LMFDB - Embedded newform 273.12.a.c.1.1

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			1.1
Root			$-84.0758$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-88.0758 q^{2} -243.000 q^{3} +5709.35 q^{4} -13401.9 q^{5} +21402.4 q^{6} +16807.0 q^{7} -322476. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-88.0758 q^{2} -243.000 q^{3} +5709.35 q^{4} -13401.9 q^{5} +21402.4 q^{6} +16807.0 q^{7} -322476. q^{8} +59049.0 q^{9} +1.18039e6 q^{10} +966243. q^{11} -1.38737e6 q^{12} -371293. q^{13} -1.48029e6 q^{14} +3.25667e6 q^{15} +1.67096e7 q^{16} -3.26911e6 q^{17} -5.20079e6 q^{18} +7.04693e6 q^{19} -7.65164e7 q^{20} -4.08410e6 q^{21} -8.51026e7 q^{22} -2.58288e7 q^{23} +7.83618e7 q^{24} +1.30784e8 q^{25} +3.27019e7 q^{26} -1.43489e7 q^{27} +9.59571e7 q^{28} -9.40200e7 q^{29} -2.86834e8 q^{30} +1.08890e8 q^{31} -8.11283e8 q^{32} -2.34797e8 q^{33} +2.87929e8 q^{34} -2.25247e8 q^{35} +3.37131e8 q^{36} -5.39687e8 q^{37} -6.20665e8 q^{38} +9.02242e7 q^{39} +4.32181e9 q^{40} +6.21045e8 q^{41} +3.59711e8 q^{42} +2.48281e8 q^{43} +5.51662e9 q^{44} -7.91372e8 q^{45} +2.27489e9 q^{46} +1.09250e8 q^{47} -4.06044e9 q^{48} +2.82475e8 q^{49} -1.15189e10 q^{50} +7.94393e8 q^{51} -2.11984e9 q^{52} +3.34527e8 q^{53} +1.26379e9 q^{54} -1.29495e10 q^{55} -5.41986e9 q^{56} -1.71240e9 q^{57} +8.28089e9 q^{58} -7.67466e9 q^{59} +1.85935e10 q^{60} -1.30287e9 q^{61} -9.59061e9 q^{62} +9.92437e8 q^{63} +3.72331e10 q^{64} +4.97605e9 q^{65} +2.06799e10 q^{66} -1.72145e10 q^{67} -1.86645e10 q^{68} +6.27640e9 q^{69} +1.98388e10 q^{70} -2.59950e10 q^{71} -1.90419e10 q^{72} +9.41694e9 q^{73} +4.75334e10 q^{74} -3.17805e10 q^{75} +4.02334e10 q^{76} +1.62396e10 q^{77} -7.94657e9 q^{78} -1.58309e10 q^{79} -2.23942e11 q^{80} +3.48678e9 q^{81} -5.46991e10 q^{82} +1.74906e10 q^{83} -2.33176e10 q^{84} +4.38124e10 q^{85} -2.18676e10 q^{86} +2.28469e10 q^{87} -3.11590e11 q^{88} +3.74891e10 q^{89} +6.97007e10 q^{90} -6.24032e9 q^{91} -1.47466e11 q^{92} -2.64604e10 q^{93} -9.62226e9 q^{94} -9.44426e10 q^{95} +1.97142e11 q^{96} -3.78023e10 q^{97} -2.48792e10 q^{98} +5.70557e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) $ 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) 16 * q - 63 * q^2 - 3888 * q^3 + 20761 * q^4 - 3168 * q^5 + 15309 * q^6 + 268912 * q^7 - 187965 * q^8 + 944784 * q^9 + 1056711 * q^10 - 466884 * q^11 - 5044923 * q^12 - 5940688 * q^13 - 1058841 * q^14 + 769824 * q^15 + 40058265 * q^16 + 1753452 * q^17 - 3720087 * q^18 + 4237800 * q^19 - 20710503 * q^20 - 65345616 * q^21 - 37479661 * q^22 - 150481440 * q^23 + 45675495 * q^24 + 150983176 * q^25 + 23391459 * q^26 - 229582512 * q^27 + 348930127 * q^28 - 111411432 * q^29 - 256780773 * q^30 - 90536236 * q^31 - 609941313 * q^32 + 113452812 * q^33 + 443745577 * q^34 - 53244576 * q^35 + 1225916289 * q^36 - 1756337900 * q^37 - 4378868973 * q^38 + 1443587184 * q^39 + 57535383 * q^40 + 649575720 * q^41 + 257298363 * q^42 - 1889554520 * q^43 - 4979587689 * q^44 - 187067232 * q^45 - 3204000867 * q^46 - 4036082940 * q^47 - 9734158395 * q^48 + 4519603984 * q^49 - 15928886862 * q^50 - 426088836 * q^51 - 7708413973 * q^52 + 511144020 * q^53 + 903981141 * q^54 - 8519365572 * q^55 - 3159127755 * q^56 - 1029785400 * q^57 - 7851149577 * q^58 + 3728287296 * q^59 + 5032652229 * q^60 + 26227205052 * q^61 + 2996618490 * q^62 + 15878984688 * q^63 + 51104408465 * q^64 + 1176256224 * q^65 + 9107557623 * q^66 - 5295680024 * q^67 + 7919540325 * q^68 + 36566989920 * q^69 + 17760141777 * q^70 + 17082800928 * q^71 - 11099145285 * q^72 + 21076301488 * q^73 + 52794333675 * q^74 - 36688911768 * q^75 + 81459179177 * q^76 - 7846919388 * q^77 - 5684124537 * q^78 - 83677977852 * q^79 - 163988465427 * q^80 + 55788550416 * q^81 - 61543728760 * q^82 - 72857072340 * q^83 - 84790020861 * q^84 - 12608565060 * q^85 - 20177818011 * q^86 + 27072977976 * q^87 - 202213679643 * q^88 + 32238476676 * q^89 + 62397727839 * q^90 - 99845143216 * q^91 - 487057197033 * q^92 + 22000305348 * q^93 + 183904776602 * q^94 - 143022915504 * q^95 + 148215739059 * q^96 + 6973535140 * q^97 - 17795940687 * q^98 - 27569033316 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−88.0758	−1.94622	−0.973110	−	0.230343i	$-0.926015\pi$
$2$	−88.0758	−1.94622	−0.973110	+	0.230343i	$0.926015\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5709.35	2.78777
$5$	−13401.9	−1.91793	−0.958965	−	0.283523i	$-0.908497\pi$
$5$	−13401.9	−1.91793	−0.958965	+	0.283523i	$0.908497\pi$
$6$	21402.4	1.12365
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	−322476.	−3.47939
$9$	59049.0	0.333333
$10$	1.18039e6	3.73271
$11$	966243.	1.80895	0.904475	−	0.426527i	$-0.140263\pi$
$11$	966243.	1.80895	0.904475	+	0.426527i	$0.140263\pi$
$12$	−1.38737e6	−1.60952
$13$	−371293.	−0.277350
$13$	−371293.	−0.277350
$14$	−1.48029e6	−0.735602
$15$	3.25667e6	1.10732
$16$	1.67096e7	3.98389
$17$	−3.26911e6	−0.558419	−0.279209	−	0.960230i	$-0.590072\pi$
$17$	−3.26911e6	−0.558419	−0.279209	+	0.960230i	$0.590072\pi$
$18$	−5.20079e6	−0.648740
$19$	7.04693e6	0.652913	0.326457	−	0.945212i	$-0.394145\pi$
$19$	7.04693e6	0.652913	0.326457	+	0.945212i	$0.394145\pi$
$20$	−7.65164e7	−5.34675
$21$	−4.08410e6	−0.218218
$22$	−8.51026e7	−3.52061
$23$	−2.58288e7	−0.836761	−0.418380	−	0.908272i	$-0.637402\pi$
$23$	−2.58288e7	−0.836761	−0.418380	+	0.908272i	$0.637402\pi$
$24$	7.83618e7	2.00883
$25$	1.30784e8	2.67846
$26$	3.27019e7	0.539784
$27$	−1.43489e7	−0.192450
$28$	9.59571e7	1.05368
$29$	−9.40200e7	−0.851199	−0.425600	−	0.904912i	$-0.639937\pi$
$29$	−9.40200e7	−0.851199	−0.425600	+	0.904912i	$0.639937\pi$
$30$	−2.86834e8	−2.15508
$31$	1.08890e8	0.683125	0.341563	−	0.939859i	$-0.389044\pi$
$31$	1.08890e8	0.683125	0.341563	+	0.939859i	$0.389044\pi$
$32$	−8.11283e8	−4.27413
$33$	−2.34797e8	−1.04440
$34$	2.87929e8	1.08680
$35$	−2.25247e8	−0.724910
$36$	3.37131e8	0.929256
$37$	−5.39687e8	−1.27948	−0.639739	−	0.768592i	$-0.720958\pi$
$37$	−5.39687e8	−1.27948	−0.639739	+	0.768592i	$0.720958\pi$
$38$	−6.20665e8	−1.27071
$39$	9.02242e7	0.160128
$40$	4.32181e9	6.67323
$41$	6.21045e8	0.837167	0.418584	−	0.908178i	$-0.362527\pi$
$41$	6.21045e8	0.837167	0.418584	+	0.908178i	$0.362527\pi$
$42$	3.59711e8	0.424700
