LMFDB - Embedded newform 6018.2.a.bc.1.13

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			1.13
Root			$3.97677$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97677 q^{5} -1.00000 q^{6} +1.13692 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97677 q^{5} -1.00000 q^{6} +1.13692 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.97677 q^{10} +3.07009 q^{11} -1.00000 q^{12} +1.25804 q^{13} +1.13692 q^{14} -3.97677 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.69872 q^{19} +3.97677 q^{20} -1.13692 q^{21} +3.07009 q^{22} -0.619707 q^{23} -1.00000 q^{24} +10.8147 q^{25} +1.25804 q^{26} -1.00000 q^{27} +1.13692 q^{28} -1.81795 q^{29} -3.97677 q^{30} +0.994381 q^{31} +1.00000 q^{32} -3.07009 q^{33} +1.00000 q^{34} +4.52126 q^{35} +1.00000 q^{36} +0.988751 q^{37} -7.69872 q^{38} -1.25804 q^{39} +3.97677 q^{40} +12.0914 q^{41} -1.13692 q^{42} -6.19494 q^{43} +3.07009 q^{44} +3.97677 q^{45} -0.619707 q^{46} +10.4864 q^{47} -1.00000 q^{48} -5.70742 q^{49} +10.8147 q^{50} -1.00000 q^{51} +1.25804 q^{52} +1.70278 q^{53} -1.00000 q^{54} +12.2091 q^{55} +1.13692 q^{56} +7.69872 q^{57} -1.81795 q^{58} +1.00000 q^{59} -3.97677 q^{60} +10.7571 q^{61} +0.994381 q^{62} +1.13692 q^{63} +1.00000 q^{64} +5.00296 q^{65} -3.07009 q^{66} -5.42097 q^{67} +1.00000 q^{68} +0.619707 q^{69} +4.52126 q^{70} +8.89395 q^{71} +1.00000 q^{72} +7.75863 q^{73} +0.988751 q^{74} -10.8147 q^{75} -7.69872 q^{76} +3.49043 q^{77} -1.25804 q^{78} -3.35038 q^{79} +3.97677 q^{80} +1.00000 q^{81} +12.0914 q^{82} -7.79561 q^{83} -1.13692 q^{84} +3.97677 q^{85} -6.19494 q^{86} +1.81795 q^{87} +3.07009 q^{88} -4.27542 q^{89} +3.97677 q^{90} +1.43029 q^{91} -0.619707 q^{92} -0.994381 q^{93} +10.4864 q^{94} -30.6161 q^{95} -1.00000 q^{96} -11.1924 q^{97} -5.70742 q^{98} +3.07009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.97677	1.77847	0.889234	−	0.457453i	$-0.151238\pi$
$5$	3.97677	1.77847	0.889234	+	0.457453i	$0.151238\pi$
$6$	−1.00000	−0.408248
$7$	1.13692	0.429714	0.214857	−	0.976646i	$-0.431072\pi$
$7$	1.13692	0.429714	0.214857	+	0.976646i	$0.431072\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.97677	1.25757
$11$	3.07009	0.925667	0.462834	−	0.886445i	$-0.346833\pi$
$11$	3.07009	0.925667	0.462834	+	0.886445i	$0.346833\pi$
$12$	−1.00000	−0.288675
$13$	1.25804	0.348919	0.174459	−	0.984664i	$-0.444182\pi$
$13$	1.25804	0.348919	0.174459	+	0.984664i	$0.444182\pi$
$14$	1.13692	0.303853
$15$	−3.97677	−1.02680
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−7.69872	−1.76621	−0.883104	−	0.469177i	$-0.844551\pi$
$19$	−7.69872	−1.76621	−0.883104	+	0.469177i	$0.844551\pi$
$20$	3.97677	0.889234
$21$	−1.13692	−0.248095
$22$	3.07009	0.654546
$23$	−0.619707	−0.129218	−0.0646089	−	0.997911i	$-0.520580\pi$
$23$	−0.619707	−0.129218	−0.0646089	+	0.997911i	$0.520580\pi$
$24$	−1.00000	−0.204124
$25$	10.8147	2.16295
$26$	1.25804	0.246723
$27$	−1.00000	−0.192450
$28$	1.13692	0.214857
$29$	−1.81795	−0.337585	−0.168793	−	0.985652i	$-0.553987\pi$
$29$	−1.81795	−0.337585	−0.168793	+	0.985652i	$0.553987\pi$
$30$	−3.97677	−0.726056
$31$	0.994381	0.178596	0.0892981	−	0.996005i	$-0.471538\pi$
$31$	0.994381	0.178596	0.0892981	+	0.996005i	$0.471538\pi$
$32$	1.00000	0.176777
$33$	−3.07009	−0.534434
$34$	1.00000	0.171499
$35$	4.52126	0.764232
$36$	1.00000	0.166667
$37$	0.988751	0.162550	0.0812748	−	0.996692i	$-0.474101\pi$
$37$	0.988751	0.162550	0.0812748	+	0.996692i	$0.474101\pi$
$38$	−7.69872	−1.24890
$39$	−1.25804	−0.201448
$40$	3.97677	0.628783
$41$	12.0914	1.88836	0.944181	−	0.329428i	$-0.106856\pi$
$41$	12.0914	1.88836	0.944181	+	0.329428i	$0.106856\pi$
$42$	−1.13692	−0.175430
$43$	−6.19494	−0.944719	−0.472360	−	0.881406i	$-0.656598\pi$
$43$	−6.19494	−0.944719	−0.472360	+	0.881406i	$0.656598\pi$
$44$	3.07009	0.462834
$45$	3.97677	0.592823
$46$	−0.619707	−0.0913708
$47$	10.4864	1.52961	0.764803	−	0.644265i	$-0.222836\pi$
$47$	10.4864	1.52961	0.764803	+	0.644265i	$0.222836\pi$
$48$	−1.00000	−0.144338
$49$	−5.70742	−0.815346
$50$	10.8147	1.52943
$51$	−1.00000	−0.140028
$52$	1.25804	0.174459
$53$	1.70278	0.233895	0.116948	−	0.993138i	$-0.462689\pi$
$53$	1.70278	0.233895	0.116948	+	0.993138i	$0.462689\pi$
$54$	−1.00000	−0.136083
$55$	12.2091	1.64627
$56$	1.13692	0.151927
$57$	7.69872	1.01972
$58$	−1.81795	−0.238709
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.97677	−0.513399
$61$	10.7571	1.37730	0.688650	−	0.725094i	$-0.258204\pi$
$61$	10.7571	1.37730	0.688650	+	0.725094i	$0.258204\pi$
$62$	0.994381	0.126287
$63$	1.13692	0.143238
$64$	1.00000	0.125000
$65$	5.00296	0.620540
$66$	−3.07009	−0.377902
$67$	−5.42097	−0.662277	−0.331138	−	0.943582i	$-0.607433\pi$
$67$	−5.42097	−0.662277	−0.331138	+	0.943582i	$0.607433\pi$
$68$	1.00000	0.121268
$69$	0.619707	0.0746040
$70$	4.52126	0.540393
$71$	8.89395	1.05552	0.527759	−	0.849394i	$-0.323033\pi$
$71$	8.89395	1.05552	0.527759	+	0.849394i	$0.323033\pi$
$72$	1.00000	0.117851
$73$	7.75863	0.908079	0.454040	−	0.890981i	$-0.349982\pi$
$73$	7.75863	0.908079	0.454040	+	0.890981i	$0.349982\pi$
$74$	0.988751	0.114940
$75$	−10.8147	−1.24878
$76$	−7.69872	−0.883104
$77$	3.49043	0.397772
$78$	−1.25804	−0.142445
$79$	−3.35038	−0.376947	−0.188474	−	0.982078i	$-0.560354\pi$
$79$	−3.35038	−0.376947	−0.188474	+	0.982078i	$0.560354\pi$
$80$	3.97677	0.444617
$81$	1.00000	0.111111
$82$	12.0914	1.33527
$83$	−7.79561	−0.855679	−0.427840	−	0.903855i	$-0.640725\pi$
$83$	−7.79561	−0.855679	−0.427840	+	0.903855i	$0.640725\pi$
