LMFDB - Embedded newform 29.12.a.a.1.5

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			1.5
Root			$-20.7036$ 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)

$f(q)$	$=$	$q-23.7036 q^{2} -804.018 q^{3} -1486.14 q^{4} +6643.74 q^{5} +19058.1 q^{6} -61145.1 q^{7} +83771.9 q^{8} +469298. q^{9} +O(q^{10})$	\(q-23.7036 q^{2} -804.018 q^{3} -1486.14 q^{4} +6643.74 q^{5} +19058.1 q^{6} -61145.1 q^{7} +83771.9 q^{8} +469298. q^{9} -157481. q^{10} +97159.7 q^{11} +1.19488e6 q^{12} +2.25195e6 q^{13} +1.44936e6 q^{14} -5.34169e6 q^{15} +1.05792e6 q^{16} -5.47274e6 q^{17} -1.11241e7 q^{18} -1.36844e7 q^{19} -9.87353e6 q^{20} +4.91618e7 q^{21} -2.30304e6 q^{22} +3.78724e7 q^{23} -6.73541e7 q^{24} -4.68878e6 q^{25} -5.33794e7 q^{26} -2.34895e8 q^{27} +9.08701e7 q^{28} +2.05111e7 q^{29} +1.26617e8 q^{30} +7.66307e7 q^{31} -1.96641e8 q^{32} -7.81182e7 q^{33} +1.29724e8 q^{34} -4.06232e8 q^{35} -6.97442e8 q^{36} +5.87994e8 q^{37} +3.24370e8 q^{38} -1.81061e9 q^{39} +5.56559e8 q^{40} -5.25000e8 q^{41} -1.16531e9 q^{42} +1.40657e9 q^{43} -1.44393e8 q^{44} +3.11790e9 q^{45} -8.97712e8 q^{46} -1.05859e9 q^{47} -8.50585e8 q^{48} +1.76140e9 q^{49} +1.11141e8 q^{50} +4.40018e9 q^{51} -3.34671e9 q^{52} +1.82460e8 q^{53} +5.56786e9 q^{54} +6.45504e8 q^{55} -5.12224e9 q^{56} +1.10025e10 q^{57} -4.86188e8 q^{58} -4.81226e9 q^{59} +7.93850e9 q^{60} +1.42171e9 q^{61} -1.81643e9 q^{62} -2.86953e10 q^{63} +2.49449e9 q^{64} +1.49614e10 q^{65} +1.85168e9 q^{66} +1.58194e9 q^{67} +8.13325e9 q^{68} -3.04501e10 q^{69} +9.62917e9 q^{70} -7.93869e9 q^{71} +3.93140e10 q^{72} -2.06263e10 q^{73} -1.39376e10 q^{74} +3.76987e9 q^{75} +2.03369e10 q^{76} -5.94084e9 q^{77} +4.29180e10 q^{78} -3.33041e10 q^{79} +7.02853e9 q^{80} +1.05725e11 q^{81} +1.24444e10 q^{82} -4.80488e9 q^{83} -7.30612e10 q^{84} -3.63595e10 q^{85} -3.33408e10 q^{86} -1.64913e10 q^{87} +8.13925e9 q^{88} -3.03829e10 q^{89} -7.39054e10 q^{90} -1.37696e11 q^{91} -5.62836e10 q^{92} -6.16125e10 q^{93} +2.50925e10 q^{94} -9.09157e10 q^{95} +1.58103e11 q^{96} -2.92126e10 q^{97} -4.17514e10 q^{98} +4.55969e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−23.7036	−0.523781	−0.261890	−	0.965098i	$-0.584346\pi$
$2$	−23.7036	−0.523781	−0.261890	+	0.965098i	$0.584346\pi$
$3$	−804.018	−1.91029	−0.955144	−	0.296141i	$-0.904300\pi$
$3$	−804.018	−1.91029	−0.955144	+	0.296141i	$0.904300\pi$
$4$	−1486.14	−0.725654
$5$	6643.74	0.950775	0.475388	−	0.879776i	$-0.342308\pi$
$5$	6643.74	0.950775	0.475388	+	0.879776i	$0.342308\pi$
$6$	19058.1	1.00057
$7$	−61145.1	−1.37506	−0.687531	−	0.726155i	$-0.741306\pi$
$7$	−61145.1	−1.37506	−0.687531	+	0.726155i	$0.741306\pi$
$8$	83771.9	0.903864
$9$	469298.	2.64920
$10$	−157481.	−0.497998
$11$	97159.7	0.181897	0.0909487	−	0.995856i	$-0.471010\pi$
$11$	97159.7	0.181897	0.0909487	+	0.995856i	$0.471010\pi$
$12$	1.19488e6	1.38621
$13$	2.25195e6	1.68217	0.841086	−	0.540901i	$-0.181917\pi$
$13$	2.25195e6	1.68217	0.841086	+	0.540901i	$0.181917\pi$
$14$	1.44936e6	0.720231
$15$	−5.34169e6	−1.81626
$16$	1.05792e6	0.252227
$17$	−5.47274e6	−0.934837	−0.467418	−	0.884036i	$-0.654816\pi$
$17$	−5.47274e6	−0.934837	−0.467418	+	0.884036i	$0.654816\pi$
$18$	−1.11241e7	−1.38760
$19$	−1.36844e7	−1.26789	−0.633944	−	0.773379i	$-0.718565\pi$
$19$	−1.36844e7	−1.26789	−0.633944	+	0.773379i	$0.718565\pi$
$20$	−9.87353e6	−0.689934
$21$	4.91618e7	2.62677
$22$	−2.30304e6	−0.0952743
$23$	3.78724e7	1.22693	0.613464	−	0.789722i	$-0.289775\pi$
$23$	3.78724e7	1.22693	0.613464	+	0.789722i	$0.289775\pi$
$24$	−6.73541e7	−1.72664
$25$	−4.68878e6	−0.0960263
$26$	−5.33794e7	−0.881090
$27$	−2.34895e8	−3.15045
$28$	9.08701e7	0.997819
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	1.26617e8	0.951320
$31$	7.66307e7	0.480744	0.240372	−	0.970681i	$-0.422731\pi$
$31$	7.66307e7	0.480744	0.240372	+	0.970681i	$0.422731\pi$
$32$	−1.96641e8	−1.03598
$33$	−7.81182e7	−0.347476
$34$	1.29724e8	0.489649
$35$	−4.06232e8	−1.30738
$36$	−6.97442e8	−1.92240
$37$	5.87994e8	1.39400	0.697001	−	0.717070i	$-0.254517\pi$
$37$	5.87994e8	1.39400	0.697001	+	0.717070i	$0.254517\pi$
$38$	3.24370e8	0.664095
$39$	−1.81061e9	−3.21344
$40$	5.56559e8	0.859372
$41$	−5.25000e8	−0.707699	−0.353849	−	0.935302i	$-0.615127\pi$
$41$	−5.25000e8	−0.707699	−0.353849	+	0.935302i	$0.615127\pi$
$42$	−1.16531e9	−1.37585
$43$	1.40657e9	1.45910	0.729550	−	0.683927i	$-0.239729\pi$
$43$	1.40657e9	1.45910	0.729550	+	0.683927i	$0.239729\pi$
$44$	−1.44393e8	−0.131994
$45$	3.11790e9	2.51880
$46$	−8.97712e8	−0.642642
$47$	−1.05859e9	−0.673273	−0.336636	−	0.941635i	$-0.609289\pi$
$47$	−1.05859e9	−0.673273	−0.336636	+	0.941635i	$0.609289\pi$
$48$	−8.50585e8	−0.481826
$49$	1.76140e9	0.890796
$50$	1.11141e8	0.0502967
$51$	4.40018e9	1.78581
$52$	−3.34671e9	−1.22067
$53$	1.82460e8	0.0599307	0.0299654	−	0.999551i	$-0.490460\pi$
$53$	1.82460e8	0.0599307	0.0299654	+	0.999551i	$0.490460\pi$
$54$	5.56786e9	1.65015
$55$	6.45504e8	0.172943
$56$	−5.12224e9	−1.24287
$57$	1.10025e10	2.42203
$58$	−4.86188e8	−0.0972636
$59$	−4.81226e9	−0.876321	−0.438160	−	0.898897i	$-0.644370\pi$
$59$	−4.81226e9	−0.876321	−0.438160	+	0.898897i	$0.644370\pi$
$60$	7.93850e9	1.31797
$61$	1.42171e9	0.215524	0.107762	−	0.994177i	$-0.465632\pi$
$61$	1.42171e9	0.215524	0.107762	+	0.994177i	$0.465632\pi$
$62$	−1.81643e9	−0.251804
$63$	−2.86953e10	−3.64282
$64$	2.49449e9	0.290397
$65$	1.49614e10	1.59937
$66$	1.85168e9	0.182001
$67$	1.58194e9	0.143146	0.0715728	−	0.997435i	$-0.477198\pi$
$67$	1.58194e9	0.143146	0.0715728	+	0.997435i	$0.477198\pi$
$68$	8.13325e9	0.678368
$69$	−3.04501e10	−2.34379
$70$	9.62917e9	0.684778
$71$	−7.93869e9	−0.522189	−0.261095	−	0.965313i	$-0.584083\pi$
$71$	−7.93869e9	−0.522189	−0.261095	+	0.965313i	$0.584083\pi$
$72$	3.93140e10	2.39452
$73$	−2.06263e10	−1.16452	−0.582258	−	0.813004i	$-0.697831\pi$
$73$	−2.06263e10	−1.16452	−0.582258	+	0.813004i	$0.697831\pi$
$74$	−1.39376e10	−0.730151
$75$	3.76987e9	0.183438
$76$	2.03369e10	0.920048
$77$	−5.94084e9	−0.250120
