LMFDB - Embedded newform 273.12.a.c.1.6

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			1.6
Root			$-37.3707$ 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)

$f(q)$	$=$	$q-41.3707 q^{2} -243.000 q^{3} -336.467 q^{4} -335.043 q^{5} +10053.1 q^{6} +16807.0 q^{7} +98647.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-41.3707 q^{2} -243.000 q^{3} -336.467 q^{4} -335.043 q^{5} +10053.1 q^{6} +16807.0 q^{7} +98647.0 q^{8} +59049.0 q^{9} +13861.0 q^{10} -167805. q^{11} +81761.4 q^{12} -371293. q^{13} -695317. q^{14} +81415.4 q^{15} -3.39201e6 q^{16} -48979.8 q^{17} -2.44290e6 q^{18} +1.41962e7 q^{19} +112731. q^{20} -4.08410e6 q^{21} +6.94222e6 q^{22} +3.84648e7 q^{23} -2.39712e7 q^{24} -4.87159e7 q^{25} +1.53606e7 q^{26} -1.43489e7 q^{27} -5.65500e6 q^{28} -8.99484e7 q^{29} -3.36821e6 q^{30} +1.22353e8 q^{31} -6.16993e7 q^{32} +4.07767e7 q^{33} +2.02633e6 q^{34} -5.63107e6 q^{35} -1.98680e7 q^{36} -6.35049e8 q^{37} -5.87307e8 q^{38} +9.02242e7 q^{39} -3.30510e7 q^{40} -4.35832e8 q^{41} +1.68962e8 q^{42} -7.21546e8 q^{43} +5.64609e7 q^{44} -1.97840e7 q^{45} -1.59131e9 q^{46} -1.84403e9 q^{47} +8.24259e8 q^{48} +2.82475e8 q^{49} +2.01541e9 q^{50} +1.19021e7 q^{51} +1.24928e8 q^{52} +2.91076e9 q^{53} +5.93624e8 q^{54} +5.62220e7 q^{55} +1.65796e9 q^{56} -3.44968e9 q^{57} +3.72122e9 q^{58} +3.37446e9 q^{59} -2.73936e7 q^{60} -2.50761e9 q^{61} -5.06181e9 q^{62} +9.92437e8 q^{63} +9.49938e9 q^{64} +1.24399e8 q^{65} -1.68696e9 q^{66} +1.35442e10 q^{67} +1.64801e7 q^{68} -9.34694e9 q^{69} +2.32961e8 q^{70} -1.32563e10 q^{71} +5.82501e9 q^{72} -8.63655e9 q^{73} +2.62724e10 q^{74} +1.18380e10 q^{75} -4.77656e9 q^{76} -2.82030e9 q^{77} -3.73264e9 q^{78} +1.81183e10 q^{79} +1.13647e9 q^{80} +3.48678e9 q^{81} +1.80307e10 q^{82} +2.48333e10 q^{83} +1.37416e9 q^{84} +1.64103e7 q^{85} +2.98508e10 q^{86} +2.18575e10 q^{87} -1.65535e10 q^{88} +5.46685e10 q^{89} +8.18476e8 q^{90} -6.24032e9 q^{91} -1.29421e10 q^{92} -2.97317e10 q^{93} +7.62888e10 q^{94} -4.75634e9 q^{95} +1.49929e10 q^{96} -3.67985e10 q^{97} -1.16862e10 q^{98} -9.90874e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−41.3707	−0.914172	−0.457086	−	0.889423i	$-0.651107\pi$
$2$	−41.3707	−0.914172	−0.457086	+	0.889423i	$0.651107\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−336.467	−0.164290
$5$	−335.043	−0.0479474	−0.0239737	−	0.999713i	$-0.507632\pi$
$5$	−335.043	−0.0479474	−0.0239737	+	0.999713i	$0.507632\pi$
$6$	10053.1	0.527797
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	98647.0	1.06436
$9$	59049.0	0.333333
$10$	13861.0	0.0438322
$11$	−167805.	−0.314157	−0.157078	−	0.987586i	$-0.550207\pi$
$11$	−167805.	−0.314157	−0.157078	+	0.987586i	$0.550207\pi$
$12$	81761.4	0.0948531
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−695317.	−0.345524
$15$	81415.4	0.0276825
$16$	−3.39201e6	−0.808718
$17$	−48979.8	−0.00836658	−0.00418329	−	0.999991i	$-0.501332\pi$
$17$	−48979.8	−0.00836658	−0.00418329	+	0.999991i	$0.501332\pi$
$18$	−2.44290e6	−0.304724
$19$	1.41962e7	1.31531	0.657655	−	0.753319i	$-0.271549\pi$
$19$	1.41962e7	1.31531	0.657655	+	0.753319i	$0.271549\pi$
$20$	112731.	0.00787730
$21$	−4.08410e6	−0.218218
$22$	6.94222e6	0.287193
$23$	3.84648e7	1.24612	0.623060	−	0.782174i	$-0.285889\pi$
$23$	3.84648e7	1.24612	0.623060	+	0.782174i	$0.285889\pi$
$24$	−2.39712e7	−0.614509
$25$	−4.87159e7	−0.997701
$26$	1.53606e7	0.253546
$27$	−1.43489e7	−0.192450
$28$	−5.65500e6	−0.0620959
$29$	−8.99484e7	−0.814337	−0.407169	−	0.913353i	$-0.633484\pi$
$29$	−8.99484e7	−0.814337	−0.407169	+	0.913353i	$0.633484\pi$
$30$	−3.36821e6	−0.0253065
$31$	1.22353e8	0.767580	0.383790	−	0.923420i	$-0.374619\pi$
$31$	1.22353e8	0.767580	0.383790	+	0.923420i	$0.374619\pi$
$32$	−6.16993e7	−0.325054
$33$	4.07767e7	0.181378
$34$	2.02633e6	0.00764849
$35$	−5.63107e6	−0.0181224
$36$	−1.98680e7	−0.0547635
$37$	−6.35049e8	−1.50556	−0.752779	−	0.658273i	$-0.771287\pi$
$37$	−6.35049e8	−1.50556	−0.752779	+	0.658273i	$0.771287\pi$
$38$	−5.87307e8	−1.20242
$39$	9.02242e7	0.160128
$40$	−3.30510e7	−0.0510334
$41$	−4.35832e8	−0.587500	−0.293750	−	0.955882i	$-0.594903\pi$
$41$	−4.35832e8	−0.587500	−0.293750	+	0.955882i	$0.594903\pi$
$42$	1.68962e8	0.199489
$43$	−7.21546e8	−0.748492	−0.374246	−	0.927329i	$-0.622099\pi$
$43$	−7.21546e8	−0.748492	−0.374246	+	0.927329i	$0.622099\pi$
$44$	5.64609e7	0.0516129
$45$	−1.97840e7	−0.0159825
$46$	−1.59131e9	−1.13917
$47$	−1.84403e9	−1.17282	−0.586408	−	0.810016i	$-0.699459\pi$
$47$	−1.84403e9	−1.17282	−0.586408	+	0.810016i	$0.699459\pi$
$48$	8.24259e8	0.466914
$49$	2.82475e8	0.142857
$50$	2.01541e9	0.912070
$51$	1.19021e7	0.00483045
$52$	1.24928e8	0.0455660
$53$	2.91076e9	0.956068	0.478034	−	0.878341i	$-0.341349\pi$
$53$	2.91076e9	0.956068	0.478034	+	0.878341i	$0.341349\pi$
$54$	5.93624e8	0.175932
$55$	5.62220e7	0.0150630
$56$	1.65796e9	0.402291
$57$	−3.44968e9	−0.759394
$58$	3.72122e9	0.744444
$59$	3.37446e9	0.614494	0.307247	−	0.951630i	$-0.400592\pi$
$59$	3.37446e9	0.614494	0.307247	+	0.951630i	$0.400592\pi$
$60$	−2.73936e7	−0.00454796
$61$	−2.50761e9	−0.380142	−0.190071	−	0.981770i	$-0.560872\pi$
$61$	−2.50761e9	−0.380142	−0.190071	+	0.981770i	$0.560872\pi$
$62$	−5.06181e9	−0.701700
$63$	9.92437e8	0.125988
$64$	9.49938e9	1.10587
$65$	1.24399e8	0.0132982
$66$	−1.68696e9	−0.165811
$67$	1.35442e10	1.22558	0.612791	−	0.790245i	$-0.290047\pi$
$67$	1.35442e10	1.22558	0.612791	+	0.790245i	$0.290047\pi$
$68$	1.64801e7	0.00137455
$69$	−9.34694e9	−0.719448
$70$	2.32961e8	0.0165670
$71$	−1.32563e10	−0.871967	−0.435984	−	0.899955i	$-0.643599\pi$
$71$	−1.32563e10	−0.871967	−0.435984	+	0.899955i	$0.643599\pi$
$72$	5.82501e9	0.354787
$73$	−8.63655e9	−0.487601	−0.243801	−	0.969825i	$-0.578394\pi$
$73$	−8.63655e9	−0.487601	−0.243801	+	0.969825i	$0.578394\pi$
$74$	2.62724e10	1.37634
$75$	1.18380e10	0.576023
$76$	−4.77656e9	−0.216093
$77$	−2.82030e9	−0.118740
$78$	−3.73264e9	−0.146385
$79$	1.81183e10	0.662472	0.331236	−	0.943548i	$-0.392534\pi$
$79$	1.81183e10	0.662472	0.331236	+	0.943548i	$0.392534\pi$
