LMFDB - Embedded newform 1205.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 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			1.9
Root			$0.596683$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.596683 q^{2} -3.22200 q^{3} -1.64397 q^{4} -1.00000 q^{5} -1.92252 q^{6} +0.0914365 q^{7} -2.17430 q^{8} +7.38130 q^{9} +O(q^{10})$	\(q+0.596683 q^{2} -3.22200 q^{3} -1.64397 q^{4} -1.00000 q^{5} -1.92252 q^{6} +0.0914365 q^{7} -2.17430 q^{8} +7.38130 q^{9} -0.596683 q^{10} +0.938184 q^{11} +5.29687 q^{12} +6.40952 q^{13} +0.0545586 q^{14} +3.22200 q^{15} +1.99057 q^{16} -5.47227 q^{17} +4.40430 q^{18} -4.62417 q^{19} +1.64397 q^{20} -0.294609 q^{21} +0.559799 q^{22} +9.45757 q^{23} +7.00559 q^{24} +1.00000 q^{25} +3.82445 q^{26} -14.1166 q^{27} -0.150319 q^{28} -0.666961 q^{29} +1.92252 q^{30} -7.51445 q^{31} +5.53633 q^{32} -3.02283 q^{33} -3.26521 q^{34} -0.0914365 q^{35} -12.1346 q^{36} +5.97202 q^{37} -2.75917 q^{38} -20.6515 q^{39} +2.17430 q^{40} -1.82336 q^{41} -0.175788 q^{42} +2.41367 q^{43} -1.54234 q^{44} -7.38130 q^{45} +5.64318 q^{46} +1.50928 q^{47} -6.41363 q^{48} -6.99164 q^{49} +0.596683 q^{50} +17.6317 q^{51} -10.5370 q^{52} -3.52075 q^{53} -8.42312 q^{54} -0.938184 q^{55} -0.198810 q^{56} +14.8991 q^{57} -0.397965 q^{58} -14.3795 q^{59} -5.29687 q^{60} -6.52207 q^{61} -4.48375 q^{62} +0.674920 q^{63} -0.677704 q^{64} -6.40952 q^{65} -1.80367 q^{66} -15.3694 q^{67} +8.99624 q^{68} -30.4723 q^{69} -0.0545586 q^{70} +6.49472 q^{71} -16.0491 q^{72} -2.73165 q^{73} +3.56340 q^{74} -3.22200 q^{75} +7.60200 q^{76} +0.0857842 q^{77} -12.3224 q^{78} -8.80094 q^{79} -1.99057 q^{80} +23.3397 q^{81} -1.08797 q^{82} -0.402706 q^{83} +0.484327 q^{84} +5.47227 q^{85} +1.44020 q^{86} +2.14895 q^{87} -2.03989 q^{88} +17.9570 q^{89} -4.40430 q^{90} +0.586064 q^{91} -15.5480 q^{92} +24.2116 q^{93} +0.900560 q^{94} +4.62417 q^{95} -17.8381 q^{96} +17.4995 q^{97} -4.17180 q^{98} +6.92502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * 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 $

$2$	0.596683	0.421919	0.210959	−	0.977495i	$-0.432341\pi$
$2$	0.596683	0.421919	0.210959	+	0.977495i	$0.432341\pi$
$3$	−3.22200	−1.86022	−0.930112	−	0.367276i	$-0.880290\pi$
$3$	−3.22200	−1.86022	−0.930112	+	0.367276i	$0.880290\pi$
$4$	−1.64397	−0.821984
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.92252	−0.784864
$7$	0.0914365	0.0345597	0.0172799	−	0.999851i	$-0.494499\pi$
$7$	0.0914365	0.0345597	0.0172799	+	0.999851i	$0.494499\pi$
$8$	−2.17430	−0.768730
$9$	7.38130	2.46043
$10$	−0.596683	−0.188688
$11$	0.938184	0.282873	0.141437	−	0.989947i	$-0.454828\pi$
$11$	0.938184	0.282873	0.141437	+	0.989947i	$0.454828\pi$
$12$	5.29687	1.52908
$13$	6.40952	1.77768	0.888840	−	0.458218i	$-0.151512\pi$
$13$	6.40952	1.77768	0.888840	+	0.458218i	$0.151512\pi$
$14$	0.0545586	0.0145814
$15$	3.22200	0.831918
$16$	1.99057	0.497643
$17$	−5.47227	−1.32722	−0.663610	−	0.748079i	$-0.730977\pi$
$17$	−5.47227	−1.32722	−0.663610	+	0.748079i	$0.730977\pi$
$18$	4.40430	1.03810
$19$	−4.62417	−1.06086	−0.530429	−	0.847729i	$-0.677969\pi$
$19$	−4.62417	−1.06086	−0.530429	+	0.847729i	$0.677969\pi$
$20$	1.64397	0.367603
$21$	−0.294609	−0.0642889
$22$	0.559799	0.119349
$23$	9.45757	1.97204	0.986020	−	0.166626i	$-0.0532871\pi$
$23$	9.45757	1.97204	0.986020	+	0.166626i	$0.0532871\pi$
$24$	7.00559	1.43001
$25$	1.00000	0.200000
$26$	3.82445	0.750037
$27$	−14.1166	−2.71673
$28$	−0.150319	−0.0284076
$29$	−0.666961	−0.123852	−0.0619258	−	0.998081i	$-0.519724\pi$
$29$	−0.666961	−0.123852	−0.0619258	+	0.998081i	$0.519724\pi$
$30$	1.92252	0.351002
$31$	−7.51445	−1.34964	−0.674818	−	0.737985i	$-0.735778\pi$
$31$	−7.51445	−1.34964	−0.674818	+	0.737985i	$0.735778\pi$
$32$	5.53633	0.978695
$33$	−3.02283	−0.526207
$34$	−3.26521	−0.559979
$35$	−0.0914365	−0.0154556
$36$	−12.1346	−2.02244
$37$	5.97202	0.981793	0.490897	−	0.871218i	$-0.336669\pi$
$37$	5.97202	0.981793	0.490897	+	0.871218i	$0.336669\pi$
$38$	−2.75917	−0.447596
$39$	−20.6515	−3.30688
$40$	2.17430	0.343786
$41$	−1.82336	−0.284761	−0.142380	−	0.989812i	$-0.545476\pi$
$41$	−1.82336	−0.284761	−0.142380	+	0.989812i	$0.545476\pi$
$42$	−0.175788	−0.0271247
$43$	2.41367	0.368081	0.184041	−	0.982919i	$-0.441082\pi$
$43$	2.41367	0.368081	0.184041	+	0.982919i	$0.441082\pi$
$44$	−1.54234	−0.232517
$45$	−7.38130	−1.10034
$46$	5.64318	0.832041
$47$	1.50928	0.220151	0.110075	−	0.993923i	$-0.464891\pi$
$47$	1.50928	0.220151	0.110075	+	0.993923i	$0.464891\pi$
$48$	−6.41363	−0.925727
$49$	−6.99164	−0.998806
$50$	0.596683	0.0843838
$51$	17.6317	2.46893
$52$	−10.5370	−1.46123
$53$	−3.52075	−0.483612	−0.241806	−	0.970325i	$-0.577740\pi$
$53$	−3.52075	−0.483612	−0.241806	+	0.970325i	$0.577740\pi$
$54$	−8.42312	−1.14624
$55$	−0.938184	−0.126505
$56$	−0.198810	−0.0265671
$57$	14.8991	1.97343
$58$	−0.397965	−0.0522553
$59$	−14.3795	−1.87206	−0.936028	−	0.351926i	$-0.885527\pi$
$59$	−14.3795	−1.87206	−0.936028	+	0.351926i	$0.885527\pi$
$60$	−5.29687	−0.683823
$61$	−6.52207	−0.835065	−0.417533	−	0.908662i	$-0.637105\pi$
$61$	−6.52207	−0.835065	−0.417533	+	0.908662i	$0.637105\pi$
$62$	−4.48375	−0.569437
$63$	0.674920	0.0850320
$64$	−0.677704	−0.0847130
$65$	−6.40952	−0.795003
$66$	−1.80367	−0.222017
$67$	−15.3694	−1.87767	−0.938835	−	0.344369i	$-0.888093\pi$
$67$	−15.3694	−1.87767	−0.938835	+	0.344369i	$0.888093\pi$
$68$	8.99624	1.09095
$69$	−30.4723	−3.66844
$70$	−0.0545586	−0.00652101
$71$	6.49472	0.770782	0.385391	−	0.922753i	$-0.374067\pi$
$71$	6.49472	0.770782	0.385391	+	0.922753i	$0.374067\pi$
$72$	−16.0491	−1.89141
$73$	−2.73165	−0.319716	−0.159858	−	0.987140i	$-0.551104\pi$
$73$	−2.73165	−0.319716	−0.159858	+	0.987140i	$0.551104\pi$
$74$	3.56340	0.414237
$75$	−3.22200	−0.372045
$76$	7.60200	0.872009
$77$	0.0857842	0.00977602
$78$	−12.3224	−1.39524
$79$	−8.80094	−0.990184	−0.495092	−	0.868841i	$-0.664866\pi$
