LMFDB - Embedded newform 4015.2.a.i.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0798923 q^{2} +0.0600931 q^{3} -1.99362 q^{4} +1.00000 q^{5} -0.00480098 q^{6} -4.79075 q^{7} +0.319059 q^{8} -2.99639 q^{9} +O(q^{10})$	\(q-0.0798923 q^{2} +0.0600931 q^{3} -1.99362 q^{4} +1.00000 q^{5} -0.00480098 q^{6} -4.79075 q^{7} +0.319059 q^{8} -2.99639 q^{9} -0.0798923 q^{10} -1.00000 q^{11} -0.119803 q^{12} -6.38456 q^{13} +0.382744 q^{14} +0.0600931 q^{15} +3.96174 q^{16} -1.67598 q^{17} +0.239388 q^{18} -7.70830 q^{19} -1.99362 q^{20} -0.287891 q^{21} +0.0798923 q^{22} -6.03887 q^{23} +0.0191733 q^{24} +1.00000 q^{25} +0.510077 q^{26} -0.360342 q^{27} +9.55093 q^{28} +4.87927 q^{29} -0.00480098 q^{30} -9.07547 q^{31} -0.954631 q^{32} -0.0600931 q^{33} +0.133898 q^{34} -4.79075 q^{35} +5.97365 q^{36} -0.534369 q^{37} +0.615834 q^{38} -0.383668 q^{39} +0.319059 q^{40} +12.3270 q^{41} +0.0230003 q^{42} -2.67683 q^{43} +1.99362 q^{44} -2.99639 q^{45} +0.482460 q^{46} -9.73663 q^{47} +0.238074 q^{48} +15.9513 q^{49} -0.0798923 q^{50} -0.100715 q^{51} +12.7284 q^{52} -2.69068 q^{53} +0.0287885 q^{54} -1.00000 q^{55} -1.52853 q^{56} -0.463216 q^{57} -0.389816 q^{58} -3.42198 q^{59} -0.119803 q^{60} -2.63093 q^{61} +0.725060 q^{62} +14.3550 q^{63} -7.84722 q^{64} -6.38456 q^{65} +0.00480098 q^{66} +9.96436 q^{67} +3.34126 q^{68} -0.362895 q^{69} +0.382744 q^{70} +0.362984 q^{71} -0.956026 q^{72} -1.00000 q^{73} +0.0426920 q^{74} +0.0600931 q^{75} +15.3674 q^{76} +4.79075 q^{77} +0.0306521 q^{78} -10.6212 q^{79} +3.96174 q^{80} +8.96751 q^{81} -0.984829 q^{82} +1.49298 q^{83} +0.573945 q^{84} -1.67598 q^{85} +0.213858 q^{86} +0.293210 q^{87} -0.319059 q^{88} -8.90487 q^{89} +0.239388 q^{90} +30.5869 q^{91} +12.0392 q^{92} -0.545374 q^{93} +0.777882 q^{94} -7.70830 q^{95} -0.0573668 q^{96} -6.72269 q^{97} -1.27439 q^{98} +2.99639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * 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 $

$2$	−0.0798923	−0.0564924	−0.0282462	−	0.999601i	$-0.508992\pi$
$2$	−0.0798923	−0.0564924	−0.0282462	+	0.999601i	$0.508992\pi$
$3$	0.0600931	0.0346948	0.0173474	−	0.999850i	$-0.494478\pi$
$3$	0.0600931	0.0346948	0.0173474	+	0.999850i	$0.494478\pi$
$4$	−1.99362	−0.996809
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.00480098	−0.00195999
$7$	−4.79075	−1.81073	−0.905367	−	0.424629i	$-0.860405\pi$
$7$	−4.79075	−1.81073	−0.905367	+	0.424629i	$0.860405\pi$
$8$	0.319059	0.112804
$9$	−2.99639	−0.998796
$10$	−0.0798923	−0.0252642
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.119803	−0.0345841
$13$	−6.38456	−1.77076	−0.885380	−	0.464869i	$-0.846101\pi$
$13$	−6.38456	−1.77076	−0.885380	+	0.464869i	$0.846101\pi$
$14$	0.382744	0.102293
$15$	0.0600931	0.0155160
$16$	3.96174	0.990436
$17$	−1.67598	−0.406484	−0.203242	−	0.979129i	$-0.565148\pi$
$17$	−1.67598	−0.406484	−0.203242	+	0.979129i	$0.565148\pi$
$18$	0.239388	0.0564244
$19$	−7.70830	−1.76840	−0.884202	−	0.467104i	$-0.845297\pi$
$19$	−7.70830	−1.76840	−0.884202	+	0.467104i	$0.845297\pi$
$20$	−1.99362	−0.445786
$21$	−0.287891	−0.0628231
$22$	0.0798923	0.0170331
$23$	−6.03887	−1.25919	−0.629596	−	0.776923i	$-0.716780\pi$
$23$	−6.03887	−1.25919	−0.629596	+	0.776923i	$0.716780\pi$
$24$	0.0191733	0.00391373
$25$	1.00000	0.200000
$26$	0.510077	0.100034
$27$	−0.360342	−0.0693478
$28$	9.55093	1.80496
$29$	4.87927	0.906057	0.453028	−	0.891496i	$-0.350344\pi$
$29$	4.87927	0.906057	0.453028	+	0.891496i	$0.350344\pi$
$30$	−0.00480098	−0.000876535 0
$31$	−9.07547	−1.63000	−0.815002	−	0.579459i	$-0.803264\pi$
$31$	−9.07547	−1.63000	−0.815002	+	0.579459i	$0.803264\pi$
$32$	−0.954631	−0.168757
$33$	−0.0600931	−0.0104609
$34$	0.133898	0.0229633
$35$	−4.79075	−0.809785
$36$	5.97365	0.995609
$37$	−0.534369	−0.0878497	−0.0439249	−	0.999035i	$-0.513986\pi$
$37$	−0.534369	−0.0878497	−0.0439249	+	0.999035i	$0.513986\pi$
$38$	0.615834	0.0999014
$39$	−0.383668	−0.0614361
$40$	0.319059	0.0504477
$41$	12.3270	1.92515	0.962574	−	0.271019i	$-0.0873608\pi$
$41$	12.3270	1.92515	0.962574	+	0.271019i	$0.0873608\pi$
$42$	0.0230003	0.00354902
$43$	−2.67683	−0.408213	−0.204106	−	0.978949i	$-0.565429\pi$
$43$	−2.67683	−0.408213	−0.204106	+	0.978949i	$0.565429\pi$
$44$	1.99362	0.300549
$45$	−2.99639	−0.446675
$46$	0.482460	0.0711348
$47$	−9.73663	−1.42023	−0.710117	−	0.704084i	$-0.751358\pi$
$47$	−9.73663	−1.42023	−0.710117	+	0.704084i	$0.751358\pi$
$48$	0.238074	0.0343630
$49$	15.9513	2.27876
$50$	−0.0798923	−0.0112985
$51$	−0.100715	−0.0141029
$52$	12.7284	1.76511
$53$	−2.69068	−0.369594	−0.184797	−	0.982777i	$-0.559163\pi$
$53$	−2.69068	−0.369594	−0.184797	+	0.982777i	$0.559163\pi$
$54$	0.0287885	0.00391762
$55$	−1.00000	−0.134840
$56$	−1.52853	−0.204259
$57$	−0.463216	−0.0613544
$58$	−0.389816	−0.0511853
$59$	−3.42198	−0.445504	−0.222752	−	0.974875i	$-0.571504\pi$
$59$	−3.42198	−0.445504	−0.222752	+	0.974875i	$0.571504\pi$
$60$	−0.119803	−0.0154665
$61$	−2.63093	−0.336856	−0.168428	−	0.985714i	$-0.553869\pi$
$61$	−2.63093	−0.336856	−0.168428	+	0.985714i	$0.553869\pi$
$62$	0.725060	0.0920828
$63$	14.3550	1.80856
$64$	−7.84722	−0.980903
$65$	−6.38456	−0.791908
$66$	0.00480098	0.000590960 0
$67$	9.96436	1.21734	0.608670	−	0.793424i	$-0.291703\pi$
$67$	9.96436	1.21734	0.608670	+	0.793424i	$0.291703\pi$
$68$	3.34126	0.405187
$69$	−0.362895	−0.0436874
$70$	0.382744	0.0457467
$71$	0.362984	0.0430782	0.0215391	−	0.999768i	$-0.493143\pi$
$71$	0.362984	0.0430782	0.0215391	+	0.999768i	$0.493143\pi$
$72$	−0.956026	−0.112669
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	0.0426920	0.00496284
$75$	0.0600931	0.00693896
$76$	15.3674	1.76276
$77$	4.79075	0.545957
