LMFDB - Embedded newform 29.12.a.a.1.1

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			1.1
Root			$-82.7218$ 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)

$f(q)$	$=$	$q-85.7218 q^{2} +234.308 q^{3} +5300.23 q^{4} -1506.26 q^{5} -20085.3 q^{6} -7069.49 q^{7} -278787. q^{8} -122247. q^{9} +O(q^{10})$	\(q-85.7218 q^{2} +234.308 q^{3} +5300.23 q^{4} -1506.26 q^{5} -20085.3 q^{6} -7069.49 q^{7} -278787. q^{8} -122247. q^{9} +129120. q^{10} +598395. q^{11} +1.24189e6 q^{12} -284167. q^{13} +606010. q^{14} -352930. q^{15} +1.30433e7 q^{16} +6.02872e6 q^{17} +1.04792e7 q^{18} -1.04134e7 q^{19} -7.98356e6 q^{20} -1.65644e6 q^{21} -5.12955e7 q^{22} +3.07410e7 q^{23} -6.53221e7 q^{24} -4.65593e7 q^{25} +2.43593e7 q^{26} -7.01503e7 q^{27} -3.74700e7 q^{28} +2.05111e7 q^{29} +3.02538e7 q^{30} +2.00119e7 q^{31} -5.47138e8 q^{32} +1.40209e8 q^{33} -5.16793e8 q^{34} +1.06485e7 q^{35} -6.47937e8 q^{36} -3.29372e8 q^{37} +8.92657e8 q^{38} -6.65825e7 q^{39} +4.19928e8 q^{40} -1.33409e8 q^{41} +1.41993e8 q^{42} -1.51972e8 q^{43} +3.17163e9 q^{44} +1.84136e8 q^{45} -2.63517e9 q^{46} +5.65222e8 q^{47} +3.05615e9 q^{48} -1.92735e9 q^{49} +3.99115e9 q^{50} +1.41258e9 q^{51} -1.50615e9 q^{52} -5.83151e9 q^{53} +6.01341e9 q^{54} -9.01341e8 q^{55} +1.97089e9 q^{56} -2.43995e9 q^{57} -1.75825e9 q^{58} -8.59503e9 q^{59} -1.87061e9 q^{60} -1.25836e10 q^{61} -1.71546e9 q^{62} +8.64223e8 q^{63} +2.01890e10 q^{64} +4.28030e8 q^{65} -1.20189e10 q^{66} +1.31795e10 q^{67} +3.19536e10 q^{68} +7.20285e9 q^{69} -9.12811e8 q^{70} -4.99850e9 q^{71} +3.40809e10 q^{72} +3.78444e9 q^{73} +2.82344e10 q^{74} -1.09092e10 q^{75} -5.51936e10 q^{76} -4.23035e9 q^{77} +5.70757e9 q^{78} -3.61053e10 q^{79} -1.96467e10 q^{80} +5.21889e9 q^{81} +1.14360e10 q^{82} -3.39624e10 q^{83} -8.77951e9 q^{84} -9.08085e9 q^{85} +1.30273e10 q^{86} +4.80592e9 q^{87} -1.66825e11 q^{88} +8.21218e10 q^{89} -1.57845e10 q^{90} +2.00891e9 q^{91} +1.62934e11 q^{92} +4.68895e9 q^{93} -4.84519e10 q^{94} +1.56854e10 q^{95} -1.28199e11 q^{96} -4.18025e10 q^{97} +1.65216e11 q^{98} -7.31519e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−85.7218	−1.89420	−0.947101	−	0.320934i	$-0.896003\pi$
$2$	−85.7218	−1.89420	−0.947101	+	0.320934i	$0.896003\pi$
$3$	234.308	0.556698	0.278349	−	0.960480i	$-0.410213\pi$
$3$	234.308	0.556698	0.278349	+	0.960480i	$0.410213\pi$
$4$	5300.23	2.58800
$5$	−1506.26	−0.215559	−0.107780	−	0.994175i	$-0.534374\pi$
$5$	−1506.26	−0.215559	−0.107780	+	0.994175i	$0.534374\pi$
$6$	−20085.3	−1.05450
$7$	−7069.49	−0.158982	−0.0794912	−	0.996836i	$-0.525330\pi$
$7$	−7069.49	−0.158982	−0.0794912	+	0.996836i	$0.525330\pi$
$8$	−278787.	−3.00800
$9$	−122247.	−0.690087
$10$	129120.	0.408313
$11$	598395.	1.12028	0.560142	−	0.828397i	$-0.310747\pi$
$11$	598395.	1.12028	0.560142	+	0.828397i	$0.310747\pi$
$12$	1.24189e6	1.44074
$13$	−284167.	−0.212268	−0.106134	−	0.994352i	$-0.533847\pi$
$13$	−284167.	−0.212268	−0.106134	+	0.994352i	$0.533847\pi$
$14$	606010.	0.301145
$15$	−352930.	−0.120001
$16$	1.30433e7	3.10976
$17$	6.02872e6	1.02981	0.514904	−	0.857248i	$-0.327828\pi$
$17$	6.02872e6	1.02981	0.514904	+	0.857248i	$0.327828\pi$
$18$	1.04792e7	1.30716
$19$	−1.04134e7	−0.964825	−0.482413	−	0.875944i	$-0.660239\pi$
$19$	−1.04134e7	−0.964825	−0.482413	+	0.875944i	$0.660239\pi$
$20$	−7.98356e6	−0.557868
$21$	−1.65644e6	−0.0885052
$22$	−5.12955e7	−2.12204
$23$	3.07410e7	0.995897	0.497949	−	0.867207i	$-0.334087\pi$
$23$	3.07410e7	0.995897	0.497949	+	0.867207i	$0.334087\pi$
$24$	−6.53221e7	−1.67455
$25$	−4.65593e7	−0.953534
$26$	2.43593e7	0.402079
$27$	−7.01503e7	−0.940869
$28$	−3.74700e7	−0.411447
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	3.02538e7	0.227307
$31$	2.00119e7	0.125545	0.0627725	−	0.998028i	$-0.480006\pi$
$31$	2.00119e7	0.125545	0.0627725	+	0.998028i	$0.480006\pi$
$32$	−5.47138e8	−2.88252
$33$	1.40209e8	0.623660
$34$	−5.16793e8	−1.95066
$35$	1.06485e7	0.0342701
$36$	−6.47937e8	−1.78595
$37$	−3.29372e8	−0.780867	−0.390433	−	0.920631i	$-0.627675\pi$
$37$	−3.29372e8	−0.780867	−0.390433	+	0.920631i	$0.627675\pi$
$38$	8.92657e8	1.82757
$39$	−6.65825e7	−0.118169
$40$	4.19928e8	0.648402
$41$	−1.33409e8	−0.179834	−0.0899172	−	0.995949i	$-0.528660\pi$
$41$	−1.33409e8	−0.179834	−0.0899172	+	0.995949i	$0.528660\pi$
$42$	1.41993e8	0.167647
$43$	−1.51972e8	−0.157647	−0.0788236	−	0.996889i	$-0.525116\pi$
$43$	−1.51972e8	−0.157647	−0.0788236	+	0.996889i	$0.525116\pi$
$44$	3.17163e9	2.89930
$45$	1.84136e8	0.148755
$46$	−2.63517e9	−1.88643
$47$	5.65222e8	0.359485	0.179743	−	0.983714i	$-0.442474\pi$
$47$	5.65222e8	0.359485	0.179743	+	0.983714i	$0.442474\pi$
$48$	3.05615e9	1.73120
$49$	−1.92735e9	−0.974725
$50$	3.99115e9	1.80619
$51$	1.41258e9	0.573292
$52$	−1.50615e9	−0.549351
$53$	−5.83151e9	−1.91542	−0.957709	−	0.287738i	$-0.907097\pi$
$53$	−5.83151e9	−1.91542	−0.957709	+	0.287738i	$0.907097\pi$
$54$	6.01341e9	1.78220
$55$	−9.01341e8	−0.241487
$56$	1.97089e9	0.478220
$57$	−2.43995e9	−0.537117
$58$	−1.75825e9	−0.351745
$59$	−8.59503e9	−1.56517	−0.782585	−	0.622544i	$-0.786099\pi$
$59$	−8.59503e9	−1.56517	−0.782585	+	0.622544i	$0.786099\pi$
$60$	−1.87061e9	−0.310564
$61$	−1.25836e10	−1.90761	−0.953807	−	0.300419i	$-0.902873\pi$
$61$	−1.25836e10	−1.90761	−0.953807	+	0.300419i	$0.902873\pi$
$62$	−1.71546e9	−0.237808
$63$	8.64223e8	0.109712
$64$	2.01890e10	2.35031
$65$	4.28030e8	0.0457563
$66$	−1.20189e10	−1.18134
$67$	1.31795e10	1.19258	0.596291	−	0.802768i	$-0.296640\pi$
$67$	1.31795e10	1.19258	0.596291	+	0.802768i	$0.296640\pi$
$68$	3.19536e10	2.66515
$69$	7.20285e9	0.554414
$70$	−9.12811e8	−0.0649145
$71$	−4.99850e9	−0.328790	−0.164395	−	0.986395i	$-0.552567\pi$
$71$	−4.99850e9	−0.328790	−0.164395	+	0.986395i	$0.552567\pi$
$72$	3.40809e10	2.07578
$73$	3.78444e9	0.213661	0.106831	−	0.994277i	$-0.465930\pi$
$73$	3.78444e9	0.213661	0.106831	+	0.994277i	$0.465930\pi$
$74$	2.82344e10	1.47912
$75$	−1.09092e10	−0.530831
$76$	−5.51936e10	−2.49697
$77$	−4.23035e9	−0.178105
