LMFDB - Embedded newform 2013.2.a.c.1.4

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			1.4
Root			$-1.03538$ 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)

$f(q)$	$=$	$q-2.03538 q^{2} +1.00000 q^{3} +2.14278 q^{4} +3.64320 q^{5} -2.03538 q^{6} -4.68983 q^{7} -0.290605 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.03538 q^{2} +1.00000 q^{3} +2.14278 q^{4} +3.64320 q^{5} -2.03538 q^{6} -4.68983 q^{7} -0.290605 q^{8} +1.00000 q^{9} -7.41529 q^{10} +1.00000 q^{11} +2.14278 q^{12} +2.53815 q^{13} +9.54560 q^{14} +3.64320 q^{15} -3.69406 q^{16} -7.26013 q^{17} -2.03538 q^{18} -7.00236 q^{19} +7.80656 q^{20} -4.68983 q^{21} -2.03538 q^{22} +2.30296 q^{23} -0.290605 q^{24} +8.27289 q^{25} -5.16610 q^{26} +1.00000 q^{27} -10.0493 q^{28} +4.04230 q^{29} -7.41529 q^{30} -7.56494 q^{31} +8.10003 q^{32} +1.00000 q^{33} +14.7771 q^{34} -17.0860 q^{35} +2.14278 q^{36} -4.60383 q^{37} +14.2525 q^{38} +2.53815 q^{39} -1.05873 q^{40} -3.50819 q^{41} +9.54560 q^{42} -4.39873 q^{43} +2.14278 q^{44} +3.64320 q^{45} -4.68740 q^{46} -12.2779 q^{47} -3.69406 q^{48} +14.9945 q^{49} -16.8385 q^{50} -7.26013 q^{51} +5.43869 q^{52} -5.26804 q^{53} -2.03538 q^{54} +3.64320 q^{55} +1.36289 q^{56} -7.00236 q^{57} -8.22761 q^{58} -1.23759 q^{59} +7.80656 q^{60} -1.00000 q^{61} +15.3975 q^{62} -4.68983 q^{63} -9.09853 q^{64} +9.24698 q^{65} -2.03538 q^{66} +6.04060 q^{67} -15.5568 q^{68} +2.30296 q^{69} +34.7765 q^{70} -12.6630 q^{71} -0.290605 q^{72} +2.01935 q^{73} +9.37055 q^{74} +8.27289 q^{75} -15.0045 q^{76} -4.68983 q^{77} -5.16610 q^{78} +1.56355 q^{79} -13.4582 q^{80} +1.00000 q^{81} +7.14050 q^{82} -13.7810 q^{83} -10.0493 q^{84} -26.4501 q^{85} +8.95310 q^{86} +4.04230 q^{87} -0.290605 q^{88} -2.49179 q^{89} -7.41529 q^{90} -11.9035 q^{91} +4.93473 q^{92} -7.56494 q^{93} +24.9902 q^{94} -25.5110 q^{95} +8.10003 q^{96} +10.3814 q^{97} -30.5196 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.03538	−1.43923	−0.719616	−	0.694372i	$-0.755682\pi$
$2$	−2.03538	−1.43923	−0.719616	+	0.694372i	$0.755682\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.14278	1.07139
$5$	3.64320	1.62929	0.814644	−	0.579962i	$-0.196933\pi$
$5$	3.64320	1.62929	0.814644	+	0.579962i	$0.196933\pi$
$6$	−2.03538	−0.830941
$7$	−4.68983	−1.77259	−0.886295	−	0.463121i	$-0.846730\pi$
$7$	−4.68983	−1.77259	−0.886295	+	0.463121i	$0.846730\pi$
$8$	−0.290605	−0.102744
$9$	1.00000	0.333333
$10$	−7.41529	−2.34492
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.14278	0.618566
$13$	2.53815	0.703956	0.351978	−	0.936008i	$-0.385509\pi$
$13$	2.53815	0.703956	0.351978	+	0.936008i	$0.385509\pi$
$14$	9.54560	2.55117
$15$	3.64320	0.940669
$16$	−3.69406	−0.923515
$17$	−7.26013	−1.76084	−0.880420	−	0.474195i	$-0.842739\pi$
$17$	−7.26013	−1.76084	−0.880420	+	0.474195i	$0.842739\pi$
$18$	−2.03538	−0.479744
$19$	−7.00236	−1.60645	−0.803226	−	0.595675i	$-0.796885\pi$
$19$	−7.00236	−1.60645	−0.803226	+	0.595675i	$0.796885\pi$
$20$	7.80656	1.74560
$21$	−4.68983	−1.02341
$22$	−2.03538	−0.433945
$23$	2.30296	0.480200	0.240100	−	0.970748i	$-0.422820\pi$
$23$	2.30296	0.480200	0.240100	+	0.970748i	$0.422820\pi$
$24$	−0.290605	−0.0593194
$25$	8.27289	1.65458
$26$	−5.16610	−1.01316
$27$	1.00000	0.192450
$28$	−10.0493	−1.89913
$29$	4.04230	0.750635	0.375318	−	0.926896i	$-0.377534\pi$
$29$	4.04230	0.750635	0.375318	+	0.926896i	$0.377534\pi$
$30$	−7.41529	−1.35384
$31$	−7.56494	−1.35870	−0.679352	−	0.733813i	$-0.737739\pi$
$31$	−7.56494	−1.35870	−0.679352	+	0.733813i	$0.737739\pi$
$32$	8.10003	1.43190
$33$	1.00000	0.174078
$34$	14.7771	2.53426
$35$	−17.0860	−2.88806
$36$	2.14278	0.357129
$37$	−4.60383	−0.756865	−0.378433	−	0.925629i	$-0.623537\pi$
$37$	−4.60383	−0.756865	−0.378433	+	0.925629i	$0.623537\pi$
$38$	14.2525	2.31206
$39$	2.53815	0.406429
$40$	−1.05873	−0.167400
$41$	−3.50819	−0.547887	−0.273943	−	0.961746i	$-0.588328\pi$
$41$	−3.50819	−0.547887	−0.273943	+	0.961746i	$0.588328\pi$
$42$	9.54560	1.47292
$43$	−4.39873	−0.670801	−0.335400	−	0.942076i	$-0.608872\pi$
$43$	−4.39873	−0.670801	−0.335400	+	0.942076i	$0.608872\pi$
$44$	2.14278	0.323036
$45$	3.64320	0.543096
$46$	−4.68740	−0.691119
$47$	−12.2779	−1.79092	−0.895458	−	0.445147i	$-0.853151\pi$
$47$	−12.2779	−1.79092	−0.895458	+	0.445147i	$0.853151\pi$
$48$	−3.69406	−0.533192
$49$	14.9945	2.14208
$50$	−16.8385	−2.38132
$51$	−7.26013	−1.01662
$52$	5.43869	0.754210
$53$	−5.26804	−0.723621	−0.361811	−	0.932252i	$-0.617841\pi$
$53$	−5.26804	−0.723621	−0.361811	+	0.932252i	$0.617841\pi$
$54$	−2.03538	−0.276980
$55$	3.64320	0.491249
$56$	1.36289	0.182123
$57$	−7.00236	−0.927485
$58$	−8.22761	−1.08034
$59$	−1.23759	−0.161120	−0.0805600	−	0.996750i	$-0.525671\pi$
$59$	−1.23759	−0.161120	−0.0805600	+	0.996750i	$0.525671\pi$
$60$	7.80656	1.00782
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	15.3975	1.95549
$63$	−4.68983	−0.590863
$64$	−9.09853	−1.13732
$65$	9.24698	1.14695
$66$	−2.03538	−0.250538
$67$	6.04060	0.737977	0.368988	−	0.929434i	$-0.379704\pi$
$67$	6.04060	0.737977	0.368988	+	0.929434i	$0.379704\pi$
$68$	−15.5568	−1.88654
$69$	2.30296	0.277244
$70$	34.7765	4.15659
$71$	−12.6630	−1.50282	−0.751412	−	0.659834i	$-0.770627\pi$
$71$	−12.6630	−1.50282	−0.751412	+	0.659834i	$0.770627\pi$
$72$	−0.290605	−0.0342481
$73$	2.01935	0.236347	0.118174	−	0.992993i	$-0.462296\pi$
$73$	2.01935	0.236347	0.118174	+	0.992993i	$0.462296\pi$
$74$	9.37055	1.08930
$75$	8.27289	0.955271
$76$	−15.0045	−1.72113
$77$	−4.68983	−0.534456
$78$	−5.16610	−0.584946
