LMFDB - Embedded newform 29.12.a.a.1.6

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			1.6
Root			$-18.9987$ 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)

$f(q)$	$=$	$q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +O(q^{10})$	\(q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +19497.9 q^{10} -480464. q^{11} -485474. q^{12} +729102. q^{13} -973741. q^{14} -275109. q^{15} +1.45516e6 q^{16} +6.80915e6 q^{17} +1.77755e6 q^{18} -1.56192e7 q^{19} +1.38626e6 q^{20} +1.37392e7 q^{21} +1.05696e7 q^{22} -3.18252e7 q^{23} +2.46641e7 q^{24} -4.80426e7 q^{25} -1.60393e7 q^{26} -8.00660e7 q^{27} -6.92307e7 q^{28} +2.05111e7 q^{29} +6.05205e6 q^{30} -3.08016e8 q^{31} -1.94747e8 q^{32} -1.49133e8 q^{33} -1.49793e8 q^{34} -3.92317e7 q^{35} +1.26379e8 q^{36} +4.28251e8 q^{37} +3.43602e8 q^{38} +2.26309e8 q^{39} -7.04276e7 q^{40} -1.00915e9 q^{41} -3.02244e8 q^{42} +3.53819e8 q^{43} +7.51473e8 q^{44} +7.16169e7 q^{45} +7.00114e8 q^{46} -2.87373e9 q^{47} +4.51672e8 q^{48} -1.80646e7 q^{49} +1.05687e9 q^{50} +2.11352e9 q^{51} -1.14036e9 q^{52} -1.08796e9 q^{53} +1.76135e9 q^{54} +4.25846e8 q^{55} +3.51721e9 q^{56} -4.84810e9 q^{57} -4.51219e8 q^{58} +9.69237e9 q^{59} +4.30286e8 q^{60} +2.73036e9 q^{61} +6.77597e9 q^{62} -3.57660e9 q^{63} +1.30402e9 q^{64} -6.46218e8 q^{65} +3.28074e9 q^{66} +5.53037e9 q^{67} -1.06499e10 q^{68} -9.87837e9 q^{69} +8.63048e8 q^{70} +1.51715e10 q^{71} -6.42060e9 q^{72} +2.05445e10 q^{73} -9.42097e9 q^{74} -1.49121e10 q^{75} +2.44293e10 q^{76} -2.12671e10 q^{77} -4.97851e9 q^{78} -2.27864e10 q^{79} -1.28974e9 q^{80} -1.05381e10 q^{81} +2.21999e10 q^{82} -6.37446e9 q^{83} -2.14888e10 q^{84} -6.03510e9 q^{85} -7.78357e9 q^{86} +6.36654e9 q^{87} -3.81780e10 q^{88} -2.92283e10 q^{89} -1.57548e9 q^{90} +3.22726e10 q^{91} +4.97764e10 q^{92} -9.56066e10 q^{93} +6.32185e10 q^{94} +1.38436e10 q^{95} -6.04483e10 q^{96} -1.24338e11 q^{97} +3.97399e8 q^{98} +3.88226e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−21.9987	−0.486107	−0.243054	−	0.970013i	$-0.578149\pi$
$2$	−21.9987	−0.486107	−0.243054	+	0.970013i	$0.578149\pi$
$3$	310.394	0.737474	0.368737	−	0.929534i	$-0.379790\pi$
$3$	310.394	0.737474	0.368737	+	0.929534i	$0.379790\pi$
$4$	−1564.06	−0.763700
$5$	−886.321	−0.126840	−0.0634200	−	0.997987i	$-0.520201\pi$
$5$	−886.321	−0.126840	−0.0634200	+	0.997987i	$0.520201\pi$
$6$	−6828.28	−0.358492
$7$	44263.6	0.995422	0.497711	−	0.867343i	$-0.334174\pi$
$7$	44263.6	0.995422	0.497711	+	0.867343i	$0.334174\pi$
$8$	79460.6	0.857348
$9$	−80802.4	−0.456132
$10$	19497.9	0.0616579
$11$	−480464.	−0.899500	−0.449750	−	0.893154i	$-0.648487\pi$
$11$	−480464.	−0.899500	−0.449750	+	0.893154i	$0.648487\pi$
$12$	−485474.	−0.563209
$13$	729102.	0.544627	0.272314	−	0.962209i	$-0.412211\pi$
$13$	729102.	0.544627	0.272314	+	0.962209i	$0.412211\pi$
$14$	−973741.	−0.483882
$15$	−275109.	−0.0935412
$16$	1.45516e6	0.346936
$17$	6.80915e6	1.16312	0.581559	−	0.813504i	$-0.302443\pi$
$17$	6.80915e6	1.16312	0.581559	+	0.813504i	$0.302443\pi$
$18$	1.77755e6	0.221729
$19$	−1.56192e7	−1.44715	−0.723574	−	0.690246i	$-0.757502\pi$
$19$	−1.56192e7	−1.44715	−0.723574	+	0.690246i	$0.757502\pi$
$20$	1.38626e6	0.0968676
$21$	1.37392e7	0.734098
$22$	1.05696e7	0.437254
$23$	−3.18252e7	−1.03102	−0.515511	−	0.856883i	$-0.672398\pi$
$23$	−3.18252e7	−1.03102	−0.515511	+	0.856883i	$0.672398\pi$
$24$	2.46641e7	0.632272
$25$	−4.80426e7	−0.983912
$26$	−1.60393e7	−0.264748
$27$	−8.00660e7	−1.07386
$28$	−6.92307e7	−0.760203
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	6.05205e6	0.0454711
$31$	−3.08016e8	−1.93234	−0.966172	−	0.257898i	$-0.916970\pi$
$31$	−3.08016e8	−1.93234	−0.966172	+	0.257898i	$0.916970\pi$
$32$	−1.94747e8	−1.02600
$33$	−1.49133e8	−0.663358
$34$	−1.49793e8	−0.565401
$35$	−3.92317e7	−0.126259
$36$	1.26379e8	0.348348
$37$	4.28251e8	1.01529	0.507643	−	0.861567i	$-0.330517\pi$
$37$	4.28251e8	1.01529	0.507643	+	0.861567i	$0.330517\pi$
$38$	3.43602e8	0.703470
$39$	2.26309e8	0.401649
$40$	−7.04276e7	−0.108746
$41$	−1.00915e9	−1.36033	−0.680163	−	0.733061i	$-0.738091\pi$
$41$	−1.00915e9	−1.36033	−0.680163	+	0.733061i	$0.738091\pi$
$42$	−3.02244e8	−0.356850
$43$	3.53819e8	0.367033	0.183516	−	0.983017i	$-0.441252\pi$
$43$	3.53819e8	0.367033	0.183516	+	0.983017i	$0.441252\pi$
$44$	7.51473e8	0.686948
$45$	7.16169e7	0.0578557
$46$	7.00114e8	0.501188
$47$	−2.87373e9	−1.82772	−0.913858	−	0.406035i	$-0.866911\pi$
$47$	−2.87373e9	−1.82772	−0.913858	+	0.406035i	$0.866911\pi$
$48$	4.51672e8	0.255857
$49$	−1.80646e7	−0.00913589
$50$	1.05687e9	0.478287
$51$	2.11352e9	0.857770
$52$	−1.14036e9	−0.415932
$53$	−1.08796e9	−0.357353	−0.178676	−	0.983908i	$-0.557182\pi$
$53$	−1.08796e9	−0.357353	−0.178676	+	0.983908i	$0.557182\pi$
$54$	1.76135e9	0.522011
$55$	4.25846e8	0.114093
$56$	3.51721e9	0.853422
$57$	−4.84810e9	−1.06724
$58$	−4.51219e8	−0.0902679
$59$	9.69237e9	1.76500	0.882499	−	0.470315i	$-0.155860\pi$
$59$	9.69237e9	1.76500	0.882499	+	0.470315i	$0.155860\pi$
$60$	4.30286e8	0.0714374
$61$	2.73036e9	0.413910	0.206955	−	0.978350i	$-0.433645\pi$
$61$	2.73036e9	0.413910	0.206955	+	0.978350i	$0.433645\pi$
$62$	6.77597e9	0.939327
$63$	−3.57660e9	−0.454043
$64$	1.30402e9	0.151808
$65$	−6.46218e8	−0.0690805
$66$	3.28074e9	0.322463
$67$	5.53037e9	0.500429	0.250215	−	0.968190i	$-0.419499\pi$
$67$	5.53037e9	0.500429	0.250215	+	0.968190i	$0.419499\pi$
$68$	−1.06499e10	−0.888273
$69$	−9.87837e9	−0.760353
$70$	8.63048e8	0.0613756
$71$	1.51715e10	0.997949	0.498974	−	0.866617i	$-0.333710\pi$
$71$	1.51715e10	0.997949	0.498974	+	0.866617i	$0.333710\pi$
$72$	−6.42060e9	−0.391063
$73$	2.05445e10	1.15990	0.579949	−	0.814653i	$-0.303072\pi$
$73$	2.05445e10	1.15990	0.579949	+	0.814653i	$0.303072\pi$
$74$	−9.42097e9	−0.493538
$75$	−1.49121e10	−0.725610
$76$	2.44293e10	1.10519
$77$	−2.12671e10	−0.895382
$78$	−4.97851e9	−0.195244
$79$	−2.27864e10	−0.833158	−0.416579	−	0.909100i	$-0.636771\pi$
$79$	−2.27864e10	−0.833158	−0.416579	+	0.909100i	$0.636771\pi$
