LMFDB - Embedded newform 6018.2.a.bc.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + \cdots - 43744 $ x^14 - 2x^13 - 49x^12 + 79x^11 + 956x^10 - 1179x^9 - 9396x^8 + 8315x^7 + 48570x^6 - 28124x^5 - 125592x^4 + 40576x^3 + 138096x^2 - 22032*x - 43744
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$3.24808$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.24808 q^{5} -1.00000 q^{6} +4.67729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.24808 q^{5} -1.00000 q^{6} +4.67729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.24808 q^{10} -0.964277 q^{11} -1.00000 q^{12} -3.76363 q^{13} +4.67729 q^{14} -3.24808 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.28135 q^{19} +3.24808 q^{20} -4.67729 q^{21} -0.964277 q^{22} +3.52257 q^{23} -1.00000 q^{24} +5.55004 q^{25} -3.76363 q^{26} -1.00000 q^{27} +4.67729 q^{28} -8.34244 q^{29} -3.24808 q^{30} +1.51849 q^{31} +1.00000 q^{32} +0.964277 q^{33} +1.00000 q^{34} +15.1922 q^{35} +1.00000 q^{36} +0.888494 q^{37} +5.28135 q^{38} +3.76363 q^{39} +3.24808 q^{40} -11.6789 q^{41} -4.67729 q^{42} +3.13009 q^{43} -0.964277 q^{44} +3.24808 q^{45} +3.52257 q^{46} -1.03935 q^{47} -1.00000 q^{48} +14.8771 q^{49} +5.55004 q^{50} -1.00000 q^{51} -3.76363 q^{52} +7.87333 q^{53} -1.00000 q^{54} -3.13205 q^{55} +4.67729 q^{56} -5.28135 q^{57} -8.34244 q^{58} +1.00000 q^{59} -3.24808 q^{60} +12.7252 q^{61} +1.51849 q^{62} +4.67729 q^{63} +1.00000 q^{64} -12.2246 q^{65} +0.964277 q^{66} -5.31844 q^{67} +1.00000 q^{68} -3.52257 q^{69} +15.1922 q^{70} +4.77564 q^{71} +1.00000 q^{72} +11.3315 q^{73} +0.888494 q^{74} -5.55004 q^{75} +5.28135 q^{76} -4.51020 q^{77} +3.76363 q^{78} -7.01971 q^{79} +3.24808 q^{80} +1.00000 q^{81} -11.6789 q^{82} +12.7137 q^{83} -4.67729 q^{84} +3.24808 q^{85} +3.13009 q^{86} +8.34244 q^{87} -0.964277 q^{88} +11.2087 q^{89} +3.24808 q^{90} -17.6036 q^{91} +3.52257 q^{92} -1.51849 q^{93} -1.03935 q^{94} +17.1542 q^{95} -1.00000 q^{96} -9.68663 q^{97} +14.8771 q^{98} -0.964277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9 + 2 * q^10 + 3 * q^11 - 14 * q^12 + 16 * q^13 + q^14 - 2 * q^15 + 14 * q^16 + 14 * q^17 + 14 * q^18 + 13 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 4 * q^23 - 14 * q^24 + 32 * q^25 + 16 * q^26 - 14 * q^27 + q^28 - 2 * q^30 - 13 * q^31 + 14 * q^32 - 3 * q^33 + 14 * q^34 + 14 * q^36 + 12 * q^37 + 13 * q^38 - 16 * q^39 + 2 * q^40 - 18 * q^41 - q^42 + 29 * q^43 + 3 * q^44 + 2 * q^45 + 4 * q^46 - 14 * q^48 + 49 * q^49 + 32 * q^50 - 14 * q^51 + 16 * q^52 + 24 * q^53 - 14 * q^54 + 15 * q^55 + q^56 - 13 * q^57 + 14 * q^59 - 2 * q^60 + 29 * q^61 - 13 * q^62 + q^63 + 14 * q^64 + 6 * q^65 - 3 * q^66 + 4 * q^67 + 14 * q^68 - 4 * q^69 - 10 * q^71 + 14 * q^72 + 18 * q^73 + 12 * q^74 - 32 * q^75 + 13 * q^76 + 20 * q^77 - 16 * q^78 + 7 * q^79 + 2 * q^80 + 14 * q^81 - 18 * q^82 + 28 * q^83 - q^84 + 2 * q^85 + 29 * q^86 + 3 * q^88 + 23 * q^89 + 2 * q^90 + 9 * q^91 + 4 * q^92 + 13 * q^93 + 5 * q^95 - 14 * q^96 - 7 * q^97 + 49 * q^98 + 3 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.24808	1.45259	0.726293	−	0.687385i	$-0.241241\pi$
$5$	3.24808	1.45259	0.726293	+	0.687385i	$0.241241\pi$
$6$	−1.00000	−0.408248
$7$	4.67729	1.76785	0.883925	−	0.467628i	$-0.154891\pi$
$7$	4.67729	1.76785	0.883925	+	0.467628i	$0.154891\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.24808	1.02713
$11$	−0.964277	−0.290740	−0.145370	−	0.989377i	$-0.546437\pi$
$11$	−0.964277	−0.290740	−0.145370	+	0.989377i	$0.546437\pi$
$12$	−1.00000	−0.288675
$13$	−3.76363	−1.04384	−0.521921	−	0.852994i	$-0.674785\pi$
$13$	−3.76363	−1.04384	−0.521921	+	0.852994i	$0.674785\pi$
$14$	4.67729	1.25006
$15$	−3.24808	−0.838651
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	5.28135	1.21162	0.605812	−	0.795608i	$-0.292848\pi$
$19$	5.28135	1.21162	0.605812	+	0.795608i	$0.292848\pi$
$20$	3.24808	0.726293
$21$	−4.67729	−1.02067
$22$	−0.964277	−0.205585
$23$	3.52257	0.734506	0.367253	−	0.930121i	$-0.380298\pi$
$23$	3.52257	0.734506	0.367253	+	0.930121i	$0.380298\pi$
$24$	−1.00000	−0.204124
$25$	5.55004	1.11001
$26$	−3.76363	−0.738108
$27$	−1.00000	−0.192450
$28$	4.67729	0.883925
$29$	−8.34244	−1.54915	−0.774576	−	0.632481i	$-0.782037\pi$
$29$	−8.34244	−1.54915	−0.774576	+	0.632481i	$0.782037\pi$
$30$	−3.24808	−0.593016
$31$	1.51849	0.272728	0.136364	−	0.990659i	$-0.456458\pi$
$31$	1.51849	0.272728	0.136364	+	0.990659i	$0.456458\pi$
$32$	1.00000	0.176777
$33$	0.964277	0.167859
$34$	1.00000	0.171499
$35$	15.1922	2.56796
$36$	1.00000	0.166667
$37$	0.888494	0.146068	0.0730338	−	0.997329i	$-0.476732\pi$
$37$	0.888494	0.146068	0.0730338	+	0.997329i	$0.476732\pi$
$38$	5.28135	0.856747
$39$	3.76363	0.602663
$40$	3.24808	0.513567
$41$	−11.6789	−1.82393	−0.911965	−	0.410267i	$-0.865435\pi$
$41$	−11.6789	−1.82393	−0.911965	+	0.410267i	$0.865435\pi$
$42$	−4.67729	−0.721722
$43$	3.13009	0.477334	0.238667	−	0.971101i	$-0.423290\pi$
$43$	3.13009	0.477334	0.238667	+	0.971101i	$0.423290\pi$
$44$	−0.964277	−0.145370
$45$	3.24808	0.484196
$46$	3.52257	0.519374
$47$	−1.03935	−0.151605	−0.0758024	−	0.997123i	$-0.524152\pi$
$47$	−1.03935	−0.151605	−0.0758024	+	0.997123i	$0.524152\pi$
$48$	−1.00000	−0.144338
$49$	14.8771	2.12529
$50$	5.55004	0.784894
$51$	−1.00000	−0.140028
$52$	−3.76363	−0.521921
$53$	7.87333	1.08148	0.540742	−	0.841188i	$-0.318143\pi$
$53$	7.87333	1.08148	0.540742	+	0.841188i	$0.318143\pi$
$54$	−1.00000	−0.136083
$55$	−3.13205	−0.422326
$56$	4.67729	0.625029
$57$	−5.28135	−0.699531
$58$	−8.34244	−1.09542
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.24808	−0.419326
$61$	12.7252	1.62930	0.814650	−	0.579952i	$-0.196929\pi$
$61$	12.7252	1.62930	0.814650	+	0.579952i	$0.196929\pi$
$62$	1.51849	0.192848
$63$	4.67729	0.589283
$64$	1.00000	0.125000
$65$	−12.2246	−1.51627
$66$	0.964277	0.118694
$67$	−5.31844	−0.649751	−0.324875	−	0.945757i	$-0.605322\pi$