$84$	−1.13692	−0.124048
$85$	3.97677	0.431342
$86$	−6.19494	−0.668017
$87$	1.81795	0.194905
$88$	3.07009	0.327273
$89$	−4.27542	−0.453194	−0.226597	−	0.973989i	$-0.572760\pi$
$89$	−4.27542	−0.453194	−0.226597	+	0.973989i	$0.572760\pi$
$90$	3.97677	0.419189
$91$	1.43029	0.149935
$92$	−0.619707	−0.0646089
$93$	−0.994381	−0.103113
$94$	10.4864	1.08159
$95$	−30.6161	−3.14114
$96$	−1.00000	−0.102062
$97$	−11.1924	−1.13642	−0.568210	−	0.822884i	$-0.692364\pi$
$97$	−11.1924	−1.13642	−0.568210	+	0.822884i	$0.692364\pi$
$98$	−5.70742	−0.576537
$99$	3.07009	0.308556
$100$	10.8147	1.08147
$101$	−1.92257	−0.191303	−0.0956513	−	0.995415i	$-0.530493\pi$
$101$	−1.92257	−0.191303	−0.0956513	+	0.995415i	$0.530493\pi$
$102$	−1.00000	−0.0990148
$103$	−6.72362	−0.662498	−0.331249	−	0.943543i	$-0.607470\pi$
$103$	−6.72362	−0.662498	−0.331249	+	0.943543i	$0.607470\pi$
$104$	1.25804	0.123361
$105$	−4.52126	−0.441229
$106$	1.70278	0.165389
$107$	6.85186	0.662394	0.331197	−	0.943562i	$-0.392547\pi$
$107$	6.85186	0.662394	0.331197	+	0.943562i	$0.392547\pi$
$108$	−1.00000	−0.0962250
$109$	2.09467	0.200633	0.100317	−	0.994956i	$-0.468014\pi$
$109$	2.09467	0.200633	0.100317	+	0.994956i	$0.468014\pi$
$110$	12.2091	1.16409
$111$	−0.988751	−0.0938481
$112$	1.13692	0.107428
$113$	−14.2454	−1.34010	−0.670048	−	0.742318i	$-0.733726\pi$
$113$	−14.2454	−1.34010	−0.670048	+	0.742318i	$0.733726\pi$
$114$	7.69872	0.721051
$115$	−2.46444	−0.229810
$116$	−1.81795	−0.168793
$117$	1.25804	0.116306
$118$	1.00000	0.0920575
$119$	1.13692	0.104221
$120$	−3.97677	−0.363028
$121$	−1.57454	−0.143140
$122$	10.7571	0.973899
$123$	−12.0914	−1.09025
$124$	0.994381	0.0892981
$125$	23.1239	2.06826
$126$	1.13692	0.101284
$127$	−5.95300	−0.528243	−0.264121	−	0.964489i	$-0.585082\pi$
$127$	−5.95300	−0.528243	−0.264121	+	0.964489i	$0.585082\pi$
$128$	1.00000	0.0883883
$129$	6.19494	0.545434
$130$	5.00296	0.438788
$131$	−4.72801	−0.413088	−0.206544	−	0.978437i	$-0.566222\pi$
$131$	−4.72801	−0.413088	−0.206544	+	0.978437i	$0.566222\pi$
$132$	−3.07009	−0.267217
$133$	−8.75279	−0.758963
$134$	−5.42097	−0.468300
$135$	−3.97677	−0.342266
$136$	1.00000	0.0857493
$137$	−4.27426	−0.365175	−0.182587	−	0.983190i	$-0.558447\pi$
$137$	−4.27426	−0.365175	−0.182587	+	0.983190i	$0.558447\pi$
$138$	0.619707	0.0527530
$139$	12.9036	1.09447	0.547236	−	0.836978i	$-0.315680\pi$
$139$	12.9036	1.09447	0.547236	+	0.836978i	$0.315680\pi$
$140$	4.52126	0.382116
$141$	−10.4864	−0.883118
$142$	8.89395	0.746363
$143$	3.86231	0.322982
$144$	1.00000	0.0833333
$145$	−7.22959	−0.600385
$146$	7.75863	0.642109
$147$	5.70742	0.470740
$148$	0.988751	0.0812748
$149$	3.21387	0.263290	0.131645	−	0.991297i	$-0.457974\pi$
$149$	3.21387	0.263290	0.131645	+	0.991297i	$0.457974\pi$
$150$	−10.8147	−0.883020
$151$	−19.3475	−1.57447	−0.787237	−	0.616650i	$-0.788489\pi$
$151$	−19.3475	−1.57447	−0.787237	+	0.616650i	$0.788489\pi$
$152$	−7.69872	−0.624449
$153$	1.00000	0.0808452
$154$	3.49043	0.281267
$155$	3.95443	0.317628
$156$	−1.25804	−0.100724
$157$	22.3783	1.78598	0.892991	−	0.450074i	$-0.148602\pi$
$157$	22.3783	1.78598	0.892991	+	0.450074i	$0.148602\pi$
$158$	−3.35038	−0.266542
$159$	−1.70278	−0.135039
$160$	3.97677	0.314392
$161$	−0.704554	−0.0555267
$162$	1.00000	0.0785674
$163$	−0.142808	−0.0111856	−0.00559279	−	0.999984i	$-0.501780\pi$
$163$	−0.142808	−0.0111856	−0.00559279	+	0.999984i	$0.501780\pi$
$164$	12.0914	0.944181
$165$	−12.2091	−0.950474
$166$	−7.79561	−0.605057
$167$	17.1066	1.32375	0.661873	−	0.749616i	$-0.269762\pi$
$167$	17.1066	1.32375	0.661873	+	0.749616i	$0.269762\pi$
$168$	−1.13692	−0.0877149
$169$	−11.4173	−0.878256
$170$	3.97677	0.305005
$171$	−7.69872	−0.588736
$172$	−6.19494	−0.472360
$173$	23.5568	1.79099	0.895496	−	0.445069i	$-0.146821\pi$
$173$	23.5568	1.79099	0.895496	+	0.445069i	$0.146821\pi$
$174$	1.81795	0.137819
$175$	12.2954	0.929448
$176$	3.07009	0.231417
$177$	−1.00000	−0.0751646
$178$	−4.27542	−0.320456
$179$	9.80221	0.732652	0.366326	−	0.930487i	$-0.380616\pi$
$179$	9.80221	0.732652	0.366326	+	0.930487i	$0.380616\pi$
$180$	3.97677	0.296411
$181$	−24.6041	−1.82881	−0.914404	−	0.404802i	$-0.867340\pi$
$181$	−24.6041	−1.82881	−0.914404	+	0.404802i	$0.867340\pi$
$182$	1.43029	0.106020
$183$	−10.7571	−0.795185
$184$	−0.619707	−0.0456854
$185$	3.93204	0.289089
$186$	−0.994381	−0.0729116
$187$	3.07009	0.224507
$188$	10.4864	0.764803
$189$	−1.13692	−0.0826984
$190$	−30.6161	−2.22112
$191$	12.0907	0.874856	0.437428	−	0.899253i	$-0.355890\pi$
$191$	12.0907	0.874856	0.437428	+	0.899253i	$0.355890\pi$
$192$	−1.00000	−0.0721688
$193$	−2.30143	−0.165661	−0.0828303	−	0.996564i	$-0.526396\pi$
$193$	−2.30143	−0.165661	−0.0828303	+	0.996564i	$0.526396\pi$
$194$	−11.1924	−0.803570
$195$	−5.00296	−0.358269
$196$	−5.70742	−0.407673
$197$	20.9107	1.48982	0.744911	−	0.667164i	$-0.232492\pi$
$197$	20.9107	1.48982	0.744911	+	0.667164i	$0.232492\pi$
$198$	3.07009	0.218182
$199$	−25.0623	−1.77662	−0.888310	−	0.459244i	$-0.848120\pi$
$199$	−25.0623	−1.77662	−0.888310	+	0.459244i	$0.848120\pi$
$200$	10.8147	0.764717
$201$	5.42097	0.382366
$202$	−1.92257	−0.135271
$203$	−2.06686	−0.145065
$204$	−1.00000	−0.0700140
$205$	48.0848	3.35839
$206$	−6.72362	−0.468457
$207$	−0.619707	−0.0430726
$208$	1.25804	0.0872296
$209$	−23.6358	−1.63492
$210$	−4.52126	−0.311996
$211$	−22.1859	−1.52734	−0.763669	−	0.645608i	$-0.776604\pi$
$211$	−22.1859	−1.52734	−0.763669	+	0.645608i	$0.776604\pi$
$212$	1.70278	0.116948