$78$	0.0306521	0.00347067
$79$	−10.6212	−1.19498	−0.597491	−	0.801876i	$-0.703836\pi$
$79$	−10.6212	−1.19498	−0.597491	+	0.801876i	$0.703836\pi$
$80$	3.96174	0.442936
$81$	8.96751	0.996390
$82$	−0.984829	−0.108756
$83$	1.49298	0.163876	0.0819380	−	0.996637i	$-0.473889\pi$
$83$	1.49298	0.163876	0.0819380	+	0.996637i	$0.473889\pi$
$84$	0.573945	0.0626226
$85$	−1.67598	−0.181785
$86$	0.213858	0.0230609
$87$	0.293210	0.0314355
$88$	−0.319059	−0.0340118
$89$	−8.90487	−0.943914	−0.471957	−	0.881621i	$-0.656452\pi$
$89$	−8.90487	−0.943914	−0.471957	+	0.881621i	$0.656452\pi$
$90$	0.239388	0.0252338
$91$	30.5869	3.20638
$92$	12.0392	1.25517
$93$	−0.545374	−0.0565526
$94$	0.777882	0.0802324
$95$	−7.70830	−0.790855
$96$	−0.0573668	−0.00585497
$97$	−6.72269	−0.682586	−0.341293	−	0.939957i	$-0.610865\pi$
$97$	−6.72269	−0.682586	−0.341293	+	0.939957i	$0.610865\pi$
$98$	−1.27439	−0.128733
$99$	2.99639	0.301148
$100$	−1.99362	−0.199362
$101$	7.05178	0.701679	0.350839	−	0.936436i	$-0.385896\pi$
$101$	7.05178	0.701679	0.350839	+	0.936436i	$0.385896\pi$
$102$	0.00804633	0.000796705 0
$103$	−10.9273	−1.07670	−0.538350	−	0.842721i	$-0.680952\pi$
$103$	−10.9273	−1.07670	−0.538350	+	0.842721i	$0.680952\pi$
$104$	−2.03705	−0.199750
$105$	−0.287891	−0.0280953
$106$	0.214965	0.0208792
$107$	−15.9814	−1.54498	−0.772490	−	0.635027i	$-0.780989\pi$
$107$	−15.9814	−1.54498	−0.772490	+	0.635027i	$0.780989\pi$
$108$	0.718384	0.0691265
$109$	7.19671	0.689320	0.344660	−	0.938728i	$-0.387994\pi$
$109$	7.19671	0.689320	0.344660	+	0.938728i	$0.387994\pi$
$110$	0.0798923	0.00761743
$111$	−0.0321119	−0.00304793
$112$	−18.9797	−1.79342
$113$	3.67521	0.345734	0.172867	−	0.984945i	$-0.444697\pi$
$113$	3.67521	0.345734	0.172867	+	0.984945i	$0.444697\pi$
$114$	0.0370074	0.00346606
$115$	−6.03887	−0.563128
$116$	−9.72739	−0.903165
$117$	19.1306	1.76863
$118$	0.273390	0.0251676
$119$	8.02919	0.736035
$120$	0.0191733	0.00175027
$121$	1.00000	0.0909091
$122$	0.210191	0.0190298
$123$	0.740766	0.0667926
$124$	18.0930	1.62480
$125$	1.00000	0.0894427
$126$	−1.14685	−0.102170
$127$	5.93047	0.526244	0.263122	−	0.964763i	$-0.415248\pi$
$127$	5.93047	0.526244	0.263122	+	0.964763i	$0.415248\pi$
$128$	2.53620	0.224170
$129$	−0.160859	−0.0141629
$130$	0.510077	0.0447367
$131$	−2.95287	−0.257993	−0.128997	−	0.991645i	$-0.541176\pi$
$131$	−2.95287	−0.257993	−0.128997	+	0.991645i	$0.541176\pi$
$132$	0.119803	0.0104275
$133$	36.9286	3.20211
$134$	−0.796075	−0.0687704
$135$	−0.360342	−0.0310133
$136$	−0.534736	−0.0458532
$137$	0.669214	0.0571748	0.0285874	−	0.999591i	$-0.490899\pi$
$137$	0.669214	0.0571748	0.0285874	+	0.999591i	$0.490899\pi$
$138$	0.0289925	0.00246801
$139$	−15.1627	−1.28609	−0.643043	−	0.765830i	$-0.722329\pi$
$139$	−15.1627	−1.28609	−0.643043	+	0.765830i	$0.722329\pi$
$140$	9.55093	0.807201
$141$	−0.585104	−0.0492747
$142$	−0.0289996	−0.00243359
$143$	6.38456	0.533904
$144$	−11.8709	−0.989244
$145$	4.87927	0.405201
$146$	0.0798923	0.00661193
$147$	0.958565	0.0790611
$148$	1.06533	0.0875694
$149$	−12.0697	−0.988789	−0.494395	−	0.869238i	$-0.664610\pi$
$149$	−12.0697	−0.988789	−0.494395	+	0.869238i	$0.664610\pi$
$150$	−0.00480098	−0.000391998 0
$151$	10.0839	0.820612	0.410306	−	0.911948i	$-0.365422\pi$
$151$	10.0839	0.820612	0.410306	+	0.911948i	$0.365422\pi$
$152$	−2.45940	−0.199484
$153$	5.02188	0.405995
$154$	−0.382744	−0.0308424
$155$	−9.07547	−0.728960
$156$	0.764888	0.0612400
$157$	−10.4380	−0.833044	−0.416522	−	0.909126i	$-0.636751\pi$
$157$	−10.4380	−0.833044	−0.416522	+	0.909126i	$0.636751\pi$
$158$	0.848555	0.0675074
$159$	−0.161692	−0.0128230
$160$	−0.954631	−0.0754702
$161$	28.9308	2.28006
$162$	−0.716435	−0.0562885
$163$	13.6845	1.07185	0.535926	−	0.844265i	$-0.319963\pi$
$163$	13.6845	1.07185	0.535926	+	0.844265i	$0.319963\pi$
$164$	−24.5752	−1.91900
$165$	−0.0600931	−0.00467824
$166$	−0.119278	−0.00925775
$167$	8.09154	0.626142	0.313071	−	0.949730i	$-0.398642\pi$
$167$	8.09154	0.626142	0.313071	+	0.949730i	$0.398642\pi$
$168$	−0.0918544	−0.00708672
$169$	27.7626	2.13559
$170$	0.133898	0.0102695
$171$	23.0971	1.76628
$172$	5.33658	0.406910
$173$	−23.5983	−1.79415	−0.897074	−	0.441881i	$-0.854311\pi$
$173$	−23.5983	−1.79415	−0.897074	+	0.441881i	$0.854311\pi$
$174$	−0.0234253	−0.00177586
$175$	−4.79075	−0.362147
$176$	−3.96174	−0.298628
$177$	−0.205638	−0.0154567
$178$	0.711431	0.0533240
$179$	−10.8577	−0.811540	−0.405770	−	0.913975i	$-0.632997\pi$
$179$	−10.8577	−0.811540	−0.405770	+	0.913975i	$0.632997\pi$
$180$	5.97365	0.445250
$181$	17.7738	1.32112	0.660560	−	0.750774i	$-0.270319\pi$
$181$	17.7738	1.32112	0.660560	+	0.750774i	$0.270319\pi$
$182$	−2.44366	−0.181136
$183$	−0.158101	−0.0116871
$184$	−1.92676	−0.142043
$185$	−0.534369	−0.0392876
$186$	0.0435712	0.00319479
$187$	1.67598	0.122560
$188$	19.4111	1.41570
$189$	1.72631	0.125571
$190$	0.615834	0.0446773
$191$	−4.35267	−0.314948	−0.157474	−	0.987523i	$-0.550335\pi$
$191$	−4.35267	−0.314948	−0.157474	+	0.987523i	$0.550335\pi$
$192$	−0.471564	−0.0340322
$193$	−12.4760	−0.898044	−0.449022	−	0.893521i	$-0.648228\pi$
$193$	−12.4760	−0.898044	−0.449022	+	0.893521i	$0.648228\pi$
$194$	0.537092	0.0385609
$195$	−0.383668	−0.0274751
$196$	−31.8008	−2.27149
$197$	−22.4733	−1.60115	−0.800577	−	0.599229i	$-0.795474\pi$
$197$	−22.4733	−1.60115	−0.800577	+	0.599229i	$0.795474\pi$
$198$	−0.239388	−0.0170126
$199$	1.42696	0.101155	0.0505774	−	0.998720i	$-0.483894\pi$
$199$	1.42696	0.101155	0.0505774	+	0.998720i	$0.483894\pi$
$200$	0.319059	0.0225609
$201$	0.598789	0.0422354
$202$	−0.563383	−0.0396395
$203$	−23.3754	−1.64063
$204$	0.200787	0.0140579
$205$	12.3270	0.860952
$206$	0.873008	0.0608254
