LMFDB - Embedded newform 91.10.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7002 x^{13} + 56252 x^{12} + 19365525 x^{11} - 172593791 x^{10} + \cdots + 15\!\cdots\!80 $ x^15 - 7x^14 - 7002x^13 + 56252x^12 + 19365525x^11 - 172593791x^10 - 26814463634x^9 + 254652735184x^8 + 19468686934379x^7 - 187275922162581x^6 - 7114485342885046x^5 + 65109704629514532x^4 + 1131832063959701151x^3 - 8977247355614269573x^2 - 47004259937698392062x + 152144189066892720880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.47100$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.47100 q^{2} -27.0742 q^{3} -499.952 q^{4} -887.663 q^{5} -93.9746 q^{6} -2401.00 q^{7} -3512.49 q^{8} -18950.0 q^{9} +O(q^{10})$	\(q+3.47100 q^{2} -27.0742 q^{3} -499.952 q^{4} -887.663 q^{5} -93.9746 q^{6} -2401.00 q^{7} -3512.49 q^{8} -18950.0 q^{9} -3081.08 q^{10} -66919.5 q^{11} +13535.8 q^{12} +28561.0 q^{13} -8333.88 q^{14} +24032.8 q^{15} +243784. q^{16} -670340. q^{17} -65775.4 q^{18} -258629. q^{19} +443789. q^{20} +65005.2 q^{21} -232278. q^{22} -1.41144e6 q^{23} +95097.8 q^{24} -1.16518e6 q^{25} +99135.3 q^{26} +1.04596e6 q^{27} +1.20039e6 q^{28} +6.64091e6 q^{29} +83417.8 q^{30} +424741. q^{31} +2.64457e6 q^{32} +1.81179e6 q^{33} -2.32675e6 q^{34} +2.13128e6 q^{35} +9.47409e6 q^{36} -1.66918e7 q^{37} -897701. q^{38} -773267. q^{39} +3.11791e6 q^{40} +3.01729e7 q^{41} +225633. q^{42} -1.77582e7 q^{43} +3.34566e7 q^{44} +1.68212e7 q^{45} -4.89913e6 q^{46} -1.47602e7 q^{47} -6.60025e6 q^{48} +5.76480e6 q^{49} -4.04434e6 q^{50} +1.81489e7 q^{51} -1.42791e7 q^{52} -6.66586e7 q^{53} +3.63052e6 q^{54} +5.94020e7 q^{55} +8.43348e6 q^{56} +7.00217e6 q^{57} +2.30506e7 q^{58} +1.53682e8 q^{59} -1.20152e7 q^{60} +5.11243e7 q^{61} +1.47428e6 q^{62} +4.54989e7 q^{63} -1.15638e8 q^{64} -2.53525e7 q^{65} +6.28874e6 q^{66} -1.97499e7 q^{67} +3.35138e8 q^{68} +3.82137e7 q^{69} +7.39767e6 q^{70} +2.05994e7 q^{71} +6.65616e7 q^{72} +3.96460e7 q^{73} -5.79372e7 q^{74} +3.15463e7 q^{75} +1.29302e8 q^{76} +1.60674e8 q^{77} -2.68401e6 q^{78} +2.76066e8 q^{79} -2.16398e8 q^{80} +3.44674e8 q^{81} +1.04730e8 q^{82} -3.41041e8 q^{83} -3.24995e7 q^{84} +5.95036e8 q^{85} -6.16386e7 q^{86} -1.79797e8 q^{87} +2.35054e8 q^{88} -7.76819e8 q^{89} +5.83864e7 q^{90} -6.85750e7 q^{91} +7.05655e8 q^{92} -1.14995e7 q^{93} -5.12326e7 q^{94} +2.29575e8 q^{95} -7.15996e7 q^{96} -7.42905e8 q^{97} +2.00096e7 q^{98} +1.26812e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) $ 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * q^99

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 $

$2$	3.47100	0.153398	0.0766990	−	0.997054i	$-0.475562\pi$
$2$	3.47100	0.153398	0.0766990	+	0.997054i	$0.475562\pi$
$3$	−27.0742	−0.192979	−0.0964895	−	0.995334i	$-0.530761\pi$
$3$	−27.0742	−0.192979	−0.0964895	+	0.995334i	$0.530761\pi$
$4$	−499.952	−0.976469
$5$	−887.663	−0.635160	−0.317580	−	0.948231i	$-0.602870\pi$
$5$	−887.663	−0.635160	−0.317580	+	0.948231i	$0.602870\pi$
$6$	−93.9746	−0.0296026
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−3512.49	−0.303187
$9$	−18950.0	−0.962759
$10$	−3081.08	−0.0974323
$11$	−66919.5	−1.37812	−0.689058	−	0.724706i	$-0.741976\pi$
$11$	−66919.5	−1.37812	−0.689058	+	0.724706i	$0.741976\pi$
$12$	13535.8	0.188438
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−8333.88	−0.0579790
$15$	24032.8	0.122573
$16$	243784.	0.929961
$17$	−670340.	−1.94659	−0.973296	−	0.229555i	$-0.926273\pi$
$17$	−670340.	−1.94659	−0.973296	+	0.229555i	$0.926273\pi$
$18$	−65775.4	−0.147685
$19$	−258629.	−0.455288	−0.227644	−	0.973744i	$-0.573102\pi$
$19$	−258629.	−0.455288	−0.227644	+	0.973744i	$0.573102\pi$
$20$	443789.	0.620214
$21$	65005.2	0.0729392
$22$	−232278.	−0.211400
$23$	−1.41144e6	−1.05169	−0.525846	−	0.850580i	$-0.676251\pi$
$23$	−1.41144e6	−1.05169	−0.525846	+	0.850580i	$0.676251\pi$
$24$	95097.8	0.0585086
$25$	−1.16518e6	−0.596572
$26$	99135.3	0.0425450
$27$	1.04596e6	0.378771
$28$	1.20039e6	0.369071
$29$	6.64091e6	1.74356	0.871780	−	0.489898i	$-0.162966\pi$
$29$	6.64091e6	1.74356	0.871780	+	0.489898i	$0.162966\pi$
$30$	83417.8	0.0188024
$31$	424741.	0.0826032	0.0413016	−	0.999147i	$-0.486850\pi$
$31$	424741.	0.0826032	0.0413016	+	0.999147i	$0.486850\pi$
$32$	2.64457e6	0.445841
$33$	1.81179e6	0.265948
$34$	−2.32675e6	−0.298603
$35$	2.13128e6	0.240068
$36$	9.47409e6	0.940104
$37$	−1.66918e7	−1.46418	−0.732091	−	0.681207i	$-0.761455\pi$
$37$	−1.66918e7	−1.46418	−0.732091	+	0.681207i	$0.761455\pi$
$38$	−897701.	−0.0698402
$39$	−773267.	−0.0535228
$40$	3.11791e6	0.192572
$41$	3.01729e7	1.66759	0.833797	−	0.552071i	$-0.186162\pi$
$41$	3.01729e7	1.66759	0.833797	+	0.552071i	$0.186162\pi$
$42$	225633.	0.0111887
$43$	−1.77582e7	−0.792118	−0.396059	−	0.918225i	$-0.629622\pi$
$43$	−1.77582e7	−0.792118	−0.396059	+	0.918225i	$0.629622\pi$
$44$	3.34566e7	1.34569
$45$	1.68212e7	0.611506
$46$	−4.89913e6	−0.161327
$47$	−1.47602e7	−0.441216	−0.220608	−	0.975363i	$-0.570804\pi$
$47$	−1.47602e7	−0.441216	−0.220608	+	0.975363i	$0.570804\pi$
$48$	−6.60025e6	−0.179463
$49$	5.76480e6	0.142857
$50$	−4.04434e6	−0.0915130
$51$	1.81489e7	0.375651
$52$	−1.42791e7	−0.270824
$53$	−6.66586e7	−1.16042	−0.580209	−	0.814467i	$-0.697029\pi$
$53$	−6.66586e7	−1.16042	−0.580209	+	0.814467i	$0.697029\pi$
$54$	3.63052e6	0.0581028
$55$	5.94020e7	0.875324
$56$	8.43348e6	0.114594
$57$	7.00217e6	0.0878610
$58$	2.30506e7	0.267459
$59$	1.53682e8	1.65116	0.825581	−	0.564284i	$-0.190848\pi$
$59$	1.53682e8	1.65116	0.825581	+	0.564284i	$0.190848\pi$
$60$	−1.20152e7	−0.119688
$61$	5.11243e7	0.472763	0.236381	−	0.971660i	$-0.424039\pi$
$61$	5.11243e7	0.472763	0.236381	+	0.971660i	$0.424039\pi$
$62$	1.47428e6	0.0126712
$63$	4.54989e7	0.363889
$64$	−1.15638e8	−0.861570
$65$	−2.53525e7	−0.176162
$66$	6.28874e6	0.0407958
$67$	−1.97499e7	−0.119737	−0.0598684	−	0.998206i	$-0.519068\pi$
$67$	−1.97499e7	−0.119737	−0.0598684	+	0.998206i	$0.519068\pi$
$68$	3.35138e8	1.90079
$69$	3.82137e7	0.202954
$70$	7.39767e6	0.0368260
$71$	2.05994e7	0.0962035	0.0481018	−	0.998842i	$-0.484683\pi$
