LMFDB - Embedded newform 6045.2.a.bh.1.8

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.287376$ 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)

$f(q)$	$=$	$q-0.287376 q^{2} -1.00000 q^{3} -1.91742 q^{4} +1.00000 q^{5} +0.287376 q^{6} -1.07674 q^{7} +1.12577 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.287376 q^{2} -1.00000 q^{3} -1.91742 q^{4} +1.00000 q^{5} +0.287376 q^{6} -1.07674 q^{7} +1.12577 q^{8} +1.00000 q^{9} -0.287376 q^{10} -2.40977 q^{11} +1.91742 q^{12} +1.00000 q^{13} +0.309430 q^{14} -1.00000 q^{15} +3.51131 q^{16} +0.378264 q^{17} -0.287376 q^{18} +5.04481 q^{19} -1.91742 q^{20} +1.07674 q^{21} +0.692509 q^{22} +3.38416 q^{23} -1.12577 q^{24} +1.00000 q^{25} -0.287376 q^{26} -1.00000 q^{27} +2.06457 q^{28} -3.29421 q^{29} +0.287376 q^{30} +1.00000 q^{31} -3.26061 q^{32} +2.40977 q^{33} -0.108704 q^{34} -1.07674 q^{35} -1.91742 q^{36} +8.21599 q^{37} -1.44976 q^{38} -1.00000 q^{39} +1.12577 q^{40} -0.318106 q^{41} -0.309430 q^{42} -1.13876 q^{43} +4.62053 q^{44} +1.00000 q^{45} -0.972525 q^{46} -5.16954 q^{47} -3.51131 q^{48} -5.84062 q^{49} -0.287376 q^{50} -0.378264 q^{51} -1.91742 q^{52} -9.13732 q^{53} +0.287376 q^{54} -2.40977 q^{55} -1.21217 q^{56} -5.04481 q^{57} +0.946677 q^{58} -4.64947 q^{59} +1.91742 q^{60} +2.40286 q^{61} -0.287376 q^{62} -1.07674 q^{63} -6.08560 q^{64} +1.00000 q^{65} -0.692509 q^{66} -8.33361 q^{67} -0.725289 q^{68} -3.38416 q^{69} +0.309430 q^{70} -5.08878 q^{71} +1.12577 q^{72} -0.510965 q^{73} -2.36108 q^{74} -1.00000 q^{75} -9.67300 q^{76} +2.59470 q^{77} +0.287376 q^{78} +14.5508 q^{79} +3.51131 q^{80} +1.00000 q^{81} +0.0914158 q^{82} +9.57096 q^{83} -2.06457 q^{84} +0.378264 q^{85} +0.327252 q^{86} +3.29421 q^{87} -2.71285 q^{88} +12.9533 q^{89} -0.287376 q^{90} -1.07674 q^{91} -6.48884 q^{92} -1.00000 q^{93} +1.48560 q^{94} +5.04481 q^{95} +3.26061 q^{96} -9.26944 q^{97} +1.67845 q^{98} -2.40977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * 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 $

$2$	−0.287376	−0.203205	−0.101603	−	0.994825i	$-0.532397\pi$
$2$	−0.287376	−0.203205	−0.101603	+	0.994825i	$0.532397\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.91742	−0.958708
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.287376	0.117321
$7$	−1.07674	−0.406971	−0.203485	−	0.979078i	$-0.565227\pi$
$7$	−1.07674	−0.406971	−0.203485	+	0.979078i	$0.565227\pi$
$8$	1.12577	0.398020
$9$	1.00000	0.333333
$10$	−0.287376	−0.0908762
$11$	−2.40977	−0.726573	−0.363286	−	0.931678i	$-0.618345\pi$
$11$	−2.40977	−0.726573	−0.363286	+	0.931678i	$0.618345\pi$
$12$	1.91742	0.553510
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.309430	0.0826987
$15$	−1.00000	−0.258199
$16$	3.51131	0.877828
$17$	0.378264	0.0917425	0.0458712	−	0.998947i	$-0.485394\pi$
$17$	0.378264	0.0917425	0.0458712	+	0.998947i	$0.485394\pi$
$18$	−0.287376	−0.0677351
$19$	5.04481	1.15736	0.578680	−	0.815555i	$-0.303568\pi$
$19$	5.04481	1.15736	0.578680	+	0.815555i	$0.303568\pi$
$20$	−1.91742	−0.428747
$21$	1.07674	0.234965
$22$	0.692509	0.147643
$23$	3.38416	0.705646	0.352823	−	0.935690i	$-0.385222\pi$
$23$	3.38416	0.705646	0.352823	+	0.935690i	$0.385222\pi$
$24$	−1.12577	−0.229797
$25$	1.00000	0.200000
$26$	−0.287376	−0.0563590
$27$	−1.00000	−0.192450
$28$	2.06457	0.390166
$29$	−3.29421	−0.611720	−0.305860	−	0.952076i	$-0.598944\pi$
$29$	−3.29421	−0.611720	−0.305860	+	0.952076i	$0.598944\pi$
$30$	0.287376	0.0524674
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.26061	−0.576399
$33$	2.40977	0.419487
$34$	−0.108704	−0.0186426
$35$	−1.07674	−0.182003
$36$	−1.91742	−0.319569
$37$	8.21599	1.35070	0.675350	−	0.737497i	$-0.263993\pi$
$37$	8.21599	1.35070	0.675350	+	0.737497i	$0.263993\pi$
$38$	−1.44976	−0.235182
$39$	−1.00000	−0.160128
$40$	1.12577	0.178000
$41$	−0.318106	−0.0496798	−0.0248399	−	0.999691i	$-0.507908\pi$
$41$	−0.318106	−0.0496798	−0.0248399	+	0.999691i	$0.507908\pi$
$42$	−0.309430	−0.0477461
$43$	−1.13876	−0.173660	−0.0868298	−	0.996223i	$-0.527674\pi$
$43$	−1.13876	−0.173660	−0.0868298	+	0.996223i	$0.527674\pi$
$44$	4.62053	0.696571
$45$	1.00000	0.149071
$46$	−0.972525	−0.143391
$47$	−5.16954	−0.754055	−0.377027	−	0.926202i	$-0.623054\pi$
$47$	−5.16954	−0.754055	−0.377027	+	0.926202i	$0.623054\pi$
$48$	−3.51131	−0.506814
$49$	−5.84062	−0.834375
$50$	−0.287376	−0.0406411
$51$	−0.378264	−0.0529676
$52$	−1.91742	−0.265898
$53$	−9.13732	−1.25511	−0.627554	−	0.778573i	$-0.715944\pi$
$53$	−9.13732	−1.25511	−0.627554	+	0.778573i	$0.715944\pi$
$54$	0.287376	0.0391069
$55$	−2.40977	−0.324933
$56$	−1.21217	−0.161982
$57$	−5.04481	−0.668202
$58$	0.946677	0.124305
$59$	−4.64947	−0.605309	−0.302654	−	0.953100i	$-0.597873\pi$
$59$	−4.64947	−0.605309	−0.302654	+	0.953100i	$0.597873\pi$
$60$	1.91742	0.247537
$61$	2.40286	0.307655	0.153828	−	0.988098i	$-0.450840\pi$
$61$	2.40286	0.307655	0.153828	+	0.988098i	$0.450840\pi$
$62$	−0.287376	−0.0364967
$63$	−1.07674	−0.135657
$64$	−6.08560	−0.760701
$65$	1.00000	0.124035
$66$	−0.692509	−0.0852420
$67$	−8.33361	−1.01811	−0.509056	−	0.860733i	$-0.670006\pi$
$67$	−8.33361	−1.01811	−0.509056	+	0.860733i	$0.670006\pi$
$68$	−0.725289	−0.0879542
$69$	−3.38416	−0.407405
$70$	0.309430	0.0369840
$71$	−5.08878	−0.603928	−0.301964	−	0.953319i	$-0.597642\pi$
$71$	−5.08878	−0.603928	−0.301964	+	0.953319i	$0.597642\pi$
$72$	1.12577	0.132673
$73$	−0.510965	−0.0598039	−0.0299020	−	0.999553i	$-0.509520\pi$
$73$	−0.510965	−0.0598039	−0.0299020	+	0.999553i	$0.509520\pi$
$74$	−2.36108	−0.274469
$75$	−1.00000	−0.115470
$76$	−9.67300	−1.10957