$79$	1.56355	0.175913	0.0879563	−	0.996124i	$-0.471966\pi$
$79$	1.56355	0.175913	0.0879563	+	0.996124i	$0.471966\pi$
$80$	−13.4582	−1.50467
$81$	1.00000	0.111111
$82$	7.14050	0.788536
$83$	−13.7810	−1.51267	−0.756333	−	0.654187i	$-0.773011\pi$
$83$	−13.7810	−1.51267	−0.756333	+	0.654187i	$0.773011\pi$
$84$	−10.0493	−1.09646
$85$	−26.4501	−2.86891
$86$	8.95310	0.965438
$87$	4.04230	0.433380
$88$	−0.290605	−0.0309786
$89$	−2.49179	−0.264129	−0.132065	−	0.991241i	$-0.542161\pi$
$89$	−2.49179	−0.264129	−0.132065	+	0.991241i	$0.542161\pi$
$90$	−7.41529	−0.781641
$91$	−11.9035	−1.24783
$92$	4.93473	0.514481
$93$	−7.56494	−0.784448
$94$	24.9902	2.57754
$95$	−25.5110	−2.61737
$96$	8.10003	0.826706
$97$	10.3814	1.05407	0.527035	−	0.849844i	$-0.323304\pi$
$97$	10.3814	1.05407	0.527035	+	0.849844i	$0.323304\pi$
$98$	−30.5196	−3.08294
$99$	1.00000	0.100504
$100$	17.7269	1.77269
$101$	17.6969	1.76091	0.880456	−	0.474129i	$-0.157237\pi$
$101$	17.6969	1.76091	0.880456	+	0.474129i	$0.157237\pi$
$102$	14.7771	1.46315
$103$	14.1535	1.39459	0.697294	−	0.716785i	$-0.254387\pi$
$103$	14.1535	1.39459	0.697294	+	0.716785i	$0.254387\pi$
$104$	−0.737598	−0.0723275
$105$	−17.0860	−1.66742
$106$	10.7225	1.04146
$107$	8.84032	0.854626	0.427313	−	0.904104i	$-0.359460\pi$
$107$	8.84032	0.854626	0.427313	+	0.904104i	$0.359460\pi$
$108$	2.14278	0.206189
$109$	6.08893	0.583214	0.291607	−	0.956538i	$-0.405810\pi$
$109$	6.08893	0.583214	0.291607	+	0.956538i	$0.405810\pi$
$110$	−7.41529	−0.707021
$111$	−4.60383	−0.436976
$112$	17.3245	1.63701
$113$	−5.34589	−0.502899	−0.251449	−	0.967870i	$-0.580907\pi$
$113$	−5.34589	−0.502899	−0.251449	+	0.967870i	$0.580907\pi$
$114$	14.2525	1.33487
$115$	8.39013	0.782384
$116$	8.66174	0.804222
$117$	2.53815	0.234652
$118$	2.51896	0.231889
$119$	34.0488	3.12125
$120$	−1.05873	−0.0966484
$121$	1.00000	0.0909091
$122$	2.03538	0.184275
$123$	−3.50819	−0.316323
$124$	−16.2100	−1.45570
$125$	11.9238	1.06649
$126$	9.54560	0.850389
$127$	−11.5221	−1.02242	−0.511211	−	0.859455i	$-0.670803\pi$
$127$	−11.5221	−1.02242	−0.511211	+	0.859455i	$0.670803\pi$
$128$	2.31891	0.204965
$129$	−4.39873	−0.387287
$130$	−18.8211	−1.65072
$131$	21.2523	1.85682	0.928409	−	0.371560i	$-0.121177\pi$
$131$	21.2523	1.85682	0.928409	+	0.371560i	$0.121177\pi$
$132$	2.14278	0.186505
$133$	32.8399	2.84758
$134$	−12.2949	−1.06212
$135$	3.64320	0.313556
$136$	2.10983	0.180916
$137$	−14.7406	−1.25937	−0.629686	−	0.776850i	$-0.716816\pi$
$137$	−14.7406	−1.25937	−0.629686	+	0.776850i	$0.716816\pi$
$138$	−4.68740	−0.399018
$139$	−15.4607	−1.31136	−0.655681	−	0.755038i	$-0.727618\pi$
$139$	−15.4607	−1.31136	−0.655681	+	0.755038i	$0.727618\pi$
$140$	−36.6115	−3.09423
$141$	−12.2779	−1.03399
$142$	25.7741	2.16291
$143$	2.53815	0.212251
$144$	−3.69406	−0.307838
$145$	14.7269	1.22300
$146$	−4.11015	−0.340159
$147$	14.9945	1.23673
$148$	−9.86498	−0.810897
$149$	6.25623	0.512530	0.256265	−	0.966607i	$-0.417508\pi$
$149$	6.25623	0.512530	0.256265	+	0.966607i	$0.417508\pi$
$150$	−16.8385	−1.37486
$151$	12.3903	1.00831	0.504155	−	0.863613i	$-0.331804\pi$
$151$	12.3903	1.00831	0.504155	+	0.863613i	$0.331804\pi$
$152$	2.03492	0.165054
$153$	−7.26013	−0.586946
$154$	9.54560	0.769206
$155$	−27.5606	−2.21372
$156$	5.43869	0.435444
$157$	−6.06191	−0.483793	−0.241897	−	0.970302i	$-0.577769\pi$
$157$	−6.06191	−0.483793	−0.241897	+	0.970302i	$0.577769\pi$
$158$	−3.18241	−0.253179
$159$	−5.26804	−0.417783
$160$	29.5100	2.33297
$161$	−10.8005	−0.851198
$162$	−2.03538	−0.159915
$163$	−0.681180	−0.0533541	−0.0266771	−	0.999644i	$-0.508493\pi$
$163$	−0.681180	−0.0533541	−0.0266771	+	0.999644i	$0.508493\pi$
$164$	−7.51726	−0.587000
$165$	3.64320	0.283623
$166$	28.0497	2.17708
$167$	9.15595	0.708508	0.354254	−	0.935149i	$-0.384735\pi$
$167$	9.15595	0.708508	0.354254	+	0.935149i	$0.384735\pi$
$168$	1.36289	0.105149
$169$	−6.55779	−0.504446
$170$	53.8360	4.12903
$171$	−7.00236	−0.535484
$172$	−9.42550	−0.718688
$173$	−24.7562	−1.88218	−0.941090	−	0.338157i	$-0.890196\pi$
$173$	−24.7562	−1.88218	−0.941090	+	0.338157i	$0.890196\pi$
$174$	−8.22761	−0.623734
$175$	−38.7985	−2.93289
$176$	−3.69406	−0.278450
$177$	−1.23759	−0.0930227
$178$	5.07174	0.380143
$179$	0.378311	0.0282763	0.0141381	−	0.999900i	$-0.495500\pi$
$179$	0.378311	0.0282763	0.0141381	+	0.999900i	$0.495500\pi$
$180$	7.80656	0.581866
$181$	−18.2472	−1.35631	−0.678153	−	0.734921i	$-0.737219\pi$
$181$	−18.2472	−1.35631	−0.678153	+	0.734921i	$0.737219\pi$
$182$	24.2282	1.79591
$183$	−1.00000	−0.0739221
$184$	−0.669250	−0.0493378
$185$	−16.7727	−1.23315
$186$	15.3975	1.12900
$187$	−7.26013	−0.530913
$188$	−26.3088	−1.91877
$189$	−4.68983	−0.341135
$190$	51.9245	3.76700
$191$	0.0423953	0.00306762	0.00153381	−	0.999999i	$-0.499512\pi$
$191$	0.0423953	0.00306762	0.00153381	+	0.999999i	$0.499512\pi$
$192$	−9.09853	−0.656630
$193$	8.68788	0.625367	0.312684	−	0.949857i	$-0.398772\pi$
$193$	8.68788	0.625367	0.312684	+	0.949857i	$0.398772\pi$
$194$	−21.1301	−1.51705
$195$	9.24698	0.662190
$196$	32.1299	2.29500
$197$	−15.2402	−1.08582	−0.542908	−	0.839792i	$-0.682677\pi$
$197$	−15.2402	−1.08582	−0.542908	+	0.839792i	$0.682677\pi$
$198$	−2.03538	−0.144648
$199$	11.7486	0.832835	0.416417	−	0.909174i	$-0.363286\pi$
$199$	11.7486	0.832835	0.416417	+	0.909174i	$0.363286\pi$
$200$	−2.40414	−0.169998
$201$	6.04060	0.426071
$202$	−36.0200	−2.53436
$203$	−18.9577	−1.33057
$204$	−15.5568	−1.08920
$205$	−12.7810	−0.892665
$206$	−28.8078	−2.00713
$207$	2.30296	0.160067