$71$	2.05994e7	0.0962035	0.0481018	+	0.998842i	$0.484683\pi$
$72$	6.65616e7	0.291896
$73$	3.96460e7	0.163398	0.0816990	−	0.996657i	$-0.473965\pi$
$73$	3.96460e7	0.163398	0.0816990	+	0.996657i	$0.473965\pi$
$74$	−5.79372e7	−0.224603
$75$	3.15463e7	0.115126
$76$	1.29302e8	0.444574
$77$	1.60674e8	0.520879
$78$	−2.68401e6	−0.00821029
$79$	2.76066e8	0.797428	0.398714	−	0.917075i	$-0.369457\pi$
$79$	2.76066e8	0.797428	0.398714	+	0.917075i	$0.369457\pi$
$80$	−2.16398e8	−0.590674
$81$	3.44674e8	0.889664
$82$	1.04730e8	0.255806
$83$	−3.41041e8	−0.788779	−0.394390	−	0.918943i	$-0.629044\pi$
$83$	−3.41041e8	−0.788779	−0.394390	+	0.918943i	$0.629044\pi$
$84$	−3.24995e7	−0.0712229
$85$	5.95036e8	1.23640
$86$	−6.16386e7	−0.121509
$87$	−1.79797e8	−0.336470
$88$	2.35054e8	0.417826
$89$	−7.76819e8	−1.31240	−0.656198	−	0.754589i	$-0.727836\pi$
$89$	−7.76819e8	−1.31240	−0.656198	+	0.754589i	$0.727836\pi$
$90$	5.83864e7	0.0938038
$91$	−6.85750e7	−0.104828
$92$	7.05655e8	1.02694
$93$	−1.14995e7	−0.0159407
$94$	−5.12326e7	−0.0676817
$95$	2.29575e8	0.289180
$96$	−7.15996e7	−0.0860379
$97$	−7.42905e8	−0.852041	−0.426020	−	0.904714i	$-0.640085\pi$
$97$	−7.42905e8	−0.852041	−0.426020	+	0.904714i	$0.640085\pi$
$98$	2.00096e7	0.0219140
$99$	1.26812e9	1.32679
$100$	5.82534e8	0.582534
$101$	9.20507e8	0.880199	0.440100	−	0.897949i	$-0.354943\pi$
$101$	9.20507e8	0.880199	0.440100	+	0.897949i	$0.354943\pi$
$102$	6.29949e7	0.0576242
$103$	−1.24228e8	−0.108756	−0.0543779	−	0.998520i	$-0.517318\pi$
$103$	−1.24228e8	−0.108756	−0.0543779	+	0.998520i	$0.517318\pi$
$104$	−1.00320e8	−0.0840888
$105$	−5.77027e7	−0.0463281
$106$	−2.31372e8	−0.178006
$107$	−1.34472e9	−0.991757	−0.495879	−	0.868392i	$-0.665154\pi$
$107$	−1.34472e9	−0.991757	−0.495879	+	0.868392i	$0.665154\pi$
$108$	−5.22929e8	−0.369859
$109$	−1.37890e9	−0.935652	−0.467826	−	0.883821i	$-0.654963\pi$
$109$	−1.37890e9	−0.935652	−0.467826	+	0.883821i	$0.654963\pi$
$110$	2.06184e8	0.134273
$111$	4.51917e8	0.282556
$112$	−5.85325e8	−0.351492
$113$	4.32803e8	0.249711	0.124855	−	0.992175i	$-0.460153\pi$
$113$	4.32803e8	0.249711	0.124855	+	0.992175i	$0.460153\pi$
$114$	2.43046e7	0.0134777
$115$	1.25289e9	0.667993
$116$	−3.32014e9	−1.70253
$117$	−5.41231e8	−0.267021
$118$	5.33431e8	0.253285
$119$	1.60949e9	0.735742
$120$	−8.44148e7	−0.0371624
$121$	2.12028e9	0.899205
$122$	1.77453e8	0.0725209
$123$	−8.16909e8	−0.321811
$124$	−2.12350e8	−0.0806594
$125$	2.76800e9	1.01408
$126$	1.57927e8	0.0558198
$127$	−3.01343e9	−1.02789	−0.513943	−	0.857824i	$-0.671816\pi$
$127$	−3.01343e9	−1.02789	−0.513943	+	0.857824i	$0.671816\pi$
$128$	−1.75540e9	−0.578004
$129$	4.80788e8	0.152862
$130$	−8.79987e7	−0.0270229
$131$	−2.35446e9	−0.698506	−0.349253	−	0.937028i	$-0.613565\pi$
$131$	−2.35446e9	−0.698506	−0.349253	+	0.937028i	$0.613565\pi$
$132$	−9.05810e8	−0.259690
$133$	6.20968e8	0.172083
$134$	−6.85518e7	−0.0183674
$135$	−9.28458e8	−0.240580
$136$	2.35456e9	0.590180
$137$	−3.92524e9	−0.951970	−0.475985	−	0.879453i	$-0.657908\pi$
$137$	−3.92524e9	−0.951970	−0.475985	+	0.879453i	$0.657908\pi$
$138$	1.32640e8	0.0311328
$139$	−6.50700e9	−1.47848	−0.739238	−	0.673445i	$-0.764814\pi$
$139$	−6.50700e9	−1.47848	−0.739238	+	0.673445i	$0.764814\pi$
$140$	−1.06554e9	−0.234419
$141$	3.99620e8	0.0851454
$142$	7.15004e7	0.0147574
$143$	−1.91129e9	−0.382221
$144$	−4.61970e9	−0.895328
$145$	−5.89489e9	−1.10744
$146$	1.37611e8	0.0250649
$147$	−1.56077e8	−0.0275684
$148$	8.34510e9	1.42973
$149$	−5.41962e9	−0.900804	−0.450402	−	0.892826i	$-0.648719\pi$
$149$	−5.41962e9	−0.900804	−0.450402	+	0.892826i	$0.648719\pi$
$150$	1.09497e8	0.0176601
$151$	−5.87519e9	−0.919657	−0.459828	−	0.888008i	$-0.652089\pi$
$151$	−5.87519e9	−0.919657	−0.459828	+	0.888008i	$0.652089\pi$
$152$	9.08431e8	0.138037
$153$	1.27029e10	1.87410
$154$	5.57699e8	0.0799018
$155$	−3.77027e8	−0.0524662
$156$	3.86596e8	0.0522633
$157$	−5.53398e9	−0.726924	−0.363462	−	0.931609i	$-0.618405\pi$
$157$	−5.53398e9	−0.726924	−0.363462	+	0.931609i	$0.618405\pi$
$158$	9.58227e8	0.122324
$159$	1.80473e9	0.223936
$160$	−2.34748e9	−0.283180
$161$	3.38888e9	0.397502
$162$	1.19636e9	0.136473
$163$	−4.59789e9	−0.510169	−0.255085	−	0.966919i	$-0.582103\pi$
$163$	−4.59789e9	−0.510169	−0.255085	+	0.966919i	$0.582103\pi$
$164$	−1.50850e10	−1.62835
$165$	−1.60826e9	−0.168919
$166$	−1.18375e9	−0.120997
$167$	1.02484e10	1.01961	0.509803	−	0.860291i	$-0.329718\pi$
$167$	1.02484e10	1.01961	0.509803	+	0.860291i	$0.329718\pi$
$168$	−2.28330e8	−0.0221142
$169$	8.15731e8	0.0769231
$170$	2.06537e9	0.189661
$171$	4.90101e9	0.438332
$172$	8.87823e9	0.773479
$173$	−2.05621e10	−1.74526	−0.872629	−	0.488383i	$-0.837587\pi$
$173$	−2.05621e10	−1.74526	−0.872629	+	0.488383i	$0.837587\pi$
$174$	−6.24077e8	−0.0516139
$175$	2.79760e9	0.225483
$176$	−1.63139e10	−1.28159
$177$	−4.16082e9	−0.318640
$178$	−2.69634e9	−0.201319
$179$	9.73555e9	0.708797	0.354399	−	0.935094i	$-0.384686\pi$
$179$	9.73555e9	0.708797	0.354399	+	0.935094i	$0.384686\pi$
$180$	−8.40980e9	−0.597117
$181$	−1.56811e10	−1.08598	−0.542992	−	0.839738i	$-0.682709\pi$
$181$	−1.56811e10	−1.08598	−0.542992	+	0.839738i	$0.682709\pi$
$182$	−2.38024e8	−0.0160805
$183$	−1.38415e9	−0.0912333
$184$	4.95768e9	0.318859
$185$	1.48167e10	0.929990
$186$	−3.99149e7	−0.00244527
$187$	4.48588e10	2.68263
$188$	7.37938e9	0.430834
$189$	−2.51134e9	−0.143162
$190$	7.96856e8	0.0443597
$191$	9.53554e9	0.518436	0.259218	−	0.965819i	$-0.416535\pi$
$191$	9.53554e9	0.518436	0.259218	+	0.965819i	$0.416535\pi$
$192$	3.13081e9	0.166265
$193$	2.25020e10	1.16738	0.583691	−	0.811976i	$-0.301608\pi$
$193$	2.25020e10	1.16738	0.583691	+	0.811976i	$0.301608\pi$
$194$	−2.57862e9	−0.130701
$195$	6.86400e8	0.0339955
$196$	−2.88212e9	−0.139496
$197$	1.00733e10	0.476511	0.238256	−	0.971202i	$-0.423424\pi$
$197$	1.00733e10	0.476511	0.238256	+	0.971202i	$0.423424\pi$
$198$	4.40166e9	0.203528
$199$	1.35648e10	0.613161	0.306581	−	0.951845i	$-0.400815\pi$
$199$	1.35648e10	0.613161	0.306581	+	0.951845i	$0.400815\pi$
$200$	4.09268e9	0.180873
