LMFDB - Embedded newform 2013.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
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			1.7
Root			$0.179763$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.179763 q^{2} -1.00000 q^{3} -1.96769 q^{4} +2.20477 q^{5} +0.179763 q^{6} +3.17177 q^{7} +0.713244 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.179763 q^{2} -1.00000 q^{3} -1.96769 q^{4} +2.20477 q^{5} +0.179763 q^{6} +3.17177 q^{7} +0.713244 q^{8} +1.00000 q^{9} -0.396336 q^{10} -1.00000 q^{11} +1.96769 q^{12} +5.02358 q^{13} -0.570167 q^{14} -2.20477 q^{15} +3.80716 q^{16} +1.08785 q^{17} -0.179763 q^{18} +3.53893 q^{19} -4.33828 q^{20} -3.17177 q^{21} +0.179763 q^{22} +1.91419 q^{23} -0.713244 q^{24} -0.139010 q^{25} -0.903056 q^{26} -1.00000 q^{27} -6.24104 q^{28} -5.13495 q^{29} +0.396336 q^{30} -0.976010 q^{31} -2.11088 q^{32} +1.00000 q^{33} -0.195555 q^{34} +6.99300 q^{35} -1.96769 q^{36} +7.67629 q^{37} -0.636169 q^{38} -5.02358 q^{39} +1.57254 q^{40} -2.80345 q^{41} +0.570167 q^{42} -7.46749 q^{43} +1.96769 q^{44} +2.20477 q^{45} -0.344102 q^{46} +5.09413 q^{47} -3.80716 q^{48} +3.06010 q^{49} +0.0249889 q^{50} -1.08785 q^{51} -9.88482 q^{52} -10.9620 q^{53} +0.179763 q^{54} -2.20477 q^{55} +2.26224 q^{56} -3.53893 q^{57} +0.923076 q^{58} +8.89797 q^{59} +4.33828 q^{60} +1.00000 q^{61} +0.175451 q^{62} +3.17177 q^{63} -7.23485 q^{64} +11.0758 q^{65} -0.179763 q^{66} -6.12066 q^{67} -2.14054 q^{68} -1.91419 q^{69} -1.25709 q^{70} +10.4162 q^{71} +0.713244 q^{72} +12.2613 q^{73} -1.37992 q^{74} +0.139010 q^{75} -6.96349 q^{76} -3.17177 q^{77} +0.903056 q^{78} +15.6773 q^{79} +8.39388 q^{80} +1.00000 q^{81} +0.503958 q^{82} +10.7598 q^{83} +6.24104 q^{84} +2.39845 q^{85} +1.34238 q^{86} +5.13495 q^{87} -0.713244 q^{88} -14.2391 q^{89} -0.396336 q^{90} +15.9336 q^{91} -3.76653 q^{92} +0.976010 q^{93} -0.915737 q^{94} +7.80250 q^{95} +2.11088 q^{96} -13.8759 q^{97} -0.550094 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.179763	−0.127112	−0.0635560	−	0.997978i	$-0.520244\pi$
$2$	−0.179763	−0.127112	−0.0635560	+	0.997978i	$0.520244\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96769	−0.983843
$5$	2.20477	0.986001	0.493001	−	0.870029i	$-0.335900\pi$
$5$	2.20477	0.986001	0.493001	+	0.870029i	$0.335900\pi$
$6$	0.179763	0.0733881
$7$	3.17177	1.19881	0.599407	−	0.800444i	$-0.295403\pi$
$7$	3.17177	1.19881	0.599407	+	0.800444i	$0.295403\pi$
$8$	0.713244	0.252170
$9$	1.00000	0.333333
$10$	−0.396336	−0.125332
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.96769	0.568022
$13$	5.02358	1.39329	0.696645	−	0.717416i	$-0.254675\pi$
$13$	5.02358	1.39329	0.696645	+	0.717416i	$0.254675\pi$
$14$	−0.570167	−0.152384
$15$	−2.20477	−0.569268
$16$	3.80716	0.951789
$17$	1.08785	0.263842	0.131921	−	0.991260i	$-0.457886\pi$
$17$	1.08785	0.263842	0.131921	+	0.991260i	$0.457886\pi$
$18$	−0.179763	−0.0423706
$19$	3.53893	0.811885	0.405943	−	0.913899i	$-0.366943\pi$
$19$	3.53893	0.811885	0.405943	+	0.913899i	$0.366943\pi$
$20$	−4.33828	−0.970070
$21$	−3.17177	−0.692136
$22$	0.179763	0.0383257
$23$	1.91419	0.399137	0.199568	−	0.979884i	$-0.436046\pi$
$23$	1.91419	0.399137	0.199568	+	0.979884i	$0.436046\pi$
$24$	−0.713244	−0.145590
$25$	−0.139010	−0.0278020
$26$	−0.903056	−0.177104
$27$	−1.00000	−0.192450
$28$	−6.24104	−1.17944
$29$	−5.13495	−0.953537	−0.476768	−	0.879029i	$-0.658192\pi$
$29$	−5.13495	−0.953537	−0.476768	+	0.879029i	$0.658192\pi$
$30$	0.396336	0.0723607
$31$	−0.976010	−0.175297	−0.0876483	−	0.996151i	$-0.527935\pi$
$31$	−0.976010	−0.175297	−0.0876483	+	0.996151i	$0.527935\pi$
$32$	−2.11088	−0.373154
$33$	1.00000	0.174078
$34$	−0.195555	−0.0335374
$35$	6.99300	1.18203
$36$	−1.96769	−0.327948
$37$	7.67629	1.26197	0.630987	−	0.775793i	$-0.282650\pi$
$37$	7.67629	1.26197	0.630987	+	0.775793i	$0.282650\pi$
$38$	−0.636169	−0.103200
$39$	−5.02358	−0.804416
$40$	1.57254	0.248640
$41$	−2.80345	−0.437826	−0.218913	−	0.975744i	$-0.570251\pi$
$41$	−2.80345	−0.437826	−0.218913	+	0.975744i	$0.570251\pi$
$42$	0.570167	0.0879787
$43$	−7.46749	−1.13878	−0.569391	−	0.822067i	$-0.692821\pi$
$43$	−7.46749	−1.13878	−0.569391	+	0.822067i	$0.692821\pi$
$44$	1.96769	0.296640
$45$	2.20477	0.328667
$46$	−0.344102	−0.0507350
$47$	5.09413	0.743055	0.371527	−	0.928422i	$-0.378834\pi$
$47$	5.09413	0.743055	0.371527	+	0.928422i	$0.378834\pi$
$48$	−3.80716	−0.549515
$49$	3.06010	0.437157
$50$	0.0249889	0.00353396
$51$	−1.08785	−0.152329
$52$	−9.88482	−1.37078
$53$	−10.9620	−1.50574	−0.752870	−	0.658169i	$-0.771331\pi$
$53$	−10.9620	−1.50574	−0.752870	+	0.658169i	$0.771331\pi$
$54$	0.179763	0.0244627
$55$	−2.20477	−0.297290
$56$	2.26224	0.302305
$57$	−3.53893	−0.468742
$58$	0.923076	0.121206
$59$	8.89797	1.15842	0.579209	−	0.815179i	$-0.303362\pi$
$59$	8.89797	1.15842	0.579209	+	0.815179i	$0.303362\pi$
$60$	4.33828	0.560070
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	0.175451	0.0222823
$63$	3.17177	0.399605
$64$	−7.23485	−0.904356
$65$	11.0758	1.37379
$66$	−0.179763	−0.0221273
$67$	−6.12066	−0.747757	−0.373879	−	0.927478i	$-0.621972\pi$
$67$	−6.12066	−0.747757	−0.373879	+	0.927478i	$0.621972\pi$
$68$	−2.14054	−0.259579
$69$	−1.91419	−0.230442
$70$	−1.25709	−0.150250
$71$	10.4162	1.23618	0.618091	−	0.786107i	$-0.287907\pi$
$71$	10.4162	1.23618	0.618091	+	0.786107i	$0.287907\pi$
$72$	0.713244	0.0840567
$73$	12.2613	1.43508	0.717538	−	0.696519i	$-0.245269\pi$
$73$	12.2613	1.43508	0.717538	+	0.696519i	$0.245269\pi$
$74$	−1.37992	−0.160412
$75$	0.139010	0.0160515
$76$	−6.96349	−0.798767