$80$	−1.28974e9	−0.0440054
$81$	−1.05381e10	−0.335812
$82$	2.21999e10	0.661265
$83$	−6.37446e9	−0.177629	−0.0888144	−	0.996048i	$-0.528308\pi$
$83$	−6.37446e9	−0.177629	−0.0888144	+	0.996048i	$0.528308\pi$
$84$	−2.14888e10	−0.560630
$85$	−6.03510e9	−0.147530
$86$	−7.78357e9	−0.178417
$87$	6.36654e9	0.136946
$88$	−3.81780e10	−0.771184
$89$	−2.92283e10	−0.554828	−0.277414	−	0.960751i	$-0.589477\pi$
$89$	−2.92283e10	−0.554828	−0.277414	+	0.960751i	$0.589477\pi$
$90$	−1.57548e9	−0.0281241
$91$	3.22726e10	0.542134
$92$	4.97764e10	0.787392
$93$	−9.56066e10	−1.42505
$94$	6.32185e10	0.888466
$95$	1.38436e10	0.183556
$96$	−6.04483e10	−0.756646
$97$	−1.24338e11	−1.47014	−0.735069	−	0.677992i	$-0.762850\pi$
$97$	−1.24338e11	−1.47014	−0.735069	+	0.677992i	$0.762850\pi$
$98$	3.97399e8	0.00444103
$99$	3.88226e10	0.410291
$100$	7.51413e10	0.751413
$101$	−2.60286e10	−0.246424	−0.123212	−	0.992380i	$-0.539320\pi$
$101$	−2.60286e10	−0.246424	−0.123212	+	0.992380i	$0.539320\pi$
$102$	−4.64948e10	−0.416968
$103$	−1.19818e11	−1.01840	−0.509200	−	0.860648i	$-0.670059\pi$
$103$	−1.19818e11	−1.01840	−0.509200	+	0.860648i	$0.670059\pi$
$104$	5.79348e10	0.466935
$105$	−1.21773e10	−0.0931130
$106$	2.39338e10	0.173712
$107$	−1.11393e11	−0.767795	−0.383897	−	0.923376i	$-0.625418\pi$
$107$	−1.11393e11	−0.767795	−0.383897	+	0.923376i	$0.625418\pi$
$108$	1.25228e11	0.820106
$109$	1.17465e11	0.731247	0.365624	−	0.930763i	$-0.380856\pi$
$109$	1.17465e11	0.731247	0.365624	+	0.930763i	$0.380856\pi$
$110$	−9.36806e9	−0.0554613
$111$	1.32927e11	0.748748
$112$	6.44104e10	0.345348
$113$	3.69905e11	1.88868	0.944340	−	0.328972i	$-0.106702\pi$
$113$	3.69905e11	1.88868	0.944340	+	0.328972i	$0.106702\pi$
$114$	1.06652e11	0.518791
$115$	2.82074e10	0.130775
$116$	−3.20806e10	−0.141815
$117$	−5.89131e10	−0.248422
$118$	−2.13220e11	−0.857978
$119$	3.01397e11	1.15779
$120$	−2.18603e10	−0.0801973
$121$	−5.44658e10	−0.190899
$122$	−6.00645e10	−0.201205
$123$	−3.13233e11	−1.00321
$124$	4.81755e11	1.47573
$125$	8.58586e10	0.251639
$126$	7.86806e10	0.220714
$127$	−5.07350e11	−1.36266	−0.681329	−	0.731977i	$-0.738598\pi$
$127$	−5.07350e11	−1.36266	−0.681329	+	0.731977i	$0.738598\pi$
$128$	3.70155e11	0.952201
$129$	1.09823e11	0.270677
$130$	1.42160e10	0.0335806
$131$	3.44791e11	0.780843	0.390422	−	0.920636i	$-0.372329\pi$
$131$	3.44791e11	0.780843	0.390422	+	0.920636i	$0.372329\pi$
$132$	2.33253e11	0.506606
$133$	−6.91360e11	−1.44052
$134$	−1.21661e11	−0.243262
$135$	7.09642e10	0.136208
$136$	5.41059e11	0.997197
$137$	5.50954e11	0.975332	0.487666	−	0.873030i	$-0.337848\pi$
$137$	5.50954e11	0.975332	0.487666	+	0.873030i	$0.337848\pi$
$138$	2.17311e11	0.369613
$139$	−9.76916e11	−1.59689	−0.798447	−	0.602065i	$-0.794345\pi$
$139$	−9.76916e11	−1.59689	−0.798447	+	0.602065i	$0.794345\pi$
$140$	6.13606e10	0.0964241
$141$	−8.91991e11	−1.34789
$142$	−3.33754e11	−0.485110
$143$	−3.50307e11	−0.489893
$144$	−1.17580e11	−0.158249
$145$	−1.81795e10	−0.0235536
$146$	−4.51953e11	−0.563835
$147$	−5.60716e9	−0.00673749
$148$	−6.69808e11	−0.775374
$149$	−5.22457e9	−0.00582809	−0.00291404	−	0.999996i	$-0.500928\pi$
$149$	−5.22457e9	−0.00582809	−0.00291404	+	0.999996i	$0.500928\pi$
$150$	3.28048e11	0.352724
$151$	2.71454e11	0.281400	0.140700	−	0.990052i	$-0.455065\pi$
$151$	2.71454e11	0.281400	0.140700	+	0.990052i	$0.455065\pi$
$152$	−1.24111e12	−1.24071
$153$	−5.50195e11	−0.530535
$154$	4.67848e11	0.435252
$155$	2.73002e11	0.245099
$156$	−3.53960e11	−0.306739
$157$	−8.51389e11	−0.712328	−0.356164	−	0.934424i	$-0.615915\pi$
$157$	−8.51389e11	−0.712328	−0.356164	+	0.934424i	$0.615915\pi$
$158$	5.01272e11	0.405004
$159$	−3.37698e11	−0.263539
$160$	1.72608e11	0.130137
$161$	−1.40870e12	−1.02630
$162$	2.31826e11	0.163241
$163$	1.66971e12	1.13661	0.568304	−	0.822819i	$-0.307600\pi$
$163$	1.66971e12	1.13661	0.568304	+	0.822819i	$0.307600\pi$
$164$	1.57836e12	1.03888
$165$	1.32180e11	0.0841403
$166$	1.40230e11	0.0863467
$167$	1.10002e12	0.655328	0.327664	−	0.944794i	$-0.393739\pi$
$167$	1.10002e12	0.655328	0.327664	+	0.944794i	$0.393739\pi$
$168$	1.09172e12	0.629377
$169$	−1.26057e12	−0.703381
$170$	1.32764e11	0.0717154
$171$	1.26207e12	0.660090
$172$	−5.53393e11	−0.280303
$173$	−1.93882e12	−0.951225	−0.475612	−	0.879655i	$-0.657774\pi$
$173$	−1.93882e12	−0.951225	−0.475612	+	0.879655i	$0.657774\pi$
$174$	−1.40056e11	−0.0665703
$175$	−2.12653e12	−0.979407
$176$	−6.99151e11	−0.312069
$177$	3.00846e12	1.30164
$178$	6.42984e11	0.269706
$179$	9.66841e11	0.393245	0.196623	−	0.980479i	$-0.437003\pi$
$179$	9.66841e11	0.393245	0.196623	+	0.980479i	$0.437003\pi$
$180$	−1.12013e11	−0.0441844
$181$	3.06155e12	1.17141	0.585705	−	0.810524i	$-0.300818\pi$
$181$	3.06155e12	1.17141	0.585705	+	0.810524i	$0.300818\pi$
$182$	−7.09956e11	−0.263535
$183$	8.47489e11	0.305248
$184$	−2.52885e12	−0.883945
$185$	−3.79568e11	−0.128779
$186$	2.10322e12	0.692730
$187$	−3.27155e12	−1.04623
$188$	4.49468e12	1.39583
$189$	−3.54401e12	−1.06894
$190$	−3.04542e11	−0.0892281
$191$	1.59095e12	0.452869	0.226435	−	0.974026i	$-0.427293\pi$
$191$	1.59095e12	0.452869	0.226435	+	0.974026i	$0.427293\pi$
$192$	4.04760e11	0.111954
$193$	−2.02014e12	−0.543021	−0.271511	−	0.962435i	$-0.587523\pi$
$193$	−2.02014e12	−0.543021	−0.271511	+	0.962435i	$0.587523\pi$
$194$	2.73527e12	0.714645
$195$	−2.00582e11	−0.0509451
$196$	2.82541e10	0.00697708
$197$	−1.30724e12	−0.313901	−0.156950	−	0.987607i	$-0.550166\pi$
$197$	−1.30724e12	−0.313901	−0.156950	+	0.987607i	$0.550166\pi$
$198$	−8.54048e11	−0.199445
$199$	2.91409e12	0.661928	0.330964	−	0.943643i	$-0.392626\pi$
$199$	2.91409e12	0.661928	0.330964	+	0.943643i	$0.392626\pi$
$200$	−3.81749e12	−0.843554
$201$	1.71659e12	0.369054
$202$	5.72595e11	0.119789
$203$	9.07896e11	0.184845
$204$	−3.30567e12	−0.655078
$205$	8.94428e11	0.172544
$206$	2.63585e12	0.495052
$207$	2.57155e12	0.470282
$208$	1.06096e12	0.188951
$209$	7.50445e12	1.30171
$210$	2.67885e11	0.0452629
