LMFDB - Embedded newform 289.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
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:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$42.3973$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.3973 q^{2} -109.740 q^{3} +1285.53 q^{4} +2498.37 q^{5} +4652.67 q^{6} -2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} +O(q^{10})$	\(q-42.3973 q^{2} -109.740 q^{3} +1285.53 q^{4} +2498.37 q^{5} +4652.67 q^{6} -2872.61 q^{7} -32795.8 q^{8} -7640.20 q^{9} -105924. q^{10} -36573.4 q^{11} -141074. q^{12} +69902.2 q^{13} +121791. q^{14} -274171. q^{15} +732260. q^{16} +323924. q^{18} +640587. q^{19} +3.21175e6 q^{20} +315239. q^{21} +1.55061e6 q^{22} -2.09284e6 q^{23} +3.59900e6 q^{24} +4.28875e6 q^{25} -2.96367e6 q^{26} +2.99844e6 q^{27} -3.69283e6 q^{28} -4.99200e6 q^{29} +1.16241e7 q^{30} +5.61791e6 q^{31} -1.42544e7 q^{32} +4.01355e6 q^{33} -7.17685e6 q^{35} -9.82174e6 q^{36} -3.47843e6 q^{37} -2.71592e7 q^{38} -7.67105e6 q^{39} -8.19361e7 q^{40} -469632. q^{41} -1.33653e7 q^{42} +3.50525e6 q^{43} -4.70163e7 q^{44} -1.90881e7 q^{45} +8.87310e7 q^{46} +1.55290e6 q^{47} -8.03580e7 q^{48} -3.21017e7 q^{49} -1.81832e8 q^{50} +8.98617e7 q^{52} +1.03903e8 q^{53} -1.27126e8 q^{54} -9.13740e7 q^{55} +9.42094e7 q^{56} -7.02978e7 q^{57} +2.11648e8 q^{58} -7.79169e7 q^{59} -3.52456e8 q^{60} -1.79259e7 q^{61} -2.38185e8 q^{62} +2.19473e7 q^{63} +2.29433e8 q^{64} +1.74642e8 q^{65} -1.70164e8 q^{66} +8.26939e7 q^{67} +2.29668e8 q^{69} +3.04279e8 q^{70} +1.03521e8 q^{71} +2.50566e8 q^{72} -1.43348e7 q^{73} +1.47476e8 q^{74} -4.70646e8 q^{75} +8.23496e8 q^{76} +1.05061e8 q^{77} +3.25232e8 q^{78} -3.90455e8 q^{79} +1.82946e9 q^{80} -1.78666e8 q^{81} +1.99111e7 q^{82} -3.47368e8 q^{83} +4.05250e8 q^{84} -1.48613e8 q^{86} +5.47821e8 q^{87} +1.19945e9 q^{88} -4.95430e7 q^{89} +8.09284e8 q^{90} -2.00802e8 q^{91} -2.69042e9 q^{92} -6.16508e8 q^{93} -6.58387e7 q^{94} +1.60043e9 q^{95} +1.56428e9 q^{96} -6.49870e8 q^{97} +1.36103e9 q^{98} +2.79428e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 7 q - q^{2} - 88 q^{3} + 2389 q^{4} - 1362 q^{5} + 11720 q^{6} - 9388 q^{7} + 16821 q^{8} + 81419 q^{9} - 154226 q^{10} - 135536 q^{11} - 198160 q^{12} + 166122 q^{13} - 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 149027 q^{18} + 777172 q^{19} + 917162 q^{20} - 3412104 q^{21} + 1222520 q^{22} - 1357764 q^{23} + 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} + 4519064 q^{27} + 3328892 q^{28} - 967002 q^{29} - 12558992 q^{30} - 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 530736 q^{35} + 4535009 q^{36} - 18296498 q^{37} - 49363020 q^{38} - 86306872 q^{39} - 127155062 q^{40} - 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} - 96696624 q^{44} - 108916410 q^{45} + 151509484 q^{46} + 56639800 q^{47} + 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} - 156226378 q^{52} + 121813562 q^{53} + 93375344 q^{54} + 40793128 q^{55} + 196175436 q^{56} - 153612960 q^{57} + 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} + 49915846 q^{61} + 73506556 q^{62} + 2185356 q^{63} + 317922057 q^{64} + 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 379683432 q^{69} + 966315960 q^{70} - 652473940 q^{71} + 655760385 q^{72} - 306656342 q^{73} - 249173874 q^{74} - 