LMFDB - Embedded newform 91.10.a.b.1.10

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:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4945 x^{11} - 8694 x^{10} + 9009530 x^{9} + 27431200 x^{8} - 7320118704 x^{7} + \cdots + 20\!\cdots\!00 $ x^13 - 4945x^11 - 8694x^10 + 9009530x^9 + 27431200x^8 - 7320118704x^7 - 28566940352x^6 + 2456696387328x^5 + 11170187661056x^4 - 201778709941248x^3 - 1417840074892800x^2 - 1725123584678400*x + 2025982720512000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$25.2754$ 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)

$f(q)$	$=$	$q+23.2754 q^{2} +5.80529 q^{3} +29.7447 q^{4} +2107.58 q^{5} +135.120 q^{6} -2401.00 q^{7} -11224.7 q^{8} -19649.3 q^{9} +O(q^{10})$	\(q+23.2754 q^{2} +5.80529 q^{3} +29.7447 q^{4} +2107.58 q^{5} +135.120 q^{6} -2401.00 q^{7} -11224.7 q^{8} -19649.3 q^{9} +49054.9 q^{10} +1021.05 q^{11} +172.676 q^{12} -28561.0 q^{13} -55884.3 q^{14} +12235.1 q^{15} -276489. q^{16} -157157. q^{17} -457345. q^{18} -565523. q^{19} +62689.4 q^{20} -13938.5 q^{21} +23765.4 q^{22} -246584. q^{23} -65162.5 q^{24} +2.48878e6 q^{25} -664769. q^{26} -228335. q^{27} -71417.0 q^{28} +1.71702e6 q^{29} +284777. q^{30} -291482. q^{31} -688343. q^{32} +5927.49 q^{33} -3.65789e6 q^{34} -5.06031e6 q^{35} -584462. q^{36} -1.36942e7 q^{37} -1.31628e7 q^{38} -165805. q^{39} -2.36570e7 q^{40} -1.84681e7 q^{41} -324424. q^{42} +1.45079e7 q^{43} +30370.9 q^{44} -4.14125e7 q^{45} -5.73934e6 q^{46} -7.95996e6 q^{47} -1.60510e6 q^{48} +5.76480e6 q^{49} +5.79274e7 q^{50} -912340. q^{51} -849538. q^{52} -4.59260e7 q^{53} -5.31460e6 q^{54} +2.15195e6 q^{55} +2.69505e7 q^{56} -3.28303e6 q^{57} +3.99644e7 q^{58} -1.39423e8 q^{59} +363930. q^{60} -1.07419e8 q^{61} -6.78436e6 q^{62} +4.71780e7 q^{63} +1.25541e8 q^{64} -6.01947e7 q^{65} +137965. q^{66} -1.85122e7 q^{67} -4.67458e6 q^{68} -1.43149e6 q^{69} -1.17781e8 q^{70} +1.35416e7 q^{71} +2.20557e8 q^{72} +1.89880e8 q^{73} -3.18738e8 q^{74} +1.44481e7 q^{75} -1.68213e7 q^{76} -2.45154e6 q^{77} -3.85917e6 q^{78} +9.86568e7 q^{79} -5.82723e8 q^{80} +3.85432e8 q^{81} -4.29852e8 q^{82} -7.47822e8 q^{83} -414596. q^{84} -3.31221e8 q^{85} +3.37678e8 q^{86} +9.96780e6 q^{87} -1.14610e7 q^{88} +7.83712e8 q^{89} -9.63894e8 q^{90} +6.85750e7 q^{91} -7.33456e6 q^{92} -1.69214e6 q^{93} -1.85271e8 q^{94} -1.19189e9 q^{95} -3.99603e6 q^{96} -3.55582e8 q^{97} +1.34178e8 q^{98} -2.00629e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) $ 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * 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 $

$2$	23.2754	1.02864	0.514319	−	0.857599i	$-0.328045\pi$
$2$	23.2754	1.02864	0.514319	+	0.857599i	$0.328045\pi$
$3$	5.80529	0.0413788	0.0206894	−	0.999786i	$-0.493414\pi$
$3$	5.80529	0.0413788	0.0206894	+	0.999786i	$0.493414\pi$
$4$	29.7447	0.0580951
$5$	2107.58	1.50806	0.754032	−	0.656838i	$-0.228106\pi$
$5$	2107.58	1.50806	0.754032	+	0.656838i	$0.228106\pi$
$6$	135.120	0.0425638
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−11224.7	−0.968879
$9$	−19649.3	−0.998288
$10$	49054.9	1.55125
$11$	1021.05	0.0210272	0.0105136	−	0.999945i	$-0.496653\pi$
$11$	1021.05	0.0210272	0.0105136	+	0.999945i	$0.496653\pi$
$12$	172.676	0.00240391
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−55884.3	−0.388788
$15$	12235.1	0.0624019
$16$	−276489.	−1.05472
$17$	−157157.	−0.456365	−0.228183	−	0.973618i	$-0.573278\pi$
$17$	−157157.	−0.456365	−0.228183	+	0.973618i	$0.573278\pi$
$18$	−457345.	−1.02688
$19$	−565523.	−0.995542	−0.497771	−	0.867309i	$-0.665848\pi$
$19$	−565523.	−0.995542	−0.497771	+	0.867309i	$0.665848\pi$
$20$	62689.4	0.0876111
$21$	−13938.5	−0.0156397
$22$	23765.4	0.0216293
$23$	−246584.	−0.183734	−0.0918669	−	0.995771i	$-0.529283\pi$
$23$	−246584.	−0.183734	−0.0918669	+	0.995771i	$0.529283\pi$
$24$	−65162.5	−0.0400910
$25$	2.48878e6	1.27426
$26$	−664769.	−0.285293
$27$	−228335.	−0.0826868
$28$	−71417.0	−0.0219579
$29$	1.71702e6	0.450801	0.225400	−	0.974266i	$-0.427631\pi$
$29$	1.71702e6	0.450801	0.225400	+	0.974266i	$0.427631\pi$
$30$	284777.	0.0641889
$31$	−291482.	−0.0566871	−0.0283435	−	0.999598i	$-0.509023\pi$
$31$	−291482.	−0.0566871	−0.0283435	+	0.999598i	$0.509023\pi$
$32$	−688343.	−0.116046
$33$	5927.49	0.000870079 0
$34$	−3.65789e6	−0.469435
$35$	−5.06031e6	−0.569994
$36$	−584462.	−0.0579956
$37$	−1.36942e7	−1.20124	−0.600619	−	0.799535i	$-0.705079\pi$
$37$	−1.36942e7	−1.20124	−0.600619	+	0.799535i	$0.705079\pi$
$38$	−1.31628e7	−1.02405
$39$	−165805.	−0.0114764
$40$	−2.36570e7	−1.46113
$41$	−1.84681e7	−1.02069	−0.510345	−	0.859970i	$-0.670482\pi$
$41$	−1.84681e7	−1.02069	−0.510345	+	0.859970i	$0.670482\pi$
$42$	−324424.	−0.0160876
$43$	1.45079e7	0.647138	0.323569	−	0.946205i	$-0.395117\pi$
$43$	1.45079e7	0.647138	0.323569	+	0.946205i	$0.395117\pi$
$44$	30370.9	0.00122157
$45$	−4.14125e7	−1.50548
$46$	−5.73934e6	−0.188996
$47$	−7.95996e6	−0.237942	−0.118971	−	0.992898i	$-0.537959\pi$
$47$	−7.95996e6	−0.237942	−0.118971	+	0.992898i	$0.537959\pi$
$48$	−1.60510e6	−0.0436431
$49$	5.76480e6	0.142857
$50$	5.79274e7	1.31075
$51$	−912340.	−0.0188839
$52$	−849538.	−0.0161127
$53$	−4.59260e7	−0.799497	−0.399749	−	0.916625i	$-0.630903\pi$
$53$	−4.59260e7	−0.799497	−0.399749	+	0.916625i	$0.630903\pi$
$54$	−5.31460e6	−0.0850547
$55$	2.15195e6	0.0317103
$56$	2.69505e7	0.366202
$57$	−3.28303e6	−0.0411943
$58$	3.99644e7	0.463711
$59$	−1.39423e8	−1.49796	−0.748981	−	0.662592i	$-0.769456\pi$
$59$	−1.39423e8	−1.49796	−0.748981	+	0.662592i	$0.769456\pi$
$60$	363930.	0.00362524
$61$	−1.07419e8	−0.993334	−0.496667	−	0.867941i	$-0.665443\pi$
$61$	−1.07419e8	−0.993334	−0.496667	+	0.867941i	$0.665443\pi$
$62$	−6.78436e6	−0.0583105
$63$	4.71780e7	0.377317
$64$	1.25541e8	0.935351
$65$	−6.01947e7	−0.418262
$66$	137965.	0.000894995 0
$67$	−1.85122e7	−0.112233	−0.0561167	−	0.998424i	$-0.517872\pi$
$67$	−1.85122e7	−0.112233	−0.0561167	+	0.998424i	$0.517872\pi$
$68$	−4.67458e6	−0.0265126
$69$	−1.43149e6	−0.00760269
$70$	−1.17781e8	−0.586318
$71$	1.35416e7	0.0632422	0.0316211	−	0.999500i	$-0.489933\pi$
