$	3.02633e10	0.267467
$287$	2.45495e10	0.213586
$288$	0	0
$289$	1.58448e11	1.33612
$290$	−1.17608e11	−0.976437
$291$	0	0
$292$	−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
$297$	0	0
$298$	−2.41217e11	−1.77188
$299$	−2.63133e10	−0.190395
$300$	0	0
$301$	7.23037e10	0.507705
$302$	−1.53693e11	−1.06322
$303$	0	0
$304$	1.14618e11	0.769701
$305$	−9.17364e9	−0.0607005
$306$	0	0
$307$	1.74144e11	1.11889	0.559443	−	0.828869i	$-0.311015\pi$
$307$	1.74144e11	1.11889	0.559443	+	0.828869i	$0.311015\pi$
$308$	1.66847e10	0.105643
$309$	0	0
$310$	−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	$0.395989\pi$
$312$	0	0
$313$	−2.43558e11	−1.43434	−0.717171	−	0.696897i	$-0.754563\pi$
$313$	−2.43558e11	−1.43434	−0.717171	+	0.696897i	$0.754563\pi$
$314$	3.72709e10	0.216365
$315$	0	0
$316$	7.51012e10	0.423697
$317$	−1.83776e11	−1.02217	−0.511083	−	0.859531i	$-0.670755\pi$
$317$	−1.83776e11	−1.02217	−0.511083	+	0.859531i	$0.670755\pi$
$318$	0	0
$319$	−1.71694e11	−0.928316
$320$	−4.54912e9	−0.0242523
$321$	0	0
$322$	−4.18142e10	−0.216757
$323$	−1.84251e11	−0.941888
$324$	0	0
$325$	−1.65258e10	−0.0821650
$326$	−3.95071e10	−0.193730
$327$	0	0
$328$	6.87098e10	0.327783
$329$	5.67714e10	0.267146
$330$	0	0
$331$	−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
$333$	0	0
$334$	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
$339$	0	0
$340$	−8.94781e10	−0.363130
$341$	−1.63819e11	−0.656100
$342$	0	0
$343$	1.38413e10	0.0539949
$344$	2.02366e11	0.779157
$345$	0	0
$346$	4.66262e11	1.74899
$347$	5.02625e11	1.86107	0.930533	−	0.366208i	$-0.119344\pi$
$347$	5.02625e11	1.86107	0.930533	+	0.366208i	$0.119344\pi$
$348$	0	0
$349$	7.14710e10	0.257879	0.128939	−	0.991652i	$-0.458843\pi$
$349$	7.14710e10	0.257879	0.128939	+	0.991652i	$0.458843\pi$
$350$	−2.62609e10	−0.0935414
$351$	0	0
$352$	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	$0.486079\pi$
$354$	0	0
$355$	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	$-0.576497\pi$
$359$	−1.49816e11	−0.476029	−0.238014	+	0.971262i	$0.576497\pi$
$360$	0	0
$361$	−2.00146e11	−0.620246
$362$	3.81246e11	1.16685
$363$	0	0
$364$	−2.76289e10	−0.0824910
$365$	1.77352e11	0.523021
$366$	0	0
$367$	−4.59514e11	−1.32221	−0.661107	−	0.750291i	$-0.729913\pi$
$367$	−4.59514e11	−1.32221	−0.661107	+	0.750291i	$0.729913\pi$
$368$	−2.03650e11	−0.578854
$369$	0	0
$370$	−4.05594e10	−0.112508
$371$	−1.37560e11	−0.376971
$372$	0	0
$373$	−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
$375$	0	0
$376$	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
$381$	0	0
$382$	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	$0.758285\pi$
$384$	0	0
$385$	−3.83380e10	−0.0889315
$386$	−3.46492e11	−0.794421
$387$	0	0
$388$	3.27980e11	0.734691
$389$	6.49908e11	1.43906	0.719530	−	0.694461i	$-0.244357\pi$
$389$	6.49908e11	1.43906	0.719530	+	0.694461i	$0.244357\pi$
$390$	0	0
$391$	3.27372e11	0.708347
$392$	3.87395e10	0.0828641