$79$	−8.80094	−0.990184	−0.495092	+	0.868841i	$0.664866\pi$
$80$	−1.99057	−0.222553
$81$	23.3397	2.59330
$82$	−1.08797	−0.120146
$83$	−0.402706	−0.0442028	−0.0221014	−	0.999756i	$-0.507036\pi$
$83$	−0.402706	−0.0442028	−0.0221014	+	0.999756i	$0.507036\pi$
$84$	0.484327	0.0528444
$85$	5.47227	0.593551
$86$	1.44020	0.155300
$87$	2.14895	0.230392
$88$	−2.03989	−0.217453
$89$	17.9570	1.90344	0.951721	−	0.306964i	$-0.0993132\pi$
$89$	17.9570	1.90344	0.951721	+	0.306964i	$0.0993132\pi$
$90$	−4.40430	−0.464254
$91$	0.586064	0.0614362
$92$	−15.5480	−1.62099
$93$	24.2116	2.51062
$94$	0.900560	0.0928857
$95$	4.62417	0.474430
$96$	−17.8381	−1.82059
$97$	17.4995	1.77680	0.888401	−	0.459068i	$-0.151816\pi$
$97$	17.4995	1.77680	0.888401	+	0.459068i	$0.151816\pi$
$98$	−4.17180	−0.421415
$99$	6.92502	0.695990
$100$	−1.64397	−0.164397
$101$	16.0553	1.59757	0.798783	−	0.601619i	$-0.205477\pi$
$101$	16.0553	1.59757	0.798783	+	0.601619i	$0.205477\pi$
$102$	10.5205	1.04169
$103$	−9.85176	−0.970722	−0.485361	−	0.874314i	$-0.661312\pi$
$103$	−9.85176	−0.970722	−0.485361	+	0.874314i	$0.661312\pi$
$104$	−13.9362	−1.36656
$105$	0.294609	0.0287509
$106$	−2.10077	−0.204045
$107$	−5.96114	−0.576285	−0.288143	−	0.957588i	$-0.593038\pi$
$107$	−5.96114	−0.576285	−0.288143	+	0.957588i	$0.593038\pi$
$108$	23.2072	2.23311
$109$	−8.70283	−0.833580	−0.416790	−	0.909003i	$-0.636845\pi$
$109$	−8.70283	−0.833580	−0.416790	+	0.909003i	$0.636845\pi$
$110$	−0.559799	−0.0533747
$111$	−19.2418	−1.82636
$112$	0.182011	0.0171984
$113$	12.3991	1.16640	0.583202	−	0.812327i	$-0.301799\pi$
$113$	12.3991	1.16640	0.583202	+	0.812327i	$0.301799\pi$
$114$	8.89004	0.832629
$115$	−9.45757	−0.881923
$116$	1.09646	0.101804
$117$	47.3106	4.37386
$118$	−8.58003	−0.789856
$119$	−0.500365	−0.0458684
$120$	−7.00559	−0.639520
$121$	−10.1198	−0.919983
$122$	−3.89161	−0.352330
$123$	5.87486	0.529718
$124$	12.3535	1.10938
$125$	−1.00000	−0.0894427
$126$	0.402714	0.0358766
$127$	12.6594	1.12334	0.561671	−	0.827361i	$-0.310159\pi$
$127$	12.6594	1.12334	0.561671	+	0.827361i	$0.310159\pi$
$128$	−11.4770	−1.01444
$129$	−7.77685	−0.684714
$130$	−3.82445	−0.335427
$131$	7.79459	0.681017	0.340508	−	0.940242i	$-0.389401\pi$
$131$	7.79459	0.681017	0.340508	+	0.940242i	$0.389401\pi$
$132$	4.96944	0.432534
$133$	−0.422818	−0.0366630
$134$	−9.17066	−0.792224
$135$	14.1166	1.21496
$136$	11.8983	1.02027
$137$	−11.1891	−0.955948	−0.477974	−	0.878374i	$-0.658629\pi$
$137$	−11.1891	−0.955948	−0.477974	+	0.878374i	$0.658629\pi$
$138$	−18.1823	−1.54778
$139$	−13.2779	−1.12622	−0.563110	−	0.826382i	$-0.690395\pi$
$139$	−13.2779	−1.12622	−0.563110	+	0.826382i	$0.690395\pi$
$140$	0.150319	0.0127043
$141$	−4.86289	−0.409529
$142$	3.87529	0.325207
$143$	6.01330	0.502858
$144$	14.6930	1.22442
$145$	0.666961	0.0553881
$146$	−1.62993	−0.134894
$147$	22.5271	1.85800
$148$	−9.81781	−0.807019
$149$	−13.4293	−1.10017	−0.550084	−	0.835109i	$-0.685404\pi$
$149$	−13.4293	−1.10017	−0.550084	+	0.835109i	$0.685404\pi$
$150$	−1.92252	−0.156973
$151$	−13.2454	−1.07789	−0.538947	−	0.842340i	$-0.681178\pi$
$151$	−13.2454	−1.07789	−0.538947	+	0.842340i	$0.681178\pi$
$152$	10.0543	0.815513
$153$	−40.3925	−3.26554
$154$	0.0511860	0.00412469
$155$	7.51445	0.603575
$156$	33.9504	2.71821
$157$	−11.4227	−0.911634	−0.455817	−	0.890074i	$-0.650653\pi$
$157$	−11.4227	−0.911634	−0.455817	+	0.890074i	$0.650653\pi$
$158$	−5.25138	−0.417777
$159$	11.3439	0.899628
$160$	−5.53633	−0.437686
$161$	0.864767	0.0681532
$162$	13.9264	1.09416
$163$	4.17420	0.326949	0.163474	−	0.986548i	$-0.447730\pi$
$163$	4.17420	0.326949	0.163474	+	0.986548i	$0.447730\pi$
$164$	2.99754	0.234069
$165$	3.02283	0.235327
$166$	−0.240288	−0.0186500
$167$	−22.4429	−1.73668	−0.868340	−	0.495969i	$-0.834813\pi$
$167$	−22.4429	−1.73668	−0.868340	+	0.495969i	$0.834813\pi$
$168$	0.640566	0.0494208
$169$	28.0819	2.16015
$170$	3.26521	0.250430
$171$	−34.1324	−2.61017
$172$	−3.96800	−0.302557
$173$	−19.0621	−1.44926	−0.724632	−	0.689136i	$-0.757990\pi$
$173$	−19.0621	−1.44926	−0.724632	+	0.689136i	$0.757990\pi$
$174$	1.28224	0.0972066
$175$	0.0914365	0.00691195
$176$	1.86752	0.140770
$177$	46.3309	3.48244
$178$	10.7147	0.803098
$179$	6.78903	0.507436	0.253718	−	0.967278i	$-0.418346\pi$
$179$	6.78903	0.507436	0.253718	+	0.967278i	$0.418346\pi$
$180$	12.1346	0.904462
$181$	−0.650357	−0.0483406	−0.0241703	−	0.999708i	$-0.507694\pi$
$181$	−0.650357	−0.0483406	−0.0241703	+	0.999708i	$0.507694\pi$
$182$	0.349694	0.0259211
$183$	21.0141	1.55341
$184$	−20.5636	−1.51597
$185$	−5.97202	−0.439071
$186$	14.4466	1.05928
$187$	−5.13399	−0.375435
$188$	−2.48120	−0.180960
$189$	−1.29077	−0.0938896
$190$	2.75917	0.200171
$191$	−13.4770	−0.975161	−0.487580	−	0.873078i	$-0.662120\pi$
$191$	−13.4770	−0.975161	−0.487580	+	0.873078i	$0.662120\pi$
$192$	2.18356	0.157585
$193$	5.46458	0.393349	0.196675	−	0.980469i	$-0.436986\pi$
$193$	5.46458	0.393349	0.196675	+	0.980469i	$0.436986\pi$
$194$	10.4416	0.749667
$195$	20.6515	1.47888
$196$	11.4940	0.821003
$197$	−20.7161	−1.47596	−0.737981	−	0.674822i	$-0.764220\pi$
$197$	−20.7161	−1.47596	−0.737981	+	0.674822i	$0.764220\pi$
$198$	4.13204	0.293651
$199$	−25.7071	−1.82233	−0.911165	−	0.412041i	$-0.864816\pi$
$199$	−25.7071	−1.82233	−0.911165	+	0.412041i	$0.864816\pi$
$200$	−2.17430	−0.153746
$201$	49.5202	3.49289
$202$	9.57996	0.674043
$203$	−0.0609846	−0.00428028
$204$	−28.9859	−2.02942
$205$	1.82336	0.127349
$206$	−5.87838	−0.409566
$207$	69.8092	4.85207
$208$	12.7586	0.884649
$209$	−4.33832	−0.300088
$210$	0.175788	0.0121305
$211$	10.6358	0.732195	0.366098	−	0.930576i	$-0.380694\pi$
$211$	10.6358	0.732195	0.366098	+	0.930576i	$0.380694\pi$
$212$	5.78801	0.397522
$213$	−20.9260	−1.43383
$214$	−3.55691	−0.243146
$215$	−2.41367	−0.164611
$216$	30.6936	2.08843
$217$	−0.687095	−0.0466430
$218$	−5.19283	−0.351703
