LMFDB - Embedded newform 649.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [649,2,Mod(1,649)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(649, 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("649.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 649 = 11 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	649.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:	$5.18229109118$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 74 x^{14} + 224 x^{13} - 719 x^{12} - 1025 x^{11} + 3506 x^{10} + \cdots + 56 $ x^17 - 3x^16 - 24x^15 + 74x^14 + 224x^13 - 719x^12 - 1025x^11 + 3506x^10 + 2357x^9 - 9053x^8 - 2358x^7 + 12050x^6 + 122x^5 - 7537x^4 + 1399x^3 + 1682x^2 - 656x + 56
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			1.14
Root			$2.26840$ of defining polynomial
Character	$\chi$	$=$	649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26840 q^{2} +1.03586 q^{3} +3.14565 q^{4} +2.26915 q^{5} +2.34976 q^{6} -2.07542 q^{7} +2.59880 q^{8} -1.92699 q^{9} +O(q^{10})$	\(q+2.26840 q^{2} +1.03586 q^{3} +3.14565 q^{4} +2.26915 q^{5} +2.34976 q^{6} -2.07542 q^{7} +2.59880 q^{8} -1.92699 q^{9} +5.14734 q^{10} +1.00000 q^{11} +3.25847 q^{12} +2.29894 q^{13} -4.70789 q^{14} +2.35053 q^{15} -0.396171 q^{16} +4.60862 q^{17} -4.37118 q^{18} -4.12915 q^{19} +7.13794 q^{20} -2.14985 q^{21} +2.26840 q^{22} +3.08800 q^{23} +2.69201 q^{24} +0.149019 q^{25} +5.21492 q^{26} -5.10369 q^{27} -6.52856 q^{28} -10.0523 q^{29} +5.33194 q^{30} +5.47519 q^{31} -6.09628 q^{32} +1.03586 q^{33} +10.4542 q^{34} -4.70943 q^{35} -6.06163 q^{36} +2.25726 q^{37} -9.36659 q^{38} +2.38139 q^{39} +5.89706 q^{40} -5.24297 q^{41} -4.87674 q^{42} +3.86613 q^{43} +3.14565 q^{44} -4.37261 q^{45} +7.00483 q^{46} +5.28226 q^{47} -0.410379 q^{48} -2.69263 q^{49} +0.338036 q^{50} +4.77391 q^{51} +7.23167 q^{52} -13.3492 q^{53} -11.5772 q^{54} +2.26915 q^{55} -5.39361 q^{56} -4.27724 q^{57} -22.8026 q^{58} -1.00000 q^{59} +7.39394 q^{60} -9.23162 q^{61} +12.4199 q^{62} +3.99931 q^{63} -13.0365 q^{64} +5.21663 q^{65} +2.34976 q^{66} +4.29418 q^{67} +14.4971 q^{68} +3.19875 q^{69} -10.6829 q^{70} +8.42036 q^{71} -5.00786 q^{72} +11.7483 q^{73} +5.12038 q^{74} +0.154364 q^{75} -12.9889 q^{76} -2.07542 q^{77} +5.40195 q^{78} -6.09227 q^{79} -0.898968 q^{80} +0.494231 q^{81} -11.8932 q^{82} +11.8769 q^{83} -6.76270 q^{84} +10.4576 q^{85} +8.76995 q^{86} -10.4128 q^{87} +2.59880 q^{88} +4.26327 q^{89} -9.91884 q^{90} -4.77127 q^{91} +9.71377 q^{92} +5.67155 q^{93} +11.9823 q^{94} -9.36965 q^{95} -6.31492 q^{96} +15.4782 q^{97} -6.10796 q^{98} -1.92699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9} - 4 q^{10} + 17 q^{11} + 2 q^{12} - 11 q^{13} + 16 q^{14} + 20 q^{15} + 39 q^{16} + 6 q^{17} - 15 q^{18} - 4 q^{19} - q^{20} - 11 q^{21} + 3 q^{22} + 36 q^{23} + 4 q^{24} + 22 q^{25} + 28 q^{26} + 13 q^{27} + 13 q^{29} - 34 q^{30} + 6 q^{31} + 16 q^{32} + 4 q^{33} - 5 q^{34} + 16 q^{35} + 34 q^{36} + 14 q^{37} + 12 q^{38} + 41 q^{39} - 54 q^{40} + 6 q^{41} - 57 q^{42} - 11 q^{43} + 23 q^{44} + 5 q^{45} + q^{46} + 25 q^{47} + 14 q^{48} + 23 q^{49} + 15 q^{50} - 4 q^{51} - 64 q^{52} - 2 q^{54} + 7 q^{55} + 43 q^{56} - 9 q^{57} - 21 q^{58} - 17 q^{59} + 15 q^{60} - 38 q^{61} - 21 q^{62} + 2 q^{63} + 43 q^{64} - 13 q^{65} - 5 q^{66} + q^{67} + 34 q^{68} - 13 q^{69} + 5 q^{70} + 89 q^{71} + 15 q^{72} - 16 q^{73} + 17 q^{74} + 2 q^{75} - q^{76} + 4 q^{77} - 58 q^{78} + 34 q^{79} - 64 q^{80} + 29 q^{81} - 17 q^{82} - 12 q^{83} - 111 q^{84} - 15 q^{85} - 21 q^{86} - 4 q^{87} + 9 q^{88} - 5 q^{89} + 7 q^{90} - 12 q^{91} + 80 q^{92} + 32 q^{93} - 25 q^{94} + 103 q^{95} - 48 q^{96} - 15 q^{97} + 8 q^{98} + 29 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9 - 4 * q^10 + 17 * q^11 + 2 * q^12 - 11 * q^13 + 16 * q^14 + 20 * q^15 + 39 * q^16 + 6 * q^17 - 15 * q^18 - 4 * q^19 - q^20 - 11 * q^21 + 3 * q^22 + 36 * q^23 + 4 * q^24 + 22 * q^25 + 28 * q^26 + 13 * q^27 + 13 * q^29 - 34 * q^30 + 6 * q^31 + 16 * q^32 + 4 * q^33 - 5 * q^34 + 16 * q^35 + 34 * q^36 + 14 * q^37 + 12 * q^38 + 41 * q^39 - 54 * q^40 + 6 * q^41 - 57 * q^42 - 11 * q^43 + 23 * q^44 + 5 * q^45 + q^46 + 25 * q^47 + 14 * q^48 + 23 * q^49 + 15 * q^50 - 4 * q^51 - 64 * q^52 - 2 * q^54 + 7 * q^55 + 43 * q^56 - 9 * q^57 - 21 * q^58 - 17 * q^59 + 15 * q^60 - 38 * q^61 - 21 * q^62 + 2 * q^63 + 43 * q^64 - 13 * q^65 - 5 * q^66 + q^67 + 34 * q^68 - 13 * q^69 + 5 * q^70 + 89 * q^71 + 15 * q^72 - 16 * q^73 + 17 * q^74 + 2 * q^75 - q^76 + 4 * q^77 - 58 * q^78 + 34 * q^79 - 64 * q^80 + 29 * q^81 - 17 * q^82 - 12 * q^83 - 111 * q^84 - 15 * q^85 - 21 * q^86 - 4 * q^87 + 9 * q^88 - 5 * q^89 + 7 * q^90 - 12 * q^91 + 80 * q^92 + 32 * q^93 - 25 * q^94 + 103 * q^95 - 48 * q^96 - 15 * q^97 + 8 * q^98 + 29 * 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 $

$2$	2.26840	1.60400	0.802002	−	0.597322i	$-0.203768\pi$
$2$	2.26840	1.60400	0.802002	+	0.597322i	$0.203768\pi$
$3$	1.03586	0.598056	0.299028	−	0.954244i	$-0.403338\pi$
$3$	1.03586	0.598056	0.299028	+	0.954244i	$0.403338\pi$
$4$	3.14565	1.57283
$5$	2.26915	1.01479	0.507396	−	0.861713i	$-0.330608\pi$
$5$	2.26915	1.01479	0.507396	+	0.861713i	$0.330608\pi$
$6$	2.34976	0.959284
$7$	−2.07542	−0.784436	−0.392218	−	0.919872i	$-0.628292\pi$
$7$	−2.07542	−0.784436	−0.392218	+	0.919872i	$0.628292\pi$
$8$	2.59880	0.918816
$9$	−1.92699	−0.642329
$10$	5.14734	1.62773
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.25847	0.940639
$13$	2.29894	0.637611	0.318806	−	0.947820i	$-0.396718\pi$
$13$	2.29894	0.637611	0.318806	+	0.947820i	$0.396718\pi$
$14$	−4.70789	−1.25824
$15$	2.35053	0.606903
$16$	−0.396171	−0.0990426
$17$	4.60862	1.11776	0.558878	−	0.829250i	$-0.311232\pi$
$17$	4.60862	1.11776	0.558878	+	0.829250i	$0.311232\pi$
$18$	−4.37118	−1.03030
$19$	−4.12915	−0.947293	−0.473646	−	0.880715i	$-0.657063\pi$
$19$	−4.12915	−0.947293	−0.473646	+	0.880715i	$0.657063\pi$
$20$	7.13794	1.59609
$21$	−2.14985	−0.469137
$22$	2.26840	0.483625
$23$	3.08800	0.643892	0.321946	−	0.946758i	$-0.395663\pi$
$23$	3.08800	0.643892	0.321946	+	0.946758i	$0.395663\pi$
$24$	2.69201	0.549504
$25$	0.149019	0.0298038
$26$	5.21492	1.02273
$27$	−5.10369	−0.982205