$213$	−8.89395	−0.609403
$214$	6.85186	0.468384
$215$	−24.6359	−1.68015
$216$	−1.00000	−0.0680414
$217$	1.13053	0.0767452
$218$	2.09467	0.141869
$219$	−7.75863	−0.524280
$220$	12.2091	0.823135
$221$	1.25804	0.0846252
$222$	−0.988751	−0.0663606
$223$	−3.62679	−0.242868	−0.121434	−	0.992600i	$-0.538749\pi$
$223$	−3.62679	−0.242868	−0.121434	+	0.992600i	$0.538749\pi$
$224$	1.13692	0.0759633
$225$	10.8147	0.720982
$226$	−14.2454	−0.947591
$227$	−7.96375	−0.528573	−0.264286	−	0.964444i	$-0.585136\pi$
$227$	−7.96375	−0.528573	−0.264286	+	0.964444i	$0.585136\pi$
$228$	7.69872	0.509860
$229$	11.7865	0.778873	0.389437	−	0.921053i	$-0.372670\pi$
$229$	11.7865	0.778873	0.389437	+	0.921053i	$0.372670\pi$
$230$	−2.46444	−0.162500
$231$	−3.49043	−0.229654
$232$	−1.81795	−0.119354
$233$	−15.0215	−0.984089	−0.492044	−	0.870570i	$-0.663750\pi$
$233$	−15.0215	−0.984089	−0.492044	+	0.870570i	$0.663750\pi$
$234$	1.25804	0.0822409
$235$	41.7022	2.72035
$236$	1.00000	0.0650945
$237$	3.35038	0.217631
$238$	1.13692	0.0736953
$239$	4.05363	0.262207	0.131104	−	0.991369i	$-0.458148\pi$
$239$	4.05363	0.262207	0.131104	+	0.991369i	$0.458148\pi$
$240$	−3.97677	−0.256700
$241$	16.4934	1.06243	0.531216	−	0.847237i	$-0.321735\pi$
$241$	16.4934	1.06243	0.531216	+	0.847237i	$0.321735\pi$
$242$	−1.57454	−0.101215
$243$	−1.00000	−0.0641500
$244$	10.7571	0.688650
$245$	−22.6971	−1.45007
$246$	−12.0914	−0.770920
$247$	−9.68533	−0.616263
$248$	0.994381	0.0631433
$249$	7.79561	0.494027
$250$	23.1239	1.46248
$251$	3.02939	0.191214	0.0956068	−	0.995419i	$-0.469521\pi$
$251$	3.02939	0.191214	0.0956068	+	0.995419i	$0.469521\pi$
$252$	1.13692	0.0716189
$253$	−1.90256	−0.119613
$254$	−5.95300	−0.373524
$255$	−3.97677	−0.249035
$256$	1.00000	0.0625000
$257$	−5.09152	−0.317600	−0.158800	−	0.987311i	$-0.550763\pi$
$257$	−5.09152	−0.317600	−0.158800	+	0.987311i	$0.550763\pi$
$258$	6.19494	0.385680
$259$	1.12413	0.0698498
$260$	5.00296	0.310270
$261$	−1.81795	−0.112528
$262$	−4.72801	−0.292098
$263$	0.115913	0.00714750	0.00357375	−	0.999994i	$-0.498862\pi$
$263$	0.115913	0.00714750	0.00357375	+	0.999994i	$0.498862\pi$
$264$	−3.07009	−0.188951
$265$	6.77158	0.415975
$266$	−8.75279	−0.536668
$267$	4.27542	0.261652
$268$	−5.42097	−0.331138
$269$	−2.51075	−0.153083	−0.0765414	−	0.997066i	$-0.524388\pi$
$269$	−2.51075	−0.153083	−0.0765414	+	0.997066i	$0.524388\pi$
$270$	−3.97677	−0.242019
$271$	−24.6022	−1.49448	−0.747238	−	0.664557i	$-0.768620\pi$
$271$	−24.6022	−1.49448	−0.747238	+	0.664557i	$0.768620\pi$
$272$	1.00000	0.0606339
$273$	−1.43029	−0.0865650
$274$	−4.27426	−0.258217
$275$	33.2022	2.00217
$276$	0.619707	0.0373020
$277$	12.0291	0.722756	0.361378	−	0.932419i	$-0.382306\pi$
$277$	12.0291	0.722756	0.361378	+	0.932419i	$0.382306\pi$
$278$	12.9036	0.773909
$279$	0.994381	0.0595321
$280$	4.52126	0.270197
$281$	−13.9052	−0.829516	−0.414758	−	0.909932i	$-0.636134\pi$
$281$	−13.9052	−0.829516	−0.414758	+	0.909932i	$0.636134\pi$
$282$	−10.4864	−0.624459
$283$	−3.44887	−0.205014	−0.102507	−	0.994732i	$-0.532686\pi$
$283$	−3.44887	−0.205014	−0.102507	+	0.994732i	$0.532686\pi$
$284$	8.89395	0.527759
$285$	30.6161	1.81354
$286$	3.86231	0.228383
$287$	13.7469	0.811454
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−7.22959	−0.424536
$291$	11.1924	0.656112
$292$	7.75863	0.454040
$293$	−27.1598	−1.58669	−0.793347	−	0.608770i	$-0.791663\pi$
$293$	−27.1598	−1.58669	−0.793347	+	0.608770i	$0.791663\pi$
$294$	5.70742	0.332864
$295$	3.97677	0.231537
$296$	0.988751	0.0574700
$297$	−3.07009	−0.178145
$298$	3.21387	0.186174
$299$	−0.779618	−0.0450865
$300$	−10.8147	−0.624389
$301$	−7.04312	−0.405959
$302$	−19.3475	−1.11332
$303$	1.92257	0.110449
$304$	−7.69872	−0.441552
$305$	42.7784	2.44948
$306$	1.00000	0.0571662
$307$	−22.6836	−1.29462	−0.647312	−	0.762225i	$-0.724107\pi$
$307$	−22.6836	−1.29462	−0.647312	+	0.762225i	$0.724107\pi$
$308$	3.49043	0.198886
$309$	6.72362	0.382494
$310$	3.95443	0.224597
$311$	10.0386	0.569234	0.284617	−	0.958641i	$-0.408134\pi$
$311$	10.0386	0.569234	0.284617	+	0.958641i	$0.408134\pi$
$312$	−1.25804	−0.0712227
$313$	−21.6502	−1.22374	−0.611871	−	0.790957i	$-0.709583\pi$
$313$	−21.6502	−1.22374	−0.611871	+	0.790957i	$0.709583\pi$
$314$	22.3783	1.26288
$315$	4.52126	0.254744
$316$	−3.35038	−0.188474
$317$	3.79216	0.212989	0.106494	−	0.994313i	$-0.466037\pi$
$317$	3.79216	0.212989	0.106494	+	0.994313i	$0.466037\pi$
$318$	−1.70278	−0.0954873
$319$	−5.58128	−0.312492
$320$	3.97677	0.222308
$321$	−6.85186	−0.382434
$322$	−0.704554	−0.0392633
$323$	−7.69872	−0.428368
$324$	1.00000	0.0555556
$325$	13.6054	0.754692
$326$	−0.142808	−0.00790939
$327$	−2.09467	−0.115836
$328$	12.0914	0.667636
$329$	11.9222	0.657292
$330$	−12.2091	−0.672087
$331$	−8.61958	−0.473775	−0.236888	−	0.971537i	$-0.576127\pi$
$331$	−8.61958	−0.473775	−0.236888	+	0.971537i	$0.576127\pi$
$332$	−7.79561	−0.427840
$333$	0.988751	0.0541832
$334$	17.1066	0.936029
$335$	−21.5580	−1.17784
$336$	−1.13692	−0.0620238
$337$	26.6845	1.45360	0.726799	−	0.686850i	$-0.241007\pi$
$337$	26.6845	1.45360	0.726799	+	0.686850i	$0.241007\pi$
$338$	−11.4173	−0.621021
$339$	14.2454	0.773704
$340$	3.97677	0.215671
$341$	3.05284	0.165321
$342$	−7.69872	−0.416299
$343$	−14.4473	−0.780079
$344$	−6.19494	−0.334009
$345$	2.46444	0.132681
$346$	23.5568	1.26642
$347$	−0.431315	−0.0231542	−0.0115771	−	0.999933i	$-0.503685\pi$
$347$	−0.431315	−0.0231542	−0.0115771	+	0.999933i	$0.503685\pi$
$348$	1.81795	0.0974525