$211$	7.99404e12	1.31587	0.657935	−	0.753075i	$-0.271430\pi$
$211$	7.99404e12	1.31587	0.657935	+	0.753075i	$0.271430\pi$
$212$	1.70164e12	0.272910
$213$	4.70915e12	0.735961
$214$	2.45049e12	0.373231
$215$	−3.13597e11	−0.0465544
$216$	−6.36209e12	−0.920671
$217$	−1.36339e13	−1.92350
$218$	−2.58409e12	−0.355465
$219$	6.37690e12	0.855395
$220$	−6.66047e11	−0.0871325
$221$	4.96456e12	0.633466
$222$	−2.92421e12	−0.363972
$223$	−8.85549e12	−1.07532	−0.537658	−	0.843163i	$-0.680691\pi$
$223$	−8.85549e12	−1.07532	−0.537658	+	0.843163i	$0.680691\pi$
$224$	−8.62019e12	−1.02130
$225$	3.88195e12	0.448793
$226$	−8.13743e12	−0.918101
$227$	−9.57786e12	−1.05469	−0.527347	−	0.849650i	$-0.676813\pi$
$227$	−9.57786e12	−1.05469	−0.527347	+	0.849650i	$0.676813\pi$
$228$	7.58271e12	0.815047
$229$	−1.53613e13	−1.61188	−0.805940	−	0.591998i	$-0.798339\pi$
$229$	−1.53613e13	−1.61188	−0.805940	+	0.591998i	$0.798339\pi$
$230$	−6.20526e11	−0.0635707
$231$	−6.60117e12	−0.660321
$232$	1.62983e12	0.159205
$233$	1.29012e13	1.23076	0.615379	−	0.788231i	$-0.289003\pi$
$233$	1.29012e13	1.23076	0.615379	+	0.788231i	$0.289003\pi$
$234$	1.29601e12	0.120760
$235$	2.54705e12	0.231827
$236$	−1.51594e13	−1.34793
$237$	−7.07278e12	−0.614432
$238$	−6.63035e12	−0.562812
$239$	−6.63263e12	−0.550170	−0.275085	−	0.961420i	$-0.588706\pi$
$239$	−6.63263e12	−0.550170	−0.275085	+	0.961420i	$0.588706\pi$
$240$	−4.00327e11	−0.0324529
$241$	1.46207e13	1.15845	0.579223	−	0.815169i	$-0.303356\pi$
$241$	1.46207e13	1.15845	0.579223	+	0.815169i	$0.303356\pi$
$242$	1.19818e12	0.0927976
$243$	1.09125e13	0.826207
$244$	−4.27044e12	−0.316103
$245$	1.60111e10	0.00115880
$246$	6.89073e12	0.487666
$247$	−1.13880e13	−0.788157
$248$	−2.44752e13	−1.65669
$249$	−1.97859e12	−0.130997
$250$	−1.88878e12	−0.122324
$251$	9.17406e12	0.581241	0.290620	−	0.956838i	$-0.406138\pi$
$251$	9.17406e12	0.581241	0.290620	+	0.956838i	$0.406138\pi$
$252$	5.59400e12	0.346753
$253$	1.52909e13	0.927405
$254$	1.11610e13	0.662399
$255$	−1.87326e12	−0.108800
$256$	−1.08136e13	−0.614680
$257$	1.33408e13	0.742249	0.371125	−	0.928583i	$-0.378972\pi$
$257$	1.33408e13	0.742249	0.371125	+	0.928583i	$0.378972\pi$
$258$	−2.41597e12	−0.131578
$259$	1.89559e13	1.01064
$260$	1.01072e12	0.0527568
$261$	−1.65735e12	−0.0847015
$262$	−7.58496e12	−0.379574
$263$	1.17880e13	0.577677	0.288838	−	0.957378i	$-0.406731\pi$
$263$	1.17880e13	0.577677	0.288838	+	0.957378i	$0.406731\pi$
$264$	−1.18502e13	−0.568729
$265$	9.64286e11	0.0453266
$266$	1.52090e13	0.700249
$267$	−9.07229e12	−0.409171
$268$	−8.64981e12	−0.382177
$269$	4.69213e12	0.203111	0.101555	−	0.994830i	$-0.467618\pi$
$269$	4.69213e12	0.203111	0.101555	+	0.994830i	$0.467618\pi$
$270$	−1.56112e12	−0.0662119
$271$	2.00690e13	0.834056	0.417028	−	0.908894i	$-0.363072\pi$
$271$	2.00690e13	0.834056	0.417028	+	0.908894i	$0.363072\pi$
$272$	9.90838e12	0.403528
$273$	1.00172e13	0.399810
$274$	−1.21203e13	−0.474116
$275$	2.30827e13	0.885029
$276$	1.54503e13	0.580681
$277$	−3.83151e13	−1.41166	−0.705832	−	0.708379i	$-0.749427\pi$
$277$	−3.83151e13	−1.41166	−0.705832	+	0.708379i	$0.749427\pi$
$278$	2.14909e13	0.776262
$279$	2.48885e13	0.881404
$280$	−3.11738e12	−0.108248
$281$	2.14260e13	0.729552	0.364776	−	0.931095i	$-0.381146\pi$
$281$	2.14260e13	0.729552	0.364776	+	0.931095i	$0.381146\pi$
$282$	1.96227e13	0.655221
$283$	−1.96008e13	−0.641873	−0.320936	−	0.947101i	$-0.603998\pi$
$283$	−1.96008e13	−0.641873	−0.320936	+	0.947101i	$0.603998\pi$
$284$	−2.37291e13	−0.762133
$285$	4.29698e12	0.135368
$286$	7.70631e12	0.238140
$287$	−4.46684e13	−1.35410
$288$	1.57360e13	0.467989
$289$	1.20926e13	0.352844
$290$	3.99925e11	0.0114496
$291$	−3.85937e13	−1.08419
$292$	−3.21328e13	−0.885814
$293$	5.83139e13	1.57761	0.788807	−	0.614642i	$-0.210699\pi$
$293$	5.83139e13	1.57761	0.788807	+	0.614642i	$0.210699\pi$
$294$	1.23350e11	0.00327514
$295$	−8.59056e12	−0.223872
$296$	3.40291e13	0.870453
$297$	3.84689e13	0.965937
$298$	1.14934e11	0.00283308
$299$	−2.32038e13	−0.561523
$300$	2.33234e13	0.554148
$301$	1.56613e13	0.365352
$302$	−5.97165e12	−0.136790
$303$	−8.07912e12	−0.181731
$304$	−2.27283e13	−0.502069
$305$	−2.41998e12	−0.0525004
$306$	1.21036e13	0.257897
$307$	−8.69471e13	−1.81968	−0.909838	−	0.414964i	$-0.863794\pi$
$307$	−8.69471e13	−1.81968	−0.909838	+	0.414964i	$0.863794\pi$
$308$	3.32629e13	0.683803
$309$	−3.71909e13	−0.751044
$310$	−6.00568e12	−0.119144
$311$	2.77778e13	0.541398	0.270699	−	0.962664i	$-0.412745\pi$
$311$	2.77778e13	0.541398	0.270699	+	0.962664i	$0.412745\pi$
$312$	1.79826e13	0.344353
$313$	−1.13541e13	−0.213629	−0.106814	−	0.994279i	$-0.534065\pi$
$313$	−1.13541e13	−0.213629	−0.106814	+	0.994279i	$0.534065\pi$
$314$	1.87295e13	0.346268
$315$	3.17002e12	0.0575908
$316$	3.56393e13	0.636282
$317$	−3.72872e13	−0.654236	−0.327118	−	0.944984i	$-0.606077\pi$
$317$	−3.72872e13	−0.654236	−0.327118	+	0.944984i	$0.606077\pi$
$318$	7.42892e12	0.128108
$319$	−9.85487e12	−0.167033
$320$	−1.15578e12	−0.0192553
$321$	−3.45756e13	−0.566229
$322$	3.09895e13	0.498893
$323$	−1.06353e14	−1.68321
$324$	1.64823e13	0.256460
$325$	−3.50279e13	−0.535865
$326$	−3.67316e13	−0.552513
$327$	3.64606e13	0.539276
$328$	−8.01874e13	−1.16627
$329$	−1.27202e14	−1.81935
$330$	−2.90779e12	−0.0409013
$331$	−1.28189e14	−1.77336	−0.886678	−	0.462388i	$-0.846993\pi$
$331$	−1.28189e14	−1.77336	−0.886678	+	0.462388i	$0.846993\pi$
$332$	9.97001e12	0.135655
$333$	−3.46037e13	−0.463104
$334$	−2.41989e13	−0.318560
$335$	−4.90168e12	−0.0634744
$336$	1.99926e13	0.254685
$337$	6.54934e13	0.820792	0.410396	−	0.911907i	$-0.365390\pi$
$337$	6.54934e13	0.820792	0.410396	+	0.911907i	$0.365390\pi$
$338$	2.77309e13	0.341919
$339$	1.14816e14	1.39285
$340$	9.43923e12	0.112669
$341$	1.47991e14	1.73814
$342$	−2.77638e13	−0.320875
$343$	−8.83231e13	−1.00452
$344$	2.81147e13	0.314675
$345$	8.75541e12	0.0964431
$346$	4.26515e13	0.462398
$347$	8.39610e13	0.895912	0.447956	−	0.894056i	$-0.352152\pi$
$347$	8.39610e13	0.895912	0.447956	+	0.894056i	$0.352152\pi$