$80$	1.13647e9	0.0387760
$81$	3.48678e9	0.111111
$82$	1.80307e10	0.537076
$83$	2.48333e10	0.691999	0.346000	−	0.938235i	$-0.387540\pi$
$83$	2.48333e10	0.691999	0.346000	+	0.938235i	$0.387540\pi$
$84$	1.37416e9	0.0358511
$85$	1.64103e7	0.000401156 0
$86$	2.98508e10	0.684250
$87$	2.18575e10	0.470158
$88$	−1.65535e10	−0.334376
$89$	5.46685e10	1.03775	0.518874	−	0.854851i	$-0.326351\pi$
$89$	5.46685e10	1.03775	0.518874	+	0.854851i	$0.326351\pi$
$90$	8.18476e8	0.0146107
$91$	−6.24032e9	−0.104828
$92$	−1.29421e10	−0.204726
$93$	−2.97317e10	−0.443163
$94$	7.62888e10	1.07216
$95$	−4.75634e9	−0.0630657
$96$	1.49929e10	0.187670
$97$	−3.67985e10	−0.435097	−0.217548	−	0.976050i	$-0.569806\pi$
$97$	−3.67985e10	−0.435097	−0.217548	+	0.976050i	$0.569806\pi$
$98$	−1.16862e10	−0.130596
$99$	−9.90874e9	−0.104719
$100$	1.63913e10	0.163913
$101$	−1.28433e10	−0.121593	−0.0607967	−	0.998150i	$-0.519364\pi$
$101$	−1.28433e10	−0.121593	−0.0607967	+	0.998150i	$0.519364\pi$
$102$	−4.92398e8	−0.00441586
$103$	−1.49949e11	−1.27450	−0.637248	−	0.770659i	$-0.719927\pi$
$103$	−1.49949e11	−1.27450	−0.637248	+	0.770659i	$0.719927\pi$
$104$	−3.66269e10	−0.295201
$105$	1.36835e9	0.0104630
$106$	−1.20420e11	−0.874011
$107$	1.96667e11	1.35557	0.677785	−	0.735261i	$-0.262940\pi$
$107$	1.96667e11	1.35557	0.677785	+	0.735261i	$0.262940\pi$
$108$	4.82793e9	0.0316177
$109$	3.02081e11	1.88052	0.940261	−	0.340456i	$-0.110581\pi$
$109$	3.02081e11	1.88052	0.940261	+	0.340456i	$0.110581\pi$
$110$	−2.32594e9	−0.0137702
$111$	1.54317e11	0.869234
$112$	−5.70095e10	−0.305667
$113$	−4.14817e10	−0.211799	−0.105900	−	0.994377i	$-0.533772\pi$
$113$	−4.14817e10	−0.211799	−0.105900	+	0.994377i	$0.533772\pi$
$114$	1.42716e11	0.694217
$115$	−1.28874e10	−0.0597483
$116$	3.02646e10	0.133788
$117$	−2.19245e10	−0.0924500
$118$	−1.39604e11	−0.561753
$119$	−8.23204e8	−0.00316227
$120$	8.03139e9	0.0294641
$121$	−2.57153e11	−0.901306
$122$	1.03742e11	0.347515
$123$	1.05907e11	0.339193
$124$	−4.11676e10	−0.126106
$125$	3.26814e10	0.0957847
$126$	−4.10578e10	−0.115175
$127$	4.18372e11	1.12368	0.561839	−	0.827247i	$-0.310094\pi$
$127$	4.18372e11	1.12368	0.561839	+	0.827247i	$0.310094\pi$
$128$	−2.66636e11	−0.685904
$129$	1.75336e11	0.432142
$130$	−5.14648e9	−0.0121569
$131$	1.54067e11	0.348913	0.174456	−	0.984665i	$-0.444183\pi$
$131$	1.54067e11	0.348913	0.174456	+	0.984665i	$0.444183\pi$
$132$	−1.37200e10	−0.0297987
$133$	2.38596e11	0.497140
$134$	−5.60333e11	−1.12039
$135$	4.80750e9	0.00922749
$136$	−4.83171e9	−0.00890507
$137$	5.72343e11	1.01320	0.506598	−	0.862182i	$-0.330903\pi$
$137$	5.72343e11	1.01320	0.506598	+	0.862182i	$0.330903\pi$
$138$	3.86689e11	0.657699
$139$	3.12240e11	0.510395	0.255198	−	0.966889i	$-0.417859\pi$
$139$	3.12240e11	0.510395	0.255198	+	0.966889i	$0.417859\pi$
$140$	1.89467e9	0.00297734
$141$	4.48100e11	0.677126
$142$	5.48421e11	0.797128
$143$	6.23050e10	0.0871313
$144$	−2.00295e11	−0.269573
$145$	3.01366e10	0.0390454
$146$	3.57300e11	0.445751
$147$	−6.86415e10	−0.0824786
$148$	2.13673e11	0.247349
$149$	−1.45681e12	−1.62509	−0.812546	−	0.582897i	$-0.801919\pi$
$149$	−1.45681e12	−1.62509	−0.812546	+	0.582897i	$0.801919\pi$
$150$	−4.89744e11	−0.526584
$151$	8.43380e11	0.874279	0.437140	−	0.899394i	$-0.355992\pi$
$151$	8.43380e11	0.874279	0.437140	+	0.899394i	$0.355992\pi$
$152$	1.40041e12	1.39996
$153$	−2.89221e9	−0.00278886
$154$	1.16678e11	0.108549
$155$	−4.09934e10	−0.0368035
$156$	−3.03574e10	−0.0263075
$157$	−2.28089e12	−1.90834	−0.954172	−	0.299260i	$-0.903260\pi$
$157$	−2.28089e12	−1.90834	−0.954172	+	0.299260i	$0.903260\pi$
$158$	−7.49565e11	−0.605613
$159$	−7.07314e11	−0.551986
$160$	2.06719e10	0.0155855
$161$	6.46477e11	0.470989
$162$	−1.44251e11	−0.101575
$163$	9.22369e11	0.627874	0.313937	−	0.949444i	$-0.398352\pi$
$163$	9.22369e11	0.627874	0.313937	+	0.949444i	$0.398352\pi$
$164$	1.46643e11	0.0965206
$165$	−1.36619e10	−0.00869663
$166$	−1.02737e12	−0.632606
$167$	3.11967e12	1.85852	0.929262	−	0.369422i	$-0.120444\pi$
$167$	3.11967e12	1.85852	0.929262	+	0.369422i	$0.120444\pi$
$168$	−4.02884e11	−0.232263
$169$	1.37858e11	0.0769231
$170$	−6.78907e8	−0.000366726 0
$171$	8.38273e11	0.438436
$172$	2.42776e11	0.122970
$173$	−2.40095e12	−1.17796	−0.588978	−	0.808149i	$-0.700469\pi$
$173$	−2.40095e12	−1.17796	−0.588978	+	0.808149i	$0.700469\pi$
$174$	−9.04258e11	−0.429805
$175$	−8.18768e11	−0.377096
$176$	5.69198e11	0.254064
$177$	−8.19993e11	−0.354778
$178$	−2.26167e12	−0.948680
$179$	2.43237e12	0.989323	0.494662	−	0.869086i	$-0.335292\pi$
$179$	2.43237e12	0.989323	0.494662	+	0.869086i	$0.335292\pi$
$180$	6.65664e9	0.00262577
$181$	−1.36684e12	−0.522980	−0.261490	−	0.965206i	$-0.584214\pi$
$181$	−1.36684e12	−0.522980	−0.261490	+	0.965206i	$0.584214\pi$
$182$	2.58166e11	0.0958312
$183$	6.09350e11	0.219475
$184$	3.79443e12	1.32632
$185$	2.12769e11	0.0721877
$186$	1.23002e12	0.405127
$187$	8.21908e9	0.00262842
$188$	6.20455e11	0.192683
$189$	−2.41162e11	−0.0727393
$190$	1.96773e11	0.0576529
$191$	−3.69529e12	−1.05188	−0.525938	−	0.850523i	$-0.676286\pi$
$191$	−3.69529e12	−1.05188	−0.525938	+	0.850523i	$0.676286\pi$
$192$	−2.30835e12	−0.638476
$193$	−4.85389e12	−1.30474	−0.652371	−	0.757900i	$-0.726226\pi$
$193$	−4.85389e12	−1.30474	−0.652371	+	0.757900i	$0.726226\pi$
$194$	1.52238e12	0.397753
$195$	−3.02290e10	−0.00767774
$196$	−9.50435e10	−0.0234701
$197$	−2.33085e12	−0.559694	−0.279847	−	0.960045i	$-0.590284\pi$
$197$	−2.33085e12	−0.559694	−0.279847	+	0.960045i	$0.590284\pi$
$198$	4.09931e11	0.0957310
$199$	6.85105e12	1.55620	0.778099	−	0.628141i	$-0.216184\pi$
$199$	6.85105e12	1.55620	0.778099	+	0.628141i	$0.216184\pi$
$200$	−4.80568e12	−1.06191
$201$	−3.29124e12	−0.707590
$202$	5.31337e11	0.111157
$203$	−1.51176e12	−0.307791
$204$	−4.00466e9	−0.000793596 0
$205$	1.46022e11	0.0281691
$206$	6.20348e12	1.16511
$207$	2.27131e12	0.415374
$208$	1.25943e12	0.224298
$209$	−2.38220e12	−0.413213
$210$	−5.66095e10	−0.00956497
$211$	7.09731e12	1.16826	0.584131	−	0.811660i	$-0.301435\pi$
