LMFDB - Embedded newform 6034.2.a.o.1.14

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.221832 q^{3} +1.00000 q^{4} -0.411075 q^{5} +0.221832 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.95079 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.221832 q^{3} +1.00000 q^{4} -0.411075 q^{5} +0.221832 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.95079 q^{9} +0.411075 q^{10} +2.69766 q^{11} -0.221832 q^{12} +1.03208 q^{13} +1.00000 q^{14} +0.0911894 q^{15} +1.00000 q^{16} +3.23250 q^{17} +2.95079 q^{18} +4.82747 q^{19} -0.411075 q^{20} +0.221832 q^{21} -2.69766 q^{22} -3.50944 q^{23} +0.221832 q^{24} -4.83102 q^{25} -1.03208 q^{26} +1.32007 q^{27} -1.00000 q^{28} +6.47535 q^{29} -0.0911894 q^{30} -9.99931 q^{31} -1.00000 q^{32} -0.598426 q^{33} -3.23250 q^{34} +0.411075 q^{35} -2.95079 q^{36} -11.7573 q^{37} -4.82747 q^{38} -0.228947 q^{39} +0.411075 q^{40} +5.63083 q^{41} -0.221832 q^{42} -2.15686 q^{43} +2.69766 q^{44} +1.21300 q^{45} +3.50944 q^{46} -1.43035 q^{47} -0.221832 q^{48} +1.00000 q^{49} +4.83102 q^{50} -0.717070 q^{51} +1.03208 q^{52} +8.04686 q^{53} -1.32007 q^{54} -1.10894 q^{55} +1.00000 q^{56} -1.07089 q^{57} -6.47535 q^{58} -4.90229 q^{59} +0.0911894 q^{60} -9.82773 q^{61} +9.99931 q^{62} +2.95079 q^{63} +1.00000 q^{64} -0.424261 q^{65} +0.598426 q^{66} +13.8647 q^{67} +3.23250 q^{68} +0.778504 q^{69} -0.411075 q^{70} -9.72897 q^{71} +2.95079 q^{72} -3.14473 q^{73} +11.7573 q^{74} +1.07167 q^{75} +4.82747 q^{76} -2.69766 q^{77} +0.228947 q^{78} +10.8134 q^{79} -0.411075 q^{80} +8.55954 q^{81} -5.63083 q^{82} -4.93994 q^{83} +0.221832 q^{84} -1.32880 q^{85} +2.15686 q^{86} -1.43644 q^{87} -2.69766 q^{88} +2.08906 q^{89} -1.21300 q^{90} -1.03208 q^{91} -3.50944 q^{92} +2.21816 q^{93} +1.43035 q^{94} -1.98445 q^{95} +0.221832 q^{96} +14.2370 q^{97} -1.00000 q^{98} -7.96023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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
$3$	−0.221832	−0.128075	−0.0640373	−	0.997948i	$-0.520398\pi$
$3$	−0.221832	−0.128075	−0.0640373	+	0.997948i	$0.520398\pi$
$4$	1.00000	0.500000
$5$	−0.411075	−0.183838	−0.0919191	−	0.995766i	$-0.529300\pi$
$5$	−0.411075	−0.183838	−0.0919191	+	0.995766i	$0.529300\pi$
$6$	0.221832	0.0905624
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.95079	−0.983597
$10$	0.411075	0.129993
$11$	2.69766	0.813375	0.406688	−	0.913567i	$-0.366684\pi$
$11$	2.69766	0.813375	0.406688	+	0.913567i	$0.366684\pi$
$12$	−0.221832	−0.0640373
$13$	1.03208	0.286247	0.143123	−	0.989705i	$-0.454285\pi$
$13$	1.03208	0.286247	0.143123	+	0.989705i	$0.454285\pi$
$14$	1.00000	0.267261
$15$	0.0911894	0.0235450
$16$	1.00000	0.250000
$17$	3.23250	0.783996	0.391998	−	0.919966i	$-0.371784\pi$
$17$	3.23250	0.783996	0.391998	+	0.919966i	$0.371784\pi$
$18$	2.95079	0.695508
$19$	4.82747	1.10750	0.553749	−	0.832683i	$-0.313197\pi$
$19$	4.82747	1.10750	0.553749	+	0.832683i	$0.313197\pi$
$20$	−0.411075	−0.0919191
$21$	0.221832	0.0484076
$22$	−2.69766	−0.575143
$23$	−3.50944	−0.731768	−0.365884	−	0.930660i	$-0.619233\pi$
$23$	−3.50944	−0.731768	−0.365884	+	0.930660i	$0.619233\pi$
$24$	0.221832	0.0452812
$25$	−4.83102	−0.966203
$26$	−1.03208	−0.202407
$27$	1.32007	0.254048
$28$	−1.00000	−0.188982
$29$	6.47535	1.20244	0.601221	−	0.799082i	$-0.294681\pi$
$29$	6.47535	1.20244	0.601221	+	0.799082i	$0.294681\pi$
$30$	−0.0911894	−0.0166488
$31$	−9.99931	−1.79593	−0.897965	−	0.440068i	$-0.854954\pi$
$31$	−9.99931	−1.79593	−0.897965	+	0.440068i	$0.854954\pi$
$32$	−1.00000	−0.176777
$33$	−0.598426	−0.104173
$34$	−3.23250	−0.554369
$35$	0.411075	0.0694843
$36$	−2.95079	−0.491798
$37$	−11.7573	−1.93289	−0.966445	−	0.256872i	$-0.917308\pi$
$37$	−11.7573	−1.93289	−0.966445	+	0.256872i	$0.917308\pi$
$38$	−4.82747	−0.783120
$39$	−0.228947	−0.0366609
$40$	0.411075	0.0649967
$41$	5.63083	0.879388	0.439694	−	0.898148i	$-0.355087\pi$
$41$	5.63083	0.879388	0.439694	+	0.898148i	$0.355087\pi$
$42$	−0.221832	−0.0342294
$43$	−2.15686	−0.328919	−0.164459	−	0.986384i	$-0.552588\pi$
$43$	−2.15686	−0.328919	−0.164459	+	0.986384i	$0.552588\pi$
$44$	2.69766	0.406688
$45$	1.21300	0.180823
$46$	3.50944	0.517438
$47$	−1.43035	−0.208637	−0.104319	−	0.994544i	$-0.533266\pi$
$47$	−1.43035	−0.208637	−0.104319	+	0.994544i	$0.533266\pi$
$48$	−0.221832	−0.0320186
$49$	1.00000	0.142857
$50$	4.83102	0.683209
$51$	−0.717070	−0.100410
$52$	1.03208	0.143123
$53$	8.04686	1.10532	0.552661	−	0.833406i	$-0.313613\pi$
$53$	8.04686	1.10532	0.552661	+	0.833406i	$0.313613\pi$
$54$	−1.32007	−0.179639
$55$	−1.10894	−0.149530
$56$	1.00000	0.133631
$57$	−1.07089	−0.141842
$58$	−6.47535	−0.850256
$59$	−4.90229	−0.638224	−0.319112	−	0.947717i	$-0.603385\pi$
$59$	−4.90229	−0.638224	−0.319112	+	0.947717i	$0.603385\pi$
$60$	0.0911894	0.0117725
$61$	−9.82773	−1.25831	−0.629156	−	0.777279i	$-0.716599\pi$
$61$	−9.82773	−1.25831	−0.629156	+	0.777279i	$0.716599\pi$
$62$	9.99931	1.26991
$63$	2.95079	0.371765
$64$	1.00000	0.125000
$65$	−0.424261	−0.0526231
$66$	0.598426	0.0736612
$67$	13.8647	1.69384	0.846919	−	0.531722i	$-0.178455\pi$
$67$	13.8647	1.69384	0.846919	+	0.531722i	$0.178455\pi$
$68$	3.23250	0.391998
$69$	0.778504	0.0937208
$70$	−0.411075	−0.0491328
$71$	−9.72897	−1.15462	−0.577308	−	0.816526i	$-0.695897\pi$
$71$	−9.72897	−1.15462	−0.577308	+	0.816526i	$0.695897\pi$
$72$	2.95079	0.347754
$73$	−3.14473	−0.368063	−0.184031	−	0.982920i	$-0.558915\pi$
$73$	−3.14473	−0.368063	−0.184031	+	0.982920i	$0.558915\pi$
$74$	11.7573	1.36676
$75$	1.07167	0.123746
$76$	4.82747	0.553749
