LMFDB - Embedded newform 6034.2.a.o.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.45476 q^{3} +1.00000 q^{4} +0.421306 q^{5} +1.45476 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.883670 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.45476 q^{3} +1.00000 q^{4} +0.421306 q^{5} +1.45476 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.883670 q^{9} -0.421306 q^{10} +5.56306 q^{11} -1.45476 q^{12} -6.08610 q^{13} +1.00000 q^{14} -0.612900 q^{15} +1.00000 q^{16} +1.25017 q^{17} +0.883670 q^{18} +2.04223 q^{19} +0.421306 q^{20} +1.45476 q^{21} -5.56306 q^{22} +5.01283 q^{23} +1.45476 q^{24} -4.82250 q^{25} +6.08610 q^{26} +5.64981 q^{27} -1.00000 q^{28} +1.55048 q^{29} +0.612900 q^{30} -10.2403 q^{31} -1.00000 q^{32} -8.09293 q^{33} -1.25017 q^{34} -0.421306 q^{35} -0.883670 q^{36} -1.18687 q^{37} -2.04223 q^{38} +8.85382 q^{39} -0.421306 q^{40} -8.49672 q^{41} -1.45476 q^{42} +7.73270 q^{43} +5.56306 q^{44} -0.372296 q^{45} -5.01283 q^{46} +7.91813 q^{47} -1.45476 q^{48} +1.00000 q^{49} +4.82250 q^{50} -1.81870 q^{51} -6.08610 q^{52} +2.13148 q^{53} -5.64981 q^{54} +2.34375 q^{55} +1.00000 q^{56} -2.97096 q^{57} -1.55048 q^{58} +5.95981 q^{59} -0.612900 q^{60} -10.4363 q^{61} +10.2403 q^{62} +0.883670 q^{63} +1.00000 q^{64} -2.56411 q^{65} +8.09293 q^{66} -3.25549 q^{67} +1.25017 q^{68} -7.29247 q^{69} +0.421306 q^{70} +9.78075 q^{71} +0.883670 q^{72} +4.82654 q^{73} +1.18687 q^{74} +7.01559 q^{75} +2.04223 q^{76} -5.56306 q^{77} -8.85382 q^{78} -9.27657 q^{79} +0.421306 q^{80} -5.56812 q^{81} +8.49672 q^{82} +7.33151 q^{83} +1.45476 q^{84} +0.526704 q^{85} -7.73270 q^{86} -2.25558 q^{87} -5.56306 q^{88} +0.964727 q^{89} +0.372296 q^{90} +6.08610 q^{91} +5.01283 q^{92} +14.8972 q^{93} -7.91813 q^{94} +0.860406 q^{95} +1.45476 q^{96} +5.02549 q^{97} -1.00000 q^{98} -4.91591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.45476	−0.839907	−0.419953	−	0.907546i	$-0.637954\pi$
$3$	−1.45476	−0.839907	−0.419953	+	0.907546i	$0.637954\pi$
$4$	1.00000	0.500000
$5$	0.421306	0.188414	0.0942070	−	0.995553i	$-0.469968\pi$
$5$	0.421306	0.188414	0.0942070	+	0.995553i	$0.469968\pi$
$6$	1.45476	0.593904
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.883670	−0.294557
$10$	−0.421306	−0.133229
$11$	5.56306	1.67733	0.838664	−	0.544650i	$-0.183337\pi$
$11$	5.56306	1.67733	0.838664	+	0.544650i	$0.183337\pi$
$12$	−1.45476	−0.419953
$13$	−6.08610	−1.68798	−0.843990	−	0.536359i	$-0.819799\pi$
$13$	−6.08610	−1.68798	−0.843990	+	0.536359i	$0.819799\pi$
$14$	1.00000	0.267261
$15$	−0.612900	−0.158250
$16$	1.00000	0.250000
$17$	1.25017	0.303210	0.151605	−	0.988441i	$-0.451556\pi$
$17$	1.25017	0.303210	0.151605	+	0.988441i	$0.451556\pi$
$18$	0.883670	0.208283
$19$	2.04223	0.468521	0.234260	−	0.972174i	$-0.424733\pi$
$19$	2.04223	0.468521	0.234260	+	0.972174i	$0.424733\pi$
$20$	0.421306	0.0942070
$21$	1.45476	0.317455
$22$	−5.56306	−1.18605
$23$	5.01283	1.04525	0.522624	−	0.852564i	$-0.324953\pi$
$23$	5.01283	1.04525	0.522624	+	0.852564i	$0.324953\pi$
$24$	1.45476	0.296952
$25$	−4.82250	−0.964500
$26$	6.08610	1.19358
$27$	5.64981	1.08731
$28$	−1.00000	−0.188982
$29$	1.55048	0.287917	0.143958	−	0.989584i	$-0.454017\pi$
$29$	1.55048	0.287917	0.143958	+	0.989584i	$0.454017\pi$
$30$	0.612900	0.111900
$31$	−10.2403	−1.83922	−0.919608	−	0.392837i	$-0.871494\pi$
$31$	−10.2403	−1.83922	−0.919608	+	0.392837i	$0.871494\pi$
$32$	−1.00000	−0.176777
$33$	−8.09293	−1.40880
$34$	−1.25017	−0.214402
$35$	−0.421306	−0.0712138
$36$	−0.883670	−0.147278
$37$	−1.18687	−0.195121	−0.0975604	−	0.995230i	$-0.531104\pi$
$37$	−1.18687	−0.195121	−0.0975604	+	0.995230i	$0.531104\pi$
$38$	−2.04223	−0.331294
$39$	8.85382	1.41775
$40$	−0.421306	−0.0666144
$41$	−8.49672	−1.32697	−0.663483	−	0.748192i	$-0.730922\pi$
$41$	−8.49672	−1.32697	−0.663483	+	0.748192i	$0.730922\pi$
$42$	−1.45476	−0.224475
$43$	7.73270	1.17923	0.589613	−	0.807686i	$-0.299280\pi$
$43$	7.73270	1.17923	0.589613	+	0.807686i	$0.299280\pi$
$44$	5.56306	0.838664
$45$	−0.372296	−0.0554986
$46$	−5.01283	−0.739101
$47$	7.91813	1.15498	0.577489	−	0.816398i	$-0.304033\pi$
$47$	7.91813	1.15498	0.577489	+	0.816398i	$0.304033\pi$
$48$	−1.45476	−0.209977
$49$	1.00000	0.142857
$50$	4.82250	0.682005
$51$	−1.81870	−0.254668
$52$	−6.08610	−0.843990
$53$	2.13148	0.292781	0.146390	−	0.989227i	$-0.453234\pi$
$53$	2.13148	0.292781	0.146390	+	0.989227i	$0.453234\pi$
$54$	−5.64981	−0.768842
$55$	2.34375	0.316032
$56$	1.00000	0.133631
$57$	−2.97096	−0.393514
$58$	−1.55048	−0.203588
$59$	5.95981	0.775902	0.387951	−	0.921680i	$-0.373183\pi$
$59$	5.95981	0.775902	0.387951	+	0.921680i	$0.373183\pi$
$60$	−0.612900	−0.0791251
$61$	−10.4363	−1.33623	−0.668116	−	0.744057i	$-0.732899\pi$
$61$	−10.4363	−1.33623	−0.668116	+	0.744057i	$0.732899\pi$
$62$	10.2403	1.30052
$63$	0.883670	0.111332
$64$	1.00000	0.125000
$65$	−2.56411	−0.318039
$66$	8.09293	0.996171
$67$	−3.25549	−0.397722	−0.198861	−	0.980028i	$-0.563724\pi$
$67$	−3.25549	−0.397722	−0.198861	+	0.980028i	$0.563724\pi$
$68$	1.25017	0.151605
$69$	−7.29247	−0.877910
$70$	0.421306	0.0503557
$71$	9.78075	1.16076	0.580381	−	0.814345i	$-0.302904\pi$
$71$	9.78075	1.16076	0.580381	+	0.814345i	$0.302904\pi$
$72$	0.883670	0.104141
$73$	4.82654	0.564904	0.282452	−	0.959281i	$-0.408852\pi$
$73$	4.82654	0.564904	0.282452	+	0.959281i	$0.408852\pi$
$74$	1.18687	0.137971
$75$	7.01559	0.810090
$76$	2.04223	0.234260
$77$	−5.56306	−0.633970
$78$	−8.85382	−1.00250
$79$	−9.27657	−1.04370	−0.521848	−	0.853039i	$-0.674757\pi$
