LMFDB - Embedded newform 299.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(1,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 19x^{8} + 18x^{7} + 127x^{6} - 109x^{5} - 357x^{4} + 252x^{3} + 400x^{2} - 192x - 128 $ x^10 - x^9 - 19x^8 + 18x^7 + 127x^6 - 109x^5 - 357x^4 + 252x^3 + 400x^2 - 192x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.29172$ of defining polynomial
Character	$\chi$	$=$	299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29172 q^{2} -2.20386 q^{3} -0.331447 q^{4} +2.25480 q^{5} +2.84678 q^{6} -4.62032 q^{7} +3.01159 q^{8} +1.85700 q^{9} +O(q^{10})$	\(q-1.29172 q^{2} -2.20386 q^{3} -0.331447 q^{4} +2.25480 q^{5} +2.84678 q^{6} -4.62032 q^{7} +3.01159 q^{8} +1.85700 q^{9} -2.91259 q^{10} -2.87359 q^{11} +0.730462 q^{12} -1.00000 q^{13} +5.96818 q^{14} -4.96927 q^{15} -3.22725 q^{16} +6.49176 q^{17} -2.39873 q^{18} +8.00718 q^{19} -0.747347 q^{20} +10.1825 q^{21} +3.71189 q^{22} +1.00000 q^{23} -6.63712 q^{24} +0.0841365 q^{25} +1.29172 q^{26} +2.51901 q^{27} +1.53139 q^{28} +2.37233 q^{29} +6.41893 q^{30} +7.98496 q^{31} -1.85446 q^{32} +6.33299 q^{33} -8.38557 q^{34} -10.4179 q^{35} -0.615496 q^{36} +1.26769 q^{37} -10.3431 q^{38} +2.20386 q^{39} +6.79054 q^{40} +3.98435 q^{41} -13.1530 q^{42} -7.41177 q^{43} +0.952442 q^{44} +4.18717 q^{45} -1.29172 q^{46} -2.81176 q^{47} +7.11241 q^{48} +14.3473 q^{49} -0.108681 q^{50} -14.3069 q^{51} +0.331447 q^{52} -6.19126 q^{53} -3.25387 q^{54} -6.47938 q^{55} -13.9145 q^{56} -17.6467 q^{57} -3.06440 q^{58} +0.769085 q^{59} +1.64705 q^{60} +11.2176 q^{61} -10.3144 q^{62} -8.57993 q^{63} +8.84995 q^{64} -2.25480 q^{65} -8.18048 q^{66} +3.12004 q^{67} -2.15167 q^{68} -2.20386 q^{69} +13.4571 q^{70} -2.22762 q^{71} +5.59252 q^{72} -5.21941 q^{73} -1.63750 q^{74} -0.185425 q^{75} -2.65395 q^{76} +13.2769 q^{77} -2.84678 q^{78} +15.4542 q^{79} -7.27681 q^{80} -11.1226 q^{81} -5.14669 q^{82} -6.74200 q^{83} -3.37497 q^{84} +14.6376 q^{85} +9.57397 q^{86} -5.22829 q^{87} -8.65407 q^{88} +1.08219 q^{89} -5.40867 q^{90} +4.62032 q^{91} -0.331447 q^{92} -17.5977 q^{93} +3.63203 q^{94} +18.0546 q^{95} +4.08696 q^{96} -5.78097 q^{97} -18.5328 q^{98} -5.33625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 3 q^{3} + 19 q^{4} + 3 q^{5} + q^{6} - 2 q^{7} + 17 q^{9}+O(q^{10}) $ 10 * q + q^2 + 3 * q^3 + 19 * q^4 + 3 * q^5 + q^6 - 2 * q^7 + 17 * q^9	\( 10 q + q^{2} + 3 q^{3} + 19 q^{4} + 3 q^{5} + q^{6} - 2 q^{7} + 17 q^{9} + 6 q^{10} + 3 q^{11} + 10 q^{12} - 10 q^{13} - 15 q^{14} + 2 q^{15} + 25 q^{16} - 3 q^{17} + q^{18} + 2 q^{19} - 19 q^{20} + 21 q^{21} + 13 q^{22} + 10 q^{23} - 35 q^{24} + 33 q^{25} - q^{26} + 6 q^{27} - 19 q^{28} + 17 q^{29} - 47 q^{30} + 5 q^{31} - 9 q^{32} - 23 q^{33} + 23 q^{34} + 3 q^{35} + 48 q^{36} + 16 q^{37} + 5 q^{38} - 3 q^{39} + 13 q^{40} - 16 q^{41} - 65 q^{42} - 9 q^{43} + 18 q^{44} + 32 q^{45} + q^{46} - 11 q^{47} + 37 q^{48} + 40 q^{49} - 30 q^{50} - 31 q^{51} - 19 q^{52} + 8 q^{53} - 73 q^{54} - 14 q^{55} - 54 q^{56} - 35 q^{57} + 17 q^{58} + 2 q^{59} - 37 q^{60} + 48 q^{61} - 19 q^{62} - 15 q^{63} + 64 q^{64} - 3 q^{65} - 84 q^{66} - 6 q^{67} - 62 q^{68} + 3 q^{69} - 44 q^{70} + 24 q^{71} - 89 q^{72} - 33 q^{73} - 28 q^{74} - 22 q^{75} - 53 q^{76} + 15 q^{77} - q^{78} + 17 q^{79} - 94 q^{80} + 30 q^{81} + 35 q^{82} - 21 q^{83} + 92 q^{84} + 58 q^{85} - 7 q^{86} + 23 q^{87} + 9 q^{88} - 16 q^{89} + 67 q^{90} + 2 q^{91} + 19 q^{92} + 15 q^{93} + 12 q^{94} - 27 q^{95} - 22 q^{96} - 40 q^{97} - 34 q^{98} - 17 q^{99}+O(q^{100}) \) 10 * q + q^2 + 3 * q^3 + 19 * q^4 + 3 * q^5 + q^6 - 2 * q^7 + 17 * q^9 + 6 * q^10 + 3 * q^11 + 10 * q^12 - 10 * q^13 - 15 * q^14 + 2 * q^15 + 25 * q^16 - 3 * q^17 + q^18 + 2 * q^19 - 19 * q^20 + 21 * q^21 + 13 * q^22 + 10 * q^23 - 35 * q^24 + 33 * q^25 - q^26 + 6 * q^27 - 19 * q^28 + 17 * q^29 - 47 * q^30 + 5 * q^31 - 9 * q^32 - 23 * q^33 + 23 * q^34 + 3 * q^35 + 48 * q^36 + 16 * q^37 + 5 * q^38 - 3 * q^39 + 13 * q^40 - 16 * q^41 - 65 * q^42 - 9 * q^43 + 18 * q^44 + 32 * q^45 + q^46 - 11 * q^47 + 37 * q^48 + 40 * q^49 - 30 * q^50 - 31 * q^51 - 19 * q^52 + 8 * q^53 - 73 * q^54 - 14 * q^55 - 54 * q^56 - 35 * q^57 + 17 * q^58 + 2 * q^59 - 37 * q^60 + 48 * q^61 - 19 * q^62 - 15 * q^63 + 64 * q^64 - 3 * q^65 - 84 * q^66 - 6 * q^67 - 62 * q^68 + 3 * q^69 - 44 * q^70 + 24 * q^71 - 89 * q^72 - 33 * q^73 - 28 * q^74 - 22 * q^75 - 53 * q^76 + 15 * q^77 - q^78 + 17 * q^79 - 94 * q^80 + 30 * q^81 + 35 * q^82 - 21 * q^83 + 92 * q^84 + 58 * q^85 - 7 * q^86 + 23 * q^87 + 9 * q^88 - 16 * q^89 + 67 * q^90 + 2 * q^91 + 19 * q^92 + 15 * q^93 + 12 * q^94 - 27 * q^95 - 22 * q^96 - 40 * q^97 - 34 * q^98 - 17 * 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 $

$2$	−1.29172	−0.913387	−0.456694	−	0.889624i	$-0.650966\pi$
$2$	−1.29172	−0.913387	−0.456694	+	0.889624i	$0.650966\pi$
$3$	−2.20386	−1.27240	−0.636200	−	0.771525i	$-0.719495\pi$
$3$	−2.20386	−1.27240	−0.636200	+	0.771525i	$0.719495\pi$
$4$	−0.331447	−0.165723
$5$	2.25480	1.00838	0.504189	−	0.863593i	$-0.331791\pi$
$5$	2.25480	1.00838	0.504189	+	0.863593i	$0.331791\pi$
$6$	2.84678	1.16219
$7$	−4.62032	−1.74632	−0.873158	−	0.487437i	$-0.837932\pi$
$7$	−4.62032	−1.74632	−0.873158	+	0.487437i	$0.837932\pi$
$8$	3.01159	1.06476
$9$	1.85700	0.619000
$10$	−2.91259	−0.921040
$11$	−2.87359	−0.866420	−0.433210	−	0.901293i	$-0.642619\pi$
$11$	−2.87359	−0.866420	−0.433210	+	0.901293i	$0.642619\pi$
$12$	0.730462	0.210866
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.96818	1.59506
$15$	−4.96927	−1.28306
$16$	−3.22725	−0.806812
$17$	6.49176	1.57448	0.787241	−	0.616645i	$-0.211509\pi$
$17$	6.49176	1.57448	0.787241	+	0.616645i	$0.211509\pi$
$18$	−2.39873	−0.565387
$19$	8.00718	1.83697	0.918486	−	0.395453i	$-0.129412\pi$
$19$	8.00718	1.83697	0.918486	+	0.395453i	$0.129412\pi$
$20$	−0.747347	−0.167112
$21$	10.1825	2.22201
$22$	3.71189	0.791377
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.63712	−1.35480
$25$	0.0841365	0.0168273
$26$	1.29172	0.253328
$27$	2.51901	0.484784
$28$	1.53139	0.289405
$29$	2.37233	0.440531	0.220266	−	0.975440i	$-0.429308\pi$
$29$	2.37233	0.440531	0.220266	+	0.975440i	$0.429308\pi$
$30$	6.41893	1.17193
$31$	7.98496	1.43414	0.717071	−	0.697000i	$-0.245482\pi$
