LMFDB - Embedded newform 91.8.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,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, 8, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-20.4545$ 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)

$f(q)$	$=$	$q+21.4545 q^{2} -57.9549 q^{3} +332.295 q^{4} +368.020 q^{5} -1243.39 q^{6} +343.000 q^{7} +4383.05 q^{8} +1171.77 q^{9} +O(q^{10})$	\(q+21.4545 q^{2} -57.9549 q^{3} +332.295 q^{4} +368.020 q^{5} -1243.39 q^{6} +343.000 q^{7} +4383.05 q^{8} +1171.77 q^{9} +7895.68 q^{10} -3956.94 q^{11} -19258.1 q^{12} +2197.00 q^{13} +7358.89 q^{14} -21328.6 q^{15} +51502.3 q^{16} +18410.7 q^{17} +25139.8 q^{18} +49599.2 q^{19} +122291. q^{20} -19878.5 q^{21} -84894.2 q^{22} -65802.0 q^{23} -254019. q^{24} +57313.6 q^{25} +47135.5 q^{26} +58837.3 q^{27} +113977. q^{28} +139239. q^{29} -457593. q^{30} -80569.9 q^{31} +543925. q^{32} +229324. q^{33} +394991. q^{34} +126231. q^{35} +389375. q^{36} -331607. q^{37} +1.06413e6 q^{38} -127327. q^{39} +1.61305e6 q^{40} +600160. q^{41} -426484. q^{42} +407204. q^{43} -1.31487e6 q^{44} +431236. q^{45} -1.41175e6 q^{46} -403277. q^{47} -2.98481e6 q^{48} +117649. q^{49} +1.22963e6 q^{50} -1.06699e6 q^{51} +730052. q^{52} -766525. q^{53} +1.26233e6 q^{54} -1.45623e6 q^{55} +1.50339e6 q^{56} -2.87452e6 q^{57} +2.98731e6 q^{58} -2.94498e6 q^{59} -7.08738e6 q^{60} -772451. q^{61} -1.72859e6 q^{62} +401919. q^{63} +5.07735e6 q^{64} +808540. q^{65} +4.92004e6 q^{66} -4.03272e6 q^{67} +6.11777e6 q^{68} +3.81355e6 q^{69} +2.70822e6 q^{70} +2.55540e6 q^{71} +5.13594e6 q^{72} -2.53403e6 q^{73} -7.11445e6 q^{74} -3.32161e6 q^{75} +1.64816e7 q^{76} -1.35723e6 q^{77} -2.73174e6 q^{78} -2.00823e6 q^{79} +1.89539e7 q^{80} -5.97258e6 q^{81} +1.28761e7 q^{82} -8.63495e6 q^{83} -6.60554e6 q^{84} +6.77549e6 q^{85} +8.73635e6 q^{86} -8.06961e6 q^{87} -1.73435e7 q^{88} -4.56488e6 q^{89} +9.25195e6 q^{90} +753571. q^{91} -2.18657e7 q^{92} +4.66942e6 q^{93} -8.65210e6 q^{94} +1.82535e7 q^{95} -3.15232e7 q^{96} +2.73971e6 q^{97} +2.52410e6 q^{98} -4.63664e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	21.4545	1.89633	0.948163	−	0.317783i	$-0.102938\pi$
$2$	21.4545	1.89633	0.948163	+	0.317783i	$0.102938\pi$
$3$	−57.9549	−1.23927	−0.619635	−	0.784890i	$-0.712719\pi$
$3$	−57.9549	−1.23927	−0.619635	+	0.784890i	$0.712719\pi$
$4$	332.295	2.59606
$5$	368.020	1.31667	0.658334	−	0.752726i	$-0.271262\pi$
$5$	368.020	1.31667	0.658334	+	0.752726i	$0.271262\pi$
$6$	−1243.39	−2.35006
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	4383.05	3.02664
$9$	1171.77	0.535791
$10$	7895.68	2.49683
$11$	−3956.94	−0.896366	−0.448183	−	0.893942i	$-0.647929\pi$
$11$	−3956.94	−0.896366	−0.448183	+	0.893942i	$0.647929\pi$
$12$	−19258.1	−3.21721
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	7358.89	0.716744
$15$	−21328.6	−1.63171
$16$	51502.3	3.14345
$17$	18410.7	0.908863	0.454431	−	0.890782i	$-0.349843\pi$
$17$	18410.7	0.908863	0.454431	+	0.890782i	$0.349843\pi$
$18$	25139.8	1.01603
$19$	49599.2	1.65896	0.829482	−	0.558534i	$-0.188636\pi$
$19$	49599.2	1.65896	0.829482	+	0.558534i	$0.188636\pi$
$20$	122291.	3.41814
$21$	−19878.5	−0.468400
$22$	−84894.2	−1.69980
$23$	−65802.0	−1.12770	−0.563848	−	0.825879i	$-0.690679\pi$
$23$	−65802.0	−1.12770	−0.563848	+	0.825879i	$0.690679\pi$
$24$	−254019.	−3.75083
$25$	57313.6	0.733614
$26$	47135.5	0.525946
$27$	58837.3	0.575281
$28$	113977.	0.981217
$29$	139239.	1.06015	0.530077	−	0.847949i	$-0.322163\pi$
$29$	139239.	1.06015	0.530077	+	0.847949i	$0.322163\pi$
$30$	−457593.	−3.09425
$31$	−80569.9	−0.485743	−0.242872	−	0.970058i	$-0.578089\pi$
$31$	−80569.9	−0.485743	−0.242872	+	0.970058i	$0.578089\pi$
$32$	543925.	2.93437
$33$	229324.	1.11084
$34$	394991.	1.72350
$35$	126231.	0.497654
$36$	389375.	1.39094
$37$	−331607.	−1.07626	−0.538130	−	0.842862i	$-0.680869\pi$
$37$	−331607.	−1.07626	−0.538130	+	0.842862i	$0.680869\pi$
$38$	1.06413e6	3.14594
$39$	−127327.	−0.343712
$40$	1.61305e6	3.98508
$41$	600160.	1.35995	0.679975	−	0.733235i	$-0.261990\pi$
$41$	600160.	1.35995	0.679975	+	0.733235i	$0.261990\pi$
$42$	−426484.	−0.888240
$43$	407204.	0.781038	0.390519	−	0.920595i	$-0.372296\pi$
$43$	407204.	0.781038	0.390519	+	0.920595i	$0.372296\pi$
$44$	−1.31487e6	−2.32702
$45$	431236.	0.705458
$46$	−1.41175e6	−2.13848
$47$	−403277.	−0.566580	−0.283290	−	0.959034i	$-0.591426\pi$
$47$	−403277.	−0.566580	−0.283290	+	0.959034i	$0.591426\pi$
$48$	−2.98481e6	−3.89558
$49$	117649.	0.142857
$50$	1.22963e6	1.39117
$51$	−1.06699e6	−1.12633
$52$	730052.	0.720016
$53$	−766525.	−0.707231	−0.353615	−	0.935391i	$-0.615048\pi$
$53$	−766525.	−0.707231	−0.353615	+	0.935391i	$0.615048\pi$
$54$	1.26233e6	1.09092
$55$	−1.45623e6	−1.18022
$56$	1.50339e6	1.14396
$57$	−2.87452e6	−2.05590
$58$	2.98731e6	2.01040
$59$	−2.94498e6	−1.86681	−0.933405	−	0.358826i	$-0.883177\pi$
$59$	−2.94498e6	−1.86681	−0.933405	+	0.358826i	$0.883177\pi$
$60$	−7.08738e6	−4.23600
$61$	−772451.	−0.435729	−0.217865	−	0.975979i	$-0.569909\pi$
$61$	−772451.	−0.435729	−0.217865	+	0.975979i	$0.569909\pi$
$62$	−1.72859e6	−0.921128
$63$	401919.	0.202510
$64$	5.07735e6	2.42107
$65$	808540.	0.365178
$66$	4.92004e6	2.10652
$67$	−4.03272e6	−1.63809	−0.819043	−	0.573733i	$-0.805495\pi$
$67$	−4.03272e6	−1.63809	−0.819043	+	0.573733i	$0.805495\pi$
$68$	6.11777e6	2.35946
$69$	3.81355e6	1.39752
$70$	2.70822e6	0.943714
$71$	2.55540e6	0.847334	0.423667	−	0.905818i	$-0.360743\pi$
$71$	2.55540e6	0.847334	0.423667	+	0.905818i	$0.360743\pi$
$72$	5.13594e6	1.62165
$73$	−2.53403e6	−0.762397	−0.381199	−	0.924493i	$-0.624489\pi$
$73$	−2.53403e6	−0.762397	−0.381199	+	0.924493i	$0.624489\pi$
$74$	−7.11445e6	−2.04094
$75$	−3.32161e6	−0.909146
$76$	1.64816e7	4.30676
$77$	−1.35723e6	−0.338795
$78$	−2.73174e6	−0.651790
