LMFDB - Embedded newform 273.12.a.c.1.14

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			1.14
Root			$72.4378$ 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)

$f(q)$	$=$	$q+68.4378 q^{2} -243.000 q^{3} +2635.73 q^{4} +3481.49 q^{5} -16630.4 q^{6} +16807.0 q^{7} +40223.3 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+68.4378 q^{2} -243.000 q^{3} +2635.73 q^{4} +3481.49 q^{5} -16630.4 q^{6} +16807.0 q^{7} +40223.3 q^{8} +59049.0 q^{9} +238265. q^{10} +564893. q^{11} -640484. q^{12} -371293. q^{13} +1.15023e6 q^{14} -846001. q^{15} -2.64519e6 q^{16} -7.43323e6 q^{17} +4.04118e6 q^{18} -5.25778e6 q^{19} +9.17628e6 q^{20} -4.08410e6 q^{21} +3.86601e7 q^{22} +6.43385e6 q^{23} -9.77426e6 q^{24} -3.67074e7 q^{25} -2.54105e7 q^{26} -1.43489e7 q^{27} +4.42988e7 q^{28} -6.05266e7 q^{29} -5.78985e7 q^{30} +1.86892e8 q^{31} -2.63408e8 q^{32} -1.37269e8 q^{33} -5.08714e8 q^{34} +5.85134e7 q^{35} +1.55638e8 q^{36} -2.81894e7 q^{37} -3.59831e8 q^{38} +9.02242e7 q^{39} +1.40037e8 q^{40} -9.05699e8 q^{41} -2.79507e8 q^{42} -9.23656e8 q^{43} +1.48891e9 q^{44} +2.05578e8 q^{45} +4.40319e8 q^{46} +1.20837e9 q^{47} +6.42781e8 q^{48} +2.82475e8 q^{49} -2.51217e9 q^{50} +1.80628e9 q^{51} -9.78630e8 q^{52} +7.69035e8 q^{53} -9.82008e8 q^{54} +1.96667e9 q^{55} +6.76033e8 q^{56} +1.27764e9 q^{57} -4.14231e9 q^{58} +3.00954e9 q^{59} -2.22984e9 q^{60} +6.04594e9 q^{61} +1.27905e10 q^{62} +9.92437e8 q^{63} -1.26097e10 q^{64} -1.29265e9 q^{65} -9.39440e9 q^{66} -1.34769e10 q^{67} -1.95920e10 q^{68} -1.56343e9 q^{69} +4.00453e9 q^{70} -1.16893e10 q^{71} +2.37515e9 q^{72} +1.04851e9 q^{73} -1.92922e9 q^{74} +8.91989e9 q^{75} -1.38581e10 q^{76} +9.49416e9 q^{77} +6.17475e9 q^{78} +1.51686e10 q^{79} -9.20920e9 q^{80} +3.48678e9 q^{81} -6.19840e10 q^{82} +3.27992e10 q^{83} -1.07646e10 q^{84} -2.58787e10 q^{85} -6.32130e10 q^{86} +1.47080e10 q^{87} +2.27219e10 q^{88} -6.18269e10 q^{89} +1.40693e10 q^{90} -6.24032e9 q^{91} +1.69579e10 q^{92} -4.54147e10 q^{93} +8.26980e10 q^{94} -1.83049e10 q^{95} +6.40082e10 q^{96} -5.58660e10 q^{97} +1.93320e10 q^{98} +3.33564e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	68.4378	1.51228	0.756138	−	0.654412i	$-0.227084\pi$
$2$	68.4378	1.51228	0.756138	+	0.654412i	$0.227084\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2635.73	1.28698
$5$	3481.49	0.498230	0.249115	−	0.968474i	$-0.419860\pi$
$5$	3481.49	0.498230	0.249115	+	0.968474i	$0.419860\pi$
$6$	−16630.4	−0.873113
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	40223.3	0.433993
$9$	59049.0	0.333333
$10$	238265.	0.753461
$11$	564893.	1.05756	0.528782	−	0.848758i	$-0.322649\pi$
$11$	564893.	1.05756	0.528782	+	0.848758i	$0.322649\pi$
$12$	−640484.	−0.743038
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	1.15023e6	0.571587
$15$	−846001.	−0.287653
$16$	−2.64519e6	−0.630663
$17$	−7.43323e6	−1.26972	−0.634861	−	0.772626i	$-0.718943\pi$
$17$	−7.43323e6	−1.26972	−0.634861	+	0.772626i	$0.718943\pi$
$18$	4.04118e6	0.504092
$19$	−5.25778e6	−0.487144	−0.243572	−	0.969883i	$-0.578319\pi$
$19$	−5.25778e6	−0.487144	−0.243572	+	0.969883i	$0.578319\pi$
$20$	9.17628e6	0.641212
$21$	−4.08410e6	−0.218218
$22$	3.86601e7	1.59933
$23$	6.43385e6	0.208434	0.104217	−	0.994555i	$-0.466766\pi$
$23$	6.43385e6	0.208434	0.104217	+	0.994555i	$0.466766\pi$
$24$	−9.77426e6	−0.250566
$25$	−3.67074e7	−0.751767
$26$	−2.54105e7	−0.419430
$27$	−1.43489e7	−0.192450
$28$	4.42988e7	0.486433
$29$	−6.05266e7	−0.547971	−0.273985	−	0.961734i	$-0.588342\pi$
$29$	−6.05266e7	−0.547971	−0.273985	+	0.961734i	$0.588342\pi$
$30$	−5.78985e7	−0.435011
$31$	1.86892e8	1.17247	0.586234	−	0.810142i	$-0.300610\pi$
$31$	1.86892e8	1.17247	0.586234	+	0.810142i	$0.300610\pi$
$32$	−2.63408e8	−1.38773
$33$	−1.37269e8	−0.610585
$34$	−5.08714e8	−1.92017
$35$	5.85134e7	0.188313
$36$	1.55638e8	0.428993
$37$	−2.81894e7	−0.0668307	−0.0334154	−	0.999442i	$-0.510638\pi$
$37$	−2.81894e7	−0.0668307	−0.0334154	+	0.999442i	$0.510638\pi$
$38$	−3.59831e8	−0.736697
$39$	9.02242e7	0.160128
$40$	1.40037e8	0.216228
$41$	−9.05699e8	−1.22088	−0.610439	−	0.792063i	$-0.709007\pi$
$41$	−9.05699e8	−1.22088	−0.610439	+	0.792063i	$0.709007\pi$
$42$	−2.79507e8	−0.330006
$43$	−9.23656e8	−0.958150	−0.479075	−	0.877774i	$-0.659028\pi$
$43$	−9.23656e8	−0.958150	−0.479075	+	0.877774i	$0.659028\pi$
$44$	1.48891e9	1.36106
$45$	2.05578e8	0.166077
$46$	4.40319e8	0.315209
$47$	1.20837e9	0.768529	0.384265	−	0.923223i	$-0.374455\pi$
$47$	1.20837e9	0.768529	0.384265	+	0.923223i	$0.374455\pi$
$48$	6.42781e8	0.364113
$49$	2.82475e8	0.142857
$50$	−2.51217e9	−1.13688
$51$	1.80628e9	0.733074
$52$	−9.78630e8	−0.356944
$53$	7.69035e8	0.252597	0.126299	−	0.991992i	$-0.459690\pi$
$53$	7.69035e8	0.252597	0.126299	+	0.991992i	$0.459690\pi$
$54$	−9.82008e8	−0.291038
$55$	1.96667e9	0.526910
$56$	6.76033e8	0.164034
$57$	1.27764e9	0.281253
$58$	−4.14231e9	−0.828683
$59$	3.00954e9	0.548042	0.274021	−	0.961724i	$-0.411646\pi$
$59$	3.00954e9	0.548042	0.274021	+	0.961724i	$0.411646\pi$
$60$	−2.22984e9	−0.370204
$61$	6.04594e9	0.916537	0.458268	−	0.888814i	$-0.348470\pi$
$61$	6.04594e9	0.916537	0.458268	+	0.888814i	$0.348470\pi$
$62$	1.27905e10	1.77310
$63$	9.92437e8	0.125988
$64$	−1.26097e10	−1.46797
$65$	−1.29265e9	−0.138184
$66$	−9.39440e9	−0.923373
$67$	−1.34769e10	−1.21949	−0.609746	−	0.792597i	$-0.708729\pi$
$67$	−1.34769e10	−1.21949	−0.609746	+	0.792597i	$0.708729\pi$
$68$	−1.95920e10	−1.63411
$69$	−1.56343e9	−0.120339
$70$	4.00453e9	0.284782
$71$	−1.16893e10	−0.768895	−0.384447	−	0.923147i	$-0.625608\pi$
$71$	−1.16893e10	−0.768895	−0.384447	+	0.923147i	$0.625608\pi$
$72$	2.37515e9	0.144664
$73$	1.04851e9	0.0591965	0.0295982	−	0.999562i	$-0.490577\pi$
$73$	1.04851e9	0.0591965	0.0295982	+	0.999562i	$0.490577\pi$
$74$	−1.92922e9	−0.101067
$75$	8.91989e9	0.434033
$76$	−1.38581e10	−0.626945
$77$	9.49416e9	0.399722
$78$	6.17475e9	0.242158
$79$	1.51686e10	0.554621	0.277311	−	0.960780i	$-0.410557\pi$
$79$	1.51686e10	0.554621	0.277311	+	0.960780i	$0.410557\pi$
