LMFDB - Embedded newform 6034.2.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.59011 q^{3} +1.00000 q^{4} +1.58456 q^{5} +2.59011 q^{6} +1.00000 q^{7} -1.00000 q^{8} +3.70867 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.59011 q^{3} +1.00000 q^{4} +1.58456 q^{5} +2.59011 q^{6} +1.00000 q^{7} -1.00000 q^{8} +3.70867 q^{9} -1.58456 q^{10} +5.04145 q^{11} -2.59011 q^{12} -2.41481 q^{13} -1.00000 q^{14} -4.10417 q^{15} +1.00000 q^{16} -2.62825 q^{17} -3.70867 q^{18} -4.64731 q^{19} +1.58456 q^{20} -2.59011 q^{21} -5.04145 q^{22} -5.45400 q^{23} +2.59011 q^{24} -2.48918 q^{25} +2.41481 q^{26} -1.83554 q^{27} +1.00000 q^{28} +9.36695 q^{29} +4.10417 q^{30} -1.16791 q^{31} -1.00000 q^{32} -13.0579 q^{33} +2.62825 q^{34} +1.58456 q^{35} +3.70867 q^{36} +1.11529 q^{37} +4.64731 q^{38} +6.25463 q^{39} -1.58456 q^{40} -11.4969 q^{41} +2.59011 q^{42} +5.09479 q^{43} +5.04145 q^{44} +5.87660 q^{45} +5.45400 q^{46} -5.58564 q^{47} -2.59011 q^{48} +1.00000 q^{49} +2.48918 q^{50} +6.80747 q^{51} -2.41481 q^{52} -0.467440 q^{53} +1.83554 q^{54} +7.98846 q^{55} -1.00000 q^{56} +12.0370 q^{57} -9.36695 q^{58} +7.18909 q^{59} -4.10417 q^{60} +11.9829 q^{61} +1.16791 q^{62} +3.70867 q^{63} +1.00000 q^{64} -3.82640 q^{65} +13.0579 q^{66} +10.0090 q^{67} -2.62825 q^{68} +14.1265 q^{69} -1.58456 q^{70} +6.06255 q^{71} -3.70867 q^{72} +5.20518 q^{73} -1.11529 q^{74} +6.44726 q^{75} -4.64731 q^{76} +5.04145 q^{77} -6.25463 q^{78} -3.99901 q^{79} +1.58456 q^{80} -6.37177 q^{81} +11.4969 q^{82} -4.52458 q^{83} -2.59011 q^{84} -4.16461 q^{85} -5.09479 q^{86} -24.2614 q^{87} -5.04145 q^{88} -3.80461 q^{89} -5.87660 q^{90} -2.41481 q^{91} -5.45400 q^{92} +3.02501 q^{93} +5.58564 q^{94} -7.36392 q^{95} +2.59011 q^{96} -6.16683 q^{97} -1.00000 q^{98} +18.6971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−2.59011	−1.49540	−0.747700	−	0.664036i	$-0.768842\pi$
$3$	−2.59011	−1.49540	−0.747700	+	0.664036i	$0.768842\pi$
$4$	1.00000	0.500000
$5$	1.58456	0.708635	0.354317	−	0.935125i	$-0.384713\pi$
$5$	1.58456	0.708635	0.354317	+	0.935125i	$0.384713\pi$
$6$	2.59011	1.05741
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	3.70867	1.23622
$10$	−1.58456	−0.501080
$11$	5.04145	1.52006	0.760028	−	0.649891i	$-0.225185\pi$
$11$	5.04145	1.52006	0.760028	+	0.649891i	$0.225185\pi$
$12$	−2.59011	−0.747700
$13$	−2.41481	−0.669749	−0.334874	−	0.942263i	$-0.608694\pi$
$13$	−2.41481	−0.669749	−0.334874	+	0.942263i	$0.608694\pi$
$14$	−1.00000	−0.267261
$15$	−4.10417	−1.05969
$16$	1.00000	0.250000
$17$	−2.62825	−0.637445	−0.318723	−	0.947848i	$-0.603254\pi$
$17$	−2.62825	−0.637445	−0.318723	+	0.947848i	$0.603254\pi$
$18$	−3.70867	−0.874142
$19$	−4.64731	−1.06617	−0.533083	−	0.846063i	$-0.678967\pi$
$19$	−4.64731	−1.06617	−0.533083	+	0.846063i	$0.678967\pi$
$20$	1.58456	0.354317
$21$	−2.59011	−0.565208
$22$	−5.04145	−1.07484
$23$	−5.45400	−1.13724	−0.568619	−	0.822601i	$-0.692522\pi$
$23$	−5.45400	−1.13724	−0.568619	+	0.822601i	$0.692522\pi$
$24$	2.59011	0.528704
$25$	−2.48918	−0.497837
$26$	2.41481	0.473584
$27$	−1.83554	−0.353250
$28$	1.00000	0.188982
$29$	9.36695	1.73940	0.869700	−	0.493581i	$-0.164312\pi$
$29$	9.36695	1.73940	0.869700	+	0.493581i	$0.164312\pi$
$30$	4.10417	0.749316
$31$	−1.16791	−0.209762	−0.104881	−	0.994485i	$-0.533446\pi$
$31$	−1.16791	−0.209762	−0.104881	+	0.994485i	$0.533446\pi$
$32$	−1.00000	−0.176777
$33$	−13.0579	−2.27309
$34$	2.62825	0.450742
$35$	1.58456	0.267839
$36$	3.70867	0.618112
$37$	1.11529	0.183353	0.0916765	−	0.995789i	$-0.470777\pi$
$37$	1.11529	0.183353	0.0916765	+	0.995789i	$0.470777\pi$
$38$	4.64731	0.753893
$39$	6.25463	1.00154
$40$	−1.58456	−0.250540
$41$	−11.4969	−1.79551	−0.897757	−	0.440490i	$-0.854805\pi$
$41$	−11.4969	−1.79551	−0.897757	+	0.440490i	$0.854805\pi$
$42$	2.59011	0.399663
$43$	5.09479	0.776948	0.388474	−	0.921460i	$-0.373002\pi$
$43$	5.09479	0.776948	0.388474	+	0.921460i	$0.373002\pi$
$44$	5.04145	0.760028
$45$	5.87660	0.876031
$46$	5.45400	0.804149
$47$	−5.58564	−0.814749	−0.407374	−	0.913261i	$-0.633556\pi$
$47$	−5.58564	−0.814749	−0.407374	+	0.913261i	$0.633556\pi$
$48$	−2.59011	−0.373850
$49$	1.00000	0.142857
$50$	2.48918	0.352024
$51$	6.80747	0.953236
$52$	−2.41481	−0.334874
$53$	−0.467440	−0.0642078	−0.0321039	−	0.999485i	$-0.510221\pi$
$53$	−0.467440	−0.0642078	−0.0321039	+	0.999485i	$0.510221\pi$
$54$	1.83554	0.249785
$55$	7.98846	1.07716
$56$	−1.00000	−0.133631
$57$	12.0370	1.59435
$58$	−9.36695	−1.22994
$59$	7.18909	0.935940	0.467970	−	0.883744i	$-0.344986\pi$
$59$	7.18909	0.935940	0.467970	+	0.883744i	$0.344986\pi$
$60$	−4.10417	−0.529846
$61$	11.9829	1.53425	0.767126	−	0.641497i	$-0.221686\pi$
$61$	11.9829	1.53425	0.767126	+	0.641497i	$0.221686\pi$
$62$	1.16791	0.148324
$63$	3.70867	0.467249
$64$	1.00000	0.125000
$65$	−3.82640	−0.474607
$66$	13.0579	1.60732
$67$	10.0090	1.22279	0.611394	−	0.791326i	$-0.290609\pi$
$67$	10.0090	1.22279	0.611394	+	0.791326i	$0.290609\pi$
$68$	−2.62825	−0.318723
$69$	14.1265	1.70063
$70$	−1.58456	−0.189391
$71$	6.06255	0.719492	0.359746	−	0.933050i	$-0.382863\pi$
$71$	6.06255	0.719492	0.359746	+	0.933050i	$0.382863\pi$
$72$	−3.70867	−0.437071
$73$	5.20518	0.609220	0.304610	−	0.952477i	$-0.401474\pi$
$73$	5.20518	0.609220	0.304610	+	0.952477i	$0.401474\pi$
$74$	−1.11529	−0.129650
$75$	6.44726	0.744466
$76$	−4.64731	−0.533083
$77$	5.04145	0.574527
$78$	−6.25463	−0.708198
$79$	−3.99901	−0.449923	−0.224962	−	0.974368i	$-0.572226\pi$
