LMFDB - Embedded newform 6018.2.a.bc.1.3

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			1.3
Root			$-3.00862$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00862 q^{5} -1.00000 q^{6} -0.900066 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00862 q^{5} -1.00000 q^{6} -0.900066 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.00862 q^{10} -6.30983 q^{11} -1.00000 q^{12} -3.45134 q^{13} -0.900066 q^{14} +3.00862 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.45211 q^{19} -3.00862 q^{20} +0.900066 q^{21} -6.30983 q^{22} -2.88558 q^{23} -1.00000 q^{24} +4.05178 q^{25} -3.45134 q^{26} -1.00000 q^{27} -0.900066 q^{28} +2.91623 q^{29} +3.00862 q^{30} -1.87668 q^{31} +1.00000 q^{32} +6.30983 q^{33} +1.00000 q^{34} +2.70795 q^{35} +1.00000 q^{36} -8.38471 q^{37} +6.45211 q^{38} +3.45134 q^{39} -3.00862 q^{40} -10.6470 q^{41} +0.900066 q^{42} -4.63613 q^{43} -6.30983 q^{44} -3.00862 q^{45} -2.88558 q^{46} -9.49357 q^{47} -1.00000 q^{48} -6.18988 q^{49} +4.05178 q^{50} -1.00000 q^{51} -3.45134 q^{52} +6.66594 q^{53} -1.00000 q^{54} +18.9839 q^{55} -0.900066 q^{56} -6.45211 q^{57} +2.91623 q^{58} +1.00000 q^{59} +3.00862 q^{60} +1.98803 q^{61} -1.87668 q^{62} -0.900066 q^{63} +1.00000 q^{64} +10.3838 q^{65} +6.30983 q^{66} +10.3412 q^{67} +1.00000 q^{68} +2.88558 q^{69} +2.70795 q^{70} -9.78989 q^{71} +1.00000 q^{72} -4.23244 q^{73} -8.38471 q^{74} -4.05178 q^{75} +6.45211 q^{76} +5.67926 q^{77} +3.45134 q^{78} +5.62862 q^{79} -3.00862 q^{80} +1.00000 q^{81} -10.6470 q^{82} +16.5675 q^{83} +0.900066 q^{84} -3.00862 q^{85} -4.63613 q^{86} -2.91623 q^{87} -6.30983 q^{88} +9.46066 q^{89} -3.00862 q^{90} +3.10644 q^{91} -2.88558 q^{92} +1.87668 q^{93} -9.49357 q^{94} -19.4119 q^{95} -1.00000 q^{96} +7.99860 q^{97} -6.18988 q^{98} -6.30983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.00862	−1.34549	−0.672747	−	0.739872i	$-0.734886\pi$
$5$	−3.00862	−1.34549	−0.672747	+	0.739872i	$0.734886\pi$
$6$	−1.00000	−0.408248
$7$	−0.900066	−0.340193	−0.170096	−	0.985427i	$-0.554408\pi$
$7$	−0.900066	−0.340193	−0.170096	+	0.985427i	$0.554408\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.00862	−0.951409
$11$	−6.30983	−1.90248	−0.951242	−	0.308445i	$-0.900191\pi$
$11$	−6.30983	−1.90248	−0.951242	+	0.308445i	$0.900191\pi$
$12$	−1.00000	−0.288675
$13$	−3.45134	−0.957231	−0.478615	−	0.878025i	$-0.658861\pi$
$13$	−3.45134	−0.957231	−0.478615	+	0.878025i	$0.658861\pi$
$14$	−0.900066	−0.240553
$15$	3.00862	0.776822
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	6.45211	1.48022	0.740108	−	0.672488i	$-0.234774\pi$
$19$	6.45211	1.48022	0.740108	+	0.672488i	$0.234774\pi$
$20$	−3.00862	−0.672747
$21$	0.900066	0.196411
$22$	−6.30983	−1.34526
$23$	−2.88558	−0.601686	−0.300843	−	0.953674i	$-0.597268\pi$
$23$	−2.88558	−0.601686	−0.300843	+	0.953674i	$0.597268\pi$
$24$	−1.00000	−0.204124
$25$	4.05178	0.810356
$26$	−3.45134	−0.676864
$27$	−1.00000	−0.192450
$28$	−0.900066	−0.170096
$29$	2.91623	0.541530	0.270765	−	0.962645i	$-0.412723\pi$
$29$	2.91623	0.541530	0.270765	+	0.962645i	$0.412723\pi$
$30$	3.00862	0.549296
$31$	−1.87668	−0.337062	−0.168531	−	0.985696i	$-0.553902\pi$
$31$	−1.87668	−0.337062	−0.168531	+	0.985696i	$0.553902\pi$
$32$	1.00000	0.176777
$33$	6.30983	1.09840
$34$	1.00000	0.171499
$35$	2.70795	0.457728
$36$	1.00000	0.166667
$37$	−8.38471	−1.37844	−0.689219	−	0.724553i	$-0.742046\pi$
$37$	−8.38471	−1.37844	−0.689219	+	0.724553i	$0.742046\pi$
$38$	6.45211	1.04667
$39$	3.45134	0.552657
$40$	−3.00862	−0.475704
$41$	−10.6470	−1.66278	−0.831389	−	0.555690i	$-0.812454\pi$
$41$	−10.6470	−1.66278	−0.831389	+	0.555690i	$0.812454\pi$
$42$	0.900066	0.138883
$43$	−4.63613	−0.707004	−0.353502	−	0.935434i	$-0.615009\pi$
$43$	−4.63613	−0.707004	−0.353502	+	0.935434i	$0.615009\pi$
$44$	−6.30983	−0.951242
$45$	−3.00862	−0.448498
$46$	−2.88558	−0.425456
$47$	−9.49357	−1.38478	−0.692389	−	0.721524i	$-0.743442\pi$
$47$	−9.49357	−1.38478	−0.692389	+	0.721524i	$0.743442\pi$
$48$	−1.00000	−0.144338
$49$	−6.18988	−0.884269
$50$	4.05178	0.573009
$51$	−1.00000	−0.140028
$52$	−3.45134	−0.478615
$53$	6.66594	0.915638	0.457819	−	0.889046i	$-0.348631\pi$
$53$	6.66594	0.915638	0.457819	+	0.889046i	$0.348631\pi$
$54$	−1.00000	−0.136083
$55$	18.9839	2.55978
$56$	−0.900066	−0.120276
$57$	−6.45211	−0.854603
$58$	2.91623	0.382919
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.00862	0.388411
$61$	1.98803	0.254541	0.127270	−	0.991868i	$-0.459378\pi$
$61$	1.98803	0.254541	0.127270	+	0.991868i	$0.459378\pi$
$62$	−1.87668	−0.238339
$63$	−0.900066	−0.113398
$64$	1.00000	0.125000
$65$	10.3838	1.28795
$66$	6.30983	0.776686
$67$	10.3412	1.26338	0.631690	−	0.775221i	$-0.282362\pi$
$67$	10.3412	1.26338	0.631690	+	0.775221i	$0.282362\pi$
$68$	1.00000	0.121268
$69$	2.88558	0.347384
$70$	2.70795	0.323663
$71$	−9.78989	−1.16185	−0.580923	−	0.813958i	$-0.697308\pi$
$71$	−9.78989	−1.16185	−0.580923	+	0.813958i	$0.697308\pi$
$72$	1.00000	0.117851
$73$	−4.23244	−0.495369	−0.247685	−	0.968841i	$-0.579670\pi$
$73$	−4.23244	−0.495369	−0.247685	+	0.968841i	$0.579670\pi$
$74$	−8.38471	−0.974702
$75$	−4.05178	−0.467860
$76$	6.45211	0.740108
$77$	5.67926	0.647212
$78$	3.45134	0.390788
$79$	5.62862	0.633269	0.316635	−	0.948548i	$-0.397447\pi$
$79$	5.62862	0.633269	0.316635	+	0.948548i	$0.397447\pi$
$80$	−3.00862	−0.336374
$81$	1.00000	0.111111
$82$	−10.6470	−1.17576
$83$	16.5675	1.81852	0.909259	−	0.416231i	$-0.136649\pi$
