LMFDB - Embedded newform 139.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [139,2,Mod(1,139)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(139, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("139.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	139.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:	$1.10992058810$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 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			1.5
Root			$1.44228$ of defining polynomial
Character	$\chi$	$=$	139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44228 q^{2} +1.01681 q^{3} +0.0801788 q^{4} +2.10270 q^{5} +1.46653 q^{6} -1.94441 q^{7} -2.76892 q^{8} -1.96609 q^{9} +O(q^{10})$	\(q+1.44228 q^{2} +1.01681 q^{3} +0.0801788 q^{4} +2.10270 q^{5} +1.46653 q^{6} -1.94441 q^{7} -2.76892 q^{8} -1.96609 q^{9} +3.03269 q^{10} -1.65710 q^{11} +0.0815268 q^{12} +2.72182 q^{13} -2.80439 q^{14} +2.13805 q^{15} -4.15393 q^{16} +4.48334 q^{17} -2.83566 q^{18} +2.23411 q^{19} +0.168592 q^{20} -1.97710 q^{21} -2.39001 q^{22} -3.67193 q^{23} -2.81548 q^{24} -0.578649 q^{25} +3.92563 q^{26} -5.04959 q^{27} -0.155900 q^{28} -6.87982 q^{29} +3.08368 q^{30} +1.29710 q^{31} -0.453290 q^{32} -1.68496 q^{33} +6.46625 q^{34} -4.08851 q^{35} -0.157639 q^{36} +9.38804 q^{37} +3.22221 q^{38} +2.76758 q^{39} -5.82222 q^{40} +10.2034 q^{41} -2.85154 q^{42} -2.68294 q^{43} -0.132864 q^{44} -4.13410 q^{45} -5.29596 q^{46} +5.68799 q^{47} -4.22377 q^{48} -3.21928 q^{49} -0.834575 q^{50} +4.55872 q^{51} +0.218232 q^{52} -0.660925 q^{53} -7.28293 q^{54} -3.48439 q^{55} +5.38392 q^{56} +2.27167 q^{57} -9.92265 q^{58} +5.46888 q^{59} +0.171427 q^{60} -2.95008 q^{61} +1.87078 q^{62} +3.82289 q^{63} +7.65409 q^{64} +5.72316 q^{65} -2.43019 q^{66} -9.39699 q^{67} +0.359469 q^{68} -3.73367 q^{69} -5.89679 q^{70} +12.6029 q^{71} +5.44396 q^{72} +9.25327 q^{73} +13.5402 q^{74} -0.588378 q^{75} +0.179128 q^{76} +3.22208 q^{77} +3.99163 q^{78} -10.6724 q^{79} -8.73447 q^{80} +0.763792 q^{81} +14.7162 q^{82} -2.94980 q^{83} -0.158521 q^{84} +9.42713 q^{85} -3.86956 q^{86} -6.99549 q^{87} +4.58839 q^{88} -10.6226 q^{89} -5.96254 q^{90} -5.29232 q^{91} -0.294411 q^{92} +1.31890 q^{93} +8.20369 q^{94} +4.69766 q^{95} -0.460911 q^{96} -4.39900 q^{97} -4.64311 q^{98} +3.25801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * 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 $

$2$	1.44228	1.01985	0.509924	−	0.860220i	$-0.329674\pi$
$2$	1.44228	1.01985	0.509924	+	0.860220i	$0.329674\pi$
$3$	1.01681	0.587057	0.293529	−	0.955950i	$-0.405170\pi$
$3$	1.01681	0.587057	0.293529	+	0.955950i	$0.405170\pi$
$4$	0.0801788	0.0400894
$5$	2.10270	0.940356	0.470178	−	0.882572i	$-0.344190\pi$
$5$	2.10270	0.940356	0.470178	+	0.882572i	$0.344190\pi$
$6$	1.46653	0.598709
$7$	−1.94441	−0.734917	−0.367459	−	0.930040i	$-0.619772\pi$
$7$	−1.94441	−0.734917	−0.367459	+	0.930040i	$0.619772\pi$
$8$	−2.76892	−0.978963
$9$	−1.96609	−0.655364
$10$	3.03269	0.959020
$11$	−1.65710	−0.499635	−0.249817	−	0.968293i	$-0.580371\pi$
$11$	−1.65710	−0.499635	−0.249817	+	0.968293i	$0.580371\pi$
$12$	0.0815268	0.0235348
$13$	2.72182	0.754896	0.377448	−	0.926031i	$-0.376802\pi$
$13$	2.72182	0.754896	0.377448	+	0.926031i	$0.376802\pi$
$14$	−2.80439	−0.749504
$15$	2.13805	0.552043
$16$	−4.15393	−1.03848
$17$	4.48334	1.08737	0.543685	−	0.839289i	$-0.317029\pi$
$17$	4.48334	1.08737	0.543685	+	0.839289i	$0.317029\pi$
$18$	−2.83566	−0.668371
$19$	2.23411	0.512539	0.256270	−	0.966605i	$-0.417506\pi$
$19$	2.23411	0.512539	0.256270	+	0.966605i	$0.417506\pi$
$20$	0.168592	0.0376983
$21$	−1.97710	−0.431438
$22$	−2.39001	−0.509551
$23$	−3.67193	−0.765651	−0.382825	−	0.923821i	$-0.625049\pi$
$23$	−3.67193	−0.765651	−0.382825	+	0.923821i	$0.625049\pi$
$24$	−2.81548	−0.574707
$25$	−0.578649	−0.115730
$26$	3.92563	0.769879
$27$	−5.04959	−0.971793
$28$	−0.155900	−0.0294624
$29$	−6.87982	−1.27755	−0.638776	−	0.769393i	$-0.720559\pi$
$29$	−6.87982	−1.27755	−0.638776	+	0.769393i	$0.720559\pi$
$30$	3.08368	0.563000
$31$	1.29710	0.232965	0.116483	−	0.993193i	$-0.462838\pi$
$31$	1.29710	0.232965	0.116483	+	0.993193i	$0.462838\pi$
$32$	−0.453290	−0.0801311
$33$	−1.68496	−0.293314
$34$	6.46625	1.10895
$35$	−4.08851	−0.691084
$36$	−0.157639	−0.0262731
$37$	9.38804	1.54338	0.771692	−	0.635997i	$-0.219411\pi$
$37$	9.38804	1.54338	0.771692	+	0.635997i	$0.219411\pi$
$38$	3.22221	0.522712
$39$	2.76758	0.443167
$40$	−5.82222	−0.920574
$41$	10.2034	1.59350	0.796750	−	0.604309i	$-0.206551\pi$
$41$	10.2034	1.59350	0.796750	+	0.604309i	$0.206551\pi$
$42$	−2.85154	−0.440002
$43$	−2.68294	−0.409145	−0.204572	−	0.978851i	$-0.565580\pi$
$43$	−2.68294	−0.409145	−0.204572	+	0.978851i	$0.565580\pi$
$44$	−0.132864	−0.0200301
$45$	−4.13410	−0.616276
$46$	−5.29596	−0.780847
$47$	5.68799	0.829679	0.414840	−	0.909895i	$-0.363838\pi$
$47$	5.68799	0.829679	0.414840	+	0.909895i	$0.363838\pi$
$48$	−4.22377	−0.609648
$49$	−3.21928	−0.459897
$50$	−0.834575	−0.118027
$51$	4.55872	0.638349
$52$	0.218232	0.0302633
$53$	−0.660925	−0.0907851	−0.0453925	−	0.998969i	$-0.514454\pi$
$53$	−0.660925	−0.0907851	−0.0453925	+	0.998969i	$0.514454\pi$
$54$	−7.28293	−0.991081
$55$	−3.48439	−0.469835
$56$	5.38392	0.719457
$57$	2.27167	0.300890
$58$	−9.92265	−1.30291
$59$	5.46888	0.711988	0.355994	−	0.934488i	$-0.384142\pi$
$59$	5.46888	0.711988	0.355994	+	0.934488i	$0.384142\pi$
$60$	0.171427	0.0221311
$61$	−2.95008	−0.377719	−0.188859	−	0.982004i	$-0.560479\pi$
$61$	−2.95008	−0.377719	−0.188859	+	0.982004i	$0.560479\pi$
$62$	1.87078	0.237589
$63$	3.82289	0.481638
$64$	7.65409	0.956761
$65$	5.72316	0.709871
$66$	−2.43019	−0.299136
