LMFDB - Embedded newform 29.12.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	29.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:	$22.2819522362$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 $ x^11 - x^10 - 15790x^9 + 14666x^8 + 87206462x^7 - 14008334x^6 - 203974096304x^5 - 388180519304x^4 + 193065378004825x^3 + 1279291654973975x^2 - 65244901875230266*x - 758324542468966858
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-56.7551$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +O(q^{10})$	\(q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +381183. q^{10} +522514. q^{11} -597963. q^{12} +1.47979e6 q^{13} +1.37472e6 q^{14} +2.50510e6 q^{15} -4.99420e6 q^{16} +4.61480e6 q^{17} +1.37017e6 q^{18} +1.36307e7 q^{19} -9.71327e6 q^{20} +9.03450e6 q^{21} -3.12229e7 q^{22} -5.58468e7 q^{23} -1.23273e7 q^{24} -8.13546e6 q^{25} -8.84253e7 q^{26} +7.85711e7 q^{27} -3.50304e7 q^{28} +2.05111e7 q^{29} -1.49692e8 q^{30} -1.47320e8 q^{31} +2.34141e8 q^{32} -2.05194e8 q^{33} -2.75758e8 q^{34} +1.46756e8 q^{35} -3.49146e7 q^{36} -1.64673e8 q^{37} -8.14503e8 q^{38} -5.81123e8 q^{39} -2.00244e8 q^{40} +9.49494e6 q^{41} -5.39858e8 q^{42} +7.59458e8 q^{43} +7.95619e8 q^{44} +1.46271e8 q^{45} +3.33713e9 q^{46} +1.65847e9 q^{47} +1.96125e9 q^{48} -1.44806e9 q^{49} +4.86136e8 q^{50} -1.81226e9 q^{51} +2.25325e9 q^{52} +3.15983e9 q^{53} -4.69503e9 q^{54} -3.33316e9 q^{55} -7.22171e8 q^{56} -5.35284e9 q^{57} -1.22565e9 q^{58} +2.72696e9 q^{59} +3.81445e9 q^{60} +2.15540e9 q^{61} +8.80314e9 q^{62} +5.27517e8 q^{63} -3.76299e9 q^{64} -9.43973e9 q^{65} +1.22614e10 q^{66} -1.36283e10 q^{67} +7.02685e9 q^{68} +2.19313e10 q^{69} -8.76942e9 q^{70} +9.15005e9 q^{71} -7.19783e8 q^{72} -2.13411e10 q^{73} +9.84006e9 q^{74} +3.19484e9 q^{75} +2.07551e10 q^{76} -1.20209e10 q^{77} +3.47251e10 q^{78} -3.95516e10 q^{79} +3.18584e10 q^{80} -2.67934e10 q^{81} -5.67371e8 q^{82} +2.56121e10 q^{83} +1.37566e10 q^{84} -2.94382e10 q^{85} -4.53815e10 q^{86} -8.05483e9 q^{87} +1.64021e10 q^{88} -6.50080e10 q^{89} -8.74042e9 q^{90} -3.40439e10 q^{91} -8.50365e10 q^{92} +5.78534e10 q^{93} -9.91019e10 q^{94} -8.69512e10 q^{95} -9.19483e10 q^{96} +1.86954e10 q^{97} +8.65290e10 q^{98} -1.19811e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) $ 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9} - 685834 q^{10} - 612246 q^{11} + 2578538 q^{12} + 1510364 q^{13} + 3955400 q^{14} - 2462818 q^{15} + 3024818 q^{16} - 3291098 q^{17} - 27885614 q^{18} - 44121388 q^{19} - 49472662 q^{20} - 46916800 q^{21} - 43435618 q^{22} - 88684076 q^{23} - 224700678 q^{24} - 44195521 q^{25} - 324999762 q^{26} - 236304286 q^{27} - 391274848 q^{28} + 225622639 q^{29} - 494910382 q^{30} - 292235934 q^{31} - 632542514 q^{32} - 1079766410 q^{33} - 1113307936 q^{34} - 1312820120 q^{35} - 2236726492 q^{36} - 1380429338 q^{37} - 1222857284 q^{38} - 1186931090 q^{39} - 2713154106 q^{40} - 1062067494 q^{41} + 205598960 q^{42} + 74588594 q^{43} + 52891466 q^{44} + 4527996830 q^{45} - 87670324 q^{46} - 1821239394 q^{47} + 2666035542 q^{48} + 4692522003 q^{49} + 9494259926 q^{50} + 8768158380 q^{51} + 3266669866 q^{52} + 7818635688 q^{53} + 17402728558 q^{54} - 191002682 q^{55} + 11263587512 q^{56} + 15495358340 q^{57} - 656356768 q^{58} + 1230002712 q^{59} + 31834046430 q^{60} - 18602654230 q^{61} + 22075953162 q^{62} - 9964531456 q^{63} + 11813658086 q^{64} + 32245789334 q^{65} + 42677188354 q^{66} + 27481284652 q^{67} + 29588811820 q^{68} - 20565315068 q^{69} + 42862666712 q^{70} - 20347168516 q^{71} + 47061083616 q^{72} - 57740010478 q^{73} - 2640709564 q^{74} - 23544691000 q^{75} - 33350650772 q^{76} + 871959792 q^{77} - 15384525342 q^{78} - 120245016462 q^{79} - 84319695274 q^{80} - 48880047865 q^{81} - 111495532412 q^{82} - 142463983824 q^{83} - 134146226376 q^{84} - 181628566552 q^{85} + 47870165542 q^{86} - 20141948318 q^{87} - 180608014462 q^{88} - 96700717270 q^{89} - 25522461244 q^{90} - 355162031176 q^{91} - 22429477796 q^{92} - 172582115142 q^{93} + 172608565078 q^{94} - 195922150708 q^{95} + 226391047758 q^{96} - 303190852014 q^{97} - 123776497136 q^{98} - 139125462440 q^{99}+O(q^{100}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9 - 685834 * q^10 - 612246 * q^11 + 2578538 * q^12 + 1510364 * q^13 + 3955400 * q^14 - 2462818 * q^15 + 3024818 * q^16 - 3291098 * q^17 - 27885614 * q^18 - 44121388 * q^19 - 49472662 * q^20 - 46916800 * q^21 - 43435618 * q^22 - 88684076 * q^23 - 224700678 * q^24 - 44195521 * q^25 - 324999762 * q^26 - 236304286 * q^27 - 391274848 * q^28 + 225622639 * q^29 - 494910382 * q^30 - 292235934 * q^31 - 632542514 * q^32 - 1079766410 * q^33 - 1113307936 * q^34 - 1312820120 * q^35 - 2236726492 * q^36 - 1380429338 * q^37 - 1222857284 * q^38 - 1186931090 * q^39 - 2713154106 * q^40 - 1062067494 * q^41 + 205598960 * q^42 + 74588594 * q^43 + 52891466 * q^44 + 4527996830 * q^45 - 87670324 * q^46 - 1821239394 * q^47 + 2666035542 * q^48 + 4692522003 * q^49 + 9494259926 * q^50 + 8768158380 * q^51 + 3266669866 * q^52 + 7818635688 * q^53 + 17402728558 * q^54 - 191002682 * q^55 + 11263587512 * q^56 + 15495358340 * q^57 - 656356768 * q^58 + 1230002712 * q^59 + 31834046430 * q^60 - 18602654230 * q^61 + 22075953162 * q^62 - 9964531456 * q^63 + 11813658086 * q^64 + 32245789334 * q^65 + 42677188354 * q^66 + 27481284652 * q^67 + 29588811820 * q^68 - 20565315068 * q^69 + 42862666712 * q^70 - 20347168516 * q^71 + 47061083616 * q^72 - 57740010478 * q^73 - 2640709564 * q^74 - 23544691000 * q^75 - 33350650772 * q^76 + 871959792 * q^77 - 15384525342 * q^78 - 120245016462 * q^79 - 84319695274 * q^80 - 48880047865 * q^81 - 111495532412 * q^82 - 142463983824 * q^83 - 134146226376 * q^84 - 181628566552 * q^85 + 47870165542 * q^86 - 20141948318 * q^87 - 180608014462 * q^88 - 96700717270 * q^89 - 25522461244 * q^90 - 355162031176 * q^91 - 22429477796 * q^92 - 172582115142 * q^93 + 172608565078 * q^94 - 195922150708 * q^95 + 226391047758 * q^96 - 303190852014 * q^97 - 123776497136 * q^98 - 139125462440 * 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 $

$2$	−59.7551	−1.32041	−0.660207	−	0.751084i	$-0.729532\pi$
$2$	−59.7551	−1.32041	−0.660207	+	0.751084i	$0.729532\pi$
$3$	−392.705	−0.933039	−0.466519	−	0.884511i	$-0.654492\pi$
$3$	−392.705	−0.933039	−0.466519	+	0.884511i	$0.654492\pi$
$4$	1522.68	0.743494
$5$	−6379.08	−0.912900	−0.456450	−	0.889749i	$-0.650879\pi$
$5$	−6379.08	−0.912900	−0.456450	+	0.889749i	$0.650879\pi$
$6$	23466.1	1.23200
$7$	−23005.8	−0.517367	−0.258683	−	0.965962i	$-0.583289\pi$
$7$	−23005.8	−0.517367	−0.258683	+	0.965962i	$0.583289\pi$
$8$	31390.8	0.338694
$9$	−22929.7	−0.129439
$10$	381183.	1.20541
$11$	522514.	0.978223	0.489112	−	0.872221i	$-0.337321\pi$
$11$	522514.	0.978223	0.489112	+	0.872221i	$0.337321\pi$
$12$	−597963.	−0.693709
$13$	1.47979e6	1.10538	0.552692	−	0.833386i	$-0.313601\pi$
$13$	1.47979e6	1.10538	0.552692	+	0.833386i	$0.313601\pi$
