LMFDB - Embedded newform 17.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$42.3973$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +O(q^{10})$	\(q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +105924. q^{10} +36573.4 q^{11} +141074. q^{12} +69902.2 q^{13} -121791. q^{14} -274171. q^{15} +732260. q^{16} +83521.0 q^{17} +323924. q^{18} +640587. q^{19} -3.21175e6 q^{20} +315239. q^{21} -1.55061e6 q^{22} +2.09284e6 q^{23} -3.59900e6 q^{24} +4.28875e6 q^{25} -2.96367e6 q^{26} -2.99844e6 q^{27} +3.69283e6 q^{28} +4.99200e6 q^{29} +1.16241e7 q^{30} -5.61791e6 q^{31} -1.42544e7 q^{32} +4.01355e6 q^{33} -3.54107e6 q^{34} -7.17685e6 q^{35} -9.82174e6 q^{36} +3.47843e6 q^{37} -2.71592e7 q^{38} +7.67105e6 q^{39} +8.19361e7 q^{40} +469632. q^{41} -1.33653e7 q^{42} +3.50525e6 q^{43} +4.70163e7 q^{44} +1.90881e7 q^{45} -8.87310e7 q^{46} +1.55290e6 q^{47} +8.03580e7 q^{48} -3.21017e7 q^{49} -1.81832e8 q^{50} +9.16557e6 q^{51} +8.98617e7 q^{52} +1.03903e8 q^{53} +1.27126e8 q^{54} -9.13740e7 q^{55} -9.42094e7 q^{56} +7.02978e7 q^{57} -2.11648e8 q^{58} -7.79169e7 q^{59} -3.52456e8 q^{60} +1.79259e7 q^{61} +2.38185e8 q^{62} -2.19473e7 q^{63} +2.29433e8 q^{64} -1.74642e8 q^{65} -1.70164e8 q^{66} +8.26939e7 q^{67} +1.07369e8 q^{68} +2.29668e8 q^{69} +3.04279e8 q^{70} -1.03521e8 q^{71} +2.50566e8 q^{72} +1.43348e7 q^{73} -1.47476e8 q^{74} +4.70646e8 q^{75} +8.23496e8 q^{76} +1.05061e8 q^{77} -3.25232e8 q^{78} +3.90455e8 q^{79} -1.82946e9 q^{80} -1.78666e8 q^{81} -1.99111e7 q^{82} -3.47368e8 q^{83} +4.05250e8 q^{84} -2.08667e8 q^{85} -1.48613e8 q^{86} +5.47821e8 q^{87} -1.19945e9 q^{88} -4.95430e7 q^{89} -8.09284e8 q^{90} +2.00802e8 q^{91} +2.69042e9 q^{92} -6.16508e8 q^{93} -6.58387e7 q^{94} -1.60043e9 q^{95} -1.56428e9 q^{96} +6.49870e8 q^{97} +1.36103e9 q^{98} -2.79428e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * 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 $

$2$	−42.3973	−1.87372	−0.936858	−	0.349711i	$-0.886280\pi$
$2$	−42.3973	−1.87372	−0.936858	+	0.349711i	$0.886280\pi$
$3$	109.740	0.782200	0.391100	−	0.920348i	$-0.372095\pi$
$3$	109.740	0.782200	0.391100	+	0.920348i	$0.372095\pi$
$4$	1285.53	2.51081
$5$	−2498.37	−1.78769	−0.893846	−	0.448375i	$-0.852003\pi$
$5$	−2498.37	−1.78769	−0.893846	+	0.448375i	$0.852003\pi$
$6$	−4652.67	−1.46562
$7$	2872.61	0.452205	0.226102	−	0.974104i	$-0.427402\pi$
$7$	2872.61	0.452205	0.226102	+	0.974104i	$0.427402\pi$
$8$	−32795.8	−2.83082
$9$	−7640.20	−0.388163
$10$	105924.	3.34962
$11$	36573.4	0.753178	0.376589	−	0.926380i	$-0.377097\pi$
$11$	36573.4	0.753178	0.376589	+	0.926380i	$0.377097\pi$
$12$	141074.	1.96396
$13$	69902.2	0.678806	0.339403	−	0.940641i	$-0.389775\pi$
$13$	69902.2	0.678806	0.339403	+	0.940641i	$0.389775\pi$
$14$	−121791.	−0.847303
$15$	−274171.	−1.39833
$16$	732260.	2.79335
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	323924.	0.727306
$19$	640587.	1.12768	0.563841	−	0.825883i	$-0.309323\pi$
$19$	640587.	1.12768	0.563841	+	0.825883i	$0.309323\pi$
$20$	−3.21175e6	−4.48855
$21$	315239.	0.353715
$22$	−1.55061e6	−1.41124
$23$	2.09284e6	1.55941	0.779707	−	0.626144i	$-0.215368\pi$
$23$	2.09284e6	1.55941	0.779707	+	0.626144i	$0.215368\pi$
$24$	−3.59900e6	−2.21427
$25$	4.28875e6	2.19584
$26$	−2.96367e6	−1.27189
$27$	−2.99844e6	−1.08582
$28$	3.69283e6	1.13540
$29$	4.99200e6	1.31064	0.655321	−	0.755351i	$-0.272534\pi$
$29$	4.99200e6	1.31064	0.655321	+	0.755351i	$0.272534\pi$
$30$	1.16241e7	2.62008
$31$	−5.61791e6	−1.09257	−0.546283	−	0.837601i	$-0.683958\pi$
$31$	−5.61791e6	−1.09257	−0.546283	+	0.837601i	$0.683958\pi$
$32$	−1.42544e7	−2.40312
$33$	4.01355e6	0.589136
$34$	−3.54107e6	−0.454443
$35$	−7.17685e6	−0.808402
$36$	−9.82174e6	−0.974602
$37$	3.47843e6	0.305123	0.152562	−	0.988294i	$-0.451248\pi$
$37$	3.47843e6	0.305123	0.152562	+	0.988294i	$0.451248\pi$
$38$	−2.71592e7	−2.11296
$39$	7.67105e6	0.530963
$40$	8.19361e7	5.06064
$41$	469632.	0.0259555	0.0129778	−	0.999916i	$-0.495869\pi$
$41$	469632.	0.0259555	0.0129778	+	0.999916i	$0.495869\pi$
$42$	−1.33653e7	−0.662760
$43$	3.50525e6	0.156355	0.0781773	−	0.996939i	$-0.475090\pi$
$43$	3.50525e6	0.156355	0.0781773	+	0.996939i	$0.475090\pi$
$44$	4.70163e7	1.89109
$45$	1.90881e7	0.693915
$46$	−8.87310e7	−2.92190
$47$	1.55290e6	0.0464197	0.0232098	−	0.999731i	$-0.492611\pi$
$47$	1.55290e6	0.0464197	0.0232098	+	0.999731i	$0.492611\pi$
$48$	8.03580e7	2.18496
$49$	−3.21017e7	−0.795511
$50$	−1.81832e8	−4.11438
$51$	9.16557e6	0.189711
$52$	8.98617e7	1.70435
$53$	1.03903e8	1.80878	0.904390	−	0.426706i	$-0.140326\pi$
$53$	1.03903e8	1.80878	0.904390	+	0.426706i	$0.140326\pi$
$54$	1.27126e8	2.03452
$55$	−9.13740e7	−1.34645
$56$	−9.42094e7	−1.28011
$57$	7.02978e7	0.882074
$58$	−2.11648e8	−2.45577
$59$	−7.79169e7	−0.837139	−0.418569	−	0.908185i	$-0.637468\pi$
$59$	−7.79169e7	−0.837139	−0.418569	+	0.908185i	$0.637468\pi$
$60$	−3.52456e8	−3.51095
$61$	1.79259e7	0.165766	0.0828831	−	0.996559i	$-0.473587\pi$
$61$	1.79259e7	0.165766	0.0828831	+	0.996559i	$0.473587\pi$
$62$	2.38185e8	2.04716
$63$	−2.19473e7	−0.175529
$64$	2.29433e8	1.70941
$65$	−1.74642e8	−1.21350
$66$	−1.70164e8	−1.10387
$67$	8.26939e7	0.501345	0.250673	−	0.968072i	$-0.419348\pi$
$67$	8.26939e7	0.501345	0.250673	+	0.968072i	$0.419348\pi$
$68$	1.07369e8	0.608960
$69$	2.29668e8	1.21977
$70$	3.04279e8	1.51472
$71$	−1.03521e8	−0.483465	−0.241732	−	0.970343i	$-0.577716\pi$
$71$	−1.03521e8	−0.483465	−0.241732	+	0.970343i	$0.577716\pi$
$72$	2.50566e8	1.09882
$73$	1.43348e7	0.0590797	0.0295399	−	0.999564i	$-0.490596\pi$
$73$	1.43348e7	0.0590797	0.0295399	+	0.999564i	$0.490596\pi$
$74$	−1.47476e8	−0.571714
$75$	4.70646e8	1.71759
$76$	8.23496e8	2.83140
$77$	1.05061e8	0.340591
$78$	−3.25232e8	−0.994873
$79$	3.90455e8	1.12784	0.563922	−	0.825828i	$-0.309292\pi$
$79$	3.90455e8	1.12784	0.563922	+	0.825828i	$0.309292\pi$
$80$	−1.82946e9	−4.99365
$81$	−1.78666e8	−0.461167
$82$	−1.99111e7	−0.0486333
