LMFDB - Embedded newform 8085.2.a.co.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 16 x^{12} + 76 x^{11} + 78 x^{10} - 532 x^{9} - 56 x^{8} + 1684 x^{7} - 471 x^{6} + \cdots + 14 $ x^14 - 4x^13 - 16x^12 + 76x^11 + 78x^10 - 532x^9 - 56x^8 + 1684x^7 - 471x^6 - 2352x^5 + 950x^4 + 1184x^3 - 340x^2 - 152*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.347588$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.347588 q^{2} -1.00000 q^{3} -1.87918 q^{4} -1.00000 q^{5} +0.347588 q^{6} +1.34836 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.347588 q^{2} -1.00000 q^{3} -1.87918 q^{4} -1.00000 q^{5} +0.347588 q^{6} +1.34836 q^{8} +1.00000 q^{9} +0.347588 q^{10} +1.00000 q^{11} +1.87918 q^{12} -5.01489 q^{13} +1.00000 q^{15} +3.28969 q^{16} -6.74730 q^{17} -0.347588 q^{18} -6.66003 q^{19} +1.87918 q^{20} -0.347588 q^{22} -2.01998 q^{23} -1.34836 q^{24} +1.00000 q^{25} +1.74311 q^{26} -1.00000 q^{27} -3.99365 q^{29} -0.347588 q^{30} -7.39618 q^{31} -3.84017 q^{32} -1.00000 q^{33} +2.34528 q^{34} -1.87918 q^{36} -3.29771 q^{37} +2.31494 q^{38} +5.01489 q^{39} -1.34836 q^{40} +6.77964 q^{41} +10.4409 q^{43} -1.87918 q^{44} -1.00000 q^{45} +0.702119 q^{46} -3.28767 q^{47} -3.28969 q^{48} -0.347588 q^{50} +6.74730 q^{51} +9.42389 q^{52} +0.122872 q^{53} +0.347588 q^{54} -1.00000 q^{55} +6.66003 q^{57} +1.38814 q^{58} -11.3232 q^{59} -1.87918 q^{60} -2.63579 q^{61} +2.57082 q^{62} -5.24459 q^{64} +5.01489 q^{65} +0.347588 q^{66} -2.00560 q^{67} +12.6794 q^{68} +2.01998 q^{69} -15.7259 q^{71} +1.34836 q^{72} -12.1577 q^{73} +1.14624 q^{74} -1.00000 q^{75} +12.5154 q^{76} -1.74311 q^{78} +2.65771 q^{79} -3.28969 q^{80} +1.00000 q^{81} -2.35652 q^{82} +1.18360 q^{83} +6.74730 q^{85} -3.62914 q^{86} +3.99365 q^{87} +1.34836 q^{88} -4.23551 q^{89} +0.347588 q^{90} +3.79591 q^{92} +7.39618 q^{93} +1.14275 q^{94} +6.66003 q^{95} +3.84017 q^{96} +4.83004 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{2} - 14 q^{3} + 20 q^{4} - 14 q^{5} - 4 q^{6} + 12 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 4 * q^2 - 14 * q^3 + 20 * q^4 - 14 * q^5 - 4 * q^6 + 12 * q^8 + 14 * q^9	$ 14 q + 4 q^{2} - 14 q^{3} + 20 q^{4} - 14 q^{5} - 4 q^{6} + 12 q^{8} + 14 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 8 q^{13} + 14 q^{15} + 32 q^{16} + 6 q^{17} + 4 q^{18} - 10 q^{19} - 20 q^{20} + 4 q^{22} + 22 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} - 14 q^{27} + 10 q^{29} + 4 q^{30} - 20 q^{31} + 28 q^{32} - 14 q^{33} - 16 q^{34} + 20 q^{36} + 20 q^{37} + 16 q^{38} + 8 q^{39} - 12 q^{40} + 22 q^{43} + 20 q^{44} - 14 q^{45} + 4 q^{46} + 8 q^{47} - 32 q^{48} + 4 q^{50} - 6 q^{51} - 4 q^{52} + 34 q^{53} - 4 q^{54} - 14 q^{55} + 10 q^{57} + 20 q^{58} - 22 q^{59} + 20 q^{60} - 6 q^{61} + 28 q^{62} + 32 q^{64} + 8 q^{65} - 4 q^{66} + 32 q^{67} + 56 q^{68} - 22 q^{69} + 4 q^{71} + 12 q^{72} - 8 q^{73} + 36 q^{74} - 14 q^{75} - 24 q^{76} + 12 q^{78} + 12 q^{79} - 32 q^{80} + 14 q^{81} + 28 q^{82} + 26 q^{83} - 6 q^{85} + 40 q^{86} - 10 q^{87} + 12 q^{88} - 10 q^{89} - 4 q^{90} + 8 q^{92} + 20 q^{93} - 28 q^{94} + 10 q^{95} - 28 q^{96} - 14 q^{97} + 14 q^{99}+O(q^{100}) $ 14 * q + 4 * q^2 - 14 * q^3 + 20 * q^4 - 14 * q^5 - 4 * q^6 + 12 * q^8 + 14 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 8 * q^13 + 14 * q^15 + 32 * q^16 + 6 * q^17 + 4 * q^18 - 10 * q^19 - 20 * q^20 + 4 * q^22 + 22 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 - 14 * q^27 + 10 * q^29 + 4 * q^30 - 20 * q^31 + 28 * q^32 - 14 * q^33 - 16 * q^34 + 20 * q^36 + 20 * q^37 + 16 * q^38 + 8 * q^39 - 12 * q^40 + 22 * q^43 + 20 * q^44 - 14 * q^45 + 4 * q^46 + 8 * q^47 - 32 * q^48 + 4 * q^50 - 6 * q^51 - 4 * q^52 + 34 * q^53 - 4 * q^54 - 14 * q^55 + 10 * q^57 + 20 * q^58 - 22 * q^59 + 20 * q^60 - 6 * q^61 + 28 * q^62 + 32 * q^64 + 8 * q^65 - 4 * q^66 + 32 * q^67 + 56 * q^68 - 22 * q^69 + 4 * q^71 + 12 * q^72 - 8 * q^73 + 36 * q^74 - 14 * q^75 - 24 * q^76 + 12 * q^78 + 12 * q^79 - 32 * q^80 + 14 * q^81 + 28 * q^82 + 26 * q^83 - 6 * q^85 + 40 * q^86 - 10 * q^87 + 12 * q^88 - 10 * q^89 - 4 * q^90 + 8 * q^92 + 20 * q^93 - 28 * q^94 + 10 * q^95 - 28 * q^96 - 14 * q^97 + 14 * 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 $

$2$	−0.347588	−0.245782	−0.122891	−	0.992420i	$-0.539216\pi$
$2$	−0.347588	−0.245782	−0.122891	+	0.992420i	$0.539216\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.87918	−0.939591
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.347588	0.141902
$7$	0	0
$7$	0	0
$8$	1.34836	0.476716
$9$	1.00000	0.333333
$10$	0.347588	0.109917
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.87918	0.542473
$13$	−5.01489	−1.39088	−0.695440	−	0.718584i	$-0.744790\pi$
$13$	−5.01489	−1.39088	−0.695440	+	0.718584i	$0.744790\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	3.28969	0.822423
$17$	−6.74730	−1.63646	−0.818231	−	0.574890i	$-0.805045\pi$
$17$	−6.74730	−1.63646	−0.818231	+	0.574890i	$0.805045\pi$
$18$	−0.347588	−0.0819272
$19$	−6.66003	−1.52792	−0.763958	−	0.645266i	$-0.776746\pi$
$19$	−6.66003	−1.52792	−0.763958	+	0.645266i	$0.776746\pi$
$20$	1.87918	0.420198
$21$	0	0
$22$	−0.347588	−0.0741059
$23$	−2.01998	−0.421195	−0.210597	−	0.977573i	$-0.567541\pi$
$23$	−2.01998	−0.421195	−0.210597	+	0.977573i	$0.567541\pi$
$24$	−1.34836	−0.275232
$25$	1.00000	0.200000
$26$	1.74311	0.341853
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.99365	−0.741603	−0.370802	−	0.928712i	$-0.620917\pi$
$29$	−3.99365	−0.741603	−0.370802	+	0.928712i	$0.620917\pi$
$30$	−0.347588	−0.0634605
$31$	−7.39618	−1.32839	−0.664196	−	0.747558i	$-0.731226\pi$
$31$	−7.39618	−1.32839	−0.664196	+	0.747558i	$0.731226\pi$
$32$	−3.84017	−0.678852
$33$	−1.00000	−0.174078
$34$	2.34528	0.402212
$35$	0	0
$36$	−1.87918	−0.313197
$37$	−3.29771	−0.542140	−0.271070	−	0.962560i	$-0.587378\pi$