$80$	−9.20920e9	−0.314215
$81$	3.48678e9	0.111111
$82$	−6.19840e10	−1.84631
$83$	3.27992e10	0.913974	0.456987	−	0.889473i	$-0.348929\pi$
$83$	3.27992e10	0.913974	0.456987	+	0.889473i	$0.348929\pi$
$84$	−1.07646e10	−0.280842
$85$	−2.58787e10	−0.632613
$86$	−6.32130e10	−1.44899
$87$	1.47080e10	0.316371
$88$	2.27219e10	0.458975
$89$	−6.18269e10	−1.17363	−0.586816	−	0.809720i	$-0.699619\pi$
$89$	−6.18269e10	−1.17363	−0.586816	+	0.809720i	$0.699619\pi$
$90$	1.40693e10	0.251154
$91$	−6.24032e9	−0.104828
$92$	1.69579e10	0.268250
$93$	−4.54147e10	−0.676924
$94$	8.26980e10	1.16223
$95$	−1.83049e10	−0.242710
$96$	6.40082e10	0.801206
$97$	−5.58660e10	−0.660546	−0.330273	−	0.943885i	$-0.607141\pi$
$97$	−5.58660e10	−0.660546	−0.330273	+	0.943885i	$0.607141\pi$
$98$	1.93320e10	0.216039
$99$	3.33564e10	0.352521
$100$	−9.67509e10	−0.967509
$101$	−1.20562e11	−1.14142	−0.570709	−	0.821153i	$-0.693331\pi$
$101$	−1.20562e11	−1.14142	−0.570709	+	0.821153i	$0.693331\pi$
$102$	1.23618e11	1.10861
$103$	−1.91328e11	−1.62620	−0.813101	−	0.582122i	$-0.802222\pi$
$103$	−1.91328e11	−1.62620	−0.813101	+	0.582122i	$0.802222\pi$
$104$	−1.49346e10	−0.120368
$105$	−1.42187e10	−0.108723
$106$	5.26310e10	0.381997
$107$	−2.48403e11	−1.71216	−0.856082	−	0.516840i	$-0.827108\pi$
$107$	−2.48403e11	−1.71216	−0.856082	+	0.516840i	$0.827108\pi$
$108$	−3.78199e10	−0.247679
$109$	−1.88296e11	−1.17218	−0.586090	−	0.810246i	$-0.699333\pi$
$109$	−1.88296e11	−1.17218	−0.586090	+	0.810246i	$0.699333\pi$
$110$	1.34595e11	0.796834
$111$	6.85002e9	0.0385847
$112$	−4.44577e10	−0.238368
$113$	3.09322e11	1.57935	0.789677	−	0.613523i	$-0.210248\pi$
$113$	3.09322e11	1.57935	0.789677	+	0.613523i	$0.210248\pi$
$114$	8.74389e10	0.425332
$115$	2.23994e10	0.103848
$116$	−1.59532e11	−0.705227
$117$	−2.19245e10	−0.0924500
$118$	2.05966e11	0.828791
$119$	−1.24930e11	−0.479910
$120$	−3.40290e10	−0.124839
$121$	3.37930e10	0.118442
$122$	4.13771e11	1.38606
$123$	2.20085e11	0.704875
$124$	4.92597e11	1.50894
$125$	−2.97791e11	−0.872783
$126$	6.79202e10	0.190529
$127$	2.25536e11	0.605752	0.302876	−	0.953030i	$-0.402053\pi$
$127$	2.25536e11	0.605752	0.302876	+	0.953030i	$0.402053\pi$
$128$	−3.23523e11	−0.832243
$129$	2.24448e11	0.553188
$130$	−8.84663e10	−0.208973
$131$	7.60909e11	1.72322	0.861610	−	0.507571i	$-0.169457\pi$
$131$	7.60909e11	1.72322	0.861610	+	0.507571i	$0.169457\pi$
$132$	−3.61805e11	−0.785811
$133$	−8.83675e10	−0.184123
$134$	−9.22331e11	−1.84421
$135$	−4.99555e10	−0.0958844
$136$	−2.98989e11	−0.551050
$137$	−5.74354e11	−1.01676	−0.508378	−	0.861134i	$-0.669755\pi$
$137$	−5.74354e11	−1.01676	−0.508378	+	0.861134i	$0.669755\pi$
$138$	−1.06997e11	−0.181986
$139$	8.10846e11	1.32543	0.662715	−	0.748871i	$-0.269404\pi$
$139$	8.10846e11	1.32543	0.662715	+	0.748871i	$0.269404\pi$
$140$	1.54226e11	0.242355
$141$	−2.93633e11	−0.443711
$142$	−7.99989e11	−1.16278
$143$	−2.09741e11	−0.293316
$144$	−1.56196e11	−0.210221
$145$	−2.10723e11	−0.273015
$146$	7.17576e10	0.0895214
$147$	−6.86415e10	−0.0824786
$148$	−7.42997e10	−0.0860098
$149$	−1.03895e12	−1.15896	−0.579481	−	0.814986i	$-0.696745\pi$
$149$	−1.03895e12	−1.15896	−0.579481	+	0.814986i	$0.696745\pi$
$150$	6.10458e11	0.656378
$151$	−1.27401e12	−1.32069	−0.660343	−	0.750964i	$-0.729589\pi$
$151$	−1.27401e12	−1.32069	−0.660343	+	0.750964i	$0.729589\pi$
$152$	−2.11485e11	−0.211417
$153$	−4.38925e11	−0.423241
$154$	6.49760e11	0.604490
$155$	6.50661e11	0.584158
$156$	2.37807e11	0.206082
$157$	−1.75079e12	−1.46482	−0.732412	−	0.680862i	$-0.761605\pi$
$157$	−1.75079e12	−1.46482	−0.732412	+	0.680862i	$0.761605\pi$
$158$	1.03811e12	0.838741
$159$	−1.86875e11	−0.145837
$160$	−9.17053e11	−0.691408
$161$	1.08134e11	0.0787805
$162$	2.38628e11	0.168031
$163$	1.96458e12	1.33733	0.668664	−	0.743565i	$-0.266867\pi$
$163$	1.96458e12	1.33733	0.668664	+	0.743565i	$0.266867\pi$
$164$	−2.38718e12	−1.57125
$165$	−4.77901e11	−0.304212
$166$	2.24470e12	1.38218
$167$	4.65300e10	0.0277200	0.0138600	−	0.999904i	$-0.495588\pi$
$167$	4.65300e10	0.0277200	0.0138600	+	0.999904i	$0.495588\pi$
$168$	−1.64276e11	−0.0947050
$169$	1.37858e11	0.0769231
$170$	−1.77108e12	−0.956686
$171$	−3.10467e11	−0.162381
$172$	−2.43451e12	−1.23312
$173$	−3.15039e12	−1.54565	−0.772825	−	0.634619i	$-0.781157\pi$
$173$	−3.15039e12	−1.54565	−0.772825	+	0.634619i	$0.781157\pi$
$174$	1.00658e12	0.478441
$175$	−6.16941e11	−0.284141
$176$	−1.49425e12	−0.666966
$177$	−7.31318e11	−0.316412
$178$	−4.23130e12	−1.77486
$179$	−1.12504e12	−0.457588	−0.228794	−	0.973475i	$-0.573478\pi$
$179$	−1.12504e12	−0.457588	−0.228794	+	0.973475i	$0.573478\pi$
$180$	5.41850e11	0.213737
$181$	1.35256e11	0.0517518	0.0258759	−	0.999665i	$-0.491763\pi$
$181$	1.35256e11	0.0517518	0.0258759	+	0.999665i	$0.491763\pi$
$182$	−4.27074e11	−0.158530
$183$	−1.46916e12	−0.529163
$184$	2.58791e11	0.0904588
$185$	−9.81410e10	−0.0332971
$186$	−3.10808e12	−1.02370
$187$	−4.19898e12	−1.34281
$188$	3.18493e12	0.989082
$189$	−2.41162e11	−0.0727393
$190$	−1.25275e12	−0.367044
$191$	8.49260e11	0.241745	0.120872	−	0.992668i	$-0.461431\pi$
$191$	8.49260e11	0.241745	0.120872	+	0.992668i	$0.461431\pi$
$192$	3.06417e12	0.847531
$193$	−3.57384e12	−0.960661	−0.480330	−	0.877088i	$-0.659483\pi$
$193$	−3.57384e12	−0.960661	−0.480330	+	0.877088i	$0.659483\pi$
$194$	−3.82335e12	−0.998929
$195$	3.14114e11	0.0797806
$196$	7.44530e11	0.183854
$197$	7.02036e8	0.000168576 0	8.42879e−5	−	1.00000i	$-0.499973\pi$
$197$	7.02036e8	0.000168576 0	8.42879e−5		1.00000i	$0.499973\pi$
$198$	2.28284e12	0.533110
$199$	−1.20032e12	−0.272650	−0.136325	−	0.990664i	$-0.543529\pi$
$199$	−1.20032e12	−0.272650	−0.136325	+	0.990664i	$0.543529\pi$
$200$	−1.47649e12	−0.326262
$201$	3.27489e12	0.704074
$202$	−8.25103e12	−1.72614
$203$	−1.01727e12	−0.207114
$204$	4.76086e12	0.943452
$205$	−3.15318e12	−0.608278
$206$	−1.30941e13	−2.45927
$207$	3.79913e11	0.0694779
$208$	9.82141e11	0.174914
$209$	−2.97009e12	−0.515186
$210$	−9.73100e11	−0.164419