$83$	16.5675	1.81852	0.909259	+	0.416231i	$0.136649\pi$
$84$	0.900066	0.0982053
$85$	−3.00862	−0.326330
$86$	−4.63613	−0.499927
$87$	−2.91623	−0.312652
$88$	−6.30983	−0.672630
$89$	9.46066	1.00283	0.501414	−	0.865207i	$-0.332813\pi$
$89$	9.46066	1.00283	0.501414	+	0.865207i	$0.332813\pi$
$90$	−3.00862	−0.317136
$91$	3.10644	0.325643
$92$	−2.88558	−0.300843
$93$	1.87668	0.194603
$94$	−9.49357	−0.979187
$95$	−19.4119	−1.99162
$96$	−1.00000	−0.102062
$97$	7.99860	0.812135	0.406067	−	0.913843i	$-0.366900\pi$
$97$	7.99860	0.812135	0.406067	+	0.913843i	$0.366900\pi$
$98$	−6.18988	−0.625272
$99$	−6.30983	−0.634161
$100$	4.05178	0.405178
$101$	−12.5529	−1.24906	−0.624531	−	0.781000i	$-0.714710\pi$
$101$	−12.5529	−1.24906	−0.624531	+	0.781000i	$0.714710\pi$
$102$	−1.00000	−0.0990148
$103$	7.50255	0.739249	0.369624	−	0.929181i	$-0.379486\pi$
$103$	7.50255	0.739249	0.369624	+	0.929181i	$0.379486\pi$
$104$	−3.45134	−0.338432
$105$	−2.70795	−0.264269
$106$	6.66594	0.647454
$107$	−19.6141	−1.89617	−0.948083	−	0.318023i	$-0.896981\pi$
$107$	−19.6141	−1.89617	−0.948083	+	0.318023i	$0.896981\pi$
$108$	−1.00000	−0.0962250
$109$	13.1725	1.26169	0.630847	−	0.775907i	$-0.282707\pi$
$109$	13.1725	1.26169	0.630847	+	0.775907i	$0.282707\pi$
$110$	18.9839	1.81004
$111$	8.38471	0.795841
$112$	−0.900066	−0.0850482
$113$	13.6376	1.28292	0.641458	−	0.767158i	$-0.278330\pi$
$113$	13.6376	1.28292	0.641458	+	0.767158i	$0.278330\pi$
$114$	−6.45211	−0.604296
$115$	8.68162	0.809565
$116$	2.91623	0.270765
$117$	−3.45134	−0.319077
$118$	1.00000	0.0920575
$119$	−0.900066	−0.0825089
$120$	3.00862	0.274648
$121$	28.8139	2.61945
$122$	1.98803	0.179987
$123$	10.6470	0.960006
$124$	−1.87668	−0.168531
$125$	2.85283	0.255164
$126$	−0.900066	−0.0801843
$127$	12.5563	1.11419	0.557097	−	0.830448i	$-0.311915\pi$
$127$	12.5563	1.11419	0.557097	+	0.830448i	$0.311915\pi$
$128$	1.00000	0.0883883
$129$	4.63613	0.408189
$130$	10.3838	0.910717
$131$	18.8034	1.64286	0.821429	−	0.570310i	$-0.193177\pi$
$131$	18.8034	1.64286	0.821429	+	0.570310i	$0.193177\pi$
$132$	6.30983	0.549200
$133$	−5.80733	−0.503559
$134$	10.3412	0.893344
$135$	3.00862	0.258941
$136$	1.00000	0.0857493
$137$	12.4290	1.06188	0.530939	−	0.847410i	$-0.321839\pi$
$137$	12.4290	1.06188	0.530939	+	0.847410i	$0.321839\pi$
$138$	2.88558	0.245637
$139$	15.7367	1.33477	0.667386	−	0.744712i	$-0.267413\pi$
$139$	15.7367	1.33477	0.667386	+	0.744712i	$0.267413\pi$
$140$	2.70795	0.228864
$141$	9.49357	0.799503
$142$	−9.78989	−0.821550
$143$	21.7774	1.82112
$144$	1.00000	0.0833333
$145$	−8.77381	−0.728626
$146$	−4.23244	−0.350279
$147$	6.18988	0.510533
$148$	−8.38471	−0.689219
$149$	−0.619076	−0.0507167	−0.0253584	−	0.999678i	$-0.508073\pi$
$149$	−0.619076	−0.0507167	−0.0253584	+	0.999678i	$0.508073\pi$
$150$	−4.05178	−0.330827
$151$	−9.41500	−0.766182	−0.383091	−	0.923711i	$-0.625140\pi$
$151$	−9.41500	−0.766182	−0.383091	+	0.923711i	$0.625140\pi$
$152$	6.45211	0.523336
$153$	1.00000	0.0808452
$154$	5.67926	0.457648
$155$	5.64623	0.453516
$156$	3.45134	0.276329
$157$	4.97505	0.397052	0.198526	−	0.980096i	$-0.436385\pi$
$157$	4.97505	0.397052	0.198526	+	0.980096i	$0.436385\pi$
$158$	5.62862	0.447789
$159$	−6.66594	−0.528644
$160$	−3.00862	−0.237852
$161$	2.59722	0.204689
$162$	1.00000	0.0785674
$163$	22.6879	1.77706	0.888528	−	0.458822i	$-0.151729\pi$
$163$	22.6879	1.77706	0.888528	+	0.458822i	$0.151729\pi$
$164$	−10.6470	−0.831389
$165$	−18.9839	−1.47789
$166$	16.5675	1.28589
$167$	−17.4833	−1.35290	−0.676450	−	0.736488i	$-0.736483\pi$
$167$	−17.4833	−1.35290	−0.676450	+	0.736488i	$0.736483\pi$
$168$	0.900066	0.0694416
$169$	−1.08822	−0.0837094
$170$	−3.00862	−0.230750
$171$	6.45211	0.493405
$172$	−4.63613	−0.353502
$173$	0.465613	0.0353999	0.0176999	−	0.999843i	$-0.494366\pi$
$173$	0.465613	0.0353999	0.0176999	+	0.999843i	$0.494366\pi$
$174$	−2.91623	−0.221079
$175$	−3.64687	−0.275678
$176$	−6.30983	−0.475621
$177$	−1.00000	−0.0751646
$178$	9.46066	0.709107
$179$	−9.29678	−0.694874	−0.347437	−	0.937703i	$-0.612948\pi$
$179$	−9.29678	−0.694874	−0.347437	+	0.937703i	$0.612948\pi$
$180$	−3.00862	−0.224249
$181$	10.5727	0.785862	0.392931	−	0.919568i	$-0.371461\pi$
$181$	10.5727	0.785862	0.392931	+	0.919568i	$0.371461\pi$
$182$	3.10644	0.230264
$183$	−1.98803	−0.146959
$184$	−2.88558	−0.212728
$185$	25.2264	1.85468
$186$	1.87668	0.137605
$187$	−6.30983	−0.461420
$188$	−9.49357	−0.692389
$189$	0.900066	0.0654702
$190$	−19.4119	−1.40829
$191$	−19.5955	−1.41788	−0.708939	−	0.705270i	$-0.750826\pi$
$191$	−19.5955	−1.41788	−0.708939	+	0.705270i	$0.750826\pi$
$192$	−1.00000	−0.0721688
$193$	−10.4285	−0.750662	−0.375331	−	0.926891i	$-0.622471\pi$
$193$	−10.4285	−0.750662	−0.375331	+	0.926891i	$0.622471\pi$
$194$	7.99860	0.574266
$195$	−10.3838	−0.743598
$196$	−6.18988	−0.442134
$197$	19.5307	1.39151	0.695753	−	0.718281i	$-0.255071\pi$
$197$	19.5307	1.39151	0.695753	+	0.718281i	$0.255071\pi$
$198$	−6.30983	−0.448420
$199$	−7.02177	−0.497760	−0.248880	−	0.968534i	$-0.580062\pi$
$199$	−7.02177	−0.497760	−0.248880	+	0.968534i	$0.580062\pi$
$200$	4.05178	0.286504
$201$	−10.3412	−0.729413
$202$	−12.5529	−0.883220
$203$	−2.62480	−0.184225
$204$	−1.00000	−0.0700140
$205$	32.0327	2.23726
$206$	7.50255	0.522728
$207$	−2.88558	−0.200562
$208$	−3.45134	−0.239308
$209$	−40.7117	−2.81609
$210$	−2.70795	−0.186867
$211$	7.31362	0.503490	0.251745	−	0.967794i	$-0.418996\pi$
$211$	7.31362	0.503490	0.251745	+	0.967794i	$0.418996\pi$
