LMFDB - Embedded newform 287.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(1,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("287.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.08727$ of defining polynomial
Character	$\chi$	$=$	287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.08727 q^{2} +2.08727 q^{3} -0.817843 q^{4} +0.209668 q^{5} +2.26943 q^{6} +1.00000 q^{7} -3.06376 q^{8} +1.35670 q^{9} +O(q^{10})$	\(q+1.08727 q^{2} +2.08727 q^{3} -0.817843 q^{4} +0.209668 q^{5} +2.26943 q^{6} +1.00000 q^{7} -3.06376 q^{8} +1.35670 q^{9} +0.227965 q^{10} +6.03819 q^{11} -1.70706 q^{12} +3.67193 q^{13} +1.08727 q^{14} +0.437633 q^{15} -1.69545 q^{16} -5.37138 q^{17} +1.47510 q^{18} -3.54285 q^{19} -0.171475 q^{20} +2.08727 q^{21} +6.56515 q^{22} -1.30362 q^{23} -6.39489 q^{24} -4.95604 q^{25} +3.99238 q^{26} -3.43002 q^{27} -0.817843 q^{28} -8.00307 q^{29} +0.475825 q^{30} -0.384208 q^{31} +4.28411 q^{32} +12.6033 q^{33} -5.84014 q^{34} +0.209668 q^{35} -1.10957 q^{36} -3.68876 q^{37} -3.85204 q^{38} +7.66432 q^{39} -0.642370 q^{40} -1.00000 q^{41} +2.26943 q^{42} +0.824527 q^{43} -4.93829 q^{44} +0.284455 q^{45} -1.41739 q^{46} +5.11625 q^{47} -3.53885 q^{48} +1.00000 q^{49} -5.38855 q^{50} -11.2115 q^{51} -3.00307 q^{52} +1.53217 q^{53} -3.72936 q^{54} +1.26601 q^{55} -3.06376 q^{56} -7.39489 q^{57} -8.70150 q^{58} +10.2669 q^{59} -0.357915 q^{60} +9.36070 q^{61} -0.417738 q^{62} +1.35670 q^{63} +8.04887 q^{64} +0.769885 q^{65} +13.7032 q^{66} +11.3638 q^{67} +4.39294 q^{68} -2.72101 q^{69} +0.227965 q^{70} -14.9494 q^{71} -4.15659 q^{72} +7.77203 q^{73} -4.01068 q^{74} -10.3446 q^{75} +2.89750 q^{76} +6.03819 q^{77} +8.33318 q^{78} -6.04703 q^{79} -0.355480 q^{80} -11.2295 q^{81} -1.08727 q^{82} +14.1871 q^{83} -1.70706 q^{84} -1.12620 q^{85} +0.896484 q^{86} -16.7046 q^{87} -18.4996 q^{88} +0.520905 q^{89} +0.309280 q^{90} +3.67193 q^{91} +1.06616 q^{92} -0.801946 q^{93} +5.56275 q^{94} -0.742821 q^{95} +8.94209 q^{96} -3.65270 q^{97} +1.08727 q^{98} +8.19200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q - q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 12 * q^6 + 5 * q^7 - 3 * q^8 + q^9	\( 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9} + 2 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - 5 q^{15} - q^{16} + 13 q^{17} + 21 q^{18} - 23 q^{20} + 4 q^{21} + q^{22} + 2 q^{23} + 2 q^{24} + 22 q^{25} + 10 q^{27} + 3 q^{28} - 5 q^{29} - 33 q^{30} + 17 q^{31} - 12 q^{32} + 3 q^{33} - 8 q^{34} - 5 q^{35} + 15 q^{36} - 7 q^{37} - 3 q^{38} + 5 q^{39} + 7 q^{40} - 5 q^{41} + 12 q^{42} + q^{43} - 47 q^{44} - 23 q^{45} - 24 q^{46} + 9 q^{47} - 19 q^{48} + 5 q^{49} + 2 q^{50} + 5 q^{51} + 20 q^{52} + 5 q^{53} + 2 q^{54} + 33 q^{55} - 3 q^{56} - 3 q^{57} - 27 q^{58} + 7 q^{59} - 16 q^{60} + 22 q^{61} - 28 q^{62} + q^{63} - 3 q^{64} - 31 q^{65} - 42 q^{66} - 3 q^{67} + 17 q^{68} - 22 q^{69} - 24 q^{71} - 12 q^{72} + 40 q^{73} - 5 q^{74} + 24 q^{75} - 19 q^{76} + 2 q^{77} + 30 q^{78} - 42 q^{79} + 24 q^{80} + 9 q^{81} + q^{82} - 12 q^{83} - 2 q^{84} - 23 q^{85} + 16 q^{86} - 32 q^{87} + 26 q^{88} + 8 q^{89} - 59 q^{90} + 5 q^{91} + 12 q^{92} - 11 q^{93} - 23 q^{94} - 17 q^{95} - 17 q^{96} + 16 q^{97} - q^{98} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 12 * q^6 + 5 * q^7 - 3 * q^8 + q^9 + 2 * q^11 - 2 * q^12 + 5 * q^13 - q^14 - 5 * q^15 - q^16 + 13 * q^17 + 21 * q^18 - 23 * q^20 + 4 * q^21 + q^22 + 2 * q^23 + 2 * q^24 + 22 * q^25 + 10 * q^27 + 3 * q^28 - 5 * q^29 - 33 * q^30 + 17 * q^31 - 12 * q^32 + 3 * q^33 - 8 * q^34 - 5 * q^35 + 15 * q^36 - 7 * q^37 - 3 * q^38 + 5 * q^39 + 7 * q^40 - 5 * q^41 + 12 * q^42 + q^43 - 47 * q^44 - 23 * q^45 - 24 * q^46 + 9 * q^47 - 19 * q^48 + 5 * q^49 + 2 * q^50 + 5 * q^51 + 20 * q^52 + 5 * q^53 + 2 * q^54 + 33 * q^55 - 3 * q^56 - 3 * q^57 - 27 * q^58 + 7 * q^59 - 16 * q^60 + 22 * q^61 - 28 * q^62 + q^63 - 3 * q^64 - 31 * q^65 - 42 * q^66 - 3 * q^67 + 17 * q^68 - 22 * q^69 - 24 * q^71 - 12 * q^72 + 40 * q^73 - 5 * q^74 + 24 * q^75 - 19 * q^76 + 2 * q^77 + 30 * q^78 - 42 * q^79 + 24 * q^80 + 9 * q^81 + q^82 - 12 * q^83 - 2 * q^84 - 23 * q^85 + 16 * q^86 - 32 * q^87 + 26 * q^88 + 8 * q^89 - 59 * q^90 + 5 * q^91 + 12 * q^92 - 11 * q^93 - 23 * q^94 - 17 * q^95 - 17 * q^96 + 16 * q^97 - q^98 - 45 * 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 $

$2$	1.08727	0.768816	0.384408	−	0.923163i	$-0.374406\pi$
$2$	1.08727	0.768816	0.384408	+	0.923163i	$0.374406\pi$
$3$	2.08727	1.20509	0.602543	−	0.798086i	$-0.294154\pi$
$3$	2.08727	1.20509	0.602543	+	0.798086i	$0.294154\pi$
$4$	−0.817843	−0.408922
$5$	0.209668	0.0937662	0.0468831	−	0.998900i	$-0.485071\pi$
$5$	0.209668	0.0937662	0.0468831	+	0.998900i	$0.485071\pi$
$6$	2.26943	0.926490
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.06376	−1.08320
$9$	1.35670	0.452232
$10$	0.227965	0.0720889
$11$	6.03819	1.82058	0.910292	−	0.413967i	$-0.135857\pi$
$11$	6.03819	1.82058	0.910292	+	0.413967i	$0.135857\pi$
$12$	−1.70706	−0.492786
$13$	3.67193	1.01841	0.509205	−	0.860645i	$-0.329939\pi$
$13$	3.67193	1.01841	0.509205	+	0.860645i	$0.329939\pi$
$14$	1.08727	0.290585
$15$	0.437633	0.112996
$16$	−1.69545	−0.423862
$17$	−5.37138	−1.30275	−0.651375	−	0.758756i	$-0.725808\pi$
$17$	−5.37138	−1.30275	−0.651375	+	0.758756i	$0.725808\pi$
$18$	1.47510	0.347684
$19$	−3.54285	−0.812786	−0.406393	−	0.913698i	$-0.633214\pi$
$19$	−3.54285	−0.812786	−0.406393	+	0.913698i	$0.633214\pi$
$20$	−0.171475	−0.0383430
$21$	2.08727	0.455480
$22$	6.56515	1.39969
$23$	−1.30362	−0.271824	−0.135912	−	0.990721i	$-0.543396\pi$
$23$	−1.30362	−0.271824	−0.135912	+	0.990721i	$0.543396\pi$
$24$	−6.39489	−1.30535
$25$	−4.95604	−0.991208
$26$	3.99238	0.782971
$27$	−3.43002	−0.660107
$28$	−0.817843	−0.154558
$29$	−8.00307	−1.48613	−0.743066	−	0.669218i	$-0.766629\pi$
$29$	−8.00307	−1.48613	−0.743066	+	0.669218i	$0.766629\pi$
$30$	0.475825	0.0868734
$31$	−0.384208	−0.0690058	−0.0345029	−	0.999405i	$-0.510985\pi$
$31$	−0.384208	−0.0690058	−0.0345029	+	0.999405i	$0.510985\pi$
$32$	4.28411	0.757330
$33$	12.6033	2.19396
$34$	−5.84014	−1.00158
$35$	0.209668	0.0354403
$36$	−1.10957	−0.184928