$14$	1.37472e6	0.683138
$15$	2.50510e6	0.851771
$16$	−4.99420e6	−1.19071
$17$	4.61480e6	0.788286	0.394143	−	0.919049i	$-0.371041\pi$
$17$	4.61480e6	0.788286	0.394143	+	0.919049i	$0.371041\pi$
$18$	1.37017e6	0.170913
$19$	1.36307e7	1.26291	0.631456	−	0.775412i	$-0.282458\pi$
$19$	1.36307e7	1.26291	0.631456	+	0.775412i	$0.282458\pi$
$20$	−9.71327e6	−0.678736
$21$	9.03450e6	0.482723
$22$	−3.12229e7	−1.29166
$23$	−5.58468e7	−1.80923	−0.904617	−	0.426225i	$-0.859843\pi$
$23$	−5.58468e7	−1.80923	−0.904617	+	0.426225i	$0.859843\pi$
$24$	−1.23273e7	−0.316014
$25$	−8.13546e6	−0.166614
$26$	−8.84253e7	−1.45956
$27$	7.85711e7	1.05381
$28$	−3.50304e7	−0.384659
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	−1.49692e8	−1.12469
$31$	−1.47320e8	−0.924215	−0.462108	−	0.886824i	$-0.652907\pi$
$31$	−1.47320e8	−0.924215	−0.462108	+	0.886824i	$0.652907\pi$
$32$	2.34141e8	1.23354
$33$	−2.05194e8	−0.912720
$34$	−2.75758e8	−1.04086
$35$	1.46756e8	0.472304
$36$	−3.49146e7	−0.0962372
$37$	−1.64673e8	−0.390403	−0.195201	−	0.980763i	$-0.562536\pi$
$37$	−1.64673e8	−0.390403	−0.195201	+	0.980763i	$0.562536\pi$
$38$	−8.14503e8	−1.66757
$39$	−5.81123e8	−1.03137
$40$	−2.00244e8	−0.309194
$41$	9.49494e6	0.0127991	0.00639957	−	0.999980i	$-0.497963\pi$
$41$	9.49494e6	0.0127991	0.00639957	+	0.999980i	$0.497963\pi$
$42$	−5.39858e8	−0.637395
$43$	7.59458e8	0.787820	0.393910	−	0.919149i	$-0.371122\pi$
$43$	7.59458e8	0.787820	0.393910	+	0.919149i	$0.371122\pi$
$44$	7.95619e8	0.727303
$45$	1.46271e8	0.118165
$46$	3.33713e9	2.38894
$47$	1.65847e9	1.05480	0.527398	−	0.849618i	$-0.323168\pi$
$47$	1.65847e9	1.05480	0.527398	+	0.849618i	$0.323168\pi$
$48$	1.96125e9	1.11098
$49$	−1.44806e9	−0.732332
$50$	4.86136e8	0.220000
$51$	−1.81226e9	−0.735501
$52$	2.25325e9	0.821846
$53$	3.15983e9	1.03788	0.518940	−	0.854811i	$-0.326327\pi$
$53$	3.15983e9	1.03788	0.518940	+	0.854811i	$0.326327\pi$
$54$	−4.69503e9	−1.39147
$55$	−3.33316e9	−0.893020
$56$	−7.22171e8	−0.175229
$57$	−5.35284e9	−1.17834
$58$	−1.22565e9	−0.245195
$59$	2.72696e9	0.496584	0.248292	−	0.968685i	$-0.420131\pi$
$59$	2.72696e9	0.496584	0.248292	+	0.968685i	$0.420131\pi$
$60$	3.81445e9	0.633286
$61$	2.15540e9	0.326748	0.163374	−	0.986564i	$-0.447762\pi$
$61$	2.15540e9	0.326748	0.163374	+	0.986564i	$0.447762\pi$
$62$	8.80314e9	1.22035
$63$	5.27517e8	0.0669674
$64$	−3.76299e9	−0.438070
$65$	−9.43973e9	−1.00910
$66$	1.22614e10	1.20517
$67$	−1.36283e10	−1.23319	−0.616594	−	0.787281i	$-0.711488\pi$
$67$	−1.36283e10	−1.23319	−0.616594	+	0.787281i	$0.711488\pi$
$68$	7.02685e9	0.586086
$69$	2.19313e10	1.68809
$70$	−8.76942e9	−0.623637
$71$	9.15005e9	0.601870	0.300935	−	0.953645i	$-0.402701\pi$
$71$	9.15005e9	0.601870	0.300935	+	0.953645i	$0.402701\pi$
$72$	−7.19783e8	−0.0438402
$73$	−2.13411e10	−1.20487	−0.602437	−	0.798166i	$-0.705804\pi$
$73$	−2.13411e10	−1.20487	−0.602437	+	0.798166i	$0.705804\pi$
$74$	9.84006e9	0.515493
$75$	3.19484e9	0.155458
$76$	2.07551e10	0.938967
$77$	−1.20209e10	−0.506100
$78$	3.47251e10	1.36183
$79$	−3.95516e10	−1.44616	−0.723078	−	0.690766i	$-0.757273\pi$
$79$	−3.95516e10	−1.44616	−0.723078	+	0.690766i	$0.757273\pi$
$80$	3.18584e10	1.08700
$81$	−2.67934e10	−0.853807
$82$	−5.67371e8	−0.0169002
$83$	2.56121e10	0.713699	0.356850	−	0.934162i	$-0.383851\pi$
$83$	2.56121e10	0.713699	0.356850	+	0.934162i	$0.383851\pi$
$84$	1.37566e10	0.358902
$85$	−2.94382e10	−0.719626
$86$	−4.53815e10	−1.04025
$87$	−8.05483e9	−0.173261
$88$	1.64021e10	0.331318
$89$	−6.50080e10	−1.23402	−0.617009	−	0.786956i	$-0.711656\pi$
$89$	−6.50080e10	−1.23402	−0.617009	+	0.786956i	$0.711656\pi$
$90$	−8.74042e9	−0.156027
$91$	−3.40439e10	−0.571889
$92$	−8.50365e10	−1.34516
$93$	5.78534e10	0.862329
$94$	−9.91019e10	−1.39277
$95$	−8.69512e10	−1.15291
$96$	−9.19483e10	−1.15094
$97$	1.86954e10	0.221050	0.110525	−	0.993873i	$-0.464747\pi$
$97$	1.86954e10	0.221050	0.110525	+	0.993873i	$0.464747\pi$
$98$	8.65290e10	0.966981
$99$	−1.19811e10	−0.126620
$100$	−1.23877e10	−0.123877
$101$	6.62726e10	0.627432	0.313716	−	0.949517i	$-0.398426\pi$
$101$	6.62726e10	0.627432	0.313716	+	0.949517i	$0.398426\pi$
$102$	1.08292e11	0.971166
$103$	5.60992e10	0.476817	0.238409	−	0.971165i	$-0.423374\pi$
$103$	5.60992e10	0.476817	0.238409	+	0.971165i	$0.423374\pi$
$104$	4.64519e10	0.374387
$105$	−5.76318e10	−0.440678
$106$	−1.88816e11	−1.37043
$107$	−8.31258e10	−0.572961	−0.286481	−	0.958086i	$-0.592485\pi$
$107$	−8.31258e10	−0.572961	−0.286481	+	0.958086i	$0.592485\pi$
$108$	1.19638e11	0.783502
$109$	−5.57921e9	−0.0347318	−0.0173659	−	0.999849i	$-0.505528\pi$
$109$	−5.57921e9	−0.0347318	−0.0173659	+	0.999849i	$0.505528\pi$
$110$	1.99173e11	1.17916
$111$	6.46679e10	0.364261
$112$	1.14896e11	0.616034
$113$	1.83190e11	0.935341	0.467670	−	0.883903i	$-0.345093\pi$
$113$	1.83190e11	0.935341	0.467670	+	0.883903i	$0.345093\pi$
$114$	3.19860e11	1.55590
$115$	3.56251e11	1.65165
$116$	3.12318e10	0.138063
$117$	−3.39313e10	−0.143080
$118$	−1.62950e11	−0.655696
$119$	−1.06167e11	−0.407833
$120$	7.86370e10	0.288489
$121$	−1.22910e10	−0.0430791
$122$	−1.28796e11	−0.431443
$123$	−3.72871e9	−0.0119421
$124$	−2.24321e11	−0.687149
$125$	3.63375e11	1.06500
$126$	−3.15219e10	−0.0884248
$127$	5.37204e11	1.44284	0.721421	−	0.692497i	$-0.243489\pi$
$127$	5.37204e11	1.44284	0.721421	+	0.692497i	$0.243489\pi$
$128$	−2.54662e11	−0.655103
$129$	−2.98243e11	−0.735067
$130$	5.64072e11	1.33244
$131$	−1.80822e11	−0.409506	−0.204753	−	0.978814i	$-0.565639\pi$
$131$	−1.80822e11	−0.409506	−0.204753	+	0.978814i	$0.565639\pi$
$132$	−3.12444e11	−0.678602
$133$	−3.13585e11	−0.653388
$134$	8.14359e11	1.62832
$135$	−5.01212e11	−0.962023
$136$	1.44862e11	0.266988
$137$	−9.68864e10	−0.171514	−0.0857570	−	0.996316i	$-0.527331\pi$
$137$	−9.68864e10	−0.171514	−0.0857570	+	0.996316i	$0.527331\pi$
$138$	−1.31051e12	−2.22897
$139$	−8.65857e11	−1.41535	−0.707677	−	0.706536i	$-0.750257\pi$
$139$	−8.65857e11	−1.41535	−0.707677	+	0.706536i	$0.750257\pi$
$140$	2.23462e11	0.351155
$141$	−6.51288e11	−0.984166
$142$	−5.46762e11	−0.794717
$143$	7.73213e11	1.08131
$144$	1.14516e11	0.154124
$145$	−1.30842e11	−0.169521
$146$	1.27524e12	1.59093
$147$	5.68660e11	0.683294
$148$	−2.50744e11	−0.290262
$149$	−1.20498e12	−1.34418	−0.672089	−	0.740471i	$-0.734603\pi$
$149$	−1.20498e12	−1.34418	−0.672089	+	0.740471i	$0.734603\pi$
$150$	−1.90908e11	−0.205268
$151$	−1.40735e12	−1.45891	−0.729457	−	0.684027i	$-0.760227\pi$
$151$	−1.40735e12	−1.45891	−0.729457	+	0.684027i	$0.760227\pi$
$152$	4.27878e11	0.427740
$153$	−1.05816e11	−0.102035
$154$	7.18308e11	0.668262
$155$	9.39768e11	0.843716
$156$	−8.84862e11	−0.766814
$157$	−9.92000e10	−0.0829973	−0.0414986	−	0.999139i	$-0.513213\pi$
$157$	−9.92000e10	−0.0829973	−0.0414986	+	0.999139i	$0.513213\pi$
$158$	2.36341e12	1.90953
$159$	−1.24088e12	−0.968381
$160$	−1.49360e12	−1.12610
$161$	1.28480e12	0.936038
$162$	1.60104e12	1.12738
$163$	−2.51668e12	−1.71315	−0.856577	−	0.516019i	$-0.827413\pi$