$78$	4.29180e10	1.68314
$79$	−3.33041e10	−1.21772	−0.608862	−	0.793276i	$-0.708374\pi$
$79$	−3.33041e10	−1.21772	−0.608862	+	0.793276i	$0.708374\pi$
$80$	7.02853e9	0.239811
$81$	1.05725e11	3.36907
$82$	1.24444e10	0.370679
$83$	−4.80488e9	−0.133891	−0.0669457	−	0.997757i	$-0.521325\pi$
$83$	−4.80488e9	−0.133891	−0.0669457	+	0.997757i	$0.521325\pi$
$84$	−7.30612e10	−1.90612
$85$	−3.63595e10	−0.888820
$86$	−3.33408e10	−0.764249
$87$	−1.64913e10	−0.354732
$88$	8.13925e9	0.164410
$89$	−3.03829e10	−0.576745	−0.288373	−	0.957518i	$-0.593114\pi$
$89$	−3.03829e10	−0.576745	−0.288373	+	0.957518i	$0.593114\pi$
$90$	−7.39054e10	−1.31930
$91$	−1.37696e11	−2.31309
$92$	−5.62836e10	−0.890325
$93$	−6.16125e10	−0.918360
$94$	2.50925e10	0.352647
$95$	−9.09157e10	−1.20548
$96$	1.58103e11	1.97901
$97$	−2.92126e10	−0.345402	−0.172701	−	0.984974i	$-0.555249\pi$
$97$	−2.92126e10	−0.345402	−0.172701	+	0.984974i	$0.555249\pi$
$98$	−4.17514e10	−0.466582
$99$	4.55969e10	0.481883
$100$	6.96818e9	0.0696818
$101$	−1.67043e9	−0.0158147	−0.00790734	−	0.999969i	$-0.502517\pi$
$101$	−1.67043e9	−0.0158147	−0.00790734	+	0.999969i	$0.502517\pi$
$102$	−1.04300e11	−0.935372
$103$	1.11501e11	0.947706	0.473853	−	0.880604i	$-0.342863\pi$
$103$	1.11501e11	0.947706	0.473853	+	0.880604i	$0.342863\pi$
$104$	1.88650e11	1.52046
$105$	3.26618e11	2.49746
$106$	−4.32495e9	−0.0313906
$107$	1.37541e11	0.948031	0.474015	−	0.880517i	$-0.342804\pi$
$107$	1.37541e11	0.948031	0.474015	+	0.880517i	$0.342804\pi$
$108$	3.49087e11	2.28614
$109$	−2.80903e11	−1.74868	−0.874340	−	0.485314i	$-0.838705\pi$
$109$	−2.80903e11	−1.74868	−0.874340	+	0.485314i	$0.838705\pi$
$110$	−1.53008e10	−0.0905845
$111$	−4.72758e11	−2.66295
$112$	−6.46864e10	−0.346828
$113$	1.69957e10	0.0867775	0.0433887	−	0.999058i	$-0.486185\pi$
$113$	1.69957e10	0.0867775	0.0433887	+	0.999058i	$0.486185\pi$
$114$	−2.60799e11	−1.26861
$115$	2.51614e11	1.16653
$116$	−3.04824e10	−0.134751
$117$	1.05684e12	4.45642
$118$	1.14068e11	0.459000
$119$	3.34631e11	1.28546
$120$	−4.47483e11	−1.64165
$121$	−2.75872e11	−0.966913
$122$	−3.36996e10	−0.112887
$123$	4.22110e11	1.35191
$124$	−1.13884e11	−0.348854
$125$	−3.55553e11	−1.04207
$126$	6.80182e11	1.90804
$127$	−3.22954e11	−0.867402	−0.433701	−	0.901057i	$-0.642792\pi$
$127$	−3.22954e11	−0.867402	−0.433701	+	0.901057i	$0.642792\pi$
$128$	3.43593e11	0.883871
$129$	−1.13091e12	−2.78730
$130$	−3.54639e11	−0.837718
$131$	−1.19707e11	−0.271099	−0.135549	−	0.990771i	$-0.543280\pi$
$131$	−1.19707e11	−0.271099	−0.135549	+	0.990771i	$0.543280\pi$
$132$	1.16094e11	0.252148
$133$	8.36734e11	1.74343
$134$	−3.74976e10	−0.0749769
$135$	−1.56058e12	−2.99537
$136$	−4.58462e11	−0.844965
$137$	1.15117e10	0.0203787	0.0101894	−	0.999948i	$-0.496757\pi$
$137$	1.15117e10	0.0203787	0.0101894	+	0.999948i	$0.496757\pi$
$138$	7.21777e11	1.22763
$139$	−1.29449e11	−0.211600	−0.105800	−	0.994387i	$-0.533740\pi$
$139$	−1.29449e11	−0.211600	−0.105800	+	0.994387i	$0.533740\pi$
$140$	6.03718e11	0.948702
$141$	8.51128e11	1.28614
$142$	1.88176e11	0.273513
$143$	2.18799e11	0.305983
$144$	4.96479e11	0.668201
$145$	1.36271e11	0.176555
$146$	4.88917e11	0.609951
$147$	−1.41619e12	−1.70168
$148$	−8.73841e11	−1.01156
$149$	1.04551e12	1.16628	0.583139	−	0.812372i	$-0.301824\pi$
$149$	1.04551e12	1.16628	0.583139	+	0.812372i	$0.301824\pi$
$150$	−8.93595e10	−0.0960812
$151$	−4.17782e11	−0.433088	−0.216544	−	0.976273i	$-0.569479\pi$
$151$	−4.17782e11	−0.433088	−0.216544	+	0.976273i	$0.569479\pi$
$152$	−1.14637e12	−1.14600
$153$	−2.56835e12	−2.47657
$154$	1.40819e11	0.131008
$155$	5.09115e11	0.457079
$156$	2.69082e12	2.33184
$157$	−1.93394e11	−0.161806	−0.0809030	−	0.996722i	$-0.525780\pi$
$157$	−1.93394e11	−0.161806	−0.0809030	+	0.996722i	$0.525780\pi$
$158$	7.89427e11	0.637820
$159$	−1.46701e11	−0.114485
$160$	−1.30643e12	−0.984980
$161$	−2.31571e12	−1.68710
$162$	−2.50607e12	−1.76466
$163$	−6.42171e11	−0.437138	−0.218569	−	0.975821i	$-0.570139\pi$
$163$	−6.42171e11	−0.437138	−0.218569	+	0.975821i	$0.570139\pi$
$164$	7.80223e11	0.513544
$165$	−5.18997e11	−0.330372
$166$	1.13893e11	0.0701297
$167$	−3.12229e11	−0.186008	−0.0930042	−	0.995666i	$-0.529647\pi$
$167$	−3.12229e11	−0.186008	−0.0930042	+	0.995666i	$0.529647\pi$
$168$	4.11837e12	2.37424
$169$	3.27912e12	1.82970
$170$	8.61851e11	0.465547
$171$	−6.42207e12	−3.35889
$172$	−2.09036e12	−1.05880
$173$	9.22108e11	0.452406	0.226203	−	0.974080i	$-0.427369\pi$
$173$	9.22108e11	0.452406	0.226203	+	0.974080i	$0.427369\pi$
$174$	3.90904e11	0.185802
$175$	2.86696e11	0.132042
$176$	1.02787e11	0.0458794
$177$	3.86915e12	1.67403
$178$	7.20184e11	0.302088
$179$	−3.84140e11	−0.156242	−0.0781210	−	0.996944i	$-0.524892\pi$
$179$	−3.84140e11	−0.156242	−0.0781210	+	0.996944i	$0.524892\pi$
$180$	−4.63363e12	−1.82777
$181$	−3.67123e11	−0.140469	−0.0702344	−	0.997531i	$-0.522375\pi$
$181$	−3.67123e11	−0.140469	−0.0702344	+	0.997531i	$0.522375\pi$
$182$	3.26389e12	1.21155
$183$	−1.14308e12	−0.411713
$184$	3.17264e12	1.10898
$185$	3.90648e12	1.32538
$186$	1.46044e12	0.481019
$187$	−5.31730e11	−0.170044
$188$	1.57322e12	0.488563
$189$	1.43627e13	4.33207
$190$	2.15503e12	0.631406
$191$	−2.26967e11	−0.0646070	−0.0323035	−	0.999478i	$-0.510284\pi$
$191$	−2.26967e11	−0.0646070	−0.0323035	+	0.999478i	$0.510284\pi$
$192$	−2.00562e12	−0.554742
$193$	1.51356e12	0.406850	0.203425	−	0.979091i	$-0.434793\pi$
$193$	1.51356e12	0.406850	0.203425	+	0.979091i	$0.434793\pi$
$194$	6.92443e11	0.180915
$195$	−1.20292e13	−3.05526
$196$	−2.61768e12	−0.646410
$197$	−7.38522e12	−1.77337	−0.886684	−	0.462375i	$-0.846997\pi$
$197$	−7.38522e12	−1.77337	−0.886684	+	0.462375i	$0.846997\pi$
$198$	−1.08081e12	−0.252401
$199$	3.16497e12	0.718915	0.359458	−	0.933161i	$-0.382962\pi$
$199$	3.16497e12	0.718915	0.359458	+	0.933161i	$0.382962\pi$
$200$	−3.92788e11	−0.0867947
$201$	−1.27191e12	−0.273449
$202$	3.95952e10	0.00828342
$203$	−1.25416e12	−0.255343
$204$	−6.53928e12	−1.29588
$205$	−3.48797e12	−0.672862
$206$	−2.64297e12	−0.496390
