LMFDB - Embedded newform 91.10.a.b.1.6

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			1.6
Root			$-5.16491$ 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)

$f(q)$	$=$	$q-7.16491 q^{2} -126.235 q^{3} -460.664 q^{4} +1492.86 q^{5} +904.459 q^{6} -2401.00 q^{7} +6969.05 q^{8} -3747.85 q^{9} +O(q^{10})$	\(q-7.16491 q^{2} -126.235 q^{3} -460.664 q^{4} +1492.86 q^{5} +904.459 q^{6} -2401.00 q^{7} +6969.05 q^{8} -3747.85 q^{9} -10696.2 q^{10} -38561.5 q^{11} +58151.7 q^{12} -28561.0 q^{13} +17203.0 q^{14} -188451. q^{15} +185927. q^{16} +236040. q^{17} +26853.0 q^{18} +909643. q^{19} -687708. q^{20} +303089. q^{21} +276290. q^{22} +1.95328e6 q^{23} -879735. q^{24} +275513. q^{25} +204637. q^{26} +2.95778e6 q^{27} +1.10605e6 q^{28} +2.90690e6 q^{29} +1.35023e6 q^{30} -5.77919e6 q^{31} -4.90031e6 q^{32} +4.86780e6 q^{33} -1.69120e6 q^{34} -3.58436e6 q^{35} +1.72650e6 q^{36} -4.43378e6 q^{37} -6.51751e6 q^{38} +3.60538e6 q^{39} +1.04038e7 q^{40} -3.24163e7 q^{41} -2.17161e6 q^{42} -3.92884e6 q^{43} +1.77639e7 q^{44} -5.59503e6 q^{45} -1.39951e7 q^{46} -5.10293e7 q^{47} -2.34704e7 q^{48} +5.76480e6 q^{49} -1.97403e6 q^{50} -2.97964e7 q^{51} +1.31570e7 q^{52} +5.66348e7 q^{53} -2.11922e7 q^{54} -5.75671e7 q^{55} -1.67327e7 q^{56} -1.14828e8 q^{57} -2.08277e7 q^{58} +1.45696e8 q^{59} +8.68125e7 q^{60} +1.60977e8 q^{61} +4.14074e7 q^{62} +8.99859e6 q^{63} -6.00845e7 q^{64} -4.26376e7 q^{65} -3.48773e7 q^{66} -2.60575e8 q^{67} -1.08735e8 q^{68} -2.46572e8 q^{69} +2.56816e7 q^{70} +1.00477e8 q^{71} -2.61190e7 q^{72} -4.23324e8 q^{73} +3.17676e7 q^{74} -3.47793e7 q^{75} -4.19040e8 q^{76} +9.25863e7 q^{77} -2.58323e7 q^{78} -2.23973e8 q^{79} +2.77564e8 q^{80} -2.99605e8 q^{81} +2.32260e8 q^{82} -1.93113e8 q^{83} -1.39622e8 q^{84} +3.52375e8 q^{85} +2.81498e7 q^{86} -3.66951e8 q^{87} -2.68737e8 q^{88} -6.08632e8 q^{89} +4.00879e7 q^{90} +6.85750e7 q^{91} -8.99808e8 q^{92} +7.29533e8 q^{93} +3.65620e8 q^{94} +1.35797e9 q^{95} +6.18588e8 q^{96} -6.40267e8 q^{97} -4.13043e7 q^{98} +1.44523e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.16491	−0.316647	−0.158324	−	0.987387i	$-0.550609\pi$
$2$	−7.16491	−0.316647	−0.158324	+	0.987387i	$0.550609\pi$
$3$	−126.235	−0.899772	−0.449886	−	0.893086i	$-0.648535\pi$
$3$	−126.235	−0.899772	−0.449886	+	0.893086i	$0.648535\pi$
$4$	−460.664	−0.899734
$5$	1492.86	1.06821	0.534103	−	0.845420i	$-0.320650\pi$
$5$	1492.86	1.06821	0.534103	+	0.845420i	$0.320650\pi$
$6$	904.459	0.284910
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	6969.05	0.601546
$9$	−3747.85	−0.190411
$10$	−10696.2	−0.338244
$11$	−38561.5	−0.794122	−0.397061	−	0.917792i	$-0.629970\pi$
$11$	−38561.5	−0.794122	−0.397061	+	0.917792i	$0.629970\pi$
$12$	58151.7	0.809556
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	17203.0	0.119681
$15$	−188451.	−0.961141
$16$	185927.	0.709257
$17$	236040.	0.685433	0.342717	−	0.939439i	$-0.388653\pi$
$17$	236040.	0.685433	0.342717	+	0.939439i	$0.388653\pi$
$18$	26853.0	0.0602930
$19$	909643.	1.60133	0.800663	−	0.599115i	$-0.204481\pi$
$19$	909643.	1.60133	0.800663	+	0.599115i	$0.204481\pi$
$20$	−687708.	−0.961101
$21$	303089.	0.340082
$22$	276290.	0.251457
$23$	1.95328e6	1.45543	0.727713	−	0.685882i	$-0.240583\pi$
$23$	1.95328e6	1.45543	0.727713	+	0.685882i	$0.240583\pi$
$24$	−879735.	−0.541254
$25$	275513.	0.141063
$26$	204637.	0.0878222
$27$	2.95778e6	1.07110
$28$	1.10605e6	0.340068
$29$	2.90690e6	0.763201	0.381601	−	0.924327i	$-0.375373\pi$
$29$	2.90690e6	0.763201	0.381601	+	0.924327i	$0.375373\pi$
$30$	1.35023e6	0.304343
$31$	−5.77919e6	−1.12393	−0.561965	−	0.827161i	$-0.689955\pi$
$31$	−5.77919e6	−1.12393	−0.561965	+	0.827161i	$0.689955\pi$
$32$	−4.90031e6	−0.826130
$33$	4.86780e6	0.714529
$34$	−1.69120e6	−0.217041
$35$	−3.58436e6	−0.403744
$36$	1.72650e6	0.171319
$37$	−4.43378e6	−0.388926	−0.194463	−	0.980910i	$-0.562296\pi$
$37$	−4.43378e6	−0.388926	−0.194463	+	0.980910i	$0.562296\pi$
$38$	−6.51751e6	−0.507055
$39$	3.60538e6	0.249552
$40$	1.04038e7	0.642575
$41$	−3.24163e7	−1.79158	−0.895789	−	0.444480i	$-0.853389\pi$
$41$	−3.24163e7	−1.79158	−0.895789	+	0.444480i	$0.853389\pi$
$42$	−2.17161e6	−0.107686
$43$	−3.92884e6	−0.175249	−0.0876247	−	0.996154i	$-0.527928\pi$
$43$	−3.92884e6	−0.175249	−0.0876247	+	0.996154i	$0.527928\pi$
$44$	1.77639e7	0.714499
$45$	−5.59503e6	−0.203398
$46$	−1.39951e7	−0.460857
$47$	−5.10293e7	−1.52538	−0.762692	−	0.646762i	$-0.776123\pi$
$47$	−5.10293e7	−1.52538	−0.762692	+	0.646762i	$0.776123\pi$
$48$	−2.34704e7	−0.638169
$49$	5.76480e6	0.142857
$50$	−1.97403e6	−0.0446672
$51$	−2.97964e7	−0.616734
$52$	1.31570e7	0.249541
$53$	5.66348e7	0.985921	0.492960	−	0.870052i	$-0.335915\pi$
$53$	5.66348e7	0.985921	0.492960	+	0.870052i	$0.335915\pi$
$54$	−2.11922e7	−0.339160
$55$	−5.75671e7	−0.848286
$56$	−1.67327e7	−0.227363
$57$	−1.14828e8	−1.44083
$58$	−2.08277e7	−0.241666
$59$	1.45696e8	1.56536	0.782678	−	0.622427i	$-0.213853\pi$
$59$	1.45696e8	1.56536	0.782678	+	0.622427i	$0.213853\pi$
$60$	8.68125e7	0.864772
$61$	1.60977e8	1.48861	0.744303	−	0.667842i	$-0.232782\pi$
$61$	1.60977e8	1.48861	0.744303	+	0.667842i	$0.232782\pi$
$62$	4.14074e7	0.355890
$63$	8.99859e6	0.0719684
$64$	−6.00845e7	−0.447665
$65$	−4.26376e7	−0.296267
$66$	−3.48773e7	−0.226254
$67$	−2.60575e8	−1.57978	−0.789888	−	0.613251i	$-0.789861\pi$
$67$	−2.60575e8	−1.57978	−0.789888	+	0.613251i	$0.789861\pi$
$68$	−1.08735e8	−0.616708
$69$	−2.46572e8	−1.30955
$70$	2.56816e7	0.127844
$71$	1.00477e8	0.469251	0.234626	−	0.972086i	$-0.424614\pi$
$71$	1.00477e8	0.469251	0.234626	+	0.972086i	$0.424614\pi$
$72$	−2.61190e7	−0.114541
$73$	−4.23324e8	−1.74470	−0.872349	−	0.488884i	$-0.837404\pi$
$73$	−4.23324e8	−1.74470	−0.872349	+	0.488884i	$0.837404\pi$
$74$	3.17676e7	0.123152
$75$	−3.47793e7	−0.126924
$76$	−4.19040e8	−1.44077
$77$	9.25863e7	0.300150
$78$	−2.58323e7	−0.0790199
$79$	−2.23973e8	−0.646956	−0.323478	−	0.946236i	$-0.604852\pi$
