LMFDB - Embedded newform 6018.2.a.bc.1.5

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			1.5
Root			$-1.69357$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69357 q^{5} -1.00000 q^{6} +3.25998 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69357 q^{5} -1.00000 q^{6} +3.25998 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.69357 q^{10} +5.34841 q^{11} -1.00000 q^{12} -0.872188 q^{13} +3.25998 q^{14} +1.69357 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -8.19698 q^{19} -1.69357 q^{20} -3.25998 q^{21} +5.34841 q^{22} +6.81251 q^{23} -1.00000 q^{24} -2.13182 q^{25} -0.872188 q^{26} -1.00000 q^{27} +3.25998 q^{28} +7.06454 q^{29} +1.69357 q^{30} +8.08471 q^{31} +1.00000 q^{32} -5.34841 q^{33} +1.00000 q^{34} -5.52099 q^{35} +1.00000 q^{36} +5.23414 q^{37} -8.19698 q^{38} +0.872188 q^{39} -1.69357 q^{40} -11.8798 q^{41} -3.25998 q^{42} +8.64072 q^{43} +5.34841 q^{44} -1.69357 q^{45} +6.81251 q^{46} +2.11402 q^{47} -1.00000 q^{48} +3.62744 q^{49} -2.13182 q^{50} -1.00000 q^{51} -0.872188 q^{52} -9.00406 q^{53} -1.00000 q^{54} -9.05791 q^{55} +3.25998 q^{56} +8.19698 q^{57} +7.06454 q^{58} +1.00000 q^{59} +1.69357 q^{60} +13.5963 q^{61} +8.08471 q^{62} +3.25998 q^{63} +1.00000 q^{64} +1.47711 q^{65} -5.34841 q^{66} -8.42336 q^{67} +1.00000 q^{68} -6.81251 q^{69} -5.52099 q^{70} +4.49841 q^{71} +1.00000 q^{72} -8.42134 q^{73} +5.23414 q^{74} +2.13182 q^{75} -8.19698 q^{76} +17.4357 q^{77} +0.872188 q^{78} -4.21233 q^{79} -1.69357 q^{80} +1.00000 q^{81} -11.8798 q^{82} +11.0390 q^{83} -3.25998 q^{84} -1.69357 q^{85} +8.64072 q^{86} -7.06454 q^{87} +5.34841 q^{88} -10.7178 q^{89} -1.69357 q^{90} -2.84331 q^{91} +6.81251 q^{92} -8.08471 q^{93} +2.11402 q^{94} +13.8822 q^{95} -1.00000 q^{96} -0.447712 q^{97} +3.62744 q^{98} +5.34841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.69357	−0.757387	−0.378694	−	0.925522i	$-0.623627\pi$
$5$	−1.69357	−0.757387	−0.378694	+	0.925522i	$0.623627\pi$
$6$	−1.00000	−0.408248
$7$	3.25998	1.23216	0.616078	−	0.787685i	$-0.288721\pi$
$7$	3.25998	1.23216	0.616078	+	0.787685i	$0.288721\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.69357	−0.535553
$11$	5.34841	1.61261	0.806304	−	0.591502i	$-0.201465\pi$
$11$	5.34841	1.61261	0.806304	+	0.591502i	$0.201465\pi$
$12$	−1.00000	−0.288675
$13$	−0.872188	−0.241902	−0.120951	−	0.992659i	$-0.538594\pi$
$13$	−0.872188	−0.241902	−0.120951	+	0.992659i	$0.538594\pi$
$14$	3.25998	0.871265
$15$	1.69357	0.437278
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−8.19698	−1.88052	−0.940258	−	0.340461i	$-0.889417\pi$
$19$	−8.19698	−1.88052	−0.940258	+	0.340461i	$0.889417\pi$
$20$	−1.69357	−0.378694
$21$	−3.25998	−0.711385
$22$	5.34841	1.14029
$23$	6.81251	1.42051	0.710253	−	0.703947i	$-0.248581\pi$
$23$	6.81251	1.42051	0.710253	+	0.703947i	$0.248581\pi$
$24$	−1.00000	−0.204124
$25$	−2.13182	−0.426365
$26$	−0.872188	−0.171050
$27$	−1.00000	−0.192450
$28$	3.25998	0.616078
$29$	7.06454	1.31185	0.655926	−	0.754825i	$-0.272278\pi$
$29$	7.06454	1.31185	0.655926	+	0.754825i	$0.272278\pi$
$30$	1.69357	0.309202
$31$	8.08471	1.45206	0.726028	−	0.687665i	$-0.241364\pi$
$31$	8.08471	1.45206	0.726028	+	0.687665i	$0.241364\pi$
$32$	1.00000	0.176777
$33$	−5.34841	−0.931039
$34$	1.00000	0.171499
$35$	−5.52099	−0.933218
$36$	1.00000	0.166667
$37$	5.23414	0.860487	0.430244	−	0.902713i	$-0.358428\pi$
$37$	5.23414	0.860487	0.430244	+	0.902713i	$0.358428\pi$
$38$	−8.19698	−1.32973
$39$	0.872188	0.139662
$40$	−1.69357	−0.267777
$41$	−11.8798	−1.85532	−0.927659	−	0.373429i	$-0.878182\pi$
$41$	−11.8798	−1.85532	−0.927659	+	0.373429i	$0.878182\pi$
$42$	−3.25998	−0.503025
$43$	8.64072	1.31770	0.658848	−	0.752276i	$-0.271044\pi$
$43$	8.64072	1.31770	0.658848	+	0.752276i	$0.271044\pi$
$44$	5.34841	0.806304
$45$	−1.69357	−0.252462
$46$	6.81251	1.00445
$47$	2.11402	0.308361	0.154180	−	0.988043i	$-0.450726\pi$
$47$	2.11402	0.308361	0.154180	+	0.988043i	$0.450726\pi$
$48$	−1.00000	−0.144338
$49$	3.62744	0.518206
$50$	−2.13182	−0.301486
$51$	−1.00000	−0.140028
$52$	−0.872188	−0.120951
$53$	−9.00406	−1.23680	−0.618402	−	0.785862i	$-0.712219\pi$
$53$	−9.00406	−1.23680	−0.618402	+	0.785862i	$0.712219\pi$
$54$	−1.00000	−0.136083
$55$	−9.05791	−1.22137
$56$	3.25998	0.435633
$57$	8.19698	1.08572
$58$	7.06454	0.927620
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.69357	0.218639
$61$	13.5963	1.74083	0.870415	−	0.492319i	$-0.163851\pi$
$61$	13.5963	1.74083	0.870415	+	0.492319i	$0.163851\pi$
$62$	8.08471	1.02676
$63$	3.25998	0.410718
$64$	1.00000	0.125000
$65$	1.47711	0.183213
$66$	−5.34841	−0.658344
