LMFDB - Embedded newform 4334.2.a.c.1.12

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			1.12
Root			$1.67869$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.67869 q^{3} +1.00000 q^{4} -2.31468 q^{5} -1.67869 q^{6} +0.643391 q^{7} -1.00000 q^{8} -0.181998 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.67869 q^{3} +1.00000 q^{4} -2.31468 q^{5} -1.67869 q^{6} +0.643391 q^{7} -1.00000 q^{8} -0.181998 q^{9} +2.31468 q^{10} -1.00000 q^{11} +1.67869 q^{12} -1.92323 q^{13} -0.643391 q^{14} -3.88563 q^{15} +1.00000 q^{16} +4.51851 q^{17} +0.181998 q^{18} +2.52486 q^{19} -2.31468 q^{20} +1.08005 q^{21} +1.00000 q^{22} +5.22610 q^{23} -1.67869 q^{24} +0.357745 q^{25} +1.92323 q^{26} -5.34159 q^{27} +0.643391 q^{28} -4.38918 q^{29} +3.88563 q^{30} +0.0236297 q^{31} -1.00000 q^{32} -1.67869 q^{33} -4.51851 q^{34} -1.48925 q^{35} -0.181998 q^{36} -7.10236 q^{37} -2.52486 q^{38} -3.22851 q^{39} +2.31468 q^{40} +4.61817 q^{41} -1.08005 q^{42} +0.191305 q^{43} -1.00000 q^{44} +0.421267 q^{45} -5.22610 q^{46} +1.10758 q^{47} +1.67869 q^{48} -6.58605 q^{49} -0.357745 q^{50} +7.58518 q^{51} -1.92323 q^{52} +6.60625 q^{53} +5.34159 q^{54} +2.31468 q^{55} -0.643391 q^{56} +4.23845 q^{57} +4.38918 q^{58} -3.43077 q^{59} -3.88563 q^{60} +6.50048 q^{61} -0.0236297 q^{62} -0.117096 q^{63} +1.00000 q^{64} +4.45166 q^{65} +1.67869 q^{66} +6.92800 q^{67} +4.51851 q^{68} +8.77301 q^{69} +1.48925 q^{70} -13.3071 q^{71} +0.181998 q^{72} -14.4572 q^{73} +7.10236 q^{74} +0.600543 q^{75} +2.52486 q^{76} -0.643391 q^{77} +3.22851 q^{78} -8.10605 q^{79} -2.31468 q^{80} -8.42088 q^{81} -4.61817 q^{82} -5.72731 q^{83} +1.08005 q^{84} -10.4589 q^{85} -0.191305 q^{86} -7.36808 q^{87} +1.00000 q^{88} +10.9118 q^{89} -0.421267 q^{90} -1.23739 q^{91} +5.22610 q^{92} +0.0396670 q^{93} -1.10758 q^{94} -5.84423 q^{95} -1.67869 q^{96} -4.52450 q^{97} +6.58605 q^{98} +0.181998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.67869	0.969192	0.484596	−	0.874738i	$-0.338967\pi$
$3$	1.67869	0.969192	0.484596	+	0.874738i	$0.338967\pi$
$4$	1.00000	0.500000
$5$	−2.31468	−1.03516	−0.517578	−	0.855636i	$-0.673166\pi$
$5$	−2.31468	−1.03516	−0.517578	+	0.855636i	$0.673166\pi$
$6$	−1.67869	−0.685323
$7$	0.643391	0.243179	0.121590	−	0.992580i	$-0.461201\pi$
$7$	0.643391	0.243179	0.121590	+	0.992580i	$0.461201\pi$
$8$	−1.00000	−0.353553
$9$	−0.181998	−0.0606660
$10$	2.31468	0.731966
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.67869	0.484596
$13$	−1.92323	−0.533408	−0.266704	−	0.963779i	$-0.585935\pi$
$13$	−1.92323	−0.533408	−0.266704	+	0.963779i	$0.585935\pi$
$14$	−0.643391	−0.171954
$15$	−3.88563	−1.00327
$16$	1.00000	0.250000
$17$	4.51851	1.09590	0.547950	−	0.836511i	$-0.315409\pi$
$17$	4.51851	1.09590	0.547950	+	0.836511i	$0.315409\pi$
$18$	0.181998	0.0428973
$19$	2.52486	0.579242	0.289621	−	0.957141i	$-0.406471\pi$
$19$	2.52486	0.579242	0.289621	+	0.957141i	$0.406471\pi$
$20$	−2.31468	−0.517578
$21$	1.08005	0.235687
$22$	1.00000	0.213201
$23$	5.22610	1.08972	0.544859	−	0.838528i	$-0.316583\pi$
$23$	5.22610	1.08972	0.544859	+	0.838528i	$0.316583\pi$
$24$	−1.67869	−0.342661
$25$	0.357745	0.0715490
$26$	1.92323	0.377176
$27$	−5.34159	−1.02799
$28$	0.643391	0.121590
$29$	−4.38918	−0.815051	−0.407525	−	0.913194i	$-0.633608\pi$
$29$	−4.38918	−0.815051	−0.407525	+	0.913194i	$0.633608\pi$
$30$	3.88563	0.709416
$31$	0.0236297	0.00424403	0.00212201	−	0.999998i	$-0.499325\pi$
$31$	0.0236297	0.00424403	0.00212201	+	0.999998i	$0.499325\pi$
$32$	−1.00000	−0.176777
$33$	−1.67869	−0.292223
$34$	−4.51851	−0.774918
$35$	−1.48925	−0.251728
$36$	−0.181998	−0.0303330
$37$	−7.10236	−1.16762	−0.583810	−	0.811890i	$-0.698439\pi$
$37$	−7.10236	−1.16762	−0.583810	+	0.811890i	$0.698439\pi$
$38$	−2.52486	−0.409586
$39$	−3.22851	−0.516975
$40$	2.31468	0.365983
$41$	4.61817	0.721236	0.360618	−	0.932714i	$-0.382566\pi$
$41$	4.61817	0.721236	0.360618	+	0.932714i	$0.382566\pi$
$42$	−1.08005	−0.166656
$43$	0.191305	0.0291737	0.0145869	−	0.999894i	$-0.495357\pi$
$43$	0.191305	0.0291737	0.0145869	+	0.999894i	$0.495357\pi$
$44$	−1.00000	−0.150756
$45$	0.421267	0.0627988
$46$	−5.22610	−0.770547
$47$	1.10758	0.161558	0.0807788	−	0.996732i	$-0.474259\pi$
$47$	1.10758	0.161558	0.0807788	+	0.996732i	$0.474259\pi$
$48$	1.67869	0.242298
$49$	−6.58605	−0.940864
$50$	−0.357745	−0.0505928
$51$	7.58518	1.06214
$52$	−1.92323	−0.266704
$53$	6.60625	0.907438	0.453719	−	0.891145i	$-0.350097\pi$
$53$	6.60625	0.907438	0.453719	+	0.891145i	$0.350097\pi$
$54$	5.34159	0.726898
$55$	2.31468	0.312111
$56$	−0.643391	−0.0859768
$57$	4.23845	0.561397
$58$	4.38918	0.576328
$59$	−3.43077	−0.446648	−0.223324	−	0.974744i	$-0.571691\pi$
$59$	−3.43077	−0.446648	−0.223324	+	0.974744i	$0.571691\pi$
$60$	−3.88563	−0.501633
$61$	6.50048	0.832301	0.416151	−	0.909296i	$-0.363379\pi$
$61$	6.50048	0.832301	0.416151	+	0.909296i	$0.363379\pi$
$62$	−0.0236297	−0.00300098
$63$	−0.117096	−0.0147527
$64$	1.00000	0.125000
$65$	4.45166	0.552160
$66$	1.67869	0.206633
$67$	6.92800	0.846390	0.423195	−	0.906039i	$-0.360909\pi$
$67$	6.92800	0.846390	0.423195	+	0.906039i	$0.360909\pi$
$68$	4.51851	0.547950
$69$	8.77301	1.05615
$70$	1.48925	0.177999
$71$	−13.3071	−1.57926	−0.789631	−	0.613582i	$-0.789728\pi$
$71$	−13.3071	−1.57926	−0.789631	+	0.613582i	$0.789728\pi$
$72$	0.181998	0.0214487
$73$	−14.4572	−1.69209	−0.846044	−	0.533113i	$-0.821022\pi$
$73$	−14.4572	−1.69209	−0.846044	+	0.533113i	$0.821022\pi$
$74$	7.10236	0.825633
$75$	0.600543	0.0693448
$76$	2.52486	0.289621
$77$	−0.643391	−0.0733212
