LMFDB - Embedded newform 273.12.a.c.1.8

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			1.8
Root			$-6.60872$ 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)

$f(q)$	$=$	$q-10.6087 q^{2} -243.000 q^{3} -1935.46 q^{4} +7850.01 q^{5} +2577.92 q^{6} +16807.0 q^{7} +42259.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-10.6087 q^{2} -243.000 q^{3} -1935.46 q^{4} +7850.01 q^{5} +2577.92 q^{6} +16807.0 q^{7} +42259.4 q^{8} +59049.0 q^{9} -83278.5 q^{10} +565609. q^{11} +470316. q^{12} -371293. q^{13} -178301. q^{14} -1.90755e6 q^{15} +3.51549e6 q^{16} -5.26713e6 q^{17} -626434. q^{18} +1.77632e7 q^{19} -1.51933e7 q^{20} -4.08410e6 q^{21} -6.00038e6 q^{22} -4.38946e7 q^{23} -1.02690e7 q^{24} +1.27945e7 q^{25} +3.93894e6 q^{26} -1.43489e7 q^{27} -3.25292e7 q^{28} +3.72483e7 q^{29} +2.02367e7 q^{30} -1.56557e8 q^{31} -1.23842e8 q^{32} -1.37443e8 q^{33} +5.58775e7 q^{34} +1.31935e8 q^{35} -1.14287e8 q^{36} +1.31605e8 q^{37} -1.88445e8 q^{38} +9.02242e7 q^{39} +3.31736e8 q^{40} -1.04040e9 q^{41} +4.33271e7 q^{42} +4.31645e7 q^{43} -1.09471e9 q^{44} +4.63535e8 q^{45} +4.65666e8 q^{46} -2.75693e8 q^{47} -8.54265e8 q^{48} +2.82475e8 q^{49} -1.35733e8 q^{50} +1.27991e9 q^{51} +7.18621e8 q^{52} -2.34009e9 q^{53} +1.52224e8 q^{54} +4.44003e9 q^{55} +7.10253e8 q^{56} -4.31647e9 q^{57} -3.95157e8 q^{58} -3.65787e9 q^{59} +3.69198e9 q^{60} +2.98602e9 q^{61} +1.66087e9 q^{62} +9.92437e8 q^{63} -5.88593e9 q^{64} -2.91465e9 q^{65} +1.45809e9 q^{66} +9.85767e9 q^{67} +1.01943e10 q^{68} +1.06664e10 q^{69} -1.39966e9 q^{70} +7.12578e9 q^{71} +2.49537e9 q^{72} -1.26352e10 q^{73} -1.39616e9 q^{74} -3.10906e9 q^{75} -3.43799e10 q^{76} +9.50618e9 q^{77} -9.57163e8 q^{78} -1.99176e10 q^{79} +2.75967e10 q^{80} +3.48678e9 q^{81} +1.10373e10 q^{82} +1.64069e10 q^{83} +7.90459e9 q^{84} -4.13470e10 q^{85} -4.57920e8 q^{86} -9.05133e9 q^{87} +2.39023e10 q^{88} +5.49390e10 q^{89} -4.91751e9 q^{90} -6.24032e9 q^{91} +8.49561e10 q^{92} +3.80433e10 q^{93} +2.92475e9 q^{94} +1.39442e11 q^{95} +3.00936e10 q^{96} -3.02288e10 q^{97} -2.99670e9 q^{98} +3.33986e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.6087	−0.234422	−0.117211	−	0.993107i	$-0.537395\pi$
$2$	−10.6087	−0.234422	−0.117211	+	0.993107i	$0.537395\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1935.46	−0.945046
$5$	7850.01	1.12340	0.561701	−	0.827340i	$-0.310147\pi$
$5$	7850.01	1.12340	0.561701	+	0.827340i	$0.310147\pi$
$6$	2577.92	0.135343
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	42259.4	0.455961
$9$	59049.0	0.333333
$10$	−83278.5	−0.263350
$11$	565609.	1.05890	0.529452	−	0.848340i	$-0.322398\pi$
$11$	565609.	1.05890	0.529452	+	0.848340i	$0.322398\pi$
$12$	470316.	0.545623
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−178301.	−0.0886031
$15$	−1.90755e6	−0.648596
$16$	3.51549e6	0.838159
$17$	−5.26713e6	−0.899715	−0.449858	−	0.893100i	$-0.648525\pi$
$17$	−5.26713e6	−0.899715	−0.449858	+	0.893100i	$0.648525\pi$
$18$	−626434.	−0.0781406
$19$	1.77632e7	1.64580	0.822900	−	0.568186i	$-0.192355\pi$
$19$	1.77632e7	1.64580	0.822900	+	0.568186i	$0.192355\pi$
$20$	−1.51933e7	−1.06167
$21$	−4.08410e6	−0.218218
$22$	−6.00038e6	−0.248230
$23$	−4.38946e7	−1.42203	−0.711014	−	0.703177i	$-0.751764\pi$
$23$	−4.38946e7	−1.42203	−0.711014	+	0.703177i	$0.751764\pi$
$24$	−1.02690e7	−0.263249
$25$	1.27945e7	0.262031
$26$	3.93894e6	0.0650169
$27$	−1.43489e7	−0.192450
$28$	−3.25292e7	−0.357194
$29$	3.72483e7	0.337223	0.168612	−	0.985683i	$-0.446072\pi$
$29$	3.72483e7	0.337223	0.168612	+	0.985683i	$0.446072\pi$
$30$	2.02367e7	0.152045
$31$	−1.56557e8	−0.982161	−0.491080	−	0.871114i	$-0.663398\pi$
$31$	−1.56557e8	−0.982161	−0.491080	+	0.871114i	$0.663398\pi$
$32$	−1.23842e8	−0.652444
$33$	−1.37443e8	−0.611358
$34$	5.58775e7	0.210913
$35$	1.31935e8	0.424606
$36$	−1.14287e8	−0.315015
$37$	1.31605e8	0.312005	0.156002	−	0.987757i	$-0.450139\pi$
$37$	1.31605e8	0.312005	0.156002	+	0.987757i	$0.450139\pi$
$38$	−1.88445e8	−0.385811
$39$	9.02242e7	0.160128
$40$	3.31736e8	0.512228
$41$	−1.04040e9	−1.40246	−0.701229	−	0.712936i	$-0.747365\pi$
$41$	−1.04040e9	−1.40246	−0.701229	+	0.712936i	$0.747365\pi$
$42$	4.33271e7	0.0511550
$43$	4.31645e7	0.0447765	0.0223883	−	0.999749i	$-0.492873\pi$
$43$	4.31645e7	0.0447765	0.0223883	+	0.999749i	$0.492873\pi$
$44$	−1.09471e9	−1.00071
$45$	4.63535e8	0.374467
$46$	4.65666e8	0.333354
$47$	−2.75693e8	−0.175342	−0.0876712	−	0.996149i	$-0.527942\pi$
$47$	−2.75693e8	−0.175342	−0.0876712	+	0.996149i	$0.527942\pi$
$48$	−8.54265e8	−0.483911
$49$	2.82475e8	0.142857
$50$	−1.35733e8	−0.0614258
$51$	1.27991e9	0.519451
$52$	7.18621e8	0.262109
$53$	−2.34009e9	−0.768625	−0.384313	−	0.923203i	$-0.625562\pi$
$53$	−2.34009e9	−0.768625	−0.384313	+	0.923203i	$0.625562\pi$
$54$	1.52224e8	0.0451145
$55$	4.44003e9	1.18957
$56$	7.10253e8	0.172337
$57$	−4.31647e9	−0.950203
$58$	−3.95157e8	−0.0790524
$59$	−3.65787e9	−0.666105	−0.333053	−	0.942908i	$-0.608079\pi$
$59$	−3.65787e9	−0.666105	−0.333053	+	0.942908i	$0.608079\pi$
$60$	3.69198e9	0.612954
$61$	2.98602e9	0.452667	0.226334	−	0.974050i	$-0.427326\pi$
$61$	2.98602e9	0.452667	0.226334	+	0.974050i	$0.427326\pi$
$62$	1.66087e9	0.230240
$63$	9.92437e8	0.125988
$64$	−5.88593e9	−0.685212
$65$	−2.91465e9	−0.311576
$66$	1.45809e9	0.143316
$67$	9.85767e9	0.891996	0.445998	−	0.895034i	$-0.352849\pi$
$67$	9.85767e9	0.891996	0.445998	+	0.895034i	$0.352849\pi$
$68$	1.01943e10	0.850273
$69$	1.06664e10	0.821009
$70$	−1.39966e9	−0.0995369
$71$	7.12578e9	0.468718	0.234359	−	0.972150i	$-0.424701\pi$
$71$	7.12578e9	0.468718	0.234359	+	0.972150i	$0.424701\pi$
$72$	2.49537e9	0.151987
$73$	−1.26352e10	−0.713356	−0.356678	−	0.934227i	$-0.616091\pi$
$73$	−1.26352e10	−0.713356	−0.356678	+	0.934227i	$0.616091\pi$
$74$	−1.39616e9	−0.0731407
$75$	−3.10906e9	−0.151284
$76$	−3.43799e10	−1.55536
$77$	9.50618e9	0.400228
$78$	−9.57163e8	−0.0375375
$79$	−1.99176e10	−0.728261	−0.364130	−	0.931348i	$-0.618634\pi$
