LMFDB - Embedded newform 91.10.a.c.1.2

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			1.2
Root			$33.1611$ 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)

$f(q)$	$=$	$q-31.1611 q^{2} -183.696 q^{3} +459.017 q^{4} -1660.96 q^{5} +5724.18 q^{6} +2401.00 q^{7} +1651.02 q^{8} +14061.3 q^{9} +O(q^{10})$	\(q-31.1611 q^{2} -183.696 q^{3} +459.017 q^{4} -1660.96 q^{5} +5724.18 q^{6} +2401.00 q^{7} +1651.02 q^{8} +14061.3 q^{9} +51757.3 q^{10} -2168.88 q^{11} -84319.6 q^{12} -28561.0 q^{13} -74817.9 q^{14} +305111. q^{15} -286464. q^{16} +32976.9 q^{17} -438165. q^{18} -448123. q^{19} -762407. q^{20} -441054. q^{21} +67584.9 q^{22} -708849. q^{23} -303286. q^{24} +805651. q^{25} +889993. q^{26} +1.03269e6 q^{27} +1.10210e6 q^{28} -7.50446e6 q^{29} -9.50762e6 q^{30} -8.49151e6 q^{31} +8.08123e6 q^{32} +398415. q^{33} -1.02760e6 q^{34} -3.98796e6 q^{35} +6.45436e6 q^{36} -1.77529e7 q^{37} +1.39640e7 q^{38} +5.24655e6 q^{39} -2.74228e6 q^{40} +2.82963e6 q^{41} +1.37438e7 q^{42} -4.58688e6 q^{43} -995553. q^{44} -2.33552e7 q^{45} +2.20885e7 q^{46} -3.19968e7 q^{47} +5.26224e7 q^{48} +5.76480e6 q^{49} -2.51050e7 q^{50} -6.05773e6 q^{51} -1.31100e7 q^{52} -1.83900e7 q^{53} -3.21798e7 q^{54} +3.60242e6 q^{55} +3.96411e6 q^{56} +8.23185e7 q^{57} +2.33847e8 q^{58} +1.45660e8 q^{59} +1.40051e8 q^{60} -1.05246e7 q^{61} +2.64605e8 q^{62} +3.37611e7 q^{63} -1.05151e8 q^{64} +4.74386e7 q^{65} -1.24151e7 q^{66} -3.52331e7 q^{67} +1.51369e7 q^{68} +1.30213e8 q^{69} +1.24269e8 q^{70} -2.70612e7 q^{71} +2.32155e7 q^{72} -3.20807e8 q^{73} +5.53201e8 q^{74} -1.47995e8 q^{75} -2.05696e8 q^{76} -5.20749e6 q^{77} -1.63488e8 q^{78} -3.48283e8 q^{79} +4.75805e8 q^{80} -4.66469e8 q^{81} -8.81745e7 q^{82} -1.46829e8 q^{83} -2.02451e8 q^{84} -5.47732e7 q^{85} +1.42932e8 q^{86} +1.37854e9 q^{87} -3.58087e6 q^{88} -3.59036e8 q^{89} +7.27773e8 q^{90} -6.85750e7 q^{91} -3.25373e8 q^{92} +1.55986e9 q^{93} +9.97057e8 q^{94} +7.44313e8 q^{95} -1.48449e9 q^{96} -1.04226e9 q^{97} -1.79638e8 q^{98} -3.04973e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−31.1611	−1.37714	−0.688570	−	0.725169i	$-0.741761\pi$
$2$	−31.1611	−1.37714	−0.688570	+	0.725169i	$0.741761\pi$
$3$	−183.696	−1.30935	−0.654673	−	0.755912i	$-0.727194\pi$
$3$	−183.696	−1.30935	−0.654673	+	0.755912i	$0.727194\pi$
$4$	459.017	0.896517
$5$	−1660.96	−1.18848	−0.594242	−	0.804286i	$-0.702548\pi$
$5$	−1660.96	−1.18848	−0.594242	+	0.804286i	$0.702548\pi$
$6$	5724.18	1.80315
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	1651.02	0.142511
$9$	14061.3	0.714387
$10$	51757.3	1.63671
$11$	−2168.88	−0.0446652	−0.0223326	−	0.999751i	$-0.507109\pi$
$11$	−2168.88	−0.0446652	−0.0223326	+	0.999751i	$0.507109\pi$
$12$	−84319.6	−1.17385
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−74817.9	−0.520510
$15$	305111.	1.55614
$16$	−286464.	−1.09277
$17$	32976.9	0.0957612	0.0478806	−	0.998853i	$-0.484753\pi$
$17$	32976.9	0.0957612	0.0478806	+	0.998853i	$0.484753\pi$
$18$	−438165.	−0.983811
$19$	−448123.	−0.788871	−0.394436	−	0.918924i	$-0.629060\pi$
$19$	−448123.	−0.788871	−0.394436	+	0.918924i	$0.629060\pi$
$20$	−762407.	−1.06550
$21$	−441054.	−0.494886
$22$	67584.9	0.0615102
$23$	−708849.	−0.528175	−0.264088	−	0.964499i	$-0.585071\pi$
$23$	−708849.	−0.528175	−0.264088	+	0.964499i	$0.585071\pi$
$24$	−303286.	−0.186596
$25$	805651.	0.412493
$26$	889993.	0.381950
$27$	1.03269e6	0.373967
$28$	1.10210e6	0.338852
$29$	−7.50446e6	−1.97028	−0.985141	−	0.171748i	$-0.945059\pi$
$29$	−7.50446e6	−1.97028	−0.985141	+	0.171748i	$0.945059\pi$
$30$	−9.50762e6	−2.14302
$31$	−8.49151e6	−1.65142	−0.825710	−	0.564095i	$-0.809225\pi$
$31$	−8.49151e6	−1.65142	−0.825710	+	0.564095i	$0.809225\pi$
$32$	8.08123e6	1.36239
$33$	398415.	0.0584822
$34$	−1.02760e6	−0.131877
$35$	−3.98796e6	−0.449205
$36$	6.45436e6	0.640460
$37$	−1.77529e7	−1.55726	−0.778632	−	0.627481i	$-0.784086\pi$
$37$	−1.77529e7	−1.55726	−0.778632	+	0.627481i	$0.784086\pi$
$38$	1.39640e7	1.08639
$39$	5.24655e6	0.363147
$40$	−2.74228e6	−0.169372
$41$	2.82963e6	0.156388	0.0781938	−	0.996938i	$-0.475085\pi$
$41$	2.82963e6	0.156388	0.0781938	+	0.996938i	$0.475085\pi$
$42$	1.37438e7	0.681528
$43$	−4.58688e6	−0.204602	−0.102301	−	0.994754i	$-0.532620\pi$
$43$	−4.58688e6	−0.204602	−0.102301	+	0.994754i	$0.532620\pi$
$44$	−995553.	−0.0400431
$45$	−2.33552e7	−0.849037
$46$	2.20885e7	0.727372
$47$	−3.19968e7	−0.956459	−0.478230	−	0.878235i	$-0.658721\pi$
$47$	−3.19968e7	−0.956459	−0.478230	+	0.878235i	$0.658721\pi$
$48$	5.26224e7	1.43082
$49$	5.76480e6	0.142857
$50$	−2.51050e7	−0.568061
$51$	−6.05773e6	−0.125385
$52$	−1.31100e7	−0.248649
$53$	−1.83900e7	−0.320141	−0.160070	−	0.987106i	$-0.551172\pi$
$53$	−1.83900e7	−0.320141	−0.160070	+	0.987106i	$0.551172\pi$
$54$	−3.21798e7	−0.515005
$55$	3.60242e6	0.0530838
$56$	3.96411e6	0.0538641
$57$	8.23185e7	1.03291
$58$	2.33847e8	2.71336
$59$	1.45660e8	1.56497	0.782487	−	0.622667i	$-0.213951\pi$
$59$	1.45660e8	1.56497	0.782487	+	0.622667i	$0.213951\pi$
$60$	1.40051e8	1.39510
$61$	−1.05246e7	−0.0973247	−0.0486624	−	0.998815i	$-0.515496\pi$
$61$	−1.05246e7	−0.0973247	−0.0486624	+	0.998815i	$0.515496\pi$
$62$	2.64605e8	2.27424
$63$	3.37611e7	0.270013
$64$	−1.05151e8	−0.783433
$65$	4.74386e7	0.329626
$66$	−1.24151e7	−0.0805382
$67$	−3.52331e7	−0.213606	−0.106803	−	0.994280i	$-0.534061\pi$
$67$	−3.52331e7	−0.213606	−0.106803	+	0.994280i	$0.534061\pi$
$68$	1.51369e7	0.0858515
$69$	1.30213e8	0.691564
$70$	1.24269e8	0.618618
$71$	−2.70612e7	−0.126382	−0.0631908	−	0.998001i	$-0.520128\pi$
$71$	−2.70612e7	−0.126382	−0.0631908	+	0.998001i	$0.520128\pi$
$72$	2.32155e7	0.101808
$73$	−3.20807e8	−1.32218	−0.661090	−	0.750306i	$-0.729906\pi$
$73$	−3.20807e8	−1.32218	−0.661090	+	0.750306i	$0.729906\pi$
$74$	5.53201e8	2.14457
$75$	−1.47995e8	−0.540096
$76$	−2.05696e8	−0.707236
$77$	−5.20749e6	−0.0168818
$78$	−1.63488e8	−0.500105
$79$	−3.48283e8	−1.00603	−0.503014	−	0.864278i	$-0.667776\pi$