$67$	−8.42336	−1.02908	−0.514539	−	0.857467i	$-0.672037\pi$
$67$	−8.42336	−1.02908	−0.514539	+	0.857467i	$0.672037\pi$
$68$	1.00000	0.121268
$69$	−6.81251	−0.820129
$70$	−5.52099	−0.659885
$71$	4.49841	0.533863	0.266932	−	0.963715i	$-0.413990\pi$
$71$	4.49841	0.533863	0.266932	+	0.963715i	$0.413990\pi$
$72$	1.00000	0.117851
$73$	−8.42134	−0.985643	−0.492822	−	0.870130i	$-0.664034\pi$
$73$	−8.42134	−0.985643	−0.492822	+	0.870130i	$0.664034\pi$
$74$	5.23414	0.608456
$75$	2.13182	0.246162
$76$	−8.19698	−0.940258
$77$	17.4357	1.98698
$78$	0.872188	0.0987559
$79$	−4.21233	−0.473924	−0.236962	−	0.971519i	$-0.576152\pi$
$79$	−4.21233	−0.473924	−0.236962	+	0.971519i	$0.576152\pi$
$80$	−1.69357	−0.189347
$81$	1.00000	0.111111
$82$	−11.8798	−1.31191
$83$	11.0390	1.21169	0.605843	−	0.795584i	$-0.292836\pi$
$83$	11.0390	1.21169	0.605843	+	0.795584i	$0.292836\pi$
$84$	−3.25998	−0.355693
$85$	−1.69357	−0.183693
$86$	8.64072	0.931752
$87$	−7.06454	−0.757398
$88$	5.34841	0.570143
$89$	−10.7178	−1.13608	−0.568041	−	0.823000i	$-0.692299\pi$
$89$	−10.7178	−1.13608	−0.568041	+	0.823000i	$0.692299\pi$
$90$	−1.69357	−0.178518
$91$	−2.84331	−0.298060
$92$	6.81251	0.710253
$93$	−8.08471	−0.838345
$94$	2.11402	0.218044
$95$	13.8822	1.42428
$96$	−1.00000	−0.102062
$97$	−0.447712	−0.0454583	−0.0227291	−	0.999742i	$-0.507236\pi$
$97$	−0.447712	−0.0454583	−0.0227291	+	0.999742i	$0.507236\pi$
$98$	3.62744	0.366427
$99$	5.34841	0.537536
$100$	−2.13182	−0.213182
$101$	−15.2331	−1.51575	−0.757877	−	0.652397i	$-0.773763\pi$
$101$	−15.2331	−1.51575	−0.757877	+	0.652397i	$0.773763\pi$
$102$	−1.00000	−0.0990148
$103$	−13.1296	−1.29370	−0.646848	−	0.762619i	$-0.723913\pi$
$103$	−13.1296	−1.29370	−0.646848	+	0.762619i	$0.723913\pi$
$104$	−0.872188	−0.0855251
$105$	5.52099	0.538794
$106$	−9.00406	−0.874552
$107$	4.99176	0.482572	0.241286	−	0.970454i	$-0.422431\pi$
$107$	4.99176	0.482572	0.241286	+	0.970454i	$0.422431\pi$
$108$	−1.00000	−0.0962250
$109$	−3.85965	−0.369687	−0.184844	−	0.982768i	$-0.559178\pi$
$109$	−3.85965	−0.369687	−0.184844	+	0.982768i	$0.559178\pi$
$110$	−9.05791	−0.863637
$111$	−5.23414	−0.496803
$112$	3.25998	0.308039
$113$	2.85200	0.268293	0.134147	−	0.990961i	$-0.457171\pi$
$113$	2.85200	0.268293	0.134147	+	0.990961i	$0.457171\pi$
$114$	8.19698	0.767718
$115$	−11.5374	−1.07587
$116$	7.06454	0.655926
$117$	−0.872188	−0.0806338
$118$	1.00000	0.0920575
$119$	3.25998	0.298842
$120$	1.69357	0.154601
$121$	17.6055	1.60050
$122$	13.5963	1.23095
$123$	11.8798	1.07117
$124$	8.08471	0.726028
$125$	12.0782	1.08031
$126$	3.25998	0.290422
$127$	13.0162	1.15500	0.577502	−	0.816389i	$-0.304027\pi$
$127$	13.0162	1.15500	0.577502	+	0.816389i	$0.304027\pi$
$128$	1.00000	0.0883883
$129$	−8.64072	−0.760773
$130$	1.47711	0.129551
$131$	5.81999	0.508495	0.254247	−	0.967139i	$-0.418172\pi$
$131$	5.81999	0.508495	0.254247	+	0.967139i	$0.418172\pi$
$132$	−5.34841	−0.465520
$133$	−26.7220	−2.31709
$134$	−8.42336	−0.727668
$135$	1.69357	0.145759
$136$	1.00000	0.0857493
$137$	−6.73352	−0.575283	−0.287642	−	0.957738i	$-0.592871\pi$
$137$	−6.73352	−0.575283	−0.287642	+	0.957738i	$0.592871\pi$
$138$	−6.81251	−0.579919
$139$	11.5918	0.983207	0.491603	−	0.870819i	$-0.336411\pi$
$139$	11.5918	0.983207	0.491603	+	0.870819i	$0.336411\pi$
$140$	−5.52099	−0.466609
$141$	−2.11402	−0.178032
$142$	4.49841	0.377498
$143$	−4.66482	−0.390092
$144$	1.00000	0.0833333
$145$	−11.9643	−0.993580
$146$	−8.42134	−0.696955
$147$	−3.62744	−0.299187
$148$	5.23414	0.430244
$149$	14.2808	1.16993	0.584964	−	0.811059i	$-0.301108\pi$
$149$	14.2808	1.16993	0.584964	+	0.811059i	$0.301108\pi$
$150$	2.13182	0.174063
$151$	10.6867	0.869669	0.434835	−	0.900510i	$-0.356807\pi$
$151$	10.6867	0.869669	0.434835	+	0.900510i	$0.356807\pi$
$152$	−8.19698	−0.664863
$153$	1.00000	0.0808452
$154$	17.4357	1.40501
$155$	−13.6920	−1.09977
$156$	0.872188	0.0698309
$157$	19.3407	1.54356	0.771780	−	0.635890i	$-0.219367\pi$
$157$	19.3407	1.54356	0.771780	+	0.635890i	$0.219367\pi$
$158$	−4.21233	−0.335115
$159$	9.00406	0.714069
$160$	−1.69357	−0.133888
$161$	22.2086	1.75028
$162$	1.00000	0.0785674
$163$	11.5555	0.905095	0.452547	−	0.891740i	$-0.350515\pi$
$163$	11.5555	0.905095	0.452547	+	0.891740i	$0.350515\pi$
$164$	−11.8798	−0.927659
$165$	9.05791	0.705157
$166$	11.0390	0.856791
$167$	0.0924743	0.00715587	0.00357794	−	0.999994i	$-0.498861\pi$
$167$	0.0924743	0.00715587	0.00357794	+	0.999994i	$0.498861\pi$
$168$	−3.25998	−0.251513
$169$	−12.2393	−0.941484
$170$	−1.69357	−0.129891
$171$	−8.19698	−0.626839
$172$	8.64072	0.658848
$173$	−19.6366	−1.49295	−0.746473	−	0.665416i	$-0.768254\pi$
