LMFDB - Embedded newform 2013.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 $ x^12 - 5x^11 - 5x^10 + 48x^9 - 173x^7 + 29x^6 + 281x^5 - 41x^4 - 201x^3 + 8x^2 + 49x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.858571$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.141429 q^{2} +1.00000 q^{3} -1.98000 q^{4} -4.38024 q^{5} -0.141429 q^{6} +3.47902 q^{7} +0.562887 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.141429 q^{2} +1.00000 q^{3} -1.98000 q^{4} -4.38024 q^{5} -0.141429 q^{6} +3.47902 q^{7} +0.562887 q^{8} +1.00000 q^{9} +0.619492 q^{10} +1.00000 q^{11} -1.98000 q^{12} -0.619218 q^{13} -0.492034 q^{14} -4.38024 q^{15} +3.88039 q^{16} +0.200614 q^{17} -0.141429 q^{18} -7.65406 q^{19} +8.67287 q^{20} +3.47902 q^{21} -0.141429 q^{22} +2.85870 q^{23} +0.562887 q^{24} +14.1865 q^{25} +0.0875752 q^{26} +1.00000 q^{27} -6.88846 q^{28} -0.407417 q^{29} +0.619492 q^{30} -0.653645 q^{31} -1.67457 q^{32} +1.00000 q^{33} -0.0283726 q^{34} -15.2390 q^{35} -1.98000 q^{36} +4.13768 q^{37} +1.08250 q^{38} -0.619218 q^{39} -2.46558 q^{40} -0.852809 q^{41} -0.492034 q^{42} -2.11255 q^{43} -1.98000 q^{44} -4.38024 q^{45} -0.404302 q^{46} -9.35524 q^{47} +3.88039 q^{48} +5.10359 q^{49} -2.00638 q^{50} +0.200614 q^{51} +1.22605 q^{52} -5.66170 q^{53} -0.141429 q^{54} -4.38024 q^{55} +1.95829 q^{56} -7.65406 q^{57} +0.0576205 q^{58} -5.55219 q^{59} +8.67287 q^{60} -1.00000 q^{61} +0.0924443 q^{62} +3.47902 q^{63} -7.52394 q^{64} +2.71232 q^{65} -0.141429 q^{66} -0.741703 q^{67} -0.397216 q^{68} +2.85870 q^{69} +2.15523 q^{70} -9.73380 q^{71} +0.562887 q^{72} +16.3153 q^{73} -0.585188 q^{74} +14.1865 q^{75} +15.1550 q^{76} +3.47902 q^{77} +0.0875752 q^{78} -11.6445 q^{79} -16.9970 q^{80} +1.00000 q^{81} +0.120612 q^{82} -13.2427 q^{83} -6.88846 q^{84} -0.878738 q^{85} +0.298776 q^{86} -0.407417 q^{87} +0.562887 q^{88} -12.6034 q^{89} +0.619492 q^{90} -2.15427 q^{91} -5.66021 q^{92} -0.653645 q^{93} +1.32310 q^{94} +33.5266 q^{95} -1.67457 q^{96} -7.90680 q^{97} -0.721795 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * 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 $

$2$	−0.141429	−0.100005	−0.0500027	−	0.998749i	$-0.515923\pi$
$2$	−0.141429	−0.100005	−0.0500027	+	0.998749i	$0.515923\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98000	−0.989999
$5$	−4.38024	−1.95890	−0.979452	−	0.201679i	$-0.935360\pi$
$5$	−4.38024	−1.95890	−0.979452	+	0.201679i	$0.935360\pi$
$6$	−0.141429	−0.0577381
$7$	3.47902	1.31495	0.657473	−	0.753478i	$-0.271625\pi$
$7$	3.47902	1.31495	0.657473	+	0.753478i	$0.271625\pi$
$8$	0.562887	0.199010
$9$	1.00000	0.333333
$10$	0.619492	0.195901
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.98000	−0.571576
$13$	−0.619218	−0.171740	−0.0858700	−	0.996306i	$-0.527367\pi$
$13$	−0.619218	−0.171740	−0.0858700	+	0.996306i	$0.527367\pi$
$14$	−0.492034	−0.131502
$15$	−4.38024	−1.13097
$16$	3.88039	0.970097
$17$	0.200614	0.0486561	0.0243280	−	0.999704i	$-0.492255\pi$
$17$	0.200614	0.0486561	0.0243280	+	0.999704i	$0.492255\pi$
$18$	−0.141429	−0.0333351
$19$	−7.65406	−1.75596	−0.877981	−	0.478696i	$-0.841109\pi$
$19$	−7.65406	−1.75596	−0.877981	+	0.478696i	$0.841109\pi$
$20$	8.67287	1.93931
$21$	3.47902	0.759185
$22$	−0.141429	−0.0301527
$23$	2.85870	0.596079	0.298040	−	0.954554i	$-0.403667\pi$
$23$	2.85870	0.596079	0.298040	+	0.954554i	$0.403667\pi$
$24$	0.562887	0.114899
$25$	14.1865	2.83730
$26$	0.0875752	0.0171749
$27$	1.00000	0.192450
$28$	−6.88846	−1.30180
$29$	−0.407417	−0.0756555	−0.0378277	−	0.999284i	$-0.512044\pi$
$29$	−0.407417	−0.0756555	−0.0378277	+	0.999284i	$0.512044\pi$
$30$	0.619492	0.113103
$31$	−0.653645	−0.117398	−0.0586991	−	0.998276i	$-0.518695\pi$
$31$	−0.653645	−0.117398	−0.0586991	+	0.998276i	$0.518695\pi$
$32$	−1.67457	−0.296025
$33$	1.00000	0.174078
$34$	−0.0283726	−0.00486587
$35$	−15.2390	−2.57585
$36$	−1.98000	−0.330000
$37$	4.13768	0.680231	0.340115	−	0.940384i	$-0.389534\pi$
$37$	4.13768	0.680231	0.340115	+	0.940384i	$0.389534\pi$
$38$	1.08250	0.175605
$39$	−0.619218	−0.0991542
$40$	−2.46558	−0.389842
$41$	−0.852809	−0.133186	−0.0665932	−	0.997780i	$-0.521213\pi$
$41$	−0.852809	−0.133186	−0.0665932	+	0.997780i	$0.521213\pi$
$42$	−0.492034	−0.0759225
$43$	−2.11255	−0.322161	−0.161080	−	0.986941i	$-0.551498\pi$
$43$	−2.11255	−0.322161	−0.161080	+	0.986941i	$0.551498\pi$
$44$	−1.98000	−0.298496
$45$	−4.38024	−0.652968
$46$	−0.404302	−0.0596111
$47$	−9.35524	−1.36460	−0.682301	−	0.731071i	$-0.739021\pi$
$47$	−9.35524	−1.36460	−0.682301	+	0.731071i	$0.739021\pi$
$48$	3.88039	0.560086
$49$	5.10359	0.729085
$50$	−2.00638	−0.283745
$51$	0.200614	0.0280916
$52$	1.22605	0.170022
$53$	−5.66170	−0.777694	−0.388847	−	0.921302i	$-0.627126\pi$
$53$	−5.66170	−0.777694	−0.388847	+	0.921302i	$0.627126\pi$
$54$	−0.141429	−0.0192460
$55$	−4.38024	−0.590632
$56$	1.95829	0.261688
$57$	−7.65406	−1.01380
$58$	0.0576205	0.00756595
$59$	−5.55219	−0.722834	−0.361417	−	0.932404i	$-0.617707\pi$
$59$	−5.55219	−0.722834	−0.361417	+	0.932404i	$0.617707\pi$
$60$	8.67287	1.11966
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	0.0924443	0.0117404
$63$	3.47902	0.438316
$64$	−7.52394	−0.940493
$65$	2.71232	0.336422
$66$	−0.141429	−0.0174087
$67$	−0.741703	−0.0906135	−0.0453067	−	0.998973i	$-0.514427\pi$
$67$	−0.741703	−0.0906135	−0.0453067	+	0.998973i	$0.514427\pi$
$68$	−0.397216	−0.0481695
$69$	2.85870	0.344146
$70$	2.15523	0.257599
$71$	−9.73380	−1.15519	−0.577595	−	0.816324i	$-0.696009\pi$
$71$	−9.73380	−1.15519	−0.577595	+	0.816324i	$0.696009\pi$
$72$	0.562887	0.0663368
$73$	16.3153	1.90957	0.954783	−	0.297305i	$-0.0960877\pi$