$77$	−3.17177	−0.361456
$78$	0.903056	0.102251
$79$	15.6773	1.76384	0.881918	−	0.471402i	$-0.156252\pi$
$79$	15.6773	1.76384	0.881918	+	0.471402i	$0.156252\pi$
$80$	8.39388	0.938465
$81$	1.00000	0.111111
$82$	0.503958	0.0556529
$83$	10.7598	1.18105	0.590523	−	0.807021i	$-0.298922\pi$
$83$	10.7598	1.18105	0.590523	+	0.807021i	$0.298922\pi$
$84$	6.24104	0.680953
$85$	2.39845	0.260148
$86$	1.34238	0.144753
$87$	5.13495	0.550525
$88$	−0.713244	−0.0760321
$89$	−14.2391	−1.50934	−0.754669	−	0.656106i	$-0.772203\pi$
$89$	−14.2391	−1.50934	−0.754669	+	0.656106i	$0.772203\pi$
$90$	−0.396336	−0.0417775
$91$	15.9336	1.67030
$92$	−3.76653	−0.392688
$93$	0.976010	0.101208
$94$	−0.915737	−0.0944511
$95$	7.80250	0.800520
$96$	2.11088	0.215440
$97$	−13.8759	−1.40888	−0.704440	−	0.709763i	$-0.748802\pi$
$97$	−13.8759	−1.40888	−0.704440	+	0.709763i	$0.748802\pi$
$98$	−0.550094	−0.0555678
$99$	−1.00000	−0.100504
$100$	0.273528	0.0273528
$101$	−3.48657	−0.346927	−0.173463	−	0.984840i	$-0.555496\pi$
$101$	−3.48657	−0.346927	−0.173463	+	0.984840i	$0.555496\pi$
$102$	0.195555	0.0193628
$103$	−19.2415	−1.89592	−0.947960	−	0.318389i	$-0.896858\pi$
$103$	−19.2415	−1.89592	−0.947960	+	0.318389i	$0.896858\pi$
$104$	3.58304	0.351346
$105$	−6.99300	−0.682447
$106$	1.97056	0.191398
$107$	2.82984	0.273571	0.136786	−	0.990601i	$-0.456323\pi$
$107$	2.82984	0.273571	0.136786	+	0.990601i	$0.456323\pi$
$108$	1.96769	0.189341
$109$	7.46781	0.715287	0.357643	−	0.933858i	$-0.383580\pi$
$109$	7.46781	0.715287	0.357643	+	0.933858i	$0.383580\pi$
$110$	0.396336	0.0377892
$111$	−7.67629	−0.728601
$112$	12.0754	1.14102
$113$	−9.07728	−0.853919	−0.426959	−	0.904271i	$-0.640415\pi$
$113$	−9.07728	−0.853919	−0.426959	+	0.904271i	$0.640415\pi$
$114$	0.636169	0.0595827
$115$	4.22035	0.393549
$116$	10.1040	0.938130
$117$	5.02358	0.464430
$118$	−1.59953	−0.147249
$119$	3.45039	0.316297
$120$	−1.57254	−0.143552
$121$	1.00000	0.0909091
$122$	−0.179763	−0.0162750
$123$	2.80345	0.252779
$124$	1.92048	0.172464
$125$	−11.3303	−1.01341
$126$	−0.570167	−0.0507945
$127$	8.94879	0.794077	0.397039	−	0.917802i	$-0.370038\pi$
$127$	8.94879	0.794077	0.397039	+	0.917802i	$0.370038\pi$
$128$	5.52231	0.488108
$129$	7.46749	0.657476
$130$	−1.99103	−0.174625
$131$	13.9885	1.22218	0.611090	−	0.791561i	$-0.290732\pi$
$131$	13.9885	1.22218	0.611090	+	0.791561i	$0.290732\pi$
$132$	−1.96769	−0.171265
$133$	11.2246	0.973300
$134$	1.10027	0.0950488
$135$	−2.20477	−0.189756
$136$	0.775901	0.0665329
$137$	19.7992	1.69156	0.845781	−	0.533530i	$-0.179135\pi$
$137$	19.7992	1.69156	0.845781	+	0.533530i	$0.179135\pi$
$138$	0.344102	0.0292919
$139$	−4.24898	−0.360394	−0.180197	−	0.983631i	$-0.557674\pi$
$139$	−4.24898	−0.360394	−0.180197	+	0.983631i	$0.557674\pi$
$140$	−13.7600	−1.16293
$141$	−5.09413	−0.429003
$142$	−1.87246	−0.157133
$143$	−5.02358	−0.420093
$144$	3.80716	0.317263
$145$	−11.3214	−0.940188
$146$	−2.20413	−0.182415
$147$	−3.06010	−0.252393
$148$	−15.1045	−1.24158
$149$	4.17125	0.341722	0.170861	−	0.985295i	$-0.445345\pi$
$149$	4.17125	0.341722	0.170861	+	0.985295i	$0.445345\pi$
$150$	−0.0249889	−0.00204034
$151$	18.0934	1.47242	0.736212	−	0.676751i	$-0.236613\pi$
$151$	18.0934	1.47242	0.736212	+	0.676751i	$0.236613\pi$
$152$	2.52412	0.204733
$153$	1.08785	0.0879472
$154$	0.570167	0.0459454
$155$	−2.15187	−0.172843
$156$	9.88482	0.791419
$157$	19.5799	1.56265	0.781323	−	0.624126i	$-0.214545\pi$
$157$	19.5799	1.56265	0.781323	+	0.624126i	$0.214545\pi$
$158$	−2.81821	−0.224205
$159$	10.9620	0.869340
$160$	−4.65399	−0.367930
$161$	6.07137	0.478491
$162$	−0.179763	−0.0141235
$163$	14.3214	1.12174	0.560870	−	0.827904i	$-0.310467\pi$
$163$	14.3214	1.12174	0.560870	+	0.827904i	$0.310467\pi$
$164$	5.51632	0.430752
$165$	2.20477	0.171641
$166$	−1.93422	−0.150125
$167$	0.178130	0.0137841	0.00689205	−	0.999976i	$-0.497806\pi$
$167$	0.178130	0.0137841	0.00689205	+	0.999976i	$0.497806\pi$
$168$	−2.26224	−0.174536
$169$	12.2363	0.941258
$170$	−0.431153	−0.0330679
$171$	3.53893	0.270628
$172$	14.6937	1.12038
$173$	0.504790	0.0383785	0.0191892	−	0.999816i	$-0.493892\pi$
$173$	0.504790	0.0383785	0.0191892	+	0.999816i	$0.493892\pi$
$174$	−0.923076	−0.0699782
$175$	−0.440907	−0.0333294
$176$	−3.80716	−0.286975
$177$	−8.89797	−0.668813
$178$	2.55966	0.191855
$179$	12.0518	0.900795	0.450397	−	0.892828i	$-0.351282\pi$
$179$	12.0518	0.900795	0.450397	+	0.892828i	$0.351282\pi$
$180$	−4.33828	−0.323357
$181$	23.8425	1.77220	0.886098	−	0.463497i	$-0.153406\pi$
$181$	23.8425	1.77220	0.886098	+	0.463497i	$0.153406\pi$
$182$	−2.86428	−0.212315
$183$	−1.00000	−0.0739221
$184$	1.36529	0.100650
$185$	16.9244	1.24431
$186$	−0.175451	−0.0128647
$187$	−1.08785	−0.0795512
$188$	−10.0236	−0.731049
$189$	−3.17177	−0.230712
$190$	−1.40260	−0.101756
$191$	−26.0154	−1.88241	−0.941205	−	0.337836i	$-0.890305\pi$
$191$	−26.0154	−1.88241	−0.941205	+	0.337836i	$0.890305\pi$
$192$	7.23485	0.522130
$193$	−3.89975	−0.280710	−0.140355	−	0.990101i	$-0.544824\pi$
$193$	−3.89975	−0.280710	−0.140355	+	0.990101i	$0.544824\pi$
$194$	2.49437	0.179086
$195$	−11.0758	−0.793155
$196$	−6.02131	−0.430093
$197$	−21.9665	−1.56505	−0.782526	−	0.622618i	$-0.786069\pi$
$197$	−21.9665	−1.56505	−0.782526	+	0.622618i	$0.786069\pi$
$198$	0.179763	0.0127752
$199$	1.14129	0.0809040	0.0404520	−	0.999181i	$-0.487120\pi$
$199$	1.14129	0.0809040	0.0404520	+	0.999181i	$0.487120\pi$
$200$	−0.0991481	−0.00701083
$201$	6.12066	0.431718
$202$	0.626758	0.0440985
$203$	−16.2869	−1.14311
$204$	2.14054	0.149868
$205$	−6.18096	−0.431697
$206$	3.45892	0.240994