$31$	7.98496	1.43414	0.717071	+	0.697000i	$0.245482\pi$
$32$	−1.85446	−0.327825
$33$	6.33299	1.10243
$34$	−8.38557	−1.43811
$35$	−10.4179	−1.76095
$36$	−0.615496	−0.102583
$37$	1.26769	0.208406	0.104203	−	0.994556i	$-0.466771\pi$
$37$	1.26769	0.208406	0.104203	+	0.994556i	$0.466771\pi$
$38$	−10.3431	−1.67787
$39$	2.20386	0.352900
$40$	6.79054	1.07368
$41$	3.98435	0.622251	0.311126	−	0.950369i	$-0.399294\pi$
$41$	3.98435	0.622251	0.311126	+	0.950369i	$0.399294\pi$
$42$	−13.1530	−2.02956
$43$	−7.41177	−1.13028	−0.565142	−	0.824993i	$-0.691179\pi$
$43$	−7.41177	−1.13028	−0.565142	+	0.824993i	$0.691179\pi$
$44$	0.952442	0.143586
$45$	4.18717	0.624186
$46$	−1.29172	−0.190454
$47$	−2.81176	−0.410138	−0.205069	−	0.978748i	$-0.565742\pi$
$47$	−2.81176	−0.410138	−0.205069	+	0.978748i	$0.565742\pi$
$48$	7.11241	1.02659
$49$	14.3473	2.04962
$50$	−0.108681	−0.0153698
$51$	−14.3069	−2.00337
$52$	0.331447	0.0459634
$53$	−6.19126	−0.850434	−0.425217	−	0.905091i	$-0.639802\pi$
$53$	−6.19126	−0.850434	−0.425217	+	0.905091i	$0.639802\pi$
$54$	−3.25387	−0.442796
$55$	−6.47938	−0.873679
$56$	−13.9145	−1.85940
$57$	−17.6467	−2.33736
$58$	−3.06440	−0.402376
$59$	0.769085	0.100126	0.0500632	−	0.998746i	$-0.484058\pi$
$59$	0.769085	0.100126	0.0500632	+	0.998746i	$0.484058\pi$
$60$	1.64705	0.212633
$61$	11.2176	1.43627	0.718135	−	0.695904i	$-0.244996\pi$
$61$	11.2176	1.43627	0.718135	+	0.695904i	$0.244996\pi$
$62$	−10.3144	−1.30993
$63$	−8.57993	−1.08097
$64$	8.84995	1.10624
$65$	−2.25480	−0.279674
$66$	−8.18048	−1.00695
$67$	3.12004	0.381174	0.190587	−	0.981670i	$-0.438961\pi$
$67$	3.12004	0.381174	0.190587	+	0.981670i	$0.438961\pi$
$68$	−2.15167	−0.260929
$69$	−2.20386	−0.265314
$70$	13.4571	1.60843
$71$	−2.22762	−0.264370	−0.132185	−	0.991225i	$-0.542199\pi$
$71$	−2.22762	−0.264370	−0.132185	+	0.991225i	$0.542199\pi$
$72$	5.59252	0.659084
$73$	−5.21941	−0.610886	−0.305443	−	0.952210i	$-0.598805\pi$
$73$	−5.21941	−0.610886	−0.305443	+	0.952210i	$0.598805\pi$
$74$	−1.63750	−0.190356
$75$	−0.185425	−0.0214110
$76$	−2.65395	−0.304429
$77$	13.2769	1.51304
$78$	−2.84678	−0.322334
$79$	15.4542	1.73873	0.869367	−	0.494166i	$-0.164527\pi$
$79$	15.4542	1.73873	0.869367	+	0.494166i	$0.164527\pi$
$80$	−7.27681	−0.813572
$81$	−11.1226	−1.23584
$82$	−5.14669	−0.568356
$83$	−6.74200	−0.740031	−0.370016	−	0.929026i	$-0.620648\pi$
$83$	−6.74200	−0.740031	−0.370016	+	0.929026i	$0.620648\pi$
$84$	−3.37497	−0.368239
$85$	14.6376	1.58767
$86$	9.57397	1.03239
$87$	−5.22829	−0.560532
$88$	−8.65407	−0.922527
$89$	1.08219	0.114712	0.0573561	−	0.998354i	$-0.481733\pi$
$89$	1.08219	0.114712	0.0573561	+	0.998354i	$0.481733\pi$
$90$	−5.40867	−0.570124
$91$	4.62032	0.484341
$92$	−0.331447	−0.0345557
$93$	−17.5977	−1.82480
$94$	3.63203	0.374615
$95$	18.0546	1.85236
$96$	4.08696	0.417124
$97$	−5.78097	−0.586968	−0.293484	−	0.955964i	$-0.594815\pi$
$97$	−5.78097	−0.586968	−0.293484	+	0.955964i	$0.594815\pi$
$98$	−18.5328	−1.87210
$99$	−5.33625	−0.536314
$100$	−0.0278868	−0.00278868
$101$	12.8777	1.28138	0.640691	−	0.767799i	$-0.278648\pi$
$101$	12.8777	1.28138	0.640691	+	0.767799i	$0.278648\pi$
$102$	18.4806	1.82985
$103$	12.2478	1.20681	0.603406	−	0.797434i	$-0.293810\pi$
$103$	12.2478	1.20681	0.603406	+	0.797434i	$0.293810\pi$
$104$	−3.01159	−0.295310
$105$	22.9596	2.24063
$106$	7.99740	0.776776
$107$	6.94179	0.671088	0.335544	−	0.942025i	$-0.391080\pi$
$107$	6.94179	0.671088	0.335544	+	0.942025i	$0.391080\pi$
$108$	−0.834919	−0.0803401
$109$	−7.89317	−0.756028	−0.378014	−	0.925800i	$-0.623393\pi$
$109$	−7.89317	−0.756028	−0.378014	+	0.925800i	$0.623393\pi$
$110$	8.36958	0.798008
$111$	−2.79380	−0.265176
$112$	14.9109	1.40895
$113$	−11.3110	−1.06405	−0.532024	−	0.846729i	$-0.678568\pi$
$113$	−11.3110	−1.06405	−0.532024	+	0.846729i	$0.678568\pi$
$114$	22.7947	2.13492
$115$	2.25480	0.210261
$116$	−0.786302	−0.0730063
$117$	−1.85700	−0.171680
$118$	−0.993447	−0.0914542
$119$	−29.9940	−2.74955
$120$	−14.9654	−1.36615
$121$	−2.74248	−0.249317
$122$	−14.4901	−1.31187
$123$	−8.78095	−0.791752
$124$	−2.64659	−0.237671
$125$	−11.0843	−0.991410
$126$	11.0829	0.987344
$127$	10.0956	0.895836	0.447918	−	0.894075i	$-0.352166\pi$
$127$	10.0956	0.895836	0.447918	+	0.894075i	$0.352166\pi$
$128$	−7.72278	−0.682604
$129$	16.3345	1.43817
$130$	2.91259	0.255451
$131$	2.57126	0.224652	0.112326	−	0.993671i	$-0.464170\pi$
$131$	2.57126	0.224652	0.112326	+	0.993671i	$0.464170\pi$
$132$	−2.09905	−0.182699
$133$	−36.9957	−3.20793
$134$	−4.03024	−0.348159
$135$	5.67988	0.488846
$136$	19.5505	1.67644
$137$	21.0806	1.80104	0.900519	−	0.434817i	$-0.143187\pi$
$137$	21.0806	1.80104	0.900519	+	0.434817i	$0.143187\pi$
$138$	2.84678	0.242334
$139$	−12.7296	−1.07971	−0.539857	−	0.841757i	$-0.681522\pi$
$139$	−12.7296	−1.07971	−0.539857	+	0.841757i	$0.681522\pi$
$140$	3.45298	0.291830
$141$	6.19674	0.521859
$142$	2.87748	0.241472
$143$	2.87359	0.240302
$144$	−5.99300	−0.499417
$145$	5.34915	0.444222
$146$	6.74204	0.557975
$147$	−31.6195	−2.60794
$148$	−0.420170	−0.0345378
$149$	−12.0268	−0.985274	−0.492637	−	0.870235i	$-0.663967\pi$
$149$	−12.0268	−0.985274	−0.492637	+	0.870235i	$0.663967\pi$
$150$	0.239518	0.0195566
$151$	−3.18265	−0.259000	−0.129500	−	0.991579i	$-0.541337\pi$
$151$	−3.18265	−0.259000	−0.129500	+	0.991579i	$0.541337\pi$
$152$	24.1143	1.95593
$153$	12.0552	0.974604
$154$	−17.1501	−1.38199
$155$	18.0045	1.44616
$156$	−0.730462	−0.0584838
$157$	20.7626	1.65703	0.828517	−	0.559964i	$-0.189185\pi$
$157$	20.7626	1.65703	0.828517	+	0.559964i	$0.189185\pi$
$158$	−19.9626	−1.58814
$159$	13.6447	1.08209
$160$	−4.18143	−0.330571
$161$	−4.62032	−0.364132
$162$	14.3673	1.12880
$163$	22.5958	1.76984	0.884919	−	0.465744i	$-0.154213\pi$
$163$	22.5958	1.76984	0.884919	+	0.465744i	$0.154213\pi$
$164$	−1.32060	−0.103122
$165$	14.2796	1.11167
$166$	8.70881	0.675935
$167$	−10.2741	−0.795031	−0.397516	−	0.917595i	$-0.630128\pi$
$167$	−10.2741	−0.795031	−0.397516	+	0.917595i	$0.630128\pi$
$168$	30.6656	2.36590
$169$	1.00000	0.0769231
$170$	−18.9078	−1.45016
$171$	14.8693	1.13709
$172$	2.45661	0.187315
$173$	11.3402	0.862181	0.431091	−	0.902309i	$-0.358129\pi$
$173$	11.3402	0.862181	0.431091	+	0.902309i	$0.358129\pi$