$79$	−2.23973e8	−0.646956	−0.323478	+	0.946236i	$0.604852\pi$
$80$	2.77564e8	0.757632
$81$	−2.99605e8	−0.773333
$82$	2.32260e8	0.567298
$83$	−1.93113e8	−0.446644	−0.223322	−	0.974745i	$-0.571690\pi$
$83$	−1.93113e8	−0.446644	−0.223322	+	0.974745i	$0.571690\pi$
$84$	−1.39622e8	−0.305983
$85$	3.52375e8	0.732184
$86$	2.81498e7	0.0554923
$87$	−3.66951e8	−0.686707
$88$	−2.68737e8	−0.477701
$89$	−6.08632e8	−1.02825	−0.514126	−	0.857715i	$-0.671884\pi$
$89$	−6.08632e8	−1.02825	−0.514126	+	0.857715i	$0.671884\pi$
$90$	4.00879e7	0.0644053
$91$	6.85750e7	0.104828
$92$	−8.99808e8	−1.30950
$93$	7.29533e8	1.01128
$94$	3.65620e8	0.483009
$95$	1.35797e9	1.71054
$96$	6.18588e8	0.743329
$97$	−6.40267e8	−0.734324	−0.367162	−	0.930157i	$-0.619671\pi$
$97$	−6.40267e8	−0.734324	−0.367162	+	0.930157i	$0.619671\pi$
$98$	−4.13043e7	−0.0452353
$99$	1.44523e8	0.151209
$100$	−1.26919e8	−0.126919
$101$	−6.83595e8	−0.653661	−0.326831	−	0.945083i	$-0.605981\pi$
$101$	−6.83595e8	−0.653661	−0.326831	+	0.945083i	$0.605981\pi$
$102$	2.13488e8	0.195287
$103$	−9.05448e8	−0.792676	−0.396338	−	0.918105i	$-0.629719\pi$
$103$	−9.05448e8	−0.792676	−0.396338	+	0.918105i	$0.629719\pi$
$104$	−1.99043e8	−0.166839
$105$	4.52470e8	0.363277
$106$	−4.05783e8	−0.312189
$107$	2.27638e9	1.67887	0.839435	−	0.543460i	$-0.182886\pi$
$107$	2.27638e9	1.67887	0.839435	+	0.543460i	$0.182886\pi$
$108$	−1.36254e9	−0.963704
$109$	−1.92885e9	−1.30882	−0.654409	−	0.756141i	$-0.727082\pi$
$109$	−1.92885e9	−1.30882	−0.654409	+	0.756141i	$0.727082\pi$
$110$	4.12463e8	0.268607
$111$	5.59696e8	0.349944
$112$	−4.46412e8	−0.268074
$113$	2.09198e9	1.20699	0.603497	−	0.797365i	$-0.293773\pi$
$113$	2.09198e9	1.20699	0.603497	+	0.797365i	$0.293773\pi$
$114$	8.22734e8	0.456234
$115$	2.91599e9	1.55469
$116$	−1.33910e9	−0.686679
$117$	1.07042e8	0.0528104
$118$	−1.04390e9	−0.495666
$119$	−5.66732e8	−0.259069
$120$	−1.31332e9	−0.578170
$121$	−8.70955e8	−0.369370
$122$	−1.15339e9	−0.471363
$123$	4.09205e9	1.61201
$124$	2.66227e9	1.01124
$125$	−2.50444e9	−0.917521
$126$	−6.44741e7	−0.0227886
$127$	−3.88176e9	−1.32407	−0.662037	−	0.749471i	$-0.730308\pi$
$127$	−3.88176e9	−1.32407	−0.662037	+	0.749471i	$0.730308\pi$
$128$	2.93946e9	0.967882
$129$	4.95956e8	0.157685
$130$	3.05495e8	0.0938121
$131$	4.31205e9	1.27927	0.639635	−	0.768678i	$-0.279085\pi$
$131$	4.31205e9	1.27927	0.639635	+	0.768678i	$0.279085\pi$
$132$	−2.24242e9	−0.642886
$133$	−2.18405e9	−0.605244
$134$	1.86699e9	0.500232
$135$	4.41556e9	1.14415
$136$	1.64497e9	0.412320
$137$	2.11266e9	0.512375	0.256187	−	0.966627i	$-0.417534\pi$
$137$	2.11266e9	0.512375	0.256187	+	0.966627i	$0.417534\pi$
$138$	1.76667e9	0.414666
$139$	−6.67911e9	−1.51758	−0.758791	−	0.651334i	$-0.774210\pi$
$139$	−6.67911e9	−1.51758	−0.758791	+	0.651334i	$0.774210\pi$
$140$	1.65119e9	0.363262
$141$	6.44165e9	1.37250
$142$	−7.19911e8	−0.148587
$143$	1.10136e9	0.220250
$144$	−6.96828e8	−0.135050
$145$	4.33960e9	0.815256
$146$	3.03308e9	0.552454
$147$	−7.27717e8	−0.128539
$148$	2.04248e9	0.349930
$149$	2.35253e9	0.391018	0.195509	−	0.980702i	$-0.437364\pi$
$149$	2.35253e9	0.391018	0.195509	+	0.980702i	$0.437364\pi$
$150$	2.49191e8	0.0401903
$151$	−6.70346e8	−0.104931	−0.0524654	−	0.998623i	$-0.516708\pi$
$151$	−6.70346e8	−0.104931	−0.0524654	+	0.998623i	$0.516708\pi$
$152$	6.33935e9	0.963271
$153$	−8.84642e8	−0.130514
$154$	−6.63372e8	−0.0950417
$155$	−8.62754e9	−1.20059
$156$	−1.66087e9	−0.224530
$157$	4.54349e9	0.596817	0.298408	−	0.954438i	$-0.403544\pi$
$157$	4.54349e9	0.596817	0.298408	+	0.954438i	$0.403544\pi$
$158$	1.60475e9	0.204857
$159$	−7.14927e9	−0.887104
$160$	−7.31548e9	−0.882477
$161$	−4.68984e9	−0.550099
$162$	2.14664e9	0.244874
$163$	5.81587e8	0.0645313	0.0322657	−	0.999479i	$-0.489728\pi$
$163$	5.81587e8	0.0645313	0.0322657	+	0.999479i	$0.489728\pi$
$164$	1.49330e10	1.61194
$165$	7.26695e9	0.763264
$166$	1.38364e9	0.141429
$167$	8.40260e9	0.835968	0.417984	−	0.908454i	$-0.362737\pi$
$167$	8.40260e9	0.835968	0.417984	+	0.908454i	$0.362737\pi$
$168$	2.11224e9	0.204575
$169$	8.15731e8	0.0769231
$170$	−2.52474e9	−0.231844
$171$	−3.40920e9	−0.304909
$172$	1.80988e9	0.157678
$173$	−2.08072e10	−1.76606	−0.883032	−	0.469313i	$-0.844502\pi$
$173$	−2.08072e10	−1.76606	−0.883032	+	0.469313i	$0.844502\pi$
$174$	2.62917e9	0.217444
$175$	−6.61508e8	−0.0533168
$176$	−7.16965e9	−0.563236
$177$	−1.83918e10	−1.40846
$178$	4.36079e9	0.325593
$179$	−8.28369e8	−0.0603095	−0.0301547	−	0.999545i	$-0.509600\pi$
$179$	−8.28369e8	−0.0603095	−0.0301547	+	0.999545i	$0.509600\pi$
$180$	2.57743e9	0.183004
$181$	2.58334e9	0.178907	0.0894536	−	0.995991i	$-0.471488\pi$
$181$	2.58334e9	0.178907	0.0894536	+	0.995991i	$0.471488\pi$
$182$	−4.91333e8	−0.0331937
$183$	−2.03209e10	−1.33941
$184$	1.36125e10	0.875506
$185$	−6.61903e9	−0.415452
$186$	−5.22704e9	−0.320219
$187$	−9.10206e9	−0.544318
$188$	2.35073e10	1.37244
$189$	−7.10163e9	−0.404837
$190$	−9.72974e9	−0.541639
$191$	−2.58753e8	−0.0140681	−0.00703405	−	0.999975i	$-0.502239\pi$
$191$	−2.58753e8	−0.0140681	−0.00703405	+	0.999975i	$0.502239\pi$
$192$	7.58474e9	0.402796
$193$	−1.87627e10	−0.973389	−0.486694	−	0.873572i	$-0.661797\pi$
$193$	−1.87627e10	−0.973389	−0.486694	+	0.873572i	$0.661797\pi$
$194$	4.58745e9	0.232522
$195$	5.38234e9	0.266573
$196$	−2.65564e9	−0.128533
$197$	−3.31287e10	−1.56713	−0.783567	−	0.621308i	$-0.786602\pi$
$197$	−3.31287e10	−1.56713	−0.783567	+	0.621308i	$0.786602\pi$
$198$	−1.03549e9	−0.0478800
$199$	2.93424e10	1.32634	0.663172	−	0.748467i	$-0.269210\pi$
$199$	2.93424e10	1.32634	0.663172	+	0.748467i	$0.269210\pi$
$200$	1.92007e9	0.0848558
$201$	3.28935e10	1.42144
$202$	4.89790e9	0.206980
$203$	−6.97947e9	−0.288463
$204$	1.37261e10	0.554897
$205$	−4.83930e10	−1.91377
$206$	6.48745e9	0.250999
$207$	−7.32062e9	−0.277129
$208$	−5.31027e9	−0.196712
$209$	−3.50772e10	−1.27165
$210$	−3.24191e9	−0.115031
$211$	4.64225e10	1.61234	0.806171	−	0.591683i	$-0.201536\pi$
