LMFDB - Embedded newform 273.12.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,12,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("273.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	273.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:	$209.757688293$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} + \cdots + 45\!\cdots\!68 $ x^16 - x^15 - 26640x^14 - 38138x^13 + 279954048x^12 + 940095168x^11 - 1473489774048x^10 - 6951601887328x^9 + 4072481535854976x^8 + 21355761647276288x^7 - 5703452025696599040x^6 - 25041700255043457024x^5 + 3737994671267475603456x^4 + 6711995200063092490240x^3 - 963518272786595267739648x^2 + 1287697466669064032092160x + 45555354651594891689197568
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-81.4415$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-85.4415 q^{2} -243.000 q^{3} +5252.25 q^{4} +8053.09 q^{5} +20762.3 q^{6} +16807.0 q^{7} -273776. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-85.4415 q^{2} -243.000 q^{3} +5252.25 q^{4} +8053.09 q^{5} +20762.3 q^{6} +16807.0 q^{7} -273776. q^{8} +59049.0 q^{9} -688068. q^{10} -763843. q^{11} -1.27630e6 q^{12} -371293. q^{13} -1.43602e6 q^{14} -1.95690e6 q^{15} +1.26353e7 q^{16} -1.13101e7 q^{17} -5.04524e6 q^{18} +1.19332e7 q^{19} +4.22969e7 q^{20} -4.08410e6 q^{21} +6.52639e7 q^{22} -2.31448e7 q^{23} +6.65277e7 q^{24} +1.60241e7 q^{25} +3.17238e7 q^{26} -1.43489e7 q^{27} +8.82746e7 q^{28} +6.17965e7 q^{29} +1.67201e8 q^{30} +2.82040e8 q^{31} -5.18881e8 q^{32} +1.85614e8 q^{33} +9.66351e8 q^{34} +1.35348e8 q^{35} +3.10140e8 q^{36} +1.13149e8 q^{37} -1.01959e9 q^{38} +9.02242e7 q^{39} -2.20474e9 q^{40} +8.17246e8 q^{41} +3.48952e8 q^{42} -1.03346e9 q^{43} -4.01190e9 q^{44} +4.75527e8 q^{45} +1.97753e9 q^{46} -9.12860e8 q^{47} -3.07037e9 q^{48} +2.82475e8 q^{49} -1.36912e9 q^{50} +2.74835e9 q^{51} -1.95013e9 q^{52} +3.83883e8 q^{53} +1.22599e9 q^{54} -6.15129e9 q^{55} -4.60136e9 q^{56} -2.89977e9 q^{57} -5.27998e9 q^{58} +7.57765e9 q^{59} -1.02781e10 q^{60} -4.32479e9 q^{61} -2.40980e10 q^{62} +9.92437e8 q^{63} +1.84570e10 q^{64} -2.99005e9 q^{65} -1.58591e10 q^{66} +5.01329e9 q^{67} -5.94034e10 q^{68} +5.62420e9 q^{69} -1.15644e10 q^{70} +2.74383e10 q^{71} -1.61662e10 q^{72} +1.00245e10 q^{73} -9.66760e9 q^{74} -3.89385e9 q^{75} +6.26762e10 q^{76} -1.28379e10 q^{77} -7.70889e9 q^{78} -1.20185e10 q^{79} +1.01753e11 q^{80} +3.48678e9 q^{81} -6.98268e10 q^{82} -5.80640e10 q^{83} -2.14507e10 q^{84} -9.10811e10 q^{85} +8.83003e10 q^{86} -1.50165e10 q^{87} +2.09122e11 q^{88} -2.43139e10 q^{89} -4.06297e10 q^{90} -6.24032e9 q^{91} -1.21563e11 q^{92} -6.85358e10 q^{93} +7.79962e10 q^{94} +9.60991e10 q^{95} +1.26088e11 q^{96} +1.17628e11 q^{97} -2.41351e10 q^{98} -4.51041e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) $ 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9 + 1056711 * q^10 - 466884 * q^11 - 5044923 * q^12 - 5940688 * q^13 - 1058841 * q^14 + 769824 * q^15 + 40058265 * q^16 + 1753452 * q^17 - 3720087 * q^18 + 4237800 * q^19 - 20710503 * q^20 - 65345616 * q^21 - 37479661 * q^22 - 150481440 * q^23 + 45675495 * q^24 + 150983176 * q^25 + 23391459 * q^26 - 229582512 * q^27 + 348930127 * q^28 - 111411432 * q^29 - 256780773 * q^30 - 90536236 * q^31 - 609941313 * q^32 + 113452812 * q^33 + 443745577 * q^34 - 53244576 * q^35 + 1225916289 * q^36 - 1756337900 * q^37 - 4378868973 * q^38 + 1443587184 * q^39 + 57535383 * q^40 + 649575720 * q^41 + 257298363 * q^42 - 1889554520 * q^43 - 4979587689 * q^44 - 187067232 * q^45 - 3204000867 * q^46 - 4036082940 * q^47 - 9734158395 * q^48 + 4519603984 * q^49 - 15928886862 * q^50 - 426088836 * q^51 - 7708413973 * q^52 + 511144020 * q^53 + 903981141 * q^54 - 8519365572 * q^55 - 3159127755 * q^56 - 1029785400 * q^57 - 7851149577 * q^58 + 3728287296 * q^59 + 5032652229 * q^60 + 26227205052 * q^61 + 2996618490 * q^62 + 15878984688 * q^63 + 51104408465 * q^64 + 1176256224 * q^65 + 9107557623 * q^66 - 5295680024 * q^67 + 7919540325 * q^68 + 36566989920 * q^69 + 17760141777 * q^70 + 17082800928 * q^71 - 11099145285 * q^72 + 21076301488 * q^73 + 52794333675 * q^74 - 36688911768 * q^75 + 81459179177 * q^76 - 7846919388 * q^77 - 5684124537 * q^78 - 83677977852 * q^79 - 163988465427 * q^80 + 55788550416 * q^81 - 61543728760 * q^82 - 72857072340 * q^83 - 84790020861 * q^84 - 12608565060 * q^85 - 20177818011 * q^86 + 27072977976 * q^87 - 202213679643 * q^88 + 32238476676 * q^89 + 62397727839 * q^90 - 99845143216 * q^91 - 487057197033 * q^92 + 22000305348 * q^93 + 183904776602 * q^94 - 143022915504 * q^95 + 148215739059 * q^96 + 6973535140 * q^97 - 17795940687 * q^98 - 27569033316 * 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 $

$2$	−85.4415	−1.88801	−0.944004	−	0.329933i	$-0.892974\pi$
$2$	−85.4415	−1.88801	−0.944004	+	0.329933i	$0.892974\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5252.25	2.56458
$5$	8053.09	1.15246	0.576232	−	0.817286i	$-0.304522\pi$
$5$	8053.09	1.15246	0.576232	+	0.817286i	$0.304522\pi$
$6$	20762.3	1.09004
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−273776.	−2.95394
$9$	59049.0	0.333333
$10$	−688068.	−2.17586
$11$	−763843.	−1.43003	−0.715013	−	0.699111i	$-0.753579\pi$
$11$	−763843.	−1.43003	−0.715013	+	0.699111i	$0.753579\pi$
$12$	−1.27630e6	−1.48066
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−1.43602e6	−0.713600
$15$	−1.95690e6	−0.665375
$16$	1.26353e7	3.01248
$17$	−1.13101e7	−1.93195	−0.965977	−	0.258628i	$-0.916729\pi$
$17$	−1.13101e7	−1.93195	−0.965977	+	0.258628i	$0.916729\pi$
$18$	−5.04524e6	−0.629336
$19$	1.19332e7	1.10564	0.552818	−	0.833302i	$-0.313553\pi$
$19$	1.19332e7	1.10564	0.552818	+	0.833302i	$0.313553\pi$
$20$	4.22969e7	2.95558
$21$	−4.08410e6	−0.218218
$22$	6.52639e7	2.69990
$23$	−2.31448e7	−0.749810	−0.374905	−	0.927063i	$-0.622325\pi$
$23$	−2.31448e7	−0.749810	−0.374905	+	0.927063i	$0.622325\pi$
$24$	6.65277e7	1.70546
$25$	1.60241e7	0.328173
$26$	3.17238e7	0.523639
$27$	−1.43489e7	−0.192450
$28$	8.82746e7	0.969319
$29$	6.17965e7	0.559467	0.279734	−	0.960078i	$-0.409754\pi$
$29$	6.17965e7	0.559467	0.279734	+	0.960078i	$0.409754\pi$
$30$	1.67201e8	1.25623
$31$	2.82040e8	1.76938	0.884692	−	0.466176i	$-0.154369\pi$
$31$	2.82040e8	1.76938	0.884692	+	0.466176i	$0.154369\pi$
$32$	−5.18881e8	−2.73365
$33$	1.85614e8	0.825626
$34$	9.66351e8	3.64755
$35$	1.35348e8	0.435590
$36$	3.10140e8	0.854859
$37$	1.13149e8	0.268250	0.134125	−	0.990964i	$-0.457178\pi$
$37$	1.13149e8	0.268250	0.134125	+	0.990964i	$0.457178\pi$