$207$	18.0948	1.25768
$208$	−25.2940	−1.75382
$209$	7.70830	0.533194
$210$	0.0230003	0.00158717
$211$	−9.01496	−0.620615	−0.310308	−	0.950636i	$-0.600432\pi$
$211$	−9.01496	−0.620615	−0.310308	+	0.950636i	$0.600432\pi$
$212$	5.36419	0.368414
$213$	0.0218128	0.00149459
$214$	1.27679	0.0872796
$215$	−2.67683	−0.182558
$216$	−0.114970	−0.00782274
$217$	43.4784	2.95150
$218$	−0.574962	−0.0389413
$219$	−0.0600931	−0.00406072
$220$	1.99362	0.134410
$221$	10.7004	0.719785
$222$	0.00256549	0.000172185 0
$223$	7.86849	0.526913	0.263457	−	0.964671i	$-0.415137\pi$
$223$	7.86849	0.526913	0.263457	+	0.964671i	$0.415137\pi$
$224$	4.57340	0.305573
$225$	−2.99639	−0.199759
$226$	−0.293621	−0.0195314
$227$	14.7919	0.981771	0.490886	−	0.871224i	$-0.336673\pi$
$227$	14.7919	0.981771	0.490886	+	0.871224i	$0.336673\pi$
$228$	0.923475	0.0611586
$229$	21.5872	1.42652	0.713261	−	0.700898i	$-0.247217\pi$
$229$	21.5872	1.42652	0.713261	+	0.700898i	$0.247217\pi$
$230$	0.482460	0.0318124
$231$	0.287891	0.0189419
$232$	1.55678	0.102207
$233$	0.387104	0.0253600	0.0126800	−	0.999920i	$-0.495964\pi$
$233$	0.387104	0.0253600	0.0126800	+	0.999920i	$0.495964\pi$
$234$	−1.52839	−0.0999140
$235$	−9.73663	−0.635148
$236$	6.82212	0.444082
$237$	−0.638263	−0.0414596
$238$	−0.641471	−0.0415804
$239$	−28.0390	−1.81369	−0.906847	−	0.421460i	$-0.861518\pi$
$239$	−28.0390	−1.81369	−0.906847	+	0.421460i	$0.861518\pi$
$240$	0.238074	0.0153676
$241$	−23.7343	−1.52886	−0.764430	−	0.644707i	$-0.776979\pi$
$241$	−23.7343	−1.52886	−0.764430	+	0.644707i	$0.776979\pi$
$242$	−0.0798923	−0.00513567
$243$	1.61991	0.103917
$244$	5.24506	0.335781
$245$	15.9513	1.01909
$246$	−0.0591815	−0.00377327
$247$	49.2141	3.13142
$248$	−2.89561	−0.183872
$249$	0.0897180	0.00568565
$250$	−0.0798923	−0.00505283
$251$	25.2944	1.59657	0.798285	−	0.602279i	$-0.205741\pi$
$251$	25.2944	1.59657	0.798285	+	0.602279i	$0.205741\pi$
$252$	−28.6183	−1.80278
$253$	6.03887	0.379661
$254$	−0.473799	−0.0297288
$255$	−0.100715	−0.00630700
$256$	15.4918	0.968239
$257$	−1.67763	−0.104647	−0.0523237	−	0.998630i	$-0.516663\pi$
$257$	−1.67763	−0.104647	−0.0523237	+	0.998630i	$0.516663\pi$
$258$	0.0128514	0.000800094 0
$259$	2.56003	0.159073
$260$	12.7284	0.789380
$261$	−14.6202	−0.904966
$262$	0.235911	0.0145746
$263$	−20.5775	−1.26886	−0.634432	−	0.772978i	$-0.718766\pi$
$263$	−20.5775	−1.26886	−0.634432	+	0.772978i	$0.718766\pi$
$264$	−0.0191733	−0.00118003
$265$	−2.69068	−0.165287
$266$	−2.95031	−0.180895
$267$	−0.535122	−0.0327489
$268$	−19.8651	−1.21345
$269$	7.99432	0.487422	0.243711	−	0.969848i	$-0.421635\pi$
$269$	7.99432	0.487422	0.243711	+	0.969848i	$0.421635\pi$
$270$	0.0287885	0.00175201
$271$	−20.5754	−1.24987	−0.624934	−	0.780678i	$-0.714874\pi$
$271$	−20.5754	−1.24987	−0.624934	+	0.780678i	$0.714874\pi$
$272$	−6.63979	−0.402596
$273$	1.83806	0.111245
$274$	−0.0534650	−0.00322994
$275$	−1.00000	−0.0603023
$276$	0.723474	0.0435480
$277$	−19.7910	−1.18913	−0.594564	−	0.804048i	$-0.702675\pi$
$277$	−19.7910	−1.18913	−0.594564	+	0.804048i	$0.702675\pi$
$278$	1.21139	0.0726541
$279$	27.1936	1.62804
$280$	−1.52853	−0.0913474
$281$	−12.0853	−0.720950	−0.360475	−	0.932769i	$-0.617385\pi$
$281$	−12.0853	−0.720950	−0.360475	+	0.932769i	$0.617385\pi$
$282$	0.0467453	0.00278364
$283$	6.12857	0.364306	0.182153	−	0.983270i	$-0.441693\pi$
$283$	6.12857	0.364306	0.182153	+	0.983270i	$0.441693\pi$
$284$	−0.723650	−0.0429408
$285$	−0.463216	−0.0274385
$286$	−0.510077	−0.0301615
$287$	−59.0554	−3.48593
$288$	2.86045	0.168553
$289$	−14.1911	−0.834771
$290$	−0.389816	−0.0228908
$291$	−0.403988	−0.0236822
$292$	1.99362	0.116668
$293$	−18.8386	−1.10056	−0.550282	−	0.834979i	$-0.685480\pi$
$293$	−18.8386	−1.10056	−0.550282	+	0.834979i	$0.685480\pi$
$294$	−0.0765820	−0.00446635
$295$	−3.42198	−0.199235
$296$	−0.170495	−0.00990984
$297$	0.360342	0.0209092
$298$	0.964277	0.0558591
$299$	38.5556	2.22973
$300$	−0.119803	−0.00691681
$301$	12.8240	0.739165
$302$	−0.805622	−0.0463583
$303$	0.423764	0.0243446
$304$	−30.5383	−1.75149
$305$	−2.63093	−0.150646
$306$	−0.401209	−0.0229356
$307$	16.9654	0.968265	0.484132	−	0.874995i	$-0.339135\pi$
$307$	16.9654	0.968265	0.484132	+	0.874995i	$0.339135\pi$
$308$	−9.55093	−0.544215
$309$	−0.656657	−0.0373559
$310$	0.725060	0.0411807
$311$	21.8317	1.23796	0.618980	−	0.785407i	$-0.287546\pi$
$311$	21.8317	1.23796	0.618980	+	0.785407i	$0.287546\pi$
$312$	−0.122413	−0.00693027
$313$	8.77860	0.496196	0.248098	−	0.968735i	$-0.420194\pi$
$313$	8.77860	0.496196	0.248098	+	0.968735i	$0.420194\pi$
$314$	0.833917	0.0470606
$315$	14.3550	0.808810
$316$	21.1747	1.19117
$317$	−18.4155	−1.03432	−0.517159	−	0.855889i	$-0.673010\pi$
$317$	−18.4155	−1.03432	−0.517159	+	0.855889i	$0.673010\pi$
$318$	0.0129179	0.000724401 0
$319$	−4.87927	−0.273186
$320$	−7.84722	−0.438673
$321$	−0.960372	−0.0536028
$322$	−2.31135	−0.128806
$323$	12.9189	0.718828
$324$	−17.8778	−0.993210
$325$	−6.38456	−0.354152
$326$	−1.09329	−0.0605515
$327$	0.432473	0.0239158
$328$	3.93303	0.217165
$329$	46.6458	2.57167
$330$	0.00480098	0.000264285 0
$331$	−12.9660	−0.712677	−0.356339	−	0.934357i	$-0.615975\pi$
$331$	−12.9660	−0.712677	−0.356339	+	0.934357i	$0.615975\pi$
$332$	−2.97644	−0.163353
$333$	1.60118	0.0877440
$334$	−0.646452	−0.0353723
$335$	9.96436	0.544411
$336$	−1.14055	−0.0622222
$337$	11.6655	0.635461	0.317730	−	0.948181i	$-0.397079\pi$
$337$	11.6655	0.635461	0.317730	+	0.948181i	$0.397079\pi$
$338$	−2.21802	−0.120644
$339$	0.220855	0.0119952
$340$	3.34126	0.181205
$341$	9.07547	0.491464
$342$	−1.84528	−0.0997812
$343$	−42.8836	−2.31550
$344$	−0.854068	−0.0460482
$345$	−0.362895	−0.0195376