$211$	4.64225e10	1.61234	0.806171	+	0.591683i	$0.201536\pi$
$212$	−2.60896e10	−0.887067
$213$	−1.26837e10	−0.422219
$214$	−1.63100e10	−0.531610
$215$	−5.86522e9	−0.187202
$216$	2.06129e10	0.644314
$217$	1.38758e10	0.424806
$218$	1.38200e10	0.414434
$219$	5.34381e10	1.56983
$220$	2.65191e10	0.763232
$221$	−6.74153e9	−0.190105
$222$	−4.01017e9	−0.110809
$223$	−2.77268e10	−0.750806	−0.375403	−	0.926862i	$-0.622496\pi$
$223$	−2.77268e10	−0.750806	−0.375403	+	0.926862i	$0.622496\pi$
$224$	1.17656e10	0.312248
$225$	−1.03258e9	−0.0268599
$226$	−1.49889e10	−0.382192
$227$	7.13956e10	1.78466	0.892329	−	0.451385i	$-0.149070\pi$
$227$	7.13956e10	1.78466	0.892329	+	0.451385i	$0.149070\pi$
$228$	5.28973e10	1.29636
$229$	−1.41177e10	−0.339238	−0.169619	−	0.985510i	$-0.554254\pi$
$229$	−1.41177e10	−0.339238	−0.169619	+	0.985510i	$0.554254\pi$
$230$	−2.08928e10	−0.492290
$231$	−1.16876e10	−0.270066
$232$	2.02583e10	0.459101
$233$	−3.41791e10	−0.759730	−0.379865	−	0.925042i	$-0.624030\pi$
$233$	−3.41791e10	−0.759730	−0.379865	+	0.925042i	$0.624030\pi$
$234$	−7.66949e8	−0.0167223
$235$	−7.61797e10	−1.62942
$236$	−6.71168e10	−1.40840
$237$	2.82732e10	0.582113
$238$	4.06058e9	0.0820336
$239$	1.14315e10	0.226628	0.113314	−	0.993559i	$-0.463853\pi$
$239$	1.14315e10	0.226628	0.113314	+	0.993559i	$0.463853\pi$
$240$	−3.50382e10	−0.681696
$241$	−5.74907e10	−1.09779	−0.548897	−	0.835890i	$-0.684952\pi$
$241$	−5.74907e10	−1.09779	−0.548897	+	0.835890i	$0.684952\pi$
$242$	6.24032e9	0.116960
$243$	−2.03975e10	−0.375274
$244$	−7.41564e10	−1.33935
$245$	8.60606e9	0.152601
$246$	−2.93192e10	−0.510439
$247$	−2.59803e10	−0.444128
$248$	−4.02755e10	−0.676096
$249$	2.43776e10	0.401877
$250$	1.79441e10	0.290531
$251$	−5.39183e10	−0.857442	−0.428721	−	0.903437i	$-0.641036\pi$
$251$	−5.39183e10	−0.857442	−0.428721	+	0.903437i	$0.641036\pi$
$252$	−4.14533e9	−0.0647525
$253$	−7.53217e10	−1.15579
$254$	2.78125e10	0.419265
$255$	−4.44819e10	−0.658798
$256$	9.70234e9	0.141188
$257$	−6.14709e10	−0.878963	−0.439482	−	0.898252i	$-0.644838\pi$
$257$	−6.14709e10	−0.878963	−0.439482	+	0.898252i	$0.644838\pi$
$258$	−3.55348e9	−0.0499304
$259$	1.06455e10	0.147000
$260$	1.96416e10	0.266562
$261$	−1.08946e10	−0.145322
$262$	−3.08954e10	−0.405078
$263$	−9.98825e10	−1.28733	−0.643663	−	0.765309i	$-0.722586\pi$
$263$	−9.98825e10	−1.28733	−0.643663	+	0.765309i	$0.722586\pi$
$264$	3.39239e10	0.429822
$265$	8.45480e10	1.05317
$266$	1.56485e10	0.191649
$267$	7.68303e10	0.925192
$268$	1.20037e11	1.42138
$269$	5.59033e10	0.650957	0.325479	−	0.945549i	$-0.394475\pi$
$269$	5.59033e10	0.650957	0.325479	+	0.945549i	$0.394475\pi$
$270$	−3.16371e10	−0.362293
$271$	8.05220e10	0.906887	0.453443	−	0.891285i	$-0.350195\pi$
$271$	8.05220e10	0.906887	0.453443	+	0.891285i	$0.350195\pi$
$272$	4.38863e10	0.486148
$273$	−8.65653e9	−0.0943217
$274$	−1.51370e10	−0.162242
$275$	−1.06242e10	−0.112021
$276$	1.13587e11	1.17825
$277$	1.43186e11	1.46130	0.730652	−	0.682750i	$-0.239216\pi$
$277$	1.43186e11	1.46130	0.730652	+	0.682750i	$0.239216\pi$
$278$	4.78552e10	0.480538
$279$	2.16595e10	0.214008
$280$	−2.49796e10	−0.242870
$281$	−5.84239e10	−0.559001	−0.279500	−	0.960146i	$-0.590169\pi$
$281$	−5.84239e10	−0.559001	−0.279500	+	0.960146i	$0.590169\pi$
$282$	−4.61539e10	−0.434597
$283$	9.17125e10	0.849942	0.424971	−	0.905207i	$-0.360284\pi$
$283$	9.17125e10	0.849942	0.424971	+	0.905207i	$0.360284\pi$
$284$	−4.62863e10	−0.422201
$285$	−1.71423e11	−1.53910
$286$	−7.89112e9	−0.0697415
$287$	7.78315e10	0.677153
$288$	1.83656e10	0.157304
$289$	−6.28731e10	−0.530181
$290$	−3.10929e10	−0.258149
$291$	8.08237e10	0.660724
$292$	1.95010e11	1.56976
$293$	1.50038e10	0.118932	0.0594658	−	0.998230i	$-0.481060\pi$
$293$	1.50038e10	0.118932	0.0594658	+	0.998230i	$0.481060\pi$
$294$	5.21403e9	0.0407015
$295$	2.17504e11	1.67212
$296$	−3.08992e10	−0.233957
$297$	−1.14057e11	−0.850583
$298$	−1.68556e10	−0.123815
$299$	−5.57878e10	−0.403663
$300$	1.60216e10	0.114198
$301$	9.43315e9	0.0662381
$302$	4.80297e9	0.0332260
$303$	8.62933e10	0.588146
$304$	1.69127e11	1.13575
$305$	2.40317e11	1.59014
$306$	6.33838e9	0.0413268
$307$	2.39921e11	1.54151	0.770753	−	0.637134i	$-0.219880\pi$
$307$	2.39921e11	1.54151	0.770753	+	0.637134i	$0.219880\pi$
$308$	−4.26512e10	−0.270055
$309$	1.14299e11	0.713228
$310$	6.18155e10	0.380163
$311$	−6.63031e10	−0.401895	−0.200947	−	0.979602i	$-0.564402\pi$
$311$	−6.63031e10	−0.401895	−0.200947	+	0.979602i	$0.564402\pi$
$312$	2.51261e10	0.150117
$313$	8.68489e8	0.00511464	0.00255732	−	0.999997i	$-0.499186\pi$
$313$	8.68489e8	0.00511464	0.00255732	+	0.999997i	$0.499186\pi$
$314$	−3.25537e10	−0.188980
$315$	1.34337e10	0.0768771
$316$	1.03177e11	0.582089
$317$	−2.62527e11	−1.46018	−0.730090	−	0.683351i	$-0.760522\pi$
$317$	−2.62527e11	−1.46018	−0.730090	+	0.683351i	$0.760522\pi$
$318$	5.12239e10	0.280899
$319$	−1.12095e11	−0.606075
$320$	−8.96980e10	−0.478198
$321$	−2.87357e11	−1.51060
$322$	3.36023e10	0.174188
$323$	2.14712e11	1.09760
$324$	1.38017e11	0.695795
$325$	−7.86894e9	−0.0391238
$326$	−4.16702e9	−0.0204337
$327$	2.43487e11	1.17764
$328$	−2.25911e11	−1.07772
$329$	1.22521e11	0.576541
$330$	−5.20671e10	−0.241685
$331$	−2.70269e11	−1.23757	−0.618786	−	0.785560i	$-0.712375\pi$
$331$	−2.70269e11	−1.23757	−0.618786	+	0.785560i	$0.712375\pi$
$332$	8.89604e10	0.401861
$333$	1.66171e10	0.0740555
$334$	−6.02039e10	−0.264707
$335$	−3.89002e11	−1.68753
$336$	5.63525e10	0.241205
$337$	4.10261e11	1.73271	0.866354	−	0.499431i	$-0.166458\pi$
$337$	4.10261e11	1.73271	0.866354	+	0.499431i	$0.166458\pi$
$338$	−5.84464e9	−0.0243575
$339$	−2.64081e11	−1.08602
$340$	−1.62327e11	−0.658771
$341$	2.22854e11	0.892538
$342$	2.44266e10	0.0965487
$343$	−1.38413e10	−0.0539949
$344$	−2.73803e10	−0.105421
$345$	−3.68098e11	−1.39887
$346$	1.49082e11	0.559219
$347$	−8.15368e10	−0.301905	−0.150953	−	0.988541i	$-0.548234\pi$
$347$	−8.15368e10	−0.301905	−0.150953	+	0.988541i	$0.548234\pi$
$348$	1.69041e11	0.617854