$38$	−1.01959e9	−2.08745
$39$	9.02242e7	0.160128
$40$	−2.20474e9	−3.40430
$41$	8.17246e8	1.10165	0.550823	−	0.834622i	$-0.314314\pi$
$41$	8.17246e8	1.10165	0.550823	+	0.834622i	$0.314314\pi$
$42$	3.48952e8	0.411997
$43$	−1.03346e9	−1.07205	−0.536027	−	0.844201i	$-0.680076\pi$
$43$	−1.03346e9	−1.07205	−0.536027	+	0.844201i	$0.680076\pi$
$44$	−4.01190e9	−3.66741
$45$	4.75527e8	0.384155
$46$	1.97753e9	1.41565
$47$	−9.12860e8	−0.580585	−0.290293	−	0.956938i	$-0.593753\pi$
$47$	−9.12860e8	−0.580585	−0.290293	+	0.956938i	$0.593753\pi$
$48$	−3.07037e9	−1.73926
$49$	2.82475e8	0.142857
$50$	−1.36912e9	−0.619594
$51$	2.74835e9	1.11541
$52$	−1.95013e9	−0.711286
$53$	3.83883e8	0.126090	0.0630451	−	0.998011i	$-0.479919\pi$
$53$	3.83883e8	0.126090	0.0630451	+	0.998011i	$0.479919\pi$
$54$	1.22599e9	0.363347
$55$	−6.15129e9	−1.64805
$56$	−4.60136e9	−1.11648
$57$	−2.89977e9	−0.638339
$58$	−5.27998e9	−1.05628
$59$	7.57765e9	1.37990	0.689951	−	0.723856i	$-0.257632\pi$
$59$	7.57765e9	1.37990	0.689951	+	0.723856i	$0.257632\pi$
$60$	−1.02781e10	−1.70641
$61$	−4.32479e9	−0.655618	−0.327809	−	0.944744i	$-0.606310\pi$
$61$	−4.32479e9	−0.655618	−0.327809	+	0.944744i	$0.606310\pi$
$62$	−2.40980e10	−3.34061
$63$	9.92437e8	0.125988
$64$	1.84570e10	2.14868
$65$	−2.99005e9	−0.319636
$66$	−1.58591e10	−1.55879
$67$	5.01329e9	0.453640	0.226820	−	0.973937i	$-0.427167\pi$
$67$	5.01329e9	0.453640	0.226820	+	0.973937i	$0.427167\pi$
$68$	−5.94034e10	−4.95464
$69$	5.62420e9	0.432903
$70$	−1.15644e10	−0.822399
$71$	2.74383e10	1.80483	0.902416	−	0.430867i	$-0.141792\pi$
$71$	2.74383e10	1.80483	0.902416	+	0.430867i	$0.141792\pi$
$72$	−1.61662e10	−0.984645
$73$	1.00245e10	0.565964	0.282982	−	0.959125i	$-0.408676\pi$
$73$	1.00245e10	0.565964	0.282982	+	0.959125i	$0.408676\pi$
$74$	−9.66760e9	−0.506459
$75$	−3.89385e9	−0.189471
$76$	6.26762e10	2.83549
$77$	−1.28379e10	−0.540499
$78$	−7.70889e9	−0.302323
$79$	−1.20185e10	−0.439441	−0.219721	−	0.975563i	$-0.570515\pi$
$79$	−1.20185e10	−0.439441	−0.219721	+	0.975563i	$0.570515\pi$
$80$	1.01753e11	3.47177
$81$	3.48678e9	0.111111
$82$	−6.98268e10	−2.07992
$83$	−5.80640e10	−1.61800	−0.808998	−	0.587812i	$-0.799990\pi$
$83$	−5.80640e10	−1.61800	−0.808998	+	0.587812i	$0.799990\pi$
$84$	−2.14507e10	−0.559637
$85$	−9.10811e10	−2.22651
$86$	8.83003e10	2.02405
$87$	−1.50165e10	−0.323009
$88$	2.09122e11	4.22421
$89$	−2.43139e10	−0.461540	−0.230770	−	0.973008i	$-0.574125\pi$
$89$	−2.43139e10	−0.461540	−0.230770	+	0.973008i	$0.574125\pi$
$90$	−4.06297e10	−0.725287
$91$	−6.24032e9	−0.104828
$92$	−1.21563e11	−1.92295
$93$	−6.85358e10	−1.02155
$94$	7.79962e10	1.09615
$95$	9.60991e10	1.27421
$96$	1.26088e11	1.57827
$97$	1.17628e11	1.39081	0.695405	−	0.718618i	$-0.255225\pi$
$97$	1.17628e11	1.39081	0.695405	+	0.718618i	$0.255225\pi$
$98$	−2.41351e10	−0.269716
$99$	−4.51041e10	−0.476676
$100$	8.41626e10	0.841626
$101$	1.26568e11	1.19828	0.599138	−	0.800646i	$-0.295510\pi$
$101$	1.26568e11	1.19828	0.599138	+	0.800646i	$0.295510\pi$
$102$	−2.34823e11	−2.10591
$103$	−9.18850e10	−0.780980	−0.390490	−	0.920607i	$-0.627694\pi$
$103$	−9.18850e10	−0.780980	−0.390490	+	0.920607i	$0.627694\pi$
$104$	1.01651e11	0.819274
$105$	−3.28896e10	−0.251488
$106$	−3.27995e10	−0.238059
$107$	6.94702e10	0.478837	0.239419	−	0.970916i	$-0.423043\pi$
$107$	6.94702e10	0.478837	0.239419	+	0.970916i	$0.423043\pi$
$108$	−7.53641e10	−0.493553
$109$	3.47768e10	0.216493	0.108247	−	0.994124i	$-0.465476\pi$
$109$	3.47768e10	0.216493	0.108247	+	0.994124i	$0.465476\pi$
$110$	5.25576e11	3.11154
$111$	−2.74951e10	−0.154874
$112$	2.12361e11	1.13861
$113$	2.16735e11	1.10662	0.553309	−	0.832976i	$-0.313365\pi$
$113$	2.16735e11	1.10662	0.553309	+	0.832976i	$0.313365\pi$
$114$	2.47761e11	1.20519
$115$	−1.86387e11	−0.864129
$116$	3.24571e11	1.43480
$117$	−2.19245e10	−0.0924500
$118$	−6.47446e11	−2.60527
$119$	−1.90089e11	−0.730210
$120$	5.35753e11	1.96548
$121$	2.98144e11	1.04498
$122$	3.69517e11	1.23781
$123$	−1.98591e11	−0.636035
$124$	1.48135e12	4.53772
$125$	−2.64174e11	−0.774256
$126$	−8.47953e10	−0.237867
$127$	2.57449e11	0.691467	0.345734	−	0.938333i	$-0.387630\pi$
$127$	2.57449e11	0.691467	0.345734	+	0.938333i	$0.387630\pi$
$128$	−5.14326e11	−1.32307
$129$	2.51131e11	0.618951
$130$	2.55475e11	0.603476
$131$	−5.15177e11	−1.16671	−0.583357	−	0.812216i	$-0.698261\pi$
$131$	−5.15177e11	−1.16671	−0.583357	+	0.812216i	$0.698261\pi$
$132$	9.74891e11	2.11738
$133$	2.00561e11	0.417891
$134$	−4.28343e11	−0.856476
$135$	−1.15553e11	−0.221792
$136$	3.09643e12	5.70687
$137$	−7.73092e11	−1.36857	−0.684287	−	0.729213i	$-0.739886\pi$
$137$	−7.73092e11	−1.36857	−0.684287	+	0.729213i	$0.739886\pi$
$138$	−4.80540e11	−0.817325
$139$	1.41717e11	0.231655	0.115827	−	0.993269i	$-0.463048\pi$
$139$	1.41717e11	0.231655	0.115827	+	0.993269i	$0.463048\pi$
$140$	7.10883e11	1.11711
$141$	2.21825e11	0.335201
$142$	−2.34437e12	−3.40754
$143$	2.83609e11	0.396618
$144$	7.46099e11	1.00416
$145$	4.97652e11	0.644766
$146$	−8.56512e11	−1.06854
$147$	−6.86415e10	−0.0824786
$148$	5.94286e11	0.687949
$149$	−1.07931e12	−1.20399	−0.601994	−	0.798501i	$-0.705627\pi$
$149$	−1.07931e12	−1.20399	−0.601994	+	0.798501i	$0.705627\pi$
$150$	3.32697e11	0.357723
$151$	−7.61202e11	−0.789090	−0.394545	−	0.918877i	$-0.629098\pi$
$151$	−7.61202e11	−0.789090	−0.394545	+	0.918877i	$0.629098\pi$
$152$	−3.26703e12	−3.26598
$153$	−6.67849e11	−0.643985
$154$	1.09689e12	1.02047
$155$	2.27130e12	2.03915
$156$	4.73880e11	0.410661
$157$	2.01629e12	1.68696	0.843480	−	0.537160i	$-0.180503\pi$
$157$	2.01629e12	1.68696	0.843480	+	0.537160i	$0.180503\pi$
$158$	1.02688e12	0.829669
$159$	−9.32835e10	−0.0727982
$160$	−4.17860e12	−3.15043
$161$	−3.88995e11	−0.283402
$162$	−2.97916e11	−0.209779
$163$	7.39508e11	0.503398	0.251699	−	0.967806i	$-0.419011\pi$
$163$	7.39508e11	0.503398	0.251699	+	0.967806i	$0.419011\pi$
$164$	4.29238e12	2.82525
$165$	1.49476e12	0.951505
$166$	4.96108e12	3.05479
$167$	−1.50716e12	−0.897879	−0.448940	−	0.893562i	$-0.648198\pi$
$167$	−1.50716e12	−0.897879	−0.448940	+	0.893562i	$0.648198\pi$
$168$	1.11813e12	0.644602
$169$	1.37858e11	0.0769231
$170$	7.78211e12	4.20367
$171$	7.04643e11	0.368545
$172$	−5.42799e12	−2.74937
$173$	2.41520e9	0.00118495	0.000592475	−	1.00000i	$-0.499811\pi$
$173$	2.41520e9	0.00118495	0.000592475		1.00000i	$0.499811\pi$
$174$	1.28304e12	0.609843
$175$	2.69317e11	0.124038
$176$	−9.65134e12	−4.30793
$177$	−1.84137e12	−0.796687
$178$	2.07742e12	0.871392