$73$	16.3153	1.90957	0.954783	+	0.297305i	$0.0960877\pi$
$74$	−0.585188	−0.0680267
$75$	14.1865	1.63812
$76$	15.1550	1.73840
$77$	3.47902	0.396471
$78$	0.0875752	0.00991594
$79$	−11.6445	−1.31011	−0.655053	−	0.755583i	$-0.727354\pi$
$79$	−11.6445	−1.31011	−0.655053	+	0.755583i	$0.727354\pi$
$80$	−16.9970	−1.90033
$81$	1.00000	0.111111
$82$	0.120612	0.0133194
$83$	−13.2427	−1.45358	−0.726788	−	0.686862i	$-0.758988\pi$
$83$	−13.2427	−1.45358	−0.726788	+	0.686862i	$0.758988\pi$
$84$	−6.88846	−0.751592
$85$	−0.878738	−0.0953125
$86$	0.298776	0.0322178
$87$	−0.407417	−0.0436797
$88$	0.562887	0.0600039
$89$	−12.6034	−1.33596	−0.667981	−	0.744178i	$-0.732841\pi$
$89$	−12.6034	−1.33596	−0.667981	+	0.744178i	$0.732841\pi$
$90$	0.619492	0.0653002
$91$	−2.15427	−0.225829
$92$	−5.66021	−0.590118
$93$	−0.653645	−0.0677799
$94$	1.32310	0.136467
$95$	33.5266	3.43976
$96$	−1.67457	−0.170910
$97$	−7.90680	−0.802814	−0.401407	−	0.915900i	$-0.631479\pi$
$97$	−7.90680	−0.802814	−0.401407	+	0.915900i	$0.631479\pi$
$98$	−0.721795	−0.0729123
$99$	1.00000	0.100504
$100$	−28.0893	−2.80893
$101$	−9.33126	−0.928495	−0.464248	−	0.885705i	$-0.653675\pi$
$101$	−9.33126	−0.928495	−0.464248	+	0.885705i	$0.653675\pi$
$102$	−0.0283726	−0.00280931
$103$	16.2562	1.60177	0.800887	−	0.598815i	$-0.204362\pi$
$103$	16.2562	1.60177	0.800887	+	0.598815i	$0.204362\pi$
$104$	−0.348549	−0.0341781
$105$	−15.2390	−1.48717
$106$	0.800727	0.0777735
$107$	−15.9877	−1.54559	−0.772793	−	0.634659i	$-0.781141\pi$
$107$	−15.9877	−1.54559	−0.772793	+	0.634659i	$0.781141\pi$
$108$	−1.98000	−0.190525
$109$	3.91244	0.374744	0.187372	−	0.982289i	$-0.440003\pi$
$109$	3.91244	0.374744	0.187372	+	0.982289i	$0.440003\pi$
$110$	0.619492	0.0590663
$111$	4.13768	0.392731
$112$	13.5000	1.27563
$113$	−4.55817	−0.428796	−0.214398	−	0.976746i	$-0.568779\pi$
$113$	−4.55817	−0.428796	−0.214398	+	0.976746i	$0.568779\pi$
$114$	1.08250	0.101386
$115$	−12.5218	−1.16766
$116$	0.806685	0.0748988
$117$	−0.619218	−0.0572467
$118$	0.785240	0.0722872
$119$	0.697941	0.0639801
$120$	−2.46558	−0.225076
$121$	1.00000	0.0909091
$122$	0.141429	0.0128044
$123$	−0.852809	−0.0768952
$124$	1.29422	0.116224
$125$	−40.2391	−3.59910
$126$	−0.492034	−0.0438339
$127$	−17.4782	−1.55094	−0.775472	−	0.631382i	$-0.782488\pi$
$127$	−17.4782	−1.55094	−0.775472	+	0.631382i	$0.782488\pi$
$128$	4.41325	0.390080
$129$	−2.11255	−0.186000
$130$	−0.383601	−0.0336440
$131$	−1.74523	−0.152482	−0.0762408	−	0.997089i	$-0.524292\pi$
$131$	−1.74523	−0.152482	−0.0762408	+	0.997089i	$0.524292\pi$
$132$	−1.98000	−0.172337
$133$	−26.6286	−2.30900
$134$	0.104898	0.00906183
$135$	−4.38024	−0.376991
$136$	0.112923	0.00968307
$137$	−8.83571	−0.754886	−0.377443	−	0.926033i	$-0.623197\pi$
$137$	−8.83571	−0.754886	−0.377443	+	0.926033i	$0.623197\pi$
$138$	−0.404302	−0.0344165
$139$	−14.0524	−1.19191	−0.595955	−	0.803018i	$-0.703226\pi$
$139$	−14.0524	−1.19191	−0.595955	+	0.803018i	$0.703226\pi$
$140$	30.1731	2.55009
$141$	−9.35524	−0.787853
$142$	1.37664	0.115525
$143$	−0.619218	−0.0517816
$144$	3.88039	0.323366
$145$	1.78459	0.148202
$146$	−2.30746	−0.190967
$147$	5.10359	0.420937
$148$	−8.19260	−0.673428
$149$	5.81012	0.475984	0.237992	−	0.971267i	$-0.423511\pi$
$149$	5.81012	0.475984	0.237992	+	0.971267i	$0.423511\pi$
$150$	−2.00638	−0.163820
$151$	−7.54804	−0.614251	−0.307125	−	0.951669i	$-0.599367\pi$
$151$	−7.54804	−0.614251	−0.307125	+	0.951669i	$0.599367\pi$
$152$	−4.30837	−0.349455
$153$	0.200614	0.0162187
$154$	−0.492034	−0.0396492
$155$	2.86312	0.229972
$156$	1.22605	0.0981625
$157$	−3.79819	−0.303129	−0.151564	−	0.988447i	$-0.548431\pi$
$157$	−3.79819	−0.303129	−0.151564	+	0.988447i	$0.548431\pi$
$158$	1.64686	0.131018
$159$	−5.66170	−0.449002
$160$	7.33503	0.579885
$161$	9.94546	0.783812
$162$	−0.141429	−0.0111117
$163$	11.3224	0.886841	0.443421	−	0.896314i	$-0.353765\pi$
$163$	11.3224	0.886841	0.443421	+	0.896314i	$0.353765\pi$
$164$	1.68856	0.131854
$165$	−4.38024	−0.341001
$166$	1.87290	0.145365
$167$	11.7529	0.909466	0.454733	−	0.890628i	$-0.349735\pi$
$167$	11.7529	0.909466	0.454733	+	0.890628i	$0.349735\pi$
$168$	1.95829	0.151086
$169$	−12.6166	−0.970505
$170$	0.124279	0.00953176
$171$	−7.65406	−0.585320
$172$	4.18284	0.318939
$173$	15.5225	1.18016	0.590078	−	0.807346i	$-0.299097\pi$
$173$	15.5225	1.18016	0.590078	+	0.807346i	$0.299097\pi$
$174$	0.0576205	0.00436820
$175$	49.3552	3.73090
$176$	3.88039	0.292495
$177$	−5.55219	−0.417328
$178$	1.78249	0.133603
$179$	15.6173	1.16729	0.583645	−	0.812009i	$-0.301626\pi$
$179$	15.6173	1.16729	0.583645	+	0.812009i	$0.301626\pi$
$180$	8.67287	0.646437
$181$	12.3823	0.920366	0.460183	−	0.887824i	$-0.347784\pi$
$181$	12.3823	0.920366	0.460183	+	0.887824i	$0.347784\pi$
$182$	0.304676	0.0225841
$183$	−1.00000	−0.0739221
$184$	1.60912	0.118626
$185$	−18.1240	−1.33251
$186$	0.0924443	0.00677835
$187$	0.200614	0.0146704
$188$	18.5234	1.35095
$189$	3.47902	0.253062
$190$	−4.74163	−0.343994
$191$	19.9985	1.44704	0.723521	−	0.690302i	$-0.242522\pi$
$191$	19.9985	1.44704	0.723521	+	0.690302i	$0.242522\pi$
$192$	−7.52394	−0.542994
$193$	2.17635	0.156657	0.0783284	−	0.996928i	$-0.475042\pi$
$193$	2.17635	0.156657	0.0783284	+	0.996928i	$0.475042\pi$
$194$	1.11825	0.0802857
$195$	2.71232	0.194233
$196$	−10.1051	−0.721793
$197$	12.8782	0.917532	0.458766	−	0.888557i	$-0.348292\pi$
$197$	12.8782	0.917532	0.458766	+	0.888557i	$0.348292\pi$
$198$	−0.141429	−0.0100509
$199$	−19.7614	−1.40085	−0.700423	−	0.713728i	$-0.747005\pi$
$199$	−19.7614	−1.40085	−0.700423	+	0.713728i	$0.747005\pi$
$200$	7.98540	0.564653
$201$	−0.741703	−0.0523157