$208$	−9.37608	−0.650115
$209$	−7.00236	−0.484363
$210$	34.7765	2.39981
$211$	−7.49488	−0.515969	−0.257984	−	0.966149i	$-0.583058\pi$
$211$	−7.49488	−0.515969	−0.257984	+	0.966149i	$0.583058\pi$
$212$	−11.2882	−0.775279
$213$	−12.6630	−0.867656
$214$	−17.9934	−1.23001
$215$	−16.0255	−1.09293
$216$	−0.290605	−0.0197731
$217$	35.4783	2.40843
$218$	−12.3933	−0.839380
$219$	2.01935	0.136455
$220$	7.80656	0.526318
$221$	−18.4273	−1.23955
$222$	9.37055	0.628910
$223$	−19.6088	−1.31310	−0.656550	−	0.754282i	$-0.727985\pi$
$223$	−19.6088	−1.31310	−0.656550	+	0.754282i	$0.727985\pi$
$224$	−37.9878	−2.53817
$225$	8.27289	0.551526
$226$	10.8809	0.723788
$227$	−10.2134	−0.677889	−0.338944	−	0.940806i	$-0.610070\pi$
$227$	−10.2134	−0.677889	−0.338944	+	0.940806i	$0.610070\pi$
$228$	−15.0045	−0.993696
$229$	−16.8612	−1.11422	−0.557109	−	0.830439i	$-0.688090\pi$
$229$	−16.8612	−1.11422	−0.557109	+	0.830439i	$0.688090\pi$
$230$	−17.0771	−1.12603
$231$	−4.68983	−0.308568
$232$	−1.17471	−0.0771235
$233$	22.2881	1.46014	0.730072	−	0.683370i	$-0.239486\pi$
$233$	22.2881	1.46014	0.730072	+	0.683370i	$0.239486\pi$
$234$	−5.16610	−0.337719
$235$	−44.7308	−2.91792
$236$	−2.65187	−0.172622
$237$	1.56355	0.101563
$238$	−69.3023	−4.49220
$239$	19.9170	1.28833	0.644163	−	0.764888i	$-0.277206\pi$
$239$	19.9170	1.28833	0.644163	+	0.764888i	$0.277206\pi$
$240$	−13.4582	−0.868723
$241$	10.8476	0.698758	0.349379	−	0.936981i	$-0.386393\pi$
$241$	10.8476	0.698758	0.349379	+	0.936981i	$0.386393\pi$
$242$	−2.03538	−0.130839
$243$	1.00000	0.0641500
$244$	−2.14278	−0.137177
$245$	54.6280	3.49006
$246$	7.14050	0.455262
$247$	−17.7730	−1.13087
$248$	2.19841	0.139599
$249$	−13.7810	−0.873338
$250$	−24.2694	−1.53493
$251$	−5.74852	−0.362843	−0.181422	−	0.983405i	$-0.558070\pi$
$251$	−5.74852	−0.362843	−0.181422	+	0.983405i	$0.558070\pi$
$252$	−10.0493	−0.633044
$253$	2.30296	0.144786
$254$	23.4519	1.47150
$255$	−26.4501	−1.65637
$256$	13.4772	0.842324
$257$	−24.2003	−1.50957	−0.754786	−	0.655971i	$-0.772259\pi$
$257$	−24.2003	−1.50957	−0.754786	+	0.655971i	$0.772259\pi$
$258$	8.95310	0.557396
$259$	21.5912	1.34161
$260$	19.8142	1.22883
$261$	4.04230	0.250212
$262$	−43.2564	−2.67239
$263$	−17.0507	−1.05139	−0.525697	−	0.850672i	$-0.676195\pi$
$263$	−17.0507	−1.05139	−0.525697	+	0.850672i	$0.676195\pi$
$264$	−0.290605	−0.0178855
$265$	−19.1925	−1.17899
$266$	−66.8417	−4.09833
$267$	−2.49179	−0.152495
$268$	12.9437	0.790660
$269$	15.6684	0.955319	0.477659	−	0.878545i	$-0.341485\pi$
$269$	15.6684	0.955319	0.477659	+	0.878545i	$0.341485\pi$
$270$	−7.41529	−0.451280
$271$	8.11046	0.492675	0.246338	−	0.969184i	$-0.420773\pi$
$271$	8.11046	0.492675	0.246338	+	0.969184i	$0.420773\pi$
$272$	26.8194	1.62616
$273$	−11.9035	−0.720433
$274$	30.0027	1.81253
$275$	8.27289	0.498874
$276$	4.93473	0.297036
$277$	−0.347564	−0.0208831	−0.0104416	−	0.999945i	$-0.503324\pi$
$277$	−0.347564	−0.0208831	−0.0104416	+	0.999945i	$0.503324\pi$
$278$	31.4685	1.88735
$279$	−7.56494	−0.452901
$280$	4.96527	0.296731
$281$	−31.5166	−1.88012	−0.940062	−	0.341003i	$-0.889233\pi$
$281$	−31.5166	−1.88012	−0.940062	+	0.341003i	$0.889233\pi$
$282$	24.9902	1.48814
$283$	−23.2867	−1.38425	−0.692127	−	0.721776i	$-0.743326\pi$
$283$	−23.2867	−1.38425	−0.692127	+	0.721776i	$0.743326\pi$
$284$	−27.1340	−1.61011
$285$	−25.5110	−1.51114
$286$	−5.16610	−0.305478
$287$	16.4528	0.971179
$288$	8.10003	0.477299
$289$	35.7094	2.10056
$290$	−29.9748	−1.76018
$291$	10.3814	0.608568
$292$	4.32702	0.253220
$293$	−13.8274	−0.807803	−0.403901	−	0.914803i	$-0.632346\pi$
$293$	−13.8274	−0.807803	−0.403901	+	0.914803i	$0.632346\pi$
$294$	−30.5196	−1.77994
$295$	−4.50877	−0.262511
$296$	1.33789	0.0777636
$297$	1.00000	0.0580259
$298$	−12.7338	−0.737650
$299$	5.84526	0.338040
$300$	17.7269	1.02347
$301$	20.6293	1.18905
$302$	−25.2190	−1.45119
$303$	17.6969	1.01666
$304$	25.8671	1.48358
$305$	−3.64320	−0.208609
$306$	14.7771	0.844752
$307$	−0.622350	−0.0355194	−0.0177597	−	0.999842i	$-0.505653\pi$
$307$	−0.622350	−0.0355194	−0.0177597	+	0.999842i	$0.505653\pi$
$308$	−10.0493	−0.572610
$309$	14.1535	0.805165
$310$	56.0963	3.18606
$311$	32.0025	1.81469	0.907347	−	0.420383i	$-0.138104\pi$
$311$	32.0025	1.81469	0.907347	+	0.420383i	$0.138104\pi$
$312$	−0.737598	−0.0417583
$313$	9.75051	0.551132	0.275566	−	0.961282i	$-0.411135\pi$
$313$	9.75051	0.551132	0.275566	+	0.961282i	$0.411135\pi$
$314$	12.3383	0.696291
$315$	−17.0860	−0.962686
$316$	3.35033	0.188471
$317$	−9.83781	−0.552547	−0.276273	−	0.961079i	$-0.589099\pi$
$317$	−9.83781	−0.552547	−0.276273	+	0.961079i	$0.589099\pi$
$318$	10.7225	0.601286
$319$	4.04230	0.226325
$320$	−33.1477	−1.85302
$321$	8.84032	0.493419
$322$	21.9831	1.22507
$323$	50.8380	2.82870
$324$	2.14278	0.119043
$325$	20.9978	1.16475
$326$	1.38646	0.0767889
$327$	6.08893	0.336719
$328$	1.01950	0.0562922
$329$	57.5813	3.17456
$330$	−7.41529	−0.408199
$331$	10.4811	0.576096	0.288048	−	0.957616i	$-0.406994\pi$
$331$	10.4811	0.576096	0.288048	+	0.957616i	$0.406994\pi$
$332$	−29.5297	−1.62065
$333$	−4.60383	−0.252288
$334$	−18.6358	−1.01971
$335$	22.0071	1.20238
$336$	17.3245	0.945131
$337$	−7.34494	−0.400105	−0.200052	−	0.979785i	$-0.564111\pi$
$337$	−7.34494	−0.400105	−0.200052	+	0.979785i	$0.564111\pi$
$338$	13.3476	0.726014
$339$	−5.34589	−0.290349
$340$	−56.6766	−3.07372
$341$	−7.56494	−0.409665
$342$	14.2525	0.770685
$343$	−37.4930	−2.02443
$344$	1.27829	0.0689209
$345$	8.39013	0.451710
$346$	50.3883	2.70889
