LMFDB - Embedded newform 91.10.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.8682610909$
Analytic rank:	$1$
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			1.8
Root			$0.714333$ 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)

$f(q)$	$=$	$q-1.28567 q^{2} -259.576 q^{3} -510.347 q^{4} -2321.41 q^{5} +333.729 q^{6} -2401.00 q^{7} +1314.40 q^{8} +47696.7 q^{9} +O(q^{10})$	\(q-1.28567 q^{2} -259.576 q^{3} -510.347 q^{4} -2321.41 q^{5} +333.729 q^{6} -2401.00 q^{7} +1314.40 q^{8} +47696.7 q^{9} +2984.56 q^{10} -69139.2 q^{11} +132474. q^{12} -28561.0 q^{13} +3086.89 q^{14} +602583. q^{15} +259608. q^{16} +163983. q^{17} -61322.1 q^{18} +406698. q^{19} +1.18473e6 q^{20} +623242. q^{21} +88890.1 q^{22} -1.12709e6 q^{23} -341186. q^{24} +3.43583e6 q^{25} +36719.9 q^{26} -7.27170e6 q^{27} +1.22534e6 q^{28} -4.49343e6 q^{29} -774721. q^{30} +6.48193e6 q^{31} -1.00674e6 q^{32} +1.79469e7 q^{33} -210828. q^{34} +5.57371e6 q^{35} -2.43419e7 q^{36} -8.27771e6 q^{37} -522879. q^{38} +7.41375e6 q^{39} -3.05126e6 q^{40} -1.76075e7 q^{41} -801282. q^{42} -8.65735e6 q^{43} +3.52850e7 q^{44} -1.10724e8 q^{45} +1.44906e6 q^{46} +5.02833e7 q^{47} -6.73880e7 q^{48} +5.76480e6 q^{49} -4.41733e6 q^{50} -4.25662e7 q^{51} +1.45760e7 q^{52} +1.74731e7 q^{53} +9.34898e6 q^{54} +1.60501e8 q^{55} -3.15587e6 q^{56} -1.05569e8 q^{57} +5.77706e6 q^{58} -9.99330e6 q^{59} -3.07526e8 q^{60} +7.07861e7 q^{61} -8.33360e6 q^{62} -1.14520e8 q^{63} -1.31625e8 q^{64} +6.63019e7 q^{65} -2.30737e7 q^{66} +2.34532e8 q^{67} -8.36885e7 q^{68} +2.92566e8 q^{69} -7.16594e6 q^{70} -3.97213e8 q^{71} +6.26925e7 q^{72} +1.87509e8 q^{73} +1.06424e7 q^{74} -8.91859e8 q^{75} -2.07557e8 q^{76} +1.66003e8 q^{77} -9.53162e6 q^{78} +1.83817e8 q^{79} -6.02657e8 q^{80} +9.48743e8 q^{81} +2.26374e7 q^{82} +6.61272e8 q^{83} -3.18070e8 q^{84} -3.80673e8 q^{85} +1.11305e7 q^{86} +1.16639e9 q^{87} -9.08765e7 q^{88} +2.46447e8 q^{89} +1.42354e8 q^{90} +6.85750e7 q^{91} +5.75207e8 q^{92} -1.68255e9 q^{93} -6.46476e7 q^{94} -9.44115e8 q^{95} +2.61326e8 q^{96} -1.04745e9 q^{97} -7.41162e6 q^{98} -3.29772e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.28567	−0.0568190	−0.0284095	−	0.999596i	$-0.509044\pi$
$2$	−1.28567	−0.0568190	−0.0284095	+	0.999596i	$0.509044\pi$
$3$	−259.576	−1.85020	−0.925101	−	0.379722i	$-0.876020\pi$
$3$	−259.576	−1.85020	−0.925101	+	0.379722i	$0.876020\pi$
$4$	−510.347	−0.996772
$5$	−2321.41	−1.66107	−0.830534	−	0.556968i	$-0.811964\pi$
$5$	−2321.41	−1.66107	−0.830534	+	0.556968i	$0.811964\pi$
$6$	333.729	0.105127
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	1314.40	0.113455
$9$	47696.7	2.42325
$10$	2984.56	0.0943802
$11$	−69139.2	−1.42383	−0.711914	−	0.702267i	$-0.752171\pi$
$11$	−69139.2	−1.42383	−0.711914	+	0.702267i	$0.752171\pi$
$12$	132474.	1.84423
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	3086.89	0.0214756
$15$	602583.	3.07331
$16$	259608.	0.990325
$17$	163983.	0.476190	0.238095	−	0.971242i	$-0.423477\pi$
$17$	163983.	0.476190	0.238095	+	0.971242i	$0.423477\pi$
$18$	−61322.1	−0.137686
$19$	406698.	0.715948	0.357974	−	0.933732i	$-0.383468\pi$
$19$	406698.	0.715948	0.357974	+	0.933732i	$0.383468\pi$
$20$	1.18473e6	1.65570
$21$	623242.	0.699310
$22$	88890.1	0.0809005
$23$	−1.12709e6	−0.839814	−0.419907	−	0.907567i	$-0.637937\pi$
$23$	−1.12709e6	−0.839814	−0.419907	+	0.907567i	$0.637937\pi$
$24$	−341186.	−0.209914
$25$	3.43583e6	1.75914
$26$	36719.9	0.0157588
$27$	−7.27170e6	−2.63329
$28$	1.22534e6	0.376744
$29$	−4.49343e6	−1.17974	−0.589871	−	0.807498i	$-0.700821\pi$
$29$	−4.49343e6	−1.17974	−0.589871	+	0.807498i	$0.700821\pi$
$30$	−774721.	−0.174622
$31$	6.48193e6	1.26060	0.630299	−	0.776352i	$-0.282932\pi$
$31$	6.48193e6	1.26060	0.630299	+	0.776352i	$0.282932\pi$
$32$	−1.00674e6	−0.169724
$33$	1.79469e7	2.63437
$34$	−210828.	−0.0270566
$35$	5.57371e6	0.627824
$36$	−2.43419e7	−2.41542
$37$	−8.27771e6	−0.726110	−0.363055	−	0.931768i	$-0.618266\pi$
$37$	−8.27771e6	−0.726110	−0.363055	+	0.931768i	$0.618266\pi$
$38$	−522879.	−0.0406794
$39$	7.41375e6	0.513154
$40$	−3.05126e6	−0.188456
$41$	−1.76075e7	−0.973128	−0.486564	−	0.873645i	$-0.661750\pi$
$41$	−1.76075e7	−0.973128	−0.486564	+	0.873645i	$0.661750\pi$
$42$	−801282.	−0.0397341
$43$	−8.65735e6	−0.386169	−0.193084	−	0.981182i	$-0.561849\pi$
$43$	−8.65735e6	−0.386169	−0.193084	+	0.981182i	$0.561849\pi$
$44$	3.52850e7	1.41923
$45$	−1.10724e8	−4.02517
$46$	1.44906e6	0.0477174
$47$	5.02833e7	1.50308	0.751542	−	0.659685i	$-0.229310\pi$
$47$	5.02833e7	1.50308	0.751542	+	0.659685i	$0.229310\pi$
$48$	−6.73880e7	−1.83230
$49$	5.76480e6	0.142857
$50$	−4.41733e6	−0.0999529
$51$	−4.25662e7	−0.881047
$52$	1.45760e7	0.276455
$53$	1.74731e7	0.304179	0.152089	−	0.988367i	$-0.451400\pi$
$53$	1.74731e7	0.304179	0.152089	+	0.988367i	$0.451400\pi$
$54$	9.34898e6	0.149621
$55$	1.60501e8	2.36507
$56$	−3.15587e6	−0.0428818
$57$	−1.05569e8	−1.32465
$58$	5.77706e6	0.0670317
$59$	−9.99330e6	−0.107368	−0.0536840	−	0.998558i	$-0.517096\pi$
$59$	−9.99330e6	−0.107368	−0.0536840	+	0.998558i	$0.517096\pi$
$60$	−3.07526e8	−3.06339
$61$	7.07861e7	0.654582	0.327291	−	0.944924i	$-0.393864\pi$
$61$	7.07861e7	0.654582	0.327291	+	0.944924i	$0.393864\pi$
$62$	−8.33360e6	−0.0716259
$63$	−1.14520e8	−0.915901
$64$	−1.31625e8	−0.980682
$65$	6.63019e7	0.460697
$66$	−2.30737e7	−0.149682
$67$	2.34532e8	1.42189	0.710944	−	0.703249i	$-0.248268\pi$
$67$	2.34532e8	1.42189	0.710944	+	0.703249i	$0.248268\pi$
$68$	−8.36885e7	−0.474652
$69$	2.92566e8	1.55383
$70$	−7.16594e6	−0.0356724
$71$	−3.97213e8	−1.85507	−0.927535	−	0.373735i	$-0.878077\pi$
$71$	−3.97213e8	−1.85507	−0.927535	+	0.373735i	$0.878077\pi$
$72$	6.26925e7	0.274928
$73$	1.87509e8	0.772806	0.386403	−	0.922330i	$-0.373717\pi$
$73$	1.87509e8	0.772806	0.386403	+	0.922330i	$0.373717\pi$
$74$	1.06424e7	0.0412569
$75$	−8.91859e8	−3.25477
$76$	−2.07557e8	−0.713636
$77$	1.66003e8	0.538156
$78$	−9.53162e6	−0.0291569