$79$	−9.27657	−1.04370	−0.521848	+	0.853039i	$0.674757\pi$
$80$	0.421306	0.0471035
$81$	−5.56812	−0.618680
$82$	8.49672	0.938306
$83$	7.33151	0.804738	0.402369	−	0.915478i	$-0.368187\pi$
$83$	7.33151	0.804738	0.402369	+	0.915478i	$0.368187\pi$
$84$	1.45476	0.158727
$85$	0.526704	0.0571291
$86$	−7.73270	−0.833838
$87$	−2.25558	−0.241823
$88$	−5.56306	−0.593025
$89$	0.964727	0.102261	0.0511304	−	0.998692i	$-0.483718\pi$
$89$	0.964727	0.102261	0.0511304	+	0.998692i	$0.483718\pi$
$90$	0.372296	0.0392434
$91$	6.08610	0.637997
$92$	5.01283	0.522624
$93$	14.8972	1.54477
$94$	−7.91813	−0.816693
$95$	0.860406	0.0882758
$96$	1.45476	0.148476
$97$	5.02549	0.510262	0.255131	−	0.966907i	$-0.417881\pi$
$97$	5.02549	0.510262	0.255131	+	0.966907i	$0.417881\pi$
$98$	−1.00000	−0.101015
$99$	−4.91591	−0.494068
$100$	−4.82250	−0.482250
$101$	−19.2626	−1.91670	−0.958348	−	0.285602i	$-0.907807\pi$
$101$	−19.2626	−1.91670	−0.958348	+	0.285602i	$0.907807\pi$
$102$	1.81870	0.180078
$103$	−6.00413	−0.591604	−0.295802	−	0.955249i	$-0.595587\pi$
$103$	−6.00413	−0.591604	−0.295802	+	0.955249i	$0.595587\pi$
$104$	6.08610	0.596791
$105$	0.612900	0.0598129
$106$	−2.13148	−0.207027
$107$	−0.940072	−0.0908802	−0.0454401	−	0.998967i	$-0.514469\pi$
$107$	−0.940072	−0.0908802	−0.0454401	+	0.998967i	$0.514469\pi$
$108$	5.64981	0.543653
$109$	0.270368	0.0258965	0.0129483	−	0.999916i	$-0.495878\pi$
$109$	0.270368	0.0258965	0.0129483	+	0.999916i	$0.495878\pi$
$110$	−2.34375	−0.223468
$111$	1.72662	0.163883
$112$	−1.00000	−0.0944911
$113$	5.40238	0.508213	0.254107	−	0.967176i	$-0.418219\pi$
$113$	5.40238	0.508213	0.254107	+	0.967176i	$0.418219\pi$
$114$	2.97096	0.278256
$115$	2.11194	0.196939
$116$	1.55048	0.143958
$117$	5.37810	0.497206
$118$	−5.95981	−0.548645
$119$	−1.25017	−0.114603
$120$	0.612900	0.0559499
$121$	19.9477	1.81343
$122$	10.4363	0.944859
$123$	12.3607	1.11453
$124$	−10.2403	−0.919608
$125$	−4.13828	−0.370139
$126$	−0.883670	−0.0787235
$127$	−7.83760	−0.695475	−0.347737	−	0.937592i	$-0.613050\pi$
$127$	−7.83760	−0.695475	−0.347737	+	0.937592i	$0.613050\pi$
$128$	−1.00000	−0.0883883
$129$	−11.2492	−0.990440
$130$	2.56411	0.224888
$131$	8.96924	0.783646	0.391823	−	0.920041i	$-0.371845\pi$
$131$	8.96924	0.783646	0.391823	+	0.920041i	$0.371845\pi$
$132$	−8.09293	−0.704399
$133$	−2.04223	−0.177084
$134$	3.25549	0.281232
$135$	2.38030	0.204864
$136$	−1.25017	−0.107201
$137$	16.0926	1.37488	0.687440	−	0.726241i	$-0.258734\pi$
$137$	16.0926	1.37488	0.687440	+	0.726241i	$0.258734\pi$
$138$	7.29247	0.620776
$139$	−18.0080	−1.52742	−0.763710	−	0.645560i	$-0.776624\pi$
$139$	−18.0080	−1.52742	−0.763710	+	0.645560i	$0.776624\pi$
$140$	−0.421306	−0.0356069
$141$	−11.5190	−0.970074
$142$	−9.78075	−0.820782
$143$	−33.8574	−2.83130
$144$	−0.883670	−0.0736391
$145$	0.653226	0.0542475
$146$	−4.82654	−0.399447
$147$	−1.45476	−0.119987
$148$	−1.18687	−0.0975604
$149$	3.13366	0.256719	0.128360	−	0.991728i	$-0.459029\pi$
$149$	3.13366	0.256719	0.128360	+	0.991728i	$0.459029\pi$
$150$	−7.01559	−0.572820
$151$	12.9380	1.05288	0.526440	−	0.850212i	$-0.323526\pi$
$151$	12.9380	1.05288	0.526440	+	0.850212i	$0.323526\pi$
$152$	−2.04223	−0.165647
$153$	−1.10474	−0.0893126
$154$	5.56306	0.448285
$155$	−4.31431	−0.346534
$156$	8.85382	0.708873
$157$	−21.0822	−1.68254	−0.841272	−	0.540612i	$-0.818193\pi$
$157$	−21.0822	−1.68254	−0.841272	+	0.540612i	$0.818193\pi$
$158$	9.27657	0.738004
$159$	−3.10079	−0.245909
$160$	−0.421306	−0.0333072
$161$	−5.01283	−0.395066
$162$	5.56812	0.437473
$163$	−22.1108	−1.73185	−0.865926	−	0.500172i	$-0.833270\pi$
$163$	−22.1108	−1.73185	−0.865926	+	0.500172i	$0.833270\pi$
$164$	−8.49672	−0.663483
$165$	−3.40960	−0.265437
$166$	−7.33151	−0.569035
$167$	21.7142	1.68029	0.840146	−	0.542360i	$-0.182469\pi$
$167$	21.7142	1.68029	0.840146	+	0.542360i	$0.182469\pi$
$168$	−1.45476	−0.112237
$169$	24.0406	1.84928
$170$	−0.526704	−0.0403964
$171$	−1.80466	−0.138006
$172$	7.73270	0.589613
$173$	−6.82214	−0.518678	−0.259339	−	0.965786i	$-0.583505\pi$
$173$	−6.82214	−0.518678	−0.259339	+	0.965786i	$0.583505\pi$
$174$	2.25558	0.170995
$175$	4.82250	0.364547
$176$	5.56306	0.419332
$177$	−8.67011	−0.651685
$178$	−0.964727	−0.0723093
$179$	−7.40284	−0.553314	−0.276657	−	0.960969i	$-0.589227\pi$
$179$	−7.40284	−0.553314	−0.276657	+	0.960969i	$0.589227\pi$
$180$	−0.372296	−0.0277493
$181$	−6.36717	−0.473268	−0.236634	−	0.971599i	$-0.576044\pi$
$181$	−6.36717	−0.473268	−0.236634	+	0.971599i	$0.576044\pi$
$182$	−6.08610	−0.451132
$183$	15.1823	1.12231
$184$	−5.01283	−0.369551
$185$	−0.500037	−0.0367635
$186$	−14.8972	−1.09232
$187$	6.95477	0.508583
$188$	7.91813	0.577489
$189$	−5.64981	−0.410963
$190$	−0.860406	−0.0624204
$191$	−0.834880	−0.0604098	−0.0302049	−	0.999544i	$-0.509616\pi$
$191$	−0.834880	−0.0604098	−0.0302049	+	0.999544i	$0.509616\pi$
$192$	−1.45476	−0.104988
$193$	−3.21837	−0.231664	−0.115832	−	0.993269i	$-0.536953\pi$
$193$	−3.21837	−0.231664	−0.115832	+	0.993269i	$0.536953\pi$
$194$	−5.02549	−0.360809
$195$	3.73017	0.267123
$196$	1.00000	0.0714286
$197$	11.2654	0.802624	0.401312	−	0.915941i	$-0.368554\pi$
$197$	11.2654	0.802624	0.401312	+	0.915941i	$0.368554\pi$
$198$	4.91591	0.349359
$199$	−5.03701	−0.357064	−0.178532	−	0.983934i	$-0.557135\pi$
$199$	−5.03701	−0.357064	−0.178532	+	0.983934i	$0.557135\pi$
$200$	4.82250	0.341002
$201$	4.73597	0.334049
$202$	19.2626	1.35531
$203$	−1.55048	−0.108822
$204$	−1.81870	−0.127334
$205$	−3.57972	−0.250019
$206$	6.00413	0.418328
$207$	−4.42968	−0.307884