$37$	−3.68876	−0.606429	−0.303214	−	0.952922i	$-0.598060\pi$
$37$	−3.68876	−0.606429	−0.303214	+	0.952922i	$0.598060\pi$
$38$	−3.85204	−0.624883
$39$	7.66432	1.22727
$40$	−0.642370	−0.101568
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	2.26943	0.350180
$43$	0.824527	0.125739	0.0628696	−	0.998022i	$-0.479975\pi$
$43$	0.824527	0.125739	0.0628696	+	0.998022i	$0.479975\pi$
$44$	−4.93829	−0.744476
$45$	0.284455	0.0424041
$46$	−1.41739	−0.208983
$47$	5.11625	0.746282	0.373141	−	0.927775i	$-0.378281\pi$
$47$	5.11625	0.746282	0.373141	+	0.927775i	$0.378281\pi$
$48$	−3.53885	−0.510790
$49$	1.00000	0.142857
$50$	−5.38855	−0.762057
$51$	−11.2115	−1.56993
$52$	−3.00307	−0.416450
$53$	1.53217	0.210460	0.105230	−	0.994448i	$-0.466442\pi$
$53$	1.53217	0.210460	0.105230	+	0.994448i	$0.466442\pi$
$54$	−3.72936	−0.507501
$55$	1.26601	0.170709
$56$	−3.06376	−0.409412
$57$	−7.39489	−0.979477
$58$	−8.70150	−1.14256
$59$	10.2669	1.33664	0.668320	−	0.743874i	$-0.267014\pi$
$59$	10.2669	1.33664	0.668320	+	0.743874i	$0.267014\pi$
$60$	−0.357915	−0.0462066
$61$	9.36070	1.19851	0.599257	−	0.800557i	$-0.295463\pi$
$61$	9.36070	1.19851	0.599257	+	0.800557i	$0.295463\pi$
$62$	−0.417738	−0.0530528
$63$	1.35670	0.170928
$64$	8.04887	1.00611
$65$	0.769885	0.0954925
$66$	13.7032	1.68675
$67$	11.3638	1.38830	0.694152	−	0.719828i	$-0.255779\pi$
$67$	11.3638	1.38830	0.694152	+	0.719828i	$0.255779\pi$
$68$	4.39294	0.532723
$69$	−2.72101	−0.327571
$70$	0.227965	0.0272471
$71$	−14.9494	−1.77416	−0.887081	−	0.461614i	$-0.847271\pi$
$71$	−14.9494	−1.77416	−0.887081	+	0.461614i	$0.847271\pi$
$72$	−4.15659	−0.489859
$73$	7.77203	0.909648	0.454824	−	0.890581i	$-0.349702\pi$
$73$	7.77203	0.909648	0.454824	+	0.890581i	$0.349702\pi$
$74$	−4.01068	−0.466232
$75$	−10.3446	−1.19449
$76$	2.89750	0.332366
$77$	6.03819	0.688116
$78$	8.33318	0.943547
$79$	−6.04703	−0.680344	−0.340172	−	0.940363i	$-0.610485\pi$
$79$	−6.04703	−0.680344	−0.340172	+	0.940363i	$0.610485\pi$
$80$	−0.355480	−0.0397439
$81$	−11.2295	−1.24772
$82$	−1.08727	−0.120069
$83$	14.1871	1.55723	0.778617	−	0.627500i	$-0.215922\pi$
$83$	14.1871	1.55723	0.778617	+	0.627500i	$0.215922\pi$
$84$	−1.70706	−0.186256
$85$	−1.12620	−0.122154
$86$	0.896484	0.0966703
$87$	−16.7046	−1.79092
$88$	−18.4996	−1.97206
$89$	0.520905	0.0552159	0.0276079	−	0.999619i	$-0.491211\pi$
$89$	0.520905	0.0552159	0.0276079	+	0.999619i	$0.491211\pi$
$90$	0.309280	0.0326010
$91$	3.67193	0.384923
$92$	1.06616	0.111155
$93$	−0.801946	−0.0831580
$94$	5.56275	0.573754
$95$	−0.742821	−0.0762118
$96$	8.94209	0.912648
$97$	−3.65270	−0.370876	−0.185438	−	0.982656i	$-0.559370\pi$
$97$	−3.65270	−0.370876	−0.185438	+	0.982656i	$0.559370\pi$
$98$	1.08727	0.109831
$99$	8.19200	0.823327
$100$	4.05326	0.405326
$101$	−2.45465	−0.244247	−0.122123	−	0.992515i	$-0.538970\pi$
$101$	−2.45465	−0.244247	−0.122123	+	0.992515i	$0.538970\pi$
$102$	−12.1899	−1.20698
$103$	−10.2479	−1.00975	−0.504876	−	0.863192i	$-0.668462\pi$
$103$	−10.2479	−1.00975	−0.504876	+	0.863192i	$0.668462\pi$
$104$	−11.2499	−1.10314
$105$	0.437633	0.0427086
$106$	1.66588	0.161805
$107$	−5.33318	−0.515578	−0.257789	−	0.966201i	$-0.582994\pi$
$107$	−5.33318	−0.515578	−0.257789	+	0.966201i	$0.582994\pi$
$108$	2.80522	0.269932
$109$	8.82638	0.845413	0.422707	−	0.906267i	$-0.361080\pi$
$109$	8.82638	0.845413	0.422707	+	0.906267i	$0.361080\pi$
$110$	1.37650	0.131244
$111$	−7.69944	−0.730799
$112$	−1.69545	−0.160205
$113$	−18.2045	−1.71253	−0.856267	−	0.516534i	$-0.827222\pi$
$113$	−18.2045	−1.71253	−0.856267	+	0.516534i	$0.827222\pi$
$114$	−8.04024	−0.753038
$115$	−0.273327	−0.0254879
$116$	6.54525	0.607711
$117$	4.98170	0.460559
$118$	11.1629	1.02763
$119$	−5.37138	−0.492393
$120$	−1.34080	−0.122398
$121$	25.4598	2.31452
$122$	10.1776	0.921437
$123$	−2.08727	−0.188203
$124$	0.314222	0.0282180
$125$	−2.08746	−0.186708
$126$	1.47510	0.131412
$127$	−13.1751	−1.16910	−0.584551	−	0.811357i	$-0.698729\pi$
$127$	−13.1751	−1.16910	−0.584551	+	0.811357i	$0.698729\pi$
$128$	0.183089	0.0161829
$129$	1.72101	0.151527
$130$	0.837073	0.0734162
$131$	13.0506	1.14023	0.570117	−	0.821563i	$-0.306898\pi$
$131$	13.0506	1.14023	0.570117	+	0.821563i	$0.306898\pi$
$132$	−10.3076	−0.897158
$133$	−3.54285	−0.307204
$134$	12.3555	1.06735
$135$	−0.719163	−0.0618957
$136$	16.4566	1.41114
$137$	12.7699	1.09100	0.545502	−	0.838109i	$-0.316339\pi$
$137$	12.7699	1.09100	0.545502	+	0.838109i	$0.316339\pi$
$138$	−2.95847	−0.251842
$139$	13.9759	1.18542	0.592712	−	0.805415i	$-0.298057\pi$
$139$	13.9759	1.18542	0.592712	+	0.805415i	$0.298057\pi$
$140$	−0.171475	−0.0144923
$141$	10.6790	0.899334
$142$	−16.2540	−1.36400
$143$	22.1718	1.85410
$144$	−2.30021	−0.191684
$145$	−1.67798	−0.139349
$146$	8.45030	0.699352
$147$	2.08727	0.172155
$148$	3.01683	0.247982
$149$	−2.02136	−0.165597	−0.0827983	−	0.996566i	$-0.526386\pi$
$149$	−2.02136	−0.165597	−0.0827983	+	0.996566i	$0.526386\pi$
$150$	−11.2474	−0.918344
$151$	11.7648	0.957406	0.478703	−	0.877977i	$-0.341107\pi$
$151$	11.7648	0.957406	0.478703	+	0.877977i	$0.341107\pi$
$152$	10.8544	0.880411
$153$	−7.28733	−0.589146
$154$	6.56515	0.529035
$155$	−0.0805560	−0.00647041
$156$	−6.26821	−0.501858
$157$	18.8859	1.50726	0.753631	−	0.657297i	$-0.228300\pi$
$157$	18.8859	1.50726	0.753631	+	0.657297i	$0.228300\pi$
$158$	−6.57475	−0.523059
$159$	3.19805	0.253622
$160$	0.898238	0.0710119
$161$	−1.30362	−0.102740
$162$	−12.2095	−0.959266
$163$	16.3263	1.27877	0.639387	−	0.768885i	$-0.279188\pi$
$163$	16.3263	1.27877	0.639387	+	0.768885i	$0.279188\pi$
$164$	0.817843	0.0638628
$165$	2.64251	0.205719
$166$	15.4252	1.19723
$167$	−22.5846	−1.74765	−0.873824	−	0.486242i	$-0.838367\pi$
$167$	−22.5846	−1.74765	−0.873824	+	0.486242i	$0.838367\pi$
$168$	−6.39489	−0.493376
$169$	0.483092	0.0371609
$170$	−1.22449	−0.0939139
$171$	−4.80658	−0.367568
$172$	−0.674334	−0.0514175
$173$	−22.2230	−1.68958	−0.844790	−	0.535097i	$-0.820275\pi$
$173$	−22.2230	−1.68958	−0.844790	+	0.535097i	$0.820275\pi$
$174$	−18.1624	−1.37689
$175$	−4.95604	−0.374641
$176$	−10.2374	−0.771675
$177$	21.4299	1.61077
$178$	0.566365	0.0424508
$179$	−10.0095	−0.748142	−0.374071	−	0.927400i	$-0.622038\pi$
