LMFDB - Embedded newform 301.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [301,2,Mod(1,301)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(301, 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("301.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 301 = 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	301.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$2.40349710084$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.301909.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 5x^{2} + 6x - 1 $ x^5 - x^4 - 6x^3 + 5x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.827330$ of defining polynomial
Character	$\chi$	$=$	301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.827330 q^{2} -1.74303 q^{3} -1.31552 q^{4} -0.781199 q^{5} +1.44206 q^{6} -1.00000 q^{7} +2.74303 q^{8} +0.0381656 q^{9} +O(q^{10})$	\(q-0.827330 q^{2} -1.74303 q^{3} -1.31552 q^{4} -0.781199 q^{5} +1.44206 q^{6} -1.00000 q^{7} +2.74303 q^{8} +0.0381656 q^{9} +0.646309 q^{10} -0.696902 q^{11} +2.29300 q^{12} +0.888017 q^{13} +0.827330 q^{14} +1.36166 q^{15} +0.361656 q^{16} +1.72051 q^{17} -0.0315755 q^{18} +7.17054 q^{19} +1.02769 q^{20} +1.74303 q^{21} +0.576568 q^{22} +5.79363 q^{23} -4.78120 q^{24} -4.38973 q^{25} -0.734683 q^{26} +5.16258 q^{27} +1.31552 q^{28} +4.84365 q^{29} -1.12654 q^{30} +2.61649 q^{31} -5.78528 q^{32} +1.21472 q^{33} -1.42343 q^{34} +0.781199 q^{35} -0.0502078 q^{36} -8.37408 q^{37} -5.93240 q^{38} -1.54784 q^{39} -2.14286 q^{40} -0.0770026 q^{41} -1.44206 q^{42} +1.00000 q^{43} +0.916793 q^{44} -0.0298149 q^{45} -4.79324 q^{46} +3.18102 q^{47} -0.630379 q^{48} +1.00000 q^{49} +3.63175 q^{50} -2.99891 q^{51} -1.16821 q^{52} -0.507343 q^{53} -4.27115 q^{54} +0.544419 q^{55} -2.74303 q^{56} -12.4985 q^{57} -4.00729 q^{58} +4.48431 q^{59} -1.79129 q^{60} -1.99341 q^{61} -2.16470 q^{62} -0.0381656 q^{63} +4.06302 q^{64} -0.693718 q^{65} -1.00498 q^{66} -4.72990 q^{67} -2.26338 q^{68} -10.0985 q^{69} -0.646309 q^{70} +13.5446 q^{71} +0.104689 q^{72} +4.89764 q^{73} +6.92813 q^{74} +7.65144 q^{75} -9.43303 q^{76} +0.696902 q^{77} +1.28058 q^{78} -5.79752 q^{79} -0.282525 q^{80} -9.11304 q^{81} +0.0637066 q^{82} +4.18723 q^{83} -2.29300 q^{84} -1.34406 q^{85} -0.827330 q^{86} -8.44264 q^{87} -1.91163 q^{88} +17.7638 q^{89} +0.0246668 q^{90} -0.888017 q^{91} -7.62166 q^{92} -4.56064 q^{93} -2.63175 q^{94} -5.60162 q^{95} +10.0839 q^{96} -12.8973 q^{97} -0.827330 q^{98} -0.0265977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9} + 7 q^{10} + 13 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{16} + q^{17} - 6 q^{18} + 18 q^{19} + 2 q^{20} - 5 q^{21} - 5 q^{22} - 5 q^{23} - 16 q^{24} - q^{25} - 4 q^{26} + 11 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 3 q^{31} - 9 q^{32} + 26 q^{33} - 15 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} + 7 q^{38} + 5 q^{39} + 4 q^{40} + 17 q^{41} + 5 q^{43} + 11 q^{44} - 20 q^{45} - q^{46} + 7 q^{47} - 13 q^{48} + 5 q^{49} + 25 q^{50} - 34 q^{52} - 30 q^{53} + 5 q^{54} + 21 q^{55} - 9 q^{57} - 46 q^{58} + 9 q^{59} - 21 q^{60} - 10 q^{61} - 19 q^{62} - 6 q^{63} - 26 q^{64} - 4 q^{65} - 29 q^{66} - 10 q^{67} + 33 q^{68} - 19 q^{69} - 7 q^{70} + 17 q^{71} - 20 q^{72} - q^{73} - 10 q^{75} + 20 q^{76} - 13 q^{77} + 29 q^{78} - 4 q^{79} + 11 q^{80} - 11 q^{81} + 28 q^{82} + 23 q^{83} - 8 q^{84} - 23 q^{85} + q^{86} - 3 q^{87} - 13 q^{88} + 35 q^{89} - 31 q^{90} + q^{91} - 25 q^{92} - 21 q^{93} - 20 q^{94} + 22 q^{95} + 22 q^{96} - 2 q^{97} + q^{98} + 18 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9 + 7 * q^10 + 13 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^16 + q^17 - 6 * q^18 + 18 * q^19 + 2 * q^20 - 5 * q^21 - 5 * q^22 - 5 * q^23 - 16 * q^24 - q^25 - 4 * q^26 + 11 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 3 * q^31 - 9 * q^32 + 26 * q^33 - 15 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 + 7 * q^38 + 5 * q^39 + 4 * q^40 + 17 * q^41 + 5 * q^43 + 11 * q^44 - 20 * q^45 - q^46 + 7 * q^47 - 13 * q^48 + 5 * q^49 + 25 * q^50 - 34 * q^52 - 30 * q^53 + 5 * q^54 + 21 * q^55 - 9 * q^57 - 46 * q^58 + 9 * q^59 - 21 * q^60 - 10 * q^61 - 19 * q^62 - 6 * q^63 - 26 * q^64 - 4 * q^65 - 29 * q^66 - 10 * q^67 + 33 * q^68 - 19 * q^69 - 7 * q^70 + 17 * q^71 - 20 * q^72 - q^73 - 10 * q^75 + 20 * q^76 - 13 * q^77 + 29 * q^78 - 4 * q^79 + 11 * q^80 - 11 * q^81 + 28 * q^82 + 23 * q^83 - 8 * q^84 - 23 * q^85 + q^86 - 3 * q^87 - 13 * q^88 + 35 * q^89 - 31 * q^90 + q^91 - 25 * q^92 - 21 * q^93 - 20 * q^94 + 22 * q^95 + 22 * q^96 - 2 * q^97 + q^98 + 18 * 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 $

$2$	−0.827330	−0.585011	−0.292505	−	0.956264i	$-0.594489\pi$
$2$	−0.827330	−0.585011	−0.292505	+	0.956264i	$0.594489\pi$
$3$	−1.74303	−1.00634	−0.503170	−	0.864187i	$-0.667833\pi$
$3$	−1.74303	−1.00634	−0.503170	+	0.864187i	$0.667833\pi$
$4$	−1.31552	−0.657762
$5$	−0.781199	−0.349363	−0.174681	−	0.984625i	$-0.555890\pi$
$5$	−0.781199	−0.349363	−0.174681	+	0.984625i	$0.555890\pi$
$6$	1.44206	0.588720
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.74303	0.969809
$9$	0.0381656	0.0127219
$10$	0.646309	0.204381
$11$	−0.696902	−0.210124	−0.105062	−	0.994466i	$-0.533504\pi$
$11$	−0.696902	−0.210124	−0.105062	+	0.994466i	$0.533504\pi$
$12$	2.29300	0.661933
$13$	0.888017	0.246291	0.123146	−	0.992389i	$-0.460702\pi$
$13$	0.888017	0.246291	0.123146	+	0.992389i	$0.460702\pi$
$14$	0.827330	0.221113
$15$	1.36166	0.351578
$16$	0.361656	0.0904140
$17$	1.72051	0.417286	0.208643	−	0.977992i	$-0.433095\pi$
$17$	1.72051	0.417286	0.208643	+	0.977992i	$0.433095\pi$
$18$	−0.0315755	−0.00744242
$19$	7.17054	1.64504	0.822518	−	0.568740i	$-0.192569\pi$
$19$	7.17054	1.64504	0.822518	+	0.568740i	$0.192569\pi$
$20$	1.02769	0.229798
$21$	1.74303	0.380361
$22$	0.576568	0.122925
$23$	5.79363	1.20805	0.604027	−	0.796964i	$-0.293562\pi$
$23$	5.79363	1.20805	0.604027	+	0.796964i	$0.293562\pi$
$24$	−4.78120	−0.975958
$25$	−4.38973	−0.877946
$26$	−0.734683	−0.144083
$27$	5.16258	0.993538
$28$	1.31552	0.248611
$29$	4.84365	0.899443	0.449721	−	0.893169i	$-0.351523\pi$
$29$	4.84365	0.899443	0.449721	+	0.893169i	$0.351523\pi$
$30$	−1.12654	−0.205677
$31$	2.61649	0.469936	0.234968	−	0.972003i	$-0.424501\pi$
