LMFDB - Embedded newform 273.12.a.c.1.16

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			1.16
Root			$92.3644$ 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)

$f(q)$	$=$	$q+88.3644 q^{2} -243.000 q^{3} +5760.27 q^{4} -1021.65 q^{5} -21472.6 q^{6} +16807.0 q^{7} +328033. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+88.3644 q^{2} -243.000 q^{3} +5760.27 q^{4} -1021.65 q^{5} -21472.6 q^{6} +16807.0 q^{7} +328033. q^{8} +59049.0 q^{9} -90277.5 q^{10} -819336. q^{11} -1.39975e6 q^{12} -371293. q^{13} +1.48514e6 q^{14} +248261. q^{15} +1.71894e7 q^{16} +3.09906e6 q^{17} +5.21783e6 q^{18} -9.03742e6 q^{19} -5.88498e6 q^{20} -4.08410e6 q^{21} -7.24002e7 q^{22} -4.70427e7 q^{23} -7.97120e7 q^{24} -4.77844e7 q^{25} -3.28091e7 q^{26} -1.43489e7 q^{27} +9.68129e7 q^{28} -5.65403e7 q^{29} +2.19374e7 q^{30} -9.85087e7 q^{31} +8.47121e8 q^{32} +1.99099e8 q^{33} +2.73846e8 q^{34} -1.71709e7 q^{35} +3.40138e8 q^{36} +8.98038e7 q^{37} -7.98586e8 q^{38} +9.02242e7 q^{39} -3.35135e8 q^{40} +6.18906e7 q^{41} -3.60889e8 q^{42} -4.55034e8 q^{43} -4.71960e9 q^{44} -6.03274e7 q^{45} -4.15690e9 q^{46} +1.44454e9 q^{47} -4.17703e9 q^{48} +2.82475e8 q^{49} -4.22244e9 q^{50} -7.53071e8 q^{51} -2.13875e9 q^{52} +1.88695e9 q^{53} -1.26793e9 q^{54} +8.37074e8 q^{55} +5.51325e9 q^{56} +2.19609e9 q^{57} -4.99616e9 q^{58} -1.01791e10 q^{59} +1.43005e9 q^{60} +6.35042e9 q^{61} -8.70467e9 q^{62} +9.92437e8 q^{63} +3.96515e10 q^{64} +3.79331e8 q^{65} +1.75932e10 q^{66} -1.30235e10 q^{67} +1.78514e10 q^{68} +1.14314e10 q^{69} -1.51729e9 q^{70} -1.68193e10 q^{71} +1.93700e10 q^{72} +1.49805e10 q^{73} +7.93547e9 q^{74} +1.16116e10 q^{75} -5.20580e10 q^{76} -1.37706e10 q^{77} +7.97261e9 q^{78} -4.30723e10 q^{79} -1.75616e10 q^{80} +3.48678e9 q^{81} +5.46893e9 q^{82} +2.80681e9 q^{83} -2.35255e10 q^{84} -3.16615e9 q^{85} -4.02088e10 q^{86} +1.37393e10 q^{87} -2.68769e11 q^{88} +1.02421e11 q^{89} -5.33079e9 q^{90} -6.24032e9 q^{91} -2.70979e11 q^{92} +2.39376e10 q^{93} +1.27646e11 q^{94} +9.23307e9 q^{95} -2.05851e11 q^{96} -8.57630e10 q^{97} +2.49608e10 q^{98} -4.83810e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	88.3644	1.95260	0.976298	−	0.216429i	$-0.0694410\pi$
$2$	88.3644	1.95260	0.976298	+	0.216429i	$0.0694410\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5760.27	2.81263
$5$	−1021.65	−0.146207	−0.0731033	−	0.997324i	$-0.523290\pi$
$5$	−1021.65	−0.146207	−0.0731033	+	0.997324i	$0.523290\pi$
$6$	−21472.6	−1.12733
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	328033.	3.53934
$9$	59049.0	0.333333
$10$	−90277.5	−0.285482
$11$	−819336.	−1.53392	−0.766959	−	0.641696i	$-0.778231\pi$
$11$	−819336.	−1.53392	−0.766959	+	0.641696i	$0.778231\pi$
$12$	−1.39975e6	−1.62388
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	1.48514e6	0.738012
$15$	248261.	0.0844124
$16$	1.71894e7	4.09828
$17$	3.09906e6	0.529371	0.264686	−	0.964335i	$-0.414732\pi$
$17$	3.09906e6	0.529371	0.264686	+	0.964335i	$0.414732\pi$
$18$	5.21783e6	0.650866
$19$	−9.03742e6	−0.837335	−0.418668	−	0.908140i	$-0.637503\pi$
$19$	−9.03742e6	−0.837335	−0.418668	+	0.908140i	$0.637503\pi$
$20$	−5.88498e6	−0.411226
$21$	−4.08410e6	−0.218218
$22$	−7.24002e7	−2.99512
$23$	−4.70427e7	−1.52401	−0.762007	−	0.647569i	$-0.775786\pi$
$23$	−4.70427e7	−1.52401	−0.762007	+	0.647569i	$0.775786\pi$
$24$	−7.97120e7	−2.04344
$25$	−4.77844e7	−0.978624
$26$	−3.28091e7	−0.541553
$27$	−1.43489e7	−0.192450
$28$	9.68129e7	1.06308
$29$	−5.65403e7	−0.511881	−0.255941	−	0.966692i	$-0.582385\pi$
$29$	−5.65403e7	−0.511881	−0.255941	+	0.966692i	$0.582385\pi$
$30$	2.19374e7	0.164823
$31$	−9.85087e7	−0.617996	−0.308998	−	0.951063i	$-0.599994\pi$
$31$	−9.85087e7	−0.617996	−0.308998	+	0.951063i	$0.599994\pi$
$32$	8.47121e8	4.46294
$33$	1.99099e8	0.885608
$34$	2.73846e8	1.03365
$35$	−1.71709e7	−0.0552609
$36$	3.40138e8	0.937545
$37$	8.98038e7	0.212905	0.106452	−	0.994318i	$-0.466051\pi$
$37$	8.98038e7	0.212905	0.106452	+	0.994318i	$0.466051\pi$
$38$	−7.98586e8	−1.63498
$39$	9.02242e7	0.160128
$40$	−3.35135e8	−0.517475
$41$	6.18906e7	0.0834283	0.0417142	−	0.999130i	$-0.486718\pi$
$41$	6.18906e7	0.0834283	0.0417142	+	0.999130i	$0.486718\pi$
$42$	−3.60889e8	−0.426092
$43$	−4.55034e8	−0.472028	−0.236014	−	0.971750i	$-0.575841\pi$
$43$	−4.55034e8	−0.472028	−0.236014	+	0.971750i	$0.575841\pi$
$44$	−4.71960e9	−4.31435
$45$	−6.03274e7	−0.0487355
$46$	−4.15690e9	−2.97579
$47$	1.44454e9	0.918738	0.459369	−	0.888246i	$-0.348076\pi$
$47$	1.44454e9	0.918738	0.459369	+	0.888246i	$0.348076\pi$
$48$	−4.17703e9	−2.36614
$49$	2.82475e8	0.142857
$50$	−4.22244e9	−1.91086
$51$	−7.53071e8	−0.305633
$52$	−2.13875e9	−0.780084
$53$	1.88695e9	0.619787	0.309893	−	0.950771i	$-0.399707\pi$
$53$	1.88695e9	0.619787	0.309893	+	0.950771i	$0.399707\pi$
$54$	−1.26793e9	−0.375777
$55$	8.37074e8	0.224269
$56$	5.51325e9	1.33775
$57$	2.19609e9	0.483436
$58$	−4.99616e9	−0.999498
$59$	−1.01791e10	−1.85363	−0.926816	−	0.375516i	$-0.877465\pi$
$59$	−1.01791e10	−1.85363	−0.926816	+	0.375516i	$0.877465\pi$
$60$	1.43005e9	0.237421
$61$	6.35042e9	0.962694	0.481347	−	0.876530i	$-0.340148\pi$
$61$	6.35042e9	0.962694	0.481347	+	0.876530i	$0.340148\pi$
$62$	−8.70467e9	−1.20670
$63$	9.92437e8	0.125988
$64$	3.96515e10	4.61604
$65$	3.79331e8	0.0405504
$66$	1.75932e10	1.72924
$67$	−1.30235e10	−1.17847	−0.589233	−	0.807963i	$-0.700570\pi$
$67$	−1.30235e10	−1.17847	−0.589233	+	0.807963i	$0.700570\pi$
$68$	1.78514e10	1.48893
$69$	1.14314e10	0.879890
$70$	−1.51729e9	−0.107902
$71$	−1.68193e10	−1.10633	−0.553167	−	0.833070i	$-0.686581\pi$
$71$	−1.68193e10	−1.10633	−0.553167	+	0.833070i	$0.686581\pi$
$72$	1.93700e10	1.17978
$73$	1.49805e10	0.845766	0.422883	−	0.906184i	$-0.361018\pi$
$73$	1.49805e10	0.845766	0.422883	+	0.906184i	$0.361018\pi$
$74$	7.93547e9	0.415717
$75$	1.16116e10	0.565009
$76$	−5.20580e10	−2.35512
$77$	−1.37706e10	−0.579767
$78$	7.97261e9	0.312666
$79$	−4.30723e10	−1.57489	−0.787444	−	0.616387i	$-0.788596\pi$