$71$	1.35416e7	0.0632422	0.0316211	+	0.999500i	$0.489933\pi$
$72$	2.20557e8	0.967220
$73$	1.89880e8	0.782574	0.391287	−	0.920269i	$-0.372030\pi$
$73$	1.89880e8	0.782574	0.391287	+	0.920269i	$0.372030\pi$
$74$	−3.18738e8	−1.23564
$75$	1.44481e7	0.0527272
$76$	−1.68213e7	−0.0578361
$77$	−2.45154e6	−0.00794752
$78$	−3.85917e6	−0.0118051
$79$	9.86568e7	0.284974	0.142487	−	0.989797i	$-0.454490\pi$
$79$	9.86568e7	0.284974	0.142487	+	0.989797i	$0.454490\pi$
$80$	−5.82723e8	−1.59058
$81$	3.85432e8	0.994866
$82$	−4.29852e8	−1.04992
$83$	−7.47822e8	−1.72961	−0.864803	−	0.502112i	$-0.832557\pi$
$83$	−7.47822e8	−1.72961	−0.864803	+	0.502112i	$0.832557\pi$
$84$	−414596.	−0.000908591 0
$85$	−3.31221e8	−0.688228
$86$	3.37678e8	0.665670
$87$	9.96780e6	0.0186536
$88$	−1.14610e7	−0.0203728
$89$	7.83712e8	1.32404	0.662021	−	0.749486i	$-0.269699\pi$
$89$	7.83712e8	1.32404	0.662021	+	0.749486i	$0.269699\pi$
$90$	−9.63894e8	−1.54859
$91$	6.85750e7	0.104828
$92$	−7.33456e6	−0.0106740
$93$	−1.69214e6	−0.00234564
$94$	−1.85271e8	−0.244756
$95$	−1.19189e9	−1.50134
$96$	−3.99603e6	−0.00480184
$97$	−3.55582e8	−0.407819	−0.203909	−	0.978990i	$-0.565365\pi$
$97$	−3.55582e8	−0.407819	−0.203909	+	0.978990i	$0.565365\pi$
$98$	1.34178e8	0.146948
$99$	−2.00629e7	−0.0209911
$100$	7.40280e7	0.0740280
$101$	1.69120e9	1.61715	0.808573	−	0.588395i	$-0.200240\pi$
$101$	1.69120e9	1.61715	0.808573	+	0.588395i	$0.200240\pi$
$102$	−2.12351e7	−0.0194246
$103$	9.75466e8	0.853974	0.426987	−	0.904258i	$-0.359575\pi$
$103$	9.75466e8	0.853974	0.426987	+	0.904258i	$0.359575\pi$
$104$	3.20588e8	0.268719
$105$	−2.93765e7	−0.0235857
$106$	−1.06895e9	−0.822393
$107$	1.24004e9	0.914555	0.457278	−	0.889324i	$-0.348825\pi$
$107$	1.24004e9	0.914555	0.457278	+	0.889324i	$0.348825\pi$
$108$	−6.79176e6	−0.00480370
$109$	−2.55400e9	−1.73301	−0.866507	−	0.499165i	$-0.833640\pi$
$109$	−2.55400e9	−1.73301	−0.866507	+	0.499165i	$0.833640\pi$
$110$	5.00875e7	0.0326184
$111$	−7.94988e7	−0.0497058
$112$	6.63849e8	0.398647
$113$	1.03971e9	0.599872	0.299936	−	0.953959i	$-0.403035\pi$
$113$	1.03971e9	0.599872	0.299936	+	0.953959i	$0.403035\pi$
$114$	−7.64138e7	−0.0423740
$115$	−5.19696e8	−0.277082
$116$	5.10723e7	0.0261893
$117$	5.61204e8	0.276875
$118$	−3.24513e9	−1.54086
$119$	3.77333e8	0.172490
$120$	−1.37335e8	−0.0604598
$121$	−2.35691e9	−0.999558
$122$	−2.50021e9	−1.02178
$123$	−1.07212e8	−0.0422349
$124$	−8.67004e6	−0.00329324
$125$	1.12894e9	0.413595
$126$	1.09809e9	0.388123
$127$	3.70881e8	0.126508	0.0632540	−	0.997997i	$-0.479852\pi$
$127$	3.70881e8	0.126508	0.0632540	+	0.997997i	$0.479852\pi$
$128$	3.27444e9	1.07818
$129$	8.42226e7	0.0267778
$130$	−1.40106e9	−0.430240
$131$	4.52022e9	1.34103	0.670516	−	0.741895i	$-0.266073\pi$
$131$	4.52022e9	1.34103	0.670516	+	0.741895i	$0.266073\pi$
$132$	176312.	5.05473e−5 0
$133$	1.35782e9	0.376279
$134$	−4.30880e8	−0.115447
$135$	−4.81235e8	−0.124697
$136$	1.76404e9	0.442163
$137$	3.28584e9	0.796900	0.398450	−	0.917190i	$-0.369548\pi$
$137$	3.28584e9	0.796900	0.398450	+	0.917190i	$0.369548\pi$
$138$	−3.33185e7	−0.00782041
$139$	3.21120e9	0.729626	0.364813	−	0.931081i	$-0.381133\pi$
$139$	3.21120e9	0.729626	0.364813	+	0.931081i	$0.381133\pi$
$140$	−1.50517e8	−0.0331139
$141$	−4.62098e7	−0.00984574
$142$	3.15186e8	0.0650533
$143$	−2.91622e7	−0.00583188
$144$	5.43281e9	1.05291
$145$	3.61876e9	0.679836
$146$	4.41952e9	0.804985
$147$	3.34663e7	0.00591126
$148$	−4.07330e8	−0.0697861
$149$	3.63968e9	0.604958	0.302479	−	0.953156i	$-0.402186\pi$
$149$	3.63968e9	0.604958	0.302479	+	0.953156i	$0.402186\pi$
$150$	3.36285e8	0.0542372
$151$	8.31285e9	1.30123	0.650615	−	0.759408i	$-0.274511\pi$
$151$	8.31285e9	1.30123	0.650615	+	0.759408i	$0.274511\pi$
$152$	6.34782e9	0.964559
$153$	3.08802e9	0.455584
$154$	−5.70607e7	−0.00817511
$155$	−6.14323e8	−0.0854877
$156$	−4.93181e6	−0.000666724 0
$157$	−7.71573e9	−1.01351	−0.506755	−	0.862090i	$-0.669155\pi$
$157$	−7.71573e9	−1.01351	−0.506755	+	0.862090i	$0.669155\pi$
$158$	2.29628e9	0.293135
$159$	−2.66613e8	−0.0330823
$160$	−1.45074e9	−0.175005
$161$	5.92048e8	0.0694449
$162$	8.97108e9	1.02336
$163$	−3.98929e9	−0.442641	−0.221321	−	0.975201i	$-0.571037\pi$
$163$	−3.98929e9	−0.442641	−0.221321	+	0.975201i	$0.571037\pi$
$164$	−5.49327e8	−0.0592971
$165$	1.24927e7	0.00131213
$166$	−1.74059e10	−1.77914
$167$	1.22618e10	1.21991	0.609956	−	0.792435i	$-0.291187\pi$
$167$	1.22618e10	1.21991	0.609956	+	0.792435i	$0.291187\pi$
$168$	1.56455e8	0.0151530
$169$	8.15731e8	0.0769231
$170$	−7.70930e9	−0.707937
$171$	1.11121e10	0.993837
$172$	4.31533e8	0.0375955
$173$	−8.11633e8	−0.0688894	−0.0344447	−	0.999407i	$-0.510966\pi$
$173$	−8.11633e8	−0.0688894	−0.0344447	+	0.999407i	$0.510966\pi$
$174$	2.32005e8	0.0191878
$175$	−5.97556e9	−0.481623
$176$	−2.82309e8	−0.0221778
$177$	−8.09391e8	−0.0619839
$178$	1.82412e10	1.36196
$179$	−1.18000e10	−0.859097	−0.429548	−	0.903044i	$-0.641327\pi$
$179$	−1.18000e10	−0.859097	−0.429548	+	0.903044i	$0.641327\pi$
$180$	−1.23180e9	−0.0874611
$181$	−4.08844e9	−0.283142	−0.141571	−	0.989928i	$-0.545215\pi$
$181$	−4.08844e9	−0.283142	−0.141571	+	0.989928i	$0.545215\pi$
$182$	1.59611e9	0.107831
$183$	−6.23596e8	−0.0411030
$184$	2.76783e9	0.178016
$185$	−2.88617e10	−1.81154
$186$	−3.93852e7	−0.00241282
$187$	−1.60465e8	−0.00959607
$188$	−2.36767e8	−0.0138232
$189$	5.48233e8	0.0312527
$190$	−2.77417e10	−1.54433
$191$	1.74897e10	0.950893	0.475446	−	0.879745i	$-0.342287\pi$
$191$	1.74897e10	0.950893	0.475446	+	0.879745i	$0.342287\pi$
$192$	7.28800e8	0.0387037
$193$	−1.29452e10	−0.671586	−0.335793	−	0.941936i	$-0.609004\pi$
$193$	−1.29452e10	−0.671586	−0.335793	+	0.941936i	$0.609004\pi$
$194$	−8.27632e9	−0.419498
$195$	−3.49447e8	−0.0173072
$196$	1.71472e8	0.00829930
$197$	−2.62497e10	−1.24173	−0.620864	−	0.783918i	$-0.713218\pi$
$197$	−2.62497e10	−1.24173	−0.620864	+	0.783918i	$0.713218\pi$
$198$	−4.66973e8	−0.0215923
$199$	−3.19560e10	−1.44448	−0.722242	−	0.691640i	$-0.756888\pi$
$199$	−3.19560e10	−1.44448	−0.722242	+	0.691640i	$0.756888\pi$
$200$	−2.79358e10	−1.23460
