LMFDB - Embedded newform 91.8.a.c.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:	$1$
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			1.4
Root			$-9.51136$ 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)

$f(q)$	$=$	$q-11.5114 q^{2} +23.9058 q^{3} +4.51150 q^{4} -301.396 q^{5} -275.188 q^{6} +343.000 q^{7} +1421.52 q^{8} -1615.51 q^{9} +O(q^{10})$	\(q-11.5114 q^{2} +23.9058 q^{3} +4.51150 q^{4} -301.396 q^{5} -275.188 q^{6} +343.000 q^{7} +1421.52 q^{8} -1615.51 q^{9} +3469.48 q^{10} +8165.11 q^{11} +107.851 q^{12} -2197.00 q^{13} -3948.40 q^{14} -7205.13 q^{15} -16941.1 q^{16} -18445.8 q^{17} +18596.7 q^{18} +25451.2 q^{19} -1359.75 q^{20} +8199.69 q^{21} -93991.6 q^{22} +100507. q^{23} +33982.6 q^{24} +12714.8 q^{25} +25290.5 q^{26} -90902.1 q^{27} +1547.44 q^{28} +1639.36 q^{29} +82940.8 q^{30} -183210. q^{31} +13060.7 q^{32} +195194. q^{33} +212337. q^{34} -103379. q^{35} -7288.38 q^{36} +564340. q^{37} -292978. q^{38} -52521.1 q^{39} -428441. q^{40} -738171. q^{41} -94389.6 q^{42} -759297. q^{43} +36836.9 q^{44} +486910. q^{45} -1.15698e6 q^{46} -1.10773e6 q^{47} -404991. q^{48} +117649. q^{49} -146365. q^{50} -440963. q^{51} -9911.76 q^{52} -822620. q^{53} +1.04641e6 q^{54} -2.46094e6 q^{55} +487582. q^{56} +608432. q^{57} -18871.3 q^{58} -768137. q^{59} -32505.9 q^{60} -1.66731e6 q^{61} +2.10900e6 q^{62} -554121. q^{63} +2.01812e6 q^{64} +662168. q^{65} -2.24694e6 q^{66} +1.69335e6 q^{67} -83218.4 q^{68} +2.40271e6 q^{69} +1.19003e6 q^{70} -3.19149e6 q^{71} -2.29648e6 q^{72} -1.83029e6 q^{73} -6.49632e6 q^{74} +303958. q^{75} +114823. q^{76} +2.80063e6 q^{77} +604589. q^{78} +4.85216e6 q^{79} +5.10599e6 q^{80} +1.36004e6 q^{81} +8.49735e6 q^{82} -3.84497e6 q^{83} +36992.9 q^{84} +5.55951e6 q^{85} +8.74055e6 q^{86} +39190.2 q^{87} +1.16069e7 q^{88} -2.37126e6 q^{89} -5.60499e6 q^{90} -753571. q^{91} +453439. q^{92} -4.37979e6 q^{93} +1.27515e7 q^{94} -7.67091e6 q^{95} +312226. q^{96} -4.74338e6 q^{97} -1.35430e6 q^{98} -1.31908e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.5114	−1.01747	−0.508735	−	0.860923i	$-0.669887\pi$
$2$	−11.5114	−1.01747	−0.508735	+	0.860923i	$0.669887\pi$
$3$	23.9058	0.511186	0.255593	−	0.966784i	$-0.417729\pi$
$3$	23.9058	0.511186	0.255593	+	0.966784i	$0.417729\pi$
$4$	4.51150	0.0352461
$5$	−301.396	−1.07831	−0.539154	−	0.842207i	$-0.681256\pi$
$5$	−301.396	−1.07831	−0.539154	+	0.842207i	$0.681256\pi$
$6$	−275.188	−0.520117
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	1421.52	0.981609
$9$	−1615.51	−0.738689
$10$	3469.48	1.09715
$11$	8165.11	1.84964	0.924821	−	0.380403i	$-0.124215\pi$
$11$	8165.11	1.84964	0.924821	+	0.380403i	$0.124215\pi$
$12$	107.851	0.0180173
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−3948.40	−0.384568
$15$	−7205.13	−0.551217
$16$	−16941.1	−1.03400
$17$	−18445.8	−0.910599	−0.455299	−	0.890338i	$-0.650468\pi$
$17$	−18445.8	−0.910599	−0.455299	+	0.890338i	$0.650468\pi$
$18$	18596.7	0.751594
$19$	25451.2	0.851278	0.425639	−	0.904893i	$-0.360049\pi$
$19$	25451.2	0.851278	0.425639	+	0.904893i	$0.360049\pi$
$20$	−1359.75	−0.0380062
$21$	8199.69	0.193210
$22$	−93991.6	−1.88196
$23$	100507.	1.72246	0.861232	−	0.508212i	$-0.169693\pi$
$23$	100507.	1.72246	0.861232	+	0.508212i	$0.169693\pi$
$24$	33982.6	0.501785
$25$	12714.8	0.162750
$26$	25290.5	0.282196
$27$	−90902.1	−0.888794
$28$	1547.44	0.0133218
$29$	1639.36	0.0124819	0.00624096	−	0.999981i	$-0.498013\pi$
$29$	1639.36	0.0124819	0.00624096	+	0.999981i	$0.498013\pi$
$30$	82940.8	0.560847
$31$	−183210.	−1.10455	−0.552274	−	0.833663i	$-0.686240\pi$
$31$	−183210.	−1.10455	−0.552274	+	0.833663i	$0.686240\pi$
$32$	13060.7	0.0704597
$33$	195194.	0.945511
$34$	212337.	0.926508
$35$	−103379.	−0.407562
$36$	−7288.38	−0.0260359
$37$	564340.	1.83162	0.915808	−	0.401615i	$-0.131551\pi$
$37$	564340.	1.83162	0.915808	+	0.401615i	$0.131551\pi$
$38$	−292978.	−0.866150
$39$	−52521.1	−0.141778
$40$	−428441.	−1.05848
$41$	−738171.	−1.67268	−0.836341	−	0.548209i	$-0.815310\pi$
$41$	−738171.	−1.67268	−0.836341	+	0.548209i	$0.815310\pi$
$42$	−94389.6	−0.196586
$43$	−759297.	−1.45637	−0.728186	−	0.685380i	$-0.759636\pi$
$43$	−759297.	−1.45637	−0.728186	+	0.685380i	$0.759636\pi$
$44$	36836.9	0.0651926
$45$	486910.	0.796535
$46$	−1.15698e6	−1.75256
$47$	−1.10773e6	−1.55630	−0.778150	−	0.628078i	$-0.783842\pi$
$47$	−1.10773e6	−1.55630	−0.778150	+	0.628078i	$0.783842\pi$
$48$	−404991.	−0.528568
$49$	117649.	0.142857
$50$	−146365.	−0.165593
$51$	−440963.	−0.465486
$52$	−9911.76	−0.00977551
$53$	−822620.	−0.758986	−0.379493	−	0.925195i	$-0.623901\pi$
$53$	−822620.	−0.758986	−0.379493	+	0.925195i	$0.623901\pi$
$54$	1.04641e6	0.904321
$55$	−2.46094e6	−1.99449
$56$	487582.	0.371013
$57$	608432.	0.435161
$58$	−18871.3	−0.0127000
$59$	−768137.	−0.486919	−0.243459	−	0.969911i	$-0.578282\pi$
$59$	−768137.	−0.486919	−0.243459	+	0.969911i	$0.578282\pi$
$60$	−32505.9	−0.0194282
$61$	−1.66731e6	−0.940508	−0.470254	−	0.882531i	$-0.655838\pi$
$61$	−1.66731e6	−0.940508	−0.470254	+	0.882531i	$0.655838\pi$
$62$	2.10900e6	1.12384
$63$	−554121.	−0.279198
$64$	2.01812e6	0.962313
$65$	662168.	0.299069
$66$	−2.24694e6	−0.962030
$67$	1.69335e6	0.687835	0.343917	−	0.939000i	$-0.388246\pi$
$67$	1.69335e6	0.687835	0.343917	+	0.939000i	$0.388246\pi$
$68$	−83218.4	−0.0320951
$69$	2.40271e6	0.880500
$70$	1.19003e6	0.414683
$71$	−3.19149e6	−1.05825	−0.529127	−	0.848543i	$-0.677480\pi$
$71$	−3.19149e6	−1.05825	−0.529127	+	0.848543i	$0.677480\pi$
$72$	−2.29648e6	−0.725103
$73$	−1.83029e6	−0.550668	−0.275334	−	0.961349i	$-0.588789\pi$
$73$	−1.83029e6	−0.550668	−0.275334	+	0.961349i	$0.588789\pi$
$74$	−6.49632e6	−1.86362
$75$	303958.	0.0831955
$76$	114823.	0.0300042
$77$	2.80063e6	0.699099
$78$	604589.	0.144254
$79$	4.85216e6	1.10724	0.553618	−	0.832771i	$-0.313247\pi$
$79$	4.85216e6	1.10724	0.553618	+	0.832771i	$0.313247\pi$