$163$	−2.51668e12	−1.71315	−0.856577	+	0.516019i	$0.827413\pi$
$164$	1.44577e10	0.00951609
$165$	1.30895e12	0.833222
$166$	−1.53045e12	−0.942379
$167$	−3.10127e12	−1.84756	−0.923782	−	0.382919i	$-0.874919\pi$
$167$	−3.10127e12	−1.84756	−0.923782	+	0.382919i	$0.874919\pi$
$168$	2.83600e11	0.163495
$169$	3.97632e11	0.221873
$170$	1.75908e12	0.950204
$171$	−3.12548e11	−0.163470
$172$	1.15641e12	0.585740
$173$	3.96206e12	1.94387	0.971936	−	0.235244i	$-0.0755888\pi$
$173$	3.96206e12	1.94387	0.971936	+	0.235244i	$0.0755888\pi$
$174$	4.81318e11	0.228776
$175$	1.87163e11	0.0862007
$176$	−2.60954e12	−1.16478
$177$	−1.07089e12	−0.463332
$178$	3.88456e12	1.62942
$179$	−3.65706e12	−1.48744	−0.743721	−	0.668490i	$-0.766941\pi$
$179$	−3.65706e12	−1.48744	−0.743721	+	0.668490i	$0.766941\pi$
$180$	2.22723e11	0.0878549
$181$	−4.32276e11	−0.165397	−0.0826987	−	0.996575i	$-0.526354\pi$
$181$	−4.32276e11	−0.165397	−0.0826987	+	0.996575i	$0.526354\pi$
$182$	2.03430e12	0.755130
$183$	−8.46436e11	−0.304869
$184$	−1.75307e12	−0.612777
$185$	1.05046e12	0.356399
$186$	−3.45704e12	−1.13863
$187$	2.41130e12	0.771120
$188$	2.52531e12	0.784235
$189$	−1.80759e12	−0.545206
$190$	5.19578e12	1.52232
$191$	1.14191e12	0.325048	0.162524	−	0.986705i	$-0.448037\pi$
$191$	1.14191e12	0.325048	0.162524	+	0.986705i	$0.448037\pi$
$192$	1.47775e12	0.408736
$193$	−2.21005e12	−0.594068	−0.297034	−	0.954867i	$-0.595997\pi$
$193$	−2.21005e12	−0.594068	−0.297034	+	0.954867i	$0.595997\pi$
$194$	−1.11715e12	−0.291878
$195$	3.70703e12	0.941533
$196$	−2.20493e12	−0.544484
$197$	4.19072e12	1.00629	0.503146	−	0.864201i	$-0.332176\pi$
$197$	4.19072e12	1.00629	0.503146	+	0.864201i	$0.332176\pi$
$198$	7.15933e11	0.167191
$199$	−4.05306e12	−0.920643	−0.460322	−	0.887752i	$-0.652266\pi$
$199$	−4.05306e12	−0.920643	−0.460322	+	0.887752i	$0.652266\pi$
$200$	−2.55379e11	−0.0564313
$201$	5.35189e12	1.15061
$202$	−3.96013e12	−0.828470
$203$	−4.71876e11	−0.0960726
$204$	−2.75948e12	−0.546841
$205$	−6.05690e10	−0.0116843
$206$	−3.35222e12	−0.629596
$207$	1.28055e12	0.234186
$208$	−7.39039e12	−1.31619
$209$	7.12222e12	1.23541
$210$	3.44380e12	0.581877
$211$	−4.84297e12	−0.797184	−0.398592	−	0.917128i	$-0.630501\pi$
$211$	−4.84297e12	−0.797184	−0.398592	+	0.917128i	$0.630501\pi$
$212$	4.81140e12	0.771657
$213$	−3.59327e12	−0.561568
$214$	4.96720e12	0.756546
$215$	−4.84464e12	−0.719201
$216$	2.46641e12	0.356919
$217$	3.38922e12	0.478158
$218$	3.33387e11	0.0458604
$219$	8.38078e12	1.12419
$220$	−5.07532e12	−0.663955
$221$	6.82896e12	0.871358
$222$	−3.86424e12	−0.480975
$223$	−1.05727e11	−0.0128383	−0.00641915	−	0.999979i	$-0.502043\pi$
$223$	−1.05727e11	−0.0128383	−0.00641915	+	0.999979i	$0.502043\pi$
$224$	−5.38660e12	−0.638191
$225$	1.86544e11	0.0215664
$226$	−1.09465e13	−1.23504
$227$	7.03256e12	0.774410	0.387205	−	0.921994i	$-0.373441\pi$
$227$	7.03256e12	0.774410	0.387205	+	0.921994i	$0.373441\pi$
$228$	−8.15064e12	−0.876093
$229$	1.66758e13	1.74981	0.874905	−	0.484294i	$-0.160923\pi$
$229$	1.66758e13	1.74981	0.874905	+	0.484294i	$0.160923\pi$
$230$	−2.12878e13	−2.18086
$231$	4.72065e12	0.472211
$232$	6.43861e11	0.0628939
$233$	−3.37844e12	−0.322298	−0.161149	−	0.986930i	$-0.551520\pi$
$233$	−3.37844e12	−0.322298	−0.161149	+	0.986930i	$0.551520\pi$
$234$	2.02757e12	0.188925
$235$	−1.05795e13	−0.962923
$236$	4.15227e12	0.369207
$237$	1.55321e13	1.34932
$238$	6.34404e12	0.538508
$239$	−4.13774e12	−0.343222	−0.171611	−	0.985165i	$-0.554897\pi$
$239$	−4.13774e12	−0.343222	−0.171611	+	0.985165i	$0.554897\pi$
$240$	−1.25110e13	−1.01421
$241$	−2.20806e13	−1.74952	−0.874758	−	0.484559i	$-0.838980\pi$
$241$	−2.20806e13	−1.74952	−0.874758	+	0.484559i	$0.838980\pi$
$242$	7.34448e11	0.0568822
$243$	−3.39676e12	−0.257176
$244$	3.28197e12	0.242936
$245$	9.23728e12	0.668545
$246$	2.22810e11	0.0157685
$247$	2.01706e13	1.39600
$248$	−4.62450e12	−0.313026
$249$	−1.00580e13	−0.665909
$250$	−2.17135e13	−1.40624
$251$	−9.99788e12	−0.633435	−0.316718	−	0.948520i	$-0.602581\pi$
$251$	−9.99788e12	−0.633435	−0.316718	+	0.948520i	$0.602581\pi$
$252$	8.03238e11	0.0497899
$253$	−2.91807e13	−1.76984
$254$	−3.21007e13	−1.90515
$255$	1.15605e13	0.671439
$256$	2.29240e13	1.30308
$257$	−1.92790e13	−1.07264	−0.536319	−	0.844016i	$-0.680185\pi$
$257$	−1.92790e13	−1.07264	−0.536319	+	0.844016i	$0.680185\pi$
$258$	1.78216e13	0.970593
$259$	3.78844e12	0.201981
$260$	−1.43737e13	−0.750263
$261$	−4.70315e11	−0.0240362
$262$	1.08051e13	0.540717
$263$	1.38093e13	0.676729	0.338364	−	0.941015i	$-0.390126\pi$
$263$	1.38093e13	0.676729	0.338364	+	0.941015i	$0.390126\pi$
$264$	−6.44120e12	−0.309133
$265$	−2.01568e13	−0.947479
$266$	1.87383e13	0.862743
$267$	2.55290e13	1.15139
$268$	−2.07514e13	−0.916869
$269$	2.07270e13	0.897219	0.448609	−	0.893728i	$-0.351919\pi$
$269$	2.07270e13	0.897219	0.448609	+	0.893728i	$0.351919\pi$
$270$	2.99500e13	1.27027
$271$	1.20155e13	0.499356	0.249678	−	0.968329i	$-0.419675\pi$
$271$	1.20155e13	0.499356	0.249678	+	0.968329i	$0.419675\pi$
$272$	−2.30472e13	−0.938620
$273$	1.33692e13	0.533594
$274$	5.78946e12	0.226470
$275$	−4.25089e12	−0.162986
$276$	3.33943e13	1.25508
$277$	3.13772e13	1.15605	0.578024	−	0.816020i	$-0.303824\pi$
$277$	3.13772e13	1.15605	0.578024	+	0.816020i	$0.303824\pi$
$278$	5.17394e13	1.86885
$279$	3.37802e12	0.119630
$280$	4.60679e12	0.159966
$281$	1.59297e13	0.542404	0.271202	−	0.962522i	$-0.412579\pi$
$281$	1.59297e13	0.542404	0.271202	+	0.962522i	$0.412579\pi$
$282$	3.89178e13	1.29951
$283$	4.36081e13	1.42805	0.714023	−	0.700123i	$-0.246871\pi$
$283$	4.36081e13	1.42805	0.714023	+	0.700123i	$0.246871\pi$
$284$	1.39326e13	0.447487
$285$	3.41462e13	1.07571
$286$	−4.62035e13	−1.42778
$287$	−2.18439e11	−0.00662185
$288$	−5.36879e12	−0.159668
$289$	−1.29755e13	−0.378605
$290$	7.81850e12	0.223838
$291$	−7.34179e12	−0.206248
$292$	−3.24957e13	−0.895818
$293$	−5.68721e13	−1.53861	−0.769303	−	0.638885i	$-0.779396\pi$
$293$	−5.68721e13	−1.53861	−0.769303	+	0.638885i	$0.779396\pi$
$294$	−3.39804e13	−0.902231
$295$	−1.73955e13	−0.453331
$296$	−5.16922e12	−0.132227
$297$	4.10545e13	1.03086
$298$	7.20040e13	1.77487
$299$	−8.26417e13	−1.99990
$300$	4.86470e12	0.115582
$301$	−1.74720e13	−0.407592
$302$	8.40965e13	1.92637
$303$	−2.60256e13	−0.585418
$304$	−6.80744e13	−1.50376
$305$	−1.37495e13	−0.298288
$306$	6.32306e12	0.134728
$307$	−8.79181e13	−1.84000	−0.919998	−	0.391922i	$-0.871810\pi$
$307$	−8.79181e13	−1.84000	−0.919998	+	0.391922i	$0.871810\pi$
$308$	−1.83039e13	−0.376283
$309$	−2.20304e13	−0.444889
$310$	−5.61560e13	−1.11405
$311$	−8.36586e12	−0.163053	−0.0815264	−	0.996671i	$-0.525980\pi$
$311$	−8.36586e12	−0.163053	−0.0815264	+	0.996671i	$0.525980\pi$
$312$	−1.82419e13	−0.349317
$313$	8.42618e12	0.158539	0.0792697	−	0.996853i	$-0.474741\pi$
$313$	8.42618e12	0.158539	0.0792697	+	0.996853i	$0.474741\pi$
$314$	5.92771e12	0.109591
$315$	−3.36508e12	−0.0611346