$207$	1.91419	0.133046
$208$	19.1255	1.32612
$209$	−3.53893	−0.244793
$210$	1.25709	0.0867471
$211$	9.40163	0.647235	0.323617	−	0.946188i	$-0.395101\pi$
$211$	9.40163	0.647235	0.323617	+	0.946188i	$0.395101\pi$
$212$	21.5697	1.48141
$213$	−10.4162	−0.713709
$214$	−0.508702	−0.0347742
$215$	−16.4641	−1.12284
$216$	−0.713244	−0.0485301
$217$	−3.09568	−0.210148
$218$	−1.34244	−0.0909215
$219$	−12.2613	−0.828541
$220$	4.33828	0.292487
$221$	5.46488	0.367608
$222$	1.37992	0.0926139
$223$	2.42729	0.162543	0.0812715	−	0.996692i	$-0.474102\pi$
$223$	2.42729	0.162543	0.0812715	+	0.996692i	$0.474102\pi$
$224$	−6.69520	−0.447342
$225$	−0.139010	−0.00926733
$226$	1.63176	0.108543
$227$	−19.4929	−1.29379	−0.646893	−	0.762581i	$-0.723932\pi$
$227$	−19.4929	−1.29379	−0.646893	+	0.762581i	$0.723932\pi$
$228$	6.96349	0.461168
$229$	14.8284	0.979889	0.489944	−	0.871754i	$-0.337017\pi$
$229$	14.8284	0.979889	0.489944	+	0.871754i	$0.337017\pi$
$230$	−0.758664	−0.0500248
$231$	3.17177	0.208687
$232$	−3.66248	−0.240453
$233$	−9.17826	−0.601288	−0.300644	−	0.953736i	$-0.597202\pi$
$233$	−9.17826	−0.601288	−0.300644	+	0.953736i	$0.597202\pi$
$234$	−0.903056	−0.0590346
$235$	11.2314	0.732653
$236$	−17.5084	−1.13970
$237$	−15.6773	−1.01835
$238$	−0.620255	−0.0402051
$239$	17.9788	1.16296	0.581478	−	0.813562i	$-0.302475\pi$
$239$	17.9788	1.16296	0.581478	+	0.813562i	$0.302475\pi$
$240$	−8.39388	−0.541823
$241$	−11.8019	−0.760226	−0.380113	−	0.924940i	$-0.624115\pi$
$241$	−11.8019	−0.760226	−0.380113	+	0.924940i	$0.624115\pi$
$242$	−0.179763	−0.0115556
$243$	−1.00000	−0.0641500
$244$	−1.96769	−0.125968
$245$	6.74680	0.431037
$246$	−0.503958	−0.0321312
$247$	17.7781	1.13119
$248$	−0.696134	−0.0442045
$249$	−10.7598	−0.681877
$250$	2.03677	0.128817
$251$	−17.0765	−1.07786	−0.538929	−	0.842351i	$-0.681171\pi$
$251$	−17.0765	−1.07786	−0.538929	+	0.842351i	$0.681171\pi$
$252$	−6.24104	−0.393148
$253$	−1.91419	−0.120344
$254$	−1.60867	−0.100937
$255$	−2.39845	−0.150197
$256$	13.4770	0.842312
$257$	18.9734	1.18353	0.591763	−	0.806112i	$-0.298432\pi$
$257$	18.9734	1.18353	0.591763	+	0.806112i	$0.298432\pi$
$258$	−1.34238	−0.0835730
$259$	24.3474	1.51287
$260$	−21.7937	−1.35159
$261$	−5.13495	−0.317846
$262$	−2.51462	−0.155354
$263$	14.6726	0.904753	0.452376	−	0.891827i	$-0.350576\pi$
$263$	14.6726	0.904753	0.452376	+	0.891827i	$0.350576\pi$
$264$	0.713244	0.0438972
$265$	−24.1685	−1.48466
$266$	−2.01778	−0.123718
$267$	14.2391	0.871417
$268$	12.0435	0.735675
$269$	−16.9485	−1.03337	−0.516685	−	0.856176i	$-0.672834\pi$
$269$	−16.9485	−1.03337	−0.516685	+	0.856176i	$0.672834\pi$
$270$	0.396336	0.0241202
$271$	6.59936	0.400883	0.200441	−	0.979706i	$-0.435762\pi$
$271$	6.59936	0.400883	0.200441	+	0.979706i	$0.435762\pi$
$272$	4.14160	0.251121
$273$	−15.9336	−0.964346
$274$	−3.55918	−0.215018
$275$	0.139010	0.00838262
$276$	3.76653	0.226718
$277$	−19.7287	−1.18538	−0.592692	−	0.805429i	$-0.701935\pi$
$277$	−19.7287	−1.18538	−0.592692	+	0.805429i	$0.701935\pi$
$278$	0.763811	0.0458104
$279$	−0.976010	−0.0584322
$280$	4.98772	0.298073
$281$	−23.8313	−1.42165	−0.710827	−	0.703367i	$-0.751679\pi$
$281$	−23.8313	−1.42165	−0.710827	+	0.703367i	$0.751679\pi$
$282$	0.915737	0.0545314
$283$	−14.5254	−0.863447	−0.431724	−	0.902006i	$-0.642094\pi$
$283$	−14.5254	−0.863447	−0.431724	+	0.902006i	$0.642094\pi$
$284$	−20.4959	−1.21621
$285$	−7.80250	−0.462180
$286$	0.903056	0.0533988
$287$	−8.89190	−0.524872
$288$	−2.11088	−0.124385
$289$	−15.8166	−0.930388
$290$	2.03517	0.119509
$291$	13.8759	0.813418
$292$	−24.1264	−1.41189
$293$	−3.05620	−0.178545	−0.0892724	−	0.996007i	$-0.528454\pi$
$293$	−3.05620	−0.178545	−0.0892724	+	0.996007i	$0.528454\pi$
$294$	0.550094	0.0320821
$295$	19.6179	1.14220
$296$	5.47507	0.318232
$297$	1.00000	0.0580259
$298$	−0.749838	−0.0434369
$299$	9.61610	0.556113
$300$	−0.273528	−0.0157921
$301$	−23.6851	−1.36519
$302$	−3.25254	−0.187163
$303$	3.48657	0.200298
$304$	13.4732	0.772743
$305$	2.20477	0.126244
$306$	−0.195555	−0.0111791
$307$	−18.3076	−1.04487	−0.522436	−	0.852679i	$-0.674976\pi$
$307$	−18.3076	−1.04487	−0.522436	+	0.852679i	$0.674976\pi$
$308$	6.24104	0.355616
$309$	19.2415	1.09461
$310$	0.386828	0.0219704
$311$	−20.8499	−1.18229	−0.591145	−	0.806565i	$-0.701324\pi$
$311$	−20.8499	−1.18229	−0.591145	+	0.806565i	$0.701324\pi$
$312$	−3.58304	−0.202850
$313$	−3.49928	−0.197791	−0.0988956	−	0.995098i	$-0.531531\pi$
$313$	−3.49928	−0.197791	−0.0988956	+	0.995098i	$0.531531\pi$
$314$	−3.51975	−0.198631
$315$	6.99300	0.394011
$316$	−30.8480	−1.73534
$317$	−18.4416	−1.03578	−0.517891	−	0.855447i	$-0.673283\pi$
$317$	−18.4416	−1.03578	−0.517891	+	0.855447i	$0.673283\pi$
$318$	−1.97056	−0.110503
$319$	5.13495	0.287502
$320$	−15.9512	−0.891696
$321$	−2.82984	−0.157947
$322$	−1.09141	−0.0608219
$323$	3.84981	0.214209
$324$	−1.96769	−0.109316
$325$	−0.698328	−0.0387362
$326$	−2.57447	−0.142587
$327$	−7.46781	−0.412971
$328$	−1.99955	−0.110407
$329$	16.1574	0.890785
$330$	−0.396336	−0.0218176
$331$	6.78274	0.372813	0.186407	−	0.982473i	$-0.440316\pi$
$331$	6.78274	0.372813	0.186407	+	0.982473i	$0.440316\pi$
$332$	−21.1720	−1.16196
$333$	7.67629	0.420658
$334$	−0.0320212	−0.00175212
$335$	−13.4946	−0.737289
$336$	−12.0754	−0.658767
$337$	35.9736	1.95961	0.979803	−	0.199965i	$-0.0640827\pi$
$337$	35.9736	1.95961	0.979803	+	0.199965i	$0.0640827\pi$
$338$	−2.19965	−0.119645
$339$	9.07728	0.493010
$340$	−4.71939	−0.255945
$341$	0.976010	0.0528539
$342$	−0.636169	−0.0344001
$343$	−12.4964	−0.674745
$344$	−5.32615	−0.287167
$345$	−4.22035	−0.227216