$79$	−1.99176e10	−0.728261	−0.364130	+	0.931348i	$0.618634\pi$
$80$	2.75967e10	0.941589
$81$	3.48678e9	0.111111
$82$	1.10373e10	0.328767
$83$	1.64069e10	0.457190	0.228595	−	0.973522i	$-0.426587\pi$
$83$	1.64069e10	0.457190	0.228595	+	0.973522i	$0.426587\pi$
$84$	7.90459e9	0.206226
$85$	−4.13470e10	−1.01074
$86$	−4.57920e8	−0.0104966
$87$	−9.05133e9	−0.194696
$88$	2.39023e10	0.482819
$89$	5.49390e10	1.04288	0.521442	−	0.853287i	$-0.325394\pi$
$89$	5.49390e10	1.04288	0.521442	+	0.853287i	$0.325394\pi$
$90$	−4.91751e9	−0.0877833
$91$	−6.24032e9	−0.104828
$92$	8.49561e10	1.34388
$93$	3.80433e10	0.567051
$94$	2.92475e9	0.0411041
$95$	1.39442e11	1.84889
$96$	3.00936e10	0.376689
$97$	−3.02288e10	−0.357418	−0.178709	−	0.983902i	$-0.557192\pi$
$97$	−3.02288e10	−0.357418	−0.178709	+	0.983902i	$0.557192\pi$
$98$	−2.99670e9	−0.0334888
$99$	3.33986e10	0.352968
$100$	−2.47632e10	−0.247632
$101$	3.80780e10	0.360501	0.180251	−	0.983621i	$-0.442309\pi$
$101$	3.80780e10	0.360501	0.180251	+	0.983621i	$0.442309\pi$
$102$	−1.35782e10	−0.121771
$103$	1.78958e11	1.52106	0.760531	−	0.649301i	$-0.224939\pi$
$103$	1.78958e11	1.52106	0.760531	+	0.649301i	$0.224939\pi$
$104$	−1.56906e10	−0.126461
$105$	−3.20602e10	−0.245146
$106$	2.48253e10	0.180183
$107$	6.36540e10	0.438747	0.219374	−	0.975641i	$-0.429599\pi$
$107$	6.36540e10	0.438747	0.219374	+	0.975641i	$0.429599\pi$
$108$	2.77717e10	0.181874
$109$	5.74423e10	0.357590	0.178795	−	0.983886i	$-0.442780\pi$
$109$	5.74423e10	0.357590	0.178795	+	0.983886i	$0.442780\pi$
$110$	−4.71030e10	−0.278862
$111$	−3.19799e10	−0.180136
$112$	5.90849e10	0.316794
$113$	−1.09894e11	−0.561104	−0.280552	−	0.959839i	$-0.590517\pi$
$113$	−1.09894e11	−0.561104	−0.280552	+	0.959839i	$0.590517\pi$
$114$	4.57922e10	0.222748
$115$	−3.44573e11	−1.59751
$116$	−7.20924e10	−0.318691
$117$	−2.19245e10	−0.0924500
$118$	3.88054e10	0.156150
$119$	−8.85247e10	−0.340060
$120$	−8.06119e10	−0.295735
$121$	3.46014e10	0.121276
$122$	−3.16779e10	−0.106115
$123$	2.52818e11	0.809710
$124$	3.03009e11	0.928187
$125$	−2.82864e11	−0.829035
$126$	−1.05285e10	−0.0295344
$127$	−4.57405e11	−1.22852	−0.614258	−	0.789105i	$-0.710545\pi$
$127$	−4.57405e11	−1.22852	−0.614258	+	0.789105i	$0.710545\pi$
$128$	3.16071e11	0.813073
$129$	−1.04890e10	−0.0258517
$130$	3.09207e10	0.0730401
$131$	6.09065e11	1.37934	0.689670	−	0.724124i	$-0.257756\pi$
$131$	6.09065e11	1.37934	0.689670	+	0.724124i	$0.257756\pi$
$132$	2.66015e11	0.577762
$133$	2.98547e11	0.622054
$134$	−1.04577e11	−0.209103
$135$	−1.12639e11	−0.216199
$136$	−2.22586e11	−0.410235
$137$	−5.75656e11	−1.01906	−0.509531	−	0.860453i	$-0.670181\pi$
$137$	−5.75656e11	−1.01906	−0.509531	+	0.860453i	$0.670181\pi$
$138$	−1.13157e11	−0.192462
$139$	−3.53586e11	−0.577981	−0.288990	−	0.957332i	$-0.593320\pi$
$139$	−3.53586e11	−0.577981	−0.288990	+	0.957332i	$0.593320\pi$
$140$	−2.55354e11	−0.401272
$141$	6.69933e10	0.101234
$142$	−7.55954e10	−0.109878
$143$	−2.10006e11	−0.293687
$144$	2.07586e11	0.279386
$145$	2.92399e11	0.378837
$146$	1.34043e11	0.167226
$147$	−6.86415e10	−0.0824786
$148$	−2.54715e11	−0.294859
$149$	−6.42699e10	−0.0716941	−0.0358470	−	0.999357i	$-0.511413\pi$
$149$	−6.42699e10	−0.0716941	−0.0358470	+	0.999357i	$0.511413\pi$
$150$	3.29831e10	0.0354642
$151$	1.55665e11	0.161369	0.0806843	−	0.996740i	$-0.474289\pi$
$151$	1.55665e11	0.161369	0.0806843	+	0.996740i	$0.474289\pi$
$152$	7.50663e11	0.750421
$153$	−3.11019e11	−0.299905
$154$	−1.00848e11	−0.0938221
$155$	−1.22897e12	−1.10336
$156$	−1.74625e11	−0.151329
$157$	−4.97462e10	−0.0416209	−0.0208105	−	0.999783i	$-0.506625\pi$
$157$	−4.97462e10	−0.0416209	−0.0208105	+	0.999783i	$0.506625\pi$
$158$	2.11300e11	0.170720
$159$	5.68641e11	0.443766
$160$	−9.72161e11	−0.732957
$161$	−7.37737e11	−0.537476
$162$	−3.69903e10	−0.0260469
$163$	−1.64466e12	−1.11955	−0.559777	−	0.828644i	$-0.689113\pi$
$163$	−1.64466e12	−1.11955	−0.559777	+	0.828644i	$0.689113\pi$
$164$	2.01365e12	1.32539
$165$	−1.07893e12	−0.686800
$166$	−1.74056e11	−0.107175
$167$	−2.35974e12	−1.40580	−0.702900	−	0.711289i	$-0.748112\pi$
$167$	−2.35974e12	−1.40580	−0.702900	+	0.711289i	$0.748112\pi$
$168$	−1.72591e11	−0.0994989
$169$	1.37858e11	0.0769231
$170$	4.38639e11	0.236940
$171$	1.04890e12	0.548600
$172$	−8.35429e10	−0.0423159
$173$	8.89407e11	0.436362	0.218181	−	0.975908i	$-0.429988\pi$
$173$	8.89407e11	0.436362	0.218181	+	0.975908i	$0.429988\pi$
$174$	9.60230e10	0.0456409
$175$	2.15037e11	0.0990385
$176$	1.98839e12	0.887529
$177$	8.88864e11	0.384576
$178$	−5.82832e11	−0.244475
$179$	−3.31920e12	−1.35003	−0.675013	−	0.737806i	$-0.735862\pi$
$179$	−3.31920e12	−1.35003	−0.675013	+	0.737806i	$0.735862\pi$
$180$	−8.97151e11	−0.353889
$181$	−2.40400e12	−0.919818	−0.459909	−	0.887966i	$-0.652118\pi$
$181$	−2.40400e12	−0.919818	−0.459909	+	0.887966i	$0.652118\pi$
$182$	6.62018e10	0.0245741
$183$	−7.25603e11	−0.261347
$184$	−1.85496e12	−0.648390
$185$	1.03310e12	0.350507
$186$	−4.03591e11	−0.132929
$187$	−2.97914e12	−0.952711
$188$	5.33591e11	0.165707
$189$	−2.41162e11	−0.0727393
$190$	−1.47930e12	−0.433421
$191$	4.02236e11	0.114498	0.0572489	−	0.998360i	$-0.481767\pi$
$191$	4.02236e11	0.114498	0.0572489	+	0.998360i	$0.481767\pi$
$192$	1.43028e12	0.395607
$193$	6.13494e10	0.0164909	0.00824546	−	0.999966i	$-0.497375\pi$
$193$	6.13494e10	0.0164909	0.00824546	+	0.999966i	$0.497375\pi$
$194$	3.20689e11	0.0837866
$195$	7.08261e11	0.179888
$196$	−5.46718e11	−0.135007
$197$	3.74520e12	0.899312	0.449656	−	0.893202i	$-0.351547\pi$
$197$	3.74520e12	0.899312	0.449656	+	0.893202i	$0.351547\pi$
$198$	−3.54317e11	−0.0827433
$199$	5.17983e12	1.17659	0.588293	−	0.808648i	$-0.299800\pi$
$199$	5.17983e12	1.17659	0.588293	+	0.808648i	$0.299800\pi$
$200$	5.40687e11	0.119476
$201$	−2.39541e12	−0.514994
$202$	−4.03959e11	−0.0845093
$203$	6.26032e11	0.127458
$204$	−2.47721e12	−0.490905
$205$	−8.16717e12	−1.57552
$206$	−1.89852e12	−0.356570
$207$	−2.59193e12	−0.474010
$208$	−1.30528e12	−0.232464
$209$	1.00470e13	1.74274
$210$	3.40118e11	0.0574676