$43$	2.48281e8	0.257554	0.128777	−	0.991674i	$-0.458895\pi$
$43$	2.48281e8	0.257554	0.128777	+	0.991674i	$0.458895\pi$
$44$	5.51662e9	5.04293
$45$	−7.91372e8	−0.639310
$46$	2.27489e9	1.62852
$47$	1.09250e8	0.0694835	0.0347418	−	0.999396i	$-0.488939\pi$
$47$	1.09250e8	0.0694835	0.0347418	+	0.999396i	$0.488939\pi$
$48$	−4.06044e9	−2.30010
$49$	2.82475e8	0.142857
$50$	−1.15189e10	−5.21287
$51$	7.94393e8	0.322403
$52$	−2.11984e9	−0.773188
$53$	3.34527e8	0.109879	0.0549394	−	0.998490i	$-0.482503\pi$
$53$	3.34527e8	0.109879	0.0549394	+	0.998490i	$0.482503\pi$
$54$	1.26379e9	0.374550
$55$	−1.29495e10	−3.46944
$56$	−5.41986e9	−1.31509
$57$	−1.71240e9	−0.376960
$58$	8.28089e9	1.65662
$59$	−7.67466e9	−1.39757	−0.698784	−	0.715333i	$-0.746275\pi$
$59$	−7.67466e9	−1.39757	−0.698784	+	0.715333i	$0.746275\pi$
$60$	1.85935e10	3.08695
$61$	−1.30287e9	−0.197508	−0.0987542	−	0.995112i	$-0.531486\pi$
$61$	−1.30287e9	−0.197508	−0.0987542	+	0.995112i	$0.531486\pi$
$62$	−9.59061e9	−1.32951
$63$	9.92437e8	0.125988
$64$	3.72331e10	4.33450
$65$	4.97605e9	0.531938
$66$	2.06799e10	2.03263
$67$	−1.72145e10	−1.55770	−0.778849	−	0.627211i	$-0.784196\pi$
$67$	−1.72145e10	−1.55770	−0.778849	+	0.627211i	$0.784196\pi$
$68$	−1.86645e10	−1.55674
$69$	6.27640e9	0.483104
$70$	1.98388e10	1.41083
$71$	−2.59950e10	−1.70989	−0.854947	−	0.518715i	$-0.826410\pi$
$71$	−2.59950e10	−1.70989	−0.854947	+	0.518715i	$0.826410\pi$
$72$	−1.90419e10	−1.15980
$73$	9.41694e9	0.531660	0.265830	−	0.964020i	$-0.414354\pi$
$73$	9.41694e9	0.531660	0.265830	+	0.964020i	$0.414354\pi$
$74$	4.75334e10	2.49014
$75$	−3.17805e10	−1.54641
$76$	4.02334e10	1.82017
$77$	1.62396e10	0.683719
$78$	−7.94657e9	−0.311644
$79$	−1.58309e10	−0.578837	−0.289419	−	0.957203i	$-0.593462\pi$
$79$	−1.58309e10	−0.578837	−0.289419	+	0.957203i	$0.593462\pi$
$80$	−2.23942e11	−7.64082
$81$	3.48678e9	0.111111
$82$	−5.46991e10	−1.62931
$83$	1.74906e10	0.487387	0.243694	−	0.969852i	$-0.421641\pi$
$83$	1.74906e10	0.487387	0.243694	+	0.969852i	$0.421641\pi$
$84$	−2.33176e10	−0.608341
$85$	4.38124e10	1.07101
$86$	−2.18676e10	−0.501256
$87$	2.28469e10	0.491440
$88$	−3.11590e11	−6.29404
$89$	3.74891e10	0.711640	0.355820	−	0.934554i	$-0.384202\pi$
$89$	3.74891e10	0.711640	0.355820	+	0.934554i	$0.384202\pi$
$90$	6.97007e10	1.24424
$91$	−6.24032e9	−0.104828
$92$	−1.47466e11	−2.33270
$93$	−2.64604e10	−0.394402
$94$	−9.62226e9	−0.135230
$95$	−9.44426e10	−1.25224
$96$	1.97142e11	2.46767
$97$	−3.78023e10	−0.446965	−0.223483	−	0.974708i	$-0.571743\pi$
$97$	−3.78023e10	−0.446965	−0.223483	+	0.974708i	$0.571743\pi$
$98$	−2.48792e10	−0.278031
$99$	5.70557e10	0.602983
$100$	7.46692e11	7.46692
$101$	1.36161e11	1.28910	0.644548	−	0.764564i	$-0.277045\pi$
$101$	1.36161e11	1.28910	0.644548	+	0.764564i	$0.277045\pi$
$102$	−6.99668e10	−0.627467
$103$	7.29756e10	0.620259	0.310130	−	0.950694i	$-0.399628\pi$
$103$	7.29756e10	0.620259	0.310130	+	0.950694i	$0.399628\pi$
$104$	1.19733e11	0.965009
$105$	5.47349e10	0.418527
$106$	−2.94637e10	−0.213848
$107$	2.71362e11	1.87042	0.935208	−	0.354098i	$-0.115212\pi$
$107$	2.71362e11	1.87042	0.935208	+	0.354098i	$0.115212\pi$
$108$	−8.19229e10	−0.536506
$109$	6.06812e9	0.0377753	0.0188877	−	0.999822i	$-0.493988\pi$
$109$	6.06812e9	0.0377753	0.0188877	+	0.999822i	$0.493988\pi$
$110$	1.14054e12	6.75229
$111$	1.31144e11	0.738707
$112$	2.80839e11	1.50577
$113$	−3.32091e11	−1.69561	−0.847805	−	0.530308i	$-0.822076\pi$
$113$	−3.32091e11	−1.69561	−0.847805	+	0.530308i	$0.822076\pi$
$114$	1.50821e11	0.733646
$115$	3.46156e11	1.60485
$116$	−5.36793e11	−2.37295
$117$	−2.19245e10	−0.0924500
$118$	6.75952e11	2.71997
$119$	−5.49439e10	−0.211062
$120$	−1.05020e12	−3.85279
$121$	6.48313e11	2.27230
$122$	1.14751e11	0.384395
$123$	−1.50914e11	−0.483339
$124$	6.21693e11	1.90439
$125$	−1.09837e12	−3.21917
$126$	−8.74097e10	−0.245201
$127$	2.44398e11	0.656412	0.328206	−	0.944606i	$-0.393556\pi$
$127$	2.44398e11	0.656412	0.328206	+	0.944606i	$0.393556\pi$
$128$	−1.61783e12	−4.16176
$129$	−6.03323e10	−0.148699
$130$	−4.38270e11	−1.03527
$131$	6.62940e11	1.50135	0.750675	−	0.660672i	$-0.229729\pi$
$131$	6.62940e11	1.50135	0.750675	+	0.660672i	$0.229729\pi$
$132$	−1.34054e12	−2.91154
$133$	1.18438e11	0.246778
$134$	1.51618e12	3.03162
$135$	1.92303e11	0.369106
$136$	1.05421e12	1.94296
$137$	−7.76673e11	−1.37491	−0.687456	−	0.726226i	$-0.741273\pi$
$137$	−7.76673e11	−1.37491	−0.687456	+	0.726226i	$0.741273\pi$
$138$	−5.52799e11	−0.940226
$139$	7.23049e11	1.18192	0.590958	−	0.806703i	$-0.298750\pi$
$139$	7.23049e11	1.18192	0.590958	+	0.806703i	$0.298750\pi$
$140$	−1.28601e12	−2.02088
$141$	−2.65477e10	−0.0401163
$142$	2.28953e12	3.32783
$143$	−3.58759e11	−0.501712
$144$	9.86687e11	1.32796
$145$	1.26005e12	1.63254
$146$	−8.29404e11	−1.03473
$147$	−6.86415e10	−0.0824786
$148$	−3.08126e12	−3.56689
$149$	6.93308e11	0.773395	0.386698	−	0.922207i	$-0.373616\pi$
$149$	6.93308e11	0.773395	0.386698	+	0.922207i	$0.373616\pi$
$150$	2.79910e12	3.00965
$151$	−7.94031e11	−0.823122	−0.411561	−	0.911382i	$-0.635016\pi$
$151$	−7.94031e11	−0.823122	−0.411561	+	0.911382i	$0.635016\pi$
$152$	−2.27247e12	−2.27174
$153$	−1.93037e11	−0.186140
$154$	−1.43032e12	−1.33067
$155$	−1.45934e12	−1.31019
$156$	5.15122e11	0.446400
$157$	1.24474e12	1.04143	0.520716	−	0.853730i	$-0.325665\pi$
$157$	1.24474e12	1.04143	0.520716	+	0.853730i	$0.325665\pi$
$158$	1.39432e12	1.12654
$159$	−8.12900e10	−0.0634385
$160$	1.08728e13	8.19748
$161$	−4.34105e11	−0.316266
$162$	−3.07101e11	−0.216247
$163$	1.59796e12	1.08777	0.543883	−	0.839161i	$-0.316954\pi$
$163$	1.59796e12	1.08777	0.543883	+	0.839161i	$0.316954\pi$
$164$	3.54577e12	2.33383
$165$	3.14674e12	2.00308
$166$	−1.54050e12	−0.948563
$167$	3.20978e12	1.91221	0.956103	−	0.293031i	$-0.0946640\pi$
$167$	3.20978e12	1.91221	0.956103	+	0.293031i	$0.0946640\pi$
$168$	1.31703e12	0.759265
$169$	1.37858e11	0.0769231
$170$	−3.85881e12	−2.08442
$171$	4.16114e11	0.217638
$172$	1.41752e12	0.718000
$173$	−2.68266e12	−1.31617	−0.658084	−	0.752945i	$-0.728633\pi$
$173$	−2.68266e12	−1.31617	−0.658084	+	0.752945i	$0.728633\pi$
$174$	−2.01226e12	−0.956450
$175$	2.19809e12	1.01236
$176$	1.61456e13	7.20665
$177$	1.86494e12	0.806887
