LMFDB - Embedded newform 91.10.a.b.1.1

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			1.1
Root			$-39.9033$ 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)

$f(q)$	$=$	$q-41.9033 q^{2} +259.004 q^{3} +1243.89 q^{4} -2349.43 q^{5} -10853.1 q^{6} -2401.00 q^{7} -30668.6 q^{8} +47400.0 q^{9} +O(q^{10})$	\(q-41.9033 q^{2} +259.004 q^{3} +1243.89 q^{4} -2349.43 q^{5} -10853.1 q^{6} -2401.00 q^{7} -30668.6 q^{8} +47400.0 q^{9} +98448.7 q^{10} +12307.2 q^{11} +322172. q^{12} -28561.0 q^{13} +100610. q^{14} -608510. q^{15} +648245. q^{16} +112626. q^{17} -1.98622e6 q^{18} +797243. q^{19} -2.92242e6 q^{20} -621868. q^{21} -515715. q^{22} -1.90356e6 q^{23} -7.94328e6 q^{24} +3.56667e6 q^{25} +1.19680e6 q^{26} +7.17880e6 q^{27} -2.98658e6 q^{28} +380444. q^{29} +2.54986e7 q^{30} -7.55351e6 q^{31} -1.14613e7 q^{32} +3.18762e6 q^{33} -4.71939e6 q^{34} +5.64097e6 q^{35} +5.89603e7 q^{36} +8.70768e6 q^{37} -3.34071e7 q^{38} -7.39741e6 q^{39} +7.20536e7 q^{40} -2.41346e7 q^{41} +2.60583e7 q^{42} -1.07086e7 q^{43} +1.53088e7 q^{44} -1.11363e8 q^{45} +7.97657e7 q^{46} +2.03326e7 q^{47} +1.67898e8 q^{48} +5.76480e6 q^{49} -1.49456e8 q^{50} +2.91705e7 q^{51} -3.55267e7 q^{52} -7.67964e7 q^{53} -3.00815e8 q^{54} -2.89150e7 q^{55} +7.36353e7 q^{56} +2.06489e8 q^{57} -1.59419e7 q^{58} +3.01260e7 q^{59} -7.56919e8 q^{60} -1.21595e8 q^{61} +3.16517e8 q^{62} -1.13807e8 q^{63} +1.48365e8 q^{64} +6.71019e7 q^{65} -1.33572e8 q^{66} +2.12824e8 q^{67} +1.40094e8 q^{68} -4.93030e8 q^{69} -2.36375e8 q^{70} -1.43710e8 q^{71} -1.45369e9 q^{72} +1.97430e8 q^{73} -3.64881e8 q^{74} +9.23782e8 q^{75} +9.91682e8 q^{76} -2.95497e7 q^{77} +3.09976e8 q^{78} -6.22951e8 q^{79} -1.52300e9 q^{80} +9.26362e8 q^{81} +1.01132e9 q^{82} -2.70749e8 q^{83} -7.73535e8 q^{84} -2.64606e8 q^{85} +4.48726e8 q^{86} +9.85364e7 q^{87} -3.77446e8 q^{88} -8.21754e8 q^{89} +4.66647e9 q^{90} +6.85750e7 q^{91} -2.36782e9 q^{92} -1.95639e9 q^{93} -8.52003e8 q^{94} -1.87306e9 q^{95} -2.96852e9 q^{96} -1.55427e9 q^{97} -2.41564e8 q^{98} +5.83363e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−41.9033	−1.85188	−0.925942	−	0.377667i	$-0.876726\pi$
$2$	−41.9033	−1.85188	−0.925942	+	0.377667i	$0.876726\pi$
$3$	259.004	1.84612	0.923061	−	0.384653i	$-0.125679\pi$
$3$	259.004	1.84612	0.923061	+	0.384653i	$0.125679\pi$
$4$	1243.89	2.42947
$5$	−2349.43	−1.68111	−0.840556	−	0.541725i	$-0.817772\pi$
$5$	−2349.43	−1.68111	−0.840556	+	0.541725i	$0.817772\pi$
$6$	−10853.1	−3.41880
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−30668.6	−2.64721
$9$	47400.0	2.40817
$10$	98448.7	3.11322
$11$	12307.2	0.253451	0.126725	−	0.991938i	$-0.459553\pi$
$11$	12307.2	0.253451	0.126725	+	0.991938i	$0.459553\pi$
$12$	322172.	4.48510
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	100610.	0.699946
$15$	−608510.	−3.10354
$16$	648245.	2.47286
$17$	112626.	0.327053	0.163526	−	0.986539i	$-0.447713\pi$
$17$	112626.	0.327053	0.163526	+	0.986539i	$0.447713\pi$
$18$	−1.98622e6	−4.45964
$19$	797243.	1.40346	0.701729	−	0.712444i	$-0.252412\pi$
$19$	797243.	1.40346	0.701729	+	0.712444i	$0.252412\pi$
$20$	−2.92242e6	−4.08421
$21$	−621868.	−0.697769
$22$	−515715.	−0.469361
$23$	−1.90356e6	−1.41838	−0.709189	−	0.705018i	$-0.750939\pi$
$23$	−1.90356e6	−1.41838	−0.709189	+	0.705018i	$0.750939\pi$
$24$	−7.94328e6	−4.88708
$25$	3.56667e6	1.82614
$26$	1.19680e6	0.513620
$27$	7.17880e6	2.59965
$28$	−2.98658e6	−0.918254
$29$	380444.	0.0998848	0.0499424	−	0.998752i	$-0.484096\pi$
$29$	380444.	0.0998848	0.0499424	+	0.998752i	$0.484096\pi$
$30$	2.54986e7	5.74739
$31$	−7.55351e6	−1.46900	−0.734499	−	0.678610i	$-0.762583\pi$
$31$	−7.55351e6	−1.46900	−0.734499	+	0.678610i	$0.762583\pi$
$32$	−1.14613e7	−1.93223
$33$	3.18762e6	0.467901
$34$	−4.71939e6	−0.605663
$35$	5.64097e6	0.635401
$36$	5.89603e7	5.85057
$37$	8.70768e6	0.763827	0.381913	−	0.924198i	$-0.375265\pi$
$37$	8.70768e6	0.763827	0.381913	+	0.924198i	$0.375265\pi$
$38$	−3.34071e7	−2.59904
$39$	−7.39741e6	−0.512022
$40$	7.20536e7	4.45026
$41$	−2.41346e7	−1.33387	−0.666933	−	0.745118i	$-0.732393\pi$
$41$	−2.41346e7	−1.33387	−0.666933	+	0.745118i	$0.732393\pi$
$42$	2.60583e7	1.29219
$43$	−1.07086e7	−0.477667	−0.238833	−	0.971061i	$-0.576765\pi$
$43$	−1.07086e7	−0.477667	−0.238833	+	0.971061i	$0.576765\pi$
$44$	1.53088e7	0.615752
$45$	−1.11363e8	−4.04840
$46$	7.97657e7	2.62667
$47$	2.03326e7	0.607788	0.303894	−	0.952706i	$-0.401713\pi$
$47$	2.03326e7	0.607788	0.303894	+	0.952706i	$0.401713\pi$
$48$	1.67898e8	4.56520
$49$	5.76480e6	0.142857
$50$	−1.49456e8	−3.38179
$51$	2.91705e7	0.603779
$52$	−3.55267e7	−0.673814
$53$	−7.67964e7	−1.33690	−0.668451	−	0.743756i	$-0.733042\pi$
$53$	−7.67964e7	−1.33690	−0.668451	+	0.743756i	$0.733042\pi$
$54$	−3.00815e8	−4.81425
$55$	−2.89150e7	−0.426079
$56$	7.36353e7	1.00055
$57$	2.06489e8	2.59095
$58$	−1.59419e7	−0.184975
$59$	3.01260e7	0.323673	0.161837	−	0.986818i	$-0.448258\pi$
$59$	3.01260e7	0.323673	0.161837	+	0.986818i	$0.448258\pi$
$60$	−7.56919e8	−7.53996
$61$	−1.21595e8	−1.12443	−0.562215	−	0.826991i	$-0.690051\pi$
$61$	−1.21595e8	−1.12443	−0.562215	+	0.826991i	$0.690051\pi$
$62$	3.16517e8	2.72041
$63$	−1.13807e8	−0.910202
$64$	1.48365e8	1.10541
$65$	6.71019e7	0.466257
$66$	−1.33572e8	−0.866498
$67$	2.12824e8	1.29028	0.645140	−	0.764065i	$-0.276799\pi$
$67$	2.12824e8	1.29028	0.645140	+	0.764065i	$0.276799\pi$
$68$	1.40094e8	0.794565
$69$	−4.93030e8	−2.61850
$70$	−2.36375e8	−1.17669
$71$	−1.43710e8	−0.671157	−0.335579	−	0.942012i	$-0.608932\pi$
$71$	−1.43710e8	−0.671157	−0.335579	+	0.942012i	$0.608932\pi$
$72$	−1.45369e9	−6.37493
$73$	1.97430e8	0.813694	0.406847	−	0.913496i	$-0.366628\pi$
$73$	1.97430e8	0.813694	0.406847	+	0.913496i	$0.366628\pi$
$74$	−3.64881e8	−1.41452
$75$	9.23782e8	3.37127
$76$	9.91682e8	3.40966
$77$	−2.95497e7	−0.0957954
$78$	3.09976e8	0.948205
$79$	−6.22951e8	−1.79942	−0.899709	−	0.436490i	$-0.856221\pi$
