LMFDB - Embedded newform 273.12.a.c.1.3

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			1.3
Root			$-68.0202$ 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)

$f(q)$	$=$	$q-72.0202 q^{2} -243.000 q^{3} +3138.91 q^{4} +10386.5 q^{5} +17500.9 q^{6} +16807.0 q^{7} -78567.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-72.0202 q^{2} -243.000 q^{3} +3138.91 q^{4} +10386.5 q^{5} +17500.9 q^{6} +16807.0 q^{7} -78567.7 q^{8} +59049.0 q^{9} -748037. q^{10} -54869.8 q^{11} -762756. q^{12} -371293. q^{13} -1.21044e6 q^{14} -2.52391e6 q^{15} -770028. q^{16} +8.38294e6 q^{17} -4.25272e6 q^{18} +2.28143e6 q^{19} +3.26022e7 q^{20} -4.08410e6 q^{21} +3.95173e6 q^{22} +3.46075e7 q^{23} +1.90920e7 q^{24} +5.90508e7 q^{25} +2.67406e7 q^{26} -1.43489e7 q^{27} +5.27557e7 q^{28} +4.87020e7 q^{29} +1.81773e8 q^{30} -1.98801e8 q^{31} +2.16364e8 q^{32} +1.33333e7 q^{33} -6.03741e8 q^{34} +1.74566e8 q^{35} +1.85350e8 q^{36} -2.17672e8 q^{37} -1.64309e8 q^{38} +9.02242e7 q^{39} -8.16042e8 q^{40} -5.94586e8 q^{41} +2.94138e8 q^{42} -9.67503e7 q^{43} -1.72231e8 q^{44} +6.13311e8 q^{45} -2.49244e9 q^{46} -1.28528e9 q^{47} +1.87117e8 q^{48} +2.82475e8 q^{49} -4.25285e9 q^{50} -2.03706e9 q^{51} -1.16546e9 q^{52} -2.30912e9 q^{53} +1.03341e9 q^{54} -5.69904e8 q^{55} -1.32049e9 q^{56} -5.54386e8 q^{57} -3.50753e9 q^{58} -3.33247e9 q^{59} -7.92235e9 q^{60} -5.51641e8 q^{61} +1.43177e10 q^{62} +9.92437e8 q^{63} -1.40056e10 q^{64} -3.85643e9 q^{65} -9.60271e8 q^{66} -1.91638e10 q^{67} +2.63133e10 q^{68} -8.40963e9 q^{69} -1.25722e10 q^{70} -2.26355e10 q^{71} -4.63934e9 q^{72} +1.35333e10 q^{73} +1.56768e10 q^{74} -1.43494e10 q^{75} +7.16119e9 q^{76} -9.22196e8 q^{77} -6.49797e9 q^{78} -1.95395e10 q^{79} -7.99788e9 q^{80} +3.48678e9 q^{81} +4.28222e10 q^{82} -2.23053e10 q^{83} -1.28196e10 q^{84} +8.70693e10 q^{85} +6.96798e9 q^{86} -1.18346e10 q^{87} +4.31099e9 q^{88} -8.54763e9 q^{89} -4.41708e10 q^{90} -6.24032e9 q^{91} +1.08630e11 q^{92} +4.83087e10 q^{93} +9.25662e10 q^{94} +2.36960e10 q^{95} -5.25765e10 q^{96} -1.38639e11 q^{97} -2.03439e10 q^{98} -3.24000e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−72.0202	−1.59144	−0.795719	−	0.605667i	$-0.792907\pi$
$2$	−72.0202	−1.59144	−0.795719	+	0.605667i	$0.792907\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	3138.91	1.53267
$5$	10386.5	1.48639	0.743196	−	0.669074i	$-0.233309\pi$
$5$	10386.5	1.48639	0.743196	+	0.669074i	$0.233309\pi$
$6$	17500.9	0.918817
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−78567.7	−0.847714
$9$	59049.0	0.333333
$10$	−748037.	−2.36550
$11$	−54869.8	−0.102724	−0.0513622	−	0.998680i	$-0.516356\pi$
$11$	−54869.8	−0.102724	−0.0513622	+	0.998680i	$0.516356\pi$
$12$	−762756.	−0.884888
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−1.21044e6	−0.601507
$15$	−2.52391e6	−0.858169
$16$	−770028.	−0.183589
$17$	8.38294e6	1.43195	0.715974	−	0.698127i	$-0.245983\pi$
$17$	8.38294e6	1.43195	0.715974	+	0.698127i	$0.245983\pi$
$18$	−4.25272e6	−0.530479
$19$	2.28143e6	0.211379	0.105689	−	0.994399i	$-0.466295\pi$
$19$	2.28143e6	0.211379	0.105689	+	0.994399i	$0.466295\pi$
$20$	3.26022e7	2.27815
$21$	−4.08410e6	−0.218218
$22$	3.95173e6	0.163479
$23$	3.46075e7	1.12116	0.560580	−	0.828100i	$-0.310578\pi$
$23$	3.46075e7	1.12116	0.560580	+	0.828100i	$0.310578\pi$
$24$	1.90920e7	0.489428
$25$	5.90508e7	1.20936
$26$	2.67406e7	0.441385
$27$	−1.43489e7	−0.192450
$28$	5.27557e7	0.579296
$29$	4.87020e7	0.440918	0.220459	−	0.975396i	$-0.429244\pi$
$29$	4.87020e7	0.440918	0.220459	+	0.975396i	$0.429244\pi$
$30$	1.81773e8	1.36572
$31$	−1.98801e8	−1.24718	−0.623591	−	0.781751i	$-0.714327\pi$
$31$	−1.98801e8	−1.24718	−0.623591	+	0.781751i	$0.714327\pi$
$32$	2.16364e8	1.13988
$33$	1.33333e7	0.0593079
$34$	−6.03741e8	−2.27886
$35$	1.74566e8	0.561803
$36$	1.85350e8	0.510891
$37$	−2.17672e8	−0.516052	−0.258026	−	0.966138i	$-0.583072\pi$
$37$	−2.17672e8	−0.516052	−0.258026	+	0.966138i	$0.583072\pi$
$38$	−1.64309e8	−0.336396
$39$	9.02242e7	0.160128
$40$	−8.16042e8	−1.26003
$41$	−5.94586e8	−0.801500	−0.400750	−	0.916187i	$-0.631250\pi$
$41$	−5.94586e8	−0.801500	−0.400750	+	0.916187i	$0.631250\pi$
$42$	2.94138e8	0.347280
$43$	−9.67503e7	−0.100363	−0.0501817	−	0.998740i	$-0.515980\pi$
$43$	−9.67503e7	−0.100363	−0.0501817	+	0.998740i	$0.515980\pi$
$44$	−1.72231e8	−0.157443
$45$	6.13311e8	0.495464
$46$	−2.49244e9	−1.78426
$47$	−1.28528e9	−0.817447	−0.408724	−	0.912658i	$-0.634026\pi$
$47$	−1.28528e9	−0.817447	−0.408724	+	0.912658i	$0.634026\pi$
$48$	1.87117e8	0.105995
$49$	2.82475e8	0.142857
$50$	−4.25285e9	−1.92462
$51$	−2.03706e9	−0.826736
$52$	−1.16546e9	−0.425087
$53$	−2.30912e9	−0.758454	−0.379227	−	0.925304i	$-0.623810\pi$
$53$	−2.30912e9	−0.758454	−0.379227	+	0.925304i	$0.623810\pi$
$54$	1.03341e9	0.306272
$55$	−5.69904e8	−0.152689
$56$	−1.32049e9	−0.320406
$57$	−5.54386e8	−0.122040
$58$	−3.50753e9	−0.701693
$59$	−3.33247e9	−0.606848	−0.303424	−	0.952856i	$-0.598130\pi$
$59$	−3.33247e9	−0.606848	−0.303424	+	0.952856i	$0.598130\pi$
$60$	−7.92235e9	−1.31529
$61$	−5.51641e8	−0.0836262	−0.0418131	−	0.999125i	$-0.513313\pi$
$61$	−5.51641e8	−0.0836262	−0.0418131	+	0.999125i	$0.513313\pi$
$62$	1.43177e10	1.98481
$63$	9.92437e8	0.125988
$64$	−1.40056e10	−1.63046
$65$	−3.85643e9	−0.412251
$66$	−9.60271e8	−0.0943848
$67$	−1.91638e10	−1.73409	−0.867043	−	0.498234i	$-0.833982\pi$
$67$	−1.91638e10	−1.73409	−0.867043	+	0.498234i	$0.833982\pi$
$68$	2.63133e10	2.19471
$69$	−8.40963e9	−0.647302
$70$	−1.25722e10	−0.894075
$71$	−2.26355e10	−1.48891	−0.744455	−	0.667673i	$-0.767291\pi$
$71$	−2.26355e10	−1.48891	−0.744455	+	0.667673i	$0.767291\pi$
$72$	−4.63934e9	−0.282571
$73$	1.35333e10	0.764060	0.382030	−	0.924150i	$-0.375225\pi$
$73$	1.35333e10	0.764060	0.382030	+	0.924150i	$0.375225\pi$
$74$	1.56768e10	0.821264
$75$	−1.43494e10	−0.698225
$76$	7.16119e9	0.323974
$77$	−9.22196e8	−0.0388261
$78$	−6.49797e9	−0.254834
$79$	−1.95395e10	−0.714436	−0.357218	−	0.934021i	$-0.616275\pi$