$67$	−5.31844	−0.649751	−0.324875	+	0.945757i	$0.605322\pi$
$68$	1.00000	0.121268
$69$	−3.52257	−0.424067
$70$	15.1922	1.81582
$71$	4.77564	0.566764	0.283382	−	0.959007i	$-0.408543\pi$
$71$	4.77564	0.566764	0.283382	+	0.959007i	$0.408543\pi$
$72$	1.00000	0.117851
$73$	11.3315	1.32626	0.663128	−	0.748506i	$-0.269228\pi$
$73$	11.3315	1.32626	0.663128	+	0.748506i	$0.269228\pi$
$74$	0.888494	0.103285
$75$	−5.55004	−0.640863
$76$	5.28135	0.605812
$77$	−4.51020	−0.513985
$78$	3.76363	0.426147
$79$	−7.01971	−0.789779	−0.394889	−	0.918729i	$-0.629217\pi$
$79$	−7.01971	−0.789779	−0.394889	+	0.918729i	$0.629217\pi$
$80$	3.24808	0.363147
$81$	1.00000	0.111111
$82$	−11.6789	−1.28971
$83$	12.7137	1.39550	0.697752	−	0.716339i	$-0.254184\pi$
$83$	12.7137	1.39550	0.697752	+	0.716339i	$0.254184\pi$
$84$	−4.67729	−0.510334
$85$	3.24808	0.352304
$86$	3.13009	0.337526
$87$	8.34244	0.894403
$88$	−0.964277	−0.102792
$89$	11.2087	1.18812	0.594061	−	0.804420i	$-0.297524\pi$
$89$	11.2087	1.18812	0.594061	+	0.804420i	$0.297524\pi$
$90$	3.24808	0.342378
$91$	−17.6036	−1.84536
$92$	3.52257	0.367253
$93$	−1.51849	−0.157460
$94$	−1.03935	−0.107201
$95$	17.1542	1.75999
$96$	−1.00000	−0.102062
$97$	−9.68663	−0.983528	−0.491764	−	0.870728i	$-0.663648\pi$
$97$	−9.68663	−0.983528	−0.491764	+	0.870728i	$0.663648\pi$
$98$	14.8771	1.50281
$99$	−0.964277	−0.0969135
$100$	5.55004	0.555004
$101$	−3.30551	−0.328911	−0.164455	−	0.986385i	$-0.552587\pi$
$101$	−3.30551	−0.328911	−0.164455	+	0.986385i	$0.552587\pi$
$102$	−1.00000	−0.0990148
$103$	−5.42804	−0.534840	−0.267420	−	0.963580i	$-0.586171\pi$
$103$	−5.42804	−0.534840	−0.267420	+	0.963580i	$0.586171\pi$
$104$	−3.76363	−0.369054
$105$	−15.1922	−1.48261
$106$	7.87333	0.764725
$107$	−9.35714	−0.904589	−0.452295	−	0.891869i	$-0.649394\pi$
$107$	−9.35714	−0.904589	−0.452295	+	0.891869i	$0.649394\pi$
$108$	−1.00000	−0.0962250
$109$	13.3923	1.28275	0.641374	−	0.767229i	$-0.278365\pi$
$109$	13.3923	1.28275	0.641374	+	0.767229i	$0.278365\pi$
$110$	−3.13205	−0.298629
$111$	−0.888494	−0.0843321
$112$	4.67729	0.441963
$113$	1.28146	0.120550	0.0602749	−	0.998182i	$-0.480802\pi$
$113$	1.28146	0.120550	0.0602749	+	0.998182i	$0.480802\pi$
$114$	−5.28135	−0.494643
$115$	11.4416	1.06693
$116$	−8.34244	−0.774576
$117$	−3.76363	−0.347948
$118$	1.00000	0.0920575
$119$	4.67729	0.428767
$120$	−3.24808	−0.296508
$121$	−10.0702	−0.915470
$122$	12.7252	1.15209
$123$	11.6789	1.05305
$124$	1.51849	0.136364
$125$	1.78657	0.159795
$126$	4.67729	0.416686
$127$	−9.40985	−0.834989	−0.417495	−	0.908679i	$-0.637092\pi$
$127$	−9.40985	−0.834989	−0.417495	+	0.908679i	$0.637092\pi$
$128$	1.00000	0.0883883
$129$	−3.13009	−0.275589
$130$	−12.2246	−1.07217
$131$	−7.66465	−0.669663	−0.334832	−	0.942278i	$-0.608679\pi$
$131$	−7.66465	−0.669663	−0.334832	+	0.942278i	$0.608679\pi$
$132$	0.964277	0.0839295
$133$	24.7024	2.14197
$134$	−5.31844	−0.459443
$135$	−3.24808	−0.279550
$136$	1.00000	0.0857493
$137$	−12.7766	−1.09158	−0.545790	−	0.837922i	$-0.683771\pi$
$137$	−12.7766	−1.09158	−0.545790	+	0.837922i	$0.683771\pi$
$138$	−3.52257	−0.299861
$139$	3.66265	0.310662	0.155331	−	0.987862i	$-0.450356\pi$
$139$	3.66265	0.310662	0.155331	+	0.987862i	$0.450356\pi$
$140$	15.1922	1.28398
$141$	1.03935	0.0875290
$142$	4.77564	0.400763
$143$	3.62918	0.303487
$144$	1.00000	0.0833333
$145$	−27.0969	−2.25028
$146$	11.3315	0.937805
$147$	−14.8771	−1.22704
$148$	0.888494	0.0730338
$149$	−20.8053	−1.70444	−0.852219	−	0.523186i	$-0.824743\pi$
$149$	−20.8053	−1.70444	−0.852219	+	0.523186i	$0.824743\pi$
$150$	−5.55004	−0.453159
$151$	0.591724	0.0481538	0.0240769	−	0.999710i	$-0.492335\pi$
$151$	0.591724	0.0481538	0.0240769	+	0.999710i	$0.492335\pi$
$152$	5.28135	0.428374
$153$	1.00000	0.0808452
$154$	−4.51020	−0.363443
$155$	4.93216	0.396161
$156$	3.76363	0.301331
$157$	−14.9091	−1.18988	−0.594938	−	0.803771i	$-0.702824\pi$
$157$	−14.9091	−1.18988	−0.594938	+	0.803771i	$0.702824\pi$
$158$	−7.01971	−0.558458
$159$	−7.87333	−0.624396
$160$	3.24808	0.256783
$161$	16.4761	1.29850
$162$	1.00000	0.0785674
$163$	−3.86070	−0.302393	−0.151197	−	0.988504i	$-0.548313\pi$
$163$	−3.86070	−0.302393	−0.151197	+	0.988504i	$0.548313\pi$
$164$	−11.6789	−0.911965
$165$	3.13205	0.243830
$166$	12.7137	0.986771
$167$	−5.61829	−0.434756	−0.217378	−	0.976087i	$-0.569751\pi$
$167$	−5.61829	−0.434756	−0.217378	+	0.976087i	$0.569751\pi$
$168$	−4.67729	−0.360861
$169$	1.16490	0.0896077
$170$	3.24808	0.249117
$171$	5.28135	0.403875
$172$	3.13009	0.238667
$173$	−14.4876	−1.10147	−0.550734	−	0.834681i	$-0.685652\pi$
$173$	−14.4876	−1.10147	−0.550734	+	0.834681i	$0.685652\pi$
$174$	8.34244	0.632439
$175$	25.9591	1.96233
$176$	−0.964277	−0.0726851
$177$	−1.00000	−0.0751646
$178$	11.2087	0.840129
$179$	15.5761	1.16421	0.582107	−	0.813112i	$-0.302228\pi$
$179$	15.5761	1.16421	0.582107	+	0.813112i	$0.302228\pi$
$180$	3.24808	0.242098
$181$	10.4407	0.776048	0.388024	−	0.921649i	$-0.373158\pi$
$181$	10.4407	0.776048	0.388024	+	0.921649i	$0.373158\pi$
$182$	−17.6036	−1.30486
$183$	−12.7252	−0.940677
$184$	3.52257	0.259687
$185$	2.88590	0.212176
$186$	−1.51849	−0.111341
$187$	−0.964277	−0.0705149
$188$	−1.03935	−0.0758024
$189$	−4.67729	−0.340223
$190$	17.1542	1.24450
$191$	−4.16668	−0.301490	−0.150745	−	0.988573i	$-0.548167\pi$
$191$	−4.16668	−0.301490	−0.150745	+	0.988573i	$0.548167\pi$
$192$	−1.00000	−0.0721688
$193$	0.335211	0.0241290	0.0120645	−	0.999927i	$-0.496160\pi$
$193$	0.335211	0.0241290	0.0120645	+	0.999927i	$0.496160\pi$
$194$	−9.68663	−0.695459
$195$	12.2246	0.875420
$196$	14.8771	1.06265
$197$	1.39648	0.0994948	0.0497474	−	0.998762i	$-0.484158\pi$
$197$	1.39648	0.0994948	0.0497474	+	0.998762i	$0.484158\pi$
$198$	−0.964277	−0.0685282
$199$	5.34040	0.378571	0.189285	−	0.981922i	$-0.439383\pi$
$199$	5.34040	0.378571	0.189285	+	0.981922i	$0.439383\pi$