$202$	1.31971	0.0928545
$203$	−1.41741	−0.0994829
$204$	−0.397216	−0.0278106
$205$	3.73551	0.260899
$206$	−2.29910	−0.160186
$207$	2.85870	0.198693
$208$	−2.40280	−0.166604
$209$	−7.65406	−0.529442
$210$	2.15523	0.148725
$211$	13.4080	0.923042	0.461521	−	0.887129i	$-0.347304\pi$
$211$	13.4080	0.923042	0.461521	+	0.887129i	$0.347304\pi$
$212$	11.2101	0.769916
$213$	−9.73380	−0.666949
$214$	2.26112	0.154567
$215$	9.25348	0.631082
$216$	0.562887	0.0382996
$217$	−2.27405	−0.154372
$218$	−0.553332	−0.0374764
$219$	16.3153	1.10249
$220$	8.67287	0.584725
$221$	−0.124224	−0.00835620
$222$	−0.585188	−0.0392752
$223$	14.3831	0.963166	0.481583	−	0.876400i	$-0.340062\pi$
$223$	14.3831	0.963166	0.481583	+	0.876400i	$0.340062\pi$
$224$	−5.82587	−0.389257
$225$	14.1865	0.945767
$226$	0.644657	0.0428819
$227$	−14.1128	−0.936701	−0.468350	−	0.883543i	$-0.655152\pi$
$227$	−14.1128	−0.936701	−0.468350	+	0.883543i	$0.655152\pi$
$228$	15.1550	1.00367
$229$	−14.0784	−0.930325	−0.465162	−	0.885225i	$-0.654004\pi$
$229$	−14.0784	−0.930325	−0.465162	+	0.885225i	$0.654004\pi$
$230$	1.77094	0.116772
$231$	3.47902	0.228903
$232$	−0.229330	−0.0150562
$233$	0.879278	0.0576034	0.0288017	−	0.999585i	$-0.490831\pi$
$233$	0.879278	0.0576034	0.0288017	+	0.999585i	$0.490831\pi$
$234$	0.0875752	0.00572497
$235$	40.9782	2.67312
$236$	10.9933	0.715605
$237$	−11.6445	−0.756390
$238$	−0.0987090	−0.00639835
$239$	9.71808	0.628610	0.314305	−	0.949322i	$-0.398229\pi$
$239$	9.71808	0.628610	0.314305	+	0.949322i	$0.398229\pi$
$240$	−16.9970	−1.09715
$241$	−0.519904	−0.0334900	−0.0167450	−	0.999860i	$-0.505330\pi$
$241$	−0.519904	−0.0334900	−0.0167450	+	0.999860i	$0.505330\pi$
$242$	−0.141429	−0.00909139
$243$	1.00000	0.0641500
$244$	1.98000	0.126756
$245$	−22.3550	−1.42821
$246$	0.120612	0.00768993
$247$	4.73953	0.301569
$248$	−0.367928	−0.0233635
$249$	−13.2427	−0.839223
$250$	5.69097	0.359929
$251$	−29.7739	−1.87931	−0.939657	−	0.342118i	$-0.888856\pi$
$251$	−29.7739	−1.87931	−0.939657	+	0.342118i	$0.888856\pi$
$252$	−6.88846	−0.433932
$253$	2.85870	0.179725
$254$	2.47193	0.155103
$255$	−0.878738	−0.0550287
$256$	14.4237	0.901483
$257$	2.98917	0.186460	0.0932298	−	0.995645i	$-0.470281\pi$
$257$	2.98917	0.186460	0.0932298	+	0.995645i	$0.470281\pi$
$258$	0.298776	0.0186010
$259$	14.3951	0.894467
$260$	−5.37039	−0.333058
$261$	−0.407417	−0.0252185
$262$	0.246826	0.0152490
$263$	22.3173	1.37614	0.688070	−	0.725644i	$-0.258458\pi$
$263$	22.3173	1.37614	0.688070	+	0.725644i	$0.258458\pi$
$264$	0.562887	0.0346433
$265$	24.7996	1.52343
$266$	3.76606	0.230912
$267$	−12.6034	−0.771318
$268$	1.46857	0.0897073
$269$	−15.4307	−0.940829	−0.470415	−	0.882445i	$-0.655896\pi$
$269$	−15.4307	−0.940829	−0.470415	+	0.882445i	$0.655896\pi$
$270$	0.619492	0.0377011
$271$	16.4228	0.997611	0.498806	−	0.866714i	$-0.333772\pi$
$271$	16.4228	0.997611	0.498806	+	0.866714i	$0.333772\pi$
$272$	0.778460	0.0472011
$273$	−2.15427	−0.130382
$274$	1.24962	0.0754926
$275$	14.1865	0.855479
$276$	−5.66021	−0.340705
$277$	22.6770	1.36253	0.681266	−	0.732036i	$-0.261430\pi$
$277$	22.6770	1.36253	0.681266	+	0.732036i	$0.261430\pi$
$278$	1.98742	0.119197
$279$	−0.653645	−0.0391327
$280$	−8.57780	−0.512622
$281$	−15.4368	−0.920881	−0.460440	−	0.887691i	$-0.652308\pi$
$281$	−15.4368	−0.920881	−0.460440	+	0.887691i	$0.652308\pi$
$282$	1.32310	0.0787895
$283$	−25.7002	−1.52772	−0.763858	−	0.645384i	$-0.776697\pi$
$283$	−25.7002	−1.52772	−0.763858	+	0.645384i	$0.776697\pi$
$284$	19.2729	1.14364
$285$	33.5266	1.98595
$286$	0.0875752	0.00517843
$287$	−2.96694	−0.175133
$288$	−1.67457	−0.0986751
$289$	−16.9598	−0.997633
$290$	−0.252392	−0.0148210
$291$	−7.90680	−0.463505
$292$	−32.3043	−1.89047
$293$	−8.73612	−0.510369	−0.255185	−	0.966892i	$-0.582136\pi$
$293$	−8.73612	−0.510369	−0.255185	+	0.966892i	$0.582136\pi$
$294$	−0.721795	−0.0420960
$295$	24.3199	1.41596
$296$	2.32905	0.135373
$297$	1.00000	0.0580259
$298$	−0.821719	−0.0476009
$299$	−1.77015	−0.102371
$300$	−28.0893	−1.62173
$301$	−7.34961	−0.423624
$302$	1.06751	0.0614283
$303$	−9.33126	−0.536067
$304$	−29.7007	−1.70345
$305$	4.38024	0.250812
$306$	−0.0283726	−0.00162196
$307$	7.16998	0.409212	0.204606	−	0.978844i	$-0.434409\pi$
$307$	7.16998	0.409212	0.204606	+	0.978844i	$0.434409\pi$
$308$	−6.88846	−0.392506
$309$	16.2562	0.924785
$310$	−0.404928	−0.0229984
$311$	14.0403	0.796154	0.398077	−	0.917352i	$-0.369678\pi$
$311$	14.0403	0.796154	0.398077	+	0.917352i	$0.369678\pi$
$312$	−0.348549	−0.0197327
$313$	23.7718	1.34366	0.671830	−	0.740706i	$-0.265509\pi$
$313$	23.7718	1.34366	0.671830	+	0.740706i	$0.265509\pi$
$314$	0.537174	0.0303145
$315$	−15.2390	−0.858618
$316$	23.0560	1.29700
$317$	14.3528	0.806136	0.403068	−	0.915170i	$-0.367944\pi$
$317$	14.3528	0.806136	0.403068	+	0.915170i	$0.367944\pi$
$318$	0.800727	0.0449026
$319$	−0.407417	−0.0228110
$320$	32.9567	1.84233
$321$	−15.9877	−0.892344
$322$	−1.40658	−0.0783854
$323$	−1.53551	−0.0854382
$324$	−1.98000	−0.110000
$325$	−8.78453	−0.487278
$326$	−1.60132	−0.0886888
$327$	3.91244	0.216358
$328$	−0.480035	−0.0265055
$329$	−32.5471	−1.79438
$330$	0.619492	0.0341019
$331$	−9.20941	−0.506195	−0.253098	−	0.967441i	$-0.581449\pi$
$331$	−9.20941	−0.506195	−0.253098	+	0.967441i	$0.581449\pi$
$332$	26.2205	1.43904
$333$	4.13768	0.226744
$334$	−1.66220	−0.0909514
$335$	3.24884	0.177503
$336$	13.5000	0.736483
$337$	28.0337	1.52710	0.763548	−	0.645752i	$-0.223456\pi$
$337$	28.0337	1.52710	0.763548	+	0.645752i	$0.223456\pi$
$338$	1.78435	0.0970557
$339$	−4.55817	−0.247566
$340$	1.73990	0.0943593
$341$	−0.653645	−0.0353969
$342$	1.08250	0.0585351