$173$	−19.6366	−1.49295	−0.746473	+	0.665416i	$0.768254\pi$
$174$	−7.06454	−0.535561
$175$	−6.94970	−0.525348
$176$	5.34841	0.403152
$177$	−1.00000	−0.0751646
$178$	−10.7178	−0.803332
$179$	0.451919	0.0337780	0.0168890	−	0.999857i	$-0.494624\pi$
$179$	0.451919	0.0337780	0.0168890	+	0.999857i	$0.494624\pi$
$180$	−1.69357	−0.126231
$181$	11.0413	0.820690	0.410345	−	0.911930i	$-0.365408\pi$
$181$	11.0413	0.820690	0.410345	+	0.911930i	$0.365408\pi$
$182$	−2.84331	−0.210760
$183$	−13.5963	−1.00507
$184$	6.81251	0.502225
$185$	−8.86438	−0.651722
$186$	−8.08471	−0.592800
$187$	5.34841	0.391115
$188$	2.11402	0.154180
$189$	−3.25998	−0.237128
$190$	13.8822	1.00712
$191$	10.8266	0.783386	0.391693	−	0.920096i	$-0.371890\pi$
$191$	10.8266	0.783386	0.391693	+	0.920096i	$0.371890\pi$
$192$	−1.00000	−0.0721688
$193$	−0.00971922	−0.000699605 0	−0.000349802	−	1.00000i	$-0.500111\pi$
$193$	−0.00971922	−0.000699605 0	−0.000349802		1.00000i	$0.500111\pi$
$194$	−0.447712	−0.0321439
$195$	−1.47711	−0.105778
$196$	3.62744	0.259103
$197$	−23.4333	−1.66955	−0.834776	−	0.550590i	$-0.814403\pi$
$197$	−23.4333	−1.66955	−0.834776	+	0.550590i	$0.814403\pi$
$198$	5.34841	0.380095
$199$	13.7943	0.977851	0.488926	−	0.872325i	$-0.337389\pi$
$199$	13.7943	0.977851	0.488926	+	0.872325i	$0.337389\pi$
$200$	−2.13182	−0.150743
$201$	8.42336	0.594138
$202$	−15.2331	−1.07180
$203$	23.0302	1.61641
$204$	−1.00000	−0.0700140
$205$	20.1193	1.40519
$206$	−13.1296	−0.914781
$207$	6.81251	0.473502
$208$	−0.872188	−0.0604754
$209$	−43.8409	−3.03254
$210$	5.52099	0.380985
$211$	12.7991	0.881124	0.440562	−	0.897722i	$-0.354779\pi$
$211$	12.7991	0.881124	0.440562	+	0.897722i	$0.354779\pi$
$212$	−9.00406	−0.618402
$213$	−4.49841	−0.308226
$214$	4.99176	0.341230
$215$	−14.6336	−0.998006
$216$	−1.00000	−0.0680414
$217$	26.3560	1.78916
$218$	−3.85965	−0.261408
$219$	8.42134	0.569061
$220$	−9.05791	−0.610684
$221$	−0.872188	−0.0586697
$222$	−5.23414	−0.351292
$223$	4.15974	0.278557	0.139278	−	0.990253i	$-0.455522\pi$
$223$	4.15974	0.278557	0.139278	+	0.990253i	$0.455522\pi$
$224$	3.25998	0.217816
$225$	−2.13182	−0.142122
$226$	2.85200	0.189712
$227$	−8.45801	−0.561378	−0.280689	−	0.959799i	$-0.590563\pi$
$227$	−8.45801	−0.561378	−0.280689	+	0.959799i	$0.590563\pi$
$228$	8.19698	0.542858
$229$	18.5289	1.22442	0.612212	−	0.790694i	$-0.290280\pi$
$229$	18.5289	1.22442	0.612212	+	0.790694i	$0.290280\pi$
$230$	−11.5374	−0.760757
$231$	−17.4357	−1.14718
$232$	7.06454	0.463810
$233$	−0.749085	−0.0490742	−0.0245371	−	0.999699i	$-0.507811\pi$
$233$	−0.749085	−0.0490742	−0.0245371	+	0.999699i	$0.507811\pi$
$234$	−0.872188	−0.0570167
$235$	−3.58023	−0.233548
$236$	1.00000	0.0650945
$237$	4.21233	0.273620
$238$	3.25998	0.211313
$239$	−15.0757	−0.975167	−0.487584	−	0.873076i	$-0.662122\pi$
$239$	−15.0757	−0.975167	−0.487584	+	0.873076i	$0.662122\pi$
$240$	1.69357	0.109319
$241$	−23.0265	−1.48327	−0.741633	−	0.670805i	$-0.765949\pi$
$241$	−23.0265	−1.48327	−0.741633	+	0.670805i	$0.765949\pi$
$242$	17.6055	1.13173
$243$	−1.00000	−0.0641500
$244$	13.5963	0.870415
$245$	−6.14333	−0.392483
$246$	11.8798	0.757430
$247$	7.14931	0.454900
$248$	8.08471	0.513379
$249$	−11.0390	−0.699567
$250$	12.0782	0.763895
$251$	1.14905	0.0725273	0.0362637	−	0.999342i	$-0.488454\pi$
$251$	1.14905	0.0725273	0.0362637	+	0.999342i	$0.488454\pi$
$252$	3.25998	0.205359
$253$	36.4361	2.29072
$254$	13.0162	0.816712
$255$	1.69357	0.106055
$256$	1.00000	0.0625000
$257$	−5.01500	−0.312827	−0.156414	−	0.987692i	$-0.549993\pi$
$257$	−5.01500	−0.312827	−0.156414	+	0.987692i	$0.549993\pi$
$258$	−8.64072	−0.537947
$259$	17.0632	1.06025
$260$	1.47711	0.0916065
$261$	7.06454	0.437284
$262$	5.81999	0.359560
$263$	27.6970	1.70787	0.853935	−	0.520380i	$-0.174210\pi$
$263$	27.6970	1.70787	0.853935	+	0.520380i	$0.174210\pi$
$264$	−5.34841	−0.329172
$265$	15.2490	0.936739
$266$	−26.7220	−1.63843
$267$	10.7178	0.655918
$268$	−8.42336	−0.514539
$269$	23.4650	1.43069	0.715343	−	0.698774i	$-0.246270\pi$
$269$	23.4650	1.43069	0.715343	+	0.698774i	$0.246270\pi$
$270$	1.69357	0.103067
$271$	12.9670	0.787689	0.393844	−	0.919177i	$-0.371145\pi$
$271$	12.9670	0.787689	0.393844	+	0.919177i	$0.371145\pi$
$272$	1.00000	0.0606339
$273$	2.84331	0.172085
$274$	−6.73352	−0.406787
$275$	−11.4019	−0.687559
$276$	−6.81251	−0.410065
$277$	6.44021	0.386955	0.193477	−	0.981105i	$-0.438023\pi$
$277$	6.44021	0.386955	0.193477	+	0.981105i	$0.438023\pi$
$278$	11.5918	0.695232
$279$	8.08471	0.484019
$280$	−5.52099	−0.329943
$281$	2.49667	0.148939	0.0744696	−	0.997223i	$-0.476274\pi$
$281$	2.49667	0.148939	0.0744696	+	0.997223i	$0.476274\pi$