$28$	−6.52856	−1.23378
$29$	−10.0523	−1.86666	−0.933329	−	0.359023i	$-0.883110\pi$
$29$	−10.0523	−1.86666	−0.933329	+	0.359023i	$0.883110\pi$
$30$	5.33194	0.973475
$31$	5.47519	0.983372	0.491686	−	0.870772i	$-0.336381\pi$
$31$	5.47519	0.983372	0.491686	+	0.870772i	$0.336381\pi$
$32$	−6.09628	−1.07768
$33$	1.03586	0.180321
$34$	10.4542	1.79288
$35$	−4.70943	−0.796039
$36$	−6.06163	−1.01027
$37$	2.25726	0.371092	0.185546	−	0.982636i	$-0.440595\pi$
$37$	2.25726	0.371092	0.185546	+	0.982636i	$0.440595\pi$
$38$	−9.36659	−1.51946
$39$	2.38139	0.381328
$40$	5.89706	0.932408
$41$	−5.24297	−0.818814	−0.409407	−	0.912352i	$-0.634264\pi$
$41$	−5.24297	−0.818814	−0.409407	+	0.912352i	$0.634264\pi$
$42$	−4.87674	−0.752497
$43$	3.86613	0.589580	0.294790	−	0.955562i	$-0.404750\pi$
$43$	3.86613	0.589580	0.294790	+	0.955562i	$0.404750\pi$
$44$	3.14565	0.474225
$45$	−4.37261	−0.651830
$46$	7.00483	1.03281
$47$	5.28226	0.770497	0.385248	−	0.922813i	$-0.374116\pi$
$47$	5.28226	0.770497	0.385248	+	0.922813i	$0.374116\pi$
$48$	−0.410379	−0.0592331
$49$	−2.69263	−0.384661
$50$	0.338036	0.0478055
$51$	4.77391	0.668481
$52$	7.23167	1.00285
$53$	−13.3492	−1.83366	−0.916829	−	0.399280i	$-0.869260\pi$
$53$	−13.3492	−1.83366	−0.916829	+	0.399280i	$0.869260\pi$
$54$	−11.5772	−1.57546
$55$	2.26915	0.305971
$56$	−5.39361	−0.720752
$57$	−4.27724	−0.566535
$58$	−22.8026	−2.99413
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	7.39394	0.954554
$61$	−9.23162	−1.18199	−0.590994	−	0.806676i	$-0.701264\pi$
$61$	−9.23162	−1.18199	−0.590994	+	0.806676i	$0.701264\pi$
$62$	12.4199	1.57733
$63$	3.99931	0.503865
$64$	−13.0365	−1.62956
$65$	5.21663	0.647043
$66$	2.34976	0.289235
$67$	4.29418	0.524618	0.262309	−	0.964984i	$-0.415516\pi$
$67$	4.29418	0.524618	0.262309	+	0.964984i	$0.415516\pi$
$68$	14.4971	1.75804
$69$	3.19875	0.385084
$70$	−10.6829	−1.27685
$71$	8.42036	0.999313	0.499657	−	0.866224i	$-0.333460\pi$
$71$	8.42036	0.999313	0.499657	+	0.866224i	$0.333460\pi$
$72$	−5.00786	−0.590182
$73$	11.7483	1.37503	0.687516	−	0.726169i	$-0.258701\pi$
$73$	11.7483	1.37503	0.687516	+	0.726169i	$0.258701\pi$
$74$	5.12038	0.595232
$75$	0.154364	0.0178244
$76$	−12.9889	−1.48993
$77$	−2.07542	−0.236516
$78$	5.40195	0.611651
$79$	−6.09227	−0.685434	−0.342717	−	0.939439i	$-0.611347\pi$
$79$	−6.09227	−0.685434	−0.342717	+	0.939439i	$0.611347\pi$
$80$	−0.898968	−0.100508
$81$	0.494231	0.0549145
$82$	−11.8932	−1.31338
$83$	11.8769	1.30366	0.651831	−	0.758364i	$-0.274001\pi$
$83$	11.8769	1.30366	0.651831	+	0.758364i	$0.274001\pi$
$84$	−6.76270	−0.737871
$85$	10.4576	1.13429
$86$	8.76995	0.945688
$87$	−10.4128	−1.11637
$88$	2.59880	0.277033
$89$	4.26327	0.451906	0.225953	−	0.974138i	$-0.427450\pi$
$89$	4.26327	0.451906	0.225953	+	0.974138i	$0.427450\pi$
$90$	−9.91884	−1.04554
$91$	−4.77127	−0.500165
$92$	9.71377	1.01273
$93$	5.67155	0.588112
$94$	11.9823	1.23588
$95$	−9.36965	−0.961306
$96$	−6.31492	−0.644514
$97$	15.4782	1.57157	0.785784	−	0.618500i	$-0.212260\pi$
$97$	15.4782	1.57157	0.785784	+	0.618500i	$0.212260\pi$
$98$	−6.10796	−0.616997
$99$	−1.92699	−0.193669
$100$	0.468763	0.0468763
$101$	−0.604749	−0.0601748	−0.0300874	−	0.999547i	$-0.509579\pi$
$101$	−0.604749	−0.0601748	−0.0300874	+	0.999547i	$0.509579\pi$
$102$	10.8291	1.07225
$103$	15.1711	1.49485	0.747427	−	0.664344i	$-0.231289\pi$
$103$	15.1711	1.49485	0.747427	+	0.664344i	$0.231289\pi$
$104$	5.97450	0.585848
$105$	−4.87833	−0.476076
$106$	−30.2814	−2.94119
$107$	7.13954	0.690205	0.345103	−	0.938565i	$-0.387844\pi$
$107$	7.13954	0.690205	0.345103	+	0.938565i	$0.387844\pi$
$108$	−16.0544	−1.54484
$109$	4.53169	0.434057	0.217028	−	0.976165i	$-0.430364\pi$
$109$	4.53169	0.434057	0.217028	+	0.976165i	$0.430364\pi$
$110$	5.14734	0.490779
$111$	2.33822	0.221934
$112$	0.822221	0.0776926
$113$	−14.7674	−1.38920	−0.694598	−	0.719398i	$-0.744418\pi$
$113$	−14.7674	−1.38920	−0.694598	+	0.719398i	$0.744418\pi$
$114$	−9.70251	−0.908723
$115$	7.00712	0.653417
$116$	−31.6209	−2.93593
$117$	−4.43003	−0.409556
$118$	−2.26840	−0.208823
$119$	−9.56484	−0.876807
$120$	6.10856	0.557632
$121$	1.00000	0.0909091
$122$	−20.9410	−1.89591
$123$	−5.43100	−0.489697
$124$	17.2230	1.54667
$125$	−11.0076	−0.984548
$126$	9.07204	0.808202
$127$	−7.53494	−0.668618	−0.334309	−	0.942464i	$-0.608503\pi$
$127$	−7.53494	−0.668618	−0.334309	+	0.942464i	$0.608503\pi$
$128$	−17.3794	−1.53614
$129$	4.00479	0.352602
$130$	11.8334	1.03786
$131$	−8.87467	−0.775384	−0.387692	−	0.921789i	$-0.626728\pi$
$131$	−8.87467	−0.775384	−0.387692	+	0.921789i	$0.626728\pi$
$132$	3.25847	0.283613
$133$	8.56973	0.743090
$134$	9.74094	0.841489
$135$	−11.5810	−0.996734
$136$	11.9769	1.02701
$137$	15.2861	1.30598	0.652990	−	0.757367i	$-0.273514\pi$
$137$	15.2861	1.30598	0.652990	+	0.757367i	$0.273514\pi$
$138$	7.25605	0.617676
$139$	−19.5142	−1.65518	−0.827588	−	0.561337i	$-0.810287\pi$
$139$	−19.5142	−1.65518	−0.827588	+	0.561337i	$0.810287\pi$
$140$	−14.8142	−1.25203
$141$	5.47170	0.460801
$142$	19.1008	1.60290
$143$	2.29894	0.192247
$144$	0.763415	0.0636179
$145$	−22.8100	−1.89427
$146$	26.6498	2.20556
$147$	−2.78919	−0.230049
$148$	7.10056	0.583663
$149$	−4.15739	−0.340587	−0.170293	−	0.985393i	$-0.554472\pi$
$149$	−4.15739	−0.340587	−0.170293	+	0.985393i	$0.554472\pi$
$150$	0.350159	0.0285904
$151$	16.4153	1.33586	0.667929	−	0.744225i	$-0.267181\pi$
$151$	16.4153	1.33586	0.667929	+	0.744225i	$0.267181\pi$
$152$	−10.7309	−0.870388
$153$	−8.88075	−0.717966
$154$	−4.70789	−0.379373
$155$	12.4240	0.997919
$156$	7.49103	0.599762
$157$	−13.3918	−1.06878	−0.534392	−	0.845237i	$-0.679459\pi$
$157$	−13.3918	−1.06878	−0.534392	+	0.845237i	$0.679459\pi$
$158$	−13.8197	−1.09944
$159$	−13.8280	−1.09663
$160$	−13.8334	−1.09362
$161$	−6.40890	−0.505092
$162$	1.12111	0.0880831
$163$	6.94584	0.544040	0.272020	−	0.962292i	$-0.412308\pi$
$163$	6.94584	0.544040	0.272020	+	0.962292i	$0.412308\pi$
$164$	−16.4926	−1.28785
$165$	2.35053	0.182988
$166$	26.9417	2.09108
$167$	3.28042	0.253847	0.126923	−	0.991913i	$-0.459490\pi$
$167$	3.28042	0.253847	0.126923	+	0.991913i	$0.459490\pi$
$168$	−5.58705	−0.431050
$169$	−7.71487	−0.593452
$170$	23.7221	1.81940