$346$	1.88532	0.101356
$347$	23.8191	1.27868	0.639339	−	0.768925i	$-0.279208\pi$
$347$	23.8191	1.27868	0.639339	+	0.768925i	$0.279208\pi$
$348$	−0.584549	−0.0313351
$349$	−8.73109	−0.467365	−0.233682	−	0.972313i	$-0.575078\pi$
$349$	−8.73109	−0.467365	−0.233682	+	0.972313i	$0.575078\pi$
$350$	0.382744	0.0204585
$351$	2.30062	0.122798
$352$	0.954631	0.0508820
$353$	11.8987	0.633304	0.316652	−	0.948542i	$-0.397441\pi$
$353$	11.8987	0.633304	0.316652	+	0.948542i	$0.397441\pi$
$354$	0.0164289	0.000873184 0
$355$	0.362984	0.0192652
$356$	17.7529	0.940902
$357$	0.482499	0.0255366
$358$	0.867444	0.0458459
$359$	−23.5543	−1.24315	−0.621575	−	0.783355i	$-0.713507\pi$
$359$	−23.5543	−1.24315	−0.621575	+	0.783355i	$0.713507\pi$
$360$	−0.956026	−0.0503870
$361$	40.4179	2.12726
$362$	−1.41999	−0.0746332
$363$	0.0600931	0.00315407
$364$	−60.9785	−3.19614
$365$	−1.00000	−0.0523424
$366$	0.0126310	0.000660234 0
$367$	15.6920	0.819117	0.409558	−	0.912284i	$-0.365683\pi$
$367$	15.6920	0.819117	0.409558	+	0.912284i	$0.365683\pi$
$368$	−23.9245	−1.24715
$369$	−36.9364	−1.92283
$370$	0.0426920	0.00221945
$371$	12.8904	0.669237
$372$	1.08727	0.0563721
$373$	9.42272	0.487890	0.243945	−	0.969789i	$-0.421558\pi$
$373$	9.42272	0.487890	0.243945	+	0.969789i	$0.421558\pi$
$374$	−0.133898	−0.00692368
$375$	0.0600931	0.00310320
$376$	−3.10656	−0.160209
$377$	−31.1520	−1.60441
$378$	−0.137919	−0.00709378
$379$	3.97336	0.204098	0.102049	−	0.994779i	$-0.467460\pi$
$379$	3.97336	0.204098	0.102049	+	0.994779i	$0.467460\pi$
$380$	15.3674	0.788331
$381$	0.356381	0.0182579
$382$	0.347745	0.0177922
$383$	2.40776	0.123031	0.0615153	−	0.998106i	$-0.480407\pi$
$383$	2.40776	0.123031	0.0615153	+	0.998106i	$0.480407\pi$
$384$	0.152408	0.00777753
$385$	4.79075	0.244159
$386$	0.996739	0.0507327
$387$	8.02083	0.407722
$388$	13.4025	0.680408
$389$	−24.6748	−1.25106	−0.625531	−	0.780199i	$-0.715118\pi$
$389$	−24.6748	−1.25106	−0.625531	+	0.780199i	$0.715118\pi$
$390$	0.0306521	0.00155213
$391$	10.1210	0.511842
$392$	5.08942	0.257054
$393$	−0.177447	−0.00895102
$394$	1.79544	0.0904531
$395$	−10.6212	−0.534412
$396$	−5.97365	−0.300187
$397$	−23.2585	−1.16731	−0.583656	−	0.812001i	$-0.698378\pi$
$397$	−23.2585	−1.16731	−0.583656	+	0.812001i	$0.698378\pi$
$398$	−0.114003	−0.00571448
$399$	2.21915	0.111097
$400$	3.96174	0.198087
$401$	−3.45005	−0.172287	−0.0861436	−	0.996283i	$-0.527454\pi$
$401$	−3.45005	−0.172287	−0.0861436	+	0.996283i	$0.527454\pi$
$402$	−0.0478387	−0.00238598
$403$	57.9429	2.88634
$404$	−14.0586	−0.699439
$405$	8.96751	0.445599
$406$	1.86751	0.0926830
$407$	0.534369	0.0264877
$408$	−0.0321340	−0.00159087
$409$	20.2671	1.00214	0.501071	−	0.865406i	$-0.332940\pi$
$409$	20.2671	1.00214	0.501071	+	0.865406i	$0.332940\pi$
$410$	−0.984829	−0.0486372
$411$	0.0402152	0.00198367
$412$	21.7849	1.07326
$413$	16.3939	0.806690
$414$	−1.44564	−0.0710492
$415$	1.49298	0.0732876
$416$	6.09490	0.298827
$417$	−0.911177	−0.0446205
$418$	−0.615834	−0.0301214
$419$	−23.5681	−1.15138	−0.575689	−	0.817669i	$-0.695266\pi$
$419$	−23.5681	−1.15138	−0.575689	+	0.817669i	$0.695266\pi$
$420$	0.573945	0.0280057
$421$	−5.56201	−0.271076	−0.135538	−	0.990772i	$-0.543276\pi$
$421$	−5.56201	−0.271076	−0.135538	+	0.990772i	$0.543276\pi$
$422$	0.720226	0.0350600
$423$	29.1747	1.41852
$424$	−0.858488	−0.0416918
$425$	−1.67598	−0.0812968
$426$	−0.00174268	−8.44330e−5 0
$427$	12.6041	0.609956
$428$	31.8608	1.54005
$429$	0.383668	0.0185237
$430$	0.213858	0.0103132
$431$	2.92329	0.140810	0.0704050	−	0.997518i	$-0.477571\pi$
$431$	2.92329	0.140810	0.0704050	+	0.997518i	$0.477571\pi$
$432$	−1.42758	−0.0686846
$433$	11.5860	0.556786	0.278393	−	0.960467i	$-0.410198\pi$
$433$	11.5860	0.556786	0.278393	+	0.960467i	$0.410198\pi$
$434$	−3.47359	−0.166737
$435$	0.293210	0.0140584
$436$	−14.3475	−0.687120
$437$	46.5494	2.22676
$438$	0.00480098	0.000229400 0
$439$	15.8499	0.756475	0.378237	−	0.925709i	$-0.376530\pi$
$439$	15.8499	0.756475	0.378237	+	0.925709i	$0.376530\pi$
$440$	−0.319059	−0.0152106
$441$	−47.7964	−2.27602
$442$	−0.854878	−0.0406624
$443$	21.7348	1.03265	0.516326	−	0.856392i	$-0.327299\pi$
$443$	21.7348	1.03265	0.516326	+	0.856392i	$0.327299\pi$
$444$	0.0640189	0.00303820
$445$	−8.90487	−0.422131
$446$	−0.628632	−0.0297666
$447$	−0.725307	−0.0343058
$448$	37.5941	1.77615
$449$	−6.87717	−0.324554	−0.162277	−	0.986745i	$-0.551884\pi$
$449$	−6.87717	−0.324554	−0.162277	+	0.986745i	$0.551884\pi$
$450$	0.239388	0.0112849
$451$	−12.3270	−0.580454
$452$	−7.32696	−0.344631
$453$	0.605970	0.0284710
$454$	−1.18176	−0.0554626
$455$	30.5869	1.43393
$456$	−0.147793	−0.00692106
$457$	−31.7620	−1.48576	−0.742882	−	0.669423i	$-0.766542\pi$
$457$	−31.7620	−1.48576	−0.742882	+	0.669423i	$0.766542\pi$
$458$	−1.72465	−0.0805877
$459$	0.603924	0.0281888
$460$	12.0392	0.561331
$461$	−8.78415	−0.409118	−0.204559	−	0.978854i	$-0.565576\pi$
$461$	−8.78415	−0.409118	−0.204559	+	0.978854i	$0.565576\pi$
$462$	−0.0230003	−0.00107007
$463$	−29.1669	−1.35550	−0.677750	−	0.735292i	$-0.737045\pi$
$463$	−29.1669	−1.35550	−0.677750	+	0.735292i	$0.737045\pi$
$464$	19.3304	0.897391
$465$	−0.545374	−0.0252911
$466$	−0.0309266	−0.00143265
$467$	34.0303	1.57474	0.787368	−	0.616484i	$-0.211443\pi$
$467$	34.0303	1.57474	0.787368	+	0.616484i	$0.211443\pi$
$468$	−38.1392	−1.76298
$469$	−47.7368	−2.20428
$470$	0.777882	0.0358810
$471$	−0.627253	−0.0289023
$472$	−1.09181	−0.0502549
$473$	2.67683	0.123081
$474$	0.0509923	0.00234215
$475$	−7.70830	−0.353681
$476$	−16.0071	−0.733686
$477$	8.06234	0.369149
$478$	2.24010	0.102460
$479$	37.8843	1.73098	0.865489	−	0.500929i	$-0.167008\pi$
$479$	37.8843	1.73098	0.865489	+	0.500929i	$0.167008\pi$
