LMFDB - Embedded newform 6045.2.a.bi.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 21 x^{16} + 97 x^{15} + 156 x^{14} - 935 x^{13} - 411 x^{12} + 4582 x^{11} + \cdots - 112 $ x^18 - 4x^17 - 21x^16 + 97x^15 + 156x^14 - 935x^13 - 411x^12 + 4582x^11 - 446x^10 - 12159x^9 + 4398x^8 + 17347x^7 - 7839x^6 - 12832x^5 + 4744x^4 + 5064x^3 - 746x^2 - 892*x - 112
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.173863$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.173863 q^{2} +1.00000 q^{3} -1.96977 q^{4} +1.00000 q^{5} -0.173863 q^{6} -4.18769 q^{7} +0.690195 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.173863 q^{2} +1.00000 q^{3} -1.96977 q^{4} +1.00000 q^{5} -0.173863 q^{6} -4.18769 q^{7} +0.690195 q^{8} +1.00000 q^{9} -0.173863 q^{10} +2.34893 q^{11} -1.96977 q^{12} -1.00000 q^{13} +0.728082 q^{14} +1.00000 q^{15} +3.81954 q^{16} +2.05254 q^{17} -0.173863 q^{18} -6.58024 q^{19} -1.96977 q^{20} -4.18769 q^{21} -0.408392 q^{22} +0.591630 q^{23} +0.690195 q^{24} +1.00000 q^{25} +0.173863 q^{26} +1.00000 q^{27} +8.24879 q^{28} -0.846471 q^{29} -0.173863 q^{30} +1.00000 q^{31} -2.04446 q^{32} +2.34893 q^{33} -0.356860 q^{34} -4.18769 q^{35} -1.96977 q^{36} +3.05606 q^{37} +1.14406 q^{38} -1.00000 q^{39} +0.690195 q^{40} -1.67092 q^{41} +0.728082 q^{42} +0.550304 q^{43} -4.62686 q^{44} +1.00000 q^{45} -0.102862 q^{46} -8.93209 q^{47} +3.81954 q^{48} +10.5367 q^{49} -0.173863 q^{50} +2.05254 q^{51} +1.96977 q^{52} -4.11691 q^{53} -0.173863 q^{54} +2.34893 q^{55} -2.89032 q^{56} -6.58024 q^{57} +0.147170 q^{58} +6.30854 q^{59} -1.96977 q^{60} -5.97516 q^{61} -0.173863 q^{62} -4.18769 q^{63} -7.28363 q^{64} -1.00000 q^{65} -0.408392 q^{66} +2.68423 q^{67} -4.04303 q^{68} +0.591630 q^{69} +0.728082 q^{70} +13.9901 q^{71} +0.690195 q^{72} +5.16145 q^{73} -0.531334 q^{74} +1.00000 q^{75} +12.9616 q^{76} -9.83660 q^{77} +0.173863 q^{78} -2.08787 q^{79} +3.81954 q^{80} +1.00000 q^{81} +0.290510 q^{82} -0.818085 q^{83} +8.24879 q^{84} +2.05254 q^{85} -0.0956773 q^{86} -0.846471 q^{87} +1.62122 q^{88} -13.7274 q^{89} -0.173863 q^{90} +4.18769 q^{91} -1.16538 q^{92} +1.00000 q^{93} +1.55296 q^{94} -6.58024 q^{95} -2.04446 q^{96} +10.8287 q^{97} -1.83194 q^{98} +2.34893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * 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 $

$2$	−0.173863	−0.122939	−0.0614697	−	0.998109i	$-0.519579\pi$
$2$	−0.173863	−0.122939	−0.0614697	+	0.998109i	$0.519579\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96977	−0.984886
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.173863	−0.0709791
$7$	−4.18769	−1.58280	−0.791398	−	0.611301i	$-0.790647\pi$
$7$	−4.18769	−1.58280	−0.791398	+	0.611301i	$0.790647\pi$
$8$	0.690195	0.244021
$9$	1.00000	0.333333
$10$	−0.173863	−0.0549802
$11$	2.34893	0.708230	0.354115	−	0.935202i	$-0.384782\pi$
$11$	2.34893	0.708230	0.354115	+	0.935202i	$0.384782\pi$
$12$	−1.96977	−0.568624
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.728082	0.194588
$15$	1.00000	0.258199
$16$	3.81954	0.954886
$17$	2.05254	0.497814	0.248907	−	0.968527i	$-0.419929\pi$
$17$	2.05254	0.497814	0.248907	+	0.968527i	$0.419929\pi$
$18$	−0.173863	−0.0409798
$19$	−6.58024	−1.50961	−0.754806	−	0.655949i	$-0.772269\pi$
$19$	−6.58024	−1.50961	−0.754806	+	0.655949i	$0.772269\pi$
$20$	−1.96977	−0.440454
$21$	−4.18769	−0.913828
$22$	−0.408392	−0.0870694
$23$	0.591630	0.123363	0.0616817	−	0.998096i	$-0.480354\pi$
$23$	0.591630	0.123363	0.0616817	+	0.998096i	$0.480354\pi$
$24$	0.690195	0.140885
$25$	1.00000	0.200000
$26$	0.173863	0.0340972
$27$	1.00000	0.192450
$28$	8.24879	1.55887
$29$	−0.846471	−0.157186	−0.0785929	−	0.996907i	$-0.525043\pi$
$29$	−0.846471	−0.157186	−0.0785929	+	0.996907i	$0.525043\pi$
$30$	−0.173863	−0.0317428
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−2.04446	−0.361414
$33$	2.34893	0.408897
$34$	−0.356860	−0.0612009
$35$	−4.18769	−0.707848
$36$	−1.96977	−0.328295
$37$	3.05606	0.502413	0.251206	−	0.967934i	$-0.419173\pi$
$37$	3.05606	0.502413	0.251206	+	0.967934i	$0.419173\pi$
$38$	1.14406	0.185591
$39$	−1.00000	−0.160128
$40$	0.690195	0.109129
$41$	−1.67092	−0.260954	−0.130477	−	0.991451i	$-0.541651\pi$
$41$	−1.67092	−0.260954	−0.130477	+	0.991451i	$0.541651\pi$
$42$	0.728082	0.112345
$43$	0.550304	0.0839206	0.0419603	−	0.999119i	$-0.486640\pi$
$43$	0.550304	0.0839206	0.0419603	+	0.999119i	$0.486640\pi$
$44$	−4.62686	−0.697526
$45$	1.00000	0.149071
$46$	−0.102862	−0.0151662
$47$	−8.93209	−1.30288	−0.651440	−	0.758700i	$-0.725835\pi$
$47$	−8.93209	−1.30288	−0.651440	+	0.758700i	$0.725835\pi$
$48$	3.81954	0.551304
$49$	10.5367	1.50525
$50$	−0.173863	−0.0245879
$51$	2.05254	0.287413
$52$	1.96977	0.273158
$53$	−4.11691	−0.565501	−0.282751	−	0.959193i	$-0.591247\pi$
$53$	−4.11691	−0.565501	−0.282751	+	0.959193i	$0.591247\pi$
$54$	−0.173863	−0.0236597
$55$	2.34893	0.316730
$56$	−2.89032	−0.386235
$57$	−6.58024	−0.871574
$58$	0.147170	0.0193243
$59$	6.30854	0.821302	0.410651	−	0.911793i	$-0.365301\pi$
$59$	6.30854	0.821302	0.410651	+	0.911793i	$0.365301\pi$
$60$	−1.96977	−0.254296
$61$	−5.97516	−0.765041	−0.382520	−	0.923947i	$-0.624944\pi$
$61$	−5.97516	−0.765041	−0.382520	+	0.923947i	$0.624944\pi$
$62$	−0.173863	−0.0220806
$63$	−4.18769	−0.527599
$64$	−7.28363	−0.910454
$65$	−1.00000	−0.124035
$66$	−0.408392	−0.0502695
$67$	2.68423	0.327930	0.163965	−	0.986466i	$-0.447572\pi$
$67$	2.68423	0.327930	0.163965	+	0.986466i	$0.447572\pi$
$68$	−4.04303	−0.490290
$69$	0.591630	0.0712239
$70$	0.728082	0.0870224
$71$	13.9901	1.66032	0.830158	−	0.557528i	$-0.188250\pi$
$71$	13.9901	1.66032	0.830158	+	0.557528i	$0.188250\pi$
$72$	0.690195	0.0813402
$73$	5.16145	0.604102	0.302051	−	0.953292i	$-0.402329\pi$
$73$	5.16145	0.604102	0.302051	+	0.953292i	$0.402329\pi$
$74$	−0.531334	−0.0617663
$75$	1.00000	0.115470
$76$	12.9616	1.48679
$77$	−9.83660	−1.12098
$78$	0.173863	0.0196861