$178$	−3.30189e12	−1.38501
$179$	−1.42958e12	−0.581455	−0.290728	−	0.956806i	$-0.593897\pi$
$179$	−1.42958e12	−0.581455	−0.290728	+	0.956806i	$0.593897\pi$
$180$	−4.51822e12	−1.78225
$181$	−4.83814e12	−1.85117	−0.925584	−	0.378542i	$-0.876425\pi$
$181$	−4.83814e12	−1.85117	−0.925584	+	0.378542i	$0.876425\pi$
$182$	5.49621e11	0.204019
$183$	3.16597e11	0.114032
$184$	8.32918e12	2.91142
$185$	7.23286e12	2.45395
$186$	2.33052e12	0.767594
$187$	−3.15875e12	−1.01015
$188$	6.23745e11	0.193704
$189$	−2.41162e11	−0.0727393
$190$	8.31811e12	2.43714
$191$	3.48943e11	0.0993279	0.0496639	−	0.998766i	$-0.484185\pi$
$191$	3.48943e11	0.0993279	0.0496639	+	0.998766i	$0.484185\pi$
$192$	−9.04763e12	−2.50252
$193$	−2.28986e12	−0.615522	−0.307761	−	0.951464i	$-0.599580\pi$
$193$	−2.28986e12	−0.615522	−0.307761	+	0.951464i	$0.599580\pi$
$194$	3.32947e12	0.869892
$195$	−1.20918e12	−0.307115
$196$	1.61275e12	0.398253
$197$	2.35434e11	0.0565333	0.0282667	−	0.999600i	$-0.491001\pi$
$197$	2.35434e11	0.0565333	0.0282667	+	0.999600i	$0.491001\pi$
$198$	−5.02522e12	−1.17354
$199$	5.99332e12	1.36137	0.680684	−	0.732578i	$-0.261683\pi$
$199$	5.99332e12	1.36137	0.680684	+	0.732578i	$0.261683\pi$
$200$	−4.21748e13	−9.31940
$201$	4.18313e12	0.899338
$202$	−1.19925e13	−2.50886
$203$	−1.58019e12	−0.321723
$204$	4.53547e12	0.898785
$205$	−8.32322e12	−1.60563
$206$	−6.42739e12	−1.20716
$207$	−1.52517e12	−0.278920
$208$	−6.20417e12	−1.10493
$209$	6.80905e12	1.18109
$210$	−4.82082e12	−0.814545
$211$	1.12195e13	1.84680	0.923398	−	0.383843i	$-0.125400\pi$
$211$	1.12195e13	1.84680	0.923398	+	0.383843i	$0.125400\pi$
$212$	1.90993e12	0.306317
$213$	6.31679e12	0.987208
$214$	−2.39004e13	−3.64024
$215$	−3.32745e12	−0.493970
$216$	4.62718e12	0.669609
$217$	1.83012e12	0.258197
$218$	−5.34455e11	−0.0735191
$219$	−2.28832e12	−0.306954
$220$	−7.39334e13	−9.67199
$221$	1.21380e12	0.154877
$222$	−1.15506e13	−1.43769
$223$	−1.04277e13	−1.26623	−0.633115	−	0.774058i	$-0.718224\pi$
$223$	−1.04277e13	−1.26623	−0.633115	+	0.774058i	$0.718224\pi$
$224$	−1.36352e13	−1.61547
$225$	7.72267e12	0.892819
$226$	2.92492e13	3.30003
$227$	−3.75088e12	−0.413039	−0.206519	−	0.978443i	$-0.566214\pi$
$227$	−3.75088e12	−0.413039	−0.206519	+	0.978443i	$0.566214\pi$
$228$	−9.77672e12	−1.05088
$229$	9.22961e12	0.968474	0.484237	−	0.874937i	$-0.339097\pi$
$229$	9.22961e12	0.968474	0.484237	+	0.874937i	$0.339097\pi$
$230$	−3.04880e13	−3.12339
$231$	−3.94623e12	−0.394745
$232$	3.03192e13	2.96165
$233$	−8.78175e12	−0.837767	−0.418884	−	0.908040i	$-0.637579\pi$
$233$	−8.78175e12	−0.837767	−0.418884	+	0.908040i	$0.637579\pi$
$234$	1.93102e12	0.179928
$235$	−1.46416e12	−0.133265
$236$	−4.38173e13	−3.89610
$237$	3.84691e12	0.334192
$238$	4.83923e12	0.410774
$239$	7.03033e12	0.583159	0.291580	−	0.956547i	$-0.405819\pi$
$239$	7.03033e12	0.583159	0.291580	+	0.956547i	$0.405819\pi$
$240$	5.44178e13	4.41143
$241$	1.59569e12	0.126431	0.0632156	−	0.998000i	$-0.479864\pi$
$241$	1.59569e12	0.126431	0.0632156	+	0.998000i	$0.479864\pi$
$242$	−5.71007e13	−4.42239
$243$	−8.47289e11	−0.0641500
$244$	−7.43852e12	−0.550608
$245$	−3.78572e12	−0.273990
$246$	1.32919e13	0.940683
$247$	−2.61648e12	−0.181086
$248$	−3.51146e13	−2.37686
$249$	−4.25021e12	−0.281393
$250$	9.67398e13	6.26520
$251$	3.17410e12	0.201101	0.100551	−	0.994932i	$-0.467940\pi$
$251$	3.17410e12	0.201101	0.100551	+	0.994932i	$0.467940\pi$
$252$	5.66617e12	0.351226
$253$	−2.49569e13	−1.51366
$254$	−2.15255e13	−1.27752
$255$	−1.06464e13	−0.618347
$256$	6.62380e13	3.76520
$257$	−1.59775e12	−0.0888949	−0.0444474	−	0.999012i	$-0.514153\pi$
$257$	−1.59775e12	−0.0888949	−0.0444474	+	0.999012i	$0.514153\pi$
$258$	5.31382e12	0.289400
$259$	−9.07053e12	−0.483597
$260$	2.84100e13	1.48292
$261$	−5.55179e12	−0.283733
$262$	−5.83889e13	−2.92196
$263$	2.51476e13	1.23237	0.616184	−	0.787602i	$-0.288678\pi$
$263$	2.51476e13	1.23237	0.616184	+	0.787602i	$0.288678\pi$
$264$	7.57165e13	3.63387
$265$	−4.48331e12	−0.210740
$266$	−1.04315e13	−0.480284
$267$	−9.10986e12	−0.410866
$268$	−9.82837e13	−4.34250
$269$	2.66015e13	1.15151	0.575756	−	0.817621i	$-0.304708\pi$
$269$	2.66015e13	1.15151	0.575756	+	0.817621i	$0.304708\pi$
$270$	−1.69373e13	−0.718361
$271$	−4.43812e12	−0.184446	−0.0922228	−	0.995738i	$-0.529397\pi$
$271$	−4.43812e12	−0.184446	−0.0922228	+	0.995738i	$0.529397\pi$
$272$	−5.46255e13	−2.22468
$273$	1.51640e12	0.0605228
$274$	6.84061e13	2.67588
$275$	1.26369e14	4.84519
$276$	3.58342e13	1.34678
$277$	3.22412e13	1.18788	0.593939	−	0.804510i	$-0.297572\pi$
$277$	3.22412e13	1.18788	0.593939	+	0.804510i	$0.297572\pi$
$278$	−6.36831e13	−2.30027
$279$	6.42987e12	0.227708
$280$	7.26367e13	2.52224
$281$	−6.18824e12	−0.210709	−0.105354	−	0.994435i	$-0.533598\pi$
$281$	−6.18824e12	−0.210709	−0.105354	+	0.994435i	$0.533598\pi$
$282$	2.33821e12	0.0780752
$283$	−4.63157e13	−1.51671	−0.758356	−	0.651841i	$-0.773997\pi$
$283$	−4.63157e13	−1.51671	−0.758356	+	0.651841i	$0.773997\pi$
$284$	−1.48415e14	−4.76679
$285$	2.29496e13	0.722982
$286$	3.15980e13	0.976442
$287$	1.04379e13	0.316419
$288$	−4.79054e13	−1.42471
$289$	−2.35848e13	−0.688169
$290$	−1.10980e14	−3.17728
$291$	9.18596e12	0.258055
$292$	5.37646e13	1.48214
$293$	−1.38698e13	−0.375231	−0.187615	−	0.982243i	$-0.560076\pi$
$293$	−1.38698e13	−0.375231	−0.187615	+	0.982243i	$0.560076\pi$
$294$	6.04566e12	0.160521
$295$	1.02855e14	2.68044
$296$	1.74036e14	4.45180
$297$	−1.38645e13	−0.348132
$298$	−6.10636e13	−1.50520
$299$	9.59005e12	0.232076
$300$	−1.81446e14	−4.31103
$301$	4.17286e12	0.0973461
$302$	6.99349e13	1.60198
$303$	−3.30871e13	−0.744260
$304$	1.17752e14	2.60113
$305$	1.74609e13	0.378808
$306$	1.70019e13	0.362268
$307$	6.33986e13	1.32684	0.663420	−	0.748247i	$-0.269104\pi$
$307$	6.33986e13	1.32684	0.663420	+	0.748247i	$0.269104\pi$
$308$	9.27178e13	1.90605
$309$	−1.77331e13	−0.358107
$310$	1.28533e14	2.54991
$311$	−4.99398e12	−0.0973341	−0.0486670	−	0.998815i	$-0.515497\pi$
$311$	−4.99398e12	−0.0973341	−0.0486670	+	0.998815i	$0.515497\pi$
$312$	−2.90952e13	−0.557148
$313$	−3.34290e13	−0.628970	−0.314485	−	0.949262i	$-0.601832\pi$
$313$	−3.34290e13	−0.628970	−0.314485	+	0.949262i	$0.601832\pi$
$314$	−1.09632e14	−2.02685