$31$	2.61649	0.469936	0.234968	+	0.972003i	$0.424501\pi$
$32$	−5.78528	−1.02270
$33$	1.21472	0.211456
$34$	−1.42343	−0.244117
$35$	0.781199	0.132047
$36$	−0.0502078	−0.00836796
$37$	−8.37408	−1.37669	−0.688345	−	0.725383i	$-0.741663\pi$
$37$	−8.37408	−1.37669	−0.688345	+	0.725383i	$0.741663\pi$
$38$	−5.93240	−0.962363
$39$	−1.54784	−0.247853
$40$	−2.14286	−0.338815
$41$	−0.0770026	−0.0120258	−0.00601289	−	0.999982i	$-0.501914\pi$
$41$	−0.0770026	−0.0120258	−0.00601289	+	0.999982i	$0.501914\pi$
$42$	−1.44206	−0.222515
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.916793	0.138212
$45$	−0.0298149	−0.00444454
$46$	−4.79324	−0.706725
$47$	3.18102	0.464000	0.232000	−	0.972716i	$-0.425473\pi$
$47$	3.18102	0.464000	0.232000	+	0.972716i	$0.425473\pi$
$48$	−0.630379	−0.0909873
$49$	1.00000	0.142857
$50$	3.63175	0.513608
$51$	−2.99891	−0.419932
$52$	−1.16821	−0.162001
$53$	−0.507343	−0.0696889	−0.0348445	−	0.999393i	$-0.511094\pi$
$53$	−0.507343	−0.0696889	−0.0348445	+	0.999393i	$0.511094\pi$
$54$	−4.27115	−0.581231
$55$	0.544419	0.0734095
$56$	−2.74303	−0.366553
$57$	−12.4985	−1.65547
$58$	−4.00729	−0.526183
$59$	4.48431	0.583807	0.291903	−	0.956448i	$-0.405711\pi$
$59$	4.48431	0.583807	0.291903	+	0.956448i	$0.405711\pi$
$60$	−1.79129	−0.231255
$61$	−1.99341	−0.255230	−0.127615	−	0.991824i	$-0.540732\pi$
$61$	−1.99341	−0.255230	−0.127615	+	0.991824i	$0.540732\pi$
$62$	−2.16470	−0.274918
$63$	−0.0381656	−0.00480841
$64$	4.06302	0.507878
$65$	−0.693718	−0.0860451
$66$	−1.00498	−0.123704
$67$	−4.72990	−0.577850	−0.288925	−	0.957352i	$-0.593298\pi$
$67$	−4.72990	−0.577850	−0.288925	+	0.957352i	$0.593298\pi$
$68$	−2.26338	−0.274475
$69$	−10.0985	−1.21571
$70$	−0.646309	−0.0772488
$71$	13.5446	1.60745	0.803726	−	0.595000i	$-0.202848\pi$
$71$	13.5446	1.60745	0.803726	+	0.595000i	$0.202848\pi$
$72$	0.104689	0.0123378
$73$	4.89764	0.573226	0.286613	−	0.958046i	$-0.407471\pi$
$73$	4.89764	0.573226	0.286613	+	0.958046i	$0.407471\pi$
$74$	6.92813	0.805379
$75$	7.65144	0.883513
$76$	−9.43303	−1.08204
$77$	0.696902	0.0794194
$78$	1.28058	0.144997
$79$	−5.79752	−0.652271	−0.326136	−	0.945323i	$-0.605747\pi$
$79$	−5.79752	−0.652271	−0.326136	+	0.945323i	$0.605747\pi$
$80$	−0.282525	−0.0315873
$81$	−9.11304	−1.01256
$82$	0.0637066	0.00703521
$83$	4.18723	0.459608	0.229804	−	0.973237i	$-0.426192\pi$
$83$	4.18723	0.459608	0.229804	+	0.973237i	$0.426192\pi$
$84$	−2.29300	−0.250187
$85$	−1.34406	−0.145784
$86$	−0.827330	−0.0892133
$87$	−8.44264	−0.905146
$88$	−1.91163	−0.203780
$89$	17.7638	1.88296	0.941480	−	0.337068i	$-0.109435\pi$
$89$	17.7638	1.88296	0.941480	+	0.337068i	$0.109435\pi$
$90$	0.0246668	0.00260011
$91$	−0.888017	−0.0930894
$92$	−7.62166	−0.794613
$93$	−4.56064	−0.472916
$94$	−2.63175	−0.271445
$95$	−5.60162	−0.574714
$96$	10.0839	1.02919
$97$	−12.8973	−1.30952	−0.654760	−	0.755837i	$-0.727230\pi$
$97$	−12.8973	−1.30952	−0.654760	+	0.755837i	$0.727230\pi$
$98$	−0.827330	−0.0835730
$99$	−0.0265977	−0.00267317
$100$	5.77480	0.577480
$101$	5.83833	0.580936	0.290468	−	0.956885i	$-0.406189\pi$
$101$	5.83833	0.580936	0.290468	+	0.956885i	$0.406189\pi$
$102$	2.48109	0.245664
$103$	1.53181	0.150934	0.0754670	−	0.997148i	$-0.475955\pi$
$103$	1.53181	0.150934	0.0754670	+	0.997148i	$0.475955\pi$
$104$	2.43586	0.238856
$105$	−1.36166	−0.132884
$106$	0.419740	0.0407688
$107$	−2.43926	−0.235813	−0.117906	−	0.993025i	$-0.537618\pi$
$107$	−2.43926	−0.235813	−0.117906	+	0.993025i	$0.537618\pi$
$108$	−6.79150	−0.653512
$109$	13.7933	1.32115	0.660577	−	0.750758i	$-0.270312\pi$
$109$	13.7933	1.32115	0.660577	+	0.750758i	$0.270312\pi$
$110$	−0.450415	−0.0429453
$111$	14.5963	1.38542
$112$	−0.361656	−0.0341733
$113$	10.7291	1.00930	0.504652	−	0.863323i	$-0.331621\pi$
$113$	10.7291	1.00930	0.504652	+	0.863323i	$0.331621\pi$
$114$	10.3404	0.968465
$115$	−4.52598	−0.422049
$116$	−6.37194	−0.591620
$117$	0.0338917	0.00313329
$118$	−3.71000	−0.341533
$119$	−1.72051	−0.157719
$120$	3.73507	0.340963
$121$	−10.5143	−0.955848
$122$	1.64921	0.149312
$123$	0.134218	0.0121020
$124$	−3.44206	−0.309106
$125$	7.33525	0.656084
$126$	0.0315755	0.00281297
$127$	−11.9459	−1.06003	−0.530015	−	0.847989i	$-0.677814\pi$
$127$	−11.9459	−1.06003	−0.530015	+	0.847989i	$0.677814\pi$
$128$	8.20909	0.725588
$129$	−1.74303	−0.153466
$130$	0.573933	0.0503373
$131$	15.7180	1.37329	0.686643	−	0.726995i	$-0.259084\pi$
$131$	15.7180	1.37329	0.686643	+	0.726995i	$0.259084\pi$
$132$	−1.59800	−0.139088
$133$	−7.17054	−0.621765
$134$	3.91319	0.338048
$135$	−4.03300	−0.347105
$136$	4.71942	0.404687
$137$	−7.11683	−0.608032	−0.304016	−	0.952667i	$-0.598328\pi$
$137$	−7.11683	−0.608032	−0.304016	+	0.952667i	$0.598328\pi$
$138$	8.35478	0.711206
$139$	19.6396	1.66581	0.832904	−	0.553417i	$-0.186677\pi$
$139$	19.6396	1.66581	0.832904	+	0.553417i	$0.186677\pi$
$140$	−1.02769	−0.0868554
$141$	−5.54463	−0.466942
$142$	−11.2059	−0.940376
$143$	−0.618861	−0.0517517
$144$	0.0138028	0.00115023
$145$	−3.78385	−0.314232
$146$	−4.05197	−0.335343
$147$	−1.74303	−0.143763
$148$	11.0163	0.905536
$149$	−3.88874	−0.318578	−0.159289	−	0.987232i	$-0.550920\pi$
$149$	−3.88874	−0.318578	−0.159289	+	0.987232i	$0.550920\pi$
$150$	−6.33027	−0.516864
$151$	7.51006	0.611160	0.305580	−	0.952166i	$-0.401150\pi$
$151$	7.51006	0.611160	0.305580	+	0.952166i	$0.401150\pi$
$152$	19.6690	1.59537
$153$	0.0656644	0.00530865
$154$	−0.576568	−0.0464612
$155$	−2.04400	−0.164178
$156$	2.03623	0.163029
$157$	20.3691	1.62563	0.812817	−	0.582520i	$-0.197933\pi$
$157$	20.3691	1.62563	0.812817	+	0.582520i	$0.197933\pi$
$158$	4.79646	0.381586
$159$	0.884316	0.0701308
$160$	4.51945	0.357294
$161$	−5.79363	−0.456602
$162$	7.53949	0.592358
$163$	14.5266	1.13781	0.568904	−	0.822404i	$-0.307367\pi$
$163$	14.5266	1.13781	0.568904	+	0.822404i	$0.307367\pi$
$164$	0.101299	0.00791011
$165$	−0.948941	−0.0738750
$166$	−3.46422	−0.268875
$167$	−19.5590	−1.51352	−0.756760	−	0.653692i	$-0.773219\pi$
$167$	−19.5590	−1.51352	−0.756760	+	0.653692i	$0.773219\pi$
$168$	4.78120	0.368878
$169$	−12.2114	−0.939341
$170$	1.11198	0.0852852
$171$	0.273668	0.0209279
$172$	−1.31552	−0.100308
$173$	−8.68253	−0.660121	−0.330060	−	0.943960i	$-0.607069\pi$
