LMFDB - Embedded newform 91.10.a.c.1.4

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			1.4
Root			$21.0054$ 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)

$f(q)$	$=$	$q-19.0054 q^{2} -267.441 q^{3} -150.796 q^{4} +1106.90 q^{5} +5082.81 q^{6} +2401.00 q^{7} +12596.7 q^{8} +51841.8 q^{9} +O(q^{10})$	\(q-19.0054 q^{2} -267.441 q^{3} -150.796 q^{4} +1106.90 q^{5} +5082.81 q^{6} +2401.00 q^{7} +12596.7 q^{8} +51841.8 q^{9} -21037.1 q^{10} +42175.5 q^{11} +40329.2 q^{12} -28561.0 q^{13} -45631.9 q^{14} -296032. q^{15} -162197. q^{16} -57128.9 q^{17} -985271. q^{18} +901112. q^{19} -166917. q^{20} -642126. q^{21} -801560. q^{22} +199593. q^{23} -3.36887e6 q^{24} -727889. q^{25} +542812. q^{26} -8.60058e6 q^{27} -362062. q^{28} +2.30695e6 q^{29} +5.62619e6 q^{30} +2.67210e6 q^{31} -3.36690e6 q^{32} -1.12795e7 q^{33} +1.08575e6 q^{34} +2.65768e6 q^{35} -7.81756e6 q^{36} +1.43536e7 q^{37} -1.71260e7 q^{38} +7.63839e6 q^{39} +1.39433e7 q^{40} +2.31999e7 q^{41} +1.22038e7 q^{42} -2.17951e7 q^{43} -6.35991e6 q^{44} +5.73838e7 q^{45} -3.79334e6 q^{46} -1.73684e6 q^{47} +4.33780e7 q^{48} +5.76480e6 q^{49} +1.38338e7 q^{50} +1.52786e7 q^{51} +4.30690e6 q^{52} -7.68965e7 q^{53} +1.63457e8 q^{54} +4.66842e7 q^{55} +3.02446e7 q^{56} -2.40994e8 q^{57} -4.38444e7 q^{58} +1.47046e7 q^{59} +4.46405e7 q^{60} -1.41914e7 q^{61} -5.07843e7 q^{62} +1.24472e8 q^{63} +1.47034e8 q^{64} -3.16143e7 q^{65} +2.14370e8 q^{66} +9.37201e7 q^{67} +8.61484e6 q^{68} -5.33794e7 q^{69} -5.05101e7 q^{70} -3.59758e8 q^{71} +6.53034e8 q^{72} +4.24967e8 q^{73} -2.72795e8 q^{74} +1.94668e8 q^{75} -1.35885e8 q^{76} +1.01263e8 q^{77} -1.45170e8 q^{78} +1.29378e8 q^{79} -1.79536e8 q^{80} +1.27975e9 q^{81} -4.40922e8 q^{82} -5.02465e8 q^{83} +9.68304e7 q^{84} -6.32362e7 q^{85} +4.14224e8 q^{86} -6.16973e8 q^{87} +5.31271e8 q^{88} -4.03796e8 q^{89} -1.09060e9 q^{90} -6.85750e7 q^{91} -3.00980e7 q^{92} -7.14630e8 q^{93} +3.30094e7 q^{94} +9.97444e8 q^{95} +9.00447e8 q^{96} +1.35910e9 q^{97} -1.09562e8 q^{98} +2.18645e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.0054	−0.839926	−0.419963	−	0.907541i	$-0.637957\pi$
$2$	−19.0054	−0.839926	−0.419963	+	0.907541i	$0.637957\pi$
$3$	−267.441	−1.90626	−0.953131	−	0.302558i	$-0.902159\pi$
$3$	−267.441	−1.90626	−0.953131	+	0.302558i	$0.902159\pi$
$4$	−150.796	−0.294524
$5$	1106.90	0.792036	0.396018	−	0.918243i	$-0.370392\pi$
$5$	1106.90	0.792036	0.396018	+	0.918243i	$0.370392\pi$
$6$	5082.81	1.60112
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	12596.7	1.08730
$9$	51841.8	2.63383
$10$	−21037.1	−0.665251
$11$	42175.5	0.868546	0.434273	−	0.900781i	$-0.357005\pi$
$11$	42175.5	0.868546	0.434273	+	0.900781i	$0.357005\pi$
$12$	40329.2	0.561441
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−45631.9	−0.317462
$15$	−296032.	−1.50983
$16$	−162197.	−0.618731
$17$	−57128.9	−0.165896	−0.0829479	−	0.996554i	$-0.526434\pi$
$17$	−57128.9	−0.165896	−0.0829479	+	0.996554i	$0.526434\pi$
$18$	−985271.	−2.21223
$19$	901112.	1.58631	0.793154	−	0.609021i	$-0.208437\pi$
$19$	901112.	1.58631	0.793154	+	0.609021i	$0.208437\pi$
$20$	−166917.	−0.233274
$21$	−642126.	−0.720499
$22$	−801560.	−0.729514
$23$	199593.	0.148720	0.0743602	−	0.997231i	$-0.476309\pi$
$23$	199593.	0.148720	0.0743602	+	0.997231i	$0.476309\pi$
$24$	−3.36887e6	−2.07269
$25$	−727889.	−0.372679
$26$	542812.	0.232954
$27$	−8.60058e6	−3.11452
$28$	−362062.	−0.111320
$29$	2.30695e6	0.605686	0.302843	−	0.953041i	$-0.402064\pi$
$29$	2.30695e6	0.605686	0.302843	+	0.953041i	$0.402064\pi$
$30$	5.62619e6	1.26814
$31$	2.67210e6	0.519668	0.259834	−	0.965653i	$-0.416332\pi$
$31$	2.67210e6	0.519668	0.259834	+	0.965653i	$0.416332\pi$
$32$	−3.36690e6	−0.567616
$33$	−1.12795e7	−1.65568
$34$	1.08575e6	0.139340
$35$	2.65768e6	0.299361
$36$	−7.81756e6	−0.775729
$37$	1.43536e7	1.25908	0.629540	−	0.776968i	$-0.283244\pi$
$37$	1.43536e7	1.25908	0.629540	+	0.776968i	$0.283244\pi$
$38$	−1.71260e7	−1.33238
$39$	7.63839e6	0.528702
$40$	1.39433e7	0.861184
$41$	2.31999e7	1.28221	0.641104	−	0.767454i	$-0.278477\pi$
$41$	2.31999e7	1.28221	0.641104	+	0.767454i	$0.278477\pi$
$42$	1.22038e7	0.605166
$43$	−2.17951e7	−0.972189	−0.486095	−	0.873906i	$-0.661579\pi$
$43$	−2.17951e7	−0.972189	−0.486095	+	0.873906i	$0.661579\pi$
$44$	−6.35991e6	−0.255808
$45$	5.73838e7	2.08609
$46$	−3.79334e6	−0.124914
$47$	−1.73684e6	−0.0519183	−0.0259592	−	0.999663i	$-0.508264\pi$
$47$	−1.73684e6	−0.0519183	−0.0259592	+	0.999663i	$0.508264\pi$
$48$	4.33780e7	1.17946
$49$	5.76480e6	0.142857
$50$	1.38338e7	0.313023
$51$	1.52786e7	0.316241
$52$	4.30690e6	0.0816864
$53$	−7.68965e7	−1.33864	−0.669322	−	0.742973i	$-0.733415\pi$
$53$	−7.68965e7	−1.33864	−0.669322	+	0.742973i	$0.733415\pi$
$54$	1.63457e8	2.61596
$55$	4.66842e7	0.687920
$56$	3.02446e7	0.410963
$57$	−2.40994e8	−3.02392
$58$	−4.38444e7	−0.508731
$59$	1.47046e7	0.157986	0.0789929	−	0.996875i	$-0.474830\pi$
$59$	1.47046e7	0.157986	0.0789929	+	0.996875i	$0.474830\pi$
$60$	4.46405e7	0.444681
$61$	−1.41914e7	−0.131232	−0.0656161	−	0.997845i	$-0.520901\pi$
$61$	−1.41914e7	−0.131232	−0.0656161	+	0.997845i	$0.520901\pi$
$62$	−5.07843e7	−0.436482
$63$	1.24472e8	0.995496
$64$	1.47034e8	1.09549
$65$	−3.16143e7	−0.219671
$66$	2.14370e8	1.39065
$67$	9.37201e7	0.568194	0.284097	−	0.958796i	$-0.408306\pi$
$67$	9.37201e7	0.568194	0.284097	+	0.958796i	$0.408306\pi$
$68$	8.61484e6	0.0488604
$69$	−5.33794e7	−0.283500
$70$	−5.05101e7	−0.251441
$71$	−3.59758e8	−1.68015	−0.840074	−	0.542471i	$-0.817489\pi$
$71$	−3.59758e8	−1.68015	−0.840074	+	0.542471i	$0.817489\pi$
$72$	6.53034e8	2.86378
$73$	4.24967e8	1.75147	0.875734	−	0.482793i	$-0.160378\pi$
$73$	4.24967e8	1.75147	0.875734	+	0.482793i	$0.160378\pi$
$74$	−2.72795e8	−1.05753
$75$	1.94668e8	0.710424
$76$	−1.35885e8	−0.467207
$77$	1.01263e8	0.328280
$78$	−1.45170e8	−0.444070
$79$	1.29378e8	0.373714	0.186857	−	0.982387i	$-0.440170\pi$