$80$	5.10599e6	1.11498
$81$	1.36004e6	0.284350
$82$	8.49735e6	1.70190
$83$	−3.84497e6	−0.738107	−0.369053	−	0.929408i	$-0.620318\pi$
$83$	−3.84497e6	−0.738107	−0.369053	+	0.929408i	$0.620318\pi$
$84$	36992.9	0.00680990
$85$	5.55951e6	0.981907
$86$	8.74055e6	1.48182
$87$	39190.2	0.00638058
$88$	1.16069e7	1.81562
$89$	−2.37126e6	−0.356545	−0.178272	−	0.983981i	$-0.557051\pi$
$89$	−2.37126e6	−0.356545	−0.178272	+	0.983981i	$0.557051\pi$
$90$	−5.60499e6	−0.810450
$91$	−753571.	−0.104828
$92$	453439.	0.0607101
$93$	−4.37979e6	−0.564629
$94$	1.27515e7	1.58349
$95$	−7.67091e6	−0.917940
$96$	312226.	0.0360180
$97$	−4.74338e6	−0.527700	−0.263850	−	0.964564i	$-0.584992\pi$
$97$	−4.74338e6	−0.527700	−0.263850	+	0.964564i	$0.584992\pi$
$98$	−1.35430e6	−0.145353
$99$	−1.31908e7	−1.36631
$100$	57363.0	0.00573630
$101$	8.69794e6	0.840024	0.420012	−	0.907519i	$-0.362026\pi$
$101$	8.69794e6	0.840024	0.420012	+	0.907519i	$0.362026\pi$
$102$	5.07608e6	0.473618
$103$	5.63467e6	0.508087	0.254043	−	0.967193i	$-0.418239\pi$
$103$	5.63467e6	0.508087	0.254043	+	0.967193i	$0.418239\pi$
$104$	−3.12308e6	−0.272249
$105$	−2.47136e6	−0.208340
$106$	9.46947e6	0.772245
$107$	−3.33224e6	−0.262962	−0.131481	−	0.991319i	$-0.541973\pi$
$107$	−3.33224e6	−0.262962	−0.131481	+	0.991319i	$0.541973\pi$
$108$	−410105.	−0.0313265
$109$	181248.	0.0134054	0.00670270	−	0.999978i	$-0.497866\pi$
$109$	181248.	0.0134054	0.00670270	+	0.999978i	$0.497866\pi$
$110$	2.83287e7	2.02933
$111$	1.34910e7	0.936297
$112$	−5.81080e6	−0.390817
$113$	−1.78210e7	−1.16187	−0.580935	−	0.813950i	$-0.697313\pi$
$113$	−1.78210e7	−1.16187	−0.580935	+	0.813950i	$0.697313\pi$
$114$	−7.00389e6	−0.442764
$115$	−3.02925e7	−1.85735
$116$	7395.97	0.000439939 0
$117$	3.54928e6	0.204875
$118$	8.84231e6	0.495426
$119$	−6.32692e6	−0.344174
$120$	−1.02422e7	−0.541079
$121$	4.71819e7	2.42118
$122$	1.91930e7	0.956939
$123$	−1.76466e7	−0.855052
$124$	−826554.	−0.0389310
$125$	1.97144e7	0.902814
$126$	6.37869e6	0.284076
$127$	−4.53740e7	−1.96560	−0.982798	−	0.184685i	$-0.940874\pi$
$127$	−4.53740e7	−1.96560	−0.982798	+	0.184685i	$0.940874\pi$
$128$	−2.49030e7	−1.04958
$129$	−1.81516e7	−0.744477
$130$	−7.62246e6	−0.304294
$131$	−4.50612e6	−0.175127	−0.0875636	−	0.996159i	$-0.527908\pi$
$131$	−4.50612e6	−0.175127	−0.0875636	+	0.996159i	$0.527908\pi$
$132$	880616.	0.0333256
$133$	8.72977e6	0.321753
$134$	−1.94927e7	−0.699852
$135$	2.73976e7	0.958394
$136$	−2.62211e7	−0.893852
$137$	−2.00557e7	−0.666372	−0.333186	−	0.942861i	$-0.608124\pi$
$137$	−2.00557e7	−0.666372	−0.333186	+	0.942861i	$0.608124\pi$
$138$	−2.76585e7	−0.895883
$139$	5.63022e7	1.77817	0.889085	−	0.457742i	$-0.151342\pi$
$139$	5.63022e7	1.77817	0.889085	+	0.457742i	$0.151342\pi$
$140$	−466394.	−0.0143650
$141$	−2.64813e7	−0.795559
$142$	3.67384e7	1.07674
$143$	−1.79387e7	−0.512998
$144$	2.73686e7	0.763807
$145$	−494097.	−0.0134594
$146$	2.10691e7	0.560289
$147$	2.81249e6	0.0730266
$148$	2.54602e6	0.0645573
$149$	−1.35095e7	−0.334571	−0.167285	−	0.985909i	$-0.553500\pi$
$149$	−1.35095e7	−0.334571	−0.167285	+	0.985909i	$0.553500\pi$
$150$	−3.49898e6	−0.0846489
$151$	−4.15725e7	−0.982624	−0.491312	−	0.870984i	$-0.663482\pi$
$151$	−4.15725e7	−0.982624	−0.491312	+	0.870984i	$0.663482\pi$
$152$	3.61795e7	0.835621
$153$	2.97995e7	0.672649
$154$	−3.22391e7	−0.711313
$155$	5.52190e7	1.19104
$156$	−236949.	−0.00499710
$157$	5.56692e7	1.14806	0.574032	−	0.818833i	$-0.305378\pi$
$157$	5.56692e7	1.14806	0.574032	+	0.818833i	$0.305378\pi$
$158$	−5.58550e7	−1.12658
$159$	−1.96654e7	−0.387983
$160$	−3.93644e6	−0.0759773
$161$	3.44740e7	0.651030
$162$	−1.56559e7	−0.289317
$163$	−1.25415e7	−0.226826	−0.113413	−	0.993548i	$-0.536178\pi$
$163$	−1.25415e7	−0.226826	−0.113413	+	0.993548i	$0.536178\pi$
$164$	−3.33026e6	−0.0589555
$165$	−5.88307e7	−1.01955
$166$	4.42608e7	0.751002
$167$	4.76687e7	0.792001	0.396000	−	0.918250i	$-0.370398\pi$
$167$	4.76687e7	0.792001	0.396000	+	0.918250i	$0.370398\pi$
$168$	1.16560e7	0.189657
$169$	4.82681e6	0.0769231
$170$	−6.39975e7	−0.999061
$171$	−4.11168e7	−0.628829
$172$	−3.42557e6	−0.0513314
$173$	−9.74049e7	−1.43028	−0.715138	−	0.698984i	$-0.753636\pi$
$173$	−9.74049e7	−1.43028	−0.715138	+	0.698984i	$0.753636\pi$
$174$	−451133.	−0.00649206
$175$	4.36119e6	0.0615137
$176$	−1.38326e8	−1.91254
$177$	−1.83629e7	−0.248906
$178$	2.72964e7	0.362774
$179$	1.24140e8	1.61781	0.808905	−	0.587939i	$-0.200061\pi$
$179$	1.24140e8	1.61781	0.808905	+	0.587939i	$0.200061\pi$
$180$	2.19669e6	0.0280747
$181$	−5.09706e7	−0.638918	−0.319459	−	0.947600i	$-0.603501\pi$
$181$	−5.09706e7	−0.638918	−0.319459	+	0.947600i	$0.603501\pi$
$182$	8.67463e6	0.106660
$183$	−3.98585e7	−0.480775
$184$	1.42873e8	1.69079
$185$	−1.70090e8	−1.97505
$186$	5.04174e7	0.574494
$187$	−1.50612e8	−1.68428
$188$	−4.99755e6	−0.0548535
$189$	−3.11794e7	−0.335932
$190$	8.83027e7	0.933977
$191$	−8.85715e7	−0.919766	−0.459883	−	0.887979i	$-0.652109\pi$
$191$	−8.85715e7	−0.919766	−0.459883	+	0.887979i	$0.652109\pi$
$192$	4.82447e7	0.491921
$193$	1.60849e7	0.161053	0.0805264	−	0.996752i	$-0.474340\pi$
$193$	1.60849e7	0.161053	0.0805264	+	0.996752i	$0.474340\pi$
$194$	5.46028e7	0.536919
$195$	1.58297e7	0.152880
$196$	530773.	0.00503516
$197$	−7.18559e7	−0.669624	−0.334812	−	0.942285i	$-0.608673\pi$
$197$	−7.18559e7	−0.669624	−0.334812	+	0.942285i	$0.608673\pi$
$198$	1.51845e8	1.39018
$199$	−1.69138e8	−1.52144	−0.760721	−	0.649079i	$-0.775154\pi$
$199$	−1.69138e8	−1.52144	−0.760721	+	0.649079i	$0.775154\pi$
$200$	1.80744e7	0.159757
$201$	4.04808e7	0.351612
$202$	−1.00125e8	−0.854699
$203$	562300.	0.00471772
$204$	−1.98940e6	−0.0164065
$205$	2.22482e8	1.80367
$206$	−6.48627e7	−0.516963
$207$	−1.62371e8	−1.27236
$208$	3.72196e7	0.286781
$209$	2.07812e8	1.57456
$210$	2.84487e7	0.211980
$211$	−2.36714e7	−0.173474	−0.0867372	−	0.996231i	$-0.527644\pi$