$179$	−10.0095	−0.748142	−0.374071	+	0.927400i	$0.622038\pi$
$180$	−0.232640	−0.0173400
$181$	10.8101	0.803511	0.401755	−	0.915747i	$-0.368400\pi$
$181$	10.8101	0.803511	0.401755	+	0.915747i	$0.368400\pi$
$182$	3.99238	0.295935
$183$	19.5383	1.44431
$184$	3.99398	0.294440
$185$	−0.773414	−0.0568625
$186$	−0.871932	−0.0639332
$187$	−32.4334	−2.37177
$188$	−4.18429	−0.305171
$189$	−3.43002	−0.249497
$190$	−0.807647	−0.0585929
$191$	−19.7693	−1.43046	−0.715229	−	0.698890i	$-0.753678\pi$
$191$	−19.7693	−1.43046	−0.715229	+	0.698890i	$0.753678\pi$
$192$	16.8002	1.21245
$193$	18.0955	1.30254	0.651270	−	0.758846i	$-0.274237\pi$
$193$	18.0955	1.30254	0.651270	+	0.758846i	$0.274237\pi$
$194$	−3.97148	−0.285135
$195$	1.60696	0.115077
$196$	−0.817843	−0.0584174
$197$	4.47538	0.318858	0.159429	−	0.987209i	$-0.449035\pi$
$197$	4.47538	0.318858	0.159429	+	0.987209i	$0.449035\pi$
$198$	8.90692	0.632987
$199$	10.1956	0.722744	0.361372	−	0.932422i	$-0.382308\pi$
$199$	10.1956	0.722744	0.361372	+	0.932422i	$0.382308\pi$
$200$	15.1841	1.07368
$201$	23.7192	1.67303
$202$	−2.66887	−0.187781
$203$	−8.00307	−0.561705
$204$	9.16926	0.641977
$205$	−0.209668	−0.0146438
$206$	−11.1422	−0.776313
$207$	−1.76862	−0.122928
$208$	−6.22556	−0.431665
$209$	−21.3924	−1.47974
$210$	0.475825	0.0328351
$211$	−14.0477	−0.967081	−0.483540	−	0.875322i	$-0.660649\pi$
$211$	−14.0477	−0.967081	−0.483540	+	0.875322i	$0.660649\pi$
$212$	−1.25308	−0.0860616
$213$	−31.2033	−2.13802
$214$	−5.79861	−0.396385
$215$	0.172877	0.0117901
$216$	10.5087	0.715029
$217$	−0.384208	−0.0260818
$218$	9.59666	0.649968
$219$	16.2223	1.09620
$220$	−1.03540	−0.0698066
$221$	−19.7233	−1.32674
$222$	−8.37138	−0.561850
$223$	−0.701496	−0.0469756	−0.0234878	−	0.999724i	$-0.507477\pi$
$223$	−0.701496	−0.0469756	−0.0234878	+	0.999724i	$0.507477\pi$
$224$	4.28411	0.286244
$225$	−6.72385	−0.448256
$226$	−19.7932	−1.31662
$227$	9.36869	0.621822	0.310911	−	0.950439i	$-0.399366\pi$
$227$	9.36869	0.621822	0.310911	+	0.950439i	$0.399366\pi$
$228$	6.04786	0.400529
$229$	12.4012	0.819496	0.409748	−	0.912199i	$-0.365617\pi$
$229$	12.4012	0.819496	0.409748	+	0.912199i	$0.365617\pi$
$230$	−0.297180	−0.0195955
$231$	12.6033	0.829239
$232$	24.5195	1.60978
$233$	9.61739	0.630056	0.315028	−	0.949082i	$-0.397986\pi$
$233$	9.61739	0.630056	0.315028	+	0.949082i	$0.397986\pi$
$234$	5.41646	0.354085
$235$	1.07271	0.0699760
$236$	−8.39674	−0.546581
$237$	−12.6218	−0.819873
$238$	−5.84014	−0.378560
$239$	−16.5603	−1.07120	−0.535600	−	0.844472i	$-0.679914\pi$
$239$	−16.5603	−1.07120	−0.535600	+	0.844472i	$0.679914\pi$
$240$	−0.741983	−0.0478948
$241$	9.29684	0.598862	0.299431	−	0.954118i	$-0.403203\pi$
$241$	9.29684	0.598862	0.299431	+	0.954118i	$0.403203\pi$
$242$	27.6816	1.77944
$243$	−13.1489	−0.843501
$244$	−7.65558	−0.490098
$245$	0.209668	0.0133952
$246$	−2.26943	−0.144693
$247$	−13.0091	−0.827750
$248$	1.17712	0.0747472
$249$	29.6123	1.87660
$250$	−2.26963	−0.143544
$251$	2.89503	0.182733	0.0913664	−	0.995817i	$-0.470877\pi$
$251$	2.89503	0.182733	0.0913664	+	0.995817i	$0.470877\pi$
$252$	−1.10957	−0.0698961
$253$	−7.87152	−0.494878
$254$	−14.3249	−0.898824
$255$	−2.35069	−0.147206
$256$	−15.8987	−0.993668
$257$	5.41470	0.337760	0.168880	−	0.985637i	$-0.445985\pi$
$257$	5.41470	0.337760	0.168880	+	0.985637i	$0.445985\pi$
$258$	1.87120	0.116496
$259$	−3.68876	−0.229209
$260$	−0.629645	−0.0390489
$261$	−10.8577	−0.672077
$262$	14.1895	0.876631
$263$	−26.7339	−1.64848	−0.824242	−	0.566238i	$-0.808398\pi$
$263$	−26.7339	−1.64848	−0.824242	+	0.566238i	$0.808398\pi$
$264$	−38.6136	−2.37650
$265$	0.321246	0.0197340
$266$	−3.85204	−0.236184
$267$	1.08727	0.0665399
$268$	−9.29377	−0.567708
$269$	−14.6488	−0.893151	−0.446576	−	0.894746i	$-0.647357\pi$
$269$	−14.6488	−0.893151	−0.446576	+	0.894746i	$0.647357\pi$
$270$	−0.781925	−0.0475864
$271$	22.8241	1.38646	0.693232	−	0.720714i	$-0.256186\pi$
$271$	22.8241	1.38646	0.693232	+	0.720714i	$0.256186\pi$
$272$	9.10688	0.552186
$273$	7.66432	0.463866
$274$	13.8843	0.838782
$275$	−29.9255	−1.80458
$276$	2.22536	0.133951
$277$	−8.31190	−0.499414	−0.249707	−	0.968321i	$-0.580334\pi$
$277$	−8.31190	−0.499414	−0.249707	+	0.968321i	$0.580334\pi$
$278$	15.1956	0.911373
$279$	−0.521254	−0.0312067
$280$	−0.642370	−0.0383890
$281$	17.3137	1.03285	0.516423	−	0.856333i	$-0.327263\pi$
$281$	17.3137	1.03285	0.516423	+	0.856333i	$0.327263\pi$
$282$	11.6110	0.691422
$283$	−14.7818	−0.878686	−0.439343	−	0.898319i	$-0.644789\pi$
$283$	−14.7818	−0.878686	−0.439343	+	0.898319i	$0.644789\pi$
$284$	12.2262	0.725493
$285$	−1.55047	−0.0918418
$286$	24.1068	1.42546
$287$	−1.00000	−0.0590281
$288$	5.81224	0.342489
$289$	11.8517	0.697158
$290$	−1.82442	−0.107134
$291$	−7.62418	−0.446937
$292$	−6.35631	−0.371975
$293$	4.99638	0.291892	0.145946	−	0.989293i	$-0.453377\pi$
$293$	4.99638	0.291892	0.145946	+	0.989293i	$0.453377\pi$
$294$	2.26943	0.132356
$295$	2.15264	0.125332
$296$	11.3015	0.656885
$297$	−20.7111	−1.20178
$298$	−2.19777	−0.127313
$299$	−4.78681	−0.276828
$300$	8.46026	0.488453
$301$	0.824527	0.0475250
$302$	12.7915	0.736069
$303$	−5.12352	−0.294338
$304$	6.00671	0.344509
$305$	1.96263	0.112380
$306$	−7.92330	−0.452945
$307$	−7.85295	−0.448192	−0.224096	−	0.974567i	$-0.571943\pi$
$307$	−7.85295	−0.448192	−0.224096	+	0.974567i	$0.571943\pi$
$308$	−4.93829	−0.281385
$309$	−21.3901	−1.21684
$310$	−0.0875861	−0.00497456
$311$	−27.0379	−1.53318	−0.766589	−	0.642138i	$-0.778048\pi$
$311$	−27.0379	−1.53318	−0.766589	+	0.642138i	$0.778048\pi$
$312$	−23.4816	−1.32938
$313$	−0.168393	−0.00951815	−0.00475907	−	0.999989i	$-0.501515\pi$
$313$	−0.168393	−0.00951815	−0.00475907	+	0.999989i	$0.501515\pi$
$314$	20.5341	1.15881
$315$	0.284455	0.0160272
$316$	4.94552	0.278207
$317$	5.33690	0.299750	0.149875	−	0.988705i	$-0.452113\pi$
$317$	5.33690	0.299750	0.149875	+	0.988705i	$0.452113\pi$
$318$	3.47715	0.194989
$319$	−48.3240	−2.70563
$320$	1.68759	0.0943390
$321$	−11.1318	−0.621316
$322$	−1.41739	−0.0789880
$323$	19.0300	1.05886
$324$	9.18394	0.510219
$325$	−18.1982	−1.00946
$326$	17.7511	0.983142
$327$	18.4230	1.01880
$328$	3.06376	0.169168
$329$	5.11625	0.282068