$79$	−3.48283e8	−1.00603	−0.503014	+	0.864278i	$0.667776\pi$
$80$	4.75805e8	1.29874
$81$	−4.66469e8	−1.20404
$82$	−8.81745e7	−0.215368
$83$	−1.46829e8	−0.339593	−0.169797	−	0.985479i	$-0.554311\pi$
$83$	−1.46829e8	−0.339593	−0.169797	+	0.985479i	$0.554311\pi$
$84$	−2.02451e8	−0.443674
$85$	−5.47732e7	−0.113811
$86$	1.42932e8	0.281765
$87$	1.37854e9	2.57978
$88$	−3.58087e6	−0.00636527
$89$	−3.59036e8	−0.606573	−0.303286	−	0.952899i	$-0.598084\pi$
$89$	−3.59036e8	−0.606573	−0.303286	+	0.952899i	$0.598084\pi$
$90$	7.27773e8	1.16924
$91$	−6.85750e7	−0.104828
$92$	−3.25373e8	−0.473518
$93$	1.55986e9	2.16228
$94$	9.97057e8	1.31718
$95$	7.44313e8	0.937561
$96$	−1.48449e9	−1.78384
$97$	−1.04226e9	−1.19537	−0.597687	−	0.801729i	$-0.703914\pi$
$97$	−1.04226e9	−1.19537	−0.597687	+	0.801729i	$0.703914\pi$
$98$	−1.79638e8	−0.196734
$99$	−3.04973e7	−0.0319082
$100$	3.69807e8	0.369807
$101$	1.84467e9	1.76389	0.881947	−	0.471348i	$-0.156232\pi$
$101$	1.84467e9	1.76389	0.881947	+	0.471348i	$0.156232\pi$
$102$	1.88766e8	0.172672
$103$	−2.94224e8	−0.257579	−0.128790	−	0.991672i	$-0.541109\pi$
$103$	−2.94224e8	−0.257579	−0.128790	+	0.991672i	$0.541109\pi$
$104$	−4.71549e7	−0.0395254
$105$	7.32572e8	0.588164
$106$	5.73054e8	0.440879
$107$	−1.05501e9	−0.778093	−0.389046	−	0.921218i	$-0.627195\pi$
$107$	−1.05501e9	−0.778093	−0.389046	+	0.921218i	$0.627195\pi$
$108$	4.74022e8	0.335267
$109$	7.00451e7	0.0475290	0.0237645	−	0.999718i	$-0.492435\pi$
$109$	7.00451e7	0.0475290	0.0237645	+	0.999718i	$0.492435\pi$
$110$	−1.12256e8	−0.0731039
$111$	3.26114e9	2.03900
$112$	−6.87801e8	−0.413030
$113$	−2.22556e9	−1.28406	−0.642030	−	0.766679i	$-0.721908\pi$
$113$	−2.22556e9	−1.28406	−0.642030	+	0.766679i	$0.721908\pi$
$114$	−2.56514e9	−1.42246
$115$	1.17737e9	0.627728
$116$	−3.44467e9	−1.76639
$117$	−4.01604e8	−0.198135
$118$	−4.53894e9	−2.15519
$119$	7.91775e7	0.0361943
$120$	5.03746e8	0.221766
$121$	−2.35324e9	−0.998005
$122$	3.27960e8	0.134030
$123$	−5.19792e8	−0.204765
$124$	−3.89775e9	−1.48053
$125$	1.90590e9	0.698242
$126$	−1.05203e9	−0.371846
$127$	−5.19626e9	−1.77245	−0.886225	−	0.463254i	$-0.846682\pi$
$127$	−5.19626e9	−1.77245	−0.886225	+	0.463254i	$0.846682\pi$
$128$	−8.60977e8	−0.283496
$129$	8.42591e8	0.267894
$130$	−1.47824e9	−0.453941
$131$	−1.68134e9	−0.498811	−0.249405	−	0.968399i	$-0.580235\pi$
$131$	−1.68134e9	−0.498811	−0.249405	+	0.968399i	$0.580235\pi$
$132$	1.82879e8	0.0524302
$133$	−1.07594e9	−0.298165
$134$	1.09790e9	0.294166
$135$	−1.71525e9	−0.444453
$136$	5.44456e7	0.0136470
$137$	−6.67999e9	−1.62007	−0.810034	−	0.586383i	$-0.800552\pi$
$137$	−6.67999e9	−1.62007	−0.810034	+	0.586383i	$0.800552\pi$
$138$	−4.05758e9	−0.952382
$139$	2.74649e9	0.624039	0.312019	−	0.950076i	$-0.398995\pi$
$139$	2.74649e9	0.624039	0.312019	+	0.950076i	$0.398995\pi$
$140$	−1.83054e9	−0.402719
$141$	5.87769e9	1.25234
$142$	8.43257e8	0.174045
$143$	6.19455e7	0.0123879
$144$	−4.02805e9	−0.780664
$145$	1.24646e10	2.34165
$146$	9.99671e9	1.82083
$147$	−1.05897e9	−0.187049
$148$	−8.14889e9	−1.39611
$149$	3.95604e9	0.657540	0.328770	−	0.944410i	$-0.393366\pi$
$149$	3.95604e9	0.657540	0.328770	+	0.944410i	$0.393366\pi$
$150$	4.61169e9	0.743789
$151$	−3.00865e9	−0.470951	−0.235475	−	0.971880i	$-0.575665\pi$
$151$	−3.00865e9	−0.470951	−0.235475	+	0.971880i	$0.575665\pi$
$152$	−7.39861e8	−0.112423
$153$	4.63697e8	0.0684105
$154$	1.62271e8	0.0232487
$155$	1.41040e10	1.96269
$156$	2.40825e9	0.325568
$157$	−1.49559e9	−0.196456	−0.0982280	−	0.995164i	$-0.531317\pi$
$157$	−1.49559e9	−0.196456	−0.0982280	+	0.995164i	$0.531317\pi$
$158$	1.08529e10	1.38544
$159$	3.37818e9	0.419175
$160$	−1.34226e10	−1.61918
$161$	−1.70195e9	−0.199632
$162$	1.45357e10	1.65813
$163$	2.89358e9	0.321064	0.160532	−	0.987031i	$-0.448679\pi$
$163$	2.89358e9	0.321064	0.160532	+	0.987031i	$0.448679\pi$
$164$	1.29885e9	0.140204
$165$	−6.61751e8	−0.0695051
$166$	4.57535e9	0.467668
$167$	6.58005e9	0.654644	0.327322	−	0.944913i	$-0.393854\pi$
$167$	6.58005e9	0.654644	0.327322	+	0.944913i	$0.393854\pi$
$168$	−7.28191e8	−0.0705267
$169$	8.15731e8	0.0769231
$170$	1.70680e9	0.156733
$171$	−6.30118e9	−0.563559
$172$	−2.10545e9	−0.183429
$173$	6.76816e9	0.574464	0.287232	−	0.957861i	$-0.407265\pi$
$173$	6.76816e9	0.574464	0.287232	+	0.957861i	$0.407265\pi$
$174$	−4.29569e10	−3.55272
$175$	1.93437e9	0.155908
$176$	6.21307e8	0.0488090
$177$	−2.67572e10	−2.04909
$178$	1.11880e10	0.835336
$179$	−4.69441e9	−0.341777	−0.170888	−	0.985290i	$-0.554664\pi$
$179$	−4.69441e9	−0.341777	−0.170888	+	0.985290i	$0.554664\pi$
$180$	−1.07204e10	−0.761176
$181$	5.31928e9	0.368383	0.184191	−	0.982890i	$-0.441033\pi$
$181$	5.31928e9	0.368383	0.184191	+	0.982890i	$0.441033\pi$
$182$	2.13687e9	0.144364
$183$	1.93334e9	0.127432
$184$	−1.17033e9	−0.0752708
$185$	2.94868e10	1.85078
$186$	−4.86070e10	−2.97776
$187$	−7.15230e7	−0.00427719
$188$	−1.46871e10	−0.857482
$189$	2.47949e9	0.141346
$190$	−2.31936e10	−1.29115
$191$	1.23028e10	0.668888	0.334444	−	0.942416i	$-0.391451\pi$
$191$	1.23028e10	0.668888	0.334444	+	0.942416i	$0.391451\pi$
$192$	1.93158e10	1.02578
$193$	−5.33716e9	−0.276887	−0.138443	−	0.990370i	$-0.544210\pi$
$193$	−5.33716e9	−0.276887	−0.138443	+	0.990370i	$0.544210\pi$
$194$	3.24781e10	1.64620
$195$	−8.71428e9	−0.431595
$196$	2.64614e9	0.128074
$197$	2.81913e10	1.33357	0.666786	−	0.745249i	$-0.267670\pi$
$197$	2.81913e10	1.33357	0.666786	+	0.745249i	$0.267670\pi$
$198$	9.50329e8	0.0439421
$199$	2.59177e10	1.17154	0.585772	−	0.810476i	$-0.300791\pi$
$199$	2.59177e10	1.17154	0.585772	+	0.810476i	$0.300791\pi$
$200$	1.33015e9	0.0587848
$201$	6.47218e9	0.279685
$202$	−5.74820e10	−2.42913
$203$	−1.80182e10	−0.744697
$204$	−2.78060e9	−0.112409
$205$	−4.69989e9	−0.185864
$206$	9.16836e9	0.354723
$207$	−9.96731e9	−0.377322
$208$	8.18171e9	0.303081
$209$	9.71927e8	0.0352351
$210$	−2.28278e10	−0.809985
$211$	4.18680e10	1.45416	0.727079	−	0.686554i	$-0.240877\pi$