$78$	3.22851	0.365556
$79$	−8.10605	−0.912002	−0.456001	−	0.889979i	$-0.650719\pi$
$79$	−8.10605	−0.912002	−0.456001	+	0.889979i	$0.650719\pi$
$80$	−2.31468	−0.258789
$81$	−8.42088	−0.935654
$82$	−4.61817	−0.509991
$83$	−5.72731	−0.628654	−0.314327	−	0.949315i	$-0.601779\pi$
$83$	−5.72731	−0.628654	−0.314327	+	0.949315i	$0.601779\pi$
$84$	1.08005	0.117844
$85$	−10.4589	−1.13443
$86$	−0.191305	−0.0206289
$87$	−7.36808	−0.789941
$88$	1.00000	0.106600
$89$	10.9118	1.15664	0.578322	−	0.815809i	$-0.303708\pi$
$89$	10.9118	1.15664	0.578322	+	0.815809i	$0.303708\pi$
$90$	−0.421267	−0.0444055
$91$	−1.23739	−0.129714
$92$	5.22610	0.544859
$93$	0.0396670	0.00411328
$94$	−1.10758	−0.114238
$95$	−5.84423	−0.599606
$96$	−1.67869	−0.171331
$97$	−4.52450	−0.459394	−0.229697	−	0.973262i	$-0.573773\pi$
$97$	−4.52450	−0.459394	−0.229697	+	0.973262i	$0.573773\pi$
$98$	6.58605	0.665291
$99$	0.181998	0.0182915
$100$	0.357745	0.0357745
$101$	14.4698	1.43980	0.719899	−	0.694078i	$-0.244188\pi$
$101$	14.4698	1.43980	0.719899	+	0.694078i	$0.244188\pi$
$102$	−7.58518	−0.751044
$103$	9.54957	0.940947	0.470474	−	0.882414i	$-0.344083\pi$
$103$	9.54957	0.940947	0.470474	+	0.882414i	$0.344083\pi$
$104$	1.92323	0.188588
$105$	−2.49998	−0.243973
$106$	−6.60625	−0.641655
$107$	−13.8740	−1.34125	−0.670626	−	0.741795i	$-0.733975\pi$
$107$	−13.8740	−1.34125	−0.670626	+	0.741795i	$0.733975\pi$
$108$	−5.34159	−0.513995
$109$	−16.5277	−1.58307	−0.791535	−	0.611124i	$-0.790718\pi$
$109$	−16.5277	−1.58307	−0.791535	+	0.611124i	$0.790718\pi$
$110$	−2.31468	−0.220696
$111$	−11.9227	−1.13165
$112$	0.643391	0.0607948
$113$	−16.2584	−1.52946	−0.764732	−	0.644349i	$-0.777129\pi$
$113$	−16.2584	−1.52946	−0.764732	+	0.644349i	$0.777129\pi$
$114$	−4.23845	−0.396967
$115$	−12.0968	−1.12803
$116$	−4.38918	−0.407525
$117$	0.350024	0.0323597
$118$	3.43077	0.315828
$119$	2.90717	0.266500
$120$	3.88563	0.354708
$121$	1.00000	0.0909091
$122$	−6.50048	−0.588526
$123$	7.75247	0.699017
$124$	0.0236297	0.00212201
$125$	10.7453	0.961092
$126$	0.117096	0.0104317
$127$	−2.24218	−0.198961	−0.0994805	−	0.995040i	$-0.531718\pi$
$127$	−2.24218	−0.198961	−0.0994805	+	0.995040i	$0.531718\pi$
$128$	−1.00000	−0.0883883
$129$	0.321142	0.0282749
$130$	−4.45166	−0.390436
$131$	−5.39166	−0.471072	−0.235536	−	0.971866i	$-0.575685\pi$
$131$	−5.39166	−0.471072	−0.235536	+	0.971866i	$0.575685\pi$
$132$	−1.67869	−0.146111
$133$	1.62447	0.140859
$134$	−6.92800	−0.598488
$135$	12.3641	1.06413
$136$	−4.51851	−0.387459
$137$	−14.7737	−1.26221	−0.631103	−	0.775699i	$-0.717398\pi$
$137$	−14.7737	−1.26221	−0.631103	+	0.775699i	$0.717398\pi$
$138$	−8.77301	−0.746808
$139$	−16.0012	−1.35720	−0.678601	−	0.734507i	$-0.737413\pi$
$139$	−16.0012	−1.35720	−0.678601	+	0.734507i	$0.737413\pi$
$140$	−1.48925	−0.125864
$141$	1.85929	0.156580
$142$	13.3071	1.11671
$143$	1.92323	0.160828
$144$	−0.181998	−0.0151665
$145$	10.1596	0.843705
$146$	14.4572	1.19649
$147$	−11.0559	−0.911878
$148$	−7.10236	−0.583810
$149$	5.89332	0.482800	0.241400	−	0.970426i	$-0.422393\pi$
$149$	5.89332	0.482800	0.241400	+	0.970426i	$0.422393\pi$
$150$	−0.600543	−0.0490342
$151$	0.779716	0.0634524	0.0317262	−	0.999497i	$-0.489900\pi$
$151$	0.779716	0.0634524	0.0317262	+	0.999497i	$0.489900\pi$
$152$	−2.52486	−0.204793
$153$	−0.822359	−0.0664838
$154$	0.643391	0.0518459
$155$	−0.0546953	−0.00439323
$156$	−3.22851	−0.258487
$157$	−16.5471	−1.32060	−0.660300	−	0.751002i	$-0.729571\pi$
$157$	−16.5471	−1.32060	−0.660300	+	0.751002i	$0.729571\pi$
$158$	8.10605	0.644882
$159$	11.0898	0.879482
$160$	2.31468	0.182992
$161$	3.36243	0.264997
$162$	8.42088	0.661607
$163$	−1.06794	−0.0836477	−0.0418238	−	0.999125i	$-0.513317\pi$
$163$	−1.06794	−0.0836477	−0.0418238	+	0.999125i	$0.513317\pi$
$164$	4.61817	0.360618
$165$	3.88563	0.302496
$166$	5.72731	0.444526
$167$	4.40074	0.340540	0.170270	−	0.985397i	$-0.445536\pi$
$167$	4.40074	0.340540	0.170270	+	0.985397i	$0.445536\pi$
$168$	−1.08005	−0.0833280
$169$	−9.30119	−0.715476
$170$	10.4589	0.802161
$171$	−0.459519	−0.0351403
$172$	0.191305	0.0145869
$173$	2.69435	0.204847	0.102424	−	0.994741i	$-0.467340\pi$
$173$	2.69435	0.204847	0.102424	+	0.994741i	$0.467340\pi$
$174$	7.36808	0.558573
$175$	0.230170	0.0173992
$176$	−1.00000	−0.0753778
$177$	−5.75919	−0.432888
$178$	−10.9118	−0.817870
$179$	0.234702	0.0175425	0.00877124	−	0.999962i	$-0.497208\pi$
$179$	0.234702	0.0175425	0.00877124	+	0.999962i	$0.497208\pi$
$180$	0.421267	0.0313994
$181$	2.18005	0.162042	0.0810209	−	0.996712i	$-0.474182\pi$
$181$	2.18005	0.162042	0.0810209	+	0.996712i	$0.474182\pi$
$182$	1.23739	0.0917214
$183$	10.9123	0.806660
$184$	−5.22610	−0.385273
$185$	16.4397	1.20867
$186$	−0.0396670	−0.00290853
$187$	−4.51851	−0.330426
$188$	1.10758	0.0807788
$189$	−3.43673	−0.249986
$190$	5.84423	0.423985
$191$	−2.81268	−0.203518	−0.101759	−	0.994809i	$-0.532447\pi$
$191$	−2.81268	−0.203518	−0.101759	+	0.994809i	$0.532447\pi$
$192$	1.67869	0.121149
$193$	−17.1448	−1.23411	−0.617057	−	0.786919i	$-0.711675\pi$
$193$	−17.1448	−1.23411	−0.617057	+	0.786919i	$0.711675\pi$
$194$	4.52450	0.324840
$195$	7.47296	0.535150
$196$	−6.58605	−0.470432
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−0.181998	−0.0129340
$199$	7.77226	0.550961	0.275481	−	0.961307i	$-0.411163\pi$
$199$	7.77226	0.550961	0.275481	+	0.961307i	$0.411163\pi$
$200$	−0.357745	−0.0252964
$201$	11.6300	0.820314
$202$	−14.4698	−1.01809
$203$	−2.82396	−0.198203
$204$	7.58518	0.531069
$205$	−10.6896	−0.746593
$206$	−9.54957	−0.665350
$207$	−0.951140	−0.0661088
$208$	−1.92323	−0.133352
