LMFDB - Embedded newform 91.8.a.e.1.7

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			1.7
Root			$-4.06937$ 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)

$f(q)$	$=$	$q+5.06937 q^{2} +91.5295 q^{3} -102.301 q^{4} -15.8892 q^{5} +463.997 q^{6} +343.000 q^{7} -1167.48 q^{8} +6190.65 q^{9} +O(q^{10})$	\(q+5.06937 q^{2} +91.5295 q^{3} -102.301 q^{4} -15.8892 q^{5} +463.997 q^{6} +343.000 q^{7} -1167.48 q^{8} +6190.65 q^{9} -80.5484 q^{10} -579.101 q^{11} -9363.61 q^{12} +2197.00 q^{13} +1738.79 q^{14} -1454.33 q^{15} +7176.18 q^{16} +25963.7 q^{17} +31382.7 q^{18} +56738.3 q^{19} +1625.49 q^{20} +31394.6 q^{21} -2935.68 q^{22} +17102.5 q^{23} -106859. q^{24} -77872.5 q^{25} +11137.4 q^{26} +366452. q^{27} -35089.4 q^{28} -48744.2 q^{29} -7372.56 q^{30} -207655. q^{31} +185817. q^{32} -53004.8 q^{33} +131620. q^{34} -5450.01 q^{35} -633313. q^{36} +379482. q^{37} +287628. q^{38} +201090. q^{39} +18550.4 q^{40} -347988. q^{41} +159151. q^{42} -899979. q^{43} +59242.9 q^{44} -98364.7 q^{45} +86699.2 q^{46} -356855. q^{47} +656833. q^{48} +117649. q^{49} -394765. q^{50} +2.37645e6 q^{51} -224756. q^{52} +1.86328e6 q^{53} +1.85768e6 q^{54} +9201.47 q^{55} -400447. q^{56} +5.19323e6 q^{57} -247102. q^{58} -2.04992e6 q^{59} +148781. q^{60} +1.21657e6 q^{61} -1.05268e6 q^{62} +2.12339e6 q^{63} +23422.0 q^{64} -34908.6 q^{65} -268701. q^{66} -2.99961e6 q^{67} -2.65613e6 q^{68} +1.56539e6 q^{69} -27628.1 q^{70} +2.26514e6 q^{71} -7.22748e6 q^{72} -2.72537e6 q^{73} +1.92373e6 q^{74} -7.12764e6 q^{75} -5.80442e6 q^{76} -198632. q^{77} +1.01940e6 q^{78} +3.48407e6 q^{79} -114024. q^{80} +2.00022e7 q^{81} -1.76408e6 q^{82} +58195.4 q^{83} -3.21172e6 q^{84} -412544. q^{85} -4.56232e6 q^{86} -4.46153e6 q^{87} +676091. q^{88} -8.32624e6 q^{89} -498647. q^{90} +753571. q^{91} -1.74962e6 q^{92} -1.90066e7 q^{93} -1.80903e6 q^{94} -901529. q^{95} +1.70077e7 q^{96} +1.77608e6 q^{97} +596406. q^{98} -3.58501e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.06937	0.448073	0.224037	−	0.974581i	$-0.428076\pi$
$2$	5.06937	0.448073	0.224037	+	0.974581i	$0.428076\pi$
$3$	91.5295	1.95721	0.978604	−	0.205755i	$-0.0659650\pi$
$3$	91.5295	1.95721	0.978604	+	0.205755i	$0.0659650\pi$
$4$	−102.301	−0.799230
$5$	−15.8892	−0.0568470	−0.0284235	−	0.999596i	$-0.509049\pi$
$5$	−15.8892	−0.0568470	−0.0284235	+	0.999596i	$0.509049\pi$
$6$	463.997	0.876972
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1167.48	−0.806187
$9$	6190.65	2.83066
$10$	−80.5484	−0.0254716
$11$	−579.101	−0.131184	−0.0655918	−	0.997847i	$-0.520894\pi$
$11$	−579.101	−0.131184	−0.0655918	+	0.997847i	$0.520894\pi$
$12$	−9363.61	−1.56426
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	1738.79	0.169356
$15$	−1454.33	−0.111261
$16$	7176.18	0.437999
$17$	25963.7	1.28173	0.640864	−	0.767655i	$-0.278576\pi$
$17$	25963.7	1.28173	0.640864	+	0.767655i	$0.278576\pi$
$18$	31382.7	1.26834
$19$	56738.3	1.89775	0.948875	−	0.315652i	$-0.102223\pi$
$19$	56738.3	1.89775	0.948875	+	0.315652i	$0.102223\pi$
$20$	1625.49	0.0454339
$21$	31394.6	0.739755
$22$	−2935.68	−0.0587799
$23$	17102.5	0.293098	0.146549	−	0.989203i	$-0.453183\pi$
$23$	17102.5	0.293098	0.146549	+	0.989203i	$0.453183\pi$
$24$	−106859.	−1.57788
$25$	−77872.5	−0.996768
$26$	11137.4	0.124273
$27$	366452.	3.58298
$28$	−35089.4	−0.302081
$29$	−48744.2	−0.371133	−0.185567	−	0.982632i	$-0.559412\pi$
$29$	−48744.2	−0.371133	−0.185567	+	0.982632i	$0.559412\pi$
$30$	−7372.56	−0.0498533
$31$	−207655.	−1.25192	−0.625960	−	0.779855i	$-0.715293\pi$
$31$	−207655.	−1.25192	−0.625960	+	0.779855i	$0.715293\pi$
$32$	185817.	1.00244
$33$	−53004.8	−0.256754
$34$	131620.	0.574308
$35$	−5450.01	−0.0214862
$36$	−633313.	−2.26235
$37$	379482.	1.23164	0.615822	−	0.787885i	$-0.288824\pi$
$37$	379482.	1.23164	0.615822	+	0.787885i	$0.288824\pi$
$38$	287628.	0.850331
$39$	201090.	0.542832
$40$	18550.4	0.0458294
$41$	−347988.	−0.788535	−0.394268	−	0.918996i	$-0.629002\pi$
$41$	−347988.	−0.788535	−0.394268	+	0.918996i	$0.629002\pi$
$42$	159151.	0.331464
$43$	−899979.	−1.72621	−0.863103	−	0.505028i	$-0.831482\pi$
$43$	−899979.	−1.72621	−0.863103	+	0.505028i	$0.831482\pi$
$44$	59242.9	0.104846
$45$	−98364.7	−0.160915
$46$	86699.2	0.131330
$47$	−356855.	−0.501359	−0.250680	−	0.968070i	$-0.580654\pi$
$47$	−356855.	−0.501359	−0.250680	+	0.968070i	$0.580654\pi$
$48$	656833.	0.857256
$49$	117649.	0.142857
$50$	−394765.	−0.446625
$51$	2.37645e6	2.50861
$52$	−224756.	−0.221667
$53$	1.86328e6	1.71915	0.859575	−	0.511010i	$-0.170729\pi$
$53$	1.86328e6	1.71915	0.859575	+	0.511010i	$0.170729\pi$
$54$	1.85768e6	1.60544
$55$	9201.47	0.00745740
$56$	−400447.	−0.304710
$57$	5.19323e6	3.71429
$58$	−247102.	−0.166295
$59$	−2.04992e6	−1.29943	−0.649717	−	0.760176i	$-0.725113\pi$
$59$	−2.04992e6	−1.29943	−0.649717	+	0.760176i	$0.725113\pi$
$60$	148781.	0.0889235
$61$	1.21657e6	0.686253	0.343126	−	0.939289i	$-0.388514\pi$
$61$	1.21657e6	0.686253	0.343126	+	0.939289i	$0.388514\pi$
$62$	−1.05268e6	−0.560952
$63$	2.12339e6	1.06989
$64$	23422.0	0.0111685
$65$	−34908.6	−0.0157665
$66$	−268701.	−0.115044
$67$	−2.99961e6	−1.21844	−0.609219	−	0.793002i	$-0.708517\pi$
$67$	−2.99961e6	−1.21844	−0.609219	+	0.793002i	$0.708517\pi$
$68$	−2.65613e6	−1.02440
$69$	1.56539e6	0.573654
$70$	−27628.1	−0.00962738
$71$	2.26514e6	0.751089	0.375545	−	0.926804i	$-0.377456\pi$
$71$	2.26514e6	0.751089	0.375545	+	0.926804i	$0.377456\pi$
$72$	−7.22748e6	−2.28204
$73$	−2.72537e6	−0.819966	−0.409983	−	0.912093i	$-0.634465\pi$
$73$	−2.72537e6	−0.819966	−0.409983	+	0.912093i	$0.634465\pi$
$74$	1.92373e6	0.551867
$75$	−7.12764e6	−1.95088
$76$	−5.80442e6	−1.51674
$77$	−198632.	−0.0495828
$78$	1.01940e6	0.243228
$79$	3.48407e6	0.795045	0.397522	−	0.917592i	$-0.369870\pi$
$79$	3.48407e6	0.795045	0.397522	+	0.917592i	$0.369870\pi$
$80$	−114024.	−0.0248990