$349$	22.1596	1.18618	0.593089	−	0.805137i	$-0.297908\pi$
$349$	22.1596	1.18618	0.593089	+	0.805137i	$0.297908\pi$
$350$	12.2954	0.657219
$351$	−1.25804	−0.0671494
$352$	3.07009	0.163636
$353$	−12.7394	−0.678048	−0.339024	−	0.940778i	$-0.610097\pi$
$353$	−12.7394	−0.678048	−0.339024	+	0.940778i	$0.610097\pi$
$354$	−1.00000	−0.0531494
$355$	35.3692	1.87720
$356$	−4.27542	−0.226597
$357$	−1.13692	−0.0601719
$358$	9.80221	0.518063
$359$	−10.6586	−0.562540	−0.281270	−	0.959629i	$-0.590756\pi$
$359$	−10.6586	−0.562540	−0.281270	+	0.959629i	$0.590756\pi$
$360$	3.97677	0.209594
$361$	40.2703	2.11949
$362$	−24.6041	−1.29316
$363$	1.57454	0.0826419
$364$	1.43029	0.0749675
$365$	30.8543	1.61499
$366$	−10.7571	−0.562281
$367$	19.1112	0.997598	0.498799	−	0.866718i	$-0.333775\pi$
$367$	19.1112	0.997598	0.498799	+	0.866718i	$0.333775\pi$
$368$	−0.619707	−0.0323045
$369$	12.0914	0.629454
$370$	3.93204	0.204417
$371$	1.93592	0.100508
$372$	−0.994381	−0.0515563
$373$	3.17300	0.164292	0.0821458	−	0.996620i	$-0.473823\pi$
$373$	3.17300	0.164292	0.0821458	+	0.996620i	$0.473823\pi$
$374$	3.07009	0.158751
$375$	−23.1239	−1.19411
$376$	10.4864	0.540797
$377$	−2.28706	−0.117790
$378$	−1.13692	−0.0584766
$379$	12.7053	0.652627	0.326313	−	0.945262i	$-0.394194\pi$
$379$	12.7053	0.652627	0.326313	+	0.945262i	$0.394194\pi$
$380$	−30.6161	−1.57057
$381$	5.95300	0.304981
$382$	12.0907	0.618616
$383$	33.6237	1.71809	0.859045	−	0.511900i	$-0.171058\pi$
$383$	33.6237	1.71809	0.859045	+	0.511900i	$0.171058\pi$
$384$	−1.00000	−0.0510310
$385$	13.8807	0.707424
$386$	−2.30143	−0.117140
$387$	−6.19494	−0.314906
$388$	−11.1924	−0.568210
$389$	−28.6873	−1.45450	−0.727251	−	0.686371i	$-0.759202\pi$
$389$	−28.6873	−1.45450	−0.727251	+	0.686371i	$0.759202\pi$
$390$	−5.00296	−0.253335
$391$	−0.619707	−0.0313399
$392$	−5.70742	−0.288268
$393$	4.72801	0.238497
$394$	20.9107	1.05346
$395$	−13.3237	−0.670389
$396$	3.07009	0.154278
$397$	7.15452	0.359075	0.179537	−	0.983751i	$-0.442540\pi$
$397$	7.15452	0.359075	0.179537	+	0.983751i	$0.442540\pi$
$398$	−25.0623	−1.25626
$399$	8.75279	0.438188
$400$	10.8147	0.540737
$401$	28.7514	1.43577	0.717887	−	0.696160i	$-0.245109\pi$
$401$	28.7514	1.43577	0.717887	+	0.696160i	$0.245109\pi$
$402$	5.42097	0.270373
$403$	1.25098	0.0623155
$404$	−1.92257	−0.0956513
$405$	3.97677	0.197608
$406$	−2.06686	−0.102576
$407$	3.03556	0.150467
$408$	−1.00000	−0.0495074
$409$	−12.9056	−0.638140	−0.319070	−	0.947731i	$-0.603371\pi$
$409$	−12.9056	−0.638140	−0.319070	+	0.947731i	$0.603371\pi$
$410$	48.0848	2.37474
$411$	4.27426	0.210834
$412$	−6.72362	−0.331249
$413$	1.13692	0.0559439
$414$	−0.619707	−0.0304569
$415$	−31.0014	−1.52180
$416$	1.25804	0.0616807
$417$	−12.9036	−0.631894
$418$	−23.6358	−1.15606
$419$	0.561324	0.0274225	0.0137112	−	0.999906i	$-0.495635\pi$
$419$	0.561324	0.0274225	0.0137112	+	0.999906i	$0.495635\pi$
$420$	−4.52126	−0.220615
$421$	7.84671	0.382425	0.191213	−	0.981549i	$-0.438758\pi$
$421$	7.84671	0.382425	0.191213	+	0.981549i	$0.438758\pi$
$422$	−22.1859	−1.07999
$423$	10.4864	0.509868
$424$	1.70278	0.0826944
$425$	10.8147	0.524592
$426$	−8.89395	−0.430913
$427$	12.2299	0.591845
$428$	6.85186	0.331197
$429$	−3.86231	−0.186474
$430$	−24.6359	−1.18805
$431$	6.79498	0.327302	0.163651	−	0.986518i	$-0.447673\pi$
$431$	6.79498	0.327302	0.163651	+	0.986518i	$0.447673\pi$
$432$	−1.00000	−0.0481125
$433$	−20.1047	−0.966170	−0.483085	−	0.875573i	$-0.660484\pi$
$433$	−20.1047	−0.966170	−0.483085	+	0.875573i	$0.660484\pi$
$434$	1.13053	0.0542671
$435$	7.22959	0.346632
$436$	2.09467	0.100317
$437$	4.77095	0.228226
$438$	−7.75863	−0.370722
$439$	−19.1000	−0.911592	−0.455796	−	0.890084i	$-0.650645\pi$
$439$	−19.1000	−0.911592	−0.455796	+	0.890084i	$0.650645\pi$
$440$	12.2091	0.582044
$441$	−5.70742	−0.271782
$442$	1.25804	0.0598390
$443$	1.06939	0.0508085	0.0254042	−	0.999677i	$-0.491913\pi$
$443$	1.06939	0.0508085	0.0254042	+	0.999677i	$0.491913\pi$
$444$	−0.988751	−0.0469240
$445$	−17.0024	−0.805991
$446$	−3.62679	−0.171734
$447$	−3.21387	−0.152011
$448$	1.13692	0.0537142
$449$	27.9046	1.31690	0.658449	−	0.752625i	$-0.271213\pi$
$449$	27.9046	1.31690	0.658449	+	0.752625i	$0.271213\pi$
$450$	10.8147	0.509812
$451$	37.1217	1.74799
$452$	−14.2454	−0.670048
$453$	19.3475	0.909023
$454$	−7.96375	−0.373758
$455$	5.68794	0.266655
$456$	7.69872	0.360526
$457$	−35.4635	−1.65891	−0.829456	−	0.558572i	$-0.811349\pi$
$457$	−35.4635	−1.65891	−0.829456	+	0.558572i	$0.811349\pi$
$458$	11.7865	0.550746
$459$	−1.00000	−0.0466760
$460$	−2.46444	−0.114905
$461$	17.2178	0.801913	0.400957	−	0.916097i	$-0.368678\pi$
$461$	17.2178	0.801913	0.400957	+	0.916097i	$0.368678\pi$
$462$	−3.49043	−0.162390
$463$	16.3314	0.758984	0.379492	−	0.925195i	$-0.376099\pi$
$463$	16.3314	0.758984	0.379492	+	0.925195i	$0.376099\pi$
$464$	−1.81795	−0.0843964
$465$	−3.95443	−0.183382
$466$	−15.0215	−0.695856
$467$	−31.4290	−1.45436	−0.727180	−	0.686447i	$-0.759169\pi$
$467$	−31.4290	−1.45436	−0.727180	+	0.686447i	$0.759169\pi$
$468$	1.25804	0.0581531
$469$	−6.16318	−0.284589
$470$	41.7022	1.92358
$471$	−22.3783	−1.03114
$472$	1.00000	0.0460287
$473$	−19.0190	−0.874496
$474$	3.35038	0.153888
$475$	−83.2597	−3.82021
$476$	1.13692	0.0521104
$477$	1.70278	0.0779651
$478$	4.05363	0.185409
$479$	36.8928	1.68567	0.842837	−	0.538170i	$-0.180884\pi$
$479$	36.8928	1.68567	0.842837	+	0.538170i	$0.180884\pi$
$480$	−3.97677	−0.181514
$481$	1.24389	0.0567166
$482$	16.4934	0.751252