$179$	−1.14518e12	−0.465782	−0.232891	−	0.972503i	$-0.574819\pi$
$179$	−1.14518e12	−0.465782	−0.232891	+	0.972503i	$0.574819\pi$
$180$	2.49759e12	0.985194
$181$	−2.11231e12	−0.808214	−0.404107	−	0.914712i	$-0.632418\pi$
$181$	−2.11231e12	−0.808214	−0.404107	+	0.914712i	$0.632418\pi$
$182$	5.33183e11	0.197917
$183$	1.05092e12	0.378521
$184$	6.33651e12	2.21489
$185$	9.11197e11	0.309149
$186$	5.85581e12	1.92870
$187$	8.63912e12	2.76275
$188$	−4.79457e12	−1.48896
$189$	−2.41162e11	−0.0727393
$190$	−8.21085e12	−2.40571
$191$	−3.12702e12	−0.890116	−0.445058	−	0.895502i	$-0.646817\pi$
$191$	−3.12702e12	−0.890116	−0.445058	+	0.895502i	$0.646817\pi$
$192$	−4.48505e12	−1.24054
$193$	−4.45408e12	−1.19727	−0.598636	−	0.801021i	$-0.704290\pi$
$193$	−4.45408e12	−1.19727	−0.598636	+	0.801021i	$0.704290\pi$
$194$	−1.00504e13	−2.62586
$195$	7.26583e11	0.184542
$196$	1.48363e12	0.366368
$197$	1.68054e12	0.403538	0.201769	−	0.979433i	$-0.435331\pi$
$197$	1.68054e12	0.403538	0.201769	+	0.979433i	$0.435331\pi$
$198$	3.85377e12	0.899968
$199$	−4.33759e12	−0.985272	−0.492636	−	0.870235i	$-0.663967\pi$
$199$	−4.33759e12	−0.985272	−0.492636	+	0.870235i	$0.663967\pi$
$200$	−4.38702e12	−0.969403
$201$	−1.21823e12	−0.261909
$202$	−1.08142e13	−2.26236
$203$	1.03861e12	0.211459
$204$	1.44350e13	2.86057
$205$	6.58136e12	1.26961
$206$	7.85079e12	1.47450
$207$	−1.36668e12	−0.249937
$208$	−4.69138e12	−0.835511
$209$	−9.11508e12	−1.58109
$210$	2.81014e12	0.474812
$211$	3.61505e12	0.595061	0.297530	−	0.954712i	$-0.403837\pi$
$211$	3.61505e12	0.595061	0.297530	+	0.954712i	$0.403837\pi$
$212$	2.01625e12	0.323368
$213$	−6.66751e12	−1.04202
$214$	−5.93564e12	−0.904049
$215$	−8.32254e12	−1.23550
$216$	3.92839e12	0.568485
$217$	4.74025e12	0.668764
$218$	−2.97139e12	−0.408741
$219$	−2.43596e12	−0.326759
$220$	−3.23081e13	−4.22656
$221$	4.19935e12	0.535828
$222$	2.34923e12	0.292404
$223$	9.05337e12	1.09934	0.549672	−	0.835381i	$-0.314753\pi$
$223$	9.05337e12	1.09934	0.549672	+	0.835381i	$0.314753\pi$
$224$	−8.72084e12	−1.03322
$225$	9.46206e11	0.109391
$226$	−1.85182e13	−2.08930
$227$	7.05927e12	0.777351	0.388676	−	0.921375i	$-0.372933\pi$
$227$	7.05927e12	0.777351	0.388676	+	0.921375i	$0.372933\pi$
$228$	−1.52303e13	−1.63707
$229$	−8.49506e12	−0.891397	−0.445699	−	0.895183i	$-0.647045\pi$
$229$	−8.49506e12	−0.891397	−0.445699	+	0.895183i	$0.647045\pi$
$230$	1.59252e13	1.63148
$231$	3.11961e12	0.312057
$232$	−1.69184e13	−1.65263
$233$	−1.34373e13	−1.28190	−0.640950	−	0.767583i	$-0.721459\pi$
$233$	−1.34373e13	−1.28190	−0.640950	+	0.767583i	$0.721459\pi$
$234$	1.87326e12	0.174546
$235$	−7.35134e12	−0.669104
$236$	3.97997e13	3.53887
$237$	2.92049e12	0.253712
$238$	1.62415e13	1.37864
$239$	1.23059e13	1.02076	0.510381	−	0.859949i	$-0.329504\pi$
$239$	1.23059e13	1.02076	0.510381	+	0.859949i	$0.329504\pi$
$240$	−2.47259e13	−2.00443
$241$	−6.61712e12	−0.524294	−0.262147	−	0.965028i	$-0.584431\pi$
$241$	−6.61712e12	−0.524294	−0.262147	+	0.965028i	$0.584431\pi$
$242$	−2.54739e13	−1.97292
$243$	−8.47289e11	−0.0641500
$244$	−2.27149e13	−1.68138
$245$	2.27480e12	0.164638
$246$	1.69679e13	1.20084
$247$	−4.43071e12	−0.306648
$248$	−7.72160e13	−5.22665
$249$	1.41096e13	0.934150
$250$	2.25714e13	1.46180
$251$	2.08534e13	1.32121	0.660604	−	0.750734i	$-0.270300\pi$
$251$	2.08534e13	1.32121	0.660604	+	0.750734i	$0.270300\pi$
$252$	5.21253e12	0.323106
$253$	1.76790e13	1.07225
$254$	−2.19969e13	−1.30550
$255$	2.21327e13	1.28547
$256$	6.14486e12	0.349295
$257$	−7.72597e12	−0.429854	−0.214927	−	0.976630i	$-0.568951\pi$
$257$	−7.72597e12	−0.429854	−0.214927	+	0.976630i	$0.568951\pi$
$258$	−2.14570e13	−1.16858
$259$	1.90169e12	0.101389
$260$	−1.57045e13	−0.819731
$261$	3.64902e12	0.186489
$262$	4.40175e13	2.20276
$263$	−1.44121e13	−0.706270	−0.353135	−	0.935572i	$-0.614884\pi$
$263$	−1.44121e13	−0.706270	−0.353135	+	0.935572i	$0.614884\pi$
$264$	−5.08167e13	−2.43885
$265$	3.09144e12	0.145314
$266$	−1.71363e13	−0.788982
$267$	5.90828e12	0.266471
$268$	2.63311e13	1.16340
$269$	−4.21199e13	−1.82327	−0.911633	−	0.411005i	$-0.865178\pi$
$269$	−4.21199e13	−1.82327	−0.911633	+	0.411005i	$0.865178\pi$
$270$	9.87302e12	0.418745
$271$	−3.75772e13	−1.56169	−0.780843	−	0.624728i	$-0.785210\pi$
$271$	−3.75772e13	−1.56169	−0.780843	+	0.624728i	$0.785210\pi$
$272$	−1.42906e14	−5.81997
$273$	1.51640e12	0.0605228
$274$	6.60542e13	2.58388
$275$	−1.22399e13	−0.469296
$276$	2.95397e13	1.11021
$277$	1.26653e13	0.466633	0.233316	−	0.972401i	$-0.425042\pi$
$277$	1.26653e13	0.466633	0.233316	+	0.972401i	$0.425042\pi$
$278$	−1.21085e13	−0.437366
$279$	1.66542e13	0.589795
$280$	−3.70551e13	−1.28671
$281$	4.15864e13	1.41601	0.708005	−	0.706208i	$-0.249596\pi$
$281$	4.15864e13	1.41601	0.708005	+	0.706208i	$0.249596\pi$
$282$	−1.89531e13	−0.632863
$283$	4.39981e13	1.44082	0.720408	−	0.693551i	$-0.243955\pi$
$283$	4.39981e13	1.44082	0.720408	+	0.693551i	$0.243955\pi$
$284$	1.44113e14	4.62863
$285$	−2.33521e13	−0.735663
$286$	−2.42320e13	−0.748818
$287$	1.37355e13	0.416383
$288$	−3.06394e13	−0.911217
$289$	9.36461e13	2.73245
$290$	−4.25202e13	−1.21732
$291$	−2.85837e13	−0.802985
$292$	5.26514e13	1.45146
$293$	−2.77921e13	−0.751880	−0.375940	−	0.926644i	$-0.622680\pi$
$293$	−2.77921e13	−0.751880	−0.375940	+	0.926644i	$0.622680\pi$
$294$	5.86483e12	0.155720
$295$	6.10235e13	1.59029
$296$	−3.09775e13	−0.792394
$297$	1.09603e13	0.275209
$298$	9.22180e13	2.27314
$299$	8.59352e12	0.207960
$300$	−2.04515e13	−0.485913
$301$	−1.73694e13	−0.405199
$302$	6.50383e13	1.48981
$303$	−3.07561e13	−0.691825
$304$	1.50779e14	3.33070
$305$	−3.48279e13	−0.755576
$306$	5.70620e13	1.21585
$307$	−8.88361e13	−1.85921	−0.929605	−	0.368558i	$-0.879852\pi$
$307$	−8.88361e13	−1.85921	−0.929605	+	0.368558i	$0.879852\pi$
$308$	−6.74279e13	−1.38615
$309$	2.23280e13	0.450899
$310$	−1.94063e14	−3.84994
$311$	−8.37420e13	−1.63215	−0.816077	−	0.577943i	$-0.803856\pi$
$311$	−8.37420e13	−1.63215	−0.816077	+	0.577943i	$0.803856\pi$
$312$	−2.47013e13	−0.473008
$313$	−2.78398e13	−0.523809	−0.261904	−	0.965094i	$-0.584351\pi$
$313$	−2.78398e13	−0.523809	−0.261904	+	0.965094i	$0.584351\pi$
$314$	−1.72275e14	−3.18500
$315$	7.99218e12	0.145197
$316$	−6.31242e13	−1.12698
$317$	2.04725e12	0.0359207	0.0179604	−	0.999839i	$-0.494283\pi$
$317$	2.04725e12	0.0359207	0.0179604	+	0.999839i	$0.494283\pi$
$318$	7.97028e12	0.137444
$319$	−4.72028e13	−0.800053
$320$	1.48636e14	2.47627
$321$	−1.68813e13	−0.276457
$322$	3.32364e13	0.535065
$323$	−1.34965e14	−2.13604