$343$	−6.59764	−0.356239
$344$	−1.18913	−0.0641134
$345$	−12.5218	−0.674150
$346$	−2.19533	−0.118022
$347$	−8.39309	−0.450564	−0.225282	−	0.974294i	$-0.572330\pi$
$347$	−8.39309	−0.450564	−0.225282	+	0.974294i	$0.572330\pi$
$348$	0.806685	0.0432429
$349$	−16.9338	−0.906444	−0.453222	−	0.891398i	$-0.649725\pi$
$349$	−16.9338	−0.906444	−0.453222	+	0.891398i	$0.649725\pi$
$350$	−6.98025	−0.373110
$351$	−0.619218	−0.0330514
$352$	−1.67457	−0.0892550
$353$	2.34107	0.124603	0.0623013	−	0.998057i	$-0.480156\pi$
$353$	2.34107	0.124603	0.0623013	+	0.998057i	$0.480156\pi$
$354$	0.785240	0.0417350
$355$	42.6364	2.26290
$356$	24.9548	1.32260
$357$	0.697941	0.0369389
$358$	−2.20873	−0.116735
$359$	6.48271	0.342144	0.171072	−	0.985259i	$-0.445277\pi$
$359$	6.48271	0.342144	0.171072	+	0.985259i	$0.445277\pi$
$360$	−2.46558	−0.129947
$361$	39.5846	2.08340
$362$	−1.75121	−0.0920415
$363$	1.00000	0.0524864
$364$	4.26545	0.223570
$365$	−71.4651	−3.74065
$366$	0.141429	0.00739261
$367$	14.6482	0.764632	0.382316	−	0.924032i	$-0.375127\pi$
$367$	14.6482	0.764632	0.382316	+	0.924032i	$0.375127\pi$
$368$	11.0928	0.578255
$369$	−0.852809	−0.0443955
$370$	2.56326	0.133258
$371$	−19.6972	−1.02263
$372$	1.29422	0.0671020
$373$	−0.0273707	−0.00141720	−0.000708602	−	1.00000i	$-0.500226\pi$
$373$	−0.0273707	−0.00141720	−0.000708602		1.00000i	$0.500226\pi$
$374$	−0.0283726	−0.00146711
$375$	−40.2391	−2.07794
$376$	−5.26594	−0.271570
$377$	0.252280	0.0129931
$378$	−0.492034	−0.0253075
$379$	−36.5143	−1.87561	−0.937807	−	0.347158i	$-0.887147\pi$
$379$	−36.5143	−1.87561	−0.937807	+	0.347158i	$0.887147\pi$
$380$	−66.3826	−3.40536
$381$	−17.4782	−0.895437
$382$	−2.82837	−0.144712
$383$	−37.0959	−1.89551	−0.947757	−	0.318994i	$-0.896655\pi$
$383$	−37.0959	−1.89551	−0.947757	+	0.318994i	$0.896655\pi$
$384$	4.41325	0.225213
$385$	−15.2390	−0.776649
$386$	−0.307798	−0.0156665
$387$	−2.11255	−0.107387
$388$	15.6555	0.794785
$389$	−30.4644	−1.54461	−0.772304	−	0.635253i	$-0.780896\pi$
$389$	−30.4644	−1.54461	−0.772304	+	0.635253i	$0.780896\pi$
$390$	−0.383601	−0.0194244
$391$	0.573495	0.0290029
$392$	2.87274	0.145095
$393$	−1.74523	−0.0880353
$394$	−1.82135	−0.0917581
$395$	51.0056	2.56637
$396$	−1.98000	−0.0994986
$397$	−17.0429	−0.855357	−0.427679	−	0.903931i	$-0.640668\pi$
$397$	−17.0429	−0.855357	−0.427679	+	0.903931i	$0.640668\pi$
$398$	2.79483	0.140092
$399$	−26.6286	−1.33310
$400$	55.0491	2.75246
$401$	−19.2375	−0.960673	−0.480337	−	0.877084i	$-0.659486\pi$
$401$	−19.2375	−0.960673	−0.480337	+	0.877084i	$0.659486\pi$
$402$	0.104898	0.00523185
$403$	0.404749	0.0201620
$404$	18.4759	0.919209
$405$	−4.38024	−0.217656
$406$	0.200463	0.00994882
$407$	4.13768	0.205097
$408$	0.112923	0.00559052
$409$	−29.2347	−1.44556	−0.722781	−	0.691077i	$-0.757136\pi$
$409$	−29.2347	−1.44556	−0.722781	+	0.691077i	$0.757136\pi$
$410$	−0.528309	−0.0260913
$411$	−8.83571	−0.435833
$412$	−32.1873	−1.58575
$413$	−19.3162	−0.950488
$414$	−0.404302	−0.0198704
$415$	58.0063	2.84742
$416$	1.03692	0.0508394
$417$	−14.0524	−0.688149
$418$	1.08250	0.0529470
$419$	38.5702	1.88428	0.942138	−	0.335226i	$-0.108813\pi$
$419$	38.5702	1.88428	0.942138	+	0.335226i	$0.108813\pi$
$420$	30.1731	1.47230
$421$	−19.3383	−0.942491	−0.471245	−	0.882002i	$-0.656195\pi$
$421$	−19.3383	−0.942491	−0.471245	+	0.882002i	$0.656195\pi$
$422$	−1.89627	−0.0923091
$423$	−9.35524	−0.454867
$424$	−3.18689	−0.154769
$425$	2.84601	0.138052
$426$	1.37664	0.0666984
$427$	−3.47902	−0.168362
$428$	31.6555	1.53013
$429$	−0.619218	−0.0298961
$430$	−1.30871	−0.0631115
$431$	−1.93628	−0.0932675	−0.0466338	−	0.998912i	$-0.514849\pi$
$431$	−1.93628	−0.0932675	−0.0466338	+	0.998912i	$0.514849\pi$
$432$	3.88039	0.186695
$433$	12.6549	0.608153	0.304077	−	0.952648i	$-0.401652\pi$
$433$	12.6549	0.608153	0.304077	+	0.952648i	$0.401652\pi$
$434$	0.321616	0.0154381
$435$	1.78459	0.0855643
$436$	−7.74662	−0.370996
$437$	−21.8806	−1.04669
$438$	−2.30746	−0.110255
$439$	−17.9604	−0.857202	−0.428601	−	0.903494i	$-0.640993\pi$
$439$	−17.9604	−0.857202	−0.428601	+	0.903494i	$0.640993\pi$
$440$	−2.46558	−0.117542
$441$	5.10359	0.243028
$442$	0.0175688	0.000835664 0
$443$	32.7510	1.55605	0.778024	−	0.628235i	$-0.216222\pi$
$443$	32.7510	1.55605	0.778024	+	0.628235i	$0.216222\pi$
$444$	−8.19260	−0.388804
$445$	55.2061	2.61702
$446$	−2.03419	−0.0963217
$447$	5.81012	0.274809
$448$	−26.1760	−1.23670
$449$	−17.7888	−0.839505	−0.419752	−	0.907639i	$-0.637883\pi$
$449$	−17.7888	−0.839505	−0.419752	+	0.907639i	$0.637883\pi$
$450$	−2.00638	−0.0945817
$451$	−0.852809	−0.0401572
$452$	9.02516	0.424508
$453$	−7.54804	−0.354638
$454$	1.99596	0.0936751
$455$	9.43623	0.442377
$456$	−4.30837	−0.201758
$457$	−4.43857	−0.207627	−0.103814	−	0.994597i	$-0.533105\pi$
$457$	−4.43857	−0.207627	−0.103814	+	0.994597i	$0.533105\pi$
$458$	1.99109	0.0930374
$459$	0.200614	0.00936387
$460$	24.7931	1.15598
$461$	−16.6012	−0.773194	−0.386597	−	0.922249i	$-0.626350\pi$
$461$	−16.6012	−0.773194	−0.386597	+	0.922249i	$0.626350\pi$
$462$	−0.492034	−0.0228915
$463$	2.16371	0.100556	0.0502781	−	0.998735i	$-0.483989\pi$
$463$	2.16371	0.100556	0.0502781	+	0.998735i	$0.483989\pi$
$464$	−1.58094	−0.0733931
$465$	2.86312	0.132774
$466$	−0.124355	−0.00576065
$467$	24.6868	1.14237	0.571185	−	0.820821i	$-0.306484\pi$
$467$	24.6868	1.14237	0.571185	+	0.820821i	$0.306484\pi$
$468$	1.22605	0.0566742
$469$	−2.58040	−0.119152
$470$	−5.79550	−0.267326
$471$	−3.79819	−0.175012
$472$	−3.12525	−0.143851
$473$	−2.11255	−0.0971352
$474$	1.64686	0.0756430
$475$	−108.584	−4.98219
$476$	−1.38192	−0.0633403
$477$	−5.66170	−0.259231