$79$	1.83817e8	0.530961	0.265481	−	0.964116i	$-0.414469\pi$
$79$	1.83817e8	0.530961	0.265481	+	0.964116i	$0.414469\pi$
$80$	−6.02657e8	−1.64500
$81$	9.48743e8	2.44887
$82$	2.26374e7	0.0552922
$83$	6.61272e8	1.52943	0.764713	−	0.644371i	$-0.222881\pi$
$83$	6.61272e8	1.52943	0.764713	+	0.644371i	$0.222881\pi$
$84$	−3.18070e8	−0.697053
$85$	−3.80673e8	−0.790983
$86$	1.11305e7	0.0219417
$87$	1.16639e9	2.18276
$88$	−9.08765e7	−0.161540
$89$	2.46447e8	0.416360	0.208180	−	0.978091i	$-0.433246\pi$
$89$	2.46447e8	0.416360	0.208180	+	0.978091i	$0.433246\pi$
$90$	1.42354e8	0.228706
$91$	6.85750e7	0.104828
$92$	5.75207e8	0.837103
$93$	−1.68255e9	−2.33236
$94$	−6.46476e7	−0.0854037
$95$	−9.44115e8	−1.18924
$96$	2.61326e8	0.314023
$97$	−1.04745e9	−1.20132	−0.600660	−	0.799505i	$-0.705095\pi$
$97$	−1.04745e9	−1.20132	−0.600660	+	0.799505i	$0.705095\pi$
$98$	−7.41162e6	−0.00811700
$99$	−3.29772e9	−3.45028
$100$	−1.75347e9	−1.75347
$101$	−8.20619e8	−0.784685	−0.392343	−	0.919819i	$-0.628335\pi$
$101$	−8.20619e8	−0.784685	−0.392343	+	0.919819i	$0.628335\pi$
$102$	5.47259e7	0.0500602
$103$	9.91880e8	0.868344	0.434172	−	0.900830i	$-0.357041\pi$
$103$	9.91880e8	0.868344	0.434172	+	0.900830i	$0.357041\pi$
$104$	−3.75405e7	−0.0314666
$105$	−1.44680e9	−1.16160
$106$	−2.24646e7	−0.0172831
$107$	−1.71919e9	−1.26794	−0.633968	−	0.773359i	$-0.718575\pi$
$107$	−1.71919e9	−1.26794	−0.633968	+	0.773359i	$0.718575\pi$
$108$	3.71109e9	2.62479
$109$	−4.14500e8	−0.281258	−0.140629	−	0.990062i	$-0.544913\pi$
$109$	−4.14500e8	−0.281258	−0.140629	+	0.990062i	$0.544913\pi$
$110$	−2.06350e8	−0.134381
$111$	2.14870e9	1.34345
$112$	−6.23318e8	−0.374308
$113$	3.04487e9	1.75678	0.878388	−	0.477948i	$-0.158619\pi$
$113$	3.04487e9	1.75678	0.878388	+	0.477948i	$0.158619\pi$
$114$	1.35727e8	0.0752652
$115$	2.61644e9	1.39499
$116$	2.29321e9	1.17593
$117$	−1.36227e9	−0.672087
$118$	1.28481e7	0.00610054
$119$	−3.93724e8	−0.179983
$120$	7.92034e8	0.348681
$121$	2.42229e9	1.02729
$122$	−9.10074e7	−0.0371927
$123$	4.57048e9	1.80048
$124$	−3.30803e9	−1.25653
$125$	−3.44197e9	−1.26099
$126$	1.47234e8	0.0520406
$127$	2.59467e9	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$127$	2.59467e9	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$128$	6.84677e8	0.225445
$129$	2.24724e9	0.714490
$130$	−8.52421e7	−0.0261764
$131$	5.73202e9	1.70054	0.850270	−	0.526347i	$-0.176439\pi$
$131$	5.73202e9	1.70054	0.850270	+	0.526347i	$0.176439\pi$
$132$	−9.15914e9	−2.62586
$133$	−9.76483e8	−0.270603
$134$	−3.01530e8	−0.0807903
$135$	1.68806e10	4.37407
$136$	2.15540e8	0.0540259
$137$	−7.17371e9	−1.73981	−0.869903	−	0.493222i	$-0.835819\pi$
$137$	−7.17371e9	−1.73981	−0.869903	+	0.493222i	$0.835819\pi$
$138$	−3.76142e8	−0.0882868
$139$	5.07140e8	0.115229	0.0576144	−	0.998339i	$-0.481651\pi$
$139$	5.07140e8	0.115229	0.0576144	+	0.998339i	$0.481651\pi$
$140$	−2.84453e9	−0.625798
$141$	−1.30523e10	−2.78101
$142$	5.10683e8	0.105403
$143$	1.97469e9	0.394899
$144$	1.23824e10	2.39980
$145$	1.04311e10	1.95963
$146$	−2.41075e8	−0.0439101
$147$	−1.49640e9	−0.264314
$148$	4.22451e9	0.723766
$149$	1.06475e10	1.76973	0.884866	−	0.465845i	$-0.154250\pi$
$149$	1.06475e10	1.76973	0.884866	+	0.465845i	$0.154250\pi$
$150$	1.14663e9	0.184933
$151$	9.32459e9	1.45960	0.729800	−	0.683661i	$-0.239613\pi$
$151$	9.32459e9	1.45960	0.729800	+	0.683661i	$0.239613\pi$
$152$	5.34564e8	0.0812276
$153$	7.82147e9	1.15392
$154$	−2.13425e8	−0.0305775
$155$	−1.50472e10	−2.09394
$156$	−3.78359e9	−0.511497
$157$	−1.33001e10	−1.74705	−0.873524	−	0.486780i	$-0.838171\pi$
$157$	−1.33001e10	−1.74705	−0.873524	+	0.486780i	$0.838171\pi$
$158$	−2.36327e8	−0.0301687
$159$	−4.53560e9	−0.562792
$160$	2.33706e9	0.281923
$161$	2.70614e9	0.317420
$162$	−1.21977e9	−0.139143
$163$	−9.44767e9	−1.04829	−0.524144	−	0.851630i	$-0.675615\pi$
$163$	−9.44767e9	−1.04829	−0.524144	+	0.851630i	$0.675615\pi$
$164$	8.98593e9	0.969986
$165$	−4.16621e10	−4.37586
$166$	−8.50175e8	−0.0869005
$167$	6.56332e9	0.652979	0.326489	−	0.945201i	$-0.394134\pi$
$167$	6.56332e9	0.652979	0.326489	+	0.945201i	$0.394134\pi$
$168$	8.19188e8	0.0793400
$169$	8.15731e8	0.0769231
$170$	4.89419e8	0.0449429
$171$	1.93982e10	1.73492
$172$	4.41826e9	0.384922
$173$	1.16847e10	0.991772	0.495886	−	0.868388i	$-0.334843\pi$
$173$	1.16847e10	0.991772	0.495886	+	0.868388i	$0.334843\pi$
$174$	−1.49959e9	−0.124022
$175$	−8.24943e9	−0.664894
$176$	−1.79491e10	−1.41005
$177$	2.59402e9	0.198652
$178$	−3.16849e8	−0.0236571
$179$	−1.59865e10	−1.16390	−0.581949	−	0.813225i	$-0.697710\pi$
$179$	−1.59865e10	−1.16390	−0.581949	+	0.813225i	$0.697710\pi$
$180$	5.65076e10	4.01218
$181$	−1.25478e10	−0.868989	−0.434495	−	0.900674i	$-0.643073\pi$
$181$	−1.25478e10	−0.868989	−0.434495	+	0.900674i	$0.643073\pi$
$182$	−8.81646e7	−0.00595625
$183$	−1.83744e10	−1.21111
$184$	−1.48145e9	−0.0952808
$185$	1.92160e10	1.20612
$186$	2.16320e9	0.132522
$187$	−1.13377e10	−0.678012
$188$	−2.56619e10	−1.49823
$189$	1.74593e10	0.995290
$190$	1.21382e9	0.0675713
$191$	−9.36897e9	−0.509380	−0.254690	−	0.967023i	$-0.581973\pi$
$191$	−9.36897e9	−0.509380	−0.254690	+	0.967023i	$0.581973\pi$
$192$	3.41667e10	1.81446
$193$	−2.78001e9	−0.144224	−0.0721122	−	0.997397i	$-0.522974\pi$
$193$	−2.78001e9	−0.144224	−0.0721122	+	0.997397i	$0.522974\pi$
$194$	1.34667e9	0.0682578
$195$	−1.72104e10	−0.852383
$196$	−2.94205e9	−0.142396
$197$	−2.77740e10	−1.31384	−0.656918	−	0.753962i	$-0.728140\pi$
$197$	−2.77740e10	−1.31384	−0.656918	+	0.753962i	$0.728140\pi$
$198$	4.23977e9	0.196042
$199$	−8.02905e9	−0.362932	−0.181466	−	0.983397i	$-0.558084\pi$
$199$	−8.02905e9	−0.362932	−0.181466	+	0.983397i	$0.558084\pi$
$200$	4.51605e9	0.199583
$201$	−6.08789e10	−2.63078
$202$	1.05504e9	0.0445851
$203$	1.07887e10	0.445900
$204$	2.17235e10	0.878202
$205$	4.08742e10	1.61643
$206$	−1.27523e9	−0.0493384
$207$	−5.37585e10	−2.03508
$208$	−7.41466e9	−0.274667
$209$	−2.81188e10	−1.01939
$210$	1.86011e9	0.0660011