$201$	5.34712e8	0.0231067
$202$	3.19508e9	0.135021
$203$	−1.59448e10	−0.659003
$204$	−9.07359e9	−0.366812
$205$	−2.67834e10	−1.05919
$206$	−4.31196e8	−0.0166829
$207$	2.67469e10	1.01253
$208$	6.96270e9	0.257925
$209$	1.73073e10	0.627439
$210$	−2.00286e8	−0.00710664
$211$	4.05313e9	0.140773	0.0703865	−	0.997520i	$-0.477577\pi$
$211$	4.05313e9	0.140773	0.0703865	+	0.997520i	$0.477577\pi$
$212$	3.33261e10	1.13311
$213$	−5.57711e8	−0.0185653
$214$	−4.66753e9	−0.152134
$215$	1.57633e10	0.503122
$216$	−3.67391e9	−0.114838
$217$	−1.01980e9	−0.0312211
$218$	−4.78617e9	−0.143527
$219$	−1.07338e9	−0.0315324
$220$	−2.96982e10	−0.854727
$221$	−1.91456e10	−0.539887
$222$	1.56860e9	0.0433436
$223$	−9.36600e9	−0.253619	−0.126810	−	0.991927i	$-0.540474\pi$
$223$	−9.36600e9	−0.253619	−0.126810	+	0.991927i	$0.540474\pi$
$224$	−6.34961e9	−0.168512
$225$	2.20801e10	0.574355
$226$	1.50226e9	0.0383052
$227$	−9.15002e9	−0.228721	−0.114360	−	0.993439i	$-0.536482\pi$
$227$	−9.15002e9	−0.228721	−0.114360	+	0.993439i	$0.536482\pi$
$228$	−3.50075e9	−0.0857935
$229$	2.54314e10	0.611096	0.305548	−	0.952177i	$-0.401160\pi$
$229$	2.54314e10	0.611096	0.305548	+	0.952177i	$0.401160\pi$
$230$	4.34877e9	0.102469
$231$	−4.35012e9	−0.100519
$232$	−2.33261e10	−0.528624
$233$	4.78761e10	1.06419	0.532093	−	0.846686i	$-0.321406\pi$
$233$	4.78761e10	1.06419	0.532093	+	0.846686i	$0.321406\pi$
$234$	−1.87861e9	−0.0409606
$235$	1.31021e10	0.280243
$236$	−7.68337e10	−1.61231
$237$	−7.47428e9	−0.153887
$238$	5.58653e9	0.112861
$239$	4.55956e10	0.903926	0.451963	−	0.892037i	$-0.350724\pi$
$239$	4.55956e10	0.903926	0.451963	+	0.892037i	$0.350724\pi$
$240$	5.85880e9	0.113988
$241$	4.91092e10	0.937748	0.468874	−	0.883265i	$-0.344660\pi$
$241$	4.91092e10	0.937748	0.468874	+	0.883265i	$0.344660\pi$
$242$	7.35949e9	0.137936
$243$	−2.99194e10	−0.550458
$244$	−2.55597e10	−0.461638
$245$	−5.11720e9	−0.0907371
$246$	−2.83549e9	−0.0493652
$247$	−7.38670e9	−0.126274
$248$	−1.49190e9	−0.0250442
$249$	9.23342e9	0.152218
$250$	9.60775e9	0.155558
$251$	5.11042e10	0.812689	0.406345	−	0.913720i	$-0.366803\pi$
$251$	5.11042e10	0.812689	0.406345	+	0.913720i	$0.366803\pi$
$252$	−2.27473e10	−0.355326
$253$	9.44532e10	1.44935
$254$	−1.04596e10	−0.157676
$255$	−1.61101e10	−0.238599
$256$	5.31136e10	0.772905
$257$	−1.43518e10	−0.205214	−0.102607	−	0.994722i	$-0.532718\pi$
$257$	−1.43518e10	−0.205214	−0.102607	+	0.994722i	$0.532718\pi$
$258$	1.66882e9	0.0234488
$259$	4.00770e10	0.553409
$260$	1.26751e10	0.172016
$261$	−1.25845e11	−1.67863
$262$	−8.17233e9	−0.107150
$263$	5.32706e10	0.686573	0.343287	−	0.939231i	$-0.388460\pi$
$263$	5.32706e10	0.686573	0.343287	+	0.939231i	$0.388460\pi$
$264$	−6.36390e9	−0.0806317
$265$	5.91704e10	0.737051
$266$	2.15538e9	0.0263971
$267$	2.10318e10	0.253265
$268$	9.87399e9	0.116919
$269$	−6.65577e10	−0.775020	−0.387510	−	0.921865i	$-0.626665\pi$
$269$	−6.65577e10	−0.775020	−0.387510	+	0.921865i	$0.626665\pi$
$270$	−3.22268e9	−0.0369046
$271$	−7.29209e9	−0.0821278	−0.0410639	−	0.999157i	$-0.513075\pi$
$271$	−7.29209e9	−0.0821278	−0.0410639	+	0.999157i	$0.513075\pi$
$272$	−1.63418e11	−1.81025
$273$	1.85661e9	0.0202297
$274$	−1.36245e10	−0.146030
$275$	7.79733e10	0.822145
$276$	−1.91050e10	−0.198179
$277$	−1.22189e11	−1.24702	−0.623510	−	0.781816i	$-0.714294\pi$
$277$	−1.22189e11	−1.24702	−0.623510	+	0.781816i	$0.714294\pi$
$278$	−2.25858e10	−0.226795
$279$	−8.04884e9	−0.0795270
$280$	−7.48609e9	−0.0727854
$281$	−4.18189e10	−0.400123	−0.200062	−	0.979783i	$-0.564114\pi$
$281$	−4.18189e10	−0.400123	−0.200062	+	0.979783i	$0.564114\pi$
$282$	1.38708e9	0.0130611
$283$	−4.98293e10	−0.461791	−0.230896	−	0.972978i	$-0.574166\pi$
$283$	−4.98293e10	−0.461791	−0.230896	+	0.972978i	$0.574166\pi$
$284$	−1.02987e10	−0.0939398
$285$	−6.21557e9	−0.0558058
$286$	−6.63409e9	−0.0586319
$287$	−7.24453e10	−0.630291
$288$	−5.01145e10	−0.429237
$289$	3.30767e11	2.78922
$290$	−2.04612e10	−0.169879
$291$	2.01136e10	0.164426
$292$	−1.98211e10	−0.159553
$293$	1.12563e11	0.892259	0.446130	−	0.894968i	$-0.352802\pi$
$293$	1.12563e11	0.892259	0.446130	+	0.894968i	$0.352802\pi$
$294$	−5.41745e8	−0.00422894
$295$	−1.36418e11	−1.04875
$296$	5.86297e10	0.443920
$297$	−6.99950e10	−0.521991
$298$	−1.88115e10	−0.138182
$299$	−4.03123e10	−0.291687
$300$	−1.57716e10	−0.112417
$301$	4.26373e10	0.299392
$302$	−2.03928e10	−0.141074
$303$	−2.49220e10	−0.169860
$304$	−6.30495e10	−0.423400
$305$	−4.53811e10	−0.300280
$306$	4.40919e10	0.287483
$307$	−3.04804e11	−1.95838	−0.979192	−	0.202937i	$-0.934951\pi$
$307$	−3.04804e11	−1.95838	−0.979192	+	0.202937i	$0.934951\pi$
$308$	−8.03292e10	−0.508622
$309$	3.36338e9	0.0209876
$310$	−1.30866e9	−0.00804822
$311$	−6.27441e10	−0.380322	−0.190161	−	0.981753i	$-0.560901\pi$
$311$	−6.27441e10	−0.380322	−0.190161	+	0.981753i	$0.560901\pi$
$312$	2.71609e9	0.0162274
$313$	−4.17710e10	−0.245994	−0.122997	−	0.992407i	$-0.539251\pi$
$313$	−4.17710e10	−0.245994	−0.122997	+	0.992407i	$0.539251\pi$
$314$	−1.92085e10	−0.111509
$315$	−4.03877e10	−0.231128
$316$	−1.38020e11	−0.778664
$317$	−6.58656e10	−0.366347	−0.183173	−	0.983081i	$-0.558637\pi$
$317$	−6.58656e10	−0.366347	−0.183173	+	0.983081i	$0.558637\pi$
$318$	6.26422e9	0.0343514
$319$	−4.44407e11	−2.40283
$320$	1.02648e11	0.547235
$321$	3.64073e10	0.191388
$322$	1.17628e10	0.0609761
$323$	1.73369e11	0.886259
$324$	−1.72321e11	−0.868729
$325$	−3.32787e10	−0.165459
$326$	−1.59593e10	−0.0782590
$327$	3.73327e10	0.180561
$328$	−1.05982e11	−0.505592
$329$	3.54392e10	0.166764
$330$	−5.58228e9	−0.0259119
$331$	3.45035e11	1.57993	0.789965	−	0.613152i	$-0.210099\pi$
$331$	3.45035e11	1.57993	0.789965	+	0.613152i	$0.210099\pi$
$332$	1.70504e11	0.770218
$333$	3.16309e11	1.40965
$334$	3.55723e10	0.156406
$335$	1.75312e10	0.0760520
$336$	1.58472e10	0.0678306
$337$	−1.05013e10	−0.0443515	−0.0221757	−	0.999754i	$-0.507059\pi$
$337$	−1.05013e10	−0.0443515	−0.0221757	+	0.999754i	$0.507059\pi$
$338$	2.83140e9	0.0117999
$339$	−1.17178e10	−0.0481890
$340$	−2.97489e11	−1.20730
