LMFDB - Embedded newform 91.8.a.e.1.4

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			1.4
Root			$10.7733$ 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)

$f(q)$	$=$	$q-9.77328 q^{2} -73.6575 q^{3} -32.4830 q^{4} +542.246 q^{5} +719.876 q^{6} +343.000 q^{7} +1568.45 q^{8} +3238.43 q^{9} +O(q^{10})$	\(q-9.77328 q^{2} -73.6575 q^{3} -32.4830 q^{4} +542.246 q^{5} +719.876 q^{6} +343.000 q^{7} +1568.45 q^{8} +3238.43 q^{9} -5299.52 q^{10} -5395.65 q^{11} +2392.61 q^{12} +2197.00 q^{13} -3352.24 q^{14} -39940.5 q^{15} -11171.0 q^{16} +18410.0 q^{17} -31650.1 q^{18} -44263.9 q^{19} -17613.8 q^{20} -25264.5 q^{21} +52733.2 q^{22} +43813.6 q^{23} -115528. q^{24} +215906. q^{25} -21471.9 q^{26} -77445.7 q^{27} -11141.7 q^{28} -134005. q^{29} +390350. q^{30} +49812.7 q^{31} -91583.3 q^{32} +397430. q^{33} -179926. q^{34} +185990. q^{35} -105194. q^{36} +329314. q^{37} +432603. q^{38} -161826. q^{39} +850483. q^{40} -550159. q^{41} +246917. q^{42} -295625. q^{43} +175267. q^{44} +1.75603e6 q^{45} -428203. q^{46} -995915. q^{47} +822831. q^{48} +117649. q^{49} -2.11011e6 q^{50} -1.35604e6 q^{51} -71365.1 q^{52} +755923. q^{53} +756899. q^{54} -2.92577e6 q^{55} +537977. q^{56} +3.26037e6 q^{57} +1.30967e6 q^{58} +2.25161e6 q^{59} +1.29739e6 q^{60} +2.50367e6 q^{61} -486834. q^{62} +1.11078e6 q^{63} +2.32496e6 q^{64} +1.19131e6 q^{65} -3.88420e6 q^{66} +2.12825e6 q^{67} -598012. q^{68} -3.22720e6 q^{69} -1.81774e6 q^{70} +630584. q^{71} +5.07930e6 q^{72} -958314. q^{73} -3.21847e6 q^{74} -1.59031e7 q^{75} +1.43782e6 q^{76} -1.85071e6 q^{77} +1.58157e6 q^{78} +7.53352e6 q^{79} -6.05745e6 q^{80} -1.37799e6 q^{81} +5.37686e6 q^{82} -833106. q^{83} +820667. q^{84} +9.98276e6 q^{85} +2.88922e6 q^{86} +9.87051e6 q^{87} -8.46279e6 q^{88} +47383.3 q^{89} -1.71621e7 q^{90} +753571. q^{91} -1.42320e6 q^{92} -3.66908e6 q^{93} +9.73336e6 q^{94} -2.40019e7 q^{95} +6.74580e6 q^{96} -8.93678e6 q^{97} -1.14982e6 q^{98} -1.74734e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.77328	−0.863844	−0.431922	−	0.901911i	$-0.642164\pi$
$2$	−9.77328	−0.863844	−0.431922	+	0.901911i	$0.642164\pi$
$3$	−73.6575	−1.57504	−0.787522	−	0.616287i	$-0.788636\pi$
$3$	−73.6575	−1.57504	−0.787522	+	0.616287i	$0.788636\pi$
$4$	−32.4830	−0.253773
$5$	542.246	1.94000	0.969999	−	0.243108i	$-0.0781671\pi$
$5$	542.246	1.94000	0.969999	+	0.243108i	$0.0781671\pi$
$6$	719.876	1.36059
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	1568.45	1.08306
$9$	3238.43	1.48076
$10$	−5299.52	−1.67586
$11$	−5395.65	−1.22228	−0.611139	−	0.791524i	$-0.709288\pi$
$11$	−5395.65	−1.22228	−0.611139	+	0.791524i	$0.709288\pi$
$12$	2392.61	0.399704
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−3352.24	−0.326502
$15$	−39940.5	−3.05558
$16$	−11171.0	−0.681826
$17$	18410.0	0.908831	0.454415	−	0.890790i	$-0.349848\pi$
$17$	18410.0	0.908831	0.454415	+	0.890790i	$0.349848\pi$
$18$	−31650.1	−1.27915
$19$	−44263.9	−1.48051	−0.740256	−	0.672325i	$-0.765296\pi$
$19$	−44263.9	−1.48051	−0.740256	+	0.672325i	$0.765296\pi$
$20$	−17613.8	−0.492319
$21$	−25264.5	−0.595311
$22$	52733.2	1.05586
$23$	43813.6	0.750865	0.375433	−	0.926850i	$-0.377494\pi$
$23$	43813.6	0.750865	0.375433	+	0.926850i	$0.377494\pi$
$24$	−115528.	−1.70587
$25$	215906.	2.76359
$26$	−21471.9	−0.239587
$27$	−77445.7	−0.757224
$28$	−11141.7	−0.0959172
$29$	−134005.	−1.02030	−0.510152	−	0.860084i	$-0.670411\pi$
$29$	−134005.	−1.02030	−0.510152	+	0.860084i	$0.670411\pi$
$30$	390350.	2.63955
$31$	49812.7	0.300313	0.150157	−	0.988662i	$-0.452022\pi$
$31$	49812.7	0.300313	0.150157	+	0.988662i	$0.452022\pi$
$32$	−91583.3	−0.494073
$33$	397430.	1.92514
$34$	−179926.	−0.785088
$35$	185990.	0.733250
$36$	−105194.	−0.375778
$37$	329314.	1.06882	0.534409	−	0.845226i	$-0.320534\pi$
$37$	329314.	1.06882	0.534409	+	0.845226i	$0.320534\pi$
$38$	432603.	1.27893
$39$	−161826.	−0.436839
$40$	850483.	2.10114
$41$	−550159.	−1.24665	−0.623325	−	0.781963i	$-0.714219\pi$
$41$	−550159.	−1.24665	−0.623325	+	0.781963i	$0.714219\pi$
$42$	246917.	0.514256
$43$	−295625.	−0.567023	−0.283512	−	0.958969i	$-0.591499\pi$
$43$	−295625.	−0.567023	−0.283512	+	0.958969i	$0.591499\pi$
$44$	175267.	0.310181
$45$	1.75603e6	2.87268
$46$	−428203.	−0.648631
$47$	−995915.	−1.39920	−0.699600	−	0.714535i	$-0.746638\pi$
$47$	−995915.	−1.39920	−0.699600	+	0.714535i	$0.746638\pi$
$48$	822831.	1.07391
$49$	117649.	0.142857
$50$	−2.11011e6	−2.38731
$51$	−1.35604e6	−1.43145
$52$	−71365.1	−0.0703840
$53$	755923.	0.697448	0.348724	−	0.937225i	$-0.386615\pi$
$53$	755923.	0.697448	0.348724	+	0.937225i	$0.386615\pi$
$54$	756899.	0.654124
$55$	−2.92577e6	−2.37122
$56$	537977.	0.409360
$57$	3.26037e6	2.33187
$58$	1.30967e6	0.881383
$59$	2.25161e6	1.42729	0.713644	−	0.700508i	$-0.247043\pi$
$59$	2.25161e6	1.42729	0.713644	+	0.700508i	$0.247043\pi$
$60$	1.29739e6	0.775425
$61$	2.50367e6	1.41229	0.706143	−	0.708070i	$-0.250434\pi$
$61$	2.50367e6	1.41229	0.706143	+	0.708070i	$0.250434\pi$
$62$	−486834.	−0.259424
$63$	1.11078e6	0.559676
$64$	2.32496e6	1.10863
$65$	1.19131e6	0.538059
$66$	−3.88420e6	−1.66302
$67$	2.12825e6	0.864491	0.432245	−	0.901756i	$-0.357721\pi$
$67$	2.12825e6	0.864491	0.432245	+	0.901756i	$0.357721\pi$
$68$	−598012.	−0.230637
$69$	−3.22720e6	−1.18265
$70$	−1.81774e6	−0.633414
$71$	630584.	0.209092	0.104546	−	0.994520i	$-0.466661\pi$
$71$	630584.	0.209092	0.104546	+	0.994520i	$0.466661\pi$
$72$	5.07930e6	1.60376
$73$	−958314.	−0.288322	−0.144161	−	0.989554i	$-0.546048\pi$
$73$	−958314.	−0.288322	−0.144161	+	0.989554i	$0.546048\pi$
$74$	−3.21847e6	−0.923292
$75$	−1.59031e7	−4.35278
$76$	1.43782e6	0.375714
$77$	−1.85071e6	−0.461977
$78$	1.58157e6	0.377361
$79$	7.53352e6	1.71911	0.859554	−	0.511045i	$-0.170742\pi$
$79$	7.53352e6	1.71911	0.859554	+	0.511045i	$0.170742\pi$
