LMFDB - Embedded newform 91.8.a.c.1.10

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 957 x^{8} + 1224 x^{7} + 310102 x^{6} - 241884 x^{5} - 40367312 x^{4} + \cdots - 4516262912 $ x^10 - 2x^9 - 957x^8 + 1224x^7 + 310102x^6 - 241884x^5 - 40367312x^4 + 11067840x^3 + 1840757376x^2 + 541859072*x - 4516262912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$21.7215$ 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)

$f(q)$	$=$	$q+19.7215 q^{2} -37.6933 q^{3} +260.937 q^{4} -267.290 q^{5} -743.369 q^{6} +343.000 q^{7} +2621.72 q^{8} -766.212 q^{9} +O(q^{10})$	\(q+19.7215 q^{2} -37.6933 q^{3} +260.937 q^{4} -267.290 q^{5} -743.369 q^{6} +343.000 q^{7} +2621.72 q^{8} -766.212 q^{9} -5271.36 q^{10} +827.140 q^{11} -9835.59 q^{12} -2197.00 q^{13} +6764.47 q^{14} +10075.1 q^{15} +18304.2 q^{16} -33502.5 q^{17} -15110.8 q^{18} -46735.7 q^{19} -69745.9 q^{20} -12928.8 q^{21} +16312.4 q^{22} -13109.5 q^{23} -98821.3 q^{24} -6680.98 q^{25} -43328.1 q^{26} +111316. q^{27} +89501.4 q^{28} +102867. q^{29} +198695. q^{30} -113909. q^{31} +25406.7 q^{32} -31177.7 q^{33} -660719. q^{34} -91680.5 q^{35} -199933. q^{36} -18161.8 q^{37} -921698. q^{38} +82812.3 q^{39} -700759. q^{40} +753837. q^{41} -254976. q^{42} -512289. q^{43} +215832. q^{44} +204801. q^{45} -258539. q^{46} -215875. q^{47} -689947. q^{48} +117649. q^{49} -131759. q^{50} +1.26282e6 q^{51} -573279. q^{52} +1.40885e6 q^{53} +2.19533e6 q^{54} -221086. q^{55} +899249. q^{56} +1.76163e6 q^{57} +2.02869e6 q^{58} +401039. q^{59} +2.62896e6 q^{60} -1.48021e6 q^{61} -2.24645e6 q^{62} -262811. q^{63} -1.84188e6 q^{64} +587236. q^{65} -614870. q^{66} +4.12271e6 q^{67} -8.74204e6 q^{68} +494141. q^{69} -1.80808e6 q^{70} -2.09432e6 q^{71} -2.00879e6 q^{72} +2.16439e6 q^{73} -358178. q^{74} +251828. q^{75} -1.21951e7 q^{76} +283709. q^{77} +1.63318e6 q^{78} -679457. q^{79} -4.89254e6 q^{80} -2.52018e6 q^{81} +1.48668e7 q^{82} -9.02864e6 q^{83} -3.37361e6 q^{84} +8.95488e6 q^{85} -1.01031e7 q^{86} -3.87740e6 q^{87} +2.16853e6 q^{88} +2.31755e6 q^{89} +4.03898e6 q^{90} -753571. q^{91} -3.42076e6 q^{92} +4.29361e6 q^{93} -4.25738e6 q^{94} +1.24920e7 q^{95} -957663. q^{96} -4.51624e6 q^{97} +2.32021e6 q^{98} -633765. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) $ 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * 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 $

$2$	19.7215	1.74315	0.871575	−	0.490262i	$-0.163099\pi$
$2$	19.7215	1.74315	0.871575	+	0.490262i	$0.163099\pi$
$3$	−37.6933	−0.806010	−0.403005	−	0.915198i	$-0.632034\pi$
$3$	−37.6933	−0.806010	−0.403005	+	0.915198i	$0.632034\pi$
$4$	260.937	2.03857
$5$	−267.290	−0.956286	−0.478143	−	0.878282i	$-0.658690\pi$
$5$	−267.290	−0.956286	−0.478143	+	0.878282i	$0.658690\pi$
$6$	−743.369	−1.40500
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	2621.72	1.81039
$9$	−766.212	−0.350348
$10$	−5271.36	−1.66695
$11$	827.140	0.187372	0.0936860	−	0.995602i	$-0.470135\pi$
$11$	827.140	0.187372	0.0936860	+	0.995602i	$0.470135\pi$
$12$	−9835.59	−1.64311
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	6764.47	0.658849
$15$	10075.1	0.770776
$16$	18304.2	1.11720
$17$	−33502.5	−1.65389	−0.826943	−	0.562285i	$-0.809922\pi$
$17$	−33502.5	−1.65389	−0.826943	+	0.562285i	$0.809922\pi$
$18$	−15110.8	−0.610709
$19$	−46735.7	−1.56319	−0.781594	−	0.623787i	$-0.785593\pi$
$19$	−46735.7	−1.56319	−0.781594	+	0.623787i	$0.785593\pi$
$20$	−69745.9	−1.94946
$21$	−12928.8	−0.304643
$22$	16312.4	0.326618
$23$	−13109.5	−0.224667	−0.112333	−	0.993671i	$-0.535832\pi$
$23$	−13109.5	−0.224667	−0.112333	+	0.993671i	$0.535832\pi$
$24$	−98821.3	−1.45919
$25$	−6680.98	−0.0855165
$26$	−43328.1	−0.483463
$27$	111316.	1.08839
$28$	89501.4	0.770507
$29$	102867.	0.783219	0.391610	−	0.920131i	$-0.371918\pi$
$29$	102867.	0.783219	0.391610	+	0.920131i	$0.371918\pi$
$30$	198695.	1.34358
$31$	−113909.	−0.686739	−0.343370	−	0.939200i	$-0.611568\pi$
$31$	−113909.	−0.686739	−0.343370	+	0.939200i	$0.611568\pi$
$32$	25406.7	0.137064
$33$	−31177.7	−0.151024
$34$	−660719.	−2.88297
$35$	−91680.5	−0.361442
$36$	−199933.	−0.714210
$37$	−18161.8	−0.0589459	−0.0294729	−	0.999566i	$-0.509383\pi$
$37$	−18161.8	−0.0589459	−0.0294729	+	0.999566i	$0.509383\pi$
$38$	−921698.	−2.72487
$39$	82812.3	0.223547
$40$	−700759.	−1.73125
$41$	753837.	1.70818	0.854091	−	0.520124i	$-0.174114\pi$
$41$	753837.	1.70818	0.854091	+	0.520124i	$0.174114\pi$
$42$	−254976.	−0.531038
$43$	−512289.	−0.982598	−0.491299	−	0.870991i	$-0.663478\pi$
$43$	−512289.	−0.982598	−0.491299	+	0.870991i	$0.663478\pi$
$44$	215832.	0.381971
$45$	204801.	0.335033
$46$	−258539.	−0.391628
$47$	−215875.	−0.303291	−0.151646	−	0.988435i	$-0.548457\pi$
$47$	−215875.	−0.303291	−0.151646	+	0.988435i	$0.548457\pi$
$48$	−689947.	−0.900475
$49$	117649.	0.142857
$50$	−131759.	−0.149068
$51$	1.26282e6	1.33305
$52$	−573279.	−0.565398
$53$	1.40885e6	1.29987	0.649936	−	0.759989i	$-0.274796\pi$
$53$	1.40885e6	1.29987	0.649936	+	0.759989i	$0.274796\pi$
$54$	2.19533e6	1.89723
$55$	−221086.	−0.179181
$56$	899249.	0.684261
$57$	1.76163e6	1.25995
$58$	2.02869e6	1.36527
$59$	401039.	0.254217	0.127108	−	0.991889i	$-0.459430\pi$
$59$	401039.	0.254217	0.127108	+	0.991889i	$0.459430\pi$
$60$	2.62896e6	1.57128
$61$	−1.48021e6	−0.834968	−0.417484	−	0.908684i	$-0.637088\pi$
$61$	−1.48021e6	−0.834968	−0.417484	+	0.908684i	$0.637088\pi$
$62$	−2.24645e6	−1.19709
$63$	−262811.	−0.132419
$64$	−1.84188e6	−0.878278
$65$	587236.	0.265226
$66$	−614870.	−0.263257
$67$	4.12271e6	1.67464	0.837319	−	0.546714i	$-0.184122\pi$
$67$	4.12271e6	1.67464	0.837319	+	0.546714i	$0.184122\pi$
$68$	−8.74204e6	−3.37157
$69$	494141.	0.181084
$70$	−1.80808e6	−0.630048
$71$	−2.09432e6	−0.694446	−0.347223	−	0.937783i	$-0.612875\pi$
$71$	−2.09432e6	−0.694446	−0.347223	+	0.937783i	$0.612875\pi$
$72$	−2.00879e6	−0.634265
$73$	2.16439e6	0.651187	0.325594	−	0.945510i	$-0.394436\pi$
$73$	2.16439e6	0.651187	0.325594	+	0.945510i	$0.394436\pi$
$74$	−358178.	−0.102752
$75$	251828.	0.0689271
$76$	−1.21951e7	−3.18667
$77$	283709.	0.0708200
$78$	1.63318e6	0.389676
$79$	−679457.	−0.155048	−0.0775242	−	0.996990i	$-0.524701\pi$
$79$	−679457.	−0.155048	−0.0775242	+	0.996990i	$0.524701\pi$
$80$	−4.89254e6	−1.06836