$341$	−2.84235e10	−0.113837
$342$	1.70114e10	0.0672393
$343$	−1.38413e10	−0.0539949
$344$	6.23753e10	0.240159
$345$	−3.39209e10	−0.128909
$346$	−7.13711e10	−0.267719
$347$	4.30594e11	1.59435	0.797177	−	0.603745i	$-0.206326\pi$
$347$	4.30594e11	1.59435	0.797177	+	0.603745i	$0.206326\pi$
$348$	8.98901e10	0.328553
$349$	3.31193e11	1.19500	0.597498	−	0.801870i	$-0.296162\pi$
$349$	3.31193e11	1.19500	0.597498	+	0.801870i	$0.296162\pi$
$350$	9.71046e9	0.0345886
$351$	2.98736e10	0.105052
$352$	−1.76973e11	−0.614420
$353$	2.10199e11	0.720517	0.360258	−	0.932853i	$-0.382689\pi$
$353$	2.10199e11	0.720517	0.360258	+	0.932853i	$0.382689\pi$
$354$	−1.44422e10	−0.0488787
$355$	−1.82853e10	−0.0611046
$356$	3.88372e11	1.28151
$357$	−4.35756e10	−0.141983
$358$	3.37921e10	0.108728
$359$	5.41785e11	1.72148	0.860741	−	0.509044i	$-0.170001\pi$
$359$	5.41785e11	1.72148	0.860741	+	0.509044i	$0.170001\pi$
$360$	−5.90843e10	−0.185400
$361$	−2.55799e11	−0.792713
$362$	−5.44292e10	−0.166588
$363$	−5.74049e10	−0.173528
$364$	3.42842e10	0.102362
$365$	−3.51923e10	−0.103784
$366$	−4.80439e9	−0.0139950
$367$	−5.93018e11	−1.70636	−0.853180	−	0.521616i	$-0.825329\pi$
$367$	−5.93018e11	−1.70636	−0.853180	+	0.521616i	$0.825329\pi$
$368$	−3.44087e11	−0.978032
$369$	−5.71777e11	−1.60549
$370$	5.14287e10	0.142659
$371$	1.60047e11	0.438597
$372$	5.74922e9	0.0155656
$373$	1.93052e11	0.516399	0.258199	−	0.966092i	$-0.416871\pi$
$373$	1.93052e11	0.516399	0.258199	+	0.966092i	$0.416871\pi$
$374$	1.55705e11	0.411510
$375$	−7.49415e10	−0.195696
$376$	5.18449e10	0.133771
$377$	1.89671e11	0.483576
$378$	−8.71688e9	−0.0219608
$379$	7.87560e11	1.96068	0.980342	−	0.197307i	$-0.0632197\pi$
$379$	7.87560e11	1.96068	0.980342	+	0.197307i	$0.0632197\pi$
$380$	−1.14777e11	−0.282376
$381$	8.15864e10	0.198360
$382$	3.30979e10	0.0795271
$383$	−5.21498e11	−1.23839	−0.619196	−	0.785237i	$-0.712541\pi$
$383$	−5.21498e11	−1.23839	−0.619196	+	0.785237i	$0.712541\pi$
$384$	4.75260e10	0.111543
$385$	−1.42624e11	−0.330842
$386$	7.81044e10	0.179074
$387$	3.36517e11	0.762619
$388$	3.71417e11	0.831992
$389$	1.20805e11	0.267493	0.133746	−	0.991016i	$-0.457299\pi$
$389$	1.20805e11	0.267493	0.133746	+	0.991016i	$0.457299\pi$
$390$	2.38250e9	0.00521485
$391$	9.46147e11	2.04721
$392$	−2.02488e10	−0.0433124
$393$	6.37451e10	0.134797
$394$	3.49644e10	0.0730959
$395$	−2.45054e11	−0.506494
$396$	−6.34002e11	−1.29557
$397$	−6.89355e11	−1.39279	−0.696395	−	0.717659i	$-0.745214\pi$
$397$	−6.89355e11	−1.39279	−0.696395	+	0.717659i	$0.745214\pi$
$398$	4.70835e10	0.0940578
$399$	−1.68122e10	−0.0332083
$400$	−2.84052e11	−0.554788
$401$	−2.46879e11	−0.476798	−0.238399	−	0.971167i	$-0.576623\pi$
$401$	−2.46879e11	−0.476798	−0.238399	+	0.971167i	$0.576623\pi$
$402$	1.85599e9	0.00354452
$403$	1.21310e10	0.0229100
$404$	−4.60210e11	−0.859487
$405$	−3.05954e11	−0.565079
$406$	−5.53445e10	−0.101090
$407$	1.11701e12	2.01781
$408$	−6.37479e10	−0.113892
$409$	5.41737e11	0.957267	0.478634	−	0.878015i	$-0.341132\pi$
$409$	5.41737e11	0.957267	0.478634	+	0.878015i	$0.341132\pi$
$410$	−9.29653e10	−0.162478
$411$	1.06273e11	0.183710
$412$	6.21082e10	0.106197
$413$	−3.68991e11	−0.624080
$414$	9.28384e10	0.155319
$415$	3.02730e11	0.501001
$416$	7.55315e10	0.123654
$417$	1.76172e11	0.285315
$418$	6.00738e10	0.0962480
$419$	8.74991e10	0.138689	0.0693443	−	0.997593i	$-0.477909\pi$
$419$	8.74991e10	0.138689	0.0693443	+	0.997593i	$0.477909\pi$
$420$	2.88486e10	0.0452379
$421$	−7.50514e11	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$421$	−7.50514e11	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$422$	1.40684e10	0.0215943
$423$	2.79705e11	0.424785
$424$	2.34137e11	0.351823
$425$	7.81066e11	1.16128
$426$	−1.93582e9	−0.00284788
$427$	−1.22749e11	−0.178687
$428$	6.72297e11	0.968420
$429$	5.17466e10	0.0737606
$430$	5.47143e10	0.0771779
$431$	−1.21883e12	−1.70136	−0.850679	−	0.525686i	$-0.823809\pi$
$431$	−1.21883e12	−1.70136	−0.850679	+	0.525686i	$0.823809\pi$
$432$	2.54987e11	0.352243
$433$	1.25571e12	1.71670	0.858349	−	0.513066i	$-0.171490\pi$
$433$	1.25571e12	1.71670	0.858349	+	0.513066i	$0.171490\pi$
$434$	−3.53974e9	−0.00478925
$435$	1.59600e11	0.213713
$436$	6.89385e11	0.913635
$437$	3.65040e11	0.478822
$438$	−3.72572e9	−0.00483701
$439$	−5.69398e11	−0.731688	−0.365844	−	0.930676i	$-0.619220\pi$
$439$	−5.69398e11	−0.731688	−0.365844	+	0.930676i	$0.619220\pi$
$440$	−2.08649e11	−0.265387
$441$	−1.09243e11	−0.137537
$442$	−6.64543e10	−0.0828177
$443$	1.10958e12	1.36880	0.684402	−	0.729105i	$-0.260063\pi$
$443$	1.10958e12	1.36880	0.684402	+	0.729105i	$0.260063\pi$
$444$	−2.25937e11	−0.275908
$445$	6.89554e11	0.833581
$446$	−3.25094e10	−0.0389047
$447$	1.46732e11	0.173836
$448$	2.77647e11	0.325643
$449$	−9.59544e11	−1.11418	−0.557091	−	0.830451i	$-0.688083\pi$
$449$	−9.59544e11	−1.11418	−0.557091	+	0.830451i	$0.688083\pi$
$450$	7.66402e10	0.0881049
$451$	−2.01916e12	−2.29814
$452$	−2.16381e11	−0.243835
$453$	1.59066e11	0.177474
$454$	−3.17597e10	−0.0350853
$455$	6.08715e10	0.0665829
$456$	−2.45950e10	−0.0266383
$457$	6.58265e11	0.705956	0.352978	−	0.935632i	$-0.385169\pi$
$457$	6.58265e11	0.705956	0.352978	+	0.935632i	$0.385169\pi$
$458$	8.82723e10	0.0937410
$459$	−7.01147e11	−0.737313
$460$	−6.26384e11	−0.652274
$461$	4.37783e11	0.451445	0.225722	−	0.974192i	$-0.427526\pi$
$461$	4.37783e11	0.451445	0.225722	+	0.974192i	$0.427526\pi$
$462$	−1.50993e10	−0.0154194
$463$	−1.14187e12	−1.15479	−0.577393	−	0.816467i	$-0.695930\pi$
$463$	−1.14187e12	−1.15479	−0.577393	+	0.816467i	$0.695930\pi$
$464$	1.61895e12	1.62144
$465$	1.02077e10	0.0101249
$466$	1.66178e11	0.163244
$467$	3.61838e11	0.352037	0.176018	−	0.984387i	$-0.443678\pi$
$467$	3.61838e11	0.352037	0.176018	+	0.984387i	$0.443678\pi$
$468$	2.70589e11	0.260738
$469$	4.74194e10	0.0452563
$470$	4.54773e10	0.0429887
$471$	1.49828e11	0.140281
$472$	−5.39807e11	−0.500610
$473$	1.18837e12	1.09163
$474$	−2.59432e10	−0.0236060
$475$	3.01349e11	0.271612
$476$	−8.04666e11	−0.718430
$477$	1.26318e12	1.11720
$478$	1.58263e11	0.138660