$81$	2.00022e7	4.18197
$82$	−1.76408e6	−0.353322
$83$	58195.4	0.0111716	0.00558580	−	0.999984i	$-0.498222\pi$
$83$	58195.4	0.0111716	0.00558580	+	0.999984i	$0.498222\pi$
$84$	−3.21172e6	−0.591234
$85$	−412544.	−0.0728624
$86$	−4.56232e6	−0.773467
$87$	−4.46153e6	−0.726385
$88$	676091.	0.105759
$89$	−8.32624e6	−1.25194	−0.625970	−	0.779847i	$-0.715297\pi$
$89$	−8.32624e6	−1.25194	−0.625970	+	0.779847i	$0.715297\pi$
$90$	−498647.	−0.0721016
$91$	753571.	0.104828
$92$	−1.74962e6	−0.234253
$93$	−1.90066e7	−2.45027
$94$	−1.80903e6	−0.224646
$95$	−901529.	−0.107881
$96$	1.70077e7	1.96199
$97$	1.77608e6	0.197588	0.0987942	−	0.995108i	$-0.468501\pi$
$97$	1.77608e6	0.197588	0.0987942	+	0.995108i	$0.468501\pi$
$98$	596406.	0.0640105
$99$	−3.58501e6	−0.371336
$100$	7.96648e6	0.796648
$101$	−4.40648e6	−0.425566	−0.212783	−	0.977099i	$-0.568253\pi$
$101$	−4.40648e6	−0.425566	−0.212783	+	0.977099i	$0.568253\pi$
$102$	1.20471e7	1.12404
$103$	3.02337e6	0.272622	0.136311	−	0.990666i	$-0.456475\pi$
$103$	3.02337e6	0.272622	0.136311	+	0.990666i	$0.456475\pi$
$104$	−2.56496e6	−0.223596
$105$	−498837.	−0.0420529
$106$	9.44568e6	0.770305
$107$	−2.19696e7	−1.73372	−0.866860	−	0.498551i	$-0.833866\pi$
$107$	−2.19696e7	−1.73372	−0.866860	+	0.498551i	$0.833866\pi$
$108$	−3.74886e7	−2.86363
$109$	−5.96120e6	−0.440901	−0.220450	−	0.975398i	$-0.570753\pi$
$109$	−5.96120e6	−0.440901	−0.220450	+	0.975398i	$0.570753\pi$
$110$	46645.7	0.00334146
$111$	3.47338e7	2.41058
$112$	2.46143e6	0.165548
$113$	−5.08342e6	−0.331422	−0.165711	−	0.986174i	$-0.552992\pi$
$113$	−5.08342e6	−0.331422	−0.165711	+	0.986174i	$0.552992\pi$
$114$	2.63264e7	1.66427
$115$	−271746.	−0.0166618
$116$	4.98660e6	0.296621
$117$	1.36009e7	0.785084
$118$	−1.03918e7	−0.582242
$119$	8.90556e6	0.484448
$120$	1.69791e6	0.0896975
$121$	−1.91518e7	−0.982791
$122$	6.16726e6	0.307491
$123$	−3.18512e7	−1.54333
$124$	2.12434e7	1.00057
$125$	2.47868e6	0.113510
$126$	1.07643e7	0.479389
$127$	2.44607e7	1.05963	0.529816	−	0.848112i	$-0.322261\pi$
$127$	2.44607e7	1.05963	0.529816	+	0.848112i	$0.322261\pi$
$128$	−2.36658e7	−0.997439
$129$	−8.23746e7	−3.37854
$130$	−176965.	−0.00706456
$131$	−2.12476e7	−0.825774	−0.412887	−	0.910782i	$-0.635480\pi$
$131$	−2.12476e7	−0.825774	−0.412887	+	0.910782i	$0.635480\pi$
$132$	5.42247e6	0.205205
$133$	1.94613e7	0.717282
$134$	−1.52061e7	−0.545949
$135$	−5.82265e6	−0.203682
$136$	−3.03122e7	−1.03331
$137$	−4.31857e6	−0.143489	−0.0717443	−	0.997423i	$-0.522857\pi$
$137$	−4.31857e6	−0.143489	−0.0717443	+	0.997423i	$0.522857\pi$
$138$	7.93553e6	0.257039
$139$	−1.67466e7	−0.528903	−0.264452	−	0.964399i	$-0.585191\pi$
$139$	−1.67466e7	−0.528903	−0.264452	+	0.964399i	$0.585191\pi$
$140$	557544.	0.0171724
$141$	−3.26627e7	−0.981264
$142$	1.14829e7	0.336543
$143$	−1.27228e6	−0.0363838
$144$	4.44253e7	1.23983
$145$	774508.	0.0210978
$146$	−1.38159e7	−0.367405
$147$	1.07684e7	0.279601
$148$	−3.88216e7	−0.984367
$149$	6.90935e7	1.71114	0.855569	−	0.517689i	$-0.173207\pi$
$149$	6.90935e7	1.71114	0.855569	+	0.517689i	$0.173207\pi$
$150$	−3.61326e7	−0.874138
$151$	−2.74329e7	−0.648413	−0.324206	−	0.945986i	$-0.605097\pi$
$151$	−2.74329e7	−0.648413	−0.324206	+	0.945986i	$0.605097\pi$
$152$	−6.62411e7	−1.52994
$153$	1.60732e8	3.62813
$154$	−1.00694e6	−0.0222167
$155$	3.29948e6	0.0711679
$156$	−2.05718e7	−0.433847
$157$	−9.21041e6	−0.189946	−0.0949730	−	0.995480i	$-0.530276\pi$
$157$	−9.21041e6	−0.189946	−0.0949730	+	0.995480i	$0.530276\pi$
$158$	1.76620e7	0.356238
$159$	1.70546e8	3.36473
$160$	−2.95248e6	−0.0569859
$161$	5.86617e6	0.110781
$162$	1.01399e8	1.87383
$163$	2.11841e7	0.383137	0.191569	−	0.981479i	$-0.438643\pi$
$163$	2.11841e7	0.383137	0.191569	+	0.981479i	$0.438643\pi$
$164$	3.55997e7	0.630221
$165$	842206.	0.0145957
$166$	295014.	0.00500569
$167$	−5.14308e7	−0.854506	−0.427253	−	0.904132i	$-0.640519\pi$
$167$	−5.14308e7	−0.854506	−0.427253	+	0.904132i	$0.640519\pi$
$168$	−3.66527e7	−0.596381
$169$	4.82681e6	0.0769231
$170$	−2.09134e6	−0.0326477
$171$	3.51247e8	5.37188
$172$	9.20691e7	1.37964
$173$	−8.67654e7	−1.27405	−0.637023	−	0.770845i	$-0.719834\pi$
$173$	−8.67654e7	−1.27405	−0.637023	+	0.770845i	$0.719834\pi$
$174$	−2.26172e7	−0.325474
$175$	−2.67103e7	−0.376743
$176$	−4.15573e6	−0.0574584
$177$	−1.87628e8	−2.54326
$178$	−4.22088e7	−0.560961
$179$	−2.19989e7	−0.286692	−0.143346	−	0.989673i	$-0.545786\pi$
$179$	−2.19989e7	−0.286692	−0.143346	+	0.989673i	$0.545786\pi$
$180$	1.00629e7	0.128608
$181$	−3.85285e7	−0.482955	−0.241478	−	0.970406i	$-0.577632\pi$
$181$	−3.85285e7	−0.482955	−0.241478	+	0.970406i	$0.577632\pi$
$182$	3.82013e6	0.0469708
$183$	1.11352e8	1.34314
$184$	−1.99669e7	−0.236292
$185$	−6.02968e6	−0.0700153
$186$	−9.63513e7	−1.09790
$187$	−1.50356e7	−0.168142
$188$	3.65068e7	0.400701
$189$	1.25693e8	1.35424
$190$	−4.57018e6	−0.0483388
$191$	1.57619e8	1.63678	0.818391	−	0.574661i	$-0.194866\pi$
$191$	1.57619e8	1.63678	0.818391	+	0.574661i	$0.194866\pi$
$192$	2.14380e6	0.0218590
$193$	−1.95891e7	−0.196139	−0.0980694	−	0.995180i	$-0.531267\pi$
$193$	−1.95891e7	−0.196139	−0.0980694	+	0.995180i	$0.531267\pi$
$194$	9.00361e6	0.0885341
$195$	−3.19517e6	−0.0308584
$196$	−1.20357e7	−0.114176
$197$	−6.61441e6	−0.0616395	−0.0308198	−	0.999525i	$-0.509812\pi$
$197$	−6.61441e6	−0.0616395	−0.0308198	+	0.999525i	$0.509812\pi$
$198$	−1.81738e7	−0.166386
$199$	9.85013e7	0.886046	0.443023	−	0.896510i	$-0.353906\pi$
$199$	9.85013e7	0.886046	0.443023	+	0.896510i	$0.353906\pi$
$200$	9.09149e7	0.803582
$201$	−2.74553e8	−2.38473
$202$	−2.23381e7	−0.190685
$203$	−1.67193e7	−0.140275
$204$	−2.43114e8	−2.00495
$205$	5.52927e6	0.0448259
$206$	1.53266e7	0.122155
$207$	1.05876e8	0.829662
$208$	1.57661e7	0.121479
$209$	−3.28572e7	−0.248954
$210$	−2.52879e6	−0.0188428
$211$	−3.57516e7	−0.262003	−0.131002	−	0.991382i	$-0.541819\pi$