$77$	−2.69766	−0.307427
$78$	0.228947	0.0259232
$79$	10.8134	1.21660	0.608302	−	0.793706i	$-0.291851\pi$
$79$	10.8134	1.21660	0.608302	+	0.793706i	$0.291851\pi$
$80$	−0.411075	−0.0459596
$81$	8.55954	0.951060
$82$	−5.63083	−0.621821
$83$	−4.93994	−0.542229	−0.271114	−	0.962547i	$-0.587392\pi$
$83$	−4.93994	−0.542229	−0.271114	+	0.962547i	$0.587392\pi$
$84$	0.221832	0.0242038
$85$	−1.32880	−0.144128
$86$	2.15686	0.232581
$87$	−1.43644	−0.154002
$88$	−2.69766	−0.287572
$89$	2.08906	0.221440	0.110720	−	0.993852i	$-0.464684\pi$
$89$	2.08906	0.221440	0.110720	+	0.993852i	$0.464684\pi$
$90$	−1.21300	−0.127861
$91$	−1.03208	−0.108191
$92$	−3.50944	−0.365884
$93$	2.21816	0.230013
$94$	1.43035	0.147529
$95$	−1.98445	−0.203601
$96$	0.221832	0.0226406
$97$	14.2370	1.44555	0.722775	−	0.691083i	$-0.242866\pi$
$97$	14.2370	1.44555	0.722775	+	0.691083i	$0.242866\pi$
$98$	−1.00000	−0.101015
$99$	−7.96023	−0.800033
$100$	−4.83102	−0.483102
$101$	9.55703	0.950960	0.475480	−	0.879727i	$-0.342274\pi$
$101$	9.55703	0.950960	0.475480	+	0.879727i	$0.342274\pi$
$102$	0.717070	0.0710005
$103$	12.1879	1.20091	0.600453	−	0.799660i	$-0.294987\pi$
$103$	12.1879	1.20091	0.600453	+	0.799660i	$0.294987\pi$
$104$	−1.03208	−0.101203
$105$	−0.0911894	−0.00889918
$106$	−8.04686	−0.781580
$107$	4.35682	0.421189	0.210595	−	0.977573i	$-0.432460\pi$
$107$	4.35682	0.421189	0.210595	+	0.977573i	$0.432460\pi$
$108$	1.32007	0.127024
$109$	−9.74842	−0.933729	−0.466864	−	0.884329i	$-0.654616\pi$
$109$	−9.74842	−0.933729	−0.466864	+	0.884329i	$0.654616\pi$
$110$	1.10894	0.105733
$111$	2.60814	0.247554
$112$	−1.00000	−0.0944911
$113$	12.6519	1.19019	0.595094	−	0.803656i	$-0.297115\pi$
$113$	12.6519	1.19019	0.595094	+	0.803656i	$0.297115\pi$
$114$	1.07089	0.100298
$115$	1.44264	0.134527
$116$	6.47535	0.601221
$117$	−3.04544	−0.281551
$118$	4.90229	0.451293
$119$	−3.23250	−0.296322
$120$	−0.0911894	−0.00832442
$121$	−3.72263	−0.338421
$122$	9.82773	0.889760
$123$	−1.24910	−0.112627
$124$	−9.99931	−0.897965
$125$	4.04128	0.361463
$126$	−2.95079	−0.262877
$127$	11.0452	0.980103	0.490051	−	0.871694i	$-0.336978\pi$
$127$	11.0452	0.980103	0.490051	+	0.871694i	$0.336978\pi$
$128$	−1.00000	−0.0883883
$129$	0.478460	0.0421261
$130$	0.424261	0.0372101
$131$	−0.360289	−0.0314786	−0.0157393	−	0.999876i	$-0.505010\pi$
$131$	−0.360289	−0.0314786	−0.0157393	+	0.999876i	$0.505010\pi$
$132$	−0.598426	−0.0520863
$133$	−4.82747	−0.418595
$134$	−13.8647	−1.19772
$135$	−0.542649	−0.0467038
$136$	−3.23250	−0.277184
$137$	−18.8902	−1.61390	−0.806948	−	0.590622i	$-0.798882\pi$
$137$	−18.8902	−1.61390	−0.806948	+	0.590622i	$0.798882\pi$
$138$	−0.778504	−0.0662706
$139$	−1.00418	−0.0851734	−0.0425867	−	0.999093i	$-0.513560\pi$
$139$	−1.00418	−0.0851734	−0.0425867	+	0.999093i	$0.513560\pi$
$140$	0.411075	0.0347422
$141$	0.317296	0.0267212
$142$	9.72897	0.816437
$143$	2.78419	0.232826
$144$	−2.95079	−0.245899
$145$	−2.66186	−0.221055
$146$	3.14473	0.260260
$147$	−0.221832	−0.0182964
$148$	−11.7573	−0.966445
$149$	−23.4796	−1.92353	−0.961764	−	0.273881i	$-0.911692\pi$
$149$	−23.4796	−1.92353	−0.961764	+	0.273881i	$0.911692\pi$
$150$	−1.07167	−0.0875017
$151$	−13.8676	−1.12853	−0.564263	−	0.825595i	$-0.690840\pi$
$151$	−13.8676	−1.12853	−0.564263	+	0.825595i	$0.690840\pi$
$152$	−4.82747	−0.391560
$153$	−9.53842	−0.771136
$154$	2.69766	0.217384
$155$	4.11047	0.330161
$156$	−0.228947	−0.0183304
$157$	15.1034	1.20538	0.602691	−	0.797975i	$-0.294095\pi$
$157$	15.1034	1.20538	0.602691	+	0.797975i	$0.294095\pi$
$158$	−10.8134	−0.860269
$159$	−1.78505	−0.141564
$160$	0.411075	0.0324983
$161$	3.50944	0.276582
$162$	−8.55954	−0.672501
$163$	−3.74783	−0.293553	−0.146776	−	0.989170i	$-0.546890\pi$
$163$	−3.74783	−0.293553	−0.146776	+	0.989170i	$0.546890\pi$
$164$	5.63083	0.439694
$165$	0.245998	0.0191509
$166$	4.93994	0.383414
$167$	−4.82949	−0.373717	−0.186858	−	0.982387i	$-0.559831\pi$
$167$	−4.82949	−0.373717	−0.186858	+	0.982387i	$0.559831\pi$
$168$	−0.221832	−0.0171147
$169$	−11.9348	−0.918063
$170$	1.32880	0.101914
$171$	−14.2449	−1.08933
$172$	−2.15686	−0.164459
$173$	−16.0147	−1.21757	−0.608787	−	0.793334i	$-0.708343\pi$
$173$	−16.0147	−1.21757	−0.608787	+	0.793334i	$0.708343\pi$
$174$	1.43644	0.108896
$175$	4.83102	0.365191
$176$	2.69766	0.203344
$177$	1.08748	0.0817402
$178$	−2.08906	−0.156582
$179$	−11.5159	−0.860741	−0.430370	−	0.902652i	$-0.641617\pi$
$179$	−11.5159	−0.860741	−0.430370	+	0.902652i	$0.641617\pi$
$180$	1.21300	0.0904114
$181$	6.66991	0.495771	0.247885	−	0.968789i	$-0.420264\pi$
$181$	6.66991	0.495771	0.247885	+	0.968789i	$0.420264\pi$
$182$	1.03208	0.0765026
$183$	2.18010	0.161158
$184$	3.50944	0.258719
$185$	4.83314	0.355339
$186$	−2.21816	−0.162644
$187$	8.72018	0.637683
$188$	−1.43035	−0.104319
$189$	−1.32007	−0.0960212
$190$	1.98445	0.143967
$191$	−16.5428	−1.19700	−0.598499	−	0.801124i	$-0.704236\pi$
$191$	−16.5428	−1.19700	−0.598499	+	0.801124i	$0.704236\pi$
$192$	−0.221832	−0.0160093
$193$	−8.71648	−0.627426	−0.313713	−	0.949518i	$-0.601573\pi$
$193$	−8.71648	−0.627426	−0.313713	+	0.949518i	$0.601573\pi$
$194$	−14.2370	−1.02216
$195$	0.0941145	0.00673968
$196$	1.00000	0.0714286
$197$	−26.5211	−1.88955	−0.944774	−	0.327723i	$-0.893719\pi$
$197$	−26.5211	−1.88955	−0.944774	+	0.327723i	$0.893719\pi$
$198$	7.96023	0.565709
$199$	−17.2484	−1.22271	−0.611355	−	0.791356i	$-0.709375\pi$
$199$	−17.2484	−1.22271	−0.611355	+	0.791356i	$0.709375\pi$
$200$	4.83102	0.341605
$201$	−3.07562	−0.216938
$202$	−9.55703	−0.672430
$203$	−6.47535	−0.454481
$204$	−0.717070	−0.0502049