$77$	2.59470	0.295694
$78$	0.287376	0.0325389
$79$	14.5508	1.63710	0.818549	−	0.574437i	$-0.194779\pi$
$79$	14.5508	1.63710	0.818549	+	0.574437i	$0.194779\pi$
$80$	3.51131	0.392577
$81$	1.00000	0.111111
$82$	0.0914158	0.0100952
$83$	9.57096	1.05055	0.525275	−	0.850933i	$-0.323962\pi$
$83$	9.57096	1.05055	0.525275	+	0.850933i	$0.323962\pi$
$84$	−2.06457	−0.225263
$85$	0.378264	0.0410285
$86$	0.327252	0.0352885
$87$	3.29421	0.353177
$88$	−2.71285	−0.289190
$89$	12.9533	1.37305	0.686523	−	0.727108i	$-0.259136\pi$
$89$	12.9533	1.37305	0.686523	+	0.727108i	$0.259136\pi$
$90$	−0.287376	−0.0302921
$91$	−1.07674	−0.112873
$92$	−6.48884	−0.676508
$93$	−1.00000	−0.103695
$94$	1.48560	0.153228
$95$	5.04481	0.517587
$96$	3.26061	0.332784
$97$	−9.26944	−0.941169	−0.470585	−	0.882355i	$-0.655957\pi$
$97$	−9.26944	−0.941169	−0.470585	+	0.882355i	$0.655957\pi$
$98$	1.67845	0.169549
$99$	−2.40977	−0.242191
$100$	−1.91742	−0.191742
$101$	13.3917	1.33252	0.666262	−	0.745717i	$-0.267893\pi$
$101$	13.3917	1.33252	0.666262	+	0.745717i	$0.267893\pi$
$102$	0.108704	0.0107633
$103$	11.9046	1.17299	0.586497	−	0.809951i	$-0.300506\pi$
$103$	11.9046	1.17299	0.586497	+	0.809951i	$0.300506\pi$
$104$	1.12577	0.110391
$105$	1.07674	0.105079
$106$	2.62584	0.255044
$107$	11.2930	1.09174	0.545868	−	0.837871i	$-0.316200\pi$
$107$	11.2930	1.09174	0.545868	+	0.837871i	$0.316200\pi$
$108$	1.91742	0.184503
$109$	−15.9679	−1.52945	−0.764723	−	0.644359i	$-0.777124\pi$
$109$	−15.9679	−1.52945	−0.764723	+	0.644359i	$0.777124\pi$
$110$	0.692509	0.0660281
$111$	−8.21599	−0.779827
$112$	−3.78078	−0.357250
$113$	−10.1959	−0.959152	−0.479576	−	0.877500i	$-0.659210\pi$
$113$	−10.1959	−0.959152	−0.479576	+	0.877500i	$0.659210\pi$
$114$	1.44976	0.135782
$115$	3.38416	0.315574
$116$	6.31638	0.586461
$117$	1.00000	0.0924500
$118$	1.33614	0.123002
$119$	−0.407294	−0.0373365
$120$	−1.12577	−0.102768
$121$	−5.19301	−0.472092
$122$	−0.690525	−0.0625172
$123$	0.318106	0.0286826
$124$	−1.91742	−0.172189
$125$	1.00000	0.0894427
$126$	0.309430	0.0275662
$127$	1.38729	0.123102	0.0615510	−	0.998104i	$-0.480395\pi$
$127$	1.38729	0.123102	0.0615510	+	0.998104i	$0.480395\pi$
$128$	8.27006	0.730977
$129$	1.13876	0.100262
$130$	−0.287376	−0.0252045
$131$	−9.38988	−0.820398	−0.410199	−	0.911996i	$-0.634541\pi$
$131$	−9.38988	−0.820398	−0.410199	+	0.911996i	$0.634541\pi$
$132$	−4.62053	−0.402165
$133$	−5.43197	−0.471012
$134$	2.39488	0.206886
$135$	−1.00000	−0.0860663
$136$	0.425838	0.0365153
$137$	12.2216	1.04416	0.522080	−	0.852897i	$-0.325156\pi$
$137$	12.2216	1.04416	0.522080	+	0.852897i	$0.325156\pi$
$138$	0.972525	0.0827868
$139$	8.70902	0.738689	0.369345	−	0.929292i	$-0.379582\pi$
$139$	8.70902	0.738689	0.369345	+	0.929292i	$0.379582\pi$
$140$	2.06457	0.174488
$141$	5.16954	0.435354
$142$	1.46239	0.122721
$143$	−2.40977	−0.201515
$144$	3.51131	0.292609
$145$	−3.29421	−0.273570
$146$	0.146839	0.0121525
$147$	5.84062	0.481726
$148$	−15.7535	−1.29493
$149$	−22.2231	−1.82059	−0.910295	−	0.413961i	$-0.864145\pi$
$149$	−22.2231	−1.82059	−0.910295	+	0.413961i	$0.864145\pi$
$150$	0.287376	0.0234641
$151$	3.29360	0.268029	0.134015	−	0.990979i	$-0.457213\pi$
$151$	3.29360	0.268029	0.134015	+	0.990979i	$0.457213\pi$
$152$	5.67930	0.460652
$153$	0.378264	0.0305808
$154$	−0.745655	−0.0600866
$155$	1.00000	0.0803219
$156$	1.91742	0.153516
$157$	−13.8944	−1.10890	−0.554448	−	0.832219i	$-0.687070\pi$
$157$	−13.8944	−1.10890	−0.554448	+	0.832219i	$0.687070\pi$
$158$	−4.18156	−0.332667
$159$	9.13732	0.724636
$160$	−3.26061	−0.257773
$161$	−3.64387	−0.287177
$162$	−0.287376	−0.0225784
$163$	24.2256	1.89750	0.948748	−	0.316033i	$-0.102351\pi$
$163$	24.2256	1.89750	0.948748	+	0.316033i	$0.102351\pi$
$164$	0.609941	0.0476284
$165$	2.40977	0.187600
$166$	−2.75046	−0.213477
$167$	−13.4729	−1.04257	−0.521284	−	0.853384i	$-0.674547\pi$
$167$	−13.4729	−1.04257	−0.521284	+	0.853384i	$0.674547\pi$
$168$	1.21217	0.0935206
$169$	1.00000	0.0769231
$170$	−0.108704	−0.00833721
$171$	5.04481	0.385787
$172$	2.18348	0.166489
$173$	−6.48079	−0.492725	−0.246363	−	0.969178i	$-0.579235\pi$
$173$	−6.48079	−0.492725	−0.246363	+	0.969178i	$0.579235\pi$
$174$	−0.946677	−0.0717674
$175$	−1.07674	−0.0813942
$176$	−8.46145	−0.637806
$177$	4.64947	0.349475
$178$	−3.72246	−0.279010
$179$	23.5437	1.75974	0.879870	−	0.475215i	$-0.157630\pi$
$179$	23.5437	1.75974	0.879870	+	0.475215i	$0.157630\pi$
$180$	−1.91742	−0.142916
$181$	−12.4770	−0.927409	−0.463704	−	0.885990i	$-0.653480\pi$
$181$	−12.4770	−0.927409	−0.463704	+	0.885990i	$0.653480\pi$
$182$	0.309430	0.0229365
$183$	−2.40286	−0.177625
$184$	3.80978	0.280861
$185$	8.21599	0.604052
$186$	0.287376	0.0210714
$187$	−0.911529	−0.0666576
$188$	9.91215	0.722918
$189$	1.07674	0.0783216
$190$	−1.44976	−0.105176
$191$	10.5570	0.763874	0.381937	−	0.924188i	$-0.375257\pi$
$191$	10.5570	0.763874	0.381937	+	0.924188i	$0.375257\pi$
$192$	6.08560	0.439191
$193$	16.6493	1.19844	0.599222	−	0.800583i	$-0.295477\pi$
$193$	16.6493	1.19844	0.599222	+	0.800583i	$0.295477\pi$
$194$	2.66381	0.191251
$195$	−1.00000	−0.0716115
$196$	11.1989	0.799921
$197$	−7.81470	−0.556774	−0.278387	−	0.960469i	$-0.589800\pi$
$197$	−7.81470	−0.556774	−0.278387	+	0.960469i	$0.589800\pi$
$198$	0.692509	0.0492145
$199$	−23.8267	−1.68903	−0.844513	−	0.535535i	$-0.820110\pi$
$199$	−23.8267	−1.68903	−0.844513	+	0.535535i	$0.820110\pi$
$200$	1.12577	0.0796039
$201$	8.33361	0.587808
$202$	−3.84845	−0.270776
$203$	3.54703	0.248952
$204$	0.725289	0.0507804
$205$	−0.318106	−0.0222175
$206$	−3.42109	−0.238359