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} - 323434416 q^{78} - 959147884 q^{79} + 692173602 q^{80} - 374486977 q^{81} - 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} - 164953236 q^{86} - 1612550856 q^{87} - 1132038848 q^{88} - 1971327114 q^{89} + 2284664662 q^{90} + 1061062864 q^{91} - 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} + 3249631512 q^{95} + 4442036640 q^{96} - 2006526254 q^{97} - 2170640009 q^{98} + 2579159272 q^{99}+O(q^{100}) \) 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 + 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 - 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 - 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 + 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 - 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	$-0.627905\pi$
$3$	−109.740	−0.782200	−0.391100	+	0.920348i	$0.627905\pi$
$4$	1285.53	2.51081
$5$	2498.37	1.78769	0.893846	−	0.448375i	$-0.147997\pi$
$5$	2498.37	1.78769	0.893846	+	0.448375i	$0.147997\pi$
$6$	4652.67	1.46562
$7$	−2872.61	−0.452205	−0.226102	−	0.974104i	$-0.572598\pi$
$7$	−2872.61	−0.452205	−0.226102	+	0.974104i	$0.572598\pi$
$8$	−32795.8	−2.83082
$9$	−7640.20	−0.388163
$10$	−105924.	−3.34962
$11$	−36573.4	−0.753178	−0.376589	−	0.926380i	$-0.622903\pi$
$11$	−36573.4	−0.753178	−0.376589	+	0.926380i	$0.622903\pi$
$12$	−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
$17$	0	0
$17$	0	0
$18$	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	$-0.784632\pi$
$23$	−2.09284e6	−1.55941	−0.779707	+	0.626144i	$0.784632\pi$
$24$	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	$-0.727466\pi$
$29$	−4.99200e6	−1.31064	−0.655321	+	0.755351i	$0.727466\pi$
$30$	1.16241e7	2.62008
$31$	5.61791e6	1.09257	0.546283	−	0.837601i	$-0.316042\pi$
$31$	5.61791e6	1.09257	0.546283	+	0.837601i	$0.316042\pi$
$32$	−1.42544e7	−2.40312
$33$	4.01355e6	0.589136
$34$	0	0
$35$	−7.17685e6	−0.808402
$36$	−9.82174e6	−0.974602
$37$	−3.47843e6	−0.305123	−0.152562	−	0.988294i	$-0.548752\pi$
$37$	−3.47843e6	−0.305123	−0.152562	+	0.988294i	$0.548752\pi$
$38$	−2.71592e7	−2.11296
$39$	−7.67105e6	−0.530963
$40$	−8.19361e7	−5.06064
$41$	−469632.	−0.0259555	−0.0129778	−	0.999916i	$-0.504131\pi$
$41$	−469632.	−0.0259555	−0.0129778	+	0.999916i	$0.504131\pi$
$42$	−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
$51$	0	0
$52$	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	$-0.526413\pi$
$61$	−1.79259e7	−0.165766	−0.0828831	+	0.996559i	$0.526413\pi$
$62$	−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	$0.419348\pi$
$68$	0	0
$69$	2.29668e8	1.21977
$70$	3.04279e8	1.51472
$71$	1.03521e8	0.483465	0.241732	−	0.970343i	$-0.422284\pi$
$71$	1.03521e8	0.483465	0.241732	+	0.970343i	$0.422284\pi$
$72$	2.50566e8	1.09882
$73$	−1.43348e7	−0.0590797	−0.0295399	−	0.999564i	$-0.509404\pi$
$73$	−1.43348e7	−0.0590797	−0.0295399	+	0.999564i	$0.509404\pi$
$74$	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	$-0.690708\pi$
$79$	−3.90455e8	−1.12784	−0.563922	+	0.825828i	$0.690708\pi$
$80$	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
$85$	0	0
$86$	−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	$-0.621557\pi$
$97$	−6.49870e8	−0.745338	−0.372669	+	0.927964i	$0.621557\pi$
$98$	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	$0.583385\pi$