$219$	8.80139	0.594743
$220$	1.54234	0.103985
$221$	−35.0746	−2.35937
$222$	−11.4813	−0.770574
$223$	11.7045	0.783791	0.391896	−	0.920010i	$-0.371819\pi$
$223$	11.7045	0.783791	0.391896	+	0.920010i	$0.371819\pi$
$224$	0.506223	0.0338234
$225$	7.38130	0.492087
$226$	7.39831	0.492128
$227$	−4.74976	−0.315253	−0.157626	−	0.987499i	$-0.550384\pi$
$227$	−4.74976	−0.315253	−0.157626	+	0.987499i	$0.550384\pi$
$228$	−24.4937	−1.62213
$229$	3.91733	0.258864	0.129432	−	0.991588i	$-0.458685\pi$
$229$	3.91733	0.258864	0.129432	+	0.991588i	$0.458685\pi$
$230$	−5.64318	−0.372100
$231$	−0.276397	−0.0181856
$232$	1.45017	0.0952084
$233$	2.05639	0.134719	0.0673593	−	0.997729i	$-0.478543\pi$
$233$	2.05639	0.134719	0.0673593	+	0.997729i	$0.478543\pi$
$234$	28.2294	1.84542
$235$	−1.50928	−0.0984543
$236$	23.6395	1.53880
$237$	28.3567	1.84196
$238$	−0.298560	−0.0193527
$239$	−4.37294	−0.282862	−0.141431	−	0.989948i	$-0.545170\pi$
$239$	−4.37294	−0.282862	−0.141431	+	0.989948i	$0.545170\pi$
$240$	6.41363	0.413998
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−6.03832	−0.388158
$243$	−32.8509	−2.10739
$244$	10.7221	0.686410
$245$	6.99164	0.446679
$246$	3.50543	0.223498
$247$	−29.6387	−1.88587
$248$	16.3386	1.03750
$249$	1.29752	0.0822271
$250$	−0.596683	−0.0377376
$251$	−10.1344	−0.639677	−0.319839	−	0.947472i	$-0.603629\pi$
$251$	−10.1344	−0.639677	−0.319839	+	0.947472i	$0.603629\pi$
$252$	−1.10955	−0.0698949
$253$	8.87294	0.557837
$254$	7.55367	0.473959
$255$	−17.6317	−1.10414
$256$	−5.49275	−0.343297
$257$	−7.65793	−0.477689	−0.238844	−	0.971058i	$-0.576769\pi$
$257$	−7.65793	−0.477689	−0.238844	+	0.971058i	$0.576769\pi$
$258$	−4.64032	−0.288894
$259$	0.546060	0.0339305
$260$	10.5370	0.653480
$261$	−4.92304	−0.304729
$262$	4.65090	0.287334
$263$	−7.22289	−0.445382	−0.222691	−	0.974889i	$-0.571484\pi$
$263$	−7.22289	−0.445382	−0.222691	+	0.974889i	$0.571484\pi$
$264$	6.57253	0.404511
$265$	3.52075	0.216278
$266$	−0.252289	−0.0154688
$267$	−57.8576	−3.54083
$268$	25.2668	1.54341
$269$	−3.86388	−0.235585	−0.117793	−	0.993038i	$-0.537582\pi$
$269$	−3.86388	−0.235585	−0.117793	+	0.993038i	$0.537582\pi$
$270$	8.42312	0.512615
$271$	−30.9680	−1.88117	−0.940587	−	0.339554i	$-0.889724\pi$
$271$	−30.9680	−1.88117	−0.940587	+	0.339554i	$0.889724\pi$
$272$	−10.8929	−0.660482
$273$	−1.88830	−0.114285
$274$	−6.67634	−0.403333
$275$	0.938184	0.0565746
$276$	50.0956	3.01540
$277$	−3.23714	−0.194501	−0.0972503	−	0.995260i	$-0.531005\pi$
$277$	−3.23714	−0.194501	−0.0972503	+	0.995260i	$0.531005\pi$
$278$	−7.92272	−0.475173
$279$	−55.4664	−3.32069
$280$	0.198810	0.0118812
$281$	15.7837	0.941577	0.470788	−	0.882246i	$-0.343970\pi$
$281$	15.7837	0.941577	0.470788	+	0.882246i	$0.343970\pi$
$282$	−2.90161	−0.172788
$283$	17.7210	1.05340	0.526702	−	0.850050i	$-0.323429\pi$
$283$	17.7210	1.05340	0.526702	+	0.850050i	$0.323429\pi$
$284$	−10.6771	−0.633571
$285$	−14.8991	−0.882546
$286$	3.58804	0.212165
$287$	−0.166721	−0.00984125
$288$	40.8653	2.40801
$289$	12.9457	0.761514
$290$	0.397965	0.0233693
$291$	−56.3834	−3.30525
$292$	4.49075	0.262801
$293$	17.6430	1.03072	0.515358	−	0.856975i	$-0.327659\pi$
$293$	17.6430	1.03072	0.515358	+	0.856975i	$0.327659\pi$
$294$	13.4415	0.783926
$295$	14.3795	0.837209
$296$	−12.9849	−0.754734
$297$	−13.2439	−0.768491
$298$	−8.01302	−0.464182
$299$	60.6185	3.50566
$300$	5.29687	0.305815
$301$	0.220697	0.0127208
$302$	−7.90330	−0.454784
$303$	−51.7304	−2.97183
$304$	−9.20474	−0.527928
$305$	6.52207	0.373452
$306$	−24.1015	−1.37779
$307$	10.5635	0.602891	0.301445	−	0.953483i	$-0.402531\pi$
$307$	10.5635	0.602891	0.301445	+	0.953483i	$0.402531\pi$
$308$	−0.141027	−0.00803574
$309$	31.7424	1.80576
$310$	4.48375	0.254660
$311$	15.5162	0.879843	0.439922	−	0.898036i	$-0.355006\pi$
$311$	15.5162	0.879843	0.439922	+	0.898036i	$0.355006\pi$
$312$	44.9024	2.54210
$313$	−16.0089	−0.904874	−0.452437	−	0.891796i	$-0.649445\pi$
$313$	−16.0089	−0.904874	−0.452437	+	0.891796i	$0.649445\pi$
$314$	−6.81576	−0.384636
$315$	−0.674920	−0.0380274
$316$	14.4685	0.813915
$317$	−5.93621	−0.333411	−0.166705	−	0.986007i	$-0.553313\pi$
$317$	−5.93621	−0.333411	−0.166705	+	0.986007i	$0.553313\pi$
$318$	6.76870	0.379570
$319$	−0.625732	−0.0350343
$320$	0.677704	0.0378848
$321$	19.2068	1.07202
$322$	0.515992	0.0287551
$323$	25.3047	1.40799
$324$	−38.3697	−2.13165
$325$	6.40952	0.355536
$326$	2.49068	0.137946
$327$	28.0405	1.55064
$328$	3.96452	0.218904
$329$	0.138003	0.00760835
$330$	1.80367	0.0992889
$331$	−24.4916	−1.34618	−0.673091	−	0.739560i	$-0.735034\pi$
$331$	−24.4916	−1.34618	−0.673091	+	0.739560i	$0.735034\pi$
$332$	0.662037	0.0363340
$333$	44.0812	2.41564
$334$	−13.3913	−0.732738
$335$	15.3694	0.839719
$336$	−0.586439	−0.0319929
$337$	4.60431	0.250813	0.125406	−	0.992105i	$-0.459977\pi$
$337$	4.60431	0.250813	0.125406	+	0.992105i	$0.459977\pi$
$338$	16.7560	0.911406
$339$	−39.9498	−2.16977
$340$	−8.99624	−0.487890
$341$	−7.04993	−0.381775
$342$	−20.3662	−1.10128
$343$	−1.27935	−0.0690782
$344$	−5.24803	−0.282955
$345$	30.4723	1.64058
$346$	−11.3740	−0.611472
$347$	6.59915	0.354261	0.177131	−	0.984187i	$-0.443319\pi$
$347$	6.59915	0.354261	0.177131	+	0.984187i	$0.443319\pi$
$348$	−3.53281	−0.189378
$349$	−9.00022	−0.481770	−0.240885	−	0.970554i	$-0.577438\pi$
$349$	−9.00022	−0.481770	−0.240885	+	0.970554i	$0.577438\pi$
$350$	0.0545586	0.00291628
$351$	−90.4803	−4.82948
$352$	5.19410	0.276846
$353$	19.2510	1.02463	0.512313	−	0.858799i	$-0.328789\pi$
$353$	19.2510	1.02463	0.512313	+	0.858799i	$0.328789\pi$
$354$	27.6449	1.46931
$355$	−6.49472	−0.344704
$356$	−29.5208	−1.56460
$357$	1.61218	0.0853255
$358$	4.05091	0.214097
$359$	−6.46996	−0.341472	−0.170736	−	0.985317i	$-0.554614\pi$
$359$	−6.46996	−0.341472	−0.170736	+	0.985317i	$0.554614\pi$
$360$	16.0491	0.845864
$361$	2.38297	0.125420
$362$	−0.388057	−0.0203958
