LMFDB - Embedded newform 91.10.a.c.1.13

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			1.13
Root			$-34.2541$ 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)

$f(q)$	$=$	$q+36.2541 q^{2} -166.815 q^{3} +802.361 q^{4} +2128.44 q^{5} -6047.74 q^{6} +2401.00 q^{7} +10526.8 q^{8} +8144.30 q^{9} +O(q^{10})$	\(q+36.2541 q^{2} -166.815 q^{3} +802.361 q^{4} +2128.44 q^{5} -6047.74 q^{6} +2401.00 q^{7} +10526.8 q^{8} +8144.30 q^{9} +77164.9 q^{10} +43107.8 q^{11} -133846. q^{12} -28561.0 q^{13} +87046.1 q^{14} -355057. q^{15} -29170.1 q^{16} +525481. q^{17} +295264. q^{18} -730842. q^{19} +1.70778e6 q^{20} -400523. q^{21} +1.56283e6 q^{22} +1.94924e6 q^{23} -1.75602e6 q^{24} +2.57715e6 q^{25} -1.03545e6 q^{26} +1.92483e6 q^{27} +1.92647e6 q^{28} -3.37235e6 q^{29} -1.28723e7 q^{30} +479891. q^{31} -6.44724e6 q^{32} -7.19103e6 q^{33} +1.90509e7 q^{34} +5.11040e6 q^{35} +6.53466e6 q^{36} +7.24197e6 q^{37} -2.64960e7 q^{38} +4.76441e6 q^{39} +2.24056e7 q^{40} +2.74246e7 q^{41} -1.45206e7 q^{42} +3.54975e7 q^{43} +3.45880e7 q^{44} +1.73347e7 q^{45} +7.06680e7 q^{46} +1.65313e6 q^{47} +4.86602e6 q^{48} +5.76480e6 q^{49} +9.34323e7 q^{50} -8.76582e7 q^{51} -2.29162e7 q^{52} +2.21254e7 q^{53} +6.97830e7 q^{54} +9.17525e7 q^{55} +2.52748e7 q^{56} +1.21916e8 q^{57} -1.22262e8 q^{58} +1.15881e8 q^{59} -2.84884e8 q^{60} +1.30109e8 q^{61} +1.73980e7 q^{62} +1.95545e7 q^{63} -2.18804e8 q^{64} -6.07905e7 q^{65} -2.60704e8 q^{66} -2.46756e8 q^{67} +4.21625e8 q^{68} -3.25163e8 q^{69} +1.85273e8 q^{70} -4.10200e8 q^{71} +8.57331e7 q^{72} +2.58619e8 q^{73} +2.62551e8 q^{74} -4.29908e8 q^{75} -5.86399e8 q^{76} +1.03502e8 q^{77} +1.72729e8 q^{78} -6.38704e8 q^{79} -6.20870e7 q^{80} -4.81395e8 q^{81} +9.94254e8 q^{82} +1.54980e8 q^{83} -3.21364e8 q^{84} +1.11846e9 q^{85} +1.28693e9 q^{86} +5.62559e8 q^{87} +4.53785e8 q^{88} -3.37453e8 q^{89} +6.28454e8 q^{90} -6.85750e7 q^{91} +1.56399e9 q^{92} -8.00530e7 q^{93} +5.99326e7 q^{94} -1.55556e9 q^{95} +1.07550e9 q^{96} -5.42438e8 q^{97} +2.08998e8 q^{98} +3.51082e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	36.2541	1.60222	0.801110	−	0.598517i	$-0.204243\pi$
$2$	36.2541	1.60222	0.801110	+	0.598517i	$0.204243\pi$
$3$	−166.815	−1.18902	−0.594511	−	0.804088i	$-0.702654\pi$
$3$	−166.815	−1.18902	−0.594511	+	0.804088i	$0.702654\pi$
$4$	802.361	1.56711
$5$	2128.44	1.52299	0.761495	−	0.648170i	$-0.224465\pi$
$5$	2128.44	1.52299	0.761495	+	0.648170i	$0.224465\pi$
$6$	−6047.74	−1.90508
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	10526.8	0.908636
$9$	8144.30	0.413773
$10$	77164.9	2.44017
$11$	43107.8	0.887745	0.443873	−	0.896090i	$-0.353604\pi$
$11$	43107.8	0.887745	0.443873	+	0.896090i	$0.353604\pi$
$12$	−133846.	−1.86333
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	87046.1	0.605582
$15$	−355057.	−1.81087
$16$	−29170.1	−0.111275
$17$	525481.	1.52594	0.762969	−	0.646435i	$-0.223741\pi$
$17$	525481.	1.52594	0.762969	+	0.646435i	$0.223741\pi$
$18$	295264.	0.662956
$19$	−730842.	−1.28657	−0.643283	−	0.765628i	$-0.722428\pi$
$19$	−730842.	−1.28657	−0.643283	+	0.765628i	$0.722428\pi$
$20$	1.70778e6	2.38670
$21$	−400523.	−0.449408
$22$	1.56283e6	1.42236
$23$	1.94924e6	1.45241	0.726206	−	0.687477i	$-0.241282\pi$
$23$	1.94924e6	1.45241	0.726206	+	0.687477i	$0.241282\pi$
$24$	−1.75602e6	−1.08039
$25$	2.57715e6	1.31950
$26$	−1.03545e6	−0.444376
$27$	1.92483e6	0.697037
$28$	1.92647e6	0.592312
$29$	−3.37235e6	−0.885404	−0.442702	−	0.896669i	$-0.645980\pi$
$29$	−3.37235e6	−0.885404	−0.442702	+	0.896669i	$0.645980\pi$
$30$	−1.28723e7	−2.90141
$31$	479891.	0.0933286	0.0466643	−	0.998911i	$-0.485141\pi$
$31$	479891.	0.0933286	0.0466643	+	0.998911i	$0.485141\pi$
$32$	−6.44724e6	−1.08692
$33$	−7.19103e6	−1.05555
$34$	1.90509e7	2.44489
$35$	5.11040e6	0.575636
$36$	6.53466e6	0.648428
$37$	7.24197e6	0.635256	0.317628	−	0.948215i	$-0.397114\pi$
$37$	7.24197e6	0.635256	0.317628	+	0.948215i	$0.397114\pi$
$38$	−2.64960e7	−2.06136
$39$	4.76441e6	0.329775
$40$	2.24056e7	1.38384
$41$	2.74246e7	1.51570	0.757849	−	0.652430i	$-0.226250\pi$
$41$	2.74246e7	1.51570	0.757849	+	0.652430i	$0.226250\pi$
$42$	−1.45206e7	−0.720051
$43$	3.54975e7	1.58340	0.791698	−	0.610913i	$-0.209197\pi$
$43$	3.54975e7	1.58340	0.791698	+	0.610913i	$0.209197\pi$
$44$	3.45880e7	1.39119
$45$	1.73347e7	0.630173
$46$	7.06680e7	2.32709
$47$	1.65313e6	0.0494158	0.0247079	−	0.999695i	$-0.492134\pi$
$47$	1.65313e6	0.0494158	0.0247079	+	0.999695i	$0.492134\pi$
$48$	4.86602e6	0.132309
$49$	5.76480e6	0.142857
$50$	9.34323e7	2.11413
$51$	−8.76582e7	−1.81437
$52$	−2.29162e7	−0.434638
$53$	2.21254e7	0.385168	0.192584	−	0.981280i	$-0.438313\pi$
$53$	2.21254e7	0.385168	0.192584	+	0.981280i	$0.438313\pi$
$54$	6.97830e7	1.11681
$55$	9.17525e7	1.35203
$56$	2.52748e7	0.343432
$57$	1.21916e8	1.52976
$58$	−1.22262e8	−1.41861
$59$	1.15881e8	1.24503	0.622514	−	0.782608i	$-0.286111\pi$
$59$	1.15881e8	1.24503	0.622514	+	0.782608i	$0.286111\pi$
$60$	−2.84884e8	−2.83783
$61$	1.30109e8	1.20316	0.601578	−	0.798814i	$-0.294539\pi$
$61$	1.30109e8	1.20316	0.601578	+	0.798814i	$0.294539\pi$
$62$	1.73980e7	0.149533
$63$	1.95545e7	0.156392
$64$	−2.18804e8	−1.63022
$65$	−6.07905e7	−0.422402
$66$	−2.60704e8	−1.69122
$67$	−2.46756e8	−1.49600	−0.747999	−	0.663700i	$-0.768985\pi$
$67$	−2.46756e8	−1.49600	−0.747999	+	0.663700i	$0.768985\pi$
$68$	4.21625e8	2.39131
$69$	−3.25163e8	−1.72695
$70$	1.85273e8	0.922297
$71$	−4.10200e8	−1.91572	−0.957862	−	0.287228i	$-0.907266\pi$
$71$	−4.10200e8	−1.91572	−0.957862	+	0.287228i	$0.907266\pi$
$72$	8.57331e7	0.375969
$73$	2.58619e8	1.06588	0.532939	−	0.846153i	$-0.321087\pi$
$73$	2.58619e8	1.06588	0.532939	+	0.846153i	$0.321087\pi$
$74$	2.62551e8	1.01782
$75$	−4.29908e8	−1.56892
$76$	−5.86399e8	−2.01619
$77$	1.03502e8	0.335536
$78$	1.72729e8	0.528373
$79$	−6.38704e8	−1.84492	−0.922461	−	0.386090i	$-0.873825\pi$
$79$	−6.38704e8	−1.84492	−0.922461	+	0.386090i	$0.873825\pi$