$79$	−6.22951e8	−1.79942	−0.899709	+	0.436490i	$0.856221\pi$
$80$	−1.52300e9	−4.15715
$81$	9.26362e8	2.39110
$82$	1.01132e9	2.47016
$83$	−2.70749e8	−0.626204	−0.313102	−	0.949720i	$-0.601368\pi$
$83$	−2.70749e8	−0.626204	−0.313102	+	0.949720i	$0.601368\pi$
$84$	−7.73535e8	−1.69521
$85$	−2.64606e8	−0.549812
$86$	4.48726e8	0.884583
$87$	9.85364e7	0.184400
$88$	−3.77446e8	−0.670938
$89$	−8.21754e8	−1.38831	−0.694156	−	0.719825i	$-0.744222\pi$
$89$	−8.21754e8	−1.38831	−0.694156	+	0.719825i	$0.744222\pi$
$90$	4.66647e9	7.49716
$91$	6.85750e7	0.104828
$92$	−2.36782e9	−3.44591
$93$	−1.95639e9	−2.71195
$94$	−8.52003e8	−1.12555
$95$	−1.87306e9	−2.35937
$96$	−2.96852e9	−3.56714
$97$	−1.55427e9	−1.78260	−0.891302	−	0.453410i	$-0.850207\pi$
$97$	−1.55427e9	−1.78260	−0.891302	+	0.453410i	$0.850207\pi$
$98$	−2.41564e8	−0.264555
$99$	5.83363e8	0.610352
$100$	4.43655e9	4.43655
$101$	−6.33132e8	−0.605408	−0.302704	−	0.953085i	$-0.597889\pi$
$101$	−6.33132e8	−0.605408	−0.302704	+	0.953085i	$0.597889\pi$
$102$	−1.22234e9	−1.11813
$103$	1.91358e9	1.67525	0.837624	−	0.546246i	$-0.183944\pi$
$103$	1.91358e9	1.67525	0.837624	+	0.546246i	$0.183944\pi$
$104$	8.75926e8	0.734205
$105$	1.46103e9	1.17303
$106$	3.21802e9	2.47579
$107$	−4.84352e8	−0.357219	−0.178609	−	0.983920i	$-0.557160\pi$
$107$	−4.84352e8	−0.357219	−0.178609	+	0.983920i	$0.557160\pi$
$108$	8.92963e9	6.31577
$109$	−7.09930e7	−0.0481722	−0.0240861	−	0.999710i	$-0.507668\pi$
$109$	−7.09930e7	−0.0481722	−0.0240861	+	0.999710i	$0.507668\pi$
$110$	1.21163e9	0.789049
$111$	2.25532e9	1.41012
$112$	−1.55644e9	−0.934653
$113$	−6.81852e8	−0.393403	−0.196701	−	0.980463i	$-0.563023\pi$
$113$	−6.81852e8	−0.393403	−0.196701	+	0.980463i	$0.563023\pi$
$114$	−8.65257e9	−4.79814
$115$	4.47228e9	2.38445
$116$	4.73230e8	0.242667
$117$	−1.35379e9	−0.667905
$118$	−1.26238e9	−0.599405
$119$	−2.70414e8	−0.123614
$120$	1.86621e10	8.21573
$121$	−2.20648e9	−0.935763
$122$	5.09525e9	2.08231
$123$	−6.25094e9	−2.46248
$124$	−9.39573e9	−3.56889
$125$	−3.79091e9	−1.38883
$126$	4.76890e9	1.68559
$127$	1.34136e9	0.457539	0.228770	−	0.973481i	$-0.426530\pi$
$127$	1.34136e9	0.457539	0.228770	+	0.973481i	$0.426530\pi$
$128$	−3.48817e8	−0.114856
$129$	−2.77357e9	−0.881831
$130$	−2.81179e9	−0.863453
$131$	−3.65346e9	−1.08389	−0.541944	−	0.840415i	$-0.682311\pi$
$131$	−3.65346e9	−1.08389	−0.541944	+	0.840415i	$0.682311\pi$
$132$	3.96505e9	1.13675
$133$	−1.91418e9	−0.530457
$134$	−8.91803e9	−2.38945
$135$	−1.68660e10	−4.37030
$136$	−3.45407e9	−0.865778
$137$	−4.29359e9	−1.04131	−0.520653	−	0.853768i	$-0.674311\pi$
$137$	−4.29359e9	−1.04131	−0.520653	+	0.853768i	$0.674311\pi$
$138$	2.06596e10	4.84916
$139$	−2.99497e9	−0.680496	−0.340248	−	0.940336i	$-0.610511\pi$
$139$	−2.99497e9	−0.680496	−0.340248	+	0.940336i	$0.610511\pi$
$140$	7.01674e9	1.54369
$141$	5.26622e9	1.12205
$142$	6.02193e9	1.24290
$143$	−3.51507e8	−0.0702946
$144$	3.07268e10	5.95506
$145$	−8.93824e8	−0.167918
$146$	−8.27299e9	−1.50687
$147$	1.49311e9	0.263732
$148$	1.08314e10	1.85570
$149$	1.02671e9	0.170650	0.0853252	−	0.996353i	$-0.472807\pi$
$149$	1.02671e9	0.170650	0.0853252	+	0.996353i	$0.472807\pi$
$150$	−3.87095e10	−6.24320
$151$	−9.01471e9	−1.41109	−0.705547	−	0.708664i	$-0.749298\pi$
$151$	−9.01471e9	−1.41109	−0.705547	+	0.708664i	$0.749298\pi$
$152$	−2.44503e10	−3.71525
$153$	5.33846e9	0.787597
$154$	1.23823e9	0.177402
$155$	1.77464e10	2.46955
$156$	−9.20155e9	−1.24394
$157$	7.02669e9	0.923002	0.461501	−	0.887140i	$-0.347311\pi$
$157$	7.02669e9	0.923002	0.461501	+	0.887140i	$0.347311\pi$
$158$	2.61037e10	3.33231
$159$	−1.98906e10	−2.46808
$160$	2.69275e10	3.24830
$161$	4.57046e9	0.536097
$162$	−3.88177e10	−4.42804
$163$	−1.44470e9	−0.160300	−0.0801502	−	0.996783i	$-0.525540\pi$
$163$	−1.44470e9	−0.160300	−0.0801502	+	0.996783i	$0.525540\pi$
$164$	−3.00207e10	−3.24059
$165$	−7.48908e9	−0.786594
$166$	1.13453e10	1.15966
$167$	1.19736e9	0.119124	0.0595622	−	0.998225i	$-0.481030\pi$
$167$	1.19736e9	0.119124	0.0595622	+	0.998225i	$0.481030\pi$
$168$	1.90718e10	1.84714
$169$	8.15731e8	0.0769231
$170$	1.10879e10	1.01819
$171$	3.77893e10	3.37976
$172$	−1.33203e10	−1.16048
$173$	−8.33487e9	−0.707443	−0.353722	−	0.935351i	$-0.615084\pi$
$173$	−8.33487e9	−0.707443	−0.353722	+	0.935351i	$0.615084\pi$
$174$	−4.12900e9	−0.341486
$175$	−8.56359e9	−0.690215
$176$	7.97811e9	0.626748
$177$	7.80274e9	0.597541
$178$	3.44342e10	2.57099
$179$	1.35207e10	0.984375	0.492188	−	0.870489i	$-0.336197\pi$
$179$	1.35207e10	0.984375	0.492188	+	0.870489i	$0.336197\pi$
$180$	−1.38523e11	−9.83547
$181$	−5.18956e8	−0.0359399	−0.0179700	−	0.999839i	$-0.505720\pi$
$181$	−5.18956e8	−0.0359399	−0.0179700	+	0.999839i	$0.505720\pi$
$182$	−2.87352e9	−0.194130
$183$	−3.14936e10	−2.07584
$184$	5.83796e10	3.75475
$185$	−2.04581e10	−1.28408
$186$	8.19792e10	5.02221
$187$	1.38611e9	0.0828917
$188$	2.52915e10	1.47660
$189$	−1.72363e10	−0.982575
$190$	7.84875e10	4.36928
$191$	−3.28460e8	−0.0178580	−0.00892900	−	0.999960i	$-0.502842\pi$
$191$	−3.28460e8	−0.0178580	−0.00892900	+	0.999960i	$0.502842\pi$
$192$	3.84272e10	2.04072
$193$	−4.90851e8	−0.0254649	−0.0127325	−	0.999919i	$-0.504053\pi$
$193$	−4.90851e8	−0.0254649	−0.0127325	+	0.999919i	$0.504053\pi$
$194$	6.51293e10	3.30117
$195$	1.73797e10	0.860767
$196$	7.17077e9	0.347067
$197$	2.61659e10	1.23776	0.618881	−	0.785485i	$-0.287586\pi$
$197$	2.61659e10	1.23776	0.618881	+	0.785485i	$0.287586\pi$
$198$	−2.44448e10	−1.13030
$199$	−1.60260e10	−0.724415	−0.362208	−	0.932097i	$-0.617977\pi$
$199$	−1.60260e10	−0.724415	−0.362208	+	0.932097i	$0.617977\pi$
$200$	−1.09385e11	−4.83417
$201$	5.51222e10	2.38201
$202$	2.65304e10	1.12115
$203$	−9.13445e8	−0.0377529
$204$	3.62849e10	1.46686
$205$	5.67023e10	2.24238
$206$	−8.01854e10	−3.10237
$207$	−9.02288e10	−3.41569
$208$	−1.85145e10	−0.685848
$209$	9.81186e9	0.355708
$210$	−6.12221e10	−2.17231