$83$	−3.47368e8	−0.803411	−0.401706	−	0.915769i	$-0.631582\pi$
$83$	−3.47368e8	−0.803411	−0.401706	+	0.915769i	$0.631582\pi$
$84$	4.05250e8	0.888110
$85$	−2.08667e8	−0.433579
$86$	−1.48613e8	−0.292964
$87$	5.47821e8	1.02518
$88$	−1.19945e9	−2.13212
$89$	−4.95430e7	−0.0837004	−0.0418502	−	0.999124i	$-0.513325\pi$
$89$	−4.95430e7	−0.0837004	−0.0418502	+	0.999124i	$0.513325\pi$
$90$	−8.09284e8	−1.30020
$91$	2.00802e8	0.306959
$92$	2.69042e9	3.91539
$93$	−6.16508e8	−0.854605
$94$	−6.58387e7	−0.0869772
$95$	−1.60043e9	−2.01595
$96$	−1.56428e9	−1.87972
$97$	6.49870e8	0.745338	0.372669	−	0.927964i	$-0.378443\pi$
$97$	6.49870e8	0.745338	0.372669	+	0.927964i	$0.378443\pi$
$98$	1.36103e9	1.49056
$99$	−2.79428e8	−0.292356
$100$	5.51334e9	5.51334
$101$	−5.41669e8	−0.517950	−0.258975	−	0.965884i	$-0.583385\pi$
$101$	−5.41669e8	−0.517950	−0.258975	+	0.965884i	$0.583385\pi$
$102$	−3.88596e8	−0.355465
$103$	1.38535e9	1.21281	0.606403	−	0.795157i	$-0.292612\pi$
$103$	1.38535e9	1.21281	0.606403	+	0.795157i	$0.292612\pi$
$104$	−2.29250e9	−1.92158
$105$	−7.87585e8	−0.632333
$106$	−4.40520e9	−3.38914
$107$	3.51366e8	0.259139	0.129569	−	0.991570i	$-0.458641\pi$
$107$	3.51366e8	0.259139	0.129569	+	0.991570i	$0.458641\pi$
$108$	−3.85460e9	−2.72629
$109$	−8.82255e8	−0.598652	−0.299326	−	0.954151i	$-0.596762\pi$
$109$	−8.82255e8	−0.598652	−0.299326	+	0.954151i	$0.596762\pi$
$110$	3.87401e9	2.52286
$111$	3.81722e8	0.238668
$112$	2.10349e9	1.26317
$113$	1.98816e9	1.14709	0.573545	−	0.819174i	$-0.305568\pi$
$113$	1.98816e9	1.14709	0.573545	+	0.819174i	$0.305568\pi$
$114$	−2.98044e9	−1.65276
$115$	−5.22871e9	−2.78775
$116$	6.41739e9	3.29077
$117$	−5.34067e8	−0.263487
$118$	3.30347e9	1.56856
$119$	2.39923e8	0.109676
$120$	8.99164e9	3.95844
$121$	−1.02034e9	−0.432723
$122$	−7.60009e8	−0.310598
$123$	5.15372e7	0.0203024
$124$	−7.22202e9	−2.74322
$125$	−5.83527e9	−2.13780
$126$	9.30507e8	0.328891
$127$	−3.59412e8	−0.122596	−0.0612980	−	0.998120i	$-0.519524\pi$
$127$	−3.59412e8	−0.122596	−0.0612980	+	0.998120i	$0.519524\pi$
$128$	−2.42907e9	−0.799826
$129$	3.84665e8	0.122301
$130$	7.40435e9	2.27375
$131$	2.17687e8	0.0645820	0.0322910	−	0.999479i	$-0.489720\pi$
$131$	2.17687e8	0.0645820	0.0322910	+	0.999479i	$0.489720\pi$
$132$	5.15955e9	1.47921
$133$	1.84015e9	0.509943
$134$	−3.50600e9	−0.939378
$135$	7.49123e9	1.94111
$136$	−2.73914e9	−0.686576
$137$	3.81268e9	0.924671	0.462336	−	0.886705i	$-0.347011\pi$
$137$	3.81268e9	0.924671	0.462336	+	0.886705i	$0.347011\pi$
$138$	−9.73731e9	−2.28551
$139$	1.05651e9	0.240054	0.120027	−	0.992771i	$-0.461702\pi$
$139$	1.05651e9	0.240054	0.120027	+	0.992771i	$0.461702\pi$
$140$	−9.22608e9	−2.02974
$141$	1.70414e8	0.0363095
$142$	4.38900e9	0.905875
$143$	2.55656e9	0.511262
$144$	−5.59461e9	−1.08427
$145$	−1.24719e10	−2.34302
$146$	−6.07757e8	−0.110699
$147$	−3.52283e9	−0.622249
$148$	4.47164e9	0.766106
$149$	1.11231e10	1.84879	0.924394	−	0.381439i	$-0.124571\pi$
$149$	1.11231e10	1.84879	0.924394	+	0.381439i	$0.124571\pi$
$150$	−1.99541e10	−3.21827
$151$	−4.54386e8	−0.0711261	−0.0355630	−	0.999367i	$-0.511322\pi$
$151$	−4.54386e8	−0.0711261	−0.0355630	+	0.999367i	$0.511322\pi$
$152$	−2.10085e10	−3.19227
$153$	−6.38117e8	−0.0941432
$154$	−4.45430e9	−0.638170
$155$	1.40357e10	1.95317
$156$	9.86139e9	1.33315
$157$	1.18078e10	1.55102	0.775512	−	0.631332i	$-0.217492\pi$
$157$	1.18078e10	1.55102	0.775512	+	0.631332i	$0.217492\pi$
$158$	−1.65542e10	−2.11326
$159$	1.14023e10	1.41483
$160$	3.56129e10	4.29603
$161$	6.01192e9	0.705175
$162$	7.57495e9	0.864096
$163$	9.05833e8	0.100509	0.0502544	−	0.998736i	$-0.483997\pi$
$163$	9.05833e8	0.100509	0.0502544	+	0.998736i	$0.483997\pi$
$164$	6.03728e8	0.0651694
$165$	−1.00273e10	−1.05319
$166$	1.47275e10	1.50536
$167$	1.08715e10	1.08159	0.540797	−	0.841153i	$-0.318123\pi$
$167$	1.08715e10	1.08159	0.540797	+	0.841153i	$0.318123\pi$
$168$	−1.03385e10	−1.00130
$169$	−5.71818e9	−0.539222
$170$	8.84691e9	0.812403
$171$	−4.89422e9	−0.437724
$172$	4.50611e9	0.392576
$173$	−2.10914e10	−1.79019	−0.895093	−	0.445880i	$-0.852891\pi$
$173$	−2.10914e10	−1.79019	−0.895093	+	0.445880i	$0.852891\pi$
$174$	−2.32261e10	−1.92090
$175$	1.23199e10	0.992970
$176$	2.67812e10	2.10389
$177$	−8.55057e9	−0.654810
$178$	2.10049e9	0.156831
$179$	−2.13633e10	−1.55535	−0.777676	−	0.628665i	$-0.783602\pi$
$179$	−2.13633e10	−1.55535	−0.777676	+	0.628665i	$0.783602\pi$
$180$	2.45384e10	1.74229
$181$	−1.23594e10	−0.855937	−0.427969	−	0.903794i	$-0.640771\pi$
$181$	−1.23594e10	−0.855937	−0.427969	+	0.903794i	$0.640771\pi$
$182$	−8.51345e9	−0.575154
$183$	1.96718e9	0.129662
$184$	−6.86364e10	−4.41443
$185$	−8.69042e9	−0.545466
$186$	2.61383e10	1.60129
$187$	3.05464e9	0.182673
$188$	1.99630e9	0.116551
$189$	−8.61334e9	−0.491013
$190$	6.78538e10	3.77731
$191$	2.02521e10	1.10108	0.550540	−	0.834809i	$-0.314422\pi$
$191$	2.02521e10	1.10108	0.550540	+	0.834809i	$0.314422\pi$
$192$	2.51779e10	1.33710
$193$	−2.75114e10	−1.42727	−0.713633	−	0.700520i	$-0.752952\pi$
$193$	−2.75114e10	−1.42727	−0.713633	+	0.700520i	$0.752952\pi$
$194$	−2.75527e10	−1.39655
$195$	−1.91652e10	−0.949197
$196$	−4.12679e10	−1.99738
$197$	1.58792e10	0.751156	0.375578	−	0.926791i	$-0.377444\pi$
$197$	1.58792e10	0.751156	0.375578	+	0.926791i	$0.377444\pi$
$198$	1.18470e10	0.547791
$199$	3.50786e10	1.58563	0.792817	−	0.609460i	$-0.208614\pi$
$199$	3.50786e10	1.58563	0.792817	+	0.609460i	$0.208614\pi$
$200$	−1.40653e11	−6.21604
$201$	9.07480e9	0.392152
$202$	2.29653e10	0.970491
$203$	1.43401e10	0.592678
$204$	1.17826e10	0.476329
$205$	−1.17332e9	−0.0464005
$206$	−5.87351e10	−2.27245
$207$	−1.59898e10	−0.605306
$208$	5.11866e10	1.89614
$209$	2.34284e10	0.849346
$210$	3.33915e10	1.18481
$211$	−2.22358e10	−0.772293	−0.386146	−	0.922438i	$-0.626194\pi$
$211$	−2.22358e10	−0.772293	−0.386146	+	0.922438i	$0.626194\pi$
$212$	1.33571e11	4.54150
$213$	−1.13603e10	−0.378166