$330$	2.87312	0.158160
$331$	−8.09405	−0.444889	−0.222445	−	0.974945i	$-0.571404\pi$
$331$	−8.09405	−0.444889	−0.222445	+	0.974945i	$0.571404\pi$
$332$	−11.6028	−0.636786
$333$	−5.00453	−0.274247
$334$	−24.5556	−1.34362
$335$	2.38261	0.130176
$336$	−3.53885	−0.193060
$337$	20.1540	1.09786	0.548929	−	0.835869i	$-0.315036\pi$
$337$	20.1540	1.09786	0.548929	+	0.835869i	$0.315036\pi$
$338$	0.525252	0.0285699
$339$	−37.9977	−2.06375
$340$	0.921058	0.0499514
$341$	−2.31992	−0.125631
$342$	−5.22605	−0.282592
$343$	1.00000	0.0539949
$344$	−2.52615	−0.136201
$345$	−0.570508	−0.0307151
$346$	−24.1624	−1.29898
$347$	18.2807	0.981359	0.490679	−	0.871340i	$-0.336749\pi$
$347$	18.2807	0.981359	0.490679	+	0.871340i	$0.336749\pi$
$348$	13.6617	0.732345
$349$	9.74567	0.521674	0.260837	−	0.965383i	$-0.416001\pi$
$349$	9.74567	0.521674	0.260837	+	0.965383i	$0.416001\pi$
$350$	−5.38855	−0.288030
$351$	−12.5948	−0.672260
$352$	25.8683	1.37878
$353$	26.2143	1.39525	0.697624	−	0.716464i	$-0.254241\pi$
$353$	26.2143	1.39525	0.697624	+	0.716464i	$0.254241\pi$
$354$	23.3000	1.23838
$355$	−3.13439	−0.166356
$356$	−0.426019	−0.0225790
$357$	−11.2115	−0.593376
$358$	−10.8830	−0.575184
$359$	0.473108	0.0249697	0.0124849	−	0.999922i	$-0.496026\pi$
$359$	0.473108	0.0249697	0.0124849	+	0.999922i	$0.496026\pi$
$360$	−0.871502	−0.0459322
$361$	−6.44820	−0.339379
$362$	11.7535	0.617752
$363$	53.1414	2.78920
$364$	−3.00307	−0.157403
$365$	1.62954	0.0852942
$366$	21.2434	1.11041
$367$	10.2670	0.535932	0.267966	−	0.963428i	$-0.413648\pi$
$367$	10.2670	0.535932	0.267966	+	0.963428i	$0.413648\pi$
$368$	2.21022	0.115216
$369$	−1.35670	−0.0706268
$370$	−0.840910	−0.0437168
$371$	1.53217	0.0795463
$372$	0.655866	0.0340051
$373$	20.1653	1.04412	0.522061	−	0.852908i	$-0.325163\pi$
$373$	20.1653	1.04412	0.522061	+	0.852908i	$0.325163\pi$
$374$	−35.2639	−1.82345
$375$	−4.35709	−0.224999
$376$	−15.6749	−0.808374
$377$	−29.3867	−1.51349
$378$	−3.72936	−0.191817
$379$	−26.8293	−1.37813	−0.689063	−	0.724701i	$-0.741978\pi$
$379$	−26.8293	−1.37813	−0.689063	+	0.724701i	$0.741978\pi$
$380$	0.607511	0.0311647
$381$	−27.5000	−1.40887
$382$	−21.4946	−1.09976
$383$	−24.1679	−1.23492	−0.617461	−	0.786602i	$-0.711839\pi$
$383$	−24.1679	−1.23492	−0.617461	+	0.786602i	$0.711839\pi$
$384$	0.382156	0.0195018
$385$	1.26601	0.0645220
$386$	19.6746	1.00141
$387$	1.11863	0.0568634
$388$	2.98734	0.151659
$389$	15.9595	0.809180	0.404590	−	0.914498i	$-0.367414\pi$
$389$	15.9595	0.809180	0.404590	+	0.914498i	$0.367414\pi$
$390$	1.74720	0.0884728
$391$	7.00224	0.354119
$392$	−3.06376	−0.154743
$393$	27.2401	1.37408
$394$	4.86595	0.245143
$395$	−1.26786	−0.0637932
$396$	−6.69977	−0.336676
$397$	−8.73399	−0.438346	−0.219173	−	0.975686i	$-0.570336\pi$
$397$	−8.73399	−0.438346	−0.219173	+	0.975686i	$0.570336\pi$
$398$	11.0853	0.555657
$399$	−7.39489	−0.370208
$400$	8.40270	0.420135
$401$	1.77238	0.0885086	0.0442543	−	0.999020i	$-0.485909\pi$
$401$	1.77238	0.0885086	0.0442543	+	0.999020i	$0.485909\pi$
$402$	25.7892	1.28625
$403$	−1.41079	−0.0702763
$404$	2.00752	0.0998778
$405$	−2.35445	−0.116994
$406$	−8.70150	−0.431848
$407$	−22.2735	−1.10405
$408$	34.3494	1.70055
$409$	−27.0895	−1.33949	−0.669746	−	0.742590i	$-0.733597\pi$
$409$	−27.0895	−1.33949	−0.669746	+	0.742590i	$0.733597\pi$
$410$	−0.227965	−0.0112584
$411$	26.6542	1.31475
$412$	8.38114	0.412909
$413$	10.2669	0.505203
$414$	−1.92297	−0.0945087
$415$	2.97457	0.146016
$416$	15.7310	0.771273
$417$	29.1716	1.42854
$418$	−23.2593	−1.13765
$419$	−18.3386	−0.895898	−0.447949	−	0.894059i	$-0.647845\pi$
$419$	−18.3386	−0.895898	−0.447949	+	0.894059i	$0.647845\pi$
$420$	−0.357915	−0.0174645
$421$	16.7202	0.814894	0.407447	−	0.913229i	$-0.366419\pi$
$421$	16.7202	0.814894	0.407447	+	0.913229i	$0.366419\pi$
$422$	−15.2736	−0.743507
$423$	6.94120	0.337493
$424$	−4.69420	−0.227970
$425$	26.6208	1.29130
$426$	−33.9265	−1.64374
$427$	9.36070	0.452996
$428$	4.36171	0.210831
$429$	46.2786	2.23435
$430$	0.187964	0.00906441
$431$	0.204738	0.00986186	0.00493093	−	0.999988i	$-0.498430\pi$
$431$	0.204738	0.00986186	0.00493093	+	0.999988i	$0.498430\pi$
$432$	5.81541	0.279794
$433$	31.9997	1.53781	0.768903	−	0.639366i	$-0.220803\pi$
$433$	31.9997	1.53781	0.768903	+	0.639366i	$0.220803\pi$
$434$	−0.417738	−0.0200521
$435$	−3.50240	−0.167927
$436$	−7.21859	−0.345708
$437$	4.61854	0.220935
$438$	17.6381	0.842779
$439$	24.9052	1.18866	0.594330	−	0.804221i	$-0.297417\pi$
$439$	24.9052	1.18866	0.594330	+	0.804221i	$0.297417\pi$
$440$	−3.87876	−0.184912
$441$	1.35670	0.0646046
$442$	−21.4446	−1.02002
$443$	19.0300	0.904142	0.452071	−	0.891982i	$-0.350685\pi$
$443$	19.0300	0.904142	0.452071	+	0.891982i	$0.350685\pi$
$444$	6.29694	0.298839
$445$	0.109217	0.00517738
$446$	−0.762716	−0.0361156
$447$	−4.21913	−0.199558
$448$	8.04887	0.380274
$449$	−5.95010	−0.280802	−0.140401	−	0.990095i	$-0.544839\pi$
$449$	−5.95010	−0.280802	−0.140401	+	0.990095i	$0.544839\pi$
$450$	−7.31064	−0.344627
$451$	−6.03819	−0.284327
$452$	14.8884	0.700292
$453$	24.5563	1.15376
$454$	10.1863	0.478067
$455$	0.769885	0.0360928
$456$	22.6561	1.06097
$457$	−31.8410	−1.48946	−0.744729	−	0.667367i	$-0.767421\pi$
$457$	−31.8410	−1.48946	−0.744729	+	0.667367i	$0.767421\pi$
$458$	13.4835	0.630042
$459$	18.4239	0.859955
$460$	0.223539	0.0104225
$461$	4.99638	0.232705	0.116352	−	0.993208i	$-0.462880\pi$
$461$	4.99638	0.232705	0.116352	+	0.993208i	$0.462880\pi$
$462$	13.7032	0.637532
$463$	17.6038	0.818119	0.409060	−	0.912508i	$-0.365857\pi$
$463$	17.6038	0.818119	0.409060	+	0.912508i	$0.365857\pi$
$464$	13.5688	0.629914
$465$	−0.168142	−0.00779740
$466$	10.4567	0.484397
$467$	−42.9444	−1.98723	−0.993614	−	0.112833i	$-0.964007\pi$
$467$	−42.9444	−1.98723	−0.993614	+	0.112833i	$0.964007\pi$
$468$	−4.07425	−0.188332
$469$	11.3638	0.524730
$470$	1.16633	0.0537987
$471$	39.4201	1.81638
$472$	−31.4554	−1.44785
$473$	4.97865	0.228919
$474$	−13.7233	−0.630331
$475$	17.5585	0.805640
$476$	4.39294	0.201350
$477$	2.07869	0.0951767
$478$	−18.0056	−0.823556
$479$	2.85249	0.130334	0.0651669	−	0.997874i	$-0.479242\pi$
$479$	2.85249	0.130334	0.0651669	+	0.997874i	$0.479242\pi$
