LMFDB - Embedded newform 273.12.a.c.1.4

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			1.4
Root			$-65.6788$ 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)

$f(q)$	$=$	$q-69.6788 q^{2} -243.000 q^{3} +2807.14 q^{4} -8533.64 q^{5} +16932.0 q^{6} +16807.0 q^{7} -52895.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-69.6788 q^{2} -243.000 q^{3} +2807.14 q^{4} -8533.64 q^{5} +16932.0 q^{6} +16807.0 q^{7} -52895.7 q^{8} +59049.0 q^{9} +594614. q^{10} -896472. q^{11} -682134. q^{12} -371293. q^{13} -1.17109e6 q^{14} +2.07367e6 q^{15} -2.06330e6 q^{16} +6.97736e6 q^{17} -4.11446e6 q^{18} +8.73840e6 q^{19} -2.39551e7 q^{20} -4.08410e6 q^{21} +6.24651e7 q^{22} -2.99957e7 q^{23} +1.28537e7 q^{24} +2.39948e7 q^{25} +2.58713e7 q^{26} -1.43489e7 q^{27} +4.71795e7 q^{28} -2.58336e7 q^{29} -1.44491e8 q^{30} -1.03902e8 q^{31} +2.52099e8 q^{32} +2.17843e8 q^{33} -4.86174e8 q^{34} -1.43425e8 q^{35} +1.65759e8 q^{36} -2.97829e7 q^{37} -6.08881e8 q^{38} +9.02242e7 q^{39} +4.51393e8 q^{40} -4.22760e8 q^{41} +2.84575e8 q^{42} +3.51751e8 q^{43} -2.51652e9 q^{44} -5.03903e8 q^{45} +2.09007e9 q^{46} +1.85963e8 q^{47} +5.01383e8 q^{48} +2.82475e8 q^{49} -1.67193e9 q^{50} -1.69550e9 q^{51} -1.04227e9 q^{52} -3.89621e9 q^{53} +9.99815e8 q^{54} +7.65017e9 q^{55} -8.89019e8 q^{56} -2.12343e9 q^{57} +1.80006e9 q^{58} -6.93019e9 q^{59} +5.82108e9 q^{60} +3.21359e9 q^{61} +7.23980e9 q^{62} +9.92437e8 q^{63} -1.33403e10 q^{64} +3.16848e9 q^{65} -1.51790e10 q^{66} +1.07796e10 q^{67} +1.95864e10 q^{68} +7.28896e9 q^{69} +9.99367e9 q^{70} +1.05896e10 q^{71} -3.12344e9 q^{72} -1.93948e10 q^{73} +2.07524e9 q^{74} -5.83074e9 q^{75} +2.45299e10 q^{76} -1.50670e10 q^{77} -6.28671e9 q^{78} -4.97021e9 q^{79} +1.76075e10 q^{80} +3.48678e9 q^{81} +2.94574e10 q^{82} +1.40537e9 q^{83} -1.14646e10 q^{84} -5.95423e10 q^{85} -2.45096e10 q^{86} +6.27757e9 q^{87} +4.74196e10 q^{88} -6.73546e10 q^{89} +3.51113e10 q^{90} -6.24032e9 q^{91} -8.42021e10 q^{92} +2.52483e10 q^{93} -1.29577e10 q^{94} -7.45703e10 q^{95} -6.12601e10 q^{96} +9.77987e10 q^{97} -1.96825e10 q^{98} -5.29358e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−69.6788	−1.53970	−0.769849	−	0.638226i	$-0.779669\pi$
$2$	−69.6788	−1.53970	−0.769849	+	0.638226i	$0.779669\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2807.14	1.37067
$5$	−8533.64	−1.22123	−0.610617	−	0.791926i	$-0.709079\pi$
$5$	−8533.64	−1.22123	−0.610617	+	0.791926i	$0.709079\pi$
$6$	16932.0	0.888945
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−52895.7	−0.570723
$9$	59049.0	0.333333
$10$	594614.	1.88033
$11$	−896472.	−1.67833	−0.839165	−	0.543877i	$-0.816956\pi$
$11$	−896472.	−1.67833	−0.839165	+	0.543877i	$0.816956\pi$
$12$	−682134.	−0.791358
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−1.17109e6	−0.581951
$15$	2.07367e6	0.705080
$16$	−2.06330e6	−0.491930
$17$	6.97736e6	1.19185	0.595926	−	0.803039i	$-0.296785\pi$
$17$	6.97736e6	1.19185	0.595926	+	0.803039i	$0.296785\pi$
$18$	−4.11446e6	−0.513233
$19$	8.73840e6	0.809631	0.404815	−	0.914398i	$-0.367336\pi$
$19$	8.73840e6	0.809631	0.404815	+	0.914398i	$0.367336\pi$
$20$	−2.39551e7	−1.67391
$21$	−4.08410e6	−0.218218
$22$	6.24651e7	2.58412
$23$	−2.99957e7	−0.971754	−0.485877	−	0.874027i	$-0.661500\pi$
$23$	−2.99957e7	−0.971754	−0.485877	+	0.874027i	$0.661500\pi$
$24$	1.28537e7	0.329507
$25$	2.39948e7	0.491414
$26$	2.58713e7	0.427036
$27$	−1.43489e7	−0.192450
$28$	4.71795e7	0.518065
$29$	−2.58336e7	−0.233882	−0.116941	−	0.993139i	$-0.537309\pi$
$29$	−2.58336e7	−0.233882	−0.116941	+	0.993139i	$0.537309\pi$
$30$	−1.44491e8	−1.08561
$31$	−1.03902e8	−0.651833	−0.325917	−	0.945398i	$-0.605673\pi$
$31$	−1.03902e8	−0.651833	−0.325917	+	0.945398i	$0.605673\pi$
$32$	2.52099e8	1.32815
$33$	2.17843e8	0.968984
$34$	−4.86174e8	−1.83509
$35$	−1.43425e8	−0.461583
$36$	1.65759e8	0.456891
$37$	−2.97829e7	−0.0706086	−0.0353043	−	0.999377i	$-0.511240\pi$
$37$	−2.97829e7	−0.0706086	−0.0353043	+	0.999377i	$0.511240\pi$
$38$	−6.08881e8	−1.24659
$39$	9.02242e7	0.160128
$40$	4.51393e8	0.696987
$41$	−4.22760e8	−0.569879	−0.284939	−	0.958546i	$-0.591973\pi$
$41$	−4.22760e8	−0.569879	−0.284939	+	0.958546i	$0.591973\pi$
$42$	2.84575e8	0.335990
$43$	3.51751e8	0.364887	0.182443	−	0.983216i	$-0.441599\pi$
$43$	3.51751e8	0.364887	0.182443	+	0.983216i	$0.441599\pi$
$44$	−2.51652e9	−2.30044
$45$	−5.03903e8	−0.407078
$46$	2.09007e9	1.49621
$47$	1.85963e8	0.118274	0.0591370	−	0.998250i	$-0.481165\pi$
$47$	1.85963e8	0.118274	0.0591370	+	0.998250i	$0.481165\pi$
$48$	5.01383e8	0.284016
$49$	2.82475e8	0.142857
$50$	−1.67193e9	−0.756629
$51$	−1.69550e9	−0.688116
$52$	−1.04227e9	−0.380156
$53$	−3.89621e9	−1.27975	−0.639874	−	0.768480i	$-0.721014\pi$
$53$	−3.89621e9	−1.27975	−0.639874	+	0.768480i	$0.721014\pi$
$54$	9.99815e8	0.296315
$55$	7.65017e9	2.04963
$56$	−8.89019e8	−0.215713
$57$	−2.12343e9	−0.467440
$58$	1.80006e9	0.360107
$59$	−6.93019e9	−1.26200	−0.630999	−	0.775783i	$-0.717355\pi$
$59$	−6.93019e9	−1.26200	−0.630999	+	0.775783i	$0.717355\pi$
$60$	5.82108e9	0.966434
$61$	3.21359e9	0.487165	0.243582	−	0.969880i	$-0.421677\pi$
$61$	3.21359e9	0.487165	0.243582	+	0.969880i	$0.421677\pi$
$62$	7.23980e9	1.00363
$63$	9.92437e8	0.125988
$64$	−1.33403e10	−1.55302
$65$	3.16848e9	0.338710
$66$	−1.51790e10	−1.49194
$67$	1.07796e10	0.975421	0.487711	−	0.873005i	$-0.337832\pi$
$67$	1.07796e10	0.975421	0.487711	+	0.873005i	$0.337832\pi$
$68$	1.95864e10	1.63364
$69$	7.28896e9	0.561042
$70$	9.99367e9	0.710699
$71$	1.05896e10	0.696562	0.348281	−	0.937390i	$-0.386765\pi$
$71$	1.05896e10	0.696562	0.348281	+	0.937390i	$0.386765\pi$
$72$	−3.12344e9	−0.190241
$73$	−1.93948e10	−1.09499	−0.547495	−	0.836809i	$-0.684418\pi$
$73$	−1.93948e10	−1.09499	−0.547495	+	0.836809i	$0.684418\pi$
$74$	2.07524e9	0.108716
$75$	−5.83074e9	−0.283718
$76$	2.45299e10	1.10974
$77$	−1.50670e10	−0.634349
$78$	−6.28671e9	−0.246549
$79$	−4.97021e9	−0.181730	−0.0908648	−	0.995863i	$-0.528963\pi$