$37$	−3.29771	−0.542140	−0.271070	+	0.962560i	$0.587378\pi$
$38$	2.31494	0.375533
$39$	5.01489	0.803025
$40$	−1.34836	−0.213194
$41$	6.77964	1.05880	0.529401	−	0.848372i	$-0.322417\pi$
$41$	6.77964	1.05880	0.529401	+	0.848372i	$0.322417\pi$
$42$	0	0
$43$	10.4409	1.59223	0.796113	−	0.605148i	$-0.206886\pi$
$43$	10.4409	1.59223	0.796113	+	0.605148i	$0.206886\pi$
$44$	−1.87918	−0.283297
$45$	−1.00000	−0.149071
$46$	0.702119	0.103522
$47$	−3.28767	−0.479556	−0.239778	−	0.970828i	$-0.577075\pi$
$47$	−3.28767	−0.479556	−0.239778	+	0.970828i	$0.577075\pi$
$48$	−3.28969	−0.474826
$49$	0	0
$50$	−0.347588	−0.0491563
$51$	6.74730	0.944811
$52$	9.42389	1.30686
$53$	0.122872	0.0168777	0.00843885	−	0.999964i	$-0.497314\pi$
$53$	0.122872	0.0168777	0.00843885	+	0.999964i	$0.497314\pi$
$54$	0.347588	0.0473007
$55$	−1.00000	−0.134840
$56$	0	0
$57$	6.66003	0.882142
$58$	1.38814	0.182272
$59$	−11.3232	−1.47415	−0.737074	−	0.675812i	$-0.763793\pi$
$59$	−11.3232	−1.47415	−0.737074	+	0.675812i	$0.763793\pi$
$60$	−1.87918	−0.242601
$61$	−2.63579	−0.337479	−0.168739	−	0.985661i	$-0.553970\pi$
$61$	−2.63579	−0.337479	−0.168739	+	0.985661i	$0.553970\pi$
$62$	2.57082	0.326494
$63$	0	0
$64$	−5.24459	−0.655574
$65$	5.01489	0.622020
$66$	0.347588	0.0427851
$67$	−2.00560	−0.245023	−0.122512	−	0.992467i	$-0.539095\pi$
$67$	−2.00560	−0.245023	−0.122512	+	0.992467i	$0.539095\pi$
$68$	12.6794	1.53761
$69$	2.01998	0.243177
$70$	0	0
$71$	−15.7259	−1.86632	−0.933161	−	0.359458i	$-0.882962\pi$
$71$	−15.7259	−1.86632	−0.933161	+	0.359458i	$0.882962\pi$
$72$	1.34836	0.158905
$73$	−12.1577	−1.42295	−0.711476	−	0.702710i	$-0.751973\pi$
$73$	−12.1577	−1.42295	−0.711476	+	0.702710i	$0.751973\pi$
$74$	1.14624	0.133248
$75$	−1.00000	−0.115470
$76$	12.5154	1.43562
$77$	0	0
$78$	−1.74311	−0.197369
$79$	2.65771	0.299015	0.149508	−	0.988761i	$-0.452231\pi$
$79$	2.65771	0.299015	0.149508	+	0.988761i	$0.452231\pi$
$80$	−3.28969	−0.367799
$81$	1.00000	0.111111
$82$	−2.35652	−0.260234
$83$	1.18360	0.129917	0.0649585	−	0.997888i	$-0.479309\pi$
$83$	1.18360	0.129917	0.0649585	+	0.997888i	$0.479309\pi$
$84$	0	0
$85$	6.74730	0.731848
$86$	−3.62914	−0.391340
$87$	3.99365	0.428165
$88$	1.34836	0.143735
$89$	−4.23551	−0.448964	−0.224482	−	0.974478i	$-0.572069\pi$
$89$	−4.23551	−0.448964	−0.224482	+	0.974478i	$0.572069\pi$
$90$	0.347588	0.0366389
$91$	0	0
$92$	3.79591	0.395751
$93$	7.39618	0.766948
$94$	1.14275	0.117866
$95$	6.66003	0.683304
$96$	3.84017	0.391936
$97$	4.83004	0.490416	0.245208	−	0.969470i	$-0.421144\pi$
$97$	4.83004	0.490416	0.245208	+	0.969470i	$0.421144\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.87918	−0.187918
$101$	−4.01994	−0.399999	−0.200000	−	0.979796i	$-0.564094\pi$
$101$	−4.01994	−0.399999	−0.200000	+	0.979796i	$0.564094\pi$
$102$	−2.34528	−0.232217
$103$	16.0626	1.58270	0.791349	−	0.611365i	$-0.209379\pi$
$103$	16.0626	1.58270	0.791349	+	0.611365i	$0.209379\pi$
$104$	−6.76185	−0.663054
$105$	0	0
$106$	−0.0427086	−0.00414823
$107$	2.58590	0.249988	0.124994	−	0.992157i	$-0.460109\pi$
$107$	2.58590	0.249988	0.124994	+	0.992157i	$0.460109\pi$
$108$	1.87918	0.180824
$109$	−14.7599	−1.41374	−0.706871	−	0.707342i	$-0.749894\pi$
$109$	−14.7599	−1.41374	−0.706871	+	0.707342i	$0.749894\pi$
$110$	0.347588	0.0331412
$111$	3.29771	0.313005
$112$	0	0
$113$	−14.3840	−1.35313	−0.676566	−	0.736382i	$-0.736533\pi$
$113$	−14.3840	−1.35313	−0.676566	+	0.736382i	$0.736533\pi$
$114$	−2.31494	−0.216814
$115$	2.01998	0.188364
$116$	7.50481	0.696804
$117$	−5.01489	−0.463627
$118$	3.93579	0.362319
$119$	0	0
$120$	1.34836	0.123087
$121$	1.00000	0.0909091
$122$	0.916169	0.0829460
$123$	−6.77964	−0.611300
$124$	13.8988	1.24815
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.0198	−1.42152	−0.710762	−	0.703432i	$-0.751650\pi$
$127$	−16.0198	−1.42152	−0.710762	+	0.703432i	$0.751650\pi$
$128$	9.50329	0.839980
$129$	−10.4409	−0.919272
$130$	−1.74311	−0.152881
$131$	12.6789	1.10776	0.553882	−	0.832595i	$-0.313146\pi$
$131$	12.6789	1.10776	0.553882	+	0.832595i	$0.313146\pi$
$132$	1.87918	0.163562
$133$	0	0
$134$	0.697122	0.0602222
$135$	1.00000	0.0860663
$136$	−9.09777	−0.780127
$137$	−2.21855	−0.189543	−0.0947716	−	0.995499i	$-0.530212\pi$
$137$	−2.21855	−0.189543	−0.0947716	+	0.995499i	$0.530212\pi$
$138$	−0.702119	−0.0597684
$139$	−13.0431	−1.10630	−0.553152	−	0.833080i	$-0.686575\pi$
$139$	−13.0431	−1.10630	−0.553152	+	0.833080i	$0.686575\pi$
$140$	0	0
$141$	3.28767	0.276872
$142$	5.46613	0.458708
$143$	−5.01489	−0.419366
$144$	3.28969	0.274141
$145$	3.99365	0.331655
$146$	4.22587	0.349735
$147$	0	0
$148$	6.19700	0.509390
$149$	−7.23453	−0.592676	−0.296338	−	0.955083i	$-0.595766\pi$
$149$	−7.23453	−0.592676	−0.296338	+	0.955083i	$0.595766\pi$
$150$	0.347588	0.0283804
$151$	−22.9862	−1.87059	−0.935296	−	0.353866i	$-0.884867\pi$
$151$	−22.9862	−1.87059	−0.935296	+	0.353866i	$0.884867\pi$
$152$	−8.98009	−0.728381
$153$	−6.74730	−0.545487
$154$	0	0
$155$	7.39618	0.594075
$156$	−9.42389	−0.754515
$157$	5.69046	0.454148	0.227074	−	0.973878i	$-0.427084\pi$
$157$	5.69046	0.454148	0.227074	+	0.973878i	$0.427084\pi$
$158$	−0.923786	−0.0734925
$159$	−0.122872	−0.00974435
$160$	3.84017	0.303592
$161$	0	0
$162$	−0.347588	−0.0273091
$163$	−6.32929	−0.495748	−0.247874	−	0.968792i	$-0.579732\pi$
$163$	−6.32929	−0.495748	−0.247874	+	0.968792i	$0.579732\pi$
$164$	−12.7402	−0.994842
$165$	1.00000	0.0778499
$166$	−0.411404	−0.0319312
$167$	−1.98587	−0.153671	−0.0768354	−	0.997044i	$-0.524482\pi$
$167$	−1.98587	−0.153671	−0.0768354	+	0.997044i	$0.524482\pi$
$168$	0	0
$169$	12.1491	0.934546
$170$	−2.34528	−0.179875
$171$	−6.66003	−0.509305
$172$	−19.6204	−1.49604
$173$	1.36999	0.104158	0.0520791	−	0.998643i	$-0.483415\pi$
$173$	1.36999	0.104158	0.0520791	+	0.998643i	$0.483415\pi$
$174$	−1.38814	−0.105235
$175$	0	0
$176$	3.28969	0.247970
$177$	11.3232	0.851100