$208$	−6.08610	−0.421995
$209$	11.3611	0.785862
$210$	−0.612900	−0.0422941
$211$	−18.4805	−1.27225	−0.636125	−	0.771586i	$-0.719464\pi$
$211$	−18.4805	−1.27225	−0.636125	+	0.771586i	$0.719464\pi$
$212$	2.13148	0.146390
$213$	−14.2287	−0.974931
$214$	0.940072	0.0642620
$215$	3.25784	0.222183
$216$	−5.64981	−0.384421
$217$	10.2403	0.695158
$218$	−0.270368	−0.0183116
$219$	−7.02146	−0.474467
$220$	2.34375	0.158016
$221$	−7.60865	−0.511813
$222$	−1.72662	−0.115883
$223$	0.384833	0.0257703	0.0128851	−	0.999917i	$-0.495898\pi$
$223$	0.384833	0.0257703	0.0128851	+	0.999917i	$0.495898\pi$
$224$	1.00000	0.0668153
$225$	4.26150	0.284100
$226$	−5.40238	−0.359361
$227$	21.5978	1.43350	0.716749	−	0.697332i	$-0.245629\pi$
$227$	21.5978	1.43350	0.716749	+	0.697332i	$0.245629\pi$
$228$	−2.97096	−0.196757
$229$	23.3157	1.54075	0.770374	−	0.637593i	$-0.220070\pi$
$229$	23.3157	1.54075	0.770374	+	0.637593i	$0.220070\pi$
$230$	−2.11194	−0.139257
$231$	8.09293	0.532476
$232$	−1.55048	−0.101794
$233$	7.24555	0.474672	0.237336	−	0.971428i	$-0.423726\pi$
$233$	7.24555	0.474672	0.237336	+	0.971428i	$0.423726\pi$
$234$	−5.37810	−0.351577
$235$	3.33596	0.217614
$236$	5.95981	0.387951
$237$	13.4952	0.876607
$238$	1.25017	0.0810364
$239$	−27.2368	−1.76180	−0.880900	−	0.473302i	$-0.843062\pi$
$239$	−27.2368	−1.76180	−0.880900	+	0.473302i	$0.843062\pi$
$240$	−0.612900	−0.0395625
$241$	21.6841	1.39679	0.698397	−	0.715711i	$-0.253897\pi$
$241$	21.6841	1.39679	0.698397	+	0.715711i	$0.253897\pi$
$242$	−19.9477	−1.28229
$243$	−8.84915	−0.567673
$244$	−10.4363	−0.668116
$245$	0.421306	0.0269163
$246$	−12.3607	−0.788090
$247$	−12.4292	−0.790853
$248$	10.2403	0.650261
$249$	−10.6656	−0.675905
$250$	4.13828	0.261728
$251$	−21.2509	−1.34135	−0.670673	−	0.741753i	$-0.733995\pi$
$251$	−21.2509	−1.34135	−0.670673	+	0.741753i	$0.733995\pi$
$252$	0.883670	0.0556660
$253$	27.8867	1.75322
$254$	7.83760	0.491775
$255$	−0.766229	−0.0479831
$256$	1.00000	0.0625000
$257$	−14.0457	−0.876147	−0.438074	−	0.898939i	$-0.644339\pi$
$257$	−14.0457	−0.876147	−0.438074	+	0.898939i	$0.644339\pi$
$258$	11.2492	0.700347
$259$	1.18687	0.0737487
$260$	−2.56411	−0.159020
$261$	−1.37011	−0.0848077
$262$	−8.96924	−0.554121
$263$	18.0466	1.11280	0.556399	−	0.830915i	$-0.312182\pi$
$263$	18.0466	1.11280	0.556399	+	0.830915i	$0.312182\pi$
$264$	8.09293	0.498085
$265$	0.898005	0.0551640
$266$	2.04223	0.125217
$267$	−1.40345	−0.0858896
$268$	−3.25549	−0.198861
$269$	−0.939086	−0.0572571	−0.0286285	−	0.999590i	$-0.509114\pi$
$269$	−0.939086	−0.0572571	−0.0286285	+	0.999590i	$0.509114\pi$
$270$	−2.38030	−0.144861
$271$	−5.74490	−0.348978	−0.174489	−	0.984659i	$-0.555827\pi$
$271$	−5.74490	−0.348978	−0.174489	+	0.984659i	$0.555827\pi$
$272$	1.25017	0.0758026
$273$	−8.85382	−0.535858
$274$	−16.0926	−0.972187
$275$	−26.8279	−1.61778
$276$	−7.29247	−0.438955
$277$	20.7704	1.24797	0.623987	−	0.781434i	$-0.285512\pi$
$277$	20.7704	1.24797	0.623987	+	0.781434i	$0.285512\pi$
$278$	18.0080	1.08005
$279$	9.04906	0.541753
$280$	0.421306	0.0251779
$281$	−6.32373	−0.377242	−0.188621	−	0.982050i	$-0.560402\pi$
$281$	−6.32373	−0.377242	−0.188621	+	0.982050i	$0.560402\pi$
$282$	11.5190	0.685946
$283$	1.31191	0.0779847	0.0389924	−	0.999240i	$-0.487585\pi$
$283$	1.31191	0.0779847	0.0389924	+	0.999240i	$0.487585\pi$
$284$	9.78075	0.580381
$285$	−1.25169	−0.0741434
$286$	33.8574	2.00203
$287$	8.49672	0.501546
$288$	0.883670	0.0520707
$289$	−15.4371	−0.908063
$290$	−0.653226	−0.0383588
$291$	−7.31090	−0.428572
$292$	4.82654	0.282452
$293$	−4.22593	−0.246882	−0.123441	−	0.992352i	$-0.539393\pi$
$293$	−4.22593	−0.246882	−0.123441	+	0.992352i	$0.539393\pi$
$294$	1.45476	0.0848434
$295$	2.51091	0.146191
$296$	1.18687	0.0689856
$297$	31.4303	1.82377
$298$	−3.13366	−0.181528
$299$	−30.5086	−1.76436
$300$	7.01559	0.405045
$301$	−7.73270	−0.445705
$302$	−12.9380	−0.744499
$303$	28.0224	1.60985
$304$	2.04223	0.117130
$305$	−4.39689	−0.251765
$306$	1.10474	0.0631535
$307$	−24.3325	−1.38873	−0.694365	−	0.719623i	$-0.744314\pi$
$307$	−24.3325	−1.38873	−0.694365	+	0.719623i	$0.744314\pi$
$308$	−5.56306	−0.316985
$309$	8.73457	0.496893
$310$	4.31431	0.245037
$311$	1.38770	0.0786890	0.0393445	−	0.999226i	$-0.487473\pi$
$311$	1.38770	0.0786890	0.0393445	+	0.999226i	$0.487473\pi$
$312$	−8.85382	−0.501249
$313$	1.89086	0.106878	0.0534388	−	0.998571i	$-0.482982\pi$
$313$	1.89086	0.106878	0.0534388	+	0.998571i	$0.482982\pi$
$314$	21.0822	1.18974
$315$	0.372296	0.0209765
$316$	−9.27657	−0.521848
$317$	−5.74132	−0.322465	−0.161232	−	0.986916i	$-0.551547\pi$
$317$	−5.74132	−0.322465	−0.161232	+	0.986916i	$0.551547\pi$
$318$	3.10079	0.173884
$319$	8.62541	0.482930
$320$	0.421306	0.0235517
$321$	1.36758	0.0763309
$322$	5.01283	0.279354
$323$	2.55314	0.142060
$324$	−5.56812	−0.309340
$325$	29.3502	1.62806
$326$	22.1108	1.22460
$327$	−0.393321	−0.0217507
$328$	8.49672	0.469153
$329$	−7.91813	−0.436541
$330$	3.40960	0.187693
$331$	4.94444	0.271771	0.135885	−	0.990725i	$-0.456612\pi$
$331$	4.94444	0.271771	0.135885	+	0.990725i	$0.456612\pi$
$332$	7.33151	0.402369
$333$	1.04880	0.0574741
$334$	−21.7142	−1.18815
$335$	−1.37156	−0.0749363
$336$	1.45476	0.0793637
$337$	3.07094	0.167285	0.0836425	−	0.996496i	$-0.473345\pi$
$337$	3.07094	0.167285	0.0836425	+	0.996496i	$0.473345\pi$
$338$	−24.0406	−1.30764
$339$	−7.85917	−0.426852
$340$	0.526704	0.0285645
$341$	−56.9676	−3.08497
$342$	1.80466	0.0975848
$343$	−1.00000	−0.0539949
$344$	−7.73270	−0.416919
$345$	−3.07236	−0.165411
$346$	6.82214	0.366761