$316$	−6.02243e13	−1.07521
$317$	−9.64046e13	−1.69150	−0.845750	−	0.533580i	$-0.820846\pi$
$317$	−9.64046e13	−1.69150	−0.845750	+	0.533580i	$0.820846\pi$
$318$	7.41491e13	1.27866
$319$	1.07174e13	0.181652
$320$	2.40044e13	0.399914
$321$	3.26439e13	0.534595
$322$	−7.67734e13	−1.23596
$323$	6.29029e13	0.995535
$324$	−4.07976e13	−0.634800
$325$	−1.20388e13	−0.184173
$326$	1.50385e14	2.26207
$327$	2.19099e12	0.0324061
$328$	2.98054e11	0.00433499
$329$	−3.81544e13	−0.545717
$330$	−7.82164e13	−1.10020
$331$	−2.88602e13	−0.399251	−0.199625	−	0.979872i	$-0.563973\pi$
$331$	−2.88602e13	−0.399251	−0.199625	+	0.979872i	$0.563973\pi$
$332$	3.89989e13	0.530631
$333$	3.77591e12	0.0505334
$334$	1.85317e14	2.43955
$335$	8.69359e13	1.12578
$336$	−4.51201e13	−0.574783
$337$	4.06845e13	0.509876	0.254938	−	0.966957i	$-0.417945\pi$
$337$	4.06845e13	0.509876	0.254938	+	0.966957i	$0.417945\pi$
$338$	−2.37606e13	−0.292964
$339$	−7.19396e13	−0.872709
$340$	−4.48248e13	−0.535038
$341$	−7.69769e13	−0.904089
$342$	1.86763e13	0.215848
$343$	7.88038e13	0.896251
$344$	2.38400e13	0.266830
$345$	−1.39902e14	−1.54105
$346$	−2.36754e14	−2.56672
$347$	−6.27388e12	−0.0669460	−0.0334730	−	0.999440i	$-0.510657\pi$
$347$	−6.27388e12	−0.0669460	−0.0334730	+	0.999440i	$0.510657\pi$
$348$	−1.22649e13	−0.128818
$349$	1.09741e12	0.0113457	0.00567283	−	0.999984i	$-0.498194\pi$
$349$	1.09741e12	0.0113457	0.00567283	+	0.999984i	$0.498194\pi$
$350$	−1.11840e13	−0.113821
$351$	1.16269e14	1.16486
$352$	1.22342e14	1.20668
$353$	5.86214e13	0.569240	0.284620	−	0.958640i	$-0.408133\pi$
$353$	5.86214e13	0.569240	0.284620	+	0.958640i	$0.408133\pi$
$354$	6.39912e13	0.611790
$355$	−5.83689e13	−0.549447
$356$	−9.89861e13	−0.917486
$357$	4.16924e13	0.380524
$358$	2.18528e14	1.96404
$359$	5.82298e13	0.515378	0.257689	−	0.966228i	$-0.417039\pi$
$359$	5.82298e13	0.515378	0.257689	+	0.966228i	$0.417039\pi$
$360$	4.59155e12	0.0400217
$361$	6.93053e13	0.594945
$362$	2.58307e13	0.218393
$363$	4.82672e12	0.0401944
$364$	−5.18378e13	−0.425196
$365$	1.36137e14	1.09993
$366$	5.05789e13	0.402553
$367$	−2.00272e14	−1.57021	−0.785104	−	0.619364i	$-0.787390\pi$
$367$	−2.00272e14	−1.57021	−0.785104	+	0.619364i	$0.787390\pi$
$368$	2.78910e14	2.15427
$369$	−2.17716e11	−0.00165671
$370$	−6.27705e13	−0.470594
$371$	−7.26945e13	−0.536964
$372$	8.80920e13	0.641136
$373$	1.06705e14	0.765219	0.382609	−	0.923910i	$-0.375026\pi$
$373$	1.06705e14	0.765219	0.382609	+	0.923910i	$0.375026\pi$
$374$	−1.44087e14	−1.01820
$375$	−1.42699e14	−0.993688
$376$	5.20606e13	0.357253
$377$	3.03523e13	0.205265
$378$	1.08013e14	0.719898
$379$	−2.74715e14	−1.80454	−0.902269	−	0.431173i	$-0.858100\pi$
$379$	−2.74715e14	−1.80454	−0.902269	+	0.431173i	$0.858100\pi$
$380$	−1.32399e14	−0.857183
$381$	−2.10963e14	−1.34623
$382$	−6.82348e13	−0.429198
$383$	1.78808e14	1.10865	0.554323	−	0.832302i	$-0.312977\pi$
$383$	1.78808e14	1.10865	0.554323	+	0.832302i	$0.312977\pi$
$384$	1.00007e14	0.611237
$385$	7.66820e13	0.462019
$386$	1.32062e14	0.784416
$387$	−1.74142e13	−0.101975
$388$	2.84671e13	0.164350
$389$	3.37178e13	0.191927	0.0959635	−	0.995385i	$-0.469407\pi$
$389$	3.37178e13	0.191927	0.0959635	+	0.995385i	$0.469407\pi$
$390$	−2.21514e14	−1.24321
$391$	−2.57722e14	−1.42619
$392$	−4.54557e13	−0.248036
$393$	7.10098e13	0.382085
$394$	−2.50417e14	−1.32872
$395$	2.52303e14	1.32020
$396$	−1.82433e13	−0.0941415
$397$	6.71565e13	0.341775	0.170887	−	0.985291i	$-0.445337\pi$
$397$	6.71565e13	0.341775	0.170887	+	0.985291i	$0.445337\pi$
$398$	2.42191e14	1.21563
$399$	1.23146e14	0.609636
$400$	4.06302e13	0.198389
$401$	3.26275e14	1.57141	0.785706	−	0.618600i	$-0.212300\pi$
$401$	3.26275e14	1.57141	0.785706	+	0.618600i	$0.212300\pi$
$402$	−3.19803e14	−1.51929
$403$	−2.18004e14	−1.02161
$404$	1.00912e14	0.466492
$405$	1.70917e14	0.779440
$406$	2.81970e13	0.126856
$407$	−8.60439e13	−0.381901
$408$	−5.68881e13	−0.249110
$409$	2.71137e14	1.17142	0.585708	−	0.810522i	$-0.300817\pi$
$409$	2.71137e14	1.17142	0.585708	+	0.810522i	$0.300817\pi$
$410$	3.61931e12	0.0154282
$411$	3.80478e13	0.160029
$412$	8.54209e13	0.354511
$413$	−6.27359e13	−0.256916
$414$	−7.65195e13	−0.309222
$415$	−1.63381e14	−0.651536
$416$	3.46480e14	1.36353
$417$	3.40026e14	1.32058
$418$	−4.25589e14	−1.63125
$419$	−4.36462e14	−1.65109	−0.825543	−	0.564339i	$-0.809131\pi$
$419$	−4.36462e14	−1.65109	−0.825543	+	0.564339i	$0.809131\pi$
$420$	−8.77546e13	−0.327641
$421$	3.35884e14	1.23776	0.618881	−	0.785485i	$-0.287586\pi$
$421$	3.35884e14	1.23776	0.618881	+	0.785485i	$0.287586\pi$
$422$	2.89392e14	1.05261
$423$	−3.80282e13	−0.136532
$424$	9.91896e13	0.351523
$425$	−3.75435e13	−0.131340
$426$	2.14716e14	0.741502
$427$	−4.95867e13	−0.169049
$428$	−1.26574e14	−0.425993
$429$	−3.03645e14	−1.00891
$430$	2.89492e14	0.949643
$431$	−3.93344e14	−1.27394	−0.636968	−	0.770890i	$-0.719812\pi$
$431$	−3.93344e14	−1.27394	−0.636968	+	0.770890i	$0.719812\pi$
$432$	−3.92400e14	−1.25478
$433$	3.57057e14	1.12734	0.563668	−	0.826001i	$-0.309390\pi$
$433$	3.57057e14	1.12734	0.563668	+	0.826001i	$0.309390\pi$
$434$	−2.02524e14	−0.631367
$435$	5.13824e13	0.158170
$436$	−8.49534e12	−0.0258229
$437$	−7.61229e14	−2.28490
$438$	−5.00794e14	−1.48440
$439$	−3.37901e14	−0.989087	−0.494543	−	0.869153i	$-0.664665\pi$
$439$	−3.37901e14	−0.989087	−0.494543	+	0.869153i	$0.664665\pi$
$440$	−1.04630e14	−0.302460
$441$	3.32036e13	0.0947923
$442$	−4.08065e14	−1.15055
$443$	4.40752e14	1.22737	0.613683	−	0.789552i	$-0.289687\pi$
$443$	4.40752e14	1.22737	0.613683	+	0.789552i	$0.289687\pi$
$444$	9.84683e13	0.270826
$445$	4.14691e14	1.12653
$446$	6.31771e12	0.0169519
$447$	4.73203e14	1.25417
$448$	8.65707e13	0.226643
$449$	−4.87159e14	−1.25984	−0.629920	−	0.776660i	$-0.716913\pi$
$449$	−4.87159e14	−1.25984	−0.629920	+	0.776660i	$0.716913\pi$
$450$	−1.11470e13	−0.0284766
$451$	4.96124e12	0.0125204
$452$	2.78939e14	0.695421
$453$	5.52674e14	1.36122
$454$	−4.20231e14	−1.02254
$455$	2.17169e14	0.522077
$456$	−1.68030e14	−0.399098
$457$	−3.43377e14	−0.805809	−0.402905	−	0.915242i	$-0.631999\pi$
$457$	−3.43377e14	−0.805809	−0.402905	+	0.915242i	$0.631999\pi$
$458$	−9.96464e14	−2.31048
$459$	3.62590e14	0.830704
$460$	5.42455e14	1.22799
$461$	1.17693e14	0.263266	0.131633	−	0.991299i	$-0.457978\pi$
$461$	1.17693e14	0.263266	0.131633	+	0.991299i	$0.457978\pi$
$462$	−2.82083e14	−0.623514
$463$	6.04064e14	1.31943	0.659717	−	0.751514i	$-0.270676\pi$
$463$	6.04064e14	1.31943	0.659717	+	0.751514i	$0.270676\pi$
$464$	−1.02437e14	−0.221109
$465$	−3.69052e14	−0.787220
$466$	2.01879e14	0.425568
$467$	−6.03902e14	−1.25812	−0.629062	−	0.777355i	$-0.716561\pi$
$467$	−6.03902e14	−1.25812	−0.629062	+	0.777355i	$0.716561\pi$
$468$	−5.16664e13	−0.106379
$469$	3.13530e14	0.638011
$470$	6.32179e14	1.27146
$471$	3.89564e13	0.0774397
$472$	8.56014e13	0.168190
$473$	3.96827e14	0.770664
$474$	−9.28124e14	−1.78166
$475$	−1.10892e14	−0.210419
$476$	−1.61658e14	−0.303221