$79$	−3.99901	−0.449923	−0.224962	+	0.974368i	$0.572226\pi$
$80$	1.58456	0.177159
$81$	−6.37177	−0.707974
$82$	11.4969	1.26962
$83$	−4.52458	−0.496638	−0.248319	−	0.968678i	$-0.579878\pi$
$83$	−4.52458	−0.496638	−0.248319	+	0.968678i	$0.579878\pi$
$84$	−2.59011	−0.282604
$85$	−4.16461	−0.451716
$86$	−5.09479	−0.549385
$87$	−24.2614	−2.60110
$88$	−5.04145	−0.537421
$89$	−3.80461	−0.403288	−0.201644	−	0.979459i	$-0.564628\pi$
$89$	−3.80461	−0.403288	−0.201644	+	0.979459i	$0.564628\pi$
$90$	−5.87660	−0.619448
$91$	−2.41481	−0.253141
$92$	−5.45400	−0.568619
$93$	3.02501	0.313679
$94$	5.58564	0.576114
$95$	−7.36392	−0.755522
$96$	2.59011	0.264352
$97$	−6.16683	−0.626147	−0.313073	−	0.949729i	$-0.601359\pi$
$97$	−6.16683	−0.626147	−0.313073	+	0.949729i	$0.601359\pi$
$98$	−1.00000	−0.101015
$99$	18.6971	1.87913
$100$	−2.48918	−0.248918
$101$	9.94159	0.989225	0.494613	−	0.869114i	$-0.335310\pi$
$101$	9.94159	0.989225	0.494613	+	0.869114i	$0.335310\pi$
$102$	−6.80747	−0.674040
$103$	10.2705	1.01198	0.505990	−	0.862540i	$-0.331127\pi$
$103$	10.2705	1.01198	0.505990	+	0.862540i	$0.331127\pi$
$104$	2.41481	0.236792
$105$	−4.10417	−0.400526
$106$	0.467440	0.0454018
$107$	2.11459	0.204425	0.102213	−	0.994763i	$-0.467408\pi$
$107$	2.11459	0.204425	0.102213	+	0.994763i	$0.467408\pi$
$108$	−1.83554	−0.176625
$109$	7.03498	0.673829	0.336914	−	0.941535i	$-0.390617\pi$
$109$	7.03498	0.673829	0.336914	+	0.941535i	$0.390617\pi$
$110$	−7.98846	−0.761670
$111$	−2.88873	−0.274186
$112$	1.00000	0.0944911
$113$	−5.84966	−0.550290	−0.275145	−	0.961403i	$-0.588726\pi$
$113$	−5.84966	−0.550290	−0.275145	+	0.961403i	$0.588726\pi$
$114$	−12.0370	−1.12737
$115$	−8.64217	−0.805887
$116$	9.36695	0.869700
$117$	−8.95575	−0.827959
$118$	−7.18909	−0.661809
$119$	−2.62825	−0.240932
$120$	4.10417	0.374658
$121$	14.4163	1.31057
$122$	−11.9829	−1.08488
$123$	29.7782	2.68501
$124$	−1.16791	−0.104881
$125$	−11.8670	−1.06142
$126$	−3.70867	−0.330395
$127$	5.47325	0.485673	0.242836	−	0.970067i	$-0.421922\pi$
$127$	5.47325	0.485673	0.242836	+	0.970067i	$0.421922\pi$
$128$	−1.00000	−0.0883883
$129$	−13.1961	−1.16185
$130$	3.82640	0.335598
$131$	10.6145	0.927395	0.463697	−	0.885994i	$-0.346522\pi$
$131$	10.6145	0.927395	0.463697	+	0.885994i	$0.346522\pi$
$132$	−13.0579	−1.13655
$133$	−4.64731	−0.402973
$134$	−10.0090	−0.864642
$135$	−2.90851	−0.250325
$136$	2.62825	0.225371
$137$	−4.96452	−0.424148	−0.212074	−	0.977254i	$-0.568022\pi$
$137$	−4.96452	−0.424148	−0.212074	+	0.977254i	$0.568022\pi$
$138$	−14.1265	−1.20253
$139$	−11.6529	−0.988385	−0.494193	−	0.869352i	$-0.664536\pi$
$139$	−11.6529	−0.988385	−0.494193	+	0.869352i	$0.664536\pi$
$140$	1.58456	0.133919
$141$	14.4674	1.21838
$142$	−6.06255	−0.508758
$143$	−12.1742	−1.01806
$144$	3.70867	0.309056
$145$	14.8425	1.23260
$146$	−5.20518	−0.430784
$147$	−2.59011	−0.213629
$148$	1.11529	0.0916765
$149$	−0.764758	−0.0626514	−0.0313257	−	0.999509i	$-0.509973\pi$
$149$	−0.764758	−0.0626514	−0.0313257	+	0.999509i	$0.509973\pi$
$150$	−6.44726	−0.526417
$151$	16.0673	1.30754	0.653770	−	0.756693i	$-0.273186\pi$
$151$	16.0673	1.30754	0.653770	+	0.756693i	$0.273186\pi$
$152$	4.64731	0.376946
$153$	−9.74733	−0.788025
$154$	−5.04145	−0.406252
$155$	−1.85061	−0.148645
$156$	6.25463	0.500771
$157$	−20.5915	−1.64338	−0.821689	−	0.569936i	$-0.806968\pi$
$157$	−20.5915	−1.64338	−0.821689	+	0.569936i	$0.806968\pi$
$158$	3.99901	0.318144
$159$	1.21072	0.0960164
$160$	−1.58456	−0.125270
$161$	−5.45400	−0.429836
$162$	6.37177	0.500613
$163$	15.7226	1.23149	0.615743	−	0.787947i	$-0.288856\pi$
$163$	15.7226	1.23149	0.615743	+	0.787947i	$0.288856\pi$
$164$	−11.4969	−0.897757
$165$	−20.6910	−1.61079
$166$	4.52458	0.351176
$167$	−12.3060	−0.952266	−0.476133	−	0.879373i	$-0.657962\pi$
$167$	−12.3060	−0.952266	−0.476133	+	0.879373i	$0.657962\pi$
$168$	2.59011	0.199831
$169$	−7.16868	−0.551437
$170$	4.16461	0.319411
$171$	−17.2353	−1.31802
$172$	5.09479	0.388474
$173$	14.8956	1.13249	0.566246	−	0.824236i	$-0.308395\pi$
$173$	14.8956	1.13249	0.566246	+	0.824236i	$0.308395\pi$
$174$	24.2614	1.83926
$175$	−2.48918	−0.188165
$176$	5.04145	0.380014
$177$	−18.6205	−1.39961
$178$	3.80461	0.285168
$179$	7.83038	0.585270	0.292635	−	0.956224i	$-0.405468\pi$
$179$	7.83038	0.585270	0.292635	+	0.956224i	$0.405468\pi$
$180$	5.87660	0.438016
$181$	11.3109	0.840730	0.420365	−	0.907355i	$-0.361902\pi$
$181$	11.3109	0.840730	0.420365	+	0.907355i	$0.361902\pi$
$182$	2.41481	0.178998
$183$	−31.0370	−2.29432
$184$	5.45400	0.402075
$185$	1.76724	0.129930
$186$	−3.02501	−0.221804
$187$	−13.2502	−0.968952
$188$	−5.58564	−0.407374
$189$	−1.83554	−0.133516
$190$	7.36392	0.534235
$191$	−4.38180	−0.317056	−0.158528	−	0.987354i	$-0.550675\pi$
$191$	−4.38180	−0.317056	−0.158528	+	0.987354i	$0.550675\pi$
$192$	−2.59011	−0.186925
$193$	12.5160	0.900922	0.450461	−	0.892796i	$-0.351260\pi$
$193$	12.5160	0.900922	0.450461	+	0.892796i	$0.351260\pi$
$194$	6.16683	0.442752
$195$	9.91081	0.709728
$196$	1.00000	0.0714286
$197$	−14.3509	−1.02246	−0.511228	−	0.859445i	$-0.670809\pi$
$197$	−14.3509	−1.02246	−0.511228	+	0.859445i	$0.670809\pi$
$198$	−18.6971	−1.32874
$199$	−16.2965	−1.15523	−0.577613	−	0.816311i	$-0.696016\pi$
$199$	−16.2965	−1.15523	−0.577613	+	0.816311i	$0.696016\pi$
$200$	2.48918	0.176012
$201$	−25.9243	−1.82856
$202$	−9.94159	−0.699488
$203$	9.36695	0.657431
$204$	6.80747	0.476618
$205$	−18.2175	−1.27236
$206$	−10.2705	−0.715577
$207$	−20.2271	−1.40588
$208$	−2.41481	−0.167437