$79$	1.29378e8	0.373714	0.186857	+	0.982387i	$0.440170\pi$
$80$	−1.79536e8	−0.490057
$81$	1.27975e9	3.30325
$82$	−4.40922e8	−1.07696
$83$	−5.02465e8	−1.16213	−0.581065	−	0.813857i	$-0.697364\pi$
$83$	−5.02465e8	−1.16213	−0.581065	+	0.813857i	$0.697364\pi$
$84$	9.68304e7	0.212205
$85$	−6.32362e7	−0.131395
$86$	4.14224e8	0.816567
$87$	−6.16973e8	−1.15460
$88$	5.31271e8	0.944374
$89$	−4.03796e8	−0.682193	−0.341097	−	0.940028i	$-0.610798\pi$
$89$	−4.03796e8	−0.682193	−0.341097	+	0.940028i	$0.610798\pi$
$90$	−1.09060e9	−1.75216
$91$	−6.85750e7	−0.104828
$92$	−3.00980e7	−0.0438018
$93$	−7.14630e8	−0.990622
$94$	3.30094e7	0.0436075
$95$	9.97444e8	1.25641
$96$	9.00447e8	1.08203
$97$	1.35910e9	1.55876	0.779379	−	0.626552i	$-0.215535\pi$
$97$	1.35910e9	1.55876	0.779379	+	0.626552i	$0.215535\pi$
$98$	−1.09562e8	−0.119989
$99$	2.18645e9	2.28761
$100$	1.09763e8	0.109763
$101$	1.70967e9	1.63480	0.817402	−	0.576067i	$-0.195413\pi$
$101$	1.70967e9	1.63480	0.817402	+	0.576067i	$0.195413\pi$
$102$	−2.90375e8	−0.265619
$103$	−1.52428e9	−1.33443	−0.667217	−	0.744863i	$-0.732515\pi$
$103$	−1.52428e9	−1.33443	−0.667217	+	0.744863i	$0.732515\pi$
$104$	−3.59774e8	−0.301564
$105$	−7.10772e8	−0.570661
$106$	1.46144e9	1.12436
$107$	1.09327e9	0.806304	0.403152	−	0.915133i	$-0.367915\pi$
$107$	1.09327e9	0.806304	0.403152	+	0.915133i	$0.367915\pi$
$108$	1.29694e9	0.917301
$109$	−2.86254e9	−1.94237	−0.971185	−	0.238325i	$-0.923402\pi$
$109$	−2.86254e9	−1.94237	−0.971185	+	0.238325i	$0.923402\pi$
$110$	−8.87250e8	−0.577802
$111$	−3.83874e9	−2.40013
$112$	−3.89434e8	−0.233858
$113$	2.73279e8	0.157671	0.0788357	−	0.996888i	$-0.474880\pi$
$113$	2.73279e8	0.157671	0.0788357	+	0.996888i	$0.474880\pi$
$114$	4.58018e9	2.53987
$115$	2.20931e8	0.117792
$116$	−3.47880e8	−0.178389
$117$	−1.48065e9	−0.730494
$118$	−2.79466e8	−0.132696
$119$	−1.37166e8	−0.0627027
$120$	−3.72902e9	−1.64164
$121$	−5.79177e8	−0.245628
$122$	2.69712e8	0.110225
$123$	−6.20461e9	−2.44423
$124$	−4.02944e8	−0.153055
$125$	−2.96762e9	−1.08721
$126$	−2.36564e9	−0.836143
$127$	4.01684e8	0.137015	0.0685075	−	0.997651i	$-0.478176\pi$
$127$	4.01684e8	0.137015	0.0685075	+	0.997651i	$0.478176\pi$
$128$	−1.07058e9	−0.352511
$129$	5.82891e9	1.85325
$130$	6.00841e8	0.184508
$131$	−3.70082e9	−1.09794	−0.548968	−	0.835843i	$-0.684979\pi$
$131$	−3.70082e9	−1.09794	−0.548968	+	0.835843i	$0.684979\pi$
$132$	1.70090e9	0.487637
$133$	2.16357e9	0.599568
$134$	−1.78118e9	−0.477240
$135$	−9.52001e9	−2.46681
$136$	−7.19634e8	−0.180379
$137$	5.32962e9	1.29257	0.646284	−	0.763097i	$-0.276322\pi$
$137$	5.32962e9	1.29257	0.646284	+	0.763097i	$0.276322\pi$
$138$	1.01450e9	0.238119
$139$	−7.24124e7	−0.0164531	−0.00822653	−	0.999966i	$-0.502619\pi$
$139$	−7.24124e7	−0.0164531	−0.00822653	+	0.999966i	$0.502619\pi$
$140$	−4.00768e8	−0.0881692
$141$	4.64504e8	0.0989699
$142$	6.83733e9	1.41120
$143$	−1.20457e9	−0.240891
$144$	−8.40856e9	−1.62964
$145$	2.55357e9	0.479725
$146$	−8.07665e9	−1.47110
$147$	−1.54174e9	−0.272323
$148$	−2.16447e9	−0.370830
$149$	9.21620e9	1.53184	0.765921	−	0.642935i	$-0.222283\pi$
$149$	9.21620e9	1.53184	0.765921	+	0.642935i	$0.222283\pi$
$150$	−3.69973e9	−0.596704
$151$	−3.96783e9	−0.621093	−0.310546	−	0.950558i	$-0.600512\pi$
$151$	−3.96783e9	−0.621093	−0.310546	+	0.950558i	$0.600512\pi$
$152$	1.13510e10	1.72480
$153$	−2.96166e9	−0.436942
$154$	−1.92455e9	−0.275731
$155$	2.95776e9	0.411595
$156$	−1.15184e9	−0.155716
$157$	5.19472e9	0.682360	0.341180	−	0.939998i	$-0.389173\pi$
$157$	5.19472e9	0.682360	0.341180	+	0.939998i	$0.389173\pi$
$158$	−2.45888e9	−0.313892
$159$	2.05653e10	2.55181
$160$	−3.72683e9	−0.449573
$161$	4.79223e8	0.0562110
$162$	−2.43220e10	−2.77449
$163$	−6.10693e9	−0.677608	−0.338804	−	0.940857i	$-0.610022\pi$
$163$	−6.10693e9	−0.677608	−0.338804	+	0.940857i	$0.610022\pi$
$164$	−3.49846e9	−0.377642
$165$	−1.24853e10	−1.31136
$166$	9.54953e9	0.976103
$167$	−6.35288e9	−0.632043	−0.316022	−	0.948752i	$-0.602347\pi$
$167$	−6.35288e9	−0.632043	−0.316022	+	0.948752i	$0.602347\pi$
$168$	−8.08866e9	−0.783402
$169$	8.15731e8	0.0769231
$170$	1.20183e9	0.110362
$171$	4.67152e10	4.17807
$172$	3.28662e9	0.286333
$173$	1.03351e10	0.877216	0.438608	−	0.898678i	$-0.355472\pi$
$173$	1.03351e10	0.877216	0.438608	+	0.898678i	$0.355472\pi$
$174$	1.17258e10	0.969775
$175$	−1.74766e9	−0.140860
$176$	−6.84072e9	−0.537396
$177$	−3.93261e9	−0.301162
$178$	7.67429e9	0.572992
$179$	−2.65864e9	−0.193562	−0.0967812	−	0.995306i	$-0.530855\pi$
$179$	−2.65864e9	−0.193562	−0.0967812	+	0.995306i	$0.530855\pi$
$180$	−8.65328e9	−0.614405
$181$	2.61993e10	1.81441	0.907205	−	0.420688i	$-0.138211\pi$
$181$	2.61993e10	1.81441	0.907205	+	0.420688i	$0.138211\pi$
$182$	1.30329e9	0.0880482
$183$	3.79536e9	0.250163
$184$	2.51421e9	0.161704
$185$	1.58881e10	0.997236
$186$	1.35818e10	0.832050
$187$	−2.40944e9	−0.144088
$188$	2.61910e8	0.0152912
$189$	−2.06500e10	−1.17718
$190$	−1.89568e10	−1.05529
$191$	2.01495e10	1.09550	0.547752	−	0.836640i	$-0.315484\pi$
$191$	2.01495e10	1.09550	0.547752	+	0.836640i	$0.315484\pi$
$192$	−3.93229e10	−2.08828
$193$	−5.59277e9	−0.290148	−0.145074	−	0.989421i	$-0.546342\pi$
$193$	−5.59277e9	−0.290148	−0.145074	+	0.989421i	$0.546342\pi$
$194$	−2.58302e10	−1.30924
$195$	8.45496e9	0.418751
$196$	−8.69312e8	−0.0420749
$197$	−1.17103e10	−0.553951	−0.276976	−	0.960877i	$-0.589332\pi$
$197$	−1.17103e10	−0.553951	−0.276976	+	0.960877i	$0.589332\pi$
$198$	−4.15543e10	−1.92142
$199$	6.16120e9	0.278501	0.139250	−	0.990257i	$-0.455531\pi$
$199$	6.16120e9	0.278501	0.139250	+	0.990257i	$0.455531\pi$
$200$	−9.16899e9	−0.405216
$201$	−2.50646e10	−1.08313
$202$	−3.24929e10	−1.37311
$203$	5.53899e9	0.228928
$204$	−2.30396e9	−0.0931407
$205$	2.56800e10	1.01555
$206$	2.89695e10	1.12083
$207$	1.03473e10	0.391705
$208$	4.63250e9	0.171605
$209$	3.80048e10	1.37778
$210$	1.35085e10	0.479313
$211$	3.71493e10	1.29027	0.645134	−	0.764070i	$-0.276802\pi$