$211$	−3.57516e7	−0.262003	−0.131002	+	0.991382i	$0.541819\pi$
$212$	−1.90617e8	−1.37400
$213$	2.07328e8	1.47004
$214$	−1.11372e8	−0.776834
$215$	1.43000e7	0.0981297
$216$	−4.27827e8	−2.88855
$217$	−7.12257e7	−0.473181
$218$	−3.02195e7	−0.197556
$219$	−2.49452e8	−1.60484
$220$	−941324.	−0.00596018
$221$	5.70423e7	0.355487
$222$	1.76079e8	1.08012
$223$	−3.67694e7	−0.222034	−0.111017	−	0.993818i	$-0.535411\pi$
$223$	−3.67694e7	−0.222034	−0.111017	+	0.993818i	$0.535411\pi$
$224$	6.37351e7	0.378888
$225$	−4.82082e8	−2.82151
$226$	−2.57698e7	−0.148501
$227$	1.29910e7	0.0737142	0.0368571	−	0.999321i	$-0.488265\pi$
$227$	1.29910e7	0.0737142	0.0368571	+	0.999321i	$0.488265\pi$
$228$	−5.31275e8	−2.96857
$229$	−4.42704e7	−0.243607	−0.121803	−	0.992554i	$-0.538868\pi$
$229$	−4.42704e7	−0.243607	−0.121803	+	0.992554i	$0.538868\pi$
$230$	−1.37758e6	−0.00746570
$231$	−1.81807e7	−0.0970437
$232$	5.69080e7	0.299203
$233$	1.80402e8	0.934320	0.467160	−	0.884173i	$-0.345277\pi$
$233$	1.80402e8	0.934320	0.467160	+	0.884173i	$0.345277\pi$
$234$	6.89478e7	0.351775
$235$	5.67015e6	0.0285008
$236$	2.09710e8	1.03855
$237$	3.18895e8	1.55607
$238$	4.51456e7	0.217068
$239$	−2.17659e8	−1.03130	−0.515648	−	0.856801i	$-0.672449\pi$
$239$	−2.17659e8	−1.03130	−0.515648	+	0.856801i	$0.672449\pi$
$240$	−1.04366e7	−0.0487324
$241$	1.16211e8	0.534795	0.267398	−	0.963586i	$-0.413836\pi$
$241$	1.16211e8	0.534795	0.267398	+	0.963586i	$0.413836\pi$
$242$	−9.70876e7	−0.440362
$243$	1.02936e9	4.60201
$244$	−1.24457e8	−0.548474
$245$	−1.86935e6	−0.00812101
$246$	−1.61466e8	−0.691523
$247$	1.24654e8	0.526341
$248$	2.42434e8	1.00928
$249$	5.32659e6	0.0218651
$250$	1.25654e7	0.0508610
$251$	2.43213e8	0.970798	0.485399	−	0.874293i	$-0.338674\pi$
$251$	2.43213e8	0.970798	0.485399	+	0.874293i	$0.338674\pi$
$252$	−2.17226e8	−0.855087
$253$	−9.90410e6	−0.0384497
$254$	1.24000e8	0.474793
$255$	−3.77599e7	−0.142607
$256$	−1.22969e8	−0.458094
$257$	7.17329e7	0.263604	0.131802	−	0.991276i	$-0.457924\pi$
$257$	7.17329e7	0.263604	0.131802	+	0.991276i	$0.457924\pi$
$258$	−4.17587e8	−1.51383
$259$	1.30162e8	0.465518
$260$	3.57121e6	0.0126011
$261$	−3.01758e8	−1.05055
$262$	−1.07712e8	−0.370007
$263$	4.01427e8	1.36070	0.680349	−	0.732888i	$-0.261828\pi$
$263$	4.01427e8	1.36070	0.680349	+	0.732888i	$0.261828\pi$
$264$	6.18823e7	0.206991
$265$	−2.96062e7	−0.0977286
$266$	9.86563e7	0.321395
$267$	−7.62096e8	−2.45031
$268$	3.06865e8	0.973812
$269$	2.35245e8	0.736863	0.368431	−	0.929655i	$-0.379895\pi$
$269$	2.35245e8	0.736863	0.368431	+	0.929655i	$0.379895\pi$
$270$	−2.95172e7	−0.0912644
$271$	−3.67493e8	−1.12165	−0.560824	−	0.827935i	$-0.689515\pi$
$271$	−3.67493e8	−1.12165	−0.560824	+	0.827935i	$0.689515\pi$
$272$	1.86320e8	0.561396
$273$	6.89740e7	0.205171
$274$	−2.18924e7	−0.0642934
$275$	4.50960e7	0.130760
$276$	−1.60141e8	−0.458482
$277$	2.10430e8	0.594878	0.297439	−	0.954741i	$-0.403867\pi$
$277$	2.10430e8	0.594878	0.297439	+	0.954741i	$0.403867\pi$
$278$	−8.48950e7	−0.236987
$279$	−1.28552e9	−3.54376
$280$	6.36279e6	0.0173219
$281$	−2.43532e8	−0.654762	−0.327381	−	0.944892i	$-0.606166\pi$
$281$	−2.43532e8	−0.654762	−0.327381	+	0.944892i	$0.606166\pi$
$282$	−1.65580e8	−0.439678
$283$	4.51678e8	1.18461	0.592307	−	0.805712i	$-0.298217\pi$
$283$	4.51678e8	1.18461	0.592307	+	0.805712i	$0.298217\pi$
$284$	−2.31728e8	−0.600293
$285$	−8.25165e7	−0.211146
$286$	−6.44968e6	−0.0163026
$287$	−1.19360e8	−0.298038
$288$	1.15033e9	2.83757
$289$	2.63776e8	0.642826
$290$	3.92627e6	0.00945337
$291$	1.62564e8	0.386721
$292$	2.78810e8	0.655342
$293$	1.67695e8	0.389479	0.194739	−	0.980855i	$-0.437614\pi$
$293$	1.67695e8	0.389479	0.194739	+	0.980855i	$0.437614\pi$
$294$	5.45888e7	0.125282
$295$	3.25716e7	0.0738690
$296$	−4.43039e8	−0.992935
$297$	−2.12213e8	−0.470028
$298$	3.50260e8	0.766715
$299$	3.75743e7	0.0812909
$300$	7.29168e8	1.55920
$301$	−3.08693e8	−0.652444
$302$	−1.39067e8	−0.290536
$303$	−4.03323e8	−0.832921
$304$	4.07165e8	0.831213
$305$	−1.93304e7	−0.0390114
$306$	8.14812e8	1.62567
$307$	2.16321e8	0.426692	0.213346	−	0.976977i	$-0.431564\pi$
$307$	2.16321e8	0.426692	0.213346	+	0.976977i	$0.431564\pi$
$308$	2.03203e7	0.0396280
$309$	2.76728e8	0.533578
$310$	1.67263e7	0.0318885
$311$	4.08196e8	0.769497	0.384748	−	0.923021i	$-0.374288\pi$
$311$	4.08196e8	0.769497	0.384748	+	0.923021i	$0.374288\pi$
$312$	−2.34770e8	−0.437624
$313$	−1.06467e8	−0.196250	−0.0981248	−	0.995174i	$-0.531284\pi$
$313$	−1.06467e8	−0.196250	−0.0981248	+	0.995174i	$0.531284\pi$
$314$	−4.66910e7	−0.0851097
$315$	−3.37391e7	−0.0608200
$316$	−3.56425e8	−0.635424
$317$	−7.93037e8	−1.39825	−0.699127	−	0.714998i	$-0.746428\pi$
$317$	−7.93037e8	−1.39825	−0.699127	+	0.714998i	$0.746428\pi$
$318$	8.64558e8	1.50765
$319$	2.82278e7	0.0486866
$320$	−372158.	−0.000634895 0
$321$	−2.01087e9	−3.39325
$322$	2.97378e7	0.0496379
$323$	1.47314e9	2.43240
$324$	−2.04626e9	−3.34236
$325$	−1.71086e8	−0.276454
$326$	1.07390e8	0.171674
$327$	−5.45626e8	−0.862934
$328$	4.06271e8	0.635707
$329$	−1.22401e8	−0.189496
$330$	4.26945e6	0.00653994
$331$	−7.95604e8	−1.20587	−0.602933	−	0.797792i	$-0.706001\pi$
$331$	−7.95604e8	−1.20587	−0.602933	+	0.797792i	$0.706001\pi$
$332$	−5.95347e6	−0.00892868
$333$	2.34924e9	3.48636
$334$	−2.60722e8	−0.382882
$335$	4.76615e7	0.0692646
$336$	2.25294e8	0.324012
$337$	−7.06625e8	−1.00574	−0.502869	−	0.864363i	$-0.667722\pi$
$337$	−7.06625e8	−1.00574	−0.502869	+	0.864363i	$0.667722\pi$
$338$	2.44689e7	0.0344672
$339$	−4.65283e8	−0.648662
$340$	4.22038e7	0.0582339
$341$	1.20253e8	0.164231
$342$	1.78060e9	2.40700
$343$	4.03536e7	0.0539949
$344$	1.05071e9	1.39164
$345$	−2.48728e7	−0.0326105
$346$	−4.39846e8	−0.570866
$347$	6.87593e8	0.883442	0.441721	−	0.897152i	$-0.354368\pi$
$347$	6.87593e8	0.883442	0.441721	+	0.897152i	$0.354368\pi$