$393$	0	0
$394$	5.40785e11	1.13055
$395$	−1.72567e11	−0.356674
$396$	0	0
$397$	−3.67168e11	−0.741836	−0.370918	−	0.928666i	$-0.620957\pi$
$397$	−3.67168e11	−0.741836	−0.370918	+	0.928666i	$0.620957\pi$
$398$	−4.26007e11	−0.851026
$399$	0	0
$400$	−1.27900e11	−0.249805
$401$	9.73985e11	1.88106	0.940530	−	0.339712i	$-0.110330\pi$
$401$	9.73985e11	1.88106	0.940530	+	0.339712i	$0.110330\pi$
$402$	0	0
$403$	2.71275e11	0.512315
$404$	3.97178e11	0.741770
$405$	0	0
$406$	4.51801e11	0.825240
$407$	−5.92121e10	−0.106964
$408$	0	0
$409$	3.58196e11	0.632944	0.316472	−	0.948602i	$-0.397502\pi$
$409$	3.58196e11	0.632944	0.316472	+	0.948602i	$0.397502\pi$
$410$	1.78932e11	0.312723
$411$	0	0
$412$	2.93783e11	0.502330
$413$	−2.03928e11	−0.344907
$414$	0	0
$415$	−4.56225e10	−0.0755027
$416$	−2.42296e11	−0.396668
$417$	0	0
$418$	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
$423$	0	0
$424$	−3.85007e11	−0.578525
$425$	2.05602e11	0.305688
$426$	0	0
$427$	3.52415e10	0.0513013
$428$	−9.13782e10	−0.131627
$429$	0	0
$430$	5.26995e11	0.743359
$431$	−8.27297e11	−1.15482	−0.577409	−	0.816455i	$-0.695936\pi$
$431$	−8.27297e11	−1.15482	−0.577409	+	0.816455i	$0.695936\pi$
$432$	0	0
$433$	8.73032e11	1.19353	0.596767	−	0.802415i	$-0.296452\pi$
$433$	8.73032e11	1.19353	0.596767	+	0.802415i	$0.296452\pi$
$434$	4.31080e11	0.583249
$435$	0	0
$436$	−3.87657e11	−0.513757
$437$	−2.17729e11	−0.285594
$438$	0	0
$439$	7.15061e11	0.918867	0.459433	−	0.888212i	$-0.348053\pi$
$439$	7.15061e11	0.918867	0.459433	+	0.888212i	$0.348053\pi$
$440$	−1.07302e11	−0.136480
$441$	0	0
$442$	6.23488e11	0.777012
$443$	−5.89691e11	−0.727457	−0.363729	−	0.931505i	$-0.618496\pi$
$443$	−5.89691e11	−0.727457	−0.363729	+	0.931505i	$0.618496\pi$
$444$	0	0
$445$	−5.60230e11	−0.677246
$446$	−3.03308e10	−0.0362975
$447$	0	0
$448$	1.74759e10	0.0204969
$449$	1.06477e12	1.23636	0.618181	−	0.786036i	$-0.287870\pi$
$449$	1.06477e12	1.23636	0.618181	+	0.786036i	$0.287870\pi$
$450$	0	0
$451$	2.61220e11	0.297312
$452$	7.72964e11	0.871037
$453$	0	0
$454$	−1.38493e12	−1.52995
$455$	6.34854e10	0.0694421
$456$	0	0
$457$	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
$459$	0	0
$460$	−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
$465$	0	0
$466$	−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	$0.753584\pi$
$468$	0	0
$469$	−5.87183e11	−0.560397
$470$	4.13786e11	0.391143
$471$	0	0
$472$	−5.70762e11	−0.529317
$473$	7.69353e11	0.706725
$474$	0	0
$475$	−1.36742e11	−0.123248
$476$	3.43739e11	0.306901
$477$	0	0
$478$	−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	$0.904922\pi$
$480$	0	0
$481$	9.80519e10	0.0835224
$482$	2.31282e12	1.95177
$483$	0	0
$484$	−4.63827e11	−0.384195
$485$	−7.53631e11	−0.618473
$486$	0	0
$487$	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
$489$	0	0
$490$	1.00884e11	0.0790569
$491$	−6.88947e11	−0.534957	−0.267479	−	0.963564i	$-0.586190\pi$
