LMFDB - Embedded newform 6034.2.a.o.1.16

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			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.684006 q^{3} +1.00000 q^{4} +2.60861 q^{5} -0.684006 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.53214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.684006 q^{3} +1.00000 q^{4} +2.60861 q^{5} -0.684006 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.53214 q^{9} -2.60861 q^{10} +0.515557 q^{11} +0.684006 q^{12} -2.30528 q^{13} +1.00000 q^{14} +1.78430 q^{15} +1.00000 q^{16} -4.22152 q^{17} +2.53214 q^{18} +6.41287 q^{19} +2.60861 q^{20} -0.684006 q^{21} -0.515557 q^{22} +7.56095 q^{23} -0.684006 q^{24} +1.80483 q^{25} +2.30528 q^{26} -3.78401 q^{27} -1.00000 q^{28} -9.57149 q^{29} -1.78430 q^{30} -2.60007 q^{31} -1.00000 q^{32} +0.352644 q^{33} +4.22152 q^{34} -2.60861 q^{35} -2.53214 q^{36} -5.64515 q^{37} -6.41287 q^{38} -1.57683 q^{39} -2.60861 q^{40} -5.21138 q^{41} +0.684006 q^{42} -5.23218 q^{43} +0.515557 q^{44} -6.60535 q^{45} -7.56095 q^{46} +13.6244 q^{47} +0.684006 q^{48} +1.00000 q^{49} -1.80483 q^{50} -2.88754 q^{51} -2.30528 q^{52} +3.72311 q^{53} +3.78401 q^{54} +1.34489 q^{55} +1.00000 q^{56} +4.38644 q^{57} +9.57149 q^{58} -7.47870 q^{59} +1.78430 q^{60} +11.6080 q^{61} +2.60007 q^{62} +2.53214 q^{63} +1.00000 q^{64} -6.01358 q^{65} -0.352644 q^{66} -2.77186 q^{67} -4.22152 q^{68} +5.17173 q^{69} +2.60861 q^{70} -13.1071 q^{71} +2.53214 q^{72} -4.14608 q^{73} +5.64515 q^{74} +1.23451 q^{75} +6.41287 q^{76} -0.515557 q^{77} +1.57683 q^{78} +14.4494 q^{79} +2.60861 q^{80} +5.00812 q^{81} +5.21138 q^{82} +0.936990 q^{83} -0.684006 q^{84} -11.0123 q^{85} +5.23218 q^{86} -6.54695 q^{87} -0.515557 q^{88} -4.79799 q^{89} +6.60535 q^{90} +2.30528 q^{91} +7.56095 q^{92} -1.77846 q^{93} -13.6244 q^{94} +16.7287 q^{95} -0.684006 q^{96} -8.69140 q^{97} -1.00000 q^{98} -1.30546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.684006	0.394911	0.197455	−	0.980312i	$-0.436732\pi$
$3$	0.684006	0.394911	0.197455	+	0.980312i	$0.436732\pi$
$4$	1.00000	0.500000
$5$	2.60861	1.16660	0.583302	−	0.812255i	$-0.301760\pi$
$5$	2.60861	1.16660	0.583302	+	0.812255i	$0.301760\pi$
$6$	−0.684006	−0.279244
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.53214	−0.844045
$10$	−2.60861	−0.824914
$11$	0.515557	0.155446	0.0777231	−	0.996975i	$-0.475235\pi$
$11$	0.515557	0.155446	0.0777231	+	0.996975i	$0.475235\pi$
$12$	0.684006	0.197455
$13$	−2.30528	−0.639370	−0.319685	−	0.947524i	$-0.603577\pi$
$13$	−2.30528	−0.639370	−0.319685	+	0.947524i	$0.603577\pi$
$14$	1.00000	0.267261
$15$	1.78430	0.460705
$16$	1.00000	0.250000
$17$	−4.22152	−1.02387	−0.511934	−	0.859025i	$-0.671071\pi$
$17$	−4.22152	−1.02387	−0.511934	+	0.859025i	$0.671071\pi$
$18$	2.53214	0.596830
$19$	6.41287	1.47121	0.735607	−	0.677409i	$-0.236897\pi$
$19$	6.41287	1.47121	0.735607	+	0.677409i	$0.236897\pi$
$20$	2.60861	0.583302
$21$	−0.684006	−0.149262
$22$	−0.515557	−0.109917
$23$	7.56095	1.57657	0.788283	−	0.615312i	$-0.210970\pi$
$23$	7.56095	1.57657	0.788283	+	0.615312i	$0.210970\pi$
$24$	−0.684006	−0.139622
$25$	1.80483	0.360965
$26$	2.30528	0.452103
$27$	−3.78401	−0.728234
$28$	−1.00000	−0.188982
$29$	−9.57149	−1.77738	−0.888690	−	0.458508i	$-0.848384\pi$
$29$	−9.57149	−1.77738	−0.888690	+	0.458508i	$0.848384\pi$
$30$	−1.78430	−0.325767
$31$	−2.60007	−0.466986	−0.233493	−	0.972359i	$-0.575016\pi$
$31$	−2.60007	−0.466986	−0.233493	+	0.972359i	$0.575016\pi$
$32$	−1.00000	−0.176777
$33$	0.352644	0.0613874
$34$	4.22152	0.723984
$35$	−2.60861	−0.440935
$36$	−2.53214	−0.422023
$37$	−5.64515	−0.928057	−0.464029	−	0.885820i	$-0.653596\pi$
$37$	−5.64515	−0.928057	−0.464029	+	0.885820i	$0.653596\pi$
$38$	−6.41287	−1.04030
$39$	−1.57683	−0.252494
$40$	−2.60861	−0.412457
$41$	−5.21138	−0.813881	−0.406940	−	0.913455i	$-0.633404\pi$
$41$	−5.21138	−0.813881	−0.406940	+	0.913455i	$0.633404\pi$
$42$	0.684006	0.105544
$43$	−5.23218	−0.797900	−0.398950	−	0.916973i	$-0.630625\pi$
$43$	−5.23218	−0.797900	−0.398950	+	0.916973i	$0.630625\pi$
$44$	0.515557	0.0777231
$45$	−6.60535	−0.984667
$46$	−7.56095	−1.11480
$47$	13.6244	1.98732	0.993659	−	0.112432i	$-0.0358642\pi$
$47$	13.6244	1.98732	0.993659	+	0.112432i	$0.0358642\pi$
$48$	0.684006	0.0987277
$49$	1.00000	0.142857
$50$	−1.80483	−0.255241
$51$	−2.88754	−0.404337
$52$	−2.30528	−0.319685
$53$	3.72311	0.511409	0.255704	−	0.966755i	$-0.417693\pi$
$53$	3.72311	0.511409	0.255704	+	0.966755i	$0.417693\pi$
$54$	3.78401	0.514939
$55$	1.34489	0.181344
$56$	1.00000	0.133631
$57$	4.38644	0.580998
$58$	9.57149	1.25680
$59$	−7.47870	−0.973644	−0.486822	−	0.873501i	$-0.661844\pi$
$59$	−7.47870	−0.973644	−0.486822	+	0.873501i	$0.661844\pi$
$60$	1.78430	0.230352
$61$	11.6080	1.48625	0.743124	−	0.669154i	$-0.233343\pi$
$61$	11.6080	1.48625	0.743124	+	0.669154i	$0.233343\pi$
$62$	2.60007	0.330209
$63$	2.53214	0.319019
$64$	1.00000	0.125000
$65$	−6.01358	−0.745892
$66$	−0.352644	−0.0434075
$67$	−2.77186	−0.338637	−0.169318	−	0.985561i	$-0.554157\pi$
$67$	−2.77186	−0.338637	−0.169318	+	0.985561i	$0.554157\pi$
$68$	−4.22152	−0.511934
$69$	5.17173	0.622603
$70$	2.60861	0.311788
$71$	−13.1071	−1.55553	−0.777764	−	0.628557i	$-0.783646\pi$
$71$	−13.1071	−1.55553	−0.777764	+	0.628557i	$0.783646\pi$
$72$	2.53214	0.298415
$73$	−4.14608	−0.485262	−0.242631	−	0.970119i	$-0.578010\pi$
$73$	−4.14608	−0.485262	−0.242631	+	0.970119i	$0.578010\pi$
$74$	5.64515	0.656235
$75$	1.23451	0.142549
$76$	6.41287	0.735607
$77$	−0.515557	−0.0587532