$348$	−9.95764e12	−0.104585
$349$	−1.07463e13	−0.111102	−0.0555509	−	0.998456i	$-0.517691\pi$
$349$	−1.07463e13	−0.111102	−0.0555509	+	0.998456i	$0.517691\pi$
$350$	4.67810e13	0.476097
$351$	−5.83763e13	−0.584853
$352$	9.35689e13	0.922884
$353$	−1.25603e13	−0.121966	−0.0609832	−	0.998139i	$-0.519424\pi$
$353$	−1.25603e13	−0.121966	−0.0609832	+	0.998139i	$0.519424\pi$
$354$	−6.61822e13	−0.632737
$355$	−1.34468e13	−0.126580
$356$	4.57147e13	0.423722
$357$	9.35520e13	0.853843
$358$	−2.12693e13	−0.191159
$359$	−1.38150e14	−1.22273	−0.611365	−	0.791349i	$-0.709379\pi$
$359$	−1.38150e14	−1.22273	−0.611365	+	0.791349i	$0.709379\pi$
$360$	5.69072e12	0.0496025
$361$	1.27468e14	1.09424
$362$	−6.73502e13	−0.569432
$363$	−1.69059e13	−0.140783
$364$	−5.04762e13	−0.414027
$365$	−1.82090e13	−0.147121
$366$	−1.86437e13	−0.148383
$367$	2.02429e14	1.58712	0.793559	−	0.608494i	$-0.208226\pi$
$367$	2.02429e14	1.58712	0.793559	+	0.608494i	$0.208226\pi$
$368$	−4.63107e13	−0.357699
$369$	8.15414e13	0.620488
$370$	8.35000e12	0.0626004
$371$	−4.81572e13	−0.355717
$372$	1.49534e14	1.08831
$373$	2.52372e13	0.180985	0.0904927	−	0.995897i	$-0.471156\pi$
$373$	2.52372e13	0.180985	0.0904927	+	0.995897i	$0.471156\pi$
$374$	7.19700e13	0.508578
$375$	2.66500e13	0.185578
$376$	−2.28349e14	−1.56699
$377$	1.49547e13	0.101135
$378$	7.79636e13	0.519621
$379$	−5.31941e13	−0.349420	−0.174710	−	0.984620i	$-0.555899\pi$
$379$	−5.31941e13	−0.349420	−0.174710	+	0.984620i	$0.555899\pi$
$380$	−2.16522e13	−0.140182
$381$	−1.57479e14	−1.00493
$382$	−3.49988e13	−0.220143
$383$	3.19109e14	1.97854	0.989272	−	0.146084i	$-0.0466669\pi$
$383$	3.19109e14	1.97854	0.989272	+	0.146084i	$0.0466669\pi$
$384$	1.14894e14	0.702224
$385$	1.88494e13	0.113570
$386$	4.44405e13	0.263967
$387$	−2.85894e13	−0.167415
$388$	1.94471e14	1.12274
$389$	−7.65689e13	−0.435842	−0.217921	−	0.975966i	$-0.569928\pi$
$389$	−7.65689e13	−0.435842	−0.217921	+	0.975966i	$0.569928\pi$
$390$	4.41256e12	0.0247648
$391$	−2.16703e14	−1.19920
$392$	−1.43543e12	−0.00783264
$393$	1.07021e14	0.575852
$394$	2.87577e13	0.152589
$395$	2.01961e13	0.105678
$396$	−6.07208e13	−0.313339
$397$	−3.97244e13	−0.202166	−0.101083	−	0.994878i	$-0.532231\pi$
$397$	−3.97244e13	−0.202166	−0.101083	+	0.994878i	$0.532231\pi$
$398$	−6.41062e13	−0.321768
$399$	−2.14594e14	−1.06235
$400$	−6.99095e13	−0.341355
$401$	3.19615e14	1.53934	0.769668	−	0.638444i	$-0.220422\pi$
$401$	3.19615e14	1.53934	0.769668	+	0.638444i	$0.220422\pi$
$402$	−3.77629e13	−0.179400
$403$	−2.24575e14	−1.05241
$404$	4.07102e13	0.188194
$405$	9.34018e12	0.0425944
$406$	−1.99726e13	−0.0898546
$407$	−2.05759e14	−0.913250
$408$	1.67942e14	0.735407
$409$	−1.92549e14	−0.831885	−0.415942	−	0.909391i	$-0.636548\pi$
$409$	−1.92549e14	−0.831885	−0.415942	+	0.909391i	$0.636548\pi$
$410$	−1.96763e13	−0.0838748
$411$	1.71013e14	0.719282
$412$	1.87403e14	0.777752
$413$	4.29019e14	1.75692
$414$	−5.65709e13	−0.228608
$415$	5.64982e12	0.0225304
$416$	−1.41990e14	−0.558786
$417$	−3.03229e14	−1.17767
$418$	−1.65088e14	−0.632771
$419$	−4.17916e13	−0.158093	−0.0790464	−	0.996871i	$-0.525188\pi$
$419$	−4.17916e13	−0.158093	−0.0790464	+	0.996871i	$0.525188\pi$
$420$	1.90460e13	0.0711103
$421$	2.60522e14	0.960048	0.480024	−	0.877255i	$-0.340628\pi$
$421$	2.60522e14	0.960048	0.480024	+	0.877255i	$0.340628\pi$
$422$	−1.75859e14	−0.639654
$423$	2.32205e14	0.833679
$424$	−8.64503e13	−0.306376
$425$	−3.27129e14	−1.14441
$426$	−1.03595e14	−0.357756
$427$	1.20856e14	0.412015
$428$	1.74224e14	0.586365
$429$	−1.08733e14	−0.361283
$430$	6.89874e12	0.0226305
$431$	−1.31690e14	−0.426508	−0.213254	−	0.976997i	$-0.568406\pi$
$431$	−1.31690e14	−0.426508	−0.213254	+	0.976997i	$0.568406\pi$
$432$	−1.16509e14	−0.372561
$433$	−1.19097e13	−0.0376026	−0.0188013	−	0.999823i	$-0.505985\pi$
$433$	−1.19097e13	−0.0376026	−0.0188013	+	0.999823i	$0.505985\pi$
$434$	2.99928e14	0.935027
$435$	−5.64280e12	−0.0173702
$436$	−1.83723e14	−0.558453
$437$	4.97084e14	1.49204
$438$	−1.40284e14	−0.415814
$439$	−5.65097e14	−1.65413	−0.827063	−	0.562110i	$-0.809990\pi$
$439$	−5.65097e14	−1.65413	−0.827063	+	0.562110i	$0.809990\pi$
$440$	3.38380e13	0.0978170
$441$	1.45967e12	0.00416717
$442$	−1.09214e14	−0.307933
$443$	−1.77548e14	−0.494419	−0.247210	−	0.968962i	$-0.579514\pi$
$443$	−1.77548e14	−0.494419	−0.247210	+	0.968962i	$0.579514\pi$
$444$	−2.07905e14	−0.571818
$445$	2.59056e13	0.0703743
$446$	1.94809e14	0.522719
$447$	−1.62168e12	−0.00429806
$448$	5.77206e13	0.151113
$449$	−7.83747e13	−0.202685	−0.101342	−	0.994852i	$-0.532314\pi$
$449$	−7.83747e13	−0.202685	−0.101342	+	0.994852i	$0.532314\pi$
$450$	−8.53980e13	−0.218162
$451$	4.84859e14	1.22361
$452$	−5.78552e14	−1.44238
$453$	8.42579e13	0.207525
$454$	2.10701e14	0.512694
$455$	−2.86039e13	−0.0687643
$456$	−3.85233e14	−0.914991
$457$	−4.40497e14	−1.03372	−0.516861	−	0.856069i	$-0.672900\pi$
$457$	−4.40497e14	−1.03372	−0.516861	+	0.856069i	$0.672900\pi$
$458$	3.37929e14	0.783547
$459$	−5.45182e14	−1.24903
$460$	−4.41179e13	−0.0998727
$461$	2.97082e14	0.664541	0.332270	−	0.943184i	$-0.392185\pi$
$461$	2.97082e14	0.664541	0.332270	+	0.943184i	$0.392185\pi$
$462$	1.45217e14	0.320987
$463$	1.07028e14	0.233776	0.116888	−	0.993145i	$-0.462708\pi$
$463$	1.07028e14	0.233776	0.116888	+	0.993145i	$0.462708\pi$
$464$	2.98469e13	0.0644245
$465$	8.47381e13	0.180754
$466$	−2.83810e14	−0.598281
$467$	−2.59277e14	−0.540158	−0.270079	−	0.962838i	$-0.587050\pi$
$467$	−2.59277e14	−0.540158	−0.270079	+	0.962838i	$0.587050\pi$
$468$	9.21435e13	0.189720
$469$	2.44794e14	0.498138
$470$	−5.60319e13	−0.112693
$471$	−2.64266e14	−0.525323
$472$	7.70162e14	1.51322
$473$	−1.69997e14	−0.330146
$474$	1.55592e14	0.298680
$475$	7.50385e14	1.42387
$476$	−4.71402e14	−0.884206
$477$	8.79101e13	0.163000
$478$	1.45909e14	0.267442
$479$	−9.69340e13	−0.175643	−0.0878215	−	0.996136i	$-0.527991\pi$
$479$	−9.69340e13	−0.175643	−0.0878215	+	0.996136i	$0.527991\pi$
$480$	5.35766e13	0.0959729