$200$	5.55004	0.392447
$201$	5.31844	0.375134
$202$	−3.30551	−0.232575
$203$	−39.0200	−2.73867
$204$	−1.00000	−0.0700140
$205$	−37.9339	−2.64942
$206$	−5.42804	−0.378189
$207$	3.52257	0.244835
$208$	−3.76363	−0.260961
$209$	−5.09268	−0.352268
$210$	−15.1922	−1.04836
$211$	10.0065	0.688875	0.344437	−	0.938809i	$-0.388070\pi$
$211$	10.0065	0.688875	0.344437	+	0.938809i	$0.388070\pi$
$212$	7.87333	0.540742
$213$	−4.77564	−0.327222
$214$	−9.35714	−0.639641
$215$	10.1668	0.693369
$216$	−1.00000	−0.0680414
$217$	7.10240	0.482142
$218$	13.3923	0.907039
$219$	−11.3315	−0.765715
$220$	−3.13205	−0.211163
$221$	−3.76363	−0.253169
$222$	−0.888494	−0.0596318
$223$	−19.4606	−1.30318	−0.651589	−	0.758572i	$-0.725897\pi$
$223$	−19.4606	−1.30318	−0.651589	+	0.758572i	$0.725897\pi$
$224$	4.67729	0.312515
$225$	5.55004	0.370003
$226$	1.28146	0.0852415
$227$	27.6168	1.83299	0.916495	−	0.400045i	$-0.131006\pi$
$227$	27.6168	1.83299	0.916495	+	0.400045i	$0.131006\pi$
$228$	−5.28135	−0.349766
$229$	12.3449	0.815774	0.407887	−	0.913032i	$-0.366266\pi$
$229$	12.3449	0.815774	0.407887	+	0.913032i	$0.366266\pi$
$230$	11.4416	0.754436
$231$	4.51020	0.296750
$232$	−8.34244	−0.547708
$233$	1.60445	0.105111	0.0525553	−	0.998618i	$-0.483263\pi$
$233$	1.60445	0.105111	0.0525553	+	0.998618i	$0.483263\pi$
$234$	−3.76363	−0.246036
$235$	−3.37589	−0.220219
$236$	1.00000	0.0650945
$237$	7.01971	0.455979
$238$	4.67729	0.303184
$239$	−12.4813	−0.807351	−0.403675	−	0.914902i	$-0.632268\pi$
$239$	−12.4813	−0.807351	−0.403675	+	0.914902i	$0.632268\pi$
$240$	−3.24808	−0.209663
$241$	16.5973	1.06913	0.534563	−	0.845129i	$-0.320476\pi$
$241$	16.5973	1.06913	0.534563	+	0.845129i	$0.320476\pi$
$242$	−10.0702	−0.647335
$243$	−1.00000	−0.0641500
$244$	12.7252	0.814650
$245$	48.3219	3.08717
$246$	11.6789	0.744617
$247$	−19.8770	−1.26474
$248$	1.51849	0.0964239
$249$	−12.7137	−0.805695
$250$	1.78657	0.112992
$251$	−2.98004	−0.188099	−0.0940494	−	0.995568i	$-0.529981\pi$
$251$	−2.98004	−0.188099	−0.0940494	+	0.995568i	$0.529981\pi$
$252$	4.67729	0.294642
$253$	−3.39673	−0.213550
$254$	−9.40985	−0.590427
$255$	−3.24808	−0.203403
$256$	1.00000	0.0625000
$257$	12.1620	0.758647	0.379324	−	0.925264i	$-0.376157\pi$
$257$	12.1620	0.758647	0.379324	+	0.925264i	$0.376157\pi$
$258$	−3.13009	−0.194871
$259$	4.15575	0.258226
$260$	−12.2246	−0.758136
$261$	−8.34244	−0.516384
$262$	−7.66465	−0.473523
$263$	19.2237	1.18538	0.592692	−	0.805429i	$-0.298065\pi$
$263$	19.2237	1.18538	0.592692	+	0.805429i	$0.298065\pi$
$264$	0.964277	0.0593471
$265$	25.5732	1.57095
$266$	24.7024	1.51460
$267$	−11.2087	−0.685963
$268$	−5.31844	−0.324875
$269$	−1.41513	−0.0862818	−0.0431409	−	0.999069i	$-0.513736\pi$
$269$	−1.41513	−0.0862818	−0.0431409	+	0.999069i	$0.513736\pi$
$270$	−3.24808	−0.197672
$271$	−11.7428	−0.713322	−0.356661	−	0.934234i	$-0.616085\pi$
$271$	−11.7428	−0.713322	−0.356661	+	0.934234i	$0.616085\pi$
$272$	1.00000	0.0606339
$273$	17.6036	1.06542
$274$	−12.7766	−0.771864
$275$	−5.35177	−0.322724
$276$	−3.52257	−0.212034
$277$	19.1118	1.14831	0.574157	−	0.818745i	$-0.305330\pi$
$277$	19.1118	1.14831	0.574157	+	0.818745i	$0.305330\pi$
$278$	3.66265	0.219671
$279$	1.51849	0.0909093
$280$	15.1922	0.907909
$281$	−26.4976	−1.58072	−0.790358	−	0.612645i	$-0.790106\pi$
$281$	−26.4976	−1.58072	−0.790358	+	0.612645i	$0.790106\pi$
$282$	1.03935	0.0618924
$283$	−25.0095	−1.48666	−0.743329	−	0.668926i	$-0.766754\pi$
$283$	−25.0095	−1.48666	−0.743329	+	0.668926i	$0.766754\pi$
$284$	4.77564	0.283382
$285$	−17.1542	−1.01613
$286$	3.62918	0.214598
$287$	−54.6254	−3.22444
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−27.0969	−1.59119
$291$	9.68663	0.567840
$292$	11.3315	0.663128
$293$	−14.1710	−0.827878	−0.413939	−	0.910305i	$-0.635847\pi$
$293$	−14.1710	−0.827878	−0.413939	+	0.910305i	$0.635847\pi$
$294$	−14.8771	−0.867648
$295$	3.24808	0.189111
$296$	0.888494	0.0516427
$297$	0.964277	0.0559530
$298$	−20.8053	−1.20522
$299$	−13.2576	−0.766708
$300$	−5.55004	−0.320432
$301$	14.6403	0.843855
$302$	0.591724	0.0340499
$303$	3.30551	0.189897
$304$	5.28135	0.302906
$305$	41.3326	2.36670
$306$	1.00000	0.0571662
$307$	−0.0848060	−0.00484013	−0.00242007	−	0.999997i	$-0.500770\pi$
$307$	−0.0848060	−0.00484013	−0.00242007	+	0.999997i	$0.500770\pi$
$308$	−4.51020	−0.256993
$309$	5.42804	0.308790
$310$	4.93216	0.280128
$311$	−30.8497	−1.74932	−0.874662	−	0.484733i	$-0.838917\pi$
$311$	−30.8497	−1.74932	−0.874662	+	0.484733i	$0.838917\pi$
$312$	3.76363	0.213074
$313$	14.5289	0.821219	0.410610	−	0.911811i	$-0.365316\pi$
$313$	14.5289	0.821219	0.410610	+	0.911811i	$0.365316\pi$
$314$	−14.9091	−0.841370
$315$	15.1922	0.855985
$316$	−7.01971	−0.394889
$317$	21.4863	1.20679	0.603396	−	0.797441i	$-0.293814\pi$
$317$	21.4863	1.20679	0.603396	+	0.797441i	$0.293814\pi$
$318$	−7.87333	−0.441514
$319$	8.04442	0.450401
$320$	3.24808	0.181573
$321$	9.35714	0.522265
$322$	16.4761	0.918175
$323$	5.28135	0.293862
$324$	1.00000	0.0555556
$325$	−20.8883	−1.15867
$326$	−3.86070	−0.213824
$327$	−13.3923	−0.740595
$328$	−11.6789	−0.644857
$329$	−4.86134	−0.268014
$330$	3.13205	0.172414
$331$	13.2725	0.729524	0.364762	−	0.931101i	$-0.381150\pi$
$331$	13.2725	0.729524	0.364762	+	0.931101i	$0.381150\pi$
$332$	12.7137	0.697752
$333$	0.888494	0.0486892
$334$	−5.61829	−0.307419
$335$	−17.2747	−0.943819
$336$	−4.67729	−0.255167
$337$	11.9625	0.651638	0.325819	−	0.945432i	$-0.394360\pi$
$337$	11.9625	0.651638	0.325819	+	0.945432i	$0.394360\pi$
$338$	1.16490	0.0633622
$339$	−1.28146	−0.0695994
$340$	3.24808	0.176152
$341$	−1.46424	−0.0792930
$342$	5.28135	0.285582
$343$	36.8433	1.98935
$344$	3.13009	0.168763
$345$	−11.4416	−0.615994
$346$	−14.4876	−0.778856
$347$	−2.95988	−0.158894	−0.0794472	−	0.996839i	$-0.525316\pi$
$347$	−2.95988	−0.158894	−0.0794472	+	0.996839i	$0.525316\pi$
$348$	8.34244	0.447202