$79$	−2.08787	−0.234904	−0.117452	−	0.993079i	$-0.537473\pi$
$79$	−2.08787	−0.234904	−0.117452	+	0.993079i	$0.537473\pi$
$80$	3.81954	0.427038
$81$	1.00000	0.111111
$82$	0.290510	0.0320815
$83$	−0.818085	−0.0897965	−0.0448983	−	0.998992i	$-0.514296\pi$
$83$	−0.818085	−0.0897965	−0.0448983	+	0.998992i	$0.514296\pi$
$84$	8.24879	0.900017
$85$	2.05254	0.222629
$86$	−0.0956773	−0.0103171
$87$	−0.846471	−0.0907512
$88$	1.62122	0.172823
$89$	−13.7274	−1.45510	−0.727551	−	0.686054i	$-0.759341\pi$
$89$	−13.7274	−1.45510	−0.727551	+	0.686054i	$0.759341\pi$
$90$	−0.173863	−0.0183267
$91$	4.18769	0.438989
$92$	−1.16538	−0.121499
$93$	1.00000	0.103695
$94$	1.55296	0.160175
$95$	−6.58024	−0.675119
$96$	−2.04446	−0.208662
$97$	10.8287	1.09949	0.549745	−	0.835333i	$-0.314725\pi$
$97$	10.8287	1.09949	0.549745	+	0.835333i	$0.314725\pi$
$98$	−1.83194	−0.185054
$99$	2.34893	0.236077
$100$	−1.96977	−0.196977
$101$	4.64198	0.461895	0.230947	−	0.972966i	$-0.425817\pi$
$101$	4.64198	0.461895	0.230947	+	0.972966i	$0.425817\pi$
$102$	−0.356860	−0.0353344
$103$	11.8241	1.16506	0.582530	−	0.812810i	$-0.302063\pi$
$103$	11.8241	1.16506	0.582530	+	0.812810i	$0.302063\pi$
$104$	−0.690195	−0.0676791
$105$	−4.18769	−0.408676
$106$	0.715777	0.0695224
$107$	−3.18496	−0.307902	−0.153951	−	0.988078i	$-0.549200\pi$
$107$	−3.18496	−0.307902	−0.153951	+	0.988078i	$0.549200\pi$
$108$	−1.96977	−0.189541
$109$	5.23596	0.501514	0.250757	−	0.968050i	$-0.419320\pi$
$109$	5.23596	0.501514	0.250757	+	0.968050i	$0.419320\pi$
$110$	−0.408392	−0.0389386
$111$	3.05606	0.290068
$112$	−15.9951	−1.51139
$113$	13.6434	1.28346	0.641731	−	0.766930i	$-0.278216\pi$
$113$	13.6434	1.28346	0.641731	+	0.766930i	$0.278216\pi$
$114$	1.14406	0.107151
$115$	0.591630	0.0551698
$116$	1.66736	0.154810
$117$	−1.00000	−0.0924500
$118$	−1.09682	−0.100970
$119$	−8.59539	−0.787938
$120$	0.690195	0.0630059
$121$	−5.48251	−0.498410
$122$	1.03886	0.0940536
$123$	−1.67092	−0.150662
$124$	−1.96977	−0.176891
$125$	1.00000	0.0894427
$126$	0.728082	0.0648627
$127$	20.4759	1.81694	0.908469	−	0.417952i	$-0.137252\pi$
$127$	20.4759	1.81694	0.908469	+	0.417952i	$0.137252\pi$
$128$	5.35528	0.473344
$129$	0.550304	0.0484516
$130$	0.173863	0.0152488
$131$	−1.22988	−0.107455	−0.0537274	−	0.998556i	$-0.517110\pi$
$131$	−1.22988	−0.107455	−0.0537274	+	0.998556i	$0.517110\pi$
$132$	−4.62686	−0.402717
$133$	27.5560	2.38941
$134$	−0.466686	−0.0403156
$135$	1.00000	0.0860663
$136$	1.41665	0.121477
$137$	−12.1252	−1.03593	−0.517964	−	0.855402i	$-0.673310\pi$
$137$	−12.1252	−1.03593	−0.517964	+	0.855402i	$0.673310\pi$
$138$	−0.102862	−0.00875622
$139$	18.6507	1.58193	0.790965	−	0.611862i	$-0.209579\pi$
$139$	18.6507	1.58193	0.790965	+	0.611862i	$0.209579\pi$
$140$	8.24879	0.697150
$141$	−8.93209	−0.752218
$142$	−2.43235	−0.204118
$143$	−2.34893	−0.196428
$144$	3.81954	0.318295
$145$	−0.846471	−0.0702956
$146$	−0.897382	−0.0742679
$147$	10.5367	0.869054
$148$	−6.01974	−0.494819
$149$	−19.9615	−1.63531	−0.817655	−	0.575708i	$-0.804726\pi$
$149$	−19.9615	−1.63531	−0.817655	+	0.575708i	$0.804726\pi$
$150$	−0.173863	−0.0141958
$151$	0.231359	0.0188277	0.00941387	−	0.999956i	$-0.497003\pi$
$151$	0.231359	0.0188277	0.00941387	+	0.999956i	$0.497003\pi$
$152$	−4.54165	−0.368376
$153$	2.05254	0.165938
$154$	1.71022	0.137813
$155$	1.00000	0.0803219
$156$	1.96977	0.157708
$157$	−13.9480	−1.11317	−0.556585	−	0.830791i	$-0.687889\pi$
$157$	−13.9480	−1.11317	−0.556585	+	0.830791i	$0.687889\pi$
$158$	0.363002	0.0288789
$159$	−4.11691	−0.326492
$160$	−2.04446	−0.161629
$161$	−2.47756	−0.195259
$162$	−0.173863	−0.0136599
$163$	19.8911	1.55799	0.778997	−	0.627028i	$-0.215729\pi$
$163$	19.8911	1.55799	0.778997	+	0.627028i	$0.215729\pi$
$164$	3.29133	0.257010
$165$	2.34893	0.182864
$166$	0.142234	0.0110395
$167$	−6.96622	−0.539062	−0.269531	−	0.962992i	$-0.586869\pi$
$167$	−6.96622	−0.539062	−0.269531	+	0.962992i	$0.586869\pi$
$168$	−2.89032	−0.222993
$169$	1.00000	0.0769231
$170$	−0.356860	−0.0273699
$171$	−6.58024	−0.503204
$172$	−1.08397	−0.0826522
$173$	12.2336	0.930103	0.465051	−	0.885284i	$-0.346036\pi$
$173$	12.2336	0.930103	0.465051	+	0.885284i	$0.346036\pi$
$174$	0.147170	0.0111569
$175$	−4.18769	−0.316559
$176$	8.97186	0.676279
$177$	6.30854	0.474179
$178$	2.38668	0.178889
$179$	−0.112346	−0.00839712	−0.00419856	−	0.999991i	$-0.501336\pi$
$179$	−0.112346	−0.00839712	−0.00419856	+	0.999991i	$0.501336\pi$
$180$	−1.96977	−0.146818
$181$	−13.1054	−0.974118	−0.487059	−	0.873369i	$-0.661930\pi$
$181$	−13.1054	−0.974118	−0.487059	+	0.873369i	$0.661930\pi$
$182$	−0.728082	−0.0539690
$183$	−5.97516	−0.441697
$184$	0.408340	0.0301032
$185$	3.05606	0.224686
$186$	−0.173863	−0.0127482
$187$	4.82128	0.352567
$188$	17.5942	1.28319
$189$	−4.18769	−0.304609
$190$	1.14406	0.0829987
$191$	16.9605	1.22722	0.613608	−	0.789611i	$-0.289718\pi$
$191$	16.9605	1.22722	0.613608	+	0.789611i	$0.289718\pi$
$192$	−7.28363	−0.525651
$193$	−12.9794	−0.934277	−0.467138	−	0.884184i	$-0.654715\pi$
$193$	−12.9794	−0.934277	−0.467138	+	0.884184i	$0.654715\pi$
$194$	−1.88271	−0.135171
$195$	−1.00000	−0.0716115
$196$	−20.7549	−1.48250
$197$	17.7630	1.26556	0.632780	−	0.774332i	$-0.281914\pi$
$197$	17.7630	1.26556	0.632780	+	0.774332i	$0.281914\pi$
$198$	−0.408392	−0.0290231
$199$	21.5632	1.52857	0.764287	−	0.644876i	$-0.223091\pi$
$199$	21.5632	1.52857	0.764287	+	0.644876i	$0.223091\pi$
$200$	0.690195	0.0488041
$201$	2.68423	0.189331
$202$	−0.807067	−0.0567850
$203$	3.54476	0.248793
$204$	−4.04303	−0.283069
$205$	−1.67092	−0.116702
$206$	−2.05576	−0.143232
$207$	0.591630	0.0411211
$208$	−3.81954	−0.264838
$209$	−15.4566	−1.06915
$210$	0.728082	0.0502424
$211$	19.1611	1.31910	0.659552	−	0.751659i	$-0.270746\pi$
$211$	19.1611	1.31910	0.659552	+	0.751659i	$0.270746\pi$
$212$	8.10938	0.556954
$213$	13.9901	0.958584
$214$	0.553746	0.0378533
$215$	0.550304	0.0375304
$216$	0.690195	0.0469618