$207$	3.38416	0.235215
$208$	3.51131	0.243466
$209$	−12.1568	−0.840906
$210$	−0.309430	−0.0213527
$211$	12.8921	0.887532	0.443766	−	0.896143i	$-0.353642\pi$
$211$	12.8921	0.887532	0.443766	+	0.896143i	$0.353642\pi$
$212$	17.5200	1.20328
$213$	5.08878	0.348678
$214$	−3.24534	−0.221847
$215$	−1.13876	−0.0776629
$216$	−1.12577	−0.0765989
$217$	−1.07674	−0.0730941
$218$	4.58878	0.310792
$219$	0.510965	0.0345278
$220$	4.62053	0.311516
$221$	0.378264	0.0254448
$222$	2.36108	0.158465
$223$	16.2151	1.08585	0.542923	−	0.839782i	$-0.317318\pi$
$223$	16.2151	1.08585	0.542923	+	0.839782i	$0.317318\pi$
$224$	3.51084	0.234578
$225$	1.00000	0.0666667
$226$	2.93006	0.194905
$227$	17.5172	1.16266	0.581330	−	0.813668i	$-0.302533\pi$
$227$	17.5172	1.16266	0.581330	+	0.813668i	$0.302533\pi$
$228$	9.67300	0.640610
$229$	17.7771	1.17474	0.587371	−	0.809318i	$-0.300163\pi$
$229$	17.7771	1.17474	0.587371	+	0.809318i	$0.300163\pi$
$230$	−0.972525	−0.0641264
$231$	−2.59470	−0.170719
$232$	−3.70853	−0.243477
$233$	−3.78171	−0.247748	−0.123874	−	0.992298i	$-0.539532\pi$
$233$	−3.78171	−0.247748	−0.123874	+	0.992298i	$0.539532\pi$
$234$	−0.287376	−0.0187863
$235$	−5.16954	−0.337224
$236$	8.91496	0.580314
$237$	−14.5508	−0.945179
$238$	0.117046	0.00758698
$239$	19.4835	1.26028	0.630140	−	0.776481i	$-0.282997\pi$
$239$	19.4835	1.26028	0.630140	+	0.776481i	$0.282997\pi$
$240$	−3.51131	−0.226654
$241$	10.9116	0.702878	0.351439	−	0.936211i	$-0.385693\pi$
$241$	10.9116	0.702878	0.351439	+	0.936211i	$0.385693\pi$
$242$	1.49235	0.0959316
$243$	−1.00000	−0.0641500
$244$	−4.60729	−0.294951
$245$	−5.84062	−0.373144
$246$	−0.0914158	−0.00582846
$247$	5.04481	0.320994
$248$	1.12577	0.0714865
$249$	−9.57096	−0.606535
$250$	−0.287376	−0.0181752
$251$	−27.1616	−1.71442	−0.857211	−	0.514965i	$-0.827805\pi$
$251$	−27.1616	−1.71442	−0.857211	+	0.514965i	$0.827805\pi$
$252$	2.06457	0.130055
$253$	−8.15504	−0.512703
$254$	−0.398673	−0.0250150
$255$	−0.378264	−0.0236878
$256$	9.79459	0.612162
$257$	−9.92385	−0.619033	−0.309517	−	0.950894i	$-0.600167\pi$
$257$	−9.92385	−0.619033	−0.309517	+	0.950894i	$0.600167\pi$
$258$	−0.327252	−0.0203738
$259$	−8.84652	−0.549696
$260$	−1.91742	−0.118913
$261$	−3.29421	−0.203907
$262$	2.69842	0.166709
$263$	1.09739	0.0676677	0.0338338	−	0.999427i	$-0.489228\pi$
$263$	1.09739	0.0676677	0.0338338	+	0.999427i	$0.489228\pi$
$264$	2.71285	0.166964
$265$	−9.13732	−0.561301
$266$	1.56102	0.0957121
$267$	−12.9533	−0.792729
$268$	15.9790	0.976072
$269$	28.4506	1.73466	0.867331	−	0.497732i	$-0.165834\pi$
$269$	28.4506	1.73466	0.867331	+	0.497732i	$0.165834\pi$
$270$	0.287376	0.0174891
$271$	−32.0733	−1.94831	−0.974157	−	0.225873i	$-0.927476\pi$
$271$	−32.0733	−1.94831	−0.974157	+	0.225873i	$0.927476\pi$
$272$	1.32820	0.0805341
$273$	1.07674	0.0651675
$274$	−3.51218	−0.212179
$275$	−2.40977	−0.145315
$276$	6.48884	0.390582
$277$	30.5051	1.83287	0.916437	−	0.400178i	$-0.131052\pi$
$277$	30.5051	1.83287	0.916437	+	0.400178i	$0.131052\pi$
$278$	−2.50276	−0.150106
$279$	1.00000	0.0598684
$280$	−1.21217	−0.0724408
$281$	−3.74879	−0.223634	−0.111817	−	0.993729i	$-0.535667\pi$
$281$	−3.74879	−0.223634	−0.111817	+	0.993729i	$0.535667\pi$
$282$	−1.48560	−0.0884662
$283$	15.0227	0.893007	0.446503	−	0.894782i	$-0.352669\pi$
$283$	15.0227	0.893007	0.446503	+	0.894782i	$0.352669\pi$
$284$	9.75731	0.578990
$285$	−5.04481	−0.298829
$286$	0.692509	0.0409489
$287$	0.342518	0.0202182
$288$	−3.26061	−0.192133
$289$	−16.8569	−0.991583
$290$	0.946677	0.0555908
$291$	9.26944	0.543384
$292$	0.979732	0.0573345
$293$	10.2822	0.600695	0.300347	−	0.953830i	$-0.402897\pi$
$293$	10.2822	0.600695	0.300347	+	0.953830i	$0.402897\pi$
$294$	−1.67845	−0.0978893
$295$	−4.64947	−0.270702
$296$	9.24931	0.537605
$297$	2.40977	0.139829
$298$	6.38639	0.369953
$299$	3.38416	0.195711
$300$	1.91742	0.110702
$301$	1.22615	0.0706744
$302$	−0.946500	−0.0544649
$303$	−13.3917	−0.769334
$304$	17.7139	1.01596
$305$	2.40286	0.137588
$306$	−0.108704	−0.00621419
$307$	1.25850	0.0718266	0.0359133	−	0.999355i	$-0.488566\pi$
$307$	1.25850	0.0718266	0.0359133	+	0.999355i	$0.488566\pi$
$308$	−4.97513	−0.283484
$309$	−11.9046	−0.677229
$310$	−0.287376	−0.0163218
$311$	14.1496	0.802349	0.401175	−	0.916002i	$-0.368602\pi$
$311$	14.1496	0.802349	0.401175	+	0.916002i	$0.368602\pi$
$312$	−1.12577	−0.0637342
$313$	−7.25919	−0.410313	−0.205157	−	0.978729i	$-0.565770\pi$
$313$	−7.25919	−0.410313	−0.205157	+	0.978729i	$0.565770\pi$
$314$	3.99292	0.225333
$315$	−1.07674	−0.0606677
$316$	−27.9000	−1.56950
$317$	10.8546	0.609657	0.304829	−	0.952407i	$-0.401401\pi$
$317$	10.8546	0.609657	0.304829	+	0.952407i	$0.401401\pi$
$318$	−2.62584	−0.147250
$319$	7.93830	0.444459
$320$	−6.08560	−0.340196
$321$	−11.2930	−0.630314
$322$	1.04716	0.0583560
$323$	1.90827	0.106179
$324$	−1.91742	−0.106523
$325$	1.00000	0.0554700
$326$	−6.96185	−0.385581
$327$	15.9679	0.883027
$328$	−0.358114	−0.0197735
$329$	5.56627	0.306878
$330$	−0.692509	−0.0381214
$331$	−1.93615	−0.106420	−0.0532102	−	0.998583i	$-0.516945\pi$
$331$	−1.93615	−0.106420	−0.0532102	+	0.998583i	$0.516945\pi$
$332$	−18.3515	−1.00717
$333$	8.21599	0.450233
$334$	3.87179	0.211855
$335$	−8.33361	−0.455314
$336$	3.78078	0.206259
$337$	6.06436	0.330346	0.165173	−	0.986265i	$-0.447182\pi$
$337$	6.06436	0.330346	0.165173	+	0.986265i	$0.447182\pi$
$338$	−0.287376	−0.0156312
$339$	10.1959	0.553767
$340$	−0.725289	−0.0393343
$341$	−2.40977	−0.130496
$342$	−1.44976	−0.0783939
$343$	13.8261	0.746537
$344$	−1.28198	−0.0691199
$345$	−3.38416	−0.182197
$346$	1.86242	0.100124