$80$	−6.20870e7	−0.169471
$81$	−4.81395e8	−1.24256
$82$	9.94254e8	2.42848
$83$	1.54980e8	0.358446	0.179223	−	0.983808i	$-0.442642\pi$
$83$	1.54980e8	0.358446	0.179223	+	0.983808i	$0.442642\pi$
$84$	−3.21364e8	−0.704272
$85$	1.11846e9	2.32399
$86$	1.28693e9	2.53695
$87$	5.62559e8	1.05276
$88$	4.53785e8	0.806637
$89$	−3.37453e8	−0.570110	−0.285055	−	0.958511i	$-0.592012\pi$
$89$	−3.37453e8	−0.570110	−0.285055	+	0.958511i	$0.592012\pi$
$90$	6.28454e8	1.00968
$91$	−6.85750e7	−0.104828
$92$	1.56399e9	2.27609
$93$	−8.00530e7	−0.110970
$94$	5.99326e7	0.0791749
$95$	−1.55556e9	−1.95943
$96$	1.07550e9	1.29238
$97$	−5.42438e8	−0.622125	−0.311063	−	0.950389i	$-0.600685\pi$
$97$	−5.42438e8	−0.622125	−0.311063	+	0.950389i	$0.600685\pi$
$98$	2.08998e8	0.228889
$99$	3.51082e8	0.367325
$100$	2.06780e9	2.06780
$101$	−1.26639e9	−1.21094	−0.605468	−	0.795870i	$-0.707014\pi$
$101$	−1.26639e9	−1.21094	−0.605468	+	0.795870i	$0.707014\pi$
$102$	−3.17797e9	−2.90703
$103$	3.72255e8	0.325891	0.162946	−	0.986635i	$-0.447901\pi$
$103$	3.72255e8	0.325891	0.162946	+	0.986635i	$0.447901\pi$
$104$	−3.00655e8	−0.252010
$105$	−8.52491e8	−0.684444
$106$	8.02138e8	0.617125
$107$	−6.94990e8	−0.512568	−0.256284	−	0.966602i	$-0.582498\pi$
$107$	−6.94990e8	−0.512568	−0.256284	+	0.966602i	$0.582498\pi$
$108$	1.54441e9	1.09233
$109$	−1.17208e9	−0.795313	−0.397656	−	0.917534i	$-0.630176\pi$
$109$	−1.17208e9	−0.795313	−0.397656	+	0.917534i	$0.630176\pi$
$110$	3.32640e9	2.16625
$111$	−1.20807e9	−0.755333
$112$	−7.00375e7	−0.0420581
$113$	−3.11053e8	−0.179466	−0.0897328	−	0.995966i	$-0.528601\pi$
$113$	−3.11053e8	−0.179466	−0.0897328	+	0.995966i	$0.528601\pi$
$114$	4.41994e9	2.45101
$115$	4.14885e9	2.21201
$116$	−2.70584e9	−1.38753
$117$	−2.32609e8	−0.114760
$118$	4.20117e9	1.99481
$119$	1.26168e9	0.576751
$120$	−3.73760e9	−1.64542
$121$	−4.99669e8	−0.211908
$122$	4.71697e9	1.92772
$123$	−4.57484e9	−1.80220
$124$	3.85045e8	0.146256
$125$	1.32820e9	0.486598
$126$	7.08929e8	0.250574
$127$	−7.17827e8	−0.244852	−0.122426	−	0.992478i	$-0.539067\pi$
$127$	−7.17827e8	−0.244852	−0.122426	+	0.992478i	$0.539067\pi$
$128$	−4.63155e9	−1.52504
$129$	−5.92152e9	−1.88269
$130$	−2.20391e9	−0.676781
$131$	−1.59686e9	−0.473746	−0.236873	−	0.971541i	$-0.576123\pi$
$131$	−1.59686e9	−0.473746	−0.236873	+	0.971541i	$0.576123\pi$
$132$	−5.76980e9	−1.65416
$133$	−1.75475e9	−0.486276
$134$	−8.94591e9	−2.39692
$135$	4.09689e9	1.06158
$136$	5.53162e9	1.38652
$137$	3.27771e9	0.794929	0.397464	−	0.917618i	$-0.369890\pi$
$137$	3.27771e9	0.794929	0.397464	+	0.917618i	$0.369890\pi$
$138$	−1.17885e10	−2.76696
$139$	−1.73472e9	−0.394152	−0.197076	−	0.980388i	$-0.563145\pi$
$139$	−1.73472e9	−0.394152	−0.197076	+	0.980388i	$0.563145\pi$
$140$	4.10038e9	0.902086
$141$	−2.75766e8	−0.0587564
$142$	−1.48714e10	−3.06941
$143$	−1.23120e9	−0.246216
$144$	−2.37570e8	−0.0460427
$145$	−7.17786e9	−1.34846
$146$	9.37601e9	1.70777
$147$	−9.61656e8	−0.169860
$148$	5.81067e9	0.995516
$149$	1.76392e9	0.293184	0.146592	−	0.989197i	$-0.453169\pi$
$149$	1.76392e9	0.293184	0.146592	+	0.989197i	$0.453169\pi$
$150$	−1.55859e10	−2.51375
$151$	7.95151e9	1.24467	0.622334	−	0.782752i	$-0.286185\pi$
$151$	7.95151e9	1.24467	0.622334	+	0.782752i	$0.286185\pi$
$152$	−7.69340e9	−1.16902
$153$	4.27967e9	0.631392
$154$	3.75236e9	0.537603
$155$	1.02142e9	0.142139
$156$	3.82277e9	0.516794
$157$	6.51392e9	0.855646	0.427823	−	0.903862i	$-0.359281\pi$
$157$	6.51392e9	0.855646	0.427823	+	0.903862i	$0.359281\pi$
$158$	−2.31557e10	−2.95597
$159$	−3.69086e9	−0.457974
$160$	−1.37226e10	−1.65537
$161$	4.68012e9	0.548960
$162$	−1.74526e10	−1.99086
$163$	−2.09402e9	−0.232347	−0.116174	−	0.993229i	$-0.537063\pi$
$163$	−2.09402e9	−0.232347	−0.116174	+	0.993229i	$0.537063\pi$
$164$	2.20044e10	2.37527
$165$	−1.53057e10	−1.60759
$166$	5.61866e9	0.574310
$167$	−1.57730e9	−0.156924	−0.0784620	−	0.996917i	$-0.525001\pi$
$167$	−1.57730e9	−0.156924	−0.0784620	+	0.996917i	$0.525001\pi$
$168$	−4.21621e9	−0.408348
$169$	8.15731e8	0.0769231
$170$	4.05487e10	3.72355
$171$	−5.95219e9	−0.532347
$172$	2.84818e10	2.48136
$173$	1.08098e10	0.917506	0.458753	−	0.888564i	$-0.348296\pi$
$173$	1.08098e10	0.917506	0.458753	+	0.888564i	$0.348296\pi$
$174$	2.03951e10	1.68676
$175$	6.18774e9	0.498725
$176$	−1.25746e9	−0.0987840
$177$	−1.93308e10	−1.48037
$178$	−1.22341e10	−0.913442
$179$	−1.26967e10	−0.924383	−0.462192	−	0.886780i	$-0.652937\pi$
$179$	−1.26967e10	−0.924383	−0.462192	+	0.886780i	$0.652937\pi$
$180$	1.39087e10	0.987550
$181$	1.90915e10	1.32217	0.661084	−	0.750312i	$-0.270097\pi$
$181$	1.90915e10	1.32217	0.661084	+	0.750312i	$0.270097\pi$
$182$	−2.48612e9	−0.167958
$183$	−2.17041e10	−1.43058
$184$	2.05192e10	1.31971
$185$	1.54141e10	0.967489
$186$	−2.90225e9	−0.177798
$187$	2.26523e10	1.35464
$188$	1.32640e9	0.0774400
$189$	4.62152e9	0.263455
$190$	−5.63953e10	−3.13944
$191$	−2.44449e10	−1.32904	−0.664521	−	0.747270i	$-0.731364\pi$
$191$	−2.44449e10	−1.32904	−0.664521	+	0.747270i	$0.731364\pi$
$192$	3.64998e10	1.93836
$193$	6.71475e9	0.348355	0.174177	−	0.984714i	$-0.444273\pi$
$193$	6.71475e9	0.348355	0.174177	+	0.984714i	$0.444273\pi$
$194$	−1.96656e10	−0.996781
$195$	1.01408e10	0.502245
$196$	4.62545e9	0.223873
$197$	1.16325e10	0.550268	0.275134	−	0.961406i	$-0.411278\pi$
$197$	1.16325e10	0.550268	0.275134	+	0.961406i	$0.411278\pi$
$198$	1.27282e10	0.588536
$199$	−3.77740e10	−1.70748	−0.853738	−	0.520703i	$-0.825670\pi$
$199$	−3.77740e10	−1.70748	−0.853738	+	0.520703i	$0.825670\pi$
$200$	2.71291e10	1.19895
$201$	4.11626e10	1.77877
$202$	−4.59118e10	−1.94019
$203$	−8.09701e9	−0.334651
$204$	−7.03335e10	−2.84333
$205$	5.83717e10	2.30839
$206$	1.34958e10	0.522149
$207$	1.58752e10	0.600969
$208$	8.33128e8	0.0308622
$209$	−3.15050e10	−1.14214
$210$	−3.09063e10	−1.09663
$211$	2.79138e9	0.0969501	0.0484751	−	0.998824i	$-0.484564\pi$
$211$	2.79138e9	0.0969501	0.0484751	+	0.998824i	$0.484564\pi$