$483$	0.704554	0.0320583
$484$	−1.57454	−0.0715700
$485$	−44.5098	−2.02109
$486$	−1.00000	−0.0453609
$487$	22.8713	1.03640	0.518200	−	0.855260i	$-0.326602\pi$
$487$	22.8713	1.03640	0.518200	+	0.855260i	$0.326602\pi$
$488$	10.7571	0.486949
$489$	0.142808	0.00645799
$490$	−22.6971	−1.02535
$491$	21.1099	0.952675	0.476338	−	0.879262i	$-0.341964\pi$
$491$	21.1099	0.952675	0.476338	+	0.879262i	$0.341964\pi$
$492$	−12.0914	−0.545123
$493$	−1.81795	−0.0818765
$494$	−9.68533	−0.435764
$495$	12.2091	0.548756
$496$	0.994381	0.0446490
$497$	10.1117	0.453570
$498$	7.79561	0.349330
$499$	30.6232	1.37088	0.685441	−	0.728128i	$-0.259610\pi$
$499$	30.6232	1.37088	0.685441	+	0.728128i	$0.259610\pi$
$500$	23.1239	1.03413
$501$	−17.1066	−0.764265
$502$	3.02939	0.135208
$503$	−33.9433	−1.51346	−0.756728	−	0.653729i	$-0.773203\pi$
$503$	−33.9433	−1.51346	−0.756728	+	0.653729i	$0.773203\pi$
$504$	1.13692	0.0506422
$505$	−7.64562	−0.340226
$506$	−1.90256	−0.0845790
$507$	11.4173	0.507061
$508$	−5.95300	−0.264121
$509$	−29.2052	−1.29450	−0.647250	−	0.762278i	$-0.724081\pi$
$509$	−29.2052	−1.29450	−0.647250	+	0.762278i	$0.724081\pi$
$510$	−3.97677	−0.176095
$511$	8.82091	0.390214
$512$	1.00000	0.0441942
$513$	7.69872	0.339907
$514$	−5.09152	−0.224577
$515$	−26.7383	−1.17823
$516$	6.19494	0.272717
$517$	32.1943	1.41591
$518$	1.12413	0.0493913
$519$	−23.5568	−1.03403
$520$	5.00296	0.219394
$521$	−38.6144	−1.69173	−0.845864	−	0.533398i	$-0.820915\pi$
$521$	−38.6144	−1.69173	−0.845864	+	0.533398i	$0.820915\pi$
$522$	−1.81795	−0.0795696
$523$	18.0494	0.789247	0.394624	−	0.918843i	$-0.370875\pi$
$523$	18.0494	0.789247	0.394624	+	0.918843i	$0.370875\pi$
$524$	−4.72801	−0.206544
$525$	−12.2954	−0.536617
$526$	0.115913	0.00505404
$527$	0.994381	0.0433159
$528$	−3.07009	−0.133609
$529$	−22.6160	−0.983303
$530$	6.77158	0.294139
$531$	1.00000	0.0433963
$532$	−8.75279	−0.379482
$533$	15.2115	0.658884
$534$	4.27542	0.185016
$535$	27.2483	1.17805
$536$	−5.42097	−0.234150
$537$	−9.80221	−0.422997
$538$	−2.51075	−0.108246
$539$	−17.5223	−0.754739
$540$	−3.97677	−0.171133
$541$	−34.8356	−1.49770	−0.748850	−	0.662740i	$-0.769394\pi$
$541$	−34.8356	−1.49770	−0.748850	+	0.662740i	$0.769394\pi$
$542$	−24.6022	−1.05675
$543$	24.6041	1.05586
$544$	1.00000	0.0428746
$545$	8.33003	0.356819
$546$	−1.43029	−0.0612107
$547$	−5.42768	−0.232071	−0.116035	−	0.993245i	$-0.537019\pi$
$547$	−5.42768	−0.232071	−0.116035	+	0.993245i	$0.537019\pi$
$548$	−4.27426	−0.182587
$549$	10.7571	0.459100
$550$	33.2022	1.41575
$551$	13.9959	0.596246
$552$	0.619707	0.0263765
$553$	−3.80910	−0.161979
$554$	12.0291	0.511066
$555$	−3.93204	−0.166906
$556$	12.9036	0.547236
$557$	23.9627	1.01533	0.507667	−	0.861553i	$-0.330508\pi$
$557$	23.9627	1.01533	0.507667	+	0.861553i	$0.330508\pi$
$558$	0.994381	0.0420955
$559$	−7.79350	−0.329630
$560$	4.52126	0.191058
$561$	−3.07009	−0.129619
$562$	−13.9052	−0.586556
$563$	−2.15708	−0.0909100	−0.0454550	−	0.998966i	$-0.514474\pi$
$563$	−2.15708	−0.0909100	−0.0454550	+	0.998966i	$0.514474\pi$
$564$	−10.4864	−0.441559
$565$	−56.6508	−2.38332
$566$	−3.44887	−0.144967
$567$	1.13692	0.0477460
$568$	8.89395	0.373182
$569$	22.0115	0.922771	0.461385	−	0.887200i	$-0.347353\pi$
$569$	22.0115	0.922771	0.461385	+	0.887200i	$0.347353\pi$
$570$	30.6161	1.28237
$571$	20.8843	0.873982	0.436991	−	0.899466i	$-0.356044\pi$
$571$	20.8843	0.873982	0.436991	+	0.899466i	$0.356044\pi$
$572$	3.86231	0.161491
$573$	−12.0907	−0.505098
$574$	13.7469	0.573785
$575$	−6.70197	−0.279491
$576$	1.00000	0.0416667
$577$	33.1087	1.37833	0.689167	−	0.724603i	$-0.257977\pi$
$577$	33.1087	1.37833	0.689167	+	0.724603i	$0.257977\pi$
$578$	1.00000	0.0415945
$579$	2.30143	0.0956442
$580$	−7.22959	−0.300192
$581$	−8.86295	−0.367697
$582$	11.1924	0.463941
$583$	5.22770	0.216509
$584$	7.75863	0.321055
$585$	5.00296	0.206847
$586$	−27.1598	−1.12196
$587$	−32.5888	−1.34508	−0.672542	−	0.740059i	$-0.734797\pi$
$587$	−32.5888	−1.34508	−0.672542	+	0.740059i	$0.734797\pi$
$588$	5.70742	0.235370
$589$	−7.65547	−0.315438
$590$	3.97677	0.163721
$591$	−20.9107	−0.860149
$592$	0.988751	0.0406374
$593$	−37.6319	−1.54536	−0.772679	−	0.634797i	$-0.781084\pi$
$593$	−37.6319	−1.54536	−0.772679	+	0.634797i	$0.781084\pi$
$594$	−3.07009	−0.125967
$595$	4.52126	0.185353
$596$	3.21387	0.131645
$597$	25.0623	1.02573
$598$	−0.779618	−0.0318810
$599$	−13.7672	−0.562513	−0.281256	−	0.959633i	$-0.590751\pi$
$599$	−13.7672	−0.562513	−0.281256	+	0.959633i	$0.590751\pi$
$600$	−10.8147	−0.441510
$601$	−7.04332	−0.287303	−0.143651	−	0.989628i	$-0.545884\pi$
$601$	−7.04332	−0.287303	−0.143651	+	0.989628i	$0.545884\pi$
$602$	−7.04312	−0.287056
$603$	−5.42097	−0.220759
$604$	−19.3475	−0.787237
$605$	−6.26159	−0.254570
$606$	1.92257	0.0780990
$607$	−17.7754	−0.721481	−0.360740	−	0.932666i	$-0.617476\pi$
$607$	−17.7754	−0.721481	−0.360740	+	0.932666i	$0.617476\pi$
$608$	−7.69872	−0.312224
$609$	2.06686	0.0837533
$610$	42.7784	1.73205
$611$	13.1924	0.533708
$612$	1.00000	0.0404226
$613$	−11.1371	−0.449823	−0.224911	−	0.974379i	$-0.572209\pi$
$613$	−11.1371	−0.449823	−0.224911	+	0.974379i	$0.572209\pi$
$614$	−22.6836	−0.915438
$615$	−48.0848	−1.93897
$616$	3.49043	0.140634
$617$	20.7290	0.834518	0.417259	−	0.908788i	$-0.362991\pi$
$617$	20.7290	0.834518	0.417259	+	0.908788i	$0.362991\pi$
$618$	6.72362	0.270464
$619$	−30.2186	−1.21459	−0.607294	−	0.794477i	$-0.707745\pi$
$619$	−30.2186	−1.21459	−0.607294	+	0.794477i	$0.707745\pi$
$620$	3.95443	0.158814