$78$	5.70757e9	0.223837
$79$	−3.61053e10	−1.32015	−0.660074	−	0.751201i	$-0.729475\pi$
$79$	−3.61053e10	−1.32015	−0.660074	+	0.751201i	$0.729475\pi$
$80$	−1.96467e10	−0.670338
$81$	5.21889e9	0.166307
$82$	1.14360e10	0.340643
$83$	−3.39624e10	−0.946387	−0.473193	−	0.880959i	$-0.656899\pi$
$83$	−3.39624e10	−0.946387	−0.473193	+	0.880959i	$0.656899\pi$
$84$	−8.77951e9	−0.229052
$85$	−9.08085e9	−0.221984
$86$	1.30273e10	0.298616
$87$	4.80592e9	0.103376
$88$	−1.66825e11	−3.36982
$89$	8.21218e10	1.55888	0.779441	−	0.626475i	$-0.215503\pi$
$89$	8.21218e10	1.55888	0.779441	+	0.626475i	$0.215503\pi$
$90$	−1.57845e10	−0.281771
$91$	2.00891e9	0.0337469
$92$	1.62934e11	2.57739
$93$	4.68895e9	0.0698908
$94$	−4.84519e10	−0.680938
$95$	1.56854e10	0.207977
$96$	−1.28199e11	−1.60469
$97$	−4.18025e10	−0.494262	−0.247131	−	0.968982i	$-0.579488\pi$
$97$	−4.18025e10	−0.494262	−0.247131	+	0.968982i	$0.579488\pi$
$98$	1.65216e11	1.84633
$99$	−7.31519e10	−0.773093
$100$	−2.46775e11	−2.46775
$101$	−1.93279e11	−1.82986	−0.914930	−	0.403613i	$-0.867754\pi$
$101$	−1.93279e11	−1.82986	−0.914930	+	0.403613i	$0.867754\pi$
$102$	−1.21089e11	−1.08593
$103$	1.18942e11	1.01095	0.505475	−	0.862841i	$-0.331317\pi$
$103$	1.18942e11	1.01095	0.505475	+	0.862841i	$0.331317\pi$
$104$	7.92221e10	0.638503
$105$	2.49503e9	0.0190781
$106$	4.99888e11	3.62819
$107$	1.74684e11	1.20404	0.602022	−	0.798480i	$-0.294362\pi$
$107$	1.74684e11	1.20404	0.602022	+	0.798480i	$0.294362\pi$
$108$	−3.71813e11	−2.43497
$109$	−4.14362e10	−0.257949	−0.128975	−	0.991648i	$-0.541169\pi$
$109$	−4.14362e10	−0.257949	−0.128975	+	0.991648i	$0.541169\pi$
$110$	7.72646e10	0.457426
$111$	−7.71744e10	−0.434707
$112$	−9.22095e10	−0.494398
$113$	−7.24493e10	−0.369916	−0.184958	−	0.982746i	$-0.559215\pi$
$113$	−7.24493e10	−0.369916	−0.184958	+	0.982746i	$0.559215\pi$
$114$	2.09157e11	1.01741
$115$	−4.63040e10	−0.214675
$116$	1.08714e11	0.480580
$117$	3.47385e10	0.146483
$118$	7.36782e11	2.96475
$119$	−4.26200e10	−0.163721
$120$	9.83924e10	0.360965
$121$	7.27646e10	0.255036
$122$	1.07869e12	3.61341
$123$	−3.12587e10	−0.100114
$124$	1.06068e11	0.324911
$125$	1.43679e11	0.421102
$126$	−7.40828e10	−0.207816
$127$	1.62132e11	0.435460	0.217730	−	0.976009i	$-0.430135\pi$
$127$	1.62132e11	0.435460	0.217730	+	0.976009i	$0.430135\pi$
$128$	−6.10103e11	−1.56945
$129$	−3.56082e10	−0.0877619
$130$	−3.66915e10	−0.0866718
$131$	4.23024e10	0.0958016	0.0479008	−	0.998852i	$-0.484747\pi$
$131$	4.23024e10	0.0958016	0.0479008	+	0.998852i	$0.484747\pi$
$132$	7.43138e11	1.61404
$133$	7.36176e10	0.153390
$134$	−1.12977e12	−2.25899
$135$	1.05665e11	0.202813
$136$	−1.68073e12	−3.09766
$137$	−9.90449e11	−1.75335	−0.876676	−	0.481082i	$-0.840244\pi$
$137$	−9.90449e11	−1.75335	−0.876676	+	0.481082i	$0.840244\pi$
$138$	−6.17442e11	−1.05017
$139$	5.58932e10	0.0913646	0.0456823	−	0.998956i	$-0.485454\pi$
$139$	5.58932e10	0.0913646	0.0456823	+	0.998956i	$0.485454\pi$
$140$	5.64397e10	0.0886912
$141$	1.32436e11	0.200125
$142$	4.28480e11	0.622795
$143$	−1.70044e11	−0.237801
$144$	−1.59450e12	−2.14601
$145$	−3.08952e10	−0.0400283
$146$	−3.24409e11	−0.404718
$147$	−4.51593e11	−0.542628
$148$	−1.74575e12	−2.02089
$149$	5.84976e11	0.652550	0.326275	−	0.945275i	$-0.394206\pi$
$149$	5.84976e11	0.652550	0.326275	+	0.945275i	$0.394206\pi$
$150$	9.35157e11	1.00550
$151$	1.14354e12	1.18543	0.592716	−	0.805412i	$-0.298056\pi$
$151$	1.14354e12	1.18543	0.592716	+	0.805412i	$0.298056\pi$
$152$	2.90313e12	2.90220
$153$	−7.36992e11	−0.710657
$154$	3.62633e11	0.337368
$155$	−3.01433e10	−0.0270624
$156$	−3.52903e11	−0.305823
$157$	−1.19892e12	−1.00309	−0.501547	−	0.865130i	$-0.667236\pi$
$157$	−1.19892e12	−1.00309	−0.501547	+	0.865130i	$0.667236\pi$
$158$	3.09502e12	2.50063
$159$	−1.36637e12	−1.06631
$160$	8.24135e11	0.621353
$161$	−2.17323e11	−0.158330
$162$	−4.47373e11	−0.315019
$163$	−2.10135e12	−1.43043	−0.715216	−	0.698904i	$-0.753671\pi$
$163$	−2.10135e12	−1.43043	−0.715216	+	0.698904i	$0.753671\pi$
$164$	−7.07097e11	−0.465413
$165$	−2.11191e11	−0.134436
$166$	2.91132e12	1.79265
$167$	2.49583e12	1.48688	0.743438	−	0.668805i	$-0.233194\pi$
$167$	2.49583e12	1.48688	0.743438	+	0.668805i	$0.233194\pi$
$168$	4.61794e11	0.266224
$169$	−1.71141e12	−0.954942
$170$	7.78427e11	0.420483
$171$	1.27301e12	0.665813
$172$	−8.05485e11	−0.407992
$173$	−1.72047e11	−0.0844100	−0.0422050	−	0.999109i	$-0.513438\pi$
$173$	−1.72047e11	−0.0844100	−0.0422050	+	0.999109i	$0.513438\pi$
$174$	−4.11973e11	−0.195816
$175$	3.29151e11	0.151595
$176$	7.80504e12	3.48382
$177$	−2.01388e12	−0.871327
$178$	−7.03963e12	−2.95284
$179$	−3.23099e12	−1.31415	−0.657074	−	0.753826i	$-0.728206\pi$
$179$	−3.23099e12	−1.31415	−0.657074	+	0.753826i	$0.728206\pi$
$180$	9.75964e11	0.384977
$181$	2.32931e12	0.891239	0.445620	−	0.895222i	$-0.352983\pi$
$181$	2.32931e12	0.891239	0.445620	+	0.895222i	$0.352983\pi$
$182$	−1.72208e11	−0.0639235
$183$	−2.94843e12	−1.06197
$184$	−8.57020e12	−2.99566
$185$	4.96121e11	0.168323
$186$	−4.01946e11	−0.132387
$187$	3.60755e12	1.15368
$188$	2.99581e12	0.930349
$189$	4.95927e11	0.149582
$190$	−1.34458e12	−0.393950
$191$	8.46740e11	0.241028	0.120514	−	0.992712i	$-0.461546\pi$
$191$	8.46740e11	0.241028	0.120514	+	0.992712i	$0.461546\pi$
$192$	4.73045e12	1.30842
$193$	−2.76009e12	−0.741921	−0.370960	−	0.928649i	$-0.620971\pi$
$193$	−2.76009e12	−0.741921	−0.370960	+	0.928649i	$0.620971\pi$
$194$	3.58339e12	0.936233
$195$	1.00291e11	0.0254725
$196$	−1.02154e13	−2.52259
$197$	4.20436e12	1.00957	0.504785	−	0.863245i	$-0.331572\pi$
$197$	4.20436e12	1.00957	0.504785	+	0.863245i	$0.331572\pi$
$198$	6.27071e12	1.46440
$199$	−7.87735e12	−1.78932	−0.894661	−	0.446746i	$-0.852583\pi$
$199$	−7.87735e12	−1.78932	−0.894661	+	0.446746i	$0.852583\pi$
$200$	1.29801e13	2.86823
$201$	3.08807e12	0.663909
$202$	1.65683e13	3.46613
$203$	−1.45003e11	−0.0295223
$204$	7.48699e12	1.48368
$205$	2.00949e11	0.0387650
$206$	−1.01959e13	−1.91494
$207$	−3.75799e12	−0.687256
$208$	−3.70647e12	−0.660104
