LMFDB - Embedded newform 9282.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.23665.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 8x + 3 $ x^4 - x^3 - 7x^2 + 8x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.300431$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.43470 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.43470 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.43470 q^{10} +5.47504 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} -1.43470 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.735132 q^{19} +1.43470 q^{20} -1.00000 q^{21} -5.47504 q^{22} +0.833838 q^{23} +1.00000 q^{24} -2.94163 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.04034 q^{29} +1.43470 q^{30} -6.28607 q^{31} -1.00000 q^{32} -5.47504 q^{33} -1.00000 q^{34} +1.43470 q^{35} +1.00000 q^{36} +8.28607 q^{37} -0.735132 q^{38} -1.00000 q^{39} -1.43470 q^{40} -1.51060 q^{41} +1.00000 q^{42} +8.51905 q^{43} +5.47504 q^{44} +1.43470 q^{45} -0.833838 q^{46} -0.909741 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.94163 q^{50} -1.00000 q^{51} +1.00000 q^{52} -5.38845 q^{53} +1.00000 q^{54} +7.85505 q^{55} -1.00000 q^{56} -0.735132 q^{57} +4.04034 q^{58} +3.34077 q^{59} -1.43470 q^{60} +9.85982 q^{61} +6.28607 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.43470 q^{65} +5.47504 q^{66} -0.395465 q^{67} +1.00000 q^{68} -0.833838 q^{69} -1.43470 q^{70} +10.1115 q^{71} -1.00000 q^{72} +7.00845 q^{73} -8.28607 q^{74} +2.94163 q^{75} +0.735132 q^{76} +5.47504 q^{77} +1.00000 q^{78} -13.3301 q^{79} +1.43470 q^{80} +1.00000 q^{81} +1.51060 q^{82} -0.169833 q^{83} -1.00000 q^{84} +1.43470 q^{85} -8.51905 q^{86} +4.04034 q^{87} -5.47504 q^{88} -6.64120 q^{89} -1.43470 q^{90} +1.00000 q^{91} +0.833838 q^{92} +6.28607 q^{93} +0.909741 q^{94} +1.05470 q^{95} +1.00000 q^{96} +15.2362 q^{97} -1.00000 q^{98} +5.47504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 9 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - q^{19} + 4 q^{20} - 4 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 5 q^{29} + 4 q^{30} + 9 q^{31} - 4 q^{32} - 9 q^{33} - 4 q^{34} + 4 q^{35} + 4 q^{36} - q^{37} + q^{38} - 4 q^{39} - 4 q^{40} + 13 q^{41} + 4 q^{42} + 7 q^{43} + 9 q^{44} + 4 q^{45} - 6 q^{46} + 11 q^{47} - 4 q^{48} + 4 q^{49} - 6 q^{50} - 4 q^{51} + 4 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} - 4 q^{56} + q^{57} + 5 q^{58} - 4 q^{60} - q^{61} - 9 q^{62} + 4 q^{63} + 4 q^{64} + 4 q^{65} + 9 q^{66} - 9 q^{67} + 4 q^{68} - 6 q^{69} - 4 q^{70} + 17 q^{71} - 4 q^{72} + 20 q^{73} + q^{74} - 6 q^{75} - q^{76} + 9 q^{77} + 4 q^{78} - 5 q^{79} + 4 q^{80} + 4 q^{81} - 13 q^{82} + 5 q^{83} - 4 q^{84} + 4 q^{85} - 7 q^{86} + 5 q^{87} - 9 q^{88} - 11 q^{89} - 4 q^{90} + 4 q^{91} + 6 q^{92} - 9 q^{93} - 11 q^{94} + 25 q^{95} + 4 q^{96} + q^{97} - 4 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 9 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - q^19 + 4 * q^20 - 4 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 5 * q^29 + 4 * q^30 + 9 * q^31 - 4 * q^32 - 9 * q^33 - 4 * q^34 + 4 * q^35 + 4 * q^36 - q^37 + q^38 - 4 * q^39 - 4 * q^40 + 13 * q^41 + 4 * q^42 + 7 * q^43 + 9 * q^44 + 4 * q^45 - 6 * q^46 + 11 * q^47 - 4 * q^48 + 4 * q^49 - 6 * q^50 - 4 * q^51 + 4 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 - 4 * q^56 + q^57 + 5 * q^58 - 4 * q^60 - q^61 - 9 * q^62 + 4 * q^63 + 4 * q^64 + 4 * q^65 + 9 * q^66 - 9 * q^67 + 4 * q^68 - 6 * q^69 - 4 * q^70 + 17 * q^71 - 4 * q^72 + 20 * q^73 + q^74 - 6 * q^75 - q^76 + 9 * q^77 + 4 * q^78 - 5 * q^79 + 4 * q^80 + 4 * q^81 - 13 * q^82 + 5 * q^83 - 4 * q^84 + 4 * q^85 - 7 * q^86 + 5 * q^87 - 9 * q^88 - 11 * q^89 - 4 * q^90 + 4 * q^91 + 6 * q^92 - 9 * q^93 - 11 * q^94 + 25 * q^95 + 4 * q^96 + q^97 - 4 * q^98 + 9 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.43470	0.641618	0.320809	−	0.947144i	$-0.396045\pi$
$5$	1.43470	0.641618	0.320809	+	0.947144i	$0.396045\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.43470	−0.453692
$11$	5.47504	1.65079	0.825393	−	0.564558i	$-0.190953\pi$
$11$	5.47504	1.65079	0.825393	+	0.564558i	$0.190953\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.00000	−0.267261
$15$	−1.43470	−0.370438
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	0.735132	0.168651	0.0843255	−	0.996438i	$-0.473126\pi$
$19$	0.735132	0.168651	0.0843255	+	0.996438i	$0.473126\pi$
$20$	1.43470	0.320809
$21$	−1.00000	−0.218218
$22$	−5.47504	−1.16728
$23$	0.833838	0.173867	0.0869337	−	0.996214i	$-0.472293\pi$
$23$	0.833838	0.173867	0.0869337	+	0.996214i	$0.472293\pi$
$24$	1.00000	0.204124
$25$	−2.94163	−0.588327
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−4.04034	−0.750272	−0.375136	−	0.926970i	$-0.622404\pi$
$29$	−4.04034	−0.750272	−0.375136	+	0.926970i	$0.622404\pi$
$30$	1.43470	0.261939
$31$	−6.28607	−1.12901	−0.564506	−	0.825429i	$-0.690933\pi$
$31$	−6.28607	−1.12901	−0.564506	+	0.825429i	$0.690933\pi$
$32$	−1.00000	−0.176777
$33$	−5.47504	−0.953082
$34$	−1.00000	−0.171499
$35$	1.43470	0.242509
$36$	1.00000	0.166667
$37$	8.28607	1.36222	0.681111	−	0.732180i	$-0.261497\pi$
$37$	8.28607	1.36222	0.681111	+	0.732180i	$0.261497\pi$
$38$	−0.735132	−0.119254
$39$	−1.00000	−0.160128
$40$	−1.43470	−0.226846
$41$	−1.51060	−0.235917	−0.117958	−	0.993019i	$-0.537635\pi$
$41$	−1.51060	−0.235917	−0.117958	+	0.993019i	$0.537635\pi$
$42$	1.00000	0.154303
$43$	8.51905	1.29914	0.649572	−	0.760300i	$-0.274948\pi$
$43$	8.51905	1.29914	0.649572	+	0.760300i	$0.274948\pi$
$44$	5.47504	0.825393
$45$	1.43470	0.213873
$46$	−0.833838	−0.122943
$47$	−0.909741	−0.132699	−0.0663497	−	0.997796i	$-0.521135\pi$
$47$	−0.909741	−0.132699	−0.0663497	+	0.997796i	$0.521135\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.94163	0.416010
$51$	−1.00000	−0.140028
$52$	1.00000	0.138675
$53$	−5.38845	−0.740161	−0.370080	−	0.929000i	$-0.620670\pi$
$53$	−5.38845	−0.740161	−0.370080	+	0.929000i	$0.620670\pi$