$214$	−1.48970e10	−0.485552
$215$	−8.75742e9	−0.279514
$216$	9.83361e10	3.07377
$217$	−1.61381e10	−0.494063
$218$	3.74052e10	1.12170
$219$	1.57310e9	0.0462122
$220$	−1.17464e11	−3.38068
$221$	5.83830e9	0.164635
$222$	−1.61840e10	−0.447195
$223$	4.29725e9	0.116364	0.0581821	−	0.998306i	$-0.481470\pi$
$223$	4.29725e9	0.116364	0.0581821	+	0.998306i	$0.481470\pi$
$224$	−4.09474e10	−1.08670
$225$	−3.27669e10	−0.852343
$226$	−8.42925e10	−2.14932
$227$	2.64486e10	0.661129	0.330565	−	0.943783i	$-0.392761\pi$
$227$	2.64486e10	0.661129	0.330565	+	0.943783i	$0.392761\pi$
$228$	9.03702e10	2.21472
$229$	−1.98494e10	−0.476966	−0.238483	−	0.971147i	$-0.576650\pi$
$229$	−1.98494e10	−0.476966	−0.238483	+	0.971147i	$0.576650\pi$
$230$	2.21683e11	5.22345
$231$	1.15293e10	0.266410
$232$	−1.63717e11	−3.71019
$233$	−2.09016e10	−0.464598	−0.232299	−	0.972644i	$-0.574625\pi$
$233$	−2.09016e10	−0.464598	−0.232299	+	0.972644i	$0.574625\pi$
$234$	2.26430e10	0.493700
$235$	−3.87972e9	−0.0829841
$236$	−1.00165e11	−2.10190
$237$	4.28484e10	0.882200
$238$	−1.01721e10	−0.205501
$239$	−3.88402e10	−0.769999	−0.385000	−	0.922917i	$-0.625798\pi$
$239$	−3.88402e10	−0.769999	−0.385000	+	0.922917i	$0.625798\pi$
$240$	−2.00764e11	−3.90603
$241$	−1.37408e10	−0.262383	−0.131192	−	0.991357i	$-0.541880\pi$
$241$	−1.37408e10	−0.262383	−0.131192	+	0.991357i	$0.541880\pi$
$242$	4.32596e10	0.810799
$243$	3.94116e10	0.725096
$244$	2.30443e10	0.416207
$245$	8.02022e10	1.42213
$246$	−2.18504e9	−0.0380410
$247$	4.47785e10	0.765478
$248$	1.84244e11	3.09286
$249$	−3.81200e10	−0.628428
$250$	2.47400e11	4.00562
$251$	−7.04853e10	−1.12090	−0.560450	−	0.828188i	$-0.689372\pi$
$251$	−7.04853e10	−1.12090	−0.560450	+	0.828188i	$0.689372\pi$
$252$	−2.82140e10	−0.440719
$253$	7.65423e10	1.17452
$254$	1.52381e10	0.229710
$255$	−2.28990e10	−0.339146
$256$	−1.44835e10	−0.210762
$257$	6.32271e10	0.904075	0.452038	−	0.891999i	$-0.350697\pi$
$257$	6.32271e10	0.904075	0.452038	+	0.891999i	$0.350697\pi$
$258$	−1.63088e10	−0.229156
$259$	9.99216e9	0.137978
$260$	−2.24508e11	−3.04686
$261$	−3.81399e10	−0.508742
$262$	−9.22934e9	−0.121008
$263$	−7.65063e9	−0.0986044	−0.0493022	−	0.998784i	$-0.515700\pi$
$263$	−7.65063e9	−0.0986044	−0.0493022	+	0.998784i	$0.515700\pi$
$264$	−1.31627e11	−1.66774
$265$	−2.59588e11	−3.23354
$266$	−7.80177e10	−0.955489
$267$	−5.43684e9	−0.0654705
$268$	1.06306e11	1.25878
$269$	5.99383e10	0.697942	0.348971	−	0.937134i	$-0.386531\pi$
$269$	5.99383e10	0.697942	0.348971	+	0.937134i	$0.386531\pi$
$270$	−3.17608e11	−3.63709
$271$	−4.61140e10	−0.519363	−0.259681	−	0.965694i	$-0.583618\pi$
$271$	−4.61140e10	−0.519363	−0.259681	+	0.965694i	$0.583618\pi$
$272$	6.11591e10	0.677487
$273$	2.20359e10	0.240104
$274$	−1.61647e11	−1.73257
$275$	1.56854e11	1.65386
$276$	2.95246e11	3.06262
$277$	3.74719e9	0.0382426	0.0191213	−	0.999817i	$-0.493913\pi$
$277$	3.74719e9	0.0382426	0.0191213	+	0.999817i	$0.493913\pi$
$278$	−4.47934e10	−0.449792
$279$	4.29220e10	0.424093
$280$	2.35370e11	2.28845
$281$	−1.09177e10	−0.104461	−0.0522305	−	0.998635i	$-0.516633\pi$
$281$	−1.09177e10	−0.104461	−0.0522305	+	0.998635i	$0.516633\pi$
$282$	−7.22511e9	−0.0680336
$283$	2.09684e10	0.194324	0.0971620	−	0.995269i	$-0.469024\pi$
$283$	2.09684e10	0.194324	0.0971620	+	0.995269i	$0.469024\pi$
$284$	−1.33079e11	−1.21389
$285$	−1.75630e11	−1.57688
$286$	−1.08391e11	−0.957960
$287$	1.34907e9	0.0117372
$288$	1.08907e11	0.932800
$289$	6.97576e9	0.0588235
$290$	5.28775e11	4.39016
$291$	7.13165e10	0.583004
$292$	1.84279e10	0.148338
$293$	−2.40168e11	−1.90375	−0.951875	−	0.306485i	$-0.900847\pi$
$293$	−2.40168e11	−1.90375	−0.951875	+	0.306485i	$0.900847\pi$
$294$	1.49359e11	1.16592
$295$	1.94666e11	1.49655
$296$	−1.14078e11	−0.863750
$297$	−1.09663e11	−0.817817
$298$	−4.71589e11	−3.46410
$299$	1.46294e11	1.05854
$300$	6.05032e11	4.31253
$301$	1.00692e10	0.0707042
$302$	1.92648e10	0.133270
$303$	−5.94426e10	−0.405141
$304$	4.69076e11	3.15001
$305$	−4.47855e10	−0.296339
$306$	2.70545e10	0.176398
$307$	−2.30483e11	−1.48087	−0.740435	−	0.672128i	$-0.765380\pi$
$307$	−2.30483e11	−1.48087	−0.740435	+	0.672128i	$0.765380\pi$
$308$	1.35059e11	0.855158
$309$	1.52028e11	0.948658
$310$	−5.95074e11	−3.65968
$311$	1.47492e11	0.894016	0.447008	−	0.894530i	$-0.352490\pi$
$311$	1.47492e11	0.894016	0.447008	+	0.894530i	$0.352490\pi$
$312$	−2.51578e11	−1.50306
$313$	1.79761e11	1.05863	0.529317	−	0.848424i	$-0.322448\pi$
$313$	1.79761e11	1.05863	0.529317	+	0.848424i	$0.322448\pi$
$314$	−5.00617e11	−2.90618
$315$	5.48326e10	0.313792
$316$	5.01943e11	2.83180
$317$	4.91432e10	0.273336	0.136668	−	0.990617i	$-0.456361\pi$
$317$	4.91432e10	0.273336	0.136668	+	0.990617i	$0.456361\pi$
$318$	−4.83425e11	−2.65099
$319$	1.82574e11	0.987146
$320$	−5.73209e11	−3.05589
$321$	3.85588e10	0.202698
$322$	−2.54889e11	−1.32130
$323$	5.35025e10	0.273503
$324$	−2.29681e11	−1.15790
$325$	2.99793e11	1.49055
$326$	−3.84049e10	−0.188325
$327$	−9.68183e10	−0.468266
$328$	−1.54019e10	−0.0734756
$329$	4.46086e9	0.0209912
$330$	4.25133e11	1.97339
$331$	2.45275e11	1.12312	0.561562	−	0.827434i	$-0.310200\pi$
$331$	2.45275e11	1.12312	0.561562	+	0.827434i	$0.310200\pi$
$332$	−4.46553e11	−2.01721
$333$	−2.65759e10	−0.118437
$334$	−4.60922e11	−2.02660
$335$	−2.06600e11	−0.896251
$336$	2.30837e11	0.988049
$337$	6.51138e10	0.275004	0.137502	−	0.990502i	$-0.456093\pi$
$337$	6.51138e10	0.275004	0.137502	+	0.990502i	$0.456093\pi$
$338$	2.42435e11	1.01035
$339$	2.18180e11	0.897254
$340$	−2.68248e11	−1.08863
$341$	−2.05466e11	−0.822896
$342$	2.07502e11	0.820170
$343$	−2.08136e11	−0.811938
$344$	−1.14957e11	−0.442612
$345$	−5.73797e11	−2.18058
$346$	8.94219e11	3.35430
$347$	−7.31021e10	−0.270675	−0.135337	−	0.990800i	$-0.543212\pi$
$347$	−7.31021e10	−0.270675	−0.135337	+	0.990800i	$0.543212\pi$
$348$	7.04242e11	2.57404
$349$	1.43103e11	0.516337	0.258169	−	0.966100i	$-0.416881\pi$
$349$	1.43103e11	0.516337	0.258169	+	0.966100i	$0.416881\pi$