$67$	−9.39699	−1.14802	−0.574012	−	0.818847i	$-0.694614\pi$
$67$	−9.39699	−1.14802	−0.574012	+	0.818847i	$0.694614\pi$
$68$	0.359469	0.0435920
$69$	−3.73367	−0.449481
$70$	−5.89679	−0.704801
$71$	12.6029	1.49568	0.747842	−	0.663877i	$-0.231090\pi$
$71$	12.6029	1.49568	0.747842	+	0.663877i	$0.231090\pi$
$72$	5.44396	0.641577
$73$	9.25327	1.08301	0.541507	−	0.840696i	$-0.317854\pi$
$73$	9.25327	1.08301	0.541507	+	0.840696i	$0.317854\pi$
$74$	13.5402	1.57402
$75$	−0.588378	−0.0679400
$76$	0.179128	0.0205474
$77$	3.22208	0.367190
$78$	3.99163	0.451963
$79$	−10.6724	−1.20073	−0.600367	−	0.799725i	$-0.704979\pi$
$79$	−10.6724	−1.20073	−0.600367	+	0.799725i	$0.704979\pi$
$80$	−8.73447	−0.976543
$81$	0.763792	0.0848658
$82$	14.7162	1.62513
$83$	−2.94980	−0.323783	−0.161891	−	0.986809i	$-0.551759\pi$
$83$	−2.94980	−0.323783	−0.161891	+	0.986809i	$0.551759\pi$
$84$	−0.158521	−0.0172961
$85$	9.42713	1.02252
$86$	−3.86956	−0.417265
$87$	−6.99549	−0.749995
$88$	4.58839	0.489124
$89$	−10.6226	−1.12599	−0.562994	−	0.826461i	$-0.690351\pi$
$89$	−10.6226	−1.12599	−0.562994	+	0.826461i	$0.690351\pi$
$90$	−5.96254	−0.628507
$91$	−5.29232	−0.554786
$92$	−0.294411	−0.0306945
$93$	1.31890	0.136764
$94$	8.20369	0.846146
$95$	4.69766	0.481970
$96$	−0.460911	−0.0470415
$97$	−4.39900	−0.446651	−0.223325	−	0.974744i	$-0.571691\pi$
$97$	−4.39900	−0.446651	−0.223325	+	0.974744i	$0.571691\pi$
$98$	−4.64311	−0.469024
$99$	3.25801	0.327443
$100$	−0.0463954	−0.00463954
$101$	18.0072	1.79178	0.895892	−	0.444272i	$-0.146538\pi$
$101$	18.0072	1.79178	0.895892	+	0.444272i	$0.146538\pi$
$102$	6.57496	0.651018
$103$	−4.12106	−0.406060	−0.203030	−	0.979173i	$-0.565079\pi$
$103$	−4.12106	−0.406060	−0.203030	+	0.979173i	$0.565079\pi$
$104$	−7.53650	−0.739015
$105$	−4.15725	−0.405706
$106$	−0.953241	−0.0925870
$107$	−4.15932	−0.402097	−0.201048	−	0.979581i	$-0.564435\pi$
$107$	−4.15932	−0.402097	−0.201048	+	0.979581i	$0.564435\pi$
$108$	−0.404870	−0.0389586
$109$	−15.3002	−1.46550	−0.732748	−	0.680500i	$-0.761762\pi$
$109$	−15.3002	−1.46550	−0.732748	+	0.680500i	$0.761762\pi$
$110$	−5.02547	−0.479160
$111$	9.54588	0.906054
$112$	8.07693	0.763199
$113$	13.3298	1.25396	0.626980	−	0.779036i	$-0.284291\pi$
$113$	13.3298	1.25396	0.626980	+	0.779036i	$0.284291\pi$
$114$	3.27639	0.306862
$115$	−7.72098	−0.719985
$116$	−0.551616	−0.0512162
$117$	−5.35134	−0.494731
$118$	7.88767	0.726119
$119$	−8.71745	−0.799127
$120$	−5.92011	−0.540429
$121$	−8.25402	−0.750365
$122$	−4.25485	−0.385216
$123$	10.3749	0.935476
$124$	0.104000	0.00933943
$125$	−11.7302	−1.04918
$126$	5.51368	0.491198
$127$	0.581539	0.0516032	0.0258016	−	0.999667i	$-0.491786\pi$
$127$	0.581539	0.0516032	0.0258016	+	0.999667i	$0.491786\pi$
$128$	11.9459	1.05588
$129$	−2.72805	−0.240191
$130$	8.25442	0.723960
$131$	−20.8834	−1.82459	−0.912296	−	0.409532i	$-0.865692\pi$
$131$	−20.8834	−1.82459	−0.912296	+	0.409532i	$0.865692\pi$
$132$	−0.135098	−0.0117588
$133$	−4.34402	−0.376674
$134$	−13.5531	−1.17081
$135$	−10.6178	−0.913832
$136$	−12.4140	−1.06450
$137$	8.21826	0.702134	0.351067	−	0.936350i	$-0.385819\pi$
$137$	8.21826	0.702134	0.351067	+	0.936350i	$0.385819\pi$
$138$	−5.38500	−0.458402
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−0.327812	−0.0277051
$141$	5.78362	0.487069
$142$	18.1769	1.52537
$143$	−4.51032	−0.377172
$144$	8.16701	0.680584
$145$	−14.4662	−1.20135
$146$	13.3458	1.10451
$147$	−3.27340	−0.269986
$148$	0.752721	0.0618733
$149$	6.64525	0.544400	0.272200	−	0.962241i	$-0.412249\pi$
$149$	6.64525	0.544400	0.272200	+	0.962241i	$0.412249\pi$
$150$	−0.848607	−0.0692885
$151$	−7.46212	−0.607259	−0.303629	−	0.952790i	$-0.598198\pi$
$151$	−7.46212	−0.607259	−0.303629	+	0.952790i	$0.598198\pi$
$152$	−6.18608	−0.501757
$153$	−8.81467	−0.712624
$154$	4.64715	0.374478
$155$	2.72740	0.219070
$156$	0.221901	0.0177663
$157$	−0.686050	−0.0547527	−0.0273764	−	0.999625i	$-0.508715\pi$
$157$	−0.686050	−0.0547527	−0.0273764	+	0.999625i	$0.508715\pi$
$158$	−15.3926	−1.22457
$159$	−0.672037	−0.0532960
$160$	−0.953133	−0.0753518
$161$	7.13974	0.562690
$162$	1.10160	0.0865502
$163$	−15.6818	−1.22829	−0.614147	−	0.789191i	$-0.710500\pi$
$163$	−15.6818	−1.22829	−0.614147	+	0.789191i	$0.710500\pi$
$164$	0.818095	0.0638825
$165$	−3.54297	−0.275820
$166$	−4.25445	−0.330209
$167$	−9.59823	−0.742733	−0.371367	−	0.928486i	$-0.621111\pi$
$167$	−9.59823	−0.742733	−0.371367	+	0.928486i	$0.621111\pi$
$168$	5.47444	0.422362
$169$	−5.59172	−0.430132
$170$	13.5966	1.04281
$171$	−4.39246	−0.335900
$172$	−0.215115	−0.0164024
$173$	7.08082	0.538345	0.269172	−	0.963092i	$-0.413250\pi$
$173$	7.08082	0.538345	0.269172	+	0.963092i	$0.413250\pi$
$174$	−10.0895	−0.764881
$175$	1.12513	0.0850518
$176$	6.88348	0.518862
$177$	5.56083	0.417978
$178$	−15.3207	−1.14834
$179$	−3.92939	−0.293696	−0.146848	−	0.989159i	$-0.546913\pi$
$179$	−3.92939	−0.293696	−0.146848	+	0.989159i	$0.546913\pi$
$180$	−0.331467	−0.0247061
$181$	21.6810	1.61154	0.805769	−	0.592230i	$-0.201752\pi$
$181$	21.6810	1.61154	0.805769	+	0.592230i	$0.201752\pi$
$182$	−7.63302	−0.565797
$183$	−2.99968	−0.221742
$184$	10.1673	0.749544
$185$	19.7402	1.45133
$186$	1.90223	0.139478
$187$	−7.42935	−0.543288
$188$	0.456056	0.0332613
$189$	9.81846	0.714188
$190$	6.77535	0.491536
$191$	17.1191	1.23870	0.619349	−	0.785116i	$-0.287397\pi$
$191$	17.1191	1.23870	0.619349	+	0.785116i	$0.287397\pi$
$192$	7.78277	0.561673
$193$	−25.1710	−1.81185	−0.905923	−	0.423442i	$-0.860822\pi$
$193$	−25.1710	−1.81185	−0.905923	+	0.423442i	$0.860822\pi$
$194$	−6.34460	−0.455516
$195$	5.81939	0.416735
$196$	−0.258118	−0.0184370
$197$	8.92502	0.635881	0.317941	−	0.948111i	$-0.397009\pi$