$480$	1.87487	0.0855755
$481$	−13.5449	−0.617594
$482$	10.1082	0.460415
$483$	−2.72101	−0.123810
$484$	−20.8221	−0.946459
$485$	−0.765853	−0.0347756
$486$	−14.2964	−0.648497
$487$	−6.23225	−0.282410	−0.141205	−	0.989980i	$-0.545098\pi$
$487$	−6.23225	−0.282410	−0.141205	+	0.989980i	$0.545098\pi$
$488$	−28.6789	−1.29823
$489$	34.0774	1.54103
$490$	0.227965	0.0102984
$491$	−2.13846	−0.0965071	−0.0482536	−	0.998835i	$-0.515366\pi$
$491$	−2.13846	−0.0965071	−0.0482536	+	0.998835i	$0.515366\pi$
$492$	1.70706	0.0769602
$493$	42.9875	1.93606
$494$	−14.1444	−0.636388
$495$	1.71760	0.0772002
$496$	0.651404	0.0292489
$497$	−14.9494	−0.670570
$498$	32.1965	1.44276
$499$	25.1110	1.12412	0.562060	−	0.827096i	$-0.310009\pi$
$499$	25.1110	1.12412	0.562060	+	0.827096i	$0.310009\pi$
$500$	1.70721	0.0763489
$501$	−47.1402	−2.10607
$502$	3.14768	0.140488
$503$	37.1641	1.65707	0.828534	−	0.559939i	$-0.189176\pi$
$503$	37.1641	1.65707	0.828534	+	0.559939i	$0.189176\pi$
$504$	−4.15659	−0.185149
$505$	−0.514660	−0.0229021
$506$	−8.55847	−0.380470
$507$	1.00834	0.0447821
$508$	10.7752	0.478071
$509$	−2.36319	−0.104747	−0.0523734	−	0.998628i	$-0.516679\pi$
$509$	−2.36319	−0.104747	−0.0523734	+	0.998628i	$0.516679\pi$
$510$	−2.55584	−0.113174
$511$	7.77203	0.343815
$512$	−17.6523	−0.780131
$513$	12.1520	0.536526
$514$	5.88725	0.259675
$515$	−2.14864	−0.0946805
$516$	−1.40752	−0.0619625
$517$	30.8929	1.35867
$518$	−4.01068	−0.176219
$519$	−46.3853	−2.03609
$520$	−2.35874	−0.103438
$521$	−2.27368	−0.0996116	−0.0498058	−	0.998759i	$-0.515860\pi$
$521$	−2.27368	−0.0996116	−0.0498058	+	0.998759i	$0.515860\pi$
$522$	−11.8053	−0.516704
$523$	−35.7432	−1.56294	−0.781471	−	0.623941i	$-0.785531\pi$
$523$	−35.7432	−1.56294	−0.781471	+	0.623941i	$0.785531\pi$
$524$	−10.6733	−0.466266
$525$	−10.3446	−0.451475
$526$	−29.0670	−1.26738
$527$	2.06373	0.0898974
$528$	−21.3683	−0.929935
$529$	−21.3006	−0.926112
$530$	0.349282	0.0151718
$531$	13.9291	0.604472
$532$	2.89750	0.125622
$533$	−3.67193	−0.159049
$534$	1.18216	0.0511569
$535$	−1.11820	−0.0483438
$536$	−34.8158	−1.50381
$537$	−20.8925	−0.901576
$538$	−15.9272	−0.686669
$539$	6.03819	0.260083
$540$	0.588163	0.0253105
$541$	−22.5224	−0.968314	−0.484157	−	0.874981i	$-0.660874\pi$
$541$	−22.5224	−0.968314	−0.484157	+	0.874981i	$0.660874\pi$
$542$	24.8159	1.06594
$543$	22.5637	0.968299
$544$	−23.0116	−0.986612
$545$	1.85060	0.0792712
$546$	8.33318	0.356627
$547$	3.63915	0.155599	0.0777994	−	0.996969i	$-0.475211\pi$
$547$	3.63915	0.155599	0.0777994	+	0.996969i	$0.475211\pi$
$548$	−10.4438	−0.446135
$549$	12.6996	0.542007
$550$	−32.5371	−1.38739
$551$	28.3537	1.20791
$552$	8.33652	0.354826
$553$	−6.04703	−0.257146
$554$	−9.03729	−0.383957
$555$	−1.61432	−0.0685242
$556$	−11.4301	−0.484745
$557$	4.80008	0.203386	0.101693	−	0.994816i	$-0.467574\pi$
$557$	4.80008	0.203386	0.101693	+	0.994816i	$0.467574\pi$
$558$	−0.566744	−0.0239922
$559$	3.02761	0.128054
$560$	−0.355480	−0.0150218
$561$	−67.6973	−2.85818
$562$	18.8246	0.794069
$563$	31.7115	1.33648	0.668241	−	0.743945i	$-0.267048\pi$
$563$	31.7115	1.33648	0.668241	+	0.743945i	$0.267048\pi$
$564$	−8.73374	−0.367757
$565$	−3.81689	−0.160578
$566$	−16.0718	−0.675548
$567$	−11.2295	−0.471593
$568$	45.8012	1.92178
$569$	−35.4970	−1.48811	−0.744055	−	0.668118i	$-0.767100\pi$
$569$	−35.4970	−1.48811	−0.744055	+	0.668118i	$0.767100\pi$
$570$	−1.68578	−0.0706095
$571$	−38.7912	−1.62336	−0.811681	−	0.584100i	$-0.801447\pi$
$571$	−38.7912	−1.62336	−0.811681	+	0.584100i	$0.801447\pi$
$572$	−18.1331	−0.758182
$573$	−41.2639	−1.72383
$574$	−1.08727	−0.0453818
$575$	6.46080	0.269434
$576$	10.9199	0.454995
$577$	−0.335828	−0.0139807	−0.00699035	−	0.999976i	$-0.502225\pi$
$577$	−0.335828	−0.0139807	−0.00699035	+	0.999976i	$0.502225\pi$
$578$	12.8860	0.535987
$579$	37.7701	1.56967
$580$	1.37233	0.0569828
$581$	14.1871	0.588579
$582$	−8.28954	−0.343613
$583$	9.25154	0.383160
$584$	−23.8116	−0.985332
$585$	1.04450	0.0431848
$586$	5.43242	0.224411
$587$	8.19386	0.338197	0.169098	−	0.985599i	$-0.445914\pi$
$587$	8.19386	0.338197	0.169098	+	0.985599i	$0.445914\pi$
$588$	−1.70706	−0.0703980
$589$	1.36119	0.0560870
$590$	2.34050	0.0963570
$591$	9.34132	0.384251
$592$	6.25410	0.257042
$593$	30.1222	1.23697	0.618486	−	0.785796i	$-0.287746\pi$
$593$	30.1222	1.23697	0.618486	+	0.785796i	$0.287746\pi$
$594$	−22.5186	−0.923948
$595$	−1.12620	−0.0461698
$596$	1.65316	0.0677160
$597$	21.2809	0.870968
$598$	−5.20456	−0.212830
$599$	−39.6072	−1.61831	−0.809153	−	0.587599i	$-0.800073\pi$
$599$	−39.6072	−1.61831	−0.809153	+	0.587599i	$0.800073\pi$
$600$	31.6933	1.29387
$601$	−35.0329	−1.42902	−0.714511	−	0.699624i	$-0.753351\pi$
$601$	−35.0329	−1.42902	−0.714511	+	0.699624i	$0.753351\pi$
$602$	0.896484	0.0365380
$603$	15.4172	0.627836
$604$	−9.62176	−0.391504
$605$	5.33809	0.217024
$606$	−5.57065	−0.226292
$607$	13.4657	0.546555	0.273278	−	0.961935i	$-0.411892\pi$
$607$	13.4657	0.546555	0.273278	+	0.961935i	$0.411892\pi$
$608$	−15.1780	−0.615547
$609$	−16.7046	−0.676903
$610$	2.13391	0.0863996
$611$	18.7865	0.760022
$612$	5.95990	0.240915
$613$	−6.49820	−0.262460	−0.131230	−	0.991352i	$-0.541893\pi$
$613$	−6.49820	−0.262460	−0.131230	+	0.991352i	$0.541893\pi$
$614$	−8.53828	−0.344577
$615$	−0.437633	−0.0176471
$616$	−18.4996	−0.745368
$617$	6.63045	0.266932	0.133466	−	0.991053i	$-0.457389\pi$
$617$	6.63045	0.266932	0.133466	+	0.991053i	$0.457389\pi$
$618$	−23.2568	−0.935525
$619$	−4.50756	−0.181174	−0.0905871	−	0.995889i	$-0.528874\pi$
$619$	−4.50756	−0.181174	−0.0905871	+	0.995889i	$0.528874\pi$
$620$	0.0658822	0.00264589
$621$	4.47144	0.179433
$622$	−29.3975	−1.17873
$623$	0.520905	0.0208696
$624$	−12.9944	−0.520194
$625$	24.3425	0.973701
$626$	−0.183089	−0.00731771
$627$	−44.6518	−1.78322
$628$	−15.4457	−0.616352
$629$	19.8137	0.790025
$630$	0.309280	0.0123220
$631$	−24.2677	−0.966081	−0.483040	−	0.875598i	$-0.660468\pi$
$631$	−24.2677	−0.966081	−0.483040	+	0.875598i	$0.660468\pi$
$632$	18.5266	0.736949
$633$	−29.3213	−1.16542
$634$	5.80265	0.230453
$635$	−2.76239	−0.109622
$636$	−2.61551	−0.103712
$637$	3.67193	0.145487
$638$	−52.5413	−2.08013