$54$	1.00000	0.136083
$55$	7.85505	1.05917
$56$	−1.00000	−0.133631
$57$	−0.735132	−0.0973707
$58$	4.04034	0.530522
$59$	3.34077	0.434931	0.217466	−	0.976068i	$-0.430221\pi$
$59$	3.34077	0.434931	0.217466	+	0.976068i	$0.430221\pi$
$60$	−1.43470	−0.185219
$61$	9.85982	1.26242	0.631210	−	0.775612i	$-0.282558\pi$
$61$	9.85982	1.26242	0.631210	+	0.775612i	$0.282558\pi$
$62$	6.28607	0.798332
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	1.43470	0.177953
$66$	5.47504	0.673931
$67$	−0.395465	−0.0483138	−0.0241569	−	0.999708i	$-0.507690\pi$
$67$	−0.395465	−0.0483138	−0.0241569	+	0.999708i	$0.507690\pi$
$68$	1.00000	0.121268
$69$	−0.833838	−0.100382
$70$	−1.43470	−0.171480
$71$	10.1115	1.20001	0.600005	−	0.799996i	$-0.295165\pi$
$71$	10.1115	1.20001	0.600005	+	0.799996i	$0.295165\pi$
$72$	−1.00000	−0.117851
$73$	7.00845	0.820277	0.410138	−	0.912023i	$-0.365480\pi$
$73$	7.00845	0.820277	0.410138	+	0.912023i	$0.365480\pi$
$74$	−8.28607	−0.963237
$75$	2.94163	0.339670
$76$	0.735132	0.0843255
$77$	5.47504	0.623939
$78$	1.00000	0.113228
$79$	−13.3301	−1.49975	−0.749876	−	0.661579i	$-0.769887\pi$
$79$	−13.3301	−1.49975	−0.749876	+	0.661579i	$0.769887\pi$
$80$	1.43470	0.160404
$81$	1.00000	0.111111
$82$	1.51060	0.166818
$83$	−0.169833	−0.0186416	−0.00932082	−	0.999957i	$-0.502967\pi$
$83$	−0.169833	−0.0186416	−0.00932082	+	0.999957i	$0.502967\pi$
$84$	−1.00000	−0.109109
$85$	1.43470	0.155615
$86$	−8.51905	−0.918633
$87$	4.04034	0.433170
$88$	−5.47504	−0.583641
$89$	−6.64120	−0.703966	−0.351983	−	0.936006i	$-0.614493\pi$
$89$	−6.64120	−0.703966	−0.351983	+	0.936006i	$0.614493\pi$
$90$	−1.43470	−0.151231
$91$	1.00000	0.104828
$92$	0.833838	0.0869337
$93$	6.28607	0.651836
$94$	0.909741	0.0938326
$95$	1.05470	0.108209
$96$	1.00000	0.102062
$97$	15.2362	1.54700	0.773499	−	0.633798i	$-0.218505\pi$
$97$	15.2362	1.54700	0.773499	+	0.633798i	$0.218505\pi$
$98$	−1.00000	−0.101015
$99$	5.47504	0.550262
$100$	−2.94163	−0.294163
$101$	18.0579	1.79683	0.898413	−	0.439152i	$-0.144721\pi$
$101$	18.0579	1.79683	0.898413	+	0.439152i	$0.144721\pi$
$102$	1.00000	0.0990148
$103$	5.20173	0.512541	0.256271	−	0.966605i	$-0.417506\pi$
$103$	5.20173	0.512541	0.256271	+	0.966605i	$0.417506\pi$
$104$	−1.00000	−0.0980581
$105$	−1.43470	−0.140012
$106$	5.38845	0.523373
$107$	−3.95375	−0.382224	−0.191112	−	0.981568i	$-0.561209\pi$
$107$	−3.95375	−0.382224	−0.191112	+	0.981568i	$0.561209\pi$
$108$	−1.00000	−0.0962250
$109$	−4.79350	−0.459134	−0.229567	−	0.973293i	$-0.573731\pi$
$109$	−4.79350	−0.459134	−0.229567	+	0.973293i	$0.573731\pi$
$110$	−7.85505	−0.748949
$111$	−8.28607	−0.786479
$112$	1.00000	0.0944911
$113$	18.6661	1.75596	0.877979	−	0.478700i	$-0.158892\pi$
$113$	18.6661	1.75596	0.877979	+	0.478700i	$0.158892\pi$
$114$	0.735132	0.0688515
$115$	1.19631	0.111556
$116$	−4.04034	−0.375136
$117$	1.00000	0.0924500
$118$	−3.34077	−0.307543
$119$	1.00000	0.0916698
$120$	1.43470	0.130970
$121$	18.9761	1.72510
$122$	−9.85982	−0.892666
$123$	1.51060	0.136207
$124$	−6.28607	−0.564506
$125$	−11.3939	−1.01910
$126$	−1.00000	−0.0890871
$127$	−5.80145	−0.514796	−0.257398	−	0.966306i	$-0.582865\pi$
$127$	−5.80145	−0.514796	−0.257398	+	0.966306i	$0.582865\pi$
$128$	−1.00000	−0.0883883
$129$	−8.51905	−0.750061
$130$	−1.43470	−0.125832
$131$	20.6661	1.80560	0.902802	−	0.430057i	$-0.141506\pi$
$131$	20.6661	1.80560	0.902802	+	0.430057i	$0.141506\pi$
$132$	−5.47504	−0.476541
$133$	0.735132	0.0637441
$134$	0.395465	0.0341630
$135$	−1.43470	−0.123479
$136$	−1.00000	−0.0857493
$137$	−18.6661	−1.59475	−0.797375	−	0.603484i	$-0.793779\pi$
$137$	−18.6661	−1.59475	−0.797375	+	0.603484i	$0.793779\pi$
$138$	0.833838	0.0709810
$139$	−15.2234	−1.29123	−0.645616	−	0.763662i	$-0.723399\pi$
$139$	−15.2234	−1.29123	−0.645616	+	0.763662i	$0.723399\pi$
$140$	1.43470	0.121254
$141$	0.909741	0.0766140
$142$	−10.1115	−0.848535
$143$	5.47504	0.457846
$144$	1.00000	0.0833333
$145$	−5.79668	−0.481388
$146$	−7.00845	−0.580023
$147$	−1.00000	−0.0824786
$148$	8.28607	0.681111
$149$	−4.43103	−0.363004	−0.181502	−	0.983391i	$-0.558096\pi$
$149$	−4.43103	−0.363004	−0.181502	+	0.983391i	$0.558096\pi$
$150$	−2.94163	−0.240183
$151$	20.5439	1.67184	0.835921	−	0.548850i	$-0.184934\pi$
$151$	20.5439	1.67184	0.835921	+	0.548850i	$0.184934\pi$
$152$	−0.735132	−0.0596271
$153$	1.00000	0.0808452
$154$	−5.47504	−0.441191
$155$	−9.01864	−0.724394
$156$	−1.00000	−0.0800641
$157$	0.0403388	0.00321939	0.00160970	−	0.999999i	$-0.499488\pi$
$157$	0.0403388	0.00321939	0.00160970	+	0.999999i	$0.499488\pi$
$158$	13.3301	1.06048
$159$	5.38845	0.427332
$160$	−1.43470	−0.113423
$161$	0.833838	0.0657157
$162$	−1.00000	−0.0785674
$163$	−23.8136	−1.86522	−0.932611	−	0.360882i	$-0.882476\pi$
$163$	−23.8136	−1.86522	−0.932611	+	0.360882i	$0.882476\pi$
$164$	−1.51060	−0.117958
$165$	−7.85505	−0.611514
$166$	0.169833	0.0131816
$167$	−4.42512	−0.342426	−0.171213	−	0.985234i	$-0.554769\pi$
$167$	−4.42512	−0.342426	−0.171213	+	0.985234i	$0.554769\pi$
$168$	1.00000	0.0771517
$169$	1.00000	0.0769231
$170$	−1.43470	−0.110037
$171$	0.735132	0.0562170
$172$	8.51905	0.649572
$173$	−5.83017	−0.443259	−0.221630	−	0.975131i	$-0.571138\pi$
$173$	−5.83017	−0.443259	−0.221630	+	0.975131i	$0.571138\pi$
$174$	−4.04034	−0.306297
$175$	−2.94163	−0.222367
$176$	5.47504	0.412697
$177$	−3.34077	−0.251108
$178$	6.64120	0.497779
$179$	12.3264	0.921319	0.460660	−	0.887577i	$-0.347613\pi$
$179$	12.3264	0.921319	0.460660	+	0.887577i	$0.347613\pi$
$180$	1.43470	0.106936
$181$	2.22229	0.165182	0.0825908	−	0.996584i	$-0.473681\pi$
$181$	2.22229	0.165182	0.0825908	+	0.996584i	$0.473681\pi$
$182$	−1.00000	−0.0741249
$183$	−9.85982	−0.728859
$184$	−0.833838	−0.0614714
$185$	11.8880	0.874026
$186$	−6.28607	−0.460917
$187$	5.47504	0.400375
$188$	−0.909741	−0.0663497
$189$	−1.00000	−0.0727393
$190$	−1.05470	−0.0765156
$191$	−15.3704	−1.11216	−0.556082	−	0.831127i	$-0.687696\pi$
$191$	−15.3704	−1.11216	−0.556082	+	0.831127i	$0.687696\pi$