$211$	4.18680e10	1.45416	0.727079	+	0.686554i	$0.240877\pi$
$212$	−8.44133e9	−0.287012
$213$	4.97103e9	0.165477
$214$	3.28754e10	1.07154
$215$	7.61860e9	0.243166
$216$	1.70499e9	0.0532943
$217$	−2.03881e10	−0.624178
$218$	−2.18269e9	−0.0654541
$219$	5.89310e10	1.73119
$220$	1.65357e9	0.0475905
$221$	−9.41853e8	−0.0265594
$222$	−1.01621e11	−2.80799
$223$	−2.89900e9	−0.0785013	−0.0392506	−	0.999229i	$-0.512497\pi$
$223$	−2.89900e9	−0.0785013	−0.0392506	+	0.999229i	$0.512497\pi$
$224$	1.94030e10	0.514936
$225$	1.13285e10	0.294680
$226$	6.93509e10	1.76833
$227$	3.64280e10	0.910582	0.455291	−	0.890343i	$-0.349535\pi$
$227$	3.64280e10	0.910582	0.455291	+	0.890343i	$0.349535\pi$
$228$	3.77856e10	0.926017
$229$	−5.37091e10	−1.29059	−0.645295	−	0.763933i	$-0.723266\pi$
$229$	−5.37091e10	−1.29059	−0.645295	+	0.763933i	$0.723266\pi$
$230$	−3.66881e10	−0.864470
$231$	9.56595e8	0.0221042
$232$	−1.23900e10	−0.280787
$233$	−5.21834e10	−1.15993	−0.579963	−	0.814643i	$-0.696933\pi$
$233$	−5.21834e10	−1.15993	−0.579963	+	0.814643i	$0.696933\pi$
$234$	1.25144e10	0.272860
$235$	5.31453e10	1.13674
$236$	6.68605e10	1.40303
$237$	6.39782e10	1.31724
$238$	−2.46726e9	−0.0498447
$239$	1.56130e10	0.309524	0.154762	−	0.987952i	$-0.450539\pi$
$239$	1.56130e10	0.309524	0.154762	+	0.987952i	$0.450539\pi$
$240$	−8.74035e10	−1.70051
$241$	1.79029e10	0.341859	0.170930	−	0.985283i	$-0.445323\pi$
$241$	1.79029e10	0.341859	0.170930	+	0.985283i	$0.445323\pi$
$242$	7.33298e10	1.37439
$243$	6.53622e10	1.20254
$244$	−4.83099e9	−0.0872533
$245$	−9.57508e9	−0.169783
$246$	1.61973e10	0.281991
$247$	1.27988e10	0.218794
$248$	−1.40197e10	−0.235345
$249$	2.69718e10	0.444645
$250$	−5.93901e10	−0.961578
$251$	−1.11916e11	−1.77976	−0.889878	−	0.456199i	$-0.849211\pi$
$251$	−1.11916e11	−1.77976	−0.889878	+	0.456199i	$0.849211\pi$
$252$	1.54969e10	0.242071
$253$	1.53741e9	0.0235910
$254$	1.61921e11	2.44091
$255$	1.00616e10	0.149017
$256$	8.06661e10	1.17385
$257$	−1.00270e11	−1.43375	−0.716874	−	0.697203i	$-0.754428\pi$
$257$	−1.00270e11	−1.43375	−0.716874	+	0.697203i	$0.754428\pi$
$258$	−2.62561e10	−0.368928
$259$	−4.26248e10	−0.588590
$260$	2.17751e10	0.295515
$261$	−1.05522e11	−1.40754
$262$	5.23926e10	0.686933
$263$	9.81760e10	1.26533	0.632666	−	0.774425i	$-0.281961\pi$
$263$	9.81760e10	1.26533	0.632666	+	0.774425i	$0.281961\pi$
$264$	6.57793e8	0.00833435
$265$	3.05450e10	0.380482
$266$	3.35276e10	0.410616
$267$	6.59535e10	0.794214
$268$	−1.61726e10	−0.191502
$269$	1.06526e11	1.24043	0.620213	−	0.784433i	$-0.287046\pi$
$269$	1.06526e11	1.24043	0.620213	+	0.784433i	$0.287046\pi$
$270$	5.34492e10	0.612075
$271$	−9.45652e10	−1.06505	−0.532525	−	0.846415i	$-0.678757\pi$
$271$	−9.45652e10	−1.06505	−0.532525	+	0.846415i	$0.678757\pi$
$272$	−9.44670e9	−0.104645
$273$	1.25970e10	0.137257
$274$	2.08156e11	2.23106
$275$	−1.74736e9	−0.0184241
$276$	5.97698e10	0.619999
$277$	−2.28335e8	−0.00233031	−0.00116515	−	0.999999i	$-0.500371\pi$
$277$	−2.28335e8	−0.00233031	−0.00116515	+	0.999999i	$0.500371\pi$
$278$	−8.55838e10	−0.859389
$279$	−1.19402e11	−1.17975
$280$	−6.58421e9	−0.0640166
$281$	2.74740e10	0.262871	0.131436	−	0.991325i	$-0.458041\pi$
$281$	2.74740e10	0.262871	0.131436	+	0.991325i	$0.458041\pi$
$282$	−1.83156e11	−1.72464
$283$	−2.21355e10	−0.205140	−0.102570	−	0.994726i	$-0.532707\pi$
$283$	−2.21355e10	−0.205140	−0.102570	+	0.994726i	$0.532707\pi$
$284$	−1.24215e10	−0.113303
$285$	−1.36727e11	−1.22759
$286$	−1.93029e9	−0.0170599
$287$	6.79394e9	0.0591089
$288$	1.13632e11	0.973276
$289$	−1.17500e11	−0.990830
$290$	−3.88410e11	−3.22478
$291$	1.91460e11	1.56516
$292$	−1.47256e11	−1.18536
$293$	−3.00864e10	−0.238487	−0.119244	−	0.992865i	$-0.538047\pi$
$293$	−3.00864e10	−0.238487	−0.119244	+	0.992865i	$0.538047\pi$
$294$	3.29988e10	0.257593
$295$	−2.41935e11	−1.85995
$296$	−2.93105e10	−0.221927
$297$	−2.23978e9	−0.0167033
$298$	−1.23275e11	−0.905526
$299$	2.02454e10	0.146490
$300$	−6.79322e10	−0.484206
$301$	−1.10131e10	−0.0773321
$302$	9.37530e10	0.648565
$303$	−3.38859e11	−2.30955
$304$	1.28371e11	0.862058
$305$	1.74810e10	0.115669
$306$	−1.44493e10	−0.0942110
$307$	−1.26253e11	−0.811185	−0.405592	−	0.914054i	$-0.632935\pi$
$307$	−1.26253e11	−0.811185	−0.405592	+	0.914054i	$0.632935\pi$
$308$	−2.39032e9	−0.0151349
$309$	5.40478e10	0.337260
$310$	−4.39498e11	−2.70289
$311$	−2.72563e11	−1.65213	−0.826066	−	0.563574i	$-0.809426\pi$
$311$	−2.72563e11	−1.65213	−0.826066	+	0.563574i	$0.809426\pi$
$312$	8.66217e9	0.0517524
$313$	2.58487e11	1.52226	0.761131	−	0.648598i	$-0.224644\pi$
$313$	2.58487e11	1.52226	0.761131	+	0.648598i	$0.224644\pi$
$314$	4.66044e10	0.270548
$315$	−5.60757e10	−0.320906
$316$	−1.59868e11	−0.901921
$317$	2.80288e11	1.55897	0.779486	−	0.626420i	$-0.215480\pi$
$317$	2.80288e11	1.55897	0.779486	+	0.626420i	$0.215480\pi$
$318$	−1.05268e11	−0.577263
$319$	1.62763e10	0.0880030
$320$	1.74651e11	0.931097
$321$	1.93802e11	1.01879
$322$	5.30346e10	0.274921
$323$	−1.47777e10	−0.0755433
$324$	−2.14117e11	−1.07944
$325$	−2.30102e10	−0.114405
$326$	−9.01672e10	−0.442150
$327$	−1.28670e10	−0.0622319
$328$	4.67178e9	0.0222869
$329$	−7.68244e10	−0.361508
$330$	2.06209e10	0.0957183
$331$	−9.04934e10	−0.414373	−0.207186	−	0.978302i	$-0.566431\pi$
$331$	−9.04934e10	−0.414373	−0.207186	+	0.978302i	$0.566431\pi$
$332$	−6.73968e10	−0.304451
$333$	−2.49629e11	−1.11249
$334$	−2.05042e11	−0.901537
$335$	5.85206e10	0.253868
$336$	1.26346e11	0.540799
$337$	−1.00307e10	−0.0423640	−0.0211820	−	0.999776i	$-0.506743\pi$
$337$	−1.00307e10	−0.0423640	−0.0211820	+	0.999776i	$0.506743\pi$
$338$	−2.54191e10	−0.105934
$339$	4.08826e11	1.68128
$340$	−2.51418e10	−0.102033
$341$	1.84171e10	0.0737610
$342$	1.96352e11	0.776100
$343$	1.38413e10	0.0539949
$344$	−7.57304e9	−0.0291580
$345$	−2.16278e11	−0.821913
$346$	−2.10904e11	−0.791118
$347$	−2.98414e11	−1.10494	−0.552468	−	0.833534i	$-0.686314\pi$
$347$	−2.98414e11	−1.10494	−0.552468	+	0.833534i	$0.686314\pi$
$348$	6.32773e11	2.31282