$211$	−2.27357e12	−0.374244	−0.187122	−	0.982337i	$-0.559916\pi$
$211$	−2.27357e12	−0.374244	−0.187122	+	0.982337i	$0.559916\pi$
$212$	4.52913e12	0.726387
$213$	−1.73156e12	−0.270614
$214$	−6.75287e11	−0.102852
$215$	3.38842e11	0.0503020
$216$	−6.06376e11	−0.0877498
$217$	−2.63125e12	−0.371222
$218$	−6.09389e11	−0.0838270
$219$	3.07035e12	0.411856
$220$	−8.59348e12	−1.12420
$221$	1.95565e12	0.249536
$222$	3.39266e11	0.0422278
$223$	8.52343e12	1.03499	0.517497	−	0.855685i	$-0.326864\pi$
$223$	8.52343e12	1.03499	0.517497	+	0.855685i	$0.326864\pi$
$224$	−2.08141e12	−0.246601
$225$	7.55502e11	0.0873437
$226$	1.16584e12	0.131535
$227$	−4.64728e12	−0.511749	−0.255874	−	0.966710i	$-0.582363\pi$
$227$	−4.64728e12	−0.511749	−0.255874	+	0.966710i	$0.582363\pi$
$228$	8.35433e12	0.897986
$229$	1.41738e13	1.48727	0.743636	−	0.668585i	$-0.233100\pi$
$229$	1.41738e13	1.48727	0.743636	+	0.668585i	$0.233100\pi$
$230$	3.65548e12	0.374491
$231$	−2.31000e12	−0.231072
$232$	1.57409e12	0.153761
$233$	−1.17362e13	−1.11961	−0.559807	−	0.828623i	$-0.689125\pi$
$233$	−1.17362e13	−1.11961	−0.559807	+	0.828623i	$0.689125\pi$
$234$	2.32591e11	0.0216723
$235$	−2.16419e12	−0.196980
$236$	7.07965e12	0.629500
$237$	4.83996e12	0.420462
$238$	9.39134e11	0.0797176
$239$	2.13022e13	1.76700	0.883498	−	0.468435i	$-0.155182\pi$
$239$	2.13022e13	1.76700	0.883498	+	0.468435i	$0.155182\pi$
$240$	−6.70599e12	−0.543627
$241$	−1.95364e13	−1.54793	−0.773965	−	0.633228i	$-0.781730\pi$
$241$	−1.95364e13	−1.54793	−0.773965	+	0.633228i	$0.781730\pi$
$242$	−3.67076e11	−0.0284297
$243$	−8.47289e11	−0.0641500
$244$	−5.77931e12	−0.427791
$245$	2.21743e12	0.160486
$246$	−2.68207e12	−0.189814
$247$	−6.59536e12	−0.456463
$248$	−6.61599e12	−0.447827
$249$	−3.98687e12	−0.263959
$250$	3.00083e12	0.194344
$251$	−4.87168e12	−0.308655	−0.154327	−	0.988020i	$-0.549321\pi$
$251$	−4.87168e12	−0.308655	−0.154327	+	0.988020i	$0.549321\pi$
$252$	−1.92082e12	−0.119065
$253$	−2.48272e13	−1.50579
$254$	4.85248e12	0.287991
$255$	1.00473e13	0.583552
$256$	8.70128e12	0.494610
$257$	−8.70274e12	−0.484199	−0.242100	−	0.970251i	$-0.577836\pi$
$257$	−8.70274e12	−0.484199	−0.242100	+	0.970251i	$0.577836\pi$
$258$	1.11275e11	0.00606021
$259$	2.21188e12	0.117927
$260$	5.64118e12	0.294453
$261$	2.19947e12	0.112408
$262$	−6.46140e12	−0.323347
$263$	−1.07494e13	−0.526778	−0.263389	−	0.964690i	$-0.584840\pi$
$263$	−1.07494e13	−0.526778	−0.263389	+	0.964690i	$0.584840\pi$
$264$	−5.80825e12	−0.278756
$265$	−1.83697e13	−0.863475
$266$	−3.16720e12	−0.145823
$267$	−1.33502e13	−0.602109
$268$	−1.90791e13	−0.842978
$269$	−2.85429e13	−1.23555	−0.617775	−	0.786355i	$-0.711966\pi$
$269$	−2.85429e13	−1.23555	−0.617775	+	0.786355i	$0.711966\pi$
$270$	1.19496e12	0.0506817
$271$	−4.58138e13	−1.90399	−0.951997	−	0.306107i	$-0.900974\pi$
$271$	−4.58138e13	−1.90399	−0.951997	+	0.306107i	$0.900974\pi$
$272$	−1.85166e13	−0.754105
$273$	1.51640e12	0.0605228
$274$	6.10698e12	0.238890
$275$	7.23667e12	0.277466
$276$	−2.06443e13	−0.775891
$277$	2.56717e13	0.945836	0.472918	−	0.881106i	$-0.343201\pi$
$277$	2.56717e13	0.945836	0.472918	+	0.881106i	$0.343201\pi$
$278$	3.75109e12	0.135491
$279$	−9.24452e12	−0.327387
$280$	5.57549e12	0.193604
$281$	−4.89722e13	−1.66750	−0.833749	−	0.552144i	$-0.813810\pi$
$281$	−4.89722e13	−1.66750	−0.833749	+	0.552144i	$0.813810\pi$
$282$	−7.10713e11	−0.0237314
$283$	4.09935e12	0.134242	0.0671211	−	0.997745i	$-0.478619\pi$
$283$	4.09935e12	0.134242	0.0671211	+	0.997745i	$0.478619\pi$
$284$	−1.37916e13	−0.442960
$285$	−3.38843e13	−1.06746
$286$	2.22790e12	0.0688466
$287$	−1.74860e13	−0.530080
$288$	−7.31275e12	−0.217481
$289$	−6.52921e12	−0.190512
$290$	−3.10198e12	−0.0888076
$291$	7.34561e12	0.206356
$292$	2.44549e13	0.674155
$293$	6.17015e12	0.166926	0.0834629	−	0.996511i	$-0.473402\pi$
$293$	6.17015e12	0.166926	0.0834629	+	0.996511i	$0.473402\pi$
$294$	7.28198e11	0.0193348
$295$	−2.87143e13	−0.748303
$296$	5.56152e12	0.142262
$297$	−8.11586e12	−0.203786
$298$	6.81822e11	0.0168067
$299$	1.62978e13	0.394400
$300$	6.01745e12	0.142970
$301$	7.25466e11	0.0169239
$302$	−1.65141e12	−0.0378283
$303$	−9.25296e12	−0.208135
$304$	6.24465e13	1.37944
$305$	2.34403e13	0.508527
$306$	3.29951e12	0.0703043
$307$	−7.97373e13	−1.66878	−0.834392	−	0.551171i	$-0.814181\pi$
$307$	−7.97373e13	−1.66878	−0.834392	+	0.551171i	$0.814181\pi$
$308$	−1.83988e13	−0.378234
$309$	−4.34869e13	−0.878186
$310$	1.30378e13	0.258652
$311$	7.63582e13	1.48824	0.744121	−	0.668045i	$-0.232869\pi$
$311$	7.63582e13	1.48824	0.744121	+	0.668045i	$0.232869\pi$
$312$	3.81282e12	0.0730122
$313$	−5.14481e13	−0.968001	−0.484001	−	0.875068i	$-0.660817\pi$
$313$	−5.14481e13	−0.968001	−0.484001	+	0.875068i	$0.660817\pi$
$314$	5.27743e11	0.00975685
$315$	7.79063e12	0.141535
$316$	3.85495e13	0.688240
$317$	−7.99481e13	−1.40276	−0.701378	−	0.712790i	$-0.747431\pi$
$317$	−7.99481e13	−1.40276	−0.701378	+	0.712790i	$0.747431\pi$
$318$	−6.03255e12	−0.104028
$319$	2.10679e13	0.357087
$320$	−4.62046e13	−0.769768
$321$	−1.54679e13	−0.253311
$322$	7.82645e12	0.125996
$323$	−9.35613e13	−1.48075
$324$	−6.74851e12	−0.105005
$325$	−4.75050e12	−0.0726744
$326$	1.74478e13	0.262448
$327$	−1.39585e13	−0.206455
$328$	−4.39667e13	−0.639467
$329$	−4.63357e12	−0.0662732
$330$	1.14460e13	0.161001
$331$	3.31082e13	0.458017	0.229009	−	0.973424i	$-0.426452\pi$
$331$	3.31082e13	0.458017	0.229009	+	0.973424i	$0.426452\pi$
$332$	−3.17548e13	−0.432066
$333$	7.77111e12	0.104002
$334$	2.50338e13	0.329550
$335$	7.73828e13	1.00207
$336$	−1.43576e13	−0.182901
$337$	−5.55440e13	−0.696102	−0.348051	−	0.937476i	$-0.613156\pi$
$337$	−5.55440e13	−0.696102	−0.348051	+	0.937476i	$0.613156\pi$
$338$	−1.46250e12	−0.0180324
$339$	2.67043e13	0.323953
$340$	8.00253e13	0.955198
$341$	−8.85498e13	−1.04001
$342$	−1.11275e13	−0.128604
$343$	4.74756e12	0.0539949
$344$	1.82410e12	0.0204163
$345$	8.37313e13	0.922322
$346$	−9.43547e12	−0.102293
$347$	−5.37715e13	−0.573773	−0.286887	−	0.957965i	$-0.592620\pi$