$211$	3.71493e10	1.29027	0.645134	+	0.764070i	$0.276802\pi$
$212$	1.15957e10	0.394263
$213$	9.62141e10	3.20280
$214$	−2.07779e10	−0.677236
$215$	−2.41251e10	−0.770009
$216$	−1.08339e11	−3.38643
$217$	6.41572e9	0.196416
$218$	5.44036e10	1.63145
$219$	−1.13654e11	−3.33876
$220$	−7.03981e9	−0.202609
$221$	1.63166e9	0.0460112
$222$	7.29567e10	2.01594
$223$	9.60813e8	0.0260176	0.0130088	−	0.999915i	$-0.495859\pi$
$223$	9.60813e8	0.0260176	0.0130088	+	0.999915i	$0.495859\pi$
$224$	−8.08392e9	−0.214539
$225$	−3.77351e10	−0.981576
$226$	−5.19376e9	−0.132432
$227$	−4.91046e10	−1.22746	−0.613728	−	0.789518i	$-0.710331\pi$
$227$	−4.91046e10	−1.22746	−0.613728	+	0.789518i	$0.710331\pi$
$228$	3.63411e10	0.890618
$229$	1.82370e10	0.438221	0.219111	−	0.975700i	$-0.429684\pi$
$229$	1.82370e10	0.438221	0.219111	+	0.975700i	$0.429684\pi$
$230$	−4.19886e9	−0.0989365
$231$	−2.70820e10	−0.625787
$232$	2.90599e10	0.658565
$233$	4.08699e10	0.908453	0.454226	−	0.890886i	$-0.349916\pi$
$233$	4.08699e10	0.908453	0.454226	+	0.890886i	$0.349916\pi$
$234$	2.81403e10	0.613561
$235$	−1.92252e9	−0.0411212
$236$	−2.21740e9	−0.0465307
$237$	−3.46011e10	−0.712396
$238$	2.60690e9	0.0526657
$239$	7.95986e10	1.57803	0.789014	−	0.614375i	$-0.210592\pi$
$239$	7.95986e10	1.57803	0.789014	+	0.614375i	$0.210592\pi$
$240$	4.80153e10	0.934177
$241$	7.82899e10	1.49496	0.747479	−	0.664285i	$-0.231264\pi$
$241$	7.82899e10	1.49496	0.747479	+	0.664285i	$0.231264\pi$
$242$	1.10075e10	0.206309
$243$	−1.72972e11	−3.18234
$244$	2.14001e9	0.0386511
$245$	6.38108e9	0.113148
$246$	1.17921e11	2.05297
$247$	−2.57367e10	−0.439963
$248$	3.36596e10	0.565037
$249$	1.34380e11	2.21532
$250$	5.64008e10	0.913177
$251$	7.26371e10	1.15512	0.577560	−	0.816349i	$-0.304005\pi$
$251$	7.26371e10	1.15512	0.577560	+	0.816349i	$0.304005\pi$
$252$	−1.87700e10	−0.293198
$253$	8.41794e9	0.129171
$254$	−7.63415e9	−0.115082
$255$	1.69120e10	0.250474
$256$	−5.49346e10	−0.799403
$257$	−2.75374e10	−0.393752	−0.196876	−	0.980428i	$-0.563080\pi$
$257$	−2.75374e10	−0.393752	−0.196876	+	0.980428i	$0.563080\pi$
$258$	−1.10780e11	−1.55659
$259$	3.44630e10	0.475887
$260$	4.76732e9	0.0646985
$261$	1.19596e11	1.59528
$262$	7.03354e10	0.922185
$263$	9.43987e10	1.21665	0.608324	−	0.793688i	$-0.291842\pi$
$263$	9.43987e10	1.21665	0.608324	+	0.793688i	$0.291842\pi$
$264$	−1.42084e11	−1.80022
$265$	−8.51170e10	−1.06025
$266$	−4.11194e10	−0.503593
$267$	1.07992e11	1.30044
$268$	−1.41327e10	−0.167347
$269$	1.52665e11	1.77768	0.888838	−	0.458221i	$-0.151513\pi$
$269$	1.52665e11	1.77768	0.888838	+	0.458221i	$0.151513\pi$
$270$	1.80931e11	2.07194
$271$	−3.55121e9	−0.0399958	−0.0199979	−	0.999800i	$-0.506366\pi$
$271$	−3.55121e9	−0.0399958	−0.0199979	+	0.999800i	$0.506366\pi$
$272$	9.26611e9	0.102645
$273$	1.83398e10	0.199831
$274$	−1.01291e11	−1.08566
$275$	−3.06991e10	−0.323689
$276$	8.04943e9	0.0834977
$277$	−1.66364e11	−1.69786	−0.848928	−	0.528509i	$-0.822751\pi$
$277$	−1.66364e11	−1.69786	−0.848928	+	0.528509i	$0.822751\pi$
$278$	1.37622e9	0.0138193
$279$	1.38527e11	1.36872
$280$	3.34779e10	0.325497
$281$	−1.32399e11	−1.26680	−0.633399	−	0.773825i	$-0.718341\pi$
$281$	−1.32399e11	−1.26680	−0.633399	+	0.773825i	$0.718341\pi$
$282$	−8.82806e9	−0.0831274
$283$	−1.71592e11	−1.59022	−0.795109	−	0.606466i	$-0.792587\pi$
$283$	−1.71592e11	−1.59022	−0.795109	+	0.606466i	$0.792587\pi$
$284$	5.42502e10	0.494845
$285$	−2.66758e11	−2.39505
$286$	2.28934e10	0.202331
$287$	5.57029e10	0.484629
$288$	−1.74546e11	−1.49501
$289$	−1.15324e11	−0.972479
$290$	−4.85315e10	−0.402933
$291$	−3.63480e11	−2.97140
$292$	−6.40835e10	−0.515850
$293$	2.68502e10	0.212835	0.106418	−	0.994322i	$-0.466062\pi$
$293$	2.68502e10	0.212835	0.106418	+	0.994322i	$0.466062\pi$
$294$	2.93014e10	0.228731
$295$	1.62765e10	0.125130
$296$	1.80808e11	1.36900
$297$	−3.62733e11	−2.70510
$298$	−1.75157e11	−1.28663
$299$	−5.70058e9	−0.0412476
$300$	−2.93552e10	−0.209237
$301$	−5.23300e10	−0.367453
$302$	7.54100e10	0.521672
$303$	−4.57236e11	−3.11637
$304$	−1.46157e11	−0.981498
$305$	−1.57085e10	−0.103941
$306$	5.62874e10	0.366999
$307$	1.80631e10	0.116057	0.0580284	−	0.998315i	$-0.481519\pi$
$307$	1.80631e10	0.116057	0.0580284	+	0.998315i	$0.481519\pi$
$308$	−1.52702e10	−0.0966864
$309$	4.07655e11	2.54378
$310$	−5.62133e10	−0.345710
$311$	−1.21312e11	−0.735327	−0.367663	−	0.929959i	$-0.619842\pi$
$311$	−1.21312e11	−0.735327	−0.367663	+	0.929959i	$0.619842\pi$
$312$	9.62183e10	0.574860
$313$	5.55168e10	0.326945	0.163473	−	0.986548i	$-0.447730\pi$
$313$	5.55168e10	0.326945	0.163473	+	0.986548i	$0.447730\pi$
$314$	−9.87274e10	−0.573132
$315$	1.37779e11	0.788468
$316$	−1.95098e10	−0.110068
$317$	−4.21508e10	−0.234444	−0.117222	−	0.993106i	$-0.537399\pi$
$317$	−4.21508e10	−0.234444	−0.117222	+	0.993106i	$0.537399\pi$
$318$	−3.90850e11	−2.14333
$319$	9.72967e10	0.526066
$320$	1.62752e11	0.867665
$321$	−2.92384e11	−1.53703
$322$	−9.10781e9	−0.0472131
$323$	−5.14795e10	−0.263162
$324$	−1.92981e11	−0.972888
$325$	2.07892e10	0.103363
$326$	1.16064e11	0.569141
$327$	7.65561e11	3.70267
$328$	2.92242e11	1.39415
$329$	−4.17016e9	−0.0196233
$330$	2.37287e11	1.10144
$331$	−3.02859e11	−1.38680	−0.693402	−	0.720551i	$-0.743889\pi$
$331$	−3.02859e11	−1.38680	−0.693402	+	0.720551i	$0.743889\pi$
$332$	7.57700e10	0.342275
$333$	7.44116e11	3.31621
$334$	1.20739e11	0.530870
$335$	1.03739e11	0.450030
$336$	1.04151e11	0.445795
$337$	−2.00922e11	−0.848578	−0.424289	−	0.905527i	$-0.639476\pi$
$337$	−2.00922e11	−0.848578	−0.424289	+	0.905527i	$0.639476\pi$
$338$	−1.55033e10	−0.0646097
$339$	−7.30859e10	−0.300563
$340$	9.53579e9	0.0386992
$341$	1.12697e11	0.451355
$342$	−8.87840e11	−3.50927
$343$	1.38413e10	0.0539949
$344$	−2.74546e11	−1.05707
$345$	−5.90859e10	−0.224542
$346$	−1.96422e11	−0.736797
$347$	−2.82429e11	−1.04575	−0.522874	−	0.852410i	$-0.675140\pi$
$347$	−2.82429e11	−1.04575	−0.522874	+	0.852410i	$0.675140\pi$