$211$	−5.23462e12	−0.861652	−0.430826	−	0.902435i	$-0.641778\pi$
$211$	−5.23462e12	−0.861652	−0.430826	+	0.902435i	$0.641778\pi$
$212$	2.02697e12	0.325088
$213$	2.84050e12	0.443922
$214$	−1.70001e13	−2.58926
$215$	−3.21570e12	−0.477379
$216$	−5.77160e11	−0.0835220
$217$	3.14109e12	0.443151
$218$	−1.28865e13	−1.77266
$219$	−2.54787e11	−0.0341771
$220$	5.18362e12	0.678123
$221$	2.75991e12	0.352157
$222$	4.68800e11	0.0583508
$223$	3.57089e12	0.433610	0.216805	−	0.976215i	$-0.430436\pi$
$223$	3.57089e12	0.433610	0.216805	+	0.976215i	$0.430436\pi$
$224$	−4.42710e12	−0.524512
$225$	−2.16753e12	−0.250589
$226$	2.11693e13	2.38842
$227$	−1.63188e12	−0.179699	−0.0898494	−	0.995955i	$-0.528639\pi$
$227$	−1.63188e12	−0.179699	−0.0898494	+	0.995955i	$0.528639\pi$
$228$	3.36752e12	0.361967
$229$	9.85983e12	1.03460	0.517302	−	0.855803i	$-0.326936\pi$
$229$	9.85983e12	1.03460	0.517302	+	0.855803i	$0.326936\pi$
$230$	1.53296e12	0.157047
$231$	−2.30708e12	−0.230779
$232$	−2.43458e12	−0.237815
$233$	−1.30585e13	−1.24577	−0.622883	−	0.782315i	$-0.714039\pi$
$233$	−1.30585e13	−1.24577	−0.622883	+	0.782315i	$0.714039\pi$
$234$	−1.50046e12	−0.139810
$235$	4.20691e12	0.382904
$236$	7.93234e12	0.705319
$237$	−3.68597e12	−0.320211
$238$	−8.54996e12	−0.725756
$239$	7.45534e12	0.618414	0.309207	−	0.950995i	$-0.399936\pi$
$239$	7.45534e12	0.618414	0.309207	+	0.950995i	$0.399936\pi$
$240$	2.23784e12	0.181412
$241$	−1.10955e12	−0.0879129	−0.0439565	−	0.999033i	$-0.513996\pi$
$241$	−1.10955e12	−0.0879129	−0.0439565	+	0.999033i	$0.513996\pi$
$242$	2.31272e12	0.179118
$243$	−8.47289e11	−0.0641500
$244$	1.59355e13	1.17956
$245$	9.83434e11	0.0711757
$246$	1.50621e13	1.06597
$247$	1.95218e12	0.135110
$248$	7.51740e12	0.508843
$249$	−7.97020e12	−0.527683
$250$	−2.03801e13	−1.31989
$251$	1.24080e13	0.786133	0.393066	−	0.919510i	$-0.371414\pi$
$251$	1.24080e13	0.786133	0.393066	+	0.919510i	$0.371414\pi$
$252$	2.61580e12	0.162144
$253$	3.63444e12	0.220432
$254$	1.54352e13	0.916064
$255$	6.28852e12	0.365240
$256$	3.68355e12	0.209386
$257$	2.13373e12	0.118716	0.0593578	−	0.998237i	$-0.481095\pi$
$257$	2.13373e12	0.118716	0.0593578	+	0.998237i	$0.481095\pi$
$258$	1.53608e13	0.836574
$259$	−4.73779e11	−0.0252596
$260$	−3.40709e12	−0.177840
$261$	−3.57404e12	−0.182657
$262$	5.20750e13	2.60598
$263$	2.97653e13	1.45866	0.729328	−	0.684164i	$-0.239833\pi$
$263$	2.97653e13	1.45866	0.729328	+	0.684164i	$0.239833\pi$
$264$	−5.52142e12	−0.264990
$265$	2.67738e12	0.125851
$266$	−6.04768e12	−0.278445
$267$	1.50239e13	0.677597
$268$	−3.55216e13	−1.56946
$269$	−3.33130e13	−1.44203	−0.721017	−	0.692917i	$-0.756325\pi$
$269$	−3.33130e13	−1.44203	−0.721017	+	0.692917i	$0.756325\pi$
$270$	−3.41885e12	−0.145004
$271$	1.57794e13	0.655781	0.327890	−	0.944716i	$-0.393662\pi$
$271$	1.57794e13	0.655781	0.327890	+	0.944716i	$0.393662\pi$
$272$	1.96623e13	0.800766
$273$	1.51640e12	0.0605228
$274$	−3.93075e13	−1.53761
$275$	−2.07358e13	−0.795042
$276$	−4.12078e12	−0.154874
$277$	3.54997e13	1.30794	0.653968	−	0.756523i	$-0.273103\pi$
$277$	3.54997e13	1.30794	0.653968	+	0.756523i	$0.273103\pi$
$278$	5.54925e13	2.00442
$279$	1.10358e13	0.390823
$280$	2.35360e12	0.0817266
$281$	−4.92480e13	−1.67689	−0.838443	−	0.544989i	$-0.816534\pi$
$281$	−4.92480e13	−1.67689	−0.838443	+	0.544989i	$0.816534\pi$
$282$	−2.00956e13	−0.671013
$283$	−1.79600e13	−0.588141	−0.294071	−	0.955784i	$-0.595010\pi$
$283$	−1.79600e13	−0.588141	−0.294071	+	0.955784i	$0.595010\pi$
$284$	−3.08099e13	−0.989552
$285$	4.44809e12	0.140129
$286$	−1.43542e13	−0.443574
$287$	−1.52221e13	−0.461449
$288$	−1.55540e13	−0.462576
$289$	2.09810e13	0.612194
$290$	−1.44214e13	−0.412875
$291$	1.35754e13	0.381367
$292$	2.76359e12	0.0761847
$293$	5.39376e13	1.45922	0.729608	−	0.683865i	$-0.239702\pi$
$293$	5.39376e13	1.45922	0.729608	+	0.683865i	$0.239702\pi$
$294$	−4.69767e12	−0.124730
$295$	1.04777e13	0.273051
$296$	−1.13387e12	−0.0290041
$297$	−8.10560e12	−0.203528
$298$	−7.11033e13	−1.75267
$299$	−2.38884e12	−0.0578091
$300$	2.35105e13	0.558592
$301$	−1.55239e13	−0.362147
$302$	−8.71905e13	−1.99724
$303$	2.92967e13	0.658998
$304$	1.39078e13	0.307224
$305$	2.10489e13	0.456646
$306$	−3.00391e13	−0.640057
$307$	−2.56574e13	−0.536972	−0.268486	−	0.963284i	$-0.586523\pi$
$307$	−2.56574e13	−0.536972	−0.268486	+	0.963284i	$0.586523\pi$
$308$	2.50241e13	0.514434
$309$	4.64928e13	0.938888
$310$	4.45298e13	0.883409
$311$	−1.84395e13	−0.359391	−0.179695	−	0.983722i	$-0.557511\pi$
$311$	−1.84395e13	−0.359391	−0.179695	+	0.983722i	$0.557511\pi$
$312$	3.62911e12	0.0694945
$313$	−1.83257e13	−0.344800	−0.172400	−	0.985027i	$-0.555152\pi$
$313$	−1.83257e13	−0.344800	−0.172400	+	0.985027i	$0.555152\pi$
$314$	−1.19820e14	−2.21522
$315$	3.45516e12	0.0627711
$316$	3.99804e13	0.713786
$317$	−5.12731e13	−0.899629	−0.449814	−	0.893122i	$-0.648510\pi$
$317$	−5.12731e13	−0.899629	−0.449814	+	0.893122i	$0.648510\pi$
$318$	−1.27893e13	−0.220546
$319$	−3.41911e13	−0.579514
$320$	−4.39007e13	−0.731385
$321$	6.03618e13	0.988518
$322$	7.40044e12	0.119138
$323$	3.90823e13	0.618538
$324$	9.19024e12	0.142998
$325$	1.36292e13	0.208503
$326$	1.34452e14	2.02241
$327$	4.57558e13	0.676758
$328$	−3.64302e13	−0.529853
$329$	2.03090e13	0.290477
$330$	−3.27065e13	−0.460052
$331$	−1.41462e13	−0.195697	−0.0978486	−	0.995201i	$-0.531196\pi$
$331$	−1.41462e13	−0.195697	−0.0978486	+	0.995201i	$0.531196\pi$
$332$	8.64500e13	1.17627
$333$	−1.66456e12	−0.0222769
$334$	3.18441e12	0.0419202
$335$	−4.69197e13	−0.607587
$336$	1.08032e13	0.137622
$337$	2.17233e13	0.272246	0.136123	−	0.990692i	$-0.456536\pi$
$337$	2.17233e13	0.272246	0.136123	+	0.990692i	$0.456536\pi$
$338$	9.43473e12	0.116329
$339$	−7.51653e13	−0.911840
$340$	−6.82094e13	−0.814161
$341$	1.05574e14	1.23996
$342$	−2.12477e13	−0.245566
$343$	4.74756e12	0.0539949
$344$	−3.71525e13	−0.415830
$345$	−5.44305e12	−0.0599566
$346$	−2.15606e14	−2.33745
$347$	1.86177e13	0.198662	0.0993308	−	0.995054i	$-0.468330\pi$
