LMFDB - Embedded newform 91.10.a.c.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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 $ x^14 - x^13 - 4752x^12 + 9346x^11 + 8576824x^10 - 26923636x^9 - 7450416552x^8 + 31594524240x^7 + 3232668379296x^6 - 15784728192704x^5 - 654706244016512x^4 + 3031992312058112x^3 + 50459693673905664x^2 - 177878730644221952x - 247584423217725440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.08476$ 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)

$f(q)$	$=$	$q+3.08476 q^{2} -166.247 q^{3} -502.484 q^{4} +1085.59 q^{5} -512.832 q^{6} +2401.00 q^{7} -3129.44 q^{8} +7955.00 q^{9} +O(q^{10})$	\(q+3.08476 q^{2} -166.247 q^{3} -502.484 q^{4} +1085.59 q^{5} -512.832 q^{6} +2401.00 q^{7} -3129.44 q^{8} +7955.00 q^{9} +3348.80 q^{10} -73889.9 q^{11} +83536.4 q^{12} -28561.0 q^{13} +7406.51 q^{14} -180476. q^{15} +247618. q^{16} -202432. q^{17} +24539.3 q^{18} -706267. q^{19} -545493. q^{20} -399159. q^{21} -227933. q^{22} -891380. q^{23} +520260. q^{24} -774612. q^{25} -88103.9 q^{26} +1.94974e6 q^{27} -1.20646e6 q^{28} -592728. q^{29} -556727. q^{30} -9.05075e6 q^{31} +2.36612e6 q^{32} +1.22840e7 q^{33} -624454. q^{34} +2.60651e6 q^{35} -3.99726e6 q^{36} +1.81578e7 q^{37} -2.17867e6 q^{38} +4.74817e6 q^{39} -3.39730e6 q^{40} +4.86353e6 q^{41} -1.23131e6 q^{42} +8.57230e6 q^{43} +3.71285e7 q^{44} +8.63589e6 q^{45} -2.74969e6 q^{46} +6.24412e7 q^{47} -4.11658e7 q^{48} +5.76480e6 q^{49} -2.38949e6 q^{50} +3.36536e7 q^{51} +1.43515e7 q^{52} +3.57021e7 q^{53} +6.01449e6 q^{54} -8.02143e7 q^{55} -7.51379e6 q^{56} +1.17415e8 q^{57} -1.82842e6 q^{58} -1.26595e8 q^{59} +9.06865e7 q^{60} -5.69643e7 q^{61} -2.79194e7 q^{62} +1.91000e7 q^{63} -1.19482e8 q^{64} -3.10056e7 q^{65} +3.78931e7 q^{66} +9.93533e7 q^{67} +1.01719e8 q^{68} +1.48189e8 q^{69} +8.04046e6 q^{70} +1.06658e8 q^{71} -2.48947e7 q^{72} +1.41961e8 q^{73} +5.60124e7 q^{74} +1.28777e8 q^{75} +3.54888e8 q^{76} -1.77410e8 q^{77} +1.46470e7 q^{78} +2.68327e7 q^{79} +2.68813e8 q^{80} -4.80717e8 q^{81} +1.50028e7 q^{82} -2.28330e8 q^{83} +2.00571e8 q^{84} -2.19759e8 q^{85} +2.64435e7 q^{86} +9.85391e7 q^{87} +2.31234e8 q^{88} +7.33561e8 q^{89} +2.66397e7 q^{90} -6.85750e7 q^{91} +4.47904e8 q^{92} +1.50466e9 q^{93} +1.92616e8 q^{94} -7.66719e8 q^{95} -3.93359e8 q^{96} -2.19803e8 q^{97} +1.77830e7 q^{98} -5.87794e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) $ 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * 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 $

$2$	3.08476	0.136328	0.0681642	−	0.997674i	$-0.478286\pi$
$2$	3.08476	0.136328	0.0681642	+	0.997674i	$0.478286\pi$
$3$	−166.247	−1.18497	−0.592485	−	0.805581i	$-0.701853\pi$
$3$	−166.247	−1.18497	−0.592485	+	0.805581i	$0.701853\pi$
$4$	−502.484	−0.981415
$5$	1085.59	0.776787	0.388394	−	0.921494i	$-0.373030\pi$
$5$	1085.59	0.776787	0.388394	+	0.921494i	$0.373030\pi$
$6$	−512.832	−0.161545
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−3129.44	−0.270123
$9$	7955.00	0.404156
$10$	3348.80	0.105898
$11$	−73889.9	−1.52166	−0.760830	−	0.648951i	$-0.775208\pi$
$11$	−73889.9	−1.52166	−0.760830	+	0.648951i	$0.775208\pi$
$12$	83536.4	1.16295
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	7406.51	0.0515273
$15$	−180476.	−0.920470
$16$	247618.	0.944589
$17$	−202432.	−0.587839	−0.293920	−	0.955830i	$-0.594960\pi$
$17$	−202432.	−0.587839	−0.293920	+	0.955830i	$0.594960\pi$
$18$	24539.3	0.0550979
$19$	−706267.	−1.24331	−0.621653	−	0.783293i	$-0.713538\pi$
$19$	−706267.	−1.24331	−0.621653	+	0.783293i	$0.713538\pi$
$20$	−545493.	−0.762350
$21$	−399159.	−0.447877
$22$	−227933.	−0.207446
$23$	−891380.	−0.664183	−0.332091	−	0.943247i	$-0.607754\pi$
$23$	−891380.	−0.664183	−0.332091	+	0.943247i	$0.607754\pi$
$24$	520260.	0.320088
$25$	−774612.	−0.396602
$26$	−88103.9	−0.0378107
$27$	1.94974e6	0.706058
$28$	−1.20646e6	−0.370940
$29$	−592728.	−0.155620	−0.0778098	−	0.996968i	$-0.524793\pi$
$29$	−592728.	−0.155620	−0.0778098	+	0.996968i	$0.524793\pi$
$30$	−556727.	−0.125486
$31$	−9.05075e6	−1.76018	−0.880089	−	0.474808i	$-0.842517\pi$
$31$	−9.05075e6	−1.76018	−0.880089	+	0.474808i	$0.842517\pi$
$32$	2.36612e6	0.398898
$33$	1.22840e7	1.80312
$34$	−624454.	−0.0801392
$35$	2.60651e6	0.293598
$36$	−3.99726e6	−0.396644
$37$	1.81578e7	1.59278	0.796389	−	0.604785i	$-0.206741\pi$
$37$	1.81578e7	1.59278	0.796389	+	0.604785i	$0.206741\pi$
$38$	−2.17867e6	−0.169498
$39$	4.74817e6	0.328652
$40$	−3.39730e6	−0.209828
$41$	4.86353e6	0.268797	0.134398	−	0.990927i	$-0.457090\pi$
$41$	4.86353e6	0.268797	0.134398	+	0.990927i	$0.457090\pi$
$42$	−1.23131e6	−0.0610584
$43$	8.57230e6	0.382375	0.191187	−	0.981554i	$-0.438766\pi$
$43$	8.57230e6	0.382375	0.191187	+	0.981554i	$0.438766\pi$
$44$	3.71285e7	1.49338
$45$	8.63589e6	0.313943
$46$	−2.74969e6	−0.0905470
$47$	6.24412e7	1.86651	0.933256	−	0.359212i	$-0.116954\pi$
$47$	6.24412e7	1.86651	0.933256	+	0.359212i	$0.116954\pi$
$48$	−4.11658e7	−1.11931
$49$	5.76480e6	0.142857
$50$	−2.38949e6	−0.0540681
$51$	3.36536e7	0.696572
$52$	1.43515e7	0.272195
$53$	3.57021e7	0.621515	0.310758	−	0.950489i	$-0.399417\pi$
$53$	3.57021e7	0.621515	0.310758	+	0.950489i	$0.399417\pi$
$54$	6.01449e6	0.0962558
$55$	−8.02143e7	−1.18201
$56$	−7.51379e6	−0.102097
$57$	1.17415e8	1.47328
$58$	−1.82842e6	−0.0212154
$59$	−1.26595e8	−1.36014	−0.680068	−	0.733149i	$-0.738050\pi$
$59$	−1.26595e8	−1.36014	−0.680068	+	0.733149i	$0.738050\pi$
$60$	9.06865e7	0.903363
$61$	−5.69643e7	−0.526767	−0.263383	−	0.964691i	$-0.584838\pi$
$61$	−5.69643e7	−0.526767	−0.263383	+	0.964691i	$0.584838\pi$
$62$	−2.79194e7	−0.239962
$63$	1.91000e7	0.152757
$64$	−1.19482e8	−0.890208
$65$	−3.10056e7	−0.215442
$66$	3.78931e7	0.245817
$67$	9.93533e7	0.602345	0.301173	−	0.953570i	$-0.402622\pi$
$67$	9.93533e7	0.602345	0.301173	+	0.953570i	$0.402622\pi$
$68$	1.01719e8	0.576914
$69$	1.48189e8	0.787037
$70$	8.04046e6	0.0400258
$71$	1.06658e8	0.498117	0.249059	−	0.968488i	$-0.419879\pi$
$71$	1.06658e8	0.498117	0.249059	+	0.968488i	$0.419879\pi$