$197$	8.92502	0.635881	0.317941	+	0.948111i	$0.397009\pi$
$198$	4.69898	0.333942
$199$	10.9052	0.773049	0.386525	−	0.922279i	$-0.373675\pi$
$199$	10.9052	0.773049	0.386525	+	0.922279i	$0.373675\pi$
$200$	1.60224	0.113295
$201$	−9.55498	−0.673956
$202$	25.9715	1.82735
$203$	13.3772	0.938894
$204$	0.365513	0.0255910
$205$	21.4547	1.49846
$206$	−5.94373	−0.414119
$207$	7.21936	0.501780
$208$	−11.3062	−0.783946
$209$	−3.70214	−0.256083
$210$	−5.99593	−0.413758
$211$	3.88066	0.267155	0.133578	−	0.991038i	$-0.457353\pi$
$211$	3.88066	0.267155	0.133578	+	0.991038i	$0.457353\pi$
$212$	−0.0529922	−0.00363952
$213$	12.8147	0.878052
$214$	−5.99892	−0.410078
$215$	−5.64142	−0.384742
$216$	13.9819	0.951349
$217$	−2.52208	−0.171210
$218$	−22.0672	−1.49458
$219$	9.40885	0.635791
$220$	−0.279374	−0.0188354
$221$	12.2028	0.820851
$222$	13.7678	0.924038
$223$	−10.3790	−0.695032	−0.347516	−	0.937674i	$-0.612975\pi$
$223$	−10.3790	−0.695032	−0.347516	+	0.937674i	$0.612975\pi$
$224$	0.881381	0.0588897
$225$	1.13768	0.0758451
$226$	19.2253	1.27885
$227$	−28.4485	−1.88819	−0.944097	−	0.329667i	$-0.893064\pi$
$227$	−28.4485	−1.88819	−0.944097	+	0.329667i	$0.893064\pi$
$228$	0.182140	0.0120625
$229$	23.3247	1.54134	0.770671	−	0.637233i	$-0.219921\pi$
$229$	23.3247	1.54134	0.770671	+	0.637233i	$0.219921\pi$
$230$	−11.1358	−0.734275
$231$	3.27625	0.215562
$232$	19.0497	1.25067
$233$	−13.8555	−0.907705	−0.453852	−	0.891077i	$-0.649951\pi$
$233$	−13.8555	−0.907705	−0.453852	+	0.891077i	$0.649951\pi$
$234$	−7.71814	−0.504551
$235$	11.9601	0.780194
$236$	0.438488	0.0285432
$237$	−10.8518	−0.704899
$238$	−12.5730	−0.814988
$239$	21.0113	1.35911	0.679555	−	0.733625i	$-0.262173\pi$
$239$	21.0113	1.35911	0.679555	+	0.733625i	$0.262173\pi$
$240$	−8.88132	−0.573287
$241$	3.16874	0.204116	0.102058	−	0.994778i	$-0.467457\pi$
$241$	3.16874	0.204116	0.102058	+	0.994778i	$0.467457\pi$
$242$	−11.9046	−0.765258
$243$	15.9254	1.02161
$244$	−0.236534	−0.0151425
$245$	−6.76917	−0.432467
$246$	14.9636	0.954043
$247$	6.08083	0.386914
$248$	−3.59156	−0.228064
$249$	−2.99940	−0.190079
$250$	−16.9183	−1.07001
$251$	5.34519	0.337385	0.168693	−	0.985669i	$-0.446045\pi$
$251$	5.34519	0.337385	0.168693	+	0.985669i	$0.446045\pi$
$252$	0.306514	0.0193086
$253$	6.08476	0.382546
$254$	0.838743	0.0526274
$255$	9.58563	0.600275
$256$	1.92124	0.120077
$257$	−9.77662	−0.609849	−0.304925	−	0.952377i	$-0.598631\pi$
$257$	−9.77662	−0.609849	−0.304925	+	0.952377i	$0.598631\pi$
$258$	−3.93462	−0.244958
$259$	−18.2542	−1.13426
$260$	0.458876	0.0284583
$261$	13.5264	0.837261
$262$	−30.1198	−1.86081
$263$	−21.2549	−1.31063	−0.655316	−	0.755355i	$-0.727464\pi$
$263$	−21.2549	−1.31063	−0.655316	+	0.755355i	$0.727464\pi$
$264$	4.66553	0.287144
$265$	−1.38973	−0.0853703
$266$	−6.26530	−0.384150
$267$	−10.8012	−0.661020
$268$	−0.753439	−0.0460236
$269$	10.6372	0.648563	0.324281	−	0.945961i	$-0.394878\pi$
$269$	10.6372	0.648563	0.324281	+	0.945961i	$0.394878\pi$
$270$	−15.3138	−0.931969
$271$	−15.6524	−0.950816	−0.475408	−	0.879766i	$-0.657699\pi$
$271$	−15.6524	−0.950816	−0.475408	+	0.879766i	$0.657699\pi$
$272$	−18.6235	−1.12922
$273$	−5.38130	−0.325691
$274$	11.8531	0.716069
$275$	0.958880	0.0578226
$276$	−0.299361	−0.0180194
$277$	−20.6725	−1.24209	−0.621044	−	0.783776i	$-0.713291\pi$
$277$	−20.6725	−1.24209	−0.621044	+	0.783776i	$0.713291\pi$
$278$	1.44228	0.0865024
$279$	−2.55021	−0.152677
$280$	11.3208	0.676546
$281$	3.32086	0.198106	0.0990530	−	0.995082i	$-0.468419\pi$
$281$	3.32086	0.198106	0.0990530	+	0.995082i	$0.468419\pi$
$282$	8.34162	0.496736
$283$	−14.6513	−0.870930	−0.435465	−	0.900206i	$-0.643416\pi$
$283$	−14.6513	−0.870930	−0.435465	+	0.900206i	$0.643416\pi$
$284$	1.01048	0.0599611
$285$	4.77664	0.282944
$286$	−6.50516	−0.384658
$287$	−19.8395	−1.17109
$288$	0.891210	0.0525150
$289$	3.10037	0.182375
$290$	−20.8644	−1.22520
$291$	−4.47296	−0.262209
$292$	0.741916	0.0434174
$293$	−0.927136	−0.0541639	−0.0270819	−	0.999633i	$-0.508621\pi$
$293$	−0.927136	−0.0541639	−0.0270819	+	0.999633i	$0.508621\pi$
$294$	−4.72117	−0.275344
$295$	11.4994	0.669522
$296$	−25.9948	−1.51092
$297$	8.36767	0.485542
$298$	9.58433	0.555205
$299$	−9.99432	−0.577987
$300$	−0.0471754	−0.00272367
$301$	5.21673	0.300687
$302$	−10.7625	−0.619311
$303$	18.3100	1.05188
$304$	−9.28032	−0.532263
$305$	−6.20313	−0.355190
$306$	−12.7132	−0.726767
$307$	32.2115	1.83841	0.919204	−	0.393782i	$-0.128833\pi$
$307$	32.2115	1.83841	0.919204	+	0.393782i	$0.128833\pi$
$308$	0.258343	0.0147204
$309$	−4.19034	−0.238380
$310$	3.93369	0.223418
$311$	32.0918	1.81976	0.909881	−	0.414870i	$-0.136173\pi$
$311$	32.0918	1.81976	0.909881	+	0.414870i	$0.136173\pi$
$312$	−7.66321	−0.433844
$313$	6.61799	0.374071	0.187035	−	0.982353i	$-0.440112\pi$
$313$	6.61799	0.374071	0.187035	+	0.982353i	$0.440112\pi$
$314$	−0.989477	−0.0558394
$315$	8.03838	0.452912
$316$	−0.855697	−0.0481367
$317$	5.92720	0.332905	0.166452	−	0.986049i	$-0.446769\pi$
$317$	5.92720	0.332905	0.166452	+	0.986049i	$0.446769\pi$
$318$	−0.969268	−0.0543538
$319$	11.4006	0.638309
$320$	16.0943	0.899696
$321$	−4.22925	−0.236054
$322$	10.2975	0.573858
$323$	10.0163	0.557320
$324$	0.0612400	0.00340222
$325$	−1.57498	−0.0873639
$326$	−22.6176	−1.25267
$327$	−15.5575	−0.860330
$328$	−28.2524	−1.55998
$329$	−11.0598	−0.609746
$330$	−5.10996	−0.281294
$331$	32.6437	1.79426	0.897131	−	0.441764i	$-0.145647\pi$
$331$	32.6437	1.79426	0.897131	+	0.441764i	$0.145647\pi$
$332$	−0.236512	−0.0129803
$333$	−18.4577	−1.01148
$334$	−13.8434	−0.757475
$335$	−19.7591	−1.07955
$336$	8.21273	0.448041
$337$	5.63098	0.306739	0.153369	−	0.988169i	$-0.450988\pi$
$337$	5.63098	0.306739	0.153369	+	0.988169i	$0.450988\pi$