$363$	32.6061	1.71137
$364$	−0.963470	−0.0504996
$365$	2.73165	0.142981
$366$	12.5388	0.655412
$367$	7.33529	0.382899	0.191450	−	0.981502i	$-0.438681\pi$
$367$	7.33529	0.382899	0.191450	+	0.981502i	$0.438681\pi$
$368$	18.8260	0.981372
$369$	−13.4587	−0.700634
$370$	−3.56340	−0.185252
$371$	−0.321925	−0.0167135
$372$	−39.8031	−2.06369
$373$	−19.9506	−1.03300	−0.516500	−	0.856287i	$-0.672766\pi$
$373$	−19.9506	−1.03300	−0.516500	+	0.856287i	$0.672766\pi$
$374$	−3.06337	−0.158403
$375$	3.22200	0.166384
$376$	−3.28161	−0.169236
$377$	−4.27490	−0.220169
$378$	−0.770181	−0.0396138
$379$	−23.4451	−1.20430	−0.602148	−	0.798384i	$-0.705688\pi$
$379$	−23.4451	−1.20430	−0.602148	+	0.798384i	$0.705688\pi$
$380$	−7.60200	−0.389974
$381$	−40.7887	−2.08967
$382$	−8.04150	−0.411439
$383$	15.0980	0.771472	0.385736	−	0.922609i	$-0.373948\pi$
$383$	15.0980	0.771472	0.385736	+	0.922609i	$0.373948\pi$
$384$	36.9791	1.88708
$385$	−0.0857842	−0.00437197
$386$	3.26063	0.165962
$387$	17.8160	0.905639
$388$	−28.7686	−1.46050
$389$	−30.5029	−1.54656	−0.773279	−	0.634066i	$-0.781385\pi$
$389$	−30.5029	−1.54656	−0.773279	+	0.634066i	$0.781385\pi$
$390$	12.3224	0.623969
$391$	−51.7544	−2.61733
$392$	15.2019	0.767812
$393$	−25.1142	−1.26684
$394$	−12.3610	−0.622736
$395$	8.80094	0.442824
$396$	−11.3845	−0.572093
$397$	−13.3211	−0.668569	−0.334284	−	0.942472i	$-0.608495\pi$
$397$	−13.3211	−0.668569	−0.334284	+	0.942472i	$0.608495\pi$
$398$	−15.3390	−0.768876
$399$	1.36232	0.0682014
$400$	1.99057	0.0995286
$401$	−2.04724	−0.102234	−0.0511171	−	0.998693i	$-0.516278\pi$
$401$	−2.04724	−0.102234	−0.0511171	+	0.998693i	$0.516278\pi$
$402$	29.5479	1.47371
$403$	−48.1640	−2.39922
$404$	−26.3945	−1.31317
$405$	−23.3397	−1.15976
$406$	−0.0363885	−0.00180593
$407$	5.60285	0.277723
$408$	−38.3365	−1.89794
$409$	−13.4604	−0.665575	−0.332787	−	0.943002i	$-0.607989\pi$
$409$	−13.4604	−0.665575	−0.332787	+	0.943002i	$0.607989\pi$
$410$	1.08797	0.0537309
$411$	36.0513	1.77828
$412$	16.1960	0.797919
$413$	−1.31481	−0.0646978
$414$	41.6540	2.04718
$415$	0.402706	0.0197681
$416$	35.4852	1.73981
$417$	42.7815	2.09502
$418$	−2.58861	−0.126613
$419$	−11.6546	−0.569366	−0.284683	−	0.958622i	$-0.591888\pi$
$419$	−11.6546	−0.569366	−0.284683	+	0.958622i	$0.591888\pi$
$420$	−0.484327	−0.0236328
$421$	−6.83090	−0.332918	−0.166459	−	0.986048i	$-0.553233\pi$
$421$	−6.83090	−0.332918	−0.166459	+	0.986048i	$0.553233\pi$
$422$	6.34618	0.308927
$423$	11.1404	0.541666
$424$	7.65516	0.371767
$425$	−5.47227	−0.265444
$426$	−12.4862	−0.604959
$427$	−0.596355	−0.0288596
$428$	9.79993	0.473697
$429$	−19.3749	−0.935428
$430$	−1.44020	−0.0694525
$431$	19.6002	0.944109	0.472054	−	0.881569i	$-0.343513\pi$
$431$	19.6002	0.944109	0.472054	+	0.881569i	$0.343513\pi$
$432$	−28.1000	−1.35196
$433$	−8.10862	−0.389676	−0.194838	−	0.980835i	$-0.562418\pi$
$433$	−8.10862	−0.389676	−0.194838	+	0.980835i	$0.562418\pi$
$434$	−0.409978	−0.0196796
$435$	−2.14895	−0.103034
$436$	14.3072	0.685189
$437$	−43.7335	−2.09205
$438$	5.25164	0.250933
$439$	34.0684	1.62600	0.812998	−	0.582267i	$-0.197834\pi$
$439$	34.0684	1.62600	0.812998	+	0.582267i	$0.197834\pi$
$440$	2.03989	0.0972479
$441$	−51.6074	−2.45750
$442$	−20.9284	−0.995464
$443$	12.5494	0.596240	0.298120	−	0.954528i	$-0.403640\pi$
$443$	12.5494	0.596240	0.298120	+	0.954528i	$0.403640\pi$
$444$	31.6330	1.50124
$445$	−17.9570	−0.851245
$446$	6.98388	0.330696
$447$	43.2691	2.04656
$448$	−0.0619669	−0.00292766
$449$	23.2022	1.09498	0.547489	−	0.836813i	$-0.315584\pi$
$449$	23.2022	1.09498	0.547489	+	0.836813i	$0.315584\pi$
$450$	4.40430	0.207621
$451$	−1.71064	−0.0805511
$452$	−20.3837	−0.958766
$453$	42.6766	2.00512
$454$	−2.83410	−0.133011
$455$	−0.586064	−0.0274751
$456$	−32.3950	−1.51704
$457$	−12.7868	−0.598140	−0.299070	−	0.954231i	$-0.596676\pi$
$457$	−12.7868	−0.598140	−0.299070	+	0.954231i	$0.596676\pi$
$458$	2.33740	0.109220
$459$	77.2496	3.60570
$460$	15.5480	0.724927
$461$	−2.71560	−0.126478	−0.0632389	−	0.997998i	$-0.520143\pi$
$461$	−2.71560	−0.126478	−0.0632389	+	0.997998i	$0.520143\pi$
$462$	−0.164922	−0.00767284
$463$	−29.7362	−1.38196	−0.690979	−	0.722875i	$-0.742820\pi$
$463$	−29.7362	−1.38196	−0.690979	+	0.722875i	$0.742820\pi$
$464$	−1.32763	−0.0616339
$465$	−24.2116	−1.12279
$466$	1.22701	0.0568403
$467$	−6.90067	−0.319325	−0.159662	−	0.987172i	$-0.551041\pi$
$467$	−6.90067	−0.319325	−0.159662	+	0.987172i	$0.551041\pi$
$468$	−77.7771	−3.59525
$469$	−1.40532	−0.0648918
$470$	−0.900560	−0.0415397
$471$	36.8041	1.69584
$472$	31.2654	1.43911
$473$	2.26447	0.104120
$474$	16.9200	0.777159
$475$	−4.62417	−0.212172
$476$	0.822585	0.0377031
$477$	−25.9877	−1.18990
$478$	−2.60926	−0.119345
$479$	33.1760	1.51585	0.757924	−	0.652342i	$-0.226214\pi$
$479$	33.1760	1.51585	0.757924	+	0.652342i	$0.226214\pi$
$480$	17.8381	0.814193
$481$	38.2777	1.74531
$482$	−0.596683	−0.0271782
$483$	−2.78628	−0.126780
$484$	16.6367	0.756212
$485$	−17.4995	−0.794610
$486$	−19.6016	−0.889146
$487$	−3.24933	−0.147241	−0.0736207	−	0.997286i	$-0.523455\pi$
$487$	−3.24933	−0.147241	−0.0736207	+	0.997286i	$0.523455\pi$
$488$	14.1809	0.641939
$489$	−13.4493	−0.608198
$490$	4.17180	0.188463
$491$	−1.81775	−0.0820340	−0.0410170	−	0.999158i	$-0.513060\pi$
$491$	−1.81775	−0.0820340	−0.0410170	+	0.999158i	$0.513060\pi$
$492$	−9.65809	−0.435420
$493$	3.64979	0.164378
$494$	−17.6849	−0.795682
$495$	−6.92502	−0.311256
$496$	−14.9580	−0.671636
$497$	0.593855	0.0266380
$498$	0.774209	0.0346932
$499$	−12.2563	−0.548667	−0.274333	−	0.961635i	$-0.588457\pi$
$499$	−12.2563	−0.548667	−0.274333	+	0.961635i	$0.588457\pi$
$500$	1.64397	0.0735205
$501$	72.3109	3.23061
$502$	−6.04702	−0.269892
$503$	−5.24664	−0.233936	−0.116968	−	0.993136i	$-0.537318\pi$
$503$	−5.24664	−0.233936	−0.116968	+	0.993136i	$0.537318\pi$
$504$	−1.46748	−0.0653666
$505$	−16.0553	−0.714453
