LMFDB - Embedded newform 4334.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.82096$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.82096 q^{3} +1.00000 q^{4} -3.88691 q^{5} -1.82096 q^{6} -1.09055 q^{7} -1.00000 q^{8} +0.315898 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.82096 q^{3} +1.00000 q^{4} -3.88691 q^{5} -1.82096 q^{6} -1.09055 q^{7} -1.00000 q^{8} +0.315898 q^{9} +3.88691 q^{10} -1.00000 q^{11} +1.82096 q^{12} +3.26389 q^{13} +1.09055 q^{14} -7.07792 q^{15} +1.00000 q^{16} +3.47492 q^{17} -0.315898 q^{18} -0.547288 q^{19} -3.88691 q^{20} -1.98586 q^{21} +1.00000 q^{22} +3.83829 q^{23} -1.82096 q^{24} +10.1081 q^{25} -3.26389 q^{26} -4.88764 q^{27} -1.09055 q^{28} +7.20072 q^{29} +7.07792 q^{30} -9.62400 q^{31} -1.00000 q^{32} -1.82096 q^{33} -3.47492 q^{34} +4.23889 q^{35} +0.315898 q^{36} +3.31784 q^{37} +0.547288 q^{38} +5.94342 q^{39} +3.88691 q^{40} -0.584852 q^{41} +1.98586 q^{42} -6.84648 q^{43} -1.00000 q^{44} -1.22787 q^{45} -3.83829 q^{46} +9.22319 q^{47} +1.82096 q^{48} -5.81069 q^{49} -10.1081 q^{50} +6.32769 q^{51} +3.26389 q^{52} -9.00877 q^{53} +4.88764 q^{54} +3.88691 q^{55} +1.09055 q^{56} -0.996591 q^{57} -7.20072 q^{58} +10.3330 q^{59} -7.07792 q^{60} -9.09127 q^{61} +9.62400 q^{62} -0.344505 q^{63} +1.00000 q^{64} -12.6865 q^{65} +1.82096 q^{66} -7.44786 q^{67} +3.47492 q^{68} +6.98938 q^{69} -4.23889 q^{70} +4.05963 q^{71} -0.315898 q^{72} -1.66387 q^{73} -3.31784 q^{74} +18.4065 q^{75} -0.547288 q^{76} +1.09055 q^{77} -5.94342 q^{78} +11.4194 q^{79} -3.88691 q^{80} -9.84790 q^{81} +0.584852 q^{82} -1.65694 q^{83} -1.98586 q^{84} -13.5067 q^{85} +6.84648 q^{86} +13.1122 q^{87} +1.00000 q^{88} -7.20384 q^{89} +1.22787 q^{90} -3.55945 q^{91} +3.83829 q^{92} -17.5249 q^{93} -9.22319 q^{94} +2.12726 q^{95} -1.82096 q^{96} -12.2357 q^{97} +5.81069 q^{98} -0.315898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * 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
$3$	1.82096	1.05133	0.525666	−	0.850691i	$-0.323816\pi$
$3$	1.82096	1.05133	0.525666	+	0.850691i	$0.323816\pi$
$4$	1.00000	0.500000
$5$	−3.88691	−1.73828	−0.869140	−	0.494566i	$-0.835327\pi$
$5$	−3.88691	−1.73828	−0.869140	+	0.494566i	$0.835327\pi$
$6$	−1.82096	−0.743404
$7$	−1.09055	−0.412191	−0.206095	−	0.978532i	$-0.566076\pi$
$7$	−1.09055	−0.412191	−0.206095	+	0.978532i	$0.566076\pi$
$8$	−1.00000	−0.353553
$9$	0.315898	0.105299
$10$	3.88691	1.22915
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.82096	0.525666
$13$	3.26389	0.905240	0.452620	−	0.891703i	$-0.350489\pi$
$13$	3.26389	0.905240	0.452620	+	0.891703i	$0.350489\pi$
$14$	1.09055	0.291463
$15$	−7.07792	−1.82751
$16$	1.00000	0.250000
$17$	3.47492	0.842792	0.421396	−	0.906877i	$-0.361540\pi$
$17$	3.47492	0.842792	0.421396	+	0.906877i	$0.361540\pi$
$18$	−0.315898	−0.0744580
$19$	−0.547288	−0.125557	−0.0627783	−	0.998027i	$-0.519996\pi$
$19$	−0.547288	−0.125557	−0.0627783	+	0.998027i	$0.519996\pi$
$20$	−3.88691	−0.869140
$21$	−1.98586	−0.433350
$22$	1.00000	0.213201
$23$	3.83829	0.800339	0.400170	−	0.916441i	$-0.368951\pi$
$23$	3.83829	0.800339	0.400170	+	0.916441i	$0.368951\pi$
$24$	−1.82096	−0.371702
$25$	10.1081	2.02162
$26$	−3.26389	−0.640102
$27$	−4.88764	−0.940628
$28$	−1.09055	−0.206095
$29$	7.20072	1.33714	0.668570	−	0.743649i	$-0.266907\pi$
$29$	7.20072	1.33714	0.668570	+	0.743649i	$0.266907\pi$
$30$	7.07792	1.29225
$31$	−9.62400	−1.72852	−0.864261	−	0.503044i	$-0.832213\pi$
$31$	−9.62400	−1.72852	−0.864261	+	0.503044i	$0.832213\pi$
$32$	−1.00000	−0.176777
$33$	−1.82096	−0.316989
$34$	−3.47492	−0.595944
$35$	4.23889	0.716504
$36$	0.315898	0.0526497
$37$	3.31784	0.545449	0.272725	−	0.962092i	$-0.412075\pi$
$37$	3.31784	0.545449	0.272725	+	0.962092i	$0.412075\pi$
$38$	0.547288	0.0887819
$39$	5.94342	0.951708
$40$	3.88691	0.614575
$41$	−0.584852	−0.0913386	−0.0456693	−	0.998957i	$-0.514542\pi$
$41$	−0.584852	−0.0913386	−0.0456693	+	0.998957i	$0.514542\pi$
$42$	1.98586	0.306424
$43$	−6.84648	−1.04408	−0.522040	−	0.852921i	$-0.674829\pi$
$43$	−6.84648	−1.04408	−0.522040	+	0.852921i	$0.674829\pi$
$44$	−1.00000	−0.150756
$45$	−1.22787	−0.183040
$46$	−3.83829	−0.565925
$47$	9.22319	1.34534	0.672670	−	0.739942i	$-0.265147\pi$
$47$	9.22319	1.34534	0.672670	+	0.739942i	$0.265147\pi$
$48$	1.82096	0.262833
$49$	−5.81069	−0.830099
$50$	−10.1081	−1.42950
$51$	6.32769	0.886054
$52$	3.26389	0.452620
$53$	−9.00877	−1.23745	−0.618725	−	0.785608i	$-0.712350\pi$
$53$	−9.00877	−1.23745	−0.618725	+	0.785608i	$0.712350\pi$
$54$	4.88764	0.665124
$55$	3.88691	0.524111
$56$	1.09055	0.145732
$57$	−0.996591	−0.132002
$58$	−7.20072	−0.945501
$59$	10.3330	1.34525	0.672624	−	0.739984i	$-0.265167\pi$
$59$	10.3330	1.34525	0.672624	+	0.739984i	$0.265167\pi$
$60$	−7.07792	−0.913755
$61$	−9.09127	−1.16402	−0.582009	−	0.813183i	$-0.697733\pi$
$61$	−9.09127	−1.16402	−0.582009	+	0.813183i	$0.697733\pi$
$62$	9.62400	1.22225
$63$	−0.344505	−0.0434035
$64$	1.00000	0.125000
$65$	−12.6865	−1.57356
$66$	1.82096	0.224145
$67$	−7.44786	−0.909901	−0.454951	−	0.890517i	$-0.650343\pi$
$67$	−7.44786	−0.909901	−0.454951	+	0.890517i	$0.650343\pi$
$68$	3.47492	0.421396
$69$	6.98938	0.841422
$70$	−4.23889	−0.506645
$71$	4.05963	0.481790	0.240895	−	0.970551i	$-0.422559\pi$
$71$	4.05963	0.481790	0.240895	+	0.970551i	$0.422559\pi$
$72$	−0.315898	−0.0372290
$73$	−1.66387	−0.194741	−0.0973706	−	0.995248i	$-0.531043\pi$
$73$	−1.66387	−0.194741	−0.0973706	+	0.995248i	$0.531043\pi$
$74$	−3.31784	−0.385691
$75$	18.4065	2.12539