$347$	1.86177e13	0.198662	0.0993308	+	0.995054i	$0.468330\pi$
$348$	3.87663e13	0.407163
$349$	−1.13332e14	−1.17169	−0.585847	−	0.810421i	$-0.699238\pi$
$349$	−1.13332e14	−1.17169	−0.585847	+	0.810421i	$0.699238\pi$
$350$	−4.22221e13	−0.429700
$351$	5.32765e12	0.0533761
$352$	−1.48798e14	−1.46761
$353$	6.63649e13	0.644433	0.322216	−	0.946666i	$-0.395572\pi$
$353$	6.63649e13	0.644433	0.322216	+	0.946666i	$0.395572\pi$
$354$	−5.00498e13	−0.478503
$355$	−4.06961e13	−0.383086
$356$	−1.62959e14	−1.51044
$357$	3.03581e13	0.277076
$358$	−7.69950e13	−0.692000
$359$	1.92535e14	1.70408	0.852039	−	0.523479i	$-0.175366\pi$
$359$	1.92535e14	1.70408	0.852039	+	0.523479i	$0.175366\pi$
$360$	8.26904e12	0.0720761
$361$	−8.88460e13	−0.762690
$362$	9.25665e12	0.0782630
$363$	−8.21169e12	−0.0683827
$364$	−1.64478e13	−0.134912
$365$	3.65037e12	0.0294935
$366$	−1.00546e14	−0.800240
$367$	−5.64786e13	−0.442813	−0.221407	−	0.975182i	$-0.571065\pi$
$367$	−5.64786e13	−0.442813	−0.221407	+	0.975182i	$0.571065\pi$
$368$	−1.70188e13	−0.131451
$369$	−5.34806e13	−0.406960
$370$	−6.71656e12	−0.0503544
$371$	1.29252e13	0.0954728
$372$	−1.19701e14	−0.871188
$373$	−2.00343e14	−1.43673	−0.718365	−	0.695666i	$-0.755109\pi$
$373$	−2.00343e14	−1.43673	−0.718365	+	0.695666i	$0.755109\pi$
$374$	−2.87369e14	−2.03070
$375$	7.23632e13	0.503901
$376$	4.86045e13	0.333536
$377$	2.24731e13	0.151980
$378$	−1.65046e13	−0.110002
$379$	−6.63639e13	−0.435929	−0.217965	−	0.975957i	$-0.569942\pi$
$379$	−6.63639e13	−0.435929	−0.217965	+	0.975957i	$0.569942\pi$
$380$	−4.82468e13	−0.312363
$381$	−5.48052e13	−0.349731
$382$	5.81215e13	0.365585
$383$	2.46460e14	1.52811	0.764053	−	0.645154i	$-0.223207\pi$
$383$	2.46460e14	1.52811	0.764053	+	0.645154i	$0.223207\pi$
$384$	7.86161e13	0.480496
$385$	3.30538e13	0.199153
$386$	−2.44586e14	−1.45278
$387$	−5.45409e13	−0.319383
$388$	−1.47248e14	−0.850110
$389$	3.76084e13	0.214073	0.107036	−	0.994255i	$-0.465864\pi$
$389$	3.76084e13	0.214073	0.107036	+	0.994255i	$0.465864\pi$
$390$	2.14973e13	0.120650
$391$	−4.78243e13	−0.264653
$392$	1.13621e13	0.0619990
$393$	−1.84901e14	−0.994901
$394$	4.80458e10	0.000254933 0
$395$	5.28093e13	0.276329
$396$	8.79186e13	0.453688
$397$	2.05786e14	1.04729	0.523645	−	0.851936i	$-0.324572\pi$
$397$	2.05786e14	1.04729	0.523645	+	0.851936i	$0.324572\pi$
$398$	−8.21473e13	−0.412322
$399$	2.14733e13	0.106304
$400$	9.70980e13	0.474111
$401$	−2.11851e14	−1.02032	−0.510160	−	0.860079i	$-0.670414\pi$
$401$	−2.11851e14	−1.02032	−0.510160	+	0.860079i	$0.670414\pi$
$402$	2.24126e14	1.06475
$403$	−6.93916e13	−0.325184
$404$	−3.17771e14	−1.46898
$405$	1.21392e13	0.0553589
$406$	−6.96198e13	−0.313213
$407$	−1.59240e13	−0.0706778
$408$	7.26543e13	0.318149
$409$	−9.92496e13	−0.428796	−0.214398	−	0.976746i	$-0.568779\pi$
$409$	−9.92496e13	−0.428796	−0.214398	+	0.976746i	$0.568779\pi$
$410$	−2.15797e14	−0.919885
$411$	1.39568e14	0.587024
$412$	−5.04291e14	−2.09289
$413$	5.05813e13	0.207140
$414$	2.60004e13	0.105070
$415$	1.14190e14	0.455369
$416$	9.78017e13	0.384887
$417$	−1.97036e14	−0.765238
$418$	−2.03266e14	−0.779104
$419$	4.76296e14	1.80177	0.900885	−	0.434057i	$-0.142918\pi$
$419$	4.76296e14	1.80177	0.900885	+	0.434057i	$0.142918\pi$
$420$	−3.74768e13	−0.139924
$421$	−6.89369e13	−0.254039	−0.127019	−	0.991900i	$-0.540541\pi$
$421$	−6.89369e13	−0.254039	−0.127019	+	0.991900i	$0.540541\pi$
$422$	−3.58246e14	−1.30306
$423$	7.13528e13	0.256176
$424$	3.09331e13	0.109625
$425$	2.72854e14	0.954535
$426$	1.94397e14	0.671332
$427$	1.01614e14	0.346418
$428$	−6.54723e14	−2.20352
$429$	5.09671e13	0.169346
$430$	−2.20075e14	−0.721929
$431$	−8.62118e13	−0.279217	−0.139608	−	0.990207i	$-0.544584\pi$
$431$	−8.62118e13	−0.279217	−0.139608	+	0.990207i	$0.544584\pi$
$432$	3.79556e13	0.121371
$433$	−3.47451e14	−1.09701	−0.548504	−	0.836148i	$-0.684802\pi$
$433$	−3.47451e14	−1.09701	−0.548504	+	0.836148i	$0.684802\pi$
$434$	2.14969e14	0.670167
$435$	5.12056e13	0.157626
$436$	−4.96297e14	−1.50857
$437$	−3.38278e13	−0.101537
$438$	−1.74371e13	−0.0516852
$439$	1.22043e14	0.357238	0.178619	−	0.983918i	$-0.442837\pi$
$439$	1.22043e14	0.357238	0.178619	+	0.983918i	$0.442837\pi$
$440$	7.91059e13	0.228675
$441$	1.66799e13	0.0476190
$442$	1.88882e14	0.532559
$443$	−6.92479e13	−0.192835	−0.0964175	−	0.995341i	$-0.530738\pi$
$443$	−6.92479e13	−0.192835	−0.0964175	+	0.995341i	$0.530738\pi$
$444$	1.80548e13	0.0496578
$445$	−2.15250e14	−0.584739
$446$	2.44384e14	0.655739
$447$	2.52464e14	0.669127
$448$	−2.11932e14	−0.554840
$449$	6.35502e14	1.64347	0.821736	−	0.569868i	$-0.193006\pi$
$449$	6.35502e14	1.64347	0.821736	+	0.569868i	$0.193006\pi$
$450$	−1.48341e14	−0.378960
$451$	−5.11623e14	−1.29116
$452$	8.15291e14	2.03260
$453$	3.09585e14	0.762499
$454$	−1.11682e14	−0.271754
$455$	−2.17256e13	−0.0522287
$456$	5.13909e13	0.122062
$457$	4.55857e14	1.06977	0.534884	−	0.844925i	$-0.320355\pi$
$457$	4.55857e14	1.06977	0.534884	+	0.844925i	$0.320355\pi$
$458$	6.74785e14	1.56461
$459$	1.06659e14	0.244358
$460$	5.90388e13	0.133650
$461$	7.15733e14	1.60102	0.800508	−	0.599322i	$-0.204563\pi$
$461$	7.15733e14	1.60102	0.800508	+	0.599322i	$0.204563\pi$
$462$	−1.57892e14	−0.349002
$463$	−6.87620e14	−1.50194	−0.750971	−	0.660335i	$-0.770414\pi$
$463$	−6.87620e14	−1.50194	−0.750971	+	0.660335i	$0.770414\pi$
$464$	1.60104e14	0.345585
$465$	−1.58111e14	−0.337264
$466$	−8.93697e14	−1.88394
$467$	1.37772e14	0.287025	0.143512	−	0.989649i	$-0.454160\pi$
$467$	1.37772e14	0.287025	0.143512	+	0.989649i	$0.454160\pi$
$468$	−5.77871e13	−0.118981
$469$	−2.26506e14	−0.460925
$470$	2.87912e14	0.579057
$471$	4.25441e14	0.845716
$472$	1.21053e14	0.237846
$473$	−5.21767e14	−1.01331
$474$	−2.52260e14	−0.484247
$475$	1.92999e14	0.366219
$476$	−3.29283e14	−0.617634
$477$	4.54107e13	0.0841991
$478$	5.10227e14	0.935212
$479$	4.62840e13	0.0838659	0.0419329	−	0.999120i	$-0.486648\pi$
$479$	4.62840e13	0.0838659	0.0419329	+	0.999120i	$0.486648\pi$
$480$	2.22844e14	0.399185
$481$	1.04665e13	0.0185355