$346$	−0.0907427	−0.00487836
$347$	−8.50844	−0.456757	−0.228379	−	0.973572i	$-0.573342\pi$
$347$	−8.50844	−0.456757	−0.228379	+	0.973572i	$0.573342\pi$
$348$	−10.1040	−0.541630
$349$	13.9195	0.745096	0.372548	−	0.928013i	$-0.378484\pi$
$349$	13.9195	0.745096	0.372548	+	0.928013i	$0.378484\pi$
$350$	0.0792589	0.00423657
$351$	−5.02358	−0.268139
$352$	2.11088	0.112510
$353$	−21.3602	−1.13689	−0.568444	−	0.822722i	$-0.692454\pi$
$353$	−21.3602	−1.13689	−0.568444	+	0.822722i	$0.692454\pi$
$354$	1.59953	0.0850140
$355$	22.9654	1.21888
$356$	28.0180	1.48495
$357$	−3.45039	−0.182614
$358$	−2.16647	−0.114502
$359$	−10.1841	−0.537495	−0.268748	−	0.963211i	$-0.586610\pi$
$359$	−10.1841	−0.537495	−0.268748	+	0.963211i	$0.586610\pi$
$360$	1.57254	0.0828800
$361$	−6.47601	−0.340842
$362$	−4.28600	−0.225267
$363$	−1.00000	−0.0524864
$364$	−31.3523	−1.64331
$365$	27.0333	1.41499
$366$	0.179763	0.00939638
$367$	−7.71600	−0.402772	−0.201386	−	0.979512i	$-0.564545\pi$
$367$	−7.71600	−0.402772	−0.201386	+	0.979512i	$0.564545\pi$
$368$	7.28763	0.379894
$369$	−2.80345	−0.145942
$370$	−3.04239	−0.158166
$371$	−34.7688	−1.80510
$372$	−1.92048	−0.0995723
$373$	−17.3992	−0.900897	−0.450448	−	0.892802i	$-0.648736\pi$
$373$	−17.3992	−0.900897	−0.450448	+	0.892802i	$0.648736\pi$
$374$	0.195555	0.0101119
$375$	11.3303	0.585095
$376$	3.63336	0.187376
$377$	−25.7958	−1.32855
$378$	0.570167	0.0293262
$379$	−2.31368	−0.118846	−0.0594230	−	0.998233i	$-0.518926\pi$
$379$	−2.31368	−0.118846	−0.0594230	+	0.998233i	$0.518926\pi$
$380$	−15.3529	−0.787585
$381$	−8.94879	−0.458461
$382$	4.67662	0.239277
$383$	−8.99228	−0.459484	−0.229742	−	0.973252i	$-0.573788\pi$
$383$	−8.99228	−0.459484	−0.229742	+	0.973252i	$0.573788\pi$
$384$	−5.52231	−0.281809
$385$	−6.99300	−0.356396
$386$	0.701032	0.0356816
$387$	−7.46749	−0.379594
$388$	27.3033	1.38612
$389$	−7.65447	−0.388097	−0.194048	−	0.980992i	$-0.562162\pi$
$389$	−7.65447	−0.388097	−0.194048	+	0.980992i	$0.562162\pi$
$390$	1.99103	0.100820
$391$	2.08235	0.105309
$392$	2.18260	0.110238
$393$	−13.9885	−0.705625
$394$	3.94878	0.198937
$395$	34.5648	1.73914
$396$	1.96769	0.0988799
$397$	26.1237	1.31111	0.655555	−	0.755147i	$-0.272435\pi$
$397$	26.1237	1.31111	0.655555	+	0.755147i	$0.272435\pi$
$398$	−0.205162	−0.0102839
$399$	−11.2246	−0.561935
$400$	−0.529232	−0.0264616
$401$	−27.3416	−1.36537	−0.682686	−	0.730712i	$-0.739188\pi$
$401$	−27.3416	−1.36537	−0.682686	+	0.730712i	$0.739188\pi$
$402$	−1.10027	−0.0548765
$403$	−4.90306	−0.244239
$404$	6.86047	0.341321
$405$	2.20477	0.109556
$406$	2.92778	0.145303
$407$	−7.67629	−0.380500
$408$	−0.775901	−0.0384128
$409$	−24.2671	−1.19993	−0.599965	−	0.800027i	$-0.704819\pi$
$409$	−24.2671	−1.19993	−0.599965	+	0.800027i	$0.704819\pi$
$410$	1.11111	0.0548738
$411$	−19.7992	−0.976624
$412$	37.8612	1.86529
$413$	28.2223	1.38873
$414$	−0.344102	−0.0169117
$415$	23.7229	1.16451
$416$	−10.6042	−0.519911
$417$	4.24898	0.208074
$418$	0.636169	0.0311161
$419$	16.5732	0.809655	0.404828	−	0.914393i	$-0.367332\pi$
$419$	16.5732	0.809655	0.404828	+	0.914393i	$0.367332\pi$
$420$	13.7600	0.671420
$421$	0.423105	0.0206209	0.0103104	−	0.999947i	$-0.496718\pi$
$421$	0.423105	0.0206209	0.0103104	+	0.999947i	$0.496718\pi$
$422$	−1.69007	−0.0822713
$423$	5.09413	0.247685
$424$	−7.81856	−0.379703
$425$	−0.151222	−0.00733532
$426$	1.87246	0.0907210
$427$	3.17177	0.153493
$428$	−5.56824	−0.269151
$429$	5.02358	0.242541
$430$	2.95964	0.142726
$431$	24.3394	1.17239	0.586195	−	0.810170i	$-0.300625\pi$
$431$	24.3394	1.17239	0.586195	+	0.810170i	$0.300625\pi$
$432$	−3.80716	−0.183172
$433$	5.45603	0.262200	0.131100	−	0.991369i	$-0.458149\pi$
$433$	5.45603	0.262200	0.131100	+	0.991369i	$0.458149\pi$
$434$	0.556489	0.0267123
$435$	11.3214	0.542818
$436$	−14.6943	−0.703730
$437$	6.77419	0.324053
$438$	2.20413	0.105317
$439$	5.71582	0.272801	0.136401	−	0.990654i	$-0.456447\pi$
$439$	5.71582	0.272801	0.136401	+	0.990654i	$0.456447\pi$
$440$	−1.57254	−0.0749677
$441$	3.06010	0.145719
$442$	−0.982386	−0.0467273
$443$	15.1986	0.722106	0.361053	−	0.932545i	$-0.382417\pi$
$443$	15.1986	0.722106	0.361053	+	0.932545i	$0.382417\pi$
$444$	15.1045	0.716829
$445$	−31.3938	−1.48821
$446$	−0.436337	−0.0206612
$447$	−4.17125	−0.197293
$448$	−22.9473	−1.08416
$449$	−1.16467	−0.0549641	−0.0274820	−	0.999622i	$-0.508749\pi$
$449$	−1.16467	−0.0549641	−0.0274820	+	0.999622i	$0.508749\pi$
$450$	0.0249889	0.00117799
$451$	2.80345	0.132010
$452$	17.8612	0.840122
$453$	−18.0934	−0.850104
$454$	3.50410	0.164456
$455$	35.1299	1.64691
$456$	−2.52412	−0.118203
$457$	15.8354	0.740748	0.370374	−	0.928883i	$-0.379230\pi$
$457$	15.8354	0.740748	0.370374	+	0.928883i	$0.379230\pi$
$458$	−2.66560	−0.124556
$459$	−1.08785	−0.0507763
$460$	−8.30431	−0.387191
$461$	14.3447	0.668097	0.334048	−	0.942556i	$-0.391585\pi$
$461$	14.3447	0.668097	0.334048	+	0.942556i	$0.391585\pi$
$462$	−0.570167	−0.0265266
$463$	24.6422	1.14522	0.572611	−	0.819827i	$-0.305931\pi$
$463$	24.6422	1.14522	0.572611	+	0.819827i	$0.305931\pi$
$464$	−19.5496	−0.907566
$465$	2.15187	0.0997907
$466$	1.64992	0.0764309
$467$	−9.26543	−0.428753	−0.214377	−	0.976751i	$-0.568772\pi$
$467$	−9.26543	−0.428753	−0.214377	+	0.976751i	$0.568772\pi$
$468$	−9.88482	−0.456926
$469$	−19.4133	−0.896422
$470$	−2.01899	−0.0931289
$471$	−19.5799	−0.902194
$472$	6.34643	0.292118
$473$	7.46749	0.343356
$474$	2.81821	0.129445
$475$	−0.491946	−0.0225720
$476$	−6.78929	−0.311187
$477$	−10.9620	−0.501914
$478$	−3.23194	−0.147825
$479$	4.42880	0.202357	0.101178	−	0.994868i	$-0.467739\pi$