$211$	1.06135e10	0.368626	0.184313	−	0.982868i	$-0.440994\pi$
$211$	1.06135e10	0.368626	0.184313	+	0.982868i	$0.440994\pi$
$212$	−8.91736e9	−0.303197
$213$	1.03107e11	3.43225
$214$	2.21031e9	0.0720429
$215$	2.00973e10	0.641452
$216$	−9.55790e9	−0.298759
$217$	−1.55631e10	−0.476461
$218$	5.32909e8	0.0159808
$219$	−4.86730e10	−1.42985
$220$	−8.19110e10	−2.35744
$221$	−4.68353e9	−0.132071
$222$	−2.76251e9	−0.0763335
$223$	−3.01614e10	−0.816733	−0.408367	−	0.912818i	$-0.633901\pi$
$223$	−3.01614e10	−0.816733	−0.408367	+	0.912818i	$0.633901\pi$
$224$	2.41719e9	0.0641496
$225$	1.63878e11	4.26284
$226$	−3.91470e9	−0.0998183
$227$	−1.29641e10	−0.324061	−0.162030	−	0.986786i	$-0.551804\pi$
$227$	−1.29641e10	−0.324061	−0.162030	+	0.986786i	$0.551804\pi$
$228$	5.38769e10	1.32037
$229$	1.68325e10	0.404473	0.202237	−	0.979337i	$-0.435179\pi$
$229$	1.68325e10	0.404473	0.202237	+	0.979337i	$0.435179\pi$
$230$	−3.36387e9	−0.0792619
$231$	−4.30905e10	−0.995698
$232$	−5.90616e9	−0.133847
$233$	5.32496e10	1.18363	0.591814	−	0.806075i	$-0.298412\pi$
$233$	5.32496e10	1.18363	0.591814	+	0.806075i	$0.298412\pi$
$234$	1.75142e9	0.0381873
$235$	−1.16728e11	−2.49672
$236$	5.10005e9	0.107021
$237$	−4.77144e10	−0.982385
$238$	5.06198e8	0.0102264
$239$	−5.89174e10	−1.16803	−0.584013	−	0.811744i	$-0.698518\pi$
$239$	−5.89174e10	−1.16803	−0.584013	+	0.811744i	$0.698518\pi$
$240$	1.56435e11	3.04358
$241$	−1.93956e10	−0.370361	−0.185181	−	0.982704i	$-0.559287\pi$
$241$	−1.93956e10	−0.370361	−0.185181	+	0.982704i	$0.559287\pi$
$242$	−3.11425e9	−0.0583694
$243$	−1.03142e11	−1.89762
$244$	−3.61255e10	−0.652469
$245$	−1.33825e10	−0.237295
$246$	−5.87612e9	−0.102302
$247$	−1.16157e10	−0.198568
$248$	8.51984e9	0.143021
$249$	−1.71650e11	−2.82975
$250$	4.42523e9	0.0716482
$251$	1.65061e10	0.262490	0.131245	−	0.991350i	$-0.458102\pi$
$251$	1.65061e10	0.262490	0.131245	+	0.991350i	$0.458102\pi$
$252$	5.84449e10	0.912944
$253$	7.79261e10	1.19575
$254$	−3.33588e9	−0.0502873
$255$	9.88136e10	1.46348
$256$	6.65117e10	0.967872
$257$	−1.65745e10	−0.236996	−0.118498	−	0.992954i	$-0.537808\pi$
$257$	−1.65745e10	−0.236996	−0.118498	+	0.992954i	$0.537808\pi$
$258$	−2.88921e9	−0.0405966
$259$	1.98748e10	0.274444
$260$	−3.38370e10	−0.459210
$261$	−2.14322e11	−2.85880
$262$	−7.36947e9	−0.0966230
$263$	1.49607e11	1.92819	0.964096	−	0.265554i	$-0.0855549\pi$
$263$	1.49607e11	1.92819	0.964096	+	0.265554i	$0.0855549\pi$
$264$	2.35894e10	0.298881
$265$	−4.05623e10	−0.505262
$266$	1.25543e9	0.0153754
$267$	−6.39718e10	−0.770349
$268$	−1.19693e11	−1.41730
$269$	−1.00734e10	−0.117298	−0.0586492	−	0.998279i	$-0.518679\pi$
$269$	−1.00734e10	−0.117298	−0.0586492	+	0.998279i	$0.518679\pi$
$270$	−2.17028e10	−0.248530
$271$	−8.62623e10	−0.971537	−0.485768	−	0.874088i	$-0.661460\pi$
$271$	−8.62623e10	−0.971537	−0.485768	+	0.874088i	$0.661460\pi$
$272$	4.25714e10	0.471582
$273$	−1.78004e10	−0.193954
$274$	9.22300e9	0.0988541
$275$	−2.37551e11	−2.50472
$276$	−1.49310e11	−1.54881
$277$	9.90950e10	1.01133	0.505665	−	0.862730i	$-0.331247\pi$
$277$	9.90950e10	1.01133	0.505665	+	0.862730i	$0.331247\pi$
$278$	−6.52013e8	−0.00654719
$279$	3.09167e11	3.05474
$280$	7.32608e9	0.0712296
$281$	−1.33553e10	−0.127784	−0.0638920	−	0.997957i	$-0.520351\pi$
$281$	−1.33553e10	−0.127784	−0.0638920	+	0.997957i	$0.520351\pi$
$282$	1.67810e10	0.158014
$283$	−1.59240e11	−1.47575	−0.737876	−	0.674936i	$-0.764171\pi$
$283$	−1.59240e11	−1.47575	−0.737876	+	0.674936i	$0.764171\pi$
$284$	2.02716e11	1.84908
$285$	2.45070e11	2.20033
$286$	−2.53879e9	−0.0224378
$287$	4.22756e10	0.367808
$288$	−4.80183e10	−0.411283
$289$	−9.16973e10	−0.773244
$290$	−1.34109e10	−0.111344
$291$	2.71892e11	2.22268
$292$	−9.56949e10	−0.770311
$293$	−1.35456e10	−0.107373	−0.0536863	−	0.998558i	$-0.517097\pi$
$293$	−1.35456e10	−0.107373	−0.0536863	+	0.998558i	$0.517097\pi$
$294$	1.92388e9	0.0150181
$295$	2.31986e10	0.178345
$296$	−1.08802e10	−0.0823806
$297$	5.02759e11	3.74935
$298$	−1.36891e10	−0.100554
$299$	3.21908e10	0.232923
$300$	4.55158e11	3.24426
$301$	2.07863e10	0.145958
$302$	−1.19883e10	−0.0829330
$303$	2.13013e11	1.45183
$304$	1.05582e11	0.709021
$305$	−1.64324e11	−1.08730
$306$	−1.00558e10	−0.0655648
$307$	1.25768e11	0.808065	0.404032	−	0.914745i	$-0.367608\pi$
$307$	1.25768e11	0.808065	0.404032	+	0.914745i	$0.367608\pi$
$308$	−8.47193e10	−0.536419
$309$	−2.57468e11	−1.60661
$310$	1.93457e10	0.118975
$311$	−4.69814e9	−0.0284776	−0.0142388	−	0.999899i	$-0.504533\pi$
$311$	−4.69814e9	−0.0284776	−0.0142388	+	0.999899i	$0.504533\pi$
$312$	9.74462e9	0.0582196
$313$	2.53839e9	0.0149489	0.00747446	−	0.999972i	$-0.497621\pi$
$313$	2.53839e9	0.0149489	0.00747446	+	0.999972i	$0.497621\pi$
$314$	1.70994e10	0.0992656
$315$	2.65848e11	1.52137
$316$	−9.38103e10	−0.529247
$317$	−1.21435e11	−0.675426	−0.337713	−	0.941249i	$-0.609653\pi$
$317$	−1.21435e11	−0.675426	−0.337713	+	0.941249i	$0.609653\pi$
$318$	5.83128e9	0.0319773
$319$	3.10672e11	1.67975
$320$	3.05556e11	1.62898
$321$	4.46261e11	2.34594
$322$	−3.47920e9	−0.0180355
$323$	6.66918e10	0.340927
$324$	−4.84188e11	−2.44097
$325$	−9.81307e10	−0.487899
$326$	1.21466e10	0.0595626
$327$	1.07594e11	0.520384
$328$	−2.31432e10	−0.110406
$329$	−1.20730e11	−0.568112
$330$	5.35636e10	0.248632
$331$	2.35732e11	1.07942	0.539712	−	0.841850i	$-0.318533\pi$
$331$	2.35732e11	1.07942	0.539712	+	0.841850i	$0.318533\pi$
$332$	−3.37478e11	−1.52449
$333$	−3.94820e11	−1.75954
$334$	−8.43824e9	−0.0371016
$335$	−5.44445e11	−2.36185
$336$	1.61799e11	0.692545
$337$	4.46170e11	1.88437	0.942184	−	0.335097i	$-0.108769\pi$
$337$	4.46170e11	1.88437	0.942184	+	0.335097i	$0.108769\pi$
$338$	−1.04876e9	−0.00437069
$339$	−7.90377e11	−3.25039
$340$	1.94275e11	0.788429
$341$	−4.48156e11	−1.79487
$342$	−2.49396e10	−0.0985763
$343$	−1.38413e10	−0.0539949
$344$	−1.13792e10	−0.0438126
$345$	−6.79165e11	−2.58101
$346$	−1.50227e10	−0.0563515
$347$	2.13209e11	0.789446	0.394723	−	0.918800i	$-0.370841\pi$