$79$	−2.00823e6	−0.458266	−0.229133	−	0.973395i	$-0.573589\pi$
$79$	−2.00823e6	−0.458266	−0.229133	+	0.973395i	$0.573589\pi$
$80$	1.89539e7	4.13888
$81$	−5.97258e6	−1.24872
$82$	1.28761e7	2.57891
$83$	−8.63495e6	−1.65763	−0.828813	−	0.559526i	$-0.810983\pi$
$83$	−8.63495e6	−1.65763	−0.828813	+	0.559526i	$0.810983\pi$
$84$	−6.60554e6	−1.21599
$85$	6.77549e6	1.19667
$86$	8.73635e6	1.48110
$87$	−8.06961e6	−1.31382
$88$	−1.73435e7	−2.71298
$89$	−4.56488e6	−0.686380	−0.343190	−	0.939266i	$-0.611507\pi$
$89$	−4.56488e6	−0.686380	−0.343190	+	0.939266i	$0.611507\pi$
$90$	9.25195e6	1.33778
$91$	753571.	0.104828
$92$	−2.18657e7	−2.92756
$93$	4.66942e6	0.601967
$94$	−8.65210e6	−1.07442
$95$	1.82535e7	2.18430
$96$	−3.15232e7	−3.63647
$97$	2.73971e6	0.304792	0.152396	−	0.988319i	$-0.451301\pi$
$97$	2.73971e6	0.304792	0.152396	+	0.988319i	$0.451301\pi$
$98$	2.52410e6	0.270904
$99$	−4.63664e6	−0.480265
$100$	1.90450e7	1.90450
$101$	1.86139e7	1.79768	0.898839	−	0.438280i	$-0.144412\pi$
$101$	1.86139e7	1.79768	0.898839	+	0.438280i	$0.144412\pi$
$102$	−2.28917e7	−2.13588
$103$	−4.55736e6	−0.410945	−0.205472	−	0.978663i	$-0.565873\pi$
$103$	−4.55736e6	−0.410945	−0.205472	+	0.978663i	$0.565873\pi$
$104$	9.62956e6	0.839440
$105$	−7.31570e6	−0.616727
$106$	−1.64454e7	−1.34114
$107$	−1.70465e6	−0.134521	−0.0672606	−	0.997735i	$-0.521426\pi$
$107$	−1.70465e6	−0.134521	−0.0672606	+	0.997735i	$0.521426\pi$
$108$	1.95514e7	1.49346
$109$	−1.42288e7	−1.05239	−0.526195	−	0.850364i	$-0.676382\pi$
$109$	−1.42288e7	−1.05239	−0.526195	+	0.850364i	$0.676382\pi$
$110$	−3.12428e7	−2.23808
$111$	1.92182e7	1.33378
$112$	1.76653e7	1.18811
$113$	2.43770e7	1.58930	0.794651	−	0.607066i	$-0.207654\pi$
$113$	2.43770e7	1.58930	0.794651	+	0.607066i	$0.207654\pi$
$114$	−6.16713e7	−3.89867
$115$	−2.42164e7	−1.48480
$116$	4.62686e7	2.75222
$117$	2.57439e6	0.148602
$118$	−6.31830e7	−3.54008
$119$	6.31486e6	0.343518
$120$	−9.34841e7	−4.93860
$121$	−3.82977e6	−0.196528
$122$	−1.65726e7	−0.826285
$123$	−3.47822e7	−1.68535
$124$	−2.67730e7	−1.26102
$125$	−7.65901e6	−0.350742
$126$	8.62296e6	0.384025
$127$	3.65627e7	1.58389	0.791946	−	0.610592i	$-0.209068\pi$
$127$	3.65627e7	1.58389	0.791946	+	0.610592i	$0.209068\pi$
$128$	3.93094e7	1.65677
$129$	−2.35995e7	−0.967917
$130$	1.73468e7	0.692497
$131$	4.30483e7	1.67304	0.836520	−	0.547936i	$-0.184586\pi$
$131$	4.30483e7	1.67304	0.836520	+	0.547936i	$0.184586\pi$
$132$	7.62034e7	2.88380
$133$	1.70125e7	0.627029
$134$	−8.65200e7	−3.10635
$135$	2.16533e7	0.757454
$136$	8.06948e7	2.75080
$137$	−6.08723e6	−0.202254	−0.101127	−	0.994874i	$-0.532245\pi$
$137$	−6.08723e6	−0.202254	−0.101127	+	0.994874i	$0.532245\pi$
$138$	8.18178e7	2.65015
$139$	−1.53650e7	−0.485266	−0.242633	−	0.970118i	$-0.578011\pi$
$139$	−1.53650e7	−0.485266	−0.242633	+	0.970118i	$0.578011\pi$
$140$	4.19459e7	1.29194
$141$	2.33719e7	0.702145
$142$	5.48248e7	1.60682
$143$	−8.69341e6	−0.248607
$144$	6.03491e7	1.68423
$145$	5.12429e7	1.39587
$146$	−5.43663e7	−1.44575
$147$	−6.81834e6	−0.177039
$148$	−1.10191e8	−2.79403
$149$	−6.92801e7	−1.71576	−0.857880	−	0.513851i	$-0.828219\pi$
$149$	−6.92801e7	−1.71576	−0.857880	+	0.513851i	$0.828219\pi$
$150$	−7.12634e7	−1.72404
$151$	−4.72439e7	−1.11667	−0.558337	−	0.829614i	$-0.688560\pi$
$151$	−4.72439e7	−1.11667	−0.558337	+	0.829614i	$0.688560\pi$
$152$	2.17396e8	5.02109
$153$	2.15731e7	0.486960
$154$	−2.91187e7	−0.642465
$155$	−2.96513e7	−0.639562
$156$	−4.23101e7	−0.892295
$157$	2.88947e7	0.595895	0.297948	−	0.954582i	$-0.403698\pi$
$157$	2.88947e7	0.595895	0.297948	+	0.954582i	$0.403698\pi$
$158$	−4.30854e7	−0.869022
$159$	4.44239e7	0.876450
$160$	2.00175e8	3.86359
$161$	−2.25701e7	−0.426229
$162$	−1.28139e8	−2.36798
$163$	3.43157e7	0.620635	0.310318	−	0.950633i	$-0.399565\pi$
$163$	3.43157e7	0.620635	0.310318	+	0.950633i	$0.399565\pi$
$164$	1.99430e8	3.53051
$165$	8.43959e7	1.46261
$166$	−1.85258e8	−3.14340
$167$	−4.49299e7	−0.746497	−0.373249	−	0.927731i	$-0.621756\pi$
$167$	−4.49299e7	−0.746497	−0.373249	+	0.927731i	$0.621756\pi$
$168$	−8.71286e7	−1.41768
$169$	4.82681e6	0.0769231
$170$	1.45365e8	2.26928
$171$	5.81190e7	0.888857
$172$	1.35312e8	2.02762
$173$	5.77523e7	0.848023	0.424012	−	0.905657i	$-0.360622\pi$
$173$	5.77523e7	0.848023	0.424012	+	0.905657i	$0.360622\pi$
$174$	−1.73129e8	−2.49143
$175$	1.96586e7	0.277280
$176$	−2.03792e8	−2.81768
$177$	1.70676e8	2.31348
$178$	−9.79372e7	−1.30160
$179$	−1.11756e8	−1.45641	−0.728205	−	0.685360i	$-0.759645\pi$
$179$	−1.11756e8	−1.45641	−0.728205	+	0.685360i	$0.759645\pi$
$180$	1.43298e8	1.83141
$181$	8.62628e7	1.08131	0.540653	−	0.841246i	$-0.318177\pi$
$181$	8.62628e7	1.08131	0.540653	+	0.841246i	$0.318177\pi$
$182$	1.61675e7	0.198789
$183$	4.47674e7	0.539986
$184$	−2.88413e8	−3.41313
$185$	−1.22038e8	−1.41708
$186$	1.00180e8	1.14153
$187$	−7.28500e7	−0.814674
$188$	−1.34007e8	−1.47087
$189$	2.01812e7	0.217436
$190$	3.91619e8	4.14215
$191$	−1.53573e8	−1.59477	−0.797387	−	0.603468i	$-0.793785\pi$
$191$	−1.53573e8	−1.59477	−0.797387	+	0.603468i	$0.793785\pi$
$192$	−2.94257e8	−3.00036
$193$	1.62516e8	1.62722	0.813609	−	0.581412i	$-0.197499\pi$
$193$	1.62516e8	1.62722	0.813609	+	0.581412i	$0.197499\pi$
$194$	5.87792e7	0.577986
$195$	−4.68589e7	−0.452554
$196$	3.90942e7	0.370865
$197$	−1.21457e6	−0.0113185	−0.00565925	−	0.999984i	$-0.501801\pi$
$197$	−1.21457e6	−0.0113185	−0.00565925	+	0.999984i	$0.501801\pi$
$198$	−9.94768e7	−0.910739
$199$	−3.17081e7	−0.285223	−0.142612	−	0.989779i	$-0.545550\pi$
$199$	−3.17081e7	−0.285223	−0.142612	+	0.989779i	$0.545550\pi$
$200$	2.51208e8	2.22039
$201$	2.33716e8	2.03003
$202$	3.99351e8	3.40898
$203$	4.77591e7	0.400701
$204$	−3.54555e8	−2.92401
$205$	2.20871e8	1.79060
$206$	−9.77759e7	−0.779285
$207$	−7.71051e7	−0.604209
$208$	1.13151e8	0.871836
$209$	−1.96261e8	−1.48704