$478$	−1.37442	−0.0628644
$479$	12.9368	0.591097	0.295548	−	0.955328i	$-0.404498\pi$
$479$	12.9368	0.591097	0.295548	+	0.955328i	$0.404498\pi$
$480$	7.33503	0.334797
$481$	−2.56213	−0.116823
$482$	0.0735294	0.00334917
$483$	9.94546	0.452534
$484$	−1.98000	−0.0899999
$485$	34.6337	1.57264
$486$	−0.141429	−0.00641534
$487$	−9.33917	−0.423198	−0.211599	−	0.977357i	$-0.567867\pi$
$487$	−9.33917	−0.423198	−0.211599	+	0.977357i	$0.567867\pi$
$488$	−0.562887	−0.0254807
$489$	11.3224	0.512018
$490$	3.16164	0.142828
$491$	−29.4687	−1.32990	−0.664951	−	0.746887i	$-0.731548\pi$
$491$	−29.4687	−1.32990	−0.664951	+	0.746887i	$0.731548\pi$
$492$	1.68856	0.0761262
$493$	−0.0817336	−0.00368110
$494$	−0.670306	−0.0301585
$495$	−4.38024	−0.196877
$496$	−2.53640	−0.113888
$497$	−33.8641	−1.51901
$498$	1.87290	0.0839267
$499$	15.5619	0.696644	0.348322	−	0.937375i	$-0.386752\pi$
$499$	15.5619	0.696644	0.348322	+	0.937375i	$0.386752\pi$
$500$	79.6734	3.56310
$501$	11.7529	0.525080
$502$	4.21089	0.187941
$503$	−20.8851	−0.931222	−0.465611	−	0.884989i	$-0.654165\pi$
$503$	−20.8851	−0.931222	−0.465611	+	0.884989i	$0.654165\pi$
$504$	1.95829	0.0872294
$505$	40.8732	1.81883
$506$	−0.404302	−0.0179734
$507$	−12.6166	−0.560322
$508$	34.6069	1.53543
$509$	27.9100	1.23709	0.618545	−	0.785750i	$-0.287723\pi$
$509$	27.9100	1.23709	0.618545	+	0.785750i	$0.287723\pi$
$510$	0.124279	0.00550316
$511$	56.7614	2.51098
$512$	−10.8664	−0.480233
$513$	−7.65406	−0.337935
$514$	−0.422756	−0.0186469
$515$	−71.2062	−3.13772
$516$	4.18284	0.184139
$517$	−9.35524	−0.411443
$518$	−2.03588	−0.0894515
$519$	15.5225	0.681364
$520$	1.52673	0.0669515
$521$	17.4201	0.763187	0.381593	−	0.924330i	$-0.375375\pi$
$521$	17.4201	0.763187	0.381593	+	0.924330i	$0.375375\pi$
$522$	0.0576205	0.00252198
$523$	−41.7759	−1.82673	−0.913367	−	0.407137i	$-0.866527\pi$
$523$	−41.7759	−1.82673	−0.913367	+	0.407137i	$0.866527\pi$
$524$	3.45556	0.150957
$525$	49.3552	2.15404
$526$	−3.15630	−0.137621
$527$	−0.131130	−0.00571213
$528$	3.88039	0.168872
$529$	−14.8279	−0.644690
$530$	−3.50738	−0.152351
$531$	−5.55219	−0.240945
$532$	52.7246	2.28590
$533$	0.528075	0.0228734
$534$	1.78249	0.0771359
$535$	70.0298	3.02765
$536$	−0.417495	−0.0180330
$537$	15.6173	0.673935
$538$	2.18235	0.0940879
$539$	5.10359	0.219827
$540$	8.67287	0.373221
$541$	−14.6695	−0.630689	−0.315345	−	0.948977i	$-0.602120\pi$
$541$	−14.6695	−0.630689	−0.315345	+	0.948977i	$0.602120\pi$
$542$	−2.32265	−0.0997664
$543$	12.3823	0.531373
$544$	−0.335943	−0.0144034
$545$	−17.1374	−0.734087
$546$	0.304676	0.0130389
$547$	42.6882	1.82521	0.912607	−	0.408837i	$-0.134066\pi$
$547$	42.6882	1.82521	0.912607	+	0.408837i	$0.134066\pi$
$548$	17.4947	0.747336
$549$	−1.00000	−0.0426790
$550$	−2.00638	−0.0855524
$551$	3.11839	0.132848
$552$	1.60912	0.0684887
$553$	−40.5114	−1.72272
$554$	−3.20719	−0.136260
$555$	−18.1240	−0.769323
$556$	27.8237	1.17999
$557$	42.2757	1.79128	0.895640	−	0.444780i	$-0.146718\pi$
$557$	42.2757	1.79128	0.895640	+	0.444780i	$0.146718\pi$
$558$	0.0924443	0.00391348
$559$	1.30813	0.0553279
$560$	−59.1330	−2.49883
$561$	0.200614	0.00846993
$562$	2.18321	0.0920930
$563$	−11.2426	−0.473819	−0.236909	−	0.971532i	$-0.576134\pi$
$563$	−11.2426	−0.473819	−0.236909	+	0.971532i	$0.576134\pi$
$564$	18.5234	0.779974
$565$	19.9659	0.839971
$566$	3.63475	0.152780
$567$	3.47902	0.146105
$568$	−5.47903	−0.229895
$569$	6.50046	0.272514	0.136257	−	0.990674i	$-0.456493\pi$
$569$	6.50046	0.272514	0.136257	+	0.990674i	$0.456493\pi$
$570$	−4.74163	−0.198605
$571$	−29.2320	−1.22332	−0.611660	−	0.791120i	$-0.709498\pi$
$571$	−29.2320	−1.22332	−0.611660	+	0.791120i	$0.709498\pi$
$572$	1.22605	0.0512637
$573$	19.9985	0.835451
$574$	0.419611	0.0175142
$575$	40.5549	1.69126
$576$	−7.52394	−0.313498
$577$	7.88529	0.328269	0.164135	−	0.986438i	$-0.447517\pi$
$577$	7.88529	0.328269	0.164135	+	0.986438i	$0.447517\pi$
$578$	2.39860	0.0997686
$579$	2.17635	0.0904459
$580$	−3.53348	−0.146720
$581$	−46.0717	−1.91138
$582$	1.11825	0.0463530
$583$	−5.66170	−0.234483
$584$	9.18368	0.380023
$585$	2.71232	0.112141
$586$	1.23554	0.0510396
$587$	−38.5604	−1.59156	−0.795779	−	0.605587i	$-0.792938\pi$
$587$	−38.5604	−1.59156	−0.795779	+	0.605587i	$0.792938\pi$
$588$	−10.1051	−0.416727
$589$	5.00304	0.206147
$590$	−3.43954	−0.141604
$591$	12.8782	0.529737
$592$	16.0558	0.659890
$593$	−45.4904	−1.86807	−0.934033	−	0.357186i	$-0.883736\pi$
$593$	−45.4904	−1.86807	−0.934033	+	0.357186i	$0.883736\pi$
$594$	−0.141429	−0.00580290
$595$	−3.05715	−0.125331
$596$	−11.5040	−0.471224
$597$	−19.7614	−0.808779
$598$	0.250351	0.0102376
$599$	20.5409	0.839277	0.419638	−	0.907691i	$-0.362157\pi$
$599$	20.5409	0.839277	0.419638	+	0.907691i	$0.362157\pi$
$600$	7.98540	0.326002
$601$	10.1809	0.415289	0.207645	−	0.978204i	$-0.433420\pi$
$601$	10.1809	0.415289	0.207645	+	0.978204i	$0.433420\pi$
$602$	1.03945	0.0423647
$603$	−0.741703	−0.0302045
$604$	14.9451	0.608107
$605$	−4.38024	−0.178082
$606$	1.31971	0.0536095
$607$	−5.51011	−0.223649	−0.111824	−	0.993728i	$-0.535669\pi$
$607$	−5.51011	−0.223649	−0.111824	+	0.993728i	$0.535669\pi$
$608$	12.8173	0.519809
$609$	−1.41741	−0.0574365
$610$	−0.619492	−0.0250825
$611$	5.79293	0.234357
$612$	−0.397216	−0.0160565
$613$	1.25326	0.0506187	0.0253094	−	0.999680i	$-0.491943\pi$
$613$	1.25326	0.0506187	0.0253094	+	0.999680i	$0.491943\pi$
$614$	−1.01404	−0.0409234
$615$	3.73551	0.150630
$616$	1.95829	0.0789019
$617$	28.7021	1.15550	0.577751	−	0.816213i	$-0.303930\pi$
$617$	28.7021	1.15550	0.577751	+	0.816213i	$0.303930\pi$
$618$	−2.29910	−0.0924834
$619$	36.5837	1.47042	0.735211	−	0.677839i	$-0.237083\pi$