$315$	−1.33006e13	−0.241637
$316$	−9.03842e13	−1.61367
$317$	−2.50776e13	−0.440007	−0.220004	−	0.975499i	$-0.570607\pi$
$317$	−2.50776e13	−0.440007	−0.220004	+	0.975499i	$0.570607\pi$
$318$	7.15969e12	0.123465
$319$	−9.08461e13	−1.53978
$320$	−4.98996e14	−8.31327
$321$	−6.59410e13	−1.07989
$322$	3.82341e13	0.615523
$323$	−2.30372e13	−0.364599
$324$	1.99073e13	0.309752
$325$	−4.85592e13	−0.742871
$326$	−1.40742e14	−2.11703
$327$	−1.47455e12	−0.0218096
$328$	−2.00273e14	−2.91283
$329$	1.83616e12	0.0262623
$330$	−2.77151e14	−3.89844
$331$	−1.09568e14	−1.51576	−0.757882	−	0.652392i	$-0.773766\pi$
$331$	−1.09568e14	−1.51576	−0.757882	+	0.652392i	$0.773766\pi$
$332$	9.98598e13	1.35872
$333$	−3.18680e13	−0.426493
$334$	−2.82704e14	−3.72157
$335$	2.30708e14	2.98756
$336$	−6.82438e13	−0.869355
$337$	2.22866e12	0.0279305	0.0139652	−	0.999902i	$-0.495555\pi$
$337$	2.22866e12	0.0279305	0.0139652	+	0.999902i	$0.495555\pi$
$338$	−1.21420e13	−0.149709
$339$	8.06981e13	0.978961
$340$	2.50140e14	2.98572
$341$	1.05215e14	1.23574
$342$	−3.66496e13	−0.423571
$343$	4.74756e12	0.0539949
$344$	−8.00649e13	−0.896129
$345$	−8.41160e13	−0.926560
$346$	2.36277e14	2.56155
$347$	1.65759e14	1.76875	0.884374	−	0.466779i	$-0.154586\pi$
$347$	1.65759e14	1.76875	0.884374	+	0.466779i	$0.154586\pi$
$348$	1.30441e14	1.37002
$349$	−7.00848e13	−0.724576	−0.362288	−	0.932066i	$-0.618004\pi$
$349$	−7.00848e13	−0.724576	−0.362288	+	0.932066i	$0.618004\pi$
$350$	−1.93598e14	−1.97028
$351$	5.32765e12	0.0533761
$352$	−7.83896e14	−7.73168
$353$	1.61695e14	1.57013	0.785066	−	0.619412i	$-0.212629\pi$
$353$	1.61695e14	1.57013	0.785066	+	0.619412i	$0.212629\pi$
$354$	−1.64256e14	−1.57038
$355$	3.48384e14	3.27946
$356$	2.14039e14	1.98389
$357$	1.33514e13	0.121857
$358$	1.25911e14	1.13164
$359$	−8.69841e13	−0.769875	−0.384937	−	0.922943i	$-0.625777\pi$
$359$	−8.69841e13	−0.769875	−0.384937	+	0.922943i	$0.625777\pi$
$360$	2.55199e14	2.22441
$361$	−6.68310e13	−0.573704
$362$	4.26123e14	3.60278
$363$	−1.57540e14	−1.31191
$364$	−3.56282e13	−0.292238
$365$	−1.26205e14	−1.01969
$366$	−2.78845e13	−0.221930
$367$	1.22953e14	0.963998	0.481999	−	0.876172i	$-0.339911\pi$
$367$	1.22953e14	0.963998	0.481999	+	0.876172i	$0.339911\pi$
$368$	−4.31590e14	−3.33356
$369$	3.66721e13	0.279056
$370$	−6.37040e14	−4.77592
$371$	5.62239e12	0.0415303
$372$	−1.51072e14	−1.09950
$373$	5.85866e13	0.420146	0.210073	−	0.977686i	$-0.432630\pi$
$373$	5.85866e13	0.420146	0.210073	+	0.977686i	$0.432630\pi$
$374$	2.78209e14	1.96598
$375$	2.66904e14	1.85859
$376$	−3.52305e13	−0.241760
$377$	3.49090e13	0.236080
$378$	2.12405e13	0.141567
$379$	−6.41085e13	−0.421114	−0.210557	−	0.977582i	$-0.567528\pi$
$379$	−6.41085e13	−0.421114	−0.210557	+	0.977582i	$0.567528\pi$
$380$	−5.39206e14	−3.49096
$381$	−5.93886e13	−0.378980
$382$	−3.07335e13	−0.193314
$383$	−2.80586e12	−0.0173969	−0.00869847	−	0.999962i	$-0.502769\pi$
$383$	−2.80586e12	−0.0173969	−0.00869847	+	0.999962i	$0.502769\pi$
$384$	3.93132e14	2.40279
$385$	−2.17643e14	−1.31132
$386$	2.01681e14	1.19794
$387$	1.46608e13	0.0858512
$388$	−2.15827e14	−1.24604
$389$	−2.86526e14	−1.63095	−0.815477	−	0.578789i	$-0.803525\pi$
$389$	−2.86526e14	−1.63095	−0.815477	+	0.578789i	$0.803525\pi$
$390$	1.06500e14	0.597712
$391$	8.44371e13	0.467263
$392$	−9.10916e13	−0.497056
$393$	−1.61094e14	−0.866805
$394$	−2.07360e13	−0.110026
$395$	2.12165e14	1.11017
$396$	3.25751e14	1.68098
$397$	−3.33362e14	−1.69655	−0.848277	−	0.529552i	$-0.822360\pi$
$397$	−3.33362e14	−1.69655	−0.848277	+	0.529552i	$0.822360\pi$
$398$	−5.27866e14	−2.64952
$399$	−2.87804e13	−0.142477
$400$	2.18535e15	10.6707
$401$	1.48196e14	0.713746	0.356873	−	0.934153i	$-0.383843\pi$
$401$	1.48196e14	0.713746	0.356873	+	0.934153i	$0.383843\pi$
$402$	−3.68432e14	−1.75031
$403$	−4.04302e13	−0.189465
$404$	7.77391e14	3.59370
$405$	−4.67297e13	−0.213103
$406$	1.39177e14	0.626144
$407$	−5.21469e14	−2.31451
$408$	−2.56173e14	−1.12177
$409$	−3.25562e14	−1.40655	−0.703277	−	0.710916i	$-0.748280\pi$
$409$	−3.25562e14	−1.40655	−0.703277	+	0.710916i	$0.748280\pi$
$410$	7.33074e14	3.12490
$411$	1.88731e14	0.793806
$412$	4.16644e14	1.72914
$413$	−1.28988e14	−0.528231
$414$	1.34330e14	0.542840
$415$	−2.34408e14	−0.934775
$416$	3.01224e14	1.18543
$417$	−1.75701e14	−0.682379
$418$	−5.99712e14	−2.29865
$419$	−8.95562e13	−0.338781	−0.169390	−	0.985549i	$-0.554180\pi$
$419$	−8.95562e13	−0.338781	−0.169390	+	0.985549i	$0.554180\pi$
$420$	3.12501e14	1.16676
$421$	−2.87090e14	−1.05795	−0.528977	−	0.848636i	$-0.677424\pi$
$421$	−2.87090e14	−1.05795	−0.528977	+	0.848636i	$0.677424\pi$
$422$	−9.88165e14	−3.59427
$423$	6.45108e12	0.0231612
$424$	−1.07877e14	−0.382311
$425$	−4.27547e14	−1.49570
$426$	−5.56356e14	−1.92132
$427$	−2.18973e13	−0.0746512
$428$	1.54930e15	5.21429
$429$	8.71785e13	0.289664
$430$	2.93068e14	0.961373
$431$	−4.24606e14	−1.37519	−0.687593	−	0.726096i	$-0.741333\pi$
$431$	−4.24606e14	−1.37519	−0.687593	+	0.726096i	$0.741333\pi$
$432$	−2.39765e14	−0.766699
$433$	4.40990e14	1.39234	0.696170	−	0.717877i	$-0.254886\pi$
$433$	4.40990e14	1.39234	0.696170	+	0.717877i	$0.254886\pi$
$434$	−1.61189e14	−0.502508
$435$	−3.06192e14	−0.942548
$436$	3.46450e13	0.105309
$437$	−1.82014e14	−0.546332
$438$	2.01545e14	0.597400
$439$	−3.86345e14	−1.13089	−0.565445	−	0.824786i	$-0.691295\pi$
$439$	−3.86345e14	−1.13089	−0.565445	+	0.824786i	$0.691295\pi$
$440$	4.17592e15	12.0715
$441$	1.66799e13	0.0476190
$442$	−1.06906e14	−0.301425
$443$	5.59438e14	1.55787	0.778935	−	0.627105i	$-0.215760\pi$
$443$	5.59438e14	1.55787	0.778935	+	0.627105i	$0.215760\pi$
$444$	7.48747e14	2.05934
$445$	−5.02428e14	−1.36488
$446$	9.18430e14	2.46436
$447$	−1.68474e14	−0.446520
$448$	6.25776e14	1.63829
$449$	−1.87991e13	−0.0486163	−0.0243081	−	0.999705i	$-0.507738\pi$
$449$	−1.87991e13	−0.0486163	−0.0243081	+	0.999705i	$0.507738\pi$
$450$	−6.80180e14	−1.73762
$451$	6.00081e14	1.51439
$452$	−1.89602e15	−4.72697
$453$	1.92950e14	0.475230
$454$	3.30362e14	0.803864
$455$	8.36325e13	0.201054
$456$	5.52210e14	1.31159
$457$	2.40929e14	0.565393	0.282696	−	0.959209i	$-0.408771\pi$
$457$	2.40929e14	0.565393	0.282696	+	0.959209i	$0.408771\pi$
$458$	−8.12905e14	−1.88486