$481$	3.12238e14	0.552953
$482$	−3.21637e14	−0.563129
$483$	−4.37252e14	−0.756872
$484$	8.51876e13	0.145790
$485$	1.10203e14	0.186472
$486$	−2.40060e14	−0.401625
$487$	4.95544e14	0.819735	0.409867	−	0.912145i	$-0.365575\pi$
$487$	4.95544e14	0.819735	0.409867	+	0.912145i	$0.365575\pi$
$488$	2.16956e14	0.354865
$489$	5.18270e14	0.838219
$490$	−3.52223e11	−0.000563300 0
$491$	−9.75658e14	−1.54294	−0.771471	−	0.636264i	$-0.780479\pi$
$491$	−9.75658e14	−1.54294	−0.771471	+	0.636264i	$0.780479\pi$
$492$	4.89915e14	0.766147
$493$	1.39664e14	0.215986
$494$	2.50521e14	0.383129
$495$	−3.44093e13	−0.0520412
$496$	−4.48212e14	−0.670401
$497$	6.71545e14	0.993380
$498$	4.35265e13	0.0636785
$499$	1.26831e15	1.83516	0.917579	−	0.397554i	$-0.130141\pi$
$499$	1.26831e15	1.83516	0.917579	+	0.397554i	$0.130141\pi$
$500$	−1.34288e14	−0.192177
$501$	3.41439e14	0.483287
$502$	−2.01817e14	−0.282545
$503$	7.13091e14	0.987463	0.493732	−	0.869614i	$-0.335632\pi$
$503$	7.13091e14	0.987463	0.493732	+	0.869614i	$0.335632\pi$
$504$	−2.84199e14	−0.389273
$505$	2.30697e13	0.0312564
$506$	−3.36380e14	−0.450819
$507$	−3.91274e14	−0.518725
$508$	7.93524e14	1.04066
$509$	−1.47779e14	−0.191719	−0.0958597	−	0.995395i	$-0.530560\pi$
$509$	−1.47779e14	−0.191719	−0.0958597	+	0.995395i	$0.530560\pi$
$510$	4.12093e13	0.0528883
$511$	9.09373e14	1.15459
$512$	−5.20193e14	−0.653400
$513$	1.25056e15	1.55403
$514$	−2.93480e14	−0.360813
$515$	1.06198e14	0.129174
$516$	−1.71770e14	−0.206716
$517$	1.38073e15	1.64403
$518$	−4.17005e14	−0.491279
$519$	−6.01798e14	−0.701504
$520$	−5.13489e13	−0.0592260
$521$	2.60928e14	0.297792	0.148896	−	0.988853i	$-0.452428\pi$
$521$	2.60928e14	0.297792	0.148896	+	0.988853i	$0.452428\pi$
$522$	3.64596e13	0.0411740
$523$	7.01208e14	0.783587	0.391794	−	0.920053i	$-0.371855\pi$
$523$	7.01208e14	0.783587	0.391794	+	0.920053i	$0.371855\pi$
$524$	−5.39273e14	−0.596330
$525$	−6.60064e14	−0.722287
$526$	−2.59322e14	−0.280813
$527$	−2.09733e15	−2.24755
$528$	−2.17012e14	−0.230143
$529$	6.00349e13	0.0630082
$530$	−2.12130e13	−0.0220336
$531$	−7.83166e14	−0.805071
$532$	1.08133e15	1.10013
$533$	−7.35770e14	−0.740871
$534$	1.99579e14	0.198901
$535$	9.87296e13	0.0973871
$536$	4.39446e14	0.429042
$537$	3.00102e14	0.290008
$538$	−1.03221e14	−0.0987336
$539$	8.67942e12	0.00821774
$540$	−1.10992e14	−0.104022
$541$	−1.43669e15	−1.33284	−0.666419	−	0.745578i	$-0.732174\pi$
$541$	−1.43669e15	−1.33284	−0.666419	+	0.745578i	$0.732174\pi$
$542$	−4.41493e14	−0.405441
$543$	9.50288e14	0.863885
$544$	−1.32606e15	−1.19335
$545$	−1.04112e14	−0.0927514
$546$	−2.20366e14	−0.194351
$547$	−9.61440e14	−0.839444	−0.419722	−	0.907653i	$-0.637872\pi$
$547$	−9.61440e14	−0.839444	−0.419722	+	0.907653i	$0.637872\pi$
$548$	−8.61724e14	−0.744861
$549$	−2.20620e14	−0.188798
$550$	−5.07790e14	−0.430219
$551$	−3.20367e14	−0.268729
$552$	−7.84941e14	−0.651887
$553$	−1.00861e15	−0.829343
$554$	8.42884e14	0.686221
$555$	−1.17816e14	−0.0949711
$556$	1.52795e15	1.21955
$557$	−2.91552e14	−0.230416	−0.115208	−	0.993341i	$-0.536753\pi$
$557$	−2.91552e14	−0.230416	−0.115208	+	0.993341i	$0.536753\pi$
$558$	−5.47514e14	−0.428457
$559$	2.57970e14	0.199896
$560$	−5.70883e13	−0.0438039
$561$	−1.01547e15	−0.771564
$562$	−4.71344e14	−0.354641
$563$	−6.42960e14	−0.479057	−0.239529	−	0.970889i	$-0.576993\pi$
$563$	−6.42960e14	−0.479057	−0.239529	+	0.970889i	$0.576993\pi$
$564$	1.39512e15	1.02939
$565$	−3.27854e14	−0.239560
$566$	4.31193e14	0.312019
$567$	−4.66456e14	−0.334275
$568$	1.20554e15	0.855589
$569$	4.54572e14	0.319511	0.159755	−	0.987157i	$-0.448929\pi$
$569$	4.54572e14	0.319511	0.159755	+	0.987157i	$0.448929\pi$
$570$	−9.45280e13	−0.0658034
$571$	−1.61565e15	−1.11391	−0.556955	−	0.830543i	$-0.688030\pi$
$571$	−1.61565e15	−1.11391	−0.556955	+	0.830543i	$0.688030\pi$
$572$	5.47900e14	0.374131
$573$	4.93822e14	0.333979
$574$	9.82647e14	0.658237
$575$	1.52897e15	1.01444
$576$	−1.05368e14	−0.0692444
$577$	−3.96128e14	−0.257851	−0.128926	−	0.991654i	$-0.541153\pi$
$577$	−3.96128e14	−0.257851	−0.128926	+	0.991654i	$0.541153\pi$
$578$	−2.66022e14	−0.171520
$579$	−6.27041e14	−0.400464
$580$	2.84337e13	0.0179879
$581$	−2.82156e14	−0.176816
$582$	8.49012e14	0.527033
$583$	5.22728e14	0.321439
$584$	1.63248e15	0.994436
$585$	5.22160e13	0.0315098
$586$	−1.28283e15	−0.766890
$587$	−6.16212e14	−0.364939	−0.182470	−	0.983211i	$-0.558409\pi$
$587$	−6.16212e14	−0.364939	−0.182470	+	0.983211i	$0.558409\pi$
$588$	8.76992e12	0.00514542
$589$	4.81096e15	2.79639
$590$	1.88981e14	0.108826
$591$	−4.05761e14	−0.231494
$592$	6.23172e14	0.352240
$593$	−1.04704e15	−0.586360	−0.293180	−	0.956057i	$-0.594714\pi$
$593$	−1.04704e15	−0.586360	−0.293180	+	0.956057i	$0.594714\pi$
$594$	−8.46265e14	−0.469549
$595$	−2.67135e14	−0.146854
$596$	8.17152e12	0.00445091
$597$	9.04516e14	0.488155
$598$	5.10454e14	0.272961
$599$	−3.29250e15	−1.74453	−0.872265	−	0.489033i	$-0.837350\pi$
$599$	−3.29250e15	−1.74453	−0.872265	+	0.489033i	$0.837350\pi$
$600$	−1.18493e15	−0.622100
$601$	−2.47950e14	−0.128990	−0.0644949	−	0.997918i	$-0.520544\pi$
$601$	−2.47950e14	−0.128990	−0.0644949	+	0.997918i	$0.520544\pi$
$602$	−3.44528e14	−0.177600
$603$	−4.46867e14	−0.228262
$604$	−4.24570e14	−0.214905
$605$	4.82742e13	0.0242137
$606$	1.77730e14	0.0883410
$607$	−2.44547e15	−1.20455	−0.602274	−	0.798290i	$-0.705738\pi$
$607$	−2.44547e15	−1.20455	−0.602274	+	0.798290i	$0.705738\pi$
$608$	3.04179e15	1.48477
$609$	2.81806e14	0.136319
$610$	5.32364e13	0.0255208
$611$	−2.09524e15	−0.995424
$612$	8.60537e14	0.405169
$613$	2.10077e15	0.980270	0.490135	−	0.871646i	$-0.336947\pi$
$613$	2.10077e15	0.980270	0.490135	+	0.871646i	$0.336947\pi$
$614$	1.91272e15	0.884558
$615$	2.77625e14	0.127247
$616$	−1.68989e15	−0.767653
$617$	−2.30636e14	−0.103839	−0.0519194	−	0.998651i	$-0.516534\pi$
$617$	−2.30636e14	−0.103839	−0.0519194	+	0.998651i	$0.516534\pi$
$618$	8.18152e14	0.365088
$619$	−1.04593e15	−0.462599	−0.231300	−	0.972883i	$-0.574298\pi$