$338$	−8.06484	−0.438670
$339$	13.5539	0.736146
$340$	0.755856	0.0409920
$341$	−2.14942	−0.116398
$342$	−6.33517	−0.342567
$343$	19.8704	1.07290
$344$	7.42886	0.400537
$345$	−7.85079	−0.422672
$346$	10.2125	0.549030
$347$	19.6551	1.05514	0.527571	−	0.849511i	$-0.323103\pi$
$347$	19.6551	1.05514	0.527571	+	0.849511i	$0.323103\pi$
$348$	−0.560890	−0.0300669
$349$	2.21624	0.118632	0.0593162	−	0.998239i	$-0.481108\pi$
$349$	2.21624	0.118632	0.0593162	+	0.998239i	$0.481108\pi$
$350$	1.62276	0.0867399
$351$	−13.7440	−0.733603
$352$	0.751147	0.0400363
$353$	−28.6867	−1.52684	−0.763419	−	0.645903i	$-0.776481\pi$
$353$	−28.6867	−1.52684	−0.763419	+	0.645903i	$0.776481\pi$
$354$	8.02029	0.426274
$355$	26.5000	1.40648
$356$	−0.851704	−0.0451402
$357$	−8.86402	−0.469133
$358$	−5.66729	−0.299526
$359$	9.67172	0.510454	0.255227	−	0.966881i	$-0.417850\pi$
$359$	9.67172	0.510454	0.255227	+	0.966881i	$0.417850\pi$
$360$	11.4470	0.603311
$361$	−14.0088	−0.737303
$362$	31.2702	1.64352
$363$	−8.39279	−0.440507
$364$	−0.424332	−0.0222410
$365$	19.4569	1.01842
$366$	−4.32638	−0.226144
$367$	25.4918	1.33066	0.665330	−	0.746549i	$-0.268291\pi$
$367$	25.4918	1.33066	0.665330	+	0.746549i	$0.268291\pi$
$368$	15.2529	0.795115
$369$	−20.0608	−1.04432
$370$	28.4710	1.48014
$371$	1.28511	0.0667195
$372$	0.105748	0.00548278
$373$	3.86874	0.200316	0.100158	−	0.994972i	$-0.468065\pi$
$373$	3.86874	0.200316	0.100158	+	0.994972i	$0.468065\pi$
$374$	−10.7152	−0.554071
$375$	−11.9274	−0.615931
$376$	−15.7496	−0.812225
$377$	−18.7256	−0.964418
$378$	14.1610	0.728363
$379$	28.5264	1.46530	0.732651	−	0.680604i	$-0.238283\pi$
$379$	28.5264	1.46530	0.732651	+	0.680604i	$0.238283\pi$
$380$	0.376653	0.0193219
$381$	0.591316	0.0302940
$382$	24.6906	1.26328
$383$	−9.01261	−0.460523	−0.230261	−	0.973129i	$-0.573958\pi$
$383$	−9.01261	−0.460523	−0.230261	+	0.973129i	$0.573958\pi$
$384$	12.1468	0.619863
$385$	6.77507	0.345290
$386$	−36.3037	−1.84781
$387$	5.27491	0.268139
$388$	−0.352706	−0.0179059
$389$	35.7699	1.81360	0.906802	−	0.421557i	$-0.138516\pi$
$389$	35.7699	1.81360	0.906802	+	0.421557i	$0.138516\pi$
$390$	8.39320	0.425006
$391$	−16.4625	−0.832546
$392$	8.91393	0.450222
$393$	−21.2345	−1.07114
$394$	12.8724	0.648502
$395$	−22.4408	−1.12912
$396$	0.261224	0.0131270
$397$	−18.1594	−0.911397	−0.455698	−	0.890134i	$-0.650610\pi$
$397$	−18.1594	−0.911397	−0.455698	+	0.890134i	$0.650610\pi$
$398$	15.7284	0.788393
$399$	−4.41705	−0.221129
$400$	2.40367	0.120183
$401$	−17.8319	−0.890483	−0.445241	−	0.895411i	$-0.646882\pi$
$401$	−17.8319	−0.890483	−0.445241	+	0.895411i	$0.646882\pi$
$402$	−13.7810	−0.687333
$403$	3.53045	0.175864
$404$	1.44380	0.0718315
$405$	1.60603	0.0798041
$406$	19.2937	0.957529
$407$	−15.5569	−0.771128
$408$	−12.6228	−0.624920
$409$	−12.7017	−0.628060	−0.314030	−	0.949413i	$-0.601679\pi$
$409$	−12.7017	−0.628060	−0.314030	+	0.949413i	$0.601679\pi$
$410$	30.9437	1.52820
$411$	8.35643	0.412192
$412$	−0.330421	−0.0162787
$413$	−10.6337	−0.523252
$414$	10.4124	0.511739
$415$	−6.20255	−0.304471
$416$	−1.23377	−0.0604906
$417$	1.01681	0.0497935
$418$	−5.33954	−0.261165
$419$	38.2854	1.87037	0.935183	−	0.354164i	$-0.115235\pi$
$419$	38.2854	1.87037	0.935183	+	0.354164i	$0.115235\pi$
$420$	−0.333323	−0.0162645
$421$	−34.9446	−1.70310	−0.851548	−	0.524277i	$-0.824336\pi$
$421$	−34.9446	−1.70310	−0.851548	+	0.524277i	$0.824336\pi$
$422$	5.59700	0.272458
$423$	−11.1831	−0.543742
$424$	1.83005	0.0888752
$425$	−2.59428	−0.125841
$426$	18.4825	0.895479
$427$	5.73616	0.277592
$428$	−0.333490	−0.0161198
$429$	−4.58615	−0.221422
$430$	−8.13652	−0.392378
$431$	8.75076	0.421509	0.210755	−	0.977539i	$-0.432408\pi$
$431$	8.75076	0.421509	0.210755	+	0.977539i	$0.432408\pi$
$432$	20.9756	1.00919
$433$	30.1605	1.44942	0.724710	−	0.689054i	$-0.241974\pi$
$433$	30.1605	1.44942	0.724710	+	0.689054i	$0.241974\pi$
$434$	−3.63756	−0.174608
$435$	−14.7094	−0.705263
$436$	−1.22675	−0.0587508
$437$	−8.20349	−0.392426
$438$	13.5702	0.648410
$439$	−21.7996	−1.04044	−0.520220	−	0.854032i	$-0.674150\pi$
$439$	−21.7996	−1.04044	−0.520220	+	0.854032i	$0.674150\pi$
$440$	9.64801	0.459951
$441$	6.32939	0.301400
$442$	17.5999	0.837143
$443$	−35.9082	−1.70605	−0.853026	−	0.521868i	$-0.825235\pi$
$443$	−35.9082	−1.70605	−0.853026	+	0.521868i	$0.825235\pi$
$444$	0.765377	0.0363232
$445$	−22.3361	−1.05883
$446$	−14.9695	−0.708827
$447$	6.75697	0.319594
$448$	−14.8827	−0.703140
$449$	−8.49151	−0.400739	−0.200369	−	0.979720i	$-0.564214\pi$
$449$	−8.49151	−0.400739	−0.200369	+	0.979720i	$0.564214\pi$
$450$	1.64085	0.0773505
$451$	−16.9080	−0.796168
$452$	1.06876	0.0502705
$453$	−7.58758	−0.356496
$454$	−41.0308	−1.92567
$455$	−11.1282	−0.521697
$456$	−6.29008	−0.294560
$457$	−22.6167	−1.05796	−0.528982	−	0.848633i	$-0.677426\pi$
$457$	−22.6167	−1.05796	−0.528982	+	0.848633i	$0.677426\pi$
$458$	33.6409	1.57193
$459$	−22.6390	−1.05670
$460$	−0.619059	−0.0288638
$461$	11.0838	0.516223	0.258111	−	0.966115i	$-0.416900\pi$
$461$	11.0838	0.516223	0.258111	+	0.966115i	$0.416900\pi$
$462$	4.72528	0.219840
$463$	38.6313	1.79535	0.897675	−	0.440659i	$-0.145255\pi$
$463$	38.6313	1.79535	0.897675	+	0.440659i	$0.145255\pi$
$464$	28.5783	1.32671
$465$	2.77326	0.128607
$466$	−19.9836	−0.925721
$467$	24.0609	1.11340	0.556702	−	0.830712i	$-0.312066\pi$
$467$	24.0609	1.11340	0.556702	+	0.830712i	$0.312066\pi$
$468$	−0.429064	−0.0198335
$469$	18.2716	0.843703
$470$	17.2499	0.795679
$471$	−0.697584	−0.0321430
$472$	−15.1429	−0.697010
$473$	4.44590	0.204423
$474$	−15.6513	−0.718890
$475$	−1.29276	−0.0593161
$476$	−0.698955	−0.0320365
$477$	1.29944	0.0594973
$478$	30.3043	1.38609