$174$	6.75351	0.511983
$175$	−0.388737	−0.0293858
$176$	9.27379	0.699038
$177$	−1.69496	−0.127401
$178$	−1.39789	−0.104777
$179$	11.5484	0.863171	0.431585	−	0.902072i	$-0.357954\pi$
$179$	11.5484	0.863171	0.431585	+	0.902072i	$0.357954\pi$
$180$	−1.38782	−0.103442
$181$	7.24156	0.538261	0.269130	−	0.963104i	$-0.413264\pi$
$181$	7.24156	0.538261	0.269130	+	0.963104i	$0.413264\pi$
$182$	−5.96818	−0.442391
$183$	−24.7221	−1.82751
$184$	3.01159	0.222017
$185$	2.85838	0.210152
$186$	22.7314	1.66675
$187$	−18.6547	−1.36416
$188$	0.931950	0.0679694
$189$	−11.6386	−0.846587
$190$	−23.3216	−1.69193
$191$	6.60898	0.478209	0.239105	−	0.970994i	$-0.423146\pi$
$191$	6.60898	0.478209	0.239105	+	0.970994i	$0.423146\pi$
$192$	−19.5040	−1.40758
$193$	−6.66223	−0.479558	−0.239779	−	0.970828i	$-0.577075\pi$
$193$	−6.66223	−0.479558	−0.239779	+	0.970828i	$0.577075\pi$
$194$	7.46742	0.536129
$195$	4.96927	0.355857
$196$	−4.75538	−0.339670
$197$	22.8526	1.62818	0.814091	−	0.580738i	$-0.197236\pi$
$197$	22.8526	1.62818	0.814091	+	0.580738i	$0.197236\pi$
$198$	6.89297	0.489862
$199$	7.57885	0.537250	0.268625	−	0.963245i	$-0.413431\pi$
$199$	7.57885	0.537250	0.268625	+	0.963245i	$0.413431\pi$
$200$	0.253384	0.0179170
$201$	−6.87614	−0.485005
$202$	−16.6345	−1.17040
$203$	−10.9609	−0.769307
$204$	4.74198	0.332005
$205$	8.98393	0.627465
$206$	−15.8208	−1.10229
$207$	1.85700	0.129070
$208$	3.22725	0.223770
$209$	−23.0093	−1.59159
$210$	−29.6575	−2.04656
$211$	9.51105	0.654767	0.327384	−	0.944891i	$-0.393833\pi$
$211$	9.51105	0.654767	0.327384	+	0.944891i	$0.393833\pi$
$212$	2.05207	0.140937
$213$	4.90937	0.336384
$214$	−8.96688	−0.612963
$215$	−16.7121	−1.13975
$216$	7.58623	0.516178
$217$	−36.8931	−2.50447
$218$	10.1958	0.690547
$219$	11.5028	0.777291
$220$	2.14757	0.144789
$221$	−6.49176	−0.436683
$222$	3.60882	0.242208
$223$	−10.6759	−0.714914	−0.357457	−	0.933930i	$-0.616356\pi$
$223$	−10.6759	−0.714914	−0.357457	+	0.933930i	$0.616356\pi$
$224$	8.56818	0.572486
$225$	0.156241	0.0104161
$226$	14.6107	0.971888
$227$	1.64852	0.109416	0.0547082	−	0.998502i	$-0.482577\pi$
$227$	1.64852	0.109416	0.0547082	+	0.998502i	$0.482577\pi$
$228$	5.84894	0.387355
$229$	−6.90725	−0.456444	−0.228222	−	0.973609i	$-0.573291\pi$
$229$	−6.90725	−0.456444	−0.228222	+	0.973609i	$0.573291\pi$
$230$	−2.91259	−0.192050
$231$	−29.2604	−1.92520
$232$	7.14449	0.469059
$233$	−24.9702	−1.63585	−0.817925	−	0.575325i	$-0.804875\pi$
$233$	−24.9702	−1.63585	−0.817925	+	0.575325i	$0.804875\pi$
$234$	2.39873	0.156810
$235$	−6.33998	−0.413574
$236$	−0.254911	−0.0165933
$237$	−34.0589	−2.21236
$238$	38.7440	2.51140
$239$	−7.74999	−0.501305	−0.250653	−	0.968077i	$-0.580645\pi$
$239$	−7.74999	−0.501305	−0.250653	+	0.968077i	$0.580645\pi$
$240$	16.0371	1.03519
$241$	−22.2290	−1.43190	−0.715949	−	0.698153i	$-0.754006\pi$
$241$	−22.2290	−1.43190	−0.715949	+	0.698153i	$0.754006\pi$
$242$	3.54253	0.227723
$243$	16.9555	1.08770
$244$	−3.71804	−0.238023
$245$	32.3504	2.06679
$246$	11.3426	0.723176
$247$	−8.00718	−0.509484
$248$	24.0474	1.52701
$249$	14.8584	0.941615
$250$	14.3179	0.905542
$251$	18.2503	1.15195	0.575974	−	0.817468i	$-0.304623\pi$
$251$	18.2503	1.15195	0.575974	+	0.817468i	$0.304623\pi$
$252$	2.84379	0.179142
$253$	−2.87359	−0.180661
$254$	−13.0407	−0.818245
$255$	−32.2593	−2.02016
$256$	−7.72418	−0.482761
$257$	6.48302	0.404400	0.202200	−	0.979344i	$-0.435191\pi$
$257$	6.48302	0.404400	0.202200	+	0.979344i	$0.435191\pi$
$258$	−21.0997	−1.31361
$259$	−5.85711	−0.363943
$260$	0.747347	0.0463485
$261$	4.40542	0.272689
$262$	−3.32136	−0.205195
$263$	8.25160	0.508816	0.254408	−	0.967097i	$-0.418119\pi$
$263$	8.25160	0.508816	0.254408	+	0.967097i	$0.418119\pi$
$264$	19.0724	1.17382
$265$	−13.9601	−0.857560
$266$	47.7883	2.93009
$267$	−2.38500	−0.145960
$268$	−1.03413	−0.0631694
$269$	−6.04655	−0.368665	−0.184332	−	0.982864i	$-0.559012\pi$
$269$	−6.04655	−0.368665	−0.184332	+	0.982864i	$0.559012\pi$
$270$	−7.33684	−0.446506
$271$	−5.22560	−0.317433	−0.158716	−	0.987324i	$-0.550736\pi$
$271$	−5.22560	−0.317433	−0.158716	+	0.987324i	$0.550736\pi$
$272$	−20.9505	−1.27031
$273$	−10.1825	−0.616275
$274$	−27.2303	−1.64504
$275$	−0.241774	−0.0145795
$276$	0.730462	0.0439686
$277$	−4.94636	−0.297198	−0.148599	−	0.988898i	$-0.547476\pi$
$277$	−4.94636	−0.297198	−0.148599	+	0.988898i	$0.547476\pi$
$278$	16.4432	0.986197
$279$	14.8281	0.887733
$280$	−31.3744	−1.87498
$281$	−7.34319	−0.438058	−0.219029	−	0.975718i	$-0.570289\pi$
$281$	−7.34319	−0.438058	−0.219029	+	0.975718i	$0.570289\pi$
$282$	−8.00448	−0.476660
$283$	−13.1298	−0.780488	−0.390244	−	0.920711i	$-0.627609\pi$
$283$	−13.1298	−0.780488	−0.390244	+	0.920711i	$0.627609\pi$
$284$	0.738338	0.0438123
$285$	−39.7898	−2.35695
$286$	−3.71189	−0.219489
$287$	−18.4090	−1.08665
$288$	−3.44372	−0.202923
$289$	25.1429	1.47900
$290$	−6.90962	−0.405747
$291$	12.7404	0.746858
$292$	1.72996	0.101238
$293$	5.30511	0.309928	0.154964	−	0.987920i	$-0.450474\pi$
$293$	5.30511	0.309928	0.154964	+	0.987920i	$0.450474\pi$
$294$	40.8438	2.38206
$295$	1.73414	0.100965
$296$	3.81775	0.221902
$297$	−7.23861	−0.420027
$298$	15.5353	0.899937
$299$	−1.00000	−0.0578315
$300$	0.0614585	0.00354831
$301$	34.2448	1.97383
$302$	4.11110	0.236567
$303$	−28.3807	−1.63043
$304$	−25.8412	−1.48209
$305$	25.2935	1.44830
$306$	−15.5720	−0.890191
$307$	3.57154	0.203839	0.101919	−	0.994793i	$-0.467502\pi$
$307$	3.57154	0.203839	0.101919	+	0.994793i	$0.467502\pi$
$308$	−4.40058	−0.250747
$309$	−26.9924	−1.53555
$310$	−23.2569	−1.32090
$311$	−9.52569	−0.540152	−0.270076	−	0.962839i	$-0.587049\pi$
$311$	−9.52569	−0.540152	−0.270076	+	0.962839i	$0.587049\pi$
$312$	6.63712	0.375753
$313$	17.3014	0.977931	0.488965	−	0.872303i	$-0.337374\pi$
$313$	17.3014	0.977931	0.488965	+	0.872303i	$0.337374\pi$
$314$	−26.8195	−1.51351
$315$	−19.3460	−1.09003
$316$	−5.12225	−0.288149
$317$	4.78710	0.268870	0.134435	−	0.990922i	$-0.457078\pi$
$317$	4.78710	0.268870	0.134435	+	0.990922i	$0.457078\pi$
$318$	−17.6252	−0.988369
$319$	−6.81711	−0.381685
$320$	19.9549	1.11551
$321$	−15.2987	−0.853892
$322$	5.96818	0.332594
$323$	51.9807	2.89228
$324$	3.68653	0.204807