$491$	−6.88947e11	−0.534957	−0.267479	+	0.963564i	$0.586190\pi$
$492$	0	0
$493$	−3.53724e12	−2.69683
$494$	−4.14670e11	−0.313279
$495$	0	0
$496$	2.09951e12	1.55758
$497$	−1.48627e11	−0.109268
$498$	0	0
$499$	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
$501$	0	0
$502$	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
$507$	0	0
$508$	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	$0.762105\pi$
$510$	0	0
$511$	−6.81317e11	−0.442033
$512$	−7.48685e11	−0.481487
$513$	0	0
$514$	7.91786e11	0.500350
$515$	−6.75053e11	−0.422869
$516$	0	0
$517$	6.04080e11	0.371867
$518$	1.55813e11	0.0950868
$519$	0	0
$520$	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	$0.311849\pi$
$522$	0	0
$523$	−1.58412e12	−0.925828	−0.462914	−	0.886403i	$-0.653196\pi$
$523$	−1.58412e12	−0.925828	−0.462914	+	0.886403i	$0.653196\pi$
$524$	5.02375e11	0.291096
$525$	0	0
$526$	3.89590e12	2.21908
$527$	−3.37501e12	−1.90602
$528$	0	0
$529$	−1.41430e12	−0.785219
$530$	−1.00262e12	−0.551945
$531$	0	0
$532$	−2.28614e11	−0.123737
$533$	−4.32565e11	−0.232156
$534$	0	0
$535$	2.09968e11	0.110806
$536$	−1.64343e12	−0.860021
$537$	0	0
$538$	1.62087e11	0.0834120
$539$	1.47279e11	0.0751609
$540$	0	0
$541$	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
$543$	0	0
$544$	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
$549$	0	0
$550$	−2.79431e11	−0.130210
$551$	2.35255e12	1.08732
$552$	0	0
$553$	6.62934e11	0.301444
$554$	−6.22594e11	−0.280809
$555$	0	0
$556$	−1.33008e12	−0.590259
$557$	−3.29033e12	−1.44841	−0.724204	−	0.689586i	$-0.757793\pi$
$557$	−3.29033e12	−1.44841	−0.724204	+	0.689586i	$0.757793\pi$
$558$	0	0
$559$	−1.27400e12	−0.551845
$560$	4.91341e11	0.211123
$561$	0	0
$562$	−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	$0.223634\pi$
$564$	0	0
$565$	−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	$-0.835809\pi$
$569$	−4.35009e12	−1.73978	−0.869888	+	0.493250i	$0.835809\pi$
$570$	0	0
$571$	−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
$573$	0	0
$574$	−6.87385e11	−0.264299
$575$	2.42959e11	0.0926890
$576$	0	0
$577$	−1.68758e12	−0.633830	−0.316915	−	0.948454i	$-0.602647\pi$
$577$	−1.68758e12	−0.633830	−0.316915	+	0.948454i	$0.602647\pi$
$578$	−4.43654e12	−1.65337
$579$	0	0
$580$	1.14247e12	0.419199
$581$	1.75263e11	0.0638114
$582$	0	0
$583$	−1.46371e12	−0.524744
$584$	−1.90689e12	−0.678373
$585$	0	0
$586$	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
$591$	0	0
$592$	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	$0.440416\pi$
$594$	0	0
$595$	−7.89842e11	−0.258353
$596$	2.34325e12	0.760694
$597$	0	0
$598$	7.36773e11	0.235602
$599$	−1.35944e12	−0.431460	−0.215730	−	0.976453i	$-0.569213\pi$
$599$	−1.35944e12	−0.431460	−0.215730	+	0.976453i	$0.569213\pi$
$600$	0	0
$601$	9.50421e11	0.297153	0.148577	−	0.988901i	$-0.452531\pi$
$601$	9.50421e11	0.297153	0.148577	+	0.988901i	$0.452531\pi$
$602$	−2.02450e12	−0.628253
$603$	0	0
$604$	1.49302e12	0.456457