$80$	−6.05745e6	−1.32274
$81$	−1.37799e6	−0.288103
$82$	5.37686e6	1.07691
$83$	−833106.	−0.159929	−0.0799645	−	0.996798i	$-0.525481\pi$
$83$	−833106.	−0.159929	−0.0799645	+	0.996798i	$0.525481\pi$
$84$	820667.	0.151074
$85$	9.98276e6	1.76313
$86$	2.88922e6	0.489820
$87$	9.87051e6	1.60702
$88$	−8.46279e6	−1.32381
$89$	47383.3	0.00712459	0.00356230	−	0.999994i	$-0.498866\pi$
$89$	47383.3	0.00712459	0.00356230	+	0.999994i	$0.498866\pi$
$90$	−1.71621e7	−2.48155
$91$	753571.	0.104828
$92$	−1.42320e6	−0.190549
$93$	−3.66908e6	−0.473007
$94$	9.73336e6	1.20869
$95$	−2.40019e7	−2.87219
$96$	6.74580e6	0.778187
$97$	−8.93678e6	−0.994214	−0.497107	−	0.867689i	$-0.665604\pi$
$97$	−8.93678e6	−0.994214	−0.497107	+	0.867689i	$0.665604\pi$
$98$	−1.14982e6	−0.123406
$99$	−1.74734e7	−1.80990
$100$	−7.01326e6	−0.701326
$101$	1.47082e7	1.42048	0.710240	−	0.703960i	$-0.248586\pi$
$101$	1.47082e7	1.42048	0.710240	+	0.703960i	$0.248586\pi$
$102$	1.32529e7	1.23655
$103$	−2.89121e6	−0.260705	−0.130353	−	0.991468i	$-0.541611\pi$
$103$	−2.89121e6	−0.260705	−0.130353	+	0.991468i	$0.541611\pi$
$104$	3.44587e6	0.300388
$105$	−1.36996e7	−1.15490
$106$	−7.38785e6	−0.602487
$107$	9.99326e6	0.788613	0.394306	−	0.918979i	$-0.370985\pi$
$107$	9.99326e6	0.788613	0.394306	+	0.918979i	$0.370985\pi$
$108$	2.51567e6	0.192163
$109$	−4.36259e6	−0.322665	−0.161332	−	0.986900i	$-0.551579\pi$
$109$	−4.36259e6	−0.322665	−0.161332	+	0.986900i	$0.551579\pi$
$110$	2.85944e7	2.04836
$111$	−2.42564e7	−1.68343
$112$	−3.83167e6	−0.257706
$113$	−801002.	−0.0522227	−0.0261113	−	0.999659i	$-0.508312\pi$
$113$	−801002.	−0.0522227	−0.0261113	+	0.999659i	$0.508312\pi$
$114$	−3.18645e7	−2.01437
$115$	2.37578e7	1.45668
$116$	4.35289e6	0.258926
$117$	7.11483e6	0.410690
$118$	−2.20057e7	−1.23296
$119$	6.31464e6	0.343506
$120$	−6.26445e7	−3.30939
$121$	9.62591e6	0.493961
$122$	−2.44691e7	−1.21999
$123$	4.05233e7	1.96353
$124$	−1.61806e6	−0.0762114
$125$	7.47110e7	3.42137
$126$	−1.08560e7	−0.483473
$127$	2.84540e7	1.23262	0.616312	−	0.787502i	$-0.288626\pi$
$127$	2.84540e7	1.23262	0.616312	+	0.787502i	$0.288626\pi$
$128$	−1.09999e7	−0.463609
$129$	2.17750e7	0.893087
$130$	−1.16431e7	−0.464799
$131$	2.99334e7	1.16334	0.581670	−	0.813425i	$-0.302400\pi$
$131$	2.99334e7	1.16334	0.581670	+	0.813425i	$0.302400\pi$
$132$	−1.29097e7	−0.488549
$133$	−1.51825e7	−0.559581
$134$	−2.08000e7	−0.746785
$135$	−4.19946e7	−1.46901
$136$	2.88751e7	0.984323
$137$	−3.00981e7	−1.00004	−0.500020	−	0.866014i	$-0.666674\pi$
$137$	−3.00981e7	−1.00004	−0.500020	+	0.866014i	$0.666674\pi$
$138$	3.15404e7	1.02162
$139$	2.66578e7	0.841923	0.420961	−	0.907079i	$-0.361693\pi$
$139$	2.66578e7	0.841923	0.420961	+	0.907079i	$0.361693\pi$
$140$	−6.04152e6	−0.186079
$141$	7.33566e7	2.20380
$142$	−6.16287e6	−0.180623
$143$	−1.18543e7	−0.338999
$144$	−3.61766e7	−1.00962
$145$	−7.26639e7	−1.97939
$146$	9.36587e6	0.249065
$147$	−8.66573e6	−0.225006
$148$	−1.06971e7	−0.271237
$149$	5.04552e7	1.24955	0.624776	−	0.780804i	$-0.285190\pi$
$149$	5.04552e7	1.24955	0.624776	+	0.780804i	$0.285190\pi$
$150$	1.55425e8	3.76012
$151$	7.18866e6	0.169914	0.0849569	−	0.996385i	$-0.472925\pi$
$151$	7.18866e6	0.169914	0.0849569	+	0.996385i	$0.472925\pi$
$152$	−6.94255e7	−1.60349
$153$	5.96196e7	1.34576
$154$	1.80875e7	0.399076
$155$	2.70108e7	0.582607
$156$	5.25657e6	0.110858
$157$	2.22228e7	0.458300	0.229150	−	0.973391i	$-0.426405\pi$
$157$	2.22228e7	0.458300	0.229150	+	0.973391i	$0.426405\pi$
$158$	−7.36272e7	−1.48504
$159$	−5.56794e7	−1.09851
$160$	−4.96607e7	−0.958501
$161$	1.50281e7	0.283800
$162$	1.34674e7	0.248876
$163$	−2.91573e7	−0.527341	−0.263670	−	0.964613i	$-0.584933\pi$
$163$	−2.91573e7	−0.527341	−0.263670	+	0.964613i	$0.584933\pi$
$164$	1.78708e7	0.316366
$165$	2.15505e8	3.73477
$166$	8.14218e6	0.138154
$167$	6.32524e7	1.05092	0.525459	−	0.850819i	$-0.323894\pi$
$167$	6.32524e7	1.05092	0.525459	+	0.850819i	$0.323894\pi$
$168$	−3.96260e7	−0.644760
$169$	4.82681e6	0.0769231
$170$	−9.75643e7	−1.52307
$171$	−1.43345e8	−2.19229
$172$	9.60276e6	0.143895
$173$	9.60420e7	1.41026	0.705131	−	0.709077i	$-0.250888\pi$
$173$	9.60420e7	1.41026	0.705131	+	0.709077i	$0.250888\pi$
$174$	−9.64672e7	−1.38822
$175$	7.40557e7	1.04454
$176$	6.02751e7	0.833380
$177$	−1.65848e8	−2.24804
$178$	−463090.	−0.00615454
$179$	−6.00804e7	−0.782973	−0.391487	−	0.920184i	$-0.628039\pi$
$179$	−6.00804e7	−0.782973	−0.391487	+	0.920184i	$0.628039\pi$
$180$	−5.70409e7	−0.729009
$181$	−1.25061e8	−1.56764	−0.783821	−	0.620987i	$-0.786732\pi$
$181$	−1.25061e8	−1.56764	−0.783821	+	0.620987i	$0.786732\pi$
$182$	−7.36486e6	−0.0905555
$183$	−1.84414e8	−2.22441
$184$	6.87193e7	0.813236
$185$	1.78569e8	2.07350
$186$	3.58590e7	0.408604
$187$	−9.93341e7	−1.11084
$188$	3.23503e7	0.355079
$189$	−2.65639e7	−0.286204
$190$	2.34577e8	2.48112
$191$	1.25052e7	0.129859	0.0649296	−	0.997890i	$-0.479318\pi$
$191$	1.25052e7	0.129859	0.0649296	+	0.997890i	$0.479318\pi$
$192$	−1.71251e8	−1.74614
$193$	2.91478e7	0.291847	0.145924	−	0.989296i	$-0.453385\pi$
$193$	2.91478e7	0.291847	0.145924	+	0.989296i	$0.453385\pi$
$194$	8.73417e7	0.858846
$195$	−8.77493e7	−0.847466
$196$	−3.82159e6	−0.0362533
$197$	1.31037e8	1.22113	0.610567	−	0.791965i	$-0.290942\pi$
$197$	1.31037e8	1.22113	0.610567	+	0.791965i	$0.290942\pi$
$198$	1.70773e8	1.56347
$199$	1.12046e8	1.00788	0.503940	−	0.863739i	$-0.331883\pi$
$199$	1.12046e8	1.00788	0.503940	+	0.863739i	$0.331883\pi$
$200$	3.38636e8	2.99315
$201$	−1.56761e8	−1.36161
$202$	−1.43748e8	−1.22707
$203$	−4.59639e7	−0.385638
$204$	4.40481e7	0.363263
$205$	−2.98321e8	−2.41850
$206$	2.82567e7	0.225209
$207$	1.41887e8	1.11185
$208$	−2.45428e7	−0.189105
$209$	2.38833e8	1.80960
$210$	1.33890e8	0.997655
$211$	−1.61207e8	−1.18140	−0.590698	−	0.806893i	$-0.701148\pi$