$349$	−28.6405	−1.53309	−0.766544	−	0.642191i	$-0.778026\pi$
$349$	−28.6405	−1.53309	−0.766544	+	0.642191i	$0.778026\pi$
$350$	25.9591	1.38757
$351$	3.76363	0.200888
$352$	−0.964277	−0.0513961
$353$	14.3844	0.765602	0.382801	−	0.923831i	$-0.374960\pi$
$353$	14.3844	0.765602	0.382801	+	0.923831i	$0.374960\pi$
$354$	−1.00000	−0.0531494
$355$	15.5117	0.823274
$356$	11.2087	0.594061
$357$	−4.67729	−0.247549
$358$	15.5761	0.823224
$359$	20.9168	1.10394	0.551972	−	0.833862i	$-0.313875\pi$
$359$	20.9168	1.10394	0.551972	+	0.833862i	$0.313875\pi$
$360$	3.24808	0.171189
$361$	8.89262	0.468032
$362$	10.4407	0.548749
$363$	10.0702	0.528547
$364$	−17.6036	−0.922679
$365$	36.8058	1.92650
$366$	−12.7252	−0.665159
$367$	−36.8894	−1.92561	−0.962804	−	0.270199i	$-0.912910\pi$
$367$	−36.8894	−1.92561	−0.962804	+	0.270199i	$0.912910\pi$
$368$	3.52257	0.183626
$369$	−11.6789	−0.607977
$370$	2.88590	0.150031
$371$	36.8259	1.91190
$372$	−1.51849	−0.0787298
$373$	−8.27987	−0.428716	−0.214358	−	0.976755i	$-0.568766\pi$
$373$	−8.27987	−0.428716	−0.214358	+	0.976755i	$0.568766\pi$
$374$	−0.964277	−0.0498616
$375$	−1.78657	−0.0922580
$376$	−1.03935	−0.0536004
$377$	31.3978	1.61707
$378$	−4.67729	−0.240574
$379$	7.63045	0.391950	0.195975	−	0.980609i	$-0.437213\pi$
$379$	7.63045	0.391950	0.195975	+	0.980609i	$0.437213\pi$
$380$	17.1542	0.879994
$381$	9.40985	0.482081
$382$	−4.16668	−0.213186
$383$	−30.8877	−1.57829	−0.789145	−	0.614208i	$-0.789476\pi$
$383$	−30.8877	−1.57829	−0.789145	+	0.614208i	$0.789476\pi$
$384$	−1.00000	−0.0510310
$385$	−14.6495	−0.746608
$386$	0.335211	0.0170618
$387$	3.13009	0.159111
$388$	−9.68663	−0.491764
$389$	2.17405	0.110228	0.0551142	−	0.998480i	$-0.482448\pi$
$389$	2.17405	0.110228	0.0551142	+	0.998480i	$0.482448\pi$
$390$	12.2246	0.619015
$391$	3.52257	0.178144
$392$	14.8771	0.751405
$393$	7.66465	0.386630
$394$	1.39648	0.0703535
$395$	−22.8006	−1.14722
$396$	−0.964277	−0.0484567
$397$	11.5219	0.578269	0.289134	−	0.957289i	$-0.406633\pi$
$397$	11.5219	0.578269	0.289134	+	0.957289i	$0.406633\pi$
$398$	5.34040	0.267690
$399$	−24.7024	−1.23667
$400$	5.55004	0.277502
$401$	−24.6706	−1.23199	−0.615996	−	0.787749i	$-0.711246\pi$
$401$	−24.6706	−1.23199	−0.615996	+	0.787749i	$0.711246\pi$
$402$	5.31844	0.265260
$403$	−5.71501	−0.284685
$404$	−3.30551	−0.164455
$405$	3.24808	0.161399
$406$	−39.0200	−1.93653
$407$	−0.856754	−0.0424677
$408$	−1.00000	−0.0495074
$409$	15.8261	0.782552	0.391276	−	0.920273i	$-0.372034\pi$
$409$	15.8261	0.782552	0.391276	+	0.920273i	$0.372034\pi$
$410$	−37.9339	−1.87342
$411$	12.7766	0.630225
$412$	−5.42804	−0.267420
$413$	4.67729	0.230154
$414$	3.52257	0.173125
$415$	41.2950	2.02709
$416$	−3.76363	−0.184527
$417$	−3.66265	−0.179361
$418$	−5.09268	−0.249091
$419$	−24.7072	−1.20703	−0.603514	−	0.797353i	$-0.706233\pi$
$419$	−24.7072	−1.20703	−0.603514	+	0.797353i	$0.706233\pi$
$420$	−15.1922	−0.741305
$421$	37.3900	1.82228	0.911138	−	0.412102i	$-0.135205\pi$
$421$	37.3900	1.82228	0.911138	+	0.412102i	$0.135205\pi$
$422$	10.0065	0.487108
$423$	−1.03935	−0.0505349
$424$	7.87333	0.382363
$425$	5.55004	0.269216
$426$	−4.77564	−0.231381
$427$	59.5197	2.88036
$428$	−9.35714	−0.452295
$429$	−3.62918	−0.175218
$430$	10.1668	0.490286
$431$	−26.2686	−1.26531	−0.632656	−	0.774433i	$-0.718035\pi$
$431$	−26.2686	−1.26531	−0.632656	+	0.774433i	$0.718035\pi$
$432$	−1.00000	−0.0481125
$433$	−14.3891	−0.691496	−0.345748	−	0.938327i	$-0.612375\pi$
$433$	−14.3891	−0.691496	−0.345748	+	0.938327i	$0.612375\pi$
$434$	7.10240	0.340926
$435$	27.0969	1.29920
$436$	13.3923	0.641374
$437$	18.6039	0.889945
$438$	−11.3315	−0.541442
$439$	−14.8704	−0.709723	−0.354862	−	0.934919i	$-0.615472\pi$
$439$	−14.8704	−0.709723	−0.354862	+	0.934919i	$0.615472\pi$
$440$	−3.13205	−0.149315
$441$	14.8771	0.708431
$442$	−3.76363	−0.179018
$443$	−15.3125	−0.727520	−0.363760	−	0.931493i	$-0.618507\pi$
$443$	−15.3125	−0.727520	−0.363760	+	0.931493i	$0.618507\pi$
$444$	−0.888494	−0.0421661
$445$	36.4069	1.72585
$446$	−19.4606	−0.921486
$447$	20.8053	0.984057
$448$	4.67729	0.220981
$449$	37.0958	1.75066	0.875330	−	0.483527i	$-0.160644\pi$
$449$	37.0958	1.75066	0.875330	+	0.483527i	$0.160644\pi$
$450$	5.55004	0.261631
$451$	11.2616	0.530290
$452$	1.28146	0.0602749
$453$	−0.591724	−0.0278016
$454$	27.6168	1.29612
$455$	−57.1779	−2.68054
$456$	−5.28135	−0.247322
$457$	24.4591	1.14415	0.572074	−	0.820202i	$-0.306139\pi$
$457$	24.4591	1.14415	0.572074	+	0.820202i	$0.306139\pi$
$458$	12.3449	0.576839
$459$	−1.00000	−0.0466760
$460$	11.4416	0.533467
$461$	29.4670	1.37241	0.686207	−	0.727406i	$-0.259274\pi$
$461$	29.4670	1.37241	0.686207	+	0.727406i	$0.259274\pi$
$462$	4.51020	0.209834
$463$	1.49629	0.0695383	0.0347692	−	0.999395i	$-0.488930\pi$
$463$	1.49629	0.0695383	0.0347692	+	0.999395i	$0.488930\pi$
$464$	−8.34244	−0.387288
$465$	−4.93216	−0.228724
$466$	1.60445	0.0743245
$467$	26.2523	1.21481	0.607405	−	0.794392i	$-0.292210\pi$
$467$	26.2523	1.21481	0.607405	+	0.794392i	$0.292210\pi$
$468$	−3.76363	−0.173974
$469$	−24.8759	−1.14866
$470$	−3.37589	−0.155718
$471$	14.9091	0.686976
$472$	1.00000	0.0460287
$473$	−3.01827	−0.138780
$474$	7.01971	0.322426
$475$	29.3117	1.34491
$476$	4.67729	0.214383
$477$	7.87333	0.360495
$478$	−12.4813	−0.570883
$479$	−19.6601	−0.898293	−0.449147	−	0.893458i	$-0.648272\pi$
$479$	−19.6601	−0.898293	−0.449147	+	0.893458i	$0.648272\pi$
$480$	−3.24808	−0.148254
$481$	−3.34396	−0.152472
$482$	16.5973	0.755986
$483$	−16.4761	−0.749687
$484$	−10.0702	−0.457735
$485$	−31.4630	−1.42866
$486$	−1.00000	−0.0453609
$487$	−30.0997	−1.36395	−0.681973	−	0.731377i	$-0.738878\pi$
$487$	−30.0997	−1.36395	−0.681973	+	0.731377i	$0.738878\pi$
$488$	12.7252	0.576045
$489$	3.86070	0.174587
$490$	48.3219	2.18296
$491$	34.0092	1.53482	0.767408	−	0.641160i	$-0.221546\pi$
$491$	34.0092	1.53482	0.767408	+	0.641160i	$0.221546\pi$