$81$	−2.52018e6	−0.526908
$82$	1.48668e7	2.97762
$83$	−9.02864e6	−1.73320	−0.866600	−	0.499003i	$-0.833700\pi$
$83$	−9.02864e6	−1.73320	−0.866600	+	0.499003i	$0.833700\pi$
$84$	−3.37361e6	−0.621037
$85$	8.95488e6	1.58159
$86$	−1.01031e7	−1.71282
$87$	−3.87740e6	−0.631282
$88$	2.16853e6	0.339216
$89$	2.31755e6	0.348469	0.174234	−	0.984704i	$-0.444255\pi$
$89$	2.31755e6	0.348469	0.174234	+	0.984704i	$0.444255\pi$
$90$	4.03898e6	0.584013
$91$	−753571.	−0.104828
$92$	−3.42076e6	−0.457999
$93$	4.29361e6	0.553519
$94$	−4.25738e6	−0.528682
$95$	1.24920e7	1.49486
$96$	−957663.	−0.110475
$97$	−4.51624e6	−0.502430	−0.251215	−	0.967931i	$-0.580830\pi$
$97$	−4.51624e6	−0.502430	−0.251215	+	0.967931i	$0.580830\pi$
$98$	2.32021e6	0.249021
$99$	−633765.	−0.0656455
$100$	−1.74331e6	−0.174331
$101$	−1.49062e7	−1.43960	−0.719800	−	0.694182i	$-0.755766\pi$
$101$	−1.49062e7	−1.43960	−0.719800	+	0.694182i	$0.755766\pi$
$102$	2.49047e7	2.32370
$103$	1.57816e7	1.42305	0.711527	−	0.702659i	$-0.248004\pi$
$103$	1.57816e7	1.42305	0.711527	+	0.702659i	$0.248004\pi$
$104$	−5.75991e6	−0.502110
$105$	3.45575e6	0.291326
$106$	2.77847e7	2.26587
$107$	−3.53700e6	−0.279121	−0.139560	−	0.990214i	$-0.544569\pi$
$107$	−3.53700e6	−0.279121	−0.139560	+	0.990214i	$0.544569\pi$
$108$	2.90466e7	2.21877
$109$	1.41938e7	1.04980	0.524900	−	0.851164i	$-0.324103\pi$
$109$	1.41938e7	1.04980	0.524900	+	0.851164i	$0.324103\pi$
$110$	−4.36015e6	−0.312340
$111$	684580.	0.0475110
$112$	6.27835e6	0.422262
$113$	1.01889e6	0.0664284	0.0332142	−	0.999448i	$-0.489426\pi$
$113$	1.01889e6	0.0664284	0.0332142	+	0.999448i	$0.489426\pi$
$114$	3.47419e7	2.19627
$115$	3.50404e6	0.214846
$116$	2.68418e7	1.59665
$117$	1.68337e6	0.0971691
$118$	7.90908e6	0.443138
$119$	−1.14914e7	−0.625110
$120$	2.64140e7	1.39540
$121$	−1.88030e7	−0.964892
$122$	−2.91920e7	−1.45547
$123$	−2.84146e7	−1.37681
$124$	−2.97231e7	−1.39997
$125$	2.26678e7	1.03806
$126$	−5.18302e6	−0.230826
$127$	1.77642e7	0.769541	0.384771	−	0.923012i	$-0.374281\pi$
$127$	1.77642e7	0.769541	0.384771	+	0.923012i	$0.374281\pi$
$128$	−3.95767e7	−1.66803
$129$	1.93099e7	0.791983
$130$	1.15812e7	0.462329
$131$	−4.16959e6	−0.162048	−0.0810240	−	0.996712i	$-0.525819\pi$
$131$	−4.16959e6	−0.162048	−0.0810240	+	0.996712i	$0.525819\pi$
$132$	−8.13542e6	−0.307873
$133$	−1.60304e7	−0.590830
$134$	8.13060e7	2.91915
$135$	−2.97538e7	−1.04082
$136$	−8.78340e7	−2.99417
$137$	−5.08735e7	−1.69032	−0.845162	−	0.534511i	$-0.820496\pi$
$137$	−5.08735e7	−1.69032	−0.845162	+	0.534511i	$0.820496\pi$
$138$	9.74520e6	0.315656
$139$	3.26158e7	1.03009	0.515046	−	0.857163i	$-0.327775\pi$
$139$	3.26158e7	1.03009	0.515046	+	0.857163i	$0.327775\pi$
$140$	−2.39228e7	−0.736826
$141$	8.13705e6	0.244456
$142$	−4.13031e7	−1.21052
$143$	−1.81723e6	−0.0519677
$144$	−1.40249e7	−0.391409
$145$	−2.74954e7	−0.748982
$146$	4.26850e7	1.13512
$147$	−4.43458e6	−0.115144
$148$	−4.73910e6	−0.120165
$149$	1.14836e7	0.284397	0.142198	−	0.989838i	$-0.454583\pi$
$149$	1.14836e7	0.284397	0.142198	+	0.989838i	$0.454583\pi$
$150$	4.96643e6	0.120150
$151$	2.94489e7	0.696065	0.348033	−	0.937482i	$-0.386850\pi$
$151$	2.94489e7	0.696065	0.348033	+	0.937482i	$0.386850\pi$
$152$	−1.22528e8	−2.82997
$153$	2.56700e7	0.579436
$154$	5.59517e6	0.123450
$155$	3.04467e7	0.656719
$156$	2.16088e7	0.455716
$157$	1.32647e7	0.273556	0.136778	−	0.990602i	$-0.456325\pi$
$157$	1.32647e7	0.273556	0.136778	+	0.990602i	$0.456325\pi$
$158$	−1.33999e7	−0.270272
$159$	−5.31045e7	−1.04771
$160$	−6.79096e6	−0.131072
$161$	−4.49656e6	−0.0849160
$162$	−4.97018e7	−0.918479
$163$	−6.97755e7	−1.26196	−0.630982	−	0.775798i	$-0.717348\pi$
$163$	−6.97755e7	−1.26196	−0.630982	+	0.775798i	$0.717348\pi$
$164$	1.96704e8	3.48225
$165$	8.33349e6	0.144422
$166$	−1.78058e8	−3.02123
$167$	−5.27839e7	−0.876988	−0.438494	−	0.898734i	$-0.644488\pi$
$167$	−5.27839e7	−0.876988	−0.438494	+	0.898734i	$0.644488\pi$
$168$	−3.38957e7	−0.551521
$169$	4.82681e6	0.0769231
$170$	1.76604e8	2.75695
$171$	3.58095e7	0.547660
$172$	−1.33675e8	−2.00310
$173$	−1.18657e7	−0.174234	−0.0871171	−	0.996198i	$-0.527765\pi$
$173$	−1.18657e7	−0.174234	−0.0871171	+	0.996198i	$0.527765\pi$
$174$	−7.64682e7	−1.10042
$175$	−2.29158e6	−0.0323222
$176$	1.51402e7	0.209332
$177$	−1.51165e7	−0.204901
$178$	4.57055e7	0.607433
$179$	−1.45452e8	−1.89555	−0.947773	−	0.318945i	$-0.896672\pi$
$179$	−1.45452e8	−1.89555	−0.947773	+	0.318945i	$0.896672\pi$
$180$	5.34401e7	0.682989
$181$	−1.87044e7	−0.234460	−0.117230	−	0.993105i	$-0.537401\pi$
$181$	−1.87044e7	−0.234460	−0.117230	+	0.993105i	$0.537401\pi$
$182$	−1.48615e7	−0.182732
$183$	5.57942e7	0.672992
$184$	−3.43694e7	−0.406733
$185$	4.85448e6	0.0563692
$186$	8.46764e7	0.964866
$187$	−2.77113e7	−0.309892
$188$	−5.63298e7	−0.618281
$189$	3.81815e7	0.411374
$190$	2.46361e8	2.60576
$191$	5172.21	5.37105e−5 0	2.68552e−5	−	1.00000i	$-0.499991\pi$
$191$	5172.21	5.37105e−5 0	2.68552e−5		1.00000i	$0.499991\pi$
$192$	6.94267e7	0.707901
$193$	−3.75386e7	−0.375862	−0.187931	−	0.982182i	$-0.560178\pi$
$193$	−3.75386e7	−0.375862	−0.187931	+	0.982182i	$0.560178\pi$
$194$	−8.90669e7	−0.875811
$195$	−2.21349e7	−0.213775
$196$	3.06990e7	0.291224
$197$	−1.29935e8	−1.21086	−0.605431	−	0.795898i	$-0.706999\pi$
$197$	−1.29935e8	−1.21086	−0.605431	+	0.795898i	$0.706999\pi$
$198$	−1.24988e7	−0.114430
$199$	−1.37264e8	−1.23473	−0.617364	−	0.786678i	$-0.711799\pi$
$199$	−1.37264e8	−1.23473	−0.617364	+	0.786678i	$0.711799\pi$
$200$	−1.75156e7	−0.154818
$201$	−1.55399e8	−1.34978
$202$	−2.93972e8	−2.50944
$203$	3.52834e7	0.296029
$204$	3.29517e8	2.71751
$205$	−2.01493e8	−1.63351
$206$	3.11237e8	2.48059
$207$	1.00447e7	0.0787116
$208$	−4.02144e7	−0.309856
$209$	−3.86570e7	−0.292898
$210$	6.81524e7	0.507825
$211$	−2.00168e8	−1.46692	−0.733460	−	0.679733i	$-0.762096\pi$
$211$	−2.00168e8	−1.46692	−0.733460	+	0.679733i	$0.762096\pi$
$212$	3.67622e8	2.64988
$213$	7.89419e7	0.559731
$214$	−6.97549e7	−0.486549
$215$	1.36930e8	0.939645
$216$	2.91840e8	1.97041
$217$	−3.90708e7	−0.259563
$218$	2.79923e8	1.82996
$219$	−8.15832e7	−0.524863
$220$	−5.76897e7	−0.365274
$221$	7.36049e7	0.458706
$222$	1.35009e7	0.0828187
$223$	2.17656e8	1.31433	0.657164	−	0.753747i	$-0.271756\pi$
$223$	2.17656e8	1.31433	0.657164	+	0.753747i	$0.271756\pi$