$347$	14.3873	0.772353	0.386176	−	0.922425i	$-0.373796\pi$
$347$	14.3873	0.772353	0.386176	+	0.922425i	$0.373796\pi$
$348$	8.66174	0.464318
$349$	−0.901220	−0.0482412	−0.0241206	−	0.999709i	$-0.507679\pi$
$349$	−0.901220	−0.0482412	−0.0241206	+	0.999709i	$0.507679\pi$
$350$	78.9696	4.22110
$351$	2.53815	0.135476
$352$	8.10003	0.431733
$353$	14.6186	0.778068	0.389034	−	0.921223i	$-0.372809\pi$
$353$	14.6186	0.778068	0.389034	+	0.921223i	$0.372809\pi$
$354$	2.51896	0.133881
$355$	−46.1339	−2.44853
$356$	−5.33935	−0.282985
$357$	34.0488	1.80205
$358$	−0.770007	−0.0406961
$359$	−30.7091	−1.62076	−0.810382	−	0.585902i	$-0.800740\pi$
$359$	−30.7091	−1.62076	−0.810382	+	0.585902i	$0.800740\pi$
$360$	−1.05873	−0.0558000
$361$	30.0330	1.58068
$362$	37.1401	1.95204
$363$	1.00000	0.0524864
$364$	−25.5065	−1.33691
$365$	7.35690	0.385078
$366$	2.03538	0.106391
$367$	−31.7475	−1.65720	−0.828602	−	0.559838i	$-0.810863\pi$
$367$	−31.7475	−1.65720	−0.828602	+	0.559838i	$0.810863\pi$
$368$	−8.50727	−0.443472
$369$	−3.50819	−0.182629
$370$	34.1388	1.77479
$371$	24.7062	1.28268
$372$	−16.2100	−0.840449
$373$	11.9713	0.619852	0.309926	−	0.950761i	$-0.399696\pi$
$373$	11.9713	0.619852	0.309926	+	0.950761i	$0.399696\pi$
$374$	14.7771	0.764107
$375$	11.9238	0.615741
$376$	3.56801	0.184006
$377$	10.2600	0.528415
$378$	9.54560	0.490973
$379$	7.27754	0.373822	0.186911	−	0.982377i	$-0.440152\pi$
$379$	7.27754	0.373822	0.186911	+	0.982377i	$0.440152\pi$
$380$	−54.6643	−2.80422
$381$	−11.5221	−0.590295
$382$	−0.0862907	−0.00441502
$383$	−32.6838	−1.67006	−0.835032	−	0.550201i	$-0.814551\pi$
$383$	−32.6838	−1.67006	−0.835032	+	0.550201i	$0.814551\pi$
$384$	2.31891	0.118337
$385$	−17.0860	−0.870783
$386$	−17.6831	−0.900048
$387$	−4.39873	−0.223600
$388$	22.2450	1.12932
$389$	19.8941	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$389$	19.8941	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$390$	−18.8211	−0.953045
$391$	−16.7198	−0.845555
$392$	−4.35748	−0.220086
$393$	21.2523	1.07203
$394$	31.0195	1.56274
$395$	5.69630	0.286612
$396$	2.14278	0.107679
$397$	23.8399	1.19649	0.598244	−	0.801314i	$-0.295865\pi$
$397$	23.8399	1.19649	0.598244	+	0.801314i	$0.295865\pi$
$398$	−23.9128	−1.19864
$399$	32.8399	1.64405
$400$	−30.5606	−1.52803
$401$	−8.95725	−0.447304	−0.223652	−	0.974669i	$-0.571798\pi$
$401$	−8.95725	−0.447304	−0.223652	+	0.974669i	$0.571798\pi$
$402$	−12.2949	−0.613215
$403$	−19.2010	−0.956468
$404$	37.9206	1.88662
$405$	3.64320	0.181032
$406$	38.5861	1.91500
$407$	−4.60383	−0.228203
$408$	2.10983	0.104452
$409$	−2.16459	−0.107032	−0.0535160	−	0.998567i	$-0.517043\pi$
$409$	−2.16459	−0.107032	−0.0535160	+	0.998567i	$0.517043\pi$
$410$	26.0142	1.28475
$411$	−14.7406	−0.727098
$412$	30.3278	1.49414
$413$	5.80408	0.285600
$414$	−4.68740	−0.230373
$415$	−50.2071	−2.46457
$416$	20.5591	1.00799
$417$	−15.4607	−0.757115
$418$	14.2525	0.697111
$419$	−14.3813	−0.702571	−0.351286	−	0.936268i	$-0.614255\pi$
$419$	−14.3813	−0.702571	−0.351286	+	0.936268i	$0.614255\pi$
$420$	−36.6115	−1.78646
$421$	−17.9478	−0.874723	−0.437362	−	0.899286i	$-0.644087\pi$
$421$	−17.9478	−0.874723	−0.437362	+	0.899286i	$0.644087\pi$
$422$	15.2549	0.742599
$423$	−12.2779	−0.596972
$424$	1.53092	0.0743479
$425$	−60.0622	−2.91344
$426$	25.7741	1.24876
$427$	4.68983	0.226957
$428$	18.9428	0.915637
$429$	2.53815	0.122543
$430$	32.6179	1.57298
$431$	3.90648	0.188168	0.0940841	−	0.995564i	$-0.470008\pi$
$431$	3.90648	0.188168	0.0940841	+	0.995564i	$0.470008\pi$
$432$	−3.69406	−0.177731
$433$	11.9670	0.575098	0.287549	−	0.957766i	$-0.407160\pi$
$433$	11.9670	0.575098	0.287549	+	0.957766i	$0.407160\pi$
$434$	−72.2119	−3.46628
$435$	14.7269	0.706100
$436$	13.0472	0.624849
$437$	−16.1261	−0.771418
$438$	−4.11015	−0.196391
$439$	−4.57537	−0.218370	−0.109185	−	0.994021i	$-0.534824\pi$
$439$	−4.57537	−0.218370	−0.109185	+	0.994021i	$0.534824\pi$
$440$	−1.05873	−0.0504730
$441$	14.9945	0.714025
$442$	37.5066	1.78401
$443$	8.48126	0.402957	0.201478	−	0.979493i	$-0.435425\pi$
$443$	8.48126	0.402957	0.201478	+	0.979493i	$0.435425\pi$
$444$	−9.86498	−0.468171
$445$	−9.07808	−0.430342
$446$	39.9113	1.88986
$447$	6.25623	0.295909
$448$	42.6706	2.01600
$449$	30.7884	1.45299	0.726496	−	0.687170i	$-0.241147\pi$
$449$	30.7884	1.45299	0.726496	+	0.687170i	$0.241147\pi$
$450$	−16.8385	−0.793773
$451$	−3.50819	−0.165194
$452$	−11.4550	−0.538800
$453$	12.3903	0.582148
$454$	20.7882	0.975639
$455$	−43.3668	−2.03307
$456$	2.03492	0.0952937
$457$	8.09871	0.378842	0.189421	−	0.981896i	$-0.439339\pi$
$457$	8.09871	0.378842	0.189421	+	0.981896i	$0.439339\pi$
$458$	34.3189	1.60362
$459$	−7.26013	−0.338874
$460$	17.9782	0.838237
$461$	11.9563	0.556859	0.278430	−	0.960457i	$-0.410186\pi$
$461$	11.9563	0.556859	0.278430	+	0.960457i	$0.410186\pi$
$462$	9.54560	0.444101
$463$	−21.2091	−0.985671	−0.492836	−	0.870122i	$-0.664040\pi$
$463$	−21.2091	−0.985671	−0.492836	+	0.870122i	$0.664040\pi$
$464$	−14.9325	−0.693223
$465$	−27.5606	−1.27809
$466$	−45.3648	−2.10149
$467$	−16.4835	−0.762766	−0.381383	−	0.924417i	$-0.624552\pi$
$467$	−16.4835	−0.762766	−0.381383	+	0.924417i	$0.624552\pi$
$468$	5.43869	0.251403
$469$	−28.3294	−1.30813
$470$	91.0442	4.19956
$471$	−6.06191	−0.279318
$472$	0.359648	0.0165542
$473$	−4.39873	−0.202254
$474$	−3.18241	−0.146173
$475$	−57.9297	−2.65800
$476$	72.9589	3.34407
$477$	−5.26804	−0.241207
$478$	−40.5388	−1.85420
$479$	−5.89367	−0.269289	−0.134644	−	0.990894i	$-0.542989\pi$
$479$	−5.89367	−0.269289	−0.134644	+	0.990894i	$0.542989\pi$