$479$	−1.32781e12	−1.15246	−0.576230	−	0.817288i	$-0.695477\pi$
$479$	−1.32781e12	−1.15246	−0.576230	+	0.817288i	$0.695477\pi$
$480$	6.35563e10	0.0546478
$481$	−4.76734e11	−0.406091
$482$	1.70458e11	0.143849
$483$	−9.17512e10	−0.0767096
$484$	−1.06004e12	−0.878046
$485$	6.59449e11	0.541182
$486$	−1.03850e11	−0.0844392
$487$	−6.49239e11	−0.523028	−0.261514	−	0.965200i	$-0.584222\pi$
$487$	−6.49239e11	−0.523028	−0.261514	+	0.965200i	$0.584222\pi$
$488$	−1.79573e11	−0.143335
$489$	1.24484e11	0.0984520
$490$	−1.77618e10	−0.0139189
$491$	−1.62504e12	−1.26182	−0.630910	−	0.775856i	$-0.717318\pi$
$491$	−1.62504e12	−1.26182	−0.630910	+	0.775856i	$0.717318\pi$
$492$	4.08415e11	0.314238
$493$	−4.45167e12	−3.39400
$494$	−2.56392e10	−0.0193702
$495$	−1.12567e12	−0.842727
$496$	1.03545e11	0.0768177
$497$	−4.94590e10	−0.0363615
$498$	3.20492e10	0.0233499
$499$	−1.29912e12	−0.937990	−0.468995	−	0.883201i	$-0.655384\pi$
$499$	−1.29912e12	−0.937990	−0.468995	+	0.883201i	$0.655384\pi$
$500$	−1.38387e12	−0.990216
$501$	−2.77468e11	−0.196763
$502$	1.77383e11	0.124665
$503$	−2.25079e12	−1.56776	−0.783881	−	0.620912i	$-0.786763\pi$
$503$	−2.25079e12	−1.56776	−0.783881	+	0.620912i	$0.786763\pi$
$504$	−1.59814e11	−0.110326
$505$	−8.17100e11	−0.559067
$506$	3.27847e11	0.222328
$507$	−2.20853e10	−0.0148445
$508$	1.50657e12	1.00370
$509$	4.22297e11	0.278861	0.139430	−	0.990232i	$-0.455473\pi$
$509$	4.22297e11	0.278861	0.139430	+	0.990232i	$0.455473\pi$
$510$	−5.59183e10	−0.0366006
$511$	−9.51901e10	−0.0617586
$512$	1.08312e12	0.696566
$513$	−2.70515e11	−0.172450
$514$	−4.98151e10	−0.0314794
$515$	1.10273e11	0.0690774
$516$	−2.40371e11	−0.149265
$517$	9.87744e11	0.608047
$518$	1.39107e11	0.0848918
$519$	5.56702e11	0.336798
$520$	8.90505e10	0.0534098
$521$	−1.08861e12	−0.647295	−0.323647	−	0.946178i	$-0.604909\pi$
$521$	−1.08861e12	−0.647295	−0.323647	+	0.946178i	$0.604909\pi$
$522$	−4.36809e11	−0.257498
$523$	5.79922e11	0.338932	0.169466	−	0.985536i	$-0.445796\pi$
$523$	5.79922e11	0.338932	0.169466	+	0.985536i	$0.445796\pi$
$524$	1.17712e12	0.682070
$525$	−7.57427e10	−0.0435135
$526$	1.84902e11	0.105319
$527$	−2.84721e11	−0.160795
$528$	4.41686e11	0.247321
$529$	1.91022e11	0.106056
$530$	2.05380e11	0.113062
$531$	−2.91228e12	−1.58967
$532$	−3.10454e11	−0.168033
$533$	8.61770e11	0.462507
$534$	7.30013e10	0.0388503
$535$	1.19366e12	0.629925
$536$	6.93712e10	0.0363026
$537$	−2.63582e11	−0.136783
$538$	−2.31022e11	−0.118887
$539$	−3.85778e11	−0.196874
$540$	4.64185e11	0.234919
$541$	1.93855e12	0.972946	0.486473	−	0.873696i	$-0.338283\pi$
$541$	1.93855e12	0.972946	0.486473	+	0.873696i	$0.338283\pi$
$542$	−2.53108e10	−0.0125982
$543$	4.24554e11	0.209572
$544$	−1.77276e12	−0.867870
$545$	1.22400e12	0.594289
$546$	6.44431e9	0.00310320
$547$	2.01859e12	0.964062	0.482031	−	0.876154i	$-0.339899\pi$
$547$	2.01859e12	0.964062	0.482031	+	0.876154i	$0.339899\pi$
$548$	1.96243e12	0.929570
$549$	−9.68805e11	−0.455156
$550$	2.70645e11	0.126116
$551$	−1.71753e12	−0.793821
$552$	−1.34225e11	−0.0615331
$553$	−6.62835e11	−0.301399
$554$	−4.24118e11	−0.191290
$555$	−4.01150e11	−0.179469
$556$	3.25319e12	1.44369
$557$	−3.33775e12	−1.46928	−0.734642	−	0.678455i	$-0.762650\pi$
$557$	−3.33775e12	−1.46928	−0.734642	+	0.678455i	$0.762650\pi$
$558$	−2.79375e10	−0.0121993
$559$	−5.07191e11	−0.219694
$560$	5.19571e11	0.223254
$561$	−1.21452e12	−0.517691
$562$	−1.45153e11	−0.0613782
$563$	6.60787e10	0.0277187	0.0138594	−	0.999904i	$-0.495588\pi$
$563$	6.60787e10	0.0277187	0.0138594	+	0.999904i	$0.495588\pi$
$564$	−1.99791e11	−0.0831419
$565$	−3.84183e11	−0.158606
$566$	−1.72958e11	−0.0708379
$567$	−8.27563e11	−0.336261
$568$	−7.23550e10	−0.0291676
$569$	3.19509e12	1.27784	0.638921	−	0.769272i	$-0.279381\pi$
$569$	3.19509e12	1.27784	0.638921	+	0.769272i	$0.279381\pi$
$570$	−2.15743e10	−0.00856050
$571$	−2.22425e12	−0.875633	−0.437816	−	0.899064i	$-0.644248\pi$
$571$	−2.22425e12	−0.875633	−0.437816	+	0.899064i	$0.644248\pi$
$572$	9.55553e11	0.373227
$573$	−2.58167e11	−0.100047
$574$	−2.51458e11	−0.0966855
$575$	1.64459e12	0.627410
$576$	2.19134e12	0.829484
$577$	−1.66950e12	−0.627040	−0.313520	−	0.949582i	$-0.601508\pi$
$577$	−1.66950e12	−0.627040	−0.313520	+	0.949582i	$0.601508\pi$
$578$	1.14809e12	0.427861
$579$	−6.09223e11	−0.225280
$580$	2.94716e12	1.08138
$581$	8.18840e11	0.298130
$582$	6.98142e10	0.0252226
$583$	4.46076e12	1.59919
$584$	−1.39256e11	−0.0495401
$585$	4.80430e11	0.169601
$586$	3.90706e11	0.136871
$587$	−5.68216e11	−0.197534	−0.0987670	−	0.995111i	$-0.531490\pi$
$587$	−5.68216e11	−0.197534	−0.0987670	+	0.995111i	$0.531490\pi$
$588$	7.80313e10	0.0269197
$589$	−1.09850e11	−0.0376082
$590$	−4.73507e11	−0.160876
$591$	−2.72726e11	−0.0919567
$592$	−4.06918e12	−1.36163
$593$	1.41463e12	0.469781	0.234891	−	0.972022i	$-0.424527\pi$
$593$	1.41463e12	0.469781	0.234891	+	0.972022i	$0.424527\pi$
$594$	−2.42953e11	−0.0800724
$595$	−1.42868e12	−0.467314
$596$	2.70955e12	0.879607
$597$	−3.67257e11	−0.118327
$598$	−1.39924e11	−0.0447442
$599$	−6.93939e11	−0.220242	−0.110121	−	0.993918i	$-0.535124\pi$
$599$	−6.93939e11	−0.220242	−0.110121	+	0.993918i	$0.535124\pi$
$600$	−1.10806e11	−0.0349046
$601$	−5.19076e11	−0.162292	−0.0811458	−	0.996702i	$-0.525858\pi$
$601$	−5.19076e11	−0.162292	−0.0811458	+	0.996702i	$0.525858\pi$
$602$	1.47994e11	0.0459262
$603$	3.74260e11	0.115278
$604$	2.93731e12	0.898016
$605$	−1.88209e12	−0.571139
$606$	−8.65043e10	−0.0260562
$607$	−2.53172e12	−0.756949	−0.378475	−	0.925612i	$-0.623551\pi$
$607$	−2.53172e12	−0.756949	−0.378475	+	0.925612i	$0.623551\pi$
$608$	−6.83961e11	−0.202986
$609$	4.31694e11	0.127174
$610$	−1.57518e11	−0.0460623
$611$	−4.21565e11	−0.122371
$612$	−6.35086e12	−1.83000
$613$	2.01999e12	0.577799	0.288899	−	0.957360i	$-0.406711\pi$
$613$	2.01999e12	0.577799	0.288899	+	0.957360i	$0.406711\pi$
$614$	−1.05797e12	−0.300412
$615$	7.25140e11	0.204401
$616$	−5.64365e11	−0.157924
$617$	1.72737e12	0.479846	0.239923	−	0.970792i	$-0.422878\pi$
$617$	1.72737e12	0.479846	0.239923	+	0.970792i	$0.422878\pi$