$79$	−4.30723e10	−1.57489	−0.787444	+	0.616387i	$0.788596\pi$
$80$	−1.75616e10	−0.599195
$81$	3.48678e9	0.111111
$82$	5.46893e9	0.162902
$83$	2.80681e9	0.0782139	0.0391069	−	0.999235i	$-0.487549\pi$
$83$	2.80681e9	0.0782139	0.0391069	+	0.999235i	$0.487549\pi$
$84$	−2.35255e10	−0.613767
$85$	−3.16615e9	−0.0773976
$86$	−4.02088e10	−0.921679
$87$	1.37393e10	0.295535
$88$	−2.68769e11	−5.42906
$89$	1.02421e11	1.94420	0.972102	−	0.234557i	$-0.0753639\pi$
$89$	1.02421e11	1.94420	0.972102	+	0.234557i	$0.0753639\pi$
$90$	−5.33079e9	−0.0951608
$91$	−6.24032e9	−0.104828
$92$	−2.70979e11	−4.28649
$93$	2.39376e10	0.356800
$94$	1.27646e11	1.79392
$95$	9.23307e9	0.122424
$96$	−2.05851e11	−2.57668
$97$	−8.57630e10	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$97$	−8.57630e10	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$98$	2.49608e10	0.278942
$99$	−4.83810e10	−0.511306
$100$	−2.75251e11	−2.75251
$101$	−1.18598e11	−1.12282	−0.561411	−	0.827537i	$-0.689741\pi$
$101$	−1.18598e11	−1.12282	−0.561411	+	0.827537i	$0.689741\pi$
$102$	−6.65447e10	−0.596777
$103$	−1.16400e11	−0.989350	−0.494675	−	0.869078i	$-0.664713\pi$
$103$	−1.16400e11	−0.989350	−0.494675	+	0.869078i	$0.664713\pi$
$104$	−1.21796e11	−0.981637
$105$	4.17252e9	0.0319049
$106$	1.66739e11	1.21019
$107$	2.77289e11	1.91127	0.955634	−	0.294557i	$-0.0951720\pi$
$107$	2.77289e11	1.91127	0.955634	+	0.294557i	$0.0951720\pi$
$108$	−8.26536e10	−0.541292
$109$	−2.29305e10	−0.142747	−0.0713735	−	0.997450i	$-0.522738\pi$
$109$	−2.29305e10	−0.142747	−0.0713735	+	0.997450i	$0.522738\pi$
$110$	7.39676e10	0.437907
$111$	−2.18223e10	−0.122921
$112$	2.88903e11	1.54900
$113$	1.28195e11	0.654544	0.327272	−	0.944930i	$-0.393871\pi$
$113$	1.28195e11	0.654544	0.327272	+	0.944930i	$0.393871\pi$
$114$	1.94056e11	0.943955
$115$	4.80611e10	0.222821
$116$	−3.25688e11	−1.43974
$117$	−2.19245e10	−0.0924500
$118$	−8.99471e11	−3.61939
$119$	5.20858e10	0.200084
$120$	8.14377e10	0.298764
$121$	3.86000e11	1.35291
$122$	5.61151e11	1.87975
$123$	−1.50394e10	−0.0481674
$124$	−5.67437e11	−1.73820
$125$	9.87041e10	0.289288
$126$	8.76961e10	0.246004
$127$	−7.06098e11	−1.89646	−0.948231	−	0.317580i	$-0.897130\pi$
$127$	−7.06098e11	−1.89646	−0.948231	+	0.317580i	$0.897130\pi$
$128$	1.76888e12	4.55033
$129$	1.10573e11	0.272525
$130$	3.35194e10	0.0791786
$131$	−1.67941e11	−0.380333	−0.190167	−	0.981752i	$-0.560903\pi$
$131$	−1.67941e11	−0.380333	−0.190167	+	0.981752i	$0.560903\pi$
$132$	1.14686e12	2.49089
$133$	−1.51892e11	−0.316483
$134$	−1.15082e12	−2.30107
$135$	1.46596e10	0.0281375
$136$	1.01659e12	1.87363
$137$	−4.95466e11	−0.877103	−0.438552	−	0.898706i	$-0.644508\pi$
$137$	−4.95466e11	−0.877103	−0.438552	+	0.898706i	$0.644508\pi$
$138$	1.01013e12	1.71807
$139$	1.03006e12	1.68376	0.841882	−	0.539661i	$-0.181448\pi$
$139$	1.03006e12	1.68376	0.841882	+	0.539661i	$0.181448\pi$
$140$	−9.89089e10	−0.155429
$141$	−3.51023e11	−0.530434
$142$	−1.48623e12	−2.16023
$143$	3.04214e11	0.425432
$144$	1.01502e12	1.36609
$145$	5.77644e10	0.0748404
$146$	1.32374e12	1.65144
$147$	−6.86415e10	−0.0824786
$148$	5.17295e11	0.598823
$149$	−1.61103e12	−1.79713	−0.898567	−	0.438836i	$-0.855391\pi$
$149$	−1.61103e12	−1.79713	−0.898567	+	0.438836i	$0.855391\pi$
$150$	1.02605e12	1.10323
$151$	2.97328e11	0.308221	0.154111	−	0.988054i	$-0.450749\pi$
$151$	2.97328e11	0.308221	0.154111	+	0.988054i	$0.450749\pi$
$152$	−2.96457e12	−2.96362
$153$	1.82996e11	0.176457
$154$	−1.21683e12	−1.13205
$155$	1.00641e11	0.0903550
$156$	5.19716e11	0.450382
$157$	1.12810e12	0.943839	0.471920	−	0.881642i	$-0.343561\pi$
$157$	1.12810e12	0.943839	0.471920	+	0.881642i	$0.343561\pi$
$158$	−3.80606e12	−3.07512
$159$	−4.58528e11	−0.357834
$160$	−8.65461e11	−0.652511
$161$	−7.90647e11	−0.576023
$162$	3.08108e11	0.216955
$163$	5.20703e11	0.354453	0.177226	−	0.984170i	$-0.443287\pi$
$163$	5.20703e11	0.354453	0.177226	+	0.984170i	$0.443287\pi$
$164$	3.56507e11	0.234653
$165$	−2.03409e11	−0.129482
$166$	2.48022e11	0.152720
$167$	−8.70065e11	−0.518336	−0.259168	−	0.965832i	$-0.583448\pi$
$167$	−8.70065e11	−0.518336	−0.259168	+	0.965832i	$0.583448\pi$
$168$	−1.33972e12	−0.772348
$169$	1.37858e11	0.0769231
$170$	−2.79775e11	−0.151126
$171$	−5.33650e11	−0.279112
$172$	−2.62112e12	−1.32764
$173$	6.44225e11	0.316070	0.158035	−	0.987433i	$-0.449484\pi$
$173$	6.44225e11	0.316070	0.158035	+	0.987433i	$0.449484\pi$
$174$	1.21407e12	0.577061
$175$	−8.03112e11	−0.369885
$176$	−1.40839e13	−6.28642
$177$	2.47352e12	1.07019
$178$	9.05033e12	3.79625
$179$	−3.07205e12	−1.24950	−0.624750	−	0.780825i	$-0.714799\pi$
$179$	−3.07205e12	−1.24950	−0.624750	+	0.780825i	$0.714799\pi$
$180$	−3.47502e11	−0.137075
$181$	−9.74738e11	−0.372954	−0.186477	−	0.982459i	$-0.559707\pi$
$181$	−9.74738e11	−0.372954	−0.186477	+	0.982459i	$0.559707\pi$
$182$	−5.51423e11	−0.204688
$183$	−1.54315e12	−0.555812
$184$	−1.54316e13	−5.39401
$185$	−9.17480e10	−0.0311281
$186$	2.11523e12	0.696686
$187$	−2.53917e12	−0.812012
$188$	8.32095e12	2.58407
$189$	−2.41162e11	−0.0727393
$190$	8.15875e11	0.239045
$191$	−4.53005e12	−1.28950	−0.644748	−	0.764395i	$-0.723038\pi$
$191$	−4.53005e12	−1.28950	−0.644748	+	0.764395i	$0.723038\pi$
$192$	−9.63531e12	−2.66507
$193$	3.68965e12	0.991791	0.495896	−	0.868382i	$-0.334840\pi$
$193$	3.68965e12	0.991791	0.495896	+	0.868382i	$0.334840\pi$
$194$	−7.57840e12	−1.98001
$195$	−9.21775e10	−0.0234118
$196$	1.62713e12	0.401805
$197$	−2.68038e12	−0.643625	−0.321812	−	0.946803i	$-0.604292\pi$
$197$	−2.68038e12	−0.643625	−0.321812	+	0.946803i	$0.604292\pi$
$198$	−4.27516e12	−0.998375
$199$	−3.97610e12	−0.903161	−0.451581	−	0.892230i	$-0.649140\pi$
$199$	−3.97610e12	−0.903161	−0.451581	+	0.892230i	$0.649140\pi$
$200$	−1.56748e13	−3.46368
$201$	3.16471e12	0.680387
$202$	−1.04799e13	−2.19242
$203$	−9.50273e11	−0.193473
$204$	−4.33789e12	−0.859633
$205$	−6.32305e10	−0.0121978
$206$	−1.02857e13	−1.93180
$207$	−2.77782e12	−0.508005