$102$	0	0
$103$	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	$-0.541359\pi$
$107$	−3.51366e8	−0.259139	−0.129569	+	0.991570i	$0.541359\pi$
$108$	3.85460e9	2.72629
$109$	8.82255e8	0.598652	0.299326	−	0.954151i	$-0.403238\pi$
$109$	8.82255e8	0.598652	0.299326	+	0.954151i	$0.403238\pi$
$110$	3.87401e9	2.52286
$111$	3.81722e8	0.238668
$112$	−2.10349e9	−1.26317
$113$	−1.98816e9	−1.14709	−0.573545	−	0.819174i	$-0.694432\pi$
$113$	−1.98816e9	−1.14709	−0.573545	+	0.819174i	$0.694432\pi$
$114$	2.98044e9	1.65276
$115$	−5.22871e9	−2.78775
$116$	−6.41739e9	−3.29077
$117$	−5.34067e8	−0.263487
$118$	3.30347e9	1.56856
$119$	0	0
$120$	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	$-0.510280\pi$
$131$	−2.17687e8	−0.0645820	−0.0322910	+	0.999479i	$0.510280\pi$
$132$	5.15955e9	1.47921
$133$	−1.84015e9	−0.509943
$134$	−3.50600e9	−0.939378
$135$	7.49123e9	1.94111
$136$	0	0
$137$	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	$-0.538298\pi$
$139$	−1.05651e9	−0.240054	−0.120027	+	0.992771i	$0.538298\pi$
$140$	−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
$153$	0	0
$154$	−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	$-0.516003\pi$
$163$	−9.05833e8	−0.100509	−0.0502544	+	0.998736i	$0.516003\pi$
$164$	−6.03728e8	−0.0651694
$165$	1.00273e10	1.05319
$166$	1.47275e10	1.50536
$167$	−1.08715e10	−1.08159	−0.540797	−	0.841153i	$-0.681877\pi$
$167$	−1.08715e10	−1.08159	−0.540797	+	0.841153i	$0.681877\pi$
$168$	−1.03385e10	−1.00130
$169$	−5.71818e9	−0.539222
$170$	0	0
$171$	−4.89422e9	−0.437724
$172$	4.50611e9	0.392576
$173$	2.10914e10	1.79019	0.895093	−	0.445880i	$-0.147109\pi$
$173$	2.10914e10	1.79019	0.895093	+	0.445880i	$0.147109\pi$
$174$	−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	$-0.359229\pi$
$181$	1.23594e10	0.855937	0.427969	+	0.903794i	$0.359229\pi$
$182$	8.51345e9	0.575154
$183$	1.96718e9	0.129662
$184$	6.86364e10	4.41443
$185$	−8.69042e9	−0.545466
$186$	2.61383e10	1.60129
$187$	0	0
$188$	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	$-0.247048\pi$
$193$	2.75114e10	1.42727	0.713633	+	0.700520i	$0.247048\pi$
$194$	2.75527e10	1.39655
$195$	−1.91652e10	−0.949197
$196$	−4.12679e10	−1.99738
$197$	−1.58792e10	−0.751156	−0.375578	−	0.926791i	$-0.622556\pi$
$197$	−1.58792e10	−0.751156	−0.375578	+	0.926791i	$0.622556\pi$
$198$	−1.18470e10	−0.547791
$199$	−3.50786e10	−1.58563	−0.792817	−	0.609460i	$-0.791386\pi$
$199$	−3.50786e10	−1.58563	−0.792817	+	0.609460i	$0.791386\pi$
$200$	−1.40653e11	−6.21604
$201$	−9.07480e9	−0.392152
$202$	2.29653e10	0.970491
$203$	1.43401e10	0.592678
$204$	0	0
$205$	−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	$-0.373806\pi$
$211$	2.22358e10	0.772293	0.386146	+	0.922438i	$0.373806\pi$
$212$	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
$221$	0	0
$222$	−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	$-0.607239\pi$
$227$	−2.64486e10	−0.661129	−0.330565	+	0.943783i	$0.607239\pi$
$228$	−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	$-0.425375\pi$
$233$	2.09016e10	0.464598	0.232299	+	0.972644i	$0.425375\pi$
$234$	2.26430e10	0.493700
$235$	3.87972e9	0.0829841
$236$	−1.00165e11	−2.10190
$237$	4.28484e10	0.882200
$238$	0	0
$239$	−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	$-0.458120\pi$
$241$	1.37408e10	0.262383	0.131192	+	0.991357i	$0.458120\pi$