$492$	11.6789	0.526523
$493$	−8.34244	−0.375725
$494$	−19.8770	−0.894310
$495$	−3.13205	−0.140775
$496$	1.51849	0.0681820
$497$	22.3371	1.00195
$498$	−12.7137	−0.569712
$499$	−26.0517	−1.16624	−0.583118	−	0.812388i	$-0.698167\pi$
$499$	−26.0517	−1.16624	−0.583118	+	0.812388i	$0.698167\pi$
$500$	1.78657	0.0798977
$501$	5.61829	0.251007
$502$	−2.98004	−0.133006
$503$	23.0932	1.02968	0.514838	−	0.857288i	$-0.327852\pi$
$503$	23.0932	1.02968	0.514838	+	0.857288i	$0.327852\pi$
$504$	4.67729	0.208343
$505$	−10.7366	−0.477771
$506$	−3.39673	−0.151003
$507$	−1.16490	−0.0517350
$508$	−9.40985	−0.417495
$509$	32.1577	1.42537	0.712684	−	0.701486i	$-0.247480\pi$
$509$	32.1577	1.42537	0.712684	+	0.701486i	$0.247480\pi$
$510$	−3.24808	−0.143827
$511$	53.0009	2.34462
$512$	1.00000	0.0441942
$513$	−5.28135	−0.233177
$514$	12.1620	0.536444
$515$	−17.6307	−0.776902
$516$	−3.13009	−0.137794
$517$	1.00222	0.0440776
$518$	4.15575	0.182593
$519$	14.4876	0.635933
$520$	−12.2246	−0.536083
$521$	4.23421	0.185504	0.0927521	−	0.995689i	$-0.470434\pi$
$521$	4.23421	0.185504	0.0927521	+	0.995689i	$0.470434\pi$
$522$	−8.34244	−0.365139
$523$	−11.6827	−0.510848	−0.255424	−	0.966829i	$-0.582215\pi$
$523$	−11.6827	−0.510848	−0.255424	+	0.966829i	$0.582215\pi$
$524$	−7.66465	−0.334832
$525$	−25.9591	−1.13295
$526$	19.2237	0.838193
$527$	1.51849	0.0661462
$528$	0.964277	0.0419648
$529$	−10.5915	−0.460501
$530$	25.5732	1.11083
$531$	1.00000	0.0433963
$532$	24.7024	1.07098
$533$	43.9549	1.90390
$534$	−11.2087	−0.485049
$535$	−30.3928	−1.31399
$536$	−5.31844	−0.229722
$537$	−15.5761	−0.672159
$538$	−1.41513	−0.0610104
$539$	−14.3456	−0.617909
$540$	−3.24808	−0.139775
$541$	15.3622	0.660472	0.330236	−	0.943898i	$-0.392872\pi$
$541$	15.3622	0.660472	0.330236	+	0.943898i	$0.392872\pi$
$542$	−11.7428	−0.504395
$543$	−10.4407	−0.448052
$544$	1.00000	0.0428746
$545$	43.4992	1.86330
$546$	17.6036	0.753364
$547$	−2.26303	−0.0967604	−0.0483802	−	0.998829i	$-0.515406\pi$
$547$	−2.26303	−0.0967604	−0.0483802	+	0.998829i	$0.515406\pi$
$548$	−12.7766	−0.545790
$549$	12.7252	0.543100
$550$	−5.35177	−0.228200
$551$	−44.0593	−1.87699
$552$	−3.52257	−0.149930
$553$	−32.8332	−1.39621
$554$	19.1118	0.811981
$555$	−2.88590	−0.122500
$556$	3.66265	0.155331
$557$	18.3576	0.777834	0.388917	−	0.921273i	$-0.372849\pi$
$557$	18.3576	0.777834	0.388917	+	0.921273i	$0.372849\pi$
$558$	1.51849	0.0642826
$559$	−11.7805	−0.498261
$560$	15.1922	0.641989
$561$	0.964277	0.0407118
$562$	−26.4976	−1.11774
$563$	7.01381	0.295597	0.147798	−	0.989018i	$-0.452781\pi$
$563$	7.01381	0.295597	0.147798	+	0.989018i	$0.452781\pi$
$564$	1.03935	0.0437645
$565$	4.16229	0.175109
$566$	−25.0095	−1.05123
$567$	4.67729	0.196428
$568$	4.77564	0.200381
$569$	34.4271	1.44326	0.721629	−	0.692280i	$-0.243394\pi$
$569$	34.4271	1.44326	0.721629	+	0.692280i	$0.243394\pi$
$570$	−17.1542	−0.718512
$571$	7.91030	0.331036	0.165518	−	0.986207i	$-0.447070\pi$
$571$	7.91030	0.331036	0.165518	+	0.986207i	$0.447070\pi$
$572$	3.62918	0.151744
$573$	4.16668	0.174066
$574$	−54.6254	−2.28002
$575$	19.5504	0.815307
$576$	1.00000	0.0416667
$577$	−17.9360	−0.746686	−0.373343	−	0.927693i	$-0.621789\pi$
$577$	−17.9360	−0.746686	−0.373343	+	0.927693i	$0.621789\pi$
$578$	1.00000	0.0415945
$579$	−0.335211	−0.0139309
$580$	−27.0969	−1.12514
$581$	59.4655	2.46704
$582$	9.68663	0.401524
$583$	−7.59207	−0.314431
$584$	11.3315	0.468903
$585$	−12.2246	−0.505424
$586$	−14.1710	−0.585398
$587$	−20.9520	−0.864780	−0.432390	−	0.901687i	$-0.642330\pi$
$587$	−20.9520	−0.864780	−0.432390	+	0.901687i	$0.642330\pi$
$588$	−14.8771	−0.613520
$589$	8.01965	0.330444
$590$	3.24808	0.133721
$591$	−1.39648	−0.0574434
$592$	0.888494	0.0365169
$593$	7.57543	0.311086	0.155543	−	0.987829i	$-0.450287\pi$
$593$	7.57543	0.311086	0.155543	+	0.987829i	$0.450287\pi$
$594$	0.964277	0.0395648
$595$	15.1922	0.622821
$596$	−20.8053	−0.852219
$597$	−5.34040	−0.218568
$598$	−13.2576	−0.542145
$599$	−30.0807	−1.22906	−0.614532	−	0.788892i	$-0.710655\pi$
$599$	−30.0807	−1.22906	−0.614532	+	0.788892i	$0.710655\pi$
$600$	−5.55004	−0.226579
$601$	6.29500	0.256779	0.128389	−	0.991724i	$-0.459019\pi$
$601$	6.29500	0.256779	0.128389	+	0.991724i	$0.459019\pi$
$602$	14.6403	0.596695
$603$	−5.31844	−0.216584
$604$	0.591724	0.0240769
$605$	−32.7087	−1.32980
$606$	3.30551	0.134277
$607$	−15.6462	−0.635061	−0.317530	−	0.948248i	$-0.602854\pi$
$607$	−15.6462	−0.635061	−0.317530	+	0.948248i	$0.602854\pi$
$608$	5.28135	0.214187
$609$	39.0200	1.58117
$610$	41.3326	1.67351
$611$	3.91173	0.158251
$612$	1.00000	0.0404226
$613$	−16.6496	−0.672469	−0.336235	−	0.941778i	$-0.609154\pi$
$613$	−16.6496	−0.672469	−0.336235	+	0.941778i	$0.609154\pi$
$614$	−0.0848060	−0.00342249
$615$	37.9339	1.52964
$616$	−4.51020	−0.181721
$617$	−14.6616	−0.590255	−0.295127	−	0.955458i	$-0.595362\pi$
$617$	−14.6616	−0.590255	−0.295127	+	0.955458i	$0.595362\pi$
$618$	5.42804	0.218348
$619$	12.5813	0.505684	0.252842	−	0.967508i	$-0.418635\pi$
$619$	12.5813	0.505684	0.252842	+	0.967508i	$0.418635\pi$
$620$	4.93216	0.198080
$621$	−3.52257	−0.141356
$622$	−30.8497	−1.23696
$623$	52.4265	2.10042
$624$	3.76363	0.150666
$625$	−21.9473	−0.877891
$626$	14.5289	0.580690
$627$	5.09268	0.203382
$628$	−14.9091	−0.594938
$629$	0.888494	0.0354266
$630$	15.1922	0.605273
$631$	24.8563	0.989512	0.494756	−	0.869032i	$-0.335257\pi$
$631$	24.8563	0.989512	0.494756	+	0.869032i	$0.335257\pi$
$632$	−7.01971	−0.279229
$633$	−10.0065	−0.397722
$634$	21.4863	0.853331
$635$	−30.5640	−1.21289
$636$	−7.87333	−0.312198
$637$	−55.9917	−2.21847
$638$	8.04442	0.318482
$639$	4.77564	0.188921
$640$	3.24808	0.128392
$641$	−23.7230	−0.937002	−0.468501	−	0.883463i	$-0.655206\pi$
$641$	−23.7230	−0.937002	−0.468501	+	0.883463i	$0.655206\pi$
$642$	9.35714	0.369297
$643$	10.1413	0.399936	0.199968	−	0.979802i	$-0.435916\pi$