$639$	−20.2818	−0.802334
$640$	0.0383878	0.00151741
$641$	22.2964	0.880653	0.440327	−	0.897838i	$-0.354863\pi$
$641$	22.2964	0.880653	0.440327	+	0.897838i	$0.354863\pi$
$642$	−12.1033	−0.477678
$643$	−16.2405	−0.640464	−0.320232	−	0.947339i	$-0.603761\pi$
$643$	−16.2405	−0.640464	−0.320232	+	0.947339i	$0.603761\pi$
$644$	1.06616	0.0420125
$645$	0.360840	0.0142081
$646$	20.6907	0.814067
$647$	13.5814	0.533939	0.266969	−	0.963705i	$-0.413978\pi$
$647$	13.5814	0.533939	0.266969	+	0.963705i	$0.413978\pi$
$648$	34.4044	1.35153
$649$	61.9937	2.43347
$650$	−19.7864	−0.776087
$651$	−0.801946	−0.0314308
$652$	−13.3524	−0.522918
$653$	−47.1222	−1.84403	−0.922016	−	0.387151i	$-0.873459\pi$
$653$	−47.1222	−1.84403	−0.922016	+	0.387151i	$0.873459\pi$
$654$	20.0308	0.783267
$655$	2.73628	0.106915
$656$	1.69545	0.0661960
$657$	10.5443	0.411372
$658$	5.56275	0.216858
$659$	5.27483	0.205478	0.102739	−	0.994708i	$-0.467239\pi$
$659$	5.27483	0.205478	0.102739	+	0.994708i	$0.467239\pi$
$660$	−2.16116	−0.0841230
$661$	−47.8044	−1.85938	−0.929689	−	0.368346i	$-0.879924\pi$
$661$	−47.8044	−1.85938	−0.929689	+	0.368346i	$0.879924\pi$
$662$	−8.80042	−0.342038
$663$	−41.1679	−1.59883
$664$	−43.4657	−1.68680
$665$	−0.742821	−0.0288054
$666$	−5.44128	−0.210845
$667$	10.4330	0.403966
$668$	18.4707	0.714651
$669$	−1.46421	−0.0566097
$670$	2.59054	0.100081
$671$	56.5217	2.18200
$672$	8.94209	0.344949
$673$	−5.11960	−0.197346	−0.0986730	−	0.995120i	$-0.531460\pi$
$673$	−5.11960	−0.197346	−0.0986730	+	0.995120i	$0.531460\pi$
$674$	21.9128	0.844051
$675$	16.9993	0.654303
$676$	−0.395094	−0.0151959
$677$	30.7985	1.18368	0.591842	−	0.806054i	$-0.298401\pi$
$677$	30.7985	1.18368	0.591842	+	0.806054i	$0.298401\pi$
$678$	−41.3137	−1.58664
$679$	−3.65270	−0.140178
$680$	3.45041	0.132317
$681$	19.5550	0.749349
$682$	−2.52238	−0.0965870
$683$	−18.8534	−0.721407	−0.360703	−	0.932681i	$-0.617463\pi$
$683$	−18.8534	−0.721407	−0.360703	+	0.932681i	$0.617463\pi$
$684$	3.93103	0.150307
$685$	2.67743	0.102299
$686$	1.08727	0.0415122
$687$	25.8847	0.987563
$688$	−1.39794	−0.0532960
$689$	5.62603	0.214335
$690$	−0.620296	−0.0236143
$691$	−6.22638	−0.236863	−0.118431	−	0.992962i	$-0.537787\pi$
$691$	−6.22638	−0.236863	−0.118431	+	0.992962i	$0.537787\pi$
$692$	18.1749	0.690906
$693$	8.19200	0.311188
$694$	19.8761	0.754485
$695$	2.93030	0.111153
$696$	51.1787	1.93992
$697$	5.37138	0.203455
$698$	10.5962	0.401071
$699$	20.0741	0.759272
$700$	4.05326	0.153199
$701$	40.6743	1.53625	0.768124	−	0.640301i	$-0.221190\pi$
$701$	40.6743	1.53625	0.768124	+	0.640301i	$0.221190\pi$
$702$	−13.6939	−0.516845
$703$	13.0687	0.492897
$704$	48.6006	1.83171
$705$	2.23904	0.0843271
$706$	28.5021	1.07269
$707$	−2.45465	−0.0923166
$708$	−17.5263	−0.658677
$709$	−47.5660	−1.78638	−0.893189	−	0.449681i	$-0.851538\pi$
$709$	−47.5660	−1.78638	−0.893189	+	0.449681i	$0.851538\pi$
$710$	−3.40793	−0.127897
$711$	−8.20398	−0.307673
$712$	−1.59593	−0.0598099
$713$	0.500862	0.0187574
$714$	−12.1899	−0.456197
$715$	4.64871	0.173852
$716$	8.18617	0.305932
$717$	−34.5659	−1.29089
$718$	0.514397	0.0191971
$719$	−0.700457	−0.0261226	−0.0130613	−	0.999915i	$-0.504158\pi$
$719$	−0.700457	−0.0261226	−0.0130613	+	0.999915i	$0.504158\pi$
$720$	−0.482279	−0.0179735
$721$	−10.2479	−0.381650
$722$	−7.01094	−0.260920
$723$	19.4050	0.721680
$724$	−8.84099	−0.328573
$725$	39.6635	1.47307
$726$	57.7791	2.14438
$727$	38.6447	1.43325	0.716625	−	0.697458i	$-0.245686\pi$
$727$	38.6447	1.43325	0.716625	+	0.697458i	$0.245686\pi$
$728$	−11.2499	−0.416949
$729$	6.24313	0.231227
$730$	1.77175	0.0655756
$731$	−4.42885	−0.163807
$732$	−15.9793	−0.590611
$733$	−31.3572	−1.15820	−0.579101	−	0.815255i	$-0.696596\pi$
$733$	−31.3572	−1.15820	−0.579101	+	0.815255i	$0.696596\pi$
$734$	11.1630	0.412033
$735$	0.437633	0.0161423
$736$	−5.58485	−0.205860
$737$	68.6166	2.52752
$738$	−1.47510	−0.0542991
$739$	51.5448	1.89611	0.948054	−	0.318110i	$-0.103048\pi$
$739$	51.5448	1.89611	0.948054	+	0.318110i	$0.103048\pi$
$740$	0.632531	0.0232523
$741$	−27.1535	−0.997510
$742$	1.66588	0.0611565
$743$	−15.7347	−0.577251	−0.288626	−	0.957442i	$-0.593198\pi$
$743$	−15.7347	−0.577251	−0.288626	+	0.957442i	$0.593198\pi$
$744$	2.45697	0.0900769
$745$	−0.423814	−0.0155274
$746$	21.9252	0.802737
$747$	19.2476	0.704231
$748$	26.5254	0.969866
$749$	−5.33318	−0.194870
$750$	−4.73733	−0.172983
$751$	−12.1375	−0.442904	−0.221452	−	0.975171i	$-0.571080\pi$
$751$	−12.1375	−0.442904	−0.221452	+	0.975171i	$0.571080\pi$
$752$	−8.67433	−0.316320
$753$	6.04271	0.220209
$754$	−31.9513	−1.16360
$755$	2.46670	0.0897723
$756$	2.80522	0.102025
$757$	−17.9846	−0.653660	−0.326830	−	0.945083i	$-0.605981\pi$
$757$	−17.9846	−0.653660	−0.326830	+	0.945083i	$0.605981\pi$
$758$	−29.1707	−1.05953
$759$	−16.4300	−0.596371
$760$	2.27582	0.0825528
$761$	23.2298	0.842079	0.421039	−	0.907042i	$-0.361665\pi$
$761$	23.2298	0.842079	0.421039	+	0.907042i	$0.361665\pi$
$762$	−29.8999	−1.08316
$763$	8.82638	0.319536
$764$	16.1682	0.584945
$765$	−1.52792	−0.0552420
$766$	−26.2770	−0.949428
$767$	37.6995	1.36125
$768$	−33.1848	−1.19745
$769$	−34.9703	−1.26106	−0.630530	−	0.776165i	$-0.717162\pi$
$769$	−34.9703	−1.26106	−0.630530	+	0.776165i	$0.717162\pi$
$770$	1.37650	0.0496055
$771$	11.3019	0.407030
$772$	−14.7992	−0.532636
$773$	−26.7805	−0.963228	−0.481614	−	0.876384i	$-0.659949\pi$
$773$	−26.7805	−0.963228	−0.481614	+	0.876384i	$0.659949\pi$
$774$	1.21626	0.0437175
$775$	1.90415	0.0683991
$776$	11.1910	0.401733
$777$	−7.69944	−0.276216
$778$	17.3523	0.622111
$779$	3.54285	0.126936
$780$	−1.31424	−0.0470573
$781$	−90.2671	−3.23001
$782$	7.61333	0.272252
$783$	27.4506	0.981006
$784$	−1.69545	−0.0605516
$785$	3.95977	0.141330
$786$	29.6173	1.05642
$787$	0.177103	0.00631303	0.00315652	−	0.999995i	$-0.498995\pi$
$787$	0.177103	0.00631303	0.00315652	+	0.999995i	$0.498995\pi$
$788$	−3.66016	−0.130388
$789$	−55.8009	−1.98657
$790$	−1.37851	−0.0490452
$791$	−18.2045	−0.647277
$792$	−25.0983	−0.891829
$793$	34.3718	1.22058
$794$	−9.49621	−0.337008
$795$	0.670528	0.0237812
$796$	−8.33837	−0.295546
$797$	−15.4863	−0.548555	−0.274277	−	0.961651i	$-0.588439\pi$