$79$	−4.97021e9	−0.181730	−0.0908648	+	0.995863i	$0.528963\pi$
$80$	1.76075e10	0.600762
$81$	3.48678e9	0.111111
$82$	2.94574e10	0.877441
$83$	1.40537e9	0.0391616	0.0195808	−	0.999808i	$-0.493767\pi$
$83$	1.40537e9	0.0391616	0.0195808	+	0.999808i	$0.493767\pi$
$84$	−1.14646e10	−0.299105
$85$	−5.95423e10	−1.45553
$86$	−2.45096e10	−0.561816
$87$	6.27757e9	0.135032
$88$	4.74196e10	0.957862
$89$	−6.73546e10	−1.27856	−0.639282	−	0.768973i	$-0.720768\pi$
$89$	−6.73546e10	−1.27856	−0.639282	+	0.768973i	$0.720768\pi$
$90$	3.51113e10	0.626778
$91$	−6.24032e9	−0.104828
$92$	−8.42021e10	−1.33196
$93$	2.52483e10	0.376336
$94$	−1.29577e10	−0.182106
$95$	−7.45703e10	−0.988749
$96$	−6.12601e10	−0.766806
$97$	9.77987e10	1.15635	0.578174	−	0.815914i	$-0.303766\pi$
$97$	9.77987e10	1.15635	0.578174	+	0.815914i	$0.303766\pi$
$98$	−1.96825e10	−0.219957
$99$	−5.29358e10	−0.559443
$100$	6.73567e10	0.673567
$101$	−5.47424e10	−0.518270	−0.259135	−	0.965841i	$-0.583437\pi$
$101$	−5.47424e10	−0.518270	−0.259135	+	0.965841i	$0.583437\pi$
$102$	1.18140e11	1.05949
$103$	1.95398e11	1.66079	0.830397	−	0.557172i	$-0.188114\pi$
$103$	1.95398e11	1.66079	0.830397	+	0.557172i	$0.188114\pi$
$104$	1.96398e10	0.158290
$105$	3.48522e10	0.266495
$106$	2.71483e11	1.97043
$107$	3.50218e10	0.241395	0.120697	−	0.992689i	$-0.461487\pi$
$107$	3.50218e10	0.241395	0.120697	+	0.992689i	$0.461487\pi$
$108$	−4.02793e10	−0.263786
$109$	1.88052e11	1.17066	0.585331	−	0.810795i	$-0.300965\pi$
$109$	1.88052e11	1.17066	0.585331	+	0.810795i	$0.300965\pi$
$110$	−5.33055e11	−3.15582
$111$	7.23725e9	0.0407659
$112$	−3.46779e10	−0.185932
$113$	2.38260e11	1.21652	0.608260	−	0.793738i	$-0.291868\pi$
$113$	2.38260e11	1.21652	0.608260	+	0.793738i	$0.291868\pi$
$114$	1.47958e11	0.719718
$115$	2.55972e11	1.18674
$116$	−7.25185e10	−0.320575
$117$	−2.19245e10	−0.0924500
$118$	4.82887e11	1.94310
$119$	1.17269e11	0.450478
$120$	−1.09688e11	−0.402406
$121$	5.18351e11	1.81679
$122$	−2.23919e11	−0.750087
$123$	1.02731e11	0.329020
$124$	−2.91668e11	−0.893450
$125$	2.11918e11	0.621103
$126$	−6.91518e10	−0.193984
$127$	−1.08959e11	−0.292647	−0.146323	−	0.989237i	$-0.546744\pi$
$127$	−1.08959e11	−0.292647	−0.146323	+	0.989237i	$0.546744\pi$
$128$	4.13238e11	1.06303
$129$	−8.54754e10	−0.210668
$130$	−2.20776e11	−0.521511
$131$	1.96232e11	0.444404	0.222202	−	0.975001i	$-0.428676\pi$
$131$	1.96232e11	0.444404	0.222202	+	0.975001i	$0.428676\pi$
$132$	6.11515e11	1.32816
$133$	1.46866e11	0.306012
$134$	−7.51111e11	−1.50185
$135$	1.22448e11	0.235027
$136$	−3.69073e11	−0.680218
$137$	1.01527e12	1.79728	0.898642	−	0.438683i	$-0.144555\pi$
$137$	1.01527e12	1.79728	0.898642	+	0.438683i	$0.144555\pi$
$138$	−5.07886e11	−0.863836
$139$	1.92508e11	0.314678	0.157339	−	0.987545i	$-0.449708\pi$
$139$	1.92508e11	0.314678	0.157339	+	0.987545i	$0.449708\pi$
$140$	−4.02613e11	−0.632679
$141$	−4.51891e10	−0.0682855
$142$	−7.37873e11	−1.07250
$143$	3.32854e11	0.465485
$144$	−1.21836e11	−0.163977
$145$	2.20455e11	0.285624
$146$	1.35141e12	1.68595
$147$	−6.86415e10	−0.0824786
$148$	−8.36047e10	−0.0967813
$149$	6.90195e11	0.769923	0.384961	−	0.922933i	$-0.374215\pi$
$149$	6.90195e11	0.769923	0.384961	+	0.922933i	$0.374215\pi$
$150$	4.06279e11	0.436840
$151$	−4.33411e10	−0.0449290	−0.0224645	−	0.999748i	$-0.507151\pi$
$151$	−4.33411e10	−0.0449290	−0.0224645	+	0.999748i	$0.507151\pi$
$152$	−4.62224e11	−0.462075
$153$	4.12006e11	0.397284
$154$	1.04985e12	0.976706
$155$	8.86666e11	0.796041
$156$	2.53272e11	0.219483
$157$	1.52920e12	1.27943	0.639714	−	0.768613i	$-0.279053\pi$
$157$	1.52920e12	1.27943	0.639714	+	0.768613i	$0.279053\pi$
$158$	3.46318e11	0.279809
$159$	9.46778e11	0.738863
$160$	−2.15132e12	−1.62198
$161$	−5.04138e11	−0.367288
$162$	−2.42955e11	−0.171078
$163$	2.42450e12	1.65040	0.825202	−	0.564838i	$-0.191061\pi$
$163$	2.42450e12	1.65040	0.825202	+	0.564838i	$0.191061\pi$
$164$	−1.18674e12	−0.781117
$165$	−1.85899e12	−1.18336
$166$	−9.79244e10	−0.0602971
$167$	−2.70780e12	−1.61315	−0.806577	−	0.591129i	$-0.798682\pi$
$167$	−2.70780e12	−1.61315	−0.806577	+	0.591129i	$0.798682\pi$
$168$	2.16032e11	0.124542
$169$	1.37858e11	0.0769231
$170$	4.14883e12	2.24108
$171$	5.15994e11	0.269877
$172$	9.87412e11	0.500140
$173$	1.97019e12	0.966616	0.483308	−	0.875450i	$-0.339435\pi$
$173$	1.97019e12	0.966616	0.483308	+	0.875450i	$0.339435\pi$
$174$	−4.37414e11	−0.207908
$175$	4.03281e11	0.185737
$176$	1.84969e12	0.825620
$177$	1.68404e12	0.728615
$178$	4.69319e12	1.96860
$179$	−8.09414e11	−0.329215	−0.164607	−	0.986359i	$-0.552636\pi$
$179$	−8.09414e11	−0.329215	−0.164607	+	0.986359i	$0.552636\pi$
$180$	−1.41452e12	−0.557971
$181$	2.39624e12	0.916850	0.458425	−	0.888733i	$-0.348414\pi$
$181$	2.39624e12	0.916850	0.458425	+	0.888733i	$0.348414\pi$
$182$	4.34818e11	0.161404
$183$	−7.80902e11	−0.281265
$184$	1.58665e12	0.554603
$185$	2.54157e11	0.0862297
$186$	−1.75927e12	−0.579444
$187$	−6.25501e12	−2.00032
$188$	5.22025e11	0.162115
$189$	−2.41162e11	−0.0727393
$190$	5.19597e12	1.52238
$191$	−2.02981e12	−0.577791	−0.288896	−	0.957361i	$-0.593288\pi$
$191$	−2.02981e12	−0.577791	−0.288896	+	0.957361i	$0.593288\pi$
$192$	3.24170e12	0.896635
$193$	−2.71671e12	−0.730261	−0.365130	−	0.930956i	$-0.618976\pi$
$193$	−2.71671e12	−0.730261	−0.365130	+	0.930956i	$0.618976\pi$
$194$	−6.81450e12	−1.78043
$195$	−7.69940e11	−0.195554
$196$	7.92947e11	0.195810
$197$	5.51146e12	1.32343	0.661717	−	0.749754i	$-0.269828\pi$
$197$	5.51146e12	1.32343	0.661717	+	0.749754i	$0.269828\pi$
$198$	3.68850e12	0.861374
$199$	−4.57352e12	−1.03886	−0.519432	−	0.854512i	$-0.673857\pi$
$199$	−4.57352e12	−1.03886	−0.519432	+	0.854512i	$0.673857\pi$
$200$	−1.26922e12	−0.280461
$201$	−2.61945e12	−0.563160
$202$	3.81438e12	0.797980
$203$	−4.34186e11	−0.0883990
$204$	−4.75950e12	−0.943181
$205$	3.60768e12	0.695955
$206$	−1.36151e13	−2.55712
$207$	−1.77122e12	−0.323918
$208$	7.66090e11	0.136437
$209$	−7.83373e12	−1.35883
$210$	−2.42846e12	−0.410322