$207$	1.77734e13	3.25038
$208$	2.38238e12	0.424289
$209$	−1.32957e12	−0.230625
$210$	−7.74203e12	−1.30812
$211$	4.52814e12	0.745360	0.372680	−	0.927960i	$-0.378439\pi$
$211$	4.52814e12	0.745360	0.372680	+	0.927960i	$0.378439\pi$
$212$	−2.71160e11	−0.0434890
$213$	6.38285e12	0.997532
$214$	−3.26023e12	−0.496560
$215$	9.34490e12	1.38728
$216$	−1.96776e13	−2.84758
$217$	−4.68559e12	−0.661053
$218$	6.65841e12	0.915925
$219$	1.65839e13	2.22456
$220$	−9.59309e11	−0.125497
$221$	−1.23243e13	−1.57256
$222$	1.12061e13	1.39480
$223$	−1.19134e13	−1.44664	−0.723319	−	0.690514i	$-0.757384\pi$
$223$	−1.19134e13	−1.44664	−0.723319	+	0.690514i	$0.757384\pi$
$224$	1.20236e13	1.42453
$225$	−2.20044e12	−0.254393
$226$	−4.02859e11	−0.0454524
$227$	1.51576e13	1.66913	0.834564	−	0.550912i	$-0.185720\pi$
$227$	1.51576e13	1.66913	0.834564	+	0.550912i	$0.185720\pi$
$228$	−1.63513e13	−1.75756
$229$	−9.21835e12	−0.967293	−0.483646	−	0.875264i	$-0.660688\pi$
$229$	−9.21835e12	−0.967293	−0.483646	+	0.875264i	$0.660688\pi$
$230$	−5.96417e12	−0.611008
$231$	4.77654e12	0.477802
$232$	1.71826e12	0.167843
$233$	1.81932e11	0.0173561	0.00867804	−	0.999962i	$-0.497238\pi$
$233$	1.81932e11	0.0173561	0.00867804	+	0.999962i	$0.497238\pi$
$234$	−2.50509e13	−2.33419
$235$	−7.03302e12	−0.640131
$236$	7.15169e12	0.635905
$237$	2.67771e13	2.32620
$238$	−7.93197e12	−0.673298
$239$	6.71911e12	0.557344	0.278672	−	0.960386i	$-0.410106\pi$
$239$	6.71911e12	0.557344	0.278672	+	0.960386i	$0.410106\pi$
$240$	−5.65107e12	−0.458109
$241$	7.28547e12	0.577250	0.288625	−	0.957442i	$-0.406802\pi$
$241$	7.28547e12	0.577250	0.288625	+	0.957442i	$0.406802\pi$
$242$	6.53915e12	0.506451
$243$	−4.33939e13	−3.28545
$244$	−2.11285e12	−0.156396
$245$	1.17023e13	0.846947
$246$	−1.00055e13	−0.708104
$247$	−3.08166e13	−2.13281
$248$	6.41950e12	0.434527
$249$	3.86321e12	0.255771
$250$	8.42788e12	0.545819
$251$	−1.88972e13	−1.19727	−0.598634	−	0.801023i	$-0.704290\pi$
$251$	−1.88972e13	−1.19727	−0.598634	+	0.801023i	$0.704290\pi$
$252$	4.26452e13	2.64343
$253$	3.67967e12	0.223175
$254$	7.65518e12	0.454328
$255$	2.92337e13	1.69790
$256$	−1.32531e13	−0.753352
$257$	−3.10860e13	−1.72955	−0.864773	−	0.502163i	$-0.832538\pi$
$257$	−3.10860e13	−1.72955	−0.864773	+	0.502163i	$0.832538\pi$
$258$	2.68066e13	1.45994
$259$	−3.59529e13	−1.91684
$260$	−2.22347e13	−1.16059
$261$	9.62585e12	0.491945
$262$	2.83749e12	0.141996
$263$	−1.64154e12	−0.0804440	−0.0402220	−	0.999191i	$-0.512807\pi$
$263$	−1.64154e12	−0.0804440	−0.0402220	+	0.999191i	$0.512807\pi$
$264$	−6.54410e12	−0.314071
$265$	1.21222e12	0.0569807
$266$	−1.98336e13	−0.913173
$267$	2.44284e13	1.10175
$268$	−2.35098e12	−0.103874
$269$	−4.31521e13	−1.86794	−0.933972	−	0.357346i	$-0.883682\pi$
$269$	−4.31521e13	−1.86794	−0.933972	+	0.357346i	$0.883682\pi$
$270$	3.69914e13	1.56892
$271$	−2.74015e12	−0.113879	−0.0569395	−	0.998378i	$-0.518134\pi$
$271$	−2.74015e12	−0.113879	−0.0569395	+	0.998378i	$0.518134\pi$
$272$	−5.78970e12	−0.235791
$273$	1.10710e14	4.41867
$274$	−2.72869e11	−0.0106740
$275$	−4.55561e11	−0.0174669
$276$	4.52530e13	1.70078
$277$	1.99734e13	0.735892	0.367946	−	0.929847i	$-0.380061\pi$
$277$	1.99734e13	0.735892	0.367946	+	0.929847i	$0.380061\pi$
$278$	3.06840e12	0.110832
$279$	3.59627e13	1.27359
$280$	−3.40308e13	−1.18169
$281$	−5.50393e13	−1.87408	−0.937040	−	0.349221i	$-0.886446\pi$
$281$	−5.50393e13	−1.87408	−0.937040	+	0.349221i	$0.886446\pi$
$282$	−2.01748e13	−0.673658
$283$	7.72019e12	0.252815	0.126407	−	0.991978i	$-0.459655\pi$
$283$	7.72019e12	0.252815	0.126407	+	0.991978i	$0.459655\pi$
$284$	1.17980e13	0.378928
$285$	7.30979e13	2.30281
$286$	−5.18632e12	−0.160268
$287$	3.21012e13	0.973130
$288$	−9.22834e13	−2.74451
$289$	−4.32102e12	−0.126081
$290$	−3.23011e12	−0.0924759
$291$	2.34874e13	0.659818
$292$	3.06535e13	0.845035
$293$	1.62367e13	0.439264	0.219632	−	0.975583i	$-0.429514\pi$
$293$	1.62367e13	0.439264	0.219632	+	0.975583i	$0.429514\pi$
$294$	3.35689e13	0.891306
$295$	−3.19714e13	−0.833184
$296$	4.92573e13	1.25999
$297$	−2.28223e13	−0.573059
$298$	−2.47823e13	−0.610874
$299$	8.52867e13	2.06391
$300$	−5.60255e12	−0.133112
$301$	−8.60049e13	−2.00635
$302$	9.90294e12	0.226843
$303$	1.34306e12	0.0302106
$304$	−1.44770e13	−0.319796
$305$	9.44545e12	0.204915
$306$	6.08791e13	1.29718
$307$	4.14278e13	0.867024	0.433512	−	0.901148i	$-0.357274\pi$
$307$	4.14278e13	0.867024	0.433512	+	0.901148i	$0.357274\pi$
$308$	8.82891e12	0.181501
$309$	−8.96488e13	−1.81039
$310$	−1.20679e13	−0.239409
$311$	−6.13636e13	−1.19599	−0.597996	−	0.801499i	$-0.704036\pi$
$311$	−6.13636e13	−1.19599	−0.597996	+	0.801499i	$0.704036\pi$
$312$	−1.51678e14	−2.90451
$313$	−4.27555e13	−0.804448	−0.402224	−	0.915541i	$-0.631763\pi$
$313$	−4.27555e13	−0.804448	−0.402224	+	0.915541i	$0.631763\pi$
$314$	4.58413e12	0.0847508
$315$	−1.90644e14	−3.46350
$316$	4.94945e13	0.883645
$317$	−8.82253e13	−1.54799	−0.773993	−	0.633194i	$-0.781744\pi$
$317$	−8.82253e13	−1.54799	−0.773993	+	0.633194i	$0.781744\pi$
$318$	3.47734e12	0.0599650
$319$	1.99286e12	0.0337775
$320$	1.65728e13	0.276102
$321$	−1.10586e14	−1.81101
$322$	5.48907e13	0.883672
$323$	7.48912e13	1.18527
$324$	−1.57122e14	−2.44478
$325$	−1.05589e13	−0.161533
$326$	1.52218e13	0.228964
$327$	2.25851e14	3.34048
$328$	−4.39803e13	−0.639664
$329$	6.47278e13	0.925792
$330$	1.23021e13	0.173042
$331$	−3.28413e13	−0.454325	−0.227163	−	0.973857i	$-0.572945\pi$
$331$	−3.28413e13	−0.454325	−0.227163	+	0.973857i	$0.572945\pi$
$332$	7.14071e12	0.0971588
$333$	2.75945e14	3.69299
$334$	7.40096e12	0.0974277
$335$	1.05100e13	0.136099
$336$	5.20091e13	0.662541
$337$	−9.63718e13	−1.20777	−0.603887	−	0.797070i	$-0.706382\pi$
$337$	−9.63718e13	−1.20777	−0.603887	+	0.797070i	$0.706382\pi$
$338$	−7.77271e13	−0.958364
$339$	−1.36648e13	−0.165770
$340$	5.40352e13	0.644975
$341$	7.44542e12	0.0874460
$342$	1.52226e14	1.75932
$343$	1.32031e13	0.150162
$344$	1.17831e14	1.31883
$345$	−2.02303e14	−2.22842
$346$	−2.18573e13	−0.236962