$348$	9.30374e10	0.340057
$349$	2.67460e11	0.965039	0.482520	−	0.875885i	$-0.339722\pi$
$349$	2.67460e11	0.965039	0.482520	+	0.875885i	$0.339722\pi$
$350$	3.32149e10	0.118312
$351$	2.45641e11	0.863812
$352$	−1.42001e11	−0.493001
$353$	3.45544e11	1.18445	0.592226	−	0.805772i	$-0.298249\pi$
$353$	3.45544e11	1.18445	0.592226	+	0.805772i	$0.298249\pi$
$354$	7.47406e10	0.252954
$355$	−3.98217e11	−1.33074
$356$	6.08911e10	0.200923
$357$	3.66840e10	0.119528
$358$	5.05284e10	0.162578
$359$	−3.21350e11	−1.02106	−0.510532	−	0.859859i	$-0.670552\pi$
$359$	−3.21350e11	−1.02106	−0.510532	+	0.859859i	$0.670552\pi$
$360$	7.22846e11	2.26822
$361$	4.89315e11	1.51637
$362$	−4.97926e11	−1.52397
$363$	1.54896e11	0.468230
$364$	1.03409e10	0.0308745
$365$	4.70398e11	1.38723
$366$	−7.21322e10	−0.210118
$367$	−4.64868e11	−1.33762	−0.668810	−	0.743433i	$-0.733196\pi$
$367$	−4.64868e11	−1.33762	−0.668810	+	0.743433i	$0.733196\pi$
$368$	−3.23733e10	−0.0920179
$369$	1.20272e12	3.37712
$370$	−3.01958e11	−0.837604
$371$	−1.84628e11	−0.505960
$372$	1.07764e11	0.291763
$373$	1.02736e10	0.0274809	0.0137404	−	0.999906i	$-0.495626\pi$
$373$	1.02736e10	0.0274809	0.0137404	+	0.999906i	$0.495626\pi$
$374$	4.57922e10	0.121023
$375$	7.93665e11	2.07251
$376$	−2.18785e10	−0.0564510
$377$	−6.58888e10	−0.167987
$378$	3.92460e11	0.988741
$379$	−1.05771e10	−0.0263323	−0.0131662	−	0.999913i	$-0.504191\pi$
$379$	−1.05771e10	−0.0263323	−0.0131662	+	0.999913i	$0.504191\pi$
$380$	−1.50411e11	−0.370044
$381$	−1.07427e11	−0.261187
$382$	−3.82949e11	−0.920143
$383$	2.12166e11	0.503827	0.251913	−	0.967750i	$-0.418940\pi$
$383$	2.12166e11	0.503827	0.251913	+	0.967750i	$0.418940\pi$
$384$	2.86316e11	0.671979
$385$	1.12089e11	0.260009
$386$	1.06293e11	0.243703
$387$	−1.12990e12	−2.56059
$388$	−2.04948e11	−0.459093
$389$	4.34127e11	0.961266	0.480633	−	0.876922i	$-0.340407\pi$
$389$	4.34127e11	0.961266	0.480633	+	0.876922i	$0.340407\pi$
$390$	−1.60689e11	−0.351720
$391$	−1.14025e10	−0.0246721
$392$	7.26174e10	0.155329
$393$	9.89752e11	2.09295
$394$	2.22559e11	0.465278
$395$	1.43209e11	0.295995
$396$	−3.29709e11	−0.673756
$397$	1.54000e11	0.311146	0.155573	−	0.987824i	$-0.450278\pi$
$397$	1.54000e11	0.311146	0.155573	+	0.987824i	$0.450278\pi$
$398$	−1.17096e11	−0.233920
$399$	−5.78628e11	−1.14293
$400$	1.18061e11	0.230588
$401$	−4.02298e11	−0.776959	−0.388480	−	0.921457i	$-0.627000\pi$
$401$	−4.02298e11	−0.776959	−0.388480	+	0.921457i	$0.627000\pi$
$402$	4.76362e11	0.909745
$403$	−7.63179e10	−0.144130
$404$	−2.57812e11	−0.481490
$405$	1.41656e12	2.61629
$406$	−1.05270e11	−0.192282
$407$	6.05370e11	1.09357
$408$	1.92460e11	0.343850
$409$	6.87811e11	1.21539	0.607693	−	0.794172i	$-0.292095\pi$
$409$	6.87811e11	1.21539	0.607693	+	0.794172i	$0.292095\pi$
$410$	−4.88058e11	−0.852991
$411$	−1.42536e12	−2.46397
$412$	2.29856e11	0.393024
$413$	3.53057e10	0.0597131
$414$	−1.96653e11	−0.329003
$415$	−5.56181e11	−0.920448
$416$	9.61620e10	0.157428
$417$	1.93661e10	0.0313638
$418$	−7.22295e11	−1.15723
$419$	1.11812e12	1.77226	0.886129	−	0.463438i	$-0.153384\pi$
$419$	1.11812e12	1.77226	0.886129	+	0.463438i	$0.153384\pi$
$420$	1.07182e11	0.168074
$421$	−7.42231e11	−1.15152	−0.575758	−	0.817620i	$-0.695293\pi$
$421$	−7.42231e11	−1.15152	−0.575758	+	0.817620i	$0.695293\pi$
$422$	−7.06036e11	−1.08373
$423$	−9.00411e10	−0.136744
$424$	−9.68640e11	−1.45551
$425$	4.15835e10	0.0618260
$426$	−1.82858e12	−2.69012
$427$	−3.40735e10	−0.0496011
$428$	−1.64861e11	−0.237476
$429$	3.22153e11	0.459202
$430$	4.58506e11	0.646750
$431$	3.20304e11	0.447110	0.223555	−	0.974691i	$-0.428234\pi$
$431$	3.20304e11	0.447110	0.223555	+	0.974691i	$0.428234\pi$
$432$	1.39498e12	1.92705
$433$	−7.07388e11	−0.967080	−0.483540	−	0.875322i	$-0.660649\pi$
$433$	−7.07388e11	−0.967080	−0.483540	+	0.875322i	$0.660649\pi$
$434$	−1.21933e11	−0.164975
$435$	−6.82930e11	−0.914481
$436$	4.31661e11	0.572076
$437$	1.79856e11	0.235916
$438$	2.16003e12	2.80431
$439$	−1.57238e11	−0.202053	−0.101027	−	0.994884i	$-0.532213\pi$
$439$	−1.57238e11	−0.202053	−0.101027	+	0.994884i	$0.532213\pi$
$440$	5.88066e11	0.747978
$441$	2.98857e11	0.376262
$442$	−3.10102e10	−0.0386460
$443$	1.21578e12	1.49981	0.749907	−	0.661544i	$-0.230098\pi$
$443$	1.21578e12	1.49981	0.749907	+	0.661544i	$0.230098\pi$
$444$	5.78869e11	0.706898
$445$	−4.46964e11	−0.540321
$446$	−1.82606e10	−0.0218529
$447$	−2.46479e12	−2.92009
$448$	3.53028e11	0.414055
$449$	−1.31962e12	−1.53229	−0.766147	−	0.642666i	$-0.777828\pi$
$449$	−1.31962e12	−1.53229	−0.766147	+	0.642666i	$0.777828\pi$
$450$	7.17168e11	0.824451
$451$	9.78466e11	1.11366
$452$	−4.12095e10	−0.0464380
$453$	1.06116e12	1.18397
$454$	9.33250e11	1.03097
$455$	−7.59059e10	−0.0830279
$456$	−3.03573e12	−3.28792
$457$	1.68107e12	1.80286	0.901432	−	0.432920i	$-0.142517\pi$
$457$	1.68107e12	1.80286	0.901432	+	0.432920i	$0.142517\pi$
$458$	−3.46600e11	−0.368073
$459$	4.91341e11	0.516685
$460$	−3.33155e10	−0.0346926
$461$	7.14657e11	0.736959	0.368480	−	0.929636i	$-0.379878\pi$
$461$	7.14657e11	0.736959	0.368480	+	0.929636i	$0.379878\pi$
$462$	5.14703e11	0.525615
$463$	−1.49469e12	−1.51160	−0.755801	−	0.654801i	$-0.772752\pi$
$463$	−1.49469e12	−1.51160	−0.755801	+	0.654801i	$0.772752\pi$
$464$	−3.74179e11	−0.374756
$465$	−7.91027e11	−0.784608
$466$	−7.76748e11	−0.763033
$467$	1.93553e12	1.88311	0.941553	−	0.336864i	$-0.109366\pi$
$467$	1.93553e12	1.88311	0.941553	+	0.336864i	$0.109366\pi$
$468$	2.23277e11	0.215148
$469$	2.25022e11	0.214757
$470$	3.65382e10	0.0345387
$471$	−1.38928e12	−1.30076
$472$	1.85229e11	0.171779
$473$	−9.19219e11	−0.844391
$474$	6.57605e11	0.598360
$475$	−6.55910e11	−0.591184
$476$	2.06842e10	0.0184675
$477$	−3.98645e12	−3.52577
$478$	−1.51280e12	−1.32543
$479$	3.52795e11	0.306205	0.153103	−	0.988210i	$-0.451074\pi$
$479$	3.52795e11	0.306205	0.153103	+	0.988210i	$0.451074\pi$
$480$	9.96708e11	0.857003
$481$	−4.09953e11	−0.349206
$482$	−1.48793e12	−1.25565