$212$	6.66594	0.457819
$213$	9.78989	0.670792
$214$	−19.6141	−1.34079
$215$	13.9484	0.951270
$216$	−1.00000	−0.0680414
$217$	1.68914	0.114666
$218$	13.1725	0.892153
$219$	4.23244	0.286002
$220$	18.9839	1.27989
$221$	−3.45134	−0.232163
$222$	8.38471	0.562745
$223$	−6.74732	−0.451834	−0.225917	−	0.974147i	$-0.572538\pi$
$223$	−6.74732	−0.451834	−0.225917	+	0.974147i	$0.572538\pi$
$224$	−0.900066	−0.0601382
$225$	4.05178	0.270119
$226$	13.6376	0.907158
$227$	−6.97645	−0.463043	−0.231522	−	0.972830i	$-0.574370\pi$
$227$	−6.97645	−0.463043	−0.231522	+	0.972830i	$0.574370\pi$
$228$	−6.45211	−0.427302
$229$	−20.3019	−1.34159	−0.670794	−	0.741644i	$-0.734046\pi$
$229$	−20.3019	−1.34159	−0.670794	+	0.741644i	$0.734046\pi$
$230$	8.68162	0.572449
$231$	−5.67926	−0.373668
$232$	2.91623	0.191460
$233$	20.5754	1.34794	0.673968	−	0.738760i	$-0.264588\pi$
$233$	20.5754	1.34794	0.673968	+	0.738760i	$0.264588\pi$
$234$	−3.45134	−0.225621
$235$	28.5625	1.86321
$236$	1.00000	0.0650945
$237$	−5.62862	−0.365618
$238$	−0.900066	−0.0583426
$239$	−9.61103	−0.621686	−0.310843	−	0.950461i	$-0.600611\pi$
$239$	−9.61103	−0.621686	−0.310843	+	0.950461i	$0.600611\pi$
$240$	3.00862	0.194205
$241$	8.42760	0.542869	0.271435	−	0.962457i	$-0.412502\pi$
$241$	8.42760	0.542869	0.271435	+	0.962457i	$0.412502\pi$
$242$	28.8139	1.85223
$243$	−1.00000	−0.0641500
$244$	1.98803	0.127270
$245$	18.6230	1.18978
$246$	10.6470	0.678827
$247$	−22.2685	−1.41691
$248$	−1.87668	−0.119170
$249$	−16.5675	−1.04992
$250$	2.85283	0.180428
$251$	−2.54876	−0.160876	−0.0804380	−	0.996760i	$-0.525632\pi$
$251$	−2.54876	−0.160876	−0.0804380	+	0.996760i	$0.525632\pi$
$252$	−0.900066	−0.0566988
$253$	18.2075	1.14470
$254$	12.5563	0.787854
$255$	3.00862	0.188407
$256$	1.00000	0.0625000
$257$	−28.3319	−1.76730	−0.883649	−	0.468151i	$-0.844920\pi$
$257$	−28.3319	−1.76730	−0.883649	+	0.468151i	$0.844920\pi$
$258$	4.63613	0.288633
$259$	7.54679	0.468935
$260$	10.3838	0.643974
$261$	2.91623	0.180510
$262$	18.8034	1.16168
$263$	12.5929	0.776512	0.388256	−	0.921552i	$-0.373078\pi$
$263$	12.5929	0.776512	0.388256	+	0.921552i	$0.373078\pi$
$264$	6.30983	0.388343
$265$	−20.0553	−1.23199
$266$	−5.80733	−0.356070
$267$	−9.46066	−0.578983
$268$	10.3412	0.631690
$269$	13.9452	0.850254	0.425127	−	0.905134i	$-0.360229\pi$
$269$	13.9452	0.850254	0.425127	+	0.905134i	$0.360229\pi$
$270$	3.00862	0.183099
$271$	−4.21240	−0.255885	−0.127943	−	0.991782i	$-0.540837\pi$
$271$	−4.21240	−0.255885	−0.127943	+	0.991782i	$0.540837\pi$
$272$	1.00000	0.0606339
$273$	−3.10644	−0.188010
$274$	12.4290	0.750861
$275$	−25.5660	−1.54169
$276$	2.88558	0.173692
$277$	6.75313	0.405756	0.202878	−	0.979204i	$-0.434970\pi$
$277$	6.75313	0.405756	0.202878	+	0.979204i	$0.434970\pi$
$278$	15.7367	0.943826
$279$	−1.87668	−0.112354
$280$	2.70795	0.161831
$281$	−13.3057	−0.793749	−0.396874	−	0.917873i	$-0.629905\pi$
$281$	−13.3057	−0.793749	−0.396874	+	0.917873i	$0.629905\pi$
$282$	9.49357	0.565334
$283$	−6.18534	−0.367680	−0.183840	−	0.982956i	$-0.558853\pi$
$283$	−6.18534	−0.367680	−0.183840	+	0.982956i	$0.558853\pi$
$284$	−9.78989	−0.580923
$285$	19.4119	1.14986
$286$	21.7774	1.28772
$287$	9.58298	0.565666
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−8.77381	−0.515216
$291$	−7.99860	−0.468886
$292$	−4.23244	−0.247685
$293$	−11.0832	−0.647489	−0.323745	−	0.946145i	$-0.604942\pi$
$293$	−11.0832	−0.647489	−0.323745	+	0.946145i	$0.604942\pi$
$294$	6.18988	0.361001
$295$	−3.00862	−0.175169
$296$	−8.38471	−0.487351
$297$	6.30983	0.366133
$298$	−0.619076	−0.0358621
$299$	9.95915	0.575952
$300$	−4.05178	−0.233930
$301$	4.17283	0.240518
$302$	−9.41500	−0.541772
$303$	12.5529	0.721146
$304$	6.45211	0.370054
$305$	−5.98121	−0.342483
$306$	1.00000	0.0571662
$307$	−30.4096	−1.73557	−0.867783	−	0.496944i	$-0.834456\pi$
$307$	−30.4096	−1.73557	−0.867783	+	0.496944i	$0.834456\pi$
$308$	5.67926	0.323606
$309$	−7.50255	−0.426805
$310$	5.64623	0.320684
$311$	11.0000	0.623753	0.311876	−	0.950123i	$-0.399043\pi$
$311$	11.0000	0.623753	0.311876	+	0.950123i	$0.399043\pi$
$312$	3.45134	0.195394
$313$	26.3895	1.49162	0.745811	−	0.666157i	$-0.232062\pi$
$313$	26.3895	1.49162	0.745811	+	0.666157i	$0.232062\pi$
$314$	4.97505	0.280758
$315$	2.70795	0.152576
$316$	5.62862	0.316635
$317$	−11.7130	−0.657866	−0.328933	−	0.944353i	$-0.606689\pi$
$317$	−11.7130	−0.657866	−0.328933	+	0.944353i	$0.606689\pi$
$318$	−6.66594	−0.373807
$319$	−18.4009	−1.03025
$320$	−3.00862	−0.168187
$321$	19.6141	1.09475
$322$	2.59722	0.144737
$323$	6.45211	0.359005
$324$	1.00000	0.0555556
$325$	−13.9841	−0.775698
$326$	22.6879	1.25657
$327$	−13.1725	−0.728440
$328$	−10.6470	−0.587881
$329$	8.54484	0.471092
$330$	−18.9839	−1.04503
$331$	−18.9951	−1.04407	−0.522033	−	0.852925i	$-0.674826\pi$
$331$	−18.9951	−1.04407	−0.522033	+	0.852925i	$0.674826\pi$
$332$	16.5675	0.909259
$333$	−8.38471	−0.459479
$334$	−17.4833	−0.956645
$335$	−31.1127	−1.69987
$336$	0.900066	0.0491026
$337$	−23.8027	−1.29662	−0.648309	−	0.761377i	$-0.724524\pi$
$337$	−23.8027	−1.29662	−0.648309	+	0.761377i	$0.724524\pi$
$338$	−1.08822	−0.0591915
$339$	−13.6376	−0.740691
$340$	−3.00862	−0.163165
$341$	11.8416	0.641256
$342$	6.45211	0.348890
$343$	11.8718	0.641015
$344$	−4.63613	−0.249963
$345$	−8.68162	−0.467403
$346$	0.465613	0.0250315
$347$	−3.69322	−0.198263	−0.0991313	−	0.995074i	$-0.531606\pi$
$347$	−3.69322	−0.198263	−0.0991313	+	0.995074i	$0.531606\pi$
$348$	−2.91623	−0.156326