$211$	9.73284e12	1.60209	0.801044	−	0.598606i	$-0.204279\pi$
$211$	9.73284e12	1.60209	0.801044	+	0.598606i	$0.204279\pi$
$212$	−1.09372e13	−1.75412
$213$	−2.57328e12	−0.402160
$214$	−2.44028e12	−0.371675
$215$	−3.00171e12	−0.445612
$216$	7.58996e11	0.109836
$217$	−1.74629e12	−0.246370
$218$	−1.31032e13	−1.80247
$219$	4.71294e12	0.632192
$220$	2.14751e13	2.80938
$221$	−2.59065e12	−0.330560
$222$	−5.04283e11	−0.0627672
$223$	−9.59844e12	−1.16553	−0.582766	−	0.812640i	$-0.698029\pi$
$223$	−9.59844e12	−1.16553	−0.582766	+	0.812640i	$0.698029\pi$
$224$	4.23703e12	0.501993
$225$	1.41687e12	0.163805
$226$	−1.66017e13	−1.87307
$227$	−1.62487e13	−1.78928	−0.894638	−	0.446791i	$-0.852567\pi$
$227$	−1.62487e13	−1.78928	−0.894638	+	0.446791i	$0.852567\pi$
$228$	−5.96076e12	−0.640708
$229$	−1.10665e13	−1.16122	−0.580612	−	0.814181i	$-0.697186\pi$
$229$	−1.10665e13	−1.16122	−0.580612	+	0.814181i	$0.697186\pi$
$230$	−1.78359e13	−1.82722
$231$	3.66128e12	0.366241
$232$	1.36649e12	0.133482
$233$	9.50085e12	0.906368	0.453184	−	0.891417i	$-0.350288\pi$
$233$	9.50085e12	0.906368	0.453184	+	0.891417i	$0.350288\pi$
$234$	1.52767e12	0.142345
$235$	−1.58694e12	−0.144440
$236$	−1.94540e13	−1.72979
$237$	1.20776e12	0.104922
$238$	−8.17113e12	−0.693600
$239$	−8.95973e12	−0.743201	−0.371601	−	0.928393i	$-0.621191\pi$
$239$	−8.95973e12	−0.743201	−0.371601	+	0.928393i	$0.621191\pi$
$240$	−4.27862e12	−0.346850
$241$	−2.13370e13	−1.69060	−0.845299	−	0.534293i	$-0.820578\pi$
$241$	−2.13370e13	−1.69060	−0.845299	+	0.534293i	$0.820578\pi$
$242$	−3.61181e13	−2.79731
$243$	−8.47289e11	−0.0641500
$244$	9.02098e12	0.667743
$245$	−2.41054e12	−0.174462
$246$	−7.15815e12	−0.506591
$247$	−3.24451e12	−0.224551
$248$	5.49600e12	0.372017
$249$	−3.41505e11	−0.0226100
$250$	−1.47662e13	−0.956312
$251$	5.02959e12	0.318659	0.159330	−	0.987225i	$-0.449067\pi$
$251$	5.02959e12	0.318659	0.159330	+	0.987225i	$0.449067\pi$
$252$	2.78590e12	0.172688
$253$	2.68903e13	1.63092
$254$	7.59215e12	0.450588
$255$	1.44688e13	0.840351
$256$	−1.47300e12	−0.0837302
$257$	1.00594e13	0.559679	0.279840	−	0.960047i	$-0.409719\pi$
$257$	1.00594e13	0.559679	0.279840	+	0.960047i	$0.409719\pi$
$258$	5.95582e12	0.324365
$259$	−5.00562e11	−0.0266876
$260$	8.89435e12	0.464260
$261$	−1.52545e12	−0.0779606
$262$	−1.36732e13	−0.684248
$263$	3.66706e13	1.79705	0.898527	−	0.438919i	$-0.144638\pi$
$263$	3.66706e13	1.79705	0.898527	+	0.438919i	$0.144638\pi$
$264$	−1.15230e13	−0.553022
$265$	3.32488e13	1.56287
$266$	−1.02335e13	−0.471166
$267$	1.63672e13	0.738179
$268$	3.02599e13	1.33698
$269$	2.37943e13	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$269$	2.37943e13	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$270$	−8.53205e12	−0.361870
$271$	4.13886e13	1.72008	0.860042	−	0.510223i	$-0.170437\pi$
$271$	4.13886e13	1.72008	0.860042	+	0.510223i	$0.170437\pi$
$272$	−1.43964e13	−0.586308
$273$	1.51640e12	0.0605228
$274$	−7.07425e13	−2.76727
$275$	−2.15107e13	−0.824754
$276$	2.04611e13	0.769005
$277$	1.81620e12	0.0669150	0.0334575	−	0.999440i	$-0.489348\pi$
$277$	1.81620e12	0.0669150	0.0334575	+	0.999440i	$0.489348\pi$
$278$	−1.34137e13	−0.484509
$279$	−6.13534e12	−0.217278
$280$	7.58656e12	0.263436
$281$	−5.02144e13	−1.70979	−0.854896	−	0.518800i	$-0.826379\pi$
$281$	−5.02144e13	−1.70979	−0.854896	+	0.518800i	$0.826379\pi$
$282$	3.14872e12	0.105139
$283$	1.48728e13	0.487043	0.243521	−	0.969896i	$-0.421697\pi$
$283$	1.48728e13	0.487043	0.243521	+	0.969896i	$0.421697\pi$
$284$	2.97265e13	0.954758
$285$	1.81206e13	0.570854
$286$	−2.31929e13	−0.716706
$287$	−7.10532e12	−0.215394
$288$	1.48862e13	0.442716
$289$	1.44117e13	0.420511
$290$	−1.53610e13	−0.439776
$291$	−2.37651e13	−0.667618
$292$	−5.44439e13	−1.50087
$293$	−3.58573e12	−0.0970076	−0.0485038	−	0.998823i	$-0.515445\pi$
$293$	−3.58573e12	−0.0970076	−0.0485038	+	0.998823i	$0.515445\pi$
$294$	4.78286e12	0.126992
$295$	5.91397e13	1.54120
$296$	1.57539e12	0.0402980
$297$	1.28634e13	0.322995
$298$	−4.80919e13	−1.18545
$299$	1.11372e13	0.269516
$300$	−1.63677e13	−0.388884
$301$	5.91187e12	0.137914
$302$	3.01996e12	0.0691771
$303$	1.33024e13	0.299223
$304$	−1.80300e13	−0.398282
$305$	−2.74236e13	−0.594943
$306$	−2.87081e13	−0.611698
$307$	3.08147e13	0.644907	0.322454	−	0.946585i	$-0.395492\pi$
$307$	3.08147e13	0.644907	0.322454	+	0.946585i	$0.395492\pi$
$308$	−4.22952e13	−0.869484
$309$	−4.74817e13	−0.958860
$310$	−6.17818e13	−1.22566
$311$	−6.43609e13	−1.25441	−0.627206	−	0.778853i	$-0.715802\pi$
$311$	−6.43609e13	−1.25441	−0.627206	+	0.778853i	$0.715802\pi$
$312$	−4.77248e12	−0.0913889
$313$	−5.65228e13	−1.06348	−0.531740	−	0.846907i	$-0.678462\pi$
$313$	−5.65228e13	−1.06348	−0.531740	+	0.846907i	$0.678462\pi$
$314$	−1.06553e14	−1.96993
$315$	−8.46909e12	−0.153861
$316$	−1.39521e13	−0.249092
$317$	−2.88898e13	−0.506896	−0.253448	−	0.967349i	$-0.581565\pi$
$317$	−2.88898e13	−0.506896	−0.253448	+	0.967349i	$0.581565\pi$
$318$	−6.59704e13	−1.13763
$319$	2.31591e13	0.392531
$320$	1.13841e14	1.89660
$321$	−8.51030e12	−0.139369
$322$	3.51277e13	0.565513
$323$	6.09710e13	0.964960
$324$	9.78788e12	0.152297
$325$	−8.90911e12	−0.136294
$326$	−1.68936e14	−2.54112
$327$	−4.56965e13	−0.675881
$328$	2.23622e13	0.325243
$329$	3.12549e12	0.0447034
$330$	1.29532e14	1.82201
$331$	−9.09171e13	−1.25774	−0.628871	−	0.777510i	$-0.716483\pi$
$331$	−9.09171e13	−1.25774	−0.628871	+	0.777510i	$0.716483\pi$
$332$	3.94506e12	0.0536778
$333$	−1.75865e12	−0.0235362
$334$	1.88676e14	2.48377
$335$	−9.19894e13	−1.19122
$336$	8.42674e12	0.107348
$337$	−1.09634e13	−0.137398	−0.0686989	−	0.997637i	$-0.521885\pi$
$337$	−1.09634e13	−0.137398	−0.0686989	+	0.997637i	$0.521885\pi$
$338$	−9.60582e12	−0.118438
$339$	−5.78971e13	−0.702358
$340$	−1.67143e14	−1.99506
$341$	9.31457e13	1.09399
$342$	−3.59538e13	−0.415529
$343$	4.74756e12	0.0539949
$344$	−1.86061e13	−0.208250
$345$	−6.22013e13	−0.685164
$346$	−1.37280e14	−1.48830
$347$	8.11014e13	0.865399	0.432700	−	0.901538i	$-0.357561\pi$