$477$	−7.24541e13	−0.134342
$478$	2.47251e14	0.453195
$479$	−6.97054e14	−1.26305	−0.631526	−	0.775355i	$-0.717571\pi$
$479$	−6.97054e14	−1.26305	−0.631526	+	0.775355i	$0.717571\pi$
$480$	5.86546e14	1.05069
$481$	−2.43682e14	−0.431545
$482$	1.31943e15	2.31009
$483$	−5.04548e14	−0.873359
$484$	−1.87152e13	−0.0320290
$485$	−1.19260e14	−0.201797
$486$	2.02974e14	0.339579
$487$	−3.79054e14	−0.627035	−0.313517	−	0.949582i	$-0.601507\pi$
$487$	−3.79054e14	−0.627035	−0.313517	+	0.949582i	$0.601507\pi$
$488$	6.76597e13	0.110668
$489$	9.88314e14	1.59844
$490$	−5.51975e14	−0.882757
$491$	2.28692e14	0.361662	0.180831	−	0.983514i	$-0.442121\pi$
$491$	2.28692e14	0.361662	0.180831	+	0.983514i	$0.442121\pi$
$492$	−5.67762e12	−0.00887888
$493$	9.46548e13	0.146381
$494$	−1.20530e15	−1.84330
$495$	7.64284e13	0.115592
$496$	7.35747e14	1.10047
$497$	−2.10504e14	−0.311387
$498$	6.01017e14	0.879276
$499$	4.01402e14	0.580800	0.290400	−	0.956905i	$-0.406212\pi$
$499$	4.01402e14	0.580800	0.290400	+	0.956905i	$0.406212\pi$
$500$	5.53303e14	0.791823
$501$	1.21789e15	1.72385
$502$	5.97424e14	0.836397
$503$	3.05669e13	0.0423280	0.0211640	−	0.999776i	$-0.493263\pi$
$503$	3.05669e13	0.0423280	0.0211640	+	0.999776i	$0.493263\pi$
$504$	1.65592e13	0.0226815
$505$	−4.22758e14	−0.572782
$506$	1.74370e15	2.33692
$507$	−1.56152e14	−0.207016
$508$	8.17988e14	1.07274
$509$	−9.50285e14	−1.23284	−0.616419	−	0.787418i	$-0.711417\pi$
$509$	−9.50285e14	−1.23284	−0.616419	+	0.787418i	$0.711417\pi$
$510$	−6.90800e14	−0.886577
$511$	4.90971e14	0.623362
$512$	−8.48278e14	−1.06550
$513$	1.07098e15	1.33087
$514$	1.15202e15	1.41633
$515$	−3.57861e14	−0.435286
$516$	−4.54127e14	−0.546518
$517$	8.66572e14	1.03183
$518$	−2.26379e14	−0.266699
$519$	−1.55592e15	−1.81371
$520$	−2.96321e14	−0.341777
$521$	−1.22076e15	−1.39322	−0.696612	−	0.717448i	$-0.745310\pi$
$521$	−1.22076e15	−1.39322	−0.696612	+	0.717448i	$0.745310\pi$
$522$	2.81038e13	0.0317378
$523$	−7.59341e14	−0.848550	−0.424275	−	0.905533i	$-0.639471\pi$
$523$	−7.59341e14	−0.848550	−0.424275	+	0.905533i	$0.639471\pi$
$524$	−2.75334e14	−0.304465
$525$	−7.34999e13	−0.0804286
$526$	−8.25176e14	−0.893562
$527$	−6.79854e14	−0.728546
$528$	1.02478e15	1.08679
$529$	2.16605e15	2.27333
$530$	1.20447e15	1.25107
$531$	−6.25284e13	−0.0642773
$532$	−4.77488e14	−0.485790
$533$	1.40506e13	0.0141480
$534$	−1.52549e15	−1.52031
$535$	5.30266e14	0.523056
$536$	−4.27802e14	−0.417673
$537$	1.43615e15	1.38784
$538$	−1.23854e15	−1.18470
$539$	−7.56631e14	−0.716384
$540$	−7.63183e14	−0.715258
$541$	1.08760e15	1.00898	0.504491	−	0.863417i	$-0.331680\pi$
$541$	1.08760e15	1.00898	0.504491	+	0.863417i	$0.331680\pi$
$542$	−7.17987e14	−0.659357
$543$	1.69757e14	0.154322
$544$	1.08051e15	0.972380
$545$	3.55903e13	0.0317066
$546$	−7.98879e14	−0.704565
$547$	−2.03385e15	−1.77578	−0.887888	−	0.460059i	$-0.847828\pi$
$547$	−2.03385e15	−1.77578	−0.887888	+	0.460059i	$0.847828\pi$
$548$	−1.47527e14	−0.127520
$549$	−4.94227e13	−0.0422940
$550$	2.54013e14	0.215209
$551$	2.79581e14	0.234517
$552$	6.88441e14	0.571744
$553$	9.09918e14	0.748193
$554$	−1.87495e15	−1.52646
$555$	−4.12522e14	−0.332534
$556$	−1.31842e15	−1.05231
$557$	1.33949e15	1.05861	0.529305	−	0.848432i	$-0.322453\pi$
$557$	1.33949e15	1.05861	0.529305	+	0.848432i	$0.322453\pi$
$558$	−2.01854e14	−0.157961
$559$	1.12384e15	0.870844
$560$	−7.32929e14	−0.562377
$561$	−9.46928e14	−0.719484
$562$	−9.51882e14	−0.716198
$563$	−2.15377e15	−1.60474	−0.802369	−	0.596829i	$-0.796427\pi$
$563$	−2.15377e15	−1.60474	−0.802369	+	0.596829i	$0.796427\pi$
$564$	−9.91701e14	−0.731722
$565$	−1.16858e15	−0.853872
$566$	−2.60581e15	−1.88561
$567$	6.16403e14	0.441731
$568$	2.87227e14	0.203850
$569$	−3.66146e14	−0.257357	−0.128679	−	0.991686i	$-0.541074\pi$
$569$	−3.66146e14	−0.257357	−0.128679	+	0.991686i	$0.541074\pi$
$570$	−2.04041e15	−1.42038
$571$	1.16726e15	0.804767	0.402384	−	0.915471i	$-0.368182\pi$
$571$	1.16726e15	0.804767	0.402384	+	0.915471i	$0.368182\pi$
$572$	1.17735e15	0.803949
$573$	−4.48433e14	−0.303282
$574$	1.30528e13	0.00874359
$575$	4.54339e14	0.301444
$576$	8.62845e13	0.0567034
$577$	1.33412e15	0.868419	0.434209	−	0.900812i	$-0.357028\pi$
$577$	1.33412e15	0.868419	0.434209	+	0.900812i	$0.357028\pi$
$578$	7.75354e14	0.499916
$579$	8.67896e14	0.554288
$580$	−1.99230e14	−0.126038
$581$	−5.89227e14	−0.369244
$582$	4.38710e14	0.272333
$583$	1.65106e15	1.01528
$584$	−6.69915e14	−0.408084
$585$	2.16450e14	0.130617
$586$	3.39840e15	2.03160
$587$	−1.53095e15	−0.906677	−0.453339	−	0.891338i	$-0.649767\pi$
$587$	−1.53095e15	−0.906677	−0.453339	+	0.891338i	$0.649767\pi$
$588$	8.65885e14	0.508025
$589$	−2.00808e15	−1.16720
$590$	1.03947e15	0.598585
$591$	−1.64572e15	−0.938909
$592$	8.22410e14	0.464857
$593$	4.73205e14	0.265002	0.132501	−	0.991183i	$-0.457699\pi$
$593$	4.73205e14	0.265002	0.132501	+	0.991183i	$0.457699\pi$
$594$	−2.45322e15	−1.36116
$595$	6.77249e14	0.372310
$596$	−1.83480e15	−0.999388
$597$	1.59166e15	0.858996
$598$	4.93827e15	2.64069
$599$	1.14171e15	0.604932	0.302466	−	0.953160i	$-0.402190\pi$
$599$	1.14171e15	0.604932	0.302466	+	0.953160i	$0.402190\pi$
$600$	1.00289e14	0.0526525
$601$	1.00013e15	0.520290	0.260145	−	0.965570i	$-0.416230\pi$
$601$	1.00013e15	0.520290	0.260145	+	0.965570i	$0.416230\pi$
$602$	1.04404e15	0.538190
$603$	3.12493e14	0.159623
$604$	−2.14294e15	−1.08469
$605$	7.84050e13	0.0393269
$606$	1.55516e15	0.772994
$607$	−1.84033e15	−0.906480	−0.453240	−	0.891388i	$-0.649732\pi$
$607$	−1.84033e15	−0.906480	−0.453240	+	0.891388i	$0.649732\pi$
$608$	3.19150e15	1.55785
$609$	1.85308e14	0.0896394
$610$	8.21601e14	0.393864
$611$	2.45419e15	1.16595
$612$	−1.61124e14	−0.0758624
$613$	−3.47262e15	−1.62041	−0.810205	−	0.586146i	$-0.800644\pi$
$613$	−3.47262e15	−1.62041	−0.810205	+	0.586146i	$0.800644\pi$
$614$	5.25356e15	2.42956
$615$	2.37857e13	0.0109019
$616$	−3.77344e14	−0.171413
$617$	3.14997e15	1.41820	0.709101	−	0.705107i	$-0.249101\pi$
$617$	3.14997e15	1.41820	0.709101	+	0.705107i	$0.249101\pi$
$618$	1.31643e15	0.587438
$619$	4.65762e14	0.205999	0.103000	−	0.994681i	$-0.467156\pi$
$619$	4.65762e14	0.205999	0.103000	+	0.994681i	$0.467156\pi$
$620$	1.43096e15	0.627298
$621$	−4.38794e15	−1.90659
$622$	4.99903e14	0.215297
$623$	1.49556e15	0.638440
$624$	2.90225e15	1.22806
$625$	−1.92076e15	−0.805625
$626$	−5.03508e14	−0.209338
$627$	−2.79693e15	−1.15268
$628$	−1.51050e14	−0.0617080
$629$	−7.59933e14	−0.307749
$630$	2.01081e14	0.0807229
$631$	−3.09320e15	−1.23097	−0.615483	−	0.788150i	$-0.711039\pi$
$631$	−3.09320e15	−1.23097	−0.615483	+	0.788150i	$0.711039\pi$
$632$	−1.24156e15	−0.489805
$633$	1.90186e15	0.743803
$634$	5.76067e15	2.23348
$635$	−3.42687e15	−1.31717
$636$	−1.88946e15	−0.719986
$637$	−2.14283e15	−0.809507
$638$	−6.40417e14	−0.239855
$639$	−2.09808e14	−0.0779054
$640$	1.62451e15	0.598044
$641$	−2.63890e15	−0.963170	−0.481585	−	0.876399i	$-0.659939\pi$
$641$	−2.63890e15	−0.963170	−0.481585	+	0.876399i	$0.659939\pi$