$347$	−5.37715e13	−0.573773	−0.286887	+	0.957965i	$0.592620\pi$
$348$	1.75184e13	0.183997
$349$	−1.19932e14	−1.23992	−0.619960	−	0.784633i	$-0.712851\pi$
$349$	−1.19932e14	−1.23992	−0.619960	+	0.784633i	$0.712851\pi$
$350$	−2.28127e12	−0.0232168
$351$	5.32765e12	0.0533761
$352$	−7.00461e13	−0.690875
$353$	−1.02896e14	−0.999161	−0.499581	−	0.866267i	$-0.666513\pi$
$353$	−1.02896e14	−0.999161	−0.499581	+	0.866267i	$0.666513\pi$
$354$	−9.42970e12	−0.0901530
$355$	5.59374e13	0.526558
$356$	−1.06332e14	−0.985573
$357$	2.15115e13	0.196334
$358$	3.52125e13	0.316475
$359$	1.87257e14	1.65737	0.828684	−	0.559716i	$-0.189090\pi$
$359$	1.87257e14	1.65737	0.828684	+	0.559716i	$0.189090\pi$
$360$	1.95887e13	0.170743
$361$	1.99042e14	1.70866
$362$	2.55033e13	0.215625
$363$	−8.40813e12	−0.0700185
$364$	1.20779e13	0.0990678
$365$	−9.91864e13	−0.801385
$366$	7.69772e12	0.0612655
$367$	7.38408e12	0.0578939	0.0289470	−	0.999581i	$-0.490785\pi$
$367$	7.38408e12	0.0578939	0.0289470	+	0.999581i	$0.490785\pi$
$368$	−1.54311e14	−1.19189
$369$	−6.14347e13	−0.467486
$370$	−1.09598e13	−0.0821664
$371$	−3.93298e13	−0.290513
$372$	−7.36311e13	−0.535889
$373$	6.39307e13	0.458470	0.229235	−	0.973371i	$-0.426378\pi$
$373$	6.39307e13	0.458470	0.229235	+	0.973371i	$0.426378\pi$
$374$	3.16048e13	0.223336
$375$	6.87360e13	0.478644
$376$	−1.16506e13	−0.0799493
$377$	−1.38300e13	−0.0935289
$378$	2.55842e12	0.0170517
$379$	1.06754e13	0.0701242	0.0350621	−	0.999385i	$-0.488837\pi$
$379$	1.06754e13	0.0701242	0.0350621	+	0.999385i	$0.488837\pi$
$380$	−2.69883e14	−1.74729
$381$	1.11149e14	0.709284
$382$	−4.26720e12	−0.0268408
$383$	6.42139e13	0.398140	0.199070	−	0.979985i	$-0.436208\pi$
$383$	6.42139e13	0.398140	0.199070	+	0.979985i	$0.436208\pi$
$384$	−7.68052e13	−0.469428
$385$	7.46236e13	0.449616
$386$	−6.50838e11	−0.00386583
$387$	2.54882e12	0.0149255
$388$	5.85065e13	0.337777
$389$	1.78968e14	1.01872	0.509359	−	0.860554i	$-0.329883\pi$
$389$	1.78968e14	1.01872	0.509359	+	0.860554i	$0.329883\pi$
$390$	−7.51374e12	−0.0421697
$391$	2.31199e14	1.27942
$392$	1.19372e13	0.0651373
$393$	−1.48003e14	−0.796362
$394$	−3.97317e13	−0.210818
$395$	−1.56353e14	−0.818129
$396$	−6.46415e13	−0.333571
$397$	−2.81498e14	−1.43261	−0.716305	−	0.697787i	$-0.754168\pi$
$397$	−2.81498e14	−1.43261	−0.716305	+	0.697787i	$0.754168\pi$
$398$	−5.49513e13	−0.275817
$399$	−7.25468e13	−0.359143
$400$	4.49790e13	0.219624
$401$	1.57151e14	0.756874	0.378437	−	0.925627i	$-0.376462\pi$
$401$	1.57151e14	0.756874	0.378437	+	0.925627i	$0.376462\pi$
$402$	2.54123e13	0.120726
$403$	5.81284e13	0.272402
$404$	−7.36983e13	−0.340690
$405$	2.73713e13	0.124822
$406$	−6.64140e12	−0.0298790
$407$	7.44366e13	0.330383
$408$	5.40883e13	0.236849
$409$	1.84435e14	0.796831	0.398415	−	0.917205i	$-0.369560\pi$
$409$	1.84435e14	0.796831	0.398415	+	0.917205i	$0.369560\pi$
$410$	8.66432e13	0.369337
$411$	1.39884e14	0.588355
$412$	−3.46366e14	−1.43748
$413$	−6.14779e13	−0.251764
$414$	2.74971e13	0.111118
$415$	1.28794e14	0.513608
$416$	4.59817e13	0.180955
$417$	8.59214e13	0.333697
$418$	−1.06586e14	−0.408537
$419$	−2.64482e14	−1.00050	−0.500251	−	0.865880i	$-0.666759\pi$
$419$	−2.64482e14	−1.00050	−0.500251	+	0.865880i	$0.666759\pi$
$420$	6.20511e13	0.231675
$421$	3.11866e14	1.14926	0.574628	−	0.818415i	$-0.305147\pi$
$421$	3.11866e14	1.14926	0.574628	+	0.818415i	$0.305147\pi$
$422$	2.41196e13	0.0877309
$423$	−1.62794e13	−0.0584475
$424$	−9.88906e13	−0.350463
$425$	−6.73903e13	−0.235753
$426$	1.83697e13	0.0634379
$427$	5.01861e13	0.171092
$428$	−1.23199e14	−0.414637
$429$	5.10316e13	0.169560
$430$	−3.59468e12	−0.0117919
$431$	−1.11029e14	−0.359594	−0.179797	−	0.983704i	$-0.557544\pi$
$431$	−1.11029e14	−0.359594	−0.179797	+	0.983704i	$0.557544\pi$
$432$	−5.04435e13	−0.161304
$433$	−5.68188e14	−1.79394	−0.896971	−	0.442090i	$-0.854237\pi$
$433$	−5.68188e14	−1.79394	−0.896971	+	0.442090i	$0.854237\pi$
$434$	2.79142e13	0.0870225
$435$	−7.10530e13	−0.218722
$436$	−1.11177e14	−0.337940
$437$	−7.79711e14	−2.34038
$438$	−3.25725e13	−0.0965481
$439$	−4.37752e14	−1.28137	−0.640683	−	0.767806i	$-0.721349\pi$
$439$	−4.37752e14	−1.28137	−0.640683	+	0.767806i	$0.721349\pi$
$440$	1.87633e14	0.542399
$441$	1.66799e13	0.0476190
$442$	−2.07469e13	−0.0584967
$443$	4.04818e13	0.112730	0.0563650	−	0.998410i	$-0.482049\pi$
$443$	4.04818e13	0.112730	0.0563650	+	0.998410i	$0.482049\pi$
$444$	6.18957e13	0.170237
$445$	4.31272e14	1.17158
$446$	−9.04226e13	−0.242625
$447$	1.56176e13	0.0413926
$448$	−9.89248e13	−0.258986
$449$	2.66473e14	0.689125	0.344562	−	0.938763i	$-0.388027\pi$
$449$	2.66473e14	0.689125	0.344562	+	0.938763i	$0.388027\pi$
$450$	−8.01490e12	−0.0204753
$451$	−5.88460e14	−1.48507
$452$	2.12695e14	0.530269
$453$	−3.78267e13	−0.0931662
$454$	4.93017e13	0.119965
$455$	−4.89866e13	−0.117764
$456$	−1.82411e14	−0.433256
$457$	4.25311e14	0.998085	0.499042	−	0.866578i	$-0.333685\pi$
$457$	4.25311e14	0.998085	0.499042	+	0.866578i	$0.333685\pi$
$458$	−1.50366e14	−0.348649
$459$	7.55776e13	0.173150
$460$	6.66906e14	1.50972
$461$	2.16389e14	0.484038	0.242019	−	0.970272i	$-0.422190\pi$
$461$	2.16389e14	0.484038	0.242019	+	0.970272i	$0.422190\pi$
$462$	2.45062e13	0.0541682
$463$	3.85356e14	0.841719	0.420859	−	0.907126i	$-0.361729\pi$
$463$	3.85356e14	0.841719	0.420859	+	0.907126i	$0.361729\pi$
$464$	1.30946e14	0.282647
$465$	2.98640e14	0.637026
$466$	1.24506e14	0.262462
$467$	−1.89006e13	−0.0393761	−0.0196881	−	0.999806i	$-0.506267\pi$
$467$	−1.89006e13	−0.0393761	−0.0196881	+	0.999806i	$0.506267\pi$
$468$	4.24338e13	0.0873696
$469$	1.65678e14	0.337143
$470$	2.29593e13	0.0461764
$471$	1.20883e13	0.0240298
$472$	−1.54579e14	−0.303718
$473$	2.44142e13	0.0474140
$474$	−5.13458e13	−0.0985653
$475$	2.27271e14	0.431251
$476$	1.71336e14	0.321373
$477$	−1.38180e14	−0.256208
$478$	−2.25989e14	−0.414222
$479$	−3.58466e14	−0.649535	−0.324768	−	0.945794i	$-0.605286\pi$
$479$	−3.58466e14	−0.649535	−0.324768	+	0.945794i	$0.605286\pi$