$209$	−2.52486	−0.174648
$210$	2.49998	0.172515
$211$	−18.8460	−1.29742	−0.648708	−	0.761038i	$-0.724690\pi$
$211$	−18.8460	−1.29742	−0.648708	+	0.761038i	$0.724690\pi$
$212$	6.60625	0.453719
$213$	−22.3385	−1.53061
$214$	13.8740	0.948409
$215$	−0.442810	−0.0301994
$216$	5.34159	0.363449
$217$	0.0152032	0.00103206
$218$	16.5277	1.11940
$219$	−24.2692	−1.63996
$220$	2.31468	0.156056
$221$	−8.69013	−0.584561
$222$	11.9227	0.800197
$223$	−16.0797	−1.07677	−0.538387	−	0.842697i	$-0.680966\pi$
$223$	−16.0797	−1.07677	−0.538387	+	0.842697i	$0.680966\pi$
$224$	−0.643391	−0.0429884
$225$	−0.0651089	−0.00434059
$226$	16.2584	1.08149
$227$	−7.04805	−0.467796	−0.233898	−	0.972261i	$-0.575148\pi$
$227$	−7.04805	−0.467796	−0.233898	+	0.972261i	$0.575148\pi$
$228$	4.23845	0.280698
$229$	−5.30988	−0.350887	−0.175443	−	0.984490i	$-0.556136\pi$
$229$	−5.30988	−0.350887	−0.175443	+	0.984490i	$0.556136\pi$
$230$	12.0968	0.797637
$231$	−1.08005	−0.0710624
$232$	4.38918	0.288164
$233$	−12.7225	−0.833478	−0.416739	−	0.909026i	$-0.636827\pi$
$233$	−12.7225	−0.833478	−0.416739	+	0.909026i	$0.636827\pi$
$234$	−0.350024	−0.0228818
$235$	−2.56370	−0.167237
$236$	−3.43077	−0.223324
$237$	−13.6075	−0.883905
$238$	−2.90717	−0.188444
$239$	5.46293	0.353367	0.176684	−	0.984268i	$-0.443463\pi$
$239$	5.46293	0.353367	0.176684	+	0.984268i	$0.443463\pi$
$240$	−3.88563	−0.250816
$241$	3.27817	0.211166	0.105583	−	0.994411i	$-0.466329\pi$
$241$	3.27817	0.211166	0.105583	+	0.994411i	$0.466329\pi$
$242$	−1.00000	−0.0642824
$243$	1.88871	0.121161
$244$	6.50048	0.416151
$245$	15.2446	0.973941
$246$	−7.75247	−0.494280
$247$	−4.85588	−0.308972
$248$	−0.0236297	−0.00150049
$249$	−9.61439	−0.609287
$250$	−10.7453	−0.679595
$251$	7.42897	0.468912	0.234456	−	0.972127i	$-0.424669\pi$
$251$	7.42897	0.468912	0.234456	+	0.972127i	$0.424669\pi$
$252$	−0.117096	−0.00737635
$253$	−5.22610	−0.328562
$254$	2.24218	0.140687
$255$	−17.5573	−1.09948
$256$	1.00000	0.0625000
$257$	6.09990	0.380501	0.190251	−	0.981736i	$-0.439070\pi$
$257$	6.09990	0.380501	0.190251	+	0.981736i	$0.439070\pi$
$258$	−0.321142	−0.0199934
$259$	−4.56960	−0.283941
$260$	4.45166	0.276080
$261$	0.798822	0.0494459
$262$	5.39166	0.333098
$263$	−19.0856	−1.17687	−0.588434	−	0.808545i	$-0.700255\pi$
$263$	−19.0856	−1.17687	−0.588434	+	0.808545i	$0.700255\pi$
$264$	1.67869	0.103316
$265$	−15.2913	−0.939340
$266$	−1.62447	−0.0996027
$267$	18.3175	1.12101
$268$	6.92800	0.423195
$269$	25.8171	1.57410	0.787048	−	0.616891i	$-0.211608\pi$
$269$	25.8171	1.57410	0.787048	+	0.616891i	$0.211608\pi$
$270$	−12.3641	−0.752454
$271$	−17.6418	−1.07166	−0.535830	−	0.844326i	$-0.680001\pi$
$271$	−17.6418	−1.07166	−0.535830	+	0.844326i	$0.680001\pi$
$272$	4.51851	0.273975
$273$	−2.07719	−0.125717
$274$	14.7737	0.892515
$275$	−0.357745	−0.0215728
$276$	8.77301	0.528073
$277$	19.7017	1.18376	0.591879	−	0.806027i	$-0.298386\pi$
$277$	19.7017	1.18376	0.591879	+	0.806027i	$0.298386\pi$
$278$	16.0012	0.959686
$279$	−0.00430056	−0.000257468 0
$280$	1.48925	0.0889994
$281$	−23.7536	−1.41702	−0.708511	−	0.705700i	$-0.750633\pi$
$281$	−23.7536	−1.41702	−0.708511	+	0.705700i	$0.750633\pi$
$282$	−1.85929	−0.110719
$283$	14.1905	0.843536	0.421768	−	0.906704i	$-0.361410\pi$
$283$	14.1905	0.843536	0.421768	+	0.906704i	$0.361410\pi$
$284$	−13.3071	−0.789631
$285$	−9.81066	−0.581133
$286$	−1.92323	−0.113723
$287$	2.97129	0.175390
$288$	0.181998	0.0107243
$289$	3.41692	0.200995
$290$	−10.1596	−0.596590
$291$	−7.59524	−0.445241
$292$	−14.4572	−0.846044
$293$	22.2453	1.29958	0.649791	−	0.760113i	$-0.274856\pi$
$293$	22.2453	1.29958	0.649791	+	0.760113i	$0.274856\pi$
$294$	11.0559	0.644795
$295$	7.94113	0.462350
$296$	7.10236	0.412816
$297$	5.34159	0.309950
$298$	−5.89332	−0.341391
$299$	−10.0510	−0.581264
$300$	0.600543	0.0346724
$301$	0.123084	0.00709444
$302$	−0.779716	−0.0448676
$303$	24.2903	1.39544
$304$	2.52486	0.144810
$305$	−15.0465	−0.861562
$306$	0.822359	0.0470112
$307$	−18.8014	−1.07305	−0.536526	−	0.843884i	$-0.680264\pi$
$307$	−18.8014	−1.07305	−0.536526	+	0.843884i	$0.680264\pi$
$308$	−0.643391	−0.0366606
$309$	16.0308	0.911959
$310$	0.0546953	0.00310648
$311$	0.917714	0.0520388	0.0260194	−	0.999661i	$-0.491717\pi$
$311$	0.917714	0.0520388	0.0260194	+	0.999661i	$0.491717\pi$
$312$	3.22851	0.182778
$313$	−7.12692	−0.402837	−0.201419	−	0.979505i	$-0.564555\pi$
$313$	−7.12692	−0.402837	−0.201419	+	0.979505i	$0.564555\pi$
$314$	16.5471	0.933805
$315$	0.271040	0.0152714
$316$	−8.10605	−0.456001
$317$	28.3578	1.59274	0.796368	−	0.604813i	$-0.206752\pi$
$317$	28.3578	1.59274	0.796368	+	0.604813i	$0.206752\pi$
$318$	−11.0898	−0.621888
$319$	4.38918	0.245747
$320$	−2.31468	−0.129395
$321$	−23.2902	−1.29993
$322$	−3.36243	−0.187381
$323$	11.4086	0.634790
$324$	−8.42088	−0.467827
$325$	−0.688026	−0.0381648
$326$	1.06794	0.0591478
$327$	−27.7450	−1.53430
$328$	−4.61817	−0.254996
$329$	0.712609	0.0392874
$330$	−3.88563	−0.213897
$331$	19.3084	1.06128	0.530642	−	0.847596i	$-0.321951\pi$
$331$	19.3084	1.06128	0.530642	+	0.847596i	$0.321951\pi$
$332$	−5.72731	−0.314327
$333$	1.29262	0.0708349
$334$	−4.40074	−0.240798
$335$	−16.0361	−0.876146
$336$	1.08005	0.0589218
$337$	−4.56364	−0.248598	−0.124299	−	0.992245i	$-0.539668\pi$
$337$	−4.56364	−0.248598	−0.124299	+	0.992245i	$0.539668\pi$
$338$	9.30119	0.505918
$339$	−27.2929	−1.48234
$340$	−10.4589	−0.567214
$341$	−0.0236297	−0.00127962
$342$	0.459519	0.0248479
$343$	−8.74114	−0.471977
$344$	−0.191305	−0.0103145
$345$	−20.3067	−1.09328
$346$	−2.69435	−0.144849