$348$	4.56421e8	0.580549
$349$	−1.02454e9	−1.29015	−0.645077	−	0.764117i	$-0.723175\pi$
$349$	−1.02454e9	−1.29015	−0.645077	+	0.764117i	$0.723175\pi$
$350$	−1.35404e8	−0.168809
$351$	8.05096e8	0.993740
$352$	−1.07607e8	−0.131504
$353$	3.72727e7	0.0451003	0.0225502	−	0.999746i	$-0.492821\pi$
$353$	3.72727e7	0.0451003	0.0225502	+	0.999746i	$0.492821\pi$
$354$	−9.51156e8	−1.13957
$355$	−3.59914e7	−0.0426972
$356$	8.51786e8	1.00059
$357$	8.15121e8	0.948164
$358$	−1.11521e8	−0.128459
$359$	1.16518e9	1.32911	0.664557	−	0.747238i	$-0.268620\pi$
$359$	1.16518e9	1.32911	0.664557	+	0.747238i	$0.268620\pi$
$360$	1.14839e8	0.129727
$361$	2.32537e9	2.60146
$362$	−1.95315e8	−0.216399
$363$	−1.75296e9	−1.92353
$364$	−7.70914e7	−0.0837821
$365$	4.33041e7	0.0466127
$366$	5.64487e8	0.601824
$367$	−6.31350e8	−0.666713	−0.333356	−	0.942801i	$-0.608181\pi$
$367$	−6.31350e8	−0.666713	−0.333356	+	0.942801i	$0.608181\pi$
$368$	1.22731e8	0.128377
$369$	−2.15427e9	−2.23207
$370$	−3.05667e7	−0.0313720
$371$	6.39107e8	0.649777
$372$	1.94440e9	1.95833
$373$	5.17231e8	0.516064	0.258032	−	0.966136i	$-0.416926\pi$
$373$	5.17231e8	0.516064	0.258032	+	0.966136i	$0.416926\pi$
$374$	−7.62211e7	−0.0753398
$375$	2.26872e8	0.222163
$376$	4.16622e8	0.404189
$377$	−1.07091e8	−0.102934
$378$	6.37185e8	0.606798
$379$	−9.29432e8	−0.876961	−0.438480	−	0.898741i	$-0.644483\pi$
$379$	−9.29432e8	−0.876961	−0.438480	+	0.898741i	$0.644483\pi$
$380$	9.22277e7	0.0862222
$381$	2.23887e9	2.07392
$382$	7.99028e8	0.733399
$383$	1.60085e9	1.45598	0.727988	−	0.685590i	$-0.240456\pi$
$383$	1.60085e9	1.45598	0.727988	+	0.685590i	$0.240456\pi$
$384$	−2.16612e9	−1.95219
$385$	3.15610e6	0.00281863
$386$	−9.93043e7	−0.0878845
$387$	−5.57145e9	−4.88630
$388$	−1.81696e8	−0.157919
$389$	−2.04556e9	−1.76193	−0.880964	−	0.473183i	$-0.843105\pi$
$389$	−2.04556e9	−1.76193	−0.880964	+	0.473183i	$0.843105\pi$
$390$	−1.61975e7	−0.0138268
$391$	4.44046e8	0.375672
$392$	−1.37353e8	−0.115170
$393$	−1.94479e9	−1.61621
$394$	−3.35309e7	−0.0276190
$395$	−5.53591e7	−0.0451960
$396$	3.66752e8	0.296783
$397$	1.28803e9	1.03314	0.516572	−	0.856244i	$-0.327208\pi$
$397$	1.28803e9	1.03314	0.516572	+	0.856244i	$0.327208\pi$
$398$	4.99339e8	0.397013
$399$	1.78128e9	1.40387
$400$	−5.58828e8	−0.436584
$401$	1.39744e9	1.08225	0.541126	−	0.840942i	$-0.317998\pi$
$401$	1.39744e9	1.08225	0.541126	+	0.840942i	$0.317998\pi$
$402$	−1.39181e9	−1.06854
$403$	−4.56218e8	−0.347220
$404$	4.50790e8	0.340125
$405$	−3.17820e8	−0.237733
$406$	−8.47561e7	−0.0628536
$407$	−2.19758e8	−0.161572
$408$	−2.77446e9	−2.02241
$409$	−1.53071e9	−1.10627	−0.553137	−	0.833091i	$-0.686569\pi$
$409$	−1.53071e9	−1.10627	−0.553137	+	0.833091i	$0.686569\pi$
$410$	2.80299e7	0.0200853
$411$	−3.95276e8	−0.280837
$412$	−3.09295e8	−0.217888
$413$	−7.03122e8	−0.491140
$414$	5.36724e8	0.371749
$415$	−924680.	−0.000635072 0
$416$	4.08239e8	0.278028
$417$	−1.53281e9	−1.03517
$418$	−1.66565e8	−0.111550
$419$	1.70414e8	0.113176	0.0565881	−	0.998398i	$-0.481978\pi$
$419$	1.70414e8	0.113176	0.0565881	+	0.998398i	$0.481978\pi$
$420$	5.10317e7	0.0336099
$421$	−1.14665e9	−0.748935	−0.374468	−	0.927240i	$-0.622175\pi$
$421$	−1.14665e9	−0.748935	−0.374468	+	0.927240i	$0.622175\pi$
$422$	−1.81238e8	−0.117397
$423$	−2.20916e9	−1.41918
$424$	−2.17535e9	−1.38596
$425$	−2.02186e9	−1.27759
$426$	1.05102e9	0.658684
$427$	4.17285e8	0.259379
$428$	2.24752e9	1.38564
$429$	−1.16452e8	−0.0712106
$430$	7.24918e7	0.0439693
$431$	−7.19547e8	−0.432901	−0.216450	−	0.976294i	$-0.569448\pi$
$431$	−7.19547e8	−0.432901	−0.216450	+	0.976294i	$0.569448\pi$
$432$	2.62973e9	1.56934
$433$	2.43815e9	1.44329	0.721644	−	0.692264i	$-0.243387\pi$
$433$	2.43815e9	1.44329	0.721644	+	0.692264i	$0.243387\pi$
$434$	−3.61069e8	−0.212020
$435$	7.08903e7	0.0412928
$436$	6.09840e8	0.352381
$437$	9.70370e8	0.556227
$438$	−1.26457e9	−0.719088
$439$	−3.13203e9	−1.76685	−0.883427	−	0.468569i	$-0.844770\pi$
$439$	−3.13203e9	−1.76685	−0.883427	+	0.468569i	$0.844770\pi$
$440$	−1.07426e7	−0.00601206
$441$	7.28324e8	0.404380
$442$	2.89169e8	0.159284
$443$	1.55735e9	0.851085	0.425543	−	0.904938i	$-0.360083\pi$
$443$	1.55735e9	0.851085	0.425543	+	0.904938i	$0.360083\pi$
$444$	−3.55332e9	−1.92661
$445$	1.32298e8	0.0711691
$446$	−1.86398e8	−0.0994876
$447$	6.32409e9	3.34905
$448$	8.03375e6	0.00422129
$449$	−6.57537e8	−0.342814	−0.171407	−	0.985200i	$-0.554831\pi$
$449$	−6.57537e8	−0.342814	−0.171407	+	0.985200i	$0.554831\pi$
$450$	−2.44385e9	−1.26424
$451$	2.01520e8	0.103443
$452$	5.20042e8	0.264883
$453$	−2.51092e9	−1.26908
$454$	6.58561e7	0.0330294
$455$	−1.19737e7	−0.00595919
$456$	−6.06301e9	−2.99441
$457$	−2.75176e9	−1.34866	−0.674332	−	0.738428i	$-0.735569\pi$
$457$	−2.75176e9	−1.34866	−0.674332	+	0.738428i	$0.735569\pi$
$458$	−2.24423e8	−0.109154
$459$	9.51447e9	4.59240
$460$	2.78001e7	0.0133166
$461$	−1.79310e9	−0.852416	−0.426208	−	0.904625i	$-0.640151\pi$
$461$	−1.79310e9	−0.852416	−0.426208	+	0.904625i	$0.640151\pi$
$462$	−9.21645e7	−0.0434827
$463$	−2.07178e9	−0.970085	−0.485042	−	0.874491i	$-0.661196\pi$
$463$	−2.07178e9	−0.970085	−0.485042	+	0.874491i	$0.661196\pi$
$464$	−3.49797e8	−0.162556
$465$	3.02000e8	0.139290
$466$	9.14525e8	0.418644
$467$	6.66713e8	0.302921	0.151461	−	0.988463i	$-0.451602\pi$
$467$	6.66713e8	0.302921	0.151461	+	0.988463i	$0.451602\pi$
$468$	−1.39139e9	−0.627463
$469$	−1.02887e9	−0.460526
$470$	2.87441e7	0.0127704
$471$	−8.43024e8	−0.371764
$472$	2.39324e9	1.04759
$473$	5.21178e8	0.226450
$474$	1.61660e9	0.697232
$475$	−4.41836e9	−1.89162
$476$	−9.11052e8	−0.387185
$477$	1.15349e10	4.86633
$478$	−1.10339e9	−0.462096
$479$	4.04833e9	1.68307	0.841534	−	0.540204i	$-0.181653\pi$
$479$	4.04833e9	1.68307	0.841534	+	0.540204i	$0.181653\pi$
$480$	−2.70239e8	−0.111533
$481$	8.33722e8	0.341597
$482$	5.89116e8	0.239627
$483$	5.36928e8	0.216821