$619$	−1.04593e15	−0.462599	−0.231300	+	0.972883i	$0.574298\pi$
$620$	−4.26990e14	−0.187182
$621$	2.54812e15	1.10717
$622$	−6.11077e14	−0.263177
$623$	−1.29375e15	−0.552287
$624$	3.29315e14	0.139347
$625$	2.26973e15	0.951994
$626$	2.49776e14	0.103846
$627$	2.32934e15	0.959978
$628$	1.33162e15	0.544004
$629$	2.91602e15	1.18090
$630$	−6.97363e13	−0.0279953
$631$	8.37986e14	0.333484	0.166742	−	0.986001i	$-0.446675\pi$
$631$	8.37986e14	0.333484	0.166742	+	0.986001i	$0.446675\pi$
$632$	−1.81062e15	−0.714306
$633$	2.48130e15	0.970420
$634$	8.20271e14	0.318029
$635$	4.49675e14	0.172840
$636$	5.28179e14	0.201264
$637$	−1.31710e13	−0.00497566
$638$	2.16795e14	0.0811960
$639$	−1.22589e15	−0.455196
$640$	−3.28076e14	−0.120777
$641$	−4.90090e15	−1.78878	−0.894390	−	0.447288i	$-0.852390\pi$
$641$	−4.90090e15	−1.78878	−0.894390	+	0.447288i	$0.852390\pi$
$642$	7.60619e14	0.275248
$643$	1.71965e15	0.616991	0.308496	−	0.951226i	$-0.400174\pi$
$643$	1.71965e15	0.616991	0.308496	+	0.951226i	$0.400174\pi$
$644$	2.20328e15	0.783787
$645$	−9.73389e13	−0.0343327
$646$	2.33964e15	0.818219
$647$	8.99014e14	0.311740	0.155870	−	0.987778i	$-0.450182\pi$
$647$	8.99014e14	0.311740	0.155870	+	0.987778i	$0.450182\pi$
$648$	−8.37367e14	−0.287908
$649$	−4.65684e15	−1.58762
$650$	7.70569e14	0.260488
$651$	−4.23189e15	−1.41853
$652$	−2.61153e15	−0.868026
$653$	1.85055e15	0.609927	0.304964	−	0.952364i	$-0.401356\pi$
$653$	1.85055e15	0.609927	0.304964	+	0.952364i	$0.401356\pi$
$654$	−8.02086e14	−0.262146
$655$	−3.05596e14	−0.0990421
$656$	−1.46847e15	−0.471947
$657$	−1.66004e15	−0.529066
$658$	2.79827e15	0.884398
$659$	−8.51169e14	−0.266776	−0.133388	−	0.991064i	$-0.542586\pi$
$659$	−8.51169e14	−0.266776	−0.133388	+	0.991064i	$0.542586\pi$
$660$	−2.06737e14	−0.0642579
$661$	5.25610e15	1.62015	0.810075	−	0.586326i	$-0.199426\pi$
$661$	5.25610e15	1.62015	0.810075	+	0.586326i	$0.199426\pi$
$662$	2.81999e15	0.862042
$663$	1.54097e15	0.467165
$664$	−5.06518e14	−0.152290
$665$	6.12767e14	0.182716
$666$	7.61236e14	0.225119
$667$	−6.52772e14	−0.191456
$668$	−1.72049e15	−0.500473
$669$	−2.74869e15	−0.793017
$670$	1.07831e14	0.0308554
$671$	−1.31184e15	−0.372313
$672$	−2.67566e15	−0.753181
$673$	6.49345e14	0.181298	0.0906490	−	0.995883i	$-0.471106\pi$
$673$	6.49345e14	0.181298	0.0906490	+	0.995883i	$0.471106\pi$
$674$	−1.44077e15	−0.398993
$675$	3.84658e15	1.05658
$676$	1.97160e15	0.537172
$677$	4.60763e15	1.24520	0.622601	−	0.782540i	$-0.286076\pi$
$677$	4.60763e15	1.24520	0.622601	+	0.782540i	$0.286076\pi$
$678$	−2.52581e15	−0.677076
$679$	−5.50363e15	−1.46341
$680$	−4.79552e14	−0.126484
$681$	−2.97291e15	−0.777809
$682$	−3.25561e15	−0.844925
$683$	−1.97762e15	−0.509131	−0.254566	−	0.967056i	$-0.581932\pi$
$683$	−1.97762e15	−0.509131	−0.254566	+	0.967056i	$0.581932\pi$
$684$	−1.97394e15	−0.504111
$685$	−4.88323e14	−0.123711
$686$	1.94299e15	0.488303
$687$	−4.76806e15	−1.18872
$688$	5.14862e14	0.127337
$689$	−7.93236e14	−0.194624
$690$	−1.92608e14	−0.0468817
$691$	−5.65502e15	−1.36554	−0.682770	−	0.730633i	$-0.739225\pi$
$691$	−5.65502e15	−1.36554	−0.682770	+	0.730633i	$0.739225\pi$
$692$	3.03242e15	0.726450
$693$	1.71843e15	0.408412
$694$	−1.84703e15	−0.435510
$695$	8.65862e14	0.202550
$696$	5.05889e14	0.117410
$697$	−6.87143e15	−1.58222
$698$	2.36406e14	0.0540074
$699$	4.00446e15	0.907653
$700$	3.32602e15	0.747973
$701$	6.37840e15	1.42319	0.711595	−	0.702590i	$-0.247973\pi$
$701$	6.37840e15	1.42319	0.711595	+	0.702590i	$0.247973\pi$
$702$	1.28420e15	0.284302
$703$	−6.68892e15	−1.46927
$704$	−6.26535e14	−0.136551
$705$	7.90591e14	0.170967
$706$	2.76311e14	0.0592887
$707$	−1.15212e15	−0.245296
$708$	−4.70540e15	−0.994062
$709$	−1.82210e15	−0.381961	−0.190980	−	0.981594i	$-0.561167\pi$
$709$	−1.82210e15	−0.381961	−0.190980	+	0.981594i	$0.561167\pi$
$710$	2.95813e14	0.0615314
$711$	1.84120e15	0.380030
$712$	−2.32250e15	−0.475680
$713$	9.80269e15	1.99229
$714$	−2.05802e15	−0.415059
$715$	3.10485e14	0.0621380
$716$	−1.51219e15	−0.300321
$717$	−2.05873e15	−0.405736
$718$	3.03912e15	0.594378
$719$	4.72441e15	0.916935	0.458467	−	0.888711i	$-0.348399\pi$
$719$	4.72441e15	0.916935	0.458467	+	0.888711i	$0.348399\pi$
$720$	1.04214e14	0.0200723
$721$	−5.30358e15	−1.01374
$722$	−2.80414e15	−0.531918
$723$	4.53819e15	0.854324
$724$	−4.78844e15	−0.894606
$725$	−9.85408e14	−0.182708
$726$	3.71908e14	0.0684359
$727$	9.76903e15	1.78407	0.892035	−	0.451966i	$-0.149277\pi$
$727$	9.76903e15	1.78407	0.892035	+	0.451966i	$0.149277\pi$
$728$	2.56440e15	0.464797
$729$	5.25397e15	0.945118
$730$	4.00575e14	0.0715169
$731$	2.40921e15	0.426902
$732$	−1.32552e15	−0.233118
$733$	−2.30118e15	−0.401678	−0.200839	−	0.979624i	$-0.564367\pi$
$733$	−2.30118e15	−0.401678	−0.200839	+	0.979624i	$0.564367\pi$
$734$	−4.45317e15	−0.771510
$735$	4.96975e12	0.000854583 0
$736$	6.19786e15	1.05783
$737$	−2.65714e15	−0.450136
$738$	−1.79381e15	−0.301624
$739$	7.78978e15	1.30011	0.650056	−	0.759886i	$-0.274745\pi$
$739$	7.78978e15	1.30011	0.650056	+	0.759886i	$0.274745\pi$
$740$	5.93665e14	0.0983484
$741$	−3.53476e15	−0.581246
$742$	1.05940e15	0.172917
$743$	−7.50411e14	−0.121580	−0.0607898	−	0.998151i	$-0.519362\pi$
$743$	−7.50411e14	−0.121580	−0.0607898	+	0.998151i	$0.519362\pi$
$744$	−7.59695e15	−1.22177
$745$	4.63065e12	0.000739234 0
$746$	−5.55187e14	−0.0879783
$747$	5.15071e14	0.0810222
$748$	5.11689e15	0.799002
$749$	−4.93063e15	−0.764280
$750$	−5.86266e14	−0.0902106
$751$	−8.59656e15	−1.31312	−0.656561	−	0.754273i	$-0.727989\pi$
$751$	−8.59656e15	−1.31312	−0.656561	+	0.754273i	$0.727989\pi$
$752$	−4.18174e15	−0.634101
$753$	2.84757e15	0.428650
$754$	−3.28984e14	−0.0491624
$755$	−2.40596e14	−0.0356927
$756$	5.54303e15	0.816351
$757$	−5.23719e15	−0.765722	−0.382861	−	0.923806i	$-0.625061\pi$
$757$	−5.23719e15	−0.765722	−0.382861	+	0.923806i	$0.625061\pi$
$758$	1.17020e15	0.169856
$759$	4.74620e15	0.683938
$760$	1.10002e15	0.157372
$761$	−5.40274e15	−0.767358	−0.383679	−	0.923466i	$-0.625343\pi$