$347$	−1.54375	−0.0828727	−0.0414364	−	0.999141i	$-0.513193\pi$
$347$	−1.54375	−0.0828727	−0.0414364	+	0.999141i	$0.513193\pi$
$348$	−7.36808	−0.394970
$349$	−5.82258	−0.311675	−0.155838	−	0.987783i	$-0.549808\pi$
$349$	−5.82258	−0.311675	−0.155838	+	0.987783i	$0.549808\pi$
$350$	−0.230170	−0.0123031
$351$	10.2731	0.548337
$352$	1.00000	0.0533002
$353$	18.4820	0.983699	0.491850	−	0.870680i	$-0.336321\pi$
$353$	18.4820	0.983699	0.491850	+	0.870680i	$0.336321\pi$
$354$	5.75919	0.306098
$355$	30.8017	1.63478
$356$	10.9118	0.578322
$357$	4.88024	0.258290
$358$	−0.234702	−0.0124044
$359$	−18.8587	−0.995326	−0.497663	−	0.867370i	$-0.665808\pi$
$359$	−18.8587	−0.995326	−0.497663	+	0.867370i	$0.665808\pi$
$360$	−0.421267	−0.0222027
$361$	−12.6251	−0.664479
$362$	−2.18005	−0.114581
$363$	1.67869	0.0881084
$364$	−1.23739	−0.0648568
$365$	33.4638	1.75158
$366$	−10.9123	−0.570395
$367$	1.11150	0.0580197	0.0290098	−	0.999579i	$-0.490765\pi$
$367$	1.11150	0.0580197	0.0290098	+	0.999579i	$0.490765\pi$
$368$	5.22610	0.272429
$369$	−0.840497	−0.0437545
$370$	−16.4397	−0.854659
$371$	4.25040	0.220670
$372$	0.0396670	0.00205664
$373$	26.8434	1.38990	0.694949	−	0.719059i	$-0.255427\pi$
$373$	26.8434	1.38990	0.694949	+	0.719059i	$0.255427\pi$
$374$	4.51851	0.233646
$375$	18.0381	0.931483
$376$	−1.10758	−0.0571192
$377$	8.44140	0.434754
$378$	3.43673	0.176766
$379$	−23.3085	−1.19728	−0.598639	−	0.801019i	$-0.704291\pi$
$379$	−23.3085	−1.19728	−0.598639	+	0.801019i	$0.704291\pi$
$380$	−5.84423	−0.299803
$381$	−3.76392	−0.192831
$382$	2.81268	0.143909
$383$	−13.9218	−0.711373	−0.355686	−	0.934605i	$-0.615753\pi$
$383$	−13.9218	−0.711373	−0.355686	+	0.934605i	$0.615753\pi$
$384$	−1.67869	−0.0856653
$385$	1.48925	0.0758990
$386$	17.1448	0.872650
$387$	−0.0348171	−0.00176985
$388$	−4.52450	−0.229697
$389$	0.315084	0.0159754	0.00798771	−	0.999968i	$-0.497457\pi$
$389$	0.315084	0.0159754	0.00798771	+	0.999968i	$0.497457\pi$
$390$	−7.47296	−0.378408
$391$	23.6142	1.19422
$392$	6.58605	0.332646
$393$	−9.05093	−0.456559
$394$	1.00000	0.0503793
$395$	18.7629	0.944064
$396$	0.181998	0.00914574
$397$	6.97165	0.349897	0.174949	−	0.984578i	$-0.444024\pi$
$397$	6.97165	0.349897	0.174949	+	0.984578i	$0.444024\pi$
$398$	−7.77226	−0.389588
$399$	2.72698	0.136520
$400$	0.357745	0.0178873
$401$	9.00430	0.449653	0.224827	−	0.974399i	$-0.427818\pi$
$401$	9.00430	0.449653	0.224827	+	0.974399i	$0.427818\pi$
$402$	−11.6300	−0.580050
$403$	−0.0454454	−0.00226380
$404$	14.4698	0.719899
$405$	19.4917	0.968548
$406$	2.82396	0.140151
$407$	7.10236	0.352051
$408$	−7.58518	−0.375522
$409$	19.1395	0.946389	0.473195	−	0.880958i	$-0.343101\pi$
$409$	19.1395	0.946389	0.473195	+	0.880958i	$0.343101\pi$
$410$	10.6896	0.527921
$411$	−24.8005	−1.22332
$412$	9.54957	0.470474
$413$	−2.20732	−0.108615
$414$	0.951140	0.0467460
$415$	13.2569	0.650756
$416$	1.92323	0.0942940
$417$	−26.8610	−1.31539
$418$	2.52486	0.123495
$419$	33.6087	1.64189	0.820946	−	0.571006i	$-0.193447\pi$
$419$	33.6087	1.64189	0.820946	+	0.571006i	$0.193447\pi$
$420$	−2.49998	−0.121987
$421$	21.5965	1.05255	0.526275	−	0.850314i	$-0.323588\pi$
$421$	21.5965	1.05255	0.526275	+	0.850314i	$0.323588\pi$
$422$	18.8460	0.917411
$423$	−0.201578	−0.00980105
$424$	−6.60625	−0.320828
$425$	1.61647	0.0784105
$426$	22.3385	1.08230
$427$	4.18235	0.202398
$428$	−13.8740	−0.670626
$429$	3.22851	0.155874
$430$	0.442810	0.0213542
$431$	−17.5132	−0.843582	−0.421791	−	0.906693i	$-0.638598\pi$
$431$	−17.5132	−0.843582	−0.421791	+	0.906693i	$0.638598\pi$
$432$	−5.34159	−0.256997
$433$	−0.219008	−0.0105248	−0.00526242	−	0.999986i	$-0.501675\pi$
$433$	−0.219008	−0.0105248	−0.00526242	+	0.999986i	$0.501675\pi$
$434$	−0.0152032	−0.000729775 0
$435$	17.0547	0.817713
$436$	−16.5277	−0.791535
$437$	13.1952	0.631210
$438$	24.2692	1.15963
$439$	−36.6468	−1.74906	−0.874528	−	0.484976i	$-0.838828\pi$
$439$	−36.6468	−1.74906	−0.874528	+	0.484976i	$0.838828\pi$
$440$	−2.31468	−0.110348
$441$	1.19865	0.0570784
$442$	8.69013	0.413347
$443$	32.0049	1.52060	0.760299	−	0.649573i	$-0.225052\pi$
$443$	32.0049	1.52060	0.760299	+	0.649573i	$0.225052\pi$
$444$	−11.9227	−0.565825
$445$	−25.2572	−1.19731
$446$	16.0797	0.761395
$447$	9.89306	0.467926
$448$	0.643391	0.0303974
$449$	5.10603	0.240969	0.120484	−	0.992715i	$-0.461555\pi$
$449$	5.10603	0.240969	0.120484	+	0.992715i	$0.461555\pi$
$450$	0.0651089	0.00306926
$451$	−4.61817	−0.217461
$452$	−16.2584	−0.764732
$453$	1.30890	0.0614976
$454$	7.04805	0.330782
$455$	2.86416	0.134274
$456$	−4.23845	−0.198484
$457$	−11.0590	−0.517316	−0.258658	−	0.965969i	$-0.583280\pi$
$457$	−11.0590	−0.517316	−0.258658	+	0.965969i	$0.583280\pi$
$458$	5.30988	0.248114
$459$	−24.1360	−1.12657
$460$	−12.0968	−0.564014
$461$	−4.67470	−0.217723	−0.108861	−	0.994057i	$-0.534720\pi$
$461$	−4.67470	−0.217723	−0.108861	+	0.994057i	$0.534720\pi$
$462$	1.08005	0.0502487
$463$	−24.7186	−1.14877	−0.574384	−	0.818586i	$-0.694758\pi$
$463$	−24.7186	−1.14877	−0.574384	+	0.818586i	$0.694758\pi$
$464$	−4.38918	−0.203763
$465$	−0.0918165	−0.00425789
$466$	12.7225	0.589358
$467$	−25.6913	−1.18885	−0.594425	−	0.804151i	$-0.702620\pi$
$467$	−25.6913	−1.18885	−0.594425	+	0.804151i	$0.702620\pi$
$468$	0.350024	0.0161799
$469$	4.45741	0.205824
$470$	2.56370	0.118255
$471$	−27.7774	−1.27991
$472$	3.43077	0.157914
$473$	−0.191305	−0.00879621
$474$	13.6075	0.625015
$475$	0.903255	0.0414442
$476$	2.90717	0.133250
$477$	−1.20232	−0.0550506
$478$	−5.46293	−0.249868
$479$	−30.9222	−1.41287	−0.706437	−	0.707776i	$-0.749698\pi$