$205$	−2.31469	−0.161665
$206$	−12.1879	−0.849169
$207$	10.3556	0.719765
$208$	1.03208	0.0715616
$209$	13.0229	0.900812
$210$	0.0911894	0.00629267
$211$	23.3007	1.60409	0.802044	−	0.597264i	$-0.203746\pi$
$211$	23.3007	1.60409	0.802044	+	0.597264i	$0.203746\pi$
$212$	8.04686	0.552661
$213$	2.15819	0.147877
$214$	−4.35682	−0.297826
$215$	0.886632	0.0604678
$216$	−1.32007	−0.0898196
$217$	9.99931	0.678797
$218$	9.74842	0.660246
$219$	0.697601	0.0471395
$220$	−1.10894	−0.0747648
$221$	3.33618	0.224416
$222$	−2.60814	−0.175047
$223$	8.38051	0.561201	0.280600	−	0.959825i	$-0.409466\pi$
$223$	8.38051	0.561201	0.280600	+	0.959825i	$0.409466\pi$
$224$	1.00000	0.0668153
$225$	14.2553	0.950355
$226$	−12.6519	−0.841590
$227$	−24.6646	−1.63705	−0.818525	−	0.574471i	$-0.805208\pi$
$227$	−24.6646	−1.63705	−0.818525	+	0.574471i	$0.805208\pi$
$228$	−1.07089	−0.0709212
$229$	−18.2297	−1.20465	−0.602326	−	0.798250i	$-0.705759\pi$
$229$	−18.2297	−1.20465	−0.602326	+	0.798250i	$0.705759\pi$
$230$	−1.44264	−0.0951249
$231$	0.598426	0.0393736
$232$	−6.47535	−0.425128
$233$	−14.3165	−0.937907	−0.468953	−	0.883223i	$-0.655369\pi$
$233$	−14.3165	−0.937907	−0.468953	+	0.883223i	$0.655369\pi$
$234$	3.04544	0.199087
$235$	0.587980	0.0383556
$236$	−4.90229	−0.319112
$237$	−2.39876	−0.155816
$238$	3.23250	0.209532
$239$	−5.50573	−0.356136	−0.178068	−	0.984018i	$-0.556985\pi$
$239$	−5.50573	−0.356136	−0.178068	+	0.984018i	$0.556985\pi$
$240$	0.0911894	0.00588625
$241$	5.36991	0.345906	0.172953	−	0.984930i	$-0.444669\pi$
$241$	5.36991	0.345906	0.172953	+	0.984930i	$0.444669\pi$
$242$	3.72263	0.239300
$243$	−5.85900	−0.375855
$244$	−9.82773	−0.629156
$245$	−0.411075	−0.0262626
$246$	1.24910	0.0796394
$247$	4.98232	0.317018
$248$	9.99931	0.634957
$249$	1.09583	0.0694457
$250$	−4.04128	−0.255593
$251$	1.40512	0.0886906	0.0443453	−	0.999016i	$-0.485880\pi$
$251$	1.40512	0.0886906	0.0443453	+	0.999016i	$0.485880\pi$
$252$	2.95079	0.185882
$253$	−9.46727	−0.595202
$254$	−11.0452	−0.693037
$255$	0.294769	0.0184592
$256$	1.00000	0.0625000
$257$	28.6316	1.78599	0.892996	−	0.450064i	$-0.148599\pi$
$257$	28.6316	1.78599	0.892996	+	0.450064i	$0.148599\pi$
$258$	−0.478460	−0.0297876
$259$	11.7573	0.730564
$260$	−0.424261	−0.0263115
$261$	−19.1074	−1.18272
$262$	0.360289	0.0222588
$263$	−10.9653	−0.676152	−0.338076	−	0.941119i	$-0.609776\pi$
$263$	−10.9653	−0.676152	−0.338076	+	0.941119i	$0.609776\pi$
$264$	0.598426	0.0368306
$265$	−3.30786	−0.203200
$266$	4.82747	0.295991
$267$	−0.463420	−0.0283608
$268$	13.8647	0.846919
$269$	−14.9861	−0.913717	−0.456858	−	0.889539i	$-0.651025\pi$
$269$	−14.9861	−0.913717	−0.456858	+	0.889539i	$0.651025\pi$
$270$	0.542649	0.0330246
$271$	10.5686	0.641996	0.320998	−	0.947080i	$-0.395982\pi$
$271$	10.5686	0.641996	0.320998	+	0.947080i	$0.395982\pi$
$272$	3.23250	0.195999
$273$	0.228947	0.0138565
$274$	18.8902	1.14120
$275$	−13.0324	−0.785886
$276$	0.778504	0.0468604
$277$	7.97481	0.479160	0.239580	−	0.970877i	$-0.422990\pi$
$277$	7.97481	0.479160	0.239580	+	0.970877i	$0.422990\pi$
$278$	1.00418	0.0602267
$279$	29.5059	1.76647
$280$	−0.411075	−0.0245664
$281$	0.922625	0.0550392	0.0275196	−	0.999621i	$-0.491239\pi$
$281$	0.922625	0.0550392	0.0275196	+	0.999621i	$0.491239\pi$
$282$	−0.317296	−0.0188947
$283$	−24.7672	−1.47226	−0.736129	−	0.676842i	$-0.763348\pi$
$283$	−24.7672	−1.47226	−0.736129	+	0.676842i	$0.763348\pi$
$284$	−9.72897	−0.577308
$285$	0.440214	0.0260761
$286$	−2.78419	−0.164633
$287$	−5.63083	−0.332377
$288$	2.95079	0.173877
$289$	−6.55097	−0.385351
$290$	2.66186	0.156310
$291$	−3.15822	−0.185138
$292$	−3.14473	−0.184031
$293$	−13.4217	−0.784103	−0.392052	−	0.919943i	$-0.628235\pi$
$293$	−13.4217	−0.784103	−0.392052	+	0.919943i	$0.628235\pi$
$294$	0.221832	0.0129375
$295$	2.01521	0.117330
$296$	11.7573	0.683380
$297$	3.56111	0.206637
$298$	23.4796	1.36014
$299$	−3.62201	−0.209466
$300$	1.07167	0.0618730
$301$	2.15686	0.124320
$302$	13.8676	0.797988
$303$	−2.12005	−0.121794
$304$	4.82747	0.276875
$305$	4.03993	0.231326
$306$	9.53842	0.545275
$307$	26.0466	1.48656	0.743279	−	0.668982i	$-0.233270\pi$
$307$	26.0466	1.48656	0.743279	+	0.668982i	$0.233270\pi$
$308$	−2.69766	−0.153713
$309$	−2.70365	−0.153806
$310$	−4.11047	−0.233459
$311$	−10.6422	−0.603463	−0.301731	−	0.953393i	$-0.597565\pi$
$311$	−10.6422	−0.603463	−0.301731	+	0.953393i	$0.597565\pi$
$312$	0.228947	0.0129616
$313$	−6.72883	−0.380336	−0.190168	−	0.981752i	$-0.560903\pi$
$313$	−6.72883	−0.380336	−0.190168	+	0.981752i	$0.560903\pi$
$314$	−15.1034	−0.852333
$315$	−1.21300	−0.0683446
$316$	10.8134	0.608302
$317$	3.89756	0.218909	0.109454	−	0.993992i	$-0.465090\pi$
$317$	3.89756	0.218909	0.109454	+	0.993992i	$0.465090\pi$
$318$	1.78505	0.100101
$319$	17.4683	0.978037
$320$	−0.411075	−0.0229798
$321$	−0.966479	−0.0539436
$322$	−3.50944	−0.195573
$323$	15.6048	0.868274
$324$	8.55954	0.475530
$325$	−4.98598	−0.276572
$326$	3.74783	0.207573
$327$	2.16251	0.119587
$328$	−5.63083	−0.310911
$329$	1.43035	0.0788576
$330$	−0.245998	−0.0135417
$331$	−11.9906	−0.659062	−0.329531	−	0.944145i	$-0.606891\pi$
$331$	−11.9906	−0.659062	−0.329531	+	0.944145i	$0.606891\pi$
$332$	−4.93994	−0.271114
$333$	34.6934	1.90119
$334$	4.82949	0.264258
$335$	−5.69941	−0.311392
$336$	0.221832	0.0121019
$337$	18.0796	0.984857	0.492428	−	0.870353i	$-0.336109\pi$
$337$	18.0796	0.984857	0.492428	+	0.870353i	$0.336109\pi$
$338$	11.9348	0.649169
$339$	−2.80659	−0.152433
$340$	−1.32880	−0.0720642
$341$	−26.9747	−1.46076
$342$	14.2449	0.770274
$343$	−1.00000	−0.0539949