$605$	1.06578e12	0.323421
$606$	0	0
$607$	3.35939e12	1.00441	0.502205	−	0.864749i	$-0.332522\pi$
$607$	3.35939e12	1.00441	0.502205	+	0.864749i	$0.332522\pi$
$608$	−2.00487e12	−0.595006
$609$	0	0
$610$	2.56862e11	0.0751131
$611$	−1.00032e12	−0.290372
$612$	0	0
$613$	−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
$615$	0	0
$616$	4.12210e11	0.115347
$617$	3.35285e10	0.00931388	0.00465694	−	0.999989i	$-0.498518\pi$
$617$	3.35285e10	0.00931388	0.00465694	+	0.999989i	$0.498518\pi$
$618$	0	0
$619$	5.51587e12	1.51010	0.755051	−	0.655666i	$-0.227612\pi$
$619$	5.51587e12	1.51010	0.755051	+	0.655666i	$0.227612\pi$
$620$	1.09008e12	0.296274
$621$	0	0
$622$	−2.96540e12	−0.794377
$623$	2.15218e12	0.572377
$624$	0	0
$625$	1.52588e11	0.0400000
$626$	6.81962e12	1.77491
$627$	0	0
$628$	−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
$633$	0	0
$634$	5.14572e12	1.26487
$635$	−2.18337e12	−0.532900
$636$	0	0
$637$	−2.43886e11	−0.0586893
$638$	4.80742e12	1.14873
$639$	0	0
$640$	1.96009e12	0.461813
$641$	−3.79136e11	−0.0887022	−0.0443511	−	0.999016i	$-0.514122\pi$
$641$	−3.79136e11	−0.0887022	−0.0443511	+	0.999016i	$0.514122\pi$
$642$	0	0
$643$	−5.15446e12	−1.18914	−0.594571	−	0.804043i	$-0.702678\pi$
$643$	−5.15446e12	−1.18914	−0.594571	+	0.804043i	$0.702678\pi$
$644$	4.06195e11	0.0930568
$645$	0	0
$646$	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	$0.402780\pi$
$648$	0	0
$649$	−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	$-0.255810\pi$
$653$	6.44986e12	1.38816	0.694082	+	0.719896i	$0.255810\pi$
$654$	0	0
$655$	−1.15435e12	−0.245049
$656$	−3.34780e12	−0.705818
$657$	0	0
$658$	−1.58960e12	−0.330576
$659$	2.79549e12	0.577396	0.288698	−	0.957420i	$-0.406778\pi$
$659$	2.79549e12	0.577396	0.288698	+	0.957420i	$0.406778\pi$
$660$	0	0
$661$	−4.93691e11	−0.100589	−0.0502943	−	0.998734i	$-0.516016\pi$
$661$	−4.93691e11	−0.100589	−0.0502943	+	0.998734i	$0.516016\pi$
$662$	1.62893e12	0.329641
$663$	0	0
$664$	4.90533e11	0.0979291
$665$	5.25309e11	0.104164
$666$	0	0
$667$	−4.17995e12	−0.817720
$668$	−6.76068e10	−0.0131370
$669$	0	0
$670$	−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
$675$	0	0
$676$	−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	$0.749286\pi$
$678$	0	0
$679$	2.89515e12	0.522705
$680$	−2.21064e12	−0.396485
$681$	0	0
$682$	4.58693e12	0.811882
$683$	−1.07677e13	−1.89334	−0.946670	−	0.322204i	$-0.895576\pi$
$683$	−1.07677e13	−1.89334	−0.946670	+	0.322204i	$0.895576\pi$
$684$	0	0
$685$	7.32735e11	0.127157
$686$	−3.87556e11	−0.0668153
$687$	0	0
$688$	−9.86005e12	−1.67776
$689$	2.42382e12	0.409746
$690$	0	0
$691$	2.02298e12	0.337552	0.168776	−	0.985654i	$-0.446019\pi$
$691$	2.02298e12	0.337552	0.168776	+	0.985654i	$0.446019\pi$
$692$	−4.52940e12	−0.750867
$693$	0	0
$694$	−1.40735e13	−2.30295
$695$	3.05626e12	0.496888
$696$	0	0
$697$	5.38168e12	0.863714
$698$	−2.00119e12	−0.319109
$699$	0	0
$700$	2.55106e11	0.0401587