$211$	−1.61207e8	−1.18140	−0.590698	+	0.806893i	$0.701148\pi$
$212$	−2.45546e7	−0.176994
$213$	−4.64472e7	−0.329330
$214$	−9.76669e7	−0.681239
$215$	−1.60301e8	−1.10002
$216$	−1.21469e8	−0.820122
$217$	1.70858e7	0.113508
$218$	4.26368e7	0.278732
$219$	7.05870e7	0.454120
$220$	9.50377e7	0.601751
$221$	4.04468e7	0.252064
$222$	2.37065e8	1.45423
$223$	−4.67109e7	−0.282066	−0.141033	−	0.990005i	$-0.545042\pi$
$223$	−4.67109e7	−0.282066	−0.141033	+	0.990005i	$0.545042\pi$
$224$	−3.14131e7	−0.186742
$225$	6.99196e8	4.09223
$226$	7.82842e6	0.0451123
$227$	−1.14409e7	−0.0649189	−0.0324595	−	0.999473i	$-0.510334\pi$
$227$	−1.14409e7	−0.0649189	−0.0324595	+	0.999473i	$0.510334\pi$
$228$	−1.05906e8	−0.591766
$229$	3.35140e8	1.84418	0.922088	−	0.386980i	$-0.126482\pi$
$229$	3.35140e8	1.84418	0.922088	+	0.386980i	$0.126482\pi$
$230$	−2.32191e8	−1.25834
$231$	1.36319e8	0.727635
$232$	−2.10180e8	−1.10505
$233$	−3.25837e6	−0.0168754	−0.00843772	−	0.999964i	$-0.502686\pi$
$233$	−3.25837e6	−0.0168754	−0.00843772	+	0.999964i	$0.502686\pi$
$234$	−6.95353e7	−0.354772
$235$	−5.40031e8	−2.71444
$236$	−7.31391e7	−0.362208
$237$	−5.54900e8	−2.70767
$238$	−6.17147e7	−0.296736
$239$	8.02647e6	0.0380305	0.0190152	−	0.999819i	$-0.493947\pi$
$239$	8.02647e6	0.0380305	0.0190152	+	0.999819i	$0.493947\pi$
$240$	4.46177e8	2.08338
$241$	−2.18177e8	−1.00403	−0.502017	−	0.864858i	$-0.667409\pi$
$241$	−2.18177e8	−1.00403	−0.502017	+	0.864858i	$0.667409\pi$
$242$	−9.40767e7	−0.426706
$243$	2.70873e8	1.21100
$244$	−8.13266e7	−0.358400
$245$	6.37947e7	0.277143
$246$	−3.96046e8	−1.69618
$247$	−9.72477e7	−0.410620
$248$	7.81285e7	0.325259
$249$	6.13645e7	0.251895
$250$	−7.30172e8	−2.95553
$251$	4.91535e8	1.96199	0.980994	−	0.194039i	$-0.0621589\pi$
$251$	4.91535e8	1.96199	0.980994	+	0.194039i	$0.0621589\pi$
$252$	−3.60815e7	−0.142031
$253$	−2.36403e8	−0.917765
$254$	−2.78089e8	−1.06480
$255$	−7.35305e8	−2.77701
$256$	−1.90090e8	−0.708142
$257$	−3.91074e6	−0.0143712	−0.00718559	−	0.999974i	$-0.502287\pi$
$257$	−3.91074e6	−0.0143712	−0.00718559	+	0.999974i	$0.502287\pi$
$258$	−2.12813e8	−0.771488
$259$	1.12955e8	0.403975
$260$	−3.86974e7	−0.136545
$261$	−4.33967e8	−1.51083
$262$	−2.92548e8	−1.00494
$263$	2.44686e8	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$263$	2.44686e8	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$264$	6.23348e8	2.08505
$265$	4.09896e8	1.35305
$266$	1.48383e8	0.483391
$267$	−3.49013e6	−0.0112215
$268$	−6.91318e7	−0.219385
$269$	−3.94462e8	−1.23559	−0.617793	−	0.786341i	$-0.711973\pi$
$269$	−3.94462e8	−1.23559	−0.617793	+	0.786341i	$0.711973\pi$
$270$	4.10425e8	1.26900
$271$	−1.93103e8	−0.589381	−0.294691	−	0.955593i	$-0.595217\pi$
$271$	−1.93103e8	−0.589381	−0.294691	+	0.955593i	$0.595217\pi$
$272$	−2.05659e8	−0.619665
$273$	−5.55062e7	−0.165109
$274$	2.94157e8	0.863878
$275$	−1.16495e9	−3.37788
$276$	1.04829e8	0.300124
$277$	−2.29853e8	−0.649788	−0.324894	−	0.945750i	$-0.605329\pi$
$277$	−2.29853e8	−0.649788	−0.324894	+	0.945750i	$0.605329\pi$
$278$	−2.60534e8	−0.727290
$279$	1.61315e8	0.444693
$280$	2.91716e8	0.794158
$281$	−1.88360e8	−0.506427	−0.253213	−	0.967410i	$-0.581488\pi$
$281$	−1.88360e8	−0.506427	−0.253213	+	0.967410i	$0.581488\pi$
$282$	−7.16935e8	−1.90374
$283$	5.30265e8	1.39072	0.695362	−	0.718660i	$-0.255244\pi$
$283$	5.30265e8	1.39072	0.695362	+	0.718660i	$0.255244\pi$
$284$	−2.04832e7	−0.0530620
$285$	1.76792e9	4.52383
$286$	1.15855e8	0.292842
$287$	−1.88704e8	−0.471189
$288$	−2.96586e8	−0.731606
$289$	−7.14097e7	−0.174026
$290$	7.10165e8	1.70988
$291$	6.58261e8	1.56593
$292$	3.11289e7	0.0731683
$293$	2.60555e7	0.0605151	0.0302575	−	0.999542i	$-0.490367\pi$
$293$	2.60555e7	0.0605151	0.0302575	+	0.999542i	$0.490367\pi$
$294$	8.46927e7	0.194370
$295$	1.22093e9	2.76894
$296$	5.16510e8	1.15760
$297$	4.17870e8	0.925537
$298$	−4.93113e8	−1.07942
$299$	9.62586e7	0.208253
$300$	5.16579e8	1.10462
$301$	−1.01399e8	−0.214315
$302$	−7.02568e7	−0.146779
$303$	−1.08337e9	−2.23732
$304$	4.94473e8	1.00945
$305$	1.35760e9	2.73983
$306$	−5.82679e8	−1.16253
$307$	−2.20100e8	−0.434146	−0.217073	−	0.976155i	$-0.569651\pi$
$307$	−2.20100e8	−0.434146	−0.217073	+	0.976155i	$0.569651\pi$
$308$	6.01165e7	0.117237
$309$	2.12960e8	0.410622
$310$	−2.63984e8	−0.503282
$311$	−6.05011e8	−1.14052	−0.570259	−	0.821465i	$-0.693157\pi$
$311$	−6.05011e8	−1.14052	−0.570259	+	0.821465i	$0.693157\pi$
$312$	−2.53815e8	−0.473124
$313$	3.49729e8	0.644654	0.322327	−	0.946628i	$-0.395535\pi$
$313$	3.49729e8	0.644654	0.322327	+	0.946628i	$0.395535\pi$
$314$	−2.17190e8	−0.395900
$315$	6.02317e8	1.08577
$316$	−2.44711e8	−0.436263
$317$	3.59961e8	0.634669	0.317335	−	0.948314i	$-0.397212\pi$
$317$	3.59961e8	0.634669	0.317335	+	0.948314i	$0.397212\pi$
$318$	5.44170e8	0.948943
$319$	7.23047e8	1.24709
$320$	1.26070e9	2.15074
$321$	−7.36079e8	−1.24210
$322$	−1.46874e8	−0.245159
$323$	−8.14899e8	−1.34553
$324$	4.47611e7	0.0731127
$325$	4.74345e8	0.766483
$326$	2.84963e8	0.455540
$327$	3.21337e8	0.508211
$328$	−8.62894e8	−1.35020
$329$	−3.41599e8	−0.528848
$330$	−2.10619e9	−3.22626
$331$	4.41046e8	0.668476	0.334238	−	0.942489i	$-0.391521\pi$
$331$	4.41046e8	0.668476	0.334238	+	0.942489i	$0.391521\pi$
$332$	2.70618e7	0.0405857
$333$	1.06646e9	1.58267
$334$	−6.18183e8	−0.907830
$335$	1.15403e9	1.67711
$336$	2.82231e8	0.405898
$337$	1.14008e8	0.162267	0.0811335	−	0.996703i	$-0.474146\pi$
$337$	1.14008e8	0.162267	0.0811335	+	0.996703i	$0.474146\pi$
$338$	−4.71738e7	−0.0664496
$339$	5.89998e7	0.0822530
$340$	−3.24270e8	−0.447435
$341$	−2.68772e8	−0.367066
$342$	1.40096e9	1.89380
$343$	4.03536e7	0.0539949
$344$	−4.63671e8	−0.614123
$345$	−1.74994e9	−2.29433
$346$	−9.38646e8	−1.21825
$347$	−1.30706e9	−1.67935	−0.839675	−	0.543089i	$-0.817255\pi$
$347$	−1.30706e9	−1.67935	−0.839675	+	0.543089i	$0.817255\pi$
