LMFDB - Embedded newform 91.10.a.c.1.12

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			1.12
Root			$-31.6981$ 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)

$f(q)$	$=$	$q+33.6981 q^{2} +231.670 q^{3} +623.565 q^{4} +224.065 q^{5} +7806.84 q^{6} +2401.00 q^{7} +3759.53 q^{8} +33987.9 q^{9} +O(q^{10})$	\(q+33.6981 q^{2} +231.670 q^{3} +623.565 q^{4} +224.065 q^{5} +7806.84 q^{6} +2401.00 q^{7} +3759.53 q^{8} +33987.9 q^{9} +7550.59 q^{10} +40187.8 q^{11} +144461. q^{12} -28561.0 q^{13} +80909.2 q^{14} +51909.2 q^{15} -192576. q^{16} +305963. q^{17} +1.14533e6 q^{18} -91205.4 q^{19} +139719. q^{20} +556239. q^{21} +1.35425e6 q^{22} +613654. q^{23} +870971. q^{24} -1.90292e6 q^{25} -962453. q^{26} +3.31402e6 q^{27} +1.49718e6 q^{28} +2.14553e6 q^{29} +1.74924e6 q^{30} +5.37624e6 q^{31} -8.41433e6 q^{32} +9.31030e6 q^{33} +1.03104e7 q^{34} +537981. q^{35} +2.11937e7 q^{36} -238209. q^{37} -3.07345e6 q^{38} -6.61672e6 q^{39} +842381. q^{40} -1.96562e7 q^{41} +1.87442e7 q^{42} -8.54327e6 q^{43} +2.50597e7 q^{44} +7.61551e6 q^{45} +2.06790e7 q^{46} -2.30819e7 q^{47} -4.46140e7 q^{48} +5.76480e6 q^{49} -6.41249e7 q^{50} +7.08823e7 q^{51} -1.78096e7 q^{52} +8.18785e6 q^{53} +1.11676e8 q^{54} +9.00469e6 q^{55} +9.02664e6 q^{56} -2.11295e7 q^{57} +7.23003e7 q^{58} -1.54420e8 q^{59} +3.23687e7 q^{60} -1.85271e8 q^{61} +1.81169e8 q^{62} +8.16050e7 q^{63} -1.84949e8 q^{64} -6.39953e6 q^{65} +3.13740e8 q^{66} +2.28058e8 q^{67} +1.90788e8 q^{68} +1.42165e8 q^{69} +1.81290e7 q^{70} -6.60946e7 q^{71} +1.27779e8 q^{72} +2.41971e8 q^{73} -8.02720e6 q^{74} -4.40849e8 q^{75} -5.68725e7 q^{76} +9.64909e7 q^{77} -2.22971e8 q^{78} -1.67385e8 q^{79} -4.31496e7 q^{80} +9.87737e7 q^{81} -6.62378e8 q^{82} -2.85737e7 q^{83} +3.46851e8 q^{84} +6.85556e7 q^{85} -2.87892e8 q^{86} +4.97054e8 q^{87} +1.51087e8 q^{88} -5.16155e8 q^{89} +2.56629e8 q^{90} -6.85750e7 q^{91} +3.82653e8 q^{92} +1.24551e9 q^{93} -7.77816e8 q^{94} -2.04360e7 q^{95} -1.94935e9 q^{96} +1.48269e9 q^{97} +1.94263e8 q^{98} +1.36590e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	33.6981	1.48926	0.744631	−	0.667477i	$-0.232626\pi$
$2$	33.6981	1.48926	0.744631	+	0.667477i	$0.232626\pi$
$3$	231.670	1.65129	0.825646	−	0.564189i	$-0.190811\pi$
$3$	231.670	1.65129	0.825646	+	0.564189i	$0.190811\pi$
$4$	623.565	1.21790
$5$	224.065	0.160328	0.0801640	−	0.996782i	$-0.474456\pi$
$5$	224.065	0.160328	0.0801640	+	0.996782i	$0.474456\pi$
$6$	7806.84	2.45921
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	3759.53	0.324511
$9$	33987.9	1.72676
$10$	7550.59	0.238770
$11$	40187.8	0.827612	0.413806	−	0.910365i	$-0.364199\pi$
$11$	40187.8	0.827612	0.413806	+	0.910365i	$0.364199\pi$
$12$	144461.	2.01111
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	80909.2	0.562888
$15$	51909.2	0.264748
$16$	−192576.	−0.734619
$17$	305963.	0.888481	0.444241	−	0.895907i	$-0.353473\pi$
$17$	305963.	0.888481	0.444241	+	0.895907i	$0.353473\pi$
$18$	1.14533e6	2.57160
$19$	−91205.4	−0.160557	−0.0802785	−	0.996772i	$-0.525581\pi$
$19$	−91205.4	−0.160557	−0.0802785	+	0.996772i	$0.525581\pi$
$20$	139719.	0.195264
$21$	556239.	0.624130
$22$	1.35425e6	1.23253
$23$	613654.	0.457244	0.228622	−	0.973515i	$-0.426578\pi$
$23$	613654.	0.457244	0.228622	+	0.973515i	$0.426578\pi$
$24$	870971.	0.535862
$25$	−1.90292e6	−0.974295
$26$	−962453.	−0.413047
$27$	3.31402e6	1.20010
$28$	1.49718e6	0.460323
$29$	2.14553e6	0.563304	0.281652	−	0.959517i	$-0.409118\pi$
$29$	2.14553e6	0.563304	0.281652	+	0.959517i	$0.409118\pi$
$30$	1.74924e6	0.394280
$31$	5.37624e6	1.04557	0.522783	−	0.852466i	$-0.324894\pi$
$31$	5.37624e6	1.04557	0.522783	+	0.852466i	$0.324894\pi$
$32$	−8.41433e6	−1.41855
$33$	9.31030e6	1.36663
$34$	1.03104e7	1.32318
$35$	537981.	0.0605983
$36$	2.11937e7	2.10303
$37$	−238209.	−0.0208954	−0.0104477	−	0.999945i	$-0.503326\pi$
$37$	−238209.	−0.0208954	−0.0104477	+	0.999945i	$0.503326\pi$
$38$	−3.07345e6	−0.239111
$39$	−6.61672e6	−0.457986
$40$	842381.	0.0520282
$41$	−1.96562e7	−1.08636	−0.543179	−	0.839617i	$-0.682779\pi$
$41$	−1.96562e7	−1.08636	−0.543179	+	0.839617i	$0.682779\pi$
$42$	1.87442e7	0.929492
$43$	−8.54327e6	−0.381080	−0.190540	−	0.981679i	$-0.561024\pi$
$43$	−8.54327e6	−0.381080	−0.190540	+	0.981679i	$0.561024\pi$
$44$	2.50597e7	1.00795
$45$	7.61551e6	0.276849
$46$	2.06790e7	0.680956
$47$	−2.30819e7	−0.689970	−0.344985	−	0.938608i	$-0.612116\pi$
$47$	−2.30819e7	−0.689970	−0.344985	+	0.938608i	$0.612116\pi$
$48$	−4.46140e7	−1.21307
$49$	5.76480e6	0.142857
$50$	−6.41249e7	−1.45098
$51$	7.08823e7	1.46714
$52$	−1.78096e7	−0.337785
$53$	8.18785e6	0.142537	0.0712686	−	0.997457i	$-0.477295\pi$
$53$	8.18785e6	0.142537	0.0712686	+	0.997457i	$0.477295\pi$
$54$	1.11676e8	1.78726
$55$	9.00469e6	0.132690
$56$	9.02664e6	0.122654
$57$	−2.11295e7	−0.265126
$58$	7.23003e7	0.838908
$59$	−1.54420e8	−1.65909	−0.829543	−	0.558443i	$-0.811399\pi$
$59$	−1.54420e8	−1.65909	−0.829543	+	0.558443i	$0.811399\pi$
$60$	3.23687e7	0.322437
$61$	−1.85271e8	−1.71326	−0.856628	−	0.515935i	$-0.827444\pi$
$61$	−1.85271e8	−1.71326	−0.856628	+	0.515935i	$0.827444\pi$
$62$	1.81169e8	1.55712
$63$	8.16050e7	0.652656
$64$	−1.84949e8	−1.37797
$65$	−6.39953e6	−0.0444670
$66$	3.13740e8	2.03527
$67$	2.28058e8	1.38264	0.691319	−	0.722550i	$-0.257030\pi$
$67$	2.28058e8	1.38264	0.691319	+	0.722550i	$0.257030\pi$
$68$	1.90788e8	1.08208
$69$	1.42165e8	0.755044
$70$	1.81290e7	0.0902468
$71$	−6.60946e7	−0.308676	−0.154338	−	0.988018i	$-0.549325\pi$
$71$	−6.60946e7	−0.308676	−0.154338	+	0.988018i	$0.549325\pi$
$72$	1.27779e8	0.560354
$73$	2.41971e8	0.997263	0.498632	−	0.866814i	$-0.333836\pi$
$73$	2.41971e8	0.997263	0.498632	+	0.866814i	$0.333836\pi$
$74$	−8.02720e6	−0.0311187
$75$	−4.40849e8	−1.60885
$76$	−5.68725e7	−0.195542
$77$	9.64909e7	0.312808
$78$	−2.22971e8	−0.682061
$79$	−1.67385e8	−0.483497	−0.241748	−	0.970339i	$-0.577721\pi$
$79$	−1.67385e8	−0.483497	−0.241748	+	0.970339i	$0.577721\pi$