$325$	−0.0841365	−0.00466705
$326$	−29.1875	−1.61655
$327$	17.3954	0.961970
$328$	11.9992	0.662546
$329$	12.9912	0.716231
$330$	−18.4454	−1.01538
$331$	−8.58277	−0.471752	−0.235876	−	0.971783i	$-0.575796\pi$
$331$	−8.58277	−0.471752	−0.235876	+	0.971783i	$0.575796\pi$
$332$	2.23461	0.122640
$333$	2.35409	0.129003
$334$	13.2713	0.726172
$335$	7.03508	0.384368
$336$	−32.8616	−1.79275
$337$	25.4229	1.38487	0.692436	−	0.721479i	$-0.256537\pi$
$337$	25.4229	1.38487	0.692436	+	0.721479i	$0.256537\pi$
$338$	−1.29172	−0.0702606
$339$	24.9278	1.35389
$340$	−4.85160	−0.263115
$341$	−22.9455	−1.24257
$342$	−19.2071	−1.03860
$343$	−33.9471	−1.83297
$344$	−22.3212	−1.20348
$345$	−4.96927	−0.267537
$346$	−14.6485	−0.787506
$347$	−1.99569	−0.107134	−0.0535671	−	0.998564i	$-0.517059\pi$
$347$	−1.99569	−0.107134	−0.0535671	+	0.998564i	$0.517059\pi$
$348$	1.73290	0.0928932
$349$	17.2693	0.924404	0.462202	−	0.886775i	$-0.347060\pi$
$349$	17.2693	0.924404	0.462202	+	0.886775i	$0.347060\pi$
$350$	0.502142	0.0268406
$351$	−2.51901	−0.134455
$352$	5.32895	0.284034
$353$	−4.09830	−0.218130	−0.109065	−	0.994035i	$-0.534786\pi$
$353$	−4.09830	−0.218130	−0.109065	+	0.994035i	$0.534786\pi$
$354$	2.18942	0.116366
$355$	−5.02285	−0.266585
$356$	−0.358689	−0.0190105
$357$	66.1026	3.49852
$358$	−14.9174	−0.788409
$359$	−22.7191	−1.19907	−0.599534	−	0.800349i	$-0.704647\pi$
$359$	−22.7191	−1.19907	−0.599534	+	0.800349i	$0.704647\pi$
$360$	12.6100	0.664607
$361$	45.1149	2.37447
$362$	−9.35410	−0.491641
$363$	6.04405	0.317230
$364$	−1.53139	−0.0802666
$365$	−11.7687	−0.616004
$366$	31.9341	1.66922
$367$	25.1909	1.31495	0.657477	−	0.753475i	$-0.271624\pi$
$367$	25.1909	1.31495	0.657477	+	0.753475i	$0.271624\pi$
$368$	−3.22725	−0.168232
$369$	7.39894	0.385173
$370$	−3.69224	−0.191951
$371$	28.6056	1.48513
$372$	5.83271	0.302412
$373$	15.0107	0.777225	0.388613	−	0.921401i	$-0.372954\pi$
$373$	15.0107	0.777225	0.388613	+	0.921401i	$0.372954\pi$
$374$	24.0967	1.24601
$375$	24.4283	1.26147
$376$	−8.46788	−0.436697
$377$	−2.37233	−0.122181
$378$	15.0339	0.773262
$379$	22.5196	1.15676	0.578378	−	0.815769i	$-0.303686\pi$
$379$	22.5196	1.15676	0.578378	+	0.815769i	$0.303686\pi$
$380$	−5.98414	−0.306980
$381$	−22.2492	−1.13986
$382$	−8.53699	−0.436790
$383$	−15.5836	−0.796283	−0.398141	−	0.917324i	$-0.630345\pi$
$383$	−15.5836	−0.796283	−0.398141	+	0.917324i	$0.630345\pi$
$384$	17.0199	0.868545
$385$	29.9368	1.52572
$386$	8.60577	0.438022
$387$	−13.7637	−0.699646
$388$	1.91608	0.0972743
$389$	−25.9932	−1.31791	−0.658954	−	0.752183i	$-0.729001\pi$
$389$	−25.9932	−1.31791	−0.658954	+	0.752183i	$0.729001\pi$
$390$	−6.41893	−0.325035
$391$	6.49176	0.328302
$392$	43.2083	2.18235
$393$	−5.66670	−0.285847
$394$	−29.5193	−1.48716
$395$	34.8462	1.75330
$396$	1.76868	0.0888797
$397$	24.0549	1.20728	0.603642	−	0.797256i	$-0.293716\pi$
$397$	24.0549	1.20728	0.603642	+	0.797256i	$0.293716\pi$
$398$	−9.78979	−0.490718
$399$	81.5334	4.08177
$400$	−0.271530	−0.0135765
$401$	−34.8926	−1.74246	−0.871228	−	0.490879i	$-0.836676\pi$
$401$	−34.8926	−1.74246	−0.871228	+	0.490879i	$0.836676\pi$
$402$	8.88208	0.442998
$403$	−7.98496	−0.397759
$404$	−4.26828	−0.212355
$405$	−25.0792	−1.24619
$406$	14.1585	0.702675
$407$	−3.64281	−0.180567
$408$	−43.0866	−2.13310
$409$	−0.512147	−0.0253240	−0.0126620	−	0.999920i	$-0.504031\pi$
$409$	−0.512147	−0.0253240	−0.0126620	+	0.999920i	$0.504031\pi$
$410$	−11.6048	−0.573118
$411$	−46.4587	−2.29164
$412$	−4.05949	−0.199997
$413$	−3.55342	−0.174852
$414$	−2.39873	−0.117891
$415$	−15.2019	−0.746231
$416$	1.85446	0.0909222
$417$	28.0543	1.37383
$418$	29.7217	1.45374
$419$	3.91510	0.191265	0.0956325	−	0.995417i	$-0.469513\pi$
$419$	3.91510	0.191265	0.0956325	+	0.995417i	$0.469513\pi$
$420$	−7.60989	−0.371324
$421$	17.2654	0.841463	0.420731	−	0.907185i	$-0.361774\pi$
$421$	17.2654	0.841463	0.420731	+	0.907185i	$0.361774\pi$
$422$	−12.2857	−0.598056
$423$	−5.22144	−0.253875
$424$	−18.6455	−0.905506
$425$	0.546194	0.0264943
$426$	−6.34155	−0.307249
$427$	−51.8290	−2.50818
$428$	−2.30083	−0.111215
$429$	−6.33299	−0.305760
$430$	21.5874	1.04104
$431$	−32.7604	−1.57801	−0.789006	−	0.614385i	$-0.789404\pi$
$431$	−32.7604	−1.57801	−0.789006	+	0.614385i	$0.789404\pi$
$432$	−8.12949	−0.391130
$433$	9.21478	0.442834	0.221417	−	0.975179i	$-0.428932\pi$
$433$	9.21478	0.442834	0.221417	+	0.975179i	$0.428932\pi$
$434$	47.6557	2.28755
$435$	−11.7888	−0.565228
$436$	2.61616	0.125292
$437$	8.00718	0.383035
$438$	−14.8585	−0.709967
$439$	12.2538	0.584843	0.292421	−	0.956290i	$-0.405539\pi$
$439$	12.2538	0.584843	0.292421	+	0.956290i	$0.405539\pi$
$440$	−19.5132	−0.930256
$441$	26.6430	1.26871
$442$	8.38557	0.398861
$443$	−14.1560	−0.672574	−0.336287	−	0.941760i	$-0.609171\pi$
$443$	−14.1560	−0.672574	−0.336287	+	0.941760i	$0.609171\pi$
$444$	0.925996	0.0439458
$445$	2.44013	0.115673
$446$	13.7904	0.652993
$447$	26.5054	1.25366
$448$	−40.8896	−1.93185
$449$	−11.7240	−0.553288	−0.276644	−	0.960972i	$-0.589222\pi$
$449$	−11.7240	−0.553288	−0.276644	+	0.960972i	$0.589222\pi$
$450$	−0.201821	−0.00951393
$451$	−11.4494	−0.539131
$452$	3.74899	0.176337
$453$	7.01411	0.329551
$454$	−2.12944	−0.0999395
$455$	10.4179	0.488399
$456$	−53.1446	−2.48872
$457$	−27.1070	−1.26801	−0.634005	−	0.773329i	$-0.718590\pi$
$457$	−27.1070	−1.26801	−0.634005	+	0.773329i	$0.718590\pi$
$458$	8.92227	0.416910
$459$	16.3528	0.763285
$460$	−0.747347	−0.0348452
$461$	20.2881	0.944909	0.472455	−	0.881355i	$-0.343368\pi$
$461$	20.2881	0.944909	0.472455	+	0.881355i	$0.343368\pi$
$462$	37.7964	1.75845
$463$	−18.2103	−0.846306	−0.423153	−	0.906058i	$-0.639077\pi$
$463$	−18.2103	−0.846306	−0.423153	+	0.906058i	$0.639077\pi$
$464$	−7.65611	−0.355426
$465$	−39.6794	−1.84009
$466$	32.2546	1.49416
$467$	8.40226	0.388810	0.194405	−	0.980921i	$-0.437722\pi$
$467$	8.40226	0.388810	0.194405	+	0.980921i	$0.437722\pi$
$468$	0.615496	0.0284513
$469$	−14.4156	−0.665650
$470$	8.18950	0.377754
$471$	−45.7578	−2.10841
$472$	2.31617	0.106610
$473$	21.2984	0.979301
$474$	43.9948	2.02075
$475$	0.673696	0.0309113
$476$	9.94141	0.455664
$477$	−11.4972	−0.526419
$478$	10.0109	0.457886
$479$	35.3034	1.61305	0.806526	−	0.591199i	$-0.201345\pi$