$482$	−7.59351e13	−0.132949
$483$	−2.62765e13	−0.0454840
$484$	8.90693e13	0.152433
$485$	−1.94497e14	−0.329104
$486$	−5.79866e13	−0.0970126
$487$	4.35951e14	0.721154	0.360577	−	0.932729i	$-0.382580\pi$
$487$	4.35951e14	0.721154	0.360577	+	0.932729i	$0.382580\pi$
$488$	2.43188e14	0.397771
$489$	−4.77393e14	−0.772106
$490$	6.73041e13	0.107637
$491$	6.19791e14	0.980161	0.490080	−	0.871677i	$-0.336967\pi$
$491$	6.19791e14	0.980161	0.490080	+	0.871677i	$0.336967\pi$
$492$	5.80085e14	0.907159
$493$	4.49908e14	0.695771
$494$	1.33603e14	0.204323
$495$	1.16130e14	0.175637
$496$	−4.94364e14	−0.739431
$497$	−1.96462e14	−0.290615
$498$	−5.45463e14	−0.798002
$499$	−1.52673e14	−0.220906	−0.110453	−	0.993881i	$-0.535230\pi$
$499$	−1.52673e14	−0.220906	−0.110453	+	0.993881i	$0.535230\pi$
$500$	−7.84897e14	−1.12325
$501$	−1.13068e13	−0.0160041
$502$	8.49176e14	1.18885
$503$	1.18696e15	1.64366	0.821831	−	0.569731i	$-0.192952\pi$
$503$	1.18696e15	1.64366	0.821831	+	0.569731i	$0.192952\pi$
$504$	3.99191e13	0.0546780
$505$	−4.19737e14	−0.568688
$506$	2.48733e14	0.333354
$507$	−3.34996e13	−0.0444116
$508$	5.94452e14	0.779590
$509$	1.39272e15	1.80682	0.903412	−	0.428773i	$-0.141054\pi$
$509$	1.39272e15	1.80682	0.903412	+	0.428773i	$0.141054\pi$
$510$	4.30373e14	0.552343
$511$	1.76223e13	0.0223742
$512$	9.14669e14	1.14889
$513$	7.54434e13	0.0937510
$514$	1.46028e14	0.179531
$515$	−6.66107e14	−0.810223
$516$	5.91586e14	0.711942
$517$	6.82598e14	0.812769
$518$	−3.24244e13	−0.0381996
$519$	7.65546e14	0.892382
$520$	−5.19947e13	−0.0599709
$521$	−1.03833e14	−0.118502	−0.0592511	−	0.998243i	$-0.518871\pi$
$521$	−1.03833e14	−0.118502	−0.0592511	+	0.998243i	$0.518871\pi$
$522$	−2.44599e14	−0.276228
$523$	−2.26986e14	−0.253653	−0.126827	−	0.991925i	$-0.540479\pi$
$523$	−2.26986e14	−0.253653	−0.126827	+	0.991925i	$0.540479\pi$
$524$	2.00555e15	2.21775
$525$	1.49917e14	0.164049
$526$	2.03707e15	2.20589
$527$	−1.38921e15	−1.48871
$528$	3.63103e14	0.385073
$529$	−9.11415e14	−0.956555
$530$	1.83234e14	0.190322
$531$	1.77710e14	0.182681
$532$	−2.32913e14	−0.236963
$533$	3.36280e14	0.338611
$534$	1.02821e15	1.02471
$535$	−8.64810e14	−0.853051
$536$	−5.42086e14	−0.529251
$537$	2.73384e14	0.264189
$538$	−2.27987e15	−2.18076
$539$	1.59568e14	0.151081
$540$	−1.31670e14	−0.123401
$541$	4.53144e14	0.420389	0.210194	−	0.977660i	$-0.432590\pi$
$541$	4.53144e14	0.420389	0.210194	+	0.977660i	$0.432590\pi$
$542$	1.07991e15	0.991722
$543$	−3.28673e13	−0.0298789
$544$	1.95798e15	1.76203
$545$	−6.55549e14	−0.584015
$546$	1.03779e14	0.0915271
$547$	7.41296e14	0.647234	0.323617	−	0.946188i	$-0.395101\pi$
$547$	7.41296e14	0.647234	0.323617	+	0.946188i	$0.395101\pi$
$548$	−1.51384e15	−1.30854
$549$	3.57007e14	0.305512
$550$	−1.41911e15	−1.20232
$551$	3.18236e14	0.266941
$552$	−6.28861e13	−0.0522264
$553$	2.54939e14	0.209627
$554$	2.42952e15	1.97796
$555$	2.38483e13	0.0192241
$556$	2.13718e15	1.70580
$557$	−1.05234e15	−0.831676	−0.415838	−	0.909439i	$-0.636512\pi$
$557$	−1.05234e15	−0.831676	−0.415838	+	0.909439i	$0.636512\pi$
$558$	7.55264e14	0.591032
$559$	3.42947e14	0.265743
$560$	−1.54779e14	−0.118762
$561$	1.02035e15	0.775273
$562$	−3.37042e15	−2.53592
$563$	3.00877e14	0.224178	0.112089	−	0.993698i	$-0.464246\pi$
$563$	3.00877e14	0.224178	0.112089	+	0.993698i	$0.464246\pi$
$564$	−7.73939e14	−0.571047
$565$	1.07690e15	0.786881
$566$	−1.22914e15	−0.889432
$567$	5.86024e13	0.0419961
$568$	−4.70181e14	−0.333695
$569$	9.20184e14	0.646781	0.323390	−	0.946266i	$-0.395177\pi$
$569$	9.20184e14	0.646781	0.323390	+	0.946266i	$0.395177\pi$
$570$	3.04418e14	0.211913
$571$	1.94242e15	1.33920	0.669598	−	0.742724i	$-0.266466\pi$
$571$	1.94242e15	1.33920	0.669598	+	0.742724i	$0.266466\pi$
$572$	−5.52822e14	−0.377491
$573$	−2.06370e14	−0.139571
$574$	−1.04177e15	−0.697838
$575$	−2.36170e14	−0.156694
$576$	−7.44593e14	−0.489322
$577$	8.72958e14	0.568233	0.284117	−	0.958790i	$-0.408300\pi$
$577$	8.72958e14	0.568233	0.284117	+	0.958790i	$0.408300\pi$
$578$	1.43590e15	0.925806
$579$	8.68443e14	0.554638
$580$	−5.55409e14	−0.351365
$581$	5.51256e14	0.345450
$582$	9.29074e14	0.576732
$583$	4.34423e14	0.267138
$584$	4.21744e13	0.0256909
$585$	−7.63298e13	−0.0460614
$586$	3.69137e15	2.20674
$587$	−2.91423e15	−1.72589	−0.862946	−	0.505296i	$-0.831383\pi$
$587$	−2.91423e15	−1.72589	−0.862946	+	0.505296i	$0.831383\pi$
$588$	−1.80921e14	−0.106148
$589$	−9.82636e14	−0.571161
$590$	7.17069e14	0.412928
$591$	−1.70595e11	−9.73273e−5 0
$592$	7.45663e13	0.0421476
$593$	1.40975e15	0.789479	0.394740	−	0.918793i	$-0.370835\pi$
$593$	1.40975e15	0.789479	0.394740	+	0.918793i	$0.370835\pi$
$594$	−5.54730e14	−0.307791
$595$	−4.34943e14	−0.239105
$596$	−2.73839e15	−1.49156
$597$	2.91678e14	0.157414
$598$	−1.63487e14	−0.0874234
$599$	−1.24793e14	−0.0661217	−0.0330608	−	0.999453i	$-0.510526\pi$
$599$	−1.24793e14	−0.0661217	−0.0330608	+	0.999453i	$0.510526\pi$
$600$	3.58787e14	0.188367
$601$	1.03295e15	0.537367	0.268683	−	0.963229i	$-0.413411\pi$
$601$	1.03295e15	0.537367	0.268683	+	0.963229i	$0.413411\pi$
$602$	−1.06242e15	−0.547666
$603$	−7.95798e14	−0.406497
$604$	−3.35795e15	−1.69970
$605$	1.17650e14	0.0590115
$606$	2.00500e15	0.996587
$607$	2.63492e14	0.129787	0.0648934	−	0.997892i	$-0.479329\pi$
$607$	2.63492e14	0.129787	0.0648934	+	0.997892i	$0.479329\pi$
$608$	1.38494e15	0.676024
$609$	2.47197e14	0.119577
$610$	1.44054e15	0.690575
$611$	−4.48658e14	−0.213152
$612$	−1.15689e15	−0.544702
$613$	3.61668e14	0.168763	0.0843815	−	0.996434i	$-0.473109\pi$
$613$	3.61668e14	0.168763	0.0843815	+	0.996434i	$0.473109\pi$
$614$	−1.75594e15	−0.812051
$615$	7.66222e14	0.351190
$616$	3.81887e14	0.173476
$617$	−1.47671e15	−0.664854	−0.332427	−	0.943129i	$-0.607868\pi$
$617$	−1.47671e15	−0.664854	−0.332427	+	0.943129i	$0.607868\pi$
$618$	3.18187e15	1.41986
$619$	−1.16495e15	−0.515240	−0.257620	−	0.966246i	$-0.582938\pi$
$619$	−1.16495e15	−0.515240	−0.257620	+	0.966246i	$0.582938\pi$
$620$	1.71497e15	0.751800