$324$	1.83135e13	0.284953
$325$	−5.94963e12	−0.0910189
$326$	−6.31847e13	−0.950419
$327$	−8.45077e12	−0.124992
$328$	−2.23743e14	−3.25419
$329$	−1.53424e13	−0.219441
$330$	−1.27715e14	−1.79645
$331$	5.51332e13	0.762710	0.381355	−	0.924429i	$-0.375458\pi$
$331$	5.51332e13	0.762710	0.381355	+	0.924429i	$0.375458\pi$
$332$	−3.04967e14	−4.14948
$333$	6.68132e12	0.0894168
$334$	1.28774e14	1.69520
$335$	4.03725e13	0.522804
$336$	−5.16036e13	−0.657377
$337$	−1.01528e14	−1.27240	−0.636199	−	0.771525i	$-0.719494\pi$
$337$	−1.01528e14	−1.27240	−0.636199	+	0.771525i	$0.719494\pi$
$338$	−1.17788e13	−0.145231
$339$	−5.26666e13	−0.638906
$340$	−4.78381e14	−5.71005
$341$	−2.15435e14	−2.53027
$342$	−6.02058e13	−0.695817
$343$	4.74756e12	0.0539949
$344$	2.82937e14	3.16678
$345$	4.52922e13	0.498905
$346$	−2.06359e11	−0.00223720
$347$	9.72058e13	1.03724	0.518621	−	0.855004i	$-0.326446\pi$
$347$	9.72058e13	1.03724	0.518621	+	0.855004i	$0.326446\pi$
$348$	−7.88707e13	−0.828380
$349$	5.50463e13	0.569100	0.284550	−	0.958661i	$-0.408156\pi$
$349$	5.50463e13	0.569100	0.284550	+	0.958661i	$0.408156\pi$
$350$	−2.30108e13	−0.234185
$351$	5.32765e12	0.0533761
$352$	3.96344e14	3.90919
$353$	9.47241e13	0.919813	0.459906	−	0.887967i	$-0.347883\pi$
$353$	9.47241e13	0.919813	0.459906	+	0.887967i	$0.347883\pi$
$354$	1.57329e14	1.50415
$355$	2.20963e14	2.08000
$356$	−1.27703e14	−1.18366
$357$	4.61915e13	0.421587
$358$	9.78461e13	0.879401
$359$	−6.11442e13	−0.541173	−0.270586	−	0.962696i	$-0.587218\pi$
$359$	−6.11442e13	−0.541173	−0.270586	+	0.962696i	$0.587218\pi$
$360$	−1.30188e14	−1.13477
$361$	2.59109e13	0.222430
$362$	1.80479e14	1.52592
$363$	−7.24490e13	−0.603317
$364$	−3.27758e13	−0.268841
$365$	8.07285e13	0.652253
$366$	−8.97926e13	−0.714652
$367$	1.88415e14	1.47724	0.738622	−	0.674119i	$-0.235477\pi$
$367$	1.88415e14	1.47724	0.738622	+	0.674119i	$0.235477\pi$
$368$	−2.92441e14	−2.25879
$369$	4.82576e13	0.367215
$370$	−7.78540e13	−0.583676
$371$	6.45191e12	0.0476576
$372$	−3.59968e14	−2.61985
$373$	−2.59905e14	−1.86388	−0.931938	−	0.362619i	$-0.881883\pi$
$373$	−2.59905e14	−1.86388	−0.931938	+	0.362619i	$0.881883\pi$
$374$	−7.38140e14	−5.21609
$375$	6.41942e13	0.447017
$376$	2.49919e14	1.71501
$377$	−2.29446e13	−0.155168
$378$	2.06053e13	0.137332
$379$	−4.36538e13	−0.286752	−0.143376	−	0.989668i	$-0.545796\pi$
$379$	−4.36538e13	−0.286752	−0.143376	+	0.989668i	$0.545796\pi$
$380$	5.04737e14	3.26780
$381$	−6.25602e13	−0.399219
$382$	2.67177e14	1.68055
$383$	−5.00699e13	−0.310444	−0.155222	−	0.987880i	$-0.549609\pi$
$383$	−5.00699e13	−0.310444	−0.155222	+	0.987880i	$0.549609\pi$
$384$	1.24981e14	0.763877
$385$	−1.03385e14	−0.622906
$386$	3.80563e14	2.26046
$387$	−6.10247e13	−0.357352
$388$	6.17815e14	3.56684
$389$	−9.34160e12	−0.0531739	−0.0265870	−	0.999647i	$-0.508464\pi$
$389$	−9.34160e12	−0.0531739	−0.0265870	+	0.999647i	$0.508464\pi$
$390$	−6.20804e13	−0.348417
$391$	2.61770e14	1.44860
$392$	−7.73350e13	−0.421991
$393$	1.25188e14	0.673602
$394$	−1.43588e14	−0.761883
$395$	−9.67859e13	−0.506440
$396$	−2.36898e14	−1.22247
$397$	1.73516e14	0.883065	0.441533	−	0.897245i	$-0.354435\pi$
$397$	1.73516e14	0.883065	0.441533	+	0.897245i	$0.354435\pi$
$398$	3.70610e14	1.86020
$399$	−4.87364e13	−0.241269
$400$	2.02468e14	0.988615
$401$	3.80819e14	1.83411	0.917054	−	0.398763i	$-0.130560\pi$
$401$	3.80819e14	1.83411	0.917054	+	0.398763i	$0.130560\pi$
$402$	1.04087e14	0.494487
$403$	−1.04720e14	−0.490739
$404$	6.64768e14	3.07307
$405$	2.80794e13	0.128052
$406$	−8.87407e13	−0.399236
$407$	−8.64278e13	−0.383605
$408$	−7.52433e14	−3.29486
$409$	−4.09780e14	−1.77041	−0.885203	−	0.465205i	$-0.845981\pi$
$409$	−4.09780e14	−1.77041	−0.885203	+	0.465205i	$0.845981\pi$
$410$	−5.62321e14	−2.39703
$411$	1.87861e14	0.790147
$412$	−4.82603e14	−2.00288
$413$	1.27358e14	0.521554
$414$	1.16771e14	0.471883
$415$	−4.67594e14	−1.86468
$416$	1.92657e14	0.758178
$417$	−3.44373e13	−0.133746
$418$	7.78807e14	2.98511
$419$	−1.19915e14	−0.453625	−0.226813	−	0.973938i	$-0.572830\pi$
$419$	−1.19915e14	−0.453625	−0.226813	+	0.973938i	$0.572830\pi$
$420$	−1.72745e14	−0.644961
$421$	−3.01588e13	−0.111138	−0.0555690	−	0.998455i	$-0.517697\pi$
$421$	−3.01588e13	−0.111138	−0.0555690	+	0.998455i	$0.517697\pi$
$422$	−3.08876e14	−1.12348
$423$	−5.39035e13	−0.193528
$424$	−1.05098e14	−0.372462
$425$	−1.81234e14	−0.634016
$426$	5.69682e14	1.96734
$427$	−7.26868e13	−0.247800
$428$	3.64875e14	1.22801
$429$	−6.89171e13	−0.228988
$430$	7.11090e14	2.33264
$431$	9.13897e13	0.295987	0.147993	−	0.988988i	$-0.452719\pi$
$431$	9.13897e13	0.295987	0.147993	+	0.988988i	$0.452719\pi$
$432$	−1.81302e14	−0.579752
$433$	6.01116e14	1.89791	0.948953	−	0.315418i	$-0.102145\pi$
$433$	6.01116e14	1.89791	0.948953	+	0.315418i	$0.102145\pi$
$434$	−4.05015e14	−1.26263
$435$	−1.20930e14	−0.372256
$436$	1.82657e14	0.555214
$437$	−2.76192e14	−0.829017
$438$	2.08132e14	0.616925
$439$	2.75739e14	0.807131	0.403565	−	0.914951i	$-0.367771\pi$
$439$	2.75739e14	0.807131	0.403565	+	0.914951i	$0.367771\pi$
$440$	1.68408e15	4.86825
$441$	1.66799e13	0.0476190
$442$	−3.58799e14	−1.01165
$443$	4.86155e13	0.135380	0.0676899	−	0.997706i	$-0.478437\pi$
$443$	4.86155e13	0.135380	0.0676899	+	0.997706i	$0.478437\pi$
$444$	−1.44411e14	−0.397187
$445$	−1.95802e14	−0.531909
$446$	−7.73534e14	−2.07557
$447$	2.62273e14	0.695123
$448$	3.10207e14	0.812124
$449$	−2.40909e14	−0.623015	−0.311507	−	0.950244i	$-0.600834\pi$
$449$	−2.40909e14	−0.623015	−0.311507	+	0.950244i	$0.600834\pi$
$450$	−8.08453e13	−0.206531
$451$	−6.24248e14	−1.57538
$452$	1.13835e15	2.83801
$453$	1.84972e14	0.455581
$454$	−6.03155e14	−1.46765
$455$	−5.02539e13	−0.120811
$456$	7.93888e14	1.88561
$457$	5.45002e14	1.27897	0.639483	−	0.768805i	$-0.279149\pi$
$457$	5.45002e14	1.27897	0.639483	+	0.768805i	$0.279149\pi$
$458$	7.25831e14	1.68297
$459$	1.62287e14	0.371805
$460$	−9.78954e14	−2.21613
$461$	7.41577e14	1.65883	0.829414	−	0.558635i	$-0.188675\pi$
$461$	7.41577e14	1.65883	0.829414	+	0.558635i	$0.188675\pi$
$462$	−2.66544e14	−0.589167
$463$	2.31282e14	0.505181	0.252590	−	0.967573i	$-0.418717\pi$
$463$	2.31282e14	0.505181	0.252590	+	0.967573i	$0.418717\pi$
$464$	7.80814e14	1.68538
$465$	−5.51925e14	−1.17730
$466$	1.14810e15	2.42024
$467$	−2.84119e14	−0.591913	−0.295956	−	0.955201i	$-0.595638\pi$
$467$	−2.84119e14	−0.591913	−0.295956	+	0.955201i	$0.595638\pi$
$468$	−1.15153e14	−0.237095
$469$	8.42584e13	0.171460
$470$	6.28110e14	1.26327
$471$	−4.89958e14	−0.973967