$80$	−4.31496e7	−0.117780
$81$	9.87737e7	0.254952
$82$	−6.62378e8	−1.61787
$83$	−2.85737e7	−0.0660869	−0.0330435	−	0.999454i	$-0.510520\pi$
$83$	−2.85737e7	−0.0660869	−0.0330435	+	0.999454i	$0.510520\pi$
$84$	3.46851e8	0.760128
$85$	6.85556e7	0.142449
$86$	−2.87892e8	−0.567528
$87$	4.97054e8	0.930180
$88$	1.51087e8	0.268569
$89$	−5.16155e8	−0.872018	−0.436009	−	0.899942i	$-0.643608\pi$
$89$	−5.16155e8	−0.872018	−0.436009	+	0.899942i	$0.643608\pi$
$90$	2.56629e8	0.412300
$91$	−6.85750e7	−0.104828
$92$	3.82653e8	0.556878
$93$	1.24551e9	1.72653
$94$	−7.77816e8	−1.02755
$95$	−2.04360e7	−0.0257418
$96$	−1.94935e9	−2.34244
$97$	1.48269e9	1.70051	0.850255	−	0.526372i	$-0.176448\pi$
$97$	1.48269e9	1.70051	0.850255	+	0.526372i	$0.176448\pi$
$98$	1.94263e8	0.212752
$99$	1.36590e9	1.42909
$100$	−1.18659e9	−1.18659
$101$	5.79267e8	0.553902	0.276951	−	0.960884i	$-0.410676\pi$
$101$	5.79267e8	0.553902	0.276951	+	0.960884i	$0.410676\pi$
$102$	2.38860e9	2.18496
$103$	1.36027e8	0.119085	0.0595427	−	0.998226i	$-0.481036\pi$
$103$	1.36027e8	0.119085	0.0595427	+	0.998226i	$0.481036\pi$
$104$	−1.07376e8	−0.0900031
$105$	1.24634e8	0.100066
$106$	2.75915e8	0.212275
$107$	1.86280e9	1.37385	0.686923	−	0.726730i	$-0.258961\pi$
$107$	1.86280e9	1.37385	0.686923	+	0.726730i	$0.258961\pi$
$108$	2.06650e9	1.46160
$109$	−9.28324e8	−0.629913	−0.314956	−	0.949106i	$-0.601990\pi$
$109$	−9.28324e8	−0.629913	−0.314956	+	0.949106i	$0.601990\pi$
$110$	3.03441e8	0.197609
$111$	−5.51858e7	−0.0345044
$112$	−4.62375e8	−0.277660
$113$	1.31593e8	0.0759241	0.0379620	−	0.999279i	$-0.487913\pi$
$113$	1.31593e8	0.0759241	0.0379620	+	0.999279i	$0.487913\pi$
$114$	−7.12026e8	−0.394843
$115$	1.37499e8	0.0733091
$116$	1.33788e9	0.686049
$117$	−9.70729e8	−0.478918
$118$	−5.20366e9	−2.47081
$119$	7.34616e8	0.335814
$120$	1.95154e8	0.0859137
$121$	−7.42890e8	−0.315058
$122$	−6.24327e9	−2.55149
$123$	−4.55375e9	−1.79389
$124$	3.35244e9	1.27339
$125$	−8.64006e8	−0.316535
$126$	2.74994e9	0.971975
$127$	1.05992e9	0.361540	0.180770	−	0.983525i	$-0.442141\pi$
$127$	1.05992e9	0.361540	0.180770	+	0.983525i	$0.442141\pi$
$128$	−1.92428e9	−0.633614
$129$	−1.97922e9	−0.629274
$130$	−2.15652e8	−0.0662230
$131$	−6.15747e9	−1.82676	−0.913380	−	0.407108i	$-0.866537\pi$
$131$	−6.15747e9	−1.82676	−0.913380	+	0.407108i	$0.866537\pi$
$132$	5.80558e9	1.66442
$133$	−2.18984e8	−0.0606848
$134$	7.68512e9	2.05911
$135$	7.42556e8	0.192410
$136$	1.15028e9	0.288322
$137$	−3.19022e9	−0.773711	−0.386855	−	0.922140i	$-0.626439\pi$
$137$	−3.19022e9	−0.773711	−0.386855	+	0.922140i	$0.626439\pi$
$138$	4.79070e9	1.12446
$139$	1.44432e9	0.328168	0.164084	−	0.986446i	$-0.447533\pi$
$139$	1.44432e9	0.328168	0.164084	+	0.986446i	$0.447533\pi$
$140$	3.35466e8	0.0738027
$141$	−5.34737e9	−1.13934
$142$	−2.22726e9	−0.459700
$143$	−1.14780e9	−0.229538
$144$	−6.54525e9	−1.26851
$145$	4.80738e8	0.0903135
$146$	8.15396e9	1.48519
$147$	1.33553e9	0.235899
$148$	−1.48539e8	−0.0254485
$149$	−7.43470e9	−1.23574	−0.617868	−	0.786282i	$-0.712003\pi$
$149$	−7.43470e9	−1.23574	−0.617868	+	0.786282i	$0.712003\pi$
$150$	−1.48558e10	−2.39599
$151$	−1.22170e10	−1.91236	−0.956179	−	0.292784i	$-0.905418\pi$
$151$	−1.22170e10	−1.91236	−0.956179	+	0.292784i	$0.905418\pi$
$152$	−3.42890e8	−0.0521025
$153$	1.03990e10	1.53420
$154$	3.25156e9	0.465853
$155$	1.20463e9	0.167633
$156$	−4.12596e9	−0.557781
$157$	−6.19658e9	−0.813961	−0.406980	−	0.913437i	$-0.633418\pi$
$157$	−6.19658e9	−0.813961	−0.406980	+	0.913437i	$0.633418\pi$
$158$	−5.64055e9	−0.720053
$159$	1.89688e9	0.235371
$160$	−1.88536e9	−0.227434
$161$	1.47338e9	0.172822
$162$	3.32849e9	0.379690
$163$	−1.14820e10	−1.27401	−0.637006	−	0.770859i	$-0.719827\pi$
$163$	−1.14820e10	−1.27401	−0.637006	+	0.770859i	$0.719827\pi$
$164$	−1.22569e10	−1.32307
$165$	2.08611e9	0.219109
$166$	−9.62882e8	−0.0984207
$167$	1.22866e10	1.22238	0.611190	−	0.791484i	$-0.290691\pi$
$167$	1.22866e10	1.22238	0.611190	+	0.791484i	$0.290691\pi$
$168$	2.09120e9	0.202537
$169$	8.15731e8	0.0769231
$170$	2.31020e9	0.212143
$171$	−3.09988e9	−0.277244
$172$	−5.32728e9	−0.464117
$173$	2.89337e9	0.245582	0.122791	−	0.992433i	$-0.460816\pi$
$173$	2.89337e9	0.245582	0.122791	+	0.992433i	$0.460816\pi$
$174$	1.67498e10	1.38528
$175$	−4.56891e9	−0.368249
$176$	−7.73920e9	−0.607980
$177$	−3.57744e10	−2.73963
$178$	−1.73935e10	−1.29866
$179$	3.35175e9	0.244024	0.122012	−	0.992529i	$-0.461065\pi$
$179$	3.35175e9	0.244024	0.122012	+	0.992529i	$0.461065\pi$
$180$	4.74877e9	0.337174
$181$	1.75144e10	1.21295	0.606474	−	0.795103i	$-0.292583\pi$
$181$	1.75144e10	1.21295	0.606474	+	0.795103i	$0.292583\pi$
$182$	−2.31085e9	−0.156117
$183$	−4.29216e10	−2.82908
$184$	2.30705e9	0.148381
$185$	−5.33743e7	−0.00335011
$186$	4.19715e10	2.57126
$187$	1.22960e10	0.735318
$188$	−1.43930e10	−0.840315
$189$	7.95695e9	0.453596
$190$	−6.88654e8	−0.0383363
$191$	−1.82065e9	−0.0989868	−0.0494934	−	0.998774i	$-0.515761\pi$
$191$	−1.82065e9	−0.0989868	−0.0494934	+	0.998774i	$0.515761\pi$
$192$	−4.28470e10	−2.27544
$193$	1.60619e10	0.833279	0.416639	−	0.909072i	$-0.363208\pi$
$193$	1.60619e10	0.833279	0.416639	+	0.909072i	$0.363208\pi$
$194$	4.99641e10	2.53250
$195$	−1.48258e9	−0.0734280
$196$	3.59473e9	0.173986
$197$	2.14119e10	1.01288	0.506439	−	0.862276i	$-0.330961\pi$
$197$	2.14119e10	1.01288	0.506439	+	0.862276i	$0.330961\pi$
$198$	4.60283e10	2.12829
$199$	5.63050e9	0.254512	0.127256	−	0.991870i	$-0.459383\pi$
$199$	5.63050e9	0.254512	0.127256	+	0.991870i	$0.459383\pi$
$200$	−7.15409e9	−0.316169
$201$	5.28341e10	2.28314
$202$	1.95202e10	0.824905
$203$	5.15141e9	0.212909
$204$	4.41997e10	1.78683
$205$	−4.40428e9	−0.174174
$206$	4.58387e9	0.177349
$207$	2.08568e10	0.789553
$208$	5.50016e9	0.203747
$209$	−3.66534e9	−0.132879
$210$	4.19993e9	0.149024
$211$	−5.31018e9	−0.184433	−0.0922163	−	0.995739i	$-0.529395\pi$
$211$	−5.31018e9	−0.184433	−0.0922163	+	0.995739i	$0.529395\pi$