$350$	−5.22331e11	−1.86054
$351$	−2.09598e11	−0.737062
$352$	−5.21332e11	−1.80998
$353$	3.76830e11	1.29169	0.645846	−	0.763467i	$-0.276505\pi$
$353$	3.76830e11	1.29169	0.645846	+	0.763467i	$0.276505\pi$
$354$	3.62521e11	1.22693
$355$	2.58634e11	0.864286
$356$	−6.36892e10	−0.210156
$357$	2.63291e10	0.0857884
$358$	9.05745e11	2.91429
$359$	−3.51198e11	−1.11590	−0.557952	−	0.829873i	$-0.688413\pi$
$359$	−3.51198e11	−1.11590	−0.557952	+	0.829873i	$0.688413\pi$
$360$	−6.26009e11	−1.96435
$361$	8.76640e10	0.271668
$362$	5.24003e11	1.60378
$363$	−1.11971e11	−0.338476
$364$	2.58137e11	0.770716
$365$	−3.58137e10	−0.105616
$366$	−8.34031e10	−0.242950
$367$	−4.78044e11	−1.37553	−0.687766	−	0.725933i	$-0.741408\pi$
$367$	−4.78044e11	−1.37553	−0.687766	+	0.725933i	$0.741408\pi$
$368$	1.53251e12	4.35599
$369$	−3.58808e9	−0.0100750
$370$	3.68451e11	1.02205
$371$	2.98472e11	0.817939
$372$	−7.92542e11	−2.14575
$373$	6.76181e11	1.80873	0.904364	−	0.426762i	$-0.140346\pi$
$373$	6.76181e11	1.80873	0.904364	+	0.426762i	$0.140346\pi$
$374$	−1.29509e11	−0.342276
$375$	−6.40361e11	−1.67218
$376$	−5.09284e10	−0.131406
$377$	3.48952e11	0.889672
$378$	3.65183e11	0.920019
$379$	−5.13122e11	−1.27745	−0.638725	−	0.769435i	$-0.720538\pi$
$379$	−5.13122e11	−1.27745	−0.638725	+	0.769435i	$0.720538\pi$
$380$	−2.05740e12	−5.06166
$381$	−3.94418e10	−0.0958946
$382$	−8.58633e11	−2.06311
$383$	−7.63819e11	−1.81383	−0.906914	−	0.421316i	$-0.861568\pi$
$383$	−7.63819e11	−1.81383	−0.906914	+	0.421316i	$0.861568\pi$
$384$	−2.66566e11	−0.625624
$385$	−2.62481e11	−0.608871
$386$	1.16641e12	2.67429
$387$	−2.67808e10	−0.0606910
$388$	8.35429e11	1.87140
$389$	3.33397e11	0.738224	0.369112	−	0.929385i	$-0.379662\pi$
$389$	3.33397e11	0.738224	0.369112	+	0.929385i	$0.379662\pi$
$390$	8.12551e11	1.77853
$391$	1.74796e11	0.378214
$392$	1.05280e12	2.25195
$393$	2.38889e10	0.0505160
$394$	−6.73235e11	−1.40745
$395$	−9.75503e11	−2.01624
$396$	−3.59214e11	−0.734049
$397$	−6.95415e11	−1.40503	−0.702517	−	0.711667i	$-0.747941\pi$
$397$	−6.95415e11	−1.40503	−0.702517	+	0.711667i	$0.747941\pi$
$398$	−1.48724e12	−2.97103
$399$	2.01938e11	0.398878
$400$	3.14048e12	6.13375
$401$	5.82880e11	1.12572	0.562859	−	0.826553i	$-0.309701\pi$
$401$	5.82880e11	1.12572	0.562859	+	0.826553i	$0.309701\pi$
$402$	−3.84747e11	−0.734782
$403$	−3.92705e11	−0.741640
$404$	−6.96334e11	−1.30047
$405$	4.46374e11	0.824425
$406$	−6.07980e11	−1.11051
$407$	1.27218e11	0.229812
$408$	−3.00592e11	−0.537040
$409$	2.34282e11	0.413985	0.206993	−	0.978343i	$-0.433632\pi$
$409$	2.34282e11	0.413985	0.206993	+	0.978343i	$0.433632\pi$
$410$	4.97455e10	0.0869413
$411$	4.18402e11	0.723278
$412$	1.78091e12	3.04512
$413$	−2.23825e11	−0.378558
$414$	6.77923e11	1.13417
$415$	8.67854e11	1.43625
$416$	−9.96417e11	−1.63125
$417$	1.15941e11	0.187770
$418$	−9.93302e11	−1.59143
$419$	−6.51621e11	−1.03284	−0.516419	−	0.856336i	$-0.672735\pi$
$419$	−6.51621e11	−1.03284	−0.516419	+	0.856336i	$0.672735\pi$
$420$	−1.01247e12	−1.58767
$421$	−5.97500e11	−0.926976	−0.463488	−	0.886103i	$-0.653402\pi$
$421$	−5.97500e11	−0.926976	−0.463488	+	0.886103i	$0.653402\pi$
$422$	9.42739e11	1.44706
$423$	−1.18644e10	−0.0180184
$424$	−3.40757e12	−5.12034
$425$	3.58201e11	0.532570
$426$	4.81648e11	0.708576
$427$	5.14939e10	0.0749602
$428$	4.51692e11	0.650648
$429$	2.80556e11	0.399909
$430$	3.71291e11	0.523729
$431$	−1.45053e11	−0.202478	−0.101239	−	0.994862i	$-0.532281\pi$
$431$	−1.45053e11	−0.202478	−0.101239	+	0.994862i	$0.532281\pi$
$432$	−2.19564e12	−3.03308
$433$	−2.07018e11	−0.283017	−0.141509	−	0.989937i	$-0.545195\pi$
$433$	−2.07018e11	−0.283017	−0.141509	+	0.989937i	$0.545195\pi$
$434$	6.84211e11	0.925734
$435$	−1.36866e12	−1.83271
$436$	−1.13417e12	−1.50310
$437$	1.34065e12	1.75853
$438$	−6.66951e10	−0.0865885
$439$	1.27742e12	1.64151	0.820757	−	0.571278i	$-0.193552\pi$
$439$	1.27742e12	1.64151	0.820757	+	0.571278i	$0.193552\pi$
$440$	2.99668e12	3.81156
$441$	2.45264e11	0.308788
$442$	−2.47529e11	−0.308479
$443$	2.56214e10	0.0316072	0.0158036	−	0.999875i	$-0.494969\pi$
$443$	2.56214e10	0.0316072	0.0158036	+	0.999875i	$0.494969\pi$
$444$	4.90716e11	0.599248
$445$	1.23777e11	0.149630
$446$	−1.82192e11	−0.218033
$447$	1.22064e12	1.44612
$448$	6.59070e11	0.773002
$449$	−6.93244e11	−0.804967	−0.402483	−	0.915427i	$-0.631853\pi$
$449$	−6.93244e11	−0.804967	−0.402483	+	0.915427i	$0.631853\pi$
$450$	1.38923e12	1.59705
$451$	1.71760e10	0.0195491
$452$	2.55584e12	2.88012
$453$	−4.98642e10	−0.0556348
$454$	−1.12135e12	−1.23877
$455$	−5.01678e11	−0.548749
$456$	−2.30547e12	−2.49700
$457$	−1.01211e12	−1.08544	−0.542721	−	0.839913i	$-0.682606\pi$
$457$	−1.01211e12	−1.08544	−0.542721	+	0.839913i	$0.682606\pi$
$458$	8.41560e11	0.893698
$459$	−2.50433e11	−0.263350
$460$	−6.72168e12	−6.99951
$461$	4.59728e11	0.474075	0.237037	−	0.971501i	$-0.423824\pi$
$461$	4.59728e11	0.474075	0.237037	+	0.971501i	$0.423824\pi$
$462$	−4.88814e11	−0.499177
$463$	−7.53078e11	−0.761598	−0.380799	−	0.924658i	$-0.624351\pi$
$463$	−7.53078e11	−0.761598	−0.380799	+	0.924658i	$0.624351\pi$
$464$	3.65544e12	3.66108
$465$	1.54027e12	1.52777
$466$	8.86170e11	0.870523
$467$	−1.22063e12	−1.18757	−0.593783	−	0.804625i	$-0.702366\pi$
$467$	−1.22063e12	−1.18757	−0.593783	+	0.804625i	$0.702366\pi$
$468$	−6.86562e11	−0.661566
$469$	2.37547e11	0.226711
$470$	1.64490e11	0.155488
$471$	1.29578e12	1.21321
$472$	2.55534e12	2.36979
$473$	1.28199e11	0.117763
$474$	−1.81666e12	−1.65299
$475$	2.74732e12	2.47621
$476$	3.08429e11	0.275375
$477$	−7.93839e11	−0.702101
$478$	1.64672e12	1.44276
$479$	1.22689e12	1.06487	0.532436	−	0.846470i	$-0.321277\pi$
$479$	1.22689e12	1.06487	0.532436	+	0.846470i	$0.321277\pi$
$480$	3.90815e12	3.36036
$481$	2.43150e11	0.207120
$482$	5.82574e11	0.491631
$483$	6.59746e11	0.551588
$484$	−1.31168e12	−1.08648
$485$	−1.62362e12	−1.33243
$486$	−1.67095e12	−1.35862