$347$	2.13209e11	0.789446	0.394723	+	0.918800i	$0.370841\pi$
$348$	−5.95262e11	−2.17571
$349$	−5.65574e10	−0.204068	−0.102034	−	0.994781i	$-0.532535\pi$
$349$	−5.65574e10	−0.204068	−0.102034	+	0.994781i	$0.532535\pi$
$350$	1.06060e10	0.0377786
$351$	2.07687e11	0.730343
$352$	6.96053e10	0.241658
$353$	1.11655e11	0.382730	0.191365	−	0.981519i	$-0.438709\pi$
$353$	1.11655e11	0.382730	0.191365	+	0.981519i	$0.438709\pi$
$354$	−3.33505e9	−0.0112872
$355$	9.22094e11	3.08140
$356$	−1.25774e11	−0.415015
$357$	1.02201e11	0.333004
$358$	2.05533e10	0.0661315
$359$	2.29961e10	0.0730684	0.0365342	−	0.999332i	$-0.488368\pi$
$359$	2.29961e10	0.0730684	0.0365342	+	0.999332i	$0.488368\pi$
$360$	−1.45535e11	−0.456674
$361$	−1.57284e11	−0.487419
$362$	1.61323e10	0.0493751
$363$	−6.28768e11	−1.90069
$364$	−3.49970e10	−0.104490
$365$	−4.35287e11	−1.28368
$366$	2.36233e10	0.0688140
$367$	7.71359e10	0.221952	0.110976	−	0.993823i	$-0.464602\pi$
$367$	7.71359e10	0.221952	0.110976	+	0.993823i	$0.464602\pi$
$368$	−2.92601e11	−0.831689
$369$	−8.39820e11	−2.35813
$370$	−2.47054e10	−0.0685305
$371$	−4.19530e10	−0.114969
$372$	8.58686e11	2.32483
$373$	−8.52871e10	−0.228136	−0.114068	−	0.993473i	$-0.536388\pi$
$373$	−8.52871e10	−0.228136	−0.114068	+	0.993473i	$0.536388\pi$
$374$	1.45765e10	0.0385240
$375$	8.93453e11	2.33309
$376$	6.60923e10	0.170532
$377$	1.28337e11	0.327201
$378$	−2.24469e10	−0.0565514
$379$	1.03922e11	0.258721	0.129361	−	0.991598i	$-0.458708\pi$
$379$	1.03922e11	0.258721	0.129361	+	0.991598i	$0.458708\pi$
$380$	4.81826e11	1.18540
$381$	−6.73513e11	−1.63751
$382$	1.20454e10	0.0289424
$383$	1.80872e11	0.429513	0.214757	−	0.976668i	$-0.431104\pi$
$383$	1.80872e11	0.429513	0.214757	+	0.976668i	$0.431104\pi$
$384$	−1.77726e11	−0.417119
$385$	−3.85362e11	−0.893914
$386$	3.57417e9	0.00819468
$387$	−4.12928e11	−0.935782
$388$	5.34561e11	1.19744
$389$	1.23614e10	0.0273712	0.0136856	−	0.999906i	$-0.495644\pi$
$389$	1.23614e10	0.0273712	0.0136856	+	0.999906i	$0.495644\pi$
$390$	2.21268e10	0.0484315
$391$	−1.84824e11	−0.399911
$392$	7.57724e9	0.0162078
$393$	−1.48790e12	−3.14634
$394$	3.57082e10	0.0746508
$395$	−4.26714e11	−0.881962
$396$	1.68298e12	3.43915
$397$	5.21354e11	1.05336	0.526679	−	0.850065i	$-0.323437\pi$
$397$	5.21354e11	1.05336	0.526679	+	0.850065i	$0.323437\pi$
$398$	1.03227e10	0.0206214
$399$	2.53472e11	0.500670
$400$	8.91968e11	1.74213
$401$	−1.55735e11	−0.300770	−0.150385	−	0.988627i	$-0.548051\pi$
$401$	−1.55735e11	−0.300770	−0.150385	+	0.988627i	$0.548051\pi$
$402$	7.82700e10	0.149478
$403$	−1.85130e11	−0.349627
$404$	4.18801e11	0.782152
$405$	−2.20242e12	−4.06774
$406$	−1.38707e10	−0.0253356
$407$	5.72315e11	1.03386
$408$	−5.59489e10	−0.0999588
$409$	1.87514e11	0.331344	0.165672	−	0.986181i	$-0.447021\pi$
$409$	1.87514e11	0.331344	0.165672	+	0.986181i	$0.447021\pi$
$410$	−5.25507e10	−0.0918440
$411$	1.86212e12	3.21899
$412$	−5.06203e11	−0.865540
$413$	2.39939e10	0.0405813
$414$	6.91156e10	0.115631
$415$	−1.53508e12	−2.54048
$416$	2.87535e10	0.0470729
$417$	−1.31641e11	−0.213197
$418$	3.61515e10	0.0579205
$419$	1.36729e11	0.216719	0.108360	−	0.994112i	$-0.465440\pi$
$419$	1.36729e11	0.216719	0.108360	+	0.994112i	$0.465440\pi$
$420$	7.38371e11	1.15785
$421$	4.42573e11	0.686618	0.343309	−	0.939223i	$-0.388452\pi$
$421$	4.42573e11	0.686618	0.343309	+	0.939223i	$0.388452\pi$
$422$	−1.36454e10	−0.0209450
$423$	2.39835e12	3.64234
$424$	2.29666e10	0.0345105
$425$	5.63419e11	0.837686
$426$	−1.32561e11	−0.195017
$427$	−1.69958e11	−0.247409
$428$	8.77385e11	1.26384
$429$	−5.12581e11	−0.730642
$430$	−2.58384e10	−0.0364467
$431$	3.54848e11	0.495330	0.247665	−	0.968846i	$-0.420337\pi$
$431$	3.54848e11	0.495330	0.247665	+	0.968846i	$0.420337\pi$
$432$	−1.88779e12	−2.60781
$433$	4.83812e11	0.661426	0.330713	−	0.943731i	$-0.392711\pi$
$433$	4.83812e11	0.661426	0.330713	+	0.943731i	$0.392711\pi$
$434$	2.00090e10	0.0270721
$435$	−2.70766e12	−3.62571
$436$	2.11539e11	0.280350
$437$	−4.58386e11	−0.601263
$438$	6.25773e10	0.0812424
$439$	1.30184e12	1.67289	0.836447	−	0.548047i	$-0.184629\pi$
$439$	1.30184e12	1.67289	0.836447	+	0.548047i	$0.184629\pi$
$440$	2.10962e11	0.268328
$441$	2.74962e11	0.346178
$442$	6.02146e9	0.00750416
$443$	−1.48839e12	−1.83612	−0.918060	−	0.396441i	$-0.870245\pi$
$443$	−1.48839e12	−1.83612	−0.918060	+	0.396441i	$0.870245\pi$
$444$	−1.09658e12	−1.33911
$445$	−5.72105e11	−0.691601
$446$	3.87776e10	0.0464060
$447$	−2.76382e12	−3.27436
$448$	3.16031e11	0.370663
$449$	−1.35614e12	−1.57469	−0.787345	−	0.616512i	$-0.788545\pi$
$449$	−1.35614e12	−1.57469	−0.787345	+	0.616512i	$0.788545\pi$
$450$	−2.10692e11	−0.242210
$451$	1.21737e12	1.38557
$452$	−1.55394e12	−1.75110
$453$	−2.42044e12	−2.70055
$454$	1.66675e10	0.0184128
$455$	−1.59191e11	−0.174127
$456$	−1.38760e11	−0.150287
$457$	7.51445e11	0.805887	0.402944	−	0.915225i	$-0.367987\pi$
$457$	7.51445e11	0.805887	0.402944	+	0.915225i	$0.367987\pi$
$458$	−2.16410e10	−0.0229818
$459$	−1.19244e12	−1.25395
$460$	−1.33529e12	−1.39048
$461$	−2.26739e11	−0.233814	−0.116907	−	0.993143i	$-0.537298\pi$
$461$	−2.26739e11	−0.233814	−0.116907	+	0.993143i	$0.537298\pi$
$462$	5.54000e10	0.0565746
$463$	−1.19647e12	−1.21001	−0.605004	−	0.796222i	$-0.706829\pi$
$463$	−1.19647e12	−1.21001	−0.605004	+	0.796222i	$0.706829\pi$
$464$	−1.16653e12	−1.16833
$465$	3.90590e12	3.87421
$466$	−6.84613e10	−0.0672525
$467$	1.56747e12	1.52502	0.762508	−	0.646978i	$-0.223968\pi$
$467$	1.56747e12	1.52502	0.762508	+	0.646978i	$0.223968\pi$
$468$	6.95229e11	0.669918
$469$	−5.63111e11	−0.537423
$470$	1.50074e11	0.141861
$471$	3.45238e12	3.23239
$472$	−1.31352e10	−0.0121814
$473$	5.98563e11	0.549838
$474$	6.13448e10	0.0558182
$475$	1.39735e12	1.25946
$476$	2.00936e11	0.179402
$477$	8.33411e11	0.737100
$478$	7.57482e10	0.0663661
$479$	−1.24621e12	−1.08164	−0.540818	−	0.841139i	$-0.681885\pi$
$479$	−1.24621e12	−1.08164	−0.540818	+	0.841139i	$0.681885\pi$
$480$	−6.06645e11	−0.521614