$347$	24.8000	1.33133	0.665667	−	0.746249i	$-0.268147\pi$
$347$	24.8000	1.33133	0.665667	+	0.746249i	$0.268147\pi$
$348$	−2.25558	−0.120912
$349$	5.91067	0.316391	0.158195	−	0.987408i	$-0.449432\pi$
$349$	5.91067	0.316391	0.158195	+	0.987408i	$0.449432\pi$
$350$	−4.82250	−0.257774
$351$	−34.3853	−1.83535
$352$	−5.56306	−0.296512
$353$	−9.18016	−0.488611	−0.244305	−	0.969698i	$-0.578560\pi$
$353$	−9.18016	−0.488611	−0.244305	+	0.969698i	$0.578560\pi$
$354$	8.67011	0.460811
$355$	4.12069	0.218704
$356$	0.964727	0.0511304
$357$	1.81870	0.0962556
$358$	7.40284	0.391252
$359$	−17.4606	−0.921537	−0.460769	−	0.887520i	$-0.652426\pi$
$359$	−17.4606	−0.921537	−0.460769	+	0.887520i	$0.652426\pi$
$360$	0.372296	0.0196217
$361$	−14.8293	−0.780489
$362$	6.36717	0.334651
$363$	−29.0191	−1.52311
$364$	6.08610	0.318998
$365$	2.03345	0.106436
$366$	−15.1823	−0.793594
$367$	−18.3687	−0.958838	−0.479419	−	0.877586i	$-0.659152\pi$
$367$	−18.3687	−0.958838	−0.479419	+	0.877586i	$0.659152\pi$
$368$	5.01283	0.261312
$369$	7.50830	0.390866
$370$	0.500037	0.0259957
$371$	−2.13148	−0.110661
$372$	14.8972	0.772385
$373$	−16.2881	−0.843364	−0.421682	−	0.906744i	$-0.638560\pi$
$373$	−16.2881	−0.843364	−0.421682	+	0.906744i	$0.638560\pi$
$374$	−6.95477	−0.359623
$375$	6.02021	0.310882
$376$	−7.91813	−0.408347
$377$	−9.43637	−0.485998
$378$	5.64981	0.290595
$379$	−16.1885	−0.831546	−0.415773	−	0.909468i	$-0.636489\pi$
$379$	−16.1885	−0.831546	−0.415773	+	0.909468i	$0.636489\pi$
$380$	0.860406	0.0441379
$381$	11.4018	0.584134
$382$	0.834880	0.0427162
$383$	−10.9908	−0.561604	−0.280802	−	0.959766i	$-0.590600\pi$
$383$	−10.9908	−0.561604	−0.280802	+	0.959766i	$0.590600\pi$
$384$	1.45476	0.0742380
$385$	−2.34375	−0.119449
$386$	3.21837	0.163811
$387$	−6.83315	−0.347349
$388$	5.02549	0.255131
$389$	−27.7972	−1.40937	−0.704687	−	0.709518i	$-0.748913\pi$
$389$	−27.7972	−1.40937	−0.704687	+	0.709518i	$0.748913\pi$
$390$	−3.73017	−0.188885
$391$	6.26688	0.316930
$392$	−1.00000	−0.0505076
$393$	−13.0481	−0.658190
$394$	−11.2654	−0.567541
$395$	−3.90828	−0.196647
$396$	−4.91591	−0.247034
$397$	−36.8589	−1.84990	−0.924948	−	0.380093i	$-0.875892\pi$
$397$	−36.8589	−1.84990	−0.924948	+	0.380093i	$0.875892\pi$
$398$	5.03701	0.252482
$399$	2.97096	0.148734
$400$	−4.82250	−0.241125
$401$	−14.9113	−0.744636	−0.372318	−	0.928105i	$-0.621437\pi$
$401$	−14.9113	−0.744636	−0.372318	+	0.928105i	$0.621437\pi$
$402$	−4.73597	−0.236208
$403$	62.3236	3.10456
$404$	−19.2626	−0.958348
$405$	−2.34588	−0.116568
$406$	1.55048	0.0769489
$407$	−6.60265	−0.327281
$408$	1.81870	0.0900389
$409$	−33.6016	−1.66149	−0.830746	−	0.556652i	$-0.812086\pi$
$409$	−33.6016	−1.66149	−0.830746	+	0.556652i	$0.812086\pi$
$410$	3.57972	0.176790
$411$	−23.4108	−1.15477
$412$	−6.00413	−0.295802
$413$	−5.95981	−0.293263
$414$	4.42968	0.217707
$415$	3.08881	0.151624
$416$	6.08610	0.298396
$417$	26.1974	1.28289
$418$	−11.3611	−0.555688
$419$	0.00271920	0.000132842 0	6.64209e−5	−	1.00000i	$-0.499979\pi$
$419$	0.00271920	0.000132842 0	6.64209e−5		1.00000i	$0.499979\pi$
$420$	0.612900	0.0299065
$421$	−20.4225	−0.995333	−0.497667	−	0.867368i	$-0.665810\pi$
$421$	−20.4225	−0.995333	−0.497667	+	0.867368i	$0.665810\pi$
$422$	18.4805	0.899617
$423$	−6.99701	−0.340206
$424$	−2.13148	−0.103514
$425$	−6.02894	−0.292446
$426$	14.2287	0.689381
$427$	10.4363	0.505049
$428$	−0.940072	−0.0454401
$429$	49.2544	2.37802
$430$	−3.25784	−0.157107
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.64981	0.271827
$433$	−28.6327	−1.37600	−0.687999	−	0.725712i	$-0.741511\pi$
$433$	−28.6327	−1.37600	−0.687999	+	0.725712i	$0.741511\pi$
$434$	−10.2403	−0.491551
$435$	−0.950288	−0.0455628
$436$	0.270368	0.0129483
$437$	10.2374	0.489720
$438$	7.02146	0.335499
$439$	23.9600	1.14355	0.571773	−	0.820412i	$-0.306256\pi$
$439$	23.9600	1.14355	0.571773	+	0.820412i	$0.306256\pi$
$440$	−2.34375	−0.111734
$441$	−0.883670	−0.0420795
$442$	7.60865	0.361907
$443$	−32.6656	−1.55199	−0.775996	−	0.630738i	$-0.782752\pi$
$443$	−32.6656	−1.55199	−0.775996	+	0.630738i	$0.782752\pi$
$444$	1.72662	0.0819417
$445$	0.406446	0.0192674
$446$	−0.384833	−0.0182224
$447$	−4.55872	−0.215620
$448$	−1.00000	−0.0472456
$449$	−4.45417	−0.210206	−0.105103	−	0.994461i	$-0.533517\pi$
$449$	−4.45417	−0.210206	−0.105103	+	0.994461i	$0.533517\pi$
$450$	−4.26150	−0.200889
$451$	−47.2678	−2.22576
$452$	5.40238	0.254107
$453$	−18.8217	−0.884322
$454$	−21.5978	−1.01364
$455$	2.56411	0.120207
$456$	2.97096	0.139128
$457$	−2.18612	−0.102262	−0.0511312	−	0.998692i	$-0.516283\pi$
$457$	−2.18612	−0.102262	−0.0511312	+	0.998692i	$0.516283\pi$
$458$	−23.3157	−1.08947
$459$	7.06322	0.329683
$460$	2.11194	0.0984696
$461$	5.15255	0.239978	0.119989	−	0.992775i	$-0.461714\pi$
$461$	5.15255	0.239978	0.119989	+	0.992775i	$0.461714\pi$
$462$	−8.09293	−0.376517
$463$	18.6944	0.868804	0.434402	−	0.900719i	$-0.356960\pi$
$463$	18.6944	0.868804	0.434402	+	0.900719i	$0.356960\pi$
$464$	1.55048	0.0719791
$465$	6.27630	0.291056
$466$	−7.24555	−0.335643
$467$	−2.07104	−0.0958362	−0.0479181	−	0.998851i	$-0.515259\pi$
$467$	−2.07104	−0.0958362	−0.0479181	+	0.998851i	$0.515259\pi$
$468$	5.37810	0.248603
$469$	3.25549	0.150325
$470$	−3.33596	−0.153876
$471$	30.6696	1.41318
$472$	−5.95981	−0.274323
$473$	43.0175	1.97795
$474$	−13.4952	−0.619855
$475$	−9.84867	−0.451888
$476$	−1.25017	−0.0573014
$477$	−1.88352	−0.0862405
$478$	27.2368	1.24578
$479$	−31.3208	−1.43108	−0.715542	−	0.698569i	$-0.753820\pi$
$479$	−31.3208	−1.43108	−0.715542	+	0.698569i	$0.753820\pi$