$209$	−23.4292	−1.62063
$210$	4.10417	0.283215
$211$	5.25694	0.361903	0.180951	−	0.983492i	$-0.442082\pi$
$211$	5.25694	0.361903	0.180951	+	0.983492i	$0.442082\pi$
$212$	−0.467440	−0.0321039
$213$	−15.7027	−1.07593
$214$	−2.11459	−0.144550
$215$	8.07297	0.550572
$216$	1.83554	0.124893
$217$	−1.16791	−0.0792827
$218$	−7.03498	−0.476469
$219$	−13.4820	−0.911028
$220$	7.98846	0.538582
$221$	6.34674	0.426928
$222$	2.88873	0.193879
$223$	−13.5084	−0.904586	−0.452293	−	0.891869i	$-0.649394\pi$
$223$	−13.5084	−0.904586	−0.452293	+	0.891869i	$0.649394\pi$
$224$	−1.00000	−0.0668153
$225$	−9.23157	−0.615438
$226$	5.84966	0.389114
$227$	−1.38269	−0.0917723	−0.0458861	−	0.998947i	$-0.514611\pi$
$227$	−1.38269	−0.0917723	−0.0458861	+	0.998947i	$0.514611\pi$
$228$	12.0370	0.797173
$229$	−17.2877	−1.14240	−0.571202	−	0.820809i	$-0.693523\pi$
$229$	−17.2877	−1.14240	−0.571202	+	0.820809i	$0.693523\pi$
$230$	8.64217	0.569848
$231$	−13.0579	−0.859148
$232$	−9.36695	−0.614971
$233$	11.2080	0.734261	0.367130	−	0.930169i	$-0.380340\pi$
$233$	11.2080	0.734261	0.367130	+	0.930169i	$0.380340\pi$
$234$	8.95575	0.585456
$235$	−8.85075	−0.577359
$236$	7.18909	0.467970
$237$	10.3579	0.672816
$238$	2.62825	0.170364
$239$	18.6411	1.20579	0.602897	−	0.797819i	$-0.294013\pi$
$239$	18.6411	1.20579	0.602897	+	0.797819i	$0.294013\pi$
$240$	−4.10417	−0.264923
$241$	11.3184	0.729085	0.364543	−	0.931187i	$-0.381225\pi$
$241$	11.3184	0.729085	0.364543	+	0.931187i	$0.381225\pi$
$242$	−14.4163	−0.926712
$243$	22.0102	1.41195
$244$	11.9829	0.767126
$245$	1.58456	0.101234
$246$	−29.7782	−1.89859
$247$	11.2224	0.714063
$248$	1.16791	0.0741622
$249$	11.7192	0.742672
$250$	11.8670	0.750537
$251$	17.9868	1.13532	0.567658	−	0.823264i	$-0.307850\pi$
$251$	17.9868	1.13532	0.567658	+	0.823264i	$0.307850\pi$
$252$	3.70867	0.233624
$253$	−27.4961	−1.72867
$254$	−5.47325	−0.343422
$255$	10.7868	0.675496
$256$	1.00000	0.0625000
$257$	23.0534	1.43803	0.719015	−	0.694995i	$-0.244593\pi$
$257$	23.0534	1.43803	0.719015	+	0.694995i	$0.244593\pi$
$258$	13.1961	0.821551
$259$	1.11529	0.0693009
$260$	−3.82640	−0.237304
$261$	34.7390	2.15029
$262$	−10.6145	−0.655767
$263$	8.66846	0.534520	0.267260	−	0.963624i	$-0.413882\pi$
$263$	8.66846	0.534520	0.267260	+	0.963624i	$0.413882\pi$
$264$	13.0579	0.803660
$265$	−0.740685	−0.0454999
$266$	4.64731	0.284945
$267$	9.85436	0.603077
$268$	10.0090	0.611394
$269$	16.8322	1.02628	0.513139	−	0.858306i	$-0.328483\pi$
$269$	16.8322	1.02628	0.513139	+	0.858306i	$0.328483\pi$
$270$	2.90851	0.177006
$271$	29.9246	1.81779	0.908894	−	0.417027i	$-0.136928\pi$
$271$	29.9246	1.81779	0.908894	+	0.417027i	$0.136928\pi$
$272$	−2.62825	−0.159361
$273$	6.25463	0.378548
$274$	4.96452	0.299918
$275$	−12.5491	−0.756740
$276$	14.1265	0.850314
$277$	−25.6489	−1.54109	−0.770545	−	0.637386i	$-0.780016\pi$
$277$	−25.6489	−1.54109	−0.770545	+	0.637386i	$0.780016\pi$
$278$	11.6529	0.698894
$279$	−4.33138	−0.259313
$280$	−1.58456	−0.0946953
$281$	−0.313785	−0.0187189	−0.00935943	−	0.999956i	$-0.502979\pi$
$281$	−0.313785	−0.0187189	−0.00935943	+	0.999956i	$0.502979\pi$
$282$	−14.4674	−0.861522
$283$	9.05343	0.538171	0.269085	−	0.963116i	$-0.413279\pi$
$283$	9.05343	0.538171	0.269085	+	0.963116i	$0.413279\pi$
$284$	6.06255	0.359746
$285$	19.0734	1.12981
$286$	12.1742	0.719874
$287$	−11.4969	−0.678641
$288$	−3.70867	−0.218536
$289$	−10.0923	−0.593664
$290$	−14.8425	−0.871579
$291$	15.9728	0.936340
$292$	5.20518	0.304610
$293$	−24.1211	−1.40917	−0.704584	−	0.709621i	$-0.748866\pi$
$293$	−24.1211	−1.40917	−0.704584	+	0.709621i	$0.748866\pi$
$294$	2.59011	0.151058
$295$	11.3915	0.663239
$296$	−1.11529	−0.0648251
$297$	−9.25378	−0.536959
$298$	0.764758	0.0443012
$299$	13.1704	0.761664
$300$	6.44726	0.372233
$301$	5.09479	0.293659
$302$	−16.0673	−0.924571
$303$	−25.7498	−1.47929
$304$	−4.64731	−0.266541
$305$	18.9875	1.08722
$306$	9.74733	0.557218
$307$	7.18851	0.410270	0.205135	−	0.978734i	$-0.434237\pi$
$307$	7.18851	0.410270	0.205135	+	0.978734i	$0.434237\pi$
$308$	5.04145	0.287263
$309$	−26.6016	−1.51331
$310$	1.85061	0.105108
$311$	26.9619	1.52887	0.764435	−	0.644701i	$-0.223018\pi$
$311$	26.9619	1.52887	0.764435	+	0.644701i	$0.223018\pi$
$312$	−6.25463	−0.354099
$313$	−7.68448	−0.434352	−0.217176	−	0.976132i	$-0.569685\pi$
$313$	−7.68448	−0.434352	−0.217176	+	0.976132i	$0.569685\pi$
$314$	20.5915	1.16204
$315$	5.87660	0.331109
$316$	−3.99901	−0.224962
$317$	−1.94251	−0.109102	−0.0545511	−	0.998511i	$-0.517373\pi$
$317$	−1.94251	−0.109102	−0.0545511	+	0.998511i	$0.517373\pi$
$318$	−1.21072	−0.0678939
$319$	47.2231	2.64398
$320$	1.58456	0.0885793
$321$	−5.47702	−0.305697
$322$	5.45400	0.303940
$323$	12.2143	0.679622
$324$	−6.37177	−0.353987
$325$	6.01092	0.333426
$326$	−15.7226	−0.870793
$327$	−18.2214	−1.00764
$328$	11.4969	0.634810
$329$	−5.58564	−0.307946
$330$	20.6910	1.13900
$331$	−6.74660	−0.370827	−0.185413	−	0.982661i	$-0.559362\pi$
$331$	−6.74660	−0.370827	−0.185413	+	0.982661i	$0.559362\pi$
$332$	−4.52458	−0.248319
$333$	4.13625	0.226665
$334$	12.3060	0.673354
$335$	15.8597	0.866510
$336$	−2.59011	−0.141302
$337$	6.08814	0.331642	0.165821	−	0.986156i	$-0.446973\pi$
$337$	6.08814	0.331642	0.165821	+	0.986156i	$0.446973\pi$
$338$	7.16868	0.389925
$339$	15.1513	0.822904
$340$	−4.16461	−0.225858
$341$	−5.88795	−0.318850
$342$	17.2353	0.931981
$343$	1.00000	0.0539949
$344$	−5.09479	−0.274692
$345$	22.3842	1.20512
$346$	−14.8956	−0.800792