$192$	−1.00000	−0.0721688
$193$	−14.1331	−1.01733	−0.508663	−	0.860966i	$-0.669860\pi$
$193$	−14.1331	−1.01733	−0.508663	+	0.860966i	$0.669860\pi$
$194$	−15.2362	−1.09389
$195$	−1.43470	−0.102741
$196$	1.00000	0.0714286
$197$	14.5667	1.03784	0.518918	−	0.854824i	$-0.326335\pi$
$197$	14.5667	1.03784	0.518918	+	0.854824i	$0.326335\pi$
$198$	−5.47504	−0.389094
$199$	−3.70866	−0.262900	−0.131450	−	0.991323i	$-0.541963\pi$
$199$	−3.70866	−0.262900	−0.131450	+	0.991323i	$0.541963\pi$
$200$	2.94163	0.208005
$201$	0.395465	0.0278940
$202$	−18.0579	−1.27055
$203$	−4.04034	−0.283576
$204$	−1.00000	−0.0700140
$205$	−2.16726	−0.151368
$206$	−5.20173	−0.362421
$207$	0.833838	0.0579558
$208$	1.00000	0.0693375
$209$	4.02488	0.278407
$210$	1.43470	0.0990038
$211$	−15.8364	−1.09022	−0.545111	−	0.838364i	$-0.683512\pi$
$211$	−15.8364	−1.09022	−0.545111	+	0.838364i	$0.683512\pi$
$212$	−5.38845	−0.370080
$213$	−10.1115	−0.692826
$214$	3.95375	0.270273
$215$	12.2223	0.833553
$216$	1.00000	0.0680414
$217$	−6.28607	−0.426727
$218$	4.79350	0.324657
$219$	−7.00845	−0.473587
$220$	7.85505	0.529587
$221$	1.00000	0.0672673
$222$	8.28607	0.556125
$223$	0.641201	0.0429380	0.0214690	−	0.999770i	$-0.493166\pi$
$223$	0.641201	0.0429380	0.0214690	+	0.999770i	$0.493166\pi$
$224$	−1.00000	−0.0668153
$225$	−2.94163	−0.196109
$226$	−18.6661	−1.24165
$227$	14.4607	0.959789	0.479895	−	0.877326i	$-0.340675\pi$
$227$	14.4607	0.959789	0.479895	+	0.877326i	$0.340675\pi$
$228$	−0.735132	−0.0486853
$229$	17.6624	1.16716	0.583582	−	0.812054i	$-0.301651\pi$
$229$	17.6624	1.16716	0.583582	+	0.812054i	$0.301651\pi$
$230$	−1.19631	−0.0788823
$231$	−5.47504	−0.360231
$232$	4.04034	0.265261
$233$	−18.0641	−1.18342	−0.591709	−	0.806152i	$-0.701546\pi$
$233$	−18.0641	−1.18342	−0.591709	+	0.806152i	$0.701546\pi$
$234$	−1.00000	−0.0653720
$235$	−1.30521	−0.0851423
$236$	3.34077	0.217466
$237$	13.3301	0.865882
$238$	−1.00000	−0.0648204
$239$	−5.59719	−0.362052	−0.181026	−	0.983478i	$-0.557942\pi$
$239$	−5.59719	−0.362052	−0.181026	+	0.983478i	$0.557942\pi$
$240$	−1.43470	−0.0926096
$241$	−5.03924	−0.324606	−0.162303	−	0.986741i	$-0.551892\pi$
$241$	−5.03924	−0.324606	−0.162303	+	0.986741i	$0.551892\pi$
$242$	−18.9761	−1.21983
$243$	−1.00000	−0.0641500
$244$	9.85982	0.631210
$245$	1.43470	0.0916597
$246$	−1.51060	−0.0963126
$247$	0.735132	0.0467754
$248$	6.28607	0.399166
$249$	0.169833	0.0107628
$250$	11.3939	0.720612
$251$	25.1650	1.58840	0.794201	−	0.607655i	$-0.207890\pi$
$251$	25.1650	1.58840	0.794201	+	0.607655i	$0.207890\pi$
$252$	1.00000	0.0629941
$253$	4.56530	0.287018
$254$	5.80145	0.364016
$255$	−1.43470	−0.0898445
$256$	1.00000	0.0625000
$257$	2.24366	0.139956	0.0699778	−	0.997549i	$-0.477707\pi$
$257$	2.24366	0.139956	0.0699778	+	0.997549i	$0.477707\pi$
$258$	8.51905	0.530373
$259$	8.28607	0.514872
$260$	1.43470	0.0889764
$261$	−4.04034	−0.250091
$262$	−20.6661	−1.27675
$263$	31.6968	1.95451	0.977255	−	0.212066i	$-0.0680191\pi$
$263$	31.6968	1.95451	0.977255	+	0.212066i	$0.0680191\pi$
$264$	5.47504	0.336965
$265$	−7.73082	−0.474900
$266$	−0.735132	−0.0450739
$267$	6.64120	0.406435
$268$	−0.395465	−0.0241569
$269$	25.8901	1.57855	0.789274	−	0.614041i	$-0.210457\pi$
$269$	25.8901	1.57855	0.789274	+	0.614041i	$0.210457\pi$
$270$	1.43470	0.0873131
$271$	−17.5281	−1.06476	−0.532379	−	0.846506i	$-0.678702\pi$
$271$	−17.5281	−1.06476	−0.532379	+	0.846506i	$0.678702\pi$
$272$	1.00000	0.0606339
$273$	−1.00000	−0.0605228
$274$	18.6661	1.12766
$275$	−16.1056	−0.971202
$276$	−0.833838	−0.0501912
$277$	−19.1045	−1.14788	−0.573938	−	0.818899i	$-0.694585\pi$
$277$	−19.1045	−1.14788	−0.573938	+	0.818899i	$0.694585\pi$
$278$	15.2234	0.913039
$279$	−6.28607	−0.376337
$280$	−1.43470	−0.0857398
$281$	3.74214	0.223238	0.111619	−	0.993751i	$-0.464396\pi$
$281$	3.74214	0.223238	0.111619	+	0.993751i	$0.464396\pi$
$282$	−0.909741	−0.0541743
$283$	29.9580	1.78082	0.890410	−	0.455159i	$-0.150418\pi$
$283$	29.9580	1.78082	0.890410	+	0.455159i	$0.150418\pi$
$284$	10.1115	0.600005
$285$	−1.05470	−0.0624748
$286$	−5.47504	−0.323746
$287$	−1.51060	−0.0891681
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	5.79668	0.340393
$291$	−15.2362	−0.893159
$292$	7.00845	0.410138
$293$	12.2218	0.714005	0.357003	−	0.934103i	$-0.383799\pi$
$293$	12.2218	0.714005	0.357003	+	0.934103i	$0.383799\pi$
$294$	1.00000	0.0583212
$295$	4.79301	0.279060
$296$	−8.28607	−0.481618
$297$	−5.47504	−0.317694
$298$	4.43103	0.256683
$299$	0.833838	0.0482221
$300$	2.94163	0.169835
$301$	8.51905	0.491030
$302$	−20.5439	−1.18217
$303$	−18.0579	−1.03740
$304$	0.735132	0.0421627
$305$	14.1459	0.809992
$306$	−1.00000	−0.0571662
$307$	−33.9781	−1.93923	−0.969617	−	0.244627i	$-0.921335\pi$
$307$	−33.9781	−1.93923	−0.969617	+	0.244627i	$0.921335\pi$
$308$	5.47504	0.311969
$309$	−5.20173	−0.295916
$310$	9.01864	0.512224
$311$	−6.34558	−0.359825	−0.179912	−	0.983683i	$-0.557581\pi$
$311$	−6.34558	−0.359825	−0.179912	+	0.983683i	$0.557581\pi$
$312$	1.00000	0.0566139
$313$	−15.4336	−0.872357	−0.436178	−	0.899860i	$-0.643668\pi$
$313$	−15.4336	−0.872357	−0.436178	+	0.899860i	$0.643668\pi$
$314$	−0.0403388	−0.00227645
$315$	1.43470	0.0808362
$316$	−13.3301	−0.749876
$317$	18.5755	1.04330	0.521652	−	0.853159i	$-0.325316\pi$
$317$	18.5755	1.04330	0.521652	+	0.853159i	$0.325316\pi$
$318$	−5.38845	−0.302169
$319$	−22.1210	−1.23854
$320$	1.43470	0.0802022
$321$	3.95375	0.220677
$322$	−0.833838	−0.0464680
$323$	0.735132	0.0409039
$324$	1.00000	0.0555556
$325$	−2.94163	−0.163172
$326$	23.8136	1.31891
$327$	4.79350	0.265081
$328$	1.51060	0.0834091
$329$	−0.909741	−0.0501556
$330$	7.85505	0.432406
$331$	25.7801	1.41700	0.708501	−	0.705710i	$-0.249372\pi$
$331$	25.7801	1.41700	0.708501	+	0.705710i	$0.249372\pi$
$332$	−0.169833	−0.00932082
$333$	8.28607	0.454074
$334$	4.42512	0.242132
$335$	−0.567375	−0.0309990
$336$	−1.00000	−0.0545545
$337$	−12.2336	−0.666408	−0.333204	−	0.942855i	$-0.608130\pi$