$78$	1.57683	0.178540
$79$	14.4494	1.62568	0.812841	−	0.582486i	$-0.197920\pi$
$79$	14.4494	1.62568	0.812841	+	0.582486i	$0.197920\pi$
$80$	2.60861	0.291651
$81$	5.00812	0.556458
$82$	5.21138	0.575501
$83$	0.936990	0.102848	0.0514240	−	0.998677i	$-0.483624\pi$
$83$	0.936990	0.102848	0.0514240	+	0.998677i	$0.483624\pi$
$84$	−0.684006	−0.0746311
$85$	−11.0123	−1.19445
$86$	5.23218	0.564201
$87$	−6.54695	−0.701907
$88$	−0.515557	−0.0549586
$89$	−4.79799	−0.508586	−0.254293	−	0.967127i	$-0.581843\pi$
$89$	−4.79799	−0.508586	−0.254293	+	0.967127i	$0.581843\pi$
$90$	6.60535	0.696265
$91$	2.30528	0.241659
$92$	7.56095	0.788283
$93$	−1.77846	−0.184418
$94$	−13.6244	−1.40525
$95$	16.7287	1.71632
$96$	−0.684006	−0.0698110
$97$	−8.69140	−0.882478	−0.441239	−	0.897390i	$-0.645461\pi$
$97$	−8.69140	−0.882478	−0.441239	+	0.897390i	$0.645461\pi$
$98$	−1.00000	−0.101015
$99$	−1.30546	−0.131204
$100$	1.80483	0.180483
$101$	5.57890	0.555121	0.277560	−	0.960708i	$-0.410474\pi$
$101$	5.57890	0.555121	0.277560	+	0.960708i	$0.410474\pi$
$102$	2.88754	0.285909
$103$	−17.5389	−1.72816	−0.864082	−	0.503352i	$-0.832100\pi$
$103$	−17.5389	−1.72816	−0.864082	+	0.503352i	$0.832100\pi$
$104$	2.30528	0.226052
$105$	−1.78430	−0.174130
$106$	−3.72311	−0.361621
$107$	1.20662	0.116648	0.0583240	−	0.998298i	$-0.481424\pi$
$107$	1.20662	0.116648	0.0583240	+	0.998298i	$0.481424\pi$
$108$	−3.78401	−0.364117
$109$	−2.86110	−0.274044	−0.137022	−	0.990568i	$-0.543753\pi$
$109$	−2.86110	−0.274044	−0.137022	+	0.990568i	$0.543753\pi$
$110$	−1.34489	−0.128230
$111$	−3.86132	−0.366500
$112$	−1.00000	−0.0944911
$113$	−19.1601	−1.80243	−0.901215	−	0.433372i	$-0.857324\pi$
$113$	−19.1601	−1.80243	−0.901215	+	0.433372i	$0.857324\pi$
$114$	−4.38644	−0.410828
$115$	19.7235	1.83923
$116$	−9.57149	−0.888690
$117$	5.83729	0.539658
$118$	7.47870	0.688470
$119$	4.22152	0.386986
$120$	−1.78430	−0.162884
$121$	−10.7342	−0.975836
$122$	−11.6080	−1.05094
$123$	−3.56461	−0.321410
$124$	−2.60007	−0.233493
$125$	−8.33495	−0.745501
$126$	−2.53214	−0.225581
$127$	2.41386	0.214195	0.107098	−	0.994248i	$-0.465844\pi$
$127$	2.41386	0.214195	0.107098	+	0.994248i	$0.465844\pi$
$128$	−1.00000	−0.0883883
$129$	−3.57884	−0.315100
$130$	6.01358	0.527425
$131$	1.48215	0.129496	0.0647482	−	0.997902i	$-0.479376\pi$
$131$	1.48215	0.129496	0.0647482	+	0.997902i	$0.479376\pi$
$132$	0.352644	0.0306937
$133$	−6.41287	−0.556066
$134$	2.77186	0.239452
$135$	−9.87100	−0.849560
$136$	4.22152	0.361992
$137$	−8.04841	−0.687622	−0.343811	−	0.939039i	$-0.611718\pi$
$137$	−8.04841	−0.687622	−0.343811	+	0.939039i	$0.611718\pi$
$138$	−5.17173	−0.440247
$139$	−22.2252	−1.88512	−0.942559	−	0.334041i	$-0.891588\pi$
$139$	−22.2252	−1.88512	−0.942559	+	0.334041i	$0.891588\pi$
$140$	−2.60861	−0.220467
$141$	9.31915	0.784814
$142$	13.1071	1.09992
$143$	−1.18850	−0.0993877
$144$	−2.53214	−0.211011
$145$	−24.9682	−2.07350
$146$	4.14608	0.343132
$147$	0.684006	0.0564158
$148$	−5.64515	−0.464029
$149$	−12.4362	−1.01882	−0.509408	−	0.860525i	$-0.670135\pi$
$149$	−12.4362	−1.01882	−0.509408	+	0.860525i	$0.670135\pi$
$150$	−1.23451	−0.100797
$151$	−15.6007	−1.26956	−0.634782	−	0.772692i	$-0.718910\pi$
$151$	−15.6007	−1.26956	−0.634782	+	0.772692i	$0.718910\pi$
$152$	−6.41287	−0.520152
$153$	10.6895	0.864191
$154$	0.515557	0.0415448
$155$	−6.78255	−0.544787
$156$	−1.57683	−0.126247
$157$	11.0875	0.884881	0.442440	−	0.896798i	$-0.354113\pi$
$157$	11.0875	0.884881	0.442440	+	0.896798i	$0.354113\pi$
$158$	−14.4494	−1.14953
$159$	2.54663	0.201961
$160$	−2.60861	−0.206228
$161$	−7.56095	−0.595886
$162$	−5.00812	−0.393475
$163$	−9.36899	−0.733836	−0.366918	−	0.930253i	$-0.619587\pi$
$163$	−9.36899	−0.733836	−0.366918	+	0.930253i	$0.619587\pi$
$164$	−5.21138	−0.406940
$165$	0.919909	0.0716148
$166$	−0.936990	−0.0727245
$167$	16.5151	1.27797	0.638987	−	0.769218i	$-0.279354\pi$
$167$	16.5151	1.27797	0.638987	+	0.769218i	$0.279354\pi$
$168$	0.684006	0.0527722
$169$	−7.68567	−0.591205
$170$	11.0123	0.844603
$171$	−16.2383	−1.24177
$172$	−5.23218	−0.398950
$173$	−16.7859	−1.27621	−0.638105	−	0.769949i	$-0.720282\pi$
$173$	−16.7859	−1.27621	−0.638105	+	0.769949i	$0.720282\pi$
$174$	6.54695	0.496323
$175$	−1.80483	−0.136432
$176$	0.515557	0.0388616
$177$	−5.11547	−0.384503
$178$	4.79799	0.359625
$179$	3.11317	0.232689	0.116345	−	0.993209i	$-0.462882\pi$
$179$	3.11317	0.232689	0.116345	+	0.993209i	$0.462882\pi$
$180$	−6.60535	−0.492333
$181$	3.58486	0.266460	0.133230	−	0.991085i	$-0.457465\pi$
$181$	3.58486	0.266460	0.133230	+	0.991085i	$0.457465\pi$
$182$	−2.30528	−0.170879
$183$	7.93991	0.586935
$184$	−7.56095	−0.557401
$185$	−14.7260	−1.08268
$186$	1.77846	0.130403
$187$	−2.17643	−0.159156
$188$	13.6244	0.993659
$189$	3.78401	0.275246
$190$	−16.7287	−1.21362
$191$	4.97179	0.359746	0.179873	−	0.983690i	$-0.442431\pi$
$191$	4.97179	0.359746	0.179873	+	0.983690i	$0.442431\pi$
$192$	0.684006	0.0493639
$193$	20.4991	1.47555	0.737777	−	0.675044i	$-0.235875\pi$
$193$	20.4991	1.47555	0.737777	+	0.675044i	$0.235875\pi$
$194$	8.69140	0.624006
$195$	−4.11332	−0.294561
$196$	1.00000	0.0714286
$197$	13.3421	0.950587	0.475293	−	0.879827i	$-0.342342\pi$
$197$	13.3421	0.950587	0.475293	+	0.879827i	$0.342342\pi$
$198$	1.30546	0.0927750
$199$	−6.33474	−0.449058	−0.224529	−	0.974467i	$-0.572084\pi$
$199$	−6.33474	−0.449058	−0.224529	+	0.974467i	$0.572084\pi$
$200$	−1.80483	−0.127620
$201$	−1.89597	−0.133731
$202$	−5.57890	−0.392530
$203$	9.57149	0.671787
$204$	−2.88754	−0.202168
$205$	−13.5944	−0.949477