$211$	−9.07175e9	−0.315079	−0.157540	−	0.987513i	$-0.550356\pi$
$211$	−9.07175e9	−0.315079	−0.157540	+	0.987513i	$0.550356\pi$
$212$	−9.55262e10	−3.24796
$213$	−3.72214e10	−1.23904
$214$	2.02960e10	0.661527
$215$	2.51591e10	0.803011
$216$	−2.20164e11	−6.88182
$217$	1.81360e10	0.555229
$218$	2.97484e9	0.0892092
$219$	5.11352e10	1.50218
$220$	−3.59670e10	−1.03515
$221$	−3.21670e9	−0.0907081
$222$	−9.45056e10	−2.61137
$223$	−5.38945e10	−1.45939	−0.729697	−	0.683771i	$-0.760339\pi$
$223$	−5.38945e10	−1.45939	−0.729697	+	0.683771i	$0.760339\pi$
$224$	2.75186e10	0.730315
$225$	1.69060e11	4.39764
$226$	2.85719e10	0.728536
$227$	−1.50876e10	−0.377141	−0.188570	−	0.982060i	$-0.560385\pi$
$227$	−1.50876e10	−0.377141	−0.188570	+	0.982060i	$0.560385\pi$
$228$	2.56849e11	6.29465
$229$	4.00195e10	0.961640	0.480820	−	0.876819i	$-0.340339\pi$
$229$	4.00195e10	0.961640	0.480820	+	0.876819i	$0.340339\pi$
$230$	−1.87403e11	−4.41573
$231$	−7.65348e9	−0.176850
$232$	−1.16677e10	−0.264416
$233$	−3.66092e10	−0.813746	−0.406873	−	0.913485i	$-0.633381\pi$
$233$	−3.66092e10	−0.813746	−0.406873	+	0.913485i	$0.633381\pi$
$234$	5.67283e10	1.23688
$235$	−4.77699e10	−1.02176
$236$	3.74734e10	0.786355
$237$	−1.61347e11	−3.32195
$238$	1.13313e10	0.228919
$239$	−1.55694e10	−0.308660	−0.154330	−	0.988019i	$-0.549322\pi$
$239$	−1.55694e10	−0.308660	−0.154330	+	0.988019i	$0.549322\pi$
$240$	−3.94464e11	−7.67461
$241$	−1.03265e10	−0.197186	−0.0985931	−	0.995128i	$-0.531434\pi$
$241$	−1.03265e10	−0.197186	−0.0985931	+	0.995128i	$0.531434\pi$
$242$	9.24588e10	1.73292
$243$	9.86310e10	1.81462
$244$	−1.51251e11	−2.73177
$245$	−1.35440e10	−0.240159
$246$	2.61935e11	4.56022
$247$	−2.27700e10	−0.389249
$248$	2.31656e11	3.88875
$249$	−7.01251e10	−1.15605
$250$	1.58852e11	2.57195
$251$	4.72412e10	0.751258	0.375629	−	0.926770i	$-0.377427\pi$
$251$	4.72412e10	0.751258	0.375629	+	0.926770i	$0.377427\pi$
$252$	−1.41564e11	−2.21131
$253$	−2.34276e10	−0.359489
$254$	−5.62074e10	−0.847309
$255$	−6.85339e10	−1.01502
$256$	−6.13465e10	−0.892709
$257$	7.36444e10	1.05303	0.526515	−	0.850166i	$-0.323498\pi$
$257$	7.36444e10	1.05303	0.526515	+	0.850166i	$0.323498\pi$
$258$	1.16222e11	1.63305
$259$	−2.09071e10	−0.288699
$260$	8.34674e10	1.13276
$261$	1.80330e10	0.240539
$262$	1.53092e11	2.00723
$263$	−5.73252e10	−0.738831	−0.369415	−	0.929264i	$-0.620442\pi$
$263$	−5.73252e10	−0.738831	−0.369415	+	0.929264i	$0.620442\pi$
$264$	−9.77599e10	−1.23863
$265$	1.80427e11	2.24748
$266$	8.02105e10	0.982345
$267$	−2.12838e11	−2.56299
$268$	2.64729e11	3.13470
$269$	1.35120e11	1.57339	0.786693	−	0.617345i	$-0.211792\pi$
$269$	1.35120e11	1.57339	0.786693	+	0.617345i	$0.211792\pi$
$270$	7.06744e11	8.09329
$271$	3.87001e9	0.0435863	0.0217932	−	0.999763i	$-0.493062\pi$
$271$	3.87001e9	0.0435863	0.0217932	+	0.999763i	$0.493062\pi$
$272$	7.30091e10	0.808755
$273$	1.77612e10	0.193526
$274$	1.79916e11	1.92838
$275$	4.38959e10	0.462836
$276$	−6.13275e11	−6.36157
$277$	−2.19549e10	−0.224064	−0.112032	−	0.993705i	$-0.535736\pi$
$277$	−2.19549e10	−0.224064	−0.112032	+	0.993705i	$0.535736\pi$
$278$	1.25499e11	1.26020
$279$	−3.58036e11	−3.53759
$280$	−1.73001e11	−1.68204
$281$	−9.96876e10	−0.953812	−0.476906	−	0.878954i	$-0.658242\pi$
$281$	−9.96876e10	−0.953812	−0.476906	+	0.878954i	$0.658242\pi$
$282$	−2.20672e11	−2.07791
$283$	−1.10342e10	−0.102259	−0.0511295	−	0.998692i	$-0.516282\pi$
$283$	−1.10342e10	−0.102259	−0.0511295	+	0.998692i	$0.516282\pi$
$284$	−1.78759e11	−1.63056
$285$	−4.85130e11	−4.35568
$286$	1.47293e10	0.130177
$287$	5.79471e10	0.504154
$288$	−5.43265e11	−4.65314
$289$	−1.05903e11	−0.893037
$290$	3.74542e10	0.310964
$291$	−4.02563e11	−3.29090
$292$	2.45582e11	1.97685
$293$	2.25402e11	1.78671	0.893354	−	0.449353i	$-0.148346\pi$
$293$	2.25402e11	1.78671	0.893354	+	0.449353i	$0.148346\pi$
$294$	−6.25661e10	−0.488400
$295$	−7.07787e10	−0.544131
$296$	−2.67052e11	−2.02201
$297$	8.83512e10	0.658883
$298$	−4.30224e10	−0.316025
$299$	5.43677e10	0.393387
$300$	1.14908e12	8.19041
$301$	2.57114e10	0.180541
$302$	3.77747e11	2.61318
$303$	−1.63984e11	−1.11766
$304$	5.16809e11	3.47055
$305$	2.85679e11	1.89029
$306$	−2.23699e11	−1.45854
$307$	−1.22466e11	−0.786850	−0.393425	−	0.919357i	$-0.628710\pi$
$307$	−1.22466e11	−0.786850	−0.393425	+	0.919357i	$0.628710\pi$
$308$	−3.67565e10	−0.232732
$309$	4.95625e11	3.09271
$310$	−7.43634e11	−4.57332
$311$	2.01037e11	1.21858	0.609290	−	0.792948i	$-0.291455\pi$
$311$	2.01037e11	1.21858	0.609290	+	0.792948i	$0.291455\pi$
$312$	2.26868e11	1.35543
$313$	2.22510e11	1.31039	0.655195	−	0.755460i	$-0.272587\pi$
$313$	2.22510e11	1.31039	0.655195	+	0.755460i	$0.272587\pi$
$314$	−2.94442e11	−1.70929
$315$	2.67382e11	1.53015
$316$	−7.74882e11	−4.37163
$317$	7.25246e10	0.403384	0.201692	−	0.979449i	$-0.435356\pi$
$317$	7.25246e10	0.403384	0.201692	+	0.979449i	$0.435356\pi$
$318$	8.33480e11	4.57060
$319$	4.68221e9	0.0253159
$320$	−3.48573e11	−1.85832
$321$	−1.25449e11	−0.659469
$322$	−1.91517e11	−0.992789
$323$	8.97900e10	0.459004
$324$	1.15229e12	5.80911
$325$	−1.01868e11	−0.506479
$326$	6.05379e10	0.296858
$327$	−1.83875e10	−0.0889317
$328$	7.40173e11	3.53103
$329$	−4.88185e10	−0.229722
$330$	3.13817e11	1.45668
$331$	−1.01725e10	−0.0465802	−0.0232901	−	0.999729i	$-0.507414\pi$
$331$	−1.01725e10	−0.0465802	−0.0232901	+	0.999729i	$0.507414\pi$
$332$	−3.36782e11	−1.52134
$333$	4.12744e11	1.83942
$334$	−5.01733e10	−0.220604
$335$	−5.00014e11	−2.16910
$336$	−4.03123e11	−1.72548
$337$	3.61649e11	1.52740	0.763699	−	0.645572i	$-0.223381\pi$
$337$	3.61649e11	1.52740	0.763699	+	0.645572i	$0.223381\pi$
$338$	−3.41818e10	−0.142453
$339$	−1.76602e11	−0.726269
$340$	−3.29140e11	−1.33575
$341$	−9.29629e10	−0.372319
$342$	−1.58350e12	−6.25892
$343$	−1.38413e10	−0.0539949
$344$	3.28418e11	1.26449
$345$	1.15834e12	4.40199
$346$	3.49259e11	1.31010
$347$	−1.88006e11	−0.696128	−0.348064	−	0.937471i	$-0.613161\pi$