$347$	−31.9663	−1.71604	−0.858021	−	0.513614i	$-0.828306\pi$
$347$	−31.9663	−1.71604	−0.858021	+	0.513614i	$0.828306\pi$
$348$	−6.31638	−0.338593
$349$	30.1622	1.61455	0.807273	−	0.590178i	$-0.200943\pi$
$349$	30.1622	1.61455	0.807273	+	0.590178i	$0.200943\pi$
$350$	0.309430	0.0165397
$351$	−1.00000	−0.0533761
$352$	7.85730	0.418796
$353$	13.3553	0.710830	0.355415	−	0.934709i	$-0.384340\pi$
$353$	13.3553	0.710830	0.355415	+	0.934709i	$0.384340\pi$
$354$	−1.33614	−0.0710152
$355$	−5.08878	−0.270085
$356$	−24.8369	−1.31635
$357$	0.407294	0.0215563
$358$	−6.76589	−0.357588
$359$	19.5027	1.02931	0.514657	−	0.857396i	$-0.327919\pi$
$359$	19.5027	1.02931	0.514657	+	0.857396i	$0.327919\pi$
$360$	1.12577	0.0593333
$361$	6.45015	0.339482
$362$	3.58559	0.188454
$363$	5.19301	0.272563
$364$	2.06457	0.108213
$365$	−0.510965	−0.0267451
$366$	0.690525	0.0360943
$367$	21.1787	1.10552	0.552760	−	0.833341i	$-0.313575\pi$
$367$	21.1787	1.10552	0.552760	+	0.833341i	$0.313575\pi$
$368$	11.8828	0.619436
$369$	−0.318106	−0.0165599
$370$	−2.36108	−0.122746
$371$	9.83855	0.510792
$372$	1.91742	0.0994133
$373$	35.1021	1.81752	0.908760	−	0.417320i	$-0.137030\pi$
$373$	35.1021	1.81752	0.908760	+	0.417320i	$0.137030\pi$
$374$	0.261951	0.0135452
$375$	−1.00000	−0.0516398
$376$	−5.81971	−0.300129
$377$	−3.29421	−0.169661
$378$	−0.309430	−0.0159154
$379$	17.2029	0.883654	0.441827	−	0.897100i	$-0.354330\pi$
$379$	17.2029	0.883654	0.441827	+	0.897100i	$0.354330\pi$
$380$	−9.67300	−0.496215
$381$	−1.38729	−0.0710730
$382$	−3.03381	−0.155223
$383$	−2.25422	−0.115185	−0.0575927	−	0.998340i	$-0.518342\pi$
$383$	−2.25422	−0.115185	−0.0575927	+	0.998340i	$0.518342\pi$
$384$	−8.27006	−0.422030
$385$	2.59470	0.132238
$386$	−4.78461	−0.243530
$387$	−1.13876	−0.0578865
$388$	17.7734	0.902306
$389$	0.445579	0.0225917	0.0112959	−	0.999936i	$-0.496404\pi$
$389$	0.445579	0.0225917	0.0112959	+	0.999936i	$0.496404\pi$
$390$	0.287376	0.0145518
$391$	1.28011	0.0647377
$392$	−6.57520	−0.332098
$393$	9.38988	0.473657
$394$	2.24576	0.113140
$395$	14.5508	0.732132
$396$	4.62053	0.232190
$397$	−11.2649	−0.565371	−0.282686	−	0.959213i	$-0.591225\pi$
$397$	−11.2649	−0.565371	−0.282686	+	0.959213i	$0.591225\pi$
$398$	6.84720	0.343219
$399$	5.43197	0.271939
$400$	3.51131	0.175566
$401$	22.4490	1.12105	0.560526	−	0.828137i	$-0.310599\pi$
$401$	22.4490	1.12105	0.560526	+	0.828137i	$0.310599\pi$
$402$	−2.39488	−0.119446
$403$	1.00000	0.0498135
$404$	−25.6775	−1.27750
$405$	1.00000	0.0496904
$406$	−1.01933	−0.0505884
$407$	−19.7986	−0.981382
$408$	−0.425838	−0.0210821
$409$	−22.3957	−1.10739	−0.553697	−	0.832718i	$-0.686783\pi$
$409$	−22.3957	−1.10739	−0.553697	+	0.832718i	$0.686783\pi$
$410$	0.0914158	0.00451471
$411$	−12.2216	−0.602846
$412$	−22.8261	−1.12456
$413$	5.00628	0.246343
$414$	−0.972525	−0.0477970
$415$	9.57096	0.469820
$416$	−3.26061	−0.159864
$417$	−8.70902	−0.426483
$418$	3.49358	0.170877
$419$	15.2118	0.743147	0.371574	−	0.928403i	$-0.378818\pi$
$419$	15.2118	0.743147	0.371574	+	0.928403i	$0.378818\pi$
$420$	−2.06457	−0.100740
$421$	−1.73074	−0.0843509	−0.0421754	−	0.999110i	$-0.513429\pi$
$421$	−1.73074	−0.0843509	−0.0421754	+	0.999110i	$0.513429\pi$
$422$	−3.70489	−0.180351
$423$	−5.16954	−0.251352
$424$	−10.2865	−0.499557
$425$	0.378264	0.0183485
$426$	−1.46239	−0.0708532
$427$	−2.58727	−0.125207
$428$	−21.6534	−1.04666
$429$	2.40977	0.116345
$430$	0.327252	0.0157815
$431$	−0.804694	−0.0387608	−0.0193804	−	0.999812i	$-0.506169\pi$
$431$	−0.804694	−0.0387608	−0.0193804	+	0.999812i	$0.506169\pi$
$432$	−3.51131	−0.168938
$433$	7.50454	0.360645	0.180323	−	0.983608i	$-0.442286\pi$
$433$	7.50454	0.360645	0.180323	+	0.983608i	$0.442286\pi$
$434$	0.309430	0.0148531
$435$	3.29421	0.157945
$436$	30.6171	1.46629
$437$	17.0725	0.816686
$438$	−0.146839	−0.00701624
$439$	39.8019	1.89964	0.949820	−	0.312796i	$-0.101266\pi$
$439$	39.8019	1.89964	0.949820	+	0.312796i	$0.101266\pi$
$440$	−2.71285	−0.129330
$441$	−5.84062	−0.278125
$442$	−0.108704	−0.00517052
$443$	18.1586	0.862743	0.431372	−	0.902174i	$-0.358030\pi$
$443$	18.1586	0.862743	0.431372	+	0.902174i	$0.358030\pi$
$444$	15.7535	0.747626
$445$	12.9533	0.614045
$446$	−4.65984	−0.220650
$447$	22.2231	1.05112
$448$	6.55264	0.309583
$449$	15.6132	0.736833	0.368416	−	0.929661i	$-0.379900\pi$
$449$	15.6132	0.736833	0.368416	+	0.929661i	$0.379900\pi$
$450$	−0.287376	−0.0135470
$451$	0.766561	0.0360960
$452$	19.5498	0.919547
$453$	−3.29360	−0.154747
$454$	−5.03403	−0.236259
$455$	−1.07674	−0.0504785
$456$	−5.67930	−0.265958
$457$	12.6063	0.589696	0.294848	−	0.955544i	$-0.404731\pi$
$457$	12.6063	0.589696	0.294848	+	0.955544i	$0.404731\pi$
$458$	−5.10870	−0.238714
$459$	−0.378264	−0.0176559
$460$	−6.48884	−0.302544
$461$	4.61520	0.214951	0.107476	−	0.994208i	$-0.465723\pi$
$461$	4.61520	0.214951	0.107476	+	0.994208i	$0.465723\pi$
$462$	0.745655	0.0346910
$463$	30.4026	1.41293	0.706465	−	0.707748i	$-0.250289\pi$
$463$	30.4026	1.41293	0.706465	+	0.707748i	$0.250289\pi$
$464$	−11.5670	−0.536985
$465$	−1.00000	−0.0463739
$466$	1.08677	0.0503437
$467$	15.5516	0.719644	0.359822	−	0.933021i	$-0.382837\pi$
$467$	15.5516	0.719644	0.359822	+	0.933021i	$0.382837\pi$
$468$	−1.91742	−0.0886326
$469$	8.97317	0.414342
$470$	1.48560	0.0685256
$471$	13.8944	0.640221
$472$	−5.23423	−0.240925
$473$	2.74415	0.126176
$474$	4.18156	0.192065
$475$	5.04481	0.231472
$476$	0.780951	0.0357948
$477$	−9.13732	−0.418369
$478$	−5.59907	−0.256096
$479$	15.5440	0.710223	0.355112	−	0.934824i	$-0.384443\pi$
$479$	15.5440	0.710223	0.355112	+	0.934824i	$0.384443\pi$