$349$	−3.47244e11	−1.25291	−0.626455	−	0.779457i	$-0.715495\pi$
$349$	−3.47244e11	−1.25291	−0.626455	+	0.779457i	$0.715495\pi$
$350$	4.73964e9	0.0168826
$351$	−8.44772e10	−0.297069
$352$	1.88963e11	0.656048
$353$	−3.04555e11	−1.04395	−0.521975	−	0.852961i	$-0.674804\pi$
$353$	−3.04555e11	−1.04395	−0.521975	+	0.852961i	$0.674804\pi$
$354$	1.31776e11	0.445986
$355$	1.49999e11	0.501257
$356$	2.80375e11	0.925154
$357$	7.15411e10	0.233103
$358$	5.93519e9	0.0190968
$359$	−3.75381e11	−1.19274	−0.596372	−	0.802708i	$-0.703392\pi$
$359$	−3.75381e11	−1.19274	−0.596372	+	0.802708i	$0.703392\pi$
$360$	−3.89920e10	−0.122353
$361$	5.04762e11	1.56424
$362$	−1.85094e10	−0.0566505
$363$	1.09945e11	0.332349
$364$	−3.15900e10	−0.0943178
$365$	−6.31965e11	−1.86370
$366$	1.45597e11	0.424120
$367$	−3.41168e11	−0.981682	−0.490841	−	0.871249i	$-0.663310\pi$
$367$	−3.41168e11	−0.981682	−0.490841	+	0.871249i	$0.663310\pi$
$368$	3.63169e11	1.03227
$369$	1.21491e11	0.341135
$370$	4.74247e10	0.131552
$371$	−1.35980e11	−0.372643
$372$	−3.36070e11	−0.909884
$373$	−6.07531e11	−1.62509	−0.812547	−	0.582895i	$-0.801920\pi$
$373$	−6.07531e11	−1.62509	−0.812547	+	0.582895i	$0.801920\pi$
$374$	6.52155e10	0.172357
$375$	3.16147e11	0.825560
$376$	−3.55626e11	−0.917588
$377$	−8.30240e10	−0.211674
$378$	5.08826e10	0.128191
$379$	−5.00656e11	−1.24642	−0.623208	−	0.782056i	$-0.714171\pi$
$379$	−5.00656e11	−1.24642	−0.623208	+	0.782056i	$0.714171\pi$
$380$	−6.25569e11	−1.53904
$381$	4.90013e11	1.19137
$382$	1.85394e9	0.00445463
$383$	4.98546e11	1.18389	0.591945	−	0.805979i	$-0.298360\pi$
$383$	4.98546e11	1.18389	0.591945	+	0.805979i	$0.298360\pi$
$384$	−3.71061e11	−0.870873
$385$	1.38219e11	0.320622
$386$	1.34433e11	0.308221
$387$	1.47247e10	0.0333693
$388$	2.94948e11	0.660697
$389$	−5.43023e10	−0.120239	−0.0601194	−	0.998191i	$-0.519148\pi$
$389$	−5.43023e10	−0.120239	−0.0601194	+	0.998191i	$0.519148\pi$
$390$	−3.85640e10	−0.0844095
$391$	4.61053e11	0.997598
$392$	4.01752e10	0.0859351
$393$	−5.44329e11	−1.15105
$394$	2.37364e11	0.496229
$395$	−3.34362e11	−0.691082
$396$	−6.65765e10	−0.136048
$397$	−4.05593e11	−0.819470	−0.409735	−	0.912205i	$-0.634379\pi$
$397$	−4.05593e11	−0.819470	−0.409735	+	0.912205i	$0.634379\pi$
$398$	−2.10235e11	−0.419983
$399$	2.75703e11	0.544582
$400$	5.12255e10	0.100050
$401$	−1.78719e11	−0.345161	−0.172581	−	0.984995i	$-0.555211\pi$
$401$	−1.78719e11	−0.345161	−0.172581	+	0.984995i	$0.555211\pi$
$402$	−2.35679e11	−0.450095
$403$	1.65059e11	0.311722
$404$	3.14908e11	0.588121
$405$	−4.47269e11	−0.826079
$406$	5.00073e10	0.0913410
$407$	1.70973e11	0.308854
$408$	−2.07652e11	−0.370994
$409$	−8.57854e11	−1.51586	−0.757929	−	0.652337i	$-0.773789\pi$
$409$	−8.57854e11	−1.51586	−0.757929	+	0.652337i	$0.773789\pi$
$410$	3.46732e11	0.605991
$411$	−2.66691e11	−0.461020
$412$	4.17107e11	0.713198
$413$	−3.49816e11	−0.591649
$414$	5.24516e10	0.0877520
$415$	−2.88292e11	−0.477107
$416$	1.39958e11	0.229127
$417$	8.43134e11	1.36548
$418$	2.51325e11	0.402664
$419$	3.65496e11	0.579321	0.289661	−	0.957129i	$-0.406458\pi$
$419$	3.65496e11	0.579321	0.289661	+	0.957129i	$0.406458\pi$
$420$	−2.08437e11	−0.326853
$421$	9.34326e11	1.44954	0.724768	−	0.688993i	$-0.241947\pi$
$421$	9.34326e11	1.44954	0.724768	+	0.688993i	$0.241947\pi$
$422$	−3.32613e11	−0.510544
$423$	1.91250e11	0.290449
$424$	3.94691e11	0.593077
$425$	6.50322e10	0.0966892
$426$	9.08776e10	0.133694
$427$	−3.86506e11	−0.562641
$428$	−1.04864e12	−1.51054
$429$	−1.39029e11	−0.198175
$430$	4.20238e10	0.0592772
$431$	−4.36830e11	−0.609768	−0.304884	−	0.952390i	$-0.598618\pi$
$431$	−4.36830e11	−0.609768	−0.304884	+	0.952390i	$0.598618\pi$
$432$	5.49933e11	0.759683
$433$	−4.32621e11	−0.591442	−0.295721	−	0.955274i	$-0.595560\pi$
$433$	−4.32621e11	−0.591442	−0.295721	+	0.955274i	$0.595560\pi$
$434$	−9.94191e10	−0.134514
$435$	−5.47808e11	−0.733544
$436$	8.88552e11	1.17759
$437$	1.77679e12	2.33061
$438$	−3.82879e11	−0.497083
$439$	−6.73759e10	−0.0865793	−0.0432897	−	0.999063i	$-0.513784\pi$
$439$	−6.73759e10	−0.0865793	−0.0432897	+	0.999063i	$0.513784\pi$
$440$	−4.01188e11	−0.510283
$441$	−2.16056e10	−0.0272015
$442$	4.83025e10	0.0601962
$443$	−3.84961e11	−0.474898	−0.237449	−	0.971400i	$-0.576311\pi$
$443$	−3.84961e11	−0.474898	−0.237449	+	0.971400i	$0.576311\pi$
$444$	−2.57832e11	−0.314857
$445$	−9.08604e11	−1.09838
$446$	1.98660e11	0.237741
$447$	−2.96970e11	−0.351827
$448$	1.44263e11	0.169201
$449$	−1.07287e12	−1.24577	−0.622884	−	0.782314i	$-0.714039\pi$
$449$	−1.07287e12	−1.24577	−0.622884	+	0.782314i	$0.714039\pi$
$450$	7.39837e9	0.00850510
$451$	1.25002e12	1.42273
$452$	−9.63702e11	−1.08597
$453$	8.46208e10	0.0944137
$454$	−5.11543e11	−0.565107
$455$	1.02373e11	0.111978
$456$	−8.00244e11	−0.866724
$457$	−1.17323e12	−1.25823	−0.629117	−	0.777311i	$-0.716583\pi$
$457$	−1.17323e12	−1.25823	−0.629117	+	0.777311i	$0.716583\pi$
$458$	1.01152e11	0.107419
$459$	6.98154e11	0.734166
$460$	−1.34329e12	−1.39881
$461$	8.33975e11	0.860001	0.430001	−	0.902829i	$-0.358513\pi$
$461$	8.33975e11	0.860001	0.430001	+	0.902829i	$0.358513\pi$
$462$	8.37405e10	0.0855158
$463$	−1.16869e11	−0.118191	−0.0590954	−	0.998252i	$-0.518822\pi$
$463$	−1.16869e11	−0.118191	−0.0590954	+	0.998252i	$0.518822\pi$
$464$	5.40472e11	0.541306
$465$	1.08909e12	1.08026
$466$	2.44890e11	0.240566
$467$	1.49944e12	1.45882	0.729410	−	0.684077i	$-0.239795\pi$
$467$	1.49944e12	1.45882	0.729410	+	0.684077i	$0.239795\pi$
$468$	−4.93106e10	−0.0475153
$469$	6.25640e11	0.597099
$470$	5.45821e11	0.515952
$471$	−5.73545e11	−0.536999
$472$	1.01536e12	0.941633
$473$	1.51502e11	0.139169
$474$	−2.02575e11	−0.184324
$475$	2.50619e11	0.225888
$476$	2.61073e11	0.233094
$477$	−2.12259e11	−0.187730
$478$	−8.19058e10	−0.0717611
$479$	−4.39521e11	−0.381478	−0.190739	−	0.981641i	$-0.561088\pi$
$479$	−4.39521e11	−0.381478	−0.190739	+	0.981641i	$0.561088\pi$
$480$	9.23467e11	0.794028
$481$	1.26633e11	0.107869