$212$	5.10565e9	0.173596
$213$	−1.53121e10	−0.509715
$214$	6.27728e10	2.04602
$215$	−1.91425e9	−0.0610978
$216$	1.24592e10	0.389446
$217$	1.29084e10	0.395186
$218$	−3.12828e10	−0.938105
$219$	5.60573e10	1.64677
$220$	5.61501e9	0.161603
$221$	−8.73860e9	−0.246420
$222$	−1.85966e9	−0.0513860
$223$	3.52420e10	0.954307	0.477154	−	0.878820i	$-0.341669\pi$
$223$	3.52420e10	0.954307	0.477154	+	0.878820i	$0.341669\pi$
$224$	−2.02028e10	−0.536162
$225$	−6.46763e10	−1.68238
$226$	4.43444e9	0.113071
$227$	6.67379e10	1.66823	0.834116	−	0.551589i	$-0.185978\pi$
$227$	6.67379e10	1.66823	0.834116	+	0.551589i	$0.185978\pi$
$228$	−1.31756e10	−0.322898
$229$	1.38631e10	0.333121	0.166561	−	0.986031i	$-0.446734\pi$
$229$	1.38631e10	0.333121	0.166561	+	0.986031i	$0.446734\pi$
$230$	4.63345e9	0.109176
$231$	2.23540e10	0.516537
$232$	8.06618e9	0.182798
$233$	−1.47931e10	−0.328820	−0.164410	−	0.986392i	$-0.552572\pi$
$233$	−1.47931e10	−0.328820	−0.164410	+	0.986392i	$0.552572\pi$
$234$	−3.27118e10	−0.713235
$235$	−5.17184e9	−0.110622
$236$	−9.62908e10	−2.02060
$237$	−3.87779e10	−0.798394
$238$	2.47552e10	0.500116
$239$	4.41252e10	0.874775	0.437388	−	0.899273i	$-0.355904\pi$
$239$	4.41252e10	0.874775	0.437388	+	0.899273i	$0.355904\pi$
$240$	−9.99646e9	−0.194489
$241$	−1.66870e10	−0.318641	−0.159321	−	0.987227i	$-0.550930\pi$
$241$	−1.66870e10	−0.318641	−0.159321	+	0.987227i	$0.550930\pi$
$242$	−2.50340e10	−0.469203
$243$	−4.23469e10	−0.779101
$244$	−1.15528e11	−2.08657
$245$	1.29169e9	0.0229040
$246$	−1.53453e11	−2.67158
$247$	2.60492e9	0.0445305
$248$	2.02122e10	0.339297
$249$	−6.61967e9	−0.109129
$250$	−2.91154e10	−0.471403
$251$	3.96693e10	0.630845	0.315423	−	0.948951i	$-0.397854\pi$
$251$	3.96693e10	0.630845	0.315423	+	0.948951i	$0.397854\pi$
$252$	5.08860e10	0.794870
$253$	2.46614e10	0.378421
$254$	3.57173e10	0.538427
$255$	1.58823e10	0.235224
$256$	2.98488e10	0.434358
$257$	−8.83822e10	−1.26376	−0.631882	−	0.775065i	$-0.717717\pi$
$257$	−8.83822e10	−1.26376	−0.631882	+	0.775065i	$0.717717\pi$
$258$	−6.66960e10	−0.937154
$259$	−5.71939e8	−0.00789771
$260$	−3.99052e9	−0.0541564
$261$	7.29220e10	0.972694
$262$	−2.07495e11	−2.72052
$263$	2.00560e10	0.258490	0.129245	−	0.991613i	$-0.458745\pi$
$263$	2.00560e10	0.258490	0.129245	+	0.991613i	$0.458745\pi$
$264$	3.50024e10	0.443486
$265$	1.83461e9	0.0228527
$266$	−7.37936e9	−0.0903756
$267$	−1.19578e11	−1.43996
$268$	1.42209e11	1.68391
$269$	−1.59150e11	−1.85319	−0.926597	−	0.376057i	$-0.877280\pi$
$269$	−1.59150e11	−1.85319	−0.926597	+	0.376057i	$0.877280\pi$
$270$	2.50228e10	0.286549
$271$	1.16802e11	1.31549	0.657747	−	0.753239i	$-0.271510\pi$
$271$	1.16802e11	1.31549	0.657747	+	0.753239i	$0.271510\pi$
$272$	−5.89211e10	−0.652695
$273$	−1.58868e10	−0.173102
$274$	−1.07505e11	−1.15226
$275$	−7.64741e10	−0.806339
$276$	8.86492e10	0.919568
$277$	2.68941e10	0.274472	0.137236	−	0.990538i	$-0.456178\pi$
$277$	2.68941e10	0.274472	0.137236	+	0.990538i	$0.456178\pi$
$278$	4.86709e10	0.488728
$279$	1.82727e11	1.80545
$280$	2.02256e9	0.0196648
$281$	−7.11370e10	−0.680639	−0.340320	−	0.940310i	$-0.610535\pi$
$281$	−7.11370e10	−0.680639	−0.340320	+	0.940310i	$0.610535\pi$
$282$	−1.80196e11	−1.69678
$283$	2.02579e11	1.87740	0.938699	−	0.344738i	$-0.112032\pi$
$283$	2.02579e11	1.87740	0.938699	+	0.344738i	$0.112032\pi$
$284$	−4.12143e10	−0.375937
$285$	−4.73440e9	−0.0425072
$286$	−3.86788e10	−0.341843
$287$	−4.71946e10	−0.410604
$288$	−2.85986e11	−2.44950
$289$	−2.49747e10	−0.210601
$290$	1.62000e10	0.134500
$291$	3.43496e11	2.80804
$292$	1.50884e11	1.21457
$293$	1.83165e11	1.45191	0.725954	−	0.687743i	$-0.241398\pi$
$293$	1.83165e11	1.45191	0.725954	+	0.687743i	$0.241398\pi$
$294$	4.50049e10	0.351315
$295$	−3.46001e10	−0.265998
$296$	−8.95554e8	−0.00678077
$297$	1.33183e11	0.993218
$298$	−2.50536e11	−1.84033
$299$	−1.75266e10	−0.126817
$300$	−2.74898e11	−1.95941
$301$	−2.05124e10	−0.144035
$302$	−4.11691e11	−2.84800
$303$	1.34199e11	0.914653
$304$	1.75640e10	0.117948
$305$	−4.15127e10	−0.274683
$306$	3.50428e11	2.28482
$307$	1.43918e11	0.924683	0.462341	−	0.886702i	$-0.347009\pi$
$307$	1.43918e11	0.924683	0.462341	+	0.886702i	$0.347009\pi$
$308$	6.01683e10	0.380969
$309$	3.15134e10	0.196645
$310$	4.05938e10	0.249650
$311$	1.71719e11	1.04087	0.520436	−	0.853900i	$-0.325769\pi$
$311$	1.71719e11	1.04087	0.520436	+	0.853900i	$0.325769\pi$
$312$	−2.48758e10	−0.148621
$313$	2.71927e11	1.60141	0.800706	−	0.599057i	$-0.204458\pi$
$313$	2.71927e11	1.60141	0.800706	+	0.599057i	$0.204458\pi$
$314$	−2.08813e11	−1.21220
$315$	1.82848e10	0.104639
$316$	−1.04375e11	−0.588851
$317$	1.42989e10	0.0795310	0.0397655	−	0.999209i	$-0.487339\pi$
$317$	1.42989e10	0.0795310	0.0397655	+	0.999209i	$0.487339\pi$
$318$	6.39212e10	0.350528
$319$	8.62240e10	0.466198
$320$	−4.14406e10	−0.220928
$321$	4.31554e11	2.26862
$322$	4.96503e10	0.257377
$323$	−2.79054e10	−0.142652
$324$	6.15918e10	0.310506
$325$	5.43493e10	0.270221
$326$	−3.86922e11	−1.89734
$327$	−2.15065e11	−1.04017
$328$	−7.38982e10	−0.352535
$329$	−5.54195e10	−0.260784
$330$	7.02982e10	0.326311
$331$	1.30274e11	0.596528	0.298264	−	0.954483i	$-0.403592\pi$
$331$	1.30274e11	0.596528	0.298264	+	0.954483i	$0.403592\pi$
$332$	−1.78176e10	−0.0804873
$333$	−8.09622e9	−0.0360814
$334$	4.14034e11	1.82044
$335$	5.10998e10	0.221676
$336$	−1.07118e11	−0.458497
$337$	−2.66692e11	−1.12635	−0.563177	−	0.826336i	$-0.690421\pi$
$337$	−2.66692e11	−1.12635	−0.563177	+	0.826336i	$0.690421\pi$
$338$	2.74886e10	0.114559
$339$	3.04861e10	0.125373
$340$	4.27489e10	0.173488
$341$	2.16059e11	0.865323
$342$	−1.04460e11	−0.412889
$343$	1.38413e10	0.0539949
$344$	−3.21187e10	−0.123665
$345$	3.18543e10	0.121055
$346$	9.75012e10	0.365736
$347$	−3.37737e11	−1.25054	−0.625268	−	0.780410i	$-0.715010\pi$
$347$	−3.37737e11	−1.25054	−0.625268	+	0.780410i	$0.715010\pi$
$348$	3.09946e11	1.13287
$349$	−6.04884e9	−0.0218252	−0.0109126	−	0.999940i	$-0.503474\pi$