$173$	−8.68253	−0.660121	−0.330060	+	0.943960i	$0.607069\pi$
$174$	6.98485	0.529520
$175$	4.38973	0.331832
$176$	−0.252039	−0.0189982
$177$	−7.81630	−0.587509
$178$	−14.6965	−1.10155
$179$	22.7984	1.70403	0.852017	−	0.523514i	$-0.175379\pi$
$179$	22.7984	1.70403	0.852017	+	0.523514i	$0.175379\pi$
$180$	0.0392223	0.00292345
$181$	5.16306	0.383767	0.191884	−	0.981418i	$-0.438540\pi$
$181$	5.16306	0.383767	0.191884	+	0.981418i	$0.438540\pi$
$182$	0.734683	0.0544583
$183$	3.47458	0.256848
$184$	15.8921	1.17158
$185$	6.54183	0.480965
$186$	3.77315	0.276661
$187$	−1.19903	−0.0876817
$188$	−4.18471	−0.305202
$189$	−5.16258	−0.375522
$190$	4.63439	0.336214
$191$	5.95018	0.430540	0.215270	−	0.976555i	$-0.430937\pi$
$191$	5.95018	0.430540	0.215270	+	0.976555i	$0.430937\pi$
$192$	−7.08198	−0.511098
$193$	−2.36060	−0.169920	−0.0849598	−	0.996384i	$-0.527076\pi$
$193$	−2.36060	−0.169920	−0.0849598	+	0.996384i	$0.527076\pi$
$194$	10.6703	0.766083
$195$	1.20917	0.0865907
$196$	−1.31552	−0.0939661
$197$	−3.08468	−0.219774	−0.109887	−	0.993944i	$-0.535049\pi$
$197$	−3.08468	−0.219774	−0.109887	+	0.993944i	$0.535049\pi$
$198$	0.0220051	0.00156383
$199$	0.206006	0.0146034	0.00730169	−	0.999973i	$-0.497676\pi$
$199$	0.206006	0.0146034	0.00730169	+	0.999973i	$0.497676\pi$
$200$	−12.0412	−0.851439
$201$	8.24438	0.581514
$202$	−4.83023	−0.339854
$203$	−4.84365	−0.339957
$204$	3.94514	0.276215
$205$	0.0601544	0.00420136
$206$	−1.26731	−0.0882980
$207$	0.221117	0.0153687
$208$	0.321157	0.0222682
$209$	−4.99717	−0.345661
$210$	1.12654	0.0777386
$211$	−18.3503	−1.26329	−0.631645	−	0.775258i	$-0.717620\pi$
$211$	−18.3503	−1.26329	−0.631645	+	0.775258i	$0.717620\pi$
$212$	0.667422	0.0458388
$213$	−23.6087	−1.61764
$214$	2.01808	0.137953
$215$	−0.781199	−0.0532773
$216$	14.1611	0.963542
$217$	−2.61649	−0.177619
$218$	−11.4116	−0.772890
$219$	−8.53676	−0.576861
$220$	−0.716197	−0.0482860
$221$	1.52784	0.102774
$222$	−12.0760	−0.810486
$223$	0.00303784	0.000203429 0	0.000101714	−	1.00000i	$-0.499968\pi$
$223$	0.00303784	0.000203429 0	0.000101714		1.00000i	$0.499968\pi$
$224$	5.78528	0.386545
$225$	−0.167537	−0.0111691
$226$	−8.87647	−0.590454
$227$	8.35174	0.554325	0.277162	−	0.960823i	$-0.410606\pi$
$227$	8.35174	0.554325	0.277162	+	0.960823i	$0.410606\pi$
$228$	16.4421	1.08890
$229$	−3.08302	−0.203732	−0.101866	−	0.994798i	$-0.532481\pi$
$229$	−3.08302	−0.203732	−0.101866	+	0.994798i	$0.532481\pi$
$230$	3.74448	0.246903
$231$	−1.21472	−0.0799230
$232$	13.2863	0.872287
$233$	−16.3988	−1.07432	−0.537159	−	0.843481i	$-0.680502\pi$
$233$	−16.3988	−1.07432	−0.537159	+	0.843481i	$0.680502\pi$
$234$	−0.0280396	−0.00183301
$235$	−2.48501	−0.162104
$236$	−5.89922	−0.384006
$237$	10.1053	0.656407
$238$	1.42343	0.0922674
$239$	−5.88830	−0.380883	−0.190441	−	0.981699i	$-0.560992\pi$
$239$	−5.88830	−0.380883	−0.190441	+	0.981699i	$0.560992\pi$
$240$	0.492451	0.0317876
$241$	−13.0415	−0.840079	−0.420040	−	0.907506i	$-0.637984\pi$
$241$	−13.0415	−0.840079	−0.420040	+	0.907506i	$0.637984\pi$
$242$	8.69882	0.559181
$243$	0.396604	0.0254422
$244$	2.62238	0.167881
$245$	−0.781199	−0.0499090
$246$	−0.111043	−0.00707982
$247$	6.36756	0.405158
$248$	7.17713	0.455748
$249$	−7.29847	−0.462522
$250$	−6.06867	−0.383816
$251$	18.7576	1.18397	0.591985	−	0.805949i	$-0.298345\pi$
$251$	18.7576	1.18397	0.591985	+	0.805949i	$0.298345\pi$
$252$	0.0502078	0.00316279
$253$	−4.03759	−0.253841
$254$	9.88322	0.620128
$255$	2.34275	0.146708
$256$	−14.9177	−0.932354
$257$	−28.9311	−1.80467	−0.902337	−	0.431031i	$-0.858150\pi$
$257$	−28.9311	−1.80467	−0.902337	+	0.431031i	$0.858150\pi$
$258$	1.44206	0.0897790
$259$	8.37408	0.520340
$260$	0.912603	0.0565972
$261$	0.184861	0.0114426
$262$	−13.0039	−0.803386
$263$	−20.1731	−1.24393	−0.621963	−	0.783047i	$-0.713664\pi$
$263$	−20.1731	−1.24393	−0.621963	+	0.783047i	$0.713664\pi$
$264$	3.33203	0.205072
$265$	0.396336	0.0243467
$266$	5.93240	0.363739
$267$	−30.9629	−1.89490
$268$	6.22230	0.380088
$269$	2.52986	0.154249	0.0771243	−	0.997021i	$-0.475426\pi$
$269$	2.52986	0.154249	0.0771243	+	0.997021i	$0.475426\pi$
$270$	3.33662	0.203060
$271$	−30.9442	−1.87972	−0.939862	−	0.341554i	$-0.889047\pi$
$271$	−30.9442	−1.87972	−0.939862	+	0.341554i	$0.889047\pi$
$272$	0.622234	0.0377285
$273$	1.54784	0.0936797
$274$	5.88797	0.355705
$275$	3.05921	0.184477
$276$	13.2848	0.799652
$277$	27.8756	1.67488	0.837442	−	0.546526i	$-0.184050\pi$
$277$	27.8756	1.67488	0.837442	+	0.546526i	$0.184050\pi$
$278$	−16.2484	−0.974516
$279$	0.0998600	0.00597846
$280$	2.14286	0.128060
$281$	9.83137	0.586491	0.293245	−	0.956037i	$-0.405265\pi$
$281$	9.83137	0.586491	0.293245	+	0.956037i	$0.405265\pi$
$282$	4.58724	0.273166
$283$	12.2207	0.726446	0.363223	−	0.931702i	$-0.381676\pi$
$283$	12.2207	0.726446	0.363223	+	0.931702i	$0.381676\pi$
$284$	−17.8183	−1.05732
$285$	9.76381	0.578358
$286$	0.512002	0.0302753
$287$	0.0770026	0.00454532
$288$	−0.220798	−0.0130107
$289$	−14.0398	−0.825873
$290$	3.13049	0.183829
$291$	22.4804	1.31782
$292$	−6.44297	−0.377047
$293$	−17.0024	−0.993288	−0.496644	−	0.867954i	$-0.665435\pi$
$293$	−17.0024	−0.993288	−0.496644	+	0.867954i	$0.665435\pi$
$294$	1.44206	0.0841029
$295$	−3.50314	−0.203960
$296$	−22.9704	−1.33513
$297$	−3.59781	−0.208766
$298$	3.21727	0.186371
$299$	5.14484	0.297534
$300$	−10.0657	−0.581141
$301$	−1.00000	−0.0576390
$302$	−6.21330	−0.357535
$303$	−10.1764	−0.584619
$304$	2.59327	0.148734
$305$	1.55725	0.0891679
$306$	−0.0543261	−0.00310562
$307$	−3.87237	−0.221008	−0.110504	−	0.993876i	$-0.535246\pi$
$307$	−3.87237	−0.221008	−0.110504	+	0.993876i	$0.535246\pi$
$308$	−0.916793	−0.0522391
$309$	−2.67000	−0.151891
$310$	1.69107	0.0960460
$311$	15.1977	0.861780	0.430890	−	0.902404i	$-0.358200\pi$
$311$	15.1977	0.861780	0.430890	+	0.902404i	$0.358200\pi$
$312$	−4.24578	−0.240370
$313$	−12.9840	−0.733898	−0.366949	−	0.930241i	$-0.619598\pi$
$313$	−12.9840	−0.733898	−0.366949	+	0.930241i	$0.619598\pi$
$314$	−16.8520	−0.951013
$315$	0.0298149	0.00167988
$316$	7.62678	0.429040
$317$	−21.7794	−1.22325	−0.611627	−	0.791147i	$-0.709485\pi$
$317$	−21.7794	−1.22325	−0.611627	+	0.791147i	$0.709485\pi$
$318$	−0.731621	−0.0410273
$319$	−3.37555	−0.188994
$320$	−3.17403	−0.177434
$321$	4.25172	0.237308
