LMFDB - Embedded newform 91.10.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 $ x^14 - x^13 - 4752x^12 + 9346x^11 + 8576824x^10 - 26923636x^9 - 7450416552x^8 + 31594524240x^7 + 3232668379296x^6 - 15784728192704x^5 - 654706244016512x^4 + 3031992312058112x^3 + 50459693673905664x^2 - 177878730644221952x - 247584423217725440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$26.5220$ 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)

$f(q)$	$=$	$q-24.5220 q^{2} +116.541 q^{3} +89.3306 q^{4} -1444.79 q^{5} -2857.83 q^{6} +2401.00 q^{7} +10364.7 q^{8} -6101.17 q^{9} +O(q^{10})$	\(q-24.5220 q^{2} +116.541 q^{3} +89.3306 q^{4} -1444.79 q^{5} -2857.83 q^{6} +2401.00 q^{7} +10364.7 q^{8} -6101.17 q^{9} +35429.2 q^{10} -49044.3 q^{11} +10410.7 q^{12} -28561.0 q^{13} -58877.4 q^{14} -168377. q^{15} -299901. q^{16} -38179.3 q^{17} +149613. q^{18} +470353. q^{19} -129064. q^{20} +279815. q^{21} +1.20267e6 q^{22} -831664. q^{23} +1.20792e6 q^{24} +134293. q^{25} +700374. q^{26} -3.00492e6 q^{27} +214483. q^{28} +6.60819e6 q^{29} +4.12896e6 q^{30} -7.30594e6 q^{31} +2.04746e6 q^{32} -5.71568e6 q^{33} +936235. q^{34} -3.46894e6 q^{35} -545021. q^{36} -9.35992e6 q^{37} -1.15340e7 q^{38} -3.32853e6 q^{39} -1.49748e7 q^{40} +2.90171e6 q^{41} -6.86164e6 q^{42} -1.76481e7 q^{43} -4.38116e6 q^{44} +8.81490e6 q^{45} +2.03941e7 q^{46} +2.29528e7 q^{47} -3.49508e7 q^{48} +5.76480e6 q^{49} -3.29314e6 q^{50} -4.44946e6 q^{51} -2.55137e6 q^{52} +6.77207e7 q^{53} +7.36867e7 q^{54} +7.08587e7 q^{55} +2.48857e7 q^{56} +5.48154e7 q^{57} -1.62046e8 q^{58} -7.91170e7 q^{59} -1.50413e7 q^{60} +1.77604e8 q^{61} +1.79157e8 q^{62} -1.46489e7 q^{63} +1.03342e8 q^{64} +4.12646e7 q^{65} +1.40160e8 q^{66} +2.62510e8 q^{67} -3.41058e6 q^{68} -9.69231e7 q^{69} +8.50655e7 q^{70} +1.12506e8 q^{71} -6.32369e7 q^{72} +7.94280e7 q^{73} +2.29524e8 q^{74} +1.56507e7 q^{75} +4.20169e7 q^{76} -1.17755e8 q^{77} +8.16224e7 q^{78} -2.11864e8 q^{79} +4.33294e8 q^{80} -2.30107e8 q^{81} -7.11558e7 q^{82} +8.26963e8 q^{83} +2.49961e7 q^{84} +5.51611e7 q^{85} +4.32768e8 q^{86} +7.70126e8 q^{87} -5.08330e8 q^{88} +6.05778e8 q^{89} -2.16159e8 q^{90} -6.85750e7 q^{91} -7.42931e7 q^{92} -8.51443e8 q^{93} -5.62850e8 q^{94} -6.79561e8 q^{95} +2.38613e8 q^{96} +1.48303e9 q^{97} -1.41365e8 q^{98} +2.99227e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) $ 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−24.5220	−1.08373	−0.541866	−	0.840465i	$-0.682282\pi$
$2$	−24.5220	−1.08373	−0.541866	+	0.840465i	$0.682282\pi$
$3$	116.541	0.830680	0.415340	−	0.909666i	$-0.363663\pi$
$3$	116.541	0.830680	0.415340	+	0.909666i	$0.363663\pi$
$4$	89.3306	0.174474
$5$	−1444.79	−1.03381	−0.516904	−	0.856043i	$-0.672916\pi$
$5$	−1444.79	−1.03381	−0.516904	+	0.856043i	$0.672916\pi$
$6$	−2857.83	−0.900234
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	10364.7	0.894649
$9$	−6101.17	−0.309971
$10$	35429.2	1.12037
$11$	−49044.3	−1.01000	−0.505000	−	0.863119i	$-0.668508\pi$
$11$	−49044.3	−1.01000	−0.505000	+	0.863119i	$0.668508\pi$
$12$	10410.7	0.144932
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−58877.4	−0.409612
$15$	−168377.	−0.858763
$16$	−299901.	−1.14403
$17$	−38179.3	−0.110869	−0.0554343	−	0.998462i	$-0.517654\pi$
$17$	−38179.3	−0.110869	−0.0554343	+	0.998462i	$0.517654\pi$
$18$	149613.	0.335926
$19$	470353.	0.828004	0.414002	−	0.910276i	$-0.364131\pi$
$19$	470353.	0.828004	0.414002	+	0.910276i	$0.364131\pi$
$20$	−129064.	−0.180372
$21$	279815.	0.313967
$22$	1.20267e6	1.09457
$23$	−831664.	−0.619687	−0.309844	−	0.950788i	$-0.600277\pi$
$23$	−831664.	−0.619687	−0.309844	+	0.950788i	$0.600277\pi$
$24$	1.20792e6	0.743166
$25$	134293.	0.0687581
$26$	700374.	0.300573
$27$	−3.00492e6	−1.08817
$28$	214483.	0.0659449
$29$	6.60819e6	1.73497	0.867485	−	0.497464i	$-0.165735\pi$
$29$	6.60819e6	1.73497	0.867485	+	0.497464i	$0.165735\pi$
$30$	4.12896e6	0.930668
$31$	−7.30594e6	−1.42085	−0.710426	−	0.703772i	$-0.751497\pi$
$31$	−7.30594e6	−1.42085	−0.710426	+	0.703772i	$0.751497\pi$
$32$	2.04746e6	0.345176
$33$	−5.71568e6	−0.838987
$34$	936235.	0.120152
$35$	−3.46894e6	−0.390743
$36$	−545021.	−0.0540819
$37$	−9.35992e6	−0.821040	−0.410520	−	0.911852i	$-0.634653\pi$
$37$	−9.35992e6	−0.821040	−0.410520	+	0.911852i	$0.634653\pi$
$38$	−1.15340e7	−0.897334
$39$	−3.32853e6	−0.230389
$40$	−1.49748e7	−0.924895
$41$	2.90171e6	0.160371	0.0801856	−	0.996780i	$-0.474449\pi$
$41$	2.90171e6	0.160371	0.0801856	+	0.996780i	$0.474449\pi$
$42$	−6.86164e6	−0.340256
$43$	−1.76481e7	−0.787210	−0.393605	−	0.919280i	$-0.628772\pi$
$43$	−1.76481e7	−0.787210	−0.393605	+	0.919280i	$0.628772\pi$
$44$	−4.38116e6	−0.176219
$45$	8.81490e6	0.320451
$46$	2.03941e7	0.671575
$47$	2.29528e7	0.686113	0.343056	−	0.939315i	$-0.388538\pi$
$47$	2.29528e7	0.686113	0.343056	+	0.939315i	$0.388538\pi$
$48$	−3.49508e7	−0.950325
$49$	5.76480e6	0.142857
$50$	−3.29314e6	−0.0745153
$51$	−4.44946e6	−0.0920962
$52$	−2.55137e6	−0.0483903
$53$	6.77207e7	1.17891	0.589454	−	0.807802i	$-0.299343\pi$
$53$	6.77207e7	1.17891	0.589454	+	0.807802i	$0.299343\pi$
$54$	7.36867e7	1.17928
$55$	7.08587e7	1.04415
$56$	2.48857e7	0.338145
$57$	5.48154e7	0.687806
$58$	−1.62046e8	−1.88024
$59$	−7.91170e7	−0.850033	−0.425016	−	0.905186i	$-0.639732\pi$
$59$	−7.91170e7	−0.850033	−0.425016	+	0.905186i	$0.639732\pi$
$60$	−1.50413e7	−0.149832
$61$	1.77604e8	1.64236	0.821182	−	0.570666i	$-0.193315\pi$
$61$	1.77604e8	1.64236	0.821182	+	0.570666i	$0.193315\pi$
$62$	1.79157e8	1.53982
$63$	−1.46489e7	−0.117158
$64$	1.03342e8	0.769955
$65$	4.12646e7	0.286727
$66$	1.40160e8	0.909236
$67$	2.62510e8	1.59151	0.795754	−	0.605620i	$-0.207075\pi$
$67$	2.62510e8	1.59151	0.795754	+	0.605620i	$0.207075\pi$
$68$	−3.41058e6	−0.0193437
$69$	−9.69231e7	−0.514762
$70$	8.50655e7	0.423460
$71$	1.12506e8	0.525429	0.262714	−	0.964874i	$-0.415382\pi$
$71$	1.12506e8	0.525429	0.262714	+	0.964874i	$0.415382\pi$
$72$	−6.32369e7	−0.277315
$73$	7.94280e7	0.327356	0.163678	−	0.986514i	$-0.447664\pi$