$643$	10.1413	0.399936	0.199968	+	0.979802i	$0.435916\pi$
$644$	16.4761	0.649248
$645$	−10.1668	−0.400317
$646$	5.28135	0.207792
$647$	−11.6714	−0.458850	−0.229425	−	0.973326i	$-0.573685\pi$
$647$	−11.6714	−0.458850	−0.229425	+	0.973326i	$0.573685\pi$
$648$	1.00000	0.0392837
$649$	−0.964277	−0.0378512
$650$	−20.8883	−0.819306
$651$	−7.10240	−0.278365
$652$	−3.86070	−0.151197
$653$	−41.7466	−1.63367	−0.816836	−	0.576870i	$-0.804274\pi$
$653$	−41.7466	−1.63367	−0.816836	+	0.576870i	$0.804274\pi$
$654$	−13.3923	−0.523679
$655$	−24.8954	−0.972744
$656$	−11.6789	−0.455983
$657$	11.3315	0.442086
$658$	−4.86134	−0.189515
$659$	−36.7387	−1.43114	−0.715569	−	0.698542i	$-0.753833\pi$
$659$	−36.7387	−1.43114	−0.715569	+	0.698542i	$0.753833\pi$
$660$	3.13205	0.121915
$661$	30.6590	1.19250	0.596249	−	0.802799i	$-0.296657\pi$
$661$	30.6590	1.19250	0.596249	+	0.802799i	$0.296657\pi$
$662$	13.2725	0.515851
$663$	3.76363	0.146167
$664$	12.7137	0.493385
$665$	80.2354	3.11140
$666$	0.888494	0.0344284
$667$	−29.3868	−1.13786
$668$	−5.61829	−0.217378
$669$	19.4606	0.752390
$670$	−17.2747	−0.667381
$671$	−12.2707	−0.473704
$672$	−4.67729	−0.180430
$673$	−36.3562	−1.40143	−0.700715	−	0.713441i	$-0.747136\pi$
$673$	−36.3562	−1.40143	−0.700715	+	0.713441i	$0.747136\pi$
$674$	11.9625	0.460778
$675$	−5.55004	−0.213621
$676$	1.16490	0.0448039
$677$	−47.4110	−1.82215	−0.911076	−	0.412238i	$-0.864747\pi$
$677$	−47.4110	−1.82215	−0.911076	+	0.412238i	$0.864747\pi$
$678$	−1.28146	−0.0492142
$679$	−45.3072	−1.73873
$680$	3.24808	0.124558
$681$	−27.6168	−1.05828
$682$	−1.46424	−0.0560686
$683$	−11.1056	−0.424943	−0.212471	−	0.977167i	$-0.568151\pi$
$683$	−11.1056	−0.424943	−0.212471	+	0.977167i	$0.568151\pi$
$684$	5.28135	0.201937
$685$	−41.4995	−1.58562
$686$	36.8433	1.40668
$687$	−12.3449	−0.470987
$688$	3.13009	0.119333
$689$	−29.6323	−1.12890
$690$	−11.4416	−0.435574
$691$	8.21029	0.312334	0.156167	−	0.987731i	$-0.450086\pi$
$691$	8.21029	0.312334	0.156167	+	0.987731i	$0.450086\pi$
$692$	−14.4876	−0.550734
$693$	−4.51020	−0.171328
$694$	−2.95988	−0.112355
$695$	11.8966	0.451263
$696$	8.34244	0.316219
$697$	−11.6789	−0.442368
$698$	−28.6405	−1.08406
$699$	−1.60445	−0.0606857
$700$	25.9591	0.981164
$701$	−11.3520	−0.428759	−0.214380	−	0.976750i	$-0.568773\pi$
$701$	−11.3520	−0.428759	−0.214380	+	0.976750i	$0.568773\pi$
$702$	3.76363	0.142049
$703$	4.69244	0.176979
$704$	−0.964277	−0.0363426
$705$	3.37589	0.127143
$706$	14.3844	0.541362
$707$	−15.4608	−0.581465
$708$	−1.00000	−0.0375823
$709$	−50.5121	−1.89702	−0.948511	−	0.316744i	$-0.897410\pi$
$709$	−50.5121	−1.89702	−0.948511	+	0.316744i	$0.897410\pi$
$710$	15.5117	0.582143
$711$	−7.01971	−0.263260
$712$	11.2087	0.420065
$713$	5.34896	0.200320
$714$	−4.67729	−0.175043
$715$	11.7879	0.440842
$716$	15.5761	0.582107
$717$	12.4813	0.466124
$718$	20.9168	0.780607
$719$	7.38868	0.275551	0.137776	−	0.990463i	$-0.456005\pi$
$719$	7.38868	0.275551	0.137776	+	0.990463i	$0.456005\pi$
$720$	3.24808	0.121049
$721$	−25.3885	−0.945517
$722$	8.89262	0.330949
$723$	−16.5973	−0.617260
$724$	10.4407	0.388024
$725$	−46.3009	−1.71957
$726$	10.0702	0.373739
$727$	7.45647	0.276545	0.138273	−	0.990394i	$-0.455845\pi$
$727$	7.45647	0.276545	0.138273	+	0.990394i	$0.455845\pi$
$728$	−17.6036	−0.652432
$729$	1.00000	0.0370370
$730$	36.8058	1.36224
$731$	3.13009	0.115770
$732$	−12.7252	−0.470339
$733$	46.6802	1.72417	0.862086	−	0.506761i	$-0.169157\pi$
$733$	46.6802	1.72417	0.862086	+	0.506761i	$0.169157\pi$
$734$	−36.8894	−1.36161
$735$	−48.3219	−1.78238
$736$	3.52257	0.129843
$737$	5.12845	0.188909
$738$	−11.6789	−0.429905
$739$	−6.14182	−0.225931	−0.112965	−	0.993599i	$-0.536035\pi$
$739$	−6.14182	−0.225931	−0.112965	+	0.993599i	$0.536035\pi$
$740$	2.88590	0.106088
$741$	19.8770	0.730201
$742$	36.8259	1.35192
$743$	−28.6196	−1.04995	−0.524975	−	0.851117i	$-0.675925\pi$
$743$	−28.6196	−1.04995	−0.524975	+	0.851117i	$0.675925\pi$
$744$	−1.51849	−0.0556704
$745$	−67.5773	−2.47584
$746$	−8.27987	−0.303148
$747$	12.7137	0.465168
$748$	−0.964277	−0.0352575
$749$	−43.7661	−1.59918
$750$	−1.78657	−0.0652362
$751$	4.81929	0.175858	0.0879292	−	0.996127i	$-0.471975\pi$
$751$	4.81929	0.175858	0.0879292	+	0.996127i	$0.471975\pi$
$752$	−1.03935	−0.0379012
$753$	2.98004	0.108599
$754$	31.3978	1.14344
$755$	1.92197	0.0699476
$756$	−4.67729	−0.170111
$757$	28.3558	1.03061	0.515305	−	0.857007i	$-0.327679\pi$
$757$	28.3558	1.03061	0.515305	+	0.857007i	$0.327679\pi$
$758$	7.63045	0.277150
$759$	3.39673	0.123293
$760$	17.1542	0.622250
$761$	2.69807	0.0978050	0.0489025	−	0.998804i	$-0.484428\pi$
$761$	2.69807	0.0978050	0.0489025	+	0.998804i	$0.484428\pi$
$762$	9.40985	0.340883
$763$	62.6396	2.26771
$764$	−4.16668	−0.150745
$765$	3.24808	0.117435
$766$	−30.8877	−1.11602
$767$	−3.76363	−0.135897
$768$	−1.00000	−0.0360844
$769$	−10.0892	−0.363827	−0.181914	−	0.983315i	$-0.558229\pi$
$769$	−10.0892	−0.363827	−0.181914	+	0.983315i	$0.558229\pi$
$770$	−14.6495	−0.527932
$771$	−12.1620	−0.438005
$772$	0.335211	0.0120645
$773$	−21.4704	−0.772236	−0.386118	−	0.922449i	$-0.626184\pi$
$773$	−21.4704	−0.772236	−0.386118	+	0.922449i	$0.626184\pi$
$774$	3.13009	0.112509
$775$	8.42765	0.302730
$776$	−9.68663	−0.347730
$777$	−4.15575	−0.149087
$778$	2.17405	0.0779433
$779$	−61.6801	−2.20992
$780$	12.2246	0.437710
$781$	−4.60504	−0.164781
$782$	3.52257	0.125967
$783$	8.34244	0.298134
$784$	14.8771	0.531324
$785$	−48.4260	−1.72840
$786$	7.66465	0.273389
$787$	42.7166	1.52268	0.761341	−	0.648352i	$-0.224541\pi$
$787$	42.7166	1.52268	0.761341	+	0.648352i	$0.224541\pi$
$788$	1.39648	0.0497474
$789$	−19.2237	−0.684381
$790$	−22.8006	−0.811208
$791$	5.99377	0.213114
$792$	−0.964277	−0.0342641
$793$	−47.8931	−1.70073
$794$	11.5219	0.408898
$795$	−25.5732	−0.906989
$796$	5.34040	0.189285
$797$	−16.2205	−0.574561	−0.287281	−	0.957846i	$-0.592751\pi$