$209$	−6.23134e12	−1.08088
$210$	−2.13879e11	−0.0361378
$211$	1.03418e13	1.70233	0.851165	−	0.524899i	$-0.175897\pi$
$211$	1.03418e13	1.70233	0.851165	+	0.524899i	$0.175897\pi$
$212$	−3.09084e13	−4.95711
$213$	−1.17119e12	−0.183037
$214$	−1.49742e13	−2.28070
$215$	2.28910e11	0.0339823
$216$	1.95570e13	2.83014
$217$	−1.41474e11	−0.0199595
$218$	3.55199e12	0.488608
$219$	8.86725e11	0.118945
$220$	−4.77732e12	−0.624970
$221$	−1.71316e12	−0.218595
$222$	6.61553e12	0.823424
$223$	4.02014e12	0.488162	0.244081	−	0.969755i	$-0.421514\pi$
$223$	4.02014e12	0.488162	0.244081	+	0.969755i	$0.421514\pi$
$224$	3.86799e12	0.458270
$225$	5.69173e12	0.658022
$226$	6.21049e12	0.700696
$227$	1.61832e13	1.78206	0.891030	−	0.453944i	$-0.149983\pi$
$227$	1.61832e13	1.78206	0.891030	+	0.453944i	$0.149983\pi$
$228$	−1.29323e13	−1.39006
$229$	1.45521e13	1.52697	0.763485	−	0.645826i	$-0.223487\pi$
$229$	1.45521e13	1.52697	0.763485	+	0.645826i	$0.223487\pi$
$230$	3.96927e12	0.406637
$231$	−9.91204e11	−0.0991510
$232$	−5.71825e12	−0.558572
$233$	1.36170e13	1.29904	0.649520	−	0.760344i	$-0.274970\pi$
$233$	1.36170e13	1.29904	0.649520	+	0.760344i	$0.274970\pi$
$234$	−2.97785e12	−0.277469
$235$	−8.51374e11	−0.0774903
$236$	−4.55557e13	−4.05067
$237$	−8.45976e12	−0.734924
$238$	3.65346e12	0.310121
$239$	3.48235e12	0.288858	0.144429	−	0.989515i	$-0.453865\pi$
$239$	3.48235e12	0.288858	0.144429	+	0.989515i	$0.453865\pi$
$240$	−4.60337e12	−0.373176
$241$	−5.57570e12	−0.441780	−0.220890	−	0.975299i	$-0.570896\pi$
$241$	−5.57570e12	−0.441780	−0.220890	+	0.975299i	$0.570896\pi$
$242$	−6.23752e12	−0.483089
$243$	1.36497e13	1.03345
$244$	−6.66960e13	−4.93691
$245$	2.90310e12	0.210111
$246$	2.67955e12	0.189635
$247$	2.95915e12	0.204802
$248$	−5.57908e12	−0.377640
$249$	−7.95765e12	−0.526852
$250$	−1.23164e13	−0.797653
$251$	−1.23140e13	−0.780177	−0.390088	−	0.920777i	$-0.627556\pi$
$251$	−1.23140e13	−0.780177	−0.390088	+	0.920777i	$0.627556\pi$
$252$	4.58058e12	0.283934
$253$	1.83952e13	1.11569
$254$	−1.38982e13	−0.824849
$255$	−2.12771e12	−0.123578
$256$	1.09519e13	0.622546
$257$	2.71133e13	1.50852	0.754258	−	0.656578i	$-0.227997\pi$
$257$	2.71133e13	1.50852	0.754258	+	0.656578i	$0.227997\pi$
$258$	3.05240e12	0.166239
$259$	2.32849e12	0.124144
$260$	2.26866e12	0.118418
$261$	−2.50742e12	−0.128146
$262$	−3.62624e12	−0.181468
$263$	1.68153e13	0.824038	0.412019	−	0.911175i	$-0.364824\pi$
$263$	1.68153e13	0.824038	0.412019	+	0.911175i	$0.364824\pi$
$264$	−3.90884e13	−1.87597
$265$	8.78380e12	0.412886
$266$	−6.31064e12	−0.290552
$267$	1.92418e13	0.867828
$268$	6.98546e13	3.08641
$269$	−3.03478e13	−1.31368	−0.656840	−	0.754030i	$-0.728107\pi$
$269$	−3.03478e13	−1.31368	−0.656840	+	0.754030i	$0.728107\pi$
$270$	−9.05780e12	−0.384169
$271$	−1.31818e13	−0.547826	−0.273913	−	0.961754i	$-0.588318\pi$
$271$	−1.31818e13	−0.547826	−0.273913	+	0.961754i	$0.588318\pi$
$272$	7.86344e13	3.20246
$273$	4.70704e11	0.0187868
$274$	8.49031e13	3.32120
$275$	−2.78608e13	−1.06823
$276$	3.81768e13	1.43483
$277$	4.85013e13	1.78696	0.893480	−	0.449103i	$-0.148256\pi$
$277$	4.85013e13	1.78696	0.893480	+	0.449103i	$0.148256\pi$
$278$	−4.79127e12	−0.173063
$279$	−2.44640e12	−0.0866370
$280$	−2.96868e12	−0.103085
$281$	−1.57905e13	−0.537663	−0.268832	−	0.963187i	$-0.586638\pi$
$281$	−1.57905e13	−0.537663	−0.268832	+	0.963187i	$0.586638\pi$
$282$	−1.13527e13	−0.379077
$283$	−3.55960e13	−1.16567	−0.582836	−	0.812590i	$-0.698057\pi$
$283$	−3.55960e13	−1.16567	−0.582836	+	0.812590i	$0.698057\pi$
$284$	−2.64932e13	−0.850910
$285$	3.67520e12	0.115780
$286$	1.45765e13	0.450442
$287$	9.43132e11	0.0285905
$288$	6.68859e13	1.98919
$289$	2.07357e12	0.0605036
$290$	2.64840e12	0.0758218
$291$	−9.79465e12	−0.275155
$292$	2.00584e13	0.552957
$293$	−6.08679e13	−1.64671	−0.823354	−	0.567528i	$-0.807900\pi$
$293$	−6.08679e13	−1.64671	−0.823354	+	0.567528i	$0.807900\pi$
$294$	3.87114e13	1.02785
$295$	1.29464e13	0.337387
$296$	9.18247e13	2.34885
$297$	−4.19776e13	−1.05404
$298$	−5.01452e13	−1.23606
$299$	−8.73556e12	−0.211397
$300$	−5.78213e13	−1.37379
$301$	1.07436e12	0.0250631
$302$	−9.80260e13	−2.24545
$303$	−4.52869e13	−1.01868
$304$	−1.35825e14	−3.00038
$305$	1.89542e13	0.411204
$306$	6.31763e13	1.34613
$307$	1.27841e12	0.0267552	0.0133776	−	0.999911i	$-0.495742\pi$
$307$	1.27841e12	0.0267552	0.0133776	+	0.999911i	$0.495742\pi$
$308$	−2.24218e13	−0.460938
$309$	2.78690e13	0.562794
$310$	2.58394e12	0.0512616
$311$	−5.67748e13	−1.10656	−0.553278	−	0.832996i	$-0.686623\pi$
$311$	−5.67748e13	−1.10656	−0.553278	+	0.832996i	$0.686623\pi$
$312$	1.85624e13	0.355454
$313$	−3.35116e13	−0.630524	−0.315262	−	0.949005i	$-0.602092\pi$
$313$	−3.35116e13	−0.630524	−0.315262	+	0.949005i	$0.602092\pi$
$314$	1.02774e14	1.90006
$315$	−1.30175e12	−0.0236493
$316$	−1.91367e14	−3.41655
$317$	−1.98376e13	−0.348066	−0.174033	−	0.984740i	$-0.555680\pi$
$317$	−1.98376e13	−0.348066	−0.174033	+	0.984740i	$0.555680\pi$
$318$	1.17128e14	2.01981
$319$	1.22738e13	0.208031
$320$	−3.04100e13	−0.506632
$321$	4.09298e13	0.670289
$322$	1.86293e13	0.299909
$323$	−6.27796e13	−0.993584
$324$	2.76613e13	0.430403
$325$	1.32306e13	0.202405
$326$	1.80132e14	2.70953
$327$	−9.70882e12	−0.143600
$328$	3.71927e13	0.540943
$329$	−3.99583e12	−0.0571518
$330$	1.81037e13	0.254648
$331$	−4.54179e13	−0.628309	−0.314155	−	0.949372i	$-0.601721\pi$
$331$	−4.54179e13	−0.628309	−0.314155	+	0.949372i	$0.601721\pi$
$332$	−1.80009e14	−2.44925
$333$	4.02647e13	0.538866
$334$	−2.13947e14	−2.81644
$335$	−1.98519e13	−0.257072
$336$	−2.16054e13	−0.275230
$337$	7.95830e13	0.997369	0.498685	−	0.866784i	$-0.333817\pi$
$337$	7.95830e13	0.997369	0.498685	+	0.866784i	$0.333817\pi$
$338$	1.46705e14	1.80885
$339$	−1.69754e13	−0.205932
$340$	−4.81306e13	−0.574497
$341$	1.19750e13	0.140646
$342$	−1.09125e14	−1.26119
$343$	2.76041e13	0.313946
$344$	4.23678e13	0.474203
$345$	−1.08494e13	−0.119509
$346$	1.47482e13	0.159890
$347$	−5.46578e13	−0.583230	−0.291615	−	0.956536i	$-0.594193\pi$