$621$	−9.23187e13	−0.0401131
$622$	−1.26196e15	−0.543499
$623$	−1.03912e15	−0.443592
$624$	−2.38660e14	−0.100987
$625$	7.55597e14	0.316920
$626$	−1.25417e15	−0.521433
$627$	7.21731e14	0.297443
$628$	−4.61461e15	−1.88520
$629$	2.09538e14	0.0848564
$630$	2.36463e14	0.0949272
$631$	4.09811e15	1.63088	0.815440	−	0.578842i	$-0.196495\pi$
$631$	4.09811e15	1.63088	0.815440	+	0.578842i	$0.196495\pi$
$632$	6.10131e14	0.240702
$633$	1.27201e15	0.497475
$634$	−3.50902e15	−1.36049
$635$	7.85199e14	0.301804
$636$	−4.92554e14	−0.187689
$637$	−1.04881e14	−0.0396214
$638$	−2.33996e15	−0.876386
$639$	−6.90241e14	−0.256298
$640$	−1.12634e15	−0.414649
$641$	−6.73941e14	−0.245982	−0.122991	−	0.992408i	$-0.539249\pi$
$641$	−6.73941e14	−0.245982	−0.122991	+	0.992408i	$0.539249\pi$
$642$	4.13103e15	1.49491
$643$	3.72880e15	1.33785	0.668927	−	0.743328i	$-0.266754\pi$
$643$	3.72880e15	1.33785	0.668927	+	0.743328i	$0.266754\pi$
$644$	2.85012e14	0.101389
$645$	7.81414e14	0.275615
$646$	2.67471e15	0.935400
$647$	3.53635e15	1.22626	0.613129	−	0.789983i	$-0.289911\pi$
$647$	3.53635e15	1.22626	0.613129	+	0.789983i	$0.289911\pi$
$648$	1.40250e14	0.0482214
$649$	1.70007e15	0.579589
$650$	9.32752e14	0.315314
$651$	−7.63285e14	−0.255853
$652$	5.17811e15	1.72111
$653$	−5.87842e15	−1.93748	−0.968742	−	0.248072i	$-0.920203\pi$
$653$	−5.87842e15	−1.93748	−0.968742	+	0.248072i	$0.920203\pi$
$654$	3.13143e15	1.02345
$655$	2.64910e15	0.858560
$656$	2.39575e15	0.769963
$657$	6.19133e13	0.0197322
$658$	1.38990e15	0.439281
$659$	−4.25033e15	−1.33215	−0.666074	−	0.745886i	$-0.732026\pi$
$659$	−4.25033e15	−1.33215	−0.666074	+	0.745886i	$0.732026\pi$
$660$	−1.25962e15	−0.391514
$661$	5.20976e15	1.60587	0.802933	−	0.596069i	$-0.203272\pi$
$661$	5.20976e15	1.60587	0.802933	+	0.596069i	$0.203272\pi$
$662$	−9.68133e14	−0.295948
$663$	−6.70657e14	−0.203318
$664$	1.31929e15	0.396658
$665$	−3.07650e14	−0.0917357
$666$	−1.13919e14	−0.0336888
$667$	−3.89419e14	−0.114216
$668$	1.22641e14	0.0356750
$669$	−8.67726e14	−0.250345
$670$	−3.21108e15	−0.918840
$671$	3.41531e15	0.969297
$672$	1.07579e15	0.302827
$673$	−5.75002e15	−1.60541	−0.802706	−	0.596375i	$-0.796607\pi$
$673$	−5.75002e15	−1.60541	−0.802706	+	0.596375i	$0.796607\pi$
$674$	1.48670e15	0.411712
$675$	5.26711e14	0.144678
$676$	3.63358e14	0.0989985
$677$	3.42405e15	0.925342	0.462671	−	0.886530i	$-0.346891\pi$
$677$	3.42405e15	0.925342	0.462671	+	0.886530i	$0.346891\pi$
$678$	−5.14415e15	−1.37895
$679$	−9.38941e14	−0.249663
$680$	−1.04093e15	−0.274550
$681$	3.96546e14	0.103749
$682$	7.22525e15	1.87516
$683$	−6.36803e15	−1.63942	−0.819712	−	0.572775i	$-0.805867\pi$
$683$	−6.36803e15	−1.63942	−0.819712	+	0.572775i	$0.805867\pi$
$684$	−8.18308e14	−0.208982
$685$	−1.99961e15	−0.506578
$686$	3.24913e14	0.0816553
$687$	−2.39594e15	−0.597329
$688$	2.44325e15	0.604270
$689$	−2.85537e14	−0.0700579
$690$	−3.72510e14	−0.0906710
$691$	−3.43644e15	−0.829810	−0.414905	−	0.909865i	$-0.636185\pi$
$691$	−3.43644e15	−0.829810	−0.414905	+	0.909865i	$0.636185\pi$
$692$	−8.30360e15	−1.98922
$693$	5.60621e14	0.133241
$694$	1.27415e15	0.300431
$695$	2.82295e15	0.660369
$696$	5.91603e14	0.137303
$697$	6.73227e15	1.55018
$698$	−7.75623e15	−1.77193
$699$	3.17322e15	0.719243
$700$	−1.62609e15	−0.365684
$701$	3.08865e15	0.689159	0.344580	−	0.938757i	$-0.388021\pi$
$701$	3.08865e15	0.689159	0.344580	+	0.938757i	$0.388021\pi$
$702$	3.64613e14	0.0807193
$703$	1.48214e14	0.0325562
$704$	−7.12316e15	−1.55247
$705$	−1.02228e15	−0.221070
$706$	4.54187e15	0.974561
$707$	−2.02629e15	−0.431415
$708$	−1.92756e15	−0.407216
$709$	1.67007e15	0.350090	0.175045	−	0.984560i	$-0.443993\pi$
$709$	1.67007e15	0.350090	0.175045	+	0.984560i	$0.443993\pi$
$710$	−2.78515e15	−0.579333
$711$	8.95691e14	0.184874
$712$	−2.48688e15	−0.509348
$713$	1.20243e15	0.244382
$714$	2.07764e15	0.419016
$715$	−7.30211e14	−0.146139
$716$	−2.96530e15	−0.588907
$717$	−1.81165e15	−0.357041
$718$	1.31766e16	2.57704
$719$	−1.28059e15	−0.248542	−0.124271	−	0.992248i	$-0.539659\pi$
$719$	−1.28059e15	−0.248542	−0.124271	+	0.992248i	$0.539659\pi$
$720$	−5.43794e14	−0.104738
$721$	−3.21566e15	−0.614647
$722$	−6.08043e15	−1.15340
$723$	2.69620e14	0.0507566
$724$	3.56500e14	0.0666035
$725$	2.22177e15	0.411946
$726$	−5.61990e14	−0.103414
$727$	−5.21108e15	−0.951674	−0.475837	−	0.879533i	$-0.657855\pi$
$727$	−5.21108e15	−0.951674	−0.475837	+	0.879533i	$0.657855\pi$
$728$	−2.51006e14	−0.0454948
$729$	2.05891e14	0.0370370
$730$	2.49823e14	0.0446023
$731$	6.86575e15	1.21658
$732$	−3.87233e15	−0.681022
$733$	6.95004e15	1.21315	0.606576	−	0.795025i	$-0.292543\pi$
$733$	6.95004e15	1.21315	0.606576	+	0.795025i	$0.292543\pi$
$734$	−3.86527e15	−0.669656
$735$	−2.38974e14	−0.0410933
$736$	−1.69473e15	−0.289250
$737$	−7.61302e15	−1.28969
$738$	−3.66010e15	−0.615435
$739$	2.58294e15	0.431091	0.215546	−	0.976494i	$-0.430847\pi$
$739$	2.58294e15	0.431091	0.215546	+	0.976494i	$0.430847\pi$
$740$	−2.58674e14	−0.0428527
$741$	−4.74379e14	−0.0780055
$742$	8.84570e14	0.144381
$743$	−4.84381e15	−0.784782	−0.392391	−	0.919799i	$-0.628352\pi$
$743$	−4.84381e15	−0.784782	−0.392391	+	0.919799i	$0.628352\pi$
$744$	−1.82673e15	−0.293780
$745$	−3.61708e15	−0.577429
$746$	−1.37110e16	−2.17273
$747$	1.93676e15	0.304658
$748$	−1.10674e16	−1.72817
$749$	−4.17490e15	−0.647137
$750$	4.95238e15	0.762038
$751$	−4.72235e15	−0.721338	−0.360669	−	0.932694i	$-0.617452\pi$
$751$	−4.72235e15	−0.721338	−0.360669	+	0.932694i	$0.617452\pi$
$752$	−3.19636e15	−0.484683
$753$	−3.01514e15	−0.453874
$754$	1.53801e15	0.229835
$755$	−4.43545e15	−0.658006
$756$	−6.35639e14	−0.0936140
$757$	4.22447e15	0.617653	0.308826	−	0.951118i	$-0.400064\pi$
$757$	4.22447e15	0.617653	0.308826	+	0.951118i	$0.400064\pi$
$758$	−4.54180e15	−0.659246
$759$	−8.83169e14	−0.127267
$760$	−7.36283e14	−0.105334
$761$	−1.46113e15	−0.207526	−0.103763	−	0.994602i	$-0.533088\pi$
$761$	−1.46113e15	−0.207526	−0.103763	+	0.994602i	$0.533088\pi$
$762$	−3.75075e15	−0.528890