$171$	7.95682	0.608473
$172$	12.1615	0.927306
$173$	−7.24350	−0.550713	−0.275357	−	0.961342i	$-0.588796\pi$
$173$	−7.24350	−0.550713	−0.275357	+	0.961342i	$0.588796\pi$
$174$	−23.6204	−1.79066
$175$	−0.309278	−0.0233792
$176$	−0.396171	−0.0298625
$177$	−1.03586	−0.0778603
$178$	9.67081	0.724858
$179$	18.5092	1.38344	0.691721	−	0.722165i	$-0.256853\pi$
$179$	18.5092	1.38344	0.691721	+	0.722165i	$0.256853\pi$
$180$	−13.7547	−1.02522
$181$	1.99782	0.148497	0.0742485	−	0.997240i	$-0.476344\pi$
$181$	1.99782	0.148497	0.0742485	+	0.997240i	$0.476344\pi$
$182$	−10.8232	−0.802267
$183$	−9.56271	−0.706896
$184$	8.02510	0.591619
$185$	5.12205	0.376581
$186$	12.8654	0.943334
$187$	4.60862	0.337016
$188$	16.6162	1.21186
$189$	10.5923	0.770477
$190$	−21.2541	−1.54194
$191$	−9.04909	−0.654769	−0.327385	−	0.944891i	$-0.606167\pi$
$191$	−9.04909	−0.654769	−0.327385	+	0.944891i	$0.606167\pi$
$192$	−13.5040	−0.974569
$193$	−2.45987	−0.177066	−0.0885328	−	0.996073i	$-0.528218\pi$
$193$	−2.45987	−0.177066	−0.0885328	+	0.996073i	$0.528218\pi$
$194$	35.1107	2.52080
$195$	5.40372	0.386968
$196$	−8.47007	−0.605005
$197$	11.3258	0.806929	0.403465	−	0.914995i	$-0.367806\pi$
$197$	11.3258	0.806929	0.403465	+	0.914995i	$0.367806\pi$
$198$	−4.37118	−0.310646
$199$	15.0247	1.06507	0.532536	−	0.846407i	$-0.321239\pi$
$199$	15.0247	1.06507	0.532536	+	0.846407i	$0.321239\pi$
$200$	0.387272	0.0273843
$201$	4.44819	0.313751
$202$	−1.37182	−0.0965206
$203$	20.8627	1.46427
$204$	15.0171	1.05140
$205$	−11.8971	−0.830926
$206$	34.4142	2.39775
$207$	−5.95053	−0.413590
$208$	−0.910773	−0.0631507
$209$	−4.12915	−0.285620
$210$	−11.0660	−0.763628
$211$	−13.2076	−0.909249	−0.454624	−	0.890683i	$-0.650226\pi$
$211$	−13.2076	−0.909249	−0.454624	+	0.890683i	$0.650226\pi$
$212$	−41.9921	−2.88403
$213$	8.72235	0.597646
$214$	16.1954	1.10709
$215$	8.77281	0.598301
$216$	−13.2635	−0.902466
$217$	−11.3633	−0.771392
$218$	10.2797	0.696228
$219$	12.1696	0.822347
$220$	7.13794	0.481240
$221$	10.5950	0.712694
$222$	5.30402	0.355982
$223$	22.9451	1.53652	0.768259	−	0.640139i	$-0.221123\pi$
$223$	22.9451	1.53652	0.768259	+	0.640139i	$0.221123\pi$
$224$	12.6524	0.845371
$225$	−0.287158	−0.0191439
$226$	−33.4983	−2.22828
$227$	−18.2469	−1.21109	−0.605545	−	0.795811i	$-0.707045\pi$
$227$	−18.2469	−1.21109	−0.605545	+	0.795811i	$0.707045\pi$
$228$	−13.4547	−0.891061
$229$	11.9211	0.787768	0.393884	−	0.919160i	$-0.371131\pi$
$229$	11.9211	0.787768	0.393884	+	0.919160i	$0.371131\pi$
$230$	15.8950	1.04808
$231$	−2.14985	−0.141450
$232$	−26.1239	−1.71512
$233$	−7.05818	−0.462397	−0.231198	−	0.972907i	$-0.574265\pi$
$233$	−7.05818	−0.462397	−0.231198	+	0.972907i	$0.574265\pi$
$234$	−10.0491	−0.656929
$235$	11.9862	0.781894
$236$	−3.14565	−0.204765
$237$	−6.31076	−0.409928
$238$	−21.6969	−1.40640
$239$	2.74671	0.177670	0.0888351	−	0.996046i	$-0.471686\pi$
$239$	2.74671	0.177670	0.0888351	+	0.996046i	$0.471686\pi$
$240$	−0.931209	−0.0601093
$241$	12.4992	0.805141	0.402571	−	0.915389i	$-0.368117\pi$
$241$	12.4992	0.805141	0.402571	+	0.915389i	$0.368117\pi$
$242$	2.26840	0.145818
$243$	15.8230	1.01505
$244$	−29.0395	−1.85906
$245$	−6.10996	−0.390351
$246$	−12.3197	−0.785475
$247$	−9.49268	−0.604005
$248$	14.2289	0.903539
$249$	12.3029	0.779664
$250$	−24.9696	−1.57922
$251$	9.02251	0.569496	0.284748	−	0.958602i	$-0.408090\pi$
$251$	9.02251	0.569496	0.284748	+	0.958602i	$0.408090\pi$
$252$	12.5804	0.792493
$253$	3.08800	0.194141
$254$	−17.0923	−1.07247
$255$	10.8327	0.678369
$256$	−13.3506	−0.834414
$257$	−19.2277	−1.19939	−0.599696	−	0.800228i	$-0.704712\pi$
$257$	−19.2277	−1.19939	−0.599696	+	0.800228i	$0.704712\pi$
$258$	9.08447	0.565574
$259$	−4.68477	−0.291097
$260$	16.4097	1.01769
$261$	19.3706	1.19901
$262$	−20.1313	−1.24372
$263$	1.97756	0.121941	0.0609707	−	0.998140i	$-0.480580\pi$
$263$	1.97756	0.121941	0.0609707	+	0.998140i	$0.480580\pi$
$264$	2.69201	0.165682
$265$	−30.2914	−1.86078
$266$	19.4396	1.19192
$267$	4.41617	0.270265
$268$	13.5080	0.825133
$269$	25.2320	1.53842	0.769211	−	0.638995i	$-0.220649\pi$
$269$	25.2320	1.53842	0.769211	+	0.638995i	$0.220649\pi$
$270$	−26.2704	−1.59877
$271$	−18.5715	−1.12814	−0.564069	−	0.825728i	$-0.690765\pi$
$271$	−18.5715	−1.12814	−0.564069	+	0.825728i	$0.690765\pi$
$272$	−1.82580	−0.110705
$273$	−4.94239	−0.299127
$274$	34.6750	2.09480
$275$	0.149019	0.00898620
$276$	10.0621	0.605670
$277$	31.3728	1.88501	0.942505	−	0.334192i	$-0.108463\pi$
$277$	31.3728	1.88501	0.942505	+	0.334192i	$0.108463\pi$
$278$	−44.2661	−2.65491
$279$	−10.5506	−0.631648
$280$	−12.2389	−0.731414
$281$	18.4898	1.10301	0.551504	−	0.834172i	$-0.314054\pi$
$281$	18.4898	1.10301	0.551504	+	0.834172i	$0.314054\pi$
$282$	12.4120	0.739126
$283$	−2.61300	−0.155327	−0.0776634	−	0.996980i	$-0.524746\pi$
$283$	−2.61300	−0.155327	−0.0776634	+	0.996980i	$0.524746\pi$
$284$	26.4875	1.57175
$285$	−9.70568	−0.574915
$286$	5.21492	0.308365
$287$	10.8814	0.642307
$288$	11.7475	0.692225
$289$	4.23941	0.249377
$290$	−51.7424	−3.03842
$291$	16.0333	0.939887
$292$	36.9560	2.16269
$293$	9.83716	0.574693	0.287346	−	0.957827i	$-0.407227\pi$
$293$	9.83716	0.574693	0.287346	+	0.957827i	$0.407227\pi$
$294$	−6.32702	−0.368999
$295$	−2.26915	−0.132115
$296$	5.86618	0.340965
$297$	−5.10369	−0.296146
$298$	−9.43064	−0.546302
$299$	7.09913	0.410553
$300$	0.485575	0.0280347
$301$	−8.02385	−0.462487
$302$	37.2365	2.14272
$303$	−0.626438	−0.0359879
$304$	1.63585	0.0938224
$305$	−20.9479	−1.19947
$306$	−20.1451	−1.15162
$307$	−30.7214	−1.75336	−0.876682	−	0.481070i	$-0.840248\pi$
$307$	−30.7214	−1.75336	−0.876682	+	0.481070i	$0.840248\pi$
$308$	−6.52856	−0.371999
$309$	15.7152	0.894007
$310$	28.1826	1.60067
$311$	−10.6057	−0.601394	−0.300697	−	0.953720i	$-0.597219\pi$
$311$	−10.6057	−0.601394	−0.300697	+	0.953720i	$0.597219\pi$
$312$	6.18877	0.350370
$313$	12.8415	0.725842	0.362921	−	0.931820i	$-0.381779\pi$
$313$	12.8415	0.725842	0.362921	+	0.931820i	$0.381779\pi$
$314$	−30.3781	−1.71433
$315$	9.07501	0.511319
$316$	−19.1642	−1.07807
$317$	18.2716	1.02623	0.513117	−	0.858319i	$-0.328491\pi$
$317$	18.2716	1.02623	0.513117	+	0.858319i	$0.328491\pi$
$318$	−31.3675	−1.75900