$480$	29.5100	1.34694
$481$	−11.6852	−0.532800
$482$	−22.0791	−1.00568
$483$	−10.8005	−0.491439
$484$	2.14278	0.0973989
$485$	37.8214	1.71738
$486$	−2.03538	−0.0923268
$487$	4.70750	0.213317	0.106659	−	0.994296i	$-0.465985\pi$
$487$	4.70750	0.213317	0.106659	+	0.994296i	$0.465985\pi$
$488$	0.290605	0.0131551
$489$	−0.681180	−0.0308040
$490$	−111.189	−5.02300
$491$	2.88342	0.130127	0.0650635	−	0.997881i	$-0.479275\pi$
$491$	2.88342	0.130127	0.0650635	+	0.997881i	$0.479275\pi$
$492$	−7.51726	−0.338904
$493$	−29.3476	−1.32175
$494$	36.1749	1.62759
$495$	3.64320	0.163750
$496$	27.9454	1.25478
$497$	59.3874	2.66389
$498$	28.0497	1.25694
$499$	33.5303	1.50102	0.750510	−	0.660859i	$-0.229808\pi$
$499$	33.5303	1.50102	0.750510	+	0.660859i	$0.229808\pi$
$500$	25.5500	1.14263
$501$	9.15595	0.409058
$502$	11.7004	0.522216
$503$	−7.09540	−0.316368	−0.158184	−	0.987410i	$-0.550564\pi$
$503$	−7.09540	−0.316368	−0.158184	+	0.987410i	$0.550564\pi$
$504$	1.36289	0.0607078
$505$	64.4734	2.86903
$506$	−4.68740	−0.208380
$507$	−6.55779	−0.291242
$508$	−24.6893	−1.09541
$509$	25.5826	1.13393	0.566965	−	0.823742i	$-0.308117\pi$
$509$	25.5826	1.13393	0.566965	+	0.823742i	$0.308117\pi$
$510$	53.8360	2.38390
$511$	−9.47042	−0.418947
$512$	−32.0690	−1.41727
$513$	−7.00236	−0.309162
$514$	49.2568	2.17262
$515$	51.5641	2.27218
$516$	−9.42550	−0.414935
$517$	−12.2779	−0.539981
$518$	−43.9463	−1.93089
$519$	−24.7562	−1.08668
$520$	−2.68722	−0.117842
$521$	−26.2764	−1.15119	−0.575596	−	0.817734i	$-0.695230\pi$
$521$	−26.2764	−1.15119	−0.575596	+	0.817734i	$0.695230\pi$
$522$	−8.22761	−0.360113
$523$	30.3176	1.32570	0.662848	−	0.748754i	$-0.269348\pi$
$523$	30.3176	1.32570	0.662848	+	0.748754i	$0.269348\pi$
$524$	45.5388	1.98937
$525$	−38.7985	−1.69330
$526$	34.7047	1.51320
$527$	54.9225	2.39246
$528$	−3.69406	−0.160763
$529$	−17.6964	−0.769408
$530$	39.0641	1.69684
$531$	−1.23759	−0.0537067
$532$	70.3685	3.05086
$533$	−8.90431	−0.385688
$534$	5.07174	0.219476
$535$	32.2070	1.39243
$536$	−1.75543	−0.0758229
$537$	0.378311	0.0163253
$538$	−31.8911	−1.37492
$539$	14.9945	0.645860
$540$	7.80656	0.335941
$541$	20.4919	0.881017	0.440508	−	0.897748i	$-0.354798\pi$
$541$	20.4919	0.881017	0.440508	+	0.897748i	$0.354798\pi$
$542$	−16.5079	−0.709074
$543$	−18.2472	−0.783064
$544$	−58.8073	−2.52134
$545$	22.1832	0.950223
$546$	24.2282	1.03687
$547$	28.8237	1.23241	0.616206	−	0.787585i	$-0.288669\pi$
$547$	28.8237	1.23241	0.616206	+	0.787585i	$0.288669\pi$
$548$	−31.5857	−1.34928
$549$	−1.00000	−0.0426790
$550$	−16.8385	−0.717995
$551$	−28.3056	−1.20586
$552$	−0.669250	−0.0284852
$553$	−7.33277	−0.311821
$554$	0.707426	0.0300556
$555$	−16.7727	−0.711960
$556$	−33.1289	−1.40498
$557$	−3.71481	−0.157402	−0.0787008	−	0.996898i	$-0.525077\pi$
$557$	−3.71481	−0.157402	−0.0787008	+	0.996898i	$0.525077\pi$
$558$	15.3975	0.651830
$559$	−11.1646	−0.472214
$560$	63.1167	2.66717
$561$	−7.26013	−0.306523
$562$	64.1483	2.70593
$563$	34.2645	1.44408	0.722038	−	0.691854i	$-0.243206\pi$
$563$	34.2645	1.44408	0.722038	+	0.691854i	$0.243206\pi$
$564$	−26.3088	−1.10780
$565$	−19.4761	−0.819367
$566$	47.3974	1.99226
$567$	−4.68983	−0.196954
$568$	3.67993	0.154406
$569$	−29.8315	−1.25060	−0.625300	−	0.780384i	$-0.715024\pi$
$569$	−29.8315	−1.25060	−0.625300	+	0.780384i	$0.715024\pi$
$570$	51.9245	2.17488
$571$	7.62436	0.319069	0.159535	−	0.987192i	$-0.449001\pi$
$571$	7.62436	0.319069	0.159535	+	0.987192i	$0.449001\pi$
$572$	5.43869	0.227403
$573$	0.0423953	0.00177109
$574$	−33.4878	−1.39775
$575$	19.0521	0.794528
$576$	−9.09853	−0.379105
$577$	13.8227	0.575446	0.287723	−	0.957714i	$-0.407102\pi$
$577$	13.8227	0.575446	0.287723	+	0.957714i	$0.407102\pi$
$578$	−72.6823	−3.02319
$579$	8.68788	0.361056
$580$	31.5564	1.31031
$581$	64.6308	2.68134
$582$	−21.1301	−0.875870
$583$	−5.26804	−0.218180
$584$	−0.586833	−0.0242833
$585$	9.24698	0.382316
$586$	28.1439	1.16262
$587$	30.3944	1.25451	0.627257	−	0.778813i	$-0.284178\pi$
$587$	30.3944	1.25451	0.627257	+	0.778813i	$0.284178\pi$
$588$	32.1299	1.32502
$589$	52.9724	2.18269
$590$	9.17707	0.377814
$591$	−15.2402	−0.626896
$592$	17.0068	0.698977
$593$	−19.1615	−0.786867	−0.393433	−	0.919353i	$-0.628713\pi$
$593$	−19.1615	−0.786867	−0.393433	+	0.919353i	$0.628713\pi$
$594$	−2.03538	−0.0835127
$595$	124.046	5.08541
$596$	13.4057	0.549119
$597$	11.7486	0.480837
$598$	−11.8973	−0.486518
$599$	−32.1514	−1.31367	−0.656836	−	0.754034i	$-0.728106\pi$
$599$	−32.1514	−1.31367	−0.656836	+	0.754034i	$0.728106\pi$
$600$	−2.40414	−0.0981485
$601$	−36.8302	−1.50233	−0.751167	−	0.660112i	$-0.770509\pi$
$601$	−36.8302	−1.50233	−0.751167	+	0.660112i	$0.770509\pi$
$602$	−41.9886	−1.71133
$603$	6.04060	0.245992
$604$	26.5497	1.08029
$605$	3.64320	0.148117
$606$	−36.0200	−1.46321
$607$	−13.7738	−0.559060	−0.279530	−	0.960137i	$-0.590179\pi$
$607$	−13.7738	−0.559060	−0.279530	+	0.960137i	$0.590179\pi$
$608$	−56.7193	−2.30027
$609$	−18.9577	−0.768204
$610$	7.41529	0.300237
$611$	−31.1631	−1.26073
$612$	−15.5568	−0.628848
$613$	45.0115	1.81800	0.908999	−	0.416799i	$-0.136848\pi$
$613$	45.0115	1.81800	0.908999	+	0.416799i	$0.136848\pi$
$614$	1.26672	0.0511206
$615$	−12.7810	−0.515380
$616$	1.36289	0.0549123
$617$	5.26769	0.212069	0.106035	−	0.994362i	$-0.466185\pi$
$617$	5.26769	0.212069	0.106035	+	0.994362i	$0.466185\pi$
$618$	−28.8078	−1.15882
$619$	0.225956	0.00908194	0.00454097	−	0.999990i	$-0.498555\pi$
$619$	0.225956	0.00908194	0.00454097	+	0.999990i	$0.498555\pi$