$322$	4.79324	0.267117
$323$	12.3370	0.686449
$324$	11.9884	0.666024
$325$	−3.89815	−0.216231
$326$	−12.0183	−0.665630
$327$	−24.0421	−1.32953
$328$	−0.211221	−0.0116627
$329$	−3.18102	−0.175375
$330$	0.785088	0.0432177
$331$	−24.5189	−1.34768	−0.673839	−	0.738878i	$-0.735356\pi$
$331$	−24.5189	−1.34768	−0.673839	+	0.738878i	$0.735356\pi$
$332$	−5.50840	−0.302313
$333$	−0.319602	−0.0175141
$334$	16.1817	0.885426
$335$	3.69499	0.201879
$336$	0.630379	0.0343900
$337$	16.3337	0.889754	0.444877	−	0.895592i	$-0.353247\pi$
$337$	16.3337	0.889754	0.444877	+	0.895592i	$0.353247\pi$
$338$	10.1029	0.549524
$339$	−18.7011	−1.01570
$340$	1.76815	0.0958913
$341$	−1.82344	−0.0987449
$342$	−0.226414	−0.0122430
$343$	−1.00000	−0.0539949
$344$	2.74303	0.147894
$345$	7.88893	0.424726
$346$	7.18332	0.386178
$347$	6.69172	0.359230	0.179615	−	0.983737i	$-0.442515\pi$
$347$	6.69172	0.359230	0.179615	+	0.983737i	$0.442515\pi$
$348$	11.1065	0.595371
$349$	18.3674	0.983185	0.491593	−	0.870825i	$-0.336415\pi$
$349$	18.3674	0.983185	0.491593	+	0.870825i	$0.336415\pi$
$350$	−3.63175	−0.194125
$351$	4.58445	0.244700
$352$	4.03177	0.214894
$353$	23.9519	1.27483	0.637415	−	0.770520i	$-0.280004\pi$
$353$	23.9519	1.27483	0.637415	+	0.770520i	$0.280004\pi$
$354$	6.46666	0.343699
$355$	−10.5810	−0.561584
$356$	−23.3687	−1.23854
$357$	2.99891	0.158719
$358$	−18.8618	−0.996878
$359$	16.1543	0.852591	0.426295	−	0.904584i	$-0.359818\pi$
$359$	16.1543	0.852591	0.426295	+	0.904584i	$0.359818\pi$
$360$	−0.0817833	−0.00431036
$361$	32.4167	1.70614
$362$	−4.27155	−0.224508
$363$	18.3268	0.961909
$364$	1.16821	0.0612307
$365$	−3.82604	−0.200264
$366$	−2.87462	−0.150259
$367$	−10.6830	−0.557649	−0.278825	−	0.960342i	$-0.589945\pi$
$367$	−10.6830	−0.557649	−0.278825	+	0.960342i	$0.589945\pi$
$368$	2.09530	0.109225
$369$	−0.00293885	−0.000152990 0
$370$	−5.41225	−0.281369
$371$	0.507343	0.0263399
$372$	5.99963	0.311066
$373$	16.5924	0.859123	0.429561	−	0.903038i	$-0.358668\pi$
$373$	16.5924	0.859123	0.429561	+	0.903038i	$0.358668\pi$
$374$	0.991993	0.0512947
$375$	−12.7856	−0.660245
$376$	8.72565	0.449991
$377$	4.30124	0.221525
$378$	4.27115	0.219684
$379$	8.35408	0.429120	0.214560	−	0.976711i	$-0.431168\pi$
$379$	8.35408	0.429120	0.214560	+	0.976711i	$0.431168\pi$
$380$	7.36907	0.378025
$381$	20.8221	1.06675
$382$	−4.92276	−0.251870
$383$	9.79918	0.500715	0.250357	−	0.968154i	$-0.419452\pi$
$383$	9.79918	0.500715	0.250357	+	0.968154i	$0.419452\pi$
$384$	−14.3087	−0.730189
$385$	−0.544419	−0.0277462
$386$	1.95299	0.0994048
$387$	0.0381656	0.00194007
$388$	16.9667	0.861353
$389$	−20.7055	−1.04981	−0.524906	−	0.851160i	$-0.675900\pi$
$389$	−20.7055	−1.04981	−0.524906	+	0.851160i	$0.675900\pi$
$390$	−1.00039	−0.0506565
$391$	9.96801	0.504104
$392$	2.74303	0.138544
$393$	−27.3969	−1.38199
$394$	2.55205	0.128570
$395$	4.52901	0.227879
$396$	0.0349899	0.00175831
$397$	−2.64882	−0.132941	−0.0664703	−	0.997788i	$-0.521174\pi$
$397$	−2.64882	−0.132941	−0.0664703	+	0.997788i	$0.521174\pi$
$398$	−0.170435	−0.00854314
$399$	12.4985	0.625707
$400$	−1.58757	−0.0793786
$401$	18.7390	0.935782	0.467891	−	0.883786i	$-0.345014\pi$
$401$	18.7390	0.935782	0.467891	+	0.883786i	$0.345014\pi$
$402$	−6.82082	−0.340192
$403$	2.32349	0.115741
$404$	−7.68047	−0.382118
$405$	7.11910	0.353751
$406$	4.00729	0.198879
$407$	5.83592	0.289276
$408$	−8.22611	−0.407253
$409$	11.6278	0.574956	0.287478	−	0.957787i	$-0.407183\pi$
$409$	11.6278	0.574956	0.287478	+	0.957787i	$0.407183\pi$
$410$	−0.0497675	−0.00245784
$411$	12.4049	0.611887
$412$	−2.01514	−0.0992787
$413$	−4.48431	−0.220658
$414$	−0.182937	−0.00899085
$415$	−3.27106	−0.160570
$416$	−5.13742	−0.251883
$417$	−34.2325	−1.67637
$418$	4.13431	0.202216
$419$	−2.30738	−0.112723	−0.0563614	−	0.998410i	$-0.517950\pi$
$419$	−2.30738	−0.112723	−0.0563614	+	0.998410i	$0.517950\pi$
$420$	1.79129	0.0874061
$421$	16.8719	0.822285	0.411142	−	0.911571i	$-0.365130\pi$
$421$	16.8719	0.822285	0.411142	+	0.911571i	$0.365130\pi$
$422$	15.1818	0.739038
$423$	0.121405	0.00590294
$424$	−1.39166	−0.0675849
$425$	−7.55258	−0.366354
$426$	19.5322	0.946339
$427$	1.99341	0.0964679
$428$	3.20891	0.155109
$429$	1.07870	0.0520799
$430$	0.646309	0.0311678
$431$	0.152662	0.00735349	0.00367674	−	0.999993i	$-0.498830\pi$
$431$	0.152662	0.00735349	0.00367674	+	0.999993i	$0.498830\pi$
$432$	1.86708	0.0898298
$433$	21.8890	1.05192	0.525959	−	0.850510i	$-0.323707\pi$
$433$	21.8890	1.05192	0.525959	+	0.850510i	$0.323707\pi$
$434$	2.16470	0.103909
$435$	6.59538	0.316224
$436$	−18.1454	−0.869006
$437$	41.5434	1.98729
$438$	7.06272	0.337470
$439$	−20.9924	−1.00191	−0.500955	−	0.865473i	$-0.667018\pi$
$439$	−20.9924	−1.00191	−0.500955	+	0.865473i	$0.667018\pi$
$440$	1.49336	0.0711932
$441$	0.0381656	0.00181741
$442$	−1.26403	−0.0601238
$443$	29.3217	1.39312	0.696559	−	0.717500i	$-0.254713\pi$
$443$	29.3217	1.39312	0.696559	+	0.717500i	$0.254713\pi$
$444$	−19.2018	−0.911277
$445$	−13.8771	−0.657836
$446$	−0.00251330	−0.000119008 0
$447$	6.77820	0.320598
$448$	−4.06302	−0.191960
$449$	−18.2721	−0.862314	−0.431157	−	0.902277i	$-0.641895\pi$
$449$	−18.2721	−0.862314	−0.431157	+	0.902277i	$0.641895\pi$
$450$	0.138608	0.00653404
$451$	0.0536633	0.00252691
$452$	−14.1143	−0.663882
$453$	−13.0903	−0.615035
$454$	−6.90965	−0.324286
$455$	0.693718	0.0325220
$456$	−34.2838	−1.60549
$457$	11.3212	0.529582	0.264791	−	0.964306i	$-0.414697\pi$
$457$	11.3212	0.529582	0.264791	+	0.964306i	$0.414697\pi$
$458$	2.55067	0.119185
$459$	8.88228	0.414589
$460$	5.95403	0.277608
$461$	−17.2772	−0.804682	−0.402341	−	0.915490i	$-0.631803\pi$
$461$	−17.2772	−0.804682	−0.402341	+	0.915490i	$0.631803\pi$
$462$	1.00498	0.0467558
$463$	22.9088	1.06466	0.532331	−	0.846536i	$-0.321316\pi$
$463$	22.9088	1.06466	0.532331	+	0.846536i	$0.321316\pi$
$464$	1.75173	0.0813222
$465$	3.56277	0.165219
$466$	13.5672	0.628487
$467$	−11.5777	−0.535750	−0.267875	−	0.963454i	$-0.586322\pi$
$467$	−11.5777	−0.535750	−0.267875	+	0.963454i	$0.586322\pi$
$468$	−0.0445853	−0.00206096
$469$	4.72990	0.218407
$470$	2.05592	0.0948327
$471$	−35.5041	−1.63594
$472$	12.3006	0.566181
$473$	−0.696902	−0.0320436
$474$	−8.36039	−0.384005
$475$	−31.4767	−1.44425
$476$	2.26338	0.103742