$472$	−2.07458e15	−4.07614
$473$	7.89400e14	1.53307
$474$	−2.49531e14	−0.479010
$475$	1.91219e14	0.362840
$476$	−9.98393e14	−1.87268
$477$	2.26679e13	0.0420300
$478$	−1.05143e15	−1.92721
$479$	−1.73156e14	−0.313757	−0.156878	−	0.987618i	$-0.550143\pi$
$479$	−1.73156e14	−0.313757	−0.156878	+	0.987618i	$0.550143\pi$
$480$	1.01540e15	1.81890
$481$	−4.20113e13	−0.0743993
$482$	5.65377e14	0.989872
$483$	9.45259e13	0.163622
$484$	1.56593e15	2.67992
$485$	9.47272e14	1.60286
$486$	7.23936e13	0.121116
$487$	−9.71549e14	−1.60715	−0.803574	−	0.595205i	$-0.797071\pi$
$487$	−9.71549e14	−1.60715	−0.803574	+	0.595205i	$0.797071\pi$
$488$	1.18403e15	1.93665
$489$	−1.79701e14	−0.290637
$490$	−1.94362e14	−0.310837
$491$	4.23365e14	0.669525	0.334763	−	0.942303i	$-0.391344\pi$
$491$	4.23365e14	0.669525	0.334763	+	0.942303i	$0.391344\pi$
$492$	−1.04305e15	−1.63116
$493$	−6.98923e14	−1.08086
$494$	3.78567e14	0.578954
$495$	−3.63228e14	−0.549351
$496$	3.56365e15	5.33023
$497$	4.61156e14	0.682162
$498$	−1.20554e15	−1.76368
$499$	−6.23180e14	−0.901697	−0.450849	−	0.892600i	$-0.648879\pi$
$499$	−6.23180e14	−0.901697	−0.450849	+	0.892600i	$0.648879\pi$
$500$	−1.38751e15	−1.98564
$501$	3.66239e14	0.518391
$502$	−1.78175e15	−2.49445
$503$	−9.28331e14	−1.28552	−0.642760	−	0.766068i	$-0.722211\pi$
$503$	−9.28331e14	−1.28552	−0.642760	+	0.766068i	$0.722211\pi$
$504$	−2.71706e14	−0.372161
$505$	1.01926e15	1.38097
$506$	−1.51052e15	−2.02441
$507$	−3.34996e13	−0.0444116
$508$	1.35219e15	1.77332
$509$	−4.82159e14	−0.625521	−0.312761	−	0.949832i	$-0.601254\pi$
$509$	−4.82159e14	−0.625521	−0.312761	+	0.949832i	$0.601254\pi$
$510$	−1.89105e15	−2.42699
$511$	1.68482e14	0.213914
$512$	5.28314e14	0.663601
$513$	−1.71228e14	−0.212780
$514$	6.60119e14	0.811568
$515$	−7.39958e14	−0.900051
$516$	1.31900e15	1.58735
$517$	6.97281e14	0.830252
$518$	−1.62483e14	−0.191424
$519$	−5.86894e11	−0.000684131 0
$520$	8.18606e14	0.944184
$521$	8.45383e14	0.964820	0.482410	−	0.875946i	$-0.339762\pi$
$521$	8.45383e14	0.964820	0.482410	+	0.875946i	$0.339762\pi$
$522$	−3.11778e14	−0.352093
$523$	1.01965e15	1.13944	0.569721	−	0.821838i	$-0.307051\pi$
$523$	1.01965e15	1.13944	0.569721	+	0.821838i	$0.307051\pi$
$524$	−2.70584e15	−2.99213
$525$	−6.54440e13	−0.0716133
$526$	1.23139e15	1.33344
$527$	−3.18990e15	−3.41837
$528$	2.34528e15	2.48718
$529$	−4.17126e14	−0.437785
$530$	−2.64137e14	−0.274355
$531$	4.47452e14	0.459967
$532$	1.05340e15	1.07171
$533$	−3.03438e14	−0.305541
$534$	−5.04812e14	−0.503099
$535$	5.59450e14	0.551843
$536$	−1.37252e15	−1.34002
$537$	2.78279e14	0.268920
$538$	3.59879e15	3.44234
$539$	−2.15767e14	−0.204290
$540$	−6.06914e14	−0.568802
$541$	−3.73294e14	−0.346311	−0.173155	−	0.984895i	$-0.555396\pi$
$541$	−3.73294e14	−0.346311	−0.173155	+	0.984895i	$0.555396\pi$
$542$	3.21065e15	2.94848
$543$	5.13292e14	0.466623
$544$	5.86859e15	5.28129
$545$	2.80061e14	0.249501
$546$	−1.29563e14	−0.114267
$547$	−1.08627e15	−0.948436	−0.474218	−	0.880407i	$-0.657269\pi$
$547$	−1.08627e15	−0.948436	−0.474218	+	0.880407i	$0.657269\pi$
$548$	−4.06048e15	−3.50981
$549$	−2.55375e14	−0.218539
$550$	1.04579e15	0.886036
$551$	7.37429e14	0.618567
$552$	−1.53977e15	−1.27877
$553$	−2.01995e14	−0.166093
$554$	−1.08214e15	−0.881007
$555$	−2.21421e14	−0.178487
$556$	7.44335e14	0.594096
$557$	−1.81624e15	−1.43539	−0.717696	−	0.696356i	$-0.754803\pi$
$557$	−1.81624e15	−1.43539	−0.717696	+	0.696356i	$0.754803\pi$
$558$	−1.42296e15	−1.11354
$559$	3.83716e14	0.297334
$560$	1.71016e15	1.31221
$561$	−2.09931e15	−1.59507
$562$	−3.55320e15	−2.67344
$563$	−2.36106e15	−1.75918	−0.879592	−	0.475728i	$-0.842184\pi$
$563$	−2.36106e15	−1.75918	−0.879592	+	0.475728i	$0.842184\pi$
$564$	1.16508e15	0.859649
$565$	1.74539e15	1.27534
$566$	−3.75926e15	−2.72027
$567$	5.86024e13	0.0419961
$568$	−7.51196e15	−5.33136
$569$	2.14496e15	1.50766	0.753829	−	0.657071i	$-0.228205\pi$
$569$	2.14496e15	1.50766	0.753829	+	0.657071i	$0.228205\pi$
$570$	1.99524e15	1.38894
$571$	−1.64159e14	−0.113179	−0.0565897	−	0.998398i	$-0.518023\pi$
$571$	−1.64159e14	−0.113179	−0.0565897	+	0.998398i	$0.518023\pi$
$572$	1.48959e15	1.01716
$573$	7.59865e14	0.513909
$574$	−1.17358e15	−0.786134
$575$	−3.70875e14	−0.246068
$576$	1.08987e15	0.716226
$577$	−2.00527e15	−1.30529	−0.652645	−	0.757664i	$-0.726340\pi$
$577$	−2.00527e15	−1.30529	−0.652645	+	0.757664i	$0.726340\pi$
$578$	−8.00126e15	−5.15888
$579$	1.08234e15	0.691245
$580$	2.61380e15	1.65355
$581$	−9.75882e14	−0.611545
$582$	2.44224e15	1.51604
$583$	−2.93226e14	−0.180312
$584$	−2.74448e15	−1.67182
$585$	−1.76560e14	−0.106545
$586$	2.37460e15	1.41956
$587$	−2.73941e15	−1.62236	−0.811179	−	0.584798i	$-0.801174\pi$
$587$	−2.73941e15	−1.62236	−0.811179	+	0.584798i	$0.801174\pi$
$588$	−3.60523e14	−0.211523
$589$	3.36564e15	1.95629
$590$	−5.21394e15	−3.00248
$591$	−4.08371e14	−0.232983
$592$	1.42966e15	0.808099
$593$	−2.62471e15	−1.46988	−0.734939	−	0.678133i	$-0.762789\pi$
$593$	−2.62471e15	−1.46988	−0.734939	+	0.678133i	$0.762789\pi$
$594$	−9.36465e14	−0.519597
$595$	−1.53080e15	−0.841541
$596$	−5.66882e15	−3.08772
$597$	1.05403e15	0.568847
$598$	−7.34243e14	−0.392630
$599$	−7.10912e14	−0.376676	−0.188338	−	0.982104i	$-0.560310\pi$
$599$	−7.10912e14	−0.376676	−0.188338	+	0.982104i	$0.560310\pi$
$600$	1.06604e15	0.559685
$601$	−2.15854e15	−1.12292	−0.561461	−	0.827503i	$-0.689761\pi$
$601$	−2.15854e15	−1.12292	−0.561461	+	0.827503i	$0.689761\pi$
$602$	1.48406e15	0.765018
$603$	2.96030e14	0.151213
$604$	−3.99803e15	−2.02368
$605$	2.40098e15	1.20430
$606$	2.62785e15	1.30617
$607$	−2.00799e14	−0.0989061	−0.0494531	−	0.998776i	$-0.515748\pi$
$607$	−2.00799e14	−0.0989061	−0.0494531	+	0.998776i	$0.515748\pi$
$608$	−6.19191e15	−3.02242
$609$	−2.52383e14	−0.122086
$610$	2.97575e15	1.42653
$611$	3.38939e14	0.161025
$612$	−3.50771e15	−1.65155
$613$	−2.09302e15	−0.976654	−0.488327	−	0.872661i	$-0.662393\pi$
$613$	−2.09302e15	−0.976654	−0.488327	+	0.872661i	$0.662393\pi$
$614$	7.59029e15	3.51020
$615$	−1.59927e15	−0.733008
$616$	3.51471e15	1.59660
$617$	1.25578e15	0.565384	0.282692	−	0.959211i	$-0.408773\pi$
$617$	1.25578e15	0.565384	0.282692	+	0.959211i	$0.408773\pi$
$618$	−1.90774e15	−0.851301
$619$	−1.82948e15	−0.809149	−0.404575	−	0.914505i	$-0.632580\pi$
$619$	−1.82948e15	−0.809149	−0.404575	+	0.914505i	$0.632580\pi$
$620$	1.19294e16	5.22956
$621$	3.32103e14	0.144301
$622$	7.15505e15	3.08152
$623$	−4.08644e14	−0.174446
$624$	1.14001e15	0.482383
$625$	−2.90984e15	−1.22048