$347$	18.1952	0.976770	0.488385	−	0.872628i	$-0.337586\pi$
$347$	18.1952	0.976770	0.488385	+	0.872628i	$0.337586\pi$
$348$	−24.2614	−1.30055
$349$	−2.26222	−0.121094	−0.0605471	−	0.998165i	$-0.519285\pi$
$349$	−2.26222	−0.121094	−0.0605471	+	0.998165i	$0.519285\pi$
$350$	2.48918	0.133053
$351$	4.43248	0.236588
$352$	−5.04145	−0.268710
$353$	9.28745	0.494321	0.247161	−	0.968975i	$-0.420502\pi$
$353$	9.28745	0.494321	0.247161	+	0.968975i	$0.420502\pi$
$354$	18.6205	0.989670
$355$	9.60644	0.509857
$356$	−3.80461	−0.201644
$357$	6.80747	0.360289
$358$	−7.83038	−0.413849
$359$	−18.1249	−0.956596	−0.478298	−	0.878198i	$-0.658746\pi$
$359$	−18.1249	−0.956596	−0.478298	+	0.878198i	$0.658746\pi$
$360$	−5.87660	−0.309724
$361$	2.59747	0.136709
$362$	−11.3109	−0.594486
$363$	−37.3397	−1.95983
$364$	−2.41481	−0.126571
$365$	8.24789	0.431714
$366$	31.0370	1.62233
$367$	−10.9146	−0.569740	−0.284870	−	0.958566i	$-0.591950\pi$
$367$	−10.9146	−0.569740	−0.284870	+	0.958566i	$0.591950\pi$
$368$	−5.45400	−0.284310
$369$	−42.6382	−2.21966
$370$	−1.76724	−0.0918746
$371$	−0.467440	−0.0242683
$372$	3.02501	0.156839
$373$	−15.7494	−0.815474	−0.407737	−	0.913099i	$-0.633682\pi$
$373$	−15.7494	−0.815474	−0.407737	+	0.913099i	$0.633682\pi$
$374$	13.2502	0.685153
$375$	30.7369	1.58725
$376$	5.58564	0.288057
$377$	−22.6194	−1.16496
$378$	1.83554	0.0944099
$379$	8.21045	0.421742	0.210871	−	0.977514i	$-0.432370\pi$
$379$	8.21045	0.421742	0.210871	+	0.977514i	$0.432370\pi$
$380$	−7.36392	−0.377761
$381$	−14.1763	−0.726275
$382$	4.38180	0.224192
$383$	17.3231	0.885169	0.442584	−	0.896727i	$-0.354062\pi$
$383$	17.3231	0.885169	0.442584	+	0.896727i	$0.354062\pi$
$384$	2.59011	0.132176
$385$	7.98846	0.407130
$386$	−12.5160	−0.637048
$387$	18.8949	0.960481
$388$	−6.16683	−0.313073
$389$	−4.09068	−0.207405	−0.103703	−	0.994608i	$-0.533069\pi$
$389$	−4.09068	−0.207405	−0.103703	+	0.994608i	$0.533069\pi$
$390$	−9.91081	−0.501853
$391$	14.3345	0.724927
$392$	−1.00000	−0.0505076
$393$	−27.4928	−1.38683
$394$	14.3509	0.722986
$395$	−6.33665	−0.318831
$396$	18.6971	0.939565
$397$	13.6092	0.683025	0.341512	−	0.939877i	$-0.389061\pi$
$397$	13.6092	0.683025	0.341512	+	0.939877i	$0.389061\pi$
$398$	16.2965	0.816868
$399$	12.0370	0.602606
$400$	−2.48918	−0.124459
$401$	10.7032	0.534493	0.267247	−	0.963628i	$-0.413886\pi$
$401$	10.7032	0.534493	0.267247	+	0.963628i	$0.413886\pi$
$402$	25.9243	1.29299
$403$	2.82028	0.140488
$404$	9.94159	0.494613
$405$	−10.0964	−0.501695
$406$	−9.36695	−0.464874
$407$	5.62270	0.278707
$408$	−6.80747	−0.337020
$409$	−0.156213	−0.00772426	−0.00386213	−	0.999993i	$-0.501229\pi$
$409$	−0.156213	−0.00772426	−0.00386213	+	0.999993i	$0.501229\pi$
$410$	18.2175	0.899697
$411$	12.8587	0.634271
$412$	10.2705	0.505990
$413$	7.18909	0.353752
$414$	20.2271	0.994108
$415$	−7.16945	−0.351935
$416$	2.41481	0.118396
$417$	30.1823	1.47803
$418$	23.4292	1.14596
$419$	9.00638	0.439991	0.219995	−	0.975501i	$-0.429396\pi$
$419$	9.00638	0.439991	0.219995	+	0.975501i	$0.429396\pi$
$420$	−4.10417	−0.200263
$421$	−4.21491	−0.205422	−0.102711	−	0.994711i	$-0.532752\pi$
$421$	−4.21491	−0.205422	−0.102711	+	0.994711i	$0.532752\pi$
$422$	−5.25694	−0.255904
$423$	−20.7153	−1.00721
$424$	0.467440	0.0227009
$425$	6.54221	0.317344
$426$	15.7027	0.760797
$427$	11.9829	0.579893
$428$	2.11459	0.102213
$429$	31.5324	1.52240
$430$	−8.07297	−0.389313
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−1.83554	−0.0883124
$433$	11.0114	0.529175	0.264588	−	0.964362i	$-0.414764\pi$
$433$	11.0114	0.529175	0.264588	+	0.964362i	$0.414764\pi$
$434$	1.16791	0.0560613
$435$	−38.4436	−1.84323
$436$	7.03498	0.336914
$437$	25.3464	1.21248
$438$	13.4820	0.644194
$439$	−4.96110	−0.236780	−0.118390	−	0.992967i	$-0.537773\pi$
$439$	−4.96110	−0.236780	−0.118390	+	0.992967i	$0.537773\pi$
$440$	−7.98846	−0.380835
$441$	3.70867	0.176603
$442$	−6.34674	−0.301884
$443$	−14.6585	−0.696446	−0.348223	−	0.937412i	$-0.613215\pi$
$443$	−14.6585	−0.696446	−0.348223	+	0.937412i	$0.613215\pi$
$444$	−2.88873	−0.137093
$445$	−6.02861	−0.285784
$446$	13.5084	0.639639
$447$	1.98081	0.0936890
$448$	1.00000	0.0472456
$449$	22.0544	1.04081	0.520406	−	0.853919i	$-0.325781\pi$
$449$	22.0544	1.04081	0.520406	+	0.853919i	$0.325781\pi$
$450$	9.23157	0.435180
$451$	−57.9611	−2.72928
$452$	−5.84966	−0.275145
$453$	−41.6161	−1.95530
$454$	1.38269	0.0648928
$455$	−3.82640	−0.179385
$456$	−12.0370	−0.563686
$457$	3.08398	0.144262	0.0721312	−	0.997395i	$-0.477020\pi$
$457$	3.08398	0.144262	0.0721312	+	0.997395i	$0.477020\pi$
$458$	17.2877	0.807802
$459$	4.82426	0.225177
$460$	−8.64217	−0.402943
$461$	25.5031	1.18780	0.593898	−	0.804540i	$-0.297588\pi$
$461$	25.5031	1.18780	0.593898	+	0.804540i	$0.297588\pi$
$462$	13.0579	0.607510
$463$	11.1882	0.519960	0.259980	−	0.965614i	$-0.416284\pi$
$463$	11.1882	0.519960	0.259980	+	0.965614i	$0.416284\pi$
$464$	9.36695	0.434850
$465$	4.79329	0.222284
$466$	−11.2080	−0.519201
$467$	15.4616	0.715478	0.357739	−	0.933822i	$-0.383548\pi$
$467$	15.4616	0.715478	0.357739	+	0.933822i	$0.383548\pi$
$468$	−8.95575	−0.413980
$469$	10.0090	0.462171
$470$	8.85075	0.408255
$471$	53.3342	2.45751
$472$	−7.18909	−0.330905
$473$	25.6851	1.18100
$474$	−10.3579	−0.475753
$475$	11.5680	0.530777
$476$	−2.62825	−0.120466
$477$	−1.73358	−0.0793752
$478$	−18.6411	−0.852625
$479$	31.1963	1.42540	0.712698	−	0.701471i	$-0.247473\pi$
$479$	31.1963	1.42540	0.712698	+	0.701471i	$0.247473\pi$
$480$	4.10417	0.187329
$481$	−2.69322	−0.122800