$797$	−15.4863	−0.548555	−0.274277	+	0.961651i	$0.588439\pi$
$798$	−8.04024	−0.284622
$799$	−27.4813	−0.972219
$800$	−21.2322	−0.750672
$801$	0.706711	0.0249704
$802$	1.92706	0.0680469
$803$	46.9290	1.65609
$804$	−19.3986	−0.684137
$805$	−0.273327	−0.00963352
$806$	−1.53391	−0.0540296
$807$	−30.5759	−1.07632
$808$	7.52045	0.264569
$809$	−12.8695	−0.452467	−0.226234	−	0.974073i	$-0.572641\pi$
$809$	−12.8695	−0.452467	−0.226234	+	0.974073i	$0.572641\pi$
$810$	−2.55993	−0.0899467
$811$	24.8951	0.874185	0.437092	−	0.899417i	$-0.356008\pi$
$811$	24.8951	0.874185	0.437092	+	0.899417i	$0.356008\pi$
$812$	6.54525	0.229693
$813$	47.6400	1.67081
$814$	−24.2173	−0.848815
$815$	3.42309	0.119906
$816$	19.0085	0.665431
$817$	−2.92118	−0.102199
$818$	−29.4537	−1.02982
$819$	4.98170	0.174075
$820$	0.171475	0.00598817
$821$	−21.8002	−0.760834	−0.380417	−	0.924815i	$-0.624220\pi$
$821$	−21.8002	−0.760834	−0.380417	+	0.924815i	$0.624220\pi$
$822$	28.9803	1.01080
$823$	−1.76071	−0.0613744	−0.0306872	−	0.999529i	$-0.509770\pi$
$823$	−1.76071	−0.0613744	−0.0306872	+	0.999529i	$0.509770\pi$
$824$	31.3970	1.09376
$825$	−62.4627	−2.17467
$826$	11.1629	0.388408
$827$	9.93134	0.345347	0.172673	−	0.984979i	$-0.444760\pi$
$827$	9.93134	0.345347	0.172673	+	0.984979i	$0.444760\pi$
$828$	1.44645	0.0502678
$829$	4.85768	0.168714	0.0843571	−	0.996436i	$-0.473116\pi$
$829$	4.85768	0.168714	0.0843571	+	0.996436i	$0.473116\pi$
$830$	3.23416	0.112259
$831$	−17.3492	−0.601837
$832$	29.5549	1.02463
$833$	−5.37138	−0.186107
$834$	31.7174	1.09828
$835$	−4.73526	−0.163870
$836$	17.4956	0.605100
$837$	1.31784	0.0455512
$838$	−19.9390	−0.688781
$839$	15.9065	0.549152	0.274576	−	0.961565i	$-0.411463\pi$
$839$	15.9065	0.549152	0.274576	+	0.961565i	$0.411463\pi$
$840$	−1.34080	−0.0462620
$841$	35.0491	1.20859
$842$	18.1794	0.626504
$843$	36.1383	1.24467
$844$	11.4888	0.395460
$845$	0.101289	0.00348444
$846$	7.54696	0.259470
$847$	25.4598	0.874808
$848$	−2.59771	−0.0892058
$849$	−30.8536	−1.05889
$850$	28.9440	0.992770
$851$	4.80875	0.164842
$852$	25.5194	0.874282
$853$	1.08814	0.0372572	0.0186286	−	0.999826i	$-0.494070\pi$
$853$	1.08814	0.0372572	0.0186286	+	0.999826i	$0.494070\pi$
$854$	10.1776	0.348271
$855$	−1.00778	−0.0344655
$856$	16.3396	0.558475
$857$	−1.53174	−0.0523232	−0.0261616	−	0.999658i	$-0.508328\pi$
$857$	−1.53174	−0.0523232	−0.0261616	+	0.999658i	$0.508328\pi$
$858$	50.3174	1.71781
$859$	10.9042	0.372047	0.186024	−	0.982545i	$-0.440440\pi$
$859$	10.9042	0.372047	0.186024	+	0.982545i	$0.440440\pi$
$860$	−0.141386	−0.00482122
$861$	−2.08727	−0.0711340
$862$	0.222605	0.00758196
$863$	−54.7487	−1.86367	−0.931834	−	0.362884i	$-0.881792\pi$
$863$	−54.7487	−1.86367	−0.931834	+	0.362884i	$0.881792\pi$
$864$	−14.6946	−0.499919
$865$	−4.65943	−0.158426
$866$	34.7923	1.18229
$867$	24.7377	0.840136
$868$	0.314222	0.0106654
$869$	−36.5131	−1.23862
$870$	−3.80806	−0.129105
$871$	41.7270	1.41386
$872$	−27.0419	−0.915753
$873$	−4.95561	−0.167722
$874$	5.02160	0.169858
$875$	−2.08746	−0.0705690
$876$	−13.2673	−0.448261
$877$	−0.0143469	−0.000484459 0	−0.000242229	−	1.00000i	$-0.500077\pi$
$877$	−0.0143469	−0.000484459 0	−0.000242229		1.00000i	$0.500077\pi$
$878$	27.0787	0.913862
$879$	10.4288	0.351755
$880$	−2.14646	−0.0723570
$881$	−56.3960	−1.90003	−0.950014	−	0.312206i	$-0.898932\pi$
$881$	−56.3960	−1.90003	−0.950014	+	0.312206i	$0.898932\pi$
$882$	1.47510	0.0496691
$883$	−26.5606	−0.893835	−0.446917	−	0.894575i	$-0.647478\pi$
$883$	−26.5606	−0.893835	−0.446917	+	0.894575i	$0.647478\pi$
$884$	16.1306	0.542531
$885$	4.49314	0.151035
$886$	20.6907	0.695119
$887$	−29.3990	−0.987121	−0.493560	−	0.869712i	$-0.664305\pi$
$887$	−29.3990	−0.987121	−0.493560	+	0.869712i	$0.664305\pi$
$888$	23.5892	0.791603
$889$	−13.1751	−0.441879
$890$	0.118748	0.00398045
$891$	−67.8057	−2.27158
$892$	0.573714	0.0192094
$893$	−18.1261	−0.606567
$894$	−4.58734	−0.153423
$895$	−2.09866	−0.0701504
$896$	0.183089	0.00611657
$897$	−9.99137	−0.333602
$898$	−6.46936	−0.215885
$899$	3.07484	0.102552
$900$	5.49905	0.183302
$901$	−8.22986	−0.274177
$902$	−6.56515	−0.218595
$903$	1.72101	0.0572717
$904$	55.7741	1.85502
$905$	2.26653	0.0753421
$906$	26.6994	0.887027
$907$	−12.9258	−0.429196	−0.214598	−	0.976702i	$-0.568844\pi$
$907$	−12.9258	−0.429196	−0.214598	+	0.976702i	$0.568844\pi$
$908$	−7.66212	−0.254276
$909$	−3.33022	−0.110456
$910$	0.837073	0.0277487
$911$	33.8152	1.12035	0.560174	−	0.828375i	$-0.310734\pi$
$911$	33.8152	1.12035	0.560174	+	0.828375i	$0.310734\pi$
$912$	12.5376	0.415163
$913$	85.6643	2.83507
$914$	−34.6198	−1.14512
$915$	4.09655	0.135428
$916$	−10.1423	−0.335110
$917$	13.0506	0.430968
$918$	20.0318	0.661147
$919$	−2.96555	−0.0978246	−0.0489123	−	0.998803i	$-0.515575\pi$
$919$	−2.96555	−0.0978246	−0.0489123	+	0.998803i	$0.515575\pi$
$920$	0.837408	0.0276085
$921$	−16.3912	−0.540110
$922$	5.43242	0.178907
$923$	−54.8930	−1.80683
$924$	−10.3076	−0.339094
$925$	18.2817	0.601097
$926$	19.1401	0.628983
$927$	−13.9032	−0.456642
$928$	−34.2860	−1.12549
$929$	−24.4362	−0.801726	−0.400863	−	0.916138i	$-0.631290\pi$
$929$	−24.4362	−0.801726	−0.400863	+	0.916138i	$0.631290\pi$
$930$	−0.182816	−0.00599477
$931$	−3.54285	−0.116112
$932$	−7.86552	−0.257644
$933$	−56.4354	−1.84761
$934$	−46.6921	−1.52781
$935$	−6.80023	−0.222391
$936$	−15.2627	−0.498878
$937$	35.9240	1.17359	0.586793	−	0.809737i	$-0.300390\pi$
$937$	35.9240	1.17359	0.586793	+	0.809737i	$0.300390\pi$
$938$	12.3555	0.403421
$939$	−0.351482	−0.0114702
$940$	−0.877310	−0.0286147
$941$	−42.9108	−1.39885	−0.699426	−	0.714705i	$-0.746561\pi$
$941$	−42.9108	−1.39885	−0.699426	+	0.714705i	$0.746561\pi$
$942$	42.8603	1.39646
$943$	1.30362	0.0424518
$944$	−17.4070	−0.566550
$945$	−0.719163	−0.0233944
$946$	5.41314	0.175996
$947$	44.6039	1.44943	0.724716	−	0.689048i	$-0.241971\pi$
$947$	44.6039	1.44943	0.724716	+	0.689048i	$0.241971\pi$
$948$	10.3226	0.335264
$949$	28.5384	0.926395
$950$	19.0909	0.619389
$951$	11.1395	0.361225
$952$	16.4566	0.533361
$953$	−12.8800	−0.417224	−0.208612	−	0.977999i	$-0.566895\pi$
$953$	−12.8800	−0.417224	−0.208612	+	0.977999i	$0.566895\pi$
$954$	2.26010	0.0731734
$955$	−4.14499	−0.134129