$347$	8.11014e13	0.865399	0.432700	+	0.901538i	$0.357561\pi$
$348$	1.76220e13	0.185084
$349$	1.60423e14	1.65854	0.829272	−	0.558846i	$-0.188756\pi$
$349$	1.60423e14	1.65854	0.829272	+	0.558846i	$0.188756\pi$
$350$	−2.81001e13	−0.285979
$351$	5.32765e12	0.0533761
$352$	−2.26000e14	−2.22907
$353$	−6.62141e13	−0.642968	−0.321484	−	0.946915i	$-0.604182\pi$
$353$	−6.62141e13	−0.642968	−0.321484	+	0.946915i	$0.604182\pi$
$354$	−1.17342e14	−1.12185
$355$	−9.03680e13	−0.850666
$356$	−1.89074e14	−1.75249
$357$	−2.84963e13	−0.260083
$358$	5.63990e13	0.506891
$359$	−2.92551e13	−0.258930	−0.129465	−	0.991584i	$-0.541326\pi$
$359$	−2.92551e13	−0.258930	−0.129465	+	0.991584i	$0.541326\pi$
$360$	2.66543e13	0.232329
$361$	−4.01307e13	−0.344498
$362$	−1.66967e14	−1.41167
$363$	−1.25959e14	−1.04892
$364$	−1.75174e13	−0.143685
$365$	1.65508e14	1.33724
$366$	5.44123e13	0.433063
$367$	−1.50824e14	−1.18252	−0.591259	−	0.806482i	$-0.701369\pi$
$367$	−1.50824e14	−1.18252	−0.591259	+	0.806482i	$0.701369\pi$
$368$	6.18903e13	0.478035
$369$	−2.49635e13	−0.189960
$370$	−1.77093e13	−0.132768
$371$	−6.54835e13	−0.483699
$372$	7.08754e13	0.515834
$373$	−2.04928e13	−0.146962	−0.0734808	−	0.997297i	$-0.523411\pi$
$373$	−2.04928e13	−0.146962	−0.0734808	+	0.997297i	$0.523411\pi$
$374$	4.35842e14	3.07989
$375$	−5.14962e13	−0.358594
$376$	−9.83667e12	−0.0675017
$377$	9.59184e12	0.0648671
$378$	1.68039e13	0.111997
$379$	2.04954e14	1.34629	0.673147	−	0.739509i	$-0.264942\pi$
$379$	2.04954e14	1.34629	0.673147	+	0.739509i	$0.264942\pi$
$380$	−2.09329e14	−1.35525
$381$	2.64771e13	0.168960
$382$	1.41434e14	0.889625
$383$	1.00545e14	0.623402	0.311701	−	0.950180i	$-0.399101\pi$
$383$	1.00545e14	0.623402	0.311701	+	0.950180i	$0.399101\pi$
$384$	−1.00417e14	−0.613741
$385$	1.28576e14	0.774689
$386$	1.89297e14	1.12438
$387$	2.07705e13	0.121629
$388$	2.74534e14	1.58497
$389$	−6.01083e13	−0.342146	−0.171073	−	0.985258i	$-0.554723\pi$
$389$	−6.01083e13	−0.342146	−0.171073	+	0.985258i	$0.554723\pi$
$390$	5.36485e13	0.301094
$391$	−2.09291e14	−1.15819
$392$	−1.49417e13	−0.0815319
$393$	−4.76844e13	−0.256577
$394$	−3.84032e14	−2.03769
$395$	4.24139e13	0.221934
$396$	−1.48598e14	−0.766813
$397$	−1.41729e14	−0.721293	−0.360646	−	0.932703i	$-0.617444\pi$
$397$	−1.41729e14	−0.721293	−0.360646	+	0.932703i	$0.617444\pi$
$398$	3.18678e14	1.59954
$399$	−3.56885e13	−0.176676
$400$	−4.95086e13	−0.241741
$401$	−1.34314e14	−0.646884	−0.323442	−	0.946248i	$-0.604840\pi$
$401$	−1.34314e14	−0.646884	−0.323442	+	0.946248i	$0.604840\pi$
$402$	1.82520e14	0.867096
$403$	3.85783e13	0.180786
$404$	−1.53669e14	−0.710378
$405$	−2.97549e13	−0.135693
$406$	3.02535e13	0.136108
$407$	2.66996e13	0.118505
$408$	8.96847e13	0.392724
$409$	1.73873e14	0.751199	0.375600	−	0.926782i	$-0.377437\pi$
$409$	1.73873e14	0.751199	0.375600	+	0.926782i	$0.377437\pi$
$410$	−2.51379e14	−1.07156
$411$	−2.46710e14	−1.03766
$412$	5.48509e14	2.27640
$413$	−1.16476e14	−0.476991
$414$	1.23416e14	0.498736
$415$	−1.19929e13	−0.0478255
$416$	−9.36026e13	−0.368362
$417$	−4.67793e13	−0.181679
$418$	5.45845e14	2.09218
$419$	3.03381e14	1.14766	0.573828	−	0.818976i	$-0.305458\pi$
$419$	3.03381e14	1.14766	0.573828	+	0.818976i	$0.305458\pi$
$420$	9.78350e13	0.365278
$421$	3.70294e13	0.136457	0.0682284	−	0.997670i	$-0.478265\pi$
$421$	3.70294e13	0.136457	0.0682284	+	0.997670i	$0.478265\pi$
$422$	−6.78173e14	−2.46673
$423$	1.09810e13	0.0394247
$424$	2.06093e14	0.730383
$425$	1.67420e14	0.585692
$426$	1.79303e14	0.619206
$427$	5.40108e13	0.184131
$428$	9.83110e13	0.330873
$429$	−8.08835e13	−0.268748
$430$	2.09156e14	0.686109
$431$	−2.62477e14	−0.850094	−0.425047	−	0.905171i	$-0.639742\pi$
$431$	−2.62477e14	−0.850094	−0.425047	+	0.905171i	$0.639742\pi$
$432$	2.96062e13	0.0946720
$433$	3.32199e12	0.0104885	0.00524427	−	0.999986i	$-0.498331\pi$
$433$	3.32199e12	0.0104885	0.00524427	+	0.999986i	$0.498331\pi$
$434$	1.21679e14	0.379335
$435$	−5.35705e13	−0.164905
$436$	5.27886e14	1.60459
$437$	−2.62114e14	−0.786761
$438$	−3.28392e14	−0.973386
$439$	3.33043e14	0.974866	0.487433	−	0.873160i	$-0.337933\pi$
$439$	3.33043e14	0.974866	0.487433	+	0.873160i	$0.337933\pi$
$440$	−4.04661e14	−1.16977
$441$	1.66799e13	0.0476190
$442$	1.80513e14	0.508963
$443$	−5.42968e14	−1.51201	−0.756003	−	0.654568i	$-0.772850\pi$
$443$	−5.42968e14	−1.51201	−0.756003	+	0.654568i	$0.772850\pi$
$444$	2.03160e13	0.0558767
$445$	5.74779e14	1.56143
$446$	6.68808e14	1.79457
$447$	−1.67717e14	−0.444515
$448$	−2.24211e14	−0.586985
$449$	2.68562e14	0.694528	0.347264	−	0.937767i	$-0.387111\pi$
$449$	2.68562e14	0.694528	0.347264	+	0.937767i	$0.387111\pi$
$450$	−9.87258e13	−0.252210
$451$	3.78992e14	0.956444
$452$	6.68828e14	1.66745
$453$	1.05319e13	0.0259398
$454$	1.13219e15	2.75495
$455$	5.32526e13	0.128020
$456$	1.12320e14	0.266779
$457$	−2.97540e14	−0.698241	−0.349121	−	0.937078i	$-0.613520\pi$
$457$	−2.97540e14	−0.698241	−0.349121	+	0.937078i	$0.613520\pi$
$458$	7.71102e14	1.78793
$459$	−1.00118e14	−0.229372
$460$	7.18550e14	1.62663
$461$	7.77771e14	1.73979	0.869895	−	0.493237i	$-0.164186\pi$
$461$	7.77771e14	1.73979	0.869895	+	0.493237i	$0.164186\pi$
$462$	−2.55114e14	−0.563902
$463$	−3.15118e14	−0.688301	−0.344151	−	0.938914i	$-0.611833\pi$
$463$	−3.15118e14	−0.688301	−0.344151	+	0.938914i	$0.611833\pi$
$464$	5.33026e13	0.115053
$465$	−2.15460e14	−0.459595
$466$	−6.62008e14	−1.39553
$467$	−2.77897e12	−0.00578951	−0.00289475	−	0.999996i	$-0.500921\pi$
$467$	−2.77897e12	−0.00578951	−0.00289475	+	0.999996i	$0.500921\pi$
$468$	−6.15450e13	−0.126719
$469$	1.81173e14	0.368675
$470$	1.10576e14	0.222394
$471$	−3.71595e14	−0.738678
$472$	3.66577e14	0.720252
$473$	−3.15335e14	−0.612400
$474$	−8.41553e13	−0.161548
$475$	2.09676e14	0.397864
$476$	3.29189e14	0.617457
$477$	−2.30067e14	−0.426583
$478$	6.24303e14	1.14431
$479$	−6.67118e14	−1.20881	−0.604404	−	0.796678i	$-0.706589\pi$
$479$	−6.67118e14	−1.20881	−0.604404	+	0.796678i	$0.706589\pi$