$72$	−2.48947e7	−0.109172
$73$	1.41961e8	0.585080	0.292540	−	0.956253i	$-0.405500\pi$
$73$	1.41961e8	0.585080	0.292540	+	0.956253i	$0.405500\pi$
$74$	5.60124e7	0.217141
$75$	1.28777e8	0.469961
$76$	3.54888e8	1.22020
$77$	−1.77410e8	−0.575134
$78$	1.46470e7	0.0448046
$79$	2.68327e7	0.0775074	0.0387537	−	0.999249i	$-0.487661\pi$
$79$	2.68327e7	0.0775074	0.0387537	+	0.999249i	$0.487661\pi$
$80$	2.68813e8	0.733745
$81$	−4.80717e8	−1.24081
$82$	1.50028e7	0.0366446
$83$	−2.28330e8	−0.528095	−0.264047	−	0.964510i	$-0.585058\pi$
$83$	−2.28330e8	−0.528095	−0.264047	+	0.964510i	$0.585058\pi$
$84$	2.00571e8	0.439553
$85$	−2.19759e8	−0.456626
$86$	2.64435e7	0.0521286
$87$	9.85391e7	0.184405
$88$	2.31234e8	0.411036
$89$	7.33561e8	1.23931	0.619656	−	0.784873i	$-0.287272\pi$
$89$	7.33561e8	1.23931	0.619656	+	0.784873i	$0.287272\pi$
$90$	2.66397e7	0.0427994
$91$	−6.85750e7	−0.104828
$92$	4.47904e8	0.651839
$93$	1.50466e9	2.08576
$94$	1.92616e8	0.254459
$95$	−7.66719e8	−0.965784
$96$	−3.93359e8	−0.472682
$97$	−2.19803e8	−0.252093	−0.126047	−	0.992024i	$-0.540229\pi$
$97$	−2.19803e8	−0.252093	−0.126047	+	0.992024i	$0.540229\pi$
$98$	1.77830e7	0.0194755
$99$	−5.87794e8	−0.614988
$100$	3.89231e8	0.389231
$101$	9.86274e8	0.943086	0.471543	−	0.881843i	$-0.343697\pi$
$101$	9.86274e8	0.943086	0.471543	+	0.881843i	$0.343697\pi$
$102$	1.03813e8	0.0949626
$103$	3.39715e8	0.297404	0.148702	−	0.988882i	$-0.452490\pi$
$103$	3.39715e8	0.297404	0.148702	+	0.988882i	$0.452490\pi$
$104$	8.93800e7	0.0749187
$105$	−4.33324e8	−0.347905
$106$	1.10132e8	0.0847302
$107$	−9.46748e8	−0.698244	−0.349122	−	0.937077i	$-0.613520\pi$
$107$	−9.46748e8	−0.698244	−0.349122	+	0.937077i	$0.613520\pi$
$108$	−9.79715e8	−0.692936
$109$	1.56922e9	1.06479	0.532395	−	0.846496i	$-0.321292\pi$
$109$	1.56922e9	1.06479	0.532395	+	0.846496i	$0.321292\pi$
$110$	−2.47442e8	−0.161141
$111$	−3.01867e9	−1.88740
$112$	5.94532e8	0.357021
$113$	−1.16998e9	−0.675034	−0.337517	−	0.941319i	$-0.609587\pi$
$113$	−1.16998e9	−0.675034	−0.337517	+	0.941319i	$0.609587\pi$
$114$	3.62196e8	0.200850
$115$	−9.67676e8	−0.515929
$116$	2.97836e8	0.152727
$117$	−2.27203e8	−0.112093
$118$	−3.90515e8	−0.185425
$119$	−4.86039e8	−0.222182
$120$	5.64790e8	0.248640
$121$	3.10176e9	1.31545
$122$	−1.75721e8	−0.0718133
$123$	−8.08546e8	−0.318516
$124$	4.54786e9	1.72747
$125$	−2.96121e9	−1.08486
$126$	5.89188e7	0.0208251
$127$	4.24344e9	1.44744	0.723722	−	0.690092i	$-0.242430\pi$
$127$	4.24344e9	1.44744	0.723722	+	0.690092i	$0.242430\pi$
$128$	−1.58002e9	−0.520258
$129$	−1.42512e9	−0.453103
$130$	−9.56450e7	−0.0293709
$131$	1.00199e9	0.297265	0.148633	−	0.988892i	$-0.452513\pi$
$131$	1.00199e9	0.297265	0.148633	+	0.988892i	$0.452513\pi$
$132$	−6.17249e9	−1.76961
$133$	−1.69575e9	−0.469925
$134$	3.06481e8	0.0821168
$135$	2.11663e9	0.548457
$136$	6.33498e8	0.158789
$137$	−2.35562e8	−0.0571299	−0.0285649	−	0.999592i	$-0.509094\pi$
$137$	−2.35562e8	−0.0571299	−0.0285649	+	0.999592i	$0.509094\pi$
$138$	4.57128e8	0.107296
$139$	−6.97682e9	−1.58522	−0.792612	−	0.609726i	$-0.791280\pi$
$139$	−6.97682e9	−1.58522	−0.792612	+	0.609726i	$0.791280\pi$
$140$	−1.30973e9	−0.288141
$141$	−1.03806e10	−2.21176
$142$	3.29015e8	0.0679076
$143$	2.11037e9	0.422033
$144$	1.96980e9	0.381761
$145$	−6.43461e8	−0.120883
$146$	4.37915e8	0.0797631
$147$	−9.58380e8	−0.169282
$148$	−9.12400e9	−1.56318
$149$	−1.05316e10	−1.75047	−0.875235	−	0.483698i	$-0.839293\pi$
$149$	−1.05316e10	−1.75047	−0.875235	+	0.483698i	$0.839293\pi$
$150$	3.97246e8	0.0640691
$151$	−3.01194e9	−0.471466	−0.235733	−	0.971818i	$-0.575749\pi$
$151$	−3.01194e9	−0.471466	−0.235733	+	0.971818i	$0.575749\pi$
$152$	2.21022e9	0.335846
$153$	−1.61034e9	−0.237579
$154$	−5.47266e8	−0.0784071
$155$	−9.82543e9	−1.36728
$156$	−2.38588e9	−0.322544
$157$	1.06781e10	1.40263	0.701317	−	0.712850i	$-0.252596\pi$
$157$	1.06781e10	1.40263	0.701317	+	0.712850i	$0.252596\pi$
$158$	8.27726e7	0.0105665
$159$	−5.93535e9	−0.736478
$160$	2.56864e9	0.309859
$161$	−2.14020e9	−0.251037
$162$	−1.48290e9	−0.169158
$163$	1.38724e10	1.53924	0.769622	−	0.638499i	$-0.220444\pi$
$163$	1.38724e10	1.53924	0.769622	+	0.638499i	$0.220444\pi$
$164$	−2.44385e9	−0.263801
$165$	1.33354e10	1.40064
$166$	−7.04344e8	−0.0719944
$167$	1.37869e10	1.37165	0.685825	−	0.727767i	$-0.259442\pi$
$167$	1.37869e10	1.37165	0.685825	+	0.727767i	$0.259442\pi$
$168$	1.24914e9	0.120982
$169$	8.15731e8	0.0769231
$170$	−6.77903e8	−0.0622511
$171$	−5.61835e9	−0.502489
$172$	−4.30745e9	−0.375268
$173$	6.55399e9	0.556286	0.278143	−	0.960540i	$-0.410281\pi$
$173$	6.55399e9	0.556286	0.278143	+	0.960540i	$0.410281\pi$
$174$	3.03970e8	0.0251396
$175$	−1.85984e9	−0.149901
$176$	−1.82965e10	−1.43734
$177$	2.10460e10	1.61172
$178$	2.26286e9	0.168954
$179$	−8.73356e9	−0.635847	−0.317924	−	0.948116i	$-0.602986\pi$
$179$	−8.73356e9	−0.635847	−0.317924	+	0.948116i	$0.602986\pi$
$180$	−4.33940e9	−0.308108
$181$	2.33318e10	1.61583	0.807913	−	0.589302i	$-0.200597\pi$
$181$	2.33318e10	1.61583	0.807913	+	0.589302i	$0.200597\pi$
$182$	−2.11537e8	−0.0142911
$183$	9.47013e9	0.624203
$184$	2.78952e9	0.179411
$185$	1.97120e10	1.23725
$186$	4.64151e9	0.284349
$187$	1.49577e10	0.894492
$188$	−3.13757e10	−1.83182
$189$	4.68133e9	0.266865
$190$	−2.36514e9	−0.131664
$191$	−8.83487e9	−0.480341	−0.240171	−	0.970731i	$-0.577203\pi$
$191$	−8.83487e9	−0.480341	−0.240171	+	0.970731i	$0.577203\pi$
$192$	1.98634e10	1.05487
$193$	−3.65167e10	−1.89445	−0.947225	−	0.320570i	$-0.896126\pi$
$193$	−3.65167e10	−1.89445	−0.947225	+	0.320570i	$0.896126\pi$
$194$	−6.78040e8	−0.0343675
$195$	5.15459e9	0.255292
$196$	−2.89672e9	−0.140202
$197$	2.39254e10	1.13178	0.565888	−	0.824482i	$-0.308533\pi$
$197$	2.39254e10	1.13178	0.565888	+	0.824482i	$0.308533\pi$
$198$	−1.81320e9	−0.0838404
$199$	2.44842e10	1.10674	0.553371	−	0.832935i	$-0.313341\pi$
$199$	2.44842e10	1.10674	0.553371	+	0.832935i	$0.313341\pi$
$200$	2.42410e9	0.107131
$201$	−1.65172e10	−0.713762
$202$	3.04242e9	0.128569