$761$	−5.40274e15	−0.767358	−0.383679	+	0.923466i	$0.625343\pi$
$762$	3.46432e15	0.488502
$763$	5.19944e15	0.727899
$764$	−2.48834e15	−0.345856
$765$	4.87650e14	0.0672931
$766$	−7.01999e15	−0.961785
$767$	7.06672e15	0.961266
$768$	−3.35647e15	−0.453311
$769$	1.68378e15	0.225783	0.112891	−	0.993607i	$-0.463989\pi$
$769$	1.68378e15	0.225783	0.112891	+	0.993607i	$0.463989\pi$
$770$	−4.14663e14	−0.0552073
$771$	4.14091e15	0.547390
$772$	3.15962e15	0.414705
$773$	−6.91163e14	−0.0900727	−0.0450363	−	0.998985i	$-0.514340\pi$
$773$	−6.91163e14	−0.0900727	−0.0450363	+	0.998985i	$0.514340\pi$
$774$	6.28930e14	0.0813818
$775$	1.47979e16	1.90126
$776$	−9.87995e15	−1.26042
$777$	5.88380e15	0.745320
$778$	1.68442e15	0.211866
$779$	1.57620e16	1.96859
$780$	3.13722e14	0.0389068
$781$	−7.28937e15	−0.897655
$782$	4.76718e15	0.582941
$783$	−1.64225e15	−0.199411
$784$	−2.62869e13	−0.00316957
$785$	7.54604e14	0.0903516
$786$	−2.35433e15	−0.279926
$787$	−8.76844e15	−1.03529	−0.517644	−	0.855596i	$-0.673191\pi$
$787$	−8.76844e15	−1.03529	−0.517644	+	0.855596i	$0.673191\pi$
$788$	2.04460e15	0.239726
$789$	3.65894e15	0.426022
$790$	−4.44288e14	−0.0513707
$791$	1.63733e16	1.88003
$792$	3.08487e15	0.351762
$793$	1.99071e15	0.225427
$794$	8.73885e14	0.0982746
$795$	2.99309e14	0.0334272
$796$	−4.55780e15	−0.505514
$797$	−9.97692e15	−1.09894	−0.549472	−	0.835512i	$-0.685171\pi$
$797$	−9.97692e15	−1.09894	−0.549472	+	0.835512i	$0.685171\pi$
$798$	4.72080e15	0.516416
$799$	−1.95677e16	−2.12585
$800$	9.35614e15	1.00949
$801$	2.36171e15	0.253074
$802$	−7.03113e15	−0.748283
$803$	−9.87090e15	−1.04333
$804$	−2.68485e15	−0.281846
$805$	1.24856e15	0.130176
$806$	4.94037e15	0.511583
$807$	1.45641e15	0.149789
$808$	−2.06825e15	−0.211271
$809$	1.81464e16	1.84108	0.920540	−	0.390648i	$-0.127749\pi$
$809$	1.81464e16	1.84108	0.920540	+	0.390648i	$0.127749\pi$
$810$	−2.05472e14	−0.0207055
$811$	1.48265e16	1.48397	0.741984	−	0.670418i	$-0.233885\pi$
$811$	1.48265e16	1.48397	0.741984	+	0.670418i	$0.233885\pi$
$812$	−1.42000e15	−0.141166
$813$	6.22931e15	0.615095
$814$	4.52644e15	0.443938
$815$	−1.47990e15	−0.144167
$816$	3.07551e15	0.297592
$817$	−5.52636e15	−0.531151
$818$	4.23583e15	0.404385
$819$	−2.60770e15	−0.247284
$820$	−1.39894e15	−0.131772
$821$	−1.98325e16	−1.85562	−0.927812	−	0.373048i	$-0.878313\pi$
$821$	−1.98325e16	−1.85562	−0.927812	+	0.373048i	$0.878313\pi$
$822$	−3.76207e15	−0.349649
$823$	−4.07918e15	−0.376594	−0.188297	−	0.982112i	$-0.560297\pi$
$823$	−4.07918e15	−0.376594	−0.188297	+	0.982112i	$0.560297\pi$
$824$	−9.52083e15	−0.873123
$825$	7.16475e15	0.652686
$826$	−9.43786e15	−0.854050
$827$	−1.50273e16	−1.35083	−0.675417	−	0.737436i	$-0.736036\pi$
$827$	−1.50273e16	−1.35083	−0.675417	+	0.737436i	$0.736036\pi$
$828$	−4.02205e15	−0.359154
$829$	1.78355e15	0.158211	0.0791054	−	0.996866i	$-0.474794\pi$
$829$	1.78355e15	0.158211	0.0791054	+	0.996866i	$0.474794\pi$
$830$	−1.24289e14	−0.0109522
$831$	−1.18928e16	−1.04107
$832$	9.50763e14	0.0826787
$833$	−1.23005e14	−0.0106261
$834$	6.67065e15	0.572473
$835$	−9.74968e14	−0.0831217
$836$	−1.17374e16	−0.994116
$837$	2.46616e16	2.07507
$838$	9.19362e14	0.0768501
$839$	2.08273e16	1.72959	0.864794	−	0.502126i	$-0.167449\pi$
$839$	2.08273e16	1.72959	0.864794	+	0.502126i	$0.167449\pi$
$840$	−9.67616e14	−0.0798302
$841$	4.20707e14	0.0344828
$842$	−5.73115e15	−0.466686
$843$	6.65050e15	0.538026
$844$	−1.25031e16	−1.00493
$845$	1.11727e15	0.0892168
$846$	−5.10820e15	−0.405257
$847$	−2.41085e15	−0.190025
$848$	−1.58316e15	−0.123979
$849$	−6.08399e15	−0.473365
$850$	7.19642e15	0.556304
$851$	−1.36292e16	−1.04678
$852$	−7.36538e15	−0.562053
$853$	−2.58806e16	−1.96225	−0.981126	−	0.193370i	$-0.938058\pi$
$853$	−2.58806e16	−1.96225	−0.981126	+	0.193370i	$0.938058\pi$
$854$	−2.65867e15	−0.200284
$855$	−1.11860e15	−0.0837259
$856$	−8.85132e15	−0.658267
$857$	−1.86002e16	−1.37443	−0.687215	−	0.726454i	$-0.741167\pi$
$857$	−1.86002e16	−1.37443	−0.687215	+	0.726454i	$0.741167\pi$
$858$	2.39199e15	0.175622
$859$	−1.99564e16	−1.45586	−0.727931	−	0.685650i	$-0.759518\pi$
$859$	−1.99564e16	−1.45586	−0.727931	+	0.685650i	$0.759518\pi$
$860$	4.90484e14	0.0355536
$861$	−1.38648e16	−0.998612
$862$	2.89701e15	0.207329
$863$	5.86095e14	0.0416782	0.0208391	−	0.999783i	$-0.493366\pi$
$863$	5.86095e14	0.0416782	0.0208391	+	0.999783i	$0.493366\pi$
$864$	1.55926e16	1.10178
$865$	1.71841e15	0.120653
$866$	2.61998e14	0.0182789
$867$	3.75349e15	0.260213
$868$	2.13242e16	1.46897
$869$	1.09481e16	0.749425
$870$	1.24134e14	0.00844377
$871$	4.03220e15	0.272547
$872$	9.33387e15	0.626933
$873$	1.00468e16	0.670577
$874$	−1.09352e16	−0.725294
$875$	3.80040e15	0.250487
$876$	−9.97383e15	−0.653265
$877$	−2.50479e16	−1.63032	−0.815162	−	0.579232i	$-0.803352\pi$
$877$	−2.50479e16	−1.63032	−0.815162	+	0.579232i	$0.803352\pi$
$878$	1.24314e16	0.804083
$879$	1.81003e16	1.16345
$880$	6.19672e14	0.0395829
$881$	−2.71552e16	−1.72379	−0.861896	−	0.507085i	$-0.830723\pi$
$881$	−2.71552e16	−1.72379	−0.861896	+	0.507085i	$0.830723\pi$
$882$	−3.21108e13	−0.00202569
$883$	−6.82561e14	−0.0427915	−0.0213958	−	0.999771i	$-0.506811\pi$
$883$	−6.82561e14	−0.0427915	−0.0213958	+	0.999771i	$0.506811\pi$
$884$	−7.76486e15	−0.483778
$885$	−2.66646e15	−0.165100
$886$	3.90583e15	0.240341
$887$	1.46682e16	0.897008	0.448504	−	0.893781i	$-0.351957\pi$
$887$	1.46682e16	0.897008	0.448504	+	0.893781i	$0.351957\pi$
$888$	1.05624e16	0.641937
$889$	−2.24571e16	−1.35642
$890$	−5.69891e14	−0.0342095
$891$	5.06320e15	0.302063
$892$	1.38505e16	0.821218
$893$	4.48854e16	2.64498
$894$	3.56748e13	0.00208932
$895$	−8.56932e14	−0.0498792
$896$	1.63844e16	0.947841
$897$	−7.20233e15	−0.414109
$898$	1.72414e15	0.0985266
$899$	−6.31777e15	−0.358827
$900$	−6.07159e15	−0.342743
$901$	−7.40811e15	−0.415644
$902$	−1.06663e16	−0.594808
$903$	4.86118e15	0.269438
$904$	2.93928e16	1.61925
$905$	−2.71352e15	−0.148582
$906$	−1.85356e15	−0.100879
$907$	1.65196e16	0.893634	0.446817	−	0.894625i	$-0.352558\pi$