$480$	5.22771e14	0.936450
$481$	1.10582e13	0.0195833
$482$	1.48674e15	2.60301
$483$	1.22506e14	0.212054
$484$	1.45508e15	2.49022
$485$	−8.34578e14	−1.41217
$486$	5.90381e13	0.0987717
$487$	−9.81062e14	−1.62288	−0.811441	−	0.584434i	$-0.801317\pi$
$487$	−9.81062e14	−1.62288	−0.811441	+	0.584434i	$0.801317\pi$
$488$	−1.69985e14	−0.278036
$489$	−5.89153e14	−0.952861
$490$	1.67964e14	0.268619
$491$	9.80830e13	0.155112	0.0775560	−	0.996988i	$-0.475288\pi$
$491$	9.80830e13	0.155112	0.0775560	+	0.996988i	$0.475288\pi$
$492$	2.88379e14	0.450978
$493$	−1.80251e14	−0.278752
$494$	2.26073e14	0.345741
$495$	4.51735e14	0.683211
$496$	2.14382e14	0.320656
$497$	1.77980e14	0.263276
$498$	2.37956e13	0.0348126
$499$	6.25519e14	0.905081	0.452540	−	0.891744i	$-0.350518\pi$
$499$	6.25519e14	0.905081	0.452540	+	0.891744i	$0.350518\pi$
$500$	5.94884e14	0.851329
$501$	6.57995e14	0.931355
$502$	−3.50456e14	−0.490639
$503$	1.22254e15	1.69293	0.846467	−	0.532441i	$-0.178725\pi$
$503$	1.22254e15	1.69293	0.846467	+	0.532441i	$0.178725\pi$
$504$	−5.24957e13	−0.0719044
$505$	4.67152e14	0.632929
$506$	−1.87369e15	−2.51113
$507$	−3.34996e13	−0.0444116
$508$	−3.05863e14	−0.401123
$509$	−8.89866e14	−1.15445	−0.577227	−	0.816584i	$-0.695865\pi$
$509$	−8.89866e14	−1.15445	−0.577227	+	0.816584i	$0.695865\pi$
$510$	−1.00817e15	−1.29389
$511$	−3.25969e14	−0.413867
$512$	−7.43676e14	−0.934111
$513$	−1.25386e14	−0.155813
$514$	−7.00926e14	−0.861737
$515$	−1.66746e15	−2.02822
$516$	−2.39941e14	−0.288756
$517$	−1.66711e14	−0.198503
$518$	3.48785e13	0.0410908
$519$	−4.78756e14	−0.558076
$520$	−1.67599e14	−0.193309
$521$	5.21685e14	0.595389	0.297694	−	0.954661i	$-0.403782\pi$
$521$	5.21685e14	0.595389	0.297694	+	0.954661i	$0.403782\pi$
$522$	1.06292e14	0.120036
$523$	3.05092e14	0.340935	0.170468	−	0.985363i	$-0.445472\pi$
$523$	3.05092e14	0.340935	0.170468	+	0.985363i	$0.445472\pi$
$524$	5.50850e14	0.609132
$525$	−9.79972e13	−0.107235
$526$	−2.55516e15	−2.76692
$527$	−7.24965e14	−0.776889
$528$	−4.49476e14	−0.476672
$529$	−5.30669e13	−0.0556951
$530$	−2.31674e15	−2.40635
$531$	−4.09221e14	−0.420666
$532$	4.12274e14	0.419442
$533$	1.56968e14	0.158056
$534$	−1.14044e15	−1.13657
$535$	−2.98863e14	−0.294800
$536$	−5.70196e14	−0.556696
$537$	1.96688e14	0.190072
$538$	−1.65796e15	−1.58588
$539$	−2.53231e14	−0.239761
$540$	3.43729e14	0.322145
$541$	1.13529e15	1.05323	0.526613	−	0.850105i	$-0.323462\pi$
$541$	1.13529e15	1.05323	0.526613	+	0.850105i	$0.323462\pi$
$542$	−2.88391e15	−2.64841
$543$	−5.82287e14	−0.529344
$544$	1.75899e15	1.58295
$545$	−1.60476e15	−1.42965
$546$	−1.05661e14	−0.0931868
$547$	7.88321e14	0.688292	0.344146	−	0.938916i	$-0.388168\pi$
$547$	7.88321e14	0.688292	0.344146	+	0.938916i	$0.388168\pi$
$548$	2.84999e15	2.46349
$549$	1.89759e14	0.162388
$550$	1.49884e15	1.26987
$551$	−2.25744e14	−0.189358
$552$	−3.85555e14	−0.320200
$553$	−8.35343e13	−0.0686873
$554$	−1.26550e14	−0.103029
$555$	−6.17601e13	−0.0497847
$556$	5.40395e14	0.431320
$557$	7.96205e14	0.629247	0.314624	−	0.949217i	$-0.398122\pi$
$557$	7.96205e14	0.629247	0.314624	+	0.949217i	$0.398122\pi$
$558$	4.27503e14	0.334542
$559$	−1.30603e14	−0.101201
$560$	2.95929e14	0.227067
$561$	1.51997e15	1.15489
$562$	3.49888e15	2.63256
$563$	1.39446e15	1.03898	0.519492	−	0.854475i	$-0.326121\pi$
$563$	1.39446e15	1.03898	0.519492	+	0.854475i	$0.326121\pi$
$564$	−1.26852e14	−0.0935970
$565$	−2.03322e15	−1.48566
$566$	−1.03632e15	−0.749899
$567$	5.86024e13	0.0419961
$568$	−5.60146e14	−0.397544
$569$	−1.12310e14	−0.0789407	−0.0394704	−	0.999221i	$-0.512567\pi$
$569$	−1.12310e14	−0.0789407	−0.0394704	+	0.999221i	$0.512567\pi$
$570$	−1.26262e15	−0.878944
$571$	−1.55142e15	−1.06962	−0.534811	−	0.844972i	$-0.679617\pi$
$571$	−1.55142e15	−1.06962	−0.534811	+	0.844972i	$0.679617\pi$
$572$	9.34367e14	0.638027
$573$	4.93243e14	0.333588
$574$	4.95090e14	0.331642
$575$	−7.19741e14	−0.477533
$576$	−7.87732e14	−0.517672
$577$	1.01495e15	0.660658	0.330329	−	0.943866i	$-0.392840\pi$
$577$	1.01495e15	0.660658	0.330329	+	0.943866i	$0.392840\pi$
$578$	−1.00419e15	−0.647460
$579$	6.60160e14	0.421616
$580$	6.18847e14	0.391498
$581$	2.36200e13	0.0148017
$582$	1.65592e15	1.02793
$583$	3.49284e15	2.14784
$584$	1.02590e15	0.624936
$585$	1.87096e14	0.112903
$586$	2.49849e14	0.149362
$587$	−1.86828e14	−0.110645	−0.0553226	−	0.998469i	$-0.517619\pi$
$587$	−1.86828e14	−0.110645	−0.0553226	+	0.998469i	$0.517619\pi$
$588$	−1.92686e14	−0.113051
$589$	−9.07941e14	−0.527744
$590$	−4.12078e15	−2.37298
$591$	−1.33928e15	−0.764085
$592$	6.14512e13	0.0347345
$593$	−9.63033e13	−0.0539312	−0.0269656	−	0.999636i	$-0.508584\pi$
$593$	−9.63033e13	−0.0539312	−0.0269656	+	0.999636i	$0.508584\pi$
$594$	−8.96306e14	−0.497314
$595$	−1.00073e15	−0.550139
$596$	1.93747e15	1.05531
$597$	1.11137e15	0.599789
$598$	−7.76027e14	−0.414973
$599$	−3.14151e15	−1.66453	−0.832264	−	0.554380i	$-0.812956\pi$
$599$	−3.14151e15	−1.66453	−0.832264	+	0.554380i	$0.812956\pi$
$600$	3.08421e14	0.161924
$601$	1.48261e15	0.771288	0.385644	−	0.922648i	$-0.373979\pi$
$601$	1.48261e15	0.771288	0.385644	+	0.922648i	$0.373979\pi$
$602$	−4.11932e14	−0.212346
$603$	6.36526e14	0.325140
$604$	−1.21664e14	−0.0615829
$605$	−4.42342e15	−2.21873
$606$	−9.26895e14	−0.460714
$607$	2.41052e15	1.18733	0.593666	−	0.804711i	$-0.297680\pi$
$607$	2.41052e15	1.18733	0.593666	+	0.804711i	$0.297680\pi$
$608$	2.20294e15	1.07531
$609$	1.05507e14	0.0510372
$610$	1.91084e15	0.916032
$611$	−6.90469e13	−0.0328033
$612$	1.15656e15	0.544546
$613$	−3.43178e15	−1.60135	−0.800676	−	0.599097i	$-0.795526\pi$
$613$	−3.43178e15	−1.60135	−0.800676	+	0.599097i	$0.795526\pi$
$614$	−2.14713e15	−0.992963
$615$	−8.76665e14	−0.401810
$616$	7.96981e14	0.362038
$617$	1.08854e15	0.490092	0.245046	−	0.969512i	$-0.421197\pi$
$617$	1.08854e15	0.490092	0.245046	+	0.969512i	$0.421197\pi$
$618$	3.30847e15	1.47636
$619$	1.12768e15	0.498754	0.249377	−	0.968406i	$-0.419774\pi$