$477$	−0.0193630	−0.000886573 0
$478$	4.87157	0.222820
$479$	−29.6293	−1.35380	−0.676899	−	0.736076i	$-0.736677\pi$
$479$	−29.6293	−1.35380	−0.676899	+	0.736076i	$0.736677\pi$
$480$	−7.87756	−0.359560
$481$	−7.43632	−0.339067
$482$	10.7897	0.491455
$483$	10.0985	0.459497
$484$	13.8319	0.628721
$485$	10.0753	0.457498
$486$	−0.328123	−0.0148839
$487$	34.5793	1.56694	0.783469	−	0.621431i	$-0.213448\pi$
$487$	34.5793	1.56694	0.783469	+	0.621431i	$0.213448\pi$
$488$	−5.46799	−0.247524
$489$	−25.3203	−1.14502
$490$	0.646309	0.0291973
$491$	−25.6780	−1.15883	−0.579415	−	0.815033i	$-0.696719\pi$
$491$	−25.6780	−1.15883	−0.579415	+	0.815033i	$0.696719\pi$
$492$	−0.176567	−0.00796027
$493$	8.33355	0.375324
$494$	−5.26807	−0.237022
$495$	0.0207781	0.000933905 0
$496$	0.946271	0.0424888
$497$	−13.5446	−0.607559
$498$	6.03825	0.270580
$499$	14.1078	0.631551	0.315775	−	0.948834i	$-0.397735\pi$
$499$	14.1078	0.631551	0.315775	+	0.948834i	$0.397735\pi$
$500$	−9.64970	−0.431548
$501$	34.0920	1.52312
$502$	−15.5187	−0.692635
$503$	5.18733	0.231292	0.115646	−	0.993291i	$-0.463106\pi$
$503$	5.18733	0.231292	0.115646	+	0.993291i	$0.463106\pi$
$504$	−0.104689	−0.00466324
$505$	−4.56090	−0.202957
$506$	3.34042	0.148500
$507$	21.2849	0.945297
$508$	15.7152	0.697247
$509$	0.113309	0.00502232	0.00251116	−	0.999997i	$-0.499201\pi$
$509$	0.113309	0.00502232	0.00251116	+	0.999997i	$0.499201\pi$
$510$	−1.93822	−0.0858260
$511$	−4.89764	−0.216659
$512$	−4.07635	−0.180151
$513$	37.0185	1.63441
$514$	23.9356	1.05575
$515$	−1.19665	−0.0527307
$516$	2.29300	0.100944
$517$	−2.21686	−0.0974974
$518$	−6.92813	−0.304405
$519$	15.1339	0.664307
$520$	−1.90289	−0.0834473
$521$	11.0502	0.484118	0.242059	−	0.970261i	$-0.422177\pi$
$521$	11.0502	0.484118	0.242059	+	0.970261i	$0.422177\pi$
$522$	−0.152941	−0.00669403
$523$	−2.24352	−0.0981022	−0.0490511	−	0.998796i	$-0.515620\pi$
$523$	−2.24352	−0.0981022	−0.0490511	+	0.998796i	$0.515620\pi$
$524$	−20.6774	−0.903295
$525$	−7.65144	−0.333936
$526$	16.6898	0.727710
$527$	4.50171	0.196098
$528$	0.439312	0.0191186
$529$	10.5661	0.459396
$530$	−0.327901	−0.0142431
$531$	0.171146	0.00742711
$532$	9.43303	0.408974
$533$	−0.0683796	−0.00296185
$534$	25.6166	1.10854
$535$	1.90555	0.0823842
$536$	−12.9743	−0.560404
$537$	−39.7384	−1.71484
$538$	−2.09303	−0.0902370
$539$	−0.696902	−0.0300177
$540$	5.30551	0.228313
$541$	25.8284	1.11045	0.555226	−	0.831700i	$-0.312632\pi$
$541$	25.8284	1.11045	0.555226	+	0.831700i	$0.312632\pi$
$542$	25.6010	1.09966
$543$	−8.99939	−0.386201
$544$	−9.95364	−0.426759
$545$	−10.7753	−0.461562
$546$	−1.28058	−0.0548036
$547$	−17.3765	−0.742964	−0.371482	−	0.928440i	$-0.621150\pi$
$547$	−17.3765	−0.742964	−0.371482	+	0.928440i	$0.621150\pi$
$548$	9.36237	0.399941
$549$	−0.0760796	−0.00324700
$550$	−2.53098	−0.107921
$551$	34.7316	1.47961
$552$	−27.7005	−1.17901
$553$	5.79752	0.246535
$554$	−23.0623	−0.979825
$555$	−11.4026	−0.484014
$556$	−25.8364	−1.09571
$557$	−42.5238	−1.80179	−0.900896	−	0.434034i	$-0.857090\pi$
$557$	−42.5238	−1.80179	−0.900896	+	0.434034i	$0.857090\pi$
$558$	−0.0826172	−0.00349747
$559$	0.888017	0.0375591
$560$	0.282525	0.0119389
$561$	2.08995	0.0882377
$562$	−8.13379	−0.343103
$563$	−39.6945	−1.67292	−0.836462	−	0.548024i	$-0.815380\pi$
$563$	−39.6945	−1.67292	−0.836462	+	0.548024i	$0.815380\pi$
$564$	7.29409	0.307137
$565$	−8.38152	−0.352613
$566$	−10.1106	−0.424979
$567$	9.11304	0.382712
$568$	37.1534	1.55892
$569$	33.8748	1.42010	0.710052	−	0.704149i	$-0.248671\pi$
$569$	33.8748	1.42010	0.710052	+	0.704149i	$0.248671\pi$
$570$	−8.07789	−0.338346
$571$	45.2450	1.89344	0.946721	−	0.322054i	$-0.104373\pi$
$571$	45.2450	1.89344	0.946721	+	0.322054i	$0.104373\pi$
$572$	0.814127	0.0340404
$573$	−10.3714	−0.433270
$574$	−0.0637066	−0.00265906
$575$	−25.4324	−1.06061
$576$	0.155068	0.00646115
$577$	−13.0842	−0.544703	−0.272351	−	0.962198i	$-0.587801\pi$
$577$	−13.0842	−0.544703	−0.272351	+	0.962198i	$0.587801\pi$
$578$	11.6156	0.483144
$579$	4.11460	0.170997
$580$	4.97775	0.206690
$581$	−4.18723	−0.173715
$582$	−18.5987	−0.770941
$583$	0.353569	0.0146433
$584$	13.4344	0.555920
$585$	−0.0264761	−0.00109465
$586$	14.0666	0.581084
$587$	13.6472	0.563281	0.281641	−	0.959520i	$-0.409121\pi$
$587$	13.6472	0.563281	0.281641	+	0.959520i	$0.409121\pi$
$588$	2.29300	0.0945619
$589$	18.7617	0.773062
$590$	2.89825	0.119319
$591$	5.37670	0.221168
$592$	−3.02854	−0.124472
$593$	−26.9871	−1.10823	−0.554113	−	0.832441i	$-0.686942\pi$
$593$	−26.9871	−1.10823	−0.554113	+	0.832441i	$0.686942\pi$
$594$	2.97658	0.122130
$595$	1.34406	0.0551012
$596$	5.11573	0.209549
$597$	−0.359076	−0.0146960
$598$	−4.25648	−0.174060
$599$	−20.4657	−0.836205	−0.418102	−	0.908400i	$-0.637305\pi$
$599$	−20.4657	−0.836205	−0.418102	+	0.908400i	$0.637305\pi$
$600$	20.9882	0.856838
$601$	−11.9356	−0.486865	−0.243432	−	0.969918i	$-0.578273\pi$
$601$	−11.9356	−0.486865	−0.243432	+	0.969918i	$0.578273\pi$
$602$	0.827330	0.0337195
$603$	−0.180519	−0.00735132
$604$	−9.87967	−0.401998
$605$	8.21378	0.333938
$606$	8.41925	0.342009
$607$	−46.2443	−1.87700	−0.938500	−	0.345280i	$-0.887784\pi$
$607$	−46.2443	−1.87700	−0.938500	+	0.345280i	$0.887784\pi$
$608$	−41.4836	−1.68238
$609$	8.44264	0.342113
$610$	−1.28836	−0.0521642
$611$	2.82480	0.114279
$612$	−0.0863831	−0.00349183
$613$	5.70807	0.230547	0.115273	−	0.993334i	$-0.463226\pi$
$613$	5.70807	0.230547	0.115273	+	0.993334i	$0.463226\pi$
$614$	3.20373	0.129292
$615$	−0.104851	−0.00422800
$616$	1.91163	0.0770216
$617$	−9.18290	−0.369690	−0.184845	−	0.982768i	$-0.559178\pi$
$617$	−9.18290	−0.369690	−0.184845	+	0.982768i	$0.559178\pi$
$618$	2.20897	0.0888579
$619$	−49.3612	−1.98399	−0.991997	−	0.126263i	$-0.959702\pi$
$619$	−49.3612	−1.98399	−0.991997	+	0.126263i	$0.959702\pi$
$620$	2.68894	0.107990
$621$	29.9100	1.20025
$622$	−12.5735	−0.504150
$623$	−17.7638	−0.711692
$624$	−0.559787	−0.0224094
$625$	16.2184	0.648734
$626$	10.7420	0.429338
$627$	8.71023	0.347853
$628$	−26.7961	−1.06928
$629$	−14.4077	−0.574473
$630$	−0.0246668	−0.000982748 0
$631$	−18.3323	−0.729799	−0.364899	−	0.931047i	$-0.618897\pi$
$631$	−18.3323	−0.729799	−0.364899	+	0.931047i	$0.618897\pi$
$632$	−15.9028	−0.632579
$633$	31.9853	1.27130