$211$	−2.36714e7	−0.173474	−0.0867372	+	0.996231i	$0.527644\pi$
$212$	−3.71125e6	−0.0267513
$213$	−7.62952e7	−0.540965
$214$	3.83587e7	0.267556
$215$	2.28850e8	1.57042
$216$	−1.29219e8	−0.872447
$217$	−6.28412e7	−0.417480
$218$	−2.08641e6	−0.0136396
$219$	−4.37546e7	−0.281494
$220$	−1.11025e7	−0.0702978
$221$	4.05255e7	0.252555
$222$	−1.55300e8	−0.952655
$223$	−2.27490e8	−1.37371	−0.686855	−	0.726795i	$-0.741009\pi$
$223$	−2.27490e8	−1.37371	−0.686855	+	0.726795i	$0.741009\pi$
$224$	4.47981e6	0.0266313
$225$	−2.05410e7	−0.120221
$226$	2.05144e8	1.18217
$227$	1.57710e8	0.894886	0.447443	−	0.894313i	$-0.352335\pi$
$227$	1.57710e8	0.894886	0.447443	+	0.894313i	$0.352335\pi$
$228$	2.74494e6	0.0153377
$229$	1.97476e8	1.08665	0.543325	−	0.839522i	$-0.317165\pi$
$229$	1.97476e8	1.08665	0.543325	+	0.839522i	$0.317165\pi$
$230$	3.48709e8	1.88980
$231$	6.69514e7	0.357370
$232$	2.33038e6	0.0122524
$233$	−8.59413e7	−0.445099	−0.222549	−	0.974921i	$-0.571438\pi$
$233$	−8.59413e7	−0.445099	−0.222549	+	0.974921i	$0.571438\pi$
$234$	−4.08571e7	−0.208455
$235$	3.33867e8	1.67817
$236$	−3.46545e6	−0.0171620
$237$	1.15995e8	0.566004
$238$	7.28315e7	0.350187
$239$	−2.62303e8	−1.24283	−0.621413	−	0.783483i	$-0.713441\pi$
$239$	−2.62303e8	−1.24283	−0.621413	+	0.783483i	$0.713441\pi$
$240$	1.22063e8	0.569960
$241$	−1.78206e7	−0.0820090	−0.0410045	−	0.999159i	$-0.513056\pi$
$241$	−1.78206e7	−0.0820090	−0.0410045	+	0.999159i	$0.513056\pi$
$242$	−5.43128e8	−2.46347
$243$	2.31316e8	1.03415
$244$	−7.52208e6	−0.0331492
$245$	−3.54590e7	−0.154044
$246$	2.03136e8	0.869990
$247$	−5.59164e7	−0.236102
$248$	−2.60438e8	−1.08423
$249$	−9.19170e7	−0.377310
$250$	−2.26940e8	−0.918587
$251$	−3.88360e8	−1.55016	−0.775079	−	0.631864i	$-0.782290\pi$
$251$	−3.88360e8	−1.55016	−0.775079	+	0.631864i	$0.782290\pi$
$252$	−2.49992e6	−0.00984064
$253$	8.20653e8	3.18594
$254$	5.22317e8	1.99994
$255$	1.32905e8	0.501937
$256$	2.83491e7	0.105608
$257$	−1.76175e8	−0.647410	−0.323705	−	0.946158i	$-0.604929\pi$
$257$	−1.76175e8	−0.647410	−0.323705	+	0.946158i	$0.604929\pi$
$258$	2.08950e8	0.757484
$259$	1.93569e8	0.692286
$260$	2.98737e6	0.0105410
$261$	−2.64841e6	−0.00922025
$262$	5.18716e7	0.178187
$263$	−2.45839e8	−0.833309	−0.416654	−	0.909065i	$-0.636797\pi$
$263$	−2.45839e8	−0.833309	−0.416654	+	0.909065i	$0.636797\pi$
$264$	2.77472e8	0.928122
$265$	2.47935e8	0.818421
$266$	−1.00492e8	−0.327374
$267$	−5.66868e7	−0.182261
$268$	7.63953e6	0.0242435
$269$	−3.98799e8	−1.24917	−0.624584	−	0.780957i	$-0.714732\pi$
$269$	−3.98799e8	−1.24917	−0.624584	+	0.780957i	$0.714732\pi$
$270$	−3.15384e8	−0.975137
$271$	−2.09254e8	−0.638678	−0.319339	−	0.947641i	$-0.603461\pi$
$271$	−2.09254e8	−0.638678	−0.319339	+	0.947641i	$0.603461\pi$
$272$	3.12493e8	0.941563
$273$	−1.80147e7	−0.0535869
$274$	2.30869e8	0.678013
$275$	1.03818e8	0.301029
$276$	1.08398e7	0.0310342
$277$	1.29079e8	0.364902	0.182451	−	0.983215i	$-0.441597\pi$
$277$	1.29079e8	0.364902	0.182451	+	0.983215i	$0.441597\pi$
$278$	−6.48115e8	−1.80924
$279$	2.95979e8	0.815917
$280$	−1.46955e8	−0.400067
$281$	−2.90525e8	−0.781109	−0.390555	−	0.920580i	$-0.627717\pi$
$281$	−2.90525e8	−0.781109	−0.390555	+	0.920580i	$0.627717\pi$
$282$	3.04836e8	0.809458
$283$	2.86057e8	0.750241	0.375120	−	0.926976i	$-0.377601\pi$
$283$	2.86057e8	0.750241	0.375120	+	0.926976i	$0.377601\pi$
$284$	−1.43984e7	−0.0372993
$285$	−1.83379e8	−0.469238
$286$	2.06499e8	0.521961
$287$	−2.53193e8	−0.632214
$288$	−2.10997e7	−0.0520478
$289$	−7.00897e7	−0.170809
$290$	5.68773e6	0.0136945
$291$	−1.13394e8	−0.269753
$292$	−8.25736e6	−0.0194089
$293$	5.16778e8	1.20024	0.600118	−	0.799911i	$-0.295120\pi$
$293$	5.16778e8	1.20024	0.600118	+	0.799911i	$0.295120\pi$
$294$	−3.23756e7	−0.0743024
$295$	2.31514e8	0.525049
$296$	8.02221e8	1.79793
$297$	−7.42226e8	−1.64395
$298$	1.55513e8	0.340416
$299$	−2.20815e8	−0.477726
$300$	1.37131e6	0.00293231
$301$	−2.60439e8	−0.550457
$302$	4.78557e8	0.999791
$303$	2.07931e8	0.429408
$304$	−4.31172e8	−0.880224
$305$	5.02522e8	1.01416
$306$	−3.43033e8	−0.684401
$307$	1.57322e8	0.310317	0.155159	−	0.987890i	$-0.450411\pi$
$307$	1.57322e8	0.310317	0.155159	+	0.987890i	$0.450411\pi$
$308$	1.26351e7	0.0246405
$309$	1.34701e8	0.259727
$310$	−6.35646e8	−1.21185
$311$	−1.02817e9	−1.93823	−0.969113	−	0.246619i	$-0.920680\pi$
$311$	−1.02817e9	−1.93823	−0.969113	+	0.246619i	$0.920680\pi$
$312$	−7.46598e7	−0.139170
$313$	−5.94891e7	−0.109656	−0.0548280	−	0.998496i	$-0.517461\pi$
$313$	−5.94891e7	−0.109656	−0.0548280	+	0.998496i	$0.517461\pi$
$314$	−6.40829e8	−1.16812
$315$	1.67010e8	0.301062
$316$	2.18905e7	0.0390257
$317$	−6.27861e8	−1.10702	−0.553511	−	0.832842i	$-0.686712\pi$
$317$	−6.27861e8	−1.10702	−0.553511	+	0.832842i	$0.686712\pi$
$318$	2.26375e8	0.394761
$319$	1.33856e7	0.0230871
$320$	−6.08253e8	−1.03767
$321$	−7.96600e7	−0.134423
$322$	−3.96843e8	−0.662404
$323$	−4.69469e8	−0.775173
$324$	6.13580e6	0.0100222
$325$	−2.79345e7	−0.0451387
$326$	1.44370e8	0.230789
$327$	4.33288e6	0.00685266
$328$	−1.04933e9	−1.64192
$329$	−3.79953e8	−0.588226
$330$	6.77221e8	1.03737
$331$	5.86045e8	0.888245	0.444123	−	0.895966i	$-0.353515\pi$
$331$	5.86045e8	0.888245	0.444123	+	0.895966i	$0.353515\pi$
$332$	−1.73466e7	−0.0260154
$333$	−9.11698e8	−1.35299
$334$	−5.48732e8	−0.805837
$335$	−5.10369e8	−0.741698
$336$	−1.38912e8	−0.199780
$337$	1.27872e9	1.82000	0.910002	−	0.414605i	$-0.136080\pi$
$337$	1.27872e9	1.82000	0.910002	+	0.414605i	$0.136080\pi$
$338$	−5.55632e7	−0.0782670
$339$	−4.26026e8	−0.593932
$340$	2.50817e7	0.0346084
$341$	−1.49593e9	−2.04302
$342$	4.73310e8	0.639815
$343$	4.03536e7	0.0539949
$344$	−1.07936e9	−1.42959
$345$	−7.24168e8	−0.949451
$346$	1.12126e9	1.45526
$347$	1.13865e9	1.46298	0.731490	−	0.681852i	$-0.238825\pi$
$347$	1.13865e9	1.46298	0.731490	+	0.681852i	$0.238825\pi$