$642$	−1.95064e15	−0.705887
$643$	1.40968e15	0.505777	0.252889	−	0.967495i	$-0.418619\pi$
$643$	1.40968e15	0.505777	0.252889	+	0.967495i	$0.418619\pi$
$644$	1.95633e15	0.695939
$645$	1.90252e15	0.671042
$646$	−3.75877e15	−1.31452
$647$	−5.04497e15	−1.74938	−0.874692	−	0.484679i	$-0.838936\pi$
$647$	−5.04497e15	−1.74938	−0.874692	+	0.484679i	$0.838936\pi$
$648$	−8.41065e14	−0.289179
$649$	1.42487e15	0.485770
$650$	7.19381e14	0.243184
$651$	−1.33097e15	−0.446140
$652$	−3.83209e15	−1.27372
$653$	−3.65428e15	−1.20442	−0.602212	−	0.798336i	$-0.705714\pi$
$653$	−3.65428e15	−1.20442	−0.602212	+	0.798336i	$0.705714\pi$
$654$	−1.30923e14	−0.0427895
$655$	1.15348e15	0.373838
$656$	−4.74196e13	−0.0152401
$657$	4.89347e14	0.155958
$658$	2.27992e15	0.720572
$659$	1.48389e15	0.465085	0.232543	−	0.972586i	$-0.425296\pi$
$659$	1.48389e15	0.465085	0.232543	+	0.972586i	$0.425296\pi$
$660$	1.99310e15	0.619496
$661$	3.44956e15	1.06330	0.531650	−	0.846964i	$-0.321572\pi$
$661$	3.44956e15	1.06330	0.531650	+	0.846964i	$0.321572\pi$
$662$	1.72455e15	0.527177
$663$	−2.68177e15	−0.813011
$664$	8.03983e14	0.241726
$665$	2.00038e15	0.596478
$666$	−2.25630e14	−0.0667250
$667$	−1.14548e15	−0.335966
$668$	−4.72223e15	−1.37365
$669$	4.15194e13	0.0119786
$670$	−5.19486e15	−1.48649
$671$	1.12623e15	0.319633
$672$	2.11535e15	0.595457
$673$	−2.06156e15	−0.575591	−0.287795	−	0.957692i	$-0.592922\pi$
$673$	−2.06156e15	−0.575591	−0.287795	+	0.957692i	$0.592922\pi$
$674$	−2.43111e15	−0.673247
$675$	−6.39213e14	−0.175580
$676$	6.05465e14	0.164961
$677$	2.89101e15	0.781290	0.390645	−	0.920541i	$-0.372252\pi$
$677$	2.89101e15	0.781290	0.390645	+	0.920541i	$0.372252\pi$
$678$	4.29876e15	1.15234
$679$	−4.30104e14	−0.114364
$680$	−9.24088e14	−0.243733
$681$	−2.76172e15	−0.722555
$682$	4.59976e15	1.19377
$683$	4.53396e15	1.16725	0.583625	−	0.812023i	$-0.301634\pi$
$683$	4.53396e15	1.16725	0.583625	+	0.812023i	$0.301634\pi$
$684$	−4.75909e14	−0.121539
$685$	6.18046e14	0.156575
$686$	−4.70893e15	−1.18342
$687$	−6.54866e15	−1.63264
$688$	−3.79289e15	−0.938066
$689$	4.67590e15	1.14725
$690$	8.35984e15	2.03483
$691$	3.83758e15	0.926677	0.463339	−	0.886181i	$-0.346651\pi$
$691$	3.83758e15	0.926677	0.463339	+	0.886181i	$0.346651\pi$
$692$	6.03294e15	1.44526
$693$	2.75635e14	0.0655091
$694$	3.74897e14	0.0883964
$695$	5.52337e15	1.29208
$696$	−2.52848e14	−0.0586824
$697$	4.38172e13	0.0100894
$698$	−6.55759e13	−0.0149810
$699$	1.32673e15	0.300717
$700$	2.84989e14	0.0640897
$701$	−5.70841e15	−1.27370	−0.636848	−	0.770989i	$-0.719762\pi$
$701$	−5.70841e15	−1.27370	−0.636848	+	0.770989i	$0.719762\pi$
$702$	−6.94768e15	−1.53810
$703$	−2.24461e15	−0.493044
$704$	−1.96622e15	−0.428530
$705$	4.15462e15	0.898445
$706$	−3.50293e15	−0.751633
$707$	−1.52466e15	−0.324612
$708$	−1.63062e15	−0.344484
$709$	−6.92299e15	−1.45124	−0.725620	−	0.688095i	$-0.758447\pi$
$709$	−6.92299e15	−1.45124	−0.725620	+	0.688095i	$0.758447\pi$
$710$	3.48784e15	0.725497
$711$	9.06908e14	0.187189
$712$	−2.04065e15	−0.417955
$713$	8.22736e15	1.67212
$714$	−2.49134e15	−0.502449
$715$	−4.93239e15	−0.987129
$716$	−5.56852e15	−1.10591
$717$	1.62491e15	0.320239
$718$	−3.47953e15	−0.680512
$719$	4.05045e15	0.786130	0.393065	−	0.919511i	$-0.371415\pi$
$719$	4.05045e15	0.786130	0.393065	+	0.919511i	$0.371415\pi$
$720$	−7.30505e14	−0.140700
$721$	−1.29061e15	−0.246689
$722$	−4.14134e15	−0.785573
$723$	8.67118e15	1.63237
$724$	−6.58216e14	−0.122972
$725$	−1.66868e14	−0.0309395
$726$	−2.88421e14	−0.0530733
$727$	−2.30565e15	−0.421071	−0.210535	−	0.977586i	$-0.567521\pi$
$727$	−2.30565e15	−0.421071	−0.210535	+	0.977586i	$0.567521\pi$
$728$	−1.06866e15	−0.193695
$729$	6.08029e15	1.09376
$730$	−8.13488e15	−1.45236
$731$	3.50475e15	0.621028
$732$	−1.28885e15	−0.226668
$733$	−2.90432e15	−0.506959	−0.253479	−	0.967341i	$-0.581575\pi$
$733$	−2.90432e15	−0.506959	−0.253479	+	0.967341i	$0.581575\pi$
$734$	1.19673e16	2.07333
$735$	−3.62753e15	−0.623779
$736$	−1.30760e16	−2.23176
$737$	−7.12096e15	−1.20633
$738$	1.30097e13	0.00218754
$739$	−1.98996e15	−0.332123	−0.166062	−	0.986115i	$-0.553105\pi$
$739$	−1.98996e15	−0.332123	−0.166062	+	0.986115i	$0.553105\pi$
$740$	1.59951e15	0.264980
$741$	−7.92110e15	−1.30252
$742$	4.34387e15	0.709015
$743$	−7.35941e15	−1.19235	−0.596176	−	0.802854i	$-0.703314\pi$
$743$	−7.35941e15	−1.19235	−0.596176	+	0.802854i	$0.703314\pi$
$744$	1.81606e15	0.292065
$745$	7.68669e15	1.22710
$746$	−6.37616e15	−1.01041
$747$	−5.87278e14	−0.0923805
$748$	3.67162e15	0.573323
$749$	1.91238e15	0.296431
$750$	8.52702e15	1.31208
$751$	−1.82500e15	−0.278768	−0.139384	−	0.990238i	$-0.544512\pi$
$751$	−1.82500e15	−0.278768	−0.139384	+	0.990238i	$0.544512\pi$
$752$	−8.28272e15	−1.25596
$753$	3.92622e15	0.591020
$754$	−1.81371e15	−0.271034
$755$	8.97761e15	1.33184
$756$	−2.75238e15	−0.405358
$757$	7.72752e15	1.12983	0.564915	−	0.825149i	$-0.308909\pi$
$757$	7.72752e15	1.12983	0.564915	+	0.825149i	$0.308909\pi$
$758$	1.64156e16	2.38274
$759$	1.14594e16	1.65132
$760$	−2.72947e15	−0.390484
$761$	−1.22550e16	−1.74060	−0.870298	−	0.492526i	$-0.836074\pi$
$761$	−1.22550e16	−1.74060	−0.870298	+	0.492526i	$0.836074\pi$
$762$	1.26061e16	1.77758
$763$	1.28354e14	0.0179691
$764$	1.73876e15	0.241671
$765$	6.75010e14	0.0931477
$766$	−1.06847e16	−1.46387
$767$	4.03534e15	0.548915
$768$	−9.00237e15	−1.21582
$769$	2.18975e15	0.293629	0.146815	−	0.989164i	$-0.453098\pi$
$769$	2.18975e15	0.293629	0.146815	+	0.989164i	$0.453098\pi$
$770$	−4.58214e15	−0.610056
$771$	7.57097e15	1.00081
$772$	−3.36519e15	−0.441686
$773$	1.21172e16	1.57912	0.789559	−	0.613675i	$-0.210310\pi$
$773$	1.21172e16	1.57912	0.789559	+	0.613675i	$0.210310\pi$
$774$	1.04059e15	0.134649
$775$	1.19852e15	0.153988
$776$	5.86864e14	0.0748683
$777$	−1.48774e15	−0.188456
$778$	−2.01481e15	−0.253423
$779$	1.29422e14	0.0161642
$780$	5.64461e15	0.700025
$781$	4.78103e15	0.588763
$782$	1.54002e16	1.88317
$783$	1.61158e15	0.195688
$784$	7.23190e15	0.871995
$785$	6.32805e14	0.0757682
$786$	−4.24320e15	−0.504510
$787$	1.10648e16	1.30642	0.653211	−	0.757176i	$-0.273422\pi$
$787$	1.10648e16	1.30642	0.653211	+	0.757176i	$0.273422\pi$
$788$	6.38111e15	0.748172
$789$	−5.42298e15	−0.631414
$790$	−1.50764e16	−1.74321
$791$	−4.21443e15	−0.483914
$792$	−3.76096e14	−0.0428855
$793$	3.18955e15	0.361182
$794$	−4.01295e15	−0.451285
$795$	7.91569e15	0.884035
$796$	−6.17150e15	−0.684493
$797$	2.33358e15	0.257041	0.128520	−	0.991707i	$-0.458977\pi$
$797$	2.33358e15	0.257041	0.128520	+	0.991707i	$0.458977\pi$
$798$	−7.35863e15	−0.804973
$799$	7.65349e15	0.831481
$800$	−1.90484e15	−0.205525
$801$	1.49062e15	0.159730
$802$	−1.94966e16	−2.07491
$803$	−1.11510e16	−1.17864
$804$	8.14920e15	0.855474
$805$	−8.19584e15	−0.854508
$806$	1.30268e16	1.34895
$807$	−8.13959e15	−0.837140
$808$	2.08035e15	0.212507
$809$	2.40076e15	0.243575	0.121787	−	0.992556i	$-0.461137\pi$