$208$	−6.38231e12	−1.13666
$209$	7.40468e12	1.28440
$210$	3.68702e11	0.0622974
$211$	5.34826e12	0.880357	0.440179	−	0.897910i	$-0.354915\pi$
$211$	5.34826e12	0.880357	0.440179	+	0.897910i	$0.354915\pi$
$212$	1.08693e13	1.74323
$213$	4.08709e12	0.638743
$214$	2.45025e13	3.73194
$215$	4.64885e11	0.0690135
$216$	−4.70692e12	−0.681147
$217$	−1.65564e12	−0.233580
$218$	−2.02624e12	−0.278727
$219$	−3.64026e12	−0.488303
$220$	4.82178e12	0.630786
$221$	−1.15066e12	−0.146821
$222$	−1.92832e12	−0.240014
$223$	1.54426e13	1.87518	0.937590	−	0.347743i	$-0.113052\pi$
$223$	1.54426e13	1.87518	0.937590	+	0.347743i	$0.113052\pi$
$224$	1.42376e13	1.68683
$225$	−2.82162e12	−0.326208
$226$	1.13279e13	1.27806
$227$	3.72499e12	0.410188	0.205094	−	0.978742i	$-0.434250\pi$
$227$	3.72499e12	0.410188	0.205094	+	0.978742i	$0.434250\pi$
$228$	1.26501e13	1.35973
$229$	−1.11113e13	−1.16592	−0.582961	−	0.812500i	$-0.698106\pi$
$229$	−1.11113e13	−1.16592	−0.582961	+	0.812500i	$0.698106\pi$
$230$	4.24690e12	0.435079
$231$	3.34625e12	0.334728
$232$	−1.85471e13	−1.81172
$233$	−1.39079e13	−1.32679	−0.663396	−	0.748269i	$-0.730885\pi$
$233$	−1.39079e13	−1.32679	−0.663396	+	0.748269i	$0.730885\pi$
$234$	−1.93734e12	−0.180518
$235$	−1.47581e12	−0.134326
$236$	−5.86344e13	−5.21359
$237$	1.04666e13	0.909262
$238$	4.60254e12	0.390682
$239$	−1.02727e13	−0.852113	−0.426056	−	0.904697i	$-0.640097\pi$
$239$	−1.02727e13	−0.852113	−0.426056	+	0.904697i	$0.640097\pi$
$240$	4.26746e12	0.345945
$241$	5.21905e12	0.413521	0.206761	−	0.978392i	$-0.433708\pi$
$241$	5.21905e12	0.413521	0.206761	+	0.978392i	$0.433708\pi$
$242$	3.41087e13	2.64168
$243$	−8.47289e11	−0.0641500
$244$	3.65801e13	2.70771
$245$	−2.88591e11	−0.0208867
$246$	−1.32895e12	−0.0940515
$247$	3.35553e12	0.232235
$248$	−3.23141e13	−2.18730
$249$	−6.82055e11	−0.0451568
$250$	8.72193e12	0.564862
$251$	−1.20702e12	−0.0764733	−0.0382367	−	0.999269i	$-0.512174\pi$
$251$	−1.20702e12	−0.0764733	−0.0382367	+	0.999269i	$0.512174\pi$
$252$	5.71671e12	0.354359
$253$	3.85438e13	2.33771
$254$	−6.23939e13	−3.70303
$255$	7.69374e11	0.0446855
$256$	7.50996e13	4.26892
$257$	−1.42800e13	−0.794504	−0.397252	−	0.917710i	$-0.630036\pi$
$257$	−1.42800e13	−0.794504	−0.397252	+	0.917710i	$0.630036\pi$
$258$	9.77074e12	0.532132
$259$	1.50933e12	0.0804705
$260$	2.18505e12	0.114053
$261$	−3.33865e12	−0.170627
$262$	−1.48400e13	−0.742637
$263$	1.97262e12	0.0966687	0.0483343	−	0.998831i	$-0.484609\pi$
$263$	1.97262e12	0.0966687	0.0483343	+	0.998831i	$0.484609\pi$
$264$	6.53109e13	3.13447
$265$	−1.92780e12	−0.0906169
$266$	−1.34218e13	−0.617964
$267$	−2.48882e13	−1.12249
$268$	−7.50190e13	−3.31459
$269$	1.71769e13	0.743544	0.371772	−	0.928324i	$-0.378750\pi$
$269$	1.71769e13	0.743544	0.371772	+	0.928324i	$0.378750\pi$
$270$	1.29538e12	0.0549411
$271$	−3.31167e13	−1.37631	−0.688154	−	0.725565i	$-0.741579\pi$
$271$	−3.31167e13	−1.37631	−0.688154	+	0.725565i	$0.741579\pi$
$272$	5.32710e13	2.16951
$273$	1.51640e12	0.0605228
$274$	−4.37816e13	−1.71263
$275$	3.91514e13	1.50113
$276$	6.58479e13	2.47481
$277$	1.15285e13	0.424749	0.212375	−	0.977188i	$-0.431880\pi$
$277$	1.15285e13	0.424749	0.212375	+	0.977188i	$0.431880\pi$
$278$	9.10207e13	3.28771
$279$	−5.81684e12	−0.205999
$280$	−5.63261e12	−0.195587
$281$	3.70520e13	1.26162	0.630808	−	0.775939i	$-0.282723\pi$
$281$	3.70520e13	1.26162	0.630808	+	0.775939i	$0.282723\pi$
$282$	−3.10180e13	−1.03572
$283$	1.19738e13	0.392108	0.196054	−	0.980593i	$-0.437187\pi$
$283$	1.19738e13	0.392108	0.196054	+	0.980593i	$0.437187\pi$
$284$	−9.68837e13	−3.11171
$285$	−2.24364e12	−0.0706815
$286$	2.68817e13	0.830698
$287$	1.04020e12	0.0315329
$288$	5.00217e13	1.48765
$289$	−2.46677e13	−0.719766
$290$	5.10432e12	0.146133
$291$	2.08404e13	0.585457
$292$	8.62917e13	2.37883
$293$	−2.83237e12	−0.0766263	−0.0383131	−	0.999266i	$-0.512198\pi$
$293$	−2.83237e12	−0.0766263	−0.0383131	+	0.999266i	$0.512198\pi$
$294$	−6.06547e12	−0.161047
$295$	1.03995e13	0.271013
$296$	2.94586e13	0.753543
$297$	1.17566e13	0.295203
$298$	−1.42358e14	−3.50908
$299$	1.74666e13	0.422686
$300$	6.68860e13	1.58916
$301$	−7.64776e12	−0.178410
$302$	2.62732e13	0.601832
$303$	2.88194e13	0.648262
$304$	−1.55348e14	−3.43163
$305$	−6.48790e12	−0.140752
$306$	1.61704e13	0.344550
$307$	−6.03266e12	−0.126255	−0.0631274	−	0.998005i	$-0.520107\pi$
$307$	−6.03266e12	−0.126255	−0.0631274	+	0.998005i	$0.520107\pi$
$308$	−7.93223e13	−1.63067
$309$	2.82853e13	0.571201
$310$	8.89312e12	0.176427
$311$	9.64194e12	0.187924	0.0939620	−	0.995576i	$-0.470047\pi$
$311$	9.64194e12	0.187924	0.0939620	+	0.995576i	$0.470047\pi$
$312$	2.95965e13	0.566749
$313$	9.54252e13	1.79543	0.897717	−	0.440573i	$-0.145225\pi$
$313$	9.54252e13	1.79543	0.897717	+	0.440573i	$0.145225\pi$
$314$	9.96836e13	1.84294
$315$	−1.01392e12	−0.0184203
$316$	−2.48109e14	−4.42958
$317$	8.55644e13	1.50130	0.750650	−	0.660701i	$-0.229741\pi$
$317$	8.55644e13	1.50130	0.750650	+	0.660701i	$0.229741\pi$
$318$	−4.05176e13	−0.698706
$319$	4.63255e13	0.785185
$320$	−4.05099e13	−0.674895
$321$	−6.73812e13	−1.10347
$322$	−6.98650e13	−1.12474
$323$	−2.80075e13	−0.443261
$324$	2.00848e13	0.312515
$325$	1.77420e13	0.271421
$326$	4.60117e13	0.692104
$327$	5.57210e12	0.0824150
$328$	2.03022e13	0.295282
$329$	2.42784e13	0.347250
$330$	−1.79741e13	−0.252826
$331$	3.39683e13	0.469915	0.234958	−	0.972006i	$-0.424505\pi$
$331$	3.39683e13	0.469915	0.234958	+	0.972006i	$0.424505\pi$
$332$	1.61680e13	0.219987
$333$	5.30283e12	0.0709683
$334$	−7.68828e13	−1.01210
$335$	1.33055e13	0.172299
$336$	−7.02033e13	−0.894317
$337$	−2.54143e13	−0.318504	−0.159252	−	0.987238i	$-0.550908\pi$
$337$	−2.54143e13	−0.318504	−0.159252	+	0.987238i	$0.550908\pi$
$338$	1.21818e13	0.150200
$339$	−3.11513e13	−0.377901
$340$	−1.82379e13	−0.217691
$341$	8.07118e13	0.947955
$342$	−4.71557e13	−0.544993
$343$	4.74756e12	0.0539949
$344$	−1.49266e14	−1.67067
$345$	−1.16789e13	−0.128646
$346$	5.69266e13	0.617158