$348$	−3.20623e8	−0.407819
$349$	8.43351e8	1.06199	0.530994	−	0.847376i	$-0.321819\pi$
$349$	8.43351e8	1.06199	0.530994	+	0.847376i	$0.321819\pi$
$350$	−7.23767e8	−0.902320
$351$	−1.70148e8	−0.210016
$352$	4.94152e8	0.603894
$353$	3.55072e8	0.429641	0.214820	−	0.976654i	$-0.431083\pi$
$353$	3.55072e8	0.429641	0.214820	+	0.976654i	$0.431083\pi$
$354$	1.62088e9	1.94196
$355$	3.41931e8	0.405639
$356$	−1.53915e6	−0.00180803
$357$	−4.65121e8	−0.541037
$358$	5.87182e8	0.676367
$359$	4.30277e8	0.490815	0.245407	−	0.969420i	$-0.421078\pi$
$359$	4.30277e8	0.490815	0.245407	+	0.969420i	$0.421078\pi$
$360$	2.75423e9	3.11130
$361$	1.06542e9	1.19191
$362$	1.22226e9	1.35420
$363$	−7.09020e8	−0.778011
$364$	−2.44782e7	−0.0266026
$365$	−5.19642e8	−0.559344
$366$	1.80233e9	1.92154
$367$	4.98575e8	0.526501	0.263251	−	0.964727i	$-0.415205\pi$
$367$	4.98575e8	0.526501	0.263251	+	0.964727i	$0.415205\pi$
$368$	−4.89444e8	−0.511959
$369$	−1.78165e9	−1.84599
$370$	−1.74520e9	−1.79118
$371$	2.59282e8	0.263611
$372$	1.19183e8	0.120036
$373$	1.28216e9	1.27927	0.639633	−	0.768681i	$-0.279087\pi$
$373$	1.28216e9	1.27927	0.639633	+	0.768681i	$0.279087\pi$
$374$	9.70820e8	0.959596
$375$	−5.50303e9	−5.38880
$376$	−1.56204e9	−1.51542
$377$	−2.94410e8	−0.282981
$378$	2.59616e8	0.247235
$379$	−1.16236e9	−1.09674	−0.548370	−	0.836236i	$-0.684751\pi$
$379$	−1.16236e9	−1.09674	−0.548370	+	0.836236i	$0.684751\pi$
$380$	7.79653e8	0.728885
$381$	−2.09585e9	−1.94144
$382$	−1.22217e8	−0.112178
$383$	5.10273e8	0.464095	0.232047	−	0.972705i	$-0.425458\pi$
$383$	5.10273e8	0.464095	0.232047	+	0.972705i	$0.425458\pi$
$384$	8.10222e8	0.730205
$385$	−1.00354e9	−0.896235
$386$	−2.84870e8	−0.252111
$387$	−9.57360e8	−0.839628
$388$	2.90293e8	0.252305
$389$	−1.23045e9	−1.05984	−0.529922	−	0.848047i	$-0.677779\pi$
$389$	−1.23045e9	−1.05984	−0.529922	+	0.848047i	$0.677779\pi$
$390$	8.57598e8	0.732079
$391$	8.06610e8	0.682410
$392$	1.84526e8	0.154724
$393$	−2.20482e9	−1.83231
$394$	−1.28067e9	−1.05487
$395$	4.08502e9	3.33507
$396$	5.67589e8	0.459305
$397$	5.91484e8	0.474434	0.237217	−	0.971457i	$-0.423765\pi$
$397$	5.91484e8	0.474434	0.237217	+	0.971457i	$0.423765\pi$
$398$	−1.09505e9	−0.870651
$399$	1.11831e9	0.881364
$400$	−2.41189e9	−1.88429
$401$	−2.37781e8	−0.184150	−0.0920751	−	0.995752i	$-0.529350\pi$
$401$	−2.37781e8	−0.184150	−0.0920751	+	0.995752i	$0.529350\pi$
$402$	1.53207e9	1.17622
$403$	1.09439e8	0.0832919
$404$	−4.77766e8	−0.360480
$405$	−7.47207e8	−0.558919
$406$	4.49218e8	0.333132
$407$	−1.77686e9	−1.30639
$408$	−2.12687e9	−1.55035
$409$	−5.91200e8	−0.427271	−0.213635	−	0.976913i	$-0.568530\pi$
$409$	−5.91200e8	−0.427271	−0.213635	+	0.976913i	$0.568530\pi$
$410$	2.91558e9	2.08921
$411$	2.21695e9	1.57511
$412$	9.39152e7	0.0661600
$413$	7.72304e8	0.539465
$414$	−1.38671e9	−0.960469
$415$	−4.51749e8	−0.310262
$416$	−2.01208e8	−0.137031
$417$	−1.96355e9	−1.32607
$418$	−2.33418e9	−1.56321
$419$	1.72110e9	1.14303	0.571514	−	0.820592i	$-0.306356\pi$
$419$	1.72110e9	1.14303	0.571514	+	0.820592i	$0.306356\pi$
$420$	4.45003e8	0.293083
$421$	−2.74845e9	−1.79515	−0.897575	−	0.440862i	$-0.854673\pi$
$421$	−2.74845e9	−1.79515	−0.897575	+	0.440862i	$0.854673\pi$
$422$	1.57552e9	1.02054
$423$	−3.22520e9	−2.07188
$424$	1.18562e9	0.755381
$425$	3.97483e9	2.51164
$426$	4.53942e8	0.284490
$427$	8.58758e8	0.533794
$428$	−3.24611e8	−0.200129
$429$	8.73155e8	0.533938
$430$	1.56667e9	0.950250
$431$	−1.97069e8	−0.118562	−0.0592812	−	0.998241i	$-0.518881\pi$
$431$	−1.97069e8	−0.118562	−0.0592812	+	0.998241i	$0.518881\pi$
$432$	8.65149e8	0.516295
$433$	−1.28666e9	−0.761651	−0.380826	−	0.924647i	$-0.624360\pi$
$433$	−1.28666e9	−0.761651	−0.380826	+	0.924647i	$0.624360\pi$
$434$	−1.66984e8	−0.0980530
$435$	5.35224e9	3.11762
$436$	1.41710e8	0.0818836
$437$	−1.93936e9	−1.11166
$438$	−6.89867e8	−0.392289
$439$	1.62511e9	0.916762	0.458381	−	0.888756i	$-0.348429\pi$
$439$	1.62511e9	0.916762	0.458381	+	0.888756i	$0.348429\pi$
$440$	−4.58891e9	−2.56818
$441$	3.80998e8	0.211538
$442$	−3.95298e8	−0.217744
$443$	5.52819e8	0.302113	0.151057	−	0.988525i	$-0.451732\pi$
$443$	5.52819e8	0.302113	0.151057	+	0.988525i	$0.451732\pi$
$444$	7.87920e8	0.427210
$445$	2.56934e7	0.0138217
$446$	4.56519e8	0.243661
$447$	−3.71641e9	−1.96810
$448$	7.97462e8	0.419022
$449$	1.06717e8	0.0556378	0.0278189	−	0.999613i	$-0.491144\pi$
$449$	1.06717e8	0.0556378	0.0278189	+	0.999613i	$0.491144\pi$
$450$	−6.83344e9	−3.53505
$451$	2.96847e9	1.52375
$452$	2.60189e7	0.0132527
$453$	−5.29499e8	−0.267622
$454$	1.11816e8	0.0560799
$455$	4.08621e8	0.203367
$456$	5.11371e9	2.52557
$457$	1.64615e9	0.806796	0.403398	−	0.915025i	$-0.367829\pi$
$457$	1.64615e9	0.806796	0.403398	+	0.915025i	$0.367829\pi$
$458$	−3.27542e9	−1.59308
$459$	−1.42578e9	−0.688189
$460$	−7.71723e8	−0.369665
$461$	1.72295e9	0.819065	0.409532	−	0.912296i	$-0.365692\pi$
$461$	1.72295e9	0.819065	0.409532	+	0.912296i	$0.365692\pi$
$462$	−1.33228e9	−0.628563
$463$	−6.38530e8	−0.298984	−0.149492	−	0.988763i	$-0.547764\pi$
$463$	−6.38530e8	−0.298984	−0.149492	+	0.988763i	$0.547764\pi$
$464$	1.49698e9	0.695669
$465$	−1.98955e9	−0.917632
$466$	3.18450e7	0.0145778
$467$	−9.68141e6	−0.00439875	−0.00219938	−	0.999998i	$-0.500700\pi$
$467$	−9.68141e6	−0.00439875	−0.00219938	+	0.999998i	$0.500700\pi$
$468$	−2.31111e8	−0.104222
$469$	7.29989e8	0.326747
$470$	5.27787e9	2.34486
$471$	−1.63688e9	−0.721842
$472$	3.53153e9	1.54585
$473$	1.59509e9	0.693060
$474$	5.42320e9	2.33901
$475$	−9.55682e9	−4.09153
$476$	−2.05118e8	−0.0871725
$477$	2.44800e9	1.03276
$478$	−7.84450e7	−0.0328524
$479$	7.11028e7	0.0295606	0.0147803	−	0.999891i	$-0.495295\pi$
$479$	7.11028e7	0.0295606	0.0147803	+	0.999891i	$0.495295\pi$
$480$	3.65788e9	1.50968
$481$	7.23502e8	0.296437
$482$	2.13230e9	0.867329
$483$	−1.10693e9	−0.446998