$484$	1.95926e9	0.785476
$485$	−2.82205e7	−0.0112323
$486$	5.21823e9	2.06204
$487$	−3.32591e9	−1.30485	−0.652423	−	0.757855i	$-0.726247\pi$
$487$	−3.32591e9	−1.30485	−0.652423	+	0.757855i	$0.726247\pi$
$488$	−1.42033e9	−0.553248
$489$	1.93897e9	0.749879
$490$	−9.47644e6	−0.00363881
$491$	−7.58319e8	−0.289112	−0.144556	−	0.989497i	$-0.546175\pi$
$491$	−7.58319e8	−0.289112	−0.144556	+	0.989497i	$0.546175\pi$
$492$	3.25842e9	1.23347
$493$	−1.26558e9	−0.475692
$494$	6.31918e8	0.235839
$495$	5.69631e7	0.0211094
$496$	−1.49017e9	−0.548340
$497$	7.76944e8	0.283885
$498$	2.70025e7	0.00979718
$499$	−5.46645e9	−1.96949	−0.984745	−	0.174004i	$-0.944329\pi$
$499$	−5.46645e9	−1.96949	−0.984745	+	0.174004i	$0.944329\pi$
$500$	−2.53573e8	−0.0907209
$501$	−4.70743e9	−1.67245
$502$	1.23294e9	0.434989
$503$	−3.19139e9	−1.11813	−0.559065	−	0.829124i	$-0.688840\pi$
$503$	−3.19139e9	−1.11813	−0.559065	+	0.829124i	$0.688840\pi$
$504$	−2.47903e9	−0.862530
$505$	7.00156e7	0.0241922
$506$	−5.02075e7	−0.0172283
$507$	4.41795e8	0.150554
$508$	−2.50236e9	−0.846890
$509$	3.28223e9	1.10320	0.551602	−	0.834107i	$-0.314017\pi$
$509$	3.28223e9	1.10320	0.551602	+	0.834107i	$0.314017\pi$
$510$	−1.91419e8	−0.0638983
$511$	−9.34803e8	−0.309918
$512$	2.40585e9	0.792179
$513$	2.07919e10	6.79960
$514$	3.63641e8	0.118114
$515$	−4.80390e7	−0.0154978
$516$	8.42704e9	2.70023
$517$	2.06655e8	0.0657701
$518$	6.59841e8	0.208586
$519$	−7.94159e9	−2.49357
$520$	4.07553e7	0.0127108
$521$	9.66030e8	0.299267	0.149633	−	0.988742i	$-0.452191\pi$
$521$	9.66030e8	0.299267	0.149633	+	0.988742i	$0.452191\pi$
$522$	−1.52972e9	−0.470724
$523$	8.42870e8	0.257635	0.128817	−	0.991668i	$-0.458882\pi$
$523$	8.42870e8	0.257635	0.128817	+	0.991668i	$0.458882\pi$
$524$	2.17367e9	0.659984
$525$	−2.44478e9	−0.737364
$526$	2.03498e9	0.609693
$527$	−5.39150e9	−1.60462
$528$	−3.80372e8	−0.112458
$529$	−3.11233e9	−0.914093
$530$	−1.50085e8	−0.0437896
$531$	−1.26903e10	−3.67826
$532$	−1.99091e9	−0.573274
$533$	−7.64530e8	−0.218700
$534$	−3.86335e9	−1.09792
$535$	3.49080e8	0.0985569
$536$	3.50200e9	0.982288
$537$	−2.01355e9	−0.561116
$538$	1.19254e9	0.330168
$539$	−6.81306e7	−0.0187405
$540$	5.95665e8	0.162789
$541$	2.80052e9	0.760411	0.380206	−	0.924902i	$-0.375853\pi$
$541$	2.80052e9	0.760411	0.380206	+	0.924902i	$0.375853\pi$
$542$	−1.86296e9	−0.502580
$543$	−3.52649e9	−0.945243
$544$	4.82449e9	1.28486
$545$	9.47189e7	0.0250639
$546$	3.49655e8	0.0919317
$547$	−4.15654e8	−0.108587	−0.0542933	−	0.998525i	$-0.517291\pi$
$547$	−4.15654e8	−0.108587	−0.0542933	+	0.998525i	$0.517291\pi$
$548$	4.41796e8	0.114680
$549$	7.53138e9	1.94255
$550$	2.28609e8	0.0585899
$551$	−2.76566e9	−0.704318
$552$	−1.82756e9	−0.462473
$553$	1.19503e9	0.300499
$554$	1.06675e9	0.266549
$555$	−5.51894e8	−0.137034
$556$	1.71321e9	0.422715
$557$	9.85661e8	0.241676	0.120838	−	0.992672i	$-0.461442\pi$
$557$	9.85661e8	0.241676	0.120838	+	0.992672i	$0.461442\pi$
$558$	−6.51678e9	−1.58786
$559$	−1.97725e9	−0.478763
$560$	−3.91102e7	−0.00941093
$561$	−1.37620e9	−0.329088
$562$	−1.23455e9	−0.293381
$563$	5.49350e9	1.29739	0.648694	−	0.761049i	$-0.275315\pi$
$563$	5.49350e9	1.29739	0.648694	+	0.761049i	$0.275315\pi$
$564$	3.34145e9	0.784256
$565$	8.07717e7	0.0188404
$566$	2.28973e9	0.530794
$567$	6.86077e9	1.58064
$568$	−2.64452e9	−0.605518
$569$	7.59035e9	1.72730	0.863652	−	0.504089i	$-0.168171\pi$
$569$	7.59035e9	1.72730	0.863652	+	0.504089i	$0.168171\pi$
$570$	−4.18307e8	−0.0946091
$571$	−1.19953e8	−0.0269641	−0.0134821	−	0.999909i	$-0.504292\pi$
$571$	−1.19953e8	−0.0269641	−0.0134821	+	0.999909i	$0.504292\pi$
$572$	1.30157e8	0.0290790
$573$	1.44268e10	3.20352
$574$	−6.05080e8	−0.133543
$575$	−1.33182e9	−0.292151
$576$	1.44997e8	0.0316142
$577$	−6.88006e9	−1.49100	−0.745499	−	0.666507i	$-0.767789\pi$
$577$	−6.88006e9	−1.49100	−0.745499	+	0.666507i	$0.767789\pi$
$578$	1.33718e9	0.288033
$579$	−1.79298e9	−0.383884
$580$	−7.92333e7	−0.0168620
$581$	1.99610e7	0.00422247
$582$	8.24096e8	0.173280
$583$	−1.07903e9	−0.225524
$584$	3.18183e9	0.661046
$585$	−2.16107e8	−0.0446297
$586$	8.50109e8	0.174515
$587$	−5.52743e9	−1.12795	−0.563975	−	0.825792i	$-0.690729\pi$
$587$	−5.52743e9	−1.12795	−0.563975	+	0.825792i	$0.690729\pi$
$588$	−1.10162e9	−0.223466
$589$	−1.17820e10	−2.37583
$590$	1.65118e8	0.0330987
$591$	−6.05414e8	−0.120641
$592$	2.72323e9	0.539459
$593$	−1.02285e9	−0.201428	−0.100714	−	0.994915i	$-0.532113\pi$
$593$	−1.02285e9	−0.201428	−0.100714	+	0.994915i	$0.532113\pi$
$594$	−1.07579e9	−0.210607
$595$	−1.41502e8	−0.0275394
$596$	−7.06836e9	−1.36759
$597$	9.01577e9	1.73417
$598$	1.90478e8	0.0364243
$599$	−1.23481e9	−0.234751	−0.117375	−	0.993088i	$-0.537448\pi$
$599$	−1.23481e9	−0.234751	−0.117375	+	0.993088i	$0.537448\pi$
$600$	8.32140e9	1.57278
$601$	3.62789e9	0.681701	0.340851	−	0.940118i	$-0.389285\pi$
$601$	3.62789e9	0.681701	0.340851	+	0.940118i	$0.389285\pi$
$602$	−1.56488e9	−0.292343
$603$	−1.85695e10	−3.44898
$604$	2.80642e9	0.518231
$605$	3.04308e8	0.0558688
$606$	−2.04459e9	−0.373210
$607$	−2.53201e9	−0.459521	−0.229760	−	0.973247i	$-0.573794\pi$
$607$	−2.53201e9	−0.459521	−0.229760	+	0.973247i	$0.573794\pi$
$608$	1.05429e10	1.90239
$609$	−1.53031e9	−0.274548
$610$	−9.79931e7	−0.0174800
$611$	−7.84010e8	−0.139052
$612$	−1.64432e10	−2.89972
$613$	4.55607e9	0.798875	0.399438	−	0.916760i	$-0.369205\pi$
$613$	4.55607e9	0.798875	0.399438	+	0.916760i	$0.369205\pi$
$614$	1.09661e9	0.191189
$615$	5.06091e8	0.0877336
$616$	2.31899e8	0.0399730
$617$	1.73058e9	0.296616	0.148308	−	0.988941i	$-0.452617\pi$
$617$	1.73058e9	0.296616	0.148308	+	0.988941i	$0.452617\pi$
$618$	1.40283e9	0.239082
$619$	3.04976e9	0.516830	0.258415	−	0.966034i	$-0.416800\pi$
$619$	3.04976e9	0.516830	0.258415	+	0.966034i	$0.416800\pi$
$620$	−3.37542e8	−0.0568796
$621$	6.26727e9	1.05017