$479$	4.42880	0.202357	0.101178	+	0.994868i	$0.467739\pi$
$480$	4.65399	0.212424
$481$	38.5625	1.75830
$482$	2.12154	0.0966337
$483$	−6.07137	−0.276257
$484$	−1.96769	−0.0894402
$485$	−30.5930	−1.38916
$486$	0.179763	0.00815423
$487$	24.2935	1.10084	0.550422	−	0.834886i	$-0.314467\pi$
$487$	24.2935	1.10084	0.550422	+	0.834886i	$0.314467\pi$
$488$	0.713244	0.0322871
$489$	−14.3214	−0.647637
$490$	−1.21283	−0.0547899
$491$	−42.5903	−1.92207	−0.961037	−	0.276420i	$-0.910852\pi$
$491$	−42.5903	−1.92207	−0.961037	+	0.276420i	$0.910852\pi$
$492$	−5.51632	−0.248695
$493$	−5.58604	−0.251583
$494$	−3.19585	−0.143788
$495$	−2.20477	−0.0990968
$496$	−3.71582	−0.166845
$497$	33.0379	1.48195
$498$	1.93422	0.0866747
$499$	29.9642	1.34138	0.670690	−	0.741737i	$-0.265998\pi$
$499$	29.9642	1.34138	0.670690	+	0.741737i	$0.265998\pi$
$500$	22.2945	0.997040
$501$	−0.178130	−0.00795825
$502$	3.06973	0.137009
$503$	23.4580	1.04594	0.522970	−	0.852351i	$-0.324824\pi$
$503$	23.4580	1.04594	0.522970	+	0.852351i	$0.324824\pi$
$504$	2.26224	0.100768
$505$	−7.68707	−0.342070
$506$	0.344102	0.0152972
$507$	−12.2363	−0.543435
$508$	−17.6084	−0.781247
$509$	12.5052	0.554284	0.277142	−	0.960829i	$-0.410613\pi$
$509$	12.5052	0.554284	0.277142	+	0.960829i	$0.410613\pi$
$510$	0.431153	0.0190918
$511$	38.8900	1.72039
$512$	−13.4673	−0.595176
$513$	−3.53893	−0.156247
$514$	−3.41072	−0.150440
$515$	−42.4230	−1.86938
$516$	−14.6937	−0.646853
$517$	−5.09413	−0.224039
$518$	−4.37677	−0.192304
$519$	−0.504790	−0.0221578
$520$	7.89976	0.346428
$521$	−17.7110	−0.775931	−0.387966	−	0.921674i	$-0.626822\pi$
$521$	−17.7110	−0.775931	−0.387966	+	0.921674i	$0.626822\pi$
$522$	0.923076	0.0404020
$523$	−24.7263	−1.08121	−0.540603	−	0.841278i	$-0.681804\pi$
$523$	−24.7263	−1.08121	−0.540603	+	0.841278i	$0.681804\pi$
$524$	−27.5249	−1.20243
$525$	0.440907	0.0192428
$526$	−2.63760	−0.115005
$527$	−1.06175	−0.0462505
$528$	3.80716	0.165685
$529$	−19.3359	−0.840690
$530$	4.34462	0.188718
$531$	8.89797	0.386139
$532$	−22.0866	−0.957574
$533$	−14.0834	−0.610019
$534$	−2.55966	−0.110767
$535$	6.23914	0.269742
$536$	−4.36552	−0.188562
$537$	−12.0518	−0.520074
$538$	3.04672	0.131354
$539$	−3.06010	−0.131808
$540$	4.33828	0.186690
$541$	−14.3455	−0.616759	−0.308380	−	0.951263i	$-0.599787\pi$
$541$	−14.3455	−0.616759	−0.308380	+	0.951263i	$0.599787\pi$
$542$	−1.18632	−0.0509570
$543$	−23.8425	−1.02318
$544$	−2.29631	−0.0984535
$545$	16.4648	0.705273
$546$	2.86428	0.122580
$547$	−13.1006	−0.560142	−0.280071	−	0.959979i	$-0.590358\pi$
$547$	−13.1006	−0.560142	−0.280071	+	0.959979i	$0.590358\pi$
$548$	−38.9586	−1.66423
$549$	1.00000	0.0426790
$550$	−0.0249889	−0.00106553
$551$	−18.1722	−0.774162
$552$	−1.36529	−0.0581105
$553$	49.7248	2.11451
$554$	3.54650	0.150676
$555$	−16.9244	−0.718402
$556$	8.36066	0.354571
$557$	26.6862	1.13073	0.565365	−	0.824841i	$-0.308735\pi$
$557$	26.6862	1.13073	0.565365	+	0.824841i	$0.308735\pi$
$558$	0.175451	0.00742743
$559$	−37.5135	−1.58665
$560$	26.6234	1.12505
$561$	1.08785	0.0459289
$562$	4.28399	0.180709
$563$	−35.8990	−1.51296	−0.756482	−	0.654015i	$-0.773083\pi$
$563$	−35.8990	−1.51296	−0.756482	+	0.654015i	$0.773083\pi$
$564$	10.0236	0.422071
$565$	−20.0133	−0.841965
$566$	2.61114	0.109754
$567$	3.17177	0.133202
$568$	7.42933	0.311728
$569$	43.3017	1.81530	0.907650	−	0.419727i	$-0.137874\pi$
$569$	43.3017	1.81530	0.907650	+	0.419727i	$0.137874\pi$
$570$	1.40260	0.0587486
$571$	18.0647	0.755983	0.377992	−	0.925809i	$-0.376615\pi$
$571$	18.0647	0.755983	0.377992	+	0.925809i	$0.376615\pi$
$572$	9.88482	0.413305
$573$	26.0154	1.08681
$574$	1.59844	0.0667175
$575$	−0.266092	−0.0110968
$576$	−7.23485	−0.301452
$577$	40.3884	1.68139	0.840696	−	0.541507i	$-0.182146\pi$
$577$	40.3884	1.68139	0.840696	+	0.541507i	$0.182146\pi$
$578$	2.84324	0.118263
$579$	3.89975	0.162068
$580$	22.2769	0.924997
$581$	34.1277	1.41585
$582$	−2.49437	−0.103395
$583$	10.9620	0.453998
$584$	8.74530	0.361883
$585$	11.0758	0.457929
$586$	0.549392	0.0226952
$587$	8.96421	0.369992	0.184996	−	0.982739i	$-0.440773\pi$
$587$	8.96421	0.369992	0.184996	+	0.982739i	$0.440773\pi$
$588$	6.02131	0.248315
$589$	−3.45403	−0.142321
$590$	−3.52659	−0.145187
$591$	21.9665	0.903583
$592$	29.2248	1.20113
$593$	−26.1692	−1.07464	−0.537321	−	0.843378i	$-0.680564\pi$
$593$	−26.1692	−1.07464	−0.537321	+	0.843378i	$0.680564\pi$
$594$	−0.179763	−0.00737578
$595$	7.60731	0.311869
$596$	−8.20770	−0.336201
$597$	−1.14129	−0.0467099
$598$	−1.72862	−0.0706886
$599$	25.8018	1.05423	0.527116	−	0.849794i	$-0.323274\pi$
$599$	25.8018	1.05423	0.527116	+	0.849794i	$0.323274\pi$
$600$	0.0991481	0.00404770
$601$	−20.9671	−0.855267	−0.427633	−	0.903952i	$-0.640653\pi$
$601$	−20.9671	−0.855267	−0.427633	+	0.903952i	$0.640653\pi$
$602$	4.25772	0.173532
$603$	−6.12066	−0.249252
$604$	−35.6022	−1.44863
$605$	2.20477	0.0896365
$606$	−0.626758	−0.0254603
$607$	15.8671	0.644025	0.322013	−	0.946735i	$-0.395641\pi$
$607$	15.8671	0.644025	0.322013	+	0.946735i	$0.395641\pi$
$608$	−7.47023	−0.302958
$609$	16.2869	0.659977
$610$	−0.396336	−0.0160472
$611$	25.5908	1.03529
$612$	−2.14054	−0.0865262
$613$	−30.5257	−1.23292	−0.616462	−	0.787385i	$-0.711434\pi$
$613$	−30.5257	−1.23292	−0.616462	+	0.787385i	$0.711434\pi$
$614$	3.29104	0.132816
$615$	6.18096	0.249240
$616$	−2.26224	−0.0911484
$617$	39.2025	1.57823	0.789116	−	0.614244i	$-0.210539\pi$
$617$	39.2025	1.57823	0.789116	+	0.614244i	$0.210539\pi$
$618$	−3.45892	−0.139138
$619$	−5.80498	−0.233322	−0.116661	−	0.993172i	$-0.537219\pi$