$76$	−0.547288	−0.0627783
$77$	1.09055	0.124280
$78$	−5.94342	−0.672960
$79$	11.4194	1.28478	0.642389	−	0.766378i	$-0.277943\pi$
$79$	11.4194	1.28478	0.642389	+	0.766378i	$0.277943\pi$
$80$	−3.88691	−0.434570
$81$	−9.84790	−1.09421
$82$	0.584852	0.0645861
$83$	−1.65694	−0.181872	−0.0909362	−	0.995857i	$-0.528986\pi$
$83$	−1.65694	−0.181872	−0.0909362	+	0.995857i	$0.528986\pi$
$84$	−1.98586	−0.216675
$85$	−13.5067	−1.46501
$86$	6.84648	0.738275
$87$	13.1122	1.40578
$88$	1.00000	0.106600
$89$	−7.20384	−0.763606	−0.381803	−	0.924244i	$-0.624697\pi$
$89$	−7.20384	−0.763606	−0.381803	+	0.924244i	$0.624697\pi$
$90$	1.22787	0.129429
$91$	−3.55945	−0.373132
$92$	3.83829	0.400170
$93$	−17.5249	−1.81725
$94$	−9.22319	−0.951300
$95$	2.12726	0.218253
$96$	−1.82096	−0.185851
$97$	−12.2357	−1.24235	−0.621175	−	0.783672i	$-0.713345\pi$
$97$	−12.2357	−1.24235	−0.621175	+	0.783672i	$0.713345\pi$
$98$	5.81069	0.586968
$99$	−0.315898	−0.0317490
$100$	10.1081	1.01081
$101$	−3.94227	−0.392271	−0.196135	−	0.980577i	$-0.562839\pi$
$101$	−3.94227	−0.392271	−0.196135	+	0.980577i	$0.562839\pi$
$102$	−6.32769	−0.626535
$103$	−7.18455	−0.707915	−0.353958	−	0.935261i	$-0.615164\pi$
$103$	−7.18455	−0.707915	−0.353958	+	0.935261i	$0.615164\pi$
$104$	−3.26389	−0.320051
$105$	7.71886	0.753283
$106$	9.00877	0.875009
$107$	9.90066	0.957133	0.478567	−	0.878051i	$-0.341157\pi$
$107$	9.90066	0.957133	0.478567	+	0.878051i	$0.341157\pi$
$108$	−4.88764	−0.470314
$109$	4.83910	0.463502	0.231751	−	0.972775i	$-0.425555\pi$
$109$	4.83910	0.463502	0.231751	+	0.972775i	$0.425555\pi$
$110$	−3.88691	−0.370603
$111$	6.04166	0.573449
$112$	−1.09055	−0.103048
$113$	6.89254	0.648396	0.324198	−	0.945989i	$-0.394906\pi$
$113$	6.89254	0.648396	0.324198	+	0.945989i	$0.394906\pi$
$114$	0.996591	0.0933393
$115$	−14.9191	−1.39121
$116$	7.20072	0.668570
$117$	1.03106	0.0953213
$118$	−10.3330	−0.951234
$119$	−3.78959	−0.347391
$120$	7.07792	0.646123
$121$	1.00000	0.0909091
$122$	9.09127	0.823085
$123$	−1.06499	−0.0960272
$124$	−9.62400	−0.864261
$125$	−19.8547	−1.77586
$126$	0.344505	0.0306909
$127$	−10.1005	−0.896271	−0.448135	−	0.893966i	$-0.647912\pi$
$127$	−10.1005	−0.896271	−0.448135	+	0.893966i	$0.647912\pi$
$128$	−1.00000	−0.0883883
$129$	−12.4672	−1.09767
$130$	12.6865	1.11268
$131$	6.17565	0.539569	0.269785	−	0.962921i	$-0.413047\pi$
$131$	6.17565	0.539569	0.269785	+	0.962921i	$0.413047\pi$
$132$	−1.82096	−0.158494
$133$	0.596848	0.0517533
$134$	7.44786	0.643398
$135$	18.9979	1.63507
$136$	−3.47492	−0.297972
$137$	−3.33455	−0.284890	−0.142445	−	0.989803i	$-0.545496\pi$
$137$	−3.33455	−0.284890	−0.142445	+	0.989803i	$0.545496\pi$
$138$	−6.98938	−0.594975
$139$	−5.84422	−0.495700	−0.247850	−	0.968798i	$-0.579724\pi$
$139$	−5.84422	−0.495700	−0.247850	+	0.968798i	$0.579724\pi$
$140$	4.23889	0.358252
$141$	16.7951	1.41440
$142$	−4.05963	−0.340677
$143$	−3.26389	−0.272940
$144$	0.315898	0.0263249
$145$	−27.9886	−2.32433
$146$	1.66387	0.137703
$147$	−10.5810	−0.872709
$148$	3.31784	0.272725
$149$	−11.8075	−0.967306	−0.483653	−	0.875260i	$-0.660690\pi$
$149$	−11.8075	−0.967306	−0.483653	+	0.875260i	$0.660690\pi$
$150$	−18.4065	−1.50288
$151$	−11.0619	−0.900207	−0.450103	−	0.892976i	$-0.648613\pi$
$151$	−11.0619	−0.900207	−0.450103	+	0.892976i	$0.648613\pi$
$152$	0.547288	0.0443909
$153$	1.09772	0.0887455
$154$	−1.09055	−0.0878794
$155$	37.4077	3.00466
$156$	5.94342	0.475854
$157$	13.4530	1.07366	0.536832	−	0.843689i	$-0.319621\pi$
$157$	13.4530	1.07366	0.536832	+	0.843689i	$0.319621\pi$
$158$	−11.4194	−0.908476
$159$	−16.4046	−1.30097
$160$	3.88691	0.307288
$161$	−4.18587	−0.329892
$162$	9.84790	0.773724
$163$	−22.8405	−1.78901	−0.894504	−	0.447059i	$-0.852471\pi$
$163$	−22.8405	−1.78901	−0.894504	+	0.447059i	$0.852471\pi$
$164$	−0.584852	−0.0456693
$165$	7.07792	0.551015
$166$	1.65694	0.128603
$167$	−19.3609	−1.49819	−0.749097	−	0.662461i	$-0.769512\pi$
$167$	−19.3609	−1.49819	−0.749097	+	0.662461i	$0.769512\pi$
$168$	1.98586	0.153212
$169$	−2.34702	−0.180540
$170$	13.5067	1.03592
$171$	−0.172888	−0.0132210
$172$	−6.84648	−0.522040
$173$	−7.67554	−0.583560	−0.291780	−	0.956485i	$-0.594248\pi$
$173$	−7.67554	−0.583560	−0.291780	+	0.956485i	$0.594248\pi$
$174$	−13.1122	−0.994036
$175$	−11.0234	−0.833293
$176$	−1.00000	−0.0753778
$177$	18.8161	1.41430
$178$	7.20384	0.539951
$179$	−5.97114	−0.446304	−0.223152	−	0.974784i	$-0.571635\pi$
$179$	−5.97114	−0.446304	−0.223152	+	0.974784i	$0.571635\pi$
$180$	−1.22787	−0.0915200
$181$	−11.1323	−0.827455	−0.413727	−	0.910401i	$-0.635773\pi$
$181$	−11.1323	−0.827455	−0.413727	+	0.910401i	$0.635773\pi$
$182$	3.55945	0.263844
$183$	−16.5548	−1.22377
$184$	−3.83829	−0.282963
$185$	−12.8962	−0.948144
$186$	17.5249	1.28499
$187$	−3.47492	−0.254111
$188$	9.22319	0.672670
$189$	5.33024	0.387718
$190$	−2.12726	−0.154328
$191$	−9.86266	−0.713637	−0.356818	−	0.934174i	$-0.616139\pi$
$191$	−9.86266	−0.713637	−0.356818	+	0.934174i	$0.616139\pi$
$192$	1.82096	0.131417
$193$	−25.6067	−1.84321	−0.921605	−	0.388128i	$-0.873122\pi$
$193$	−25.6067	−1.84321	−0.921605	+	0.388128i	$0.873122\pi$
$194$	12.2357	0.878475
$195$	−23.1016	−1.65434
$196$	−5.81069	−0.415049
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	0.315898	0.0224499
$199$	−10.5538	−0.748137	−0.374068	−	0.927401i	$-0.622037\pi$
$199$	−10.5538	−0.748137	−0.374068	+	0.927401i	$0.622037\pi$
$200$	−10.1081	−0.714751
$201$	−13.5623	−0.956609
$202$	3.94227	0.277377
$203$	−7.85278	−0.551157
$204$	6.32769	0.443027
$205$	2.27327	0.158772