$347$	−5.46578e13	−0.583230	−0.291615	+	0.956536i	$0.594193\pi$
$348$	2.54725e13	0.267538
$349$	−9.78873e13	−1.01201	−0.506007	−	0.862530i	$-0.668879\pi$
$349$	−9.78873e13	−1.01201	−0.506007	+	0.862530i	$0.668879\pi$
$350$	−2.82154e13	−0.287152
$351$	1.99344e13	0.199716
$352$	−3.27405e14	−3.22924
$353$	1.31032e14	1.27238	0.636189	−	0.771533i	$-0.280510\pi$
$353$	1.31032e14	1.27238	0.636189	+	0.771533i	$0.280510\pi$
$354$	1.72634e14	1.65047
$355$	7.52906e12	0.0708736
$356$	4.35265e14	4.03440
$357$	−9.98620e12	−0.0911434
$358$	2.76967e14	2.48926
$359$	2.77646e13	0.245738	0.122869	−	0.992423i	$-0.460790\pi$
$359$	2.77646e13	0.245738	0.122869	+	0.992423i	$0.460790\pi$
$360$	−5.13348e13	−0.447454
$361$	−8.05095e12	−0.0691127
$362$	−1.99672e14	−1.68819
$363$	1.70493e13	0.141978
$364$	1.06477e13	0.0873371
$365$	−5.70037e12	−0.0460567
$366$	2.52745e14	2.01158
$367$	−1.08509e14	−0.850754	−0.425377	−	0.905016i	$-0.639858\pi$
$367$	−1.08509e14	−0.850754	−0.425377	+	0.905016i	$0.639858\pi$
$368$	4.00964e14	3.09700
$369$	1.63088e13	0.124101
$370$	−4.25284e13	−0.318838
$371$	4.12258e13	0.304518
$372$	2.48525e13	0.180878
$373$	−4.02186e13	−0.288422	−0.144211	−	0.989547i	$-0.546064\pi$
$373$	−4.02186e13	−0.288422	−0.144211	+	0.989547i	$0.546064\pi$
$374$	−3.09246e14	−2.18530
$375$	3.36650e13	0.234427
$376$	−1.57577e14	−1.08133
$377$	−5.82859e12	−0.0394172
$378$	−4.25118e13	−0.283338
$379$	−1.80219e14	−1.18382	−0.591908	−	0.806005i	$-0.701625\pi$
$379$	−1.80219e14	−1.18382	−0.591908	+	0.806005i	$0.701625\pi$
$380$	8.31361e13	0.538245
$381$	3.79888e13	0.242420
$382$	−7.25841e13	−0.456555
$383$	−1.41856e14	−0.879535	−0.439768	−	0.898112i	$-0.644939\pi$
$383$	−1.41856e14	−0.879535	−0.439768	+	0.898112i	$0.644939\pi$
$384$	−1.42952e14	−0.873711
$385$	6.37202e12	0.0383922
$386$	2.36600e14	1.40535
$387$	1.85781e13	0.108790
$388$	−2.21563e14	−1.27915
$389$	2.91132e14	1.65717	0.828586	−	0.559862i	$-0.189146\pi$
$389$	2.91132e14	1.65717	0.828586	+	0.559862i	$0.189146\pi$
$390$	−8.59712e12	−0.0482500
$391$	1.85329e14	1.02558
$392$	5.37321e14	2.93197
$393$	9.91178e12	0.0533326
$394$	−3.60406e14	−1.91233
$395$	5.43842e13	0.284570
$396$	−3.87722e14	−2.00077
$397$	1.35401e14	0.689086	0.344543	−	0.938771i	$-0.388034\pi$
$397$	1.35401e14	0.689086	0.344543	+	0.938771i	$0.388034\pi$
$398$	6.75261e14	3.38934
$399$	1.72492e13	0.0853921
$400$	−6.07286e14	−2.96527
$401$	9.06673e12	0.0436673	0.0218337	−	0.999762i	$-0.493050\pi$
$401$	9.06673e12	0.0436673	0.0218337	+	0.999762i	$0.493050\pi$
$402$	−2.64715e14	−1.25758
$403$	−5.68673e12	−0.0266492
$404$	−1.02443e15	−4.73569
$405$	−7.86103e12	−0.0358490
$406$	1.24300e13	0.0559212
$407$	−1.97094e14	−0.874792
$408$	−3.93809e14	−1.72446
$409$	8.87571e13	0.383464	0.191732	−	0.981447i	$-0.438589\pi$
$409$	8.87571e13	0.383464	0.191732	+	0.981447i	$0.438589\pi$
$410$	−1.72257e13	−0.0734287
$411$	−2.32070e14	−0.976088
$412$	6.30419e14	2.61634
$413$	6.07625e13	0.248834
$414$	3.22142e14	1.30180
$415$	5.11563e13	0.204002
$416$	1.55479e14	0.611867
$417$	1.30962e13	0.0508625
$418$	5.34162e14	2.04740
$419$	−2.74320e13	−0.103772	−0.0518860	−	0.998653i	$-0.516523\pi$
$419$	−2.74320e13	−0.103772	−0.0518860	+	0.998653i	$0.516523\pi$
$420$	1.32243e13	0.0493742
$421$	4.33872e14	1.59886	0.799429	−	0.600760i	$-0.205135\pi$
$421$	4.33872e14	1.59886	0.799429	+	0.600760i	$0.205135\pi$
$422$	−8.86520e14	−3.22456
$423$	−6.90966e13	−0.248076
$424$	1.62575e15	5.76158
$425$	−2.80693e14	−0.981957
$426$	1.00396e14	0.346709
$427$	8.89596e13	0.303277
$428$	9.25865e14	3.11607
$429$	−3.98426e13	−0.132383
$430$	−1.96225e13	−0.0643693
$431$	3.83089e14	1.24072	0.620361	−	0.784316i	$-0.286986\pi$
$431$	3.83089e14	1.24072	0.620361	+	0.784316i	$0.286986\pi$
$432$	−9.14991e14	−2.92588
$433$	9.06861e13	0.286324	0.143162	−	0.989699i	$-0.454273\pi$
$433$	9.06861e13	0.286324	0.143162	+	0.989699i	$0.454273\pi$
$434$	1.21274e13	0.0378073
$435$	−7.23899e12	−0.0222837
$436$	−2.19621e14	−0.667573
$437$	−3.20119e14	−0.960867
$438$	−7.60117e13	−0.225306
$439$	−2.09425e14	−0.613019	−0.306510	−	0.951868i	$-0.599161\pi$
$439$	−2.09425e14	−0.613019	−0.306510	+	0.951868i	$0.599161\pi$
$440$	2.51283e14	0.726395
$441$	2.35612e14	0.672645
$442$	1.46855e14	0.414064
$443$	−1.56421e14	−0.435585	−0.217793	−	0.975995i	$-0.569886\pi$
$443$	−1.56421e14	−0.435585	−0.217793	+	0.975995i	$0.569886\pi$
$444$	−4.09042e14	−1.12502
$445$	−1.23697e14	−0.336031
$446$	−3.44614e14	−0.924678
$447$	1.37065e14	0.363274
$448$	−1.42726e14	−0.373659
$449$	−4.22292e14	−1.09209	−0.546045	−	0.837756i	$-0.683867\pi$
$449$	−4.22292e14	−1.09209	−0.546045	+	0.837756i	$0.683867\pi$
$450$	−4.87905e14	−1.24643
$451$	−7.98311e13	−0.201466
$452$	−3.83998e14	−0.957344
$453$	2.67939e14	0.659928
$454$	−1.38725e15	−3.37558
$455$	−3.02596e12	−0.00727445
$456$	6.80226e14	1.61565
$457$	4.05203e14	0.950898	0.475449	−	0.879743i	$-0.342286\pi$
$457$	4.05203e14	0.950898	0.475449	+	0.879743i	$0.342286\pi$
$458$	−1.24743e15	−2.89239
$459$	−4.22917e14	−0.968914
$460$	−2.45422e14	−0.555579
$461$	−5.53814e14	−1.23882	−0.619410	−	0.785067i	$-0.712628\pi$
$461$	−5.53814e14	−1.23882	−0.619410	+	0.785067i	$0.712628\pi$
$462$	8.49678e13	0.187812
$463$	−2.46478e14	−0.538372	−0.269186	−	0.963088i	$-0.586755\pi$
$463$	−2.46478e14	−0.538372	−0.269186	+	0.963088i	$0.586755\pi$
$464$	2.67533e14	0.577469
$465$	−7.06281e12	−0.0150656
$466$	−1.16727e15	−2.46065
$467$	3.13903e14	0.653961	0.326981	−	0.945031i	$-0.393969\pi$
$467$	3.13903e14	0.653961	0.326981	+	0.945031i	$0.393969\pi$
$468$	1.84122e14	0.379100
$469$	−9.31726e13	−0.189600
$470$	7.29814e13	0.146782
$471$	−2.80916e14	−0.558421
$472$	2.39619e15	4.70803
$473$	−9.09390e13	−0.176610
$474$	7.25186e14	1.39209
$475$	4.84841e14	0.919994
$476$	−2.25896e14	−0.423711
$477$	7.12883e14	1.32181
$478$	−2.98514e14	−0.547156
$479$	2.29175e14	0.415262	0.207631	−	0.978207i	$-0.433425\pi$
$479$	2.29175e14	0.415262	0.207631	+	0.978207i	$0.433425\pi$
$480$	1.93101e14	0.345906
$481$	9.35965e13	0.165753