$282$	−2.11402	−0.125888
$283$	5.33765	0.317290	0.158645	−	0.987336i	$-0.449287\pi$
$283$	5.33765	0.317290	0.158645	+	0.987336i	$0.449287\pi$
$284$	4.49841	0.266932
$285$	−13.8822	−0.822308
$286$	−4.66482	−0.275837
$287$	−38.7280	−2.28604
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−11.9643	−0.702567
$291$	0.447712	0.0262454
$292$	−8.42134	−0.492822
$293$	32.0747	1.87382	0.936912	−	0.349566i	$-0.113671\pi$
$293$	32.0747	1.87382	0.936912	+	0.349566i	$0.113671\pi$
$294$	−3.62744	−0.211557
$295$	−1.69357	−0.0986034
$296$	5.23414	0.304228
$297$	−5.34841	−0.310346
$298$	14.2808	0.827265
$299$	−5.94179	−0.343622
$300$	2.13182	0.123081
$301$	28.1685	1.62361
$302$	10.6867	0.614949
$303$	15.2331	0.875121
$304$	−8.19698	−0.470129
$305$	−23.0263	−1.31848
$306$	1.00000	0.0571662
$307$	−4.21824	−0.240748	−0.120374	−	0.992729i	$-0.538409\pi$
$307$	−4.21824	−0.240748	−0.120374	+	0.992729i	$0.538409\pi$
$308$	17.4357	0.993491
$309$	13.1296	0.746915
$310$	−13.6920	−0.777654
$311$	29.6866	1.68337	0.841686	−	0.539967i	$-0.181563\pi$
$311$	29.6866	1.68337	0.841686	+	0.539967i	$0.181563\pi$
$312$	0.872188	0.0493779
$313$	2.46778	0.139487	0.0697437	−	0.997565i	$-0.477782\pi$
$313$	2.46778	0.139487	0.0697437	+	0.997565i	$0.477782\pi$
$314$	19.3407	1.09146
$315$	−5.52099	−0.311073
$316$	−4.21233	−0.236962
$317$	−17.5247	−0.984286	−0.492143	−	0.870514i	$-0.663786\pi$
$317$	−17.5247	−0.984286	−0.492143	+	0.870514i	$0.663786\pi$
$318$	9.00406	0.504923
$319$	37.7841	2.11550
$320$	−1.69357	−0.0946734
$321$	−4.99176	−0.278613
$322$	22.2086	1.23764
$323$	−8.19698	−0.456092
$324$	1.00000	0.0555556
$325$	1.85935	0.103138
$326$	11.5555	0.639999
$327$	3.85965	0.213439
$328$	−11.8798	−0.655954
$329$	6.89164	0.379948
$330$	9.05791	0.498621
$331$	−2.76351	−0.151897	−0.0759483	−	0.997112i	$-0.524198\pi$
$331$	−2.76351	−0.151897	−0.0759483	+	0.997112i	$0.524198\pi$
$332$	11.0390	0.605843
$333$	5.23414	0.286829
$334$	0.0924743	0.00505997
$335$	14.2655	0.779410
$336$	−3.25998	−0.177846
$337$	−17.1206	−0.932620	−0.466310	−	0.884621i	$-0.654417\pi$
$337$	−17.1206	−0.932620	−0.466310	+	0.884621i	$0.654417\pi$
$338$	−12.2393	−0.665729
$339$	−2.85200	−0.154899
$340$	−1.69357	−0.0918467
$341$	43.2404	2.34160
$342$	−8.19698	−0.443242
$343$	−10.9944	−0.593644
$344$	8.64072	0.465876
$345$	11.5374	0.621155
$346$	−19.6366	−1.05567
$347$	14.8909	0.799385	0.399693	−	0.916649i	$-0.369117\pi$
$347$	14.8909	0.799385	0.399693	+	0.916649i	$0.369117\pi$
$348$	−7.06454	−0.378699
$349$	7.01012	0.375243	0.187622	−	0.982241i	$-0.439922\pi$
$349$	7.01012	0.375243	0.187622	+	0.982241i	$0.439922\pi$
$350$	−6.94970	−0.371477
$351$	0.872188	0.0465540
$352$	5.34841	0.285071
$353$	−9.62932	−0.512517	−0.256259	−	0.966608i	$-0.582490\pi$
$353$	−9.62932	−0.512517	−0.256259	+	0.966608i	$0.582490\pi$
$354$	−1.00000	−0.0531494
$355$	−7.61837	−0.404341
$356$	−10.7178	−0.568041
$357$	−3.25998	−0.172536
$358$	0.451919	0.0238847
$359$	23.3764	1.23376	0.616879	−	0.787058i	$-0.288397\pi$
$359$	23.3764	1.23376	0.616879	+	0.787058i	$0.288397\pi$
$360$	−1.69357	−0.0892589
$361$	48.1905	2.53634
$362$	11.0413	0.580316
$363$	−17.6055	−0.924051
$364$	−2.84331	−0.149030
$365$	14.2621	0.746513
$366$	−13.5963	−0.710691
$367$	24.6623	1.28736	0.643679	−	0.765295i	$-0.277407\pi$
$367$	24.6623	1.28736	0.643679	+	0.765295i	$0.277407\pi$
$368$	6.81251	0.355126
$369$	−11.8798	−0.618439
$370$	−8.86438	−0.460837
$371$	−29.3530	−1.52393
$372$	−8.08471	−0.419173
$373$	22.3356	1.15649	0.578246	−	0.815863i	$-0.303737\pi$
$373$	22.3356	1.15649	0.578246	+	0.815863i	$0.303737\pi$
$374$	5.34841	0.276560
$375$	−12.0782	−0.623717
$376$	2.11402	0.109022
$377$	−6.16161	−0.317339
$378$	−3.25998	−0.167675
$379$	5.75391	0.295559	0.147779	−	0.989020i	$-0.452787\pi$
$379$	5.75391	0.295559	0.147779	+	0.989020i	$0.452787\pi$
$380$	13.8822	0.712140
$381$	−13.0162	−0.666842
$382$	10.8266	0.553938
$383$	−26.5189	−1.35505	−0.677527	−	0.735498i	$-0.736948\pi$
$383$	−26.5189	−1.35505	−0.677527	+	0.735498i	$0.736948\pi$
$384$	−1.00000	−0.0510310
$385$	−29.5286	−1.50491
$386$	−0.00971922	−0.000494695 0
$387$	8.64072	0.439232
$388$	−0.447712	−0.0227291
$389$	−10.4405	−0.529354	−0.264677	−	0.964337i	$-0.585265\pi$
$389$	−10.4405	−0.529354	−0.264677	+	0.964337i	$0.585265\pi$
$390$	−1.47711	−0.0747964
$391$	6.81251	0.344523
$392$	3.62744	0.183214
$393$	−5.81999	−0.293580
$394$	−23.4333	−1.18055
$395$	7.13387	0.358944
$396$	5.34841	0.268768
$397$	20.0503	1.00630	0.503148	−	0.864200i	$-0.332175\pi$
$397$	20.0503	1.00630	0.503148	+	0.864200i	$0.332175\pi$
$398$	13.7943	0.691445