$206$	7.18455	0.500572
$207$	1.21251	0.0842753
$208$	3.26389	0.226310
$209$	0.547288	0.0378567
$210$	−7.71886	−0.532652
$211$	6.84907	0.471509	0.235755	−	0.971813i	$-0.424244\pi$
$211$	6.84907	0.471509	0.235755	+	0.971813i	$0.424244\pi$
$212$	−9.00877	−0.618725
$213$	7.39244	0.506521
$214$	−9.90066	−0.676795
$215$	26.6117	1.81490
$216$	4.88764	0.332562
$217$	10.4955	0.712481
$218$	−4.83910	−0.327745
$219$	−3.02984	−0.204738
$220$	3.88691	0.262056
$221$	11.3418	0.762929
$222$	−6.04166	−0.405489
$223$	−5.37519	−0.359949	−0.179975	−	0.983671i	$-0.557602\pi$
$223$	−5.37519	−0.359949	−0.179975	+	0.983671i	$0.557602\pi$
$224$	1.09055	0.0728658
$225$	3.19313	0.212875
$226$	−6.89254	−0.458485
$227$	−12.7753	−0.847927	−0.423963	−	0.905679i	$-0.639362\pi$
$227$	−12.7753	−0.847927	−0.423963	+	0.905679i	$0.639362\pi$
$228$	−0.996591	−0.0660008
$229$	16.0711	1.06201	0.531004	−	0.847369i	$-0.321815\pi$
$229$	16.0711	1.06201	0.531004	+	0.847369i	$0.321815\pi$
$230$	14.9191	0.983737
$231$	1.98586	0.130660
$232$	−7.20072	−0.472751
$233$	−8.11215	−0.531444	−0.265722	−	0.964050i	$-0.585610\pi$
$233$	−8.11215	−0.531444	−0.265722	+	0.964050i	$0.585610\pi$
$234$	−1.03106	−0.0674024
$235$	−35.8498	−2.33858
$236$	10.3330	0.672624
$237$	20.7942	1.35073
$238$	3.78959	0.245643
$239$	−1.63315	−0.105639	−0.0528197	−	0.998604i	$-0.516821\pi$
$239$	−1.63315	−0.105639	−0.0528197	+	0.998604i	$0.516821\pi$
$240$	−7.07792	−0.456878
$241$	−14.7552	−0.950468	−0.475234	−	0.879860i	$-0.657637\pi$
$241$	−14.7552	−0.950468	−0.475234	+	0.879860i	$0.657637\pi$
$242$	−1.00000	−0.0642824
$243$	−3.26971	−0.209752
$244$	−9.09127	−0.582009
$245$	22.5857	1.44294
$246$	1.06499	0.0679015
$247$	−1.78629	−0.113659
$248$	9.62400	0.611125
$249$	−3.01722	−0.191208
$250$	19.8547	1.25572
$251$	5.29266	0.334070	0.167035	−	0.985951i	$-0.446581\pi$
$251$	5.29266	0.334070	0.167035	+	0.985951i	$0.446581\pi$
$252$	−0.344505	−0.0217017
$253$	−3.83829	−0.241311
$254$	10.1005	0.633759
$255$	−24.5952	−1.54021
$256$	1.00000	0.0625000
$257$	−6.26950	−0.391081	−0.195540	−	0.980696i	$-0.562646\pi$
$257$	−6.26950	−0.391081	−0.195540	+	0.980696i	$0.562646\pi$
$258$	12.4672	0.776173
$259$	−3.61829	−0.224829
$260$	−12.6865	−0.786781
$261$	2.27470	0.140800
$262$	−6.17565	−0.381533
$263$	4.45805	0.274895	0.137447	−	0.990509i	$-0.456110\pi$
$263$	4.45805	0.274895	0.137447	+	0.990509i	$0.456110\pi$
$264$	1.82096	0.112072
$265$	35.0163	2.15103
$266$	−0.596848	−0.0365951
$267$	−13.1179	−0.802803
$268$	−7.44786	−0.454951
$269$	−12.8850	−0.785612	−0.392806	−	0.919621i	$-0.628496\pi$
$269$	−12.8850	−0.785612	−0.392806	+	0.919621i	$0.628496\pi$
$270$	−18.9979	−1.15617
$271$	8.53005	0.518164	0.259082	−	0.965855i	$-0.416580\pi$
$271$	8.53005	0.518164	0.259082	+	0.965855i	$0.416580\pi$
$272$	3.47492	0.210698
$273$	−6.48162	−0.392286
$274$	3.33455	0.201447
$275$	−10.1081	−0.609541
$276$	6.98938	0.420711
$277$	−5.55846	−0.333975	−0.166988	−	0.985959i	$-0.553404\pi$
$277$	−5.55846	−0.333975	−0.166988	+	0.985959i	$0.553404\pi$
$278$	5.84422	0.350513
$279$	−3.04021	−0.182012
$280$	−4.23889	−0.253322
$281$	29.7164	1.77273	0.886365	−	0.462986i	$-0.153222\pi$
$281$	29.7164	1.77273	0.886365	+	0.462986i	$0.153222\pi$
$282$	−16.7951	−1.00013
$283$	−7.62350	−0.453170	−0.226585	−	0.973991i	$-0.572756\pi$
$283$	−7.62350	−0.453170	−0.226585	+	0.973991i	$0.572756\pi$
$284$	4.05963	0.240895
$285$	3.87366	0.229456
$286$	3.26389	0.192998
$287$	0.637813	0.0376489
$288$	−0.315898	−0.0186145
$289$	−4.92493	−0.289702
$290$	27.9886	1.64355
$291$	−22.2808	−1.30612
$292$	−1.66387	−0.0973706
$293$	−22.1426	−1.29358	−0.646792	−	0.762666i	$-0.723890\pi$
$293$	−22.1426	−1.29358	−0.646792	+	0.762666i	$0.723890\pi$
$294$	10.5810	0.617099
$295$	−40.1637	−2.33842
$296$	−3.31784	−0.192845
$297$	4.88764	0.283610
$298$	11.8075	0.683989
$299$	12.5278	0.724499
$300$	18.4065	1.06270
$301$	7.46647	0.430360
$302$	11.0619	0.636542
$303$	−7.17873	−0.412407
$304$	−0.547288	−0.0313891
$305$	35.3370	2.02339
$306$	−1.09772	−0.0627526
$307$	−32.1397	−1.83431	−0.917155	−	0.398531i	$-0.869520\pi$
$307$	−32.1397	−1.83431	−0.917155	+	0.398531i	$0.869520\pi$
$308$	1.09055	0.0621401
$309$	−13.0828	−0.744254
$310$	−37.4077	−2.12461
$311$	−10.9108	−0.618693	−0.309346	−	0.950949i	$-0.600110\pi$
$311$	−10.9108	−0.618693	−0.309346	+	0.950949i	$0.600110\pi$
$312$	−5.94342	−0.336480
$313$	31.7610	1.79524	0.897620	−	0.440770i	$-0.145295\pi$
$313$	31.7610	1.79524	0.897620	+	0.440770i	$0.145295\pi$
$314$	−13.4530	−0.759195
$315$	1.33906	0.0754474
$316$	11.4194	0.642389
$317$	9.74886	0.547550	0.273775	−	0.961794i	$-0.411728\pi$
$317$	9.74886	0.547550	0.273775	+	0.961794i	$0.411728\pi$
$318$	16.4046	0.919925
$319$	−7.20072	−0.403163
$320$	−3.88691	−0.217285
$321$	18.0287	1.00626
$322$	4.18587	0.233269
$323$	−1.90178	−0.105818
$324$	−9.84790	−0.547106
$325$	32.9917	1.83005
$326$	22.8405	1.26502
$327$	8.81181	0.487294
$328$	0.584852	0.0322931
$329$	−10.0584	−0.554537
$330$	−7.07792	−0.389627
$331$	23.2019	1.27529	0.637645	−	0.770330i	$-0.279909\pi$
$331$	23.2019	1.27529	0.637645	+	0.770330i	$0.279909\pi$
$332$	−1.65694	−0.0909362
$333$	1.04810	0.0574355
$334$	19.3609	1.05938
$335$	28.9492	1.58166
$336$	−1.98586	−0.108337
$337$	−1.32620	−0.0722425	−0.0361213	−	0.999347i	$-0.511500\pi$
$337$	−1.32620	−0.0722425	−0.0361213	+	0.999347i	$0.511500\pi$
$338$	2.34702	0.127661
$339$	12.5510	0.681679
$340$	−13.5067	−0.732504
$341$	9.62400	0.521169
$342$	0.172888	0.00934869
$343$	13.9708	0.754350
$344$	6.84648	0.369138