$217$	−4.18769	−0.284279
$218$	−0.910337	−0.0616558
$219$	5.16145	0.348778
$220$	−4.62686	−0.311943
$221$	−2.05254	−0.138069
$222$	−0.531334	−0.0356608
$223$	23.2999	1.56028	0.780139	−	0.625606i	$-0.215148\pi$
$223$	23.2999	1.56028	0.780139	+	0.625606i	$0.215148\pi$
$224$	8.56158	0.572044
$225$	1.00000	0.0666667
$226$	−2.37208	−0.157788
$227$	7.56819	0.502318	0.251159	−	0.967946i	$-0.419188\pi$
$227$	7.56819	0.502318	0.251159	+	0.967946i	$0.419188\pi$
$228$	12.9616	0.858401
$229$	−5.38349	−0.355751	−0.177876	−	0.984053i	$-0.556922\pi$
$229$	−5.38349	−0.355751	−0.177876	+	0.984053i	$0.556922\pi$
$230$	−0.102862	−0.00678254
$231$	−9.83660	−0.647201
$232$	−0.584230	−0.0383566
$233$	28.3667	1.85837	0.929184	−	0.369619i	$-0.120512\pi$
$233$	28.3667	1.85837	0.929184	+	0.369619i	$0.120512\pi$
$234$	0.173863	0.0113657
$235$	−8.93209	−0.582666
$236$	−12.4264	−0.808889
$237$	−2.08787	−0.135622
$238$	1.49442	0.0968686
$239$	−2.78225	−0.179969	−0.0899844	−	0.995943i	$-0.528682\pi$
$239$	−2.78225	−0.179969	−0.0899844	+	0.995943i	$0.528682\pi$
$240$	3.81954	0.246551
$241$	−6.94989	−0.447682	−0.223841	−	0.974626i	$-0.571860\pi$
$241$	−6.94989	−0.447682	−0.223841	+	0.974626i	$0.571860\pi$
$242$	0.953203	0.0612742
$243$	1.00000	0.0641500
$244$	11.7697	0.753478
$245$	10.5367	0.673166
$246$	0.290510	0.0185223
$247$	6.58024	0.418691
$248$	0.690195	0.0438274
$249$	−0.818085	−0.0518440
$250$	−0.173863	−0.0109960
$251$	14.0883	0.889247	0.444624	−	0.895717i	$-0.353337\pi$
$251$	14.0883	0.889247	0.444624	+	0.895717i	$0.353337\pi$
$252$	8.24879	0.519625
$253$	1.38970	0.0873696
$254$	−3.55998	−0.223373
$255$	2.05254	0.128535
$256$	13.6362	0.852262
$257$	23.1880	1.44643	0.723213	−	0.690625i	$-0.242664\pi$
$257$	23.1880	1.44643	0.723213	+	0.690625i	$0.242664\pi$
$258$	−0.0956773	−0.00595661
$259$	−12.7978	−0.795218
$260$	1.96977	0.122160
$261$	−0.846471	−0.0523952
$262$	0.213829	0.0132104
$263$	−3.73469	−0.230291	−0.115145	−	0.993349i	$-0.536733\pi$
$263$	−3.73469	−0.230291	−0.115145	+	0.993349i	$0.536733\pi$
$264$	1.62122	0.0997793
$265$	−4.11691	−0.252900
$266$	−4.79095	−0.293752
$267$	−13.7274	−0.840103
$268$	−5.28731	−0.322974
$269$	12.6713	0.772583	0.386291	−	0.922377i	$-0.373756\pi$
$269$	12.6713	0.772583	0.386291	+	0.922377i	$0.373756\pi$
$270$	−0.173863	−0.0105809
$271$	−5.12759	−0.311479	−0.155740	−	0.987798i	$-0.549776\pi$
$271$	−5.12759	−0.311479	−0.155740	+	0.987798i	$0.549776\pi$
$272$	7.83977	0.475356
$273$	4.18769	0.253450
$274$	2.10812	0.127356
$275$	2.34893	0.141646
$276$	−1.16538	−0.0701474
$277$	10.2533	0.616058	0.308029	−	0.951377i	$-0.400331\pi$
$277$	10.2533	0.616058	0.308029	+	0.951377i	$0.400331\pi$
$278$	−3.24265	−0.194481
$279$	1.00000	0.0598684
$280$	−2.89032	−0.172730
$281$	5.58114	0.332943	0.166471	−	0.986046i	$-0.446763\pi$
$281$	5.58114	0.332943	0.166471	+	0.986046i	$0.446763\pi$
$282$	1.55296	0.0924772
$283$	13.4387	0.798851	0.399425	−	0.916766i	$-0.369210\pi$
$283$	13.4387	0.798851	0.399425	+	0.916766i	$0.369210\pi$
$284$	−27.5572	−1.63522
$285$	−6.58024	−0.389780
$286$	0.408392	0.0241487
$287$	6.99729	0.413037
$288$	−2.04446	−0.120471
$289$	−12.7871	−0.752181
$290$	0.147170	0.00864210
$291$	10.8287	0.634790
$292$	−10.1669	−0.594971
$293$	2.80378	0.163798	0.0818992	−	0.996641i	$-0.473901\pi$
$293$	2.80378	0.163798	0.0818992	+	0.996641i	$0.473901\pi$
$294$	−1.83194	−0.106841
$295$	6.30854	0.367297
$296$	2.10927	0.122599
$297$	2.34893	0.136299
$298$	3.47056	0.201044
$299$	−0.591630	−0.0342148
$300$	−1.96977	−0.113725
$301$	−2.30450	−0.132829
$302$	−0.0402247	−0.00231467
$303$	4.64198	0.266675
$304$	−25.1335	−1.44151
$305$	−5.97516	−0.342137
$306$	−0.356860	−0.0204003
$307$	7.65687	0.437001	0.218500	−	0.975837i	$-0.429884\pi$
$307$	7.65687	0.437001	0.218500	+	0.975837i	$0.429884\pi$
$308$	19.3759	1.10404
$309$	11.8241	0.672647
$310$	−0.173863	−0.00987473
$311$	14.8281	0.840827	0.420413	−	0.907333i	$-0.361885\pi$
$311$	14.8281	0.840827	0.420413	+	0.907333i	$0.361885\pi$
$312$	−0.690195	−0.0390746
$313$	1.55273	0.0877654	0.0438827	−	0.999037i	$-0.486027\pi$
$313$	1.55273	0.0877654	0.0438827	+	0.999037i	$0.486027\pi$
$314$	2.42503	0.136852
$315$	−4.18769	−0.235949
$316$	4.11263	0.231353
$317$	6.23442	0.350160	0.175080	−	0.984554i	$-0.443982\pi$
$317$	6.23442	0.350160	0.175080	+	0.984554i	$0.443982\pi$
$318$	0.715777	0.0401388
$319$	−1.98830	−0.111324
$320$	−7.28363	−0.407167
$321$	−3.18496	−0.177767
$322$	0.430755	0.0240050
$323$	−13.5062	−0.751505
$324$	−1.96977	−0.109432
$325$	−1.00000	−0.0554700
$326$	−3.45832	−0.191539
$327$	5.23596	0.289549
$328$	−1.15326	−0.0636781
$329$	37.4048	2.06219
$330$	−0.408392	−0.0224812
$331$	26.2735	1.44412	0.722061	−	0.691829i	$-0.243195\pi$
$331$	26.2735	1.44412	0.722061	+	0.691829i	$0.243195\pi$
$332$	1.61144	0.0884393
$333$	3.05606	0.167471
$334$	1.21116	0.0662719
$335$	2.68423	0.146655
$336$	−15.9951	−0.872602
$337$	−14.6657	−0.798892	−0.399446	−	0.916757i	$-0.630797\pi$
$337$	−14.6657	−0.798892	−0.399446	+	0.916757i	$0.630797\pi$
$338$	−0.173863	−0.00945687
$339$	13.6434	0.741007
$340$	−4.04303	−0.219264
$341$	2.34893	0.127202
$342$	1.14406	0.0618635
$343$	−14.8107	−0.799702
$344$	0.379817	0.0204784
$345$	0.591630	0.0318523
$346$	−2.12696	−0.114346
$347$	−4.30599	−0.231157	−0.115579	−	0.993298i	$-0.536872\pi$
$347$	−4.30599	−0.231157	−0.115579	+	0.993298i	$0.536872\pi$
$348$	1.66736	0.0893796
$349$	9.97616	0.534012	0.267006	−	0.963695i	$-0.413966\pi$
$349$	9.97616	0.534012	0.267006	+	0.963695i	$0.413966\pi$
$350$	0.728082	0.0389176
$351$	−1.00000	−0.0533761
$352$	−4.80231	−0.255964
$353$	8.17485	0.435104	0.217552	−	0.976049i	$-0.430193\pi$
$353$	8.17485	0.435104	0.217552	+	0.976049i	$0.430193\pi$
$354$	−1.09682	−0.0582953
$355$	13.9901	0.742516
$356$	27.0398	1.43311
$357$	−8.59539	−0.454916
$358$	0.0195327	0.00103234
$359$	−20.2459	−1.06854	−0.534268	−	0.845315i	$-0.679413\pi$