$319$	−10.0523	−0.562818
$320$	−29.5817	−1.65367
$321$	7.39559	0.412782
$322$	−14.5380	−0.810169
$323$	−19.0297	−1.05884
$324$	1.55468	0.0863710
$325$	0.342586	0.0190033
$326$	15.7560	0.872642
$327$	4.69421	0.259590
$328$	−13.6254	−0.752339
$329$	−10.9629	−0.604405
$330$	5.33194	0.293514
$331$	18.6864	1.02709	0.513547	−	0.858061i	$-0.328331\pi$
$331$	18.6864	1.02709	0.513547	+	0.858061i	$0.328331\pi$
$332$	37.3607	2.05044
$333$	−4.34971	−0.238363
$334$	7.44132	0.407171
$335$	9.74412	0.532378
$336$	0.851709	0.0464645
$337$	−30.5674	−1.66511	−0.832556	−	0.553941i	$-0.813123\pi$
$337$	−30.5674	−1.66511	−0.832556	+	0.553941i	$0.813123\pi$
$338$	−17.5004	−0.951898
$339$	−15.2970	−0.830818
$340$	32.8961	1.78404
$341$	5.47519	0.296498
$342$	18.0493	0.975993
$343$	20.1163	1.08618
$344$	10.0473	0.541715
$345$	7.25842	0.390780
$346$	−16.4312	−0.883346
$347$	5.08285	0.272861	0.136431	−	0.990650i	$-0.456437\pi$
$347$	5.08285	0.272861	0.136431	+	0.990650i	$0.456437\pi$
$348$	−32.7550	−1.75585
$349$	−28.2997	−1.51485	−0.757423	−	0.652924i	$-0.773542\pi$
$349$	−28.2997	−1.51485	−0.757423	+	0.652924i	$0.773542\pi$
$350$	−0.701567	−0.0375003
$351$	−11.7331	−0.626265
$352$	−6.09628	−0.324933
$353$	−11.3913	−0.606296	−0.303148	−	0.952943i	$-0.598038\pi$
$353$	−11.3913	−0.606296	−0.303148	+	0.952943i	$0.598038\pi$
$354$	−2.34976	−0.124888
$355$	19.1070	1.01410
$356$	13.4108	0.710769
$357$	−9.90787	−0.524380
$358$	41.9863	2.21905
$359$	20.5607	1.08515	0.542577	−	0.840006i	$-0.317449\pi$
$359$	20.5607	1.08515	0.542577	+	0.840006i	$0.317449\pi$
$360$	−11.3636	−0.598912
$361$	−1.95009	−0.102636
$362$	4.53187	0.238190
$363$	1.03586	0.0543688
$364$	−15.0088	−0.786673
$365$	26.6585	1.39537
$366$	−21.6921	−1.13386
$367$	3.34572	0.174645	0.0873226	−	0.996180i	$-0.472169\pi$
$367$	3.34572	0.174645	0.0873226	+	0.996180i	$0.472169\pi$
$368$	−1.22337	−0.0637728
$369$	10.1031	0.525947
$370$	11.6189	0.604037
$371$	27.7053	1.43839
$372$	17.8407	0.924999
$373$	−11.9141	−0.616888	−0.308444	−	0.951242i	$-0.599808\pi$
$373$	−11.9141	−0.616888	−0.308444	+	0.951242i	$0.599808\pi$
$374$	10.4542	0.540575
$375$	−11.4024	−0.588815
$376$	13.7276	0.707945
$377$	−23.1095	−1.19020
$378$	24.0276	1.23585
$379$	−15.0145	−0.771241	−0.385621	−	0.922657i	$-0.626013\pi$
$379$	−15.0145	−0.771241	−0.385621	+	0.922657i	$0.626013\pi$
$380$	−29.4737	−1.51197
$381$	−7.80517	−0.399871
$382$	−20.5270	−1.05025
$383$	−10.7199	−0.547759	−0.273880	−	0.961764i	$-0.588307\pi$
$383$	−10.7199	−0.547759	−0.273880	+	0.961764i	$0.588307\pi$
$384$	−18.0027	−0.918699
$385$	−4.70943	−0.240015
$386$	−5.57999	−0.284014
$387$	−7.44998	−0.378704
$388$	48.6889	2.47181
$389$	−16.3076	−0.826829	−0.413414	−	0.910543i	$-0.635664\pi$
$389$	−16.3076	−0.826829	−0.413414	+	0.910543i	$0.635664\pi$
$390$	12.2578	0.620699
$391$	14.2314	0.719714
$392$	−6.99761	−0.353433
$393$	−9.19295	−0.463723
$394$	25.6915	1.29432
$395$	−13.8242	−0.695573
$396$	−6.06163	−0.304608
$397$	−18.7931	−0.943198	−0.471599	−	0.881813i	$-0.656323\pi$
$397$	−18.7931	−0.943198	−0.471599	+	0.881813i	$0.656323\pi$
$398$	34.0821	1.70838
$399$	8.87708	0.444410
$400$	−0.0590370	−0.00295185
$401$	−12.1815	−0.608316	−0.304158	−	0.952622i	$-0.598375\pi$
$401$	−12.1815	−0.608316	−0.304158	+	0.952622i	$0.598375\pi$
$402$	10.0903	0.503258
$403$	12.5871	0.627010
$404$	−1.90233	−0.0946445
$405$	1.12148	0.0557269
$406$	47.3250	2.34870
$407$	2.25726	0.111888
$408$	12.4065	0.614211
$409$	−15.1805	−0.750628	−0.375314	−	0.926898i	$-0.622465\pi$
$409$	−15.1805	−0.750628	−0.375314	+	0.926898i	$0.622465\pi$
$410$	−26.9873	−1.33281
$411$	15.8343	0.781049
$412$	47.7231	2.35115
$413$	2.07542	0.102125
$414$	−13.4982	−0.663400
$415$	26.9505	1.32295
$416$	−14.0150	−0.687142
$417$	−20.2141	−0.989888
$418$	−9.36659	−0.458135
$419$	−21.2808	−1.03963	−0.519817	−	0.854278i	$-0.674000\pi$
$419$	−21.2808	−1.03963	−0.519817	+	0.854278i	$0.674000\pi$
$420$	−15.3455	−0.748786
$421$	38.9887	1.90019	0.950095	−	0.311959i	$-0.100985\pi$
$421$	38.9887	1.90019	0.950095	+	0.311959i	$0.100985\pi$
$422$	−29.9602	−1.45844
$423$	−10.1788	−0.494912
$424$	−34.6921	−1.68479
$425$	0.686773	0.0333134
$426$	19.7858	0.958626
$427$	19.1595	0.927194
$428$	22.4585	1.08557
$429$	2.38139	0.114975
$430$	19.9003	0.959677
$431$	4.76778	0.229656	0.114828	−	0.993385i	$-0.463368\pi$
$431$	4.76778	0.229656	0.114828	+	0.993385i	$0.463368\pi$
$432$	2.02193	0.0972802
$433$	−2.32875	−0.111913	−0.0559563	−	0.998433i	$-0.517821\pi$
$433$	−2.32875	−0.111913	−0.0559563	+	0.998433i	$0.517821\pi$
$434$	−25.7766	−1.23732
$435$	−23.6281	−1.13288
$436$	14.2551	0.682696
$437$	−12.7508	−0.609954
$438$	27.6056	1.31905
$439$	−28.4735	−1.35897	−0.679483	−	0.733692i	$-0.737796\pi$
$439$	−28.4735	−1.35897	−0.679483	+	0.733692i	$0.737796\pi$
$440$	5.89706	0.281132
$441$	5.18865	0.247079
$442$	24.0336	1.14316
$443$	28.4050	1.34956	0.674782	−	0.738017i	$-0.264238\pi$
$443$	28.4050	1.34956	0.674782	+	0.738017i	$0.264238\pi$
$444$	7.35522	0.349063
$445$	9.67398	0.458590
$446$	52.0488	2.46458
$447$	−4.30649	−0.203690
$448$	27.0562	1.27829
$449$	12.5233	0.591012	0.295506	−	0.955341i	$-0.404512\pi$
$449$	12.5233	0.591012	0.295506	+	0.955341i	$0.404512\pi$
$450$	−0.651390	−0.0307068
$451$	−5.24297	−0.246882
$452$	−46.4530	−2.18497
$453$	17.0040	0.798918
$454$	−41.3914	−1.94259
$455$	−10.8267	−0.507564
$456$	−11.1157	−0.520541
$457$	6.58325	0.307951	0.153976	−	0.988075i	$-0.450792\pi$
$457$	6.58325	0.307951	0.153976	+	0.988075i	$0.450792\pi$
$458$	27.0419	1.26358
$459$	−23.5210	−1.09786
$460$	22.0420	1.02771
$461$	4.33692	0.201990	0.100995	−	0.994887i	$-0.467797\pi$
$461$	4.33692	0.201990	0.100995	+	0.994887i	$0.467797\pi$
$462$	−4.87674	−0.226886
$463$	−8.25570	−0.383675	−0.191837	−	0.981427i	$-0.561445\pi$
$463$	−8.25570	−0.383675	−0.191837	+	0.981427i	$0.561445\pi$
$464$	3.98241	0.184879
$465$	12.8696	0.596812
$466$	−16.0108	−0.741686
$467$	26.5118	1.22682	0.613411	−	0.789764i	$-0.289797\pi$
$467$	26.5118	1.22682	0.613411	+	0.789764i	$0.289797\pi$
$468$	−13.9353	−0.644161
$469$	−8.91224	−0.411529
$470$	27.1896	1.25416
$471$	−13.8721	−0.639193
$472$	−2.59880	−0.119620
$473$	3.86613	0.177765
$474$	−14.3154	−0.657526