$242$	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
$255$	0	0
$256$	−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	$-0.613469\pi$
$269$	−5.99383e10	−0.697942	−0.348971	+	0.937134i	$0.613469\pi$
$270$	−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	$0.583618\pi$
$272$	0	0
$273$	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	$-0.506087\pi$
$277$	−3.74719e9	−0.0382426	−0.0191213	+	0.999817i	$0.506087\pi$
$278$	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	$-0.530976\pi$
$283$	−2.09684e10	−0.194324	−0.0971620	+	0.995269i	$0.530976\pi$
$284$	1.33079e11	1.21389
$285$	−1.75630e11	−1.57688
$286$	1.08391e11	0.957960
$287$	1.34907e9	0.0117372
$288$	1.08907e11	0.932800
$289$	0	0
$290$	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
$306$	0	0
$307$	−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	$-0.647510\pi$
$311$	−1.47492e11	−0.894016	−0.447008	+	0.894530i	$0.647510\pi$
$312$	2.51578e11	1.50306
$313$	−1.79761e11	−1.05863	−0.529317	−	0.848424i	$-0.677552\pi$
$313$	−1.79761e11	−1.05863	−0.529317	+	0.848424i	$0.677552\pi$
$314$	−5.00617e11	−2.90618
$315$	5.48326e10	0.313792
$316$	−5.01943e11	−2.83180
$317$	−4.91432e10	−0.273336	−0.136668	−	0.990617i	$-0.543639\pi$
$317$	−4.91432e10	−0.273336	−0.136668	+	0.990617i	$0.543639\pi$
$318$	4.83425e11	2.65099
$319$	1.82574e11	0.987146
$320$	5.73209e11	3.05589
$321$	3.85588e10	0.202698
$322$	−2.54889e11	−1.32130
$323$	0	0
$324$	−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	$-0.543907\pi$
$337$	−6.51138e10	−0.275004	−0.137502	+	0.990502i	$0.543907\pi$
$338$	2.42435e11	1.01035
$339$	2.18180e11	0.897254
$340$	0	0
$341$	−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	$-0.456788\pi$
$347$	7.31021e10	0.270675	0.135337	+	0.990800i	$0.456788\pi$
$348$	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
$357$	0	0
$358$	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	$-0.258592\pi$
$367$	4.78044e11	1.37553	0.687766	+	0.725933i	$0.258592\pi$
$368$	−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	$0.140346\pi$
$374$	0	0
$375$	−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	$-0.279462\pi$
$379$	5.13122e11	1.27745	0.638725	+	0.769435i	$0.279462\pi$
$380$	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
$391$	0	0
$392$	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	$-0.252059\pi$
$397$	6.95415e11	1.40503	0.702517	+	0.711667i	$0.252059\pi$
$398$	1.48724e12	2.97103
$399$	2.01938e11	0.398878
$400$	3.14048e12	6.13375
$401$	−5.82880e11	−1.12572	−0.562859	−	0.826553i	$-0.690299\pi$
$401$	−5.82880e11	−1.12572	−0.562859	+	0.826553i	$0.690299\pi$
$402$	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
$408$	0	0
$409$	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	$-0.327265\pi$
$419$	6.51621e11	1.03284	0.516419	+	0.856336i	$0.327265\pi$
$420$	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
$425$	0	0
$426$	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	$-0.467719\pi$
$431$	1.45053e11	0.202478	0.101239	+	0.994862i	$0.467719\pi$
$432$	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	$-0.806448\pi$
$439$	−1.27742e12	−1.64151	−0.820757	+	0.571278i	$0.806448\pi$
$440$	2.99668e12	3.81156
$441$	2.45264e11	0.308788
$442$	0	0
$443$	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	$-0.368147\pi$