$619$	1.12768e15	0.498754	0.249377	+	0.968406i	$0.419774\pi$
$620$	2.48899e15	1.09111
$621$	4.30406e14	0.187014
$622$	4.48459e15	1.93142
$623$	−1.13203e15	−0.483251
$624$	−1.86160e14	−0.0787718
$625$	−2.98006e15	−1.24993
$626$	3.93844e15	1.63744
$627$	1.90360e15	0.784519
$628$	4.29267e15	1.75368
$629$	−2.07806e14	−0.0841550
$630$	5.90116e14	0.236900
$631$	4.31662e14	0.171784	0.0858919	−	0.996304i	$-0.472626\pi$
$631$	4.31662e14	0.171784	0.0858919	+	0.996304i	$0.472626\pi$
$632$	2.62903e14	0.103717
$633$	−2.36508e15	−0.924965
$634$	2.01301e15	0.780467
$635$	9.29819e14	0.357390
$636$	2.65774e15	1.01274
$637$	−1.04881e14	−0.0396214
$638$	−1.61370e15	−0.604379
$639$	6.25307e14	0.232187
$640$	−3.52643e15	−1.29821
$641$	2.80860e15	1.02511	0.512555	−	0.858654i	$-0.328699\pi$
$641$	2.80860e15	1.02511	0.512555	+	0.858654i	$0.328699\pi$
$642$	5.92988e14	0.214587
$643$	5.14744e15	1.84685	0.923424	−	0.383781i	$-0.125378\pi$
$643$	5.14744e15	1.84685	0.923424	+	0.383781i	$0.125378\pi$
$644$	−1.41518e15	−0.503432
$645$	7.29416e14	0.257274
$646$	−4.24838e15	−1.48575
$647$	−4.79076e15	−1.66123	−0.830617	−	0.556844i	$-0.812012\pi$
$647$	−4.79076e15	−1.66123	−0.830617	+	0.556844i	$0.812012\pi$
$648$	−1.84436e14	−0.0634137
$649$	6.21272e15	2.11805
$650$	6.20776e14	0.209851
$651$	4.24348e14	0.142242
$652$	6.80590e15	2.26216
$653$	−4.82004e15	−1.58865	−0.794324	−	0.607494i	$-0.792175\pi$
$653$	−4.82004e15	−1.58865	−0.794324	+	0.607494i	$0.792175\pi$
$654$	3.18408e15	1.04065
$655$	−1.67457e15	−0.542722
$656$	8.72282e14	0.280340
$657$	−1.14524e15	−0.364996
$658$	−2.17780e14	−0.0688297
$659$	−2.71767e15	−0.851779	−0.425890	−	0.904775i	$-0.640039\pi$
$659$	−2.71767e15	−0.851779	−0.425890	+	0.904775i	$0.640039\pi$
$660$	−5.21844e15	−1.62199
$661$	−5.37344e14	−0.165632	−0.0828160	−	0.996565i	$-0.526391\pi$
$661$	−5.37344e14	−0.165632	−0.0828160	+	0.996565i	$0.526391\pi$
$662$	6.33499e15	1.93654
$663$	6.29527e14	0.190849
$664$	−7.43380e13	−0.0223505
$665$	−1.25330e15	−0.373712
$666$	1.22541e14	0.0362387
$667$	7.74898e14	0.227275
$668$	−7.60116e15	−2.21110
$669$	2.33242e15	0.672920
$670$	6.40971e15	1.83412
$671$	−2.88089e15	−0.817623
$672$	−1.02960e15	−0.289826
$673$	−4.27385e15	−1.19326	−0.596632	−	0.802515i	$-0.703495\pi$
$673$	−4.27385e15	−1.19326	−0.596632	+	0.802515i	$0.703495\pi$
$674$	7.63915e14	0.211551
$675$	−3.44299e14	−0.0945726
$676$	3.86988e14	0.105436
$677$	−1.08439e15	−0.293053	−0.146527	−	0.989207i	$-0.546809\pi$
$677$	−1.08439e15	−0.293053	−0.146527	+	0.989207i	$0.546809\pi$
$678$	4.03420e15	1.08142
$679$	1.64370e15	0.437058
$680$	3.14953e15	0.830705
$681$	3.94844e15	1.03304
$682$	−6.49028e15	−1.68442
$683$	−4.17016e15	−1.07359	−0.536796	−	0.843712i	$-0.680366\pi$
$683$	−4.17016e15	−1.07359	−0.536796	+	0.843712i	$0.680366\pi$
$684$	1.44846e15	0.369913
$685$	−8.66391e15	−2.19490
$686$	−3.30804e14	−0.0831359
$687$	2.68916e15	0.670432
$688$	−7.25768e14	−0.179499
$689$	1.44663e15	0.354938
$690$	4.33411e15	1.05495
$691$	−1.29754e15	−0.313323	−0.156661	−	0.987652i	$-0.550073\pi$
$691$	−1.29754e15	−0.313323	−0.156661	+	0.987652i	$0.550073\pi$
$692$	5.53059e15	1.32491
$693$	−8.89692e14	−0.211450
$694$	−5.65105e15	−1.33245
$695$	−1.64279e15	−0.384296
$696$	−3.32057e14	−0.0770658
$697$	−2.94975e15	−0.679211
$698$	−1.11781e16	−2.55366
$699$	−2.30871e15	−0.523292
$700$	1.13206e15	0.254584
$701$	1.60609e15	0.358361	0.179180	−	0.983816i	$-0.442655\pi$
$701$	1.60609e15	0.358361	0.179180	+	0.983816i	$0.442655\pi$
$702$	−3.71224e14	−0.0821830
$703$	−2.60255e14	−0.0571669
$704$	1.19592e16	2.60647
$705$	3.85627e14	0.0833926
$706$	4.61372e15	0.989977
$707$	−9.20055e14	−0.195888
$708$	4.72732e15	0.998693
$709$	−6.62938e15	−1.38969	−0.694847	−	0.719158i	$-0.744528\pi$
$709$	−6.62938e15	−1.38969	−0.694847	+	0.719158i	$0.744528\pi$
$710$	6.29674e15	1.30977
$711$	−2.93486e14	−0.0605765
$712$	3.56277e15	0.729706
$713$	3.11663e15	0.633421
$714$	1.98559e15	0.400450
$715$	−2.84045e15	−0.568466
$716$	−2.27214e15	−0.451245
$717$	2.17721e15	0.429088
$718$	2.03846e15	0.398674
$719$	8.59398e15	1.66796	0.833979	−	0.551795i	$-0.186057\pi$
$719$	8.59398e15	1.66796	0.833979	+	0.551795i	$0.186057\pi$
$720$	1.03970e15	0.200254
$721$	3.28406e15	0.627721
$722$	2.79626e15	0.530423
$723$	5.18490e15	0.976067
$724$	6.72658e15	1.25670
$725$	−6.19873e14	−0.114933
$726$	8.77670e15	1.61503
$727$	−4.63477e15	−0.846426	−0.423213	−	0.906030i	$-0.639098\pi$
$727$	−4.63477e15	−0.846426	−0.423213	+	0.906030i	$0.639098\pi$
$728$	3.30086e14	0.0598281
$729$	2.05891e14	0.0370370
$730$	−1.15324e16	−2.05894
$731$	2.45429e15	0.434891
$732$	−2.19210e15	−0.385522
$733$	9.26638e15	1.61748	0.808739	−	0.588168i	$-0.200151\pi$
$733$	9.26638e15	1.61748	0.808739	+	0.588168i	$0.200151\pi$
$734$	1.05093e16	1.82072
$735$	5.85761e14	0.100726
$736$	−7.56189e15	−1.29063
$737$	−9.66364e15	−1.63708
$738$	1.73943e15	0.292480
$739$	−1.35050e15	−0.225398	−0.112699	−	0.993629i	$-0.535950\pi$
$739$	−1.35050e15	−0.225398	−0.112699	+	0.993629i	$0.535950\pi$
$740$	7.13452e14	0.118193
$741$	7.88415e14	0.129645
$742$	4.56282e15	0.744751
$743$	−1.24892e15	−0.202347	−0.101173	−	0.994869i	$-0.532260\pi$
$743$	−1.24892e15	−0.202347	−0.101173	+	0.994869i	$0.532260\pi$
$744$	−1.33553e15	−0.214784
$745$	−5.88987e15	−0.940256
$746$	1.42792e15	0.226277
$747$	8.29856e13	0.0130539
$748$	−1.75587e16	−2.74178
$749$	5.88612e14	0.0912386
$750$	3.58819e15	0.552127
$751$	9.42935e15	1.44033	0.720165	−	0.693803i	$-0.244066\pi$
$751$	9.42935e15	1.44033	0.720165	+	0.693803i	$0.244066\pi$
$752$	−3.83699e14	−0.0581825
$753$	−1.22219e15	−0.183978
$754$	−6.68348e14	−0.0998758
$755$	3.69857e14	0.0548688
$756$	−6.76975e14	−0.0997017
$757$	−3.10111e15	−0.453408	−0.226704	−	0.973964i	$-0.572795\pi$
$757$	−3.10111e15	−0.453408	−0.226704	+	0.973964i	$0.572795\pi$
$758$	−1.42809e16	−2.07289
$759$	−6.53435e15	−0.941613
$760$	3.94445e15	0.564302
$761$	7.93065e15	1.12640	0.563201	−	0.826320i	$-0.309570\pi$
$761$	7.93065e15	1.12640	0.563201	+	0.826320i	$0.309570\pi$