$482$	−11.3184	−0.515541
$483$	14.1265	0.642777
$484$	14.4163	0.655284
$485$	−9.77168	−0.443709
$486$	−22.0102	−0.998403
$487$	14.6184	0.662423	0.331211	−	0.943557i	$-0.392543\pi$
$487$	14.6184	0.662423	0.331211	+	0.943557i	$0.392543\pi$
$488$	−11.9829	−0.542440
$489$	−40.7232	−1.84157
$490$	−1.58456	−0.0715829
$491$	14.8609	0.670661	0.335330	−	0.942101i	$-0.391152\pi$
$491$	14.8609	0.670661	0.335330	+	0.942101i	$0.391152\pi$
$492$	29.7782	1.34251
$493$	−24.6187	−1.10877
$494$	−11.2224	−0.504919
$495$	29.6266	1.33162
$496$	−1.16791	−0.0524406
$497$	6.06255	0.271942
$498$	−11.7192	−0.525149
$499$	−30.3089	−1.35681	−0.678407	−	0.734686i	$-0.737330\pi$
$499$	−30.3089	−1.35681	−0.678407	+	0.734686i	$0.737330\pi$
$500$	−11.8670	−0.530710
$501$	31.8739	1.42402
$502$	−17.9868	−0.802790
$503$	10.7540	0.479499	0.239750	−	0.970835i	$-0.422935\pi$
$503$	10.7540	0.479499	0.239750	+	0.970835i	$0.422935\pi$
$504$	−3.70867	−0.165197
$505$	15.7530	0.700999
$506$	27.4961	1.22235
$507$	18.5677	0.824619
$508$	5.47325	0.242836
$509$	−10.5661	−0.468334	−0.234167	−	0.972196i	$-0.575236\pi$
$509$	−10.5661	−0.468334	−0.234167	+	0.972196i	$0.575236\pi$
$510$	−10.7868	−0.477648
$511$	5.20518	0.230264
$512$	−1.00000	−0.0441942
$513$	8.53031	0.376623
$514$	−23.0534	−1.01684
$515$	16.2741	0.717123
$516$	−13.1961	−0.580924
$517$	−28.1597	−1.23846
$518$	−1.11529	−0.0490031
$519$	−38.5813	−1.69353
$520$	3.82640	0.167799
$521$	−20.8863	−0.915045	−0.457523	−	0.889198i	$-0.651263\pi$
$521$	−20.8863	−0.915045	−0.457523	+	0.889198i	$0.651263\pi$
$522$	−34.7390	−1.52048
$523$	−14.2288	−0.622182	−0.311091	−	0.950380i	$-0.600694\pi$
$523$	−14.2288	−0.622182	−0.311091	+	0.950380i	$0.600694\pi$
$524$	10.6145	0.463697
$525$	6.44726	0.281382
$526$	−8.66846	−0.377963
$527$	3.06956	0.133712
$528$	−13.0579	−0.568273
$529$	6.74617	0.293312
$530$	0.740685	0.0321733
$531$	26.6620	1.15703
$532$	−4.64731	−0.201486
$533$	27.7629	1.20254
$534$	−9.85436	−0.426440
$535$	3.35068	0.144863
$536$	−10.0090	−0.432321
$537$	−20.2816	−0.875214
$538$	−16.8322	−0.725688
$539$	5.04145	0.217151
$540$	−2.90851	−0.125162
$541$	4.15906	0.178812	0.0894060	−	0.995995i	$-0.471503\pi$
$541$	4.15906	0.178812	0.0894060	+	0.995995i	$0.471503\pi$
$542$	−29.9246	−1.28537
$543$	−29.2964	−1.25723
$544$	2.62825	0.112685
$545$	11.1473	0.477498
$546$	−6.25463	−0.267674
$547$	−2.69746	−0.115335	−0.0576674	−	0.998336i	$-0.518366\pi$
$547$	−2.69746	−0.115335	−0.0576674	+	0.998336i	$0.518366\pi$
$548$	−4.96452	−0.212074
$549$	44.4406	1.89668
$550$	12.5491	0.535096
$551$	−43.5311	−1.85449
$552$	−14.1265	−0.601263
$553$	−3.99901	−0.170055
$554$	25.6489	1.08972
$555$	−4.57735	−0.194298
$556$	−11.6529	−0.494193
$557$	25.5570	1.08288	0.541442	−	0.840738i	$-0.317879\pi$
$557$	25.5570	1.08288	0.541442	+	0.840738i	$0.317879\pi$
$558$	4.33138	0.183362
$559$	−12.3030	−0.520360
$560$	1.58456	0.0669597
$561$	34.3195	1.44897
$562$	0.313785	0.0132362
$563$	40.2959	1.69827	0.849135	−	0.528176i	$-0.177124\pi$
$563$	40.2959	1.69827	0.849135	+	0.528176i	$0.177124\pi$
$564$	14.4674	0.609188
$565$	−9.26911	−0.389954
$566$	−9.05343	−0.380544
$567$	−6.37177	−0.267589
$568$	−6.06255	−0.254379
$569$	6.26556	0.262666	0.131333	−	0.991338i	$-0.458074\pi$
$569$	6.26556	0.262666	0.131333	+	0.991338i	$0.458074\pi$
$570$	−19.0734	−0.798895
$571$	36.8590	1.54250	0.771251	−	0.636531i	$-0.219631\pi$
$571$	36.8590	1.54250	0.771251	+	0.636531i	$0.219631\pi$
$572$	−12.1742	−0.509028
$573$	11.3494	0.474126
$574$	11.4969	0.479871
$575$	13.5760	0.566159
$576$	3.70867	0.154528
$577$	39.6136	1.64914	0.824569	−	0.565762i	$-0.191418\pi$
$577$	39.6136	1.64914	0.824569	+	0.565762i	$0.191418\pi$
$578$	10.0923	0.419784
$579$	−32.4179	−1.34724
$580$	14.8425	0.616299
$581$	−4.52458	−0.187711
$582$	−15.9728	−0.662092
$583$	−2.35658	−0.0975995
$584$	−5.20518	−0.215392
$585$	−14.1909	−0.586721
$586$	24.1211	0.996432
$587$	−24.3064	−1.00323	−0.501616	−	0.865090i	$-0.667261\pi$
$587$	−24.3064	−1.00323	−0.501616	+	0.865090i	$0.667261\pi$
$588$	−2.59011	−0.106814
$589$	5.42762	0.223641
$590$	−11.3915	−0.468981
$591$	37.1703	1.52898
$592$	1.11529	0.0458382
$593$	−15.6884	−0.644247	−0.322124	−	0.946698i	$-0.604397\pi$
$593$	−15.6884	−0.644247	−0.322124	+	0.946698i	$0.604397\pi$
$594$	9.25378	0.379687
$595$	−4.16461	−0.170733
$596$	−0.764758	−0.0313257
$597$	42.2096	1.72753
$598$	−13.1704	−0.538578
$599$	8.19101	0.334675	0.167338	−	0.985900i	$-0.446483\pi$
$599$	8.19101	0.334675	0.167338	+	0.985900i	$0.446483\pi$
$600$	−6.44726	−0.263208
$601$	−2.00265	−0.0816899	−0.0408449	−	0.999165i	$-0.513005\pi$
$601$	−2.00265	−0.0816899	−0.0408449	+	0.999165i	$0.513005\pi$
$602$	−5.09479	−0.207648
$603$	37.1199	1.51164
$604$	16.0673	0.653770
$605$	22.8434	0.928714
$606$	25.7498	1.04601
$607$	2.23296	0.0906329	0.0453165	−	0.998973i	$-0.485570\pi$
$607$	2.23296	0.0906329	0.0453165	+	0.998973i	$0.485570\pi$
$608$	4.64731	0.188473
$609$	−24.2614	−0.983123
$610$	−18.9875	−0.768783
$611$	13.4883	0.545677
$612$	−9.74733	−0.394013
$613$	−40.5018	−1.63585	−0.817925	−	0.575324i	$-0.804876\pi$
$613$	−40.5018	−1.63585	−0.817925	+	0.575324i	$0.804876\pi$
$614$	−7.18851	−0.290105
$615$	47.1853	1.90269
$616$	−5.04145	−0.203126
$617$	23.2066	0.934261	0.467130	−	0.884188i	$-0.345288\pi$
$617$	23.2066	0.934261	0.467130	+	0.884188i	$0.345288\pi$
$618$	26.6016	1.07007
$619$	16.8541	0.677422	0.338711	−	0.940890i	$-0.390009\pi$
$619$	16.8541	0.677422	0.338711	+	0.940890i	$0.390009\pi$