$480$	−0.0573668	−0.00261842
$481$	3.41171	0.155561
$482$	1.89619	0.0863689
$483$	1.73854	0.0791063
$484$	−1.99362	−0.0906190
$485$	−6.72269	−0.305262
$486$	−0.129418	−0.00587054
$487$	31.2736	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$487$	31.2736	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$488$	−0.839422	−0.0379988
$489$	0.822344	0.0371877
$490$	−1.27439	−0.0575710
$491$	−39.4167	−1.77885	−0.889425	−	0.457082i	$-0.848895\pi$
$491$	−39.4167	−1.77885	−0.889425	+	0.457082i	$0.848895\pi$
$492$	−1.47680	−0.0665794
$493$	−8.17754	−0.368298
$494$	−3.93183	−0.176901
$495$	2.99639	0.134678
$496$	−35.9547	−1.61441
$497$	−1.73897	−0.0780033
$498$	−0.00716778	−0.000321196 0
$499$	24.7344	1.10726	0.553632	−	0.832761i	$-0.313241\pi$
$499$	24.7344	1.10726	0.553632	+	0.832761i	$0.313241\pi$
$500$	−1.99362	−0.0891573
$501$	0.486246	0.0217239
$502$	−2.02083	−0.0901941
$503$	−17.3127	−0.771935	−0.385967	−	0.922512i	$-0.626132\pi$
$503$	−17.3127	−0.771935	−0.385967	+	0.922512i	$0.626132\pi$
$504$	4.58008	0.204013
$505$	7.05178	0.313800
$506$	−0.482460	−0.0214479
$507$	1.66834	0.0740938
$508$	−11.8231	−0.524565
$509$	15.8127	0.700885	0.350442	−	0.936584i	$-0.386031\pi$
$509$	15.8127	0.700885	0.350442	+	0.936584i	$0.386031\pi$
$510$	0.00804633	0.000356297 0
$511$	4.79075	0.211930
$512$	−6.31007	−0.278868
$513$	2.77762	0.122635
$514$	0.134029	0.00591178
$515$	−10.9273	−0.481515
$516$	0.320692	0.0141177
$517$	9.73663	0.428216
$518$	−0.204527	−0.00898639
$519$	−1.41810	−0.0622476
$520$	−2.03705	−0.0893307
$521$	6.60043	0.289170	0.144585	−	0.989492i	$-0.453815\pi$
$521$	6.60043	0.289170	0.144585	+	0.989492i	$0.453815\pi$
$522$	1.16804	0.0511237
$523$	10.2591	0.448597	0.224299	−	0.974520i	$-0.427991\pi$
$523$	10.2591	0.448597	0.224299	+	0.974520i	$0.427991\pi$
$524$	5.88688	0.257170
$525$	−0.287891	−0.0125646
$526$	1.64399	0.0716812
$527$	15.2103	0.662570
$528$	−0.238074	−0.0103608
$529$	13.4680	0.585565
$530$	0.214965	0.00933748
$531$	10.2536	0.444968
$532$	−73.6214	−3.19189
$533$	−78.7022	−3.40897
$534$	0.0427521	0.00185006
$535$	−15.9814	−0.690936
$536$	3.17922	0.137321
$537$	−0.652471	−0.0281562
$538$	−0.638685	−0.0275357
$539$	−15.9513	−0.687072
$540$	0.718384	0.0309143
$541$	35.0754	1.50801	0.754004	−	0.656870i	$-0.228120\pi$
$541$	35.0754	1.50801	0.754004	+	0.656870i	$0.228120\pi$
$542$	1.64382	0.0706080
$543$	1.06809	0.0458359
$544$	1.59994	0.0685969
$545$	7.19671	0.308273
$546$	−0.146847	−0.00628447
$547$	−39.7325	−1.69884	−0.849419	−	0.527720i	$-0.823047\pi$
$547$	−39.7325	−1.69884	−0.849419	+	0.527720i	$0.823047\pi$
$548$	−1.33416	−0.0569923
$549$	7.88328	0.336450
$550$	0.0798923	0.00340662
$551$	−37.6108	−1.60228
$552$	−0.115785	−0.00492814
$553$	50.8837	2.16380
$554$	1.58115	0.0671767
$555$	−0.0321119	−0.00136307
$556$	30.2287	1.28198
$557$	−31.0950	−1.31754	−0.658769	−	0.752345i	$-0.728923\pi$
$557$	−31.0950	−1.31754	−0.658769	+	0.752345i	$0.728923\pi$
$558$	−2.17256	−0.0919719
$559$	17.0904	0.722847
$560$	−18.9797	−0.802040
$561$	0.100715	0.00425218
$562$	0.965524	0.0407282
$563$	−7.11983	−0.300065	−0.150032	−	0.988681i	$-0.547938\pi$
$563$	−7.11983	−0.300065	−0.150032	+	0.988681i	$0.547938\pi$
$564$	1.16647	0.0491174
$565$	3.67521	0.154617
$566$	−0.489625	−0.0205805
$567$	−42.9611	−1.80420
$568$	0.115813	0.00485942
$569$	−32.1614	−1.34828	−0.674139	−	0.738605i	$-0.735485\pi$
$569$	−32.1614	−1.34828	−0.674139	+	0.738605i	$0.735485\pi$
$570$	0.0370074	0.00155007
$571$	−25.4342	−1.06439	−0.532195	−	0.846622i	$-0.678633\pi$
$571$	−25.4342	−1.06439	−0.532195	+	0.846622i	$0.678633\pi$
$572$	−12.7284	−0.532200
$573$	−0.261566	−0.0109271
$574$	4.71807	0.196929
$575$	−6.03887	−0.251838
$576$	23.5133	0.979722
$577$	1.80469	0.0751302	0.0375651	−	0.999294i	$-0.488040\pi$
$577$	1.80469	0.0751302	0.0375651	+	0.999294i	$0.488040\pi$
$578$	1.13376	0.0471582
$579$	−0.749724	−0.0311575
$580$	−9.72739	−0.403908
$581$	−7.15251	−0.296736
$582$	0.0322755	0.00133786
$583$	2.69068	0.111437
$584$	−0.319059	−0.0132028
$585$	19.1306	0.790954
$586$	1.50506	0.0621735
$587$	−19.9232	−0.822320	−0.411160	−	0.911563i	$-0.634876\pi$
$587$	−19.9232	−0.822320	−0.411160	+	0.911563i	$0.634876\pi$
$588$	−1.91101	−0.0788088
$589$	69.9565	2.88251
$590$	0.273390	0.0112553
$591$	−1.35049	−0.0555517
$592$	−2.11703	−0.0870095
$593$	15.7461	0.646616	0.323308	−	0.946294i	$-0.395205\pi$
$593$	15.7461	0.646616	0.323308	+	0.946294i	$0.395205\pi$
$594$	−0.0287885	−0.00118121
$595$	8.02919	0.329165
$596$	24.0624	0.985633
$597$	0.0857507	0.00350954
$598$	−3.08029	−0.125963
$599$	−27.1931	−1.11108	−0.555540	−	0.831490i	$-0.687488\pi$
$599$	−27.1931	−1.11108	−0.555540	+	0.831490i	$0.687488\pi$
$600$	0.0191733	0.000782746 0
$601$	15.2742	0.623048	0.311524	−	0.950238i	$-0.399161\pi$
$601$	15.2742	0.623048	0.311524	+	0.950238i	$0.399161\pi$
$602$	−1.02454	−0.0417572
$603$	−29.8571	−1.21587
$604$	−20.1033	−0.817993
$605$	1.00000	0.0406558
$606$	−0.0338555	−0.00137528
$607$	−28.9770	−1.17614	−0.588070	−	0.808810i	$-0.700112\pi$
$607$	−28.9770	−1.17614	−0.588070	+	0.808810i	$0.700112\pi$
$608$	7.35858	0.298430
$609$	−1.40470	−0.0569213
$610$	0.210191	0.00851038
$611$	62.1641	2.51489
$612$	−10.0117	−0.404699
$613$	−24.0262	−0.970410	−0.485205	−	0.874400i	$-0.661255\pi$
$613$	−24.0262	−0.970410	−0.485205	+	0.874400i	$0.661255\pi$
$614$	−1.35540	−0.0546996
$615$	0.740766	0.0298706
$616$	1.52853	0.0615864
$617$	−36.9946	−1.48935	−0.744673	−	0.667429i	$-0.767395\pi$
$617$	−36.9946	−1.48935	−0.744673	+	0.667429i	$0.767395\pi$
$618$	0.0524618	0.00211032
$619$	−21.3139	−0.856676	−0.428338	−	0.903619i	$-0.640901\pi$