$349$	−6.04884e9	−0.0218252	−0.0109126	+	0.999940i	$0.503474\pi$
$350$	−1.53964e11	−0.548419
$351$	−9.46516e10	−0.332848
$352$	−3.38153e11	−1.17401
$353$	−5.31224e11	−1.82092	−0.910461	−	0.413596i	$-0.864273\pi$
$353$	−5.31224e11	−1.82092	−0.910461	+	0.413596i	$0.864273\pi$
$354$	−1.20553e12	−4.08003
$355$	−1.48095e10	−0.0494895
$356$	−3.21856e11	−1.06203
$357$	1.70188e11	0.554528
$358$	1.12948e11	0.363416
$359$	−6.38841e10	−0.202987	−0.101493	−	0.994836i	$-0.532362\pi$
$359$	−6.38841e10	−0.202987	−0.101493	+	0.994836i	$0.532362\pi$
$360$	2.86308e10	0.0898405
$361$	−3.14369e11	−0.974221
$362$	5.90204e11	1.80640
$363$	−1.72105e11	−0.520252
$364$	−4.27609e10	−0.127671
$365$	5.42172e10	0.159889
$366$	−1.44638e12	−4.21325
$367$	2.94437e11	0.847217	0.423609	−	0.905845i	$-0.360763\pi$
$367$	2.94437e11	0.847217	0.423609	+	0.905845i	$0.360763\pi$
$368$	−1.18175e11	−0.335900
$369$	−6.68074e11	−1.87588
$370$	−1.79862e9	−0.00498920
$371$	1.96590e10	0.0538740
$372$	7.76658e11	2.10275
$373$	−1.82124e11	−0.487167	−0.243583	−	0.969880i	$-0.578323\pi$
$373$	−1.82124e11	−0.487167	−0.243583	+	0.969880i	$0.578323\pi$
$374$	4.14351e11	1.09508
$375$	−2.00164e11	−0.522692
$376$	−8.67770e10	−0.223903
$377$	−6.12784e10	−0.156233
$378$	2.68135e11	0.675522
$379$	7.60858e11	1.89421	0.947103	−	0.320931i	$-0.103996\pi$
$379$	7.60858e11	1.89421	0.947103	+	0.320931i	$0.103996\pi$
$380$	−1.27431e10	−0.0313509
$381$	2.45551e11	0.597007
$382$	−6.13527e10	−0.147417
$383$	5.01446e11	1.19078	0.595388	−	0.803438i	$-0.296998\pi$
$383$	5.01446e11	1.19078	0.595388	+	0.803438i	$0.296998\pi$
$384$	−4.45799e11	−1.04628
$385$	2.16203e10	0.0501519
$386$	5.41258e11	1.24097
$387$	−2.90368e11	−0.658035
$388$	9.24557e11	2.07105
$389$	8.95743e11	1.98340	0.991700	−	0.128571i	$-0.0410390\pi$
$389$	8.95743e11	1.98340	0.991700	+	0.128571i	$0.0410390\pi$
$390$	−4.99601e10	−0.109354
$391$	1.87755e11	0.406253
$392$	2.16730e10	0.0463587
$393$	−1.42650e12	−3.01651
$394$	7.21542e11	1.50844
$395$	−3.75051e10	−0.0775181
$396$	8.51727e11	1.74049
$397$	1.44199e11	0.291343	0.145672	−	0.989333i	$-0.453466\pi$
$397$	1.44199e11	0.291343	0.145672	+	0.989333i	$0.453466\pi$
$398$	1.89737e11	0.379035
$399$	−5.07320e10	−0.100208
$400$	3.66457e11	0.715736
$401$	−3.15644e11	−0.609605	−0.304802	−	0.952416i	$-0.598590\pi$
$401$	−3.15644e11	−0.609605	−0.304802	+	0.952416i	$0.598590\pi$
$402$	1.78041e12	3.40019
$403$	−1.53551e11	−0.289988
$404$	3.61211e11	0.674597
$405$	2.21318e10	0.0408760
$406$	1.73593e11	0.317077
$407$	−9.57308e9	−0.0172933
$408$	2.66485e11	0.476103
$409$	5.40025e11	0.954243	0.477121	−	0.878837i	$-0.341680\pi$
$409$	5.40025e11	0.954243	0.477121	+	0.878837i	$0.341680\pi$
$410$	−1.48416e11	−0.259390
$411$	−7.39079e11	−1.27762
$412$	8.48218e10	0.145034
$413$	−3.70762e11	−0.627075
$414$	7.02836e11	1.17585
$415$	−6.40238e9	−0.0105956
$416$	2.40322e11	0.393435
$417$	3.34605e11	0.541901
$418$	−1.23515e11	−0.197892
$419$	−3.59581e11	−0.569946	−0.284973	−	0.958536i	$-0.591985\pi$
$419$	−3.59581e11	−0.569946	−0.284973	+	0.958536i	$0.591985\pi$
$420$	7.77174e10	0.121870
$421$	3.53786e11	0.548872	0.274436	−	0.961605i	$-0.411509\pi$
$421$	3.53786e11	0.548872	0.274436	+	0.961605i	$0.411509\pi$
$422$	−1.78943e11	−0.274668
$423$	−7.84504e11	−1.19142
$424$	3.07825e10	0.0462549
$425$	−5.82223e11	−0.865643
$426$	−5.15990e11	−0.759099
$427$	−4.44834e11	−0.647550
$428$	1.16157e12	1.67321
$429$	−2.65911e11	−0.379035
$430$	−6.45067e10	−0.0909906
$431$	1.08550e12	1.51524	0.757622	−	0.652694i	$-0.226361\pi$
$431$	1.08550e12	1.51524	0.757622	+	0.652694i	$0.226361\pi$
$432$	−6.38200e11	−0.881617
$433$	6.31815e11	0.863763	0.431882	−	0.901930i	$-0.357850\pi$
$433$	6.31815e11	0.863763	0.431882	+	0.901930i	$0.357850\pi$
$434$	4.34988e11	0.588536
$435$	1.11373e11	0.149134
$436$	−5.78870e11	−0.767171
$437$	−5.59685e10	−0.0734138
$438$	1.88903e12	2.45248
$439$	−4.14022e11	−0.532026	−0.266013	−	0.963969i	$-0.585706\pi$
$439$	−4.14022e11	−0.532026	−0.266013	+	0.963969i	$0.585706\pi$
$440$	3.38534e10	0.0430592
$441$	1.95934e11	0.246681
$442$	−2.94475e11	−0.366984
$443$	9.15087e11	1.12887	0.564437	−	0.825476i	$-0.309093\pi$
$443$	9.15087e11	1.12887	0.564437	+	0.825476i	$0.309093\pi$
$444$	−3.44119e10	−0.0420229
$445$	−1.15652e11	−0.139809
$446$	1.18759e12	1.42121
$447$	−1.72240e12	−2.04056
$448$	−4.44062e11	−0.520825
$449$	−1.42443e12	−1.65398	−0.826992	−	0.562214i	$-0.809950\pi$
$449$	−1.42443e12	−1.65398	−0.826992	+	0.562214i	$0.809950\pi$
$450$	−2.17947e12	−2.50550
$451$	−7.89940e11	−0.899083
$452$	8.20567e10	0.0924680
$453$	−2.83031e12	−3.15786
$454$	2.24894e12	2.48443
$455$	−1.53653e10	−0.0168070
$456$	−7.94372e10	−0.0860364
$457$	−8.67525e11	−0.930377	−0.465189	−	0.885212i	$-0.654013\pi$
$457$	−8.67525e11	−0.930377	−0.465189	+	0.885212i	$0.654013\pi$
$458$	4.67162e11	0.496104
$459$	1.01397e12	1.06627
$460$	8.57393e10	0.0892832
$461$	4.20750e11	0.433881	0.216940	−	0.976185i	$-0.430392\pi$
$461$	4.20750e11	0.433881	0.216940	+	0.976185i	$0.430392\pi$
$462$	7.53289e11	0.769259
$463$	−7.72123e11	−0.780858	−0.390429	−	0.920633i	$-0.627673\pi$
$463$	−7.72123e11	−0.780858	−0.390429	+	0.920633i	$0.627673\pi$
$464$	−4.13177e11	−0.413814
$465$	2.79076e11	0.276812
$466$	−4.98501e11	−0.489699
$467$	1.06827e12	1.03934	0.519668	−	0.854369i	$-0.326056\pi$
$467$	1.06827e12	1.03934	0.519668	+	0.854369i	$0.326056\pi$
$468$	−6.05313e11	−0.583275
$469$	5.47567e11	0.522588
$470$	−1.74282e11	−0.164745
$471$	−1.43556e12	−1.34409
$472$	−5.80546e11	−0.538391
$473$	−3.43335e11	−0.315386
$474$	−1.30674e12	−1.18902
$475$	1.73556e11	0.156430
$476$	4.58081e11	0.408989
$477$	2.78288e11	0.246128
$478$	1.48694e12	1.30277
$479$	2.03857e12	1.76936	0.884678	−	0.466203i	$-0.154378\pi$
$479$	2.03857e12	1.76936	0.884678	+	0.466203i	$0.154378\pi$
$480$	−4.36781e11	−0.375559
$481$	6.80348e9	0.00579533
$482$	−5.62322e11	−0.474540
$483$	3.41338e11	0.285380
$484$	−4.63240e11	−0.383709