$797$	−16.2205	−0.574561	−0.287281	+	0.957846i	$0.592751\pi$
$798$	−24.7024	−0.874455
$799$	−1.03935	−0.0367695
$800$	5.55004	0.196223
$801$	11.2087	0.396041
$802$	−24.6706	−0.871150
$803$	−10.9267	−0.385596
$804$	5.31844	0.187567
$805$	53.5156	1.88618
$806$	−5.71501	−0.201303
$807$	1.41513	0.0498148
$808$	−3.30551	−0.116288
$809$	2.93257	0.103104	0.0515519	−	0.998670i	$-0.483583\pi$
$809$	2.93257	0.103104	0.0515519	+	0.998670i	$0.483583\pi$
$810$	3.24808	0.114126
$811$	−12.1081	−0.425172	−0.212586	−	0.977142i	$-0.568189\pi$
$811$	−12.1081	−0.425172	−0.212586	+	0.977142i	$0.568189\pi$
$812$	−39.0200	−1.36933
$813$	11.7428	0.411837
$814$	−0.856754	−0.0300292
$815$	−12.5399	−0.439252
$816$	−1.00000	−0.0350070
$817$	16.5311	0.578349
$818$	15.8261	0.553348
$819$	−17.6036	−0.615119
$820$	−37.9339	−1.32471
$821$	−9.10570	−0.317791	−0.158896	−	0.987295i	$-0.550793\pi$
$821$	−9.10570	−0.317791	−0.158896	+	0.987295i	$0.550793\pi$
$822$	12.7766	0.445636
$823$	29.2078	1.01812	0.509060	−	0.860731i	$-0.329993\pi$
$823$	29.2078	1.01812	0.509060	+	0.860731i	$0.329993\pi$
$824$	−5.42804	−0.189095
$825$	5.35177	0.186325
$826$	4.67729	0.162744
$827$	1.13959	0.0396273	0.0198137	−	0.999804i	$-0.493693\pi$
$827$	1.13959	0.0396273	0.0198137	+	0.999804i	$0.493693\pi$
$828$	3.52257	0.122418
$829$	26.0509	0.904785	0.452393	−	0.891819i	$-0.350571\pi$
$829$	26.0509	0.904785	0.452393	+	0.891819i	$0.350571\pi$
$830$	41.2950	1.43337
$831$	−19.1118	−0.662979
$832$	−3.76363	−0.130480
$833$	14.8771	0.515460
$834$	−3.66265	−0.126827
$835$	−18.2487	−0.631521
$836$	−5.09268	−0.176134
$837$	−1.51849	−0.0524865
$838$	−24.7072	−0.853497
$839$	11.2082	0.386950	0.193475	−	0.981105i	$-0.438024\pi$
$839$	11.2082	0.386950	0.193475	+	0.981105i	$0.438024\pi$
$840$	−15.1922	−0.524182
$841$	40.5963	1.39987
$842$	37.3900	1.28854
$843$	26.4976	0.912627
$844$	10.0065	0.344437
$845$	3.78369	0.130163
$846$	−1.03935	−0.0357336
$847$	−47.1011	−1.61841
$848$	7.87333	0.270371
$849$	25.0095	0.858322
$850$	5.55004	0.190365
$851$	3.12978	0.107287
$852$	−4.77564	−0.163611
$853$	31.9926	1.09541	0.547703	−	0.836673i	$-0.315502\pi$
$853$	31.9926	1.09541	0.547703	+	0.836673i	$0.315502\pi$
$854$	59.5197	2.03672
$855$	17.1542	0.586663
$856$	−9.35714	−0.319821
$857$	−51.1641	−1.74773	−0.873866	−	0.486167i	$-0.838395\pi$
$857$	−51.1641	−1.74773	−0.873866	+	0.486167i	$0.838395\pi$
$858$	−3.62918	−0.123898
$859$	−27.2627	−0.930191	−0.465095	−	0.885261i	$-0.653980\pi$
$859$	−27.2627	−0.930191	−0.465095	+	0.885261i	$0.653980\pi$
$860$	10.1668	0.346684
$861$	54.6254	1.86163
$862$	−26.2686	−0.894711
$863$	−30.4257	−1.03570	−0.517852	−	0.855470i	$-0.673268\pi$
$863$	−30.4257	−1.03570	−0.517852	+	0.855470i	$0.673268\pi$
$864$	−1.00000	−0.0340207
$865$	−47.0568	−1.59998
$866$	−14.3891	−0.488961
$867$	−1.00000	−0.0339618
$868$	7.10240	0.241071
$869$	6.76894	0.229621
$870$	27.0969	0.918672
$871$	20.0166	0.678237
$872$	13.3923	0.453520
$873$	−9.68663	−0.327843
$874$	18.6039	0.629286
$875$	8.35630	0.282494
$876$	−11.3315	−0.382857
$877$	44.8983	1.51611	0.758055	−	0.652191i	$-0.226150\pi$
$877$	44.8983	1.51611	0.758055	+	0.652191i	$0.226150\pi$
$878$	−14.8704	−0.501850
$879$	14.1710	0.477976
$880$	−3.13205	−0.105581
$881$	33.2650	1.12073	0.560363	−	0.828247i	$-0.310662\pi$
$881$	33.2650	1.12073	0.560363	+	0.828247i	$0.310662\pi$
$882$	14.8771	0.500937
$883$	−13.6913	−0.460747	−0.230374	−	0.973102i	$-0.573995\pi$
$883$	−13.6913	−0.460747	−0.230374	+	0.973102i	$0.573995\pi$
$884$	−3.76363	−0.126585
$885$	−3.24808	−0.109183
$886$	−15.3125	−0.514435
$887$	19.1500	0.642994	0.321497	−	0.946911i	$-0.395814\pi$
$887$	19.1500	0.642994	0.321497	+	0.946911i	$0.395814\pi$
$888$	−0.888494	−0.0298159
$889$	−44.0126	−1.47614
$890$	36.4069	1.22036
$891$	−0.964277	−0.0323045
$892$	−19.4606	−0.651589
$893$	−5.48917	−0.183688
$894$	20.8053	0.695834
$895$	50.5925	1.69112
$896$	4.67729	0.156257
$897$	13.2576	0.442659
$898$	37.0958	1.23790
$899$	−12.6679	−0.422497
$900$	5.55004	0.185001
$901$	7.87333	0.262299
$902$	11.2616	0.374972
$903$	−14.6403	−0.487200
$904$	1.28146	0.0426208
$905$	33.9121	1.12728
$906$	−0.591724	−0.0196587
$907$	−1.14076	−0.0378785	−0.0189392	−	0.999821i	$-0.506029\pi$
$907$	−1.14076	−0.0378785	−0.0189392	+	0.999821i	$0.506029\pi$
$908$	27.6168	0.916495
$909$	−3.30551	−0.109637
$910$	−57.1779	−1.89543
$911$	−35.5515	−1.17787	−0.588937	−	0.808179i	$-0.700453\pi$
$911$	−35.5515	−1.17787	−0.588937	+	0.808179i	$0.700453\pi$
$912$	−5.28135	−0.174883
$913$	−12.2595	−0.405730
$914$	24.4591	0.809035
$915$	−41.3326	−1.36641
$916$	12.3449	0.407887
$917$	−35.8498	−1.18386
$918$	−1.00000	−0.0330049
$919$	15.2232	0.502165	0.251083	−	0.967966i	$-0.419213\pi$
$919$	15.2232	0.502165	0.251083	+	0.967966i	$0.419213\pi$
$920$	11.4416	0.377218
$921$	0.0848060	0.00279445
$922$	29.4670	0.970443
$923$	−17.9737	−0.591613
$924$	4.51020	0.148375
$925$	4.93118	0.162136
$926$	1.49629	0.0491710
$927$	−5.42804	−0.178280
$928$	−8.34244	−0.273854
$929$	−23.4988	−0.770971	−0.385485	−	0.922714i	$-0.625966\pi$
$929$	−23.4988	−0.770971	−0.385485	+	0.922714i	$0.625966\pi$
$930$	−4.93216	−0.161732
$931$	78.5709	2.57506
$932$	1.60445	0.0525553
$933$	30.8497	1.00997
$934$	26.2523	0.859001
$935$	−3.13205	−0.102429
$936$	−3.76363	−0.123018
$937$	13.4115	0.438133	0.219067	−	0.975710i	$-0.429699\pi$
$937$	13.4115	0.438133	0.219067	+	0.975710i	$0.429699\pi$
$938$	−24.8759	−0.812226
$939$	−14.5289	−0.474131
$940$	−3.37589	−0.110109
$941$	−56.1574	−1.83068	−0.915339	−	0.402683i	$-0.868078\pi$
$941$	−56.1574	−1.83068	−0.915339	+	0.402683i	$0.868078\pi$
$942$	14.9091	0.485765
$943$	−41.1395	−1.33969
$944$	1.00000	0.0325472
$945$	−15.1922	−0.494203
$946$	−3.01827	−0.0981324
$947$	13.1193	0.426319	0.213160	−	0.977017i	$-0.431625\pi$
$947$	13.1193	0.426319	0.213160	+	0.977017i	$0.431625\pi$
$948$	7.01971	0.227989