$224$	8.71449e6	0.0518053
$225$	5.11904e6	0.0299606
$226$	2.00941e7	0.115795
$227$	−9.53549e7	−0.541069	−0.270534	−	0.962710i	$-0.587200\pi$
$227$	−9.53549e7	−0.541069	−0.270534	+	0.962710i	$0.587200\pi$
$228$	4.59674e8	2.56849
$229$	−5.73437e7	−0.315545	−0.157772	−	0.987475i	$-0.550431\pi$
$229$	−5.73437e7	−0.315545	−0.157772	+	0.987475i	$0.550431\pi$
$230$	6.91049e7	0.374508
$231$	−1.06939e7	−0.0570816
$232$	2.69688e8	1.41793
$233$	−1.97192e8	−1.02128	−0.510638	−	0.859796i	$-0.670591\pi$
$233$	−1.97192e8	−1.02128	−0.510638	+	0.859796i	$0.670591\pi$
$234$	3.31985e7	0.169380
$235$	5.77013e7	0.290033
$236$	1.04646e8	0.518239
$237$	2.56110e7	0.124970
$238$	−2.26627e8	−1.08966
$239$	3.94751e8	1.87038	0.935192	−	0.354142i	$-0.115227\pi$
$239$	3.94751e8	1.87038	0.935192	+	0.354142i	$0.115227\pi$
$240$	1.84416e8	0.861112
$241$	8.84427e7	0.407008	0.203504	−	0.979074i	$-0.434767\pi$
$241$	8.84427e7	0.407008	0.203504	+	0.979074i	$0.434767\pi$
$242$	−3.70823e8	−1.68195
$243$	−1.48455e8	−0.663701
$244$	−3.86243e8	−1.70214
$245$	−3.14464e7	−0.136612
$246$	−5.60379e8	−2.39999
$247$	1.02678e8	0.433551
$248$	−2.98637e8	−1.24326
$249$	3.40319e8	1.39698
$250$	4.47043e8	1.80950
$251$	3.37842e8	1.34852	0.674258	−	0.738496i	$-0.264464\pi$
$251$	3.37842e8	1.34852	0.674258	+	0.738496i	$0.264464\pi$
$252$	−6.85770e7	−0.269946
$253$	−1.08434e7	−0.0420963
$254$	3.50336e8	1.34143
$255$	−3.37540e8	−1.27478
$256$	−5.44751e8	−2.02936
$257$	−5.08006e8	−1.86682	−0.933412	−	0.358808i	$-0.883183\pi$
$257$	−5.08006e8	−1.86682	−0.933412	+	0.358808i	$0.883183\pi$
$258$	3.80820e8	1.38055
$259$	−6.22951e6	−0.0222795
$260$	1.53232e8	0.540682
$261$	−7.88179e7	−0.274400
$262$	−8.22305e7	−0.282474
$263$	2.82727e8	0.958345	0.479173	−	0.877721i	$-0.340937\pi$
$263$	2.82727e8	0.958345	0.479173	+	0.877721i	$0.340937\pi$
$264$	−8.17391e7	−0.273411
$265$	−3.76573e8	−1.24305
$266$	−3.16142e8	−1.02990
$267$	−8.73562e7	−0.280869
$268$	1.07577e9	3.41387
$269$	−2.41153e8	−0.755370	−0.377685	−	0.925934i	$-0.623280\pi$
$269$	−2.41153e8	−0.755370	−0.377685	+	0.925934i	$0.623280\pi$
$270$	−5.86789e8	−1.81430
$271$	5.32234e7	0.162446	0.0812232	−	0.996696i	$-0.474117\pi$
$271$	5.32234e7	0.162446	0.0812232	+	0.996696i	$0.474117\pi$
$272$	−6.13237e8	−1.84772
$273$	2.84046e7	0.0844928
$274$	−1.00330e9	−2.94649
$275$	−5.52611e6	−0.0160234
$276$	1.28940e8	0.369152
$277$	3.06655e6	0.00866904	0.00433452	−	0.999991i	$-0.498620\pi$
$277$	3.06655e6	0.00866904	0.00433452	+	0.999991i	$0.498620\pi$
$278$	6.43232e8	1.79560
$279$	8.72784e7	0.240598
$280$	−2.40360e8	−0.654350
$281$	−4.43851e8	−1.19334	−0.596671	−	0.802486i	$-0.703510\pi$
$281$	−4.43851e8	−1.19334	−0.596671	+	0.802486i	$0.703510\pi$
$282$	1.60475e8	0.426123
$283$	2.44859e8	0.642190	0.321095	−	0.947047i	$-0.395949\pi$
$283$	2.44859e8	0.642190	0.321095	+	0.947047i	$0.395949\pi$
$284$	−5.46486e8	−1.41568
$285$	−4.70865e8	−1.20487
$286$	−3.58384e7	−0.0905874
$287$	2.58566e8	0.645632
$288$	−1.94669e7	−0.0480201
$289$	7.12077e8	1.73534
$290$	−5.42249e8	−1.30559
$291$	1.70232e8	0.404963
$292$	5.64770e8	1.32749
$293$	3.72397e8	0.864908	0.432454	−	0.901656i	$-0.357648\pi$
$293$	3.72397e8	0.864908	0.432454	+	0.901656i	$0.357648\pi$
$294$	−8.74566e7	−0.200714
$295$	−1.07194e8	−0.243104
$296$	−4.76152e7	−0.106715
$297$	9.20743e7	0.203935
$298$	2.26473e8	0.495746
$299$	2.88016e7	0.0623113
$300$	6.57114e7	0.140513
$301$	−1.75715e8	−0.371387
$302$	5.80777e8	1.21335
$303$	5.61864e8	1.16033
$304$	−8.55461e8	−1.74640
$305$	3.95646e8	0.798468
$306$	5.06250e8	1.01004
$307$	−3.26577e8	−0.644172	−0.322086	−	0.946710i	$-0.604384\pi$
$307$	−3.26577e8	−0.644172	−0.322086	+	0.946710i	$0.604384\pi$
$308$	7.40302e7	0.144372
$309$	−5.94862e8	−1.14699
$310$	6.00455e8	1.14476
$311$	1.08181e8	0.203933	0.101967	−	0.994788i	$-0.467486\pi$
$311$	1.08181e8	0.203933	0.101967	+	0.994788i	$0.467486\pi$
$312$	2.17110e8	0.404706
$313$	4.38420e8	0.808138	0.404069	−	0.914729i	$-0.367596\pi$
$313$	4.38420e8	0.808138	0.404069	+	0.914729i	$0.367596\pi$
$314$	2.61599e8	0.476850
$315$	7.02467e7	0.126631
$316$	−1.77296e8	−0.316077
$317$	−3.44382e7	−0.0607202	−0.0303601	−	0.999539i	$-0.509665\pi$
$317$	−3.44382e7	−0.0607202	−0.0303601	+	0.999539i	$0.509665\pi$
$318$	−1.04730e9	−1.82632
$319$	8.50855e7	0.146753
$320$	4.92317e8	0.839885
$321$	1.33321e8	0.224974
$322$	−8.86788e7	−0.148021
$323$	1.56576e9	2.58534
$324$	−6.57610e8	−1.07414
$325$	1.46781e7	0.0237180
$326$	−1.37608e9	−2.19979
$327$	−5.35013e8	−0.846149
$328$	1.97635e9	3.09247
$329$	−7.40451e7	−0.114633
$330$	1.64349e8	0.251749
$331$	1.61372e7	0.0244585	0.0122293	−	0.999925i	$-0.496107\pi$
$331$	1.61372e7	0.0244585	0.0122293	+	0.999925i	$0.496107\pi$
$332$	−2.35591e9	−3.53325
$333$	1.39158e7	0.0206516
$334$	−1.04098e9	−1.52872
$335$	−1.10196e9	−1.60143
$336$	−2.36652e8	−0.340348
$337$	−6.90869e8	−0.983311	−0.491656	−	0.870790i	$-0.663608\pi$
$337$	−6.90869e8	−0.983311	−0.491656	+	0.870790i	$0.663608\pi$
$338$	9.51919e7	0.134088
$339$	−3.84055e7	−0.0535419
$340$	2.33666e9	3.22418
$341$	−9.42187e7	−0.128676
$342$	7.06216e8	0.954654
$343$	4.03536e7	0.0539949
$344$	−1.34308e9	−1.77888
$345$	−1.32079e8	−0.173168
$346$	−2.34010e8	−0.303716
$347$	−7.32745e8	−0.941455	−0.470728	−	0.882279i	$-0.656009\pi$
$347$	−7.32745e8	−0.941455	−0.470728	+	0.882279i	$0.656009\pi$
$348$	−1.01176e9	−1.28691
$349$	1.05422e9	1.32752	0.663762	−	0.747944i	$-0.268959\pi$
$349$	1.05422e9	1.32752	0.663762	+	0.747944i	$0.268959\pi$
$350$	−4.51933e7	−0.0563424
$351$	−2.44562e8	−0.301866
$352$	2.10149e7	0.0256819
$353$	8.71811e8	1.05490	0.527449	−	0.849586i	$-0.323148\pi$
$353$	8.71811e8	1.05490	0.527449	+	0.849586i	$0.323148\pi$
$354$	−2.98120e8	−0.357173
$355$	5.59791e8	0.664090
$356$	6.04735e8	0.710379
$357$	4.33147e8	0.503845
$358$	−2.86853e9	−3.30422
$359$	−1.02521e9	−1.16945	−0.584724	−	0.811233i	$-0.698797\pi$
$359$	−1.02521e9	−1.16945	−0.584724	+	0.811233i	$0.698797\pi$
$360$	5.36930e8	0.606539
$361$	1.29036e9	1.44356
$362$	−3.68878e8	−0.408698
$363$	7.08748e8	0.777712
$364$	−1.96635e8	−0.213700
$365$	−5.78521e8	−0.622721
$366$	1.10034e9	1.17313
$367$	1.32639e9	1.40068	0.700341	−	0.713808i	$-0.253031\pi$
$367$	1.32639e9	1.40068	0.700341	+	0.713808i	$0.253031\pi$