$347$	5.46073e12	0.0582691	0.0291346	−	0.999575i	$-0.490725\pi$
$347$	5.46073e12	0.0582691	0.0291346	+	0.999575i	$0.490725\pi$
$348$	2.45084e13	0.257412
$349$	1.74524e14	1.80433	0.902163	−	0.431395i	$-0.141979\pi$
$349$	1.74524e14	1.80433	0.902163	+	0.431395i	$0.141979\pi$
$350$	−6.79573e12	−0.0691611
$351$	−5.28972e14	−5.29961
$352$	−1.91056e13	−0.188441
$353$	1.76562e14	1.71449	0.857246	−	0.514908i	$-0.172174\pi$
$353$	1.76562e14	1.71449	0.857246	+	0.514908i	$0.172174\pi$
$354$	−9.17127e13	−0.876822
$355$	−5.27426e13	−0.496484
$356$	4.51532e13	0.418517
$357$	−2.69050e14	−2.45560
$358$	9.10551e12	0.0818366
$359$	1.66347e14	1.47230	0.736149	−	0.676820i	$-0.236642\pi$
$359$	1.66347e14	1.47230	0.736149	+	0.676820i	$0.236642\pi$
$360$	2.61192e14	2.27665
$361$	7.07726e13	0.607541
$362$	8.70215e12	0.0735748
$363$	2.21806e14	1.84708
$364$	2.04635e14	1.67850
$365$	−1.37036e14	−1.10719
$366$	2.70951e13	0.215647
$367$	−1.94799e14	−1.52730	−0.763648	−	0.645632i	$-0.776594\pi$
$367$	−1.94799e14	−1.52730	−0.763648	+	0.645632i	$0.776594\pi$
$368$	4.00658e13	0.309465
$369$	−2.46382e14	−1.87484
$370$	−9.25977e13	−0.694210
$371$	−1.11565e13	−0.0824085
$372$	9.15648e13	0.666411
$373$	−1.50997e14	−1.08286	−0.541428	−	0.840747i	$-0.682116\pi$
$373$	−1.50997e14	−1.08286	−0.541428	+	0.840747i	$0.682116\pi$
$374$	1.26039e13	0.0890659
$375$	2.85871e14	1.99066
$376$	−8.86803e13	−0.608547
$377$	4.61901e13	0.312372
$378$	−3.40447e14	−2.26905
$379$	−1.39626e14	−0.917173	−0.458586	−	0.888650i	$-0.651644\pi$
$379$	−1.39626e14	−0.917173	−0.458586	+	0.888650i	$0.651644\pi$
$380$	1.35113e14	0.874759
$381$	2.59661e14	1.65699
$382$	5.37994e12	0.0338399
$383$	6.01897e13	0.373189	0.186595	−	0.982437i	$-0.440255\pi$
$383$	6.01897e13	0.373189	0.186595	+	0.982437i	$0.440255\pi$
$384$	−2.76255e14	−1.68845
$385$	−3.94694e13	−0.237808
$386$	−3.58768e13	−0.213100
$387$	6.60102e14	3.86545
$388$	4.34139e13	0.250642
$389$	−2.30214e14	−1.31042	−0.655208	−	0.755449i	$-0.727419\pi$
$389$	−2.30214e14	−1.31042	−0.655208	+	0.755449i	$0.727419\pi$
$390$	2.85136e14	1.60028
$391$	−2.07266e14	−1.14698
$392$	1.47555e14	0.805159
$393$	9.62466e13	0.517876
$394$	1.75056e14	0.928856
$395$	−2.21264e14	−1.15778
$396$	−6.77633e13	−0.349680
$397$	2.16304e14	1.10082	0.550411	−	0.834894i	$-0.314471\pi$
$397$	2.16304e14	1.10082	0.550411	+	0.834894i	$0.314471\pi$
$398$	−7.50212e13	−0.376554
$399$	−6.72749e14	−3.33045
$400$	−4.96034e12	−0.0242204
$401$	2.59235e14	1.24853	0.624265	−	0.781212i	$-0.285398\pi$
$401$	2.59235e14	1.24853	0.624265	+	0.781212i	$0.285398\pi$
$402$	3.01488e13	0.143228
$403$	1.72569e14	0.808694
$404$	2.48249e12	0.0114760
$405$	7.02410e14	3.20323
$406$	2.97280e13	0.133744
$407$	5.71293e13	0.253565
$408$	3.68611e14	1.61413
$409$	1.21534e14	0.525071	0.262536	−	0.964922i	$-0.415441\pi$
$409$	1.21534e14	0.525071	0.262536	+	0.964922i	$0.415441\pi$
$410$	8.26774e13	0.352432
$411$	−9.25563e12	−0.0389292
$412$	−1.65706e14	−0.687706
$413$	2.94246e14	1.20500
$414$	−4.21295e14	−1.70249
$415$	−3.19224e13	−0.127301
$416$	−4.42826e14	−1.74269
$417$	1.04079e14	0.404217
$418$	3.15157e13	0.120797
$419$	−3.00046e14	−1.13504	−0.567519	−	0.823360i	$-0.692097\pi$
$419$	−3.00046e14	−1.13504	−0.567519	+	0.823360i	$0.692097\pi$
$420$	−4.85400e14	−1.81229
$421$	−6.52194e11	−0.00240340	−0.00120170	−	0.999999i	$-0.500383\pi$
$421$	−6.52194e11	−0.00240340	−0.00120170	+	0.999999i	$0.500383\pi$
$422$	−1.07333e14	−0.390405
$423$	−4.96796e14	−1.78364
$424$	1.52850e13	0.0541693
$425$	2.56605e13	0.0897689
$426$	−1.51297e14	−0.522488
$427$	−8.69303e13	−0.296359
$428$	−2.04405e14	−0.687942
$429$	−1.75918e14	−0.584515
$430$	−2.21508e14	−0.726629
$431$	−7.67212e12	−0.0248479	−0.0124240	−	0.999923i	$-0.503955\pi$
$431$	−7.67212e12	−0.0248479	−0.0124240	+	0.999923i	$0.503955\pi$
$432$	−2.48499e14	−0.794630
$433$	−3.59957e14	−1.13649	−0.568247	−	0.822858i	$-0.692378\pi$
$433$	−3.59957e14	−1.13649	−0.568247	+	0.822858i	$0.692378\pi$
$434$	1.11065e14	0.346247
$435$	−1.09564e14	−0.337270
$436$	4.17460e14	1.26894
$437$	−5.18261e14	−1.55561
$438$	−3.93099e14	−1.16518
$439$	−1.45149e13	−0.0424872	−0.0212436	−	0.999774i	$-0.506763\pi$
$439$	−1.45149e13	−0.0424872	−0.0212436	+	0.999774i	$0.506763\pi$
$440$	5.40751e13	0.156317
$441$	8.26620e14	2.35990
$442$	2.92131e14	0.823675
$443$	1.97208e14	0.549166	0.274583	−	0.961563i	$-0.411460\pi$
$443$	1.97208e14	0.549166	0.274583	+	0.961563i	$0.411460\pi$
$444$	7.02584e14	1.93238
$445$	−2.01856e14	−0.548355
$446$	2.82391e14	0.757721
$447$	−8.40606e14	−2.22793
$448$	−1.52526e14	−0.399314
$449$	3.49615e14	0.904138	0.452069	−	0.891983i	$-0.350686\pi$
$449$	3.49615e14	0.904138	0.452069	+	0.891983i	$0.350686\pi$
$450$	5.21583e13	0.133246
$451$	−5.10089e13	−0.128729
$452$	−2.52579e13	−0.0629704
$453$	3.35904e14	0.827323
$454$	−3.59291e14	−0.874257
$455$	−9.14816e14	−2.19923
$456$	9.21700e14	2.18919
$457$	7.08412e14	1.66244	0.831222	−	0.555940i	$-0.187642\pi$
$457$	7.08412e14	1.66244	0.831222	+	0.555940i	$0.187642\pi$
$458$	2.18508e14	0.506649
$459$	1.28552e15	2.94516
$460$	−3.73934e14	−0.846499
$461$	9.39784e13	0.210220	0.105110	−	0.994461i	$-0.466481\pi$
$461$	9.39784e13	0.210220	0.105110	+	0.994461i	$0.466481\pi$
$462$	−1.13221e14	−0.250263
$463$	−2.32182e14	−0.507146	−0.253573	−	0.967316i	$-0.581606\pi$
$463$	−2.32182e14	−0.507146	−0.253573	+	0.967316i	$0.581606\pi$
$464$	2.16991e13	0.0468374
$465$	−4.09338e14	−0.873154
$466$	−4.31245e12	−0.00909078
$467$	3.22971e14	0.672855	0.336427	−	0.941709i	$-0.390781\pi$
$467$	3.22971e14	0.672855	0.336427	+	0.941709i	$0.390781\pi$
$468$	−1.57061e15	−3.23382
$469$	−9.67277e13	−0.196834
$470$	1.66708e14	0.335288
$471$	1.55492e14	0.309096
$472$	−4.03132e14	−0.792075
$473$	1.36662e14	0.265407
$474$	−6.34714e14	−1.21842
$475$	6.41632e13	0.121751
$476$	−4.97308e14	−0.932798
$477$	8.56280e13	0.158769
$478$	−1.59267e14	−0.291926
$479$	−1.04417e15	−1.89202	−0.946008	−	0.324142i	$-0.894924\pi$
$479$	−1.04417e15	−1.89202	−0.946008	+	0.324142i	$0.894924\pi$