$449$	6.93244e11	0.804967	0.402483	+	0.915427i	$0.368147\pi$
$450$	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
$459$	0	0
$460$	−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
$476$	0	0
$477$	−7.93839e11	−0.702101
$478$	1.64672e12	1.44276
$479$	−1.22689e12	−1.06487	−0.532436	−	0.846470i	$-0.678723\pi$
$479$	−1.22689e12	−1.06487	−0.532436	+	0.846470i	$0.678723\pi$
$480$	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	$-0.790549\pi$
$487$	−1.96428e12	−1.58242	−0.791211	+	0.611543i	$0.790549\pi$
$488$	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
$493$	0	0
$494$	−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	$-0.814222\pi$
$499$	−2.31148e12	−1.66893	−0.834464	+	0.551063i	$0.814222\pi$
$500$	7.50144e12	5.36759
$501$	1.19303e12	0.846024
$502$	2.98839e12	2.10025
$503$	2.10646e12	1.46723	0.733615	−	0.679565i	$-0.237832\pi$
$503$	2.10646e12	1.46723	0.733615	+	0.679565i	$0.237832\pi$
$504$	−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	$0.674241\pi$
$510$	0	0
$511$	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	$-0.462931\pi$
$521$	3.90823e11	0.232386	0.116193	+	0.993227i	$0.462931\pi$
$522$	−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
$527$	0	0
$528$	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	$-0.618640\pi$
$541$	−1.45109e12	−0.728296	−0.364148	+	0.931341i	$0.618640\pi$
$542$	1.95511e12	0.973138
$543$	−1.35631e12	−0.669515
$544$	0	0
$545$	2.20420e12	1.07021
$546$	−9.34264e11	−0.449886
$547$	2.60966e10	0.0124635	0.00623177	−	0.999981i	$-0.498016\pi$
$547$	2.60966e10	0.0124635	0.00623177	+	0.999981i	$0.498016\pi$
$548$	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
$561$	0	0
$562$	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	$-0.664872\pi$
$571$	−2.51532e12	−0.990216	−0.495108	+	0.868831i	$0.664872\pi$
$572$	−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	$0.398846\pi$
$578$	0	0
$579$	−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
$595$	0	0
$596$	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	$-0.543788\pi$
$601$	−8.77198e11	−0.274260	−0.137130	+	0.990553i	$0.543788\pi$
$602$	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	$-0.447679\pi$
$607$	1.09458e12	0.327265	0.163632	+	0.986521i	$0.447679\pi$
$608$	−9.13121e12	−2.70995
$609$	−1.57367e12	−0.463593
$610$	1.89879e12	0.555254
$611$	1.08551e11	0.0315100
$612$	0	0
$613$	−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	$-0.366858\pi$
$617$	2.92442e12	0.812376	0.406188	+	0.913790i	$0.366858\pi$
$618$	6.44557e12	1.77751
$619$	−1.52167e12	−0.416593	−0.208296	−	0.978066i	$-0.566792\pi$
$619$	−1.52167e12	−0.416593	−0.208296	+	0.978066i	$0.566792\pi$
$620$	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
$629$	0	0
$630$	−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	$-0.628803\pi$
$641$	−3.36551e12	−0.787389	−0.393694	+	0.919241i	$0.628803\pi$
$642$	−1.63479e12	−0.379799
$643$	1.05715e12	0.243887	0.121943	−	0.992537i	$-0.461087\pi$
$643$	1.05715e12	0.243887	0.121943	+	0.992537i	$0.461087\pi$
$644$	7.72852e12	1.77056
$645$	−9.61036e11	−0.218636
$646$	0	0
$647$	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	$-0.262751\pi$
$653$	6.30246e12	1.35644	0.678220	+	0.734859i	$0.262751\pi$
$654$	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