$344$	2.15686	0.116290
$345$	−0.320023	−0.0172295
$346$	16.0147	0.860954
$347$	−2.39193	−0.128405	−0.0642026	−	0.997937i	$-0.520450\pi$
$347$	−2.39193	−0.128405	−0.0642026	+	0.997937i	$0.520450\pi$
$348$	−1.43644	−0.0770012
$349$	−22.7148	−1.21590	−0.607948	−	0.793977i	$-0.708007\pi$
$349$	−22.7148	−1.21590	−0.607948	+	0.793977i	$0.708007\pi$
$350$	−4.83102	−0.258229
$351$	1.36242	0.0727204
$352$	−2.69766	−0.143786
$353$	8.04665	0.428280	0.214140	−	0.976803i	$-0.431305\pi$
$353$	8.04665	0.428280	0.214140	+	0.976803i	$0.431305\pi$
$354$	−1.08748	−0.0577991
$355$	3.99934	0.212263
$356$	2.08906	0.110720
$357$	0.717070	0.0379514
$358$	11.5159	0.608636
$359$	−29.5548	−1.55984	−0.779920	−	0.625879i	$-0.784740\pi$
$359$	−29.5548	−1.55984	−0.779920	+	0.625879i	$0.784740\pi$
$360$	−1.21300	−0.0639305
$361$	4.30450	0.226553
$362$	−6.66991	−0.350563
$363$	0.825796	0.0433431
$364$	−1.03208	−0.0540955
$365$	1.29272	0.0676641
$366$	−2.18010	−0.113956
$367$	−28.0323	−1.46328	−0.731638	−	0.681694i	$-0.761244\pi$
$367$	−28.0323	−1.46328	−0.731638	+	0.681694i	$0.761244\pi$
$368$	−3.50944	−0.182942
$369$	−16.6154	−0.864963
$370$	−4.83314	−0.251263
$371$	−8.04686	−0.417772
$372$	2.21816	0.115006
$373$	−9.34169	−0.483694	−0.241847	−	0.970314i	$-0.577753\pi$
$373$	−9.34169	−0.483694	−0.241847	+	0.970314i	$0.577753\pi$
$374$	−8.72018	−0.450910
$375$	−0.896485	−0.0462943
$376$	1.43035	0.0737645
$377$	6.68306	0.344195
$378$	1.32007	0.0678973
$379$	5.84057	0.300010	0.150005	−	0.988685i	$-0.452071\pi$
$379$	5.84057	0.300010	0.150005	+	0.988685i	$0.452071\pi$
$380$	−1.98445	−0.101800
$381$	−2.45017	−0.125526
$382$	16.5428	0.846405
$383$	−17.8660	−0.912910	−0.456455	−	0.889746i	$-0.650881\pi$
$383$	−17.8660	−0.912910	−0.456455	+	0.889746i	$0.650881\pi$
$384$	0.221832	0.0113203
$385$	1.10894	0.0565168
$386$	8.71648	0.443657
$387$	6.36445	0.323523
$388$	14.2370	0.722775
$389$	12.8723	0.652650	0.326325	−	0.945258i	$-0.394190\pi$
$389$	12.8723	0.652650	0.326325	+	0.945258i	$0.394190\pi$
$390$	−0.0941145	−0.00476567
$391$	−11.3442	−0.573703
$392$	−1.00000	−0.0505076
$393$	0.0799236	0.00403161
$394$	26.5211	1.33611
$395$	−4.44512	−0.223658
$396$	−7.96023	−0.400017
$397$	−17.4765	−0.877119	−0.438560	−	0.898702i	$-0.644511\pi$
$397$	−17.4765	−0.877119	−0.438560	+	0.898702i	$0.644511\pi$
$398$	17.2484	0.864586
$399$	1.07089	0.0536114
$400$	−4.83102	−0.241551
$401$	−29.0219	−1.44928	−0.724641	−	0.689126i	$-0.757995\pi$
$401$	−29.0219	−1.44928	−0.724641	+	0.689126i	$0.757995\pi$
$402$	3.07562	0.153398
$403$	−10.3201	−0.514079
$404$	9.55703	0.475480
$405$	−3.51861	−0.174841
$406$	6.47535	0.321366
$407$	−31.7172	−1.57217
$408$	0.717070	0.0355002
$409$	3.52099	0.174102	0.0870508	−	0.996204i	$-0.472256\pi$
$409$	3.52099	0.174102	0.0870508	+	0.996204i	$0.472256\pi$
$410$	2.31469	0.114315
$411$	4.19044	0.206699
$412$	12.1879	0.600453
$413$	4.90229	0.241226
$414$	−10.3556	−0.508950
$415$	2.03068	0.0996824
$416$	−1.03208	−0.0506017
$417$	0.222759	0.0109085
$418$	−13.0229	−0.636970
$419$	−21.0423	−1.02798	−0.513991	−	0.857795i	$-0.671834\pi$
$419$	−21.0423	−1.02798	−0.513991	+	0.857795i	$0.671834\pi$
$420$	−0.0911894	−0.00444959
$421$	−19.3095	−0.941086	−0.470543	−	0.882377i	$-0.655942\pi$
$421$	−19.3095	−0.941086	−0.470543	+	0.882377i	$0.655942\pi$
$422$	−23.3007	−1.13426
$423$	4.22065	0.205215
$424$	−8.04686	−0.390790
$425$	−15.6162	−0.757499
$426$	−2.15819	−0.104565
$427$	9.82773	0.475597
$428$	4.35682	0.210595
$429$	−0.617622	−0.0298191
$430$	−0.886632	−0.0427572
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.32007	0.0635121
$433$	40.7932	1.96040	0.980199	−	0.198016i	$-0.0634497\pi$
$433$	40.7932	1.96040	0.980199	+	0.198016i	$0.0634497\pi$
$434$	−9.99931	−0.479982
$435$	0.590484	0.0283115
$436$	−9.74842	−0.466864
$437$	−16.9417	−0.810432
$438$	−0.697601	−0.0333327
$439$	19.3451	0.923293	0.461647	−	0.887064i	$-0.347259\pi$
$439$	19.3451	0.923293	0.461647	+	0.887064i	$0.347259\pi$
$440$	1.10894	0.0528667
$441$	−2.95079	−0.140514
$442$	−3.33618	−0.158686
$443$	38.2976	1.81958	0.909788	−	0.415074i	$-0.136244\pi$
$443$	38.2976	1.81958	0.909788	+	0.415074i	$0.136244\pi$
$444$	2.60814	0.123777
$445$	−0.858760	−0.0407091
$446$	−8.38051	−0.396829
$447$	5.20853	0.246355
$448$	−1.00000	−0.0472456
$449$	4.79531	0.226305	0.113152	−	0.993578i	$-0.463905\pi$
$449$	4.79531	0.226305	0.113152	+	0.993578i	$0.463905\pi$
$450$	−14.2553	−0.672002
$451$	15.1901	0.715272
$452$	12.6519	0.595094
$453$	3.07626	0.144535
$454$	24.6646	1.15757
$455$	0.424261	0.0198897
$456$	1.07089	0.0501488
$457$	15.9209	0.744746	0.372373	−	0.928083i	$-0.378544\pi$
$457$	15.9209	0.744746	0.372373	+	0.928083i	$0.378544\pi$
$458$	18.2297	0.851818
$459$	4.26713	0.199173
$460$	1.44264	0.0672635
$461$	−8.44686	−0.393410	−0.196705	−	0.980463i	$-0.563024\pi$
$461$	−8.44686	−0.393410	−0.196705	+	0.980463i	$0.563024\pi$
$462$	−0.598426	−0.0278413
$463$	19.4628	0.904515	0.452257	−	0.891888i	$-0.350619\pi$
$463$	19.4628	0.904515	0.452257	+	0.891888i	$0.350619\pi$
$464$	6.47535	0.300611
$465$	−0.911831	−0.0422852
$466$	14.3165	0.663200
$467$	−13.0097	−0.602018	−0.301009	−	0.953621i	$-0.597323\pi$
$467$	−13.0097	−0.602018	−0.301009	+	0.953621i	$0.597323\pi$
$468$	−3.04544	−0.140776
$469$	−13.8647	−0.640211
$470$	−0.587980	−0.0271215
$471$	−3.35041	−0.154379
$472$	4.90229	0.225646
$473$	−5.81849	−0.267534
$474$	2.39876	0.110179
$475$	−23.3216	−1.07007
$476$	−3.23250	−0.148161
$477$	−23.7446	−1.08719
$478$	5.50573	0.251826
$479$	26.3565	1.20426	0.602130	−	0.798398i	$-0.294319\pi$