$349$	4.74116e11	1.71069	0.855343	−	0.518061i	$-0.173346\pi$
$349$	4.74116e11	1.71069	0.855343	+	0.518061i	$0.173346\pi$
$350$	−6.02771e10	−0.214707
$351$	−2.94946e10	−0.103720
$352$	−1.75272e10	−0.0608515
$353$	5.42384e11	1.85918	0.929588	−	0.368600i	$-0.120163\pi$
$353$	5.42384e11	1.85918	0.929588	+	0.368600i	$0.120163\pi$
$354$	8.33786e11	2.82189
$355$	4.49474e10	0.150203
$356$	−1.64804e11	−0.543803
$357$	−1.45446e10	−0.0473909
$358$	1.46283e11	0.470675
$359$	8.05321e10	0.255885	0.127942	−	0.991782i	$-0.459163\pi$
$359$	8.05321e10	0.255885	0.127942	+	0.991782i	$0.459163\pi$
$360$	−3.85599e10	−0.120997
$361$	−1.21873e11	−0.377682
$362$	−1.65755e11	−0.507315
$363$	4.32282e11	1.30673
$364$	−3.14770e10	−0.0939805
$365$	5.32846e11	1.57139
$366$	−6.02450e10	−0.175491
$367$	−9.90111e10	−0.284896	−0.142448	−	0.989802i	$-0.545497\pi$
$367$	−9.90111e10	−0.284896	−0.142448	+	0.989802i	$0.545497\pi$
$368$	2.03060e11	0.577177
$369$	3.97882e10	0.111721
$370$	−9.18843e11	−2.54879
$371$	−4.41545e10	−0.121002
$372$	7.16001e11	1.93852
$373$	−5.64158e11	−1.50908	−0.754538	−	0.656257i	$-0.772139\pi$
$373$	−5.64158e11	−1.50908	−0.754538	+	0.656257i	$0.772139\pi$
$374$	2.22874e9	0.00589029
$375$	−3.50107e11	−0.914240
$376$	−5.28275e10	−0.136306
$377$	2.14335e11	0.546458
$378$	−7.72636e10	−0.194653
$379$	−1.87576e11	−0.466982	−0.233491	−	0.972359i	$-0.575015\pi$
$379$	−1.87576e11	−0.466982	−0.233491	+	0.972359i	$0.575015\pi$
$380$	3.41652e11	0.840539
$381$	9.54533e11	2.32075
$382$	−3.83369e11	−0.921153
$383$	−2.75353e11	−0.653877	−0.326938	−	0.945046i	$-0.606017\pi$
$383$	−2.75353e11	−0.653877	−0.326938	+	0.945046i	$0.606017\pi$
$384$	1.58158e11	0.371194
$385$	8.64941e9	0.0200638
$386$	1.66312e11	0.381312
$387$	−6.44973e10	−0.146165
$388$	−4.78416e11	−1.07167
$389$	5.23050e11	1.15816	0.579082	−	0.815269i	$-0.303411\pi$
$389$	5.23050e11	1.15816	0.579082	+	0.815269i	$0.303411\pi$
$390$	2.71547e11	0.594366
$391$	−2.33756e10	−0.0505787
$392$	9.51782e9	0.0203587
$393$	3.08856e11	0.653116
$394$	−8.78472e11	−1.83652
$395$	5.78482e11	1.19565
$396$	−1.39987e10	−0.0286062
$397$	−1.33964e11	−0.270665	−0.135333	−	0.990800i	$-0.543210\pi$
$397$	−1.33964e11	−0.270665	−0.135333	+	0.990800i	$0.543210\pi$
$398$	−8.07627e11	−1.61338
$399$	1.97647e11	0.390402
$400$	−2.30790e11	−0.450762
$401$	8.10802e11	1.56590	0.782952	−	0.622082i	$-0.213713\pi$
$401$	8.10802e11	1.56590	0.782952	+	0.622082i	$0.213713\pi$
$402$	−2.01681e11	−0.385165
$403$	2.42526e11	0.458022
$404$	8.46735e11	1.58136
$405$	7.74785e11	1.43098
$406$	5.61468e11	1.02555
$407$	3.85040e10	0.0695555
$408$	−1.00014e10	−0.0178687
$409$	−4.86152e10	−0.0859048	−0.0429524	−	0.999077i	$-0.513676\pi$
$409$	−4.86152e10	−0.0859048	−0.0429524	+	0.999077i	$0.513676\pi$
$410$	1.46454e11	0.255961
$411$	1.22709e12	2.12123
$412$	−1.35054e11	−0.230924
$413$	3.49730e11	0.591504
$414$	3.10593e11	0.519625
$415$	2.43876e11	0.403601
$416$	−2.30808e11	−0.377860
$417$	−5.04520e11	−0.817082
$418$	−3.02863e10	−0.0485237
$419$	−6.91424e11	−1.09593	−0.547963	−	0.836503i	$-0.684597\pi$
$419$	−6.91424e11	−1.09593	−0.547963	+	0.836503i	$0.684597\pi$
$420$	3.36263e11	0.527299
$421$	−3.17438e11	−0.492481	−0.246241	−	0.969209i	$-0.579195\pi$
$421$	−3.17438e11	−0.492481	−0.246241	+	0.969209i	$0.579195\pi$
$422$	−1.30466e12	−2.00258
$423$	−4.49916e11	−0.683282
$424$	−3.03624e10	−0.0456236
$425$	2.65679e10	0.0395009
$426$	−1.54903e11	−0.227886
$427$	−2.52697e10	−0.0367853
$428$	−4.84269e11	−0.697573
$429$	−1.13791e10	−0.0162200
$430$	−2.37404e11	−0.334873
$431$	7.71117e11	1.07640	0.538198	−	0.842818i	$-0.319105\pi$
$431$	7.71117e11	1.07640	0.538198	+	0.842818i	$0.319105\pi$
$432$	−2.95829e11	−0.408661
$433$	3.28343e11	0.448882	0.224441	−	0.974488i	$-0.427944\pi$
$433$	3.28343e11	0.448882	0.224441	+	0.974488i	$0.427944\pi$
$434$	6.35317e11	0.859581
$435$	−2.28969e12	−3.06603
$436$	3.21519e10	0.0426105
$437$	3.17651e11	0.416662
$438$	−1.83636e12	−2.38409
$439$	−3.77562e11	−0.485175	−0.242587	−	0.970130i	$-0.577996\pi$
$439$	−3.77562e11	−0.485175	−0.242587	+	0.970130i	$0.577996\pi$
$440$	5.94768e9	0.00756502
$441$	8.10604e10	0.102055
$442$	2.93492e10	0.0365760
$443$	−1.02879e12	−1.26914	−0.634569	−	0.772866i	$-0.718822\pi$
$443$	−1.02879e12	−1.26914	−0.634569	+	0.772866i	$0.718822\pi$
$444$	1.49692e12	1.82800
$445$	5.96343e11	0.720902
$446$	9.03362e10	0.108107
$447$	−7.26709e11	−0.860948
$448$	−2.52467e11	−0.296110
$449$	3.88014e11	0.450545	0.225273	−	0.974296i	$-0.427673\pi$
$449$	3.88014e11	0.450545	0.225273	+	0.974296i	$0.427673\pi$
$450$	−3.53008e11	−0.405816
$451$	−6.13714e9	−0.00698508
$452$	−1.02157e12	−1.15118
$453$	5.52677e11	0.616637
$454$	−1.13514e12	−1.25400
$455$	1.13900e11	0.124587
$456$	1.35910e11	0.147200
$457$	7.08194e11	0.759503	0.379752	−	0.925089i	$-0.376009\pi$
$457$	7.08194e11	0.759503	0.379752	+	0.925089i	$0.376009\pi$
$458$	1.67364e12	1.77732
$459$	3.40549e10	0.0358115
$460$	5.40431e11	0.562769
$461$	−1.80238e11	−0.185862	−0.0929311	−	0.995673i	$-0.529624\pi$
$461$	−1.80238e11	−0.185862	−0.0929311	+	0.995673i	$0.529624\pi$
$462$	−2.98086e10	−0.0304406
$463$	−8.36615e11	−0.846079	−0.423040	−	0.906111i	$-0.639037\pi$
$463$	−8.36615e11	−0.846079	−0.423040	+	0.906111i	$0.639037\pi$
$464$	2.14976e12	2.15307
$465$	−2.59086e12	−2.56983
$466$	1.62609e12	1.59738
$467$	6.45255e11	0.627777	0.313889	−	0.949460i	$-0.398368\pi$
$467$	6.45255e11	0.627777	0.313889	+	0.949460i	$0.398368\pi$
$468$	−1.84343e11	−0.177632
$469$	−8.45946e10	−0.0807356
$470$	−1.65607e12	−1.56545
$471$	2.74735e11	0.257229
$472$	2.40488e11	0.223026
$473$	9.94840e9	0.00913856
$474$	−1.99363e12	−1.81402
$475$	−3.61031e11	−0.325404
$476$	3.63438e10	0.0324488
$477$	−2.58587e11	−0.228704
$478$	−4.86518e11	−0.426258
$479$	1.17577e12	1.02050	0.510249	−	0.860027i	$-0.329553\pi$
$479$	1.17577e12	1.02050	0.510249	+	0.860027i	$0.329553\pi$
$480$	2.46567e12	2.12007
$481$	5.07041e11	0.431907
$482$	−5.57876e11	−0.470788