$349$	29.6507	1.58717	0.793583	−	0.608462i	$-0.208213\pi$
$349$	29.6507	1.58717	0.793583	+	0.608462i	$0.208213\pi$
$350$	−3.64687	−0.194933
$351$	3.45134	0.184219
$352$	−6.30983	−0.336315
$353$	−9.09492	−0.484074	−0.242037	−	0.970267i	$-0.577815\pi$
$353$	−9.09492	−0.484074	−0.242037	+	0.970267i	$0.577815\pi$
$354$	−1.00000	−0.0531494
$355$	29.4540	1.56326
$356$	9.46066	0.501414
$357$	0.900066	0.0476365
$358$	−9.29678	−0.491350
$359$	30.5704	1.61344	0.806722	−	0.590932i	$-0.201240\pi$
$359$	30.5704	1.61344	0.806722	+	0.590932i	$0.201240\pi$
$360$	−3.00862	−0.158568
$361$	22.6298	1.19104
$362$	10.5727	0.555688
$363$	−28.8139	−1.51234
$364$	3.10644	0.162822
$365$	12.7338	0.666517
$366$	−1.98803	−0.103916
$367$	26.2188	1.36861	0.684306	−	0.729195i	$-0.260105\pi$
$367$	26.2188	1.36861	0.684306	+	0.729195i	$0.260105\pi$
$368$	−2.88558	−0.150422
$369$	−10.6470	−0.554260
$370$	25.2264	1.31146
$371$	−5.99979	−0.311493
$372$	1.87668	0.0973015
$373$	12.3238	0.638103	0.319052	−	0.947737i	$-0.396636\pi$
$373$	12.3238	0.638103	0.319052	+	0.947737i	$0.396636\pi$
$374$	−6.30983	−0.326273
$375$	−2.85283	−0.147319
$376$	−9.49357	−0.489593
$377$	−10.0649	−0.518369
$378$	0.900066	0.0462944
$379$	6.80047	0.349317	0.174658	−	0.984629i	$-0.444118\pi$
$379$	6.80047	0.349317	0.174658	+	0.984629i	$0.444118\pi$
$380$	−19.4119	−0.995812
$381$	−12.5563	−0.643280
$382$	−19.5955	−1.00259
$383$	4.42187	0.225947	0.112974	−	0.993598i	$-0.463962\pi$
$383$	4.42187	0.225947	0.112974	+	0.993598i	$0.463962\pi$
$384$	−1.00000	−0.0510310
$385$	−17.0867	−0.870820
$386$	−10.4285	−0.530798
$387$	−4.63613	−0.235668
$388$	7.99860	0.406067
$389$	−3.04080	−0.154174	−0.0770872	−	0.997024i	$-0.524562\pi$
$389$	−3.04080	−0.154174	−0.0770872	+	0.997024i	$0.524562\pi$
$390$	−10.3838	−0.525803
$391$	−2.88558	−0.145930
$392$	−6.18988	−0.312636
$393$	−18.8034	−0.948505
$394$	19.5307	0.983943
$395$	−16.9344	−0.852061
$396$	−6.30983	−0.317081
$397$	−15.5357	−0.779716	−0.389858	−	0.920875i	$-0.627476\pi$
$397$	−15.5357	−0.779716	−0.389858	+	0.920875i	$0.627476\pi$
$398$	−7.02177	−0.351970
$399$	5.80733	0.290730
$400$	4.05178	0.202589
$401$	2.97913	0.148771	0.0743853	−	0.997230i	$-0.476301\pi$
$401$	2.97913	0.148771	0.0743853	+	0.997230i	$0.476301\pi$
$402$	−10.3412	−0.515773
$403$	6.47708	0.322647
$404$	−12.5529	−0.624531
$405$	−3.00862	−0.149499
$406$	−2.62480	−0.130267
$407$	52.9060	2.62246
$408$	−1.00000	−0.0495074
$409$	−15.1112	−0.747198	−0.373599	−	0.927590i	$-0.621876\pi$
$409$	−15.1112	−0.747198	−0.373599	+	0.927590i	$0.621876\pi$
$410$	32.0327	1.58198
$411$	−12.4290	−0.613076
$412$	7.50255	0.369624
$413$	−0.900066	−0.0442894
$414$	−2.88558	−0.141819
$415$	−49.8452	−2.44681
$416$	−3.45134	−0.169216
$417$	−15.7367	−0.770631
$418$	−40.7117	−1.99128
$419$	−17.5780	−0.858743	−0.429371	−	0.903128i	$-0.641265\pi$
$419$	−17.5780	−0.858743	−0.429371	+	0.903128i	$0.641265\pi$
$420$	−2.70795	−0.132135
$421$	15.2171	0.741636	0.370818	−	0.928706i	$-0.379077\pi$
$421$	15.2171	0.741636	0.370818	+	0.928706i	$0.379077\pi$
$422$	7.31362	0.356021
$423$	−9.49357	−0.461593
$424$	6.66594	0.323727
$425$	4.05178	0.196540
$426$	9.78989	0.474322
$427$	−1.78935	−0.0865929
$428$	−19.6141	−0.948083
$429$	−21.7774	−1.05142
$430$	13.9484	0.672649
$431$	−13.0660	−0.629368	−0.314684	−	0.949196i	$-0.601899\pi$
$431$	−13.0660	−0.629368	−0.314684	+	0.949196i	$0.601899\pi$
$432$	−1.00000	−0.0481125
$433$	12.8460	0.617338	0.308669	−	0.951170i	$-0.400117\pi$
$433$	12.8460	0.617338	0.308669	+	0.951170i	$0.400117\pi$
$434$	1.68914	0.0810813
$435$	8.77381	0.420672
$436$	13.1725	0.630847
$437$	−18.6181	−0.890626
$438$	4.23244	0.202234
$439$	1.69640	0.0809645	0.0404823	−	0.999180i	$-0.487111\pi$
$439$	1.69640	0.0809645	0.0404823	+	0.999180i	$0.487111\pi$
$440$	18.9839	0.905020
$441$	−6.18988	−0.294756
$442$	−3.45134	−0.164164
$443$	14.9806	0.711751	0.355876	−	0.934533i	$-0.384183\pi$
$443$	14.9806	0.711751	0.355876	+	0.934533i	$0.384183\pi$
$444$	8.38471	0.397921
$445$	−28.4635	−1.34930
$446$	−6.74732	−0.319495
$447$	0.619076	0.0292813
$448$	−0.900066	−0.0425241
$449$	23.3819	1.10346	0.551730	−	0.834023i	$-0.313968\pi$
$449$	23.3819	1.10346	0.551730	+	0.834023i	$0.313968\pi$
$450$	4.05178	0.191003
$451$	67.1806	3.16341
$452$	13.6376	0.641458
$453$	9.41500	0.442355
$454$	−6.97645	−0.327421
$455$	−9.34608	−0.438151
$456$	−6.45211	−0.302148
$457$	33.9039	1.58596	0.792978	−	0.609250i	$-0.208529\pi$
$457$	33.9039	1.58596	0.792978	+	0.609250i	$0.208529\pi$
$458$	−20.3019	−0.948645
$459$	−1.00000	−0.0466760
$460$	8.68162	0.404783
$461$	−17.9890	−0.837832	−0.418916	−	0.908025i	$-0.637590\pi$
$461$	−17.9890	−0.837832	−0.418916	+	0.908025i	$0.637590\pi$
$462$	−5.67926	−0.264223
$463$	−16.5135	−0.767445	−0.383723	−	0.923448i	$-0.625358\pi$
$463$	−16.5135	−0.767445	−0.383723	+	0.923448i	$0.625358\pi$
$464$	2.91623	0.135382
$465$	−5.64623	−0.261837
$466$	20.5754	0.953135
$467$	−11.5177	−0.532974	−0.266487	−	0.963839i	$-0.585863\pi$
$467$	−11.5177	−0.532974	−0.266487	+	0.963839i	$0.585863\pi$
$468$	−3.45134	−0.159538
$469$	−9.30777	−0.429793
$470$	28.5625	1.31749
$471$	−4.97505	−0.229238
$472$	1.00000	0.0460287
$473$	29.2532	1.34506
$474$	−5.62862	−0.258531
$475$	26.1426	1.19950
$476$	−0.900066	−0.0412545
$477$	6.66594	0.305213
$478$	−9.61103	−0.439598
$479$	−38.0671	−1.73933	−0.869665	−	0.493643i	$-0.835665\pi$
$479$	−38.0671	−1.73933	−0.869665	+	0.493643i	$0.835665\pi$
$480$	3.00862	0.137324
$481$	28.9385	1.31948