$949$	−42.6477	−1.38440
$950$	29.3117	0.950996
$951$	−21.4863	−0.696742
$952$	4.67729	0.151592
$953$	−11.0575	−0.358189	−0.179094	−	0.983832i	$-0.557317\pi$
$953$	−11.0575	−0.358189	−0.179094	+	0.983832i	$0.557317\pi$
$954$	7.87333	0.254908
$955$	−13.5337	−0.437941
$956$	−12.4813	−0.403675
$957$	−8.04442	−0.260039
$958$	−19.6601	−0.635189
$959$	−59.7600	−1.92975
$960$	−3.24808	−0.104831
$961$	−28.6942	−0.925619
$962$	−3.34396	−0.107814
$963$	−9.35714	−0.301530
$964$	16.5973	0.534563
$965$	1.08879	0.0350495
$966$	−16.4761	−0.530109
$967$	−34.6909	−1.11558	−0.557792	−	0.829981i	$-0.688351\pi$
$967$	−34.6909	−1.11558	−0.557792	+	0.829981i	$0.688351\pi$
$968$	−10.0702	−0.323668
$969$	−5.28135	−0.169661
$970$	−31.4630	−1.01022
$971$	6.05085	0.194181	0.0970905	−	0.995276i	$-0.469046\pi$
$971$	6.05085	0.194181	0.0970905	+	0.995276i	$0.469046\pi$
$972$	−1.00000	−0.0320750
$973$	17.1313	0.549204
$974$	−30.0997	−0.964456
$975$	20.8883	0.668960
$976$	12.7252	0.407325
$977$	6.87914	0.220083	0.110042	−	0.993927i	$-0.464902\pi$
$977$	6.87914	0.220083	0.110042	+	0.993927i	$0.464902\pi$
$978$	3.86070	0.123451
$979$	−10.8083	−0.345435
$980$	48.3219	1.54359
$981$	13.3923	0.427582
$982$	34.0092	1.08528
$983$	−4.23662	−0.135127	−0.0675636	−	0.997715i	$-0.521523\pi$
$983$	−4.23662	−0.135127	−0.0675636	+	0.997715i	$0.521523\pi$
$984$	11.6789	0.372308
$985$	4.53587	0.144525
$986$	−8.34244	−0.265677
$987$	4.86134	0.154738
$988$	−19.8770	−0.632372
$989$	11.0259	0.350604
$990$	−3.13205	−0.0995431
$991$	17.8050	0.565594	0.282797	−	0.959180i	$-0.408738\pi$
$991$	17.8050	0.565594	0.282797	+	0.959180i	$0.408738\pi$
$992$	1.51849	0.0482120
$993$	−13.2725	−0.421191
$994$	22.3371	0.708489
$995$	17.3461	0.549907
$996$	−12.7137	−0.402848
$997$	60.4739	1.91523	0.957614	−	0.288056i	$-0.0930088\pi$
$997$	60.4739	1.91523	0.957614	+	0.288056i	$0.0930088\pi$
$998$	−26.0517	−0.824653
$999$	−0.888494	−0.0281107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bc.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bc.1.12	✓	14	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.24808 q^{5} -1.00000 q^{6} +4.67729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.24808 q^{5} -1.00000 q^{6} +4.67729 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.24808 q^{10} -0.964277 q^{11} -1.00000 q^{12} -3.76363 q^{13} +4.67729 q^{14} -3.24808 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.28135 q^{19} +3.24808 q^{20} -4.67729 q^{21} -0.964277 q^{22} +3.52257 q^{23} -1.00000 q^{24} +5.55004 q^{25} -3.76363 q^{26} -1.00000 q^{27} +4.67729 q^{28} -8.34244 q^{29} -3.24808 q^{30} +1.51849 q^{31} +1.00000 q^{32} +0.964277 q^{33} +1.00000 q^{34} +15.1922 q^{35} +1.00000 q^{36} +0.888494 q^{37} +5.28135 q^{38} +3.76363 q^{39} +3.24808 q^{40} -11.6789 q^{41} -4.67729 q^{42} +3.13009 q^{43} -0.964277 q^{44} +3.24808 q^{45} +3.52257 q^{46} -1.03935 q^{47} -1.00000 q^{48} +14.8771 q^{49} +5.55004 q^{50} -1.00000 q^{51} -3.76363 q^{52} +7.87333 q^{53} -1.00000 q^{54} -3.13205 q^{55} +4.67729 q^{56} -5.28135 q^{57} -8.34244 q^{58} +1.00000 q^{59} -3.24808 q^{60} +12.7252 q^{61} +1.51849 q^{62} +4.67729 q^{63} +1.00000 q^{64} -12.2246 q^{65} +0.964277 q^{66} -5.31844 q^{67} +1.00000 q^{68} -3.52257 q^{69} +15.1922 q^{70} +4.77564 q^{71} +1.00000 q^{72} +11.3315 q^{73} +0.888494 q^{74} -5.55004 q^{75} +5.28135 q^{76} -4.51020 q^{77} +3.76363 q^{78} -7.01971 q^{79} +3.24808 q^{80} +1.00000 q^{81} -11.6789 q^{82} +12.7137 q^{83} -4.67729 q^{84} +3.24808 q^{85} +3.13009 q^{86} +8.34244 q^{87} -0.964277 q^{88} +11.2087 q^{89} +3.24808 q^{90} -17.6036 q^{91} +3.52257 q^{92} -1.51849 q^{93} -1.03935 q^{94} +17.1542 q^{95} -1.00000 q^{96} -9.68663 q^{97} +14.8771 q^{98} -0.964277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9} + 2 q^{10} + 3 q^{11} - 14 q^{12} + 16 q^{13} + q^{14} - 2 q^{15} + 14 q^{16} + 14 q^{17} + 14 q^{18} + 13 q^{19} + 2 q^{20} - q^{21} + 3 q^{22} + 4 q^{23} - 14 q^{24} + 32 q^{25} + 16 q^{26} - 14 q^{27} + q^{28} - 2 q^{30} - 13 q^{31} + 14 q^{32} - 3 q^{33} + 14 q^{34} + 14 q^{36} + 12 q^{37} + 13 q^{38} - 16 q^{39} + 2 q^{40} - 18 q^{41} - q^{42} + 29 q^{43} + 3 q^{44} + 2 q^{45} + 4 q^{46} - 14 q^{48} + 49 q^{49} + 32 q^{50} - 14 q^{51} + 16 q^{52} + 24 q^{53} - 14 q^{54} + 15 q^{55} + q^{56} - 13 q^{57} + 14 q^{59} - 2 q^{60} + 29 q^{61} - 13 q^{62} + q^{63} + 14 q^{64} + 6 q^{65} - 3 q^{66} + 4 q^{67} + 14 q^{68} - 4 q^{69} - 10 q^{71} + 14 q^{72} + 18 q^{73} + 12 q^{74} - 32 q^{75} + 13 q^{76} + 20 q^{77} - 16 q^{78} + 7 q^{79} + 2 q^{80} + 14 q^{81} - 18 q^{82} + 28 q^{83} - q^{84} + 2 q^{85} + 29 q^{86} + 3 q^{88} + 23 q^{89} + 2 q^{90} + 9 q^{91} + 4 q^{92} + 13 q^{93} + 5 q^{95} - 14 q^{96} - 7 q^{97} + 49 q^{98} + 3 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 - 14 * q^3 + 14 * q^4 + 2 * q^5 - 14 * q^6 + q^7 + 14 * q^8 + 14 * q^9 + 2 * q^10 + 3 * q^11 - 14 * q^12 + 16 * q^13 + q^14 - 2 * q^15 + 14 * q^16 + 14 * q^17 + 14 * q^18 + 13 * q^19 + 2 * q^20 - q^21 + 3 * q^22 + 4 * q^23 - 14 * q^24 + 32 * q^25 + 16 * q^26 - 14 * q^27 + q^28 - 2 * q^30 - 13 * q^31 + 14 * q^32 - 3 * q^33 + 14 * q^34 + 14 * q^36 + 12 * q^37 + 13 * q^38 - 16 * q^39 + 2 * q^40 - 18 * q^41 - q^42 + 29 * q^43 + 3 * q^44 + 2 * q^45 + 4 * q^46 - 14 * q^48 + 49 * q^49 + 32 * q^50 - 14 * q^51 + 16 * q^52 + 24 * q^53 - 14 * q^54 + 15 * q^55 + q^56 - 13 * q^57 + 14 * q^59 - 2 * q^60 + 29 * q^61 - 13 * q^62 + q^63 + 14 * q^64 + 6 * q^65 - 3 * q^66 + 4 * q^67 + 14 * q^68 - 4 * q^69 - 10 * q^71 + 14 * q^72 + 18 * q^73 + 12 * q^74 - 32 * q^75 + 13 * q^76 + 20 * q^77 - 16 * q^78 + 7 * q^79 + 2 * q^80 + 14 * q^81 - 18 * q^82 + 28 * q^83 - q^84 + 2 * q^85 + 29 * q^86 + 3 * q^88 + 23 * q^89 + 2 * q^90 + 9 * q^91 + 4 * q^92 + 13 * q^93 + 5 * q^95 - 14 * q^96 - 7 * q^97 + 49 * q^98 + 3 * q^99

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