$79$	−1.95395e10	−0.714436	−0.357218	+	0.934021i	$0.616275\pi$
$80$	−7.99788e9	−0.272885
$81$	3.48678e9	0.111111
$82$	4.28222e10	1.27554
$83$	−2.23053e10	−0.621554	−0.310777	−	0.950483i	$-0.600589\pi$
$83$	−2.23053e10	−0.621554	−0.310777	+	0.950483i	$0.600589\pi$
$84$	−1.28196e10	−0.334456
$85$	8.70693e10	2.12844
$86$	6.96798e9	0.159722
$87$	−1.18346e10	−0.254564
$88$	4.31099e9	0.0870808
$89$	−8.54763e9	−0.162256	−0.0811280	−	0.996704i	$-0.525852\pi$
$89$	−8.54763e9	−0.162256	−0.0811280	+	0.996704i	$0.525852\pi$
$90$	−4.41708e10	−0.788500
$91$	−6.24032e9	−0.104828
$92$	1.08630e11	1.71837
$93$	4.83087e10	0.720061
$94$	9.25662e10	1.30092
$95$	2.36960e10	0.314192
$96$	−5.25765e10	−0.658112
$97$	−1.38639e11	−1.63923	−0.819617	−	0.572911i	$-0.805814\pi$
$97$	−1.38639e11	−1.63923	−0.819617	+	0.572911i	$0.805814\pi$
$98$	−2.03439e10	−0.227348
$99$	−3.24000e9	−0.0342414
$100$	1.85355e11	1.85355
$101$	1.02717e11	0.972466	0.486233	−	0.873829i	$-0.338371\pi$
$101$	1.02717e11	0.972466	0.486233	+	0.873829i	$0.338371\pi$
$102$	1.46709e11	1.31570
$103$	−1.89741e10	−0.161271	−0.0806357	−	0.996744i	$-0.525695\pi$
$103$	−1.89741e10	−0.161271	−0.0806357	+	0.996744i	$0.525695\pi$
$104$	2.91716e10	0.235113
$105$	−4.24194e10	−0.324357
$106$	1.66303e11	1.20703
$107$	6.90189e10	0.475727	0.237863	−	0.971299i	$-0.423553\pi$
$107$	6.90189e10	0.475727	0.237863	+	0.971299i	$0.423553\pi$
$108$	−4.50400e10	−0.294963
$109$	−1.66287e11	−1.03517	−0.517585	−	0.855632i	$-0.673169\pi$
$109$	−1.66287e11	−1.03517	−0.517585	+	0.855632i	$0.673169\pi$
$110$	4.10446e10	0.242994
$111$	5.28943e10	0.297943
$112$	−1.29419e10	−0.0693901
$113$	−8.46513e10	−0.432217	−0.216109	−	0.976369i	$-0.569337\pi$
$113$	−8.46513e10	−0.432217	−0.216109	+	0.976369i	$0.569337\pi$
$114$	3.99270e10	0.194218
$115$	3.59451e11	1.66648
$116$	1.52871e11	0.675783
$117$	−2.19245e10	−0.0924500
$118$	2.40005e11	0.965760
$119$	1.40892e11	0.541226
$120$	1.98298e11	0.727481
$121$	−2.82301e11	−0.989448
$122$	3.97293e10	0.133086
$123$	1.44484e11	0.462746
$124$	−6.24020e11	−1.91152
$125$	1.06178e11	0.311192
$126$	−7.14755e10	−0.200502
$127$	6.05760e11	1.62697	0.813486	−	0.581584i	$-0.197567\pi$
$127$	6.05760e11	1.62697	0.813486	+	0.581584i	$0.197567\pi$
$128$	5.65571e11	1.45490
$129$	2.35103e10	0.0579449
$130$	2.77741e11	0.656071
$131$	−3.67870e11	−0.833109	−0.416555	−	0.909111i	$-0.636763\pi$
$131$	−3.67870e11	−0.833109	−0.416555	+	0.909111i	$0.636763\pi$
$132$	4.18522e10	0.0908996
$133$	3.83439e10	0.0798937
$134$	1.38018e12	2.75969
$135$	−1.49035e11	−0.286056
$136$	−6.58629e11	−1.21388
$137$	−2.88591e11	−0.510881	−0.255440	−	0.966825i	$-0.582220\pi$
$137$	−2.88591e11	−0.510881	−0.255440	+	0.966825i	$0.582220\pi$
$138$	6.05664e11	1.03014
$139$	−4.45630e11	−0.728439	−0.364219	−	0.931313i	$-0.618664\pi$
$139$	−4.45630e11	−0.728439	−0.364219	+	0.931313i	$0.618664\pi$
$140$	5.47946e11	0.861060
$141$	3.12323e11	0.471953
$142$	1.63021e12	2.36951
$143$	2.03728e10	0.0284906
$144$	−4.54694e10	−0.0611963
$145$	5.05842e11	0.655377
$146$	−9.74670e11	−1.21595
$147$	−6.86415e10	−0.0824786
$148$	−6.83253e11	−0.790938
$149$	4.94332e11	0.551435	0.275718	−	0.961239i	$-0.411085\pi$
$149$	4.94332e11	0.551435	0.275718	+	0.961239i	$0.411085\pi$
$150$	1.03344e12	1.11118
$151$	−6.45835e11	−0.669496	−0.334748	−	0.942308i	$-0.608651\pi$
$151$	−6.45835e11	−0.669496	−0.334748	+	0.942308i	$0.608651\pi$
$152$	−1.79246e11	−0.179189
$153$	4.95004e11	0.477316
$154$	6.64167e10	0.0617894
$155$	−2.06485e12	−1.85380
$156$	2.83206e11	0.245424
$157$	2.25304e12	1.88504	0.942522	−	0.334144i	$-0.108447\pi$
$157$	2.25304e12	1.88504	0.942522	+	0.334144i	$0.108447\pi$
$158$	1.40724e12	1.13698
$159$	5.61116e11	0.437894
$160$	2.24726e12	1.69431
$161$	5.81649e11	0.423759
$162$	−2.51119e11	−0.176826
$163$	−1.69121e12	−1.15124	−0.575619	−	0.817718i	$-0.695239\pi$
$163$	−1.69121e12	−1.15124	−0.575619	+	0.817718i	$0.695239\pi$
$164$	−1.86635e12	−1.22844
$165$	1.38487e11	0.0881548
$166$	1.60643e12	0.989163
$167$	−2.14256e10	−0.0127642	−0.00638209	−	0.999980i	$-0.502031\pi$
$167$	−2.14256e10	−0.0127642	−0.00638209	+	0.999980i	$0.502031\pi$
$168$	3.20878e11	0.184986
$169$	1.37858e11	0.0769231
$170$	−6.27075e12	−3.38727
$171$	1.34716e11	0.0704596
$172$	−3.03691e11	−0.153824
$173$	−8.20851e11	−0.402727	−0.201363	−	0.979517i	$-0.564537\pi$
$173$	−8.20851e11	−0.402727	−0.201363	+	0.979517i	$0.564537\pi$
$174$	8.52330e11	0.405123
$175$	9.92467e11	0.457095
$176$	4.22512e10	0.0188590
$177$	8.09790e11	0.350364
$178$	6.15602e11	0.258220
$179$	−2.51132e11	−0.102143	−0.0510716	−	0.998695i	$-0.516264\pi$
$179$	−2.51132e11	−0.102143	−0.0510716	+	0.998695i	$0.516264\pi$
$180$	1.92513e12	0.759384
$181$	−2.70122e12	−1.03354	−0.516770	−	0.856124i	$-0.672866\pi$
$181$	−2.70122e12	−1.03354	−0.516770	+	0.856124i	$0.672866\pi$
$182$	4.49429e11	0.166828
$183$	1.34049e11	0.0482816
$184$	−2.71904e12	−0.950423
$185$	−2.26085e12	−0.767055
$186$	−3.47921e12	−1.14593
$187$	−4.59970e11	−0.147096
$188$	−4.03438e12	−1.25288
$189$	−2.41162e11	−0.0727393
$190$	−1.70659e12	−0.500016
$191$	3.09580e12	0.881230	0.440615	−	0.897696i	$-0.354760\pi$
$191$	3.09580e12	0.881230	0.440615	+	0.897696i	$0.354760\pi$
$192$	3.40336e12	0.941349
$193$	4.71878e12	1.26842	0.634212	−	0.773159i	$-0.281325\pi$
$193$	4.71878e12	1.26842	0.634212	+	0.773159i	$0.281325\pi$
$194$	9.98482e12	2.60874
$195$	9.37112e11	0.238013
$196$	8.86665e11	0.218953
$197$	−2.27060e12	−0.545227	−0.272613	−	0.962124i	$-0.587888\pi$
$197$	−2.27060e12	−0.545227	−0.272613	+	0.962124i	$0.587888\pi$
$198$	2.33346e11	0.0544931
$199$	1.25545e12	0.285171	0.142586	−	0.989782i	$-0.454458\pi$
$199$	1.25545e12	0.285171	0.142586	+	0.989782i	$0.454458\pi$
$200$	−4.63949e12	−1.02519
$201$	4.65681e12	1.00117
$202$	−7.39769e12	−1.54762
$203$	8.18535e11	0.166651
$204$	−6.39414e12	−1.26712
$205$	−6.17566e12	−1.19134
$206$	1.36652e12	0.256653
$207$	2.04354e12	0.373720
$208$	2.85906e11	0.0509184
$209$	−1.25181e11	−0.0217137