$475$	−0.615323	−0.0282330
$476$	−30.0877	−1.37907
$477$	25.7238	1.17781
$478$	6.23066	0.284984
$479$	−18.1845	−0.830869	−0.415435	−	0.909623i	$-0.636371\pi$
$479$	−18.1845	−0.830869	−0.415435	+	0.909623i	$0.636371\pi$
$480$	−14.3295	−0.654048
$481$	5.18931	0.236612
$482$	28.3531	1.29145
$483$	−6.63875	−0.302073
$484$	3.14565	0.142984
$485$	35.1222	1.59482
$486$	35.8930	1.62814
$487$	−15.9817	−0.724199	−0.362100	−	0.932139i	$-0.617940\pi$
$487$	−15.9817	−0.724199	−0.362100	+	0.932139i	$0.617940\pi$
$488$	−23.9912	−1.08603
$489$	7.19494	0.325367
$490$	−13.8598	−0.626124
$491$	40.4421	1.82513	0.912564	−	0.408935i	$-0.134100\pi$
$491$	40.4421	1.82513	0.912564	+	0.408935i	$0.134100\pi$
$492$	−17.0840	−0.770208
$493$	−46.3271	−2.08647
$494$	−21.5332	−0.968826
$495$	−4.37261	−0.196534
$496$	−2.16911	−0.0973958
$497$	−17.4758	−0.783897
$498$	27.9079	1.25058
$499$	−30.2399	−1.35373	−0.676863	−	0.736109i	$-0.736661\pi$
$499$	−30.2399	−1.35373	−0.676863	+	0.736109i	$0.736661\pi$
$500$	−34.6260	−1.54852
$501$	3.39807	0.151815
$502$	20.4667	0.913474
$503$	10.2442	0.456768	0.228384	−	0.973571i	$-0.426656\pi$
$503$	10.2442	0.456768	0.228384	+	0.973571i	$0.426656\pi$
$504$	10.3934	0.462960
$505$	−1.37226	−0.0610649
$506$	7.00483	0.311402
$507$	−7.99156	−0.354918
$508$	−23.7023	−1.05162
$509$	−23.5876	−1.04550	−0.522750	−	0.852486i	$-0.675094\pi$
$509$	−23.5876	−1.04550	−0.522750	+	0.852486i	$0.675094\pi$
$510$	24.5729	1.08811
$511$	−24.3826	−1.07862
$512$	4.47431	0.197738
$513$	21.0739	0.930436
$514$	−43.6162	−1.92383
$515$	34.4255	1.51697
$516$	12.5977	0.554582
$517$	5.28226	0.232314
$518$	−10.6269	−0.466921
$519$	−7.50328	−0.329358
$520$	13.5570	0.594514
$521$	−2.82716	−0.123860	−0.0619301	−	0.998080i	$-0.519726\pi$
$521$	−2.82716	−0.123860	−0.0619301	+	0.998080i	$0.519726\pi$
$522$	43.9402	1.92321
$523$	−26.1883	−1.14514	−0.572568	−	0.819857i	$-0.694053\pi$
$523$	−26.1883	−1.14514	−0.572568	+	0.819857i	$0.694053\pi$
$524$	−27.9166	−1.21954
$525$	−0.320370	−0.0139821
$526$	4.48589	0.195594
$527$	25.2331	1.09917
$528$	−0.410379	−0.0178594
$529$	−13.4643	−0.585403
$530$	−68.7130	−2.98470
$531$	1.92699	0.0836241
$532$	26.9574	1.16875
$533$	−12.0533	−0.522085
$534$	10.0176	0.433506
$535$	16.2007	0.700415
$536$	11.1597	0.482027
$537$	19.1730	0.827376
$538$	57.2364	2.46763
$539$	−2.69263	−0.115980
$540$	−36.4298	−1.56769
$541$	16.9301	0.727882	0.363941	−	0.931422i	$-0.381431\pi$
$541$	16.9301	0.727882	0.363941	+	0.931422i	$0.381431\pi$
$542$	−42.1276	−1.80954
$543$	2.06947	0.0888096
$544$	−28.0955	−1.20458
$545$	10.2831	0.440478
$546$	−11.2113	−0.479801
$547$	−7.94456	−0.339685	−0.169842	−	0.985471i	$-0.554326\pi$
$547$	−7.94456	−0.339685	−0.169842	+	0.985471i	$0.554326\pi$
$548$	48.0848	2.05408
$549$	17.7892	0.759225
$550$	0.338036	0.0144139
$551$	41.5073	1.76827
$552$	8.31292	0.353821
$553$	12.6440	0.537679
$554$	71.1662	3.02356
$555$	5.30575	0.225217
$556$	−61.3850	−2.60330
$557$	−9.01890	−0.382143	−0.191071	−	0.981576i	$-0.561196\pi$
$557$	−9.01890	−0.382143	−0.191071	+	0.981576i	$0.561196\pi$
$558$	−23.9330	−1.01317
$559$	8.88801	0.375923
$560$	1.86574	0.0788418
$561$	4.77391	0.201555
$562$	41.9423	1.76923
$563$	−20.0229	−0.843864	−0.421932	−	0.906627i	$-0.638648\pi$
$563$	−20.0229	−0.843864	−0.421932	+	0.906627i	$0.638648\pi$
$564$	17.2121	0.724759
$565$	−33.5093	−1.40975
$566$	−5.92734	−0.249145
$567$	−1.02574	−0.0430769
$568$	21.8829	0.918185
$569$	−1.12340	−0.0470953	−0.0235477	−	0.999723i	$-0.507496\pi$
$569$	−1.12340	−0.0470953	−0.0235477	+	0.999723i	$0.507496\pi$
$570$	−22.0164	−0.922166
$571$	−17.1392	−0.717253	−0.358627	−	0.933481i	$-0.616755\pi$
$571$	−17.1392	−0.717253	−0.358627	+	0.933481i	$0.616755\pi$
$572$	7.23167	0.302371
$573$	−9.37363	−0.391589
$574$	24.6833	1.03026
$575$	0.460171	0.0191905
$576$	25.1211	1.04671
$577$	−21.2175	−0.883297	−0.441648	−	0.897188i	$-0.645606\pi$
$577$	−21.2175	−0.883297	−0.441648	+	0.897188i	$0.645606\pi$
$578$	9.61669	0.400001
$579$	−2.54810	−0.105895
$580$	−71.7525	−2.97936
$581$	−24.6496	−1.02264
$582$	36.3699	1.50758
$583$	−13.3492	−0.552869
$584$	30.5315	1.26340
$585$	−10.0524	−0.415614
$586$	22.3146	0.921809
$587$	19.2539	0.794694	0.397347	−	0.917668i	$-0.369931\pi$
$587$	19.2539	0.794694	0.397347	+	0.917668i	$0.369931\pi$
$588$	−8.77384	−0.361827
$589$	−22.6079	−0.931542
$590$	−5.14734	−0.211912
$591$	11.7320	0.482589
$592$	−0.894261	−0.0367539
$593$	−27.4194	−1.12598	−0.562989	−	0.826464i	$-0.690349\pi$
$593$	−27.4194	−1.12598	−0.562989	+	0.826464i	$0.690349\pi$
$594$	−11.5772	−0.475019
$595$	−21.7040	−0.889777
$596$	−13.0777	−0.535684
$597$	15.5635	0.636973
$598$	16.1037	0.658528
$599$	8.03022	0.328106	0.164053	−	0.986452i	$-0.447543\pi$
$599$	8.03022	0.328106	0.164053	+	0.986452i	$0.447543\pi$
$600$	0.401161	0.0163773
$601$	−6.93033	−0.282694	−0.141347	−	0.989960i	$-0.545143\pi$
$601$	−6.93033	−0.282694	−0.141347	+	0.989960i	$0.545143\pi$
$602$	−18.2013	−0.741831
$603$	−8.27483	−0.336977
$604$	51.6368	2.10107
$605$	2.26915	0.0922539
$606$	−1.42101	−0.0577247
$607$	−25.5298	−1.03622	−0.518112	−	0.855313i	$-0.673365\pi$
$607$	−25.5298	−1.03622	−0.518112	+	0.855313i	$0.673365\pi$
$608$	25.1725	1.02088
$609$	21.6109	0.875718
$610$	−47.5183	−1.92396
$611$	12.1436	0.491278
$612$	−27.9358	−1.12924
$613$	−14.1051	−0.569700	−0.284850	−	0.958572i	$-0.591944\pi$
$613$	−14.1051	−0.569700	−0.284850	+	0.958572i	$0.591944\pi$
$614$	−69.6886	−2.81240
$615$	−12.3237	−0.496941
$616$	−5.39361	−0.217315
$617$	−40.6949	−1.63832	−0.819158	−	0.573568i	$-0.805559\pi$
$617$	−40.6949	−1.63832	−0.819158	+	0.573568i	$0.805559\pi$
$618$	35.6484	1.43399
$619$	10.6491	0.428025	0.214012	−	0.976831i	$-0.431347\pi$
$619$	10.6491	0.428025	0.214012	+	0.976831i	$0.431347\pi$
$620$	39.0816	1.56955
$621$	−15.7602	−0.632434
$622$	−24.0580	−0.964637
$623$	−8.84808	−0.354491
$624$	−0.943437	−0.0377677
$625$	−25.7229	−1.02892
$626$	29.1296	1.16425
$627$	−4.27724	−0.170817
$628$	−42.1261	−1.68101
$629$	10.4029	0.414790
$630$	20.5858	0.820157
$631$	−23.5068	−0.935792	−0.467896	−	0.883783i	$-0.654988\pi$
$631$	−23.5068	−0.935792	−0.467896	+	0.883783i	$0.654988\pi$
$632$	−15.8326	−0.629788