$347$	−5.16476e13	−0.551109	−0.275555	−	0.961285i	$-0.588862\pi$
$347$	−5.16476e13	−0.551109	−0.275555	+	0.961285i	$0.588862\pi$
$348$	7.91422e13	0.831232
$349$	4.31030e13	0.445623	0.222812	−	0.974862i	$-0.428477\pi$
$349$	4.31030e13	0.445623	0.222812	+	0.974862i	$0.428477\pi$
$350$	−7.09665e13	−0.722236
$351$	5.32765e12	0.0533761
$352$	−6.94077e14	−6.84578
$353$	−7.47176e13	−0.725542	−0.362771	−	0.931878i	$-0.618169\pi$
$353$	−7.47176e13	−0.725542	−0.362771	+	0.931878i	$0.618169\pi$
$354$	2.18571e14	2.08966
$355$	1.71834e13	0.161753
$356$	5.89970e14	5.46834
$357$	−1.26569e13	−0.115518
$358$	−2.71460e14	−2.43977
$359$	1.40180e14	1.24070	0.620348	−	0.784327i	$-0.286991\pi$
$359$	1.40180e14	1.24070	0.620348	+	0.784327i	$0.286991\pi$
$360$	−1.97894e13	−0.172492
$361$	−3.48154e13	−0.298869
$362$	−8.61321e13	−0.728229
$363$	−9.37980e13	−0.781101
$364$	−3.59460e13	−0.294844
$365$	−1.53048e13	−0.123656
$366$	−1.36360e14	−1.08528
$367$	1.20173e14	0.942204	0.471102	−	0.882079i	$-0.343856\pi$
$367$	1.20173e14	0.942204	0.471102	+	0.882079i	$0.343856\pi$
$368$	−8.08636e14	−6.24583
$369$	3.65458e12	0.0278094
$370$	−8.10726e12	−0.0607806
$371$	3.17139e13	0.234257
$372$	1.37887e14	1.00355
$373$	7.53606e13	0.540438	0.270219	−	0.962799i	$-0.412904\pi$
$373$	7.53606e13	0.540438	0.270219	+	0.962799i	$0.412904\pi$
$374$	−2.24372e14	−1.58553
$375$	−2.39851e13	−0.167020
$376$	4.73857e14	3.25173
$377$	2.09930e13	0.141970
$378$	−2.13102e13	−0.142031
$379$	−2.35858e14	−1.54930	−0.774648	−	0.632392i	$-0.782073\pi$
$379$	−2.35858e14	−1.54930	−0.774648	+	0.632392i	$0.782073\pi$
$380$	5.31850e13	0.344334
$381$	1.71582e14	1.09492
$382$	−4.00296e14	−2.51787
$383$	−1.95745e14	−1.21366	−0.606831	−	0.794831i	$-0.707560\pi$
$383$	−1.95745e14	−1.21366	−0.606831	+	0.794831i	$0.707560\pi$
$384$	−4.29837e14	−2.62713
$385$	1.40687e13	0.0847657
$386$	3.26034e14	1.93657
$387$	−2.68693e13	−0.157343
$388$	−4.94018e14	−2.85213
$389$	7.45447e13	0.424320	0.212160	−	0.977235i	$-0.431950\pi$
$389$	7.45447e13	0.424320	0.212160	+	0.977235i	$0.431950\pi$
$390$	−8.14521e12	−0.0457138
$391$	−1.45788e14	−0.806769
$392$	9.26612e13	0.505620
$393$	4.08096e13	0.219585
$394$	−2.36851e14	−1.25674
$395$	4.40048e13	0.230259
$396$	−2.78688e14	−1.43812
$397$	3.80265e14	1.93525	0.967627	−	0.252384i	$-0.0812147\pi$
$397$	3.80265e14	1.93525	0.967627	+	0.252384i	$0.0812147\pi$
$398$	−3.51346e14	−1.76351
$399$	3.69097e13	0.182722
$400$	−8.21385e14	−4.01067
$401$	1.45243e14	0.699524	0.349762	−	0.936839i	$-0.386262\pi$
$401$	1.45243e14	0.699524	0.349762	+	0.936839i	$0.386262\pi$
$402$	2.79648e14	1.32852
$403$	3.65756e13	0.171401
$404$	−6.83159e14	−3.15809
$405$	−3.56227e12	−0.0162452
$406$	−8.39704e13	−0.377775
$407$	−7.35795e13	−0.326579
$408$	−2.47032e14	−1.08174
$409$	3.05173e14	1.31846	0.659232	−	0.751940i	$-0.270882\pi$
$409$	3.05173e14	1.31846	0.659232	+	0.751940i	$0.270882\pi$
$410$	−5.58733e12	−0.0238173
$411$	1.20398e14	0.506396
$412$	−6.70498e14	−2.78268
$413$	−1.71080e14	−0.700607
$414$	−2.45461e14	−0.991929
$415$	−2.86758e12	−0.0114354
$416$	−3.14530e14	−1.23780
$417$	−2.50305e14	−0.972122
$418$	6.54310e14	2.50792
$419$	−3.02764e14	−1.14532	−0.572659	−	0.819793i	$-0.694088\pi$
$419$	−3.02764e14	−1.14532	−0.572659	+	0.819793i	$0.694088\pi$
$420$	2.40349e13	0.0897368
$421$	3.53420e13	0.130238	0.0651192	−	0.997877i	$-0.479257\pi$
$421$	3.53420e13	0.130238	0.0651192	+	0.997877i	$0.479257\pi$
$422$	4.72596e14	1.71898
$423$	8.52987e13	0.306246
$424$	6.18981e14	2.19364
$425$	−1.48086e14	−0.518055
$426$	3.61153e14	1.24721
$427$	1.06731e14	0.363864
$428$	1.59726e15	5.37570
$429$	−7.39239e13	−0.245624
$430$	4.10793e13	0.134756
$431$	−3.35573e14	−1.08683	−0.543416	−	0.839464i	$-0.682869\pi$
$431$	−3.35573e14	−1.08683	−0.543416	+	0.839464i	$0.682869\pi$
$432$	−2.46649e14	−0.788714
$433$	−1.91248e14	−0.603829	−0.301914	−	0.953335i	$-0.597626\pi$
$433$	−1.91248e14	−0.603829	−0.301914	+	0.953335i	$0.597626\pi$
$434$	−1.46299e14	−0.456088
$435$	−1.40367e13	−0.0432091
$436$	−1.32086e14	−0.401495
$437$	4.25144e14	1.27611
$438$	−3.21669e14	−0.953459
$439$	4.62864e14	1.35487	0.677437	−	0.735581i	$-0.263091\pi$
$439$	4.62864e14	1.35487	0.677437	+	0.735581i	$0.263091\pi$
$440$	2.74588e14	0.793765
$441$	1.66799e13	0.0476190
$442$	−1.01677e14	−0.286683
$443$	4.40139e14	1.22566	0.612829	−	0.790215i	$-0.290031\pi$
$443$	4.40139e14	1.22566	0.612829	+	0.790215i	$0.290031\pi$
$444$	−1.25703e14	−0.345731
$445$	−1.04638e14	−0.284255
$446$	1.36457e15	3.66147
$447$	3.91481e14	1.03758
$448$	6.66423e14	1.74470
$449$	−3.59098e14	−0.928662	−0.464331	−	0.885662i	$-0.653705\pi$
$449$	−3.59098e14	−0.928662	−0.464331	+	0.885662i	$0.653705\pi$
$450$	−2.49331e14	−0.636952
$451$	−5.07092e13	−0.127972
$452$	7.38437e14	1.84099
$453$	−7.22507e13	−0.177952
$454$	3.29157e14	0.800932
$455$	6.37542e12	0.0153266
$456$	7.20391e14	1.71105
$457$	3.30623e14	0.775880	0.387940	−	0.921685i	$-0.373187\pi$
$457$	3.30623e14	0.775880	0.387940	+	0.921685i	$0.373187\pi$
$458$	−9.81843e14	−2.27657
$459$	−4.44681e13	−0.101878
$460$	2.76845e14	0.626714
$461$	3.46668e14	0.775460	0.387730	−	0.921773i	$-0.373259\pi$
$461$	3.46668e14	0.775460	0.387730	+	0.921773i	$0.373259\pi$
$462$	2.95690e14	0.653590
$463$	7.33943e14	1.60312	0.801561	−	0.597912i	$-0.204003\pi$
$463$	7.33943e14	1.60312	0.801561	+	0.597912i	$0.204003\pi$
$464$	−9.71895e14	−2.09783
$465$	−2.44559e13	−0.0521665
$466$	−1.22896e15	−2.59069
$467$	6.84234e14	1.42548	0.712741	−	0.701428i	$-0.247454\pi$
$467$	6.84234e14	1.42548	0.712741	+	0.701428i	$0.247454\pi$
$468$	−1.26291e14	−0.260028
$469$	−2.18886e14	−0.445418
$470$	−1.30410e14	−0.262284
$471$	−2.74127e14	−0.544926
$472$	−3.33908e15	−6.56064
$473$	3.72826e14	0.724052
$474$	9.24873e14	1.77542
$475$	4.31847e14	0.819436
$476$	3.00029e14	0.562762
$477$	1.11422e14	0.206596
$478$	−9.07743e14	−1.66383
$479$	−1.12631e14	−0.204086	−0.102043	−	0.994780i	$-0.532538\pi$