$618$	1.16743e10	0.00321946
$619$	4.86914e12	1.33304	0.666522	−	0.745486i	$-0.267782\pi$
$619$	4.86914e12	1.33304	0.666522	+	0.745486i	$0.267782\pi$
$620$	1.88495e11	0.0512316
$621$	−1.47631e12	−0.398351
$622$	−2.17785e11	−0.0583407
$623$	1.86514e12	0.496039
$624$	−1.88510e11	−0.0497741
$625$	−1.81314e11	−0.0475303
$626$	−1.44987e11	−0.0377351
$627$	−4.68582e11	−0.121083
$628$	2.76672e12	0.709819
$629$	1.11892e13	2.85016
$630$	−1.40186e11	−0.0354545
$631$	−1.72218e12	−0.432460	−0.216230	−	0.976342i	$-0.569376\pi$
$631$	−1.72218e12	−0.432460	−0.216230	+	0.976342i	$0.569376\pi$
$632$	−9.69680e11	−0.241769
$633$	−1.09735e11	−0.0271662
$634$	−2.28620e11	−0.0561969
$635$	2.67491e12	0.652872
$636$	−9.02278e11	−0.218667
$637$	1.64648e11	0.0396214
$638$	−1.54254e12	−0.368589
$639$	−3.90357e11	−0.0926208
$640$	1.55820e12	0.367125
$641$	8.13580e12	1.90344	0.951720	−	0.306969i	$-0.0993147\pi$
$641$	8.13580e12	1.90344	0.951720	+	0.306969i	$0.0993147\pi$
$642$	1.26370e11	0.0293586
$643$	−1.06886e12	−0.246588	−0.123294	−	0.992370i	$-0.539346\pi$
$643$	−1.06886e12	−0.246588	−0.123294	+	0.992370i	$0.539346\pi$
$644$	−1.69428e12	−0.388149
$645$	−4.26778e11	−0.0970919
$646$	6.01765e11	0.135950
$647$	7.19980e12	1.61529	0.807646	−	0.589668i	$-0.200741\pi$
$647$	7.19980e12	1.61529	0.807646	+	0.589668i	$0.200741\pi$
$648$	−1.21066e12	−0.269734
$649$	−1.02843e13	−2.27549
$650$	−1.15510e11	−0.0253811
$651$	2.76104e10	0.00602501
$652$	2.29873e12	0.498165
$653$	8.69807e12	1.87203	0.936017	−	0.351955i	$-0.114483\pi$
$653$	8.69807e12	1.87203	0.936017	+	0.351955i	$0.114483\pi$
$654$	1.29582e11	0.0276977
$655$	2.08997e12	0.443663
$656$	7.35567e12	1.55080
$657$	−7.51292e11	−0.157313
$658$	1.23009e11	0.0255813
$659$	8.59515e12	1.77529	0.887645	−	0.460529i	$-0.152340\pi$
$659$	8.59515e12	1.77529	0.887645	+	0.460529i	$0.152340\pi$
$660$	8.04054e11	0.164944
$661$	−7.38727e12	−1.50514	−0.752571	−	0.658511i	$-0.771186\pi$
$661$	−7.38727e12	−1.50514	−0.752571	+	0.658511i	$0.771186\pi$
$662$	1.19762e12	0.242358
$663$	5.18351e11	0.104187
$664$	1.19790e12	0.239147
$665$	−5.51210e11	−0.109300
$666$	1.09791e12	0.216238
$667$	−9.37328e12	−1.83369
$668$	−5.12371e12	−0.995614
$669$	2.53577e11	0.0489432
$670$	6.08509e10	0.0116662
$671$	−3.42121e12	−0.651522
$672$	1.71911e11	0.0325193
$673$	−2.94205e12	−0.552819	−0.276409	−	0.961040i	$-0.589145\pi$
$673$	−2.94205e12	−0.552819	−0.276409	+	0.961040i	$0.589145\pi$
$674$	−3.64500e10	−0.00680343
$675$	−1.21873e12	−0.225964
$676$	−4.07826e11	−0.0751130
$677$	4.17442e12	0.763743	0.381871	−	0.924215i	$-0.375280\pi$
$677$	4.17442e12	0.763743	0.381871	+	0.924215i	$0.375280\pi$
$678$	−4.06725e10	−0.00739210
$679$	1.78371e12	0.322041
$680$	−2.09006e12	−0.374859
$681$	2.47730e11	0.0441383
$682$	−9.86580e10	−0.0174623
$683$	−2.74715e12	−0.483047	−0.241523	−	0.970395i	$-0.577647\pi$
$683$	−2.74715e12	−0.483047	−0.241523	+	0.970395i	$0.577647\pi$
$684$	−2.45027e12	−0.428018
$685$	3.48429e12	0.604654
$686$	−4.80431e10	−0.00828272
$687$	−6.88534e11	−0.117929
$688$	−4.32915e12	−0.736639
$689$	−1.90384e12	−0.321842
$690$	−1.17740e11	−0.0197743
$691$	−1.06051e13	−1.76955	−0.884776	−	0.466017i	$-0.845688\pi$
$691$	−1.06051e13	−1.76955	−0.884776	+	0.466017i	$0.845688\pi$
$692$	1.02801e13	1.70419
$693$	−3.04477e12	−0.501481
$694$	1.49459e12	0.244571
$695$	5.77602e12	0.939068
$696$	6.31536e11	0.102013
$697$	−2.02261e13	−3.24612
$698$	1.14957e12	0.183310
$699$	−1.29621e12	−0.205366
$700$	−1.39866e12	−0.220177
$701$	−5.72338e12	−0.895203	−0.447602	−	0.894233i	$-0.647722\pi$
$701$	−5.72338e12	−0.895203	−0.447602	+	0.894233i	$0.647722\pi$
$702$	1.03691e11	0.0161148
$703$	4.31698e12	0.666624
$704$	7.73844e12	1.18734
$705$	−3.54728e11	−0.0540810
$706$	7.29600e11	0.110526
$707$	−2.21014e12	−0.332684
$708$	2.08021e12	0.311142
$709$	9.64455e12	1.43342	0.716710	−	0.697371i	$-0.245647\pi$
$709$	9.64455e12	1.43342	0.716710	+	0.697371i	$0.245647\pi$
$710$	−6.34683e10	−0.00937333
$711$	−5.23145e12	−0.767731
$712$	2.72857e12	0.397901
$713$	−5.99498e11	−0.0868731
$714$	−1.51251e11	−0.0217799
$715$	1.69658e12	0.242771
$716$	−4.86731e12	−0.692119
$717$	−1.23447e12	−0.174439
$718$	1.88054e12	0.264072
$719$	−4.51584e12	−0.630171	−0.315086	−	0.949063i	$-0.602033\pi$
$719$	−4.51584e12	−0.630171	−0.315086	+	0.949063i	$0.602033\pi$
$720$	4.10073e12	0.568677
$721$	2.98272e11	0.0411059
$722$	−8.87878e11	−0.121601
$723$	−1.32959e12	−0.180966
$724$	7.83981e12	1.06043
$725$	−7.73785e12	−1.04016
$726$	−1.99252e11	−0.0266188
$727$	1.50309e12	0.199563	0.0997814	−	0.995009i	$-0.468186\pi$
$727$	1.50309e12	0.199563	0.0997814	+	0.995009i	$0.468186\pi$
$728$	2.40869e11	0.0317826
$729$	−5.97418e12	−0.783437
$730$	−1.22153e11	−0.0159202
$731$	1.19040e13	1.54193
$732$	6.92009e11	0.0890865
$733$	−6.45399e12	−0.825772	−0.412886	−	0.910783i	$-0.635479\pi$
$733$	−6.45399e12	−0.825772	−0.412886	+	0.910783i	$0.635479\pi$
$734$	−2.05837e12	−0.261752
$735$	1.38544e11	0.0175104
$736$	−3.73266e12	−0.468887
$737$	1.32165e12	0.165011
$738$	−1.98464e12	−0.246279
$739$	−1.89421e12	−0.233629	−0.116815	−	0.993154i	$-0.537268\pi$
$739$	−1.89421e12	−0.233629	−0.116815	+	0.993154i	$0.537268\pi$
$740$	−7.40763e12	−0.908106
$741$	1.99989e11	0.0243682
$742$	5.55524e11	0.0672799
$743$	−9.45139e12	−1.13775	−0.568874	−	0.822425i	$-0.692621\pi$
$743$	−9.45139e12	−1.13775	−0.568874	+	0.822425i	$0.692621\pi$
$744$	4.03920e10	0.00483300
$745$	4.81079e12	0.572155
$746$	6.70085e11	0.0792146
$747$	6.46273e12	0.759404
$748$	−2.24273e13	−2.61950
$749$	3.22868e12	0.374849
$750$	−2.60122e11	−0.0300194
$751$	−3.66013e12	−0.419872	−0.209936	−	0.977715i	$-0.567326\pi$
$751$	−3.66013e12	−0.419872	−0.209936	+	0.977715i	$0.567326\pi$
$752$	−3.59829e12	−0.410314
$753$	−1.38361e12	−0.156832
$754$	6.58349e11	0.0741797
$755$	5.21519e12	0.584129
$756$	1.25555e12	0.139793
$757$	2.00245e12	0.221631	0.110815	−	0.993841i	$-0.464654\pi$
$757$	2.00245e12	0.221631	0.110815	+	0.993841i	$0.464654\pi$
$758$	2.73362e12	0.300765
$759$	−2.55725e12	−0.279695
$760$	−8.06380e11	−0.0876756