$620$	−59.0562	−2.37175
$621$	2.30296	0.0924146
$622$	−65.1372	−2.61176
$623$	11.6861	0.468193
$624$	−9.37608	−0.375344
$625$	2.07621	0.0830483
$626$	−19.8460	−0.793206
$627$	−7.00236	−0.279647
$628$	−12.9893	−0.518330
$629$	33.4244	1.33272
$630$	34.7765	1.38553
$631$	13.9516	0.555403	0.277701	−	0.960667i	$-0.410427\pi$
$631$	13.9516	0.555403	0.277701	+	0.960667i	$0.410427\pi$
$632$	−0.454373	−0.0180740
$633$	−7.49488	−0.297895
$634$	20.0237	0.795243
$635$	−41.9773	−1.66582
$636$	−11.2882	−0.447608
$637$	38.0584	1.50793
$638$	−8.22761	−0.325734
$639$	−12.6630	−0.500941
$640$	8.44826	0.333947
$641$	−8.58714	−0.339172	−0.169586	−	0.985515i	$-0.554243\pi$
$641$	−8.58714	−0.339172	−0.169586	+	0.985515i	$0.554243\pi$
$642$	−17.9934	−0.710144
$643$	5.01284	0.197687	0.0988435	−	0.995103i	$-0.468486\pi$
$643$	5.01284	0.197687	0.0988435	+	0.995103i	$0.468486\pi$
$644$	−23.1430	−0.911964
$645$	−16.0255	−0.631002
$646$	−103.475	−4.07116
$647$	−17.2188	−0.676942	−0.338471	−	0.940977i	$-0.609910\pi$
$647$	−17.2188	−0.676942	−0.338471	+	0.940977i	$0.609910\pi$
$648$	−0.290605	−0.0114160
$649$	−1.23759	−0.0485795
$650$	−42.7386	−1.67635
$651$	35.4783	1.39051
$652$	−1.45962	−0.0571630
$653$	40.0846	1.56863	0.784316	−	0.620361i	$-0.213014\pi$
$653$	40.0846	1.56863	0.784316	+	0.620361i	$0.213014\pi$
$654$	−12.3933	−0.484616
$655$	77.4261	3.02529
$656$	12.9595	0.505982
$657$	2.01935	0.0787824
$658$	−117.200	−4.56893
$659$	44.6994	1.74124	0.870622	−	0.491953i	$-0.163717\pi$
$659$	44.6994	1.74124	0.870622	+	0.491953i	$0.163717\pi$
$660$	7.80656	0.303870
$661$	18.9406	0.736703	0.368351	−	0.929687i	$-0.379922\pi$
$661$	18.9406	0.736703	0.368351	+	0.929687i	$0.379922\pi$
$662$	−21.3331	−0.829135
$663$	−18.4273	−0.715657
$664$	4.00484	0.155418
$665$	119.642	4.63953
$666$	9.37055	0.363102
$667$	9.30924	0.360455
$668$	19.6191	0.759088
$669$	−19.6088	−0.758119
$670$	−44.7928	−1.73050
$671$	−1.00000	−0.0386046
$672$	−37.9878	−1.46541
$673$	5.92807	0.228510	0.114255	−	0.993451i	$-0.463552\pi$
$673$	5.92807	0.228510	0.114255	+	0.993451i	$0.463552\pi$
$674$	14.9498	0.575843
$675$	8.27289	0.318424
$676$	−14.0519	−0.540457
$677$	1.69010	0.0649558	0.0324779	−	0.999472i	$-0.489660\pi$
$677$	1.69010	0.0649558	0.0324779	+	0.999472i	$0.489660\pi$
$678$	10.8809	0.417879
$679$	−48.6870	−1.86843
$680$	7.68651	0.294764
$681$	−10.2134	−0.391379
$682$	15.3975	0.589602
$683$	−41.8817	−1.60256	−0.801279	−	0.598291i	$-0.795847\pi$
$683$	−41.8817	−1.60256	−0.801279	+	0.598291i	$0.795847\pi$
$684$	−15.0045	−0.573711
$685$	−53.7028	−2.05188
$686$	76.3126	2.91363
$687$	−16.8612	−0.643294
$688$	16.2492	0.619495
$689$	−13.3711	−0.509398
$690$	−17.0771	−0.650115
$691$	8.60093	0.327195	0.163597	−	0.986527i	$-0.447690\pi$
$691$	8.60093	0.327195	0.163597	+	0.986527i	$0.447690\pi$
$692$	−53.0470	−2.01654
$693$	−4.68983	−0.178152
$694$	−29.2837	−1.11159
$695$	−56.3265	−2.13658
$696$	−1.17471	−0.0445273
$697$	25.4699	0.964741
$698$	1.83433	0.0694303
$699$	22.2881	0.843015
$700$	−83.1364	−3.14226
$701$	28.0591	1.05978	0.529888	−	0.848068i	$-0.322234\pi$
$701$	28.0591	1.05978	0.529888	+	0.848068i	$0.322234\pi$
$702$	−5.16610	−0.194982
$703$	32.2377	1.21587
$704$	−9.09853	−0.342914
$705$	−44.7308	−1.68466
$706$	−29.7544	−1.11982
$707$	−82.9957	−3.12137
$708$	−2.65187	−0.0996634
$709$	42.8777	1.61031	0.805154	−	0.593066i	$-0.202083\pi$
$709$	42.8777	1.61031	0.805154	+	0.593066i	$0.202083\pi$
$710$	93.9000	3.52400
$711$	1.56355	0.0586375
$712$	0.724125	0.0271377
$713$	−17.4218	−0.652450
$714$	−69.3023	−2.59357
$715$	9.24698	0.345818
$716$	0.810636	0.0302949
$717$	19.9170	0.743815
$718$	62.5047	2.33265
$719$	39.3106	1.46604	0.733019	−	0.680208i	$-0.238110\pi$
$719$	39.3106	1.46604	0.733019	+	0.680208i	$0.238110\pi$
$720$	−13.4582	−0.501557
$721$	−66.3776	−2.47203
$722$	−61.1286	−2.27497
$723$	10.8476	0.403428
$724$	−39.0997	−1.45313
$725$	33.4414	1.24198
$726$	−2.03538	−0.0755401
$727$	−20.5914	−0.763693	−0.381846	−	0.924226i	$-0.624712\pi$
$727$	−20.5914	−0.763693	−0.381846	+	0.924226i	$0.624712\pi$
$728$	3.45921	0.128207
$729$	1.00000	0.0370370
$730$	−14.9741	−0.554216
$731$	31.9354	1.18117
$732$	−2.14278	−0.0791993
$733$	−33.3897	−1.23328	−0.616639	−	0.787246i	$-0.711506\pi$
$733$	−33.3897	−1.23328	−0.616639	+	0.787246i	$0.711506\pi$
$734$	64.6182	2.38510
$735$	54.6280	2.01499
$736$	18.6540	0.687597
$737$	6.04060	0.222508
$738$	7.14050	0.262845
$739$	6.75881	0.248627	0.124313	−	0.992243i	$-0.460327\pi$
$739$	6.75881	0.248627	0.124313	+	0.992243i	$0.460327\pi$
$740$	−35.9401	−1.32118
$741$	−17.7730	−0.652909
$742$	−50.2866	−1.84608
$743$	−24.0448	−0.882119	−0.441060	−	0.897478i	$-0.645397\pi$
$743$	−24.0448	−0.882119	−0.441060	+	0.897478i	$0.645397\pi$
$744$	2.19841	0.0805975
$745$	22.7927	0.835059
$746$	−24.3662	−0.892111
$747$	−13.7810	−0.504222
$748$	−15.5568	−0.568814
$749$	−41.4596	−1.51490
$750$	−24.2694	−0.886194
$751$	11.0501	0.403224	0.201612	−	0.979465i	$-0.435382\pi$
$751$	11.0501	0.403224	0.201612	+	0.979465i	$0.435382\pi$
$752$	45.3553	1.65394
$753$	−5.74852	−0.209488
$754$	−20.8829	−0.760511
$755$	45.1403	1.64283
$756$	−10.0493	−0.365488
$757$	−6.93705	−0.252131	−0.126066	−	0.992022i	$-0.540235\pi$
$757$	−6.93705	−0.252131	−0.126066	+	0.992022i	$0.540235\pi$
$758$	−14.8126	−0.538017
$759$	2.30296	0.0835921
$760$	7.41361	0.268920
$761$	−31.8639	−1.15506	−0.577532	−	0.816368i	$-0.695984\pi$
$761$	−31.8639	−1.15506	−0.577532	+	0.816368i	$0.695984\pi$
$762$	23.4519	0.849572