$481$	2.36420e11	0.201387
$482$	2.49363e10	0.0210436
$483$	−7.02450e11	−0.587291
$484$	−1.23621e12	−1.02397
$485$	2.43155e12	1.99547
$486$	1.32607e11	0.107821
$487$	1.20576e12	0.971360	0.485680	−	0.874137i	$-0.338572\pi$
$487$	1.20576e12	0.971360	0.485680	+	0.874137i	$0.338572\pi$
$488$	9.30412e10	0.0742653
$489$	2.45239e12	1.93954
$490$	1.72054e10	0.0134829
$491$	1.04648e12	0.812578	0.406289	−	0.913745i	$-0.366823\pi$
$491$	1.04648e12	0.812578	0.406289	+	0.913745i	$0.366823\pi$
$492$	−2.33253e12	−1.79467
$493$	−7.36848e11	−0.561781
$494$	1.49339e10	0.0112824
$495$	7.65536e12	5.73115
$496$	1.68276e12	1.24840
$497$	9.53707e11	0.701151
$498$	2.20685e11	0.160783
$499$	8.35494e11	0.603241	0.301621	−	0.953428i	$-0.402472\pi$
$499$	8.35494e11	0.603241	0.301621	+	0.953428i	$0.402472\pi$
$500$	1.75660e12	1.25692
$501$	−1.70368e12	−1.20814
$502$	−2.12214e10	−0.0149144
$503$	1.56190e12	1.08792	0.543961	−	0.839111i	$-0.316924\pi$
$503$	1.56190e12	1.08792	0.543961	+	0.839111i	$0.316924\pi$
$504$	−1.50525e11	−0.103913
$505$	1.90500e12	1.30342
$506$	−1.00187e11	−0.0679414
$507$	−2.11744e11	−0.142323
$508$	−1.32418e12	−0.882187
$509$	−1.26338e12	−0.834266	−0.417133	−	0.908845i	$-0.636965\pi$
$509$	−1.26338e12	−0.834266	−0.417133	+	0.908845i	$0.636965\pi$
$510$	−1.27041e11	−0.0831533
$511$	−4.50210e11	−0.292093
$512$	−4.36067e11	−0.280439
$513$	−2.95739e12	−1.88530
$514$	2.13093e10	0.0134659
$515$	−2.30256e12	−1.44238
$516$	−1.14687e12	−0.712183
$517$	−3.47655e12	−2.14013
$518$	−2.55524e10	−0.0155936
$519$	−3.03308e12	−1.83498
$520$	8.71470e10	0.0522682
$521$	1.23357e12	0.733488	0.366744	−	0.930322i	$-0.380472\pi$
$521$	1.23357e12	0.733488	0.366744	+	0.930322i	$0.380472\pi$
$522$	2.75547e11	0.162434
$523$	1.92980e12	1.12786	0.563930	−	0.825823i	$-0.309289\pi$
$523$	1.92980e12	1.12786	0.563930	+	0.825823i	$0.309289\pi$
$524$	−2.92532e12	−1.69505
$525$	2.14135e12	1.23019
$526$	−1.92345e11	−0.109558
$527$	1.06293e12	0.600284
$528$	4.65915e12	2.60888
$529$	−5.30821e11	−0.294712
$530$	5.21496e10	0.0287085
$531$	−4.76648e11	−0.260179
$532$	4.98345e11	0.269729
$533$	5.02887e11	0.269897
$534$	8.22464e10	0.0437705
$535$	3.99095e12	2.10613
$536$	3.08268e11	0.161320
$537$	4.14971e12	2.15344
$538$	1.29511e10	0.00666478
$539$	−3.98574e11	−0.203404
$540$	−8.61497e12	−4.35995
$541$	−3.06493e12	−1.53827	−0.769136	−	0.639085i	$-0.779313\pi$
$541$	−3.06493e12	−1.53827	−0.769136	+	0.639085i	$0.779313\pi$
$542$	1.10905e11	0.0552017
$543$	3.25711e12	1.60781
$544$	−1.65089e11	−0.0808207
$545$	9.62225e11	0.467189
$546$	2.28854e10	0.0110203
$547$	2.42647e12	1.15886	0.579431	−	0.815022i	$-0.303275\pi$
$547$	2.42647e12	1.15886	0.579431	+	0.815022i	$0.303275\pi$
$548$	3.66108e12	1.73419
$549$	3.37627e12	1.58621
$550$	3.05411e11	0.142316
$551$	−1.82747e12	−0.844633
$552$	3.84548e11	0.176289
$553$	−4.41344e11	−0.200684
$554$	−1.27403e11	−0.0574628
$555$	−4.98801e12	−2.23156
$556$	−2.58817e11	−0.114857
$557$	−2.31305e12	−1.01821	−0.509105	−	0.860704i	$-0.670024\pi$
$557$	−2.31305e12	−1.01821	−0.509105	+	0.860704i	$0.670024\pi$
$558$	−3.97486e11	−0.173567
$559$	2.47263e11	0.107104
$560$	1.44698e12	0.621750
$561$	2.94299e12	1.25446
$562$	1.71705e10	0.00726057
$563$	1.35408e12	0.568009	0.284005	−	0.958823i	$-0.408337\pi$
$563$	1.35408e12	0.568009	0.284005	+	0.958823i	$0.408337\pi$
$564$	6.66122e12	2.77203
$565$	−7.06841e12	−2.91812
$566$	2.04730e11	0.0838508
$567$	−2.27793e12	−0.925587
$568$	−5.22096e11	−0.210466
$569$	−4.44136e12	−1.77628	−0.888140	−	0.459574i	$-0.848002\pi$
$569$	−4.44136e12	−1.77628	−0.888140	+	0.459574i	$0.848002\pi$
$570$	−3.15078e11	−0.125021
$571$	1.84308e12	0.725573	0.362787	−	0.931872i	$-0.381825\pi$
$571$	1.84308e12	0.725573	0.362787	+	0.931872i	$0.381825\pi$
$572$	−1.00778e12	−0.393624
$573$	2.43196e12	0.942455
$574$	−5.43523e10	−0.0208985
$575$	−3.87249e12	−1.47736
$576$	−6.27808e12	−2.37643
$577$	4.08691e11	0.153498	0.0767492	−	0.997050i	$-0.475546\pi$
$577$	4.08691e11	0.153498	0.0767492	+	0.997050i	$0.475546\pi$
$578$	1.17892e11	0.0439349
$579$	7.21624e11	0.266844
$580$	−5.32348e12	−1.95330
$581$	−1.58771e12	−0.578069
$582$	−3.49562e11	−0.126291
$583$	−1.20808e12	−0.433098
$584$	2.46462e11	0.0876784
$585$	3.16238e12	1.11638
$586$	1.74151e10	0.00610081
$587$	1.53916e12	0.535072	0.267536	−	0.963548i	$-0.413791\pi$
$587$	1.53916e12	0.535072	0.267536	+	0.963548i	$0.413791\pi$
$588$	7.63686e11	0.263461
$589$	2.63619e12	0.902522
$590$	−2.98256e10	−0.0101334
$591$	7.20948e12	2.43086
$592$	−2.14896e12	−0.719085
$593$	−1.83390e12	−0.609018	−0.304509	−	0.952509i	$-0.598492\pi$
$593$	−1.83390e12	−0.609018	−0.304509	+	0.952509i	$0.598492\pi$
$594$	−6.46381e11	−0.213034
$595$	9.13996e11	0.298963
$596$	−5.43390e12	−1.76402
$597$	2.08415e12	0.671497
$598$	−4.13867e10	−0.0132344
$599$	−4.41887e12	−1.40246	−0.701230	−	0.712935i	$-0.747366\pi$
$599$	−4.41887e12	−1.40246	−0.701230	+	0.712935i	$0.747366\pi$
$600$	−1.17226e12	−0.369269
$601$	9.68840e11	0.302912	0.151456	−	0.988464i	$-0.451604\pi$
$601$	9.68840e11	0.302912	0.151456	+	0.988464i	$0.451604\pi$
$602$	−2.67243e10	−0.00829319
$603$	1.11864e13	3.44558
$604$	−4.75878e12	−1.45489
$605$	−5.62312e12	−1.70639
$606$	−2.73864e11	−0.0824913
$607$	1.02230e12	0.305654	0.152827	−	0.988253i	$-0.451162\pi$
$607$	1.02230e12	0.305654	0.152827	+	0.988253i	$0.451162\pi$
$608$	−4.09440e11	−0.121513
$609$	−2.80049e12	−0.825006
$610$	2.11266e11	0.0617796
$611$	−1.43614e12	−0.416880
$612$	−3.99167e12	−1.15020
$613$	−2.99442e12	−0.856526	−0.428263	−	0.903654i	$-0.640874\pi$
$613$	−2.99442e12	−0.856526	−0.428263	+	0.903654i	$0.640874\pi$
$614$	−1.61695e11	−0.0459134
$615$	−1.06100e13	−2.99072
$616$	2.18194e11	0.0610563
$617$	1.41114e12	0.392001	0.196001	−	0.980604i	$-0.437205\pi$
$617$	1.41114e12	0.392001	0.196001	+	0.980604i	$0.437205\pi$
$618$	3.31019e11	0.0912860
$619$	1.20474e12	0.329826	0.164913	−	0.986308i	$-0.447266\pi$
$619$	1.20474e12	0.329826	0.164913	+	0.986308i	$0.447266\pi$