$368$	−2.39959e8	−0.250998
$369$	−5.77599e8	−0.598458
$370$	9.57375e7	0.0982599
$371$	4.83237e8	0.491306
$372$	1.12036e9	1.12839
$373$	3.56019e8	0.355216	0.177608	−	0.984101i	$-0.443164\pi$
$373$	3.56019e8	0.355216	0.177608	+	0.984101i	$0.443164\pi$
$374$	−5.46507e8	−0.540188
$375$	−8.54425e8	−0.836690
$376$	−5.65963e8	−0.549074
$377$	−2.25999e8	−0.217226
$378$	7.52997e8	0.717087
$379$	1.88912e8	0.178247	0.0891234	−	0.996021i	$-0.471593\pi$
$379$	1.88912e8	0.178247	0.0891234	+	0.996021i	$0.471593\pi$
$380$	3.25963e9	3.04737
$381$	−6.69591e8	−0.620258
$382$	102004.	9.36254e−5 0
$383$	1.48845e9	1.35375	0.676876	−	0.736097i	$-0.263333\pi$
$383$	1.48845e9	1.35375	0.676876	+	0.736097i	$0.263333\pi$
$384$	1.49178e9	1.34445
$385$	−7.58327e7	−0.0677242
$386$	−7.40318e8	−0.655183
$387$	3.92522e8	0.344251
$388$	−1.17845e9	−1.02424
$389$	−1.40268e9	−1.20819	−0.604096	−	0.796912i	$-0.706466\pi$
$389$	−1.40268e9	−1.20819	−0.604096	+	0.796912i	$0.706466\pi$
$390$	−4.36533e8	−0.372642
$391$	4.39201e8	0.371573
$392$	3.08442e8	0.258626
$393$	1.57166e8	0.130612
$394$	−2.56251e9	−2.11071
$395$	1.81612e8	0.148271
$396$	−1.65373e8	−0.133823
$397$	−3.42516e8	−0.274735	−0.137368	−	0.990520i	$-0.543864\pi$
$397$	−3.42516e8	−0.274735	−0.137368	+	0.990520i	$0.543864\pi$
$398$	−2.70705e9	−2.15232
$399$	6.04238e8	0.476215
$400$	−1.22290e8	−0.0955391
$401$	−2.04952e9	−1.58725	−0.793627	−	0.608404i	$-0.791810\pi$
$401$	−2.04952e9	−1.58725	−0.793627	+	0.608404i	$0.791810\pi$
$402$	−3.06470e9	−2.35286
$403$	2.50258e8	0.190467
$404$	−3.88958e9	−2.93473
$405$	6.73620e8	0.503875
$406$	6.95841e8	0.516023
$407$	−1.50224e7	−0.0110448
$408$	3.31076e9	2.41333
$409$	−9.49171e8	−0.685982	−0.342991	−	0.939339i	$-0.611440\pi$
$409$	−9.49171e8	−0.685982	−0.342991	+	0.939339i	$0.611440\pi$
$410$	−3.97375e9	−2.84745
$411$	1.91759e9	1.36242
$412$	4.11801e9	2.90100
$413$	1.37556e8	0.0960849
$414$	1.98095e8	0.137206
$415$	2.41327e9	1.65744
$416$	−5.58185e7	−0.0380147
$417$	−1.22940e9	−0.830264
$418$	−7.62374e8	−0.510565
$419$	1.67352e9	1.11143	0.555713	−	0.831374i	$-0.312445\pi$
$419$	1.67352e9	1.11143	0.555713	+	0.831374i	$0.312445\pi$
$420$	9.01732e8	0.593889
$421$	1.62025e9	1.05826	0.529132	−	0.848540i	$-0.322518\pi$
$421$	1.62025e9	1.05826	0.529132	+	0.848540i	$0.322518\pi$
$422$	−3.94761e9	−2.55706
$423$	1.65406e8	0.106258
$424$	3.69362e9	2.35327
$425$	2.23829e8	0.141435
$426$	1.55685e9	0.975694
$427$	−5.07713e8	−0.315588
$428$	−9.22934e8	−0.569007
$429$	6.84974e7	0.0418864
$430$	2.70046e9	1.63794
$431$	−1.30425e9	−0.784675	−0.392337	−	0.919821i	$-0.628333\pi$
$431$	−1.30425e9	−0.784675	−0.392337	+	0.919821i	$0.628333\pi$
$432$	2.03756e9	1.21595
$433$	1.30502e9	0.772522	0.386261	−	0.922390i	$-0.373766\pi$
$433$	1.30502e9	0.772522	0.386261	+	0.922390i	$0.373766\pi$
$434$	−7.70534e8	−0.452457
$435$	1.03639e9	0.603687
$436$	3.70369e9	2.14009
$437$	6.12682e8	0.351197
$438$	−1.60894e9	−0.914915
$439$	−1.49705e9	−0.844523	−0.422262	−	0.906474i	$-0.638764\pi$
$439$	−1.49705e9	−0.844523	−0.422262	+	0.906474i	$0.638764\pi$
$440$	−5.79626e8	−0.324387
$441$	−9.01440e7	−0.0500497
$442$	1.45160e9	0.799593
$443$	3.31367e8	0.181091	0.0905453	−	0.995892i	$-0.471139\pi$
$443$	3.31367e8	0.181091	0.0905453	+	0.995892i	$0.471139\pi$
$444$	1.78632e8	0.0968545
$445$	−6.19458e8	−0.333236
$446$	4.29250e9	2.29107
$447$	−4.32854e8	−0.229227
$448$	−6.31766e8	−0.331958
$449$	2.50438e9	1.30568	0.652842	−	0.757494i	$-0.273576\pi$
$449$	2.50438e9	1.30568	0.652842	+	0.757494i	$0.273576\pi$
$450$	1.00955e8	0.0522257
$451$	6.23529e8	0.320066
$452$	2.65867e8	0.135419
$453$	−1.11003e9	−0.561036
$454$	−1.88054e9	−0.943164
$455$	2.01422e8	0.100246
$456$	4.61849e9	2.28099
$457$	3.97072e9	1.94609	0.973044	−	0.230620i	$-0.0740753\pi$
$457$	3.97072e9	1.94609	0.973044	+	0.230620i	$0.0740753\pi$
$458$	−1.13090e9	−0.550042
$459$	−3.72938e9	−1.80008
$460$	9.14334e8	0.437978
$461$	−3.43489e9	−1.63290	−0.816449	−	0.577418i	$-0.804060\pi$
$461$	−3.43489e9	−1.63290	−0.816449	+	0.577418i	$0.804060\pi$
$462$	−2.10901e8	−0.0995018
$463$	−2.92597e9	−1.37005	−0.685024	−	0.728520i	$-0.740208\pi$
$463$	−2.92597e9	−1.37005	−0.685024	+	0.728520i	$0.740208\pi$
$464$	1.88290e9	0.875014
$465$	−1.14764e9	−0.529322
$466$	−3.88892e9	−1.78024
$467$	−2.22257e9	−1.00983	−0.504914	−	0.863170i	$-0.668476\pi$
$467$	−2.22257e9	−1.00983	−0.504914	+	0.863170i	$0.668476\pi$
$468$	4.39253e8	0.198086
$469$	1.41409e9	0.632954
$470$	1.13795e9	0.505571
$471$	−4.99989e8	−0.220489
$472$	1.05141e9	0.460230
$473$	−4.23735e8	−0.184111
$474$	5.05087e8	0.217842
$475$	3.12240e8	0.133678
$476$	−2.99852e9	−1.27433
$477$	−1.07948e9	−0.455408
$478$	7.78508e9	3.26036
$479$	4.17730e9	1.73669	0.868343	−	0.495963i	$-0.165185\pi$
$479$	4.17730e9	1.73669	0.868343	+	0.495963i	$0.165185\pi$
$480$	2.55974e8	0.105646
$481$	3.99015e7	0.0163486
$482$	1.74422e9	0.709475
$483$	1.69490e8	0.0684432
$484$	−4.90640e9	−1.96700
$485$	1.20715e9	0.480467
$486$	−2.92775e9	−1.15693
$487$	1.67420e9	0.656834	0.328417	−	0.944533i	$-0.393485\pi$
$487$	1.67420e9	0.656834	0.328417	+	0.944533i	$0.393485\pi$
$488$	−3.88070e9	−1.51161
$489$	2.63007e9	1.01715
$490$	−6.20170e8	−0.238136
$491$	2.82592e9	1.07740	0.538698	−	0.842499i	$-0.318916\pi$
$491$	2.82592e9	1.07740	0.538698	+	0.842499i	$0.318916\pi$
$492$	−7.41444e9	−2.80673
$493$	−3.44630e9	−1.29536
$494$	2.02497e9	0.755744
$495$	1.69399e8	0.0627759
$496$	−2.08502e9	−0.767226
$497$	−7.18352e8	−0.262476
$498$	6.71161e9	2.43514
$499$	−4.37978e9	−1.57798	−0.788989	−	0.614408i	$-0.789395\pi$
$499$	−4.37978e9	−1.57798	−0.788989	+	0.614408i	$0.789395\pi$
$500$	5.91487e9	2.11617
$501$	1.98960e9	0.706861
$502$	6.66275e9	2.35067
$503$	−1.81237e9	−0.634978	−0.317489	−	0.948262i	$-0.602840\pi$
$503$	−1.81237e9	−0.634978	−0.317489	+	0.948262i	$0.602840\pi$
$504$	−6.89015e8	−0.239730
$505$	3.98428e9	1.37667
$506$	−2.13848e8	−0.0733801
$507$	−1.81939e8	−0.0620008
$508$	4.63533e9	1.56876
$509$	−3.95573e9	−1.32958	−0.664790	−	0.747030i	$-0.731479\pi$
$509$	−3.95573e9	−1.32958	−0.664790	+	0.747030i	$0.731479\pi$
$510$	−6.65678e9	−2.22213
$511$	7.42386e8	0.246126
$512$	−5.67748e9	−1.86944
$513$	−5.20245e9	−1.70137
$514$	−1.00186e10	−3.25415
$515$	−4.21827e9	−1.36085
$516$	5.03867e9	1.61451
$517$	−1.78559e8	−0.0568283