$479$	−30.9222	−1.41287	−0.706437	+	0.707776i	$0.749698\pi$
$480$	3.88563	0.177354
$481$	13.6595	0.622818
$482$	−3.27817	−0.149317
$483$	5.64448	0.256833
$484$	1.00000	0.0454545
$485$	10.4728	0.475545
$486$	−1.88871	−0.0856738
$487$	−13.5069	−0.612057	−0.306029	−	0.952022i	$-0.599000\pi$
$487$	−13.5069	−0.612057	−0.306029	+	0.952022i	$0.599000\pi$
$488$	−6.50048	−0.294263
$489$	−1.79274	−0.0810707
$490$	−15.2446	−0.688681
$491$	33.4034	1.50747	0.753737	−	0.657176i	$-0.228249\pi$
$491$	33.4034	1.50747	0.753737	+	0.657176i	$0.228249\pi$
$492$	7.75247	0.349508
$493$	−19.8326	−0.893213
$494$	4.85588	0.218476
$495$	−0.421267	−0.0189345
$496$	0.0236297	0.00106101
$497$	−8.56167	−0.384043
$498$	9.61439	0.430831
$499$	20.7435	0.928605	0.464303	−	0.885677i	$-0.346305\pi$
$499$	20.7435	0.928605	0.464303	+	0.885677i	$0.346305\pi$
$500$	10.7453	0.480546
$501$	7.38749	0.330049
$502$	−7.42897	−0.331571
$503$	27.3266	1.21843	0.609215	−	0.793005i	$-0.291484\pi$
$503$	27.3266	1.21843	0.609215	+	0.793005i	$0.291484\pi$
$504$	0.117096	0.00521587
$505$	−33.4930	−1.49042
$506$	5.22610	0.232329
$507$	−15.6138	−0.693434
$508$	−2.24218	−0.0994805
$509$	18.9126	0.838288	0.419144	−	0.907920i	$-0.362330\pi$
$509$	18.9126	0.838288	0.419144	+	0.907920i	$0.362330\pi$
$510$	17.5573	0.777449
$511$	−9.30164	−0.411480
$512$	−1.00000	−0.0441942
$513$	−13.4867	−0.595454
$514$	−6.09990	−0.269055
$515$	−22.1042	−0.974028
$516$	0.321142	0.0141375
$517$	−1.10758	−0.0487114
$518$	4.56960	0.200777
$519$	4.52297	0.198537
$520$	−4.45166	−0.195218
$521$	0.819046	0.0358831	0.0179415	−	0.999839i	$-0.494289\pi$
$521$	0.819046	0.0358831	0.0179415	+	0.999839i	$0.494289\pi$
$522$	−0.798822	−0.0349635
$523$	−35.1472	−1.53688	−0.768439	−	0.639923i	$-0.778966\pi$
$523$	−35.1472	−1.53688	−0.768439	+	0.639923i	$0.778966\pi$
$524$	−5.39166	−0.235536
$525$	0.386384	0.0168632
$526$	19.0856	0.832171
$527$	0.106771	0.00465103
$528$	−1.67869	−0.0730556
$529$	4.31216	0.187485
$530$	15.2913	0.664214
$531$	0.624392	0.0270963
$532$	1.62447	0.0704297
$533$	−8.88179	−0.384713
$534$	−18.3175	−0.792674
$535$	32.1139	1.38841
$536$	−6.92800	−0.299244
$537$	0.393993	0.0170020
$538$	−25.8171	−1.11305
$539$	6.58605	0.283681
$540$	12.3641	0.532065
$541$	18.7426	0.805809	0.402904	−	0.915242i	$-0.368001\pi$
$541$	18.7426	0.805809	0.402904	+	0.915242i	$0.368001\pi$
$542$	17.6418	0.757778
$543$	3.65963	0.157050
$544$	−4.51851	−0.193729
$545$	38.2564	1.63873
$546$	2.07719	0.0888956
$547$	22.3444	0.955378	0.477689	−	0.878529i	$-0.341475\pi$
$547$	22.3444	0.955378	0.477689	+	0.878529i	$0.341475\pi$
$548$	−14.7737	−0.631103
$549$	−1.18307	−0.0504924
$550$	0.357745	0.0152543
$551$	−11.0821	−0.472111
$552$	−8.77301	−0.373404
$553$	−5.21536	−0.221780
$554$	−19.7017	−0.837044
$555$	27.5972	1.17143
$556$	−16.0012	−0.678601
$557$	11.8259	0.501078	0.250539	−	0.968107i	$-0.419392\pi$
$557$	11.8259	0.501078	0.250539	+	0.968107i	$0.419392\pi$
$558$	0.00430056	0.000182057 0
$559$	−0.367923	−0.0155615
$560$	−1.48925	−0.0629321
$561$	−7.58518	−0.320246
$562$	23.7536	1.00199
$563$	−40.4179	−1.70341	−0.851705	−	0.524021i	$-0.824431\pi$
$563$	−40.4179	−1.70341	−0.851705	+	0.524021i	$0.824431\pi$
$564$	1.85929	0.0782902
$565$	37.6331	1.58323
$566$	−14.1905	−0.596470
$567$	−5.41792	−0.227531
$568$	13.3071	0.558353
$569$	16.8676	0.707128	0.353564	−	0.935410i	$-0.384970\pi$
$569$	16.8676	0.707128	0.353564	+	0.935410i	$0.384970\pi$
$570$	9.81066	0.410923
$571$	19.0921	0.798979	0.399490	−	0.916738i	$-0.369187\pi$
$571$	19.0921	0.798979	0.399490	+	0.916738i	$0.369187\pi$
$572$	1.92323	0.0804142
$573$	−4.72162	−0.197249
$574$	−2.97129	−0.124019
$575$	1.86961	0.0779682
$576$	−0.181998	−0.00758325
$577$	16.1754	0.673391	0.336695	−	0.941614i	$-0.390691\pi$
$577$	16.1754	0.673391	0.336695	+	0.941614i	$0.390691\pi$
$578$	−3.41692	−0.142125
$579$	−28.7809	−1.19609
$580$	10.1596	0.421853
$581$	−3.68490	−0.152876
$582$	7.59524	0.314833
$583$	−6.60625	−0.273603
$584$	14.4572	0.598243
$585$	−0.810193	−0.0334974
$586$	−22.2453	−0.918944
$587$	1.58797	0.0655425	0.0327713	−	0.999463i	$-0.489567\pi$
$587$	1.58797	0.0655425	0.0327713	+	0.999463i	$0.489567\pi$
$588$	−11.0559	−0.455939
$589$	0.0596617	0.00245832
$590$	−7.94113	−0.326931
$591$	−1.67869	−0.0690521
$592$	−7.10236	−0.291905
$593$	−35.9886	−1.47788	−0.738938	−	0.673774i	$-0.764672\pi$
$593$	−35.9886	−1.47788	−0.738938	+	0.673774i	$0.764672\pi$
$594$	−5.34159	−0.219168
$595$	−6.72917	−0.275869
$596$	5.89332	0.241400
$597$	13.0472	0.533987
$598$	10.0510	0.411016
$599$	−18.0210	−0.736317	−0.368159	−	0.929763i	$-0.620012\pi$
$599$	−18.0210	−0.736317	−0.368159	+	0.929763i	$0.620012\pi$
$600$	−0.600543	−0.0245171
$601$	11.7347	0.478669	0.239335	−	0.970937i	$-0.423071\pi$
$601$	11.7347	0.478669	0.239335	+	0.970937i	$0.423071\pi$
$602$	−0.123084	−0.00501652
$603$	−1.26088	−0.0513471
$604$	0.779716	0.0317262
$605$	−2.31468	−0.0941051
$606$	−24.2903	−0.986727
$607$	−15.1983	−0.616881	−0.308440	−	0.951244i	$-0.599807\pi$
$607$	−15.1983	−0.616881	−0.308440	+	0.951244i	$0.599807\pi$
$608$	−2.52486	−0.102396
$609$	−4.74056	−0.192097
$610$	15.0465	0.609216
$611$	−2.13013	−0.0861760
$612$	−0.822359	−0.0332419
$613$	−29.3396	−1.18501	−0.592507	−	0.805565i	$-0.701862\pi$
$613$	−29.3396	−1.18501	−0.592507	+	0.805565i	$0.701862\pi$
$614$	18.8014	0.758762
$615$	−17.9445	−0.723592
$616$	0.643391	0.0259230
$617$	−22.5801	−0.909041	−0.454520	−	0.890736i	$-0.650189\pi$
$617$	−22.5801	−0.909041	−0.454520	+	0.890736i	$0.650189\pi$
$618$	−16.0308	−0.644853
$619$	−7.90740	−0.317825	−0.158913	−	0.987293i	$-0.550799\pi$