$210$	−1.56955e8	−1.16952
$211$	−1.29291e8	−0.947499	−0.473749	−	0.880660i	$-0.657100\pi$
$211$	−1.29291e8	−0.947499	−0.473749	+	0.880660i	$0.657100\pi$
$212$	−2.54713e8	−1.83601
$213$	−1.48098e8	−1.05008
$214$	−3.65723e7	−0.255096
$215$	1.49859e8	1.02837
$216$	2.57887e8	1.74117
$217$	−2.76355e7	−0.183594
$218$	−3.05273e8	−1.99568
$219$	1.46859e8	0.944816
$220$	−4.83899e8	−3.06391
$221$	4.04482e7	0.252073
$222$	4.12318e8	2.52928
$223$	1.08405e8	0.654611	0.327306	−	0.944919i	$-0.393859\pi$
$223$	1.08405e8	0.654611	0.327306	+	0.944919i	$0.393859\pi$
$224$	1.86566e8	1.10909
$225$	6.71586e7	0.393064
$226$	5.22997e8	3.01384
$227$	−2.18762e8	−1.24131	−0.620656	−	0.784083i	$-0.713134\pi$
$227$	−2.18762e8	−1.24131	−0.620656	+	0.784083i	$0.713134\pi$
$228$	−9.55188e8	−5.33724
$229$	2.06490e7	0.113625	0.0568126	−	0.998385i	$-0.481906\pi$
$229$	2.06490e7	0.113625	0.0568126	+	0.998385i	$0.481906\pi$
$230$	−5.19551e8	−2.81567
$231$	7.86583e7	0.419858
$232$	6.10293e8	3.20871
$233$	4.41473e7	0.228643	0.114322	−	0.993444i	$-0.463531\pi$
$233$	4.41473e7	0.228643	0.114322	+	0.993444i	$0.463531\pi$
$234$	5.52322e7	0.281797
$235$	−1.48414e8	−0.745997
$236$	−9.78602e8	−4.84634
$237$	1.16387e8	0.567915
$238$	1.35482e8	0.651422
$239$	2.96903e8	1.40677	0.703383	−	0.710811i	$-0.251672\pi$
$239$	2.96903e8	1.40677	0.703383	+	0.710811i	$0.251672\pi$
$240$	−1.09847e9	−5.12919
$241$	6.20616e7	0.285604	0.142802	−	0.989751i	$-0.454389\pi$
$241$	6.20616e7	0.285604	0.142802	+	0.989751i	$0.454389\pi$
$242$	−8.21657e7	−0.372681
$243$	2.17463e8	0.972219
$244$	−2.56682e8	−1.13118
$245$	4.32972e7	0.188095
$246$	−7.46235e8	−3.19597
$247$	1.08969e8	0.460114
$248$	−3.53142e8	−1.47017
$249$	5.00438e8	2.05425
$250$	−1.64320e8	−0.665121
$251$	1.46602e8	0.585171	0.292585	−	0.956239i	$-0.405484\pi$
$251$	1.46602e8	0.585171	0.292585	+	0.956239i	$0.405484\pi$
$252$	1.33556e8	0.525727
$253$	2.60375e8	1.01083
$254$	7.84434e8	3.00358
$255$	−3.92673e8	−1.48300
$256$	1.93464e8	0.720709
$257$	−1.74246e8	−0.640319	−0.320160	−	0.947364i	$-0.603737\pi$
$257$	−1.74246e8	−0.640319	−0.320160	+	0.947364i	$0.603737\pi$
$258$	−5.06315e8	−1.83549
$259$	−1.13741e8	−0.406788
$260$	2.68674e8	0.948022
$261$	1.63157e8	0.568021
$262$	9.23579e8	3.17263
$263$	6.67763e7	0.226348	0.113174	−	0.993575i	$-0.463898\pi$
$263$	6.67763e7	0.226348	0.113174	+	0.993575i	$0.463898\pi$
$264$	1.00514e9	3.36212
$265$	−2.82097e8	−0.931188
$266$	3.64995e8	1.18905
$267$	2.64557e8	0.850610
$268$	−1.34005e9	−4.25256
$269$	1.25914e8	0.394404	0.197202	−	0.980363i	$-0.436814\pi$
$269$	1.25914e8	0.394404	0.197202	+	0.980363i	$0.436814\pi$
$270$	4.64561e8	1.43638
$271$	−2.29438e8	−0.700281	−0.350140	−	0.936697i	$-0.613866\pi$
$271$	−2.29438e8	−0.700281	−0.350140	+	0.936697i	$0.613866\pi$
$272$	9.48192e8	2.85696
$273$	−4.36732e7	−0.129911
$274$	−1.30598e8	−0.383540
$275$	−2.26787e8	−0.657587
$276$	1.26722e9	3.62804
$277$	2.44611e8	0.691508	0.345754	−	0.938325i	$-0.387623\pi$
$277$	2.44611e8	0.691508	0.345754	+	0.938325i	$0.387623\pi$
$278$	−3.29648e8	−0.920224
$279$	−9.44097e7	−0.260257
$280$	5.53276e8	1.50622
$281$	3.03651e8	0.816398	0.408199	−	0.912893i	$-0.366157\pi$
$281$	3.03651e8	0.816398	0.408199	+	0.912893i	$0.366157\pi$
$282$	5.01432e8	1.33150
$283$	6.42389e8	1.68479	0.842394	−	0.538862i	$-0.181145\pi$
$283$	6.42389e8	1.68479	0.842394	+	0.538862i	$0.181145\pi$
$284$	8.49147e8	2.19973
$285$	−1.05788e9	−2.70694
$286$	−1.86513e8	−0.471441
$287$	2.05855e8	0.514013
$288$	6.37358e8	1.57221
$289$	−7.13861e7	−0.173969
$290$	1.09939e9	2.64703
$291$	−1.58780e8	−0.377720
$292$	−8.42045e8	−1.97923
$293$	−1.82926e8	−0.424852	−0.212426	−	0.977177i	$-0.568136\pi$
$293$	−1.82926e8	−0.424852	−0.212426	+	0.977177i	$0.568136\pi$
$294$	−1.46284e8	−0.335723
$295$	−1.08381e9	−2.45797
$296$	−1.45345e9	−3.25746
$297$	−2.32816e8	−0.515662
$298$	−1.48637e9	−3.25364
$299$	−1.44567e8	−0.312766
$300$	−1.10375e9	−2.36019
$301$	1.39671e8	0.295205
$302$	−1.01359e9	−2.11758
$303$	−1.07877e9	−2.22781
$304$	2.55447e9	5.21487
$305$	−2.84277e8	−0.573711
$306$	4.62841e8	0.923436
$307$	−2.22234e8	−0.438356	−0.219178	−	0.975685i	$-0.570338\pi$
$307$	−2.22234e8	−0.438356	−0.219178	+	0.975685i	$0.570338\pi$
$308$	−4.51002e8	−0.879530
$309$	2.64122e8	0.509271
$310$	−6.36154e8	−1.21282
$311$	3.37759e8	0.636715	0.318358	−	0.947971i	$-0.396869\pi$
$311$	3.37759e8	0.636715	0.318358	+	0.947971i	$0.396869\pi$
$312$	−5.58080e8	−1.04029
$313$	−7.44664e8	−1.37264	−0.686318	−	0.727301i	$-0.740774\pi$
$313$	−7.44664e8	−1.37264	−0.686318	+	0.727301i	$0.740774\pi$
$314$	6.19922e8	1.13001
$315$	1.47914e8	0.266638
$316$	−6.67323e8	−1.18968
$317$	2.03277e7	0.0358411	0.0179205	−	0.999839i	$-0.494295\pi$
$317$	2.03277e7	0.0358411	0.0179205	+	0.999839i	$0.494295\pi$
$318$	9.53093e8	1.66204
$319$	−5.50963e8	−0.950287
$320$	1.86856e9	3.18774
$321$	9.87926e7	0.166708
$322$	−4.84230e8	−0.808269
$323$	9.13154e8	1.50777
$324$	−1.98466e9	−3.24174
$325$	1.25918e8	0.203468
$326$	7.36226e8	1.17693
$327$	8.24632e8	1.30420
$328$	2.63053e9	4.11609
$329$	−1.38324e8	−0.214147
$330$	1.81067e9	2.77358
$331$	8.04493e8	1.21934	0.609669	−	0.792656i	$-0.291302\pi$
$331$	8.04493e8	1.21934	0.609669	+	0.792656i	$0.291302\pi$
$332$	−2.86935e9	−4.30329
$333$	−3.88568e8	−0.576650
$334$	−9.63949e8	−1.41560
$335$	−1.48412e9	−2.15681
$336$	−1.02379e9	−1.47239
$337$	1.45891e8	0.207646	0.103823	−	0.994596i	$-0.466892\pi$
$337$	1.45891e8	0.207646	0.103823	+	0.994596i	$0.466892\pi$
$338$	1.03557e8	0.145871
$339$	−1.41277e9	−1.96958
$340$	2.25146e9	3.10662
$341$	3.18810e8	0.435404
$342$	1.24691e9	1.68556
$343$	4.03536e7	0.0539949
$344$	1.78479e9	2.36392
$345$	1.40346e9	1.84007
$346$	1.23905e9	1.60813
$347$	−6.38212e8	−0.819996	−0.409998	−	0.912086i	$-0.634471\pi$
$347$	−6.38212e8	−0.819996	−0.409998	+	0.912086i	$0.634471\pi$