$620$	7.67931e12	2.08718
$621$	8.19585e12	2.21148
$622$	6.04024e9	0.00161807
$623$	−5.91719e11	−0.157369
$624$	1.92467e12	0.508189
$625$	1.27962e12	0.335446
$626$	−3.26353e9	−0.000849382 0
$627$	7.29897e12	1.88607
$628$	6.78764e12	1.74141
$629$	−1.35741e12	−0.345766
$630$	−3.41792e11	−0.0864429
$631$	−6.21974e12	−1.56185	−0.780926	−	0.624624i	$-0.785252\pi$
$631$	−6.21974e12	−1.56185	−0.780926	+	0.624624i	$0.785252\pi$
$632$	2.41608e11	0.0602400
$633$	−2.75500e12	−0.682032
$634$	1.56125e11	0.0383771
$635$	−6.02329e12	−1.47012
$636$	2.31473e12	0.560975
$637$	−1.64648e11	−0.0396214
$638$	−3.99421e11	−0.0954417
$639$	−1.89457e13	−4.49529
$640$	−1.58942e12	−0.374480
$641$	−4.43577e12	−1.03779	−0.518893	−	0.854839i	$-0.673656\pi$
$641$	−4.43577e12	−1.03779	−0.518893	+	0.854839i	$0.673656\pi$
$642$	−5.73743e11	−0.133294
$643$	7.91422e12	1.82582	0.912911	−	0.408158i	$-0.133829\pi$
$643$	7.91422e12	1.82582	0.912911	+	0.408158i	$0.133829\pi$
$644$	−1.38107e12	−0.316395
$645$	−5.21677e12	−1.18682
$646$	−8.57435e10	−0.0193711
$647$	2.97398e12	0.667219	0.333610	−	0.942711i	$-0.391733\pi$
$647$	2.97398e12	0.667219	0.333610	+	0.942711i	$0.391733\pi$
$648$	1.24703e12	0.277836
$649$	6.90929e11	0.152874
$650$	1.26163e11	0.0277219
$651$	4.03981e12	0.881549
$652$	4.82159e12	1.04490
$653$	−2.06624e12	−0.444704	−0.222352	−	0.974966i	$-0.571373\pi$
$653$	−2.06624e12	−0.444704	−0.222352	+	0.974966i	$0.571373\pi$
$654$	−1.38330e11	−0.0295677
$655$	−1.33064e13	−2.82471
$656$	−4.57104e12	−0.963713
$657$	8.94359e12	1.87270
$658$	1.55219e11	0.0322796
$659$	1.54574e12	0.319267	0.159633	−	0.987176i	$-0.448969\pi$
$659$	1.54574e12	0.319267	0.159633	+	0.987176i	$0.448969\pi$
$660$	2.12621e13	4.36174
$661$	−6.02290e12	−1.22715	−0.613577	−	0.789635i	$-0.710270\pi$
$661$	−6.02290e12	−1.22715	−0.613577	+	0.789635i	$0.710270\pi$
$662$	−3.03073e11	−0.0613318
$663$	1.21573e12	0.244358
$664$	8.69174e11	0.173520
$665$	2.26682e12	0.449490
$666$	5.07607e11	0.0999755
$667$	5.06450e12	0.990764
$668$	−3.34957e12	−0.650871
$669$	7.82919e12	1.51112
$670$	6.99976e11	0.134198
$671$	−4.89410e12	−0.932012
$672$	−6.27444e11	−0.118690
$673$	9.32388e12	1.75198	0.875989	−	0.482331i	$-0.160210\pi$
$673$	9.32388e12	1.75198	0.875989	+	0.482331i	$0.160210\pi$
$674$	−5.73626e11	−0.107068
$675$	−2.49843e13	−4.63234
$676$	−4.16306e11	−0.0766747
$677$	−7.86978e12	−1.43984	−0.719919	−	0.694058i	$-0.755821\pi$
$677$	−7.86978e12	−1.43984	−0.719919	+	0.694058i	$0.755821\pi$
$678$	1.01616e12	0.184684
$679$	2.51492e12	0.454056
$680$	−5.00356e11	−0.0897406
$681$	3.36518e12	0.599578
$682$	5.76179e11	0.101983
$683$	2.04270e12	0.359179	0.179590	−	0.983742i	$-0.442523\pi$
$683$	2.04270e12	0.359179	0.179590	+	0.983742i	$0.442523\pi$
$684$	−9.89981e12	−1.72932
$685$	1.66531e13	2.88994
$686$	1.77953e10	0.00306794
$687$	−4.36932e12	−0.748357
$688$	−2.24752e12	−0.382433
$689$	−4.99050e11	−0.0843640
$690$	8.73181e11	0.146650
$691$	7.32959e12	1.22301	0.611503	−	0.791242i	$-0.290565\pi$
$691$	7.32959e12	1.22301	0.611503	+	0.791242i	$0.290565\pi$
$692$	−5.96328e12	−0.988570
$693$	7.91782e12	1.30408
$694$	−2.74116e11	−0.0448555
$695$	−1.17728e12	−0.191403
$696$	1.53310e12	0.247644
$697$	−2.88734e12	−0.463393
$698$	7.27140e10	0.0115949
$699$	−1.38223e13	−2.18995
$700$	4.21007e12	0.662748
$701$	−3.68447e12	−0.576294	−0.288147	−	0.957586i	$-0.593039\pi$
$701$	−3.68447e12	−0.576294	−0.288147	+	0.957586i	$0.593039\pi$
$702$	−2.67016e11	−0.0414974
$703$	−3.36653e12	−0.519857
$704$	9.10044e12	1.39632
$705$	3.02999e13	4.61944
$706$	−1.43552e11	−0.0217464
$707$	1.97031e12	0.296583
$708$	−1.32385e12	−0.198011
$709$	−4.91181e9	−0.000730017 0	−0.000365009	−	1.00000i	$-0.500116\pi$
$709$	−4.91181e9	−0.000730017 0	−0.000365009		1.00000i	$0.500116\pi$
$710$	−1.18551e12	−0.175082
$711$	8.76745e12	1.28665
$712$	3.23930e11	0.0472379
$713$	−7.30572e12	−1.05867
$714$	−1.31397e11	−0.0189210
$715$	−4.58406e12	−0.655954
$716$	8.15866e12	1.16014
$717$	1.52935e13	2.16108
$718$	−2.95653e10	−0.00415167
$719$	−1.18560e13	−1.65447	−0.827236	−	0.561854i	$-0.810088\pi$
$719$	−1.18560e13	−1.65447	−0.827236	+	0.561854i	$0.810088\pi$
$720$	−2.87448e13	−3.98623
$721$	−2.38150e12	−0.328203
$722$	2.02215e11	0.0276947
$723$	5.03463e12	0.685243
$724$	6.40374e12	0.866184
$725$	−1.54387e13	−2.07534
$726$	8.08386e11	0.107995
$727$	5.43147e12	0.721128	0.360564	−	0.932734i	$-0.382584\pi$
$727$	5.43147e12	0.721128	0.360564	+	0.932734i	$0.382584\pi$
$728$	9.01348e10	0.0118933
$729$	8.09915e12	1.06210
$730$	5.59634e11	0.0729376
$731$	−1.41966e12	−0.183890
$732$	9.37731e12	1.20720
$733$	1.02717e13	1.31424	0.657118	−	0.753788i	$-0.271775\pi$
$733$	1.02717e13	1.31424	0.657118	+	0.753788i	$0.271775\pi$
$734$	−9.91711e10	−0.0126111
$735$	3.47377e12	0.439044
$736$	1.13469e12	0.142537
$737$	−1.62154e13	−2.02452
$738$	1.07973e12	0.133986
$739$	6.87695e12	0.848196	0.424098	−	0.905616i	$-0.360591\pi$
$739$	6.87695e12	0.848196	0.424098	+	0.905616i	$0.360591\pi$
$740$	−9.80682e12	−1.20222
$741$	3.01516e12	0.367391
$742$	5.39376e10	0.00653241
$743$	1.75401e12	0.211146	0.105573	−	0.994412i	$-0.466332\pi$
$743$	1.75401e12	0.211146	0.105573	+	0.994412i	$0.466332\pi$
$744$	−2.21155e12	−0.264617
$745$	−2.47171e13	−2.93964
$746$	1.09651e11	0.0129625
$747$	3.15405e13	3.70617
$748$	5.78616e12	0.675823
$749$	4.12778e12	0.479235
$750$	−1.14868e12	−0.132564
$751$	1.00633e13	1.15441	0.577207	−	0.816598i	$-0.304143\pi$
$751$	1.00633e13	1.15441	0.577207	+	0.816598i	$0.304143\pi$
$752$	1.30539e13	1.48854
$753$	−4.28459e12	−0.485660
$754$	−1.64998e11	−0.0185913
$755$	−2.16462e13	−2.42449
$756$	−8.91032e12	−0.992077
$757$	1.56802e12	0.173548	0.0867741	−	0.996228i	$-0.472344\pi$
$757$	1.56802e12	0.173548	0.0867741	+	0.996228i	$0.472344\pi$
$758$	−1.33609e11	−0.0147003
$759$	−2.02278e13	−2.21238
$760$	−1.24094e12	−0.134924
$761$	−1.85312e12	−0.200296	−0.100148	−	0.994973i	$-0.531932\pi$
$761$	−1.85312e12	−0.200296	−0.100148	+	0.994973i	$0.531932\pi$