$479$	−1.12631e14	−0.204086	−0.102043	+	0.994780i	$0.532538\pi$
$480$	2.10307e14	0.376727
$481$	−3.33435e13	−0.0590492
$482$	4.61179e14	0.807441
$483$	1.92127e14	0.332567
$484$	2.22347e15	3.80523
$485$	8.76197e13	0.148259
$486$	−7.48702e13	−0.125259
$487$	−6.66535e14	−1.10259	−0.551295	−	0.834311i	$-0.685866\pi$
$487$	−6.66535e14	−1.10259	−0.551295	+	0.834311i	$0.685866\pi$
$488$	2.08315e15	3.40730
$489$	−1.26531e14	−0.204644
$490$	−2.55012e13	−0.0407832
$491$	1.01477e15	1.60479	0.802394	−	0.596795i	$-0.203559\pi$
$491$	1.01477e15	1.60479	0.802394	+	0.596795i	$0.203559\pi$
$492$	−8.66312e13	−0.135477
$493$	−1.75222e14	−0.270975
$494$	2.96509e14	0.453461
$495$	4.94284e13	0.0747563
$496$	−1.69331e15	−2.53272
$497$	−2.82682e14	−0.418155
$498$	−6.02694e13	−0.0881730
$499$	−9.33311e13	−0.135043	−0.0675217	−	0.997718i	$-0.521509\pi$
$499$	−9.33311e13	−0.135043	−0.0675217	+	0.997718i	$0.521509\pi$
$500$	5.68563e14	0.813661
$501$	2.11426e14	0.299261
$502$	−1.06658e14	−0.149322
$503$	−9.26596e14	−1.28312	−0.641559	−	0.767074i	$-0.721712\pi$
$503$	−9.26596e14	−1.28312	−0.641559	+	0.767074i	$0.721712\pi$
$504$	3.25552e14	0.445915
$505$	1.21166e14	0.164164
$506$	3.40590e15	4.56461
$507$	−3.34996e13	−0.0444116
$508$	−4.06732e15	−5.33406
$509$	−1.60046e14	−0.207634	−0.103817	−	0.994596i	$-0.533106\pi$
$509$	−1.60046e14	−0.207634	−0.103817	+	0.994596i	$0.533106\pi$
$510$	6.79853e13	0.0872528
$511$	2.51777e14	0.319669
$512$	3.01347e15	3.78514
$513$	1.29677e14	0.161145
$514$	−1.26184e15	−1.55135
$515$	1.18920e14	0.144649
$516$	6.36932e14	0.766514
$517$	−1.18356e15	−1.40927
$518$	1.33371e14	0.157126
$519$	−1.56547e14	−0.182483
$520$	1.24433e14	0.143522
$521$	9.93135e14	1.13345	0.566723	−	0.823909i	$-0.308211\pi$
$521$	9.93135e14	1.13345	0.566723	+	0.823909i	$0.308211\pi$
$522$	−2.95018e14	−0.333166
$523$	−9.97503e14	−1.11469	−0.557346	−	0.830280i	$-0.688180\pi$
$523$	−9.97503e14	−1.11469	−0.557346	+	0.830280i	$0.688180\pi$
$524$	−9.67385e14	−1.06974
$525$	1.95156e14	0.213553
$526$	1.74309e14	0.188755
$527$	−3.05284e14	−0.327149
$528$	3.42239e15	3.62947
$529$	1.26021e15	1.32262
$530$	−1.70349e14	−0.176938
$531$	−6.01066e14	−0.617877
$532$	−8.74939e14	−0.890151
$533$	−2.29796e13	−0.0231389
$534$	−2.19923e15	−2.19176
$535$	−2.83292e14	−0.279440
$536$	−4.27214e15	−4.17099
$537$	7.46507e14	0.721399
$538$	1.51782e15	1.45184
$539$	−2.31442e14	−0.219131
$540$	8.44430e13	0.0791404
$541$	9.33331e13	0.0865866	0.0432933	−	0.999062i	$-0.486215\pi$
$541$	9.33331e13	0.0865866	0.0432933	+	0.999062i	$0.486215\pi$
$542$	−2.92634e15	−2.68737
$543$	2.36861e14	0.215325
$544$	2.62528e15	2.36255
$545$	2.34269e13	0.0208705
$546$	1.33996e14	0.118177
$547$	3.27112e14	0.285605	0.142803	−	0.989751i	$-0.454389\pi$
$547$	3.27112e14	0.285605	0.142803	+	0.989751i	$0.454389\pi$
$548$	−2.85402e15	−2.46697
$549$	3.74986e14	0.320898
$550$	3.45960e15	2.93110
$551$	5.10979e14	0.428616
$552$	3.74987e15	3.11423
$553$	−7.23917e14	−0.595251
$554$	1.01871e15	0.829364
$555$	2.22948e13	0.0179718
$556$	5.93343e15	4.73581
$557$	2.63953e14	0.208604	0.104302	−	0.994546i	$-0.466739\pi$
$557$	2.63953e14	0.208604	0.104302	+	0.994546i	$0.466739\pi$
$558$	−5.14002e14	−0.402232
$559$	1.68951e14	0.130917
$560$	−2.95157e14	−0.226474
$561$	6.17018e14	0.468816
$562$	3.27408e15	2.46343
$563$	−2.90714e14	−0.216606	−0.108303	−	0.994118i	$-0.534542\pi$
$563$	−2.90714e14	−0.216606	−0.108303	+	0.994118i	$0.534542\pi$
$564$	−2.02199e15	−1.49192
$565$	−1.30970e14	−0.0956986
$566$	1.05806e15	0.765629
$567$	5.86024e13	0.0419961
$568$	−5.51728e15	−3.91570
$569$	−2.14560e15	−1.50811	−0.754054	−	0.656813i	$-0.771904\pi$
$569$	−2.14560e15	−1.50811	−0.754054	+	0.656813i	$0.771904\pi$
$570$	−1.98258e14	−0.138012
$571$	−2.53896e14	−0.175048	−0.0875242	−	0.996162i	$-0.527896\pi$
$571$	−2.53896e14	−0.175048	−0.0875242	+	0.996162i	$0.527896\pi$
$572$	1.75235e15	1.19659
$573$	1.10080e15	0.744491
$574$	9.19163e13	0.0615711
$575$	2.24790e15	1.49144
$576$	2.34138e15	1.53868
$577$	−1.93022e15	−1.25643	−0.628216	−	0.778039i	$-0.716215\pi$
$577$	−1.93022e15	−1.25643	−0.628216	+	0.778039i	$0.716215\pi$
$578$	−2.17975e15	−1.40541
$579$	−8.96586e14	−0.572611
$580$	3.32739e14	0.210499
$581$	4.71741e13	0.0295621
$582$	1.84155e15	1.14316
$583$	−1.54604e15	−0.950703
$584$	4.91409e15	2.99345
$585$	2.23991e13	0.0135168
$586$	−2.50281e14	−0.149620
$587$	2.75845e14	0.163364	0.0816819	−	0.996658i	$-0.473971\pi$
$587$	2.75845e14	0.163364	0.0816819	+	0.996658i	$0.473971\pi$
$588$	−3.95394e14	−0.231982
$589$	8.90264e14	0.517470
$590$	9.18944e14	0.529179
$591$	6.51333e14	0.371597
$592$	1.54368e15	0.872543
$593$	2.28455e15	1.27938	0.639690	−	0.768633i	$-0.279063\pi$
$593$	2.28455e15	1.27938	0.639690	+	0.768633i	$0.279063\pi$
$594$	1.03886e15	0.576412
$595$	−5.32135e13	−0.0292535
$596$	−9.28000e15	−5.05468
$597$	9.66192e14	0.521441
$598$	1.54343e15	0.825334
$599$	−8.19998e14	−0.434475	−0.217238	−	0.976119i	$-0.569705\pi$
$599$	−8.19998e14	−0.434475	−0.217238	+	0.976119i	$0.569705\pi$
$600$	3.80899e15	1.99976
$601$	−1.94659e15	−1.01266	−0.506332	−	0.862339i	$-0.668999\pi$
$601$	−1.94659e15	−1.01266	−0.506332	+	0.862339i	$0.668999\pi$
$602$	−6.75790e14	−0.348362
$603$	−7.69026e14	−0.392822
$604$	1.71269e15	0.866913
$605$	−3.94357e14	−0.197804
$606$	2.54661e15	1.26579
$607$	−1.79707e14	−0.0885172	−0.0442586	−	0.999020i	$-0.514093\pi$
$607$	−1.79707e14	−0.0885172	−0.0442586	+	0.999020i	$0.514093\pi$
$608$	−7.65579e15	−3.73698
$609$	2.30916e14	0.111702
$610$	−5.73300e14	−0.274832
$611$	−5.36348e14	−0.254812
$612$	1.05411e15	0.496309
$613$	−2.46205e15	−1.14885	−0.574426	−	0.818556i	$-0.694775\pi$
$613$	−2.46205e15	−1.14885	−0.574426	+	0.818556i	$0.694775\pi$
$614$	−5.33073e14	−0.246525
$615$	1.53650e13	0.00704239
$616$	−4.51721e15	−2.05199
$617$	1.02774e15	0.462716	0.231358	−	0.972869i	$-0.425683\pi$
$617$	1.02774e15	0.462716	0.231358	+	0.972869i	$0.425683\pi$
$618$	2.49941e15	1.11533
$619$	4.28906e15	1.89698	0.948492	−	0.316800i	$-0.102609\pi$