$348$	−2.68149e9	−3.41075
$349$	5.47535e8	0.689483	0.344741	−	0.938698i	$-0.387967\pi$
$349$	5.47535e8	0.689483	0.344741	+	0.938698i	$0.387967\pi$
$350$	4.21764e8	0.525814
$351$	1.29266e8	0.159554
$352$	−2.15228e9	−2.63027
$353$	−1.18800e8	−0.143749	−0.0718746	−	0.997414i	$-0.522898\pi$
$353$	−1.18800e8	−0.143749	−0.0718746	+	0.997414i	$0.522898\pi$
$354$	3.66177e9	4.38712
$355$	9.40438e8	1.11566
$356$	−1.51689e9	−1.78188
$357$	−3.65977e8	−0.425711
$358$	−2.39766e9	−2.76183
$359$	−3.95266e8	−0.450878	−0.225439	−	0.974257i	$-0.572382\pi$
$359$	−3.95266e8	−0.450878	−0.225439	+	0.974257i	$0.572382\pi$
$360$	1.89013e9	2.13517
$361$	1.56621e9	1.75216
$362$	1.85072e9	2.05051
$363$	2.21954e8	0.243551
$364$	2.50408e8	0.272141
$365$	−9.32573e8	−1.00382
$366$	9.60461e8	1.02399
$367$	−7.08721e8	−0.748417	−0.374209	−	0.927345i	$-0.622086\pi$
$367$	−7.08721e8	−0.748417	−0.374209	+	0.927345i	$0.622086\pi$
$368$	−3.38895e9	−3.54485
$369$	7.03251e8	0.728649
$370$	−2.61826e9	−2.68724
$371$	−2.62918e8	−0.267308
$372$	1.55163e9	1.56274
$373$	−1.04724e9	−1.04488	−0.522438	−	0.852677i	$-0.674978\pi$
$373$	−1.04724e9	−1.04488	−0.522438	+	0.852677i	$0.674978\pi$
$374$	−1.56296e9	−1.54489
$375$	4.43877e8	0.434664
$376$	−1.76758e9	−1.71483
$377$	3.05909e8	0.294034
$378$	4.32978e8	0.412329
$379$	1.38424e9	1.30609	0.653046	−	0.757318i	$-0.273491\pi$
$379$	1.38424e9	1.30609	0.653046	+	0.757318i	$0.273491\pi$
$380$	6.06554e9	5.67058
$381$	−2.11899e9	−1.96287
$382$	−3.29484e9	−3.02421
$383$	−6.78514e7	−0.0617111	−0.0308555	−	0.999524i	$-0.509823\pi$
$383$	−6.78514e7	−0.0617111	−0.0308555	+	0.999524i	$0.509823\pi$
$384$	−2.27818e9	−2.05318
$385$	−4.99488e8	−0.446080
$386$	3.48670e9	3.08574
$387$	4.77151e8	0.418473
$388$	9.10394e8	0.791258
$389$	4.66805e8	0.402080	0.201040	−	0.979583i	$-0.435568\pi$
$389$	4.66805e8	0.402080	0.201040	+	0.979583i	$0.435568\pi$
$390$	−1.00533e9	−0.858191
$391$	−1.21146e9	−1.02492
$392$	5.15661e8	0.432378
$393$	−2.49486e9	−2.07335
$394$	−2.60579e7	−0.0214636
$395$	−7.39067e8	−0.603384
$396$	−1.54073e9	−1.24679
$397$	1.13367e9	0.909324	0.454662	−	0.890664i	$-0.349760\pi$
$397$	1.13367e9	0.909324	0.454662	+	0.890664i	$0.349760\pi$
$398$	−6.80282e8	−0.540877
$399$	−9.85959e8	−0.777059
$400$	2.95178e9	2.30608
$401$	−2.42658e8	−0.187927	−0.0939634	−	0.995576i	$-0.529954\pi$
$401$	−2.42658e8	−0.187927	−0.0939634	+	0.995576i	$0.529954\pi$
$402$	5.01426e9	3.84960
$403$	−1.77012e8	−0.134721
$404$	6.18530e9	4.66687
$405$	−2.19803e9	−1.64415
$406$	1.02465e9	0.759860
$407$	1.31215e9	0.964723
$408$	−4.67666e9	−3.40899
$409$	8.57583e8	0.619790	0.309895	−	0.950771i	$-0.399706\pi$
$409$	8.57583e8	0.619790	0.309895	+	0.950771i	$0.399706\pi$
$410$	4.73867e9	3.39557
$411$	3.52785e8	0.250648
$412$	−1.51439e9	−1.06683
$413$	−1.01013e9	−0.705588
$414$	−1.65425e9	−1.14578
$415$	−3.17783e9	−2.18254
$416$	1.19500e9	0.813847
$417$	8.90476e8	0.601376
$418$	−4.21068e9	−2.81991
$419$	2.01001e9	1.33490	0.667452	−	0.744653i	$-0.267385\pi$
$419$	2.01001e9	1.33490	0.667452	+	0.744653i	$0.267385\pi$
$420$	−2.43097e9	−1.60106
$421$	1.21619e9	0.794351	0.397176	−	0.917743i	$-0.369990\pi$
$421$	1.21619e9	0.794351	0.397176	+	0.917743i	$0.369990\pi$
$422$	−2.77387e9	−1.79677
$423$	−4.72550e8	−0.303568
$424$	−3.35972e9	−2.14054
$425$	1.05518e9	0.666754
$426$	−3.17737e9	−1.99129
$427$	−2.64951e8	−0.164690
$428$	−5.66445e8	−0.349225
$429$	5.03826e8	0.308092
$430$	3.21515e9	1.95012
$431$	1.80990e9	1.08889	0.544444	−	0.838797i	$-0.316741\pi$
$431$	1.80990e9	1.08889	0.544444	+	0.838797i	$0.316741\pi$
$432$	3.03026e9	1.80837
$433$	1.31114e9	0.776144	0.388072	−	0.921629i	$-0.373141\pi$
$433$	1.31114e9	0.776144	0.388072	+	0.921629i	$0.373141\pi$
$434$	−5.92905e8	−0.348154
$435$	−2.96978e9	−1.72986
$436$	−4.72818e9	−2.73206
$437$	−3.26373e9	−1.87081
$438$	3.15079e9	1.79168
$439$	−9.08435e8	−0.512470	−0.256235	−	0.966615i	$-0.582482\pi$
$439$	−9.08435e8	−0.512470	−0.256235	+	0.966615i	$0.582482\pi$
$440$	−6.38274e9	−3.57210
$441$	1.37858e8	0.0765415
$442$	8.67796e8	0.478013
$443$	1.75993e9	0.961796	0.480898	−	0.876777i	$-0.340311\pi$
$443$	1.75993e9	0.961796	0.480898	+	0.876777i	$0.340311\pi$
$444$	6.38613e9	3.46256
$445$	−1.67997e9	−0.903734
$446$	2.32578e9	1.24136
$447$	4.01512e9	2.12629
$448$	1.74153e9	0.915078
$449$	−1.48143e9	−0.772358	−0.386179	−	0.922424i	$-0.626205\pi$
$449$	−1.48143e9	−0.772358	−0.386179	+	0.922424i	$0.626205\pi$
$450$	1.44085e9	0.745377
$451$	−2.37480e9	−1.21901
$452$	8.10037e9	4.12592
$453$	2.73802e9	1.38386
$454$	−4.69342e9	−2.35393
$455$	2.77329e8	0.138024
$456$	−1.25991e10	−6.22249
$457$	−3.76896e9	−1.84721	−0.923603	−	0.383351i	$-0.874770\pi$
$457$	−3.76896e9	−1.84721	−0.923603	+	0.383351i	$0.874770\pi$
$458$	4.43014e8	0.215471
$459$	1.08323e9	0.522851
$460$	−8.04701e9	−3.85462
$461$	2.52786e9	1.20171	0.600855	−	0.799358i	$-0.294827\pi$
$461$	2.52786e9	1.20171	0.600855	+	0.799358i	$0.294827\pi$
$462$	1.68757e9	0.796188
$463$	−1.87727e8	−0.0879007	−0.0439504	−	0.999034i	$-0.513994\pi$
$463$	−1.87727e8	−0.0879007	−0.0439504	+	0.999034i	$0.513994\pi$
$464$	7.17115e9	3.33254
$465$	1.71844e9	0.792591
$466$	9.47159e8	0.433583
$467$	3.11191e9	1.41390	0.706948	−	0.707266i	$-0.250072\pi$
$467$	3.11191e9	1.41390	0.706948	+	0.707266i	$0.250072\pi$
$468$	8.55457e8	0.385778
$469$	−1.38322e9	−0.619138
$470$	−3.18415e9	−1.41465
$471$	−1.67459e9	−0.738475
$472$	−1.29080e10	−5.65017
$473$	−1.61128e9	−0.700096
$474$	2.49701e9	1.07695
$475$	2.84271e9	1.21704
$476$	2.09840e9	0.891791
$477$	−8.98195e8	−0.378928
$478$	6.36990e9	2.66769
$479$	2.73570e8	0.113735	0.0568675	−	0.998382i	$-0.481889\pi$
$479$	2.73570e8	0.113735	0.0568675	+	0.998382i	$0.481889\pi$
$480$	−1.16011e10	−4.78803
$481$	−7.28540e8	−0.298501
$482$	1.33150e9	0.541598
$483$	1.30805e9	0.528213