$73$	7.94280e7	0.327356	0.163678	+	0.986514i	$0.447664\pi$
$74$	2.29524e8	0.889787
$75$	1.56507e7	0.0571160
$76$	4.20169e7	0.144465
$77$	−1.17755e8	−0.381744
$78$	8.16224e7	0.249680
$79$	−2.11864e8	−0.611976	−0.305988	−	0.952035i	$-0.598987\pi$
$79$	−2.11864e8	−0.611976	−0.305988	+	0.952035i	$0.598987\pi$
$80$	4.33294e8	1.18271
$81$	−2.30107e8	−0.593946
$82$	−7.11558e7	−0.173799
$83$	8.26963e8	1.91265	0.956323	−	0.292311i	$-0.0944242\pi$
$83$	8.26963e8	1.91265	0.956323	+	0.292311i	$0.0944242\pi$
$84$	2.49961e7	0.0547791
$85$	5.51611e7	0.114617
$86$	4.32768e8	0.853124
$87$	7.70126e8	1.44120
$88$	−5.08330e8	−0.903595
$89$	6.05778e8	1.02343	0.511716	−	0.859155i	$-0.329010\pi$
$89$	6.05778e8	1.02343	0.511716	+	0.859155i	$0.329010\pi$
$90$	−2.16159e8	−0.347283
$91$	−6.85750e7	−0.104828
$92$	−7.42931e7	−0.108119
$93$	−8.51443e8	−1.18027
$94$	−5.62850e8	−0.743562
$95$	−6.79561e8	−0.855997
$96$	2.38613e8	0.286730
$97$	1.48303e9	1.70090	0.850449	−	0.526058i	$-0.176330\pi$
$97$	1.48303e9	1.70090	0.850449	+	0.526058i	$0.176330\pi$
$98$	−1.41365e8	−0.154819
$99$	2.99227e8	0.313071
$100$	1.19965e7	0.0119965
$101$	−8.04195e8	−0.768980	−0.384490	−	0.923129i	$-0.625623\pi$
$101$	−8.04195e8	−0.768980	−0.384490	+	0.923129i	$0.625623\pi$
$102$	1.09110e8	0.0998076
$103$	−1.18538e9	−1.03775	−0.518874	−	0.854851i	$-0.673649\pi$
$103$	−1.18538e9	−1.03775	−0.518874	+	0.854851i	$0.673649\pi$
$104$	−2.96027e8	−0.248131
$105$	−4.04274e8	−0.324582
$106$	−1.66065e9	−1.27762
$107$	−9.70896e7	−0.0716054	−0.0358027	−	0.999359i	$-0.511399\pi$
$107$	−9.70896e7	−0.0716054	−0.0358027	+	0.999359i	$0.511399\pi$
$108$	−2.68431e8	−0.189857
$109$	−2.04052e7	−0.0138459	−0.00692294	−	0.999976i	$-0.502204\pi$
$109$	−2.04052e7	−0.0138459	−0.00692294	+	0.999976i	$0.502204\pi$
$110$	−1.73760e9	−1.13157
$111$	−1.09082e9	−0.682021
$112$	−7.20063e8	−0.432404
$113$	2.69885e9	1.55713	0.778566	−	0.627562i	$-0.215947\pi$
$113$	2.69885e9	1.55713	0.778566	+	0.627562i	$0.215947\pi$
$114$	−1.34419e9	−0.745397
$115$	1.20158e9	0.640638
$116$	5.90314e8	0.302707
$117$	1.74255e8	0.0859706
$118$	1.94011e9	0.921207
$119$	−9.16686e7	−0.0419044
$120$	−1.74518e9	−0.768291
$121$	4.73963e7	0.0201006
$122$	−4.35522e9	−1.77988
$123$	3.38168e8	0.133217
$124$	−6.52644e8	−0.247901
$125$	2.62783e9	0.962725
$126$	3.59221e8	0.126968
$127$	3.35303e9	1.14372	0.571860	−	0.820351i	$-0.306222\pi$
$127$	3.35303e9	1.14372	0.571860	+	0.820351i	$0.306222\pi$
$128$	−3.58245e9	−1.17960
$129$	−2.05673e9	−0.653919
$130$	−1.01189e9	−0.310735
$131$	−1.24654e9	−0.369817	−0.184909	−	0.982756i	$-0.559199\pi$
$131$	−1.24654e9	−0.369817	−0.184909	+	0.982756i	$0.559199\pi$
$132$	−5.10585e8	−0.146381
$133$	1.12932e9	0.312956
$134$	−6.43727e9	−1.72477
$135$	4.34147e9	1.12495
$136$	−3.95718e8	−0.0991884
$137$	6.14218e9	1.48963	0.744817	−	0.667269i	$-0.232537\pi$
$137$	6.14218e9	1.48963	0.744817	+	0.667269i	$0.232537\pi$
$138$	2.37675e9	0.557863
$139$	−3.37584e9	−0.767035	−0.383518	−	0.923534i	$-0.625287\pi$
$139$	−3.37584e9	−0.767035	−0.383518	+	0.923534i	$0.625287\pi$
$140$	−3.09883e8	−0.0681744
$141$	2.67495e9	0.569940
$142$	−2.75888e9	−0.569424
$143$	1.40075e9	0.280124
$144$	1.82975e9	0.354617
$145$	−9.54745e9	−1.79362
$146$	−1.94774e9	−0.354766
$147$	6.71836e8	0.118669
$148$	−8.36127e8	−0.143250
$149$	−1.88476e9	−0.313269	−0.156634	−	0.987657i	$-0.550064\pi$
$149$	−1.88476e9	−0.313269	−0.156634	+	0.987657i	$0.550064\pi$
$150$	−3.83787e8	−0.0618984
$151$	−2.86811e9	−0.448951	−0.224475	−	0.974480i	$-0.572067\pi$
$151$	−2.86811e9	−0.448951	−0.224475	+	0.974480i	$0.572067\pi$
$152$	4.87507e9	0.740773
$153$	2.32938e8	0.0343661
$154$	2.88760e9	0.413708
$155$	1.05556e10	1.46889
$156$	−2.97340e8	−0.0401969
$157$	−4.92639e9	−0.647113	−0.323557	−	0.946209i	$-0.604879\pi$
$157$	−4.92639e9	−0.647113	−0.323557	+	0.946209i	$0.604879\pi$
$158$	5.19533e9	0.663217
$159$	7.89224e9	0.979295
$160$	−2.95815e9	−0.356845
$161$	−1.99683e9	−0.234220
$162$	5.64269e9	0.643678
$163$	−2.80810e9	−0.311579	−0.155790	−	0.987790i	$-0.549792\pi$
$163$	−2.80810e9	−0.311579	−0.155790	+	0.987790i	$0.549792\pi$
$164$	2.59211e8	0.0279806
$165$	8.25796e9	0.867351
$166$	−2.02788e10	−2.07280
$167$	1.13192e10	1.12614	0.563070	−	0.826409i	$-0.309620\pi$
$167$	1.13192e10	1.12614	0.563070	+	0.826409i	$0.309620\pi$
$168$	2.90021e9	0.280891
$169$	8.15731e8	0.0769231
$170$	−1.35266e9	−0.124214
$171$	−2.86970e9	−0.256658
$172$	−1.57652e9	−0.137348
$173$	−2.16249e10	−1.83547	−0.917734	−	0.397196i	$-0.869983\pi$
$173$	−2.16249e10	−1.83547	−0.917734	+	0.397196i	$0.869983\pi$
$174$	−1.88851e10	−1.56188
$175$	3.22438e8	0.0259881
$176$	1.47085e10	1.15547
$177$	−9.22038e9	−0.706105
$178$	−1.48549e10	−1.10912
$179$	−1.14517e10	−0.833740	−0.416870	−	0.908966i	$-0.636873\pi$
$179$	−1.14517e10	−0.833740	−0.416870	+	0.908966i	$0.636873\pi$
$180$	7.87441e8	0.0559103
$181$	−2.25155e10	−1.55930	−0.779648	−	0.626218i	$-0.784602\pi$
$181$	−2.25155e10	−1.55930	−0.779648	+	0.626218i	$0.784602\pi$
$182$	1.68160e9	0.113606
$183$	2.06982e10	1.36428
$184$	−8.61996e9	−0.554402
$185$	1.35231e10	0.848798
$186$	2.08791e10	1.27910
$187$	1.87248e9	0.111977
$188$	2.05039e9	0.119709
$189$	−7.21480e9	−0.411288
$190$	1.66642e10	0.927671
$191$	7.30694e9	0.397270	0.198635	−	0.980074i	$-0.436349\pi$
$191$	7.30694e9	0.397270	0.198635	+	0.980074i	$0.436349\pi$
$192$	1.20435e10	0.639586
$193$	−5.56638e9	−0.288778	−0.144389	−	0.989521i	$-0.546122\pi$
$193$	−5.56638e9	−0.288778	−0.144389	+	0.989521i	$0.546122\pi$
$194$	−3.63670e10	−1.84332
$195$	4.80903e9	0.238178
$196$	5.14973e8	0.0249248
$197$	−1.58629e10	−0.750387	−0.375193	−	0.926947i	$-0.622424\pi$
$197$	−1.58629e10	−0.750387	−0.375193	+	0.926947i	$0.622424\pi$
$198$	−7.33767e9	−0.339285
$199$	3.43415e9	0.155232	0.0776158	−	0.996983i	$-0.475269\pi$
$199$	3.43415e9	0.155232	0.0776158	+	0.996983i	$0.475269\pi$
$200$	1.39191e9	0.0615143
$201$	3.05932e10	1.32203
$202$	1.97205e10	0.833368
$203$	1.58663e10	0.655757