$359$	−20.2459	−1.06854	−0.534268	+	0.845315i	$0.679413\pi$
$360$	0.690195	0.0363764
$361$	24.2996	1.27893
$362$	2.27854	0.119757
$363$	−5.48251	−0.287757
$364$	−8.24879	−0.432354
$365$	5.16145	0.270162
$366$	1.03886	0.0543019
$367$	−12.6386	−0.659730	−0.329865	−	0.944028i	$-0.607003\pi$
$367$	−12.6386	−0.659730	−0.329865	+	0.944028i	$0.607003\pi$
$368$	2.25976	0.117798
$369$	−1.67092	−0.0869846
$370$	−0.531334	−0.0276227
$371$	17.2403	0.895074
$372$	−1.96977	−0.102128
$373$	−10.7010	−0.554077	−0.277039	−	0.960859i	$-0.589353\pi$
$373$	−10.7010	−0.554077	−0.277039	+	0.960859i	$0.589353\pi$
$374$	−0.838240	−0.0433443
$375$	1.00000	0.0516398
$376$	−6.16488	−0.317930
$377$	0.846471	0.0435955
$378$	0.728082	0.0374485
$379$	3.17541	0.163110	0.0815550	−	0.996669i	$-0.474011\pi$
$379$	3.17541	0.163110	0.0815550	+	0.996669i	$0.474011\pi$
$380$	12.9616	0.664915
$381$	20.4759	1.04901
$382$	−2.94879	−0.150873
$383$	10.3219	0.527427	0.263713	−	0.964601i	$-0.415053\pi$
$383$	10.3219	0.527427	0.263713	+	0.964601i	$0.415053\pi$
$384$	5.35528	0.273286
$385$	−9.83660	−0.501319
$386$	2.25663	0.114859
$387$	0.550304	0.0279735
$388$	−21.3301	−1.08287
$389$	−36.1603	−1.83340	−0.916701	−	0.399575i	$-0.869158\pi$
$389$	−36.1603	−1.83340	−0.916701	+	0.399575i	$0.869158\pi$
$390$	0.173863	0.00880387
$391$	1.21434	0.0614120
$392$	7.27239	0.367311
$393$	−1.22988	−0.0620391
$394$	−3.08832	−0.155587
$395$	−2.08787	−0.105052
$396$	−4.62686	−0.232509
$397$	−26.7032	−1.34020	−0.670098	−	0.742273i	$-0.733748\pi$
$397$	−26.7032	−1.34020	−0.670098	+	0.742273i	$0.733748\pi$
$398$	−3.74903	−0.187922
$399$	27.5560	1.37953
$400$	3.81954	0.190977
$401$	−2.42847	−0.121272	−0.0606361	−	0.998160i	$-0.519313\pi$
$401$	−2.42847	−0.121272	−0.0606361	+	0.998160i	$0.519313\pi$
$402$	−0.466686	−0.0232762
$403$	−1.00000	−0.0498135
$404$	−9.14365	−0.454914
$405$	1.00000	0.0496904
$406$	−0.616300	−0.0305865
$407$	7.17848	0.355824
$408$	1.41665	0.0701347
$409$	23.1223	1.14333	0.571663	−	0.820488i	$-0.306298\pi$
$409$	23.1223	1.14333	0.571663	+	0.820488i	$0.306298\pi$
$410$	0.290510	0.0143473
$411$	−12.1252	−0.598094
$412$	−23.2907	−1.14745
$413$	−26.4182	−1.29995
$414$	−0.102862	−0.00505540
$415$	−0.818085	−0.0401582
$416$	2.04446	0.100238
$417$	18.6507	0.913327
$418$	2.68732	0.131441
$419$	−23.9205	−1.16860	−0.584298	−	0.811539i	$-0.698630\pi$
$419$	−23.9205	−1.16860	−0.584298	+	0.811539i	$0.698630\pi$
$420$	8.24879	0.402500
$421$	−20.3440	−0.991506	−0.495753	−	0.868464i	$-0.665108\pi$
$421$	−20.3440	−0.991506	−0.495753	+	0.868464i	$0.665108\pi$
$422$	−3.33140	−0.162170
$423$	−8.93209	−0.434293
$424$	−2.84147	−0.137994
$425$	2.05254	0.0995628
$426$	−2.43235	−0.117848
$427$	25.0221	1.21090
$428$	6.27365	0.303248
$429$	−2.34893	−0.113408
$430$	−0.0956773	−0.00461397
$431$	2.93559	0.141402	0.0707011	−	0.997498i	$-0.477476\pi$
$431$	2.93559	0.141402	0.0707011	+	0.997498i	$0.477476\pi$
$432$	3.81954	0.183768
$433$	−2.14818	−0.103235	−0.0516174	−	0.998667i	$-0.516438\pi$
$433$	−2.14818	−0.103235	−0.0516174	+	0.998667i	$0.516438\pi$
$434$	0.728082	0.0349490
$435$	−0.846471	−0.0405852
$436$	−10.3136	−0.493934
$437$	−3.89307	−0.186231
$438$	−0.897382	−0.0428786
$439$	0.614439	0.0293256	0.0146628	−	0.999892i	$-0.495333\pi$
$439$	0.614439	0.0293256	0.0146628	+	0.999892i	$0.495333\pi$
$440$	1.62122	0.0772887
$441$	10.5367	0.501749
$442$	0.356860	0.0169741
$443$	22.0469	1.04748	0.523740	−	0.851878i	$-0.324536\pi$
$443$	22.0469	1.04748	0.523740	+	0.851878i	$0.324536\pi$
$444$	−6.01974	−0.285684
$445$	−13.7274	−0.650741
$446$	−4.05098	−0.191820
$447$	−19.9615	−0.944147
$448$	30.5016	1.44106
$449$	−20.0274	−0.945153	−0.472576	−	0.881290i	$-0.656676\pi$
$449$	−20.0274	−0.945153	−0.472576	+	0.881290i	$0.656676\pi$
$450$	−0.173863	−0.00819596
$451$	−3.92488	−0.184815
$452$	−26.8744	−1.26406
$453$	0.231359	0.0108702
$454$	−1.31582	−0.0617547
$455$	4.18769	0.196322
$456$	−4.54165	−0.212682
$457$	−26.4678	−1.23811	−0.619056	−	0.785346i	$-0.712485\pi$
$457$	−26.4678	−1.23811	−0.619056	+	0.785346i	$0.712485\pi$
$458$	0.935987	0.0437358
$459$	2.05254	0.0958043
$460$	−1.16538	−0.0543359
$461$	15.0802	0.702353	0.351176	−	0.936309i	$-0.385782\pi$
$461$	15.0802	0.702353	0.351176	+	0.936309i	$0.385782\pi$
$462$	1.71022	0.0795664
$463$	−10.4332	−0.484871	−0.242435	−	0.970168i	$-0.577946\pi$
$463$	−10.4332	−0.484871	−0.242435	+	0.970168i	$0.577946\pi$
$464$	−3.23313	−0.150094
$465$	1.00000	0.0463739
$466$	−4.93191	−0.228466
$467$	−12.2023	−0.564655	−0.282328	−	0.959318i	$-0.591107\pi$
$467$	−12.2023	−0.564655	−0.282328	+	0.959318i	$0.591107\pi$
$468$	1.96977	0.0910527
$469$	−11.2407	−0.519047
$470$	1.55296	0.0716325
$471$	−13.9480	−0.642689
$472$	4.35412	0.200415
$473$	1.29263	0.0594351
$474$	0.363002	0.0166732
$475$	−6.58024	−0.301922
$476$	16.9310	0.776029
$477$	−4.11691	−0.188500
$478$	0.483729	0.0221252
$479$	−38.0854	−1.74017	−0.870084	−	0.492904i	$-0.835935\pi$
$479$	−38.0854	−1.74017	−0.870084	+	0.492904i	$0.835935\pi$
$480$	−2.04446	−0.0933166
$481$	−3.05606	−0.139344
$482$	1.20832	0.0550377
$483$	−2.47756	−0.112733
$484$	10.7993	0.490877
$485$	10.8287	0.491707
$486$	−0.173863	−0.00788656
$487$	15.5712	0.705597	0.352799	−	0.935699i	$-0.385230\pi$
$487$	15.5712	0.705597	0.352799	+	0.935699i	$0.385230\pi$
$488$	−4.12402	−0.186686
$489$	19.8911	0.899508
$490$	−1.83194	−0.0827587
$491$	11.0132	0.497019	0.248510	−	0.968629i	$-0.420059\pi$
$491$	11.0132	0.497019	0.248510	+	0.968629i	$0.420059\pi$
$492$	3.29133	0.148385
$493$	−1.73742	−0.0782493
$494$	−1.14406	−0.0514736
$495$	2.34893	0.105577
$496$	3.81954	0.171503
$497$	−58.5860	−2.62794
$498$	0.142234	0.00637367
$499$	37.4325	1.67571	0.837854	−	0.545894i	$-0.183810\pi$
$499$	37.4325	1.67571	0.837854	+	0.545894i	$0.183810\pi$
$500$	−1.96977	−0.0880909
$501$	−6.96622	−0.311228
$502$	−2.44943	−0.109324
$503$	−35.2395	−1.57125	−0.785626	−	0.618701i	$-0.787659\pi$