$484$	−1.27261e9	−0.510197
$485$	1.00827e9	0.401310
$486$	4.66557e9	1.84365
$487$	4.11444e8	0.161421	0.0807104	−	0.996738i	$-0.474281\pi$
$487$	4.11444e8	0.161421	0.0807104	+	0.996738i	$0.474281\pi$
$488$	−3.38569e9	−1.31880
$489$	−1.98876e9	−0.769134
$490$	9.28919e8	0.356690
$491$	−4.56732e9	−1.74131	−0.870655	−	0.491895i	$-0.836304\pi$
$491$	−4.56732e9	−1.74131	−0.870655	+	0.491895i	$0.836304\pi$
$492$	−1.15580e10	−4.37525
$493$	2.56349e9	0.963535
$494$	2.33788e9	0.872526
$495$	−1.70638e9	−0.632349
$496$	−4.14953e9	−1.52691
$497$	8.76502e8	0.320262
$498$	1.07366e10	3.89552
$499$	2.29418e9	0.826562	0.413281	−	0.910604i	$-0.364383\pi$
$499$	2.29418e9	0.826562	0.413281	+	0.910604i	$0.364383\pi$
$500$	−2.54505e9	−0.910546
$501$	2.60391e9	0.925112
$502$	3.14528e9	1.10968
$503$	1.58482e8	0.0555254	0.0277627	−	0.999615i	$-0.491162\pi$
$503$	1.58482e8	0.0555254	0.0277627	+	0.999615i	$0.491162\pi$
$504$	1.76163e9	0.612925
$505$	6.85027e9	2.36694
$506$	5.58621e9	1.91686
$507$	−2.79737e8	−0.0953285
$508$	1.21496e10	4.11187
$509$	1.66384e9	0.559242	0.279621	−	0.960110i	$-0.409791\pi$
$509$	1.66384e9	0.559242	0.279621	+	0.960110i	$0.409791\pi$
$510$	−8.42460e9	−2.81225
$511$	−8.69172e8	−0.288159
$512$	−8.80942e8	−0.290070
$513$	2.91828e9	0.954370
$514$	−3.73836e9	−1.21425
$515$	−1.67720e9	−0.541077
$516$	−7.84199e9	−2.51277
$517$	1.59574e9	0.507863
$518$	−2.44026e9	−0.771403
$519$	−3.34703e9	−1.05093
$520$	3.54387e9	1.10526
$521$	4.75766e9	1.47388	0.736939	−	0.675959i	$-0.236271\pi$
$521$	4.75766e9	1.47388	0.736939	+	0.675959i	$0.236271\pi$
$522$	3.50045e9	1.07715
$523$	−6.17825e9	−1.88847	−0.944235	−	0.329274i	$-0.893196\pi$
$523$	−6.17825e9	−1.88847	−0.944235	+	0.329274i	$0.893196\pi$
$524$	1.43047e10	4.34331
$525$	−1.13931e9	−0.343625
$526$	1.43265e9	0.429230
$527$	−1.48334e9	−0.441474
$528$	1.18107e10	3.49187
$529$	9.25079e8	0.271697
$530$	−6.05224e9	−1.76584
$531$	−3.45085e9	−1.00022
$532$	5.65318e9	1.62780
$533$	1.31855e9	0.377183
$534$	5.67594e9	1.61303
$535$	−6.27343e8	−0.177120
$536$	−1.76756e10	−4.95790
$537$	6.47679e9	1.80489
$538$	2.70142e9	0.747920
$539$	−4.65530e8	−0.128052
$540$	7.19529e9	1.96639
$541$	−6.89344e9	−1.87174	−0.935871	−	0.352344i	$-0.885385\pi$
$541$	−6.89344e9	−1.87174	−0.935871	+	0.352344i	$0.885385\pi$
$542$	−4.92247e9	−1.32796
$543$	−4.99935e9	−1.34003
$544$	1.00140e10	2.66694
$545$	−5.23650e9	−1.38565
$546$	−9.36985e8	−0.246353
$547$	2.50406e9	0.654169	0.327084	−	0.944995i	$-0.393934\pi$
$547$	2.50406e9	0.654169	0.327084	+	0.944995i	$0.393934\pi$
$548$	−2.02276e9	−0.525063
$549$	−9.05139e8	−0.233460
$550$	−4.86559e9	−1.24700
$551$	6.90616e9	1.75876
$552$	1.67150e10	4.22979
$553$	−6.88821e8	−0.173208
$554$	5.24801e9	1.31132
$555$	7.07269e9	1.75614
$556$	−5.10571e9	−1.25978
$557$	1.68359e9	0.412804	0.206402	−	0.978467i	$-0.433825\pi$
$557$	1.68359e9	0.412804	0.206402	+	0.978467i	$0.433825\pi$
$558$	−2.02551e9	−0.493532
$559$	8.94627e8	0.216621
$560$	6.50118e9	1.56435
$561$	4.22201e9	1.00960
$562$	6.51467e9	1.54816
$563$	6.19180e8	0.146230	0.0731152	−	0.997324i	$-0.476706\pi$
$563$	6.19180e8	0.146230	0.0731152	+	0.997324i	$0.476706\pi$
$564$	7.76637e9	1.82281
$565$	8.97124e9	2.09258
$566$	1.37821e10	3.19491
$567$	−2.04860e9	−0.471971
$568$	1.12004e10	2.56458
$569$	3.42963e9	0.780468	0.390234	−	0.920716i	$-0.372394\pi$
$569$	3.42963e9	0.780468	0.390234	+	0.920716i	$0.372394\pi$
$570$	−2.26963e10	−5.13325
$571$	−4.28991e9	−0.964322	−0.482161	−	0.876083i	$-0.660148\pi$
$571$	−4.28991e9	−0.964322	−0.482161	+	0.876083i	$0.660148\pi$
$572$	−2.88878e9	−0.645398
$573$	8.90034e9	1.97636
$574$	4.41651e9	0.974737
$575$	−3.77135e9	−0.827293
$576$	5.94950e9	1.29719
$577$	−5.28606e9	−1.14556	−0.572778	−	0.819710i	$-0.694134\pi$
$577$	−5.28606e9	−1.14556	−0.572778	+	0.819710i	$0.694134\pi$
$578$	−1.53155e9	−0.329902
$579$	−9.41861e9	−2.01656
$580$	1.70278e10	3.62376
$581$	−2.96179e9	−0.626524
$582$	−3.40654e9	−0.716281
$583$	3.03310e9	0.633938
$584$	−1.11068e10	−2.30751
$585$	9.47426e8	0.195659
$586$	−3.92458e9	−0.805659
$587$	−1.76980e9	−0.361153	−0.180576	−	0.983561i	$-0.557796\pi$
$587$	−1.76980e9	−0.361153	−0.180576	+	0.983561i	$0.557796\pi$
$588$	−2.26570e9	−0.459602
$589$	−3.99620e9	−0.805830
$590$	−2.32526e10	−4.66111
$591$	7.03901e7	0.0140267
$592$	−1.70785e10	−3.38317
$593$	−2.25369e9	−0.443816	−0.221908	−	0.975068i	$-0.571228\pi$
$593$	−2.25369e9	−0.443816	−0.221908	+	0.975068i	$0.571228\pi$
$594$	−4.99495e9	−0.977864
$595$	2.32399e9	0.452299
$596$	−2.30214e10	−4.45421
$597$	1.83764e9	0.353469
$598$	−3.10161e9	−0.593107
$599$	8.55681e9	1.62674	0.813369	−	0.581747i	$-0.197631\pi$
$599$	8.55681e9	1.62674	0.813369	+	0.581747i	$0.197631\pi$
$600$	−1.45588e10	−2.75166
$601$	−7.40943e8	−0.139227	−0.0696136	−	0.997574i	$-0.522177\pi$
$601$	−7.40943e8	−0.139227	−0.0696136	+	0.997574i	$0.522177\pi$
$602$	2.99657e9	0.559805
$603$	−4.72544e9	−0.877671
$604$	−1.56989e10	−2.89895
$605$	−1.40943e9	−0.258762
$606$	−2.31444e10	−4.22465
$607$	2.78806e9	0.505989	0.252994	−	0.967468i	$-0.418585\pi$
$607$	2.78806e9	0.505989	0.252994	+	0.967468i	$0.418585\pi$
$608$	2.69782e10	4.86801
$609$	−2.76788e9	−0.496577
$610$	−6.09903e9	−1.08794
$611$	−8.86000e8	−0.157141
$612$	7.16865e9	1.26418
$613$	3.41393e9	0.598609	0.299305	−	0.954158i	$-0.403245\pi$
$613$	3.41393e9	0.598609	0.299305	+	0.954158i	$0.403245\pi$
$614$	−4.76793e9	−0.831266
$615$	−1.28005e10	−2.21904
$616$	−5.94881e9	−1.02541
$617$	−4.91692e9	−0.842742	−0.421371	−	0.906888i	$-0.638451\pi$
$617$	−4.91692e9	−0.842742	−0.421371	+	0.906888i	$0.638451\pi$
$618$	5.66659e9	0.965745
$619$	4.67165e9	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$619$	4.67165e9	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$620$	−9.85299e9	−1.66034
$621$	−3.87162e9	−0.648741