$178$	1.47221	0.110347
$179$	−15.3966	−1.15079	−0.575397	−	0.817874i	$-0.695153\pi$
$179$	−15.3966	−1.15079	−0.575397	+	0.817874i	$0.695153\pi$
$180$	1.87918	0.140066
$181$	−5.74788	−0.427236	−0.213618	−	0.976917i	$-0.568525\pi$
$181$	−5.74788	−0.427236	−0.213618	+	0.976917i	$0.568525\pi$
$182$	0	0
$183$	2.63579	0.194843
$184$	−2.72365	−0.200790
$185$	3.29771	0.242452
$186$	−2.57082	−0.188502
$187$	−6.74730	−0.493412
$188$	6.17814	0.450587
$189$	0	0
$190$	−2.31494	−0.167944
$191$	−10.9350	−0.791226	−0.395613	−	0.918417i	$-0.629468\pi$
$191$	−10.9350	−0.791226	−0.395613	+	0.918417i	$0.629468\pi$
$192$	5.24459	0.378496
$193$	22.1226	1.59242	0.796209	−	0.605021i	$-0.206835\pi$
$193$	22.1226	1.59242	0.796209	+	0.605021i	$0.206835\pi$
$194$	−1.67886	−0.120535
$195$	−5.01489	−0.359124
$196$	0	0
$197$	6.46630	0.460705	0.230352	−	0.973107i	$-0.426012\pi$
$197$	6.46630	0.460705	0.230352	+	0.973107i	$0.426012\pi$
$198$	−0.347588	−0.0247020
$199$	−14.7563	−1.04605	−0.523025	−	0.852318i	$-0.675196\pi$
$199$	−14.7563	−1.04605	−0.523025	+	0.852318i	$0.675196\pi$
$200$	1.34836	0.0953432
$201$	2.00560	0.141464
$202$	1.39728	0.0983125
$203$	0	0
$204$	−12.6794	−0.887737
$205$	−6.77964	−0.473511
$206$	−5.58317	−0.388998
$207$	−2.01998	−0.140398
$208$	−16.4974	−1.14389
$209$	−6.66003	−0.460684
$210$	0	0
$211$	1.13874	0.0783941	0.0391970	−	0.999232i	$-0.487520\pi$
$211$	1.13874	0.0783941	0.0391970	+	0.999232i	$0.487520\pi$
$212$	−0.230898	−0.0158581
$213$	15.7259	1.07752
$214$	−0.898825	−0.0614424
$215$	−10.4409	−0.712065
$216$	−1.34836	−0.0917440
$217$	0	0
$218$	5.13036	0.347472
$219$	12.1577	0.821542
$220$	1.87918	0.126694
$221$	33.8370	2.27612
$222$	−1.14624	−0.0769308
$223$	11.2347	0.752334	0.376167	−	0.926552i	$-0.377242\pi$
$223$	11.2347	0.752334	0.376167	+	0.926552i	$0.377242\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	4.99969	0.332575
$227$	−24.8791	−1.65128	−0.825642	−	0.564195i	$-0.809187\pi$
$227$	−24.8791	−1.65128	−0.825642	+	0.564195i	$0.809187\pi$
$228$	−12.5154	−0.828853
$229$	12.4385	0.821962	0.410981	−	0.911644i	$-0.365186\pi$
$229$	12.4385	0.821962	0.410981	+	0.911644i	$0.365186\pi$
$230$	−0.702119	−0.0462964
$231$	0	0
$232$	−5.38487	−0.353534
$233$	13.9051	0.910952	0.455476	−	0.890248i	$-0.349469\pi$
$233$	13.9051	0.910952	0.455476	+	0.890248i	$0.349469\pi$
$234$	1.74311	0.113951
$235$	3.28767	0.214464
$236$	21.2783	1.38510
$237$	−2.65771	−0.172637
$238$	0	0
$239$	1.70575	0.110336	0.0551678	−	0.998477i	$-0.482431\pi$
$239$	1.70575	0.110336	0.0551678	+	0.998477i	$0.482431\pi$
$240$	3.28969	0.212349
$241$	−26.5528	−1.71041	−0.855207	−	0.518286i	$-0.826570\pi$
$241$	−26.5528	−1.71041	−0.855207	+	0.518286i	$0.826570\pi$
$242$	−0.347588	−0.0223438
$243$	−1.00000	−0.0641500
$244$	4.95314	0.317092
$245$	0	0
$246$	2.35652	0.150246
$247$	33.3993	2.12515
$248$	−9.97268	−0.633266
$249$	−1.18360	−0.0750076
$250$	0.347588	0.0219834
$251$	19.2768	1.21674	0.608370	−	0.793654i	$-0.291824\pi$
$251$	19.2768	1.21674	0.608370	+	0.793654i	$0.291824\pi$
$252$	0	0
$253$	−2.01998	−0.126995
$254$	5.56827	0.349385
$255$	−6.74730	−0.422533
$256$	7.18596	0.449122
$257$	−7.76175	−0.484164	−0.242082	−	0.970256i	$-0.577830\pi$
$257$	−7.76175	−0.484164	−0.242082	+	0.970256i	$0.577830\pi$
$258$	3.62914	0.225940
$259$	0	0
$260$	−9.42389	−0.584445
$261$	−3.99365	−0.247201
$262$	−4.40704	−0.272268
$263$	30.7074	1.89350	0.946751	−	0.321967i	$-0.104344\pi$
$263$	30.7074	1.89350	0.946751	+	0.321967i	$0.104344\pi$
$264$	−1.34836	−0.0829856
$265$	−0.122872	−0.00754794
$266$	0	0
$267$	4.23551	0.259209
$268$	3.76889	0.230222
$269$	−3.02165	−0.184233	−0.0921166	−	0.995748i	$-0.529363\pi$
$269$	−3.02165	−0.184233	−0.0921166	+	0.995748i	$0.529363\pi$
$270$	−0.347588	−0.0211535
$271$	6.44257	0.391358	0.195679	−	0.980668i	$-0.437309\pi$
$271$	6.44257	0.391358	0.195679	+	0.980668i	$0.437309\pi$
$272$	−22.1966	−1.34586
$273$	0	0
$274$	0.771139	0.0465862
$275$	1.00000	0.0603023
$276$	−3.79591	−0.228487
$277$	7.34215	0.441147	0.220573	−	0.975370i	$-0.429207\pi$
$277$	7.34215	0.441147	0.220573	+	0.975370i	$0.429207\pi$
$278$	4.53363	0.271909
$279$	−7.39618	−0.442798
$280$	0	0
$281$	9.19709	0.548652	0.274326	−	0.961637i	$-0.411545\pi$
$281$	9.19709	0.548652	0.274326	+	0.961637i	$0.411545\pi$
$282$	−1.14275	−0.0680500
$283$	11.6068	0.689952	0.344976	−	0.938612i	$-0.387887\pi$
$283$	11.6068	0.689952	0.344976	+	0.938612i	$0.387887\pi$
$284$	29.5519	1.75358
$285$	−6.66003	−0.394506
$286$	1.74311	0.103072
$287$	0	0
$288$	−3.84017	−0.226284
$289$	28.5261	1.67801
$290$	−1.38814	−0.0815147
$291$	−4.83004	−0.283142
$292$	22.8466	1.33699
$293$	−11.7691	−0.687560	−0.343780	−	0.939050i	$-0.611708\pi$
$293$	−11.7691	−0.687560	−0.343780	+	0.939050i	$0.611708\pi$
$294$	0	0
$295$	11.3232	0.659259
$296$	−4.44649	−0.258447
$297$	−1.00000	−0.0580259
$298$	2.51463	0.145669
$299$	10.1300	0.585831
$300$	1.87918	0.108495
$301$	0	0
$302$	7.98972	0.459757
$303$	4.01994	0.230940
$304$	−21.9095	−1.25659
$305$	2.63579	0.150925
$306$	2.34528	0.134071
$307$	−0.926562	−0.0528817	−0.0264408	−	0.999650i	$-0.508417\pi$
$307$	−0.926562	−0.0528817	−0.0264408	+	0.999650i	$0.508417\pi$
$308$	0	0
$309$	−16.0626	−0.913771
$310$	−2.57082	−0.146013
$311$	26.7389	1.51622	0.758111	−	0.652126i	$-0.226123\pi$
$311$	26.7389	1.51622	0.758111	+	0.652126i	$0.226123\pi$
$312$	6.76185	0.382815
$313$	−19.4391	−1.09876	−0.549382	−	0.835571i	$-0.685137\pi$
$313$	−19.4391	−1.09876	−0.549382	+	0.835571i	$0.685137\pi$
$314$	−1.97793	−0.111621
$315$	0	0
$316$	−4.99432	−0.280952
$317$	−21.0239	−1.18082	−0.590410	−	0.807103i	$-0.701034\pi$
$317$	−21.0239	−1.18082	−0.590410	+	0.807103i	$0.701034\pi$
$318$	0.0427086	0.00239498
$319$	−3.99365	−0.223602
$320$	5.24459	0.293182
$321$	−2.58590	−0.144331
$322$	0	0
$323$	44.9372	2.50037
$324$	−1.87918	−0.104399