$619$	−7.90740	−0.317825	−0.158913	+	0.987293i	$0.550799\pi$
$620$	−0.0546953	−0.00219662
$621$	−27.9157	−1.12022
$622$	−0.917714	−0.0367970
$623$	7.02053	0.281271
$624$	−3.22851	−0.129244
$625$	−26.6607	−1.06643
$626$	7.12692	0.284849
$627$	−4.23845	−0.169267
$628$	−16.5471	−0.660300
$629$	−32.0921	−1.27959
$630$	−0.271040	−0.0107985
$631$	−40.5908	−1.61590	−0.807948	−	0.589254i	$-0.799422\pi$
$631$	−40.5908	−1.61590	−0.807948	+	0.589254i	$0.799422\pi$
$632$	8.10605	0.322441
$633$	−31.6367	−1.25744
$634$	−28.3578	−1.12623
$635$	5.18992	0.205956
$636$	11.0898	0.439741
$637$	12.6665	0.501864
$638$	−4.38918	−0.173769
$639$	2.42186	0.0958075
$640$	2.31468	0.0914958
$641$	9.97427	0.393960	0.196980	−	0.980407i	$-0.436887\pi$
$641$	9.97427	0.393960	0.196980	+	0.980407i	$0.436887\pi$
$642$	23.2902	0.919191
$643$	10.5070	0.414357	0.207178	−	0.978303i	$-0.433572\pi$
$643$	10.5070	0.414357	0.207178	+	0.978303i	$0.433572\pi$
$644$	3.36243	0.132498
$645$	−0.743340	−0.0292690
$646$	−11.4086	−0.448865
$647$	33.4773	1.31613	0.658064	−	0.752962i	$-0.271376\pi$
$647$	33.4773	1.31613	0.658064	+	0.752962i	$0.271376\pi$
$648$	8.42088	0.330804
$649$	3.43077	0.134669
$650$	0.688026	0.0269866
$651$	0.0255214	0.00100026
$652$	−1.06794	−0.0418238
$653$	−45.8844	−1.79559	−0.897797	−	0.440410i	$-0.854833\pi$
$653$	−45.8844	−1.79559	−0.897797	+	0.440410i	$0.854833\pi$
$654$	27.7450	1.08491
$655$	12.4800	0.487633
$656$	4.61817	0.180309
$657$	2.63118	0.102652
$658$	−0.712609	−0.0277804
$659$	−31.8651	−1.24129	−0.620644	−	0.784092i	$-0.713129\pi$
$659$	−31.8651	−1.24129	−0.620644	+	0.784092i	$0.713129\pi$
$660$	3.88563	0.151248
$661$	−2.93712	−0.114241	−0.0571205	−	0.998367i	$-0.518192\pi$
$661$	−2.93712	−0.114241	−0.0571205	+	0.998367i	$0.518192\pi$
$662$	−19.3084	−0.750442
$663$	−14.5880	−0.566552
$664$	5.72731	0.222263
$665$	−3.76013	−0.145812
$666$	−1.29262	−0.0500878
$667$	−22.9383	−0.888175
$668$	4.40074	0.170270
$669$	−26.9928	−1.04360
$670$	16.0361	0.619529
$671$	−6.50048	−0.250948
$672$	−1.08005	−0.0416640
$673$	41.5115	1.60015	0.800076	−	0.599899i	$-0.204793\pi$
$673$	41.5115	1.60015	0.800076	+	0.599899i	$0.204793\pi$
$674$	4.56364	0.175785
$675$	−1.91093	−0.0735516
$676$	−9.30119	−0.357738
$677$	3.70533	0.142408	0.0712038	−	0.997462i	$-0.477316\pi$
$677$	3.70533	0.142408	0.0712038	+	0.997462i	$0.477316\pi$
$678$	27.2929	1.04818
$679$	−2.91103	−0.111715
$680$	10.4589	0.401081
$681$	−11.8315	−0.453384
$682$	0.0236297	0.000904829 0
$683$	−12.2838	−0.470027	−0.235013	−	0.971992i	$-0.575513\pi$
$683$	−12.2838	−0.470027	−0.235013	+	0.971992i	$0.575513\pi$
$684$	−0.459519	−0.0175701
$685$	34.1965	1.30658
$686$	8.74114	0.333738
$687$	−8.91364	−0.340077
$688$	0.191305	0.00729343
$689$	−12.7053	−0.484034
$690$	20.3067	0.773063
$691$	29.3849	1.11785	0.558927	−	0.829217i	$-0.311213\pi$
$691$	29.3849	1.11785	0.558927	+	0.829217i	$0.311213\pi$
$692$	2.69435	0.102424
$693$	0.117096	0.00444811
$694$	1.54375	0.0585999
$695$	37.0376	1.40492
$696$	7.36808	0.279286
$697$	20.8672	0.790402
$698$	5.82258	0.220388
$699$	−21.3571	−0.807801
$700$	0.230170	0.00869961
$701$	−12.8789	−0.486428	−0.243214	−	0.969973i	$-0.578202\pi$
$701$	−12.8789	−0.486428	−0.243214	+	0.969973i	$0.578202\pi$
$702$	−10.2731	−0.387733
$703$	−17.9324	−0.676335
$704$	−1.00000	−0.0376889
$705$	−4.30366	−0.162085
$706$	−18.4820	−0.695580
$707$	9.30974	0.350129
$708$	−5.75919	−0.216444
$709$	−14.2852	−0.536493	−0.268247	−	0.963350i	$-0.586444\pi$
$709$	−14.2852	−0.536493	−0.268247	+	0.963350i	$0.586444\pi$
$710$	−30.8017	−1.15597
$711$	1.47528	0.0553275
$712$	−10.9118	−0.408935
$713$	0.123491	0.00462479
$714$	−4.88024	−0.182638
$715$	−4.45166	−0.166483
$716$	0.234702	0.00877124
$717$	9.17056	0.342481
$718$	18.8587	0.703802
$719$	40.1304	1.49661	0.748305	−	0.663355i	$-0.230868\pi$
$719$	40.1304	1.49661	0.748305	+	0.663355i	$0.230868\pi$
$720$	0.421267	0.0156997
$721$	6.14411	0.228819
$722$	12.6251	0.469858
$723$	5.50304	0.204660
$724$	2.18005	0.0810209
$725$	−1.57021	−0.0583161
$726$	−1.67869	−0.0623021
$727$	−7.69823	−0.285512	−0.142756	−	0.989758i	$-0.545596\pi$
$727$	−7.69823	−0.285512	−0.142756	+	0.989758i	$0.545596\pi$
$728$	1.23739	0.0458607
$729$	28.4332	1.05308
$730$	−33.4638	−1.23855
$731$	0.864413	0.0319715
$732$	10.9123	0.403330
$733$	−49.5900	−1.83165	−0.915825	−	0.401578i	$-0.868462\pi$
$733$	−49.5900	−1.83165	−0.915825	+	0.401578i	$0.868462\pi$
$734$	−1.11150	−0.0410261
$735$	25.5910	0.943937
$736$	−5.22610	−0.192637
$737$	−6.92800	−0.255196
$738$	0.840497	0.0309391
$739$	−23.5235	−0.865324	−0.432662	−	0.901556i	$-0.642426\pi$
$739$	−23.5235	−0.865324	−0.432662	+	0.901556i	$0.642426\pi$
$740$	16.4397	0.604335
$741$	−8.15151	−0.299453
$742$	−4.25040	−0.156037
$743$	15.5609	0.570874	0.285437	−	0.958397i	$-0.407861\pi$
$743$	15.5609	0.570874	0.285437	+	0.958397i	$0.407861\pi$
$744$	−0.0396670	−0.00145426
$745$	−13.6412	−0.499773
$746$	−26.8434	−0.982806
$747$	1.04236	0.0381379
$748$	−4.51851	−0.165213
$749$	−8.92643	−0.326165
$750$	−18.0381	−0.658658
$751$	−6.22154	−0.227027	−0.113514	−	0.993536i	$-0.536211\pi$
$751$	−6.22154	−0.227027	−0.113514	+	0.993536i	$0.536211\pi$
$752$	1.10758	0.0403894
$753$	12.4709	0.454466
$754$	−8.44140	−0.307418
$755$	−1.80479	−0.0656831
$756$	−3.43673	−0.124993
$757$	28.9015	1.05044	0.525221	−	0.850966i	$-0.323983\pi$
$757$	28.9015	1.05044	0.525221	+	0.850966i	$0.323983\pi$
$758$	23.3085	0.846603
$759$	−8.77301	−0.318440
$760$	5.84423	0.211993
$761$	−21.2100	−0.768863	−0.384431	−	0.923154i	$-0.625602\pi$