$622$	7.24644e9	1.20742
$623$	−1.56575e9	−0.259427
$624$	−6.55763e9	−1.08044
$625$	−7.29629e9	−1.19542
$626$	−1.59764e10	−2.60297
$627$	1.13743e10	1.84284
$628$	9.60158e9	1.54698
$629$	−6.10510e9	−0.978173
$630$	3.17342e9	0.505633
$631$	−4.89335e9	−0.775360	−0.387680	−	0.921794i	$-0.626723\pi$
$631$	−4.89335e9	−0.775360	−0.387680	+	0.921794i	$0.626723\pi$
$632$	−8.80215e9	−1.38701
$633$	7.49303e9	1.17421
$634$	4.36121e8	0.0679664
$635$	1.34558e10	2.08546
$636$	1.47619e10	2.27531
$637$	2.58475e8	0.0396214
$638$	−1.18206e10	−1.80205
$639$	2.99435e9	0.453994
$640$	1.44667e10	2.18141
$641$	−3.13608e9	−0.470310	−0.235155	−	0.971958i	$-0.575560\pi$
$641$	−3.13608e9	−0.470310	−0.235155	+	0.971958i	$0.575560\pi$
$642$	2.11954e9	0.316133
$643$	−6.75599e9	−1.00219	−0.501096	−	0.865392i	$-0.667070\pi$
$643$	−6.75599e9	−1.00219	−0.501096	+	0.865392i	$0.667070\pi$
$644$	−7.49993e9	−1.10651
$645$	−8.68507e9	−1.27443
$646$	1.95912e10	2.85922
$647$	8.28130e9	1.20208	0.601040	−	0.799219i	$-0.294753\pi$
$647$	8.28130e9	1.20208	0.601040	+	0.799219i	$0.294753\pi$
$648$	−2.61781e10	−3.77943
$649$	1.16531e10	1.67334
$650$	2.70151e9	0.385842
$651$	1.60161e9	0.227522
$652$	1.14029e10	1.61120
$653$	−4.00554e9	−0.562944	−0.281472	−	0.959569i	$-0.590823\pi$
$653$	−4.00554e9	−0.562944	−0.281472	+	0.959569i	$0.590823\pi$
$654$	1.76921e10	2.47318
$655$	1.58426e10	2.20284
$656$	3.09096e10	4.27494
$657$	−2.96931e9	−0.408485
$658$	−2.96767e9	−0.406093
$659$	−7.39356e9	−1.00636	−0.503181	−	0.864181i	$-0.667837\pi$
$659$	−7.39356e9	−1.00636	−0.503181	+	0.864181i	$0.667837\pi$
$660$	2.80444e10	3.79701
$661$	−2.42892e9	−0.327120	−0.163560	−	0.986533i	$-0.552298\pi$
$661$	−2.42892e9	−0.327120	−0.163560	+	0.986533i	$0.552298\pi$
$662$	1.72600e10	2.31227
$663$	−2.34417e9	−0.312387
$664$	−3.78474e10	−5.01704
$665$	6.26094e9	0.825589
$666$	−8.33653e9	−1.09352
$667$	−9.16224e9	−1.19553
$668$	−1.49300e10	−1.93795
$669$	−6.28262e9	−0.811240
$670$	−3.18411e10	−4.09002
$671$	3.05655e9	0.390573
$672$	−1.08124e10	−1.37446
$673$	1.63332e9	0.206547	0.103273	−	0.994653i	$-0.467068\pi$
$673$	1.63332e9	0.206547	0.103273	+	0.994653i	$0.467068\pi$
$674$	3.13002e9	0.393765
$675$	3.37218e9	0.422034
$676$	1.60393e9	0.199697
$677$	−8.03237e9	−0.994909	−0.497454	−	0.867490i	$-0.665732\pi$
$677$	−8.03237e9	−0.994909	−0.497454	+	0.867490i	$0.665732\pi$
$678$	−3.03103e10	−3.73496
$679$	9.39722e8	0.115201
$680$	2.96973e10	3.62189
$681$	1.26783e10	1.53832
$682$	6.83992e9	0.825668
$683$	−8.15621e8	−0.0979526	−0.0489763	−	0.998800i	$-0.515596\pi$
$683$	−8.15621e8	−0.0979526	−0.0489763	+	0.998800i	$0.515596\pi$
$684$	1.93127e10	2.30752
$685$	−2.24022e9	−0.266302
$686$	8.65766e8	0.102392
$687$	−1.19671e9	−0.140812
$688$	2.09719e10	2.45515
$689$	−1.68406e9	−0.196150
$690$	3.01106e10	3.48937
$691$	−2.74837e9	−0.316886	−0.158443	−	0.987368i	$-0.550647\pi$
$691$	−2.74837e9	−0.316886	−0.158443	+	0.987368i	$0.550647\pi$
$692$	1.91908e10	2.20152
$693$	−1.59037e9	−0.181523
$694$	−1.36925e10	−1.55498
$695$	−5.65462e9	−0.638935
$696$	−3.53695e10	−3.97646
$697$	1.10493e10	1.23601
$698$	1.17471e10	1.30748
$699$	−2.55856e9	−0.283351
$700$	6.53245e9	0.719834
$701$	9.43733e9	1.03475	0.517375	−	0.855758i	$-0.326909\pi$
$701$	9.43733e9	1.03475	0.517375	+	0.855758i	$0.326909\pi$
$702$	2.77333e9	0.302567
$703$	−1.64474e10	−1.78548
$704$	−2.00908e10	−2.17016
$705$	8.60132e9	0.924492
$706$	−2.54880e9	−0.272595
$707$	6.38455e9	0.679458
$708$	5.67148e10	6.00593
$709$	4.12614e9	0.434792	0.217396	−	0.976083i	$-0.430244\pi$
$709$	4.12614e9	0.434792	0.217396	+	0.976083i	$0.430244\pi$
$710$	2.01766e10	2.11565
$711$	−2.35319e9	−0.245535
$712$	−2.00081e10	−2.07743
$713$	5.30166e9	0.547770
$714$	−7.85185e9	−0.807288
$715$	−3.19935e9	−0.327333
$716$	−3.71358e10	−3.78092
$717$	−1.72070e10	−1.74336
$718$	−8.48024e9	−0.855013
$719$	8.21156e9	0.823900	0.411950	−	0.911206i	$-0.364848\pi$
$719$	8.21156e9	0.823900	0.411950	+	0.911206i	$0.364848\pi$
$720$	2.22097e10	2.21757
$721$	−1.56317e9	−0.155322
$722$	3.36022e10	3.32267
$723$	−3.59678e9	−0.353940
$724$	2.86647e10	2.80713
$725$	7.98031e9	0.777744
$726$	4.76191e9	0.461852
$727$	−1.95125e10	−1.88340	−0.941698	−	0.336460i	$-0.890770\pi$
$727$	−1.95125e10	−1.88340	−0.941698	+	0.336460i	$0.890770\pi$
$728$	3.30294e9	0.317279
$729$	4.58963e8	0.0438764
$730$	−2.00079e10	−1.90358
$731$	7.49689e9	0.709856
$732$	1.48760e10	1.40183
$733$	−5.50452e9	−0.516245	−0.258122	−	0.966112i	$-0.583104\pi$
$733$	−5.50452e9	−0.516245	−0.258122	+	0.966112i	$0.583104\pi$
$734$	−1.52052e10	−1.41924
$735$	−2.50928e9	−0.233101
$736$	−3.57914e10	−3.30907
$737$	1.59573e10	1.46832
$738$	1.50879e10	1.38176
$739$	6.54719e9	0.596759	0.298380	−	0.954447i	$-0.403554\pi$
$739$	6.54719e9	0.596759	0.298380	+	0.954447i	$0.403554\pi$
$740$	−4.05526e10	−3.67881
$741$	−6.31531e9	−0.570205
$742$	−5.64078e9	−0.506903
$743$	−2.12398e10	−1.89972	−0.949860	−	0.312676i	$-0.898775\pi$
$743$	−2.12398e10	−1.89972	−0.949860	+	0.312676i	$0.898775\pi$
$744$	2.04663e10	1.82194
$745$	−2.54964e10	−2.25909
$746$	−2.24680e10	−1.98143
$747$	−1.01182e10	−0.888140
$748$	−2.42077e10	−2.11494
$749$	−5.84693e8	−0.0508442
$750$	9.52316e9	0.824265
$751$	1.73021e10	1.49059	0.745296	−	0.666734i	$-0.232308\pi$
$751$	1.73021e10	1.49059	0.745296	+	0.666734i	$0.232308\pi$
$752$	−2.07697e10	−1.78102
$753$	−8.49632e9	−0.725185
$754$	6.56312e9	0.557585
$755$	−1.73867e10	−1.47029
$756$	6.70612e9	0.564475
$757$	6.08797e9	0.510078	0.255039	−	0.966931i	$-0.417912\pi$
$757$	6.08797e9	0.510078	0.255039	+	0.966931i	$0.417912\pi$
$758$	2.96981e10	2.47678
$759$	−1.50900e10	−1.25269
$760$	8.00059e10	6.61111
$761$	1.92333e10	1.58201	0.791004	−	0.611811i	$-0.209559\pi$
$761$	1.92333e10	1.58201	0.791004	+	0.611811i	$0.209559\pi$
$762$	−4.54618e10	−3.72224
$763$	−4.88049e9	−0.397766