$621$	0.619707	0.0248680
$622$	10.0386	0.402509
$623$	−4.86079	−0.194744
$624$	−1.25804	−0.0503621
$625$	37.8849	1.51539
$626$	−21.6502	−0.865316
$627$	23.6358	0.943922
$628$	22.3783	0.892991
$629$	0.988751	0.0394241
$630$	4.52126	0.180131
$631$	−1.46915	−0.0584859	−0.0292429	−	0.999572i	$-0.509310\pi$
$631$	−1.46915	−0.0584859	−0.0292429	+	0.999572i	$0.509310\pi$
$632$	−3.35038	−0.133271
$633$	22.1859	0.881809
$634$	3.79216	0.150606
$635$	−23.6737	−0.939463
$636$	−1.70278	−0.0675197
$637$	−7.18019	−0.284489
$638$	−5.58128	−0.220965
$639$	8.89395	0.351839
$640$	3.97677	0.157196
$641$	4.81753	0.190281	0.0951405	−	0.995464i	$-0.469670\pi$
$641$	4.81753	0.190281	0.0951405	+	0.995464i	$0.469670\pi$
$642$	−6.85186	−0.270421
$643$	−28.7004	−1.13183	−0.565916	−	0.824463i	$-0.691477\pi$
$643$	−28.7004	−1.13183	−0.565916	+	0.824463i	$0.691477\pi$
$644$	−0.704554	−0.0277633
$645$	24.6359	0.970037
$646$	−7.69872	−0.302902
$647$	−4.01167	−0.157715	−0.0788575	−	0.996886i	$-0.525127\pi$
$647$	−4.01167	−0.157715	−0.0788575	+	0.996886i	$0.525127\pi$
$648$	1.00000	0.0392837
$649$	3.07009	0.120512
$650$	13.6054	0.533648
$651$	−1.13053	−0.0443089
$652$	−0.142808	−0.00559279
$653$	11.9377	0.467159	0.233579	−	0.972338i	$-0.424956\pi$
$653$	11.9377	0.467159	0.233579	+	0.972338i	$0.424956\pi$
$654$	−2.09467	−0.0819081
$655$	−18.8022	−0.734664
$656$	12.0914	0.472090
$657$	7.75863	0.302693
$658$	11.9222	0.464776
$659$	−14.8828	−0.579753	−0.289877	−	0.957064i	$-0.593614\pi$
$659$	−14.8828	−0.579753	−0.289877	+	0.957064i	$0.593614\pi$
$660$	−12.2091	−0.475237
$661$	14.5325	0.565251	0.282625	−	0.959230i	$-0.408795\pi$
$661$	14.5325	0.565251	0.282625	+	0.959230i	$0.408795\pi$
$662$	−8.61958	−0.335010
$663$	−1.25804	−0.0488584
$664$	−7.79561	−0.302528
$665$	−34.8079	−1.34979
$666$	0.988751	0.0383133
$667$	1.12660	0.0436221
$668$	17.1066	0.661873
$669$	3.62679	0.140220
$670$	−21.5580	−0.832857
$671$	33.0252	1.27492
$672$	−1.13692	−0.0438575
$673$	38.3450	1.47809	0.739045	−	0.673656i	$-0.235277\pi$
$673$	38.3450	1.47809	0.739045	+	0.673656i	$0.235277\pi$
$674$	26.6845	1.02785
$675$	−10.8147	−0.416259
$676$	−11.4173	−0.439128
$677$	−44.6853	−1.71739	−0.858697	−	0.512483i	$-0.828726\pi$
$677$	−44.6853	−1.71739	−0.858697	+	0.512483i	$0.828726\pi$
$678$	14.2454	0.547092
$679$	−12.7249	−0.488335
$680$	3.97677	0.152502
$681$	7.96375	0.305172
$682$	3.05284	0.116899
$683$	−2.74009	−0.104847	−0.0524234	−	0.998625i	$-0.516695\pi$
$683$	−2.74009	−0.104847	−0.0524234	+	0.998625i	$0.516695\pi$
$684$	−7.69872	−0.294368
$685$	−16.9978	−0.649451
$686$	−14.4473	−0.551599
$687$	−11.7865	−0.449683
$688$	−6.19494	−0.236180
$689$	2.14217	0.0816104
$690$	2.46444	0.0938194
$691$	25.3287	0.963549	0.481774	−	0.876295i	$-0.339992\pi$
$691$	25.3287	0.963549	0.481774	+	0.876295i	$0.339992\pi$
$692$	23.5568	0.895496
$693$	3.49043	0.132591
$694$	−0.431315	−0.0163725
$695$	51.3149	1.94648
$696$	1.81795	0.0689093
$697$	12.0914	0.457995
$698$	22.1596	0.838754
$699$	15.0215	0.568164
$700$	12.2954	0.464724
$701$	34.0332	1.28542	0.642708	−	0.766111i	$-0.277811\pi$
$701$	34.0332	1.28542	0.642708	+	0.766111i	$0.277811\pi$
$702$	−1.25804	−0.0474818
$703$	−7.61212	−0.287096
$704$	3.07009	0.115708
$705$	−41.7022	−1.57060
$706$	−12.7394	−0.479452
$707$	−2.18580	−0.0822053
$708$	−1.00000	−0.0375823
$709$	−18.8998	−0.709799	−0.354899	−	0.934905i	$-0.615485\pi$
$709$	−18.8998	−0.709799	−0.354899	+	0.934905i	$0.615485\pi$
$710$	35.3692	1.32738
$711$	−3.35038	−0.125649
$712$	−4.27542	−0.160228
$713$	−0.616225	−0.0230778
$714$	−1.13692	−0.0425480
$715$	15.3595	0.574414
$716$	9.80221	0.366326
$717$	−4.05363	−0.151385
$718$	−10.6586	−0.397776
$719$	−35.2523	−1.31469	−0.657345	−	0.753589i	$-0.728321\pi$
$719$	−35.2523	−1.31469	−0.657345	+	0.753589i	$0.728321\pi$
$720$	3.97677	0.148206
$721$	−7.64419	−0.284684
$722$	40.2703	1.49871
$723$	−16.4934	−0.613395
$724$	−24.6041	−0.914404
$725$	−19.6607	−0.730180
$726$	1.57454	0.0584367
$727$	13.4734	0.499701	0.249851	−	0.968284i	$-0.419619\pi$
$727$	13.4734	0.499701	0.249851	+	0.968284i	$0.419619\pi$
$728$	1.43029	0.0530100
$729$	1.00000	0.0370370
$730$	30.8543	1.14197
$731$	−6.19494	−0.229128
$732$	−10.7571	−0.397592
$733$	17.1698	0.634180	0.317090	−	0.948395i	$-0.397294\pi$
$733$	17.1698	0.634180	0.317090	+	0.948395i	$0.397294\pi$
$734$	19.1112	0.705408
$735$	22.6971	0.837197
$736$	−0.619707	−0.0228427
$737$	−16.6429	−0.613048
$738$	12.0914	0.445091
$739$	−6.64752	−0.244533	−0.122267	−	0.992497i	$-0.539016\pi$
$739$	−6.64752	−0.244533	−0.122267	+	0.992497i	$0.539016\pi$
$740$	3.93204	0.144545
$741$	9.68533	0.355799
$742$	1.93592	0.0710698
$743$	33.7608	1.23856	0.619281	−	0.785169i	$-0.287424\pi$
$743$	33.7608	1.23856	0.619281	+	0.785169i	$0.287424\pi$
$744$	−0.994381	−0.0364558
$745$	12.7808	0.468253
$746$	3.17300	0.116172
$747$	−7.79561	−0.285226
$748$	3.07009	0.112254
$749$	7.78998	0.284640
$750$	−23.1239	−0.844365
$751$	32.2701	1.17755	0.588777	−	0.808296i	$-0.299610\pi$
$751$	32.2701	1.17755	0.588777	+	0.808296i	$0.299610\pi$
$752$	10.4864	0.382401
$753$	−3.02939	−0.110397
$754$	−2.28706	−0.0832900
$755$	−76.9405	−2.80015
$756$	−1.13692	−0.0413492
$757$	−37.1035	−1.34855	−0.674275	−	0.738481i	$-0.735544\pi$
$757$	−37.1035	−1.34855	−0.674275	+	0.738481i	$0.735544\pi$
$758$	12.7053	0.461477
$759$	1.90256	0.0690584
$760$	−30.6161	−1.11056
$761$	−32.3348	−1.17214	−0.586068	−	0.810262i	$-0.699325\pi$
$761$	−32.3348	−1.17214	−0.586068	+	0.810262i	$0.699325\pi$