$485$	3.32220e11	0.272639
$486$	−1.42701e12	−1.16028
$487$	1.75171e12	1.41118	0.705589	−	0.708621i	$-0.250682\pi$
$487$	1.75171e12	1.41118	0.705589	+	0.708621i	$0.250682\pi$
$488$	−6.96531e11	−0.555970
$489$	−2.66003e12	−2.10376
$490$	4.35276e10	0.0341101
$491$	2.22528e12	1.72790	0.863950	−	0.503577i	$-0.167983\pi$
$491$	2.22528e12	1.72790	0.863950	+	0.503577i	$0.167983\pi$
$492$	−2.83956e12	−2.18478
$493$	6.56451e11	0.500485
$494$	8.77809e10	0.0663176
$495$	3.06051e11	0.229124
$496$	−1.03533e12	−0.768092
$497$	−1.58693e11	−0.116669
$498$	−2.23071e11	−0.162521
$499$	−1.32859e12	−0.959266	−0.479633	−	0.877469i	$-0.659230\pi$
$499$	−1.32859e12	−0.959266	−0.479633	+	0.877469i	$0.659230\pi$
$500$	−5.38764e11	−0.385508
$501$	2.84642e12	2.01851
$502$	1.33678e12	0.939494
$503$	9.06407e11	0.631346	0.315673	−	0.948868i	$-0.397770\pi$
$503$	9.06407e11	0.631346	0.315673	+	0.948868i	$0.397770\pi$
$504$	3.06797e11	0.211794
$505$	1.29794e11	0.0888060
$506$	8.31043e11	0.563568
$507$	1.88980e11	0.127022
$508$	6.60928e11	0.440319
$509$	3.13864e11	0.207258	0.103629	−	0.994616i	$-0.466955\pi$
$509$	3.13864e11	0.207258	0.103629	+	0.994616i	$0.466955\pi$
$510$	5.35203e11	0.350310
$511$	5.80971e11	0.376930
$512$	1.99108e12	1.28049
$513$	−3.02256e11	−0.192685
$514$	−2.97832e12	−1.88207
$515$	3.04790e10	0.0190927
$516$	−1.23417e12	−0.766393
$517$	−9.27609e11	−0.571028
$518$	−1.92733e10	−0.0117618
$519$	6.70307e11	0.405528
$520$	−2.40593e10	−0.0144300
$521$	3.14067e10	0.0186746	0.00933731	−	0.999956i	$-0.497028\pi$
$521$	3.14067e10	0.0186746	0.00933731	+	0.999956i	$0.497028\pi$
$522$	2.45734e12	1.44860
$523$	−2.09698e11	−0.122557	−0.0612784	−	0.998121i	$-0.519518\pi$
$523$	−2.09698e11	−0.122557	−0.0612784	+	0.998121i	$0.519518\pi$
$524$	−3.83958e12	−2.22481
$525$	−1.05848e12	−0.608086
$526$	6.75850e11	0.384959
$527$	1.64493e12	0.928965
$528$	−1.79294e12	−1.00395
$529$	−1.42458e12	−0.790928
$530$	6.18230e10	0.0340337
$531$	−5.24841e12	−2.86485
$532$	−1.36551e11	−0.0739081
$533$	5.61401e11	0.301301
$534$	−4.02954e12	−2.14447
$535$	4.17388e11	0.220266
$536$	8.57391e11	0.448681
$537$	7.76500e11	0.402955
$538$	−5.36305e12	−2.75989
$539$	2.31675e11	0.118230
$540$	4.63032e11	0.234336
$541$	−2.33414e12	−1.17149	−0.585745	−	0.810495i	$-0.699198\pi$
$541$	−2.33414e12	−1.17149	−0.585745	+	0.810495i	$0.699198\pi$
$542$	3.93601e12	1.95911
$543$	4.05756e12	2.00293
$544$	−2.57447e12	−1.26036
$545$	−2.08005e11	−0.100993
$546$	−5.35354e11	−0.257795
$547$	−3.16022e12	−1.50930	−0.754648	−	0.656130i	$-0.772192\pi$
$547$	−3.16022e12	−1.50930	−0.754648	+	0.656130i	$0.772192\pi$
$548$	−1.98931e12	−0.942303
$549$	−6.29696e12	−2.95839
$550$	−2.57704e12	−1.20085
$551$	−1.95684e11	−0.0904424
$552$	5.34475e11	0.245020
$553$	−4.01890e11	−0.182745
$554$	9.06283e11	0.408761
$555$	−1.23652e10	−0.00553202
$556$	9.00627e11	0.399676
$557$	4.49057e12	1.97676	0.988379	−	0.152011i	$-0.0485750\pi$
$557$	4.49057e12	1.97676	0.988379	+	0.152011i	$0.0485750\pi$
$558$	6.15757e12	2.68878
$559$	2.44004e11	0.105693
$560$	−1.03602e11	−0.0445167
$561$	2.84860e12	1.21423
$562$	−2.39718e12	−1.01365
$563$	−1.23835e12	−0.519464	−0.259732	−	0.965681i	$-0.583634\pi$
$563$	−1.23835e12	−0.519464	−0.259732	+	0.965681i	$0.583634\pi$
$564$	−3.33443e12	−1.38761
$565$	2.94854e10	0.0121728
$566$	6.82655e12	2.79594
$567$	2.37156e11	0.0963628
$568$	−2.48485e11	−0.100169
$569$	4.24675e11	0.169845	0.0849223	−	0.996388i	$-0.472936\pi$
$569$	4.24675e11	0.169845	0.0849223	+	0.996388i	$0.472936\pi$
$570$	−1.59540e11	−0.0633044
$571$	−8.65756e10	−0.0340826	−0.0170413	−	0.999855i	$-0.505425\pi$
$571$	−8.65756e10	−0.0340826	−0.0170413	+	0.999855i	$0.505425\pi$
$572$	−7.15730e11	−0.279555
$573$	−4.21791e11	−0.163456
$574$	−1.59037e12	−0.611497
$575$	−1.16773e12	−0.445491
$576$	−6.28602e12	−2.37944
$577$	4.74305e12	1.78142	0.890711	−	0.454571i	$-0.150207\pi$
$577$	4.74305e12	1.78142	0.890711	+	0.454571i	$0.150207\pi$
$578$	−8.41601e11	−0.313640
$579$	3.72107e12	1.37599
$580$	2.99772e11	0.109993
$581$	−6.86055e10	−0.0249785
$582$	1.15752e13	4.18190
$583$	3.29051e11	0.117966
$584$	9.09697e11	0.323623
$585$	−2.17507e11	−0.0767841
$586$	6.17233e12	2.16227
$587$	−1.90663e12	−0.662819	−0.331410	−	0.943487i	$-0.607524\pi$
$587$	−1.90663e12	−0.662819	−0.331410	+	0.943487i	$0.607524\pi$
$588$	8.32790e11	0.287301
$589$	−4.90342e11	−0.167873
$590$	−1.16596e12	−0.396141
$591$	4.96049e12	1.67256
$592$	4.58733e10	0.0153501
$593$	−5.24383e11	−0.174142	−0.0870708	−	0.996202i	$-0.527751\pi$
$593$	−5.24383e11	−0.174142	−0.0870708	+	0.996202i	$0.527751\pi$
$594$	4.48802e12	1.47916
$595$	1.64602e11	0.0538405
$596$	−4.63602e12	−1.50500
$597$	1.30442e12	0.420273
$598$	−5.90613e11	−0.188863
$599$	−2.46292e12	−0.781681	−0.390841	−	0.920458i	$-0.627816\pi$
$599$	−2.46292e12	−0.781681	−0.390841	+	0.920458i	$0.627816\pi$
$600$	−1.65739e12	−0.522088
$601$	−8.09916e11	−0.253224	−0.126612	−	0.991952i	$-0.540410\pi$
$601$	−8.09916e11	−0.253224	−0.126612	+	0.991952i	$0.540410\pi$
$602$	−6.91229e11	−0.214505
$603$	7.75121e12	2.38749
$604$	−7.61811e12	−2.32906
$605$	−1.66456e11	−0.0505126
$606$	4.52225e12	1.36216
$607$	−5.91972e12	−1.76991	−0.884956	−	0.465674i	$-0.845812\pi$
$607$	−5.91972e12	−1.76991	−0.884956	+	0.465674i	$0.845812\pi$
$608$	7.67432e11	0.227758
$609$	1.19343e12	0.351575
$610$	−1.39890e12	−0.409075
$611$	6.59241e11	0.191363
$612$	6.48447e12	1.86850
$613$	−4.83544e12	−1.38313	−0.691567	−	0.722312i	$-0.743079\pi$
$613$	−4.83544e12	−1.38313	−0.691567	+	0.722312i	$0.743079\pi$
$614$	4.84977e12	1.37709
$615$	−1.02034e12	−0.287611
$616$	3.62761e11	0.101510
$617$	−9.92147e11	−0.275609	−0.137804	−	0.990459i	$-0.544005\pi$
$617$	−9.92147e11	−0.275609	−0.137804	+	0.990459i	$0.544005\pi$
$618$	1.06194e12	0.292855
$619$	−6.33450e11	−0.173422	−0.0867110	−	0.996234i	$-0.527636\pi$
$619$	−6.33450e11	−0.173422	−0.0867110	+	0.996234i	$0.527636\pi$
$620$	7.51165e11	0.204161