$663$	0	0
$664$	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	$-0.424504\pi$
$673$	2.50086e12	0.469918	0.234959	+	0.972005i	$0.424504\pi$
$674$	2.76065e12	0.515279
$675$	1.28596e13	2.38429
$676$	−7.35091e12	−1.35388
$677$	−1.03159e13	−1.88737	−0.943687	−	0.330839i	$-0.892668\pi$
$677$	−1.03159e13	−1.88737	−0.943687	+	0.330839i	$0.892668\pi$
$678$	−9.25023e12	−1.68120
$679$	1.86682e12	0.337045
$680$	0	0
$681$	2.90246e12	0.517136
$682$	8.71121e12	1.54187
$683$	−9.27753e12	−1.63132	−0.815660	−	0.578531i	$-0.803626\pi$
$683$	−9.27753e12	−1.63132	−0.815660	+	0.578531i	$0.803626\pi$
$684$	−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	$-0.542287\pi$
$691$	−1.58767e12	−0.264917	−0.132458	+	0.991189i	$0.542287\pi$
$692$	2.71137e13	4.49481
$693$	−8.02686e11	−0.132205
$694$	−3.09934e12	−0.507167
$695$	−2.63957e12	−0.429142
$696$	−1.79662e13	−2.90212
$697$	0	0
$698$	−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	$-0.475510\pi$
$709$	1.03429e12	0.153722	0.0768609	+	0.997042i	$0.475510\pi$
$710$	−1.09654e13	−1.61943
$711$	2.98315e12	0.437787
$712$	1.62480e12	0.236941
$713$	−1.17574e13	−1.70376
$714$	0	0
$715$	−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	$-0.695930\pi$
$719$	−8.27525e12	−1.15478	−0.577392	+	0.816467i	$0.695930\pi$
$720$	−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
$731$	0	0
$732$	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	$-0.697857\pi$
$743$	−9.67486e12	−1.16465	−0.582325	+	0.812956i	$0.697857\pi$
$744$	2.02189e13	2.41924
$745$	2.77896e13	3.30506
$746$	−2.86683e13	−3.38904
$747$	2.65396e12	0.311854
$748$	0	0
$749$	1.00934e12	0.117184
$750$	2.71496e13	3.13320
$751$	−5.48720e12	−0.629464	−0.314732	−	0.949181i	$-0.601915\pi$
$751$	−5.48720e12	−0.629464	−0.314732	+	0.949181i	$0.601915\pi$
$752$	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
$765$	0	0
$766$	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
$782$	0	0
$783$	−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	$-0.600428\pi$
$787$	−6.67867e12	−0.620589	−0.310294	+	0.950641i	$0.600428\pi$
$788$	−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
$799$	0	0
$800$	−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	$-0.586774\pi$
$809$	−6.56062e12	−0.538488	−0.269244	+	0.963072i	$0.586774\pi$
$810$	1.89251e13	1.54474
$811$	−1.03164e13	−0.837403	−0.418702	−	0.908124i	$-0.637515\pi$
$811$	−1.03164e13	−0.837403	−0.418702	+	0.908124i	$0.637515\pi$
$812$	1.84346e13	1.48810
$813$	5.06053e12	0.406246
$814$	−5.39370e12	−0.430603
$815$	−2.26311e12	−0.179679
$816$	0	0
$817$	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	$-0.153816\pi$
$821$	2.30549e13	1.77100	0.885500	+	0.464639i	$0.153816\pi$
$822$	1.77391e13	1.35522
$823$	1.48191e12	0.112596	0.0562979	−	0.998414i	$-0.482070\pi$
$823$	1.48191e12	0.112596	0.0562979	+	0.998414i	$0.482070\pi$
$824$	−4.54336e13	−3.43324
$825$	1.72131e13	1.29365
$826$	−9.48956e12	−0.709310
$827$	−1.73025e13	−1.28627	−0.643137	−	0.765751i	$-0.722368\pi$
$827$	−1.73025e13	−1.28627	−0.643137	+	0.765751i	$0.722368\pi$
$828$	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
$833$	0	0
$834$	−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	$-0.546473\pi$
$839$	−4.17604e12	−0.290962	−0.145481	+	0.989361i	$0.546473\pi$