$626$	2.37868e15	0.988956
$627$	2.21497e15	0.912842
$628$	1.05901e16	4.32634
$629$	−1.27972e15	−0.518247
$630$	−6.82864e14	−0.274133
$631$	−3.62896e15	−1.44418	−0.722090	−	0.691800i	$-0.756818\pi$
$631$	−3.62896e15	−1.44418	−0.722090	+	0.691800i	$0.756818\pi$
$632$	3.29038e15	1.29808
$633$	−8.78458e14	−0.343558
$634$	−1.74920e14	−0.0678186
$635$	2.07326e15	0.796891
$636$	−4.89948e14	−0.186697
$637$	−1.04881e14	−0.0396214
$638$	4.03308e15	1.51051
$639$	1.62021e15	0.601610
$640$	−4.14191e15	−1.52479
$641$	−2.58370e15	−0.943023	−0.471512	−	0.881860i	$-0.656291\pi$
$641$	−2.58370e15	−0.943023	−0.471512	+	0.881860i	$0.656291\pi$
$642$	1.44236e15	0.521953
$643$	−2.12651e15	−0.762969	−0.381485	−	0.924375i	$-0.624587\pi$
$643$	−2.12651e15	−0.762969	−0.381485	+	0.924375i	$0.624587\pi$
$644$	−2.04310e15	−0.726805
$645$	2.02238e15	0.713319
$646$	1.15317e16	4.03286
$647$	−3.79093e15	−1.31454	−0.657268	−	0.753657i	$-0.728288\pi$
$647$	−3.79093e15	−1.31454	−0.657268	+	0.753657i	$0.728288\pi$
$648$	−9.54599e14	−0.328215
$649$	−5.78813e15	−1.97330
$650$	5.08345e14	0.171844
$651$	−1.15188e15	−0.386111
$652$	3.88409e15	1.29100
$653$	−2.56060e15	−0.843955	−0.421977	−	0.906606i	$-0.638664\pi$
$653$	−2.56060e15	−0.843955	−0.421977	+	0.906606i	$0.638664\pi$
$654$	7.22047e14	0.235987
$655$	−4.14876e15	−1.34459
$656$	1.03261e16	3.31868
$657$	5.91939e14	0.188655
$658$	1.31088e15	0.414306
$659$	−6.67060e14	−0.209072	−0.104536	−	0.994521i	$-0.533336\pi$
$659$	−6.67060e14	−0.209072	−0.104536	+	0.994521i	$0.533336\pi$
$660$	7.85088e15	2.44021
$661$	3.63231e15	1.11963	0.559816	−	0.828617i	$-0.310872\pi$
$661$	3.63231e15	1.11963	0.559816	+	0.828617i	$0.310872\pi$
$662$	−4.71067e15	−1.44000
$663$	−1.02044e15	−0.309360
$664$	1.58965e16	4.77946
$665$	1.61514e15	0.481604
$666$	−5.70862e14	−0.168820
$667$	−1.43027e15	−0.419494
$668$	−7.91597e15	−2.30268
$669$	−2.19997e15	−0.634706
$670$	−3.44948e15	−0.987058
$671$	3.30346e15	0.937551
$672$	2.11916e15	0.596532
$673$	1.60730e15	0.448760	0.224380	−	0.974502i	$-0.427964\pi$
$673$	1.60730e15	0.448760	0.224380	+	0.974502i	$0.427964\pi$
$674$	8.67474e15	2.40230
$675$	−2.29928e14	−0.0631570
$676$	7.24068e14	0.197275
$677$	−5.15043e14	−0.139189	−0.0695947	−	0.997575i	$-0.522171\pi$
$677$	−5.15043e14	−0.139189	−0.0695947	+	0.997575i	$0.522171\pi$
$678$	4.49991e15	1.20626
$679$	1.97698e15	0.525677
$680$	2.49358e16	6.57696
$681$	−1.71540e15	−0.448804
$682$	1.84071e16	4.77716
$683$	6.98363e15	1.79791	0.898953	−	0.438045i	$-0.144329\pi$
$683$	6.98363e15	1.79791	0.898953	+	0.438045i	$0.144329\pi$
$684$	3.70097e15	0.945163
$685$	−6.22578e15	−1.57723
$686$	−4.05639e14	−0.101943
$687$	2.06430e15	0.514648
$688$	−1.30580e16	−3.22954
$689$	−1.42533e14	−0.0349711
$690$	−3.86983e15	−0.941937
$691$	−6.84269e15	−1.65233	−0.826167	−	0.563426i	$-0.809483\pi$
$691$	−6.84269e15	−1.65233	−0.826167	+	0.563426i	$0.809483\pi$
$692$	1.26853e13	0.00303890
$693$	−7.58065e14	−0.180166
$694$	−8.30541e15	−1.95832
$695$	1.14126e15	0.266974
$696$	4.11117e15	0.954146
$697$	−9.24312e15	−2.12833
$698$	−4.70324e15	−1.07446
$699$	3.26526e15	0.740105
$700$	1.41452e15	0.318105
$701$	−3.02022e15	−0.673892	−0.336946	−	0.941524i	$-0.609394\pi$
$701$	−3.02022e15	−0.673892	−0.336946	+	0.941524i	$0.609394\pi$
$702$	−4.55202e14	−0.100774
$703$	1.35023e15	0.296587
$704$	−1.40983e16	−3.07267
$705$	1.78638e15	0.386307
$706$	−8.09337e15	−1.73661
$707$	2.12723e15	0.452906
$708$	−9.67133e15	−2.04317
$709$	4.15720e15	0.871457	0.435729	−	0.900078i	$-0.356491\pi$
$709$	4.15720e15	0.871457	0.435729	+	0.900078i	$0.356491\pi$
$710$	−1.88794e16	−3.92706
$711$	−7.09680e14	−0.146480
$712$	6.65657e15	1.36336
$713$	−6.52778e15	−1.32670
$714$	−3.94667e15	−0.795960
$715$	2.28393e15	0.457088
$716$	−6.01479e15	−1.19453
$717$	−2.99033e15	−0.589337
$718$	5.22426e15	1.02174
$719$	2.21409e15	0.429722	0.214861	−	0.976645i	$-0.431070\pi$
$719$	2.21409e15	0.429722	0.214861	+	0.976645i	$0.431070\pi$
$720$	6.00840e15	1.15726
$721$	−1.54431e15	−0.295183
$722$	−2.21387e15	−0.419950
$723$	1.60796e15	0.302701
$724$	−1.10944e16	−2.07273
$725$	9.90232e14	0.183602
$726$	6.19015e15	1.13907
$727$	−5.01733e15	−0.916290	−0.458145	−	0.888877i	$-0.651486\pi$
$727$	−5.01733e15	−0.916290	−0.458145	+	0.888877i	$0.651486\pi$
$728$	1.70845e15	0.309657
$729$	2.05891e14	0.0370370
$730$	−6.89756e15	−1.23146
$731$	1.16885e16	2.07116
$732$	5.51972e15	0.970747
$733$	−3.99723e14	−0.0697730	−0.0348865	−	0.999391i	$-0.511107\pi$
$733$	−3.99723e14	−0.0697730	−0.0348865	+	0.999391i	$0.511107\pi$
$734$	−1.60985e16	−2.78905
$735$	−5.52776e14	−0.0950536
$736$	1.20094e16	2.04972
$737$	−3.82936e15	−0.648717
$738$	−4.12320e15	−0.693305
$739$	−5.53787e15	−0.924269	−0.462135	−	0.886810i	$-0.652916\pi$
$739$	−5.53787e15	−0.924269	−0.462135	+	0.886810i	$0.652916\pi$
$740$	4.78584e15	0.792836
$741$	1.07666e15	0.177043
$742$	−5.51261e14	−0.0899780
$743$	3.67629e15	0.595622	0.297811	−	0.954625i	$-0.403743\pi$
$743$	3.67629e15	0.595622	0.297811	+	0.954625i	$0.403743\pi$
$744$	1.87635e16	3.01761
$745$	−8.69179e15	−1.38755
$746$	2.22067e16	3.51901
$747$	−3.42862e15	−0.539332
$748$	4.53749e16	7.08527
$749$	1.16759e15	0.180983
$750$	−5.48485e15	−0.843972
$751$	7.63847e14	0.116677	0.0583387	−	0.998297i	$-0.481420\pi$
$751$	7.63847e14	0.116677	0.0583387	+	0.998297i	$0.481420\pi$
$752$	−1.15342e16	−1.74900
$753$	−5.06738e15	−0.762800
$754$	1.96042e15	0.292959
$755$	−6.13003e15	−0.909398
$756$	−1.26664e15	−0.186546
$757$	8.23903e15	1.20462	0.602308	−	0.798264i	$-0.294248\pi$
$757$	8.23903e15	1.20462	0.602308	+	0.798264i	$0.294248\pi$
$758$	3.72985e15	0.541390
$759$	−4.29600e15	−0.619063
$760$	−2.63097e16	−3.76392
$761$	2.54839e15	0.361951	0.180976	−	0.983488i	$-0.442075\pi$
$761$	2.54839e15	0.361951	0.180976	+	0.983488i	$0.442075\pi$
$762$	5.34524e15	0.753728
$763$	5.84494e14	0.0818267
$764$	−1.64239e16	−2.28277
$765$	−5.37825e15	−0.742169
$766$	4.27805e15	0.586121
$767$	−2.81353e15	−0.382716
$768$	−1.49320e15	−0.201665
$769$	6.77648e15	0.908676	0.454338	−	0.890829i	$-0.349876\pi$
$769$	6.77648e15	0.908676	0.454338	+	0.890829i	$0.349876\pi$
$770$	8.83335e15	1.17605
$771$	1.87741e15	0.248176
$772$	−2.33939e16	−3.07049
$773$	1.08648e16	1.41591	0.707955	−	0.706257i	$-0.249618\pi$
$773$	1.08648e16	1.41591	0.707955	+	0.706257i	$0.249618\pi$
$774$	5.21405e15	0.674683
$775$	4.51944e15	0.580664
$776$	−3.22039e16	−4.10836
$777$	−4.62111e14	−0.0585370
$778$	7.98161e14	0.100393
$779$	9.75236e15	1.21802
$780$	3.81620e15	0.473272