$479$	29.1169	1.33038	0.665192	−	0.746672i	$-0.268350\pi$
$479$	29.1169	1.33038	0.665192	+	0.746672i	$0.268350\pi$
$480$	−0.969158	−0.0442358
$481$	25.5525	1.16509
$482$	4.57021	0.208168
$483$	7.25978	0.330331
$484$	−0.661797	−0.0300817
$485$	−9.24978	−0.420011
$486$	22.9689	1.04189
$487$	−28.2034	−1.27802	−0.639008	−	0.769200i	$-0.720655\pi$
$487$	−28.2034	−1.27802	−0.639008	+	0.769200i	$0.720655\pi$
$488$	8.16854	0.369773
$489$	−15.9455	−0.721079
$490$	−9.76306	−0.441050
$491$	−12.4287	−0.560900	−0.280450	−	0.959869i	$-0.590484\pi$
$491$	−12.4287	−0.560900	−0.280450	+	0.959869i	$0.590484\pi$
$492$	0.831849	0.0375027
$493$	−30.8446	−1.38917
$494$	8.77027	0.394593
$495$	6.85063	0.307913
$496$	−5.38804	−0.241930
$497$	−24.5051	−1.09920
$498$	−4.32598	−0.193852
$499$	39.4279	1.76503	0.882517	−	0.470281i	$-0.155848\pi$
$499$	39.4279	1.76503	0.882517	+	0.470281i	$0.155848\pi$
$500$	−0.940516	−0.0420611
$501$	−9.75960	−0.436027
$502$	7.70927	0.344082
$503$	40.2997	1.79687	0.898437	−	0.439102i	$-0.144703\pi$
$503$	40.2997	1.79687	0.898437	+	0.439102i	$0.144703\pi$
$504$	−10.5853	−0.471506
$505$	37.8638	1.68492
$506$	8.77595	0.390139
$507$	−5.68573	−0.252512
$508$	0.0466271	0.00206874
$509$	34.6004	1.53364	0.766819	−	0.641863i	$-0.221838\pi$
$509$	34.6004	1.53364	0.766819	+	0.641863i	$0.221838\pi$
$510$	13.8252	0.612189
$511$	−17.9921	−0.795925
$512$	−21.1209	−0.933421
$513$	−11.2813	−0.498082
$514$	−14.1007	−0.621953
$515$	−8.66535	−0.381841
$516$	−0.218732	−0.00962912
$517$	−9.42558	−0.414537
$518$	−26.3277	−1.15677
$519$	7.19987	0.316039
$520$	−15.8470	−0.694937
$521$	−7.86638	−0.344632	−0.172316	−	0.985042i	$-0.555125\pi$
$521$	−7.86638	−0.344632	−0.172316	+	0.985042i	$0.555125\pi$
$522$	19.5088	0.853879
$523$	−7.66833	−0.335313	−0.167656	−	0.985846i	$-0.553620\pi$
$523$	−7.66833	−0.335313	−0.167656	+	0.985846i	$0.553620\pi$
$524$	−1.67441	−0.0731468
$525$	1.14405	0.0499303
$526$	−30.6555	−1.33664
$527$	5.81532	0.253319
$528$	6.99921	0.304602
$529$	−9.51691	−0.413779
$530$	−2.00438	−0.0870648
$531$	−10.7523	−0.466611
$532$	−0.348298	−0.0151006
$533$	27.7717	1.20293
$534$	−15.5783	−0.674140
$535$	−8.74581	−0.378114
$536$	26.0196	1.12387
$537$	−3.99545	−0.172417
$538$	15.3419	0.661435
$539$	5.33467	0.229780
$540$	−0.851320	−0.0366350
$541$	−15.0954	−0.649004	−0.324502	−	0.945885i	$-0.605197\pi$
$541$	−15.0954	−0.649004	−0.324502	+	0.945885i	$0.605197\pi$
$542$	−22.5752	−0.969687
$543$	22.0455	0.946065
$544$	−2.03225	−0.0871322
$545$	−32.1718	−1.37809
$546$	−7.76135	−0.332155
$547$	2.88384	0.123304	0.0616521	−	0.998098i	$-0.480363\pi$
$547$	2.88384	0.123304	0.0616521	+	0.998098i	$0.480363\pi$
$548$	0.658930	0.0281481
$549$	5.80012	0.247543
$550$	1.38298	0.0589703
$551$	−15.3703	−0.654795
$552$	10.3382	0.440025
$553$	20.7514	0.882440
$554$	−29.8155	−1.26674
$555$	20.0721	0.852014
$556$	0.0801788	0.00340034
$557$	−4.00819	−0.169832	−0.0849162	−	0.996388i	$-0.527062\pi$
$557$	−4.00819	−0.169832	−0.0849162	+	0.996388i	$0.527062\pi$
$558$	−3.67812	−0.155707
$559$	−7.30247	−0.308861
$560$	16.9834	0.717679
$561$	−7.55426	−0.318941
$562$	4.78962	0.202038
$563$	16.1490	0.680599	0.340299	−	0.940317i	$-0.389472\pi$
$563$	16.1490	0.680599	0.340299	+	0.940317i	$0.389472\pi$
$564$	0.463724	0.0195263
$565$	28.0285	1.17917
$566$	−21.1313	−0.888216
$567$	−1.48512	−0.0623694
$568$	−34.8964	−1.46422
$569$	−19.4554	−0.815613	−0.407807	−	0.913068i	$-0.633706\pi$
$569$	−19.4554	−0.815613	−0.407807	+	0.913068i	$0.633706\pi$
$570$	6.88927	0.288560
$571$	−33.8282	−1.41567	−0.707833	−	0.706380i	$-0.750327\pi$
$571$	−33.8282	−1.41567	−0.707833	+	0.706380i	$0.750327\pi$
$572$	−0.361632	−0.0151206
$573$	17.4070	0.727186
$574$	−28.6142	−1.19433
$575$	2.12476	0.0886086
$576$	−15.0486	−0.627026
$577$	−42.0018	−1.74856	−0.874278	−	0.485425i	$-0.838665\pi$
$577$	−42.0018	−1.74856	−0.874278	+	0.485425i	$0.838665\pi$
$578$	4.47161	0.185995
$579$	−25.5942	−1.06366
$580$	−1.15988	−0.0481615
$581$	5.73562	0.237954
$582$	−6.45127	−0.267414
$583$	1.09522	0.0453594
$584$	−25.6216	−1.06023
$585$	−11.2523	−0.465224
$586$	−1.33719	−0.0552389
$587$	−37.3166	−1.54022	−0.770110	−	0.637911i	$-0.779799\pi$
$587$	−37.3166	−1.54022	−0.770110	+	0.637911i	$0.779799\pi$
$588$	−0.262457	−0.0108236
$589$	2.89785	0.119404
$590$	16.5854	0.682811
$591$	9.07507	0.373299
$592$	−38.9972	−1.60278
$593$	−1.45651	−0.0598115	−0.0299057	−	0.999553i	$-0.509521\pi$
$593$	−1.45651	−0.0598115	−0.0299057	+	0.999553i	$0.509521\pi$
$594$	12.0686	0.495179
$595$	−18.3302	−0.751465
$596$	0.532808	0.0218247
$597$	11.0886	0.453824
$598$	−14.4146	−0.589458
$599$	−31.2287	−1.27597	−0.637985	−	0.770048i	$-0.720232\pi$
$599$	−31.2287	−1.27597	−0.637985	+	0.770048i	$0.720232\pi$
$600$	1.62917	0.0665107
$601$	24.4099	0.995699	0.497849	−	0.867263i	$-0.334123\pi$
$601$	24.4099	0.995699	0.497849	+	0.867263i	$0.334123\pi$
$602$	7.52400	0.306655
$603$	18.4753	0.752374
$604$	−0.598304	−0.0243446
$605$	−17.3557	−0.705611
$606$	26.4081	1.07276
$607$	16.7206	0.678667	0.339334	−	0.940666i	$-0.389798\pi$
$607$	16.7206	0.678667	0.339334	+	0.940666i	$0.389798\pi$
$608$	−1.01270	−0.0410704
$609$	13.6021	0.551185
$610$	−8.94667	−0.362240
$611$	15.4817	0.626321
$612$	−0.706749	−0.0285686
$613$	−13.3978	−0.541132	−0.270566	−	0.962701i	$-0.587211\pi$
$613$	−13.3978	−0.541132	−0.270566	+	0.962701i	$0.587211\pi$
$614$	46.4581	1.87490
$615$	21.8154	0.879681
$616$	−8.92170	−0.359466
$617$	29.1852	1.17495	0.587475	−	0.809242i	$-0.300122\pi$
$617$	29.1852	1.17495	0.587475	+	0.809242i	$0.300122\pi$
$618$	−6.04366	−0.243112
$619$	7.18553	0.288811	0.144405	−	0.989519i	$-0.453873\pi$
$619$	7.18553	0.288811	0.144405	+	0.989519i	$0.453873\pi$