$763$	−28.5561	−1.03380
$764$	0.0908438	0.00328661
$765$	−26.4501	−0.956304
$766$	66.5240	2.40361
$767$	−3.14118	−0.113421
$768$	13.4772	0.486316
$769$	−10.0504	−0.362427	−0.181214	−	0.983444i	$-0.558003\pi$
$769$	−10.0504	−0.362427	−0.181214	+	0.983444i	$0.558003\pi$
$770$	34.7765	1.25326
$771$	−24.2003	−0.871552
$772$	18.6162	0.670011
$773$	13.4269	0.482931	0.241466	−	0.970409i	$-0.422372\pi$
$773$	13.4269	0.482931	0.241466	+	0.970409i	$0.422372\pi$
$774$	8.95310	0.321813
$775$	−62.5839	−2.24808
$776$	−3.01688	−0.108300
$777$	21.5912	0.774580
$778$	−40.4920	−1.45171
$779$	24.5656	0.880153
$780$	19.8142	0.709463
$781$	−12.6630	−0.453118
$782$	34.0311	1.21695
$783$	4.04230	0.144460
$784$	−55.3907	−1.97824
$785$	−22.0847	−0.788238
$786$	−43.2564	−1.54291
$787$	−31.4820	−1.12221	−0.561107	−	0.827743i	$-0.689624\pi$
$787$	−31.4820	−1.12221	−0.561107	+	0.827743i	$0.689624\pi$
$788$	−32.6562	−1.16333
$789$	−17.0507	−0.607022
$790$	−11.5941	−0.412501
$791$	25.0713	0.891434
$792$	−0.290605	−0.0103262
$793$	−2.53815	−0.0901324
$794$	−48.5232	−1.72202
$795$	−19.1925	−0.680688
$796$	25.1746	0.892289
$797$	−15.0762	−0.534025	−0.267012	−	0.963693i	$-0.586036\pi$
$797$	−15.0762	−0.534025	−0.267012	+	0.963693i	$0.586036\pi$
$798$	−66.8417	−2.36617
$799$	89.1391	3.15351
$800$	67.0106	2.36918
$801$	−2.49179	−0.0880430
$802$	18.2314	0.643774
$803$	2.01935	0.0712614
$804$	12.9437	0.456488
$805$	−39.3483	−1.38685
$806$	39.0813	1.37658
$807$	15.6684	0.551553
$808$	−5.14281	−0.180923
$809$	−49.6145	−1.74435	−0.872177	−	0.489190i	$-0.837292\pi$
$809$	−49.6145	−1.74435	−0.872177	+	0.489190i	$0.837292\pi$
$810$	−7.41529	−0.260547
$811$	45.0796	1.58296	0.791480	−	0.611195i	$-0.209311\pi$
$811$	45.0796	1.58296	0.791480	+	0.611195i	$0.209311\pi$
$812$	−40.6221	−1.42556
$813$	8.11046	0.284446
$814$	9.37055	0.328438
$815$	−2.48167	−0.0869292
$816$	26.8194	0.938865
$817$	30.8015	1.07761
$818$	4.40576	0.154044
$819$	−11.9035	−0.415942
$820$	−27.3869	−0.956391
$821$	−33.9818	−1.18597	−0.592987	−	0.805212i	$-0.702051\pi$
$821$	−33.9818	−1.18597	−0.592987	+	0.805212i	$0.702051\pi$
$822$	30.0027	1.04646
$823$	13.7180	0.478179	0.239090	−	0.970998i	$-0.423151\pi$
$823$	13.7180	0.478179	0.239090	+	0.970998i	$0.423151\pi$
$824$	−4.11308	−0.143286
$825$	8.27289	0.288025
$826$	−11.8135	−0.411044
$827$	−47.0665	−1.63666	−0.818332	−	0.574746i	$-0.805101\pi$
$827$	−47.0665	−1.63666	−0.818332	+	0.574746i	$0.805101\pi$
$828$	4.93473	0.171494
$829$	−23.2955	−0.809086	−0.404543	−	0.914519i	$-0.632569\pi$
$829$	−23.2955	−0.809086	−0.404543	+	0.914519i	$0.632569\pi$
$830$	102.191	3.54708
$831$	−0.347564	−0.0120569
$832$	−23.0934	−0.800621
$833$	−108.862	−3.77185
$834$	31.4685	1.08966
$835$	33.3569	1.15436
$836$	−15.0045	−0.518941
$837$	−7.56494	−0.261483
$838$	29.2714	1.01116
$839$	56.1331	1.93793	0.968965	−	0.247199i	$-0.0795103\pi$
$839$	56.1331	1.93793	0.968965	+	0.247199i	$0.0795103\pi$
$840$	4.96527	0.171318
$841$	−12.6598	−0.436546
$842$	36.5307	1.25893
$843$	−31.5166	−1.08549
$844$	−16.0598	−0.552803
$845$	−23.8913	−0.821887
$846$	24.9902	0.859181
$847$	−4.68983	−0.161145
$848$	19.4605	0.668275
$849$	−23.2867	−0.799199
$850$	122.249	4.19312
$851$	−10.6024	−0.363447
$852$	−27.1340	−0.929596
$853$	18.0999	0.619729	0.309864	−	0.950781i	$-0.399716\pi$
$853$	18.0999	0.619729	0.309864	+	0.950781i	$0.399716\pi$
$854$	−9.54560	−0.326644
$855$	−25.5110	−0.872457
$856$	−2.56904	−0.0878079
$857$	7.44500	0.254316	0.127158	−	0.991882i	$-0.459414\pi$
$857$	7.44500	0.254316	0.127158	+	0.991882i	$0.459414\pi$
$858$	−5.16610	−0.176368
$859$	54.7631	1.86849	0.934247	−	0.356626i	$-0.116073\pi$
$859$	54.7631	1.86849	0.934247	+	0.356626i	$0.116073\pi$
$860$	−34.3390	−1.17095
$861$	16.4528	0.560710
$862$	−7.95117	−0.270818
$863$	18.6756	0.635724	0.317862	−	0.948137i	$-0.397035\pi$
$863$	18.6756	0.635724	0.317862	+	0.948137i	$0.397035\pi$
$864$	8.10003	0.275569
$865$	−90.1917	−3.06661
$866$	−24.3574	−0.827700
$867$	35.7094	1.21276
$868$	76.0221	2.58036
$869$	1.56355	0.0530396
$870$	−29.9748	−1.01624
$871$	15.3320	0.519503
$872$	−1.76947	−0.0599219
$873$	10.3814	0.351357
$874$	32.8228	1.11025
$875$	−55.9205	−1.89046
$876$	4.32702	0.146196
$877$	36.5218	1.23325	0.616626	−	0.787256i	$-0.288499\pi$
$877$	36.5218	1.23325	0.616626	+	0.787256i	$0.288499\pi$
$878$	9.31262	0.314286
$879$	−13.8274	−0.466385
$880$	−13.4582	−0.453676
$881$	−38.1820	−1.28638	−0.643192	−	0.765705i	$-0.722390\pi$
$881$	−38.1820	−1.28638	−0.643192	+	0.765705i	$0.722390\pi$
$882$	−30.5196	−1.02765
$883$	13.5685	0.456618	0.228309	−	0.973589i	$-0.426680\pi$
$883$	13.5685	0.456618	0.228309	+	0.973589i	$0.426680\pi$
$884$	−39.4856	−1.32804
$885$	−4.50877	−0.151561
$886$	−17.2626	−0.579948
$887$	16.2525	0.545707	0.272853	−	0.962056i	$-0.412033\pi$
$887$	16.2525	0.545707	0.272853	+	0.962056i	$0.412033\pi$
$888$	1.33789	0.0448968
$889$	54.0367	1.81233
$890$	18.4773	0.619362
$891$	1.00000	0.0335013
$892$	−42.0172	−1.40684
$893$	85.9742	2.87702
$894$	−12.7338	−0.425882
$895$	1.37826	0.0460702
$896$	−10.8753	−0.363319
$897$	5.84526	0.195167
$898$	−62.6661	−2.09119
$899$	−30.5797	−1.01989
$900$	17.7269	0.590898
$901$	38.2467	1.27418
$902$	7.14050	0.237753
$903$	20.6293	0.686501
$904$	1.55354	0.0516700
$905$	−66.4783	−2.20981
$906$	−25.2190	−0.837845
$907$	41.4074	1.37491	0.687455	−	0.726227i	$-0.258728\pi$
$907$	41.4074	1.37491	0.687455	+	0.726227i	$0.258728\pi$
$908$	−21.8851	−0.726282
$909$	17.6969	0.586970
$910$	88.2680	2.92606