$619$	36.5837	1.47042	0.735211	+	0.677839i	$0.237083\pi$
$620$	−5.66898	−0.227672
$621$	2.85870	0.114715
$622$	−1.98571	−0.0796196
$623$	−43.8476	−1.75672
$624$	−2.40280	−0.0961891
$625$	105.324	4.21298
$626$	−3.36201	−0.134373
$627$	−7.65406	−0.305674
$628$	7.52042	0.300097
$629$	0.830077	0.0330974
$630$	2.15523	0.0858663
$631$	−25.9863	−1.03450	−0.517248	−	0.855835i	$-0.673044\pi$
$631$	−25.9863	−1.03450	−0.517248	+	0.855835i	$0.673044\pi$
$632$	−6.55452	−0.260725
$633$	13.4080	0.532918
$634$	−2.02991	−0.0806179
$635$	76.5589	3.03815
$636$	11.2101	0.444511
$637$	−3.16023	−0.125213
$638$	0.0576205	0.00228122
$639$	−9.73380	−0.385063
$640$	−19.3311	−0.764128
$641$	28.9062	1.14173	0.570863	−	0.821045i	$-0.306609\pi$
$641$	28.9062	1.14173	0.570863	+	0.821045i	$0.306609\pi$
$642$	2.26112	0.0892391
$643$	13.0035	0.512808	0.256404	−	0.966570i	$-0.417462\pi$
$643$	13.0035	0.512808	0.256404	+	0.966570i	$0.417462\pi$
$644$	−19.6920	−0.775973
$645$	9.25348	0.364355
$646$	0.217166	0.00854427
$647$	−33.8921	−1.33244	−0.666219	−	0.745757i	$-0.732088\pi$
$647$	−33.8921	−1.33244	−0.666219	+	0.745757i	$0.732088\pi$
$648$	0.562887	0.0221123
$649$	−5.55219	−0.217943
$650$	1.24239	0.0487304
$651$	−2.27405	−0.0891269
$652$	−22.4184	−0.877972
$653$	4.14256	0.162111	0.0810554	−	0.996710i	$-0.474171\pi$
$653$	4.14256	0.162111	0.0810554	+	0.996710i	$0.474171\pi$
$654$	−0.553332	−0.0216370
$655$	7.64454	0.298697
$656$	−3.30923	−0.129204
$657$	16.3153	0.636522
$658$	4.60310	0.179447
$659$	−15.4764	−0.602876	−0.301438	−	0.953486i	$-0.597467\pi$
$659$	−15.4764	−0.602876	−0.301438	+	0.953486i	$0.597467\pi$
$660$	8.67287	0.337591
$661$	−36.2493	−1.40993	−0.704967	−	0.709240i	$-0.749038\pi$
$661$	−36.2493	−1.40993	−0.704967	+	0.709240i	$0.749038\pi$
$662$	1.30248	0.0506222
$663$	−0.124224	−0.00482445
$664$	−7.45414	−0.289277
$665$	116.640	4.52310
$666$	−0.585188	−0.0226756
$667$	−1.16468	−0.0450967
$668$	−23.2707	−0.900370
$669$	14.3831	0.556084
$670$	−0.459480	−0.0177512
$671$	−1.00000	−0.0386046
$672$	−5.82587	−0.224738
$673$	27.8448	1.07334	0.536670	−	0.843792i	$-0.319682\pi$
$673$	27.8448	1.07334	0.536670	+	0.843792i	$0.319682\pi$
$674$	−3.96478	−0.152718
$675$	14.1865	0.546039
$676$	24.9808	0.960799
$677$	25.6658	0.986415	0.493208	−	0.869912i	$-0.335824\pi$
$677$	25.6658	0.986415	0.493208	+	0.869912i	$0.335824\pi$
$678$	0.644657	0.0247579
$679$	−27.5079	−1.05566
$680$	−0.494630	−0.0189682
$681$	−14.1128	−0.540804
$682$	0.0924443	0.00353988
$683$	−4.82600	−0.184662	−0.0923309	−	0.995728i	$-0.529432\pi$
$683$	−4.82600	−0.184662	−0.0923309	+	0.995728i	$0.529432\pi$
$684$	15.1550	0.579467
$685$	38.7025	1.47875
$686$	0.933097	0.0356258
$687$	−14.0784	−0.537123
$688$	−8.19751	−0.312527
$689$	3.50582	0.133561
$690$	1.77094	0.0674185
$691$	−26.4961	−1.00796	−0.503980	−	0.863715i	$-0.668131\pi$
$691$	−26.4961	−1.00796	−0.503980	+	0.863715i	$0.668131\pi$
$692$	−30.7346	−1.16835
$693$	3.47902	0.132157
$694$	1.18702	0.0450588
$695$	61.5529	2.33484
$696$	−0.229330	−0.00869272
$697$	−0.171086	−0.00648033
$698$	2.39492	0.0906492
$699$	0.879278	0.0332574
$700$	−97.7231	−3.69359
$701$	−8.85844	−0.334579	−0.167289	−	0.985908i	$-0.553501\pi$
$701$	−8.85844	−0.334579	−0.167289	+	0.985908i	$0.553501\pi$
$702$	0.0875752	0.00330531
$703$	−31.6701	−1.19446
$704$	−7.52394	−0.283569
$705$	40.9782	1.54333
$706$	−0.331095	−0.0124609
$707$	−32.4637	−1.22092
$708$	10.9933	0.413155
$709$	20.0969	0.754754	0.377377	−	0.926060i	$-0.376826\pi$
$709$	20.0969	0.754754	0.377377	+	0.926060i	$0.376826\pi$
$710$	−6.03002	−0.226302
$711$	−11.6445	−0.436702
$712$	−7.09431	−0.265870
$713$	−1.86857	−0.0699786
$714$	−0.0987090	−0.00369409
$715$	2.71232	0.101435
$716$	−30.9222	−1.15562
$717$	9.71808	0.362928
$718$	−0.916842	−0.0342162
$719$	−7.95144	−0.296539	−0.148269	−	0.988947i	$-0.547370\pi$
$719$	−7.95144	−0.296539	−0.148269	+	0.988947i	$0.547370\pi$
$720$	−16.9970	−0.633442
$721$	56.5558	2.10625
$722$	−5.59840	−0.208351
$723$	−0.519904	−0.0193354
$724$	−24.5168	−0.911161
$725$	−5.77983	−0.214657
$726$	−0.141429	−0.00524892
$727$	23.2508	0.862326	0.431163	−	0.902274i	$-0.358103\pi$
$727$	23.2508	0.862326	0.431163	+	0.902274i	$0.358103\pi$
$728$	−1.21261	−0.0449423
$729$	1.00000	0.0370370
$730$	10.1072	0.374085
$731$	−0.423807	−0.0156751
$732$	1.98000	0.0731828
$733$	−0.683312	−0.0252387	−0.0126193	−	0.999920i	$-0.504017\pi$
$733$	−0.683312	−0.0252387	−0.0126193	+	0.999920i	$0.504017\pi$
$734$	−2.07168	−0.0764673
$735$	−22.3550	−0.824575
$736$	−4.78709	−0.176455
$737$	−0.741703	−0.0273210
$738$	0.120612	0.00443978
$739$	0.0496377	0.00182595	0.000912976	−	1.00000i	$-0.499709\pi$
$739$	0.0496377	0.00182595	0.000912976		1.00000i	$0.499709\pi$
$740$	35.8856	1.31918
$741$	4.73953	0.174111
$742$	2.78575	0.102268
$743$	30.8209	1.13071	0.565354	−	0.824848i	$-0.308740\pi$
$743$	30.8209	1.13071	0.565354	+	0.824848i	$0.308740\pi$
$744$	−0.367928	−0.0134889
$745$	−25.4497	−0.932407
$746$	0.00387101	0.000141728 0
$747$	−13.2427	−0.484525
$748$	−0.397216	−0.0145236
$749$	−55.6214	−2.03236
$750$	5.69097	0.207805
$751$	−3.18118	−0.116083	−0.0580415	−	0.998314i	$-0.518486\pi$
$751$	−3.18118	−0.116083	−0.0580415	+	0.998314i	$0.518486\pi$
$752$	−36.3019	−1.32380
$753$	−29.7739	−1.08502
$754$	−0.0356797	−0.00129938
$755$	33.0622	1.20326
$756$	−6.88846	−0.250531
$757$	−17.7747	−0.646033	−0.323017	−	0.946393i	$-0.604697\pi$
$757$	−17.7747	−0.646033	−0.323017	+	0.946393i	$0.604697\pi$
$758$	5.16418	0.187571
$759$	2.85870	0.103764
$760$	18.8717	0.684548
$761$	39.5169	1.43249	0.716244	−	0.697850i	$-0.245860\pi$