$480$	3.26061	0.148826
$481$	8.21599	0.374617
$482$	−3.13573	−0.142828
$483$	3.64387	0.165802
$484$	9.95716	0.452598
$485$	−9.26944	−0.420904
$486$	0.287376	0.0130356
$487$	−25.6603	−1.16278	−0.581389	−	0.813626i	$-0.697491\pi$
$487$	−25.6603	−1.16278	−0.581389	+	0.813626i	$0.697491\pi$
$488$	2.70507	0.122453
$489$	−24.2256	−1.09552
$490$	1.67845	0.0758248
$491$	−10.2500	−0.462577	−0.231288	−	0.972885i	$-0.574294\pi$
$491$	−10.2500	−0.462577	−0.231288	+	0.972885i	$0.574294\pi$
$492$	−0.609941	−0.0274982
$493$	−1.24608	−0.0561207
$494$	−1.44976	−0.0652276
$495$	−2.40977	−0.108311
$496$	3.51131	0.157663
$497$	5.47932	0.245781
$498$	2.75046	0.123251
$499$	−29.7229	−1.33058	−0.665290	−	0.746585i	$-0.731692\pi$
$499$	−29.7229	−1.33058	−0.665290	+	0.746585i	$0.731692\pi$
$500$	−1.91742	−0.0857494
$501$	13.4729	0.601926
$502$	7.80557	0.348380
$503$	36.8784	1.64433	0.822163	−	0.569252i	$-0.192767\pi$
$503$	36.8784	1.64433	0.822163	+	0.569252i	$0.192767\pi$
$504$	−1.21217	−0.0539942
$505$	13.3917	0.595923
$506$	2.34356	0.104184
$507$	−1.00000	−0.0444116
$508$	−2.66001	−0.118019
$509$	−12.0039	−0.532062	−0.266031	−	0.963964i	$-0.585712\pi$
$509$	−12.0039	−0.532062	−0.266031	+	0.963964i	$0.585712\pi$
$510$	0.108704	0.00481349
$511$	0.550179	0.0243385
$512$	−19.3549	−0.855372
$513$	−5.04481	−0.222734
$514$	2.85187	0.125791
$515$	11.9046	0.524579
$516$	−2.18348	−0.0961223
$517$	12.4574	0.547876
$518$	2.54227	0.111701
$519$	6.48079	0.284475
$520$	1.12577	0.0493683
$521$	−27.7634	−1.21634	−0.608168	−	0.793808i	$-0.708095\pi$
$521$	−27.7634	−1.21634	−0.608168	+	0.793808i	$0.708095\pi$
$522$	0.946677	0.0414349
$523$	36.0726	1.57735	0.788673	−	0.614813i	$-0.210768\pi$
$523$	36.0726	1.57735	0.788673	+	0.614813i	$0.210768\pi$
$524$	18.0043	0.786522
$525$	1.07674	0.0469930
$526$	−0.315362	−0.0137504
$527$	0.378264	0.0164774
$528$	8.46145	0.368237
$529$	−11.5475	−0.502064
$530$	2.62584	0.114059
$531$	−4.64947	−0.201770
$532$	10.4153	0.451563
$533$	−0.318106	−0.0137787
$534$	3.72246	0.161087
$535$	11.2930	0.488239
$536$	−9.38173	−0.405229
$537$	−23.5437	−1.01599
$538$	−8.17600	−0.352492
$539$	14.0746	0.606234
$540$	1.91742	0.0825124
$541$	36.1399	1.55378	0.776889	−	0.629638i	$-0.216797\pi$
$541$	36.1399	1.55378	0.776889	+	0.629638i	$0.216797\pi$
$542$	9.21708	0.395908
$543$	12.4770	0.535440
$544$	−1.23337	−0.0528803
$545$	−15.9679	−0.683989
$546$	−0.309430	−0.0132424
$547$	18.6929	0.799251	0.399626	−	0.916678i	$-0.369140\pi$
$547$	18.6929	0.799251	0.399626	+	0.916678i	$0.369140\pi$
$548$	−23.4338	−1.00104
$549$	2.40286	0.102552
$550$	0.692509	0.0295287
$551$	−16.6187	−0.707980
$552$	−3.80978	−0.162155
$553$	−15.6675	−0.666251
$554$	−8.76643	−0.372450
$555$	−8.21599	−0.348749
$556$	−16.6988	−0.708187
$557$	−34.0394	−1.44230	−0.721148	−	0.692781i	$-0.756385\pi$
$557$	−34.0394	−1.44230	−0.721148	+	0.692781i	$0.756385\pi$
$558$	−0.287376	−0.0121656
$559$	−1.13876	−0.0481645
$560$	−3.78078	−0.159767
$561$	0.911529	0.0384848
$562$	1.07731	0.0454437
$563$	−10.6931	−0.450659	−0.225329	−	0.974283i	$-0.572346\pi$
$563$	−10.6931	−0.450659	−0.225329	+	0.974283i	$0.572346\pi$
$564$	−9.91215	−0.417377
$565$	−10.1959	−0.428946
$566$	−4.31716	−0.181464
$567$	−1.07674	−0.0452190
$568$	−5.72880	−0.240375
$569$	−9.51454	−0.398870	−0.199435	−	0.979911i	$-0.563911\pi$
$569$	−9.51454	−0.398870	−0.199435	+	0.979911i	$0.563911\pi$
$570$	1.44976	0.0607236
$571$	1.29748	0.0542978	0.0271489	−	0.999631i	$-0.491357\pi$
$571$	1.29748	0.0542978	0.0271489	+	0.999631i	$0.491357\pi$
$572$	4.62053	0.193194
$573$	−10.5570	−0.441023
$574$	−0.0984314	−0.00410845
$575$	3.38416	0.141129
$576$	−6.08560	−0.253567
$577$	22.4632	0.935153	0.467577	−	0.883953i	$-0.345127\pi$
$577$	22.4632	0.935153	0.467577	+	0.883953i	$0.345127\pi$
$578$	4.84427	0.201495
$579$	−16.6493	−0.691922
$580$	6.31638	0.262273
$581$	−10.3055	−0.427543
$582$	−2.66381	−0.110419
$583$	22.0188	0.911927
$584$	−0.575229	−0.0238031
$585$	1.00000	0.0413449
$586$	−2.95486	−0.122064
$587$	−19.7692	−0.815964	−0.407982	−	0.912990i	$-0.633767\pi$
$587$	−19.7692	−0.815964	−0.407982	+	0.912990i	$0.633767\pi$
$588$	−11.1989	−0.461835
$589$	5.04481	0.207868
$590$	1.33614	0.0550082
$591$	7.81470	0.321454
$592$	28.8489	1.18568
$593$	24.1044	0.989851	0.494925	−	0.868935i	$-0.335195\pi$
$593$	24.1044	0.989851	0.494925	+	0.868935i	$0.335195\pi$
$594$	−0.692509	−0.0284140
$595$	−0.407294	−0.0166974
$596$	42.6110	1.74541
$597$	23.8267	0.975160
$598$	−0.972525	−0.0397695
$599$	29.4034	1.20139	0.600695	−	0.799478i	$-0.294890\pi$
$599$	29.4034	1.20139	0.600695	+	0.799478i	$0.294890\pi$
$600$	−1.12577	−0.0459594
$601$	41.8736	1.70806	0.854029	−	0.520225i	$-0.174152\pi$
$601$	41.8736	1.70806	0.854029	+	0.520225i	$0.174152\pi$
$602$	−0.352367	−0.0143614
$603$	−8.33361	−0.339371
$604$	−6.31519	−0.256962
$605$	−5.19301	−0.211126
$606$	3.84845	0.156333
$607$	−0.335008	−0.0135976	−0.00679878	−	0.999977i	$-0.502164\pi$
$607$	−0.335008	−0.0135976	−0.00679878	+	0.999977i	$0.502164\pi$
$608$	−16.4491	−0.667101
$609$	−3.54703	−0.143733
$610$	−0.690525	−0.0279585
$611$	−5.16954	−0.209137
$612$	−0.725289	−0.0293181
$613$	20.9737	0.847119	0.423560	−	0.905868i	$-0.360780\pi$
$613$	20.9737	0.847119	0.423560	+	0.905868i	$0.360780\pi$
$614$	−0.361663	−0.0145955
$615$	0.318106	0.0128273
$616$	2.92104	0.117692
$617$	−26.8288	−1.08009	−0.540043	−	0.841638i	$-0.681592\pi$
$617$	−26.8288	−1.08009	−0.540043	+	0.841638i	$0.681592\pi$
$618$	3.42109	0.137617
$619$	−49.5795	−1.99277	−0.996385	−	0.0849554i	$-0.972925\pi$