$210$	3.05506e12	0.516194
$211$	−7.68169e12	−1.26445	−0.632227	−	0.774783i	$-0.717859\pi$
$211$	−7.68169e12	−1.26445	−0.632227	+	0.774783i	$0.717859\pi$
$212$	−7.24813e12	−1.16246
$213$	5.50042e12	0.859622
$214$	−4.97076e12	−0.757089
$215$	−1.00489e12	−0.149179
$216$	1.12736e12	0.163143
$217$	−3.34125e12	−0.471391
$218$	1.19760e13	1.64741
$219$	−3.28859e12	−0.441130
$220$	−1.78888e12	−0.234021
$221$	−3.11253e12	−0.397151
$222$	−3.80946e12	−0.474157
$223$	−9.73111e11	−0.118164	−0.0590821	−	0.998253i	$-0.518817\pi$
$223$	−9.73111e11	−0.118164	−0.0590821	+	0.998253i	$0.518817\pi$
$224$	3.63643e12	0.430836
$225$	3.48689e12	0.403120
$226$	6.09661e12	0.687847
$227$	2.99000e12	0.329253	0.164626	−	0.986356i	$-0.447358\pi$
$227$	2.99000e12	0.329253	0.164626	+	0.986356i	$0.447358\pi$
$228$	−1.74017e12	−0.187047
$229$	1.32586e13	1.39124	0.695622	−	0.718408i	$-0.255129\pi$
$229$	1.32586e13	1.39124	0.695622	+	0.718408i	$0.255129\pi$
$230$	−2.58877e13	−2.65210
$231$	2.24094e11	0.0224163
$232$	−3.82641e12	−0.373772
$233$	−1.04644e13	−0.998293	−0.499147	−	0.866518i	$-0.666353\pi$
$233$	−1.04644e13	−0.998293	−0.499147	+	0.866518i	$0.666353\pi$
$234$	1.57901e12	0.147128
$235$	−1.33495e13	−1.21505
$236$	−1.04603e13	−0.930099
$237$	4.74809e12	0.412480
$238$	−1.01471e13	−0.861327
$239$	3.09290e12	0.256554	0.128277	−	0.991738i	$-0.459055\pi$
$239$	3.09290e12	0.256554	0.128277	+	0.991738i	$0.459055\pi$
$240$	1.94348e12	0.157550
$241$	3.96827e12	0.314418	0.157209	−	0.987565i	$-0.449750\pi$
$241$	3.96827e12	0.314418	0.157209	+	0.987565i	$0.449750\pi$
$242$	2.03314e13	1.57464
$243$	−8.47289e11	−0.0641500
$244$	−1.73155e12	−0.128172
$245$	2.93392e12	0.212342
$246$	−1.04058e13	−0.736432
$247$	−8.47077e11	−0.0586259
$248$	1.56194e13	1.05725
$249$	5.42019e12	0.358854
$250$	−7.64695e12	−0.495243
$251$	−1.83874e13	−1.16497	−0.582486	−	0.812841i	$-0.697920\pi$
$251$	−1.83874e13	−1.16497	−0.582486	+	0.812841i	$0.697920\pi$
$252$	3.11517e12	0.193099
$253$	−1.89891e12	−0.115170
$254$	−4.36270e13	−2.58922
$255$	−2.11578e13	−1.22885
$256$	−1.20491e13	−0.684914
$257$	−1.81562e13	−1.01017	−0.505083	−	0.863071i	$-0.668538\pi$
$257$	−1.81562e13	−1.01017	−0.505083	+	0.863071i	$0.668538\pi$
$258$	−1.69322e12	−0.0922156
$259$	−3.65841e12	−0.195049
$260$	−1.21050e13	−0.631845
$261$	2.87580e12	0.146973
$262$	2.64941e13	1.32584
$263$	1.31793e13	0.645854	0.322927	−	0.946424i	$-0.395333\pi$
$263$	1.31793e13	0.645854	0.322927	+	0.946424i	$0.395333\pi$
$264$	−1.04757e12	−0.0502761
$265$	−2.39836e13	−1.12736
$266$	−2.76154e12	−0.127146
$267$	2.07707e12	0.0936785
$268$	−6.01535e13	−2.65778
$269$	−1.95765e13	−0.847416	−0.423708	−	0.905799i	$-0.639272\pi$
$269$	−1.95765e13	−0.847416	−0.423708	+	0.905799i	$0.639272\pi$
$270$	1.07335e13	0.455241
$271$	6.04703e12	0.251311	0.125655	−	0.992074i	$-0.459897\pi$
$271$	6.04703e12	0.251311	0.125655	+	0.992074i	$0.459897\pi$
$272$	−6.45510e12	−0.262890
$273$	1.51640e12	0.0605228
$274$	2.07844e13	0.813035
$275$	−3.24010e12	−0.124231
$276$	−2.63971e13	−0.992102
$277$	4.19521e13	1.54566	0.772832	−	0.634610i	$-0.218839\pi$
$277$	4.19521e13	1.54566	0.772832	+	0.634610i	$0.218839\pi$
$278$	3.20944e13	1.15926
$279$	−1.17390e13	−0.415728
$280$	−1.37152e13	−0.476248
$281$	2.28404e13	0.777712	0.388856	−	0.921299i	$-0.372870\pi$
$281$	2.28404e13	0.777712	0.388856	+	0.921299i	$0.372870\pi$
$282$	−2.24936e13	−0.751084
$283$	4.50394e13	1.47492	0.737458	−	0.675393i	$-0.236026\pi$
$283$	4.50394e13	1.47492	0.737458	+	0.675393i	$0.236026\pi$
$284$	−7.10507e13	−2.28201
$285$	−5.75812e12	−0.181399
$286$	−1.46725e12	−0.0453410
$287$	−9.99321e12	−0.302939
$288$	1.27761e13	0.379961
$289$	3.60019e13	1.05048
$290$	−3.64309e13	−1.04299
$291$	3.36893e13	0.946413
$292$	4.24798e13	1.17105
$293$	1.09077e12	0.0295094	0.0147547	−	0.999891i	$-0.495303\pi$
$293$	1.09077e12	0.0295094	0.0147547	+	0.999891i	$0.495303\pi$
$294$	4.94357e12	0.131260
$295$	−3.46126e13	−0.902014
$296$	1.71020e13	0.437464
$297$	7.87321e11	0.0197693
$298$	−3.56019e13	−0.877575
$299$	−1.28495e13	−0.310954
$300$	−4.50413e13	−1.07015
$301$	−1.62608e12	−0.0379338
$302$	4.65132e13	1.06546
$303$	−2.49602e13	−0.561453
$304$	−1.75676e12	−0.0388068
$305$	−5.72961e12	−0.124301
$306$	−3.56503e13	−0.759619
$307$	5.11602e11	0.0107071	0.00535354	−	0.999986i	$-0.498296\pi$
$307$	5.11602e11	0.0107071	0.00535354	+	0.999986i	$0.498296\pi$
$308$	−2.89469e12	−0.0595077
$309$	4.61072e12	0.0931101
$310$	1.48711e14	2.95021
$311$	−7.70245e13	−1.50123	−0.750615	−	0.660740i	$-0.770242\pi$
$311$	−7.70245e13	−1.50123	−0.750615	+	0.660740i	$0.770242\pi$
$312$	−7.08871e12	−0.135743
$313$	2.41275e13	0.453960	0.226980	−	0.973899i	$-0.427115\pi$
$313$	2.41275e13	0.453960	0.226980	+	0.973899i	$0.427115\pi$
$314$	−1.62265e14	−2.99993
$315$	1.03079e13	0.187268
$316$	−6.13326e13	−1.09500
$317$	−9.86801e13	−1.73143	−0.865713	−	0.500541i	$-0.833134\pi$
$317$	−9.86801e13	−1.73143	−0.865713	+	0.500541i	$0.833134\pi$
$318$	−4.04117e13	−0.696880
$319$	−2.67227e12	−0.0452930
$320$	−1.45469e14	−2.42351
$321$	−1.67716e13	−0.274661
$322$	−4.18905e13	−0.674385
$323$	1.91251e13	0.302684
$324$	1.09447e13	0.170297
$325$	−2.19252e13	−0.335416
$326$	1.21801e14	1.83212
$327$	4.04076e13	0.597655
$328$	4.67153e13	0.679443
$329$	−2.16017e13	−0.308966
$330$	−9.97383e12	−0.140293
$331$	1.74708e13	0.241691	0.120845	−	0.992671i	$-0.461439\pi$
$331$	1.74708e13	0.241691	0.120845	+	0.992671i	$0.461439\pi$
$332$	−7.00144e13	−0.952638
$333$	−1.28533e13	−0.172017
$334$	1.54308e12	0.0203134
$335$	−1.99045e14	−2.57753
$336$	3.14487e12	0.0400624
$337$	−3.26051e13	−0.408622	−0.204311	−	0.978906i	$-0.565495\pi$
$337$	−3.26051e13	−0.408622	−0.204311	+	0.978906i	$0.565495\pi$
$338$	−9.92860e12	−0.122418
$339$	2.05703e13	0.249541
$340$	2.73303e14	3.26220
$341$	1.09082e13	0.128116
$342$	−9.70227e12	−0.112132
$343$	4.74756e12	0.0539949
$344$	7.60145e12	0.0850795
$345$	−8.73465e13	−0.962145
$346$	5.91179e13	0.640915