$325$	−5.01489	−0.278176
$326$	2.19998	0.121846
$327$	14.7599	0.816225
$328$	9.14137	0.504748
$329$	0	0
$330$	−0.347588	−0.0191341
$331$	−16.3167	−0.896847	−0.448424	−	0.893821i	$-0.648014\pi$
$331$	−16.3167	−0.896847	−0.448424	+	0.893821i	$0.648014\pi$
$332$	−2.22420	−0.122069
$333$	−3.29771	−0.180713
$334$	0.690262	0.0377695
$335$	2.00560	0.109578
$336$	0	0
$337$	−25.6641	−1.39801	−0.699006	−	0.715116i	$-0.746374\pi$
$337$	−25.6641	−1.39801	−0.699006	+	0.715116i	$0.746374\pi$
$338$	−4.22288	−0.229694
$339$	14.3840	0.781231
$340$	−12.6794	−0.687638
$341$	−7.39618	−0.400526
$342$	2.31494	0.125178
$343$	0	0
$344$	14.0781	0.759039
$345$	−2.01998	−0.108752
$346$	−0.476191	−0.0256002
$347$	−4.76571	−0.255837	−0.127918	−	0.991785i	$-0.540830\pi$
$347$	−4.76571	−0.255837	−0.127918	+	0.991785i	$0.540830\pi$
$348$	−7.50481	−0.402300
$349$	18.0025	0.963652	0.481826	−	0.876267i	$-0.339974\pi$
$349$	18.0025	0.963652	0.481826	+	0.876267i	$0.339974\pi$
$350$	0	0
$351$	5.01489	0.267675
$352$	−3.84017	−0.204682
$353$	11.6636	0.620789	0.310395	−	0.950608i	$-0.399539\pi$
$353$	11.6636	0.620789	0.310395	+	0.950608i	$0.399539\pi$
$354$	−3.93579	−0.209185
$355$	15.7259	0.834645
$356$	7.95931	0.421842
$357$	0	0
$358$	5.35166	0.282844
$359$	−24.0430	−1.26894	−0.634470	−	0.772948i	$-0.718782\pi$
$359$	−24.0430	−1.26894	−0.634470	+	0.772948i	$0.718782\pi$
$360$	−1.34836	−0.0710646
$361$	25.3560	1.33452
$362$	1.99789	0.105007
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	12.1577	0.636364
$366$	−0.916169	−0.0478889
$367$	−27.3682	−1.42861	−0.714303	−	0.699836i	$-0.753256\pi$
$367$	−27.3682	−1.42861	−0.714303	+	0.699836i	$0.753256\pi$
$368$	−6.64511	−0.346400
$369$	6.77964	0.352934
$370$	−1.14624	−0.0595904
$371$	0	0
$372$	−13.8988	−0.720618
$373$	4.56059	0.236138	0.118069	−	0.993005i	$-0.462330\pi$
$373$	4.56059	0.236138	0.118069	+	0.993005i	$0.462330\pi$
$374$	2.34528	0.121271
$375$	1.00000	0.0516398
$376$	−4.43295	−0.228612
$377$	20.0277	1.03148
$378$	0	0
$379$	16.4305	0.843980	0.421990	−	0.906600i	$-0.361332\pi$
$379$	16.4305	0.843980	0.421990	+	0.906600i	$0.361332\pi$
$380$	−12.5154	−0.642027
$381$	16.0198	0.820718
$382$	3.80086	0.194469
$383$	−23.2209	−1.18653	−0.593266	−	0.805006i	$-0.702162\pi$
$383$	−23.2209	−1.18653	−0.593266	+	0.805006i	$0.702162\pi$
$384$	−9.50329	−0.484963
$385$	0	0
$386$	−7.68954	−0.391387
$387$	10.4409	0.530742
$388$	−9.07652	−0.460791
$389$	34.7279	1.76078	0.880388	−	0.474254i	$-0.157282\pi$
$389$	34.7279	1.76078	0.880388	+	0.474254i	$0.157282\pi$
$390$	1.74311	0.0882660
$391$	13.6294	0.689269
$392$	0	0
$393$	−12.6789	−0.639568
$394$	−2.24761	−0.113233
$395$	−2.65771	−0.133724
$396$	−1.87918	−0.0944325
$397$	36.5302	1.83340	0.916700	−	0.399576i	$-0.130843\pi$
$397$	36.5302	1.83340	0.916700	+	0.399576i	$0.130843\pi$
$398$	5.12912	0.257100
$399$	0	0
$400$	3.28969	0.164485
$401$	−15.0295	−0.750536	−0.375268	−	0.926916i	$-0.622449\pi$
$401$	−15.0295	−0.750536	−0.375268	+	0.926916i	$0.622449\pi$
$402$	−0.697122	−0.0347693
$403$	37.0910	1.84763
$404$	7.55421	0.375836
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−3.29771	−0.163461
$408$	9.09777	0.450407
$409$	−24.7663	−1.22462	−0.612308	−	0.790619i	$-0.709759\pi$
$409$	−24.7663	−1.22462	−0.612308	+	0.790619i	$0.709759\pi$
$410$	2.35652	0.116380
$411$	2.21855	0.109433
$412$	−30.1846	−1.48709
$413$	0	0
$414$	0.702119	0.0345073
$415$	−1.18360	−0.0581006
$416$	19.2580	0.944202
$417$	13.0431	0.638725
$418$	2.31494	0.113228
$419$	26.8156	1.31003	0.655013	−	0.755617i	$-0.272663\pi$
$419$	26.8156	1.31003	0.655013	+	0.755617i	$0.272663\pi$
$420$	0	0
$421$	−16.2065	−0.789856	−0.394928	−	0.918712i	$-0.629230\pi$
$421$	−16.2065	−0.789856	−0.394928	+	0.918712i	$0.629230\pi$
$422$	−0.395812	−0.0192678
$423$	−3.28767	−0.159852
$424$	0.165675	0.00804587
$425$	−6.74730	−0.327292
$426$	−5.46613	−0.264835
$427$	0	0
$428$	−4.85937	−0.234887
$429$	5.01489	0.242121
$430$	3.62914	0.175013
$431$	15.5894	0.750917	0.375458	−	0.926839i	$-0.377485\pi$
$431$	15.5894	0.750917	0.375458	+	0.926839i	$0.377485\pi$
$432$	−3.28969	−0.158275
$433$	−3.51006	−0.168683	−0.0843413	−	0.996437i	$-0.526879\pi$
$433$	−3.51006	−0.168683	−0.0843413	+	0.996437i	$0.526879\pi$
$434$	0	0
$435$	−3.99365	−0.191481
$436$	27.7366	1.32834
$437$	13.4531	0.643550
$438$	−4.22587	−0.201920
$439$	−27.4559	−1.31040	−0.655200	−	0.755456i	$-0.727416\pi$
$439$	−27.4559	−1.31040	−0.655200	+	0.755456i	$0.727416\pi$
$440$	−1.34836	−0.0642803
$441$	0	0
$442$	−11.7613	−0.559429
$443$	11.4141	0.542302	0.271151	−	0.962537i	$-0.412596\pi$
$443$	11.4141	0.542302	0.271151	+	0.962537i	$0.412596\pi$
$444$	−6.19700	−0.294097
$445$	4.23551	0.200783
$446$	−3.90506	−0.184910
$447$	7.23453	0.342182
$448$	0	0
$449$	30.7671	1.45199	0.725995	−	0.687700i	$-0.241380\pi$
$449$	30.7671	1.45199	0.725995	+	0.687700i	$0.241380\pi$
$450$	−0.347588	−0.0163854
$451$	6.77964	0.319241
$452$	27.0301	1.27139
$453$	22.9862	1.07999
$454$	8.64766	0.405855
$455$	0	0
$456$	8.98009	0.420531
$457$	17.1327	0.801436	0.400718	−	0.916201i	$-0.368761\pi$
$457$	17.1327	0.801436	0.400718	+	0.916201i	$0.368761\pi$
$458$	−4.32348	−0.202023
$459$	6.74730	0.314937
$460$	−3.79591	−0.176985
$461$	11.7378	0.546685	0.273343	−	0.961917i	$-0.411871\pi$
$461$	11.7378	0.546685	0.273343	+	0.961917i	$0.411871\pi$
$462$	0	0
$463$	4.36060	0.202654	0.101327	−	0.994853i	$-0.467691\pi$
$463$	4.36060	0.202654	0.101327	+	0.994853i	$0.467691\pi$
$464$	−13.1379	−0.609912
$465$	−7.39618	−0.342990
$466$	−4.83323	−0.223895
$467$	42.2154	1.95349	0.976747	−	0.214395i	$-0.0687780\pi$
$467$	42.2154	1.95349	0.976747	+	0.214395i	$0.0687780\pi$
$468$	9.42389	0.435620
$469$	0	0
$470$	−1.14275	−0.0527113
$471$	−5.69046	−0.262202
$472$	−15.2676	−0.702750
$473$	10.4409	0.480074
$474$	0.923786	0.0424309
$475$	−6.66003	−0.305583
$476$	0	0