$503$	−35.2395	−1.57125	−0.785626	+	0.618701i	$0.787659\pi$
$504$	−2.89032	−0.128745
$505$	4.64198	0.206566
$506$	−0.241617	−0.0107412
$507$	1.00000	0.0444116
$508$	−40.3328	−1.78948
$509$	35.0859	1.55515	0.777577	−	0.628788i	$-0.216449\pi$
$509$	35.0859	1.55515	0.777577	+	0.628788i	$0.216449\pi$
$510$	−0.356860	−0.0158020
$511$	−21.6145	−0.956170
$512$	−13.0814	−0.578121
$513$	−6.58024	−0.290525
$514$	−4.03152	−0.177823
$515$	11.8241	0.521030
$516$	−1.08397	−0.0477193
$517$	−20.9809	−0.922739
$518$	2.22506	0.0977635
$519$	12.2336	0.536995
$520$	−0.690195	−0.0302670
$521$	−7.06308	−0.309439	−0.154720	−	0.987958i	$-0.549447\pi$
$521$	−7.06308	−0.309439	−0.154720	+	0.987958i	$0.549447\pi$
$522$	0.147170	0.00644144
$523$	24.2522	1.06047	0.530236	−	0.847850i	$-0.322103\pi$
$523$	24.2522	1.06047	0.530236	+	0.847850i	$0.322103\pi$
$524$	2.42258	0.105831
$525$	−4.18769	−0.182766
$526$	0.649322	0.0283118
$527$	2.05254	0.0894100
$528$	8.97186	0.390450
$529$	−22.6500	−0.984781
$530$	0.715777	0.0310914
$531$	6.30854	0.273767
$532$	−54.2790	−2.35329
$533$	1.67092	0.0723755
$534$	2.38668	0.103282
$535$	−3.18496	−0.137698
$536$	1.85264	0.0800218
$537$	−0.112346	−0.00484808
$538$	−2.20306	−0.0949809
$539$	24.7501	1.06606
$540$	−1.96977	−0.0847655
$541$	21.3919	0.919711	0.459855	−	0.887994i	$-0.347901\pi$
$541$	21.3919	0.919711	0.459855	+	0.887994i	$0.347901\pi$
$542$	0.891496	0.0382930
$543$	−13.1054	−0.562408
$544$	−4.19634	−0.179917
$545$	5.23596	0.224284
$546$	−0.728082	−0.0311590
$547$	28.0374	1.19879	0.599396	−	0.800452i	$-0.295407\pi$
$547$	28.0374	1.19879	0.599396	+	0.800452i	$0.295407\pi$
$548$	23.8839	1.02027
$549$	−5.97516	−0.255014
$550$	−0.408392	−0.0174139
$551$	5.56999	0.237289
$552$	0.408340	0.0173801
$553$	8.74334	0.371805
$554$	−1.78266	−0.0757378
$555$	3.05606	0.129722
$556$	−36.7376	−1.55802
$557$	−22.1587	−0.938893	−0.469446	−	0.882961i	$-0.655547\pi$
$557$	−22.1587	−0.938893	−0.469446	+	0.882961i	$0.655547\pi$
$558$	−0.173863	−0.00736019
$559$	−0.550304	−0.0232754
$560$	−15.9951	−0.675915
$561$	4.82128	0.203555
$562$	−0.970351	−0.0409318
$563$	17.0731	0.719544	0.359772	−	0.933040i	$-0.382854\pi$
$563$	17.0731	0.719544	0.359772	+	0.933040i	$0.382854\pi$
$564$	17.5942	0.740849
$565$	13.6434	0.573982
$566$	−2.33649	−0.0982102
$567$	−4.18769	−0.175866
$568$	9.65587	0.405151
$569$	25.7885	1.08111	0.540556	−	0.841308i	$-0.318214\pi$
$569$	25.7885	1.08111	0.540556	+	0.841308i	$0.318214\pi$
$570$	1.14406	0.0479193
$571$	−32.7376	−1.37002	−0.685012	−	0.728531i	$-0.740203\pi$
$571$	−32.7376	−1.37002	−0.685012	+	0.728531i	$0.740203\pi$
$572$	4.62686	0.193459
$573$	16.9605	0.708534
$574$	−1.21657	−0.0507785
$575$	0.591630	0.0246727
$576$	−7.28363	−0.303485
$577$	−23.9013	−0.995023	−0.497511	−	0.867457i	$-0.665753\pi$
$577$	−23.9013	−0.995023	−0.497511	+	0.867457i	$0.665753\pi$
$578$	2.22319	0.0924727
$579$	−12.9794	−0.539405
$580$	1.66736	0.0692331
$581$	3.42588	0.142130
$582$	−1.88271	−0.0780407
$583$	−9.67035	−0.400505
$584$	3.56240	0.147413
$585$	−1.00000	−0.0413449
$586$	−0.487472	−0.0201373
$587$	42.0582	1.73593	0.867964	−	0.496626i	$-0.165428\pi$
$587$	42.0582	1.73593	0.867964	+	0.496626i	$0.165428\pi$
$588$	−20.7549	−0.855919
$589$	−6.58024	−0.271134
$590$	−1.09682	−0.0451553
$591$	17.7630	0.730671
$592$	11.6728	0.479747
$593$	−3.05635	−0.125509	−0.0627545	−	0.998029i	$-0.519989\pi$
$593$	−3.05635	−0.125509	−0.0627545	+	0.998029i	$0.519989\pi$
$594$	−0.408392	−0.0167565
$595$	−8.59539	−0.352377
$596$	39.3196	1.61059
$597$	21.5632	0.882523
$598$	0.102862	0.00420635
$599$	24.6774	1.00829	0.504146	−	0.863618i	$-0.331807\pi$
$599$	24.6774	1.00829	0.504146	+	0.863618i	$0.331807\pi$
$600$	0.690195	0.0281771
$601$	21.5421	0.878719	0.439359	−	0.898311i	$-0.355205\pi$
$601$	21.5421	0.878719	0.439359	+	0.898311i	$0.355205\pi$
$602$	0.400667	0.0163299
$603$	2.68423	0.109310
$604$	−0.455725	−0.0185432
$605$	−5.48251	−0.222896
$606$	−0.807067	−0.0327849
$607$	−26.9635	−1.09441	−0.547207	−	0.836997i	$-0.684309\pi$
$607$	−26.9635	−1.09441	−0.547207	+	0.836997i	$0.684309\pi$
$608$	13.4531	0.545594
$609$	3.54476	0.143641
$610$	1.03886	0.0420621
$611$	8.93209	0.361354
$612$	−4.04303	−0.163430
$613$	−1.29379	−0.0522557	−0.0261279	−	0.999659i	$-0.508318\pi$
$613$	−1.29379	−0.0522557	−0.0261279	+	0.999659i	$0.508318\pi$
$614$	−1.33124	−0.0537246
$615$	−1.67092	−0.0673780
$616$	−6.78917	−0.273543
$617$	45.0960	1.81549	0.907747	−	0.419517i	$-0.137801\pi$
$617$	45.0960	1.81549	0.907747	+	0.419517i	$0.137801\pi$
$618$	−2.05576	−0.0826948
$619$	18.8185	0.756378	0.378189	−	0.925728i	$-0.376547\pi$
$619$	18.8185	0.756378	0.378189	+	0.925728i	$0.376547\pi$
$620$	−1.96977	−0.0791079
$621$	0.591630	0.0237413
$622$	−2.57806	−0.103371
$623$	57.4860	2.30313
$624$	−3.81954	−0.152904
$625$	1.00000	0.0400000
$626$	−0.269961	−0.0107898
$627$	−15.4566	−0.617275
$628$	27.4743	1.09634
$629$	6.27268	0.250108
$630$	0.728082	0.0290075
$631$	−11.6938	−0.465524	−0.232762	−	0.972534i	$-0.574776\pi$
$631$	−11.6938	−0.465524	−0.232762	+	0.972534i	$0.574776\pi$
$632$	−1.44104	−0.0573213
$633$	19.1611	0.761586
$634$	−1.08393	−0.0430484
$635$	20.4759	0.812560
$636$	8.10938	0.321558
$637$	−10.5367	−0.417480
$638$	0.345692	0.0136861
$639$	13.9901	0.553439
$640$	5.35528	0.211686
$641$	−19.5968	−0.774028	−0.387014	−	0.922074i	$-0.626494\pi$
$641$	−19.5968	−0.774028	−0.387014	+	0.922074i	$0.626494\pi$
$642$	0.553746	0.0218546
$643$	−35.3064	−1.39235	−0.696175	−	0.717872i	$-0.745116\pi$
$643$	−35.3064	−1.39235	−0.696175	+	0.717872i	$0.745116\pi$
$644$	4.88023	0.192308
$645$	0.550304	0.0216682
$646$	2.34822	0.0923896
$647$	47.5282	1.86852	0.934262	−	0.356586i	$-0.116059\pi$
$647$	47.5282	1.86852	0.934262	+	0.356586i	$0.116059\pi$
$648$	0.690195	0.0271134
$649$	14.8183	0.581671
$650$	0.173863	0.00681945
$651$	−4.18769	−0.164128
$652$	−39.1810	−1.53445
$653$	33.8872	1.32611	0.663054	−	0.748571i	$-0.269260\pi$