$482$	8.42760	0.383866
$483$	−2.59722	−0.118177
$484$	28.8139	1.30972
$485$	−24.0647	−1.09272
$486$	−1.00000	−0.0453609
$487$	32.1500	1.45685	0.728427	−	0.685123i	$-0.240252\pi$
$487$	32.1500	1.45685	0.728427	+	0.685123i	$0.240252\pi$
$488$	1.98803	0.0899937
$489$	−22.6879	−1.02598
$490$	18.6230	0.841301
$491$	−23.8092	−1.07450	−0.537248	−	0.843424i	$-0.680536\pi$
$491$	−23.8092	−1.07450	−0.537248	+	0.843424i	$0.680536\pi$
$492$	10.6470	0.480003
$493$	2.91623	0.131340
$494$	−22.2685	−1.00191
$495$	18.9839	0.853261
$496$	−1.87668	−0.0842656
$497$	8.81155	0.395252
$498$	−16.5675	−0.742407
$499$	32.0084	1.43289	0.716446	−	0.697642i	$-0.245768\pi$
$499$	32.0084	1.43289	0.716446	+	0.697642i	$0.245768\pi$
$500$	2.85283	0.127582
$501$	17.4833	0.781097
$502$	−2.54876	−0.113757
$503$	17.1037	0.762615	0.381308	−	0.924448i	$-0.375474\pi$
$503$	17.1037	0.762615	0.381308	+	0.924448i	$0.375474\pi$
$504$	−0.900066	−0.0400921
$505$	37.7669	1.68061
$506$	18.2075	0.809424
$507$	1.08822	0.0483296
$508$	12.5563	0.557097
$509$	−16.2102	−0.718503	−0.359252	−	0.933241i	$-0.616968\pi$
$509$	−16.2102	−0.718503	−0.359252	+	0.933241i	$0.616968\pi$
$510$	3.00862	0.133224
$511$	3.80947	0.168521
$512$	1.00000	0.0441942
$513$	−6.45211	−0.284868
$514$	−28.3319	−1.24967
$515$	−22.5723	−0.994655
$516$	4.63613	0.204094
$517$	59.9028	2.63452
$518$	7.54679	0.331587
$519$	−0.465613	−0.0204381
$520$	10.3838	0.455359
$521$	−37.0654	−1.62387	−0.811933	−	0.583751i	$-0.801585\pi$
$521$	−37.0654	−1.62387	−0.811933	+	0.583751i	$0.801585\pi$
$522$	2.91623	0.127640
$523$	2.92636	0.127961	0.0639803	−	0.997951i	$-0.479621\pi$
$523$	2.92636	0.127961	0.0639803	+	0.997951i	$0.479621\pi$
$524$	18.8034	0.821429
$525$	3.64687	0.159163
$526$	12.5929	0.549077
$527$	−1.87668	−0.0817497
$528$	6.30983	0.274600
$529$	−14.6734	−0.637974
$530$	−20.0553	−0.871145
$531$	1.00000	0.0433963
$532$	−5.80733	−0.251780
$533$	36.7464	1.59166
$534$	−9.46066	−0.409403
$535$	59.0113	2.55128
$536$	10.3412	0.446672
$537$	9.29678	0.401186
$538$	13.9452	0.601220
$539$	39.0571	1.68231
$540$	3.00862	0.129470
$541$	5.91770	0.254422	0.127211	−	0.991876i	$-0.459397\pi$
$541$	5.91770	0.254422	0.127211	+	0.991876i	$0.459397\pi$
$542$	−4.21240	−0.180938
$543$	−10.5727	−0.453717
$544$	1.00000	0.0428746
$545$	−39.6310	−1.69760
$546$	−3.10644	−0.132943
$547$	18.9175	0.808854	0.404427	−	0.914570i	$-0.367471\pi$
$547$	18.9175	0.808854	0.404427	+	0.914570i	$0.367471\pi$
$548$	12.4290	0.530939
$549$	1.98803	0.0848469
$550$	−25.5660	−1.09014
$551$	18.8158	0.801581
$552$	2.88558	0.122819
$553$	−5.06613	−0.215434
$554$	6.75313	0.286913
$555$	−25.2264	−1.07080
$556$	15.7367	0.667386
$557$	6.41783	0.271932	0.135966	−	0.990714i	$-0.456586\pi$
$557$	6.41783	0.271932	0.135966	+	0.990714i	$0.456586\pi$
$558$	−1.87668	−0.0794464
$559$	16.0009	0.676765
$560$	2.70795	0.114432
$561$	6.30983	0.266401
$562$	−13.3057	−0.561265
$563$	36.9623	1.55777	0.778887	−	0.627164i	$-0.215785\pi$
$563$	36.9623	1.55777	0.778887	+	0.627164i	$0.215785\pi$
$564$	9.49357	0.399751
$565$	−41.0303	−1.72616
$566$	−6.18534	−0.259989
$567$	−0.900066	−0.0377992
$568$	−9.78989	−0.410775
$569$	4.01251	0.168213	0.0841066	−	0.996457i	$-0.473196\pi$
$569$	4.01251	0.168213	0.0841066	+	0.996457i	$0.473196\pi$
$570$	19.4119	0.813077
$571$	−18.3996	−0.769997	−0.384999	−	0.922917i	$-0.625798\pi$
$571$	−18.3996	−0.769997	−0.384999	+	0.922917i	$0.625798\pi$
$572$	21.7774	0.910558
$573$	19.5955	0.818612
$574$	9.58298	0.399986
$575$	−11.6918	−0.487580
$576$	1.00000	0.0416667
$577$	−33.7552	−1.40525	−0.702625	−	0.711561i	$-0.747989\pi$
$577$	−33.7552	−1.40525	−0.702625	+	0.711561i	$0.747989\pi$
$578$	1.00000	0.0415945
$579$	10.4285	0.433395
$580$	−8.77381	−0.364313
$581$	−14.9118	−0.618647
$582$	−7.99860	−0.331553
$583$	−42.0609	−1.74199
$584$	−4.23244	−0.175139
$585$	10.3838	0.429316
$586$	−11.0832	−0.457844
$587$	30.8747	1.27434	0.637168	−	0.770725i	$-0.280106\pi$
$587$	30.8747	1.27434	0.637168	+	0.770725i	$0.280106\pi$
$588$	6.18988	0.255266
$589$	−12.1086	−0.498925
$590$	−3.00862	−0.123863
$591$	−19.5307	−0.803386
$592$	−8.38471	−0.344609
$593$	27.4714	1.12812	0.564058	−	0.825735i	$-0.309240\pi$
$593$	27.4714	1.12812	0.564058	+	0.825735i	$0.309240\pi$
$594$	6.30983	0.258895
$595$	2.70795	0.111015
$596$	−0.619076	−0.0253584
$597$	7.02177	0.287382
$598$	9.95915	0.407260
$599$	16.1252	0.658858	0.329429	−	0.944180i	$-0.393144\pi$
$599$	16.1252	0.658858	0.329429	+	0.944180i	$0.393144\pi$
$600$	−4.05178	−0.165413
$601$	−8.88247	−0.362324	−0.181162	−	0.983453i	$-0.557986\pi$
$601$	−8.88247	−0.362324	−0.181162	+	0.983453i	$0.557986\pi$
$602$	4.17283	0.170072
$603$	10.3412	0.421127
$604$	−9.41500	−0.383091
$605$	−86.6900	−3.52445
$606$	12.5529	0.509927
$607$	−12.6602	−0.513861	−0.256930	−	0.966430i	$-0.582711\pi$
$607$	−12.6602	−0.513861	−0.256930	+	0.966430i	$0.582711\pi$
$608$	6.45211	0.261668
$609$	2.62480	0.106362
$610$	−5.98121	−0.242172
$611$	32.7656	1.32555
$612$	1.00000	0.0404226
$613$	24.4368	0.986994	0.493497	−	0.869747i	$-0.335718\pi$
$613$	24.4368	0.986994	0.493497	+	0.869747i	$0.335718\pi$
$614$	−30.4096	−1.22723
$615$	−32.0327	−1.29168
$616$	5.67926	0.228824
$617$	1.72492	0.0694429	0.0347214	−	0.999397i	$-0.488946\pi$
$617$	1.72492	0.0694429	0.0347214	+	0.999397i	$0.488946\pi$
$618$	−7.50255	−0.301797
$619$	−49.5522	−1.99167	−0.995837	−	0.0911572i	$-0.970943\pi$
$619$	−49.5522	−1.99167	−0.995837	+	0.0911572i	$0.970943\pi$
$620$	5.64623	0.226758