$487$	1.96428e12	1.58242	0.791211	−	0.611543i	$-0.209451\pi$
$487$	1.96428e12	1.58242	0.791211	+	0.611543i	$0.209451\pi$
$488$	−5.87892e11	−0.469255
$489$	9.94058e10	0.0786180
$490$	−3.40036e12	−2.66466
$491$	−2.27273e12	−1.76474	−0.882371	−	0.470554i	$-0.844054\pi$
$491$	−2.27273e12	−1.76474	−0.882371	+	0.470554i	$0.844054\pi$
$492$	6.62529e10	0.0509755
$493$	4.16937e11	0.317877
$494$	−1.89849e12	−1.43429
$495$	6.98116e11	0.522642
$496$	−4.11377e12	−3.05192
$497$	−2.97374e11	−0.218625
$498$	1.61619e12	1.17750
$499$	2.31148e12	1.66893	0.834464	−	0.551063i	$-0.185778\pi$
$499$	2.31148e12	1.66893	0.834464	+	0.551063i	$0.185778\pi$
$500$	−7.50144e12	−5.36759
$501$	1.19303e12	0.846024
$502$	2.98839e12	2.10025
$503$	−2.10646e12	−1.46723	−0.733615	−	0.679565i	$-0.762168\pi$
$503$	−2.10646e12	−1.46723	−0.733615	+	0.679565i	$0.762168\pi$
$504$	7.19779e11	0.496891
$505$	1.35329e12	0.925935
$506$	−3.24519e12	−2.20071
$507$	−6.27511e11	−0.421780
$508$	−4.62037e11	−0.307815
$509$	−1.57634e12	−1.04093	−0.520464	−	0.853884i	$-0.674241\pi$
$509$	−1.57634e12	−1.04093	−0.520464	+	0.853884i	$0.674241\pi$
$510$	9.70858e11	0.635462
$511$	4.11782e10	0.0267161
$512$	1.85774e12	1.19473
$513$	−1.92076e12	−1.22446
$514$	−2.68066e12	−1.69398
$515$	−3.46112e12	−2.16812
$516$	4.94499e11	0.307073
$517$	5.67946e10	0.0349623
$518$	−4.23641e11	−0.258532
$519$	−2.31456e12	−1.40028
$520$	5.72752e12	3.43520
$521$	−3.90823e11	−0.232386	−0.116193	−	0.993227i	$-0.537069\pi$
$521$	−3.90823e11	−0.232386	−0.116193	+	0.993227i	$0.537069\pi$
$522$	1.61703e12	0.953237
$523$	−2.52838e12	−1.47770	−0.738849	−	0.673871i	$-0.764630\pi$
$523$	−2.52838e12	−1.47770	−0.738849	+	0.673871i	$0.764630\pi$
$524$	2.79844e11	0.162153
$525$	1.35198e12	0.776701
$526$	3.24366e11	0.184757
$527$	−4.69214e11	−0.264986
$528$	2.93896e12	1.64566
$529$	2.57884e12	1.43177
$530$	1.10058e13	6.05874
$531$	5.95301e11	0.324946
$532$	2.36558e12	1.28037
$533$	3.28283e10	0.0176188
$534$	2.30507e11	0.122673
$535$	−8.77843e11	−0.463260
$536$	−2.71201e12	−1.41922
$537$	−2.34440e12	−1.21660
$538$	−2.54123e12	−1.30774
$539$	−1.17407e12	−0.599161
$540$	9.63022e12	4.87376
$541$	1.45109e12	0.728296	0.364148	−	0.931341i	$-0.381360\pi$
$541$	1.45109e12	0.728296	0.364148	+	0.931341i	$0.381360\pi$
$542$	1.95511e12	0.973138
$543$	−1.35631e12	−0.669515
$544$	−1.19054e12	−0.582842
$545$	2.20420e12	1.07021
$546$	−9.34264e11	−0.449886
$547$	−2.60966e10	−0.0124635	−0.00623177	−	0.999981i	$-0.501984\pi$
$547$	−2.60966e10	−0.0124635	−0.00623177	+	0.999981i	$0.501984\pi$
$548$	4.90133e12	2.32167
$549$	−1.36957e11	−0.0643442
$550$	−6.65019e12	−3.09886
$551$	3.19781e12	1.47799
$552$	−7.53214e12	−3.45297
$553$	1.12162e12	0.510016
$554$	−1.58871e11	−0.0716557
$555$	−9.53684e11	−0.426664
$556$	1.35818e12	0.602729
$557$	−2.42622e12	−1.06803	−0.534013	−	0.845477i	$-0.679317\pi$
$557$	−2.42622e12	−1.06803	−0.534013	+	0.845477i	$0.679317\pi$
$558$	−1.81978e12	−0.794629
$559$	2.45025e11	0.106134
$560$	−5.25532e12	−2.25815
$561$	3.35216e11	0.142887
$562$	4.62883e11	0.195730
$563$	−3.14392e12	−1.31881	−0.659406	−	0.751787i	$-0.729192\pi$
$563$	−3.14392e12	−1.31881	−0.659406	+	0.751787i	$0.729192\pi$
$564$	2.19073e11	0.0911662
$565$	−4.96716e12	−2.05064
$566$	−8.89004e11	−0.364108
$567$	−5.13236e11	−0.208542
$568$	3.39504e12	1.36860
$569$	−4.68855e12	−1.87514	−0.937570	−	0.347798i	$-0.886930\pi$
$569$	−4.68855e12	−1.87514	−0.937570	+	0.347798i	$0.886930\pi$
$570$	7.44626e12	2.95462
$571$	2.51532e12	0.990216	0.495108	−	0.868831i	$-0.335128\pi$
$571$	2.51532e12	0.990216	0.495108	+	0.868831i	$0.335128\pi$
$572$	3.28654e12	1.28368
$573$	2.22245e12	0.861265
$574$	−5.71969e10	−0.0219922
$575$	8.97569e12	3.42423
$576$	−1.75291e12	−0.663528
$577$	1.66387e12	0.624924	0.312462	−	0.949930i	$-0.398846\pi$
$577$	1.66387e12	0.624924	0.312462	+	0.949930i	$0.398846\pi$
$578$	−2.95754e11	−0.110219
$579$	−3.01909e12	−1.11641
$580$	−1.60330e13	−5.88288
$581$	−9.97850e11	−0.363306
$582$	−3.02363e12	−1.09238
$583$	3.80007e12	1.36233
$584$	−4.70121e11	−0.167244
$585$	1.33430e12	0.471034
$586$	1.01825e13	3.56709
$587$	1.10214e12	0.383147	0.191573	−	0.981478i	$-0.438641\pi$
$587$	1.10214e12	0.383147	0.191573	+	0.981478i	$0.438641\pi$
$588$	−4.52872e12	−1.56235
$589$	−3.59876e12	−1.23207
$590$	−8.25330e12	−2.80410
$591$	1.74258e12	0.587555
$592$	2.54711e12	0.852316
$593$	−1.47081e12	−0.488438	−0.244219	−	0.969720i	$-0.578532\pi$
$593$	−1.47081e12	−0.488438	−0.244219	+	0.969720i	$0.578532\pi$
$594$	4.64942e12	1.53236
$595$	−5.99418e11	−0.196066
$596$	1.42991e13	4.64195
$597$	3.84951e12	1.24028
$598$	−6.20250e12	−1.98340
$599$	3.93181e12	1.24788	0.623938	−	0.781473i	$-0.285532\pi$
$599$	3.93181e12	1.24788	0.623938	+	0.781473i	$0.285532\pi$
$600$	−1.54352e13	−4.86219
$601$	8.77198e11	0.274260	0.137130	−	0.990553i	$-0.456212\pi$
$601$	8.77198e11	0.274260	0.137130	+	0.990553i	$0.456212\pi$
$602$	−4.26907e11	−0.132480
$603$	−6.31798e11	−0.194603
$604$	−5.84129e11	−0.178584
$605$	2.54919e12	0.773575
$606$	2.52021e12	0.759119
$607$	−1.09458e12	−0.327265	−0.163632	−	0.986521i	$-0.552321\pi$
$607$	−1.09458e12	−0.327265	−0.163632	+	0.986521i	$0.552321\pi$
$608$	−9.13121e12	−2.70995
$609$	1.57367e12	0.463593
$610$	1.89879e12	0.555254
$611$	1.08551e11	0.0315100
$612$	−8.20322e11	−0.236376
$613$	−4.47212e12	−1.27921	−0.639605	−	0.768704i	$-0.720902\pi$
$613$	−4.47212e12	−1.27921	−0.639605	+	0.768704i	$0.720902\pi$
$614$	9.77188e12	2.77473
$615$	−1.28759e11	−0.0362945
$616$	−3.44555e12	−0.964152
$617$	−2.92442e12	−0.812376	−0.406188	−	0.913790i	$-0.633142\pi$
$617$	−2.92442e12	−0.812376	−0.406188	+	0.913790i	$0.633142\pi$
$618$	−6.44557e12	−1.77751
$619$	1.52167e12	0.416593	0.208296	−	0.978066i	$-0.433208\pi$
$619$	1.52167e12	0.416593	0.208296	+	0.978066i	$0.433208\pi$
$620$	1.80433e13	4.90404
$621$	−6.27527e12	−1.69325
$622$	−6.25325e12	−1.67513
$623$	−1.42318e11	−0.0378497
$624$	5.61720e12	1.48316