$483$	3.12641e11	0.261387
$484$	−1.08018e12	−0.894728
$485$	1.73115e12	1.42068
$486$	−2.03676e12	−1.65606
$487$	1.48367e11	0.119524	0.0597621	−	0.998213i	$-0.480966\pi$
$487$	1.48367e11	0.119524	0.0597621	+	0.998213i	$0.480966\pi$
$488$	−1.73764e10	−0.0138698
$489$	−5.31539e11	−0.420383
$490$	2.98370e11	0.233816
$491$	−1.67861e12	−1.30342	−0.651708	−	0.758470i	$-0.725947\pi$
$491$	−1.67861e12	−1.30342	−0.651708	+	0.758470i	$0.725947\pi$
$492$	−2.38593e11	−0.183576
$493$	−2.47474e11	−0.188677
$494$	−3.98827e11	−0.301309
$495$	5.06546e10	0.0379224
$496$	2.43252e12	1.80463
$497$	−6.49739e10	−0.0477678
$498$	−8.40474e11	−0.612339
$499$	−6.00497e11	−0.433569	−0.216785	−	0.976219i	$-0.569557\pi$
$499$	−6.00497e11	−0.433569	−0.216785	+	0.976219i	$0.569557\pi$
$500$	8.74842e11	0.625986
$501$	−1.20873e12	−0.857156
$502$	3.48743e12	2.45097
$503$	−7.25643e9	−0.00505437	−0.00252718	−	0.999997i	$-0.500804\pi$
$503$	−7.25643e9	−0.00505437	−0.00252718	+	0.999997i	$0.500804\pi$
$504$	5.57404e10	0.0384798
$505$	−3.06392e12	−2.09636
$506$	−4.79074e10	−0.0324882
$507$	−1.49847e11	−0.100719
$508$	−2.38517e12	−1.58903
$509$	2.50852e12	1.65648	0.828241	−	0.560371i	$-0.189342\pi$
$509$	2.50852e12	1.65648	0.828241	+	0.560371i	$0.189342\pi$
$510$	−3.13532e11	−0.205218
$511$	−7.70257e11	−0.499737
$512$	−2.07283e12	−1.33306
$513$	−4.62772e11	−0.295011
$514$	3.12453e12	1.97447
$515$	4.88693e11	0.306129
$516$	3.86763e11	0.240172
$517$	6.93974e10	0.0427204
$518$	1.32824e12	0.810572
$519$	−1.24329e12	−0.752173
$520$	7.83222e10	0.0469753
$521$	1.83929e12	1.09366	0.546829	−	0.837244i	$-0.315835\pi$
$521$	1.83929e12	1.09366	0.546829	+	0.837244i	$0.315835\pi$
$522$	3.28819e12	1.93839
$523$	−2.67195e12	−1.56160	−0.780801	−	0.624779i	$-0.785189\pi$
$523$	−2.67195e12	−1.56160	−0.780801	+	0.624779i	$0.785189\pi$
$524$	−7.71765e11	−0.447192
$525$	−3.55336e11	−0.204137
$526$	−3.05928e12	−1.74254
$527$	−2.80024e11	−0.158142
$528$	−1.14132e11	−0.0639078
$529$	−1.29869e12	−0.721031
$530$	−9.51818e11	−0.523978
$531$	2.04817e12	1.11800
$532$	−4.93876e11	−0.267310
$533$	−8.08170e10	−0.0433741
$534$	−2.05519e12	−1.09374
$535$	1.75233e12	0.924750
$536$	−5.81706e10	−0.0304412
$537$	8.62345e11	0.447504
$538$	−3.31948e12	−1.70824
$539$	−1.25032e10	−0.00638074
$540$	−7.87329e11	−0.398460
$541$	7.07819e10	0.0355250	0.0177625	−	0.999842i	$-0.494346\pi$
$541$	7.07819e10	0.0355250	0.0177625	+	0.999842i	$0.494346\pi$
$542$	2.94676e12	1.46672
$543$	−9.77131e11	−0.482340
$544$	2.66494e11	0.130464
$545$	−1.16342e11	−0.0564874
$546$	−3.92536e11	−0.189022
$547$	2.46809e12	1.17874	0.589369	−	0.807864i	$-0.299376\pi$
$547$	2.46809e12	1.17874	0.589369	+	0.807864i	$0.299376\pi$
$548$	−3.06623e12	−1.45242
$549$	−1.47990e11	−0.0695275
$550$	5.44498e10	0.0253726
$551$	3.36292e12	1.55430
$552$	2.14984e11	0.0985555
$553$	−8.36227e11	−0.380243
$554$	7.11517e9	0.00320916
$555$	−5.41662e12	−2.42331
$556$	1.26068e12	0.559461
$557$	−3.04875e12	−1.34207	−0.671033	−	0.741427i	$-0.734149\pi$
$557$	−3.04875e12	−1.34207	−0.671033	+	0.741427i	$0.734149\pi$
$558$	3.72069e12	1.62469
$559$	1.31006e11	0.0567463
$560$	1.14241e12	0.490879
$561$	1.31385e10	0.00560032
$562$	−8.56121e11	−0.362011
$563$	−2.04691e12	−0.858638	−0.429319	−	0.903153i	$-0.641246\pi$
$563$	−2.04691e12	−0.858638	−0.429319	+	0.903153i	$0.641246\pi$
$564$	2.69796e12	1.12274
$565$	3.69655e12	1.52609
$566$	6.89766e11	0.282506
$567$	−1.11999e12	−0.455084
$568$	−4.46786e10	−0.0180108
$569$	−1.21106e12	−0.484353	−0.242176	−	0.970232i	$-0.577861\pi$
$569$	−1.21106e12	−0.484353	−0.242176	+	0.970232i	$0.577861\pi$
$570$	4.26058e12	1.69057
$571$	−2.71050e12	−1.06706	−0.533528	−	0.845782i	$-0.679134\pi$
$571$	−2.71050e12	−1.06706	−0.533528	+	0.845782i	$0.679134\pi$
$572$	2.84340e10	0.0111060
$573$	−2.25998e12	−0.875806
$574$	−2.11707e11	−0.0814013
$575$	−5.71085e11	−0.217869
$576$	−1.47855e12	−0.559674
$577$	−3.60856e11	−0.135532	−0.0677661	−	0.997701i	$-0.521587\pi$
$577$	−3.60856e11	−0.135532	−0.0677661	+	0.997701i	$0.521587\pi$
$578$	3.66145e12	1.36451
$579$	9.80416e11	0.362541
$580$	5.72145e12	2.09933
$581$	−3.52535e11	−0.128354
$582$	−5.96610e12	−2.15544
$583$	3.98858e10	0.0142991
$584$	−5.29659e11	−0.188425
$585$	6.67047e11	0.235480
$586$	9.37525e11	0.328431
$587$	−2.53212e12	−0.880263	−0.440132	−	0.897933i	$-0.645068\pi$
$587$	−2.53212e12	−0.880263	−0.440132	+	0.897933i	$0.645068\pi$
$588$	−4.86086e11	−0.167693
$589$	3.80524e12	1.30276
$590$	7.53898e12	2.56141
$591$	−5.17862e12	−1.74611
$592$	5.08558e12	1.70174
$593$	5.57792e11	0.185236	0.0926182	−	0.995702i	$-0.470476\pi$
$593$	5.57792e11	0.185236	0.0926182	+	0.995702i	$0.470476\pi$
$594$	6.97942e10	0.0230028
$595$	−1.31510e11	−0.0430164
$596$	1.81589e12	0.589496
$597$	−4.76099e12	−1.53396
$598$	−6.30870e11	−0.201737
$599$	−5.40325e12	−1.71488	−0.857441	−	0.514582i	$-0.827947\pi$
$599$	−5.40325e12	−1.71488	−0.857441	+	0.514582i	$0.827947\pi$
$600$	−2.44343e11	−0.0769696
$601$	3.75368e10	0.0117361	0.00586803	−	0.999983i	$-0.498132\pi$
$601$	3.75368e10	0.0117361	0.00586803	+	0.999983i	$0.498132\pi$
$602$	3.43180e11	0.106497
$603$	−4.95422e11	−0.152597
$604$	−1.38102e12	−0.422215
$605$	3.90864e12	1.18611
$606$	1.05592e13	3.18057
$607$	−2.89398e12	−0.865260	−0.432630	−	0.901571i	$-0.642414\pi$
$607$	−2.89398e12	−0.865260	−0.432630	+	0.901571i	$0.642414\pi$
$608$	−3.62139e12	−1.07475
$609$	3.30987e12	0.975065
$610$	−5.44727e11	−0.159292
$611$	9.13861e11	0.265274
$612$	2.12845e11	0.0613312
$613$	−3.90117e12	−1.11589	−0.557946	−	0.829877i	$-0.688411\pi$
$613$	−3.90117e12	−1.11589	−0.557946	+	0.829877i	$0.688411\pi$
$614$	3.93419e12	1.11712
$615$	8.63352e11	0.243360
$616$	−8.59768e9	−0.00240585
$617$	4.57281e12	1.27028	0.635141	−	0.772396i	$-0.280942\pi$
$617$	4.57281e12	1.27028	0.635141	+	0.772396i	$0.280942\pi$
$618$	−1.68419e12	−0.464455
$619$	−7.82457e10	−0.0214216	−0.0107108	−	0.999943i	$-0.503409\pi$
$619$	−7.82457e10	−0.0214216	−0.0107108	+	0.999943i	$0.503409\pi$