$399$	26.7220	1.33777
$400$	−2.13182	−0.106591
$401$	27.4728	1.37193	0.685963	−	0.727636i	$-0.259381\pi$
$401$	27.4728	1.37193	0.685963	+	0.727636i	$0.259381\pi$
$402$	8.42336	0.420119
$403$	−7.05139	−0.351255
$404$	−15.2331	−0.757877
$405$	−1.69357	−0.0841541
$406$	23.0302	1.14297
$407$	27.9943	1.38763
$408$	−1.00000	−0.0495074
$409$	−26.2901	−1.29996	−0.649981	−	0.759950i	$-0.725223\pi$
$409$	−26.2901	−1.29996	−0.649981	+	0.759950i	$0.725223\pi$
$410$	20.1193	0.993622
$411$	6.73352	0.332140
$412$	−13.1296	−0.646848
$413$	3.25998	0.160413
$414$	6.81251	0.334816
$415$	−18.6953	−0.917715
$416$	−0.872188	−0.0427625
$417$	−11.5918	−0.567655
$418$	−43.8409	−2.14433
$419$	−21.7764	−1.06385	−0.531923	−	0.846793i	$-0.678530\pi$
$419$	−21.7764	−1.06385	−0.531923	+	0.846793i	$0.678530\pi$
$420$	5.52099	0.269397
$421$	−22.5632	−1.09966	−0.549832	−	0.835276i	$-0.685308\pi$
$421$	−22.5632	−1.09966	−0.549832	+	0.835276i	$0.685308\pi$
$422$	12.7991	0.623049
$423$	2.11402	0.102787
$424$	−9.00406	−0.437276
$425$	−2.13182	−0.103409
$426$	−4.49841	−0.217949
$427$	44.3237	2.14497
$428$	4.99176	0.241286
$429$	4.66482	0.225220
$430$	−14.6336	−0.705697
$431$	−20.8086	−1.00231	−0.501157	−	0.865356i	$-0.667092\pi$
$431$	−20.8086	−1.00231	−0.501157	+	0.865356i	$0.667092\pi$
$432$	−1.00000	−0.0481125
$433$	−10.9005	−0.523842	−0.261921	−	0.965089i	$-0.584356\pi$
$433$	−10.9005	−0.523842	−0.261921	+	0.965089i	$0.584356\pi$
$434$	26.3560	1.26513
$435$	11.9643	0.573644
$436$	−3.85965	−0.184844
$437$	−55.8420	−2.67129
$438$	8.42134	0.402387
$439$	8.77870	0.418984	0.209492	−	0.977810i	$-0.432819\pi$
$439$	8.77870	0.418984	0.209492	+	0.977810i	$0.432819\pi$
$440$	−9.05791	−0.431819
$441$	3.62744	0.172735
$442$	−0.872188	−0.0414858
$443$	−36.9950	−1.75769	−0.878843	−	0.477111i	$-0.841684\pi$
$443$	−36.9950	−1.75769	−0.878843	+	0.477111i	$0.841684\pi$
$444$	−5.23414	−0.248401
$445$	18.1513	0.860454
$446$	4.15974	0.196969
$447$	−14.2808	−0.675459
$448$	3.25998	0.154019
$449$	−35.1087	−1.65688	−0.828442	−	0.560075i	$-0.810772\pi$
$449$	−35.1087	−1.65688	−0.828442	+	0.560075i	$0.810772\pi$
$450$	−2.13182	−0.100495
$451$	−63.5382	−2.99190
$452$	2.85200	0.134147
$453$	−10.6867	−0.502104
$454$	−8.45801	−0.396954
$455$	4.81535	0.225747
$456$	8.19698	0.383859
$457$	21.7100	1.01555	0.507776	−	0.861489i	$-0.330468\pi$
$457$	21.7100	1.01555	0.507776	+	0.861489i	$0.330468\pi$
$458$	18.5289	0.865798
$459$	−1.00000	−0.0466760
$460$	−11.5374	−0.537936
$461$	4.25372	0.198115	0.0990577	−	0.995082i	$-0.468417\pi$
$461$	4.25372	0.198115	0.0990577	+	0.995082i	$0.468417\pi$
$462$	−17.4357	−0.811182
$463$	−31.3122	−1.45520	−0.727602	−	0.686000i	$-0.759365\pi$
$463$	−31.3122	−1.45520	−0.727602	+	0.686000i	$0.759365\pi$
$464$	7.06454	0.327963
$465$	13.6920	0.634952
$466$	−0.749085	−0.0347007
$467$	−17.8953	−0.828096	−0.414048	−	0.910255i	$-0.635885\pi$
$467$	−17.8953	−0.828096	−0.414048	+	0.910255i	$0.635885\pi$
$468$	−0.872188	−0.0403169
$469$	−27.4600	−1.26798
$470$	−3.58023	−0.165144
$471$	−19.3407	−0.891175
$472$	1.00000	0.0460287
$473$	46.2141	2.12493
$474$	4.21233	0.193479
$475$	17.4745	0.801786
$476$	3.25998	0.149421
$477$	−9.00406	−0.412268
$478$	−15.0757	−0.689547
$479$	−13.5206	−0.617772	−0.308886	−	0.951099i	$-0.599956\pi$
$479$	−13.5206	−0.617772	−0.308886	+	0.951099i	$0.599956\pi$
$480$	1.69357	0.0773005
$481$	−4.56515	−0.208153
$482$	−23.0265	−1.04883
$483$	−22.2086	−1.01053
$484$	17.6055	0.800251
$485$	0.758232	0.0344295
$486$	−1.00000	−0.0453609
$487$	28.7702	1.30370	0.651851	−	0.758347i	$-0.273993\pi$
$487$	28.7702	1.30370	0.651851	+	0.758347i	$0.273993\pi$
$488$	13.5963	0.615476
$489$	−11.5555	−0.522557
$490$	−6.14333	−0.277527
$491$	−38.9666	−1.75854	−0.879269	−	0.476326i	$-0.841968\pi$
$491$	−38.9666	−1.75854	−0.879269	+	0.476326i	$0.841968\pi$
$492$	11.8798	0.535584
$493$	7.06454	0.318171
$494$	7.14931	0.321663
$495$	−9.05791	−0.407123
$496$	8.08471	0.363014
$497$	14.6647	0.657802
$498$	−11.0390	−0.494669
$499$	−8.87761	−0.397416	−0.198708	−	0.980059i	$-0.563675\pi$
$499$	−8.87761	−0.397416	−0.198708	+	0.980059i	$0.563675\pi$
$500$	12.0782	0.540155
$501$	−0.0924743	−0.00413145
$502$	1.14905	0.0512846
$503$	−19.2085	−0.856463	−0.428232	−	0.903669i	$-0.640863\pi$
$503$	−19.2085	−0.856463	−0.428232	+	0.903669i	$0.640863\pi$
$504$	3.25998	0.145211
$505$	25.7984	1.14801
$506$	36.4361	1.61978
$507$	12.2393	0.543566
$508$	13.0162	0.577502
$509$	19.3842	0.859190	0.429595	−	0.903022i	$-0.358656\pi$
$509$	19.3842	0.859190	0.429595	+	0.903022i	$0.358656\pi$
$510$	1.69357	0.0749925
$511$	−27.4534	−1.21447
$512$	1.00000	0.0441942