$781$	−2.09586e16	−2.58096
$782$	−2.23660e16	−2.73497
$783$	−8.86712e14	−0.107670
$784$	3.56915e15	0.430354
$785$	1.62374e16	1.94416
$786$	−1.06962e16	−1.27177
$787$	6.41445e15	0.757354	0.378677	−	0.925529i	$-0.376379\pi$
$787$	6.41445e15	0.757354	0.378677	+	0.925529i	$0.376379\pi$
$788$	8.82662e15	1.03490
$789$	3.50214e15	0.407765
$790$	8.26954e15	0.956164
$791$	3.64266e15	0.418262
$792$	1.23484e16	1.40807
$793$	1.60576e15	0.181836
$794$	−1.48255e16	−1.66723
$795$	−7.51220e14	−0.0838973
$796$	−2.27821e16	−2.52681
$797$	−6.94319e15	−0.764783	−0.382392	−	0.924000i	$-0.624899\pi$
$797$	−6.94319e15	−0.764783	−0.382392	+	0.924000i	$0.624899\pi$
$798$	4.16411e15	0.455519
$799$	1.03245e16	1.12166
$800$	−8.31460e15	−0.897111
$801$	−1.43571e15	−0.153847
$802$	−3.25378e16	−3.46281
$803$	−7.65717e15	−0.809343
$804$	−6.39845e15	−0.671686
$805$	−3.13261e15	−0.326610
$806$	8.94741e15	0.926519
$807$	1.02351e16	1.05266
$808$	−3.46514e16	−3.53963
$809$	1.64346e16	1.66741	0.833707	−	0.552207i	$-0.186214\pi$
$809$	1.64346e16	1.66741	0.833707	+	0.552207i	$0.186214\pi$
$810$	−2.39914e15	−0.241762
$811$	−1.08054e16	−1.08150	−0.540749	−	0.841184i	$-0.681859\pi$
$811$	−1.08054e16	−1.08150	−0.540749	+	0.841184i	$0.681859\pi$
$812$	5.45506e15	0.542302
$813$	9.13126e15	0.901639
$814$	7.38453e15	0.724250
$815$	5.95532e15	0.580148
$816$	3.47261e16	3.36016
$817$	−1.23325e16	−1.18530
$818$	3.50122e16	3.34254
$819$	−3.68485e14	−0.0349428
$820$	3.45669e16	3.25600
$821$	−1.43731e16	−1.34482	−0.672410	−	0.740179i	$-0.734741\pi$
$821$	−1.43731e16	−1.34482	−0.672410	+	0.740179i	$0.734741\pi$
$822$	−1.60512e16	−1.49180
$823$	−5.47150e14	−0.0505135	−0.0252568	−	0.999681i	$-0.508040\pi$
$823$	−5.47150e14	−0.0505135	−0.0252568	+	0.999681i	$0.508040\pi$
$824$	2.51559e16	2.30696
$825$	2.97429e15	0.270948
$826$	−1.08816e16	−0.984699
$827$	−1.17334e16	−1.05473	−0.527367	−	0.849637i	$-0.676821\pi$
$827$	−1.17334e16	−1.05473	−0.527367	+	0.849637i	$0.676821\pi$
$828$	−7.17815e15	−0.640982
$829$	−1.76415e16	−1.56490	−0.782450	−	0.622714i	$-0.786030\pi$
$829$	−1.76415e16	−1.56490	−0.782450	+	0.622714i	$0.786030\pi$
$830$	3.99520e16	3.52054
$831$	−3.07766e15	−0.269411
$832$	−6.85296e15	−0.595936
$833$	−3.19482e15	−0.275993
$834$	2.94237e15	0.252513
$835$	−1.21373e16	−1.03477
$836$	−4.78747e16	−4.05482
$837$	−4.04697e15	−0.340518
$838$	1.02457e16	0.856448
$839$	−1.43593e16	−1.19246	−0.596229	−	0.802814i	$-0.703335\pi$
$839$	−1.43593e16	−1.19246	−0.596229	+	0.802814i	$0.703335\pi$
$840$	9.00440e15	0.742880
$841$	−8.38171e15	−0.686996
$842$	2.57681e15	0.209829
$843$	−1.01055e16	−0.817533
$844$	1.89872e16	1.52608
$845$	1.11019e15	0.0886511
$846$	4.60559e15	0.365383
$847$	5.01090e15	0.394964
$848$	4.85045e15	0.379844
$849$	−1.06915e16	−0.831855
$850$	1.54849e16	1.19703
$851$	−2.61881e15	−0.201137
$852$	−3.50195e16	−2.67234
$853$	4.70434e15	0.356680	0.178340	−	0.983969i	$-0.442927\pi$
$853$	4.70434e15	0.356680	0.178340	+	0.983969i	$0.442927\pi$
$854$	6.21047e15	0.467849
$855$	5.67455e15	0.424735
$856$	−1.90193e16	−1.41445
$857$	2.41359e16	1.78348	0.891740	−	0.452547i	$-0.149485\pi$
$857$	2.41359e16	1.78348	0.891740	+	0.452547i	$0.149485\pi$
$858$	5.88838e15	0.432330
$859$	−2.29146e16	−1.67167	−0.835835	−	0.548980i	$-0.815016\pi$
$859$	−2.29146e16	−1.67167	−0.835835	+	0.548980i	$0.815016\pi$
$860$	−4.37121e16	−3.16855
$861$	−3.33772e15	−0.240399
$862$	−7.80848e15	−0.558826
$863$	−5.87430e15	−0.417731	−0.208866	−	0.977944i	$-0.566977\pi$
$863$	−5.87430e15	−0.417731	−0.208866	+	0.977944i	$0.566977\pi$
$864$	7.44538e15	0.526091
$865$	1.94498e13	0.00136561
$866$	−5.13602e16	−3.58326
$867$	−2.27560e16	−1.57758
$868$	2.48970e16	1.71510
$869$	9.18023e15	0.628413
$870$	1.03324e16	0.702822
$871$	−1.86140e15	−0.125817
$872$	−9.52107e15	−0.639507
$873$	6.94584e15	0.463604
$874$	2.35983e16	1.56519
$875$	−4.43997e15	−0.292641
$876$	−1.27943e16	−0.838000
$877$	9.65356e15	0.628333	0.314166	−	0.949368i	$-0.398275\pi$
$877$	9.65356e15	0.628333	0.314166	+	0.949368i	$0.398275\pi$
$878$	−2.35596e16	−1.52387
$879$	6.75347e15	0.434098
$880$	−7.77231e16	−4.96473
$881$	−4.62485e15	−0.293583	−0.146791	−	0.989167i	$-0.546895\pi$
$881$	−4.62485e15	−0.293583	−0.146791	+	0.989167i	$0.546895\pi$
$882$	−1.42515e15	−0.0899052
$883$	−8.06211e15	−0.505434	−0.252717	−	0.967540i	$-0.581324\pi$
$883$	−8.06211e15	−0.505434	−0.252717	+	0.967540i	$0.581324\pi$
$884$	2.20561e16	1.37417
$885$	−1.48287e16	−0.918153
$886$	−4.15378e15	−0.255598
$887$	−1.13706e16	−0.695352	−0.347676	−	0.937615i	$-0.613029\pi$
$887$	−1.13706e16	−0.695352	−0.347676	+	0.937615i	$0.613029\pi$
$888$	7.52752e15	0.457489
$889$	4.32695e15	0.261350
$890$	1.67296e16	1.00425
$891$	−2.66335e15	−0.158892
$892$	4.75506e16	2.81935
$893$	−1.08933e16	−0.641916
$894$	−2.24090e16	−1.31240
$895$	−9.22225e15	−0.536797
$896$	−8.64428e15	−0.500075
$897$	−2.08823e15	−0.120066
$898$	2.05836e16	1.17626
$899$	1.74291e16	0.989912
$900$	4.96972e15	0.280542
$901$	−4.34174e15	−0.243600
$902$	5.33367e16	2.97433
$903$	4.22075e15	0.233942
$904$	−5.93369e16	−3.26888
$905$	−1.70107e16	−0.931438
$906$	−1.58043e16	−0.860142
$907$	1.85203e16	1.00186	0.500931	−	0.865487i	$-0.332991\pi$
$907$	1.85203e16	1.00186	0.500931	+	0.865487i	$0.332991\pi$
$908$	3.70771e16	1.99358
$909$	7.47372e15	0.399425
$910$	4.29377e15	0.228092
$911$	−3.26336e16	−1.72311	−0.861557	−	0.507660i	$-0.830511\pi$
$911$	−3.26336e16	−1.72311	−0.861557	+	0.507660i	$0.830511\pi$
$912$	−3.66393e16	−1.92298
$913$	4.43518e16	2.31378
$914$	−4.65658e16	−2.41470
$915$	8.46318e15	0.436232
$916$	−4.46182e16	−2.28606
$917$	−8.65857e15	−0.440976
$918$	−1.38661e16	−0.701971
$919$	1.85187e16	0.931915	0.465957	−	0.884807i	$-0.345710\pi$
$919$	1.85187e16	0.931915	0.465957	+	0.884807i	$0.345710\pi$
$920$	5.10285e16	2.55258
$921$	2.15872e16	1.07342
$922$	−6.33615e16	−3.13188
$923$	−1.01877e16	−0.500570
$924$	1.63850e16	0.800295
$925$	1.81311e15	0.0880326
$926$	−1.97611e16	−0.953786
$927$	−5.42571e15	−0.260327
$928$	−3.20650e16	−1.52939
$929$	1.99057e16	0.943826	0.471913	−	0.881645i	$-0.343564\pi$
$929$	1.99057e16	0.943826	0.471913	+	0.881645i	$0.343564\pi$
$930$	4.71573e16	2.22276
$931$	3.37083e15	0.157948
$932$	−7.05761e16	−3.28753
$933$	2.03493e16	0.942325
$934$	2.42756e16	1.11754
$935$	6.95716e16	3.18396
$936$	6.00240e15	0.273091
$937$	−1.64080e15	−0.0742142	−0.0371071	−	0.999311i	$-0.511814\pi$
$937$	−1.64080e15	−0.0742142	−0.0371071	+	0.999311i	$0.511814\pi$
$938$	−7.19916e15	−0.323718
$939$	6.76508e15	0.302421