$480$	0.612900	0.0279749
$481$	7.22343	0.329360
$482$	−21.6841	−0.987682
$483$	7.29247	0.331819
$484$	19.9477	0.906713
$485$	2.11727	0.0961404
$486$	8.84915	0.401406
$487$	−21.9057	−0.992643	−0.496321	−	0.868139i	$-0.665316\pi$
$487$	−21.9057	−0.992643	−0.496321	+	0.868139i	$0.665316\pi$
$488$	10.4363	0.472430
$489$	32.1660	1.45459
$490$	−0.421306	−0.0190327
$491$	−31.3320	−1.41399	−0.706996	−	0.707218i	$-0.749950\pi$
$491$	−31.3320	−1.41399	−0.706996	+	0.707218i	$0.749950\pi$
$492$	12.3607	0.557264
$493$	1.93836	0.0872993
$494$	12.4292	0.559218
$495$	−2.07110	−0.0930892
$496$	−10.2403	−0.459804
$497$	−9.78075	−0.438727
$498$	10.6656	0.477937
$499$	−8.41497	−0.376706	−0.188353	−	0.982101i	$-0.560315\pi$
$499$	−8.41497	−0.376706	−0.188353	+	0.982101i	$0.560315\pi$
$500$	−4.13828	−0.185070
$501$	−31.5889	−1.41129
$502$	21.2509	0.948475
$503$	−28.2155	−1.25807	−0.629033	−	0.777378i	$-0.716549\pi$
$503$	−28.2155	−1.25807	−0.629033	+	0.777378i	$0.716549\pi$
$504$	−0.883670	−0.0393618
$505$	−8.11544	−0.361132
$506$	−27.8867	−1.23971
$507$	−34.9734	−1.55322
$508$	−7.83760	−0.347737
$509$	−42.3484	−1.87706	−0.938530	−	0.345197i	$-0.887812\pi$
$509$	−42.3484	−1.87706	−0.938530	+	0.345197i	$0.887812\pi$
$510$	0.766229	0.0339292
$511$	−4.82654	−0.213514
$512$	−1.00000	−0.0441942
$513$	11.5382	0.509426
$514$	14.0457	0.619530
$515$	−2.52958	−0.111467
$516$	−11.2492	−0.495220
$517$	44.0491	1.93728
$518$	−1.18687	−0.0521482
$519$	9.92459	0.435641
$520$	2.56411	0.112444
$521$	−11.8638	−0.519763	−0.259881	−	0.965641i	$-0.583683\pi$
$521$	−11.8638	−0.519763	−0.259881	+	0.965641i	$0.583683\pi$
$522$	1.37011	0.0599681
$523$	44.3106	1.93757	0.968784	−	0.247907i	$-0.0797428\pi$
$523$	44.3106	1.93757	0.968784	+	0.247907i	$0.0797428\pi$
$524$	8.96924	0.391823
$525$	−7.01559	−0.306185
$526$	−18.0466	−0.786867
$527$	−12.8021	−0.557670
$528$	−8.09293	−0.352200
$529$	2.12845	0.0925414
$530$	−0.898005	−0.0390068
$531$	−5.26651	−0.228547
$532$	−2.04223	−0.0885421
$533$	51.7119	2.23989
$534$	1.40345	0.0607331
$535$	−0.396058	−0.0171231
$536$	3.25549	0.140616
$537$	10.7694	0.464733
$538$	0.939086	0.0404869
$539$	5.56306	0.239618
$540$	2.38030	0.102432
$541$	−13.6392	−0.586395	−0.293197	−	0.956052i	$-0.594719\pi$
$541$	−13.6392	−0.586395	−0.293197	+	0.956052i	$0.594719\pi$
$542$	5.74490	0.246764
$543$	9.26271	0.397501
$544$	−1.25017	−0.0536005
$545$	0.113908	0.00487927
$546$	8.85382	0.378909
$547$	10.2923	0.440067	0.220034	−	0.975492i	$-0.429383\pi$
$547$	10.2923	0.440067	0.220034	+	0.975492i	$0.429383\pi$
$548$	16.0926	0.687440
$549$	9.22225	0.393596
$550$	26.8279	1.14394
$551$	3.16644	0.134895
$552$	7.29247	0.310388
$553$	9.27657	0.394480
$554$	−20.7704	−0.882451
$555$	0.727435	0.0308779
$556$	−18.0080	−0.763710
$557$	5.68100	0.240712	0.120356	−	0.992731i	$-0.461596\pi$
$557$	5.68100	0.240712	0.120356	+	0.992731i	$0.461596\pi$
$558$	−9.04906	−0.383077
$559$	−47.0620	−1.99051
$560$	−0.421306	−0.0178034
$561$	−10.1175	−0.427162
$562$	6.32373	0.266750
$563$	29.4415	1.24081	0.620406	−	0.784281i	$-0.286968\pi$
$563$	29.4415	1.24081	0.620406	+	0.784281i	$0.286968\pi$
$564$	−11.5190	−0.485037
$565$	2.27606	0.0957544
$566$	−1.31191	−0.0551435
$567$	5.56812	0.233839
$568$	−9.78075	−0.410391
$569$	−7.69948	−0.322779	−0.161390	−	0.986891i	$-0.551598\pi$
$569$	−7.69948	−0.322779	−0.161390	+	0.986891i	$0.551598\pi$
$570$	1.25169	0.0524273
$571$	17.6540	0.738798	0.369399	−	0.929271i	$-0.379564\pi$
$571$	17.6540	0.738798	0.369399	+	0.929271i	$0.379564\pi$
$572$	−33.8574	−1.41565
$573$	1.21455	0.0507386
$574$	−8.49672	−0.354646
$575$	−24.1744	−1.00814
$576$	−0.883670	−0.0368196
$577$	46.2083	1.92368	0.961839	−	0.273616i	$-0.0882199\pi$
$577$	46.2083	1.92368	0.961839	+	0.273616i	$0.0882199\pi$
$578$	15.4371	0.642098
$579$	4.68196	0.194576
$580$	0.653226	0.0271237
$581$	−7.33151	−0.304162
$582$	7.31090	0.303046
$583$	11.8575	0.491089
$584$	−4.82654	−0.199724
$585$	2.26583	0.0936805
$586$	4.22593	0.174572
$587$	20.1481	0.831600	0.415800	−	0.909456i	$-0.363502\pi$
$587$	20.1481	0.831600	0.415800	+	0.909456i	$0.363502\pi$
$588$	−1.45476	−0.0599933
$589$	−20.9131	−0.861711
$590$	−2.51091	−0.103372
$591$	−16.3884	−0.674129
$592$	−1.18687	−0.0487802
$593$	15.4440	0.634208	0.317104	−	0.948391i	$-0.397290\pi$
$593$	15.4440	0.634208	0.317104	+	0.948391i	$0.397290\pi$
$594$	−31.4303	−1.28960
$595$	−0.526704	−0.0215928
$596$	3.13366	0.128360
$597$	7.32765	0.299901
$598$	30.5086	1.24759
$599$	38.9589	1.59182	0.795909	−	0.605417i	$-0.206994\pi$
$599$	38.9589	1.59182	0.795909	+	0.605417i	$0.206994\pi$
$600$	−7.01559	−0.286410
$601$	−4.82773	−0.196927	−0.0984636	−	0.995141i	$-0.531393\pi$
$601$	−4.82773	−0.196927	−0.0984636	+	0.995141i	$0.531393\pi$
$602$	7.73270	0.315161
$603$	2.87678	0.117152
$604$	12.9380	0.526440
$605$	8.40409	0.341675
$606$	−28.0224	−1.13833
$607$	−45.7025	−1.85501	−0.927505	−	0.373812i	$-0.878051\pi$
$607$	−45.7025	−1.85501	−0.927505	+	0.373812i	$0.878051\pi$
$608$	−2.04223	−0.0828235
$609$	2.25558	0.0914005
$610$	4.39689	0.178025
$611$	−48.1905	−1.94958
$612$	−1.10474	−0.0446563
$613$	34.6858	1.40095	0.700473	−	0.713679i	$-0.252972\pi$
$613$	34.6858	1.40095	0.700473	+	0.713679i	$0.252972\pi$
$614$	24.3325	0.981980
$615$	5.20764	0.209992
$616$	5.56306	0.224142
$617$	−33.7853	−1.36015	−0.680073	−	0.733144i	$-0.738052\pi$
$617$	−33.7853	−1.36015	−0.680073	+	0.733144i	$0.738052\pi$
$618$	−8.73457	−0.351356
$619$	28.3535	1.13962	0.569811	−	0.821776i	$-0.307016\pi$