$506$	5.29434	0.235362
$507$	−90.4799	−4.01835
$508$	−20.8117	−0.923370
$509$	−38.3672	−1.70060	−0.850298	−	0.526301i	$-0.823579\pi$
$509$	−38.3672	−1.70060	−0.850298	+	0.526301i	$0.823579\pi$
$510$	−10.5205	−0.465857
$511$	−0.249773	−0.0110493
$512$	19.6766	0.869593
$513$	65.2774	2.88207
$514$	−4.56936	−0.201546
$515$	9.85176	0.434120
$516$	12.7849	0.562824
$517$	1.41598	0.0622746
$518$	0.325825	0.0143159
$519$	61.4181	2.69596
$520$	13.9362	0.611142
$521$	18.6227	0.815876	0.407938	−	0.913010i	$-0.366248\pi$
$521$	18.6227	0.815876	0.407938	+	0.913010i	$0.366248\pi$
$522$	−2.93750	−0.128571
$523$	−26.1292	−1.14255	−0.571274	−	0.820759i	$-0.693551\pi$
$523$	−26.1292	−1.14255	−0.571274	+	0.820759i	$0.693551\pi$
$524$	−12.8141	−0.559785
$525$	−0.294609	−0.0128578
$526$	−4.30978	−0.187915
$527$	41.1211	1.79126
$528$	−6.01716	−0.261863
$529$	66.4457	2.88894
$530$	2.10077	0.0912518
$531$	−106.140	−4.60607
$532$	0.695100	0.0301364
$533$	−11.6868	−0.506213
$534$	−34.5227	−1.49394
$535$	5.96114	0.257723
$536$	33.4176	1.44342
$537$	−21.8743	−0.943945
$538$	−2.30552	−0.0993978
$539$	−6.55944	−0.282535
$540$	−23.2072	−0.998679
$541$	27.4175	1.17877	0.589386	−	0.807852i	$-0.299370\pi$
$541$	27.4175	1.17877	0.589386	+	0.807852i	$0.299370\pi$
$542$	−18.4781	−0.793703
$543$	2.09545	0.0899244
$544$	−30.2963	−1.29894
$545$	8.70283	0.372788
$546$	−1.12672	−0.0482190
$547$	7.78442	0.332838	0.166419	−	0.986055i	$-0.446780\pi$
$547$	7.78442	0.332838	0.166419	+	0.986055i	$0.446780\pi$
$548$	18.3945	0.785775
$549$	−48.1413	−2.05462
$550$	0.559799	0.0238699
$551$	3.08414	0.131389
$552$	66.2559	2.82004
$553$	−0.804727	−0.0342205
$554$	−1.93155	−0.0820635
$555$	19.2418	0.816771
$556$	21.8285	0.925735
$557$	31.6184	1.33971	0.669857	−	0.742490i	$-0.266355\pi$
$557$	31.6184	1.33971	0.669857	+	0.742490i	$0.266355\pi$
$558$	−33.0959	−1.40106
$559$	15.4705	0.654330
$560$	−0.182011	−0.00769136
$561$	16.5417	0.698393
$562$	9.41788	0.397269
$563$	−13.8213	−0.582498	−0.291249	−	0.956647i	$-0.594071\pi$
$563$	−13.8213	−0.582498	−0.291249	+	0.956647i	$0.594071\pi$
$564$	7.99444	0.336627
$565$	−12.3991	−0.521632
$566$	10.5738	0.444451
$567$	2.13410	0.0896238
$568$	−14.1215	−0.592523
$569$	8.73989	0.366395	0.183198	−	0.983076i	$-0.441355\pi$
$569$	8.73989	0.366395	0.183198	+	0.983076i	$0.441355\pi$
$570$	−8.89004	−0.372363
$571$	−11.5163	−0.481944	−0.240972	−	0.970532i	$-0.577466\pi$
$571$	−11.5163	−0.481944	−0.240972	+	0.970532i	$0.577466\pi$
$572$	−9.88568	−0.413341
$573$	43.4229	1.81402
$574$	−0.0994799	−0.00415221
$575$	9.45757	0.394408
$576$	−5.00234	−0.208431
$577$	−6.75615	−0.281262	−0.140631	−	0.990062i	$-0.544913\pi$
$577$	−6.75615	−0.281262	−0.140631	+	0.990062i	$0.544913\pi$
$578$	7.72451	0.321297
$579$	−17.6069	−0.731718
$580$	−1.09646	−0.0455282
$581$	−0.0368221	−0.00152764
$582$	−33.6430	−1.39455
$583$	−3.30311	−0.136801
$584$	5.93942	0.245775
$585$	−47.3106	−1.95605
$586$	10.5273	0.434879
$587$	−1.71413	−0.0707498	−0.0353749	−	0.999374i	$-0.511263\pi$
$587$	−1.71413	−0.0707498	−0.0353749	+	0.999374i	$0.511263\pi$
$588$	−37.0338	−1.52725
$589$	34.7481	1.43177
$590$	8.58003	0.353234
$591$	66.7473	2.74562
$592$	11.8877	0.488582
$593$	27.1227	1.11380	0.556898	−	0.830581i	$-0.311992\pi$
$593$	27.1227	1.11380	0.556898	+	0.830581i	$0.311992\pi$
$594$	−7.90243	−0.324241
$595$	0.500365	0.0205130
$596$	22.0773	0.904321
$597$	82.8285	3.38994
$598$	36.1700	1.47910
$599$	29.0181	1.18565	0.592824	−	0.805332i	$-0.298013\pi$
$599$	29.0181	1.18565	0.592824	+	0.805332i	$0.298013\pi$
$600$	7.00559	0.286002
$601$	−6.46669	−0.263782	−0.131891	−	0.991264i	$-0.542105\pi$
$601$	−6.46669	−0.263782	−0.131891	+	0.991264i	$0.542105\pi$
$602$	0.131687	0.00536714
$603$	−113.446	−4.61988
$604$	21.7750	0.886012
$605$	10.1198	0.411429
$606$	−30.8666	−1.25387
$607$	16.5728	0.672669	0.336335	−	0.941743i	$-0.390813\pi$
$607$	16.5728	0.672669	0.336335	+	0.941743i	$0.390813\pi$
$608$	−25.6010	−1.03826
$609$	0.196493	0.00796228
$610$	3.89161	0.157567
$611$	9.67373	0.391357
$612$	66.4040	2.68422
$613$	21.8721	0.883407	0.441704	−	0.897161i	$-0.354374\pi$
$613$	21.8721	0.883407	0.441704	+	0.897161i	$0.354374\pi$
$614$	6.30306	0.254371
$615$	−5.87486	−0.236897
$616$	−0.186520	−0.00751512
$617$	10.5044	0.422891	0.211446	−	0.977390i	$-0.432183\pi$
$617$	10.5044	0.422891	0.211446	+	0.977390i	$0.432183\pi$
$618$	18.9402	0.761885
$619$	23.9195	0.961406	0.480703	−	0.876884i	$-0.340382\pi$
$619$	23.9195	0.961406	0.480703	+	0.876884i	$0.340382\pi$
$620$	−12.3535	−0.496129
$621$	−133.508	−5.35751
$622$	9.25826	0.371222
$623$	1.64193	0.0657825
$624$	−41.1082	−1.64565
$625$	1.00000	0.0400000
$626$	−9.55222	−0.381783
$627$	13.9781	0.558231
$628$	18.7786	0.749349
$629$	−32.6805	−1.30306
$630$	−0.402714	−0.0160445
$631$	−14.4550	−0.575444	−0.287722	−	0.957714i	$-0.592898\pi$
$631$	−14.4550	−0.575444	−0.287722	+	0.957714i	$0.592898\pi$
$632$	19.1359	0.761184
$633$	−34.2684	−1.36205
$634$	−3.54204	−0.140672
$635$	−12.6594	−0.502374
$636$	−18.6490	−0.739480
$637$	−44.8130	−1.77556
$638$	−0.373364	−0.0147816
$639$	47.9395	1.89646
$640$	11.4770	0.453670
$641$	10.0263	0.396017	0.198008	−	0.980200i	$-0.436553\pi$
$641$	10.0263	0.396017	0.198008	+	0.980200i	$0.436553\pi$
$642$	11.4604	0.452305
$643$	−22.8415	−0.900781	−0.450391	−	0.892832i	$-0.648715\pi$
$643$	−22.8415	−0.900781	−0.450391	+	0.892832i	$0.648715\pi$
$644$	−1.42165	−0.0560209
$645$	7.77685	0.306213
$646$	15.0989	0.594059
$647$	5.91891	0.232697	0.116348	−	0.993208i	$-0.462881\pi$
$647$	5.91891	0.232697	0.116348	+	0.993208i	$0.462881\pi$
$648$	−50.7474	−1.99355
$649$	−13.4906	−0.529554
$650$	3.82445	0.150007
$651$	2.21382	0.0867665
$652$	−6.86226	−0.268747
$653$	−7.83832	−0.306737	−0.153369	−	0.988169i	$-0.549012\pi$
$653$	−7.83832	−0.306737	−0.153369	+	0.988169i	$0.549012\pi$
$654$	16.7313	0.654246