$206$	17.5389	1.22200
$207$	−19.1454	−1.33069
$208$	−2.30528	−0.159843
$209$	3.30620	0.228695
$210$	1.78430	0.123129
$211$	14.0019	0.963928	0.481964	−	0.876191i	$-0.339924\pi$
$211$	14.0019	0.963928	0.481964	+	0.876191i	$0.339924\pi$
$212$	3.72311	0.255704
$213$	−8.96534	−0.614295
$214$	−1.20662	−0.0824826
$215$	−13.6487	−0.930834
$216$	3.78401	0.257469
$217$	2.60007	0.176504
$218$	2.86110	0.193778
$219$	−2.83594	−0.191635
$220$	1.34489	0.0906721
$221$	9.73179	0.654631
$222$	3.86132	0.259155
$223$	−13.1667	−0.881710	−0.440855	−	0.897578i	$-0.645325\pi$
$223$	−13.1667	−0.881710	−0.440855	+	0.897578i	$0.645325\pi$
$224$	1.00000	0.0668153
$225$	−4.57007	−0.304671
$226$	19.1601	1.27451
$227$	7.12819	0.473115	0.236557	−	0.971618i	$-0.423981\pi$
$227$	7.12819	0.473115	0.236557	+	0.971618i	$0.423981\pi$
$228$	4.38644	0.290499
$229$	−4.66053	−0.307976	−0.153988	−	0.988073i	$-0.549212\pi$
$229$	−4.66053	−0.307976	−0.153988	+	0.988073i	$0.549212\pi$
$230$	−19.7235	−1.30053
$231$	−0.352644	−0.0232023
$232$	9.57149	0.628399
$233$	13.2009	0.864816	0.432408	−	0.901678i	$-0.357664\pi$
$233$	13.2009	0.864816	0.432408	+	0.901678i	$0.357664\pi$
$234$	−5.83729	−0.381596
$235$	35.5406	2.31841
$236$	−7.47870	−0.486822
$237$	9.88345	0.641999
$238$	−4.22152	−0.273640
$239$	8.22498	0.532029	0.266015	−	0.963969i	$-0.414293\pi$
$239$	8.22498	0.532029	0.266015	+	0.963969i	$0.414293\pi$
$240$	1.78430	0.115176
$241$	−12.7676	−0.822431	−0.411216	−	0.911538i	$-0.634896\pi$
$241$	−12.7676	−0.822431	−0.411216	+	0.911538i	$0.634896\pi$
$242$	10.7342	0.690021
$243$	14.7776	0.947985
$244$	11.6080	0.743124
$245$	2.60861	0.166658
$246$	3.56461	0.227271
$247$	−14.7835	−0.940650
$248$	2.60007	0.165104
$249$	0.640906	0.0406158
$250$	8.33495	0.527149
$251$	10.9273	0.689726	0.344863	−	0.938653i	$-0.387925\pi$
$251$	10.9273	0.689726	0.344863	+	0.938653i	$0.387925\pi$
$252$	2.53214	0.159510
$253$	3.89810	0.245071
$254$	−2.41386	−0.151459
$255$	−7.53246	−0.471701
$256$	1.00000	0.0625000
$257$	−29.6655	−1.85048	−0.925240	−	0.379382i	$-0.876137\pi$
$257$	−29.6655	−1.85048	−0.925240	+	0.379382i	$0.876137\pi$
$258$	3.57884	0.222809
$259$	5.64515	0.350773
$260$	−6.01358	−0.372946
$261$	24.2363	1.50019
$262$	−1.48215	−0.0915678
$263$	5.93821	0.366166	0.183083	−	0.983097i	$-0.441392\pi$
$263$	5.93821	0.366166	0.183083	+	0.983097i	$0.441392\pi$
$264$	−0.352644	−0.0217037
$265$	9.71214	0.596612
$266$	6.41287	0.393198
$267$	−3.28185	−0.200846
$268$	−2.77186	−0.169318
$269$	−8.82154	−0.537859	−0.268929	−	0.963160i	$-0.586670\pi$
$269$	−8.82154	−0.537859	−0.268929	+	0.963160i	$0.586670\pi$
$270$	9.87100	0.600730
$271$	30.0642	1.82627	0.913135	−	0.407657i	$-0.133654\pi$
$271$	30.0642	1.82627	0.913135	+	0.407657i	$0.133654\pi$
$272$	−4.22152	−0.255967
$273$	1.57683	0.0954339
$274$	8.04841	0.486222
$275$	0.930491	0.0561107
$276$	5.17173	0.311302
$277$	−22.7539	−1.36715	−0.683575	−	0.729880i	$-0.739576\pi$
$277$	−22.7539	−1.36715	−0.683575	+	0.729880i	$0.739576\pi$
$278$	22.2252	1.33298
$279$	6.58372	0.394157
$280$	2.60861	0.155894
$281$	−9.69524	−0.578370	−0.289185	−	0.957273i	$-0.593384\pi$
$281$	−9.69524	−0.578370	−0.289185	+	0.957273i	$0.593384\pi$
$282$	−9.31915	−0.554947
$283$	4.42760	0.263193	0.131597	−	0.991303i	$-0.457990\pi$
$283$	4.42760	0.263193	0.131597	+	0.991303i	$0.457990\pi$
$284$	−13.1071	−0.777764
$285$	11.4425	0.677795
$286$	1.18850	0.0702777
$287$	5.21138	0.307618
$288$	2.53214	0.149208
$289$	0.821193	0.0483055
$290$	24.9682	1.46619
$291$	−5.94497	−0.348500
$292$	−4.14608	−0.242631
$293$	29.6012	1.72932	0.864659	−	0.502359i	$-0.167534\pi$
$293$	29.6012	1.72932	0.864659	+	0.502359i	$0.167534\pi$
$294$	−0.684006	−0.0398920
$295$	−19.5090	−1.13586
$296$	5.64515	0.328118
$297$	−1.95087	−0.113201
$298$	12.4362	0.720411
$299$	−17.4301	−1.00801
$300$	1.23451	0.0712746
$301$	5.23218	0.301578
$302$	15.6007	0.897717
$303$	3.81600	0.219223
$304$	6.41287	0.367803
$305$	30.2806	1.73386
$306$	−10.6895	−0.611075
$307$	−3.91114	−0.223220	−0.111610	−	0.993752i	$-0.535601\pi$
$307$	−3.91114	−0.223220	−0.111610	+	0.993752i	$0.535601\pi$
$308$	−0.515557	−0.0293766
$309$	−11.9967	−0.682470
$310$	6.78255	0.385223
$311$	−21.2467	−1.20479	−0.602396	−	0.798197i	$-0.705787\pi$
$311$	−21.2467	−1.20479	−0.602396	+	0.798197i	$0.705787\pi$
$312$	1.57683	0.0892702
$313$	9.15299	0.517358	0.258679	−	0.965963i	$-0.416713\pi$
$313$	9.15299	0.517358	0.258679	+	0.965963i	$0.416713\pi$
$314$	−11.0875	−0.625705
$315$	6.60535	0.372169
$316$	14.4494	0.812841
$317$	−24.0490	−1.35073	−0.675363	−	0.737486i	$-0.736013\pi$
$317$	−24.0490	−1.35073	−0.675363	+	0.737486i	$0.736013\pi$
$318$	−2.54663	−0.142808
$319$	−4.93465	−0.276287
$320$	2.60861	0.145826
$321$	0.825332	0.0460656
$322$	7.56095	0.421355
$323$	−27.0720	−1.50633
$324$	5.00812	0.278229
$325$	−4.16064	−0.230791
$326$	9.36899	0.518900
$327$	−1.95701	−0.108223
$328$	5.21138	0.287750
$329$	−13.6244	−0.751136
$330$	−0.919909	−0.0506393
$331$	9.59094	0.527166	0.263583	−	0.964637i	$-0.415096\pi$
$331$	9.59094	0.527166	0.263583	+	0.964637i	$0.415096\pi$
$332$	0.936990	0.0514240
$333$	14.2943	0.783322
$334$	−16.5151	−0.903663
$335$	−7.23069	−0.395055
$336$	−0.684006	−0.0373156
$337$	−7.56335	−0.412002	−0.206001	−	0.978552i	$-0.566045\pi$
$337$	−7.56335	−0.412002	−0.206001	+	0.978552i	$0.566045\pi$
$338$	7.68567	0.418045
$339$	−13.1056	−0.711799
$340$	−11.0123	−0.597224
$341$	−1.34048	−0.0725912
$342$	16.2383	0.878065
$343$	−1.00000	−0.0539949
$344$	5.23218	0.282100
$345$	13.4910	0.726332