$621$	2.03366e12	0.548739
$622$	5.78663e12	1.55013
$623$	−1.23929e12	−0.329592
$624$	1.27422e12	0.336445
$625$	3.52305e12	0.923545
$626$	9.16345e12	2.38492
$627$	−8.49149e11	−0.219422
$628$	−3.86397e12	−0.991323
$629$	−7.28830e10	−0.0185651
$630$	6.16165e11	0.155835
$631$	−6.23202e12	−1.56494	−0.782468	−	0.622690i	$-0.786040\pi$
$631$	−6.23202e12	−1.56494	−0.782468	+	0.622690i	$0.786040\pi$
$632$	−6.29288e11	−0.156900
$633$	−1.23021e12	−0.304552
$634$	4.81847e11	0.118442
$635$	2.37491e11	0.0579649
$636$	1.18283e12	0.286658
$637$	−1.64648e11	−0.0396214
$638$	2.90559e12	0.694290
$639$	−2.24642e12	−0.533011
$640$	−4.31165e11	−0.101586
$641$	−5.59437e12	−1.30885	−0.654426	−	0.756126i	$-0.727090\pi$
$641$	−5.59437e12	−1.30885	−0.654426	+	0.756126i	$0.727090\pi$
$642$	1.45426e13	3.37857
$643$	−3.41860e12	−0.788677	−0.394339	−	0.918965i	$-0.629026\pi$
$643$	−3.41860e12	−0.788677	−0.394339	+	0.918965i	$0.629026\pi$
$644$	9.18750e11	0.210480
$645$	−4.43474e11	−0.100890
$646$	−9.40362e11	−0.212446
$647$	−1.61545e12	−0.362430	−0.181215	−	0.983444i	$-0.558003\pi$
$647$	−1.61545e12	−0.362430	−0.181215	+	0.983444i	$0.558003\pi$
$648$	3.71343e11	0.0827347
$649$	−6.20579e12	−1.37308
$650$	1.83147e12	0.402429
$651$	2.99048e12	0.652568
$652$	−7.15977e12	−1.55162
$653$	5.49044e12	1.18167	0.590837	−	0.806791i	$-0.298797\pi$
$653$	5.49044e12	1.18167	0.590837	+	0.806791i	$0.298797\pi$
$654$	−7.24728e12	−1.54908
$655$	−1.37968e12	−0.292881
$656$	3.78532e12	0.798059
$657$	8.22408e12	1.72204
$658$	−1.86754e12	−0.388376
$659$	−8.99038e12	−1.85692	−0.928461	−	0.371430i	$-0.878868\pi$
$659$	−8.99038e12	−1.85692	−0.928461	+	0.371430i	$0.878868\pi$
$660$	1.30083e12	0.266853
$661$	−8.32299e11	−0.169579	−0.0847896	−	0.996399i	$-0.527022\pi$
$661$	−8.32299e11	−0.169579	−0.0847896	+	0.996399i	$0.527022\pi$
$662$	4.38998e12	0.888386
$663$	−2.02447e12	−0.406912
$664$	−1.07424e11	−0.0214459
$665$	−4.90667e10	−0.00972948
$666$	−2.72828e11	−0.0537346
$667$	1.31661e12	0.257568
$668$	7.66147e12	1.48874
$669$	8.16450e12	1.57584
$670$	1.72197e12	0.330133
$671$	−7.44561e12	−1.41791
$672$	−4.68038e12	−0.885360
$673$	3.52571e12	0.662489	0.331245	−	0.943545i	$-0.392531\pi$
$673$	3.52571e12	0.662489	0.331245	+	0.943545i	$0.392531\pi$
$674$	−8.98701e12	−1.67744
$675$	−6.30631e12	−1.16925
$676$	5.08661e11	0.0936846
$677$	7.04729e12	1.28936	0.644678	−	0.764454i	$-0.276991\pi$
$677$	7.04729e12	1.28936	0.644678	+	0.764454i	$0.276991\pi$
$678$	1.02733e12	0.186713
$679$	3.55995e12	0.642732
$680$	2.57737e11	0.0462261
$681$	1.54612e13	2.75474
$682$	7.28079e12	1.28869
$683$	−2.92523e12	−0.514359	−0.257180	−	0.966364i	$-0.582793\pi$
$683$	−2.92523e12	−0.514359	−0.257180	+	0.966364i	$0.582793\pi$
$684$	−1.93298e12	−0.337656
$685$	−7.14819e11	−0.124048
$686$	4.66426e11	0.0804126
$687$	3.21167e12	0.550080
$688$	1.64523e12	0.279948
$689$	−2.33853e11	−0.0395327
$690$	1.07343e12	0.180282
$691$	2.22828e12	0.371807	0.185904	−	0.982568i	$-0.440479\pi$
$691$	2.22828e12	0.371807	0.185904	+	0.982568i	$0.440479\pi$
$692$	1.80420e12	0.299094
$693$	3.27952e12	0.540146
$694$	−1.13811e13	−1.86237
$695$	3.23622e11	0.0526146
$696$	1.86869e12	0.301853
$697$	−6.01407e12	−0.965208
$698$	−2.03835e11	−0.0325034
$699$	−3.42712e12	−0.542978
$700$	−2.84901e12	−0.448490
$701$	−1.51930e12	−0.237636	−0.118818	−	0.992916i	$-0.537911\pi$
$701$	−1.51930e12	−0.237636	−0.118818	+	0.992916i	$0.537911\pi$
$702$	−3.18958e12	−0.495698
$703$	2.17259e10	0.00335490
$704$	−7.43267e12	−1.14043
$705$	−1.19816e12	−0.182669
$706$	−1.79013e13	−2.71183
$707$	1.39082e12	0.209355
$708$	−2.23077e13	−3.33660
$709$	1.03221e13	1.53412	0.767061	−	0.641574i	$-0.221718\pi$
$709$	1.03221e13	1.53412	0.767061	+	0.641574i	$0.221718\pi$
$710$	−4.99053e11	−0.0737028
$711$	−5.68905e12	−0.834885
$712$	−1.94050e12	−0.282979
$713$	3.29915e12	0.478079
$714$	5.73504e12	0.825837
$715$	−2.57183e11	−0.0368015
$716$	2.09003e12	0.297197
$717$	1.02225e13	1.44451
$718$	−2.15277e12	−0.302300
$719$	−8.65348e12	−1.20757	−0.603783	−	0.797149i	$-0.706340\pi$
$719$	−8.65348e12	−1.20757	−0.603783	+	0.797149i	$0.706340\pi$
$720$	−1.46656e12	−0.203378
$721$	3.26601e11	0.0450100
$722$	−1.05937e13	−1.45087
$723$	−3.86588e12	−0.526170
$724$	1.09214e13	1.47725
$725$	−4.08277e12	−0.548825
$726$	−5.79962e12	−0.774792
$727$	−9.16346e12	−1.21662	−0.608310	−	0.793700i	$-0.708152\pi$
$727$	−9.16346e12	−1.21662	−0.608310	+	0.793700i	$0.708152\pi$
$728$	−2.57810e11	−0.0340180
$729$	−1.17547e13	−1.54147
$730$	1.82702e12	0.238117
$731$	−2.61392e12	−0.338582
$732$	−2.67644e13	−3.44554
$733$	−6.06753e12	−0.776325	−0.388163	−	0.921591i	$-0.626890\pi$
$733$	−6.06753e12	−0.776325	−0.388163	+	0.921591i	$0.626890\pi$
$734$	9.92198e12	1.26173
$735$	2.99246e11	0.0378212
$736$	−5.16349e12	−0.648624
$737$	9.16514e12	1.14429
$738$	−2.25129e13	−2.79368
$739$	6.22808e12	0.768164	0.384082	−	0.923299i	$-0.374518\pi$
$739$	6.22808e12	0.768164	0.384082	+	0.923299i	$0.374518\pi$
$740$	−3.32824e10	−0.00408011
$741$	6.03481e11	0.0735328
$742$	6.62473e11	0.0802325
$743$	−3.53737e12	−0.425825	−0.212912	−	0.977071i	$-0.568295\pi$
$743$	−3.53737e12	−0.425825	−0.212912	+	0.977071i	$0.568295\pi$
$744$	4.68255e12	0.560279
$745$	−1.66586e12	−0.198123
$746$	−6.13724e12	−0.725519
$747$	−9.71161e11	−0.114117
$748$	7.66733e12	0.895544
$749$	4.47257e12	0.519265
$750$	−6.74516e12	−0.778425
$751$	−8.26282e12	−0.947870	−0.473935	−	0.880560i	$-0.657167\pi$
$751$	−8.26282e12	−0.947870	−0.473935	+	0.880560i	$0.657167\pi$
$752$	4.44501e12	0.506865
$753$	9.19018e12	1.04171
$754$	−2.06497e12	−0.232671
$755$	−2.73741e12	−0.306605
$756$	4.96168e12	0.552434
$757$	−1.61061e12	−0.178262	−0.0891311	−	0.996020i	$-0.528409\pi$
$757$	−1.61061e12	−0.178262	−0.0891311	+	0.996020i	$0.528409\pi$
$758$	2.56395e13	2.82097
$759$	5.71330e12	0.624884
$760$	−7.68297e10	−0.00835349
$761$	−4.03650e12	−0.436289	−0.218144	−	0.975916i	$-0.570000\pi$