$633$	−13.6813	−0.543782
$634$	41.4473	1.64608
$635$	−17.0979	−0.678508
$636$	−43.4981	−1.72481
$637$	−6.19019	−0.245264
$638$	−22.8026	−0.902763
$639$	−16.2259	−0.641887
$640$	−39.4365	−1.55886
$641$	18.4119	0.727225	0.363613	−	0.931550i	$-0.381543\pi$
$641$	18.4119	0.727225	0.363613	+	0.931550i	$0.381543\pi$
$642$	16.7762	0.662103
$643$	17.9372	0.707375	0.353688	−	0.935364i	$-0.384928\pi$
$643$	17.9372	0.707375	0.353688	+	0.935364i	$0.384928\pi$
$644$	−20.1602	−0.794422
$645$	9.08744	0.357818
$646$	−43.1671	−1.69839
$647$	31.4808	1.23764	0.618820	−	0.785533i	$-0.287611\pi$
$647$	31.4808	1.23764	0.618820	+	0.785533i	$0.287611\pi$
$648$	1.28441	0.0504564
$649$	−1.00000	−0.0392534
$650$	0.777124	0.0304813
$651$	−11.7709	−0.461336
$652$	21.8492	0.855681
$653$	28.6331	1.12050	0.560249	−	0.828324i	$-0.310705\pi$
$653$	28.6331	1.12050	0.560249	+	0.828324i	$0.310705\pi$
$654$	10.6484	0.416384
$655$	−20.1379	−0.786853
$656$	2.07711	0.0810975
$657$	−22.6388	−0.883222
$658$	−24.8683	−0.969468
$659$	−50.5938	−1.97085	−0.985427	−	0.170096i	$-0.945592\pi$
$659$	−50.5938	−1.97085	−0.985427	+	0.170096i	$0.945592\pi$
$660$	7.39394	0.287809
$661$	−46.1019	−1.79316	−0.896578	−	0.442885i	$-0.853955\pi$
$661$	−46.1019	−1.79316	−0.896578	+	0.442885i	$0.853955\pi$
$662$	42.3882	1.64746
$663$	10.9749	0.426231
$664$	30.8658	1.19783
$665$	19.4460	0.754082
$666$	−9.86690	−0.382335
$667$	−31.0414	−1.20193
$668$	10.3191	0.399257
$669$	23.7680	0.918924
$670$	22.1036	0.853937
$671$	−9.23162	−0.356383
$672$	13.1061	0.505580
$673$	−0.472567	−0.0182161	−0.00910806	−	0.999959i	$-0.502899\pi$
$673$	−0.472567	−0.0182161	−0.00910806	+	0.999959i	$0.502899\pi$
$674$	−69.3392	−2.67084
$675$	−0.760548	−0.0292735
$676$	−24.2683	−0.933397
$677$	31.3813	1.20608	0.603041	−	0.797711i	$-0.293956\pi$
$677$	31.3813	1.20608	0.603041	+	0.797711i	$0.293956\pi$
$678$	−34.6997	−1.33263
$679$	−32.1237	−1.23279
$680$	27.1773	1.04220
$681$	−18.9013	−0.724300
$682$	12.4199	0.475584
$683$	−33.0698	−1.26538	−0.632691	−	0.774404i	$-0.718050\pi$
$683$	−33.0698	−1.26538	−0.632691	+	0.774404i	$0.718050\pi$
$684$	25.0294	0.957023
$685$	34.6864	1.32530
$686$	45.6318	1.74223
$687$	12.3486	0.471130
$688$	−1.53165	−0.0583935
$689$	−30.6891	−1.16916
$690$	16.4650	0.626813
$691$	24.8231	0.944314	0.472157	−	0.881514i	$-0.343476\pi$
$691$	24.8231	0.944314	0.472157	+	0.881514i	$0.343476\pi$
$692$	−22.7856	−0.866177
$693$	3.99931	0.151921
$694$	11.5299	0.437671
$695$	−44.2806	−1.67966
$696$	−27.0608	−1.02574
$697$	−24.1629	−0.915233
$698$	−64.1951	−2.42982
$699$	−7.31132	−0.276539
$700$	−0.972881	−0.0367714
$701$	19.7553	0.746148	0.373074	−	0.927802i	$-0.378304\pi$
$701$	19.7553	0.746148	0.373074	+	0.927802i	$0.378304\pi$
$702$	−26.6153	−1.00453
$703$	−9.32058	−0.351532
$704$	−13.0365	−0.491331
$705$	12.4161	0.467617
$706$	−25.8400	−0.972501
$707$	1.25511	0.0472032
$708$	−3.25847	−0.122461
$709$	−44.0104	−1.65285	−0.826423	−	0.563049i	$-0.809628\pi$
$709$	−44.0104	−1.65285	−0.826423	+	0.563049i	$0.809628\pi$
$710$	43.3424	1.62661
$711$	11.7397	0.440274
$712$	11.0794	0.415218
$713$	16.9074	0.633186
$714$	−22.4750	−0.841107
$715$	5.21663	0.195091
$716$	58.2235	2.17591
$717$	2.84522	0.106257
$718$	46.6400	1.74059
$719$	−0.620419	−0.0231377	−0.0115689	−	0.999933i	$-0.503683\pi$
$719$	−0.620419	−0.0231377	−0.0115689	+	0.999933i	$0.503683\pi$
$720$	1.73230	0.0645590
$721$	−31.4865	−1.17262
$722$	−4.42359	−0.164629
$723$	12.9474	0.481520
$724$	6.28446	0.233560
$725$	−1.49798	−0.0556336
$726$	2.34976	0.0872077
$727$	50.6797	1.87960	0.939802	−	0.341719i	$-0.111009\pi$
$727$	50.6797	1.87960	0.939802	+	0.341719i	$0.111009\pi$
$728$	−12.3996	−0.459560
$729$	14.9078	0.552141
$730$	60.4723	2.23818
$731$	17.8175	0.659006
$732$	−30.0810	−1.11182
$733$	−44.0989	−1.62883	−0.814416	−	0.580282i	$-0.802942\pi$
$733$	−44.0989	−1.62883	−0.814416	+	0.580282i	$0.802942\pi$
$734$	7.58945	0.280132
$735$	−6.32909	−0.233452
$736$	−18.8253	−0.693910
$737$	4.29418	0.158178
$738$	22.9180	0.843622
$739$	−21.5894	−0.794179	−0.397090	−	0.917780i	$-0.629980\pi$
$739$	−21.5894	−0.794179	−0.397090	+	0.917780i	$0.629980\pi$
$740$	16.1122	0.592297
$741$	−9.83313	−0.361229
$742$	62.8468	2.30718
$743$	3.56975	0.130961	0.0654807	−	0.997854i	$-0.479142\pi$
$743$	3.56975	0.130961	0.0654807	+	0.997854i	$0.479142\pi$
$744$	14.7392	0.540367
$745$	−9.43372	−0.345625
$746$	−27.0260	−0.989491
$747$	−22.8867	−0.837380
$748$	14.4971	0.530068
$749$	−14.8176	−0.541422
$750$	−25.8651	−0.944461
$751$	−5.20425	−0.189906	−0.0949529	−	0.995482i	$-0.530270\pi$
$751$	−5.20425	−0.189906	−0.0949529	+	0.995482i	$0.530270\pi$
$752$	−2.09268	−0.0763120
$753$	9.34610	0.340591
$754$	−52.4218	−1.90909
$755$	37.2487	1.35562
$756$	33.3197	1.21183
$757$	−24.4433	−0.888407	−0.444204	−	0.895926i	$-0.646513\pi$
$757$	−24.4433	−0.888407	−0.444204	+	0.895926i	$0.646513\pi$
$758$	−34.0589	−1.23707
$759$	3.19875	0.116107
$760$	−24.3499	−0.883263
$761$	−22.3227	−0.809199	−0.404599	−	0.914494i	$-0.632589\pi$
$761$	−22.3227	−0.809199	−0.404599	+	0.914494i	$0.632589\pi$
$762$	−17.7053	−0.641395
$763$	−9.40516	−0.340490
$764$	−28.4653	−1.02984
$765$	−20.1517	−0.728587
$766$	−24.3170	−0.878607
$767$	−2.29894	−0.0830099
$768$	−13.8294	−0.499026
$769$	9.37347	0.338016	0.169008	−	0.985615i	$-0.445944\pi$
$769$	9.37347	0.338016	0.169008	+	0.985615i	$0.445944\pi$
$770$	−10.6829	−0.384985
$771$	−19.9173	−0.717305
$772$	−7.73791	−0.278494
$773$	−10.2681	−0.369319	−0.184660	−	0.982803i	$-0.559118\pi$
$773$	−10.2681	−0.369319	−0.184660	+	0.982803i	$0.559118\pi$
$774$	−16.8996	−0.607442
$775$	0.815908	0.0293083
$776$	40.2247	1.44398
$777$	−4.85278	−0.174093
$778$	−36.9922	−1.32624
$779$	21.6490	0.775656
$780$	16.9982	0.608634
$781$	8.42036	0.301304
$782$	32.2826	1.15442
$783$	51.3036	1.83344
$784$	1.06674	0.0380978
$785$	−30.3880	−1.08459
$786$	−20.8533	−0.743813
$787$	21.6578	0.772017	0.386009	−	0.922495i	$-0.373854\pi$
$787$	21.6578	0.772017	0.386009	+	0.922495i	$0.373854\pi$
$788$	35.6270	1.26916
$789$	2.04848	0.0729278
$790$	−31.3590	−1.11570
$791$	30.6485	1.08974
$792$	−5.00786	−0.177947
$793$	−21.2230	−0.753649
$794$	−42.6303	−1.51289
$795$	−31.3777	−1.11285