$655$	−7.79459	−0.304560
$656$	−3.62952	−0.141709
$657$	−20.1631	−0.786639
$658$	0.0823441	0.00321011
$659$	8.38247	0.326535	0.163267	−	0.986582i	$-0.447797\pi$
$659$	8.38247	0.326535	0.163267	+	0.986582i	$0.447797\pi$
$660$	−4.96944	−0.193435
$661$	4.45841	0.173412	0.0867060	−	0.996234i	$-0.472366\pi$
$661$	4.45841	0.173412	0.0867060	+	0.996234i	$0.472366\pi$
$662$	−14.6138	−0.567980
$663$	113.010	4.38896
$664$	0.875603	0.0339800
$665$	0.422818	0.0163962
$666$	26.3026	1.01920
$667$	−6.30784	−0.244240
$668$	36.8954	1.42752
$669$	−37.7119	−1.45803
$670$	9.17066	0.354293
$671$	−6.11890	−0.236217
$672$	−1.63105	−0.0629192
$673$	−31.5701	−1.21694	−0.608470	−	0.793577i	$-0.708216\pi$
$673$	−31.5701	−1.21694	−0.608470	+	0.793577i	$0.708216\pi$
$674$	2.74732	0.105823
$675$	−14.1166	−0.543347
$676$	−46.1657	−1.77561
$677$	−15.6023	−0.599645	−0.299823	−	0.953995i	$-0.596928\pi$
$677$	−15.6023	−0.599645	−0.299823	+	0.953995i	$0.596928\pi$
$678$	−23.8374	−0.915469
$679$	1.60009	0.0614058
$680$	−11.8983	−0.456280
$681$	15.3037	0.586441
$682$	−4.20658	−0.161078
$683$	−24.0372	−0.919756	−0.459878	−	0.887982i	$-0.652107\pi$
$683$	−24.0372	−0.919756	−0.459878	+	0.887982i	$0.652107\pi$
$684$	56.1126	2.14552
$685$	11.1891	0.427513
$686$	−0.763365	−0.0291454
$687$	−12.6216	−0.481546
$688$	4.80458	0.183173
$689$	−22.5663	−0.859708
$690$	18.1823	0.692190
$691$	−21.8219	−0.830143	−0.415072	−	0.909789i	$-0.636243\pi$
$691$	−21.8219	−0.830143	−0.415072	+	0.909789i	$0.636243\pi$
$692$	31.3375	1.19127
$693$	0.633199	0.0240532
$694$	3.93761	0.149469
$695$	13.2779	0.503661
$696$	−4.67246	−0.177109
$697$	9.97790	0.377940
$698$	−5.37028	−0.203268
$699$	−6.62569	−0.250607
$700$	−0.150319	−0.00568151
$701$	−36.9054	−1.39390	−0.696949	−	0.717120i	$-0.745460\pi$
$701$	−36.9054	−1.39390	−0.696949	+	0.717120i	$0.745460\pi$
$702$	−53.9881	−2.03765
$703$	−27.6156	−1.04154
$704$	−0.635811	−0.0239630
$705$	4.86289	0.183147
$706$	11.4867	0.432309
$707$	1.46804	0.0552115
$708$	−76.1666	−2.86251
$709$	18.5895	0.698145	0.349072	−	0.937096i	$-0.386497\pi$
$709$	18.5895	0.698145	0.349072	+	0.937096i	$0.386497\pi$
$710$	−3.87529	−0.145437
$711$	−64.9624	−2.43628
$712$	−39.0439	−1.46323
$713$	−71.0685	−2.66154
$714$	0.961960	0.0360004
$715$	−6.01330	−0.224885
$716$	−11.1610	−0.417105
$717$	14.0896	0.526187
$718$	−3.86052	−0.144073
$719$	21.3723	0.797052	0.398526	−	0.917157i	$-0.369522\pi$
$719$	21.3723	0.797052	0.398526	+	0.917157i	$0.369522\pi$
$720$	−14.6930	−0.547576
$721$	−0.900810	−0.0335479
$722$	1.42188	0.0529169
$723$	3.22200	0.119828
$724$	1.06917	0.0397353
$725$	−0.666961	−0.0247703
$726$	19.4555	0.722061
$727$	4.55494	0.168933	0.0844667	−	0.996426i	$-0.473081\pi$
$727$	4.55494	0.168933	0.0844667	+	0.996426i	$0.473081\pi$
$728$	−1.27428	−0.0472278
$729$	35.8266	1.32691
$730$	1.62993	0.0603265
$731$	−13.2083	−0.488525
$732$	−34.5466	−1.27688
$733$	−6.73245	−0.248669	−0.124334	−	0.992240i	$-0.539680\pi$
$733$	−6.73245	−0.248669	−0.124334	+	0.992240i	$0.539680\pi$
$734$	4.37685	0.161552
$735$	−22.5271	−0.830924
$736$	52.3603	1.93003
$737$	−14.4193	−0.531142
$738$	−8.03061	−0.295611
$739$	−7.18344	−0.264247	−0.132124	−	0.991233i	$-0.542180\pi$
$739$	−7.18344	−0.264247	−0.132124	+	0.991233i	$0.542180\pi$
$740$	9.81781	0.360910
$741$	95.4960	3.50813
$742$	−0.192087	−0.00705175
$743$	30.4874	1.11847	0.559237	−	0.829008i	$-0.311094\pi$
$743$	30.4874	1.11847	0.559237	+	0.829008i	$0.311094\pi$
$744$	−52.6431	−1.92999
$745$	13.4293	0.492010
$746$	−11.9042	−0.435843
$747$	−2.97250	−0.108758
$748$	8.44013	0.308602
$749$	−0.545066	−0.0199163
$750$	1.92252	0.0702004
$751$	29.4839	1.07588	0.537942	−	0.842982i	$-0.319202\pi$
$751$	29.4839	1.07588	0.537942	+	0.842982i	$0.319202\pi$
$752$	3.00432	0.109556
$753$	32.6530	1.18994
$754$	−2.55076	−0.0928933
$755$	13.2454	0.482049
$756$	2.12198	0.0771758
$757$	−7.20199	−0.261761	−0.130880	−	0.991398i	$-0.541780\pi$
$757$	−7.20199	−0.261761	−0.130880	+	0.991398i	$0.541780\pi$
$758$	−13.9893	−0.508115
$759$	−28.5886	−1.03770
$760$	−10.0543	−0.364709
$761$	−3.55723	−0.128950	−0.0644748	−	0.997919i	$-0.520537\pi$
$761$	−3.55723	−0.128950	−0.0644748	+	0.997919i	$0.520537\pi$
$762$	−24.3379	−0.881671
$763$	−0.795756	−0.0288083
$764$	22.1558	0.801567
$765$	40.3925	1.46039
$766$	9.00873	0.325499
$767$	−92.1659	−3.32792
$768$	17.6977	0.638609
$769$	−9.11046	−0.328532	−0.164266	−	0.986416i	$-0.552525\pi$
$769$	−9.11046	−0.328532	−0.164266	+	0.986416i	$0.552525\pi$
$770$	−0.0511860	−0.00184462
$771$	24.6739	0.888608
$772$	−8.98361	−0.323327
$773$	14.7015	0.528777	0.264388	−	0.964416i	$-0.414830\pi$
$773$	14.7015	0.528777	0.264388	+	0.964416i	$0.414830\pi$
$774$	10.6305	0.382106
$775$	−7.51445	−0.269927
$776$	−38.0490	−1.36588
$777$	−1.75941	−0.0631184
$778$	−18.2006	−0.652522
$779$	8.43152	0.302090
$780$	−33.9504	−1.21562
$781$	6.09324	0.218033
$782$	−30.8810	−1.10430
$783$	9.41520	0.336472
$784$	−13.9174	−0.497048
$785$	11.4227	0.407695
$786$	−14.9852	−0.534505
$787$	41.7194	1.48713	0.743567	−	0.668661i	$-0.233132\pi$
$787$	41.7194	1.48713	0.743567	+	0.668661i	$0.233132\pi$
$788$	34.0566	1.21322
$789$	23.2722	0.828511
$790$	5.25138	0.186836
$791$	1.13373	0.0403106
$792$	−15.0570	−0.535028
$793$	−41.8033	−1.48448
$794$	−7.94850	−0.282082
$795$	−11.3439	−0.402326
$796$	42.2617	1.49793
$797$	39.9649	1.41563	0.707815	−	0.706398i	$-0.249681\pi$
$797$	39.9649	1.41563	0.707815	+	0.706398i	$0.249681\pi$
$798$	0.812874	0.0287754
$799$	−8.25917	−0.292188
$800$	5.53633	0.195739
$801$	132.546	4.68329
$802$	−1.22155	−0.0431346
$803$	−2.56279	−0.0904389
$804$	−81.4097	−2.87110
$805$	−0.864767	−0.0304790
$806$	−28.7387	−1.01228
$807$	12.4494	0.438241
$808$	−34.9091	−1.22810
$809$	48.1327	1.69226	0.846128	−	0.532980i	$-0.178928\pi$
$809$	48.1327	1.69226	0.846128	+	0.532980i	$0.178928\pi$
$810$	−13.9264	−0.489324