$348$	176807.	0.000224891 0
$349$	−9.59006e8	−1.20763	−0.603813	−	0.797126i	$-0.706353\pi$
$349$	−9.59006e8	−1.20763	−0.603813	+	0.797126i	$0.706353\pi$
$350$	−5.02032e7	−0.0625883
$351$	1.99712e8	0.246507
$352$	1.06642e8	0.130325
$353$	1.12980e8	0.136707	0.0683536	−	0.997661i	$-0.478225\pi$
$353$	1.12980e8	0.136707	0.0683536	+	0.997661i	$0.478225\pi$
$354$	2.11382e8	0.253255
$355$	9.61905e8	1.14112
$356$	−1.06979e7	−0.0125668
$357$	−1.51250e8	−0.175937
$358$	−1.42903e9	−1.64607
$359$	−2.35730e8	−0.268896	−0.134448	−	0.990921i	$-0.542926\pi$
$359$	−2.35730e8	−0.268896	−0.134448	+	0.990921i	$0.542926\pi$
$360$	6.92152e8	0.781885
$361$	−2.46107e8	−0.275326
$362$	5.86742e8	0.650080
$363$	1.12792e9	1.23767
$364$	−3.39974e6	−0.00369479
$365$	5.51643e8	0.593791
$366$	4.58825e8	0.489174
$367$	1.21921e9	1.28750	0.643748	−	0.765238i	$-0.277379\pi$
$367$	1.21921e9	1.28750	0.643748	+	0.765238i	$0.277379\pi$
$368$	−1.70271e9	−1.78103
$369$	1.19252e9	1.23559
$370$	1.95797e9	2.00955
$371$	−2.82159e8	−0.286870
$372$	−1.97594e7	−0.0199010
$373$	1.62860e9	1.62492	0.812462	−	0.583013i	$-0.198127\pi$
$373$	1.62860e9	1.62492	0.812462	+	0.583013i	$0.198127\pi$
$374$	1.73375e9	1.71371
$375$	4.71289e8	0.461506
$376$	−1.57467e9	−1.52768
$377$	−3.60167e6	−0.00346186
$378$	3.58918e8	0.341801
$379$	−7.52232e8	−0.709765	−0.354882	−	0.934911i	$-0.615479\pi$
$379$	−7.52232e8	−0.709765	−0.354882	+	0.934911i	$0.615479\pi$
$380$	−3.46073e7	−0.0323538
$381$	−1.08470e9	−1.00479
$382$	1.01958e9	0.935835
$383$	−7.70245e7	−0.0700540	−0.0350270	−	0.999386i	$-0.511152\pi$
$383$	−7.70245e7	−0.0700540	−0.0350270	+	0.999386i	$0.511152\pi$
$384$	−5.95327e8	−0.536533
$385$	−8.44101e8	−0.753845
$386$	−1.85159e8	−0.163866
$387$	1.22665e9	1.07581
$388$	−2.13998e7	−0.0185993
$389$	−6.01354e8	−0.517973	−0.258986	−	0.965881i	$-0.583388\pi$
$389$	−6.01354e8	−0.517973	−0.258986	+	0.965881i	$0.583388\pi$
$390$	−1.82221e8	−0.155551
$391$	−1.85394e9	−1.56847
$392$	1.67241e8	0.140230
$393$	−1.07722e8	−0.0895226
$394$	8.27160e8	0.681322
$395$	−1.46242e9	−1.19394
$396$	−5.95104e7	−0.0481571
$397$	−1.83806e9	−1.47433	−0.737163	−	0.675715i	$-0.763835\pi$
$397$	−1.83806e9	−1.47433	−0.737163	+	0.675715i	$0.763835\pi$
$398$	1.94701e9	1.54802
$399$	2.08692e8	0.164476
$400$	−2.15403e8	−0.168284
$401$	1.40955e9	1.09163	0.545817	−	0.837905i	$-0.316220\pi$
$401$	1.40955e9	1.09163	0.545817	+	0.837905i	$0.316220\pi$
$402$	−4.65990e8	−0.357754
$403$	4.02513e8	0.306346
$404$	3.92407e7	0.0296075
$405$	−4.09910e8	−0.306617
$406$	−6.47285e6	−0.00480014
$407$	4.60790e9	3.38784
$408$	−6.26838e8	−0.456925
$409$	2.23639e9	1.61628	0.808140	−	0.588990i	$-0.200474\pi$
$409$	2.23639e9	1.61628	0.808140	+	0.588990i	$0.200474\pi$
$410$	−2.56107e9	−1.83518
$411$	−4.79448e8	−0.340640
$412$	2.54208e7	0.0179081
$413$	−2.63471e8	−0.184038
$414$	1.86911e9	1.29459
$415$	1.15886e9	0.795907
$416$	−2.86943e7	−0.0195420
$417$	1.34595e9	0.908976
$418$	−2.39220e9	−1.60207
$419$	1.46487e9	0.972859	0.486429	−	0.873720i	$-0.338299\pi$
$419$	1.46487e9	0.972859	0.486429	+	0.873720i	$0.338299\pi$
$420$	−1.11495e7	−0.00734318
$421$	1.43831e9	0.939430	0.469715	−	0.882818i	$-0.344357\pi$
$421$	1.43831e9	0.939430	0.469715	+	0.882818i	$0.344357\pi$
$422$	2.72490e8	0.176505
$423$	1.78956e9	1.14962
$424$	−1.16937e9	−0.745027
$425$	−2.34536e8	−0.148200
$426$	8.78262e8	0.550415
$427$	−5.71888e8	−0.355479
$428$	−1.50334e7	−0.00926839
$429$	−4.28840e8	−0.262238
$430$	−2.63437e9	−1.59785
$431$	−7.35475e8	−0.442484	−0.221242	−	0.975219i	$-0.571011\pi$
$431$	−7.35475e8	−0.442484	−0.221242	+	0.975219i	$0.571011\pi$
$432$	1.53998e9	0.919016
$433$	1.13801e9	0.673658	0.336829	−	0.941566i	$-0.390646\pi$
$433$	1.13801e9	0.673658	0.336829	+	0.941566i	$0.390646\pi$
$434$	7.23388e8	0.424773
$435$	−1.18118e7	−0.00688024
$436$	817699.	0.000472488 0
$437$	2.55803e9	1.46630
$438$	5.03675e8	0.286412
$439$	2.06154e9	1.16297	0.581483	−	0.813559i	$-0.302473\pi$
$439$	2.06154e9	1.16297	0.581483	+	0.813559i	$0.302473\pi$
$440$	−3.49827e9	−1.95780
$441$	−1.90063e8	−0.105527
$442$	−4.66504e8	−0.256967
$443$	1.06794e9	0.583624	0.291812	−	0.956476i	$-0.405742\pi$
$443$	1.06794e9	0.583624	0.291812	+	0.956476i	$0.405742\pi$
$444$	6.08646e7	0.0330008
$445$	7.14689e8	0.384465
$446$	2.61872e9	1.39771
$447$	−3.22956e8	−0.171028
$448$	6.92214e8	0.363720
$449$	−5.31935e7	−0.0277330	−0.0138665	−	0.999904i	$-0.504414\pi$
$449$	−5.31935e7	−0.0277330	−0.0138665	+	0.999904i	$0.504414\pi$
$450$	2.36455e8	0.122322
$451$	−6.02725e9	−3.09386
$452$	−8.03995e7	−0.0409514
$453$	−9.93825e8	−0.502304
$454$	−1.81545e9	−0.910520
$455$	2.27124e8	0.113037
$456$	8.64899e8	0.427158
$457$	−4.22053e8	−0.206852	−0.103426	−	0.994637i	$-0.532981\pi$
$457$	−4.22053e8	−0.206852	−0.103426	+	0.994637i	$0.532981\pi$
$458$	−2.27322e9	−1.10563
$459$	1.67677e9	0.809335
$460$	−1.36665e8	−0.0654643
$461$	8.15164e8	0.387518	0.193759	−	0.981049i	$-0.437932\pi$
$461$	8.15164e8	0.387518	0.193759	+	0.981049i	$0.437932\pi$
$462$	−7.70702e8	−0.363613
$463$	−8.00723e8	−0.374929	−0.187464	−	0.982271i	$-0.560027\pi$
$463$	−8.00723e8	−0.374929	−0.187464	+	0.982271i	$0.560027\pi$
$464$	−2.77726e7	−0.0129064
$465$	1.32005e9	0.608845
$466$	9.89302e8	0.452875
$467$	−1.74070e9	−0.790887	−0.395444	−	0.918490i	$-0.629409\pi$
$467$	−1.74070e9	−0.790887	−0.395444	+	0.918490i	$0.629409\pi$
$468$	1.60126e7	0.00722106
$469$	5.80818e8	0.259977
$470$	−3.84327e9	−1.70749
$471$	1.33082e9	0.586875
$472$	−1.09192e9	−0.477964
$473$	−6.19975e9	−2.69377
$474$	−1.33526e9	−0.575892
$475$	3.23608e8	0.138545
$476$	−2.85439e7	−0.0121308
$477$	1.32895e9	0.560654
$478$	3.01946e9	1.26454
$479$	−2.49945e9	−1.03913	−0.519565	−	0.854431i	$-0.673906\pi$
$479$	−2.49945e9	−1.03913	−0.519565	+	0.854431i	$0.673906\pi$
$480$	−9.41039e7	−0.0388386
$481$	−1.23985e9	−0.507999
$482$	2.05139e8	0.0834417
$483$	8.24129e8	0.332798