$347$	−1.88006e11	−0.696128	−0.348064	+	0.937471i	$0.613161\pi$
$348$	1.22568e11	0.447993
$349$	8.94676e10	0.322813	0.161407	−	0.986888i	$-0.448397\pi$
$349$	8.94676e10	0.322813	0.161407	+	0.986888i	$0.448397\pi$
$350$	3.58843e11	1.27820
$351$	−2.05034e11	−0.721013
$352$	−1.41057e11	−0.489726
$353$	−2.48773e11	−0.852741	−0.426370	−	0.904549i	$-0.640208\pi$
$353$	−2.48773e11	−0.852741	−0.426370	+	0.904549i	$0.640208\pi$
$354$	−3.26961e11	−1.10658
$355$	3.37636e11	1.12829
$356$	−1.02217e12	−3.37286
$357$	−7.00384e10	−0.228207
$358$	−5.66563e11	−1.82295
$359$	5.66435e11	1.79980	0.899901	−	0.436093i	$-0.143638\pi$
$359$	5.66435e11	1.79980	0.899901	+	0.436093i	$0.143638\pi$
$360$	3.41534e12	10.7170
$361$	3.12908e11	0.969694
$362$	2.17460e10	0.0665566
$363$	−5.71486e11	−1.72753
$364$	8.52997e10	0.254678
$365$	−4.63848e11	−1.36791
$366$	1.31969e12	3.84421
$367$	1.71557e11	0.493640	0.246820	−	0.969061i	$-0.420614\pi$
$367$	1.71557e11	0.493640	0.246820	+	0.969061i	$0.420614\pi$
$368$	−1.23398e12	−3.50745
$369$	−1.14398e12	−3.21217
$370$	8.57261e11	2.37796
$371$	1.84388e11	0.505301
$372$	−2.43353e12	−6.58860
$373$	−1.33693e11	−0.357617	−0.178809	−	0.983884i	$-0.557224\pi$
$373$	−1.33693e11	−0.357617	−0.178809	+	0.983884i	$0.557224\pi$
$374$	−5.80827e10	−0.153506
$375$	−9.81861e11	−2.56395
$376$	−6.23572e11	−1.60895
$377$	−1.08659e10	−0.0277031
$378$	7.22258e11	1.81961
$379$	6.89315e11	1.71610	0.858048	−	0.513570i	$-0.171677\pi$
$379$	6.89315e11	1.71610	0.858048	+	0.513570i	$0.171677\pi$
$380$	−2.32988e12	−5.73202
$381$	3.47417e11	0.844673
$382$	1.37636e10	0.0330709
$383$	2.18117e11	0.517959	0.258979	−	0.965883i	$-0.416614\pi$
$383$	2.18117e11	0.517959	0.258979	+	0.965883i	$0.416614\pi$
$384$	−9.03448e10	−0.212038
$385$	6.94248e10	0.161043
$386$	2.05683e10	0.0471580
$387$	−5.07588e11	−1.15030
$388$	−1.93334e12	−4.33078
$389$	1.39717e11	0.309368	0.154684	−	0.987964i	$-0.450564\pi$
$389$	1.39717e11	0.309368	0.154684	+	0.987964i	$0.450564\pi$
$390$	−7.28265e11	−1.59404
$391$	−2.14390e11	−0.463884
$392$	−1.76798e11	−0.378173
$393$	−9.46261e11	−2.00099
$394$	−1.09644e12	−2.29219
$395$	1.46358e12	3.02502
$396$	7.25639e11	1.48283
$397$	7.10484e11	1.43548	0.717740	−	0.696312i	$-0.245177\pi$
$397$	7.10484e11	1.43548	0.717740	+	0.696312i	$0.245177\pi$
$398$	6.71545e11	1.34153
$399$	−4.95780e11	−0.979289
$400$	2.31208e12	4.51578
$401$	1.55457e11	0.300235	0.150117	−	0.988668i	$-0.452035\pi$
$401$	1.55457e11	0.300235	0.150117	+	0.988668i	$0.452035\pi$
$402$	−2.30980e12	−4.41121
$403$	2.15736e11	0.407427
$404$	−7.87546e11	−1.47082
$405$	−2.17642e12	−4.01971
$406$	3.82764e10	0.0699140
$407$	1.07168e11	0.193593
$408$	−8.94618e11	−1.59833
$409$	−1.06029e12	−1.87356	−0.936782	−	0.349913i	$-0.886211\pi$
$409$	−1.06029e12	−1.87356	−0.936782	+	0.349913i	$0.886211\pi$
$410$	−2.37602e12	−4.15262
$411$	−1.11206e12	−1.92238
$412$	2.38028e12	4.06997
$413$	−7.23325e10	−0.122337
$414$	3.78089e12	6.32546
$415$	6.36105e11	1.05272
$416$	3.27346e11	0.535905
$417$	−7.75707e11	−1.25628
$418$	−4.11150e11	−0.658729
$419$	8.49092e9	0.0134583	0.00672917	−	0.999977i	$-0.497858\pi$
$419$	8.49092e9	0.0134583	0.00672917	+	0.999977i	$0.497858\pi$
$420$	1.81736e12	2.84984
$421$	−4.54165e11	−0.704603	−0.352301	−	0.935887i	$-0.614601\pi$
$421$	−4.54165e11	−0.704603	−0.352301	+	0.935887i	$0.614601\pi$
$422$	3.80137e11	0.583490
$423$	9.63764e11	1.46366
$424$	2.35524e12	3.53906
$425$	4.01699e11	0.597243
$426$	1.55970e12	2.29455
$427$	2.91950e11	0.424995
$428$	−6.02480e11	−0.867852
$429$	−9.10417e10	−0.129772
$430$	−1.05425e12	−1.48708
$431$	−8.40545e11	−1.17331	−0.586656	−	0.809837i	$-0.699556\pi$
$431$	−8.40545e11	−1.17331	−0.586656	+	0.809837i	$0.699556\pi$
$432$	4.65362e12	6.42856
$433$	−7.89202e11	−1.07893	−0.539464	−	0.842008i	$-0.681373\pi$
$433$	−7.89202e11	−1.07893	−0.539464	+	0.842008i	$0.681373\pi$
$434$	−7.59958e11	−1.02822
$435$	−2.31504e11	−0.309996
$436$	−8.83074e10	−0.117033
$437$	−1.51760e12	−1.99063
$438$	−2.14274e12	−2.78186
$439$	−2.69062e11	−0.345749	−0.172875	−	0.984944i	$-0.555306\pi$
$439$	−2.69062e11	−0.345749	−0.172875	+	0.984944i	$0.555306\pi$
$440$	8.86781e11	1.12792
$441$	2.73251e11	0.344024
$442$	1.34791e11	0.167981
$443$	−2.02148e10	−0.0249374	−0.0124687	−	0.999922i	$-0.503969\pi$
$443$	−2.02148e10	−0.0249374	−0.0124687	+	0.999922i	$0.503969\pi$
$444$	2.80537e12	3.42584
$445$	1.93065e12	2.33391
$446$	2.25836e12	2.70263
$447$	2.65921e11	0.315042
$448$	−3.56225e11	−0.417805
$449$	5.37841e11	0.624519	0.312259	−	0.949997i	$-0.398914\pi$
$449$	5.37841e11	0.624519	0.312259	+	0.949997i	$0.398914\pi$
$450$	−7.08419e12	−8.14392
$451$	−2.97030e11	−0.338069
$452$	−8.48149e11	−0.955760
$453$	−2.33485e12	−2.60505
$454$	6.32220e11	0.698420
$455$	−1.61112e11	−0.176228
$456$	−6.33272e12	−6.85881
$457$	−1.66356e11	−0.178408	−0.0892041	−	0.996013i	$-0.528432\pi$
$457$	−1.66356e11	−0.178408	−0.0892041	+	0.996013i	$0.528432\pi$
$458$	−1.67695e12	−1.78084
$459$	8.08517e11	0.850222
$460$	5.56302e12	5.79296
$461$	−2.03732e11	−0.210090	−0.105045	−	0.994467i	$-0.533499\pi$
$461$	−2.03732e11	−0.210090	−0.105045	+	0.994467i	$0.533499\pi$
$462$	3.20706e11	0.327506
$463$	1.13048e12	1.14327	0.571633	−	0.820510i	$-0.306310\pi$
$463$	1.13048e12	1.14327	0.571633	+	0.820510i	$0.306310\pi$
$464$	2.46621e11	0.247001
$465$	4.59639e12	4.55909
$466$	1.53405e12	1.50696
$467$	−3.99938e11	−0.389105	−0.194553	−	0.980892i	$-0.562325\pi$
$467$	−3.99938e11	−0.389105	−0.194553	+	0.980892i	$0.562325\pi$
$468$	−1.68396e12	−1.62266
$469$	−5.10990e11	−0.487680
$470$	2.00172e12	1.89218
$471$	1.81994e12	1.70397
$472$	−9.23921e11	−0.856833
$473$	−1.31793e11	−0.121065
$474$	6.76096e12	6.15186
$475$	2.84351e12	2.56291
$476$	−3.36366e11	−0.300317
$477$	−3.64015e12	−3.21948
$478$	6.52409e11	0.571603
$479$	−1.89301e12	−1.64302	−0.821510	−	0.570193i	$-0.806868\pi$
$479$	−1.89301e12	−1.64302	−0.821510	+	0.570193i	$0.806868\pi$