$518$	−1.22855e8	−0.0388364
$519$	4.47259e8	0.140434
$520$	1.53957e9	0.480161
$521$	3.91752e9	1.21361	0.606804	−	0.794851i	$-0.292451\pi$
$521$	3.91752e9	1.21361	0.606804	+	0.794851i	$0.292451\pi$
$522$	−1.55441e9	−0.478319
$523$	−5.02928e9	−1.53727	−0.768635	−	0.639687i	$-0.779064\pi$
$523$	−5.02928e9	−1.53727	−0.768635	+	0.639687i	$0.779064\pi$
$524$	−1.08800e9	−0.330347
$525$	8.63771e7	0.0260520
$526$	5.57580e9	1.67054
$527$	3.81623e9	1.13579
$528$	−5.70683e8	−0.168724
$529$	−3.23297e9	−0.949525
$530$	−7.42658e9	−2.16682
$531$	−3.07280e8	−0.0890644
$532$	−4.18291e9	−1.20445
$533$	−1.65618e9	−0.473764
$534$	−1.72279e9	−0.489597
$535$	9.45405e8	0.266919
$536$	1.08086e10	3.03174
$537$	5.48258e9	1.52783
$538$	−4.75589e9	−1.31672
$539$	9.73122e7	0.0267674
$540$	−7.76387e9	−2.12178
$541$	−1.70186e9	−0.462096	−0.231048	−	0.972942i	$-0.574216\pi$
$541$	−1.70186e9	−0.462096	−0.231048	+	0.972942i	$0.574216\pi$
$542$	1.04965e9	0.283169
$543$	7.05030e8	0.188977
$544$	−8.51187e8	−0.226688
$545$	−3.79387e9	−1.00391
$546$	5.60181e8	0.147284
$547$	−4.66266e9	−1.21809	−0.609043	−	0.793137i	$-0.708446\pi$
$547$	−4.66266e9	−1.21809	−0.609043	+	0.793137i	$0.708446\pi$
$548$	−1.32748e10	−3.44584
$549$	1.13416e9	0.292530
$550$	−1.08983e8	−0.0279312
$551$	−4.80757e9	−1.22432
$552$	1.29550e9	0.327831
$553$	−2.33054e8	−0.0586028
$554$	6.04769e7	0.0151114
$555$	−1.82982e8	−0.0454341
$556$	8.51066e9	2.09991
$557$	−6.47466e9	−1.58754	−0.793768	−	0.608221i	$-0.791883\pi$
$557$	−6.47466e9	−1.58754	−0.793768	+	0.608221i	$0.791883\pi$
$558$	1.72126e9	0.419398
$559$	1.12550e9	0.272524
$560$	−1.67814e9	−0.403804
$561$	1.04453e9	0.249776
$562$	−8.75341e9	−2.08018
$563$	−5.15612e9	−1.21771	−0.608855	−	0.793282i	$-0.708371\pi$
$563$	−5.15612e9	−1.21771	−0.608855	+	0.793282i	$0.708371\pi$
$564$	2.12326e9	0.498340
$565$	−2.72340e8	−0.0635245
$566$	4.82898e9	1.11943
$567$	−8.64423e8	−0.199152
$568$	−5.49071e9	−1.25722
$569$	−2.62426e9	−0.597191	−0.298595	−	0.954380i	$-0.596518\pi$
$569$	−2.62426e9	−0.597191	−0.298595	+	0.954380i	$0.596518\pi$
$570$	−9.28616e9	−2.10027
$571$	5.17728e9	1.16379	0.581896	−	0.813263i	$-0.302311\pi$
$571$	5.17728e9	1.16379	0.581896	+	0.813263i	$0.302311\pi$
$572$	−4.74182e8	−0.105940
$573$	−194958.	−4.32912e−5 0
$574$	5.09931e9	1.12543
$575$	8.75843e7	0.0192127
$576$	1.41127e9	0.307703
$577$	3.83929e9	0.832024	0.416012	−	0.909359i	$-0.363427\pi$
$577$	3.83929e9	0.832024	0.416012	+	0.909359i	$0.363427\pi$
$578$	1.40432e10	3.02496
$579$	1.41496e9	0.302948
$580$	−7.17456e9	−1.52685
$581$	−3.09682e9	−0.655088
$582$	3.35723e9	0.705912
$583$	1.16532e9	0.243560
$584$	5.67442e9	1.17890
$585$	−4.49947e8	−0.0929215
$586$	7.34423e9	1.50766
$587$	−8.04509e9	−1.64171	−0.820857	−	0.571134i	$-0.806504\pi$
$587$	−8.04509e9	−1.64171	−0.820857	+	0.571134i	$0.806504\pi$
$588$	−1.15715e9	−0.234730
$589$	5.32362e9	1.07350
$590$	−2.11402e9	−0.423767
$591$	4.89769e9	0.975967
$592$	−3.32438e8	−0.0658544
$593$	2.51014e9	0.494317	0.247159	−	0.968975i	$-0.420503\pi$
$593$	2.51014e9	0.494317	0.247159	+	0.968975i	$0.420503\pi$
$594$	1.81584e9	0.355489
$595$	3.07152e9	0.597784
$596$	2.99649e9	0.579763
$597$	5.17395e9	0.995203
$598$	5.68010e8	0.108618
$599$	9.34498e9	1.77658	0.888290	−	0.459283i	$-0.151894\pi$
$599$	9.34498e9	1.77658	0.888290	+	0.459283i	$0.151894\pi$
$600$	6.60223e8	0.124785
$601$	−9.42663e9	−1.77131	−0.885657	−	0.464339i	$-0.846292\pi$
$601$	−9.42663e9	−1.77131	−0.885657	+	0.464339i	$0.846292\pi$
$602$	−3.46537e9	−0.647383
$603$	−3.15887e9	−0.586707
$604$	7.68432e9	1.41898
$605$	5.02586e9	0.922713
$606$	1.10808e10	2.02263
$607$	−4.96368e9	−0.900831	−0.450415	−	0.892819i	$-0.648724\pi$
$607$	−4.96368e9	−0.900831	−0.450415	+	0.892819i	$0.648724\pi$
$608$	−1.18740e9	−0.214257
$609$	−1.32995e9	−0.238602
$610$	7.80274e9	1.39185
$611$	4.74277e8	0.0841179
$612$	6.69825e9	1.18122
$613$	1.22009e9	0.213935	0.106967	−	0.994263i	$-0.465886\pi$
$613$	1.22009e9	0.213935	0.106967	+	0.994263i	$0.465886\pi$
$614$	−6.44059e9	−1.12289
$615$	7.59496e9	1.31663
$616$	7.43805e8	0.128211
$617$	6.85957e9	1.17571	0.587853	−	0.808968i	$-0.299973\pi$
$617$	6.85957e9	1.17571	0.587853	+	0.808968i	$0.299973\pi$
$618$	−1.17316e10	−1.99938
$619$	6.19500e9	1.04984	0.524921	−	0.851151i	$-0.324095\pi$
$619$	6.19500e9	1.04984	0.524921	+	0.851151i	$0.324095\pi$
$620$	7.94469e9	1.33877
$621$	−1.45930e9	−0.244526
$622$	2.13348e9	0.355487
$623$	7.94919e8	0.131709
$624$	1.51581e9	0.249747
$625$	−5.53693e9	−0.907170
$626$	8.64630e9	1.40871
$627$	1.45711e9	0.236079
$628$	3.46124e9	0.557664
$629$	6.08466e8	0.0974898
$630$	1.38537e9	0.220736
$631$	4.08090e9	0.646626	0.323313	−	0.946292i	$-0.395203\pi$
$631$	4.08090e9	0.646626	0.323313	+	0.946292i	$0.395203\pi$
$632$	−1.78134e9	−0.280697
$633$	7.54500e9	1.18235
$634$	−6.79173e8	−0.105844
$635$	−4.74819e9	−0.735902
$636$	−1.38569e10	−2.13583
$637$	−2.58475e8	−0.0396214
$638$	1.67801e9	0.255813
$639$	1.60469e9	0.243298
$640$	1.05785e10	1.59512
$641$	−9.92656e9	−1.48866	−0.744330	−	0.667812i	$-0.767231\pi$
$641$	−9.92656e9	−1.48866	−0.744330	+	0.667812i	$0.767231\pi$
$642$	2.62930e9	0.392163
$643$	9.26393e9	1.37422	0.687111	−	0.726553i	$-0.258879\pi$
$643$	9.26393e9	1.37422	0.687111	+	0.726553i	$0.258879\pi$
$644$	−1.17332e9	−0.173107
$645$	−5.16135e9	−0.757363
$646$	3.08792e10	4.50663
$647$	9.25281e9	1.34310	0.671550	−	0.740959i	$-0.265629\pi$
$647$	9.25281e9	1.34310	0.671550	+	0.740959i	$0.265629\pi$
$648$	−6.60721e9	−0.953906
$649$	3.31715e8	0.0476331
$650$	2.89474e8	0.0413441
$651$	1.47271e9	0.209210
$652$	−1.82070e10	−2.57260
$653$	1.08773e10	1.52870	0.764352	−	0.644799i	$-0.223059\pi$
$653$	1.08773e10	1.52870	0.764352	+	0.644799i	$0.223059\pi$
$654$	−1.05512e10	−1.47496
$655$	1.11449e9	0.154964
$656$	1.37984e10	1.90838
$657$	−1.65838e9	−0.228142
$658$	−1.46028e9	−0.199823
$659$	5.51538e9	0.750717	0.375358	−	0.926880i	$-0.377520\pi$
$659$	5.51538e9	0.750717	0.375358	+	0.926880i	$0.377520\pi$
$660$	2.17452e9	0.294414
$661$	4.83533e8	0.0651210	0.0325605	−	0.999470i	$-0.489634\pi$
$661$	4.83533e8	0.0651210	0.0325605	+	0.999470i	$0.489634\pi$
$662$	3.18250e8	0.0426349
$663$	−2.77442e9	−0.369721
$664$	−2.36705e10	−3.13776
$665$	4.28476e9	0.565002
$666$	2.74440e8	0.0359988