$761$	39.5169	1.43249	0.716244	+	0.697850i	$0.245860\pi$
$762$	2.47193	0.0895485
$763$	13.6115	0.492768
$764$	−39.5970	−1.43257
$765$	−0.878738	−0.0317708
$766$	5.24644	0.189561
$767$	3.43801	0.124139
$768$	14.4237	0.520471
$769$	−28.3672	−1.02295	−0.511475	−	0.859298i	$-0.670901\pi$
$769$	−28.3672	−1.02295	−0.511475	+	0.859298i	$0.670901\pi$
$770$	2.15523	0.0776690
$771$	2.98917	0.107652
$772$	−4.30916	−0.155090
$773$	40.3211	1.45025	0.725125	−	0.688617i	$-0.241782\pi$
$773$	40.3211	1.45025	0.725125	+	0.688617i	$0.241782\pi$
$774$	0.298776	0.0107393
$775$	−9.27295	−0.333094
$776$	−4.45063	−0.159768
$777$	14.3951	0.516421
$778$	4.30855	0.154469
$779$	6.52745	0.233870
$780$	−5.37039	−0.192291
$781$	−9.73380	−0.348303
$782$	−0.0811087	−0.00290044
$783$	−0.407417	−0.0145599
$784$	19.8039	0.707283
$785$	16.6370	0.593800
$786$	0.246826	0.00880400
$787$	46.5564	1.65956	0.829778	−	0.558094i	$-0.188467\pi$
$787$	46.5564	1.65956	0.829778	+	0.558094i	$0.188467\pi$
$788$	−25.4988	−0.908356
$789$	22.3173	0.794515
$790$	−7.21366	−0.256651
$791$	−15.8580	−0.563844
$792$	0.562887	0.0200013
$793$	0.619218	0.0219891
$794$	2.41035	0.0855403
$795$	24.7996	0.879551
$796$	39.1274	1.38684
$797$	29.4881	1.04452	0.522261	−	0.852785i	$-0.325089\pi$
$797$	29.4881	1.04452	0.522261	+	0.852785i	$0.325089\pi$
$798$	3.76606	0.133317
$799$	−1.87679	−0.0663962
$800$	−23.7563	−0.839913
$801$	−12.6034	−0.445321
$802$	2.72073	0.0960724
$803$	16.3153	0.575756
$804$	1.46857	0.0517925
$805$	−43.5635	−1.53541
$806$	−0.0572431	−0.00201630
$807$	−15.4307	−0.543188
$808$	−5.25244	−0.184780
$809$	28.9898	1.01923	0.509613	−	0.860404i	$-0.329789\pi$
$809$	28.9898	1.01923	0.509613	+	0.860404i	$0.329789\pi$
$810$	0.619492	0.0217667
$811$	−38.9028	−1.36606	−0.683031	−	0.730389i	$-0.739339\pi$
$811$	−38.9028	−1.36606	−0.683031	+	0.730389i	$0.739339\pi$
$812$	2.80648	0.0984880
$813$	16.4228	0.575971
$814$	−0.585188	−0.0205108
$815$	−49.5950	−1.73724
$816$	0.778460	0.0272516
$817$	16.1696	0.565702
$818$	4.13463	0.144564
$819$	−2.15427	−0.0752763
$820$	−7.39630	−0.258290
$821$	−0.388487	−0.0135583	−0.00677914	−	0.999977i	$-0.502158\pi$
$821$	−0.388487	−0.0135583	−0.00677914	+	0.999977i	$0.502158\pi$
$822$	1.24962	0.0435857
$823$	−51.6999	−1.80215	−0.901073	−	0.433667i	$-0.857219\pi$
$823$	−51.6999	−1.80215	−0.901073	+	0.433667i	$0.857219\pi$
$824$	9.15041	0.318770
$825$	14.1865	0.493911
$826$	2.73187	0.0950538
$827$	−32.0395	−1.11412	−0.557061	−	0.830472i	$-0.688071\pi$
$827$	−32.0395	−1.11412	−0.557061	+	0.830472i	$0.688071\pi$
$828$	−5.66021	−0.196706
$829$	−44.9452	−1.56101	−0.780506	−	0.625149i	$-0.785038\pi$
$829$	−44.9452	−1.56101	−0.780506	+	0.625149i	$0.785038\pi$
$830$	−8.20376	−0.284757
$831$	22.6770	0.786658
$832$	4.65896	0.161520
$833$	1.02385	0.0354744
$834$	1.98742	0.0688186
$835$	−51.4805	−1.78156
$836$	15.1550	0.524147
$837$	−0.653645	−0.0225933
$838$	−5.45493	−0.188438
$839$	30.7211	1.06061	0.530305	−	0.847807i	$-0.322078\pi$
$839$	30.7211	1.06061	0.530305	+	0.847807i	$0.322078\pi$
$840$	−8.57780	−0.295962
$841$	−28.8340	−0.994276
$842$	2.73499	0.0942541
$843$	−15.4368	−0.531671
$844$	−26.5477	−0.913810
$845$	55.2636	1.90113
$846$	1.32310	0.0454891
$847$	3.47902	0.119541
$848$	−21.9696	−0.754438
$849$	−25.7002	−0.882028
$850$	−0.402509	−0.0138059
$851$	11.8284	0.405471
$852$	19.2729	0.660279
$853$	−0.0565190	−0.00193517	−0.000967587	−	1.00000i	$-0.500308\pi$
$853$	−0.0565190	−0.00193517	−0.000967587		1.00000i	$0.500308\pi$
$854$	0.492034	0.0168371
$855$	33.5266	1.14659
$856$	−8.99924	−0.307588
$857$	6.53000	0.223061	0.111530	−	0.993761i	$-0.464425\pi$
$857$	6.53000	0.223061	0.111530	+	0.993761i	$0.464425\pi$
$858$	0.0875752	0.00298977
$859$	6.95640	0.237349	0.118675	−	0.992933i	$-0.462135\pi$
$859$	6.95640	0.237349	0.118675	+	0.992933i	$0.462135\pi$
$860$	−18.3219	−0.624770
$861$	−2.96694	−0.101113
$862$	0.273846	0.00932725
$863$	−5.23914	−0.178342	−0.0891712	−	0.996016i	$-0.528422\pi$
$863$	−5.23914	−0.178342	−0.0891712	+	0.996016i	$0.528422\pi$
$864$	−1.67457	−0.0569701
$865$	−67.9924	−2.31181
$866$	−1.78976	−0.0608186
$867$	−16.9598	−0.575983
$868$	4.50261	0.152828
$869$	−11.6445	−0.395012
$870$	−0.252392	−0.00855689
$871$	0.459276	0.0155620
$872$	2.20226	0.0745779
$873$	−7.90680	−0.267605
$874$	3.09455	0.104675
$875$	−139.993	−4.73262
$876$	−32.3043	−1.09146
$877$	−30.1228	−1.01717	−0.508587	−	0.861011i	$-0.669832\pi$
$877$	−30.1228	−1.01717	−0.508587	+	0.861011i	$0.669832\pi$
$878$	2.54012	0.0857248
$879$	−8.73612	−0.294662
$880$	−16.9970	−0.572970
$881$	−43.9634	−1.48117	−0.740583	−	0.671965i	$-0.765451\pi$
$881$	−43.9634	−1.48117	−0.740583	+	0.671965i	$0.765451\pi$
$882$	−0.721795	−0.0243041
$883$	4.24591	0.142886	0.0714432	−	0.997445i	$-0.477240\pi$
$883$	4.24591	0.142886	0.0714432	+	0.997445i	$0.477240\pi$
$884$	0.245963	0.00827262
$885$	24.3199	0.817506
$886$	−4.63194	−0.155613
$887$	−6.84223	−0.229740	−0.114870	−	0.993381i	$-0.536645\pi$
$887$	−6.84223	−0.229740	−0.114870	+	0.993381i	$0.536645\pi$
$888$	2.32905	0.0781577
$889$	−60.8072	−2.03941
$890$	−7.80774	−0.261716
$891$	1.00000	0.0335013
$892$	−28.4786	−0.953534
$893$	71.6055	2.39619
$894$	−0.821719	−0.0274824
$895$	−68.4074	−2.28661
$896$	15.3538	0.512934
$897$	−1.77015	−0.0591037
$898$	2.51585	0.0839549
$899$	0.266306	0.00888181
$900$	−28.0893	−0.936309
$901$	−1.13582	−0.0378395
$902$	0.120612	0.00401594
$903$	−7.34961	−0.244580
$904$	−2.56573	−0.0853350
$905$	−54.2373	−1.80291
$906$	1.06751	0.0354657
$907$	−6.48343	−0.215279	−0.107639	−	0.994190i	$-0.534329\pi$
$907$	−6.48343	−0.215279	−0.107639	+	0.994190i	$0.534329\pi$
$908$	27.9434	0.927333