$480$	6.97432e12	5.99675
$481$	−2.48700e11	−0.211847
$482$	4.32715e11	0.365166
$483$	1.18377e12	0.989700
$484$	−2.74462e12	−2.27341
$485$	3.65165e12	2.99676
$486$	−4.13297e12	−3.36046
$487$	7.11530e11	0.573209	0.286605	−	0.958049i	$-0.407473\pi$
$487$	7.11530e11	0.573209	0.286605	+	0.958049i	$0.407473\pi$
$488$	3.72916e12	2.97661
$489$	−3.74184e11	−0.295934
$490$	5.67537e11	0.444746
$491$	−8.59143e11	−0.667112	−0.333556	−	0.942730i	$-0.608249\pi$
$491$	−8.59143e11	−0.667112	−0.333556	+	0.942730i	$0.608249\pi$
$492$	−7.77548e12	−5.98252
$493$	4.28478e10	0.0326676
$494$	9.54141e11	0.720844
$495$	−1.37057e12	−1.02607
$496$	−4.89653e12	−3.63262
$497$	3.45048e11	0.253674
$498$	2.93847e12	2.14087
$499$	−2.18426e12	−1.57708	−0.788538	−	0.614986i	$-0.789162\pi$
$499$	−2.18426e12	−1.57708	−0.788538	+	0.614986i	$0.789162\pi$
$500$	−4.71548e12	−3.37412
$501$	3.10121e11	0.219918
$502$	−1.97956e12	−1.39124
$503$	−3.06321e11	−0.213364	−0.106682	−	0.994293i	$-0.534023\pi$
$503$	−3.06321e11	−0.213364	−0.106682	+	0.994293i	$0.534023\pi$
$504$	3.49031e12	2.40950
$505$	1.48750e12	1.01776
$506$	9.81696e11	0.665732
$507$	2.11277e11	0.142009
$508$	1.66850e12	1.11158
$509$	2.40717e12	1.58956	0.794780	−	0.606897i	$-0.207586\pi$
$509$	2.40717e12	1.58956	0.794780	+	0.606897i	$0.207586\pi$
$510$	2.87180e12	1.87970
$511$	−4.74030e11	−0.307547
$512$	2.74922e12	1.76805
$513$	5.72324e12	3.64850
$514$	−3.08595e12	−1.95009
$515$	−4.49582e12	−2.81628
$516$	−3.45001e12	−2.14238
$517$	2.50238e11	0.154044
$518$	8.76079e11	0.534638
$519$	−2.15876e12	−1.30603
$520$	−2.05792e12	−1.23428
$521$	−2.24797e11	−0.133666	−0.0668329	−	0.997764i	$-0.521289\pi$
$521$	−2.24797e11	−0.133666	−0.0668329	+	0.997764i	$0.521289\pi$
$522$	−7.55643e11	−0.445451
$523$	7.89841e11	0.461617	0.230809	−	0.972999i	$-0.425863\pi$
$523$	7.89841e11	0.461617	0.230809	+	0.972999i	$0.425863\pi$
$524$	−4.54451e12	−2.63327
$525$	−2.21800e12	−1.27422
$526$	2.40212e12	1.36823
$527$	−8.50720e11	−0.480440
$528$	2.06636e12	1.15705
$529$	1.82240e12	1.01180
$530$	−7.56051e12	−4.16207
$531$	1.42797e12	0.779460
$532$	−2.38103e12	−1.28873
$533$	6.89307e11	0.369948
$534$	8.91860e12	4.74636
$535$	1.13795e12	0.600524
$536$	−6.52701e12	−3.41564
$537$	3.50191e12	1.81728
$538$	−5.66199e12	−2.91373
$539$	7.09488e10	0.0362073
$540$	−2.09795e13	−10.6175
$541$	7.61057e11	0.381970	0.190985	−	0.981593i	$-0.438832\pi$
$541$	7.61057e11	0.381970	0.190985	+	0.981593i	$0.438832\pi$
$542$	−1.62166e11	−0.0807168
$543$	−1.34412e11	−0.0663495
$544$	−1.29084e12	−0.631941
$545$	1.66793e11	0.0809828
$546$	−7.44252e11	−0.358388
$547$	−5.65093e11	−0.269884	−0.134942	−	0.990854i	$-0.543085\pi$
$547$	−5.65093e11	−0.269884	−0.134942	+	0.990854i	$0.543085\pi$
$548$	−5.34075e12	−2.52982
$549$	−5.76361e12	−2.70782
$550$	−1.83939e12	−0.857118
$551$	3.03306e11	0.140184
$552$	1.51205e13	6.93173
$553$	1.49571e12	0.680116
$554$	9.19981e11	0.414940
$555$	−5.29871e12	−2.37057
$556$	−3.72541e12	−1.65324
$557$	−2.55584e12	−1.12508	−0.562542	−	0.826769i	$-0.690176\pi$
$557$	−2.55584e12	−1.12508	−0.562542	+	0.826769i	$0.690176\pi$
$558$	1.50029e13	6.55121
$559$	3.05849e11	0.132481
$560$	3.65673e12	1.57126
$561$	3.59008e11	0.153028
$562$	4.17724e12	1.76635
$563$	−1.61893e12	−0.679111	−0.339556	−	0.940586i	$-0.610277\pi$
$563$	−1.61893e12	−0.679111	−0.339556	+	0.940586i	$0.610277\pi$
$564$	6.55059e12	2.72599
$565$	1.60196e12	0.661354
$566$	4.62369e11	0.189372
$567$	−2.22420e12	−0.903752
$568$	4.40738e12	1.77670
$569$	3.43649e12	1.37439	0.687195	−	0.726473i	$-0.258842\pi$
$569$	3.43649e12	1.37439	0.687195	+	0.726473i	$0.258842\pi$
$570$	2.03286e13	8.06622
$571$	8.12728e11	0.319950	0.159975	−	0.987121i	$-0.448859\pi$
$571$	8.12728e11	0.319950	0.159975	+	0.987121i	$0.448859\pi$
$572$	−4.37236e11	−0.170779
$573$	−8.50724e10	−0.0329680
$574$	−2.42818e12	−0.933634
$575$	−6.78939e12	−2.59015
$576$	7.03251e12	2.66201
$577$	−1.43153e12	−0.537661	−0.268830	−	0.963188i	$-0.586637\pi$
$577$	−1.43153e12	−0.537661	−0.268830	+	0.963188i	$0.586637\pi$
$578$	4.43770e12	1.65380
$579$	−1.27132e11	−0.0470113
$580$	−1.11182e12	−0.407951
$581$	6.50069e11	0.236683
$582$	1.68687e13	6.09437
$583$	−9.45152e11	−0.338839
$584$	−6.05491e12	−2.15402
$585$	3.18063e12	1.12282
$586$	−9.44510e12	−3.30877
$587$	2.63412e12	0.915724	0.457862	−	0.889023i	$-0.348615\pi$
$587$	2.63412e12	0.915724	0.457862	+	0.889023i	$0.348615\pi$
$588$	1.85726e12	0.640729
$589$	−6.02198e12	−2.06168
$590$	2.96587e12	1.00767
$591$	6.77706e12	2.28506
$592$	5.64471e12	1.88884
$593$	−1.61955e12	−0.537833	−0.268916	−	0.963164i	$-0.586666\pi$
$593$	−1.61955e12	−0.537833	−0.268916	+	0.963164i	$0.586666\pi$
$594$	−3.70221e12	−1.22017
$595$	6.35318e11	0.207809
$596$	1.27711e12	0.414590
$597$	−4.15081e12	−1.33736
$598$	−2.27819e12	−0.728508
$599$	1.21019e12	0.384090	0.192045	−	0.981386i	$-0.438488\pi$
$599$	1.21019e12	0.384090	0.192045	+	0.981386i	$0.438488\pi$
$600$	−2.83311e13	−8.92448
$601$	−1.16942e12	−0.365626	−0.182813	−	0.983148i	$-0.558520\pi$
$601$	−1.16942e12	−0.365626	−0.182813	+	0.983148i	$0.558520\pi$
$602$	−1.07739e12	−0.334341
$603$	1.00878e13	3.10721
$604$	−1.12133e13	−3.42821
$605$	5.18396e12	1.57312
$606$	6.87146e12	2.06977
$607$	3.25270e12	0.972512	0.486256	−	0.873816i	$-0.338362\pi$
$607$	3.25270e12	0.972512	0.486256	+	0.873816i	$0.338362\pi$
$608$	−9.13744e12	−2.71181
$609$	−2.36586e11	−0.0696965
$610$	−1.19709e13	−3.50060
$611$	−5.80719e11	−0.168570
$612$	6.64045e12	1.91344
$613$	4.68116e12	1.33900	0.669502	−	0.742811i	$-0.266508\pi$
$613$	4.68116e12	1.33900	0.669502	+	0.742811i	$0.266508\pi$
$614$	5.13172e12	1.45715
$615$	1.46861e13	4.13970
$616$	9.06248e11	0.253591
$617$	−2.51723e12	−0.699261	−0.349630	−	0.936888i	$-0.613693\pi$
$617$	−2.51723e12	−0.699261	−0.349630	+	0.936888i	$0.613693\pi$
$618$	−2.07683e13	−5.72735
$619$	−4.58262e12	−1.25460	−0.627301	−	0.778777i	$-0.715841\pi$
$619$	−4.58262e12	−1.25460	−0.627301	+	0.778777i	$0.715841\pi$