$761$	−21.2100	−0.768863	−0.384431	+	0.923154i	$0.625602\pi$
$762$	3.76392	0.136352
$763$	−10.6338	−0.384969
$764$	−2.81268	−0.101759
$765$	1.90350	0.0688211
$766$	13.9218	0.503016
$767$	6.59815	0.238245
$768$	1.67869	0.0605745
$769$	6.86386	0.247517	0.123758	−	0.992312i	$-0.460505\pi$
$769$	6.86386	0.247517	0.123758	+	0.992312i	$0.460505\pi$
$770$	−1.48925	−0.0536687
$771$	10.2398	0.368779
$772$	−17.1448	−0.617057
$773$	−7.13723	−0.256708	−0.128354	−	0.991728i	$-0.540969\pi$
$773$	−7.13723	−0.256708	−0.128354	+	0.991728i	$0.540969\pi$
$774$	0.0348171	0.00125147
$775$	0.00845342	0.000303656 0
$776$	4.52450	0.162420
$777$	−7.67094	−0.275193
$778$	−0.315084	−0.0112963
$779$	11.6602	0.417770
$780$	7.47296	0.267575
$781$	13.3071	0.476165
$782$	−23.6142	−0.844442
$783$	23.4452	0.837864
$784$	−6.58605	−0.235216
$785$	38.3012	1.36703
$786$	9.05093	0.322836
$787$	−4.15581	−0.148138	−0.0740692	−	0.997253i	$-0.523599\pi$
$787$	−4.15581	−0.148138	−0.0740692	+	0.997253i	$0.523599\pi$
$788$	−1.00000	−0.0356235
$789$	−32.0388	−1.14061
$790$	−18.7629	−0.667554
$791$	−10.4605	−0.371934
$792$	−0.181998	−0.00646702
$793$	−12.5019	−0.443956
$794$	−6.97165	−0.247415
$795$	−25.6694	−0.910401
$796$	7.77226	0.275481
$797$	−12.6187	−0.446977	−0.223488	−	0.974707i	$-0.571744\pi$
$797$	−12.6187	−0.446977	−0.223488	+	0.974707i	$0.571744\pi$
$798$	−2.72698	−0.0965342
$799$	5.00462	0.177051
$800$	−0.357745	−0.0126482
$801$	−1.98592	−0.0701689
$802$	−9.00430	−0.317953
$803$	14.4572	0.510184
$804$	11.6300	0.410157
$805$	−7.78295	−0.274313
$806$	0.0454454	0.00160075
$807$	43.3389	1.52560
$808$	−14.4698	−0.509046
$809$	−17.3070	−0.608480	−0.304240	−	0.952595i	$-0.598403\pi$
$809$	−17.3070	−0.608480	−0.304240	+	0.952595i	$0.598403\pi$
$810$	−19.4917	−0.684867
$811$	−0.741534	−0.0260388	−0.0130194	−	0.999915i	$-0.504144\pi$
$811$	−0.741534	−0.0260388	−0.0130194	+	0.999915i	$0.504144\pi$
$812$	−2.82396	−0.0991016
$813$	−29.6151	−1.03865
$814$	−7.10236	−0.248938
$815$	2.47194	0.0865884
$816$	7.58518	0.265534
$817$	0.483017	0.0168986
$818$	−19.1395	−0.669198
$819$	0.225202	0.00786920
$820$	−10.6896	−0.373296
$821$	32.5359	1.13551	0.567755	−	0.823198i	$-0.307812\pi$
$821$	32.5359	1.13551	0.567755	+	0.823198i	$0.307812\pi$
$822$	24.8005	0.865019
$823$	11.5845	0.403809	0.201904	−	0.979405i	$-0.435287\pi$
$823$	11.5845	0.403809	0.201904	+	0.979405i	$0.435287\pi$
$824$	−9.54957	−0.332675
$825$	−0.600543	−0.0209082
$826$	2.20732	0.0768027
$827$	9.72244	0.338082	0.169041	−	0.985609i	$-0.445933\pi$
$827$	9.72244	0.338082	0.169041	+	0.985609i	$0.445933\pi$
$828$	−0.951140	−0.0330544
$829$	41.7451	1.44987	0.724934	−	0.688819i	$-0.241870\pi$
$829$	41.7451	1.44987	0.724934	+	0.688819i	$0.241870\pi$
$830$	−13.2569	−0.460154
$831$	33.0730	1.14729
$832$	−1.92323	−0.0666760
$833$	−29.7591	−1.03109
$834$	26.8610	0.930121
$835$	−10.1863	−0.352512
$836$	−2.52486	−0.0873240
$837$	−0.126220	−0.00436281
$838$	−33.6087	−1.16099
$839$	33.6065	1.16022	0.580112	−	0.814537i	$-0.303009\pi$
$839$	33.6065	1.16022	0.580112	+	0.814537i	$0.303009\pi$
$840$	2.49998	0.0862576
$841$	−9.73508	−0.335692
$842$	−21.5965	−0.744266
$843$	−39.8750	−1.37337
$844$	−18.8460	−0.648708
$845$	21.5293	0.740630
$846$	0.201578	0.00693039
$847$	0.643391	0.0221072
$848$	6.60625	0.226859
$849$	23.8214	0.817549
$850$	−1.61647	−0.0554446
$851$	−37.1177	−1.27238
$852$	−22.3385	−0.765304
$853$	−6.02631	−0.206337	−0.103168	−	0.994664i	$-0.532898\pi$
$853$	−6.02631	−0.206337	−0.103168	+	0.994664i	$0.532898\pi$
$854$	−4.18235	−0.143117
$855$	1.06364	0.0363757
$856$	13.8740	0.474205
$857$	43.5606	1.48800	0.744001	−	0.668179i	$-0.232926\pi$
$857$	43.5606	1.48800	0.744001	+	0.668179i	$0.232926\pi$
$858$	−3.22851	−0.110219
$859$	35.5704	1.21365	0.606823	−	0.794837i	$-0.292444\pi$
$859$	35.5704	1.21365	0.606823	+	0.794837i	$0.292444\pi$
$860$	−0.442810	−0.0150997
$861$	4.98787	0.169986
$862$	17.5132	0.596502
$863$	31.2524	1.06384	0.531922	−	0.846793i	$-0.321470\pi$
$863$	31.2524	1.06384	0.531922	+	0.846793i	$0.321470\pi$
$864$	5.34159	0.181725
$865$	−6.23655	−0.212049
$866$	0.219008	0.00744219
$867$	5.73595	0.194803
$868$	0.0152032	0.000516029 0
$869$	8.10605	0.274979
$870$	−17.0547	−0.578210
$871$	−13.3241	−0.451471
$872$	16.5277	0.559700
$873$	0.823451	0.0278696
$874$	−13.1952	−0.446333
$875$	6.91346	0.233717
$876$	−24.2692	−0.819979
$877$	45.7884	1.54616	0.773082	−	0.634307i	$-0.218714\pi$
$877$	45.7884	1.54616	0.773082	+	0.634307i	$0.218714\pi$
$878$	36.6468	1.23677
$879$	37.3429	1.25955
$880$	2.31468	0.0780279
$881$	52.8534	1.78068	0.890338	−	0.455301i	$-0.150468\pi$
$881$	52.8534	1.78068	0.890338	+	0.455301i	$0.150468\pi$
$882$	−1.19865	−0.0403606
$883$	53.6027	1.80387	0.901936	−	0.431869i	$-0.142146\pi$
$883$	53.6027	1.80387	0.901936	+	0.431869i	$0.142146\pi$
$884$	−8.69013	−0.292281
$885$	13.3307	0.448106
$886$	−32.0049	−1.07523
$887$	36.5233	1.22633	0.613166	−	0.789954i	$-0.289896\pi$
$887$	36.5233	1.22633	0.613166	+	0.789954i	$0.289896\pi$
$888$	11.9227	0.400098
$889$	−1.44260	−0.0483831
$890$	25.2572	0.846624
$891$	8.42088	0.282110
$892$	−16.0797	−0.538387
$893$	2.79649	0.0935809
$894$	−9.89306	−0.330873
$895$	−0.543261	−0.0181592
$896$	−0.643391	−0.0214942
$897$	−16.8725	−0.563357
$898$	−5.10603	−0.170390
$899$	−0.103715	−0.00345910
$900$	−0.0651089	−0.00217030
$901$	29.8504	0.994460
$902$	4.61817	0.153768
$903$	0.206620	0.00687587
$904$	16.2584	0.540747
$905$	−5.04612	−0.167739
$906$	−1.30890	−0.0434853
$907$	0.0922302	0.00306245	0.00153123	−	0.999999i	$-0.499513\pi$