$764$	−5.10317e10	−4.14012
$765$	7.93934e9	0.641165
$766$	−1.45572e9	−0.117024
$767$	−6.47012e9	−0.517760
$768$	−1.12122e10	−0.893153
$769$	4.91707e9	0.389910	0.194955	−	0.980812i	$-0.437544\pi$
$769$	4.91707e9	0.389910	0.194955	+	0.980812i	$0.437544\pi$
$770$	−1.07163e10	−0.845913
$771$	1.00984e10	0.793529
$772$	5.40033e10	4.22435
$773$	1.69143e10	1.31712	0.658559	−	0.752529i	$-0.271166\pi$
$773$	1.69143e10	1.31712	0.658559	+	0.752529i	$0.271166\pi$
$774$	1.02370e10	0.793561
$775$	−4.61775e9	−0.356348
$776$	1.20083e10	0.922498
$777$	6.59186e9	0.504120
$778$	1.00151e10	0.762475
$779$	2.97674e10	2.25611
$780$	−1.55710e10	−1.17486
$781$	−1.01116e10	−0.759521
$782$	−2.59912e10	−1.94358
$783$	8.19248e9	0.609887
$784$	6.05919e9	0.449064
$785$	1.06338e10	0.784596
$786$	−5.35260e10	−3.93175
$787$	−1.05413e10	−0.770871	−0.385436	−	0.922735i	$-0.625949\pi$
$787$	−1.05413e10	−0.770871	−0.385436	+	0.922735i	$0.625949\pi$
$788$	−4.03594e8	−0.0293835
$789$	−3.87002e9	−0.280507
$790$	−1.58563e10	−1.14421
$791$	8.36133e9	0.600700
$792$	−2.03226e10	−1.45359
$793$	−1.69708e9	−0.120850
$794$	2.43222e10	1.72438
$795$	1.63489e10	1.15399
$796$	−1.05365e10	−0.740456
$797$	1.03772e10	0.726065	0.363032	−	0.931777i	$-0.381741\pi$
$797$	1.03772e10	0.726065	0.363032	+	0.931777i	$0.381741\pi$
$798$	−2.11533e10	−1.47356
$799$	−7.42460e9	−0.514943
$800$	3.11743e10	2.15269
$801$	−5.34901e9	−0.367756
$802$	−5.20610e9	−0.356371
$803$	1.00270e10	0.683387
$804$	7.76627e10	5.27007
$805$	−8.30624e9	−0.561202
$806$	−3.79770e9	−0.255475
$807$	−7.29735e9	−0.488774
$808$	8.15855e10	5.44093
$809$	1.94726e10	1.29302	0.646510	−	0.762906i	$-0.276228\pi$
$809$	1.94726e10	1.29302	0.646510	+	0.762906i	$0.276228\pi$
$810$	−4.71576e10	−3.11784
$811$	1.31550e9	0.0865998	0.0432999	−	0.999062i	$-0.486213\pi$
$811$	1.31550e9	0.0865998	0.0432999	+	0.999062i	$0.486213\pi$
$812$	1.58701e10	1.04024
$813$	1.32970e10	0.867837
$814$	2.81515e10	1.82943
$815$	1.26289e10	0.817170
$816$	−5.49524e10	−3.54055
$817$	2.01970e10	1.29571
$818$	1.83990e10	1.17532
$819$	8.83015e8	0.0561661
$820$	7.33942e10	4.64851
$821$	2.19897e10	1.38682	0.693409	−	0.720545i	$-0.256108\pi$
$821$	2.19897e10	1.38682	0.693409	+	0.720545i	$0.256108\pi$
$822$	7.56882e9	0.475310
$823$	1.47417e10	0.921826	0.460913	−	0.887445i	$-0.347522\pi$
$823$	1.47417e10	0.921826	0.460913	+	0.887445i	$0.347522\pi$
$824$	−1.99751e10	−1.24378
$825$	1.31434e10	0.814928
$826$	−2.16718e10	−1.33802
$827$	−1.94790e10	−1.19756	−0.598781	−	0.800913i	$-0.704348\pi$
$827$	−1.94790e10	−1.19756	−0.598781	+	0.800913i	$0.704348\pi$
$828$	−2.56217e10	−1.56856
$829$	−1.26005e10	−0.768154	−0.384077	−	0.923301i	$-0.625480\pi$
$829$	−1.26005e10	−0.768154	−0.384077	+	0.923301i	$0.625480\pi$
$830$	−6.81788e10	−4.13881
$831$	−1.41764e10	−0.856965
$832$	1.11549e10	0.671483
$833$	2.16600e9	0.129838
$834$	1.91047e10	1.14041
$835$	−1.65351e10	−0.982889
$836$	−6.52166e10	−3.86044
$837$	−4.74052e9	−0.279439
$838$	4.31238e10	2.53141
$839$	−1.39227e10	−0.813872	−0.406936	−	0.913457i	$-0.633403\pi$
$839$	−1.39227e10	−0.813872	−0.406936	+	0.913457i	$0.633403\pi$
$840$	−3.20651e10	−1.86661
$841$	2.13775e9	0.123928
$842$	2.60927e10	1.50635
$843$	−1.75980e10	−1.01174
$844$	−4.29627e10	−2.45976
$845$	1.77636e9	0.101282
$846$	−1.01383e10	−0.575664
$847$	−1.31361e9	−0.0742805
$848$	−3.94778e10	−2.22314
$849$	−3.72296e10	−2.08791
$850$	2.26384e10	1.26438
$851$	2.18204e10	1.21369
$852$	−4.92122e10	−2.72605
$853$	−3.26613e10	−1.80182	−0.900911	−	0.434004i	$-0.857100\pi$
$853$	−3.26613e10	−1.80182	−0.900911	+	0.434004i	$0.857100\pi$
$854$	−5.68439e9	−0.312306
$855$	2.13890e10	1.17033
$856$	−7.47154e9	−0.407148
$857$	−2.41294e10	−1.30952	−0.654761	−	0.755836i	$-0.727231\pi$
$857$	−2.41294e10	−1.30952	−0.654761	+	0.755836i	$0.727231\pi$
$858$	1.08093e10	0.584242
$859$	6.13516e9	0.330255	0.165128	−	0.986272i	$-0.447196\pi$
$859$	6.13516e9	0.330255	0.165128	+	0.986272i	$0.447196\pi$
$860$	4.97974e10	2.66970
$861$	−1.19303e10	−0.637001
$862$	3.88304e10	2.06489
$863$	−2.79398e10	−1.47974	−0.739870	−	0.672750i	$-0.765113\pi$
$863$	−2.79398e10	−1.47974	−0.739870	+	0.672750i	$0.765113\pi$
$864$	3.20031e10	1.68808
$865$	2.12540e10	1.11656
$866$	2.81299e10	1.47182
$867$	4.13718e9	0.215594
$868$	−9.18313e9	−0.476619
$869$	7.94643e9	0.410774
$870$	−6.37151e10	−3.28038
$871$	−8.85989e9	−0.454323
$872$	−6.23657e10	−3.18521
$873$	3.21033e9	0.163305
$874$	−7.00216e10	−3.54766
$875$	−2.62704e9	−0.132568
$876$	4.88007e10	2.45280
$877$	2.32137e10	1.16211	0.581054	−	0.813865i	$-0.302641\pi$
$877$	2.32137e10	1.16211	0.581054	+	0.813865i	$0.302641\pi$
$878$	−1.94900e10	−0.971810
$879$	1.06014e10	0.526507
$880$	−7.49994e10	−3.70995
$881$	1.29500e10	0.638050	0.319025	−	0.947746i	$-0.396645\pi$
$881$	1.29500e10	0.638050	0.319025	+	0.947746i	$0.396645\pi$
$882$	2.95767e9	0.145148
$883$	−1.70222e10	−0.832057	−0.416029	−	0.909352i	$-0.636578\pi$
$883$	−1.70222e10	−0.832057	−0.416029	+	0.909352i	$0.636578\pi$
$884$	1.34408e10	0.654396
$885$	6.28121e10	3.04609
$886$	3.77585e10	1.82388
$887$	1.41891e10	0.682690	0.341345	−	0.939938i	$-0.389118\pi$
$887$	1.41891e10	0.682690	0.341345	+	0.939938i	$0.389118\pi$
$888$	8.42345e10	4.03687
$889$	1.25410e10	0.598655
$890$	−3.60428e10	−1.71378
$891$	2.36332e10	1.11931
$892$	3.60225e10	1.69941
$893$	−2.00022e10	−0.939935
$894$	8.61424e10	4.03214
$895$	−4.11283e10	−1.91761
$896$	1.34831e10	0.626200
$897$	8.37837e9	0.387602
$898$	−3.17833e10	−1.46464
$899$	−1.12185e10	−0.514963
$900$	2.23165e10	1.02041
$901$	−1.41122e10	−0.642775
$902$	−5.09501e10	−2.31165
$903$	−8.09462e9	−0.365838
$904$	1.06846e11	4.81025
$905$	3.17464e10	1.42372
$906$	5.87427e10	2.62425
$907$	−2.21194e9	−0.0984345	−0.0492173	−	0.998788i	$-0.515673\pi$
$907$	−2.21194e9	−0.0984345	−0.0492173	+	0.998788i	$0.515673\pi$