$204$	−3.97473e8	−0.0160684
$205$	−4.19236e9	−0.165793
$206$	2.90681e10	1.12464
$207$	5.07412e9	0.192085
$208$	8.56548e9	0.317298
$209$	−2.30681e10	−0.836284
$210$	9.91363e9	0.351760
$211$	1.15845e10	0.402351	0.201175	−	0.979555i	$-0.435524\pi$
$211$	1.15845e10	0.402351	0.201175	+	0.979555i	$0.435524\pi$
$212$	6.04953e9	0.205689
$213$	1.31116e10	0.436463
$214$	2.38083e9	0.0776010
$215$	2.54978e10	0.813823
$216$	−3.11451e10	−0.973527
$217$	−1.75416e10	−0.537031
$218$	5.00376e8	0.0150052
$219$	9.25663e9	0.271928
$220$	6.32985e9	0.182176
$221$	1.09044e9	0.0307494
$222$	2.67490e10	0.739128
$223$	−4.95641e9	−0.134213	−0.0671066	−	0.997746i	$-0.521377\pi$
$223$	−4.95641e9	−0.134213	−0.0671066	+	0.997746i	$0.521377\pi$
$224$	4.91595e9	0.130464
$225$	−8.19345e8	−0.0213130
$226$	−6.61813e10	−1.68751
$227$	−1.27893e10	−0.319692	−0.159846	−	0.987142i	$-0.551100\pi$
$227$	−1.27893e10	−0.319692	−0.159846	+	0.987142i	$0.551100\pi$
$228$	4.89670e9	0.120004
$229$	5.87188e10	1.41097	0.705485	−	0.708725i	$-0.250729\pi$
$229$	5.87188e10	1.41097	0.705485	+	0.708725i	$0.250729\pi$
$230$	−2.94652e10	−0.694279
$231$	−1.37233e10	−0.317107
$232$	6.84921e10	1.55219
$233$	4.93019e10	1.09588	0.547939	−	0.836518i	$-0.315413\pi$
$233$	4.93019e10	1.09588	0.547939	+	0.836518i	$0.315413\pi$
$234$	−4.27310e9	−0.0931690
$235$	−3.31620e10	−0.709309
$236$	−7.06757e9	−0.148308
$237$	−2.46908e10	−0.508356
$238$	2.24790e9	0.0454131
$239$	9.01844e10	1.78789	0.893946	−	0.448175i	$-0.147926\pi$
$239$	9.01844e10	1.78789	0.893946	+	0.448175i	$0.147926\pi$
$240$	5.04966e10	0.982453
$241$	3.29788e10	0.629735	0.314868	−	0.949136i	$-0.398040\pi$
$241$	3.29788e10	0.629735	0.314868	+	0.949136i	$0.398040\pi$
$242$	−1.16225e9	−0.0217837
$243$	3.23288e10	0.594787
$244$	1.58655e10	0.286550
$245$	−8.32893e9	−0.147687
$246$	−8.29258e9	−0.144372
$247$	−1.34337e10	−0.229647
$248$	−7.57240e10	−1.27116
$249$	9.63752e10	1.58880
$250$	−6.44398e10	−1.04334
$251$	2.44144e10	0.388253	0.194127	−	0.980976i	$-0.437813\pi$
$251$	2.44144e10	0.388253	0.194127	+	0.980976i	$0.437813\pi$
$252$	−1.30860e9	−0.0204410
$253$	4.07884e10	0.625884
$254$	−8.22230e10	−1.23949
$255$	6.42854e9	0.0952098
$256$	3.49380e10	0.508415
$257$	−1.08665e11	−1.55379	−0.776894	−	0.629632i	$-0.783206\pi$
$257$	−1.08665e11	−1.55379	−0.776894	+	0.629632i	$0.783206\pi$
$258$	5.04353e10	0.708673
$259$	−2.24732e10	−0.310324
$260$	3.68620e9	0.0500263
$261$	−4.03177e10	−0.537791
$262$	3.05678e10	0.400782
$263$	−6.96905e9	−0.0898200	−0.0449100	−	0.998991i	$-0.514300\pi$
$263$	−6.96905e9	−0.0898200	−0.0449100	+	0.998991i	$0.514300\pi$
$264$	−5.92414e10	−0.750598
$265$	−9.78421e10	−1.21876
$266$	−2.76932e10	−0.339160
$267$	7.05981e10	0.850143
$268$	2.34502e10	0.277677
$269$	−1.57135e10	−0.182974	−0.0914868	−	0.995806i	$-0.529162\pi$
$269$	−1.57135e10	−0.182974	−0.0914868	+	0.995806i	$0.529162\pi$
$270$	−1.06462e11	−1.21915
$271$	2.65566e9	0.0299096	0.0149548	−	0.999888i	$-0.495240\pi$
$271$	2.65566e9	0.0299096	0.0149548	+	0.999888i	$0.495240\pi$
$272$	1.14500e10	0.126837
$273$	−7.99180e9	−0.0870789
$274$	−1.50619e11	−1.61436
$275$	−6.58632e9	−0.0694457
$276$	−8.65820e9	−0.0898125
$277$	1.49354e11	1.52425	0.762127	−	0.647428i	$-0.224155\pi$
$277$	1.49354e11	1.52425	0.762127	+	0.647428i	$0.224155\pi$
$278$	8.27825e10	0.831260
$279$	4.45748e10	0.440423
$280$	−3.59546e10	−0.349577
$281$	6.48073e10	0.620077	0.310038	−	0.950724i	$-0.399658\pi$
$281$	6.48073e10	0.620077	0.310038	+	0.950724i	$0.399658\pi$
$282$	−6.55952e10	−0.617662
$283$	5.82399e10	0.539736	0.269868	−	0.962897i	$-0.413020\pi$
$283$	5.82399e10	0.539736	0.269868	+	0.962897i	$0.413020\pi$
$284$	1.00502e10	0.0916736
$285$	−7.91968e10	−0.711059
$286$	−3.43494e10	−0.303579
$287$	6.96700e9	0.0606146
$288$	−1.24919e10	−0.106995
$289$	−1.17130e11	−0.987708
$290$	2.34123e11	1.94381
$291$	1.72834e11	1.41290
$292$	7.09535e9	0.0571151
$293$	−1.14689e11	−0.909116	−0.454558	−	0.890717i	$-0.650203\pi$
$293$	−1.14689e11	−0.909116	−0.454558	+	0.890717i	$0.650203\pi$
$294$	−1.64748e10	−0.128605
$295$	1.14307e11	0.878770
$296$	−9.70129e10	−0.734542
$297$	1.47374e11	1.09905
$298$	4.62180e10	0.339499
$299$	2.37532e10	0.171870
$300$	1.39808e9	0.00996524
$301$	−4.23731e10	−0.297537
$302$	7.03318e10	0.486542
$303$	−9.37218e10	−0.638776
$304$	−1.41059e11	−0.947264
$305$	−2.56601e11	−1.69789
$306$	−5.71213e9	−0.0372436
$307$	−1.33714e11	−0.859118	−0.429559	−	0.903039i	$-0.641331\pi$
$307$	−1.33714e11	−0.859118	−0.429559	+	0.903039i	$0.641331\pi$
$308$	−1.05192e10	−0.0666044
$309$	−1.38146e11	−0.862036
$310$	−2.58844e11	−1.59188
$311$	6.82682e10	0.413806	0.206903	−	0.978361i	$-0.433662\pi$
$311$	6.82682e10	0.413806	0.206903	+	0.978361i	$0.433662\pi$
$312$	−3.44993e10	−0.206117
$313$	−1.44719e11	−0.852270	−0.426135	−	0.904660i	$-0.640125\pi$
$313$	−1.44719e11	−0.852270	−0.426135	+	0.904660i	$0.640125\pi$
$314$	1.20805e11	0.701297
$315$	2.11646e10	0.121119
$316$	−1.89259e10	−0.106774
$317$	2.38329e11	1.32560	0.662798	−	0.748799i	$-0.269369\pi$
$317$	2.38329e11	1.32560	0.662798	+	0.748799i	$0.269369\pi$
$318$	−1.93534e11	−1.06129
$319$	−3.24094e11	−1.75232
$320$	−1.49307e11	−0.795985
$321$	−1.13149e10	−0.0594811
$322$	4.89662e10	0.253831
$323$	−1.79578e10	−0.0917996
$324$	−2.05556e10	−0.103628
$325$	−3.83555e9	−0.0190701
$326$	6.88603e10	0.337668
$327$	−2.37804e9	−0.0115015
$328$	3.00754e10	0.143476
$329$	5.51097e10	0.259326
$330$	−2.02502e11	−0.939975
$331$	−3.16229e11	−1.44802	−0.724011	−	0.689788i	$-0.757704\pi$
$331$	−3.16229e11	−1.44802	−0.724011	+	0.689788i	$0.757704\pi$
$332$	7.38731e10	0.333707
$333$	5.71064e10	0.254499
$334$	−2.77571e11	−1.22043
$335$	−3.79271e11	−1.64531
$336$	−8.39170e10	−0.359189
$337$	−2.91650e11	−1.23176	−0.615881	−	0.787839i	$-0.711200\pi$
$337$	−2.91650e11	−1.23176	−0.615881	+	0.787839i	$0.711200\pi$
$338$	−2.00034e10	−0.0833640
$339$	3.14527e11	1.29348
$340$	4.92758e9	0.0199976
$341$	3.58315e11	1.43506
$342$	7.03709e10	0.278148
$343$	1.38413e10	0.0539949