$909$	−9.33126	−0.309498
$910$	−1.33455	−0.0442401
$911$	8.70271	0.288334	0.144167	−	0.989553i	$-0.453950\pi$
$911$	8.70271	0.288334	0.144167	+	0.989553i	$0.453950\pi$
$912$	−29.7007	−0.983489
$913$	−13.2427	−0.438270
$914$	0.627742	0.0207639
$915$	4.38024	0.144806
$916$	27.8751	0.921021
$917$	−6.07170	−0.200505
$918$	−0.0283726	−0.000936436 0
$919$	−8.83448	−0.291422	−0.145711	−	0.989327i	$-0.546547\pi$
$919$	−8.83448	−0.291422	−0.145711	+	0.989327i	$0.546547\pi$
$920$	−7.04834	−0.232377
$921$	7.16998	0.236259
$922$	2.34789	0.0773235
$923$	6.02734	0.198392
$924$	−6.88846	−0.226614
$925$	58.6993	1.93002
$926$	−0.306011	−0.0100562
$927$	16.2562	0.533925
$928$	0.682249	0.0223959
$929$	6.31541	0.207202	0.103601	−	0.994619i	$-0.466963\pi$
$929$	6.31541	0.207202	0.103601	+	0.994619i	$0.466963\pi$
$930$	−0.404928	−0.0132781
$931$	−39.0632	−1.28024
$932$	−1.74097	−0.0570273
$933$	14.0403	0.459660
$934$	−3.49143	−0.114243
$935$	−0.878738	−0.0287378
$936$	−0.348549	−0.0113927
$937$	−0.170347	−0.00556500	−0.00278250	−	0.999996i	$-0.500886\pi$
$937$	−0.170347	−0.00556500	−0.00278250	+	0.999996i	$0.500886\pi$
$938$	0.364943	0.0119158
$939$	23.7718	0.775762
$940$	−81.1367	−2.64639
$941$	39.7386	1.29544	0.647720	−	0.761879i	$-0.275723\pi$
$941$	39.7386	1.29544	0.647720	+	0.761879i	$0.275723\pi$
$942$	0.537174	0.0175021
$943$	−2.43792	−0.0793897
$944$	−21.5447	−0.701219
$945$	−15.2390	−0.495723
$946$	0.298776	0.00971403
$947$	31.4329	1.02143	0.510715	−	0.859750i	$-0.329381\pi$
$947$	31.4329	1.02143	0.510715	+	0.859750i	$0.329381\pi$
$948$	23.0560	0.748825
$949$	−10.1027	−0.327949
$950$	15.3570	0.498246
$951$	14.3528	0.465423
$952$	0.392862	0.0127327
$953$	−2.45917	−0.0796602	−0.0398301	−	0.999206i	$-0.512682\pi$
$953$	−2.45917	−0.0796602	−0.0398301	+	0.999206i	$0.512682\pi$
$954$	0.800727	0.0259245
$955$	−87.5984	−2.83462
$956$	−19.2418	−0.622323
$957$	−0.407417	−0.0131699
$958$	−1.82963	−0.0591128
$959$	−30.7396	−0.992634
$960$	32.9567	1.06367
$961$	−30.5727	−0.986218
$962$	0.362358	0.0116829
$963$	−15.9877	−0.515195
$964$	1.02941	0.0331550
$965$	−9.53292	−0.306876
$966$	−1.40658	−0.0452558
$967$	43.2651	1.39131	0.695657	−	0.718375i	$-0.255114\pi$
$967$	43.2651	1.39131	0.695657	+	0.718375i	$0.255114\pi$
$968$	0.562887	0.0180919
$969$	−1.53551	−0.0493277
$970$	−4.89821	−0.157272
$971$	−3.78573	−0.121490	−0.0607450	−	0.998153i	$-0.519348\pi$
$971$	−3.78573	−0.121490	−0.0607450	+	0.998153i	$0.519348\pi$
$972$	−1.98000	−0.0635085
$973$	−48.8886	−1.56730
$974$	1.32083	0.0423221
$975$	−8.78453	−0.281330
$976$	−3.88039	−0.124208
$977$	−26.7510	−0.855839	−0.427919	−	0.903817i	$-0.640753\pi$
$977$	−26.7510	−0.855839	−0.427919	+	0.903817i	$0.640753\pi$
$978$	−1.60132	−0.0512045
$979$	−12.6034	−0.402808
$980$	44.2628	1.41392
$981$	3.91244	0.124915
$982$	4.16772	0.132997
$983$	8.12004	0.258989	0.129495	−	0.991580i	$-0.458665\pi$
$983$	8.12004	0.258989	0.129495	+	0.991580i	$0.458665\pi$
$984$	−0.480035	−0.0153030
$985$	−56.4095	−1.79736
$986$	0.0115595	0.000368129 0
$987$	−32.5471	−1.03598
$988$	−9.38425	−0.298553
$989$	−6.03914	−0.192033
$990$	0.619492	0.0196888
$991$	40.3920	1.28309	0.641546	−	0.767084i	$-0.278293\pi$
$991$	40.3920	1.28309	0.641546	+	0.767084i	$0.278293\pi$
$992$	1.09458	0.0347528
$993$	−9.20941	−0.292252
$994$	4.78936	0.151909
$995$	86.5595	2.74412
$996$	26.2205	0.830830
$997$	−9.53486	−0.301972	−0.150986	−	0.988536i	$-0.548245\pi$
$997$	−9.53486	−0.301972	−0.150986	+	0.988536i	$0.548245\pi$
$998$	−2.20090	−0.0696681
$999$	4.13768	0.130910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.7	✓	12
3.2	odd	2		6039.2.a.f.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.7	✓	12	1.1	even	1	trivial
6039.2.a.f.1.6		12	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.141429 q^{2} +1.00000 q^{3} -1.98000 q^{4} -4.38024 q^{5} -0.141429 q^{6} +3.47902 q^{7} +0.562887 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.141429 q^{2} +1.00000 q^{3} -1.98000 q^{4} -4.38024 q^{5} -0.141429 q^{6} +3.47902 q^{7} +0.562887 q^{8} +1.00000 q^{9} +0.619492 q^{10} +1.00000 q^{11} -1.98000 q^{12} -0.619218 q^{13} -0.492034 q^{14} -4.38024 q^{15} +3.88039 q^{16} +0.200614 q^{17} -0.141429 q^{18} -7.65406 q^{19} +8.67287 q^{20} +3.47902 q^{21} -0.141429 q^{22} +2.85870 q^{23} +0.562887 q^{24} +14.1865 q^{25} +0.0875752 q^{26} +1.00000 q^{27} -6.88846 q^{28} -0.407417 q^{29} +0.619492 q^{30} -0.653645 q^{31} -1.67457 q^{32} +1.00000 q^{33} -0.0283726 q^{34} -15.2390 q^{35} -1.98000 q^{36} +4.13768 q^{37} +1.08250 q^{38} -0.619218 q^{39} -2.46558 q^{40} -0.852809 q^{41} -0.492034 q^{42} -2.11255 q^{43} -1.98000 q^{44} -4.38024 q^{45} -0.404302 q^{46} -9.35524 q^{47} +3.88039 q^{48} +5.10359 q^{49} -2.00638 q^{50} +0.200614 q^{51} +1.22605 q^{52} -5.66170 q^{53} -0.141429 q^{54} -4.38024 q^{55} +1.95829 q^{56} -7.65406 q^{57} +0.0576205 q^{58} -5.55219 q^{59} +8.67287 q^{60} -1.00000 q^{61} +0.0924443 q^{62} +3.47902 q^{63} -7.52394 q^{64} +2.71232 q^{65} -0.141429 q^{66} -0.741703 q^{67} -0.397216 q^{68} +2.85870 q^{69} +2.15523 q^{70} -9.73380 q^{71} +0.562887 q^{72} +16.3153 q^{73} -0.585188 q^{74} +14.1865 q^{75} +15.1550 q^{76} +3.47902 q^{77} +0.0875752 q^{78} -11.6445 q^{79} -16.9970 q^{80} +1.00000 q^{81} +0.120612 q^{82} -13.2427 q^{83} -6.88846 q^{84} -0.878738 q^{85} +0.298776 q^{86} -0.407417 q^{87} +0.562887 q^{88} -12.6034 q^{89} +0.619492 q^{90} -2.15427 q^{91} -5.66021 q^{92} -0.653645 q^{93} +1.32310 q^{94} +33.5266 q^{95} -1.67457 q^{96} -7.90680 q^{97} -0.721795 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

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