$811$	−38.1641	−1.34012	−0.670061	−	0.742306i	$-0.733732\pi$
$811$	−38.1641	−1.34012	−0.670061	+	0.742306i	$0.733732\pi$
$812$	0.100257	0.00351832
$813$	99.7790	3.49940
$814$	3.34313	0.117177
$815$	−4.17420	−0.146216
$816$	35.0971	1.22864
$817$	−11.1612	−0.390482
$818$	−8.03161	−0.280819
$819$	4.32591	0.151160
$820$	−2.99754	−0.104679
$821$	25.8745	0.903025	0.451512	−	0.892265i	$-0.350885\pi$
$821$	25.8745	0.903025	0.451512	+	0.892265i	$0.350885\pi$
$822$	21.5112	0.750289
$823$	−0.237610	−0.00828258	−0.00414129	−	0.999991i	$-0.501318\pi$
$823$	−0.237610	−0.00828258	−0.00414129	+	0.999991i	$0.501318\pi$
$824$	21.4206	0.746223
$825$	−3.02283	−0.105241
$826$	−0.784528	−0.0272972
$827$	−22.1323	−0.769615	−0.384807	−	0.922997i	$-0.625732\pi$
$827$	−22.1323	−0.769615	−0.384807	+	0.922997i	$0.625732\pi$
$828$	−114.764	−3.98833
$829$	−17.4722	−0.606834	−0.303417	−	0.952858i	$-0.598128\pi$
$829$	−17.4722	−0.606834	−0.303417	+	0.952858i	$0.598128\pi$
$830$	0.240288	0.00834053
$831$	10.4301	0.361815
$832$	−4.34375	−0.150593
$833$	38.2601	1.32564
$834$	25.5270	0.883929
$835$	22.4429	0.776667
$836$	7.13207	0.246668
$837$	106.078	3.66660
$838$	−6.95412	−0.240226
$839$	2.59302	0.0895208	0.0447604	−	0.998998i	$-0.485748\pi$
$839$	2.59302	0.0895208	0.0447604	+	0.998998i	$0.485748\pi$
$840$	−0.640566	−0.0221016
$841$	−28.5552	−0.984661
$842$	−4.07589	−0.140464
$843$	−50.8551	−1.75154
$844$	−17.4848	−0.601853
$845$	−28.0819	−0.966046
$846$	6.64731	0.228539
$847$	−0.925320	−0.0317944
$848$	−7.00831	−0.240666
$849$	−57.0971	−1.95957
$850$	−3.26521	−0.111996
$851$	56.4808	1.93614
$852$	34.4017	1.17858
$853$	−14.2813	−0.488984	−0.244492	−	0.969651i	$-0.578621\pi$
$853$	−14.2813	−0.488984	−0.244492	+	0.969651i	$0.578621\pi$
$854$	−0.355835	−0.0121764
$855$	34.1324	1.16730
$856$	12.9613	0.443008
$857$	5.29985	0.181039	0.0905196	−	0.995895i	$-0.471147\pi$
$857$	5.29985	0.181039	0.0905196	+	0.995895i	$0.471147\pi$
$858$	−11.5607	−0.394675
$859$	−46.6430	−1.59144	−0.795719	−	0.605666i	$-0.792907\pi$
$859$	−46.6430	−1.59144	−0.795719	+	0.605666i	$0.792907\pi$
$860$	3.96800	0.135308
$861$	0.537177	0.0183069
$862$	11.6951	0.398337
$863$	7.04585	0.239843	0.119922	−	0.992783i	$-0.461736\pi$
$863$	7.04585	0.239843	0.119922	+	0.992783i	$0.461736\pi$
$864$	−78.1540	−2.65885
$865$	19.0621	0.648130
$866$	−4.83828	−0.164411
$867$	−41.7112	−1.41659
$868$	1.12956	0.0383399
$869$	−8.25690	−0.280096
$870$	−1.28224	−0.0434721
$871$	−98.5103	−3.33789
$872$	18.9225	0.640797
$873$	129.169	4.37171
$874$	−26.0950	−0.882678
$875$	−0.0914365	−0.00309112
$876$	−14.4692	−0.488869
$877$	−9.94520	−0.335825	−0.167913	−	0.985802i	$-0.553703\pi$
$877$	−9.94520	−0.335825	−0.167913	+	0.985802i	$0.553703\pi$
$878$	20.3280	0.686038
$879$	−56.8459	−1.91736
$880$	−1.86752	−0.0629541
$881$	2.95289	0.0994854	0.0497427	−	0.998762i	$-0.484160\pi$
$881$	2.95289	0.0994854	0.0497427	+	0.998762i	$0.484160\pi$
$882$	−30.7933	−1.03686
$883$	47.0985	1.58499	0.792495	−	0.609878i	$-0.208781\pi$
$883$	47.0985	1.58499	0.792495	+	0.609878i	$0.208781\pi$
$884$	57.6615	1.93937
$885$	−46.3309	−1.55740
$886$	7.48803	0.251565
$887$	30.3790	1.02003	0.510013	−	0.860167i	$-0.329640\pi$
$887$	30.3790	1.02003	0.510013	+	0.860167i	$0.329640\pi$
$888$	41.8375	1.40397
$889$	1.15753	0.0388224
$890$	−10.7147	−0.359156
$891$	21.8969	0.733575
$892$	−19.2418	−0.644264
$893$	−6.97915	−0.233548
$894$	25.8180	0.863482
$895$	−6.78903	−0.226932
$896$	−1.04942	−0.0350587
$897$	−195.313	−6.52131
$898$	13.8444	0.461992
$899$	5.01185	0.167154
$900$	−12.1346	−0.404488
$901$	19.2665	0.641860
$902$	−1.02071	−0.0339860
$903$	−0.711088	−0.0236635
$904$	−26.9592	−0.896650
$905$	0.650357	0.0216186
$906$	25.4644	0.845999
$907$	3.94698	0.131057	0.0655287	−	0.997851i	$-0.479127\pi$
$907$	3.94698	0.131057	0.0655287	+	0.997851i	$0.479127\pi$
$908$	7.80846	0.259133
$909$	118.509	3.93071
$910$	−0.349694	−0.0115923
$911$	−32.1864	−1.06638	−0.533192	−	0.845994i	$-0.679008\pi$
$911$	−32.1864	−1.06638	−0.533192	+	0.845994i	$0.679008\pi$
$912$	29.6577	0.982065
$913$	−0.377813	−0.0125038
$914$	−7.62965	−0.252366
$915$	−21.0141	−0.694705
$916$	−6.43996	−0.212782
$917$	0.712710	0.0235358
$918$	46.0936	1.52132
$919$	−22.6485	−0.747106	−0.373553	−	0.927609i	$-0.621861\pi$
$919$	−22.6485	−0.747106	−0.373553	+	0.927609i	$0.621861\pi$
$920$	20.5636	0.677961
$921$	−34.0356	−1.12151
$922$	−1.62035	−0.0533634
$923$	41.6280	1.37020
$924$	0.454388	0.0149483
$925$	5.97202	0.196359
$926$	−17.7431	−0.583074
$927$	−72.7188	−2.38840
$928$	−3.69252	−0.121213
$929$	9.27409	0.304273	0.152137	−	0.988359i	$-0.451385\pi$
$929$	9.27409	0.304273	0.152137	+	0.988359i	$0.451385\pi$
$930$	−14.4466	−0.473724
$931$	32.3305	1.05959
$932$	−3.38064	−0.110737
$933$	−49.9932	−1.63671
$934$	−4.11751	−0.134729
$935$	5.13399	0.167900
$936$	−102.867	−3.36232
$937$	−37.3432	−1.21995	−0.609975	−	0.792420i	$-0.708821\pi$
$937$	−37.3432	−1.21995	−0.609975	+	0.792420i	$0.708821\pi$
$938$	−0.838533	−0.0273791
$939$	51.5806	1.68327
$940$	2.48120	0.0809279
$941$	37.4044	1.21935	0.609674	−	0.792652i	$-0.291300\pi$
$941$	37.4044	1.21935	0.609674	+	0.792652i	$0.291300\pi$
$942$	21.9604	0.715508
$943$	−17.2445	−0.561559
$944$	−28.6235	−0.931615
$945$	1.29077	0.0419887
$946$	1.35117	0.0439303
$947$	−38.2457	−1.24282	−0.621409	−	0.783486i	$-0.713440\pi$
$947$	−38.2457	−1.24282	−0.621409	+	0.783486i	$0.713440\pi$
$948$	−46.6175	−1.51407
$949$	−17.5086	−0.568352
$950$	−2.75917	−0.0895192
$951$	19.1265	0.620218
$952$	1.08794	0.0352604
$953$	−16.0014	−0.518336	−0.259168	−	0.965832i	$-0.583448\pi$
$953$	−16.0014	−0.518336	−0.259168	+	0.965832i	$0.583448\pi$
$954$	−15.5064	−0.502040
$955$	13.4770	0.436105
$956$	7.18898	0.232508
$957$	2.01611	0.0651716
$958$	19.7956	0.639565
$959$	−1.02309	−0.0330373
$960$	−2.18356	−0.0704742
$961$	25.4670	0.821515
$962$	22.8397	0.736381
$963$	−44.0010	−1.41791