$344$	−1.82918e11	−0.704276
$345$	1.40033e11	0.532165
$346$	5.30287e11	1.98915
$347$	−5.46530e10	−0.202363	−0.101182	−	0.994868i	$-0.532262\pi$
$347$	−5.46530e10	−0.202363	−0.101182	+	0.994868i	$0.532262\pi$
$348$	6.87959e10	0.251452
$349$	−4.66258e10	−0.168233	−0.0841166	−	0.996456i	$-0.526807\pi$
$349$	−4.66258e10	−0.168233	−0.0841166	+	0.996456i	$0.526807\pi$
$350$	−7.90684e9	−0.0281641
$351$	8.58234e10	0.301803
$352$	−1.00416e11	−0.348627
$353$	2.93801e11	1.00709	0.503544	−	0.863969i	$-0.332029\pi$
$353$	2.93801e11	1.00709	0.503544	+	0.863969i	$0.332029\pi$
$354$	2.26103e11	0.765228
$355$	−1.62548e11	−0.543192
$356$	5.41145e10	0.178562
$357$	−1.06832e10	−0.0348091
$358$	2.80819e11	0.903550
$359$	4.75889e11	1.51210	0.756051	−	0.654513i	$-0.227126\pi$
$359$	4.75889e11	1.51210	0.756051	+	0.654513i	$0.227126\pi$
$360$	9.13640e10	0.286691
$361$	−1.01456e11	−0.314409
$362$	5.52127e11	1.68986
$363$	5.52361e9	0.0166972
$364$	−6.12584e9	−0.0182898
$365$	−1.14757e11	−0.338423
$366$	−5.07563e11	−1.47851
$367$	6.30522e11	1.81427	0.907137	−	0.420835i	$-0.138263\pi$
$367$	6.30522e11	1.81427	0.907137	+	0.420835i	$0.138263\pi$
$368$	2.49417e11	0.708943
$369$	−1.77038e10	−0.0497105
$370$	−3.31615e11	−0.919869
$371$	1.62597e11	0.445585
$372$	−7.60599e10	−0.205927
$373$	−5.81257e11	−1.55481	−0.777407	−	0.628998i	$-0.783465\pi$
$373$	−5.81257e11	−1.55481	−0.777407	+	0.628998i	$0.783465\pi$
$374$	−4.59170e10	−0.121353
$375$	3.06250e11	0.799716
$376$	2.37899e11	0.613830
$377$	−1.88737e11	−0.481194
$378$	1.76922e11	0.445726
$379$	−2.27515e11	−0.566414	−0.283207	−	0.959059i	$-0.591398\pi$
$379$	−2.27515e11	−0.566414	−0.283207	+	0.959059i	$0.591398\pi$
$380$	−6.07056e10	−0.149349
$381$	3.90765e11	0.950066
$382$	−1.79181e11	−0.430534
$383$	3.35067e11	0.795679	0.397839	−	0.917455i	$-0.369760\pi$
$383$	3.35067e11	0.795679	0.397839	+	0.917455i	$0.369760\pi$
$384$	−4.17502e11	−0.979870
$385$	1.70132e11	0.394650
$386$	1.36499e11	0.312958
$387$	1.07674e11	0.244012
$388$	1.32480e11	0.296762
$389$	6.97803e11	1.54511	0.772556	−	0.634947i	$-0.218978\pi$
$389$	6.97803e11	1.54511	0.772556	+	0.634947i	$0.218978\pi$
$390$	−1.17927e11	−0.258121
$391$	3.17524e10	0.0687038
$392$	5.97505e10	0.127807
$393$	−1.45274e11	−0.307200
$394$	3.88991e11	0.813218
$395$	3.06098e11	0.632665
$396$	2.67302e10	0.0546227
$397$	3.64945e10	0.0737343	0.0368672	−	0.999320i	$-0.488262\pi$
$397$	3.64945e10	0.0737343	0.0368672	+	0.999320i	$0.488262\pi$
$398$	−8.42123e10	−0.168229
$399$	1.31612e11	0.259966
$400$	−4.02747e10	−0.0786615
$401$	8.83833e11	1.70695	0.853474	−	0.521135i	$-0.174491\pi$
$401$	8.83833e11	1.70695	0.853474	+	0.521135i	$0.174491\pi$
$402$	−7.50207e11	−1.43273
$403$	2.08665e11	0.394073
$404$	−7.18392e10	−0.134167
$405$	3.32456e11	0.614026
$406$	−3.89074e11	−0.710664
$407$	4.59051e11	0.829251
$408$	−4.61174e10	−0.0823938
$409$	−2.60141e11	−0.459678	−0.229839	−	0.973229i	$-0.573820\pi$
$409$	−2.60141e11	−0.459678	−0.229839	+	0.973229i	$0.573820\pi$
$410$	1.02805e11	0.179675
$411$	7.15816e11	1.23741
$412$	−1.05891e11	−0.181060
$413$	−1.89960e11	−0.321282
$414$	−1.24428e11	−0.208169
$415$	−1.19479e12	−1.97731
$416$	−5.84774e10	−0.0957345
$417$	−3.93424e11	−0.637160
$418$	5.65678e11	0.906308
$419$	5.18597e11	0.821991	0.410995	−	0.911637i	$-0.365181\pi$
$419$	5.18597e11	0.821991	0.410995	+	0.911637i	$0.365181\pi$
$420$	−3.61141e10	−0.0566310
$421$	8.95089e11	1.38866	0.694332	−	0.719655i	$-0.255700\pi$
$421$	8.95089e11	1.38866	0.694332	+	0.719655i	$0.255700\pi$
$422$	−2.84075e11	−0.436040
$423$	−1.40039e11	−0.212675
$424$	7.01906e11	1.05471
$425$	−5.12722e9	−0.00762311
$426$	−3.21523e11	−0.473009
$427$	4.26428e11	0.620755
$428$	−8.67307e9	−0.0124933
$429$	1.63245e11	0.232693
$430$	−6.25259e11	−0.881966
$431$	−8.16697e11	−1.14002	−0.570011	−	0.821637i	$-0.693061\pi$
$431$	−8.16697e11	−1.14002	−0.570011	+	0.821637i	$0.693061\pi$
$432$	9.01178e11	1.24490
$433$	1.05283e11	0.143934	0.0719668	−	0.997407i	$-0.477072\pi$
$433$	1.05283e11	0.143934	0.0719668	+	0.997407i	$0.477072\pi$
$434$	4.30155e11	0.581998
$435$	−1.11267e12	−1.48993
$436$	−1.82281e9	−0.00241575
$437$	−3.91175e11	−0.513104
$438$	−2.26991e11	−0.294697
$439$	−3.99014e11	−0.512741	−0.256371	−	0.966579i	$-0.582527\pi$
$439$	−3.99014e11	−0.512741	−0.256371	+	0.966579i	$0.582527\pi$
$440$	7.34431e11	0.934144
$441$	−3.51720e10	−0.0442816
$442$	−2.67398e10	−0.0333241
$443$	1.28403e12	1.58401	0.792003	−	0.610517i	$-0.209038\pi$
$443$	1.28403e12	1.58401	0.792003	+	0.610517i	$0.209038\pi$
$444$	−9.74432e10	−0.118995
$445$	−8.75222e11	−1.05803
$446$	1.21541e11	0.145451
$447$	−2.19651e11	−0.260226
$448$	2.48123e11	0.291016
$449$	−8.97598e11	−1.04225	−0.521127	−	0.853479i	$-0.674488\pi$
$449$	−8.97598e11	−1.04225	−0.521127	+	0.853479i	$0.674488\pi$
$450$	2.00920e10	0.0230976
$451$	−1.42312e11	−0.161975
$452$	2.41090e11	0.271679
$453$	−3.34252e11	−0.372934
$454$	3.13621e11	0.346460
$455$	9.90764e10	0.108372
$456$	5.68147e11	0.615345
$457$	3.99985e11	0.428964	0.214482	−	0.976728i	$-0.431194\pi$
$457$	3.99985e11	0.428964	0.214482	+	0.976728i	$0.431194\pi$
$458$	−1.43991e12	−1.52911
$459$	1.14726e11	0.120643
$460$	1.07338e11	0.111774
$461$	−1.87092e12	−1.92930	−0.964651	−	0.263530i	$-0.915113\pi$
$461$	−1.87092e12	−1.92930	−0.964651	+	0.263530i	$0.915113\pi$
$462$	3.36524e11	0.343659
$463$	−9.15849e11	−0.926210	−0.463105	−	0.886303i	$-0.653265\pi$
$463$	−9.15849e11	−0.926210	−0.463105	+	0.886303i	$0.653265\pi$
$464$	−1.98181e12	−1.98486
$465$	1.23016e12	1.22017
$466$	−1.20898e12	−1.18764
$467$	4.39124e11	0.427230	0.213615	−	0.976918i	$-0.431476\pi$
$467$	4.39124e11	0.427230	0.213615	+	0.976918i	$0.431476\pi$
$468$	1.55663e10	0.0149996
$469$	6.30286e11	0.601533
$470$	8.13200e11	0.768700
$471$	−5.74127e11	−0.537544
$472$	−8.20025e11	−0.760481
$473$	8.65540e11	0.795082
$474$	6.05469e11	0.550921
$475$	6.31652e10	0.0569320
$476$	−8.18881e9	−0.00731121
$477$	−4.13175e11	−0.365428
$478$	−2.21151e12	−1.93759