$619$	−49.5795	−1.99277	−0.996385	+	0.0849554i	$0.972925\pi$
$620$	−1.91742	−0.0770052
$621$	−3.38416	−0.135802
$622$	−4.06625	−0.163042
$623$	−13.9474	−0.558790
$624$	−3.51131	−0.140565
$625$	1.00000	0.0400000
$626$	2.08611	0.0833779
$627$	12.1568	0.485497
$628$	26.6414	1.06311
$629$	3.10781	0.123917
$630$	0.309430	0.0123280
$631$	−30.1353	−1.19967	−0.599833	−	0.800125i	$-0.704766\pi$
$631$	−30.1353	−1.19967	−0.599833	+	0.800125i	$0.704766\pi$
$632$	16.3809	0.651597
$633$	−12.8921	−0.512417
$634$	−3.11936	−0.123886
$635$	1.38729	0.0550529
$636$	−17.5200	−0.694714
$637$	−5.84062	−0.231414
$638$	−2.28127	−0.0903165
$639$	−5.08878	−0.201309
$640$	8.27006	0.326903
$641$	−47.7547	−1.88620	−0.943099	−	0.332512i	$-0.892104\pi$
$641$	−47.7547	−1.88620	−0.943099	+	0.332512i	$0.892104\pi$
$642$	3.24534	0.128083
$643$	−25.7266	−1.01456	−0.507280	−	0.861781i	$-0.669349\pi$
$643$	−25.7266	−1.01456	−0.507280	+	0.861781i	$0.669349\pi$
$644$	6.98682	0.275319
$645$	1.13876	0.0448387
$646$	−0.548391	−0.0215761
$647$	−20.9903	−0.825215	−0.412608	−	0.910909i	$-0.635382\pi$
$647$	−20.9903	−0.825215	−0.412608	+	0.910909i	$0.635382\pi$
$648$	1.12577	0.0442244
$649$	11.2041	0.439801
$650$	−0.287376	−0.0112718
$651$	1.07674	0.0422009
$652$	−46.4506	−1.81914
$653$	−6.70137	−0.262245	−0.131122	−	0.991366i	$-0.541858\pi$
$653$	−6.70137	−0.262245	−0.131122	+	0.991366i	$0.541858\pi$
$654$	−4.58878	−0.179436
$655$	−9.38988	−0.366893
$656$	−1.11697	−0.0436103
$657$	−0.510965	−0.0199346
$658$	−1.59961	−0.0623593
$659$	9.15243	0.356528	0.178264	−	0.983983i	$-0.442952\pi$
$659$	9.15243	0.356528	0.178264	+	0.983983i	$0.442952\pi$
$660$	−4.62053	−0.179854
$661$	−14.7736	−0.574626	−0.287313	−	0.957837i	$-0.592762\pi$
$661$	−14.7736	−0.574626	−0.287313	+	0.957837i	$0.592762\pi$
$662$	0.556402	0.0216252
$663$	−0.378264	−0.0146906
$664$	10.7747	0.418140
$665$	−5.43197	−0.210643
$666$	−2.36108	−0.0914898
$667$	−11.1481	−0.431658
$668$	25.8332	0.999517
$669$	−16.2151	−0.626914
$670$	2.39488	0.0925222
$671$	−5.79035	−0.223534
$672$	−3.51084	−0.135433
$673$	38.3930	1.47994	0.739970	−	0.672640i	$-0.234840\pi$
$673$	38.3930	1.47994	0.739970	+	0.672640i	$0.234840\pi$
$674$	−1.74275	−0.0671281
$675$	−1.00000	−0.0384900
$676$	−1.91742	−0.0737467
$677$	−22.3881	−0.860445	−0.430223	−	0.902723i	$-0.641565\pi$
$677$	−22.3881	−0.860445	−0.430223	+	0.902723i	$0.641565\pi$
$678$	−2.93006	−0.112528
$679$	9.98081	0.383028
$680$	0.425838	0.0163301
$681$	−17.5172	−0.671262
$682$	0.692509	0.0265175
$683$	−0.884348	−0.0338386	−0.0169193	−	0.999857i	$-0.505386\pi$
$683$	−0.884348	−0.0338386	−0.0169193	+	0.999857i	$0.505386\pi$
$684$	−9.67300	−0.369857
$685$	12.2216	0.466962
$686$	−3.97327	−0.151700
$687$	−17.7771	−0.678238
$688$	−3.99855	−0.152443
$689$	−9.13732	−0.348104
$690$	0.972525	0.0370234
$691$	51.3435	1.95320	0.976599	−	0.215070i	$-0.0689981\pi$
$691$	51.3435	1.95320	0.976599	+	0.215070i	$0.0689981\pi$
$692$	12.4264	0.472380
$693$	2.59470	0.0985647
$694$	9.18634	0.348709
$695$	8.70902	0.330352
$696$	3.70853	0.140571
$697$	−0.120328	−0.00455774
$698$	−8.66788	−0.328084
$699$	3.78171	0.143037
$700$	2.06457	0.0780332
$701$	−29.6727	−1.12072	−0.560362	−	0.828248i	$-0.689338\pi$
$701$	−29.6727	−1.12072	−0.560362	+	0.828248i	$0.689338\pi$
$702$	0.287376	0.0108463
$703$	41.4481	1.56325
$704$	14.6649	0.552704
$705$	5.16954	0.194696
$706$	−3.83798	−0.144444
$707$	−14.4194	−0.542299
$708$	−8.91496	−0.335045
$709$	−11.6049	−0.435832	−0.217916	−	0.975967i	$-0.569926\pi$
$709$	−11.6049	−0.435832	−0.217916	+	0.975967i	$0.569926\pi$
$710$	1.46239	0.0548826
$711$	14.5508	0.545699
$712$	14.5824	0.546500
$713$	3.38416	0.126738
$714$	−0.117046	−0.00438035
$715$	−2.40977	−0.0901202
$716$	−45.1431	−1.68708
$717$	−19.4835	−0.727623
$718$	−5.60461	−0.209162
$719$	26.0217	0.970444	0.485222	−	0.874391i	$-0.338739\pi$
$719$	26.0217	0.970444	0.485222	+	0.874391i	$0.338739\pi$
$720$	3.51131	0.130859
$721$	−12.8182	−0.477375
$722$	−1.85362	−0.0689845
$723$	−10.9116	−0.405807
$724$	23.9236	0.889114
$725$	−3.29421	−0.122344
$726$	−1.49235	−0.0553861
$727$	31.7167	1.17631	0.588153	−	0.808750i	$-0.299855\pi$
$727$	31.7167	1.17631	0.588153	+	0.808750i	$0.299855\pi$
$728$	−1.21217	−0.0449259
$729$	1.00000	0.0370370
$730$	0.146839	0.00543475
$731$	−0.430753	−0.0159320
$732$	4.60729	0.170290
$733$	−20.1847	−0.745541	−0.372770	−	0.927924i	$-0.621592\pi$
$733$	−20.1847	−0.745541	−0.372770	+	0.927924i	$0.621592\pi$
$734$	−6.08624	−0.224647
$735$	5.84062	0.215435
$736$	−11.0344	−0.406734
$737$	20.0821	0.739733
$738$	0.0914158	0.00336506
$739$	37.9143	1.39470	0.697349	−	0.716731i	$-0.254363\pi$
$739$	37.9143	1.39470	0.697349	+	0.716731i	$0.254363\pi$
$740$	−15.7535	−0.579109
$741$	−5.04481	−0.185326
$742$	−2.82736	−0.103796
$743$	13.0426	0.478486	0.239243	−	0.970960i	$-0.423101\pi$
$743$	13.0426	0.478486	0.239243	+	0.970960i	$0.423101\pi$
$744$	−1.12577	−0.0412727
$745$	−22.2231	−0.814192
$746$	−10.0875	−0.369330
$747$	9.57096	0.350183
$748$	1.74778	0.0639051
$749$	−12.1597	−0.444305
$750$	0.287376	0.0104935
$751$	−18.8873	−0.689206	−0.344603	−	0.938748i	$-0.611987\pi$
$751$	−18.8873	−0.689206	−0.344603	+	0.938748i	$0.611987\pi$
$752$	−18.1519	−0.661930
$753$	27.1616	0.989822
$754$	0.946677	0.0344759
$755$	3.29360	0.119866
$756$	−2.06457	−0.0750875
$757$	13.8985	0.505148	0.252574	−	0.967578i	$-0.418723\pi$
$757$	13.8985	0.505148	0.252574	+	0.967578i	$0.418723\pi$
$758$	−4.94370	−0.179563
$759$	8.15504	0.296009
$760$	5.67930	0.206010
$761$	−36.4598	−1.32167	−0.660833	−	0.750533i	$-0.729797\pi$