$484$	2.12861e8	0.0853370
$485$	1.42964e9	0.569023
$486$	−2.66276e9	−1.05222
$487$	−3.88076e8	−0.152253	−0.0761265	−	0.997098i	$-0.524255\pi$
$487$	−3.88076e8	−0.152253	−0.0761265	+	0.997098i	$0.524255\pi$
$488$	−2.37012e9	−0.923211
$489$	−2.99815e8	−0.115950
$490$	4.08181e8	0.156735
$491$	−1.73317e9	−0.660778	−0.330389	−	0.943845i	$-0.607180\pi$
$491$	−1.73317e9	−0.660778	−0.330389	+	0.943845i	$0.607180\pi$
$492$	−7.96125e7	−0.0301372
$493$	−3.02394e7	−0.0113660
$494$	6.43674e8	0.240227
$495$	3.97567e9	1.47330
$496$	3.10379e9	1.14211
$497$	−1.09468e9	−0.399982
$498$	1.05809e9	0.383902
$499$	2.45395e9	0.884127	0.442063	−	0.896984i	$-0.354247\pi$
$499$	2.45395e9	0.884127	0.442063	+	0.896984i	$0.354247\pi$
$500$	8.89415e7	0.0318207
$501$	1.13956e9	0.404860
$502$	4.47055e9	1.57724
$503$	2.23819e9	0.784169	0.392084	−	0.919929i	$-0.371754\pi$
$503$	2.23819e9	0.784169	0.392084	+	0.919929i	$0.371754\pi$
$504$	−7.87694e8	−0.274063
$505$	−2.62153e9	−0.905805
$506$	−9.44684e9	−3.24160
$507$	1.15389e8	0.0393220
$508$	−2.04705e8	−0.0692796
$509$	1.62022e9	0.544580	0.272290	−	0.962215i	$-0.412219\pi$
$509$	1.62022e9	0.544580	0.272290	+	0.962215i	$0.412219\pi$
$510$	−1.52991e9	−0.510706
$511$	−6.27790e8	−0.208133
$512$	2.86125e9	0.942131
$513$	−2.31357e9	−0.756610
$514$	2.02802e9	0.658720
$515$	−1.69827e9	−0.547874
$516$	−8.18910e7	−0.0262399
$517$	−9.04478e9	−2.87860
$518$	−2.22824e9	−0.704381
$519$	−2.32854e9	−0.731137
$520$	9.41286e8	0.293569
$521$	1.97614e9	0.612189	0.306095	−	0.952001i	$-0.400978\pi$
$521$	1.97614e9	0.612189	0.306095	+	0.952001i	$0.400978\pi$
$522$	3.04868e7	0.00938133
$523$	−5.67139e8	−0.173354	−0.0866769	−	0.996236i	$-0.527625\pi$
$523$	−5.67139e8	−0.173354	−0.0866769	+	0.996236i	$0.527625\pi$
$524$	−2.03294e7	−0.00617255
$525$	1.04258e8	0.0314449
$526$	2.82994e9	0.847867
$527$	3.37947e9	1.00580
$528$	−3.30680e9	−0.977662
$529$	6.69689e9	1.96688
$530$	−2.85407e9	−0.832719
$531$	1.24093e9	0.359682
$532$	3.93844e7	0.0113405
$533$	1.62176e9	0.463919
$534$	6.52543e8	0.185445
$535$	1.00433e9	0.283555
$536$	2.40713e9	0.675184
$537$	2.96768e9	0.827002
$538$	4.59072e9	1.27099
$539$	9.60617e8	0.264235
$540$	1.23604e8	0.0337796
$541$	−1.24208e9	−0.337256	−0.168628	−	0.985680i	$-0.553934\pi$
$541$	−1.24208e9	−0.337256	−0.168628	+	0.985680i	$0.553934\pi$
$542$	2.40880e9	0.649836
$543$	−1.21849e9	−0.326606
$544$	−2.40915e8	−0.0641605
$545$	−5.46274e7	−0.0144552
$546$	2.07374e8	0.0545231
$547$	−6.42413e9	−1.67826	−0.839129	−	0.543932i	$-0.816935\pi$
$547$	−6.42413e9	−1.67826	−0.839129	+	0.543932i	$0.816935\pi$
$548$	−9.04814e7	−0.0234870
$549$	2.69356e9	0.694743
$550$	−1.19509e9	−0.306288
$551$	4.17237e7	0.0106256
$552$	3.41550e9	0.864306
$553$	1.66429e9	0.418496
$554$	−1.48587e9	−0.371277
$555$	−4.06614e9	−1.00962
$556$	2.54007e8	0.0626735
$557$	−2.72192e9	−0.667395	−0.333697	−	0.942680i	$-0.608296\pi$
$557$	−2.72192e9	−0.667395	−0.333697	+	0.942680i	$0.608296\pi$
$558$	−3.40712e9	−0.830171
$559$	1.66818e9	0.403925
$560$	1.75136e9	0.421421
$561$	−3.60051e9	−0.860982
$562$	3.34434e9	0.794756
$563$	4.65154e9	1.09854	0.549272	−	0.835644i	$-0.314905\pi$
$563$	4.65154e9	1.09854	0.549272	+	0.835644i	$0.314905\pi$
$564$	−1.19470e8	−0.0280403
$565$	5.37119e9	1.25286
$566$	−3.29291e9	−0.763348
$567$	4.66492e8	0.107474
$568$	−4.53678e9	−1.03879
$569$	−1.93553e9	−0.440461	−0.220231	−	0.975448i	$-0.570681\pi$
$569$	−1.93553e9	−0.440461	−0.220231	+	0.975448i	$0.570681\pi$
$570$	2.11095e9	0.477436
$571$	1.43480e9	0.322526	0.161263	−	0.986911i	$-0.448443\pi$
$571$	1.43480e9	0.322526	0.161263	+	0.986911i	$0.448443\pi$
$572$	−8.09306e7	−0.0180812
$573$	−2.11737e9	−0.470172
$574$	2.91459e9	0.643260
$575$	1.27793e9	0.280331
$576$	−3.26029e9	−0.710850
$577$	−4.15398e9	−0.900222	−0.450111	−	0.892973i	$-0.648616\pi$
$577$	−4.15398e9	−0.900222	−0.450111	+	0.892973i	$0.648616\pi$
$578$	8.06829e8	0.173794
$579$	3.84523e8	0.0823279
$580$	−2.22912e6	−0.000474390 0
$581$	−1.31882e9	−0.278978
$582$	1.30532e9	0.274465
$583$	−6.71678e9	−1.40385
$584$	−2.60180e9	−0.540541
$585$	−1.06974e9	−0.220919
$586$	−5.94881e9	−1.22121
$587$	3.56244e9	0.726967	0.363483	−	0.931601i	$-0.381587\pi$
$587$	3.56244e9	0.726967	0.363483	+	0.931601i	$0.381587\pi$
$588$	1.26886e7	0.00257390
$589$	−4.66293e9	−0.940277
$590$	−2.66504e9	−0.534222
$591$	−1.71777e9	−0.342302
$592$	−9.56055e9	−1.89390
$593$	5.37876e9	1.05923	0.529615	−	0.848238i	$-0.322336\pi$
$593$	5.37876e9	1.05923	0.529615	+	0.848238i	$0.322336\pi$
$594$	8.54403e9	1.67267
$595$	1.90691e9	0.371126
$596$	−6.09482e7	−0.0117923
$597$	−4.04338e9	−0.777740
$598$	2.54188e9	0.486072
$599$	6.26420e9	1.19089	0.595446	−	0.803396i	$-0.296976\pi$
$599$	6.26420e9	1.19089	0.595446	+	0.803396i	$0.296976\pi$
$600$	4.32083e8	0.0816654
$601$	4.78903e8	0.0899885	0.0449942	−	0.998987i	$-0.485673\pi$
$601$	4.78903e8	0.0899885	0.0449942	+	0.998987i	$0.485673\pi$
$602$	2.99801e9	0.560074
$603$	−2.73562e9	−0.508096
$604$	−1.87554e8	−0.0346336
$605$	−1.42204e10	−2.61077
$606$	−2.39357e9	−0.436910
$607$	5.46225e9	0.991313	0.495657	−	0.868519i	$-0.334927\pi$
$607$	5.46225e9	0.991313	0.495657	+	0.868519i	$0.334927\pi$
$608$	3.32410e8	0.0599808
$609$	1.34422e7	0.00241163
$610$	−5.78471e9	−1.03188
$611$	2.43369e9	0.431640
$612$	1.34440e8	0.0237083
$613$	3.36384e9	0.589826	0.294913	−	0.955524i	$-0.404709\pi$
$613$	3.36384e9	0.589826	0.294913	+	0.955524i	$0.404709\pi$
$614$	−1.81099e9	−0.315739
$615$	5.31862e9	0.922010
$616$	3.98116e9	0.686242
$617$	−7.89816e8	−0.135372	−0.0676858	−	0.997707i	$-0.521562\pi$
$617$	−7.89816e8	−0.135372	−0.0676858	+	0.997707i	$0.521562\pi$
$618$	−1.55060e9	−0.264264
$619$	5.58082e9	0.945760	0.472880	−	0.881127i	$-0.343214\pi$
$619$	5.58082e9	0.945760	0.472880	+	0.881127i	$0.343214\pi$
$620$	2.49120e8	0.0419796
$621$	−9.13633e9	−1.53092
$622$	1.18357e10	1.97209
$623$	−8.13342e8	−0.134761