$482$	4.11916e11	0.347613
$483$	5.92019e11	0.494964
$484$	4.01218e11	0.332335
$485$	−9.55830e11	−0.784409
$486$	1.46146e11	0.118830
$487$	−8.36177e11	−0.673625	−0.336812	−	0.941572i	$-0.609349\pi$
$487$	−8.36177e11	−0.673625	−0.336812	+	0.941572i	$0.609349\pi$
$488$	1.12186e12	0.895465
$489$	−7.34164e10	−0.0580635
$490$	−6.16616e10	−0.0483206
$491$	2.59587e11	0.201565	0.100783	−	0.994908i	$-0.467865\pi$
$491$	2.59587e11	0.201565	0.100783	+	0.994908i	$0.467865\pi$
$492$	−1.88506e12	−1.45038
$493$	6.86144e11	0.523124
$494$	1.86147e11	0.140632
$495$	2.15753e11	0.161523
$496$	−1.07451e12	−0.797155
$497$	−2.41246e11	−0.177360
$498$	−1.74663e11	−0.127253
$499$	−1.39033e12	−1.00384	−0.501920	−	0.864914i	$-0.667373\pi$
$499$	−1.39033e12	−1.00384	−0.501920	+	0.864914i	$0.667373\pi$
$500$	1.15371e12	0.825526
$501$	−1.06070e12	−0.752181
$502$	3.86320e11	0.271507
$503$	3.54763e11	0.247106	0.123553	−	0.992338i	$-0.460571\pi$
$503$	3.54763e11	0.247106	0.123553	+	0.992338i	$0.460571\pi$
$504$	6.27116e10	0.0432923
$505$	−1.02051e12	−0.698244
$506$	5.39673e11	0.365977
$507$	−1.02973e11	−0.0692132
$508$	1.78819e12	1.19132
$509$	1.02245e12	0.675171	0.337585	−	0.941295i	$-0.390390\pi$
$509$	1.02245e12	0.675171	0.337585	+	0.941295i	$0.390390\pi$
$510$	3.18709e11	0.208607
$511$	1.01640e12	0.659434
$512$	−1.57452e12	−1.01259
$513$	2.69052e12	1.71518
$514$	4.40434e11	0.278321
$515$	−1.35171e12	−0.846741
$516$	−2.28469e11	−0.141874
$517$	1.96777e12	1.21134
$518$	−7.62741e10	−0.0465472
$519$	2.62659e12	1.58905
$520$	−2.97144e11	−0.178218
$521$	1.17132e12	0.696473	0.348237	−	0.937407i	$-0.386781\pi$
$521$	1.17132e12	0.696473	0.348237	+	0.937407i	$0.386781\pi$
$522$	7.80590e10	0.0460157
$523$	2.57925e12	1.50742	0.753712	−	0.657205i	$-0.228262\pi$
$523$	2.57925e12	1.50742	0.753712	+	0.657205i	$0.228262\pi$
$524$	−1.98640e12	−1.15100
$525$	8.35051e10	0.0479729
$526$	7.15649e11	0.407628
$527$	−1.36412e12	−0.770379
$528$	9.05057e11	0.506784
$529$	2.01417e12	1.11827
$530$	−6.05779e11	−0.333482
$531$	−5.46046e11	−0.298060
$532$	1.00611e12	0.544559
$533$	9.25841e11	0.496894
$534$	−5.50483e11	−0.292960
$535$	3.39832e12	1.79338
$536$	−1.81596e12	−0.950308
$537$	1.04569e11	0.0542648
$538$	−4.00542e11	−0.206124
$539$	−2.22300e11	−0.113446
$540$	−2.03409e12	−1.02943
$541$	4.79435e11	0.240625	0.120313	−	0.992736i	$-0.461610\pi$
$541$	4.79435e11	0.240625	0.120313	+	0.992736i	$0.461610\pi$
$542$	−5.76933e11	−0.287163
$543$	−3.26106e11	−0.160976
$544$	−1.15667e12	−0.566257
$545$	−2.87951e12	−1.39809
$546$	6.20232e10	0.0298667
$547$	−2.93279e11	−0.140067	−0.0700337	−	0.997545i	$-0.522311\pi$
$547$	−2.93279e11	−0.140067	−0.0700337	+	0.997545i	$0.522311\pi$
$548$	−9.73228e11	−0.461001
$549$	−6.03318e11	−0.283446
$550$	7.61216e10	0.0354712
$551$	2.64424e12	1.22213
$552$	−1.71837e12	−0.787755
$553$	5.37760e11	0.244526
$554$	−1.02591e12	−0.462718
$555$	8.35549e11	0.373812
$556$	3.07683e12	1.36542
$557$	1.22072e12	0.537361	0.268681	−	0.963229i	$-0.413412\pi$
$557$	1.22072e12	0.537361	0.268681	+	0.963229i	$0.413412\pi$
$558$	−1.55189e11	−0.0677651
$559$	1.12212e11	0.0486055
$560$	−6.66431e11	−0.286358
$561$	1.14899e12	0.489762
$562$	4.18602e11	0.177006
$563$	−3.00695e12	−1.26136	−0.630680	−	0.776043i	$-0.717224\pi$
$563$	−3.00695e12	−1.26136	−0.630680	+	0.776043i	$0.717224\pi$
$564$	−2.96744e12	−1.23488
$565$	3.12304e12	1.28932
$566$	−6.57112e11	−0.269132
$567$	7.19352e11	0.292293
$568$	7.00231e11	0.282276
$569$	−7.70728e11	−0.308245	−0.154122	−	0.988052i	$-0.549255\pi$
$569$	−7.70728e11	−0.308245	−0.154122	+	0.988052i	$0.549255\pi$
$570$	1.22823e12	0.487352
$571$	−3.28373e12	−1.29272	−0.646360	−	0.763033i	$-0.723710\pi$
$571$	−3.28373e12	−1.29272	−0.646360	+	0.763033i	$0.723710\pi$
$572$	−5.07355e11	−0.198166
$573$	3.26636e10	0.0126581
$574$	−5.57655e11	−0.214419
$575$	5.38156e11	0.205307
$576$	2.25188e11	0.0852401
$577$	−1.91275e12	−0.718401	−0.359200	−	0.933260i	$-0.616951\pi$
$577$	−1.91275e12	−0.718401	−0.359200	+	0.933260i	$0.616951\pi$
$578$	4.50480e11	0.167880
$579$	2.36849e12	0.875828
$580$	−1.99910e12	−0.733514
$581$	4.63665e11	0.168815
$582$	−5.79095e11	−0.209217
$583$	−2.18393e12	−0.782941
$584$	−2.95017e12	−1.04952
$585$	1.59800e11	0.0564123
$586$	−1.07501e11	−0.0376594
$587$	−8.28457e11	−0.288004	−0.144002	−	0.989577i	$-0.545997\pi$
$587$	−8.28457e11	−0.288004	−0.144002	+	0.989577i	$0.545997\pi$
$588$	3.35233e11	0.115651
$589$	−5.25700e12	−1.79978
$590$	−1.55839e12	−0.529473
$591$	4.18198e12	1.41006
$592$	−8.24361e11	−0.275848
$593$	−2.70681e12	−0.898900	−0.449450	−	0.893305i	$-0.648380\pi$
$593$	−2.70681e12	−0.898900	−0.449450	+	0.893305i	$0.648380\pi$
$594$	8.17205e11	0.269335
$595$	−8.46053e11	−0.276739
$596$	−1.08372e12	−0.351812
$597$	−3.70402e12	−1.19341
$598$	3.99714e11	0.127819
$599$	−1.07154e12	−0.340086	−0.170043	−	0.985437i	$-0.554391\pi$
$599$	−1.07154e12	−0.340086	−0.170043	+	0.985437i	$0.554391\pi$
$600$	−2.42379e11	−0.0763509
$601$	−3.08594e12	−0.964833	−0.482417	−	0.875942i	$-0.660241\pi$
$601$	−3.08594e12	−0.964833	−0.482417	+	0.875942i	$0.660241\pi$
$602$	−6.75877e10	−0.0209741
$603$	9.76595e11	0.300806
$604$	3.08804e11	0.0944098
$605$	−1.30022e12	−0.394563
$606$	−6.18284e11	−0.186235
$607$	3.45618e12	1.03335	0.516675	−	0.856182i	$-0.327170\pi$
$607$	3.45618e12	1.03335	0.516675	+	0.856182i	$0.327170\pi$
$608$	−4.45753e12	−1.32290
$609$	8.81050e11	0.259551
$610$	−1.72185e12	−0.503513
$611$	1.45745e12	0.423065
$612$	4.07523e11	0.117428
$613$	1.88640e12	0.539587	0.269794	−	0.962918i	$-0.413045\pi$
$613$	1.88640e12	0.539587	0.269794	+	0.962918i	$0.413045\pi$
$614$	−1.71901e12	−0.488114
$615$	6.10887e12	1.72196
$616$	6.45238e11	0.180554
$617$	5.46037e12	1.51684	0.758419	−	0.651768i	$-0.225972\pi$
$617$	5.46037e12	1.51684	0.758419	+	0.651768i	$0.225972\pi$
$618$	−8.18940e11	−0.225842
$619$	1.63926e12	0.448787	0.224393	−	0.974499i	$-0.427960\pi$
$619$	1.63926e12	0.448787	0.224393	+	0.974499i	$0.427960\pi$