$345$	−27.1671	−1.46263
$346$	7.67554	0.412640
$347$	−3.63407	−0.195087	−0.0975436	−	0.995231i	$-0.531099\pi$
$347$	−3.63407	−0.195087	−0.0975436	+	0.995231i	$0.531099\pi$
$348$	13.1122	0.702890
$349$	6.36792	0.340867	0.170433	−	0.985369i	$-0.445483\pi$
$349$	6.36792	0.340867	0.170433	+	0.985369i	$0.445483\pi$
$350$	11.0234	0.589227
$351$	−15.9527	−0.851494
$352$	1.00000	0.0533002
$353$	−7.43083	−0.395503	−0.197752	−	0.980252i	$-0.563364\pi$
$353$	−7.43083	−0.395503	−0.197752	+	0.980252i	$0.563364\pi$
$354$	−18.8161	−1.00006
$355$	−15.7795	−0.837486
$356$	−7.20384	−0.381803
$357$	−6.90070	−0.365224
$358$	5.97114	0.315585
$359$	0.902092	0.0476106	0.0238053	−	0.999717i	$-0.492422\pi$
$359$	0.902092	0.0476106	0.0238053	+	0.999717i	$0.492422\pi$
$360$	1.22787	0.0647144
$361$	−18.7005	−0.984236
$362$	11.1323	0.585099
$363$	1.82096	0.0955757
$364$	−3.55945	−0.186566
$365$	6.46732	0.338515
$366$	16.5548	0.865335
$367$	32.0077	1.67079	0.835393	−	0.549653i	$-0.185240\pi$
$367$	32.0077	1.67079	0.835393	+	0.549653i	$0.185240\pi$
$368$	3.83829	0.200085
$369$	−0.184754	−0.00961790
$370$	12.8962	0.670439
$371$	9.82456	0.510065
$372$	−17.5249	−0.908625
$373$	17.7364	0.918354	0.459177	−	0.888345i	$-0.348144\pi$
$373$	17.7364	0.918354	0.459177	+	0.888345i	$0.348144\pi$
$374$	3.47492	0.179684
$375$	−36.1547	−1.86702
$376$	−9.22319	−0.475650
$377$	23.5024	1.21043
$378$	−5.33024	−0.274158
$379$	30.5595	1.56973	0.784867	−	0.619664i	$-0.212731\pi$
$379$	30.5595	1.56973	0.784867	+	0.619664i	$0.212731\pi$
$380$	2.12726	0.109126
$381$	−18.3925	−0.942278
$382$	9.86266	0.504617
$383$	27.1035	1.38492	0.692461	−	0.721455i	$-0.256526\pi$
$383$	27.1035	1.38492	0.692461	+	0.721455i	$0.256526\pi$
$384$	−1.82096	−0.0929255
$385$	−4.23889	−0.216034
$386$	25.6067	1.30335
$387$	−2.16279	−0.109941
$388$	−12.2357	−0.621175
$389$	27.3398	1.38618	0.693090	−	0.720851i	$-0.256249\pi$
$389$	27.3398	1.38618	0.693090	+	0.720851i	$0.256249\pi$
$390$	23.1016	1.16979
$391$	13.3378	0.674519
$392$	5.81069	0.293484
$393$	11.2456	0.567267
$394$	1.00000	0.0503793
$395$	−44.3861	−2.23331
$396$	−0.315898	−0.0158745
$397$	−12.6017	−0.632461	−0.316230	−	0.948682i	$-0.602417\pi$
$397$	−12.6017	−0.632461	−0.316230	+	0.948682i	$0.602417\pi$
$398$	10.5538	0.529013
$399$	1.08684	0.0544099
$400$	10.1081	0.505405
$401$	−10.6022	−0.529448	−0.264724	−	0.964324i	$-0.585281\pi$
$401$	−10.6022	−0.529448	−0.264724	+	0.964324i	$0.585281\pi$
$402$	13.5623	0.676425
$403$	−31.4117	−1.56473
$404$	−3.94227	−0.196135
$405$	38.2780	1.90205
$406$	7.85278	0.389727
$407$	−3.31784	−0.164459
$408$	−6.32769	−0.313268
$409$	−23.2296	−1.14863	−0.574314	−	0.818635i	$-0.694731\pi$
$409$	−23.2296	−1.14863	−0.574314	+	0.818635i	$0.694731\pi$
$410$	−2.27327	−0.112269
$411$	−6.07208	−0.299514
$412$	−7.18455	−0.353958
$413$	−11.2688	−0.554499
$414$	−1.21251	−0.0595916
$415$	6.44037	0.316145
$416$	−3.26389	−0.160025
$417$	−10.6421	−0.521146
$418$	−0.547288	−0.0267687
$419$	36.8537	1.80042	0.900209	−	0.435457i	$-0.143413\pi$
$419$	36.8537	1.80042	0.900209	+	0.435457i	$0.143413\pi$
$420$	7.71886	0.376642
$421$	28.7678	1.40206	0.701029	−	0.713132i	$-0.252724\pi$
$421$	28.7678	1.40206	0.701029	+	0.713132i	$0.252724\pi$
$422$	−6.84907	−0.333407
$423$	2.91359	0.141664
$424$	9.00877	0.437504
$425$	35.1248	1.70380
$426$	−7.39244	−0.358165
$427$	9.91452	0.479797
$428$	9.90066	0.478567
$429$	−5.94342	−0.286951
$430$	−26.6117	−1.28333
$431$	−13.9491	−0.671905	−0.335953	−	0.941879i	$-0.609058\pi$
$431$	−13.9491	−0.671905	−0.335953	+	0.941879i	$0.609058\pi$
$432$	−4.88764	−0.235157
$433$	−10.6592	−0.512249	−0.256124	−	0.966644i	$-0.582446\pi$
$433$	−10.6592	−0.512249	−0.256124	+	0.966644i	$0.582446\pi$
$434$	−10.4955	−0.503800
$435$	−50.9661	−2.44364
$436$	4.83910	0.231751
$437$	−2.10065	−0.100488
$438$	3.02984	0.144771
$439$	19.0508	0.909245	0.454622	−	0.890684i	$-0.349774\pi$
$439$	19.0508	0.909245	0.454622	+	0.890684i	$0.349774\pi$
$440$	−3.88691	−0.185301
$441$	−1.83559	−0.0874089
$442$	−11.3418	−0.539473
$443$	4.10757	0.195156	0.0975782	−	0.995228i	$-0.468890\pi$
$443$	4.10757	0.195156	0.0975782	+	0.995228i	$0.468890\pi$
$444$	6.04166	0.286724
$445$	28.0007	1.32736
$446$	5.37519	0.254522
$447$	−21.5009	−1.01696
$448$	−1.09055	−0.0515239
$449$	−14.2031	−0.670285	−0.335143	−	0.942167i	$-0.608785\pi$
$449$	−14.2031	−0.670285	−0.335143	+	0.942167i	$0.608785\pi$
$450$	−3.19313	−0.150526
$451$	0.584852	0.0275396
$452$	6.89254	0.324198
$453$	−20.1433	−0.946417
$454$	12.7753	0.599575
$455$	13.8353	0.648608
$456$	0.996591	0.0466696
$457$	−34.7936	−1.62758	−0.813788	−	0.581162i	$-0.802598\pi$
$457$	−34.7936	−1.62758	−0.813788	+	0.581162i	$0.802598\pi$
$458$	−16.0711	−0.750953
$459$	−16.9842	−0.792753
$460$	−14.9191	−0.695607
$461$	−7.34457	−0.342071	−0.171035	−	0.985265i	$-0.554711\pi$
$461$	−7.34457	−0.342071	−0.171035	+	0.985265i	$0.554711\pi$
$462$	−1.98586	−0.0923905
$463$	29.4797	1.37004	0.685020	−	0.728524i	$-0.259794\pi$
$463$	29.4797	1.37004	0.685020	+	0.728524i	$0.259794\pi$
$464$	7.20072	0.334285
$465$	68.1179	3.15889
$466$	8.11215	0.375788
$467$	−34.0030	−1.57347	−0.786735	−	0.617291i	$-0.788230\pi$
$467$	−34.0030	−1.57347	−0.786735	+	0.617291i	$0.788230\pi$
$468$	1.03106	0.0476607
$469$	8.12230	0.375053
$470$	35.8498	1.65363
$471$	24.4973	1.12878
$472$	−10.3330	−0.475617
$473$	6.84648	0.314802
$474$	−20.7942	−0.955110
$475$	−5.53204	−0.253828
$476$	−3.78959	−0.173696
$477$	−2.84586	−0.130303
$478$	1.63315	0.0746984
$479$	−21.2955	−0.973015	−0.486507	−	0.873676i	$-0.661729\pi$