$624$	8.89766e8	0.146599
$625$	−6.93519e9	−1.13626
$626$	6.84801e8	0.111572
$627$	4.96792e9	0.804893
$628$	2.51152e8	0.0404648
$629$	−1.04097e10	−1.66787
$630$	−1.92251e9	−0.306321
$631$	−7.62952e9	−1.20891	−0.604455	−	0.796639i	$-0.706609\pi$
$631$	−7.62952e9	−1.20891	−0.604455	+	0.796639i	$0.706609\pi$
$632$	6.89745e9	1.08687
$633$	−5.65884e8	−0.0886777
$634$	7.22754e9	1.12636
$635$	1.36756e10	2.11952
$636$	−8.87204e7	−0.0136749
$637$	−2.58475e8	−0.0396214
$638$	−1.54086e8	−0.0234904
$639$	5.15590e9	0.781720
$640$	7.50569e9	1.13178
$641$	7.41046e8	0.111133	0.0555663	−	0.998455i	$-0.482304\pi$
$641$	7.41046e8	0.111133	0.0555663	+	0.998455i	$0.482304\pi$
$642$	9.16995e8	0.136771
$643$	−2.66540e9	−0.395388	−0.197694	−	0.980264i	$-0.563345\pi$
$643$	−2.66540e9	−0.395388	−0.197694	+	0.980264i	$0.563345\pi$
$644$	1.55529e8	0.0229463
$645$	5.47083e9	0.802776
$646$	5.40423e9	0.788715
$647$	2.53599e9	0.368114	0.184057	−	0.982916i	$-0.441077\pi$
$647$	2.53599e9	0.368114	0.184057	+	0.982916i	$0.441077\pi$
$648$	1.93332e9	0.279120
$649$	−6.27192e9	−0.900626
$650$	3.21564e8	0.0459273
$651$	−1.50227e9	−0.213410
$652$	−5.65809e7	−0.00799472
$653$	3.39054e9	0.476511	0.238256	−	0.971202i	$-0.423424\pi$
$653$	3.39054e9	0.476511	0.238256	+	0.971202i	$0.423424\pi$
$654$	−4.98773e7	−0.00697238
$655$	1.35813e9	0.188841
$656$	1.25054e10	1.72956
$657$	2.95686e9	0.406773
$658$	4.37378e9	0.598503
$659$	−8.84416e9	−1.20381	−0.601904	−	0.798568i	$-0.705591\pi$
$659$	−8.84416e9	−1.20381	−0.601904	+	0.798568i	$0.705591\pi$
$660$	−2.65414e8	−0.0359353
$661$	−6.20676e9	−0.835911	−0.417955	−	0.908468i	$-0.637253\pi$
$661$	−6.20676e9	−0.835911	−0.417955	+	0.908468i	$0.637253\pi$
$662$	−6.74618e9	−0.903763
$663$	9.68795e8	0.129102
$664$	−5.46570e9	−0.724532
$665$	−2.63112e9	−0.346949
$666$	1.04949e10	1.37663
$667$	1.64768e8	0.0214997
$668$	2.15057e8	0.0279149
$669$	−5.43833e9	−0.702221
$670$	5.87504e9	0.754656
$671$	−1.36138e10	−1.73960
$672$	1.07094e8	0.0136135
$673$	1.76630e9	0.223363	0.111682	−	0.993744i	$-0.464376\pi$
$673$	1.76630e9	0.223363	0.111682	+	0.993744i	$0.464376\pi$
$674$	−1.47199e10	−1.85180
$675$	−1.15581e9	−0.144651
$676$	2.17761e7	0.00271124
$677$	−5.83167e9	−0.722325	−0.361162	−	0.932503i	$-0.617620\pi$
$677$	−5.83167e9	−0.722325	−0.361162	+	0.932503i	$0.617620\pi$
$678$	4.90414e9	0.604309
$679$	−1.62698e9	−0.199452
$680$	7.90296e9	0.963848
$681$	3.77018e9	0.457453
$682$	1.72202e10	2.07871
$683$	4.08372e9	0.490437	0.245219	−	0.969468i	$-0.421140\pi$
$683$	4.08372e9	0.490437	0.245219	+	0.969468i	$0.421140\pi$
$684$	−1.85498e8	−0.0221638
$685$	6.04473e9	0.718554
$686$	−4.64525e8	−0.0549382
$687$	4.72082e9	0.555481
$688$	1.28633e10	1.50589
$689$	1.80730e9	0.210505
$690$	8.33616e9	0.966038
$691$	1.04320e9	0.120280	0.0601402	−	0.998190i	$-0.480845\pi$
$691$	1.04320e9	0.120280	0.0601402	+	0.998190i	$0.480845\pi$
$692$	−4.39442e8	−0.0504116
$693$	−4.52446e9	−0.516417
$694$	−1.31075e10	−1.48854
$695$	−1.69693e10	−1.91742
$696$	5.57097e7	0.00626324
$697$	1.36162e10	1.52314
$698$	1.10395e10	1.22872
$699$	−2.05450e9	−0.227528
$700$	1.96755e7	0.00216812
$701$	5.53065e9	0.606406	0.303203	−	0.952926i	$-0.401944\pi$
$701$	5.53065e9	0.606406	0.303203	+	0.952926i	$0.401944\pi$
$702$	−2.29896e9	−0.250814
$703$	1.43631e10	1.55921
$704$	1.64781e10	1.77993
$705$	7.98137e9	0.857858
$706$	−1.30056e9	−0.139096
$707$	2.98339e9	0.317499
$708$	−8.28444e7	−0.00877297
$709$	−1.54751e10	−1.63069	−0.815344	−	0.578977i	$-0.803452\pi$
$709$	−1.54751e10	−1.63069	−0.815344	+	0.578977i	$0.803452\pi$
$710$	−1.10728e10	−1.16106
$711$	−7.83872e9	−0.817903
$712$	−3.37079e9	−0.349987
$713$	−1.84140e10	−1.90254
$714$	1.74110e9	0.179011
$715$	5.40668e9	0.553171
$716$	5.60059e8	0.0570215
$717$	−6.27056e9	−0.635316
$718$	2.71358e9	0.273594
$719$	−1.67550e9	−0.168110	−0.0840551	−	0.996461i	$-0.526787\pi$
$719$	−1.67550e9	−0.168110	−0.0840551	+	0.996461i	$0.526787\pi$
$720$	−8.24879e9	−0.823620
$721$	1.93269e9	0.192039
$722$	2.83302e9	0.280136
$723$	−4.26015e8	−0.0419219
$724$	−2.29954e8	−0.0225194
$725$	2.08442e7	0.00203143
$726$	−1.29839e10	−1.25929
$727$	−1.85212e10	−1.78771	−0.893857	−	0.448352i	$-0.852011\pi$
$727$	−1.85212e10	−1.78771	−0.893857	+	0.448352i	$0.852011\pi$
$728$	−1.07122e9	−0.102901
$729$	2.55539e9	0.244293
$730$	−6.35017e9	−0.604164
$731$	1.40059e10	1.32617
$732$	−1.79821e8	−0.0169454
$733$	6.30733e9	0.591537	0.295768	−	0.955260i	$-0.404424\pi$
$733$	6.30733e9	0.591537	0.295768	+	0.955260i	$0.404424\pi$
$734$	−1.40347e10	−1.30999
$735$	−8.47676e8	−0.0787452
$736$	1.31269e9	0.121364
$737$	1.38264e10	1.27225
$738$	−1.37276e10	−1.25718
$739$	−4.89349e9	−0.446029	−0.223015	−	0.974815i	$-0.571590\pi$
$739$	−4.89349e9	−0.446029	−0.223015	+	0.974815i	$0.571590\pi$
$740$	−7.67361e8	−0.0696127
$741$	−1.33673e9	−0.120692
$742$	3.24803e9	0.291881
$743$	−5.97118e9	−0.534071	−0.267035	−	0.963687i	$-0.586044\pi$
$743$	−5.97118e9	−0.534071	−0.267035	+	0.963687i	$0.586044\pi$
$744$	−6.22597e9	−0.554245
$745$	4.07172e9	0.360771
$746$	−1.87474e10	−1.65331
$747$	6.21159e9	0.545231
$748$	−6.79487e8	−0.0593644
$749$	−1.14296e9	−0.0993904
$750$	−5.42517e9	−0.469569
$751$	3.33059e9	0.286934	0.143467	−	0.989655i	$-0.454175\pi$
$751$	3.33059e9	0.286934	0.143467	+	0.989655i	$0.454175\pi$
$752$	1.87663e10	1.60922
$753$	−9.28405e9	−0.792419
$754$	4.14602e7	0.00352234
$755$	1.25298e10	1.05957
$756$	−1.40666e8	−0.0118403
$757$	1.37350e10	1.15078	0.575392	−	0.817878i	$-0.304850\pi$
$757$	1.37350e10	1.15078	0.575392	+	0.817878i	$0.304850\pi$
$758$	8.65921e9	0.722165
$759$	1.96184e10	1.62861
$760$	−1.09044e10	−0.901058
$761$	−1.96227e9	−0.161404	−0.0807018	−	0.996738i	$-0.525716\pi$
$761$	−1.96227e9	−0.161404	−0.0807018	+	0.996738i	$0.525716\pi$
$762$	1.24864e10	1.02234
$763$	6.21680e7	0.00506677
$764$	−3.99590e8	−0.0324182
$765$	−8.98146e9	−0.725324