$619$	−5.80498	−0.233322	−0.116661	+	0.993172i	$0.537219\pi$
$620$	4.23421	0.170050
$621$	−1.91419	−0.0768139
$622$	3.74805	0.150283
$623$	−45.1630	−1.80942
$624$	−19.1255	−0.765635
$625$	−24.2856	−0.971425
$626$	0.629043	0.0251416
$627$	3.53893	0.141331
$628$	−38.5271	−1.53740
$629$	8.35063	0.332961
$630$	−1.25709	−0.0500835
$631$	−10.9232	−0.434845	−0.217423	−	0.976078i	$-0.569765\pi$
$631$	−10.9232	−0.434845	−0.217423	+	0.976078i	$0.569765\pi$
$632$	11.1818	0.444787
$633$	−9.40163	−0.373681
$634$	3.31512	0.131660
$635$	19.7300	0.782961
$636$	−21.5697	−0.855294
$637$	15.3726	0.609086
$638$	−0.923076	−0.0365449
$639$	10.4162	0.412060
$640$	12.1754	0.481275
$641$	−20.5925	−0.813355	−0.406677	−	0.913572i	$-0.633313\pi$
$641$	−20.5925	−0.813355	−0.406677	+	0.913572i	$0.633313\pi$
$642$	0.508702	0.0200769
$643$	−32.4513	−1.27975	−0.639877	−	0.768477i	$-0.721015\pi$
$643$	−32.4513	−1.27975	−0.639877	+	0.768477i	$0.721015\pi$
$644$	−11.9465	−0.470760
$645$	16.4641	0.648272
$646$	−0.692055	−0.0272285
$647$	24.4762	0.962258	0.481129	−	0.876650i	$-0.340227\pi$
$647$	24.4762	0.962258	0.481129	+	0.876650i	$0.340227\pi$
$648$	0.713244	0.0280189
$649$	−8.89797	−0.349276
$650$	0.125534	0.00492384
$651$	3.09568	0.121329
$652$	−28.1800	−1.10362
$653$	9.38845	0.367399	0.183699	−	0.982982i	$-0.441193\pi$
$653$	9.38845	0.367399	0.183699	+	0.982982i	$0.441193\pi$
$654$	1.34244	0.0524935
$655$	30.8413	1.20507
$656$	−10.6732	−0.416718
$657$	12.2613	0.478359
$658$	−2.90450	−0.113229
$659$	5.44984	0.212296	0.106148	−	0.994350i	$-0.466148\pi$
$659$	5.44984	0.212296	0.106148	+	0.994350i	$0.466148\pi$
$660$	−4.33828	−0.168867
$661$	5.23046	0.203441	0.101721	−	0.994813i	$-0.467565\pi$
$661$	5.23046	0.203441	0.101721	+	0.994813i	$0.467565\pi$
$662$	−1.21929	−0.0473890
$663$	−5.46488	−0.212239
$664$	7.67439	0.297824
$665$	24.7477	0.959675
$666$	−1.37992	−0.0534707
$667$	−9.82929	−0.380592
$668$	−0.350503	−0.0135614
$669$	−2.42729	−0.0938443
$670$	2.42584	0.0937182
$671$	−1.00000	−0.0386046
$672$	6.69520	0.258273
$673$	−50.7702	−1.95705	−0.978523	−	0.206136i	$-0.933911\pi$
$673$	−50.7702	−1.95705	−0.978523	+	0.206136i	$0.933911\pi$
$674$	−6.46673	−0.249089
$675$	0.139010	0.00535050
$676$	−24.0773	−0.926049
$677$	−38.0216	−1.46129	−0.730645	−	0.682757i	$-0.760781\pi$
$677$	−38.0216	−1.46129	−0.730645	+	0.682757i	$0.760781\pi$
$678$	−1.63176	−0.0626675
$679$	−44.0110	−1.68899
$680$	1.71068	0.0656015
$681$	19.4929	0.746968
$682$	−0.175451	−0.00671836
$683$	20.3542	0.778831	0.389416	−	0.921062i	$-0.372677\pi$
$683$	20.3542	0.778831	0.389416	+	0.921062i	$0.372677\pi$
$684$	−6.96349	−0.266256
$685$	43.6527	1.66788
$686$	2.24640	0.0857681
$687$	−14.8284	−0.565739
$688$	−28.4299	−1.08388
$689$	−55.0683	−2.09793
$690$	0.758664	0.0288818
$691$	−2.62631	−0.0999094	−0.0499547	−	0.998751i	$-0.515908\pi$
$691$	−2.62631	−0.0999094	−0.0499547	+	0.998751i	$0.515908\pi$
$692$	−0.993268	−0.0377584
$693$	−3.17177	−0.120485
$694$	1.52951	0.0580593
$695$	−9.36801	−0.355349
$696$	3.66248	0.138826
$697$	−3.04973	−0.115517
$698$	−2.50222	−0.0947106
$699$	9.17826	0.347154
$700$	0.867566	0.0327909
$701$	36.7376	1.38756	0.693780	−	0.720187i	$-0.255944\pi$
$701$	36.7376	1.38756	0.693780	+	0.720187i	$0.255944\pi$
$702$	0.903056	0.0340836
$703$	27.1658	1.02458
$704$	7.23485	0.272674
$705$	−11.2314	−0.422997
$706$	3.83978	0.144512
$707$	−11.0586	−0.415901
$708$	17.5084	0.658006
$709$	29.6385	1.11310	0.556549	−	0.830815i	$-0.312125\pi$
$709$	29.6385	1.11310	0.556549	+	0.830815i	$0.312125\pi$
$710$	−4.12833	−0.154934
$711$	15.6773	0.587946
$712$	−10.1559	−0.380610
$713$	−1.86827	−0.0699673
$714$	0.620255	0.0232124
$715$	−11.0758	−0.414212
$716$	−23.7142	−0.886240
$717$	−17.9788	−0.671432
$718$	1.83072	0.0683220
$719$	20.2891	0.756655	0.378327	−	0.925672i	$-0.376499\pi$
$719$	20.2891	0.756655	0.378327	+	0.925672i	$0.376499\pi$
$720$	8.39388	0.312822
$721$	−61.0295	−2.27286
$722$	1.16415	0.0433251
$723$	11.8019	0.438916
$724$	−46.9145	−1.74356
$725$	0.713810	0.0265102
$726$	0.179763	0.00667164
$727$	−12.1406	−0.450271	−0.225136	−	0.974327i	$-0.572283\pi$
$727$	−12.1406	−0.450271	−0.225136	+	0.974327i	$0.572283\pi$
$728$	11.3646	0.421199
$729$	1.00000	0.0370370
$730$	−4.85959	−0.179862
$731$	−8.12349	−0.300458
$732$	1.96769	0.0727277
$733$	3.41541	0.126151	0.0630755	−	0.998009i	$-0.479909\pi$
$733$	3.41541	0.126151	0.0630755	+	0.998009i	$0.479909\pi$
$734$	1.38705	0.0511971
$735$	−6.74680	−0.248859
$736$	−4.04062	−0.148939
$737$	6.12066	0.225457
$738$	0.503958	0.0185510
$739$	11.0875	0.407862	0.203931	−	0.978985i	$-0.434628\pi$
$739$	11.0875	0.407862	0.203931	+	0.978985i	$0.434628\pi$
$740$	−33.3019	−1.22420
$741$	−17.7781	−0.653094
$742$	6.25015	0.229450
$743$	−15.5926	−0.572036	−0.286018	−	0.958224i	$-0.592332\pi$
$743$	−15.5926	−0.572036	−0.286018	+	0.958224i	$0.592332\pi$
$744$	0.696134	0.0255215
$745$	9.19662	0.336938
$746$	3.12774	0.114515
$747$	10.7598	0.393682
$748$	2.14054	0.0782659
$749$	8.97560	0.327961
$750$	−2.03677	−0.0743725
$751$	2.31000	0.0842932	0.0421466	−	0.999111i	$-0.486580\pi$
$751$	2.31000	0.0842932	0.0421466	+	0.999111i	$0.486580\pi$
$752$	19.3941	0.707231
$753$	17.0765	0.622302
$754$	4.63715	0.168875
$755$	39.8918	1.45181
$756$	6.24104	0.226984
$757$	23.7474	0.863116	0.431558	−	0.902085i	$-0.357964\pi$
$757$	23.7474	0.863116	0.431558	+	0.902085i	$0.357964\pi$
$758$	0.415916	0.0151067
$759$	1.91419	0.0694808
$760$	5.56509	0.201867
$761$	−7.80814	−0.283045	−0.141523	−	0.989935i	$-0.545200\pi$
$761$	−7.80814	−0.283045	−0.141523	+	0.989935i	$0.545200\pi$