$483$	−1.28164e11	−0.107153
$484$	8.73378e10	0.0723433
$485$	1.50439e12	1.23459
$486$	3.28739e12	2.67293
$487$	−3.66997e11	−0.295653	−0.147826	−	0.989013i	$-0.547228\pi$
$487$	−3.66997e11	−0.295653	−0.147826	+	0.989013i	$0.547228\pi$
$488$	−1.78764e11	−0.142689
$489$	1.63324e12	1.29170
$490$	−1.21275e11	−0.0950359
$491$	−4.95596e11	−0.384823	−0.192412	−	0.981314i	$-0.561631\pi$
$491$	−4.95596e11	−0.384823	−0.192412	+	0.981314i	$0.561631\pi$
$492$	9.35633e11	0.719884
$493$	−1.31793e11	−0.100481
$494$	4.89134e11	0.369536
$495$	2.42019e12	1.81187
$496$	−4.33406e11	−0.321534
$497$	−8.63779e11	−0.635037
$498$	−2.55394e12	−1.86071
$499$	2.02736e12	1.46379	0.731893	−	0.681419i	$-0.238637\pi$
$499$	2.02736e12	1.46379	0.731893	+	0.681419i	$0.238637\pi$
$500$	4.47507e11	0.320210
$501$	1.69902e12	1.20484
$502$	−1.38049e12	−0.970215
$503$	−1.11109e12	−0.773913	−0.386956	−	0.922098i	$-0.626474\pi$
$503$	−1.11109e12	−0.773913	−0.386956	+	0.922098i	$0.626474\pi$
$504$	1.56794e12	1.08241
$505$	1.89244e12	1.29482
$506$	−1.59986e11	−0.108494
$507$	−2.18160e11	−0.146636
$508$	−6.05726e10	−0.0403543
$509$	1.02850e12	0.679163	0.339581	−	0.940577i	$-0.389715\pi$
$509$	1.02850e12	0.679163	0.339581	+	0.940577i	$0.389715\pi$
$510$	−3.21418e11	−0.210380
$511$	1.02035e12	0.661993
$512$	1.59219e12	1.02395
$513$	−7.75008e12	−4.94058
$514$	5.23357e11	0.330723
$515$	−1.68723e12	−1.05692
$516$	−8.78979e11	−0.545827
$517$	−7.32523e10	−0.0450935
$518$	−6.54981e11	−0.399710
$519$	−2.76403e12	−1.67220
$520$	−3.98235e11	−0.238850
$521$	−1.54044e12	−0.915957	−0.457979	−	0.888963i	$-0.651426\pi$
$521$	−1.54044e12	−0.915957	−0.457979	+	0.888963i	$0.651426\pi$
$522$	−2.27297e12	−1.33991
$523$	1.73399e12	1.01342	0.506711	−	0.862116i	$-0.330861\pi$
$523$	1.73399e12	1.01342	0.506711	+	0.862116i	$0.330861\pi$
$524$	5.58071e11	0.323369
$525$	4.67397e11	0.268515
$526$	−1.79408e12	−1.02189
$527$	−1.52654e11	−0.0862107
$528$	1.82949e12	1.02442
$529$	−1.76132e12	−0.977882
$530$	1.61768e12	0.890535
$531$	7.62311e11	0.416109
$532$	−3.26259e11	−0.176587
$533$	−6.62612e11	−0.355621
$534$	−2.05242e12	−1.09227
$535$	1.21014e12	0.638622
$536$	1.18056e12	0.617799
$537$	7.11030e11	0.368981
$538$	−2.90144e12	−1.49312
$539$	2.43133e11	0.124078
$540$	1.43558e12	0.726535
$541$	1.11808e12	0.561157	0.280578	−	0.959831i	$-0.409474\pi$
$541$	1.11808e12	0.561157	0.280578	+	0.959831i	$0.409474\pi$
$542$	6.74920e10	0.0335935
$543$	−7.00676e12	−3.45874
$544$	1.92347e11	0.0941652
$545$	−3.16855e12	−1.53843
$546$	−3.48554e11	−0.167843
$547$	2.38569e11	0.113939	0.0569694	−	0.998376i	$-0.481856\pi$
$547$	2.38569e11	0.113939	0.0569694	+	0.998376i	$0.481856\pi$
$548$	−8.03688e11	−0.380693
$549$	−7.35707e11	−0.345644
$550$	5.83447e11	0.271875
$551$	2.07882e12	0.960804
$552$	−6.72404e11	−0.308251
$553$	3.10637e11	0.141251
$554$	3.16181e12	1.42607
$555$	−4.24912e12	−1.90099
$556$	1.09195e10	0.00484583
$557$	2.87679e12	1.26637	0.633183	−	0.774002i	$-0.281748\pi$
$557$	2.87679e12	1.26637	0.633183	+	0.774002i	$0.281748\pi$
$558$	−2.63275e12	−1.14962
$559$	6.22490e11	0.269637
$560$	−4.31066e11	−0.185224
$561$	6.44383e11	0.274670
$562$	2.51630e12	1.06402
$563$	3.95108e12	1.65740	0.828701	−	0.559692i	$-0.189081\pi$
$563$	3.95108e12	1.65740	0.828701	+	0.559692i	$0.189081\pi$
$564$	−7.00455e10	−0.0291491
$565$	3.02493e11	0.124881
$566$	3.26116e12	1.33567
$567$	3.07267e12	1.24851
$568$	−4.53176e12	−1.82683
$569$	6.25346e11	0.250101	0.125050	−	0.992150i	$-0.460091\pi$
$569$	6.25346e11	0.250101	0.125050	+	0.992150i	$0.460091\pi$
$570$	5.06982e12	2.01167
$571$	−1.34562e12	−0.529736	−0.264868	−	0.964285i	$-0.585328\pi$
$571$	−1.34562e12	−0.529736	−0.264868	+	0.964285i	$0.585328\pi$
$572$	1.81646e11	0.0709484
$573$	−5.38881e12	−2.08832
$574$	−1.05865e12	−0.407053
$575$	−1.45282e11	−0.0554250
$576$	7.62249e12	2.88533
$577$	−4.52799e12	−1.70065	−0.850324	−	0.526260i	$-0.823594\pi$
$577$	−4.52799e12	−1.70065	−0.850324	+	0.526260i	$0.823594\pi$
$578$	2.19178e12	0.816810
$579$	1.49574e12	0.553098
$580$	−3.85070e11	−0.141291
$581$	−1.20642e12	−0.439244
$582$	6.90806e12	2.49576
$583$	−3.24315e12	−1.16267
$584$	5.35317e12	1.90438
$585$	−1.63894e12	−0.578578
$586$	−5.10298e11	−0.178766
$587$	−7.70494e11	−0.267854	−0.133927	−	0.990991i	$-0.542759\pi$
$587$	−7.70494e11	−0.267854	−0.133927	+	0.990991i	$0.542759\pi$
$588$	2.32490e11	0.0802058
$589$	2.40786e12	0.824353
$590$	−3.09341e11	−0.105100
$591$	3.13183e12	1.05598
$592$	−2.32811e12	−0.779031
$593$	3.90361e12	1.29634	0.648172	−	0.761494i	$-0.275534\pi$
$593$	3.90361e12	1.29634	0.648172	+	0.761494i	$0.275534\pi$
$594$	6.89388e12	2.27209
$595$	−1.51830e11	−0.0496628
$596$	−1.38977e12	−0.451165
$597$	−1.64776e12	−0.530896
$598$	1.08342e11	0.0346449
$599$	3.03859e12	0.964387	0.482193	−	0.876065i	$-0.339840\pi$
$599$	3.03859e12	0.964387	0.482193	+	0.876065i	$0.339840\pi$
$600$	2.45216e12	0.772448
$601$	−2.62760e12	−0.821532	−0.410766	−	0.911741i	$-0.634739\pi$
$601$	−2.62760e12	−0.821532	−0.410766	+	0.911741i	$0.634739\pi$
$602$	9.94551e11	0.308633
$603$	4.85862e12	1.49653
$604$	5.98335e11	0.182927
$605$	−6.41093e11	−0.194546
$606$	8.68993e12	2.61752
$607$	3.72904e12	1.11493	0.557465	−	0.830200i	$-0.311774\pi$
$607$	3.72904e12	1.11493	0.557465	+	0.830200i	$0.311774\pi$
$608$	−3.03395e12	−0.900415
$609$	−1.48135e12	−0.436396
$610$	2.98546e11	0.0873025
$611$	4.96060e10	0.0143996
$612$	4.46608e11	0.128690
$613$	1.95102e12	0.558072	0.279036	−	0.960281i	$-0.409985\pi$
$613$	1.95102e12	0.558072	0.279036	+	0.960281i	$0.409985\pi$
$614$	−3.43296e11	−0.0974791
$615$	−6.86790e12	−1.93591
$616$	1.27558e12	0.356940
$617$	−4.20008e12	−1.16674	−0.583370	−	0.812207i	$-0.698266\pi$
$617$	−4.20008e12	−1.16674	−0.583370	+	0.812207i	$0.698266\pi$
$618$	−7.74763e12	−2.13659
$619$	2.91252e12	0.797371	0.398685	−	0.917088i	$-0.369467\pi$
$619$	2.91252e12	0.797371	0.398685	+	0.917088i	$0.369467\pi$
$620$	−4.46020e11	−0.121225