$479$	−21.2955	−0.973015	−0.486507	+	0.873676i	$0.661729\pi$
$480$	7.07792	0.323061
$481$	10.8291	0.493763
$482$	14.7552	0.672082
$483$	−7.62230	−0.346827
$484$	1.00000	0.0454545
$485$	47.5593	2.15955
$486$	3.26971	0.148317
$487$	31.2140	1.41444	0.707222	−	0.706992i	$-0.249948\pi$
$487$	31.2140	1.41444	0.707222	+	0.706992i	$0.249948\pi$
$488$	9.09127	0.411542
$489$	−41.5917	−1.88084
$490$	−22.5857	−1.02032
$491$	−11.3272	−0.511189	−0.255594	−	0.966784i	$-0.582271\pi$
$491$	−11.3272	−0.511189	−0.255594	+	0.966784i	$0.582271\pi$
$492$	−1.06499	−0.0480136
$493$	25.0219	1.12693
$494$	1.78629	0.0803690
$495$	1.22787	0.0551886
$496$	−9.62400	−0.432130
$497$	−4.42725	−0.198589
$498$	3.01722	0.135205
$499$	−7.57017	−0.338887	−0.169444	−	0.985540i	$-0.554197\pi$
$499$	−7.57017	−0.338887	−0.169444	+	0.985540i	$0.554197\pi$
$500$	−19.8547	−0.887931
$501$	−35.2555	−1.57510
$502$	−5.29266	−0.236223
$503$	25.6771	1.14488	0.572442	−	0.819945i	$-0.305996\pi$
$503$	25.6771	1.14488	0.572442	+	0.819945i	$0.305996\pi$
$504$	0.344505	0.0153455
$505$	15.3233	0.681877
$506$	3.83829	0.170633
$507$	−4.27382	−0.189807
$508$	−10.1005	−0.448135
$509$	−31.3827	−1.39102	−0.695508	−	0.718519i	$-0.744820\pi$
$509$	−31.3827	−1.39102	−0.695508	+	0.718519i	$0.744820\pi$
$510$	24.5952	1.08909
$511$	1.81454	0.0802706
$512$	−1.00000	−0.0441942
$513$	2.67495	0.118102
$514$	6.26950	0.276536
$515$	27.9257	1.23056
$516$	−12.4672	−0.548837
$517$	−9.22319	−0.405636
$518$	3.61829	0.158978
$519$	−13.9769	−0.613516
$520$	12.6865	0.556338
$521$	18.7721	0.822423	0.411211	−	0.911540i	$-0.365106\pi$
$521$	18.7721	0.822423	0.411211	+	0.911540i	$0.365106\pi$
$522$	−2.27470	−0.0995608
$523$	2.01319	0.0880305	0.0440153	−	0.999031i	$-0.485985\pi$
$523$	2.01319	0.0880305	0.0440153	+	0.999031i	$0.485985\pi$
$524$	6.17565	0.269785
$525$	−20.0732	−0.876068
$526$	−4.45805	−0.194380
$527$	−33.4426	−1.45678
$528$	−1.82096	−0.0792471
$529$	−8.26752	−0.359457
$530$	−35.0163	−1.52101
$531$	3.26419	0.141654
$532$	0.596848	0.0258766
$533$	−1.90889	−0.0826834
$534$	13.1179	0.567668
$535$	−38.4830	−1.66377
$536$	7.44786	0.321699
$537$	−10.8732	−0.469214
$538$	12.8850	0.555511
$539$	5.81069	0.250284
$540$	18.9979	0.817537
$541$	−4.73529	−0.203586	−0.101793	−	0.994806i	$-0.532458\pi$
$541$	−4.73529	−0.203586	−0.101793	+	0.994806i	$0.532458\pi$
$542$	−8.53005	−0.366397
$543$	−20.2714	−0.869930
$544$	−3.47492	−0.148986
$545$	−18.8092	−0.805696
$546$	6.48162	0.277388
$547$	9.14618	0.391062	0.195531	−	0.980697i	$-0.437357\pi$
$547$	9.14618	0.391062	0.195531	+	0.980697i	$0.437357\pi$
$548$	−3.33455	−0.142445
$549$	−2.87192	−0.122570
$550$	10.1081	0.431011
$551$	−3.94087	−0.167887
$552$	−6.98938	−0.297488
$553$	−12.4534	−0.529574
$554$	5.55846	0.236156
$555$	−23.4834	−0.996815
$556$	−5.84422	−0.247850
$557$	−22.8845	−0.969646	−0.484823	−	0.874612i	$-0.661116\pi$
$557$	−22.8845	−0.969646	−0.484823	+	0.874612i	$0.661116\pi$
$558$	3.04021	0.128702
$559$	−22.3462	−0.945143
$560$	4.23889	0.179126
$561$	−6.32769	−0.267155
$562$	−29.7164	−1.25351
$563$	15.9072	0.670407	0.335204	−	0.942146i	$-0.391195\pi$
$563$	15.9072	0.670407	0.335204	+	0.942146i	$0.391195\pi$
$564$	16.7951	0.707200
$565$	−26.7907	−1.12709
$566$	7.62350	0.320440
$567$	10.7397	0.451024
$568$	−4.05963	−0.170338
$569$	−29.9372	−1.25503	−0.627517	−	0.778603i	$-0.715929\pi$
$569$	−29.9372	−1.25503	−0.627517	+	0.778603i	$0.715929\pi$
$570$	−3.87366	−0.162250
$571$	−18.1916	−0.761294	−0.380647	−	0.924720i	$-0.624299\pi$
$571$	−18.1916	−0.761294	−0.380647	+	0.924720i	$0.624299\pi$
$572$	−3.26389	−0.136470
$573$	−17.9595	−0.750269
$574$	−0.637813	−0.0266218
$575$	38.7978	1.61798
$576$	0.315898	0.0131624
$577$	0.205385	0.00855027	0.00427514	−	0.999991i	$-0.498639\pi$
$577$	0.205385	0.00855027	0.00427514	+	0.999991i	$0.498639\pi$
$578$	4.92493	0.204850
$579$	−46.6288	−1.93783
$580$	−27.9886	−1.16216
$581$	1.80698	0.0749662
$582$	22.2808	0.923569
$583$	9.00877	0.373105
$584$	1.66387	0.0688514
$585$	−4.00763	−0.165695
$586$	22.1426	0.914702
$587$	−14.6464	−0.604520	−0.302260	−	0.953226i	$-0.597741\pi$
$587$	−14.6464	−0.604520	−0.302260	+	0.953226i	$0.597741\pi$
$588$	−10.5810	−0.436355
$589$	5.26710	0.217027
$590$	40.1637	1.65351
$591$	−1.82096	−0.0749043
$592$	3.31784	0.136362
$593$	−44.8203	−1.84055	−0.920275	−	0.391272i	$-0.872035\pi$
$593$	−44.8203	−1.84055	−0.920275	+	0.391272i	$0.872035\pi$
$594$	−4.88764	−0.200542
$595$	14.7298	0.603863
$596$	−11.8075	−0.483653
$597$	−19.2180	−0.786540
$598$	−12.5278	−0.512298
$599$	−41.6384	−1.70130	−0.850649	−	0.525734i	$-0.823791\pi$
$599$	−41.6384	−1.70130	−0.850649	+	0.525734i	$0.823791\pi$
$600$	−18.4065	−0.751440
$601$	−4.93808	−0.201429	−0.100714	−	0.994915i	$-0.532113\pi$
$601$	−4.93808	−0.201429	−0.100714	+	0.994915i	$0.532113\pi$
$602$	−7.46647	−0.304310
$603$	−2.35277	−0.0958121
$604$	−11.0619	−0.450103
$605$	−3.88691	−0.158026
$606$	7.17873	0.291616
$607$	−3.92191	−0.159185	−0.0795926	−	0.996827i	$-0.525362\pi$
$607$	−3.92191	−0.159185	−0.0795926	+	0.996827i	$0.525362\pi$
$608$	0.547288	0.0221955
$609$	−14.2996	−0.579450
$610$	−35.3370	−1.43075
$611$	30.1035	1.21786
$612$	1.09772	0.0443728
$613$	42.3164	1.70914	0.854572	−	0.519333i	$-0.173820\pi$
$613$	42.3164	1.70914	0.854572	+	0.519333i	$0.173820\pi$
$614$	32.1397	1.29705
$615$	4.13954	0.166922
$616$	−1.09055	−0.0439397
$617$	−7.57391	−0.304914	−0.152457	−	0.988310i	$-0.548719\pi$
$617$	−7.57391	−0.304914	−0.152457	+	0.988310i	$0.548719\pi$
$618$	13.0828	0.526267