$211$	7.09731e12	1.16826	0.584131	+	0.811660i	$0.301435\pi$
$212$	−9.79374e11	−0.157073
$213$	3.22127e12	0.503430
$214$	−8.13627e12	−1.23922
$215$	2.41749e11	0.0358883
$216$	−1.41548e12	−0.204836
$217$	2.05638e12	0.290118
$218$	−1.24973e13	−1.71912
$219$	2.09868e12	0.281517
$220$	−1.89168e10	−0.00247471
$221$	1.81859e10	0.00232047
$222$	−6.38419e12	−0.794629
$223$	1.02373e13	1.24310	0.621551	−	0.783374i	$-0.286503\pi$
$223$	1.02373e13	1.24310	0.621551	+	0.783374i	$0.286503\pi$
$224$	−1.03698e12	−0.122859
$225$	−2.87662e12	−0.332567
$226$	1.71612e12	0.193621
$227$	−1.06971e13	−1.17794	−0.588968	−	0.808156i	$-0.700466\pi$
$227$	−1.06971e13	−1.17794	−0.588968	+	0.808156i	$0.700466\pi$
$228$	1.16070e12	0.124761
$229$	−1.41550e13	−1.48530	−0.742648	−	0.669681i	$-0.766431\pi$
$229$	−1.41550e13	−1.48530	−0.742648	+	0.669681i	$0.766431\pi$
$230$	5.33159e11	0.0546202
$231$	6.85334e11	0.0685546
$232$	−8.87314e12	−0.866749
$233$	−7.50958e12	−0.716404	−0.358202	−	0.933644i	$-0.616610\pi$
$233$	−7.50958e12	−0.716404	−0.358202	+	0.933644i	$0.616610\pi$
$234$	9.07031e11	0.0845152
$235$	6.17830e11	0.0562336
$236$	−1.13539e12	−0.100955
$237$	−4.40274e12	−0.382478
$238$	3.40565e10	0.00289086
$239$	−9.42879e12	−0.782109	−0.391055	−	0.920367i	$-0.627890\pi$
$239$	−9.42879e12	−0.782109	−0.391055	+	0.920367i	$0.627890\pi$
$240$	−2.76162e11	−0.0223873
$241$	1.91573e13	1.51789	0.758945	−	0.651155i	$-0.225715\pi$
$241$	1.91573e13	1.51789	0.758945	+	0.651155i	$0.225715\pi$
$242$	1.06386e13	0.823948
$243$	−8.47289e11	−0.0641500
$244$	8.43728e11	0.0624538
$245$	−9.46413e10	−0.00684964
$246$	−4.38145e12	−0.310081
$247$	−5.27096e12	−0.364801
$248$	1.20697e13	0.816983
$249$	−6.03450e12	−0.399526
$250$	−1.35205e12	−0.0875636
$251$	−1.43679e13	−0.910307	−0.455154	−	0.890413i	$-0.650416\pi$
$251$	−1.43679e13	−0.910307	−0.455154	+	0.890413i	$0.650416\pi$
$252$	−3.33922e11	−0.0206986
$253$	−6.45459e12	−0.391477
$254$	−1.73083e13	−1.02723
$255$	−3.98771e9	−0.000231608 0
$256$	−8.42383e12	−0.478839
$257$	1.62702e13	0.905236	0.452618	−	0.891705i	$-0.350490\pi$
$257$	1.62702e13	0.905236	0.452618	+	0.891705i	$0.350490\pi$
$258$	−7.25375e12	−0.395052
$259$	−1.06733e13	−0.569047
$260$	−4.18562e10	−0.00218477
$261$	−5.31136e12	−0.271446
$262$	−6.37385e12	−0.318966
$263$	8.77423e12	0.429984	0.214992	−	0.976616i	$-0.431027\pi$
$263$	8.77423e12	0.429984	0.214992	+	0.976616i	$0.431027\pi$
$264$	4.02250e12	0.193052
$265$	−9.75229e11	−0.0458410
$266$	−9.87087e12	−0.454471
$267$	−1.32844e13	−0.599144
$268$	−4.55718e12	−0.201351
$269$	7.78663e12	0.337064	0.168532	−	0.985696i	$-0.446097\pi$
$269$	7.78663e12	0.337064	0.168532	+	0.985696i	$0.446097\pi$
$270$	−1.98890e11	−0.00843551
$271$	−2.54766e13	−1.05879	−0.529396	−	0.848375i	$-0.677581\pi$
$271$	−2.54766e13	−1.05879	−0.529396	+	0.848375i	$0.677581\pi$
$272$	1.66140e11	0.00676621
$273$	1.51640e12	0.0605228
$274$	−2.36782e13	−0.926235
$275$	8.17478e12	0.313434
$276$	3.14493e12	0.118198
$277$	−3.70111e13	−1.36362	−0.681810	−	0.731529i	$-0.738807\pi$
$277$	−3.70111e13	−1.36362	−0.681810	+	0.731529i	$0.738807\pi$
$278$	−1.29176e13	−0.466589
$279$	7.22480e12	0.255860
$280$	−5.55488e11	−0.0192888
$281$	2.87923e13	0.980375	0.490187	−	0.871617i	$-0.336928\pi$
$281$	2.87923e13	0.980375	0.490187	+	0.871617i	$0.336928\pi$
$282$	−1.85382e13	−0.619009
$283$	−1.79126e13	−0.586589	−0.293295	−	0.956022i	$-0.594752\pi$
$283$	−1.79126e13	−0.586589	−0.293295	+	0.956022i	$0.594752\pi$
$284$	4.46029e12	0.143256
$285$	1.15579e12	0.0364110
$286$	−2.57760e12	−0.0796530
$287$	−7.32502e12	−0.222054
$288$	−3.64328e12	−0.108351
$289$	−3.42695e13	−0.999930
$290$	−1.24677e12	−0.0356942
$291$	8.94204e12	0.251203
$292$	2.90591e12	0.0801082
$293$	−5.92929e13	−1.60410	−0.802049	−	0.597259i	$-0.796257\pi$
$293$	−5.92929e13	−1.60410	−0.802049	+	0.597259i	$0.796257\pi$
$294$	2.83975e12	0.0753996
$295$	−1.13059e12	−0.0294634
$296$	−6.26456e13	−1.60246
$297$	2.40782e12	0.0604594
$298$	6.02692e13	1.48561
$299$	−1.42817e13	−0.345612
$300$	−3.98308e12	−0.0946350
$301$	−1.21270e13	−0.282904
$302$	−3.48912e13	−0.799241
$303$	3.12093e12	0.0702020
$304$	−4.81537e13	−1.06371
$305$	8.40158e11	0.0182269
$306$	1.19653e11	0.00254950
$307$	7.45676e13	1.56059	0.780295	−	0.625412i	$-0.215069\pi$
$307$	7.45676e13	1.56059	0.780295	+	0.625412i	$0.215069\pi$
$308$	9.48939e11	0.0195078
$309$	3.64375e13	0.735830
$310$	1.69592e12	0.0336447
$311$	−7.14810e13	−1.39318	−0.696592	−	0.717467i	$-0.745301\pi$
$311$	−7.14810e13	−1.39318	−0.696592	+	0.717467i	$0.745301\pi$
$312$	8.90035e12	0.170434
$313$	−3.33154e12	−0.0626832	−0.0313416	−	0.999509i	$-0.509978\pi$
$313$	−3.33154e12	−0.0626832	−0.0313416	+	0.999509i	$0.509978\pi$
$314$	9.43620e13	1.74455
$315$	−3.32509e11	−0.00604081
$316$	−6.09619e12	−0.108838
$317$	3.24500e13	0.569363	0.284681	−	0.958622i	$-0.408112\pi$
$317$	3.24500e13	0.569363	0.284681	+	0.958622i	$0.408112\pi$
$318$	2.92621e13	0.504610
$319$	1.50938e13	0.255829
$320$	−3.18270e12	−0.0530238
$321$	−4.77902e13	−0.782638
$322$	−2.67452e13	−0.430565
$323$	−6.95328e11	−0.0110046
$324$	−1.17319e12	−0.0182545
$325$	1.80879e13	0.276712
$326$	−3.81590e13	−0.573985
$327$	−7.34058e13	−1.08572
$328$	−4.29935e13	−0.625312
$329$	−3.09926e13	−0.443283
$330$	5.65204e11	0.00795021
$331$	9.52552e12	0.131776	0.0658878	−	0.997827i	$-0.479012\pi$
$331$	9.52552e12	0.131776	0.0658878	+	0.997827i	$0.479012\pi$
$332$	−8.35559e12	−0.113689
$333$	−3.74990e13	−0.501853
$334$	−1.29063e14	−1.69901
$335$	−4.53789e12	−0.0587635
$336$	1.38533e13	0.176477
$337$	1.20827e14	1.51426	0.757129	−	0.653266i	$-0.226602\pi$
$337$	1.20827e14	1.51426	0.757129	+	0.653266i	$0.226602\pi$
$338$	−5.70330e12	−0.0703209
$339$	1.00800e13	0.122282
$340$	−5.52154e9	−6.59061e−5 0
$341$	−2.05314e13	−0.241140
$342$	−3.46799e13	−0.400806
$343$	4.74756e12	0.0539949
$344$	−7.11783e13	−0.796666
$345$	3.13163e12	0.0344957
$346$	9.93288e13	1.07685
$347$	−9.23674e13	−0.985613	−0.492807	−	0.870139i	$-0.664029\pi$