$766$	8.86657e8	0.0712779
$767$	1.68760e9	0.135047
$768$	6.77707e8	0.0539856
$769$	−1.39126e10	−1.10323	−0.551616	−	0.834098i	$-0.685989\pi$
$769$	−1.39126e10	−1.10323	−0.551616	+	0.834098i	$0.685989\pi$
$770$	9.71675e9	0.767015
$771$	−4.21162e9	−0.330947
$772$	7.25671e7	0.00567648
$773$	−2.28851e10	−1.78207	−0.891035	−	0.453935i	$-0.850020\pi$
$773$	−2.28851e10	−1.78207	−0.891035	+	0.453935i	$0.850020\pi$
$774$	−1.41205e10	−1.09460
$775$	−2.32949e9	−0.179765
$776$	−6.74281e9	−0.517994
$777$	4.62741e9	0.353887
$778$	6.92241e9	0.527022
$779$	−1.87874e10	−1.42392
$780$	7.14155e7	0.00538842
$781$	−2.60589e10	−1.95739
$782$	2.13414e10	1.59588
$783$	−1.49021e8	−0.0110938
$784$	−1.99311e9	−0.147715
$785$	−1.67785e10	−1.23797
$786$	1.24003e9	0.0910866
$787$	−2.79341e9	−0.204279	−0.102139	−	0.994770i	$-0.532569\pi$
$787$	−2.79341e9	−0.204279	−0.102139	+	0.994770i	$0.532569\pi$
$788$	−3.24178e8	−0.0236016
$789$	−5.87699e9	−0.425976
$790$	1.68345e10	1.21480
$791$	−6.11261e9	−0.439146
$792$	−1.87511e10	−1.34118
$793$	3.66309e9	0.260850
$794$	2.11586e10	1.50008
$795$	5.92708e9	0.418365
$796$	−7.63066e8	−0.0536249
$797$	−3.24938e9	−0.227351	−0.113675	−	0.993518i	$-0.536262\pi$
$797$	−3.24938e9	−0.227351	−0.113675	+	0.993518i	$0.536262\pi$
$798$	−2.40233e9	−0.167349
$799$	2.04331e10	1.41717
$800$	1.66064e8	0.0114673
$801$	3.83080e9	0.263375
$802$	−1.62259e10	−1.11070
$803$	−1.49445e10	−1.01854
$804$	1.82629e8	0.0123929
$805$	−1.03903e10	−0.702012
$806$	−4.63348e9	−0.311698
$807$	−9.53361e9	−0.638558
$808$	1.23643e10	0.824574
$809$	8.68513e9	0.576709	0.288354	−	0.957524i	$-0.406892\pi$
$809$	8.68513e9	0.576709	0.288354	+	0.957524i	$0.406892\pi$
$810$	4.71862e9	0.311974
$811$	−2.04298e10	−1.34491	−0.672453	−	0.740140i	$-0.734759\pi$
$811$	−2.04298e10	−1.34491	−0.672453	+	0.740140i	$0.734759\pi$
$812$	2.53682e6	0.000166281 0
$813$	−5.00240e9	−0.326483
$814$	−5.30432e10	−3.44702
$815$	3.77996e9	0.244588
$816$	7.47040e9	0.481314
$817$	−1.93251e10	−1.23978
$818$	−2.57439e10	−1.64452
$819$	1.21740e9	0.0774356
$820$	1.00373e9	0.0635722
$821$	−3.30893e9	−0.208682	−0.104341	−	0.994542i	$-0.533273\pi$
$821$	−3.30893e9	−0.208682	−0.104341	+	0.994542i	$0.533273\pi$
$822$	5.51911e9	0.346591
$823$	2.44310e10	1.52772	0.763858	−	0.645385i	$-0.223303\pi$
$823$	2.44310e10	1.52772	0.763858	+	0.645385i	$0.223303\pi$
$824$	8.00980e9	0.498742
$825$	2.48185e9	0.153882
$826$	3.03291e9	0.187253
$827$	1.79678e10	1.10465	0.552326	−	0.833628i	$-0.313740\pi$
$827$	1.79678e10	1.10465	0.552326	+	0.833628i	$0.313740\pi$
$828$	−7.32536e8	−0.0448459
$829$	5.72608e9	0.349073	0.174537	−	0.984651i	$-0.444157\pi$
$829$	5.72608e9	0.349073	0.174537	+	0.984651i	$0.444157\pi$
$830$	−1.33400e10	−0.809812
$831$	3.08574e9	0.186533
$832$	−4.43380e9	−0.266898
$833$	−2.17013e9	−0.130086
$834$	−1.54937e10	−0.924856
$835$	−1.43672e10	−0.854021
$836$	9.37544e8	0.0554970
$837$	1.66542e10	0.981715
$838$	−1.68626e10	−0.989855
$839$	2.01482e10	1.17779	0.588897	−	0.808208i	$-0.299562\pi$
$839$	2.01482e10	1.17779	0.588897	+	0.808208i	$0.299562\pi$
$840$	−3.51309e9	−0.204509
$841$	−1.72472e10	−0.999844
$842$	−1.65569e10	−0.955842
$843$	−6.94524e9	−0.399292
$844$	−1.06793e8	−0.00611429
$845$	−1.45478e9	−0.0829468
$846$	−2.06003e10	−1.16971
$847$	1.61834e10	0.915118
$848$	1.39361e10	0.784794
$849$	6.83843e9	0.383513
$850$	2.69983e9	0.150789
$851$	5.67203e10	3.15489
$852$	−3.44206e8	−0.0190669
$853$	2.16479e10	1.19425	0.597124	−	0.802149i	$-0.296310\pi$
$853$	2.16479e10	1.19425	0.597124	+	0.802149i	$0.296310\pi$
$854$	6.58321e9	0.361689
$855$	1.23925e10	0.678072
$856$	−4.73685e9	−0.258126
$857$	2.26970e10	1.23179	0.615895	−	0.787829i	$-0.288795\pi$
$857$	2.26970e10	1.23179	0.615895	+	0.787829i	$0.288795\pi$
$858$	4.93654e9	0.266819
$859$	3.63609e9	0.195731	0.0978654	−	0.995200i	$-0.468799\pi$
$859$	3.63609e9	0.195731	0.0978654	+	0.995200i	$0.468799\pi$
$860$	1.03245e9	0.0553511
$861$	−6.05278e9	−0.323179
$862$	8.46631e9	0.450214
$863$	3.06452e10	1.62302	0.811512	−	0.584336i	$-0.198645\pi$
$863$	3.06452e10	1.62302	0.811512	+	0.584336i	$0.198645\pi$
$864$	−1.18724e9	−0.0626241
$865$	2.93575e10	1.54228
$866$	−1.31001e10	−0.685427
$867$	−1.67555e9	−0.0873154
$868$	−2.83508e8	−0.0147145
$869$	3.96184e10	2.04799
$870$	1.35970e8	0.00700044
$871$	−3.72028e9	−0.190771
$872$	2.57648e8	0.0131589
$873$	7.66299e9	0.389806
$874$	−2.94465e10	−1.49191
$875$	6.76204e9	0.341232
$876$	−1.97399e8	−0.00992157
$877$	−5.57383e9	−0.279033	−0.139516	−	0.990220i	$-0.544555\pi$
$877$	−5.57383e9	−0.279033	−0.139516	+	0.990220i	$0.544555\pi$
$878$	−2.37312e10	−1.18328
$879$	1.23540e10	0.613544
$880$	4.16910e10	2.06231
$881$	1.74820e10	0.861340	0.430670	−	0.902509i	$-0.358277\pi$
$881$	1.74820e10	0.861340	0.430670	+	0.902509i	$0.358277\pi$
$882$	2.18789e9	0.107371
$883$	1.37811e10	0.673631	0.336815	−	0.941571i	$-0.390650\pi$
$883$	1.37811e10	0.673631	0.336815	+	0.941571i	$0.390650\pi$
$884$	1.82831e8	0.00890157
$885$	5.53452e9	0.268398
$886$	−1.22934e10	−0.593820
$887$	−2.27458e10	−1.09438	−0.547190	−	0.837009i	$-0.684302\pi$
$887$	−2.27458e10	−1.09438	−0.547190	+	0.837009i	$0.684302\pi$
$888$	1.91777e10	0.919077
$889$	−1.55633e10	−0.742925
$890$	−8.22704e9	−0.391182
$891$	1.11048e10	0.525945
$892$	−1.02632e9	−0.0484179
$893$	−2.81932e10	−1.32484
$894$	3.71767e9	0.174016
$895$	−3.74155e10	−1.74450
$896$	−8.54174e9	−0.396706
$897$	−5.27875e9	−0.244207
$898$	6.12329e8	0.0282175
$899$	−3.00348e8	−0.0137869
$900$	−9.26706e7	−0.00423734
$901$	1.51739e10	0.691132
$902$	6.93818e10	3.14791
$903$	−6.22601e9	−0.281386
$904$	−2.53329e10	−1.14050
$905$	1.53624e10	0.688951
$906$	1.14403e10	0.511079
$907$	2.46167e10	1.09548	0.547740	−	0.836649i	$-0.315488\pi$
$907$	2.46167e10	1.09548	0.547740	+	0.836649i	$0.315488\pi$
$908$	7.11507e8	0.0315412
$909$	−1.40516e10	−0.620516
$910$	−2.61450e9	−0.115012