$479$	35.3034	1.61305	0.806526	+	0.591199i	$0.201345\pi$
$480$	9.21530	0.420619
$481$	−1.26769	−0.0578015
$482$	28.7138	1.30788
$483$	10.1825	0.463321
$484$	0.908987	0.0413176
$485$	−13.0349	−0.591886
$486$	−21.9019	−0.993488
$487$	4.79191	0.217142	0.108571	−	0.994089i	$-0.465372\pi$
$487$	4.79191	0.217142	0.108571	+	0.994089i	$0.465372\pi$
$488$	33.7829	1.52928
$489$	−49.7980	−2.25194
$490$	−41.7879	−1.88778
$491$	−10.6858	−0.482243	−0.241121	−	0.970495i	$-0.577515\pi$
$491$	−10.6858	−0.482243	−0.241121	+	0.970495i	$0.577515\pi$
$492$	2.91042	0.131212
$493$	15.4006	0.693609
$494$	10.3431	0.465357
$495$	−12.0322	−0.540807
$496$	−25.7695	−1.15708
$497$	10.2923	0.461674
$498$	−19.1930	−0.860059
$499$	22.3100	0.998733	0.499366	−	0.866391i	$-0.333566\pi$
$499$	22.3100	0.998733	0.499366	+	0.866391i	$0.333566\pi$
$500$	3.67386	0.164300
$501$	22.6426	1.01160
$502$	−23.5744	−1.05218
$503$	−13.4572	−0.600029	−0.300015	−	0.953935i	$-0.596992\pi$
$503$	−13.4572	−0.600029	−0.300015	+	0.953935i	$0.596992\pi$
$504$	−25.8392	−1.15097
$505$	29.0367	1.29212
$506$	3.71189	0.165014
$507$	−2.20386	−0.0978769
$508$	−3.34614	−0.148461
$509$	−18.6738	−0.827704	−0.413852	−	0.910344i	$-0.635817\pi$
$509$	−18.6738	−0.827704	−0.413852	+	0.910344i	$0.635817\pi$
$510$	41.6701	1.84519
$511$	24.1153	1.06680
$512$	25.4231	1.12355
$513$	20.1702	0.890536
$514$	−8.37428	−0.369374
$515$	27.6164	1.21692
$516$	−5.41402	−0.238339
$517$	8.07986	0.355352
$518$	7.56578	0.332421
$519$	−24.9923	−1.09704
$520$	−6.79054	−0.297785
$521$	−17.3777	−0.761330	−0.380665	−	0.924713i	$-0.624305\pi$
$521$	−17.3777	−0.761330	−0.380665	+	0.924713i	$0.624305\pi$
$522$	−5.69059	−0.249071
$523$	−39.5940	−1.73132	−0.865661	−	0.500630i	$-0.833102\pi$
$523$	−39.5940	−1.73132	−0.865661	+	0.500630i	$0.833102\pi$
$524$	−0.852236	−0.0372301
$525$	0.856723	0.0373905
$526$	−10.6588	−0.464746
$527$	51.8365	2.25803
$528$	−20.4381	−0.889456
$529$	1.00000	0.0434783
$530$	18.0326	0.783284
$531$	1.42819	0.0619782
$532$	12.2621	0.531630
$533$	−3.98435	−0.172581
$534$	3.08076	0.133318
$535$	15.6524	0.676711
$536$	9.39628	0.405858
$537$	−25.4511	−1.09830
$538$	7.81049	0.336734
$539$	−41.2284	−1.77583
$540$	−1.88258	−0.0810132
$541$	−3.09712	−0.133156	−0.0665778	−	0.997781i	$-0.521208\pi$
$541$	−3.09712	−0.133156	−0.0665778	+	0.997781i	$0.521208\pi$
$542$	6.75004	0.289939
$543$	−15.9594	−0.684883
$544$	−12.0387	−0.516154
$545$	−17.7975	−0.762363
$546$	13.1530	0.562898
$547$	−19.2550	−0.823285	−0.411642	−	0.911345i	$-0.635045\pi$
$547$	−19.2550	−0.823285	−0.411642	+	0.911345i	$0.635045\pi$
$548$	−6.98709	−0.298474
$549$	20.8311	0.889051
$550$	0.312305	0.0133167
$551$	18.9957	0.809244
$552$	−6.63712	−0.282495
$553$	−71.4034	−3.03638
$554$	6.38934	0.271457
$555$	−6.29947	−0.267398
$556$	4.21920	0.178934
$557$	−26.7341	−1.13276	−0.566381	−	0.824144i	$-0.691657\pi$
$557$	−26.7341	−1.13276	−0.566381	+	0.824144i	$0.691657\pi$
$558$	−19.1538	−0.810845
$559$	7.41177	0.313485
$560$	33.6212	1.42075
$561$	41.1122	1.73576
$562$	9.48538	0.400117
$563$	−41.5239	−1.75003	−0.875013	−	0.484100i	$-0.839147\pi$
$563$	−41.5239	−1.75003	−0.875013	+	0.484100i	$0.839147\pi$
$564$	−2.05389	−0.0864843
$565$	−25.5040	−1.07296
$566$	16.9601	0.712888
$567$	51.3897	2.15817
$568$	−6.70868	−0.281490
$569$	11.8665	0.497471	0.248736	−	0.968571i	$-0.419985\pi$
$569$	11.8665	0.497471	0.248736	+	0.968571i	$0.419985\pi$
$570$	51.3975	2.15280
$571$	30.9433	1.29494	0.647469	−	0.762092i	$-0.275828\pi$
$571$	30.9433	1.29494	0.647469	+	0.762092i	$0.275828\pi$
$572$	−0.952442	−0.0398236
$573$	−14.5653	−0.608473
$574$	23.7793	0.992530
$575$	0.0841365	0.00350873
$576$	16.4343	0.684764
$577$	−9.36343	−0.389805	−0.194902	−	0.980823i	$-0.562439\pi$
$577$	−9.36343	−0.389805	−0.194902	+	0.980823i	$0.562439\pi$
$578$	−32.4778	−1.35090
$579$	14.6826	0.610189
$580$	−1.77296	−0.0736180
$581$	31.1502	1.29233
$582$	−16.4571	−0.682171
$583$	17.7911	0.736833
$584$	−15.7187	−0.650445
$585$	−4.18717	−0.173118
$586$	−6.85275	−0.283084
$587$	25.5527	1.05467	0.527336	−	0.849657i	$-0.323191\pi$
$587$	25.5527	1.05467	0.527336	+	0.849657i	$0.323191\pi$
$588$	10.4802	0.432196
$589$	63.9370	2.63448
$590$	−2.24003	−0.0922204
$591$	−50.3640	−2.07170
$592$	−4.09114	−0.168145
$593$	−12.1423	−0.498624	−0.249312	−	0.968423i	$-0.580204\pi$
$593$	−12.1423	−0.498624	−0.249312	+	0.968423i	$0.580204\pi$
$594$	9.35030	0.383647
$595$	−67.6306	−2.77258
$596$	3.98624	0.163283
$597$	−16.7027	−0.683597
$598$	1.29172	0.0528226
$599$	−30.3220	−1.23892	−0.619461	−	0.785027i	$-0.712649\pi$
$599$	−30.3220	−1.23892	−0.619461	+	0.785027i	$0.712649\pi$
$600$	−0.558424	−0.0227976
$601$	2.32636	0.0948943	0.0474471	−	0.998874i	$-0.484891\pi$
$601$	2.32636	0.0948943	0.0474471	+	0.998874i	$0.484891\pi$
$602$	−44.2348	−1.80288
$603$	5.79392	0.235947
$604$	1.05488	0.0429224
$605$	−6.18376	−0.251405
$606$	36.6601	1.48921
$607$	−5.81404	−0.235984	−0.117992	−	0.993015i	$-0.537646\pi$
$607$	−5.81404	−0.235984	−0.117992	+	0.993015i	$0.537646\pi$
$608$	−14.8490	−0.602205
$609$	24.1564	0.978866
$610$	−32.6723	−1.32286
$611$	2.81176	0.113752
$612$	−3.99565	−0.161515
$613$	0.708390	0.0286116	0.0143058	−	0.999898i	$-0.495446\pi$
$613$	0.708390	0.0286116	0.0143058	+	0.999898i	$0.495446\pi$
$614$	−4.61345	−0.186184
$615$	−19.7993	−0.798386
$616$	39.9846	1.61102
$617$	−26.8906	−1.08257	−0.541287	−	0.840838i	$-0.682063\pi$
$617$	−26.8906	−1.08257	−0.541287	+	0.840838i	$0.682063\pi$
$618$	34.8668	1.40255
$619$	22.3158	0.896949	0.448475	−	0.893796i	$-0.351967\pi$
$619$	22.3158	0.896949	0.448475	+	0.893796i	$0.351967\pi$
$620$	−5.96754	−0.239662
$621$	2.51901	0.101085
$622$	12.3046	0.493368
$623$	−5.00007	−0.200324
$624$	−7.11241	−0.284724
$625$	−25.4136	−1.01654
$626$	−22.3486	−0.893230
$627$	50.7094	2.02514
$628$	−6.88168	−0.274609
$629$	8.22951	0.328132
$630$	24.9898	0.995616
$631$	−7.12096	−0.283481	−0.141740	−	0.989904i	$-0.545270\pi$
$631$	−7.12096	−0.283481	−0.141740	+	0.989904i	$0.545270\pi$
$632$	46.5417	1.85133
$633$	−20.9610	−0.833125
$634$	−6.18362	−0.245583
$635$	22.7635	0.903342
$636$	−4.52248	−0.179328
$637$	−14.3473	−0.568463
$638$	8.80584	0.348626
$639$	−4.13669	−0.163645
$640$	−17.4134	−0.688323