$911$	−8.80278	−0.291649	−0.145824	−	0.989310i	$-0.546583\pi$
$911$	−8.80278	−0.291649	−0.145824	+	0.989310i	$0.546583\pi$
$912$	25.8671	0.856547
$913$	−13.7810	−0.456086
$914$	−16.4840	−0.545241
$915$	−3.64320	−0.120440
$916$	−36.1297	−1.19376
$917$	−99.6695	−3.29138
$918$	14.7771	0.487718
$919$	−27.7544	−0.915534	−0.457767	−	0.889072i	$-0.651351\pi$
$919$	−27.7544	−0.915534	−0.457767	+	0.889072i	$0.651351\pi$
$920$	−2.43821	−0.0803855
$921$	−0.622350	−0.0205071
$922$	−24.3356	−0.801450
$923$	−32.1406	−1.05792
$924$	−10.0493	−0.330597
$925$	−38.0870	−1.25229
$926$	43.1686	1.41861
$927$	14.1535	0.464863
$928$	32.7427	1.07483
$929$	−16.2422	−0.532889	−0.266444	−	0.963850i	$-0.585849\pi$
$929$	−16.2422	−0.532889	−0.266444	+	0.963850i	$0.585849\pi$
$930$	56.0963	1.83947
$931$	−104.997	−3.44114
$932$	47.7585	1.56438
$933$	32.0025	1.04771
$934$	33.5502	1.09780
$935$	−26.4501	−0.865010
$936$	−0.737598	−0.0241092
$937$	27.3746	0.894289	0.447144	−	0.894462i	$-0.352441\pi$
$937$	27.3746	0.894289	0.447144	+	0.894462i	$0.352441\pi$
$938$	57.6611	1.88270
$939$	9.75051	0.318196
$940$	−95.8481	−3.12622
$941$	32.4459	1.05771	0.528854	−	0.848713i	$-0.322622\pi$
$941$	32.4459	1.05771	0.528854	+	0.848713i	$0.322622\pi$
$942$	12.3383	0.402004
$943$	−8.07921	−0.263095
$944$	4.57172	0.148797
$945$	−17.0860	−0.555807
$946$	8.95310	0.291090
$947$	−45.6348	−1.48293	−0.741466	−	0.670990i	$-0.765869\pi$
$947$	−45.6348	−1.48293	−0.741466	+	0.670990i	$0.765869\pi$
$948$	3.35033	0.108814
$949$	5.12542	0.166378
$950$	117.909	3.82547
$951$	−9.83781	−0.319013
$952$	−9.89473	−0.320690
$953$	−11.1355	−0.360715	−0.180358	−	0.983601i	$-0.557726\pi$
$953$	−11.1355	−0.360715	−0.180358	+	0.983601i	$0.557726\pi$
$954$	10.7225	0.347153
$955$	0.154455	0.00499803
$956$	42.6777	1.38030
$957$	4.04230	0.130669
$958$	11.9959	0.387569
$959$	69.1308	2.23235
$960$	−33.1477	−1.06984
$961$	26.2284	0.846077
$962$	23.7839	0.766823
$963$	8.84032	0.284875
$964$	23.2441	0.748641
$965$	31.6517	1.01890
$966$	21.9831	0.707295
$967$	33.3918	1.07381	0.536904	−	0.843643i	$-0.319594\pi$
$967$	33.3918	1.07381	0.536904	+	0.843643i	$0.319594\pi$
$968$	−0.290605	−0.00934039
$969$	50.8380	1.63315
$970$	−76.9810	−2.47171
$971$	−56.3438	−1.80816	−0.904080	−	0.427363i	$-0.859443\pi$
$971$	−56.3438	−1.80816	−0.904080	+	0.427363i	$0.859443\pi$
$972$	2.14278	0.0687296
$973$	72.5082	2.32451
$974$	−9.58156	−0.307013
$975$	20.9978	0.672469
$976$	3.69406	0.118244
$977$	47.5197	1.52029	0.760145	−	0.649753i	$-0.225128\pi$
$977$	47.5197	1.52029	0.760145	+	0.649753i	$0.225128\pi$
$978$	1.38646	0.0443341
$979$	−2.49179	−0.0796379
$980$	117.056	3.73921
$981$	6.08893	0.194405
$982$	−5.86887	−0.187283
$983$	−20.7775	−0.662700	−0.331350	−	0.943508i	$-0.607504\pi$
$983$	−20.7775	−0.662700	−0.331350	+	0.943508i	$0.607504\pi$
$984$	1.01950	0.0325003
$985$	−55.5229	−1.76911
$986$	59.7335	1.90230
$987$	57.5813	1.83283
$988$	−38.0836	−1.21160
$989$	−10.1301	−0.322119
$990$	−7.41529	−0.235674
$991$	24.1060	0.765753	0.382877	−	0.923799i	$-0.374933\pi$
$991$	24.1060	0.765753	0.382877	+	0.923799i	$0.374933\pi$
$992$	−61.2763	−1.94552
$993$	10.4811	0.332609
$994$	−120.876	−3.83396
$995$	42.8024	1.35693
$996$	−29.5297	−0.935684
$997$	−13.9288	−0.441130	−0.220565	−	0.975372i	$-0.570790\pi$
$997$	−13.9288	−0.441130	−0.220565	+	0.975372i	$0.570790\pi$
$998$	−68.2468	−2.16032
$999$	−4.60383	−0.145659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.4	✓	12
3.2	odd	2		6039.2.a.f.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.4	✓	12	1.1	even	1	trivial
6039.2.a.f.1.9		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)

\(f(q)\)	\(=\)	\(q-2.03538 q^{2} +1.00000 q^{3} +2.14278 q^{4} +3.64320 q^{5} -2.03538 q^{6} -4.68983 q^{7} -0.290605 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.03538 q^{2} +1.00000 q^{3} +2.14278 q^{4} +3.64320 q^{5} -2.03538 q^{6} -4.68983 q^{7} -0.290605 q^{8} +1.00000 q^{9} -7.41529 q^{10} +1.00000 q^{11} +2.14278 q^{12} +2.53815 q^{13} +9.54560 q^{14} +3.64320 q^{15} -3.69406 q^{16} -7.26013 q^{17} -2.03538 q^{18} -7.00236 q^{19} +7.80656 q^{20} -4.68983 q^{21} -2.03538 q^{22} +2.30296 q^{23} -0.290605 q^{24} +8.27289 q^{25} -5.16610 q^{26} +1.00000 q^{27} -10.0493 q^{28} +4.04230 q^{29} -7.41529 q^{30} -7.56494 q^{31} +8.10003 q^{32} +1.00000 q^{33} +14.7771 q^{34} -17.0860 q^{35} +2.14278 q^{36} -4.60383 q^{37} +14.2525 q^{38} +2.53815 q^{39} -1.05873 q^{40} -3.50819 q^{41} +9.54560 q^{42} -4.39873 q^{43} +2.14278 q^{44} +3.64320 q^{45} -4.68740 q^{46} -12.2779 q^{47} -3.69406 q^{48} +14.9945 q^{49} -16.8385 q^{50} -7.26013 q^{51} +5.43869 q^{52} -5.26804 q^{53} -2.03538 q^{54} +3.64320 q^{55} +1.36289 q^{56} -7.00236 q^{57} -8.22761 q^{58} -1.23759 q^{59} +7.80656 q^{60} -1.00000 q^{61} +15.3975 q^{62} -4.68983 q^{63} -9.09853 q^{64} +9.24698 q^{65} -2.03538 q^{66} +6.04060 q^{67} -15.5568 q^{68} +2.30296 q^{69} +34.7765 q^{70} -12.6630 q^{71} -0.290605 q^{72} +2.01935 q^{73} +9.37055 q^{74} +8.27289 q^{75} -15.0045 q^{76} -4.68983 q^{77} -5.16610 q^{78} +1.56355 q^{79} -13.4582 q^{80} +1.00000 q^{81} +7.14050 q^{82} -13.7810 q^{83} -10.0493 q^{84} -26.4501 q^{85} +8.95310 q^{86} +4.04230 q^{87} -0.290605 q^{88} -2.49179 q^{89} -7.41529 q^{90} -11.9035 q^{91} +4.93473 q^{92} -7.56494 q^{93} +24.9902 q^{94} -25.5110 q^{95} +8.10003 q^{96} +10.3814 q^{97} -30.5196 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 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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