$907$	1.65196e16	0.893634	0.446817	+	0.894625i	$0.352558\pi$
$908$	1.49803e16	0.805469
$909$	2.10317e15	0.112402
$910$	6.29249e14	0.0334268
$911$	−2.65587e16	−1.40235	−0.701173	−	0.712991i	$-0.747340\pi$
$911$	−2.65587e16	−1.40235	−0.701173	+	0.712991i	$0.747340\pi$
$912$	−7.05475e15	−0.370263
$913$	3.06270e15	0.159777
$914$	9.69037e15	0.502500
$915$	−7.51148e14	−0.0387177
$916$	2.40259e16	1.23099
$917$	1.52617e16	0.777268
$918$	1.19933e16	0.607161
$919$	1.23677e16	0.622378	0.311189	−	0.950348i	$-0.399273\pi$
$919$	1.23677e16	0.622378	0.311189	+	0.950348i	$0.399273\pi$
$920$	2.24137e15	0.112120
$921$	−2.69879e16	−1.34196
$922$	−6.53543e15	−0.323038
$923$	1.10616e16	0.543510
$924$	1.03246e16	0.504287
$925$	−2.05743e16	−0.998952
$926$	−2.35447e15	−0.113640
$927$	9.68160e15	0.464525
$928$	−3.99448e15	−0.190523
$929$	−2.12065e16	−1.00550	−0.502751	−	0.864432i	$-0.667679\pi$
$929$	−2.12065e16	−1.00550	−0.502751	+	0.864432i	$0.667679\pi$
$930$	−1.86413e15	−0.0878658
$931$	2.82155e14	0.0132210
$932$	−2.01782e16	−0.939929
$933$	8.62208e15	0.399267
$934$	5.70376e15	0.262575
$935$	2.89965e15	0.132703
$936$	−4.68127e15	−0.212984
$937$	4.75067e15	0.214876	0.107438	−	0.994212i	$-0.465735\pi$
$937$	4.75067e15	0.214876	0.107438	+	0.994212i	$0.465735\pi$
$938$	−5.38515e15	−0.242149
$939$	−3.52425e15	−0.157546
$940$	−3.98373e15	−0.177046
$941$	1.38698e16	0.612813	0.306406	−	0.951901i	$-0.400873\pi$
$941$	1.38698e16	0.612813	0.306406	+	0.951901i	$0.400873\pi$
$942$	5.81352e15	0.255364
$943$	3.21163e16	1.40253
$944$	1.41039e16	0.612342
$945$	3.14113e15	0.135585
$946$	3.73972e15	0.160486
$947$	−5.40709e15	−0.230695	−0.115348	−	0.993325i	$-0.536798\pi$
$947$	−5.40709e15	−0.230695	−0.115348	+	0.993325i	$0.536798\pi$
$948$	1.10622e16	0.469242
$949$	1.49790e16	0.631713
$950$	−1.65075e16	−0.692152
$951$	−1.15737e16	−0.482482
$952$	2.39492e16	0.992631
$953$	−2.32910e16	−0.959793	−0.479896	−	0.877325i	$-0.659326\pi$
$953$	−2.32910e16	−0.959793	−0.479896	+	0.877325i	$0.659326\pi$
$954$	−1.93391e15	−0.0792355
$955$	−1.41009e15	−0.0574419
$956$	1.03738e16	0.420165
$957$	−3.05890e15	−0.123183
$958$	2.13242e15	0.0853814
$959$	2.43872e16	0.970867
$960$	−3.58748e14	−0.0142003
$961$	6.94656e16	2.73396
$962$	−6.86884e15	−0.268795
$963$	9.00078e15	0.350216
$964$	−2.28677e16	−0.884704
$965$	1.79050e15	0.0688768
$966$	9.61897e15	0.367921
$967$	−4.20715e16	−1.60008	−0.800042	−	0.599944i	$-0.795189\pi$
$967$	−4.20715e16	−1.60008	−0.800042	+	0.599944i	$0.795189\pi$
$968$	−4.32789e15	−0.163667
$969$	−3.30115e16	−1.24132
$970$	−2.42433e15	−0.0906456
$971$	−4.86896e16	−1.81022	−0.905108	−	0.425181i	$-0.860210\pi$
$971$	−4.86896e16	−1.81022	−0.905108	+	0.425181i	$0.860210\pi$
$972$	−1.70677e16	−0.630974
$973$	−4.32418e16	−1.58958
$974$	−1.09013e16	−0.398479
$975$	−1.08725e16	−0.395187
$976$	3.97311e15	0.143601
$977$	−3.15141e15	−0.113262	−0.0566311	−	0.998395i	$-0.518036\pi$
$977$	−3.15141e15	−0.113262	−0.0566311	+	0.998395i	$0.518036\pi$
$978$	−1.14013e16	−0.407464
$979$	1.40431e16	0.499068
$980$	−2.50422e13	−0.000884972 0
$981$	−9.49148e15	−0.333545
$982$	2.14632e16	0.750036
$983$	1.18477e16	0.411709	0.205855	−	0.978583i	$-0.434003\pi$
$983$	1.18477e16	0.411709	0.205855	+	0.978583i	$0.434003\pi$
$984$	−2.48897e16	−0.860096
$985$	1.15864e15	0.0398151
$986$	−3.07242e15	−0.104992
$987$	−3.94827e16	−1.34172
$988$	1.78114e16	0.601915
$989$	−1.12604e16	−0.378419
$990$	7.56961e14	0.0252976
$991$	3.30955e16	1.09993	0.549963	−	0.835189i	$-0.314642\pi$
$991$	3.30955e16	1.09993	0.549963	+	0.835189i	$0.314642\pi$
$992$	5.99852e16	1.98258
$993$	−3.97891e16	−1.30780
$994$	−1.47731e16	−0.482889
$995$	−2.58282e15	−0.0839589
$996$	3.09463e15	0.100042
$997$	1.17372e15	0.0377346	0.0188673	−	0.999822i	$-0.493994\pi$
$997$	1.17372e15	0.0377346	0.0188673	+	0.999822i	$0.493994\pi$
$998$	−2.79013e16	−0.892084
$999$	−3.42883e16	−1.09028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.6	✓	11
3.2	odd	2		261.12.a.a.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.6	✓	11	1.1	even	1	trivial
261.12.a.a.1.6		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)

\(f(q)\)	\(=\)	\(q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +O(q^{10})\)	\(q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +19497.9 q^{10} -480464. q^{11} -485474. q^{12} +729102. q^{13} -973741. q^{14} -275109. q^{15} +1.45516e6 q^{16} +6.80915e6 q^{17} +1.77755e6 q^{18} -1.56192e7 q^{19} +1.38626e6 q^{20} +1.37392e7 q^{21} +1.05696e7 q^{22} -3.18252e7 q^{23} +2.46641e7 q^{24} -4.80426e7 q^{25} -1.60393e7 q^{26} -8.00660e7 q^{27} -6.92307e7 q^{28} +2.05111e7 q^{29} +6.05205e6 q^{30} -3.08016e8 q^{31} -1.94747e8 q^{32} -1.49133e8 q^{33} -1.49793e8 q^{34} -3.92317e7 q^{35} +1.26379e8 q^{36} +4.28251e8 q^{37} +3.43602e8 q^{38} +2.26309e8 q^{39} -7.04276e7 q^{40} -1.00915e9 q^{41} -3.02244e8 q^{42} +3.53819e8 q^{43} +7.51473e8 q^{44} +7.16169e7 q^{45} +7.00114e8 q^{46} -2.87373e9 q^{47} +4.51672e8 q^{48} -1.80646e7 q^{49} +1.05687e9 q^{50} +2.11352e9 q^{51} -1.14036e9 q^{52} -1.08796e9 q^{53} +1.76135e9 q^{54} +4.25846e8 q^{55} +3.51721e9 q^{56} -4.84810e9 q^{57} -4.51219e8 q^{58} +9.69237e9 q^{59} +4.30286e8 q^{60} +2.73036e9 q^{61} +6.77597e9 q^{62} -3.57660e9 q^{63} +1.30402e9 q^{64} -6.46218e8 q^{65} +3.28074e9 q^{66} +5.53037e9 q^{67} -1.06499e10 q^{68} -9.87837e9 q^{69} +8.63048e8 q^{70} +1.51715e10 q^{71} -6.42060e9 q^{72} +2.05445e10 q^{73} -9.42097e9 q^{74} -1.49121e10 q^{75} +2.44293e10 q^{76} -2.12671e10 q^{77} -4.97851e9 q^{78} -2.27864e10 q^{79} -1.28974e9 q^{80} -1.05381e10 q^{81} +2.21999e10 q^{82} -6.37446e9 q^{83} -2.14888e10 q^{84} -6.03510e9 q^{85} -7.78357e9 q^{86} +6.36654e9 q^{87} -3.81780e10 q^{88} -2.92283e10 q^{89} -1.57548e9 q^{90} +3.22726e10 q^{91} +4.97764e10 q^{92} -9.56066e10 q^{93} +6.32185e10 q^{94} +1.38436e10 q^{95} -6.04483e10 q^{96} -1.24338e11 q^{97} +3.97399e8 q^{98} +3.88226e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 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