$620$	6.47399e12	1.75958
$621$	−7.32020e11	−0.197520
$622$	8.49336e12	2.27522
$623$	−8.62046e11	−0.229263
$624$	−1.50295e12	−0.396838
$625$	−4.73916e12	−1.24234
$626$	−8.05476e12	−2.09637
$627$	−1.78539e11	−0.0461349
$628$	−6.86503e11	−0.176126
$629$	−5.85436e11	−0.149125
$630$	1.74738e12	0.441932
$631$	7.59017e12	1.90599	0.952993	−	0.302993i	$-0.0979860\pi$
$631$	7.59017e12	1.90599	0.952993	+	0.302993i	$0.0979860\pi$
$632$	−5.75023e11	−0.143370
$633$	−7.69100e12	−1.90400
$634$	−8.73410e12	−2.14692
$635$	8.63076e12	2.10653
$636$	1.55064e12	0.375798
$637$	−1.64648e11	−0.0396214
$638$	−5.07188e11	−0.121193
$639$	−3.80515e11	−0.0902854
$640$	1.43004e12	0.336930
$641$	−8.44275e12	−1.97525	−0.987627	−	0.156823i	$-0.949875\pi$
$641$	−8.44275e12	−1.97525	−0.987627	+	0.156823i	$0.949875\pi$
$642$	−6.03909e12	−1.40302
$643$	−5.90952e12	−1.36334	−0.681668	−	0.731661i	$-0.738745\pi$
$643$	−5.90952e12	−1.36334	−0.681668	+	0.731661i	$0.738745\pi$
$644$	−7.81221e11	−0.178973
$645$	−1.39951e12	−0.318388
$646$	4.60490e11	0.104034
$647$	−3.06115e11	−0.0686776	−0.0343388	−	0.999410i	$-0.510933\pi$
$647$	−3.06115e11	−0.0686776	−0.0343388	+	0.999410i	$0.510933\pi$
$648$	−7.70151e11	−0.171589
$649$	−3.15920e11	−0.0698998
$650$	7.17024e11	0.157552
$651$	3.74522e12	0.817265
$652$	1.32820e12	0.287839
$653$	−2.75098e12	−0.592078	−0.296039	−	0.955176i	$-0.595666\pi$
$653$	−2.75098e12	−0.592078	−0.296039	+	0.955176i	$0.595666\pi$
$654$	4.00951e11	0.0857021
$655$	2.79264e12	0.592828
$656$	−8.10588e11	−0.170896
$657$	−4.51095e12	−0.944548
$658$	2.39393e12	0.497847
$659$	−8.30422e11	−0.171520	−0.0857599	−	0.996316i	$-0.527332\pi$
$659$	−8.30422e11	−0.171520	−0.0857599	+	0.996316i	$0.527332\pi$
$660$	−3.03755e11	−0.0623125
$661$	6.29780e12	1.28316	0.641582	−	0.767054i	$-0.278278\pi$
$661$	6.29780e12	1.28316	0.641582	+	0.767054i	$0.278278\pi$
$662$	2.81988e12	0.570649
$663$	1.73015e11	0.0347754
$664$	−2.42417e11	−0.0483958
$665$	1.78710e12	0.354365
$666$	7.77872e12	1.53205
$667$	5.31952e12	1.04065
$668$	3.02035e12	0.586900
$669$	5.32536e11	0.102785
$670$	−1.82357e12	−0.349611
$671$	2.28267e10	0.00434703
$672$	−3.56426e12	−0.674230
$673$	7.18852e12	1.35074	0.675370	−	0.737479i	$-0.263984\pi$
$673$	7.18852e12	1.35074	0.675370	+	0.737479i	$0.263984\pi$
$674$	3.12568e11	0.0583411
$675$	8.31987e11	0.154259
$676$	3.74434e11	0.0689628
$677$	−4.60851e12	−0.843162	−0.421581	−	0.906791i	$-0.638525\pi$
$677$	−4.60851e12	−0.843162	−0.421581	+	0.906791i	$0.638525\pi$
$678$	−1.27395e13	−2.31536
$679$	−2.50247e12	−0.451809
$680$	−9.04318e10	−0.0162193
$681$	−6.69168e12	−1.19227
$682$	−5.73898e11	−0.101579
$683$	5.50395e12	0.967791	0.483895	−	0.875126i	$-0.339221\pi$
$683$	5.50395e12	0.967791	0.483895	+	0.875126i	$0.339221\pi$
$684$	−2.89235e12	−0.505240
$685$	1.10952e13	1.92542
$686$	−4.31310e11	−0.0743586
$687$	9.86616e12	1.68983
$688$	1.31398e12	0.223583
$689$	5.25238e11	0.0887911
$690$	6.73946e12	1.13189
$691$	7.67282e12	1.28028	0.640138	−	0.768260i	$-0.278877\pi$
$691$	7.67282e12	1.28028	0.640138	+	0.768260i	$0.278877\pi$
$692$	3.10670e12	0.515017
$693$	−7.32239e10	−0.0120602
$694$	9.29893e12	1.52165
$695$	−4.56180e12	−0.741660
$696$	2.27600e12	0.367647
$697$	9.33124e10	0.0149759
$698$	−1.47740e13	−2.35586
$699$	9.58588e12	1.51874
$700$	8.87907e11	0.139774
$701$	−9.37860e11	−0.146692	−0.0733461	−	0.997307i	$-0.523368\pi$
$701$	−9.37860e11	−0.146692	−0.0733461	+	0.997307i	$0.523368\pi$
$702$	9.19087e11	0.142837
$703$	7.95550e12	1.22848
$704$	2.28059e11	0.0349922
$705$	−9.76259e12	−1.48838
$706$	−1.69013e13	−2.56035
$707$	4.42905e12	0.666690
$708$	−1.22820e13	−1.83705
$709$	8.95196e12	1.33049	0.665243	−	0.746627i	$-0.268328\pi$
$709$	8.95196e12	1.33049	0.665243	+	0.746627i	$0.268328\pi$
$710$	−1.40061e12	−0.206850
$711$	−4.89730e12	−0.718693
$712$	−5.92777e11	−0.0864433
$713$	6.01920e12	0.872240
$714$	4.53227e11	0.0652640
$715$	−1.02889e11	−0.0147228
$716$	−2.15481e12	−0.306409
$717$	−2.86804e12	−0.405274
$718$	−2.50947e12	−0.352389
$719$	−4.59577e11	−0.0641325	−0.0320662	−	0.999486i	$-0.510209\pi$
$719$	−4.59577e11	−0.0641325	−0.0320662	+	0.999486i	$0.510209\pi$
$720$	6.69042e12	0.927806
$721$	−7.06432e11	−0.0973557
$722$	3.79771e12	0.520121
$723$	−3.28870e12	−0.447612
$724$	2.44164e12	0.330261
$725$	−6.04598e12	−0.812728
$726$	−1.34704e13	−1.79956
$727$	−1.01063e13	−1.34180	−0.670898	−	0.741549i	$-0.734091\pi$
$727$	−1.01063e13	−1.34180	−0.670898	+	0.741549i	$0.734091\pi$
$728$	−1.13219e11	−0.0149392
$729$	−2.82526e12	−0.370497
$730$	−1.66041e13	−2.16403
$731$	−1.51261e11	−0.0195929
$732$	8.87434e11	0.114245
$733$	1.25171e13	1.60153	0.800765	−	0.598979i	$-0.204427\pi$
$733$	1.25171e13	1.60153	0.800765	+	0.598979i	$0.204427\pi$
$734$	3.08530e12	0.392342
$735$	1.75891e12	0.222305
$736$	−5.72837e12	−0.719583
$737$	7.64164e10	0.00954076
$738$	−1.23985e12	−0.153856
$739$	−1.26664e13	−1.56226	−0.781128	−	0.624370i	$-0.785356\pi$
$739$	−1.26664e13	−1.56226	−0.781128	+	0.624370i	$0.785356\pi$
$740$	1.35349e13	1.65926
$741$	−2.35110e12	−0.286476
$742$	1.37590e12	0.166637
$743$	2.79839e12	0.336867	0.168433	−	0.985713i	$-0.446129\pi$
$743$	2.79839e12	0.336867	0.168433	+	0.985713i	$0.446129\pi$
$744$	2.57536e12	0.308148
$745$	−6.57081e12	−0.781476
$746$	1.75798e13	2.07821
$747$	−2.06460e12	−0.242601
$748$	−3.28303e10	−0.00383457
$749$	−2.53309e12	−0.294091
$750$	1.09097e13	1.25904
$751$	1.15286e13	1.32251	0.661253	−	0.750163i	$-0.270025\pi$
$751$	1.15286e13	1.32251	0.661253	+	0.750163i	$0.270025\pi$
$752$	9.16595e12	1.04519
$753$	2.05585e13	2.33032
$754$	−6.67892e12	−0.752549
$755$	4.99724e12	0.559717
$756$	1.13813e12	0.126719
$757$	−8.40849e12	−0.930651	−0.465325	−	0.885140i	$-0.654063\pi$
$757$	−8.40849e12	−0.930651	−0.465325	+	0.885140i	$0.654063\pi$
$758$	5.84507e12	0.643100
$759$	−2.82416e11	−0.0308888
$760$	1.22888e12	0.133613
$761$	−1.19871e13	−1.29563	−0.647816	−	0.761797i	$-0.724318\pi$