$484$	−3.12678e8	−0.125354
$485$	−4.84593e9	−1.92877
$486$	−2.64732e9	−1.04611
$487$	−3.42955e9	−1.34550	−0.672752	−	0.739868i	$-0.734888\pi$
$487$	−3.42955e9	−1.34550	−0.672752	+	0.739868i	$0.734888\pi$
$488$	3.92687e9	1.52960
$489$	2.14766e9	0.830585
$490$	−6.23484e8	−0.239408
$491$	4.63944e7	0.0176881	0.00884403	−	0.999961i	$-0.497185\pi$
$491$	4.63944e7	0.0176881	0.00884403	+	0.999961i	$0.497185\pi$
$492$	−1.31632e9	−0.498291
$493$	−2.46704e9	−0.927283
$494$	9.50430e8	0.354712
$495$	−9.47491e9	−3.51121
$496$	−5.56460e8	−0.204761
$497$	2.16290e8	0.0790295
$498$	−5.99733e8	−0.217598
$499$	1.82432e9	0.657277	0.328638	−	0.944456i	$-0.393410\pi$
$499$	1.82432e9	0.657277	0.328638	+	0.944456i	$0.393410\pi$
$500$	−2.42684e9	−0.868251
$501$	−4.65901e9	−1.65524
$502$	−4.80391e9	−1.69485
$503$	−9.48076e8	−0.332166	−0.166083	−	0.986112i	$-0.553112\pi$
$503$	−9.48076e8	−0.332166	−0.166083	+	0.986112i	$0.553112\pi$
$504$	1.74220e9	0.606165
$505$	7.97547e9	2.75573
$506$	2.31044e9	0.792806
$507$	−3.55531e8	−0.121157
$508$	−9.24271e8	−0.312807
$509$	8.34472e8	0.280479	0.140239	−	0.990118i	$-0.455213\pi$
$509$	8.34472e8	0.280479	0.140239	+	0.990118i	$0.455213\pi$
$510$	7.18635e9	2.39890
$511$	−3.28702e8	−0.108975
$512$	3.26579e9	1.07533
$513$	3.42805e9	1.12108
$514$	3.82207e7	0.0124145
$515$	−1.56775e9	−0.505768
$516$	−7.07316e8	−0.226641
$517$	5.37361e9	1.71021
$518$	−1.10394e9	−0.348972
$519$	−7.07422e9	−2.22123
$520$	1.86851e9	0.582752
$521$	3.03761e9	0.941021	0.470511	−	0.882394i	$-0.344070\pi$
$521$	3.03761e9	0.941021	0.470511	+	0.882394i	$0.344070\pi$
$522$	4.24128e9	1.30512
$523$	2.21284e9	0.676385	0.338192	−	0.941077i	$-0.390185\pi$
$523$	2.21284e9	0.676385	0.338192	+	0.941077i	$0.390185\pi$
$524$	−9.72325e8	−0.295224
$525$	−5.45476e9	−1.64520
$526$	−2.39139e9	−0.716473
$527$	9.17054e8	0.272934
$528$	−4.43971e9	−1.31261
$529$	−1.48519e9	−0.436202
$530$	−4.00603e9	−1.16882
$531$	7.29169e9	2.11348
$532$	4.93173e8	0.142007
$533$	−1.20870e9	−0.345758
$534$	3.41101e7	0.00969367
$535$	5.41880e9	1.52991
$536$	3.33804e9	0.936300
$537$	4.42537e9	1.23322
$538$	3.85519e9	1.06735
$539$	−6.34793e8	−0.174611
$540$	1.36411e9	0.372796
$541$	5.94862e9	1.61520	0.807599	−	0.589732i	$-0.200766\pi$
$541$	5.94862e9	1.61520	0.807599	+	0.589732i	$0.200766\pi$
$542$	1.88725e9	0.509134
$543$	9.21168e9	2.46910
$544$	−1.68605e9	−0.449029
$545$	−2.36560e9	−0.625969
$546$	5.42477e8	0.142629
$547$	−4.86977e9	−1.27219	−0.636096	−	0.771610i	$-0.719452\pi$
$547$	−4.86977e9	−1.27219	−0.636096	+	0.771610i	$0.719452\pi$
$548$	9.77675e8	0.253783
$549$	8.10796e9	2.09126
$550$	1.13854e10	2.91796
$551$	5.93160e9	1.51057
$552$	−5.06169e9	−1.28088
$553$	2.58400e9	0.649762
$554$	2.24642e9	0.561316
$555$	−1.31529e10	−3.26586
$556$	−8.65924e8	−0.213657
$557$	−7.51461e9	−1.84253	−0.921263	−	0.388941i	$-0.872841\pi$
$557$	−7.51461e9	−1.84253	−0.921263	+	0.388941i	$0.872841\pi$
$558$	−1.57658e9	−0.384145
$559$	−6.49487e8	−0.157264
$560$	−2.07771e9	−0.499949
$561$	7.31670e9	1.74963
$562$	1.84090e9	0.437474
$563$	6.43656e9	1.52011	0.760054	−	0.649860i	$-0.225173\pi$
$563$	6.43656e9	1.52011	0.760054	+	0.649860i	$0.225173\pi$
$564$	−2.38284e9	−0.559265
$565$	−4.34340e8	−0.101312
$566$	−5.18243e9	−1.20137
$567$	−4.72649e8	−0.108893
$568$	9.89036e8	0.226461
$569$	−3.63837e9	−0.827969	−0.413985	−	0.910284i	$-0.635863\pi$
$569$	−3.63837e9	−0.827969	−0.413985	+	0.910284i	$0.635863\pi$
$570$	−1.72784e10	−3.90788
$571$	2.39039e8	0.0537332	0.0268666	−	0.999639i	$-0.491447\pi$
$571$	2.39039e8	0.0537332	0.0268666	+	0.999639i	$0.491447\pi$
$572$	3.85061e8	0.0860287
$573$	−9.21100e8	−0.204534
$574$	1.84426e9	0.407034
$575$	9.45962e9	2.07509
$576$	7.52923e9	1.64162
$577$	−7.25878e9	−1.57307	−0.786536	−	0.617545i	$-0.788128\pi$
$577$	−7.25878e9	−1.57307	−0.786536	+	0.617545i	$0.788128\pi$
$578$	6.97907e8	0.150332
$579$	−2.14696e9	−0.459672
$580$	2.36034e9	0.502315
$581$	−2.85755e8	−0.0604475
$582$	−6.43337e9	−1.35272
$583$	−4.07870e9	−0.852475
$584$	−1.50306e9	−0.312271
$585$	3.85799e9	0.796738
$586$	−2.54648e8	−0.0522756
$587$	−1.87500e9	−0.382621	−0.191310	−	0.981530i	$-0.561274\pi$
$587$	−1.87500e9	−0.382621	−0.191310	+	0.981530i	$0.561274\pi$
$588$	2.81489e8	0.0571005
$589$	−2.20490e9	−0.444617
$590$	−1.19325e10	−2.39193
$591$	−9.65189e9	−1.92334
$592$	−3.67877e9	−0.728748
$593$	−7.50994e9	−1.47892	−0.739461	−	0.673200i	$-0.764919\pi$
$593$	−7.50994e9	−1.47892	−0.739461	+	0.673200i	$0.764919\pi$
$594$	−4.08396e9	−0.799520
$595$	3.42409e9	0.666401
$596$	−1.63894e9	−0.317103
$597$	−8.25299e9	−1.58745
$598$	−9.40762e8	−0.179898
$599$	1.70825e9	0.324757	0.162378	−	0.986729i	$-0.448083\pi$
$599$	1.70825e9	0.324757	0.162378	+	0.986729i	$0.448083\pi$
$600$	−2.49431e10	−4.71434
$601$	3.59846e9	0.676170	0.338085	−	0.941115i	$-0.390221\pi$
$601$	3.59846e9	0.676170	0.338085	+	0.941115i	$0.390221\pi$
$602$	9.91003e8	0.185135
$603$	6.89218e9	1.28011
$604$	−2.33509e8	−0.0431196
$605$	5.21961e9	0.958284
$606$	1.05881e10	1.93269
$607$	−8.91852e9	−1.61857	−0.809287	−	0.587414i	$-0.800146\pi$
$607$	−8.91852e9	−1.61857	−0.809287	+	0.587414i	$0.800146\pi$
$608$	4.05383e9	0.731481
$609$	3.38558e9	0.607397
$610$	−1.32682e10	−2.36679
$611$	−2.18802e9	−0.388068
$612$	−1.93662e9	−0.341519
$613$	3.71170e9	0.650821	0.325410	−	0.945573i	$-0.394498\pi$
$613$	3.71170e9	0.650821	0.325410	+	0.945573i	$0.394498\pi$
$614$	2.15110e9	0.375035
$615$	2.19736e10	3.80924
$616$	−2.90274e9	−0.500351
$617$	1.12250e10	1.92392	0.961960	−	0.273191i	$-0.0880792\pi$
$617$	1.12250e10	1.92392	0.961960	+	0.273191i	$0.0880792\pi$
$618$	−2.08132e9	−0.354714
$619$	9.00878e9	1.52668	0.763341	−	0.645996i	$-0.223558\pi$
$619$	9.00878e9	1.52668	0.763341	+	0.645996i	$0.223558\pi$
$620$	−8.77389e8	−0.147850
$621$	−3.39318e9	−0.568573
$622$	5.91294e9	0.985230