$620$	0.218680	0.00878240
$621$	18.5417	0.744054
$622$	46.2855	1.85588
$623$	20.6546	0.827509
$624$	−11.4963	−0.460221
$625$	−21.7719	−0.870877
$626$	9.54501	0.381495
$627$	−3.76439	−0.150335
$628$	−0.0550066	−0.00219500
$629$	42.0898	1.67823
$630$	11.5936	0.461901
$631$	−23.3041	−0.927720	−0.463860	−	0.885909i	$-0.653536\pi$
$631$	−23.3041	−0.927720	−0.463860	+	0.885909i	$0.653536\pi$
$632$	29.5509	1.17547
$633$	3.94590	0.156836
$634$	8.54870	0.339512
$635$	1.22280	0.0485254
$636$	−0.0538832	−0.00213661
$637$	−8.76227	−0.347174
$638$	16.4428	0.650978
$639$	−24.7784	−0.980217
$640$	25.1187	0.992905
$641$	45.0737	1.78031	0.890153	−	0.455662i	$-0.150598\pi$
$641$	45.0737	1.78031	0.890153	+	0.455662i	$0.150598\pi$
$642$	−6.09978	−0.240739
$643$	7.19585	0.283777	0.141888	−	0.989883i	$-0.454683\pi$
$643$	7.19585	0.283777	0.141888	+	0.989883i	$0.454683\pi$
$644$	0.572456	0.0225579
$645$	−5.73627	−0.225865
$646$	14.4463	0.568382
$647$	−26.2361	−1.03145	−0.515723	−	0.856755i	$-0.672477\pi$
$647$	−26.2361	−1.03145	−0.515723	+	0.856755i	$0.672477\pi$
$648$	−2.11488	−0.0830805
$649$	−9.06249	−0.355734
$650$	−2.27156	−0.0890979
$651$	−2.56449	−0.100510
$652$	−1.25735	−0.0492416
$653$	6.64240	0.259937	0.129969	−	0.991518i	$-0.458512\pi$
$653$	6.64240	0.259937	0.129969	+	0.991518i	$0.458512\pi$
$654$	−22.4383	−0.877405
$655$	−43.9116	−1.71577
$656$	−42.3841	−1.65482
$657$	−18.1928	−0.709768
$658$	−15.9513	−0.621848
$659$	11.1361	0.433802	0.216901	−	0.976194i	$-0.430405\pi$
$659$	11.1361	0.433802	0.216901	+	0.976194i	$0.430405\pi$
$660$	−0.284071	−0.0110575
$661$	−4.92047	−0.191384	−0.0956920	−	0.995411i	$-0.530506\pi$
$661$	−4.92047	−0.191384	−0.0956920	+	0.995411i	$0.530506\pi$
$662$	47.0815	1.82987
$663$	12.4080	0.481887
$664$	8.16778	0.316971
$665$	−9.13417	−0.354208
$666$	−26.6213	−1.03155
$667$	25.2622	0.978158
$668$	−0.769574	−0.0297757
$669$	−10.5535	−0.408024
$670$	−28.4981	−1.10098
$671$	4.88858	0.188721
$672$	0.896199	0.0345716
$673$	−30.4163	−1.17246	−0.586231	−	0.810144i	$-0.699389\pi$
$673$	−30.4163	−1.17246	−0.586231	+	0.810144i	$0.699389\pi$
$674$	8.12146	0.312827
$675$	2.92194	0.112465
$676$	−0.448337	−0.0172437
$677$	−16.4659	−0.632834	−0.316417	−	0.948620i	$-0.602480\pi$
$677$	−16.4659	−0.632834	−0.316417	+	0.948620i	$0.602480\pi$
$678$	19.5485	0.750757
$679$	8.55345	0.328251
$680$	−26.1030	−1.00100
$681$	−28.9268	−1.10848
$682$	−3.10007	−0.118708
$683$	32.9941	1.26248	0.631242	−	0.775586i	$-0.282546\pi$
$683$	32.9941	1.26248	0.631242	+	0.775586i	$0.282546\pi$
$684$	−0.352182	−0.0134660
$685$	17.2805	0.660256
$686$	28.6588	1.09420
$687$	23.7169	0.904856
$688$	11.1447	0.424889
$689$	−1.79892	−0.0685333
$690$	−11.3231	−0.431061
$691$	−1.55254	−0.0590614	−0.0295307	−	0.999564i	$-0.509401\pi$
$691$	−1.55254	−0.0590614	−0.0295307	+	0.999564i	$0.509401\pi$
$692$	0.567732	0.0215819
$693$	−6.33491	−0.240643
$694$	28.3482	1.07608
$695$	2.10270	0.0797600
$696$	19.3700	0.734218
$697$	45.7453	1.73273
$698$	3.19644	0.120987
$699$	−14.0885	−0.532875
$700$	0.0902116	0.00340968
$701$	32.4721	1.22645	0.613227	−	0.789907i	$-0.289871\pi$
$701$	32.4721	1.22645	0.613227	+	0.789907i	$0.289871\pi$
$702$	−19.8228	−0.748163
$703$	20.9739	0.791045
$704$	−12.6836	−0.478031
$705$	12.1612	0.458019
$706$	−41.3743	−1.55714
$707$	−35.0134	−1.31681
$708$	0.445861	0.0167565
$709$	−25.8801	−0.971947	−0.485974	−	0.873973i	$-0.661535\pi$
$709$	−25.8801	−0.971947	−0.485974	+	0.873973i	$0.661535\pi$
$710$	38.2205	1.43439
$711$	20.9828	0.786918
$712$	29.4131	1.10230
$713$	−4.76285	−0.178370
$714$	−12.7844	−0.478445
$715$	−9.48386	−0.354676
$716$	−0.315054	−0.0117741
$717$	21.3646	0.797875
$718$	13.9494	0.520585
$719$	14.6407	0.546005	0.273002	−	0.962013i	$-0.411983\pi$
$719$	14.6407	0.546005	0.273002	+	0.962013i	$0.411983\pi$
$720$	17.1728	0.639991
$721$	8.01301	0.298420
$722$	−20.2046	−0.751937
$723$	3.22201	0.119828
$724$	1.73836	0.0646056
$725$	3.98100	0.147851
$726$	−12.1048	−0.449250
$727$	27.5259	1.02088	0.510440	−	0.859913i	$-0.329483\pi$
$727$	27.5259	1.02088	0.510440	+	0.859913i	$0.329483\pi$
$728$	14.6540	0.543115
$729$	13.9018	0.514880
$730$	28.0623	1.03863
$731$	−12.0285	−0.444892
$732$	−0.240510	−0.00888952
$733$	24.7837	0.915407	0.457703	−	0.889105i	$-0.348672\pi$
$733$	24.7837	0.915407	0.457703	+	0.889105i	$0.348672\pi$
$734$	36.7664	1.35707
$735$	−6.88298	−0.253883
$736$	1.66445	0.0613525
$737$	15.5718	0.573593
$738$	−28.9333	−1.06505
$739$	−16.8509	−0.619870	−0.309935	−	0.950758i	$-0.600307\pi$
$739$	−16.8509	−0.619870	−0.309935	+	0.950758i	$0.600307\pi$
$740$	1.58275	0.0581830
$741$	6.18306	0.227141
$742$	1.85349	0.0680438
$743$	−19.8239	−0.727270	−0.363635	−	0.931542i	$-0.618464\pi$
$743$	−19.8239	−0.727270	−0.363635	+	0.931542i	$0.618464\pi$
$744$	−3.65194	−0.133887
$745$	13.9730	0.511930
$746$	5.57982	0.204292
$747$	5.79958	0.212196
$748$	−0.595677	−0.0217801
$749$	8.08742	0.295508
$750$	−17.2027	−0.628156
$751$	−11.5453	−0.421294	−0.210647	−	0.977562i	$-0.567557\pi$
$751$	−11.5453	−0.421294	−0.210647	+	0.977562i	$0.567557\pi$
$752$	−23.6275	−0.861607
$753$	5.43506	0.198064
$754$	−27.0076	−0.983559
$755$	−15.6906	−0.571040
$756$	0.787232	0.0286314
$757$	−38.2106	−1.38879	−0.694393	−	0.719596i	$-0.744327\pi$
$757$	−38.2106	−1.38879	−0.694393	+	0.719596i	$0.744327\pi$
$758$	41.1431	1.49439
$759$	6.18707	0.224576
$760$	−13.0075	−0.471830
$761$	−7.74559	−0.280777	−0.140389	−	0.990096i	$-0.544835\pi$
$761$	−7.74559	−0.280777	−0.140389	+	0.990096i	$0.544835\pi$
$762$	0.852845	0.0308953
$763$	29.7499	1.07702
$764$	1.37259	0.0496586
$765$	−18.5346	−0.670120
$766$	−12.9987	−0.469663
$767$	14.8853	0.537477