$762$	8.65914e11	0.0930417
$763$	9.95215e11	0.106306
$764$	4.78142e12	0.507735
$765$	−1.81569e13	−1.91675
$766$	−2.32541e11	−0.0244045
$767$	2.85419e11	0.0297785
$768$	−1.72648e13	−1.79076
$769$	−1.27293e13	−1.31261	−0.656305	−	0.754496i	$-0.727881\pi$
$769$	−1.27293e13	−1.31261	−0.656305	+	0.754496i	$0.727881\pi$
$770$	4.95448e11	0.0507913
$771$	4.30234e12	0.438491
$772$	1.41877e12	0.143759
$773$	−1.63622e13	−1.64829	−0.824146	−	0.566377i	$-0.808345\pi$
$773$	−1.63622e13	−1.64829	−0.824146	+	0.566377i	$0.808345\pi$
$774$	5.30887e11	0.0531702
$775$	2.22708e13	2.21757
$776$	−1.37676e12	−0.136295
$777$	−5.15902e12	−0.507777
$778$	−1.58926e10	−0.00155521
$779$	−7.16094e12	−0.696709
$780$	8.78326e12	0.849631
$781$	2.74630e13	2.64130
$782$	2.37622e11	0.0227225
$783$	3.26748e13	3.10660
$784$	1.49659e12	0.141475
$785$	3.08749e13	2.90197
$786$	1.91294e12	0.178772
$787$	−1.77706e12	−0.165126	−0.0825630	−	0.996586i	$-0.526311\pi$
$787$	−1.77706e12	−0.165126	−0.0825630	+	0.996586i	$0.526311\pi$
$788$	1.41744e13	1.30959
$789$	−3.88343e13	−3.56754
$790$	5.48612e11	0.0501122
$791$	−7.31074e12	−0.663999
$792$	−4.33451e12	−0.391451
$793$	−2.02172e12	−0.181548
$794$	−6.70288e11	−0.0598507
$795$	1.05290e13	0.934836
$796$	4.09760e12	0.361760
$797$	7.67413e12	0.673700	0.336850	−	0.941558i	$-0.390638\pi$
$797$	7.67413e12	0.673700	0.336850	+	0.941558i	$0.390638\pi$
$798$	−3.25880e11	−0.0284476
$799$	8.24562e12	0.715753
$800$	−3.45899e12	−0.298569
$801$	1.17547e13	1.00894
$802$	2.00223e11	0.0170895
$803$	−1.29643e13	−1.10034
$804$	3.10694e13	2.62229
$805$	−6.28207e12	−0.527256
$806$	2.38016e11	0.0198655
$807$	2.61482e12	0.217026
$808$	−1.07862e12	−0.0890262
$809$	2.81208e12	0.230812	0.115406	−	0.993318i	$-0.463183\pi$
$809$	2.81208e12	0.230812	0.115406	+	0.993318i	$0.463183\pi$
$810$	2.83159e12	0.231125
$811$	−1.15496e13	−0.937508	−0.468754	−	0.883329i	$-0.655297\pi$
$811$	−1.15496e13	−0.937508	−0.468754	+	0.883329i	$0.655297\pi$
$812$	−5.50599e12	−0.444461
$813$	2.23916e13	1.79754
$814$	−7.35807e11	−0.0587427
$815$	2.19319e13	1.74128
$816$	−1.10505e13	−0.872523
$817$	−3.52093e12	−0.276477
$818$	−2.41081e11	−0.0188267
$819$	3.27080e12	0.254025
$820$	−2.08600e13	−1.61121
$821$	1.80937e13	1.38990	0.694950	−	0.719058i	$-0.255427\pi$
$821$	1.80937e13	1.38990	0.694950	+	0.719058i	$0.255427\pi$
$822$	−2.39407e12	−0.182900
$823$	−1.01799e13	−0.773470	−0.386735	−	0.922191i	$-0.626397\pi$
$823$	−1.01799e13	−0.773470	−0.386735	+	0.922191i	$0.626397\pi$
$824$	1.30373e12	0.0985176
$825$	6.16625e13	4.63424
$826$	−3.08482e10	−0.00230579
$827$	−1.10490e13	−0.821387	−0.410693	−	0.911774i	$-0.634713\pi$
$827$	−1.10490e13	−0.821387	−0.410693	+	0.911774i	$0.634713\pi$
$828$	2.74355e13	2.02851
$829$	8.42801e11	0.0619769	0.0309884	−	0.999520i	$-0.490134\pi$
$829$	8.42801e11	0.0619769	0.0309884	+	0.999520i	$0.490134\pi$
$830$	1.97361e12	0.144348
$831$	−2.57227e13	−1.87116
$832$	3.75934e12	0.271992
$833$	9.45332e11	0.0680271
$834$	1.69247e11	0.0121136
$835$	−1.52362e13	−1.08464
$836$	1.43504e13	1.01610
$837$	−4.71346e13	−3.31952
$838$	−1.75788e11	−0.0123138
$839$	−1.27758e13	−0.890143	−0.445071	−	0.895495i	$-0.646822\pi$
$839$	−1.27758e13	−0.890143	−0.445071	+	0.895495i	$0.646822\pi$
$840$	−1.90167e12	−0.131789
$841$	5.68376e12	0.391790
$842$	−5.69001e11	−0.0390130
$843$	3.46673e12	0.236426
$844$	−5.41655e12	−0.367436
$845$	−1.89365e12	−0.127774
$846$	−3.08348e12	−0.206954
$847$	−5.81591e12	−0.388278
$848$	4.53616e12	0.301236
$849$	4.13349e13	2.73044
$850$	−7.24370e11	−0.0475965
$851$	9.32973e12	0.609798
$852$	−5.26203e13	−3.42117
$853$	−2.59022e13	−1.67520	−0.837599	−	0.546286i	$-0.816041\pi$
$853$	−2.59022e13	−1.67520	−0.837599	+	0.546286i	$0.816041\pi$
$854$	2.18509e11	0.0140575
$855$	−4.50312e13	−2.88181
$856$	−2.25970e12	−0.143853
$857$	1.81086e13	1.14676	0.573378	−	0.819291i	$-0.305632\pi$
$857$	1.81086e13	1.14676	0.573378	+	0.819291i	$0.305632\pi$
$858$	6.59009e11	0.0415144
$859$	5.34942e12	0.335226	0.167613	−	0.985853i	$-0.446394\pi$
$859$	5.34942e12	0.335226	0.167613	+	0.985853i	$0.446394\pi$
$860$	−1.02566e13	−0.639381
$861$	−1.09737e13	−0.680519
$862$	−4.56217e11	−0.0281442
$863$	−7.09781e12	−0.435588	−0.217794	−	0.975995i	$-0.569886\pi$
$863$	−7.09781e12	−0.435588	−0.217794	+	0.975995i	$0.569886\pi$
$864$	7.32072e12	0.446932
$865$	−2.71251e13	−1.64740
$866$	−6.22022e11	−0.0375816
$867$	2.38024e13	1.43066
$868$	7.94259e12	0.474923
$869$	−1.27089e13	−0.755997
$870$	3.48116e12	0.206009
$871$	−6.69847e12	−0.394361
$872$	−5.44818e11	−0.0319100
$873$	−4.99597e13	−2.91109
$874$	5.89332e11	0.0341632
$875$	8.26417e12	0.476610
$876$	2.48401e13	1.42523
$877$	4.71691e12	0.269252	0.134626	−	0.990896i	$-0.457017\pi$
$877$	4.71691e12	0.269252	0.134626	+	0.990896i	$0.457017\pi$
$878$	−1.67374e12	−0.0950522
$879$	3.51611e12	0.198661
$880$	4.16672e13	2.34219
$881$	−1.71502e13	−0.959128	−0.479564	−	0.877507i	$-0.659205\pi$
$881$	−1.71502e13	−0.959128	−0.479564	+	0.877507i	$0.659205\pi$
$882$	−3.53510e11	−0.0196695
$883$	−1.94555e13	−1.07701	−0.538505	−	0.842622i	$-0.681011\pi$
$883$	−1.94555e13	−1.07701	−0.538505	+	0.842622i	$0.681011\pi$
$884$	2.39023e12	0.131645
$885$	−6.02179e12	−0.329975
$886$	1.91358e12	0.104327
$887$	1.88348e13	1.02166	0.510828	−	0.859683i	$-0.329339\pi$
$887$	1.88348e13	1.02166	0.510828	+	0.859683i	$0.329339\pi$
$888$	2.82424e12	0.152421
$889$	−6.22979e12	−0.334515
$890$	7.35537e11	0.0392961
$891$	−6.55954e13	−3.48677
$892$	1.53928e13	0.814096
$893$	2.04501e13	1.07613
$894$	3.55336e12	0.186046
$895$	3.71113e13	1.93331
$896$	−1.64391e12	−0.0852103
$897$	−8.35597e12	−0.430954
$898$	1.74354e12	0.0894723
$899$	−2.91261e13	−1.48718
$900$	−8.36346e13	−4.24908
$901$	2.86530e12	0.144847
$902$	−1.56513e12	−0.0787265
$903$	−5.39563e12	−0.270052
$904$	4.00218e12	0.199314
$905$	2.91287e13	1.44345
$906$	3.11188e12	0.153443
$907$	−2.57877e13	−1.26526	−0.632630	−	0.774454i	$-0.718025\pi$
$907$	−2.57877e13	−1.26526	−0.632630	+	0.774454i	$0.718025\pi$