$620$	2.20746e13	5.99970
$621$	−1.36653e13	−3.68729
$622$	−8.42411e12	−2.25667
$623$	1.97303e12	0.524733
$624$	−4.79533e12	−1.26616
$625$	1.94031e12	0.508640
$626$	−9.32392e12	−2.42669
$627$	2.54131e12	0.656680
$628$	8.74043e12	2.24241
$629$	9.80709e11	0.249812
$630$	−1.12042e13	−2.83366
$631$	4.48445e11	0.112610	0.0563050	−	0.998414i	$-0.482068\pi$
$631$	4.48445e11	0.112610	0.0563050	+	0.998414i	$0.482068\pi$
$632$	1.91050e13	4.76344
$633$	−2.34962e12	−0.581675
$634$	−3.03902e12	−0.747020
$635$	−3.15142e12	−0.769174
$636$	−2.47416e13	−5.99614
$637$	−1.64648e11	−0.0396214
$638$	−1.96200e11	−0.0468821
$639$	−6.81184e12	−1.61626
$640$	8.19519e11	0.193085
$641$	3.27712e12	0.766709	0.383355	−	0.923601i	$-0.374769\pi$
$641$	3.27712e12	0.766709	0.383355	+	0.923601i	$0.374769\pi$
$642$	5.25673e12	1.22126
$643$	−3.05276e12	−0.704277	−0.352139	−	0.935948i	$-0.614545\pi$
$643$	−3.05276e12	−0.704277	−0.352139	+	0.935948i	$0.614545\pi$
$644$	5.68514e12	1.30243
$645$	6.51630e12	1.48246
$646$	−3.76250e12	−0.850023
$647$	8.65230e12	1.94116	0.970582	−	0.240770i	$-0.0774001\pi$
$647$	8.65230e12	1.94116	0.970582	+	0.240770i	$0.0774001\pi$
$648$	−2.84102e13	−6.32976
$649$	3.70768e11	0.0820353
$650$	4.26860e12	0.937941
$651$	4.69729e12	1.02502
$652$	−1.79705e12	−0.389445
$653$	−8.47359e12	−1.82372	−0.911860	−	0.410500i	$-0.865354\pi$
$653$	−8.47359e12	−1.82372	−0.911860	+	0.410500i	$0.865354\pi$
$654$	7.70495e11	0.164691
$655$	8.58354e12	1.82214
$656$	−1.56451e13	−3.29846
$657$	9.35819e12	1.95951
$658$	2.04566e12	0.425419
$659$	4.90167e12	1.01242	0.506209	−	0.862411i	$-0.331047\pi$
$659$	4.90167e12	1.01242	0.506209	+	0.862411i	$0.331047\pi$
$660$	−9.31559e12	−1.91101
$661$	1.59013e12	0.323986	0.161993	−	0.986792i	$-0.448208\pi$
$661$	1.59013e12	0.323986	0.161993	+	0.986792i	$0.448208\pi$
$662$	4.26261e11	0.0862611
$663$	−8.33138e11	−0.167458
$664$	8.30350e12	1.65770
$665$	4.49722e12	0.891758
$666$	−1.72953e13	−3.40640
$667$	−7.24199e11	−0.141674
$668$	1.48938e12	0.289409
$669$	−1.39589e13	−2.69422
$670$	2.09522e13	4.01693
$671$	−1.49650e12	−0.284988
$672$	7.12742e12	1.34825
$673$	−8.56787e12	−1.60992	−0.804962	−	0.593326i	$-0.797814\pi$
$673$	−8.56787e12	−1.60992	−0.804962	+	0.593326i	$0.797814\pi$
$674$	−1.51543e13	−2.82856
$675$	2.56044e13	4.74732
$676$	1.01468e12	0.186882
$677$	8.70357e12	1.59239	0.796193	−	0.605042i	$-0.206844\pi$
$677$	8.70357e12	1.59239	0.796193	+	0.605042i	$0.206844\pi$
$678$	7.40022e12	1.34497
$679$	3.73181e12	0.673761
$680$	8.11509e12	1.45547
$681$	−3.90774e12	−0.696248
$682$	3.89546e12	0.689491
$683$	−2.82448e12	−0.496645	−0.248322	−	0.968677i	$-0.579879\pi$
$683$	−2.82448e12	−0.496645	−0.248322	+	0.968677i	$0.579879\pi$
$684$	4.70057e13	8.21103
$685$	1.00875e13	1.75055
$686$	5.79996e11	0.0999923
$687$	1.03652e13	1.77530
$688$	−6.94180e12	−1.18120
$689$	2.19338e12	0.370790
$690$	−4.85382e13	−8.15198
$691$	−1.08958e13	−1.81806	−0.909029	−	0.416732i	$-0.863175\pi$
$691$	−1.08958e13	−1.81806	−0.909029	+	0.416732i	$0.863175\pi$
$692$	−1.03677e13	−1.71871
$693$	−1.40065e12	−0.230691
$694$	7.87808e12	1.28915
$695$	7.03645e12	1.14399
$696$	−3.02197e12	−0.488145
$697$	−2.71817e12	−0.436244
$698$	−3.74899e12	−0.597813
$699$	−9.48193e12	−1.50228
$700$	−1.06522e13	−1.67686
$701$	−3.24305e12	−0.507250	−0.253625	−	0.967303i	$-0.581623\pi$
$701$	−3.24305e12	−0.507250	−0.253625	+	0.967303i	$0.581623\pi$
$702$	8.59159e12	1.33523
$703$	6.94214e12	1.07200
$704$	1.82597e12	0.280167
$705$	−1.23726e13	−1.88629
$706$	1.04244e13	1.57918
$707$	1.52015e12	0.228823
$708$	9.70575e12	1.45171
$709$	5.03607e12	0.748486	0.374243	−	0.927331i	$-0.377903\pi$
$709$	5.03607e12	0.748486	0.374243	+	0.927331i	$0.377903\pi$
$710$	−1.41481e13	−2.08946
$711$	−2.95279e13	−4.33330
$712$	2.52021e13	3.67516
$713$	1.43786e13	2.08360
$714$	2.93484e12	0.422613
$715$	8.25840e11	0.118173
$716$	1.68183e13	2.39151
$717$	−4.03253e12	−0.569825
$718$	−2.37355e13	−3.33302
$719$	3.77528e12	0.526828	0.263414	−	0.964683i	$-0.415151\pi$
$719$	3.77528e12	0.526828	0.263414	+	0.964683i	$0.415151\pi$
$720$	−7.21903e13	−10.0111
$721$	−4.59451e12	−0.633185
$722$	−1.31119e13	−1.79576
$723$	−2.67460e12	−0.364030
$724$	−6.45524e11	−0.0873150
$725$	1.35692e12	0.182403
$726$	2.39472e13	3.19919
$727$	−2.44283e12	−0.324331	−0.162166	−	0.986764i	$-0.551848\pi$
$727$	−2.44283e12	−0.324331	−0.162166	+	0.986764i	$0.551848\pi$
$728$	−2.10310e12	−0.277503
$729$	7.31222e12	0.958905
$730$	1.94368e13	2.53321
$731$	−1.20607e12	−0.156222
$732$	−3.91746e13	−5.04318
$733$	−9.58679e12	−1.22661	−0.613303	−	0.789847i	$-0.710160\pi$
$733$	−9.58679e12	−1.22661	−0.613303	+	0.789847i	$0.710160\pi$
$734$	−7.18880e12	−0.914164
$735$	−3.50794e12	−0.443363
$736$	2.18173e13	2.74064
$737$	2.61928e12	0.327022
$738$	4.79364e13	5.94856
$739$	−2.00677e12	−0.247512	−0.123756	−	0.992313i	$-0.539494\pi$
$739$	−2.00677e12	−0.247512	−0.123756	+	0.992313i	$0.539494\pi$
$740$	−2.54476e13	−3.11963
$741$	−5.89753e12	−0.718601
$742$	−7.72648e12	−0.935759
$743$	1.08845e12	0.131027	0.0655134	−	0.997852i	$-0.479131\pi$
$743$	1.08845e12	0.131027	0.0655134	+	0.997852i	$0.479131\pi$
$744$	5.99997e13	7.17911
$745$	−2.41217e12	−0.286883
$746$	5.60218e12	0.662266
$747$	−1.28335e13	−1.50800
$748$	1.72417e12	0.201383
$749$	1.16293e12	0.135016
$750$	4.11432e13	4.74813
$751$	−4.54919e12	−0.521861	−0.260930	−	0.965358i	$-0.584029\pi$
$751$	−4.54919e12	−0.521861	−0.260930	+	0.965358i	$0.584029\pi$
$752$	1.31805e13	1.50297
$753$	1.22356e13	1.38691
$754$	4.55315e11	0.0513028
$755$	2.11794e13	2.37221
$756$	−2.14400e13	−2.38714
$757$	4.16269e12	0.460726	0.230363	−	0.973105i	$-0.426009\pi$
$757$	4.16269e12	0.460726	0.230363	+	0.973105i	$0.426009\pi$
$758$	−2.88846e13	−3.17801
$759$	−6.06784e12	−0.663661
$760$	5.74442e13	6.24575
$761$	−8.79234e12	−0.950328	−0.475164	−	0.879897i	$-0.657611\pi$
$761$	−8.79234e12	−0.950328	−0.475164	+	0.879897i	$0.657611\pi$