$701$	−8.66031e11	−0.135457	−0.0677286	−	0.997704i	$-0.521575\pi$
$701$	−8.66031e11	−0.135457	−0.0677286	+	0.997704i	$0.521575\pi$
$702$	0	0
$703$	8.11328e11	0.125285
$704$	1.85953e11	0.0285317
$705$	0	0
$706$	−7.14268e11	−0.108203
$707$	3.50597e12	0.527741
$708$	0	0
$709$	−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
$711$	0	0
$712$	6.02360e12	0.878407
$713$	−3.98824e12	−0.577934
$714$	0	0
$715$	6.75521e11	0.0966633
$716$	−5.52040e12	−0.784986
$717$	0	0
$718$	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	$0.518154\pi$
$720$	0	0
$721$	2.59328e12	0.357389
$722$	5.60408e12	0.767515
$723$	0	0
$724$	−3.70353e12	−0.500947
$725$	−2.62517e12	−0.352887
$726$	0	0
$727$	3.13227e12	0.415867	0.207933	−	0.978143i	$-0.433326\pi$
$727$	3.13227e12	0.415867	0.207933	+	0.978143i	$0.433326\pi$
$728$	−6.82595e11	−0.0900683
$729$	0	0
$730$	−4.96587e12	−0.647205
$731$	1.58503e13	2.05309
$732$	0	0
$733$	−1.33197e13	−1.70422	−0.852112	−	0.523360i	$-0.824678\pi$
$733$	−1.33197e13	−1.70422	−0.852112	+	0.523360i	$0.824678\pi$
$734$	1.28664e13	1.63616
$735$	0	0
$736$	3.56220e12	0.447474
$737$	−6.24796e12	−0.780072
$738$	0	0
$739$	−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
$741$	0	0
$742$	3.85167e12	0.466478
$743$	−7.91108e12	−0.952327	−0.476164	−	0.879357i	$-0.657973\pi$
$743$	−7.91108e12	−0.952327	−0.476164	+	0.879357i	$0.657973\pi$
$744$	0	0
$745$	−5.38430e12	−0.640362
$746$	1.41184e13	1.66902
$747$	0	0
$748$	3.65758e12	0.427205
$749$	−8.06614e11	−0.0936478
$750$	0	0
$751$	−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
$753$	0	0
$754$	−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
$759$	0	0
$760$	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	$0.374566\pi$
$762$	0	0
$763$	−3.42192e12	−0.365519
$764$	−4.96011e11	−0.0526709
$765$	0	0
$766$	1.71034e13	1.79495
$767$	3.59325e12	0.374894
$768$	0	0
$769$	−4.97052e12	−0.512546	−0.256273	−	0.966604i	$-0.582495\pi$
$769$	−4.97052e12	−0.512546	−0.256273	+	0.966604i	$0.582495\pi$
$770$	1.07346e12	0.110047
$771$	0	0
$772$	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	$0.689944\pi$
$774$	0	0
$775$	−2.50477e12	−0.249408
$776$	8.10304e12	0.802177
$777$	0	0
$778$	−1.81974e13	−1.78075
$779$	−3.57925e12	−0.348236
$780$	0	0
$781$	−1.58147e12	−0.152101
$782$	−9.16642e12	−0.876535
$783$	0	0
$784$	−1.88753e12	−0.178432
$785$	8.31940e11	0.0781949
$786$	0	0
$787$	−6.23763e12	−0.579607	−0.289803	−	0.957086i	$-0.593590\pi$
$787$	−6.23763e12	−0.579607	−0.289803	+	0.957086i	$0.593590\pi$
$788$	−5.25334e12	−0.485364
$789$	0	0
$790$	4.83188e12	0.441361
$791$	6.82311e12	0.619710
$792$	0	0
$793$	−6.20960e11	−0.0557615
$794$	1.02807e13	0.917975
$795$	0	0
$796$	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
$801$	0	0
$802$	−2.72716e13	−2.32769
$803$	−7.24960e12	−0.615310
$804$	0	0
$805$	−9.33353e11	−0.0783365
$806$	−7.59570e12	−0.633957
$807$	0	0
$808$	9.81263e12	0.809906