$620$	3.97440e12	1.08021
$621$	5.77739e12	1.55890
$622$	4.75056e11	0.127259
$623$	1.46133e12	0.388643
$624$	6.70339e11	0.176996
$625$	−4.27690e12	−1.12116
$626$	−6.22265e9	−0.00161954
$627$	4.42796e12	1.14419
$628$	−2.09302e12	−0.536977
$629$	−1.04655e12	−0.266583
$630$	−9.62510e10	−0.0243429
$631$	−4.68169e12	−1.17563	−0.587815	−	0.808996i	$-0.700012\pi$
$631$	−4.68169e12	−1.17563	−0.587815	+	0.808996i	$0.700012\pi$
$632$	−1.56088e12	−0.389174
$633$	−5.86012e12	−1.45074
$634$	1.88098e12	0.462362
$635$	−5.79494e12	−1.41438
$636$	3.29341e12	0.798158
$637$	−1.64648e11	−0.0396214
$638$	8.03147e11	0.191912
$639$	−3.76574e11	−0.0893503
$640$	4.38821e12	1.03390
$641$	−1.28766e12	−0.301259	−0.150629	−	0.988590i	$-0.548130\pi$
$641$	−1.28766e12	−0.301259	−0.150629	+	0.988590i	$0.548130\pi$
$642$	2.05889e12	0.478328
$643$	−1.58508e12	−0.365682	−0.182841	−	0.983143i	$-0.558529\pi$
$643$	−1.58508e12	−0.365682	−0.182841	+	0.983143i	$0.558529\pi$
$644$	2.16044e12	0.494943
$645$	7.40394e11	0.168440
$646$	−1.53839e12	−0.347553
$647$	1.48764e12	0.333757	0.166878	−	0.985978i	$-0.446631\pi$
$647$	1.48764e12	0.333757	0.166878	+	0.985978i	$0.446631\pi$
$648$	−2.08796e12	−0.465195
$649$	−5.61825e12	−1.24308
$650$	5.63803e10	0.0123884
$651$	−1.75161e12	−0.382228
$652$	−2.67916e11	−0.0580611
$653$	8.87142e11	0.190934	0.0954672	−	0.995433i	$-0.469566\pi$
$653$	8.87142e11	0.190934	0.0954672	+	0.995433i	$0.469566\pi$
$654$	−1.74457e12	−0.372896
$655$	6.43729e12	1.36652
$656$	−6.02707e12	−1.27069
$657$	1.58656e12	0.332209
$658$	−8.77854e11	−0.182560
$659$	−5.56173e12	−1.14875	−0.574375	−	0.818593i	$-0.694755\pi$
$659$	−5.56173e12	−1.14875	−0.574375	+	0.818593i	$0.694755\pi$
$660$	−3.34762e12	−0.686734
$661$	2.50799e12	0.510997	0.255499	−	0.966809i	$-0.417760\pi$
$661$	2.50799e12	0.510997	0.255499	+	0.966809i	$0.417760\pi$
$662$	1.93645e12	0.391874
$663$	8.51014e11	0.171051
$664$	−1.34582e12	−0.268677
$665$	−3.26049e12	−0.646525
$666$	−1.19060e11	−0.0234495
$667$	5.67800e12	1.11078
$668$	−3.87078e12	−0.752149
$669$	3.50008e12	0.675554
$670$	2.78717e12	0.534350
$671$	−6.20753e12	−1.18214
$672$	−1.48523e12	−0.280952
$673$	3.98622e12	0.749020	0.374510	−	0.927223i	$-0.377811\pi$
$673$	3.98622e12	0.749020	0.374510	+	0.927223i	$0.377811\pi$
$674$	−2.93948e12	−0.548657
$675$	8.14909e11	0.151092
$676$	−3.75778e11	−0.0692103
$677$	1.91572e12	0.350497	0.175248	−	0.984524i	$-0.443927\pi$
$677$	1.91572e12	0.350497	0.175248	+	0.984524i	$0.443927\pi$
$678$	1.89211e12	0.343885
$679$	1.53728e12	0.277549
$680$	2.45572e12	0.440442
$681$	−9.01259e12	−1.60579
$682$	−1.59673e12	−0.282620
$683$	−5.04848e12	−0.887702	−0.443851	−	0.896101i	$-0.646388\pi$
$683$	−5.04848e12	−0.887702	−0.443851	+	0.896101i	$0.646388\pi$
$684$	1.57050e12	0.274337
$685$	3.15392e12	0.547321
$686$	9.91716e10	0.0170973
$687$	1.78214e12	0.305237
$688$	−7.30480e11	−0.124297
$689$	−1.61755e12	−0.273445
$690$	2.63739e12	0.442949
$691$	2.74401e12	0.457861	0.228931	−	0.973443i	$-0.426477\pi$
$691$	2.74401e12	0.457861	0.228931	+	0.973443i	$0.426477\pi$
$692$	9.58514e12	1.58899
$693$	−3.46999e11	−0.0571517
$694$	5.84204e11	0.0955975
$695$	−9.97100e12	−1.62109
$696$	−2.55730e12	−0.413086
$697$	−7.65153e12	−1.22801
$698$	2.48797e12	0.396731
$699$	4.31458e12	0.683584
$700$	3.04733e11	0.0479709
$701$	−4.07457e12	−0.637309	−0.318655	−	0.947871i	$-0.603231\pi$
$701$	−4.07457e12	−0.637309	−0.318655	+	0.947871i	$0.603231\pi$
$702$	6.05272e11	0.0940661
$703$	−4.03316e12	−0.622796
$704$	2.31695e12	0.355500
$705$	9.61650e12	1.46611
$706$	2.18211e12	0.330564
$707$	1.64131e12	0.247061
$708$	8.47246e12	1.26724
$709$	−2.34218e12	−0.348106	−0.174053	−	0.984736i	$-0.555686\pi$
$709$	−2.34218e12	−0.348106	−0.174053	+	0.984736i	$0.555686\pi$
$710$	−1.07473e12	−0.158722
$711$	8.39419e11	0.123187
$712$	−4.24159e12	−0.618541
$713$	−1.12884e13	−1.63580
$714$	−5.12586e11	−0.0738116
$715$	1.64417e12	0.235272
$716$	3.81600e11	0.0542625
$717$	−1.44305e12	−0.203914
$718$	2.68957e12	0.377679
$719$	−6.50489e12	−0.907737	−0.453868	−	0.891069i	$-0.649956\pi$
$719$	−6.50489e12	−0.907737	−0.453868	+	0.891069i	$0.649956\pi$
$720$	−1.04027e12	−0.144261
$721$	2.17398e12	0.299604
$722$	−3.61658e12	−0.495313
$723$	7.25731e12	0.987764
$724$	−1.19005e12	−0.160969
$725$	8.00890e11	0.107659
$726$	−7.87743e11	−0.105237
$727$	−1.02131e13	−1.35598	−0.677990	−	0.735071i	$-0.737149\pi$
$727$	−1.02131e13	−1.35598	−0.677990	+	0.735071i	$0.737149\pi$
$728$	4.77902e11	0.0630591
$729$	8.47200e12	1.11099
$730$	4.52797e12	0.590134
$731$	−9.27364e11	−0.120122
$732$	9.36110e12	1.20511
$733$	−5.45066e12	−0.697399	−0.348699	−	0.937235i	$-0.613377\pi$
$733$	−5.45066e12	−0.697399	−0.348699	+	0.937235i	$0.613377\pi$
$734$	2.44444e12	0.310847
$735$	−1.08638e12	−0.137306
$736$	−9.57169e12	−1.20237
$737$	1.00482e13	1.25454
$738$	−8.70474e11	−0.108020
$739$	8.37248e12	1.03265	0.516326	−	0.856392i	$-0.327299\pi$
$739$	8.37248e12	1.03265	0.516326	+	0.856392i	$0.327299\pi$
$740$	3.04915e12	0.373797
$741$	3.27961e12	0.399614
$742$	9.74286e11	0.117996
$743$	8.15780e10	0.00982027	0.00491013	−	0.999988i	$-0.498437\pi$
$743$	8.15780e10	0.00982027	0.00491013	+	0.999988i	$0.498437\pi$
$744$	5.08415e12	0.608332
$745$	3.51200e12	0.417687
$746$	4.35291e12	0.514582
$747$	7.23760e11	0.0850457
$748$	4.19299e12	0.489741
$749$	−5.46558e12	−0.634553
$750$	−2.26517e12	−0.261411
$751$	9.45039e12	1.08410	0.542051	−	0.840346i	$-0.317648\pi$
$751$	9.45039e12	1.08410	0.542051	+	0.840346i	$0.317648\pi$
$752$	−9.48774e12	−1.08189
$753$	6.80635e12	0.771502
$754$	5.94859e11	0.0670260
$755$	−1.00073e12	−0.112088
$756$	3.27147e12	0.364246
$757$	3.85281e12	0.426429	0.213214	−	0.977005i	$-0.431607\pi$
$757$	3.85281e12	0.426429	0.213214	+	0.977005i	$0.431607\pi$
$758$	3.58716e12	0.394674
$759$	9.50819e12	1.03994
$760$	9.46377e12	1.02897
$761$	−8.36687e12	−0.904341	−0.452170	−	0.891932i	$-0.649350\pi$
$761$	−8.36687e12	−0.904341	−0.452170	+	0.891932i	$0.649350\pi$