$619$	−30.5874	−1.22941	−0.614706	−	0.788757i	$-0.710725\pi$
$619$	−30.5874	−1.22941	−0.614706	+	0.788757i	$0.710725\pi$
$620$	37.4077	1.50233
$621$	−18.7602	−0.752821
$622$	10.9108	0.437482
$623$	7.85618	0.314751
$624$	5.94342	0.237927
$625$	26.6332	1.06533
$626$	−31.7610	−1.26943
$627$	0.996591	0.0398000
$628$	13.4530	0.536832
$629$	11.5292	0.459700
$630$	−1.33906	−0.0533494
$631$	7.05855	0.280997	0.140498	−	0.990081i	$-0.455130\pi$
$631$	7.05855	0.280997	0.140498	+	0.990081i	$0.455130\pi$
$632$	−11.4194	−0.454238
$633$	12.4719	0.495713
$634$	−9.74886	−0.387177
$635$	39.2596	1.55797
$636$	−16.4046	−0.650485
$637$	−18.9655	−0.751439
$638$	7.20072	0.285079
$639$	1.28243	0.0507322
$640$	3.88691	0.153644
$641$	−14.2751	−0.563834	−0.281917	−	0.959439i	$-0.590970\pi$
$641$	−14.2751	−0.563834	−0.281917	+	0.959439i	$0.590970\pi$
$642$	−18.0287	−0.711537
$643$	−17.2234	−0.679226	−0.339613	−	0.940565i	$-0.610296\pi$
$643$	−17.2234	−0.679226	−0.339613	+	0.940565i	$0.610296\pi$
$644$	−4.18587	−0.164946
$645$	48.4589	1.90807
$646$	1.90178	0.0748247
$647$	32.4830	1.27704	0.638518	−	0.769607i	$-0.279548\pi$
$647$	32.4830	1.27704	0.638518	+	0.769607i	$0.279548\pi$
$648$	9.84790	0.386862
$649$	−10.3330	−0.405608
$650$	−32.9917	−1.29404
$651$	19.1119	0.749054
$652$	−22.8405	−0.894504
$653$	21.9812	0.860191	0.430096	−	0.902783i	$-0.358480\pi$
$653$	21.9812	0.860191	0.430096	+	0.902783i	$0.358480\pi$
$654$	−8.81181	−0.344569
$655$	−24.0042	−0.937923
$656$	−0.584852	−0.0228346
$657$	−0.525614	−0.0205062
$658$	10.0584	0.392117
$659$	33.8745	1.31956	0.659782	−	0.751457i	$-0.270649\pi$
$659$	33.8745	1.31956	0.659782	+	0.751457i	$0.270649\pi$
$660$	7.07792	0.275508
$661$	33.6277	1.30797	0.653984	−	0.756509i	$-0.273096\pi$
$661$	33.6277	1.30797	0.653984	+	0.756509i	$0.273096\pi$
$662$	−23.2019	−0.901767
$663$	20.6529	0.802092
$664$	1.65694	0.0643016
$665$	−2.31990	−0.0899617
$666$	−1.04810	−0.0406131
$667$	27.6385	1.07017
$668$	−19.3609	−0.749097
$669$	−9.78800	−0.378426
$670$	−28.9492	−1.11841
$671$	9.09127	0.350964
$672$	1.98586	0.0766061
$673$	31.1793	1.20188	0.600938	−	0.799296i	$-0.294794\pi$
$673$	31.1793	1.20188	0.600938	+	0.799296i	$0.294794\pi$
$674$	1.32620	0.0510832
$675$	−49.4048	−1.90159
$676$	−2.34702	−0.0902698
$677$	0.185564	0.00713181	0.00356591	−	0.999994i	$-0.498865\pi$
$677$	0.185564	0.00713181	0.00356591	+	0.999994i	$0.498865\pi$
$678$	−12.5510	−0.482020
$679$	13.3437	0.512086
$680$	13.5067	0.517959
$681$	−23.2633	−0.891453
$682$	−9.62400	−0.368522
$683$	−39.9372	−1.52816	−0.764078	−	0.645124i	$-0.776806\pi$
$683$	−39.9372	−1.52816	−0.764078	+	0.645124i	$0.776806\pi$
$684$	−0.172888	−0.00661052
$685$	12.9611	0.495218
$686$	−13.9708	−0.533406
$687$	29.2648	1.11652
$688$	−6.84648	−0.261020
$689$	−29.4036	−1.12019
$690$	27.1671	1.03423
$691$	−13.4415	−0.511340	−0.255670	−	0.966764i	$-0.582296\pi$
$691$	−13.4415	−0.511340	−0.255670	+	0.966764i	$0.582296\pi$
$692$	−7.67554	−0.291780
$693$	0.344505	0.0130866
$694$	3.63407	0.137947
$695$	22.7160	0.861666
$696$	−13.1122	−0.497018
$697$	−2.03231	−0.0769794
$698$	−6.36792	−0.241029
$699$	−14.7719	−0.558725
$700$	−11.0234	−0.416647
$701$	22.9883	0.868256	0.434128	−	0.900851i	$-0.357057\pi$
$701$	22.9883	0.868256	0.434128	+	0.900851i	$0.357057\pi$
$702$	15.9527	0.602097
$703$	−1.81581	−0.0684848
$704$	−1.00000	−0.0376889
$705$	−65.2810	−2.45862
$706$	7.43083	0.279663
$707$	4.29927	0.161691
$708$	18.8161	0.707151
$709$	44.5086	1.67156	0.835778	−	0.549067i	$-0.185017\pi$
$709$	44.5086	1.67156	0.835778	+	0.549067i	$0.185017\pi$
$710$	15.7795	0.592192
$711$	3.60736	0.135287
$712$	7.20384	0.269975
$713$	−36.9397	−1.38340
$714$	6.90070	0.258252
$715$	12.6865	0.474447
$716$	−5.97114	−0.223152
$717$	−2.97390	−0.111062
$718$	−0.902092	−0.0336658
$719$	−2.49428	−0.0930210	−0.0465105	−	0.998918i	$-0.514810\pi$
$719$	−2.49428	−0.0930210	−0.0465105	+	0.998918i	$0.514810\pi$
$720$	−1.22787	−0.0457600
$721$	7.83515	0.291796
$722$	18.7005	0.695960
$723$	−26.8687	−0.999257
$724$	−11.1323	−0.413727
$725$	72.7856	2.70319
$726$	−1.82096	−0.0675822
$727$	14.9176	0.553261	0.276631	−	0.960976i	$-0.410782\pi$
$727$	14.9176	0.553261	0.276631	+	0.960976i	$0.410782\pi$
$728$	3.55945	0.131922
$729$	23.5897	0.873692
$730$	−6.46732	−0.239366
$731$	−23.7910	−0.879941
$732$	−16.5548	−0.611885
$733$	−15.1208	−0.558498	−0.279249	−	0.960219i	$-0.590085\pi$
$733$	−15.1208	−0.558498	−0.279249	+	0.960219i	$0.590085\pi$
$734$	−32.0077	−1.18142
$735$	41.1276	1.51701
$736$	−3.83829	−0.141481
$737$	7.44786	0.274346
$738$	0.184754	0.00680088
$739$	−38.4120	−1.41301	−0.706504	−	0.707709i	$-0.749729\pi$
$739$	−38.4120	−1.41301	−0.706504	+	0.707709i	$0.749729\pi$
$740$	−12.8962	−0.474072
$741$	−3.25276	−0.119493
$742$	−9.82456	−0.360671
$743$	−13.6068	−0.499186	−0.249593	−	0.968351i	$-0.580297\pi$
$743$	−13.6068	−0.499186	−0.249593	+	0.968351i	$0.580297\pi$
$744$	17.5249	0.642495
$745$	45.8946	1.68145
$746$	−17.7364	−0.649374
$747$	−0.523424	−0.0191511
$748$	−3.47492	−0.127056
$749$	−10.7972	−0.394522
$750$	36.1547	1.32018
$751$	8.81088	0.321513	0.160757	−	0.986994i	$-0.448607\pi$
$751$	8.81088	0.321513	0.160757	+	0.986994i	$0.448607\pi$
$752$	9.22319	0.336335
$753$	9.63772	0.351218
$754$	−23.5024	−0.855906
$755$	42.9968	1.56481
$756$	5.33024	0.193859
$757$	25.9191	0.942046	0.471023	−	0.882121i	$-0.343885\pi$
$757$	25.9191	0.942046	0.471023	+	0.882121i	$0.343885\pi$
$758$	−30.5595	−1.10997
$759$	−6.98938	−0.253698
$760$	−2.12726	−0.0771639
$761$	−18.4125	−0.667452	−0.333726	−	0.942670i	$-0.608306\pi$