$347$	−1.75533e14	−1.87304	−0.936519	−	0.350617i	$-0.885972\pi$
$347$	−1.75533e14	−1.87304	−0.936519	+	0.350617i	$0.885972\pi$
$348$	−3.71477e13	−0.390163
$349$	−1.62935e13	−0.168452	−0.0842258	−	0.996447i	$-0.526842\pi$
$349$	−1.62935e13	−0.168452	−0.0842258	+	0.996447i	$0.526842\pi$
$350$	−7.14777e13	−0.727439
$351$	5.32765e12	0.0533761
$352$	−1.18719e13	−0.117094
$353$	−1.30829e14	−1.27041	−0.635203	−	0.772345i	$-0.719084\pi$
$353$	−1.30829e14	−1.27041	−0.635203	+	0.772345i	$0.719084\pi$
$354$	−5.83212e13	−0.557582
$355$	−2.35103e14	−2.21310
$356$	−2.68302e13	−0.248685
$357$	−3.42368e13	−0.312477
$358$	1.80865e13	0.162555
$359$	1.06773e14	0.945019	0.472509	−	0.881326i	$-0.343348\pi$
$359$	1.06773e14	0.945019	0.472509	+	0.881326i	$0.343348\pi$
$360$	−4.81865e13	−0.420012
$361$	−1.11285e14	−0.955319
$362$	1.94542e14	1.64481
$363$	6.85991e13	0.571258
$364$	−1.95878e13	−0.160668
$365$	1.40563e14	1.13569
$366$	−9.65422e12	−0.0768371
$367$	−2.16483e13	−0.169730	−0.0848652	−	0.996392i	$-0.527046\pi$
$367$	−2.16483e13	−0.169730	−0.0848652	+	0.996392i	$0.527046\pi$
$368$	−2.66488e13	−0.205833
$369$	−3.51097e13	−0.267167
$370$	1.62827e14	1.22072
$371$	−3.88094e13	−0.286669
$372$	1.51637e14	1.10362
$373$	1.24228e14	0.890881	0.445441	−	0.895311i	$-0.353047\pi$
$373$	1.24228e14	0.890881	0.445441	+	0.895311i	$0.353047\pi$
$374$	3.31271e13	0.234094
$375$	−2.58012e13	−0.179667
$376$	1.00982e14	0.692961
$377$	−1.80827e13	−0.122289
$378$	1.73685e13	0.115760
$379$	2.17734e14	1.43025	0.715124	−	0.698998i	$-0.246370\pi$
$379$	2.17734e14	1.43025	0.715124	+	0.698998i	$0.246370\pi$
$380$	7.43796e13	0.481553
$381$	−1.47200e14	−0.939333
$382$	−2.22960e14	−1.40242
$383$	9.73543e13	0.603617	0.301809	−	0.953368i	$-0.402410\pi$
$383$	9.73543e13	0.603617	0.301809	+	0.953368i	$0.402410\pi$
$384$	−1.37434e14	−0.839986
$385$	−9.57837e12	−0.0577109
$386$	−3.39847e14	−2.01862
$387$	−5.71301e12	−0.0334545
$388$	−4.35176e14	−2.51241
$389$	6.00957e13	0.342074	0.171037	−	0.985265i	$-0.445288\pi$
$389$	6.00957e13	0.342074	0.171037	+	0.985265i	$0.445288\pi$
$390$	−6.74910e13	−0.378783
$391$	2.90113e14	1.60544
$392$	−2.21934e13	−0.121102
$393$	8.93923e13	0.480996
$394$	1.63529e14	0.867694
$395$	−2.02946e14	−1.06193
$396$	−1.01701e13	−0.0524809
$397$	2.20423e14	1.12178	0.560891	−	0.827889i	$-0.310459\pi$
$397$	2.20423e14	1.12178	0.560891	+	0.827889i	$0.310459\pi$
$398$	−9.04175e13	−0.453832
$399$	−9.31757e12	−0.0461266
$400$	−4.54708e13	−0.222025
$401$	−1.19980e14	−0.577850	−0.288925	−	0.957352i	$-0.593298\pi$
$401$	−1.19980e14	−0.577850	−0.288925	+	0.957352i	$0.593298\pi$
$402$	−3.35384e14	−1.59331
$403$	7.38136e13	0.345906
$404$	3.22419e14	1.49047
$405$	3.62154e13	0.165155
$406$	−5.89510e13	−0.265215
$407$	1.19436e13	0.0530110
$408$	1.60047e14	0.700835
$409$	2.83112e14	1.22315	0.611575	−	0.791187i	$-0.290536\pi$
$409$	2.83112e14	1.22315	0.611575	+	0.791187i	$0.290536\pi$
$410$	4.44772e14	1.89595
$411$	7.01276e13	0.294957
$412$	−5.95582e13	−0.247176
$413$	−5.60088e13	−0.229367
$414$	−1.47176e14	−0.594752
$415$	−2.31674e14	−0.923872
$416$	−8.03345e13	−0.316147
$417$	1.08288e14	0.420564
$418$	9.01558e12	0.0345561
$419$	5.05660e14	1.91285	0.956427	−	0.291972i	$-0.0943115\pi$
$419$	5.05660e14	1.91285	0.956427	+	0.291972i	$0.0943115\pi$
$420$	−1.33151e14	−0.497133
$421$	4.07129e14	1.50031	0.750154	−	0.661263i	$-0.229979\pi$
$421$	4.07129e14	1.50031	0.750154	+	0.661263i	$0.229979\pi$
$422$	5.53237e14	2.01230
$423$	−7.58945e13	−0.272482
$424$	1.81422e14	0.642952
$425$	4.95020e14	1.73174
$426$	−3.96141e14	−1.36803
$427$	−9.27143e12	−0.0316077
$428$	2.16644e14	0.729133
$429$	−4.95058e12	−0.0164491
$430$	7.23727e13	0.237410
$431$	−1.02067e14	−0.330567	−0.165283	−	0.986246i	$-0.552854\pi$
$431$	−1.02067e14	−0.330567	−0.165283	+	0.986246i	$0.552854\pi$
$432$	1.10491e13	0.0353317
$433$	3.71741e14	1.17370	0.586850	−	0.809696i	$-0.300368\pi$
$433$	3.71741e14	1.17370	0.586850	+	0.809696i	$0.300368\pi$
$434$	2.40638e14	0.750189
$435$	−1.22920e14	−0.378382
$436$	−5.21959e14	−1.58658
$437$	7.89545e13	0.236990
$438$	2.36845e14	0.702031
$439$	2.76343e13	0.0808899	0.0404449	−	0.999182i	$-0.487122\pi$
$439$	2.76343e13	0.0808899	0.0404449	+	0.999182i	$0.487122\pi$
$440$	4.47760e13	0.129436
$441$	1.66799e13	0.0476190
$442$	2.24165e14	0.632041
$443$	5.21741e14	1.45290	0.726448	−	0.687222i	$-0.241170\pi$
$443$	5.21741e14	1.45290	0.726448	+	0.687222i	$0.241170\pi$
$444$	1.66031e14	0.456648
$445$	−8.87798e13	−0.241176
$446$	7.00837e13	0.188051
$447$	−1.20123e14	−0.318371
$448$	−2.35392e14	−0.616258
$449$	−3.32038e12	−0.00858682	−0.00429341	−	0.999991i	$-0.501367\pi$
$449$	−3.32038e12	−0.00858682	−0.00429341	+	0.999991i	$0.501367\pi$
$450$	−2.51127e14	−0.641541
$451$	3.26248e13	0.0823335
$452$	−2.65713e14	−0.662448
$453$	1.56938e14	0.386534
$454$	−2.15341e14	−0.523985
$455$	−6.48150e13	−0.155816
$456$	4.35569e13	0.103455
$457$	−9.43177e13	−0.221337	−0.110669	−	0.993857i	$-0.535299\pi$
$457$	−9.43177e13	−0.221337	−0.110669	+	0.993857i	$0.535299\pi$
$458$	−9.54889e14	−2.21408
$459$	−1.20286e14	−0.275579
$460$	1.12828e15	2.55417
$461$	−5.47693e13	−0.122513	−0.0612565	−	0.998122i	$-0.519511\pi$
$461$	−5.47693e13	−0.122513	−0.0612565	+	0.998122i	$0.519511\pi$
$462$	−1.61393e13	−0.0356741
$463$	−4.18485e14	−0.914081	−0.457040	−	0.889446i	$-0.651090\pi$
$463$	−4.18485e14	−0.914081	−0.457040	+	0.889446i	$0.651090\pi$
$464$	−3.75019e13	−0.0809477
$465$	5.01758e14	1.07029
$466$	7.53651e14	1.58872
$467$	−6.64068e14	−1.38347	−0.691735	−	0.722151i	$-0.743153\pi$
$467$	−6.64068e14	−1.38347	−0.691735	+	0.722151i	$0.743153\pi$
$468$	−6.88190e13	−0.141696
$469$	−3.22086e14	−0.655423
$470$	9.61437e14	1.93367
$471$	−5.47490e14	−1.08833
$472$	2.61824e14	0.514433
$473$	5.30866e12	0.0103098
$474$	−3.41958e14	−0.656436
$475$	1.34720e14	0.255633
$476$	4.42248e14	0.829522
$477$	−1.36351e14	−0.252818
$478$	−2.22752e14	−0.408289
$479$	3.72281e14	0.674568	0.337284	−	0.941403i	$-0.390492\pi$