$212$	1.77526e10	0.603601
$213$	6.84276e10	2.27784
$214$	−2.51962e10	−0.821247
$215$	7.55544e10	2.41150
$216$	2.02622e10	0.633353
$217$	1.15222e9	0.0352749
$218$	−4.24927e10	−1.27427
$219$	−4.31416e10	−1.26735
$220$	7.36186e10	2.11878
$221$	−1.50083e10	−0.423219
$222$	−4.37975e10	−1.21021
$223$	−2.82013e10	−0.763656	−0.381828	−	0.924233i	$-0.624705\pi$
$223$	−2.82013e10	−0.763656	−0.381828	+	0.924233i	$0.624705\pi$
$224$	−1.54798e10	−0.410818
$225$	2.09891e10	0.545974
$226$	−1.12769e10	−0.287543
$227$	−2.49158e10	−0.622813	−0.311407	−	0.950277i	$-0.600800\pi$
$227$	−2.49158e10	−0.622813	−0.311407	+	0.950277i	$0.600800\pi$
$228$	9.78202e10	2.39730
$229$	4.61661e9	0.110934	0.0554668	−	0.998461i	$-0.482335\pi$
$229$	4.61661e9	0.110934	0.0554668	+	0.998461i	$0.482335\pi$
$230$	1.50413e11	3.54413
$231$	−1.72657e10	−0.398960
$232$	−3.54999e10	−0.804510
$233$	−3.52050e10	−0.782534	−0.391267	−	0.920277i	$-0.627963\pi$
$233$	−3.52050e10	−0.782534	−0.391267	+	0.920277i	$0.627963\pi$
$234$	−8.43304e9	−0.183871
$235$	3.51859e9	0.0752598
$236$	9.29786e10	1.95110
$237$	1.06546e11	2.19365
$238$	4.57411e10	0.924082
$239$	−3.07099e10	−0.608818	−0.304409	−	0.952541i	$-0.598459\pi$
$239$	−3.07099e10	−0.608818	−0.304409	+	0.952541i	$0.598459\pi$
$240$	1.03571e10	0.201505
$241$	−6.56655e10	−1.25389	−0.626946	−	0.779063i	$-0.715695\pi$
$241$	−6.56655e10	−1.25389	−0.626946	+	0.779063i	$0.715695\pi$
$242$	−1.81151e10	−0.339524
$243$	4.24176e10	0.780400
$244$	1.04394e11	1.88548
$245$	1.22701e10	0.217570
$246$	−1.65857e11	−2.88752
$247$	2.08736e10	0.356829
$248$	5.05170e9	0.0848017
$249$	−2.58530e10	−0.426201
$250$	4.81529e10	0.779637
$251$	−3.89631e10	−0.619615	−0.309808	−	0.950799i	$-0.600265\pi$
$251$	−3.89631e10	−0.619615	−0.309808	+	0.950799i	$0.600265\pi$
$252$	1.56897e10	0.245083
$253$	8.40274e10	1.28937
$254$	−2.60242e10	−0.392306
$255$	−1.86576e11	−2.76328
$256$	−5.58852e10	−0.813237
$257$	8.77992e10	1.25543	0.627713	−	0.778445i	$-0.283991\pi$
$257$	8.77992e10	1.25543	0.627713	+	0.778445i	$0.283991\pi$
$258$	−2.14679e11	−3.01649
$259$	1.73880e10	0.240104
$260$	−4.87759e10	−0.661950
$261$	−2.74654e10	−0.366356
$262$	−5.78927e10	−0.759046
$263$	−9.79310e10	−1.26217	−0.631087	−	0.775712i	$-0.717391\pi$
$263$	−9.79310e10	−1.26217	−0.631087	+	0.775712i	$0.717391\pi$
$264$	−7.56982e10	−0.959109
$265$	4.70928e10	0.586608
$266$	−6.36170e10	−0.779122
$267$	5.62923e10	0.677873
$268$	−1.97987e11	−2.34439
$269$	−7.73982e10	−0.901251	−0.450625	−	0.892713i	$-0.648799\pi$
$269$	−7.73982e10	−0.901251	−0.450625	+	0.892713i	$0.648799\pi$
$270$	1.48529e11	1.70089
$271$	9.39115e10	1.05769	0.528843	−	0.848719i	$-0.322626\pi$
$271$	9.39115e10	1.05769	0.528843	+	0.848719i	$0.322626\pi$
$272$	−1.53284e10	−0.169799
$273$	1.14393e10	0.124643
$274$	1.18831e11	1.27365
$275$	1.11095e11	1.17138
$276$	−2.60898e11	−2.70632
$277$	3.78054e10	0.385829	0.192914	−	0.981216i	$-0.438206\pi$
$277$	3.78054e10	0.385829	0.192914	+	0.981216i	$0.438206\pi$
$278$	−6.28908e10	−0.631518
$279$	3.90837e9	0.0386169
$280$	5.37959e10	0.523044
$281$	−1.75269e11	−1.67697	−0.838487	−	0.544921i	$-0.816559\pi$
$281$	−1.75269e11	−1.67697	−0.838487	+	0.544921i	$0.816559\pi$
$282$	−9.99767e9	−0.0941407
$283$	−1.66180e11	−1.54007	−0.770036	−	0.638000i	$-0.779762\pi$
$283$	−1.66180e11	−1.54007	−0.770036	+	0.638000i	$0.779762\pi$
$284$	−3.29128e11	−3.00215
$285$	2.59490e11	2.32980
$286$	−4.46361e10	−0.394493
$287$	6.58464e10	0.572880
$288$	−5.25082e10	−0.449740
$289$	1.57543e11	1.32849
$290$	−2.60227e11	−2.16053
$291$	9.04870e10	0.739720
$292$	2.07506e11	1.67035
$293$	−1.62063e11	−1.28464	−0.642319	−	0.766438i	$-0.722028\pi$
$293$	−1.62063e11	−1.28464	−0.642319	+	0.766438i	$0.722028\pi$
$294$	−3.48640e10	−0.272154
$295$	2.46647e11	1.89617
$296$	7.62345e10	0.577216
$297$	8.29751e10	0.618791
$298$	6.39494e10	0.469746
$299$	−5.56722e10	−0.402827
$300$	−3.44941e11	−2.45866
$301$	8.52294e10	0.598467
$302$	2.88275e11	1.99423
$303$	2.11253e11	1.43983
$304$	2.13188e10	0.143163
$305$	2.76929e11	1.83239
$306$	1.55156e11	1.01163
$307$	1.82605e11	1.17325	0.586626	−	0.809858i	$-0.300456\pi$
$307$	1.82605e11	1.17325	0.586626	+	0.809858i	$0.300456\pi$
$308$	8.30457e10	0.525822
$309$	−6.20977e10	−0.387492
$310$	3.70307e10	0.227737
$311$	2.81282e11	1.70498	0.852491	−	0.522741i	$-0.175091\pi$
$311$	2.81282e11	1.70498	0.852491	+	0.522741i	$0.175091\pi$
$312$	5.01538e10	0.299646
$313$	−2.00687e11	−1.18187	−0.590934	−	0.806720i	$-0.701240\pi$
$313$	−2.00687e11	−1.18187	−0.590934	+	0.806720i	$0.701240\pi$
$314$	2.36157e11	1.37093
$315$	4.16206e10	0.238183
$316$	−5.12471e11	−2.89120
$317$	8.92731e10	0.496540	0.248270	−	0.968691i	$-0.420138\pi$
$317$	8.92731e10	0.496540	0.248270	+	0.968691i	$0.420138\pi$
$318$	−1.33809e11	−0.733775
$319$	−1.45374e11	−0.786013
$320$	−4.65712e11	−2.48280
$321$	1.15935e11	0.609455
$322$	1.69674e11	0.879556
$323$	−3.84044e11	−1.96322
$324$	−3.86252e11	−1.94724
$325$	−7.36060e10	−0.365964
$326$	−7.59169e10	−0.372271
$327$	1.95521e11	0.945644
$328$	2.88692e11	1.37722
$329$	3.96915e9	0.0186774
$330$	−5.54895e11	−2.57571
$331$	2.08591e11	0.955147	0.477573	−	0.878592i	$-0.341516\pi$
$331$	2.08591e11	0.955147	0.477573	+	0.878592i	$0.341516\pi$
$332$	1.24350e11	0.561725
$333$	5.89807e10	0.262852
$334$	−5.71835e10	−0.251427
$335$	−5.25206e11	−2.27839
$336$	1.16833e10	0.0500080
$337$	3.64080e11	1.53767	0.768833	−	0.639449i	$-0.220838\pi$
$337$	3.64080e11	1.53767	0.768833	+	0.639449i	$0.220838\pi$
$338$	2.95736e10	0.123248
$339$	5.18883e10	0.213388
$340$	8.97406e11	3.64195
$341$	2.06870e10	0.0828520
$342$	−2.15791e11	−0.852937
$343$	1.38413e10	0.0539949
$344$	3.73674e11	1.43873
$345$	−6.92091e11	−2.63013
$346$	3.91899e11	1.47005
$347$	−4.18976e11	−1.55134	−0.775670	−	0.631139i	$-0.782588\pi$
$347$	−4.18976e11	−1.55134	−0.775670	+	0.631139i	$0.782588\pi$
$348$	4.51375e11	1.64980