$201$	−1.07469e8	−0.00464408
$202$	3.93634e10	1.66346
$203$	−4.12257e9	−0.170387
$204$	−2.71373e7	−0.00109706
$205$	−3.89230e10	−1.53927
$206$	2.27044e10	0.878430
$207$	4.84520e9	0.183419
$208$	7.89679e9	0.292527
$209$	−5.77428e8	−0.0209334
$210$	−6.83751e8	−0.0242611
$211$	−2.75509e10	−0.956897	−0.478448	−	0.878116i	$-0.658801\pi$
$211$	−2.75509e10	−0.956897	−0.478448	+	0.878116i	$0.658801\pi$
$212$	−1.36605e9	−0.0464469
$213$	7.86128e7	0.00261689
$214$	2.88625e10	0.940746
$215$	3.05766e10	0.975925
$216$	2.56299e9	0.0801134
$217$	6.99848e8	0.0214257
$218$	−5.94454e10	−1.78264
$219$	1.10231e9	0.0323820
$220$	6.40091e7	0.00184221
$221$	4.48855e9	0.126573
$222$	−1.85037e9	−0.0511293
$223$	4.13976e10	1.12099	0.560497	−	0.828156i	$-0.310610\pi$
$223$	4.13976e10	1.12099	0.560497	+	0.828156i	$0.310610\pi$
$224$	1.65271e9	0.0438612
$225$	−4.89028e10	−1.27207
$226$	2.41997e10	0.617051
$227$	−4.29846e9	−0.107448	−0.0537238	−	0.998556i	$-0.517109\pi$
$227$	−4.29846e9	−0.107448	−0.0537238	+	0.998556i	$0.517109\pi$
$228$	−9.76526e7	−0.00239319
$229$	2.19791e10	0.528142	0.264071	−	0.964503i	$-0.414935\pi$
$229$	2.19791e10	0.528142	0.264071	+	0.964503i	$0.414935\pi$
$230$	−1.20961e10	−0.285017
$231$	−1.42319e7	−0.000328859 0
$232$	−1.92730e10	−0.436771
$233$	−2.12302e10	−0.471902	−0.235951	−	0.971765i	$-0.575820\pi$
$233$	−2.12302e10	−0.471902	−0.235951	+	0.971765i	$0.575820\pi$
$234$	1.30622e10	0.284804
$235$	−1.67763e10	−0.358831
$236$	−4.14710e9	−0.0870242
$237$	5.72731e8	0.0117919
$238$	8.78259e9	0.177430
$239$	−7.02316e10	−1.39233	−0.696165	−	0.717882i	$-0.745112\pi$
$239$	−7.02316e10	−1.39233	−0.696165	+	0.717882i	$0.745112\pi$
$240$	−3.38287e9	−0.0658165
$241$	−6.44986e10	−1.23161	−0.615806	−	0.787898i	$-0.711169\pi$
$241$	−6.44986e10	−1.23161	−0.615806	+	0.787898i	$0.711169\pi$
$242$	−5.48579e10	−1.02818
$243$	6.73186e9	0.123853
$244$	−3.19513e9	−0.0577078
$245$	1.21498e10	0.215438
$246$	−2.49541e9	−0.0434444
$247$	1.61519e10	0.276114
$248$	3.27180e9	0.0549229
$249$	−4.34132e9	−0.0715690
$250$	2.62765e10	0.425440
$251$	5.19508e10	0.826152	0.413076	−	0.910697i	$-0.364454\pi$
$251$	5.19508e10	0.826152	0.413076	+	0.910697i	$0.364454\pi$
$252$	1.40329e9	0.0219203
$253$	−2.51775e8	−0.00386340
$254$	8.63241e9	0.130131
$255$	−1.92283e9	−0.0284781
$256$	1.19372e10	0.173708
$257$	1.00839e11	1.44188	0.720938	−	0.693000i	$-0.243711\pi$
$257$	1.00839e11	1.44188	0.720938	+	0.693000i	$0.243711\pi$
$258$	1.96031e9	0.0275446
$259$	3.28798e10	0.454026
$260$	−1.79047e9	−0.0242990
$261$	−3.37383e10	−0.450029
$262$	1.05210e11	1.37943
$263$	1.29585e11	1.67014	0.835069	−	0.550145i	$-0.185428\pi$
$263$	1.29585e11	1.67014	0.835069	+	0.550145i	$0.185428\pi$
$264$	−6.65343e7	−0.000843001 0
$265$	−9.67928e10	−1.20569
$266$	3.16039e10	0.387055
$267$	4.54967e9	0.0547872
$268$	−5.50640e8	−0.00652021
$269$	−9.97175e10	−1.16114	−0.580572	−	0.814209i	$-0.697171\pi$
$269$	−9.97175e10	−1.16114	−0.580572	+	0.814209i	$0.697171\pi$
$270$	−1.12010e10	−0.128268
$271$	6.02173e10	0.678203	0.339101	−	0.940750i	$-0.389877\pi$
$271$	6.02173e10	0.678203	0.339101	+	0.940750i	$0.389877\pi$
$272$	4.34520e10	0.481338
$273$	3.98097e8	0.00433768
$274$	7.64793e10	0.819721
$275$	2.54117e9	0.0267940
$276$	−4.25792e7	−0.000441679 0
$277$	1.56097e10	0.159307	0.0796535	−	0.996823i	$-0.474619\pi$
$277$	1.56097e10	0.159307	0.0796535	+	0.996823i	$0.474619\pi$
$278$	7.47419e10	0.750521
$279$	5.72742e9	0.0565900
$280$	5.68004e10	0.552255
$281$	1.35891e11	1.30021	0.650104	−	0.759845i	$-0.274725\pi$
$281$	1.35891e11	1.30021	0.650104	+	0.759845i	$0.274725\pi$
$282$	−1.07555e9	−0.0101277
$283$	−6.53367e10	−0.605506	−0.302753	−	0.953069i	$-0.597906\pi$
$283$	−6.53367e10	−0.605506	−0.302753	+	0.953069i	$0.597906\pi$
$284$	4.02791e8	0.00367406
$285$	−6.91925e9	−0.0621237
$286$	−6.78763e8	−0.00599889
$287$	4.43418e10	0.385785
$288$	1.35255e10	0.115847
$289$	−9.38896e10	−0.791731
$290$	8.42282e10	0.699305
$291$	−2.06426e9	−0.0168751
$292$	5.64791e9	0.0454637
$293$	−1.42114e11	−1.12651	−0.563253	−	0.826284i	$-0.690451\pi$
$293$	−1.42114e11	−1.12651	−0.563253	+	0.826284i	$0.690451\pi$
$294$	7.78942e8	0.00608054
$295$	−2.93846e11	−2.25902
$296$	1.53713e11	1.16385
$297$	−2.33142e8	−0.00173867
$298$	8.47151e10	0.622283
$299$	7.04268e9	0.0509586
$300$	4.29754e8	0.00306319
$301$	−3.48335e10	−0.244595
$302$	1.93485e11	1.33849
$303$	9.81792e9	0.0669156
$304$	1.56361e11	1.05002
$305$	−2.26394e11	−1.49801
$306$	7.18749e10	0.468631
$307$	−1.04322e11	−0.670278	−0.335139	−	0.942169i	$-0.608783\pi$
$307$	−1.04322e11	−0.670278	−0.335139	+	0.942169i	$0.608783\pi$
$308$	−7.29204e7	−0.000461712 0
$309$	5.66286e9	0.0353364
$310$	−1.42986e10	−0.0879359
$311$	−2.16872e11	−1.31456	−0.657281	−	0.753646i	$-0.728293\pi$
$311$	−2.16872e11	−1.31456	−0.657281	+	0.753646i	$0.728293\pi$
$312$	1.86111e9	0.0111193
$313$	−1.62420e11	−0.956510	−0.478255	−	0.878221i	$-0.658731\pi$
$313$	−1.62420e11	−0.956510	−0.478255	+	0.878221i	$0.658731\pi$
$314$	−1.79587e11	−1.04254
$315$	9.94315e10	0.569019
$316$	2.93452e9	0.0165556
$317$	−3.55310e9	−0.0197625	−0.00988124	−	0.999951i	$-0.503145\pi$
$317$	−3.55310e9	−0.0197625	−0.00988124	+	0.999951i	$0.503145\pi$
$318$	−6.20554e9	−0.0340296
$319$	1.75317e9	0.00947906
$320$	2.64587e11	1.41057
$321$	7.19881e9	0.0378432
$322$	1.37801e10	0.0714336
$323$	8.88758e10	0.454331
$324$	1.14645e10	0.0577969
$325$	−7.10821e10	−0.353415
$326$	−9.28524e10	−0.455317
$327$	−1.48267e10	−0.0717100
$328$	2.07298e11	0.988925
$329$	1.91119e10	0.0899335
$330$	2.90772e8	0.00134971
$331$	−1.56690e11	−0.717488	−0.358744	−	0.933436i	$-0.616795\pi$
$331$	−1.56690e11	−0.717488	−0.358744	+	0.933436i	$0.616795\pi$
$332$	−2.22438e10	−0.100482
$333$	2.69082e11	1.19918
$334$	2.85397e11	1.25485
$335$	−3.90160e10	−0.169255
$336$	3.85383e9	0.0164955
$337$	−4.13287e11	−1.74549	−0.872744	−	0.488179i	$-0.837661\pi$
$337$	−4.13287e11	−1.74549	−0.872744	+	0.488179i	$0.837661\pi$
$338$	1.89865e10	0.0791260
$339$	6.03581e9	0.0248220
$340$	−9.85206e9	−0.0399827
$341$	−2.97618e8	−0.00119197
$342$	2.58640e11	1.02230