$768$	1.95354	0.0704923
$769$	−3.48152	−0.125547	−0.0627734	−	0.998028i	$-0.519995\pi$
$769$	−3.48152	−0.125547	−0.0627734	+	0.998028i	$0.519995\pi$
$770$	9.77157	0.352143
$771$	−9.94100	−0.358016
$772$	−2.01818	−0.0726358
$773$	−4.93133	−0.177367	−0.0886837	−	0.996060i	$-0.528266\pi$
$773$	−4.93133	−0.177367	−0.0886837	+	0.996060i	$0.528266\pi$
$774$	7.60791	0.273461
$775$	−0.750563	−0.0269610
$776$	12.1805	0.437254
$777$	−18.5611	−0.665875
$778$	51.5902	1.84960
$779$	22.7955	0.816732
$780$	0.466591	0.0167066
$781$	−20.8842	−0.747296
$782$	−23.7436	−0.849071
$783$	34.7403	1.24152
$784$	13.3726	0.477594
$785$	−1.44256	−0.0514871
$786$	−30.6262	−1.09240
$787$	−9.56773	−0.341053	−0.170526	−	0.985353i	$-0.554547\pi$
$787$	−9.56773	−0.341053	−0.170526	+	0.985353i	$0.554547\pi$
$788$	0.715597	0.0254921
$789$	−21.6122	−0.769415
$790$	−32.3659	−1.15153
$791$	−25.9185	−0.921556
$792$	−9.02119	−0.320554
$793$	−8.02957	−0.285138
$794$	−26.1911	−0.929486
$795$	−1.41309	−0.0501173
$796$	0.874366	0.0309911
$797$	15.0726	0.533898	0.266949	−	0.963711i	$-0.413984\pi$
$797$	15.0726	0.533898	0.266949	+	0.963711i	$0.413984\pi$
$798$	−6.37064	−0.225518
$799$	25.5012	0.902169
$800$	0.262296	0.00927356
$801$	20.8849	0.737933
$802$	−25.7186	−0.908157
$803$	−15.3336	−0.541111
$804$	−0.766107	−0.0270185
$805$	15.0127	0.529129
$806$	5.09191	0.179355
$807$	10.8161	0.380743
$808$	−49.8606	−1.75409
$809$	−23.5580	−0.828254	−0.414127	−	0.910219i	$-0.635913\pi$
$809$	−23.5580	−0.828254	−0.414127	+	0.910219i	$0.635913\pi$
$810$	2.31634	0.0813881
$811$	47.7098	1.67532	0.837658	−	0.546195i	$-0.183924\pi$
$811$	47.7098	1.67532	0.837658	+	0.546195i	$0.183924\pi$
$812$	1.07257	0.0376397
$813$	−15.9156	−0.558183
$814$	−22.4375	−0.786433
$815$	−32.9742	−1.15503
$816$	−18.9366	−0.662914
$817$	−5.99398	−0.209703
$818$	−18.3195	−0.640526
$819$	10.4052	0.363587
$820$	1.72021	0.0600723
$821$	4.87978	0.170306	0.0851528	−	0.996368i	$-0.472862\pi$
$821$	4.87978	0.170306	0.0851528	+	0.996368i	$0.472862\pi$
$822$	12.0523	0.420374
$823$	27.1236	0.945469	0.472735	−	0.881205i	$-0.343267\pi$
$823$	27.1236	0.945469	0.472735	+	0.881205i	$0.343267\pi$
$824$	11.4109	0.397517
$825$	0.975002	0.0339452
$826$	−15.3369	−0.533638
$827$	−52.5172	−1.82620	−0.913101	−	0.407733i	$-0.866319\pi$
$827$	−52.5172	−1.82620	−0.913101	+	0.407733i	$0.866319\pi$
$828$	0.578839	0.0201161
$829$	5.14938	0.178845	0.0894226	−	0.995994i	$-0.471498\pi$
$829$	5.14938	0.178845	0.0894226	+	0.995994i	$0.471498\pi$
$830$	−8.94583	−0.310514
$831$	−21.0200	−0.729177
$832$	20.8330	0.722255
$833$	−14.4331	−0.500078
$834$	1.46653	0.0507818
$835$	−20.1822	−0.698434
$836$	−0.296833	−0.0102662
$837$	−6.54979	−0.226394
$838$	55.2184	1.90749
$839$	−6.54789	−0.226058	−0.113029	−	0.993592i	$-0.536055\pi$
$839$	−6.54789	−0.226058	−0.113029	+	0.993592i	$0.536055\pi$
$840$	11.5111	0.397171
$841$	18.3320	0.632137
$842$	−50.4000	−1.73690
$843$	3.37669	0.116299
$844$	0.311146	0.0107101
$845$	−11.7577	−0.404478
$846$	−16.1292	−0.554534
$847$	16.0492	0.551456
$848$	2.74544	0.0942787
$849$	−14.8976	−0.511286
$850$	−3.74169	−0.128339
$851$	−34.4722	−1.18169
$852$	1.02747	0.0352006
$853$	−17.0529	−0.583880	−0.291940	−	0.956437i	$-0.594301\pi$
$853$	−17.0529	−0.583880	−0.291940	+	0.956437i	$0.594301\pi$
$854$	8.27316	0.283102
$855$	−9.23603	−0.315866
$856$	11.5169	0.393638
$857$	−27.6000	−0.942798	−0.471399	−	0.881920i	$-0.656251\pi$
$857$	−27.6000	−0.942798	−0.471399	+	0.881920i	$0.656251\pi$
$858$	−6.61453	−0.225816
$859$	4.93570	0.168404	0.0842019	−	0.996449i	$-0.473166\pi$
$859$	4.93570	0.168404	0.0842019	+	0.996449i	$0.473166\pi$
$860$	−0.452322	−0.0154241
$861$	−20.1731	−0.687497
$862$	12.6211	0.429875
$863$	−36.0972	−1.22876	−0.614381	−	0.789010i	$-0.710594\pi$
$863$	−36.0972	−1.22876	−0.614381	+	0.789010i	$0.710594\pi$
$864$	2.28893	0.0778709
$865$	14.8888	0.506236
$866$	43.4999	1.47819
$867$	3.15250	0.107064
$868$	−0.202218	−0.00686371
$869$	17.6852	0.599928
$870$	−21.2151	−0.719261
$871$	−25.5769	−0.866639
$872$	42.3652	1.43467
$873$	8.64883	0.292719
$874$	−11.8318	−0.400215
$875$	22.8084	0.771063
$876$	0.754390	0.0254885
$877$	44.8926	1.51592	0.757958	−	0.652303i	$-0.226197\pi$
$877$	44.8926	1.51592	0.757958	+	0.652303i	$0.226197\pi$
$878$	−31.4413	−1.06109
$879$	−0.942724	−0.0317973
$880$	14.4739	0.487915
$881$	23.9726	0.807658	0.403829	−	0.914835i	$-0.367679\pi$
$881$	23.9726	0.807658	0.403829	+	0.914835i	$0.367679\pi$
$882$	9.12877	0.307382
$883$	−3.36329	−0.113184	−0.0565918	−	0.998397i	$-0.518023\pi$
$883$	−3.36329	−0.113184	−0.0565918	+	0.998397i	$0.518023\pi$
$884$	0.978409	0.0329074
$885$	11.6928	0.393048
$886$	−51.7898	−1.73991
$887$	−11.3959	−0.382636	−0.191318	−	0.981528i	$-0.561276\pi$
$887$	−11.3959	−0.382636	−0.191318	+	0.981528i	$0.561276\pi$
$888$	−26.4318	−0.886993
$889$	−1.13075	−0.0379241
$890$	−32.2149	−1.07985
$891$	−1.26568	−0.0424019
$892$	−0.832179	−0.0278634
$893$	12.7076	0.425243
$894$	9.74546	0.325937
$895$	−8.26233	−0.276179
$896$	−23.2278	−0.775985
$897$	−10.1624	−0.339311
$898$	−12.2472	−0.408693
$899$	−8.92378	−0.297625
$900$	0.0912176	0.00304059
$901$	−2.96316	−0.0987171
$902$	−24.3862	−0.811971
$903$	5.30444	0.176521
$904$	−36.9091	−1.22758
$905$	45.5887	1.51542
$906$	−10.9434	−0.363571
$907$	14.5687	0.483745	0.241873	−	0.970308i	$-0.422238\pi$
$907$	14.5687	0.483745	0.241873	+	0.970308i	$0.422238\pi$
$908$	−2.28097	−0.0756966
$909$	−35.4038	−1.17427
$910$	−16.0500	−0.532051
$911$	−11.3880	−0.377301	−0.188651	−	0.982044i	$-0.560411\pi$
$911$	−11.3880	−0.377301	−0.188651	+	0.982044i	$0.560411\pi$
$912$	−9.43635	−0.312469
$913$	4.88812	0.161773
$914$	−32.6196	−1.07896