$459$	4.69081e13	0.107468
$460$	1.97633e15	4.47395
$461$	2.18518e12	0.00488800	0.00244400	−	0.999997i	$-0.499222\pi$
$461$	2.18518e12	0.00488800	0.00244400	+	0.999997i	$0.499222\pi$
$462$	3.47568e14	0.768260
$463$	−2.69300e14	−0.588221	−0.294110	−	0.955771i	$-0.595023\pi$
$463$	−2.69300e14	−0.588221	−0.294110	+	0.955771i	$0.595023\pi$
$464$	−1.57104e15	−3.39108
$465$	3.54620e14	0.756437
$466$	7.73460e14	1.63048
$467$	2.73339e14	0.569453	0.284727	−	0.958609i	$-0.408097\pi$
$467$	2.73339e14	0.569453	0.284727	+	0.958609i	$0.408097\pi$
$468$	−1.25175e14	−0.257729
$469$	−2.89324e14	−0.588755
$470$	1.28957e14	0.259362
$471$	−3.02472e14	−0.601271
$472$	2.47490e15	4.86269
$473$	2.39900e14	0.465901
$474$	−3.38820e14	−0.650411
$475$	9.21627e14	1.74880
$476$	−3.13694e14	−0.588393
$477$	1.97535e13	0.0366263
$478$	−6.19202e14	−1.13496
$479$	1.44477e14	0.261790	0.130895	−	0.991396i	$-0.458215\pi$
$479$	1.44477e14	0.261790	0.130895	+	0.991396i	$0.458215\pi$
$480$	−2.64208e15	−4.73282
$481$	2.00382e14	0.354863
$482$	−1.40542e14	−0.246063
$483$	1.05487e14	0.182596
$484$	3.70145e15	6.33464
$485$	5.06625e14	0.857248
$486$	7.46256e13	0.124850
$487$	−1.54874e14	−0.256193	−0.128097	−	0.991762i	$-0.540887\pi$
$487$	−1.54874e14	−0.256193	−0.128097	+	0.991762i	$0.540887\pi$
$488$	4.20144e14	0.687209
$489$	−3.88305e14	−0.628022
$490$	3.33430e14	0.533245
$491$	−1.00549e15	−1.59012	−0.795060	−	0.606530i	$-0.792561\pi$
$491$	−1.00549e15	−1.59012	−0.795060	+	0.606530i	$0.792561\pi$
$492$	−8.61621e14	−1.34744
$493$	3.07361e14	0.475326
$494$	2.30448e14	0.352432
$495$	−7.64657e14	−1.15648
$496$	1.81952e15	2.72149
$497$	−4.36898e14	−0.646279
$498$	3.74341e14	0.547653
$499$	−5.41005e14	−0.782796	−0.391398	−	0.920222i	$-0.628008\pi$
$499$	−5.41005e14	−0.782796	−0.391398	+	0.920222i	$0.628008\pi$
$500$	−6.27098e15	−8.97429
$501$	−7.79976e14	−1.10401
$502$	−2.79561e14	−0.391387
$503$	2.17448e14	0.301115	0.150557	−	0.988601i	$-0.451893\pi$
$503$	2.17448e14	0.301115	0.150557	+	0.988601i	$0.451893\pi$
$504$	−3.20037e14	−0.438362
$505$	−1.82482e15	−2.47240
$506$	2.19810e15	2.94591
$507$	−3.34996e13	−0.0444116
$508$	1.39535e15	1.82992
$509$	−4.82712e14	−0.626239	−0.313120	−	0.949714i	$-0.601374\pi$
$509$	−4.82712e14	−0.626239	−0.313120	+	0.949714i	$0.601374\pi$
$510$	9.37691e14	1.20344
$511$	1.58270e14	0.200949
$512$	−2.52066e15	−3.16614
$513$	−1.01116e14	−0.125653
$514$	1.40723e14	0.173009
$515$	−9.78016e14	−1.18961
$516$	−3.44459e14	−0.414537
$517$	1.05562e14	0.125692
$518$	7.98894e14	0.941186
$519$	6.51885e14	0.759890
$520$	−1.60466e15	−1.85082
$521$	−9.80262e13	−0.111875	−0.0559377	−	0.998434i	$-0.517815\pi$
$521$	−9.80262e13	−0.111875	−0.0559377	+	0.998434i	$0.517815\pi$
$522$	4.88978e14	0.552207
$523$	4.41445e14	0.493307	0.246654	−	0.969104i	$-0.420669\pi$
$523$	4.41445e14	0.493307	0.246654	+	0.969104i	$0.420669\pi$
$524$	3.78495e15	4.18542
$525$	−5.34135e14	−0.584487
$526$	−2.21490e15	−2.39846
$527$	−3.55974e14	−0.381470
$528$	−3.92337e15	−4.16076
$529$	−2.85683e14	−0.299832
$530$	3.94871e14	0.410146
$531$	−4.53181e14	−0.465856
$532$	6.76203e14	0.687960
$533$	−2.30590e14	−0.232188
$534$	8.02359e14	0.799635
$535$	−3.63678e15	−3.58733
$536$	5.55128e15	5.41984
$537$	3.47387e14	0.335703
$538$	−2.34295e15	−2.24110
$539$	2.72940e14	0.258421
$540$	1.09793e15	1.02898
$541$	1.26578e15	1.17429	0.587143	−	0.809483i	$-0.300253\pi$
$541$	1.26578e15	1.17429	0.587143	+	0.809483i	$0.300253\pi$
$542$	3.90891e14	0.358971
$543$	1.17567e15	1.06877
$544$	2.65217e15	2.38675
$545$	−8.13246e13	−0.0724505
$546$	−1.33558e14	−0.117791
$547$	−1.51359e14	−0.132153	−0.0660767	−	0.997815i	$-0.521048\pi$
$547$	−1.51359e14	−0.132153	−0.0660767	+	0.997815i	$0.521048\pi$
$548$	−4.43430e15	−3.83294
$549$	−7.69330e13	−0.0658362
$550$	−1.11301e16	−9.42981
$551$	−6.62553e14	−0.555759
$552$	−2.02399e15	−1.68091
$553$	−2.66070e14	−0.218780
$554$	−2.83967e15	−2.31187
$555$	−1.75759e15	−1.41679
$556$	4.12814e15	3.29491
$557$	6.00776e14	0.474798	0.237399	−	0.971412i	$-0.423705\pi$
$557$	6.00776e14	0.474798	0.237399	+	0.971412i	$0.423705\pi$
$558$	−5.66316e14	−0.443170
$559$	−9.21851e13	−0.0714325
$560$	−3.76379e15	−2.88796
$561$	7.67576e14	0.583211
$562$	5.45034e14	0.410085
$563$	1.79235e15	1.33544	0.667722	−	0.744411i	$-0.267269\pi$
$563$	1.79235e15	1.33544	0.667722	+	0.744411i	$0.267269\pi$
$564$	−1.51570e14	−0.111835
$565$	4.45067e15	3.25206
$566$	4.07930e15	2.95185
$567$	5.86024e13	0.0419961
$568$	8.38278e15	5.94939
$569$	−7.18981e14	−0.505359	−0.252679	−	0.967550i	$-0.581312\pi$
$569$	−7.18981e14	−0.505359	−0.252679	+	0.967550i	$0.581312\pi$
$570$	−2.02130e15	−1.40708
$571$	1.32240e15	0.911724	0.455862	−	0.890050i	$-0.349331\pi$
$571$	1.32240e15	0.911724	0.455862	+	0.890050i	$0.349331\pi$
$572$	−2.04828e15	−1.39866
$573$	−8.47932e13	−0.0573470
$574$	−9.19328e14	−0.615822
$575$	−3.37800e15	−2.24123
$576$	2.19858e15	1.44483
$577$	1.29152e15	0.840685	0.420343	−	0.907365i	$-0.361910\pi$
$577$	1.29152e15	0.840685	0.420343	+	0.907365i	$0.361910\pi$
$578$	2.07725e15	1.33933
$579$	5.56436e14	0.355372
$580$	7.19407e15	4.55115
$581$	2.93964e14	0.184215
$582$	−8.09061e14	−0.502233
$583$	3.23234e14	0.198765
$584$	−3.03674e15	−1.84985
$585$	2.93831e14	0.177313
$586$	1.22159e15	0.730281
$587$	−1.83623e15	−1.08747	−0.543737	−	0.839256i	$-0.682991\pi$
$587$	−1.83623e15	−1.08747	−0.543737	+	0.839256i	$0.682991\pi$
$588$	−3.91898e14	−0.229931
$589$	7.67343e14	0.446021
$590$	−9.05907e15	−5.21672
$591$	−5.72104e13	−0.0326395
$592$	−9.01798e15	−5.09729
$593$	−1.32174e15	−0.740194	−0.370097	−	0.928993i	$-0.620676\pi$
$593$	−1.32174e15	−0.740194	−0.370097	+	0.928993i	$0.620676\pi$
$594$	1.22113e15	0.677542
$595$	7.36355e14	0.404803
$596$	3.95834e15	2.15605
$597$	−1.45638e15	−0.785986
$598$	−8.44652e14	−0.451670
$599$	3.75903e15	1.99172	0.995859	−	0.0909106i	$-0.0289777\pi$
$599$	3.75903e15	1.99172	0.995859	+	0.0909106i	$0.0289777\pi$
$600$	1.02485e16	5.38056
$601$	−4.00228e14	−0.208208	−0.104104	−	0.994566i	$-0.533198\pi$
$601$	−4.00228e14	−0.208208	−0.104104	+	0.994566i	$0.533198\pi$
$602$	−3.67528e14	−0.189457
$603$	−1.01650e15	−0.519233
$604$	−4.53340e15	−2.29467
$605$	−8.68866e15	−4.35811
$606$	2.91418e15	1.44849