$479$	2.00347e11	0.173889	0.0869446	−	0.996213i	$-0.472290\pi$
$479$	2.00347e11	0.173889	0.0869446	+	0.996213i	$0.472290\pi$
$480$	−3.44746e11	−0.296424
$481$	2.67329e11	0.227716
$482$	−8.08707e11	−0.682464
$483$	−2.32712e11	−0.194562
$484$	4.23394e9	0.00350704
$485$	−2.14267e12	−1.75840
$486$	−7.92769e11	−0.644590
$487$	−8.93718e11	−0.719980	−0.359990	−	0.932956i	$-0.617220\pi$
$487$	−8.93718e11	−0.719980	−0.359990	+	0.932956i	$0.617220\pi$
$488$	1.84082e12	1.46934
$489$	−3.27259e11	−0.258822
$490$	2.04242e11	0.160053
$491$	−1.11154e12	−0.863098	−0.431549	−	0.902089i	$-0.642033\pi$
$491$	−1.11154e12	−0.863098	−0.431549	+	0.902089i	$0.642033\pi$
$492$	3.02088e10	0.0232429
$493$	−2.52296e11	−0.192353
$494$	3.29423e11	0.248876
$495$	−4.32321e11	−0.323655
$496$	2.19106e12	1.62550
$497$	2.70127e11	0.198593
$498$	−2.36332e12	−1.72183
$499$	−1.53332e12	−1.10708	−0.553542	−	0.832821i	$-0.686724\pi$
$499$	−1.53332e12	−1.10708	−0.553542	+	0.832821i	$0.686724\pi$
$500$	2.34746e11	0.167970
$501$	1.31916e12	0.935462
$502$	−5.98692e11	−0.420762
$503$	1.20226e12	0.837419	0.418710	−	0.908120i	$-0.362483\pi$
$503$	1.20226e12	0.837419	0.418710	+	0.908120i	$0.362483\pi$
$504$	−1.51832e11	−0.104815
$505$	1.16189e12	0.794978
$506$	−1.00021e12	−0.678291
$507$	9.50662e10	0.0638984
$508$	2.99528e11	0.199549
$509$	1.45703e12	0.962140	0.481070	−	0.876682i	$-0.340248\pi$
$509$	1.45703e12	0.962140	0.481070	+	0.876682i	$0.340248\pi$
$510$	−1.57641e11	−0.103182
$511$	1.90707e11	0.123729
$512$	9.77462e11	0.628615
$513$	−1.41337e12	−0.901006
$514$	2.66469e12	1.68389
$515$	1.71263e12	1.07283
$516$	−1.83729e11	−0.114092
$517$	−1.12570e12	−0.692974
$518$	5.51088e11	0.336308
$519$	−2.52019e12	−1.52469
$520$	4.27696e11	0.256520
$521$	5.55078e11	0.330053	0.165027	−	0.986289i	$-0.447229\pi$
$521$	5.55078e11	0.330053	0.165027	+	0.986289i	$0.447229\pi$
$522$	9.88672e11	0.582821
$523$	1.40050e12	0.818513	0.409256	−	0.912419i	$-0.365788\pi$
$523$	1.40050e12	0.818513	0.409256	+	0.912419i	$0.365788\pi$
$524$	−1.11355e11	−0.0645234
$525$	3.75773e10	0.0215878
$526$	1.70895e11	0.0973407
$527$	2.78936e11	0.157528
$528$	1.71414e12	0.959828
$529$	−1.10949e12	−0.615988
$530$	2.39929e12	1.32081
$531$	4.82706e11	0.263486
$532$	1.00883e11	0.0546027
$533$	−8.28757e10	−0.0444790
$534$	−1.73121e12	−0.921327
$535$	1.40274e11	0.0740262
$536$	2.72084e12	1.42384
$537$	−1.33459e12	−0.692571
$538$	3.85328e11	0.198294
$539$	−2.82731e11	−0.144286
$540$	3.87826e11	0.196275
$541$	2.63329e12	1.32163	0.660817	−	0.750547i	$-0.270210\pi$
$541$	2.63329e12	1.32163	0.660817	+	0.750547i	$0.270210\pi$
$542$	−6.51222e10	−0.0324140
$543$	−2.62399e12	−1.29528
$544$	−7.81706e10	−0.0382691
$545$	2.94812e10	0.0143140
$546$	1.95975e11	0.0943701
$547$	−1.50399e12	−0.718293	−0.359147	−	0.933281i	$-0.616932\pi$
$547$	−1.50399e12	−0.718293	−0.359147	+	0.933281i	$0.616932\pi$
$548$	5.48684e11	0.259902
$549$	−1.08359e12	−0.509086
$550$	1.61510e11	0.0752605
$551$	3.10818e12	1.43656
$552$	−1.00458e12	−0.460531
$553$	−5.08684e11	−0.231305
$554$	−3.66246e12	−1.65188
$555$	1.57600e12	0.705079
$556$	−3.01566e11	−0.133828
$557$	1.05623e12	0.464955	0.232478	−	0.972602i	$-0.425317\pi$
$557$	1.05623e12	0.464955	0.232478	+	0.972602i	$0.425317\pi$
$558$	−1.09306e12	−0.477300
$559$	5.04048e11	0.218333
$560$	1.04034e12	0.447022
$561$	2.18221e11	0.0930172
$562$	−1.58921e12	−0.671997
$563$	3.84939e10	0.0161475	0.00807373	−	0.999967i	$-0.497430\pi$
$563$	3.84939e10	0.0161475	0.00807373	+	0.999967i	$0.497430\pi$
$564$	2.38955e11	0.0994396
$565$	−3.89927e12	−1.60978
$566$	−1.42816e12	−0.584929
$567$	−5.52487e11	−0.224491
$568$	1.16609e12	0.470074
$569$	−1.89165e12	−0.756548	−0.378274	−	0.925694i	$-0.623482\pi$
$569$	−1.89165e12	−0.756548	−0.378274	+	0.925694i	$0.623482\pi$
$570$	1.94207e12	0.770597
$571$	2.93464e12	1.15529	0.577647	−	0.816287i	$-0.303971\pi$
$571$	2.93464e12	1.15529	0.577647	+	0.816287i	$0.303971\pi$
$572$	1.25130e11	0.0488743
$573$	8.51559e11	0.330004
$574$	−1.70845e11	−0.0656900
$575$	−1.11687e11	−0.0426085
$576$	−6.30504e11	−0.238664
$577$	−2.79641e12	−1.05029	−0.525145	−	0.851013i	$-0.675989\pi$
$577$	−2.79641e12	−1.05029	−0.525145	+	0.851013i	$0.675989\pi$
$578$	2.87227e12	1.07041
$579$	−6.48712e11	−0.239882
$580$	−8.52880e11	−0.312941
$581$	1.98554e12	0.722912
$582$	−4.23825e12	−1.53121
$583$	−3.32131e12	−1.19070
$584$	8.23248e11	0.292869
$585$	−2.51762e11	−0.0888770
$586$	2.81242e12	0.985238
$587$	3.15440e11	0.109659	0.0548296	−	0.998496i	$-0.482538\pi$
$587$	3.15440e11	0.109659	0.0548296	+	0.998496i	$0.482538\pi$
$588$	6.00156e10	0.0207046
$589$	−3.43637e12	−1.17647
$590$	−2.80305e12	−0.952351
$591$	−1.84868e12	−0.623331
$592$	2.80705e12	0.939297
$593$	3.56707e11	0.118458	0.0592291	−	0.998244i	$-0.481136\pi$
$593$	3.56707e11	0.118458	0.0592291	+	0.998244i	$0.481136\pi$
$594$	−3.61391e12	−1.19107
$595$	1.32442e11	0.0433210
$596$	−1.68366e11	−0.0546572
$597$	4.00219e11	0.128948
$598$	−5.82476e11	−0.186261
$599$	−3.98197e12	−1.26380	−0.631898	−	0.775052i	$-0.717724\pi$
$599$	−3.98197e12	−1.26380	−0.631898	+	0.775052i	$0.717724\pi$
$600$	1.62215e11	0.0510987
$601$	4.00682e12	1.25275	0.626375	−	0.779522i	$-0.284538\pi$
$601$	4.00682e12	1.25275	0.626375	+	0.779522i	$0.284538\pi$
$602$	1.03908e12	0.322451
$603$	−1.60162e12	−0.493322
$604$	−2.56210e11	−0.0783302
$605$	−6.84776e10	−0.0207802
$606$	2.29825e12	0.692262
$607$	−2.41208e12	−0.721178	−0.360589	−	0.932725i	$-0.617424\pi$
$607$	−2.41208e12	−0.721178	−0.360589	+	0.932725i	$0.617424\pi$
$608$	9.63027e11	0.285807
$609$	1.84907e12	0.544724
$610$	6.29238e12	1.84006
$611$	−6.55555e11	−0.190293
$612$	2.08085e10	0.00599598
$613$	6.21660e12	1.77820	0.889101	−	0.457712i	$-0.151331\pi$
$613$	6.21660e12	1.77820	0.889101	+	0.457712i	$0.151331\pi$
$614$	3.27893e12	0.931053
$615$	−4.88582e11	−0.137721
$616$	−1.22050e12	−0.341527
$617$	−3.76305e12	−1.04534	−0.522669	−	0.852536i	$-0.675064\pi$
$617$	−3.76305e12	−1.04534	−0.522669	+	0.852536i	$0.675064\pi$
$618$	3.38762e12	0.934216