$762$	5.95300	0.215654
$763$	2.38146	0.0862147
$764$	12.0907	0.437428
$765$	3.97677	0.143781
$766$	33.6237	1.21487
$767$	1.25804	0.0454253
$768$	−1.00000	−0.0360844
$769$	14.3729	0.518300	0.259150	−	0.965837i	$-0.416558\pi$
$769$	14.3729	0.518300	0.259150	+	0.965837i	$0.416558\pi$
$770$	13.8807	0.500225
$771$	5.09152	0.183367
$772$	−2.30143	−0.0828303
$773$	24.4646	0.879932	0.439966	−	0.898014i	$-0.354990\pi$
$773$	24.4646	0.879932	0.439966	+	0.898014i	$0.354990\pi$
$774$	−6.19494	−0.222672
$775$	10.7540	0.386294
$776$	−11.1924	−0.401785
$777$	−1.12413	−0.0403278
$778$	−28.6873	−1.02849
$779$	−93.0884	−3.33524
$780$	−5.00296	−0.179135
$781$	27.3052	0.977058
$782$	−0.619707	−0.0221607
$783$	1.81795	0.0649683
$784$	−5.70742	−0.203837
$785$	88.9935	3.17631
$786$	4.72801	0.168643
$787$	−3.89407	−0.138809	−0.0694043	−	0.997589i	$-0.522110\pi$
$787$	−3.89407	−0.138809	−0.0694043	+	0.997589i	$0.522110\pi$
$788$	20.9107	0.744911
$789$	−0.115913	−0.00412661
$790$	−13.3237	−0.474036
$791$	−16.1958	−0.575857
$792$	3.07009	0.109091
$793$	13.5329	0.480566
$794$	7.15452	0.253904
$795$	−6.77158	−0.240163
$796$	−25.0623	−0.888310
$797$	3.43866	0.121803	0.0609017	−	0.998144i	$-0.480602\pi$
$797$	3.43866	0.121803	0.0609017	+	0.998144i	$0.480602\pi$
$798$	8.75279	0.309846
$799$	10.4864	0.370984
$800$	10.8147	0.382359
$801$	−4.27542	−0.151065
$802$	28.7514	1.01525
$803$	23.8197	0.840579
$804$	5.42097	0.191183
$805$	−2.80185	−0.0987524
$806$	1.25098	0.0440637
$807$	2.51075	0.0883824
$808$	−1.92257	−0.0676357
$809$	−1.48127	−0.0520786	−0.0260393	−	0.999661i	$-0.508290\pi$
$809$	−1.48127	−0.0520786	−0.0260393	+	0.999661i	$0.508290\pi$
$810$	3.97677	0.139730
$811$	8.88731	0.312076	0.156038	−	0.987751i	$-0.450128\pi$
$811$	8.88731	0.312076	0.156038	+	0.987751i	$0.450128\pi$
$812$	−2.06686	−0.0725325
$813$	24.6022	0.862836
$814$	3.03556	0.106396
$815$	−0.567914	−0.0198932
$816$	−1.00000	−0.0350070
$817$	47.6931	1.66857
$818$	−12.9056	−0.451233
$819$	1.43029	0.0499783
$820$	48.0848	1.67919
$821$	5.05498	0.176420	0.0882101	−	0.996102i	$-0.471885\pi$
$821$	5.05498	0.176420	0.0882101	+	0.996102i	$0.471885\pi$
$822$	4.27426	0.149082
$823$	−32.3500	−1.12765	−0.563825	−	0.825894i	$-0.690671\pi$
$823$	−32.3500	−1.12765	−0.563825	+	0.825894i	$0.690671\pi$
$824$	−6.72362	−0.234229
$825$	−33.2022	−1.15595
$826$	1.13692	0.0395583
$827$	−26.8236	−0.932747	−0.466374	−	0.884588i	$-0.654440\pi$
$827$	−26.8236	−0.932747	−0.466374	+	0.884588i	$0.654440\pi$
$828$	−0.619707	−0.0215363
$829$	24.9193	0.865484	0.432742	−	0.901518i	$-0.357546\pi$
$829$	24.9193	0.865484	0.432742	+	0.901518i	$0.357546\pi$
$830$	−31.0014	−1.07607
$831$	−12.0291	−0.417283
$832$	1.25804	0.0436148
$833$	−5.70742	−0.197751
$834$	−12.9036	−0.446817
$835$	68.0289	2.35424
$836$	−23.6358	−0.817461
$837$	−0.994381	−0.0343709
$838$	0.561324	0.0193906
$839$	−28.9776	−1.00042	−0.500209	−	0.865904i	$-0.666744\pi$
$839$	−28.9776	−1.00042	−0.500209	+	0.865904i	$0.666744\pi$
$840$	−4.52126	−0.155998
$841$	−25.6950	−0.886036
$842$	7.84671	0.270416
$843$	13.9052	0.478921
$844$	−22.1859	−0.763669
$845$	−45.4041	−1.56195
$846$	10.4864	0.360531
$847$	−1.79012	−0.0615092
$848$	1.70278	0.0584738
$849$	3.44887	0.118365
$850$	10.8147	0.370942
$851$	−0.612736	−0.0210043
$852$	−8.89395	−0.304702
$853$	12.1731	0.416800	0.208400	−	0.978044i	$-0.433174\pi$
$853$	12.1731	0.416800	0.208400	+	0.978044i	$0.433174\pi$
$854$	12.2299	0.418497
$855$	−30.6161	−1.04705
$856$	6.85186	0.234192
$857$	−24.2868	−0.829620	−0.414810	−	0.909908i	$-0.636152\pi$
$857$	−24.2868	−0.829620	−0.414810	+	0.909908i	$0.636152\pi$
$858$	−3.86231	−0.131857
$859$	−12.4375	−0.424362	−0.212181	−	0.977230i	$-0.568057\pi$
$859$	−12.4375	−0.424362	−0.212181	+	0.977230i	$0.568057\pi$
$860$	−24.6359	−0.840076
$861$	−13.7469	−0.468493
$862$	6.79498	0.231438
$863$	−50.1625	−1.70755	−0.853776	−	0.520640i	$-0.825693\pi$
$863$	−50.1625	−1.70755	−0.853776	+	0.520640i	$0.825693\pi$
$864$	−1.00000	−0.0340207
$865$	93.6802	3.18522
$866$	−20.1047	−0.683186
$867$	−1.00000	−0.0339618
$868$	1.13053	0.0383726
$869$	−10.2860	−0.348928
$870$	7.22959	0.245106
$871$	−6.81981	−0.231081
$872$	2.09467	0.0709345
$873$	−11.1924	−0.378807
$874$	4.77095	0.161380
$875$	26.2899	0.888761
$876$	−7.75863	−0.262140
$877$	−47.1513	−1.59219	−0.796093	−	0.605175i	$-0.793103\pi$
$877$	−47.1513	−1.59219	−0.796093	+	0.605175i	$0.793103\pi$
$878$	−19.1000	−0.644593
$879$	27.1598	0.916078
$880$	12.2091	0.411567
$881$	52.3604	1.76407	0.882034	−	0.471187i	$-0.156174\pi$
$881$	52.3604	1.76407	0.882034	+	0.471187i	$0.156174\pi$
$882$	−5.70742	−0.192179
$883$	−2.56333	−0.0862630	−0.0431315	−	0.999069i	$-0.513733\pi$
$883$	−2.56333	−0.0862630	−0.0431315	+	0.999069i	$0.513733\pi$
$884$	1.25804	0.0423126
$885$	−3.97677	−0.133678
$886$	1.06939	0.0359270
$887$	−7.81811	−0.262506	−0.131253	−	0.991349i	$-0.541900\pi$
$887$	−7.81811	−0.262506	−0.131253	+	0.991349i	$0.541900\pi$
$888$	−0.988751	−0.0331803
$889$	−6.76805	−0.226993
$890$	−17.0024	−0.569921
$891$	3.07009	0.102852
$892$	−3.62679	−0.121434
$893$	−80.7322	−2.70160
$894$	−3.21387	−0.107488
$895$	38.9812	1.30300
$896$	1.13692	0.0379817
$897$	0.779618	0.0260307
$898$	27.9046	0.931188
$899$	−1.80774	−0.0602915
$900$	10.8147	0.360491
$901$	1.70278	0.0567279
$902$	37.1217	1.23602
$903$	7.04312	0.234380
$904$	−14.2454	−0.473795
$905$	−97.8450	−3.25248
$906$	19.3475	0.642776
$907$	−46.4656	−1.54287	−0.771433	−	0.636310i	$-0.780460\pi$