$479$	26.3565	1.20426	0.602130	+	0.798398i	$0.294319\pi$
$480$	−0.0911894	−0.00416221
$481$	−12.1345	−0.553283
$482$	−5.36991	−0.244593
$483$	−0.778504	−0.0354231
$484$	−3.72263	−0.169210
$485$	−5.85248	−0.265748
$486$	5.85900	0.265769
$487$	20.2132	0.915948	0.457974	−	0.888966i	$-0.348575\pi$
$487$	20.2132	0.915948	0.457974	+	0.888966i	$0.348575\pi$
$488$	9.82773	0.444880
$489$	0.831388	0.0375967
$490$	0.411075	0.0185705
$491$	−38.2693	−1.72707	−0.863535	−	0.504289i	$-0.831755\pi$
$491$	−38.2693	−1.72707	−0.863535	+	0.504289i	$0.831755\pi$
$492$	−1.24910	−0.0563136
$493$	20.9316	0.942710
$494$	−4.98232	−0.224165
$495$	3.27225	0.147077
$496$	−9.99931	−0.448982
$497$	9.72897	0.436404
$498$	−1.09583	−0.0491055
$499$	−16.0592	−0.718911	−0.359455	−	0.933162i	$-0.617037\pi$
$499$	−16.0592	−0.718911	−0.359455	+	0.933162i	$0.617037\pi$
$500$	4.04128	0.180732
$501$	1.07133	0.0478636
$502$	−1.40512	−0.0627137
$503$	−17.4700	−0.778949	−0.389474	−	0.921037i	$-0.627343\pi$
$503$	−17.4700	−0.778949	−0.389474	+	0.921037i	$0.627343\pi$
$504$	−2.95079	−0.131439
$505$	−3.92866	−0.174823
$506$	9.46727	0.420871
$507$	2.64752	0.117580
$508$	11.0452	0.490051
$509$	−22.2212	−0.984936	−0.492468	−	0.870331i	$-0.663905\pi$
$509$	−22.2212	−0.984936	−0.492468	+	0.870331i	$0.663905\pi$
$510$	−0.294769	−0.0130526
$511$	3.14473	0.139115
$512$	−1.00000	−0.0441942
$513$	6.37262	0.281358
$514$	−28.6316	−1.26289
$515$	−5.01013	−0.220773
$516$	0.478460	0.0210630
$517$	−3.85859	−0.169701
$518$	−11.7573	−0.516587
$519$	3.55256	0.155940
$520$	0.424261	0.0186051
$521$	28.2887	1.23935	0.619676	−	0.784858i	$-0.287264\pi$
$521$	28.2887	1.23935	0.619676	+	0.784858i	$0.287264\pi$
$522$	19.1074	0.836309
$523$	−31.4607	−1.37568	−0.687840	−	0.725862i	$-0.741441\pi$
$523$	−31.4607	−1.37568	−0.687840	+	0.725862i	$0.741441\pi$
$524$	−0.360289	−0.0157393
$525$	−1.07167	−0.0467716
$526$	10.9653	0.478111
$527$	−32.3227	−1.40800
$528$	−0.598426	−0.0260432
$529$	−10.6839	−0.464516
$530$	3.30786	0.143684
$531$	14.4656	0.627755
$532$	−4.82747	−0.209298
$533$	5.81145	0.251722
$534$	0.463420	0.0200541
$535$	−1.79098	−0.0774307
$536$	−13.8647	−0.598862
$537$	2.55460	0.110239
$538$	14.9861	0.646095
$539$	2.69766	0.116196
$540$	−0.542649	−0.0233519
$541$	20.6081	0.886011	0.443005	−	0.896519i	$-0.353912\pi$
$541$	20.6081	0.886011	0.443005	+	0.896519i	$0.353912\pi$
$542$	−10.5686	−0.453960
$543$	−1.47960	−0.0634956
$544$	−3.23250	−0.138592
$545$	4.00733	0.171655
$546$	−0.228947	−0.00979804
$547$	−16.6055	−0.710001	−0.355001	−	0.934866i	$-0.615519\pi$
$547$	−16.6055	−0.710001	−0.355001	+	0.934866i	$0.615519\pi$
$548$	−18.8902	−0.806948
$549$	28.9996	1.23767
$550$	13.0324	0.555705
$551$	31.2596	1.33170
$552$	−0.778504	−0.0331353
$553$	−10.8134	−0.459833
$554$	−7.97481	−0.338817
$555$	−1.07214	−0.0455099
$556$	−1.00418	−0.0425867
$557$	23.7054	1.00443	0.502216	−	0.864742i	$-0.332518\pi$
$557$	23.7054	1.00443	0.502216	+	0.864742i	$0.332518\pi$
$558$	−29.5059	−1.24908
$559$	−2.22605	−0.0941518
$560$	0.411075	0.0173711
$561$	−1.93441	−0.0816709
$562$	−0.922625	−0.0389186
$563$	−22.9763	−0.968338	−0.484169	−	0.874975i	$-0.660878\pi$
$563$	−22.9763	−0.968338	−0.484169	+	0.874975i	$0.660878\pi$
$564$	0.317296	0.0133606
$565$	−5.20087	−0.218802
$566$	24.7672	1.04104
$567$	−8.55954	−0.359467
$568$	9.72897	0.408219
$569$	2.82039	0.118237	0.0591185	−	0.998251i	$-0.481171\pi$
$569$	2.82039	0.118237	0.0591185	+	0.998251i	$0.481171\pi$
$570$	−0.440214	−0.0184386
$571$	19.3631	0.810319	0.405159	−	0.914246i	$-0.367216\pi$
$571$	19.3631	0.810319	0.405159	+	0.914246i	$0.367216\pi$
$572$	2.78419	0.116413
$573$	3.66972	0.153305
$574$	5.63083	0.235026
$575$	16.9541	0.707037
$576$	−2.95079	−0.122950
$577$	−34.2113	−1.42424	−0.712118	−	0.702060i	$-0.752264\pi$
$577$	−34.2113	−1.42424	−0.712118	+	0.702060i	$0.752264\pi$
$578$	6.55097	0.272484
$579$	1.93359	0.0803573
$580$	−2.66186	−0.110528
$581$	4.93994	0.204943
$582$	3.15822	0.130912
$583$	21.7077	0.899041
$584$	3.14473	0.130130
$585$	1.25190	0.0517599
$586$	13.4217	0.554445
$587$	−43.9822	−1.81534	−0.907669	−	0.419687i	$-0.862140\pi$
$587$	−43.9822	−1.81534	−0.907669	+	0.419687i	$0.862140\pi$
$588$	−0.221832	−0.00914818
$589$	−48.2714	−1.98899
$590$	−2.01521	−0.0829648
$591$	5.88321	0.242003
$592$	−11.7573	−0.483223
$593$	−41.3498	−1.69803	−0.849017	−	0.528366i	$-0.822805\pi$
$593$	−41.3498	−1.69803	−0.849017	+	0.528366i	$0.822805\pi$
$594$	−3.56111	−0.146114
$595$	1.32880	0.0544754
$596$	−23.4796	−0.961764
$597$	3.82625	0.156598
$598$	3.62201	0.148115
$599$	21.2651	0.868870	0.434435	−	0.900703i	$-0.356948\pi$
$599$	21.2651	0.868870	0.434435	+	0.900703i	$0.356948\pi$
$600$	−1.07167	−0.0437508
$601$	−28.0849	−1.14561	−0.572804	−	0.819692i	$-0.694145\pi$
$601$	−28.0849	−1.14561	−0.572804	+	0.819692i	$0.694145\pi$
$602$	−2.15686	−0.0879072
$603$	−40.9117	−1.66605
$604$	−13.8676	−0.564263
$605$	1.53028	0.0622147
$606$	2.12005	0.0861212
$607$	−42.7629	−1.73569	−0.867846	−	0.496834i	$-0.834496\pi$
$607$	−42.7629	−1.73569	−0.867846	+	0.496834i	$0.834496\pi$
$608$	−4.82747	−0.195780
$609$	1.43644	0.0582074
$610$	−4.03993	−0.163572
$611$	−1.47623	−0.0597218
$612$	−9.53842	−0.385568
$613$	−31.9115	−1.28889	−0.644447	−	0.764649i	$-0.722912\pi$
$613$	−31.9115	−1.28889	−0.644447	+	0.764649i	$0.722912\pi$
$614$	−26.0466	−1.05115
$615$	0.513472	0.0207052
$616$	2.69766	0.108692
$617$	−4.13680	−0.166541	−0.0832706	−	0.996527i	$-0.526537\pi$
$617$	−4.13680	−0.166541	−0.0832706	+	0.996527i	$0.526537\pi$
$618$	2.70365	0.108757