$908$	−7.26935e10	−3.22251
$909$	2.18112e10	0.963179
$910$	5.94995e9	0.261739
$911$	−1.35193e10	−0.592435	−0.296217	−	0.955121i	$-0.595725\pi$
$911$	−1.35193e10	−0.592435	−0.296217	+	0.955121i	$0.595725\pi$
$912$	−1.48044e11	−6.46263
$913$	3.41680e10	1.48584
$914$	−8.08612e10	−3.50290
$915$	1.64753e10	0.710983
$916$	6.86156e9	0.294977
$917$	1.47656e10	0.632350
$918$	2.32402e10	0.991497
$919$	−2.13982e8	−0.00909437	−0.00454719	−	0.999990i	$-0.501447\pi$
$919$	−2.13982e8	−0.00909437	−0.00454719	+	0.999990i	$0.501447\pi$
$920$	−1.06142e11	−4.49396
$921$	1.28796e10	0.543242
$922$	5.42340e10	2.27884
$923$	5.61421e9	0.235008
$924$	2.61378e10	1.08997
$925$	−1.90056e10	−0.789559
$926$	−4.02758e9	−0.166689
$927$	−5.34020e9	−0.220180
$928$	7.57359e10	3.11088
$929$	−1.98996e10	−0.814308	−0.407154	−	0.913359i	$-0.633479\pi$
$929$	−1.98996e10	−0.814308	−0.407154	+	0.913359i	$0.633479\pi$
$930$	3.68682e10	1.50301
$931$	5.83529e9	0.236995
$932$	1.46699e10	0.593571
$933$	−1.95748e10	−0.789062
$934$	6.67643e10	2.68121
$935$	−2.68102e10	−1.07265
$936$	1.12837e10	0.449764
$937$	1.63524e10	0.649373	0.324686	−	0.945822i	$-0.394741\pi$
$937$	1.63524e10	0.649373	0.324686	+	0.945822i	$0.394741\pi$
$938$	−2.96764e10	−1.17409
$939$	4.31570e10	1.70107
$940$	−4.93172e10	−1.93665
$941$	2.48061e10	0.970500	0.485250	−	0.874376i	$-0.338729\pi$
$941$	2.48061e10	0.970500	0.485250	+	0.874376i	$0.338729\pi$
$942$	−3.59275e10	−1.40039
$943$	−3.94917e10	−1.53361
$944$	−1.51673e11	−5.86822
$945$	7.42709e9	0.286291
$946$	−3.45692e10	−1.32761
$947$	2.71990e10	1.04070	0.520352	−	0.853952i	$-0.325801\pi$
$947$	2.71990e10	1.04070	0.520352	+	0.853952i	$0.325801\pi$
$948$	3.86747e10	1.47434
$949$	−5.56726e9	−0.211451
$950$	6.09888e10	2.30790
$951$	−1.17809e9	−0.0444168
$952$	2.76783e10	1.03971
$953$	−4.18779e9	−0.156733	−0.0783663	−	0.996925i	$-0.524970\pi$
$953$	−4.18779e9	−0.156733	−0.0783663	+	0.996925i	$0.524970\pi$
$954$	−1.92703e10	−0.718571
$955$	−5.65181e10	−2.09979
$956$	9.86594e10	3.65204
$957$	3.19310e10	1.17766
$958$	5.86931e9	0.215679
$959$	−2.08792e9	−0.0764449
$960$	−1.08293e11	−3.95047
$961$	−2.10211e10	−0.764054
$962$	−1.56305e10	−0.566055
$963$	−1.99746e9	−0.0720752
$964$	2.06228e10	0.741443
$965$	5.98092e10	2.14251
$966$	2.80635e10	1.00166
$967$	−4.05099e10	−1.44068	−0.720342	−	0.693619i	$-0.756015\pi$
$967$	−4.05099e10	−1.44068	−0.720342	+	0.693619i	$0.756015\pi$
$968$	−1.67861e10	−0.594819
$969$	−5.29218e10	−1.86853
$970$	2.16319e10	0.761016
$971$	2.12395e10	0.744523	0.372261	−	0.928128i	$-0.378583\pi$
$971$	2.12395e10	0.744523	0.372261	+	0.928128i	$0.378583\pi$
$972$	7.22621e10	2.52394
$973$	−5.27019e9	−0.183413
$974$	8.82732e9	0.306107
$975$	−7.29757e9	−0.252152
$976$	−3.97830e10	−1.36969
$977$	−4.95442e10	−1.69966	−0.849830	−	0.527056i	$-0.823296\pi$
$977$	−4.95442e10	−1.69966	−0.849830	+	0.527056i	$0.823296\pi$
$978$	−4.26679e10	−1.45853
$979$	1.80630e10	0.615248
$980$	1.43874e10	0.488306
$981$	−1.66730e10	−0.563861
$982$	−9.79894e10	−3.30209
$983$	2.16480e10	0.726910	0.363455	−	0.931612i	$-0.381597\pi$
$983$	2.16480e10	0.726910	0.363455	+	0.931612i	$0.381597\pi$
$984$	−1.52452e11	−5.10094
$985$	−4.46984e8	−0.0149027
$986$	5.49984e10	1.82718
$987$	8.01656e9	0.265386
$988$	3.62100e10	1.19448
$989$	−2.67948e10	−0.880773
$990$	−3.66095e10	−1.19914
$991$	−5.12814e10	−1.67379	−0.836897	−	0.547361i	$-0.815632\pi$
$991$	−5.12814e10	−1.67379	−0.836897	+	0.547361i	$0.815632\pi$
$992$	−4.38240e10	−1.42535
$993$	−4.66244e10	−1.51109
$994$	1.88049e10	0.607322
$995$	−1.16692e10	−0.375544
$996$	1.66293e11	5.33294
$997$	−1.54006e10	−0.492157	−0.246078	−	0.969250i	$-0.579142\pi$
$997$	−1.54006e10	−0.492157	−0.246078	+	0.969250i	$0.579142\pi$
$998$	4.92204e10	1.56743
$999$	−1.95109e10	−0.619152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.12	✓	12	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+21.4545 q^{2} -57.9549 q^{3} +332.295 q^{4} +368.020 q^{5} -1243.39 q^{6} +343.000 q^{7} +4383.05 q^{8} +1171.77 q^{9} +O(q^{10})\)	\(q+21.4545 q^{2} -57.9549 q^{3} +332.295 q^{4} +368.020 q^{5} -1243.39 q^{6} +343.000 q^{7} +4383.05 q^{8} +1171.77 q^{9} +7895.68 q^{10} -3956.94 q^{11} -19258.1 q^{12} +2197.00 q^{13} +7358.89 q^{14} -21328.6 q^{15} +51502.3 q^{16} +18410.7 q^{17} +25139.8 q^{18} +49599.2 q^{19} +122291. q^{20} -19878.5 q^{21} -84894.2 q^{22} -65802.0 q^{23} -254019. q^{24} +57313.6 q^{25} +47135.5 q^{26} +58837.3 q^{27} +113977. q^{28} +139239. q^{29} -457593. q^{30} -80569.9 q^{31} +543925. q^{32} +229324. q^{33} +394991. q^{34} +126231. q^{35} +389375. q^{36} -331607. q^{37} +1.06413e6 q^{38} -127327. q^{39} +1.61305e6 q^{40} +600160. q^{41} -426484. q^{42} +407204. q^{43} -1.31487e6 q^{44} +431236. q^{45} -1.41175e6 q^{46} -403277. q^{47} -2.98481e6 q^{48} +117649. q^{49} +1.22963e6 q^{50} -1.06699e6 q^{51} +730052. q^{52} -766525. q^{53} +1.26233e6 q^{54} -1.45623e6 q^{55} +1.50339e6 q^{56} -2.87452e6 q^{57} +2.98731e6 q^{58} -2.94498e6 q^{59} -7.08738e6 q^{60} -772451. q^{61} -1.72859e6 q^{62} +401919. q^{63} +5.07735e6 q^{64} +808540. q^{65} +4.92004e6 q^{66} -4.03272e6 q^{67} +6.11777e6 q^{68} +3.81355e6 q^{69} +2.70822e6 q^{70} +2.55540e6 q^{71} +5.13594e6 q^{72} -2.53403e6 q^{73} -7.11445e6 q^{74} -3.32161e6 q^{75} +1.64816e7 q^{76} -1.35723e6 q^{77} -2.73174e6 q^{78} -2.00823e6 q^{79} +1.89539e7 q^{80} -5.97258e6 q^{81} +1.28761e7 q^{82} -8.63495e6 q^{83} -6.60554e6 q^{84} +6.77549e6 q^{85} +8.73635e6 q^{86} -8.06961e6 q^{87} -1.73435e7 q^{88} -4.56488e6 q^{89} +9.25195e6 q^{90} +753571. q^{91} -2.18657e7 q^{92} +4.66942e6 q^{93} -8.65210e6 q^{94} +1.82535e7 q^{95} -3.15232e7 q^{96} +2.73971e6 q^{97} +2.52410e6 q^{98} -4.63664e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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