$619$	−9.25376e10	−0.0253344	−0.0126672	−	0.999920i	$-0.504032\pi$
$619$	−9.25376e10	−0.0253344	−0.0126672	+	0.999920i	$0.504032\pi$
$620$	9.42934e11	0.256282
$621$	2.49908e12	0.674323
$622$	−1.67407e12	−0.448454
$623$	1.45447e12	0.386821
$624$	9.98231e11	0.263573
$625$	−4.05895e12	−1.06403
$626$	3.54882e12	0.923632
$627$	−2.68839e12	−0.694684
$628$	−4.40077e11	−0.112904
$629$	3.57356e11	0.0910275
$630$	−5.18999e11	−0.131260
$631$	−3.16267e12	−0.794186	−0.397093	−	0.917778i	$-0.629981\pi$
$631$	−3.16267e12	−0.794186	−0.397093	+	0.917778i	$0.629981\pi$
$632$	−2.19591e12	−0.547503
$633$	1.35007e12	0.334224
$634$	−5.84432e12	−1.43659
$635$	−4.84442e12	−1.18239
$636$	7.05019e11	0.170861
$637$	−1.64648e11	−0.0396214
$638$	7.94746e12	1.89904
$639$	−6.86419e11	−0.162868
$640$	5.17588e12	1.21948
$641$	−2.83995e12	−0.664431	−0.332216	−	0.943203i	$-0.607796\pi$
$641$	−2.83995e12	−0.664431	−0.332216	+	0.943203i	$0.607796\pi$
$642$	2.77465e11	0.0644616
$643$	3.30900e12	0.763392	0.381696	−	0.924288i	$-0.375340\pi$
$643$	3.30900e12	0.763392	0.381696	+	0.924288i	$0.375340\pi$
$644$	−1.78378e11	−0.0408652
$645$	2.97155e12	0.676026
$646$	4.40361e11	0.0994861
$647$	3.86165e12	0.866370	0.433185	−	0.901305i	$-0.357390\pi$
$647$	3.86165e12	0.866370	0.433185	+	0.901305i	$0.357390\pi$
$648$	−2.38499e12	−0.531373
$649$	3.88024e12	0.858533
$650$	9.40555e10	0.0206668
$651$	−2.04431e12	−0.446101
$652$	−2.50849e11	−0.0543624
$653$	4.49538e12	0.967513	0.483757	−	0.875203i	$-0.339272\pi$
$653$	4.49538e12	0.967513	0.483757	+	0.875203i	$0.339272\pi$
$654$	5.83144e10	0.0124645
$655$	1.80100e12	0.382320
$656$	−8.70226e11	−0.183470
$657$	−4.84603e11	−0.101471
$658$	−1.35140e12	−0.281040
$659$	8.70852e11	0.179870	0.0899352	−	0.995948i	$-0.471334\pi$
$659$	8.70852e11	0.179870	0.0899352	+	0.995948i	$0.471334\pi$
$660$	7.37688e11	0.151330
$661$	9.47768e12	1.93106	0.965530	−	0.260293i	$-0.0838192\pi$
$661$	9.47768e12	1.93106	0.965530	+	0.260293i	$0.0838192\pi$
$662$	7.75457e12	1.56927
$663$	1.27081e11	0.0255429
$664$	8.57124e12	1.71115
$665$	−1.63163e12	−0.323536
$666$	−1.40037e12	−0.275808
$667$	−5.49580e12	−1.07514
$668$	1.01115e12	0.196482
$669$	−5.77625e11	−0.111488
$670$	9.30051e12	1.78308
$671$	−8.71049e12	−1.65879
$672$	5.72910e11	0.108374
$673$	4.88363e12	0.917645	0.458822	−	0.888528i	$-0.348271\pi$
$673$	4.88363e12	0.917645	0.458822	+	0.888528i	$0.348271\pi$
$674$	7.15185e12	1.33490
$675$	−4.03540e11	−0.0748203
$676$	7.28697e10	0.0134211
$677$	−6.72067e12	−1.22960	−0.614800	−	0.788683i	$-0.710763\pi$
$677$	−6.72067e12	−1.22960	−0.614800	+	0.788683i	$0.710763\pi$
$678$	−7.71284e12	−1.40178
$679$	3.56076e12	0.642879
$680$	5.71729e11	0.102542
$681$	−1.49048e12	−0.265562
$682$	−8.78661e12	−1.55522
$683$	−4.22767e12	−0.743375	−0.371688	−	0.928358i	$-0.621221\pi$
$683$	−4.22767e12	−0.743375	−0.371688	+	0.928358i	$0.621221\pi$
$684$	−2.56352e11	−0.0447800
$685$	−8.87415e12	−1.54000
$686$	−3.39417e11	−0.0585160
$687$	6.84316e12	1.17206
$688$	5.29269e12	0.900594
$689$	−1.93417e12	−0.326970
$690$	−3.43391e12	−0.576723
$691$	9.91172e11	0.165386	0.0826928	−	0.996575i	$-0.473648\pi$
$691$	9.91172e11	0.165386	0.0826928	+	0.996575i	$0.473648\pi$
$692$	−1.93177e12	−0.320241
$693$	7.18445e11	0.118330
$694$	1.34020e12	0.219307
$695$	4.87738e12	0.792967
$696$	7.98214e12	1.28937
$697$	−1.10785e11	−0.0177801
$698$	1.14336e12	0.182320
$699$	5.74570e12	0.910324
$700$	2.88036e10	0.00453425
$701$	−4.83583e11	−0.0756380	−0.0378190	−	0.999285i	$-0.512041\pi$
$701$	−4.83583e11	−0.0756380	−0.0378190	+	0.999285i	$0.512041\pi$
$702$	−2.10457e12	−0.327073
$703$	−4.40246e12	−0.679825
$704$	−5.06832e12	−0.777655
$705$	−3.86474e12	−0.589208
$706$	−7.20461e12	−1.09141
$707$	−1.93087e12	−0.290647
$708$	−8.23662e11	−0.123197
$709$	−8.97502e12	−1.33391	−0.666956	−	0.745097i	$-0.732403\pi$
$709$	−8.97502e12	−1.33391	−0.666956	+	0.745097i	$0.732403\pi$
$710$	3.98600e12	0.588675
$711$	1.29261e12	0.189695
$712$	6.27872e12	0.915611
$713$	6.07609e12	0.880483
$714$	2.61973e11	0.0377237
$715$	−2.02380e12	−0.289594
$716$	−1.02299e12	−0.145466
$717$	1.05102e13	1.48516
$718$	−1.16698e13	−1.63871
$719$	−1.11693e13	−1.55865	−0.779323	−	0.626622i	$-0.784437\pi$
$719$	−1.11693e13	−1.55865	−0.779323	+	0.626622i	$0.784437\pi$
$720$	−2.64360e12	−0.366606
$721$	−2.84611e12	−0.392232
$722$	2.48791e12	0.340735
$723$	3.84339e12	0.523108
$724$	−2.01133e12	−0.272056
$725$	8.87435e11	0.119293
$726$	−1.35450e11	−0.0180953
$727$	−2.20700e12	−0.293021	−0.146510	−	0.989209i	$-0.546804\pi$
$727$	−2.20700e12	−0.293021	−0.146510	+	0.989209i	$0.546804\pi$
$728$	−7.10760e11	−0.0937847
$729$	8.29683e12	1.08802
$730$	2.81407e12	0.366760
$731$	6.73793e11	0.0872768
$732$	1.84898e12	0.238031
$733$	1.33520e12	0.170836	0.0854179	−	0.996345i	$-0.472777\pi$
$733$	1.33520e12	0.170836	0.0854179	+	0.996345i	$0.472777\pi$
$734$	−1.54617e13	−1.96619
$735$	−9.70663e11	−0.122680
$736$	−1.70280e12	−0.213901
$737$	−1.28746e13	−1.60742
$738$	4.34133e11	0.0538728
$739$	−8.52891e12	−1.05195	−0.525973	−	0.850501i	$-0.676299\pi$
$739$	−8.52891e12	−1.05195	−0.525973	+	0.850501i	$0.676299\pi$
$740$	1.20803e12	0.148093
$741$	−1.56558e12	−0.190763
$742$	−3.98722e12	−0.482895
$743$	1.44790e13	1.74296	0.871481	−	0.490429i	$-0.163160\pi$
$743$	1.44790e13	1.74296	0.871481	+	0.490429i	$0.163160\pi$
$744$	−8.82496e12	−1.05593
$745$	2.72308e12	0.323859
$746$	1.42536e13	1.68500
$747$	−5.04544e12	−0.592866
$748$	1.67270e11	0.0195371
$749$	−2.33112e11	−0.0270643
$750$	−7.50988e12	−0.866677
$751$	8.79536e12	1.00896	0.504480	−	0.863423i	$-0.331684\pi$
$751$	8.79536e12	1.00896	0.504480	+	0.863423i	$0.331684\pi$
$752$	−6.88358e12	−0.784936
$753$	2.84529e12	0.322514
$754$	4.62821e12	0.521485
$755$	4.14381e12	0.464129
$756$	−6.44503e11	−0.0717591
$757$	3.51435e12	0.388968	0.194484	−	0.980906i	$-0.437697\pi$
$757$	3.51435e12	0.388968	0.194484	+	0.980906i	$0.437697\pi$
$758$	5.57914e12	0.613841
$759$	4.75352e12	0.519909
$760$	−7.04346e12	−0.765816