$346$	16.7859	0.902417
$347$	−13.9127	−0.746871	−0.373435	−	0.927656i	$-0.621820\pi$
$347$	−13.9127	−0.746871	−0.373435	+	0.927656i	$0.621820\pi$
$348$	−6.54695	−0.350953
$349$	−6.36993	−0.340975	−0.170487	−	0.985360i	$-0.554534\pi$
$349$	−6.36993	−0.340975	−0.170487	+	0.985360i	$0.554534\pi$
$350$	1.80483	0.0964720
$351$	8.72322	0.465611
$352$	−0.515557	−0.0274793
$353$	−3.61228	−0.192262	−0.0961312	−	0.995369i	$-0.530647\pi$
$353$	−3.61228	−0.192262	−0.0961312	+	0.995369i	$0.530647\pi$
$354$	5.11547	0.271884
$355$	−34.1913	−1.81469
$356$	−4.79799	−0.254293
$357$	2.88754	0.152825
$358$	−3.11317	−0.164536
$359$	−29.2042	−1.54134	−0.770670	−	0.637234i	$-0.780078\pi$
$359$	−29.2042	−1.54134	−0.770670	+	0.637234i	$0.780078\pi$
$360$	6.60535	0.348132
$361$	22.1249	1.16447
$362$	−3.58486	−0.188416
$363$	−7.34225	−0.385368
$364$	2.30528	0.120830
$365$	−10.8155	−0.566108
$366$	−7.93991	−0.415026
$367$	9.30809	0.485879	0.242939	−	0.970042i	$-0.421888\pi$
$367$	9.30809	0.485879	0.242939	+	0.970042i	$0.421888\pi$
$368$	7.56095	0.394142
$369$	13.1959	0.686952
$370$	14.7260	0.765567
$371$	−3.72311	−0.193294
$372$	−1.77846	−0.0922089
$373$	−17.5053	−0.906388	−0.453194	−	0.891412i	$-0.649715\pi$
$373$	−17.5053	−0.906388	−0.453194	+	0.891412i	$0.649715\pi$
$374$	2.17643	0.112541
$375$	−5.70115	−0.294406
$376$	−13.6244	−0.702623
$377$	22.0650	1.13640
$378$	−3.78401	−0.194629
$379$	−19.5290	−1.00314	−0.501569	−	0.865118i	$-0.667244\pi$
$379$	−19.5290	−1.00314	−0.501569	+	0.865118i	$0.667244\pi$
$380$	16.7287	0.858162
$381$	1.65109	0.0845881
$382$	−4.97179	−0.254379
$383$	0.0837791	0.00428091	0.00214046	−	0.999998i	$-0.499319\pi$
$383$	0.0837791	0.00428091	0.00214046	+	0.999998i	$0.499319\pi$
$384$	−0.684006	−0.0349055
$385$	−1.34489	−0.0685417
$386$	−20.4991	−1.04337
$387$	13.2486	0.673464
$388$	−8.69140	−0.441239
$389$	0.217766	0.0110412	0.00552058	−	0.999985i	$-0.498243\pi$
$389$	0.217766	0.0110412	0.00552058	+	0.999985i	$0.498243\pi$
$390$	4.11332	0.208286
$391$	−31.9187	−1.61420
$392$	−1.00000	−0.0505076
$393$	1.01380	0.0511395
$394$	−13.3421	−0.672166
$395$	37.6927	1.89653
$396$	−1.30546	−0.0656019
$397$	30.7524	1.54342	0.771709	−	0.635976i	$-0.219402\pi$
$397$	30.7524	1.54342	0.771709	+	0.635976i	$0.219402\pi$
$398$	6.33474	0.317532
$399$	−4.38644	−0.219597
$400$	1.80483	0.0902413
$401$	1.83254	0.0915129	0.0457565	−	0.998953i	$-0.485430\pi$
$401$	1.83254	0.0915129	0.0457565	+	0.998953i	$0.485430\pi$
$402$	1.89597	0.0945623
$403$	5.99389	0.298577
$404$	5.57890	0.277560
$405$	13.0642	0.649166
$406$	−9.57149	−0.475025
$407$	−2.91040	−0.144263
$408$	2.88754	0.142955
$409$	15.7459	0.778583	0.389291	−	0.921115i	$-0.372720\pi$
$409$	15.7459	0.778583	0.389291	+	0.921115i	$0.372720\pi$
$410$	13.5944	0.671381
$411$	−5.50516	−0.271549
$412$	−17.5389	−0.864082
$413$	7.47870	0.368003
$414$	19.1454	0.940943
$415$	2.44424	0.119983
$416$	2.30528	0.113026
$417$	−15.2022	−0.744453
$418$	−3.30620	−0.161712
$419$	3.08967	0.150940	0.0754702	−	0.997148i	$-0.475954\pi$
$419$	3.08967	0.150940	0.0754702	+	0.997148i	$0.475954\pi$
$420$	−1.78430	−0.0870650
$421$	1.89959	0.0925805	0.0462902	−	0.998928i	$-0.485260\pi$
$421$	1.89959	0.0925805	0.0462902	+	0.998928i	$0.485260\pi$
$422$	−14.0019	−0.681600
$423$	−34.4988	−1.67739
$424$	−3.72311	−0.180810
$425$	−7.61910	−0.369581
$426$	8.96534	0.434372
$427$	−11.6080	−0.561749
$428$	1.20662	0.0583240
$429$	−0.812944	−0.0392493
$430$	13.6487	0.658199
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−3.78401	−0.182058
$433$	26.0158	1.25024	0.625120	−	0.780529i	$-0.285050\pi$
$433$	26.0158	1.25024	0.625120	+	0.780529i	$0.285050\pi$
$434$	−2.60007	−0.124807
$435$	−17.0784	−0.818847
$436$	−2.86110	−0.137022
$437$	48.4874	2.31947
$438$	2.83594	0.135507
$439$	−0.0920981	−0.00439560	−0.00219780	−	0.999998i	$-0.500700\pi$
$439$	−0.0920981	−0.00439560	−0.00219780	+	0.999998i	$0.500700\pi$
$440$	−1.34489	−0.0641149
$441$	−2.53214	−0.120578
$442$	−9.73179	−0.462894
$443$	1.83843	0.0873466	0.0436733	−	0.999046i	$-0.486094\pi$
$443$	1.83843	0.0873466	0.0436733	+	0.999046i	$0.486094\pi$
$444$	−3.86132	−0.183250
$445$	−12.5161	−0.593319
$446$	13.1667	0.623463
$447$	−8.50645	−0.402341
$448$	−1.00000	−0.0472456
$449$	−37.1734	−1.75432	−0.877161	−	0.480197i	$-0.840565\pi$
$449$	−37.1734	−1.75432	−0.877161	+	0.480197i	$0.840565\pi$
$450$	4.57007	0.215435
$451$	−2.68676	−0.126515
$452$	−19.1601	−0.901215
$453$	−10.6709	−0.501364
$454$	−7.12819	−0.334543
$455$	6.01358	0.281921
$456$	−4.38644	−0.205414
$457$	36.1844	1.69263	0.846317	−	0.532679i	$-0.178815\pi$
$457$	36.1844	1.69263	0.846317	+	0.532679i	$0.178815\pi$
$458$	4.66053	0.217772
$459$	15.9743	0.745615
$460$	19.7235	0.919615
$461$	36.7535	1.71178	0.855890	−	0.517158i	$-0.173010\pi$
$461$	36.7535	1.71178	0.855890	+	0.517158i	$0.173010\pi$
$462$	0.352644	0.0164065
$463$	−28.6229	−1.33022	−0.665111	−	0.746745i	$-0.731616\pi$
$463$	−28.6229	−1.33022	−0.665111	+	0.746745i	$0.731616\pi$
$464$	−9.57149	−0.444345
$465$	−4.63930	−0.215143
$466$	−13.2009	−0.611518
$467$	−13.0958	−0.606002	−0.303001	−	0.952990i	$-0.597989\pi$
$467$	−13.0958	−0.606002	−0.303001	+	0.952990i	$0.597989\pi$
$468$	5.83729	0.269829
$469$	2.77186	0.127993
$470$	−35.5406	−1.63937
$471$	7.58393	0.349449
$472$	7.47870	0.344235
$473$	−2.69749	−0.124031
$474$	−9.88345	−0.453962
$475$	11.5741	0.531057
$476$	4.22152	0.193493
$477$	−9.42743	−0.431652
$478$	−8.22498	−0.376202
$479$	−11.1810	−0.510875	−0.255437	−	0.966826i	$-0.582219\pi$