$762$	−1.45579e13	−1.56424
$763$	1.70454e11	0.0182074
$764$	−4.08568e11	−0.0433855
$765$	−1.25423e13	−1.32404
$766$	−9.13984e12	−0.959199
$767$	−8.60428e11	−0.0897709
$768$	−1.58890e13	−1.64805
$769$	3.95119e12	0.407436	0.203718	−	0.979030i	$-0.434697\pi$
$769$	3.95119e12	0.407436	0.203718	+	0.979030i	$0.434697\pi$
$770$	−2.90913e12	−0.298232
$771$	1.90742e13	1.94402
$772$	−6.10565e11	−0.0618662
$773$	6.04750e12	0.609212	0.304606	−	0.952478i	$-0.401475\pi$
$773$	6.04750e12	0.609212	0.304606	+	0.952478i	$0.401475\pi$
$774$	2.12696e13	2.13022
$775$	−2.69409e13	−2.68259
$776$	4.76674e13	4.71893
$777$	−5.41503e12	−0.532974
$778$	−5.85460e12	−0.572913
$779$	−1.92411e13	−1.87202
$780$	2.16184e13	2.09121
$781$	−1.76867e12	−0.170105
$782$	8.98367e12	0.859060
$783$	2.73113e12	0.259665
$784$	3.73700e12	0.353265
$785$	−1.65087e13	−1.55167
$786$	3.96515e13	3.70560
$787$	−5.87922e12	−0.546302	−0.273151	−	0.961971i	$-0.588066\pi$
$787$	−5.87922e12	−0.546302	−0.273151	+	0.961971i	$0.588066\pi$
$788$	3.25475e13	3.00711
$789$	−1.48475e13	−1.36397
$790$	−6.13288e13	−5.60199
$791$	1.63713e12	0.148692
$792$	−1.78909e13	−1.61573
$793$	3.47288e12	0.311861
$794$	−2.97716e13	−2.65834
$795$	4.67314e13	4.14912
$796$	−1.99346e13	−1.75995
$797$	−7.81011e12	−0.685637	−0.342819	−	0.939402i	$-0.611382\pi$
$797$	−7.81011e12	−0.685637	−0.342819	+	0.939402i	$0.611382\pi$
$798$	2.07748e13	1.81353
$799$	2.28997e12	0.198779
$800$	−4.08787e13	−3.52852
$801$	−3.89511e13	−3.34329
$802$	−6.51417e12	−0.555999
$803$	2.42982e12	0.206231
$804$	6.85659e13	5.78703
$805$	−1.07379e13	−0.901239
$806$	−9.04005e12	−0.754507
$807$	3.49967e13	2.90466
$808$	1.94173e13	1.60264
$809$	2.57998e12	0.211762	0.105881	−	0.994379i	$-0.466234\pi$
$809$	2.57998e12	0.211762	0.105881	+	0.994379i	$0.466234\pi$
$810$	9.11992e13	7.44403
$811$	5.96757e12	0.484400	0.242200	−	0.970226i	$-0.422131\pi$
$811$	5.96757e12	0.484400	0.242200	+	0.970226i	$0.422131\pi$
$812$	−1.13622e12	−0.0917196
$813$	1.00235e12	0.0804657
$814$	−4.49068e12	−0.358511
$815$	3.39422e12	0.269483
$816$	1.89096e13	1.49306
$817$	−8.53736e12	−0.670385
$818$	4.44296e13	3.46962
$819$	3.25045e12	0.252445
$820$	7.05314e13	5.44779
$821$	−4.32633e11	−0.0332335	−0.0166167	−	0.999862i	$-0.505290\pi$
$821$	−4.32633e11	−0.0332335	−0.0166167	+	0.999862i	$0.505290\pi$
$822$	4.65989e13	3.56002
$823$	−5.47374e12	−0.415896	−0.207948	−	0.978140i	$-0.566678\pi$
$823$	−5.47374e12	−0.415896	−0.207948	+	0.978140i	$0.566678\pi$
$824$	−5.86868e13	−4.43474
$825$	1.13692e13	0.854452
$826$	3.03097e12	0.226554
$827$	1.29308e13	0.961283	0.480642	−	0.876917i	$-0.340404\pi$
$827$	1.29308e13	0.961283	0.480642	+	0.876917i	$0.340404\pi$
$828$	−1.12235e14	−8.29833
$829$	−8.22906e12	−0.605139	−0.302569	−	0.953127i	$-0.597844\pi$
$829$	−8.22906e12	−0.605139	−0.302569	+	0.953127i	$0.597844\pi$
$830$	−2.66549e13	−1.94951
$831$	−5.68639e12	−0.413649
$832$	−4.23746e12	−0.306585
$833$	6.49265e11	0.0467218
$834$	3.25047e13	2.32648
$835$	−2.81311e12	−0.200261
$836$	1.22049e13	0.864181
$837$	−5.42251e13	−3.81888
$838$	−3.55798e11	−0.0249233
$839$	−1.46544e13	−1.02103	−0.510517	−	0.859867i	$-0.670546\pi$
$839$	−1.46544e13	−1.02103	−0.510517	+	0.859867i	$0.670546\pi$
$840$	−4.48078e13	−3.10525
$841$	−1.43624e13	−0.990023
$842$	1.90310e13	1.30484
$843$	−2.58195e13	−1.76085
$844$	−1.12843e13	−0.765476
$845$	−1.91650e12	−0.129316
$846$	−4.03849e13	−2.71052
$847$	5.29776e12	0.353685
$848$	−4.97829e13	−3.30597
$849$	−2.85789e12	−0.188782
$850$	−1.68325e13	−1.10602
$851$	−1.65756e13	−1.08340
$852$	−4.62993e13	−3.01021
$853$	−1.67124e13	−1.08086	−0.540430	−	0.841389i	$-0.681738\pi$
$853$	−1.67124e13	−1.08086	−0.540430	+	0.841389i	$0.681738\pi$
$854$	−1.22337e13	−0.787041
$855$	−8.87831e13	−5.68176
$856$	1.48544e13	0.945634
$857$	2.52492e13	1.59895	0.799473	−	0.600702i	$-0.205112\pi$
$857$	2.52492e13	1.59895	0.799473	+	0.600702i	$0.205112\pi$
$858$	3.81495e12	0.240323
$859$	5.44673e12	0.341324	0.170662	−	0.985330i	$-0.445409\pi$
$859$	5.44673e12	0.341324	0.170662	+	0.985330i	$0.445409\pi$
$860$	3.12951e13	1.95089
$861$	1.50085e13	0.930729
$862$	3.52216e13	2.17284
$863$	5.68330e12	0.348781	0.174390	−	0.984677i	$-0.444205\pi$
$863$	5.68330e12	0.348781	0.174390	+	0.984677i	$0.444205\pi$
$864$	−8.22784e13	−5.02312
$865$	1.95822e13	1.18929
$866$	3.30702e13	1.99805
$867$	−2.74294e13	−1.64865
$868$	2.25591e13	1.34891
$869$	−7.66681e12	−0.456064
$870$	9.70078e12	0.574077
$871$	−6.07846e12	−0.357859
$872$	2.17726e12	0.127522
$873$	−7.36725e13	−4.29281
$874$	6.35926e13	3.68642
$875$	9.10198e12	0.524928
$876$	6.36066e13	3.64950
$877$	9.29256e12	0.530441	0.265221	−	0.964188i	$-0.414555\pi$
$877$	9.29256e12	0.530441	0.265221	+	0.964188i	$0.414555\pi$
$878$	1.12746e13	0.640287
$879$	5.83800e13	3.29848
$880$	−1.87440e13	−1.05363
$881$	−9.31941e11	−0.0521191	−0.0260596	−	0.999660i	$-0.508296\pi$
$881$	−9.31941e11	−0.0521191	−0.0260596	+	0.999660i	$0.508296\pi$
$882$	−1.14501e13	−0.637092
$883$	9.39742e10	0.00520218	0.00260109	−	0.999997i	$-0.499172\pi$
$883$	9.39742e10	0.00520218	0.00260109	+	0.999997i	$0.499172\pi$
$884$	−4.00122e12	−0.220373
$885$	−1.83320e13	−1.00453
$886$	8.47066e11	0.0461812
$887$	−3.18276e13	−1.72643	−0.863213	−	0.504840i	$-0.831552\pi$
$887$	−3.18276e13	−1.72643	−0.863213	+	0.504840i	$0.831552\pi$
$888$	−6.91676e13	−3.73288
$889$	−3.22060e12	−0.172933
$890$	−8.09007e13	−4.32212
$891$	1.14010e13	0.606027
$892$	−6.70388e13	−3.54555
$893$	1.62100e13	0.853005
$894$	−1.11430e13	−0.583420
$895$	−3.17659e13	−1.65484
$896$	8.37509e11	0.0434114
$897$	1.40814e13	0.726241
$898$	−2.25373e13	−1.15654
$899$	−2.87369e12	−0.146731
$900$	2.10292e14	10.6839
$901$	−8.64925e12	−0.437237
$902$	1.24465e13	0.626065
$903$	6.65934e12	0.333301
$904$	2.09114e13	1.04142
$905$	1.21925e12	0.0604191
$906$	9.78378e13	4.82425
$907$	−1.44676e12	−0.0709845	−0.0354923	−	0.999370i	$-0.511300\pi$