$482$	4.77959e14	0.836821
$483$	−5.09205e13	−0.0881421
$484$	3.85669e14	0.660033
$485$	6.29656e13	0.106543
$486$	−1.17008e15	−1.95757
$487$	−2.16926e14	−0.358841	−0.179420	−	0.983773i	$-0.557422\pi$
$487$	−2.16926e14	−0.358841	−0.179420	+	0.983773i	$0.557422\pi$
$488$	3.50815e15	5.73811
$489$	−4.92363e14	−0.796319
$490$	−2.48859e14	−0.397992
$491$	−1.19339e15	−1.88727	−0.943637	−	0.330982i	$-0.892620\pi$
$491$	−1.19339e15	−1.88727	−0.943637	+	0.330982i	$0.892620\pi$
$492$	−1.65678e14	−0.259094
$493$	1.23656e14	0.191230
$494$	−2.53664e14	−0.387936
$495$	1.10186e14	0.166647
$496$	2.61022e14	0.390416
$497$	3.53368e13	0.0522718
$498$	6.82145e14	0.997964
$499$	2.45455e14	0.355156	0.177578	−	0.984107i	$-0.443174\pi$
$499$	2.45455e14	0.355156	0.177578	+	0.984107i	$0.443174\pi$
$500$	7.61531e14	1.08981
$501$	5.84793e14	0.827741
$502$	1.05558e15	1.47781
$503$	2.39448e13	0.0331579	0.0165790	−	0.999863i	$-0.494723\pi$
$503$	2.39448e13	0.0331579	0.0165790	+	0.999863i	$0.494723\pi$
$504$	−2.40935e14	−0.330013
$505$	2.91130e14	0.394443
$506$	−1.57687e15	−2.11334
$507$	−4.00997e14	−0.531615
$508$	8.59337e14	1.12697
$509$	7.32323e14	0.950069	0.475034	−	0.879967i	$-0.342436\pi$
$509$	7.32323e14	0.950069	0.475034	+	0.879967i	$0.342436\pi$
$510$	1.82392e14	0.234082
$511$	−2.67541e13	−0.0339684
$512$	3.10669e14	0.390223
$513$	7.30505e14	0.907774
$514$	−2.32420e15	−2.85744
$515$	−1.79158e14	−0.217919
$516$	−1.88732e14	−0.227128
$517$	3.38226e14	0.402725
$518$	−1.99603e14	−0.235154
$519$	−4.03120e13	−0.0469909
$520$	−1.19329e14	−0.137635
$521$	3.34135e14	0.381341	0.190671	−	0.981654i	$-0.438934\pi$
$521$	3.34135e14	0.381341	0.190671	+	0.981654i	$0.438934\pi$
$522$	2.14941e14	0.242734
$523$	−4.01114e13	−0.0448238	−0.0224119	−	0.999749i	$-0.507135\pi$
$523$	−4.01114e13	−0.0448238	−0.0224119	+	0.999749i	$0.507135\pi$
$524$	2.24213e14	0.247935
$525$	7.71226e13	0.0843928
$526$	−1.44144e15	−1.56090
$527$	1.20646e14	0.129287
$528$	1.82878e15	1.93944
$529$	−7.80235e12	−0.00818878
$530$	−7.52963e14	−0.782090
$531$	1.05072e15	1.08010
$532$	3.90190e14	0.396975
$533$	3.79103e13	0.0381731
$534$	−1.64944e15	−1.64384
$535$	−2.63120e14	−0.259542
$536$	−3.67429e15	−3.58729
$537$	−7.57047e14	−0.731584
$538$	2.60147e15	2.48838
$539$	−1.15332e15	−1.09197
$540$	5.60049e14	0.524880
$541$	3.82729e14	0.355063	0.177532	−	0.984115i	$-0.443189\pi$
$541$	3.82729e14	0.355063	0.177532	+	0.984115i	$0.443189\pi$
$542$	1.12997e15	1.03769
$543$	5.45775e14	0.496152
$544$	−3.29854e15	−2.96844
$545$	6.24139e13	0.0556033
$546$	−4.03497e13	−0.0355861
$547$	1.10953e15	0.968742	0.484371	−	0.874863i	$-0.339048\pi$
$547$	1.10953e15	0.968742	0.484371	+	0.874863i	$0.339048\pi$
$548$	−5.24961e15	−4.53768
$549$	1.53830e15	1.31642
$550$	2.38828e15	2.02344
$551$	−2.13591e14	−0.179164
$552$	−2.00806e15	−1.66768
$553$	2.55246e14	0.209880
$554$	−4.15762e15	−3.38486
$555$	1.16245e14	0.0937051
$556$	2.96247e14	0.236452
$557$	9.17117e14	0.724805	0.362402	−	0.932022i	$-0.381957\pi$
$557$	9.17117e14	0.724805	0.362402	+	0.932022i	$0.381957\pi$
$558$	2.09710e14	0.164108
$559$	4.31853e13	0.0334635
$560$	1.38892e14	0.106572
$561$	8.45278e14	0.642250
$562$	1.35359e15	1.01844
$563$	−1.33076e15	−0.991522	−0.495761	−	0.868459i	$-0.665111\pi$
$563$	−1.33076e15	−0.991522	−0.495761	+	0.868459i	$0.665111\pi$
$564$	7.01942e14	0.517924
$565$	1.09128e14	0.0797387
$566$	3.05136e15	2.20802
$567$	−3.68949e13	−0.0264399
$568$	1.39352e15	0.989001
$569$	−1.00669e15	−0.707584	−0.353792	−	0.935324i	$-0.615108\pi$
$569$	−1.00669e15	−0.707584	−0.353792	+	0.935324i	$0.615108\pi$
$570$	−3.15045e14	−0.219311
$571$	−2.06731e15	−1.42530	−0.712652	−	0.701518i	$-0.752506\pi$
$571$	−2.06731e15	−1.42530	−0.712652	+	0.701518i	$0.752506\pi$
$572$	−9.01272e14	−0.615429
$573$	1.98398e14	0.134180
$574$	−8.08470e13	−0.0541562
$575$	−1.43128e15	−0.949622
$576$	−2.46805e15	−1.62192
$577$	7.80901e14	0.508310	0.254155	−	0.967163i	$-0.418203\pi$
$577$	7.80901e14	0.508310	0.254155	+	0.967163i	$0.418203\pi$
$578$	−1.77750e14	−0.114606
$579$	−6.46710e14	−0.413026
$580$	−1.63752e14	−0.103593
$581$	2.40097e14	0.150459
$582$	8.39615e14	0.521199
$583$	−3.48954e15	−2.14581
$584$	−1.05506e15	−0.642694
$585$	−5.23254e13	−0.0315758
$586$	5.21771e15	3.11920
$587$	2.95350e15	1.74915	0.874574	−	0.484891i	$-0.161141\pi$
$587$	2.95350e15	1.74915	0.874574	+	0.484891i	$0.161141\pi$
$588$	−2.39355e15	−1.40432
$589$	−2.08393e14	−0.121129
$590$	−1.10979e15	−0.639079
$591$	9.85115e14	0.562025
$592$	−4.29609e15	−2.42831
$593$	−1.10716e14	−0.0620026	−0.0310013	−	0.999519i	$-0.509870\pi$
$593$	−1.10716e14	−0.0620026	−0.0310013	+	0.999519i	$0.509870\pi$
$594$	3.59840e15	1.99657
$595$	6.41970e13	0.0352916
$596$	3.10051e15	1.68880
$597$	−1.84573e15	−0.996112
$598$	7.48828e14	0.400429
$599$	−2.23003e14	−0.118158	−0.0590791	−	0.998253i	$-0.518816\pi$
$599$	−2.23003e14	−0.118158	−0.0590791	+	0.998253i	$0.518816\pi$
$600$	3.04135e15	1.59674
$601$	2.38409e15	1.24026	0.620130	−	0.784499i	$-0.287080\pi$
$601$	2.38409e15	1.24026	0.620130	+	0.784499i	$0.287080\pi$
$602$	−9.20963e13	−0.0474746
$603$	−1.61116e15	−0.822986
$604$	6.06101e15	3.06790
$605$	−1.09603e14	−0.0549752
$606$	3.88207e15	1.92959
$607$	9.55050e14	0.470423	0.235211	−	0.971944i	$-0.424422\pi$
$607$	9.55050e14	0.470423	0.235211	+	0.971944i	$0.424422\pi$
$608$	5.69758e15	2.78113
$609$	−3.39754e13	−0.0164350
$610$	−1.62479e15	−0.778903
$611$	−1.60617e14	−0.0763073
$612$	−3.90623e15	−1.83918
$613$	3.30769e15	1.54345	0.771725	−	0.635956i	$-0.219394\pi$
$613$	3.30769e15	1.54345	0.771725	+	0.635956i	$0.219394\pi$
$614$	−1.09587e14	−0.0506798
$615$	4.70839e13	0.0215804
$616$	1.17937e15	0.535742
$617$	−4.36956e15	−1.96730	−0.983648	−	0.180104i	$-0.942357\pi$
$617$	−4.36956e15	−1.96730	−0.983648	+	0.180104i	$0.942357\pi$
$618$	−2.38898e15	−1.06605
$619$	−2.19128e13	−0.00969169	−0.00484585	−	0.999988i	$-0.501542\pi$
$619$	−2.19128e13	−0.00969169	−0.00484585	+	0.999988i	$0.501542\pi$
$620$	−1.59766e14	−0.0700376