$479$	−11.1810	−0.510875	−0.255437	+	0.966826i	$0.582219\pi$
$480$	−1.78430	−0.0814418
$481$	13.0137	0.593372
$482$	12.7676	0.581547
$483$	−5.17173	−0.235322
$484$	−10.7342	−0.487918
$485$	−22.6724	−1.02950
$486$	−14.7776	−0.670327
$487$	−37.4028	−1.69488	−0.847442	−	0.530889i	$-0.821858\pi$
$487$	−37.4028	−1.69488	−0.847442	+	0.530889i	$0.821858\pi$
$488$	−11.6080	−0.525468
$489$	−6.40844	−0.289800
$490$	−2.60861	−0.117845
$491$	13.6835	0.617530	0.308765	−	0.951138i	$-0.400084\pi$
$491$	13.6835	0.617530	0.308765	+	0.951138i	$0.400084\pi$
$492$	−3.56461	−0.160705
$493$	40.4062	1.81980
$494$	14.7835	0.665140
$495$	−3.40543	−0.153063
$496$	−2.60007	−0.116746
$497$	13.1071	0.587934
$498$	−0.640906	−0.0287197
$499$	−4.12045	−0.184457	−0.0922283	−	0.995738i	$-0.529399\pi$
$499$	−4.12045	−0.184457	−0.0922283	+	0.995738i	$0.529399\pi$
$500$	−8.33495	−0.372750
$501$	11.2964	0.504685
$502$	−10.9273	−0.487710
$503$	17.3818	0.775018	0.387509	−	0.921866i	$-0.373336\pi$
$503$	17.3818	0.775018	0.387509	+	0.921866i	$0.373336\pi$
$504$	−2.53214	−0.112790
$505$	14.5531	0.647606
$506$	−3.89810	−0.173292
$507$	−5.25704	−0.233473
$508$	2.41386	0.107098
$509$	−23.6117	−1.04657	−0.523286	−	0.852157i	$-0.675294\pi$
$509$	−23.6117	−1.04657	−0.523286	+	0.852157i	$0.675294\pi$
$510$	7.53246	0.333543
$511$	4.14608	0.183412
$512$	−1.00000	−0.0441942
$513$	−24.2664	−1.07139
$514$	29.6655	1.30849
$515$	−45.7522	−2.01608
$516$	−3.57884	−0.157550
$517$	7.02414	0.308921
$518$	−5.64515	−0.248034
$519$	−11.4817	−0.503990
$520$	6.01358	0.263713
$521$	−39.5634	−1.73330	−0.866652	−	0.498912i	$-0.833733\pi$
$521$	−39.5634	−1.73330	−0.866652	+	0.498912i	$0.833733\pi$
$522$	−24.2363	−1.06079
$523$	−11.6416	−0.509052	−0.254526	−	0.967066i	$-0.581919\pi$
$523$	−11.6416	−0.509052	−0.254526	+	0.967066i	$0.581919\pi$
$524$	1.48215	0.0647482
$525$	−1.23451	−0.0538785
$526$	−5.93821	−0.258918
$527$	10.9762	0.478132
$528$	0.352644	0.0153469
$529$	34.1679	1.48556
$530$	−9.71214	−0.421868
$531$	18.9371	0.821800
$532$	−6.41287	−0.278033
$533$	12.0137	0.520371
$534$	3.28185	0.142020
$535$	3.14759	0.136082
$536$	2.77186	0.119726
$537$	2.12943	0.0918916
$538$	8.82154	0.380324
$539$	0.515557	0.0222066
$540$	−9.87100	−0.424780
$541$	33.4858	1.43967	0.719833	−	0.694147i	$-0.244218\pi$
$541$	33.4858	1.43967	0.719833	+	0.694147i	$0.244218\pi$
$542$	−30.0642	−1.29137
$543$	2.45206	0.105228
$544$	4.22152	0.180996
$545$	−7.46348	−0.319700
$546$	−1.57683	−0.0674820
$547$	4.04000	0.172738	0.0863689	−	0.996263i	$-0.472474\pi$
$547$	4.04000	0.172738	0.0863689	+	0.996263i	$0.472474\pi$
$548$	−8.04841	−0.343811
$549$	−29.3929	−1.25446
$550$	−0.930491	−0.0396763
$551$	−61.3807	−2.61491
$552$	−5.17173	−0.220124
$553$	−14.4494	−0.614450
$554$	22.7539	0.966721
$555$	−10.0727	−0.427560
$556$	−22.2252	−0.942559
$557$	−1.48009	−0.0627135	−0.0313567	−	0.999508i	$-0.509983\pi$
$557$	−1.48009	−0.0627135	−0.0313567	+	0.999508i	$0.509983\pi$
$558$	−6.58372	−0.278711
$559$	12.0617	0.510154
$560$	−2.60861	−0.110234
$561$	−1.48869	−0.0628526
$562$	9.69524	0.408969
$563$	3.43172	0.144630	0.0723148	−	0.997382i	$-0.476961\pi$
$563$	3.43172	0.144630	0.0723148	+	0.997382i	$0.476961\pi$
$564$	9.31915	0.392407
$565$	−49.9811	−2.10272
$566$	−4.42760	−0.186106
$567$	−5.00812	−0.210321
$568$	13.1071	0.549962
$569$	−12.1740	−0.510360	−0.255180	−	0.966894i	$-0.582135\pi$
$569$	−12.1740	−0.510360	−0.255180	+	0.966894i	$0.582135\pi$
$570$	−11.4425	−0.479273
$571$	−15.3935	−0.644197	−0.322098	−	0.946706i	$-0.604388\pi$
$571$	−15.3935	−0.644197	−0.322098	+	0.946706i	$0.604388\pi$
$572$	−1.18850	−0.0496939
$573$	3.40073	0.142068
$574$	−5.21138	−0.217519
$575$	13.6462	0.569086
$576$	−2.53214	−0.105506
$577$	35.1138	1.46181	0.730903	−	0.682481i	$-0.239099\pi$
$577$	35.1138	1.46181	0.730903	+	0.682481i	$0.239099\pi$
$578$	−0.821193	−0.0341571
$579$	14.0215	0.582713
$580$	−24.9682	−1.03675
$581$	−0.936990	−0.0388729
$582$	5.94497	0.246427
$583$	1.91948	0.0794966
$584$	4.14608	0.171566
$585$	15.2272	0.629567
$586$	−29.6012	−1.22281
$587$	−22.5491	−0.930701	−0.465351	−	0.885126i	$-0.654072\pi$
$587$	−22.5491	−0.930701	−0.465351	+	0.885126i	$0.654072\pi$
$588$	0.684006	0.0282079
$589$	−16.6739	−0.687036
$590$	19.5090	0.803172
$591$	9.12609	0.375397
$592$	−5.64515	−0.232014
$593$	29.6158	1.21617	0.608087	−	0.793870i	$-0.291937\pi$
$593$	29.6158	1.21617	0.608087	+	0.793870i	$0.291937\pi$
$594$	1.95087	0.0800453
$595$	11.0123	0.451459
$596$	−12.4362	−0.509408
$597$	−4.33300	−0.177338
$598$	17.4301	0.712771
$599$	26.1787	1.06963	0.534816	−	0.844968i	$-0.320381\pi$
$599$	26.1787	1.06963	0.534816	+	0.844968i	$0.320381\pi$
$600$	−1.23451	−0.0503987
$601$	5.92015	0.241488	0.120744	−	0.992684i	$-0.461472\pi$
$601$	5.92015	0.241488	0.120744	+	0.992684i	$0.461472\pi$
$602$	−5.23218	−0.213248
$603$	7.01873	0.285825
$604$	−15.6007	−0.634782
$605$	−28.0013	−1.13841
$606$	−3.81600	−0.155014
$607$	27.6658	1.12292	0.561459	−	0.827504i	$-0.310240\pi$
$607$	27.6658	1.12292	0.561459	+	0.827504i	$0.310240\pi$
$608$	−6.41287	−0.260076
$609$	6.54695	0.265296
$610$	−30.2806	−1.22603
$611$	−31.4080	−1.27063
$612$	10.6895	0.432095
$613$	−17.3428	−0.700468	−0.350234	−	0.936662i	$-0.613898\pi$
$613$	−17.3428	−0.700468	−0.350234	+	0.936662i	$0.613898\pi$
$614$	3.91114	0.157841
$615$	−9.29867	−0.374959
$616$	0.515557	0.0207724
$617$	35.4455	1.42698	0.713491	−	0.700664i	$-0.247113\pi$
$617$	35.4455	1.42698	0.713491	+	0.700664i	$0.247113\pi$
$618$	11.9967	0.482579
$619$	−6.33323	−0.254554	−0.127277	−	0.991867i	$-0.540624\pi$