$621$	−1.71662e12	−0.463192
$622$	2.30557e12	0.617620
$623$	−9.69515e11	−0.257845
$624$	−1.23892e12	−0.327124
$625$	−1.86322e12	−0.488431
$626$	−1.05512e12	−0.274610
$627$	−1.01641e13	−2.62641
$628$	−7.83345e11	−0.200972
$629$	−8.20005e11	−0.208876
$630$	−2.61853e12	−0.662255
$631$	2.13779e12	0.536825	0.268413	−	0.963304i	$-0.413501\pi$
$631$	2.13779e12	0.536825	0.268413	+	0.963304i	$0.413501\pi$
$632$	1.62974e12	0.406341
$633$	−9.93525e12	−2.45959
$634$	8.01090e11	0.196915
$635$	4.44626e11	0.108521
$636$	−3.10117e12	−0.751569
$637$	−1.64648e11	−0.0396214
$638$	−1.84916e12	−0.441856
$639$	−1.86505e13	−4.42523
$640$	−1.18503e12	−0.279202
$641$	−9.75006e11	−0.228111	−0.114055	−	0.993474i	$-0.536384\pi$
$641$	−9.75006e11	−0.228111	−0.114055	+	0.993474i	$0.536384\pi$
$642$	5.55687e12	1.29099
$643$	6.33218e12	1.46084	0.730422	−	0.682996i	$-0.239323\pi$
$643$	6.33218e12	1.46084	0.730422	+	0.682996i	$0.239323\pi$
$644$	−7.22652e10	−0.0165555
$645$	6.45204e12	1.46784
$646$	9.78387e11	0.221037
$647$	−5.28295e12	−1.18524	−0.592621	−	0.805482i	$-0.701907\pi$
$647$	−5.28295e12	−1.18524	−0.592621	+	0.805482i	$0.701907\pi$
$648$	1.61206e13	3.59164
$649$	6.20172e11	0.137218
$650$	−3.95107e11	−0.0868170
$651$	−1.71583e12	−0.374420
$652$	9.20903e11	0.199572
$653$	−5.00453e11	−0.107710	−0.0538548	−	0.998549i	$-0.517151\pi$
$653$	−5.00453e11	−0.107710	−0.0538548	+	0.998549i	$0.517151\pi$
$654$	−1.45498e13	−3.10997
$655$	−4.09645e12	−0.869605
$656$	−3.76294e12	−0.793342
$657$	2.20310e13	4.61308
$658$	7.92555e10	0.0164821
$659$	8.50338e12	1.75634	0.878168	−	0.478353i	$-0.158766\pi$
$659$	8.50338e12	1.75634	0.878168	+	0.478353i	$0.158766\pi$
$660$	1.88274e12	0.386226
$661$	8.25796e12	1.68254	0.841272	−	0.540613i	$-0.181808\pi$
$661$	8.25796e12	1.68254	0.841272	+	0.540613i	$0.181808\pi$
$662$	5.75595e12	1.16481
$663$	−4.36372e11	−0.0877095
$664$	−6.32939e12	−1.26359
$665$	2.39486e12	0.474879
$666$	−1.41422e13	−2.78537
$667$	4.60452e11	0.0900778
$668$	9.57993e11	0.186152
$669$	−2.56961e11	−0.0495964
$670$	−1.97160e12	−0.377992
$671$	−5.98529e11	−0.113981
$672$	2.16197e12	0.408967
$673$	−3.22415e12	−0.605826	−0.302913	−	0.953018i	$-0.597959\pi$
$673$	−3.22415e12	−0.605826	−0.302913	+	0.953018i	$0.597959\pi$
$674$	3.81859e12	0.712743
$675$	6.26027e12	1.16072
$676$	−1.23009e11	−0.0226557
$677$	4.21817e12	0.771748	0.385874	−	0.922552i	$-0.373900\pi$
$677$	4.21817e12	0.771748	0.385874	+	0.922552i	$0.373900\pi$
$678$	1.38902e12	0.252450
$679$	3.26320e12	0.589155
$680$	−7.96566e11	−0.142867
$681$	1.31326e13	2.33985
$682$	−2.14185e12	−0.379105
$683$	1.30473e12	0.229417	0.114709	−	0.993399i	$-0.463407\pi$
$683$	1.30473e12	0.229417	0.114709	+	0.993399i	$0.463407\pi$
$684$	−7.04450e12	−1.23054
$685$	5.89938e12	1.02376
$686$	−2.63059e11	−0.0453517
$687$	−4.87732e12	−0.835364
$688$	3.53509e12	0.601524
$689$	2.19624e12	0.371273
$690$	1.12295e12	0.188599
$691$	−4.02848e12	−0.672187	−0.336093	−	0.941829i	$-0.609106\pi$
$691$	−4.02848e12	−0.672187	−0.336093	+	0.941829i	$0.609106\pi$
$692$	−1.55849e12	−0.258362
$693$	5.24967e12	0.864634
$694$	5.36766e12	0.878350
$695$	−8.01536e10	−0.0130314
$696$	−7.77182e12	−1.25540
$697$	−1.32538e12	−0.212713
$698$	−5.08318e12	−0.810562
$699$	−1.09303e13	−1.73175
$700$	2.63541e11	0.0414866
$701$	4.56350e12	0.713785	0.356892	−	0.934146i	$-0.383836\pi$
$701$	4.56350e12	0.713785	0.356892	+	0.934146i	$0.383836\pi$
$702$	−4.66850e12	−0.725538
$703$	1.29342e13	1.99729
$704$	6.20122e12	0.951481
$705$	5.14161e11	0.0783877
$706$	−6.56719e12	−0.994852
$707$	4.10491e12	0.617898
$708$	5.93023e11	0.0886997
$709$	5.91122e12	0.878555	0.439277	−	0.898351i	$-0.355235\pi$
$709$	5.91122e12	0.878555	0.439277	+	0.898351i	$0.355235\pi$
$710$	7.56826e12	1.11772
$711$	6.70719e12	0.984300
$712$	−5.08649e12	−0.741752
$713$	5.33334e11	0.0772852
$714$	−6.97192e11	−0.100395
$715$	−1.33335e12	−0.190795
$716$	4.00914e11	0.0570089
$717$	−2.12879e13	−3.00814
$718$	6.10737e12	0.857619
$719$	3.95121e12	0.551380	0.275690	−	0.961247i	$-0.411094\pi$
$719$	3.95121e12	0.551380	0.275690	+	0.961247i	$0.411094\pi$
$720$	−9.30747e12	−1.29073
$721$	−3.65980e12	−0.504369
$722$	−9.29961e12	−1.27364
$723$	−2.09379e13	−2.84978
$724$	−3.95076e12	−0.534388
$725$	−1.67920e12	−0.225726
$726$	−2.94385e12	−0.393279
$727$	1.29602e13	1.72071	0.860353	−	0.509699i	$-0.170243\pi$
$727$	1.29602e13	1.72071	0.860353	+	0.509699i	$0.170243\pi$
$728$	−8.63817e11	−0.113980
$729$	2.10705e13	2.76313
$730$	−8.94007e12	−1.16517
$731$	1.24513e12	0.161282
$732$	−5.72327e11	−0.0736791
$733$	−4.00618e11	−0.0512581	−0.0256291	−	0.999672i	$-0.508159\pi$
$733$	−4.00618e11	−0.0512581	−0.0256291	+	0.999672i	$0.508159\pi$
$734$	8.83499e12	1.12350
$735$	−1.70656e12	−0.215690
$736$	−6.72010e11	−0.0844162
$737$	3.95269e12	0.493502
$738$	−2.28582e13	−2.83653
$739$	4.11302e12	0.507296	0.253648	−	0.967297i	$-0.418370\pi$
$739$	4.11302e12	0.507296	0.253648	+	0.967297i	$0.418370\pi$
$740$	−2.39586e12	−0.293710
$741$	6.88304e12	0.838684
$742$	3.50893e12	0.424969
$743$	5.64643e12	0.679711	0.339856	−	0.940478i	$-0.389622\pi$
$743$	5.64643e12	0.679711	0.339856	+	0.940478i	$0.389622\pi$
$744$	−9.00197e12	−1.07711
$745$	1.02015e13	1.21327
$746$	−1.95252e11	−0.0230819
$747$	−2.60487e13	−3.06086
$748$	3.63335e11	0.0424375
$749$	2.62493e12	0.304754
$750$	−1.50839e13	−1.74075
$751$	1.42031e13	1.62931	0.814654	−	0.579948i	$-0.196927\pi$
$751$	1.42031e13	1.62931	0.814654	+	0.579948i	$0.196927\pi$
$752$	2.81710e11	0.0321235
$753$	−1.94262e13	−2.20196
$754$	1.25224e12	0.141097
$755$	−4.39200e12	−0.491928
$756$	3.11395e12	0.346707
$757$	1.06020e13	1.17343	0.586714	−	0.809794i	$-0.300421\pi$
$757$	1.06020e13	1.17343	0.586714	+	0.809794i	$0.300421\pi$
$758$	2.01021e11	0.0221172
$759$	−2.25130e12	−0.246233
$760$	1.25645e13	1.36610
$761$	2.55088e12	0.275714	0.137857	−	0.990452i	$-0.455979\pi$
$761$	2.55088e12	0.275714	0.137857	+	0.990452i	$0.455979\pi$