$667$	−1.34854e9	−0.175963
$668$	−1.37733e10	−1.78780
$669$	−8.20419e9	−1.05936
$670$	−2.17323e10	−2.79154
$671$	−1.22434e9	−0.156450
$672$	−3.28478e8	−0.0417556
$673$	−2.75215e9	−0.348033	−0.174016	−	0.984743i	$-0.555675\pi$
$673$	−2.75215e9	−0.348033	−0.174016	+	0.984743i	$0.555675\pi$
$674$	−1.36250e10	−1.71406
$675$	−7.43703e8	−0.0930757
$676$	1.25949e9	0.156813
$677$	−1.11271e10	−1.37823	−0.689116	−	0.724651i	$-0.742001\pi$
$677$	−1.11271e10	−1.37823	−0.689116	+	0.724651i	$0.742001\pi$
$678$	−7.57413e8	−0.0933316
$679$	−1.54907e9	−0.189901
$680$	2.34772e10	2.86329
$681$	3.59425e9	0.436107
$682$	−1.85813e9	−0.224301
$683$	−1.27298e9	−0.152879	−0.0764397	−	0.997074i	$-0.524355\pi$
$683$	−1.27298e9	−0.152879	−0.0764397	+	0.997074i	$0.524355\pi$
$684$	9.34402e9	1.11644
$685$	1.35980e10	1.61643
$686$	7.95833e8	0.0941212
$687$	2.16147e9	0.254332
$688$	−9.37706e9	−1.09776
$689$	−3.09525e9	−0.360520
$690$	−2.60480e9	−0.301857
$691$	−4.52770e9	−0.522041	−0.261020	−	0.965333i	$-0.584059\pi$
$691$	−4.52770e9	−0.522041	−0.261020	+	0.965333i	$0.584059\pi$
$692$	−3.09621e9	−0.355189
$693$	−2.17381e8	−0.0248117
$694$	−1.44508e10	−1.64110
$695$	−8.71787e9	−0.985062
$696$	−1.01655e10	−1.14286
$697$	−2.52554e10	−2.82514
$698$	2.07908e10	2.31407
$699$	7.43282e9	0.823159
$700$	−5.97957e8	−0.0658911
$701$	−1.06195e10	−1.16437	−0.582185	−	0.813056i	$-0.697802\pi$
$701$	−1.06195e10	−1.16437	−0.582185	+	0.813056i	$0.697802\pi$
$702$	−4.82313e9	−0.526198
$703$	8.48806e8	0.0921436
$704$	−1.52350e9	−0.164565
$705$	−2.17495e9	−0.233770
$706$	1.71934e10	1.83885
$707$	−5.11282e9	−0.544117
$708$	−3.94445e9	−0.417706
$709$	−1.58292e10	−1.66801	−0.834003	−	0.551760i	$-0.813957\pi$
$709$	−1.58292e10	−1.66801	−0.834003	+	0.551760i	$0.813957\pi$
$710$	1.10399e10	1.15761
$711$	5.20608e8	0.0543209
$712$	6.07596e9	0.630863
$713$	1.49329e9	0.154288
$714$	8.54231e9	0.878277
$715$	4.85727e8	0.0496960
$716$	−3.79539e10	−3.86421
$717$	−1.48795e10	−1.50755
$718$	−2.02186e10	−2.03852
$719$	−8.31614e9	−0.834393	−0.417197	−	0.908816i	$-0.636987\pi$
$719$	−8.31614e9	−0.834393	−0.417197	+	0.908816i	$0.636987\pi$
$720$	3.74872e9	0.374299
$721$	5.41309e9	0.537864
$722$	2.54478e10	2.51634
$723$	−3.33370e9	−0.328052
$724$	−4.88067e9	−0.477963
$725$	−6.87253e8	−0.0669782
$726$	1.39776e10	1.35567
$727$	7.60595e9	0.734147	0.367074	−	0.930192i	$-0.380360\pi$
$727$	7.60595e9	0.734147	0.367074	+	0.930192i	$0.380360\pi$
$728$	−1.97565e9	−0.189780
$729$	1.11074e10	1.06186
$730$	−1.14093e10	−1.08550
$731$	1.71630e10	1.62511
$732$	1.45588e10	1.37194
$733$	4.18398e9	0.392397	0.196198	−	0.980564i	$-0.437140\pi$
$733$	4.18398e9	0.392397	0.196198	+	0.980564i	$0.437140\pi$
$734$	2.61584e10	2.44160
$735$	1.18532e9	0.110111
$736$	−3.33069e8	−0.0307937
$737$	3.41006e9	0.313780
$738$	−1.13911e10	−1.04320
$739$	4.46939e9	0.407373	0.203687	−	0.979036i	$-0.434708\pi$
$739$	4.46939e9	0.407373	0.203687	+	0.979036i	$0.434708\pi$
$740$	1.26671e9	0.114913
$741$	−3.87029e9	−0.349446
$742$	9.53016e9	0.856419
$743$	−8.11858e9	−0.726138	−0.363069	−	0.931762i	$-0.618271\pi$
$743$	−8.11858e9	−0.726138	−0.363069	+	0.931762i	$0.618271\pi$
$744$	1.12566e10	1.00208
$745$	−3.06944e9	−0.271965
$746$	7.02123e9	0.619195
$747$	6.91784e9	0.607224
$748$	−7.23089e9	−0.631737
$749$	−1.21319e9	−0.105498
$750$	−1.68505e10	−1.45848
$751$	8.61793e9	0.742443	0.371222	−	0.928544i	$-0.378939\pi$
$751$	8.61793e9	0.742443	0.371222	+	0.928544i	$0.378939\pi$
$752$	−3.95142e9	−0.338837
$753$	−1.27344e10	−1.08692
$754$	−4.45704e9	−0.378657
$755$	−7.87141e9	−0.665638
$756$	9.96298e9	0.838616
$757$	1.53225e10	1.28379	0.641897	−	0.766791i	$-0.278148\pi$
$757$	1.53225e10	1.28379	0.641897	+	0.766791i	$0.278148\pi$
$758$	3.72562e9	0.310711
$759$	4.08724e8	0.0339300
$760$	3.27505e10	2.70626
$761$	−1.00154e10	−0.823801	−0.411900	−	0.911229i	$-0.635135\pi$
$761$	−1.00154e10	−0.823801	−0.411900	+	0.911229i	$0.635135\pi$
$762$	−1.32053e10	−1.08120
$763$	4.86848e9	0.396787
$764$	1.34962e6	0.000109493 0
$765$	−6.86133e9	−0.554107
$766$	2.93545e10	2.35979
$767$	−8.81082e8	−0.0705070
$768$	2.05335e10	1.63568
$769$	1.06115e10	0.841459	0.420729	−	0.907186i	$-0.361774\pi$
$769$	1.06115e10	0.841459	0.420729	+	0.907186i	$0.361774\pi$
$770$	−1.49553e9	−0.118053
$771$	1.91485e10	1.50468
$772$	−9.79522e9	−0.766221
$773$	2.28147e9	0.177659	0.0888293	−	0.996047i	$-0.471687\pi$
$773$	2.28147e9	0.177659	0.0888293	+	0.996047i	$0.471687\pi$
$774$	7.74112e9	0.600082
$775$	7.61023e8	0.0587276
$776$	−1.18403e10	−0.909592
$777$	2.34811e8	0.0179575
$778$	−2.76630e10	−2.10606
$779$	−3.52311e10	−2.67021
$780$	−5.77582e9	−0.435795
$781$	−1.73230e9	−0.130120
$782$	8.66169e9	0.647708
$783$	1.14508e10	0.852451
$784$	2.15347e9	0.159600
$785$	−3.54551e9	−0.261598
$786$	3.09954e9	0.227677
$787$	−1.90675e10	−1.39438	−0.697190	−	0.716887i	$-0.745567\pi$
$787$	−1.90675e10	−1.39438	−0.697190	+	0.716887i	$0.745567\pi$
$788$	−3.39049e10	−2.46843
$789$	−1.06569e10	−0.772436
$790$	3.58166e9	0.258458
$791$	3.49480e8	0.0251076
$792$	−1.66155e9	−0.118844
$793$	3.25203e9	0.231578
$794$	−6.75493e9	−0.478905
$795$	1.41943e10	1.00191
$796$	−3.58173e10	−2.51708
$797$	−6.37094e9	−0.445758	−0.222879	−	0.974846i	$-0.571546\pi$
$797$	−6.37094e9	−0.445758	−0.222879	+	0.974846i	$0.571546\pi$
$798$	1.19165e10	0.830113
$799$	7.23235e9	0.501609
$800$	−1.69741e8	−0.0117212
$801$	−1.77573e9	−0.122085
$802$	−4.04196e10	−2.76682
$803$	1.79026e9	0.122014
$804$	−4.05493e10	−2.75161
$805$	1.20189e9	0.0812041
$806$	4.93546e9	0.332013
$807$	9.08986e9	0.608835
$808$	−3.90798e10	−2.60623
$809$	−3.56810e9	−0.236929	−0.118464	−	0.992958i	$-0.537797\pi$
$809$	−3.56810e9	−0.236929	−0.118464	+	0.992958i	$0.537797\pi$
$810$	1.32848e10	0.878329
$811$	2.62050e10	1.72509	0.862545	−	0.505980i	$-0.168869\pi$
$811$	2.62050e10	1.72509	0.862545	+	0.505980i	$0.168869\pi$
$812$	9.20675e9	0.603476
$813$	−2.00617e9	−0.130933
$814$	−2.96264e8	−0.0192528
$815$	1.86503e10	1.20680
$816$	2.31150e10	1.48928
$817$	2.39422e10	1.53599
$818$	−1.87191e10	−1.19577
$819$	5.77395e8	0.0367265
$820$	−5.25771e10	−3.33003
$821$	−2.20019e10	−1.38758	−0.693792	−	0.720175i	$-0.744061\pi$
$821$	−2.20019e10	−1.38758	−0.693792	+	0.720175i	$0.744061\pi$
$822$	3.78178e10	2.37490