$349$	1.17690e11	0.424642	0.212321	−	0.977200i	$-0.431898\pi$
$349$	1.17690e11	0.424642	0.212321	+	0.977200i	$0.431898\pi$
$350$	2.24331e11	0.799067
$351$	−5.49751e10	−0.193323
$352$	−2.77926e11	−0.964911
$353$	−9.49329e9	−0.0325410	−0.0162705	−	0.999868i	$-0.505179\pi$
$353$	−9.49329e9	−0.0325410	−0.0162705	+	0.999868i	$0.505179\pi$
$354$	−7.00820e11	−2.37187
$355$	−8.73088e11	−2.91763
$356$	−2.70759e11	−0.893426
$357$	−2.10467e11	−0.685769
$358$	−4.60307e11	−1.48107
$359$	2.21163e11	0.702729	0.351364	−	0.936239i	$-0.385718\pi$
$359$	2.21163e11	0.702729	0.351364	+	0.936239i	$0.385718\pi$
$360$	1.82478e11	0.572598
$361$	2.11442e11	0.655253
$362$	6.92145e11	2.11840
$363$	8.33524e10	0.251964
$364$	−5.50218e10	−0.164278
$365$	5.50456e11	1.62332
$366$	−7.86862e11	−2.29210
$367$	5.16287e11	1.48557	0.742786	−	0.669529i	$-0.233504\pi$
$367$	5.16287e11	1.48557	0.742786	+	0.669529i	$0.233504\pi$
$368$	−5.68596e10	−0.161618
$369$	2.23354e11	0.627155
$370$	5.58825e11	1.55013
$371$	5.31232e10	0.145580
$372$	−6.42314e10	−0.173902
$373$	3.32716e11	0.889986	0.444993	−	0.895534i	$-0.353206\pi$
$373$	3.32716e11	0.889986	0.444993	+	0.895534i	$0.353206\pi$
$374$	8.21240e11	2.17044
$375$	−2.21565e11	−0.578575
$376$	1.74021e10	0.0449009
$377$	9.63177e10	0.245567
$378$	1.67549e11	0.422113
$379$	−4.11081e11	−1.02341	−0.511706	−	0.859161i	$-0.670986\pi$
$379$	−4.11081e11	−1.02341	−0.511706	+	0.859161i	$0.670986\pi$
$380$	−1.24812e12	−3.07064
$381$	1.19744e11	0.291134
$382$	−8.86229e11	−2.12942
$383$	−7.34558e11	−1.74434	−0.872171	−	0.489201i	$-0.837288\pi$
$383$	−7.34558e11	−1.74434	−0.872171	+	0.489201i	$0.837288\pi$
$384$	7.72613e11	1.81331
$385$	2.20298e11	0.511018
$386$	2.43437e11	0.558141
$387$	2.89102e11	0.655167
$388$	−4.35231e11	−0.974939
$389$	7.93230e11	1.75641	0.878205	−	0.478284i	$-0.158741\pi$
$389$	7.93230e11	1.75641	0.878205	+	0.478284i	$0.158741\pi$
$390$	3.67645e11	0.804707
$391$	1.02429e12	2.21629
$392$	6.06847e10	0.129805
$393$	2.66380e11	0.563295
$394$	4.21725e11	0.881651
$395$	−1.35945e12	−2.80980
$396$	2.81695e11	0.575639
$397$	2.72888e10	0.0551349	0.0275674	−	0.999620i	$-0.491224\pi$
$397$	2.72888e10	0.0551349	0.0275674	+	0.999620i	$0.491224\pi$
$398$	−1.36946e12	−2.73575
$399$	2.92719e11	0.578193
$400$	−7.51758e10	−0.146828
$401$	−3.99757e11	−0.772053	−0.386026	−	0.922488i	$-0.626153\pi$
$401$	−3.99757e11	−0.772053	−0.386026	+	0.922488i	$0.626153\pi$
$402$	1.49231e12	2.84999
$403$	−1.37062e10	−0.0258847
$404$	−1.01610e12	−1.89767
$405$	−1.02462e12	−1.89242
$406$	−2.93550e11	−0.536185
$407$	3.12185e11	0.563945
$408$	−9.22757e11	−1.64861
$409$	−2.63237e11	−0.465148	−0.232574	−	0.972579i	$-0.574715\pi$
$409$	−2.63237e11	−0.465148	−0.232574	+	0.972579i	$0.574715\pi$
$410$	2.11621e12	3.69856
$411$	−5.46772e11	−0.945188
$412$	2.98682e11	0.510707
$413$	2.78231e11	0.470577
$414$	5.75541e11	0.962885
$415$	3.29866e11	0.545911
$416$	1.84140e11	0.301458
$417$	2.89378e11	0.468655
$418$	−1.14218e12	−1.82997
$419$	−1.14730e12	−1.81850	−0.909248	−	0.416254i	$-0.863343\pi$
$419$	−1.14730e12	−1.81850	−0.909248	+	0.416254i	$0.863343\pi$
$420$	−6.84005e11	−1.07260
$421$	2.85921e11	0.443585	0.221792	−	0.975094i	$-0.428809\pi$
$421$	2.85921e11	0.443585	0.221792	+	0.975094i	$0.428809\pi$
$422$	1.01199e11	0.155336
$423$	1.34635e10	0.0204469
$424$	2.32909e11	0.349978
$425$	1.35424e12	2.01348
$426$	2.48078e12	3.64960
$427$	3.12391e11	0.454750
$428$	−5.57632e11	−0.803251
$429$	2.05383e11	0.292756
$430$	2.73916e12	3.86375
$431$	−9.10442e11	−1.27088	−0.635440	−	0.772150i	$-0.719181\pi$
$431$	−9.10442e11	−1.27088	−0.635440	+	0.772150i	$0.719181\pi$
$432$	−5.61476e10	−0.0775629
$433$	6.62331e9	0.00905481	0.00452741	−	0.999990i	$-0.498559\pi$
$433$	6.62331e9	0.00905481	0.00452741	+	0.999990i	$0.498559\pi$
$434$	4.17726e10	0.0565181
$435$	1.19738e12	1.60335
$436$	−9.40431e11	−1.24634
$437$	−1.42459e12	−1.86863
$438$	−1.56406e12	−2.03058
$439$	2.02207e11	0.259840	0.129920	−	0.991524i	$-0.458528\pi$
$439$	2.02207e11	0.259840	0.129920	+	0.991524i	$0.458528\pi$
$440$	9.65857e11	1.22850
$441$	4.69503e10	0.0591105
$442$	−5.44111e11	−0.678090
$443$	1.03584e11	0.127784	0.0638922	−	0.997957i	$-0.479649\pi$
$443$	1.03584e11	0.127784	0.0638922	+	0.997957i	$0.479649\pi$
$444$	−9.69308e11	−1.18369
$445$	−7.18251e11	−0.868272
$446$	−1.02241e12	−1.22354
$447$	−2.94249e11	−0.348603
$448$	−5.25348e11	−0.616164
$449$	9.35615e11	1.08640	0.543198	−	0.839604i	$-0.317213\pi$
$449$	9.35615e11	1.08640	0.543198	+	0.839604i	$0.317213\pi$
$450$	7.60941e11	0.874771
$451$	1.18221e12	1.34555
$452$	−2.49576e11	−0.281242
$453$	−1.32643e12	−1.47994
$454$	−9.03299e11	−0.997884
$455$	−1.45958e11	−0.159653
$456$	1.28338e12	1.38999
$457$	−1.53349e12	−1.64459	−0.822296	−	0.569060i	$-0.807307\pi$
$457$	−1.53349e12	−1.64459	−0.822296	+	0.569060i	$0.807307\pi$
$458$	1.67371e11	0.177740
$459$	1.01146e12	1.06363
$460$	3.32887e12	3.46647
$461$	2.62636e11	0.270832	0.135416	−	0.990789i	$-0.456763\pi$
$461$	2.62636e11	0.270832	0.135416	+	0.990789i	$0.456763\pi$
$462$	−6.25951e11	−0.639222
$463$	8.78762e11	0.888703	0.444351	−	0.895853i	$-0.353434\pi$
$463$	8.78762e11	0.888703	0.444351	+	0.895853i	$0.353434\pi$
$464$	9.83719e10	0.0985235
$465$	−1.70388e11	−0.169006
$466$	−1.27633e12	−1.25379
$467$	8.84893e11	0.860924	0.430462	−	0.902609i	$-0.358351\pi$
$467$	8.84893e11	0.860924	0.430462	+	0.902609i	$0.358351\pi$
$468$	−1.86637e11	−0.179842
$469$	−5.92461e11	−0.565434
$470$	1.27563e11	0.120583
$471$	−1.08662e12	−1.01738
$472$	1.21986e12	1.13128
$473$	1.53022e12	1.40565
$474$	3.86272e12	3.51472
$475$	−1.88349e12	−1.69763
$476$	1.01232e12	0.903832
$477$	1.80196e11	0.159372
$478$	−1.11336e12	−0.975460
$479$	5.98750e10	0.0519679	0.0259840	−	0.999662i	$-0.491728\pi$
$479$	5.98750e10	0.0519679	0.0259840	+	0.999662i	$0.491728\pi$
$480$	2.28914e12	1.96828
$481$	−2.06838e11	−0.176188
$482$	−2.38064e12	−2.00901
$483$	−7.80716e11	−0.652726