$620$	−1.85061	−0.0743224
$621$	10.0110	0.401729
$622$	−26.9619	−1.08107
$623$	−3.80461	−0.152428
$624$	6.25463	0.250386
$625$	−6.35804	−0.254321
$626$	7.68448	0.307134
$627$	60.6842	2.42349
$628$	−20.5915	−0.821689
$629$	−2.93127	−0.116877
$630$	−5.87660	−0.234129
$631$	3.50314	0.139458	0.0697290	−	0.997566i	$-0.477787\pi$
$631$	3.50314	0.139458	0.0697290	+	0.997566i	$0.477787\pi$
$632$	3.99901	0.159072
$633$	−13.6161	−0.541190
$634$	1.94251	0.0771469
$635$	8.67267	0.344164
$636$	1.21072	0.0480082
$637$	−2.41481	−0.0956784
$638$	−47.2231	−1.86958
$639$	22.4840	0.889453
$640$	−1.58456	−0.0626350
$641$	32.8677	1.29820	0.649098	−	0.760705i	$-0.275147\pi$
$641$	32.8677	1.29820	0.649098	+	0.760705i	$0.275147\pi$
$642$	5.47702	0.216161
$643$	−44.8624	−1.76920	−0.884601	−	0.466349i	$-0.845569\pi$
$643$	−44.8624	−1.76920	−0.884601	+	0.466349i	$0.845569\pi$
$644$	−5.45400	−0.214918
$645$	−20.9099	−0.823326
$646$	−12.2143	−0.480565
$647$	22.2291	0.873915	0.436958	−	0.899482i	$-0.356056\pi$
$647$	22.2291	0.873915	0.436958	+	0.899482i	$0.356056\pi$
$648$	6.37177	0.250307
$649$	36.2435	1.42268
$650$	−6.01092	−0.235767
$651$	3.02501	0.118559
$652$	15.7226	0.615743
$653$	16.5019	0.645770	0.322885	−	0.946438i	$-0.395347\pi$
$653$	16.5019	0.645770	0.322885	+	0.946438i	$0.395347\pi$
$654$	18.2214	0.712512
$655$	16.8193	0.657184
$656$	−11.4969	−0.448879
$657$	19.3043	0.753132
$658$	5.58564	0.217751
$659$	4.61810	0.179896	0.0899478	−	0.995946i	$-0.471330\pi$
$659$	4.61810	0.179896	0.0899478	+	0.995946i	$0.471330\pi$
$660$	−20.6910	−0.805396
$661$	25.7890	1.00307	0.501537	−	0.865136i	$-0.332768\pi$
$661$	25.7890	1.00307	0.501537	+	0.865136i	$0.332768\pi$
$662$	6.74660	0.262214
$663$	−16.4388	−0.638429
$664$	4.52458	0.175588
$665$	−7.36392	−0.285560
$666$	−4.13625	−0.160277
$667$	−51.0874	−1.97811
$668$	−12.3060	−0.476133
$669$	34.9881	1.35272
$670$	−15.8597	−0.612715
$671$	60.4112	2.33215
$672$	2.59011	0.0999157
$673$	−37.9879	−1.46433	−0.732163	−	0.681130i	$-0.761489\pi$
$673$	−37.9879	−1.46433	−0.732163	+	0.681130i	$0.761489\pi$
$674$	−6.08814	−0.234506
$675$	4.56899	0.175861
$676$	−7.16868	−0.275718
$677$	−11.0978	−0.426523	−0.213262	−	0.976995i	$-0.568409\pi$
$677$	−11.0978	−0.426523	−0.213262	+	0.976995i	$0.568409\pi$
$678$	−15.1513	−0.581881
$679$	−6.16683	−0.236661
$680$	4.16461	0.159706
$681$	3.58132	0.137236
$682$	5.88795	0.225461
$683$	38.8859	1.48793	0.743964	−	0.668219i	$-0.232943\pi$
$683$	38.8859	1.48793	0.743964	+	0.668219i	$0.232943\pi$
$684$	−17.2353	−0.659010
$685$	−7.86656	−0.300566
$686$	−1.00000	−0.0381802
$687$	44.7771	1.70835
$688$	5.09479	0.194237
$689$	1.12878	0.0430031
$690$	−22.3842	−0.852151
$691$	−28.8565	−1.09775	−0.548876	−	0.835904i	$-0.684944\pi$
$691$	−28.8565	−1.09775	−0.548876	+	0.835904i	$0.684944\pi$
$692$	14.8956	0.566246
$693$	18.6971	0.710244
$694$	−18.1952	−0.690681
$695$	−18.4647	−0.700404
$696$	24.2614	0.919628
$697$	30.2168	1.14454
$698$	2.26222	0.0856265
$699$	−29.0300	−1.09801
$700$	−2.48918	−0.0940823
$701$	−35.9859	−1.35917	−0.679585	−	0.733597i	$-0.737840\pi$
$701$	−35.9859	−1.35917	−0.679585	+	0.733597i	$0.737840\pi$
$702$	−4.43248	−0.167293
$703$	−5.18311	−0.195485
$704$	5.04145	0.190007
$705$	22.9244	0.863384
$706$	−9.28745	−0.349538
$707$	9.94159	0.373892
$708$	−18.6205	−0.699803
$709$	21.3965	0.803562	0.401781	−	0.915736i	$-0.368391\pi$
$709$	21.3965	0.803562	0.401781	+	0.915736i	$0.368391\pi$
$710$	−9.60644	−0.360523
$711$	−14.8310	−0.556206
$712$	3.80461	0.142584
$713$	6.36977	0.238550
$714$	−6.80747	−0.254763
$715$	−19.2906	−0.721429
$716$	7.83038	0.292635
$717$	−48.2826	−1.80315
$718$	18.1249	0.676415
$719$	16.7914	0.626215	0.313107	−	0.949718i	$-0.398630\pi$
$719$	16.7914	0.626215	0.313107	+	0.949718i	$0.398630\pi$
$720$	5.87660	0.219008
$721$	10.2705	0.382492
$722$	−2.59747	−0.0966680
$723$	−29.3160	−1.09027
$724$	11.3109	0.420365
$725$	−23.3161	−0.865937
$726$	37.3397	1.38581
$727$	33.9293	1.25837	0.629184	−	0.777256i	$-0.283389\pi$
$727$	33.9293	1.25837	0.629184	+	0.777256i	$0.283389\pi$
$728$	2.41481	0.0894989
$729$	−37.8935	−1.40346
$730$	−8.24789	−0.305268
$731$	−13.3904	−0.495262
$732$	−31.0370	−1.14716
$733$	36.8012	1.35928	0.679641	−	0.733545i	$-0.262136\pi$
$733$	36.8012	1.35928	0.679641	+	0.733545i	$0.262136\pi$
$734$	10.9146	0.402867
$735$	−4.10417	−0.151385
$736$	5.45400	0.201037
$737$	50.4597	1.85871
$738$	42.6382	1.56954
$739$	−37.9444	−1.39581	−0.697905	−	0.716191i	$-0.745884\pi$
$739$	−37.9444	−1.39581	−0.697905	+	0.716191i	$0.745884\pi$
$740$	1.76724	0.0649651
$741$	−29.0672	−1.06781
$742$	0.467440	0.0171603
$743$	−10.0536	−0.368830	−0.184415	−	0.982848i	$-0.559039\pi$
$743$	−10.0536	−0.368830	−0.184415	+	0.982848i	$0.559039\pi$
$744$	−3.02501	−0.110902
$745$	−1.21180	−0.0443970
$746$	15.7494	0.576627
$747$	−16.7802	−0.613955
$748$	−13.2502	−0.484476
$749$	2.11459	0.0772654
$750$	−30.7369	−1.12235
$751$	−0.874200	−0.0319000	−0.0159500	−	0.999873i	$-0.505077\pi$
$751$	−0.874200	−0.0319000	−0.0159500	+	0.999873i	$0.505077\pi$
$752$	−5.58564	−0.203687
$753$	−46.5878	−1.69775
$754$	22.6194	0.823751
$755$	25.4596	0.926568
$756$	−1.83554	−0.0667579
$757$	−32.9791	−1.19865	−0.599323	−	0.800507i	$-0.704563\pi$
$757$	−32.9791	−1.19865	−0.599323	+	0.800507i	$0.704563\pi$
$758$	−8.21045	−0.298217
$759$	71.2180	2.58505
$760$	7.36392	0.267117
$761$	28.4895	1.03274	0.516372	−	0.856365i	$-0.327282\pi$
$761$	28.4895	1.03274	0.516372	+	0.856365i	$0.327282\pi$
$762$	14.1763	0.513554