$762$	1.60867	0.0582758
$763$	23.6862	0.857496
$764$	51.1902	1.85199
$765$	2.39845	0.0867160
$766$	1.61648	0.0584059
$767$	44.6997	1.61401
$768$	−13.4770	−0.486309
$769$	−24.6045	−0.887261	−0.443630	−	0.896210i	$-0.646310\pi$
$769$	−24.6045	−0.887261	−0.443630	+	0.896210i	$0.646310\pi$
$770$	1.25709	0.0453022
$771$	−18.9734	−0.683310
$772$	7.67348	0.276175
$773$	−0.312960	−0.0112564	−0.00562819	−	0.999984i	$-0.501792\pi$
$773$	−0.312960	−0.0112564	−0.00562819	+	0.999984i	$0.501792\pi$
$774$	1.34238	0.0482509
$775$	0.135675	0.00487359
$776$	−9.89688	−0.355277
$777$	−24.3474	−0.873458
$778$	1.37599	0.0493317
$779$	−9.92122	−0.355464
$780$	21.7937	0.780340
$781$	−10.4162	−0.372723
$782$	−0.374330	−0.0133860
$783$	5.13495	0.183508
$784$	11.6503	0.416081
$785$	43.1691	1.54077
$786$	2.51462	0.0896934
$787$	9.32767	0.332495	0.166248	−	0.986084i	$-0.446835\pi$
$787$	9.32767	0.332495	0.166248	+	0.986084i	$0.446835\pi$
$788$	43.2233	1.53976
$789$	−14.6726	−0.522359
$790$	−6.21349	−0.221066
$791$	−28.7910	−1.02369
$792$	−0.713244	−0.0253440
$793$	5.02358	0.178393
$794$	−4.69608	−0.166658
$795$	24.1685	0.857170
$796$	−2.24570	−0.0795968
$797$	10.3564	0.366842	0.183421	−	0.983034i	$-0.441283\pi$
$797$	10.3564	0.366842	0.183421	+	0.983034i	$0.441283\pi$
$798$	2.01778	0.0714286
$799$	5.54163	0.196049
$800$	0.293433	0.0103744
$801$	−14.2391	−0.503113
$802$	4.91501	0.173555
$803$	−12.2613	−0.432692
$804$	−12.0435	−0.424742
$805$	13.3859	0.471793
$806$	0.881391	0.0310457
$807$	16.9485	0.596616
$808$	−2.48678	−0.0874845
$809$	−21.7280	−0.763917	−0.381958	−	0.924180i	$-0.624750\pi$
$809$	−21.7280	−0.763917	−0.381958	+	0.924180i	$0.624750\pi$
$810$	−0.396336	−0.0139258
$811$	13.2505	0.465286	0.232643	−	0.972562i	$-0.425263\pi$
$811$	13.2505	0.465286	0.232643	+	0.972562i	$0.425263\pi$
$812$	32.0474	1.12464
$813$	−6.59936	−0.231450
$814$	1.37992	0.0483660
$815$	31.5754	1.10604
$816$	−4.14160	−0.144985
$817$	−26.4269	−0.924560
$818$	4.36233	0.152525
$819$	15.9336	0.556766
$820$	12.1622	0.424722
$821$	−16.6433	−0.580856	−0.290428	−	0.956897i	$-0.593798\pi$
$821$	−16.6433	−0.580856	−0.290428	+	0.956897i	$0.593798\pi$
$822$	3.55918	0.124141
$823$	−19.5756	−0.682364	−0.341182	−	0.939997i	$-0.610827\pi$
$823$	−19.5756	−0.682364	−0.341182	+	0.939997i	$0.610827\pi$
$824$	−13.7239	−0.478094
$825$	−0.139010	−0.00483971
$826$	−5.07333	−0.176524
$827$	20.1005	0.698964	0.349482	−	0.936943i	$-0.386358\pi$
$827$	20.1005	0.698964	0.349482	+	0.936943i	$0.386358\pi$
$828$	−3.76653	−0.130896
$829$	55.2719	1.91967	0.959835	−	0.280564i	$-0.0905214\pi$
$829$	55.2719	1.91967	0.959835	+	0.280564i	$0.0905214\pi$
$830$	−4.26451	−0.148023
$831$	19.7287	0.684382
$832$	−36.3449	−1.26003
$833$	3.32892	0.115340
$834$	−0.763811	−0.0264486
$835$	0.392734	0.0135911
$836$	6.96349	0.240837
$837$	0.976010	0.0337358
$838$	−2.97926	−0.102917
$839$	−9.09374	−0.313951	−0.156975	−	0.987603i	$-0.550174\pi$
$839$	−9.09374	−0.313951	−0.156975	+	0.987603i	$0.550174\pi$
$840$	−4.98772	−0.172093
$841$	−2.63226	−0.0907676
$842$	−0.0760589	−0.00262116
$843$	23.8313	0.820793
$844$	−18.4994	−0.636777
$845$	26.9783	0.928081
$846$	−0.915737	−0.0314837
$847$	3.17177	0.108983
$848$	−41.7339	−1.43315
$849$	14.5254	0.498511
$850$	0.0271841	0.000932407 0
$851$	14.6939	0.503700
$852$	20.4959	0.702178
$853$	−30.4639	−1.04307	−0.521533	−	0.853231i	$-0.674639\pi$
$853$	−30.4639	−1.04307	−0.521533	+	0.853231i	$0.674639\pi$
$854$	−0.570167	−0.0195107
$855$	7.80250	0.266840
$856$	2.01837	0.0689865
$857$	−36.7917	−1.25678	−0.628391	−	0.777898i	$-0.716286\pi$
$857$	−36.7917	−1.25678	−0.628391	+	0.777898i	$0.716286\pi$
$858$	−0.903056	−0.0308298
$859$	−19.7020	−0.672225	−0.336112	−	0.941822i	$-0.609112\pi$
$859$	−19.7020	−0.672225	−0.336112	+	0.941822i	$0.609112\pi$
$860$	32.3961	1.10470
$861$	8.89190	0.303035
$862$	−4.37534	−0.149025
$863$	−40.6000	−1.38204	−0.691020	−	0.722836i	$-0.742838\pi$
$863$	−40.6000	−1.38204	−0.691020	+	0.722836i	$0.742838\pi$
$864$	2.11088	0.0718135
$865$	1.11294	0.0378412
$866$	−0.980794	−0.0333287
$867$	15.8166	0.537160
$868$	6.09131	0.206753
$869$	−15.6773	−0.531817
$870$	−2.03517	−0.0689986
$871$	−30.7476	−1.04184
$872$	5.32638	0.180374
$873$	−13.8759	−0.469627
$874$	−1.21775	−0.0411910
$875$	−35.9371	−1.21490
$876$	24.1264	0.815154
$877$	32.5425	1.09888	0.549441	−	0.835532i	$-0.314841\pi$
$877$	32.5425	1.09888	0.549441	+	0.835532i	$0.314841\pi$
$878$	−1.02750	−0.0346763
$879$	3.05620	0.103083
$880$	−8.39388	−0.282958
$881$	9.99390	0.336703	0.168352	−	0.985727i	$-0.446156\pi$
$881$	9.99390	0.336703	0.168352	+	0.985727i	$0.446156\pi$
$882$	−0.550094	−0.0185226
$883$	−47.6765	−1.60444	−0.802221	−	0.597028i	$-0.796348\pi$
$883$	−47.6765	−1.60444	−0.802221	+	0.597028i	$0.796348\pi$
$884$	−10.7532	−0.361668
$885$	−19.6179	−0.659450
$886$	−2.73215	−0.0917883
$887$	−32.5954	−1.09445	−0.547224	−	0.836986i	$-0.684315\pi$
$887$	−32.5954	−1.09445	−0.547224	+	0.836986i	$0.684315\pi$
$888$	−5.47507	−0.183731
$889$	28.3835	0.951951
$890$	5.64346	0.189169
$891$	−1.00000	−0.0335013
$892$	−4.77613	−0.159917
$893$	18.0277	0.603275
$894$	0.749838	0.0250783
$895$	26.5714	0.888185
$896$	17.5155	0.585151
$897$	−9.61610	−0.321072
$898$	0.209365	0.00698659
$899$	5.01177	0.167152
$900$	0.273528	0.00911759
$901$	−11.9249	−0.397277
$902$	−0.503958	−0.0167800
$903$	23.6851	0.788192
$904$	−6.47432	−0.215333
$905$	52.5671	1.74739
$906$	3.25254	0.108058
$907$	11.8687	0.394094	0.197047	−	0.980394i	$-0.436865\pi$
$907$	11.8687	0.394094	0.197047	+	0.980394i	$0.436865\pi$
$908$	38.3558	1.27288