$823$	−1.50413e10	−0.940557	−0.470279	−	0.882518i	$-0.655847\pi$
$823$	−1.50413e10	−0.940557	−0.470279	+	0.882518i	$0.655847\pi$
$824$	4.13749e10	2.57627
$825$	2.08297e8	0.0129150
$826$	2.71281e9	0.167490
$827$	−1.70192e10	−1.04633	−0.523167	−	0.852230i	$-0.675250\pi$
$827$	−1.70192e10	−1.04633	−0.523167	+	0.852230i	$0.675250\pi$
$828$	2.62102e9	0.160459
$829$	−2.24482e10	−1.36849	−0.684244	−	0.729253i	$-0.739868\pi$
$829$	−2.24482e10	−1.36849	−0.684244	+	0.729253i	$0.739868\pi$
$830$	4.75932e10	2.88916
$831$	−1.15589e8	−0.00698733
$832$	4.04662e9	0.243591
$833$	−3.94153e9	−0.236270
$834$	−2.42456e10	−1.44727
$835$	1.41086e10	0.838651
$836$	−1.00870e10	−0.597093
$837$	−1.26799e10	−0.747443
$838$	3.30042e10	1.93738
$839$	6.85489e9	0.400713	0.200357	−	0.979723i	$-0.435790\pi$
$839$	6.85489e9	0.400713	0.200357	+	0.979723i	$0.435790\pi$
$840$	9.05999e9	0.527412
$841$	−6.66824e9	−0.386567
$842$	3.19537e10	1.84471
$843$	1.67302e10	0.961846
$844$	−5.22313e10	−2.99042
$845$	−1.29016e9	−0.0735605
$846$	3.26205e9	0.185223
$847$	−6.44943e9	−0.364695
$848$	2.57880e10	1.45222
$849$	−9.22955e9	−0.517611
$850$	4.41425e9	0.246542
$851$	2.38093e8	0.0132432
$852$	2.05989e10	1.14105
$853$	−1.29247e10	−0.713016	−0.356508	−	0.934292i	$-0.616033\pi$
$853$	−1.29247e10	−0.713016	−0.356508	+	0.934292i	$0.616033\pi$
$854$	−1.00129e10	−0.550118
$855$	−9.57151e9	−0.523720
$856$	−9.27301e9	−0.505316
$857$	2.00943e10	1.09053	0.545267	−	0.838263i	$-0.316428\pi$
$857$	2.00943e10	1.09053	0.545267	+	0.838263i	$0.316428\pi$
$858$	1.35087e9	0.0730143
$859$	1.71602e10	0.923731	0.461865	−	0.886950i	$-0.347180\pi$
$859$	1.71602e10	0.923731	0.461865	+	0.886950i	$0.347180\pi$
$860$	3.57301e10	1.91553
$861$	−9.74622e9	−0.520386
$862$	−2.57217e10	−1.36781
$863$	2.05372e10	1.08769	0.543844	−	0.839187i	$-0.316968\pi$
$863$	2.05372e10	1.08769	0.543844	+	0.839187i	$0.316968\pi$
$864$	2.82818e9	0.149180
$865$	3.17159e9	0.166618
$866$	2.57370e10	1.34662
$867$	−2.68406e10	−1.39870
$868$	−1.01950e10	−0.529138
$869$	−5.62006e8	−0.0290517
$870$	2.04392e10	1.05232
$871$	−9.05760e9	−0.464461
$872$	3.72122e10	1.90054
$873$	3.46039e9	0.176025
$874$	1.20830e10	0.612188
$875$	7.77506e9	0.392352
$876$	−2.12881e10	−1.06997
$877$	−3.71793e10	−1.86124	−0.930621	−	0.365985i	$-0.880732\pi$
$877$	−3.71793e10	−1.86124	−0.930621	+	0.365985i	$0.880732\pi$
$878$	−2.95241e10	−1.47213
$879$	−1.40369e10	−0.697125
$880$	−4.04682e9	−0.200182
$881$	−4.96727e9	−0.244738	−0.122369	−	0.992485i	$-0.539049\pi$
$881$	−4.96727e9	−0.244738	−0.122369	+	0.992485i	$0.539049\pi$
$882$	−1.77777e9	−0.0872442
$883$	−6.51783e9	−0.318596	−0.159298	−	0.987231i	$-0.550923\pi$
$883$	−6.51783e9	−0.318596	−0.159298	+	0.987231i	$0.550923\pi$
$884$	1.92063e10	0.935104
$885$	4.04049e9	0.195944
$886$	6.53505e9	0.315668
$887$	2.90108e9	0.139581	0.0697906	−	0.997562i	$-0.477767\pi$
$887$	2.90108e9	0.139581	0.0697906	+	0.997562i	$0.477767\pi$
$888$	1.79478e9	0.0860131
$889$	6.09311e9	0.290859
$890$	−1.22166e10	−0.580880
$891$	−2.08455e9	−0.0987278
$892$	5.67946e10	2.67935
$893$	1.00891e10	0.474101
$894$	−8.53652e9	−0.399576
$895$	3.88779e10	1.81269
$896$	−1.35748e10	−0.630458
$897$	−1.08563e9	−0.0502236
$898$	4.93901e10	2.27600
$899$	−1.17175e10	−0.537868
$900$	1.33575e9	0.0610767
$901$	−4.72001e10	−2.14984
$902$	1.22969e10	0.557922
$903$	6.62330e9	0.299342
$904$	2.67125e9	0.120261
$905$	4.99949e9	0.224211
$906$	−2.18914e10	−0.977969
$907$	2.03940e10	0.907563	0.453781	−	0.891113i	$-0.350075\pi$
$907$	2.03940e10	0.907563	0.453781	+	0.891113i	$0.350075\pi$
$908$	−2.48816e10	−1.10301
$909$	1.14213e10	0.504361
$910$	3.97234e9	0.174744
$911$	2.24329e10	0.983039	0.491520	−	0.870867i	$-0.336442\pi$
$911$	2.24329e10	0.983039	0.491520	+	0.870867i	$0.336442\pi$
$912$	3.22452e10	1.40761
$913$	−7.46795e9	−0.324753
$914$	7.83085e10	3.39232
$915$	−1.49132e10	−0.643573
$916$	−1.49631e10	−0.643261
$917$	−1.43017e9	−0.0612484
$918$	−7.35489e10	−3.13781
$919$	2.76064e10	1.17329	0.586646	−	0.809843i	$-0.300448\pi$
$919$	2.76064e10	1.17329	0.586646	+	0.809843i	$0.300448\pi$
$920$	9.18661e9	0.388953
$921$	1.23098e10	0.519209
$922$	−6.77410e10	−2.84639
$923$	4.60122e9	0.192605
$924$	−2.79045e9	−0.116365
$925$	1.21339e8	0.00504085
$926$	−5.77044e10	−2.38820
$927$	−1.20921e10	−0.498564
$928$	2.61351e9	0.107351
$929$	−1.28569e10	−0.526117	−0.263058	−	0.964780i	$-0.584731\pi$
$929$	−1.28569e10	−0.526117	−0.263058	+	0.964780i	$0.584731\pi$
$930$	−2.26332e10	−0.922688
$931$	−5.49841e9	−0.223313
$932$	−5.14547e10	−2.08194
$933$	−4.07769e9	−0.164372
$934$	−4.38325e10	−1.76028
$935$	7.40695e9	0.296346
$936$	4.41331e9	0.175914
$937$	−1.00158e10	−0.397739	−0.198869	−	0.980026i	$-0.563727\pi$
$937$	−1.00158e10	−0.397739	−0.198869	+	0.980026i	$0.563727\pi$
$938$	2.78880e10	1.10333
$939$	−1.65255e10	−0.651367
$940$	1.50564e10	0.591253
$941$	−2.14718e10	−0.840048	−0.420024	−	0.907513i	$-0.637978\pi$
$941$	−2.14718e10	−0.840048	−0.420024	+	0.907513i	$0.637978\pi$
$942$	−9.86053e9	−0.384346
$943$	−9.88243e9	−0.383772
$944$	7.34070e9	0.284011
$945$	−1.02055e10	−0.393392
$946$	−8.35669e9	−0.320934
$947$	2.30987e10	0.883819	0.441909	−	0.897060i	$-0.354301\pi$
$947$	2.30987e10	0.883819	0.441909	+	0.897060i	$0.354301\pi$
$948$	6.68286e9	0.254761
$949$	−4.75517e9	−0.180607
$950$	6.15784e9	0.233022
$951$	1.29809e9	0.0489411
$952$	−3.01271e10	−1.13169
$953$	3.67962e10	1.37714	0.688569	−	0.725171i	$-0.258239\pi$
$953$	3.67962e10	1.37714	0.688569	+	0.725171i	$0.258239\pi$
$954$	−2.12890e10	−0.793844
$955$	−1.38248e6	−5.13626e−5 0
$956$	1.03005e11	3.81291
$957$	−3.20716e9	−0.118285
$958$	8.23826e10	3.02731
$959$	−1.74496e10	−0.638882
$960$	−1.85571e10	−0.676956
$961$	−1.45374e10	−0.528389
$962$	7.86918e8	0.0284981
$963$	2.71009e9	0.0977894
$964$	2.30780e10	0.829714
$965$	1.00337e10	0.359431
$966$	3.34260e9	0.119307
$967$	3.13628e10	1.11538	0.557688	−	0.830050i	$-0.311688\pi$
$967$	3.13628e10	1.11538	0.557688	+	0.830050i	$0.311688\pi$
$968$	−4.92962e10	−1.74683
$969$	−5.90188e10	−2.08381
$970$	2.38067e10	0.837526
$971$	4.18010e10	1.46527	0.732637	−	0.680620i	$-0.238289\pi$
$971$	4.18010e10	1.46527	0.732637	+	0.680620i	$0.238289\pi$
$972$	−3.87374e10	−1.35300
$973$	1.11872e10	0.389338
$974$	3.30177e10	1.14496
$975$	−5.53267e8	−0.0191170