$763$	7.03498	0.254683
$764$	−4.38180	−0.158528
$765$	−15.4452	−0.558422
$766$	−17.3231	−0.625909
$767$	−17.3603	−0.626844
$768$	−2.59011	−0.0934626
$769$	−2.64173	−0.0952632	−0.0476316	−	0.998865i	$-0.515167\pi$
$769$	−2.64173	−0.0952632	−0.0476316	+	0.998865i	$0.515167\pi$
$770$	−7.98846	−0.287884
$771$	−59.7108	−2.15043
$772$	12.5160	0.450461
$773$	−7.79531	−0.280378	−0.140189	−	0.990125i	$-0.544771\pi$
$773$	−7.79531	−0.280378	−0.140189	+	0.990125i	$0.544771\pi$
$774$	−18.8949	−0.679163
$775$	2.90714	0.104427
$776$	6.16683	0.221376
$777$	−2.88873	−0.103633
$778$	4.09068	0.146658
$779$	53.4297	1.91432
$780$	9.91081	0.354864
$781$	30.5641	1.09367
$782$	−14.3345	−0.512601
$783$	−17.1934	−0.614442
$784$	1.00000	0.0357143
$785$	−32.6283	−1.16456
$786$	27.4928	0.980635
$787$	39.3366	1.40220	0.701099	−	0.713064i	$-0.252693\pi$
$787$	39.3366	1.40220	0.701099	+	0.713064i	$0.252693\pi$
$788$	−14.3509	−0.511228
$789$	−22.4523	−0.799322
$790$	6.33665	0.225448
$791$	−5.84966	−0.207990
$792$	−18.6971	−0.664372
$793$	−28.9364	−1.02756
$794$	−13.6092	−0.482972
$795$	1.91845	0.0680406
$796$	−16.2965	−0.577613
$797$	−32.0092	−1.13382	−0.566911	−	0.823779i	$-0.691862\pi$
$797$	−32.0092	−1.13382	−0.566911	+	0.823779i	$0.691862\pi$
$798$	−12.0370	−0.426107
$799$	14.6805	0.519358
$800$	2.48918	0.0880060
$801$	−14.1100	−0.498554
$802$	−10.7032	−0.377944
$803$	26.2417	0.926048
$804$	−25.9243	−0.914280
$805$	−8.64217	−0.304597
$806$	−2.82028	−0.0993400
$807$	−43.5973	−1.53470
$808$	−9.94159	−0.349744
$809$	8.07350	0.283849	0.141925	−	0.989877i	$-0.454671\pi$
$809$	8.07350	0.283849	0.141925	+	0.989877i	$0.454671\pi$
$810$	10.0964	0.354752
$811$	0.448051	0.0157332	0.00786660	−	0.999969i	$-0.497496\pi$
$811$	0.448051	0.0157332	0.00786660	+	0.999969i	$0.497496\pi$
$812$	9.36695	0.328716
$813$	−77.5080	−2.71832
$814$	−5.62270	−0.197075
$815$	24.9133	0.872674
$816$	6.80747	0.238309
$817$	−23.6770	−0.828355
$818$	0.156213	0.00546188
$819$	−8.95575	−0.312939
$820$	−18.2175	−0.636182
$821$	42.0681	1.46819	0.734093	−	0.679049i	$-0.237608\pi$
$821$	42.0681	1.46819	0.734093	+	0.679049i	$0.237608\pi$
$822$	−12.8587	−0.448497
$823$	4.48408	0.156305	0.0781526	−	0.996941i	$-0.475098\pi$
$823$	4.48408	0.156305	0.0781526	+	0.996941i	$0.475098\pi$
$824$	−10.2705	−0.357789
$825$	32.5036	1.13163
$826$	−7.18909	−0.250140
$827$	26.5877	0.924547	0.462273	−	0.886737i	$-0.347034\pi$
$827$	26.5877	0.924547	0.462273	+	0.886737i	$0.347034\pi$
$828$	−20.2271	−0.702941
$829$	14.5388	0.504952	0.252476	−	0.967603i	$-0.418755\pi$
$829$	14.5388	0.504952	0.252476	+	0.967603i	$0.418755\pi$
$830$	7.16945	0.248855
$831$	66.4334	2.30455
$832$	−2.41481	−0.0837186
$833$	−2.62825	−0.0910636
$834$	−30.1823	−1.04513
$835$	−19.4995	−0.674809
$836$	−23.4292	−0.810315
$837$	2.14374	0.0740984
$838$	−9.00638	−0.311120
$839$	28.2297	0.974596	0.487298	−	0.873236i	$-0.337983\pi$
$839$	28.2297	0.974596	0.487298	+	0.873236i	$0.337983\pi$
$840$	4.10417	0.141607
$841$	58.7398	2.02551
$842$	4.21491	0.145255
$843$	0.812739	0.0279922
$844$	5.25694	0.180951
$845$	−11.3592	−0.390767
$846$	20.7153	0.712206
$847$	14.4163	0.495348
$848$	−0.467440	−0.0160520
$849$	−23.4494	−0.804781
$850$	−6.54221	−0.224396
$851$	−6.08281	−0.208516
$852$	−15.7027	−0.537964
$853$	−33.0583	−1.13189	−0.565947	−	0.824442i	$-0.691489\pi$
$853$	−33.0583	−1.13189	−0.565947	+	0.824442i	$0.691489\pi$
$854$	−11.9829	−0.410046
$855$	−27.3104	−0.933994
$856$	−2.11459	−0.0722752
$857$	21.2528	0.725982	0.362991	−	0.931793i	$-0.381756\pi$
$857$	21.2528	0.725982	0.362991	+	0.931793i	$0.381756\pi$
$858$	−31.5324	−1.07650
$859$	9.08639	0.310024	0.155012	−	0.987913i	$-0.450458\pi$
$859$	9.08639	0.310024	0.155012	+	0.987913i	$0.450458\pi$
$860$	8.07297	0.275286
$861$	29.7782	1.01484
$862$	1.00000	0.0340601
$863$	11.3833	0.387493	0.193747	−	0.981052i	$-0.437936\pi$
$863$	11.3833	0.387493	0.193747	+	0.981052i	$0.437936\pi$
$864$	1.83554	0.0624463
$865$	23.6029	0.802523
$866$	−11.0114	−0.374183
$867$	26.1401	0.887765
$868$	−1.16791	−0.0396413
$869$	−20.1608	−0.683908
$870$	38.4436	1.30336
$871$	−24.1698	−0.818961
$872$	−7.03498	−0.238234
$873$	−22.8707	−0.774057
$874$	−25.3464	−0.857356
$875$	−11.8670	−0.401179
$876$	−13.4820	−0.455514
$877$	−1.99391	−0.0673297	−0.0336648	−	0.999433i	$-0.510718\pi$
$877$	−1.99391	−0.0673297	−0.0336648	+	0.999433i	$0.510718\pi$
$878$	4.96110	0.167429
$879$	62.4762	2.10727
$880$	7.98846	0.269291
$881$	−55.6491	−1.87487	−0.937433	−	0.348164i	$-0.886805\pi$
$881$	−55.6491	−1.87487	−0.937433	+	0.348164i	$0.886805\pi$
$882$	−3.70867	−0.124877
$883$	54.1401	1.82196	0.910979	−	0.412452i	$-0.135328\pi$
$883$	54.1401	1.82196	0.910979	+	0.412452i	$0.135328\pi$
$884$	6.34674	0.213464
$885$	−29.5053	−0.991809
$886$	14.6585	0.492462
$887$	−13.8679	−0.465637	−0.232819	−	0.972520i	$-0.574795\pi$
$887$	−13.8679	−0.465637	−0.232819	+	0.972520i	$0.574795\pi$
$888$	2.88873	0.0969395
$889$	5.47325	0.183567
$890$	6.02861	0.202080
$891$	−32.1230	−1.07616
$892$	−13.5084	−0.452293
$893$	25.9582	0.868657
$894$	−1.98081	−0.0662481
$895$	12.4077	0.414743
$896$	−1.00000	−0.0334077
$897$	−34.1128	−1.13899
$898$	−22.0544	−0.735965
$899$	−10.9397	−0.364860
$900$	−9.23157	−0.307719
$901$	1.22855	0.0409290
$902$	57.9611	1.92989
$903$	−13.1961	−0.439137
$904$	5.84966	0.194557
$905$	17.9227	0.595770
$906$	41.6161	1.38260
$907$	40.1412	1.33287	0.666433	−	0.745565i	$-0.267820\pi$
$907$	40.1412	1.33287	0.666433	+	0.745565i	$0.267820\pi$