$619$	28.3535	1.13962	0.569811	+	0.821776i	$0.307016\pi$
$620$	−4.31431	−0.173267
$621$	28.3215	1.13650
$622$	−1.38770	−0.0556415
$623$	−0.964727	−0.0386510
$624$	8.85382	0.354437
$625$	22.3690	0.894761
$626$	−1.89086	−0.0755739
$627$	−16.5277	−0.660051
$628$	−21.0822	−0.841272
$629$	−1.48379	−0.0591627
$630$	−0.372296	−0.0148326
$631$	−36.3342	−1.44644	−0.723220	−	0.690617i	$-0.757339\pi$
$631$	−36.3342	−1.44644	−0.723220	+	0.690617i	$0.757339\pi$
$632$	9.27657	0.369002
$633$	26.8847	1.06857
$634$	5.74132	0.228017
$635$	−3.30203	−0.131037
$636$	−3.10079	−0.122954
$637$	−6.08610	−0.241140
$638$	−8.62541	−0.341483
$639$	−8.64295	−0.341910
$640$	−0.421306	−0.0166536
$641$	−11.5337	−0.455552	−0.227776	−	0.973714i	$-0.573145\pi$
$641$	−11.5337	−0.455552	−0.227776	+	0.973714i	$0.573145\pi$
$642$	−1.36758	−0.0539741
$643$	−18.6206	−0.734326	−0.367163	−	0.930157i	$-0.619671\pi$
$643$	−18.6206	−0.734326	−0.367163	+	0.930157i	$0.619671\pi$
$644$	−5.01283	−0.197533
$645$	−4.73937	−0.186613
$646$	−2.55314	−0.100452
$647$	−29.1576	−1.14630	−0.573152	−	0.819449i	$-0.694280\pi$
$647$	−29.1576	−1.14630	−0.573152	+	0.819449i	$0.694280\pi$
$648$	5.56812	0.218736
$649$	33.1548	1.30144
$650$	−29.3502	−1.15121
$651$	−14.8972	−0.583868
$652$	−22.1108	−0.865926
$653$	13.9118	0.544409	0.272205	−	0.962239i	$-0.412247\pi$
$653$	13.9118	0.544409	0.272205	+	0.962239i	$0.412247\pi$
$654$	0.393321	0.0153800
$655$	3.77880	0.147650
$656$	−8.49672	−0.331741
$657$	−4.26507	−0.166396
$658$	7.91813	0.308681
$659$	5.15640	0.200865	0.100432	−	0.994944i	$-0.467977\pi$
$659$	5.15640	0.200865	0.100432	+	0.994944i	$0.467977\pi$
$660$	−3.40960	−0.132719
$661$	−30.6012	−1.19025	−0.595124	−	0.803634i	$-0.702897\pi$
$661$	−30.6012	−1.19025	−0.595124	+	0.803634i	$0.702897\pi$
$662$	−4.94444	−0.192171
$663$	11.0688	0.429875
$664$	−7.33151	−0.284518
$665$	−0.860406	−0.0333651
$666$	−1.04880	−0.0406403
$667$	7.77228	0.300944
$668$	21.7142	0.840146
$669$	−0.559840	−0.0216446
$670$	1.37156	0.0529880
$671$	−58.0579	−2.24130
$672$	−1.45476	−0.0561186
$673$	−37.3339	−1.43912	−0.719559	−	0.694432i	$-0.755656\pi$
$673$	−37.3339	−1.43912	−0.719559	+	0.694432i	$0.755656\pi$
$674$	−3.07094	−0.118288
$675$	−27.2462	−1.04871
$676$	24.0406	0.924639
$677$	−24.9450	−0.958715	−0.479358	−	0.877620i	$-0.659130\pi$
$677$	−24.9450	−0.958715	−0.479358	+	0.877620i	$0.659130\pi$
$678$	7.85917	0.301830
$679$	−5.02549	−0.192861
$680$	−0.526704	−0.0201982
$681$	−31.4197	−1.20400
$682$	56.9676	2.18140
$683$	−3.53073	−0.135100	−0.0675498	−	0.997716i	$-0.521518\pi$
$683$	−3.53073	−0.135100	−0.0675498	+	0.997716i	$0.521518\pi$
$684$	−1.80466	−0.0690029
$685$	6.77990	0.259047
$686$	1.00000	0.0381802
$687$	−33.9188	−1.29408
$688$	7.73270	0.294806
$689$	−12.9724	−0.494208
$690$	3.07236	0.116963
$691$	39.5636	1.50507	0.752536	−	0.658551i	$-0.228830\pi$
$691$	39.5636	1.50507	0.752536	+	0.658551i	$0.228830\pi$
$692$	−6.82214	−0.259339
$693$	4.91591	0.186740
$694$	−24.8000	−0.941396
$695$	−7.58689	−0.287787
$696$	2.25558	0.0854974
$697$	−10.6223	−0.402350
$698$	−5.91067	−0.223722
$699$	−10.5405	−0.398680
$700$	4.82250	0.182273
$701$	−20.9005	−0.789402	−0.394701	−	0.918810i	$-0.629152\pi$
$701$	−20.9005	−0.789402	−0.394701	+	0.918810i	$0.629152\pi$
$702$	34.3853	1.29779
$703$	−2.42387	−0.0914181
$704$	5.56306	0.209666
$705$	−4.85303	−0.182776
$706$	9.18016	0.345500
$707$	19.2626	0.724443
$708$	−8.67011	−0.325843
$709$	−22.6792	−0.851734	−0.425867	−	0.904786i	$-0.640031\pi$
$709$	−22.6792	−0.851734	−0.425867	+	0.904786i	$0.640031\pi$
$710$	−4.12069	−0.154647
$711$	8.19742	0.307427
$712$	−0.964727	−0.0361547
$713$	−51.3330	−1.92244
$714$	−1.81870	−0.0680630
$715$	−14.2643	−0.533456
$716$	−7.40284	−0.276657
$717$	39.6230	1.47975
$718$	17.4606	0.651625
$719$	−22.5148	−0.839662	−0.419831	−	0.907602i	$-0.637911\pi$
$719$	−22.5148	−0.839662	−0.419831	+	0.907602i	$0.637911\pi$
$720$	−0.372296	−0.0138746
$721$	6.00413	0.223605
$722$	14.8293	0.551889
$723$	−31.5451	−1.17318
$724$	−6.36717	−0.236634
$725$	−7.47718	−0.277696
$726$	29.0191	1.07700
$727$	−53.3657	−1.97923	−0.989613	−	0.143759i	$-0.954081\pi$
$727$	−53.3657	−1.97923	−0.989613	+	0.143759i	$0.954081\pi$
$728$	−6.08610	−0.225566
$729$	29.5778	1.09547
$730$	−2.03345	−0.0752615
$731$	9.66718	0.357553
$732$	15.1823	0.561156
$733$	−32.9013	−1.21524	−0.607618	−	0.794229i	$-0.707875\pi$
$733$	−32.9013	−1.21524	−0.607618	+	0.794229i	$0.707875\pi$
$734$	18.3687	0.678001
$735$	−0.612900	−0.0226072
$736$	−5.01283	−0.184775
$737$	−18.1105	−0.667110
$738$	−7.50830	−0.276384
$739$	6.33006	0.232855	0.116428	−	0.993199i	$-0.462856\pi$
$739$	6.33006	0.232855	0.116428	+	0.993199i	$0.462856\pi$
$740$	−0.500037	−0.0183817
$741$	18.0816	0.664243
$742$	2.13148	0.0782490
$743$	−11.9398	−0.438029	−0.219014	−	0.975722i	$-0.570284\pi$
$743$	−11.9398	−0.438029	−0.219014	+	0.975722i	$0.570284\pi$
$744$	−14.8972	−0.546159
$745$	1.32023	0.0483695
$746$	16.2881	0.596348
$747$	−6.47863	−0.237041
$748$	6.95477	0.254292
$749$	0.940072	0.0343495
$750$	−6.02021	−0.219827
$751$	−25.5843	−0.933583	−0.466792	−	0.884367i	$-0.654590\pi$
$751$	−25.5843	−0.933583	−0.466792	+	0.884367i	$0.654590\pi$
$752$	7.91813	0.288745
$753$	30.9150	1.12661
$754$	9.43637	0.343652
$755$	5.45087	0.198377
$756$	−5.64981	−0.205482
$757$	−43.8733	−1.59460	−0.797302	−	0.603581i	$-0.793740\pi$
$757$	−43.8733	−1.59460	−0.797302	+	0.603581i	$0.793740\pi$
$758$	16.1885	0.587992
$759$	−40.5685	−1.47254
$760$	−0.860406	−0.0312102
$761$	3.13588	0.113676	0.0568378	−	0.998383i	$-0.481898\pi$