$347$	−9.23674e13	−0.985613	−0.492807	+	0.870139i	$0.664029\pi$
$348$	−7.35430e12	−0.0772424
$349$	−1.22711e14	−1.26866	−0.634330	−	0.773062i	$-0.718724\pi$
$349$	−1.22711e14	−1.26866	−0.634330	+	0.773062i	$0.718724\pi$
$350$	3.38730e13	0.344730
$351$	5.32765e12	0.0533761
$352$	1.03535e13	0.102118
$353$	−1.52789e14	−1.48365	−0.741826	−	0.670592i	$-0.766040\pi$
$353$	−1.52789e14	−1.48365	−0.741826	+	0.670592i	$0.766040\pi$
$354$	3.39237e13	0.324328
$355$	4.44142e12	0.0418086
$356$	−1.83941e13	−0.170492
$357$	2.00039e11	0.00182574
$358$	−1.00629e14	−0.904411
$359$	−1.51944e14	−1.34482	−0.672408	−	0.740181i	$-0.734740\pi$
$359$	−1.51944e14	−1.34482	−0.672408	+	0.740181i	$0.734740\pi$
$360$	−1.95163e12	−0.0170111
$361$	8.50424e13	0.730039
$362$	5.65471e13	0.478094
$363$	6.24882e13	0.520369
$364$	2.09966e12	0.0172223
$365$	2.89362e12	0.0233792
$366$	−2.52092e13	−0.200638
$367$	−9.94466e13	−0.779698	−0.389849	−	0.920879i	$-0.627473\pi$
$367$	−9.94466e13	−0.779698	−0.389849	+	0.920879i	$0.627473\pi$
$368$	−1.30473e14	−1.00776
$369$	−2.57354e13	−0.195833
$370$	−8.80238e12	−0.0659919
$371$	4.89211e13	0.361360
$372$	1.00037e13	0.0728074
$373$	1.04403e14	0.748710	0.374355	−	0.927285i	$-0.377864\pi$
$373$	1.04403e14	0.748710	0.374355	+	0.927285i	$0.377864\pi$
$374$	−3.40029e11	−0.00240282
$375$	−7.94159e12	−0.0553013
$376$	−1.81908e14	−1.24830
$377$	3.33972e13	0.225856
$378$	9.97704e12	0.0664962
$379$	1.25664e13	0.0825456	0.0412728	−	0.999148i	$-0.486859\pi$
$379$	1.25664e13	0.0825456	0.0412728	+	0.999148i	$0.486859\pi$
$380$	1.60035e12	0.0103611
$381$	−1.01664e14	−0.648756
$382$	1.52876e14	0.961595
$383$	2.19835e14	1.36302	0.681511	−	0.731808i	$-0.261323\pi$
$383$	2.19835e14	1.36302	0.681511	+	0.731808i	$0.261323\pi$
$384$	6.47925e13	0.396007
$385$	9.44923e11	0.00569328
$386$	2.00809e14	1.19276
$387$	−4.26066e13	−0.249497
$388$	1.23815e13	0.0714822
$389$	−3.80170e13	−0.216399	−0.108200	−	0.994129i	$-0.534509\pi$
$389$	−3.80170e13	−0.216399	−0.108200	+	0.994129i	$0.534509\pi$
$390$	1.25059e12	0.00701877
$391$	−1.88400e12	−0.0104258
$392$	2.78653e13	0.152052
$393$	−3.74382e13	−0.201445
$394$	9.64290e13	0.511657
$395$	−6.07039e12	−0.0317638
$396$	3.33396e12	0.0172043
$397$	2.29382e14	1.16738	0.583688	−	0.811978i	$-0.301609\pi$
$397$	2.29382e14	1.16738	0.583688	+	0.811978i	$0.301609\pi$
$398$	−2.83433e14	−1.42263
$399$	−5.79788e13	−0.287024
$400$	1.65245e14	0.806859
$401$	−3.84869e14	−1.85361	−0.926806	−	0.375541i	$-0.877457\pi$
$401$	−3.84869e14	−1.85361	−0.926806	+	0.375541i	$0.877457\pi$
$402$	1.36161e14	0.646859
$403$	−4.54286e13	−0.212888
$404$	4.32135e12	0.0199766
$405$	−1.16822e12	−0.00532749
$406$	6.25426e13	0.281373
$407$	1.06565e14	0.472981
$408$	1.17411e12	0.00514134
$409$	1.30983e14	0.565898	0.282949	−	0.959135i	$-0.408687\pi$
$409$	1.30983e14	0.565898	0.282949	+	0.959135i	$0.408687\pi$
$410$	−6.04104e12	−0.0257514
$411$	−1.39079e14	−0.584969
$412$	5.04528e13	0.209387
$413$	5.67145e13	0.232257
$414$	−9.39655e13	−0.379723
$415$	−8.32024e12	−0.0331796
$416$	2.29085e13	0.0901537
$417$	−7.58742e13	−0.294677
$418$	9.85533e13	0.377748
$419$	−5.28075e13	−0.199764	−0.0998822	−	0.994999i	$-0.531847\pi$
$419$	−5.28075e13	−0.199764	−0.0998822	+	0.994999i	$0.531847\pi$
$420$	−4.60404e11	−0.00171897
$421$	−1.14300e14	−0.421207	−0.210603	−	0.977572i	$-0.567543\pi$
$421$	−1.14300e14	−0.421207	−0.210603	+	0.977572i	$0.567543\pi$
$422$	−2.93620e14	−1.06799
$423$	−1.08888e14	−0.390939
$424$	2.87138e14	1.01760
$425$	2.38609e12	0.00834735
$426$	−1.33266e14	−0.460222
$427$	−4.21454e13	−0.143680
$428$	−6.61721e13	−0.222707
$429$	−1.51401e13	−0.0503053
$430$	−1.00013e13	−0.0328081
$431$	6.52231e13	0.211240	0.105620	−	0.994407i	$-0.466317\pi$
$431$	6.52231e13	0.211240	0.105620	+	0.994407i	$0.466317\pi$
$432$	4.86716e13	0.155638
$433$	2.39836e14	0.757235	0.378617	−	0.925553i	$-0.376400\pi$
$433$	2.39836e14	0.757235	0.378617	+	0.925553i	$0.376400\pi$
$434$	−8.50738e13	−0.265218
$435$	−7.32319e12	−0.0225429
$436$	−1.01640e14	−0.308952
$437$	5.46054e14	1.63903
$438$	−8.68239e13	−0.257355
$439$	2.26264e14	0.662309	0.331154	−	0.943577i	$-0.392562\pi$
$439$	2.26264e14	0.662309	0.331154	+	0.943577i	$0.392562\pi$
$440$	5.54613e12	0.0160325
$441$	1.66799e13	0.0476190
$442$	−7.52362e11	−0.00212131
$443$	−1.76041e14	−0.490222	−0.245111	−	0.969495i	$-0.578824\pi$
$443$	−1.76041e14	−0.490222	−0.245111	+	0.969495i	$0.578824\pi$
$444$	−5.19225e13	−0.142807
$445$	−1.83163e13	−0.0497574
$446$	−4.23522e14	−1.13641
$447$	3.54005e14	0.938248
$448$	1.59656e14	0.417981
$449$	4.90170e14	1.26763	0.633814	−	0.773486i	$-0.281489\pi$
$449$	4.90170e14	1.26763	0.633814	+	0.773486i	$0.281489\pi$
$450$	1.19008e14	0.304023
$451$	7.31349e13	0.184567
$452$	1.39572e13	0.0347966
$453$	−2.04941e14	−0.504765
$454$	4.42544e14	1.07684
$455$	2.09078e12	0.00502626
$456$	−3.40301e14	−0.808270
$457$	3.01761e14	0.708148	0.354074	−	0.935217i	$-0.384796\pi$
$457$	3.01761e14	0.708148	0.354074	+	0.935217i	$0.384796\pi$
$458$	5.85600e14	1.35782
$459$	7.02807e11	0.00161015
$460$	4.33616e12	0.00981607
$461$	3.91642e14	0.876060	0.438030	−	0.898960i	$-0.355676\pi$
$461$	3.91642e14	0.876060	0.438030	+	0.898960i	$0.355676\pi$
$462$	−2.83527e13	−0.0626706
$463$	4.34843e14	0.949811	0.474905	−	0.880037i	$-0.342482\pi$
$463$	4.34843e14	0.949811	0.474905	+	0.880037i	$0.342482\pi$
$464$	3.05106e14	0.658569
$465$	9.96139e12	0.0212485
$466$	3.10676e14	0.654916
$467$	−4.21299e14	−0.877703	−0.438852	−	0.898560i	$-0.644615\pi$
$467$	−4.21299e14	−0.877703	−0.438852	+	0.898560i	$0.644615\pi$
$468$	7.37686e12	0.0151887
$469$	2.27638e14	0.463226
$470$	−2.55600e13	−0.0514071
$471$	5.54257e14	1.10178
$472$	3.32880e14	0.654044
$473$	1.21079e14	0.235144
$474$	1.82144e14	0.349651
$475$	−6.91581e14	−1.31229
$476$	2.76981e11	0.000519531 0
$477$	1.71877e14	0.318689
$478$	3.90075e14	0.714982
$479$	−3.72285e14	−0.674575	−0.337287	−	0.941402i	$-0.609509\pi$
$479$	−3.72285e14	−0.674575	−0.337287	+	0.941402i	$0.609509\pi$
$480$	−5.02328e12	−0.00899830