$343$	−1.38413e10	−0.0539949
$344$	−1.62847e11	−0.626998
$345$	−3.01698e9	−0.0114653
$346$	−1.88911e10	−0.0708622
$347$	−3.84674e11	−1.42433	−0.712164	−	0.702013i	$-0.752285\pi$
$347$	−3.84674e11	−1.42433	−0.712164	+	0.702013i	$0.752285\pi$
$348$	2.96489e8	0.00108368
$349$	−3.58266e10	−0.129268	−0.0646341	−	0.997909i	$-0.520588\pi$
$349$	−3.58266e10	−0.129268	−0.0646341	+	0.997909i	$0.520588\pi$
$350$	−1.39084e11	−0.495416
$351$	6.52148e9	0.0229332
$352$	−7.02833e8	−0.00244012
$353$	4.59958e11	1.57664	0.788319	−	0.615267i	$-0.210952\pi$
$353$	4.59958e11	1.57664	0.788319	+	0.615267i	$0.210952\pi$
$354$	−1.88389e10	−0.0637589
$355$	2.85400e10	0.0953733
$356$	2.33113e10	0.0769203
$357$	2.19053e9	0.00713743
$358$	−2.74649e11	−0.883699
$359$	3.71831e11	1.18147	0.590733	−	0.806867i	$-0.298839\pi$
$359$	3.71831e11	1.18147	0.590733	+	0.806867i	$0.298839\pi$
$360$	4.64843e11	1.45863
$361$	−2.87097e9	−0.00889704
$362$	−9.51600e10	−0.291250
$363$	−1.36825e10	−0.0413605
$364$	2.03974e9	0.00609002
$365$	4.00187e11	1.18017
$366$	−1.45144e10	−0.0422801
$367$	−2.42585e10	−0.0698018	−0.0349009	−	0.999391i	$-0.511112\pi$
$367$	−2.42585e10	−0.0698018	−0.0349009	+	0.999391i	$0.511112\pi$
$368$	6.81776e10	0.193788
$369$	3.62884e11	1.01894
$370$	−6.71768e11	−1.86342
$371$	1.10268e11	0.302182
$372$	−5.03321e7	−0.000136270 0
$373$	8.96950e9	0.0239927	0.0119963	−	0.999928i	$-0.496181\pi$
$373$	8.96950e9	0.0239927	0.0119963	+	0.999928i	$0.496181\pi$
$374$	−3.73489e9	−0.00987087
$375$	6.55381e9	0.0171141
$376$	8.93481e10	0.230537
$377$	−4.90398e10	−0.125030
$378$	1.27603e10	0.0321477
$379$	3.34521e10	0.0832811	0.0416406	−	0.999133i	$-0.486742\pi$
$379$	3.34521e10	0.0832811	0.0416406	+	0.999133i	$0.486742\pi$
$380$	−3.54523e10	−0.0872205
$381$	2.15307e9	0.00523475
$382$	4.07079e11	0.978124
$383$	−2.27604e11	−0.540488	−0.270244	−	0.962792i	$-0.587104\pi$
$383$	−2.27604e11	−0.540488	−0.270244	+	0.962792i	$0.587104\pi$
$384$	1.90091e10	0.0446139
$385$	−5.16683e9	−0.0119854
$386$	−3.01305e11	−0.690818
$387$	−2.85070e11	−0.646030
$388$	−1.05767e10	−0.0236923
$389$	2.89623e11	0.641297	0.320649	−	0.947198i	$-0.396099\pi$
$389$	2.89623e11	0.641297	0.320649	+	0.947198i	$0.396099\pi$
$390$	−8.13353e9	−0.0178028
$391$	3.87523e10	0.0838498
$392$	−6.47081e10	−0.138411
$393$	2.62412e10	0.0554903
$394$	−6.10973e11	−1.27729
$395$	2.07927e11	0.429759
$396$	−5.96766e8	−0.00121948
$397$	−1.96938e11	−0.397898	−0.198949	−	0.980010i	$-0.563753\pi$
$397$	−1.96938e11	−0.397898	−0.198949	+	0.980010i	$0.563753\pi$
$398$	−7.43788e11	−1.48585
$399$	7.88254e9	0.0155700
$400$	−6.88119e11	−1.34398
$401$	−8.47710e11	−1.63719	−0.818593	−	0.574375i	$-0.805245\pi$
$401$	−8.47710e11	−1.63719	−0.818593	+	0.574375i	$0.805245\pi$
$402$	−2.50138e9	−0.00477708
$403$	8.32502e9	0.0157222
$404$	5.03043e10	0.0939483
$405$	8.12329e11	1.50032
$406$	−9.59545e10	−0.175266
$407$	−1.39825e10	−0.0252586
$408$	1.02407e10	0.0182962
$409$	−3.91261e11	−0.691372	−0.345686	−	0.938350i	$-0.612354\pi$
$409$	−3.91261e11	−0.691372	−0.345686	+	0.938350i	$0.612354\pi$
$410$	−9.05948e11	−1.58335
$411$	1.90752e10	0.0329748
$412$	2.90150e10	0.0496117
$413$	3.34755e11	0.566176
$414$	1.12774e11	0.188672
$415$	−1.57610e12	−2.60836
$416$	1.96598e10	0.0321853
$417$	1.86419e10	0.0301911
$418$	−1.34399e10	−0.0215329
$419$	1.68612e11	0.267254	0.133627	−	0.991032i	$-0.457338\pi$
$419$	1.68612e11	0.267254	0.133627	+	0.991032i	$0.457338\pi$
$420$	−8.73796e8	−0.00137021
$421$	1.02677e11	0.159295	0.0796475	−	0.996823i	$-0.474621\pi$
$421$	1.02677e11	0.159295	0.0796475	+	0.996823i	$0.474621\pi$
$422$	−6.41259e11	−0.984300
$423$	1.56408e11	0.237534
$424$	5.15505e11	0.774616
$425$	−3.91129e11	−0.581526
$426$	1.82975e9	0.00269183
$427$	2.57912e11	0.375445
$428$	3.68847e10	0.0531312
$429$	−1.69295e8	−0.000241316 0
$430$	7.11683e11	1.00387
$431$	1.07352e12	1.49852	0.749259	−	0.662278i	$-0.230410\pi$
$431$	1.07352e12	1.49852	0.749259	+	0.662278i	$0.230410\pi$
$432$	6.31321e10	0.0872114
$433$	8.85538e11	1.21063	0.605315	−	0.795986i	$-0.293047\pi$
$433$	8.85538e11	1.21063	0.605315	+	0.795986i	$0.293047\pi$
$434$	1.62893e10	0.0220393
$435$	2.10080e10	0.0281308
$436$	−7.59680e10	−0.100680
$437$	1.39449e11	0.182915
$438$	2.56566e10	0.0333093
$439$	−9.62102e11	−1.23632	−0.618160	−	0.786052i	$-0.712122\pi$
$439$	−9.62102e11	−1.23632	−0.618160	+	0.786052i	$0.712122\pi$
$440$	−2.41550e10	−0.0307234
$441$	−1.13274e11	−0.142613
$442$	1.04473e11	0.130198
$443$	−6.61066e11	−0.815507	−0.407754	−	0.913092i	$-0.633688\pi$
$443$	−6.61066e11	−0.815507	−0.407754	+	0.913092i	$0.633688\pi$
$444$	−2.36467e9	−0.00288767
$445$	1.65174e12	1.99674
$446$	9.63547e11	1.15310
$447$	2.11294e10	0.0250325
$448$	−3.01423e11	−0.353529
$449$	1.18730e11	0.137865	0.0689324	−	0.997621i	$-0.478041\pi$
$449$	1.18730e11	0.137865	0.0689324	+	0.997621i	$0.478041\pi$
$450$	−1.13823e12	−1.30850
$451$	−1.88568e10	−0.0214622
$452$	3.09258e10	0.0348496
$453$	4.82585e10	0.0538433
$454$	−1.00048e11	−0.110525
$455$	1.44527e11	0.158088
$456$	3.68509e10	0.0399123
$457$	−4.98833e11	−0.534974	−0.267487	−	0.963561i	$-0.586193\pi$
$457$	−4.98833e11	−0.534974	−0.267487	+	0.963561i	$0.586193\pi$
$458$	5.11573e11	0.543266
$459$	3.58844e10	0.0377354
$460$	−1.54582e10	−0.0160971
$461$	−1.32821e12	−1.36966	−0.684831	−	0.728702i	$-0.740124\pi$
$461$	−1.32821e12	−1.36966	−0.684831	+	0.728702i	$0.740124\pi$
$462$	−3.31254e8	−0.000338276 0
$463$	−1.23923e11	−0.125325	−0.0626626	−	0.998035i	$-0.519959\pi$
$463$	−1.23923e11	−0.125325	−0.0626626	+	0.998035i	$0.519959\pi$
$464$	−4.74737e11	−0.475469
$465$	−3.56632e9	−0.00353738
$466$	−4.94141e11	−0.485416
$467$	−7.67914e11	−0.747114	−0.373557	−	0.927607i	$-0.621862\pi$
$467$	−7.67914e11	−0.747114	−0.373557	+	0.927607i	$0.621862\pi$
$468$	1.66928e10	0.0160851
$469$	4.44478e10	0.0424202
$470$	−3.90475e11	−0.369107
$471$	−4.47920e10	−0.0419379
$472$	1.56498e12	1.45134
$473$	1.48133e10	0.0136075
$474$	1.33305e10	0.0121296
$475$	−1.40746e12	−1.26857
$476$	1.12237e10	0.0100208
$477$	9.02413e11	0.798129
$478$	−1.63467e12	−1.43220