$915$	−6.30742	−0.208517
$916$	1.87015	0.0617915
$917$	40.6059	1.34092
$918$	−32.6519	−1.07767
$919$	−8.63177	−0.284736	−0.142368	−	0.989814i	$-0.545472\pi$
$919$	−8.63177	−0.284736	−0.142368	+	0.989814i	$0.545472\pi$
$920$	21.3788	0.704838
$921$	32.7531	1.07925
$922$	15.9859	0.526469
$923$	34.3026	1.12909
$924$	0.262686	0.00864174
$925$	−5.43238	−0.178616
$926$	55.7173	1.83098
$927$	8.10237	0.266117
$928$	3.11855	0.102372
$929$	21.2022	0.695623	0.347812	−	0.937564i	$-0.386925\pi$
$929$	21.2022	0.695623	0.347812	+	0.937564i	$0.386925\pi$
$930$	3.99982	0.131159
$931$	−7.19221	−0.235715
$932$	−1.11092	−0.0363893
$933$	32.6314	1.06830
$934$	34.7026	1.13550
$935$	−15.6217	−0.510885
$936$	14.8175	0.484324
$937$	−39.4766	−1.28964	−0.644822	−	0.764333i	$-0.723068\pi$
$937$	−39.4766	−1.28964	−0.644822	+	0.764333i	$0.723068\pi$
$938$	26.3528	0.860449
$939$	6.72926	0.219601
$940$	0.958950	0.0312775
$941$	8.73780	0.284844	0.142422	−	0.989806i	$-0.454511\pi$
$941$	8.73780	0.284844	0.142422	+	0.989806i	$0.454511\pi$
$942$	−1.00611	−0.0327809
$943$	−37.4661	−1.22007
$944$	−22.7174	−0.739387
$945$	20.6453	0.671591
$946$	6.41225	0.208480
$947$	−9.63654	−0.313145	−0.156573	−	0.987666i	$-0.550045\pi$
$947$	−9.63654	−0.313145	−0.156573	+	0.987666i	$0.550045\pi$
$948$	−0.870083	−0.0282590
$949$	25.1857	0.817562
$950$	−1.86453	−0.0604934
$951$	6.02686	0.195434
$952$	24.1380	0.782316
$953$	19.1476	0.620251	0.310125	−	0.950696i	$-0.399629\pi$
$953$	19.1476	0.620251	0.310125	+	0.950696i	$0.399629\pi$
$954$	1.87416	0.0606782
$955$	35.9964	1.16482
$956$	1.68466	0.0544859
$957$	11.5922	0.374724
$958$	41.9948	1.35679
$959$	−15.9797	−0.516010
$960$	16.3648	0.528173
$961$	−29.3175	−0.945727
$962$	36.8539	1.18822
$963$	8.17761	0.263520
$964$	0.254066	0.00818290
$965$	−52.9270	−1.70378
$966$	10.4706	0.336888
$967$	−36.4956	−1.17362	−0.586810	−	0.809725i	$-0.699616\pi$
$967$	−36.4956	−1.17362	−0.586810	+	0.809725i	$0.699616\pi$
$968$	22.8547	0.734579
$969$	10.1847	0.327179
$970$	−13.3408	−0.428347
$971$	−12.8734	−0.413128	−0.206564	−	0.978433i	$-0.566228\pi$
$971$	−12.8734	−0.413128	−0.206564	+	0.978433i	$0.566228\pi$
$972$	1.27688	0.0409559
$973$	−1.94441	−0.0623349
$974$	−40.6772	−1.30338
$975$	−1.60146	−0.0512876
$976$	12.2544	0.392254
$977$	−27.8335	−0.890473	−0.445236	−	0.895413i	$-0.646880\pi$
$977$	−27.8335	−0.890473	−0.445236	+	0.895413i	$0.646880\pi$
$978$	−22.9979	−0.735391
$979$	17.6027	0.562583
$980$	−0.542744	−0.0173373
$981$	30.0816	0.960433
$982$	−17.9257	−0.572033
$983$	27.1809	0.866936	0.433468	−	0.901169i	$-0.357290\pi$
$983$	27.1809	0.866936	0.433468	+	0.901169i	$0.357290\pi$
$984$	−28.7274	−0.915796
$985$	18.7666	0.597955
$986$	−44.4866	−1.41674
$987$	−11.2457	−0.357955
$988$	0.487553	0.0155111
$989$	9.85158	0.313262
$990$	9.88054	0.314024
$991$	27.9355	0.887399	0.443700	−	0.896176i	$-0.353666\pi$
$991$	27.9355	0.887399	0.443700	+	0.896176i	$0.353666\pi$
$992$	−0.587960	−0.0186678
$993$	33.1926	1.05333
$994$	−35.3433	−1.12102
$995$	22.9304	0.726942
$996$	−0.240488	−0.00762015
$997$	26.9778	0.854397	0.427198	−	0.904158i	$-0.359501\pi$
$997$	26.9778	0.854397	0.427198	+	0.904158i	$0.359501\pi$
$998$	56.8661	1.80007
$999$	−47.4057	−1.49985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	139.2.a.c.1.5	✓	7
3.2	odd	2		1251.2.a.k.1.3		7
4.3	odd	2		2224.2.a.o.1.3		7
5.4	even	2		3475.2.a.e.1.3		7
7.6	odd	2		6811.2.a.p.1.5		7
8.3	odd	2		8896.2.a.bd.1.5		7
8.5	even	2		8896.2.a.be.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.5	✓	7	1.1	even	1	trivial
1251.2.a.k.1.3		7	3.2	odd	2
2224.2.a.o.1.3		7	4.3	odd	2
3475.2.a.e.1.3		7	5.4	even	2
6811.2.a.p.1.5		7	7.6	odd	2
8896.2.a.bd.1.5		7	8.3	odd	2
8896.2.a.be.1.3		7	8.5	even	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:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)

\(f(q)\)	\(=\)	\(q+1.44228 q^{2} +1.01681 q^{3} +0.0801788 q^{4} +2.10270 q^{5} +1.46653 q^{6} -1.94441 q^{7} -2.76892 q^{8} -1.96609 q^{9} +O(q^{10})\)	\(q+1.44228 q^{2} +1.01681 q^{3} +0.0801788 q^{4} +2.10270 q^{5} +1.46653 q^{6} -1.94441 q^{7} -2.76892 q^{8} -1.96609 q^{9} +3.03269 q^{10} -1.65710 q^{11} +0.0815268 q^{12} +2.72182 q^{13} -2.80439 q^{14} +2.13805 q^{15} -4.15393 q^{16} +4.48334 q^{17} -2.83566 q^{18} +2.23411 q^{19} +0.168592 q^{20} -1.97710 q^{21} -2.39001 q^{22} -3.67193 q^{23} -2.81548 q^{24} -0.578649 q^{25} +3.92563 q^{26} -5.04959 q^{27} -0.155900 q^{28} -6.87982 q^{29} +3.08368 q^{30} +1.29710 q^{31} -0.453290 q^{32} -1.68496 q^{33} +6.46625 q^{34} -4.08851 q^{35} -0.157639 q^{36} +9.38804 q^{37} +3.22221 q^{38} +2.76758 q^{39} -5.82222 q^{40} +10.2034 q^{41} -2.85154 q^{42} -2.68294 q^{43} -0.132864 q^{44} -4.13410 q^{45} -5.29596 q^{46} +5.68799 q^{47} -4.22377 q^{48} -3.21928 q^{49} -0.834575 q^{50} +4.55872 q^{51} +0.218232 q^{52} -0.660925 q^{53} -7.28293 q^{54} -3.48439 q^{55} +5.38392 q^{56} +2.27167 q^{57} -9.92265 q^{58} +5.46888 q^{59} +0.171427 q^{60} -2.95008 q^{61} +1.87078 q^{62} +3.82289 q^{63} +7.65409 q^{64} +5.72316 q^{65} -2.43019 q^{66} -9.39699 q^{67} +0.359469 q^{68} -3.73367 q^{69} -5.89679 q^{70} +12.6029 q^{71} +5.44396 q^{72} +9.25327 q^{73} +13.5402 q^{74} -0.588378 q^{75} +0.179128 q^{76} +3.22208 q^{77} +3.99163 q^{78} -10.6724 q^{79} -8.73447 q^{80} +0.763792 q^{81} +14.7162 q^{82} -2.94980 q^{83} -0.158521 q^{84} +9.42713 q^{85} -3.86956 q^{86} -6.99549 q^{87} +4.58839 q^{88} -10.6226 q^{89} -5.96254 q^{90} -5.29232 q^{91} -0.294411 q^{92} +1.31890 q^{93} +8.20369 q^{94} +4.69766 q^{95} -0.460911 q^{96} -4.39900 q^{97} -4.64311 q^{98} +3.25801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

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