$619$	4.28906e15	1.89698	0.948492	+	0.316800i	$0.102609\pi$
$620$	5.79722e14	0.254136
$621$	6.75011e14	0.293297
$622$	8.52005e14	0.366940
$623$	1.72138e15	0.734840
$624$	1.55090e15	0.656249
$625$	2.23238e15	0.936328
$626$	8.43220e15	3.50576
$627$	−1.79934e15	−0.741551
$628$	6.49815e15	2.65468
$629$	2.78307e14	0.112706
$630$	−8.95947e13	−0.0359674
$631$	−2.57864e14	−0.102619	−0.0513096	−	0.998683i	$-0.516340\pi$
$631$	−2.57864e14	−0.102619	−0.0513096	+	0.998683i	$0.516340\pi$
$632$	−1.41292e16	−5.57407
$633$	−1.29963e15	−0.508274
$634$	7.56085e15	2.93143
$635$	7.21384e14	0.277275
$636$	−2.64125e15	−1.00646
$637$	−1.04881e14	−0.0396214
$638$	4.09353e15	1.53315
$639$	−9.93162e14	−0.368778
$640$	−1.80717e15	−0.665288
$641$	3.02473e15	1.10400	0.551998	−	0.833845i	$-0.313865\pi$
$641$	3.02473e15	1.10400	0.551998	+	0.833845i	$0.313865\pi$
$642$	−5.95410e15	−2.15463
$643$	3.17115e15	1.13777	0.568887	−	0.822416i	$-0.307374\pi$
$643$	3.17115e15	1.13777	0.568887	+	0.822416i	$0.307374\pi$
$644$	−4.55434e15	−1.62014
$645$	−1.12967e14	−0.0398450
$646$	−2.47486e15	−0.865511
$647$	−3.03976e15	−1.05406	−0.527030	−	0.849847i	$-0.676694\pi$
$647$	−3.03976e15	−1.05406	−0.527030	+	0.849847i	$0.676694\pi$
$648$	1.14378e15	0.393260
$649$	8.34011e15	2.84332
$650$	1.56776e15	0.529976
$651$	4.02320e14	0.134858
$652$	2.99939e15	0.996947
$653$	2.43874e15	0.803792	0.401896	−	0.915685i	$-0.368351\pi$
$653$	2.43874e15	0.803792	0.401896	+	0.915685i	$0.368351\pi$
$654$	4.92375e14	0.160923
$655$	1.71577e14	0.0556072
$656$	1.06386e15	0.341912
$657$	8.84582e14	0.281922
$658$	2.14535e15	0.678040
$659$	1.85499e15	0.581397	0.290699	−	0.956815i	$-0.406112\pi$
$659$	1.85499e15	0.581397	0.290699	+	0.956815i	$0.406112\pi$
$660$	−1.17169e15	−0.364185
$661$	−3.90726e15	−1.20438	−0.602192	−	0.798352i	$-0.705706\pi$
$661$	−3.90726e15	−1.20438	−0.602192	+	0.798352i	$0.705706\pi$
$662$	3.00159e15	0.917555
$663$	2.79610e14	0.0847672
$664$	9.20727e14	0.276826
$665$	1.55180e14	0.0462719
$666$	4.68581e14	0.138572
$667$	2.65981e15	0.780115
$668$	−5.01182e15	−1.45789
$669$	−3.75255e15	−1.08264
$670$	1.17573e15	0.336431
$671$	−5.20313e15	−1.47669
$672$	−3.45973e15	−0.973893
$673$	2.82259e15	0.788071	0.394036	−	0.919095i	$-0.371079\pi$
$673$	2.82259e15	0.788071	0.394036	+	0.919095i	$0.371079\pi$
$674$	−2.24572e15	−0.621909
$675$	6.85653e14	0.188336
$676$	7.94103e14	0.216356
$677$	1.70016e15	0.459465	0.229733	−	0.973254i	$-0.426215\pi$
$677$	1.70016e15	0.459465	0.229733	+	0.973254i	$0.426215\pi$
$678$	−2.75267e15	−0.737888
$679$	−1.44142e15	−0.383271
$680$	−1.03860e15	−0.273936
$681$	−9.05173e14	−0.236822
$682$	7.13205e15	1.85097
$683$	8.19023e14	0.210854	0.105427	−	0.994427i	$-0.466379\pi$
$683$	8.19023e14	0.210854	0.105427	+	0.994427i	$0.466379\pi$
$684$	−3.07397e15	−0.785039
$685$	5.06193e14	0.128238
$686$	4.19516e14	0.105430
$687$	2.70004e15	0.673145
$688$	−7.82177e15	−1.93450
$689$	−7.00610e14	−0.171898
$690$	−1.03200e15	−0.251193
$691$	−1.38003e15	−0.333242	−0.166621	−	0.986021i	$-0.553286\pi$
$691$	−1.38003e15	−0.333242	−0.166621	+	0.986021i	$0.553286\pi$
$692$	3.71091e15	0.888991
$693$	−8.13139e14	−0.193256
$694$	−4.56381e15	−1.07609
$695$	−1.05236e15	−0.246177
$696$	4.50695e15	1.04600
$697$	1.91803e14	0.0441646
$698$	3.80877e15	0.870122
$699$	3.37961e15	0.766023
$700$	−4.62614e15	−1.04035
$701$	5.73640e14	0.127994	0.0639971	−	0.997950i	$-0.479615\pi$
$701$	5.73640e14	0.127994	0.0639971	+	0.997950i	$0.479615\pi$
$702$	4.70775e14	0.104222
$703$	−8.11595e14	−0.178273
$704$	−3.24879e16	−7.08063
$705$	3.58623e14	0.0775529
$706$	−6.60238e15	−1.41669
$707$	−1.99328e15	−0.424387
$708$	1.42482e16	3.01007
$709$	−6.39009e15	−1.33953	−0.669766	−	0.742573i	$-0.733605\pi$
$709$	−6.39009e15	−1.33953	−0.669766	+	0.742573i	$0.733605\pi$
$710$	1.51840e15	0.315839
$711$	−2.54338e15	−0.524962
$712$	3.35973e16	6.88121
$713$	4.63412e15	0.941834
$714$	−1.11842e15	−0.225561
$715$	−3.10800e14	−0.0622010
$716$	−1.76958e16	−3.51439
$717$	2.49627e15	0.491967
$718$	1.23869e16	2.42258
$719$	−7.77315e14	−0.150865	−0.0754324	−	0.997151i	$-0.524034\pi$
$719$	−7.77315e14	−0.150865	−0.0754324	+	0.997151i	$0.524034\pi$
$720$	−1.03699e15	−0.199732
$721$	−1.95634e15	−0.373939
$722$	−3.07644e15	−0.583571
$723$	−1.26823e15	−0.238747
$724$	−5.61476e15	−1.04898
$725$	2.70174e15	0.500939
$726$	−8.28841e15	−1.52517
$727$	3.74973e15	0.684796	0.342398	−	0.939555i	$-0.388761\pi$
$727$	3.74973e15	0.684796	0.342398	+	0.939555i	$0.388761\pi$
$728$	−2.04703e15	−0.371024
$729$	2.05891e14	0.0370370
$730$	−1.35240e15	−0.241451
$731$	−1.41018e15	−0.249878
$732$	−8.88898e15	−1.56329
$733$	−6.08226e15	−1.06168	−0.530839	−	0.847472i	$-0.678123\pi$
$733$	−6.08226e15	−1.06168	−0.530839	+	0.847472i	$0.678123\pi$
$734$	1.06191e16	1.83974
$735$	7.01275e13	0.0120589
$736$	−3.98509e16	−6.80158
$737$	1.06706e16	1.80767
$738$	3.22935e14	0.0543006
$739$	5.54723e13	0.00925832	0.00462916	−	0.999989i	$-0.498526\pi$
$739$	5.54723e13	0.00925832	0.00462916	+	0.999989i	$0.498526\pi$
$740$	−5.28494e14	−0.0875519
$741$	−8.15394e14	−0.134081
$742$	2.80238e15	0.457410
$743$	4.74148e15	0.768202	0.384101	−	0.923291i	$-0.374511\pi$
$743$	4.74148e15	0.768202	0.384101	+	0.923291i	$0.374511\pi$
$744$	7.85233e15	1.26284
$745$	1.64591e15	0.262753
$746$	6.65920e15	1.05526
$747$	1.65739e14	0.0260713
$748$	−1.46263e16	−2.28389
$749$	4.66039e15	0.722391
$750$	−2.11943e15	−0.326123
$751$	1.03493e16	1.58086	0.790428	−	0.612555i	$-0.209858\pi$
$751$	1.03493e16	1.58086	0.790428	+	0.612555i	$0.209858\pi$
$752$	2.48308e16	3.76524
$753$	2.93307e14	0.0441519
$754$	1.85504e15	0.277211
$755$	−3.03765e14	−0.0450639
$756$	−1.38916e15	−0.204589
$757$	−1.08087e16	−1.58032	−0.790158	−	0.612903i	$-0.790002\pi$
$757$	−1.08087e16	−1.58032	−0.790158	+	0.612903i	$0.790002\pi$
$758$	−2.08414e16	−3.02515
$759$	−9.36614e15	−1.34968
$760$	3.02875e15	0.433300
$761$	−1.21643e16	−1.72771	−0.863855	−	0.503740i	$-0.831957\pi$