$907$	0.0922302	0.00306245	0.00153123	+	0.999999i	$0.499513\pi$
$908$	−7.04805	−0.233898
$909$	−2.63347	−0.0873468
$910$	−2.86416	−0.0949460
$911$	24.3820	0.807811	0.403905	−	0.914801i	$-0.367652\pi$
$911$	24.3820	0.807811	0.403905	+	0.914801i	$0.367652\pi$
$912$	4.23845	0.140349
$913$	5.72731	0.189546
$914$	11.0590	0.365798
$915$	−25.2585	−0.835019
$916$	−5.30988	−0.175443
$917$	−3.46895	−0.114555
$918$	24.1360	0.796607
$919$	−43.8871	−1.44770	−0.723851	−	0.689957i	$-0.757630\pi$
$919$	−43.8871	−1.44770	−0.723851	+	0.689957i	$0.757630\pi$
$920$	12.0968	0.398818
$921$	−31.5617	−1.03999
$922$	4.67470	0.153953
$923$	25.5926	0.842390
$924$	−1.08005	−0.0355312
$925$	−2.54083	−0.0835421
$926$	24.7186	0.812302
$927$	−1.73800	−0.0570835
$928$	4.38918	0.144082
$929$	−42.6553	−1.39948	−0.699738	−	0.714400i	$-0.746700\pi$
$929$	−42.6553	−1.39948	−0.699738	+	0.714400i	$0.746700\pi$
$930$	0.0918165	0.00301078
$931$	−16.6288	−0.544988
$932$	−12.7225	−0.416739
$933$	1.54056	0.0504356
$934$	25.6913	0.840643
$935$	10.4589	0.342043
$936$	−0.350024	−0.0114409
$937$	−51.2718	−1.67498	−0.837489	−	0.546455i	$-0.815977\pi$
$937$	−51.2718	−1.67498	−0.837489	+	0.546455i	$0.815977\pi$
$938$	−4.45741	−0.145540
$939$	−11.9639	−0.390427
$940$	−2.56370	−0.0836187
$941$	−9.25851	−0.301819	−0.150909	−	0.988548i	$-0.548220\pi$
$941$	−9.25851	−0.301819	−0.150909	+	0.988548i	$0.548220\pi$
$942$	27.7774	0.905036
$943$	24.1350	0.785944
$944$	−3.43077	−0.111662
$945$	7.95494	0.258774
$946$	0.191305	0.00621986
$947$	60.9928	1.98200	0.991000	−	0.133865i	$-0.0427387\pi$
$947$	60.9928	1.98200	0.991000	+	0.133865i	$0.0427387\pi$
$948$	−13.6075	−0.441952
$949$	27.8045	0.902573
$950$	−0.903255	−0.0293055
$951$	47.6041	1.54367
$952$	−2.90717	−0.0942219
$953$	4.35862	0.141189	0.0705947	−	0.997505i	$-0.477510\pi$
$953$	4.35862	0.141189	0.0705947	+	0.997505i	$0.477510\pi$
$954$	1.20232	0.0389267
$955$	6.51046	0.210673
$956$	5.46293	0.176684
$957$	7.36808	0.238176
$958$	30.9222	0.999052
$959$	−9.50530	−0.306942
$960$	−3.88563	−0.125408
$961$	−30.9994	−0.999982
$962$	−13.6595	−0.440399
$963$	2.52504	0.0813684
$964$	3.27817	0.105583
$965$	39.6848	1.27750
$966$	−5.64448	−0.181608
$967$	14.5663	0.468422	0.234211	−	0.972186i	$-0.424749\pi$
$967$	14.5663	0.468422	0.234211	+	0.972186i	$0.424749\pi$
$968$	−1.00000	−0.0321412
$969$	19.1515	0.615234
$970$	−10.4728	−0.336261
$971$	−32.9880	−1.05864	−0.529318	−	0.848424i	$-0.677552\pi$
$971$	−32.9880	−1.05864	−0.529318	+	0.848424i	$0.677552\pi$
$972$	1.88871	0.0605805
$973$	−10.2950	−0.330043
$974$	13.5069	0.432790
$975$	−1.15498	−0.0369890
$976$	6.50048	0.208075
$977$	−16.4904	−0.527576	−0.263788	−	0.964581i	$-0.584972\pi$
$977$	−16.4904	−0.527576	−0.263788	+	0.964581i	$0.584972\pi$
$978$	1.79274	0.0573256
$979$	−10.9118	−0.348741
$980$	15.2446	0.486971
$981$	3.00801	0.0960385
$982$	−33.4034	−1.06594
$983$	3.75753	0.119847	0.0599233	−	0.998203i	$-0.480914\pi$
$983$	3.75753	0.119847	0.0599233	+	0.998203i	$0.480914\pi$
$984$	−7.75247	−0.247140
$985$	2.31468	0.0737518
$986$	19.8326	0.631597
$987$	1.19625	0.0380771
$988$	−4.85588	−0.154486
$989$	0.999779	0.0317911
$990$	0.421267	0.0133887
$991$	10.2386	0.325240	0.162620	−	0.986689i	$-0.448006\pi$
$991$	10.2386	0.325240	0.162620	+	0.986689i	$0.448006\pi$
$992$	−0.0236297	−0.000750245 0
$993$	32.4128	1.02859
$994$	8.56167	0.271560
$995$	−17.9903	−0.570331
$996$	−9.61439	−0.304644
$997$	42.1588	1.33518	0.667592	−	0.744527i	$-0.267325\pi$
$997$	42.1588	1.33518	0.667592	+	0.744527i	$0.267325\pi$
$998$	−20.7435	−0.656623
$999$	37.9379	1.20030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.12	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.67869 q^{3} +1.00000 q^{4} -2.31468 q^{5} -1.67869 q^{6} +0.643391 q^{7} -1.00000 q^{8} -0.181998 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.67869 q^{3} +1.00000 q^{4} -2.31468 q^{5} -1.67869 q^{6} +0.643391 q^{7} -1.00000 q^{8} -0.181998 q^{9} +2.31468 q^{10} -1.00000 q^{11} +1.67869 q^{12} -1.92323 q^{13} -0.643391 q^{14} -3.88563 q^{15} +1.00000 q^{16} +4.51851 q^{17} +0.181998 q^{18} +2.52486 q^{19} -2.31468 q^{20} +1.08005 q^{21} +1.00000 q^{22} +5.22610 q^{23} -1.67869 q^{24} +0.357745 q^{25} +1.92323 q^{26} -5.34159 q^{27} +0.643391 q^{28} -4.38918 q^{29} +3.88563 q^{30} +0.0236297 q^{31} -1.00000 q^{32} -1.67869 q^{33} -4.51851 q^{34} -1.48925 q^{35} -0.181998 q^{36} -7.10236 q^{37} -2.52486 q^{38} -3.22851 q^{39} +2.31468 q^{40} +4.61817 q^{41} -1.08005 q^{42} +0.191305 q^{43} -1.00000 q^{44} +0.421267 q^{45} -5.22610 q^{46} +1.10758 q^{47} +1.67869 q^{48} -6.58605 q^{49} -0.357745 q^{50} +7.58518 q^{51} -1.92323 q^{52} +6.60625 q^{53} +5.34159 q^{54} +2.31468 q^{55} -0.643391 q^{56} +4.23845 q^{57} +4.38918 q^{58} -3.43077 q^{59} -3.88563 q^{60} +6.50048 q^{61} -0.0236297 q^{62} -0.117096 q^{63} +1.00000 q^{64} +4.45166 q^{65} +1.67869 q^{66} +6.92800 q^{67} +4.51851 q^{68} +8.77301 q^{69} +1.48925 q^{70} -13.3071 q^{71} +0.181998 q^{72} -14.4572 q^{73} +7.10236 q^{74} +0.600543 q^{75} +2.52486 q^{76} -0.643391 q^{77} +3.22851 q^{78} -8.10605 q^{79} -2.31468 q^{80} -8.42088 q^{81} -4.61817 q^{82} -5.72731 q^{83} +1.08005 q^{84} -10.4589 q^{85} -0.191305 q^{86} -7.36808 q^{87} +1.00000 q^{88} +10.9118 q^{89} -0.421267 q^{90} -1.23739 q^{91} +5.22610 q^{92} +0.0396670 q^{93} -1.10758 q^{94} -5.84423 q^{95} -1.67869 q^{96} -4.52450 q^{97} +6.58605 q^{98} +0.181998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 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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