$479$	7.86943e11	0.683020	0.341510	−	0.939878i	$-0.389062\pi$
$479$	7.86943e11	0.683020	0.341510	+	0.939878i	$0.389062\pi$
$480$	−8.42196e9	−0.00724148
$481$	3.91120e11	0.333164
$482$	−1.50123e12	−1.26688
$483$	3.43701e9	0.00287355
$484$	−7.01054e10	−0.0580694
$485$	−7.49419e11	−0.615017
$486$	1.56687e11	0.127400
$487$	1.78948e12	1.44161	0.720803	−	0.693140i	$-0.243773\pi$
$487$	1.78948e12	1.44161	0.720803	+	0.693140i	$0.243773\pi$
$488$	1.20574e12	0.962420
$489$	−2.31590e10	−0.0183160
$490$	2.82791e11	0.221607
$491$	1.36586e12	1.06057	0.530284	−	0.847820i	$-0.322085\pi$
$491$	1.36586e12	1.06057	0.530284	+	0.847820i	$0.322085\pi$
$492$	−3.18900e9	−0.00245364
$493$	−2.69841e11	−0.205730
$494$	3.75942e11	0.284021
$495$	−4.22843e10	−0.0316560
$496$	8.05914e10	0.0597890
$497$	−3.25134e10	−0.0239033
$498$	−1.01046e11	−0.0736186
$499$	7.83609e11	0.565779	0.282890	−	0.959152i	$-0.408707\pi$
$499$	7.83609e11	0.565779	0.282890	+	0.959152i	$0.408707\pi$
$500$	3.35800e10	0.0240279
$501$	7.11830e10	0.0504785
$502$	1.20918e12	0.849811
$503$	−1.53430e12	−1.06870	−0.534348	−	0.845264i	$-0.679443\pi$
$503$	−1.53430e12	−1.06870	−0.534348	+	0.845264i	$0.679443\pi$
$504$	−5.29558e11	−0.365575
$505$	3.56435e12	2.43876
$506$	−5.86016e9	−0.00397404
$507$	4.73555e9	0.00318299
$508$	1.10317e10	0.00734950
$509$	8.45328e11	0.558207	0.279104	−	0.960261i	$-0.409963\pi$
$509$	8.45328e11	0.558207	0.279104	+	0.960261i	$0.409963\pi$
$510$	−4.47547e10	−0.0292936
$511$	−4.55901e11	−0.295785
$512$	−1.39867e12	−0.899500
$513$	1.29129e11	0.0823181
$514$	2.34706e12	1.48317
$515$	2.05588e12	1.28785
$516$	2.50517e9	0.00155566
$517$	−8.12753e9	−0.00500324
$518$	7.65291e11	0.467028
$519$	−4.71176e9	−0.00285056
$520$	6.75667e11	0.405245
$521$	1.81981e12	1.08207	0.541036	−	0.841000i	$-0.318032\pi$
$521$	1.81981e12	1.08207	0.541036	+	0.841000i	$0.318032\pi$
$522$	−7.85272e11	−0.462917
$523$	1.65029e12	0.964501	0.482250	−	0.876033i	$-0.339820\pi$
$523$	1.65029e12	0.964501	0.482250	+	0.876033i	$0.339820\pi$
$524$	1.34453e11	0.0779073
$525$	−3.46899e10	−0.0199290
$526$	3.01613e12	1.71797
$527$	4.58084e10	0.0258700
$528$	−1.63888e9	−0.000917689 0
$529$	−1.74035e12	−0.966242
$530$	−2.25289e12	−1.24022
$531$	2.73957e12	1.49540
$532$	4.03880e10	0.0218600
$533$	5.27466e11	0.283088
$534$	1.05895e11	0.0563562
$535$	2.61349e12	1.37921
$536$	2.07794e11	0.108740
$537$	−6.85022e10	−0.0355484
$538$	−2.32097e12	−1.19440
$539$	5.88616e9	0.00300388
$540$	−1.43142e10	−0.00724428
$541$	1.10324e12	0.553710	0.276855	−	0.960912i	$-0.410708\pi$
$541$	1.10324e12	0.553710	0.276855	+	0.960912i	$0.410708\pi$
$542$	1.40158e12	0.697625
$543$	−2.37345e10	−0.0117161
$544$	1.08178e11	0.0529593
$545$	−5.38277e12	−2.61349
$546$	9.26588e9	0.00446190
$547$	−5.95738e11	−0.284520	−0.142260	−	0.989829i	$-0.545437\pi$
$547$	−5.95738e11	−0.284520	−0.142260	+	0.989829i	$0.545437\pi$
$548$	9.77363e10	0.0462960
$549$	2.11070e12	0.991633
$550$	5.91468e10	0.0275613
$551$	−9.71016e11	−0.448791
$552$	1.60680e10	0.00736608
$553$	−2.36875e11	−0.107710
$554$	3.63322e11	0.163869
$555$	−1.67550e11	−0.0749596
$556$	9.55161e10	0.0423877
$557$	−3.95418e12	−1.74063	−0.870317	−	0.492492i	$-0.836086\pi$
$557$	−3.95418e12	−1.74063	−0.870317	+	0.492492i	$0.836086\pi$
$558$	1.33308e11	0.0582106
$559$	−4.14360e11	−0.179484
$560$	1.39912e12	0.601185
$561$	−9.31546e8	−0.000397074 0
$562$	3.16292e12	1.33744
$563$	−4.66904e11	−0.195857	−0.0979286	−	0.995193i	$-0.531222\pi$
$563$	−4.66904e11	−0.195857	−0.0979286	+	0.995193i	$0.531222\pi$
$564$	−1.37450e9	−0.000571989 0
$565$	2.19127e12	0.904646
$566$	−1.52074e12	−0.622846
$567$	−9.25421e11	−0.376024
$568$	−1.52000e11	−0.0612740
$569$	−3.91480e12	−1.56569	−0.782843	−	0.622219i	$-0.786231\pi$
$569$	−3.91480e12	−1.56569	−0.782843	+	0.622219i	$0.786231\pi$
$570$	−1.61048e11	−0.0639027
$571$	4.09712e12	1.61293	0.806466	−	0.591281i	$-0.201378\pi$
$571$	4.09712e12	1.61293	0.806466	+	0.591281i	$0.201378\pi$
$572$	−8.67422e8	−0.000338804 0
$573$	1.01533e11	0.0393468
$574$	1.03207e12	0.396832
$575$	−6.13693e11	−0.234124
$576$	−2.46679e12	−0.933749
$577$	−3.32182e12	−1.24763	−0.623813	−	0.781574i	$-0.714417\pi$
$577$	−3.32182e12	−1.24763	−0.623813	+	0.781574i	$0.714417\pi$
$578$	−2.18532e12	−0.814404
$579$	−7.51507e10	−0.0277894
$580$	1.07639e11	0.0394952
$581$	1.79552e12	0.653729
$582$	−4.80464e10	−0.0173583
$583$	−4.68928e10	−0.0168112
$584$	−2.13134e12	−0.758219
$585$	1.18278e12	0.417545
$586$	−3.30777e12	−1.15877
$587$	7.32887e11	0.254780	0.127390	−	0.991853i	$-0.459340\pi$
$587$	7.32887e11	0.254780	0.127390	+	0.991853i	$0.459340\pi$
$588$	9.95446e8	0.000343415 0
$589$	1.64840e11	0.0564344
$590$	−6.83938e12	−2.32371
$591$	−1.52387e11	−0.0513812
$592$	3.78629e12	1.26697
$593$	5.75444e12	1.91098	0.955492	−	0.295017i	$-0.0953254\pi$
$593$	5.75444e12	1.91098	0.955492	+	0.295017i	$0.0953254\pi$
$594$	−5.42648e9	−0.00178846
$595$	7.95261e11	0.260126
$596$	1.08261e11	0.0351451
$597$	−1.85513e11	−0.0597711
$598$	1.63921e11	0.0524179
$599$	−6.22236e12	−1.97485	−0.987426	−	0.158084i	$-0.949468\pi$
$599$	−6.22236e12	−1.97485	−0.987426	+	0.158084i	$0.949468\pi$
$600$	−1.62175e11	−0.0510862
$601$	−1.69359e12	−0.529508	−0.264754	−	0.964316i	$-0.585291\pi$
$601$	−1.69359e12	−0.529508	−0.264754	+	0.964316i	$0.585291\pi$
$602$	−8.10764e11	−0.251600
$603$	3.63752e11	0.112041
$604$	2.47263e11	0.0755951
$605$	−4.96737e12	−1.50740
$606$	2.28516e11	0.0688319
$607$	2.65847e12	0.794846	0.397423	−	0.917636i	$-0.369905\pi$
$607$	2.65847e12	0.794846	0.397423	+	0.917636i	$0.369905\pi$
$608$	3.89274e11	0.115529
$609$	−2.39327e10	−0.00705040
$610$	−5.26940e12	−1.54091
$611$	2.27344e11	0.0659931
$612$	9.18522e10	0.0264672
$613$	4.10992e12	1.17560	0.587802	−	0.809005i	$-0.299994\pi$
$613$	4.10992e12	1.17560	0.587802	+	0.809005i	$0.299994\pi$
$614$	−2.42815e12	−0.689473
$615$	−2.25959e11	−0.0636930
$616$	2.75178e10	0.00770018
$617$	−6.11970e12	−1.69999	−0.849996	−	0.526789i	$-0.823396\pi$
$617$	−6.11970e12	−1.69999	−0.849996	+	0.526789i	$0.823396\pi$
$618$	1.31805e11	0.0363484