$481$	2.35789e14	0.417567
$482$	−7.92550e14	−1.38761
$483$	−1.57094e14	−0.271926
$484$	8.65234e13	0.148076
$485$	1.23291e13	0.0208618
$486$	3.50529e13	0.0586441
$487$	−5.84872e14	−0.967502	−0.483751	−	0.875206i	$-0.660726\pi$
$487$	−5.84872e14	−0.967502	−0.483751	+	0.875206i	$0.660726\pi$
$488$	−2.47369e14	−0.404609
$489$	−2.24136e14	−0.362503
$490$	3.91538e12	0.00626174
$491$	−1.07279e15	−1.69655	−0.848274	−	0.529558i	$-0.822358\pi$
$491$	−1.07279e15	−1.69655	−0.848274	+	0.529558i	$0.822358\pi$
$492$	−3.56342e13	−0.0557262
$493$	4.40565e12	0.00681322
$494$	2.18063e14	0.333491
$495$	3.31985e12	0.00502100
$496$	−4.15021e14	−0.620756
$497$	−2.22798e14	−0.329573
$498$	2.49652e14	0.365235
$499$	1.05041e15	1.51987	0.759937	−	0.649997i	$-0.225230\pi$
$499$	1.05041e15	1.51987	0.759937	+	0.649997i	$0.225230\pi$
$500$	−1.09962e13	−0.0157365
$501$	−7.58080e14	−1.07302
$502$	5.94410e14	0.832177
$503$	−9.32550e14	−1.29136	−0.645681	−	0.763607i	$-0.723427\pi$
$503$	−9.32550e14	−1.29136	−0.645681	+	0.763607i	$0.723427\pi$
$504$	9.79009e13	0.134097
$505$	4.30307e12	0.00583009
$506$	2.67031e14	0.357877
$507$	−3.34996e13	−0.0444116
$508$	−1.40768e14	−0.184609
$509$	1.21853e15	1.58084	0.790418	−	0.612568i	$-0.209863\pi$
$509$	1.21853e15	1.58084	0.790418	+	0.612568i	$0.209863\pi$
$510$	1.64974e11	0.000211729 0
$511$	−1.45155e14	−0.184296
$512$	8.94569e14	1.12365
$513$	−2.03700e14	−0.253131
$514$	−6.73111e14	−0.827541
$515$	5.02393e13	0.0611088
$516$	−5.89946e13	−0.0709968
$517$	3.09438e14	0.368448
$518$	4.41560e14	0.520207
$519$	5.83430e14	0.680093
$520$	1.22716e13	0.0141541
$521$	−1.21714e15	−1.38910	−0.694551	−	0.719443i	$-0.744397\pi$
$521$	−1.21714e15	−1.38910	−0.694551	+	0.719443i	$0.744397\pi$
$522$	2.19735e14	0.248148
$523$	1.58024e15	1.76589	0.882945	−	0.469477i	$-0.155558\pi$
$523$	1.58024e15	1.76589	0.882945	+	0.469477i	$0.155558\pi$
$524$	−5.18384e13	−0.0573230
$525$	1.98961e14	0.217716
$526$	−3.62996e14	−0.393079
$527$	−5.99281e12	−0.00642202
$528$	−1.38315e14	−0.146684
$529$	5.26729e14	0.552816
$530$	4.03459e13	0.0419066
$531$	1.99258e14	0.204831
$532$	−8.02796e13	−0.0816754
$533$	1.61821e14	0.162943
$534$	5.49586e14	0.547721
$535$	−6.58920e13	−0.0649961
$536$	1.33610e15	1.30446
$537$	−5.91066e14	−0.571186
$538$	−3.22138e14	−0.308134
$539$	−4.74009e13	−0.0448795
$540$	−1.61756e12	−0.00151599
$541$	−1.10910e15	−1.02893	−0.514465	−	0.857511i	$-0.672010\pi$
$541$	−1.10910e15	−1.02893	−0.514465	+	0.857511i	$0.672010\pi$
$542$	1.05398e15	0.967917
$543$	3.32142e14	0.301943
$544$	3.02202e12	0.00271959
$545$	−1.01210e14	−0.0901662
$546$	−6.27344e13	−0.0553282
$547$	−5.12831e14	−0.447759	−0.223879	−	0.974617i	$-0.571872\pi$
$547$	−5.12831e14	−0.447759	−0.223879	+	0.974617i	$0.571872\pi$
$548$	−1.92574e14	−0.166458
$549$	−1.48072e14	−0.126714
$550$	−3.38196e14	−0.286533
$551$	−1.27693e15	−1.07111
$552$	−9.22048e14	−0.765753
$553$	3.04514e14	0.250391
$554$	1.53117e15	1.24658
$555$	−5.17028e13	−0.0416776
$556$	−1.05058e14	−0.0838531
$557$	−1.05328e15	−0.832414	−0.416207	−	0.909270i	$-0.636641\pi$
$557$	−1.05328e15	−0.832414	−0.416207	+	0.909270i	$0.636641\pi$
$558$	−2.98895e14	−0.233900
$559$	2.67905e14	0.207594
$560$	1.91006e13	0.0146559
$561$	−1.99724e12	−0.00151752
$562$	−1.19116e15	−0.896231
$563$	−6.85740e14	−0.510932	−0.255466	−	0.966818i	$-0.582229\pi$
$563$	−6.85740e14	−0.510932	−0.255466	+	0.966818i	$0.582229\pi$
$564$	−1.50771e14	−0.111245
$565$	1.38981e13	0.0101552
$566$	7.41058e14	0.536243
$567$	5.86024e13	0.0419961
$568$	−1.30769e15	−0.928088
$569$	−1.33364e15	−0.937392	−0.468696	−	0.883360i	$-0.655276\pi$
$569$	−1.33364e15	−0.937392	−0.468696	+	0.883360i	$0.655276\pi$
$570$	−4.78159e13	−0.0332859
$571$	2.27533e15	1.56872	0.784361	−	0.620305i	$-0.212991\pi$
$571$	2.27533e15	1.56872	0.784361	+	0.620305i	$0.212991\pi$
$572$	−2.09635e13	−0.0143148
$573$	8.97954e14	0.607301
$574$	3.03041e14	0.202995
$575$	−1.87384e15	−1.24326
$576$	5.60929e14	0.368624
$577$	1.97105e13	0.0128301	0.00641505	−	0.999979i	$-0.497958\pi$
$577$	1.97105e13	0.0128301	0.00641505	+	0.999979i	$0.497958\pi$
$578$	1.41775e15	0.914108
$579$	1.17950e15	0.753293
$580$	−1.01400e13	−0.00641478
$581$	4.17374e14	0.261551
$582$	−3.69938e14	−0.229643
$583$	−4.88441e14	−0.300355
$584$	−8.51970e14	−0.518984
$585$	7.34564e12	0.00443274
$586$	2.45299e15	1.46642
$587$	2.33373e15	1.38211	0.691053	−	0.722804i	$-0.257147\pi$
$587$	2.33373e15	1.38211	0.691053	+	0.722804i	$0.257147\pi$
$588$	2.30956e13	0.0135504
$589$	1.73694e15	1.00961
$590$	4.67732e13	0.0269346
$591$	5.66398e14	0.323140
$592$	2.15409e15	1.21757
$593$	−1.46795e15	−0.822074	−0.411037	−	0.911619i	$-0.634833\pi$
$593$	−1.46795e15	−0.822074	−0.411037	+	0.911619i	$0.634833\pi$
$594$	−9.96133e13	−0.0552703
$595$	2.75809e11	0.000151623 0
$596$	4.90168e14	0.266987
$597$	−1.66480e15	−0.898472
$598$	5.90844e14	0.315948
$599$	−1.25723e15	−0.666140	−0.333070	−	0.942902i	$-0.608085\pi$
$599$	−1.25723e15	−0.666140	−0.333070	+	0.942902i	$0.608085\pi$
$600$	1.16778e15	0.613096
$601$	−1.97279e15	−1.02629	−0.513147	−	0.858301i	$-0.671520\pi$
$601$	−1.97279e15	−1.02629	−0.513147	+	0.858301i	$0.671520\pi$
$602$	5.01703e14	0.258622
$603$	7.99772e14	0.408527
$604$	−2.83769e14	−0.143636
$605$	8.61573e13	0.0432153
$606$	−1.29115e14	−0.0641766
$607$	−3.46544e15	−1.70695	−0.853476	−	0.521133i	$-0.825510\pi$
$607$	−3.46544e15	−1.70695	−0.853476	+	0.521133i	$0.825510\pi$
$608$	−8.75897e14	−0.427546
$609$	3.67358e14	0.177703
$610$	−3.47579e13	−0.0166625
$611$	6.84676e14	0.325281
$612$	9.73132e11	0.000458183 0
$613$	2.07469e15	0.968101	0.484051	−	0.875040i	$-0.339165\pi$
$613$	2.07469e15	0.968101	0.484051	+	0.875040i	$0.339165\pi$
$614$	−3.08491e15	−1.42665
$615$	−3.54834e13	−0.0162634
$616$	−2.78215e14	−0.126382
$617$	−7.15598e14	−0.322182	−0.161091	−	0.986940i	$-0.551501\pi$
$617$	−7.15598e14	−0.322182	−0.161091	+	0.986940i	$0.551501\pi$
$618$	−1.50745e15	−0.672675
$619$	3.32049e15	1.46860	0.734300	−	0.678825i	$-0.237511\pi$
$619$	3.32049e15	1.46860	0.734300	+	0.678825i	$0.237511\pi$