$480$	1.05040e15	1.88160
$481$	1.32413e15	2.34495
$482$	−1.72692e14	−0.302352
$483$	1.86187e15	3.22285
$484$	4.09984e14	0.701644
$485$	−1.94081e14	−0.328400
$486$	1.02859e15	1.72085
$487$	−8.32567e14	−1.37724	−0.688620	−	0.725122i	$-0.741783\pi$
$487$	−8.32567e14	−1.37724	−0.688620	+	0.725122i	$0.741783\pi$
$488$	1.19099e14	0.194804
$489$	5.16317e14	0.835060
$490$	−2.77386e14	−0.443615
$491$	−8.03776e14	−1.27112	−0.635560	−	0.772051i	$-0.719231\pi$
$491$	−8.03776e14	−1.27112	−0.635560	+	0.772051i	$0.719231\pi$
$492$	−6.27314e14	−0.981018
$493$	−1.12252e14	−0.173595
$494$	7.30465e14	1.11712
$495$	3.02934e14	0.458162
$496$	8.10690e13	0.121257
$497$	4.85412e14	0.718042
$498$	−9.15720e13	−0.133968
$499$	−4.84727e13	−0.0701365	−0.0350682	−	0.999385i	$-0.511165\pi$
$499$	−4.84727e13	−0.0701365	−0.0350682	+	0.999385i	$0.511165\pi$
$500$	5.28401e14	0.756185
$501$	2.51038e14	0.355330
$502$	4.47931e14	0.627106
$503$	−7.87706e13	−0.109079	−0.0545394	−	0.998512i	$-0.517369\pi$
$503$	−7.87706e13	−0.109079	−0.0545394	+	0.998512i	$0.517369\pi$
$504$	−2.40386e15	−3.29261
$505$	−1.10979e13	−0.0150362
$506$	−8.72214e13	−0.116895
$507$	−2.63648e15	−3.49526
$508$	4.79954e14	0.629433
$509$	−1.16339e15	−1.50931	−0.754654	−	0.656123i	$-0.772195\pi$
$509$	−1.16339e15	−1.50931	−0.754654	+	0.656123i	$0.772195\pi$
$510$	−6.92944e14	−0.889328
$511$	1.26120e15	1.60128
$512$	−3.89531e14	−0.489280
$513$	3.21440e15	3.99442
$514$	7.36849e14	0.905903
$515$	7.40784e14	0.901056
$516$	1.68069e15	2.02262
$517$	−1.02853e14	−0.122466
$518$	8.52215e14	1.00400
$519$	−7.41392e14	−0.864226
$520$	1.25334e15	1.44561
$521$	3.02892e14	0.345684	0.172842	−	0.984950i	$-0.444705\pi$
$521$	3.02892e14	0.345684	0.172842	+	0.984950i	$0.444705\pi$
$522$	−2.28167e14	−0.257671
$523$	−9.73299e14	−1.08764	−0.543822	−	0.839200i	$-0.683023\pi$
$523$	−9.73299e14	−1.08764	−0.543822	+	0.839200i	$0.683023\pi$
$524$	1.77901e14	0.196724
$525$	−2.30509e14	−0.252239
$526$	3.89103e13	0.0421350
$527$	−4.19380e14	−0.449417
$528$	−8.26425e13	−0.0876430
$529$	4.81506e14	0.505354
$530$	−2.87339e13	−0.0298454
$531$	−2.25839e15	−2.32155
$532$	−1.24350e15	−1.26512
$533$	−1.18228e15	−1.19047
$534$	−5.79041e14	−0.577075
$535$	9.13789e14	0.901364
$536$	1.32522e14	0.129384
$537$	3.08856e14	0.298468
$538$	1.02286e15	0.978393
$539$	1.71137e14	0.162033
$540$	2.31924e15	2.17360
$541$	−6.67127e14	−0.618905	−0.309452	−	0.950915i	$-0.600146\pi$
$541$	−6.67127e14	−0.618905	−0.309452	+	0.950915i	$0.600146\pi$
$542$	6.49516e13	0.0596477
$543$	2.95174e14	0.268336
$544$	1.07617e15	0.968468
$545$	−1.86625e15	−1.66260
$546$	−2.62422e15	−2.31442
$547$	1.44083e15	1.25801	0.629005	−	0.777402i	$-0.283463\pi$
$547$	1.44083e15	1.25801	0.629005	+	0.777402i	$0.283463\pi$
$548$	−1.71080e13	−0.0147879
$549$	6.67204e14	0.570967
$550$	1.07984e13	0.00914884
$551$	−2.80683e14	−0.235441
$552$	−2.55086e15	−2.11847
$553$	2.03638e15	1.67445
$554$	−4.73443e14	−0.385446
$555$	−3.14088e15	−2.53186
$556$	1.92379e14	0.153548
$557$	7.07734e14	0.559328	0.279664	−	0.960098i	$-0.409777\pi$
$557$	7.07734e14	0.559328	0.279664	+	0.960098i	$0.409777\pi$
$558$	−8.52445e14	−0.667081
$559$	3.16753e15	2.45446
$560$	−4.29760e14	−0.329755
$561$	4.27520e14	0.324834
$562$	1.30463e15	0.981607
$563$	1.93114e14	0.143886	0.0719428	−	0.997409i	$-0.477080\pi$
$563$	1.93114e14	0.143886	0.0719428	+	0.997409i	$0.477080\pi$
$564$	−1.26489e15	−0.933296
$565$	1.12915e14	0.0825059
$566$	−1.82996e14	−0.132420
$567$	−6.46457e15	−4.63268
$568$	−6.65038e14	−0.471988
$569$	1.78850e13	0.0125711	0.00628554	−	0.999980i	$-0.497999\pi$
$569$	1.78850e13	0.0125711	0.00628554	+	0.999980i	$0.497999\pi$
$570$	−1.73268e15	−1.20617
$571$	−2.69139e15	−1.85557	−0.927786	−	0.373112i	$-0.878291\pi$
$571$	−2.69139e15	−1.85557	−0.927786	+	0.373112i	$0.878291\pi$
$572$	−3.25166e14	−0.222038
$573$	1.82486e14	0.123418
$574$	−7.60914e14	−0.509707
$575$	−1.77575e14	−0.117817
$576$	1.17066e15	0.769321
$577$	−8.36258e14	−0.544344	−0.272172	−	0.962249i	$-0.587742\pi$
$577$	−8.36258e14	−0.544344	−0.272172	+	0.962249i	$0.587742\pi$
$578$	1.02424e14	0.0660386
$579$	−1.21693e15	−0.777200
$580$	−2.02517e14	−0.128117
$581$	2.93795e14	0.184109
$582$	−5.56737e14	−0.345600
$583$	1.77277e13	0.0109012
$584$	−1.72790e15	−1.05256
$585$	7.02136e15	4.23705
$586$	−3.84868e14	−0.230078
$587$	7.39762e14	0.438109	0.219055	−	0.975713i	$-0.429703\pi$
$587$	7.39762e14	0.438109	0.219055	+	0.975713i	$0.429703\pi$
$588$	2.10466e15	1.23483
$589$	−1.04865e15	−0.609530
$590$	7.57838e14	0.436406
$591$	5.93785e15	3.38765
$592$	6.22049e14	0.351605
$593$	−2.54616e15	−1.42588	−0.712942	−	0.701223i	$-0.752638\pi$
$593$	−2.54616e15	−1.42588	−0.712942	+	0.701223i	$0.752638\pi$
$594$	5.40971e14	0.300157
$595$	2.22320e15	1.22218
$596$	−1.55377e15	−0.846314
$597$	−2.54469e15	−1.37334
$598$	−2.02160e15	−1.08103
$599$	3.54163e15	1.87653	0.938265	−	0.345917i	$-0.112432\pi$
$599$	3.54163e15	1.87653	0.938265	+	0.345917i	$0.112432\pi$
$600$	3.15809e14	0.165803
$601$	2.88090e15	1.49871	0.749357	−	0.662166i	$-0.230363\pi$
$601$	2.88090e15	1.49871	0.749357	+	0.662166i	$0.230363\pi$
$602$	2.03863e15	1.05089
$603$	7.42401e14	0.379222
$604$	6.20882e14	0.314272
$605$	−1.83282e15	−0.919317
$606$	−3.18353e13	−0.0158237
$607$	1.11481e15	0.549116	0.274558	−	0.961571i	$-0.411468\pi$
$607$	1.11481e15	0.549116	0.274558	+	0.961571i	$0.411468\pi$
$608$	2.69092e15	1.31350
$609$	1.00836e15	0.487778
$610$	−2.23891e14	−0.107330
$611$	−2.38390e15	−1.13256
$612$	3.81692e15	1.79713
$613$	3.23230e14	0.150827	0.0754136	−	0.997152i	$-0.475972\pi$
$613$	3.23230e14	0.150827	0.0754136	+	0.997152i	$0.475972\pi$
$614$	−9.81990e14	−0.454131
$615$	2.80439e15	1.28536
$616$	−4.97675e14	−0.226075
$617$	3.72116e15	1.67537	0.837684	−	0.546156i	$-0.183909\pi$
$617$	3.72116e15	1.67537	0.837684	+	0.546156i	$0.183909\pi$
$618$	2.12500e15	0.948249
$619$	−2.61579e15	−1.15692	−0.578461	−	0.815710i	$-0.696347\pi$
$619$	−2.61579e15	−1.15692	−0.578461	+	0.815710i	$0.696347\pi$