$619$	−6.33323	−0.254554	−0.127277	+	0.991867i	$0.540624\pi$
$620$	−6.78255	−0.272394
$621$	−28.6107	−1.14811
$622$	21.2467	0.851917
$623$	4.79799	0.192228
$624$	−1.57683	−0.0631236
$625$	−30.7667	−1.23067
$626$	−9.15299	−0.365827
$627$	2.26146	0.0903140
$628$	11.0875	0.442440
$629$	23.8311	0.950208
$630$	−6.60535	−0.263163
$631$	12.2847	0.489048	0.244524	−	0.969643i	$-0.421368\pi$
$631$	12.2847	0.489048	0.244524	+	0.969643i	$0.421368\pi$
$632$	−14.4494	−0.574765
$633$	9.57736	0.380666
$634$	24.0490	0.955107
$635$	6.29681	0.249881
$636$	2.54663	0.100980
$637$	−2.30528	−0.0913386
$638$	4.93465	0.195364
$639$	33.1890	1.31294
$640$	−2.60861	−0.103114
$641$	21.8270	0.862114	0.431057	−	0.902325i	$-0.358141\pi$
$641$	21.8270	0.862114	0.431057	+	0.902325i	$0.358141\pi$
$642$	−0.825332	−0.0325733
$643$	−8.90949	−0.351356	−0.175678	−	0.984448i	$-0.556212\pi$
$643$	−8.90949	−0.351356	−0.175678	+	0.984448i	$0.556212\pi$
$644$	−7.56095	−0.297943
$645$	−9.33579	−0.367596
$646$	27.0720	1.06513
$647$	14.3586	0.564496	0.282248	−	0.959341i	$-0.408920\pi$
$647$	14.3586	0.564496	0.282248	+	0.959341i	$0.408920\pi$
$648$	−5.00812	−0.196738
$649$	−3.85570	−0.151349
$650$	4.16064	0.163194
$651$	1.77846	0.0697034
$652$	−9.36899	−0.366918
$653$	−5.57204	−0.218051	−0.109025	−	0.994039i	$-0.534773\pi$
$653$	−5.57204	−0.218051	−0.109025	+	0.994039i	$0.534773\pi$
$654$	1.95701	0.0765251
$655$	3.86636	0.151071
$656$	−5.21138	−0.203470
$657$	10.4984	0.409583
$658$	13.6244	0.531133
$659$	22.3004	0.868702	0.434351	−	0.900744i	$-0.356978\pi$
$659$	22.3004	0.868702	0.434351	+	0.900744i	$0.356978\pi$
$660$	0.919909	0.0358074
$661$	−4.77521	−0.185734	−0.0928670	−	0.995679i	$-0.529603\pi$
$661$	−4.77521	−0.185734	−0.0928670	+	0.995679i	$0.529603\pi$
$662$	−9.59094	−0.372762
$663$	6.65660	0.258521
$664$	−0.936990	−0.0363622
$665$	−16.7287	−0.648709
$666$	−14.2943	−0.553892
$667$	−72.3695	−2.80216
$668$	16.5151	0.638987
$669$	−9.00613	−0.348197
$670$	7.23069	0.279346
$671$	5.98457	0.231032
$672$	0.684006	0.0263861
$673$	14.3149	0.551797	0.275899	−	0.961187i	$-0.411025\pi$
$673$	14.3149	0.551797	0.275899	+	0.961187i	$0.411025\pi$
$674$	7.56335	0.291329
$675$	−6.82949	−0.262867
$676$	−7.68567	−0.295603
$677$	0.333662	0.0128237	0.00641184	−	0.999979i	$-0.497959\pi$
$677$	0.333662	0.0128237	0.00641184	+	0.999979i	$0.497959\pi$
$678$	13.1056	0.503318
$679$	8.69140	0.333545
$680$	11.0123	0.422301
$681$	4.87572	0.186838
$682$	1.34048	0.0513297
$683$	−32.0621	−1.22682	−0.613411	−	0.789764i	$-0.710203\pi$
$683$	−32.0621	−1.22682	−0.613411	+	0.789764i	$0.710203\pi$
$684$	−16.2383	−0.620885
$685$	−20.9951	−0.802183
$686$	1.00000	0.0381802
$687$	−3.18783	−0.121623
$688$	−5.23218	−0.199475
$689$	−8.58283	−0.326980
$690$	−13.4910	−0.513594
$691$	11.9558	0.454819	0.227409	−	0.973799i	$-0.426974\pi$
$691$	11.9558	0.454819	0.227409	+	0.973799i	$0.426974\pi$
$692$	−16.7859	−0.638105
$693$	1.30546	0.0495903
$694$	13.9127	0.528117
$695$	−57.9768	−2.19919
$696$	6.54695	0.248162
$697$	21.9999	0.833306
$698$	6.36993	0.241105
$699$	9.02946	0.341525
$700$	−1.80483	−0.0682160
$701$	31.3573	1.18435	0.592175	−	0.805809i	$-0.298269\pi$
$701$	31.3573	1.18435	0.592175	+	0.805809i	$0.298269\pi$
$702$	−8.72322	−0.329237
$703$	−36.2016	−1.36537
$704$	0.515557	0.0194308
$705$	24.3100	0.915567
$706$	3.61228	0.135950
$707$	−5.57890	−0.209816
$708$	−5.11547	−0.192251
$709$	−18.0920	−0.679461	−0.339731	−	0.940523i	$-0.610336\pi$
$709$	−18.0920	−0.679461	−0.339731	+	0.940523i	$0.610336\pi$
$710$	34.1913	1.28318
$711$	−36.5878	−1.37215
$712$	4.79799	0.179812
$713$	−19.6590	−0.736234
$714$	−2.88754	−0.108063
$715$	−3.10034	−0.115946
$716$	3.11317	0.116345
$717$	5.62593	0.210104
$718$	29.2042	1.08989
$719$	−3.44855	−0.128609	−0.0643045	−	0.997930i	$-0.520483\pi$
$719$	−3.44855	−0.128609	−0.0643045	+	0.997930i	$0.520483\pi$
$720$	−6.60535	−0.246167
$721$	17.5389	0.653184
$722$	−22.1249	−0.823404
$723$	−8.73309	−0.324787
$724$	3.58486	0.133230
$725$	−17.2749	−0.641573
$726$	7.34225	0.272497
$727$	38.8166	1.43963	0.719814	−	0.694167i	$-0.244227\pi$
$727$	38.8166	1.43963	0.719814	+	0.694167i	$0.244227\pi$
$728$	−2.30528	−0.0854395
$729$	−4.91639	−0.182088
$730$	10.8155	0.400299
$731$	22.0877	0.816945
$732$	7.93991	0.293468
$733$	25.1023	0.927174	0.463587	−	0.886051i	$-0.346562\pi$
$733$	25.1023	0.927174	0.463587	+	0.886051i	$0.346562\pi$
$734$	−9.30809	−0.343568
$735$	1.78430	0.0658150
$736$	−7.56095	−0.278700
$737$	−1.42905	−0.0526398
$738$	−13.1959	−0.485749
$739$	−28.4879	−1.04794	−0.523972	−	0.851736i	$-0.675550\pi$
$739$	−28.4879	−1.04794	−0.523972	+	0.851736i	$0.675550\pi$
$740$	−14.7260	−0.541338
$741$	−10.1120	−0.371473
$742$	3.72311	0.136680
$743$	6.84196	0.251007	0.125504	−	0.992093i	$-0.459945\pi$
$743$	6.84196	0.251007	0.125504	+	0.992093i	$0.459945\pi$
$744$	1.77846	0.0652015
$745$	−32.4412	−1.18855
$746$	17.5053	0.640913
$747$	−2.37259	−0.0868083
$748$	−2.17643	−0.0795782
$749$	−1.20662	−0.0440888
$750$	5.70115	0.208177
$751$	4.19545	0.153094	0.0765471	−	0.997066i	$-0.475610\pi$
$751$	4.19545	0.153094	0.0765471	+	0.997066i	$0.475610\pi$
$752$	13.6244	0.496830
$753$	7.47435	0.272380
$754$	−22.0650	−0.803559
$755$	−40.6960	−1.48108
$756$	3.78401	0.137623
$757$	−8.30679	−0.301915	−0.150958	−	0.988540i	$-0.548236\pi$
$757$	−8.30679	−0.301915	−0.150958	+	0.988540i	$0.548236\pi$
$758$	19.5290	0.709325
$759$	2.66632	0.0967814
$760$	−16.7287	−0.606812
$761$	−12.3316	−0.447019	−0.223509	−	0.974702i	$-0.571751\pi$