$619$	−21.3139	−0.856676	−0.428338	+	0.903619i	$0.640901\pi$
$620$	18.0930	0.726633
$621$	2.17606	0.0873222
$622$	−1.74418	−0.0699353
$623$	42.6610	1.70918
$624$	−1.52000	−0.0608485
$625$	1.00000	0.0400000
$626$	−0.701343	−0.0280313
$627$	0.463216	0.0184991
$628$	20.8094	0.830385
$629$	0.895590	0.0357095
$630$	−1.14685	−0.0456916
$631$	−21.6860	−0.863307	−0.431653	−	0.902040i	$-0.642070\pi$
$631$	−21.6860	−0.863307	−0.431653	+	0.902040i	$0.642070\pi$
$632$	−3.38880	−0.134799
$633$	−0.541737	−0.0215321
$634$	1.47126	0.0584311
$635$	5.93047	0.235344
$636$	0.322351	0.0127821
$637$	−101.842	−4.03514
$638$	0.389816	0.0154330
$639$	−1.08764	−0.0430264
$640$	2.53620	0.100252
$641$	11.9142	0.470582	0.235291	−	0.971925i	$-0.424396\pi$
$641$	11.9142	0.470582	0.235291	+	0.971925i	$0.424396\pi$
$642$	0.0767263	0.00302815
$643$	3.41577	0.134705	0.0673524	−	0.997729i	$-0.478545\pi$
$643$	3.41577	0.134705	0.0673524	+	0.997729i	$0.478545\pi$
$644$	−57.6769	−2.27279
$645$	−0.160859	−0.00633382
$646$	−1.03212	−0.0406083
$647$	−11.2990	−0.444209	−0.222104	−	0.975023i	$-0.571293\pi$
$647$	−11.2990	−0.444209	−0.222104	+	0.975023i	$0.571293\pi$
$648$	2.86117	0.112397
$649$	3.42198	0.134325
$650$	0.510077	0.0200069
$651$	2.61275	0.102402
$652$	−27.2816	−1.06843
$653$	−5.25346	−0.205584	−0.102792	−	0.994703i	$-0.532778\pi$
$653$	−5.25346	−0.205584	−0.102792	+	0.994703i	$0.532778\pi$
$654$	−0.0345512	−0.00135106
$655$	−2.95287	−0.115378
$656$	48.8363	1.90674
$657$	2.99639	0.116900
$658$	−3.72664	−0.145280
$659$	−7.67161	−0.298844	−0.149422	−	0.988774i	$-0.547741\pi$
$659$	−7.67161	−0.298844	−0.149422	+	0.988774i	$0.547741\pi$
$660$	0.119803	0.00466331
$661$	−28.0562	−1.09126	−0.545630	−	0.838026i	$-0.683710\pi$
$661$	−28.0562	−1.09126	−0.545630	+	0.838026i	$0.683710\pi$
$662$	1.03589	0.0402608
$663$	0.643019	0.0249728
$664$	0.476350	0.0184860
$665$	36.9286	1.43203
$666$	−0.127922	−0.00495687
$667$	−29.4653	−1.14090
$668$	−16.1314	−0.624144
$669$	0.472842	0.0182811
$670$	−0.796075	−0.0307551
$671$	2.63093	0.101566
$672$	0.274830	0.0106018
$673$	−28.2684	−1.08967	−0.544834	−	0.838544i	$-0.683407\pi$
$673$	−28.2684	−1.08967	−0.544834	+	0.838544i	$0.683407\pi$
$674$	−0.931984	−0.0358987
$675$	−0.360342	−0.0138696
$676$	−55.3481	−2.12877
$677$	11.0991	0.426572	0.213286	−	0.976990i	$-0.431583\pi$
$677$	11.0991	0.426572	0.213286	+	0.976990i	$0.431583\pi$
$678$	−0.0176446	−0.000677636 0
$679$	32.2068	1.23598
$680$	−0.534736	−0.0205062
$681$	0.888890	0.0340624
$682$	−0.725060	−0.0277640
$683$	29.2814	1.12042	0.560211	−	0.828350i	$-0.310720\pi$
$683$	29.2814	1.12042	0.560211	+	0.828350i	$0.310720\pi$
$684$	−46.0467	−1.76064
$685$	0.669214	0.0255694
$686$	3.42607	0.130808
$687$	1.29724	0.0494929
$688$	−10.6049	−0.404309
$689$	17.1788	0.654462
$690$	0.0289925	0.00110373
$691$	40.7757	1.55118	0.775590	−	0.631237i	$-0.217453\pi$
$691$	40.7757	1.55118	0.775590	+	0.631237i	$0.217453\pi$
$692$	47.0460	1.78842
$693$	−14.3550	−0.545300
$694$	−1.90297	−0.0722356
$695$	−15.1627	−0.575156
$696$	0.0935515	0.00354606
$697$	−20.6597	−0.782542
$698$	0.697547	0.0264025
$699$	0.0232623	0.000879860 0
$700$	9.55093	0.360991
$701$	−1.68022	−0.0634610	−0.0317305	−	0.999496i	$-0.510102\pi$
$701$	−1.68022	−0.0634610	−0.0317305	+	0.999496i	$0.510102\pi$
$702$	−0.183802	−0.00693717
$703$	4.11908	0.155354
$704$	7.84722	0.295753
$705$	−0.585104	−0.0220363
$706$	−0.950614	−0.0357768
$707$	−33.7834	−1.27055
$708$	0.409963	0.0154073
$709$	40.1223	1.50682	0.753412	−	0.657549i	$-0.228407\pi$
$709$	40.1223	1.50682	0.753412	+	0.657549i	$0.228407\pi$
$710$	−0.0289996	−0.00108834
$711$	31.8253	1.19354
$712$	−2.84118	−0.106478
$713$	54.8056	2.05249
$714$	−0.0385480	−0.00144262
$715$	6.38456	0.238769
$716$	21.6460	0.808950
$717$	−1.68495	−0.0629257
$718$	1.88181	0.0702285
$719$	−42.8964	−1.59977	−0.799883	−	0.600156i	$-0.795105\pi$
$719$	−42.8964	−1.59977	−0.799883	+	0.600156i	$0.795105\pi$
$720$	−11.8709	−0.442403
$721$	52.3501	1.94962
$722$	−3.22908	−0.120174
$723$	−1.42627	−0.0530434
$724$	−35.4342	−1.31690
$725$	4.87927	0.181211
$726$	−0.00480098	−0.000178181 0
$727$	5.71356	0.211904	0.105952	−	0.994371i	$-0.466211\pi$
$727$	5.71356	0.211904	0.105952	+	0.994371i	$0.466211\pi$
$728$	9.75902	0.361693
$729$	−26.8052	−0.992785
$730$	0.0798923	0.00295695
$731$	4.48631	0.165932
$732$	0.315192	0.0116498
$733$	−17.9951	−0.664664	−0.332332	−	0.943162i	$-0.607835\pi$
$733$	−17.9951	−0.664664	−0.332332	+	0.943162i	$0.607835\pi$
$734$	−1.25367	−0.0462739
$735$	0.958565	0.0353572
$736$	5.76490	0.212497
$737$	−9.96436	−0.367042
$738$	2.95093	0.108625
$739$	44.3625	1.63190	0.815951	−	0.578121i	$-0.196214\pi$
$739$	44.3625	1.63190	0.815951	+	0.578121i	$0.196214\pi$
$740$	1.06533	0.0391622
$741$	2.95743	0.108644
$742$	−1.02984	−0.0378068
$743$	−14.1028	−0.517382	−0.258691	−	0.965960i	$-0.583291\pi$
$743$	−14.1028	−0.517382	−0.258691	+	0.965960i	$0.583291\pi$
$744$	−0.174007	−0.00637939
$745$	−12.0697	−0.442200
$746$	−0.752803	−0.0275621
$747$	−4.47356	−0.163679
$748$	−3.34126	−0.122168
$749$	76.5629	2.79755
$750$	−0.00480098	−0.000175307 0
$751$	−12.6804	−0.462715	−0.231357	−	0.972869i	$-0.574317\pi$
$751$	−12.6804	−0.462715	−0.231357	+	0.972869i	$0.574317\pi$
$752$	−38.5740	−1.40665
$753$	1.52002	0.0553927
$754$	2.48880	0.0906369
$755$	10.0839	0.366989
$756$	−3.44160	−0.125170
$757$	−20.9990	−0.763220	−0.381610	−	0.924323i	$-0.624630\pi$
$757$	−20.9990	−0.763220	−0.381610	+	0.924323i	$0.624630\pi$
$758$	−0.317440	−0.0115300
$759$	0.362895	0.0131723
$760$	−2.45940	−0.0892120
$761$	−14.2085	−0.515058	−0.257529	−	0.966271i	$-0.582908\pi$
$761$	−14.2085	−0.515058	−0.257529	+	0.966271i	$0.582908\pi$