$621$	2.88558	0.115795
$622$	11.0000	0.441060
$623$	−8.51522	−0.341155
$624$	3.45134	0.138164
$625$	−28.8420	−1.15368
$626$	26.3895	1.05474
$627$	40.7117	1.62587
$628$	4.97505	0.198526
$629$	−8.38471	−0.334320
$630$	2.70795	0.107888
$631$	−43.5747	−1.73468	−0.867341	−	0.497714i	$-0.834173\pi$
$631$	−43.5747	−1.73468	−0.867341	+	0.497714i	$0.834173\pi$
$632$	5.62862	0.223895
$633$	−7.31362	−0.290690
$634$	−11.7130	−0.465181
$635$	−37.7772	−1.49914
$636$	−6.66594	−0.264322
$637$	21.3634	0.846449
$638$	−18.4009	−0.728498
$639$	−9.78989	−0.387282
$640$	−3.00862	−0.118926
$641$	38.2685	1.51152	0.755758	−	0.654851i	$-0.227269\pi$
$641$	38.2685	1.51152	0.755758	+	0.654851i	$0.227269\pi$
$642$	19.6141	0.774107
$643$	−2.11096	−0.0832482	−0.0416241	−	0.999133i	$-0.513253\pi$
$643$	−2.11096	−0.0832482	−0.0416241	+	0.999133i	$0.513253\pi$
$644$	2.59722	0.102345
$645$	−13.9484	−0.549216
$646$	6.45211	0.253855
$647$	−16.1599	−0.635310	−0.317655	−	0.948206i	$-0.602895\pi$
$647$	−16.1599	−0.635310	−0.317655	+	0.948206i	$0.602895\pi$
$648$	1.00000	0.0392837
$649$	−6.30983	−0.247682
$650$	−13.9841	−0.548501
$651$	−1.68914	−0.0662026
$652$	22.6879	0.888528
$653$	7.65544	0.299580	0.149790	−	0.988718i	$-0.452140\pi$
$653$	7.65544	0.299580	0.149790	+	0.988718i	$0.452140\pi$
$654$	−13.1725	−0.515085
$655$	−56.5722	−2.21046
$656$	−10.6470	−0.415695
$657$	−4.23244	−0.165123
$658$	8.54484	0.333112
$659$	−1.00286	−0.0390657	−0.0195329	−	0.999809i	$-0.506218\pi$
$659$	−1.00286	−0.0390657	−0.0195329	+	0.999809i	$0.506218\pi$
$660$	−18.9839	−0.738946
$661$	−33.0060	−1.28378	−0.641892	−	0.766795i	$-0.721850\pi$
$661$	−33.0060	−1.28378	−0.641892	+	0.766795i	$0.721850\pi$
$662$	−18.9951	−0.738266
$663$	3.45134	0.134039
$664$	16.5675	0.642943
$665$	17.4720	0.677536
$666$	−8.38471	−0.324901
$667$	−8.41502	−0.325831
$668$	−17.4833	−0.676450
$669$	6.74732	0.260866
$670$	−31.1127	−1.20199
$671$	−12.5441	−0.484260
$672$	0.900066	0.0347208
$673$	10.1688	0.391979	0.195989	−	0.980606i	$-0.437208\pi$
$673$	10.1688	0.391979	0.195989	+	0.980606i	$0.437208\pi$
$674$	−23.8027	−0.916848
$675$	−4.05178	−0.155953
$676$	−1.08822	−0.0418547
$677$	−13.1017	−0.503540	−0.251770	−	0.967787i	$-0.581013\pi$
$677$	−13.1017	−0.503540	−0.251770	+	0.967787i	$0.581013\pi$
$678$	−13.6376	−0.523748
$679$	−7.19927	−0.276283
$680$	−3.00862	−0.115375
$681$	6.97645	0.267338
$682$	11.8416	0.453436
$683$	14.1758	0.542423	0.271211	−	0.962520i	$-0.412576\pi$
$683$	14.1758	0.542423	0.271211	+	0.962520i	$0.412576\pi$
$684$	6.45211	0.246703
$685$	−37.3940	−1.42875
$686$	11.8718	0.453266
$687$	20.3019	0.774566
$688$	−4.63613	−0.176751
$689$	−23.0065	−0.876476
$690$	−8.68162	−0.330504
$691$	−21.0961	−0.802535	−0.401268	−	0.915961i	$-0.631430\pi$
$691$	−21.0961	−0.802535	−0.401268	+	0.915961i	$0.631430\pi$
$692$	0.465613	0.0176999
$693$	5.67926	0.215737
$694$	−3.69322	−0.140193
$695$	−47.3458	−1.79593
$696$	−2.91623	−0.110539
$697$	−10.6470	−0.403283
$698$	29.6507	1.12230
$699$	−20.5754	−0.778232
$700$	−3.64687	−0.137839
$701$	−1.29234	−0.0488110	−0.0244055	−	0.999702i	$-0.507769\pi$
$701$	−1.29234	−0.0488110	−0.0244055	+	0.999702i	$0.507769\pi$
$702$	3.45134	0.130263
$703$	−54.0991	−2.04039
$704$	−6.30983	−0.237811
$705$	−28.5625	−1.07573
$706$	−9.09492	−0.342292
$707$	11.2985	0.424922
$708$	−1.00000	−0.0375823
$709$	−0.783095	−0.0294097	−0.0147049	−	0.999892i	$-0.504681\pi$
$709$	−0.783095	−0.0294097	−0.0147049	+	0.999892i	$0.504681\pi$
$710$	29.4540	1.10539
$711$	5.62862	0.211090
$712$	9.46066	0.354553
$713$	5.41533	0.202806
$714$	0.900066	0.0336841
$715$	−65.5198	−2.45030
$716$	−9.29678	−0.347437
$717$	9.61103	0.358930
$718$	30.5704	1.14088
$719$	−36.8972	−1.37603	−0.688017	−	0.725695i	$-0.741518\pi$
$719$	−36.8972	−1.37603	−0.688017	+	0.725695i	$0.741518\pi$
$720$	−3.00862	−0.112125
$721$	−6.75279	−0.251487
$722$	22.6298	0.842193
$723$	−8.42760	−0.313426
$724$	10.5727	0.392931
$725$	11.8159	0.438832
$726$	−28.8139	−1.06938
$727$	−37.0865	−1.37546	−0.687731	−	0.725966i	$-0.741393\pi$
$727$	−37.0865	−1.37546	−0.687731	+	0.725966i	$0.741393\pi$
$728$	3.10644	0.115132
$729$	1.00000	0.0370370
$730$	12.7338	0.471298
$731$	−4.63613	−0.171474
$732$	−1.98803	−0.0734796
$733$	−24.1112	−0.890568	−0.445284	−	0.895389i	$-0.646897\pi$
$733$	−24.1112	−0.890568	−0.445284	+	0.895389i	$0.646897\pi$
$734$	26.2188	0.967755
$735$	−18.6230	−0.686919
$736$	−2.88558	−0.106364
$737$	−65.2512	−2.40356
$738$	−10.6470	−0.391921
$739$	38.9573	1.43307	0.716534	−	0.697552i	$-0.245728\pi$
$739$	38.9573	1.43307	0.716534	+	0.697552i	$0.245728\pi$
$740$	25.2264	0.927340
$741$	22.2685	0.818053
$742$	−5.99979	−0.220259
$743$	4.79014	0.175733	0.0878667	−	0.996132i	$-0.471995\pi$
$743$	4.79014	0.175733	0.0878667	+	0.996132i	$0.471995\pi$
$744$	1.87668	0.0688026
$745$	1.86256	0.0682391
$746$	12.3238	0.451207
$747$	16.5675	0.606173
$748$	−6.30983	−0.230710
$749$	17.6540	0.645062
$750$	−2.85283	−0.104170
$751$	−3.63152	−0.132516	−0.0662580	−	0.997803i	$-0.521106\pi$
$751$	−3.63152	−0.132516	−0.0662580	+	0.997803i	$0.521106\pi$
$752$	−9.49357	−0.346195
$753$	2.54876	0.0928819
$754$	−10.0649	−0.366542
$755$	28.3261	1.03089
$756$	0.900066	0.0327351
$757$	44.0688	1.60171	0.800854	−	0.598859i	$-0.204379\pi$
$757$	44.0688	1.60171	0.800854	+	0.598859i	$0.204379\pi$
$758$	6.80047	0.247004
$759$	−18.2075	−0.660892
$760$	−19.4119	−0.704145
$761$	14.8836	0.539530	0.269765	−	0.962926i	$-0.413054\pi$