$607$	1.50336e15	0.740498	0.370249	−	0.928933i	$-0.379272\pi$
$607$	1.50336e15	0.740498	0.370249	+	0.928933i	$0.379272\pi$
$608$	−5.71705e15	−2.79063
$609$	3.83987e14	0.185747
$610$	−1.53789e15	−0.737243
$611$	−4.05636e13	−0.0192713
$612$	−1.10212e15	−0.518914
$613$	−1.77000e15	−0.825924	−0.412962	−	0.910748i	$-0.635506\pi$
$613$	−1.77000e15	−0.825924	−0.412962	+	0.910748i	$0.635506\pi$
$614$	−5.58388e15	−2.58232
$615$	2.02254e15	0.927010
$616$	−5.23690e15	−2.37892
$617$	−6.28931e14	−0.283162	−0.141581	−	0.989927i	$-0.545219\pi$
$617$	−6.28931e14	−0.283162	−0.141581	+	0.989927i	$0.545219\pi$
$618$	1.56186e15	0.696954
$619$	1.27006e15	0.561728	0.280864	−	0.959748i	$-0.409379\pi$
$619$	1.27006e15	0.561728	0.280864	+	0.959748i	$0.409379\pi$
$620$	−8.33190e15	−3.65250
$621$	3.70615e14	0.161035
$622$	4.39849e14	0.189433
$623$	6.30080e14	0.268975
$624$	1.50761e15	0.637932
$625$	8.33435e15	3.49568
$626$	2.94429e15	1.22411
$627$	−1.65460e15	−0.681901
$628$	7.10666e15	2.90327
$629$	1.76429e15	0.714484
$630$	1.17146e15	0.470278
$631$	2.62244e15	1.04362	0.521812	−	0.853060i	$-0.325256\pi$
$631$	2.62244e15	1.04362	0.521812	+	0.853060i	$0.325256\pi$
$632$	5.10509e15	2.01400
$633$	−2.72633e15	−1.06625
$634$	2.20873e15	0.856351
$635$	−3.27540e15	−1.25895
$636$	−4.64113e14	−0.176852
$637$	−1.04881e14	−0.0396214
$638$	8.00135e15	2.99674
$639$	−1.53498e15	−0.569965
$640$	2.16820e16	7.98196
$641$	−1.80604e15	−0.659186	−0.329593	−	0.944123i	$-0.606912\pi$
$641$	−1.80604e15	−0.659186	−0.329593	+	0.944123i	$0.606912\pi$
$642$	5.80781e15	2.10169
$643$	2.19272e14	0.0786723	0.0393361	−	0.999226i	$-0.487476\pi$
$643$	2.19272e14	0.0786723	0.0393361	+	0.999226i	$0.487476\pi$
$644$	−2.47846e15	−0.881676
$645$	8.08571e14	0.285194
$646$	2.02902e15	0.709589
$647$	1.55330e15	0.538621	0.269310	−	0.963053i	$-0.413204\pi$
$647$	1.55330e15	0.538621	0.269310	+	0.963053i	$0.413204\pi$
$648$	−1.12441e15	−0.386599
$649$	−7.41558e15	−2.52813
$650$	4.27689e15	1.44579
$651$	−4.44719e14	−0.149070
$652$	9.12334e15	3.03244
$653$	1.58385e15	0.522025	0.261012	−	0.965335i	$-0.415944\pi$
$653$	1.58385e15	0.522025	0.261012	+	0.965335i	$0.415944\pi$
$654$	1.29872e14	0.0424463
$655$	−8.88468e15	−2.87948
$656$	1.03774e16	3.33518
$657$	5.56061e14	0.177220
$658$	−1.61721e14	−0.0511122
$659$	2.46153e15	0.771498	0.385749	−	0.922604i	$-0.373943\pi$
$659$	2.46153e15	0.771498	0.385749	+	0.922604i	$0.373943\pi$
$660$	1.79658e16	5.58413
$661$	1.14409e15	0.352655	0.176328	−	0.984332i	$-0.443578\pi$
$661$	1.14409e15	0.352655	0.176328	+	0.984332i	$0.443578\pi$
$662$	9.65033e15	2.95001
$663$	−2.94952e14	−0.0894185
$664$	−5.64030e15	−1.69581
$665$	−1.58730e15	−0.473303
$666$	2.80680e15	0.830048
$667$	2.42842e15	0.712250
$668$	1.83258e16	5.33079
$669$	2.53394e15	0.731058
$670$	−2.03198e16	−5.81444
$671$	−1.25888e15	−0.357283
$672$	3.31336e15	0.932691
$673$	−2.59131e15	−0.723496	−0.361748	−	0.932276i	$-0.617820\pi$
$673$	−2.59131e15	−0.723496	−0.361748	+	0.932276i	$0.617820\pi$
$674$	−1.96291e14	−0.0543589
$675$	−1.87661e15	−0.515469
$676$	7.87082e14	0.214444
$677$	2.25648e15	0.609809	0.304905	−	0.952383i	$-0.401375\pi$
$677$	2.25648e15	0.609809	0.304905	+	0.952383i	$0.401375\pi$
$678$	−7.10756e15	−1.90527
$679$	−6.35343e14	−0.168937
$680$	−1.41285e16	−3.72645
$681$	9.11463e14	0.238468
$682$	−9.26686e15	−2.40502
$683$	5.97129e14	0.153728	0.0768642	−	0.997042i	$-0.475509\pi$
$683$	5.97129e14	0.153728	0.0768642	+	0.997042i	$0.475509\pi$
$684$	2.37574e15	0.606724
$685$	1.04089e16	2.63699
$686$	−4.18145e14	−0.105086
$687$	−2.24279e15	−0.559149
$688$	4.14869e15	1.02606
$689$	−1.24207e14	−0.0304749
$690$	7.40858e15	1.80329
$691$	7.80419e15	1.88451	0.942255	−	0.334897i	$-0.108702\pi$
$691$	7.80419e15	1.88451	0.942255	+	0.334897i	$0.108702\pi$
$692$	−1.53162e16	−3.66917
$693$	9.58934e14	0.227906
$694$	−1.45994e16	−3.44237
$695$	−9.69026e15	−2.26683
$696$	−7.36757e15	−1.70991
$697$	−2.03026e15	−0.467490
$698$	6.17278e15	1.41018
$699$	2.13396e15	0.483685
$700$	1.25497e16	2.82223
$701$	−6.06863e15	−1.35407	−0.677036	−	0.735950i	$-0.736736\pi$
$701$	−6.06863e15	−1.35407	−0.677036	+	0.735950i	$0.736736\pi$
$702$	−4.69237e14	−0.103881
$703$	−3.80314e15	−0.835388
$704$	3.59762e16	7.84089
$705$	3.55791e14	0.0769404
$706$	−1.42414e16	−3.05582
$707$	2.28846e15	0.487233
$708$	1.06476e16	2.24941
$709$	−6.42694e15	−1.34726	−0.673628	−	0.739071i	$-0.735265\pi$
$709$	−6.42694e15	−1.34726	−0.673628	+	0.739071i	$0.735265\pi$
$710$	−3.06842e16	−6.38254
$711$	−9.34799e14	−0.192946
$712$	−1.20894e16	−2.47607
$713$	−2.81251e15	−0.571612
$714$	−1.17593e15	−0.237160
$715$	4.80807e15	0.962249
$716$	−8.16196e15	−1.62096
$717$	−1.70837e15	−0.336687
$718$	7.66119e15	1.49835
$719$	7.57171e15	1.46955	0.734776	−	0.678310i	$-0.237287\pi$
$719$	7.57171e15	1.46955	0.734776	+	0.678310i	$0.237287\pi$
$720$	−1.32235e16	−2.54694
$721$	1.22650e15	0.234436
$722$	5.88619e15	1.11655
$723$	−3.87752e14	−0.0729951
$724$	−2.76226e16	−5.16063
$725$	−1.22963e16	−2.27990
$726$	1.38755e16	2.55327
$727$	−4.48914e15	−0.819830	−0.409915	−	0.912124i	$-0.634442\pi$
$727$	−4.48914e15	−0.819830	−0.409915	+	0.912124i	$0.634442\pi$
$728$	2.01236e15	0.364739
$729$	2.05891e14	0.0370370
$730$	1.11156e16	1.98453
$731$	−8.11658e14	−0.143823
$732$	1.80756e15	0.317894
$733$	−6.39691e15	−1.11660	−0.558301	−	0.829638i	$-0.688547\pi$
$733$	−6.39691e15	−1.11660	−0.558301	+	0.829638i	$0.688547\pi$
$734$	−1.08292e16	−1.87615
$735$	9.19930e14	0.158188
$736$	2.09545e16	3.57642
$737$	−1.66334e16	−2.81780
$738$	−3.22993e15	−0.543104
$739$	2.63169e15	0.439228	0.219614	−	0.975587i	$-0.429520\pi$
$739$	2.63169e15	0.439228	0.219614	+	0.975587i	$0.429520\pi$
$740$	4.12949e16	6.84104
$741$	6.35804e14	0.104550
$742$	−4.95197e14	−0.0808270
$743$	−3.59566e15	−0.582560	−0.291280	−	0.956638i	$-0.594081\pi$
$743$	−3.59566e15	−0.582560	−0.291280	+	0.956638i	$0.594081\pi$
$744$	8.53285e15	1.37228
$745$	−9.29167e15	−1.48332
$746$	−5.16006e15	−0.817696
$747$	1.03280e15	0.162462
$748$	−1.80344e16	−2.81607
$749$	4.56078e15	0.706951
$750$	−2.35078e16	−3.61722
$751$	−8.29732e15	−1.26741	−0.633706	−	0.773574i	$-0.718467\pi$
$751$	−8.29732e15	−1.26741	−0.633706	+	0.773574i	$0.718467\pi$