$621$	−2.15649e15	−0.937008
$622$	4.86684e15	2.09604
$623$	−5.80560e14	−0.247835
$624$	−8.68455e14	−0.367479
$625$	2.05698e15	0.862762
$626$	2.87268e15	1.19434
$627$	−1.46005e15	−0.601723
$628$	−6.35455e15	−2.59601
$629$	−1.98569e15	−0.804143
$630$	1.11588e14	0.0447967
$631$	−2.46904e15	−0.982577	−0.491288	−	0.870997i	$-0.663474\pi$
$631$	−2.46904e15	−0.982577	−0.491288	+	0.870997i	$0.663474\pi$
$632$	1.00657e16	3.97101
$633$	2.42317e15	0.947684
$634$	1.70051e15	0.659308
$635$	−2.44214e14	−0.0938673
$636$	−7.24207e15	−2.75962
$637$	5.47688e14	0.206903
$638$	−1.05213e15	−0.394054
$639$	6.11050e14	0.226894
$640$	9.18976e14	0.338310
$641$	4.93142e14	0.179992	0.0899959	−	0.995942i	$-0.471315\pi$
$641$	4.93142e14	0.179992	0.0899959	+	0.995942i	$0.471315\pi$
$642$	−3.50858e15	−1.26966
$643$	−3.23186e15	−1.15956	−0.579779	−	0.814774i	$-0.696861\pi$
$643$	−3.23186e15	−1.15956	−0.579779	+	0.814774i	$0.696861\pi$
$644$	−1.15186e15	−0.409759
$645$	5.36353e13	0.0189179
$646$	5.38158e15	1.88205
$647$	−3.57806e15	−1.24072	−0.620361	−	0.784317i	$-0.713014\pi$
$647$	−3.57806e15	−1.24072	−0.620361	+	0.784317i	$0.713014\pi$
$648$	−1.45496e15	−0.500252
$649$	−5.14322e15	−1.75343
$650$	−1.13415e15	−0.383396
$651$	−3.31485e13	−0.0111114
$652$	−1.11377e16	−3.70196
$653$	1.86179e15	0.613631	0.306816	−	0.951769i	$-0.400736\pi$
$653$	1.86179e15	0.613631	0.306816	+	0.951769i	$0.400736\pi$
$654$	8.32258e14	0.272007
$655$	−6.37186e13	−0.0206509
$656$	−1.74009e15	−0.559243
$657$	−4.62636e14	−0.147445
$658$	3.42530e14	0.108257
$659$	2.15375e15	0.675034	0.337517	−	0.941319i	$-0.390413\pi$
$659$	2.15375e15	0.675034	0.337517	+	0.941319i	$0.390413\pi$
$660$	−1.11936e15	−0.347920
$661$	9.87662e14	0.304439	0.152219	−	0.988347i	$-0.451358\pi$
$661$	9.87662e14	0.304439	0.152219	+	0.988347i	$0.451358\pi$
$662$	3.89331e15	1.19014
$663$	−4.01407e14	−0.121692
$664$	9.46829e15	2.84673
$665$	−1.10888e14	−0.0330646
$666$	−3.45156e15	−1.02072
$667$	6.30533e14	0.184933
$668$	1.32285e16	3.84804
$669$	9.41950e14	0.271759
$670$	1.70174e15	0.486947
$671$	−7.52996e15	−2.13707
$672$	9.06301e14	0.255118
$673$	−3.49944e15	−0.977048	−0.488524	−	0.872550i	$-0.662465\pi$
$673$	−3.49944e15	−0.977048	−0.488524	+	0.872550i	$0.662465\pi$
$674$	−6.82200e15	−1.88922
$675$	3.26615e15	0.897150
$676$	−9.07087e15	−2.47139
$677$	−1.40384e14	−0.0379386	−0.0189693	−	0.999820i	$-0.506038\pi$
$677$	−1.40384e14	−0.0379386	−0.0189693	+	0.999820i	$0.506038\pi$
$678$	1.45517e15	0.390076
$679$	2.95522e14	0.0785790
$680$	2.53163e15	0.667730
$681$	3.79185e15	0.992070
$682$	−1.02652e15	−0.266412
$683$	−4.41379e15	−1.13631	−0.568157	−	0.822920i	$-0.692343\pi$
$683$	−4.41379e15	−1.13631	−0.568157	+	0.822920i	$0.692343\pi$
$684$	6.74724e15	1.72313
$685$	1.49188e15	0.377951
$686$	−2.36627e15	−0.594678
$687$	3.40967e15	0.850061
$688$	−1.98221e15	−0.490245
$689$	1.65712e15	0.406582
$690$	9.30031e14	0.226374
$691$	−4.16695e15	−1.00621	−0.503105	−	0.864225i	$-0.667809\pi$
$691$	−4.16695e15	−1.00621	−0.503105	+	0.864225i	$0.667809\pi$
$692$	−9.11891e14	−0.218454
$693$	5.17147e14	0.122908
$694$	4.68536e15	1.10476
$695$	−8.41900e13	−0.0196945
$696$	−1.33983e15	−0.310956
$697$	−8.04284e14	−0.185195
$698$	8.39108e15	1.91696
$699$	3.19056e15	0.723174
$700$	1.74457e15	0.392329
$701$	1.15347e14	0.0257369	0.0128685	−	0.999917i	$-0.495904\pi$
$701$	1.15347e14	0.0257369	0.0128685	+	0.999917i	$0.495904\pi$
$702$	−1.70881e15	−0.378303
$703$	3.42989e15	0.753400
$704$	1.20810e16	2.63302
$705$	−1.99484e14	−0.0431387
$706$	−1.12323e16	−2.41014
$707$	1.36639e15	0.290916
$708$	−1.06741e16	−2.25500
$709$	8.73974e15	1.83208	0.916039	−	0.401088i	$-0.131368\pi$
$709$	8.73974e15	1.83208	0.916039	+	0.401088i	$0.131368\pi$
$710$	−6.45405e14	−0.134249
$711$	4.41376e15	0.911016
$712$	−2.28945e16	−4.68912
$713$	6.15186e14	0.125030
$714$	8.56035e14	0.172644
$715$	2.56131e14	0.0512601
$716$	−1.71250e16	−3.40102
$717$	8.15943e14	0.160807
$718$	−2.38004e15	−0.465478
$719$	−7.62293e14	−0.147949	−0.0739747	−	0.997260i	$-0.523568\pi$
$719$	−7.62293e14	−0.147949	−0.0739747	+	0.997260i	$0.523568\pi$
$720$	2.40174e15	0.462591
$721$	−8.40858e14	−0.160723
$722$	6.90143e14	0.130913
$723$	−1.30643e15	−0.245938
$724$	1.23459e16	2.30653
$725$	−9.54985e14	−0.177067
$726$	−1.46150e15	−0.268935
$727$	−5.14284e15	−0.939212	−0.469606	−	0.882876i	$-0.655604\pi$
$727$	−5.14284e15	−0.939212	−0.469606	+	0.882876i	$0.655604\pi$
$728$	−5.60060e14	−0.101511
$729$	2.27373e15	0.409014
$730$	4.88646e14	0.0872407
$731$	−9.16195e14	−0.162346
$732$	−1.56274e16	−2.74837
$733$	−4.01404e15	−0.700663	−0.350332	−	0.936626i	$-0.613931\pi$
$733$	−4.01404e15	−0.700663	−0.350332	+	0.936626i	$0.613931\pi$
$734$	9.30162e15	1.61150
$735$	6.80219e14	0.116968
$736$	−1.68196e16	−2.87069
$737$	7.88656e15	1.33603
$738$	−1.39802e15	−0.235073
$739$	3.88766e15	0.648850	0.324425	−	0.945911i	$-0.394829\pi$
$739$	3.88766e15	0.648850	0.324425	+	0.945911i	$0.394829\pi$
$740$	2.62956e15	0.435621
$741$	6.93351e14	0.114013
$742$	−3.53395e15	−0.576819
$743$	2.10387e15	0.340863	0.170432	−	0.985370i	$-0.445484\pi$
$743$	2.10387e15	0.340863	0.170432	+	0.985370i	$0.445484\pi$
$744$	−1.30722e15	−0.210232
$745$	−8.81129e14	−0.140663
$746$	3.44761e15	0.546329
$747$	4.15179e15	0.653089
$748$	1.91209e16	2.98572
$749$	−1.23493e15	−0.191422
$750$	−2.88583e15	−0.444052
$751$	4.83508e15	0.738557	0.369279	−	0.929319i	$-0.379605\pi$
$751$	4.83508e15	0.738557	0.369279	+	0.929319i	$0.379605\pi$
$752$	7.37236e15	1.11791
$753$	−2.88526e15	−0.434323
$754$	4.99637e14	0.0746642
$755$	−1.72247e15	−0.255531
$756$	2.62853e15	0.387118
$757$	−8.12261e15	−1.18759	−0.593797	−	0.804615i	$-0.702372\pi$
$757$	−8.12261e15	−1.18759	−0.593797	+	0.804615i	$0.702372\pi$
$758$	1.54487e16	2.24239
$759$	4.31015e15	0.621101
$760$	−4.37288e15	−0.625595
$761$	3.35823e15	0.476974	0.238487	−	0.971146i	$-0.423349\pi$
$761$	3.35823e15	0.476974	0.238487	+	0.971146i	$0.423349\pi$
$762$	−3.25647e15	−0.459192
$763$	2.92933e14	0.0410094
$764$	4.48792e15	0.623780