$796$	47.2625	1.67517
$797$	−41.7478	−1.47878	−0.739392	−	0.673275i	$-0.764887\pi$
$797$	−41.7478	−1.47878	−0.739392	+	0.673275i	$0.764887\pi$
$798$	20.1368	0.712835
$799$	24.3439	0.861227
$800$	−0.908463	−0.0321190
$801$	−8.21526	−0.290272
$802$	−27.6326	−0.975741
$803$	11.7483	0.414588
$804$	13.9925	0.493476
$805$	−14.5427	−0.512564
$806$	28.5527	1.00573
$807$	26.1369	0.920063
$808$	−1.57162	−0.0552896
$809$	21.5260	0.756812	0.378406	−	0.925640i	$-0.376472\pi$
$809$	21.5260	0.756812	0.378406	+	0.925640i	$0.376472\pi$
$810$	2.54397	0.0893861
$811$	−25.7619	−0.904623	−0.452312	−	0.891860i	$-0.649401\pi$
$811$	−25.7619	−0.904623	−0.452312	+	0.891860i	$0.649401\pi$
$812$	65.6268	2.30305
$813$	−19.2375	−0.674690
$814$	5.12038	0.179469
$815$	15.7611	0.552088
$816$	−1.89128	−0.0662081
$817$	−15.9639	−0.558504
$818$	−34.4355	−1.20401
$819$	9.19417	0.321270
$820$	−37.4240	−1.30690
$821$	33.1665	1.15752	0.578759	−	0.815499i	$-0.303537\pi$
$821$	33.1665	1.15752	0.578759	+	0.815499i	$0.303537\pi$
$822$	35.9186	1.25281
$823$	36.8089	1.28308	0.641539	−	0.767090i	$-0.278296\pi$
$823$	36.8089	1.28308	0.641539	+	0.767090i	$0.278296\pi$
$824$	39.4268	1.37350
$825$	0.154364	0.00537425
$826$	4.70789	0.163809
$827$	8.71948	0.303206	0.151603	−	0.988441i	$-0.451556\pi$
$827$	8.71948	0.303206	0.151603	+	0.988441i	$0.451556\pi$
$828$	−18.7183	−0.650506
$829$	−33.9513	−1.17918	−0.589588	−	0.807704i	$-0.700710\pi$
$829$	−33.9513	−1.17918	−0.589588	+	0.807704i	$0.700710\pi$
$830$	61.1346	2.12201
$831$	32.4980	1.12734
$832$	−29.9701	−1.03903
$833$	−12.4093	−0.429957
$834$	−45.8537	−1.58778
$835$	7.44375	0.257602
$836$	−12.9889	−0.449230
$837$	−27.9436	−0.965873
$838$	−48.2734	−1.66758
$839$	−3.51199	−0.121247	−0.0606236	−	0.998161i	$-0.519309\pi$
$839$	−3.51199	−0.121247	−0.0606236	+	0.998161i	$0.519309\pi$
$840$	−12.6778	−0.437427
$841$	72.0479	2.48441
$842$	88.4420	3.04791
$843$	19.1529	0.659661
$844$	−41.5465	−1.43009
$845$	−17.5062	−0.602230
$846$	−23.0897	−0.793841
$847$	−2.07542	−0.0713123
$848$	5.28857	0.181610
$849$	−2.70671	−0.0928941
$850$	1.55788	0.0534348
$851$	6.97042	0.238943
$852$	27.4375	0.939993
$853$	47.1591	1.61470	0.807348	−	0.590076i	$-0.200902\pi$
$853$	47.1591	1.61470	0.807348	+	0.590076i	$0.200902\pi$
$854$	43.4615	1.48722
$855$	18.0552	0.617474
$856$	18.5543	0.634172
$857$	3.92247	0.133989	0.0669945	−	0.997753i	$-0.478659\pi$
$857$	3.92247	0.133989	0.0669945	+	0.997753i	$0.478659\pi$
$858$	5.40195	0.184420
$859$	57.6757	1.96787	0.983935	−	0.178525i	$-0.0571324\pi$
$859$	57.6757	1.96787	0.983935	+	0.178525i	$0.0571324\pi$
$860$	27.5962	0.941024
$861$	11.2716	0.384136
$862$	10.8153	0.368369
$863$	27.8102	0.946670	0.473335	−	0.880882i	$-0.343050\pi$
$863$	27.8102	0.946670	0.473335	+	0.880882i	$0.343050\pi$
$864$	31.1135	1.05850
$865$	−16.4366	−0.558860
$866$	−5.28254	−0.179508
$867$	4.39145	0.149141
$868$	−35.7451	−1.21327
$869$	−6.09227	−0.206666
$870$	−53.5981	−1.81714
$871$	9.87207	0.334502
$872$	11.7770	0.398818
$873$	−29.8262	−1.00946
$874$	−28.9240	−0.978369
$875$	22.8454	0.772314
$876$	38.2814	1.29341
$877$	26.6580	0.900178	0.450089	−	0.892984i	$-0.351392\pi$
$877$	26.6580	0.900178	0.450089	+	0.892984i	$0.351392\pi$
$878$	−64.5894	−2.17979
$879$	10.1900	0.343699
$880$	−0.898968	−0.0303042
$881$	21.1079	0.711142	0.355571	−	0.934649i	$-0.384286\pi$
$881$	21.1079	0.711142	0.355571	+	0.934649i	$0.384286\pi$
$882$	11.7700	0.396315
$883$	−25.1804	−0.847387	−0.423694	−	0.905806i	$-0.639267\pi$
$883$	−25.1804	−0.847387	−0.423694	+	0.905806i	$0.639267\pi$
$884$	33.3280	1.12094
$885$	−2.35053	−0.0790121
$886$	64.4341	2.16471
$887$	35.7728	1.20113	0.600567	−	0.799575i	$-0.294942\pi$
$887$	35.7728	1.20113	0.600567	+	0.799575i	$0.294942\pi$
$888$	6.07657	0.203916
$889$	15.6382	0.524488
$890$	21.9445	0.735581
$891$	0.494231	0.0165574
$892$	72.1774	2.41668
$893$	−21.8113	−0.729886
$894$	−9.76886	−0.326720
$895$	42.0000	1.40391
$896$	36.0697	1.20500
$897$	7.35373	0.245534
$898$	28.4079	0.947985
$899$	−55.0380	−1.83562
$900$	−0.903299	−0.0301100
$901$	−61.5216	−2.04958
$902$	−11.8932	−0.395999
$903$	−8.31162	−0.276593
$904$	−38.3775	−1.27642
$905$	4.53335	0.150694
$906$	38.5720	1.28147
$907$	−48.2289	−1.60141	−0.800707	−	0.599057i	$-0.795542\pi$
$907$	−48.2289	−1.60141	−0.800707	+	0.599057i	$0.795542\pi$
$908$	−57.3985	−1.90484
$909$	1.16534	0.0386520
$910$	−24.5593	−0.814134
$911$	15.1547	0.502099	0.251050	−	0.967974i	$-0.419224\pi$
$911$	15.1547	0.502099	0.251050	+	0.967974i	$0.419224\pi$
$912$	1.69452	0.0561111
$913$	11.8769	0.393069
$914$	14.9335	0.493955
$915$	−21.6992	−0.717352
$916$	37.4996	1.23902
$917$	18.4187	0.608238
$918$	−53.3551	−1.76098
$919$	14.3189	0.472338	0.236169	−	0.971712i	$-0.424108\pi$
$919$	14.3189	0.472338	0.236169	+	0.971712i	$0.424108\pi$
$920$	18.2101	0.600370
$921$	−31.8232	−1.04861
$922$	9.83788	0.323993
$923$	19.3579	0.637173
$924$	−6.76270	−0.222476
$925$	0.336375	0.0110600
$926$	−18.7273	−0.615416
$927$	−29.2345	−0.960188
$928$	61.2814	2.01166
$929$	25.1411	0.824854	0.412427	−	0.910991i	$-0.364681\pi$
$929$	25.1411	0.824854	0.412427	+	0.910991i	$0.364681\pi$
$930$	29.1934	0.957288
$931$	11.1183	0.364386
$932$	−22.2026	−0.727270
$933$	−10.9861	−0.359667
$934$	60.1396	1.96783
$935$	10.4576	0.342001
$936$	−11.5128	−0.376307
$937$	10.1053	0.330125	0.165063	−	0.986283i	$-0.447217\pi$
$937$	10.1053	0.330125	0.165063	+	0.986283i	$0.447217\pi$
$938$	−20.2166	−0.660094
$939$	13.3020	0.434095
$940$	37.7045	1.22978
$941$	−47.1296	−1.53638	−0.768191	−	0.640221i	$-0.778843\pi$
$941$	−47.1296	−1.53638	−0.768191	+	0.640221i	$0.778843\pi$
$942$	−31.4676	−1.02527
$943$	−16.1903	−0.527228
$944$	0.396171	0.0128943
$945$	24.0355	0.781874
$946$	8.76995	0.285136
$947$	−23.8984	−0.776595	−0.388297	−	0.921534i	$-0.626937\pi$
$947$	−23.8984	−0.776595	−0.388297	+	0.921534i	$0.626937\pi$
$948$	−19.8515	−0.644746
$949$	27.0086	0.876736
$950$	−1.39580	−0.0452858
$951$	18.9269	0.613745
$952$	−24.8571	−0.805624
$953$	26.1231	0.846211	0.423106	−	0.906080i	$-0.360940\pi$
$953$	26.1231	0.846211	0.423106	+	0.906080i	$0.360940\pi$
$954$	58.3519	1.88921
$955$	−20.5337	−0.664455
$956$	8.64021	0.279444