$203$	−1.42314e9	−0.0588187
$204$	−1.69104e10	−0.683626
$205$	5.27981e9	0.208798
$206$	1.04794e9	0.0405447
$207$	−7.09093e9	−0.268433
$208$	−7.07223e9	−0.261982
$209$	5.21860e10	1.89189
$210$	−1.33670e9	−0.0474294
$211$	−5.48925e9	−0.190652	−0.0953260	−	0.995446i	$-0.530389\pi$
$211$	−5.48925e9	−0.190652	−0.0953260	+	0.995446i	$0.530389\pi$
$212$	−1.79397e10	−0.609964
$213$	−1.77316e10	−0.590254
$214$	−2.92049e9	−0.0951906
$215$	9.30603e9	0.297024
$216$	−6.10161e9	−0.190723
$217$	−2.17308e10	−0.665285
$218$	4.84066e9	0.145161
$219$	−2.36005e10	−0.693303
$220$	4.03064e10	1.16004
$221$	5.78165e9	0.163037
$222$	−9.31189e9	−0.257306
$223$	−5.11371e9	−0.138473	−0.0692364	−	0.997600i	$-0.522056\pi$
$223$	−5.11371e9	−0.138473	−0.0692364	+	0.997600i	$0.522056\pi$
$224$	5.68105e9	0.150769
$225$	−6.16204e9	−0.160289
$226$	−3.60911e9	−0.0920264
$227$	3.13866e10	0.784562	0.392281	−	0.919845i	$-0.371686\pi$
$227$	3.13866e10	0.784562	0.392281	+	0.919845i	$0.371686\pi$
$228$	−5.89990e10	−1.44590
$229$	−1.27952e10	−0.307459	−0.153729	−	0.988113i	$-0.549128\pi$
$229$	−1.27952e10	−0.307459	−0.153729	+	0.988113i	$0.549128\pi$
$230$	−2.98505e9	−0.0703358
$231$	2.94938e10	0.681516
$232$	1.85491e9	0.0420365
$233$	2.58613e10	0.574842	0.287421	−	0.957804i	$-0.407202\pi$
$233$	2.58613e10	0.574842	0.287421	+	0.957804i	$0.407202\pi$
$234$	−7.00866e8	−0.0152814
$235$	6.77857e10	1.44988
$236$	6.36120e10	1.33486
$237$	−4.46086e9	−0.0918440
$238$	−1.49931e9	−0.0302898
$239$	9.33767e9	0.185118	0.0925588	−	0.995707i	$-0.470495\pi$
$239$	9.33767e9	0.185118	0.0925588	+	0.995707i	$0.470495\pi$
$240$	−4.46893e10	−0.869466
$241$	−2.37161e10	−0.452862	−0.226431	−	0.974027i	$-0.572706\pi$
$241$	−2.37161e10	−0.452862	−0.226431	+	0.974027i	$0.572706\pi$
$242$	9.56820e9	0.179333
$243$	4.15408e10	0.764270
$244$	2.86237e10	0.516977
$245$	6.25823e9	0.110970
$246$	−2.49417e9	−0.0434228
$247$	2.01717e10	0.344831
$248$	2.83238e10	0.475465
$249$	3.79592e10	0.625777
$250$	−9.13464e9	−0.147898
$251$	−8.35823e10	−1.32918	−0.664588	−	0.747210i	$-0.731393\pi$
$251$	−8.35823e10	−1.32918	−0.664588	+	0.747210i	$0.731393\pi$
$252$	−9.59742e9	−0.149917
$253$	6.58639e10	1.01066
$254$	1.30900e10	0.197328
$255$	3.65342e10	0.541088
$256$	5.63006e10	0.819282
$257$	1.02077e11	1.45959	0.729793	−	0.683668i	$-0.239616\pi$
$257$	1.02077e11	1.45959	0.729793	+	0.683668i	$0.239616\pi$
$258$	−4.39615e9	−0.0617708
$259$	4.35969e10	0.602013
$260$	1.55798e10	0.211438
$261$	−4.71515e9	−0.0628946
$262$	3.09091e9	0.0405257
$263$	−8.45689e10	−1.08996	−0.544979	−	0.838450i	$-0.683462\pi$
$263$	−8.45689e10	−1.08996	−0.544979	+	0.838450i	$0.683462\pi$
$264$	−3.84419e10	−0.487065
$265$	3.87579e10	0.482785
$266$	−5.23098e9	−0.0640642
$267$	−1.21952e11	−1.46855
$268$	−4.99234e10	−0.591150
$269$	−5.45200e10	−0.634850	−0.317425	−	0.948283i	$-0.602818\pi$
$269$	−5.45200e10	−0.634850	−0.317425	+	0.948283i	$0.602818\pi$
$270$	6.52929e9	0.0747703
$271$	−1.62533e11	−1.83055	−0.915274	−	0.402833i	$-0.868026\pi$
$271$	−1.62533e11	−1.83055	−0.915274	+	0.402833i	$0.868026\pi$
$272$	−5.01258e10	−0.555266
$273$	1.14004e10	0.124219
$274$	−7.26654e8	−0.00778843
$275$	5.72360e10	0.603493
$276$	−7.44627e10	−0.772410
$277$	−7.74877e10	−0.790813	−0.395407	−	0.918506i	$-0.629396\pi$
$277$	−7.74877e10	−0.790813	−0.395407	+	0.918506i	$0.629396\pi$
$278$	−2.15218e10	−0.216111
$279$	−7.19987e10	−0.711386
$280$	−8.15692e9	−0.0793076
$281$	9.25756e10	0.885764	0.442882	−	0.896580i	$-0.353956\pi$
$281$	9.25756e10	0.885764	0.442882	+	0.896580i	$0.353956\pi$
$282$	−3.20218e10	−0.301526
$283$	1.17167e11	1.08584	0.542920	−	0.839784i	$-0.317319\pi$
$283$	1.17167e11	1.08584	0.542920	+	0.839784i	$0.317319\pi$
$284$	−5.35940e10	−0.488859
$285$	1.27465e11	1.14443
$286$	6.50998e9	0.0575351
$287$	1.16773e10	0.101596
$288$	1.88225e10	0.161217
$289$	−7.76093e10	−0.654445
$290$	−1.98492e9	−0.0164798
$291$	3.65416e10	0.298723
$292$	−7.13330e10	−0.574206
$293$	2.13545e11	1.69272	0.846360	−	0.532612i	$-0.178789\pi$
$293$	2.13545e11	1.69272	0.846360	+	0.532612i	$0.178789\pi$
$294$	−2.95637e9	−0.0230779
$295$	−1.37431e11	−1.05654
$296$	−5.68237e10	−0.430246
$297$	−1.44066e11	−1.07438
$298$	−3.24874e10	−0.238639
$299$	2.54587e10	0.184211
$300$	−6.47083e10	−0.461227
$301$	2.05821e10	0.144524
$302$	−9.29113e9	−0.0642743
$303$	−1.63965e11	−1.11753
$304$	−1.74885e11	−1.17441
$305$	−6.18401e10	−0.409186
$306$	−4.96753e9	−0.0323887
$307$	−1.53250e11	−0.984642	−0.492321	−	0.870414i	$-0.663851\pi$
$307$	−1.53250e11	−0.984642	−0.492321	+	0.870414i	$0.663851\pi$
$308$	8.91455e10	0.564444
$309$	−5.64766e10	−0.352416
$310$	−3.03091e10	−0.186400
$311$	−2.79871e11	−1.69643	−0.848216	−	0.529650i	$-0.822323\pi$
$311$	−2.79871e11	−1.69643	−0.848216	+	0.529650i	$0.822323\pi$
$312$	−1.48591e10	−0.0887765
$313$	−9.51524e9	−0.0560364	−0.0280182	−	0.999607i	$-0.508920\pi$
$313$	−9.51524e9	−0.0560364	−0.0280182	+	0.999607i	$0.508920\pi$
$314$	3.29393e10	0.191219
$315$	2.07348e10	0.118659
$316$	−1.34830e10	−0.0760669
$317$	−2.82632e11	−1.57201	−0.786005	−	0.618221i	$-0.787854\pi$
$317$	−2.82632e11	−1.57201	−0.786005	+	0.618221i	$0.787854\pi$
$318$	−1.83091e10	−0.100403
$319$	4.37966e10	0.236800
$320$	−1.29709e11	−0.691502
$321$	1.57394e11	0.827399
$322$	−6.60202e9	−0.0342236
$323$	1.42971e11	0.730864
$324$	2.41553e11	1.21775
$325$	2.21237e10	0.109997
$326$	4.27931e10	0.209843
$327$	−2.60877e11	−1.26175
$328$	−1.52201e10	−0.0726082
$329$	1.49921e11	0.705475
$330$	4.11364e10	0.190948
$331$	−3.31451e11	−1.51773	−0.758864	−	0.651249i	$-0.774245\pi$
$331$	−3.31451e11	−1.51773	−0.758864	+	0.651249i	$0.774245\pi$
$332$	1.14732e11	0.518280
$333$	1.44445e11	0.643730
$334$	4.25294e10	0.186995
$335$	1.07857e11	0.467894
$336$	−9.88390e10	−0.423060
$337$	3.70972e11	1.56677	0.783387	−	0.621534i	$-0.213490\pi$
$337$	3.70972e11	1.56677	0.783387	+	0.621534i	$0.213490\pi$
$338$	2.51633e9	0.0104868
$339$	1.94506e11	0.799896
$340$	1.10425e11	0.448139
$341$	6.68758e11	2.67839
$342$	−1.73313e10	−0.0685036