$337$	−12.2336	−0.666408	−0.333204	+	0.942855i	$0.608130\pi$
$338$	−1.00000	−0.0543928
$339$	−18.6661	−1.01380
$340$	1.43470	0.0778076
$341$	−34.4165	−1.86376
$342$	−0.735132	−0.0397514
$343$	1.00000	0.0539949
$344$	−8.51905	−0.459316
$345$	−1.19631	−0.0644071
$346$	5.83017	0.313432
$347$	28.9697	1.55517	0.777587	−	0.628775i	$-0.216443\pi$
$347$	28.9697	1.55517	0.777587	+	0.628775i	$0.216443\pi$
$348$	4.04034	0.216585
$349$	−15.5572	−0.832755	−0.416378	−	0.909192i	$-0.636701\pi$
$349$	−15.5572	−0.832755	−0.416378	+	0.909192i	$0.636701\pi$
$350$	2.94163	0.157237
$351$	−1.00000	−0.0533761
$352$	−5.47504	−0.291821
$353$	−12.9107	−0.687166	−0.343583	−	0.939122i	$-0.611641\pi$
$353$	−12.9107	−0.687166	−0.343583	+	0.939122i	$0.611641\pi$
$354$	3.34077	0.177560
$355$	14.5069	0.769948
$356$	−6.64120	−0.351983
$357$	−1.00000	−0.0529256
$358$	−12.3264	−0.651471
$359$	27.0556	1.42794	0.713971	−	0.700175i	$-0.246895\pi$
$359$	27.0556	1.42794	0.713971	+	0.700175i	$0.246895\pi$
$360$	−1.43470	−0.0756154
$361$	−18.4596	−0.971557
$362$	−2.22229	−0.116801
$363$	−18.9761	−0.995985
$364$	1.00000	0.0524142
$365$	10.0550	0.526304
$366$	9.85982	0.515381
$367$	−20.1862	−1.05371	−0.526856	−	0.849954i	$-0.676629\pi$
$367$	−20.1862	−1.05371	−0.526856	+	0.849954i	$0.676629\pi$
$368$	0.833838	0.0434668
$369$	−1.51060	−0.0786389
$370$	−11.8880	−0.618030
$371$	−5.38845	−0.279755
$372$	6.28607	0.325918
$373$	−0.783949	−0.0405914	−0.0202957	−	0.999794i	$-0.506461\pi$
$373$	−0.783949	−0.0405914	−0.0202957	+	0.999794i	$0.506461\pi$
$374$	−5.47504	−0.283108
$375$	11.3939	0.588377
$376$	0.909741	0.0469163
$377$	−4.04034	−0.208088
$378$	1.00000	0.0514344
$379$	−3.27108	−0.168024	−0.0840120	−	0.996465i	$-0.526773\pi$
$379$	−3.27108	−0.168024	−0.0840120	+	0.996465i	$0.526773\pi$
$380$	1.05470	0.0541047
$381$	5.80145	0.297217
$382$	15.3704	0.786419
$383$	35.8466	1.83167	0.915837	−	0.401550i	$-0.131528\pi$
$383$	35.8466	1.83167	0.915837	+	0.401550i	$0.131528\pi$
$384$	1.00000	0.0510310
$385$	7.85505	0.400330
$386$	14.1331	0.719358
$387$	8.51905	0.433048
$388$	15.2362	0.773499
$389$	−5.46770	−0.277223	−0.138612	−	0.990347i	$-0.544264\pi$
$389$	−5.46770	−0.277223	−0.138612	+	0.990347i	$0.544264\pi$
$390$	1.43470	0.0726489
$391$	0.833838	0.0421690
$392$	−1.00000	−0.0505076
$393$	−20.6661	−1.04247
$394$	−14.5667	−0.733861
$395$	−19.1247	−0.962268
$396$	5.47504	0.275131
$397$	10.6820	0.536116	0.268058	−	0.963403i	$-0.413618\pi$
$397$	10.6820	0.536116	0.268058	+	0.963403i	$0.413618\pi$
$398$	3.70866	0.185898
$399$	−0.735132	−0.0368027
$400$	−2.94163	−0.147082
$401$	−19.5281	−0.975189	−0.487594	−	0.873070i	$-0.662125\pi$
$401$	−19.5281	−0.975189	−0.487594	+	0.873070i	$0.662125\pi$
$402$	−0.395465	−0.0197240
$403$	−6.28607	−0.313132
$404$	18.0579	0.898413
$405$	1.43470	0.0712909
$406$	4.04034	0.200519
$407$	45.3666	2.24874
$408$	1.00000	0.0495074
$409$	−18.5950	−0.919461	−0.459731	−	0.888058i	$-0.652054\pi$
$409$	−18.5950	−0.919461	−0.459731	+	0.888058i	$0.652054\pi$
$410$	2.16726	0.107034
$411$	18.6661	0.920730
$412$	5.20173	0.256271
$413$	3.34077	0.164389
$414$	−0.833838	−0.0409809
$415$	−0.243660	−0.0119608
$416$	−1.00000	−0.0490290
$417$	15.2234	0.745493
$418$	−4.02488	−0.196863
$419$	−4.26376	−0.208299	−0.104149	−	0.994562i	$-0.533212\pi$
$419$	−4.26376	−0.208299	−0.104149	+	0.994562i	$0.533212\pi$
$420$	−1.43470	−0.0700062
$421$	6.59973	0.321651	0.160826	−	0.986983i	$-0.448584\pi$
$421$	6.59973	0.321651	0.160826	+	0.986983i	$0.448584\pi$
$422$	15.8364	0.770903
$423$	−0.909741	−0.0442331
$424$	5.38845	0.261686
$425$	−2.94163	−0.142690
$426$	10.1115	0.489902
$427$	9.85982	0.477150
$428$	−3.95375	−0.191112
$429$	−5.47504	−0.264337
$430$	−12.2223	−0.589411
$431$	−12.5769	−0.605809	−0.302905	−	0.953021i	$-0.597956\pi$
$431$	−12.5769	−0.605809	−0.302905	+	0.953021i	$0.597956\pi$
$432$	−1.00000	−0.0481125
$433$	−6.04625	−0.290564	−0.145282	−	0.989390i	$-0.546409\pi$
$433$	−6.04625	−0.290564	−0.145282	+	0.989390i	$0.546409\pi$
$434$	6.28607	0.301741
$435$	5.79668	0.277929
$436$	−4.79350	−0.229567
$437$	0.612982	0.0293229
$438$	7.00845	0.334877
$439$	36.7240	1.75274	0.876369	−	0.481640i	$-0.159959\pi$
$439$	36.7240	1.75274	0.876369	+	0.481640i	$0.159959\pi$
$440$	−7.85505	−0.374475
$441$	1.00000	0.0476190
$442$	−1.00000	−0.0475651
$443$	32.7138	1.55428	0.777139	−	0.629329i	$-0.216670\pi$
$443$	32.7138	1.55428	0.777139	+	0.629329i	$0.216670\pi$
$444$	−8.28607	−0.393240
$445$	−9.52814	−0.451677
$446$	−0.641201	−0.0303618
$447$	4.43103	0.209580
$448$	1.00000	0.0472456
$449$	−23.8491	−1.12551	−0.562755	−	0.826624i	$-0.690259\pi$
$449$	−23.8491	−1.12551	−0.562755	+	0.826624i	$0.690259\pi$
$450$	2.94163	0.138670
$451$	−8.27062	−0.389448
$452$	18.6661	0.877979
$453$	−20.5439	−0.965238
$454$	−14.4607	−0.678674
$455$	1.43470	0.0672598
$456$	0.735132	0.0344257
$457$	1.98675	0.0929361	0.0464680	−	0.998920i	$-0.485203\pi$
$457$	1.98675	0.0929361	0.0464680	+	0.998920i	$0.485203\pi$
$458$	−17.6624	−0.825310
$459$	−1.00000	−0.0466760
$460$	1.19631	0.0557782
$461$	−30.8373	−1.43624	−0.718119	−	0.695920i	$-0.754997\pi$
$461$	−30.8373	−1.43624	−0.718119	+	0.695920i	$0.754997\pi$
$462$	5.47504	0.254722
$463$	−33.8869	−1.57486	−0.787429	−	0.616405i	$-0.788588\pi$
$463$	−33.8869	−1.57486	−0.787429	+	0.616405i	$0.788588\pi$
$464$	−4.04034	−0.187568
$465$	9.01864	0.418229
$466$	18.0641	0.836803
$467$	4.51428	0.208896	0.104448	−	0.994530i	$-0.466692\pi$
$467$	4.51428	0.208896	0.104448	+	0.994530i	$0.466692\pi$
$468$	1.00000	0.0462250
$469$	−0.395465	−0.0182609
$470$	1.30521	0.0602047
$471$	−0.0403388	−0.00185872
$472$	−3.34077	−0.153771
$473$	46.6421	2.14461
$474$	−13.3301	−0.612271
$475$	−2.16249	−0.0992218
$476$	1.00000	0.0458349
$477$	−5.38845	−0.246720
$478$	5.59719	0.256010
$479$	1.89331	0.0865075	0.0432537	−	0.999064i	$-0.486228\pi$
$479$	1.89331	0.0865075	0.0432537	+	0.999064i	$0.486228\pi$
$480$	1.43470	0.0654848
$481$	8.28607	0.377812