$484$	−4.00915e11	−0.332084
$485$	−1.15455e12	−0.947491
$486$	1.53781e12	1.25037
$487$	3.16083e11	0.254637	0.127318	−	0.991862i	$-0.459363\pi$
$487$	3.16083e11	0.254637	0.127318	+	0.991862i	$0.459363\pi$
$488$	1.36962e12	1.09323
$489$	3.49315e11	0.276266
$490$	4.44840e11	0.348595
$491$	6.15781e11	0.478145	0.239072	−	0.971002i	$-0.423157\pi$
$491$	6.15781e11	0.478145	0.239072	+	0.971002i	$0.423157\pi$
$492$	−3.67067e12	−2.82424
$493$	−1.77211e12	−1.35107
$494$	7.56753e11	0.571719
$495$	7.47259e11	0.559433
$496$	−1.39985e10	−0.0103852
$497$	−9.84890e11	−0.724076
$498$	−9.37278e11	−0.682867
$499$	−2.42258e12	−1.74915	−0.874573	−	0.484894i	$-0.838858\pi$
$499$	−2.42258e12	−1.74915	−0.874573	+	0.484894i	$0.838858\pi$
$500$	1.06570e12	0.762552
$501$	2.63117e11	0.186586
$502$	−1.41257e12	−0.992760
$503$	−4.11652e11	−0.286731	−0.143365	−	0.989670i	$-0.545792\pi$
$503$	−4.11652e11	−0.286731	−0.143365	+	0.989670i	$0.545792\pi$
$504$	2.05845e11	0.142103
$505$	−2.69544e12	−1.84424
$506$	3.04634e12	2.06586
$507$	−1.36076e11	−0.0914632
$508$	−5.75956e11	−0.383710
$509$	2.25798e12	1.49104	0.745520	−	0.666483i	$-0.232201\pi$
$509$	2.25798e12	1.49104	0.745520	+	0.666483i	$0.232201\pi$
$510$	−6.76414e12	−4.42738
$511$	6.20945e11	0.402864
$512$	3.45285e11	0.222056
$513$	−1.40675e12	−0.896784
$514$	3.18308e12	2.01147
$515$	7.92323e11	0.496329
$516$	−4.75119e12	−2.95039
$517$	7.12625e10	0.0438686
$518$	6.30385e11	0.384700
$519$	−1.80323e12	−1.09094
$520$	−6.39927e11	−0.383809
$521$	4.60392e11	0.273752	0.136876	−	0.990588i	$-0.456294\pi$
$521$	4.60392e11	0.273752	0.136876	+	0.990588i	$0.456294\pi$
$522$	−9.95734e11	−0.586984
$523$	−2.63675e12	−1.54103	−0.770516	−	0.637421i	$-0.780001\pi$
$523$	−2.63675e12	−1.54103	−0.770516	+	0.637421i	$0.780001\pi$
$524$	−1.28126e12	−0.742413
$525$	−1.03221e12	−0.592994
$526$	−3.55040e12	−2.02228
$527$	2.52173e11	0.142414
$528$	2.09763e11	0.117456
$529$	1.99838e12	1.10950
$530$	1.70731e12	0.939875
$531$	9.43772e11	0.515160
$532$	−1.40794e12	−0.762049
$533$	−7.83273e11	−0.420379
$534$	2.04083e12	1.08610
$535$	−1.47925e12	−0.780636
$536$	−2.59754e12	−1.35932
$537$	2.11800e12	1.09911
$538$	−2.80600e12	−1.44400
$539$	2.48508e11	0.126821
$540$	3.28719e12	1.66361
$541$	−2.33082e11	−0.116982	−0.0584912	−	0.998288i	$-0.518629\pi$
$541$	−2.33082e11	−0.116982	−0.0584912	+	0.998288i	$0.518629\pi$
$542$	3.40468e12	1.69465
$543$	−3.18475e12	−1.57209
$544$	−3.38790e12	−1.65858
$545$	−2.49471e12	−1.21125
$546$	4.14723e11	0.199706
$547$	1.82746e12	0.872782	0.436391	−	0.899757i	$-0.356256\pi$
$547$	1.82746e12	0.872782	0.436391	+	0.899757i	$0.356256\pi$
$548$	2.62991e12	1.24574
$549$	1.05964e12	0.497833
$550$	4.02766e12	1.87681
$551$	2.46465e12	1.13913
$552$	−3.42291e12	−1.56917
$553$	−1.53353e12	−0.697315
$554$	1.37060e12	0.618182
$555$	−2.57131e12	−1.15037
$556$	−1.39187e12	−0.617679
$557$	−1.31844e12	−0.580379	−0.290190	−	0.956969i	$-0.593718\pi$
$557$	−1.31844e12	−0.580379	−0.290190	+	0.956969i	$0.593718\pi$
$558$	1.41695e11	0.0618727
$559$	−1.01384e12	−0.439155
$560$	−1.49071e11	−0.0640541
$561$	−3.77875e12	−1.61070
$562$	−6.35422e12	−2.68688
$563$	3.22229e12	1.35169	0.675845	−	0.737043i	$-0.263779\pi$
$563$	3.22229e12	1.35169	0.675845	+	0.737043i	$0.263779\pi$
$564$	−2.21264e11	−0.0920778
$565$	−6.62059e11	−0.273324
$566$	−6.02473e12	−2.46753
$567$	−1.15583e12	−0.469645
$568$	−4.31808e12	−1.74070
$569$	7.01148e11	0.280417	0.140209	−	0.990122i	$-0.455223\pi$
$569$	7.01148e11	0.280417	0.140209	+	0.990122i	$0.455223\pi$
$570$	9.40759e12	3.73286
$571$	2.49034e12	0.980385	0.490193	−	0.871614i	$-0.336926\pi$
$571$	2.49034e12	0.980385	0.490193	+	0.871614i	$0.336926\pi$
$572$	−9.87867e11	−0.385848
$573$	4.07778e12	1.58026
$574$	2.38720e12	0.917880
$575$	5.02349e12	1.91646
$576$	−1.78200e12	−0.674540
$577$	−1.62515e12	−0.610384	−0.305192	−	0.952291i	$-0.598721\pi$
$577$	−1.62515e12	−0.610384	−0.305192	+	0.952291i	$0.598721\pi$
$578$	5.71157e12	2.12853
$579$	−1.12012e12	−0.414202
$580$	−5.75923e12	−2.11319
$581$	3.72107e11	0.135480
$582$	3.28052e12	1.18519
$583$	9.53778e11	0.341931
$584$	2.72242e12	0.968496
$585$	−4.95096e11	−0.174778
$586$	−5.87546e12	−2.05827
$587$	3.20635e12	1.11465	0.557326	−	0.830294i	$-0.311827\pi$
$587$	3.20635e12	1.11465	0.557326	+	0.830294i	$0.311827\pi$
$588$	−7.71595e11	−0.266190
$589$	−3.50724e11	−0.120073
$590$	8.94197e12	3.03808
$591$	−1.94047e12	−0.654281
$592$	−2.11249e11	−0.0706882
$593$	5.88754e12	1.95518	0.977592	−	0.210510i	$-0.0675123\pi$
$593$	5.88754e12	1.95518	0.977592	+	0.210510i	$0.0675123\pi$
$594$	3.00819e12	0.991439
$595$	2.68542e12	0.878386
$596$	1.41530e12	0.459452
$597$	6.30128e12	2.03023
$598$	−2.01835e12	−0.645417
$599$	−2.71579e12	−0.861938	−0.430969	−	0.902367i	$-0.641828\pi$
$599$	−2.71579e12	−0.861938	−0.430969	+	0.902367i	$0.641828\pi$
$600$	−4.52554e12	−1.42557
$601$	2.54821e12	0.796709	0.398355	−	0.917232i	$-0.369581\pi$
$601$	2.54821e12	0.796709	0.398355	+	0.917232i	$0.369581\pi$
$602$	3.08992e12	0.958876
$603$	−2.00965e12	−0.619004
$604$	6.37998e12	1.95053
$605$	−1.06352e12	−0.322735
$606$	7.65879e12	2.30692
$607$	4.56076e11	0.136360	0.0681802	−	0.997673i	$-0.478281\pi$
$607$	4.56076e11	0.136360	0.0681802	+	0.997673i	$0.478281\pi$
$608$	4.71191e12	1.39840
$609$	1.35070e12	0.397908
$610$	1.00398e13	2.93590
$611$	−4.72149e10	−0.0137055
$612$	3.43384e12	0.989462
$613$	−2.43450e12	−0.696365	−0.348183	−	0.937427i	$-0.613201\pi$
$613$	−2.43450e12	−0.696365	−0.348183	+	0.937427i	$0.613201\pi$
$614$	6.62020e12	1.87981
$615$	−9.73728e12	−2.74473
$616$	1.08954e12	0.304880
$617$	2.93769e12	0.816062	0.408031	−	0.912968i	$-0.366216\pi$
$617$	2.93769e12	0.816062	0.408031	+	0.912968i	$0.366216\pi$
$618$	−2.25130e12	−0.620847
$619$	2.29646e12	0.628710	0.314355	−	0.949305i	$-0.398212\pi$
$619$	2.29646e12	0.628710	0.314355	+	0.949305i	$0.398212\pi$
$620$	8.19548e11	0.222747
$621$	3.75196e12	1.01238
$622$	1.01976e13	2.73176