$343$	1.38413e10	0.0539949
$344$	−2.68265e10	−0.103288
$345$	1.60873e11	0.611360
$346$	2.02175e10	0.0758377
$347$	1.91484e11	0.709006	0.354503	−	0.935055i	$-0.384650\pi$
$347$	1.91484e11	0.709006	0.354503	+	0.935055i	$0.384650\pi$
$348$	−4.95144e10	−0.180977
$349$	−2.29776e11	−0.829067	−0.414534	−	0.910034i	$-0.636055\pi$
$349$	−2.29776e11	−0.829067	−0.414534	+	0.910034i	$0.636055\pi$
$350$	−5.73718e9	−0.0204358
$351$	−5.56866e10	−0.195825
$352$	−1.74832e11	−0.606987
$353$	2.72568e11	0.934307	0.467153	−	0.884176i	$-0.345280\pi$
$353$	2.72568e11	0.934307	0.467153	+	0.884176i	$0.345280\pi$
$354$	6.49219e10	0.219724
$355$	1.15787e11	0.386931
$356$	−3.68603e11	−1.21628
$357$	8.08024e10	0.263280
$358$	−2.69410e10	−0.0866841
$359$	−2.33350e11	−0.741452	−0.370726	−	0.928742i	$-0.620891\pi$
$359$	−2.33350e11	−0.741452	−0.370726	+	0.928742i	$0.620891\pi$
$360$	−2.70255e10	−0.0848033
$361$	1.76126e11	0.545808
$362$	7.19730e10	0.220283
$363$	−5.15658e11	−1.55877
$364$	3.44578e10	0.102880
$365$	1.54112e11	0.454483
$366$	2.92131e10	0.0850967
$367$	−1.39194e11	−0.400519	−0.200259	−	0.979743i	$-0.564178\pi$
$367$	−1.39194e11	−0.400519	−0.200259	+	0.979743i	$0.564178\pi$
$368$	−2.20722e11	−0.627380
$369$	3.86893e10	0.108636
$370$	6.08067e10	0.168672
$371$	8.57206e10	0.234911
$372$	−7.56067e11	−2.04700
$373$	−1.12433e11	−0.300748	−0.150374	−	0.988629i	$-0.548048\pi$
$373$	−1.12433e11	−0.300748	−0.150374	+	0.988629i	$0.548048\pi$
$374$	4.61408e10	0.121945
$375$	4.92292e11	1.28553
$376$	−1.95406e11	−0.504188
$377$	1.69289e10	0.0431611
$378$	1.44408e10	0.0363813
$379$	7.93597e11	1.97571	0.987856	−	0.155371i	$-0.0496572\pi$
$379$	7.93597e11	1.97571	0.987856	+	0.155371i	$0.0496572\pi$
$380$	3.85264e11	0.947834
$381$	−7.05459e11	−1.71518
$382$	−2.72535e10	−0.0654842
$383$	6.15184e11	1.46087	0.730434	−	0.682983i	$-0.239318\pi$
$383$	6.15184e11	1.46087	0.730434	+	0.682983i	$0.239318\pi$
$384$	2.62674e11	0.616491
$385$	−1.92595e11	−0.446756
$386$	−1.12645e11	−0.258267
$387$	6.81926e10	0.154539
$388$	1.10448e11	0.247408
$389$	8.16683e11	1.80834	0.904170	−	0.427172i	$-0.140490\pi$
$389$	8.16683e11	1.80834	0.904170	+	0.427172i	$0.140490\pi$
$390$	1.59007e10	0.0348036
$391$	1.80444e11	0.390433
$392$	−1.80406e10	−0.0385890
$393$	−1.66578e11	−0.352250
$394$	7.38040e10	0.154293
$395$	2.91294e10	0.0602067
$396$	2.95357e11	0.603558
$397$	3.95604e11	0.799289	0.399644	−	0.916670i	$-0.369134\pi$
$397$	3.95604e11	0.799289	0.399644	+	0.916670i	$0.369134\pi$
$398$	7.55278e10	0.150880
$399$	2.81913e11	0.556848
$400$	−1.91808e11	−0.374626
$401$	−7.81872e11	−1.51003	−0.755015	−	0.655707i	$-0.772371\pi$
$401$	−7.81872e11	−1.51003	−0.755015	+	0.655707i	$0.772371\pi$
$402$	−5.09515e10	−0.0973060
$403$	2.58498e11	0.488186
$404$	−4.95587e11	−0.925558
$405$	−5.21863e11	−0.963848
$406$	−4.39005e9	−0.00801866
$407$	−1.34168e12	−2.42367
$408$	−1.05317e11	−0.188160
$409$	2.64838e11	0.467979	0.233989	−	0.972239i	$-0.424822\pi$
$409$	2.64838e11	0.467979	0.233989	+	0.972239i	$0.424822\pi$
$410$	1.62870e10	0.0284651
$411$	3.91615e10	0.0676973
$412$	−1.70702e11	−0.291877
$413$	−3.03954e11	−0.514083
$414$	−2.18738e10	−0.0365951
$415$	−2.47874e11	−0.410217
$416$	−6.75787e10	−0.110634
$417$	1.15987e12	1.87844
$418$	1.60981e11	0.257918
$419$	−2.02389e11	−0.320791	−0.160396	−	0.987053i	$-0.551277\pi$
$419$	−2.02389e11	−0.320791	−0.160396	+	0.987053i	$0.551277\pi$
$420$	2.17738e11	0.341439
$421$	1.00580e12	1.56042	0.780209	−	0.625519i	$-0.215113\pi$
$421$	1.00580e12	1.56042	0.780209	+	0.625519i	$0.215113\pi$
$422$	−1.69330e10	−0.0259913
$423$	4.96720e11	0.754362
$424$	−1.11728e11	−0.167886
$425$	1.56806e11	0.233138
$426$	−5.46977e10	−0.0804685
$427$	−1.36771e11	−0.199099
$428$	4.75726e11	0.685267
$429$	−3.50842e11	−0.500096
$430$	2.87069e10	0.0404928
$431$	−9.63053e11	−1.34432	−0.672160	−	0.740406i	$-0.734633\pi$
$431$	−9.63053e11	−1.34432	−0.672160	+	0.740406i	$0.734633\pi$
$432$	4.82792e11	0.666935
$433$	−5.27511e11	−0.721167	−0.360583	−	0.932727i	$-0.617422\pi$
$433$	−5.27511e11	−0.721167	−0.360583	+	0.932727i	$0.617422\pi$
$434$	−6.70345e10	−0.0906973
$435$	1.06973e11	0.143243
$436$	−7.88507e11	−1.04500
$437$	6.29552e11	0.825782
$438$	−7.28020e10	−0.0945169
$439$	2.42991e11	0.312248	0.156124	−	0.987737i	$-0.450100\pi$
$439$	2.42991e11	0.312248	0.156124	+	0.987737i	$0.450100\pi$
$440$	2.51026e11	0.319287
$441$	4.58590e10	0.0577365
$442$	1.78350e10	0.0222266
$443$	−3.38258e11	−0.417284	−0.208642	−	0.977992i	$-0.566904\pi$
$443$	−3.38258e11	−0.417284	−0.208642	+	0.977992i	$0.566904\pi$
$444$	1.51684e12	1.85232
$445$	7.96348e11	0.962682
$446$	−1.57746e10	−0.0188778
$447$	1.75084e12	2.07426
$448$	−2.86876e11	−0.336467
$449$	−1.16855e12	−1.35687	−0.678435	−	0.734660i	$-0.737342\pi$
$449$	−1.16855e12	−1.35687	−0.678435	+	0.734660i	$0.737342\pi$
$450$	−1.90084e10	−0.0218519
$451$	−3.59365e11	−0.409017
$452$	5.87897e11	0.662488
$453$	5.00726e11	0.558674
$454$	9.68201e10	0.106958
$455$	−7.44445e10	−0.0814294
$456$	−3.67442e11	−0.397967
$457$	−8.10759e11	−0.869499	−0.434750	−	0.900551i	$-0.643163\pi$
$457$	−8.10759e11	−0.869499	−0.434750	+	0.900551i	$0.643163\pi$
$458$	−3.94701e10	−0.0419154
$459$	−3.94690e11	−0.415049
$460$	4.86242e11	0.506340
$461$	3.26414e11	0.336600	0.168300	−	0.985736i	$-0.446172\pi$
$461$	3.26414e11	0.336600	0.168300	+	0.985736i	$0.446172\pi$
$462$	9.09812e10	0.0929101
$463$	−7.39356e11	−0.747721	−0.373860	−	0.927485i	$-0.621966\pi$
$463$	−7.39356e11	−0.747721	−0.373860	+	0.927485i	$0.621966\pi$
$464$	−1.46770e11	−0.146997
$465$	1.63345e12	1.62019
$466$	7.97759e10	0.0783674
$467$	−4.11121e11	−0.399985	−0.199993	−	0.979797i	$-0.564092\pi$
$467$	−4.11121e11	−0.399985	−0.199993	+	0.979797i	$0.564092\pi$
$468$	1.14166e11	0.110009
$469$	2.38547e11	0.227665
$470$	2.09103e11	0.197660
$471$	−1.77519e12	−1.66208
$472$	3.96172e11	0.367404
$473$	−6.33406e11	−0.581845
$474$	−1.37607e10	−0.0125209
$475$	5.47083e11	0.493097
$476$	2.44227e11	0.218053
$477$	2.84010e11	0.251189
$478$	2.88045e10	0.0252368