$907$	−46.4656	−1.54287	−0.771433	+	0.636310i	$0.780460\pi$
$908$	−7.96375	−0.264286
$909$	−1.92257	−0.0637675
$910$	5.68794	0.188553
$911$	−25.6149	−0.848660	−0.424330	−	0.905508i	$-0.639490\pi$
$911$	−25.6149	−0.848660	−0.424330	+	0.905508i	$0.639490\pi$
$912$	7.69872	0.254930
$913$	−23.9332	−0.792074
$914$	−35.4635	−1.17303
$915$	−42.7784	−1.41421
$916$	11.7865	0.389437
$917$	−5.37535	−0.177510
$918$	−1.00000	−0.0330049
$919$	−8.03734	−0.265127	−0.132564	−	0.991174i	$-0.542321\pi$
$919$	−8.03734	−0.265127	−0.132564	+	0.991174i	$0.542321\pi$
$920$	−2.46444	−0.0812500
$921$	22.6836	0.747452
$922$	17.2178	0.567038
$923$	11.1890	0.368290
$924$	−3.49043	−0.114827
$925$	10.6931	0.351586
$926$	16.3314	0.536683
$927$	−6.72362	−0.220833
$928$	−1.81795	−0.0596772
$929$	50.8953	1.66982	0.834910	−	0.550386i	$-0.185519\pi$
$929$	50.8953	1.66982	0.834910	+	0.550386i	$0.185519\pi$
$930$	−3.95443	−0.129671
$931$	43.9399	1.44007
$932$	−15.0215	−0.492044
$933$	−10.0386	−0.328647
$934$	−31.4290	−1.02839
$935$	12.2091	0.399279
$936$	1.25804	0.0411204
$937$	6.47597	0.211561	0.105780	−	0.994390i	$-0.466266\pi$
$937$	6.47597	0.211561	0.105780	+	0.994390i	$0.466266\pi$
$938$	−6.16318	−0.201235
$939$	21.6502	0.706528
$940$	41.7022	1.36018
$941$	−45.9334	−1.49739	−0.748693	−	0.662916i	$-0.769318\pi$
$941$	−45.9334	−1.49739	−0.748693	+	0.662916i	$0.769318\pi$
$942$	−22.3783	−0.729124
$943$	−7.49313	−0.244010
$944$	1.00000	0.0325472
$945$	−4.52126	−0.147076
$946$	−19.0190	−0.618362
$947$	−10.7594	−0.349633	−0.174816	−	0.984601i	$-0.555933\pi$
$947$	−10.7594	−0.349633	−0.174816	+	0.984601i	$0.555933\pi$
$948$	3.35038	0.108815
$949$	9.76070	0.316846
$950$	−83.2597	−2.70130
$951$	−3.79216	−0.122969
$952$	1.13692	0.0368476
$953$	−35.4256	−1.14755	−0.573774	−	0.819014i	$-0.694521\pi$
$953$	−35.4256	−1.14755	−0.573774	+	0.819014i	$0.694521\pi$
$954$	1.70278	0.0551296
$955$	48.0822	1.55590
$956$	4.05363	0.131104
$957$	5.58128	0.180417
$958$	36.8928	1.19195
$959$	−4.85947	−0.156920
$960$	−3.97677	−0.128350
$961$	−30.0112	−0.968103
$962$	1.24389	0.0401047
$963$	6.85186	0.220798
$964$	16.4934	0.531216
$965$	−9.15227	−0.294622
$966$	0.704554	0.0226687
$967$	22.4829	0.723000	0.361500	−	0.932372i	$-0.382265\pi$
$967$	22.4829	0.723000	0.361500	+	0.932372i	$0.382265\pi$
$968$	−1.57454	−0.0506076
$969$	7.69872	0.247319
$970$	−44.5098	−1.42912
$971$	−38.9249	−1.24916	−0.624580	−	0.780961i	$-0.714730\pi$
$971$	−38.9249	−1.24916	−0.624580	+	0.780961i	$0.714730\pi$
$972$	−1.00000	−0.0320750
$973$	14.6704	0.470310
$974$	22.8713	0.732845
$975$	−13.6054	−0.435722
$976$	10.7571	0.344325
$977$	−20.9642	−0.670705	−0.335353	−	0.942093i	$-0.608855\pi$
$977$	−20.9642	−0.670705	−0.335353	+	0.942093i	$0.608855\pi$
$978$	0.142808	0.00456649
$979$	−13.1259	−0.419507
$980$	−22.6971	−0.725034
$981$	2.09467	0.0668777
$982$	21.1099	0.673643
$983$	18.7624	0.598426	0.299213	−	0.954186i	$-0.403276\pi$
$983$	18.7624	0.598426	0.299213	+	0.954186i	$0.403276\pi$
$984$	−12.0914	−0.385460
$985$	83.1570	2.64960
$986$	−1.81795	−0.0578954
$987$	−11.9222	−0.379488
$988$	−9.68533	−0.308131
$989$	3.83905	0.122075
$990$	12.2091	0.388029
$991$	3.86458	0.122763	0.0613813	−	0.998114i	$-0.480449\pi$
$991$	3.86458	0.122763	0.0613813	+	0.998114i	$0.480449\pi$
$992$	0.994381	0.0315716
$993$	8.61958	0.273534
$994$	10.1117	0.320722
$995$	−99.6672	−3.15966
$996$	7.79561	0.247013
$997$	−19.7787	−0.626397	−0.313198	−	0.949688i	$-0.601400\pi$
$997$	−19.7787	−0.626397	−0.313198	+	0.949688i	$0.601400\pi$
$998$	30.6232	0.969360
$999$	−0.988751	−0.0312827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bc.1.13	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bc.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97677 q^{5} -1.00000 q^{6} +1.13692 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97677 q^{5} -1.00000 q^{6} +1.13692 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.97677 q^{10} +3.07009 q^{11} -1.00000 q^{12} +1.25804 q^{13} +1.13692 q^{14} -3.97677 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -7.69872 q^{19} +3.97677 q^{20} -1.13692 q^{21} +3.07009 q^{22} -0.619707 q^{23} -1.00000 q^{24} +10.8147 q^{25} +1.25804 q^{26} -1.00000 q^{27} +1.13692 q^{28} -1.81795 q^{29} -3.97677 q^{30} +0.994381 q^{31} +1.00000 q^{32} -3.07009 q^{33} +1.00000 q^{34} +4.52126 q^{35} +1.00000 q^{36} +0.988751 q^{37} -7.69872 q^{38} -1.25804 q^{39} +3.97677 q^{40} +12.0914 q^{41} -1.13692 q^{42} -6.19494 q^{43} +3.07009 q^{44} +3.97677 q^{45} -0.619707 q^{46} +10.4864 q^{47} -1.00000 q^{48} -5.70742 q^{49} +10.8147 q^{50} -1.00000 q^{51} +1.25804 q^{52} +1.70278 q^{53} -1.00000 q^{54} +12.2091 q^{55} +1.13692 q^{56} +7.69872 q^{57} -1.81795 q^{58} +1.00000 q^{59} -3.97677 q^{60} +10.7571 q^{61} +0.994381 q^{62} +1.13692 q^{63} +1.00000 q^{64} +5.00296 q^{65} -3.07009 q^{66} -5.42097 q^{67} +1.00000 q^{68} +0.619707 q^{69} +4.52126 q^{70} +8.89395 q^{71} +1.00000 q^{72} +7.75863 q^{73} +0.988751 q^{74} -10.8147 q^{75} -7.69872 q^{76} +3.49043 q^{77} -1.25804 q^{78} -3.35038 q^{79} +3.97677 q^{80} +1.00000 q^{81} +12.0914 q^{82} -7.79561 q^{83} -1.13692 q^{84} +3.97677 q^{85} -6.19494 q^{86} +1.81795 q^{87} +3.07009 q^{88} -4.27542 q^{89} +3.97677 q^{90} +1.43029 q^{91} -0.619707 q^{92} -0.994381 q^{93} +10.4864 q^{94} -30.6161 q^{95} -1.00000 q^{96} -11.1924 q^{97} -5.70742 q^{98} +3.07009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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