$480$	2.36235e14	0.423173
$481$	−4.88638e13	−0.0865346
$482$	2.07256e14	0.362869
$483$	1.79270e14	0.310312
$484$	−6.69694e13	−0.114611
$485$	−2.37297e14	−0.401524
$486$	8.98865e12	0.0150382
$487$	2.94241e14	0.486737	0.243369	−	0.969934i	$-0.421748\pi$
$487$	2.94241e14	0.486737	0.243369	+	0.969934i	$0.421748\pi$
$488$	1.26187e14	0.206399
$489$	3.99653e14	0.646374
$490$	−2.35241e13	−0.0376214
$491$	−9.01207e14	−1.42520	−0.712601	−	0.701569i	$-0.752483\pi$
$491$	−9.01207e14	−1.42520	−0.712601	+	0.701569i	$0.752483\pi$
$492$	−4.89317e14	−0.765213
$493$	−1.96192e14	−0.303405
$494$	6.99684e13	0.107005
$495$	2.62179e14	0.396524
$496$	−5.50374e14	−0.823207
$497$	1.19763e14	0.177159
$498$	4.22956e13	0.0618777
$499$	4.72576e14	0.683783	0.341892	−	0.939739i	$-0.388932\pi$
$499$	4.72576e14	0.683783	0.341892	+	0.939739i	$0.388932\pi$
$500$	5.47471e14	0.783477
$501$	5.73417e14	0.811639
$502$	5.16822e13	0.0723554
$503$	4.70637e13	0.0651722	0.0325861	−	0.999469i	$-0.489626\pi$
$503$	4.70637e13	0.0651722	0.0325861	+	0.999469i	$0.489626\pi$
$504$	4.19397e13	0.0574457
$505$	2.98913e14	0.404988
$506$	2.63385e14	0.352990
$507$	−3.34996e13	−0.0444116
$508$	8.85287e14	1.16100
$509$	3.88421e14	0.503913	0.251956	−	0.967739i	$-0.418926\pi$
$509$	3.88421e14	0.503913	0.251956	+	0.967739i	$0.418926\pi$
$510$	−1.06589e14	−0.136797
$511$	−2.12360e14	−0.269623
$512$	−7.39622e14	−0.929020
$513$	−2.54883e14	−0.316734
$514$	9.23249e13	0.113507
$515$	1.40482e15	1.70876
$516$	2.03009e13	0.0244311
$517$	−1.55934e14	−0.185671
$518$	−2.34652e13	−0.0276446
$519$	−2.16126e14	−0.251934
$520$	−1.23171e14	−0.142066
$521$	6.06307e14	0.691966	0.345983	−	0.938241i	$-0.387545\pi$
$521$	6.06307e14	0.691966	0.345983	+	0.938241i	$0.387545\pi$
$522$	−2.33336e13	−0.0263508
$523$	6.61968e14	0.739737	0.369869	−	0.929084i	$-0.379403\pi$
$523$	6.61968e14	0.739737	0.369869	+	0.929084i	$0.379403\pi$
$524$	−1.17882e15	−1.30354
$525$	−5.22540e13	−0.0571799
$526$	1.14037e14	0.123488
$527$	8.24605e14	0.883665
$528$	−4.83180e14	−0.512415
$529$	9.73929e14	1.02217
$530$	1.94879e14	0.202417
$531$	−2.15994e14	−0.222035
$532$	−5.77824e14	−0.587870
$533$	3.86294e14	0.388972
$534$	1.41628e14	0.141147
$535$	4.99684e14	0.492890
$536$	4.16579e14	0.406716
$537$	8.06566e14	0.779438
$538$	3.02803e14	0.289640
$539$	1.59770e14	0.151272
$540$	2.18008e14	0.204318
$541$	1.64104e15	1.52242	0.761208	−	0.648508i	$-0.224607\pi$
$541$	1.64104e15	1.52242	0.761208	+	0.648508i	$0.224607\pi$
$542$	4.86026e14	0.446338
$543$	5.84172e14	0.531057
$544$	6.52292e14	0.587014
$545$	4.50922e14	0.401718
$546$	−1.60870e13	−0.0141879
$547$	−1.00490e15	−0.877390	−0.438695	−	0.898636i	$-0.644559\pi$
$547$	−1.00490e15	−0.877390	−0.438695	+	0.898636i	$0.644559\pi$
$548$	1.11416e15	0.963060
$549$	1.76322e14	0.150889
$550$	−7.67718e13	−0.0650440
$551$	6.61650e14	0.555002
$552$	4.50755e14	0.374348
$553$	−3.34754e14	−0.275257
$554$	−2.72344e14	−0.221724
$555$	−2.51042e14	−0.202365
$556$	6.84350e14	0.546219
$557$	1.75631e15	1.38803	0.694013	−	0.719962i	$-0.255841\pi$
$557$	1.75631e15	1.38803	0.694013	+	0.719962i	$0.255841\pi$
$558$	9.80725e13	0.0767466
$559$	−1.60267e13	−0.0124188
$560$	4.63817e14	0.355887
$561$	7.23930e14	0.550048
$562$	5.19533e14	0.390898
$563$	1.55277e14	0.115694	0.0578470	−	0.998325i	$-0.481576\pi$
$563$	1.55277e14	0.115694	0.0578470	+	0.998325i	$0.481576\pi$
$564$	−1.29663e14	−0.0956708
$565$	−8.62670e14	−0.630345
$566$	−4.34888e13	−0.0314693
$567$	5.86024e13	0.0419961
$568$	3.01131e14	0.213717
$569$	−1.58200e15	−1.11196	−0.555979	−	0.831196i	$-0.687656\pi$
$569$	−1.58200e15	−1.11196	−0.555979	+	0.831196i	$0.687656\pi$
$570$	3.59469e14	0.250236
$571$	−9.43143e14	−0.650248	−0.325124	−	0.945671i	$-0.605406\pi$
$571$	−9.43143e14	−0.650248	−0.325124	+	0.945671i	$0.605406\pi$
$572$	4.06458e14	0.277548
$573$	−9.77432e13	−0.0661053
$574$	1.85504e14	0.124262
$575$	−5.61609e14	−0.372616
$576$	−3.47558e14	−0.228404
$577$	1.68693e15	1.09807	0.549035	−	0.835799i	$-0.314995\pi$
$577$	1.68693e15	1.09807	0.549035	+	0.835799i	$0.314995\pi$
$578$	6.92665e13	0.0446602
$579$	−1.49079e13	−0.00952104
$580$	−5.65926e14	−0.358018
$581$	2.75751e14	0.172802
$582$	−7.79275e13	−0.0483742
$583$	−1.32357e15	−0.813900
$584$	−5.33955e14	−0.325263
$585$	−1.72107e14	−0.103859
$586$	−6.54574e13	−0.0391311
$587$	−2.10137e15	−1.24450	−0.622249	−	0.782820i	$-0.713781\pi$
$587$	−2.10137e15	−1.24450	−0.622249	+	0.782820i	$0.713781\pi$
$588$	1.32853e14	0.0779461
$589$	−2.78095e15	−1.61644
$590$	3.04622e14	0.175419
$591$	−9.10083e14	−0.519218
$592$	4.62655e14	0.261510
$593$	−1.65475e15	−0.926686	−0.463343	−	0.886179i	$-0.653350\pi$
$593$	−1.65475e15	−0.926686	−0.463343	+	0.886179i	$0.653350\pi$
$594$	8.60989e13	0.0477719
$595$	−6.94920e14	−0.382024
$596$	1.24392e14	0.0677542
$597$	−1.25870e15	−0.679302
$598$	−1.72898e14	−0.0924559
$599$	−2.70948e15	−1.43562	−0.717809	−	0.696240i	$-0.754855\pi$
$599$	−2.70948e15	−1.43562	−0.717809	+	0.696240i	$0.754855\pi$
$600$	−1.31387e14	−0.0689795
$601$	1.18239e15	0.615109	0.307555	−	0.951530i	$-0.400489\pi$
$601$	1.18239e15	0.615109	0.307555	+	0.951530i	$0.400489\pi$
$602$	−7.69626e12	−0.00396734
$603$	5.82086e14	0.297332
$604$	−3.01283e14	−0.152501
$605$	2.71621e14	0.136241
$606$	9.81620e13	0.0487915
$607$	5.79245e14	0.285315	0.142657	−	0.989772i	$-0.454435\pi$
$607$	5.79245e14	0.285315	0.142657	+	0.989772i	$0.454435\pi$
$608$	−2.19983e15	−1.07379
$609$	−1.52126e14	−0.0735881
$610$	−2.48671e14	−0.119210
$611$	1.02363e14	0.0486312
$612$	6.01963e14	0.283424
$613$	−2.96026e15	−1.38133	−0.690665	−	0.723174i	$-0.742682\pi$
$613$	−2.96026e15	−1.38133	−0.690665	+	0.723174i	$0.742682\pi$
$614$	8.45910e14	0.391199
$615$	1.98462e15	0.909629
$616$	4.01725e14	0.182488
$617$	−2.48177e14	−0.111736	−0.0558681	−	0.998438i	$-0.517793\pi$
$617$	−2.48177e14	−0.111736	−0.0558681	+	0.998438i	$0.517793\pi$
$618$	4.61340e14	0.205866
$619$	4.23381e15	1.87255	0.936273	−	0.351272i	$-0.114251\pi$