$762$	−1.84489e15	−0.260147
$763$	3.16058e15	0.442468
$764$	−5.69794e15	−0.791963
$765$	−3.51591e15	−0.485177
$766$	−7.00587e15	−0.959851
$767$	2.57313e15	0.350015
$768$	3.57939e14	0.0483417
$769$	−8.90447e15	−1.19402	−0.597012	−	0.802232i	$-0.703646\pi$
$769$	−8.90447e15	−1.19402	−0.597012	+	0.802232i	$0.703646\pi$
$770$	−8.95905e15	−1.19279
$771$	−2.44443e15	−0.323131
$772$	−7.62618e15	−1.00095
$773$	−2.52946e15	−0.329640	−0.164820	−	0.986324i	$-0.552704\pi$
$773$	−2.52946e15	−0.329640	−0.164820	+	0.986324i	$0.552704\pi$
$774$	−1.44726e15	−0.187272
$775$	−2.49312e15	−0.320320
$776$	−5.17313e15	−0.659955
$777$	1.21636e14	0.0154081
$778$	4.18827e15	0.526802
$779$	−3.69424e15	−0.461391
$780$	−2.16133e15	−0.268040
$781$	−9.49331e15	−1.16906
$782$	1.45831e16	1.78326
$783$	3.70684e14	0.0450106
$784$	−5.82832e14	−0.0702757
$785$	−1.30496e16	−1.56248
$786$	3.32259e15	0.395051
$787$	−2.31157e15	−0.272926	−0.136463	−	0.990645i	$-0.543574\pi$
$787$	−2.31157e15	−0.272926	−0.136463	+	0.990645i	$0.543574\pi$
$788$	1.54714e16	1.81399
$789$	−8.91095e15	−1.03753
$790$	−2.95535e15	−0.341712
$791$	4.00443e15	0.459801
$792$	2.80008e15	0.319287
$793$	−1.19318e15	−0.135115
$794$	9.87552e15	1.11057
$795$	−8.07946e15	−0.902325
$796$	−1.28385e16	−1.42394
$797$	−4.55532e15	−0.501763	−0.250881	−	0.968018i	$-0.580720\pi$
$797$	−4.55532e15	−0.501763	−0.250881	+	0.968018i	$0.580720\pi$
$798$	2.48673e15	0.272028
$799$	1.29753e15	0.140965
$800$	6.04907e15	0.652670
$801$	−3.97722e15	−0.426188
$802$	9.35882e15	0.996007
$803$	1.73869e16	1.83775
$804$	−7.35315e15	−0.771907
$805$	4.30213e15	0.448545
$806$	−2.68809e15	−0.278356
$807$	−5.78202e15	−0.594668
$808$	2.89564e15	0.295789
$809$	8.22276e15	0.834259	0.417129	−	0.908847i	$-0.363036\pi$
$809$	8.22276e15	0.834259	0.417129	+	0.908847i	$0.363036\pi$
$810$	2.07329e15	0.208926
$811$	5.02418e15	0.502864	0.251432	−	0.967875i	$-0.419098\pi$
$811$	5.02418e15	0.502864	0.251432	+	0.967875i	$0.419098\pi$
$812$	−1.21882e15	−0.121166
$813$	−1.00574e16	−0.993091
$814$	−1.86039e15	−0.182461
$815$	−2.06898e16	−2.01553
$816$	3.49833e15	0.338505
$817$	3.07374e15	0.295424
$818$	−1.21153e16	−1.15662
$819$	−3.68485e14	−0.0349428
$820$	1.01272e16	0.953927
$821$	3.09589e15	0.289666	0.144833	−	0.989456i	$-0.453735\pi$
$821$	3.09589e15	0.289666	0.144833	+	0.989456i	$0.453735\pi$
$822$	1.71904e16	1.59769
$823$	−6.68332e14	−0.0617012	−0.0308506	−	0.999524i	$-0.509822\pi$
$823$	−6.68332e14	−0.0617012	−0.0308506	+	0.999524i	$0.509822\pi$
$824$	−1.03357e16	−0.947854
$825$	5.22710e15	0.476172
$826$	8.11589e15	0.734422
$827$	−4.06670e15	−0.365563	−0.182781	−	0.983154i	$-0.558510\pi$
$827$	−4.06670e15	−0.365563	−0.182781	+	0.983154i	$0.558510\pi$
$828$	−4.97205e15	−0.443985
$829$	−4.83804e15	−0.429161	−0.214580	−	0.976706i	$-0.568838\pi$
$829$	−4.83804e15	−0.429161	−0.214580	+	0.976706i	$0.568838\pi$
$830$	8.35651e14	0.0736369
$831$	−4.41335e14	−0.0386334
$832$	4.95317e15	0.430729
$833$	1.97093e15	0.170265
$834$	3.25953e15	0.279732
$835$	2.31074e16	1.97004
$836$	−2.19904e16	−1.86251
$837$	1.49089e15	0.125445
$838$	−2.11392e16	−1.76704
$839$	−5.75907e15	−0.478257	−0.239129	−	0.970988i	$-0.576862\pi$
$839$	−5.75907e15	−0.478257	−0.239129	+	0.970988i	$0.576862\pi$
$840$	−1.84353e15	−0.152095
$841$	−1.15331e16	−0.945299
$842$	−2.58017e15	−0.210102
$843$	1.22021e16	0.987149
$844$	2.73214e16	2.19594
$845$	−1.17643e15	−0.0939411
$846$	−7.65140e14	−0.0607021
$847$	8.71193e15	0.686682
$848$	8.03906e15	0.629547
$849$	−3.61409e15	−0.281194
$850$	−1.16657e16	−0.901790
$851$	8.93360e14	0.0686142
$852$	−7.22355e15	−0.551230
$853$	−1.54688e16	−1.17283	−0.586417	−	0.810009i	$-0.699462\pi$
$853$	−1.54688e16	−1.17283	−0.586417	+	0.810009i	$0.699462\pi$
$854$	−3.76341e15	−0.283506
$855$	−4.40330e15	−0.329583
$856$	−1.85250e15	−0.137770
$857$	3.67451e15	0.271522	0.135761	−	0.990742i	$-0.456652\pi$
$857$	3.67451e15	0.271522	0.135761	+	0.990742i	$0.456652\pi$
$858$	5.63587e15	0.413791
$859$	−9.25548e15	−0.675206	−0.337603	−	0.941289i	$-0.609616\pi$
$859$	−9.25548e15	−0.675206	−0.337603	+	0.941289i	$0.609616\pi$
$860$	−8.42621e15	−0.610789
$861$	1.72659e15	0.124358
$862$	1.82891e16	1.30889
$863$	1.04164e16	0.740728	0.370364	−	0.928887i	$-0.379233\pi$
$863$	1.04164e16	0.740728	0.370364	+	0.928887i	$0.379233\pi$
$864$	−3.61735e15	−0.255602
$865$	−1.68129e16	−1.18047
$866$	−2.31472e14	−0.0161492
$867$	−3.50204e15	−0.242782
$868$	−4.90207e15	−0.337692
$869$	4.45566e15	0.305002
$870$	3.73273e15	0.253905
$871$	−4.00240e15	−0.270533
$872$	−9.94712e15	−0.668124
$873$	5.77491e15	0.385449
$874$	1.82638e16	1.21138
$875$	3.56171e15	0.234755
$876$	1.32299e16	0.866528
$877$	−6.19237e15	−0.403050	−0.201525	−	0.979483i	$-0.564590\pi$
$877$	−6.19237e15	−0.403050	−0.201525	+	0.979483i	$0.564590\pi$
$878$	−2.32060e16	−1.50100
$879$	8.71332e14	0.0560073
$880$	−1.57846e16	−1.00828
$881$	−1.08017e16	−0.685683	−0.342842	−	0.939393i	$-0.611389\pi$
$881$	−1.08017e16	−0.685683	−0.342842	+	0.939393i	$0.611389\pi$
$882$	−1.16223e15	−0.0733190
$883$	2.71395e16	1.70145	0.850723	−	0.525615i	$-0.176165\pi$
$883$	2.71395e16	1.70145	0.850723	+	0.525615i	$0.176165\pi$
$884$	−7.27230e15	−0.453090
$885$	−1.43709e16	−0.889810
$886$	3.78333e16	2.32803
$887$	−2.60367e16	−1.59223	−0.796114	−	0.605146i	$-0.793115\pi$
$887$	−2.60367e16	−1.59223	−0.796114	+	0.605146i	$0.793115\pi$
$888$	−3.82820e14	−0.0232661
$889$	−1.83128e15	−0.110610
$890$	−4.00500e16	−2.40412
$891$	−3.12581e15	−0.186481
$892$	−2.69441e16	−1.59756
$893$	1.62502e15	0.0957582
$894$	1.16863e16	0.684419
$895$	6.90724e15	0.402048
$896$	6.94530e15	0.401788
$897$	−2.70634e15	−0.155605
$898$	−1.87131e16	−1.06936
$899$	2.68418e15	0.152452
$900$	3.97735e15	0.224522
$901$	−2.71852e16	−1.52527
$902$	−2.64077e16	−1.47264
$903$	−1.43658e15	−0.0796248
$904$	−1.26029e16	−0.694297
$905$	−2.04486e16	−1.11969
$906$	−7.33849e14	−0.0399394
$907$	−2.29470e16	−1.24133	−0.620664	−	0.784077i	$-0.713137\pi$