$622$	2.06929e9	0.344791
$623$	−2.85590e9	−0.473189
$624$	1.44306e9	0.237760
$625$	6.04441e9	0.990316
$626$	−5.39719e8	−0.0879342
$627$	−3.00741e9	−0.487254
$628$	9.42238e8	0.151811
$629$	9.85277e9	1.57863
$630$	−1.71036e8	−0.0272518
$631$	4.30394e8	0.0681967	0.0340983	−	0.999418i	$-0.489144\pi$
$631$	4.30394e8	0.0681967	0.0340983	+	0.999418i	$0.489144\pi$
$632$	−4.06759e9	−0.640955
$633$	−3.27233e9	−0.512795
$634$	−4.02020e9	−0.626520
$635$	−3.88661e8	−0.0602370
$636$	−1.74471e10	−2.68920
$637$	2.58475e8	0.0396214
$638$	1.43097e8	0.0218152
$639$	1.40227e10	2.12608
$640$	3.76031e8	0.0567014
$641$	1.10248e10	1.65336	0.826679	−	0.562673i	$-0.190227\pi$
$641$	1.10248e10	1.65336	0.826679	+	0.562673i	$0.190227\pi$
$642$	−1.01938e10	−1.52042
$643$	7.45141e9	1.10535	0.552675	−	0.833397i	$-0.313607\pi$
$643$	7.45141e9	1.10535	0.552675	+	0.833397i	$0.313607\pi$
$644$	−6.00118e8	−0.0885393
$645$	1.30887e9	0.192060
$646$	7.46789e9	1.08989
$647$	1.00806e10	1.46326	0.731629	−	0.681703i	$-0.238760\pi$
$647$	1.00806e10	1.46326	0.731629	+	0.681703i	$0.238760\pi$
$648$	−2.33523e10	−3.37145
$649$	1.18711e9	0.170465
$650$	−8.67298e8	−0.123872
$651$	−6.51925e9	−0.926113
$652$	−2.16717e9	−0.306215
$653$	−9.47413e9	−1.33151	−0.665753	−	0.746172i	$-0.731890\pi$
$653$	−9.47413e9	−1.33151	−0.665753	+	0.746172i	$0.731890\pi$
$654$	−2.76598e9	−0.386658
$655$	3.37609e8	0.0469428
$656$	−2.49723e9	−0.345378
$657$	−1.68718e10	−2.32105
$658$	−6.20497e8	−0.0849081
$659$	−1.76640e9	−0.240431	−0.120216	−	0.992748i	$-0.538359\pi$
$659$	−1.76640e9	−0.240431	−0.120216	+	0.992748i	$0.538359\pi$
$660$	−8.61589e7	−0.0116653
$661$	−1.38665e10	−1.86751	−0.933756	−	0.357911i	$-0.883489\pi$
$661$	−1.38665e10	−1.86751	−0.933756	+	0.357911i	$0.883489\pi$
$662$	−4.03321e9	−0.540316
$663$	5.22105e9	0.695762
$664$	−6.79421e7	−0.00900639
$665$	−3.09224e8	−0.0407754
$666$	1.19092e10	1.56215
$667$	−8.33650e8	−0.108779
$668$	5.26144e9	0.682947
$669$	−3.36549e9	−0.434567
$670$	2.41614e8	0.0310356
$671$	−7.04519e8	−0.0900251
$672$	5.83364e9	0.741562
$673$	5.33230e9	0.674313	0.337157	−	0.941449i	$-0.390535\pi$
$673$	5.33230e9	0.674313	0.337157	+	0.941449i	$0.390535\pi$
$674$	−3.58215e9	−0.450644
$675$	−2.85366e10	−3.57140
$676$	−4.93790e8	−0.0614793
$677$	−9.37389e9	−1.16107	−0.580536	−	0.814234i	$-0.697157\pi$
$677$	−9.37389e9	−1.16107	−0.580536	+	0.814234i	$0.697157\pi$
$678$	−2.35869e9	−0.290648
$679$	6.09195e8	0.0746814
$680$	4.81638e8	0.0587408
$681$	1.18906e9	0.144274
$682$	6.09608e8	0.0735877
$683$	−6.22969e9	−0.748160	−0.374080	−	0.927397i	$-0.622041\pi$
$683$	−6.22969e9	−0.748160	−0.374080	+	0.927397i	$0.622041\pi$
$684$	−3.59331e10	−4.29337
$685$	6.86187e7	0.00815691
$686$	2.04567e8	0.0241937
$687$	−4.05205e9	−0.476788
$688$	−6.45841e9	−0.756077
$689$	4.09364e9	0.476806
$690$	−1.26090e8	−0.0146119
$691$	−7.58458e9	−0.874497	−0.437248	−	0.899341i	$-0.644047\pi$
$691$	−7.58458e9	−0.874497	−0.437248	+	0.899341i	$0.644047\pi$
$692$	8.87622e9	1.01826
$693$	−1.22966e9	−0.140352
$694$	3.48566e9	0.395847
$695$	2.66091e8	0.0300666
$696$	5.20877e9	0.585602
$697$	−9.03507e9	−1.01069
$698$	−5.19379e9	−0.578084
$699$	1.65121e10	1.82866
$700$	2.73250e9	0.301104
$701$	7.37533e9	0.808665	0.404332	−	0.914612i	$-0.367504\pi$
$701$	7.37533e9	0.808665	0.404332	+	0.914612i	$0.367504\pi$
$702$	4.08133e9	0.445268
$703$	2.15312e10	2.33735
$704$	−1.35637e7	−0.00146512
$705$	5.18986e8	0.0557820
$706$	1.88949e8	0.0202083
$707$	−1.51142e9	−0.160849
$708$	1.91946e10	2.03265
$709$	−5.05378e8	−0.0532543	−0.0266271	−	0.999645i	$-0.508477\pi$
$709$	−5.05378e8	−0.0532543	−0.0266271	+	0.999645i	$0.508477\pi$
$710$	−1.82454e8	−0.0191315
$711$	2.15686e10	2.25050
$712$	9.72074e9	1.00930
$713$	−3.55143e9	−0.366936
$714$	4.13215e9	0.424847
$715$	2.02156e7	0.00206831
$716$	2.25052e9	0.229133
$717$	−1.99222e10	−2.01846
$718$	5.90672e9	0.595540
$719$	−1.01941e9	−0.102281	−0.0511407	−	0.998691i	$-0.516286\pi$
$719$	−1.01941e9	−0.102281	−0.0511407	+	0.998691i	$0.516286\pi$
$720$	−7.05883e8	−0.0704805
$721$	1.03702e9	0.103041
$722$	1.17881e10	1.16564
$723$	1.06367e10	1.04670
$724$	3.94152e9	0.385992
$725$	3.79583e9	0.369934
$726$	−8.88638e9	−0.861880
$727$	1.25881e10	1.21504	0.607520	−	0.794305i	$-0.292165\pi$
$727$	1.25881e10	1.21504	0.607520	+	0.794305i	$0.292165\pi$
$728$	−8.79782e8	−0.0845114
$729$	5.04724e10	4.82511
$730$	2.19524e8	0.0208859
$731$	−2.33668e10	−2.21253
$732$	−1.13915e10	−1.07348
$733$	9.07874e9	0.851455	0.425727	−	0.904851i	$-0.360018\pi$
$733$	9.07874e9	0.851455	0.425727	+	0.904851i	$0.360018\pi$
$734$	−3.20055e9	−0.298736
$735$	−1.71101e8	−0.0158945
$736$	3.17794e9	0.293814
$737$	1.73708e9	0.159839
$738$	−1.09208e10	−1.00013
$739$	9.17639e9	0.836405	0.418202	−	0.908354i	$-0.362660\pi$
$739$	9.17639e9	0.836405	0.418202	+	0.908354i	$0.362660\pi$
$740$	6.16845e8	0.0559584
$741$	1.14095e10	1.03016
$742$	3.23987e9	0.291148
$743$	7.27430e9	0.650624	0.325312	−	0.945607i	$-0.394531\pi$
$743$	7.27430e9	0.650624	0.325312	+	0.945607i	$0.394531\pi$
$744$	2.21898e10	1.97537
$745$	−1.09784e9	−0.0972731
$746$	2.62204e9	0.231235
$747$	3.60267e8	0.0316230
$748$	1.53817e9	0.134384
$749$	−7.53558e9	−0.655285
$750$	1.15010e9	0.0995455
$751$	−1.92362e10	−1.65722	−0.828611	−	0.559825i	$-0.810868\pi$
$751$	−1.92362e10	−1.65722	−0.828611	+	0.559825i	$0.810868\pi$
$752$	−2.56085e9	−0.219595
$753$	2.22612e10	1.90005
$754$	−5.42884e8	−0.0461219
$755$	4.35887e8	0.0368604
$756$	−1.28586e10	−1.08235
$757$	1.16902e10	0.979460	0.489730	−	0.871874i	$-0.337095\pi$
$757$	1.16902e10	0.979460	0.489730	+	0.871874i	$0.337095\pi$
$758$	−4.71163e9	−0.392943
$759$	−9.06517e8	−0.0752541
$760$	1.05252e9	0.0869727
$761$	−1.38651e9	−0.114045	−0.0570226	−	0.998373i	$-0.518161\pi$
$761$	−1.38651e9	−0.114045	−0.0570226	+	0.998373i	$0.518161\pi$
$762$	1.13497e10	0.929268
$763$	−2.04469e9	−0.166645