$482$	5.03924	0.229531
$483$	−0.833838	−0.0379410
$484$	18.9761	0.862548
$485$	21.8593	0.992581
$486$	1.00000	0.0453609
$487$	−21.7691	−0.986452	−0.493226	−	0.869901i	$-0.664182\pi$
$487$	−21.7691	−0.986452	−0.493226	+	0.869901i	$0.664182\pi$
$488$	−9.85982	−0.446333
$489$	23.8136	1.07689
$490$	−1.43470	−0.0648132
$491$	−22.2515	−1.00419	−0.502097	−	0.864811i	$-0.667438\pi$
$491$	−22.2515	−1.00419	−0.502097	+	0.864811i	$0.667438\pi$
$492$	1.51060	0.0681033
$493$	−4.04034	−0.181968
$494$	−0.735132	−0.0330752
$495$	7.85505	0.353058
$496$	−6.28607	−0.282253
$497$	10.1115	0.453561
$498$	−0.169833	−0.00761042
$499$	24.8088	1.11059	0.555296	−	0.831652i	$-0.312605\pi$
$499$	24.8088	1.11059	0.555296	+	0.831652i	$0.312605\pi$
$500$	−11.3939	−0.509549
$501$	4.42512	0.197700
$502$	−25.1650	−1.12317
$503$	−25.9257	−1.15597	−0.577984	−	0.816048i	$-0.696161\pi$
$503$	−25.9257	−1.15597	−0.577984	+	0.816048i	$0.696161\pi$
$504$	−1.00000	−0.0445435
$505$	25.9077	1.15288
$506$	−4.56530	−0.202952
$507$	−1.00000	−0.0444116
$508$	−5.80145	−0.257398
$509$	−12.7535	−0.565287	−0.282644	−	0.959225i	$-0.591211\pi$
$509$	−12.7535	−0.565287	−0.282644	+	0.959225i	$0.591211\pi$
$510$	1.43470	0.0635296
$511$	7.00845	0.310035
$512$	−1.00000	−0.0441942
$513$	−0.735132	−0.0324569
$514$	−2.24366	−0.0989636
$515$	7.46292	0.328856
$516$	−8.51905	−0.375030
$517$	−4.98087	−0.219058
$518$	−8.28607	−0.364069
$519$	5.83017	0.255916
$520$	−1.43470	−0.0629158
$521$	0.0913621	0.00400265	0.00200132	−	0.999998i	$-0.499363\pi$
$521$	0.0913621	0.00400265	0.00200132	+	0.999998i	$0.499363\pi$
$522$	4.04034	0.176841
$523$	40.2063	1.75810	0.879050	−	0.476729i	$-0.158178\pi$
$523$	40.2063	1.75810	0.879050	+	0.476729i	$0.158178\pi$
$524$	20.6661	0.902802
$525$	2.94163	0.128383
$526$	−31.6968	−1.38205
$527$	−6.28607	−0.273826
$528$	−5.47504	−0.238271
$529$	−22.3047	−0.969770
$530$	7.73082	0.335805
$531$	3.34077	0.144977
$532$	0.735132	0.0318720
$533$	−1.51060	−0.0654315
$534$	−6.64120	−0.287393
$535$	−5.67245	−0.245241
$536$	0.395465	0.0170815
$537$	−12.3264	−0.531924
$538$	−25.8901	−1.11620
$539$	5.47504	0.235827
$540$	−1.43470	−0.0617397
$541$	−31.7206	−1.36377	−0.681887	−	0.731457i	$-0.738841\pi$
$541$	−31.7206	−1.36377	−0.681887	+	0.731457i	$0.738841\pi$
$542$	17.5281	0.752898
$543$	−2.22229	−0.0953677
$544$	−1.00000	−0.0428746
$545$	−6.87724	−0.294589
$546$	1.00000	0.0427960
$547$	30.8341	1.31837	0.659186	−	0.751980i	$-0.270901\pi$
$547$	30.8341	1.31837	0.659186	+	0.751980i	$0.270901\pi$
$548$	−18.6661	−0.797375
$549$	9.85982	0.420807
$550$	16.1056	0.686743
$551$	−2.97018	−0.126534
$552$	0.833838	0.0354905
$553$	−13.3301	−0.566853
$554$	19.1045	0.811670
$555$	−11.8880	−0.504619
$556$	−15.2234	−0.645616
$557$	23.6932	1.00391	0.501956	−	0.864893i	$-0.332614\pi$
$557$	23.6932	1.00391	0.501956	+	0.864893i	$0.332614\pi$
$558$	6.28607	0.266111
$559$	8.51905	0.360317
$560$	1.43470	0.0606272
$561$	−5.47504	−0.231156
$562$	−3.74214	−0.157853
$563$	−36.6659	−1.54528	−0.772641	−	0.634843i	$-0.781065\pi$
$563$	−36.6659	−1.54528	−0.772641	+	0.634843i	$0.781065\pi$
$564$	0.909741	0.0383070
$565$	26.7802	1.12665
$566$	−29.9580	−1.25923
$567$	1.00000	0.0419961
$568$	−10.1115	−0.424268
$569$	−36.9256	−1.54800	−0.774002	−	0.633183i	$-0.781748\pi$
$569$	−36.9256	−1.54800	−0.774002	+	0.633183i	$0.781748\pi$
$570$	1.05470	0.0441763
$571$	10.0458	0.420402	0.210201	−	0.977658i	$-0.432588\pi$
$571$	10.0458	0.420402	0.210201	+	0.977658i	$0.432588\pi$
$572$	5.47504	0.228923
$573$	15.3704	0.642109
$574$	1.51060	0.0630514
$575$	−2.45285	−0.102291
$576$	1.00000	0.0416667
$577$	−20.1633	−0.839408	−0.419704	−	0.907661i	$-0.637866\pi$
$577$	−20.1633	−0.839408	−0.419704	+	0.907661i	$0.637866\pi$
$578$	−1.00000	−0.0415945
$579$	14.1331	0.587353
$580$	−5.79668	−0.240694
$581$	−0.169833	−0.00704588
$582$	15.2362	0.631559
$583$	−29.5020	−1.22185
$584$	−7.00845	−0.290012
$585$	1.43470	0.0593176
$586$	−12.2218	−0.504878
$587$	46.9631	1.93838	0.969188	−	0.246322i	$-0.0792220\pi$
$587$	46.9631	1.93838	0.969188	+	0.246322i	$0.0792220\pi$
$588$	−1.00000	−0.0412393
$589$	−4.62110	−0.190409
$590$	−4.79301	−0.197325
$591$	−14.5667	−0.599195
$592$	8.28607	0.340556
$593$	42.9877	1.76529	0.882647	−	0.470036i	$-0.155759\pi$
$593$	42.9877	1.76529	0.882647	+	0.470036i	$0.155759\pi$
$594$	5.47504	0.224644
$595$	1.43470	0.0588170
$596$	−4.43103	−0.181502
$597$	3.70866	0.151785
$598$	−0.833838	−0.0340982
$599$	−25.8427	−1.05591	−0.527953	−	0.849274i	$-0.677040\pi$
$599$	−25.8427	−1.05591	−0.527953	+	0.849274i	$0.677040\pi$
$600$	−2.94163	−0.120092
$601$	−13.2193	−0.539225	−0.269612	−	0.962969i	$-0.586896\pi$
$601$	−13.2193	−0.539225	−0.269612	+	0.962969i	$0.586896\pi$
$602$	−8.51905	−0.347211
$603$	−0.395465	−0.0161046
$604$	20.5439	0.835921
$605$	27.2250	1.10685
$606$	18.0579	0.733551
$607$	27.0032	1.09603	0.548013	−	0.836470i	$-0.315385\pi$
$607$	27.0032	1.09603	0.548013	+	0.836470i	$0.315385\pi$
$608$	−0.735132	−0.0298136
$609$	4.04034	0.163723
$610$	−14.1459	−0.572751
$611$	−0.909741	−0.0368042
$612$	1.00000	0.0404226
$613$	32.4159	1.30926	0.654632	−	0.755947i	$-0.272823\pi$
$613$	32.4159	1.30926	0.654632	+	0.755947i	$0.272823\pi$
$614$	33.9781	1.37125
$615$	2.16726	0.0873925
$616$	−5.47504	−0.220596
$617$	−10.9877	−0.442349	−0.221174	−	0.975234i	$-0.570989\pi$
$617$	−10.9877	−0.442349	−0.221174	+	0.975234i	$0.570989\pi$
$618$	5.20173	0.209244
$619$	30.3931	1.22160	0.610800	−	0.791785i	$-0.290848\pi$
$619$	30.3931	1.22160	0.610800	+	0.791785i	$0.290848\pi$
$620$	−9.01864	−0.362197
$621$	−0.833838	−0.0334608
$622$	6.34558	0.254434
$623$	−6.64120	−0.266074
$624$	−1.00000	−0.0400320
$625$	−1.63863	−0.0655453
$626$	15.4336	0.616849
$627$	−4.02488	−0.160738
$628$	0.0403388	0.00160970
$629$	8.28607	0.330387
$630$	−1.43470	−0.0571599
$631$	−46.3964	−1.84701	−0.923506	−	0.383584i	$-0.874690\pi$
$631$	−46.3964	−1.84701	−0.923506	+	0.383584i	$0.874690\pi$
$632$	13.3301	0.530242