$641$	−14.6322	−0.577939	−0.288969	−	0.957338i	$-0.593313\pi$
$641$	−14.6322	−0.577939	−0.288969	+	0.957338i	$0.593313\pi$
$642$	19.7618	0.779934
$643$	15.7665	0.621769	0.310885	−	0.950448i	$-0.399375\pi$
$643$	15.7665	0.621769	0.310885	+	0.950448i	$0.399375\pi$
$644$	1.53139	0.0603452
$645$	36.8311	1.45022
$646$	−67.1447	−2.64177
$647$	−19.6092	−0.770915	−0.385458	−	0.922726i	$-0.625956\pi$
$647$	−19.6092	−0.770915	−0.385458	+	0.922726i	$0.625956\pi$
$648$	−33.4965	−1.31587
$649$	−2.21004	−0.0867515
$650$	0.108681	0.00426283
$651$	81.3072	3.18668
$652$	−7.48930	−0.293304
$653$	30.5836	1.19683	0.598413	−	0.801187i	$-0.295798\pi$
$653$	30.5836	1.19683	0.598413	+	0.801187i	$0.295798\pi$
$654$	−22.4701	−0.878651
$655$	5.79769	0.226535
$656$	−12.8585	−0.502040
$657$	−9.69244	−0.378138
$658$	−16.7811	−0.654196
$659$	−22.6248	−0.881338	−0.440669	−	0.897670i	$-0.645259\pi$
$659$	−22.6248	−0.881338	−0.440669	+	0.897670i	$0.645259\pi$
$660$	−4.73294	−0.184229
$661$	−42.9035	−1.66875	−0.834376	−	0.551196i	$-0.814172\pi$
$661$	−42.9035	−1.66875	−0.834376	+	0.551196i	$0.814172\pi$
$662$	11.0866	0.430892
$663$	14.3069	0.555635
$664$	−20.3041	−0.787953
$665$	−83.4180	−3.23481
$666$	−3.04084	−0.117830
$667$	2.37233	0.0918571
$668$	3.40531	0.131755
$669$	23.5283	0.909656
$670$	−9.08739	−0.351077
$671$	−32.2349	−1.24441
$672$	−18.8831	−0.728430
$673$	17.2197	0.663772	0.331886	−	0.943319i	$-0.392315\pi$
$673$	17.2197	0.663772	0.331886	+	0.943319i	$0.392315\pi$
$674$	−32.8394	−1.26493
$675$	0.211941	0.00815761
$676$	−0.331447	−0.0127479
$677$	15.3806	0.591125	0.295562	−	0.955323i	$-0.404493\pi$
$677$	15.3806	0.591125	0.295562	+	0.955323i	$0.404493\pi$
$678$	−32.1999	−1.23663
$679$	26.7099	1.02503
$680$	44.0825	1.69049
$681$	−3.63312	−0.139221
$682$	29.6393	1.13495
$683$	51.5782	1.97358	0.986792	−	0.161990i	$-0.0517911\pi$
$683$	51.5782	1.97358	0.986792	+	0.161990i	$0.0517911\pi$
$684$	−4.92839	−0.188442
$685$	47.5326	1.81613
$686$	43.8503	1.67421
$687$	15.2226	0.580779
$688$	23.9196	0.911928
$689$	6.19126	0.235868
$690$	6.41893	0.244365
$691$	−30.7530	−1.16990	−0.584950	−	0.811070i	$-0.698886\pi$
$691$	−30.7530	−1.16990	−0.584950	+	0.811070i	$0.698886\pi$
$692$	−3.75868	−0.142884
$693$	24.6552	0.936573
$694$	2.57788	0.0978551
$695$	−28.7028	−1.08876
$696$	−15.7455	−0.596830
$697$	25.8655	0.979724
$698$	−22.3072	−0.844339
$699$	55.0307	2.08145
$700$	0.128846	0.00486991
$701$	−8.32757	−0.314528	−0.157264	−	0.987557i	$-0.550267\pi$
$701$	−8.32757	−0.314528	−0.157264	+	0.987557i	$0.550267\pi$
$702$	3.25387	0.122810
$703$	10.1506	0.382836
$704$	−25.4311	−0.958471
$705$	13.9724	0.526232
$706$	5.29387	0.199237
$707$	−59.4992	−2.23770
$708$	0.561788	0.0211133
$709$	38.6733	1.45241	0.726203	−	0.687480i	$-0.241283\pi$
$709$	38.6733	1.45241	0.726203	+	0.687480i	$0.241283\pi$
$710$	6.48814	0.243496
$711$	28.6985	1.07628
$712$	3.25912	0.122141
$713$	7.98496	0.299039
$714$	−85.3863	−3.19550
$715$	6.47938	0.242315
$716$	−3.82769	−0.143048
$717$	17.0799	0.637861
$718$	29.3468	1.09521
$719$	1.67429	0.0624406	0.0312203	−	0.999513i	$-0.490061\pi$
$719$	1.67429	0.0624406	0.0312203	+	0.999513i	$0.490061\pi$
$720$	−13.5130	−0.503601
$721$	−56.5887	−2.10747
$722$	−58.2760	−2.16881
$723$	48.9897	1.82195
$724$	−2.40019	−0.0892024
$725$	0.199600	0.00741295
$726$	−7.80725	−0.289754
$727$	−38.0656	−1.41177	−0.705887	−	0.708324i	$-0.749452\pi$
$727$	−38.0656	−1.41177	−0.705887	+	0.708324i	$0.749452\pi$
$728$	13.9145	0.515706
$729$	−3.99991	−0.148145
$730$	15.2020	0.562650
$731$	−48.1154	−1.77961
$732$	8.19405	0.302861
$733$	−17.4371	−0.644053	−0.322027	−	0.946731i	$-0.604364\pi$
$733$	−17.4371	−0.644053	−0.322027	+	0.946731i	$0.604364\pi$
$734$	−32.5397	−1.20106
$735$	−71.2958	−2.62979
$736$	−1.85446	−0.0683562
$737$	−8.96572	−0.330257
$738$	−9.55739	−0.351813
$739$	−10.3472	−0.380629	−0.190314	−	0.981723i	$-0.560951\pi$
$739$	−10.3472	−0.380629	−0.190314	+	0.981723i	$0.560951\pi$
$740$	−0.947401	−0.0348271
$741$	17.6467	0.648268
$742$	−36.9505	−1.35650
$743$	−23.4465	−0.860170	−0.430085	−	0.902789i	$-0.641516\pi$
$743$	−23.4465	−0.860170	−0.430085	+	0.902789i	$0.641516\pi$
$744$	−52.9971	−1.94297
$745$	−27.1181	−0.993529
$746$	−19.3897	−0.709908
$747$	−12.5199	−0.458079
$748$	6.18302	0.226074
$749$	−32.0733	−1.17193
$750$	−31.5546	−1.15221
$751$	−41.6909	−1.52132	−0.760661	−	0.649149i	$-0.775125\pi$
$751$	−41.6909	−1.52132	−0.760661	+	0.649149i	$0.775125\pi$
$752$	9.07427	0.330904
$753$	−40.2211	−1.46574
$754$	3.06440	0.111599
$755$	−7.17624	−0.261170
$756$	3.85759	0.140299
$757$	−0.0544526	−0.00197911	−0.000989556	−	1.00000i	$-0.500315\pi$
$757$	−0.0544526	−0.00197911	−0.000989556		1.00000i	$0.500315\pi$
$758$	−29.0892	−1.05657
$759$	6.33299	0.229873
$760$	54.3730	1.97232
$761$	7.48555	0.271351	0.135675	−	0.990753i	$-0.456680\pi$
$761$	7.48555	0.271351	0.135675	+	0.990753i	$0.456680\pi$
$762$	28.7398	1.04113
$763$	36.4690	1.32026
$764$	−2.19052	−0.0792504
$765$	27.1821	0.982770
$766$	20.1297	0.727315
$767$	−0.769085	−0.0277701
$768$	17.0230	0.614265
$769$	−20.3283	−0.733056	−0.366528	−	0.930407i	$-0.619454\pi$
$769$	−20.3283	−0.733056	−0.366528	+	0.930407i	$0.619454\pi$
$770$	−38.6701	−1.39357
$771$	−14.2877	−0.514558
$772$	2.20817	0.0794739
$773$	−25.0561	−0.901205	−0.450602	−	0.892725i	$-0.648791\pi$
$773$	−25.0561	−0.901205	−0.450602	+	0.892725i	$0.648791\pi$
$774$	17.7789	0.639048
$775$	0.671827	0.0241327
$776$	−17.4099	−0.624979
$777$	12.9083	0.463081
$778$	33.5761	1.20376
$779$	31.9034	1.14306
$780$	−1.64705	−0.0589738
$781$	6.40127	0.229056
$782$	−8.38557	−0.299867
$783$	5.97594	0.213563
$784$	−46.3025	−1.65366
$785$	46.8155	1.67092
$786$	7.31982	0.261089
$787$	−40.6841	−1.45023	−0.725117	−	0.688626i	$-0.758214\pi$
$787$	−40.6841	−1.45023	−0.725117	+	0.688626i	$0.758214\pi$
$788$	−7.57442	−0.269828
$789$	−18.1854	−0.647417
$790$	−45.0117	−1.60144
$791$	52.2603	1.85816
$792$	−16.0706	−0.571044
$793$	−11.2176	−0.398350
$794$	−31.0724	−1.10272
$795$	30.7660	1.09116
$796$	−2.51198	−0.0890349
$797$	41.5622	1.47221	0.736104	−	0.676869i	$-0.236663\pi$
$797$	41.5622	1.47221	0.736104	+	0.676869i	$0.236663\pi$
$798$	−105.319	−3.72824
$799$	−18.2533	−0.645755
$800$	−0.156027	−0.00551640