$762$	−0.0284721	−0.00103143
$763$	−34.4777	−1.24818
$764$	8.67756	0.313943
$765$	5.02188	0.181566
$766$	−0.192361	−0.00695030
$767$	21.8479	0.788880
$768$	0.930952	0.0335928
$769$	44.3201	1.59822	0.799112	−	0.601182i	$-0.205303\pi$
$769$	44.3201	1.59822	0.799112	+	0.601182i	$0.205303\pi$
$770$	−0.382744	−0.0137931
$771$	−0.100814	−0.00363072
$772$	24.8724	0.895178
$773$	30.1716	1.08520	0.542598	−	0.839992i	$-0.317441\pi$
$773$	30.1716	1.08520	0.542598	+	0.839992i	$0.317441\pi$
$774$	−0.640802	−0.0230332
$775$	−9.07547	−0.326001
$776$	−2.14494	−0.0769988
$777$	0.153840	0.00551899
$778$	1.97133	0.0706755
$779$	−95.0199	−3.40444
$780$	0.764888	0.0273874
$781$	−0.362984	−0.0129886
$782$	−0.808591	−0.0289152
$783$	−1.75820	−0.0628331
$784$	63.1951	2.25697
$785$	−10.4380	−0.372549
$786$	0.0141766	0.000505664 0
$787$	−52.7275	−1.87953	−0.939766	−	0.341820i	$-0.888957\pi$
$787$	−52.7275	−1.87953	−0.939766	+	0.341820i	$0.888957\pi$
$788$	44.8031	1.59604
$789$	−1.23657	−0.0440230
$790$	0.848555	0.0301902
$791$	−17.6070	−0.626033
$792$	0.956026	0.0339709
$793$	16.7973	0.596490
$794$	1.85818	0.0659443
$795$	−0.161692	−0.00573461
$796$	−2.84482	−0.100832
$797$	−8.48529	−0.300564	−0.150282	−	0.988643i	$-0.548018\pi$
$797$	−8.48529	−0.300564	−0.150282	+	0.988643i	$0.548018\pi$
$798$	−0.177293	−0.00627611
$799$	16.3184	0.577302
$800$	−0.954631	−0.0337513
$801$	26.6825	0.942778
$802$	0.275632	0.00973292
$803$	1.00000	0.0352892
$804$	−1.19376	−0.0421006
$805$	28.9308	1.01968
$806$	−4.62919	−0.163056
$807$	0.480404	0.0169110
$808$	2.24994	0.0791525
$809$	−21.5383	−0.757248	−0.378624	−	0.925551i	$-0.623603\pi$
$809$	−21.5383	−0.757248	−0.378624	+	0.925551i	$0.623603\pi$
$810$	−0.716435	−0.0251730
$811$	−28.1066	−0.986955	−0.493478	−	0.869758i	$-0.664275\pi$
$811$	−28.1066	−0.986955	−0.493478	+	0.869758i	$0.664275\pi$
$812$	46.6015	1.63539
$813$	−1.23644	−0.0433639
$814$	−0.0426920	−0.00149635
$815$	13.6845	0.479347
$816$	−0.399006	−0.0139680
$817$	20.6338	0.721886
$818$	−1.61918	−0.0566134
$819$	−91.6502	−3.20252
$820$	−24.5752	−0.858205
$821$	23.3533	0.815035	0.407518	−	0.913197i	$-0.366395\pi$
$821$	23.3533	0.815035	0.407518	+	0.913197i	$0.366395\pi$
$822$	−0.00321288	−0.000112062 0
$823$	−14.4197	−0.502641	−0.251320	−	0.967904i	$-0.580865\pi$
$823$	−14.4197	−0.502641	−0.251320	+	0.967904i	$0.580865\pi$
$824$	−3.48646	−0.121457
$825$	−0.0600931	−0.00209217
$826$	−1.30974	−0.0455718
$827$	−44.2066	−1.53721	−0.768607	−	0.639721i	$-0.779050\pi$
$827$	−44.2066	−1.53721	−0.768607	+	0.639721i	$0.779050\pi$
$828$	−36.0741	−1.25366
$829$	23.8277	0.827571	0.413786	−	0.910374i	$-0.364206\pi$
$829$	23.8277	0.827571	0.413786	+	0.910374i	$0.364206\pi$
$830$	−0.119278	−0.00414019
$831$	−1.18931	−0.0412566
$832$	50.1011	1.73694
$833$	−26.7340	−0.926280
$834$	0.0727960	0.00252072
$835$	8.09154	0.280019
$836$	−15.3674	−0.531492
$837$	3.27027	0.113037
$838$	1.88291	0.0650441
$839$	54.2133	1.87165	0.935826	−	0.352464i	$-0.114656\pi$
$839$	54.2133	1.87165	0.935826	+	0.352464i	$0.114656\pi$
$840$	−0.0918544	−0.00316928
$841$	−5.19276	−0.179061
$842$	0.444362	0.0153137
$843$	−0.726245	−0.0250132
$844$	17.9724	0.618635
$845$	27.7626	0.955064
$846$	−2.33084	−0.0801358
$847$	−4.79075	−0.164612
$848$	−10.6598	−0.366059
$849$	0.368285	0.0126395
$850$	0.133898	0.00459265
$851$	3.22699	0.110620
$852$	−0.0434864	−0.00148982
$853$	21.3378	0.730591	0.365296	−	0.930892i	$-0.380968\pi$
$853$	21.3378	0.730591	0.365296	+	0.930892i	$0.380968\pi$
$854$	−1.00697	−0.0344579
$855$	23.0971	0.789903
$856$	−5.09901	−0.174281
$857$	−23.0156	−0.786196	−0.393098	−	0.919497i	$-0.628597\pi$
$857$	−23.0156	−0.786196	−0.393098	+	0.919497i	$0.628597\pi$
$858$	−0.0306521	−0.00104645
$859$	−20.5749	−0.702006	−0.351003	−	0.936374i	$-0.614159\pi$
$859$	−20.5749	−0.702006	−0.351003	+	0.936374i	$0.614159\pi$
$860$	5.33658	0.181976
$861$	−3.54883	−0.120944
$862$	−0.233549	−0.00795470
$863$	−37.4541	−1.27495	−0.637477	−	0.770469i	$-0.720022\pi$
$863$	−37.4541	−1.27495	−0.637477	+	0.770469i	$0.720022\pi$
$864$	0.343994	0.0117029
$865$	−23.5983	−0.802367
$866$	−0.925630	−0.0314542
$867$	−0.852788	−0.0289622
$868$	−86.6792	−2.94208
$869$	10.6212	0.360301
$870$	−0.0234253	−0.000794190 0
$871$	−63.6181	−2.15562
$872$	2.29618	0.0777583
$873$	20.1438	0.681765
$874$	−3.71894	−0.125795
$875$	−4.79075	−0.161957
$876$	0.119803	0.00404776
$877$	−48.1643	−1.62639	−0.813196	−	0.581990i	$-0.802274\pi$
$877$	−48.1643	−1.62639	−0.813196	+	0.581990i	$0.802274\pi$
$878$	−1.26629	−0.0427351
$879$	−1.13207	−0.0381838
$880$	−3.96174	−0.133550
$881$	28.2279	0.951021	0.475510	−	0.879710i	$-0.342263\pi$
$881$	28.2279	0.951021	0.475510	+	0.879710i	$0.342263\pi$
$882$	3.81856	0.128578
$883$	−48.9522	−1.64737	−0.823686	−	0.567047i	$-0.808086\pi$
$883$	−48.9522	−1.64737	−0.823686	+	0.567047i	$0.808086\pi$
$884$	−21.3325	−0.717488
$885$	−0.205638	−0.00691243
$886$	−1.73644	−0.0583370
$887$	−6.56104	−0.220298	−0.110149	−	0.993915i	$-0.535133\pi$
$887$	−6.56104	−0.220298	−0.110149	+	0.993915i	$0.535133\pi$
$888$	−0.0102456	−0.000343820 0
$889$	−28.4114	−0.952889
$890$	0.711431	0.0238472
$891$	−8.96751	−0.300423
$892$	−15.6868	−0.525232
$893$	75.0528	2.51155
$894$	0.0579464	0.00193802
$895$	−10.8577	−0.362932
$896$	−12.1503	−0.405913
$897$	2.31693	0.0773599
$898$	0.549433	0.0183348
$899$	−44.2817	−1.47688
$900$	5.97365	0.199122
$901$	4.50952	0.150234
$902$	0.984829	0.0327912
$903$	0.770637	0.0256452
$904$	1.17261	0.0390004
$905$	17.7738	0.590822
$906$	−0.0484124	−0.00160839
$907$	−58.7534	−1.95087	−0.975437	−	0.220280i	$-0.929303\pi$
$907$	−58.7534	−1.95087	−0.975437	+	0.220280i	$0.929303\pi$
$908$	−29.4893	−0.978638