$633$	15.8364	0.629439
$634$	−18.5755	−0.737727
$635$	−8.32335	−0.330302
$636$	5.38845	0.213666
$637$	1.00000	0.0396214
$638$	22.1210	0.875779
$639$	10.1115	0.400003
$640$	−1.43470	−0.0567115
$641$	−27.1657	−1.07298	−0.536490	−	0.843907i	$-0.680250\pi$
$641$	−27.1657	−1.07298	−0.536490	+	0.843907i	$0.680250\pi$
$642$	−3.95375	−0.156042
$643$	25.2347	0.995160	0.497580	−	0.867418i	$-0.334222\pi$
$643$	25.2347	0.995160	0.497580	+	0.867418i	$0.334222\pi$
$644$	0.833838	0.0328578
$645$	−12.2223	−0.481252
$646$	−0.735132	−0.0289234
$647$	21.7222	0.853988	0.426994	−	0.904254i	$-0.359573\pi$
$647$	21.7222	0.853988	0.426994	+	0.904254i	$0.359573\pi$
$648$	−1.00000	−0.0392837
$649$	18.2909	0.717979
$650$	2.94163	0.115380
$651$	6.28607	0.246371
$652$	−23.8136	−0.932611
$653$	43.5211	1.70311	0.851556	−	0.524264i	$-0.175659\pi$
$653$	43.5211	1.70311	0.851556	+	0.524264i	$0.175659\pi$
$654$	−4.79350	−0.187441
$655$	29.6496	1.15851
$656$	−1.51060	−0.0589792
$657$	7.00845	0.273426
$658$	0.909741	0.0354654
$659$	−4.12549	−0.160706	−0.0803532	−	0.996766i	$-0.525605\pi$
$659$	−4.12549	−0.160706	−0.0803532	+	0.996766i	$0.525605\pi$
$660$	−7.85505	−0.305757
$661$	−1.03382	−0.0402109	−0.0201055	−	0.999798i	$-0.506400\pi$
$661$	−1.03382	−0.0402109	−0.0201055	+	0.999798i	$0.506400\pi$
$662$	−25.7801	−1.00197
$663$	−1.00000	−0.0388368
$664$	0.169833	0.00659082
$665$	1.05470	0.0408993
$666$	−8.28607	−0.321079
$667$	−3.36899	−0.130448
$668$	−4.42512	−0.171213
$669$	−0.641201	−0.0247903
$670$	0.567375	0.0219196
$671$	53.9829	2.08399
$672$	1.00000	0.0385758
$673$	45.6857	1.76105	0.880526	−	0.473997i	$-0.157189\pi$
$673$	45.6857	1.76105	0.880526	+	0.473997i	$0.157189\pi$
$674$	12.2336	0.471221
$675$	2.94163	0.113223
$676$	1.00000	0.0384615
$677$	−27.1538	−1.04361	−0.521804	−	0.853066i	$-0.674741\pi$
$677$	−27.1538	−1.04361	−0.521804	+	0.853066i	$0.674741\pi$
$678$	18.6661	0.716867
$679$	15.2362	0.584710
$680$	−1.43470	−0.0550183
$681$	−14.4607	−0.554135
$682$	34.4165	1.31788
$683$	28.1572	1.07741	0.538703	−	0.842496i	$-0.318914\pi$
$683$	28.1572	1.07741	0.538703	+	0.842496i	$0.318914\pi$
$684$	0.735132	0.0281085
$685$	−26.7802	−1.02322
$686$	−1.00000	−0.0381802
$687$	−17.6624	−0.673863
$688$	8.51905	0.324786
$689$	−5.38845	−0.205284
$690$	1.19631	0.0455427
$691$	−15.1510	−0.576371	−0.288186	−	0.957575i	$-0.593052\pi$
$691$	−15.1510	−0.576371	−0.288186	+	0.957575i	$0.593052\pi$
$692$	−5.83017	−0.221630
$693$	5.47504	0.207980
$694$	−28.9697	−1.09967
$695$	−21.8410	−0.828477
$696$	−4.04034	−0.153149
$697$	−1.51060	−0.0572182
$698$	15.5572	0.588847
$699$	18.0641	0.683246
$700$	−2.94163	−0.111183
$701$	20.3062	0.766954	0.383477	−	0.923550i	$-0.374727\pi$
$701$	20.3062	0.766954	0.383477	+	0.923550i	$0.374727\pi$
$702$	1.00000	0.0377426
$703$	6.09136	0.229740
$704$	5.47504	0.206348
$705$	1.30521	0.0491569
$706$	12.9107	0.485900
$707$	18.0579	0.679136
$708$	−3.34077	−0.125554
$709$	15.8311	0.594550	0.297275	−	0.954792i	$-0.403922\pi$
$709$	15.8311	0.594550	0.297275	+	0.954792i	$0.403922\pi$
$710$	−14.5069	−0.544435
$711$	−13.3301	−0.499917
$712$	6.64120	0.248890
$713$	−5.24157	−0.196298
$714$	1.00000	0.0374241
$715$	7.85505	0.293762
$716$	12.3264	0.460660
$717$	5.59719	0.209031
$718$	−27.0556	−1.00971
$719$	−7.21528	−0.269084	−0.134542	−	0.990908i	$-0.542956\pi$
$719$	−7.21528	−0.269084	−0.134542	+	0.990908i	$0.542956\pi$
$720$	1.43470	0.0534682
$721$	5.20173	0.193722
$722$	18.4596	0.686994
$723$	5.03924	0.187411
$724$	2.22229	0.0825908
$725$	11.8852	0.441405
$726$	18.9761	0.704268
$727$	32.4258	1.20260	0.601302	−	0.799022i	$-0.294649\pi$
$727$	32.4258	1.20260	0.601302	+	0.799022i	$0.294649\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−10.0550	−0.372153
$731$	8.51905	0.315088
$732$	−9.85982	−0.364429
$733$	20.3888	0.753076	0.376538	−	0.926401i	$-0.377114\pi$
$733$	20.3888	0.753076	0.376538	+	0.926401i	$0.377114\pi$
$734$	20.1862	0.745088
$735$	−1.43470	−0.0529197
$736$	−0.833838	−0.0307357
$737$	−2.16519	−0.0797558
$738$	1.51060	0.0556061
$739$	−38.6085	−1.42024	−0.710118	−	0.704082i	$-0.751359\pi$
$739$	−38.6085	−1.42024	−0.710118	+	0.704082i	$0.751359\pi$
$740$	11.8880	0.437013
$741$	−0.735132	−0.0270058
$742$	5.38845	0.197816
$743$	42.3157	1.55241	0.776207	−	0.630478i	$-0.217141\pi$
$743$	42.3157	1.55241	0.776207	+	0.630478i	$0.217141\pi$
$744$	−6.28607	−0.230459
$745$	−6.35720	−0.232910
$746$	0.783949	0.0287024
$747$	−0.169833	−0.00621388
$748$	5.47504	0.200187
$749$	−3.95375	−0.144467
$750$	−11.3939	−0.416045
$751$	24.9856	0.911739	0.455870	−	0.890047i	$-0.349328\pi$
$751$	24.9856	0.911739	0.455870	+	0.890047i	$0.349328\pi$
$752$	−0.909741	−0.0331748
$753$	−25.1650	−0.917065
$754$	4.04034	0.147140
$755$	29.4744	1.07268
$756$	−1.00000	−0.0363696
$757$	47.2754	1.71825	0.859126	−	0.511764i	$-0.171008\pi$
$757$	47.2754	1.71825	0.859126	+	0.511764i	$0.171008\pi$
$758$	3.27108	0.118811
$759$	−4.56530	−0.165710
$760$	−1.05470	−0.0382578
$761$	28.9944	1.05105	0.525523	−	0.850779i	$-0.323869\pi$
$761$	28.9944	1.05105	0.525523	+	0.850779i	$0.323869\pi$
$762$	−5.80145	−0.210164
$763$	−4.79350	−0.173536
$764$	−15.3704	−0.556082
$765$	1.43470	0.0518717
$766$	−35.8466	−1.29519
$767$	3.34077	0.120628
$768$	−1.00000	−0.0360844
$769$	−26.3050	−0.948584	−0.474292	−	0.880368i	$-0.657296\pi$
$769$	−26.3050	−0.948584	−0.474292	+	0.880368i	$0.657296\pi$
$770$	−7.85505	−0.283076
$771$	−2.24366	−0.0808035
$772$	−14.1331	−0.508663
$773$	−7.36100	−0.264757	−0.132378	−	0.991199i	$-0.542261\pi$
$773$	−7.36100	−0.264757	−0.132378	+	0.991199i	$0.542261\pi$
$774$	−8.51905	−0.306211
$775$	18.4913	0.664228
$776$	−15.2362	−0.546946
$777$	−8.28607	−0.297261
$778$	5.46770	0.196026
$779$	−1.11049	−0.0397876
$780$	−1.43470	−0.0513705
$781$	55.3607	1.98096
$782$	−0.833838	−0.0298180
$783$	4.04034	0.144390
$784$	1.00000	0.0357143
$785$	0.0578742	0.00206562
$786$	20.6661	0.737135
$787$	−19.5052	−0.695285	−0.347642	−	0.937627i	$-0.613018\pi$