$801$	2.00963	0.0710068
$802$	45.0717	1.59154
$803$	14.9984	0.529284
$804$	2.27907	0.0803767
$805$	−10.4179	−0.367183
$806$	10.3144	0.363308
$807$	13.3258	0.469089
$808$	38.7824	1.36436
$809$	−21.3693	−0.751303	−0.375652	−	0.926761i	$-0.622581\pi$
$809$	−21.3693	−0.751303	−0.375652	+	0.926761i	$0.622581\pi$
$810$	32.3954	1.13826
$811$	−18.4698	−0.648563	−0.324281	−	0.945961i	$-0.605122\pi$
$811$	−18.4698	−0.648563	−0.324281	+	0.945961i	$0.605122\pi$
$812$	3.63297	0.127492
$813$	11.5165	0.403901
$814$	4.70551	0.164928
$815$	50.9491	1.78467
$816$	46.1720	1.61634
$817$	−59.3474	−2.07630
$818$	0.661553	0.0231306
$819$	8.57993	0.299807
$820$	−2.97769	−0.103986
$821$	27.3574	0.954781	0.477390	−	0.878691i	$-0.341583\pi$
$821$	27.3574	0.954781	0.477390	+	0.878691i	$0.341583\pi$
$822$	60.0119	2.09315
$823$	47.2891	1.64839	0.824197	−	0.566303i	$-0.191627\pi$
$823$	47.2891	1.64839	0.824197	+	0.566303i	$0.191627\pi$
$824$	36.8853	1.28496
$825$	0.532836	0.0185510
$826$	4.59004	0.159708
$827$	−37.5519	−1.30581	−0.652903	−	0.757442i	$-0.726449\pi$
$827$	−37.5519	−1.30581	−0.652903	+	0.757442i	$0.726449\pi$
$828$	−0.615496	−0.0213900
$829$	13.0682	0.453878	0.226939	−	0.973909i	$-0.427128\pi$
$829$	13.0682	0.453878	0.226939	+	0.973909i	$0.427128\pi$
$830$	19.6367	0.681598
$831$	10.9011	0.378154
$832$	−8.84995	−0.306817
$833$	93.1395	3.22709
$834$	−36.2385	−1.25484
$835$	−23.1660	−0.801693
$836$	7.62637	0.263763
$837$	20.1142	0.695250
$838$	−5.05723	−0.174699
$839$	17.0069	0.587144	0.293572	−	0.955937i	$-0.405156\pi$
$839$	17.0069	0.587144	0.293572	+	0.955937i	$0.405156\pi$
$840$	69.1449	2.38573
$841$	−23.3720	−0.805932
$842$	−22.3021	−0.768581
$843$	16.1834	0.557385
$844$	−3.15240	−0.108510
$845$	2.25480	0.0775676
$846$	6.74467	0.231887
$847$	12.6711	0.435386
$848$	19.9807	0.686141
$849$	28.9363	0.993092
$850$	−0.705532	−0.0241996
$851$	1.26769	0.0434557
$852$	−1.62719	−0.0557467
$853$	−12.1131	−0.414743	−0.207371	−	0.978262i	$-0.566491\pi$
$853$	−12.1131	−0.414743	−0.207371	+	0.978262i	$0.566491\pi$
$854$	66.9488	2.29094
$855$	33.5274	1.14661
$856$	20.9058	0.714546
$857$	−28.3077	−0.966973	−0.483486	−	0.875352i	$-0.660630\pi$
$857$	−28.3077	−0.966973	−0.483486	+	0.875352i	$0.660630\pi$
$858$	8.18048	0.279277
$859$	50.4601	1.72168	0.860839	−	0.508877i	$-0.169939\pi$
$859$	50.4601	1.72168	0.860839	+	0.508877i	$0.169939\pi$
$860$	5.53916	0.188884
$861$	40.5708	1.38265
$862$	42.3174	1.44134
$863$	24.1646	0.822574	0.411287	−	0.911506i	$-0.365079\pi$
$863$	24.1646	0.822574	0.411287	+	0.911506i	$0.365079\pi$
$864$	−4.67140	−0.158924
$865$	25.5700	0.869405
$866$	−11.9030	−0.404479
$867$	−55.4115	−1.88187
$868$	12.2281	0.415048
$869$	−44.4091	−1.50647
$870$	15.2278	0.516272
$871$	−3.12004	−0.105719
$872$	−23.7710	−0.804987
$873$	−10.7353	−0.363333
$874$	−10.3431	−0.349860
$875$	51.2130	1.73132
$876$	−3.81258	−0.128815
$877$	45.8917	1.54965	0.774827	−	0.632174i	$-0.217837\pi$
$877$	45.8917	1.54965	0.774827	+	0.632174i	$0.217837\pi$
$878$	−15.8286	−0.534188
$879$	−11.6917	−0.394352
$880$	20.9106	0.704895
$881$	−36.0320	−1.21395	−0.606975	−	0.794721i	$-0.707617\pi$
$881$	−36.0320	−1.21395	−0.606975	+	0.794721i	$0.707617\pi$
$882$	−34.4154	−1.15883
$883$	−14.1619	−0.476586	−0.238293	−	0.971193i	$-0.576588\pi$
$883$	−14.1619	−0.476586	−0.238293	+	0.971193i	$0.576588\pi$
$884$	2.15167	0.0723685
$885$	−3.82179	−0.128468
$886$	18.2857	0.614320
$887$	22.9705	0.771273	0.385636	−	0.922651i	$-0.373982\pi$
$887$	22.9705	0.771273	0.385636	+	0.922651i	$0.373982\pi$
$888$	−8.41378	−0.282348
$889$	−46.6447	−1.56441
$890$	−3.15198	−0.105655
$891$	31.9616	1.07076
$892$	3.53851	0.118478
$893$	−22.5143	−0.753412
$894$	−34.2377	−1.14508
$895$	26.0395	0.870403
$896$	35.6817	1.19204
$897$	2.20386	0.0735847
$898$	15.1441	0.505366
$899$	18.9430	0.631784
$900$	−0.0517857	−0.00172619
$901$	−40.1921	−1.33899
$902$	14.7895	0.492435
$903$	−75.4706	−2.51151
$904$	−34.0640	−1.13295
$905$	16.3283	0.542771
$906$	−9.06030	−0.301008
$907$	−27.7732	−0.922193	−0.461097	−	0.887350i	$-0.652544\pi$
$907$	−27.7732	−0.922193	−0.461097	+	0.887350i	$0.652544\pi$
$908$	−0.546398	−0.0181328
$909$	23.9139	0.793175
$910$	−13.4571	−0.446098
$911$	25.4557	0.843384	0.421692	−	0.906739i	$-0.361436\pi$
$911$	25.4557	0.843384	0.421692	+	0.906739i	$0.361436\pi$
$912$	56.9503	1.88581
$913$	19.3738	0.641178
$914$	35.0147	1.15818
$915$	−55.7434	−1.84282
$916$	2.28939	0.0756435
$917$	−11.8801	−0.392314
$918$	−21.1234	−0.697175
$919$	42.6157	1.40576	0.702881	−	0.711307i	$-0.251896\pi$
$919$	42.6157	1.40576	0.702881	+	0.711307i	$0.251896\pi$
$920$	6.79054	0.223877
$921$	−7.87118	−0.259364
$922$	−26.2066	−0.863068
$923$	2.22762	0.0733231
$924$	9.69827	0.319050
$925$	0.106659	0.00350691
$926$	23.5228	0.773006
$927$	22.7441	0.747016
$928$	−4.39939	−0.144417
$929$	52.0648	1.70819	0.854095	−	0.520117i	$-0.174112\pi$
$929$	52.0648	1.70819	0.854095	+	0.520117i	$0.174112\pi$
$930$	51.2549	1.68072
$931$	114.882	3.76510
$932$	8.27627	0.271098
$933$	20.9933	0.687290
$934$	−10.8534	−0.355134
$935$	−42.0626	−1.37559
$936$	−5.59252	−0.182797
$937$	34.7061	1.13380	0.566899	−	0.823787i	$-0.308143\pi$
$937$	34.7061	1.13380	0.566899	+	0.823787i	$0.308143\pi$
$938$	18.6210	0.607997
$939$	−38.1298	−1.24432
$940$	2.10136	0.0685389
$941$	15.4385	0.503281	0.251641	−	0.967821i	$-0.419030\pi$
$941$	15.4385	0.503281	0.251641	+	0.967821i	$0.419030\pi$
$942$	59.1065	1.92579
$943$	3.98435	0.129748
$944$	−2.48203	−0.0807832
$945$	−26.2429	−0.853680
$946$	−27.5117	−0.894481
$947$	46.6751	1.51674	0.758368	−	0.651827i	$-0.225997\pi$
$947$	46.6751	1.51674	0.758368	+	0.651827i	$0.225997\pi$
$948$	11.2887	0.366640
$949$	5.21941	0.169429
$950$	−0.870230	−0.0282340
$951$	−10.5501	−0.342111
$952$	−90.3296	−2.92760
$953$	−21.7759	−0.705390	−0.352695	−	0.935738i	$-0.614735\pi$
$953$	−21.7759	−0.705390	−0.352695	+	0.935738i	$0.614735\pi$
$954$	14.8512	0.480824
$955$	14.9020	0.482216
$956$	2.56871	0.0830780
$957$	15.0240	0.485656
$958$	−45.6022	−1.47334
$959$	−97.3991	−3.14518
$960$	−43.9778	−1.41938
$961$	32.7596	1.05676
$962$	1.63750	0.0527951
$963$	12.8909	0.415403
$964$	7.36774	0.237299
$965$	−15.0220	−0.483576
$966$	−13.1530	−0.423192