$976$	−2.70942e10	−0.932827
$977$	−2.49112e10	−0.854602	−0.427301	−	0.904109i	$-0.640536\pi$
$977$	−2.49112e10	−0.854602	−0.427301	+	0.904109i	$0.640536\pi$
$978$	5.18690e10	1.77305
$979$	1.91694e9	0.0652933
$980$	−8.20554e9	−0.278494
$981$	−1.08755e10	−0.367796
$982$	5.57314e10	1.87806
$983$	4.82462e10	1.62004	0.810020	−	0.586402i	$-0.199456\pi$
$983$	4.82462e10	1.62004	0.810020	+	0.586402i	$0.199456\pi$
$984$	−7.44952e10	−2.49256
$985$	3.47304e10	1.15793
$986$	−6.79662e10	−2.25800
$987$	2.79101e9	0.0923956
$988$	2.67926e10	0.883824
$989$	6.71586e9	0.220757
$990$	3.34080e9	0.109428
$991$	−7.04655e9	−0.229995	−0.114998	−	0.993366i	$-0.536686\pi$
$991$	−7.04655e9	−0.229995	−0.114998	+	0.993366i	$0.536686\pi$
$992$	−2.89405e9	−0.0941272
$993$	−6.08265e8	−0.0197138
$994$	−1.41670e10	−0.457535
$995$	3.66894e10	1.18075
$996$	8.88020e10	2.84784
$997$	5.44384e10	1.73969	0.869845	−	0.493325i	$-0.164219\pi$
$997$	5.44384e10	1.73969	0.869845	+	0.493325i	$0.164219\pi$
$998$	−8.63759e10	−2.75065
$999$	−2.02171e9	−0.0641564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.c.1.10	✓	10	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)

\(f(q)\)	\(=\)	\(q+19.7215 q^{2} -37.6933 q^{3} +260.937 q^{4} -267.290 q^{5} -743.369 q^{6} +343.000 q^{7} +2621.72 q^{8} -766.212 q^{9} +O(q^{10})\)	\(q+19.7215 q^{2} -37.6933 q^{3} +260.937 q^{4} -267.290 q^{5} -743.369 q^{6} +343.000 q^{7} +2621.72 q^{8} -766.212 q^{9} -5271.36 q^{10} +827.140 q^{11} -9835.59 q^{12} -2197.00 q^{13} +6764.47 q^{14} +10075.1 q^{15} +18304.2 q^{16} -33502.5 q^{17} -15110.8 q^{18} -46735.7 q^{19} -69745.9 q^{20} -12928.8 q^{21} +16312.4 q^{22} -13109.5 q^{23} -98821.3 q^{24} -6680.98 q^{25} -43328.1 q^{26} +111316. q^{27} +89501.4 q^{28} +102867. q^{29} +198695. q^{30} -113909. q^{31} +25406.7 q^{32} -31177.7 q^{33} -660719. q^{34} -91680.5 q^{35} -199933. q^{36} -18161.8 q^{37} -921698. q^{38} +82812.3 q^{39} -700759. q^{40} +753837. q^{41} -254976. q^{42} -512289. q^{43} +215832. q^{44} +204801. q^{45} -258539. q^{46} -215875. q^{47} -689947. q^{48} +117649. q^{49} -131759. q^{50} +1.26282e6 q^{51} -573279. q^{52} +1.40885e6 q^{53} +2.19533e6 q^{54} -221086. q^{55} +899249. q^{56} +1.76163e6 q^{57} +2.02869e6 q^{58} +401039. q^{59} +2.62896e6 q^{60} -1.48021e6 q^{61} -2.24645e6 q^{62} -262811. q^{63} -1.84188e6 q^{64} +587236. q^{65} -614870. q^{66} +4.12271e6 q^{67} -8.74204e6 q^{68} +494141. q^{69} -1.80808e6 q^{70} -2.09432e6 q^{71} -2.00879e6 q^{72} +2.16439e6 q^{73} -358178. q^{74} +251828. q^{75} -1.21951e7 q^{76} +283709. q^{77} +1.63318e6 q^{78} -679457. q^{79} -4.89254e6 q^{80} -2.52018e6 q^{81} +1.48668e7 q^{82} -9.02864e6 q^{83} -3.37361e6 q^{84} +8.95488e6 q^{85} -1.01031e7 q^{86} -3.87740e6 q^{87} +2.16853e6 q^{88} +2.31755e6 q^{89} +4.03898e6 q^{90} -753571. q^{91} -3.42076e6 q^{92} +4.29361e6 q^{93} -4.25738e6 q^{94} +1.24920e7 q^{95} -957663. q^{96} -4.51624e6 q^{97} +2.32021e6 q^{98} -633765. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9} + 9420 q^{10} + 876 q^{11} - 8765 q^{12} - 21970 q^{13} - 6174 q^{14} - 5320 q^{15} + 41370 q^{16} + 6294 q^{17} - 16027 q^{18} - 97401 q^{19} - 166650 q^{20} - 27440 q^{21} + 74171 q^{22} - 15255 q^{23} + 196187 q^{24} + 162145 q^{25} + 39546 q^{26} - 181820 q^{27} + 229810 q^{28} - 340533 q^{29} - 325020 q^{30} - 148675 q^{31} - 642762 q^{32} - 624400 q^{33} - 1161518 q^{34} - 317961 q^{35} - 773917 q^{36} - 621782 q^{37} - 805092 q^{38} + 175760 q^{39} - 350478 q^{40} - 2043336 q^{41} - 486717 q^{42} - 1801391 q^{43} - 3953667 q^{44} - 1908807 q^{45} - 2707731 q^{46} - 1624701 q^{47} - 6068625 q^{48} + 1176490 q^{49} - 6891516 q^{50} + 1811700 q^{51} - 1471990 q^{52} - 199965 q^{53} - 2895913 q^{54} + 739086 q^{55} - 1673154 q^{56} + 2159088 q^{57} + 2071092 q^{58} - 8098908 q^{59} + 8096436 q^{60} + 2271618 q^{61} - 8910225 q^{62} + 1238916 q^{63} + 8099930 q^{64} + 2036619 q^{65} - 5999191 q^{66} + 1970272 q^{67} - 1766238 q^{68} - 4622962 q^{69} + 3231060 q^{70} - 7145820 q^{71} + 984975 q^{72} + 1409431 q^{73} - 5498643 q^{74} - 8857892 q^{75} - 2749534 q^{76} + 300468 q^{77} + 3117543 q^{78} - 9011055 q^{79} - 23850522 q^{80} + 11613490 q^{81} + 27962597 q^{82} - 15006567 q^{83} - 3006395 q^{84} - 9416628 q^{85} + 38357850 q^{86} - 15828996 q^{87} + 42205269 q^{88} - 11472777 q^{89} + 53425712 q^{90} - 7535710 q^{91} + 16755837 q^{92} + 36339848 q^{93} + 5133371 q^{94} + 29637939 q^{95} + 65329611 q^{96} + 3228571 q^{97} - 2117682 q^{98} + 19367194 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 80 * q^3 + 670 * q^4 - 927 * q^5 - 1419 * q^6 + 3430 * q^7 - 4878 * q^8 + 3612 * q^9 + 9420 * q^10 + 876 * q^11 - 8765 * q^12 - 21970 * q^13 - 6174 * q^14 - 5320 * q^15 + 41370 * q^16 + 6294 * q^17 - 16027 * q^18 - 97401 * q^19 - 166650 * q^20 - 27440 * q^21 + 74171 * q^22 - 15255 * q^23 + 196187 * q^24 + 162145 * q^25 + 39546 * q^26 - 181820 * q^27 + 229810 * q^28 - 340533 * q^29 - 325020 * q^30 - 148675 * q^31 - 642762 * q^32 - 624400 * q^33 - 1161518 * q^34 - 317961 * q^35 - 773917 * q^36 - 621782 * q^37 - 805092 * q^38 + 175760 * q^39 - 350478 * q^40 - 2043336 * q^41 - 486717 * q^42 - 1801391 * q^43 - 3953667 * q^44 - 1908807 * q^45 - 2707731 * q^46 - 1624701 * q^47 - 6068625 * q^48 + 1176490 * q^49 - 6891516 * q^50 + 1811700 * q^51 - 1471990 * q^52 - 199965 * q^53 - 2895913 * q^54 + 739086 * q^55 - 1673154 * q^56 + 2159088 * q^57 + 2071092 * q^58 - 8098908 * q^59 + 8096436 * q^60 + 2271618 * q^61 - 8910225 * q^62 + 1238916 * q^63 + 8099930 * q^64 + 2036619 * q^65 - 5999191 * q^66 + 1970272 * q^67 - 1766238 * q^68 - 4622962 * q^69 + 3231060 * q^70 - 7145820 * q^71 + 984975 * q^72 + 1409431 * q^73 - 5498643 * q^74 - 8857892 * q^75 - 2749534 * q^76 + 300468 * q^77 + 3117543 * q^78 - 9011055 * q^79 - 23850522 * q^80 + 11613490 * q^81 + 27962597 * q^82 - 15006567 * q^83 - 3006395 * q^84 - 9416628 * q^85 + 38357850 * q^86 - 15828996 * q^87 + 42205269 * q^88 - 11472777 * q^89 + 53425712 * q^90 - 7535710 * q^91 + 16755837 * q^92 + 36339848 * q^93 + 5133371 * q^94 + 29637939 * q^95 + 65329611 * q^96 + 3228571 * q^97 - 2117682 * q^98 + 19367194 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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