$479$	1.94552e12	1.68860	0.844300	−	0.535871i	$-0.180017\pi$
$479$	1.94552e12	1.68860	0.844300	+	0.535871i	$0.180017\pi$
$480$	−4.27028e11	−0.367173
$481$	−5.18605e11	−0.441757
$482$	−7.31584e10	−0.0617380
$483$	3.55802e11	0.297472
$484$	−1.55859e12	−1.29100
$485$	−2.38617e11	−0.195823
$486$	1.28144e11	0.104192
$487$	−8.20232e11	−0.660779	−0.330390	−	0.943845i	$-0.607180\pi$
$487$	−8.20232e11	−0.660779	−0.330390	+	0.943845i	$0.607180\pi$
$488$	1.78266e11	0.142292
$489$	−2.30624e12	−1.82396
$490$	1.93051e10	0.0151283
$491$	1.26406e11	0.0981522	0.0490761	−	0.998795i	$-0.484372\pi$
$491$	1.26406e11	0.0981522	0.0490761	+	0.998795i	$0.484372\pi$
$492$	4.06281e11	0.312596
$493$	1.19987e11	0.0914793
$494$	6.22249e10	0.0470103
$495$	−6.38105e11	−0.477715
$496$	−2.24113e12	−1.66265
$497$	2.56086e11	0.188271
$498$	1.17095e11	0.0853112
$499$	−1.94781e12	−1.40635	−0.703175	−	0.711017i	$-0.748235\pi$
$499$	−1.94781e12	−1.40635	−0.703175	+	0.711017i	$0.748235\pi$
$500$	1.48796e12	1.06470
$501$	−2.29203e12	−1.62536
$502$	−2.57831e11	−0.181205
$503$	1.31525e10	0.00916122	0.00458061	−	0.999990i	$-0.498542\pi$
$503$	1.31525e10	0.00916122	0.00458061	+	0.999990i	$0.498542\pi$
$504$	−5.97722e10	−0.0412631
$505$	1.07069e12	0.732577
$506$	2.03175e11	0.137782
$507$	−1.35613e11	−0.0911516
$508$	−2.13226e12	−1.42054
$509$	5.10979e11	0.337422	0.168711	−	0.985666i	$-0.446040\pi$
$509$	5.10979e11	0.337422	0.168711	+	0.985666i	$0.446040\pi$
$510$	1.12699e11	0.0737658
$511$	3.40848e11	0.221140
$512$	9.82647e11	0.631950
$513$	−1.37704e12	−0.877846
$514$	3.14884e11	0.198983
$515$	3.68793e11	0.231020
$516$	7.16099e11	0.444682
$517$	−4.61377e12	−2.84020
$518$	1.34486e11	0.0820716
$519$	−1.08958e12	−0.659183
$520$	9.70303e10	0.0581959
$521$	−1.82723e12	−1.08649	−0.543243	−	0.839575i	$-0.682804\pi$
$521$	−1.82723e12	−1.08649	−0.543243	+	0.839575i	$0.682804\pi$
$522$	−1.45451e10	−0.00857432
$523$	1.58552e12	0.926647	0.463324	−	0.886189i	$-0.346657\pi$
$523$	1.58552e12	0.926647	0.463324	+	0.886189i	$0.346657\pi$
$524$	−5.03486e11	−0.291740
$525$	3.09193e11	0.177629
$526$	−2.60875e11	−0.148592
$527$	1.83216e12	1.03470
$528$	3.04173e12	1.70321
$529$	−1.00659e12	−0.558861
$530$	1.19559e11	0.0658174
$531$	−1.00706e12	−0.549707
$532$	8.52086e11	0.461191
$533$	−1.38907e11	−0.0745508
$534$	−3.76193e11	−0.200205
$535$	−1.02778e12	−0.542387
$536$	−3.10920e11	−0.162707
$537$	1.45193e12	0.753460
$538$	−1.68181e11	−0.0865481
$539$	−4.25960e11	−0.217380
$540$	−1.06357e12	−0.538264
$541$	1.06832e12	0.536185	0.268092	−	0.963393i	$-0.413607\pi$
$541$	1.06832e12	0.536185	0.268092	+	0.963393i	$0.413607\pi$
$542$	−5.01377e11	−0.249556
$543$	−3.87884e12	−1.91471
$544$	−4.78977e11	−0.234488
$545$	1.70353e12	0.827115
$546$	3.51674e10	0.0169345
$547$	−2.73522e12	−1.30632	−0.653159	−	0.757221i	$-0.726556\pi$
$547$	−2.73522e12	−1.30632	−0.653159	+	0.757221i	$0.726556\pi$
$548$	1.18366e11	0.0560681
$549$	−4.53151e11	−0.212896
$550$	1.76559e11	0.0822733
$551$	4.18624e11	0.193483
$552$	−4.63749e11	−0.212597
$553$	6.44254e10	0.0292950
$554$	−2.39031e11	−0.107810
$555$	−3.27705e12	−1.46610
$556$	3.50574e12	1.55576
$557$	−9.11438e11	−0.401216	−0.200608	−	0.979672i	$-0.564292\pi$
$557$	−9.11438e11	−0.401216	−0.200608	+	0.979672i	$0.564292\pi$
$558$	−2.22099e11	−0.0969822
$559$	−2.44833e11	−0.106052
$560$	6.45420e11	0.277329
$561$	−2.48666e12	−1.05995
$562$	2.85573e11	0.120755
$563$	1.63294e12	0.684988	0.342494	−	0.939520i	$-0.388728\pi$
$563$	1.63294e12	0.684988	0.342494	+	0.939520i	$0.388728\pi$
$564$	5.21611e12	2.17066
$565$	−1.27012e12	−0.524358
$566$	3.61432e11	0.148031
$567$	−1.15420e12	−0.468984
$568$	−3.33781e11	−0.134553
$569$	3.01323e12	1.20511	0.602556	−	0.798076i	$-0.294149\pi$
$569$	3.01323e12	1.20511	0.602556	+	0.798076i	$0.294149\pi$
$570$	3.93198e11	0.156018
$571$	4.21895e12	1.66089	0.830447	−	0.557098i	$-0.188085\pi$
$571$	4.21895e12	1.66089	0.830447	+	0.557098i	$0.188085\pi$
$572$	−1.06043e12	−0.414189
$573$	1.46877e12	0.569190
$574$	3.60218e10	0.0138504
$575$	6.90474e11	0.263416
$576$	−9.50477e11	−0.359783
$577$	1.58020e12	0.593501	0.296751	−	0.954955i	$-0.404097\pi$
$577$	1.58020e12	0.593501	0.296751	+	0.954955i	$0.404097\pi$
$578$	−2.39406e11	−0.0892195
$579$	6.07078e12	2.24487
$580$	3.23329e11	0.118637
$581$	−5.48221e11	−0.199601
$582$	1.12722e11	0.0407245
$583$	−2.63802e12	−0.945735
$584$	−4.44258e11	−0.158044
$585$	−2.46650e11	−0.0870721
$586$	6.58735e11	0.230766
$587$	−1.09865e11	−0.0381935	−0.0190968	−	0.999818i	$-0.506079\pi$
$587$	−1.09865e11	−0.0381935	−0.0190968	+	0.999818i	$0.506079\pi$
$588$	4.81571e11	0.166135
$589$	6.39224e12	2.18844
$590$	−4.23941e11	−0.144036
$591$	−3.97751e12	−1.34112
$592$	4.49620e12	1.50452
$593$	2.07777e12	0.690005	0.345002	−	0.938602i	$-0.387878\pi$
$593$	2.07777e12	0.690005	0.345002	+	0.938602i	$0.387878\pi$
$594$	−4.44410e11	−0.146469
$595$	−5.27640e11	−0.172588
$596$	5.29194e12	1.71794
$597$	−4.07041e12	−1.31146
$598$	7.85340e10	0.0251132
$599$	2.21392e12	0.702652	0.351326	−	0.936253i	$-0.385731\pi$
$599$	2.21392e12	0.702652	0.351326	+	0.936253i	$0.385731\pi$
$600$	−4.03000e11	−0.126947
$601$	−9.95109e10	−0.0311126	−0.0155563	−	0.999879i	$-0.504952\pi$
$601$	−9.95109e10	−0.0311126	−0.0155563	+	0.999879i	$0.504952\pi$
$602$	6.34908e10	0.0197027
$603$	7.90355e11	0.243441
$604$	1.51345e12	0.462704
$605$	3.36725e12	1.02182
$606$	−5.05792e11	−0.152351
$607$	−5.12881e12	−1.53344	−0.766722	−	0.641979i	$-0.778113\pi$
$607$	−5.12881e12	−1.53344	−0.766722	+	0.641979i	$0.778113\pi$
$608$	−1.67111e12	−0.495952
$609$	2.36592e11	0.0696984
$610$	−1.90762e11	−0.0557837
$611$	−1.78338e12	−0.517677
$612$	8.09173e11	0.233163
$613$	8.95100e11	0.256035	0.128018	−	0.991772i	$-0.459139\pi$
$613$	8.95100e11	0.256035	0.128018	+	0.991772i	$0.459139\pi$
$614$	−4.72740e11	−0.134235
$615$	−8.77752e11	−0.247419
$616$	5.55193e11	0.155357
$617$	1.70023e12	0.472307	0.236153	−	0.971716i	$-0.424113\pi$
$617$	1.70023e12	0.472307	0.236153	+	0.971716i	$0.424113\pi$