$761$	−1.21643e16	−1.72771	−0.863855	+	0.503740i	$0.831957\pi$
$762$	1.51617e16	2.13794
$763$	−3.85392e14	−0.0539533
$764$	−2.60944e16	−3.62688
$765$	−1.86958e14	−0.0257992
$766$	−1.72969e16	−2.36979
$767$	3.77943e15	0.514105
$768$	−1.82492e16	−2.46466
$769$	3.76596e14	0.0504988	0.0252494	−	0.999681i	$-0.491962\pi$
$769$	3.76596e14	0.0504988	0.0252494	+	0.999681i	$0.491962\pi$
$770$	1.24317e15	0.165513
$771$	3.47004e15	0.458707
$772$	2.12534e16	2.78955
$773$	−1.32794e16	−1.73058	−0.865289	−	0.501273i	$-0.832865\pi$
$773$	−1.32794e16	−1.73058	−0.865289	+	0.501273i	$0.832865\pi$
$774$	−2.37429e15	−0.307226
$775$	4.70718e15	0.604785
$776$	−2.81331e16	−3.58904
$777$	−3.66768e14	−0.0464596
$778$	6.58710e15	0.828527
$779$	−5.59331e14	−0.0698575
$780$	−5.30968e14	−0.0658488
$781$	1.37806e16	1.69703
$782$	−1.28825e16	−1.57530
$783$	8.11292e14	0.0985116
$784$	4.85558e15	0.585468
$785$	−1.15252e15	−0.137996
$786$	3.60612e15	0.428762
$787$	1.37437e16	1.62272	0.811359	−	0.584548i	$-0.198728\pi$
$787$	1.37437e16	1.62272	0.811359	+	0.584548i	$0.198728\pi$
$788$	−1.54397e16	−1.81028
$789$	−4.79346e14	−0.0558117
$790$	3.88846e15	0.449603
$791$	2.15457e15	0.247394
$792$	−1.58706e16	−1.80969
$793$	−2.35787e15	−0.267003
$794$	3.36019e16	3.77877
$795$	4.68455e14	0.0523177
$796$	−2.29034e16	−2.54026
$797$	5.87693e15	0.647335	0.323668	−	0.946171i	$-0.395084\pi$
$797$	5.87693e15	0.647335	0.323668	+	0.946171i	$0.395084\pi$
$798$	3.26151e15	0.356782
$799$	4.47671e15	0.486353
$800$	−4.04792e16	−4.36754
$801$	6.04783e15	0.648068
$802$	1.28344e16	1.36589
$803$	−1.22740e16	−1.29734
$804$	1.82296e16	1.91368
$805$	8.07764e14	0.0842184
$806$	3.23198e15	0.334677
$807$	−4.17398e15	−0.429285
$808$	−3.89042e16	−3.97405
$809$	−1.38519e16	−1.40537	−0.702686	−	0.711500i	$-0.748016\pi$
$809$	−1.38519e16	−1.40537	−0.702686	+	0.711500i	$0.748016\pi$
$810$	−3.14778e14	−0.0317203
$811$	3.59854e14	0.0360173	0.0180086	−	0.999838i	$-0.494267\pi$
$811$	3.59854e14	0.0360173	0.0180086	+	0.999838i	$0.494267\pi$
$812$	−5.47384e15	−0.544169
$813$	8.04735e15	0.794612
$814$	−6.50181e15	−0.637676
$815$	−5.31976e14	−0.0518234
$816$	−1.29448e16	−1.25257
$817$	4.11233e15	0.395245
$818$	2.69664e16	2.57443
$819$	−3.68485e14	−0.0349428
$820$	−3.64225e14	−0.0343079
$821$	−1.69565e16	−1.58653	−0.793264	−	0.608877i	$-0.791620\pi$
$821$	−1.69565e16	−1.58653	−0.793264	+	0.608877i	$0.791620\pi$
$822$	1.06389e16	0.988787
$823$	−5.88363e14	−0.0543183	−0.0271591	−	0.999631i	$-0.508646\pi$
$823$	−5.88363e14	−0.0543183	−0.0271591	+	0.999631i	$0.508646\pi$
$824$	−3.81832e16	−3.50165
$825$	−9.51380e15	−0.866677
$826$	−1.51174e16	−1.36800
$827$	1.93841e15	0.174247	0.0871235	−	0.996198i	$-0.472233\pi$
$827$	1.93841e15	0.174247	0.0871235	+	0.996198i	$0.472233\pi$
$828$	−1.60010e16	−1.42883
$829$	−1.75829e16	−1.55970	−0.779848	−	0.625969i	$-0.784704\pi$
$829$	−1.75829e16	−1.55970	−0.779848	+	0.625969i	$0.784704\pi$
$830$	−2.53392e14	−0.0223287
$831$	−2.80141e15	−0.245229
$832$	−1.47223e16	−1.28026
$833$	8.75407e14	0.0756245
$834$	−2.21180e16	−1.89816
$835$	8.88902e14	0.0757841
$836$	4.26530e16	3.61256
$837$	1.41349e15	0.118933
$838$	−2.67535e16	−2.23635
$839$	−4.04180e15	−0.335648	−0.167824	−	0.985817i	$-0.553674\pi$
$839$	−4.04180e15	−0.335648	−0.167824	+	0.985817i	$0.553674\pi$
$840$	1.36872e15	0.112922
$841$	−9.00370e15	−0.737977
$842$	3.12297e15	0.254303
$843$	−9.00365e15	−0.728395
$844$	3.08074e16	2.47612
$845$	−1.40843e14	−0.0112467
$846$	7.53737e15	0.597975
$847$	6.48750e15	0.511350
$848$	3.24355e16	2.54006
$849$	−2.90963e15	−0.226384
$850$	−1.30856e16	−1.01155
$851$	−4.22461e15	−0.324470
$852$	2.35427e16	1.79655
$853$	−5.61795e15	−0.425950	−0.212975	−	0.977058i	$-0.568315\pi$
$853$	−5.61795e15	−0.425950	−0.212975	+	0.977058i	$0.568315\pi$
$854$	9.43127e15	0.710480
$855$	5.45204e14	0.0408080
$856$	9.09599e16	6.76463
$857$	2.26306e16	1.67225	0.836124	−	0.548540i	$-0.184816\pi$
$857$	2.26306e16	1.67225	0.836124	+	0.548540i	$0.184816\pi$
$858$	−6.53225e15	−0.479604
$859$	1.66157e16	1.21215	0.606073	−	0.795409i	$-0.292744\pi$
$859$	1.66157e16	1.21215	0.606073	+	0.795409i	$0.292744\pi$
$860$	2.67787e15	0.194110
$861$	−2.52768e14	−0.0182056
$862$	−2.96527e16	−2.12214
$863$	2.00361e16	1.42480	0.712400	−	0.701774i	$-0.247608\pi$
$863$	2.00361e16	1.42480	0.712400	+	0.701774i	$0.247608\pi$
$864$	−1.21553e16	−0.858893
$865$	−6.58172e14	−0.0462116
$866$	−1.68995e16	−1.17903
$867$	5.99426e15	0.415557
$868$	−9.53692e15	−0.656976
$869$	3.52907e16	2.41575
$870$	−1.24035e15	−0.0843700
$871$	4.83554e15	0.326847
$872$	−7.52195e15	−0.505230
$873$	−5.06422e15	−0.338014
$874$	3.75676e16	2.49173
$875$	1.65892e15	0.109340
$876$	−2.09689e16	−1.37342
$877$	1.59538e16	1.03841	0.519203	−	0.854651i	$-0.326229\pi$
$877$	1.59538e16	1.03841	0.519203	+	0.854651i	$0.326229\pi$
$878$	4.09008e16	2.64552
$879$	6.88265e14	0.0442402
$880$	1.43888e16	0.919116
$881$	6.71833e15	0.426475	0.213238	−	0.977000i	$-0.431599\pi$
$881$	6.71833e15	0.426475	0.213238	+	0.977000i	$0.431599\pi$
$882$	1.47391e15	0.0929808
$883$	−1.75667e16	−1.10130	−0.550650	−	0.834736i	$-0.685620\pi$
$883$	−1.75667e16	−1.10130	−0.550650	+	0.834736i	$0.685620\pi$
$884$	−6.62810e15	−0.412954
$885$	−2.52707e15	−0.156469
$886$	3.88927e16	2.39322
$887$	2.89279e16	1.76904	0.884519	−	0.466504i	$-0.154487\pi$
$887$	2.89279e16	1.76904	0.884519	+	0.466504i	$0.154487\pi$
$888$	−7.15845e15	−0.435058
$889$	−1.18674e16	−0.716796
$890$	−9.24627e15	−0.555036
$891$	−2.85685e15	−0.170435
$892$	8.89535e16	5.27419
$893$	−1.30549e16	−0.769292
$894$	3.45930e16	2.02597
$895$	3.13855e15	0.182685
$896$	2.97295e16	1.71986
$897$	−4.24439e15	−0.244038
$898$	−3.17315e16	−1.81330
$899$	5.56972e15	0.316341
$900$	−1.62533e16	−0.917503
$901$	5.84776e15	0.328097
$902$	−4.48089e15	−0.249878
$903$	1.85840e15	0.103005
$904$	4.20521e16	2.31665
$905$	9.95840e14	0.0545284
$906$	−6.38439e15	−0.347468
$907$	5.41547e15	0.292952	0.146476	−	0.989214i	$-0.453207\pi$