$809$	2.40076e15	0.243575	0.121787	+	0.992556i	$0.461137\pi$
$810$	−1.02132e16	−1.02918
$811$	−2.60209e15	−0.260440	−0.130220	−	0.991485i	$-0.541568\pi$
$811$	−2.60209e15	−0.260440	−0.130220	+	0.991485i	$0.541568\pi$
$812$	−7.18514e14	−0.0714294
$813$	−4.71854e15	−0.465919
$814$	5.14157e15	0.504268
$815$	1.60541e16	1.56394
$816$	9.05077e15	0.875769
$817$	1.03519e16	0.994947
$818$	−1.62018e16	−1.54675
$819$	7.80617e14	0.0740247
$820$	−9.22269e13	−0.00868723
$821$	1.18775e16	1.11132	0.555659	−	0.831410i	$-0.312466\pi$
$821$	1.18775e16	1.11132	0.555659	+	0.831410i	$0.312466\pi$
$822$	−2.27355e15	−0.211305
$823$	−1.52923e16	−1.41180	−0.705901	−	0.708311i	$-0.749457\pi$
$823$	−1.52923e16	−1.41180	−0.705901	+	0.708311i	$0.749457\pi$
$824$	1.76100e15	0.161495
$825$	1.66935e15	0.152072
$826$	3.74879e15	0.339235
$827$	−1.82433e16	−1.63992	−0.819959	−	0.572422i	$-0.806004\pi$
$827$	−1.82433e16	−1.63992	−0.819959	+	0.572422i	$0.806004\pi$
$828$	1.94987e15	0.174116
$829$	1.24346e16	1.10302	0.551508	−	0.834170i	$-0.314053\pi$
$829$	1.24346e16	1.10302	0.551508	+	0.834170i	$0.314053\pi$
$830$	9.76288e15	0.860297
$831$	−1.23220e16	−1.07864
$832$	−5.56846e15	−0.484236
$833$	−6.68250e15	−0.577287
$834$	−2.03183e16	−1.74371
$835$	1.97833e16	1.68664
$836$	1.08448e16	0.918520
$837$	−1.15751e16	−0.973948
$838$	2.60809e16	2.18012
$839$	−1.21441e16	−1.00850	−0.504249	−	0.863558i	$-0.668231\pi$
$839$	−1.21441e16	−1.00850	−0.504249	+	0.863558i	$0.668231\pi$
$840$	−1.80911e15	−0.149255
$841$	4.20707e14	0.0344828
$842$	−2.00708e16	−1.63436
$843$	−6.25568e15	−0.506084
$844$	−7.37428e15	−0.592702
$845$	−2.53653e15	−0.202548
$846$	2.27238e15	0.180279
$847$	2.82764e14	0.0222877
$848$	−1.57808e16	−1.23581
$849$	−1.71251e16	−1.33242
$850$	2.24342e15	0.173423
$851$	9.19645e15	0.706330
$852$	−5.47139e15	−0.417522
$853$	3.30637e15	0.250687	0.125343	−	0.992113i	$-0.459997\pi$
$853$	3.30637e15	0.250687	0.125343	+	0.992113i	$0.459997\pi$
$854$	2.96306e15	0.223214
$855$	1.99377e15	0.149232
$856$	−2.60939e15	−0.194058
$857$	−1.61448e16	−1.19299	−0.596495	−	0.802617i	$-0.703441\pi$
$857$	−1.61448e16	−1.19299	−0.596495	+	0.802617i	$0.703441\pi$
$858$	1.81443e16	1.33217
$859$	−2.41473e16	−1.76160	−0.880799	−	0.473491i	$-0.842994\pi$
$859$	−2.41473e16	−1.76160	−0.880799	+	0.473491i	$0.842994\pi$
$860$	−7.37682e15	−0.534722
$861$	8.57820e13	0.00617844
$862$	2.35043e16	1.68212
$863$	−4.67556e14	−0.0332487	−0.0166243	−	0.999862i	$-0.505292\pi$
$863$	−4.67556e14	−0.0332487	−0.0166243	+	0.999862i	$0.505292\pi$
$864$	1.83967e16	1.29991
$865$	−2.52743e16	−1.77456
$866$	−2.13360e16	−1.48855
$867$	5.09555e15	0.353253
$868$	5.16069e15	0.355508
$869$	−2.06663e16	−1.41466
$870$	−3.07036e15	−0.208850
$871$	−2.01670e16	−1.36315
$872$	−1.75136e14	−0.0117634
$873$	−4.28681e14	−0.0286125
$874$	4.54874e16	3.01702
$875$	−8.35975e15	−0.550996
$876$	1.27612e16	0.835832
$877$	−2.90591e16	−1.89140	−0.945701	−	0.325037i	$-0.894623\pi$
$877$	−2.90591e16	−1.89140	−0.945701	+	0.325037i	$0.894623\pi$
$878$	2.01913e16	1.30600
$879$	2.23340e16	1.43558
$880$	1.66465e16	1.06333
$881$	−1.38771e16	−0.880907	−0.440453	−	0.897775i	$-0.645182\pi$
$881$	−1.38771e16	−0.880907	−0.440453	+	0.897775i	$0.645182\pi$
$882$	−1.98409e15	−0.125165
$883$	−2.19395e16	−1.37544	−0.687721	−	0.725975i	$-0.741389\pi$
$883$	−2.19395e16	−1.37544	−0.687721	+	0.725975i	$0.741389\pi$
$884$	1.03983e16	0.647850
$885$	6.83129e15	0.422975
$886$	−2.63372e16	−1.62063
$887$	8.16450e15	0.499286	0.249643	−	0.968338i	$-0.419687\pi$
$887$	8.16450e15	0.499286	0.249643	+	0.968338i	$0.419687\pi$
$888$	2.02998e15	0.123373
$889$	−1.23588e16	−0.746478
$890$	−2.47799e16	−1.48749
$891$	−1.39999e16	−0.835213
$892$	−1.60987e14	−0.00954520
$893$	2.26060e16	1.33211
$894$	−2.82763e16	−1.65602
$895$	2.33287e16	1.35789
$896$	5.85872e15	0.338929
$897$	3.24538e16	1.86598
$898$	2.91102e16	1.66351
$899$	−3.02171e15	−0.171623
$900$	2.84046e14	0.0160345
$901$	1.45820e16	0.818145
$902$	−2.96459e14	−0.0165321
$903$	6.86132e15	0.380299
$904$	5.75048e15	0.316794
$905$	2.75752e15	0.150991
$906$	−3.30251e16	−1.79738
$907$	3.62086e16	1.95872	0.979359	−	0.202129i	$-0.0647859\pi$
$907$	3.62086e16	1.95872	0.979359	+	0.202129i	$0.0647859\pi$
$908$	1.07083e16	0.575769
$909$	−1.51961e15	−0.0812142
$910$	−1.29769e16	−0.689358
$911$	3.03810e16	1.60417	0.802086	−	0.597209i	$-0.203724\pi$
$911$	3.03810e16	1.60417	0.802086	+	0.597209i	$0.203724\pi$
$912$	2.67332e16	1.40307
$913$	1.33827e16	0.698157
$914$	2.05185e16	1.06400
$915$	5.39948e15	0.278315
$916$	2.53918e16	1.30097
$917$	4.15997e15	0.211865
$918$	−2.16666e16	−1.09687
$919$	−1.65057e16	−0.830613	−0.415306	−	0.909682i	$-0.636326\pi$
$919$	−1.65057e16	−0.830613	−0.415306	+	0.909682i	$0.636326\pi$
$920$	1.11830e16	0.559404
$921$	3.45259e16	1.71679
$922$	−7.03276e15	−0.347621
$923$	1.35402e16	0.665297
$924$	7.18802e15	0.351086
$925$	1.33969e15	0.0650467
$926$	−3.60959e16	−1.74220
$927$	−1.28634e15	−0.0617188
$928$	4.80250e15	0.229062
$929$	−3.43050e16	−1.62656	−0.813281	−	0.581872i	$-0.802321\pi$
$929$	−3.43050e16	−1.62656	−0.813281	+	0.581872i	$0.802321\pi$
$930$	2.20527e16	1.03946
$931$	−1.97380e16	−0.924870
$932$	−5.14427e15	−0.239627
$933$	3.28532e15	0.152135
$934$	3.60863e16	1.66125
$935$	−1.53819e16	−0.703955
$936$	−1.06513e15	−0.0484603
$937$	−1.98495e16	−0.897803	−0.448901	−	0.893581i	$-0.648185\pi$
$937$	−1.98495e16	−0.897803	−0.448901	+	0.893581i	$0.648185\pi$
$938$	−1.87350e16	−0.842438
$939$	−3.30900e15	−0.147923
$940$	−1.61091e16	−0.715928
$941$	−3.49305e16	−1.54334	−0.771671	−	0.636022i	$-0.780579\pi$
$941$	−3.49305e16	−1.54334	−0.771671	+	0.636022i	$0.780579\pi$
$942$	−2.32784e15	−0.102252
$943$	−5.30261e14	−0.0231566
$944$	−1.36190e16	−0.591287
$945$	1.15308e16	0.497719
$946$	−2.37125e16	−1.01760
$947$	1.18034e16	0.503595	0.251797	−	0.967780i	$-0.418978\pi$
$947$	1.18034e16	0.503595	0.251797	+	0.967780i	$0.418978\pi$
$948$	2.36504e16	1.00321
$949$	−3.15805e16	−1.33185
$950$	6.62636e15	0.277840
$951$	3.78586e16	1.57823
$952$	−3.33267e15	−0.138131
$953$	3.85229e16	1.58748	0.793740	−	0.608257i	$-0.208131\pi$
$953$	3.85229e16	1.58748	0.793740	+	0.608257i	$0.208131\pi$
$954$	4.32951e15	0.177387
$955$	−7.28432e15	−0.296736
$956$	−6.30044e15	−0.255183
$957$	−4.20876e15	−0.169488
$958$	4.16526e16	1.66775
$959$	2.22895e15	0.0887356
$960$	−9.42666e15	−0.373135
$961$	−3.70521e15	−0.145826
$962$	1.45613e16	0.569818
$963$	1.90605e15	0.0741636
$964$	−3.36217e16	−1.30076
$965$	1.40981e16	0.542325
$966$	3.01493e16	1.15320
$967$	−1.53557e16	−0.584013	−0.292007	−	0.956416i	$-0.594323\pi$
$967$	−1.53557e16	−0.584013	−0.292007	+	0.956416i	$0.594323\pi$
$968$	−3.85823e14	−0.0145906
$969$	−2.47023e16	−0.928873
$970$	7.12637e15	0.266455
$971$	2.11866e15	0.0787689	0.0393845	−	0.999224i	$-0.487460\pi$
$971$	2.11866e15	0.0787689	0.0393845	+	0.999224i	$0.487460\pi$
$972$	−5.17216e15	−0.191209
$973$	1.99198e16	0.732257
$974$	2.26504e16	0.827946
$975$	4.72770e15	0.171840