$618$	−1.74217e11	−0.0480443
$619$	3.73247e12	1.02185	0.510926	−	0.859625i	$-0.329303\pi$
$619$	3.73247e12	1.02185	0.510926	+	0.859625i	$0.329303\pi$
$620$	4.93712e12	1.34187
$621$	−1.73796e12	−0.468952
$622$	−8.63336e11	−0.231272
$623$	1.76128e12	0.468416
$624$	1.17574e12	0.310441
$625$	−1.70176e12	−0.446106
$626$	−2.93522e10	−0.00763935
$627$	−8.67575e12	−2.24183
$628$	−5.36556e12	−1.37657
$629$	−3.67571e12	−0.936297
$630$	6.39618e10	0.0161766
$631$	−7.13571e12	−1.79186	−0.895931	−	0.444192i	$-0.853491\pi$
$631$	−7.13571e12	−1.79186	−0.895931	+	0.444192i	$0.853491\pi$
$632$	−8.39715e10	−0.0209365
$633$	9.12569e11	0.225917
$634$	−8.71853e11	−0.214310
$635$	4.60665e12	1.12436
$636$	2.98242e12	0.722790
$637$	−1.64648e11	−0.0396214
$638$	1.35102e11	0.0322826
$639$	8.48466e11	0.201317
$640$	−1.71526e12	−0.404130
$641$	4.85808e12	1.13659	0.568295	−	0.822825i	$-0.307603\pi$
$641$	4.85808e12	1.13659	0.568295	+	0.822825i	$0.307603\pi$
$642$	4.85522e11	0.112798
$643$	1.67543e12	0.386525	0.193262	−	0.981147i	$-0.438093\pi$
$643$	1.67543e12	0.386525	0.193262	+	0.981147i	$0.438093\pi$
$644$	1.07542e12	0.246372
$645$	−1.54710e12	−0.351965
$646$	4.41031e11	0.0996375
$647$	4.83673e12	1.08513	0.542566	−	0.840013i	$-0.317453\pi$
$647$	4.83673e12	1.08513	0.542566	+	0.840013i	$0.317453\pi$
$648$	1.50437e12	0.335173
$649$	9.35408e12	2.06967
$650$	6.82464e10	0.0149958
$651$	3.61268e12	0.788343
$652$	−6.97067e12	−1.51064
$653$	−1.12662e12	−0.242476	−0.121238	−	0.992623i	$-0.538686\pi$
$653$	−1.12662e12	−0.242476	−0.121238	+	0.992623i	$0.538686\pi$
$654$	−8.04745e11	−0.172012
$655$	1.08776e12	0.230912
$656$	1.20430e12	0.253902
$657$	1.12930e12	0.236464
$658$	4.62471e11	0.0961764
$659$	8.10152e11	0.167333	0.0836666	−	0.996494i	$-0.473337\pi$
$659$	8.10152e11	0.167333	0.0836666	+	0.996494i	$0.473337\pi$
$660$	−6.70082e12	−1.37461
$661$	−5.62857e11	−0.114681	−0.0573405	−	0.998355i	$-0.518262\pi$
$661$	−5.62857e11	−0.114681	−0.0573405	+	0.998355i	$0.518262\pi$
$662$	−1.02245e12	−0.206910
$663$	−9.61181e11	−0.193194
$664$	7.14546e11	0.142651
$665$	−1.84089e12	−0.365032
$666$	4.45579e11	0.0877588
$667$	5.28346e11	0.103360
$668$	−6.92771e12	−1.34616
$669$	8.50139e11	0.164086
$670$	3.32714e11	0.0637873
$671$	4.20908e12	0.801560
$672$	−9.44456e11	−0.178657
$673$	−1.36587e12	−0.256650	−0.128325	−	0.991732i	$-0.540960\pi$
$673$	−1.36587e12	−0.256650	−0.128325	+	0.991732i	$0.540960\pi$
$674$	1.14436e12	0.213596
$675$	−1.51030e12	−0.280024
$676$	−4.09892e11	−0.0754934
$677$	7.49125e12	1.37058	0.685291	−	0.728269i	$-0.259675\pi$
$677$	7.49125e12	1.37058	0.685291	+	0.728269i	$0.259675\pi$
$678$	6.00003e11	0.109049
$679$	−5.27748e11	−0.0952823
$680$	6.87722e11	0.123345
$681$	−5.21792e12	−0.929683
$682$	2.06296e12	0.365141
$683$	1.36794e12	0.240532	0.120266	−	0.992742i	$-0.461625\pi$
$683$	1.36794e12	0.240532	0.120266	+	0.992742i	$0.461625\pi$
$684$	2.82313e12	0.493150
$685$	−2.55725e11	−0.0443778
$686$	4.26971e10	0.00736105
$687$	2.12716e12	0.364329
$688$	2.12266e12	0.361187
$689$	−1.01969e12	−0.172377
$690$	4.96255e11	0.0833458
$691$	−2.37601e10	−0.00396458	−0.00198229	−	0.999998i	$-0.500631\pi$
$691$	−2.37601e10	−0.00396458	−0.00198229	+	0.999998i	$0.500631\pi$
$692$	−3.29328e12	−0.545947
$693$	−1.41129e12	−0.232444
$694$	5.90682e11	0.0966576
$695$	−7.57399e12	−1.23138
$696$	−3.08372e11	−0.0498120
$697$	−9.84532e11	−0.158009
$698$	−7.08803e11	−0.113025
$699$	−4.29936e12	−0.681171
$700$	9.34543e11	0.147115
$701$	1.22889e13	1.92212	0.961062	−	0.276333i	$-0.0891191\pi$
$701$	1.22889e13	1.92212	0.961062	+	0.276333i	$0.0891191\pi$
$702$	−1.71780e11	−0.0266966
$703$	−1.28243e13	−1.98031
$704$	8.82848e12	1.35459
$705$	−1.12692e13	−1.71807
$706$	8.40809e11	0.127373
$707$	2.36804e12	0.356453
$708$	−1.05753e13	−1.58177
$709$	1.19782e11	0.0178026	0.00890130	−	0.999960i	$-0.497167\pi$
$709$	1.19782e11	0.0178026	0.00890130	+	0.999960i	$0.497167\pi$
$710$	3.57176e11	0.0527497
$711$	2.13454e11	0.0313251
$712$	−2.29564e12	−0.334767
$713$	8.06765e12	1.16908
$714$	2.49256e11	0.0358925
$715$	2.29100e12	0.327830
$716$	4.38848e12	0.624030
$717$	−1.55236e12	−0.219359
$718$	−7.19830e11	−0.101081
$719$	1.06178e13	1.48168	0.740840	−	0.671682i	$-0.234428\pi$
$719$	1.06178e13	1.48168	0.740840	+	0.671682i	$0.234428\pi$
$720$	2.13841e12	0.296547
$721$	8.15656e11	0.112408
$722$	5.43305e11	0.0744092
$723$	3.94272e12	0.536629
$724$	−1.17239e13	−1.58580
$725$	4.59134e11	0.0617190
$726$	−1.59068e12	−0.212505
$727$	2.57533e12	0.341922	0.170961	−	0.985278i	$-0.445313\pi$
$727$	2.57533e12	0.341922	0.170961	+	0.985278i	$0.445313\pi$
$728$	2.14601e11	0.0283166
$729$	2.55592e12	0.335176
$730$	4.75398e11	0.0619589
$731$	−1.73531e12	−0.224775
$732$	−4.75859e12	−0.612602
$733$	−2.17972e12	−0.278890	−0.139445	−	0.990230i	$-0.544532\pi$
$733$	−2.17972e12	−0.278890	−0.139445	+	0.990230i	$0.544532\pi$
$734$	−4.29380e11	−0.0546021
$735$	−1.04041e12	−0.131496
$736$	−2.10911e12	−0.264941
$737$	−7.34120e12	−0.916565
$738$	1.19347e11	0.0148101
$739$	9.05230e12	1.11650	0.558250	−	0.829673i	$-0.311473\pi$
$739$	9.05230e12	1.11650	0.558250	+	0.829673i	$0.311473\pi$
$740$	−9.90496e12	−1.21425
$741$	−3.35348e12	−0.408614
$742$	2.64428e11	0.0320250
$743$	2.85455e12	0.343627	0.171813	−	0.985129i	$-0.445037\pi$
$743$	2.85455e12	0.343627	0.171813	+	0.985129i	$0.445037\pi$
$744$	−4.70874e12	−0.563412
$745$	−1.14330e13	−1.35974
$746$	−3.46828e11	−0.0410005
$747$	−1.81637e12	−0.213433
$748$	−7.51599e12	−0.877867
$749$	−2.27314e12	−0.263911
$750$	1.51860e12	0.175254
$751$	−2.98977e12	−0.342971	−0.171486	−	0.985187i	$-0.554857\pi$
$751$	−2.98977e12	−0.342971	−0.171486	+	0.985187i	$0.554857\pi$
$752$	1.54616e13	1.76309
$753$	1.38953e13	1.57504
$754$	5.22216e10	0.00588409
$755$	−3.26975e12	−0.366229
$756$	−2.35230e12	−0.261905
$757$	−1.62545e13	−1.79904	−0.899520	−	0.436879i	$-0.856084\pi$
$757$	−1.62545e13	−1.79904	−0.899520	+	0.436879i	$0.856084\pi$
$758$	2.44806e12	0.269346
$759$	−1.09497e13	−1.19760
$760$	2.39940e12	0.260881