$761$	−36.4598	−1.32167	−0.660833	+	0.750533i	$0.729797\pi$
$762$	0.398673	0.0144424
$763$	17.1933	0.622440
$764$	−20.2421	−0.732332
$765$	0.378264	0.0136762
$766$	0.647808	0.0234063
$767$	−4.64947	−0.167882
$768$	−9.79459	−0.353432
$769$	23.9579	0.863943	0.431972	−	0.901887i	$-0.357818\pi$
$769$	23.9579	0.863943	0.431972	+	0.901887i	$0.357818\pi$
$770$	−0.745655	−0.0268715
$771$	9.92385	0.357399
$772$	−31.9236	−1.14896
$773$	34.0037	1.22303	0.611514	−	0.791234i	$-0.290561\pi$
$773$	34.0037	1.22303	0.611514	+	0.791234i	$0.290561\pi$
$774$	0.327252	0.0117628
$775$	1.00000	0.0359211
$776$	−10.4353	−0.374604
$777$	8.84652	0.317367
$778$	−0.128048	−0.00459076
$779$	−1.60478	−0.0574973
$780$	1.91742	0.0686545
$781$	12.2628	0.438797
$782$	−0.367871	−0.0131550
$783$	3.29421	0.117726
$784$	−20.5082	−0.732437
$785$	−13.8944	−0.495913
$786$	−2.69842	−0.0962496
$787$	−15.5770	−0.555260	−0.277630	−	0.960688i	$-0.589549\pi$
$787$	−15.5770	−0.555260	−0.277630	+	0.960688i	$0.589549\pi$
$788$	14.9840	0.533784
$789$	−1.09739	−0.0390680
$790$	−4.18156	−0.148773
$791$	10.9784	0.390347
$792$	−2.71285	−0.0963968
$793$	2.40286	0.0853282
$794$	3.23727	0.114886
$795$	9.13732	0.324067
$796$	45.6856	1.61928
$797$	−12.3212	−0.436439	−0.218219	−	0.975900i	$-0.570025\pi$
$797$	−12.3212	−0.436439	−0.218219	+	0.975900i	$0.570025\pi$
$798$	−1.56102	−0.0552594
$799$	−1.95545	−0.0691789
$800$	−3.26061	−0.115280
$801$	12.9533	0.457682
$802$	−6.45131	−0.227804
$803$	1.23131	0.0434519
$804$	−15.9790	−0.563536
$805$	−3.64387	−0.128430
$806$	−0.287376	−0.0101224
$807$	−28.4506	−1.00151
$808$	15.0760	0.530371
$809$	−15.0947	−0.530702	−0.265351	−	0.964152i	$-0.585488\pi$
$809$	−15.0947	−0.530702	−0.265351	+	0.964152i	$0.585488\pi$
$810$	−0.287376	−0.0100974
$811$	−18.4691	−0.648539	−0.324269	−	0.945965i	$-0.605118\pi$
$811$	−18.4691	−0.648539	−0.324269	+	0.945965i	$0.605118\pi$
$812$	−6.80112	−0.238673
$813$	32.0733	1.12486
$814$	5.68965	0.199422
$815$	24.2256	0.848586
$816$	−1.32820	−0.0464964
$817$	−5.74484	−0.200987
$818$	6.43597	0.225028
$819$	−1.07674	−0.0376245
$820$	0.609941	0.0213000
$821$	−32.8771	−1.14742	−0.573710	−	0.819059i	$-0.694496\pi$
$821$	−32.8771	−1.14742	−0.573710	+	0.819059i	$0.694496\pi$
$822$	3.51218	0.122501
$823$	37.8492	1.31934	0.659671	−	0.751555i	$-0.270696\pi$
$823$	37.8492	1.31934	0.659671	+	0.751555i	$0.270696\pi$
$824$	13.4018	0.466875
$825$	2.40977	0.0838974
$826$	−1.43868	−0.0500582
$827$	−22.5280	−0.783374	−0.391687	−	0.920099i	$-0.628108\pi$
$827$	−22.5280	−0.783374	−0.391687	+	0.920099i	$0.628108\pi$
$828$	−6.48884	−0.225503
$829$	−26.6391	−0.925214	−0.462607	−	0.886564i	$-0.653086\pi$
$829$	−26.6391	−0.925214	−0.462607	+	0.886564i	$0.653086\pi$
$830$	−2.75046	−0.0954699
$831$	−30.5051	−1.05821
$832$	−6.08560	−0.210980
$833$	−2.20930	−0.0765476
$834$	2.50276	0.0866635
$835$	−13.4729	−0.466250
$836$	23.3097	0.806183
$837$	−1.00000	−0.0345651
$838$	−4.37152	−0.151011
$839$	−52.4236	−1.80986	−0.904932	−	0.425557i	$-0.860078\pi$
$839$	−52.4236	−1.80986	−0.904932	+	0.425557i	$0.860078\pi$
$840$	1.21217	0.0418237
$841$	−18.1482	−0.625798
$842$	0.497371	0.0171405
$843$	3.74879	0.129115
$844$	−24.7196	−0.850883
$845$	1.00000	0.0344010
$846$	1.48560	0.0510760
$847$	5.59155	0.192128
$848$	−32.0840	−1.10177
$849$	−15.0227	−0.515578
$850$	−0.108704	−0.00372851
$851$	27.8042	0.953116
$852$	−9.75731	−0.334280
$853$	47.0067	1.60948	0.804739	−	0.593629i	$-0.202305\pi$
$853$	47.0067	1.60948	0.804739	+	0.593629i	$0.202305\pi$
$854$	0.743518	0.0254427
$855$	5.04481	0.172529
$856$	12.7133	0.434533
$857$	22.3366	0.763003	0.381501	−	0.924368i	$-0.375407\pi$
$857$	22.3366	0.763003	0.381501	+	0.924368i	$0.375407\pi$
$858$	−0.692509	−0.0236419
$859$	38.2764	1.30597	0.652987	−	0.757369i	$-0.273516\pi$
$859$	38.2764	1.30597	0.652987	+	0.757369i	$0.273516\pi$
$860$	2.18348	0.0744560
$861$	−0.342518	−0.0116730
$862$	0.231249	0.00787639
$863$	−3.98863	−0.135774	−0.0678872	−	0.997693i	$-0.521626\pi$
$863$	−3.98863	−0.135774	−0.0678872	+	0.997693i	$0.521626\pi$
$864$	3.26061	0.110928
$865$	−6.48079	−0.220354
$866$	−2.15662	−0.0732850
$867$	16.8569	0.572491
$868$	2.06457	0.0700759
$869$	−35.0642	−1.18947
$870$	−0.946677	−0.0320954
$871$	−8.33361	−0.282374
$872$	−17.9762	−0.608750
$873$	−9.26944	−0.313723
$874$	−4.90621	−0.165955
$875$	−1.07674	−0.0364006
$876$	−0.979732	−0.0331021
$877$	11.3112	0.381954	0.190977	−	0.981595i	$-0.438834\pi$
$877$	11.3112	0.381954	0.190977	+	0.981595i	$0.438834\pi$
$878$	−11.4381	−0.386017
$879$	−10.2822	−0.346811
$880$	−8.46145	−0.285235
$881$	−45.6362	−1.53752	−0.768762	−	0.639535i	$-0.779127\pi$
$881$	−45.6362	−1.53752	−0.768762	+	0.639535i	$0.779127\pi$
$882$	1.67845	0.0565164
$883$	−7.23848	−0.243594	−0.121797	−	0.992555i	$-0.538866\pi$
$883$	−7.23848	−0.243594	−0.121797	+	0.992555i	$0.538866\pi$
$884$	−0.725289	−0.0243941
$885$	4.64947	0.156290
$886$	−5.21835	−0.175314
$887$	45.3405	1.52238	0.761192	−	0.648526i	$-0.224614\pi$
$887$	45.3405	1.52238	0.761192	+	0.648526i	$0.224614\pi$
$888$	−9.24931	−0.310387
$889$	−1.49376	−0.0500990
$890$	−3.72246	−0.124777
$891$	−2.40977	−0.0807303
$892$	−31.0912	−1.04101
$893$	−26.0794	−0.872713
$894$	−6.38639	−0.213593
$895$	23.5437	0.786979
$896$	−8.90474	−0.297487
$897$	−3.38416	−0.112994
$898$	−4.48686	−0.149728
$899$	−3.29421	−0.109868
$900$	−1.91742	−0.0639138
$901$	−3.45632	−0.115147
$902$	−0.220291	−0.00733489
$903$	−1.22615	−0.0408039
$904$	−11.4783	−0.381762
$905$	−12.4770	−0.414750
$906$	0.946500	0.0314454
$907$	18.2301	0.605319	0.302660	−	0.953099i	$-0.402125\pi$