$634$	18.0188	0.715616
$635$	9.33214	0.370335
$636$	−1.16334	−0.0461294
$637$	0.888017	0.0351845
$638$	2.79269	0.110564
$639$	0.516938	0.0204498
$640$	−6.41294	−0.253494
$641$	40.6992	1.60752	0.803761	−	0.594952i	$-0.202829\pi$
$641$	40.6992	1.60752	0.803761	+	0.594952i	$0.202829\pi$
$642$	−3.51758	−0.138828
$643$	24.5896	0.969721	0.484860	−	0.874592i	$-0.338870\pi$
$643$	24.5896	0.969721	0.484860	+	0.874592i	$0.338870\pi$
$644$	7.62166	0.300335
$645$	1.36166	0.0536152
$646$	−10.2068	−0.401580
$647$	−3.85515	−0.151561	−0.0757807	−	0.997125i	$-0.524145\pi$
$647$	−3.85515	−0.151561	−0.0757807	+	0.997125i	$0.524145\pi$
$648$	−24.9974	−0.981990
$649$	−3.12512	−0.122672
$650$	3.22506	0.126497
$651$	4.56064	0.178745
$652$	−19.1101	−0.748408
$653$	−3.46817	−0.135720	−0.0678600	−	0.997695i	$-0.521617\pi$
$653$	−3.46817	−0.135720	−0.0678600	+	0.997695i	$0.521617\pi$
$654$	19.8908	0.777790
$655$	−12.2789	−0.479775
$656$	−0.0278485	−0.00108730
$657$	0.186921	0.00729250
$658$	2.63175	0.102596
$659$	−31.9397	−1.24419	−0.622097	−	0.782940i	$-0.713719\pi$
$659$	−31.9397	−1.24419	−0.622097	+	0.782940i	$0.713719\pi$
$660$	1.24836	0.0485922
$661$	−42.5042	−1.65322	−0.826612	−	0.562773i	$-0.809735\pi$
$661$	−42.5042	−1.65322	−0.826612	+	0.562773i	$0.809735\pi$
$662$	20.2852	0.788407
$663$	−2.66308	−0.103426
$664$	11.4857	0.445732
$665$	5.60162	0.217222
$666$	0.264416	0.0102459
$667$	28.0623	1.08658
$668$	25.7304	0.995537
$669$	−0.00529506	−0.000204719 0
$670$	−3.05698	−0.118101
$671$	1.38921	0.0536299
$672$	−10.0839	−0.388996
$673$	−31.0236	−1.19587	−0.597936	−	0.801544i	$-0.704012\pi$
$673$	−31.0236	−1.19587	−0.597936	+	0.801544i	$0.704012\pi$
$674$	−13.5134	−0.520516
$675$	−22.6623	−0.872273
$676$	16.0644	0.617863
$677$	42.4270	1.63060	0.815301	−	0.579038i	$-0.196572\pi$
$677$	42.4270	1.63060	0.815301	+	0.579038i	$0.196572\pi$
$678$	15.4720	0.594198
$679$	12.8973	0.494952
$680$	−3.68681	−0.141383
$681$	−14.5574	−0.557839
$682$	1.50859	0.0577668
$683$	41.8306	1.60060	0.800301	−	0.599599i	$-0.204673\pi$
$683$	41.8306	1.60060	0.800301	+	0.599599i	$0.204673\pi$
$684$	−0.360017	−0.0137656
$685$	5.55966	0.212424
$686$	0.827330	0.0315876
$687$	5.37381	0.205023
$688$	0.361656	0.0137880
$689$	−0.450529	−0.0171638
$690$	−6.52675	−0.248469
$691$	42.6781	1.62355	0.811776	−	0.583968i	$-0.198501\pi$
$691$	42.6781	1.62355	0.811776	+	0.583968i	$0.198501\pi$
$692$	11.4221	0.434203
$693$	0.0265977	0.00101036
$694$	−5.53626	−0.210154
$695$	−15.3424	−0.581971
$696$	−23.1584	−0.877818
$697$	−0.132484	−0.00501819
$698$	−15.1959	−0.575174
$699$	28.5836	1.08113
$700$	−5.77480	−0.218267
$701$	0.00811386	0.000306456 0	0.000153228	−	1.00000i	$-0.499951\pi$
$701$	0.00811386	0.000306456 0	0.000153228		1.00000i	$0.499951\pi$
$702$	−3.79286	−0.143152
$703$	−60.0467	−2.26470
$704$	−2.83153	−0.106717
$705$	4.33146	0.163132
$706$	−19.8161	−0.745790
$707$	−5.83833	−0.219573
$708$	10.2825	0.386441
$709$	−34.2787	−1.28736	−0.643682	−	0.765293i	$-0.722594\pi$
$709$	−34.2787	−1.28736	−0.643682	+	0.765293i	$0.722594\pi$
$710$	8.75402	0.328532
$711$	−0.221266	−0.00829811
$712$	48.7267	1.82611
$713$	15.1590	0.567709
$714$	−2.48109	−0.0928524
$715$	0.483454	0.0180801
$716$	−29.9919	−1.12085
$717$	10.2635	0.383298
$718$	−13.3649	−0.498775
$719$	12.0297	0.448632	0.224316	−	0.974516i	$-0.427985\pi$
$719$	12.0297	0.448632	0.224316	+	0.974516i	$0.427985\pi$
$720$	−0.0107827	−0.000401849 0
$721$	−1.53181	−0.0570477
$722$	−26.8193	−0.998110
$723$	22.7318	0.845406
$724$	−6.79213	−0.252428
$725$	−21.2623	−0.789662
$726$	−15.1623	−0.562727
$727$	−36.3986	−1.34995	−0.674975	−	0.737841i	$-0.735846\pi$
$727$	−36.3986	−1.34995	−0.674975	+	0.737841i	$0.735846\pi$
$728$	−2.43586	−0.0902789
$729$	26.6478	0.986957
$730$	3.16539	0.117156
$731$	1.72051	0.0636355
$732$	−4.57090	−0.168945
$733$	−21.5239	−0.795003	−0.397502	−	0.917602i	$-0.630123\pi$
$733$	−21.5239	−0.795003	−0.397502	+	0.917602i	$0.630123\pi$
$734$	8.83838	0.326231
$735$	1.36166	0.0502254
$736$	−33.5177	−1.23548
$737$	3.29628	0.121420
$738$	0.00243140	8.95010e−5 0
$739$	−16.6998	−0.614311	−0.307155	−	0.951659i	$-0.599377\pi$
$739$	−16.6998	−0.614311	−0.307155	+	0.951659i	$0.599377\pi$
$740$	−8.60594	−0.316360
$741$	−11.0989	−0.407727
$742$	−0.419740	−0.0154091
$743$	−0.535415	−0.0196425	−0.00982124	−	0.999952i	$-0.503126\pi$
$743$	−0.535415	−0.0196425	−0.00982124	+	0.999952i	$0.503126\pi$
$744$	−12.5100	−0.458638
$745$	3.03788	0.111299
$746$	−13.7274	−0.502596
$747$	0.159808	0.00584706
$748$	1.57735	0.0576737
$749$	2.43926	0.0891288
$750$	10.5779	0.386250
$751$	−38.9114	−1.41990	−0.709948	−	0.704254i	$-0.751281\pi$
$751$	−38.9114	−1.41990	−0.709948	+	0.704254i	$0.751281\pi$
$752$	1.15044	0.0419521
$753$	−32.6951	−1.19148
$754$	−3.55854	−0.129595
$755$	−5.86685	−0.213517
$756$	6.79150	0.247004
$757$	−5.15962	−0.187530	−0.0937648	−	0.995594i	$-0.529890\pi$
$757$	−5.15962	−0.187530	−0.0937648	+	0.995594i	$0.529890\pi$
$758$	−6.91158	−0.251040
$759$	7.03766	0.255451
$760$	−15.3654	−0.557363
$761$	8.57657	0.310900	0.155450	−	0.987844i	$-0.450317\pi$
$761$	8.57657	0.310900	0.155450	+	0.987844i	$0.450317\pi$
$762$	−17.2268	−0.624060
$763$	−13.7933	−0.499350
$764$	−7.82761	−0.283193
$765$	−0.0512969	−0.00185464
$766$	−8.10715	−0.292923
$767$	3.98214	0.143787
$768$	26.0020	0.938266
$769$	−17.9062	−0.645713	−0.322857	−	0.946448i	$-0.604643\pi$
$769$	−17.9062	−0.645713	−0.322857	+	0.946448i	$0.604643\pi$
$770$	0.450415	0.0162318
$771$	50.4279	1.81612
$772$	3.10543	0.111767
$773$	−33.7537	−1.21404	−0.607018	−	0.794688i	$-0.707635\pi$
$773$	−33.7537	−1.21404	−0.607018	+	0.794688i	$0.707635\pi$
$774$	−0.0315755	−0.00113496
$775$	−11.4857	−0.412579
$776$	−35.3777	−1.26998
$777$	−14.5963	−0.523640
$778$	17.1303	0.614152
$779$	−0.552151	−0.0197828
$780$	−1.59070	−0.0569561
$781$	−9.43928	−0.337764
$782$	−8.24683	−0.294906
$783$	25.0057	0.893631
$784$	0.361656	0.0129163
$785$	−15.9123	−0.567936
$786$	22.6663	0.808481
$787$	5.54969	0.197825	0.0989126	−	0.995096i	$-0.468464\pi$
$787$	5.54969	0.197825	0.0989126	+	0.995096i	$0.468464\pi$
$788$	4.05798	0.144559
$789$	35.1624	1.25181
$790$	−3.74699	−0.133312
$791$	−10.7291	−0.381481
$792$	−0.0729583	−0.00259246
$793$	−1.77018	−0.0628610