$761$	−18.4125	−0.667452	−0.333726	+	0.942670i	$0.608306\pi$
$762$	18.3925	0.666291
$763$	−5.27730	−0.191051
$764$	−9.86266	−0.356818
$765$	−4.26675	−0.154265
$766$	−27.1035	−0.979288
$767$	33.7259	1.21777
$768$	1.82096	0.0657083
$769$	−13.6395	−0.491854	−0.245927	−	0.969288i	$-0.579092\pi$
$769$	−13.6395	−0.491854	−0.245927	+	0.969288i	$0.579092\pi$
$770$	4.23889	0.152759
$771$	−11.4165	−0.411156
$772$	−25.6067	−0.921605
$773$	28.3936	1.02125	0.510623	−	0.859804i	$-0.329415\pi$
$773$	28.3936	1.02125	0.510623	+	0.859804i	$0.329415\pi$
$774$	2.16279	0.0777400
$775$	−97.2804	−3.49441
$776$	12.2357	0.439237
$777$	−6.58876	−0.236370
$778$	−27.3398	−0.980178
$779$	0.320083	0.0114682
$780$	−23.1016	−0.827168
$781$	−4.05963	−0.145265
$782$	−13.3378	−0.476957
$783$	−35.1946	−1.25775
$784$	−5.81069	−0.207525
$785$	−52.2905	−1.86633
$786$	−11.2456	−0.401118
$787$	18.2801	0.651617	0.325808	−	0.945436i	$-0.394364\pi$
$787$	18.2801	0.651617	0.325808	+	0.945436i	$0.394364\pi$
$788$	−1.00000	−0.0356235
$789$	8.11793	0.289006
$790$	44.3861	1.57919
$791$	−7.51669	−0.267263
$792$	0.315898	0.0112250
$793$	−29.6729	−1.05372
$794$	12.6017	0.447217
$795$	63.7633	2.26145
$796$	−10.5538	−0.374068
$797$	21.6800	0.767944	0.383972	−	0.923345i	$-0.374556\pi$
$797$	21.6800	0.767944	0.383972	+	0.923345i	$0.374556\pi$
$798$	−1.08684	−0.0384736
$799$	32.0499	1.13384
$800$	−10.1081	−0.357375
$801$	−2.27568	−0.0804073
$802$	10.6022	0.374377
$803$	1.66387	0.0587167
$804$	−13.5623	−0.478304
$805$	16.2701	0.573446
$806$	31.4117	1.10643
$807$	−23.4631	−0.825939
$808$	3.94227	0.138689
$809$	−27.9184	−0.981559	−0.490780	−	0.871284i	$-0.663288\pi$
$809$	−27.9184	−0.981559	−0.490780	+	0.871284i	$0.663288\pi$
$810$	−38.2780	−1.34495
$811$	−27.3163	−0.959204	−0.479602	−	0.877486i	$-0.659219\pi$
$811$	−27.3163	−0.959204	−0.479602	+	0.877486i	$0.659219\pi$
$812$	−7.85278	−0.275579
$813$	15.5329	0.544762
$814$	3.31784	0.116290
$815$	88.7792	3.10980
$816$	6.32769	0.221514
$817$	3.74700	0.131091
$818$	23.2296	0.812203
$819$	−1.12443	−0.0392906
$820$	2.27327	0.0793860
$821$	−20.4755	−0.714600	−0.357300	−	0.933990i	$-0.616303\pi$
$821$	−20.4755	−0.714600	−0.357300	+	0.933990i	$0.616303\pi$
$822$	6.07208	0.211788
$823$	32.4705	1.13185	0.565925	−	0.824457i	$-0.308519\pi$
$823$	32.4705	1.13185	0.565925	+	0.824457i	$0.308519\pi$
$824$	7.18455	0.250286
$825$	−18.4065	−0.640830
$826$	11.2688	0.392090
$827$	5.97058	0.207617	0.103809	−	0.994597i	$-0.466897\pi$
$827$	5.97058	0.207617	0.103809	+	0.994597i	$0.466897\pi$
$828$	1.21251	0.0421376
$829$	−15.8653	−0.551023	−0.275512	−	0.961298i	$-0.588847\pi$
$829$	−15.8653	−0.551023	−0.275512	+	0.961298i	$0.588847\pi$
$830$	−6.44037	−0.223549
$831$	−10.1217	−0.351119
$832$	3.26389	0.113155
$833$	−20.1917	−0.699600
$834$	10.6421	0.368506
$835$	75.2542	2.60428
$836$	0.547288	0.0189284
$837$	47.0387	1.62589
$838$	−36.8537	−1.27309
$839$	−20.3767	−0.703483	−0.351742	−	0.936097i	$-0.614410\pi$
$839$	−20.3767	−0.703483	−0.351742	+	0.936097i	$0.614410\pi$
$840$	−7.71886	−0.266326
$841$	22.8504	0.787946
$842$	−28.7678	−0.991405
$843$	54.1124	1.86373
$844$	6.84907	0.235755
$845$	9.12265	0.313829
$846$	−2.91359	−0.100171
$847$	−1.09055	−0.0374719
$848$	−9.00877	−0.309362
$849$	−13.8821	−0.476432
$850$	−35.1248	−1.20477
$851$	12.7348	0.436544
$852$	7.39244	0.253261
$853$	−45.2729	−1.55011	−0.775057	−	0.631891i	$-0.782279\pi$
$853$	−45.2729	−1.55011	−0.775057	+	0.631891i	$0.782279\pi$
$854$	−9.91452	−0.339268
$855$	0.671999	0.0229819
$856$	−9.90066	−0.338398
$857$	−7.45980	−0.254822	−0.127411	−	0.991850i	$-0.540667\pi$
$857$	−7.45980	−0.254822	−0.127411	+	0.991850i	$0.540667\pi$
$858$	5.94342	0.202905
$859$	−35.7486	−1.21973	−0.609863	−	0.792507i	$-0.708775\pi$
$859$	−35.7486	−1.21973	−0.609863	+	0.792507i	$0.708775\pi$
$860$	26.6117	0.907451
$861$	1.16143	0.0395815
$862$	13.9491	0.475109
$863$	−10.7229	−0.365012	−0.182506	−	0.983205i	$-0.558421\pi$
$863$	−10.7229	−0.365012	−0.182506	+	0.983205i	$0.558421\pi$
$864$	4.88764	0.166281
$865$	29.8342	1.01439
$866$	10.6592	0.362215
$867$	−8.96810	−0.304573
$868$	10.4955	0.356240
$869$	−11.4194	−0.387375
$870$	50.9661	1.72791
$871$	−24.3090	−0.823680
$872$	−4.83910	−0.163873
$873$	−3.86525	−0.130819
$874$	2.10065	0.0710556
$875$	21.6527	0.731994
$876$	−3.02984	−0.102369
$877$	−26.6879	−0.901186	−0.450593	−	0.892729i	$-0.648787\pi$
$877$	−26.6879	−0.901186	−0.450593	+	0.892729i	$0.648787\pi$
$878$	−19.0508	−0.642933
$879$	−40.3208	−1.35999
$880$	3.88691	0.131028
$881$	7.92418	0.266972	0.133486	−	0.991051i	$-0.457383\pi$
$881$	7.92418	0.266972	0.133486	+	0.991051i	$0.457383\pi$
$882$	1.83559	0.0618075
$883$	−51.7412	−1.74123	−0.870615	−	0.491964i	$-0.836279\pi$
$883$	−51.7412	−1.74123	−0.870615	+	0.491964i	$0.836279\pi$
$884$	11.3418	0.381465
$885$	−73.1365	−2.45846
$886$	−4.10757	−0.137996
$887$	−55.1378	−1.85135	−0.925673	−	0.378323i	$-0.876501\pi$
$887$	−55.1378	−1.85135	−0.925673	+	0.378323i	$0.876501\pi$
$888$	−6.04166	−0.202745
$889$	11.0151	0.369435
$890$	−28.0007	−0.938586
$891$	9.84790	0.329917
$892$	−5.37519	−0.179975
$893$	−5.04775	−0.168916
$894$	21.5009	0.719099
$895$	23.2093	0.775801
$896$	1.09055	0.0364329
$897$	22.8126	0.761689
$898$	14.2031	0.473963
$899$	−69.2998	−2.31128
$900$	3.19313	0.106438
$901$	−31.3048	−1.04291
$902$	−0.584852	−0.0194734
$903$	13.5961	0.452451
$904$	−6.89254	−0.229243
$905$	43.2702	1.43835
$906$	20.1433	0.669218
$907$	18.5370	0.615510	0.307755	−	0.951466i	$-0.400422\pi$