$761$	14.8836	0.539530	0.269765	+	0.962926i	$0.413054\pi$
$762$	−12.5563	−0.454867
$763$	−11.8561	−0.429220
$764$	−19.5955	−0.708939
$765$	−3.00862	−0.108777
$766$	4.42187	0.159769
$767$	−3.45134	−0.124621
$768$	−1.00000	−0.0360844
$769$	38.5505	1.39017	0.695083	−	0.718930i	$-0.255368\pi$
$769$	38.5505	1.39017	0.695083	+	0.718930i	$0.255368\pi$
$770$	−17.0867	−0.615763
$771$	28.3319	1.02035
$772$	−10.4285	−0.375331
$773$	−20.3296	−0.731205	−0.365603	−	0.930771i	$-0.619137\pi$
$773$	−20.3296	−0.731205	−0.365603	+	0.930771i	$0.619137\pi$
$774$	−4.63613	−0.166642
$775$	−7.60392	−0.273141
$776$	7.99860	0.287133
$777$	−7.54679	−0.270740
$778$	−3.04080	−0.109018
$779$	−68.6955	−2.46127
$780$	−10.3838	−0.371799
$781$	61.7725	2.21039
$782$	−2.88558	−0.103188
$783$	−2.91623	−0.104217
$784$	−6.18988	−0.221067
$785$	−14.9680	−0.534231
$786$	−18.8034	−0.670694
$787$	−22.5890	−0.805211	−0.402605	−	0.915374i	$-0.631895\pi$
$787$	−22.5890	−0.805211	−0.402605	+	0.915374i	$0.631895\pi$
$788$	19.5307	0.695753
$789$	−12.5929	−0.448319
$790$	−16.9344	−0.602498
$791$	−12.2747	−0.436439
$792$	−6.30983	−0.224210
$793$	−6.86136	−0.243654
$794$	−15.5357	−0.551342
$795$	20.0553	0.711287
$796$	−7.02177	−0.248880
$797$	27.1780	0.962693	0.481347	−	0.876530i	$-0.340148\pi$
$797$	27.1780	0.962693	0.481347	+	0.876530i	$0.340148\pi$
$798$	5.80733	0.205577
$799$	−9.49357	−0.335858
$800$	4.05178	0.143252
$801$	9.46066	0.334276
$802$	2.97913	0.105197
$803$	26.7059	0.942432
$804$	−10.3412	−0.364706
$805$	−7.81403	−0.275408
$806$	6.47708	0.228146
$807$	−13.9452	−0.490894
$808$	−12.5529	−0.441610
$809$	26.9265	0.946684	0.473342	−	0.880879i	$-0.343047\pi$
$809$	26.9265	0.946684	0.473342	+	0.880879i	$0.343047\pi$
$810$	−3.00862	−0.105712
$811$	−3.66557	−0.128716	−0.0643578	−	0.997927i	$-0.520500\pi$
$811$	−3.66557	−0.128716	−0.0643578	+	0.997927i	$0.520500\pi$
$812$	−2.62480	−0.0921123
$813$	4.21240	0.147735
$814$	52.9060	1.85436
$815$	−68.2593	−2.39102
$816$	−1.00000	−0.0350070
$817$	−29.9129	−1.04652
$818$	−15.1112	−0.528349
$819$	3.10644	0.108548
$820$	32.0327	1.11863
$821$	23.0145	0.803212	0.401606	−	0.915813i	$-0.368452\pi$
$821$	23.0145	0.803212	0.401606	+	0.915813i	$0.368452\pi$
$822$	−12.4290	−0.433510
$823$	−34.0813	−1.18800	−0.593999	−	0.804466i	$-0.702452\pi$
$823$	−34.0813	−1.18800	−0.593999	+	0.804466i	$0.702452\pi$
$824$	7.50255	0.261364
$825$	25.5660	0.890095
$826$	−0.900066	−0.0313173
$827$	−38.2376	−1.32965	−0.664826	−	0.746998i	$-0.731494\pi$
$827$	−38.2376	−1.32965	−0.664826	+	0.746998i	$0.731494\pi$
$828$	−2.88558	−0.100281
$829$	−18.9552	−0.658340	−0.329170	−	0.944271i	$-0.606769\pi$
$829$	−18.9552	−0.658340	−0.329170	+	0.944271i	$0.606769\pi$
$830$	−49.8452	−1.73015
$831$	−6.75313	−0.234264
$832$	−3.45134	−0.119654
$833$	−6.18988	−0.214467
$834$	−15.7367	−0.544918
$835$	52.6007	1.82032
$836$	−40.7117	−1.40804
$837$	1.87668	0.0648677
$838$	−17.5780	−0.607223
$839$	−28.6843	−0.990292	−0.495146	−	0.868810i	$-0.664885\pi$
$839$	−28.6843	−0.990292	−0.495146	+	0.868810i	$0.664885\pi$
$840$	−2.70795	−0.0934333
$841$	−20.4956	−0.706745
$842$	15.2171	0.524416
$843$	13.3057	0.458271
$844$	7.31362	0.251745
$845$	3.27404	0.112631
$846$	−9.49357	−0.326396
$847$	−25.9344	−0.891117
$848$	6.66594	0.228909
$849$	6.18534	0.212280
$850$	4.05178	0.138975
$851$	24.1948	0.829387
$852$	9.78989	0.335396
$853$	51.2994	1.75646	0.878229	−	0.478240i	$-0.158725\pi$
$853$	51.2994	1.75646	0.878229	+	0.478240i	$0.158725\pi$
$854$	−1.78935	−0.0612305
$855$	−19.4119	−0.663875
$856$	−19.6141	−0.670396
$857$	11.6952	0.399502	0.199751	−	0.979847i	$-0.435987\pi$
$857$	11.6952	0.399502	0.199751	+	0.979847i	$0.435987\pi$
$858$	−21.7774	−0.743468
$859$	27.4679	0.937194	0.468597	−	0.883412i	$-0.344760\pi$
$859$	27.4679	0.937194	0.468597	+	0.883412i	$0.344760\pi$
$860$	13.9484	0.475635
$861$	−9.58298	−0.326587
$862$	−13.0660	−0.445030
$863$	4.97839	0.169466	0.0847331	−	0.996404i	$-0.472996\pi$
$863$	4.97839	0.169466	0.0847331	+	0.996404i	$0.472996\pi$
$864$	−1.00000	−0.0340207
$865$	−1.40085	−0.0476304
$866$	12.8460	0.436524
$867$	−1.00000	−0.0339618
$868$	1.68914	0.0573331
$869$	−35.5156	−1.20478
$870$	8.77381	0.297460
$871$	−35.6911	−1.20935
$872$	13.1725	0.446076
$873$	7.99860	0.270712
$874$	−18.6181	−0.629767
$875$	−2.56773	−0.0868051
$876$	4.23244	0.143001
$877$	25.7564	0.869731	0.434866	−	0.900495i	$-0.356796\pi$
$877$	25.7564	0.869731	0.434866	+	0.900495i	$0.356796\pi$
$878$	1.69640	0.0572506
$879$	11.0832	0.373828
$880$	18.9839	0.639946
$881$	37.1556	1.25181	0.625903	−	0.779901i	$-0.284731\pi$
$881$	37.1556	1.25181	0.625903	+	0.779901i	$0.284731\pi$
$882$	−6.18988	−0.208424
$883$	57.1780	1.92419	0.962096	−	0.272711i	$-0.0879204\pi$
$883$	57.1780	1.92419	0.962096	+	0.272711i	$0.0879204\pi$
$884$	−3.45134	−0.116081
$885$	3.00862	0.101134
$886$	14.9806	0.503284
$887$	−19.0563	−0.639848	−0.319924	−	0.947443i	$-0.603657\pi$
$887$	−19.0563	−0.639848	−0.319924	+	0.947443i	$0.603657\pi$
$888$	8.38471	0.281372
$889$	−11.3015	−0.379041
$890$	−28.4635	−0.954099
$891$	−6.30983	−0.211387
$892$	−6.74732	−0.225917
$893$	−61.2536	−2.04977
$894$	0.619076	0.0207050
$895$	27.9705	0.934950
$896$	−0.900066	−0.0300691
$897$	−9.95915	−0.332526
$898$	23.3819	0.780264
$899$	−5.47284	−0.182529
$900$	4.05178	0.135059
$901$	6.66594	0.222075
$902$	67.1806	2.23687
$903$	−4.17283	−0.138863
$904$	13.6376	0.453579
$905$	−31.8092	−1.05737
$906$	9.41500	0.312792
$907$	1.74262	0.0578628	0.0289314	−	0.999581i	$-0.490790\pi$