$752$	1.82552e15	0.276815
$753$	−7.71306e14	−0.116106
$754$	−3.07464e15	−0.459464
$755$	1.06416e16	1.57869
$756$	−1.37688e15	−0.202780
$757$	−2.03120e15	−0.296979	−0.148489	−	0.988914i	$-0.547441\pi$
$757$	−2.03120e15	−0.296979	−0.148489	+	0.988914i	$0.547441\pi$
$758$	5.64641e15	0.819581
$759$	6.06452e15	0.873911
$760$	3.04555e16	4.35704
$761$	−5.23714e15	−0.743838	−0.371919	−	0.928265i	$-0.621300\pi$
$761$	−5.23714e15	−0.743838	−0.371919	+	0.928265i	$0.621300\pi$
$762$	5.23070e15	0.737577
$763$	1.01987e14	0.0142777
$764$	1.99224e15	0.276903
$765$	2.58708e15	0.357003
$766$	2.47128e14	0.0338583
$767$	2.84955e15	0.387616
$768$	−1.60958e16	−2.17384
$769$	2.37472e15	0.318432	0.159216	−	0.987244i	$-0.449103\pi$
$769$	2.37472e15	0.318432	0.159216	+	0.987244i	$0.449103\pi$
$770$	1.91691e16	2.55213
$771$	3.88253e14	0.0513235
$772$	−1.30736e16	−1.71593
$773$	−1.06877e16	−1.39283	−0.696416	−	0.717639i	$-0.745223\pi$
$773$	−1.06877e16	−1.39283	−0.696416	+	0.717639i	$0.745223\pi$
$774$	−1.29126e15	−0.167085
$775$	1.42411e16	1.82972
$776$	1.21904e16	1.55517
$777$	2.20414e15	0.279205
$778$	2.52360e16	3.17419
$779$	4.37647e15	0.546597
$780$	−6.90363e15	−0.856165
$781$	−2.51175e16	−3.09311
$782$	−7.43687e15	−0.909396
$783$	1.34908e15	0.163813
$784$	4.72006e15	0.569127
$785$	−1.66819e16	−1.99739
$786$	1.41885e16	1.68699
$787$	5.76104e15	0.680205	0.340102	−	0.940388i	$-0.389538\pi$
$787$	5.76104e15	0.680205	0.340102	+	0.940388i	$0.389538\pi$
$788$	1.34417e15	0.157602
$789$	−6.11087e15	−0.711508
$790$	−1.86866e16	−2.16063
$791$	−5.58146e15	−0.640880
$792$	−1.83991e16	−2.09801
$793$	4.83745e14	0.0547790
$794$	2.93611e16	3.30187
$795$	1.08944e15	0.121671
$796$	3.42179e16	3.79518
$797$	1.19610e16	1.31749	0.658746	−	0.752365i	$-0.271087\pi$
$797$	1.19610e16	1.31749	0.658746	+	0.752365i	$0.271087\pi$
$798$	2.53486e15	0.277292
$799$	−3.57149e14	−0.0388009
$800$	−1.06103e17	−11.4481
$801$	2.21370e15	0.237213
$802$	−1.30525e16	−1.38911
$803$	9.09904e15	0.961746
$804$	2.38829e16	2.50715
$805$	5.81785e15	0.606576
$806$	3.56093e15	0.368740
$807$	−6.46417e15	−0.664826
$808$	−4.39088e16	−4.48527
$809$	−5.67680e15	−0.575952	−0.287976	−	0.957638i	$-0.592982\pi$
$809$	−5.67680e15	−0.575952	−0.287976	+	0.957638i	$0.592982\pi$
$810$	4.11576e15	0.414746
$811$	2.09739e15	0.209925	0.104962	−	0.994476i	$-0.466528\pi$
$811$	2.09739e15	0.209925	0.104962	+	0.994476i	$0.466528\pi$
$812$	−9.02188e15	−0.896890
$813$	1.07846e15	0.106490
$814$	4.59288e16	4.50454
$815$	−2.14158e16	−2.08626
$816$	1.32740e16	1.28442
$817$	1.74962e15	0.168160
$818$	2.86742e16	2.73746
$819$	−3.68485e14	−0.0349428
$820$	−4.75202e16	−4.47612
$821$	9.60765e15	0.898938	0.449469	−	0.893296i	$-0.351613\pi$
$821$	9.60765e15	0.898938	0.449469	+	0.893296i	$0.351613\pi$
$822$	−1.66227e16	−1.54492
$823$	−9.40279e15	−0.868076	−0.434038	−	0.900895i	$-0.642912\pi$
$823$	−9.40279e15	−0.868076	−0.434038	+	0.900895i	$0.642912\pi$
$824$	−2.35329e16	−2.15812
$825$	−3.07077e16	−2.79737
$826$	1.13607e16	1.02805
$827$	6.48063e15	0.582555	0.291278	−	0.956639i	$-0.405920\pi$
$827$	6.48063e15	0.582555	0.291278	+	0.956639i	$0.405920\pi$
$828$	−8.70770e15	−0.777565
$829$	1.52038e16	1.34866	0.674330	−	0.738430i	$-0.264432\pi$
$829$	1.52038e16	1.34866	0.674330	+	0.738430i	$0.264432\pi$
$830$	2.06456e16	1.81928
$831$	−7.83461e15	−0.685822
$832$	−1.38244e16	−1.20217
$833$	−9.23441e14	−0.0797741
$834$	1.54750e16	1.32806
$835$	−4.30173e16	−3.66748
$836$	3.88752e16	3.29260
$837$	−1.56246e15	−0.131467
$838$	7.88773e15	0.659341
$839$	4.66734e15	0.387595	0.193798	−	0.981042i	$-0.437919\pi$
$839$	4.66734e15	0.387595	0.193798	+	0.981042i	$0.437919\pi$
$840$	−1.76507e16	−1.45622
$841$	−3.36075e15	−0.275460
$842$	2.52857e16	2.05901
$843$	1.50374e15	0.121653
$844$	6.40559e16	5.14844
$845$	−1.84757e15	−0.147533
$846$	−5.68185e14	−0.0450767
$847$	1.08962e16	0.858848
$848$	5.58982e15	0.437744
$849$	1.12547e16	0.875674
$850$	3.76566e16	2.91096
$851$	1.39395e16	1.07062
$852$	3.60648e16	2.75211
$853$	2.11779e16	1.60569	0.802847	−	0.596185i	$-0.203318\pi$
$853$	2.11779e16	1.60569	0.802847	+	0.596185i	$0.203318\pi$
$854$	1.92862e15	0.145288
$855$	−5.57674e15	−0.417414
$856$	−8.75079e16	−6.50791
$857$	6.44287e15	0.476085	0.238043	−	0.971255i	$-0.423494\pi$
$857$	6.44287e15	0.476085	0.238043	+	0.971255i	$0.423494\pi$
$858$	−7.67831e15	−0.563749
$859$	−2.98846e15	−0.218014	−0.109007	−	0.994041i	$-0.534767\pi$
$859$	−2.98846e15	−0.218014	−0.109007	+	0.994041i	$0.534767\pi$
$860$	−1.89976e16	−1.37707
$861$	−2.53641e15	−0.182685
$862$	3.73975e16	2.67641
$863$	6.52500e15	0.464003	0.232002	−	0.972715i	$-0.425473\pi$
$863$	6.52500e15	0.464003	0.232002	+	0.972715i	$0.425473\pi$
$864$	1.16410e16	0.822556
$865$	3.59528e16	2.52432
$866$	−3.88405e16	−2.70980
$867$	5.73112e15	0.397314
$868$	1.04488e16	0.719794
$869$	−1.52965e16	−1.04709
$870$	2.69682e16	1.83441
$871$	6.39163e15	0.432028
$872$	−1.95683e15	−0.131435
$873$	−2.23219e15	−0.148988
$874$	1.60310e16	1.06328
$875$	−1.84603e16	−1.21673
$876$	−1.30648e16	−0.855717
$877$	−1.10842e16	−0.721450	−0.360725	−	0.932672i	$-0.617471\pi$
$877$	−1.10842e16	−0.721450	−0.360725	+	0.932672i	$0.617471\pi$
$878$	3.40276e16	2.20096
$879$	3.37036e15	0.216640
$880$	−2.16382e17	−13.8219
$881$	−8.89292e14	−0.0564517	−0.0282258	−	0.999602i	$-0.508986\pi$
$881$	−8.89292e14	−0.0564517	−0.0282258	+	0.999602i	$0.508986\pi$
$882$	−1.46909e15	−0.0926771
$883$	−2.11288e16	−1.32462	−0.662309	−	0.749231i	$-0.730423\pi$
$883$	−2.11288e16	−1.32462	−0.662309	+	0.749231i	$0.730423\pi$
$884$	6.92999e15	0.431763
$885$	−2.49939e16	−1.54755
$886$	−4.92729e16	−3.03196
$887$	6.69059e14	0.0409152	0.0204576	−	0.999791i	$-0.493488\pi$
$887$	6.69059e14	0.0409152	0.0204576	+	0.999791i	$0.493488\pi$
$888$	−4.22909e16	−2.57025
$889$	4.10759e15	0.248100
$890$	4.42517e16	2.65635
$891$	3.36908e15	0.200994
$892$	−5.95355e16	−3.52996
$893$	7.69875e14	0.0453667
$894$	1.48385e16	0.869026
$895$	1.91591e16	1.11519
$896$	−2.71908e16	−1.57300
$897$	−2.33038e15	−0.133989
$898$	1.65574e15	0.0946179
$899$	−1.02379e16	−0.581476
$900$	4.40914e16	2.48897
$901$	−1.09360e15	−0.0613583
$902$	−5.28526e16	−2.94734
$903$	−1.01401e15	−0.0562028