$620$	−7.56616e14	−0.331681
$621$	−8.89603e15	−3.86538
$622$	1.45454e15	0.626438
$623$	1.85776e15	0.793060
$624$	−1.91548e15	−0.810515
$625$	−2.13326e15	−0.894753
$626$	1.01346e15	0.421354
$627$	1.06900e15	0.440561
$628$	2.87410e14	0.117415
$629$	−3.21794e15	−1.30316
$630$	4.51896e15	1.81412
$631$	−3.66804e15	−1.45973	−0.729864	−	0.683592i	$-0.760417\pi$
$631$	−3.66804e15	−1.45973	−0.729864	+	0.683592i	$0.760417\pi$
$632$	−2.78995e15	−1.10066
$633$	−3.64070e15	−1.42385
$634$	2.09126e15	0.810805
$635$	−2.14562e15	−0.824704
$636$	2.18018e14	0.0830765
$637$	3.96658e15	1.49847
$638$	−4.72379e13	−0.0176920
$639$	−3.72561e15	−1.38338
$640$	2.28274e15	0.840363
$641$	1.27860e15	0.466676	0.233338	−	0.972396i	$-0.425035\pi$
$641$	1.27860e15	0.466676	0.233338	+	0.972396i	$0.425035\pi$
$642$	2.62128e15	0.948573
$643$	−1.13237e15	−0.406281	−0.203140	−	0.979150i	$-0.565115\pi$
$643$	−1.13237e15	−0.406281	−0.203140	+	0.979150i	$0.565115\pi$
$644$	3.44147e15	1.22425
$645$	−7.51347e15	−2.65010
$646$	−1.77519e15	−0.620821
$647$	4.36102e15	1.51222	0.756109	−	0.654445i	$-0.227098\pi$
$647$	4.36102e15	1.51222	0.756109	+	0.654445i	$0.227098\pi$
$648$	8.85678e15	3.04518
$649$	−4.67558e14	−0.159400
$650$	2.50284e14	0.0846078
$651$	3.76730e15	1.26280
$652$	9.54355e14	0.317211
$653$	2.45898e13	0.00810460	0.00405230	−	0.999992i	$-0.498710\pi$
$653$	2.45898e13	0.00810460	0.00405230	+	0.999992i	$0.498710\pi$
$654$	−5.35348e15	−1.74968
$655$	−7.95302e14	−0.257754
$656$	−5.55407e14	−0.178501
$657$	−9.67988e15	−3.08504
$658$	−1.53428e15	−0.484912
$659$	−5.68040e15	−1.78037	−0.890183	−	0.455603i	$-0.849424\pi$
$659$	−5.68040e15	−1.78037	−0.890183	+	0.455603i	$0.849424\pi$
$660$	7.71302e14	0.239736
$661$	−1.05643e15	−0.325637	−0.162818	−	0.986656i	$-0.552058\pi$
$661$	−1.05643e15	−0.325637	−0.162818	+	0.986656i	$0.552058\pi$
$662$	7.78458e14	0.237967
$663$	9.90900e15	3.00404
$664$	−4.02513e14	−0.121020
$665$	5.55905e15	1.65761
$666$	−6.54088e15	−1.93432
$667$	7.76806e14	0.227835
$668$	4.64016e14	0.134978
$669$	9.57861e15	2.76350
$670$	−2.49125e14	−0.0712862
$671$	1.38132e14	0.0392032
$672$	−9.66723e15	−2.72127
$673$	−4.89396e15	−1.36640	−0.683200	−	0.730231i	$-0.739412\pi$
$673$	−4.89396e15	−1.36640	−0.683200	+	0.730231i	$0.739412\pi$
$674$	2.28436e15	0.632609
$675$	1.10137e15	0.302526
$676$	−4.87323e15	−1.32773
$677$	−5.87421e14	−0.158749	−0.0793746	−	0.996845i	$-0.525292\pi$
$677$	−5.87421e14	−0.158749	−0.0793746	+	0.996845i	$0.525292\pi$
$678$	3.23906e14	0.0868271
$679$	1.78620e15	0.474950
$680$	−3.04590e15	−0.803372
$681$	−1.21870e16	−3.18851
$682$	−1.76483e14	−0.0458025
$683$	2.10799e15	0.542694	0.271347	−	0.962482i	$-0.412531\pi$
$683$	2.10799e15	0.542694	0.271347	+	0.962482i	$0.412531\pi$
$684$	9.54408e15	2.43739
$685$	7.64809e13	0.0193756
$686$	−3.12962e14	−0.0786519
$687$	7.41172e15	1.84781
$688$	1.48804e15	0.368025
$689$	4.10890e14	0.100814
$690$	4.79530e15	1.16720
$691$	−9.03002e14	−0.218052	−0.109026	−	0.994039i	$-0.534773\pi$
$691$	−9.03002e14	−0.218052	−0.109026	+	0.994039i	$0.534773\pi$
$692$	−1.37038e15	−0.328290
$693$	−2.78803e15	−0.662619
$694$	−1.29439e14	−0.0305203
$695$	−8.60023e14	−0.201184
$696$	−1.38151e15	−0.320629
$697$	2.87319e15	0.661583
$698$	−4.13685e15	−0.945071
$699$	−1.46277e14	−0.0331551
$700$	−4.26070e14	−0.0958168
$701$	8.20073e15	1.82980	0.914900	−	0.403681i	$-0.132269\pi$
$701$	8.20073e15	1.82980	0.914900	+	0.403681i	$0.132269\pi$
$702$	1.25385e16	2.77583
$703$	−8.04634e15	−1.76744
$704$	2.42364e14	0.0528225
$705$	5.65468e15	1.22283
$706$	−4.18515e15	−0.898018
$707$	1.02139e14	0.0217462
$708$	−5.75009e15	−1.21476
$709$	−3.41692e15	−0.716277	−0.358139	−	0.933668i	$-0.616588\pi$
$709$	−3.41692e15	−0.716277	−0.358139	+	0.933668i	$0.616588\pi$
$710$	1.25019e15	0.260049
$711$	−1.56296e16	−3.22600
$712$	−2.54523e15	−0.521299
$713$	2.90219e15	0.589838
$714$	6.37745e15	1.28619
$715$	1.45364e15	0.290921
$716$	5.70886e14	0.113378
$717$	−5.40228e15	−1.06469
$718$	−3.94303e15	−0.771161
$719$	4.14792e15	0.805048	0.402524	−	0.915409i	$-0.368133\pi$
$719$	4.14792e15	0.805048	0.402524	+	0.915409i	$0.368133\pi$
$720$	3.29848e15	0.635309
$721$	−6.81773e15	−1.30315
$722$	−1.67757e15	−0.318218
$723$	−5.85765e15	−1.10271
$724$	5.45596e14	0.101932
$725$	−9.61723e13	−0.0178316
$726$	−5.25760e15	−0.967467
$727$	8.28661e14	0.151334	0.0756672	−	0.997133i	$-0.475891\pi$
$727$	8.28661e14	0.151334	0.0756672	+	0.997133i	$0.475891\pi$
$728$	−1.15350e16	−2.09072
$729$	1.61606e16	2.90708
$730$	3.24824e15	0.579926
$731$	−7.69780e15	−1.36402
$732$	1.69877e15	0.298761
$733$	2.10145e15	0.366815	0.183408	−	0.983037i	$-0.441287\pi$
$733$	2.10145e15	0.366815	0.183408	+	0.983037i	$0.441287\pi$
$734$	4.61744e15	0.799969
$735$	−9.40883e15	−1.61791
$736$	−7.44727e15	−1.27107
$737$	1.53701e14	0.0260378
$738$	5.84014e15	0.982004
$739$	2.96614e15	0.495049	0.247524	−	0.968882i	$-0.420383\pi$
$739$	2.96614e15	0.495049	0.247524	+	0.968882i	$0.420383\pi$
$740$	−5.80557e15	−0.961769
$741$	2.47771e16	4.07428
$742$	2.64450e14	0.0431640
$743$	7.23073e15	1.17150	0.585751	−	0.810491i	$-0.300799\pi$
$743$	7.23073e15	1.17150	0.585751	+	0.810491i	$0.300799\pi$
$744$	−5.16139e15	−0.830072
$745$	6.94607e15	1.10887
$746$	3.57918e15	0.567179
$747$	−2.25492e15	−0.354705
$748$	7.90224e14	0.123393
$749$	−8.40998e15	−1.30360
$750$	−6.77617e15	−1.04267
$751$	−2.89034e15	−0.441499	−0.220749	−	0.975331i	$-0.570850\pi$
$751$	−2.89034e15	−0.441499	−0.220749	+	0.975331i	$0.570850\pi$
$752$	−1.11990e15	−0.169818
$753$	1.51937e16	2.28713
$754$	−1.09487e15	−0.163614
$755$	−2.77564e15	−0.411770
$756$	−2.13449e16	−3.14358
$757$	1.13817e15	0.166410	0.0832048	−	0.996532i	$-0.473484\pi$
$757$	1.13817e15	0.166410	0.0832048	+	0.996532i	$0.473484\pi$
$758$	3.30964e15	0.480397
$759$	−2.95852e15	−0.426329
$760$	−7.61617e15	−1.08959
$761$	9.58101e15	1.36080	0.680402	−	0.732839i	$-0.261805\pi$
$761$	9.58101e15	1.36080	0.680402	+	0.732839i	$0.261805\pi$
$762$	−6.15490e15	−0.867898
$763$	1.71758e16	2.40454