$619$	−2.66319e12	−0.729112	−0.364556	−	0.931181i	$-0.618779\pi$
$619$	−2.66319e12	−0.729112	−0.364556	+	0.931181i	$0.618779\pi$
$620$	−1.82728e10	−0.00496642
$621$	5.63038e10	0.0151924
$622$	−5.04777e12	−1.35221
$623$	−1.88169e12	−0.500441
$624$	4.58431e10	0.0121044
$625$	−2.48157e12	−0.650528
$626$	−3.78039e12	−0.983903
$627$	−3.35214e9	−0.000866199 0
$628$	−2.29502e11	−0.0588800
$629$	2.15214e12	0.548204
$630$	2.31431e12	0.585314
$631$	−2.07377e12	−0.520750	−0.260375	−	0.965508i	$-0.583846\pi$
$631$	−2.07377e12	−0.520750	−0.260375	+	0.965508i	$0.583846\pi$
$632$	−1.10739e12	−0.276105
$633$	−1.59941e11	−0.0395952
$634$	−8.27000e10	−0.0203284
$635$	7.81663e11	0.190782
$636$	−7.93034e9	−0.00192192
$637$	−1.64648e11	−0.0396214
$638$	4.08057e10	0.00975051
$639$	−2.66083e11	−0.0631339
$640$	6.90116e12	1.62597
$641$	1.46439e12	0.342608	0.171304	−	0.985218i	$-0.445202\pi$
$641$	1.46439e12	0.342608	0.171304	+	0.985218i	$0.445202\pi$
$642$	1.67555e11	0.0389269
$643$	−3.33149e12	−0.768581	−0.384290	−	0.923212i	$-0.625554\pi$
$643$	−3.33149e12	−0.768581	−0.384290	+	0.923212i	$0.625554\pi$
$644$	1.76103e10	0.00403441
$645$	1.77506e11	0.0403826
$646$	2.06862e12	0.467342
$647$	3.87227e12	0.868752	0.434376	−	0.900732i	$-0.356969\pi$
$647$	3.87227e12	0.868752	0.434376	+	0.900732i	$0.356969\pi$
$648$	−4.32635e12	−0.963905
$649$	−1.42358e11	−0.0314979
$650$	−1.65446e12	−0.363536
$651$	4.06282e9	0.000886570 0
$652$	−1.18660e11	−0.0257153
$653$	−6.72846e12	−1.44813	−0.724063	−	0.689734i	$-0.757728\pi$
$653$	−6.72846e12	−1.44813	−0.724063	+	0.689734i	$0.757728\pi$
$654$	−3.45098e11	−0.0737636
$655$	9.52674e12	2.02236
$656$	5.10621e12	1.07654
$657$	−3.73100e12	−0.781234
$658$	4.44836e11	0.0925090
$659$	7.01775e12	1.44949	0.724743	−	0.689020i	$-0.241959\pi$
$659$	7.01775e12	1.44949	0.724743	+	0.689020i	$0.241959\pi$
$660$	3.71591e8	7.62286e−5 0
$661$	4.58087e12	0.933343	0.466672	−	0.884431i	$-0.345453\pi$
$661$	4.58087e12	0.933343	0.466672	+	0.884431i	$0.345453\pi$
$662$	−3.64702e12	−0.738035
$663$	2.60573e10	0.00523744
$664$	8.39408e12	1.67578
$665$	2.86172e12	0.567453
$666$	6.26299e12	1.23352
$667$	−4.23390e11	−0.0828274
$668$	3.64722e11	0.0708709
$669$	2.40325e11	0.0463854
$670$	−9.08114e11	−0.174102
$671$	−1.09680e11	−0.0208870
$672$	9.59446e9	0.00181493
$673$	−7.91486e12	−1.48722	−0.743610	−	0.668614i	$-0.766888\pi$
$673$	−7.91486e12	−1.48722	−0.743610	+	0.668614i	$0.766888\pi$
$674$	−9.61941e12	−1.79547
$675$	−5.68276e11	−0.105364
$676$	2.42637e10	0.00446885
$677$	−6.75089e11	−0.123513	−0.0617564	−	0.998091i	$-0.519670\pi$
$677$	−6.75089e11	−0.123513	−0.0617564	+	0.998091i	$0.519670\pi$
$678$	1.40486e11	0.0255328
$679$	8.53753e11	0.154141
$680$	3.71785e12	0.666810
$681$	−2.49538e10	−0.00444605
$682$	−6.92718e9	−0.00122610
$683$	−4.64165e12	−0.816168	−0.408084	−	0.912944i	$-0.633803\pi$
$683$	−4.64165e12	−0.816168	−0.408084	+	0.912944i	$0.633803\pi$
$684$	3.30527e11	0.0577371
$685$	6.92518e12	1.20178
$686$	−3.22162e11	−0.0555412
$687$	1.27595e11	0.0218539
$688$	−4.01127e12	−0.682549
$689$	1.31169e12	0.221741
$690$	−7.02215e10	−0.0117937
$691$	−3.16598e12	−0.528272	−0.264136	−	0.964485i	$-0.585087\pi$
$691$	−3.16598e12	−0.528272	−0.264136	+	0.964485i	$0.585087\pi$
$692$	−2.41418e10	−0.00400213
$693$	4.81711e10	0.00793391
$694$	−8.95344e12	−1.46512
$695$	6.76787e12	1.10032
$696$	−1.11885e11	−0.0180731
$697$	2.90238e12	0.465808
$698$	−8.33879e11	−0.132970
$699$	−1.23247e11	−0.0195267
$700$	−1.77741e11	−0.0279800
$701$	−1.68452e12	−0.263479	−0.131740	−	0.991284i	$-0.542056\pi$
$701$	−1.68452e12	−0.263479	−0.131740	+	0.991284i	$0.542056\pi$
$702$	1.51790e11	0.0235899
$703$	7.74440e12	1.19588
$704$	1.28183e11	0.0196678
$705$	−9.73911e10	−0.0148480
$706$	1.07057e13	1.62179
$707$	−4.06058e12	−0.611224
$708$	−2.40751e10	−0.00360096
$709$	−6.23827e12	−0.927162	−0.463581	−	0.886054i	$-0.653436\pi$
$709$	−6.23827e12	−0.927162	−0.463581	+	0.886054i	$0.653436\pi$
$710$	6.64281e11	0.0981046
$711$	−1.93854e12	−0.284486
$712$	−8.79692e12	−1.28284
$713$	7.18747e10	0.0104153
$714$	5.09854e10	0.00734183
$715$	−6.14619e10	−0.00879485
$716$	−3.50986e11	−0.0499093
$717$	−4.07715e11	−0.0576129
$718$	8.65453e12	1.21530
$719$	8.01498e12	1.11847	0.559233	−	0.829011i	$-0.311096\pi$
$719$	8.01498e12	1.11847	0.559233	+	0.829011i	$0.311096\pi$
$720$	1.14501e13	1.58786
$721$	−2.34209e12	−0.322772
$722$	−6.68229e10	−0.00915183
$723$	−3.74433e11	−0.0509626
$724$	−1.21609e11	−0.0164491
$725$	4.27329e12	0.574436
$726$	−3.18466e11	−0.0425450
$727$	−6.54485e12	−0.868950	−0.434475	−	0.900684i	$-0.643066\pi$
$727$	−6.54485e12	−0.868950	−0.434475	+	0.900684i	$0.643066\pi$
$728$	−7.69733e11	−0.101566
$729$	−7.54737e12	−0.989741
$730$	9.31451e12	1.21397
$731$	−2.28002e12	−0.295331
$732$	−1.85487e10	−0.00238788
$733$	1.08068e13	1.38270	0.691350	−	0.722520i	$-0.257016\pi$
$733$	1.08068e13	1.38270	0.691350	+	0.722520i	$0.257016\pi$
$734$	−5.64627e11	−0.0718008
$735$	7.05330e10	0.00891455
$736$	1.69734e11	0.0213216
$737$	−1.89019e10	−0.00235995
$738$	8.44628e12	1.04812
$739$	−9.81171e12	−1.21017	−0.605083	−	0.796163i	$-0.706860\pi$
$739$	−9.81171e12	−1.21017	−0.605083	+	0.796163i	$0.706860\pi$
$740$	−8.58482e11	−0.105242
$741$	9.37665e10	0.0114252
$742$	2.56654e12	0.310835
$743$	−1.47142e13	−1.77127	−0.885637	−	0.464379i	$-0.846278\pi$
$743$	−1.47142e13	−1.77127	−0.885637	+	0.464379i	$0.846278\pi$
$744$	1.89937e10	0.00227264
$745$	7.67094e12	0.912316
$746$	2.08769e11	0.0246798
$747$	1.46942e13	1.72664
$748$	−4.77298e9	−0.000557484 0
$749$	−2.97734e12	−0.345669
$750$	1.52543e11	0.0176042
$751$	1.58935e13	1.82322	0.911612	−	0.411052i	$-0.134839\pi$
$751$	1.58935e13	1.82322	0.911612	+	0.411052i	$0.134839\pi$
$752$	2.20084e12	0.250962
$753$	3.01589e11	0.0341852
$754$	−1.14142e12	−0.128610
$755$	1.75200e13	1.96234
$756$	1.63070e10	0.00181563
$757$	−3.02281e12	−0.334564	−0.167282	−	0.985909i	$-0.553499\pi$
$757$	−3.02281e12	−0.334564	−0.167282	+	0.985909i	$0.553499\pi$
$758$	7.78610e11	0.0856661
$759$	−1.46162e9	−0.000159863 0
$760$	1.33786e13	1.45462