$794$	2.19145	0.0777717
$795$	−0.690827	−0.0245011
$796$	−0.271006	−0.00960556
$797$	−13.6043	−0.481889	−0.240944	−	0.970539i	$-0.577457\pi$
$797$	−13.6043	−0.481889	−0.240944	+	0.970539i	$0.577457\pi$
$798$	−10.3404	−0.366045
$799$	5.47299	0.193620
$800$	25.3958	0.897877
$801$	0.677966	0.0239548
$802$	−15.5033	−0.547442
$803$	−3.41318	−0.120449
$804$	−10.8457	−0.382498
$805$	4.52598	0.159520
$806$	−1.92229	−0.0677099
$807$	−4.40964	−0.155227
$808$	16.0147	0.563397
$809$	8.13035	0.285848	0.142924	−	0.989734i	$-0.454350\pi$
$809$	8.13035	0.285848	0.142924	+	0.989734i	$0.454350\pi$
$810$	−5.88984	−0.206948
$811$	19.4073	0.681483	0.340742	−	0.940157i	$-0.389322\pi$
$811$	19.4073	0.681483	0.340742	+	0.940157i	$0.389322\pi$
$812$	6.37194	0.223611
$813$	53.9367	1.89164
$814$	−4.82823	−0.169229
$815$	−11.3481	−0.397508
$816$	−1.08457	−0.0379677
$817$	7.17054	0.250866
$818$	−9.62001	−0.336356
$819$	−0.0338917	−0.00118427
$820$	−0.0791346	−0.00276350
$821$	−37.8657	−1.32152	−0.660761	−	0.750596i	$-0.729766\pi$
$821$	−37.8657	−1.32152	−0.660761	+	0.750596i	$0.729766\pi$
$822$	−10.2629	−0.357961
$823$	51.9902	1.81226	0.906132	−	0.422996i	$-0.139022\pi$
$823$	51.9902	1.81226	0.906132	+	0.422996i	$0.139022\pi$
$824$	4.20181	0.146377
$825$	−5.33231	−0.185647
$826$	3.71000	0.129087
$827$	45.1280	1.56925	0.784627	−	0.619968i	$-0.212854\pi$
$827$	45.1280	1.56925	0.784627	+	0.619968i	$0.212854\pi$
$828$	−0.290885	−0.0101090
$829$	22.2045	0.771195	0.385597	−	0.922667i	$-0.373995\pi$
$829$	22.2045	0.771195	0.385597	+	0.922667i	$0.373995\pi$
$830$	2.70624	0.0939351
$831$	−48.5882	−1.68550
$832$	3.60803	0.125086
$833$	1.72051	0.0596122
$834$	28.3215	0.980695
$835$	15.2795	0.528768
$836$	6.57390	0.227363
$837$	13.5079	0.466900
$838$	1.90896	0.0659441
$839$	50.2345	1.73429	0.867144	−	0.498058i	$-0.165953\pi$
$839$	50.2345	1.73429	0.867144	+	0.498058i	$0.165953\pi$
$840$	−3.73507	−0.128872
$841$	−5.53909	−0.191003
$842$	−13.9586	−0.481045
$843$	−17.1364	−0.590209
$844$	24.1403	0.830945
$845$	9.53955	0.328171
$846$	−0.100442	−0.00345328
$847$	10.5143	0.361277
$848$	−0.183484	−0.00630086
$849$	−21.3011	−0.731053
$850$	6.24848	0.214321
$851$	−48.5163	−1.66312
$852$	31.0579	1.06403
$853$	43.1299	1.47674	0.738370	−	0.674396i	$-0.235596\pi$
$853$	43.1299	1.47674	0.738370	+	0.674396i	$0.235596\pi$
$854$	−1.64921	−0.0564347
$855$	−0.213789	−0.00731143
$856$	−6.69098	−0.228693
$857$	49.3637	1.68623	0.843116	−	0.537732i	$-0.180719\pi$
$857$	49.3637	1.68623	0.843116	+	0.537732i	$0.180719\pi$
$858$	−0.892437	−0.0304673
$859$	0.446642	0.0152392	0.00761961	−	0.999971i	$-0.497575\pi$
$859$	0.446642	0.0152392	0.00761961	+	0.999971i	$0.497575\pi$
$860$	1.02769	0.0350438
$861$	−0.134218	−0.00457414
$862$	−0.126302	−0.00430187
$863$	−5.59736	−0.190536	−0.0952682	−	0.995452i	$-0.530371\pi$
$863$	−5.59736	−0.190536	−0.0952682	+	0.995452i	$0.530371\pi$
$864$	−29.8669	−1.01609
$865$	6.78279	0.230622
$866$	−18.1094	−0.615383
$867$	24.4719	0.831109
$868$	3.44206	0.116831
$869$	4.04030	0.137058
$870$	−5.45656	−0.184995
$871$	−4.20023	−0.142319
$872$	37.8354	1.28127
$873$	−0.492232	−0.0166595
$874$	−34.3701	−1.16259
$875$	−7.33525	−0.247977
$876$	11.2303	0.379437
$877$	36.0324	1.21673	0.608364	−	0.793658i	$-0.291826\pi$
$877$	36.0324	1.21673	0.608364	+	0.793658i	$0.291826\pi$
$878$	17.3676	0.586128
$879$	29.6357	0.999586
$880$	0.196893	0.00663725
$881$	42.5554	1.43373	0.716864	−	0.697213i	$-0.245577\pi$
$881$	42.5554	1.43373	0.716864	+	0.697213i	$0.245577\pi$
$882$	−0.0315755	−0.00106320
$883$	8.53974	0.287385	0.143693	−	0.989622i	$-0.454102\pi$
$883$	8.53974	0.287385	0.143693	+	0.989622i	$0.454102\pi$
$884$	−2.00992	−0.0676008
$885$	6.10608	0.205254
$886$	−24.2588	−0.814989
$887$	41.1276	1.38093	0.690465	−	0.723366i	$-0.257406\pi$
$887$	41.1276	1.38093	0.690465	+	0.723366i	$0.257406\pi$
$888$	40.0382	1.34359
$889$	11.9459	0.400653
$890$	11.4809	0.384841
$891$	6.35090	0.212763
$892$	−0.00399635	−0.000133808 0
$893$	22.8096	0.763296
$894$	−5.60781	−0.187553
$895$	−17.8101	−0.595326
$896$	−8.20909	−0.274247
$897$	−8.96762	−0.299420
$898$	15.1171	0.504463
$899$	12.6734	0.422681
$900$	0.220398	0.00734662
$901$	−0.872890	−0.0290802
$902$	−0.0443973	−0.00147827
$903$	1.74303	0.0580045
$904$	29.4301	0.978832
$905$	−4.03338	−0.134074
$906$	10.8300	0.359802
$907$	−19.7324	−0.655204	−0.327602	−	0.944816i	$-0.606240\pi$
$907$	−19.7324	−0.655204	−0.327602	+	0.944816i	$0.606240\pi$
$908$	−10.9869	−0.364614
$909$	0.222823	0.00739058
$910$	−0.573933	−0.0190257
$911$	−18.2788	−0.605605	−0.302802	−	0.953053i	$-0.597922\pi$
$911$	−18.2788	−0.605605	−0.302802	+	0.953053i	$0.597922\pi$
$912$	−4.52016	−0.149677
$913$	−2.91809	−0.0965746
$914$	−9.36635	−0.309811
$915$	−2.71434	−0.0897333
$916$	4.05579	0.134007
$917$	−15.7180	−0.519053
$918$	−7.34857	−0.242539
$919$	−2.16840	−0.0715290	−0.0357645	−	0.999360i	$-0.511387\pi$
$919$	−2.16840	−0.0715290	−0.0357645	+	0.999360i	$0.511387\pi$
$920$	−12.4149	−0.409307
$921$	6.74967	0.222409
$922$	14.2940	0.470747
$923$	12.0279	0.395902
$924$	1.59800	0.0525703
$925$	36.7599	1.20866
$926$	−18.9531	−0.622839
$927$	0.0584625	0.00192016
$928$	−28.0218	−0.919862
$929$	−0.0192950	−0.000633049 0	−0.000316525	−	1.00000i	$-0.500101\pi$
$929$	−0.0192950	−0.000633049 0	−0.000316525		1.00000i	$0.500101\pi$
$930$	−2.94758	−0.0966551
$931$	7.17054	0.235005
$932$	21.5730	0.706646
$933$	−26.4900	−0.867244
$934$	9.57855	0.313420
$935$	0.936681	0.0306327
$936$	0.0929660	0.00303869
$937$	37.8989	1.23810	0.619052	−	0.785350i	$-0.287517\pi$
$937$	37.8989	1.23810	0.619052	+	0.785350i	$0.287517\pi$
$938$	−3.91319	−0.127770
$939$	22.6315	0.738552
$940$	3.26909	0.106626
$941$	55.9313	1.82331	0.911653	−	0.410960i	$-0.134806\pi$
$941$	55.9313	1.82331	0.911653	+	0.410960i	$0.134806\pi$
$942$	29.3736	0.957043
$943$	−0.446124	−0.0145278
$944$	1.62178	0.0527843
$945$	4.03300	0.131193
$946$	0.576568	0.0187459
$947$	−32.7199	−1.06325	−0.531627	−	0.846978i	$-0.678419\pi$
$947$	−32.7199	−1.06325	−0.531627	+	0.846978i	$0.678419\pi$
$948$	−13.2937	−0.431760
$949$	4.34919	0.141181
$950$	26.0416	0.844902
$951$	37.9622	1.23101
$952$	−4.71942	−0.152957
$953$	−42.8612	−1.38841	−0.694205	−	0.719777i	$-0.744244\pi$