$764$	3.37305e14	0.0468823
$765$	−1.70634e16	−2.35466
$766$	−1.42671e15	−0.195469
$767$	−1.08370e16	−1.47412
$768$	1.06557e16	1.43912
$769$	1.45157e16	1.94645	0.973223	−	0.229864i	$-0.0738280\pi$
$769$	1.45157e16	1.94645	0.973223	+	0.229864i	$0.0738280\pi$
$770$	9.35567e14	0.124559
$771$	2.49937e16	3.30393
$772$	−2.24936e15	−0.295232
$773$	−4.19629e15	−0.546862	−0.273431	−	0.961892i	$-0.588159\pi$
$773$	−4.19629e15	−0.546862	−0.273431	+	0.961892i	$0.588159\pi$
$774$	−1.56468e16	−2.02465
$775$	−3.59305e14	−0.0461640
$776$	−2.44719e15	−0.312197
$777$	2.89068e16	3.66172
$778$	5.45690e15	0.686370
$779$	7.18432e15	0.897283
$780$	1.78771e16	2.21706
$781$	−7.71320e14	−0.0949848
$782$	4.91294e15	0.600765
$783$	−4.81797e15	−0.585024
$784$	1.86341e15	0.224683
$785$	−1.28486e15	−0.153841
$786$	−2.28139e15	−0.271254
$787$	−1.22676e16	−1.44844	−0.724218	−	0.689571i	$-0.757799\pi$
$787$	−1.22676e16	−1.44844	−0.724218	+	0.689571i	$0.757799\pi$
$788$	1.09755e16	1.28685
$789$	1.31982e15	0.153671
$790$	5.24475e15	0.606424
$791$	−1.03920e15	−0.119324
$792$	3.81973e15	0.435557
$793$	3.20161e15	0.362549
$794$	−5.12719e15	−0.576589
$795$	−9.74643e14	−0.108850
$796$	−4.70359e15	−0.521684
$797$	−2.55928e15	−0.281902	−0.140951	−	0.990017i	$-0.545016\pi$
$797$	−2.55928e15	−0.281902	−0.140951	+	0.990017i	$0.545016\pi$
$798$	1.59466e16	1.74442
$799$	5.79340e15	0.629400
$800$	9.22008e14	0.0994809
$801$	−1.42586e16	−1.52791
$802$	−6.14480e15	−0.653956
$803$	−2.00404e15	−0.211822
$804$	1.89023e15	0.198430
$805$	−1.53850e16	−1.60406
$806$	−4.09050e15	−0.423578
$807$	3.46950e16	3.56831
$808$	−1.39935e14	−0.0142943
$809$	1.63176e16	1.65553	0.827767	−	0.561072i	$-0.189611\pi$
$809$	1.63176e16	1.65553	0.827767	+	0.561072i	$0.189611\pi$
$810$	−1.66497e16	−1.67779
$811$	−9.57950e15	−0.958800	−0.479400	−	0.877596i	$-0.659146\pi$
$811$	−9.57950e15	−0.958800	−0.479400	+	0.877596i	$0.659146\pi$
$812$	1.86385e15	0.185290
$813$	2.20313e15	0.217542
$814$	−1.35417e15	−0.132813
$815$	−4.26642e15	−0.415620
$816$	4.65503e15	0.450429
$817$	−1.92481e16	−1.84998
$818$	−2.88078e15	−0.275022
$819$	−6.46204e16	−6.12785
$820$	5.18361e15	0.488265
$821$	−3.68665e15	−0.344941	−0.172470	−	0.985015i	$-0.555175\pi$
$821$	−3.68665e15	−0.344941	−0.172470	+	0.985015i	$0.555175\pi$
$822$	2.19392e14	0.0203904
$823$	−8.96942e15	−0.828066	−0.414033	−	0.910262i	$-0.635880\pi$
$823$	−8.96942e15	−0.828066	−0.414033	+	0.910262i	$0.635880\pi$
$824$	9.34064e15	0.856598
$825$	3.66279e14	0.0333669
$826$	−6.97470e15	−0.631153
$827$	1.09711e16	0.986208	0.493104	−	0.869970i	$-0.335862\pi$
$827$	1.09711e16	0.986208	0.493104	+	0.869970i	$0.335862\pi$
$828$	−2.64138e16	−2.35865
$829$	−1.49044e16	−1.32210	−0.661052	−	0.750340i	$-0.729890\pi$
$829$	−1.49044e16	−1.32210	−0.661052	+	0.750340i	$0.729890\pi$
$830$	7.56675e14	0.0666776
$831$	−1.60590e16	−1.40577
$832$	5.61748e15	0.488498
$833$	−9.63966e15	−0.832749
$834$	−2.46705e15	−0.211721
$835$	−2.07437e15	−0.176852
$836$	1.97593e15	0.167354
$837$	−1.80002e16	−1.51456
$838$	7.11217e15	0.594511
$839$	5.79244e15	0.481028	0.240514	−	0.970646i	$-0.422684\pi$
$839$	5.79244e15	0.481028	0.240514	+	0.970646i	$0.422684\pi$
$840$	2.73614e16	2.25737
$841$	4.20707e14	0.0344828
$842$	1.54594e13	0.00125885
$843$	4.42526e16	3.58004
$844$	−6.72944e15	−0.540873
$845$	2.17857e16	1.73964
$846$	1.17759e16	0.934234
$847$	1.68682e16	1.32957
$848$	1.93027e14	0.0151162
$849$	−6.20717e15	−0.482949
$850$	−6.08246e14	−0.0470192
$851$	2.22687e16	1.71034
$852$	−9.48580e15	−0.723863
$853$	−5.68904e15	−0.431340	−0.215670	−	0.976466i	$-0.569194\pi$
$853$	−5.68904e15	−0.431340	−0.215670	+	0.976466i	$0.569194\pi$
$854$	2.06056e15	0.155227
$855$	−4.26666e16	−3.19355
$856$	1.15221e16	0.856891
$857$	−4.29917e15	−0.317680	−0.158840	−	0.987304i	$-0.550775\pi$
$857$	−4.29917e15	−0.317680	−0.158840	+	0.987304i	$0.550775\pi$
$858$	4.16990e15	0.306158
$859$	−2.27698e16	−1.66110	−0.830552	−	0.556941i	$-0.811975\pi$
$859$	−2.27698e16	−1.66110	−0.830552	+	0.556941i	$0.811975\pi$
$860$	−1.38878e16	−1.00668
$861$	−2.58099e16	−1.85896
$862$	1.81857e14	0.0130149
$863$	3.35556e15	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$863$	3.35556e15	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$864$	4.61900e16	3.26379
$865$	6.12625e15	0.430136
$866$	8.53227e15	0.595273
$867$	3.47418e15	0.240850
$868$	6.96344e15	0.479695
$869$	−3.23582e15	−0.221501
$870$	2.59707e15	0.176656
$871$	3.56245e15	0.240796
$872$	−2.35317e16	−1.58057
$873$	−1.37094e16	−0.915040
$874$	1.22846e16	0.814798
$875$	2.17403e16	1.43292
$876$	−2.46460e16	−1.61426
$877$	−1.29197e15	−0.0840917	−0.0420459	−	0.999116i	$-0.513388\pi$
$877$	−1.29197e15	−0.0840917	−0.0420459	+	0.999116i	$0.513388\pi$
$878$	3.44054e14	0.0222540
$879$	−1.30546e16	−0.839121
$880$	6.82890e14	0.0436210
$881$	−1.43080e16	−0.908263	−0.454132	−	0.890935i	$-0.650050\pi$
$881$	−1.43080e16	−0.908263	−0.454132	+	0.890935i	$0.650050\pi$
$882$	−1.95939e16	−1.23607
$883$	2.31801e16	1.45322	0.726609	−	0.687051i	$-0.241095\pi$
$883$	2.31801e16	1.45322	0.726609	+	0.687051i	$0.241095\pi$
$884$	1.83157e16	1.14113
$885$	2.57056e16	1.59162
$886$	−4.67454e15	−0.287643
$887$	−1.42457e16	−0.871174	−0.435587	−	0.900147i	$-0.643459\pi$
$887$	−1.42457e16	−0.871174	−0.435587	+	0.900147i	$0.643459\pi$
$888$	−3.96038e16	−2.40694
$889$	1.97471e16	1.19273
$890$	4.78472e15	0.287218
$891$	1.02722e16	0.612825
$892$	1.77050e16	1.04976
$893$	1.44862e16	0.853634
$894$	1.99254e16	1.16695
$895$	−2.55213e15	−0.148551
$896$	−2.10090e16	−1.21538
$897$	−6.85721e16	−3.94266
$898$	−8.28713e15	−0.473570
$899$	1.57178e15	0.0892719
$900$	3.27016e15	0.184601
$901$	−9.98554e14	−0.0560254
$902$	1.20909e15	0.0674255
$903$	6.91495e16	3.83272
$904$	1.42376e15	0.0784350
$905$	−2.43907e15	−0.133554
$906$	−7.96214e15	−0.433336
$907$	−9.32604e15	−0.504495	−0.252248	−	0.967663i	$-0.581170\pi$
$907$	−9.32604e15	−0.504495	−0.252248	+	0.967663i	$0.581170\pi$
$908$	−2.25264e16	−1.21121
$909$	−7.83929e14	−0.0418963