$908$	−1.38269	−0.0458861
$909$	36.8701	1.22290
$910$	3.82640	0.126844
$911$	−42.5776	−1.41066	−0.705329	−	0.708880i	$-0.749201\pi$
$911$	−42.5776	−1.41066	−0.705329	+	0.708880i	$0.749201\pi$
$912$	12.0370	0.398586
$913$	−22.8105	−0.754917
$914$	−3.08398	−0.102009
$915$	−49.1798	−1.62584
$916$	−17.2877	−0.571202
$917$	10.6145	0.350522
$918$	−4.82426	−0.159224
$919$	20.3187	0.670253	0.335126	−	0.942173i	$-0.391221\pi$
$919$	20.3187	0.670253	0.335126	+	0.942173i	$0.391221\pi$
$920$	8.64217	0.284924
$921$	−18.6190	−0.613518
$922$	−25.5031	−0.839899
$923$	−14.6399	−0.481879
$924$	−13.0579	−0.429574
$925$	−2.77617	−0.0912799
$926$	−11.1882	−0.367667
$927$	38.0898	1.25103
$928$	−9.36695	−0.307485
$929$	−42.9241	−1.40829	−0.704147	−	0.710054i	$-0.748670\pi$
$929$	−42.9241	−1.40829	−0.704147	+	0.710054i	$0.748670\pi$
$930$	−4.79329	−0.157178
$931$	−4.64731	−0.152309
$932$	11.2080	0.367130
$933$	−69.8343	−2.28627
$934$	−15.4616	−0.505919
$935$	−20.9957	−0.686633
$936$	8.95575	0.292728
$937$	−39.3547	−1.28566	−0.642831	−	0.766008i	$-0.722240\pi$
$937$	−39.3547	−1.28566	−0.642831	+	0.766008i	$0.722240\pi$
$938$	−10.0090	−0.326804
$939$	19.9036	0.649531
$940$	−8.85075	−0.288680
$941$	56.0521	1.82725	0.913623	−	0.406563i	$-0.133273\pi$
$941$	56.0521	1.82725	0.913623	+	0.406563i	$0.133273\pi$
$942$	−53.3342	−1.73772
$943$	62.7042	2.04193
$944$	7.18909	0.233985
$945$	−2.90851	−0.0946139
$946$	−25.6851	−0.835096
$947$	28.2009	0.916407	0.458203	−	0.888847i	$-0.348493\pi$
$947$	28.2009	0.916407	0.458203	+	0.888847i	$0.348493\pi$
$948$	10.3579	0.336408
$949$	−12.5695	−0.408024
$950$	−11.5680	−0.375316
$951$	5.03131	0.163151
$952$	2.62825	0.0851822
$953$	−24.9380	−0.807821	−0.403910	−	0.914799i	$-0.632349\pi$
$953$	−24.9380	−0.807821	−0.403910	+	0.914799i	$0.632349\pi$
$954$	1.73358	0.0561268
$955$	−6.94321	−0.224677
$956$	18.6411	0.602897
$957$	−122.313	−3.95382
$958$	−31.1963	−1.00791
$959$	−4.96452	−0.160313
$960$	−4.10417	−0.132462
$961$	−29.6360	−0.956000
$962$	2.69322	0.0868330
$963$	7.84232	0.252715
$964$	11.3184	0.364543
$965$	19.8323	0.638425
$966$	−14.1265	−0.454512
$967$	−14.9992	−0.482343	−0.241172	−	0.970482i	$-0.577532\pi$
$967$	−14.9992	−0.482343	−0.241172	+	0.970482i	$0.577532\pi$
$968$	−14.4163	−0.463356
$969$	−31.6364	−1.01631
$970$	9.77168	0.313750
$971$	−29.4553	−0.945264	−0.472632	−	0.881260i	$-0.656696\pi$
$971$	−29.4553	−0.945264	−0.472632	+	0.881260i	$0.656696\pi$
$972$	22.0102	0.705977
$973$	−11.6529	−0.373575
$974$	−14.6184	−0.468404
$975$	−15.5689	−0.498605
$976$	11.9829	0.383563
$977$	58.8055	1.88136	0.940678	−	0.339302i	$-0.110191\pi$
$977$	58.8055	1.88136	0.940678	+	0.339302i	$0.110191\pi$
$978$	40.7232	1.30218
$979$	−19.1808	−0.613020
$980$	1.58456	0.0506168
$981$	26.0904	0.833003
$982$	−14.8609	−0.474229
$983$	−33.1113	−1.05609	−0.528043	−	0.849218i	$-0.677074\pi$
$983$	−33.1113	−1.05609	−0.528043	+	0.849218i	$0.677074\pi$
$984$	−29.7782	−0.949296
$985$	−22.7397	−0.724548
$986$	24.6187	0.784020
$987$	14.4674	0.460503
$988$	11.2224	0.357031
$989$	−27.7870	−0.883575
$990$	−29.6266	−0.941595
$991$	13.6696	0.434230	0.217115	−	0.976146i	$-0.430335\pi$
$991$	13.6696	0.434230	0.217115	+	0.976146i	$0.430335\pi$
$992$	1.16791	0.0370811
$993$	17.4744	0.554535
$994$	−6.06255	−0.192292
$995$	−25.8227	−0.818633
$996$	11.7192	0.371336
$997$	33.4829	1.06041	0.530207	−	0.847868i	$-0.322114\pi$
$997$	33.4829	1.06041	0.530207	+	0.847868i	$0.322114\pi$
$998$	30.3089	0.959413
$999$	−2.04716	−0.0647693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.4	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.4	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.59011 q^{3} +1.00000 q^{4} +1.58456 q^{5} +2.59011 q^{6} +1.00000 q^{7} -1.00000 q^{8} +3.70867 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.59011 q^{3} +1.00000 q^{4} +1.58456 q^{5} +2.59011 q^{6} +1.00000 q^{7} -1.00000 q^{8} +3.70867 q^{9} -1.58456 q^{10} +5.04145 q^{11} -2.59011 q^{12} -2.41481 q^{13} -1.00000 q^{14} -4.10417 q^{15} +1.00000 q^{16} -2.62825 q^{17} -3.70867 q^{18} -4.64731 q^{19} +1.58456 q^{20} -2.59011 q^{21} -5.04145 q^{22} -5.45400 q^{23} +2.59011 q^{24} -2.48918 q^{25} +2.41481 q^{26} -1.83554 q^{27} +1.00000 q^{28} +9.36695 q^{29} +4.10417 q^{30} -1.16791 q^{31} -1.00000 q^{32} -13.0579 q^{33} +2.62825 q^{34} +1.58456 q^{35} +3.70867 q^{36} +1.11529 q^{37} +4.64731 q^{38} +6.25463 q^{39} -1.58456 q^{40} -11.4969 q^{41} +2.59011 q^{42} +5.09479 q^{43} +5.04145 q^{44} +5.87660 q^{45} +5.45400 q^{46} -5.58564 q^{47} -2.59011 q^{48} +1.00000 q^{49} +2.48918 q^{50} +6.80747 q^{51} -2.41481 q^{52} -0.467440 q^{53} +1.83554 q^{54} +7.98846 q^{55} -1.00000 q^{56} +12.0370 q^{57} -9.36695 q^{58} +7.18909 q^{59} -4.10417 q^{60} +11.9829 q^{61} +1.16791 q^{62} +3.70867 q^{63} +1.00000 q^{64} -3.82640 q^{65} +13.0579 q^{66} +10.0090 q^{67} -2.62825 q^{68} +14.1265 q^{69} -1.58456 q^{70} +6.06255 q^{71} -3.70867 q^{72} +5.20518 q^{73} -1.11529 q^{74} +6.44726 q^{75} -4.64731 q^{76} +5.04145 q^{77} -6.25463 q^{78} -3.99901 q^{79} +1.58456 q^{80} -6.37177 q^{81} +11.4969 q^{82} -4.52458 q^{83} -2.59011 q^{84} -4.16461 q^{85} -5.09479 q^{86} -24.2614 q^{87} -5.04145 q^{88} -3.80461 q^{89} -5.87660 q^{90} -2.41481 q^{91} -5.45400 q^{92} +3.02501 q^{93} +5.58564 q^{94} -7.36392 q^{95} +2.59011 q^{96} -6.16683 q^{97} -1.00000 q^{98} +18.6971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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