$762$	−3.51090e12	−0.377243
$763$	4.63117e12	0.494686
$764$	1.19198e11	0.0126576
$765$	−1.32065e12	−0.139415
$766$	−3.57204e12	−0.374875
$767$	−4.16122e12	−0.434151
$768$	−1.22477e12	−0.127037
$769$	3.89711e12	0.401859	0.200930	−	0.979606i	$-0.435604\pi$
$769$	3.89711e12	0.401859	0.200930	+	0.979606i	$0.435604\pi$
$770$	−9.90324e11	−0.101524
$771$	7.75975e12	0.790866
$772$	8.64328e12	0.875792
$773$	1.80881e13	1.82215	0.911075	−	0.412240i	$-0.135254\pi$
$773$	1.80881e13	1.82215	0.911075	+	0.412240i	$0.135254\pi$
$774$	−1.05501e11	−0.0105663
$775$	−1.59224e12	−0.158545
$776$	−4.46205e12	−0.441730
$777$	−1.34383e12	−0.132267
$778$	3.89071e11	0.0380733
$779$	−2.94872e13	−2.86890
$780$	−2.47945e12	−0.239845
$781$	−3.87456e12	−0.372643
$782$	−3.30340e12	−0.315887
$783$	8.59798e12	0.817463
$784$	1.07183e12	0.101322
$785$	6.78280e12	0.637523
$786$	3.90007e12	0.364477
$787$	−9.05135e12	−0.841060	−0.420530	−	0.907279i	$-0.638156\pi$
$787$	−9.05135e12	−0.841060	−0.420530	+	0.907279i	$0.638156\pi$
$788$	1.52612e13	1.41000
$789$	1.26086e13	1.15830
$790$	2.39567e12	0.218829
$791$	−5.02285e12	−0.456201
$792$	1.00719e12	0.0909593
$793$	−4.59767e12	−0.412865
$794$	2.90604e12	0.259483
$795$	−1.06729e13	−0.947609
$796$	−1.35170e13	−1.19336
$797$	1.03900e13	0.912123	0.456062	−	0.889948i	$-0.349260\pi$
$797$	1.03900e13	0.912123	0.456062	+	0.889948i	$0.349260\pi$
$798$	−1.97539e12	−0.172440
$799$	−1.20449e13	−1.04555
$800$	−1.35010e12	−0.116536
$801$	2.28106e12	0.195790
$802$	1.28051e12	0.109294
$803$	1.63240e13	1.38550
$804$	−1.51529e13	−1.27892
$805$	−7.00128e12	−0.587619
$806$	−1.18264e12	−0.0987060
$807$	−7.05693e12	−0.585713
$808$	−4.76401e12	−0.393207
$809$	5.10565e12	0.419066	0.209533	−	0.977802i	$-0.432806\pi$
$809$	5.10565e12	0.419066	0.209533	+	0.977802i	$0.432806\pi$
$810$	3.20464e12	0.261576
$811$	1.61240e13	1.30882	0.654410	−	0.756140i	$-0.272917\pi$
$811$	1.61240e13	1.30882	0.654410	+	0.756140i	$0.272917\pi$
$812$	3.21519e12	0.259540
$813$	−1.01647e13	−0.815991
$814$	−1.22501e12	−0.0977979
$815$	8.68230e11	0.0689327
$816$	−5.53996e12	−0.437422
$817$	−3.57384e12	−0.280631
$818$	6.14645e12	0.479993
$819$	−2.57009e11	−0.0199604
$820$	2.22929e13	1.72189
$821$	−9.23711e12	−0.709565	−0.354782	−	0.934949i	$-0.615445\pi$
$821$	−9.23711e12	−0.709565	−0.354782	+	0.934949i	$0.615445\pi$
$822$	1.91082e12	0.145981
$823$	2.72000e12	0.206666	0.103333	−	0.994647i	$-0.467049\pi$
$823$	2.72000e12	0.206666	0.103333	+	0.994647i	$0.467049\pi$
$824$	−6.31011e12	−0.476831
$825$	1.34114e12	0.100793
$826$	2.50640e12	0.187344
$827$	1.83766e13	1.36612	0.683062	−	0.730360i	$-0.260648\pi$
$827$	1.83766e13	1.36612	0.683062	+	0.730360i	$0.260648\pi$
$828$	3.37235e12	0.249342
$829$	−7.49488e12	−0.551150	−0.275575	−	0.961280i	$-0.588868\pi$
$829$	−7.49488e12	−0.551150	−0.275575	+	0.961280i	$0.588868\pi$
$830$	2.06559e12	0.151075
$831$	−1.80750e13	−1.31484
$832$	1.71607e12	0.124160
$833$	1.36072e12	0.0979190
$834$	−6.04098e12	−0.432375
$835$	1.25439e13	0.892986
$836$	1.61588e13	1.14415
$837$	−1.70936e13	−1.20384
$838$	−2.61875e12	−0.183441
$839$	−2.33267e13	−1.62527	−0.812633	−	0.582776i	$-0.801967\pi$
$839$	−2.33267e13	−1.62527	−0.812633	+	0.582776i	$0.801967\pi$
$840$	3.15329e12	0.218528
$841$	−6.05708e12	−0.417524
$842$	−6.69436e12	−0.458992
$843$	7.37512e12	0.502973
$844$	−2.13852e13	−1.45068
$845$	1.21777e12	0.0821697
$846$	−1.37029e12	−0.0919699
$847$	2.09116e12	0.139609
$848$	1.05300e13	0.699271
$849$	−1.15773e13	−0.764754
$850$	−4.65950e11	−0.0306164
$851$	−8.66044e12	−0.566053
$852$	5.84292e12	0.379885
$853$	1.32039e13	0.853949	0.426975	−	0.904264i	$-0.359579\pi$
$853$	1.32039e13	0.853949	0.426975	+	0.904264i	$0.359579\pi$
$854$	2.76928e12	0.178159
$855$	−5.08947e12	−0.325706
$856$	1.58642e13	1.00992
$857$	−5.40702e12	−0.342408	−0.171204	−	0.985236i	$-0.554766\pi$
$857$	−5.40702e12	−0.342408	−0.171204	+	0.985236i	$0.554766\pi$
$858$	9.96131e11	0.0627515
$859$	2.10673e13	1.32020	0.660101	−	0.751177i	$-0.270513\pi$
$859$	2.10673e13	1.32020	0.660101	+	0.751177i	$0.270513\pi$
$860$	2.70190e12	0.168433
$861$	−9.82501e12	−0.609283
$862$	3.12985e12	0.193081
$863$	3.05132e13	1.87258	0.936288	−	0.351232i	$-0.114237\pi$
$863$	3.05132e13	1.87258	0.936288	+	0.351232i	$0.114237\pi$
$864$	−1.44940e13	−0.884866
$865$	−3.10623e13	−1.88652
$866$	3.09969e12	0.187279
$867$	7.93675e12	0.477042
$868$	−6.39210e12	−0.382212
$869$	8.63676e12	0.513762
$870$	3.92499e12	0.232275
$871$	7.44227e12	0.438151
$872$	−1.34423e13	−0.787314
$873$	2.39962e12	0.139823
$874$	−1.27305e13	−0.737982
$875$	6.01317e12	0.346790
$876$	−2.46170e13	−1.41243
$877$	2.57937e13	1.47237	0.736183	−	0.676783i	$-0.236626\pi$
$877$	2.57937e13	1.47237	0.736183	+	0.676783i	$0.236626\pi$
$878$	4.82742e11	0.0274151
$879$	−1.89400e12	−0.107011
$880$	−1.07033e13	−0.601652
$881$	−2.29434e13	−1.28312	−0.641558	−	0.767075i	$-0.721712\pi$
$881$	−2.29434e13	−1.28312	−0.641558	+	0.767075i	$0.721712\pi$
$882$	1.54802e11	0.00861328
$883$	−9.07578e12	−0.502413	−0.251207	−	0.967933i	$-0.580827\pi$
$883$	−9.07578e12	−0.502413	−0.251207	+	0.967933i	$0.580827\pi$
$884$	3.10558e12	0.171044
$885$	−2.74565e13	−1.50453
$886$	2.75821e12	0.150375
$887$	−3.57097e12	−0.193700	−0.0968502	−	0.995299i	$-0.530877\pi$
$887$	−3.57097e12	−0.193700	−0.0968502	+	0.995299i	$0.530877\pi$
$888$	3.90055e12	0.210508
$889$	9.32012e12	0.500453
$890$	6.51006e12	0.347801
$891$	1.15532e13	0.614121
$892$	1.27727e13	0.675526
$893$	−4.64184e13	−2.44264
$894$	2.12776e12	0.111405
$895$	−1.23664e12	−0.0644229
$896$	−7.05764e12	−0.365825
$897$	7.04234e12	0.363204
$898$	7.68699e12	0.394469
$899$	−1.67995e13	−0.857785
$900$	4.75674e11	0.0241667
$901$	1.33681e13	0.675783
$902$	−8.95629e12	−0.450504
$903$	−1.19079e12	−0.0595992
$904$	1.45791e13	0.726063
$905$	3.85657e12	0.191110
$906$	−6.06300e11	−0.0298959
$907$	−1.18012e13	−0.579022	−0.289511	−	0.957175i	$-0.593493\pi$
$907$	−1.18012e13	−0.579022	−0.289511	+	0.957175i	$0.593493\pi$