$619$	42.6718	1.71513	0.857563	−	0.514379i	$-0.171978\pi$
$619$	42.6718	1.71513	0.857563	+	0.514379i	$0.171978\pi$
$620$	4.11047	0.165080
$621$	−4.63271	−0.185904
$622$	10.6422	0.426713
$623$	−2.08906	−0.0836964
$624$	−0.228947	−0.00916522
$625$	22.4938	0.899753
$626$	6.72883	0.268938
$627$	−2.88889	−0.115371
$628$	15.1034	0.602691
$629$	−38.0055	−1.51538
$630$	1.21300	0.0483269
$631$	−22.2863	−0.887202	−0.443601	−	0.896224i	$-0.646299\pi$
$631$	−22.2863	−0.887202	−0.443601	+	0.896224i	$0.646299\pi$
$632$	−10.8134	−0.430135
$633$	−5.16884	−0.205443
$634$	−3.89756	−0.154792
$635$	−4.54040	−0.180180
$636$	−1.78505	−0.0707818
$637$	1.03208	0.0408924
$638$	−17.4683	−0.691577
$639$	28.7082	1.13568
$640$	0.411075	0.0162492
$641$	12.3625	0.488290	0.244145	−	0.969739i	$-0.421493\pi$
$641$	12.3625	0.488290	0.244145	+	0.969739i	$0.421493\pi$
$642$	0.966479	0.0381439
$643$	−19.4852	−0.768422	−0.384211	−	0.923245i	$-0.625526\pi$
$643$	−19.4852	−0.768422	−0.384211	+	0.923245i	$0.625526\pi$
$644$	3.50944	0.138291
$645$	−0.196683	−0.00774439
$646$	−15.6048	−0.613962
$647$	−40.4253	−1.58928	−0.794642	−	0.607078i	$-0.792341\pi$
$647$	−40.4253	−1.58928	−0.794642	+	0.607078i	$0.792341\pi$
$648$	−8.55954	−0.336250
$649$	−13.2247	−0.519116
$650$	4.98598	0.195566
$651$	−2.21816	−0.0869367
$652$	−3.74783	−0.146776
$653$	34.0850	1.33385	0.666925	−	0.745125i	$-0.267610\pi$
$653$	34.0850	1.33385	0.666925	+	0.745125i	$0.267610\pi$
$654$	−2.16251	−0.0845607
$655$	0.148106	0.00578698
$656$	5.63083	0.219847
$657$	9.27944	0.362026
$658$	−1.43035	−0.0557607
$659$	−10.5283	−0.410125	−0.205063	−	0.978749i	$-0.565740\pi$
$659$	−10.5283	−0.410125	−0.205063	+	0.978749i	$0.565740\pi$
$660$	0.245998	0.00957546
$661$	−9.06445	−0.352566	−0.176283	−	0.984339i	$-0.556407\pi$
$661$	−9.06445	−0.352566	−0.176283	+	0.984339i	$0.556407\pi$
$662$	11.9906	0.466027
$663$	−0.740071	−0.0287420
$664$	4.93994	0.191707
$665$	1.98445	0.0769538
$666$	−34.6934	−1.34434
$667$	−22.7248	−0.879909
$668$	−4.82949	−0.186858
$669$	−1.85906	−0.0718755
$670$	5.69941	0.220188
$671$	−26.5119	−1.02348
$672$	−0.221832	−0.00855734
$673$	47.8457	1.84431	0.922157	−	0.386815i	$-0.126425\pi$
$673$	47.8457	1.84431	0.922157	+	0.386815i	$0.126425\pi$
$674$	−18.0796	−0.696399
$675$	−6.37730	−0.245462
$676$	−11.9348	−0.459031
$677$	26.8123	1.03048	0.515240	−	0.857046i	$-0.327703\pi$
$677$	26.8123	1.03048	0.515240	+	0.857046i	$0.327703\pi$
$678$	2.80659	0.107786
$679$	−14.2370	−0.546367
$680$	1.32880	0.0509571
$681$	5.47140	0.209664
$682$	26.9747	1.03292
$683$	30.9076	1.18265	0.591324	−	0.806434i	$-0.298606\pi$
$683$	30.9076	1.18265	0.591324	+	0.806434i	$0.298606\pi$
$684$	−14.2449	−0.544666
$685$	7.76528	0.296696
$686$	1.00000	0.0381802
$687$	4.04392	0.154285
$688$	−2.15686	−0.0822296
$689$	8.30498	0.316394
$690$	0.320023	0.0121831
$691$	−32.3054	−1.22895	−0.614477	−	0.788935i	$-0.710633\pi$
$691$	−32.3054	−1.22895	−0.614477	+	0.788935i	$0.710633\pi$
$692$	−16.0147	−0.608787
$693$	7.96023	0.302384
$694$	2.39193	0.0907963
$695$	0.412793	0.0156581
$696$	1.43644	0.0544480
$697$	18.2016	0.689436
$698$	22.7148	0.859768
$699$	3.17586	0.120122
$700$	4.83102	0.182595
$701$	37.0343	1.39876	0.699382	−	0.714748i	$-0.253458\pi$
$701$	37.0343	1.39876	0.699382	+	0.714748i	$0.253458\pi$
$702$	−1.36242	−0.0514211
$703$	−56.7581	−2.14067
$704$	2.69766	0.101672
$705$	−0.130432	−0.00491237
$706$	−8.04665	−0.302840
$707$	−9.55703	−0.359429
$708$	1.08748	0.0408701
$709$	40.2325	1.51096	0.755482	−	0.655170i	$-0.227403\pi$
$709$	40.2325	1.51096	0.755482	+	0.655170i	$0.227403\pi$
$710$	−3.99934	−0.150092
$711$	−31.9081	−1.19665
$712$	−2.08906	−0.0782908
$713$	35.0919	1.31420
$714$	−0.717070	−0.0268357
$715$	−1.14451	−0.0428023
$716$	−11.5159	−0.430370
$717$	1.22134	0.0456119
$718$	29.5548	1.10297
$719$	27.6523	1.03126	0.515628	−	0.856813i	$-0.327559\pi$
$719$	27.6523	1.03126	0.515628	+	0.856813i	$0.327559\pi$
$720$	1.21300	0.0452057
$721$	−12.1879	−0.453900
$722$	−4.30450	−0.160197
$723$	−1.19122	−0.0443018
$724$	6.66991	0.247885
$725$	−31.2825	−1.16180
$726$	−0.825796	−0.0306482
$727$	−44.3167	−1.64362	−0.821808	−	0.569765i	$-0.807034\pi$
$727$	−44.3167	−1.64362	−0.821808	+	0.569765i	$0.807034\pi$
$728$	1.03208	0.0382513
$729$	−24.3789	−0.902922
$730$	−1.29272	−0.0478457
$731$	−6.97205	−0.257871
$732$	2.18010	0.0805788
$733$	9.31173	0.343937	0.171968	−	0.985102i	$-0.444987\pi$
$733$	9.31173	0.343937	0.171968	+	0.985102i	$0.444987\pi$
$734$	28.0323	1.03469
$735$	0.0911894	0.00336357
$736$	3.50944	0.129359
$737$	37.4021	1.37773
$738$	16.6154	0.611621
$739$	−24.7344	−0.909870	−0.454935	−	0.890525i	$-0.650337\pi$
$739$	−24.7344	−0.909870	−0.454935	+	0.890525i	$0.650337\pi$
$740$	4.83314	0.177670
$741$	−1.10524	−0.0406019
$742$	8.04686	0.295410
$743$	−3.03246	−0.111250	−0.0556251	−	0.998452i	$-0.517715\pi$
$743$	−3.03246	−0.111250	−0.0556251	+	0.998452i	$0.517715\pi$
$744$	−2.21816	−0.0813218
$745$	9.65189	0.353618
$746$	9.34169	0.342023
$747$	14.5767	0.533334
$748$	8.72018	0.318841
$749$	−4.35682	−0.159195
$750$	0.896485	0.0327350
$751$	−0.275430	−0.0100506	−0.00502529	−	0.999987i	$-0.501600\pi$
$751$	−0.275430	−0.0100506	−0.00502529	+	0.999987i	$0.501600\pi$
$752$	−1.43035	−0.0521594
$753$	−0.311701	−0.0113590
$754$	−6.68306	−0.243383
$755$	5.70060	0.207466
$756$	−1.32007	−0.0480106
$757$	−33.9531	−1.23404	−0.617022	−	0.786946i	$-0.711661\pi$
$757$	−33.9531	−1.23404	−0.617022	+	0.786946i	$0.711661\pi$
$758$	−5.84057	−0.212139
$759$	2.10014	0.0762302
$760$	1.98445	0.0719837
$761$	40.0635	1.45230	0.726150	−	0.687536i	$-0.241308\pi$