$909$	−3.48657	−0.115642
$910$	−6.31507	−0.209342
$911$	−22.8072	−0.755636	−0.377818	−	0.925880i	$-0.623326\pi$
$911$	−22.8072	−0.755636	−0.377818	+	0.925880i	$0.623326\pi$
$912$	−13.4732	−0.446144
$913$	−10.7598	−0.356099
$914$	−2.84662	−0.0941579
$915$	−2.20477	−0.0728873
$916$	−29.1776	−0.964056
$917$	44.3682	1.46517
$918$	0.195555	0.00645428
$919$	55.9065	1.84419	0.922093	−	0.386969i	$-0.126478\pi$
$919$	55.9065	1.84419	0.922093	+	0.386969i	$0.126478\pi$
$920$	3.01014	0.0992413
$921$	18.3076	0.603257
$922$	−2.57864	−0.0849231
$923$	52.3268	1.72236
$924$	−6.24104	−0.205315
$925$	−1.06708	−0.0350854
$926$	−4.42977	−0.145571
$927$	−19.2415	−0.631973
$928$	10.8392	0.355816
$929$	−42.5584	−1.39630	−0.698149	−	0.715953i	$-0.745993\pi$
$929$	−42.5584	−1.39630	−0.698149	+	0.715953i	$0.745993\pi$
$930$	−0.386828	−0.0126846
$931$	10.8295	0.354921
$932$	18.0599	0.591573
$933$	20.8499	0.682595
$934$	1.66559	0.0544996
$935$	−2.39845	−0.0784376
$936$	3.58304	0.117115
$937$	−18.2206	−0.595242	−0.297621	−	0.954684i	$-0.596193\pi$
$937$	−18.2206	−0.595242	−0.297621	+	0.954684i	$0.596193\pi$
$938$	3.48980	0.113946
$939$	3.49928	0.114195
$940$	−22.0998	−0.720815
$941$	−30.8164	−1.00458	−0.502292	−	0.864698i	$-0.667510\pi$
$941$	−30.8164	−1.00458	−0.502292	+	0.864698i	$0.667510\pi$
$942$	3.51975	0.114680
$943$	−5.36635	−0.174752
$944$	33.8760	1.10257
$945$	−6.99300	−0.227482
$946$	−1.34238	−0.0436446
$947$	−52.0370	−1.69098	−0.845488	−	0.533994i	$-0.820690\pi$
$947$	−52.0370	−1.69098	−0.845488	+	0.533994i	$0.820690\pi$
$948$	30.8480	1.00190
$949$	61.5956	1.99948
$950$	0.0884339	0.00286917
$951$	18.4416	0.598009
$952$	2.46098	0.0797607
$953$	−19.4381	−0.629662	−0.314831	−	0.949148i	$-0.601948\pi$
$953$	−19.4381	−0.629662	−0.314831	+	0.949148i	$0.601948\pi$
$954$	1.97056	0.0637992
$955$	−57.3579	−1.85606
$956$	−35.3767	−1.14416
$957$	−5.13495	−0.165989
$958$	−0.796135	−0.0257220
$959$	62.7985	2.02787
$960$	15.9512	0.514821
$961$	−30.0474	−0.969271
$962$	−6.93212	−0.223500
$963$	2.82984	0.0911905
$964$	23.2224	0.747942
$965$	−8.59803	−0.276781
$966$	1.09141	0.0351155
$967$	−30.8565	−0.992280	−0.496140	−	0.868243i	$-0.665250\pi$
$967$	−30.8565	−0.992280	−0.496140	+	0.868243i	$0.665250\pi$
$968$	0.713244	0.0229245
$969$	−3.84981	−0.123674
$970$	5.49951	0.176578
$971$	−5.96171	−0.191320	−0.0956601	−	0.995414i	$-0.530496\pi$
$971$	−5.96171	−0.191320	−0.0956601	+	0.995414i	$0.530496\pi$
$972$	1.96769	0.0631135
$973$	−13.4768	−0.432046
$974$	−4.36708	−0.139930
$975$	0.698328	0.0223644
$976$	3.80716	0.121864
$977$	4.76596	0.152477	0.0762383	−	0.997090i	$-0.475709\pi$
$977$	4.76596	0.152477	0.0762383	+	0.997090i	$0.475709\pi$
$978$	2.57447	0.0823224
$979$	14.2391	0.455083
$980$	−13.2756	−0.424073
$981$	7.46781	0.238429
$982$	7.65618	0.244318
$983$	52.1600	1.66365	0.831823	−	0.555042i	$-0.187298\pi$
$983$	52.1600	1.66365	0.831823	+	0.555042i	$0.187298\pi$
$984$	1.99955	0.0637433
$985$	−48.4311	−1.54314
$986$	1.00417	0.0319791
$987$	−16.1574	−0.514295
$988$	−34.9817	−1.11291
$989$	−14.2942	−0.454530
$990$	0.396336	0.0125964
$991$	20.1207	0.639156	0.319578	−	0.947560i	$-0.396459\pi$
$991$	20.1207	0.639156	0.319578	+	0.947560i	$0.396459\pi$
$992$	2.06024	0.0654126
$993$	−6.78274	−0.215244
$994$	−5.93900	−0.188374
$995$	2.51628	0.0797714
$996$	21.1720	0.670859
$997$	15.9577	0.505384	0.252692	−	0.967547i	$-0.418684\pi$
$997$	15.9577	0.505384	0.252692	+	0.967547i	$0.418684\pi$
$998$	−5.38646	−0.170505
$999$	−7.67629	−0.242867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.7	✓	14
3.2	odd	2		6039.2.a.j.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.7	✓	14	1.1	even	1	trivial
6039.2.a.j.1.8		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.179763 q^{2} -1.00000 q^{3} -1.96769 q^{4} +2.20477 q^{5} +0.179763 q^{6} +3.17177 q^{7} +0.713244 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.179763 q^{2} -1.00000 q^{3} -1.96769 q^{4} +2.20477 q^{5} +0.179763 q^{6} +3.17177 q^{7} +0.713244 q^{8} +1.00000 q^{9} -0.396336 q^{10} -1.00000 q^{11} +1.96769 q^{12} +5.02358 q^{13} -0.570167 q^{14} -2.20477 q^{15} +3.80716 q^{16} +1.08785 q^{17} -0.179763 q^{18} +3.53893 q^{19} -4.33828 q^{20} -3.17177 q^{21} +0.179763 q^{22} +1.91419 q^{23} -0.713244 q^{24} -0.139010 q^{25} -0.903056 q^{26} -1.00000 q^{27} -6.24104 q^{28} -5.13495 q^{29} +0.396336 q^{30} -0.976010 q^{31} -2.11088 q^{32} +1.00000 q^{33} -0.195555 q^{34} +6.99300 q^{35} -1.96769 q^{36} +7.67629 q^{37} -0.636169 q^{38} -5.02358 q^{39} +1.57254 q^{40} -2.80345 q^{41} +0.570167 q^{42} -7.46749 q^{43} +1.96769 q^{44} +2.20477 q^{45} -0.344102 q^{46} +5.09413 q^{47} -3.80716 q^{48} +3.06010 q^{49} +0.0249889 q^{50} -1.08785 q^{51} -9.88482 q^{52} -10.9620 q^{53} +0.179763 q^{54} -2.20477 q^{55} +2.26224 q^{56} -3.53893 q^{57} +0.923076 q^{58} +8.89797 q^{59} +4.33828 q^{60} +1.00000 q^{61} +0.175451 q^{62} +3.17177 q^{63} -7.23485 q^{64} +11.0758 q^{65} -0.179763 q^{66} -6.12066 q^{67} -2.14054 q^{68} -1.91419 q^{69} -1.25709 q^{70} +10.4162 q^{71} +0.713244 q^{72} +12.2613 q^{73} -1.37992 q^{74} +0.139010 q^{75} -6.96349 q^{76} -3.17177 q^{77} +0.903056 q^{78} +15.6773 q^{79} +8.39388 q^{80} +1.00000 q^{81} +0.503958 q^{82} +10.7598 q^{83} +6.24104 q^{84} +2.39845 q^{85} +1.34238 q^{86} +5.13495 q^{87} -0.713244 q^{88} -14.2391 q^{89} -0.396336 q^{90} +15.9336 q^{91} -3.76653 q^{92} +0.976010 q^{93} -0.915737 q^{94} +7.80250 q^{95} +2.11088 q^{96} -13.8759 q^{97} -0.550094 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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