$765$	1.11011e15	0.153189
$766$	1.21601e16	1.66602
$767$	2.44242e15	0.332236
$768$	2.56613e15	0.346570
$769$	−1.21660e14	−0.0163137	−0.00815686	−	0.999967i	$-0.502596\pi$
$769$	−1.21660e14	−0.0163137	−0.00815686	+	0.999967i	$0.502596\pi$
$770$	−5.46222e14	−0.0727227
$771$	6.35286e15	0.839789
$772$	−1.46291e16	−1.92009
$773$	−3.05158e15	−0.397684	−0.198842	−	0.980032i	$-0.563718\pi$
$773$	−3.05158e15	−0.397684	−0.198842	+	0.980032i	$0.563718\pi$
$774$	−1.59254e15	−0.206071
$775$	−9.31742e14	−0.119712
$776$	1.16540e16	1.48674
$777$	5.45584e14	0.0691108
$778$	−2.49564e16	−3.13902
$779$	1.38924e15	0.173509
$780$	5.31565e14	0.0659229
$781$	−2.99107e15	−0.368338
$782$	−1.58867e16	−1.94266
$783$	−1.43886e15	−0.174715
$784$	−2.51390e16	−3.03116
$785$	1.80589e15	0.216226
$786$	−8.49656e14	−0.101023
$787$	9.93889e15	1.17348	0.586742	−	0.809774i	$-0.300410\pi$
$787$	9.93889e15	1.17348	0.586742	+	0.809774i	$0.300410\pi$
$788$	2.22841e16	2.61277
$789$	3.93995e15	0.458741
$790$	−4.66191e15	−0.539033
$791$	5.12180e14	0.0588101
$792$	2.03938e16	2.32547
$793$	3.57584e15	0.404926
$794$	−1.16068e16	−1.30527
$795$	2.05811e15	0.229853
$796$	−4.17518e16	−4.63077
$797$	6.66631e15	0.734285	0.367143	−	0.930165i	$-0.380336\pi$
$797$	6.66631e15	0.734285	0.367143	+	0.930165i	$0.380336\pi$
$798$	−1.47863e15	−0.161750
$799$	3.40757e15	0.370201
$800$	2.54744e16	2.74858
$801$	−1.00391e16	−1.07576
$802$	−7.77217e14	−0.0827148
$803$	2.26459e15	0.239361
$804$	1.63675e16	1.71820
$805$	3.27346e14	0.0341295
$806$	4.87477e14	0.0504790
$807$	−7.11073e15	−0.731324
$808$	5.38839e16	5.50422
$809$	−1.50060e16	−1.52246	−0.761232	−	0.648479i	$-0.775405\pi$
$809$	−1.50060e16	−1.52246	−0.761232	+	0.648479i	$0.775405\pi$
$810$	6.73862e14	0.0679052
$811$	9.15416e15	0.916229	0.458115	−	0.888893i	$-0.348525\pi$
$811$	9.15416e15	0.916229	0.458115	+	0.888893i	$0.348525\pi$
$812$	−7.68552e14	−0.0764038
$813$	−3.08859e15	−0.304974
$814$	1.68953e16	1.65703
$815$	3.16519e15	0.308342
$816$	1.84246e16	1.78280
$817$	1.58254e15	0.152102
$818$	−7.60843e15	−0.726360
$819$	−2.45583e14	−0.0232883
$820$	1.06508e15	0.100324
$821$	1.78031e16	1.66574	0.832872	−	0.553466i	$-0.186695\pi$
$821$	1.78031e16	1.66574	0.832872	+	0.553466i	$0.186695\pi$
$822$	1.98935e16	1.84891
$823$	1.32521e16	1.22345	0.611724	−	0.791071i	$-0.290476\pi$
$823$	1.32521e16	1.22345	0.611724	+	0.791071i	$0.290476\pi$
$824$	−3.31595e16	−3.04094
$825$	−6.52801e15	−0.594681
$826$	−5.20867e15	−0.471343
$827$	−1.40611e16	−1.26398	−0.631989	−	0.774977i	$-0.717761\pi$
$827$	−1.40611e16	−1.26398	−0.631989	+	0.774977i	$0.717761\pi$
$828$	−1.99182e16	−1.77862
$829$	−1.03566e16	−0.918686	−0.459343	−	0.888259i	$-0.651915\pi$
$829$	−1.03566e16	−0.918686	−0.459343	+	0.888259i	$0.651915\pi$
$830$	−4.38522e15	−0.386422
$831$	1.13642e16	0.994798
$832$	−5.73705e15	−0.498897
$833$	−1.16194e16	−1.00378
$834$	−1.12263e15	−0.0963439
$835$	−3.75938e15	−0.320510
$836$	−3.30275e16	−2.79732
$837$	−1.40384e15	−0.118121
$838$	2.35152e15	0.196565
$839$	9.68827e15	0.804554	0.402277	−	0.915518i	$-0.368219\pi$
$839$	9.68827e15	0.804554	0.402277	+	0.915518i	$0.368219\pi$
$840$	−6.95584e14	−0.0573870
$841$	4.20707e14	0.0344828
$842$	−3.71923e16	−3.02856
$843$	−3.69983e15	−0.299316
$844$	5.48141e16	4.40564
$845$	2.57784e15	0.205846
$846$	5.92309e15	0.469906
$847$	−5.14409e14	−0.0405462
$848$	−7.60621e16	−5.95650
$849$	−8.34043e15	−0.648927
$850$	2.40615e16	1.86003
$851$	−1.01252e16	−0.777663
$852$	−6.20756e15	−0.473700
$853$	1.46435e16	1.11026	0.555132	−	0.831762i	$-0.312668\pi$
$853$	1.46435e16	1.11026	0.555132	+	0.831762i	$0.312668\pi$
$854$	−7.62578e15	−0.574468
$855$	−1.91749e15	−0.143522
$856$	−4.86997e16	−3.62177
$857$	−9.45909e15	−0.698964	−0.349482	−	0.936943i	$-0.613642\pi$
$857$	−9.45909e15	−0.698964	−0.349482	+	0.936943i	$0.613642\pi$
$858$	3.41538e15	0.250761
$859$	4.86873e15	0.355184	0.177592	−	0.984104i	$-0.443169\pi$
$859$	4.86873e15	0.355184	0.177592	+	0.984104i	$0.443169\pi$
$860$	1.21327e15	0.0879463
$861$	2.20983e14	0.0159163
$862$	−3.28391e16	−2.35018
$863$	−1.48573e15	−0.105652	−0.0528262	−	0.998604i	$-0.516823\pi$
$863$	−1.48573e15	−0.105652	−0.0528262	+	0.998604i	$0.516823\pi$
$864$	3.83819e16	2.71207
$865$	2.59149e14	0.0181954
$866$	−7.77378e15	−0.542355
$867$	4.85854e14	0.0336822
$868$	−7.49846e14	−0.0516552
$869$	−2.16052e16	−1.47894
$870$	6.20540e14	0.0422098
$871$	−3.74518e15	−0.253147
$872$	1.15519e16	0.775912
$873$	5.11022e15	0.341084
$874$	2.74412e16	1.82008
$875$	−1.01574e15	−0.0669478
$876$	4.69985e15	0.307830
$877$	−1.05639e16	−0.687583	−0.343791	−	0.939046i	$-0.611711\pi$
$877$	−1.05639e16	−0.687583	−0.343791	+	0.939046i	$0.611711\pi$
$878$	1.79523e16	1.16118
$879$	−1.42618e16	−0.916720
$880$	−1.17565e16	−0.750968
$881$	−8.44930e15	−0.536356	−0.268178	−	0.963369i	$-0.586422\pi$
$881$	−8.44930e15	−0.536356	−0.268178	+	0.963369i	$0.586422\pi$
$882$	−2.01971e16	−1.27413
$883$	−2.60928e16	−1.63583	−0.817913	−	0.575342i	$-0.804869\pi$
$883$	−2.60928e16	−1.63583	−0.817913	+	0.575342i	$0.804869\pi$
$884$	−9.08016e15	−0.565726
$885$	3.03344e15	0.187823
$886$	1.34087e16	0.825087
$887$	2.69034e16	1.64523	0.822615	−	0.568598i	$-0.192514\pi$
$887$	2.69034e16	1.64523	0.822615	+	0.568598i	$0.192514\pi$
$888$	2.15153e16	1.30760
$889$	−1.14619e15	−0.0692304
$890$	1.06036e16	0.636512
$891$	3.12295e15	0.186311
$892$	2.13077e16	1.26337
$893$	−5.88590e15	−0.346840
$894$	−1.17494e16	−0.688114
$895$	4.86673e15	0.283277
$896$	4.31312e15	0.249515
$897$	−2.04681e15	−0.117684
$898$	3.61997e16	2.06864
$899$	4.10468e14	0.0233131
$900$	3.01675e16	1.70296
$901$	−3.51565e16	−1.97251
$902$	6.84327e15	0.381617
$903$	2.51732e14	0.0139526
$904$	2.01980e16	1.11271
$905$	−3.50855e15	−0.192115
$906$	−2.29683e16	−1.25004
$907$	2.07428e15	0.112209	0.0561045	−	0.998425i	$-0.482132\pi$
$907$	2.07428e15	0.112209	0.0561045	+	0.998425i	$0.482132\pi$
$908$	8.57748e16	4.61198
$909$	2.36278e16	1.26276
$910$	2.59391e14	0.0137793