$907$	18.5370	0.615510	0.307755	+	0.951466i	$0.400422\pi$
$908$	−12.7753	−0.423963
$909$	−1.24536	−0.0413059
$910$	−13.8353	−0.458635
$911$	51.2220	1.69706	0.848530	−	0.529147i	$-0.177488\pi$
$911$	51.2220	1.69706	0.848530	+	0.529147i	$0.177488\pi$
$912$	−0.996591	−0.0330004
$913$	1.65694	0.0548366
$914$	34.7936	1.15087
$915$	64.3472	2.12725
$916$	16.0711	0.531004
$917$	−6.73489	−0.222406
$918$	16.9842	0.560561
$919$	48.6085	1.60345	0.801724	−	0.597695i	$-0.203917\pi$
$919$	48.6085	1.60345	0.801724	+	0.597695i	$0.203917\pi$
$920$	14.9191	0.491868
$921$	−58.5251	−1.92847
$922$	7.34457	0.241880
$923$	13.2502	0.436136
$924$	1.98586	0.0653299
$925$	33.5370	1.10269
$926$	−29.4797	−0.968764
$927$	−2.26959	−0.0745431
$928$	−7.20072	−0.236375
$929$	49.8615	1.63590	0.817951	−	0.575288i	$-0.195110\pi$
$929$	49.8615	1.63590	0.817951	+	0.575288i	$0.195110\pi$
$930$	−68.1179	−2.23367
$931$	3.18012	0.104224
$932$	−8.11215	−0.265722
$933$	−19.8681	−0.650451
$934$	34.0030	1.11261
$935$	13.5067	0.441717
$936$	−1.03106	−0.0337012
$937$	9.49840	0.310299	0.155150	−	0.987891i	$-0.450414\pi$
$937$	9.49840	0.310299	0.155150	+	0.987891i	$0.450414\pi$
$938$	−8.12230	−0.265203
$939$	57.8356	1.88739
$940$	−35.8498	−1.16929
$941$	43.6556	1.42313	0.711566	−	0.702619i	$-0.247986\pi$
$941$	43.6556	1.42313	0.711566	+	0.702619i	$0.247986\pi$
$942$	−24.4973	−0.798166
$943$	−2.24483	−0.0731018
$944$	10.3330	0.336312
$945$	−20.7182	−0.673963
$946$	−6.84648	−0.222598
$947$	−4.15282	−0.134949	−0.0674743	−	0.997721i	$-0.521494\pi$
$947$	−4.15282	−0.134949	−0.0674743	+	0.997721i	$0.521494\pi$
$948$	20.7942	0.675365
$949$	−5.43069	−0.176288
$950$	5.53204	0.179483
$951$	17.7523	0.575657
$952$	3.78959	0.122821
$953$	12.1850	0.394712	0.197356	−	0.980332i	$-0.436765\pi$
$953$	12.1850	0.394712	0.197356	+	0.980332i	$0.436765\pi$
$954$	2.84586	0.0921380
$955$	38.3353	1.24050
$956$	−1.63315	−0.0528197
$957$	−13.1122	−0.423858
$958$	21.2955	0.688025
$959$	3.63651	0.117429
$960$	−7.07792	−0.228439
$961$	61.6214	1.98779
$962$	−10.8291	−0.349143
$963$	3.12760	0.100786
$964$	−14.7552	−0.475234
$965$	99.5310	3.20402
$966$	7.62230	0.245243
$967$	42.9186	1.38017	0.690085	−	0.723728i	$-0.257573\pi$
$967$	42.9186	1.38017	0.690085	+	0.723728i	$0.257573\pi$
$968$	−1.00000	−0.0321412
$969$	−3.46307	−0.111250
$970$	−47.5593	−1.52704
$971$	19.4106	0.622916	0.311458	−	0.950260i	$-0.399183\pi$
$971$	19.4106	0.622916	0.311458	+	0.950260i	$0.399183\pi$
$972$	−3.26971	−0.104876
$973$	6.37344	0.204323
$974$	−31.2140	−1.00016
$975$	60.0767	1.92399
$976$	−9.09127	−0.291004
$977$	13.2107	0.422649	0.211325	−	0.977416i	$-0.432222\pi$
$977$	13.2107	0.422649	0.211325	+	0.977416i	$0.432222\pi$
$978$	41.5917	1.32996
$979$	7.20384	0.230236
$980$	22.5857	0.721472
$981$	1.52866	0.0488065
$982$	11.3272	0.361465
$983$	−0.958718	−0.0305783	−0.0152892	−	0.999883i	$-0.504867\pi$
$983$	−0.958718	−0.0305783	−0.0152892	+	0.999883i	$0.504867\pi$
$984$	1.06499	0.0339507
$985$	3.88691	0.123847
$986$	−25.0219	−0.796861
$987$	−18.3159	−0.583003
$988$	−1.78629	−0.0568294
$989$	−26.2788	−0.835617
$990$	−1.22787	−0.0390243
$991$	−52.9775	−1.68288	−0.841442	−	0.540347i	$-0.818293\pi$
$991$	−52.9775	−1.68288	−0.841442	+	0.540347i	$0.818293\pi$
$992$	9.62400	0.305562
$993$	42.2497	1.34075
$994$	4.42725	0.140424
$995$	41.0216	1.30047
$996$	−3.01722	−0.0956042
$997$	11.1684	0.353707	0.176854	−	0.984237i	$-0.443408\pi$
$997$	11.1684	0.353707	0.176854	+	0.984237i	$0.443408\pi$
$998$	7.57017	0.239630
$999$	−16.2164	−0.513065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.13	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.13	✓	17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.82096 q^{3} +1.00000 q^{4} -3.88691 q^{5} -1.82096 q^{6} -1.09055 q^{7} -1.00000 q^{8} +0.315898 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.82096 q^{3} +1.00000 q^{4} -3.88691 q^{5} -1.82096 q^{6} -1.09055 q^{7} -1.00000 q^{8} +0.315898 q^{9} +3.88691 q^{10} -1.00000 q^{11} +1.82096 q^{12} +3.26389 q^{13} +1.09055 q^{14} -7.07792 q^{15} +1.00000 q^{16} +3.47492 q^{17} -0.315898 q^{18} -0.547288 q^{19} -3.88691 q^{20} -1.98586 q^{21} +1.00000 q^{22} +3.83829 q^{23} -1.82096 q^{24} +10.1081 q^{25} -3.26389 q^{26} -4.88764 q^{27} -1.09055 q^{28} +7.20072 q^{29} +7.07792 q^{30} -9.62400 q^{31} -1.00000 q^{32} -1.82096 q^{33} -3.47492 q^{34} +4.23889 q^{35} +0.315898 q^{36} +3.31784 q^{37} +0.547288 q^{38} +5.94342 q^{39} +3.88691 q^{40} -0.584852 q^{41} +1.98586 q^{42} -6.84648 q^{43} -1.00000 q^{44} -1.22787 q^{45} -3.83829 q^{46} +9.22319 q^{47} +1.82096 q^{48} -5.81069 q^{49} -10.1081 q^{50} +6.32769 q^{51} +3.26389 q^{52} -9.00877 q^{53} +4.88764 q^{54} +3.88691 q^{55} +1.09055 q^{56} -0.996591 q^{57} -7.20072 q^{58} +10.3330 q^{59} -7.07792 q^{60} -9.09127 q^{61} +9.62400 q^{62} -0.344505 q^{63} +1.00000 q^{64} -12.6865 q^{65} +1.82096 q^{66} -7.44786 q^{67} +3.47492 q^{68} +6.98938 q^{69} -4.23889 q^{70} +4.05963 q^{71} -0.315898 q^{72} -1.66387 q^{73} -3.31784 q^{74} +18.4065 q^{75} -0.547288 q^{76} +1.09055 q^{77} -5.94342 q^{78} +11.4194 q^{79} -3.88691 q^{80} -9.84790 q^{81} +0.584852 q^{82} -1.65694 q^{83} -1.98586 q^{84} -13.5067 q^{85} +6.84648 q^{86} +13.1122 q^{87} +1.00000 q^{88} -7.20384 q^{89} +1.22787 q^{90} -3.55945 q^{91} +3.83829 q^{92} -17.5249 q^{93} -9.22319 q^{94} +2.12726 q^{95} -1.82096 q^{96} -12.2357 q^{97} +5.81069 q^{98} -0.315898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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