$787$	−19.5052	−0.695285	−0.347642	+	0.937627i	$0.613018\pi$
$788$	14.5667	0.518918
$789$	−31.6968	−1.12844
$790$	19.1247	0.680426
$791$	18.6661	0.663689
$792$	−5.47504	−0.194547
$793$	9.85982	0.350133
$794$	−10.6820	−0.379091
$795$	7.73082	0.274184
$796$	−3.70866	−0.131450
$797$	4.15437	0.147155	0.0735777	−	0.997289i	$-0.476558\pi$
$797$	4.15437	0.147155	0.0735777	+	0.997289i	$0.476558\pi$
$798$	0.735132	0.0260234
$799$	−0.909741	−0.0321843
$800$	2.94163	0.104002
$801$	−6.64120	−0.234655
$802$	19.5281	0.689563
$803$	38.3715	1.35410
$804$	0.395465	0.0139470
$805$	1.19631	0.0421644
$806$	6.28607	0.221418
$807$	−25.8901	−0.911375
$808$	−18.0579	−0.635274
$809$	−27.1787	−0.955553	−0.477777	−	0.878481i	$-0.658557\pi$
$809$	−27.1787	−0.955553	−0.477777	+	0.878481i	$0.658557\pi$
$810$	−1.43470	−0.0504103
$811$	−41.5313	−1.45836	−0.729180	−	0.684322i	$-0.760098\pi$
$811$	−41.5313	−1.45836	−0.729180	+	0.684322i	$0.760098\pi$
$812$	−4.04034	−0.141788
$813$	17.5281	0.614739
$814$	−45.3666	−1.59010
$815$	−34.1654	−1.19676
$816$	−1.00000	−0.0350070
$817$	6.26263	0.219102
$818$	18.5950	0.650157
$819$	1.00000	0.0349428
$820$	−2.16726	−0.0756842
$821$	50.0441	1.74655	0.873276	−	0.487225i	$-0.161991\pi$
$821$	50.0441	1.74655	0.873276	+	0.487225i	$0.161991\pi$
$822$	−18.6661	−0.651054
$823$	−28.9732	−1.00994	−0.504971	−	0.863136i	$-0.668497\pi$
$823$	−28.9732	−1.00994	−0.504971	+	0.863136i	$0.668497\pi$
$824$	−5.20173	−0.181211
$825$	16.1056	0.560724
$826$	−3.34077	−0.116240
$827$	−21.3135	−0.741143	−0.370571	−	0.928804i	$-0.620838\pi$
$827$	−21.3135	−0.741143	−0.370571	+	0.928804i	$0.620838\pi$
$828$	0.833838	0.0289779
$829$	−21.6713	−0.752676	−0.376338	−	0.926482i	$-0.622817\pi$
$829$	−21.6713	−0.752676	−0.376338	+	0.926482i	$0.622817\pi$
$830$	0.243660	0.00845757
$831$	19.1045	0.662726
$832$	1.00000	0.0346688
$833$	1.00000	0.0346479
$834$	−15.2234	−0.527143
$835$	−6.34872	−0.219707
$836$	4.02488	0.139203
$837$	6.28607	0.217279
$838$	4.26376	0.147289
$839$	24.7708	0.855185	0.427592	−	0.903972i	$-0.359362\pi$
$839$	24.7708	0.855185	0.427592	+	0.903972i	$0.359362\pi$
$840$	1.43470	0.0495019
$841$	−12.6757	−0.437092
$842$	−6.59973	−0.227442
$843$	−3.74214	−0.128886
$844$	−15.8364	−0.545111
$845$	1.43470	0.0493552
$846$	0.909741	0.0312775
$847$	18.9761	0.652025
$848$	−5.38845	−0.185040
$849$	−29.9580	−1.02816
$850$	2.94163	0.100897
$851$	6.90925	0.236846
$852$	−10.1115	−0.346413
$853$	−0.215589	−0.00738161	−0.00369081	−	0.999993i	$-0.501175\pi$
$853$	−0.215589	−0.00738161	−0.00369081	+	0.999993i	$0.501175\pi$
$854$	−9.85982	−0.337396
$855$	1.05470	0.0360698
$856$	3.95375	0.135136
$857$	17.9183	0.612079	0.306039	−	0.952019i	$-0.400996\pi$
$857$	17.9183	0.612079	0.306039	+	0.952019i	$0.400996\pi$
$858$	5.47504	0.186915
$859$	26.0686	0.889448	0.444724	−	0.895668i	$-0.353302\pi$
$859$	26.0686	0.889448	0.444724	+	0.895668i	$0.353302\pi$
$860$	12.2223	0.416777
$861$	1.51060	0.0514812
$862$	12.5769	0.428372
$863$	23.4691	0.798898	0.399449	−	0.916755i	$-0.369201\pi$
$863$	23.4691	0.798898	0.399449	+	0.916755i	$0.369201\pi$
$864$	1.00000	0.0340207
$865$	−8.36455	−0.284403
$866$	6.04625	0.205460
$867$	−1.00000	−0.0339618
$868$	−6.28607	−0.213363
$869$	−72.9828	−2.47577
$870$	−5.79668	−0.196526
$871$	−0.395465	−0.0133998
$872$	4.79350	0.162328
$873$	15.2362	0.515666
$874$	−0.612982	−0.0207344
$875$	−11.3939	−0.385183
$876$	−7.00845	−0.236793
$877$	−51.3728	−1.73474	−0.867368	−	0.497667i	$-0.834190\pi$
$877$	−51.3728	−1.73474	−0.867368	+	0.497667i	$0.834190\pi$
$878$	−36.7240	−1.23937
$879$	−12.2218	−0.412231
$880$	7.85505	0.264794
$881$	45.9759	1.54897	0.774484	−	0.632593i	$-0.218009\pi$
$881$	45.9759	1.54897	0.774484	+	0.632593i	$0.218009\pi$
$882$	−1.00000	−0.0336718
$883$	25.4149	0.855279	0.427640	−	0.903949i	$-0.359345\pi$
$883$	25.4149	0.855279	0.427640	+	0.903949i	$0.359345\pi$
$884$	1.00000	0.0336336
$885$	−4.79301	−0.161115
$886$	−32.7138	−1.09904
$887$	11.4422	0.384191	0.192096	−	0.981376i	$-0.438472\pi$
$887$	11.4422	0.384191	0.192096	+	0.981376i	$0.438472\pi$
$888$	8.28607	0.278062
$889$	−5.80145	−0.194575
$890$	9.52814	0.319384
$891$	5.47504	0.183421
$892$	0.641201	0.0214690
$893$	−0.668780	−0.0223799
$894$	−4.43103	−0.148196
$895$	17.6847	0.591135
$896$	−1.00000	−0.0334077
$897$	−0.833838	−0.0278411
$898$	23.8491	0.795856
$899$	25.3979	0.847066
$900$	−2.94163	−0.0980544
$901$	−5.38845	−0.179515
$902$	8.27062	0.275381
$903$	−8.51905	−0.283496
$904$	−18.6661	−0.620825
$905$	3.18832	0.105983
$906$	20.5439	0.682526
$907$	−59.0602	−1.96106	−0.980531	−	0.196363i	$-0.937087\pi$
$907$	−59.0602	−1.96106	−0.980531	+	0.196363i	$0.937087\pi$
$908$	14.4607	0.479895
$909$	18.0579	0.598942
$910$	−1.43470	−0.0475599
$911$	−39.4029	−1.30548	−0.652739	−	0.757583i	$-0.726380\pi$
$911$	−39.4029	−1.30548	−0.652739	+	0.757583i	$0.726380\pi$
$912$	−0.735132	−0.0243427
$913$	−0.929845	−0.0307734
$914$	−1.98675	−0.0657157
$915$	−14.1459	−0.467649
$916$	17.6624	0.583582
$917$	20.6661	0.682454
$918$	1.00000	0.0330049
$919$	2.53451	0.0836058	0.0418029	−	0.999126i	$-0.486690\pi$
$919$	2.53451	0.0836058	0.0418029	+	0.999126i	$0.486690\pi$
$920$	−1.19631	−0.0394411
$921$	33.9781	1.11962
$922$	30.8373	1.01557
$923$	10.1115	0.332823
$924$	−5.47504	−0.180116
$925$	−24.3746	−0.801432
$926$	33.8869	1.11359
$927$	5.20173	0.170847
$928$	4.04034	0.132631
$929$	−31.1569	−1.02223	−0.511113	−	0.859514i	$-0.670766\pi$
$929$	−31.1569	−1.02223	−0.511113	+	0.859514i	$0.670766\pi$
$930$	−9.01864	−0.295733
$931$	0.735132	0.0240930
$932$	−18.0641	−0.591709
$933$	6.34558	0.207745
$934$	−4.51428	−0.147712
$935$	7.85505	0.256887
$936$	−1.00000	−0.0326860
$937$	51.0027	1.66619	0.833093	−	0.553134i	$-0.186568\pi$
$937$	51.0027	1.66619	0.833093	+	0.553134i	$0.186568\pi$
$938$	0.395465	0.0129124
$939$	15.4336	0.503655
$940$	−1.30521	−0.0425711
$941$	28.9327	0.943179	0.471589	−	0.881818i	$-0.343680\pi$
$941$	28.9327	0.943179	0.471589	+	0.881818i	$0.343680\pi$