$809$	−1.92205e13	−1.57760	−0.788801	−	0.614649i	$-0.789298\pi$
$809$	−1.92205e13	−1.57760	−0.788801	+	0.614649i	$0.789298\pi$
$810$	0	0
$811$	−1.70316e13	−1.38249	−0.691246	−	0.722620i	$-0.742938\pi$
$811$	−1.70316e13	−1.38249	−0.691246	+	0.722620i	$0.742938\pi$
$812$	−4.38892e12	−0.354288
$813$	0	0
$814$	1.65794e12	0.132361
$815$	−8.81855e11	−0.0700145
$816$	0	0
$817$	−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	$-0.671352\pi$
$821$	−1.33485e13	−1.02539	−0.512694	+	0.858572i	$0.671352\pi$
$822$	0	0
$823$	−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
$825$	0	0
$826$	5.71000e12	0.426801
$827$	−1.64651e13	−1.22402	−0.612012	−	0.790849i	$-0.709639\pi$
$827$	−1.64651e13	−1.22402	−0.612012	+	0.790849i	$0.709639\pi$
$828$	0	0
$829$	−5.91786e12	−0.435181	−0.217590	−	0.976040i	$-0.569820\pi$
$829$	−5.91786e12	−0.435181	−0.217590	+	0.976040i	$0.569820\pi$
$830$	1.27743e12	0.0934298
$831$	0	0
$832$	−3.07928e11	−0.0222789
$833$	3.03426e12	0.218348
$834$	0	0
$835$	1.55347e11	0.0110589
$836$	−2.43259e12	−0.172242
$837$	0	0
$838$	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
$843$	0	0
$844$	−1.05978e13	−0.718913
$845$	5.50919e12	0.371734
$846$	0	0
$847$	−4.09430e12	−0.273341
$848$	1.87590e13	1.24574
$849$	0	0
$850$	−5.75687e12	−0.378269
$851$	−1.44154e12	−0.0942203
$852$	0	0
$853$	2.26446e13	1.46452	0.732258	−	0.681027i	$-0.238466\pi$
$853$	2.26446e13	1.46452	0.732258	+	0.681027i	$0.238466\pi$
$854$	−9.86761e11	−0.0634821
$855$	0	0
$856$	−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	$0.375694\pi$
$858$	0	0
$859$	−9.44258e12	−0.591727	−0.295864	−	0.955230i	$-0.595607\pi$
$859$	−9.44258e12	−0.591727	−0.295864	+	0.955230i	$0.595607\pi$
$860$	−5.11938e12	−0.319135
$861$	0	0
$862$	2.31643e13	1.42901
$863$	−8.80380e12	−0.540283	−0.270142	−	0.962821i	$-0.587071\pi$
$863$	−8.80380e12	−0.540283	−0.270142	+	0.962821i	$0.587071\pi$
$864$	0	0
$865$	1.04076e13	0.632090
$866$	−2.44449e13	−1.47692
$867$	0	0
$868$	−4.18763e12	−0.250397
$869$	7.05399e12	0.419610
$870$	0	0
$871$	1.03463e13	0.609119
$872$	−9.57740e12	−0.560949
$873$	0	0
$874$	6.09641e12	0.353405
$875$	−5.86182e11	−0.0338062
$876$	0	0
$877$	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
$879$	0	0
$880$	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
$885$	0	0
$886$	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	$0.268450\pi$
$888$	0	0
$889$	8.38764e12	0.450383
$890$	1.56864e13	0.838049
$891$	0	0
$892$	2.94642e11	0.0155830
$893$	−8.27714e12	−0.435561
$894$	0	0
$895$	1.26847e13	0.660812
$896$	−7.52988e12	−0.390303
$897$	0	0
$898$	−2.98134e13	−1.52992
$899$	4.30928e13	2.20032
$900$	0	0
$901$	−3.01555e13	−1.52442
$902$	−7.31416e12	−0.367905
$903$	0	0
$904$	1.90968e13	0.951047
$905$	8.50995e12	0.421704
$906$	0	0
$907$	−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
$909$	0	0
$910$	−1.77759e12	−0.0859302
$911$	1.26965e13	0.610733	0.305367	−	0.952235i	$-0.401221\pi$