$761$	3.13588	0.113676	0.0568378	+	0.998383i	$0.481898\pi$
$762$	−11.4018	−0.413045
$763$	−0.270368	−0.00978797
$764$	−0.834880	−0.0302049
$765$	−0.465432	−0.0168277
$766$	10.9908	0.397114
$767$	−36.2720	−1.30971
$768$	−1.45476	−0.0524942
$769$	48.7499	1.75797	0.878983	−	0.476853i	$-0.158223\pi$
$769$	48.7499	1.75797	0.878983	+	0.476853i	$0.158223\pi$
$770$	2.34375	0.0844631
$771$	20.4332	0.735882
$772$	−3.21837	−0.115832
$773$	33.2237	1.19497	0.597486	−	0.801879i	$-0.296166\pi$
$773$	33.2237	1.19497	0.597486	+	0.801879i	$0.296166\pi$
$774$	6.83315	0.245613
$775$	49.3840	1.77392
$776$	−5.02549	−0.180405
$777$	−1.72662	−0.0619421
$778$	27.7972	0.996578
$779$	−17.3523	−0.621711
$780$	3.73017	0.133562
$781$	54.4109	1.94698
$782$	−6.26688	−0.224103
$783$	8.75991	0.313054
$784$	1.00000	0.0357143
$785$	−8.88207	−0.317015
$786$	13.0481	0.465410
$787$	−19.0906	−0.680508	−0.340254	−	0.940334i	$-0.610513\pi$
$787$	−19.0906	−0.680508	−0.340254	+	0.940334i	$0.610513\pi$
$788$	11.2654	0.401312
$789$	−26.2534	−0.934647
$790$	3.90828	0.139050
$791$	−5.40238	−0.192086
$792$	4.91591	0.174679
$793$	63.5164	2.25553
$794$	36.8589	1.30807
$795$	−1.30638	−0.0463326
$796$	−5.03701	−0.178532
$797$	−26.4991	−0.938646	−0.469323	−	0.883027i	$-0.655502\pi$
$797$	−26.4991	−0.938646	−0.469323	+	0.883027i	$0.655502\pi$
$798$	−2.97096	−0.105171
$799$	9.89900	0.350201
$800$	4.82250	0.170501
$801$	−0.852500	−0.0301216
$802$	14.9113	0.526537
$803$	26.8504	0.947529
$804$	4.73597	0.167025
$805$	−2.11194	−0.0744360
$806$	−62.3236	−2.19526
$807$	1.36615	0.0480906
$808$	19.2626	0.677655
$809$	27.8214	0.978150	0.489075	−	0.872242i	$-0.337334\pi$
$809$	27.8214	0.978150	0.489075	+	0.872242i	$0.337334\pi$
$810$	2.34588	0.0824260
$811$	7.17728	0.252028	0.126014	−	0.992028i	$-0.459782\pi$
$811$	7.17728	0.252028	0.126014	+	0.992028i	$0.459782\pi$
$812$	−1.55048	−0.0544111
$813$	8.35745	0.293109
$814$	6.60265	0.231423
$815$	−9.31543	−0.326305
$816$	−1.81870	−0.0636671
$817$	15.7920	0.552491
$818$	33.6016	1.17485
$819$	−5.37810	−0.187926
$820$	−3.57972	−0.125009
$821$	−36.1211	−1.26064	−0.630318	−	0.776337i	$-0.717075\pi$
$821$	−36.1211	−1.26064	−0.630318	+	0.776337i	$0.717075\pi$
$822$	23.4108	0.816546
$823$	43.0564	1.50085	0.750426	−	0.660954i	$-0.229848\pi$
$823$	43.0564	1.50085	0.750426	+	0.660954i	$0.229848\pi$
$824$	6.00413	0.209164
$825$	39.0282	1.35879
$826$	5.95981	0.207368
$827$	−13.1069	−0.455771	−0.227886	−	0.973688i	$-0.573181\pi$
$827$	−13.1069	−0.455771	−0.227886	+	0.973688i	$0.573181\pi$
$828$	−4.42968	−0.153942
$829$	−3.12297	−0.108465	−0.0542326	−	0.998528i	$-0.517271\pi$
$829$	−3.12297	−0.108465	−0.0542326	+	0.998528i	$0.517271\pi$
$830$	−3.08881	−0.107214
$831$	−30.2160	−1.04818
$832$	−6.08610	−0.210998
$833$	1.25017	0.0433158
$834$	−26.1974	−0.907140
$835$	9.14832	0.316591
$836$	11.3611	0.392931
$837$	−57.8559	−1.99979
$838$	−0.00271920	−9.39333e−5 0
$839$	−24.5878	−0.848864	−0.424432	−	0.905460i	$-0.639526\pi$
$839$	−24.5878	−0.848864	−0.424432	+	0.905460i	$0.639526\pi$
$840$	−0.612900	−0.0211471
$841$	−26.5960	−0.917104
$842$	20.4225	0.703807
$843$	9.19952	0.316848
$844$	−18.4805	−0.636125
$845$	10.1285	0.348430
$846$	6.99701	0.240562
$847$	−19.9477	−0.685411
$848$	2.13148	0.0731952
$849$	−1.90851	−0.0654999
$850$	6.02894	0.206791
$851$	−5.94959	−0.203949
$852$	−14.2287	−0.487466
$853$	30.3475	1.03908	0.519539	−	0.854447i	$-0.326104\pi$
$853$	30.3475	1.03908	0.519539	+	0.854447i	$0.326104\pi$
$854$	−10.4363	−0.357123
$855$	−0.760315	−0.0260022
$856$	0.940072	0.0321310
$857$	−44.6388	−1.52483	−0.762415	−	0.647088i	$-0.775987\pi$
$857$	−44.6388	−1.52483	−0.762415	+	0.647088i	$0.775987\pi$
$858$	−49.2544	−1.68152
$859$	34.3547	1.17217	0.586083	−	0.810251i	$-0.300669\pi$
$859$	34.3547	1.17217	0.586083	+	0.810251i	$0.300669\pi$
$860$	3.25784	0.111091
$861$	−12.3607	−0.421252
$862$	1.00000	0.0340601
$863$	21.5850	0.734763	0.367382	−	0.930070i	$-0.380254\pi$
$863$	21.5850	0.734763	0.367382	+	0.930070i	$0.380254\pi$
$864$	−5.64981	−0.192211
$865$	−2.87421	−0.0977262
$866$	28.6327	0.972977
$867$	22.4573	0.762689
$868$	10.2403	0.347579
$869$	−51.6061	−1.75062
$870$	0.950288	0.0322178
$871$	19.8133	0.671347
$872$	−0.270368	−0.00915581
$873$	−4.44088	−0.150301
$874$	−10.2374	−0.346284
$875$	4.13828	0.139899
$876$	−7.02146	−0.237233
$877$	31.9786	1.07984	0.539920	−	0.841716i	$-0.318454\pi$
$877$	31.9786	1.07984	0.539920	+	0.841716i	$0.318454\pi$
$878$	−23.9600	−0.808610
$879$	6.14773	0.207358
$880$	2.34375	0.0790080
$881$	−7.55641	−0.254582	−0.127291	−	0.991865i	$-0.540628\pi$
$881$	−7.55641	−0.254582	−0.127291	+	0.991865i	$0.540628\pi$
$882$	0.883670	0.0297547
$883$	15.6788	0.527633	0.263817	−	0.964573i	$-0.415019\pi$
$883$	15.6788	0.527633	0.263817	+	0.964573i	$0.415019\pi$
$884$	−7.60865	−0.255907
$885$	−3.65277	−0.122787
$886$	32.6656	1.09742
$887$	12.5032	0.419816	0.209908	−	0.977721i	$-0.432683\pi$
$887$	12.5032	0.419816	0.209908	+	0.977721i	$0.432683\pi$
$888$	−1.72662	−0.0579415
$889$	7.83760	0.262865
$890$	−0.406446	−0.0136241
$891$	−30.9758	−1.03773
$892$	0.384833	0.0128851
$893$	16.1707	0.541131
$894$	4.55872	0.152466
$895$	−3.11886	−0.104252
$896$	1.00000	0.0334077
$897$	44.3827	1.48190
$898$	4.45417	0.148638
$899$	−15.8774	−0.529541
$900$	4.26150	0.142050
$901$	2.66471	0.0887742
$902$	47.2678	1.57385
$903$	11.2492	0.374351
$904$	−5.40238	−0.179680
$905$	−2.68253	−0.0891702
$906$	18.8217	0.625310
$907$	−50.5690	−1.67912	−0.839558	−	0.543270i	$-0.817186\pi$