$763$	−3.16468e15	−0.443042
$764$	2.23842e15	0.311121
$765$	−1.52811e15	−0.210871
$766$	1.68672e16	2.31092
$767$	−1.11742e15	−0.151999
$768$	−8.95102e14	−0.120889
$769$	4.54971e15	0.610083	0.305041	−	0.952339i	$-0.401330\pi$
$769$	4.54971e15	0.610083	0.305041	+	0.952339i	$0.401330\pi$
$770$	2.26213e15	0.301175
$771$	−5.18497e14	−0.0685405
$772$	−9.41970e15	−1.23635
$773$	−1.50519e15	−0.196157	−0.0980783	−	0.995179i	$-0.531270\pi$
$773$	−1.50519e15	−0.196157	−0.0980783	+	0.995179i	$0.531270\pi$
$774$	−3.73266e15	−0.482996
$775$	−6.86031e15	−0.881422
$776$	−2.24712e15	−0.286672
$777$	1.15128e14	0.0145837
$778$	2.57384e15	0.323738
$779$	4.76196e15	0.594744
$780$	8.27922e14	0.102676
$781$	−6.60320e15	−0.813156
$782$	−3.27299e15	−0.400228
$783$	8.68491e14	0.105457
$784$	−7.47201e14	−0.0900947
$785$	−6.09534e15	−0.729819
$786$	−1.26542e16	−1.50457
$787$	−3.40004e15	−0.401442	−0.200721	−	0.979648i	$-0.564329\pi$
$787$	−3.40004e15	−0.401442	−0.200721	+	0.979648i	$0.564329\pi$
$788$	1.85038e12	0.000216954 0
$789$	−7.23296e15	−0.842156
$790$	3.61415e15	0.417886
$791$	5.19878e15	0.596940
$792$	1.34170e15	0.152992
$793$	−2.24482e15	−0.254202
$794$	1.40835e16	1.58379
$795$	−6.50604e14	−0.0726604
$796$	−3.16373e15	−0.350895
$797$	4.93714e14	0.0543820	0.0271910	−	0.999630i	$-0.491344\pi$
$797$	4.93714e14	0.0543820	0.0271910	+	0.999630i	$0.491344\pi$
$798$	1.46959e15	0.160760
$799$	−8.98207e15	−0.975819
$800$	9.66903e15	1.04325
$801$	−3.65082e15	−0.391211
$802$	−1.44986e16	−1.54301
$803$	5.92295e14	0.0626041
$804$	8.63174e15	0.906129
$805$	3.76466e14	0.0392508
$806$	−4.74901e15	−0.491768
$807$	8.09505e15	0.832559
$808$	−4.84942e15	−0.495367
$809$	7.00301e15	0.710506	0.355253	−	0.934770i	$-0.384395\pi$
$809$	7.00301e15	0.710506	0.355253	+	0.934770i	$0.384395\pi$
$810$	8.30780e14	0.0837179
$811$	−1.19498e16	−1.19604	−0.598022	−	0.801480i	$-0.704046\pi$
$811$	−1.19498e16	−1.19604	−0.598022	+	0.801480i	$0.704046\pi$
$812$	−2.68126e15	−0.266551
$813$	−3.83439e15	−0.378615
$814$	−1.08980e15	−0.106884
$815$	6.83966e15	0.666296
$816$	−4.77794e15	−0.462323
$817$	4.85638e15	0.466757
$818$	−6.79242e15	−0.648458
$819$	−3.68485e14	−0.0349428
$820$	−8.31094e15	−0.782842
$821$	−1.00099e16	−0.936576	−0.468288	−	0.883576i	$-0.655129\pi$
$821$	−1.00099e16	−0.936576	−0.468288	+	0.883576i	$0.655129\pi$
$822$	9.55173e15	0.887742
$823$	−1.16216e16	−1.07292	−0.536459	−	0.843927i	$-0.680238\pi$
$823$	−1.16216e16	−1.07292	−0.536459	+	0.843927i	$0.680238\pi$
$824$	−7.69586e15	−0.705760
$825$	5.03879e15	0.459018
$826$	3.46167e15	0.313253
$827$	−1.16988e16	−1.05163	−0.525814	−	0.850600i	$-0.676239\pi$
$827$	−1.16988e16	−1.05163	−0.525814	+	0.850600i	$0.676239\pi$
$828$	1.00135e15	0.0894167
$829$	1.61662e16	1.43403	0.717014	−	0.697059i	$-0.245508\pi$
$829$	1.61662e16	1.43403	0.717014	+	0.697059i	$0.245508\pi$
$830$	7.81491e15	0.688644
$831$	−8.62643e15	−0.755137
$832$	4.68191e15	0.407141
$833$	−2.09970e15	−0.181389
$834$	−1.34847e16	−1.15725
$835$	1.61994e14	0.0138109
$836$	−7.82836e15	−0.663035
$837$	−2.68169e15	−0.225641
$838$	3.25966e16	2.72478
$839$	−2.92069e15	−0.242546	−0.121273	−	0.992619i	$-0.538698\pi$
$839$	−2.92069e15	−0.242546	−0.121273	+	0.992619i	$0.538698\pi$
$840$	−5.71925e14	−0.0471849
$841$	−8.53704e15	−0.699728
$842$	−4.71789e15	−0.384177
$843$	1.19673e16	0.968151
$844$	−1.37971e16	−1.10893
$845$	4.79953e14	0.0383254
$846$	4.88323e15	0.387410
$847$	5.67959e14	0.0447670
$848$	−2.03424e15	−0.159304
$849$	4.36429e15	0.339563
$850$	1.86736e16	1.44352
$851$	−1.81366e14	−0.0139298
$852$	7.48679e15	0.571318
$853$	5.41837e15	0.410817	0.205409	−	0.978676i	$-0.434148\pi$
$853$	5.41837e15	0.410817	0.205409	+	0.978676i	$0.434148\pi$
$854$	6.95425e15	0.523880
$855$	−1.08089e15	−0.0809033
$856$	−9.99157e15	−0.743067
$857$	7.90458e15	0.584096	0.292048	−	0.956404i	$-0.405663\pi$
$857$	7.90458e15	0.584096	0.292048	+	0.956404i	$0.405663\pi$
$858$	3.48807e15	0.256098
$859$	7.29614e15	0.532269	0.266134	−	0.963936i	$-0.414254\pi$
$859$	7.29614e15	0.532269	0.266134	+	0.963936i	$0.414254\pi$
$860$	−8.47572e15	−0.614377
$861$	3.69896e15	0.266418
$862$	−5.90015e15	−0.422253
$863$	7.92090e15	0.563268	0.281634	−	0.959522i	$-0.409124\pi$
$863$	7.92090e15	0.563268	0.281634	+	0.959522i	$0.409124\pi$
$864$	3.77962e15	0.267069
$865$	−1.09681e16	−0.770089
$866$	−2.37788e16	−1.65898
$867$	−5.09839e15	−0.353450
$868$	8.27908e15	0.570327
$869$	8.56864e15	0.586548
$870$	3.50440e15	0.238373
$871$	5.00388e15	0.338226
$872$	−7.57387e15	−0.508718
$873$	−3.29883e15	−0.220182
$874$	−2.31510e15	−0.153552
$875$	−5.00497e15	−0.329881
$876$	−6.71552e14	−0.0439852
$877$	1.31560e16	0.856303	0.428151	−	0.903707i	$-0.359165\pi$
$877$	1.31560e16	0.856303	0.428151	+	0.903707i	$0.359165\pi$
$878$	8.35236e15	0.540243
$879$	−1.31068e16	−0.842479
$880$	−5.20222e15	−0.332303
$881$	1.35898e16	0.862672	0.431336	−	0.902191i	$-0.358042\pi$
$881$	1.35898e16	0.862672	0.431336	+	0.902191i	$0.358042\pi$
$882$	1.14153e15	0.0720132
$883$	1.94005e15	0.121627	0.0608133	−	0.998149i	$-0.480631\pi$
$883$	1.94005e15	0.121627	0.0608133	+	0.998149i	$0.480631\pi$
$884$	7.27438e15	0.453220
$885$	−2.54607e15	−0.157646
$886$	−4.73917e15	−0.291620
$887$	2.27701e16	1.39247	0.696234	−	0.717815i	$-0.254858\pi$
$887$	2.27701e16	1.39247	0.696234	+	0.717815i	$0.254858\pi$
$888$	2.75530e14	0.0167455
$889$	3.79058e15	0.228953
$890$	−1.47312e16	−0.884287
$891$	1.96966e15	0.117507
$892$	9.41192e15	0.558048
$893$	−6.35333e15	−0.374385
$894$	1.72781e16	1.01190
$895$	−3.91680e15	−0.227984
$896$	−5.43745e15	−0.314558
$897$	5.80489e14	0.0333761
$898$	4.34924e16	2.48538
$899$	−1.13119e16	−0.642478
$900$	−5.71304e15	−0.322503
$901$	−5.71641e15	−0.320728
$902$	−3.50144e16	−1.95259
$903$	3.77230e15	0.209086
$904$	1.24420e16	0.685428
$905$	4.70893e14	0.0257843
$906$	2.11873e16	1.15311
$907$	3.17945e16	1.71993	0.859966	−	0.510351i	$-0.170484\pi$
$907$	3.17945e16	1.71993	0.859966	+	0.510351i	$0.170484\pi$
$908$	−4.30120e15	−0.231269