$479$	3.72281e14	0.674568	0.337284	+	0.941403i	$0.390492\pi$
$480$	−5.46085e14	−0.978213
$481$	8.08201e13	0.143127
$482$	−2.85795e14	−0.500376
$483$	−1.41341e14	−0.244657
$484$	−8.86118e14	−1.51650
$485$	−1.43997e15	−2.43655
$486$	6.10219e13	0.102091
$487$	6.95896e13	0.115116	0.0575579	−	0.998342i	$-0.481669\pi$
$487$	6.95896e13	0.115116	0.0575579	+	0.998342i	$0.481669\pi$
$488$	4.33412e13	0.0708911
$489$	4.10964e14	0.664668
$490$	−2.11302e14	−0.337928
$491$	1.14475e15	1.81034	0.905171	−	0.425047i	$-0.139742\pi$
$491$	1.14475e15	1.81034	0.905171	+	0.425047i	$0.139742\pi$
$492$	4.53524e14	0.709238
$493$	4.08266e14	0.631372
$494$	6.10067e13	0.0932995
$495$	−3.36522e13	−0.0508962
$496$	1.53083e14	0.228969
$497$	−3.80434e14	−0.562755
$498$	−3.90363e14	−0.571094
$499$	−9.79136e14	−1.41674	−0.708370	−	0.705842i	$-0.750569\pi$
$499$	−9.79136e14	−1.41674	−0.708370	+	0.705842i	$0.750569\pi$
$500$	3.33283e14	0.476956
$501$	5.20643e12	0.00736940
$502$	1.32427e15	1.85398
$503$	8.22443e13	0.113889	0.0569445	−	0.998377i	$-0.481864\pi$
$503$	8.22443e13	0.113889	0.0569445	+	0.998377i	$0.481864\pi$
$504$	−7.79735e13	−0.106802
$505$	1.06687e15	1.44547
$506$	1.36760e14	0.183286
$507$	−3.34996e13	−0.0444116
$508$	1.90143e15	2.49361
$509$	4.86891e14	0.631660	0.315830	−	0.948816i	$-0.397717\pi$
$509$	4.86891e14	0.631660	0.315830	+	0.948816i	$0.397717\pi$
$510$	1.52379e15	1.95564
$511$	2.27454e14	0.288788
$512$	−2.90509e14	−0.364901
$513$	−3.27360e13	−0.0406799
$514$	1.30761e15	1.60762
$515$	−1.97075e14	−0.239713
$516$	7.37968e13	0.0888105
$517$	7.05230e13	0.0839717
$518$	2.63480e14	0.310409
$519$	1.99467e14	0.232515
$520$	3.02991e14	0.349471
$521$	−1.86024e14	−0.212306	−0.106153	−	0.994350i	$-0.533853\pi$
$521$	−1.86024e14	−0.212306	−0.106153	+	0.994350i	$0.533853\pi$
$522$	−2.07116e14	−0.233898
$523$	−1.18067e15	−1.31938	−0.659688	−	0.751540i	$-0.729311\pi$
$523$	−1.18067e15	−1.31938	−0.659688	+	0.751540i	$0.729311\pi$
$524$	−1.15471e15	−1.27688
$525$	−2.41170e14	−0.263904
$526$	−9.49173e14	−1.02784
$527$	−1.66654e15	−1.78590
$528$	−1.02670e13	−0.0108883
$529$	2.44873e14	0.257001
$530$	1.72731e15	1.79412
$531$	−1.96779e14	−0.202283
$532$	1.20358e14	0.122451
$533$	2.20766e14	0.222296
$534$	−1.49591e14	−0.149083
$535$	7.16864e14	0.707116
$536$	1.50566e15	1.47001
$537$	6.10250e13	0.0589724
$538$	1.40990e15	1.34861
$539$	−1.54993e13	−0.0146749
$540$	−4.67807e14	−0.438430
$541$	−1.21630e15	−1.12838	−0.564191	−	0.825645i	$-0.690812\pi$
$541$	−1.21630e15	−1.12838	−0.564191	+	0.825645i	$0.690812\pi$
$542$	−4.35508e14	−0.399945
$543$	6.56396e14	0.596715
$544$	1.81377e15	1.63226
$545$	−1.72713e15	−1.53867
$546$	−1.09211e14	−0.0963182
$547$	1.61350e15	1.40877	0.704384	−	0.709819i	$-0.251223\pi$
$547$	1.61350e15	1.40877	0.704384	+	0.709819i	$0.251223\pi$
$548$	−9.05861e14	−0.783013
$549$	−3.25738e13	−0.0278754
$550$	2.33353e14	0.197705
$551$	1.11110e14	0.0932007
$552$	6.60726e14	0.548727
$553$	−3.28400e14	−0.270032
$554$	−3.02140e15	−2.45983
$555$	5.49386e14	0.442859
$556$	−1.39879e15	−1.11646
$557$	−4.11057e14	−0.324862	−0.162431	−	0.986720i	$-0.551933\pi$
$557$	−4.11057e14	−0.324862	−0.162431	+	0.986720i	$0.551933\pi$
$558$	8.45447e14	0.661604
$559$	3.59227e13	0.0278358
$560$	−1.34420e14	−0.103141
$561$	1.11773e14	0.0849259
$562$	−1.64497e15	−1.23768
$563$	−2.10559e15	−1.56883	−0.784417	−	0.620234i	$-0.787038\pi$
$563$	−2.10559e15	−1.56883	−0.784417	+	0.620234i	$0.787038\pi$
$564$	9.80355e14	0.723350
$565$	−8.79229e14	−0.642445
$566$	−3.24375e15	−2.34724
$567$	5.86024e13	0.0419961
$568$	1.77842e15	1.26217
$569$	−2.68415e15	−1.88664	−0.943319	−	0.331886i	$-0.892315\pi$
$569$	−2.68415e15	−1.88664	−0.943319	+	0.331886i	$0.892315\pi$
$570$	4.14701e14	0.288685
$571$	−9.50779e14	−0.655512	−0.327756	−	0.944762i	$-0.606292\pi$
$571$	−9.50779e14	−0.655512	−0.327756	+	0.944762i	$0.606292\pi$
$572$	6.39483e13	0.0436667
$573$	−7.52279e14	−0.508778
$574$	7.19713e14	0.482108
$575$	2.04360e15	1.35589
$576$	−8.27016e14	−0.543488
$577$	−2.98377e15	−1.94222	−0.971111	−	0.238630i	$-0.923302\pi$
$577$	−2.98377e15	−1.94222	−0.971111	+	0.238630i	$0.923302\pi$
$578$	−2.59286e15	−1.67177
$579$	−1.14666e15	−0.732325
$580$	1.58779e15	1.00448
$581$	−3.74885e14	−0.234925
$582$	−2.42631e15	−1.50616
$583$	1.26701e14	0.0779117
$584$	−1.06328e15	−0.647704
$585$	−2.27718e14	−0.137417
$586$	−7.85572e13	−0.0469623
$587$	−2.34472e15	−1.38861	−0.694307	−	0.719679i	$-0.744289\pi$
$587$	−2.34472e15	−1.38861	−0.694307	+	0.719679i	$0.744289\pi$
$588$	−2.15460e14	−0.126413
$589$	−4.53550e14	−0.263628
$590$	2.49281e15	1.43550
$591$	5.51757e14	0.314787
$592$	1.67613e14	0.0947414
$593$	1.69092e15	0.946942	0.473471	−	0.880809i	$-0.343001\pi$
$593$	1.69092e15	0.946942	0.473471	+	0.880809i	$0.343001\pi$
$594$	−5.67030e13	−0.0314616
$595$	1.46337e15	0.804474
$596$	1.55167e15	0.845169
$597$	−3.05073e14	−0.164644
$598$	9.25427e14	0.494864
$599$	−1.61129e13	−0.00853739	−0.00426869	−	0.999991i	$-0.501359\pi$
$599$	−1.61129e13	−0.00853739	−0.00426869	+	0.999991i	$0.501359\pi$
$600$	1.12740e15	0.591895
$601$	1.63144e15	0.848713	0.424357	−	0.905495i	$-0.360500\pi$
$601$	1.63144e15	0.848713	0.424357	+	0.905495i	$0.360500\pi$
$602$	1.17111e14	0.0603693
$603$	−1.13160e15	−0.578028
$604$	−2.02722e15	−1.02612
$605$	−2.93211e15	−1.47071
$606$	1.79764e15	0.893518
$607$	−2.08154e15	−1.02529	−0.512646	−	0.858600i	$-0.671335\pi$
$607$	−2.08154e15	−1.02529	−0.512646	+	0.858600i	$0.671335\pi$
$608$	4.93619e14	0.240947
$609$	−1.98904e14	−0.0962162
$610$	4.12648e14	0.197818
$611$	4.77216e14	0.226719
$612$	1.55378e15	0.731569
$613$	−1.27712e15	−0.595933	−0.297967	−	0.954576i	$-0.596308\pi$
$613$	−1.27712e15	−0.595933	−0.297967	+	0.954576i	$0.596308\pi$
$614$	−3.68457e13	−0.0170396
$615$	1.50068e15	0.687822
$616$	7.24548e13	0.0329134
$617$	−2.00426e15	−0.902372	−0.451186	−	0.892430i	$-0.648999\pi$
$617$	−2.00426e15	−0.902372	−0.451186	+	0.892430i	$0.648999\pi$
$618$	−3.32065e14	−0.148179
$619$	−2.69075e15	−1.19008	−0.595038	−	0.803698i	$-0.702863\pi$