$761$	40.0635	1.45230	0.726150	+	0.687536i	$0.241308\pi$
$762$	2.45017	0.0887604
$763$	9.74842	0.352916
$764$	−16.5428	−0.598499
$765$	3.92101	0.141764
$766$	17.8660	0.645525
$767$	−5.05954	−0.182689
$768$	−0.221832	−0.00800466
$769$	32.6864	1.17870	0.589351	−	0.807877i	$-0.299383\pi$
$769$	32.6864	1.17870	0.589351	+	0.807877i	$0.299383\pi$
$770$	−1.10894	−0.0399634
$771$	−6.35140	−0.228740
$772$	−8.71648	−0.313713
$773$	23.2719	0.837031	0.418515	−	0.908210i	$-0.362551\pi$
$773$	23.2719	0.837031	0.418515	+	0.908210i	$0.362551\pi$
$774$	−6.36445	−0.228766
$775$	48.3068	1.73523
$776$	−14.2370	−0.511079
$777$	−2.60814	−0.0935667
$778$	−12.8723	−0.461493
$779$	27.1827	0.973921
$780$	0.0941145	0.00336984
$781$	−26.2455	−0.939136
$782$	11.3442	0.405669
$783$	8.54794	0.305479
$784$	1.00000	0.0357143
$785$	−6.20862	−0.221595
$786$	−0.0799236	−0.00285078
$787$	27.6875	0.986952	0.493476	−	0.869760i	$-0.335726\pi$
$787$	27.6875	0.986952	0.493476	+	0.869760i	$0.335726\pi$
$788$	−26.5211	−0.944774
$789$	2.43246	0.0865978
$790$	4.44512	0.158150
$791$	−12.6519	−0.449849
$792$	7.96023	0.282855
$793$	−10.1430	−0.360187
$794$	17.4765	0.620217
$795$	0.733789	0.0260248
$796$	−17.2484	−0.611355
$797$	−35.0191	−1.24044	−0.620219	−	0.784428i	$-0.712956\pi$
$797$	−35.0191	−1.24044	−0.620219	+	0.784428i	$0.712956\pi$
$798$	−1.07089	−0.0379090
$799$	−4.62359	−0.163571
$800$	4.83102	0.170802
$801$	−6.16438	−0.217808
$802$	29.0219	1.02480
$803$	−8.48342	−0.299373
$804$	−3.07562	−0.108469
$805$	−1.44264	−0.0508464
$806$	10.3201	0.363508
$807$	3.32438	0.117024
$808$	−9.55703	−0.336215
$809$	30.0569	1.05674	0.528372	−	0.849013i	$-0.322803\pi$
$809$	30.0569	1.05674	0.528372	+	0.849013i	$0.322803\pi$
$810$	3.51861	0.123631
$811$	−25.2332	−0.886056	−0.443028	−	0.896508i	$-0.646096\pi$
$811$	−25.2332	−0.886056	−0.443028	+	0.896508i	$0.646096\pi$
$812$	−6.47535	−0.227240
$813$	−2.34445	−0.0822234
$814$	31.7172	1.11169
$815$	1.54064	0.0539663
$816$	−0.717070	−0.0251025
$817$	−10.4122	−0.364277
$818$	−3.52099	−0.123108
$819$	3.04544	0.106416
$820$	−2.31469	−0.0808326
$821$	−23.3449	−0.814742	−0.407371	−	0.913263i	$-0.633554\pi$
$821$	−23.3449	−0.814742	−0.407371	+	0.913263i	$0.633554\pi$
$822$	−4.19044	−0.146158
$823$	50.3312	1.75444	0.877218	−	0.480093i	$-0.159397\pi$
$823$	50.3312	1.75444	0.877218	+	0.480093i	$0.159397\pi$
$824$	−12.1879	−0.424584
$825$	2.89101	0.100652
$826$	−4.90229	−0.170573
$827$	−38.6433	−1.34376	−0.671880	−	0.740660i	$-0.734513\pi$
$827$	−38.6433	−1.34376	−0.671880	+	0.740660i	$0.734513\pi$
$828$	10.3556	0.359882
$829$	−28.5680	−0.992207	−0.496104	−	0.868263i	$-0.665236\pi$
$829$	−28.5680	−0.992207	−0.496104	+	0.868263i	$0.665236\pi$
$830$	−2.03068	−0.0704861
$831$	−1.76907	−0.0613682
$832$	1.03208	0.0357808
$833$	3.23250	0.111999
$834$	−0.222759	−0.00771350
$835$	1.98528	0.0687035
$836$	13.0229	0.450406
$837$	−13.1998	−0.456253
$838$	21.0423	0.726894
$839$	34.8981	1.20482	0.602408	−	0.798189i	$-0.294208\pi$
$839$	34.8981	1.20482	0.602408	+	0.798189i	$0.294208\pi$
$840$	0.0911894	0.00314633
$841$	12.9302	0.445869
$842$	19.3095	0.665448
$843$	−0.204667	−0.00704912
$844$	23.3007	0.802044
$845$	4.90610	0.168775
$846$	−4.22065	−0.145109
$847$	3.72263	0.127911
$848$	8.04686	0.276330
$849$	5.49415	0.188559
$850$	15.6162	0.535633
$851$	41.2615	1.41443
$852$	2.15819	0.0739385
$853$	48.9648	1.67652	0.838262	−	0.545268i	$-0.183572\pi$
$853$	48.9648	1.67652	0.838262	+	0.545268i	$0.183572\pi$
$854$	−9.82773	−0.336298
$855$	5.85571	0.200261
$856$	−4.35682	−0.148913
$857$	40.2388	1.37453	0.687266	−	0.726406i	$-0.258811\pi$
$857$	40.2388	1.37453	0.687266	+	0.726406i	$0.258811\pi$
$858$	0.617622	0.0210853
$859$	−42.9080	−1.46400	−0.732001	−	0.681304i	$-0.761413\pi$
$859$	−42.9080	−1.46400	−0.732001	+	0.681304i	$0.761413\pi$
$860$	0.886632	0.0302339
$861$	1.24910	0.0425691
$862$	1.00000	0.0340601
$863$	29.9474	1.01942	0.509710	−	0.860346i	$-0.329753\pi$
$863$	29.9474	1.01942	0.509710	+	0.860346i	$0.329753\pi$
$864$	−1.32007	−0.0449098
$865$	6.58323	0.223837
$866$	−40.7932	−1.38621
$867$	1.45321	0.0493536
$868$	9.99931	0.339399
$869$	29.1709	0.989556
$870$	−0.590484	−0.0200193
$871$	14.3094	0.484855
$872$	9.74842	0.330123
$873$	−42.0105	−1.42184
$874$	16.9417	0.573062
$875$	−4.04128	−0.136620
$876$	0.697601	0.0235697
$877$	−20.6428	−0.697059	−0.348530	−	0.937298i	$-0.613319\pi$
$877$	−20.6428	−0.697059	−0.348530	+	0.937298i	$0.613319\pi$
$878$	−19.3451	−0.652867
$879$	2.97735	0.100424
$880$	−1.10894	−0.0373824
$881$	−10.8370	−0.365109	−0.182554	−	0.983196i	$-0.558437\pi$
$881$	−10.8370	−0.365109	−0.182554	+	0.983196i	$0.558437\pi$
$882$	2.95079	0.0993583
$883$	24.5565	0.826393	0.413197	−	0.910642i	$-0.364412\pi$
$883$	24.5565	0.826393	0.413197	+	0.910642i	$0.364412\pi$
$884$	3.33618	0.112208
$885$	−0.447037	−0.0150270
$886$	−38.2976	−1.28663
$887$	−49.6041	−1.66554	−0.832771	−	0.553617i	$-0.813247\pi$
$887$	−49.6041	−1.66554	−0.832771	+	0.553617i	$0.813247\pi$
$888$	−2.60814	−0.0875236
$889$	−11.0452	−0.370444
$890$	0.858760	0.0287857
$891$	23.0907	0.773569
$892$	8.38051	0.280600
$893$	−6.90496	−0.231066
$894$	−5.20853	−0.174199
$895$	4.73391	0.158237
$896$	1.00000	0.0334077
$897$	0.803475	0.0268273
$898$	−4.79531	−0.160022
$899$	−64.7491	−2.15950
$900$	14.2553	0.475177
$901$	26.0115	0.866567
$902$	−15.1901	−0.505774
$903$	−0.478460	−0.0159222
$904$	−12.6519	−0.420795
$905$	−2.74183	−0.0911417
$906$	−3.07626	−0.102202
$907$	3.85954	0.128154	0.0640769	−	0.997945i	$-0.479590\pi$