$761$	−4.03650e12	−0.436289	−0.218144	+	0.975916i	$0.570000\pi$
$762$	8.27462e12	0.889100
$763$	−2.22891e12	−0.238085
$764$	−1.13530e12	−0.120556
$765$	2.33006e12	0.245975
$766$	1.68978e13	1.77338
$767$	4.41038e12	0.460148
$768$	6.91508e12	0.717252
$769$	−1.61331e12	−0.166360	−0.0831799	−	0.996535i	$-0.526508\pi$
$769$	−1.61331e12	−0.166360	−0.0831799	+	0.996535i	$0.526508\pi$
$770$	7.28563e11	0.0746893
$771$	−2.04755e13	−2.08684
$772$	1.00157e13	1.01485
$773$	7.59378e12	0.764980	0.382490	−	0.923960i	$-0.375067\pi$
$773$	7.59378e12	0.764980	0.382490	+	0.923960i	$0.375067\pi$
$774$	−9.78486e12	−0.979987
$775$	−1.02306e13	−1.01869
$776$	5.57424e12	0.551833
$777$	−1.32501e11	−0.0130414
$778$	3.01849e13	2.95380
$779$	1.79275e12	0.174422
$780$	−9.24484e11	−0.0894280
$781$	−2.65619e12	−0.255464
$782$	6.32700e12	0.605017
$783$	7.11031e12	0.676022
$784$	−1.11016e12	−0.104946
$785$	−1.38844e12	−0.130501
$786$	−4.80704e13	−4.49238
$787$	1.87749e13	1.74458	0.872290	−	0.488989i	$-0.162634\pi$
$787$	1.87749e13	1.74458	0.872290	+	0.488989i	$0.162634\pi$
$788$	1.33517e13	1.23359
$789$	4.64637e12	0.426842
$790$	−1.26385e12	−0.115445
$791$	3.15955e11	0.0286966
$792$	5.13514e12	0.463756
$793$	5.29151e12	0.475171
$794$	4.85924e12	0.433887
$795$	4.25024e11	0.0377365
$796$	3.51098e12	0.309970
$797$	9.76262e12	0.857046	0.428523	−	0.903531i	$-0.359034\pi$
$797$	9.76262e12	0.857046	0.428523	+	0.903531i	$0.359034\pi$
$798$	−1.70957e12	−0.149236
$799$	−7.06219e12	−0.613026
$800$	1.60118e13	1.38209
$801$	−1.75430e13	−1.50577
$802$	−1.06366e13	−0.907861
$803$	9.72426e12	0.825347
$804$	3.29455e13	2.78063
$805$	3.30134e11	0.0277082
$806$	−5.17438e12	−0.431867
$807$	−3.68702e13	−3.06016
$808$	2.17777e12	0.179747
$809$	1.80157e13	1.47871	0.739355	−	0.673315i	$-0.235130\pi$
$809$	1.80157e13	1.47871	0.739355	+	0.673315i	$0.235130\pi$
$810$	7.45799e11	0.0608750
$811$	−1.72722e13	−1.40202	−0.701010	−	0.713151i	$-0.747267\pi$
$811$	−1.72722e13	−1.40202	−0.701010	+	0.713151i	$0.747267\pi$
$812$	3.21224e12	0.259302
$813$	2.70595e13	2.17226
$814$	−3.22595e11	−0.0257542
$815$	−2.57272e12	−0.204260
$816$	−1.36502e13	−1.07779
$817$	7.79192e11	0.0611850
$818$	1.81978e13	1.42112
$819$	−2.33072e12	−0.181014
$820$	−2.74635e12	−0.212126
$821$	−8.51791e12	−0.654318	−0.327159	−	0.944969i	$-0.606091\pi$
$821$	−8.51791e12	−0.654318	−0.327159	+	0.944969i	$0.606091\pi$
$822$	−2.49056e13	−1.90271
$823$	1.64446e13	1.24946	0.624732	−	0.780840i	$-0.285208\pi$
$823$	1.64446e13	1.24946	0.624732	+	0.780840i	$0.285208\pi$
$824$	5.11399e11	0.0386445
$825$	−1.77167e13	−1.33150
$826$	−1.24940e13	−0.933879
$827$	−1.93833e13	−1.44096	−0.720481	−	0.693475i	$-0.756079\pi$
$827$	−1.93833e13	−1.44096	−0.720481	+	0.693475i	$0.756079\pi$
$828$	1.30056e13	0.961597
$829$	−1.45904e13	−1.07293	−0.536464	−	0.843923i	$-0.680240\pi$
$829$	−1.45904e13	−1.07293	−0.536464	+	0.843923i	$0.680240\pi$
$830$	−2.15748e11	−0.0157796
$831$	6.23056e12	0.453234
$832$	5.28232e12	0.382181
$833$	1.76381e12	0.126926
$834$	1.12756e13	0.807033
$835$	2.75299e12	0.195982
$836$	−2.28558e12	−0.161833
$837$	1.78170e13	1.25478
$838$	−1.21172e13	−0.848799
$839$	1.58942e13	1.10742	0.553708	−	0.832711i	$-0.313212\pi$
$839$	1.58942e13	1.10742	0.553708	+	0.832711i	$0.313212\pi$
$840$	4.68566e11	0.0324723
$841$	−9.90386e12	−0.682688
$842$	1.19219e13	0.817414
$843$	−1.64803e13	−1.12393
$844$	−3.31124e12	−0.224621
$845$	1.82777e11	0.0123329
$846$	−2.64363e13	−1.77433
$847$	−1.78368e12	−0.119081
$848$	−1.57678e12	−0.104711
$849$	4.69315e13	3.10013
$850$	−1.96198e13	−1.28917
$851$	−1.46178e11	−0.00955429
$852$	−9.54810e12	−0.620782
$853$	3.20135e12	0.207044	0.103522	−	0.994627i	$-0.466989\pi$
$853$	3.20135e12	0.207044	0.103522	+	0.994627i	$0.466989\pi$
$854$	−1.49901e13	−0.964371
$855$	−6.94576e11	−0.0444500
$856$	7.00324e12	0.445828
$857$	−1.13802e13	−0.720668	−0.360334	−	0.932823i	$-0.617337\pi$
$857$	−1.13802e13	−0.720668	−0.360334	+	0.932823i	$0.617337\pi$
$858$	−8.96072e12	−0.564482
$859$	8.79469e12	0.551127	0.275563	−	0.961283i	$-0.411136\pi$
$859$	8.79469e12	0.551127	0.275563	+	0.961283i	$0.411136\pi$
$860$	−1.19366e12	−0.0744110
$861$	−1.09336e13	−0.678028
$862$	3.65794e13	2.25659
$863$	1.55496e13	0.954266	0.477133	−	0.878831i	$-0.341676\pi$
$863$	1.55496e13	0.954266	0.477133	+	0.878831i	$0.341676\pi$
$864$	−2.78852e13	−1.70240
$865$	6.48304e11	0.0393737
$866$	2.12910e13	1.28637
$867$	−5.78588e12	−0.347763
$868$	8.04920e12	0.481298
$869$	−6.72681e12	−0.400148
$870$	3.75305e12	0.222100
$871$	−6.51356e12	−0.383475
$872$	−3.49006e12	−0.204413
$873$	5.03937e13	2.93638
$874$	−1.88604e12	−0.109332
$875$	−2.07448e12	−0.119639
$876$	3.49554e13	2.00561
$877$	−1.32707e13	−0.757520	−0.378760	−	0.925495i	$-0.623649\pi$
$877$	−1.32707e13	−0.757520	−0.378760	+	0.925495i	$0.623649\pi$
$878$	−1.39518e13	−0.792326
$879$	4.24339e13	2.39752
$880$	−1.73409e12	−0.0974762
$881$	−3.59506e12	−0.201055	−0.100527	−	0.994934i	$-0.532053\pi$
$881$	−3.59506e12	−0.201055	−0.100527	+	0.994934i	$0.532053\pi$
$882$	6.60260e12	0.367372
$883$	8.03617e12	0.444863	0.222431	−	0.974948i	$-0.428601\pi$
$883$	8.03617e12	0.444863	0.222431	+	0.974948i	$0.428601\pi$
$884$	−5.44909e12	−0.300116
$885$	−8.01580e12	−0.439240
$886$	3.08367e13	1.68119
$887$	1.42555e13	0.773263	0.386631	−	0.922234i	$-0.373639\pi$
$887$	1.42555e13	0.773263	0.386631	+	0.922234i	$0.373639\pi$
$888$	−2.07473e11	−0.0111970
$889$	2.54486e12	0.136649
$890$	−3.89727e12	−0.208212
$891$	3.96949e12	0.211001
$892$	2.19757e13	1.16225
$893$	2.10519e12	0.110780
$894$	−5.80416e13	−3.03893
$895$	7.51011e11	0.0391240
$896$	−4.62021e12	−0.239483
$897$	−4.06038e12	−0.209411
$898$	−4.80005e13	−2.46321
$899$	1.15349e13	0.588971
$900$	−4.03299e13	−2.04897
$901$	2.50518e12	0.126642
$902$	−2.66195e13	−1.33897
$903$	−4.75210e12	−0.237843
$904$	4.94728e11	0.0246382
$905$	3.92438e12	0.194470
$906$	−9.53764e13	−4.70288
$907$	−2.85005e13	−1.39836	−0.699180	−	0.714946i	$-0.746451\pi$