$619$	−2.69075e15	−1.19008	−0.595038	+	0.803698i	$0.702863\pi$
$620$	−6.48137e15	−2.84127
$621$	−4.96580e14	−0.215767
$622$	5.54732e15	2.38911
$623$	−1.43660e14	−0.0613270
$624$	−6.94751e13	−0.0293977
$625$	−1.78053e15	−0.746807
$626$	−1.73767e15	−0.722449
$627$	3.04190e13	0.0125364
$628$	7.07210e15	2.88915
$629$	−1.82473e15	−0.738960
$630$	−7.42379e14	−0.298025
$631$	2.25077e15	0.895716	0.447858	−	0.894105i	$-0.352187\pi$
$631$	2.25077e15	0.895716	0.447858	+	0.894105i	$0.352187\pi$
$632$	1.53517e15	0.605637
$633$	1.86665e15	0.730033
$634$	7.10696e15	2.75545
$635$	6.29172e15	2.41832
$636$	1.76129e15	0.671147
$637$	−1.04881e14	−0.0396214
$638$	1.92457e14	0.0720810
$639$	−1.33660e15	−0.496303
$640$	5.87429e15	2.16255
$641$	2.47916e15	0.904867	0.452434	−	0.891798i	$-0.350556\pi$
$641$	2.47916e15	0.904867	0.452434	+	0.891798i	$0.350556\pi$
$642$	1.20789e15	0.437106
$643$	−2.98504e14	−0.107100	−0.0535501	−	0.998565i	$-0.517054\pi$
$643$	−2.98504e14	−0.107100	−0.0535501	+	0.998565i	$0.517054\pi$
$644$	1.82575e15	0.649483
$645$	2.44189e14	0.0861288
$646$	−1.37739e15	−0.481702
$647$	−1.41307e15	−0.489993	−0.244996	−	0.969524i	$-0.578787\pi$
$647$	−1.41307e15	−0.489993	−0.244996	+	0.969524i	$0.578787\pi$
$648$	−2.73949e14	−0.0941904
$649$	1.82852e14	0.0623380
$650$	1.57905e15	0.533794
$651$	8.11925e14	0.272158
$652$	−5.30855e15	−1.76447
$653$	4.39715e15	1.44927	0.724635	−	0.689133i	$-0.242008\pi$
$653$	4.39715e15	1.44927	0.724635	+	0.689133i	$0.242008\pi$
$654$	−2.91017e15	−0.951131
$655$	−3.82087e15	−1.23833
$656$	4.57848e14	0.147147
$657$	7.99127e14	0.254687
$658$	1.55576e15	0.491700
$659$	−1.80382e14	−0.0565358	−0.0282679	−	0.999600i	$-0.508999\pi$
$659$	−1.80382e14	−0.0565358	−0.0282679	+	0.999600i	$0.508999\pi$
$660$	4.34697e14	0.135112
$661$	−3.59188e15	−1.10717	−0.553585	−	0.832793i	$-0.686740\pi$
$661$	−3.59188e15	−1.10717	−0.553585	+	0.832793i	$0.686740\pi$
$662$	−1.25825e15	−0.384636
$663$	7.56344e14	0.229295
$664$	1.75248e15	0.526899
$665$	3.98258e14	0.118753
$666$	9.25699e14	0.273755
$667$	1.68546e15	0.494340
$668$	−6.72531e13	−0.0195633
$669$	2.36466e14	0.0682221
$670$	1.43352e16	4.10198
$671$	3.02684e13	0.00859044
$672$	−8.83653e14	−0.248743
$673$	5.31465e14	0.148386	0.0741928	−	0.997244i	$-0.476362\pi$
$673$	5.31465e14	0.148386	0.0741928	+	0.997244i	$0.476362\pi$
$674$	2.34823e15	0.650295
$675$	−8.47315e14	−0.232742
$676$	4.32726e14	0.117898
$677$	−1.52468e15	−0.412041	−0.206020	−	0.978548i	$-0.566051\pi$
$677$	−1.52468e15	−0.412041	−0.206020	+	0.978548i	$0.566051\pi$
$678$	−1.48148e15	−0.397129
$679$	−2.33011e15	−0.619573
$680$	−6.84083e15	−1.80431
$681$	−7.26571e14	−0.190094
$682$	−7.85610e14	−0.203888
$683$	−1.28588e15	−0.331043	−0.165522	−	0.986206i	$-0.552931\pi$
$683$	−1.28588e15	−0.331043	−0.165522	+	0.986206i	$0.552931\pi$
$684$	4.22861e14	0.107991
$685$	−2.99744e15	−0.759369
$686$	−3.41920e14	−0.0859295
$687$	−3.22185e15	−0.803235
$688$	7.45004e13	0.0184256
$689$	8.57360e14	0.210357
$690$	6.29071e15	1.53119
$691$	−2.93689e14	−0.0709183	−0.0354592	−	0.999371i	$-0.511289\pi$
$691$	−2.93689e14	−0.0709183	−0.0354592	+	0.999371i	$0.511289\pi$
$692$	−2.57658e15	−0.617248
$693$	−5.44547e13	−0.0129420
$694$	1.26419e16	2.98082
$695$	−4.62853e15	−1.08275
$696$	9.29817e14	0.215798
$697$	−4.98438e15	−1.14771
$698$	1.17346e15	0.268080
$699$	2.54286e15	0.576365
$700$	3.11527e15	0.700577
$701$	6.49037e15	1.44817	0.724087	−	0.689709i	$-0.242262\pi$
$701$	6.49037e15	1.44817	0.724087	+	0.689709i	$0.242262\pi$
$702$	−3.83698e14	−0.0849446
$703$	−4.96603e14	−0.109082
$704$	7.68483e14	0.167488
$705$	3.24394e15	0.701508
$706$	9.42232e15	2.02177
$707$	1.72636e15	0.367558
$708$	2.54186e15	0.536993
$709$	6.48647e15	1.35973	0.679867	−	0.733335i	$-0.262037\pi$
$709$	6.48647e15	1.35973	0.679867	+	0.733335i	$0.262037\pi$
$710$	1.69321e16	3.52201
$711$	−1.15379e15	−0.238145
$712$	6.71568e14	0.137547
$713$	−6.88003e15	−1.39829
$714$	2.46574e15	0.497287
$715$	2.11601e14	0.0423482
$716$	−7.88280e14	−0.156552
$717$	−7.51576e14	−0.148121
$718$	−7.68979e15	−1.50394
$719$	1.10548e15	0.214556	0.107278	−	0.994229i	$-0.465786\pi$
$719$	1.10548e15	0.214556	0.107278	+	0.994229i	$0.465786\pi$
$720$	−4.72267e14	−0.0909617
$721$	−3.18898e14	−0.0609549
$722$	8.01480e15	1.52033
$723$	−9.64289e14	−0.181529
$724$	−8.47889e15	−1.58408
$725$	2.87589e15	0.533229
$726$	−4.94052e15	−0.909121
$727$	−4.93429e15	−0.901126	−0.450563	−	0.892745i	$-0.648777\pi$
$727$	−4.93429e15	−0.901126	−0.450563	+	0.892745i	$0.648777\pi$
$728$	4.90288e14	0.0888645
$729$	2.05891e14	0.0370370
$730$	−1.01234e16	−1.80738
$731$	−8.11052e14	−0.143715
$732$	4.20767e14	0.0739999
$733$	−1.02451e16	−1.78832	−0.894159	−	0.447749i	$-0.852226\pi$
$733$	−1.02451e16	−1.78832	−0.894159	+	0.447749i	$0.852226\pi$
$734$	1.55911e15	0.270115
$735$	−7.12943e14	−0.122596
$736$	7.48784e15	1.27799
$737$	1.05151e15	0.178133
$738$	2.52861e15	0.425179
$739$	−5.63366e15	−0.940256	−0.470128	−	0.882598i	$-0.655792\pi$
$739$	−5.63366e15	−0.940256	−0.470128	+	0.882598i	$0.655792\pi$
$740$	−7.09660e15	−1.17564
$741$	2.05840e14	0.0338477
$742$	2.79506e15	0.456215
$743$	−7.62785e15	−1.23584	−0.617922	−	0.786240i	$-0.712025\pi$
$743$	−7.62785e15	−1.23584	−0.617922	+	0.786240i	$0.712025\pi$
$744$	−3.79551e15	−0.610406
$745$	5.13437e15	0.819649
$746$	−8.94691e15	−1.41778
$747$	−1.31711e15	−0.207185
$748$	−1.44381e15	−0.225450
$749$	1.16000e15	0.179808
$750$	1.85821e15	0.285929
$751$	−1.18592e16	−1.81149	−0.905743	−	0.423827i	$-0.860686\pi$
$751$	−1.18592e16	−1.81149	−0.905743	+	0.423827i	$0.860686\pi$
$752$	9.89701e14	0.150074
$753$	4.46814e15	0.672597
$754$	1.30232e15	0.194615
$755$	−6.70795e15	−0.995134
$756$	−7.56987e14	−0.111485
$757$	3.75419e15	0.548894	0.274447	−	0.961602i	$-0.411505\pi$
$757$	3.75419e15	0.548894	0.274447	+	0.961602i	$0.411505\pi$
$758$	−1.56813e16	−2.27615
$759$	4.61435e14	0.0664937
$760$	−1.86174e15	−0.266345