$477$	0.122872	0.00562590
$478$	−0.592896	−0.0271185
$479$	6.91601	0.316001	0.158000	−	0.987439i	$-0.449495\pi$
$479$	6.91601	0.316001	0.158000	+	0.987439i	$0.449495\pi$
$480$	−3.84017	−0.175279
$481$	16.5376	0.754052
$482$	9.22942	0.420388
$483$	0	0
$484$	−1.87918	−0.0854174
$485$	−4.83004	−0.219321
$486$	0.347588	0.0157669
$487$	12.3325	0.558837	0.279418	−	0.960169i	$-0.409858\pi$
$487$	12.3325	0.558837	0.279418	+	0.960169i	$0.409858\pi$
$488$	−3.55399	−0.160881
$489$	6.32929	0.286220
$490$	0	0
$491$	−3.43571	−0.155051	−0.0775257	−	0.996990i	$-0.524702\pi$
$491$	−3.43571	−0.155051	−0.0775257	+	0.996990i	$0.524702\pi$
$492$	12.7402	0.574372
$493$	26.9464	1.21360
$494$	−11.6092	−0.522322
$495$	−1.00000	−0.0449467
$496$	−24.3312	−1.09250
$497$	0	0
$498$	0.411404	0.0184355
$499$	41.2730	1.84763	0.923817	−	0.382836i	$-0.125052\pi$
$499$	41.2730	1.84763	0.923817	+	0.382836i	$0.125052\pi$
$500$	1.87918	0.0840396
$501$	1.98587	0.0887219
$502$	−6.70037	−0.299052
$503$	29.4718	1.31408	0.657040	−	0.753855i	$-0.271808\pi$
$503$	29.4718	1.31408	0.657040	+	0.753855i	$0.271808\pi$
$504$	0	0
$505$	4.01994	0.178885
$506$	0.702119	0.0312130
$507$	−12.1491	−0.539561
$508$	30.1041	1.33565
$509$	−37.2472	−1.65095	−0.825477	−	0.564436i	$-0.809094\pi$
$509$	−37.2472	−1.65095	−0.825477	+	0.564436i	$0.809094\pi$
$510$	2.34528	0.103851
$511$	0	0
$512$	−21.5043	−0.950366
$513$	6.66003	0.294047
$514$	2.69789	0.118999
$515$	−16.0626	−0.707804
$516$	19.6204	0.863740
$517$	−3.28767	−0.144592
$518$	0	0
$519$	−1.36999	−0.0601358
$520$	6.76185	0.296527
$521$	37.5521	1.64519	0.822594	−	0.568628i	$-0.192526\pi$
$521$	37.5521	1.64519	0.822594	+	0.568628i	$0.192526\pi$
$522$	1.38814	0.0607575
$523$	19.3450	0.845898	0.422949	−	0.906154i	$-0.360995\pi$
$523$	19.3450	0.845898	0.422949	+	0.906154i	$0.360995\pi$
$524$	−23.8260	−1.04085
$525$	0	0
$526$	−10.6735	−0.465388
$527$	49.9043	2.17386
$528$	−3.28969	−0.143166
$529$	−18.9197	−0.822595
$530$	0.0427086	0.00185514
$531$	−11.3232	−0.491383
$532$	0	0
$533$	−33.9992	−1.47267
$534$	−1.47221	−0.0637089
$535$	−2.58590	−0.111798
$536$	−2.70426	−0.116806
$537$	15.3966	0.664412
$538$	1.05029	0.0452811
$539$	0	0
$540$	−1.87918	−0.0808672
$541$	−15.7777	−0.678335	−0.339167	−	0.940726i	$-0.610145\pi$
$541$	−15.7777	−0.678335	−0.339167	+	0.940726i	$0.610145\pi$
$542$	−2.23936	−0.0961886
$543$	5.74788	0.246665
$544$	25.9108	1.11092
$545$	14.7599	0.632245
$546$	0	0
$547$	8.87509	0.379472	0.189736	−	0.981835i	$-0.439237\pi$
$547$	8.87509	0.379472	0.189736	+	0.981835i	$0.439237\pi$
$548$	4.16905	0.178093
$549$	−2.63579	−0.112493
$550$	−0.347588	−0.0148212
$551$	26.5979	1.13311
$552$	2.72365	0.115926
$553$	0	0
$554$	−2.55204	−0.108426
$555$	−3.29771	−0.139980
$556$	24.5104	1.03947
$557$	−13.5912	−0.575879	−0.287940	−	0.957649i	$-0.592970\pi$
$557$	−13.5912	−0.575879	−0.287940	+	0.957649i	$0.592970\pi$
$558$	2.57082	0.108831
$559$	−52.3601	−2.21460
$560$	0	0
$561$	6.74730	0.284871
$562$	−3.19679	−0.134849
$563$	−36.4577	−1.53651	−0.768255	−	0.640144i	$-0.778875\pi$
$563$	−36.4577	−1.53651	−0.768255	+	0.640144i	$0.778875\pi$
$564$	−6.17814	−0.260147
$565$	14.3840	0.605139
$566$	−4.03437	−0.169577
$567$	0	0
$568$	−21.2041	−0.889705
$569$	7.76037	0.325332	0.162666	−	0.986681i	$-0.447991\pi$
$569$	7.76037	0.325332	0.162666	+	0.986681i	$0.447991\pi$
$570$	2.31494	0.0969623
$571$	14.1459	0.591988	0.295994	−	0.955190i	$-0.404349\pi$
$571$	14.1459	0.591988	0.295994	+	0.955190i	$0.404349\pi$
$572$	9.42389	0.394033
$573$	10.9350	0.456814
$574$	0	0
$575$	−2.01998	−0.0842389
$576$	−5.24459	−0.218525
$577$	25.6912	1.06954	0.534768	−	0.844999i	$-0.320399\pi$
$577$	25.6912	1.06954	0.534768	+	0.844999i	$0.320399\pi$
$578$	−9.91532	−0.412423
$579$	−22.1226	−0.919383
$580$	−7.50481	−0.311620
$581$	0	0
$582$	1.67886	0.0695910
$583$	0.122872	0.00508882
$584$	−16.3929	−0.678344
$585$	5.01489	0.207340
$586$	4.09081	0.168990
$587$	−0.253241	−0.0104524	−0.00522618	−	0.999986i	$-0.501664\pi$
$587$	−0.253241	−0.0104524	−0.00522618	+	0.999986i	$0.501664\pi$
$588$	0	0
$589$	49.2588	2.02967
$590$	−3.93579	−0.162034
$591$	−6.46630	−0.265988
$592$	−10.8485	−0.445869
$593$	9.00865	0.369941	0.184970	−	0.982744i	$-0.440781\pi$
$593$	9.00865	0.369941	0.184970	+	0.982744i	$0.440781\pi$
$594$	0.347588	0.0142617
$595$	0	0
$596$	13.5950	0.556873
$597$	14.7563	0.603937
$598$	−3.52105	−0.143986
$599$	−6.81061	−0.278274	−0.139137	−	0.990273i	$-0.544433\pi$
$599$	−6.81061	−0.278274	−0.139137	+	0.990273i	$0.544433\pi$
$600$	−1.34836	−0.0550464
$601$	26.0442	1.06236	0.531182	−	0.847258i	$-0.321748\pi$
$601$	26.0442	1.06236	0.531182	+	0.847258i	$0.321748\pi$
$602$	0	0
$603$	−2.00560	−0.0816744
$604$	43.1953	1.75759
$605$	−1.00000	−0.0406558
$606$	−1.39728	−0.0567607
$607$	−18.1258	−0.735705	−0.367852	−	0.929884i	$-0.619907\pi$
$607$	−18.1258	−0.735705	−0.367852	+	0.929884i	$0.619907\pi$
$608$	25.5756	1.03723
$609$	0	0
$610$	−0.916169	−0.0370946
$611$	16.4873	0.667005
$612$	12.6794	0.512535
$613$	−28.8173	−1.16392	−0.581960	−	0.813217i	$-0.697714\pi$
$613$	−28.8173	−1.16392	−0.581960	+	0.813217i	$0.697714\pi$
$614$	0.322062	0.0129973
$615$	6.77964	0.273382
$616$	0	0
$617$	21.7161	0.874256	0.437128	−	0.899399i	$-0.355996\pi$
$617$	21.7161	0.874256	0.437128	+	0.899399i	$0.355996\pi$
$618$	5.58317	0.224588
$619$	5.77750	0.232217	0.116109	−	0.993237i	$-0.462958\pi$
$619$	5.77750	0.232217	0.116109	+	0.993237i	$0.462958\pi$
$620$	−13.8988	−0.558188
$621$	2.01998	0.0810589
$622$	−9.29410	−0.372659
$623$	0	0
$624$	16.4974	0.660426
$625$	1.00000	0.0400000
$626$	6.75680	0.270056
$627$	6.66003	0.265976
$628$	−10.6934	−0.426714
$629$	22.2507	0.887192
$630$	0	0
$631$	−26.0137	−1.03559	−0.517796	−	0.855504i	$-0.673247\pi$
$631$	−26.0137	−1.03559	−0.517796	+	0.855504i	$0.673247\pi$
$632$	3.58353	0.142545
$633$	−1.13874	−0.0452608