$761$	−8.96733e12	−0.969242	−0.484621	−	0.874724i	$-0.661043\pi$
$761$	−8.96733e12	−0.969242	−0.484621	+	0.874724i	$0.661043\pi$
$762$	5.01136e10	0.00538466
$763$	6.13216e12	0.655018
$764$	5.20225e11	0.0552422
$765$	6.50826e12	0.687050
$766$	−5.29759e12	−0.555966
$767$	3.98206e12	0.415460
$768$	6.92986e10	0.00718785
$769$	−1.42486e13	−1.46927	−0.734637	−	0.678461i	$-0.762647\pi$
$769$	−1.42486e13	−1.46927	−0.734637	+	0.678461i	$0.762647\pi$
$770$	−1.20260e11	−0.0123286
$771$	5.85397e11	0.0596631
$772$	−3.85052e11	−0.0390158
$773$	−9.80263e12	−0.987495	−0.493747	−	0.869605i	$-0.664373\pi$
$773$	−9.80263e12	−0.987495	−0.493747	+	0.869605i	$0.664373\pi$
$774$	−6.63513e12	−0.664530
$775$	−7.25435e11	−0.0722339
$776$	3.99130e12	0.395127
$777$	1.90877e11	0.0187870
$778$	6.74109e12	0.659662
$779$	1.04441e13	1.01614
$780$	−1.03942e10	−0.00100546
$781$	1.38267e10	0.00132980
$782$	9.01975e11	0.0862510
$783$	−3.92056e11	−0.0372753
$784$	−1.59390e12	−0.150674
$785$	−1.62615e13	−1.52844
$786$	6.10774e11	0.0570794
$787$	−1.38063e13	−1.28289	−0.641446	−	0.767168i	$-0.721665\pi$
$787$	−1.38063e13	−1.28289	−0.641446	+	0.767168i	$0.721665\pi$
$788$	−7.80790e11	−0.0721383
$789$	7.52276e11	0.0691083
$790$	4.83960e12	0.442066
$791$	−2.49634e12	−0.226730
$792$	2.25200e11	0.0203379
$793$	3.06798e12	0.275501
$794$	−4.58381e12	−0.409293
$795$	−5.61910e11	−0.0498901
$796$	−9.50520e11	−0.0839175
$797$	1.20343e13	1.05647	0.528235	−	0.849098i	$-0.322854\pi$
$797$	1.20343e13	1.05647	0.528235	+	0.849098i	$0.322854\pi$
$798$	1.83469e11	0.0160159
$799$	1.25096e12	0.108588
$800$	−1.71313e12	−0.147872
$801$	−1.53994e13	−1.32177
$802$	−1.97308e13	−1.68407
$803$	1.93877e11	0.0164553
$804$	−3.19662e9	−0.000269798 0
$805$	1.24779e12	0.104727
$806$	1.93768e11	0.0161724
$807$	−5.78889e11	−0.0480468
$808$	−1.89832e13	−1.56682
$809$	−8.87892e12	−0.728772	−0.364386	−	0.931248i	$-0.618721\pi$
$809$	−8.87892e12	−0.728772	−0.364386	+	0.931248i	$0.618721\pi$
$810$	1.89073e13	1.54329
$811$	1.34373e13	1.09073	0.545367	−	0.838197i	$-0.316390\pi$
$811$	1.34373e13	1.09073	0.545367	+	0.838197i	$0.316390\pi$
$812$	−1.22625e11	−0.00989863
$813$	3.49579e11	0.0280632
$814$	−3.25448e11	−0.0259820
$815$	−8.40777e12	−0.667531
$816$	2.52251e11	0.0199172
$817$	−8.20456e12	−0.644253
$818$	−9.10677e12	−0.711172
$819$	−1.34745e12	−0.104649
$820$	−1.15775e12	−0.0894238
$821$	9.58444e12	0.736245	0.368123	−	0.929777i	$-0.380001\pi$
$821$	9.58444e12	0.736245	0.368123	+	0.929777i	$0.380001\pi$
$822$	4.43984e11	0.0339191
$823$	9.02467e12	0.685697	0.342848	−	0.939391i	$-0.388608\pi$
$823$	9.02467e12	0.685697	0.342848	+	0.939391i	$0.388608\pi$
$824$	−1.09493e13	−0.827397
$825$	1.47522e10	0.00110870
$826$	7.79156e12	0.582390
$827$	−1.75354e13	−1.30359	−0.651794	−	0.758396i	$-0.725983\pi$
$827$	−1.75354e13	−1.30359	−0.651794	+	0.758396i	$0.725983\pi$
$828$	1.44119e11	0.0106558
$829$	1.61887e13	1.19046	0.595232	−	0.803554i	$-0.297060\pi$
$829$	1.61887e13	1.19046	0.595232	+	0.803554i	$0.297060\pi$
$830$	−3.66843e13	−2.68305
$831$	9.06187e10	0.00659194
$832$	−3.58557e12	−0.259420
$833$	−9.05977e11	−0.0651951
$834$	4.33898e11	0.0310557
$835$	2.58427e13	1.83970
$836$	−1.71754e10	−0.00121613
$837$	6.65556e10	0.00468727
$838$	3.92451e12	0.274908
$839$	−6.07117e12	−0.423003	−0.211502	−	0.977378i	$-0.567835\pi$
$839$	−6.07117e12	−0.423003	−0.211502	+	0.977378i	$0.567835\pi$
$840$	3.29742e11	0.0228517
$841$	−1.15590e13	−0.796779
$842$	2.38984e12	0.163857
$843$	7.88887e11	0.0538011
$844$	−8.19494e11	−0.0555910
$845$	1.71922e12	0.116005
$846$	3.64045e12	0.244337
$847$	5.65893e12	0.377797
$848$	1.26980e13	0.843246
$849$	−3.79298e11	−0.0250551
$850$	−9.10368e12	−0.598180
$851$	3.37677e12	0.220708
$852$	2.33831e9	0.000152028 0
$853$	−1.58313e13	−1.02387	−0.511935	−	0.859024i	$-0.671071\pi$
$853$	−1.58313e13	−1.02387	−0.511935	+	0.859024i	$0.671071\pi$
$854$	6.00301e12	0.386197
$855$	2.34198e13	1.49877
$856$	−1.39191e13	−0.886093
$857$	−4.61902e12	−0.292507	−0.146253	−	0.989247i	$-0.546721\pi$
$857$	−4.61902e12	−0.292507	−0.146253	+	0.989247i	$0.546721\pi$
$858$	−3.94041e9	−0.000248227 0
$859$	−1.79350e13	−1.12391	−0.561957	−	0.827166i	$-0.689951\pi$
$859$	−1.79350e13	−1.12391	−0.561957	+	0.827166i	$0.689951\pi$
$860$	9.09492e11	0.0566965
$861$	2.57417e11	0.0159633
$862$	2.49866e13	1.54143
$863$	−6.96081e12	−0.427180	−0.213590	−	0.976923i	$-0.568516\pi$
$863$	−6.96081e12	−0.427180	−0.213590	+	0.976923i	$0.568516\pi$
$864$	1.57173e11	0.00959546
$865$	−1.71058e12	−0.103890
$866$	2.06113e13	1.24530
$867$	−5.45056e11	−0.0327609
$868$	2.08168e10	0.00124473
$869$	1.00734e11	0.00599219
$870$	4.88969e11	0.0289364
$871$	5.28728e11	0.0311279
$872$	2.86679e13	1.67908
$873$	6.98694e12	0.407121
$874$	3.24573e12	0.188153
$875$	−2.71058e12	−0.156324
$876$	3.27877e10	0.00188123
$877$	2.25535e13	1.28741	0.643703	−	0.765276i	$-0.277397\pi$
$877$	2.25535e13	1.28741	0.643703	+	0.765276i	$0.277397\pi$
$878$	−2.23933e13	−1.27173
$879$	−8.25015e11	−0.0466135
$880$	−5.94990e11	−0.0334455
$881$	2.00364e13	1.12054	0.560271	−	0.828309i	$-0.310697\pi$
$881$	2.00364e13	1.12054	0.560271	+	0.828309i	$0.310697\pi$
$882$	−2.63651e12	−0.146697
$883$	−9.56779e11	−0.0529649	−0.0264825	−	0.999649i	$-0.508431\pi$
$883$	−9.56779e11	−0.0529649	−0.0264825	+	0.999649i	$0.508431\pi$
$884$	1.33511e11	0.00735327
$885$	−1.70586e12	−0.0934756
$886$	−1.53866e13	−0.838861
$887$	−3.07403e13	−1.66745	−0.833723	−	0.552183i	$-0.813795\pi$
$887$	−3.07403e13	−1.66745	−0.833723	+	0.552183i	$0.813795\pi$
$888$	8.92350e11	0.0481589
$889$	−8.90486e11	−0.0478155
$890$	3.84449e13	2.05392
$891$	3.93545e11	0.0209192
$892$	1.23136e12	0.0651243
$893$	4.50154e12	0.236881
$894$	4.91796e11	0.0257493
$895$	−2.48694e13	−1.29557
$896$	−7.86194e12	−0.407515
$897$	4.08848e10	0.00210861
$898$	2.76350e12	0.141813
$899$	−5.00481e11	−0.0255546
$900$	−1.45460e12	−0.0739013
$901$	7.21758e12	0.364863
$902$	−4.38901e11	−0.0220768
$903$	−2.02218e11	−0.0101211
$904$	−1.16704e13	−0.581203
$905$	−8.61672e12	−0.426995
$906$	1.12324e12	0.0553853
$907$	1.25478e13	0.615650	0.307825	−	0.951443i	$-0.400399\pi$