$957$	−10.4128	−0.336597
$958$	−41.2497	−1.33272
$959$	−31.7251	−1.02446
$960$	−30.6426	−0.988986
$961$	−1.02233	−0.0329785
$962$	11.7714	0.379527
$963$	−13.7578	−0.443339
$964$	39.3180	1.26635
$965$	−5.58181	−0.179685
$966$	−15.0594	−0.484527
$967$	31.3308	1.00753	0.503766	−	0.863840i	$-0.331948\pi$
$967$	31.3308	1.00753	0.503766	+	0.863840i	$0.331948\pi$
$968$	2.59880	0.0835287
$969$	−19.7122	−0.633247
$970$	79.6713	2.55809
$971$	−45.0198	−1.44476	−0.722378	−	0.691499i	$-0.756951\pi$
$971$	−45.0198	−1.44476	−0.722378	+	0.691499i	$0.756951\pi$
$972$	49.7737	1.59649
$973$	40.5002	1.29838
$974$	−36.2529	−1.16162
$975$	0.354873	0.0113650
$976$	3.65730	0.117067
$977$	47.0313	1.50467	0.752333	−	0.658783i	$-0.228929\pi$
$977$	47.0313	1.50467	0.752333	+	0.658783i	$0.228929\pi$
$978$	16.3210	0.521889
$979$	4.26327	0.136255
$980$	−19.2198	−0.613954
$981$	−8.73249	−0.278807
$982$	91.7390	2.92751
$983$	−34.7291	−1.10769	−0.553843	−	0.832621i	$-0.686839\pi$
$983$	−34.7291	−1.10769	−0.553843	+	0.832621i	$0.686839\pi$
$984$	−14.1141	−0.449941
$985$	25.6999	0.818866
$986$	−105.088	−3.34670
$987$	−11.3561	−0.361468
$988$	−29.8607	−0.949995
$989$	11.9386	0.379626
$990$	−9.91884	−0.315242
$991$	16.1975	0.514530	0.257265	−	0.966341i	$-0.417179\pi$
$991$	16.1975	0.514530	0.257265	+	0.966341i	$0.417179\pi$
$992$	−33.3783	−1.05976
$993$	19.3565	0.614261
$994$	−39.6422	−1.25737
$995$	34.0932	1.08083
$996$	38.7006	1.22628
$997$	−35.0371	−1.10964	−0.554819	−	0.831971i	$-0.687212\pi$
$997$	−35.0371	−1.10964	−0.554819	+	0.831971i	$0.687212\pi$
$998$	−68.5964	−2.17138
$999$	−11.5204	−0.364488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	649.2.a.f.1.14	✓	17
3.2	odd	2		5841.2.a.z.1.4		17
11.10	odd	2		7139.2.a.r.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
649.2.a.f.1.14	✓	17	1.1	even	1	trivial
5841.2.a.z.1.4		17	3.2	odd	2
7139.2.a.r.1.4		17	11.10	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:	\( N \)	\(=\)	\( 649 = 11 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	649.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26840 q^{2} +1.03586 q^{3} +3.14565 q^{4} +2.26915 q^{5} +2.34976 q^{6} -2.07542 q^{7} +2.59880 q^{8} -1.92699 q^{9} +O(q^{10})\)	\(q+2.26840 q^{2} +1.03586 q^{3} +3.14565 q^{4} +2.26915 q^{5} +2.34976 q^{6} -2.07542 q^{7} +2.59880 q^{8} -1.92699 q^{9} +5.14734 q^{10} +1.00000 q^{11} +3.25847 q^{12} +2.29894 q^{13} -4.70789 q^{14} +2.35053 q^{15} -0.396171 q^{16} +4.60862 q^{17} -4.37118 q^{18} -4.12915 q^{19} +7.13794 q^{20} -2.14985 q^{21} +2.26840 q^{22} +3.08800 q^{23} +2.69201 q^{24} +0.149019 q^{25} +5.21492 q^{26} -5.10369 q^{27} -6.52856 q^{28} -10.0523 q^{29} +5.33194 q^{30} +5.47519 q^{31} -6.09628 q^{32} +1.03586 q^{33} +10.4542 q^{34} -4.70943 q^{35} -6.06163 q^{36} +2.25726 q^{37} -9.36659 q^{38} +2.38139 q^{39} +5.89706 q^{40} -5.24297 q^{41} -4.87674 q^{42} +3.86613 q^{43} +3.14565 q^{44} -4.37261 q^{45} +7.00483 q^{46} +5.28226 q^{47} -0.410379 q^{48} -2.69263 q^{49} +0.338036 q^{50} +4.77391 q^{51} +7.23167 q^{52} -13.3492 q^{53} -11.5772 q^{54} +2.26915 q^{55} -5.39361 q^{56} -4.27724 q^{57} -22.8026 q^{58} -1.00000 q^{59} +7.39394 q^{60} -9.23162 q^{61} +12.4199 q^{62} +3.99931 q^{63} -13.0365 q^{64} +5.21663 q^{65} +2.34976 q^{66} +4.29418 q^{67} +14.4971 q^{68} +3.19875 q^{69} -10.6829 q^{70} +8.42036 q^{71} -5.00786 q^{72} +11.7483 q^{73} +5.12038 q^{74} +0.154364 q^{75} -12.9889 q^{76} -2.07542 q^{77} +5.40195 q^{78} -6.09227 q^{79} -0.898968 q^{80} +0.494231 q^{81} -11.8932 q^{82} +11.8769 q^{83} -6.76270 q^{84} +10.4576 q^{85} +8.76995 q^{86} -10.4128 q^{87} +2.59880 q^{88} +4.26327 q^{89} -9.91884 q^{90} -4.77127 q^{91} +9.71377 q^{92} +5.67155 q^{93} +11.9823 q^{94} -9.36965 q^{95} -6.31492 q^{96} +15.4782 q^{97} -6.10796 q^{98} -1.92699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9	\( 17 q + 3 q^{2} + 4 q^{3} + 23 q^{4} + 7 q^{5} - 5 q^{6} + 4 q^{7} + 9 q^{8} + 29 q^{9} - 4 q^{10} + 17 q^{11} + 2 q^{12} - 11 q^{13} + 16 q^{14} + 20 q^{15} + 39 q^{16} + 6 q^{17} - 15 q^{18} - 4 q^{19} - q^{20} - 11 q^{21} + 3 q^{22} + 36 q^{23} + 4 q^{24} + 22 q^{25} + 28 q^{26} + 13 q^{27} + 13 q^{29} - 34 q^{30} + 6 q^{31} + 16 q^{32} + 4 q^{33} - 5 q^{34} + 16 q^{35} + 34 q^{36} + 14 q^{37} + 12 q^{38} + 41 q^{39} - 54 q^{40} + 6 q^{41} - 57 q^{42} - 11 q^{43} + 23 q^{44} + 5 q^{45} + q^{46} + 25 q^{47} + 14 q^{48} + 23 q^{49} + 15 q^{50} - 4 q^{51} - 64 q^{52} - 2 q^{54} + 7 q^{55} + 43 q^{56} - 9 q^{57} - 21 q^{58} - 17 q^{59} + 15 q^{60} - 38 q^{61} - 21 q^{62} + 2 q^{63} + 43 q^{64} - 13 q^{65} - 5 q^{66} + q^{67} + 34 q^{68} - 13 q^{69} + 5 q^{70} + 89 q^{71} + 15 q^{72} - 16 q^{73} + 17 q^{74} + 2 q^{75} - q^{76} + 4 q^{77} - 58 q^{78} + 34 q^{79} - 64 q^{80} + 29 q^{81} - 17 q^{82} - 12 q^{83} - 111 q^{84} - 15 q^{85} - 21 q^{86} - 4 q^{87} + 9 q^{88} - 5 q^{89} + 7 q^{90} - 12 q^{91} + 80 q^{92} + 32 q^{93} - 25 q^{94} + 103 q^{95} - 48 q^{96} - 15 q^{97} + 8 q^{98} + 29 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + 4 * q^3 + 23 * q^4 + 7 * q^5 - 5 * q^6 + 4 * q^7 + 9 * q^8 + 29 * q^9 - 4 * q^10 + 17 * q^11 + 2 * q^12 - 11 * q^13 + 16 * q^14 + 20 * q^15 + 39 * q^16 + 6 * q^17 - 15 * q^18 - 4 * q^19 - q^20 - 11 * q^21 + 3 * q^22 + 36 * q^23 + 4 * q^24 + 22 * q^25 + 28 * q^26 + 13 * q^27 + 13 * q^29 - 34 * q^30 + 6 * q^31 + 16 * q^32 + 4 * q^33 - 5 * q^34 + 16 * q^35 + 34 * q^36 + 14 * q^37 + 12 * q^38 + 41 * q^39 - 54 * q^40 + 6 * q^41 - 57 * q^42 - 11 * q^43 + 23 * q^44 + 5 * q^45 + q^46 + 25 * q^47 + 14 * q^48 + 23 * q^49 + 15 * q^50 - 4 * q^51 - 64 * q^52 - 2 * q^54 + 7 * q^55 + 43 * q^56 - 9 * q^57 - 21 * q^58 - 17 * q^59 + 15 * q^60 - 38 * q^61 - 21 * q^62 + 2 * q^63 + 43 * q^64 - 13 * q^65 - 5 * q^66 + q^67 + 34 * q^68 - 13 * q^69 + 5 * q^70 + 89 * q^71 + 15 * q^72 - 16 * q^73 + 17 * q^74 + 2 * q^75 - q^76 + 4 * q^77 - 58 * q^78 + 34 * q^79 - 64 * q^80 + 29 * q^81 - 17 * q^82 - 12 * q^83 - 111 * q^84 - 15 * q^85 - 21 * q^86 - 4 * q^87 + 9 * q^88 - 5 * q^89 + 7 * q^90 - 12 * q^91 + 80 * q^92 + 32 * q^93 - 25 * q^94 + 103 * q^95 - 48 * q^96 - 15 * q^97 + 8 * q^98 + 29 * q^99

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