$953$	−42.8612	−1.38841	−0.694205	+	0.719777i	$0.744244\pi$
$954$	0.0160196	0.000518655 0
$955$	−4.64827	−0.150415
$956$	7.74621	0.250530
$957$	5.88369	0.190193
$958$	24.5132	0.791987
$959$	7.11683	0.229814
$960$	5.53244	0.178559
$961$	−24.1540	−0.779160
$962$	6.15229	0.198358
$963$	−0.0930959	−0.00299997
$964$	17.1565	0.552573
$965$	1.84410	0.0593636
$966$	−8.35478	−0.268811
$967$	−18.3233	−0.589239	−0.294619	−	0.955615i	$-0.595193\pi$
$967$	−18.3233	−0.589239	−0.294619	+	0.955615i	$0.595193\pi$
$968$	−28.8412	−0.926990
$969$	−21.5038	−0.690802
$970$	−8.33563	−0.267641
$971$	46.0753	1.47863	0.739313	−	0.673362i	$-0.235151\pi$
$971$	46.0753	1.47863	0.739313	+	0.673362i	$0.235151\pi$
$972$	−0.521743	−0.0167349
$973$	−19.6396	−0.629616
$974$	−28.6085	−0.916676
$975$	6.79461	0.217602
$976$	−0.720929	−0.0230764
$977$	−14.5864	−0.466660	−0.233330	−	0.972398i	$-0.574962\pi$
$977$	−14.5864	−0.466660	−0.233330	+	0.972398i	$0.574962\pi$
$978$	20.9482	0.669851
$979$	−12.3796	−0.395655
$980$	1.02769	0.0328283
$981$	0.526428	0.0168075
$982$	21.2441	0.677928
$983$	26.0391	0.830518	0.415259	−	0.909703i	$-0.363691\pi$
$983$	26.0391	0.830518	0.415259	+	0.909703i	$0.363691\pi$
$984$	0.368165	0.0117367
$985$	2.40975	0.0767810
$986$	−6.89460	−0.219569
$987$	5.54463	0.176487
$988$	−8.37668	−0.266498
$989$	5.79363	0.184227
$990$	−0.0171903	−0.000546345 0
$991$	−54.9341	−1.74504	−0.872520	−	0.488578i	$-0.837516\pi$
$991$	−54.9341	−1.74504	−0.872520	+	0.488578i	$0.837516\pi$
$992$	−15.1371	−0.480605
$993$	42.7372	1.35622
$994$	11.2059	0.355429
$995$	−0.160932	−0.00510188
$996$	9.60132	0.304230
$997$	2.64673	0.0838229	0.0419115	−	0.999121i	$-0.486655\pi$
$997$	2.64673	0.0838229	0.0419115	+	0.999121i	$0.486655\pi$
$998$	−11.6718	−0.369464
$999$	−43.2318	−1.36780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	301.2.a.c.1.2	✓	5
3.2	odd	2		2709.2.a.j.1.4		5
4.3	odd	2		4816.2.a.r.1.5		5
5.4	even	2		7525.2.a.f.1.4		5
7.6	odd	2		2107.2.a.g.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
301.2.a.c.1.2	✓	5	1.1	even	1	trivial
2107.2.a.g.1.2		5	7.6	odd	2
2709.2.a.j.1.4		5	3.2	odd	2
4816.2.a.r.1.5		5	4.3	odd	2
7525.2.a.f.1.4		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 301 = 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	301.a (trivial)

\(f(q)\)	\(=\)	\(q-0.827330 q^{2} -1.74303 q^{3} -1.31552 q^{4} -0.781199 q^{5} +1.44206 q^{6} -1.00000 q^{7} +2.74303 q^{8} +0.0381656 q^{9} +O(q^{10})\)	\(q-0.827330 q^{2} -1.74303 q^{3} -1.31552 q^{4} -0.781199 q^{5} +1.44206 q^{6} -1.00000 q^{7} +2.74303 q^{8} +0.0381656 q^{9} +0.646309 q^{10} -0.696902 q^{11} +2.29300 q^{12} +0.888017 q^{13} +0.827330 q^{14} +1.36166 q^{15} +0.361656 q^{16} +1.72051 q^{17} -0.0315755 q^{18} +7.17054 q^{19} +1.02769 q^{20} +1.74303 q^{21} +0.576568 q^{22} +5.79363 q^{23} -4.78120 q^{24} -4.38973 q^{25} -0.734683 q^{26} +5.16258 q^{27} +1.31552 q^{28} +4.84365 q^{29} -1.12654 q^{30} +2.61649 q^{31} -5.78528 q^{32} +1.21472 q^{33} -1.42343 q^{34} +0.781199 q^{35} -0.0502078 q^{36} -8.37408 q^{37} -5.93240 q^{38} -1.54784 q^{39} -2.14286 q^{40} -0.0770026 q^{41} -1.44206 q^{42} +1.00000 q^{43} +0.916793 q^{44} -0.0298149 q^{45} -4.79324 q^{46} +3.18102 q^{47} -0.630379 q^{48} +1.00000 q^{49} +3.63175 q^{50} -2.99891 q^{51} -1.16821 q^{52} -0.507343 q^{53} -4.27115 q^{54} +0.544419 q^{55} -2.74303 q^{56} -12.4985 q^{57} -4.00729 q^{58} +4.48431 q^{59} -1.79129 q^{60} -1.99341 q^{61} -2.16470 q^{62} -0.0381656 q^{63} +4.06302 q^{64} -0.693718 q^{65} -1.00498 q^{66} -4.72990 q^{67} -2.26338 q^{68} -10.0985 q^{69} -0.646309 q^{70} +13.5446 q^{71} +0.104689 q^{72} +4.89764 q^{73} +6.92813 q^{74} +7.65144 q^{75} -9.43303 q^{76} +0.696902 q^{77} +1.28058 q^{78} -5.79752 q^{79} -0.282525 q^{80} -9.11304 q^{81} +0.0637066 q^{82} +4.18723 q^{83} -2.29300 q^{84} -1.34406 q^{85} -0.827330 q^{86} -8.44264 q^{87} -1.91163 q^{88} +17.7638 q^{89} +0.0246668 q^{90} -0.888017 q^{91} -7.62166 q^{92} -4.56064 q^{93} -2.63175 q^{94} -5.60162 q^{95} +10.0839 q^{96} -12.8973 q^{97} -0.827330 q^{98} -0.0265977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - 5 q^{7} + 6 q^{9} + 7 q^{10} + 13 q^{11} + 8 q^{12} - q^{13} - q^{14} - 5 q^{16} + q^{17} - 6 q^{18} + 18 q^{19} + 2 q^{20} - 5 q^{21} - 5 q^{22} - 5 q^{23} - 16 q^{24} - q^{25} - 4 q^{26} + 11 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 3 q^{31} - 9 q^{32} + 26 q^{33} - 15 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} + 7 q^{38} + 5 q^{39} + 4 q^{40} + 17 q^{41} + 5 q^{43} + 11 q^{44} - 20 q^{45} - q^{46} + 7 q^{47} - 13 q^{48} + 5 q^{49} + 25 q^{50} - 34 q^{52} - 30 q^{53} + 5 q^{54} + 21 q^{55} - 9 q^{57} - 46 q^{58} + 9 q^{59} - 21 q^{60} - 10 q^{61} - 19 q^{62} - 6 q^{63} - 26 q^{64} - 4 q^{65} - 29 q^{66} - 10 q^{67} + 33 q^{68} - 19 q^{69} - 7 q^{70} + 17 q^{71} - 20 q^{72} - q^{73} - 10 q^{75} + 20 q^{76} - 13 q^{77} + 29 q^{78} - 4 q^{79} + 11 q^{80} - 11 q^{81} + 28 q^{82} + 23 q^{83} - 8 q^{84} - 23 q^{85} + q^{86} - 3 q^{87} - 13 q^{88} + 35 q^{89} - 31 q^{90} + q^{91} - 25 q^{92} - 21 q^{93} - 20 q^{94} + 22 q^{95} + 22 q^{96} - 2 q^{97} + q^{98} + 18 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - 5 * q^7 + 6 * q^9 + 7 * q^10 + 13 * q^11 + 8 * q^12 - q^13 - q^14 - 5 * q^16 + q^17 - 6 * q^18 + 18 * q^19 + 2 * q^20 - 5 * q^21 - 5 * q^22 - 5 * q^23 - 16 * q^24 - q^25 - 4 * q^26 + 11 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 3 * q^31 - 9 * q^32 + 26 * q^33 - 15 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 + 7 * q^38 + 5 * q^39 + 4 * q^40 + 17 * q^41 + 5 * q^43 + 11 * q^44 - 20 * q^45 - q^46 + 7 * q^47 - 13 * q^48 + 5 * q^49 + 25 * q^50 - 34 * q^52 - 30 * q^53 + 5 * q^54 + 21 * q^55 - 9 * q^57 - 46 * q^58 + 9 * q^59 - 21 * q^60 - 10 * q^61 - 19 * q^62 - 6 * q^63 - 26 * q^64 - 4 * q^65 - 29 * q^66 - 10 * q^67 + 33 * q^68 - 19 * q^69 - 7 * q^70 + 17 * q^71 - 20 * q^72 - q^73 - 10 * q^75 + 20 * q^76 - 13 * q^77 + 29 * q^78 - 4 * q^79 + 11 * q^80 - 11 * q^81 + 28 * q^82 + 23 * q^83 - 8 * q^84 - 23 * q^85 + q^86 - 3 * q^87 - 13 * q^88 + 35 * q^89 - 31 * q^90 + q^91 - 25 * q^92 - 21 * q^93 - 20 * q^94 + 22 * q^95 + 22 * q^96 - 2 * q^97 + q^98 + 18 * q^99

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