$761$	−1.19871e13	−1.29563	−0.647816	+	0.761797i	$0.724318\pi$
$762$	−2.97443e13	−3.19600
$763$	1.68178e11	0.0179643
$764$	5.64719e12	0.599670
$765$	−7.70181e11	−0.0813048
$766$	8.58032e12	0.900480
$767$	−4.16020e12	−0.434046
$768$	−1.48181e13	−1.53697
$769$	3.39698e12	0.350288	0.175144	−	0.984543i	$-0.443961\pi$
$769$	3.39698e12	0.350288	0.175144	+	0.984543i	$0.443961\pi$
$770$	−2.69525e11	−0.0276307
$771$	1.84193e13	1.87727
$772$	−2.44984e12	−0.248234
$773$	1.45175e13	1.46246	0.731228	−	0.682133i	$-0.238948\pi$
$773$	1.45175e13	1.46246	0.731228	+	0.682133i	$0.238948\pi$
$774$	2.00981e12	0.201289
$775$	−6.84120e12	−0.681200
$776$	−1.72080e12	−0.170354
$777$	7.83001e12	0.770668
$778$	−1.62988e13	−1.59496
$779$	−1.26802e12	−0.123370
$780$	−4.00000e12	−0.386932
$781$	5.86925e10	0.00564486
$782$	7.28411e11	0.0696540
$783$	−7.74977e12	−0.736820
$784$	−1.65141e12	−0.156111
$785$	2.48412e12	0.233485
$786$	−9.62432e12	−0.899432
$787$	−1.78281e13	−1.65660	−0.828300	−	0.560284i	$-0.810692\pi$
$787$	−1.78281e13	−1.65660	−0.828300	+	0.560284i	$0.810692\pi$
$788$	1.29403e13	1.19557
$789$	−1.80346e13	−1.65676
$790$	−1.80262e13	−1.64658
$791$	−5.34356e12	−0.485329
$792$	−5.03517e10	−0.00454727
$793$	3.00594e11	0.0269930
$794$	4.17448e12	0.372744
$795$	−5.61101e12	−0.498183
$796$	1.18967e13	1.05031
$797$	−5.09625e12	−0.447392	−0.223696	−	0.974659i	$-0.571812\pi$
$797$	−5.09625e12	−0.447392	−0.223696	+	0.974659i	$0.571812\pi$
$798$	−6.15890e12	−0.537638
$799$	−1.05516e12	−0.0915917
$800$	6.51065e12	0.561978
$801$	−5.04850e12	−0.433328
$802$	−2.52655e13	−2.15647
$803$	6.95792e11	0.0590554
$804$	2.97084e12	0.250742
$805$	2.82686e12	0.237259
$806$	−7.55739e12	−0.630760
$807$	−1.95684e13	−1.62415
$808$	3.04559e12	0.251374
$809$	−1.58582e13	−1.30162	−0.650811	−	0.759240i	$-0.725571\pi$
$809$	−1.58582e13	−1.30162	−0.650811	+	0.759240i	$0.725571\pi$
$810$	−2.41432e13	−1.97066
$811$	−8.27659e12	−0.671827	−0.335914	−	0.941893i	$-0.609045\pi$
$811$	−8.27659e12	−0.671827	−0.335914	+	0.941893i	$0.609045\pi$
$812$	−8.27066e12	−0.667633
$813$	1.73713e13	1.39452
$814$	−1.19983e12	−0.0957877
$815$	−4.80611e12	−0.381579
$816$	1.73532e12	0.137017
$817$	2.05549e12	0.161404
$818$	1.51491e12	0.118303
$819$	−9.64251e11	−0.0748881
$820$	−2.15733e12	−0.166630
$821$	1.81620e13	1.39515	0.697575	−	0.716512i	$-0.254263\pi$
$821$	1.81620e13	1.39515	0.697575	+	0.716512i	$0.254263\pi$
$822$	−3.82375e13	−2.92123
$823$	−1.73956e11	−0.0132172	−0.00660861	−	0.999978i	$-0.502104\pi$
$823$	−1.73956e11	−0.0132172	−0.00660861	+	0.999978i	$0.502104\pi$
$824$	−4.85771e11	−0.0367078
$825$	3.20984e11	0.0241235
$826$	−1.08980e13	−0.814585
$827$	−6.27403e12	−0.466414	−0.233207	−	0.972427i	$-0.574922\pi$
$827$	−6.27403e12	−0.466414	−0.233207	+	0.972427i	$0.574922\pi$
$828$	−4.57516e12	−0.338275
$829$	−3.58695e12	−0.263773	−0.131886	−	0.991265i	$-0.542103\pi$
$829$	−3.58695e12	−0.263773	−0.131886	+	0.991265i	$0.542103\pi$
$830$	−7.59945e12	−0.555816
$831$	4.19442e10	0.00305118
$832$	3.00321e12	0.217285
$833$	1.90105e11	0.0136802
$834$	1.57214e13	1.12524
$835$	−1.09292e13	−0.778034
$836$	4.46130e11	0.0315888
$837$	−8.76910e12	−0.617576
$838$	2.15456e13	1.50924
$839$	1.66816e13	1.16228	0.581138	−	0.813805i	$-0.302608\pi$
$839$	1.66816e13	1.16228	0.581138	+	0.813805i	$0.302608\pi$
$840$	1.20949e12	0.0838198
$841$	4.18098e13	2.88201
$842$	9.89173e12	0.678216
$843$	−5.04687e12	−0.344190
$844$	1.92181e13	1.30368
$845$	−1.35489e12	−0.0914218
$846$	1.40199e13	0.940975
$847$	−5.65014e12	−0.377210
$848$	5.26809e12	0.349842
$849$	4.06620e12	0.268599
$850$	−8.27885e11	−0.0543983
$851$	1.25841e13	0.822509
$852$	2.28179e12	0.148353
$853$	1.55052e13	1.00278	0.501390	−	0.865221i	$-0.332822\pi$
$853$	1.55052e13	1.00278	0.501390	+	0.865221i	$0.332822\pi$
$854$	7.87432e11	0.0506585
$855$	1.04660e13	0.669781
$856$	−1.74185e12	−0.110887
$857$	−2.15563e13	−1.36509	−0.682544	−	0.730845i	$-0.739126\pi$
$857$	−2.15563e13	−1.36509	−0.682544	+	0.730845i	$0.739126\pi$
$858$	3.54587e11	0.0223373
$859$	2.44363e13	1.53132	0.765661	−	0.643244i	$-0.222412\pi$
$859$	2.44363e13	1.53132	0.765661	+	0.643244i	$0.222412\pi$
$860$	3.49706e12	0.218002
$861$	−1.24802e12	−0.0773941
$862$	−2.40289e13	−1.48235
$863$	2.00361e12	0.122960	0.0614801	−	0.998108i	$-0.480418\pi$
$863$	2.00361e12	0.122960	0.0614801	+	0.998108i	$0.480418\pi$
$864$	8.34540e12	0.509490
$865$	−1.12416e13	−0.682742
$866$	−1.02315e13	−0.618174
$867$	2.15844e13	1.29734
$868$	−9.35849e12	−0.559586
$869$	7.55384e11	0.0449344
$870$	7.13495e13	4.22235
$871$	1.00629e12	0.0592437
$872$	1.15646e11	0.00677340
$873$	−1.46555e13	−0.853960
$874$	−9.89838e12	−0.573803
$875$	4.57608e12	0.263911
$876$	2.70503e13	1.55204
$877$	−2.95900e13	−1.68907	−0.844535	−	0.535501i	$-0.820123\pi$
$877$	−2.95900e13	−1.68907	−0.844535	+	0.535501i	$0.820123\pi$
$878$	1.17653e13	0.668154
$879$	5.52675e12	0.312263
$880$	−1.03196e12	−0.0580086
$881$	3.40701e13	1.90538	0.952691	−	0.303942i	$-0.0983028\pi$
$881$	3.40701e13	1.90538	0.952691	+	0.303942i	$0.0983028\pi$
$882$	−2.52594e12	−0.140544
$883$	3.28392e13	1.81790	0.908948	−	0.416910i	$-0.136887\pi$
$883$	3.28392e13	1.81790	0.908948	+	0.416910i	$0.136887\pi$
$884$	−4.32326e11	−0.0238109
$885$	4.44426e13	2.43531
$886$	3.20582e13	1.74778
$887$	2.46024e13	1.33451	0.667255	−	0.744829i	$-0.267469\pi$
$887$	2.46024e13	1.33451	0.667255	+	0.744829i	$0.267469\pi$
$888$	5.38422e12	0.290579
$889$	−1.24762e13	−0.669923
$890$	−1.85827e13	−0.992784
$891$	1.01172e12	0.0537786
$892$	−1.33069e12	−0.0703777
$893$	1.43385e13	0.754523
$894$	2.26451e13	1.18565
$895$	7.79721e12	0.406196
$896$	−2.06720e12	−0.107151
$897$	−3.71901e12	−0.191805
$898$	−1.20909e13	−0.620464
$899$	6.37242e13	3.25376
$900$	5.19996e12	0.264185
$901$	−6.06446e11	−0.0306571
$902$	1.91240e11	0.00961944
$903$	2.02306e12	0.101254
$904$	−3.67444e12	−0.182993
$905$	−8.83509e12	−0.437817
$906$	−1.72221e13	−0.849196
$907$	1.74939e13	0.858331	0.429166	−	0.903226i	$-0.358808\pi$