$840$	−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
$850$	0	0
$851$	7.27981e12	0.475814
$852$	−1.46041e13	−0.949503
$853$	−6.57843e12	−0.425453	−0.212727	−	0.977112i	$-0.568234\pi$
$853$	−6.57843e12	−0.425453	−0.212727	+	0.977112i	$0.568234\pi$
$854$	−2.18321e12	−0.140454
$855$	−1.22276e13	−0.782516
$856$	1.15233e13	0.733576
$857$	2.26445e13	1.43400	0.716999	−	0.697074i	$-0.245515\pi$
$857$	2.26445e13	1.43400	0.716999	+	0.697074i	$0.245515\pi$
$858$	−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
$867$	0	0
$868$	−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	$-0.668495\pi$
$877$	−1.76925e13	−1.00993	−0.504965	+	0.863140i	$0.668495\pi$
$878$	5.41593e13	3.07573
$879$	2.63559e13	1.48911
$880$	−6.69095e13	−3.76111
$881$	1.40172e13	0.783919	0.391959	−	0.919983i	$-0.371797\pi$
$881$	1.40172e13	0.783919	0.391959	+	0.919983i	$0.371797\pi$
$882$	−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	$0.566760\pi$
$884$	0	0
$885$	2.13625e13	1.17060
$886$	−1.08628e12	−0.0592229
$887$	4.64548e12	0.251985	0.125992	−	0.992031i	$-0.459789\pi$
$887$	4.64548e12	0.251985	0.125992	+	0.992031i	$0.459789\pi$
$888$	−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
$901$	0	0
$902$	−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	$-0.282022\pi$
$907$	2.57831e13	1.26503	0.632517	+	0.774546i	$0.282022\pi$
$908$	−3.40006e13	−1.65997
$909$	4.13846e12	0.201049
$910$	2.12698e13	1.02820
$911$	−3.74022e13	−1.79914	−0.899568	−	0.436781i	$-0.856118\pi$
$911$	−3.74022e13	−1.79914	−0.899568	+	0.436781i	$0.856118\pi$
$912$	−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
$918$	0	0
$919$	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	$-0.544631\pi$
$929$	−6.34542e12	−0.279505	−0.139752	+	0.990186i	$0.544631\pi$
$930$	6.53033e13	2.86261
$931$	−2.05640e13	−0.897084
$932$	2.68697e13	1.16652
$933$	1.61857e13	0.699300
$934$	5.17514e13	2.22516
$935$	0	0
$936$	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	$-0.688376\pi$
$941$	−2.68353e13	−1.11571	−0.557857	+	0.829937i	$0.688376\pi$
$942$	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	$-0.417243\pi$
$947$	1.27250e13	0.514140	0.257070	+	0.966393i	$0.417243\pi$
$948$	5.50831e13	2.21503
$949$	−1.00203e12	−0.0401037
$950$	−1.16479e14	−4.63972
$951$	5.39296e12	0.213804
$952$	0	0
$953$	−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
$969$	0	0
$970$	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	$-0.392461\pi$
$983$	1.94063e13	0.662906	0.331453	+	0.943472i	$0.392461\pi$
$984$	−1.69020e12	−0.0574726
$985$	−3.96722e13	−1.34284
$986$	0	0
$987$	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	$-0.516710\pi$
$991$	−3.18629e12	−0.104943	−0.0524716	+	0.998622i	$0.516710\pi$
$992$	−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	$-0.389659\pi$
$997$	2.11989e13	0.679492	0.339746	+	0.940517i	$0.389659\pi$
$998$	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	289.10.a.b.1.1		7
17.16	even	2		17.10.a.b.1.1	✓	7
51.50	odd	2		153.10.a.f.1.7		7
68.67	odd	2		272.10.a.g.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.1	✓	7	17.16	even	2
153.10.a.f.1.7		7	51.50	odd	2
272.10.a.g.1.3		7	68.67	odd	2
289.10.a.b.1.1		7	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

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

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