$761$	1.51129e12	0.163349	0.0816745	−	0.996659i	$-0.473973\pi$
$761$	1.51129e12	0.163349	0.0816745	+	0.996659i	$0.473973\pi$
$762$	−9.58236e12	−1.02962
$763$	−4.89928e10	−0.00523325
$764$	6.52734e11	0.0693132
$765$	−3.36547e11	−0.0355279
$766$	−8.21654e12	−0.862302
$767$	2.25966e12	0.235757
$768$	4.07171e12	0.422330
$769$	−1.22659e13	−1.26483	−0.632413	−	0.774631i	$-0.717936\pi$
$769$	−1.22659e13	−1.26483	−0.632413	+	0.774631i	$0.717936\pi$
$770$	−4.17198e12	−0.427695
$771$	−1.26640e13	−1.29070
$772$	−4.97248e11	−0.0503843
$773$	8.10306e12	0.816284	0.408142	−	0.912918i	$-0.366177\pi$
$773$	8.10306e12	0.816284	0.408142	+	0.912918i	$0.366177\pi$
$774$	−2.64039e12	−0.264444
$775$	−9.81138e11	−0.0976950
$776$	1.53712e13	1.52171
$777$	−2.61905e12	−0.257780
$778$	−1.71116e13	−1.67449
$779$	1.36483e12	0.132788
$780$	4.29593e11	0.0415558
$781$	−5.51779e12	−0.530683
$782$	−7.78633e11	−0.0744565
$783$	−1.98571e13	−1.88794
$784$	−1.72887e12	−0.163433
$785$	7.11760e12	0.668990
$786$	3.56241e12	0.332922
$787$	6.31120e12	0.586443	0.293221	−	0.956045i	$-0.405273\pi$
$787$	6.31120e12	0.586443	0.293221	+	0.956045i	$0.405273\pi$
$788$	−1.41704e12	−0.130923
$789$	−8.12181e11	−0.0746116
$790$	−7.50616e12	−0.685639
$791$	6.47994e12	0.588541
$792$	3.10141e12	0.280089
$793$	−5.07256e12	−0.455510
$794$	−8.94919e11	−0.0799082
$795$	−1.14026e13	−1.01240
$796$	3.06775e11	0.0270839
$797$	1.02585e12	0.0900580	0.0450290	−	0.998986i	$-0.485662\pi$
$797$	1.02585e12	0.0900580	0.0450290	+	0.998986i	$0.485662\pi$
$798$	−3.22739e12	−0.281734
$799$	−8.76323e11	−0.0760683
$800$	2.74960e11	0.0237336
$801$	−3.69595e12	−0.317234
$802$	−2.16734e13	−1.84987
$803$	−3.89549e12	−0.330630
$804$	2.73291e12	0.230660
$805$	2.88499e12	0.242138
$806$	−5.11689e12	−0.427069
$807$	−1.83127e12	−0.151993
$808$	−8.33526e12	−0.687967
$809$	1.43138e13	1.17486	0.587429	−	0.809276i	$-0.300140\pi$
$809$	1.43138e13	1.17486	0.587429	+	0.809276i	$0.300140\pi$
$810$	−8.15251e12	−0.665440
$811$	1.53992e13	1.24998	0.624990	−	0.780633i	$-0.285103\pi$
$811$	1.53992e13	1.24998	0.624990	+	0.780633i	$0.285103\pi$
$812$	1.41734e12	0.114412
$813$	3.09494e11	0.0248453
$814$	−1.12569e13	−0.898685
$815$	4.05711e12	0.322113
$816$	1.33440e12	0.105361
$817$	−8.30084e12	−0.651813
$818$	6.37918e12	0.498167
$819$	4.18387e11	0.0324938
$820$	−3.74506e11	−0.0289265
$821$	4.49933e12	0.345624	0.172812	−	0.984955i	$-0.444715\pi$
$821$	4.49933e12	0.345624	0.172812	+	0.984955i	$0.444715\pi$
$822$	−1.75533e13	−1.34102
$823$	1.17134e13	0.889984	0.444992	−	0.895535i	$-0.353207\pi$
$823$	1.17134e13	0.889984	0.444992	+	0.895535i	$0.353207\pi$
$824$	−1.22862e13	−0.928420
$825$	−7.67577e11	−0.0576871
$826$	4.65820e12	0.348184
$827$	−6.84762e12	−0.509055	−0.254528	−	0.967066i	$-0.581920\pi$
$827$	−6.84762e12	−0.509055	−0.254528	+	0.967066i	$0.581920\pi$
$828$	4.53274e11	0.0335139
$829$	4.55576e12	0.335016	0.167508	−	0.985871i	$-0.446428\pi$
$829$	4.55576e12	0.335016	0.167508	+	0.985871i	$0.446428\pi$
$830$	2.92986e13	2.14287
$831$	1.74059e13	1.26617
$832$	−2.95154e12	−0.213547
$833$	−2.20096e11	−0.0158384
$834$	9.64756e12	0.690511
$835$	−1.63539e13	−1.16421
$836$	−2.06069e12	−0.145910
$837$	2.19537e13	1.54612
$838$	−1.27171e13	−0.890817
$839$	2.33133e13	1.62433	0.812165	−	0.583428i	$-0.198289\pi$
$839$	2.33133e13	1.62433	0.812165	+	0.583428i	$0.198289\pi$
$840$	−4.19019e12	−0.290387
$841$	2.91611e13	2.01012
$842$	−2.19494e13	−1.50494
$843$	7.55272e12	0.515085
$844$	1.03485e12	0.0701996
$845$	−1.17856e12	−0.0795237
$846$	3.43404e12	0.230483
$847$	1.13798e11	0.00759733
$848$	−2.03095e13	−1.34871
$849$	6.78734e12	0.448348
$850$	1.25730e11	0.00826140
$851$	7.78431e12	0.508788
$852$	1.17127e12	0.0761514
$853$	2.01490e13	1.30312	0.651559	−	0.758598i	$-0.274115\pi$
$853$	2.01490e13	1.30312	0.651559	+	0.758598i	$0.274115\pi$
$854$	−1.04569e13	−0.672732
$855$	4.14611e12	0.265334
$856$	−1.00631e12	−0.0640616
$857$	−1.14927e12	−0.0727796	−0.0363898	−	0.999338i	$-0.511586\pi$
$857$	−1.14927e12	−0.0727796	−0.0363898	+	0.999338i	$0.511586\pi$
$858$	−4.00311e12	−0.252177
$859$	−5.31835e12	−0.333279	−0.166639	−	0.986018i	$-0.553292\pi$
$859$	−5.31835e12	−0.333279	−0.166639	+	0.986018i	$0.553292\pi$
$860$	2.27774e12	0.141991
$861$	8.11942e11	0.0503513
$862$	2.00271e13	1.23548
$863$	1.23472e13	0.757741	0.378870	−	0.925450i	$-0.376313\pi$
$863$	1.23472e13	0.757741	0.378870	+	0.925450i	$0.376313\pi$
$864$	−6.15244e12	−0.375609
$865$	3.12434e13	1.89752
$866$	−2.58175e12	−0.155985
$867$	−1.36505e13	−0.820469
$868$	−1.56700e12	−0.0936979
$869$	1.03907e13	0.618096
$870$	2.72850e13	1.61468
$871$	−7.49754e12	−0.441405
$872$	−2.11494e11	−0.0123872
$873$	−9.04823e12	−0.527230
$874$	9.59242e12	0.556067
$875$	6.30942e12	0.363876
$876$	8.26900e11	0.0474444
$877$	2.74263e13	1.56556	0.782779	−	0.622300i	$-0.213802\pi$
$877$	2.74263e13	1.56556	0.782779	+	0.622300i	$0.213802\pi$
$878$	9.78465e12	0.555674
$879$	−1.33660e13	−0.755184
$880$	−2.12506e13	−1.19454
$881$	2.71067e13	1.51595	0.757974	−	0.652285i	$-0.226189\pi$
$881$	2.71067e13	1.51595	0.757974	+	0.652285i	$0.226189\pi$
$882$	8.62489e11	0.0479894
$883$	1.87457e13	1.03772	0.518859	−	0.854860i	$-0.326357\pi$
$883$	1.87457e13	1.03772	0.518859	+	0.854860i	$0.326357\pi$
$884$	9.74097e10	0.00536496
$885$	1.33215e13	0.729977
$886$	−3.14869e13	−1.71664
$887$	−2.39367e13	−1.29840	−0.649199	−	0.760618i	$-0.724896\pi$
$887$	−2.39367e13	−1.29840	−0.649199	+	0.760618i	$0.724896\pi$
$888$	−1.13060e13	−0.610169
$889$	8.05061e12	0.432286
$890$	2.14622e13	1.14662
$891$	1.12854e13	0.599886
$892$	−4.42759e11	−0.0234167
$893$	1.07959e13	0.568104
$894$	5.38630e12	0.282015
$895$	1.65453e13	0.861927
$896$	−8.60145e12	−0.445847
$897$	2.76822e12	0.142769
$898$	2.20109e13	1.12952
$899$	−4.82791e13	−2.46513
$900$	−7.31926e10	−0.00371857
$901$	−2.58553e12	−0.130704
$902$	3.48979e12	0.175537
$903$	−4.93821e12	−0.247158
$904$	2.79728e13	1.39309
$905$	3.25302e13	1.61201
$906$	8.19655e12	0.404161
$907$	−1.89356e13	−0.929067	−0.464534	−	0.885556i	$-0.653778\pi$