$761$	−1.14658e12	−0.123929	−0.0619647	−	0.998078i	$-0.519737\pi$
$761$	−1.14658e12	−0.123929	−0.0619647	+	0.998078i	$0.519737\pi$
$762$	−2.17617e12	−0.233828
$763$	3.76769e12	0.402453
$764$	4.43938e12	0.471414
$765$	−1.74818e12	−0.184548
$766$	1.89770e12	0.199158
$767$	3.61568e12	0.377234
$768$	−9.35980e12	−0.970825
$769$	1.16605e13	1.20240	0.601201	−	0.799098i	$-0.294689\pi$
$769$	1.16605e13	1.20240	0.601201	+	0.799098i	$0.294689\pi$
$770$	−5.94108e11	−0.0609056
$771$	−1.69700e13	−1.72957
$772$	1.83490e13	1.85924
$773$	−1.59062e13	−1.60236	−0.801180	−	0.598424i	$-0.795794\pi$
$773$	−1.59062e13	−1.60236	−0.801180	+	0.598424i	$0.795794\pi$
$774$	2.10358e11	0.0210681
$775$	7.01082e12	0.698090
$776$	6.87861e11	0.0680962
$777$	−7.24784e12	−0.713368
$778$	2.51927e12	0.246528
$779$	−3.43495e12	−0.334196
$780$	−2.59010e12	−0.250548
$781$	−7.88096e12	−0.757965
$782$	5.56625e11	0.0532271
$783$	−1.15567e12	−0.109876
$784$	1.42747e12	0.134941
$785$	1.15920e13	1.08955
$786$	−5.13854e11	−0.0480218
$787$	1.54472e13	1.43537	0.717686	−	0.696366i	$-0.245201\pi$
$787$	1.54472e13	1.43537	0.717686	+	0.696366i	$0.245201\pi$
$788$	−1.20221e13	−1.11074
$789$	1.40593e13	1.29157
$790$	8.98573e10	0.00820789
$791$	−2.80912e12	−0.255139
$792$	1.83947e12	0.166122
$793$	1.62696e12	0.146099
$794$	1.22035e12	0.108966
$795$	−6.44338e12	−0.572086
$796$	−1.23029e13	−1.08617
$797$	−5.55982e12	−0.488088	−0.244044	−	0.969764i	$-0.578474\pi$
$797$	−5.55982e12	−0.488088	−0.244044	+	0.969764i	$0.578474\pi$
$798$	8.69633e11	0.0759142
$799$	−1.26401e13	−1.09721
$800$	−1.83282e12	−0.158203
$801$	5.83547e12	0.500875
$802$	−2.41189e12	−0.205860
$803$	−1.04895e13	−0.890293
$804$	8.29961e12	0.700496
$805$	−2.32339e12	−0.195003
$806$	7.97406e11	0.0665536
$807$	9.06378e12	0.752278
$808$	−3.08649e12	−0.254749
$809$	1.51333e13	1.24212	0.621061	−	0.783762i	$-0.286702\pi$
$809$	1.51333e13	1.24212	0.621061	+	0.783762i	$0.286702\pi$
$810$	−1.60982e12	−0.131400
$811$	−1.53373e13	−1.24496	−0.622479	−	0.782637i	$-0.713874\pi$
$811$	−1.53373e13	−1.24496	−0.622479	+	0.782637i	$0.713874\pi$
$812$	7.15105e11	0.0577255
$813$	2.70207e13	2.16914
$814$	−4.13875e12	−0.330415
$815$	1.50598e13	1.19567
$816$	8.33326e12	0.657975
$817$	−6.05433e12	−0.475409
$818$	8.16963e11	0.0637988
$819$	−5.45514e11	−0.0423670
$820$	−2.65302e12	−0.204917
$821$	−6.03037e12	−0.463233	−0.231617	−	0.972807i	$-0.574402\pi$
$821$	−6.03037e12	−0.463233	−0.231617	+	0.972807i	$0.574402\pi$
$822$	1.20804e11	0.00922906
$823$	−1.28556e13	−0.976768	−0.488384	−	0.872629i	$-0.662413\pi$
$823$	−1.28556e13	−0.976768	−0.488384	+	0.872629i	$0.662413\pi$
$824$	−1.06312e12	−0.0803359
$825$	−9.51530e12	−0.715121
$826$	−9.37627e11	−0.0700842
$827$	8.44807e11	0.0628034	0.0314017	−	0.999507i	$-0.490003\pi$
$827$	8.44807e11	0.0628034	0.0314017	+	0.999507i	$0.490003\pi$
$828$	3.56308e12	0.263444
$829$	5.69666e12	0.418914	0.209457	−	0.977818i	$-0.432830\pi$
$829$	5.69666e12	0.418914	0.209457	+	0.977818i	$0.432830\pi$
$830$	−7.64631e11	−0.0559243
$831$	1.28821e13	0.937091
$832$	3.41252e12	0.246899
$833$	−1.16698e12	−0.0839770
$834$	3.57793e12	0.256086
$835$	1.49670e13	1.06548
$836$	−2.62226e13	−1.85673
$837$	−1.76466e13	−1.24279
$838$	−6.24320e11	−0.0437330
$839$	2.07492e13	1.44568	0.722841	−	0.691015i	$-0.242836\pi$
$839$	2.07492e13	1.44568	0.722841	+	0.691015i	$0.242836\pi$
$840$	1.35606e12	0.0939772
$841$	−1.41558e13	−0.975783
$842$	3.10264e12	0.212729
$843$	−1.53904e13	−1.04960
$844$	2.75826e12	0.187109
$845$	8.85552e11	0.0597529
$846$	1.53226e12	0.102841
$847$	7.44733e12	0.497193
$848$	8.84049e12	0.587077
$849$	−1.94786e13	−1.28669
$850$	4.83710e11	0.0317833
$851$	−1.61855e13	−1.05790
$852$	8.90984e12	0.579284
$853$	6.79991e12	0.439777	0.219889	−	0.975525i	$-0.429431\pi$
$853$	6.79991e12	0.439777	0.219889	+	0.975525i	$0.429431\pi$
$854$	−4.21907e11	−0.0271429
$855$	−6.09925e12	−0.390327
$856$	2.96279e12	0.188612
$857$	2.01152e13	1.27383	0.636913	−	0.770936i	$-0.280211\pi$
$857$	2.01152e13	1.27383	0.636913	+	0.770936i	$0.280211\pi$
$858$	−1.08226e12	−0.0681774
$859$	4.71324e12	0.295359	0.147679	−	0.989035i	$-0.452820\pi$
$859$	4.71324e12	0.295359	0.147679	+	0.989035i	$0.452820\pi$
$860$	−4.67613e12	−0.291504
$861$	−1.94132e12	−0.120388
$862$	−2.97079e12	−0.183269
$863$	9.25794e12	0.568153	0.284077	−	0.958802i	$-0.408313\pi$
$863$	9.25794e12	0.568153	0.284077	+	0.958802i	$0.408313\pi$
$864$	4.61332e12	0.281645
$865$	7.11497e12	0.432116
$866$	−1.62724e12	−0.0983156
$867$	1.29023e13	0.775498
$868$	1.09194e13	0.652920
$869$	−1.98267e12	−0.117940
$870$	3.29987e11	0.0195281
$871$	−2.83763e12	−0.167061
$872$	−4.91078e12	−0.287625
$873$	−1.74853e12	−0.101885
$874$	1.94202e12	0.112578
$875$	−7.10987e12	−0.410039
$876$	1.18589e13	0.680418
$877$	1.50686e13	0.860151	0.430075	−	0.902793i	$-0.358487\pi$
$877$	1.50686e13	0.860151	0.430075	+	0.902793i	$0.358487\pi$
$878$	7.49570e11	0.0425684
$879$	−3.55012e13	−2.00582
$880$	−1.98625e13	−1.11651
$881$	6.49041e12	0.362978	0.181489	−	0.983393i	$-0.441908\pi$
$881$	6.49041e12	0.362978	0.181489	+	0.983393i	$0.441908\pi$
$882$	1.41464e11	0.00787113
$883$	1.78441e13	0.987807	0.493903	−	0.869517i	$-0.335570\pi$
$883$	1.78441e13	0.987807	0.493903	+	0.869517i	$0.335570\pi$
$884$	−2.90519e12	−0.160007
$885$	2.28474e13	1.25196
$886$	−1.04345e12	−0.0568877
$887$	9.72872e12	0.527715	0.263858	−	0.964562i	$-0.415005\pi$
$887$	9.72872e12	0.527715	0.263858	+	0.964562i	$0.415005\pi$
$888$	9.44677e12	0.509829
$889$	1.01885e13	0.547082
$890$	2.45654e12	0.131241
$891$	3.55201e13	1.88810
$892$	2.56956e12	0.135899
$893$	−4.41002e13	−2.32064
$894$	5.40092e12	0.282780
$895$	−9.48110e12	−0.493918
$896$	−3.79364e12	−0.196639
$897$	−4.23243e12	−0.218285
$898$	−3.60469e12	−0.184980
$899$	5.36463e12	0.273918
$900$	3.09633e12	0.157310
$901$	−7.22723e12	−0.365351
$902$	−1.10856e12	−0.0557607
$903$	−3.42171e12	−0.171257
$904$	3.66139e12	0.182342
$905$	2.53288e13	1.25515
$906$	1.54462e12	0.0761631
$907$	−1.75482e13	−0.860993	−0.430496	−	0.902592i	$-0.641661\pi$