$761$	−12.3316	−0.447019	−0.223509	+	0.974702i	$0.571751\pi$
$762$	−1.65109	−0.0598128
$763$	2.86110	0.103579
$764$	4.97179	0.179873
$765$	27.8846	1.00817
$766$	−0.0837791	−0.00302706
$767$	17.2405	0.622519
$768$	0.684006	0.0246819
$769$	−45.7837	−1.65100	−0.825501	−	0.564401i	$-0.809107\pi$
$769$	−45.7837	−1.65100	−0.825501	+	0.564401i	$0.809107\pi$
$770$	1.34489	0.0484663
$771$	−20.2913	−0.730775
$772$	20.4991	0.737777
$773$	−0.814831	−0.0293075	−0.0146537	−	0.999893i	$-0.504665\pi$
$773$	−0.814831	−0.0293075	−0.0146537	+	0.999893i	$0.504665\pi$
$774$	−13.2486	−0.476211
$775$	−4.69267	−0.168566
$776$	8.69140	0.312003
$777$	3.86132	0.138524
$778$	−0.217766	−0.00780728
$779$	−33.4199	−1.19739
$780$	−4.11332	−0.147280
$781$	−6.75746	−0.241801
$782$	31.9187	1.14141
$783$	36.2186	1.29435
$784$	1.00000	0.0357143
$785$	28.9230	1.03231
$786$	−1.01380	−0.0361611
$787$	2.27416	0.0810652	0.0405326	−	0.999178i	$-0.487095\pi$
$787$	2.27416	0.0810652	0.0405326	+	0.999178i	$0.487095\pi$
$788$	13.3421	0.475293
$789$	4.06177	0.144603
$790$	−37.6927	−1.34105
$791$	19.1601	0.681255
$792$	1.30546	0.0463875
$793$	−26.7596	−0.950263
$794$	−30.7524	−1.09136
$795$	6.64316	0.235608
$796$	−6.33474	−0.224529
$797$	−20.7613	−0.735402	−0.367701	−	0.929944i	$-0.619855\pi$
$797$	−20.7613	−0.735402	−0.367701	+	0.929944i	$0.619855\pi$
$798$	4.38644	0.155278
$799$	−57.5155	−2.03475
$800$	−1.80483	−0.0638102
$801$	12.1492	0.429270
$802$	−1.83254	−0.0647094
$803$	−2.13754	−0.0754321
$804$	−1.89597	−0.0668656
$805$	−19.7235	−0.695163
$806$	−5.99389	−0.211126
$807$	−6.03398	−0.212406
$808$	−5.57890	−0.196265
$809$	−53.4289	−1.87846	−0.939231	−	0.343286i	$-0.888460\pi$
$809$	−53.4289	−1.87846	−0.939231	+	0.343286i	$0.888460\pi$
$810$	−13.0642	−0.459030
$811$	−1.67141	−0.0586911	−0.0293455	−	0.999569i	$-0.509342\pi$
$811$	−1.67141	−0.0586911	−0.0293455	+	0.999569i	$0.509342\pi$
$812$	9.57149	0.335893
$813$	20.5641	0.721214
$814$	2.91040	0.102009
$815$	−24.4400	−0.856096
$816$	−2.88754	−0.101084
$817$	−33.5533	−1.17388
$818$	−15.7459	−0.550541
$819$	−5.83729	−0.203971
$820$	−13.5944	−0.474738
$821$	−35.0855	−1.22449	−0.612246	−	0.790667i	$-0.709734\pi$
$821$	−35.0855	−1.22449	−0.612246	+	0.790667i	$0.709734\pi$
$822$	5.50516	0.192014
$823$	45.3253	1.57994	0.789970	−	0.613145i	$-0.210096\pi$
$823$	45.3253	1.57994	0.789970	+	0.613145i	$0.210096\pi$
$824$	17.5389	0.610998
$825$	0.636461	0.0221587
$826$	−7.47870	−0.260217
$827$	−0.399547	−0.0138936	−0.00694680	−	0.999976i	$-0.502211\pi$
$827$	−0.399547	−0.0138936	−0.00694680	+	0.999976i	$0.502211\pi$
$828$	−19.1454	−0.665347
$829$	21.4857	0.746230	0.373115	−	0.927785i	$-0.378290\pi$
$829$	21.4857	0.746230	0.373115	+	0.927785i	$0.378290\pi$
$830$	−2.44424	−0.0848407
$831$	−15.5638	−0.539902
$832$	−2.30528	−0.0799213
$833$	−4.22152	−0.146267
$834$	15.2022	0.526408
$835$	43.0813	1.49089
$836$	3.30620	0.114347
$837$	9.83868	0.340075
$838$	−3.08967	−0.106731
$839$	−8.70535	−0.300542	−0.150271	−	0.988645i	$-0.548015\pi$
$839$	−8.70535	−0.300542	−0.150271	+	0.988645i	$0.548015\pi$
$840$	1.78430	0.0615643
$841$	62.6133	2.15908
$842$	−1.89959	−0.0654643
$843$	−6.63160	−0.228404
$844$	14.0019	0.481964
$845$	−20.0489	−0.689703
$846$	34.4988	1.18609
$847$	10.7342	0.368832
$848$	3.72311	0.127852
$849$	3.02850	0.103938
$850$	7.61910	0.261333
$851$	−42.6827	−1.46314
$852$	−8.96534	−0.307147
$853$	41.6102	1.42471	0.712353	−	0.701821i	$-0.247630\pi$
$853$	41.6102	1.42471	0.712353	+	0.701821i	$0.247630\pi$
$854$	11.6080	0.397216
$855$	−42.3592	−1.44866
$856$	−1.20662	−0.0412413
$857$	21.8500	0.746382	0.373191	−	0.927754i	$-0.378264\pi$
$857$	21.8500	0.746382	0.373191	+	0.927754i	$0.378264\pi$
$858$	0.812944	0.0277534
$859$	−29.3047	−0.999864	−0.499932	−	0.866065i	$-0.666642\pi$
$859$	−29.3047	−0.999864	−0.499932	+	0.866065i	$0.666642\pi$
$860$	−13.6487	−0.465417
$861$	3.56461	0.121482
$862$	1.00000	0.0340601
$863$	−36.9108	−1.25646	−0.628230	−	0.778028i	$-0.716220\pi$
$863$	−36.9108	−1.25646	−0.628230	+	0.778028i	$0.716220\pi$
$864$	3.78401	0.128735
$865$	−43.7879	−1.48883
$866$	−26.0158	−0.884053
$867$	0.561701	0.0190764
$868$	2.60007	0.0882520
$869$	7.44947	0.252706
$870$	17.0784	0.579013
$871$	6.38992	0.216514
$872$	2.86110	0.0968891
$873$	22.0078	0.744851
$874$	−48.4874	−1.64011
$875$	8.33495	0.281773
$876$	−2.83594	−0.0958176
$877$	−46.9446	−1.58521	−0.792603	−	0.609738i	$-0.791275\pi$
$877$	−46.9446	−1.58521	−0.792603	+	0.609738i	$0.791275\pi$
$878$	0.0920981	0.00310816
$879$	20.2474	0.682927
$880$	1.34489	0.0453361
$881$	−34.9929	−1.17894	−0.589471	−	0.807789i	$-0.700664\pi$
$881$	−34.9929	−1.17894	−0.589471	+	0.807789i	$0.700664\pi$
$882$	2.53214	0.0852615
$883$	9.32960	0.313966	0.156983	−	0.987601i	$-0.449823\pi$
$883$	9.32960	0.313966	0.156983	+	0.987601i	$0.449823\pi$
$884$	9.73179	0.327315
$885$	−13.3443	−0.448562
$886$	−1.83843	−0.0617634
$887$	1.52741	0.0512855	0.0256428	−	0.999671i	$-0.491837\pi$
$887$	1.52741	0.0512855	0.0256428	+	0.999671i	$0.491837\pi$
$888$	3.86132	0.129577
$889$	−2.41386	−0.0809583
$890$	12.5161	0.419540
$891$	2.58197	0.0864993
$892$	−13.1667	−0.440855
$893$	87.3713	2.92377
$894$	8.50645	0.284498
$895$	8.12104	0.271456
$896$	1.00000	0.0334077
$897$	−11.9223	−0.398074
$898$	37.1734	1.24049
$899$	24.8865	0.830011
$900$	−4.57007	−0.152336
$901$	−15.7172	−0.523615
$902$	2.68676	0.0894594
$903$	3.57884	0.119096
$904$	19.1601	0.637255
$905$	9.35148	0.310854
$906$	10.6709	0.354518
$907$	−15.2199	−0.505369	−0.252684	−	0.967549i	$-0.581313\pi$