$910$	2.16844e16	1.15191
$911$	2.12964e16	1.12449	0.562245	−	0.826970i	$-0.309938\pi$
$911$	2.12964e16	1.12449	0.562245	+	0.826970i	$0.309938\pi$
$912$	1.16397e16	0.610902
$913$	−4.66840e14	−0.0243545
$914$	−1.67919e16	−0.870756
$915$	−7.59431e15	−0.391447
$916$	1.36997e16	0.701919
$917$	7.31949e15	0.372777
$918$	−3.04714e16	−1.54262
$919$	−2.59517e16	−1.30596	−0.652981	−	0.757374i	$-0.726482\pi$
$919$	−2.59517e16	−1.30596	−0.652981	+	0.757374i	$0.726482\pi$
$920$	2.10782e16	1.05439
$921$	−3.33087e16	−1.65627
$922$	−2.22763e15	−0.110109
$923$	−1.78775e16	−0.878412
$924$	−7.09860e15	−0.346719
$925$	−2.75698e15	−0.133861
$926$	5.50355e15	0.265633
$927$	5.23272e16	2.51067
$928$	−4.03334e15	−0.192376
$929$	−7.00548e15	−0.332163	−0.166082	−	0.986112i	$-0.553112\pi$
$929$	−7.00548e15	−0.332163	−0.166082	+	0.986112i	$0.553112\pi$
$930$	9.70278e15	0.457341
$931$	−2.41036e16	−1.12943
$932$	−2.70376e14	−0.0125945
$933$	4.93374e16	2.28469
$934$	−7.65559e15	−0.352428
$935$	−3.53268e15	−0.161674
$936$	8.85332e16	4.02800
$937$	7.63705e15	0.345428	0.172714	−	0.984972i	$-0.444746\pi$
$937$	7.63705e15	0.345428	0.172714	+	0.984972i	$0.444746\pi$
$938$	2.29280e15	0.103098
$939$	3.43762e16	1.53673
$940$	1.04520e16	0.464513
$941$	−1.44859e16	−0.640033	−0.320017	−	0.947412i	$-0.603689\pi$
$941$	−1.44859e16	−0.640033	−0.320017	+	0.947412i	$0.603689\pi$
$942$	−3.68572e15	−0.161899
$943$	−1.98830e16	−0.868296
$944$	−5.09097e15	−0.221032
$945$	9.54219e16	4.11882
$946$	−3.23938e15	−0.139015
$947$	−3.99797e16	−1.70575	−0.852873	−	0.522119i	$-0.825142\pi$
$947$	−3.99797e16	−1.70575	−0.852873	+	0.522119i	$0.825142\pi$
$948$	−3.97945e16	−1.68802
$949$	−4.64494e16	−1.95892
$950$	−1.52090e15	−0.0637706
$951$	7.09347e16	2.95710
$952$	2.80327e16	1.16188
$953$	9.97633e15	0.411112	0.205556	−	0.978645i	$-0.434100\pi$
$953$	9.97633e15	0.411112	0.205556	+	0.978645i	$0.434100\pi$
$954$	−2.02969e15	−0.0831600
$955$	−1.50791e15	−0.0614268
$956$	−9.98553e15	−0.404439
$957$	−1.60229e15	−0.0645247
$958$	2.47505e16	0.991002
$959$	−7.03885e14	−0.0280220
$960$	−1.33248e16	−0.527435
$961$	−1.95362e16	−0.768885
$962$	−3.13868e16	−1.22824
$963$	6.45479e16	2.51153
$964$	−1.08272e16	−0.418884
$965$	1.00557e16	0.386823
$966$	−4.41331e16	−1.68807
$967$	7.08033e15	0.269283	0.134641	−	0.990894i	$-0.457012\pi$
$967$	7.08033e15	0.269283	0.134641	+	0.990894i	$0.457012\pi$
$968$	−2.31103e16	−0.873958
$969$	−6.02139e16	−2.26420
$970$	4.60042e15	0.172010
$971$	−1.86946e15	−0.0695043	−0.0347521	−	0.999396i	$-0.511064\pi$
$971$	−1.86946e15	−0.0695043	−0.0347521	+	0.999396i	$0.511064\pi$
$972$	6.44894e16	2.38410
$973$	7.91514e15	0.290963
$974$	1.97348e16	0.721372
$975$	8.48956e15	0.308574
$976$	1.50405e15	0.0543610
$977$	−2.08248e16	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$977$	−2.08248e16	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$978$	−1.22386e16	−0.437388
$979$	−2.95199e15	−0.104908
$980$	−1.73912e16	−0.614590
$981$	−1.31827e17	−4.63261
$982$	1.90524e16	0.665789
$983$	−1.48242e16	−0.515143	−0.257571	−	0.966259i	$-0.582922\pi$
$983$	−1.48242e16	−0.515143	−0.257571	+	0.966259i	$0.582922\pi$
$984$	3.53609e16	1.22194
$985$	−4.90655e16	−1.68608
$986$	2.66078e15	0.0909256
$987$	−5.20423e16	−1.76853
$988$	4.57978e16	1.54768
$989$	5.32702e16	1.79021
$990$	−7.18063e15	−0.239977
$991$	2.21328e16	0.735584	0.367792	−	0.929908i	$-0.380114\pi$
$991$	2.21328e16	0.735584	0.367792	+	0.929908i	$0.380114\pi$
$992$	−1.50688e16	−0.498039
$993$	2.64050e16	0.867892
$994$	−1.15060e16	−0.376097
$995$	2.10273e16	0.683527
$996$	−5.74126e15	−0.185601
$997$	−5.35383e16	−1.72124	−0.860619	−	0.509249i	$-0.829923\pi$
$997$	−5.35383e16	−1.72124	−0.860619	+	0.509249i	$0.829923\pi$
$998$	1.14898e15	0.0367361
$999$	−1.38117e17	−4.39174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.5	✓	11
3.2	odd	2		261.12.a.a.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.5	✓	11	1.1	even	1	trivial
261.12.a.a.1.7		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)

\(f(q)\)	\(=\)	\(q-23.7036 q^{2} -804.018 q^{3} -1486.14 q^{4} +6643.74 q^{5} +19058.1 q^{6} -61145.1 q^{7} +83771.9 q^{8} +469298. q^{9} +O(q^{10})\)	\(q-23.7036 q^{2} -804.018 q^{3} -1486.14 q^{4} +6643.74 q^{5} +19058.1 q^{6} -61145.1 q^{7} +83771.9 q^{8} +469298. q^{9} -157481. q^{10} +97159.7 q^{11} +1.19488e6 q^{12} +2.25195e6 q^{13} +1.44936e6 q^{14} -5.34169e6 q^{15} +1.05792e6 q^{16} -5.47274e6 q^{17} -1.11241e7 q^{18} -1.36844e7 q^{19} -9.87353e6 q^{20} +4.91618e7 q^{21} -2.30304e6 q^{22} +3.78724e7 q^{23} -6.73541e7 q^{24} -4.68878e6 q^{25} -5.33794e7 q^{26} -2.34895e8 q^{27} +9.08701e7 q^{28} +2.05111e7 q^{29} +1.26617e8 q^{30} +7.66307e7 q^{31} -1.96641e8 q^{32} -7.81182e7 q^{33} +1.29724e8 q^{34} -4.06232e8 q^{35} -6.97442e8 q^{36} +5.87994e8 q^{37} +3.24370e8 q^{38} -1.81061e9 q^{39} +5.56559e8 q^{40} -5.25000e8 q^{41} -1.16531e9 q^{42} +1.40657e9 q^{43} -1.44393e8 q^{44} +3.11790e9 q^{45} -8.97712e8 q^{46} -1.05859e9 q^{47} -8.50585e8 q^{48} +1.76140e9 q^{49} +1.11141e8 q^{50} +4.40018e9 q^{51} -3.34671e9 q^{52} +1.82460e8 q^{53} +5.56786e9 q^{54} +6.45504e8 q^{55} -5.12224e9 q^{56} +1.10025e10 q^{57} -4.86188e8 q^{58} -4.81226e9 q^{59} +7.93850e9 q^{60} +1.42171e9 q^{61} -1.81643e9 q^{62} -2.86953e10 q^{63} +2.49449e9 q^{64} +1.49614e10 q^{65} +1.85168e9 q^{66} +1.58194e9 q^{67} +8.13325e9 q^{68} -3.04501e10 q^{69} +9.62917e9 q^{70} -7.93869e9 q^{71} +3.93140e10 q^{72} -2.06263e10 q^{73} -1.39376e10 q^{74} +3.76987e9 q^{75} +2.03369e10 q^{76} -5.94084e9 q^{77} +4.29180e10 q^{78} -3.33041e10 q^{79} +7.02853e9 q^{80} +1.05725e11 q^{81} +1.24444e10 q^{82} -4.80488e9 q^{83} -7.30612e10 q^{84} -3.63595e10 q^{85} -3.33408e10 q^{86} -1.64913e10 q^{87} +8.13925e9 q^{88} -3.03829e10 q^{89} -7.39054e10 q^{90} -1.37696e11 q^{91} -5.62836e10 q^{92} -6.16125e10 q^{93} +2.50925e10 q^{94} -9.09157e10 q^{95} +1.58103e11 q^{96} -2.92126e10 q^{97} -4.17514e10 q^{98} +4.55969e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more