$761$	7.22055e12	0.780440	0.390220	−	0.920722i	$-0.372399\pi$
$761$	7.22055e12	0.780440	0.390220	+	0.920722i	$0.372399\pi$
$762$	2.83186e11	0.0304281
$763$	3.31075e12	0.353643
$764$	−4.76732e12	−0.506237
$765$	−1.12759e13	−1.19035
$766$	−1.81012e12	−0.189967
$767$	4.38932e12	0.457950
$768$	−1.43801e12	−0.149154
$769$	−2.14278e12	−0.220958	−0.110479	−	0.993878i	$-0.535238\pi$
$769$	−2.14278e12	−0.220958	−0.110479	+	0.993878i	$0.535238\pi$
$770$	−4.95049e11	−0.0507504
$771$	3.88563e11	0.0396020
$772$	−1.12499e13	−1.13991
$773$	5.48075e12	0.552119	0.276059	−	0.961141i	$-0.410971\pi$
$773$	5.48075e12	0.552119	0.276059	+	0.961141i	$0.410971\pi$
$774$	1.16805e12	0.116984
$775$	−4.94900e11	−0.0492787
$776$	2.60944e12	0.258327
$777$	−1.08505e12	−0.106796
$778$	4.19315e11	0.0410329
$779$	−7.80359e12	−0.759235
$780$	−3.43167e11	−0.0331956
$781$	−1.37850e12	−0.132580
$782$	3.28408e12	0.314039
$783$	6.94611e12	0.660410
$784$	1.40536e12	0.132852
$785$	4.91231e12	0.461713
$786$	2.21259e11	0.0206776
$787$	−1.12601e13	−1.04630	−0.523149	−	0.852241i	$-0.675243\pi$
$787$	−1.12601e13	−1.04630	−0.523149	+	0.852241i	$0.675243\pi$
$788$	−5.03616e12	−0.465298
$789$	−1.44226e12	−0.132494
$790$	−8.50583e11	−0.0776953
$791$	−1.03916e12	−0.0943818
$792$	−4.45427e12	−0.402266
$793$	1.46016e12	0.131121
$794$	−2.39275e12	−0.213651
$795$	−1.60199e12	−0.142235
$796$	−6.78176e12	−0.598733
$797$	1.77125e13	1.55496	0.777479	−	0.628909i	$-0.216498\pi$
$797$	1.77125e13	1.55496	0.777479	+	0.628909i	$0.216498\pi$
$798$	−5.83552e10	−0.00509409
$799$	9.89433e12	0.858867
$800$	−3.08139e12	−0.265976
$801$	1.47207e13	1.26352
$802$	−8.56918e11	−0.0731399
$803$	−2.65309e12	−0.225181
$804$	−2.67331e11	−0.0225630
$805$	−3.00818e12	−0.252477
$806$	4.21068e10	0.00351435
$807$	1.80200e12	0.149563
$808$	−3.23327e12	−0.266865
$809$	−8.51223e12	−0.698675	−0.349338	−	0.936997i	$-0.613593\pi$
$809$	−8.51223e12	−0.698675	−0.349338	+	0.936997i	$0.613593\pi$
$810$	−1.06197e12	−0.0866820
$811$	−2.11618e13	−1.71774	−0.858872	−	0.512190i	$-0.828834\pi$
$811$	−2.11618e13	−1.71774	−0.858872	+	0.512190i	$0.828834\pi$
$812$	7.97165e12	0.643496
$813$	1.97427e11	0.0158489
$814$	3.87713e12	0.309529
$815$	4.08138e12	0.324039
$816$	4.42441e12	0.349341
$817$	4.59277e12	0.360641
$818$	1.88037e12	0.146843
$819$	1.29949e12	0.100925
$820$	1.33904e13	1.03427
$821$	5.44921e12	0.418591	0.209295	−	0.977852i	$-0.432883\pi$
$821$	5.44921e12	0.418591	0.209295	+	0.977852i	$0.432883\pi$
$822$	3.68873e11	0.0281808
$823$	2.59067e13	1.96840	0.984198	−	0.177070i	$-0.0566618\pi$
$823$	2.59067e13	1.96840	0.984198	+	0.177070i	$0.0566618\pi$
$824$	4.36350e11	0.0329733
$825$	−2.11106e12	−0.158657
$826$	−1.28077e12	−0.0957327
$827$	1.79863e13	1.33711	0.668556	−	0.743662i	$-0.266913\pi$
$827$	1.79863e13	1.33711	0.668556	+	0.743662i	$0.266913\pi$
$828$	−1.33721e13	−0.988700
$829$	4.93981e12	0.363258	0.181629	−	0.983367i	$-0.441863\pi$
$829$	4.93981e12	0.363258	0.181629	+	0.983367i	$0.441863\pi$
$830$	1.05078e12	0.0768526
$831$	3.30817e12	0.240649
$832$	−3.30273e12	−0.238956
$833$	−3.86437e12	−0.278084
$834$	6.11493e11	0.0437667
$835$	−9.09714e12	−0.647613
$836$	−8.65283e12	−0.612675
$837$	4.44261e11	0.0312877
$838$	3.03710e11	0.0212746
$839$	−2.04762e13	−1.42666	−0.713329	−	0.700829i	$-0.752814\pi$
$839$	−2.04762e13	−1.42666	−0.713329	+	0.700829i	$0.752814\pi$
$840$	2.02680e11	0.0140460
$841$	2.95946e13	2.04000
$842$	−2.60503e12	−0.178611
$843$	1.13221e12	0.0772155
$844$	−2.02637e12	−0.137460
$845$	−7.24094e11	−0.0488585
$846$	9.70857e11	0.0651611
$847$	−5.09079e12	−0.339867
$848$	−1.62503e13	−1.07914
$849$	1.34909e12	0.0891161
$850$	2.71108e12	0.178138
$851$	2.35595e13	1.53987
$852$	2.78829e11	0.0181284
$853$	−2.13392e13	−1.38009	−0.690046	−	0.723766i	$-0.742410\pi$
$853$	−2.13392e13	−1.38009	−0.690046	+	0.723766i	$0.742410\pi$
$854$	−4.26064e11	−0.0274103
$855$	−4.35045e12	−0.278411
$856$	4.72332e12	0.300687
$857$	−1.63219e13	−1.03361	−0.516804	−	0.856104i	$-0.672878\pi$
$857$	−1.63219e13	−1.03361	−0.516804	+	0.856104i	$0.672878\pi$
$858$	1.79613e11	0.0113147
$859$	−1.21069e13	−0.758689	−0.379345	−	0.925255i	$-0.623851\pi$
$859$	−1.21069e13	−0.758689	−0.379345	+	0.925255i	$0.623851\pi$
$860$	−7.88088e12	−0.491283
$861$	1.96140e12	0.121633
$862$	−4.23056e12	−0.260985
$863$	−1.60574e13	−0.985431	−0.492716	−	0.870190i	$-0.663996\pi$
$863$	−1.60574e13	−0.985431	−0.492716	+	0.870190i	$0.663996\pi$
$864$	2.76611e12	0.168872
$865$	1.82522e13	1.10852
$866$	4.35857e12	0.263338
$867$	−8.95527e12	−0.538261
$868$	5.09853e11	0.0304864
$869$	−1.84742e13	−1.09895
$870$	5.53970e11	0.0327831
$871$	−5.64076e11	−0.0332090
$872$	4.84338e12	0.283677
$873$	1.40780e13	0.820310
$874$	1.26706e12	0.0734504
$875$	−6.64598e12	−0.383286
$876$	5.36641e11	0.0307904
$877$	1.69401e13	0.966983	0.483491	−	0.875349i	$-0.339368\pi$
$877$	1.69401e13	0.966983	0.483491	+	0.875349i	$0.339368\pi$
$878$	−1.97638e12	−0.112240
$879$	−3.04755e12	−0.172187
$880$	1.44812e13	0.814017
$881$	2.48617e13	1.39040	0.695200	−	0.718817i	$-0.255316\pi$
$881$	2.48617e13	1.39040	0.695200	+	0.718817i	$0.255316\pi$
$882$	−3.79182e11	−0.0210979
$883$	−1.38568e13	−0.767077	−0.383539	−	0.923525i	$-0.625295\pi$
$883$	−1.38568e13	−0.767077	−0.383539	+	0.923525i	$0.625295\pi$
$884$	9.57187e12	0.527183
$885$	3.69341e12	0.202387
$886$	3.85135e12	0.209972
$887$	3.51693e13	1.90769	0.953845	−	0.300300i	$-0.0970868\pi$
$887$	3.51693e13	1.90769	0.953845	+	0.300300i	$0.0970868\pi$
$888$	−1.58735e12	−0.0856673
$889$	7.23526e12	0.388504
$890$	2.39344e12	0.127870
$891$	−2.30654e13	−1.22606
$892$	4.68255e12	0.247651
$893$	3.81741e12	0.200880
$894$	5.09306e11	0.0266661
$895$	−8.64189e12	−0.450200
$896$	4.21471e12	0.218465
$897$	1.09142e12	0.0562894
$898$	−3.33058e12	−0.170913
$899$	2.82067e12	0.144024
$900$	−1.10390e13	−0.560840
$901$	4.46839e13	2.25886
$902$	−7.00851e12	−0.352530
$903$	−1.15437e12	−0.0577765
$904$	−1.52022e12	−0.0757090
$905$	1.39195e13	0.689773
$906$	5.52119e11	0.0272242
$907$	3.65440e13	1.79301	0.896507	−	0.443030i	$-0.146097\pi$