$623$	−8.10226e11	−0.215481
$624$	−1.38978e11	−0.0366958
$625$	−2.20649e12	−0.578418
$626$	−7.27571e12	−1.89361
$627$	5.25550e12	1.35803
$628$	5.22652e12	1.34089
$629$	3.80552e12	0.969361
$630$	1.50892e12	0.381622
$631$	6.09950e12	1.53166	0.765829	−	0.643044i	$-0.222329\pi$
$631$	6.09950e12	1.53166	0.765829	+	0.643044i	$0.222329\pi$
$632$	−6.72349e12	−1.67636
$633$	−4.65645e11	−0.115276
$634$	3.23652e12	0.795566
$635$	−1.52786e12	−0.372907
$636$	−2.96140e12	−0.717695
$637$	−1.64648e11	−0.0396214
$638$	−5.27042e12	−1.25937
$639$	−3.34079e12	−0.792675
$640$	−9.85800e12	−2.32262
$641$	−1.88700e12	−0.441480	−0.220740	−	0.975333i	$-0.570847\pi$
$641$	−1.88700e12	−0.441480	−0.220740	+	0.975333i	$0.570847\pi$
$642$	4.20311e12	0.976481
$643$	−5.70855e12	−1.31697	−0.658485	−	0.752594i	$-0.728803\pi$
$643$	−5.70855e12	−1.31697	−0.658485	+	0.752594i	$0.728803\pi$
$644$	3.75515e12	0.860282
$645$	−1.26036e13	−2.86732
$646$	−1.39232e13	−3.14551
$647$	−6.03413e12	−1.35377	−0.676886	−	0.736088i	$-0.736671\pi$
$647$	−6.03413e12	−1.35377	−0.676886	+	0.736088i	$0.736671\pi$
$648$	−5.06753e12	−1.12904
$649$	4.99538e12	1.10527
$650$	−2.66852e12	−0.586355
$651$	−1.92207e11	−0.0419426
$652$	−1.68016e12	−0.364113
$653$	−3.28882e12	−0.707833	−0.353917	−	0.935277i	$-0.615150\pi$
$653$	−3.28882e12	−0.707833	−0.353917	+	0.935277i	$0.615150\pi$
$654$	7.08843e12	1.51513
$655$	−3.39883e12	−0.721511
$656$	−7.99979e11	−0.168660
$657$	2.10627e12	0.441032
$658$	1.43898e11	0.0299253
$659$	−1.29201e12	−0.266859	−0.133430	−	0.991058i	$-0.542599\pi$
$659$	−1.29201e12	−0.266859	−0.133430	+	0.991058i	$0.542599\pi$
$660$	−1.22807e13	−2.51927
$661$	−4.91713e12	−1.00186	−0.500928	−	0.865489i	$-0.667008\pi$
$661$	−4.91713e12	−1.00186	−0.500928	+	0.865489i	$0.667008\pi$
$662$	7.56229e12	1.53036
$663$	2.50361e12	0.503217
$664$	1.63144e12	0.325697
$665$	−3.73489e12	−0.740595
$666$	2.13829e12	0.421147
$667$	−6.57352e12	−1.28597
$668$	−1.26556e12	−0.245917
$669$	4.70441e12	0.908003
$670$	−1.90409e13	−3.65048
$671$	5.60869e12	1.06810
$672$	2.58227e12	0.488472
$673$	7.81572e12	1.46859	0.734296	−	0.678830i	$-0.237513\pi$
$673$	7.81572e12	1.46859	0.734296	+	0.678830i	$0.237513\pi$
$674$	1.31994e13	2.46368
$675$	4.96058e12	0.919741
$676$	6.54510e11	0.120547
$677$	−8.00743e12	−1.46502	−0.732511	−	0.680755i	$-0.761652\pi$
$677$	−8.00743e12	−1.46502	−0.732511	+	0.680755i	$0.761652\pi$
$678$	1.88116e12	0.341895
$679$	−1.30239e12	−0.235141
$680$	1.17737e13	2.11166
$681$	4.15633e12	0.740538
$682$	7.49989e11	0.132747
$683$	−6.26724e11	−0.110200	−0.0551002	−	0.998481i	$-0.517548\pi$
$683$	−6.26724e11	−0.110200	−0.0551002	+	0.998481i	$0.517548\pi$
$684$	−4.77581e12	−0.834246
$685$	6.97643e12	1.21067
$686$	5.01804e11	0.0865118
$687$	−7.70120e11	−0.131903
$688$	−1.03547e12	−0.176193
$689$	−6.31925e11	−0.106826
$690$	−2.50911e13	−4.21405
$691$	6.81882e12	1.13778	0.568890	−	0.822414i	$-0.307373\pi$
$691$	6.81882e12	1.13778	0.568890	+	0.822414i	$0.307373\pi$
$692$	8.67334e12	1.43783
$693$	8.42949e11	0.138836
$694$	−1.51896e13	−2.48559
$695$	−3.69226e12	−0.600289
$696$	5.92193e12	0.956580
$697$	1.44111e13	2.31286
$698$	4.26673e12	0.680371
$699$	5.87273e12	0.930450
$700$	4.96480e12	0.781557
$701$	−6.80541e12	−1.06444	−0.532222	−	0.846605i	$-0.678643\pi$
$701$	−6.80541e12	−1.06444	−0.532222	+	0.846605i	$0.678643\pi$
$702$	−1.99307e12	−0.309746
$703$	−5.29273e12	−0.817299
$704$	−9.43214e12	−1.44722
$705$	−5.86953e11	−0.0894855
$706$	−3.44171e11	−0.0521378
$707$	−3.04060e12	−0.457691
$708$	−1.55102e13	−2.31990
$709$	8.21818e12	1.22143	0.610714	−	0.791851i	$-0.290883\pi$
$709$	8.21818e12	1.22143	0.610714	+	0.791851i	$0.290883\pi$
$710$	−3.16530e13	−4.67469
$711$	−5.20180e12	−0.763379
$712$	−3.55229e12	−0.518023
$713$	9.35422e11	0.135552
$714$	−7.63031e12	−1.09875
$715$	−2.62054e12	−0.374985
$716$	−1.01873e13	−1.44861
$717$	5.12287e12	0.723898
$718$	8.01807e12	1.12593
$719$	−5.58560e12	−0.779453	−0.389726	−	0.920931i	$-0.627430\pi$
$719$	−5.58560e12	−0.779453	−0.389726	+	0.920931i	$0.627430\pi$
$720$	−5.05655e11	−0.0701226
$721$	8.93783e11	0.123175
$722$	7.66565e12	1.04986
$723$	1.09540e13	1.49091
$724$	1.53183e13	2.07198
$725$	−8.69105e12	−1.16829
$726$	3.02187e12	0.403702
$727$	1.11646e13	1.48231	0.741157	−	0.671332i	$-0.234278\pi$
$727$	1.11646e13	1.48231	0.741157	+	0.671332i	$0.234278\pi$
$728$	−7.21872e11	−0.0952509
$729$	2.39941e12	0.314652
$730$	1.99563e13	2.60092
$731$	1.86533e13	2.41616
$732$	−1.74145e13	−2.24187
$733$	3.62658e12	0.464013	0.232006	−	0.972714i	$-0.425471\pi$
$733$	3.62658e12	0.464013	0.232006	+	0.972714i	$0.425471\pi$
$734$	1.87175e13	2.38021
$735$	−2.04683e12	−0.258696
$736$	−1.25672e13	−1.57866
$737$	−1.06371e13	−1.32806
$738$	8.09750e12	1.00484
$739$	−6.28280e12	−0.774914	−0.387457	−	0.921888i	$-0.626646\pi$
$739$	−6.28280e12	−0.774914	−0.387457	+	0.921888i	$0.626646\pi$
$740$	1.23677e13	1.51616
$741$	−3.48203e12	−0.424278
$742$	1.92593e12	0.233251
$743$	−1.19933e13	−1.44374	−0.721872	−	0.692026i	$-0.756718\pi$
$743$	−1.19933e13	−1.44374	−0.721872	+	0.692026i	$0.756718\pi$
$744$	−8.42699e11	−0.100831
$745$	3.75441e12	0.446517
$746$	1.20623e13	1.42595
$747$	1.26220e12	0.148316
$748$	1.81753e13	2.12288
$749$	−1.66867e12	−0.193732
$750$	−8.03263e12	−0.927005
$751$	−1.51642e13	−1.73956	−0.869779	−	0.493441i	$-0.835739\pi$
$751$	−1.51642e13	−1.73956	−0.869779	+	0.493441i	$0.835739\pi$
$752$	−4.82219e10	−0.00549875
$753$	6.49964e12	0.736736
$754$	3.49191e12	0.393452
$755$	1.69243e13	1.89562
$756$	3.70812e12	0.412863
$757$	−9.26562e11	−0.102552	−0.0512758	−	0.998685i	$-0.516329\pi$
$757$	−9.26562e11	−0.102552	−0.0512758	+	0.998685i	$0.516329\pi$
$758$	−1.49034e13	−1.63973
$759$	−1.40170e13	−1.53309
$760$	−1.63750e13	−1.78041
$761$	1.47223e13	1.59128	0.795638	−	0.605772i	$-0.207136\pi$
$761$	1.47223e13	1.59128	0.795638	+	0.605772i	$0.207136\pi$
$762$	4.34123e12	0.466461
$763$	−2.81416e12	−0.300600