$653$	33.8872	1.32611	0.663054	+	0.748571i	$0.269260\pi$
$654$	−0.910337	−0.0355970
$655$	−1.22988	−0.0480553
$656$	−6.38215	−0.249181
$657$	5.16145	0.201367
$658$	−6.50330	−0.253525
$659$	−14.4462	−0.562743	−0.281371	−	0.959599i	$-0.590789\pi$
$659$	−14.4462	−0.562743	−0.281371	+	0.959599i	$0.590789\pi$
$660$	−4.62686	−0.180100
$661$	44.6311	1.73595	0.867974	−	0.496609i	$-0.165422\pi$
$661$	44.6311	1.73595	0.867974	+	0.496609i	$0.165422\pi$
$662$	−4.56798	−0.177540
$663$	−2.05254	−0.0797140
$664$	−0.564638	−0.0219122
$665$	27.5560	1.06858
$666$	−0.531334	−0.0205888
$667$	−0.500798	−0.0193910
$668$	13.7219	0.530915
$669$	23.2999	0.900827
$670$	−0.466686	−0.0180297
$671$	−14.0353	−0.541825
$672$	8.56158	0.330270
$673$	−18.8642	−0.727161	−0.363580	−	0.931563i	$-0.618446\pi$
$673$	−18.8642	−0.727161	−0.363580	+	0.931563i	$0.618446\pi$
$674$	2.54982	0.0982152
$675$	1.00000	0.0384900
$676$	−1.96977	−0.0757605
$677$	−20.8061	−0.799642	−0.399821	−	0.916593i	$-0.630928\pi$
$677$	−20.8061	−0.799642	−0.399821	+	0.916593i	$0.630928\pi$
$678$	−2.37208	−0.0910990
$679$	−45.3473	−1.74027
$680$	1.41665	0.0543261
$681$	7.56819	0.290013
$682$	−0.408392	−0.0156381
$683$	−43.2698	−1.65567	−0.827836	−	0.560970i	$-0.810428\pi$
$683$	−43.2698	−1.65567	−0.827836	+	0.560970i	$0.810428\pi$
$684$	12.9616	0.495598
$685$	−12.1252	−0.463281
$686$	2.57502	0.0983148
$687$	−5.38349	−0.205393
$688$	2.10191	0.0801346
$689$	4.11691	0.156842
$690$	−0.102862	−0.00391590
$691$	10.7779	0.410009	0.205005	−	0.978761i	$-0.434279\pi$
$691$	10.7779	0.410009	0.205005	+	0.978761i	$0.434279\pi$
$692$	−24.0974	−0.916045
$693$	−9.83660	−0.373661
$694$	0.748649	0.0284183
$695$	18.6507	0.707460
$696$	−0.584230	−0.0221452
$697$	−3.42963	−0.129906
$698$	−1.73448	−0.0656511
$699$	28.3667	1.07293
$700$	8.24879	0.311775
$701$	−27.9542	−1.05581	−0.527907	−	0.849302i	$-0.677023\pi$
$701$	−27.9542	−1.05581	−0.527907	+	0.849302i	$0.677023\pi$
$702$	0.173863	0.00656202
$703$	−20.1096	−0.758448
$704$	−17.1088	−0.644811
$705$	−8.93209	−0.336402
$706$	−1.42130	−0.0534914
$707$	−19.4392	−0.731085
$708$	−12.4264	−0.467012
$709$	−29.6728	−1.11438	−0.557192	−	0.830383i	$-0.688121\pi$
$709$	−29.6728	−1.11438	−0.557192	+	0.830383i	$0.688121\pi$
$710$	−2.43235	−0.0912844
$711$	−2.08787	−0.0783012
$712$	−9.47457	−0.355075
$713$	0.591630	0.0221567
$714$	1.49442	0.0559271
$715$	−2.34893	−0.0878451
$716$	0.221296	0.00827021
$717$	−2.78225	−0.103905
$718$	3.52000	0.131365
$719$	−14.4317	−0.538211	−0.269105	−	0.963111i	$-0.586728\pi$
$719$	−14.4317	−0.538211	−0.269105	+	0.963111i	$0.586728\pi$
$720$	3.81954	0.142346
$721$	−49.5155	−1.84405
$722$	−4.22479	−0.157230
$723$	−6.94989	−0.258469
$724$	25.8147	0.959395
$725$	−0.846471	−0.0314371
$726$	0.953203	0.0353767
$727$	15.1319	0.561209	0.280605	−	0.959823i	$-0.409465\pi$
$727$	15.1319	0.561209	0.280605	+	0.959823i	$0.409465\pi$
$728$	2.89032	0.107122
$729$	1.00000	0.0370370
$730$	−0.897382	−0.0332136
$731$	1.12952	0.0417768
$732$	11.7697	0.435021
$733$	10.5604	0.390056	0.195028	−	0.980798i	$-0.437520\pi$
$733$	10.5604	0.390056	0.195028	+	0.980798i	$0.437520\pi$
$734$	2.19738	0.0811067
$735$	10.5367	0.388653
$736$	−1.20957	−0.0445852
$737$	6.30507	0.232250
$738$	0.290510	0.0106938
$739$	41.5024	1.52669	0.763345	−	0.645992i	$-0.223556\pi$
$739$	41.5024	1.52669	0.763345	+	0.645992i	$0.223556\pi$
$740$	−6.01974	−0.221290
$741$	6.58024	0.241731
$742$	−2.99745	−0.110040
$743$	−32.5711	−1.19492	−0.597459	−	0.801899i	$-0.703823\pi$
$743$	−32.5711	−1.19492	−0.597459	+	0.801899i	$0.703823\pi$
$744$	0.690195	0.0253038
$745$	−19.9615	−0.731333
$746$	1.86050	0.0681179
$747$	−0.818085	−0.0299322
$748$	−9.49682	−0.347238
$749$	13.3376	0.487346
$750$	−0.173863	−0.00634856
$751$	−15.9523	−0.582108	−0.291054	−	0.956707i	$-0.594006\pi$
$751$	−15.9523	−0.582108	−0.291054	+	0.956707i	$0.594006\pi$
$752$	−34.1165	−1.24410
$753$	14.0883	0.513407
$754$	−0.147170	−0.00535960
$755$	0.231359	0.00842002
$756$	8.24879	0.300006
$757$	−37.0069	−1.34504	−0.672519	−	0.740080i	$-0.734788\pi$
$757$	−37.0069	−1.34504	−0.672519	+	0.740080i	$0.734788\pi$
$758$	−0.552085	−0.0200526
$759$	1.38970	0.0504429
$760$	−4.54165	−0.164743
$761$	15.8830	0.575759	0.287880	−	0.957667i	$-0.407050\pi$
$761$	15.8830	0.575759	0.287880	+	0.957667i	$0.407050\pi$
$762$	−3.55998	−0.128965
$763$	−21.9266	−0.793795
$764$	−33.4082	−1.20867
$765$	2.05254	0.0742097
$766$	−1.79460	−0.0648415
$767$	−6.30854	−0.227788
$768$	13.6362	0.492053
$769$	−15.4307	−0.556447	−0.278223	−	0.960516i	$-0.589746\pi$
$769$	−15.4307	−0.556447	−0.278223	+	0.960516i	$0.589746\pi$
$770$	1.71022	0.0616319
$771$	23.1880	0.835095
$772$	25.5664	0.920156
$773$	21.1156	0.759475	0.379738	−	0.925094i	$-0.376014\pi$
$773$	21.1156	0.759475	0.379738	+	0.925094i	$0.376014\pi$
$774$	−0.0956773	−0.00343905
$775$	1.00000	0.0359211
$776$	7.47392	0.268298
$777$	−12.7978	−0.459119
$778$	6.28693	0.225397
$779$	10.9951	0.393939
$780$	1.96977	0.0705291
$781$	32.8617	1.17589
$782$	−0.211129	−0.00754995
$783$	−0.846471	−0.0302504
$784$	40.2455	1.43734
$785$	−13.9480	−0.497824
$786$	0.213829	0.00762704
$787$	35.6165	1.26959	0.634795	−	0.772681i	$-0.281085\pi$
$787$	35.6165	1.26959	0.634795	+	0.772681i	$0.281085\pi$
$788$	−34.9890	−1.24643
$789$	−3.73469	−0.132958
$790$	0.363002	0.0129150
$791$	−57.1343	−2.03146
$792$	1.62122	0.0576076
$793$	5.97516	0.212184
$794$	4.64269	0.164763
$795$	−4.11691	−0.146012
$796$	−42.4746	−1.50547
$797$	30.6597	1.08602	0.543011	−	0.839725i	$-0.317284\pi$
$797$	30.6597	1.08602	0.543011	+	0.839725i	$0.317284\pi$
$798$	−4.79095	−0.169598
$799$	−18.3335	−0.648592
$800$	−2.04446	−0.0722827
$801$	−13.7274	−0.485034
$802$	0.422220	0.0149091
$803$	12.1239	0.427843
$804$	−5.28731	−0.186469
$805$	−2.47756	−0.0873225
$806$	0.173863	0.00612405
$807$	12.6713	0.446051
$808$	3.20387	0.112712
$809$	4.11946	0.144833	0.0724163	−	0.997374i	$-0.476929\pi$