$907$	−15.2199	−0.505369	−0.252684	+	0.967549i	$0.581313\pi$
$908$	7.12819	0.236557
$909$	−14.1265	−0.468547
$910$	−6.01358	−0.199348
$911$	−11.3990	−0.377664	−0.188832	−	0.982009i	$-0.560470\pi$
$911$	−11.3990	−0.377664	−0.188832	+	0.982009i	$0.560470\pi$
$912$	4.38644	0.145250
$913$	0.483071	0.0159873
$914$	−36.1844	−1.19687
$915$	20.7121	0.684721
$916$	−4.66053	−0.153988
$917$	−1.48215	−0.0489450
$918$	−15.9743	−0.527229
$919$	14.3092	0.472018	0.236009	−	0.971751i	$-0.424161\pi$
$919$	14.3092	0.472018	0.236009	+	0.971751i	$0.424161\pi$
$920$	−19.7235	−0.650266
$921$	−2.67524	−0.0881521
$922$	−36.7535	−1.21041
$923$	30.2156	0.994558
$924$	−0.352644	−0.0116011
$925$	−10.1885	−0.334996
$926$	28.6229	0.940608
$927$	44.4110	1.45865
$928$	9.57149	0.314199
$929$	60.5468	1.98648	0.993238	−	0.116098i	$-0.0370388\pi$
$929$	60.5468	1.98648	0.993238	+	0.116098i	$0.0370388\pi$
$930$	4.63930	0.152129
$931$	6.41287	0.210173
$932$	13.2009	0.432408
$933$	−14.5329	−0.475786
$934$	13.0958	0.428508
$935$	−5.67745	−0.185673
$936$	−5.83729	−0.190798
$937$	25.3495	0.828132	0.414066	−	0.910247i	$-0.364108\pi$
$937$	25.3495	0.828132	0.414066	+	0.910247i	$0.364108\pi$
$938$	−2.77186	−0.0905044
$939$	6.26070	0.204310
$940$	35.5406	1.15921
$941$	−6.57423	−0.214314	−0.107157	−	0.994242i	$-0.534175\pi$
$941$	−6.57423	−0.214314	−0.107157	+	0.994242i	$0.534175\pi$
$942$	−7.58393	−0.247098
$943$	−39.4030	−1.28314
$944$	−7.47870	−0.243411
$945$	9.87100	0.321104
$946$	2.69749	0.0877029
$947$	55.6299	1.80773	0.903864	−	0.427819i	$-0.140718\pi$
$947$	55.6299	1.80773	0.903864	+	0.427819i	$0.140718\pi$
$948$	9.88345	0.321000
$949$	9.55788	0.310262
$950$	−11.5741	−0.375514
$951$	−16.4496	−0.533416
$952$	−4.22152	−0.136820
$953$	7.10285	0.230084	0.115042	−	0.993361i	$-0.463300\pi$
$953$	7.10285	0.230084	0.115042	+	0.993361i	$0.463300\pi$
$954$	9.42743	0.305224
$955$	12.9694	0.419681
$956$	8.22498	0.266015
$957$	−3.37533	−0.109109
$958$	11.1810	0.361243
$959$	8.04841	0.259897
$960$	1.78430	0.0575881
$961$	−24.2397	−0.781924
$962$	−13.0137	−0.419578
$963$	−3.05532	−0.0984562
$964$	−12.7676	−0.411216
$965$	53.4740	1.72139
$966$	5.17173	0.166398
$967$	5.09074	0.163707	0.0818536	−	0.996644i	$-0.473916\pi$
$967$	5.09074	0.163707	0.0818536	+	0.996644i	$0.473916\pi$
$968$	10.7342	0.345010
$969$	−18.5174	−0.594865
$970$	22.6724	0.727968
$971$	−7.66099	−0.245853	−0.122926	−	0.992416i	$-0.539228\pi$
$971$	−7.66099	−0.245853	−0.122926	+	0.992416i	$0.539228\pi$
$972$	14.7776	0.473992
$973$	22.2252	0.712507
$974$	37.4028	1.19846
$975$	−2.84590	−0.0911417
$976$	11.6080	0.371562
$977$	−5.05875	−0.161844	−0.0809218	−	0.996720i	$-0.525786\pi$
$977$	−5.05875	−0.161844	−0.0809218	+	0.996720i	$0.525786\pi$
$978$	6.40844	0.204919
$979$	−2.47364	−0.0790578
$980$	2.60861	0.0833289
$981$	7.24469	0.231305
$982$	−13.6835	−0.436660
$983$	−51.1348	−1.63095	−0.815474	−	0.578794i	$-0.803524\pi$
$983$	−51.1348	−1.63095	−0.815474	+	0.578794i	$0.803524\pi$
$984$	3.56461	0.113636
$985$	34.8043	1.10896
$986$	−40.4062	−1.28679
$987$	−9.31915	−0.296632
$988$	−14.7835	−0.470325
$989$	−39.5603	−1.25794
$990$	3.40543	0.108232
$991$	−10.6113	−0.337078	−0.168539	−	0.985695i	$-0.553905\pi$
$991$	−10.6113	−0.337078	−0.168539	+	0.985695i	$0.553905\pi$
$992$	2.60007	0.0825522
$993$	6.56026	0.208183
$994$	−13.1071	−0.415732
$995$	−16.5249	−0.523873
$996$	0.640906	0.0203079
$997$	−21.3103	−0.674905	−0.337452	−	0.941343i	$-0.609565\pi$
$997$	−21.3103	−0.674905	−0.337452	+	0.941343i	$0.609565\pi$
$998$	4.12045	0.130431
$999$	21.3613	0.675842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.684006 q^{3} +1.00000 q^{4} +2.60861 q^{5} -0.684006 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.53214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.684006 q^{3} +1.00000 q^{4} +2.60861 q^{5} -0.684006 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.53214 q^{9} -2.60861 q^{10} +0.515557 q^{11} +0.684006 q^{12} -2.30528 q^{13} +1.00000 q^{14} +1.78430 q^{15} +1.00000 q^{16} -4.22152 q^{17} +2.53214 q^{18} +6.41287 q^{19} +2.60861 q^{20} -0.684006 q^{21} -0.515557 q^{22} +7.56095 q^{23} -0.684006 q^{24} +1.80483 q^{25} +2.30528 q^{26} -3.78401 q^{27} -1.00000 q^{28} -9.57149 q^{29} -1.78430 q^{30} -2.60007 q^{31} -1.00000 q^{32} +0.352644 q^{33} +4.22152 q^{34} -2.60861 q^{35} -2.53214 q^{36} -5.64515 q^{37} -6.41287 q^{38} -1.57683 q^{39} -2.60861 q^{40} -5.21138 q^{41} +0.684006 q^{42} -5.23218 q^{43} +0.515557 q^{44} -6.60535 q^{45} -7.56095 q^{46} +13.6244 q^{47} +0.684006 q^{48} +1.00000 q^{49} -1.80483 q^{50} -2.88754 q^{51} -2.30528 q^{52} +3.72311 q^{53} +3.78401 q^{54} +1.34489 q^{55} +1.00000 q^{56} +4.38644 q^{57} +9.57149 q^{58} -7.47870 q^{59} +1.78430 q^{60} +11.6080 q^{61} +2.60007 q^{62} +2.53214 q^{63} +1.00000 q^{64} -6.01358 q^{65} -0.352644 q^{66} -2.77186 q^{67} -4.22152 q^{68} +5.17173 q^{69} +2.60861 q^{70} -13.1071 q^{71} +2.53214 q^{72} -4.14608 q^{73} +5.64515 q^{74} +1.23451 q^{75} +6.41287 q^{76} -0.515557 q^{77} +1.57683 q^{78} +14.4494 q^{79} +2.60861 q^{80} +5.00812 q^{81} +5.21138 q^{82} +0.936990 q^{83} -0.684006 q^{84} -11.0123 q^{85} +5.23218 q^{86} -6.54695 q^{87} -0.515557 q^{88} -4.79799 q^{89} +6.60535 q^{90} +2.30528 q^{91} +7.56095 q^{92} -1.77846 q^{93} -13.6244 q^{94} +16.7287 q^{95} -0.684006 q^{96} -8.69140 q^{97} -1.00000 q^{98} -1.30546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 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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