$907$	−50.5690	−1.67912	−0.839558	+	0.543270i	$0.817186\pi$
$908$	21.5978	0.716749
$909$	17.0217	0.564576
$910$	−2.56411	−0.0849995
$911$	39.4732	1.30781	0.653903	−	0.756578i	$-0.273130\pi$
$911$	39.4732	1.30781	0.653903	+	0.756578i	$0.273130\pi$
$912$	−2.97096	−0.0983784
$913$	40.7857	1.34981
$914$	2.18612	0.0723104
$915$	6.39642	0.211459
$916$	23.3157	0.770374
$917$	−8.96924	−0.296190
$918$	−7.06322	−0.233121
$919$	2.92399	0.0964536	0.0482268	−	0.998836i	$-0.484643\pi$
$919$	2.92399	0.0964536	0.0482268	+	0.998836i	$0.484643\pi$
$920$	−2.11194	−0.0696285
$921$	35.3980	1.16640
$922$	−5.15255	−0.169690
$923$	−59.5266	−1.95934
$924$	8.09293	0.266238
$925$	5.72370	0.188194
$926$	−18.6944	−0.614337
$927$	5.30567	0.174261
$928$	−1.55048	−0.0508969
$929$	46.4458	1.52384	0.761919	−	0.647672i	$-0.224257\pi$
$929$	46.4458	1.52384	0.761919	+	0.647672i	$0.224257\pi$
$930$	−6.27630	−0.205808
$931$	2.04223	0.0669315
$932$	7.24555	0.237336
$933$	−2.01877	−0.0660914
$934$	2.07104	0.0677665
$935$	2.93009	0.0958241
$936$	−5.37810	−0.175789
$937$	−39.3835	−1.28660	−0.643301	−	0.765614i	$-0.722436\pi$
$937$	−39.3835	−1.28660	−0.643301	+	0.765614i	$0.722436\pi$
$938$	−3.25549	−0.106296
$939$	−2.75075	−0.0897673
$940$	3.33596	0.108807
$941$	46.1167	1.50336	0.751681	−	0.659527i	$-0.229243\pi$
$941$	46.1167	1.50336	0.751681	+	0.659527i	$0.229243\pi$
$942$	−30.6696	−0.999269
$943$	−42.5926	−1.38701
$944$	5.95981	0.193975
$945$	−2.38030	−0.0774312
$946$	−43.0175	−1.39862
$947$	6.28538	0.204248	0.102124	−	0.994772i	$-0.467436\pi$
$947$	6.28538	0.204248	0.102124	+	0.994772i	$0.467436\pi$
$948$	13.4952	0.438303
$949$	−29.3748	−0.953547
$950$	9.84867	0.319533
$951$	8.35225	0.270840
$952$	1.25017	0.0405182
$953$	5.22209	0.169160	0.0845801	−	0.996417i	$-0.473045\pi$
$953$	5.22209	0.169160	0.0845801	+	0.996417i	$0.473045\pi$
$954$	1.88352	0.0609813
$955$	−0.351740	−0.0113821
$956$	−27.2368	−0.880900
$957$	−12.5479	−0.405616
$958$	31.3208	1.01193
$959$	−16.0926	−0.519656
$960$	−0.612900	−0.0197813
$961$	73.8642	2.38272
$962$	−7.22343	−0.232893
$963$	0.830713	0.0267694
$964$	21.6841	0.698397
$965$	−1.35592	−0.0436486
$966$	−7.29247	−0.234631
$967$	−20.1474	−0.647897	−0.323949	−	0.946075i	$-0.605010\pi$
$967$	−20.1474	−0.647897	−0.323949	+	0.946075i	$0.605010\pi$
$968$	−19.9477	−0.641143
$969$	−3.71420	−0.119317
$970$	−2.11727	−0.0679815
$971$	−25.1109	−0.805847	−0.402923	−	0.915234i	$-0.632006\pi$
$971$	−25.1109	−0.805847	−0.402923	+	0.915234i	$0.632006\pi$
$972$	−8.84915	−0.283837
$973$	18.0080	0.577310
$974$	21.9057	0.701904
$975$	−42.6976	−1.36742
$976$	−10.4363	−0.334058
$977$	−60.0204	−1.92022	−0.960111	−	0.279618i	$-0.909792\pi$
$977$	−60.0204	−1.92022	−0.960111	+	0.279618i	$0.909792\pi$
$978$	−32.1660	−1.02855
$979$	5.36684	0.171525
$980$	0.421306	0.0134581
$981$	−0.238916	−0.00762799
$982$	31.3320	0.999843
$983$	−5.43899	−0.173477	−0.0867384	−	0.996231i	$-0.527644\pi$
$983$	−5.43899	−0.173477	−0.0867384	+	0.996231i	$0.527644\pi$
$984$	−12.3607	−0.394045
$985$	4.74617	0.151226
$986$	−1.93836	−0.0617299
$987$	11.5190	0.366654
$988$	−12.4292	−0.395427
$989$	38.7627	1.23258
$990$	2.07110	0.0658240
$991$	−25.4993	−0.810012	−0.405006	−	0.914314i	$-0.632731\pi$
$991$	−25.4993	−0.810012	−0.405006	+	0.914314i	$0.632731\pi$
$992$	10.2403	0.325131
$993$	−7.19298	−0.228262
$994$	9.78075	0.310226
$995$	−2.12212	−0.0672758
$996$	−10.6656	−0.337952
$997$	−11.9264	−0.377713	−0.188857	−	0.982005i	$-0.560478\pi$
$997$	−11.9264	−0.377713	−0.188857	+	0.982005i	$0.560478\pi$
$998$	8.41497	0.266371
$999$	−6.70561	−0.212156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.45476 q^{3} +1.00000 q^{4} +0.421306 q^{5} +1.45476 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.883670 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.45476 q^{3} +1.00000 q^{4} +0.421306 q^{5} +1.45476 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.883670 q^{9} -0.421306 q^{10} +5.56306 q^{11} -1.45476 q^{12} -6.08610 q^{13} +1.00000 q^{14} -0.612900 q^{15} +1.00000 q^{16} +1.25017 q^{17} +0.883670 q^{18} +2.04223 q^{19} +0.421306 q^{20} +1.45476 q^{21} -5.56306 q^{22} +5.01283 q^{23} +1.45476 q^{24} -4.82250 q^{25} +6.08610 q^{26} +5.64981 q^{27} -1.00000 q^{28} +1.55048 q^{29} +0.612900 q^{30} -10.2403 q^{31} -1.00000 q^{32} -8.09293 q^{33} -1.25017 q^{34} -0.421306 q^{35} -0.883670 q^{36} -1.18687 q^{37} -2.04223 q^{38} +8.85382 q^{39} -0.421306 q^{40} -8.49672 q^{41} -1.45476 q^{42} +7.73270 q^{43} +5.56306 q^{44} -0.372296 q^{45} -5.01283 q^{46} +7.91813 q^{47} -1.45476 q^{48} +1.00000 q^{49} +4.82250 q^{50} -1.81870 q^{51} -6.08610 q^{52} +2.13148 q^{53} -5.64981 q^{54} +2.34375 q^{55} +1.00000 q^{56} -2.97096 q^{57} -1.55048 q^{58} +5.95981 q^{59} -0.612900 q^{60} -10.4363 q^{61} +10.2403 q^{62} +0.883670 q^{63} +1.00000 q^{64} -2.56411 q^{65} +8.09293 q^{66} -3.25549 q^{67} +1.25017 q^{68} -7.29247 q^{69} +0.421306 q^{70} +9.78075 q^{71} +0.883670 q^{72} +4.82654 q^{73} +1.18687 q^{74} +7.01559 q^{75} +2.04223 q^{76} -5.56306 q^{77} -8.85382 q^{78} -9.27657 q^{79} +0.421306 q^{80} -5.56812 q^{81} +8.49672 q^{82} +7.33151 q^{83} +1.45476 q^{84} +0.526704 q^{85} -7.73270 q^{86} -2.25558 q^{87} -5.56306 q^{88} +0.964727 q^{89} +0.372296 q^{90} +6.08610 q^{91} +5.01283 q^{92} +14.8972 q^{93} -7.91813 q^{94} +0.860406 q^{95} +1.45476 q^{96} +5.02549 q^{97} -1.00000 q^{98} -4.91591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 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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