$907$	18.2301	0.605319	0.302660	+	0.953099i	$0.402125\pi$
$908$	−33.5878	−1.11465
$909$	13.3917	0.444175
$910$	0.309430	0.0102575
$911$	−46.4499	−1.53895	−0.769477	−	0.638675i	$-0.779483\pi$
$911$	−46.4499	−1.53895	−0.769477	+	0.638675i	$0.779483\pi$
$912$	−17.7139	−0.586566
$913$	−23.0638	−0.763301
$914$	−3.62273	−0.119829
$915$	−2.40286	−0.0794362
$916$	−34.0860	−1.12623
$917$	10.1105	0.333878
$918$	0.108704	0.00358776
$919$	−22.4815	−0.741595	−0.370798	−	0.928714i	$-0.620916\pi$
$919$	−22.4815	−0.741595	−0.370798	+	0.928714i	$0.620916\pi$
$920$	3.80978	0.125605
$921$	−1.25850	−0.0414691
$922$	−1.32630	−0.0436792
$923$	−5.08878	−0.167499
$924$	4.97513	0.163670
$925$	8.21599	0.270140
$926$	−8.73698	−0.287115
$927$	11.9046	0.390998
$928$	10.7411	0.352595
$929$	−10.0878	−0.330971	−0.165485	−	0.986212i	$-0.552919\pi$
$929$	−10.0878	−0.330971	−0.165485	+	0.986212i	$0.552919\pi$
$930$	0.287376	0.00942342
$931$	−29.4649	−0.965672
$932$	7.25110	0.237518
$933$	−14.1496	−0.463237
$934$	−4.46916	−0.146236
$935$	−0.911529	−0.0298102
$936$	1.12577	0.0367969
$937$	3.94800	0.128976	0.0644878	−	0.997918i	$-0.479459\pi$
$937$	3.94800	0.128976	0.0644878	+	0.997918i	$0.479459\pi$
$938$	−2.57867	−0.0841965
$939$	7.25919	0.236895
$940$	9.91215	0.323299
$941$	−60.0194	−1.95658	−0.978288	−	0.207249i	$-0.933549\pi$
$941$	−60.0194	−1.95658	−0.978288	+	0.207249i	$0.933549\pi$
$942$	−3.99292	−0.130096
$943$	−1.07652	−0.0350563
$944$	−16.3257	−0.531357
$945$	1.07674	0.0350265
$946$	−0.788603	−0.0256397
$947$	37.9340	1.23269	0.616345	−	0.787476i	$-0.288613\pi$
$947$	37.9340	1.23269	0.616345	+	0.787476i	$0.288613\pi$
$948$	27.9000	0.906150
$949$	−0.510965	−0.0165866
$950$	−1.44976	−0.0470363
$951$	−10.8546	−0.351986
$952$	−0.458519	−0.0148607
$953$	28.5082	0.923472	0.461736	−	0.887017i	$-0.347227\pi$
$953$	28.5082	0.923472	0.461736	+	0.887017i	$0.347227\pi$
$954$	2.62584	0.0850148
$955$	10.5570	0.341615
$956$	−37.3579	−1.20824
$957$	−7.93830	−0.256609
$958$	−4.46697	−0.144321
$959$	−13.1595	−0.424943
$960$	6.08560	0.196412
$961$	1.00000	0.0322581
$962$	−2.36108	−0.0761241
$963$	11.2930	0.363912
$964$	−20.9221	−0.673854
$965$	16.6493	0.535960
$966$	−1.04716	−0.0336918
$967$	5.60181	0.180142	0.0900711	−	0.995935i	$-0.471291\pi$
$967$	5.60181	0.180142	0.0900711	+	0.995935i	$0.471291\pi$
$968$	−5.84614	−0.187902
$969$	−1.90827	−0.0613025
$970$	2.66381	0.0855298
$971$	−12.7765	−0.410016	−0.205008	−	0.978760i	$-0.565722\pi$
$971$	−12.7765	−0.410016	−0.205008	+	0.978760i	$0.565722\pi$
$972$	1.91742	0.0615011
$973$	−9.37738	−0.300625
$974$	7.37414	0.236283
$975$	−1.00000	−0.0320256
$976$	8.43720	0.270068
$977$	46.4750	1.48687	0.743433	−	0.668811i	$-0.233196\pi$
$977$	46.4750	1.48687	0.743433	+	0.668811i	$0.233196\pi$
$978$	6.96185	0.222615
$979$	−31.2145	−0.997618
$980$	11.1989	0.357736
$981$	−15.9679	−0.509816
$982$	2.94561	0.0939981
$983$	−16.6620	−0.531435	−0.265717	−	0.964051i	$-0.585609\pi$
$983$	−16.6620	−0.531435	−0.265717	+	0.964051i	$0.585609\pi$
$984$	0.358114	0.0114162
$985$	−7.81470	−0.248997
$986$	0.358094	0.0114040
$987$	−5.56627	−0.177176
$988$	−9.67300	−0.307739
$989$	−3.85375	−0.122542
$990$	0.692509	0.0220094
$991$	4.87161	0.154752	0.0773759	−	0.997002i	$-0.475346\pi$
$991$	4.87161	0.154752	0.0773759	+	0.997002i	$0.475346\pi$
$992$	−3.26061	−0.103524
$993$	1.93615	0.0614418
$994$	−1.57462	−0.0499440
$995$	−23.8267	−0.755356
$996$	18.3515	0.581490
$997$	10.7439	0.340262	0.170131	−	0.985421i	$-0.445581\pi$
$997$	10.7439	0.340262	0.170131	+	0.985421i	$0.445581\pi$
$998$	8.54164	0.270381
$999$	−8.21599	−0.259942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.8	✓	17	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)

\(f(q)\)	\(=\)	\(q-0.287376 q^{2} -1.00000 q^{3} -1.91742 q^{4} +1.00000 q^{5} +0.287376 q^{6} -1.07674 q^{7} +1.12577 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.287376 q^{2} -1.00000 q^{3} -1.91742 q^{4} +1.00000 q^{5} +0.287376 q^{6} -1.07674 q^{7} +1.12577 q^{8} +1.00000 q^{9} -0.287376 q^{10} -2.40977 q^{11} +1.91742 q^{12} +1.00000 q^{13} +0.309430 q^{14} -1.00000 q^{15} +3.51131 q^{16} +0.378264 q^{17} -0.287376 q^{18} +5.04481 q^{19} -1.91742 q^{20} +1.07674 q^{21} +0.692509 q^{22} +3.38416 q^{23} -1.12577 q^{24} +1.00000 q^{25} -0.287376 q^{26} -1.00000 q^{27} +2.06457 q^{28} -3.29421 q^{29} +0.287376 q^{30} +1.00000 q^{31} -3.26061 q^{32} +2.40977 q^{33} -0.108704 q^{34} -1.07674 q^{35} -1.91742 q^{36} +8.21599 q^{37} -1.44976 q^{38} -1.00000 q^{39} +1.12577 q^{40} -0.318106 q^{41} -0.309430 q^{42} -1.13876 q^{43} +4.62053 q^{44} +1.00000 q^{45} -0.972525 q^{46} -5.16954 q^{47} -3.51131 q^{48} -5.84062 q^{49} -0.287376 q^{50} -0.378264 q^{51} -1.91742 q^{52} -9.13732 q^{53} +0.287376 q^{54} -2.40977 q^{55} -1.21217 q^{56} -5.04481 q^{57} +0.946677 q^{58} -4.64947 q^{59} +1.91742 q^{60} +2.40286 q^{61} -0.287376 q^{62} -1.07674 q^{63} -6.08560 q^{64} +1.00000 q^{65} -0.692509 q^{66} -8.33361 q^{67} -0.725289 q^{68} -3.38416 q^{69} +0.309430 q^{70} -5.08878 q^{71} +1.12577 q^{72} -0.510965 q^{73} -2.36108 q^{74} -1.00000 q^{75} -9.67300 q^{76} +2.59470 q^{77} +0.287376 q^{78} +14.5508 q^{79} +3.51131 q^{80} +1.00000 q^{81} +0.0914158 q^{82} +9.57096 q^{83} -2.06457 q^{84} +0.378264 q^{85} +0.327252 q^{86} +3.29421 q^{87} -2.71285 q^{88} +12.9533 q^{89} -0.287376 q^{90} -1.07674 q^{91} -6.48884 q^{92} -1.00000 q^{93} +1.48560 q^{94} +5.04481 q^{95} +3.26061 q^{96} -9.26944 q^{97} +1.67845 q^{98} -2.40977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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