$634$	7.30765	0.290224
$635$	16.0198	0.635725
$636$	0.230898	0.00915571
$637$	0	0
$638$	1.38814	0.0549572
$639$	−15.7259	−0.622107
$640$	−9.50329	−0.375651
$641$	40.9566	1.61769	0.808845	−	0.588023i	$-0.200093\pi$
$641$	40.9566	1.61769	0.808845	+	0.588023i	$0.200093\pi$
$642$	0.898825	0.0354738
$643$	−38.2803	−1.50963	−0.754815	−	0.655938i	$-0.772273\pi$
$643$	−38.2803	−1.50963	−0.754815	+	0.655938i	$0.772273\pi$
$644$	0	0
$645$	10.4409	0.411111
$646$	−15.6196	−0.614546
$647$	−23.5620	−0.926318	−0.463159	−	0.886275i	$-0.653284\pi$
$647$	−23.5620	−0.926318	−0.463159	+	0.886275i	$0.653284\pi$
$648$	1.34836	0.0529684
$649$	−11.3232	−0.444473
$650$	1.74311	0.0683705
$651$	0	0
$652$	11.8939	0.465801
$653$	14.0238	0.548793	0.274397	−	0.961617i	$-0.411522\pi$
$653$	14.0238	0.548793	0.274397	+	0.961617i	$0.411522\pi$
$654$	−5.13036	−0.200613
$655$	−12.6789	−0.495407
$656$	22.3030	0.870784
$657$	−12.1577	−0.474317
$658$	0	0
$659$	−6.63019	−0.258276	−0.129138	−	0.991627i	$-0.541221\pi$
$659$	−6.63019	−0.258276	−0.129138	+	0.991627i	$0.541221\pi$
$660$	−1.87918	−0.0731471
$661$	−20.4716	−0.796251	−0.398126	−	0.917331i	$-0.630339\pi$
$661$	−20.4716	−0.796251	−0.398126	+	0.917331i	$0.630339\pi$
$662$	5.67149	0.220429
$663$	−33.8370	−1.31412
$664$	1.59591	0.0619334
$665$	0	0
$666$	1.14624	0.0444160
$667$	8.06710	0.312359
$668$	3.73180	0.144388
$669$	−11.2347	−0.434360
$670$	−0.697122	−0.0269322
$671$	−2.63579	−0.101754
$672$	0	0
$673$	−8.69344	−0.335107	−0.167554	−	0.985863i	$-0.553587\pi$
$673$	−8.69344	−0.335107	−0.167554	+	0.985863i	$0.553587\pi$
$674$	8.92052	0.343606
$675$	−1.00000	−0.0384900
$676$	−22.8304	−0.878092
$677$	37.6462	1.44686	0.723431	−	0.690397i	$-0.242564\pi$
$677$	37.6462	1.44686	0.723431	+	0.690397i	$0.242564\pi$
$678$	−4.99969	−0.192012
$679$	0	0
$680$	9.09777	0.348883
$681$	24.8791	0.953369
$682$	2.57082	0.0984418
$683$	2.38574	0.0912879	0.0456439	−	0.998958i	$-0.485466\pi$
$683$	2.38574	0.0912879	0.0456439	+	0.998958i	$0.485466\pi$
$684$	12.5154	0.478539
$685$	2.21855	0.0847663
$686$	0	0
$687$	−12.4385	−0.474560
$688$	34.3475	1.30948
$689$	−0.616187	−0.0234749
$690$	0.702119	0.0267292
$691$	−35.7192	−1.35882	−0.679412	−	0.733757i	$-0.737765\pi$
$691$	−35.7192	−1.35882	−0.679412	+	0.733757i	$0.737765\pi$
$692$	−2.57446	−0.0978662
$693$	0	0
$694$	1.65650	0.0628800
$695$	13.0431	0.494754
$696$	5.38487	0.204113
$697$	−45.7443	−1.73269
$698$	−6.25744	−0.236848
$699$	−13.9051	−0.525939
$700$	0	0
$701$	−15.6255	−0.590167	−0.295084	−	0.955471i	$-0.595348\pi$
$701$	−15.6255	−0.590167	−0.295084	+	0.955471i	$0.595348\pi$
$702$	−1.74311	−0.0657896
$703$	21.9628	0.828344
$704$	−5.24459	−0.197663
$705$	−3.28767	−0.123821
$706$	−4.05411	−0.152579
$707$	0	0
$708$	−21.2783	−0.799687
$709$	−4.84127	−0.181818	−0.0909089	−	0.995859i	$-0.528977\pi$
$709$	−4.84127	−0.181818	−0.0909089	+	0.995859i	$0.528977\pi$
$710$	−5.46613	−0.205140
$711$	2.65771	0.0996718
$712$	−5.71098	−0.214028
$713$	14.9401	0.559512
$714$	0	0
$715$	5.01489	0.187546
$716$	28.9330	1.08128
$717$	−1.70575	−0.0637023
$718$	8.35704	0.311882
$719$	−9.56443	−0.356693	−0.178346	−	0.983968i	$-0.557075\pi$
$719$	−9.56443	−0.356693	−0.178346	+	0.983968i	$0.557075\pi$
$720$	−3.28969	−0.122600
$721$	0	0
$722$	−8.81342	−0.328002
$723$	26.5528	0.987508
$724$	10.8013	0.401428
$725$	−3.99365	−0.148321
$726$	0.347588	0.0129002
$727$	−42.5014	−1.57629	−0.788146	−	0.615489i	$-0.788959\pi$
$727$	−42.5014	−1.57629	−0.788146	+	0.615489i	$0.788959\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.22587	−0.156406
$731$	−70.4481	−2.60562
$732$	−4.95314	−0.183073
$733$	−43.5150	−1.60726	−0.803631	−	0.595128i	$-0.797101\pi$
$733$	−43.5150	−1.60726	−0.803631	+	0.595128i	$0.797101\pi$
$734$	9.51283	0.351125
$735$	0	0
$736$	7.75706	0.285929
$737$	−2.00560	−0.0738772
$738$	−2.35652	−0.0867447
$739$	−42.7758	−1.57354	−0.786768	−	0.617249i	$-0.788247\pi$
$739$	−42.7758	−1.57354	−0.786768	+	0.617249i	$0.788247\pi$
$740$	−6.19700	−0.227806
$741$	−33.3993	−1.22695
$742$	0	0
$743$	−20.8130	−0.763553	−0.381777	−	0.924255i	$-0.624688\pi$
$743$	−20.8130	−0.763553	−0.381777	+	0.924255i	$0.624688\pi$
$744$	9.97268	0.365616
$745$	7.23453	0.265053
$746$	−1.58520	−0.0580384
$747$	1.18360	0.0433056
$748$	12.6794	0.463605
$749$	0	0
$750$	−0.347588	−0.0126921
$751$	−33.4933	−1.22219	−0.611094	−	0.791558i	$-0.709270\pi$
$751$	−33.4933	−1.22219	−0.611094	+	0.791558i	$0.709270\pi$
$752$	−10.8154	−0.394398
$753$	−19.2768	−0.702485
$754$	−6.96139	−0.253519
$755$	22.9862	0.836554
$756$	0	0
$757$	9.87997	0.359094	0.179547	−	0.983749i	$-0.442537\pi$
$757$	9.87997	0.359094	0.179547	+	0.983749i	$0.442537\pi$
$758$	−5.71105	−0.207435
$759$	2.01998	0.0733206
$760$	8.98009	0.325742
$761$	3.64441	0.132110	0.0660549	−	0.997816i	$-0.478959\pi$
$761$	3.64441	0.132110	0.0660549	+	0.997816i	$0.478959\pi$
$762$	−5.56827	−0.201717
$763$	0	0
$764$	20.5488	0.743429
$765$	6.74730	0.243949
$766$	8.07129	0.291628
$767$	56.7843	2.05036
$768$	−7.18596	−0.259301
$769$	50.1493	1.80843	0.904214	−	0.427079i	$-0.140457\pi$
$769$	50.1493	1.80843	0.904214	+	0.427079i	$0.140457\pi$
$770$	0	0
$771$	7.76175	0.279532
$772$	−41.5724	−1.49622
$773$	16.1611	0.581274	0.290637	−	0.956833i	$-0.406133\pi$
$773$	16.1611	0.581274	0.290637	+	0.956833i	$0.406133\pi$
$774$	−3.62914	−0.130447
$775$	−7.39618	−0.265679
$776$	6.51261	0.233789
$777$	0	0
$778$	−12.0710	−0.432766
$779$	−45.1526	−1.61776
$780$	9.42389	0.337429
$781$	−15.7259	−0.562717
$782$	−4.73741	−0.169410
$783$	3.99365	0.142722
$784$	0	0
$785$	−5.69046	−0.203101
$786$	4.40704	0.157194
$787$	−1.98414	−0.0707271	−0.0353635	−	0.999375i	$-0.511259\pi$
$787$	−1.98414	−0.0707271	−0.0353635	+	0.999375i	$0.511259\pi$
$788$	−12.1514	−0.432874
$789$	−30.7074	−1.09321
$790$	0.923786	0.0328668
$791$	0	0
$792$	1.34836	0.0479117
$793$	13.2182	0.469392