$907$	5.41547e15	0.292952	0.146476	+	0.989214i	$0.453207\pi$
$908$	2.14570e16	1.15371
$909$	−7.00311e15	−0.374274
$910$	5.63360e14	0.0299267
$911$	−8.38417e15	−0.442700	−0.221350	−	0.975194i	$-0.571046\pi$
$911$	−8.38417e15	−0.442700	−0.221350	+	0.975194i	$0.571046\pi$
$912$	3.77495e16	1.98125
$913$	−2.29972e15	−0.119974
$914$	2.92153e16	1.51498
$915$	1.57656e15	0.0812633
$916$	−6.40041e16	−3.27931
$917$	−2.82258e15	−0.143752
$918$	−3.92940e15	−0.198926
$919$	4.94161e15	0.248676	0.124338	−	0.992240i	$-0.460319\pi$
$919$	4.94161e15	0.248676	0.124338	+	0.992240i	$0.460319\pi$
$920$	1.57656e16	0.788640
$921$	1.46594e15	0.0728933
$922$	3.06332e16	1.51416
$923$	6.24488e15	0.306842
$924$	1.92753e16	0.941469
$925$	−4.29122e15	−0.208354
$926$	6.48545e16	3.13025
$927$	−6.87333e15	−0.329783
$928$	−4.78965e16	−2.28449
$929$	−2.63592e16	−1.24981	−0.624907	−	0.780699i	$-0.714863\pi$
$929$	−2.63592e16	−1.24981	−0.624907	+	0.780699i	$0.714863\pi$
$930$	−2.16103e15	−0.101860
$931$	−2.55285e15	−0.119619
$932$	−8.01131e16	−3.73178
$933$	−2.34299e15	−0.108498
$934$	6.04619e16	2.78339
$935$	2.59414e15	0.118722
$936$	−7.19195e15	−0.327212
$937$	−2.30382e16	−1.04203	−0.521015	−	0.853547i	$-0.674446\pi$
$937$	−2.30382e16	−1.04203	−0.521015	+	0.853547i	$0.674446\pi$
$938$	−1.93418e16	−0.869722
$939$	−2.31883e16	−1.03659
$940$	−8.50110e15	−0.377808
$941$	−2.47643e16	−1.09416	−0.547082	−	0.837079i	$-0.684261\pi$
$941$	−2.47643e16	−1.09416	−0.547082	+	0.837079i	$0.684261\pi$
$942$	−2.42231e16	−1.06402
$943$	−2.91150e15	−0.127146
$944$	−1.74973e17	−7.59669
$945$	2.46383e14	0.0106350
$946$	3.29445e16	1.41378
$947$	3.98279e16	1.69927	0.849635	−	0.527371i	$-0.176822\pi$
$947$	3.98279e16	1.69927	0.849635	+	0.527371i	$0.176822\pi$
$948$	6.02904e16	2.55742
$949$	−5.56215e15	−0.234573
$950$	3.81599e16	1.60003
$951$	−2.07922e16	−0.866776
$952$	1.70859e16	0.708164
$953$	−3.60996e16	−1.48762	−0.743810	−	0.668391i	$-0.766983\pi$
$953$	−3.60996e16	−1.48762	−0.743810	+	0.668391i	$0.766983\pi$
$954$	9.84577e15	0.403398
$955$	4.62813e15	0.188533
$956$	−5.91737e16	−2.39668
$957$	−1.12571e16	−0.453326
$958$	−9.95257e15	−0.398497
$959$	−8.32730e15	−0.331514
$960$	9.84391e15	0.389651
$961$	−1.57045e16	−0.618081
$962$	−2.94638e15	−0.115299
$963$	1.63736e16	0.637089
$964$	3.00632e16	1.16308
$965$	−3.76953e15	−0.145006
$966$	1.69772e16	0.649370
$967$	−1.67483e16	−0.636980	−0.318490	−	0.947926i	$-0.603176\pi$
$967$	−1.67483e16	−0.636980	−0.318490	+	0.947926i	$0.603176\pi$
$968$	1.26621e17	4.78840
$969$	6.80581e15	0.255917
$970$	7.74247e15	0.289491
$971$	−1.94424e16	−0.722842	−0.361421	−	0.932403i	$-0.617708\pi$
$971$	−1.94424e16	−0.722842	−0.361421	+	0.932403i	$0.617708\pi$
$972$	−4.88061e15	−0.180431
$973$	1.73122e16	0.636403
$974$	−5.88980e16	−2.15291
$975$	−4.31131e15	−0.156705
$976$	1.09160e17	3.94539
$977$	−4.16984e16	−1.49865	−0.749323	−	0.662205i	$-0.769621\pi$
$977$	−4.16984e16	−1.49865	−0.749323	+	0.662205i	$0.769621\pi$
$978$	−1.11808e16	−0.399586
$979$	−8.39168e16	−2.98225
$980$	−1.66236e15	−0.0587465
$981$	−1.35402e15	−0.0475823
$982$	8.96692e16	3.13350
$983$	−4.76975e16	−1.65749	−0.828746	−	0.559625i	$-0.810945\pi$
$983$	−4.76975e16	−1.65749	−0.828746	+	0.559625i	$0.810945\pi$
$984$	−4.93343e15	−0.170481
$985$	2.73841e15	0.0941022
$986$	−1.54834e16	−0.529106
$987$	−5.89965e15	−0.200485
$988$	1.93288e16	0.653192
$989$	2.14060e16	0.719377
$990$	4.36771e15	0.145969
$991$	−2.96670e16	−0.985982	−0.492991	−	0.870034i	$-0.664096\pi$
$991$	−2.96670e16	−0.985982	−0.492991	+	0.870034i	$0.664096\pi$
$992$	−8.34489e16	−2.75808
$993$	−8.25430e15	−0.271306
$994$	−2.49790e16	−0.816488
$995$	4.06218e15	0.132048
$996$	−3.92883e15	−0.127010
$997$	1.56858e16	0.504294	0.252147	−	0.967689i	$-0.418863\pi$
$997$	1.56858e16	0.504294	0.252147	+	0.967689i	$0.418863\pi$
$998$	−8.24715e15	−0.263685
$999$	−1.28859e15	−0.0409735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+88.3644 q^{2} -243.000 q^{3} +5760.27 q^{4} -1021.65 q^{5} -21472.6 q^{6} +16807.0 q^{7} +328033. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+88.3644 q^{2} -243.000 q^{3} +5760.27 q^{4} -1021.65 q^{5} -21472.6 q^{6} +16807.0 q^{7} +328033. q^{8} +59049.0 q^{9} -90277.5 q^{10} -819336. q^{11} -1.39975e6 q^{12} -371293. q^{13} +1.48514e6 q^{14} +248261. q^{15} +1.71894e7 q^{16} +3.09906e6 q^{17} +5.21783e6 q^{18} -9.03742e6 q^{19} -5.88498e6 q^{20} -4.08410e6 q^{21} -7.24002e7 q^{22} -4.70427e7 q^{23} -7.97120e7 q^{24} -4.77844e7 q^{25} -3.28091e7 q^{26} -1.43489e7 q^{27} +9.68129e7 q^{28} -5.65403e7 q^{29} +2.19374e7 q^{30} -9.85087e7 q^{31} +8.47121e8 q^{32} +1.99099e8 q^{33} +2.73846e8 q^{34} -1.71709e7 q^{35} +3.40138e8 q^{36} +8.98038e7 q^{37} -7.98586e8 q^{38} +9.02242e7 q^{39} -3.35135e8 q^{40} +6.18906e7 q^{41} -3.60889e8 q^{42} -4.55034e8 q^{43} -4.71960e9 q^{44} -6.03274e7 q^{45} -4.15690e9 q^{46} +1.44454e9 q^{47} -4.17703e9 q^{48} +2.82475e8 q^{49} -4.22244e9 q^{50} -7.53071e8 q^{51} -2.13875e9 q^{52} +1.88695e9 q^{53} -1.26793e9 q^{54} +8.37074e8 q^{55} +5.51325e9 q^{56} +2.19609e9 q^{57} -4.99616e9 q^{58} -1.01791e10 q^{59} +1.43005e9 q^{60} +6.35042e9 q^{61} -8.70467e9 q^{62} +9.92437e8 q^{63} +3.96515e10 q^{64} +3.79331e8 q^{65} +1.75932e10 q^{66} -1.30235e10 q^{67} +1.78514e10 q^{68} +1.14314e10 q^{69} -1.51729e9 q^{70} -1.68193e10 q^{71} +1.93700e10 q^{72} +1.49805e10 q^{73} +7.93547e9 q^{74} +1.16116e10 q^{75} -5.20580e10 q^{76} -1.37706e10 q^{77} +7.97261e9 q^{78} -4.30723e10 q^{79} -1.75616e10 q^{80} +3.48678e9 q^{81} +5.46893e9 q^{82} +2.80681e9 q^{83} -2.35255e10 q^{84} -3.16615e9 q^{85} -4.02088e10 q^{86} +1.37393e10 q^{87} -2.68769e11 q^{88} +1.02421e11 q^{89} -5.33079e9 q^{90} -6.24032e9 q^{91} -2.70979e11 q^{92} +2.39376e10 q^{93} +1.27646e11 q^{94} +9.23307e9 q^{95} -2.05851e11 q^{96} -8.57630e10 q^{97} +2.49608e10 q^{98} -4.83810e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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