$761$	−4.79297e15	−0.680752	−0.340376	−	0.940289i	$-0.610554\pi$
$761$	−4.79297e15	−0.680752	−0.340376	+	0.940289i	$0.610554\pi$
$762$	1.06014e16	1.49489
$763$	−2.79478e15	−0.391257
$764$	9.71744e15	1.35064
$765$	5.14135e15	0.709479
$766$	−7.01148e15	−0.960619
$767$	1.23732e15	0.168309
$768$	2.92794e15	0.395435
$769$	−1.07639e16	−1.44336	−0.721680	−	0.692227i	$-0.756630\pi$
$769$	−1.07639e16	−1.44336	−0.721680	+	0.692227i	$0.756630\pi$
$770$	6.89836e14	0.0918432
$771$	4.41196e15	0.583220
$772$	1.48118e16	1.94408
$773$	−3.60788e15	−0.470181	−0.235091	−	0.971973i	$-0.575539\pi$
$773$	−3.60788e15	−0.470181	−0.235091	+	0.971973i	$0.575539\pi$
$774$	4.11452e14	0.0532407
$775$	−1.17394e16	−1.50829
$776$	1.08926e16	1.38960
$777$	8.88995e14	0.112612
$778$	−4.32810e15	−0.544390
$779$	−1.35650e15	−0.169420
$780$	2.94151e15	0.364796
$781$	1.24200e15	0.152947
$782$	−2.08940e16	−2.55496
$783$	−6.98821e14	−0.0848547
$784$	−2.17514e14	−0.0262270
$785$	2.34012e16	2.80191
$786$	−6.43806e15	−0.765474
$787$	1.99937e15	0.236065	0.118033	−	0.993010i	$-0.462341\pi$
$787$	1.99937e15	0.236065	0.118033	+	0.993010i	$0.462341\pi$
$788$	−7.12723e15	−0.835654
$789$	−3.20256e15	−0.372884
$790$	1.46162e16	1.69000
$791$	−1.42273e15	−0.163363
$792$	2.54560e14	0.0290269
$793$	2.04820e14	0.0231937
$794$	−1.58749e16	−1.78525
$795$	5.82802e15	0.650882
$796$	3.94073e15	0.437074
$797$	2.19280e14	0.0241534	0.0120767	−	0.999927i	$-0.496156\pi$
$797$	2.19280e14	0.0241534	0.0120767	+	0.999927i	$0.496156\pi$
$798$	6.71054e14	0.0734076
$799$	−1.07744e16	−1.17054
$800$	1.27765e16	1.37853
$801$	−5.04729e14	−0.0540853
$802$	8.64099e15	0.919611
$803$	−7.42568e14	−0.0784876
$804$	1.46173e16	1.53447
$805$	6.04129e15	0.629872
$806$	−5.31607e15	−0.550488
$807$	4.75708e15	0.489256
$808$	−8.07023e15	−0.824373
$809$	1.84828e16	1.87521	0.937605	−	0.347701i	$-0.113038\pi$
$809$	1.84828e16	1.87521	0.937605	+	0.347701i	$0.113038\pi$
$810$	−2.60824e15	−0.262833
$811$	1.30720e16	1.30837	0.654183	−	0.756337i	$-0.273013\pi$
$811$	1.30720e16	1.30837	0.654183	+	0.756337i	$0.273013\pi$
$812$	2.56931e15	0.255422
$813$	−1.46943e15	−0.145094
$814$	−8.60181e14	−0.0843637
$815$	−1.75657e16	−1.71119
$816$	1.56859e15	0.151780
$817$	−2.20729e14	−0.0212147
$818$	−2.03898e16	−1.94657
$819$	−3.68485e14	−0.0349428
$820$	−1.93848e16	−1.82594
$821$	5.54032e15	0.518379	0.259190	−	0.965826i	$-0.416545\pi$
$821$	5.54032e15	0.518379	0.259190	+	0.965826i	$0.416545\pi$
$822$	−5.05060e15	−0.469406
$823$	−1.33182e16	−1.22955	−0.614775	−	0.788702i	$-0.710753\pi$
$823$	−1.33182e16	−1.22955	−0.614775	+	0.788702i	$0.710753\pi$
$824$	1.49076e15	0.136712
$825$	7.87345e14	0.0717247
$826$	4.03376e15	0.365023
$827$	−3.48404e14	−0.0313186	−0.0156593	−	0.999877i	$-0.504985\pi$
$827$	−3.48404e14	−0.0313186	−0.0156593	+	0.999877i	$0.504985\pi$
$828$	6.41450e15	0.572790
$829$	8.61235e15	0.763962	0.381981	−	0.924170i	$-0.375242\pi$
$829$	8.61235e15	0.763962	0.381981	+	0.924170i	$0.375242\pi$
$830$	1.66852e16	1.47028
$831$	−1.01944e16	−0.892390
$832$	5.20017e15	0.452209
$833$	2.36797e15	0.204564
$834$	−7.79893e15	−0.669302
$835$	−2.22537e14	−0.0189726
$836$	−3.92933e14	−0.0332800
$837$	2.85258e15	0.240020
$838$	−3.64178e16	−3.04419
$839$	3.52097e15	0.292396	0.146198	−	0.989255i	$-0.453296\pi$
$839$	3.52097e15	0.292396	0.146198	+	0.989255i	$0.453296\pi$
$840$	3.33280e15	0.274962
$841$	−9.82862e15	−0.805591
$842$	−2.93215e16	−2.38764
$843$	−5.55021e15	−0.449012
$844$	−2.41122e16	−1.93799
$845$	1.43186e15	0.114338
$846$	5.46594e15	0.433639
$847$	−4.74463e15	−0.373976
$848$	1.77809e15	0.139244
$849$	−1.09446e16	−0.851543
$850$	−3.56514e16	−2.75596
$851$	−7.53310e15	−0.578577
$852$	1.72653e16	1.31752
$853$	5.94306e15	0.450599	0.225300	−	0.974290i	$-0.427664\pi$
$853$	5.94306e15	0.450599	0.225300	+	0.974290i	$0.427664\pi$
$854$	6.67730e14	0.0503017
$855$	1.39922e15	0.104731
$856$	−5.42266e15	−0.403280
$857$	−1.70470e16	−1.25966	−0.629829	−	0.776734i	$-0.716875\pi$
$857$	−1.70470e16	−1.25966	−0.629829	+	0.776734i	$0.716875\pi$
$858$	3.56542e14	0.0261776
$859$	−4.41501e15	−0.322084	−0.161042	−	0.986948i	$-0.551486\pi$
$859$	−4.41501e15	−0.322084	−0.161042	+	0.986948i	$0.551486\pi$
$860$	−3.15428e15	−0.228643
$861$	2.42835e15	0.174902
$862$	7.35087e15	0.526076
$863$	5.48468e15	0.390024	0.195012	−	0.980801i	$-0.437525\pi$
$863$	5.48468e15	0.390024	0.195012	+	0.980801i	$0.437525\pi$
$864$	−3.10459e15	−0.219371
$865$	−8.52575e15	−0.598610
$866$	−2.67729e16	−1.86787
$867$	−8.74845e15	−0.606493
$868$	−1.04879e16	−0.722487
$869$	1.07213e15	0.0733900
$870$	8.85270e15	0.602171
$871$	7.11539e15	0.480949
$872$	1.30648e16	0.877527
$873$	−8.18650e15	−0.546412
$874$	−5.68632e15	−0.377154
$875$	1.78453e15	0.117620
$876$	−1.03226e16	−0.676108
$877$	−2.63676e16	−1.71622	−0.858109	−	0.513467i	$-0.828361\pi$
$877$	−2.63676e16	−1.71622	−0.858109	+	0.513467i	$0.828361\pi$
$878$	−1.99023e15	−0.128731
$879$	−2.65056e14	−0.0170372
$880$	4.38841e14	0.0280319
$881$	1.60495e16	1.01881	0.509406	−	0.860526i	$-0.329865\pi$
$881$	1.60495e16	1.01881	0.509406	+	0.860526i	$0.329865\pi$
$882$	−1.20129e15	−0.0757827
$883$	2.51258e16	1.57520	0.787602	−	0.616184i	$-0.211322\pi$
$883$	2.51258e16	1.57520	0.787602	+	0.616184i	$0.211322\pi$
$884$	−9.76995e15	−0.608702
$885$	8.41086e15	0.520778
$886$	−3.75759e16	−2.31219
$887$	−2.20145e16	−1.34626	−0.673130	−	0.739524i	$-0.735051\pi$
$887$	−2.20145e16	−1.34626	−0.673130	+	0.739524i	$0.735051\pi$
$888$	−4.15578e15	−0.252570
$889$	1.01810e16	0.614938
$890$	6.39394e15	0.383816
$891$	−1.91319e14	−0.0114138
$892$	−3.05451e15	−0.181107
$893$	−2.93227e15	−0.172791
$894$	8.65127e15	0.506668
$895$	−2.60837e15	−0.151825
$896$	9.50556e15	0.549900
$897$	3.12244e15	0.179529
$898$	2.39134e14	0.0136654
$899$	−9.68203e15	−0.549905
$900$	1.09450e16	0.617851
$901$	−1.93572e16	−1.08607
$902$	−2.34964e15	−0.131029
$903$	3.95138e14	0.0219011
$904$	6.65086e15	0.366397
$905$	−2.80561e16	−1.53625
$906$	−1.13027e16	−0.615144