$513$	8.19698	0.361906
$514$	−5.01500	−0.221202
$515$	22.2358	0.979828
$516$	−8.64072	−0.380386
$517$	11.3066	0.497265
$518$	17.0632	0.749713
$519$	19.6366	0.861953
$520$	1.47711	0.0647756
$521$	−36.4590	−1.59730	−0.798650	−	0.601796i	$-0.794452\pi$
$521$	−36.4590	−1.59730	−0.798650	+	0.601796i	$0.794452\pi$
$522$	7.06454	0.309207
$523$	0.852629	0.0372829	0.0186414	−	0.999826i	$-0.494066\pi$
$523$	0.852629	0.0372829	0.0186414	+	0.999826i	$0.494066\pi$
$524$	5.81999	0.254247
$525$	6.94970	0.303310
$526$	27.6970	1.20765
$527$	8.08471	0.352175
$528$	−5.34841	−0.232760
$529$	23.4102	1.01784
$530$	15.2490	0.662374
$531$	1.00000	0.0433963
$532$	−26.7220	−1.15854
$533$	10.3614	0.448804
$534$	10.7178	0.463804
$535$	−8.45389	−0.365493
$536$	−8.42336	−0.363834
$537$	−0.451919	−0.0195017
$538$	23.4650	1.01165
$539$	19.4011	0.835663
$540$	1.69357	0.0728796
$541$	−1.19156	−0.0512290	−0.0256145	−	0.999672i	$-0.508154\pi$
$541$	−1.19156	−0.0512290	−0.0256145	+	0.999672i	$0.508154\pi$
$542$	12.9670	0.556980
$543$	−11.0413	−0.473826
$544$	1.00000	0.0428746
$545$	6.53658	0.279996
$546$	2.84331	0.121683
$547$	20.7868	0.888779	0.444390	−	0.895834i	$-0.353421\pi$
$547$	20.7868	0.888779	0.444390	+	0.895834i	$0.353421\pi$
$548$	−6.73352	−0.287642
$549$	13.5963	0.580277
$550$	−11.4019	−0.486178
$551$	−57.9079	−2.46696
$552$	−6.81251	−0.289960
$553$	−13.7321	−0.583948
$554$	6.44021	0.273618
$555$	8.86438	0.376272
$556$	11.5918	0.491603
$557$	−31.3490	−1.32830	−0.664150	−	0.747599i	$-0.731206\pi$
$557$	−31.3490	−1.32830	−0.664150	+	0.747599i	$0.731206\pi$
$558$	8.08471	0.342253
$559$	−7.53633	−0.318753
$560$	−5.52099	−0.233305
$561$	−5.34841	−0.225810
$562$	2.49667	0.105316
$563$	16.1945	0.682517	0.341258	−	0.939970i	$-0.389147\pi$
$563$	16.1945	0.682517	0.341258	+	0.939970i	$0.389147\pi$
$564$	−2.11402	−0.0890161
$565$	−4.83005	−0.203202
$566$	5.33765	0.224358
$567$	3.25998	0.136906
$568$	4.49841	0.188749
$569$	−42.3281	−1.77448	−0.887242	−	0.461303i	$-0.847382\pi$
$569$	−42.3281	−1.77448	−0.887242	+	0.461303i	$0.847382\pi$
$570$	−13.8822	−0.581460
$571$	27.8340	1.16481	0.582407	−	0.812897i	$-0.302111\pi$
$571$	27.8340	1.16481	0.582407	+	0.812897i	$0.302111\pi$
$572$	−4.66482	−0.195046
$573$	−10.8266	−0.452288
$574$	−38.7280	−1.61647
$575$	−14.5231	−0.605654
$576$	1.00000	0.0416667
$577$	−15.6901	−0.653187	−0.326593	−	0.945165i	$-0.605901\pi$
$577$	−15.6901	−0.653187	−0.326593	+	0.945165i	$0.605901\pi$
$578$	1.00000	0.0415945
$579$	0.00971922	0.000403917 0
$580$	−11.9643	−0.496790
$581$	35.9868	1.49298
$582$	0.447712	0.0185583
$583$	−48.1575	−1.99448
$584$	−8.42134	−0.348478
$585$	1.47711	0.0610710
$586$	32.0747	1.32499
$587$	22.6597	0.935264	0.467632	−	0.883923i	$-0.345107\pi$
$587$	22.6597	0.935264	0.467632	+	0.883923i	$0.345107\pi$
$588$	−3.62744	−0.149593
$589$	−66.2702	−2.73062
$590$	−1.69357	−0.0697231
$591$	23.4333	0.963916
$592$	5.23414	0.215122
$593$	−35.3406	−1.45126	−0.725631	−	0.688084i	$-0.758452\pi$
$593$	−35.3406	−1.45126	−0.725631	+	0.688084i	$0.758452\pi$
$594$	−5.34841	−0.219448
$595$	−5.52099	−0.226339
$596$	14.2808	0.584964
$597$	−13.7943	−0.564563
$598$	−5.94179	−0.242978
$599$	−45.3261	−1.85198	−0.925988	−	0.377554i	$-0.876765\pi$
$599$	−45.3261	−1.85198	−0.925988	+	0.377554i	$0.876765\pi$
$600$	2.13182	0.0870314
$601$	−10.3727	−0.423110	−0.211555	−	0.977366i	$-0.567853\pi$
$601$	−10.3727	−0.423110	−0.211555	+	0.977366i	$0.567853\pi$
$602$	28.1685	1.14806
$603$	−8.42336	−0.343026
$604$	10.6867	0.434835
$605$	−29.8162	−1.21220
$606$	15.2331	0.618804
$607$	45.5614	1.84928	0.924640	−	0.380843i	$-0.124366\pi$
$607$	45.5614	1.84928	0.924640	+	0.380843i	$0.124366\pi$
$608$	−8.19698	−0.332432
$609$	−23.0302	−0.933232
$610$	−23.0263	−0.932308
$611$	−1.84382	−0.0745929
$612$	1.00000	0.0404226
$613$	−9.65543	−0.389979	−0.194989	−	0.980805i	$-0.562467\pi$
$613$	−9.65543	−0.389979	−0.194989	+	0.980805i	$0.562467\pi$
$614$	−4.21824	−0.170234
$615$	−20.1193	−0.811289
$616$	17.4357	0.702504
$617$	−2.90063	−0.116775	−0.0583875	−	0.998294i	$-0.518596\pi$
$617$	−2.90063	−0.116775	−0.0583875	+	0.998294i	$0.518596\pi$
$618$	13.1296	0.528149
$619$	19.5455	0.785598	0.392799	−	0.919624i	$-0.371507\pi$
$619$	19.5455	0.785598	0.392799	+	0.919624i	$0.371507\pi$
$620$	−13.6920	−0.549884
$621$	−6.81251	−0.273376
$622$	29.6866	1.19032
$623$	−34.9397	−1.39983
$624$	0.872188	0.0349155
$625$	−9.79620	−0.391848
$626$	2.46778	0.0986325
$627$	43.8409	1.75084
$628$	19.3407	0.771780
$629$	5.23414	0.208699
$630$	−5.52099	−0.219962
$631$	−29.3601	−1.16881	−0.584403	−	0.811463i	$-0.698671\pi$