$907$	1.74939e13	0.858331	0.429166	+	0.903226i	$0.358808\pi$
$908$	1.67211e13	0.816352
$909$	2.59384e13	1.26010
$910$	−3.54925e12	−0.171574
$911$	−3.56240e13	−1.71360	−0.856801	−	0.515648i	$-0.827551\pi$
$911$	−3.56240e13	−1.71360	−0.856801	+	0.515648i	$0.827551\pi$
$912$	−2.35813e13	−1.12873
$913$	3.18454e11	0.0151680
$914$	−2.20681e13	−1.04594
$915$	−3.21119e12	−0.151451
$916$	−2.46534e13	−1.15704
$917$	−4.03691e12	−0.188533
$918$	−1.06119e12	−0.0493175
$919$	−1.60302e12	−0.0741342	−0.0370671	−	0.999313i	$-0.511802\pi$
$919$	−1.60302e12	−0.0741342	−0.0370671	+	0.999313i	$0.511802\pi$
$920$	1.94386e12	0.0894581
$921$	2.31922e13	1.06212
$922$	5.61641e12	0.255958
$923$	7.72894e11	0.0350520
$924$	4.39093e11	0.0198168
$925$	−1.43027e13	−0.642361
$926$	2.60699e13	1.16517
$927$	−4.13716e12	−0.184011
$928$	−6.06452e13	−2.68430
$929$	1.79784e13	0.791919	0.395959	−	0.918268i	$-0.370412\pi$
$929$	1.79784e13	0.791919	0.395959	+	0.918268i	$0.370412\pi$
$930$	8.07341e13	3.53902
$931$	−2.58334e12	−0.112696
$932$	−2.39530e13	−1.03989
$933$	5.00687e13	2.16321
$934$	−2.01069e13	−0.864538
$935$	1.18797e11	0.00508337
$936$	−6.63057e11	−0.0282364
$937$	−2.91204e13	−1.23415	−0.617077	−	0.786902i	$-0.711683\pi$
$937$	−2.91204e13	−1.23415	−0.617077	+	0.786902i	$0.711683\pi$
$938$	2.63606e12	0.111184
$939$	−4.74831e13	−1.99317
$940$	2.43946e13	1.01910
$941$	−1.49397e13	−0.621139	−0.310569	−	0.950551i	$-0.600520\pi$
$941$	−1.49397e13	−0.621139	−0.310569	+	0.950551i	$0.600520\pi$
$942$	−8.56105e12	−0.354240
$943$	−2.00578e12	−0.0826001
$944$	−4.17265e13	−1.71016
$945$	−4.11832e12	−0.167988
$946$	−3.10003e11	−0.0125851
$947$	−2.05716e13	−0.831177	−0.415589	−	0.909553i	$-0.636424\pi$
$947$	−2.05716e13	−0.831177	−0.415589	+	0.909553i	$0.636424\pi$
$948$	2.93671e13	1.18093
$949$	9.16256e12	0.366707
$950$	1.12501e13	0.448127
$951$	−5.14879e13	−2.04123
$952$	1.30724e11	0.00515809
$953$	−4.75899e13	−1.86894	−0.934472	−	0.356035i	$-0.884128\pi$
$953$	−4.75899e13	−1.86894	−0.934472	+	0.356035i	$0.884128\pi$
$954$	8.05788e12	0.314958
$955$	−2.04344e13	−0.794963
$956$	7.16661e12	0.277494
$957$	−2.98989e12	−0.115226
$958$	−3.66383e13	−1.40537
$959$	−1.60387e13	−0.612328
$960$	−3.20826e13	−1.21913
$961$	4.56662e13	1.72719
$962$	−1.58000e13	−0.594797
$963$	−1.48348e13	−0.555859
$964$	8.21774e12	0.306483
$965$	8.86479e12	0.329075
$966$	−9.74224e12	−0.359966
$967$	7.90376e11	0.0290680	0.0145340	−	0.999894i	$-0.495374\pi$
$967$	7.90376e11	0.0290680	0.0145340	+	0.999894i	$0.495374\pi$
$968$	−3.88526e12	−0.142227
$969$	2.71461e12	0.0989123
$970$	−5.39447e13	−1.95648
$971$	−2.71117e13	−0.978746	−0.489373	−	0.872075i	$-0.662774\pi$
$971$	−2.71117e13	−0.978746	−0.489373	+	0.872075i	$0.662774\pi$
$972$	3.00023e13	1.07809
$973$	6.59432e12	0.235864
$974$	−4.62327e12	−0.164602
$975$	4.22689e12	0.149796
$976$	3.01493e12	0.106354
$977$	−9.61551e12	−0.337634	−0.168817	−	0.985647i	$-0.553995\pi$
$977$	−9.61551e12	−0.337634	−0.168817	+	0.985647i	$0.553995\pi$
$978$	1.65634e13	0.578927
$979$	7.78707e11	0.0270927
$980$	−4.39512e12	−0.152214
$981$	9.84924e11	0.0339541
$982$	5.23074e13	1.79499
$983$	−1.83268e13	−0.626031	−0.313016	−	0.949748i	$-0.601339\pi$
$983$	−1.83268e13	−0.626031	−0.313016	+	0.949748i	$0.601339\pi$
$984$	−8.58188e11	−0.0291813
$985$	−4.68244e13	−1.58493
$986$	7.71156e12	0.259834
$987$	1.41123e13	0.473339
$988$	5.87488e12	0.196152
$989$	3.25140e12	0.108066
$990$	−1.57846e12	−0.0522245
$991$	−5.20026e13	−1.71275	−0.856374	−	0.516355i	$-0.827288\pi$
$991$	−5.20026e13	−1.71275	−0.856374	+	0.516355i	$0.827288\pi$
$992$	−6.86219e13	−2.24988
$993$	1.66233e13	0.542557
$994$	2.02466e12	0.0657829
$995$	−4.30483e13	−1.39236
$996$	1.23805e13	0.398632
$997$	−1.11097e13	−0.356103	−0.178052	−	0.984021i	$-0.556979\pi$
$997$	−1.11097e13	−0.356103	−0.178052	+	0.984021i	$0.556979\pi$
$998$	1.87122e13	0.597086
$999$	−1.83333e13	−0.582365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-31.1611 q^{2} -183.696 q^{3} +459.017 q^{4} -1660.96 q^{5} +5724.18 q^{6} +2401.00 q^{7} +1651.02 q^{8} +14061.3 q^{9} +O(q^{10})\)	\(q-31.1611 q^{2} -183.696 q^{3} +459.017 q^{4} -1660.96 q^{5} +5724.18 q^{6} +2401.00 q^{7} +1651.02 q^{8} +14061.3 q^{9} +51757.3 q^{10} -2168.88 q^{11} -84319.6 q^{12} -28561.0 q^{13} -74817.9 q^{14} +305111. q^{15} -286464. q^{16} +32976.9 q^{17} -438165. q^{18} -448123. q^{19} -762407. q^{20} -441054. q^{21} +67584.9 q^{22} -708849. q^{23} -303286. q^{24} +805651. q^{25} +889993. q^{26} +1.03269e6 q^{27} +1.10210e6 q^{28} -7.50446e6 q^{29} -9.50762e6 q^{30} -8.49151e6 q^{31} +8.08123e6 q^{32} +398415. q^{33} -1.02760e6 q^{34} -3.98796e6 q^{35} +6.45436e6 q^{36} -1.77529e7 q^{37} +1.39640e7 q^{38} +5.24655e6 q^{39} -2.74228e6 q^{40} +2.82963e6 q^{41} +1.37438e7 q^{42} -4.58688e6 q^{43} -995553. q^{44} -2.33552e7 q^{45} +2.20885e7 q^{46} -3.19968e7 q^{47} +5.26224e7 q^{48} +5.76480e6 q^{49} -2.51050e7 q^{50} -6.05773e6 q^{51} -1.31100e7 q^{52} -1.83900e7 q^{53} -3.21798e7 q^{54} +3.60242e6 q^{55} +3.96411e6 q^{56} +8.23185e7 q^{57} +2.33847e8 q^{58} +1.45660e8 q^{59} +1.40051e8 q^{60} -1.05246e7 q^{61} +2.64605e8 q^{62} +3.37611e7 q^{63} -1.05151e8 q^{64} +4.74386e7 q^{65} -1.24151e7 q^{66} -3.52331e7 q^{67} +1.51369e7 q^{68} +1.30213e8 q^{69} +1.24269e8 q^{70} -2.70612e7 q^{71} +2.32155e7 q^{72} -3.20807e8 q^{73} +5.53201e8 q^{74} -1.47995e8 q^{75} -2.05696e8 q^{76} -5.20749e6 q^{77} -1.63488e8 q^{78} -3.48283e8 q^{79} +4.75805e8 q^{80} -4.66469e8 q^{81} -8.81745e7 q^{82} -1.46829e8 q^{83} -2.02451e8 q^{84} -5.47732e7 q^{85} +1.42932e8 q^{86} +1.37854e9 q^{87} -3.58087e6 q^{88} -3.59036e8 q^{89} +7.27773e8 q^{90} -6.85750e7 q^{91} -3.25373e8 q^{92} +1.55986e9 q^{93} +9.97057e8 q^{94} +7.44313e8 q^{95} -1.48449e9 q^{96} -1.04226e9 q^{97} -1.79638e8 q^{98} -3.04973e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 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

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