$911$	1.26965e13	0.610733	0.305367	+	0.952235i	$0.401221\pi$
$912$	0	0
$913$	1.86490e12	0.0888254
$914$	−4.32029e13	−2.04765
$915$	0	0
$916$	−1.17715e13	−0.552463
$917$	4.43456e12	0.207104
$918$	0	0
$919$	−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
$921$	0	0
$922$	−2.34830e13	−1.07020
$923$	2.61882e12	0.118768
$924$	0	0
$925$	−9.05345e11	−0.0406608
$926$	2.41309e13	1.07851
$927$	0	0
$928$	−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	$0.637129\pi$
$930$	0	0
$931$	−2.01803e12	−0.0880346
$932$	2.05460e12	0.0891980
$933$	0	0
$934$	4.11561e13	1.76959
$935$	−8.40437e12	−0.359627
$936$	0	0
$937$	8.65559e12	0.366833	0.183416	−	0.983035i	$-0.441284\pi$
$937$	8.65559e12	0.366833	0.183416	+	0.983035i	$0.441284\pi$
$938$	1.64411e13	0.693456
$939$	0	0
$940$	−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	$0.752054\pi$
$942$	0	0
$943$	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	$-0.660095\pi$
$947$	−2.38597e13	−0.964030	−0.482015	+	0.876163i	$0.660095\pi$
$948$	0	0
$949$	1.20049e13	0.480464
$950$	3.82878e12	0.152512
$951$	0	0
$952$	8.49238e12	0.335091
$953$	4.83481e13	1.89872	0.949360	−	0.314189i	$-0.101733\pi$
$953$	4.83481e13	1.89872	0.949360	+	0.314189i	$0.101733\pi$
$954$	0	0
$955$	1.13973e12	0.0443391
$956$	7.52123e12	0.291225
$957$	0	0
$958$	6.16636e13	2.36529
$959$	−2.81488e12	−0.107467
$960$	0	0
$961$	1.46768e13	0.555106
$962$	−2.74545e12	−0.103354
$963$	0	0
$964$	−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
$969$	0	0
$970$	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	$0.543943\pi$
$972$	0	0
$973$	−1.17409e13	−0.419947
$974$	−3.64203e13	−1.29667
$975$	0	0
$976$	−4.80587e12	−0.169531
$977$	−2.97018e13	−1.04293	−0.521467	−	0.853272i	$-0.674615\pi$
$977$	−2.97018e13	−1.04293	−0.521467	+	0.853272i	$0.674615\pi$
$978$	0	0
$979$	2.29004e13	0.796749
$980$	−9.80016e11	−0.0339403
$981$	0	0
$982$	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	$0.440785\pi$
$984$	0	0
$985$	1.20711e13	0.408586
$986$	9.90428e13	3.33716
$987$	0	0
$988$	4.02822e12	0.134495
$989$	1.87302e13	0.622528
$990$	0	0
$991$	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
$993$	0	0
$994$	4.16154e12	0.135212
$995$	−9.50909e12	−0.307564
$996$	0	0
$997$	1.64214e13	0.526360	0.263180	−	0.964747i	$-0.415229\pi$
$997$	1.64214e13	0.526360	0.263180	+	0.964747i	$0.415229\pi$
$998$	−4.94788e13	−1.57882
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.10.a.a.1.1		1
3.2	odd	2		35.10.a.a.1.1	✓	1
15.2	even	4		175.10.b.a.99.2		2
15.8	even	4		175.10.b.a.99.1		2
15.14	odd	2		175.10.a.a.1.1		1
21.20	even	2		245.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.a.1.1	✓	1	3.2	odd	2
175.10.a.a.1.1		1	15.14	odd	2
175.10.b.a.99.1		2	15.8	even	4
175.10.b.a.99.2		2	15.2	even	4
245.10.a.b.1.1		1	21.20	even	2
315.10.a.a.1.1		1	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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