$956$	13.5438	0.438037
$957$	−100.865	−3.26051
$958$	3.10143	0.100203
$959$	12.7699	0.412361
$960$	3.52245	0.113687
$961$	−30.8524	−0.995238
$962$	−14.7270	−0.474816
$963$	−7.23552	−0.233161
$964$	−7.60336	−0.244888
$965$	3.79403	0.122134
$966$	−2.95847	−0.0951874
$967$	49.0909	1.57866	0.789329	−	0.613970i	$-0.210429\pi$
$967$	49.0909	1.57866	0.789329	+	0.613970i	$0.210429\pi$
$968$	−78.0025	−2.50710
$969$	39.7207	1.27601
$970$	−0.832689	−0.0267360
$971$	−5.24060	−0.168179	−0.0840895	−	0.996458i	$-0.526798\pi$
$971$	−5.24060	−0.168179	−0.0840895	+	0.996458i	$0.526798\pi$
$972$	10.7537	0.344926
$973$	13.9759	0.448048
$974$	−6.77614	−0.217121
$975$	−37.9847	−1.21648
$976$	−15.8706	−0.508004
$977$	44.0772	1.41015	0.705077	−	0.709130i	$-0.250912\pi$
$977$	44.0772	1.41015	0.705077	+	0.709130i	$0.250912\pi$
$978$	37.0513	1.18477
$979$	3.14533	0.100525
$980$	−0.171475	−0.00547757
$981$	11.9747	0.382323
$982$	−2.32508	−0.0741963
$983$	−54.1938	−1.72851	−0.864256	−	0.503052i	$-0.832211\pi$
$983$	−54.1938	−1.72851	−0.864256	+	0.503052i	$0.832211\pi$
$984$	6.39489	0.203862
$985$	0.938341	0.0298980
$986$	46.7390	1.48847
$987$	10.6790	0.339916
$988$	10.6394	0.338485
$989$	−1.07487	−0.0341789
$990$	1.86749	0.0593528
$991$	−0.908400	−0.0288563	−0.0144281	−	0.999896i	$-0.504593\pi$
$991$	−0.908400	−0.0288563	−0.0144281	+	0.999896i	$0.504593\pi$
$992$	−1.64599	−0.0522602
$993$	−16.8945	−0.536130
$994$	−16.2540	−0.515545
$995$	2.13768	0.0677689
$996$	−24.2182	−0.767382
$997$	36.8530	1.16715	0.583573	−	0.812061i	$-0.301654\pi$
$997$	36.8530	1.16715	0.583573	+	0.812061i	$0.301654\pi$
$998$	27.3024	0.864242
$999$	12.6525	0.400308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.a.e.1.4	✓	5
3.2	odd	2		2583.2.a.r.1.2		5
4.3	odd	2		4592.2.a.bb.1.2		5
5.4	even	2		7175.2.a.n.1.2		5
7.6	odd	2		2009.2.a.n.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.4	✓	5	1.1	even	1	trivial
2009.2.a.n.1.4		5	7.6	odd	2
2583.2.a.r.1.2		5	3.2	odd	2
4592.2.a.bb.1.2		5	4.3	odd	2
7175.2.a.n.1.2		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.a (trivial)

\(f(q)\)	\(=\)	\(q+1.08727 q^{2} +2.08727 q^{3} -0.817843 q^{4} +0.209668 q^{5} +2.26943 q^{6} +1.00000 q^{7} -3.06376 q^{8} +1.35670 q^{9} +O(q^{10})\)	\(q+1.08727 q^{2} +2.08727 q^{3} -0.817843 q^{4} +0.209668 q^{5} +2.26943 q^{6} +1.00000 q^{7} -3.06376 q^{8} +1.35670 q^{9} +0.227965 q^{10} +6.03819 q^{11} -1.70706 q^{12} +3.67193 q^{13} +1.08727 q^{14} +0.437633 q^{15} -1.69545 q^{16} -5.37138 q^{17} +1.47510 q^{18} -3.54285 q^{19} -0.171475 q^{20} +2.08727 q^{21} +6.56515 q^{22} -1.30362 q^{23} -6.39489 q^{24} -4.95604 q^{25} +3.99238 q^{26} -3.43002 q^{27} -0.817843 q^{28} -8.00307 q^{29} +0.475825 q^{30} -0.384208 q^{31} +4.28411 q^{32} +12.6033 q^{33} -5.84014 q^{34} +0.209668 q^{35} -1.10957 q^{36} -3.68876 q^{37} -3.85204 q^{38} +7.66432 q^{39} -0.642370 q^{40} -1.00000 q^{41} +2.26943 q^{42} +0.824527 q^{43} -4.93829 q^{44} +0.284455 q^{45} -1.41739 q^{46} +5.11625 q^{47} -3.53885 q^{48} +1.00000 q^{49} -5.38855 q^{50} -11.2115 q^{51} -3.00307 q^{52} +1.53217 q^{53} -3.72936 q^{54} +1.26601 q^{55} -3.06376 q^{56} -7.39489 q^{57} -8.70150 q^{58} +10.2669 q^{59} -0.357915 q^{60} +9.36070 q^{61} -0.417738 q^{62} +1.35670 q^{63} +8.04887 q^{64} +0.769885 q^{65} +13.7032 q^{66} +11.3638 q^{67} +4.39294 q^{68} -2.72101 q^{69} +0.227965 q^{70} -14.9494 q^{71} -4.15659 q^{72} +7.77203 q^{73} -4.01068 q^{74} -10.3446 q^{75} +2.89750 q^{76} +6.03819 q^{77} +8.33318 q^{78} -6.04703 q^{79} -0.355480 q^{80} -11.2295 q^{81} -1.08727 q^{82} +14.1871 q^{83} -1.70706 q^{84} -1.12620 q^{85} +0.896484 q^{86} -16.7046 q^{87} -18.4996 q^{88} +0.520905 q^{89} +0.309280 q^{90} +3.67193 q^{91} +1.06616 q^{92} -0.801946 q^{93} +5.56275 q^{94} -0.742821 q^{95} +8.94209 q^{96} -3.65270 q^{97} +1.08727 q^{98} +8.19200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q - q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 12 * q^6 + 5 * q^7 - 3 * q^8 + q^9	\( 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9} + 2 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - 5 q^{15} - q^{16} + 13 q^{17} + 21 q^{18} - 23 q^{20} + 4 q^{21} + q^{22} + 2 q^{23} + 2 q^{24} + 22 q^{25} + 10 q^{27} + 3 q^{28} - 5 q^{29} - 33 q^{30} + 17 q^{31} - 12 q^{32} + 3 q^{33} - 8 q^{34} - 5 q^{35} + 15 q^{36} - 7 q^{37} - 3 q^{38} + 5 q^{39} + 7 q^{40} - 5 q^{41} + 12 q^{42} + q^{43} - 47 q^{44} - 23 q^{45} - 24 q^{46} + 9 q^{47} - 19 q^{48} + 5 q^{49} + 2 q^{50} + 5 q^{51} + 20 q^{52} + 5 q^{53} + 2 q^{54} + 33 q^{55} - 3 q^{56} - 3 q^{57} - 27 q^{58} + 7 q^{59} - 16 q^{60} + 22 q^{61} - 28 q^{62} + q^{63} - 3 q^{64} - 31 q^{65} - 42 q^{66} - 3 q^{67} + 17 q^{68} - 22 q^{69} - 24 q^{71} - 12 q^{72} + 40 q^{73} - 5 q^{74} + 24 q^{75} - 19 q^{76} + 2 q^{77} + 30 q^{78} - 42 q^{79} + 24 q^{80} + 9 q^{81} + q^{82} - 12 q^{83} - 2 q^{84} - 23 q^{85} + 16 q^{86} - 32 q^{87} + 26 q^{88} + 8 q^{89} - 59 q^{90} + 5 q^{91} + 12 q^{92} - 11 q^{93} - 23 q^{94} - 17 q^{95} - 17 q^{96} + 16 q^{97} - q^{98} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 12 * q^6 + 5 * q^7 - 3 * q^8 + q^9 + 2 * q^11 - 2 * q^12 + 5 * q^13 - q^14 - 5 * q^15 - q^16 + 13 * q^17 + 21 * q^18 - 23 * q^20 + 4 * q^21 + q^22 + 2 * q^23 + 2 * q^24 + 22 * q^25 + 10 * q^27 + 3 * q^28 - 5 * q^29 - 33 * q^30 + 17 * q^31 - 12 * q^32 + 3 * q^33 - 8 * q^34 - 5 * q^35 + 15 * q^36 - 7 * q^37 - 3 * q^38 + 5 * q^39 + 7 * q^40 - 5 * q^41 + 12 * q^42 + q^43 - 47 * q^44 - 23 * q^45 - 24 * q^46 + 9 * q^47 - 19 * q^48 + 5 * q^49 + 2 * q^50 + 5 * q^51 + 20 * q^52 + 5 * q^53 + 2 * q^54 + 33 * q^55 - 3 * q^56 - 3 * q^57 - 27 * q^58 + 7 * q^59 - 16 * q^60 + 22 * q^61 - 28 * q^62 + q^63 - 3 * q^64 - 31 * q^65 - 42 * q^66 - 3 * q^67 + 17 * q^68 - 22 * q^69 - 24 * q^71 - 12 * q^72 + 40 * q^73 - 5 * q^74 + 24 * q^75 - 19 * q^76 + 2 * q^77 + 30 * q^78 - 42 * q^79 + 24 * q^80 + 9 * q^81 + q^82 - 12 * q^83 - 2 * q^84 - 23 * q^85 + 16 * q^86 - 32 * q^87 + 26 * q^88 + 8 * q^89 - 59 * q^90 + 5 * q^91 + 12 * q^92 - 11 * q^93 - 23 * q^94 - 17 * q^95 - 17 * q^96 + 16 * q^97 - q^98 - 45 * q^99

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