$907$	1.74262	0.0578628	0.0289314	+	0.999581i	$0.490790\pi$
$908$	−6.97645	−0.231522
$909$	−12.5529	−0.416354
$910$	−9.34608	−0.309820
$911$	−16.6418	−0.551367	−0.275684	−	0.961248i	$-0.588904\pi$
$911$	−16.6418	−0.551367	−0.275684	+	0.961248i	$0.588904\pi$
$912$	−6.45211	−0.213651
$913$	−104.538	−3.45970
$914$	33.9039	1.12144
$915$	5.98121	0.197733
$916$	−20.3019	−0.670794
$917$	−16.9243	−0.558889
$918$	−1.00000	−0.0330049
$919$	50.1227	1.65340	0.826698	−	0.562646i	$-0.190217\pi$
$919$	50.1227	1.65340	0.826698	+	0.562646i	$0.190217\pi$
$920$	8.68162	0.286225
$921$	30.4096	1.00203
$922$	−17.9890	−0.592437
$923$	33.7883	1.11216
$924$	−5.67926	−0.186834
$925$	−33.9730	−1.11703
$926$	−16.5135	−0.542666
$927$	7.50255	0.246416
$928$	2.91623	0.0957299
$929$	15.0452	0.493619	0.246809	−	0.969064i	$-0.420618\pi$
$929$	15.0452	0.493619	0.246809	+	0.969064i	$0.420618\pi$
$930$	−5.64623	−0.185147
$931$	−39.9378	−1.30891
$932$	20.5754	0.673968
$933$	−11.0000	−0.360124
$934$	−11.5177	−0.376869
$935$	18.9839	0.620839
$936$	−3.45134	−0.112811
$937$	−2.20295	−0.0719673	−0.0359836	−	0.999352i	$-0.511456\pi$
$937$	−2.20295	−0.0719673	−0.0359836	+	0.999352i	$0.511456\pi$
$938$	−9.30777	−0.303910
$939$	−26.3895	−0.861189
$940$	28.5625	0.931607
$941$	−16.1287	−0.525782	−0.262891	−	0.964826i	$-0.584676\pi$
$941$	−16.1287	−0.525782	−0.262891	+	0.964826i	$0.584676\pi$
$942$	−4.97505	−0.162096
$943$	30.7228	1.00047
$944$	1.00000	0.0325472
$945$	−2.70795	−0.0880898
$946$	29.2532	0.951103
$947$	24.9729	0.811511	0.405755	−	0.913982i	$-0.367009\pi$
$947$	24.9729	0.811511	0.405755	+	0.913982i	$0.367009\pi$
$948$	−5.62862	−0.182809
$949$	14.6076	0.474183
$950$	26.1426	0.848177
$951$	11.7130	0.379819
$952$	−0.900066	−0.0291713
$953$	−20.2275	−0.655234	−0.327617	−	0.944811i	$-0.606245\pi$
$953$	−20.2275	−0.655234	−0.327617	+	0.944811i	$0.606245\pi$
$954$	6.66594	0.215818
$955$	58.9553	1.90775
$956$	−9.61103	−0.310843
$957$	18.4009	0.594816
$958$	−38.0671	−1.22989
$959$	−11.1869	−0.361243
$960$	3.00862	0.0971027
$961$	−27.4781	−0.886389
$962$	28.9385	0.933015
$963$	−19.6141	−0.632055
$964$	8.42760	0.271435
$965$	31.3755	1.01001
$966$	−2.59722	−0.0835641
$967$	−8.05279	−0.258960	−0.129480	−	0.991582i	$-0.541331\pi$
$967$	−8.05279	−0.258960	−0.129480	+	0.991582i	$0.541331\pi$
$968$	28.8139	0.926114
$969$	−6.45211	−0.207272
$970$	−24.0647	−0.772672
$971$	12.0673	0.387258	0.193629	−	0.981075i	$-0.437974\pi$
$971$	12.0673	0.387258	0.193629	+	0.981075i	$0.437974\pi$
$972$	−1.00000	−0.0320750
$973$	−14.1641	−0.454080
$974$	32.1500	1.03015
$975$	13.9841	0.447849
$976$	1.98803	0.0636352
$977$	27.5259	0.880630	0.440315	−	0.897843i	$-0.354867\pi$
$977$	27.5259	0.880630	0.440315	+	0.897843i	$0.354867\pi$
$978$	−22.6879	−0.725480
$979$	−59.6951	−1.90786
$980$	18.6230	0.594890
$981$	13.1725	0.420565
$982$	−23.8092	−0.759784
$983$	−61.2253	−1.95278	−0.976391	−	0.216010i	$-0.930696\pi$
$983$	−61.2253	−1.95278	−0.976391	+	0.216010i	$0.930696\pi$
$984$	10.6470	0.339413
$985$	−58.7605	−1.87226
$986$	2.91623	0.0928716
$987$	−8.54484	−0.271985
$988$	−22.2685	−0.708454
$989$	13.3780	0.425394
$990$	18.9839	0.603347
$991$	6.96487	0.221247	0.110623	−	0.993862i	$-0.464715\pi$
$991$	6.96487	0.221247	0.110623	+	0.993862i	$0.464715\pi$
$992$	−1.87668	−0.0595848
$993$	18.9951	0.602792
$994$	8.81155	0.279485
$995$	21.1258	0.669734
$996$	−16.5675	−0.524961
$997$	42.1420	1.33465	0.667325	−	0.744767i	$-0.267439\pi$
$997$	42.1420	1.33465	0.667325	+	0.744767i	$0.267439\pi$
$998$	32.0084	1.01321
$999$	8.38471	0.265280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bc.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bc.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00862 q^{5} -1.00000 q^{6} -0.900066 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.00862 q^{5} -1.00000 q^{6} -0.900066 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.00862 q^{10} -6.30983 q^{11} -1.00000 q^{12} -3.45134 q^{13} -0.900066 q^{14} +3.00862 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.45211 q^{19} -3.00862 q^{20} +0.900066 q^{21} -6.30983 q^{22} -2.88558 q^{23} -1.00000 q^{24} +4.05178 q^{25} -3.45134 q^{26} -1.00000 q^{27} -0.900066 q^{28} +2.91623 q^{29} +3.00862 q^{30} -1.87668 q^{31} +1.00000 q^{32} +6.30983 q^{33} +1.00000 q^{34} +2.70795 q^{35} +1.00000 q^{36} -8.38471 q^{37} +6.45211 q^{38} +3.45134 q^{39} -3.00862 q^{40} -10.6470 q^{41} +0.900066 q^{42} -4.63613 q^{43} -6.30983 q^{44} -3.00862 q^{45} -2.88558 q^{46} -9.49357 q^{47} -1.00000 q^{48} -6.18988 q^{49} +4.05178 q^{50} -1.00000 q^{51} -3.45134 q^{52} +6.66594 q^{53} -1.00000 q^{54} +18.9839 q^{55} -0.900066 q^{56} -6.45211 q^{57} +2.91623 q^{58} +1.00000 q^{59} +3.00862 q^{60} +1.98803 q^{61} -1.87668 q^{62} -0.900066 q^{63} +1.00000 q^{64} +10.3838 q^{65} +6.30983 q^{66} +10.3412 q^{67} +1.00000 q^{68} +2.88558 q^{69} +2.70795 q^{70} -9.78989 q^{71} +1.00000 q^{72} -4.23244 q^{73} -8.38471 q^{74} -4.05178 q^{75} +6.45211 q^{76} +5.67926 q^{77} +3.45134 q^{78} +5.62862 q^{79} -3.00862 q^{80} +1.00000 q^{81} -10.6470 q^{82} +16.5675 q^{83} +0.900066 q^{84} -3.00862 q^{85} -4.63613 q^{86} -2.91623 q^{87} -6.30983 q^{88} +9.46066 q^{89} -3.00862 q^{90} +3.10644 q^{91} -2.88558 q^{92} +1.87668 q^{93} -9.49357 q^{94} -19.4119 q^{95} -1.00000 q^{96} +7.99860 q^{97} -6.18988 q^{98} -6.30983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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