$909$	−21.1299	−0.700834
$910$	−2.44366	−0.0810064
$911$	23.2911	0.771667	0.385834	−	0.922568i	$-0.373914\pi$
$911$	23.2911	0.771667	0.385834	+	0.922568i	$0.373914\pi$
$912$	−1.83514	−0.0607676
$913$	−1.49298	−0.0494105
$914$	2.53754	0.0839343
$915$	−0.158101	−0.00522665
$916$	−43.0366	−1.42197
$917$	14.1465	0.467157
$918$	−0.0482489	−0.00159245
$919$	23.5468	0.776737	0.388369	−	0.921504i	$-0.373039\pi$
$919$	23.5468	0.776737	0.388369	+	0.921504i	$0.373039\pi$
$920$	−1.92676	−0.0635234
$921$	1.01950	0.0335937
$922$	0.701786	0.0231121
$923$	−2.31749	−0.0762812
$924$	−0.573945	−0.0188814
$925$	−0.534369	−0.0175699
$926$	2.33021	0.0765755
$927$	32.7425	1.07540
$928$	−4.65790	−0.152903
$929$	−28.5447	−0.936520	−0.468260	−	0.883591i	$-0.655119\pi$
$929$	−28.5447	−0.936520	−0.468260	+	0.883591i	$0.655119\pi$
$930$	0.0435712	0.00142875
$931$	−122.958	−4.02977
$932$	−0.771736	−0.0252791
$933$	1.31193	0.0429508
$934$	−2.71876	−0.0889605
$935$	1.67598	0.0548103
$936$	6.10381	0.199509
$937$	−23.4140	−0.764903	−0.382452	−	0.923975i	$-0.624920\pi$
$937$	−23.4140	−0.764903	−0.382452	+	0.923975i	$0.624920\pi$
$938$	3.81380	0.124525
$939$	0.527534	0.0172154
$940$	19.4111	0.633121
$941$	20.8093	0.678365	0.339183	−	0.940721i	$-0.389850\pi$
$941$	20.8093	0.678365	0.339183	+	0.940721i	$0.389850\pi$
$942$	0.0501127	0.00163276
$943$	−74.4410	−2.42413
$944$	−13.5570	−0.441243
$945$	1.72631	0.0561568
$946$	−0.213858	−0.00695313
$947$	−20.7918	−0.675641	−0.337821	−	0.941210i	$-0.609690\pi$
$947$	−20.7918	−0.675641	−0.337821	+	0.941210i	$0.609690\pi$
$948$	1.27245	0.0413273
$949$	6.38456	0.207252
$950$	0.615834	0.0199803
$951$	−1.10665	−0.0358855
$952$	2.56179	0.0830280
$953$	−18.6536	−0.604248	−0.302124	−	0.953269i	$-0.597696\pi$
$953$	−18.6536	−0.604248	−0.302124	+	0.953269i	$0.597696\pi$
$954$	−0.644119	−0.0208541
$955$	−4.35267	−0.140849
$956$	55.8991	1.80791
$957$	−0.293210	−0.00947815
$958$	−3.02666	−0.0977870
$959$	−3.20604	−0.103528
$960$	−0.471564	−0.0152197
$961$	51.3642	1.65691
$962$	−0.272570	−0.00878799
$963$	47.8865	1.54312
$964$	47.3171	1.52398
$965$	−12.4760	−0.401618
$966$	−0.138896	−0.00446890
$967$	−13.4051	−0.431080	−0.215540	−	0.976495i	$-0.569151\pi$
$967$	−13.4051	−0.431080	−0.215540	+	0.976495i	$0.569151\pi$
$968$	0.319059	0.0102550
$969$	0.776339	0.0249396
$970$	0.537092	0.0172450
$971$	0.385018	0.0123558	0.00617790	−	0.999981i	$-0.498034\pi$
$971$	0.385018	0.0123558	0.00617790	+	0.999981i	$0.498034\pi$
$972$	−3.22948	−0.103586
$973$	72.6410	2.32876
$974$	−2.49852	−0.0800579
$975$	−0.383668	−0.0122872
$976$	−10.4231	−0.333634
$977$	52.0013	1.66367	0.831834	−	0.555024i	$-0.187291\pi$
$977$	52.0013	1.66367	0.831834	+	0.555024i	$0.187291\pi$
$978$	−0.0656990	−0.00210082
$979$	8.90487	0.284601
$980$	−31.8008	−1.01584
$981$	−21.5641	−0.688490
$982$	3.14909	0.100491
$983$	−3.50787	−0.111884	−0.0559418	−	0.998434i	$-0.517816\pi$
$983$	−3.50787	−0.111884	−0.0559418	+	0.998434i	$0.517816\pi$
$984$	0.236348	0.00753450
$985$	−22.4733	−0.716058
$986$	0.653322	0.0208060
$987$	2.80309	0.0892234
$988$	−98.1141	−3.12143
$989$	16.1650	0.514019
$990$	−0.239388	−0.00760826
$991$	−30.6959	−0.975089	−0.487544	−	0.873098i	$-0.662107\pi$
$991$	−30.6959	−0.975089	−0.487544	+	0.873098i	$0.662107\pi$
$992$	8.66373	0.275074
$993$	−0.779169	−0.0247262
$994$	0.138930	0.00440659
$995$	1.42696	0.0452378
$996$	−0.178863	−0.00566750
$997$	−2.36342	−0.0748503	−0.0374251	−	0.999299i	$-0.511916\pi$
$997$	−2.36342	−0.0748503	−0.0374251	+	0.999299i	$0.511916\pi$
$998$	−1.97609	−0.0625520
$999$	0.192555	0.00609219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.i.1.18	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.i.1.18	✓	38	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0798923 q^{2} +0.0600931 q^{3} -1.99362 q^{4} +1.00000 q^{5} -0.00480098 q^{6} -4.79075 q^{7} +0.319059 q^{8} -2.99639 q^{9} +O(q^{10})\)	\(q-0.0798923 q^{2} +0.0600931 q^{3} -1.99362 q^{4} +1.00000 q^{5} -0.00480098 q^{6} -4.79075 q^{7} +0.319059 q^{8} -2.99639 q^{9} -0.0798923 q^{10} -1.00000 q^{11} -0.119803 q^{12} -6.38456 q^{13} +0.382744 q^{14} +0.0600931 q^{15} +3.96174 q^{16} -1.67598 q^{17} +0.239388 q^{18} -7.70830 q^{19} -1.99362 q^{20} -0.287891 q^{21} +0.0798923 q^{22} -6.03887 q^{23} +0.0191733 q^{24} +1.00000 q^{25} +0.510077 q^{26} -0.360342 q^{27} +9.55093 q^{28} +4.87927 q^{29} -0.00480098 q^{30} -9.07547 q^{31} -0.954631 q^{32} -0.0600931 q^{33} +0.133898 q^{34} -4.79075 q^{35} +5.97365 q^{36} -0.534369 q^{37} +0.615834 q^{38} -0.383668 q^{39} +0.319059 q^{40} +12.3270 q^{41} +0.0230003 q^{42} -2.67683 q^{43} +1.99362 q^{44} -2.99639 q^{45} +0.482460 q^{46} -9.73663 q^{47} +0.238074 q^{48} +15.9513 q^{49} -0.0798923 q^{50} -0.100715 q^{51} +12.7284 q^{52} -2.69068 q^{53} +0.0287885 q^{54} -1.00000 q^{55} -1.52853 q^{56} -0.463216 q^{57} -0.389816 q^{58} -3.42198 q^{59} -0.119803 q^{60} -2.63093 q^{61} +0.725060 q^{62} +14.3550 q^{63} -7.84722 q^{64} -6.38456 q^{65} +0.00480098 q^{66} +9.96436 q^{67} +3.34126 q^{68} -0.362895 q^{69} +0.382744 q^{70} +0.362984 q^{71} -0.956026 q^{72} -1.00000 q^{73} +0.0426920 q^{74} +0.0600931 q^{75} +15.3674 q^{76} +4.79075 q^{77} +0.0306521 q^{78} -10.6212 q^{79} +3.96174 q^{80} +8.96751 q^{81} -0.984829 q^{82} +1.49298 q^{83} +0.573945 q^{84} -1.67598 q^{85} +0.213858 q^{86} +0.293210 q^{87} -0.319059 q^{88} -8.90487 q^{89} +0.239388 q^{90} +30.5869 q^{91} +12.0392 q^{92} -0.545374 q^{93} +0.777882 q^{94} -7.70830 q^{95} -0.0573668 q^{96} -6.72269 q^{97} -1.27439 q^{98} +2.99639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * q^99

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