$623$	1.62525e7	0.00269284
$624$	1.80776e9	0.297848
$625$	2.36441e10	3.87385
$626$	−3.41800e9	−0.556881
$627$	−1.75918e10	−2.85019
$628$	−7.21862e8	−0.116304
$629$	6.06267e9	0.971375
$630$	−5.88661e9	−0.937937
$631$	−7.95970e9	−1.26123	−0.630615	−	0.776096i	$-0.717197\pi$
$631$	−7.95970e9	−1.26123	−0.630615	+	0.776096i	$0.717197\pi$
$632$	1.18159e10	1.86190
$633$	1.18741e10	1.86075
$634$	−3.51800e9	−0.548255
$635$	1.54291e10	2.39129
$636$	1.80863e9	0.278773
$637$	2.58475e8	0.0396214
$638$	−7.06654e9	−1.07729
$639$	2.04210e9	0.309617
$640$	−5.96463e9	−0.899401
$641$	−8.77037e9	−1.31527	−0.657635	−	0.753337i	$-0.728443\pi$
$641$	−8.77037e9	−1.31527	−0.657635	+	0.753337i	$0.728443\pi$
$642$	7.19390e9	1.07298
$643$	−5.02017e8	−0.0744698	−0.0372349	−	0.999307i	$-0.511855\pi$
$643$	−5.02017e8	−0.0744698	−0.0372349	+	0.999307i	$0.511855\pi$
$644$	−4.88156e8	−0.0720209
$645$	1.18074e10	1.73259
$646$	7.96424e9	1.16233
$647$	−1.87111e9	−0.271603	−0.135802	−	0.990736i	$-0.543361\pi$
$647$	−1.87111e9	−0.271603	−0.135802	+	0.990736i	$0.543361\pi$
$648$	−2.16130e9	−0.312034
$649$	−1.21489e10	−1.74454
$650$	−4.63591e9	−0.662122
$651$	−1.25850e9	−0.178780
$652$	9.47117e8	0.133825
$653$	6.54530e9	0.919884	0.459942	−	0.887949i	$-0.347870\pi$
$653$	6.54530e9	0.919884	0.459942	+	0.887949i	$0.347870\pi$
$654$	−3.14052e9	−0.439015
$655$	1.62313e10	2.25688
$656$	6.14584e9	0.849998
$657$	−3.10343e9	−0.426937
$658$	3.33854e9	0.456842
$659$	7.45930e9	1.01531	0.507656	−	0.861560i	$-0.330512\pi$
$659$	7.45930e9	1.01531	0.507656	+	0.861560i	$0.330512\pi$
$660$	−7.00024e9	−0.947784
$661$	−6.56757e9	−0.884503	−0.442252	−	0.896891i	$-0.645820\pi$
$661$	−6.56757e9	−0.884503	−0.442252	+	0.896891i	$0.645820\pi$
$662$	−4.31047e9	−0.577460
$663$	−2.97921e9	−0.397012
$664$	−1.30668e9	−0.173213
$665$	−8.23265e9	−1.08559
$666$	−1.04228e10	−1.36718
$667$	−5.87126e9	−0.766110
$668$	−2.05462e9	−0.266695
$669$	3.44061e9	0.444267
$670$	−1.12787e10	−1.44876
$671$	−1.35089e10	−1.72620
$672$	2.31381e9	0.294127
$673$	2.61763e9	0.331020	0.165510	−	0.986208i	$-0.447073\pi$
$673$	2.61763e9	0.331020	0.165510	+	0.986208i	$0.447073\pi$
$674$	−1.11423e9	−0.140173
$675$	−1.67210e10	−2.09266
$676$	−1.56789e8	−0.0195210
$677$	−1.46420e10	−1.81359	−0.906797	−	0.421567i	$-0.861480\pi$
$677$	−1.46420e10	−1.81359	−0.906797	+	0.421567i	$0.861480\pi$
$678$	−5.76622e8	−0.0710538
$679$	−3.06531e9	−0.375778
$680$	1.56574e10	1.90958
$681$	8.42712e8	0.102250
$682$	2.62679e9	0.317088
$683$	−3.74565e9	−0.449836	−0.224918	−	0.974378i	$-0.572211\pi$
$683$	−3.74565e9	−0.449836	−0.224918	+	0.974378i	$0.572211\pi$
$684$	4.65628e9	0.556344
$685$	−1.63206e10	−1.94007
$686$	−3.94387e8	−0.0466432
$687$	−2.46856e10	−2.90466
$688$	3.30243e9	0.386611
$689$	1.66076e9	0.193437
$690$	1.71026e10	1.98194
$691$	−7.38265e8	−0.0851215	−0.0425607	−	0.999094i	$-0.513552\pi$
$691$	−7.38265e8	−0.0851215	−0.0425607	+	0.999094i	$0.513552\pi$
$692$	−3.11973e9	−0.357887
$693$	−5.99339e9	−0.684079
$694$	1.27742e10	1.45070
$695$	1.44551e10	1.63333
$696$	1.54813e10	1.74051
$697$	−1.01284e10	−1.13299
$698$	−8.24231e9	−0.917392
$699$	2.40004e8	0.0265796
$700$	−2.40555e9	−0.265076
$701$	6.66935e9	0.731257	0.365629	−	0.930761i	$-0.380854\pi$
$701$	6.66935e9	0.731257	0.365629	+	0.930761i	$0.380854\pi$
$702$	1.66291e9	0.181421
$703$	−1.45767e10	−1.58240
$704$	−1.25447e10	−1.35505
$705$	3.97773e10	4.27537
$706$	−3.47022e9	−0.371143
$707$	5.04492e9	0.536891
$708$	5.38724e9	0.570493
$709$	−1.46387e10	−1.54255	−0.771277	−	0.636499i	$-0.780382\pi$
$709$	−1.46387e10	−1.54255	−0.771277	+	0.636499i	$0.780382\pi$
$710$	−3.34179e9	−0.350409
$711$	2.43968e10	2.54559
$712$	7.43180e7	0.00771639
$713$	2.18248e9	0.225495
$714$	4.54575e9	0.467372
$715$	−6.42792e9	−0.657657
$716$	1.95159e9	0.198698
$717$	−5.91210e8	−0.0598997
$718$	−4.20522e9	−0.423988
$719$	3.66906e9	0.368132	0.184066	−	0.982914i	$-0.441074\pi$
$719$	3.66906e9	0.368132	0.184066	+	0.982914i	$0.441074\pi$
$720$	−1.96166e10	−1.95867
$721$	−9.91687e8	−0.0985374
$722$	−1.04126e10	−1.02963
$723$	1.60703e10	1.58140
$724$	4.06235e9	0.397825
$725$	−2.89325e10	−2.81970
$726$	6.92946e9	0.672080
$727$	−3.33935e9	−0.322323	−0.161162	−	0.986928i	$-0.551524\pi$
$727$	−3.33935e9	−0.322323	−0.161162	+	0.986928i	$0.551524\pi$
$728$	1.18193e9	0.113536
$729$	−1.69382e10	−1.61927
$730$	5.07861e9	0.483186
$731$	−5.44246e9	−0.515328
$732$	5.99031e9	0.564496
$733$	−4.00922e9	−0.376007	−0.188004	−	0.982168i	$-0.560202\pi$
$733$	−4.00922e9	−0.376007	−0.188004	+	0.982168i	$0.560202\pi$
$734$	−4.87272e9	−0.454815
$735$	−4.69896e9	−0.436512
$736$	−4.01260e9	−0.370982
$737$	−1.14833e10	−1.05665
$738$	1.74126e10	1.59465
$739$	−1.25526e9	−0.114414	−0.0572069	−	0.998362i	$-0.518219\pi$
$739$	−1.25526e9	−0.114414	−0.0572069	+	0.998362i	$0.518219\pi$
$740$	−5.80045e9	−0.526200
$741$	7.16303e9	0.646745
$742$	−2.53403e9	−0.227718
$743$	1.10974e9	0.0992564	0.0496282	−	0.998768i	$-0.484196\pi$
$743$	1.10974e9	0.0992564	0.0496282	+	0.998768i	$0.484196\pi$
$744$	−5.75475e9	−0.512297
$745$	2.73592e10	2.42413
$746$	−1.25309e10	−1.10509
$747$	−2.69796e9	−0.236817
$748$	3.22667e9	0.281902
$749$	3.42769e9	0.298068
$750$	5.37827e10	4.65509
$751$	−3.26140e9	−0.280973	−0.140486	−	0.990083i	$-0.544867\pi$
$751$	−3.26140e9	−0.280973	−0.140486	+	0.990083i	$0.544867\pi$
$752$	1.11254e10	0.954011
$753$	−3.62052e10	−3.09022
$754$	2.87735e9	0.244452
$755$	3.89802e9	0.329633
$756$	8.62874e8	0.0726308
$757$	−2.00403e10	−1.67907	−0.839536	−	0.543305i	$-0.817173\pi$
$757$	−2.00403e10	−1.67907	−0.839536	+	0.543305i	$0.817173\pi$
$758$	1.13601e10	0.947412
$759$	1.74129e10	1.44552
$760$	−3.76457e10	−3.11077
$761$	1.33041e10	1.09431	0.547153	−	0.837033i	$-0.315712\pi$
$761$	1.33041e10	1.09431	0.547153	+	0.837033i	$0.315712\pi$
$762$	2.04834e10	1.67710