$907$	−1.89356e13	−0.929067	−0.464534	+	0.885556i	$0.653778\pi$
$908$	−1.14248e12	−0.0557779
$909$	4.90653e12	0.238362
$910$	−2.42956e12	−0.117447
$911$	−1.54738e13	−0.744329	−0.372164	−	0.928167i	$-0.621384\pi$
$911$	−1.54738e13	−0.744329	−0.372164	+	0.928167i	$0.621384\pi$
$912$	−1.64392e13	−0.786873
$913$	−4.05578e13	−1.93177
$914$	−9.80845e12	−0.464882
$915$	−2.99046e13	−1.41040
$916$	5.24539e12	0.246177
$917$	−2.99295e12	−0.139778
$918$	−2.81331e12	−0.130745
$919$	−4.01068e13	−1.85481	−0.927403	−	0.374064i	$-0.877964\pi$
$919$	−4.01068e13	−1.85481	−0.927403	+	0.374064i	$0.877964\pi$
$920$	1.24540e13	0.573146
$921$	−1.55831e13	−0.713652
$922$	4.58787e13	2.09085
$923$	−3.21329e12	−0.145728
$924$	−1.22591e12	−0.0553269
$925$	−1.25697e12	−0.0564532
$926$	2.24585e13	1.00376
$927$	7.23223e12	0.321672
$928$	1.35300e13	0.598869
$929$	−7.66966e12	−0.337835	−0.168918	−	0.985630i	$-0.554027\pi$
$929$	−7.66966e12	−0.337835	−0.168918	+	0.985630i	$0.554027\pi$
$930$	−3.01659e13	−1.32234
$931$	2.71149e12	0.118286
$932$	4.40417e12	0.191202
$933$	7.95605e12	0.343740
$934$	−1.07682e13	−0.463003
$935$	−2.70534e12	−0.115763
$936$	1.80611e12	0.0769135
$937$	3.99384e13	1.69263	0.846315	−	0.532682i	$-0.178816\pi$
$937$	3.99384e13	1.69263	0.846315	+	0.532682i	$0.178816\pi$
$938$	−1.54559e13	−0.651901
$939$	−1.68658e13	−0.707964
$940$	−2.96238e12	−0.123756
$941$	3.40763e13	1.41677	0.708384	−	0.705827i	$-0.249424\pi$
$941$	3.40763e13	1.41677	0.708384	+	0.705827i	$0.249424\pi$
$942$	1.40788e13	0.582553
$943$	−2.41325e12	−0.0993800
$944$	2.37273e13	0.972465
$945$	1.04239e13	0.425193
$946$	−2.12248e13	−0.861655
$947$	4.06183e13	1.64114	0.820572	−	0.571543i	$-0.193655\pi$
$947$	4.06183e13	1.64114	0.820572	+	0.571543i	$0.193655\pi$
$948$	−2.20565e12	−0.0886948
$949$	−2.26854e12	−0.0907923
$950$	−1.54894e12	−0.0616990
$951$	2.77752e13	1.10115
$952$	−9.50119e11	−0.0374897
$953$	−3.52201e13	−1.38316	−0.691580	−	0.722300i	$-0.743085\pi$
$953$	−3.52201e13	−1.38316	−0.691580	+	0.722300i	$0.743085\pi$
$954$	1.01319e13	0.396025
$955$	−1.05570e13	−0.410701
$956$	8.05623e12	0.311940
$957$	−3.77703e13	−1.45562
$958$	−4.91291e12	−0.188449
$959$	1.47474e13	0.563029
$960$	−1.74004e13	−0.661209
$961$	2.69372e13	1.01882
$962$	−6.55545e12	−0.246783
$963$	5.92359e11	0.0221956
$964$	2.94602e12	0.109872
$965$	8.04224e12	0.298541
$966$	5.70658e12	0.210853
$967$	−3.37167e13	−1.24001	−0.620006	−	0.784597i	$-0.712870\pi$
$967$	−3.37167e13	−1.24001	−0.620006	+	0.784597i	$0.712870\pi$
$968$	4.91249e11	0.0179830
$969$	−2.09282e12	−0.0762560
$970$	5.25427e13	1.90563
$971$	1.80759e13	0.652549	0.326275	−	0.945275i	$-0.394207\pi$
$971$	1.80759e13	0.652549	0.326275	+	0.945275i	$0.394207\pi$
$972$	2.88795e12	0.103775
$973$	−8.10539e12	−0.289912
$974$	2.19158e13	0.780265
$975$	−4.46999e11	−0.0158411
$976$	−5.32638e13	−1.87892
$977$	−4.63670e13	−1.62811	−0.814055	−	0.580788i	$-0.802744\pi$
$977$	−4.63670e13	−1.62811	−0.814055	+	0.580788i	$0.802744\pi$
$978$	8.02506e12	0.280494
$979$	−2.97100e13	−1.03367
$980$	−7.44028e11	−0.0257675
$981$	1.24495e11	0.00429183
$982$	2.72573e13	0.935367
$983$	−5.77325e13	−1.97210	−0.986051	−	0.166445i	$-0.946771\pi$
$983$	−5.77325e13	−1.97210	−0.986051	+	0.166445i	$0.946771\pi$
$984$	3.50502e12	0.119183
$985$	2.29186e13	0.775755
$986$	6.18683e12	0.208460
$987$	6.42255e12	0.215417
$988$	−1.20004e12	−0.0400674
$989$	1.46773e13	0.487824
$990$	1.06014e13	0.350755
$991$	−4.60521e13	−1.51676	−0.758381	−	0.651811i	$-0.774010\pi$
$991$	−4.60521e13	−1.51676	−0.758381	+	0.651811i	$0.774010\pi$
$992$	−1.49586e13	−0.490443
$993$	−3.68536e13	−1.20284
$994$	−6.62408e12	−0.215222
$995$	−4.96162e12	−0.160480
$996$	8.60926e12	0.277203
$997$	1.55999e13	0.500026	0.250013	−	0.968242i	$-0.419565\pi$
$997$	1.55999e13	0.500026	0.250013	+	0.968242i	$0.419565\pi$
$998$	3.76002e13	1.19978
$999$	2.81258e13	0.893428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.3	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-24.5220 q^{2} +116.541 q^{3} +89.3306 q^{4} -1444.79 q^{5} -2857.83 q^{6} +2401.00 q^{7} +10364.7 q^{8} -6101.17 q^{9} +O(q^{10})\)	\(q-24.5220 q^{2} +116.541 q^{3} +89.3306 q^{4} -1444.79 q^{5} -2857.83 q^{6} +2401.00 q^{7} +10364.7 q^{8} -6101.17 q^{9} +35429.2 q^{10} -49044.3 q^{11} +10410.7 q^{12} -28561.0 q^{13} -58877.4 q^{14} -168377. q^{15} -299901. q^{16} -38179.3 q^{17} +149613. q^{18} +470353. q^{19} -129064. q^{20} +279815. q^{21} +1.20267e6 q^{22} -831664. q^{23} +1.20792e6 q^{24} +134293. q^{25} +700374. q^{26} -3.00492e6 q^{27} +214483. q^{28} +6.60819e6 q^{29} +4.12896e6 q^{30} -7.30594e6 q^{31} +2.04746e6 q^{32} -5.71568e6 q^{33} +936235. q^{34} -3.46894e6 q^{35} -545021. q^{36} -9.35992e6 q^{37} -1.15340e7 q^{38} -3.32853e6 q^{39} -1.49748e7 q^{40} +2.90171e6 q^{41} -6.86164e6 q^{42} -1.76481e7 q^{43} -4.38116e6 q^{44} +8.81490e6 q^{45} +2.03941e7 q^{46} +2.29528e7 q^{47} -3.49508e7 q^{48} +5.76480e6 q^{49} -3.29314e6 q^{50} -4.44946e6 q^{51} -2.55137e6 q^{52} +6.77207e7 q^{53} +7.36867e7 q^{54} +7.08587e7 q^{55} +2.48857e7 q^{56} +5.48154e7 q^{57} -1.62046e8 q^{58} -7.91170e7 q^{59} -1.50413e7 q^{60} +1.77604e8 q^{61} +1.79157e8 q^{62} -1.46489e7 q^{63} +1.03342e8 q^{64} +4.12646e7 q^{65} +1.40160e8 q^{66} +2.62510e8 q^{67} -3.41058e6 q^{68} -9.69231e7 q^{69} +8.50655e7 q^{70} +1.12506e8 q^{71} -6.32369e7 q^{72} +7.94280e7 q^{73} +2.29524e8 q^{74} +1.56507e7 q^{75} +4.20169e7 q^{76} -1.17755e8 q^{77} +8.16224e7 q^{78} -2.11864e8 q^{79} +4.33294e8 q^{80} -2.30107e8 q^{81} -7.11558e7 q^{82} +8.26963e8 q^{83} +2.49961e7 q^{84} +5.51611e7 q^{85} +4.32768e8 q^{86} +7.70126e8 q^{87} -5.08330e8 q^{88} +6.05778e8 q^{89} -2.16159e8 q^{90} -6.85750e7 q^{91} -7.42931e7 q^{92} -8.51443e8 q^{93} -5.62850e8 q^{94} -6.79561e8 q^{95} +2.38613e8 q^{96} +1.48303e9 q^{97} -1.41365e8 q^{98} +2.99227e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Introduction

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