$904$	1.07092e17	5.89969
$905$	6.48404e16	3.55041
$906$	−1.69942e16	−0.924901
$907$	−3.32321e16	−1.79770	−0.898851	−	0.438254i	$-0.855597\pi$
$907$	−3.32321e16	−1.79770	−0.898851	+	0.438254i	$0.855597\pi$
$908$	−2.14151e16	−1.15146
$909$	8.04018e15	0.429699
$910$	−7.36600e15	−0.391295
$911$	1.78276e16	0.941331	0.470666	−	0.882312i	$-0.344014\pi$
$911$	1.78276e16	0.941331	0.470666	+	0.882312i	$0.344014\pi$
$912$	−2.86137e16	−1.50176
$913$	1.69001e16	0.881659
$914$	−2.12200e16	−1.10038
$915$	−4.24301e15	−0.218705
$916$	5.26951e16	2.69988
$917$	1.11420e16	0.567457
$918$	−4.13147e15	−0.209156
$919$	−1.37212e16	−0.690488	−0.345244	−	0.938513i	$-0.612204\pi$
$919$	−1.37212e16	−0.690488	−0.345244	+	0.938513i	$0.612204\pi$
$920$	−1.11627e17	−5.58389
$921$	−1.54059e16	−0.766051
$922$	−1.92461e14	−0.00951312
$923$	9.65177e15	0.474239
$924$	−2.25304e16	−1.10046
$925$	−7.05825e16	−3.42703
$926$	2.37188e16	1.14481
$927$	4.30914e15	0.206753
$928$	7.62768e16	3.63813
$929$	2.01407e16	0.954969	0.477484	−	0.878640i	$-0.341549\pi$
$929$	2.01407e16	0.954969	0.477484	+	0.878640i	$0.341549\pi$
$930$	−3.12335e16	−1.47219
$931$	1.99058e15	0.0932733
$932$	−5.01381e16	−2.33550
$933$	1.21354e15	0.0561959
$934$	−2.40745e16	−1.10828
$935$	4.23334e16	1.93740
$936$	7.07013e15	0.321670
$937$	−1.07677e16	−0.487030	−0.243515	−	0.969897i	$-0.578301\pi$
$937$	−1.07677e16	−0.487030	−0.243515	+	0.969897i	$0.578301\pi$
$938$	2.54825e16	1.14585
$939$	8.12325e15	0.363136
$940$	−8.35939e15	−0.371511
$941$	−3.92545e15	−0.173439	−0.0867194	−	0.996233i	$-0.527638\pi$
$941$	−3.92545e15	−0.173439	−0.0867194	+	0.996233i	$0.527638\pi$
$942$	2.66405e16	1.17020
$943$	−1.60409e16	−0.700508
$944$	−1.28241e17	−5.56775
$945$	3.23204e15	0.139509
$946$	−2.11294e16	−0.906746
$947$	2.33959e16	0.998195	0.499098	−	0.866546i	$-0.333665\pi$
$947$	2.33959e16	0.998195	0.499098	+	0.866546i	$0.333665\pi$
$948$	2.19634e16	0.931650
$949$	−3.49644e15	−0.147456
$950$	−8.11730e16	−3.40355
$951$	6.09386e15	0.254038
$952$	1.77181e16	0.734368
$953$	3.62494e16	1.49379	0.746896	−	0.664940i	$-0.231543\pi$
$953$	3.62494e16	1.49379	0.746896	+	0.664940i	$0.231543\pi$
$954$	−1.73980e15	−0.0712827
$955$	−4.67652e15	−0.190504
$956$	4.01386e16	1.62571
$957$	2.20756e16	0.888990
$958$	−1.27249e16	−0.509500
$959$	−1.30535e16	−0.519668
$960$	1.21256e17	4.79967
$961$	−1.35514e16	−0.533340
$962$	−1.76488e16	−0.690642
$963$	1.60237e16	0.623472
$964$	9.11034e15	0.352461
$965$	3.06886e16	1.18053
$966$	−9.29089e15	−0.355372
$967$	−4.05463e15	−0.154208	−0.0771038	−	0.997023i	$-0.524567\pi$
$967$	−4.05463e15	−0.154208	−0.0771038	+	0.997023i	$0.524567\pi$
$968$	−2.09066e17	−7.90621
$969$	5.59803e15	0.210501
$970$	−4.46214e16	−1.66839
$971$	2.07744e16	0.772366	0.386183	−	0.922422i	$-0.373793\pi$
$971$	2.07744e16	0.772366	0.386183	+	0.922422i	$0.373793\pi$
$972$	−4.83747e15	−0.178835
$973$	1.21523e16	0.446722
$974$	1.36406e16	0.498608
$975$	1.17999e16	0.428897
$976$	−2.17704e16	−0.786851
$977$	1.01946e16	0.366394	0.183197	−	0.983076i	$-0.441355\pi$
$977$	1.01946e16	0.366394	0.183197	+	0.983076i	$0.441355\pi$
$978$	3.42003e16	1.22227
$979$	3.62236e16	1.28732
$980$	−2.16140e16	−0.763821
$981$	3.58316e14	0.0125918
$982$	8.85595e16	3.09472
$983$	−1.06518e16	−0.370151	−0.185075	−	0.982724i	$-0.559253\pi$
$983$	−1.06518e16	−0.370151	−0.185075	+	0.982724i	$0.559253\pi$
$984$	4.86662e16	1.68172
$985$	−3.15527e15	−0.108427
$986$	−2.70711e16	−0.925088
$987$	−4.46187e14	−0.0151626
$988$	−1.49384e16	−0.504825
$989$	−6.41281e15	−0.215511
$990$	6.73478e16	2.25076
$991$	7.22558e15	0.240142	0.120071	−	0.992765i	$-0.461688\pi$
$991$	7.22558e15	0.240142	0.120071	+	0.992765i	$0.461688\pi$
$992$	−8.83409e16	−2.91976
$993$	2.66251e16	0.875127
$994$	3.84802e16	1.25780
$995$	−8.03221e16	−2.61101
$996$	−2.42659e16	−0.784459
$997$	−2.31554e16	−0.744439	−0.372219	−	0.928145i	$-0.621403\pi$
$997$	−2.31554e16	−0.744439	−0.372219	+	0.928145i	$0.621403\pi$
$998$	4.76495e16	1.52349
$999$	7.74392e15	0.246236

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.12.a.c.1.1	✓	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q-88.0758 q^{2} -243.000 q^{3} +5709.35 q^{4} -13401.9 q^{5} +21402.4 q^{6} +16807.0 q^{7} -322476. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-88.0758 q^{2} -243.000 q^{3} +5709.35 q^{4} -13401.9 q^{5} +21402.4 q^{6} +16807.0 q^{7} -322476. q^{8} +59049.0 q^{9} +1.18039e6 q^{10} +966243. q^{11} -1.38737e6 q^{12} -371293. q^{13} -1.48029e6 q^{14} +3.25667e6 q^{15} +1.67096e7 q^{16} -3.26911e6 q^{17} -5.20079e6 q^{18} +7.04693e6 q^{19} -7.65164e7 q^{20} -4.08410e6 q^{21} -8.51026e7 q^{22} -2.58288e7 q^{23} +7.83618e7 q^{24} +1.30784e8 q^{25} +3.27019e7 q^{26} -1.43489e7 q^{27} +9.59571e7 q^{28} -9.40200e7 q^{29} -2.86834e8 q^{30} +1.08890e8 q^{31} -8.11283e8 q^{32} -2.34797e8 q^{33} +2.87929e8 q^{34} -2.25247e8 q^{35} +3.37131e8 q^{36} -5.39687e8 q^{37} -6.20665e8 q^{38} +9.02242e7 q^{39} +4.32181e9 q^{40} +6.21045e8 q^{41} +3.59711e8 q^{42} +2.48281e8 q^{43} +5.51662e9 q^{44} -7.91372e8 q^{45} +2.27489e9 q^{46} +1.09250e8 q^{47} -4.06044e9 q^{48} +2.82475e8 q^{49} -1.15189e10 q^{50} +7.94393e8 q^{51} -2.11984e9 q^{52} +3.34527e8 q^{53} +1.26379e9 q^{54} -1.29495e10 q^{55} -5.41986e9 q^{56} -1.71240e9 q^{57} +8.28089e9 q^{58} -7.67466e9 q^{59} +1.85935e10 q^{60} -1.30287e9 q^{61} -9.59061e9 q^{62} +9.92437e8 q^{63} +3.72331e10 q^{64} +4.97605e9 q^{65} +2.06799e10 q^{66} -1.72145e10 q^{67} -1.86645e10 q^{68} +6.27640e9 q^{69} +1.98388e10 q^{70} -2.59950e10 q^{71} -1.90419e10 q^{72} +9.41694e9 q^{73} +4.75334e10 q^{74} -3.17805e10 q^{75} +4.02334e10 q^{76} +1.62396e10 q^{77} -7.94657e9 q^{78} -1.58309e10 q^{79} -2.23942e11 q^{80} +3.48678e9 q^{81} -5.46991e10 q^{82} +1.74906e10 q^{83} -2.33176e10 q^{84} +4.38124e10 q^{85} -2.18676e10 q^{86} +2.28469e10 q^{87} -3.11590e11 q^{88} +3.74891e10 q^{89} +6.97007e10 q^{90} -6.24032e9 q^{91} -1.47466e11 q^{92} -2.64604e10 q^{93} -9.62226e9 q^{94} -9.44426e10 q^{95} +1.97142e11 q^{96} -3.78023e10 q^{97} -2.48792e10 q^{98} +5.70557e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) 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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