$908$	−3.28894e13	−1.60572
$909$	2.56201e12	0.124464
$910$	−7.33493e11	−0.0354576
$911$	−2.33182e13	−1.12166	−0.560832	−	0.827930i	$-0.689518\pi$
$911$	−2.33182e13	−1.12166	−0.560832	+	0.827930i	$0.689518\pi$
$912$	−2.13497e13	−1.02192
$913$	7.44675e12	0.354690
$914$	8.40611e12	0.398416
$915$	−3.03363e13	−1.43076
$916$	6.50352e12	0.305224
$917$	−1.03532e13	−0.483519
$918$	−5.00221e12	−0.232472
$919$	2.96256e13	1.37008	0.685042	−	0.728503i	$-0.259784\pi$
$919$	2.96256e13	1.37008	0.685042	+	0.728503i	$0.259784\pi$
$920$	2.03217e13	0.935220
$921$	−3.02863e13	−1.38700
$922$	−5.97536e12	−0.272317
$923$	−2.86973e12	−0.130147
$924$	5.38405e12	0.242988
$925$	−1.22157e12	−0.0548630
$926$	8.37354e11	0.0374248
$927$	3.39348e12	0.150934
$928$	−1.42447e13	−0.630504
$929$	−4.06451e12	−0.179035	−0.0895175	−	0.995985i	$-0.528532\pi$
$929$	−4.06451e12	−0.179035	−0.0895175	+	0.995985i	$0.528532\pi$
$930$	−7.80325e12	−0.342060
$931$	5.24391e12	0.228761
$932$	1.57451e13	0.683555
$933$	8.36974e12	0.361614
$934$	−1.07433e13	−0.461931
$935$	−1.35881e13	−0.581443
$936$	7.45984e11	0.0317679
$937$	−3.35724e13	−1.42283	−0.711416	−	0.702771i	$-0.751946\pi$
$937$	−3.35724e13	−1.42283	−0.711416	+	0.702771i	$0.751946\pi$
$938$	−4.48265e12	−0.189070
$939$	−1.09633e11	−0.00460201
$940$	3.50932e13	1.46605
$941$	−2.66151e13	−1.10656	−0.553280	−	0.832995i	$-0.686624\pi$
$941$	−2.66151e13	−1.10656	−0.553280	+	0.832995i	$0.686624\pi$
$942$	4.10940e12	0.170039
$943$	−6.33182e13	−2.60751
$944$	2.70888e13	1.11024
$945$	−1.06018e13	−0.432449
$946$	−1.08550e12	−0.0440676
$947$	2.07453e13	0.838193	0.419096	−	0.907942i	$-0.362347\pi$
$947$	2.07453e13	0.838193	0.419096	+	0.907942i	$0.362347\pi$
$948$	−1.30244e13	−0.523747
$949$	1.20906e13	0.483892
$950$	−1.79566e12	−0.0715267
$951$	3.31399e13	1.31383
$952$	−3.94958e12	−0.155842
$953$	1.58116e13	0.620950	0.310475	−	0.950581i	$-0.399512\pi$
$953$	1.58116e13	0.620950	0.310475	+	0.950581i	$0.399512\pi$
$954$	1.52082e12	0.0594441
$955$	−3.86283e11	−0.0150276
$956$	−5.26609e12	−0.203905
$957$	1.41502e13	0.545329
$958$	3.14913e12	0.120794
$959$	−5.07250e12	−0.193659
$960$	1.13230e13	0.430269
$961$	6.95942e12	0.263219
$962$	−9.07316e11	−0.0341563
$963$	−8.53152e12	−0.319675
$964$	2.64839e13	0.987723
$965$	−2.80101e13	−1.03978
$966$	−4.24176e12	−0.156729
$967$	−3.24017e13	−1.19165	−0.595826	−	0.803114i	$-0.703175\pi$
$967$	−3.24017e13	−1.19165	−0.595826	+	0.803114i	$0.703175\pi$
$968$	−6.06973e12	−0.222193
$969$	−2.71041e13	−0.987591
$970$	6.84844e12	0.248381
$971$	3.80616e13	1.37404	0.687021	−	0.726637i	$-0.258918\pi$
$971$	3.80616e13	1.37404	0.687021	+	0.726637i	$0.258918\pi$
$972$	9.39640e12	0.337647
$973$	1.60365e13	0.573592
$974$	5.99113e12	0.213301
$975$	9.93332e11	0.0352025
$976$	2.99301e13	1.05580
$977$	−1.78648e13	−0.627297	−0.313649	−	0.949539i	$-0.601551\pi$
$977$	−1.78648e13	−0.627297	−0.313649	+	0.949539i	$0.601551\pi$
$978$	5.26022e11	0.0183856
$979$	2.34698e13	0.816558
$980$	−3.96450e12	−0.137300
$981$	7.22904e12	0.249213
$982$	−1.85992e12	−0.0638251
$983$	2.64353e13	0.903012	0.451506	−	0.892268i	$-0.350887\pi$
$983$	2.64353e13	0.903012	0.451506	+	0.892268i	$0.350887\pi$
$984$	2.85177e13	0.969699
$985$	−4.94565e13	−1.67402
$986$	−4.91616e12	−0.165646
$987$	−1.54664e13	−0.518755
$988$	1.19682e13	0.399597
$989$	−7.67415e12	−0.255063
$990$	−1.54585e12	−0.0511457
$991$	3.04117e13	1.00163	0.500817	−	0.865553i	$-0.333033\pi$
$991$	3.04117e13	1.00163	0.500817	+	0.865553i	$0.333033\pi$
$992$	2.83198e13	0.928513
$993$	3.41173e13	1.11353
$994$	1.72851e12	0.0561606
$995$	4.38041e13	1.41681
$996$	−1.12299e13	−0.361583
$997$	3.85450e13	1.23549	0.617746	−	0.786378i	$-0.288046\pi$
$997$	3.85450e13	1.23549	0.617746	+	0.786378i	$0.288046\pi$
$998$	9.96157e12	0.317863
$999$	−1.31142e13	−0.416577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.6	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-7.16491 q^{2} -126.235 q^{3} -460.664 q^{4} +1492.86 q^{5} +904.459 q^{6} -2401.00 q^{7} +6969.05 q^{8} -3747.85 q^{9} +O(q^{10})\)	\(q-7.16491 q^{2} -126.235 q^{3} -460.664 q^{4} +1492.86 q^{5} +904.459 q^{6} -2401.00 q^{7} +6969.05 q^{8} -3747.85 q^{9} -10696.2 q^{10} -38561.5 q^{11} +58151.7 q^{12} -28561.0 q^{13} +17203.0 q^{14} -188451. q^{15} +185927. q^{16} +236040. q^{17} +26853.0 q^{18} +909643. q^{19} -687708. q^{20} +303089. q^{21} +276290. q^{22} +1.95328e6 q^{23} -879735. q^{24} +275513. q^{25} +204637. q^{26} +2.95778e6 q^{27} +1.10605e6 q^{28} +2.90690e6 q^{29} +1.35023e6 q^{30} -5.77919e6 q^{31} -4.90031e6 q^{32} +4.86780e6 q^{33} -1.69120e6 q^{34} -3.58436e6 q^{35} +1.72650e6 q^{36} -4.43378e6 q^{37} -6.51751e6 q^{38} +3.60538e6 q^{39} +1.04038e7 q^{40} -3.24163e7 q^{41} -2.17161e6 q^{42} -3.92884e6 q^{43} +1.77639e7 q^{44} -5.59503e6 q^{45} -1.39951e7 q^{46} -5.10293e7 q^{47} -2.34704e7 q^{48} +5.76480e6 q^{49} -1.97403e6 q^{50} -2.97964e7 q^{51} +1.31570e7 q^{52} +5.66348e7 q^{53} -2.11922e7 q^{54} -5.75671e7 q^{55} -1.67327e7 q^{56} -1.14828e8 q^{57} -2.08277e7 q^{58} +1.45696e8 q^{59} +8.68125e7 q^{60} +1.60977e8 q^{61} +4.14074e7 q^{62} +8.99859e6 q^{63} -6.00845e7 q^{64} -4.26376e7 q^{65} -3.48773e7 q^{66} -2.60575e8 q^{67} -1.08735e8 q^{68} -2.46572e8 q^{69} +2.56816e7 q^{70} +1.00477e8 q^{71} -2.61190e7 q^{72} -4.23324e8 q^{73} +3.17676e7 q^{74} -3.47793e7 q^{75} -4.19040e8 q^{76} +9.25863e7 q^{77} -2.58323e7 q^{78} -2.23973e8 q^{79} +2.77564e8 q^{80} -2.99605e8 q^{81} +2.32260e8 q^{82} -1.93113e8 q^{83} -1.39622e8 q^{84} +3.52375e8 q^{85} +2.81498e7 q^{86} -3.66951e8 q^{87} -2.68737e8 q^{88} -6.08632e8 q^{89} +4.00879e7 q^{90} +6.85750e7 q^{91} -8.99808e8 q^{92} +7.29533e8 q^{93} +3.65620e8 q^{94} +1.35797e9 q^{95} +6.18588e8 q^{96} -6.40267e8 q^{97} -4.13043e7 q^{98} +1.44523e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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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