$967$	−2.21202	−0.0711337	−0.0355669	−	0.999367i	$-0.511324\pi$
$967$	−2.21202	−0.0711337	−0.0355669	+	0.999367i	$0.511324\pi$
$968$	−8.25923	−0.265462
$969$	−114.558	−3.68014
$970$	16.8376	0.540621
$971$	1.61738	0.0519042	0.0259521	−	0.999663i	$-0.491738\pi$
$971$	1.61738	0.0519042	0.0259521	+	0.999663i	$0.491738\pi$
$972$	−5.61985	−0.180257
$973$	58.8150	1.88552
$974$	−6.18983	−0.198335
$975$	0.185425	0.00593836
$976$	−36.2021	−1.15880
$977$	−3.08743	−0.0987757	−0.0493878	−	0.998780i	$-0.515727\pi$
$977$	−3.08743	−0.0987757	−0.0493878	+	0.998780i	$0.515727\pi$
$978$	64.3253	2.05690
$979$	−3.10978	−0.0993889
$980$	−10.7224	−0.342516
$981$	−14.6576	−0.467981
$982$	13.8031	0.440475
$983$	−50.2341	−1.60222	−0.801109	−	0.598518i	$-0.795756\pi$
$983$	−50.2341	−1.60222	−0.801109	+	0.598518i	$0.795756\pi$
$984$	−26.4446	−0.843024
$985$	51.5282	1.64182
$986$	−19.8934	−0.633534
$987$	−28.6309	−0.911331
$988$	2.65395	0.0844335
$989$	−7.41177	−0.235681
$990$	15.5423	0.493967
$991$	46.3446	1.47218	0.736092	−	0.676881i	$-0.236669\pi$
$991$	46.3446	1.47218	0.736092	+	0.676881i	$0.236669\pi$
$992$	−14.8078	−0.470147
$993$	18.9152	0.600257
$994$	−13.2949	−0.421687
$995$	17.0888	0.541752
$996$	−4.92478	−0.156048
$997$	−24.3039	−0.769711	−0.384856	−	0.922977i	$-0.625749\pi$
$997$	−24.3039	−0.769711	−0.384856	+	0.922977i	$0.625749\pi$
$998$	−28.8184	−0.912230
$999$	3.19332	0.101032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.a.g.1.4	✓	10
3.2	odd	2		2691.2.a.bc.1.7		10
4.3	odd	2		4784.2.a.bh.1.9		10
5.4	even	2		7475.2.a.w.1.7		10
13.12	even	2		3887.2.a.p.1.7		10
23.22	odd	2		6877.2.a.o.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.a.g.1.4	✓	10	1.1	even	1	trivial
2691.2.a.bc.1.7		10	3.2	odd	2
3887.2.a.p.1.7		10	13.12	even	2
4784.2.a.bh.1.9		10	4.3	odd	2
6877.2.a.o.1.4		10	23.22	odd	2
7475.2.a.w.1.7		10	5.4	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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29172 q^{2} -2.20386 q^{3} -0.331447 q^{4} +2.25480 q^{5} +2.84678 q^{6} -4.62032 q^{7} +3.01159 q^{8} +1.85700 q^{9} +O(q^{10})\)	\(q-1.29172 q^{2} -2.20386 q^{3} -0.331447 q^{4} +2.25480 q^{5} +2.84678 q^{6} -4.62032 q^{7} +3.01159 q^{8} +1.85700 q^{9} -2.91259 q^{10} -2.87359 q^{11} +0.730462 q^{12} -1.00000 q^{13} +5.96818 q^{14} -4.96927 q^{15} -3.22725 q^{16} +6.49176 q^{17} -2.39873 q^{18} +8.00718 q^{19} -0.747347 q^{20} +10.1825 q^{21} +3.71189 q^{22} +1.00000 q^{23} -6.63712 q^{24} +0.0841365 q^{25} +1.29172 q^{26} +2.51901 q^{27} +1.53139 q^{28} +2.37233 q^{29} +6.41893 q^{30} +7.98496 q^{31} -1.85446 q^{32} +6.33299 q^{33} -8.38557 q^{34} -10.4179 q^{35} -0.615496 q^{36} +1.26769 q^{37} -10.3431 q^{38} +2.20386 q^{39} +6.79054 q^{40} +3.98435 q^{41} -13.1530 q^{42} -7.41177 q^{43} +0.952442 q^{44} +4.18717 q^{45} -1.29172 q^{46} -2.81176 q^{47} +7.11241 q^{48} +14.3473 q^{49} -0.108681 q^{50} -14.3069 q^{51} +0.331447 q^{52} -6.19126 q^{53} -3.25387 q^{54} -6.47938 q^{55} -13.9145 q^{56} -17.6467 q^{57} -3.06440 q^{58} +0.769085 q^{59} +1.64705 q^{60} +11.2176 q^{61} -10.3144 q^{62} -8.57993 q^{63} +8.84995 q^{64} -2.25480 q^{65} -8.18048 q^{66} +3.12004 q^{67} -2.15167 q^{68} -2.20386 q^{69} +13.4571 q^{70} -2.22762 q^{71} +5.59252 q^{72} -5.21941 q^{73} -1.63750 q^{74} -0.185425 q^{75} -2.65395 q^{76} +13.2769 q^{77} -2.84678 q^{78} +15.4542 q^{79} -7.27681 q^{80} -11.1226 q^{81} -5.14669 q^{82} -6.74200 q^{83} -3.37497 q^{84} +14.6376 q^{85} +9.57397 q^{86} -5.22829 q^{87} -8.65407 q^{88} +1.08219 q^{89} -5.40867 q^{90} +4.62032 q^{91} -0.331447 q^{92} -17.5977 q^{93} +3.63203 q^{94} +18.0546 q^{95} +4.08696 q^{96} -5.78097 q^{97} -18.5328 q^{98} -5.33625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 3 q^{3} + 19 q^{4} + 3 q^{5} + q^{6} - 2 q^{7} + 17 q^{9}+O(q^{10}) \) 10 * q + q^2 + 3 * q^3 + 19 * q^4 + 3 * q^5 + q^6 - 2 * q^7 + 17 * q^9	\( 10 q + q^{2} + 3 q^{3} + 19 q^{4} + 3 q^{5} + q^{6} - 2 q^{7} + 17 q^{9} + 6 q^{10} + 3 q^{11} + 10 q^{12} - 10 q^{13} - 15 q^{14} + 2 q^{15} + 25 q^{16} - 3 q^{17} + q^{18} + 2 q^{19} - 19 q^{20} + 21 q^{21} + 13 q^{22} + 10 q^{23} - 35 q^{24} + 33 q^{25} - q^{26} + 6 q^{27} - 19 q^{28} + 17 q^{29} - 47 q^{30} + 5 q^{31} - 9 q^{32} - 23 q^{33} + 23 q^{34} + 3 q^{35} + 48 q^{36} + 16 q^{37} + 5 q^{38} - 3 q^{39} + 13 q^{40} - 16 q^{41} - 65 q^{42} - 9 q^{43} + 18 q^{44} + 32 q^{45} + q^{46} - 11 q^{47} + 37 q^{48} + 40 q^{49} - 30 q^{50} - 31 q^{51} - 19 q^{52} + 8 q^{53} - 73 q^{54} - 14 q^{55} - 54 q^{56} - 35 q^{57} + 17 q^{58} + 2 q^{59} - 37 q^{60} + 48 q^{61} - 19 q^{62} - 15 q^{63} + 64 q^{64} - 3 q^{65} - 84 q^{66} - 6 q^{67} - 62 q^{68} + 3 q^{69} - 44 q^{70} + 24 q^{71} - 89 q^{72} - 33 q^{73} - 28 q^{74} - 22 q^{75} - 53 q^{76} + 15 q^{77} - q^{78} + 17 q^{79} - 94 q^{80} + 30 q^{81} + 35 q^{82} - 21 q^{83} + 92 q^{84} + 58 q^{85} - 7 q^{86} + 23 q^{87} + 9 q^{88} - 16 q^{89} + 67 q^{90} + 2 q^{91} + 19 q^{92} + 15 q^{93} + 12 q^{94} - 27 q^{95} - 22 q^{96} - 40 q^{97} - 34 q^{98} - 17 q^{99}+O(q^{100}) \) 10 * q + q^2 + 3 * q^3 + 19 * q^4 + 3 * q^5 + q^6 - 2 * q^7 + 17 * q^9 + 6 * q^10 + 3 * q^11 + 10 * q^12 - 10 * q^13 - 15 * q^14 + 2 * q^15 + 25 * q^16 - 3 * q^17 + q^18 + 2 * q^19 - 19 * q^20 + 21 * q^21 + 13 * q^22 + 10 * q^23 - 35 * q^24 + 33 * q^25 - q^26 + 6 * q^27 - 19 * q^28 + 17 * q^29 - 47 * q^30 + 5 * q^31 - 9 * q^32 - 23 * q^33 + 23 * q^34 + 3 * q^35 + 48 * q^36 + 16 * q^37 + 5 * q^38 - 3 * q^39 + 13 * q^40 - 16 * q^41 - 65 * q^42 - 9 * q^43 + 18 * q^44 + 32 * q^45 + q^46 - 11 * q^47 + 37 * q^48 + 40 * q^49 - 30 * q^50 - 31 * q^51 - 19 * q^52 + 8 * q^53 - 73 * q^54 - 14 * q^55 - 54 * q^56 - 35 * q^57 + 17 * q^58 + 2 * q^59 - 37 * q^60 + 48 * q^61 - 19 * q^62 - 15 * q^63 + 64 * q^64 - 3 * q^65 - 84 * q^66 - 6 * q^67 - 62 * q^68 + 3 * q^69 - 44 * q^70 + 24 * q^71 - 89 * q^72 - 33 * q^73 - 28 * q^74 - 22 * q^75 - 53 * q^76 + 15 * q^77 - q^78 + 17 * q^79 - 94 * q^80 + 30 * q^81 + 35 * q^82 - 21 * q^83 + 92 * q^84 + 58 * q^85 - 7 * q^86 + 23 * q^87 + 9 * q^88 - 16 * q^89 + 67 * q^90 + 2 * q^91 + 19 * q^92 + 15 * q^93 + 12 * q^94 - 27 * q^95 - 22 * q^96 - 40 * q^97 - 34 * q^98 - 17 * q^99

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