$764$	−1.61246e10	−1.30817
$765$	−2.55391e9	−0.206249
$766$	8.11529e9	0.652384
$767$	−4.50367e9	−0.360398
$768$	−1.12553e10	−0.896585
$769$	2.25594e10	1.78890	0.894449	−	0.447169i	$-0.147568\pi$
$769$	2.25594e10	1.78890	0.894449	+	0.447169i	$0.147568\pi$
$770$	1.59995e7	0.00126295
$771$	6.56568e9	0.515928
$772$	2.00399e9	0.156760
$773$	−1.40228e10	−1.09196	−0.545980	−	0.837798i	$-0.683842\pi$
$773$	−1.40228e10	−1.09196	−0.545980	+	0.837798i	$0.683842\pi$
$774$	−2.82438e10	−2.18942
$775$	1.61706e10	1.24787
$776$	−2.07354e9	−0.159293
$777$	1.19137e10	0.911114
$778$	−1.03697e10	−0.789473
$779$	−1.97443e10	−1.49644
$780$	3.26871e8	0.0246629
$781$	−1.31175e9	−0.0985306
$782$	2.25103e9	0.168329
$783$	−1.78624e10	−1.32976
$784$	8.44271e8	0.0625713
$785$	1.46346e8	0.0107979
$786$	−9.85884e9	−0.724181
$787$	1.61699e10	1.18248	0.591241	−	0.806495i	$-0.298638\pi$
$787$	1.61699e10	1.18248	0.591241	+	0.806495i	$0.298638\pi$
$788$	6.76664e8	0.0492642
$789$	3.67425e10	2.66317
$790$	−2.80636e8	−0.0202511
$791$	−1.74361e9	−0.125266
$792$	4.18544e9	0.299367
$793$	2.67281e9	0.190332
$794$	6.52952e9	0.462924
$795$	−2.70984e9	−0.191275
$796$	−1.00768e10	−0.708154
$797$	−1.70285e10	−1.19144	−0.595720	−	0.803192i	$-0.703133\pi$
$797$	−1.70285e10	−1.19144	−0.595720	+	0.803192i	$0.703133\pi$
$798$	9.02996e9	0.629036
$799$	−9.26528e9	−0.642606
$800$	−1.44700e10	−0.999203
$801$	−5.15448e10	−3.54382
$802$	7.08415e9	0.484928
$803$	1.57827e9	0.107566
$804$	2.80872e10	1.90595
$805$	−9.32090e7	−0.00629756
$806$	−2.31274e9	−0.155580
$807$	2.15318e10	1.44219
$808$	5.14450e9	0.343086
$809$	1.06844e10	0.709461	0.354731	−	0.934969i	$-0.384573\pi$
$809$	1.06844e10	0.709461	0.354731	+	0.934969i	$0.384573\pi$
$810$	−1.61115e9	−0.106522
$811$	1.17027e9	0.0770392	0.0385196	−	0.999258i	$-0.487736\pi$
$811$	1.17027e9	0.0770392	0.0385196	+	0.999258i	$0.487736\pi$
$812$	1.71040e9	0.112112
$813$	−3.36364e10	−2.19530
$814$	−1.11404e9	−0.0723959
$815$	−3.36600e8	−0.0217802
$816$	1.70538e10	1.09877
$817$	−5.10633e10	−3.27591
$818$	−7.75976e9	−0.495691
$819$	4.66510e9	0.296734
$820$	−5.65652e8	−0.0358262
$821$	2.76919e10	1.74643	0.873217	−	0.487331i	$-0.162029\pi$
$821$	2.76919e10	1.74643	0.873217	+	0.487331i	$0.162029\pi$
$822$	−2.00380e9	−0.125836
$823$	1.47605e10	0.923001	0.461500	−	0.887140i	$-0.347311\pi$
$823$	1.47605e10	0.923001	0.461500	+	0.887140i	$0.347311\pi$
$824$	−3.52974e9	−0.219784
$825$	4.12762e9	0.255924
$826$	−3.56438e9	−0.220067
$827$	6.34407e9	0.390031	0.195015	−	0.980800i	$-0.437524\pi$
$827$	6.34407e9	0.390031	0.195015	+	0.980800i	$0.437524\pi$
$828$	−1.08313e10	−0.663091
$829$	1.54701e9	0.0943087	0.0471544	−	0.998888i	$-0.484985\pi$
$829$	1.54701e9	0.0943087	0.0471544	+	0.998888i	$0.484985\pi$
$830$	−4.68754e6	−0.000284559 0
$831$	1.92605e10	1.16430
$832$	5.14581e7	0.00309758
$833$	3.05461e9	0.183104
$834$	−7.77039e9	−0.463833
$835$	8.17195e8	0.0485762
$836$	3.36134e9	0.198971
$837$	−7.60957e10	−4.48560
$838$	8.63889e8	0.0507112
$839$	1.72472e10	1.00821	0.504105	−	0.863642i	$-0.331822\pi$
$839$	1.72472e10	1.00821	0.504105	+	0.863642i	$0.331822\pi$
$840$	5.82383e8	0.0339025
$841$	−1.48739e10	−0.862260
$842$	−5.81281e9	−0.335578
$843$	−2.22903e10	−1.28150
$844$	3.65744e9	0.209401
$845$	−7.66943e7	−0.00437285
$846$	−1.11991e10	−0.635895
$847$	−6.56907e9	−0.371460
$848$	1.33713e10	0.752986
$849$	4.13419e10	2.31853
$850$	−1.02496e10	−0.572452
$851$	6.49011e9	0.360993
$852$	−2.12099e10	−1.17490
$853$	1.46409e10	0.807691	0.403846	−	0.914827i	$-0.367673\pi$
$853$	1.46409e10	0.807691	0.403846	+	0.914827i	$0.367673\pi$
$854$	2.11537e9	0.116221
$855$	−5.58105e9	−0.305376
$856$	2.56492e10	1.39770
$857$	−2.91869e9	−0.158400	−0.0792001	−	0.996859i	$-0.525237\pi$
$857$	−2.91869e9	−0.158400	−0.0792001	+	0.996859i	$0.525237\pi$
$858$	−5.90336e8	−0.0319076
$859$	−2.48464e10	−1.33748	−0.668741	−	0.743495i	$-0.733167\pi$
$859$	−2.48464e10	−1.33748	−0.668741	+	0.743495i	$0.733167\pi$
$860$	−1.46291e9	−0.0784282
$861$	−1.09250e10	−0.583323
$862$	−3.64765e9	−0.193971
$863$	−1.35902e10	−0.719759	−0.359880	−	0.932999i	$-0.617182\pi$
$863$	−1.35902e10	−0.719759	−0.359880	+	0.932999i	$0.617182\pi$
$864$	6.80929e10	3.59173
$865$	1.37863e9	0.0724257
$866$	1.23599e10	0.646699
$867$	2.41433e10	1.25814
$868$	7.28649e9	0.378181
$869$	−2.01763e9	−0.104297
$870$	3.59369e8	0.0185022
$871$	−6.59014e9	−0.337934
$872$	6.95960e9	0.355449
$873$	1.09951e10	0.559305
$874$	4.91917e9	0.249231
$875$	8.50188e8	0.0429029
$876$	2.55193e10	1.28264
$877$	−1.72722e10	−0.864669	−0.432334	−	0.901713i	$-0.642310\pi$
$877$	−1.72722e10	−0.864669	−0.432334	+	0.901713i	$0.642310\pi$
$878$	−1.58774e10	−0.791680
$879$	1.53491e10	0.762291
$880$	6.60314e7	0.00326634
$881$	−2.10680e10	−1.03802	−0.519012	−	0.854767i	$-0.673700\pi$
$881$	−2.10680e10	−1.03802	−0.519012	+	0.854767i	$0.673700\pi$
$882$	3.69214e9	0.181192
$883$	−1.96551e10	−0.960754	−0.480377	−	0.877062i	$-0.659500\pi$
$883$	−1.96551e10	−0.960754	−0.480377	+	0.877062i	$0.659500\pi$
$884$	−5.83551e9	−0.284116
$885$	2.98126e9	0.144577
$886$	7.89478e9	0.381349
$887$	−1.51365e10	−0.728269	−0.364135	−	0.931346i	$-0.618635\pi$
$887$	−1.51365e10	−0.728269	−0.364135	+	0.931346i	$0.618635\pi$
$888$	−4.05511e10	−1.94338
$889$	8.39001e9	0.400503
$890$	6.70665e8	0.0318890
$891$	−1.15833e10	−0.548607
$892$	3.76157e9	0.177456
$893$	−2.02473e10	−0.951454
$894$	3.20592e10	1.50062
$895$	3.49546e8	0.0162976
$896$	−8.11737e9	−0.376996
$897$	3.43916e9	0.159103
$898$	−3.33330e9	−0.153606
$899$	1.01220e10	0.464629
$900$	4.93177e10	2.25504
$901$	4.83778e10	2.20348
$902$	1.02158e9	0.0463500
$903$	−2.82545e10	−1.27697
$904$	5.93481e9	0.267188
$905$	6.12188e8	0.0274546
$906$	−1.27288e10	−0.568640
$907$	1.59379e10	0.709260	0.354630	−	0.935007i	$-0.384607\pi$
$907$	1.59379e10	0.709260	0.354630	+	0.935007i	$0.384607\pi$