$907$	−1.75482e13	−0.860993	−0.430496	+	0.902592i	$0.641661\pi$
$908$	−1.57713e13	−0.769981
$909$	7.84581e12	0.381154
$910$	−2.29644e11	−0.0111011
$911$	3.01706e13	1.45128	0.725641	−	0.688074i	$-0.241544\pi$
$911$	3.01706e13	1.45128	0.725641	+	0.688074i	$0.241544\pi$
$912$	2.90740e13	1.39164
$913$	1.68713e13	0.803581
$914$	−2.50100e12	−0.118537
$915$	1.02807e13	0.484873
$916$	6.42937e12	0.301744
$917$	2.40579e12	0.112356
$918$	−1.21752e12	−0.0565829
$919$	5.65006e12	0.261296	0.130648	−	0.991429i	$-0.458294\pi$
$919$	5.65006e12	0.261296	0.130648	+	0.991429i	$0.458294\pi$
$920$	3.02829e12	0.139364
$921$	2.54773e13	1.16677
$922$	1.00691e12	0.0458882
$923$	−3.04626e12	−0.138153
$924$	−1.48202e13	−0.668850
$925$	−1.40653e13	−0.631698
$926$	−2.28074e12	−0.101936
$927$	2.70243e12	0.120198
$928$	−1.40246e12	−0.0620763
$929$	−3.57237e13	−1.57357	−0.786783	−	0.617229i	$-0.788255\pi$
$929$	−3.57237e13	−1.57357	−0.786783	+	0.617229i	$0.788255\pi$
$930$	5.03879e12	0.220878
$931$	−4.07149e12	−0.177615
$932$	−1.29949e13	−0.564158
$933$	4.65277e13	2.01022
$934$	−1.26821e12	−0.0545294
$935$	1.62379e13	0.694830
$936$	7.11018e11	0.0302788
$937$	2.04740e13	0.867710	0.433855	−	0.900983i	$-0.357153\pi$
$937$	2.04740e13	0.867710	0.433855	+	0.900983i	$0.357153\pi$
$938$	7.35861e11	0.0310372
$939$	1.58188e12	0.0664015
$940$	−3.40613e13	−1.42294
$941$	3.83999e13	1.59653	0.798264	−	0.602307i	$-0.205752\pi$
$941$	3.83999e13	1.59653	0.798264	+	0.602307i	$0.205752\pi$
$942$	−5.47605e12	−0.226589
$943$	−4.33525e12	−0.178530
$944$	−3.13472e13	−1.28477
$945$	5.08202e12	0.207297
$946$	−1.95391e12	−0.0793220
$947$	1.96134e13	0.792462	0.396231	−	0.918151i	$-0.370318\pi$
$947$	1.96134e13	0.792462	0.396231	+	0.918151i	$0.370318\pi$
$948$	2.24151e12	0.0901370
$949$	−4.05454e12	−0.162272
$950$	1.68762e12	0.0672231
$951$	4.69867e13	1.86279
$952$	1.52103e12	0.0600166
$953$	2.76463e12	0.108572	0.0542862	−	0.998525i	$-0.482712\pi$
$953$	2.76463e12	0.108572	0.0542862	+	0.998525i	$0.482712\pi$
$954$	8.76103e11	0.0342442
$955$	−9.59107e12	−0.373123
$956$	−4.69203e12	−0.181677
$957$	−7.28104e12	−0.280601
$958$	6.00147e12	0.230204
$959$	−5.65585e11	−0.0215931
$960$	2.15636e13	0.819410
$961$	5.54764e13	2.09823
$962$	−1.59977e12	−0.0602241
$963$	−7.53138e12	−0.282199
$964$	1.19170e13	0.444446
$965$	−3.96422e13	−1.47158
$966$	1.09756e12	0.0405539
$967$	−4.29185e13	−1.57843	−0.789215	−	0.614117i	$-0.789512\pi$
$967$	−4.29185e13	−1.57843	−0.789215	+	0.614117i	$0.789512\pi$
$968$	−9.70679e12	−0.355334
$969$	−2.37685e13	−0.866052
$970$	−7.36076e11	−0.0266962
$971$	−4.45700e12	−0.160900	−0.0804500	−	0.996759i	$-0.525636\pi$
$971$	−4.45700e12	−0.160900	−0.0804500	+	0.996759i	$0.525636\pi$
$972$	−2.08736e13	−0.750066
$973$	−1.67513e13	−0.599159
$974$	−2.53022e12	−0.0900830
$975$	−3.67800e12	−0.130344
$976$	−1.41054e13	−0.497578
$977$	−1.11884e12	−0.0392864	−0.0196432	−	0.999807i	$-0.506253\pi$
$977$	−1.11884e12	−0.0392864	−0.0196432	+	0.999807i	$0.506253\pi$
$978$	−7.11421e12	−0.248658
$979$	−5.42027e13	−1.88581
$980$	−3.14466e12	−0.108907
$981$	1.24831e13	0.430341
$982$	3.89932e11	0.0133809
$983$	−3.88458e13	−1.32695	−0.663473	−	0.748200i	$-0.730918\pi$
$983$	−3.88458e13	−1.32695	−0.663473	+	0.748200i	$0.730918\pi$
$984$	2.53030e12	0.0860386
$985$	2.59732e13	0.879149
$986$	3.70131e11	0.0124712
$987$	−2.49239e13	−0.835968
$988$	−1.01360e13	−0.338422
$989$	−7.64118e12	−0.253967
$990$	−1.96840e12	−0.0651261
$991$	−6.47486e11	−0.0213255	−0.0106627	−	0.999943i	$-0.503394\pi$
$991$	−6.47486e11	−0.0213255	−0.0106627	+	0.999943i	$0.503394\pi$
$992$	−2.14151e13	−0.702131
$993$	5.51028e13	1.79846
$994$	7.89965e11	0.0256666
$995$	2.65798e13	0.859703
$996$	−1.90739e13	−0.614147
$997$	−2.85877e13	−0.916327	−0.458164	−	0.888868i	$-0.651493\pi$
$997$	−2.85877e13	−0.916327	−0.458164	+	0.888868i	$0.651493\pi$
$998$	−6.00852e12	−0.191726
$999$	3.54030e13	1.12459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.8	✓	14	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)

\(f(q)\)	\(=\)	\(q+3.08476 q^{2} -166.247 q^{3} -502.484 q^{4} +1085.59 q^{5} -512.832 q^{6} +2401.00 q^{7} -3129.44 q^{8} +7955.00 q^{9} +O(q^{10})\)	\(q+3.08476 q^{2} -166.247 q^{3} -502.484 q^{4} +1085.59 q^{5} -512.832 q^{6} +2401.00 q^{7} -3129.44 q^{8} +7955.00 q^{9} +3348.80 q^{10} -73889.9 q^{11} +83536.4 q^{12} -28561.0 q^{13} +7406.51 q^{14} -180476. q^{15} +247618. q^{16} -202432. q^{17} +24539.3 q^{18} -706267. q^{19} -545493. q^{20} -399159. q^{21} -227933. q^{22} -891380. q^{23} +520260. q^{24} -774612. q^{25} -88103.9 q^{26} +1.94974e6 q^{27} -1.20646e6 q^{28} -592728. q^{29} -556727. q^{30} -9.05075e6 q^{31} +2.36612e6 q^{32} +1.22840e7 q^{33} -624454. q^{34} +2.60651e6 q^{35} -3.99726e6 q^{36} +1.81578e7 q^{37} -2.17867e6 q^{38} +4.74817e6 q^{39} -3.39730e6 q^{40} +4.86353e6 q^{41} -1.23131e6 q^{42} +8.57230e6 q^{43} +3.71285e7 q^{44} +8.63589e6 q^{45} -2.74969e6 q^{46} +6.24412e7 q^{47} -4.11658e7 q^{48} +5.76480e6 q^{49} -2.38949e6 q^{50} +3.36536e7 q^{51} +1.43515e7 q^{52} +3.57021e7 q^{53} +6.01449e6 q^{54} -8.02143e7 q^{55} -7.51379e6 q^{56} +1.17415e8 q^{57} -1.82842e6 q^{58} -1.26595e8 q^{59} +9.06865e7 q^{60} -5.69643e7 q^{61} -2.79194e7 q^{62} +1.91000e7 q^{63} -1.19482e8 q^{64} -3.10056e7 q^{65} +3.78931e7 q^{66} +9.93533e7 q^{67} +1.01719e8 q^{68} +1.48189e8 q^{69} +8.04046e6 q^{70} +1.06658e8 q^{71} -2.48947e7 q^{72} +1.41961e8 q^{73} +5.60124e7 q^{74} +1.28777e8 q^{75} +3.54888e8 q^{76} -1.77410e8 q^{77} +1.46470e7 q^{78} +2.68327e7 q^{79} +2.68813e8 q^{80} -4.80717e8 q^{81} +1.50028e7 q^{82} -2.28330e8 q^{83} +2.00571e8 q^{84} -2.19759e8 q^{85} +2.64435e7 q^{86} +9.85391e7 q^{87} +2.31234e8 q^{88} +7.33561e8 q^{89} +2.66397e7 q^{90} -6.85750e7 q^{91} +4.47904e8 q^{92} +1.50466e9 q^{93} +1.92616e8 q^{94} -7.66719e8 q^{95} -3.93359e8 q^{96} -2.19803e8 q^{97} +1.77830e7 q^{98} -5.87794e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Introduction

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