$964$	1.64397	0.0529487
$965$	−5.46458	−0.175911
$966$	−1.66253	−0.0534910
$967$	57.3667	1.84479	0.922394	−	0.386251i	$-0.126230\pi$
$967$	57.3667	1.84479	0.922394	+	0.386251i	$0.126230\pi$
$968$	22.0035	0.707218
$969$	−81.5319	−2.61918
$970$	−10.4416	−0.335261
$971$	−23.3616	−0.749711	−0.374855	−	0.927083i	$-0.622308\pi$
$971$	−23.3616	−0.749711	−0.374855	+	0.927083i	$0.622308\pi$
$972$	54.0059	1.73224
$973$	−1.21409	−0.0389218
$974$	−1.93882	−0.0621239
$975$	−20.6515	−0.661377
$976$	−12.9826	−0.415564
$977$	21.2763	0.680690	0.340345	−	0.940301i	$-0.389456\pi$
$977$	21.2763	0.680690	0.340345	+	0.940301i	$0.389456\pi$
$978$	−8.02497	−0.256610
$979$	16.8470	0.538432
$980$	−11.4940	−0.367164
$981$	−64.2382	−2.05097
$982$	−1.08462	−0.0346117
$983$	20.2377	0.645481	0.322741	−	0.946487i	$-0.395396\pi$
$983$	20.2377	0.645481	0.322741	+	0.946487i	$0.395396\pi$
$984$	−12.7737	−0.407210
$985$	20.7161	0.660070
$986$	2.17777	0.0693544
$987$	−0.444646	−0.0141532
$988$	48.7251	1.55015
$989$	22.8275	0.725871
$990$	−4.13204	−0.131325
$991$	−0.318692	−0.0101236	−0.00506179	−	0.999987i	$-0.501611\pi$
$991$	−0.318692	−0.0101236	−0.00506179	+	0.999987i	$0.501611\pi$
$992$	−41.6025	−1.32088
$993$	78.9121	2.50420
$994$	0.354343	0.0112391
$995$	25.7071	0.814971
$996$	−2.13308	−0.0675894
$997$	44.7214	1.41634	0.708170	−	0.706042i	$-0.249521\pi$
$997$	44.7214	1.41634	0.708170	+	0.706042i	$0.249521\pi$
$998$	−7.31312	−0.231493
$999$	−84.3043	−2.66727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.c.1.9	✓	15
5.4	even	2		6025.2.a.i.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.9	✓	15	1.1	even	1	trivial
6025.2.a.i.1.7		15	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+0.596683 q^{2} -3.22200 q^{3} -1.64397 q^{4} -1.00000 q^{5} -1.92252 q^{6} +0.0914365 q^{7} -2.17430 q^{8} +7.38130 q^{9} +O(q^{10})\)	\(q+0.596683 q^{2} -3.22200 q^{3} -1.64397 q^{4} -1.00000 q^{5} -1.92252 q^{6} +0.0914365 q^{7} -2.17430 q^{8} +7.38130 q^{9} -0.596683 q^{10} +0.938184 q^{11} +5.29687 q^{12} +6.40952 q^{13} +0.0545586 q^{14} +3.22200 q^{15} +1.99057 q^{16} -5.47227 q^{17} +4.40430 q^{18} -4.62417 q^{19} +1.64397 q^{20} -0.294609 q^{21} +0.559799 q^{22} +9.45757 q^{23} +7.00559 q^{24} +1.00000 q^{25} +3.82445 q^{26} -14.1166 q^{27} -0.150319 q^{28} -0.666961 q^{29} +1.92252 q^{30} -7.51445 q^{31} +5.53633 q^{32} -3.02283 q^{33} -3.26521 q^{34} -0.0914365 q^{35} -12.1346 q^{36} +5.97202 q^{37} -2.75917 q^{38} -20.6515 q^{39} +2.17430 q^{40} -1.82336 q^{41} -0.175788 q^{42} +2.41367 q^{43} -1.54234 q^{44} -7.38130 q^{45} +5.64318 q^{46} +1.50928 q^{47} -6.41363 q^{48} -6.99164 q^{49} +0.596683 q^{50} +17.6317 q^{51} -10.5370 q^{52} -3.52075 q^{53} -8.42312 q^{54} -0.938184 q^{55} -0.198810 q^{56} +14.8991 q^{57} -0.397965 q^{58} -14.3795 q^{59} -5.29687 q^{60} -6.52207 q^{61} -4.48375 q^{62} +0.674920 q^{63} -0.677704 q^{64} -6.40952 q^{65} -1.80367 q^{66} -15.3694 q^{67} +8.99624 q^{68} -30.4723 q^{69} -0.0545586 q^{70} +6.49472 q^{71} -16.0491 q^{72} -2.73165 q^{73} +3.56340 q^{74} -3.22200 q^{75} +7.60200 q^{76} +0.0857842 q^{77} -12.3224 q^{78} -8.80094 q^{79} -1.99057 q^{80} +23.3397 q^{81} -1.08797 q^{82} -0.402706 q^{83} +0.484327 q^{84} +5.47227 q^{85} +1.44020 q^{86} +2.14895 q^{87} -2.03989 q^{88} +17.9570 q^{89} -4.40430 q^{90} +0.586064 q^{91} -15.5480 q^{92} +24.2116 q^{93} +0.900560 q^{94} +4.62417 q^{95} -17.8381 q^{96} +17.4995 q^{97} -4.17180 q^{98} +6.92502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9	\( 15 q + 2 q^{2} - 7 q^{3} + 6 q^{4} - 15 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 2 q^{10} - 10 q^{11} - 6 q^{12} - 8 q^{13} - 5 q^{14} + 7 q^{15} - 16 q^{16} - q^{17} - 3 q^{18} - 30 q^{19} - 6 q^{20} - 11 q^{21} - 5 q^{22} + 19 q^{23} - 14 q^{24} + 15 q^{25} - 18 q^{26} - 22 q^{27} - 20 q^{28} - 12 q^{29} + 5 q^{30} - 22 q^{31} - 2 q^{32} + 4 q^{33} - 29 q^{34} + 3 q^{35} - 7 q^{36} - 12 q^{37} - 18 q^{38} - 17 q^{39} - 3 q^{40} - 13 q^{41} - q^{42} - 25 q^{43} - 20 q^{44} - 6 q^{45} - 7 q^{46} + 16 q^{47} - 22 q^{48} - 24 q^{49} + 2 q^{50} - 27 q^{51} - 15 q^{52} - 4 q^{53} - 43 q^{54} + 10 q^{55} - 3 q^{56} + 22 q^{57} - 20 q^{58} - 50 q^{59} + 6 q^{60} - 41 q^{61} + 12 q^{62} + 6 q^{63} - 53 q^{64} + 8 q^{65} + 5 q^{66} - 43 q^{67} + 5 q^{68} - 50 q^{69} + 5 q^{70} - 14 q^{71} + 32 q^{72} - 10 q^{73} - 26 q^{74} - 7 q^{75} - 13 q^{76} - 7 q^{77} + 3 q^{78} - 44 q^{79} + 16 q^{80} + 7 q^{81} - 19 q^{82} + 7 q^{83} - 42 q^{84} + q^{85} + 7 q^{86} + 10 q^{87} - 28 q^{88} + 4 q^{89} + 3 q^{90} - 50 q^{91} + 25 q^{92} + 22 q^{93} - 14 q^{94} + 30 q^{95} + 14 q^{96} + 9 q^{97} + 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 - 7 * q^3 + 6 * q^4 - 15 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 6 * q^9 - 2 * q^10 - 10 * q^11 - 6 * q^12 - 8 * q^13 - 5 * q^14 + 7 * q^15 - 16 * q^16 - q^17 - 3 * q^18 - 30 * q^19 - 6 * q^20 - 11 * q^21 - 5 * q^22 + 19 * q^23 - 14 * q^24 + 15 * q^25 - 18 * q^26 - 22 * q^27 - 20 * q^28 - 12 * q^29 + 5 * q^30 - 22 * q^31 - 2 * q^32 + 4 * q^33 - 29 * q^34 + 3 * q^35 - 7 * q^36 - 12 * q^37 - 18 * q^38 - 17 * q^39 - 3 * q^40 - 13 * q^41 - q^42 - 25 * q^43 - 20 * q^44 - 6 * q^45 - 7 * q^46 + 16 * q^47 - 22 * q^48 - 24 * q^49 + 2 * q^50 - 27 * q^51 - 15 * q^52 - 4 * q^53 - 43 * q^54 + 10 * q^55 - 3 * q^56 + 22 * q^57 - 20 * q^58 - 50 * q^59 + 6 * q^60 - 41 * q^61 + 12 * q^62 + 6 * q^63 - 53 * q^64 + 8 * q^65 + 5 * q^66 - 43 * q^67 + 5 * q^68 - 50 * q^69 + 5 * q^70 - 14 * q^71 + 32 * q^72 - 10 * q^73 - 26 * q^74 - 7 * q^75 - 13 * q^76 - 7 * q^77 + 3 * q^78 - 44 * q^79 + 16 * q^80 + 7 * q^81 - 19 * q^82 + 7 * q^83 - 42 * q^84 + q^85 + 7 * q^86 + 10 * q^87 - 28 * q^88 + 4 * q^89 + 3 * q^90 - 50 * q^91 + 25 * q^92 + 22 * q^93 - 14 * q^94 + 30 * q^95 + 14 * q^96 + 9 * q^97 + 2 * q^98 - 46 * q^99

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