$625$	6.20223e12	1.62588
$626$	−7.62139e12	−1.98358
$627$	2.57103e12	0.664359
$628$	1.51793e13	3.89433
$629$	2.90522e11	0.0740033
$630$	−2.32476e12	−0.587956
$631$	−6.61053e12	−1.65998	−0.829992	−	0.557775i	$-0.811655\pi$
$631$	−6.61053e12	−1.65998	−0.829992	+	0.557775i	$0.811655\pi$
$632$	−1.28053e13	−3.19273
$633$	−2.44015e12	−0.604088
$634$	−2.08354e12	−0.512154
$635$	8.97946e11	0.219164
$636$	1.46580e13	3.55236
$637$	−2.24398e12	−0.539998
$638$	−7.74066e12	−1.84963
$639$	7.90919e11	0.187663
$640$	6.06873e12	1.42984
$641$	3.36551e12	0.787389	0.393694	−	0.919241i	$-0.371197\pi$
$641$	3.36551e12	0.787389	0.393694	+	0.919241i	$0.371197\pi$
$642$	−1.63479e12	−0.379799
$643$	−1.05715e12	−0.243887	−0.121943	−	0.992537i	$-0.538913\pi$
$643$	−1.05715e12	−0.243887	−0.121943	+	0.992537i	$0.538913\pi$
$644$	7.72852e12	1.77056
$645$	−9.61036e11	−0.218636
$646$	−2.26836e12	−0.512467
$647$	3.32786e12	0.746613	0.373307	−	0.927708i	$-0.378224\pi$
$647$	3.32786e12	0.746613	0.373307	+	0.927708i	$0.378224\pi$
$648$	5.85948e12	1.30548
$649$	−2.84968e12	−0.630515
$650$	−1.27104e13	−2.79287
$651$	−1.77099e12	−0.386456
$652$	1.16448e12	0.252358
$653$	−6.30246e12	−1.35644	−0.678220	−	0.734859i	$-0.737249\pi$
$653$	−6.30246e12	−1.35644	−0.678220	+	0.734859i	$0.737249\pi$
$654$	4.10484e12	0.877397
$655$	−5.43863e11	−0.115453
$656$	3.43893e11	0.0725029
$657$	−1.09521e11	−0.0229325
$658$	−1.89129e11	−0.0393315
$659$	2.83854e12	0.586287	0.293143	−	0.956069i	$-0.405299\pi$
$659$	2.83854e12	0.586287	0.293143	+	0.956069i	$0.405299\pi$
$660$	−1.28905e13	−2.64437
$661$	6.58551e12	1.34178	0.670892	−	0.741555i	$-0.265911\pi$
$661$	6.58551e12	1.34178	0.670892	+	0.741555i	$0.265911\pi$
$662$	−1.03990e13	−2.10442
$663$	6.40694e11	0.128777
$664$	1.13922e13	2.27432
$665$	−4.59740e12	−0.911621
$666$	1.12675e12	0.221918
$667$	1.04475e13	2.04383
$668$	1.39757e13	2.71568
$669$	4.71579e11	0.0910201
$670$	8.75931e12	1.67932
$671$	6.55609e11	0.124851
$672$	−4.49355e12	−0.850018
$673$	−2.50086e12	−0.469918	−0.234959	−	0.972005i	$-0.575496\pi$
$673$	−2.50086e12	−0.469918	−0.234959	+	0.972005i	$0.575496\pi$
$674$	−2.76065e12	−0.515279
$675$	−1.28596e13	−2.38429
$676$	−7.35091e12	−1.35388
$677$	1.03159e13	1.88737	0.943687	−	0.330839i	$-0.107332\pi$
$677$	1.03159e13	1.88737	0.943687	+	0.330839i	$0.107332\pi$
$678$	−9.25023e12	−1.68120
$679$	1.86682e12	0.337045
$680$	6.84339e12	1.22739
$681$	2.90246e12	0.517136
$682$	8.71121e12	1.54187
$683$	9.27753e12	1.63132	0.815660	−	0.578531i	$-0.196374\pi$
$683$	9.27753e12	1.63132	0.815660	+	0.578531i	$0.196374\pi$
$684$	−6.29168e12	−1.09904
$685$	−9.52550e12	−1.65303
$686$	8.82440e12	1.52134
$687$	−2.17826e12	−0.373083
$688$	2.56675e12	0.436753
$689$	7.26304e12	1.22781
$690$	2.43275e13	4.08579
$691$	1.58767e12	0.264917	0.132458	−	0.991189i	$-0.457713\pi$
$691$	1.58767e12	0.264917	0.132458	+	0.991189i	$0.457713\pi$
$692$	−2.71137e13	−4.49481
$693$	−8.02686e11	−0.132205
$694$	3.09934e12	0.507167
$695$	−2.63957e12	−0.429142
$696$	−1.79662e13	−2.90212
$697$	3.92241e10	0.00629514
$698$	−6.06717e12	−0.967469
$699$	−2.29373e12	−0.363408
$700$	1.58376e13	2.49316
$701$	−1.15310e13	−1.80358	−0.901791	−	0.432172i	$-0.857747\pi$
$701$	−1.15310e13	−1.80358	−0.901791	+	0.432172i	$0.857747\pi$
$702$	8.88638e12	1.38105
$703$	2.22824e12	0.344082
$704$	8.39113e12	1.28749
$705$	−4.25759e11	−0.0649102
$706$	−1.59766e13	−2.42026
$707$	−1.55600e12	−0.234220
$708$	−1.09921e13	−1.64410
$709$	−1.03429e12	−0.153722	−0.0768609	−	0.997042i	$-0.524490\pi$
$709$	−1.03429e12	−0.153722	−0.0768609	+	0.997042i	$0.524490\pi$
$710$	−1.09654e13	−1.61943
$711$	−2.98315e12	−0.437787
$712$	1.62480e12	0.236941
$713$	−1.17574e13	−1.70376
$714$	−1.11628e12	−0.160743
$715$	−6.38724e12	−0.913979
$716$	−2.74632e13	−3.90519
$717$	−4.26231e12	−0.602294
$718$	1.48899e13	2.09089
$719$	8.27525e12	1.15478	0.577392	−	0.816467i	$-0.304070\pi$
$719$	8.27525e12	1.15478	0.577392	+	0.816467i	$0.304070\pi$
$720$	1.39774e13	1.93835
$721$	3.97956e12	0.548437
$722$	−3.71672e12	−0.509029
$723$	−1.50791e12	−0.205236
$724$	−1.58884e13	−2.14909
$725$	2.14095e13	2.87796
$726$	4.74729e12	0.634207
$727$	5.25612e12	0.697848	0.348924	−	0.937151i	$-0.386547\pi$
$727$	5.25612e12	0.697848	0.348924	+	0.937151i	$0.386547\pi$
$728$	−6.58544e12	−0.868948
$729$	7.84169e12	1.02834
$730$	1.51841e12	0.197895
$731$	2.92762e11	0.0379215
$732$	2.52887e12	0.325557
$733$	7.86667e12	1.00652	0.503261	−	0.864134i	$-0.332133\pi$
$733$	7.86667e12	1.00652	0.503261	+	0.864134i	$0.332133\pi$
$734$	2.02678e13	2.57735
$735$	8.80136e12	1.11239
$736$	−2.98323e13	−3.74746
$737$	3.02439e12	0.377602
$738$	1.52125e11	0.0188776
$739$	−8.65193e12	−1.06712	−0.533560	−	0.845762i	$-0.679146\pi$
$739$	−8.65193e12	−1.06712	−0.533560	+	0.845762i	$0.679146\pi$
$740$	−1.11718e13	−1.36956
$741$	4.91397e12	0.598757
$742$	−1.26544e13	−1.53258
$743$	9.67486e12	1.16465	0.582325	−	0.812956i	$-0.302143\pi$
$743$	9.67486e12	1.16465	0.582325	+	0.812956i	$0.302143\pi$
$744$	2.02189e13	2.41924
$745$	−2.77896e13	−3.30506
$746$	−2.86683e13	−3.38904
$747$	2.65396e12	0.311854
$748$	3.92685e12	0.458656
$749$	1.00934e12	0.117184
$750$	2.71496e13	3.13320
$751$	5.48720e12	0.629464	0.314732	−	0.949181i	$-0.398085\pi$
$751$	5.48720e12	0.629464	0.314732	+	0.949181i	$0.398085\pi$
$752$	1.13712e12	0.129666
$753$	−7.73503e12	−0.876768
$754$	−1.47946e13	−1.66699
$755$	1.13523e12	0.127151
$756$	−1.10727e13	−1.23284
$757$	1.33117e13	1.47333	0.736667	−	0.676255i	$-0.236398\pi$
$757$	1.33117e13	1.47333	0.736667	+	0.676255i	$0.236398\pi$
$758$	2.17550e13	2.39358
$759$	8.39973e12	0.918708
$760$	5.24872e13	5.70680
$761$	9.94914e12	1.07536	0.537681	−	0.843148i	$-0.319301\pi$
$761$	9.94914e12	1.07536	0.537681	+	0.843148i	$0.319301\pi$
$762$	1.67223e12	0.179679
$763$	−2.53437e12	−0.270713
$764$	2.60347e13	2.76460
$765$	1.59426e12	0.168299
$766$	3.23839e13	3.39860
$767$	−5.44656e12	−0.568255