$794$	−12.6975	−0.450616
$795$	0.122872	0.00435781
$796$	27.7299	0.982859
$797$	51.5265	1.82516	0.912582	−	0.408895i	$-0.134086\pi$
$797$	51.5265	1.82516	0.912582	+	0.408895i	$0.134086\pi$
$798$	0	0
$799$	22.1829	0.784776
$800$	−3.84017	−0.135770
$801$	−4.23551	−0.149655
$802$	5.22406	0.184468
$803$	−12.1577	−0.429036
$804$	−3.76889	−0.132919
$805$	0	0
$806$	−12.8924	−0.454115
$807$	3.02165	0.106367
$808$	−5.42032	−0.190686
$809$	−17.6089	−0.619096	−0.309548	−	0.950884i	$-0.600178\pi$
$809$	−17.6089	−0.619096	−0.309548	+	0.950884i	$0.600178\pi$
$810$	0.347588	0.0122130
$811$	−25.3295	−0.889439	−0.444719	−	0.895670i	$-0.646697\pi$
$811$	−25.3295	−0.889439	−0.444719	+	0.895670i	$0.646697\pi$
$812$	0	0
$813$	−6.44257	−0.225951
$814$	1.14624	0.0401758
$815$	6.32929	0.221705
$816$	22.1966	0.777035
$817$	−69.5369	−2.43279
$818$	8.60847	0.300988
$819$	0	0
$820$	12.7402	0.444907
$821$	−29.6759	−1.03570	−0.517848	−	0.855473i	$-0.673267\pi$
$821$	−29.6759	−1.03570	−0.517848	+	0.855473i	$0.673267\pi$
$822$	−0.771139	−0.0268966
$823$	12.0825	0.421169	0.210585	−	0.977576i	$-0.432463\pi$
$823$	12.0825	0.421169	0.210585	+	0.977576i	$0.432463\pi$
$824$	21.6581	0.754497
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	27.1635	0.944568	0.472284	−	0.881447i	$-0.343430\pi$
$827$	27.1635	0.944568	0.472284	+	0.881447i	$0.343430\pi$
$828$	3.79591	0.131917
$829$	−24.2861	−0.843492	−0.421746	−	0.906714i	$-0.638583\pi$
$829$	−24.2861	−0.843492	−0.421746	+	0.906714i	$0.638583\pi$
$830$	0.411404	0.0142801
$831$	−7.34215	−0.254696
$832$	26.3010	0.911825
$833$	0	0
$834$	−4.53363	−0.156987
$835$	1.98587	0.0687237
$836$	12.5154	0.432855
$837$	7.39618	0.255649
$838$	−9.32076	−0.321980
$839$	−54.1983	−1.87113	−0.935567	−	0.353148i	$-0.885111\pi$
$839$	−54.1983	−1.87113	−0.935567	+	0.353148i	$0.885111\pi$
$840$	0	0
$841$	−13.0507	−0.450025
$842$	5.63317	0.194132
$843$	−9.19709	−0.316765
$844$	−2.13990	−0.0736584
$845$	−12.1491	−0.417942
$846$	1.14275	0.0392887
$847$	0	0
$848$	0.404210	0.0138806
$849$	−11.6068	−0.398344
$850$	2.34528	0.0804424
$851$	6.66130	0.228347
$852$	−29.5519	−1.01243
$853$	12.8053	0.438444	0.219222	−	0.975675i	$-0.429648\pi$
$853$	12.8053	0.438444	0.219222	+	0.975675i	$0.429648\pi$
$854$	0	0
$855$	6.66003	0.227768
$856$	3.48671	0.119173
$857$	22.8845	0.781721	0.390860	−	0.920450i	$-0.372178\pi$
$857$	22.8845	0.781721	0.390860	+	0.920450i	$0.372178\pi$
$858$	−1.74311	−0.0595089
$859$	−11.4340	−0.390124	−0.195062	−	0.980791i	$-0.562491\pi$
$859$	−11.4340	−0.390124	−0.195062	+	0.980791i	$0.562491\pi$
$860$	19.6204	0.669050
$861$	0	0
$862$	−5.41870	−0.184561
$863$	−54.6634	−1.86076	−0.930382	−	0.366593i	$-0.880524\pi$
$863$	−54.6634	−1.86076	−0.930382	+	0.366593i	$0.880524\pi$
$864$	3.84017	0.130645
$865$	−1.36999	−0.0465810
$866$	1.22005	0.0414591
$867$	−28.5261	−0.968797
$868$	0	0
$869$	2.65771	0.0901565
$870$	1.38814	0.0470625
$871$	10.0579	0.340798
$872$	−19.9016	−0.673953
$873$	4.83004	0.163472
$874$	−4.67613	−0.158173
$875$	0	0
$876$	−22.8466	−0.771914
$877$	−12.9230	−0.436378	−0.218189	−	0.975907i	$-0.570015\pi$
$877$	−12.9230	−0.436378	−0.218189	+	0.975907i	$0.570015\pi$
$878$	9.54334	0.322072
$879$	11.7691	0.396963
$880$	−3.28969	−0.110896
$881$	44.8915	1.51243	0.756217	−	0.654321i	$-0.227046\pi$
$881$	44.8915	1.51243	0.756217	+	0.654321i	$0.227046\pi$
$882$	0	0
$883$	48.2755	1.62460	0.812300	−	0.583240i	$-0.198215\pi$
$883$	48.2755	1.62460	0.812300	+	0.583240i	$0.198215\pi$
$884$	−63.5859	−2.13862
$885$	−11.3232	−0.380624
$886$	−3.96742	−0.133288
$887$	42.3022	1.42037	0.710185	−	0.704015i	$-0.248611\pi$
$887$	42.3022	1.42037	0.710185	+	0.704015i	$0.248611\pi$
$888$	4.44649	0.149214
$889$	0	0
$890$	−1.47221	−0.0493487
$891$	1.00000	0.0335013
$892$	−21.1121	−0.706887
$893$	21.8960	0.732722
$894$	−2.51463	−0.0841020
$895$	15.3966	0.514651
$896$	0	0
$897$	−10.1300	−0.338230
$898$	−10.6943	−0.356872
$899$	29.5378	0.985140
$900$	−1.87918	−0.0626394
$901$	−0.829052	−0.0276197
$902$	−2.35652	−0.0784635
$903$	0	0
$904$	−19.3947	−0.645059
$905$	5.74788	0.191066
$906$	−7.98972	−0.265441
$907$	1.83812	0.0610337	0.0305169	−	0.999534i	$-0.490285\pi$
$907$	1.83812	0.0610337	0.0305169	+	0.999534i	$0.490285\pi$
$908$	46.7524	1.55153
$909$	−4.01994	−0.133333
$910$	0	0
$911$	39.2538	1.30054	0.650268	−	0.759705i	$-0.274657\pi$
$911$	39.2538	1.30054	0.650268	+	0.759705i	$0.274657\pi$
$912$	21.9095	0.725495
$913$	1.18360	0.0391714
$914$	−5.95513	−0.196978
$915$	−2.63579	−0.0871366
$916$	−23.3743	−0.772309
$917$	0	0
$918$	−2.34528	−0.0774057
$919$	11.8067	0.389468	0.194734	−	0.980856i	$-0.437616\pi$
$919$	11.8067	0.389468	0.194734	+	0.980856i	$0.437616\pi$
$920$	2.72365	0.0897961
$921$	0.926562	0.0305313
$922$	−4.07992	−0.134365
$923$	78.8637	2.59583
$924$	0	0
$925$	−3.29771	−0.108428
$926$	−1.51569	−0.0498086
$927$	16.0626	0.527566
$928$	15.3363	0.503439
$929$	−30.6459	−1.00546	−0.502729	−	0.864444i	$-0.667671\pi$
$929$	−30.6459	−1.00546	−0.502729	+	0.864444i	$0.667671\pi$
$930$	2.57082	0.0843005
$931$	0	0
$932$	−26.1302	−0.855923
$933$	−26.7389	−0.875391
$934$	−14.6735	−0.480133
$935$	6.74730	0.220660
$936$	−6.76185	−0.221018
$937$	−33.6566	−1.09951	−0.549757	−	0.835325i	$-0.685280\pi$
$937$	−33.6566	−1.09951	−0.549757	+	0.835325i	$0.685280\pi$
$938$	0	0
$939$	19.4391	0.634372
$940$	−6.17814	−0.201509
$941$	5.23071	0.170516	0.0852581	−	0.996359i	$-0.472829\pi$
$941$	5.23071	0.170516	0.0852581	+	0.996359i	$0.472829\pi$
$942$	1.97793	0.0644445
$943$	−13.6947	−0.445962
$944$	−37.2497	−1.21237
$945$	0	0
$946$	−3.62914	−0.117993
$947$	9.46090	0.307438	0.153719	−	0.988115i	$-0.450875\pi$
$947$	9.46090	0.307438	0.153719	+	0.988115i	$0.450875\pi$
$948$	4.99432	0.162208
$949$	60.9696	1.97916
$950$	2.31494	0.0751067
$951$	21.0239	0.681747
$952$	0	0
$953$	−50.8195	−1.64620	−0.823102	−	0.567894i	$-0.807758\pi$