$809$	4.11946	0.144833	0.0724163	+	0.997374i	$0.476929\pi$
$810$	−0.173863	−0.00610891
$811$	−47.8601	−1.68060	−0.840298	−	0.542124i	$-0.817620\pi$
$811$	−47.8601	−1.68060	−0.840298	+	0.542124i	$0.817620\pi$
$812$	−6.98236	−0.245033
$813$	−5.12759	−0.179833
$814$	−1.24807	−0.0437448
$815$	19.8911	0.696756
$816$	7.83977	0.274447
$817$	−3.62114	−0.126687
$818$	−4.02011	−0.140560
$819$	4.18769	0.146330
$820$	3.29133	0.114938
$821$	−46.4792	−1.62213	−0.811067	−	0.584953i	$-0.801113\pi$
$821$	−46.4792	−1.62213	−0.811067	+	0.584953i	$0.801113\pi$
$822$	2.10812	0.0735293
$823$	31.0092	1.08091	0.540457	−	0.841372i	$-0.318251\pi$
$823$	31.0092	1.08091	0.540457	+	0.841372i	$0.318251\pi$
$824$	8.16090	0.284298
$825$	2.34893	0.0817794
$826$	4.59313	0.159816
$827$	−5.92917	−0.206178	−0.103089	−	0.994672i	$-0.532873\pi$
$827$	−5.92917	−0.206178	−0.103089	+	0.994672i	$0.532873\pi$
$828$	−1.16538	−0.0404996
$829$	50.2636	1.74573	0.872864	−	0.487964i	$-0.162260\pi$
$829$	50.2636	1.74573	0.872864	+	0.487964i	$0.162260\pi$
$830$	0.142234	0.00493703
$831$	10.2533	0.355681
$832$	7.28363	0.252515
$833$	21.6270	0.749332
$834$	−3.24265	−0.112284
$835$	−6.96622	−0.241076
$836$	30.4459	1.05299
$837$	1.00000	0.0345651
$838$	4.15889	0.143666
$839$	24.4219	0.843139	0.421570	−	0.906796i	$-0.361479\pi$
$839$	24.4219	0.843139	0.421570	+	0.906796i	$0.361479\pi$
$840$	−2.89032	−0.0997255
$841$	−28.2835	−0.975293
$842$	3.53706	0.121895
$843$	5.58114	0.192225
$844$	−37.7430	−1.29917
$845$	1.00000	0.0344010
$846$	1.55296	0.0533917
$847$	22.9590	0.788882
$848$	−15.7247	−0.539989
$849$	13.4387	0.461217
$850$	−0.356860	−0.0122402
$851$	1.80806	0.0619793
$852$	−27.5572	−0.944096
$853$	0.441606	0.0151203	0.00756015	−	0.999971i	$-0.497594\pi$
$853$	0.441606	0.0151203	0.00756015	+	0.999971i	$0.497594\pi$
$854$	−4.35041	−0.148868
$855$	−6.58024	−0.225040
$856$	−2.19824	−0.0751344
$857$	6.86468	0.234493	0.117246	−	0.993103i	$-0.462593\pi$
$857$	6.86468	0.234493	0.117246	+	0.993103i	$0.462593\pi$
$858$	0.408392	0.0139423
$859$	1.99001	0.0678981	0.0339491	−	0.999424i	$-0.489192\pi$
$859$	1.99001	0.0678981	0.0339491	+	0.999424i	$0.489192\pi$
$860$	−1.08397	−0.0369632
$861$	6.99729	0.238467
$862$	−0.510388	−0.0173839
$863$	−26.3265	−0.896163	−0.448081	−	0.893993i	$-0.647893\pi$
$863$	−26.3265	−0.896163	−0.448081	+	0.893993i	$0.647893\pi$
$864$	−2.04446	−0.0695541
$865$	12.2336	0.415955
$866$	0.373488	0.0126916
$867$	−12.7871	−0.434272
$868$	8.24879	0.279982
$869$	−4.90427	−0.166366
$870$	0.147170	0.00498952
$871$	−2.68423	−0.0909515
$872$	3.61383	0.122380
$873$	10.8287	0.366496
$874$	0.676859	0.0228951
$875$	−4.18769	−0.141570
$876$	−10.1669	−0.343507
$877$	−9.62165	−0.324900	−0.162450	−	0.986717i	$-0.551940\pi$
$877$	−9.62165	−0.324900	−0.162450	+	0.986717i	$0.551940\pi$
$878$	−0.106828	−0.00360527
$879$	2.80378	0.0945690
$880$	8.97186	0.302441
$881$	0.986118	0.0332231	0.0166116	−	0.999862i	$-0.494712\pi$
$881$	0.986118	0.0332231	0.0166116	+	0.999862i	$0.494712\pi$
$882$	−1.83194	−0.0616847
$883$	−51.6526	−1.73825	−0.869123	−	0.494595i	$-0.835316\pi$
$883$	−51.6526	−1.73825	−0.869123	+	0.494595i	$0.835316\pi$
$884$	4.04303	0.135982
$885$	6.30854	0.212059
$886$	−3.83313	−0.128777
$887$	43.1936	1.45030	0.725150	−	0.688591i	$-0.241771\pi$
$887$	43.1936	1.45030	0.725150	+	0.688591i	$0.241771\pi$
$888$	2.10927	0.0707826
$889$	−85.7465	−2.87584
$890$	2.38668	0.0800017
$891$	2.34893	0.0786922
$892$	−45.8955	−1.53670
$893$	58.7753	1.96684
$894$	3.47056	0.116073
$895$	−0.112346	−0.00375531
$896$	−22.4262	−0.749208
$897$	−0.591630	−0.0197539
$898$	3.48202	0.116197
$899$	−0.846471	−0.0282314
$900$	−1.96977	−0.0656591
$901$	−8.45013	−0.281514
$902$	0.682389	0.0227211
$903$	−2.30450	−0.0766890
$904$	9.41660	0.313191
$905$	−13.1054	−0.435639
$906$	−0.0402247	−0.00133638
$907$	10.5040	0.348781	0.174390	−	0.984677i	$-0.444205\pi$
$907$	10.5040	0.348781	0.174390	+	0.984677i	$0.444205\pi$
$908$	−14.9076	−0.494726
$909$	4.64198	0.153965
$910$	−0.728082	−0.0241357
$911$	−3.36837	−0.111599	−0.0557996	−	0.998442i	$-0.517771\pi$
$911$	−3.36837	−0.111599	−0.0557996	+	0.998442i	$0.517771\pi$
$912$	−25.1335	−0.832254
$913$	−1.92163	−0.0635966
$914$	4.60176	0.152213
$915$	−5.97516	−0.197533
$916$	10.6042	0.350374
$917$	5.15034	0.170079
$918$	−0.356860	−0.0117781
$919$	−27.1388	−0.895228	−0.447614	−	0.894227i	$-0.647726\pi$
$919$	−27.1388	−0.895228	−0.447614	+	0.894227i	$0.647726\pi$
$920$	0.408340	0.0134626
$921$	7.65687	0.252302
$922$	−2.62187	−0.0863468
$923$	−13.9901	−0.460489
$924$	19.3759	0.637419
$925$	3.05606	0.100483
$926$	1.81394	0.0596097
$927$	11.8241	0.388353
$928$	1.73058	0.0568091
$929$	−33.4437	−1.09725	−0.548626	−	0.836068i	$-0.684849\pi$
$929$	−33.4437	−1.09725	−0.548626	+	0.836068i	$0.684849\pi$
$930$	−0.173863	−0.00570118
$931$	−69.3342	−2.27234
$932$	−55.8760	−1.83028
$933$	14.8281	0.485452
$934$	2.12152	0.0694184
$935$	4.82128	0.157673
$936$	−0.690195	−0.0225597
$937$	56.5367	1.84697	0.923487	−	0.383630i	$-0.125326\pi$
$937$	56.5367	1.84697	0.923487	+	0.383630i	$0.125326\pi$
$938$	1.95434	0.0638113
$939$	1.55273	0.0506714
$940$	17.5942	0.573859
$941$	−14.5585	−0.474594	−0.237297	−	0.971437i	$-0.576261\pi$
$941$	−14.5585	−0.474594	−0.237297	+	0.971437i	$0.576261\pi$
$942$	2.42503	0.0790117
$943$	−0.988565	−0.0321921
$944$	24.0958	0.784250
$945$	−4.18769	−0.136225
$946$	−0.224740	−0.00730691
$947$	−29.1978	−0.948802	−0.474401	−	0.880309i	$-0.657335\pi$
$947$	−29.1978	−0.948802	−0.474401	+	0.880309i	$0.657335\pi$
$948$	4.11263	0.133572
$949$	−5.16145	−0.167548
$950$	1.14406	0.0371181
$951$	6.23442	0.202165
$952$	−5.93249	−0.192273
$953$	23.9734	0.776574	0.388287	−	0.921538i	$-0.373067\pi$
$953$	23.9734	0.776574	0.388287	+	0.921538i	$0.373067\pi$
$954$	0.715777	0.0231741
$955$	16.9605	0.548828
$956$	5.48039	0.177249
$957$	−1.98830	−0.0642728
$958$	6.62163	0.213935
$959$	50.7767	1.63966
$960$	−7.28363	−0.235078