$768$	−1.58941e12	−0.164858
$769$	5.14283e12	0.530315	0.265157	−	0.964205i	$-0.414576\pi$
$769$	5.14283e12	0.530315	0.265157	+	0.964205i	$0.414576\pi$
$770$	1.11285e13	1.14085
$771$	6.93853e12	0.707168
$772$	−3.53668e13	−3.58359
$773$	−3.51233e12	−0.353824	−0.176912	−	0.984227i	$-0.556611\pi$
$773$	−3.51233e12	−0.353824	−0.176912	+	0.984227i	$0.556611\pi$
$774$	1.13543e12	0.113718
$775$	−2.40938e13	−2.39910
$776$	−2.13130e13	−2.10992
$777$	1.09654e12	0.107927
$778$	−1.41351e13	−1.38322
$779$	3.00840e11	0.0292696
$780$	−2.46375e13	−2.38325
$781$	−3.78610e12	−0.364135
$782$	−7.41090e12	−0.708665
$783$	−1.49682e13	−1.42312
$784$	−2.35068e13	−2.22214
$785$	−2.95002e13	−2.77275
$786$	−1.01282e12	−0.0946527
$787$	6.67867e12	0.620589	0.310294	−	0.950641i	$-0.399572\pi$
$787$	6.67867e12	0.620589	0.310294	+	0.950641i	$0.399572\pi$
$788$	2.04132e13	1.88601
$789$	−8.39577e11	−0.0771284
$790$	4.13587e13	3.77785
$791$	5.71119e12	0.518719
$792$	9.16405e12	0.827607
$793$	1.25306e12	0.112523
$794$	2.94838e13	2.63263
$795$	−2.84871e13	−2.52928
$796$	4.50947e13	3.98122
$797$	−4.54726e12	−0.399197	−0.199599	−	0.979878i	$-0.563964\pi$
$797$	−4.54726e12	−0.399197	−0.199599	+	0.979878i	$0.563964\pi$
$798$	−8.56163e12	−0.747384
$799$	1.29699e11	0.0112584
$800$	−6.11337e13	−5.27687
$801$	3.78519e11	0.0324894
$802$	−2.47126e13	−2.10927
$803$	5.24272e11	0.0444976
$804$	1.16660e13	0.984620
$805$	−1.50200e13	−1.26063
$806$	1.66496e13	1.38962
$807$	6.57761e12	0.545931
$808$	1.77645e13	1.46623
$809$	6.56062e12	0.538488	0.269244	−	0.963072i	$-0.413226\pi$
$809$	6.56062e12	0.538488	0.269244	+	0.963072i	$0.413226\pi$
$810$	−1.89251e13	−1.54474
$811$	1.03164e13	0.837403	0.418702	−	0.908124i	$-0.362485\pi$
$811$	1.03164e13	0.837403	0.418702	+	0.908124i	$0.362485\pi$
$812$	1.84346e13	1.48810
$813$	−5.06053e12	−0.406246
$814$	−5.39370e12	−0.430603
$815$	−2.26311e12	−0.179679
$816$	6.71158e12	0.529931
$817$	2.24542e12	0.176318
$818$	−9.93295e12	−0.775690
$819$	−1.53417e12	−0.119150
$820$	−1.50834e12	−0.116503
$821$	−2.30549e13	−1.77100	−0.885500	−	0.464639i	$-0.846184\pi$
$821$	−2.30549e13	−1.77100	−0.885500	+	0.464639i	$0.846184\pi$
$822$	−1.77391e13	−1.35522
$823$	−1.48191e12	−0.112596	−0.0562979	−	0.998414i	$-0.517930\pi$
$823$	−1.48191e12	−0.112596	−0.0562979	+	0.998414i	$0.517930\pi$
$824$	−4.54336e13	−3.43324
$825$	1.72131e13	1.29365
$826$	9.48956e12	0.709310
$827$	1.73025e13	1.28627	0.643137	−	0.765751i	$-0.277632\pi$
$827$	1.73025e13	1.28627	0.643137	+	0.765751i	$0.277632\pi$
$828$	−2.05554e13	−1.51981
$829$	−2.31346e13	−1.70124	−0.850622	−	0.525778i	$-0.823774\pi$
$829$	−2.31346e13	−1.70124	−0.850622	+	0.525778i	$0.823774\pi$
$830$	−3.67947e13	−2.69113
$831$	4.11216e11	0.0299134
$832$	1.60379e13	1.16036
$833$	−2.68117e12	−0.192940
$834$	−4.91561e12	−0.351828
$835$	−2.71610e13	−1.93356
$836$	3.01180e13	2.13255
$837$	1.68450e13	1.18633
$838$	2.76270e13	1.93524
$839$	4.17604e12	0.290962	0.145481	−	0.989361i	$-0.453527\pi$
$839$	4.17604e12	0.290962	0.145481	+	0.989361i	$0.453527\pi$
$840$	2.58295e13	1.79002
$841$	1.04129e13	0.717780
$842$	2.53324e13	1.73689
$843$	−1.19811e12	−0.0817095
$844$	−2.85849e13	−1.93908
$845$	1.42862e13	0.963962
$846$	5.03021e11	0.0337613
$847$	−2.93103e12	−0.195679
$848$	7.60839e13	5.05256
$849$	2.30107e12	0.152000
$850$	−1.51868e13	−0.997884
$851$	7.27981e12	0.475814
$852$	−1.46041e13	−0.949503
$853$	6.57843e12	0.425453	0.212727	−	0.977112i	$-0.431766\pi$
$853$	6.57843e12	0.425453	0.212727	+	0.977112i	$0.431766\pi$
$854$	−2.18321e12	−0.140454
$855$	1.22276e13	0.782516
$856$	−1.15233e13	−0.733576
$857$	−2.26445e13	−1.43400	−0.716999	−	0.697074i	$-0.754485\pi$
$857$	−2.26445e13	−1.43400	−0.716999	+	0.697074i	$0.754485\pi$
$858$	−1.18948e13	−0.749316
$859$	−1.95924e13	−1.22777	−0.613886	−	0.789395i	$-0.710395\pi$
$859$	−1.95924e13	−1.22777	−0.613886	+	0.789395i	$0.710395\pi$
$860$	−1.12580e13	−0.701805
$861$	1.48046e11	0.00918086
$862$	6.14986e12	0.379387
$863$	8.76018e12	0.537606	0.268803	−	0.963195i	$-0.413372\pi$
$863$	8.76018e12	0.537606	0.268803	+	0.963195i	$0.413372\pi$
$864$	4.27411e13	2.60936
$865$	5.26942e13	3.20030
$866$	8.77703e12	0.530294
$867$	7.65517e11	0.0460118
$868$	−2.07460e13	−1.24050
$869$	1.42802e13	0.849467
$870$	5.80276e13	3.43398
$871$	5.78049e12	0.340316
$872$	2.89342e13	1.69468
$873$	−4.96514e12	−0.289312
$874$	−5.68399e13	−3.29497
$875$	−1.67624e13	−0.966721
$876$	2.02227e12	0.116030
$877$	1.76925e13	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$877$	1.76925e13	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$878$	−5.41593e13	−3.07573
$879$	−2.63559e13	−1.48911
$880$	−6.69095e13	−3.76111
$881$	−1.40172e13	−0.783919	−0.391959	−	0.919983i	$-0.628203\pi$
$881$	−1.40172e13	−0.783919	−0.391959	+	0.919983i	$0.628203\pi$
$882$	−1.03985e13	−0.578580
$883$	−7.52196e12	−0.416397	−0.208199	−	0.978087i	$-0.566760\pi$
$883$	−7.52196e12	−0.416397	−0.208199	+	0.978087i	$0.566760\pi$
$884$	7.50534e12	0.413366
$885$	2.13625e13	1.17060
$886$	−1.08628e12	−0.0592229
$887$	−4.64548e12	−0.251985	−0.125992	−	0.992031i	$-0.540211\pi$
$887$	−4.64548e12	−0.251985	−0.125992	+	0.992031i	$0.540211\pi$
$888$	−1.25189e13	−0.675626
$889$	−1.03245e12	−0.0554384
$890$	−5.24782e12	−0.280365
$891$	−6.53440e12	−0.347341
$892$	5.52427e12	0.292168
$893$	9.94765e11	0.0523467
$894$	−5.17520e13	−2.70962
$895$	5.33734e13	2.78049
$896$	−6.97777e12	−0.361685
$897$	1.60543e13	0.827991
$898$	2.93917e13	1.50828
$899$	−2.80446e13	−1.43196
$900$	−4.21230e13	−2.14007
$901$	8.67807e12	0.438694
$902$	−7.28217e11	−0.0366295
$903$	1.10499e12	0.0553049
$904$	−6.52031e13	−3.24721
$905$	3.08783e13	1.53015
$906$	2.11411e12	0.104244
$907$	−2.57831e13	−1.26503	−0.632517	−	0.774546i	$-0.717978\pi$
$907$	−2.57831e13	−1.26503	−0.632517	+	0.774546i	$0.717978\pi$
$908$	3.40006e13	1.65997
$909$	4.13846e12	0.201049
$910$	2.12698e13	1.02820
$911$	3.74022e13	1.79914	0.899568	−	0.436781i	$-0.143882\pi$