$620$	1.37929e13	0.00604646
$621$	−5.51927e14	−0.239816
$622$	2.95722e15	1.27361
$623$	9.18813e14	0.392232
$624$	−3.06041e14	−0.129499
$625$	2.36775e15	0.993108
$626$	1.37828e14	0.0573032
$627$	5.78875e14	0.238569
$628$	7.67444e14	0.313522
$629$	3.11046e13	0.0125964
$630$	1.37561e13	0.00552234
$631$	1.41030e15	0.561242	0.280621	−	0.959819i	$-0.409460\pi$
$631$	1.41030e15	0.561242	0.280621	+	0.959819i	$0.409460\pi$
$632$	1.78731e15	0.705109
$633$	−1.72465e15	−0.674496
$634$	−1.34248e15	−0.520495
$635$	−1.40172e14	−0.0538775
$636$	2.37988e14	0.0906861
$637$	−1.04881e14	−0.0396214
$638$	−6.24441e14	−0.233872
$639$	−7.82769e14	−0.290656
$640$	8.93344e13	0.0328873
$641$	−3.17728e15	−1.15967	−0.579837	−	0.814733i	$-0.696884\pi$
$641$	−3.17728e15	−1.15967	−0.579837	+	0.814733i	$0.696884\pi$
$642$	1.97711e15	0.715466
$643$	−2.15907e15	−0.774650	−0.387325	−	0.921943i	$-0.626601\pi$
$643$	−2.15907e15	−0.774650	−0.387325	+	0.921943i	$0.626601\pi$
$644$	−2.17518e14	−0.0773790
$645$	−5.87450e13	−0.0207201
$646$	2.87662e13	0.0100601
$647$	5.05672e14	0.175346	0.0876729	−	0.996149i	$-0.472057\pi$
$647$	5.05672e14	0.175346	0.0876729	+	0.996149i	$0.472057\pi$
$648$	3.43961e14	0.118262
$649$	−5.66252e14	−0.193047
$650$	−7.48307e14	−0.252963
$651$	−4.99700e14	−0.167500
$652$	−3.10346e14	−0.103154
$653$	9.87951e14	0.325621	0.162811	−	0.986657i	$-0.447944\pi$
$653$	9.87951e14	0.325621	0.162811	+	0.986657i	$0.447944\pi$
$654$	3.03685e15	0.992534
$655$	−5.16190e13	−0.0167295
$656$	1.47835e15	0.475122
$657$	−5.09980e14	−0.162534
$658$	1.28219e15	0.405237
$659$	−5.39788e15	−1.69182	−0.845908	−	0.533329i	$-0.820941\pi$
$659$	−5.39788e15	−1.69182	−0.845908	+	0.533329i	$0.820941\pi$
$660$	4.59679e12	0.00142877
$661$	1.62009e15	0.499381	0.249691	−	0.968326i	$-0.419671\pi$
$661$	1.62009e15	0.499381	0.249691	+	0.968326i	$0.419671\pi$
$662$	−3.94077e14	−0.120465
$663$	−4.41917e12	−0.00133973
$664$	2.44974e15	0.736537
$665$	−7.99399e13	−0.0238366
$666$	1.55136e15	0.458779
$667$	−3.45984e15	−1.01476
$668$	−1.04967e15	−0.305338
$669$	−2.48765e15	−0.717705
$670$	1.87736e14	0.0537199
$671$	4.20791e14	0.119424
$672$	2.51986e14	0.0709326
$673$	−4.65049e15	−1.29842	−0.649211	−	0.760608i	$-0.724901\pi$
$673$	−4.65049e15	−1.29842	−0.649211	+	0.760608i	$0.724901\pi$
$674$	−4.99870e15	−1.38429
$675$	6.99020e14	0.192008
$676$	−4.63848e13	−0.0126377
$677$	−1.86212e15	−0.503233	−0.251616	−	0.967827i	$-0.580962\pi$
$677$	−1.86212e15	−0.503233	−0.251616	+	0.967827i	$0.580962\pi$
$678$	−4.17018e14	−0.111787
$679$	−6.18472e14	−0.164451
$680$	1.61883e12	0.000426975 0
$681$	2.59938e15	0.680082
$682$	8.49399e14	0.220444
$683$	2.33245e15	0.600480	0.300240	−	0.953864i	$-0.402933\pi$
$683$	2.33245e15	0.600480	0.300240	+	0.953864i	$0.402933\pi$
$684$	−2.82051e14	−0.0720309
$685$	−1.91760e14	−0.0485802
$686$	−1.96410e14	−0.0493606
$687$	3.43965e15	0.857537
$688$	2.44749e15	0.605320
$689$	−1.08074e15	−0.265166
$690$	−1.29558e14	−0.0315350
$691$	4.93407e15	1.19145	0.595725	−	0.803188i	$-0.296865\pi$
$691$	4.93407e15	1.19145	0.595725	+	0.803188i	$0.296865\pi$
$692$	8.07838e14	0.193527
$693$	−1.66536e14	−0.0395800
$694$	3.82130e15	0.901020
$695$	−1.04614e14	−0.0244722
$696$	2.15617e15	0.500418
$697$	2.13470e13	0.00491537
$698$	5.07666e15	1.15977
$699$	1.82483e15	0.413616
$700$	2.75488e14	0.0619532
$701$	5.07900e14	0.113326	0.0566629	−	0.998393i	$-0.481954\pi$
$701$	5.07900e14	0.113326	0.0566629	+	0.998393i	$0.481954\pi$
$702$	−2.20408e14	−0.0487949
$703$	−9.01529e15	−1.98027
$704$	−1.59405e15	−0.347417
$705$	−1.50133e14	−0.0324665
$706$	6.32100e15	1.35631
$707$	−2.15858e14	−0.0459580
$708$	2.75900e14	0.0582867
$709$	−3.82699e15	−0.802238	−0.401119	−	0.916026i	$-0.631379\pi$
$709$	−3.82699e15	−0.802238	−0.401119	+	0.916026i	$0.631379\pi$
$710$	−1.83744e14	−0.0382202
$711$	1.06986e15	0.220824
$712$	5.39288e15	1.10454
$713$	4.70626e15	0.956497
$714$	−8.27573e12	−0.00166904
$715$	−2.08748e13	−0.00417773
$716$	−8.18412e14	−0.162536
$717$	2.29120e15	0.451551
$718$	6.28601e15	1.22939
$719$	−4.52496e15	−0.878225	−0.439112	−	0.898432i	$-0.644707\pi$
$719$	−4.52496e15	−0.878225	−0.439112	+	0.898432i	$0.644707\pi$
$720$	6.71074e13	0.0129253
$721$	−2.52019e15	−0.481714
$722$	−3.51826e15	−0.667381
$723$	−4.65522e15	−0.876354
$724$	4.59896e14	0.0859206
$725$	4.38191e15	0.812465
$726$	−2.58518e15	−0.475707
$727$	4.60621e15	0.841210	0.420605	−	0.907244i	$-0.361818\pi$
$727$	4.60621e15	0.841210	0.420605	+	0.907244i	$0.361818\pi$
$728$	−6.15589e14	−0.111575
$729$	2.05891e14	0.0370370
$730$	−1.19711e14	−0.0213726
$731$	3.53412e13	0.00626232
$732$	−2.05026e14	−0.0360577
$733$	4.27153e15	0.745610	0.372805	−	0.927910i	$-0.378396\pi$
$733$	4.27153e15	0.745610	0.372805	+	0.927910i	$0.378396\pi$
$734$	4.11417e15	0.712778
$735$	2.29978e13	0.00395464
$736$	−2.37325e15	−0.405056
$737$	−2.27279e15	−0.385024
$738$	1.06469e15	0.179025
$739$	−1.24314e15	−0.207479	−0.103740	−	0.994604i	$-0.533081\pi$
$739$	−1.24314e15	−0.207479	−0.103740	+	0.994604i	$0.533081\pi$
$740$	−7.15895e13	−0.0118597
$741$	1.28084e15	0.210618
$742$	−2.02390e15	−0.330345
$743$	4.37560e15	0.708923	0.354461	−	0.935071i	$-0.384664\pi$
$743$	4.37560e15	0.708923	0.354461	+	0.935071i	$0.384664\pi$
$744$	−2.93294e15	−0.471685
$745$	4.88094e14	0.0779190
$746$	−4.31922e15	−0.684450
$747$	1.46638e15	0.230666
$748$	−2.76545e12	−0.000431824 0
$749$	3.30539e15	0.512357
$750$	3.28549e14	0.0505549
$751$	−5.32766e15	−0.813798	−0.406899	−	0.913473i	$-0.633390\pi$
$751$	−5.32766e15	−0.813798	−0.406899	+	0.913473i	$0.633390\pi$
$752$	6.25497e15	0.948478
$753$	3.49140e15	0.525566
$754$	−1.38166e15	−0.206472
$755$	−2.82569e14	−0.0419195
$756$	8.11430e13	0.0119504
$757$	−2.89374e15	−0.423090	−0.211545	−	0.977368i	$-0.567850\pi$
$757$	−2.89374e15	−0.423090	−0.211545	+	0.977368i	$0.567850\pi$
$758$	−5.19879e14	−0.0754609
$759$	1.56847e15	0.226019
$760$	−4.69199e14	−0.0671247
$761$	3.90539e15	0.554687	0.277344	−	0.960771i	$-0.410546\pi$