$911$	1.42172e16	0.750696	0.375348	−	0.926884i	$-0.377523\pi$
$911$	1.42172e16	0.750696	0.375348	+	0.926884i	$0.377523\pi$
$912$	−3.18249e16	−1.67031
$913$	−2.03229e16	−1.06022
$914$	−3.47348e16	−1.80119
$915$	4.44112e15	0.228916
$916$	7.71295e16	3.95180
$917$	−2.99056e14	−0.0152308
$918$	3.62532e16	1.83532
$919$	−3.08777e16	−1.55385	−0.776925	−	0.629593i	$-0.783222\pi$
$919$	−3.08777e16	−1.55385	−0.776925	+	0.629593i	$0.783222\pi$
$920$	1.29090e16	0.645742
$921$	2.99541e14	0.0148946
$922$	4.74739e16	2.34658
$923$	1.42041e15	0.0697916
$924$	−5.25361e15	−0.256603
$925$	1.53353e16	0.744583
$926$	2.11285e16	1.01979
$927$	−1.45402e16	−0.697643
$928$	−1.12224e16	−0.535270
$929$	3.68373e16	1.74663	0.873315	−	0.487156i	$-0.161966\pi$
$929$	3.68373e16	1.74663	0.873315	+	0.487156i	$0.161966\pi$
$930$	6.05437e14	0.0285373
$931$	2.00703e16	0.940439
$932$	7.21731e16	3.36192
$933$	−1.33028e16	−0.616018
$934$	−2.69083e16	−1.23874
$935$	−5.43393e15	−0.248685
$936$	−9.68465e15	−0.440623
$937$	−4.33816e16	−1.96217	−0.981087	−	0.193565i	$-0.937995\pi$
$937$	−4.33816e16	−1.96217	−0.981087	+	0.193565i	$0.937995\pi$
$938$	7.98693e15	0.359140
$939$	−7.85204e15	−0.351012
$940$	−4.51248e15	−0.200545
$941$	1.78920e16	0.790528	0.395264	−	0.918568i	$-0.370653\pi$
$941$	1.78920e16	0.790528	0.395264	+	0.918568i	$0.370653\pi$
$942$	2.40807e16	1.05776
$943$	−4.10111e15	−0.179097
$944$	−1.12108e17	−4.86731
$945$	−7.46998e14	−0.0322437
$946$	7.79546e15	0.334534
$947$	−9.07033e15	−0.386989	−0.193494	−	0.981101i	$-0.561982\pi$
$947$	−9.07033e15	−0.386989	−0.193494	+	0.981101i	$0.561982\pi$
$948$	−4.48387e16	−1.90199
$949$	−1.07541e15	−0.0453535
$950$	−4.15615e16	−1.74265
$951$	−4.64809e15	−0.193768
$952$	1.18819e16	0.492474
$953$	−1.41782e16	−0.584266	−0.292133	−	0.956378i	$-0.594365\pi$
$953$	−1.41782e16	−0.584266	−0.292133	+	0.956378i	$0.594365\pi$
$954$	−6.11097e16	−2.50377
$955$	−1.27542e15	−0.0519557
$956$	1.84573e16	0.747566
$957$	2.87584e15	0.115811
$958$	−1.96453e16	−0.786590
$959$	7.00197e15	0.278752
$960$	−7.12531e15	−0.282041
$961$	−2.50080e16	−0.984238
$962$	−8.02327e15	−0.313970
$963$	−2.13545e16	−0.830894
$964$	−2.95525e16	−1.14333
$965$	4.15742e15	0.159928
$966$	4.36500e15	0.166959
$967$	−1.91949e16	−0.730028	−0.365014	−	0.931002i	$-0.618936\pi$
$967$	−1.91949e16	−0.730028	−0.365014	+	0.931002i	$0.618936\pi$
$968$	−2.02859e16	−0.767148
$969$	−1.47098e16	−0.553127
$970$	−5.39753e15	−0.201814
$971$	3.56830e16	1.32665	0.663324	−	0.748332i	$-0.269145\pi$
$971$	3.56830e16	1.32665	0.663324	+	0.748332i	$0.269145\pi$
$972$	7.23468e16	2.67458
$973$	−3.95137e14	−0.0145254
$974$	1.85953e16	0.679717
$975$	3.10003e15	0.112678
$976$	−1.64131e17	−5.93223
$977$	3.12998e16	1.12492	0.562460	−	0.826824i	$-0.309855\pi$
$977$	3.12998e16	1.12492	0.562460	+	0.826824i	$0.309855\pi$
$978$	4.22063e16	1.50839
$979$	4.91413e16	1.74639
$980$	1.53871e16	0.543768
$981$	5.06544e15	0.178007
$982$	1.02300e17	3.57488
$983$	4.86496e16	1.69058	0.845289	−	0.534310i	$-0.179428\pi$
$983$	4.86496e16	1.69058	0.845289	+	0.534310i	$0.179428\pi$
$984$	8.71454e15	0.301142
$985$	−6.33289e15	−0.217622
$986$	−1.06000e16	−0.362229
$987$	−9.36255e14	−0.0318163
$988$	1.56842e16	0.530027
$989$	−4.67176e15	−0.157000
$990$	−9.44535e15	−0.315664
$991$	1.35365e16	0.449885	0.224942	−	0.974372i	$-0.427781\pi$
$991$	1.35365e16	0.449885	0.224942	+	0.974372i	$0.427781\pi$
$992$	−1.09493e16	−0.361886
$993$	−1.06418e16	−0.349779
$994$	−3.02914e15	−0.0990134
$995$	1.18654e16	0.385704
$996$	−4.21774e16	−1.36350
$997$	3.72028e15	0.119606	0.0598028	−	0.998210i	$-0.480953\pi$
$997$	3.72028e15	0.119606	0.0598028	+	0.998210i	$0.480953\pi$
$998$	−2.10409e16	−0.672738
$999$	2.31055e16	0.734693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.1	✓	11
3.2	odd	2		261.12.a.a.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.1	✓	11	1.1	even	1	trivial
261.12.a.a.1.11		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)

\(f(q)\)	\(=\)	\(q-85.7218 q^{2} +234.308 q^{3} +5300.23 q^{4} -1506.26 q^{5} -20085.3 q^{6} -7069.49 q^{7} -278787. q^{8} -122247. q^{9} +O(q^{10})\)	\(q-85.7218 q^{2} +234.308 q^{3} +5300.23 q^{4} -1506.26 q^{5} -20085.3 q^{6} -7069.49 q^{7} -278787. q^{8} -122247. q^{9} +129120. q^{10} +598395. q^{11} +1.24189e6 q^{12} -284167. q^{13} +606010. q^{14} -352930. q^{15} +1.30433e7 q^{16} +6.02872e6 q^{17} +1.04792e7 q^{18} -1.04134e7 q^{19} -7.98356e6 q^{20} -1.65644e6 q^{21} -5.12955e7 q^{22} +3.07410e7 q^{23} -6.53221e7 q^{24} -4.65593e7 q^{25} +2.43593e7 q^{26} -7.01503e7 q^{27} -3.74700e7 q^{28} +2.05111e7 q^{29} +3.02538e7 q^{30} +2.00119e7 q^{31} -5.47138e8 q^{32} +1.40209e8 q^{33} -5.16793e8 q^{34} +1.06485e7 q^{35} -6.47937e8 q^{36} -3.29372e8 q^{37} +8.92657e8 q^{38} -6.65825e7 q^{39} +4.19928e8 q^{40} -1.33409e8 q^{41} +1.41993e8 q^{42} -1.51972e8 q^{43} +3.17163e9 q^{44} +1.84136e8 q^{45} -2.63517e9 q^{46} +5.65222e8 q^{47} +3.05615e9 q^{48} -1.92735e9 q^{49} +3.99115e9 q^{50} +1.41258e9 q^{51} -1.50615e9 q^{52} -5.83151e9 q^{53} +6.01341e9 q^{54} -9.01341e8 q^{55} +1.97089e9 q^{56} -2.43995e9 q^{57} -1.75825e9 q^{58} -8.59503e9 q^{59} -1.87061e9 q^{60} -1.25836e10 q^{61} -1.71546e9 q^{62} +8.64223e8 q^{63} +2.01890e10 q^{64} +4.28030e8 q^{65} -1.20189e10 q^{66} +1.31795e10 q^{67} +3.19536e10 q^{68} +7.20285e9 q^{69} -9.12811e8 q^{70} -4.99850e9 q^{71} +3.40809e10 q^{72} +3.78444e9 q^{73} +2.82344e10 q^{74} -1.09092e10 q^{75} -5.51936e10 q^{76} -4.23035e9 q^{77} +5.70757e9 q^{78} -3.61053e10 q^{79} -1.96467e10 q^{80} +5.21889e9 q^{81} +1.14360e10 q^{82} -3.39624e10 q^{83} -8.77951e9 q^{84} -9.08085e9 q^{85} +1.30273e10 q^{86} +4.80592e9 q^{87} -1.66825e11 q^{88} +8.21218e10 q^{89} -1.57845e10 q^{90} +2.00891e9 q^{91} +1.62934e11 q^{92} +4.68895e9 q^{93} -4.84519e10 q^{94} +1.56854e10 q^{95} -1.28199e11 q^{96} -4.18025e10 q^{97} +1.65216e11 q^{98} -7.31519e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 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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