$908$	6.61620e12	0.323015
$909$	−3.91409e13	−1.90149
$910$	2.04666e11	0.00989373
$911$	1.29729e13	0.624029	0.312015	−	0.950077i	$-0.398996\pi$
$911$	1.29729e13	0.624029	0.312015	+	0.950077i	$0.398996\pi$
$912$	−2.74066e13	−1.31183
$913$	−4.57198e13	−2.17764
$914$	−9.66108e11	−0.0457897
$915$	4.26545e13	2.01173
$916$	−8.59043e12	−0.403167
$917$	−1.37626e13	−0.642744
$918$	1.53308e12	0.0712479
$919$	−2.88785e12	−0.133553	−0.0667766	−	0.997768i	$-0.521271\pi$
$919$	−2.88785e12	−0.133553	−0.0667766	+	0.997768i	$0.521271\pi$
$920$	3.43904e12	0.158268
$921$	−3.26463e13	−1.49508
$922$	2.91510e11	0.0132851
$923$	1.13448e13	0.514504
$924$	2.19911e13	0.992483
$925$	−2.84408e13	−1.27733
$926$	1.53827e12	0.0687515
$927$	4.73094e13	2.10421
$928$	4.52372e12	0.200230
$929$	1.29356e13	0.569793	0.284897	−	0.958558i	$-0.408041\pi$
$929$	1.29356e13	0.569793	0.284897	+	0.958558i	$0.408041\pi$
$930$	−5.02169e12	−0.220129
$931$	2.34454e12	0.102278
$932$	−2.71758e13	−1.17981
$933$	1.21952e12	0.0526894
$934$	−2.01525e12	−0.0866499
$935$	2.63195e13	1.12622
$936$	−1.79056e12	−0.0762514
$937$	6.98136e12	0.295877	0.147939	−	0.988997i	$-0.452736\pi$
$937$	6.98136e12	0.295877	0.147939	+	0.988997i	$0.452736\pi$
$938$	7.23974e11	0.0305358
$939$	−6.58906e11	−0.0276585
$940$	5.95719e13	2.48866
$941$	1.71817e13	0.714354	0.357177	−	0.934037i	$-0.383739\pi$
$941$	1.71817e13	0.714354	0.357177	+	0.934037i	$0.383739\pi$
$942$	−4.43861e12	−0.183661
$943$	1.98452e13	0.817247
$944$	−2.59434e12	−0.106329
$945$	−4.05303e13	−1.65324
$946$	−7.69553e11	−0.0312412
$947$	2.44132e13	0.986393	0.493196	−	0.869918i	$-0.335828\pi$
$947$	2.44132e13	0.986393	0.493196	+	0.869918i	$0.335828\pi$
$948$	2.43509e13	0.979214
$949$	−5.35546e12	−0.214338
$950$	−1.79652e12	−0.0715610
$951$	3.15217e13	1.24967
$952$	−5.17510e11	−0.0204199
$953$	2.24777e13	0.882742	0.441371	−	0.897325i	$-0.354492\pi$
$953$	2.24777e13	0.882742	0.441371	+	0.897325i	$0.354492\pi$
$954$	−1.07149e12	−0.0418813
$955$	2.17492e13	0.846114
$956$	3.00683e13	1.16426
$957$	−8.06431e13	−3.10787
$958$	1.60221e12	0.0614575
$959$	1.72241e13	0.657585
$960$	−7.93149e13	−3.01394
$961$	1.55758e13	0.589107
$962$	−3.03957e11	−0.0114426
$963$	−8.19999e13	−3.07252
$964$	9.89847e12	0.369166
$965$	6.45355e12	0.239566
$966$	9.03117e11	0.0333693
$967$	−5.86015e12	−0.215521	−0.107760	−	0.994177i	$-0.534368\pi$
$967$	−5.86015e12	−0.215521	−0.107760	+	0.994177i	$0.534368\pi$
$968$	3.18385e12	0.116550
$969$	−1.73116e13	−0.630783
$970$	−3.12617e12	−0.113381
$971$	−4.04150e13	−1.45900	−0.729501	−	0.683980i	$-0.760248\pi$
$971$	−4.04150e13	−1.45900	−0.729501	+	0.683980i	$0.760248\pi$
$972$	5.26384e13	1.89149
$973$	−1.21764e12	−0.0435524
$974$	−1.55020e12	−0.0551917
$975$	2.54724e13	0.902711
$976$	1.83766e13	0.648249
$977$	−7.43343e12	−0.261014	−0.130507	−	0.991447i	$-0.541661\pi$
$977$	−7.43343e12	−0.261014	−0.130507	+	0.991447i	$0.541661\pi$
$978$	−3.15296e12	−0.110203
$979$	−1.70392e13	−0.592825
$980$	6.82971e12	0.236529
$981$	−1.97703e13	−0.681558
$982$	−1.34543e12	−0.0461699
$983$	3.35637e13	1.14651	0.573257	−	0.819375i	$-0.305680\pi$
$983$	3.35637e13	1.14651	0.573257	+	0.819375i	$0.305680\pi$
$984$	6.00743e12	0.204273
$985$	6.44750e13	2.18237
$986$	9.47341e11	0.0319198
$987$	3.13387e13	1.05112
$988$	5.92805e12	0.197927
$989$	9.75762e12	0.324310
$990$	−9.84224e12	−0.325639
$991$	3.38918e13	1.11625	0.558127	−	0.829755i	$-0.311520\pi$
$991$	3.38918e13	1.11625	0.558127	+	0.829755i	$0.311520\pi$
$992$	−6.52562e12	−0.213954
$993$	−6.11903e13	−1.99715
$994$	−1.22615e12	−0.0398387
$995$	1.86387e13	0.602855
$996$	8.76012e13	2.82061
$997$	2.49255e13	0.798943	0.399471	−	0.916746i	$-0.369194\pi$
$997$	2.49255e13	0.798943	0.399471	+	0.916746i	$0.369194\pi$
$998$	−1.07417e12	−0.0342756
$999$	6.01930e13	1.91206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.8	✓	13

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

\(f(q)\)	\(=\)	\(q-1.28567 q^{2} -259.576 q^{3} -510.347 q^{4} -2321.41 q^{5} +333.729 q^{6} -2401.00 q^{7} +1314.40 q^{8} +47696.7 q^{9} +O(q^{10})\)	\(q-1.28567 q^{2} -259.576 q^{3} -510.347 q^{4} -2321.41 q^{5} +333.729 q^{6} -2401.00 q^{7} +1314.40 q^{8} +47696.7 q^{9} +2984.56 q^{10} -69139.2 q^{11} +132474. q^{12} -28561.0 q^{13} +3086.89 q^{14} +602583. q^{15} +259608. q^{16} +163983. q^{17} -61322.1 q^{18} +406698. q^{19} +1.18473e6 q^{20} +623242. q^{21} +88890.1 q^{22} -1.12709e6 q^{23} -341186. q^{24} +3.43583e6 q^{25} +36719.9 q^{26} -7.27170e6 q^{27} +1.22534e6 q^{28} -4.49343e6 q^{29} -774721. q^{30} +6.48193e6 q^{31} -1.00674e6 q^{32} +1.79469e7 q^{33} -210828. q^{34} +5.57371e6 q^{35} -2.43419e7 q^{36} -8.27771e6 q^{37} -522879. q^{38} +7.41375e6 q^{39} -3.05126e6 q^{40} -1.76075e7 q^{41} -801282. q^{42} -8.65735e6 q^{43} +3.52850e7 q^{44} -1.10724e8 q^{45} +1.44906e6 q^{46} +5.02833e7 q^{47} -6.73880e7 q^{48} +5.76480e6 q^{49} -4.41733e6 q^{50} -4.25662e7 q^{51} +1.45760e7 q^{52} +1.74731e7 q^{53} +9.34898e6 q^{54} +1.60501e8 q^{55} -3.15587e6 q^{56} -1.05569e8 q^{57} +5.77706e6 q^{58} -9.99330e6 q^{59} -3.07526e8 q^{60} +7.07861e7 q^{61} -8.33360e6 q^{62} -1.14520e8 q^{63} -1.31625e8 q^{64} +6.63019e7 q^{65} -2.30737e7 q^{66} +2.34532e8 q^{67} -8.36885e7 q^{68} +2.92566e8 q^{69} -7.16594e6 q^{70} -3.97213e8 q^{71} +6.26925e7 q^{72} +1.87509e8 q^{73} +1.06424e7 q^{74} -8.91859e8 q^{75} -2.07557e8 q^{76} +1.66003e8 q^{77} -9.53162e6 q^{78} +1.83817e8 q^{79} -6.02657e8 q^{80} +9.48743e8 q^{81} +2.26374e7 q^{82} +6.61272e8 q^{83} -3.18070e8 q^{84} -3.80673e8 q^{85} +1.11305e7 q^{86} +1.16639e9 q^{87} -9.08765e7 q^{88} +2.46447e8 q^{89} +1.42354e8 q^{90} +6.85750e7 q^{91} +5.75207e8 q^{92} -1.68255e9 q^{93} -6.46476e7 q^{94} -9.44115e8 q^{95} +2.61326e8 q^{96} -1.04745e9 q^{97} -7.41162e6 q^{98} -3.29772e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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

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