$911$	3.74022e13	1.79914	0.899568	+	0.436781i	$0.143882\pi$
$912$	5.14763e13	2.46394
$913$	−1.27044e13	−0.605112
$914$	4.29110e13	2.03381
$915$	−4.91475e12	−0.231796
$916$	−2.55170e13	−1.19757
$917$	6.25329e11	0.0292043
$918$	1.06177e13	0.493444
$919$	9.74612e12	0.450726	0.225363	−	0.974275i	$-0.427643\pi$
$919$	9.74612e12	0.450726	0.225363	+	0.974275i	$0.427643\pi$
$920$	1.71480e14	7.89164
$921$	−2.52932e13	−1.15834
$922$	−1.94912e13	−0.888281
$923$	−7.23633e12	−0.328179
$924$	1.48214e13	0.668905
$925$	1.49181e13	0.670002
$926$	3.19285e13	1.42702
$927$	−1.05843e13	−0.470766
$928$	−7.11582e13	−3.14963
$929$	6.34542e12	0.279505	0.139752	−	0.990186i	$-0.455369\pi$
$929$	6.34542e12	0.279505	0.139752	+	0.990186i	$0.455369\pi$
$930$	−6.53033e13	−2.86261
$931$	−2.05640e13	−0.897084
$932$	−2.68697e13	−1.16652
$933$	1.61857e13	0.699300
$934$	5.17514e13	2.22516
$935$	−7.63164e12	−0.326562
$936$	1.75151e13	0.745886
$937$	−2.80091e13	−1.18706	−0.593528	−	0.804813i	$-0.702265\pi$
$937$	−2.80091e13	−1.18706	−0.593528	+	0.804813i	$0.702265\pi$
$938$	−1.00714e13	−0.424791
$939$	1.97269e13	0.828064
$940$	−4.98751e12	−0.208357
$941$	2.68353e13	1.11571	0.557857	−	0.829937i	$-0.311624\pi$
$941$	2.68353e13	1.11571	0.557857	+	0.829937i	$0.311624\pi$
$942$	−5.49376e13	−2.27321
$943$	9.82866e11	0.0404755
$944$	−5.70554e13	−2.33842
$945$	2.15193e13	0.877781
$946$	−5.43528e12	−0.220654
$947$	−1.27250e13	−0.514140	−0.257070	−	0.966393i	$-0.582757\pi$
$947$	−1.27250e13	−0.514140	−0.257070	+	0.966393i	$0.582757\pi$
$948$	5.50831e13	2.21503
$949$	1.00203e12	0.0401037
$950$	−1.16479e14	−4.63972
$951$	5.39296e12	0.213804
$952$	−7.86846e12	−0.310473
$953$	−2.88311e13	−1.13225	−0.566125	−	0.824319i	$-0.691558\pi$
$953$	−2.88311e13	−1.13225	−0.566125	+	0.824319i	$0.691558\pi$
$954$	3.36566e13	1.31554
$955$	−5.05972e13	−1.96839
$956$	−4.99303e13	−1.93332
$957$	2.00356e13	0.772146
$958$	−5.20170e13	−1.99527
$959$	1.09523e13	0.418141
$960$	−6.29038e13	−2.39032
$961$	5.12133e12	0.193699
$962$	−1.03089e13	−0.388083
$963$	−2.68451e12	−0.100588
$964$	−1.76643e13	−0.658794
$965$	6.87338e13	2.55151
$966$	−2.79715e13	−1.03352
$967$	3.76299e13	1.38393	0.691964	−	0.721932i	$-0.256745\pi$
$967$	3.76299e13	1.38393	0.691964	+	0.721932i	$0.256745\pi$
$968$	3.34628e13	1.22496
$969$	5.87134e12	0.213934
$970$	6.88371e13	2.49660
$971$	−5.14050e13	−1.85575	−0.927873	−	0.372895i	$-0.878365\pi$
$971$	−5.14050e13	−1.85575	−0.927873	+	0.372895i	$0.878365\pi$
$972$	5.06649e13	1.82058
$973$	3.03495e12	0.108553
$974$	−8.32801e13	−2.96501
$975$	3.28992e13	1.16591
$976$	1.31264e13	0.463043
$977$	−2.18727e13	−0.768027	−0.384013	−	0.923328i	$-0.625458\pi$
$977$	−2.18727e13	−0.768027	−0.384013	+	0.923328i	$0.625458\pi$
$978$	−4.21454e12	−0.147308
$979$	−1.81195e12	−0.0630413
$980$	1.03103e14	3.57069
$981$	6.74060e12	0.232374
$982$	9.63577e13	3.30663
$983$	−1.94063e13	−0.662906	−0.331453	−	0.943472i	$-0.607539\pi$
$983$	−1.94063e13	−0.662906	−0.331453	+	0.943472i	$0.607539\pi$
$984$	−1.69020e12	−0.0574726
$985$	−3.96722e13	−1.34284
$986$	−1.76770e13	−0.595611
$987$	4.89533e11	0.0164193
$988$	5.75642e13	1.92197
$989$	7.33593e12	0.243822
$990$	−2.95982e13	−0.979281
$991$	3.18629e12	0.104943	0.0524716	−	0.998622i	$-0.483290\pi$
$991$	3.18629e12	0.104943	0.0524716	+	0.998622i	$0.483290\pi$
$992$	8.00802e13	2.62556
$993$	2.69164e13	0.878509
$994$	1.26079e13	0.409641
$995$	−8.76394e13	−2.83462
$996$	−4.90046e13	−1.57786
$997$	−2.11989e13	−0.679492	−0.339746	−	0.940517i	$-0.610341\pi$
$997$	−2.11989e13	−0.679492	−0.339746	+	0.940517i	$0.610341\pi$
$998$	−9.80005e13	−3.12709
$999$	−1.04299e13	−0.331309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.b.1.1	✓	7
3.2	odd	2		153.10.a.f.1.7		7
4.3	odd	2		272.10.a.g.1.3		7
17.16	even	2		289.10.a.b.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.1	✓	7	1.1	even	1	trivial
153.10.a.f.1.7		7	3.2	odd	2
272.10.a.g.1.3		7	4.3	odd	2
289.10.a.b.1.1		7	17.16	even	2

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +O(q^{10})\)	\(q-42.3973 q^{2} +109.740 q^{3} +1285.53 q^{4} -2498.37 q^{5} -4652.67 q^{6} +2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +105924. q^{10} +36573.4 q^{11} +141074. q^{12} +69902.2 q^{13} -121791. q^{14} -274171. q^{15} +732260. q^{16} +83521.0 q^{17} +323924. q^{18} +640587. q^{19} -3.21175e6 q^{20} +315239. q^{21} -1.55061e6 q^{22} +2.09284e6 q^{23} -3.59900e6 q^{24} +4.28875e6 q^{25} -2.96367e6 q^{26} -2.99844e6 q^{27} +3.69283e6 q^{28} +4.99200e6 q^{29} +1.16241e7 q^{30} -5.61791e6 q^{31} -1.42544e7 q^{32} +4.01355e6 q^{33} -3.54107e6 q^{34} -7.17685e6 q^{35} -9.82174e6 q^{36} +3.47843e6 q^{37} -2.71592e7 q^{38} +7.67105e6 q^{39} +8.19361e7 q^{40} +469632. q^{41} -1.33653e7 q^{42} +3.50525e6 q^{43} +4.70163e7 q^{44} +1.90881e7 q^{45} -8.87310e7 q^{46} +1.55290e6 q^{47} +8.03580e7 q^{48} -3.21017e7 q^{49} -1.81832e8 q^{50} +9.16557e6 q^{51} +8.98617e7 q^{52} +1.03903e8 q^{53} +1.27126e8 q^{54} -9.13740e7 q^{55} -9.42094e7 q^{56} +7.02978e7 q^{57} -2.11648e8 q^{58} -7.79169e7 q^{59} -3.52456e8 q^{60} +1.79259e7 q^{61} +2.38185e8 q^{62} -2.19473e7 q^{63} +2.29433e8 q^{64} -1.74642e8 q^{65} -1.70164e8 q^{66} +8.26939e7 q^{67} +1.07369e8 q^{68} +2.29668e8 q^{69} +3.04279e8 q^{70} -1.03521e8 q^{71} +2.50566e8 q^{72} +1.43348e7 q^{73} -1.47476e8 q^{74} +4.70646e8 q^{75} +8.23496e8 q^{76} +1.05061e8 q^{77} -3.25232e8 q^{78} +3.90455e8 q^{79} -1.82946e9 q^{80} -1.78666e8 q^{81} -1.99111e7 q^{82} -3.47368e8 q^{83} +4.05250e8 q^{84} -2.08667e8 q^{85} -1.48613e8 q^{86} +5.47821e8 q^{87} -1.19945e9 q^{88} -4.95430e7 q^{89} -8.09284e8 q^{90} +2.00802e8 q^{91} +2.69042e9 q^{92} -6.16508e8 q^{93} -6.58387e7 q^{94} -1.60043e9 q^{95} -1.56428e9 q^{96} +6.49870e8 q^{97} +1.36103e9 q^{98} -2.79428e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Introduction

L-functions

Modular forms

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