$911$	1.80092e10	0.789187	0.394594	−	0.918856i	$-0.370885\pi$
$911$	1.80092e10	0.789187	0.394594	+	0.918856i	$0.370885\pi$
$912$	−1.03075e10	−0.449958
$913$	−3.13946e10	−1.36523
$914$	4.85840e9	0.210466
$915$	1.20132e10	0.518424
$916$	8.90912e8	0.0383002
$917$	−1.54560e9	−0.0661918
$918$	−1.93019e10	−0.823474
$919$	2.01851e10	0.857881	0.428940	−	0.903333i	$-0.358887\pi$
$919$	2.01851e10	0.857881	0.428940	+	0.903333i	$0.358887\pi$
$920$	−4.30615e10	−1.82319
$921$	3.76092e9	0.158630
$922$	−9.38364e9	−0.394288
$923$	7.01171e9	0.293507
$924$	3.02051e8	0.0125959
$925$	7.17549e9	0.298095
$926$	9.21742e9	0.381479
$927$	−9.10287e9	−0.375318
$928$	2.14112e7	0.000879472 0
$929$	−1.17886e10	−0.482398	−0.241199	−	0.970476i	$-0.577541\pi$
$929$	−1.17886e10	−0.482398	−0.241199	+	0.970476i	$0.577541\pi$
$930$	−1.51956e10	−0.619482
$931$	2.99431e9	0.121611
$932$	−3.87724e8	−0.0156880
$933$	−2.45793e10	−0.990794
$934$	2.00378e10	0.804705
$935$	4.53940e10	1.81618
$936$	5.04538e9	0.201107
$937$	3.55634e10	1.41226	0.706130	−	0.708082i	$-0.250439\pi$
$937$	3.55634e10	1.41226	0.706130	+	0.708082i	$0.250439\pi$
$938$	−6.68601e9	−0.264519
$939$	−1.42214e9	−0.0560546
$940$	1.50624e9	0.0591490
$941$	1.29049e10	0.504882	0.252441	−	0.967612i	$-0.418767\pi$
$941$	1.29049e10	0.504882	0.252441	+	0.967612i	$0.418767\pi$
$942$	−1.53195e10	−0.597128
$943$	−7.41916e10	−2.88114
$944$	1.30131e10	0.503476
$945$	9.39737e9	0.362239
$946$	7.13675e10	2.74083
$947$	3.57581e10	1.36820	0.684099	−	0.729389i	$-0.260195\pi$
$947$	3.57581e10	1.36820	0.684099	+	0.729389i	$0.260195\pi$
$948$	5.23310e8	0.0199494
$949$	4.02115e9	0.152728
$950$	−3.72517e9	−0.140966
$951$	−1.50095e10	−0.565894
$952$	−8.99385e9	−0.337844
$953$	−1.55603e10	−0.582363	−0.291181	−	0.956668i	$-0.594048\pi$
$953$	−1.55603e10	−0.582363	−0.291181	+	0.956668i	$0.594048\pi$
$954$	−1.52981e10	−0.570449
$955$	2.66951e10	0.991792
$956$	−1.18338e9	−0.0438048
$957$	3.19993e8	0.0118018
$958$	2.87721e10	1.05728
$959$	−6.87911e9	−0.251865
$960$	−1.45408e10	−0.530443
$961$	6.05347e9	0.220025
$962$	1.42724e10	0.516874
$963$	5.38328e9	0.194247
$964$	−8.03974e7	−0.00289050
$965$	−4.84794e9	−0.173665
$966$	−9.48685e9	−0.338612
$967$	1.36197e9	0.0484368	0.0242184	−	0.999707i	$-0.492290\pi$
$967$	1.36197e9	0.0484368	0.0242184	+	0.999707i	$0.492290\pi$
$968$	6.70700e10	2.37665
$969$	−1.12230e10	−0.396257
$970$	−1.64571e10	−0.578964
$971$	−4.41825e10	−1.54875	−0.774377	−	0.632724i	$-0.781937\pi$
$971$	−4.41825e10	−1.54875	−0.774377	+	0.632724i	$0.781937\pi$
$972$	1.04358e9	0.0364497
$973$	1.93116e10	0.672085
$974$	4.46729e9	0.154913
$975$	−6.67797e8	−0.0230743
$976$	2.82461e10	0.972489
$977$	−1.47857e10	−0.507238	−0.253619	−	0.967304i	$-0.581621\pi$
$977$	−1.47857e10	−0.507238	−0.253619	+	0.967304i	$0.581621\pi$
$978$	3.45127e9	0.117976
$979$	−1.93616e10	−0.659480
$980$	−1.59973e8	−0.00542945
$981$	−2.92808e8	−0.00990242
$982$	1.99511e10	0.672322
$983$	−1.09926e10	−0.369117	−0.184559	−	0.982822i	$-0.559086\pi$
$983$	−1.09926e10	−0.369117	−0.184559	+	0.982822i	$0.559086\pi$
$984$	−2.50850e10	−0.839326
$985$	2.16571e10	0.722061
$986$	3.48096e8	0.0115646
$987$	−9.08309e9	−0.300693
$988$	−2.52267e8	−0.00832167
$989$	−7.63149e10	−2.50855
$990$	−4.57654e10	−1.49904
$991$	−2.24046e10	−0.731272	−0.365636	−	0.930758i	$-0.619149\pi$
$991$	−2.24046e10	−0.731272	−0.365636	+	0.930758i	$0.619149\pi$
$992$	−2.39285e9	−0.0778261
$993$	1.40099e10	0.454059
$994$	1.26013e10	0.406970
$995$	5.09776e10	1.64058
$996$	−4.14684e8	−0.0132987
$997$	1.69909e10	0.542979	0.271489	−	0.962441i	$-0.412484\pi$
$997$	1.69909e10	0.542979	0.271489	+	0.962441i	$0.412484\pi$
$998$	−2.82484e10	−0.899573
$999$	−5.12997e10	−1.62793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.c.1.4	✓	10

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

\(f(q)\)	\(=\)	\(q-11.5114 q^{2} +23.9058 q^{3} +4.51150 q^{4} -301.396 q^{5} -275.188 q^{6} +343.000 q^{7} +1421.52 q^{8} -1615.51 q^{9} +O(q^{10})\)	\(q-11.5114 q^{2} +23.9058 q^{3} +4.51150 q^{4} -301.396 q^{5} -275.188 q^{6} +343.000 q^{7} +1421.52 q^{8} -1615.51 q^{9} +3469.48 q^{10} +8165.11 q^{11} +107.851 q^{12} -2197.00 q^{13} -3948.40 q^{14} -7205.13 q^{15} -16941.1 q^{16} -18445.8 q^{17} +18596.7 q^{18} +25451.2 q^{19} -1359.75 q^{20} +8199.69 q^{21} -93991.6 q^{22} +100507. q^{23} +33982.6 q^{24} +12714.8 q^{25} +25290.5 q^{26} -90902.1 q^{27} +1547.44 q^{28} +1639.36 q^{29} +82940.8 q^{30} -183210. q^{31} +13060.7 q^{32} +195194. q^{33} +212337. q^{34} -103379. q^{35} -7288.38 q^{36} +564340. q^{37} -292978. q^{38} -52521.1 q^{39} -428441. q^{40} -738171. q^{41} -94389.6 q^{42} -759297. q^{43} +36836.9 q^{44} +486910. q^{45} -1.15698e6 q^{46} -1.10773e6 q^{47} -404991. q^{48} +117649. q^{49} -146365. q^{50} -440963. q^{51} -9911.76 q^{52} -822620. q^{53} +1.04641e6 q^{54} -2.46094e6 q^{55} +487582. q^{56} +608432. q^{57} -18871.3 q^{58} -768137. q^{59} -32505.9 q^{60} -1.66731e6 q^{61} +2.10900e6 q^{62} -554121. q^{63} +2.01812e6 q^{64} +662168. q^{65} -2.24694e6 q^{66} +1.69335e6 q^{67} -83218.4 q^{68} +2.40271e6 q^{69} +1.19003e6 q^{70} -3.19149e6 q^{71} -2.29648e6 q^{72} -1.83029e6 q^{73} -6.49632e6 q^{74} +303958. q^{75} +114823. q^{76} +2.80063e6 q^{77} +604589. q^{78} +4.85216e6 q^{79} +5.10599e6 q^{80} +1.36004e6 q^{81} +8.49735e6 q^{82} -3.84497e6 q^{83} +36992.9 q^{84} +5.55951e6 q^{85} +8.74055e6 q^{86} +39190.2 q^{87} +1.16069e7 q^{88} -2.37126e6 q^{89} -5.60499e6 q^{90} -753571. q^{91} +453439. q^{92} -4.37979e6 q^{93} +1.27515e7 q^{94} -7.67091e6 q^{95} +312226. q^{96} -4.74338e6 q^{97} -1.35430e6 q^{98} -1.31908e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 80 q^{3} + 670 q^{4} - 927 q^{5} - 1419 q^{6} + 3430 q^{7} - 4878 q^{8} + 3612 q^{9}+O(q^{10}) \) 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

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