$909$	−7.11909e15	−0.380472
$910$	−1.48685e15	−0.0789842
$911$	1.55297e15	0.0819994	0.0409997	−	0.999159i	$-0.486946\pi$
$911$	1.55297e15	0.0819994	0.0409997	+	0.999159i	$0.486946\pi$
$912$	−3.37960e15	−0.177376
$913$	1.85280e16	0.966586
$914$	3.11979e16	1.61779
$915$	−5.11488e15	−0.263645
$916$	2.59879e16	1.33151
$917$	1.27886e16	0.651316
$918$	7.29949e15	0.369537
$919$	1.18817e16	0.597923	0.298961	−	0.954265i	$-0.403360\pi$
$919$	1.18817e16	0.597923	0.298961	+	0.954265i	$0.403360\pi$
$920$	9.00977e14	0.0450693
$921$	6.23475e15	0.310021
$922$	4.89832e16	2.42118
$923$	4.34015e15	0.213253
$924$	−6.08086e15	−0.297009
$925$	1.03476e15	0.0502411
$926$	−4.70592e16	−2.27135
$927$	−1.12977e16	−0.542067
$928$	1.59432e16	0.760435
$929$	−2.21695e16	−1.05116	−0.525580	−	0.850744i	$-0.676152\pi$
$929$	−2.21695e16	−1.05116	−0.525580	+	0.850744i	$0.676152\pi$
$930$	−1.08208e16	−0.510036
$931$	−1.48519e15	−0.0695920
$932$	−3.44188e16	−1.60328
$933$	4.48080e15	0.207494
$934$	9.42884e15	0.434061
$935$	−1.46187e16	−0.669029
$936$	−8.81875e14	−0.0401227
$937$	2.52413e16	1.14168	0.570839	−	0.821062i	$-0.306618\pi$
$937$	2.52413e16	1.14168	0.570839	+	0.821062i	$0.306618\pi$
$938$	−1.55016e16	−0.697046
$939$	4.45316e15	0.199071
$940$	1.10883e16	0.492790
$941$	−1.97665e15	−0.0873347	−0.0436673	−	0.999046i	$-0.513904\pi$
$941$	−1.97665e15	−0.0873347	−0.0436673	+	0.999046i	$0.513904\pi$
$942$	2.91163e16	1.27896
$943$	−5.82713e15	−0.254472
$944$	−7.96080e15	−0.345629
$945$	−8.39603e14	−0.0362409
$946$	−3.57086e16	−1.53240
$947$	1.56686e16	0.668504	0.334252	−	0.942484i	$-0.391516\pi$
$947$	1.56686e16	0.668504	0.334252	+	0.942484i	$0.391516\pi$
$948$	−9.71524e15	−0.412105
$949$	−3.89304e14	−0.0164182
$950$	1.32084e16	0.553824
$951$	1.24594e16	0.519401
$952$	−5.02511e15	−0.208277
$953$	3.87197e15	0.159559	0.0797795	−	0.996813i	$-0.474578\pi$
$953$	3.87197e15	0.159559	0.0797795	+	0.996813i	$0.474578\pi$
$954$	3.10781e15	0.127332
$955$	2.95669e15	0.120444
$956$	1.96503e16	0.795886
$957$	8.30844e15	0.334583
$958$	3.16757e15	0.126828
$959$	−9.65316e15	−0.384297
$960$	1.06679e16	0.422265
$961$	9.52005e15	0.374680
$962$	7.16306e14	0.0280308
$963$	−1.46679e16	−0.570721
$964$	−2.92448e15	−0.113142
$965$	−1.24423e16	−0.478630
$966$	−1.79831e15	−0.0687843
$967$	−4.48172e16	−1.70451	−0.852254	−	0.523129i	$-0.824765\pi$
$967$	−4.48172e16	−1.70451	−0.852254	+	0.523129i	$0.824765\pi$
$968$	1.35926e15	0.0514031
$969$	−9.49700e15	−0.357113
$970$	−1.33109e16	−0.497696
$971$	−4.31794e16	−1.60535	−0.802676	−	0.596415i	$-0.796591\pi$
$971$	−4.31794e16	−1.60535	−0.802676	+	0.596415i	$0.796591\pi$
$972$	−2.23323e15	−0.0825598
$973$	1.36279e16	0.500966
$974$	2.98355e16	1.09058
$975$	−3.31189e15	−0.120379
$976$	−1.59927e16	−0.578026
$977$	−3.39705e16	−1.22091	−0.610453	−	0.792053i	$-0.709012\pi$
$977$	−3.39705e16	−1.22091	−0.610453	+	0.792053i	$0.709012\pi$
$978$	−3.26717e16	−1.16764
$979$	−3.49256e16	−1.24119
$980$	2.59207e15	0.0916017
$981$	−1.11187e16	−0.390727
$982$	4.24172e16	1.48227
$983$	4.91544e16	1.70812	0.854059	−	0.520175i	$-0.174133\pi$
$983$	4.91544e16	1.70812	0.854059	+	0.520175i	$0.174133\pi$
$984$	8.85253e15	0.305911
$985$	2.44413e12	8.39895e−5 0
$986$	3.07907e16	1.05220
$987$	−4.93509e15	−0.167707
$988$	5.14542e15	0.173883
$989$	−5.94266e15	−0.199711
$990$	7.94767e15	0.265611
$991$	1.74861e16	0.581149	0.290575	−	0.956852i	$-0.406154\pi$
$991$	1.74861e16	0.581149	0.290575	+	0.956852i	$0.406154\pi$
$992$	−4.92289e16	−1.62707
$993$	3.43752e15	0.112986
$994$	−1.34454e16	−0.439490
$995$	−4.17890e15	−0.135842
$996$	−2.10073e16	−0.679117
$997$	−3.59421e16	−1.15553	−0.577763	−	0.816205i	$-0.696074\pi$
$997$	−3.59421e16	−1.15553	−0.577763	+	0.816205i	$0.696074\pi$
$998$	−1.04486e16	−0.334072
$999$	4.04487e14	0.0128616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.14	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+68.4378 q^{2} -243.000 q^{3} +2635.73 q^{4} +3481.49 q^{5} -16630.4 q^{6} +16807.0 q^{7} +40223.3 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+68.4378 q^{2} -243.000 q^{3} +2635.73 q^{4} +3481.49 q^{5} -16630.4 q^{6} +16807.0 q^{7} +40223.3 q^{8} +59049.0 q^{9} +238265. q^{10} +564893. q^{11} -640484. q^{12} -371293. q^{13} +1.15023e6 q^{14} -846001. q^{15} -2.64519e6 q^{16} -7.43323e6 q^{17} +4.04118e6 q^{18} -5.25778e6 q^{19} +9.17628e6 q^{20} -4.08410e6 q^{21} +3.86601e7 q^{22} +6.43385e6 q^{23} -9.77426e6 q^{24} -3.67074e7 q^{25} -2.54105e7 q^{26} -1.43489e7 q^{27} +4.42988e7 q^{28} -6.05266e7 q^{29} -5.78985e7 q^{30} +1.86892e8 q^{31} -2.63408e8 q^{32} -1.37269e8 q^{33} -5.08714e8 q^{34} +5.85134e7 q^{35} +1.55638e8 q^{36} -2.81894e7 q^{37} -3.59831e8 q^{38} +9.02242e7 q^{39} +1.40037e8 q^{40} -9.05699e8 q^{41} -2.79507e8 q^{42} -9.23656e8 q^{43} +1.48891e9 q^{44} +2.05578e8 q^{45} +4.40319e8 q^{46} +1.20837e9 q^{47} +6.42781e8 q^{48} +2.82475e8 q^{49} -2.51217e9 q^{50} +1.80628e9 q^{51} -9.78630e8 q^{52} +7.69035e8 q^{53} -9.82008e8 q^{54} +1.96667e9 q^{55} +6.76033e8 q^{56} +1.27764e9 q^{57} -4.14231e9 q^{58} +3.00954e9 q^{59} -2.22984e9 q^{60} +6.04594e9 q^{61} +1.27905e10 q^{62} +9.92437e8 q^{63} -1.26097e10 q^{64} -1.29265e9 q^{65} -9.39440e9 q^{66} -1.34769e10 q^{67} -1.95920e10 q^{68} -1.56343e9 q^{69} +4.00453e9 q^{70} -1.16893e10 q^{71} +2.37515e9 q^{72} +1.04851e9 q^{73} -1.92922e9 q^{74} +8.91989e9 q^{75} -1.38581e10 q^{76} +9.49416e9 q^{77} +6.17475e9 q^{78} +1.51686e10 q^{79} -9.20920e9 q^{80} +3.48678e9 q^{81} -6.19840e10 q^{82} +3.27992e10 q^{83} -1.07646e10 q^{84} -2.58787e10 q^{85} -6.32130e10 q^{86} +1.47080e10 q^{87} +2.27219e10 q^{88} -6.18269e10 q^{89} +1.40693e10 q^{90} -6.24032e9 q^{91} +1.69579e10 q^{92} -4.54147e10 q^{93} +8.26980e10 q^{94} -1.83049e10 q^{95} +6.40082e10 q^{96} -5.58660e10 q^{97} +1.93320e10 q^{98} +3.33564e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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

Modular forms

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