$907$	−2.85005e13	−1.39836	−0.699180	+	0.714946i	$0.746451\pi$
$908$	4.16154e13	2.03174
$909$	1.96881e13	0.956458
$910$	−5.17781e11	−0.0250299
$911$	−3.45047e13	−1.65976	−0.829880	−	0.557941i	$-0.811591\pi$
$911$	−3.45047e13	−1.65976	−0.829880	+	0.557941i	$0.811591\pi$
$912$	4.06904e12	0.194767
$913$	−1.14831e12	−0.0546944
$914$	−2.92340e13	−1.38557
$915$	−9.61724e12	−0.453582
$916$	8.64457e12	0.405708
$917$	−1.47841e13	−0.690450
$918$	3.41688e13	1.58795
$919$	2.93845e12	0.135893	0.0679466	−	0.997689i	$-0.478355\pi$
$919$	2.93845e12	0.135893	0.0679466	+	0.997689i	$0.478355\pi$
$920$	5.16931e11	0.0237896
$921$	3.33415e13	1.52692
$922$	1.41785e13	0.646162
$923$	1.88773e12	0.0856114
$924$	1.39392e13	0.629091
$925$	4.53292e11	0.0203583
$926$	−2.60191e13	−1.16290
$927$	4.62328e12	0.205632
$928$	−1.80532e13	−0.799076
$929$	2.68674e12	0.118346	0.0591731	−	0.998248i	$-0.481154\pi$
$929$	2.68674e12	0.118346	0.0591731	+	0.998248i	$0.481154\pi$
$930$	9.40435e12	0.412245
$931$	−5.25781e11	−0.0229367
$932$	−9.22447e12	−0.400470
$933$	3.97822e13	1.71878
$934$	3.59988e13	1.54784
$935$	2.75510e12	0.117892
$936$	−3.64949e12	−0.155414
$937$	−2.02950e13	−0.860123	−0.430061	−	0.902800i	$-0.641508\pi$
$937$	−2.02950e13	−0.860123	−0.430061	+	0.902800i	$0.641508\pi$
$938$	1.84520e13	0.778270
$939$	6.29974e13	2.64440
$940$	−3.22498e12	−0.134726
$941$	−4.10361e13	−1.70613	−0.853066	−	0.521803i	$-0.825260\pi$
$941$	−4.10361e13	−1.70613	−0.853066	+	0.521803i	$0.825260\pi$
$942$	−4.83757e13	−2.00170
$943$	−1.20621e13	−0.496731
$944$	2.97375e13	1.21880
$945$	1.78288e12	0.0727241
$946$	−1.15698e13	−0.469693
$947$	3.62404e13	1.46426	0.732130	−	0.681165i	$-0.238526\pi$
$947$	3.62404e13	1.46426	0.732130	+	0.681165i	$0.238526\pi$
$948$	−2.41806e13	−0.972364
$949$	−6.91092e12	−0.276591
$950$	5.84853e12	0.232965
$951$	3.31263e12	0.131329
$952$	2.76182e12	0.108975
$953$	−3.21086e12	−0.126096	−0.0630482	−	0.998010i	$-0.520082\pi$
$953$	−3.21086e12	−0.126096	−0.0630482	+	0.998010i	$0.520082\pi$
$954$	9.37778e12	0.366549
$955$	−4.07946e11	−0.0158704
$956$	2.75150e13	1.06539
$957$	1.99755e13	0.769828
$958$	6.86959e13	2.63503
$959$	−7.65973e12	−0.292435
$960$	−9.60053e12	−0.364817
$961$	2.46435e12	0.0932065
$962$	2.29265e11	0.00863077
$963$	6.33125e13	2.37231
$964$	−1.04054e13	−0.388073
$965$	3.59893e12	0.133598
$966$	1.15025e13	0.425005
$967$	−2.39693e13	−0.881527	−0.440763	−	0.897623i	$-0.645292\pi$
$967$	−2.39693e13	−0.881527	−0.440763	+	0.897623i	$0.645292\pi$
$968$	−2.79292e12	−0.102240
$969$	−6.46485e12	−0.235560
$970$	1.11952e13	0.406031
$971$	−4.28783e13	−1.54793	−0.773965	−	0.633228i	$-0.781729\pi$
$971$	−4.28783e13	−1.54793	−0.773965	+	0.633228i	$0.781729\pi$
$972$	−2.64061e13	−0.948867
$973$	3.46781e12	0.124036
$974$	5.90294e13	2.10161
$975$	1.25911e13	0.446213
$976$	3.56786e13	1.25859
$977$	−4.90691e12	−0.172299	−0.0861495	−	0.996282i	$-0.527456\pi$
$977$	−4.90691e12	−0.172299	−0.0861495	+	0.996282i	$0.527456\pi$
$978$	−8.96382e13	−3.13306
$979$	−2.07431e13	−0.721693
$980$	8.05454e11	0.0278948
$981$	−3.15518e13	−1.08771
$982$	7.49880e13	2.57330
$983$	4.75895e12	0.162563	0.0812813	−	0.996691i	$-0.474099\pi$
$983$	4.75895e12	0.162563	0.0812813	+	0.996691i	$0.474099\pi$
$984$	−1.71200e13	−0.582137
$985$	4.79767e12	0.162393
$986$	2.21212e13	0.745354
$987$	−1.28390e13	−0.430631
$988$	1.62433e12	0.0542337
$989$	−5.24261e12	−0.174247
$990$	1.03133e13	0.341225
$991$	1.91602e13	0.631058	0.315529	−	0.948916i	$-0.397818\pi$
$991$	1.91602e13	0.631058	0.315529	+	0.948916i	$0.397818\pi$
$992$	−4.52375e13	−1.48319
$993$	3.01805e13	0.985041
$994$	−5.34766e12	−0.173750
$995$	1.26160e12	0.0408054
$996$	−4.12780e12	−0.132908
$997$	−3.33739e13	−1.06974	−0.534870	−	0.844934i	$-0.679640\pi$
$997$	−3.33739e13	−1.06974	−0.534870	+	0.844934i	$0.679640\pi$
$998$	−4.47711e13	−1.42860
$999$	−7.89428e11	−0.0250766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+33.6981 q^{2} +231.670 q^{3} +623.565 q^{4} +224.065 q^{5} +7806.84 q^{6} +2401.00 q^{7} +3759.53 q^{8} +33987.9 q^{9} +O(q^{10})\)	\(q+33.6981 q^{2} +231.670 q^{3} +623.565 q^{4} +224.065 q^{5} +7806.84 q^{6} +2401.00 q^{7} +3759.53 q^{8} +33987.9 q^{9} +7550.59 q^{10} +40187.8 q^{11} +144461. q^{12} -28561.0 q^{13} +80909.2 q^{14} +51909.2 q^{15} -192576. q^{16} +305963. q^{17} +1.14533e6 q^{18} -91205.4 q^{19} +139719. q^{20} +556239. q^{21} +1.35425e6 q^{22} +613654. q^{23} +870971. q^{24} -1.90292e6 q^{25} -962453. q^{26} +3.31402e6 q^{27} +1.49718e6 q^{28} +2.14553e6 q^{29} +1.74924e6 q^{30} +5.37624e6 q^{31} -8.41433e6 q^{32} +9.31030e6 q^{33} +1.03104e7 q^{34} +537981. q^{35} +2.11937e7 q^{36} -238209. q^{37} -3.07345e6 q^{38} -6.61672e6 q^{39} +842381. q^{40} -1.96562e7 q^{41} +1.87442e7 q^{42} -8.54327e6 q^{43} +2.50597e7 q^{44} +7.61551e6 q^{45} +2.06790e7 q^{46} -2.30819e7 q^{47} -4.46140e7 q^{48} +5.76480e6 q^{49} -6.41249e7 q^{50} +7.08823e7 q^{51} -1.78096e7 q^{52} +8.18785e6 q^{53} +1.11676e8 q^{54} +9.00469e6 q^{55} +9.02664e6 q^{56} -2.11295e7 q^{57} +7.23003e7 q^{58} -1.54420e8 q^{59} +3.23687e7 q^{60} -1.85271e8 q^{61} +1.81169e8 q^{62} +8.16050e7 q^{63} -1.84949e8 q^{64} -6.39953e6 q^{65} +3.13740e8 q^{66} +2.28058e8 q^{67} +1.90788e8 q^{68} +1.42165e8 q^{69} +1.81290e7 q^{70} -6.60946e7 q^{71} +1.27779e8 q^{72} +2.41971e8 q^{73} -8.02720e6 q^{74} -4.40849e8 q^{75} -5.68725e7 q^{76} +9.64909e7 q^{77} -2.22971e8 q^{78} -1.67385e8 q^{79} -4.31496e7 q^{80} +9.87737e7 q^{81} -6.62378e8 q^{82} -2.85737e7 q^{83} +3.46851e8 q^{84} +6.85556e7 q^{85} -2.87892e8 q^{86} +4.97054e8 q^{87} +1.51087e8 q^{88} -5.16155e8 q^{89} +2.56629e8 q^{90} -6.85750e7 q^{91} +3.82653e8 q^{92} +1.24551e9 q^{93} -7.77816e8 q^{94} -2.04360e7 q^{95} -1.94935e9 q^{96} +1.48269e9 q^{97} +1.94263e8 q^{98} +1.36590e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 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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