$619$	4.23381e15	1.87255	0.936273	+	0.351272i	$0.114251\pi$
$620$	2.37862e15	1.04273
$621$	6.29840e14	0.273670
$622$	−8.10062e14	−0.348876
$623$	9.23360e14	0.394173
$624$	3.17183e14	0.134213
$625$	−2.84522e15	−1.19337
$626$	5.45799e14	0.226921
$627$	−2.44143e15	−1.00617
$628$	9.62815e13	0.0393337
$629$	−6.93178e14	−0.280716
$630$	−8.26486e13	−0.0331790
$631$	1.65012e15	0.656682	0.328341	−	0.944559i	$-0.393511\pi$
$631$	1.65012e15	0.656682	0.328341	+	0.944559i	$0.393511\pi$
$632$	−8.41703e14	−0.332059
$633$	5.52477e14	0.216070
$634$	8.48147e14	0.328837
$635$	−3.59063e15	−1.38012
$636$	−1.10058e15	−0.419380
$637$	−1.04881e14	−0.0396214
$638$	−2.23504e14	−0.0837089
$639$	4.20770e14	0.156239
$640$	2.48116e15	0.913407
$641$	1.61205e15	0.588382	0.294191	−	0.955747i	$-0.404950\pi$
$641$	1.61205e15	0.588382	0.294191	+	0.955747i	$0.404950\pi$
$642$	1.64095e14	0.0593816
$643$	1.93481e15	0.694191	0.347095	−	0.937830i	$-0.387168\pi$
$643$	1.93481e15	0.694191	0.347095	+	0.937830i	$0.387168\pi$
$644$	1.42786e15	0.507940
$645$	−8.23385e13	−0.0290419
$646$	9.92565e14	0.347121
$647$	−1.38416e15	−0.479968	−0.239984	−	0.970777i	$-0.577142\pi$
$647$	−1.38416e15	−0.479968	−0.239984	+	0.970777i	$0.577142\pi$
$648$	1.47349e14	0.0506624
$649$	−2.06893e15	−0.705341
$650$	5.03968e13	0.0170365
$651$	6.39394e14	0.214325
$652$	3.18317e15	1.05803
$653$	−2.74612e15	−0.905101	−0.452550	−	0.891739i	$-0.649486\pi$
$653$	−2.74612e15	−0.905101	−0.452550	+	0.891739i	$0.649486\pi$
$654$	1.48081e14	0.0483975
$655$	4.78116e15	1.54955
$656$	−3.65753e15	−1.17548
$657$	−7.46096e14	−0.237785
$658$	4.91562e13	0.0155359
$659$	3.74005e15	1.17222	0.586108	−	0.810233i	$-0.300659\pi$
$659$	3.74005e15	1.17222	0.586108	+	0.810233i	$0.300659\pi$
$660$	2.08822e15	0.649058
$661$	−1.48350e15	−0.457277	−0.228638	−	0.973511i	$-0.573427\pi$
$661$	−1.48350e15	−0.457277	−0.228638	+	0.973511i	$0.573427\pi$
$662$	−3.51236e14	−0.107369
$663$	−4.75223e14	−0.144070
$664$	6.93344e14	0.208461
$665$	2.34359e15	0.698817
$666$	−8.24416e13	−0.0243802
$667$	−1.63500e15	−0.479541
$668$	4.56717e15	1.32855
$669$	−2.07119e15	−0.597554
$670$	−8.20932e14	−0.234907
$671$	1.68892e15	0.479330
$672$	5.05783e14	0.142375
$673$	4.85886e15	1.35660	0.678300	−	0.734785i	$-0.262717\pi$
$673$	4.85886e15	1.35660	0.678300	+	0.734785i	$0.262717\pi$
$674$	5.89251e14	0.163182
$675$	−1.83587e14	−0.0504279
$676$	−2.66819e14	−0.0726959
$677$	−3.57508e15	−0.966157	−0.483078	−	0.875577i	$-0.660481\pi$
$677$	−3.57508e15	−0.966157	−0.483078	+	0.875577i	$0.660481\pi$
$678$	−2.83298e14	−0.0759417
$679$	−5.08056e14	−0.135091
$680$	−1.74730e15	−0.460859
$681$	1.12929e15	0.295458
$682$	9.39400e14	0.243802
$683$	−4.30577e15	−1.10850	−0.554252	−	0.832349i	$-0.686996\pi$
$683$	−4.30577e15	−1.10850	−0.554252	+	0.832349i	$0.686996\pi$
$684$	−2.03010e15	−0.518453
$685$	−4.51891e15	−1.14481
$686$	−5.03655e13	−0.0126576
$687$	−3.44423e15	−0.858677
$688$	1.51745e14	0.0375298
$689$	8.68858e14	0.213178
$690$	−8.88282e14	−0.216212
$691$	−1.63764e15	−0.395448	−0.197724	−	0.980258i	$-0.563355\pi$
$691$	−1.63764e15	−0.395448	−0.197724	+	0.980258i	$0.563355\pi$
$692$	−1.72141e15	−0.412383
$693$	5.61331e14	0.133409
$694$	5.70447e14	0.134505
$695$	−2.77565e15	−0.649305
$696$	−3.82503e14	−0.0887737
$697$	5.47994e15	1.26181
$698$	1.27232e15	0.290664
$699$	2.85189e15	0.646409
$700$	−4.16194e14	−0.0935959
$701$	−6.14278e15	−1.37062	−0.685308	−	0.728253i	$-0.740333\pi$
$701$	−6.14278e15	−1.37062	−0.685308	+	0.728253i	$0.740333\pi$
$702$	−5.65195e13	−0.0125125
$703$	2.33772e15	0.513498
$704$	−3.32913e15	−0.725573
$705$	5.25898e14	0.113726
$706$	1.09159e15	0.234225
$707$	6.39977e14	0.136257
$708$	−1.72036e15	−0.363442
$709$	−7.63988e15	−1.60152	−0.800760	−	0.598986i	$-0.795571\pi$
$709$	−7.63988e15	−1.60152	−0.800760	+	0.598986i	$0.795571\pi$
$710$	−5.93424e14	−0.123437
$711$	−1.17611e15	−0.242754
$712$	2.32169e15	0.475514
$713$	6.87200e15	1.39666
$714$	−2.28209e14	−0.0460250
$715$	−1.64855e15	−0.329928
$716$	6.42417e15	1.27584
$717$	−5.17643e15	−1.02018
$718$	−1.98656e15	−0.388523
$719$	−6.49776e15	−1.26112	−0.630558	−	0.776142i	$-0.717174\pi$
$719$	−6.49776e15	−1.26112	−0.630558	+	0.776142i	$0.717174\pi$
$720$	1.62956e15	0.313863
$721$	3.00775e15	0.574908
$722$	−2.11158e15	−0.400547
$723$	4.74735e15	0.893698
$724$	4.65283e15	0.869271
$725$	4.76573e14	0.0883629
$726$	8.91995e13	0.0164139
$727$	4.58929e15	0.838120	0.419060	−	0.907959i	$-0.362360\pi$
$727$	4.58929e15	0.838120	0.419060	+	0.907959i	$0.362360\pi$
$728$	−2.63712e14	−0.0477977
$729$	2.05891e14	0.0370370
$730$	1.05224e15	0.187862
$731$	−2.27353e14	−0.0402861
$732$	1.40437e15	0.246985
$733$	9.38624e15	1.63840	0.819200	−	0.573509i	$-0.194418\pi$
$733$	9.38624e15	1.63840	0.819200	+	0.573509i	$0.194418\pi$
$734$	−7.83356e13	−0.0135716
$735$	−5.38836e14	−0.0926566
$736$	5.43600e15	0.927794
$737$	5.57558e15	0.944538
$738$	6.51744e14	0.109589
$739$	−1.00188e15	−0.167214	−0.0836069	−	0.996499i	$-0.526644\pi$
$739$	−1.00188e15	−0.167214	−0.0836069	+	0.996499i	$0.526644\pi$
$740$	−1.99951e15	−0.331245
$741$	1.60267e15	0.263539
$742$	4.17239e14	0.0681026
$743$	−6.83203e15	−1.10691	−0.553454	−	0.832880i	$-0.686691\pi$
$743$	−6.83203e15	−1.10691	−0.553454	+	0.832880i	$0.686691\pi$
$744$	1.60768e15	0.258553
$745$	−5.04519e14	−0.0805412
$746$	−6.78223e14	−0.107475
$747$	9.68810e14	0.152397
$748$	5.76598e15	0.900357
$749$	1.06983e15	0.165831
$750$	−7.29201e14	−0.112205
$751$	−7.57633e13	−0.0115728	−0.00578641	−	0.999983i	$-0.501842\pi$
$751$	−7.57633e13	−0.0115728	−0.00578641	+	0.999983i	$0.501842\pi$
$752$	−9.69196e14	−0.146965
$753$	1.18382e15	0.178202
$754$	1.46719e14	0.0219252
$755$	1.22197e15	0.181282
$756$	4.66758e14	0.0687420
$757$	−9.63682e15	−1.40899	−0.704493	−	0.709711i	$-0.748825\pi$
$757$	−9.63682e15	−1.40899	−0.704493	+	0.709711i	$0.748825\pi$
$758$	−1.13252e14	−0.0164386
$759$	6.03301e15	0.869369
$760$	5.89271e15	0.843024
$761$	1.13636e16	1.61399	0.806995	−	0.590558i	$-0.201092\pi$