$763$	−1.49637e9	−0.121956
$764$	−4.06205e8	−0.0329548
$765$	3.23285e10	2.61078
$766$	−4.98704e9	−0.400905
$767$	4.94680e9	0.395859
$768$	1.40016e10	1.11536
$769$	1.77213e10	1.40525	0.702625	−	0.711560i	$-0.252011\pi$
$769$	1.77213e10	1.40525	0.702625	+	0.711560i	$0.252011\pi$
$770$	9.80788e9	0.774208
$771$	2.88055e8	0.0226353
$772$	−9.46808e8	−0.0740630
$773$	−5.65358e9	−0.440246	−0.220123	−	0.975472i	$-0.570646\pi$
$773$	−5.65358e9	−0.440246	−0.220123	+	0.975472i	$0.570646\pi$
$774$	9.35654e9	0.725307
$775$	1.07549e10	0.829944
$776$	−1.40168e10	−1.07680
$777$	−8.31995e9	−0.636279
$778$	1.20256e10	0.915540
$779$	2.43521e10	1.84568
$780$	2.85036e9	0.215064
$781$	−3.40241e9	−0.255569
$782$	−7.88323e9	−0.589496
$783$	1.03781e10	0.772598
$784$	−1.31426e9	−0.0974037
$785$	1.20502e10	0.889101
$786$	2.15483e10	1.58283
$787$	−1.38346e10	−1.01170	−0.505852	−	0.862620i	$-0.668822\pi$
$787$	−1.38346e10	−1.01170	−0.505852	+	0.862620i	$0.668822\pi$
$788$	−4.25648e9	−0.309891
$789$	−1.80230e10	−1.30634
$790$	−3.99241e10	−2.88098
$791$	−2.74744e8	−0.0197383
$792$	−2.74061e10	−1.96024
$793$	5.50056e9	0.391697
$794$	−5.78074e9	−0.409837
$795$	−3.01919e10	−2.13111
$796$	−3.63957e9	−0.255773
$797$	1.94695e10	1.36223	0.681116	−	0.732175i	$-0.261495\pi$
$797$	1.94695e10	1.36223	0.681116	+	0.732175i	$0.261495\pi$
$798$	−1.09295e10	−0.761362
$799$	−1.83348e10	−1.27164
$800$	−1.97734e10	−1.36542
$801$	1.53447e8	0.0105498
$802$	2.32390e9	0.159077
$803$	5.17073e9	0.352409
$804$	5.09208e9	0.345540
$805$	8.14892e9	0.550572
$806$	−1.06957e9	−0.0719512
$807$	2.90551e10	1.94610
$808$	2.30690e10	1.53847
$809$	1.59345e10	1.05808	0.529038	−	0.848598i	$-0.322553\pi$
$809$	1.59345e10	1.05808	0.529038	+	0.848598i	$0.322553\pi$
$810$	7.30267e9	0.482819
$811$	−1.34016e10	−0.882235	−0.441118	−	0.897449i	$-0.645418\pi$
$811$	−1.34016e10	−0.882235	−0.441118	+	0.897449i	$0.645418\pi$
$812$	1.49304e9	0.0978647
$813$	1.42235e10	0.928301
$814$	1.73658e10	1.12852
$815$	−1.58105e10	−1.02304
$816$	1.51483e10	0.975999
$817$	1.30855e10	0.839485
$818$	5.77797e9	0.369095
$819$	2.44039e9	0.155226
$820$	9.69036e9	0.613750
$821$	2.58548e9	0.163057	0.0815285	−	0.996671i	$-0.474020\pi$
$821$	2.58548e9	0.163057	0.0815285	+	0.996671i	$0.474020\pi$
$822$	−2.16669e10	−1.36065
$823$	−2.67909e9	−0.167528	−0.0837640	−	0.996486i	$-0.526694\pi$
$823$	−2.67909e9	−0.167528	−0.0837640	+	0.996486i	$0.526694\pi$
$824$	−4.53471e9	−0.282361
$825$	8.58075e10	5.32030
$826$	−7.54794e9	−0.466013
$827$	−2.04833e10	−1.25931	−0.629653	−	0.776876i	$-0.716803\pi$
$827$	−2.04833e10	−1.25931	−0.629653	+	0.776876i	$0.716803\pi$
$828$	−4.60892e9	−0.282159
$829$	−1.79506e10	−1.09430	−0.547151	−	0.837034i	$-0.684288\pi$
$829$	−1.79506e10	−1.09430	−0.547151	+	0.837034i	$0.684288\pi$
$830$	4.41507e9	0.268018
$831$	1.69304e10	1.02344
$832$	5.10794e9	0.307478
$833$	2.16592e9	0.129833
$834$	1.91903e10	1.14551
$835$	3.42983e10	2.03878
$836$	−7.75799e9	−0.459227
$837$	−3.85778e9	−0.227404
$838$	−1.68208e10	−0.987399
$839$	−3.36661e10	−1.96800	−0.984001	−	0.178164i	$-0.942984\pi$
$839$	−3.36661e10	−1.96800	−0.984001	+	0.178164i	$0.942984\pi$
$840$	−2.14871e10	−1.25083
$841$	7.07571e8	0.0410189
$842$	2.68614e10	1.55073
$843$	1.38741e10	0.797645
$844$	5.23648e9	0.299807
$845$	2.61732e9	0.149231
$846$	3.15208e10	1.78978
$847$	3.30169e9	0.186700
$848$	−8.44444e9	−0.475538
$849$	−3.90580e10	−2.19045
$850$	−3.88471e10	−2.16967
$851$	1.44284e10	0.802538
$852$	1.50874e9	0.0835751
$853$	6.85632e9	0.378242	0.189121	−	0.981954i	$-0.439436\pi$
$853$	6.85632e9	0.378242	0.189121	+	0.981954i	$0.439436\pi$
$854$	−8.39289e9	−0.461115
$855$	−7.77285e10	−4.25303
$856$	1.56739e10	0.854119
$857$	1.42472e10	0.773211	0.386605	−	0.922245i	$-0.373648\pi$
$857$	1.42472e10	0.773211	0.386605	+	0.922245i	$0.373648\pi$
$858$	−8.53359e9	−0.461239
$859$	−3.50138e10	−1.88479	−0.942394	−	0.334504i	$-0.891431\pi$
$859$	−3.50138e10	−1.88479	−0.942394	+	0.334504i	$0.891431\pi$
$860$	5.20706e9	0.279157
$861$	1.38995e10	0.742144
$862$	1.92601e9	0.102419
$863$	−7.75733e9	−0.410842	−0.205421	−	0.978674i	$-0.565856\pi$
$863$	−7.75733e9	−0.410842	−0.205421	+	0.978674i	$0.565856\pi$
$864$	7.09273e9	0.374124
$865$	5.20784e10	2.73591
$866$	1.25749e10	0.657948
$867$	5.25986e9	0.274099
$868$	−5.54996e8	−0.0288052
$869$	−4.06483e10	−2.10123
$870$	−5.23090e10	−2.69314
$871$	4.67576e9	0.239767
$872$	−6.84248e9	−0.349467
$873$	−2.89411e10	−1.47220
$874$	1.89539e10	0.960305
$875$	2.56259e10	1.29316
$876$	−2.29287e9	−0.115243
$877$	1.70030e10	0.851190	0.425595	−	0.904914i	$-0.360065\pi$
$877$	1.70030e10	0.851190	0.425595	+	0.904914i	$0.360065\pi$
$878$	−1.58827e10	−0.791940
$879$	−1.91919e9	−0.0953139
$880$	3.26839e10	1.61676
$881$	1.61992e10	0.798139	0.399069	−	0.916921i	$-0.369333\pi$
$881$	1.61992e10	0.798139	0.399069	+	0.916921i	$0.369333\pi$
$882$	−3.72360e9	−0.182736
$883$	2.66957e10	1.30491	0.652453	−	0.757829i	$-0.273740\pi$
$883$	2.66957e10	1.30491	0.652453	+	0.757829i	$0.273740\pi$
$884$	−1.31383e9	−0.0639672
$885$	−8.99306e10	−4.36120
$886$	−5.40286e9	−0.260979
$887$	−3.56567e10	−1.71557	−0.857784	−	0.514010i	$-0.828159\pi$
$887$	−3.56567e10	−1.71557	−0.857784	+	0.514010i	$0.828159\pi$
$888$	−3.80449e10	−1.82327
$889$	9.75974e9	0.465888
$890$	−2.51109e8	−0.0119398
$891$	7.43514e9	0.352141
$892$	1.51731e9	0.0715808
$893$	4.40830e10	2.07153
$894$	3.63215e10	1.70013
$895$	−3.25783e10	−1.51897
$896$	−3.77295e9	−0.175228
$897$	−7.09017e9	−0.328007
$898$	−1.04297e9	−0.0480624
$899$	−6.67518e9	−0.306411
$900$	−2.27119e10	−1.03850
$901$	1.39166e10	0.633862
$902$	−2.90116e10	−1.31628
$903$	7.46882e9	0.337555
$904$	−1.25633e9	−0.0565605
$905$	−6.78138e10	−3.04122
$906$	5.17494e9	0.231184
$907$	2.50702e10	1.11566	0.557830	−	0.829955i	$-0.311634\pi$
$907$	2.50702e10	1.11566	0.557830	+	0.829955i	$0.311634\pi$