$942$	0.0403388	0.00131431
$943$	−1.25960	−0.0410182
$944$	3.34077	0.108733
$945$	−1.43470	−0.0466708
$946$	−46.6421	−1.51647
$947$	15.4388	0.501695	0.250847	−	0.968027i	$-0.419291\pi$
$947$	15.4388	0.501695	0.250847	+	0.968027i	$0.419291\pi$
$948$	13.3301	0.432941
$949$	7.00845	0.227504
$950$	2.16249	0.0701604
$951$	−18.5755	−0.602352
$952$	−1.00000	−0.0324102
$953$	46.2366	1.49775	0.748876	−	0.662710i	$-0.230594\pi$
$953$	46.2366	1.49775	0.748876	+	0.662710i	$0.230594\pi$
$954$	5.38845	0.174458
$955$	−22.0520	−0.713585
$956$	−5.59719	−0.181026
$957$	22.1210	0.715071
$958$	−1.89331	−0.0611700
$959$	−18.6661	−0.602759
$960$	−1.43470	−0.0463048
$961$	8.51474	0.274669
$962$	−8.28607	−0.267154
$963$	−3.95375	−0.127408
$964$	−5.03924	−0.162303
$965$	−20.2768	−0.652734
$966$	0.833838	0.0268283
$967$	11.8874	0.382273	0.191136	−	0.981563i	$-0.438783\pi$
$967$	11.8874	0.382273	0.191136	+	0.981563i	$0.438783\pi$
$968$	−18.9761	−0.609914
$969$	−0.735132	−0.0236159
$970$	−21.8593	−0.701861
$971$	38.5816	1.23814	0.619071	−	0.785335i	$-0.287509\pi$
$971$	38.5816	1.23814	0.619071	+	0.785335i	$0.287509\pi$
$972$	−1.00000	−0.0320750
$973$	−15.2234	−0.488040
$974$	21.7691	0.697527
$975$	2.94163	0.0942076
$976$	9.85982	0.315605
$977$	−23.1194	−0.739656	−0.369828	−	0.929100i	$-0.620583\pi$
$977$	−23.1194	−0.739656	−0.369828	+	0.929100i	$0.620583\pi$
$978$	−23.8136	−0.761474
$979$	−36.3608	−1.16210
$980$	1.43470	0.0458298
$981$	−4.79350	−0.153045
$982$	22.2515	0.710072
$983$	42.0223	1.34030	0.670152	−	0.742224i	$-0.266229\pi$
$983$	42.0223	1.34030	0.670152	+	0.742224i	$0.266229\pi$
$984$	−1.51060	−0.0481563
$985$	20.8989	0.665895
$986$	4.04034	0.128671
$987$	0.909741	0.0289574
$988$	0.735132	0.0233877
$989$	7.10351	0.225879
$990$	−7.85505	−0.249650
$991$	61.4286	1.95134	0.975672	−	0.219236i	$-0.0703564\pi$
$991$	61.4286	1.95134	0.975672	+	0.219236i	$0.0703564\pi$
$992$	6.28607	0.199583
$993$	−25.7801	−0.818106
$994$	−10.1115	−0.320716
$995$	−5.32081	−0.168681
$996$	0.169833	0.00538138
$997$	9.84593	0.311824	0.155912	−	0.987771i	$-0.450168\pi$
$997$	9.84593	0.311824	0.155912	+	0.987771i	$0.450168\pi$
$998$	−24.8088	−0.785308
$999$	−8.28607	−0.262160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bj.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bj.1.3	✓	4	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.43470 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.43470 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.43470 q^{10} +5.47504 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} -1.43470 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.735132 q^{19} +1.43470 q^{20} -1.00000 q^{21} -5.47504 q^{22} +0.833838 q^{23} +1.00000 q^{24} -2.94163 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -4.04034 q^{29} +1.43470 q^{30} -6.28607 q^{31} -1.00000 q^{32} -5.47504 q^{33} -1.00000 q^{34} +1.43470 q^{35} +1.00000 q^{36} +8.28607 q^{37} -0.735132 q^{38} -1.00000 q^{39} -1.43470 q^{40} -1.51060 q^{41} +1.00000 q^{42} +8.51905 q^{43} +5.47504 q^{44} +1.43470 q^{45} -0.833838 q^{46} -0.909741 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.94163 q^{50} -1.00000 q^{51} +1.00000 q^{52} -5.38845 q^{53} +1.00000 q^{54} +7.85505 q^{55} -1.00000 q^{56} -0.735132 q^{57} +4.04034 q^{58} +3.34077 q^{59} -1.43470 q^{60} +9.85982 q^{61} +6.28607 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.43470 q^{65} +5.47504 q^{66} -0.395465 q^{67} +1.00000 q^{68} -0.833838 q^{69} -1.43470 q^{70} +10.1115 q^{71} -1.00000 q^{72} +7.00845 q^{73} -8.28607 q^{74} +2.94163 q^{75} +0.735132 q^{76} +5.47504 q^{77} +1.00000 q^{78} -13.3301 q^{79} +1.43470 q^{80} +1.00000 q^{81} +1.51060 q^{82} -0.169833 q^{83} -1.00000 q^{84} +1.43470 q^{85} -8.51905 q^{86} +4.04034 q^{87} -5.47504 q^{88} -6.64120 q^{89} -1.43470 q^{90} +1.00000 q^{91} +0.833838 q^{92} +6.28607 q^{93} +0.909741 q^{94} +1.05470 q^{95} +1.00000 q^{96} +15.2362 q^{97} -1.00000 q^{98} +5.47504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} + 9 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - q^{19} + 4 q^{20} - 4 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 5 q^{29} + 4 q^{30} + 9 q^{31} - 4 q^{32} - 9 q^{33} - 4 q^{34} + 4 q^{35} + 4 q^{36} - q^{37} + q^{38} - 4 q^{39} - 4 q^{40} + 13 q^{41} + 4 q^{42} + 7 q^{43} + 9 q^{44} + 4 q^{45} - 6 q^{46} + 11 q^{47} - 4 q^{48} + 4 q^{49} - 6 q^{50} - 4 q^{51} + 4 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} - 4 q^{56} + q^{57} + 5 q^{58} - 4 q^{60} - q^{61} - 9 q^{62} + 4 q^{63} + 4 q^{64} + 4 q^{65} + 9 q^{66} - 9 q^{67} + 4 q^{68} - 6 q^{69} - 4 q^{70} + 17 q^{71} - 4 q^{72} + 20 q^{73} + q^{74} - 6 q^{75} - q^{76} + 9 q^{77} + 4 q^{78} - 5 q^{79} + 4 q^{80} + 4 q^{81} - 13 q^{82} + 5 q^{83} - 4 q^{84} + 4 q^{85} - 7 q^{86} + 5 q^{87} - 9 q^{88} - 11 q^{89} - 4 q^{90} + 4 q^{91} + 6 q^{92} - 9 q^{93} - 11 q^{94} + 25 q^{95} + 4 q^{96} + q^{97} - 4 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 + 9 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - q^19 + 4 * q^20 - 4 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 5 * q^29 + 4 * q^30 + 9 * q^31 - 4 * q^32 - 9 * q^33 - 4 * q^34 + 4 * q^35 + 4 * q^36 - q^37 + q^38 - 4 * q^39 - 4 * q^40 + 13 * q^41 + 4 * q^42 + 7 * q^43 + 9 * q^44 + 4 * q^45 - 6 * q^46 + 11 * q^47 - 4 * q^48 + 4 * q^49 - 6 * q^50 - 4 * q^51 + 4 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 - 4 * q^56 + q^57 + 5 * q^58 - 4 * q^60 - q^61 - 9 * q^62 + 4 * q^63 + 4 * q^64 + 4 * q^65 + 9 * q^66 - 9 * q^67 + 4 * q^68 - 6 * q^69 - 4 * q^70 + 17 * q^71 - 4 * q^72 + 20 * q^73 + q^74 - 6 * q^75 - q^76 + 9 * q^77 + 4 * q^78 - 5 * q^79 + 4 * q^80 + 4 * q^81 - 13 * q^82 + 5 * q^83 - 4 * q^84 + 4 * q^85 - 7 * q^86 + 5 * q^87 - 9 * q^88 - 11 * q^89 - 4 * q^90 + 4 * q^91 + 6 * q^92 - 9 * q^93 - 11 * q^94 + 25 * q^95 + 4 * q^96 + q^97 - 4 * q^98 + 9 * q^99

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