$764$	−1.96136e13	−2.08275
$765$	9.10905e12	0.961605
$766$	−2.66308e13	−2.79482
$767$	−3.30969e12	−0.345309
$768$	9.32251e12	0.966957
$769$	−5.00088e12	−0.515677	−0.257839	−	0.966188i	$-0.583010\pi$
$769$	−5.00088e12	−0.515677	−0.257839	+	0.966188i	$0.583010\pi$
$770$	7.98670e12	0.818764
$771$	−1.46462e13	−1.49273
$772$	5.38765e12	0.545911
$773$	−8.46485e12	−0.852730	−0.426365	−	0.904551i	$-0.640206\pi$
$773$	−8.46485e12	−0.852730	−0.426365	+	0.904551i	$0.640206\pi$
$774$	1.04811e13	1.04972
$775$	1.23675e12	0.123147
$776$	−5.71012e12	−0.565285
$777$	−2.90058e12	−0.285489
$778$	2.87578e13	2.81416
$779$	−2.00430e13	−1.95005
$780$	8.13656e12	0.787073
$781$	−1.76828e13	−1.70067
$782$	3.71347e13	3.55099
$783$	−6.49120e12	−0.617159
$784$	−1.68160e11	−0.0158965
$785$	1.38645e13	1.30314
$786$	9.65738e12	0.902522
$787$	4.37741e12	0.406753	0.203376	−	0.979101i	$-0.434808\pi$
$787$	4.37741e12	0.406753	0.203376	+	0.979101i	$0.434808\pi$
$788$	9.33344e12	0.862331
$789$	1.63364e13	1.50075
$790$	−4.92855e13	−4.50192
$791$	−7.46838e11	−0.0678316
$792$	3.69576e12	0.333765
$793$	−3.71603e12	−0.333695
$794$	9.89330e11	0.0883382
$795$	−7.85579e12	−0.697490
$796$	−3.03084e13	−2.67580
$797$	−4.41467e11	−0.0387558	−0.0193779	−	0.999812i	$-0.506169\pi$
$797$	−4.41467e11	−0.0387558	−0.0193779	+	0.999812i	$0.506169\pi$
$798$	1.06123e13	0.926393
$799$	8.68686e11	0.0754054
$800$	−1.66155e13	−1.43420
$801$	−2.74832e12	−0.235896
$802$	−1.44929e13	−1.23700
$803$	1.11485e13	0.946229
$804$	3.30273e13	2.78753
$805$	9.96139e12	0.836062
$806$	−4.96904e11	−0.0414730
$807$	1.29112e13	1.07161
$808$	−1.33310e13	−1.10030
$809$	9.18962e12	0.754274	0.377137	−	0.926157i	$-0.376909\pi$
$809$	9.18962e12	0.754274	0.377137	+	0.926157i	$0.376909\pi$
$810$	−3.71468e13	−3.03207
$811$	−2.42346e13	−1.96717	−0.983585	−	0.180447i	$-0.942246\pi$
$811$	−2.42346e13	−1.96717	−0.983585	+	0.180447i	$0.942246\pi$
$812$	−6.49672e12	−0.524436
$813$	−1.56659e13	−1.25761
$814$	1.13180e13	0.903565
$815$	−4.45701e12	−0.353862
$816$	2.55700e12	0.201895
$817$	−2.59430e13	−2.03714
$818$	−9.54341e12	−0.745270
$819$	−5.58495e11	−0.0433752
$820$	4.68351e13	3.61751
$821$	9.59483e12	0.737043	0.368522	−	0.929619i	$-0.379864\pi$
$821$	9.59483e12	0.737043	0.368522	+	0.929619i	$0.379864\pi$
$822$	−1.98227e13	−1.51440
$823$	8.78641e12	0.667594	0.333797	−	0.942645i	$-0.391670\pi$
$823$	8.78641e12	0.667594	0.333797	+	0.942645i	$0.391670\pi$
$824$	3.91864e12	0.296116
$825$	−1.85324e13	−1.39280
$826$	1.00870e13	0.753968
$827$	1.76469e13	1.31188	0.655941	−	0.754812i	$-0.272272\pi$
$827$	1.76469e13	1.31188	0.655941	+	0.754812i	$0.272272\pi$
$828$	1.27376e13	0.941785
$829$	−9.87352e12	−0.726067	−0.363033	−	0.931776i	$-0.618259\pi$
$829$	−9.87352e12	−0.726067	−0.363033	+	0.931776i	$0.618259\pi$
$830$	1.19590e13	0.874669
$831$	−6.30651e12	−0.458759
$832$	6.24926e12	0.452141
$833$	3.02929e12	0.217991
$834$	1.04911e13	0.750889
$835$	−3.35719e12	−0.238994
$836$	−2.52783e13	−1.78986
$837$	9.23708e11	0.0650534
$838$	−4.15942e13	−2.91363
$839$	5.54138e12	0.386090	0.193045	−	0.981190i	$-0.438164\pi$
$839$	5.54138e12	0.386090	0.193045	+	0.981190i	$0.438164\pi$
$840$	−8.97398e12	−0.621911
$841$	−3.13441e12	−0.216060
$842$	1.03658e13	0.710721
$843$	2.92375e13	1.99396
$844$	2.23970e12	0.151932
$845$	1.73624e12	0.117153
$846$	4.88109e11	0.0327605
$847$	−1.19971e12	−0.0800939
$848$	−6.45402e11	−0.0428597
$849$	2.77214e13	1.83118
$850$	4.90969e13	3.22604
$851$	1.41163e13	0.922654
$852$	5.49036e13	3.56962
$853$	−8.98490e12	−0.581089	−0.290545	−	0.956861i	$-0.593836\pi$
$853$	−8.98490e12	−0.581089	−0.290545	+	0.956861i	$0.593836\pi$
$854$	1.13254e13	0.728610
$855$	−1.26689e13	−0.810759
$856$	−7.31599e12	−0.465738
$857$	−2.42067e13	−1.53293	−0.766465	−	0.642287i	$-0.777986\pi$
$857$	−2.42067e13	−1.53293	−0.766465	+	0.642287i	$0.777986\pi$
$858$	7.44598e12	0.469060
$859$	2.19676e13	1.37662	0.688308	−	0.725418i	$-0.258354\pi$
$859$	2.19676e13	1.37662	0.688308	+	0.725418i	$0.258354\pi$
$860$	6.06219e13	3.77908
$861$	−1.09842e13	−0.681167
$862$	−3.30073e13	−2.03623
$863$	2.60407e13	1.59810	0.799050	−	0.601265i	$-0.205336\pi$
$863$	2.60407e13	1.59810	0.799050	+	0.601265i	$0.205336\pi$
$864$	−1.24098e13	−0.757625
$865$	2.30080e13	1.39735
$866$	2.40122e11	0.0145078
$867$	−2.62805e13	−1.57960
$868$	9.24494e11	0.0552796
$869$	−2.75331e13	−1.63782
$870$	4.34098e13	2.56892
$871$	7.04759e12	0.414915
$872$	−1.23382e13	−0.722650
$873$	−4.41778e12	−0.257419
$874$	−5.16471e13	−2.99395
$875$	3.18902e12	0.183917
$876$	−3.46151e13	−1.98608
$877$	2.27235e13	1.29711	0.648555	−	0.761168i	$-0.275374\pi$
$877$	2.27235e13	1.29711	0.648555	+	0.761168i	$0.275374\pi$
$878$	7.33083e12	0.416321
$879$	2.70346e13	1.52746
$880$	−2.67643e12	−0.150447
$881$	9.48493e12	0.530447	0.265224	−	0.964187i	$-0.414554\pi$
$881$	9.48493e12	0.530447	0.265224	+	0.964187i	$0.414554\pi$
$882$	1.70214e12	0.0947080
$883$	−1.50500e13	−0.833130	−0.416565	−	0.909106i	$-0.636766\pi$
$883$	−1.50500e13	−0.833130	−0.416565	+	0.909106i	$0.636766\pi$
$884$	−1.20420e13	−0.663231
$885$	−4.11445e13	−2.25459
$886$	3.75536e12	0.204739
$887$	1.05055e13	0.569851	0.284926	−	0.958550i	$-0.408031\pi$
$887$	1.05055e13	0.569851	0.284926	+	0.958550i	$0.408031\pi$
$888$	−1.27171e13	−0.686323
$889$	−1.72350e12	−0.0925452
$890$	−2.60395e13	−1.39116
$891$	−2.07519e13	−1.10308
$892$	−2.26276e13	−1.19673
$893$	−1.20817e12	−0.0635767
$894$	−1.06677e13	−0.558539
$895$	−2.70242e13	−1.40783
$896$	−1.11204e13	−0.576412
$897$	9.28697e12	0.478970
$898$	3.39199e13	1.74065
$899$	−1.61836e12	−0.0826335
$900$	1.68408e13	0.855602
$901$	1.16265e13	0.587743
$902$	4.28600e13	2.15587
$903$	−1.42176e13	−0.711591
$904$	−3.27438e12	−0.163069
$905$	4.06352e13	2.01365
$906$	−4.80886e13	−2.37119
$907$	2.00145e13	0.982001	0.491001	−	0.871159i	$-0.336631\pi$
$907$	2.00145e13	0.982001	0.491001	+	0.871159i	$0.336631\pi$
$908$	−1.99914e13	−0.976017