$908$	−1.32900e9	−0.0589146
$909$	−2.72790e10	−1.20463
$910$	−6.06989e7	−0.00267015
$911$	2.83676e9	0.124310	0.0621552	−	0.998066i	$-0.480203\pi$
$911$	2.83676e9	0.124310	0.0621552	+	0.998066i	$0.480203\pi$
$912$	3.72676e10	1.62686
$913$	−3.37010e7	−0.00146553
$914$	−1.39497e10	−0.604301
$915$	−1.76930e9	−0.0763534
$916$	4.52892e9	0.194698
$917$	−7.28794e9	−0.312113
$918$	4.82324e10	2.05773
$919$	−4.50629e10	−1.91521	−0.957603	−	0.288093i	$-0.906979\pi$
$919$	−4.50629e10	−1.91521	−0.957603	+	0.288093i	$0.906979\pi$
$920$	3.17259e8	0.0134325
$921$	1.97998e10	0.835124
$922$	−9.08990e9	−0.381945
$923$	4.97652e9	0.208315
$924$	1.85991e9	0.0775603
$925$	−2.95512e10	−1.22766
$926$	−1.05026e10	−0.434669
$927$	1.87166e10	0.771700
$928$	−9.05748e9	−0.372040
$929$	−3.82088e10	−1.56354	−0.781768	−	0.623569i	$-0.785682\pi$
$929$	−3.82088e10	−1.56354	−0.781768	+	0.623569i	$0.785682\pi$
$930$	1.53095e9	0.0624123
$931$	6.67521e9	0.271107
$932$	−1.84554e10	−0.746737
$933$	3.73619e10	1.50606
$934$	3.37982e9	0.135731
$935$	2.38904e8	0.00955836
$936$	−1.58788e10	−0.632924
$937$	−6.36608e9	−0.252804	−0.126402	−	0.991979i	$-0.540343\pi$
$937$	−6.36608e9	−0.252804	−0.126402	+	0.991979i	$0.540343\pi$
$938$	−5.21571e9	−0.206349
$939$	−9.74485e9	−0.384101
$940$	−5.80065e8	−0.0227787
$941$	−6.10568e9	−0.238875	−0.119437	−	0.992842i	$-0.538109\pi$
$941$	−6.10568e9	−0.238875	−0.119437	+	0.992842i	$0.538109\pi$
$942$	−4.27360e9	−0.166577
$943$	−5.95148e9	−0.231118
$944$	−1.47106e10	−0.569151
$945$	−1.99717e9	−0.0769845
$946$	2.64205e9	0.101466
$947$	−1.13940e10	−0.435966	−0.217983	−	0.975953i	$-0.569948\pi$
$947$	−1.13940e10	−0.435966	−0.217983	+	0.975953i	$0.569948\pi$
$948$	−3.26234e10	−1.24366
$949$	−5.98764e9	−0.227418
$950$	−2.23983e10	−0.847583
$951$	−7.25863e10	−2.73667
$952$	−1.03971e10	−0.390555
$953$	5.48399e9	0.205244	0.102622	−	0.994720i	$-0.467277\pi$
$953$	5.48399e9	0.205244	0.102622	+	0.994720i	$0.467277\pi$
$954$	5.84749e10	2.18047
$955$	−2.50444e9	−0.0930463
$956$	2.22668e10	0.824242
$957$	2.58368e9	0.0952898
$958$	2.05225e10	0.754138
$959$	−1.48127e9	−0.0542336
$960$	−3.40634e7	−0.00124262
$961$	1.56080e10	0.567303
$962$	4.22645e9	0.153060
$963$	−1.36006e11	−4.90757
$964$	−1.18886e10	−0.427424
$965$	3.11255e8	0.0111499
$966$	2.72189e9	0.0971517
$967$	2.68619e10	0.955309	0.477655	−	0.878548i	$-0.341487\pi$
$967$	2.68619e10	0.955309	0.477655	+	0.878548i	$0.341487\pi$
$968$	2.23594e10	0.792313
$969$	1.34836e11	4.76071
$970$	−1.43060e8	−0.00503290
$971$	−3.77276e10	−1.32249	−0.661244	−	0.750171i	$-0.729971\pi$
$971$	−3.77276e10	−1.32249	−0.661244	+	0.750171i	$0.729971\pi$
$972$	−1.05306e11	−3.67806
$973$	−5.74410e9	−0.199907
$974$	−1.68603e10	−0.584666
$975$	−1.56594e10	−0.541077
$976$	8.73035e9	0.300578
$977$	3.73201e10	1.28030	0.640150	−	0.768250i	$-0.278872\pi$
$977$	3.73201e10	1.28030	0.640150	+	0.768250i	$0.278872\pi$
$978$	9.82938e9	0.336001
$979$	4.82173e9	0.164234
$980$	1.91238e8	0.00649056
$981$	−3.69037e10	−1.24804
$982$	−3.84420e9	−0.129544
$983$	4.23260e10	1.42125	0.710624	−	0.703572i	$-0.248413\pi$
$983$	4.23260e10	1.42125	0.710624	+	0.703572i	$0.248413\pi$
$984$	3.71857e10	1.24421
$985$	1.05098e8	0.00350402
$986$	−6.41570e9	−0.213145
$987$	−1.12033e10	−0.370883
$988$	−1.27523e10	−0.420668
$989$	−1.53919e10	−0.505948
$990$	2.88767e8	0.00945855
$991$	9.53829e8	0.0311324	0.0155662	−	0.999879i	$-0.495045\pi$
$991$	9.53829e8	0.0311324	0.0155662	+	0.999879i	$0.495045\pi$
$992$	−3.85857e10	−1.25498
$993$	−7.28212e10	−2.36013
$994$	3.93862e9	0.127201
$995$	−1.56511e9	−0.0503691
$996$	−5.44918e8	−0.0174753
$997$	1.79682e10	0.574210	0.287105	−	0.957899i	$-0.407307\pi$
$997$	1.79682e10	0.574210	0.287105	+	0.957899i	$0.407307\pi$
$998$	−2.77115e10	−0.882476
$999$	1.39062e11	4.41295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+5.06937 q^{2} +91.5295 q^{3} -102.301 q^{4} -15.8892 q^{5} +463.997 q^{6} +343.000 q^{7} -1167.48 q^{8} +6190.65 q^{9} +O(q^{10})\)	\(q+5.06937 q^{2} +91.5295 q^{3} -102.301 q^{4} -15.8892 q^{5} +463.997 q^{6} +343.000 q^{7} -1167.48 q^{8} +6190.65 q^{9} -80.5484 q^{10} -579.101 q^{11} -9363.61 q^{12} +2197.00 q^{13} +1738.79 q^{14} -1454.33 q^{15} +7176.18 q^{16} +25963.7 q^{17} +31382.7 q^{18} +56738.3 q^{19} +1625.49 q^{20} +31394.6 q^{21} -2935.68 q^{22} +17102.5 q^{23} -106859. q^{24} -77872.5 q^{25} +11137.4 q^{26} +366452. q^{27} -35089.4 q^{28} -48744.2 q^{29} -7372.56 q^{30} -207655. q^{31} +185817. q^{32} -53004.8 q^{33} +131620. q^{34} -5450.01 q^{35} -633313. q^{36} +379482. q^{37} +287628. q^{38} +201090. q^{39} +18550.4 q^{40} -347988. q^{41} +159151. q^{42} -899979. q^{43} +59242.9 q^{44} -98364.7 q^{45} +86699.2 q^{46} -356855. q^{47} +656833. q^{48} +117649. q^{49} -394765. q^{50} +2.37645e6 q^{51} -224756. q^{52} +1.86328e6 q^{53} +1.85768e6 q^{54} +9201.47 q^{55} -400447. q^{56} +5.19323e6 q^{57} -247102. q^{58} -2.04992e6 q^{59} +148781. q^{60} +1.21657e6 q^{61} -1.05268e6 q^{62} +2.12339e6 q^{63} +23422.0 q^{64} -34908.6 q^{65} -268701. q^{66} -2.99961e6 q^{67} -2.65613e6 q^{68} +1.56539e6 q^{69} -27628.1 q^{70} +2.26514e6 q^{71} -7.22748e6 q^{72} -2.72537e6 q^{73} +1.92373e6 q^{74} -7.12764e6 q^{75} -5.80442e6 q^{76} -198632. q^{77} +1.01940e6 q^{78} +3.48407e6 q^{79} -114024. q^{80} +2.00022e7 q^{81} -1.76408e6 q^{82} +58195.4 q^{83} -3.21172e6 q^{84} -412544. q^{85} -4.56232e6 q^{86} -4.46153e6 q^{87} +676091. q^{88} -8.32624e6 q^{89} -498647. q^{90} +753571. q^{91} -1.74962e6 q^{92} -1.90066e7 q^{93} -1.80903e6 q^{94} -901529. q^{95} +1.70077e7 q^{96} +1.77608e6 q^{97} +596406. q^{98} -3.58501e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 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

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Database

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