$961$	1.00000	0.0322581
$962$	0.531334	0.0171309
$963$	−3.18496	−0.102634
$964$	13.6897	0.440915
$965$	−12.9794	−0.417821
$966$	0.430755	0.0138593
$967$	−12.0080	−0.386150	−0.193075	−	0.981184i	$-0.561846\pi$
$967$	−12.0080	−0.386150	−0.193075	+	0.981184i	$0.561846\pi$
$968$	−3.78400	−0.121622
$969$	−13.5062	−0.433882
$970$	−1.88271	−0.0604501
$971$	40.8015	1.30938	0.654692	−	0.755896i	$-0.272799\pi$
$971$	40.8015	1.30938	0.654692	+	0.755896i	$0.272799\pi$
$972$	−1.96977	−0.0631805
$973$	−78.1032	−2.50387
$974$	−2.70724	−0.0867457
$975$	−1.00000	−0.0320256
$976$	−22.8224	−0.730527
$977$	10.5200	0.336564	0.168282	−	0.985739i	$-0.446178\pi$
$977$	10.5200	0.336564	0.168282	+	0.985739i	$0.446178\pi$
$978$	−3.45832	−0.110585
$979$	−32.2447	−1.03055
$980$	−20.7549	−0.662992
$981$	5.23596	0.167171
$982$	−1.91479	−0.0611033
$983$	−8.71731	−0.278039	−0.139019	−	0.990290i	$-0.544395\pi$
$983$	−8.71731	−0.278039	−0.139019	+	0.990290i	$0.544395\pi$
$984$	−1.15326	−0.0367646
$985$	17.7630	0.565976
$986$	0.302071	0.00961991
$987$	37.4048	1.19061
$988$	−12.9616	−0.412363
$989$	0.325576	0.0103527
$990$	−0.408392	−0.0129795
$991$	−34.9358	−1.10977	−0.554886	−	0.831927i	$-0.687238\pi$
$991$	−34.9358	−1.10977	−0.554886	+	0.831927i	$0.687238\pi$
$992$	−2.04446	−0.0649118
$993$	26.2735	0.833765
$994$	10.1859	0.323078
$995$	21.5632	0.683599
$996$	1.61144	0.0510605
$997$	−51.5358	−1.63216	−0.816078	−	0.577942i	$-0.803856\pi$
$997$	−51.5358	−1.63216	−0.816078	+	0.577942i	$0.803856\pi$
$998$	−6.50811	−0.206011
$999$	3.05606	0.0966894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bi.1.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bi.1.9	✓	18	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.173863 q^{2} +1.00000 q^{3} -1.96977 q^{4} +1.00000 q^{5} -0.173863 q^{6} -4.18769 q^{7} +0.690195 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.173863 q^{2} +1.00000 q^{3} -1.96977 q^{4} +1.00000 q^{5} -0.173863 q^{6} -4.18769 q^{7} +0.690195 q^{8} +1.00000 q^{9} -0.173863 q^{10} +2.34893 q^{11} -1.96977 q^{12} -1.00000 q^{13} +0.728082 q^{14} +1.00000 q^{15} +3.81954 q^{16} +2.05254 q^{17} -0.173863 q^{18} -6.58024 q^{19} -1.96977 q^{20} -4.18769 q^{21} -0.408392 q^{22} +0.591630 q^{23} +0.690195 q^{24} +1.00000 q^{25} +0.173863 q^{26} +1.00000 q^{27} +8.24879 q^{28} -0.846471 q^{29} -0.173863 q^{30} +1.00000 q^{31} -2.04446 q^{32} +2.34893 q^{33} -0.356860 q^{34} -4.18769 q^{35} -1.96977 q^{36} +3.05606 q^{37} +1.14406 q^{38} -1.00000 q^{39} +0.690195 q^{40} -1.67092 q^{41} +0.728082 q^{42} +0.550304 q^{43} -4.62686 q^{44} +1.00000 q^{45} -0.102862 q^{46} -8.93209 q^{47} +3.81954 q^{48} +10.5367 q^{49} -0.173863 q^{50} +2.05254 q^{51} +1.96977 q^{52} -4.11691 q^{53} -0.173863 q^{54} +2.34893 q^{55} -2.89032 q^{56} -6.58024 q^{57} +0.147170 q^{58} +6.30854 q^{59} -1.96977 q^{60} -5.97516 q^{61} -0.173863 q^{62} -4.18769 q^{63} -7.28363 q^{64} -1.00000 q^{65} -0.408392 q^{66} +2.68423 q^{67} -4.04303 q^{68} +0.591630 q^{69} +0.728082 q^{70} +13.9901 q^{71} +0.690195 q^{72} +5.16145 q^{73} -0.531334 q^{74} +1.00000 q^{75} +12.9616 q^{76} -9.83660 q^{77} +0.173863 q^{78} -2.08787 q^{79} +3.81954 q^{80} +1.00000 q^{81} +0.290510 q^{82} -0.818085 q^{83} +8.24879 q^{84} +2.05254 q^{85} -0.0956773 q^{86} -0.846471 q^{87} +1.62122 q^{88} -13.7274 q^{89} -0.173863 q^{90} +4.18769 q^{91} -1.16538 q^{92} +1.00000 q^{93} +1.55296 q^{94} -6.58024 q^{95} -2.04446 q^{96} +10.8287 q^{97} -1.83194 q^{98} +2.34893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9	\( 18 q + 4 q^{2} + 18 q^{3} + 22 q^{4} + 18 q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 18 q^{9} + 4 q^{10} + 6 q^{11} + 22 q^{12} - 18 q^{13} + 5 q^{14} + 18 q^{15} + 30 q^{16} + 18 q^{17} + 4 q^{18} + 12 q^{19} + 22 q^{20} + 8 q^{21} + 7 q^{22} + 32 q^{23} + 9 q^{24} + 18 q^{25} - 4 q^{26} + 18 q^{27} + 10 q^{28} + 7 q^{29} + 4 q^{30} + 18 q^{31} + 22 q^{32} + 6 q^{33} + 15 q^{34} + 8 q^{35} + 22 q^{36} + 3 q^{37} + 32 q^{38} - 18 q^{39} + 9 q^{40} + 4 q^{41} + 5 q^{42} + 14 q^{43} - 5 q^{44} + 18 q^{45} + 10 q^{46} + 23 q^{47} + 30 q^{48} + 28 q^{49} + 4 q^{50} + 18 q^{51} - 22 q^{52} + 35 q^{53} + 4 q^{54} + 6 q^{55} - 7 q^{56} + 12 q^{57} - 6 q^{58} + 28 q^{59} + 22 q^{60} + 19 q^{61} + 4 q^{62} + 8 q^{63} + 43 q^{64} - 18 q^{65} + 7 q^{66} + 34 q^{67} + 55 q^{68} + 32 q^{69} + 5 q^{70} - 8 q^{71} + 9 q^{72} + 22 q^{74} + 18 q^{75} + 2 q^{76} + 21 q^{77} - 4 q^{78} + 4 q^{79} + 30 q^{80} + 18 q^{81} + 29 q^{82} + 11 q^{83} + 10 q^{84} + 18 q^{85} - 22 q^{86} + 7 q^{87} - 31 q^{88} + 17 q^{89} + 4 q^{90} - 8 q^{91} + 33 q^{92} + 18 q^{93} - 14 q^{94} + 12 q^{95} + 22 q^{96} + 32 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 + 18 * q^3 + 22 * q^4 + 18 * q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 18 * q^9 + 4 * q^10 + 6 * q^11 + 22 * q^12 - 18 * q^13 + 5 * q^14 + 18 * q^15 + 30 * q^16 + 18 * q^17 + 4 * q^18 + 12 * q^19 + 22 * q^20 + 8 * q^21 + 7 * q^22 + 32 * q^23 + 9 * q^24 + 18 * q^25 - 4 * q^26 + 18 * q^27 + 10 * q^28 + 7 * q^29 + 4 * q^30 + 18 * q^31 + 22 * q^32 + 6 * q^33 + 15 * q^34 + 8 * q^35 + 22 * q^36 + 3 * q^37 + 32 * q^38 - 18 * q^39 + 9 * q^40 + 4 * q^41 + 5 * q^42 + 14 * q^43 - 5 * q^44 + 18 * q^45 + 10 * q^46 + 23 * q^47 + 30 * q^48 + 28 * q^49 + 4 * q^50 + 18 * q^51 - 22 * q^52 + 35 * q^53 + 4 * q^54 + 6 * q^55 - 7 * q^56 + 12 * q^57 - 6 * q^58 + 28 * q^59 + 22 * q^60 + 19 * q^61 + 4 * q^62 + 8 * q^63 + 43 * q^64 - 18 * q^65 + 7 * q^66 + 34 * q^67 + 55 * q^68 + 32 * q^69 + 5 * q^70 - 8 * q^71 + 9 * q^72 + 22 * q^74 + 18 * q^75 + 2 * q^76 + 21 * q^77 - 4 * q^78 + 4 * q^79 + 30 * q^80 + 18 * q^81 + 29 * q^82 + 11 * q^83 + 10 * q^84 + 18 * q^85 - 22 * q^86 + 7 * q^87 - 31 * q^88 + 17 * q^89 + 4 * q^90 - 8 * q^91 + 33 * q^92 + 18 * q^93 - 14 * q^94 + 12 * q^95 + 22 * q^96 + 32 * q^97 + 20 * q^98 + 6 * q^99

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