$909$	−1.03139e13	−0.501053
$910$	−5.29158e12	−0.255799
$911$	−1.18505e13	−0.570038	−0.285019	−	0.958522i	$-0.592000\pi$
$911$	−1.18505e13	−0.570038	−0.285019	+	0.958522i	$0.592000\pi$
$912$	−3.55629e12	−0.170224
$913$	6.68084e12	0.318209
$914$	−5.55953e13	−2.63500
$915$	−4.61959e13	−2.17876
$916$	3.70419e12	0.173845
$917$	−3.83406e12	−0.179059
$918$	3.66697e13	1.70418
$919$	2.15844e13	0.998206	0.499103	−	0.866543i	$-0.333663\pi$
$919$	2.15844e13	0.998206	0.499103	+	0.866543i	$0.333663\pi$
$920$	4.36740e13	2.00991
$921$	−3.04614e13	−1.39502
$922$	9.52163e12	0.433933
$923$	1.17157e13	0.531326
$924$	−1.38533e13	−0.625214
$925$	1.86636e13	0.838221
$926$	3.18587e13	1.42390
$927$	3.03175e12	0.134845
$928$	2.17423e13	0.962367
$929$	−1.61104e13	−0.709638	−0.354819	−	0.934935i	$-0.615457\pi$
$929$	−1.61104e13	−0.709638	−0.354819	+	0.934935i	$0.615457\pi$
$930$	−6.17728e12	−0.270785
$931$	−4.21316e12	−0.183795
$932$	−2.82471e13	−1.22632
$933$	−4.69221e13	−2.02726
$934$	3.20810e13	1.37939
$935$	4.82142e13	2.06311
$936$	−2.44862e12	−0.104275
$937$	2.92171e13	1.23825	0.619126	−	0.785291i	$-0.287487\pi$
$937$	2.92171e13	1.23825	0.619126	+	0.785291i	$0.287487\pi$
$938$	−2.14791e13	−0.905950
$939$	3.34776e13	1.40527
$940$	2.82317e12	0.117940
$941$	1.55829e13	0.647882	0.323941	−	0.946077i	$-0.394992\pi$
$941$	1.55829e13	0.647882	0.323941	+	0.946077i	$0.394992\pi$
$942$	−3.93945e13	−1.63007
$943$	5.34571e13	2.20142
$944$	−3.38027e12	−0.138541
$945$	9.83664e12	0.401240
$946$	5.54766e13	2.25216
$947$	3.01152e13	1.21677	0.608387	−	0.793640i	$-0.291817\pi$
$947$	3.01152e13	1.21677	0.608387	+	0.793640i	$0.291817\pi$
$948$	8.54880e13	3.43770
$949$	−7.38642e12	−0.295622
$950$	−6.82842e13	−2.71997
$951$	−1.48921e13	−0.590397
$952$	1.32814e13	0.524056
$953$	−2.09287e13	−0.821908	−0.410954	−	0.911656i	$-0.634804\pi$
$953$	−2.09287e13	−0.821908	−0.410954	+	0.911656i	$0.634804\pi$
$954$	6.53285e12	0.255350
$955$	−5.20296e13	−2.02412
$956$	−2.46404e13	−0.954085
$957$	2.42507e13	0.934587
$958$	2.17071e12	0.0832641
$959$	7.86979e12	0.300455
$960$	7.76878e13	2.95211
$961$	−2.62093e13	−0.991290
$962$	−7.49872e12	−0.282292
$963$	−5.66020e12	−0.212087
$964$	−5.26874e13	−1.96499
$965$	1.42920e13	0.530541
$966$	−2.83042e13	−1.04581
$967$	−2.49667e13	−0.918209	−0.459104	−	0.888382i	$-0.651830\pi$
$967$	−2.49667e13	−0.918209	−0.459104	+	0.888382i	$0.651830\pi$
$968$	−5.25990e12	−0.192548
$969$	6.40643e13	2.33431
$970$	−4.18572e13	−1.51809
$971$	1.46151e13	0.527614	0.263807	−	0.964575i	$-0.415022\pi$
$971$	1.46151e13	0.527614	0.263807	+	0.964575i	$0.415022\pi$
$972$	3.40342e13	1.22297
$973$	−4.16507e12	−0.148975
$974$	1.14593e13	0.407984
$975$	1.22786e13	0.435139
$976$	−3.79528e12	−0.133881
$977$	1.49672e13	0.525552	0.262776	−	0.964857i	$-0.415362\pi$
$977$	1.49672e13	0.525552	0.262776	+	0.964857i	$0.415362\pi$
$978$	1.26641e13	0.442639
$979$	−1.45469e13	−0.506112
$980$	9.84501e12	0.340956
$981$	−9.54577e12	−0.329079
$982$	2.23246e13	0.766094
$983$	−5.93014e12	−0.202570	−0.101285	−	0.994857i	$-0.532295\pi$
$983$	−5.93014e12	−0.202570	−0.101285	+	0.994857i	$0.532295\pi$
$984$	−4.81582e13	−1.63754
$985$	2.47591e13	0.838053
$986$	−6.42461e13	−2.16472
$987$	−6.62115e11	−0.0222078
$988$	1.67481e13	0.559191
$989$	6.91931e13	2.29974
$990$	2.70912e13	0.896335
$991$	−2.39086e12	−0.0787451	−0.0393725	−	0.999225i	$-0.512536\pi$
$991$	−2.39086e12	−0.0787451	−0.0393725	+	0.999225i	$0.512536\pi$
$992$	−3.09397e12	−0.101441
$993$	−3.47962e13	−1.13569
$994$	−3.57063e13	−1.16013
$995$	−8.03999e13	−2.60047
$996$	−2.07434e13	−0.667904
$997$	−1.77355e13	−0.568481	−0.284241	−	0.958753i	$-0.591741\pi$
$997$	−1.77355e13	−0.568481	−0.284241	+	0.958753i	$0.591741\pi$
$998$	−8.78285e13	−2.80252
$999$	1.39396e13	0.442797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.13	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+36.2541 q^{2} -166.815 q^{3} +802.361 q^{4} +2128.44 q^{5} -6047.74 q^{6} +2401.00 q^{7} +10526.8 q^{8} +8144.30 q^{9} +O(q^{10})\)	\(q+36.2541 q^{2} -166.815 q^{3} +802.361 q^{4} +2128.44 q^{5} -6047.74 q^{6} +2401.00 q^{7} +10526.8 q^{8} +8144.30 q^{9} +77164.9 q^{10} +43107.8 q^{11} -133846. q^{12} -28561.0 q^{13} +87046.1 q^{14} -355057. q^{15} -29170.1 q^{16} +525481. q^{17} +295264. q^{18} -730842. q^{19} +1.70778e6 q^{20} -400523. q^{21} +1.56283e6 q^{22} +1.94924e6 q^{23} -1.75602e6 q^{24} +2.57715e6 q^{25} -1.03545e6 q^{26} +1.92483e6 q^{27} +1.92647e6 q^{28} -3.37235e6 q^{29} -1.28723e7 q^{30} +479891. q^{31} -6.44724e6 q^{32} -7.19103e6 q^{33} +1.90509e7 q^{34} +5.11040e6 q^{35} +6.53466e6 q^{36} +7.24197e6 q^{37} -2.64960e7 q^{38} +4.76441e6 q^{39} +2.24056e7 q^{40} +2.74246e7 q^{41} -1.45206e7 q^{42} +3.54975e7 q^{43} +3.45880e7 q^{44} +1.73347e7 q^{45} +7.06680e7 q^{46} +1.65313e6 q^{47} +4.86602e6 q^{48} +5.76480e6 q^{49} +9.34323e7 q^{50} -8.76582e7 q^{51} -2.29162e7 q^{52} +2.21254e7 q^{53} +6.97830e7 q^{54} +9.17525e7 q^{55} +2.52748e7 q^{56} +1.21916e8 q^{57} -1.22262e8 q^{58} +1.15881e8 q^{59} -2.84884e8 q^{60} +1.30109e8 q^{61} +1.73980e7 q^{62} +1.95545e7 q^{63} -2.18804e8 q^{64} -6.07905e7 q^{65} -2.60704e8 q^{66} -2.46756e8 q^{67} +4.21625e8 q^{68} -3.25163e8 q^{69} +1.85273e8 q^{70} -4.10200e8 q^{71} +8.57331e7 q^{72} +2.58619e8 q^{73} +2.62551e8 q^{74} -4.29908e8 q^{75} -5.86399e8 q^{76} +1.03502e8 q^{77} +1.72729e8 q^{78} -6.38704e8 q^{79} -6.20870e7 q^{80} -4.81395e8 q^{81} +9.94254e8 q^{82} +1.54980e8 q^{83} -3.21364e8 q^{84} +1.11846e9 q^{85} +1.28693e9 q^{86} +5.62559e8 q^{87} +4.53785e8 q^{88} -3.37453e8 q^{89} +6.28454e8 q^{90} -6.85750e7 q^{91} +1.56399e9 q^{92} -8.00530e7 q^{93} +5.99326e7 q^{94} -1.55556e9 q^{95} +1.07550e9 q^{96} -5.42438e8 q^{97} +2.08998e8 q^{98} +3.51082e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 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

L-functions

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