$761$	3.90539e15	0.554687	0.277344	+	0.960771i	$0.410546\pi$
$762$	4.20592e15	0.593074
$763$	5.07708e15	0.710770
$764$	1.24334e15	0.172813
$765$	9.69015e11	0.000133719 0
$766$	−9.09471e15	−1.24604
$767$	−1.25291e15	−0.170430
$768$	2.04699e15	0.276458
$769$	−1.21703e16	−1.63195	−0.815977	−	0.578085i	$-0.803800\pi$
$769$	−1.21703e16	−1.63195	−0.815977	+	0.578085i	$0.803800\pi$
$770$	−3.90921e13	−0.00520463
$771$	−3.95367e15	−0.522638
$772$	1.63317e15	0.214357
$773$	−2.92041e15	−0.380590	−0.190295	−	0.981727i	$-0.560944\pi$
$773$	−2.92041e15	−0.380590	−0.190295	+	0.981727i	$0.560944\pi$
$774$	1.76266e15	0.228083
$775$	−5.96051e15	−0.765816
$776$	−3.63006e15	−0.463100
$777$	2.59360e15	0.328540
$778$	1.57279e15	0.197826
$779$	−6.18716e15	−0.772744
$780$	1.01710e13	0.00126138
$781$	2.22447e15	0.273934
$782$	7.79423e13	0.00953094
$783$	1.29066e15	0.156719
$784$	−9.58159e14	−0.115531
$785$	7.64197e14	0.0915002
$786$	1.54885e15	0.184155
$787$	−9.47089e15	−1.11823	−0.559113	−	0.829091i	$-0.688858\pi$
$787$	−9.47089e15	−1.11823	−0.559113	+	0.829091i	$0.688858\pi$
$788$	7.84255e14	0.0919524
$789$	−2.13214e15	−0.248251
$790$	2.51136e14	0.0290376
$791$	−6.97182e14	−0.0800526
$792$	−9.77467e14	−0.111459
$793$	9.31059e14	0.105433
$794$	−9.48967e15	−1.06718
$795$	2.36981e14	0.0264663
$796$	−2.30515e15	−0.255668
$797$	−7.51916e15	−0.828225	−0.414113	−	0.910226i	$-0.635908\pi$
$797$	−7.51916e15	−0.828225	−0.414113	+	0.910226i	$0.635908\pi$
$798$	2.39862e15	0.262389
$799$	9.03203e13	0.00981247
$800$	3.00574e15	0.324307
$801$	3.22812e15	0.345916
$802$	1.59223e16	1.69452
$803$	1.44926e15	0.153183
$804$	1.10739e15	0.116250
$805$	−2.16598e14	−0.0225827
$806$	1.87941e15	0.194617
$807$	−1.89215e15	−0.194604
$808$	−1.26696e15	−0.129419
$809$	3.62657e15	0.367942	0.183971	−	0.982932i	$-0.441105\pi$
$809$	3.62657e15	0.367942	0.183971	+	0.982932i	$0.441105\pi$
$810$	4.83302e13	0.00487024
$811$	−2.00263e15	−0.200440	−0.100220	−	0.994965i	$-0.531955\pi$
$811$	−2.00263e15	−0.200440	−0.100220	+	0.994965i	$0.531955\pi$
$812$	5.08658e14	0.0505670
$813$	6.19082e15	0.611294
$814$	−4.40865e15	−0.432386
$815$	−3.09033e14	−0.0301050
$816$	−4.03720e13	−0.00390647
$817$	−1.02432e16	−0.984499
$818$	−5.41888e15	−0.517328
$819$	−3.68485e14	−0.0349428
$820$	−4.91317e13	−0.00462791
$821$	−1.90716e16	−1.78443	−0.892217	−	0.451608i	$-0.850851\pi$
$821$	−1.90716e16	−1.78443	−0.892217	+	0.451608i	$0.850851\pi$
$822$	5.75381e15	0.534762
$823$	5.30225e15	0.489509	0.244755	−	0.969585i	$-0.421293\pi$
$823$	5.30225e15	0.489509	0.244755	+	0.969585i	$0.421293\pi$
$824$	−1.47920e16	−1.35652
$825$	−1.98647e15	−0.180961
$826$	−2.34632e15	−0.212323
$827$	−5.28776e15	−0.475326	−0.237663	−	0.971348i	$-0.576381\pi$
$827$	−5.28776e15	−0.475326	−0.237663	+	0.971348i	$0.576381\pi$
$828$	−7.64219e14	−0.0682419
$829$	−1.08973e16	−0.966653	−0.483327	−	0.875440i	$-0.660572\pi$
$829$	−1.08973e16	−0.966653	−0.483327	+	0.875440i	$0.660572\pi$
$830$	3.44214e14	0.0303319
$831$	8.99370e15	0.787286
$832$	−3.52705e15	−0.306714
$833$	−1.38356e13	−0.00119523
$834$	3.13897e15	0.269385
$835$	−1.04522e15	−0.0891115
$836$	8.01532e14	0.0678869
$837$	−1.75563e15	−0.147721
$838$	2.18468e15	0.182619
$839$	2.82658e15	0.234731	0.117365	−	0.993089i	$-0.462555\pi$
$839$	2.82658e15	0.234731	0.117365	+	0.993089i	$0.462555\pi$
$840$	1.34984e14	0.0111364
$841$	−4.10980e15	−0.336855
$842$	4.72868e15	0.385055
$843$	−6.99654e15	−0.566020
$844$	−2.38801e15	−0.191934
$845$	−4.61885e13	−0.00368827
$846$	4.50478e15	0.357385
$847$	−4.32197e15	−0.340662
$848$	−9.87332e15	−0.773190
$849$	4.35277e15	0.338667
$850$	−9.87144e13	−0.00763091
$851$	−2.44270e16	−1.87611
$852$	−1.08385e15	−0.0827088
$853$	−1.07402e16	−0.814314	−0.407157	−	0.913358i	$-0.633480\pi$
$853$	−1.07402e16	−0.814314	−0.407157	+	0.913358i	$0.633480\pi$
$854$	1.74359e15	0.131348
$855$	−2.80857e14	−0.0210219
$856$	1.94007e16	1.44282
$857$	−1.52126e16	−1.12411	−0.562055	−	0.827100i	$-0.689989\pi$
$857$	−1.52126e16	−1.12411	−0.562055	+	0.827100i	$0.689989\pi$
$858$	6.26356e14	0.0459877
$859$	7.54484e15	0.550412	0.275206	−	0.961385i	$-0.411254\pi$
$859$	7.54484e15	0.550412	0.275206	+	0.961385i	$0.411254\pi$
$860$	−8.13404e13	−0.00589610
$861$	1.77998e15	0.128203
$862$	−2.69833e15	−0.193110
$863$	−2.70835e16	−1.92595	−0.962976	−	0.269586i	$-0.913113\pi$
$863$	−2.70835e16	−1.92595	−0.962976	+	0.269586i	$0.913113\pi$
$864$	8.85318e14	0.0625567
$865$	8.04420e14	0.0564799
$866$	−9.92217e15	−0.692243
$867$	8.32749e15	0.577310
$868$	−6.91903e14	−0.0476636
$869$	−3.04034e15	−0.208120
$870$	3.02965e14	0.0206080
$871$	−5.02887e15	−0.339915
$872$	2.97994e16	2.00155
$873$	−2.17291e15	−0.145032
$874$	−2.25906e16	−1.49836
$875$	5.49277e14	0.0362032
$876$	−7.06137e14	−0.0462505
$877$	−2.46809e16	−1.60643	−0.803217	−	0.595686i	$-0.796880\pi$
$877$	−2.46809e16	−1.60643	−0.803217	+	0.595686i	$0.796880\pi$
$878$	−9.36070e15	−0.605464
$879$	1.44082e16	0.926126
$880$	−1.90706e14	−0.0121817
$881$	−8.87922e15	−0.563647	−0.281824	−	0.959466i	$-0.590939\pi$
$881$	−8.87922e15	−0.563647	−0.281824	+	0.959466i	$0.590939\pi$
$882$	−6.90058e14	−0.0435320
$883$	−1.36250e16	−0.854188	−0.427094	−	0.904207i	$-0.640463\pi$
$883$	−1.36250e16	−0.854188	−0.427094	+	0.904207i	$0.640463\pi$
$884$	−6.11894e12	−0.000381231 0
$885$	2.74733e14	0.0170107
$886$	7.28293e15	0.448147
$887$	1.64891e15	0.100837	0.0504183	−	0.998728i	$-0.483945\pi$
$887$	1.64891e15	0.100837	0.0504183	+	0.998728i	$0.483945\pi$
$888$	1.52229e16	0.925179
$889$	7.03157e15	0.424710
$890$	7.57757e14	0.0454868
$891$	−5.85101e14	−0.0349063
$892$	−3.44449e15	−0.204230
$893$	−2.61783e16	−1.54262
$894$	−1.46454e16	−0.857719
$895$	−8.14949e14	−0.0474355
$896$	−4.48134e15	−0.259247
$897$	3.47045e15	0.199539
$898$	−2.02787e16	−1.15883
$899$	−1.10054e16	−0.625069
$900$	9.67888e14	0.0546376
$901$	−1.42568e14	−0.00799903
$902$	−3.02564e15	−0.168726
$903$	2.94687e15	0.163334
$904$	−4.09204e15	−0.225431
$905$	4.57950e14	0.0250756
$906$	8.47857e15	0.461442
$907$	1.02159e16	0.552634	0.276317	−	0.961066i	$-0.410886\pi$