$631$	−29.3601	−1.16881	−0.584403	+	0.811463i	$0.698671\pi$
$632$	−4.21233	−0.167557
$633$	−12.7991	−0.508717
$634$	−17.5247	−0.695995
$635$	−22.0439	−0.874786
$636$	9.00406	0.357034
$637$	−3.16381	−0.125355
$638$	37.7841	1.49589
$639$	4.49841	0.177954
$640$	−1.69357	−0.0669442
$641$	3.41394	0.134843	0.0674214	−	0.997725i	$-0.478523\pi$
$641$	3.41394	0.134843	0.0674214	+	0.997725i	$0.478523\pi$
$642$	−4.99176	−0.197009
$643$	−10.3725	−0.409053	−0.204526	−	0.978861i	$-0.565565\pi$
$643$	−10.3725	−0.409053	−0.204526	+	0.978861i	$0.565565\pi$
$644$	22.2086	0.875142
$645$	14.6336	0.576199
$646$	−8.19698	−0.322506
$647$	12.7423	0.500950	0.250475	−	0.968123i	$-0.419413\pi$
$647$	12.7423	0.500950	0.250475	+	0.968123i	$0.419413\pi$
$648$	1.00000	0.0392837
$649$	5.34841	0.209944
$650$	1.85935	0.0729298
$651$	−26.3560	−1.03297
$652$	11.5555	0.452547
$653$	12.7096	0.497365	0.248683	−	0.968585i	$-0.420002\pi$
$653$	12.7096	0.497365	0.248683	+	0.968585i	$0.420002\pi$
$654$	3.85965	0.150924
$655$	−9.85655	−0.385127
$656$	−11.8798	−0.463829
$657$	−8.42134	−0.328548
$658$	6.89164	0.268664
$659$	18.2871	0.712363	0.356182	−	0.934417i	$-0.384078\pi$
$659$	18.2871	0.712363	0.356182	+	0.934417i	$0.384078\pi$
$660$	9.05791	0.352579
$661$	32.4373	1.26166	0.630832	−	0.775919i	$-0.282714\pi$
$661$	32.4373	1.26166	0.630832	+	0.775919i	$0.282714\pi$
$662$	−2.76351	−0.107407
$663$	0.872188	0.0338730
$664$	11.0390	0.428395
$665$	45.2555	1.75493
$666$	5.23414	0.202819
$667$	48.1272	1.86349
$668$	0.0924743	0.00357794
$669$	−4.15974	−0.160825
$670$	14.2655	0.551126
$671$	72.7187	2.80727
$672$	−3.25998	−0.125756
$673$	−31.9094	−1.23002	−0.615008	−	0.788521i	$-0.710847\pi$
$673$	−31.9094	−1.23002	−0.615008	+	0.788521i	$0.710847\pi$
$674$	−17.1206	−0.659462
$675$	2.13182	0.0820540
$676$	−12.2393	−0.470742
$677$	6.97296	0.267993	0.133996	−	0.990982i	$-0.457219\pi$
$677$	6.97296	0.267993	0.133996	+	0.990982i	$0.457219\pi$
$678$	−2.85200	−0.109530
$679$	−1.45953	−0.0560117
$680$	−1.69357	−0.0649454
$681$	8.45801	0.324111
$682$	43.2404	1.65576
$683$	28.6314	1.09555	0.547775	−	0.836626i	$-0.315475\pi$
$683$	28.6314	1.09555	0.547775	+	0.836626i	$0.315475\pi$
$684$	−8.19698	−0.313419
$685$	11.4037	0.435712
$686$	−10.9944	−0.419770
$687$	−18.5289	−0.706921
$688$	8.64072	0.329424
$689$	7.85324	0.299185
$690$	11.5374	0.439223
$691$	−25.8516	−0.983440	−0.491720	−	0.870753i	$-0.663632\pi$
$691$	−25.8516	−0.983440	−0.491720	+	0.870753i	$0.663632\pi$
$692$	−19.6366	−0.746473
$693$	17.4357	0.662328
$694$	14.8909	0.565251
$695$	−19.6316	−0.744668
$696$	−7.06454	−0.267781
$697$	−11.8798	−0.449981
$698$	7.01012	0.265337
$699$	0.749085	0.0283330
$700$	−6.94970	−0.262674
$701$	−19.1129	−0.721886	−0.360943	−	0.932588i	$-0.617545\pi$
$701$	−19.1129	−0.721886	−0.360943	+	0.932588i	$0.617545\pi$
$702$	0.872188	0.0329186
$703$	−42.9042	−1.61816
$704$	5.34841	0.201576
$705$	3.58023	0.134839
$706$	−9.62932	−0.362404
$707$	−49.6597	−1.86764
$708$	−1.00000	−0.0375823
$709$	41.3007	1.55108	0.775540	−	0.631299i	$-0.217478\pi$
$709$	41.3007	1.55108	0.775540	+	0.631299i	$0.217478\pi$
$710$	−7.61837	−0.285912
$711$	−4.21233	−0.157975
$712$	−10.7178	−0.401666
$713$	55.0771	2.06265
$714$	−3.25998	−0.122002
$715$	7.90020	0.295451
$716$	0.451919	0.0168890
$717$	15.0757	0.563013
$718$	23.3764	0.872399
$719$	27.5366	1.02694	0.513470	−	0.858107i	$-0.328360\pi$
$719$	27.5366	1.02694	0.513470	+	0.858107i	$0.328360\pi$
$720$	−1.69357	−0.0631156
$721$	−42.8021	−1.59403
$722$	48.1905	1.79347
$723$	23.0265	0.856365
$724$	11.0413	0.410345
$725$	−15.0604	−0.559328
$726$	−17.6055	−0.653402
$727$	−23.3004	−0.864165	−0.432083	−	0.901834i	$-0.642221\pi$
$727$	−23.3004	−0.864165	−0.432083	+	0.901834i	$0.642221\pi$
$728$	−2.84331	−0.105380
$729$	1.00000	0.0370370
$730$	14.2621	0.527865
$731$	8.64072	0.319588
$732$	−13.5963	−0.502534
$733$	15.6247	0.577111	0.288555	−	0.957463i	$-0.406825\pi$
$733$	15.6247	0.577111	0.288555	+	0.957463i	$0.406825\pi$
$734$	24.6623	0.910300
$735$	6.14333	0.226600
$736$	6.81251	0.251112
$737$	−45.0516	−1.65950
$738$	−11.8798	−0.437303
$739$	−42.7669	−1.57320	−0.786602	−	0.617460i	$-0.788162\pi$
$739$	−42.7669	−1.57320	−0.786602	+	0.617460i	$0.788162\pi$
$740$	−8.86438	−0.325861
$741$	−7.14931	−0.262637
$742$	−29.3530	−1.07758
$743$	−19.0678	−0.699531	−0.349766	−	0.936837i	$-0.613739\pi$
$743$	−19.0678	−0.699531	−0.349766	+	0.936837i	$0.613739\pi$
$744$	−8.08471	−0.296400
$745$	−24.1855	−0.886089
$746$	22.3356	0.817763
$747$	11.0390	0.403895
$748$	5.34841	0.195557
$749$	16.2730	0.594603
$750$	−12.0782	−0.441035
$751$	−23.1655	−0.845321	−0.422661	−	0.906288i	$-0.638904\pi$