$908$	3.71636e8	0.0164747
$909$	4.76315e10	2.10339
$910$	−3.99357e9	−0.175677
$911$	−3.00614e10	−1.31733	−0.658665	−	0.752436i	$-0.728879\pi$
$911$	−3.00614e10	−1.31733	−0.658665	+	0.752436i	$0.728879\pi$
$912$	−3.64217e10	−1.58993
$913$	4.49515e9	0.195478
$914$	−1.60883e10	−0.696946
$915$	−9.99978e10	−4.31535
$916$	−1.08863e10	−0.468002
$917$	1.02672e10	0.439701
$918$	1.39345e10	0.594488
$919$	−4.52726e10	−1.92412	−0.962059	−	0.272843i	$-0.912036\pi$
$919$	−4.52726e10	−1.92412	−0.962059	+	0.272843i	$0.912036\pi$
$920$	3.72628e10	1.57768
$921$	1.62120e10	0.683800
$922$	−1.68388e10	−0.707544
$923$	1.38539e9	0.0579918
$924$	−4.42803e9	−0.184654
$925$	7.11007e10	2.95378
$926$	6.24053e9	0.258275
$927$	−9.36300e9	−0.386043
$928$	1.22727e10	0.504104
$929$	−1.41933e10	−0.580804	−0.290402	−	0.956905i	$-0.593789\pi$
$929$	−1.41933e10	−0.580804	−0.290402	+	0.956905i	$0.593789\pi$
$930$	1.94444e10	0.792691
$931$	−5.20760e9	−0.211502
$932$	1.05842e8	0.00428253
$933$	4.45636e10	1.79637
$934$	9.46192e7	0.00379984
$935$	−5.38635e10	−2.15503
$936$	1.11592e10	0.444804
$937$	−1.85102e10	−0.735060	−0.367530	−	0.930012i	$-0.619796\pi$
$937$	−1.85102e10	−0.735060	−0.367530	+	0.930012i	$0.619796\pi$
$938$	−7.13439e9	−0.282258
$939$	−2.57602e10	−1.01536
$940$	1.75418e10	0.688853
$941$	1.83728e10	0.718807	0.359404	−	0.933182i	$-0.382980\pi$
$941$	1.83728e10	0.718807	0.359404	+	0.933182i	$0.382980\pi$
$942$	1.59976e10	0.623559
$943$	−2.41045e10	−0.936066
$944$	−2.51529e10	−0.973163
$945$	−1.44042e10	−0.555235
$946$	−1.55892e10	−0.598696
$947$	−4.54440e10	−1.73881	−0.869404	−	0.494102i	$-0.835497\pi$
$947$	−4.54440e10	−1.73881	−0.869404	+	0.494102i	$0.835497\pi$
$948$	1.80248e10	0.687134
$949$	−2.10542e9	−0.0799661
$950$	9.34015e10	3.53445
$951$	−2.65138e10	−0.999632
$952$	9.90416e9	0.372039
$953$	−2.88434e9	−0.107950	−0.0539748	−	0.998542i	$-0.517189\pi$
$953$	−2.88434e9	−0.107950	−0.0539748	+	0.998542i	$0.517189\pi$
$954$	−2.39250e10	−0.892140
$955$	6.78088e9	0.251927
$956$	−2.60723e8	−0.00965112
$957$	−5.32578e10	−1.96423
$958$	−6.94908e8	−0.0255357
$959$	−1.03236e10	−0.377979
$960$	−9.28601e10	−3.38751
$961$	−2.50313e10	−0.909812
$962$	−7.07099e9	−0.256075
$963$	3.23625e10	1.16775
$964$	7.08702e9	0.254797
$965$	1.58053e10	0.566183
$966$	1.08183e10	0.386137
$967$	4.83268e10	1.71868	0.859341	−	0.511404i	$-0.170874\pi$
$967$	4.83268e10	1.71868	0.859341	+	0.511404i	$0.170874\pi$
$968$	1.50977e10	0.534992
$969$	6.00234e10	2.11928
$970$	4.73607e10	1.66616
$971$	3.06038e9	0.107277	0.0536386	−	0.998560i	$-0.482918\pi$
$971$	3.06038e9	0.107277	0.0536386	+	0.998560i	$0.482918\pi$
$972$	−8.79875e9	−0.307319
$973$	9.14362e9	0.318217
$974$	3.35179e10	1.16231
$975$	−3.49391e10	−1.20724
$976$	−2.79686e10	−0.962933
$977$	−5.49630e9	−0.188556	−0.0942778	−	0.995546i	$-0.530054\pi$
$977$	−5.49630e9	−0.188556	−0.0942778	+	0.995546i	$0.530054\pi$
$978$	−2.09897e10	−0.717496
$979$	−2.55664e8	−0.00870822
$980$	−2.07224e9	−0.0703313
$981$	−1.41279e10	−0.477790
$982$	−4.53426e8	−0.0152797
$983$	−9.94767e9	−0.334029	−0.167014	−	0.985954i	$-0.553413\pi$
$983$	−9.94767e9	−0.334029	−0.167014	+	0.985954i	$0.553413\pi$
$984$	6.35586e10	2.12663
$985$	7.10545e10	2.36900
$986$	2.41111e10	0.801028
$987$	2.51613e10	0.832958
$988$	3.15889e9	0.104204
$989$	−1.29524e10	−0.425758
$990$	9.26009e10	3.03314
$991$	4.97432e10	1.62359	0.811794	−	0.583943i	$-0.198491\pi$
$991$	4.97432e10	1.62359	0.811794	+	0.583943i	$0.198491\pi$
$992$	−4.56201e9	−0.148377
$993$	−3.24864e10	−1.05288
$994$	−2.11386e9	−0.0682692
$995$	6.07562e10	1.95528
$996$	−1.99330e9	−0.0639242
$997$	6.73788e9	0.215323	0.107661	−	0.994188i	$-0.465664\pi$
$997$	6.73788e9	0.215323	0.107661	+	0.994188i	$0.465664\pi$
$998$	−1.78296e10	−0.567785
$999$	−2.55039e10	−0.809334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-9.77328 q^{2} -73.6575 q^{3} -32.4830 q^{4} +542.246 q^{5} +719.876 q^{6} +343.000 q^{7} +1568.45 q^{8} +3238.43 q^{9} +O(q^{10})\)	\(q-9.77328 q^{2} -73.6575 q^{3} -32.4830 q^{4} +542.246 q^{5} +719.876 q^{6} +343.000 q^{7} +1568.45 q^{8} +3238.43 q^{9} -5299.52 q^{10} -5395.65 q^{11} +2392.61 q^{12} +2197.00 q^{13} -3352.24 q^{14} -39940.5 q^{15} -11171.0 q^{16} +18410.0 q^{17} -31650.1 q^{18} -44263.9 q^{19} -17613.8 q^{20} -25264.5 q^{21} +52733.2 q^{22} +43813.6 q^{23} -115528. q^{24} +215906. q^{25} -21471.9 q^{26} -77445.7 q^{27} -11141.7 q^{28} -134005. q^{29} +390350. q^{30} +49812.7 q^{31} -91583.3 q^{32} +397430. q^{33} -179926. q^{34} +185990. q^{35} -105194. q^{36} +329314. q^{37} +432603. q^{38} -161826. q^{39} +850483. q^{40} -550159. q^{41} +246917. q^{42} -295625. q^{43} +175267. q^{44} +1.75603e6 q^{45} -428203. q^{46} -995915. q^{47} +822831. q^{48} +117649. q^{49} -2.11011e6 q^{50} -1.35604e6 q^{51} -71365.1 q^{52} +755923. q^{53} +756899. q^{54} -2.92577e6 q^{55} +537977. q^{56} +3.26037e6 q^{57} +1.30967e6 q^{58} +2.25161e6 q^{59} +1.29739e6 q^{60} +2.50367e6 q^{61} -486834. q^{62} +1.11078e6 q^{63} +2.32496e6 q^{64} +1.19131e6 q^{65} -3.88420e6 q^{66} +2.12825e6 q^{67} -598012. q^{68} -3.22720e6 q^{69} -1.81774e6 q^{70} +630584. q^{71} +5.07930e6 q^{72} -958314. q^{73} -3.21847e6 q^{74} -1.59031e7 q^{75} +1.43782e6 q^{76} -1.85071e6 q^{77} +1.58157e6 q^{78} +7.53352e6 q^{79} -6.05745e6 q^{80} -1.37799e6 q^{81} +5.37686e6 q^{82} -833106. q^{83} +820667. q^{84} +9.98276e6 q^{85} +2.88922e6 q^{86} +9.87051e6 q^{87} -8.46279e6 q^{88} +47383.3 q^{89} -1.71621e7 q^{90} +753571. q^{91} -1.42320e6 q^{92} -3.66908e6 q^{93} +9.73336e6 q^{94} -2.40019e7 q^{95} +6.74580e6 q^{96} -8.93678e6 q^{97} -1.14982e6 q^{98} -1.74734e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 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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