$761$	1.13636e16	1.61399	0.806995	+	0.590558i	$0.201092\pi$
$762$	−1.17915e15	−0.166272
$763$	9.65432e14	0.135156
$764$	−7.78509e14	−0.108206
$765$	−2.44150e15	−0.336914
$766$	−6.81227e14	−0.0933327
$767$	1.35814e15	0.184744
$768$	−2.11441e15	−0.285563
$769$	−3.98712e15	−0.534643	−0.267322	−	0.963607i	$-0.586139\pi$
$769$	−3.98712e15	−0.534643	−0.267322	+	0.963607i	$0.586139\pi$
$770$	−7.91661e14	−0.105400
$771$	2.11477e15	0.279552
$772$	−1.18739e14	−0.0155847
$773$	2.50470e15	0.326414	0.163207	−	0.986592i	$-0.447816\pi$
$773$	2.50470e15	0.326414	0.163207	+	0.986592i	$0.447816\pi$
$774$	−2.70397e13	−0.00349886
$775$	−2.00306e15	−0.257357
$776$	−1.27745e15	−0.162969
$777$	−5.37486e14	−0.0680850
$778$	−1.89863e15	−0.238809
$779$	−1.84809e16	−2.30817
$780$	−1.37081e15	−0.170003
$781$	4.03040e15	0.496327
$782$	−2.45272e15	−0.299924
$783$	−5.34472e14	−0.0648986
$784$	9.93040e14	0.119737
$785$	−3.90508e14	−0.0467570
$786$	1.57012e15	0.186685
$787$	−8.06708e15	−0.952479	−0.476239	−	0.879316i	$-0.658000\pi$
$787$	−8.06708e15	−0.952479	−0.476239	+	0.879316i	$0.658000\pi$
$788$	−7.24866e15	−0.849892
$789$	2.61211e15	0.304136
$790$	1.65870e15	0.191787
$791$	−1.84699e15	−0.212077
$792$	1.41140e15	0.160940
$793$	−1.10869e15	−0.125547
$794$	2.98634e15	0.335835
$795$	4.46384e15	0.498528
$796$	−1.00253e16	−1.11193
$797$	−8.65777e15	−0.953642	−0.476821	−	0.879000i	$-0.658211\pi$
$797$	−8.65777e15	−0.953642	−0.476821	+	0.879000i	$0.658211\pi$
$798$	7.69629e14	0.0841910
$799$	1.45211e15	0.157758
$800$	−1.58450e15	−0.170961
$801$	3.24409e15	0.347628
$802$	−1.66717e15	−0.177428
$803$	−7.14658e15	−0.755375
$804$	4.63622e15	0.486694
$805$	−5.79124e15	−0.603802
$806$	−6.16668e14	−0.0638570
$807$	6.93592e15	0.713345
$808$	1.60915e15	0.164375
$809$	−1.29582e16	−1.31471	−0.657353	−	0.753583i	$-0.728324\pi$
$809$	−1.29582e16	−1.31471	−0.657353	+	0.753583i	$0.728324\pi$
$810$	−2.90374e14	−0.0292611
$811$	−1.09750e16	−1.09848	−0.549238	−	0.835666i	$-0.685082\pi$
$811$	−1.09750e16	−1.09848	−0.549238	+	0.835666i	$0.685082\pi$
$812$	−1.21166e15	−0.120454
$813$	1.11328e16	1.09927
$814$	−7.89677e14	−0.0774489
$815$	−1.29106e16	−1.25771
$816$	4.49953e15	0.435383
$817$	7.66741e14	0.0736932
$818$	−1.95662e15	−0.186794
$819$	−3.68485e14	−0.0349428
$820$	1.58072e16	1.48894
$821$	−1.40462e16	−1.31423	−0.657117	−	0.753788i	$-0.728224\pi$
$821$	−1.40462e16	−1.31423	−0.657117	+	0.753788i	$0.728224\pi$
$822$	−1.48400e15	−0.137923
$823$	−1.71565e16	−1.58391	−0.791954	−	0.610581i	$-0.790936\pi$
$823$	−1.71565e16	−1.58391	−0.791954	+	0.610581i	$0.790936\pi$
$824$	7.56266e15	0.693546
$825$	−1.75851e15	−0.160195
$826$	6.52202e14	0.0590190
$827$	−2.79350e15	−0.251113	−0.125556	−	0.992086i	$-0.540072\pi$
$827$	−2.79350e15	−0.251113	−0.125556	+	0.992086i	$0.540072\pi$
$828$	5.01657e15	0.447961
$829$	−2.18766e16	−1.94057	−0.970284	−	0.241967i	$-0.922207\pi$
$829$	−2.18766e16	−1.94057	−0.970284	+	0.241967i	$0.922207\pi$
$830$	−1.36634e15	−0.120401
$831$	−6.23822e15	−0.546079
$832$	2.18540e15	0.190044
$833$	−1.48783e15	−0.128531
$834$	−9.11515e14	−0.0782259
$835$	−1.85240e16	−1.57928
$836$	−1.94456e16	−1.64697
$837$	2.24642e15	0.189017
$838$	2.80581e15	0.234540
$839$	8.88511e15	0.737856	0.368928	−	0.929458i	$-0.379725\pi$
$839$	8.88511e15	0.737856	0.368928	+	0.929458i	$0.379725\pi$
$840$	−1.35484e15	−0.111777
$841$	−1.08131e16	−0.886281
$842$	−3.30850e15	−0.269411
$843$	1.19003e16	0.962730
$844$	4.40039e15	0.353678
$845$	1.08219e15	0.0864155
$846$	1.72703e14	0.0137014
$847$	5.81545e14	0.0458379
$848$	−8.22656e15	−0.644230
$849$	−9.96141e14	−0.0775048
$850$	7.14924e14	0.0552657
$851$	−5.77673e15	−0.443680
$852$	3.35137e15	0.255743
$853$	2.00288e16	1.51857	0.759284	−	0.650759i	$-0.225549\pi$
$853$	2.00288e16	1.51857	0.759284	+	0.650759i	$0.225549\pi$
$854$	−5.32410e14	−0.0401077
$855$	8.23388e15	0.616298
$856$	2.68997e15	0.200052
$857$	6.57226e15	0.485646	0.242823	−	0.970071i	$-0.421927\pi$
$857$	6.57226e15	0.485646	0.242823	+	0.970071i	$0.421927\pi$
$858$	−5.41380e14	−0.0397486
$859$	−2.25314e16	−1.64371	−0.821856	−	0.569695i	$-0.807061\pi$
$859$	−2.25314e16	−1.64371	−0.821856	+	0.569695i	$0.807061\pi$
$860$	−6.55813e14	−0.0475377
$861$	4.24911e15	0.306042
$862$	1.17788e15	0.0842967
$863$	−1.12538e16	−0.800273	−0.400137	−	0.916455i	$-0.631037\pi$
$863$	−1.12538e16	−0.800273	−0.400137	+	0.916455i	$0.631037\pi$
$864$	1.77700e15	0.125563
$865$	6.98185e15	0.490210
$866$	6.02774e15	0.420539
$867$	1.58660e15	0.109992
$868$	5.09267e15	0.350822
$869$	−1.12655e16	−0.771158
$870$	7.53782e14	0.0512731
$871$	−3.66009e15	−0.247395
$872$	2.42747e15	0.163047
$873$	−1.78498e15	−0.119139
$874$	8.27173e15	0.548635
$875$	−4.75410e15	−0.313346
$876$	−5.94253e15	−0.389223
$877$	−1.74524e16	−1.13594	−0.567972	−	0.823048i	$-0.692272\pi$
$877$	−1.74524e16	−1.13594	−0.567972	+	0.823048i	$0.692272\pi$
$878$	4.64399e15	0.300380
$879$	−1.49935e15	−0.0963747
$880$	1.56089e16	0.997052
$881$	−1.58773e16	−1.00788	−0.503940	−	0.863739i	$-0.668117\pi$
$881$	−1.58773e16	−1.00788	−0.503940	+	0.863739i	$0.668117\pi$
$882$	−1.76952e14	−0.0111629
$883$	8.49501e15	0.532574	0.266287	−	0.963894i	$-0.414203\pi$
$883$	8.49501e15	0.532574	0.266287	+	0.963894i	$0.414203\pi$
$884$	−3.78507e15	−0.235823
$885$	6.97759e15	0.432033
$886$	−4.29460e14	−0.0264264
$887$	−1.12820e16	−0.689935	−0.344967	−	0.938615i	$-0.612110\pi$
$887$	−1.12820e16	−0.689935	−0.344967	+	0.938615i	$0.612110\pi$
$888$	−1.35145e15	−0.0821351
$889$	−7.68761e15	−0.464335
$890$	−4.57524e15	−0.274643
$891$	1.97216e15	0.117656
$892$	−1.64967e16	−0.978117
$893$	−4.89719e15	−0.288579
$894$	−1.65683e14	−0.00970333
$895$	−2.60558e16	−1.51662
$896$	5.31220e15	0.307313
$897$	−3.96036e15	−0.227707
$898$	−2.82693e15	−0.161546
$899$	−5.83147e15	−0.331207
$900$	−1.46224e15	−0.0825439
$901$	1.23255e16	0.691544
$902$	6.24281e15	0.348132
$903$	−1.76288e14	−0.00977103
$904$	−4.64405e15	−0.255841
$905$	−1.88714e16	−1.03333
$906$	4.01293e14	0.0218402