$907$	1.25478e13	0.615650	0.307825	+	0.951443i	$0.400399\pi$
$908$	−1.27856e11	−0.00624218
$909$	−3.32309e13	−1.61438
$910$	3.36393e12	0.162615
$911$	1.29432e13	0.622599	0.311299	−	0.950312i	$-0.399236\pi$
$911$	1.29432e13	0.622599	0.311299	+	0.950312i	$0.399236\pi$
$912$	9.07719e11	0.0434485
$913$	−7.63565e11	−0.0363687
$914$	−1.16105e13	−0.550294
$915$	−1.31428e12	−0.0619859
$916$	6.53762e11	0.0306824
$917$	−1.08531e13	−0.506862
$918$	8.35224e11	0.0388160
$919$	3.09503e13	1.43135	0.715673	−	0.698436i	$-0.246120\pi$
$919$	3.09503e13	1.43135	0.715673	+	0.698436i	$0.246120\pi$
$920$	5.83342e12	0.268459
$921$	−6.05622e11	−0.0277353
$922$	−3.09147e13	−1.40889
$923$	−3.86761e11	−0.0175402
$924$	−4.23324e8	−1.91051e−5 0
$925$	−3.40819e13	−1.53069
$926$	−2.88436e12	−0.128914
$927$	−1.91672e13	−0.852512
$928$	−1.18190e12	−0.0523136
$929$	1.32711e13	0.584569	0.292284	−	0.956331i	$-0.405585\pi$
$929$	1.32711e13	0.584569	0.292284	+	0.956331i	$0.405585\pi$
$930$	−8.30075e10	−0.00363868
$931$	−3.26013e12	−0.142220
$932$	−6.31485e11	−0.0274152
$933$	−1.25900e12	−0.0543950
$934$	−1.78735e13	−0.768509
$935$	−3.38193e11	−0.0144715
$936$	−6.29934e12	−0.268258
$937$	−2.78627e13	−1.18085	−0.590426	−	0.807092i	$-0.701040\pi$
$937$	−2.78627e13	−1.18085	−0.590426	+	0.807092i	$0.701040\pi$
$938$	1.03454e12	0.0436350
$939$	−9.42894e11	−0.0395793
$940$	−4.99005e11	−0.0208463
$941$	−1.43896e13	−0.598269	−0.299135	−	0.954211i	$-0.596698\pi$
$941$	−1.43896e13	−0.598269	−0.299135	+	0.954211i	$0.596698\pi$
$942$	−1.04255e12	−0.0431389
$943$	4.55392e12	0.187535
$944$	3.85489e13	1.57993
$945$	1.15545e12	0.0471310
$946$	3.44786e11	0.0139971
$947$	−2.13339e13	−0.861977	−0.430988	−	0.902358i	$-0.641835\pi$
$947$	−2.13339e13	−0.861977	−0.430988	+	0.902358i	$0.641835\pi$
$948$	1.70357e10	0.000685051 0
$949$	−5.42315e12	−0.217047
$950$	−3.27593e13	−1.30490
$951$	−2.06268e10	−0.000817748 0
$952$	−4.23545e12	−0.167122
$953$	−6.24389e12	−0.245209	−0.122605	−	0.992456i	$-0.539125\pi$
$953$	−6.24389e12	−0.245209	−0.122605	+	0.992456i	$0.539125\pi$
$954$	2.10040e13	0.820985
$955$	3.68609e13	1.43401
$956$	−2.08902e12	−0.0808875
$957$	1.01776e10	0.000392232 0
$958$	1.83164e13	0.702580
$959$	−7.88930e12	−0.301200
$960$	1.53601e12	0.0583676
$961$	−2.63547e13	−0.996787
$962$	9.10349e12	0.342705
$963$	−2.43660e13	−0.912989
$964$	−1.91849e12	−0.0715506
$965$	−2.72831e13	−1.01279
$966$	7.99977e10	0.00295584
$967$	−2.21839e13	−0.815865	−0.407932	−	0.913012i	$-0.633750\pi$
$967$	−2.21839e13	−0.815865	−0.407932	+	0.913012i	$0.633750\pi$
$968$	2.64555e13	0.968450
$969$	5.15949e11	0.0187997
$970$	−1.74430e13	−0.632629
$971$	3.98867e13	1.43993	0.719965	−	0.694011i	$-0.244158\pi$
$971$	3.98867e13	1.43993	0.719965	+	0.694011i	$0.244158\pi$
$972$	2.00237e11	0.00719526
$973$	−7.71009e12	−0.275773
$974$	4.16509e13	1.48289
$975$	−4.12652e11	−0.0146239
$976$	2.97000e13	1.04769
$977$	−2.44168e13	−0.857360	−0.428680	−	0.903456i	$-0.641021\pi$
$977$	−2.44168e13	−0.857360	−0.428680	+	0.903456i	$0.641021\pi$
$978$	−5.39035e11	−0.0188405
$979$	8.00210e11	0.0278408
$980$	3.61392e11	0.0125159
$981$	5.01843e13	1.73005
$982$	3.17909e13	1.09094
$983$	1.58080e12	0.0539990	0.0269995	−	0.999635i	$-0.491405\pi$
$983$	1.58080e12	0.0539990	0.0269995	+	0.999635i	$0.491405\pi$
$984$	1.20343e12	0.0409205
$985$	−5.53234e13	−1.87260
$986$	−6.28067e12	−0.211621
$987$	1.10950e11	0.00372134
$988$	4.80434e11	0.0160408
$989$	−3.57741e12	−0.118901
$990$	−9.84185e11	−0.0325625
$991$	3.14087e13	1.03447	0.517236	−	0.855843i	$-0.326961\pi$
$991$	3.14087e13	1.03447	0.517236	+	0.855843i	$0.326961\pi$
$992$	2.00640e11	0.00657831
$993$	−9.09629e11	−0.0296888
$994$	−7.56762e11	−0.0245878
$995$	−6.73498e13	−2.17837
$996$	−1.29131e11	−0.00415781
$997$	1.36281e13	0.436826	0.218413	−	0.975856i	$-0.429912\pi$
$997$	1.36281e13	0.436826	0.218413	+	0.975856i	$0.429912\pi$
$998$	1.82388e13	0.581982
$999$	3.12687e12	0.0993266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.10	✓	13	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)

\(f(q)\)	\(=\)	\(q+23.2754 q^{2} +5.80529 q^{3} +29.7447 q^{4} +2107.58 q^{5} +135.120 q^{6} -2401.00 q^{7} -11224.7 q^{8} -19649.3 q^{9} +O(q^{10})\)	\(q+23.2754 q^{2} +5.80529 q^{3} +29.7447 q^{4} +2107.58 q^{5} +135.120 q^{6} -2401.00 q^{7} -11224.7 q^{8} -19649.3 q^{9} +49054.9 q^{10} +1021.05 q^{11} +172.676 q^{12} -28561.0 q^{13} -55884.3 q^{14} +12235.1 q^{15} -276489. q^{16} -157157. q^{17} -457345. q^{18} -565523. q^{19} +62689.4 q^{20} -13938.5 q^{21} +23765.4 q^{22} -246584. q^{23} -65162.5 q^{24} +2.48878e6 q^{25} -664769. q^{26} -228335. q^{27} -71417.0 q^{28} +1.71702e6 q^{29} +284777. q^{30} -291482. q^{31} -688343. q^{32} +5927.49 q^{33} -3.65789e6 q^{34} -5.06031e6 q^{35} -584462. q^{36} -1.36942e7 q^{37} -1.31628e7 q^{38} -165805. q^{39} -2.36570e7 q^{40} -1.84681e7 q^{41} -324424. q^{42} +1.45079e7 q^{43} +30370.9 q^{44} -4.14125e7 q^{45} -5.73934e6 q^{46} -7.95996e6 q^{47} -1.60510e6 q^{48} +5.76480e6 q^{49} +5.79274e7 q^{50} -912340. q^{51} -849538. q^{52} -4.59260e7 q^{53} -5.31460e6 q^{54} +2.15195e6 q^{55} +2.69505e7 q^{56} -3.28303e6 q^{57} +3.99644e7 q^{58} -1.39423e8 q^{59} +363930. q^{60} -1.07419e8 q^{61} -6.78436e6 q^{62} +4.71780e7 q^{63} +1.25541e8 q^{64} -6.01947e7 q^{65} +137965. q^{66} -1.85122e7 q^{67} -4.67458e6 q^{68} -1.43149e6 q^{69} -1.17781e8 q^{70} +1.35416e7 q^{71} +2.20557e8 q^{72} +1.89880e8 q^{73} -3.18738e8 q^{74} +1.44481e7 q^{75} -1.68213e7 q^{76} -2.45154e6 q^{77} -3.85917e6 q^{78} +9.86568e7 q^{79} -5.82723e8 q^{80} +3.85432e8 q^{81} -4.29852e8 q^{82} -7.47822e8 q^{83} -414596. q^{84} -3.31221e8 q^{85} +3.37678e8 q^{86} +9.96780e6 q^{87} -1.14610e7 q^{88} +7.83712e8 q^{89} -9.63894e8 q^{90} +6.85750e7 q^{91} -7.33456e6 q^{92} -1.69214e6 q^{93} -1.85271e8 q^{94} -1.19189e9 q^{95} -3.99603e6 q^{96} -3.55582e8 q^{97} +1.34178e8 q^{98} -2.00629e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * q^99

Introduction

L-functions

Modular forms

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