$907$	3.65440e13	1.79301	0.896507	+	0.443030i	$0.146097\pi$
$908$	4.57457e12	0.223339
$909$	−1.74436e13	−0.847420
$910$	2.11285e11	0.0102137
$911$	−2.88466e13	−1.38759	−0.693795	−	0.720172i	$-0.744063\pi$
$911$	−2.88466e13	−1.38759	−0.693795	+	0.720172i	$0.744063\pi$
$912$	1.70701e12	0.0817072
$913$	2.28223e13	1.08703
$914$	2.28484e12	0.108292
$915$	1.22866e12	0.0579477
$916$	−1.27145e13	−0.596717
$917$	5.65306e12	0.264011
$918$	−2.43368e12	−0.113102
$919$	3.24580e13	1.50107	0.750537	−	0.660828i	$-0.229795\pi$
$919$	3.24580e13	1.50107	0.750537	+	0.660828i	$0.229795\pi$
$920$	−4.40075e12	−0.202526
$921$	8.25232e12	0.377927
$922$	1.51954e12	0.0692507
$923$	5.88338e11	0.0266821
$924$	2.17485e12	0.0981534
$925$	1.94489e13	0.873490
$926$	−3.96342e12	−0.177142
$927$	2.35412e12	0.104706
$928$	1.75623e13	0.777350
$929$	2.72256e13	1.19924	0.599621	−	0.800284i	$-0.295318\pi$
$929$	2.72256e13	1.19924	0.599621	+	0.800284i	$0.295318\pi$
$930$	3.54310e10	0.00155314
$931$	−1.49094e12	−0.0650411
$932$	−2.39358e13	−1.03914
$933$	1.69875e12	0.0733942
$934$	1.25594e12	0.0540017
$935$	−3.98195e13	−1.70390
$936$	1.90107e12	0.0809573
$937$	−1.75576e13	−0.744108	−0.372054	−	0.928211i	$-0.621346\pi$
$937$	−1.75576e13	−0.744108	−0.372054	+	0.928211i	$0.621346\pi$
$938$	1.64593e11	0.00694222
$939$	1.13092e12	0.0474718
$940$	−6.55040e12	−0.273648
$941$	1.34040e13	0.557288	0.278644	−	0.960394i	$-0.410115\pi$
$941$	1.34040e13	0.557288	0.278644	+	0.960394i	$0.410115\pi$
$942$	5.20054e11	0.0215189
$943$	−4.25874e13	−1.75380
$944$	3.74652e13	1.53552
$945$	2.22923e12	0.0909309
$946$	4.12483e12	0.167454
$947$	−4.00173e13	−1.61686	−0.808431	−	0.588591i	$-0.799683\pi$
$947$	−4.00173e13	−1.61686	−0.808431	+	0.588591i	$0.799683\pi$
$948$	3.73678e12	0.150266
$949$	1.13233e12	0.0453185
$950$	1.04598e12	0.0416647
$951$	1.78326e12	0.0706972
$952$	−5.65330e12	−0.223067
$953$	1.38920e13	0.545565	0.272782	−	0.962076i	$-0.412056\pi$
$953$	1.38920e13	0.545565	0.272782	+	0.962076i	$0.412056\pi$
$954$	4.38450e12	0.171377
$955$	−8.46435e12	−0.329290
$956$	−2.27956e13	−0.882656
$957$	1.20320e13	0.463695
$958$	−4.60883e12	−0.176785
$959$	9.42450e12	0.359811
$960$	−2.77910e12	−0.105605
$961$	−2.62592e13	−0.993177
$962$	−1.65475e12	−0.0622936
$963$	2.54825e13	0.954823
$964$	−2.45522e13	−0.915682
$965$	−1.99742e13	−0.741474
$966$	−3.18469e11	−0.0117671
$967$	−3.62497e13	−1.33317	−0.666584	−	0.745430i	$-0.732244\pi$
$967$	−3.62497e13	−1.33317	−0.666584	+	0.745430i	$0.732244\pi$
$968$	−7.44745e12	−0.272627
$969$	−4.69383e12	−0.171029
$970$	2.28895e12	0.0830163
$971$	−4.29735e12	−0.155137	−0.0775683	−	0.996987i	$-0.524716\pi$
$971$	−4.29735e12	−0.155137	−0.0775683	+	0.996987i	$0.524716\pi$
$972$	1.49583e13	0.537505
$973$	1.56233e13	0.558811
$974$	−2.25351e12	−0.0802314
$975$	9.00994e11	0.0319302
$976$	1.24633e13	0.439651
$977$	1.79329e13	0.629689	0.314845	−	0.949143i	$-0.398048\pi$
$977$	1.79329e13	0.629689	0.314845	+	0.949143i	$0.398048\pi$
$978$	4.32085e11	0.0151023
$979$	5.19844e13	1.80863
$980$	2.55836e12	0.0886020
$981$	2.61302e13	0.900808
$982$	−5.64052e12	−0.193561
$983$	6.56003e12	0.224086	0.112043	−	0.993703i	$-0.464261\pi$
$983$	6.56003e12	0.224086	0.112043	+	0.993703i	$0.464261\pi$
$984$	2.86938e12	0.0975687
$985$	−8.94168e12	−0.302661
$986$	−1.54517e13	−0.520633
$987$	−9.59488e11	−0.0321820
$988$	3.69300e12	0.123303
$989$	2.50646e13	0.833064
$990$	−3.90719e12	−0.129273
$991$	3.90458e13	1.28600	0.643002	−	0.765864i	$-0.277689\pi$
$991$	3.90458e13	1.28600	0.643002	+	0.765864i	$0.277689\pi$
$992$	1.12326e12	0.0368279
$993$	−9.34156e12	−0.304893
$994$	−1.71672e11	−0.00557779
$995$	−1.20410e13	−0.389456
$996$	−4.61627e12	−0.148636
$997$	3.38178e13	1.08397	0.541985	−	0.840388i	$-0.317673\pi$
$997$	3.38178e13	1.08397	0.541985	+	0.840388i	$0.317673\pi$
$998$	−4.50926e12	−0.143886
$999$	−1.74589e13	−0.554590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.8	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.8	✓	15	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+3.47100 q^{2} -27.0742 q^{3} -499.952 q^{4} -887.663 q^{5} -93.9746 q^{6} -2401.00 q^{7} -3512.49 q^{8} -18950.0 q^{9} +O(q^{10})\)	\(q+3.47100 q^{2} -27.0742 q^{3} -499.952 q^{4} -887.663 q^{5} -93.9746 q^{6} -2401.00 q^{7} -3512.49 q^{8} -18950.0 q^{9} -3081.08 q^{10} -66919.5 q^{11} +13535.8 q^{12} +28561.0 q^{13} -8333.88 q^{14} +24032.8 q^{15} +243784. q^{16} -670340. q^{17} -65775.4 q^{18} -258629. q^{19} +443789. q^{20} +65005.2 q^{21} -232278. q^{22} -1.41144e6 q^{23} +95097.8 q^{24} -1.16518e6 q^{25} +99135.3 q^{26} +1.04596e6 q^{27} +1.20039e6 q^{28} +6.64091e6 q^{29} +83417.8 q^{30} +424741. q^{31} +2.64457e6 q^{32} +1.81179e6 q^{33} -2.32675e6 q^{34} +2.13128e6 q^{35} +9.47409e6 q^{36} -1.66918e7 q^{37} -897701. q^{38} -773267. q^{39} +3.11791e6 q^{40} +3.01729e7 q^{41} +225633. q^{42} -1.77582e7 q^{43} +3.34566e7 q^{44} +1.68212e7 q^{45} -4.89913e6 q^{46} -1.47602e7 q^{47} -6.60025e6 q^{48} +5.76480e6 q^{49} -4.04434e6 q^{50} +1.81489e7 q^{51} -1.42791e7 q^{52} -6.66586e7 q^{53} +3.63052e6 q^{54} +5.94020e7 q^{55} +8.43348e6 q^{56} +7.00217e6 q^{57} +2.30506e7 q^{58} +1.53682e8 q^{59} -1.20152e7 q^{60} +5.11243e7 q^{61} +1.47428e6 q^{62} +4.54989e7 q^{63} -1.15638e8 q^{64} -2.53525e7 q^{65} +6.28874e6 q^{66} -1.97499e7 q^{67} +3.35138e8 q^{68} +3.82137e7 q^{69} +7.39767e6 q^{70} +2.05994e7 q^{71} +6.65616e7 q^{72} +3.96460e7 q^{73} -5.79372e7 q^{74} +3.15463e7 q^{75} +1.29302e8 q^{76} +1.60674e8 q^{77} -2.68401e6 q^{78} +2.76066e8 q^{79} -2.16398e8 q^{80} +3.44674e8 q^{81} +1.04730e8 q^{82} -3.41041e8 q^{83} -3.24995e7 q^{84} +5.95036e8 q^{85} -6.16386e7 q^{86} -1.79797e8 q^{87} +2.35054e8 q^{88} -7.76819e8 q^{89} +5.83864e7 q^{90} -6.85750e7 q^{91} +7.05655e8 q^{92} -1.14995e7 q^{93} -5.12326e7 q^{94} +2.29575e8 q^{95} -7.15996e7 q^{96} -7.42905e8 q^{97} +2.00096e7 q^{98} +1.26812e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * q^99

Introduction

L-functions

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