$976$	−1.07645e16	−0.389063
$977$	−2.31006e16	−0.830239	−0.415119	−	0.909767i	$-0.636260\pi$
$977$	−2.31006e16	−0.830239	−0.415119	+	0.909767i	$0.636260\pi$
$978$	−5.90568e16	−2.11060
$979$	−3.39676e16	−1.20715
$980$	1.40654e16	0.497060
$981$	1.27930e14	0.00449565
$982$	−1.36655e16	−0.477544
$983$	3.15129e16	1.09508	0.547538	−	0.836781i	$-0.315565\pi$
$983$	3.15129e16	1.09508	0.547538	+	0.836781i	$0.315565\pi$
$984$	−1.17047e14	−0.00404471
$985$	−2.67329e16	−0.918644
$986$	−5.65611e15	−0.193284
$987$	1.49834e16	0.509175
$988$	3.07133e16	1.03792
$989$	−4.24133e16	−1.42535
$990$	−4.56699e15	−0.152629
$991$	9.24891e15	0.307387	0.153694	−	0.988119i	$-0.450883\pi$
$991$	9.24891e15	0.307387	0.153694	+	0.988119i	$0.450883\pi$
$992$	−3.44937e16	−1.14005
$993$	1.13336e16	0.372517
$994$	1.25787e16	0.411160
$995$	2.58548e16	0.840455
$996$	−1.53151e16	−0.495099
$997$	−7.77459e14	−0.0249950	−0.0124975	−	0.999922i	$-0.503978\pi$
$997$	−7.77459e14	−0.0249950	−0.0124975	+	0.999922i	$0.503978\pi$
$998$	−2.39858e16	−0.766897
$999$	−1.29385e16	−0.411410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.3	✓	11
3.2	odd	2		261.12.a.a.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.3	✓	11	1.1	even	1	trivial
261.12.a.a.1.9		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +O(q^{10})\)	\(q-59.7551 q^{2} -392.705 q^{3} +1522.68 q^{4} -6379.08 q^{5} +23466.1 q^{6} -23005.8 q^{7} +31390.8 q^{8} -22929.7 q^{9} +381183. q^{10} +522514. q^{11} -597963. q^{12} +1.47979e6 q^{13} +1.37472e6 q^{14} +2.50510e6 q^{15} -4.99420e6 q^{16} +4.61480e6 q^{17} +1.37017e6 q^{18} +1.36307e7 q^{19} -9.71327e6 q^{20} +9.03450e6 q^{21} -3.12229e7 q^{22} -5.58468e7 q^{23} -1.23273e7 q^{24} -8.13546e6 q^{25} -8.84253e7 q^{26} +7.85711e7 q^{27} -3.50304e7 q^{28} +2.05111e7 q^{29} -1.49692e8 q^{30} -1.47320e8 q^{31} +2.34141e8 q^{32} -2.05194e8 q^{33} -2.75758e8 q^{34} +1.46756e8 q^{35} -3.49146e7 q^{36} -1.64673e8 q^{37} -8.14503e8 q^{38} -5.81123e8 q^{39} -2.00244e8 q^{40} +9.49494e6 q^{41} -5.39858e8 q^{42} +7.59458e8 q^{43} +7.95619e8 q^{44} +1.46271e8 q^{45} +3.33713e9 q^{46} +1.65847e9 q^{47} +1.96125e9 q^{48} -1.44806e9 q^{49} +4.86136e8 q^{50} -1.81226e9 q^{51} +2.25325e9 q^{52} +3.15983e9 q^{53} -4.69503e9 q^{54} -3.33316e9 q^{55} -7.22171e8 q^{56} -5.35284e9 q^{57} -1.22565e9 q^{58} +2.72696e9 q^{59} +3.81445e9 q^{60} +2.15540e9 q^{61} +8.80314e9 q^{62} +5.27517e8 q^{63} -3.76299e9 q^{64} -9.43973e9 q^{65} +1.22614e10 q^{66} -1.36283e10 q^{67} +7.02685e9 q^{68} +2.19313e10 q^{69} -8.76942e9 q^{70} +9.15005e9 q^{71} -7.19783e8 q^{72} -2.13411e10 q^{73} +9.84006e9 q^{74} +3.19484e9 q^{75} +2.07551e10 q^{76} -1.20209e10 q^{77} +3.47251e10 q^{78} -3.95516e10 q^{79} +3.18584e10 q^{80} -2.67934e10 q^{81} -5.67371e8 q^{82} +2.56121e10 q^{83} +1.37566e10 q^{84} -2.94382e10 q^{85} -4.53815e10 q^{86} -8.05483e9 q^{87} +1.64021e10 q^{88} -6.50080e10 q^{89} -8.74042e9 q^{90} -3.40439e10 q^{91} -8.50365e10 q^{92} +5.78534e10 q^{93} -9.91019e10 q^{94} -8.69512e10 q^{95} -9.19483e10 q^{96} +1.86954e10 q^{97} +8.65290e10 q^{98} -1.19811e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9} - 685834 q^{10} - 612246 q^{11} + 2578538 q^{12} + 1510364 q^{13} + 3955400 q^{14} - 2462818 q^{15} + 3024818 q^{16} - 3291098 q^{17} - 27885614 q^{18} - 44121388 q^{19} - 49472662 q^{20} - 46916800 q^{21} - 43435618 q^{22} - 88684076 q^{23} - 224700678 q^{24} - 44195521 q^{25} - 324999762 q^{26} - 236304286 q^{27} - 391274848 q^{28} + 225622639 q^{29} - 494910382 q^{30} - 292235934 q^{31} - 632542514 q^{32} - 1079766410 q^{33} - 1113307936 q^{34} - 1312820120 q^{35} - 2236726492 q^{36} - 1380429338 q^{37} - 1222857284 q^{38} - 1186931090 q^{39} - 2713154106 q^{40} - 1062067494 q^{41} + 205598960 q^{42} + 74588594 q^{43} + 52891466 q^{44} + 4527996830 q^{45} - 87670324 q^{46} - 1821239394 q^{47} + 2666035542 q^{48} + 4692522003 q^{49} + 9494259926 q^{50} + 8768158380 q^{51} + 3266669866 q^{52} + 7818635688 q^{53} + 17402728558 q^{54} - 191002682 q^{55} + 11263587512 q^{56} + 15495358340 q^{57} - 656356768 q^{58} + 1230002712 q^{59} + 31834046430 q^{60} - 18602654230 q^{61} + 22075953162 q^{62} - 9964531456 q^{63} + 11813658086 q^{64} + 32245789334 q^{65} + 42677188354 q^{66} + 27481284652 q^{67} + 29588811820 q^{68} - 20565315068 q^{69} + 42862666712 q^{70} - 20347168516 q^{71} + 47061083616 q^{72} - 57740010478 q^{73} - 2640709564 q^{74} - 23544691000 q^{75} - 33350650772 q^{76} + 871959792 q^{77} - 15384525342 q^{78} - 120245016462 q^{79} - 84319695274 q^{80} - 48880047865 q^{81} - 111495532412 q^{82} - 142463983824 q^{83} - 134146226376 q^{84} - 181628566552 q^{85} + 47870165542 q^{86} - 20141948318 q^{87} - 180608014462 q^{88} - 96700717270 q^{89} - 25522461244 q^{90} - 355162031176 q^{91} - 22429477796 q^{92} - 172582115142 q^{93} + 172608565078 q^{94} - 195922150708 q^{95} + 226391047758 q^{96} - 303190852014 q^{97} - 123776497136 q^{98} - 139125462440 q^{99}+O(q^{100}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9 - 685834 * q^10 - 612246 * q^11 + 2578538 * q^12 + 1510364 * q^13 + 3955400 * q^14 - 2462818 * q^15 + 3024818 * q^16 - 3291098 * q^17 - 27885614 * q^18 - 44121388 * q^19 - 49472662 * q^20 - 46916800 * q^21 - 43435618 * q^22 - 88684076 * q^23 - 224700678 * q^24 - 44195521 * q^25 - 324999762 * q^26 - 236304286 * q^27 - 391274848 * q^28 + 225622639 * q^29 - 494910382 * q^30 - 292235934 * q^31 - 632542514 * q^32 - 1079766410 * q^33 - 1113307936 * q^34 - 1312820120 * q^35 - 2236726492 * q^36 - 1380429338 * q^37 - 1222857284 * q^38 - 1186931090 * q^39 - 2713154106 * q^40 - 1062067494 * q^41 + 205598960 * q^42 + 74588594 * q^43 + 52891466 * q^44 + 4527996830 * q^45 - 87670324 * q^46 - 1821239394 * q^47 + 2666035542 * q^48 + 4692522003 * q^49 + 9494259926 * q^50 + 8768158380 * q^51 + 3266669866 * q^52 + 7818635688 * q^53 + 17402728558 * q^54 - 191002682 * q^55 + 11263587512 * q^56 + 15495358340 * q^57 - 656356768 * q^58 + 1230002712 * q^59 + 31834046430 * q^60 - 18602654230 * q^61 + 22075953162 * q^62 - 9964531456 * q^63 + 11813658086 * q^64 + 32245789334 * q^65 + 42677188354 * q^66 + 27481284652 * q^67 + 29588811820 * q^68 - 20565315068 * q^69 + 42862666712 * q^70 - 20347168516 * q^71 + 47061083616 * q^72 - 57740010478 * q^73 - 2640709564 * q^74 - 23544691000 * q^75 - 33350650772 * q^76 + 871959792 * q^77 - 15384525342 * q^78 - 120245016462 * q^79 - 84319695274 * q^80 - 48880047865 * q^81 - 111495532412 * q^82 - 142463983824 * q^83 - 134146226376 * q^84 - 181628566552 * q^85 + 47870165542 * q^86 - 20141948318 * q^87 - 180608014462 * q^88 - 96700717270 * q^89 - 25522461244 * q^90 - 355162031176 * q^91 - 22429477796 * q^92 - 172582115142 * q^93 + 172608565078 * q^94 - 195922150708 * q^95 + 226391047758 * q^96 - 303190852014 * q^97 - 123776497136 * q^98 - 139125462440 * q^99

Introduction

L-functions

Modular forms

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