$907$	−1.44676e12	−0.0709845	−0.0354923	+	0.999370i	$0.511300\pi$
$908$	−1.87673e13	−0.916252
$909$	−3.00104e13	−1.45792
$910$	6.75112e12	0.326354
$911$	−1.77022e13	−0.851518	−0.425759	−	0.904837i	$-0.639993\pi$
$911$	−1.77022e13	−0.851518	−0.425759	+	0.904837i	$0.639993\pi$
$912$	1.33855e14	6.40706
$913$	−3.33218e12	−0.158712
$914$	6.97086e12	0.330391
$915$	7.39920e13	3.48971
$916$	4.97799e13	2.33628
$917$	8.77197e12	0.409671
$918$	−3.38796e13	−1.57451
$919$	−4.22444e13	−1.95366	−0.976831	−	0.214011i	$-0.931347\pi$
$919$	−4.22444e13	−1.95366	−0.976831	+	0.214011i	$0.931347\pi$
$920$	−1.37159e14	−6.31216
$921$	−3.17191e13	−1.45262
$922$	8.53706e12	0.389063
$923$	4.10450e12	0.186146
$924$	−9.52008e12	−0.429652
$925$	3.10575e13	1.39485
$926$	−4.73707e13	−2.11719
$927$	9.07037e13	4.03428
$928$	−4.36038e12	−0.193001
$929$	3.55847e13	1.56745	0.783723	−	0.621110i	$-0.213318\pi$
$929$	3.55847e13	1.56745	0.783723	+	0.621110i	$0.213318\pi$
$930$	−1.92604e14	−8.44290
$931$	4.59595e12	0.200494
$932$	−4.55378e13	−1.97697
$933$	5.20693e13	2.24965
$934$	1.67587e13	0.720577
$935$	−3.25657e12	−0.139350
$936$	4.15188e13	1.76809
$937$	2.21360e13	0.938148	0.469074	−	0.883159i	$-0.344588\pi$
$937$	2.21360e13	0.938148	0.469074	+	0.883159i	$0.344588\pi$
$938$	2.14122e13	0.903126
$939$	5.76310e13	2.41914
$940$	−5.94205e13	−2.48234
$941$	−3.32302e13	−1.38159	−0.690796	−	0.723050i	$-0.742740\pi$
$941$	−3.32302e13	−1.38159	−0.690796	+	0.723050i	$0.742740\pi$
$942$	−7.62616e13	−3.15556
$943$	4.59417e13	1.89193
$944$	1.95290e13	0.800399
$945$	4.04954e13	1.65182
$946$	5.52259e12	0.224198
$947$	1.60585e12	0.0648830	0.0324415	−	0.999474i	$-0.489672\pi$
$947$	1.60585e12	0.0648830	0.0324415	+	0.999474i	$0.489672\pi$
$948$	−2.00697e14	−8.07057
$949$	−5.63881e12	−0.225678
$950$	−1.19152e14	−4.74620
$951$	1.87841e13	0.744696
$952$	8.29323e12	0.327233
$953$	−5.45972e12	−0.214413	−0.107207	−	0.994237i	$-0.534191\pi$
$953$	−5.45972e12	−0.214413	−0.107207	+	0.994237i	$0.534191\pi$
$954$	1.52534e14	5.96210
$955$	7.71693e11	0.0300213
$956$	−1.93666e13	−0.749881
$957$	1.21271e12	0.0467362
$958$	7.93234e13	3.04268
$959$	1.03089e13	0.393577
$960$	−9.02818e13	−3.43068
$961$	3.06159e13	1.15796
$962$	1.04214e13	0.392317
$963$	−2.29583e13	−0.860242
$964$	−1.28450e13	−0.479058
$965$	1.15322e12	0.0428093
$966$	−4.96037e13	−1.83281
$967$	−1.45807e13	−0.536241	−0.268121	−	0.963385i	$-0.586403\pi$
$967$	−1.45807e13	−0.536241	−0.268121	+	0.963385i	$0.586403\pi$
$968$	6.76696e13	2.47716
$969$	2.32560e13	0.847378
$970$	−1.53016e14	−5.54964
$971$	5.21737e13	1.88350	0.941748	−	0.336319i	$-0.109182\pi$
$971$	5.21737e13	1.88350	0.941748	+	0.336319i	$0.109182\pi$
$972$	1.22686e14	4.40856
$973$	7.19091e12	0.257203
$974$	−2.98155e13	−1.06152
$975$	−2.63841e13	−0.935023
$976$	−7.88236e13	−2.78056
$977$	6.24034e12	0.219120	0.109560	−	0.993980i	$-0.465056\pi$
$977$	6.24034e12	0.219120	0.109560	+	0.993980i	$0.465056\pi$
$978$	1.56795e13	0.548035
$979$	−1.01135e13	−0.351869
$980$	−1.68472e13	−0.583459
$981$	−3.36506e12	−0.116007
$982$	3.60009e13	1.23541
$983$	4.07607e13	1.39236	0.696179	−	0.717869i	$-0.254882\pi$
$983$	4.07607e13	1.39236	0.696179	+	0.717869i	$0.254882\pi$
$984$	1.91708e14	6.51871
$985$	−6.14748e13	−2.08082
$986$	−1.79546e12	−0.0604965
$987$	−1.26442e13	−0.424096
$988$	−2.83234e13	−0.945670
$989$	2.03845e13	0.677512
$990$	5.74313e13	1.90016
$991$	2.74798e13	0.905070	0.452535	−	0.891747i	$-0.350520\pi$
$991$	2.74798e13	0.905070	0.452535	+	0.891747i	$0.350520\pi$
$992$	8.65731e13	2.83844
$993$	−2.63471e12	−0.0859927
$994$	−1.44586e13	−0.469774
$995$	3.76520e13	1.21782
$996$	−8.72278e13	−2.80859
$997$	4.13353e13	1.32493	0.662464	−	0.749093i	$-0.269511\pi$
$997$	4.13353e13	1.32493	0.662464	+	0.749093i	$0.269511\pi$
$998$	9.15279e13	2.92056
$999$	6.25107e13	1.98568

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-41.9033 q^{2} +259.004 q^{3} +1243.89 q^{4} -2349.43 q^{5} -10853.1 q^{6} -2401.00 q^{7} -30668.6 q^{8} +47400.0 q^{9} +O(q^{10})\)	\(q-41.9033 q^{2} +259.004 q^{3} +1243.89 q^{4} -2349.43 q^{5} -10853.1 q^{6} -2401.00 q^{7} -30668.6 q^{8} +47400.0 q^{9} +98448.7 q^{10} +12307.2 q^{11} +322172. q^{12} -28561.0 q^{13} +100610. q^{14} -608510. q^{15} +648245. q^{16} +112626. q^{17} -1.98622e6 q^{18} +797243. q^{19} -2.92242e6 q^{20} -621868. q^{21} -515715. q^{22} -1.90356e6 q^{23} -7.94328e6 q^{24} +3.56667e6 q^{25} +1.19680e6 q^{26} +7.17880e6 q^{27} -2.98658e6 q^{28} +380444. q^{29} +2.54986e7 q^{30} -7.55351e6 q^{31} -1.14613e7 q^{32} +3.18762e6 q^{33} -4.71939e6 q^{34} +5.64097e6 q^{35} +5.89603e7 q^{36} +8.70768e6 q^{37} -3.34071e7 q^{38} -7.39741e6 q^{39} +7.20536e7 q^{40} -2.41346e7 q^{41} +2.60583e7 q^{42} -1.07086e7 q^{43} +1.53088e7 q^{44} -1.11363e8 q^{45} +7.97657e7 q^{46} +2.03326e7 q^{47} +1.67898e8 q^{48} +5.76480e6 q^{49} -1.49456e8 q^{50} +2.91705e7 q^{51} -3.55267e7 q^{52} -7.67964e7 q^{53} -3.00815e8 q^{54} -2.89150e7 q^{55} +7.36353e7 q^{56} +2.06489e8 q^{57} -1.59419e7 q^{58} +3.01260e7 q^{59} -7.56919e8 q^{60} -1.21595e8 q^{61} +3.16517e8 q^{62} -1.13807e8 q^{63} +1.48365e8 q^{64} +6.71019e7 q^{65} -1.33572e8 q^{66} +2.12824e8 q^{67} +1.40094e8 q^{68} -4.93030e8 q^{69} -2.36375e8 q^{70} -1.43710e8 q^{71} -1.45369e9 q^{72} +1.97430e8 q^{73} -3.64881e8 q^{74} +9.23782e8 q^{75} +9.91682e8 q^{76} -2.95497e7 q^{77} +3.09976e8 q^{78} -6.22951e8 q^{79} -1.52300e9 q^{80} +9.26362e8 q^{81} +1.01132e9 q^{82} -2.70749e8 q^{83} -7.73535e8 q^{84} -2.64606e8 q^{85} +4.48726e8 q^{86} +9.85364e7 q^{87} -3.77446e8 q^{88} -8.21754e8 q^{89} +4.66647e9 q^{90} +6.85750e7 q^{91} -2.36782e9 q^{92} -1.95639e9 q^{93} -8.52003e8 q^{94} -1.87306e9 q^{95} -2.96852e9 q^{96} -1.55427e9 q^{97} -2.41564e8 q^{98} +5.83363e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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

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