$953$	−50.8195	−1.64620	−0.823102	+	0.567894i	$0.807758\pi$
$954$	−0.0427086	−0.00138274
$955$	10.9350	0.353847
$956$	−3.20541	−0.103670
$957$	3.99365	0.129097
$958$	−2.40392	−0.0776671
$959$	0	0
$960$	−5.24459	−0.169269
$961$	23.7035	0.764628
$962$	−5.74828	−0.185332
$963$	2.58590	0.0833293
$964$	49.8975	1.60709
$965$	−22.1226	−0.712151
$966$	0	0
$967$	−13.0192	−0.418668	−0.209334	−	0.977844i	$-0.567130\pi$
$967$	−13.0192	−0.418668	−0.209334	+	0.977844i	$0.567130\pi$
$968$	1.34836	0.0433378
$969$	−44.9372	−1.44359
$970$	1.67886	0.0539050
$971$	6.30362	0.202293	0.101146	−	0.994872i	$-0.467749\pi$
$971$	6.30362	0.202293	0.101146	+	0.994872i	$0.467749\pi$
$972$	1.87918	0.0602748
$973$	0	0
$974$	−4.28661	−0.137352
$975$	5.01489	0.160605
$976$	−8.67095	−0.277550
$977$	−38.2773	−1.22460	−0.612299	−	0.790626i	$-0.709755\pi$
$977$	−38.2773	−1.22460	−0.612299	+	0.790626i	$0.709755\pi$
$978$	−2.19998	−0.0703477
$979$	−4.23551	−0.135368
$980$	0	0
$981$	−14.7599	−0.471247
$982$	1.19421	0.0381088
$983$	54.2405	1.73000	0.865002	−	0.501768i	$-0.167317\pi$
$983$	54.2405	1.73000	0.865002	+	0.501768i	$0.167317\pi$
$984$	−9.14137	−0.291416
$985$	−6.46630	−0.206033
$986$	−9.36623	−0.298282
$987$	0	0
$988$	−62.7634	−1.99677
$989$	−21.0904	−0.670637
$990$	0.347588	0.0110471
$991$	58.7693	1.86687	0.933434	−	0.358749i	$-0.116797\pi$
$991$	58.7693	1.86687	0.933434	+	0.358749i	$0.116797\pi$
$992$	28.4026	0.901783
$993$	16.3167	0.517795
$994$	0	0
$995$	14.7563	0.467807
$996$	2.22420	0.0704765
$997$	−0.604991	−0.0191603	−0.00958014	−	0.999954i	$-0.503049\pi$
$997$	−0.604991	−0.0191603	−0.00958014	+	0.999954i	$0.503049\pi$
$998$	−14.3460	−0.454114
$999$	3.29771	0.104335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.co.1.6	✓	14
7.6	odd	2		8085.2.a.cp.1.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8085.2.a.co.1.6	✓	14	1.1	even	1	trivial
8085.2.a.cp.1.6	yes	14	7.6	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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-0.347588 q^{2} -1.00000 q^{3} -1.87918 q^{4} -1.00000 q^{5} +0.347588 q^{6} +1.34836 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.347588 q^{2} -1.00000 q^{3} -1.87918 q^{4} -1.00000 q^{5} +0.347588 q^{6} +1.34836 q^{8} +1.00000 q^{9} +0.347588 q^{10} +1.00000 q^{11} +1.87918 q^{12} -5.01489 q^{13} +1.00000 q^{15} +3.28969 q^{16} -6.74730 q^{17} -0.347588 q^{18} -6.66003 q^{19} +1.87918 q^{20} -0.347588 q^{22} -2.01998 q^{23} -1.34836 q^{24} +1.00000 q^{25} +1.74311 q^{26} -1.00000 q^{27} -3.99365 q^{29} -0.347588 q^{30} -7.39618 q^{31} -3.84017 q^{32} -1.00000 q^{33} +2.34528 q^{34} -1.87918 q^{36} -3.29771 q^{37} +2.31494 q^{38} +5.01489 q^{39} -1.34836 q^{40} +6.77964 q^{41} +10.4409 q^{43} -1.87918 q^{44} -1.00000 q^{45} +0.702119 q^{46} -3.28767 q^{47} -3.28969 q^{48} -0.347588 q^{50} +6.74730 q^{51} +9.42389 q^{52} +0.122872 q^{53} +0.347588 q^{54} -1.00000 q^{55} +6.66003 q^{57} +1.38814 q^{58} -11.3232 q^{59} -1.87918 q^{60} -2.63579 q^{61} +2.57082 q^{62} -5.24459 q^{64} +5.01489 q^{65} +0.347588 q^{66} -2.00560 q^{67} +12.6794 q^{68} +2.01998 q^{69} -15.7259 q^{71} +1.34836 q^{72} -12.1577 q^{73} +1.14624 q^{74} -1.00000 q^{75} +12.5154 q^{76} -1.74311 q^{78} +2.65771 q^{79} -3.28969 q^{80} +1.00000 q^{81} -2.35652 q^{82} +1.18360 q^{83} +6.74730 q^{85} -3.62914 q^{86} +3.99365 q^{87} +1.34836 q^{88} -4.23551 q^{89} +0.347588 q^{90} +3.79591 q^{92} +7.39618 q^{93} +1.14275 q^{94} +6.66003 q^{95} +3.84017 q^{96} +4.83004 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{2} - 14 q^{3} + 20 q^{4} - 14 q^{5} - 4 q^{6} + 12 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 4 * q^2 - 14 * q^3 + 20 * q^4 - 14 * q^5 - 4 * q^6 + 12 * q^8 + 14 * q^9	\( 14 q + 4 q^{2} - 14 q^{3} + 20 q^{4} - 14 q^{5} - 4 q^{6} + 12 q^{8} + 14 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 8 q^{13} + 14 q^{15} + 32 q^{16} + 6 q^{17} + 4 q^{18} - 10 q^{19} - 20 q^{20} + 4 q^{22} + 22 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} - 14 q^{27} + 10 q^{29} + 4 q^{30} - 20 q^{31} + 28 q^{32} - 14 q^{33} - 16 q^{34} + 20 q^{36} + 20 q^{37} + 16 q^{38} + 8 q^{39} - 12 q^{40} + 22 q^{43} + 20 q^{44} - 14 q^{45} + 4 q^{46} + 8 q^{47} - 32 q^{48} + 4 q^{50} - 6 q^{51} - 4 q^{52} + 34 q^{53} - 4 q^{54} - 14 q^{55} + 10 q^{57} + 20 q^{58} - 22 q^{59} + 20 q^{60} - 6 q^{61} + 28 q^{62} + 32 q^{64} + 8 q^{65} - 4 q^{66} + 32 q^{67} + 56 q^{68} - 22 q^{69} + 4 q^{71} + 12 q^{72} - 8 q^{73} + 36 q^{74} - 14 q^{75} - 24 q^{76} + 12 q^{78} + 12 q^{79} - 32 q^{80} + 14 q^{81} + 28 q^{82} + 26 q^{83} - 6 q^{85} + 40 q^{86} - 10 q^{87} + 12 q^{88} - 10 q^{89} - 4 q^{90} + 8 q^{92} + 20 q^{93} - 28 q^{94} + 10 q^{95} - 28 q^{96} - 14 q^{97} + 14 q^{99}+O(q^{100}) \) 14 * q + 4 * q^2 - 14 * q^3 + 20 * q^4 - 14 * q^5 - 4 * q^6 + 12 * q^8 + 14 * q^9 - 4 * q^10 + 14 * q^11 - 20 * q^12 - 8 * q^13 + 14 * q^15 + 32 * q^16 + 6 * q^17 + 4 * q^18 - 10 * q^19 - 20 * q^20 + 4 * q^22 + 22 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 - 14 * q^27 + 10 * q^29 + 4 * q^30 - 20 * q^31 + 28 * q^32 - 14 * q^33 - 16 * q^34 + 20 * q^36 + 20 * q^37 + 16 * q^38 + 8 * q^39 - 12 * q^40 + 22 * q^43 + 20 * q^44 - 14 * q^45 + 4 * q^46 + 8 * q^47 - 32 * q^48 + 4 * q^50 - 6 * q^51 - 4 * q^52 + 34 * q^53 - 4 * q^54 - 14 * q^55 + 10 * q^57 + 20 * q^58 - 22 * q^59 + 20 * q^60 - 6 * q^61 + 28 * q^62 + 32 * q^64 + 8 * q^65 - 4 * q^66 + 32 * q^67 + 56 * q^68 - 22 * q^69 + 4 * q^71 + 12 * q^72 - 8 * q^73 + 36 * q^74 - 14 * q^75 - 24 * q^76 + 12 * q^78 + 12 * q^79 - 32 * q^80 + 14 * q^81 + 28 * q^82 + 26 * q^83 - 6 * q^85 + 40 * q^86 - 10 * q^87 + 12 * q^88 - 10 * q^89 - 4 * q^90 + 8 * q^92 + 20 * q^93 - 28 * q^94 + 10 * q^95 - 28 * q^96 - 14 * q^97 + 14 * q^99

Introduction

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