$907$	3.85954	0.128154	0.0640769	+	0.997945i	$0.479590\pi$
$908$	−24.6646	−0.818525
$909$	−28.2008	−0.935361
$910$	−0.424261	−0.0140641
$911$	−27.2553	−0.903010	−0.451505	−	0.892269i	$-0.649113\pi$
$911$	−27.2553	−0.903010	−0.451505	+	0.892269i	$0.649113\pi$
$912$	−1.07089	−0.0354606
$913$	−13.3263	−0.441035
$914$	−15.9209	−0.526615
$915$	−0.896184	−0.0296269
$916$	−18.2297	−0.602326
$917$	0.360289	0.0118978
$918$	−4.26713	−0.140836
$919$	−24.8487	−0.819682	−0.409841	−	0.912157i	$-0.634416\pi$
$919$	−24.8487	−0.819682	−0.409841	+	0.912157i	$0.634416\pi$
$920$	−1.44264	−0.0475625
$921$	−5.77796	−0.190390
$922$	8.44686	0.278183
$923$	−10.0410	−0.330505
$924$	0.598426	0.0196868
$925$	56.7998	1.86757
$926$	−19.4628	−0.639588
$927$	−35.9638	−1.18121
$928$	−6.47535	−0.212564
$929$	−10.1215	−0.332077	−0.166039	−	0.986119i	$-0.553098\pi$
$929$	−10.1215	−0.332077	−0.166039	+	0.986119i	$0.553098\pi$
$930$	0.911831	0.0299001
$931$	4.82747	0.158214
$932$	−14.3165	−0.468953
$933$	2.36077	0.0772882
$934$	13.0097	0.425691
$935$	−3.58465	−0.117230
$936$	3.04544	0.0995434
$937$	25.6471	0.837855	0.418928	−	0.908020i	$-0.362406\pi$
$937$	25.6471	0.837855	0.418928	+	0.908020i	$0.362406\pi$
$938$	13.8647	0.452697
$939$	1.49267	0.0487114
$940$	0.587980	0.0191778
$941$	35.0238	1.14174	0.570872	−	0.821039i	$-0.306605\pi$
$941$	35.0238	1.14174	0.570872	+	0.821039i	$0.306605\pi$
$942$	3.35041	0.109162
$943$	−19.7610	−0.643508
$944$	−4.90229	−0.159556
$945$	0.542649	0.0176524
$946$	5.81849	0.189175
$947$	−50.2805	−1.63390	−0.816948	−	0.576712i	$-0.804336\pi$
$947$	−50.2805	−1.63390	−0.816948	+	0.576712i	$0.804336\pi$
$948$	−2.39876	−0.0779080
$949$	−3.24560	−0.105357
$950$	23.3216	0.756653
$951$	−0.864601	−0.0280366
$952$	3.23250	0.104766
$953$	−3.76232	−0.121873	−0.0609367	−	0.998142i	$-0.519409\pi$
$953$	−3.76232	−0.121873	−0.0609367	+	0.998142i	$0.519409\pi$
$954$	23.7446	0.768760
$955$	6.80035	0.220054
$956$	−5.50573	−0.178068
$957$	−3.87502	−0.125262
$958$	−26.3565	−0.851541
$959$	18.8902	0.609996
$960$	0.0911894	0.00294313
$961$	68.9862	2.22536
$962$	12.1345	0.391230
$963$	−12.8561	−0.414280
$964$	5.36991	0.172953
$965$	3.58313	0.115345
$966$	0.778504	0.0250479
$967$	20.7851	0.668404	0.334202	−	0.942501i	$-0.391533\pi$
$967$	20.7851	0.668404	0.334202	+	0.942501i	$0.391533\pi$
$968$	3.72263	0.119650
$969$	−3.46164	−0.111204
$970$	5.85248	0.187912
$971$	−49.0963	−1.57558	−0.787788	−	0.615946i	$-0.788774\pi$
$971$	−49.0963	−1.57558	−0.787788	+	0.615946i	$0.788774\pi$
$972$	−5.85900	−0.187927
$973$	1.00418	0.0321925
$974$	−20.2132	−0.647673
$975$	1.10605	0.0354219
$976$	−9.82773	−0.314578
$977$	16.6112	0.531440	0.265720	−	0.964050i	$-0.414390\pi$
$977$	16.6112	0.531440	0.265720	+	0.964050i	$0.414390\pi$
$978$	−0.831388	−0.0265849
$979$	5.63557	0.180114
$980$	−0.411075	−0.0131313
$981$	28.7655	0.918413
$982$	38.2693	1.22122
$983$	12.0990	0.385898	0.192949	−	0.981209i	$-0.438195\pi$
$983$	12.0990	0.385898	0.192949	+	0.981209i	$0.438195\pi$
$984$	1.24910	0.0398197
$985$	10.9021	0.347371
$986$	−20.9316	−0.666597
$987$	−0.317296	−0.0100996
$988$	4.98232	0.158509
$989$	7.56937	0.240692
$990$	−3.27225	−0.103999
$991$	−4.12919	−0.131168	−0.0655840	−	0.997847i	$-0.520891\pi$
$991$	−4.12919	−0.131168	−0.0655840	+	0.997847i	$0.520891\pi$
$992$	9.99931	0.317478
$993$	2.65989	0.0844091
$994$	−9.72897	−0.308584
$995$	7.09040	0.224781
$996$	1.09583	0.0347228
$997$	21.8953	0.693433	0.346716	−	0.937970i	$-0.387297\pi$
$997$	21.8953	0.693433	0.346716	+	0.937970i	$0.387297\pi$
$998$	16.0592	0.508347
$999$	−15.5205	−0.491048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.14	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.221832 q^{3} +1.00000 q^{4} -0.411075 q^{5} +0.221832 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.95079 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.221832 q^{3} +1.00000 q^{4} -0.411075 q^{5} +0.221832 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.95079 q^{9} +0.411075 q^{10} +2.69766 q^{11} -0.221832 q^{12} +1.03208 q^{13} +1.00000 q^{14} +0.0911894 q^{15} +1.00000 q^{16} +3.23250 q^{17} +2.95079 q^{18} +4.82747 q^{19} -0.411075 q^{20} +0.221832 q^{21} -2.69766 q^{22} -3.50944 q^{23} +0.221832 q^{24} -4.83102 q^{25} -1.03208 q^{26} +1.32007 q^{27} -1.00000 q^{28} +6.47535 q^{29} -0.0911894 q^{30} -9.99931 q^{31} -1.00000 q^{32} -0.598426 q^{33} -3.23250 q^{34} +0.411075 q^{35} -2.95079 q^{36} -11.7573 q^{37} -4.82747 q^{38} -0.228947 q^{39} +0.411075 q^{40} +5.63083 q^{41} -0.221832 q^{42} -2.15686 q^{43} +2.69766 q^{44} +1.21300 q^{45} +3.50944 q^{46} -1.43035 q^{47} -0.221832 q^{48} +1.00000 q^{49} +4.83102 q^{50} -0.717070 q^{51} +1.03208 q^{52} +8.04686 q^{53} -1.32007 q^{54} -1.10894 q^{55} +1.00000 q^{56} -1.07089 q^{57} -6.47535 q^{58} -4.90229 q^{59} +0.0911894 q^{60} -9.82773 q^{61} +9.99931 q^{62} +2.95079 q^{63} +1.00000 q^{64} -0.424261 q^{65} +0.598426 q^{66} +13.8647 q^{67} +3.23250 q^{68} +0.778504 q^{69} -0.411075 q^{70} -9.72897 q^{71} +2.95079 q^{72} -3.14473 q^{73} +11.7573 q^{74} +1.07167 q^{75} +4.82747 q^{76} -2.69766 q^{77} +0.228947 q^{78} +10.8134 q^{79} -0.411075 q^{80} +8.55954 q^{81} -5.63083 q^{82} -4.93994 q^{83} +0.221832 q^{84} -1.32880 q^{85} +2.15686 q^{86} -1.43644 q^{87} -2.69766 q^{88} +2.08906 q^{89} -1.21300 q^{90} -1.03208 q^{91} -3.50944 q^{92} +2.21816 q^{93} +1.43035 q^{94} -1.98445 q^{95} +0.221832 q^{96} +14.2370 q^{97} -1.00000 q^{98} -7.96023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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