$940$	−3.86111e16	−1.71597
$941$	−3.81330e16	−1.68484	−0.842419	−	0.538823i	$-0.818869\pi$
$941$	−3.81330e16	−1.68484	−0.842419	+	0.538823i	$0.818869\pi$
$942$	4.18628e16	1.83886
$943$	−1.89150e16	−0.826025
$944$	9.57455e16	4.15693
$945$	−1.94210e15	−0.0838294
$946$	−6.74476e16	−2.89444
$947$	6.18471e15	0.263873	0.131936	−	0.991258i	$-0.457881\pi$
$947$	6.18471e15	0.263873	0.131936	+	0.991258i	$0.457881\pi$
$948$	1.53392e16	0.650663
$949$	−3.72204e15	−0.156970
$950$	−1.63380e16	−0.685045
$951$	−4.97482e14	−0.0207388
$952$	5.20418e16	2.15699
$953$	3.57430e16	1.47292	0.736461	−	0.676480i	$-0.236496\pi$
$953$	3.57430e16	1.47292	0.736461	+	0.676480i	$0.236496\pi$
$954$	−1.93678e15	−0.0793531
$955$	−2.51821e16	−1.02583
$956$	6.46336e16	2.61782
$957$	1.14703e16	0.461911
$958$	1.47947e16	0.592375
$959$	−1.29934e16	−0.517272
$960$	−3.61185e16	−1.42968
$961$	5.41383e16	2.13072
$962$	3.58951e15	0.140466
$963$	4.10215e15	0.159612
$964$	−3.47548e16	−1.34459
$965$	−3.58691e16	−1.37981
$966$	−8.07644e15	−0.308920
$967$	1.56698e16	0.595960	0.297980	−	0.954572i	$-0.403687\pi$
$967$	1.56698e16	0.595960	0.297980	+	0.954572i	$0.403687\pi$
$968$	−8.16248e16	−3.08679
$969$	3.27966e16	1.23324
$970$	−8.09364e16	−3.02621
$971$	−1.05307e16	−0.391519	−0.195759	−	0.980652i	$-0.562717\pi$
$971$	−1.05307e16	−0.391519	−0.195759	+	0.980652i	$0.562717\pi$
$972$	−4.45018e15	−0.164518
$973$	2.38184e15	0.0875572
$974$	8.30107e16	3.03431
$975$	1.44576e15	0.0525498
$976$	−5.46448e16	−1.97504
$977$	1.49941e15	0.0538891	0.0269446	−	0.999637i	$-0.491422\pi$
$977$	1.49941e15	0.0538891	0.0269446	+	0.999637i	$0.491422\pi$
$978$	1.53539e16	0.548725
$979$	1.85720e16	0.660015
$980$	1.19478e16	0.422226
$981$	2.05354e15	0.0721644
$982$	−3.61730e16	−1.26407
$983$	2.30235e15	0.0800068	0.0400034	−	0.999200i	$-0.487263\pi$
$983$	2.30235e15	0.0800068	0.0400034	+	0.999200i	$0.487263\pi$
$984$	5.43695e16	1.87881
$985$	1.35335e16	0.465063
$986$	5.97171e16	2.04068
$987$	3.72821e15	0.126694
$988$	−2.32712e16	−0.786423
$989$	2.39193e16	0.803837
$990$	3.10347e16	1.03718
$991$	2.32084e15	0.0771329	0.0385665	−	0.999256i	$-0.487721\pi$
$991$	2.32084e15	0.0771329	0.0385665	+	0.999256i	$0.487721\pi$
$992$	−1.46346e17	−4.83688
$993$	−1.33974e16	−0.440351
$994$	−3.94019e16	−1.28793
$995$	−3.49310e16	−1.13549
$996$	7.41069e16	2.39570
$997$	−5.73575e16	−1.84403	−0.922013	−	0.387158i	$-0.873457\pi$
$997$	−5.73575e16	−1.84403	−0.922013	+	0.387158i	$0.873457\pi$
$998$	5.32455e16	1.70241
$999$	−1.62356e15	−0.0516248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.2	✓	16	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q-85.4415 q^{2} -243.000 q^{3} +5252.25 q^{4} +8053.09 q^{5} +20762.3 q^{6} +16807.0 q^{7} -273776. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-85.4415 q^{2} -243.000 q^{3} +5252.25 q^{4} +8053.09 q^{5} +20762.3 q^{6} +16807.0 q^{7} -273776. q^{8} +59049.0 q^{9} -688068. q^{10} -763843. q^{11} -1.27630e6 q^{12} -371293. q^{13} -1.43602e6 q^{14} -1.95690e6 q^{15} +1.26353e7 q^{16} -1.13101e7 q^{17} -5.04524e6 q^{18} +1.19332e7 q^{19} +4.22969e7 q^{20} -4.08410e6 q^{21} +6.52639e7 q^{22} -2.31448e7 q^{23} +6.65277e7 q^{24} +1.60241e7 q^{25} +3.17238e7 q^{26} -1.43489e7 q^{27} +8.82746e7 q^{28} +6.17965e7 q^{29} +1.67201e8 q^{30} +2.82040e8 q^{31} -5.18881e8 q^{32} +1.85614e8 q^{33} +9.66351e8 q^{34} +1.35348e8 q^{35} +3.10140e8 q^{36} +1.13149e8 q^{37} -1.01959e9 q^{38} +9.02242e7 q^{39} -2.20474e9 q^{40} +8.17246e8 q^{41} +3.48952e8 q^{42} -1.03346e9 q^{43} -4.01190e9 q^{44} +4.75527e8 q^{45} +1.97753e9 q^{46} -9.12860e8 q^{47} -3.07037e9 q^{48} +2.82475e8 q^{49} -1.36912e9 q^{50} +2.74835e9 q^{51} -1.95013e9 q^{52} +3.83883e8 q^{53} +1.22599e9 q^{54} -6.15129e9 q^{55} -4.60136e9 q^{56} -2.89977e9 q^{57} -5.27998e9 q^{58} +7.57765e9 q^{59} -1.02781e10 q^{60} -4.32479e9 q^{61} -2.40980e10 q^{62} +9.92437e8 q^{63} +1.84570e10 q^{64} -2.99005e9 q^{65} -1.58591e10 q^{66} +5.01329e9 q^{67} -5.94034e10 q^{68} +5.62420e9 q^{69} -1.15644e10 q^{70} +2.74383e10 q^{71} -1.61662e10 q^{72} +1.00245e10 q^{73} -9.66760e9 q^{74} -3.89385e9 q^{75} +6.26762e10 q^{76} -1.28379e10 q^{77} -7.70889e9 q^{78} -1.20185e10 q^{79} +1.01753e11 q^{80} +3.48678e9 q^{81} -6.98268e10 q^{82} -5.80640e10 q^{83} -2.14507e10 q^{84} -9.10811e10 q^{85} +8.83003e10 q^{86} -1.50165e10 q^{87} +2.09122e11 q^{88} -2.43139e10 q^{89} -4.06297e10 q^{90} -6.24032e9 q^{91} -1.21563e11 q^{92} -6.85358e10 q^{93} +7.79962e10 q^{94} +9.60991e10 q^{95} +1.26088e11 q^{96} +1.17628e11 q^{97} -2.41351e10 q^{98} -4.51041e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9 + 1056711 * q^10 - 466884 * q^11 - 5044923 * q^12 - 5940688 * q^13 - 1058841 * q^14 + 769824 * q^15 + 40058265 * q^16 + 1753452 * q^17 - 3720087 * q^18 + 4237800 * q^19 - 20710503 * q^20 - 65345616 * q^21 - 37479661 * q^22 - 150481440 * q^23 + 45675495 * q^24 + 150983176 * q^25 + 23391459 * q^26 - 229582512 * q^27 + 348930127 * q^28 - 111411432 * q^29 - 256780773 * q^30 - 90536236 * q^31 - 609941313 * q^32 + 113452812 * q^33 + 443745577 * q^34 - 53244576 * q^35 + 1225916289 * q^36 - 1756337900 * q^37 - 4378868973 * q^38 + 1443587184 * q^39 + 57535383 * q^40 + 649575720 * q^41 + 257298363 * q^42 - 1889554520 * q^43 - 4979587689 * q^44 - 187067232 * q^45 - 3204000867 * q^46 - 4036082940 * q^47 - 9734158395 * q^48 + 4519603984 * q^49 - 15928886862 * q^50 - 426088836 * q^51 - 7708413973 * q^52 + 511144020 * q^53 + 903981141 * q^54 - 8519365572 * q^55 - 3159127755 * q^56 - 1029785400 * q^57 - 7851149577 * q^58 + 3728287296 * q^59 + 5032652229 * q^60 + 26227205052 * q^61 + 2996618490 * q^62 + 15878984688 * q^63 + 51104408465 * q^64 + 1176256224 * q^65 + 9107557623 * q^66 - 5295680024 * q^67 + 7919540325 * q^68 + 36566989920 * q^69 + 17760141777 * q^70 + 17082800928 * q^71 - 11099145285 * q^72 + 21076301488 * q^73 + 52794333675 * q^74 - 36688911768 * q^75 + 81459179177 * q^76 - 7846919388 * q^77 - 5684124537 * q^78 - 83677977852 * q^79 - 163988465427 * q^80 + 55788550416 * q^81 - 61543728760 * q^82 - 72857072340 * q^83 - 84790020861 * q^84 - 12608565060 * q^85 - 20177818011 * q^86 + 27072977976 * q^87 - 202213679643 * q^88 + 32238476676 * q^89 + 62397727839 * q^90 - 99845143216 * q^91 - 487057197033 * q^92 + 22000305348 * q^93 + 183904776602 * q^94 - 143022915504 * q^95 + 148215739059 * q^96 + 6973535140 * q^97 - 17795940687 * q^98 - 27569033316 * q^99

Introduction

L-functions

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