$762$	2.04169e12	0.219377
$763$	−6.87296e12	−0.734147
$764$	−3.03848e12	−0.322653
$765$	−3.27827e12	−0.346074
$766$	−4.03229e12	−0.423177
$767$	−4.19977e11	−0.0438174
$768$	1.46918e13	1.52387
$769$	−9.28818e12	−0.957772	−0.478886	−	0.877877i	$-0.658959\pi$
$769$	−9.28818e12	−0.957772	−0.478886	+	0.877877i	$0.658959\pi$
$770$	−2.13029e12	−0.218388
$771$	7.36462e12	0.750595
$772$	8.43371e11	0.0854556
$773$	3.41861e12	0.344383	0.172192	−	0.985063i	$-0.444915\pi$
$773$	3.41861e12	0.344383	0.172192	+	0.985063i	$0.444915\pi$
$774$	2.14741e13	2.15070
$775$	−1.94499e12	−0.193669
$776$	1.71202e13	1.69485
$777$	−9.21682e12	−0.907166
$778$	−8.25073e12	−0.807392
$779$	2.09057e13	2.03398
$780$	−1.27498e12	−0.123332
$781$	−1.51730e13	−1.45929
$782$	2.16709e11	0.0207227
$783$	−1.98411e13	−1.88642
$784$	−9.35031e11	−0.0883901
$785$	5.75005e12	0.540453
$786$	−1.88106e13	−1.75793
$787$	−1.35710e12	−0.126103	−0.0630517	−	0.998010i	$-0.520083\pi$
$787$	−1.35710e12	−0.126103	−0.0630517	+	0.998010i	$0.520083\pi$
$788$	1.76588e12	0.163152
$789$	−2.52461e13	−2.31925
$790$	−2.72174e12	−0.248614
$791$	6.56142e11	0.0595942
$792$	2.75420e13	2.48733
$793$	4.05320e11	0.0363973
$794$	−2.92683e12	−0.261340
$795$	2.27638e13	2.02112
$796$	−9.29088e11	−0.0820253
$797$	−1.96286e13	−1.72316	−0.861581	−	0.507619i	$-0.830526\pi$
$797$	−1.96286e13	−1.72316	−0.861581	+	0.507619i	$0.830526\pi$
$798$	1.09970e13	0.959980
$799$	9.92240e10	0.00861304
$800$	2.45073e12	0.211539
$801$	−2.09335e13	−1.79678
$802$	7.64582e12	0.652588
$803$	1.79232e13	1.52123
$804$	3.77966e12	0.319007
$805$	5.30454e11	0.0445212
$806$	1.45045e12	0.121058
$807$	−4.08288e13	−3.38872
$808$	2.15362e13	1.77753
$809$	−1.73959e13	−1.42783	−0.713917	−	0.700231i	$-0.753080\pi$
$809$	−1.73959e13	−1.42783	−0.713917	+	0.700231i	$0.753080\pi$
$810$	−2.69222e13	−2.19749
$811$	−1.63150e13	−1.32432	−0.662159	−	0.749363i	$-0.730360\pi$
$811$	−1.63150e13	−1.32432	−0.662159	+	0.749363i	$0.730360\pi$
$812$	−8.35260e11	−0.0674248
$813$	9.49740e11	0.0762425
$814$	−1.15053e13	−0.918516
$815$	−6.75978e12	−0.536690
$816$	−2.47814e12	−0.195668
$817$	−1.96398e13	−1.54219
$818$	−1.30721e13	−1.02083
$819$	−3.55505e12	−0.276101
$820$	−3.87246e12	−0.299106
$821$	−8.07431e12	−0.620242	−0.310121	−	0.950697i	$-0.600370\pi$
$821$	−8.07431e12	−0.620242	−0.310121	+	0.950697i	$0.600370\pi$
$822$	2.70895e13	2.06956
$823$	−1.79696e13	−1.36534	−0.682669	−	0.730728i	$-0.739181\pi$
$823$	−1.79696e13	−1.36534	−0.682669	+	0.730728i	$0.739181\pi$
$824$	−1.92009e13	−1.45094
$825$	8.21020e12	0.617036
$826$	−6.70997e11	−0.0501545
$827$	−1.81645e13	−1.35036	−0.675178	−	0.737655i	$-0.735933\pi$
$827$	−1.81645e13	−1.35036	−0.675178	+	0.737655i	$0.735933\pi$
$828$	−1.56033e12	−0.115367
$829$	5.49500e10	0.00404084	0.00202042	−	0.999998i	$-0.499357\pi$
$829$	5.49500e10	0.00404084	0.00202042	+	0.999998i	$0.499357\pi$
$830$	1.05704e13	0.773108
$831$	4.44926e13	3.23656
$832$	−4.19943e12	−0.303833
$833$	−3.29337e11	−0.0236994
$834$	−3.68059e11	−0.0263433
$835$	−7.03203e12	−0.500601
$836$	−5.73100e12	−0.405790
$837$	−2.29816e13	−1.61851
$838$	−2.12503e13	−1.48857
$839$	1.71556e13	1.19530	0.597650	−	0.801757i	$-0.296101\pi$
$839$	1.71556e13	1.19530	0.597650	+	0.801757i	$0.296101\pi$
$840$	−8.95337e12	−0.620483
$841$	−9.18513e12	−0.633145
$842$	1.41064e13	0.967188
$843$	3.54091e13	2.41485
$844$	−5.60199e12	−0.380015
$845$	9.02935e11	0.0609258
$846$	1.71126e12	0.114855
$847$	−1.39060e12	−0.0928385
$848$	1.24723e13	0.828260
$849$	4.58906e13	3.03137
$850$	−7.90309e11	−0.0519292
$851$	2.86488e12	0.187251
$852$	−1.45087e13	−0.943304
$853$	−6.34053e12	−0.410067	−0.205034	−	0.978755i	$-0.565730\pi$
$853$	−6.34053e12	−0.410067	−0.205034	+	0.978755i	$0.565730\pi$
$854$	6.47579e11	0.0416613
$855$	5.17093e13	3.30918
$856$	1.37715e13	0.876698
$857$	2.45040e13	1.55176	0.775879	−	0.630882i	$-0.217307\pi$
$857$	2.45040e13	1.55176	0.775879	+	0.630882i	$0.217307\pi$
$858$	−6.12262e12	−0.385696
$859$	1.27478e13	0.798848	0.399424	−	0.916766i	$-0.369210\pi$
$859$	1.27478e13	0.798848	0.399424	+	0.916766i	$0.369210\pi$
$860$	3.63798e12	0.226786
$861$	−1.48973e13	−0.923830
$862$	−6.08749e12	−0.375539
$863$	−1.31810e13	−0.808910	−0.404455	−	0.914558i	$-0.632539\pi$
$863$	−1.31810e13	−0.808910	−0.404455	+	0.914558i	$0.632539\pi$
$864$	2.89573e13	1.76785
$865$	1.14399e13	0.694787
$866$	1.34442e13	0.812275
$867$	3.08424e13	1.85380
$868$	−9.67468e11	−0.0578493
$869$	5.45659e12	0.324588
$870$	1.29793e13	0.768096
$871$	−2.67674e12	−0.157589
$872$	−3.60585e13	−2.11195
$873$	7.04582e13	4.10551
$874$	−3.41822e12	−0.198152
$875$	−7.12527e12	−0.410927
$876$	1.71386e13	0.983346
$877$	−2.25809e13	−1.28897	−0.644487	−	0.764616i	$-0.722929\pi$
$877$	−2.25809e13	−1.28897	−0.644487	+	0.764616i	$0.722929\pi$
$878$	2.98836e12	0.169710
$879$	−7.18085e12	−0.405720
$880$	−7.57202e12	−0.425637
$881$	−8.60920e11	−0.0481472	−0.0240736	−	0.999710i	$-0.507664\pi$
$881$	−8.60920e11	−0.0481472	−0.0240736	+	0.999710i	$0.507664\pi$
$882$	−5.67989e12	−0.316032
$883$	−1.72958e13	−0.957454	−0.478727	−	0.877964i	$-0.658902\pi$
$883$	−1.72958e13	−0.957454	−0.478727	+	0.877964i	$0.658902\pi$
$884$	−2.46048e11	−0.0135514
$885$	−4.35302e12	−0.238531
$886$	−2.31063e13	−1.25973
$887$	−2.43457e13	−1.32058	−0.660291	−	0.751010i	$-0.729567\pi$
$887$	−2.43457e13	−1.32058	−0.660291	+	0.751010i	$0.729567\pi$
$888$	−4.83554e13	−2.60968
$889$	9.64444e11	0.0517868
$890$	8.49470e12	0.453830
$891$	5.39739e13	2.86903
$892$	−1.44887e11	−0.00766282
$893$	−1.56509e12	−0.0823585
$894$	4.68443e13	2.45266
$895$	−2.94286e12	−0.153308
$896$	−2.57046e12	−0.133237
$897$	1.52457e12	0.0786288
$898$	2.50799e13	1.28701
$899$	6.16441e12	0.314755
$900$	5.69032e12	0.289098
$901$	4.39301e12	0.222075
$902$	−1.85961e13	−0.935390
$903$	1.39952e13	0.700462
$904$	3.44240e12	0.171437
$905$	2.90001e13	1.43708
$906$	−2.01677e13	−0.994443
$907$	−3.74150e11	−0.0183575	−0.00917873	−	0.999958i	$-0.502922\pi$