$907$	−2.39382e16	−1.29495	−0.647473	−	0.762089i	$-0.724174\pi$
$907$	−2.39382e16	−1.29495	−0.647473	+	0.762089i	$0.724174\pi$
$908$	9.38536e15	0.504637
$909$	6.06533e15	0.324155
$910$	4.66799e15	0.247972
$911$	2.18881e16	1.15573	0.577866	−	0.816132i	$-0.303886\pi$
$911$	2.18881e16	1.15573	0.577866	+	0.816132i	$0.303886\pi$
$912$	4.26893e14	0.0224051
$913$	1.22389e15	0.0638487
$914$	6.79278e15	0.352244
$915$	1.39229e15	0.0717654
$916$	4.16177e16	2.13232
$917$	−6.18279e15	−0.314886
$918$	8.66303e15	0.438566
$919$	−2.30665e16	−1.16077	−0.580385	−	0.814342i	$-0.697098\pi$
$919$	−2.30665e16	−1.16077	−0.580385	+	0.814342i	$0.697098\pi$
$920$	−2.82412e16	−1.41270
$921$	−1.24319e14	−0.00618173
$922$	3.94450e15	0.194972
$923$	8.40439e15	0.412949
$924$	7.03410e14	0.0343568
$925$	−1.28537e16	−0.624093
$926$	3.01394e16	1.45470
$927$	−1.12040e15	−0.0537571
$928$	1.05374e16	0.502595
$929$	2.27055e16	1.07657	0.538287	−	0.842761i	$-0.319072\pi$
$929$	2.27055e16	1.07657	0.538287	+	0.842761i	$0.319072\pi$
$930$	−3.61367e16	−1.70330
$931$	6.44446e14	0.0301970
$932$	−3.28469e16	−1.53006
$933$	1.87170e16	0.866735
$934$	4.78263e16	2.20171
$935$	−4.77747e15	−0.218642
$936$	1.72256e15	0.0783712
$937$	−2.97054e16	−1.34359	−0.671796	−	0.740736i	$-0.734477\pi$
$937$	−2.97054e16	−1.34359	−0.671796	+	0.740736i	$0.734477\pi$
$938$	2.31967e16	1.04306
$939$	−5.86297e15	−0.262094
$940$	−4.19030e16	−1.86227
$941$	3.25186e16	1.43678	0.718388	−	0.695642i	$-0.244880\pi$
$941$	3.25186e16	1.43678	0.718388	+	0.695642i	$0.244880\pi$
$942$	3.94303e16	1.73201
$943$	−2.05772e16	−0.898610
$944$	2.56609e15	0.111411
$945$	−2.50482e15	−0.108119
$946$	−3.82331e14	−0.0164073
$947$	6.73968e15	0.287551	0.143775	−	0.989610i	$-0.454076\pi$
$947$	6.73968e15	0.287551	0.143775	+	0.989610i	$0.454076\pi$
$948$	1.49038e16	0.632197
$949$	−5.02481e15	−0.211912
$950$	−9.70257e15	−0.406824
$951$	2.39793e16	0.999639
$952$	−1.10696e16	−0.458805
$953$	9.97765e15	0.411166	0.205583	−	0.978640i	$-0.434091\pi$
$953$	9.97765e15	0.411166	0.205583	+	0.978640i	$0.434091\pi$
$954$	9.82005e15	0.402344
$955$	3.21544e16	1.30985
$956$	9.70836e15	0.393212
$957$	6.49361e14	0.0261499
$958$	−2.68118e16	−1.07353
$959$	−4.85035e15	−0.193095
$960$	3.53489e16	1.39921
$961$	1.41135e16	0.555464
$962$	−5.82068e15	−0.227778
$963$	4.07550e15	0.158576
$964$	1.24560e16	0.481899
$965$	4.90115e16	1.88537
$966$	1.01794e16	0.389357
$967$	−2.22025e16	−0.844416	−0.422208	−	0.906499i	$-0.638745\pi$
$967$	−2.22025e16	−0.844416	−0.422208	+	0.906499i	$0.638745\pi$
$968$	2.21797e16	0.838768
$969$	−4.64739e15	−0.174754
$970$	1.03707e17	3.87761
$971$	−3.61492e16	−1.34398	−0.671990	−	0.740560i	$-0.734560\pi$
$971$	−3.61492e16	−1.34398	−0.671990	+	0.740560i	$0.734560\pi$
$972$	−2.65956e15	−0.0983209
$973$	−7.48970e15	−0.275324
$974$	−5.01186e15	−0.183200
$975$	5.32781e15	0.193653
$976$	4.24779e14	0.0153528
$977$	2.03981e16	0.733112	0.366556	−	0.930396i	$-0.380537\pi$
$977$	2.03981e16	0.733112	0.366556	+	0.930396i	$0.380537\pi$
$978$	−2.95977e16	−1.05778
$979$	4.69006e14	0.0166676
$980$	9.20933e15	0.325450
$981$	−9.81906e15	−0.345056
$982$	−8.24448e16	−2.88105
$983$	−3.81698e15	−0.132640	−0.0663202	−	0.997798i	$-0.521126\pi$
$983$	−3.81698e15	−0.132640	−0.0663202	+	0.997798i	$0.521126\pi$
$984$	−1.13518e16	−0.392276
$985$	−2.35836e16	−0.810421
$986$	−2.94034e16	−1.00479
$987$	5.24922e15	0.178382
$988$	−2.65890e15	−0.0898543
$989$	−3.34829e15	−0.112524
$990$	2.42364e15	0.0809981
$991$	4.37998e16	1.45568	0.727841	−	0.685746i	$-0.240524\pi$
$991$	4.37998e16	1.45568	0.727841	+	0.685746i	$0.240524\pi$
$992$	−4.30135e16	−1.42164
$993$	−4.24542e15	−0.139540
$994$	2.73989e16	0.895589
$995$	1.30397e16	0.423877
$996$	1.70135e16	0.550006
$997$	−1.61014e15	−0.0517656	−0.0258828	−	0.999665i	$-0.508240\pi$
$997$	−1.61014e15	−0.0517656	−0.0258828	+	0.999665i	$0.508240\pi$
$998$	7.05176e16	2.25465
$999$	3.12336e15	0.0993142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.12.a.c.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-72.0202 q^{2} -243.000 q^{3} +3138.91 q^{4} +10386.5 q^{5} +17500.9 q^{6} +16807.0 q^{7} -78567.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-72.0202 q^{2} -243.000 q^{3} +3138.91 q^{4} +10386.5 q^{5} +17500.9 q^{6} +16807.0 q^{7} -78567.7 q^{8} +59049.0 q^{9} -748037. q^{10} -54869.8 q^{11} -762756. q^{12} -371293. q^{13} -1.21044e6 q^{14} -2.52391e6 q^{15} -770028. q^{16} +8.38294e6 q^{17} -4.25272e6 q^{18} +2.28143e6 q^{19} +3.26022e7 q^{20} -4.08410e6 q^{21} +3.95173e6 q^{22} +3.46075e7 q^{23} +1.90920e7 q^{24} +5.90508e7 q^{25} +2.67406e7 q^{26} -1.43489e7 q^{27} +5.27557e7 q^{28} +4.87020e7 q^{29} +1.81773e8 q^{30} -1.98801e8 q^{31} +2.16364e8 q^{32} +1.33333e7 q^{33} -6.03741e8 q^{34} +1.74566e8 q^{35} +1.85350e8 q^{36} -2.17672e8 q^{37} -1.64309e8 q^{38} +9.02242e7 q^{39} -8.16042e8 q^{40} -5.94586e8 q^{41} +2.94138e8 q^{42} -9.67503e7 q^{43} -1.72231e8 q^{44} +6.13311e8 q^{45} -2.49244e9 q^{46} -1.28528e9 q^{47} +1.87117e8 q^{48} +2.82475e8 q^{49} -4.25285e9 q^{50} -2.03706e9 q^{51} -1.16546e9 q^{52} -2.30912e9 q^{53} +1.03341e9 q^{54} -5.69904e8 q^{55} -1.32049e9 q^{56} -5.54386e8 q^{57} -3.50753e9 q^{58} -3.33247e9 q^{59} -7.92235e9 q^{60} -5.51641e8 q^{61} +1.43177e10 q^{62} +9.92437e8 q^{63} -1.40056e10 q^{64} -3.85643e9 q^{65} -9.60271e8 q^{66} -1.91638e10 q^{67} +2.63133e10 q^{68} -8.40963e9 q^{69} -1.25722e10 q^{70} -2.26355e10 q^{71} -4.63934e9 q^{72} +1.35333e10 q^{73} +1.56768e10 q^{74} -1.43494e10 q^{75} +7.16119e9 q^{76} -9.22196e8 q^{77} -6.49797e9 q^{78} -1.95395e10 q^{79} -7.99788e9 q^{80} +3.48678e9 q^{81} +4.28222e10 q^{82} -2.23053e10 q^{83} -1.28196e10 q^{84} +8.70693e10 q^{85} +6.96798e9 q^{86} -1.18346e10 q^{87} +4.31099e9 q^{88} -8.54763e9 q^{89} -4.41708e10 q^{90} -6.24032e9 q^{91} +1.08630e11 q^{92} +4.83087e10 q^{93} +9.25662e10 q^{94} +2.36960e10 q^{95} -5.25765e10 q^{96} -1.38639e11 q^{97} -2.03439e10 q^{98} -3.24000e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more