$907$	−2.29470e16	−1.24133	−0.620664	+	0.784077i	$0.713137\pi$
$908$	−4.56124e16	−2.45251
$909$	−3.23248e15	−0.172757
$910$	−3.71058e15	−0.197112
$911$	−1.26887e14	−0.00669989	−0.00334994	−	0.999994i	$-0.501066\pi$
$911$	−1.26887e14	−0.00669989	−0.00334994	+	0.999994i	$0.501066\pi$
$912$	4.38128e15	0.229948
$913$	−1.25987e15	−0.0657261
$914$	2.07322e16	1.07508
$915$	6.66393e15	0.343490
$916$	−3.10652e16	−1.59166
$917$	3.29807e15	0.167969
$918$	6.97607e15	0.353164
$919$	−1.75468e16	−0.883006	−0.441503	−	0.897260i	$-0.645554\pi$
$919$	−1.75468e16	−0.883006	−0.441503	+	0.897260i	$0.645554\pi$
$920$	−1.35399e16	−0.677300
$921$	−7.48798e15	−0.372337
$922$	−5.41942e16	−2.67875
$923$	−3.93186e15	−0.193192
$924$	1.02777e16	0.501997
$925$	−7.14636e14	−0.0346981
$926$	2.19571e16	1.05978
$927$	1.15381e16	0.553598
$928$	−6.51263e15	−0.310629
$929$	−1.89078e16	−0.896509	−0.448254	−	0.893906i	$-0.647954\pi$
$929$	−1.89078e16	−0.896509	−0.448254	+	0.893906i	$0.647954\pi$
$930$	1.50130e16	0.707637
$931$	2.46838e15	0.115662
$932$	2.66702e16	1.24233
$933$	1.56397e16	0.724235
$934$	1.93636e14	0.00891410
$935$	5.33780e16	2.44286
$936$	1.15971e15	0.0527634
$937$	1.03996e16	0.470380	0.235190	−	0.971949i	$-0.424429\pi$
$937$	1.03996e16	0.470380	0.235190	+	0.971949i	$0.424429\pi$
$938$	−1.26239e16	−0.567648
$939$	1.37350e16	0.614001
$940$	−4.45477e15	−0.197980
$941$	−1.27405e16	−0.562917	−0.281459	−	0.959573i	$-0.590818\pi$
$941$	−1.27405e16	−0.562917	−0.281459	+	0.959573i	$0.590818\pi$
$942$	2.58923e16	1.13734
$943$	1.26810e16	0.553781
$944$	1.42991e16	0.620815
$945$	2.05799e15	0.0888317
$946$	2.19721e16	0.942912
$947$	−3.55556e16	−1.51699	−0.758496	−	0.651678i	$-0.774065\pi$
$947$	−3.55556e16	−1.51699	−0.758496	+	0.651678i	$0.774065\pi$
$948$	3.39035e15	0.143813
$949$	7.20116e15	0.303695
$950$	−1.46100e16	−0.612590
$951$	7.02023e15	0.292657
$952$	−6.20301e15	−0.257098
$953$	1.67046e16	0.688374	0.344187	−	0.938901i	$-0.388155\pi$
$953$	1.67046e16	0.688374	0.344187	+	0.938901i	$0.388155\pi$
$954$	1.60308e16	0.656809
$955$	1.73216e16	0.705619
$956$	−2.51512e16	−1.01869
$957$	−5.62767e15	−0.226628
$958$	4.64840e16	1.86120
$959$	1.70636e16	0.679309
$960$	−2.76635e16	−1.09500
$961$	−1.46128e16	−0.575113
$962$	−7.70522e14	−0.0301524
$963$	2.06800e15	0.0804649
$964$	−5.98960e16	−2.31726
$965$	2.31834e16	0.891820
$966$	−8.53604e15	−0.326499
$967$	−4.25554e16	−1.61849	−0.809243	−	0.587474i	$-0.800122\pi$
$967$	−4.25554e16	−1.61849	−0.809243	+	0.587474i	$0.800122\pi$
$968$	−2.74186e16	−1.03688
$969$	−1.48159e16	−0.557120
$970$	5.81524e16	2.17432
$971$	−3.37519e16	−1.25485	−0.627425	−	0.778677i	$-0.715891\pi$
$971$	−3.37519e16	−1.25485	−0.627425	+	0.778677i	$0.715891\pi$
$972$	−2.37845e15	−0.0879287
$973$	3.23547e15	0.118937
$974$	6.83592e16	2.49875
$975$	2.16491e15	0.0786892
$976$	−6.63061e15	−0.239651
$977$	−3.92325e16	−1.41002	−0.705012	−	0.709196i	$-0.749058\pi$
$977$	−3.92325e16	−1.41002	−0.705012	+	0.709196i	$0.749058\pi$
$978$	4.10515e16	1.46712
$979$	6.03815e16	2.14585
$980$	−6.76672e15	−0.239130
$981$	1.11043e16	0.390220
$982$	−6.83431e15	−0.238826
$983$	−2.36974e15	−0.0823485	−0.0411742	−	0.999152i	$-0.513110\pi$
$983$	−2.36974e15	−0.0823485	−0.0411742	+	0.999152i	$0.513110\pi$
$984$	−5.43401e15	−0.187779
$985$	−4.70328e16	−1.61622
$986$	1.25596e16	0.429195
$987$	−7.59493e14	−0.0258095
$988$	−9.10777e15	−0.307786
$989$	−1.05510e16	−0.354580
$990$	−3.14763e16	−1.05194
$991$	4.33811e16	1.44177	0.720884	−	0.693056i	$-0.243736\pi$
$991$	4.33811e16	1.44177	0.720884	+	0.693056i	$0.243736\pi$
$992$	−2.61937e16	−0.865731
$993$	2.20928e16	0.726157
$994$	−1.24014e16	−0.405365
$995$	3.90288e16	1.26870
$996$	−9.58650e14	−0.0309909
$997$	−1.80200e16	−0.579338	−0.289669	−	0.957127i	$-0.593545\pi$
$997$	−1.80200e16	−0.579338	−0.289669	+	0.957127i	$0.593545\pi$
$998$	−4.35854e16	−1.39355
$999$	4.27352e14	0.0135886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-69.6788 q^{2} -243.000 q^{3} +2807.14 q^{4} -8533.64 q^{5} +16932.0 q^{6} +16807.0 q^{7} -52895.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-69.6788 q^{2} -243.000 q^{3} +2807.14 q^{4} -8533.64 q^{5} +16932.0 q^{6} +16807.0 q^{7} -52895.7 q^{8} +59049.0 q^{9} +594614. q^{10} -896472. q^{11} -682134. q^{12} -371293. q^{13} -1.17109e6 q^{14} +2.07367e6 q^{15} -2.06330e6 q^{16} +6.97736e6 q^{17} -4.11446e6 q^{18} +8.73840e6 q^{19} -2.39551e7 q^{20} -4.08410e6 q^{21} +6.24651e7 q^{22} -2.99957e7 q^{23} +1.28537e7 q^{24} +2.39948e7 q^{25} +2.58713e7 q^{26} -1.43489e7 q^{27} +4.71795e7 q^{28} -2.58336e7 q^{29} -1.44491e8 q^{30} -1.03902e8 q^{31} +2.52099e8 q^{32} +2.17843e8 q^{33} -4.86174e8 q^{34} -1.43425e8 q^{35} +1.65759e8 q^{36} -2.97829e7 q^{37} -6.08881e8 q^{38} +9.02242e7 q^{39} +4.51393e8 q^{40} -4.22760e8 q^{41} +2.84575e8 q^{42} +3.51751e8 q^{43} -2.51652e9 q^{44} -5.03903e8 q^{45} +2.09007e9 q^{46} +1.85963e8 q^{47} +5.01383e8 q^{48} +2.82475e8 q^{49} -1.67193e9 q^{50} -1.69550e9 q^{51} -1.04227e9 q^{52} -3.89621e9 q^{53} +9.99815e8 q^{54} +7.65017e9 q^{55} -8.89019e8 q^{56} -2.12343e9 q^{57} +1.80006e9 q^{58} -6.93019e9 q^{59} +5.82108e9 q^{60} +3.21359e9 q^{61} +7.23980e9 q^{62} +9.92437e8 q^{63} -1.33403e10 q^{64} +3.16848e9 q^{65} -1.51790e10 q^{66} +1.07796e10 q^{67} +1.95864e10 q^{68} +7.28896e9 q^{69} +9.99367e9 q^{70} +1.05896e10 q^{71} -3.12344e9 q^{72} -1.93948e10 q^{73} +2.07524e9 q^{74} -5.83074e9 q^{75} +2.45299e10 q^{76} -1.50670e10 q^{77} -6.28671e9 q^{78} -4.97021e9 q^{79} +1.76075e10 q^{80} +3.48678e9 q^{81} +2.94574e10 q^{82} +1.40537e9 q^{83} -1.14646e10 q^{84} -5.95423e10 q^{85} -2.45096e10 q^{86} +6.27757e9 q^{87} +4.74196e10 q^{88} -6.73546e10 q^{89} +3.51113e10 q^{90} -6.24032e9 q^{91} -8.42021e10 q^{92} +2.52483e10 q^{93} -1.29577e10 q^{94} -7.45703e10 q^{95} -6.12601e10 q^{96} +9.77987e10 q^{97} -1.96825e10 q^{98} -5.29358e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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