$907$	−1.45358e16	−0.786320	−0.393160	−	0.919470i	$-0.628618\pi$
$907$	−1.45358e16	−0.786320	−0.393160	+	0.919470i	$0.628618\pi$
$908$	8.99461e15	0.483627
$909$	2.24847e15	0.120167
$910$	5.19685e14	0.0276066
$911$	2.36672e14	0.0124967	0.00624835	−	0.999980i	$-0.498011\pi$
$911$	2.36672e14	0.0124967	0.00624835	+	0.999980i	$0.498011\pi$
$912$	−1.51745e16	−0.796422
$913$	9.27987e15	0.484120
$914$	−4.51200e15	−0.233973
$915$	−5.69599e15	−0.293598
$916$	−2.74327e16	−1.40554
$917$	1.02365e16	0.521341
$918$	−8.01781e14	−0.0405902
$919$	−1.96128e16	−0.986972	−0.493486	−	0.869754i	$-0.664278\pi$
$919$	−1.96128e16	−0.986972	−0.493486	+	0.869754i	$0.664278\pi$
$920$	−1.45614e16	−0.728402
$921$	1.93762e16	0.963473
$922$	−2.29561e15	−0.113469
$923$	−2.64575e15	−0.129999
$924$	4.47091e15	0.218373
$925$	1.68381e15	0.0817550
$926$	−4.08814e15	−0.197317
$927$	1.05673e16	0.507021
$928$	−4.61290e15	−0.220019
$929$	8.02487e15	0.380497	0.190249	−	0.981736i	$-0.439071\pi$
$929$	8.02487e15	0.380497	0.190249	+	0.981736i	$0.439071\pi$
$930$	−3.16819e15	−0.149333
$931$	5.01767e15	0.235114
$932$	2.27148e16	1.05809
$933$	−1.85550e16	−0.859236
$934$	2.00511e14	0.00923062
$935$	−2.33862e16	−1.07028
$936$	−9.26514e14	−0.0421536
$937$	2.88710e16	1.30585	0.652926	−	0.757422i	$-0.273541\pi$
$937$	2.88710e16	1.30585	0.652926	+	0.757422i	$0.273541\pi$
$938$	−1.75763e15	−0.0790336
$939$	1.25019e16	0.558876
$940$	4.18869e15	0.186155
$941$	3.79236e16	1.67558	0.837792	−	0.545989i	$-0.183846\pi$
$941$	3.79236e16	1.67558	0.837792	+	0.545989i	$0.183846\pi$
$942$	−1.28242e14	−0.00563312
$943$	4.56681e16	1.99434
$944$	−1.28592e16	−0.558302
$945$	−1.89312e15	−0.0817154
$946$	−2.59003e14	−0.0111149
$947$	−1.80094e16	−0.768376	−0.384188	−	0.923255i	$-0.625519\pi$
$947$	−1.80094e16	−0.768376	−0.384188	+	0.923255i	$0.625519\pi$
$948$	−9.36753e15	−0.397356
$949$	4.69136e15	0.197849
$950$	−2.41106e15	−0.101095
$951$	1.94274e16	0.809882
$952$	−3.74100e15	−0.155054
$953$	1.61850e16	0.666963	0.333482	−	0.942757i	$-0.391776\pi$
$953$	1.61850e16	0.666963	0.333482	+	0.942757i	$0.391776\pi$
$954$	1.46591e15	0.0600608
$955$	3.15755e15	0.128627
$956$	−4.12294e16	−1.66989
$957$	−5.11951e15	−0.206164
$958$	3.80286e15	0.152265
$959$	−9.67506e15	−0.385169
$960$	1.12277e16	0.444426
$961$	−8.98459e14	−0.0353606
$962$	5.18383e14	0.0202856
$963$	3.75870e15	0.146249
$964$	3.78119e16	1.46287
$965$	4.81593e14	0.0185259
$966$	−1.90183e15	−0.0727439
$967$	1.90754e16	0.725485	0.362742	−	0.931889i	$-0.381841\pi$
$967$	1.90754e16	0.725485	0.362742	+	0.931889i	$0.381841\pi$
$968$	1.46223e15	0.0552970
$969$	2.27354e16	0.854913
$970$	2.51741e15	0.0941260
$971$	−8.27824e15	−0.307774	−0.153887	−	0.988088i	$-0.549179\pi$
$971$	−8.27824e15	−0.307774	−0.153887	+	0.988088i	$0.549179\pi$
$972$	1.63989e15	0.0606248
$973$	−5.94272e15	−0.218456
$974$	−3.12152e15	−0.114102
$975$	1.15437e15	0.0419586
$976$	1.04973e16	0.379407
$977$	2.74953e16	0.988184	0.494092	−	0.869410i	$-0.335501\pi$
$977$	2.74953e16	0.988184	0.494092	+	0.869410i	$0.335501\pi$
$978$	−4.23980e15	−0.151524
$979$	3.10740e16	1.10431
$980$	−4.29174e15	−0.151667
$981$	3.39191e15	0.119197
$982$	9.56065e15	0.334098
$983$	−3.98993e16	−1.38650	−0.693252	−	0.720695i	$-0.743823\pi$
$983$	−3.98993e16	−1.38650	−0.693252	+	0.720695i	$0.743823\pi$
$984$	1.06839e16	0.369196
$985$	2.93998e16	1.01029
$986$	2.08134e15	0.0711247
$987$	1.12596e15	0.0382629
$988$	1.27650e16	0.431379
$989$	−1.89469e15	−0.0636735
$990$	−2.78139e15	−0.0929540
$991$	−4.28702e16	−1.42479	−0.712394	−	0.701780i	$-0.752389\pi$
$991$	−4.28702e16	−1.42479	−0.712394	+	0.701780i	$0.752389\pi$
$992$	1.93883e16	0.640805
$993$	−8.04530e15	−0.264436
$994$	−1.27053e15	−0.0415299
$995$	4.06617e16	1.32178
$996$	7.71641e15	0.249453
$997$	−9.47475e15	−0.304610	−0.152305	−	0.988334i	$-0.548670\pi$
$997$	−9.47475e15	−0.304610	−0.152305	+	0.988334i	$0.548670\pi$
$998$	−5.01342e15	−0.160294
$999$	−1.88838e15	−0.0600454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-10.6087 q^{2} -243.000 q^{3} -1935.46 q^{4} +7850.01 q^{5} +2577.92 q^{6} +16807.0 q^{7} +42259.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-10.6087 q^{2} -243.000 q^{3} -1935.46 q^{4} +7850.01 q^{5} +2577.92 q^{6} +16807.0 q^{7} +42259.4 q^{8} +59049.0 q^{9} -83278.5 q^{10} +565609. q^{11} +470316. q^{12} -371293. q^{13} -178301. q^{14} -1.90755e6 q^{15} +3.51549e6 q^{16} -5.26713e6 q^{17} -626434. q^{18} +1.77632e7 q^{19} -1.51933e7 q^{20} -4.08410e6 q^{21} -6.00038e6 q^{22} -4.38946e7 q^{23} -1.02690e7 q^{24} +1.27945e7 q^{25} +3.93894e6 q^{26} -1.43489e7 q^{27} -3.25292e7 q^{28} +3.72483e7 q^{29} +2.02367e7 q^{30} -1.56557e8 q^{31} -1.23842e8 q^{32} -1.37443e8 q^{33} +5.58775e7 q^{34} +1.31935e8 q^{35} -1.14287e8 q^{36} +1.31605e8 q^{37} -1.88445e8 q^{38} +9.02242e7 q^{39} +3.31736e8 q^{40} -1.04040e9 q^{41} +4.33271e7 q^{42} +4.31645e7 q^{43} -1.09471e9 q^{44} +4.63535e8 q^{45} +4.65666e8 q^{46} -2.75693e8 q^{47} -8.54265e8 q^{48} +2.82475e8 q^{49} -1.35733e8 q^{50} +1.27991e9 q^{51} +7.18621e8 q^{52} -2.34009e9 q^{53} +1.52224e8 q^{54} +4.44003e9 q^{55} +7.10253e8 q^{56} -4.31647e9 q^{57} -3.95157e8 q^{58} -3.65787e9 q^{59} +3.69198e9 q^{60} +2.98602e9 q^{61} +1.66087e9 q^{62} +9.92437e8 q^{63} -5.88593e9 q^{64} -2.91465e9 q^{65} +1.45809e9 q^{66} +9.85767e9 q^{67} +1.01943e10 q^{68} +1.06664e10 q^{69} -1.39966e9 q^{70} +7.12578e9 q^{71} +2.49537e9 q^{72} -1.26352e10 q^{73} -1.39616e9 q^{74} -3.10906e9 q^{75} -3.43799e10 q^{76} +9.50618e9 q^{77} -9.57163e8 q^{78} -1.99176e10 q^{79} +2.75967e10 q^{80} +3.48678e9 q^{81} +1.10373e10 q^{82} +1.64069e10 q^{83} +7.90459e9 q^{84} -4.13470e10 q^{85} -4.57920e8 q^{86} -9.05133e9 q^{87} +2.39023e10 q^{88} +5.49390e10 q^{89} -4.91751e9 q^{90} -6.24032e9 q^{91} +8.49561e10 q^{92} +3.80433e10 q^{93} +2.92475e9 q^{94} +1.39442e11 q^{95} +3.00936e10 q^{96} -3.02288e10 q^{97} -2.99670e9 q^{98} +3.33986e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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