$907$	1.02159e16	0.552634	0.276317	+	0.961066i	$0.410886\pi$
$908$	3.59920e15	0.193524
$909$	−7.58386e14	−0.0405311
$910$	−8.64968e13	−0.00459486
$911$	−8.31181e14	−0.0438879	−0.0219439	−	0.999759i	$-0.506986\pi$
$911$	−8.31181e14	−0.0438879	−0.0219439	+	0.999759i	$0.506986\pi$
$912$	1.17014e16	0.614136
$913$	−4.16717e15	−0.217396
$914$	−1.24841e16	−0.647369
$915$	−2.04158e14	−0.0105233
$916$	4.76267e15	0.244020
$917$	2.58940e15	0.131877
$918$	−2.90756e13	−0.00147195
$919$	1.89639e15	0.0954318	0.0477159	−	0.998861i	$-0.484806\pi$
$919$	1.89639e15	0.0954318	0.0477159	+	0.998861i	$0.484806\pi$
$920$	−1.27130e15	−0.0635938
$921$	−1.81199e16	−0.901007
$922$	−1.62025e16	−0.800869
$923$	4.92196e15	0.241840
$924$	−2.30592e14	−0.0112629
$925$	3.09369e16	1.50210
$926$	−1.79898e16	−0.868290
$927$	−8.85432e15	−0.424832
$928$	5.54975e15	0.264703
$929$	−2.21251e16	−1.04906	−0.524528	−	0.851393i	$-0.675758\pi$
$929$	−2.21251e16	−1.04906	−0.524528	+	0.851393i	$0.675758\pi$
$930$	−4.12109e14	−0.0194248
$931$	4.01008e15	0.187901
$932$	2.52672e15	0.117698
$933$	1.73699e16	0.804355
$934$	1.74294e16	0.802371
$935$	−2.75374e12	−0.000126026 0
$936$	−2.16278e15	−0.0984002
$937$	−3.28940e15	−0.148782	−0.0743908	−	0.997229i	$-0.523701\pi$
$937$	−3.28940e15	−0.148782	−0.0743908	+	0.997229i	$0.523701\pi$
$938$	−9.41752e15	−0.423468
$939$	8.09564e14	0.0361902
$940$	−2.07879e14	−0.00923864
$941$	1.06884e16	0.472248	0.236124	−	0.971723i	$-0.424123\pi$
$941$	1.06884e16	0.472248	0.236124	+	0.971723i	$0.424123\pi$
$942$	−2.29300e16	−1.00722
$943$	−1.67642e16	−0.732095
$944$	−1.14462e16	−0.496953
$945$	8.07997e13	0.00348766
$946$	−5.00913e15	−0.214962
$947$	−8.74933e15	−0.373293	−0.186646	−	0.982427i	$-0.559762\pi$
$947$	−8.74933e15	−0.373293	−0.186646	+	0.982427i	$0.559762\pi$
$948$	1.48137e15	0.0628375
$949$	3.20669e15	0.135236
$950$	2.86112e16	1.19965
$951$	−7.88536e15	−0.328722
$952$	−8.12066e13	−0.00336580
$953$	3.98003e16	1.64012	0.820060	−	0.572277i	$-0.193940\pi$
$953$	3.98003e16	1.64012	0.820060	+	0.572277i	$0.193940\pi$
$954$	−7.11069e15	−0.291337
$955$	1.23808e15	0.0504348
$956$	3.17247e15	0.128493
$957$	−3.66780e15	−0.147703
$958$	1.54017e16	0.616677
$959$	9.61937e15	0.382952
$960$	7.73396e14	0.0306133
$961$	−1.04383e16	−0.410821
$962$	−9.75475e15	−0.381727
$963$	1.16130e16	0.451856
$964$	−6.44579e15	−0.249375
$965$	1.62626e15	0.0625591
$966$	6.49909e15	0.248587
$967$	7.95672e15	0.302614	0.151307	−	0.988487i	$-0.451652\pi$
$967$	7.95672e15	0.302614	0.151307	+	0.988487i	$0.451652\pi$
$968$	−2.53674e16	−0.959315
$969$	1.68965e14	0.00635354
$970$	−5.10062e14	−0.0190712
$971$	−1.39864e16	−0.519998	−0.259999	−	0.965609i	$-0.583722\pi$
$971$	−1.39864e16	−0.519998	−0.259999	+	0.965609i	$0.583722\pi$
$972$	2.85084e14	0.0105392
$973$	5.24781e15	0.192911
$974$	2.41966e16	0.884462
$975$	−4.39535e15	−0.159760
$976$	8.50585e15	0.307428
$977$	7.04353e13	0.00253145	0.00126573	−	0.999999i	$-0.499597\pi$
$977$	7.04353e13	0.00253145	0.00126573	+	0.999999i	$0.499597\pi$
$978$	9.27264e15	0.331390
$979$	−9.17366e15	−0.326015
$980$	3.18437e13	0.00112533
$981$	1.78376e16	0.626840
$982$	4.43820e16	1.55094
$983$	−2.51147e16	−0.872737	−0.436369	−	0.899768i	$-0.643736\pi$
$983$	−2.51147e16	−0.872737	−0.436369	+	0.899768i	$0.643736\pi$
$984$	1.04474e16	0.361024
$985$	7.80936e14	0.0268359
$986$	−1.82265e14	−0.00622845
$987$	7.53121e15	0.255930
$988$	1.77350e15	0.0599333
$989$	−2.77541e16	−0.932712
$990$	−1.37345e14	−0.00459006
$991$	1.59790e16	0.531060	0.265530	−	0.964103i	$-0.414453\pi$
$991$	1.59790e16	0.531060	0.265530	+	0.964103i	$0.414453\pi$
$992$	−7.54907e15	−0.249505
$993$	−2.31470e15	−0.0760806
$994$	9.21730e15	0.301286
$995$	−2.29540e15	−0.0746158
$996$	2.03041e15	0.0656383
$997$	−2.69128e16	−0.865239	−0.432619	−	0.901577i	$-0.642411\pi$
$997$	−2.69128e16	−0.865239	−0.432619	+	0.901577i	$0.642411\pi$
$998$	−4.34563e16	−1.38943
$999$	9.11225e15	0.289745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-41.3707 q^{2} -243.000 q^{3} -336.467 q^{4} -335.043 q^{5} +10053.1 q^{6} +16807.0 q^{7} +98647.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-41.3707 q^{2} -243.000 q^{3} -336.467 q^{4} -335.043 q^{5} +10053.1 q^{6} +16807.0 q^{7} +98647.0 q^{8} +59049.0 q^{9} +13861.0 q^{10} -167805. q^{11} +81761.4 q^{12} -371293. q^{13} -695317. q^{14} +81415.4 q^{15} -3.39201e6 q^{16} -48979.8 q^{17} -2.44290e6 q^{18} +1.41962e7 q^{19} +112731. q^{20} -4.08410e6 q^{21} +6.94222e6 q^{22} +3.84648e7 q^{23} -2.39712e7 q^{24} -4.87159e7 q^{25} +1.53606e7 q^{26} -1.43489e7 q^{27} -5.65500e6 q^{28} -8.99484e7 q^{29} -3.36821e6 q^{30} +1.22353e8 q^{31} -6.16993e7 q^{32} +4.07767e7 q^{33} +2.02633e6 q^{34} -5.63107e6 q^{35} -1.98680e7 q^{36} -6.35049e8 q^{37} -5.87307e8 q^{38} +9.02242e7 q^{39} -3.30510e7 q^{40} -4.35832e8 q^{41} +1.68962e8 q^{42} -7.21546e8 q^{43} +5.64609e7 q^{44} -1.97840e7 q^{45} -1.59131e9 q^{46} -1.84403e9 q^{47} +8.24259e8 q^{48} +2.82475e8 q^{49} +2.01541e9 q^{50} +1.19021e7 q^{51} +1.24928e8 q^{52} +2.91076e9 q^{53} +5.93624e8 q^{54} +5.62220e7 q^{55} +1.65796e9 q^{56} -3.44968e9 q^{57} +3.72122e9 q^{58} +3.37446e9 q^{59} -2.73936e7 q^{60} -2.50761e9 q^{61} -5.06181e9 q^{62} +9.92437e8 q^{63} +9.49938e9 q^{64} +1.24399e8 q^{65} -1.68696e9 q^{66} +1.35442e10 q^{67} +1.64801e7 q^{68} -9.34694e9 q^{69} +2.32961e8 q^{70} -1.32563e10 q^{71} +5.82501e9 q^{72} -8.63655e9 q^{73} +2.62724e10 q^{74} +1.18380e10 q^{75} -4.77656e9 q^{76} -2.82030e9 q^{77} -3.73264e9 q^{78} +1.81183e10 q^{79} +1.13647e9 q^{80} +3.48678e9 q^{81} +1.80307e10 q^{82} +2.48333e10 q^{83} +1.37416e9 q^{84} +1.64103e7 q^{85} +2.98508e10 q^{86} +2.18575e10 q^{87} -1.65535e10 q^{88} +5.46685e10 q^{89} +8.18476e8 q^{90} -6.24032e9 q^{91} -1.29421e10 q^{92} -2.97317e10 q^{93} +7.62888e10 q^{94} -4.75634e9 q^{95} +1.49929e10 q^{96} -3.67985e10 q^{97} -1.16862e10 q^{98} -9.90874e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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