$907$	−3.74150e11	−0.0183575	−0.00917873	+	0.999958i	$0.502922\pi$
$908$	7.40480e12	0.361516
$909$	8.86322e13	4.30580
$910$	1.44262e12	0.0697373
$911$	1.84324e12	0.0886646	0.0443323	−	0.999017i	$-0.485884\pi$
$911$	1.84324e12	0.0886646	0.0443323	+	0.999017i	$0.485884\pi$
$912$	3.90885e13	1.87099
$913$	−2.11917e13	−1.00936
$914$	−3.19493e13	−1.51427
$915$	4.20110e12	0.198138
$916$	−2.75007e12	−0.129067
$917$	−8.88567e12	−0.414981
$918$	−9.33812e12	−0.433978
$919$	2.19490e13	1.01507	0.507534	−	0.861632i	$-0.330557\pi$
$919$	2.19490e13	1.01507	0.507534	+	0.861632i	$0.330557\pi$
$920$	2.78299e12	0.128076
$921$	−4.83082e12	−0.221235
$922$	−1.35823e13	−0.618991
$923$	1.02750e13	0.465989
$924$	4.08387e12	0.184310
$925$	−1.04478e13	−0.469233
$926$	2.84072e13	1.26963
$927$	−7.90214e13	−3.51468
$928$	−7.76726e12	−0.343797
$929$	3.11770e13	1.37329	0.686647	−	0.726991i	$-0.259082\pi$
$929$	3.11770e13	1.37329	0.686647	+	0.726991i	$0.259082\pi$
$930$	1.50337e13	0.659013
$931$	5.19473e12	0.226615
$932$	−6.16304e12	−0.267561
$933$	3.24437e13	1.40173
$934$	−3.67855e13	−1.58167
$935$	−2.66702e12	−0.114123
$936$	−1.86513e13	−0.794270
$937$	−2.96885e12	−0.125823	−0.0629116	−	0.998019i	$-0.520039\pi$
$937$	−2.96885e12	−0.125823	−0.0629116	+	0.998019i	$0.520039\pi$
$938$	−4.27662e12	−0.180380
$939$	−1.48475e13	−0.623243
$940$	2.89909e11	0.0121112
$941$	−1.59563e13	−0.663405	−0.331702	−	0.943384i	$-0.607623\pi$
$941$	−1.59563e13	−0.663405	−0.331702	+	0.943384i	$0.607623\pi$
$942$	2.64038e13	1.09254
$943$	4.63054e12	0.190691
$944$	−2.38503e12	−0.0977508
$945$	−2.28575e13	−0.932366
$946$	1.74701e13	0.709226
$947$	−2.52843e13	−1.02159	−0.510794	−	0.859703i	$-0.670648\pi$
$947$	−2.52843e13	−1.02159	−0.510794	+	0.859703i	$0.670648\pi$
$948$	5.21772e12	0.209818
$949$	−1.21375e13	−0.485770
$950$	1.24658e13	0.496551
$951$	1.12728e13	0.446911
$952$	−1.72784e12	−0.0681770
$953$	2.10071e13	0.824987	0.412494	−	0.910960i	$-0.364658\pi$
$953$	2.10071e13	0.824987	0.412494	+	0.910960i	$0.364658\pi$
$954$	7.57639e13	2.96138
$955$	2.23036e13	0.867679
$956$	−1.20032e13	−0.464768
$957$	−2.60211e13	−1.00282
$958$	−6.70499e12	−0.257190
$959$	1.27964e13	0.488545
$960$	−4.35266e13	−1.65400
$961$	−1.92995e13	−0.729946
$962$	7.79130e12	0.293307
$963$	5.66768e13	2.12367
$964$	−1.18058e13	−0.440302
$965$	−6.19066e12	−0.229808
$966$	2.43580e12	0.0900005
$967$	−4.79247e13	−1.76255	−0.881273	−	0.472607i	$-0.843313\pi$
$967$	−4.79247e13	−1.76255	−0.881273	+	0.472607i	$0.843313\pi$
$968$	−7.29571e12	−0.267072
$969$	1.37677e13	0.501656
$970$	−2.85915e13	−1.03697
$971$	2.38996e13	0.862787	0.431394	−	0.902164i	$-0.358022\pi$
$971$	2.38996e13	0.862787	0.431394	+	0.902164i	$0.358022\pi$
$972$	2.60835e13	0.937278
$973$	−1.73862e11	−0.00621867
$974$	6.97490e12	0.248326
$975$	−5.55990e12	−0.197036
$976$	2.30180e12	0.0811975
$977$	−1.19374e13	−0.419166	−0.209583	−	0.977791i	$-0.567211\pi$
$977$	−1.19374e13	−0.419166	−0.209583	+	0.977791i	$0.567211\pi$
$978$	−3.10404e13	−1.08493
$979$	−1.70303e13	−0.592516
$980$	−9.62244e11	−0.0333248
$981$	−1.48399e14	−5.11588
$982$	9.41898e12	0.323223
$983$	3.21445e13	1.09803	0.549017	−	0.835811i	$-0.315002\pi$
$983$	3.21445e13	1.09803	0.549017	+	0.835811i	$0.315002\pi$
$984$	−7.81574e13	−2.65762
$985$	−1.29622e13	−0.438749
$986$	2.50478e12	0.0843964
$987$	1.11527e12	0.0374071
$988$	3.88100e12	0.129580
$989$	−4.35015e12	−0.144584
$990$	−4.59966e13	−1.52183
$991$	2.91766e13	0.960955	0.480477	−	0.877007i	$-0.340463\pi$
$991$	2.91766e13	0.960955	0.480477	+	0.877007i	$0.340463\pi$
$992$	−8.99670e12	−0.294972
$993$	8.09970e13	2.64361
$994$	1.64164e13	0.533384
$995$	6.81986e12	0.220583
$996$	−2.02640e13	−0.652467
$997$	5.28401e13	1.69370	0.846848	−	0.531834i	$-0.178497\pi$
$997$	5.28401e13	1.69370	0.846848	+	0.531834i	$0.178497\pi$
$998$	−3.85306e13	−1.22947
$999$	−1.23449e14	−3.92142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-19.0054 q^{2} -267.441 q^{3} -150.796 q^{4} +1106.90 q^{5} +5082.81 q^{6} +2401.00 q^{7} +12596.7 q^{8} +51841.8 q^{9} +O(q^{10})\)	\(q-19.0054 q^{2} -267.441 q^{3} -150.796 q^{4} +1106.90 q^{5} +5082.81 q^{6} +2401.00 q^{7} +12596.7 q^{8} +51841.8 q^{9} -21037.1 q^{10} +42175.5 q^{11} +40329.2 q^{12} -28561.0 q^{13} -45631.9 q^{14} -296032. q^{15} -162197. q^{16} -57128.9 q^{17} -985271. q^{18} +901112. q^{19} -166917. q^{20} -642126. q^{21} -801560. q^{22} +199593. q^{23} -3.36887e6 q^{24} -727889. q^{25} +542812. q^{26} -8.60058e6 q^{27} -362062. q^{28} +2.30695e6 q^{29} +5.62619e6 q^{30} +2.67210e6 q^{31} -3.36690e6 q^{32} -1.12795e7 q^{33} +1.08575e6 q^{34} +2.65768e6 q^{35} -7.81756e6 q^{36} +1.43536e7 q^{37} -1.71260e7 q^{38} +7.63839e6 q^{39} +1.39433e7 q^{40} +2.31999e7 q^{41} +1.22038e7 q^{42} -2.17951e7 q^{43} -6.35991e6 q^{44} +5.73838e7 q^{45} -3.79334e6 q^{46} -1.73684e6 q^{47} +4.33780e7 q^{48} +5.76480e6 q^{49} +1.38338e7 q^{50} +1.52786e7 q^{51} +4.30690e6 q^{52} -7.68965e7 q^{53} +1.63457e8 q^{54} +4.66842e7 q^{55} +3.02446e7 q^{56} -2.40994e8 q^{57} -4.38444e7 q^{58} +1.47046e7 q^{59} +4.46405e7 q^{60} -1.41914e7 q^{61} -5.07843e7 q^{62} +1.24472e8 q^{63} +1.47034e8 q^{64} -3.16143e7 q^{65} +2.14370e8 q^{66} +9.37201e7 q^{67} +8.61484e6 q^{68} -5.33794e7 q^{69} -5.05101e7 q^{70} -3.59758e8 q^{71} +6.53034e8 q^{72} +4.24967e8 q^{73} -2.72795e8 q^{74} +1.94668e8 q^{75} -1.35885e8 q^{76} +1.01263e8 q^{77} -1.45170e8 q^{78} +1.29378e8 q^{79} -1.79536e8 q^{80} +1.27975e9 q^{81} -4.40922e8 q^{82} -5.02465e8 q^{83} +9.68304e7 q^{84} -6.32362e7 q^{85} +4.14224e8 q^{86} -6.16973e8 q^{87} +5.31271e8 q^{88} -4.03796e8 q^{89} -1.09060e9 q^{90} -6.85750e7 q^{91} -3.00980e7 q^{92} -7.14630e8 q^{93} +3.30094e7 q^{94} +9.97444e8 q^{95} +9.00447e8 q^{96} +1.35910e9 q^{97} -1.09562e8 q^{98} +2.18645e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Introduction

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