$751$	−23.1655	−0.845321	−0.422661	+	0.906288i	$0.638904\pi$
$752$	2.11402	0.0770902
$753$	−1.14905	−0.0418737
$754$	−6.16161	−0.224393
$755$	−18.0986	−0.658676
$756$	−3.25998	−0.118564
$757$	1.95453	0.0710384	0.0355192	−	0.999369i	$-0.488692\pi$
$757$	1.95453	0.0710384	0.0355192	+	0.999369i	$0.488692\pi$
$758$	5.75391	0.208992
$759$	−36.4361	−1.32255
$760$	13.8822	0.503559
$761$	6.30047	0.228392	0.114196	−	0.993458i	$-0.463571\pi$
$761$	6.30047	0.228392	0.114196	+	0.993458i	$0.463571\pi$
$762$	−13.0162	−0.471529
$763$	−12.5824	−0.455512
$764$	10.8266	0.391693
$765$	−1.69357	−0.0612311
$766$	−26.5189	−0.958168
$767$	−0.872188	−0.0314929
$768$	−1.00000	−0.0360844
$769$	−36.2604	−1.30758	−0.653791	−	0.756675i	$-0.726823\pi$
$769$	−36.2604	−1.30758	−0.653791	+	0.756675i	$0.726823\pi$
$770$	−29.5286	−1.06414
$771$	5.01500	0.180611
$772$	−0.00971922	−0.000349802 0
$773$	−15.6856	−0.564171	−0.282086	−	0.959389i	$-0.591026\pi$
$773$	−15.6856	−0.564171	−0.282086	+	0.959389i	$0.591026\pi$
$774$	8.64072	0.310584
$775$	−17.2352	−0.619106
$776$	−0.447712	−0.0160719
$777$	−17.0632	−0.612138
$778$	−10.4405	−0.374310
$779$	97.3788	3.48896
$780$	−1.47711	−0.0528891
$781$	24.0594	0.860912
$782$	6.81251	0.243615
$783$	−7.06454	−0.252466
$784$	3.62744	0.129552
$785$	−32.7549	−1.16907
$786$	−5.81999	−0.207592
$787$	−40.0891	−1.42902	−0.714511	−	0.699624i	$-0.753351\pi$
$787$	−40.0891	−1.42902	−0.714511	+	0.699624i	$0.753351\pi$
$788$	−23.4333	−0.834776
$789$	−27.6970	−0.986039
$790$	7.13387	0.253812
$791$	9.29744	0.330579
$792$	5.34841	0.190048
$793$	−11.8585	−0.421109
$794$	20.0503	0.711559
$795$	−15.2490	−0.540826
$796$	13.7943	0.488926
$797$	0.717534	0.0254164	0.0127082	−	0.999919i	$-0.495955\pi$
$797$	0.717534	0.0254164	0.0127082	+	0.999919i	$0.495955\pi$
$798$	26.7220	0.945947
$799$	2.11402	0.0747885
$800$	−2.13182	−0.0753714
$801$	−10.7178	−0.378694
$802$	27.4728	0.970098
$803$	−45.0408	−1.58946
$804$	8.42336	0.297069
$805$	−37.6118	−1.32564
$806$	−7.05139	−0.248375
$807$	−23.4650	−0.826007
$808$	−15.2331	−0.535900
$809$	−29.9676	−1.05361	−0.526803	−	0.849988i	$-0.676609\pi$
$809$	−29.9676	−1.05361	−0.526803	+	0.849988i	$0.676609\pi$
$810$	−1.69357	−0.0595059
$811$	−43.0911	−1.51313	−0.756566	−	0.653918i	$-0.773124\pi$
$811$	−43.0911	−1.51313	−0.756566	+	0.653918i	$0.773124\pi$
$812$	23.0302	0.808203
$813$	−12.9670	−0.454772
$814$	27.9943	0.981201
$815$	−19.5700	−0.685507
$816$	−1.00000	−0.0350070
$817$	−70.8278	−2.47795
$818$	−26.2901	−0.919212
$819$	−2.84331	−0.0993534
$820$	20.1193	0.702597
$821$	−0.422522	−0.0147461	−0.00737305	−	0.999973i	$-0.502347\pi$
$821$	−0.422522	−0.0147461	−0.00737305	+	0.999973i	$0.502347\pi$
$822$	6.73352	0.234859
$823$	−10.6003	−0.369504	−0.184752	−	0.982785i	$-0.559148\pi$
$823$	−10.6003	−0.369504	−0.184752	+	0.982785i	$0.559148\pi$
$824$	−13.1296	−0.457390
$825$	11.4019	0.396962
$826$	3.25998	0.113429
$827$	−47.2538	−1.64317	−0.821587	−	0.570083i	$-0.806911\pi$
$827$	−47.2538	−1.64317	−0.821587	+	0.570083i	$0.806911\pi$
$828$	6.81251	0.236751
$829$	−0.450112	−0.0156330	−0.00781652	−	0.999969i	$-0.502488\pi$
$829$	−0.450112	−0.0156330	−0.00781652	+	0.999969i	$0.502488\pi$
$830$	−18.6953	−0.648922
$831$	−6.44021	−0.223409
$832$	−0.872188	−0.0302377
$833$	3.62744	0.125684
$834$	−11.5918	−0.401393
$835$	−0.156612	−0.00541977
$836$	−43.8409	−1.51627
$837$	−8.08471	−0.279448
$838$	−21.7764	−0.752253
$839$	−4.77877	−0.164981	−0.0824907	−	0.996592i	$-0.526287\pi$
$839$	−4.77877	−0.164981	−0.0824907	+	0.996592i	$0.526287\pi$
$840$	5.52099	0.190492
$841$	20.9077	0.720956
$842$	−22.5632	−0.777579
$843$	−2.49667	−0.0859900
$844$	12.7991	0.440562
$845$	20.7281	0.713068
$846$	2.11402	0.0726813
$847$	57.3936	1.97207
$848$	−9.00406	−0.309201
$849$	−5.33765	−0.183188
$850$	−2.13182	−0.0731210
$851$	35.6576	1.22233
$852$	−4.49841	−0.154113
$853$	53.1197	1.81878	0.909392	−	0.415939i	$-0.136547\pi$
$853$	53.1197	1.81878	0.909392	+	0.415939i	$0.136547\pi$
$854$	44.3237	1.51672
$855$	13.8822	0.474760
$856$	4.99176	0.170615
$857$	−30.3500	−1.03674	−0.518369	−	0.855157i	$-0.673461\pi$
$857$	−30.3500	−1.03674	−0.518369	+	0.855157i	$0.673461\pi$
$858$	4.66482	0.159254
$859$	−17.4264	−0.594582	−0.297291	−	0.954787i	$-0.596083\pi$
$859$	−17.4264	−0.594582	−0.297291	+	0.954787i	$0.596083\pi$
$860$	−14.6336	−0.499003
$861$	38.7280	1.31985
$862$	−20.8086	−0.708743
$863$	−14.9876	−0.510184	−0.255092	−	0.966917i	$-0.582106\pi$
$863$	−14.9876	−0.510184	−0.255092	+	0.966917i	$0.582106\pi$
$864$	−1.00000	−0.0340207
$865$	33.2560	1.13074
$866$	−10.9005	−0.370413
$867$	−1.00000	−0.0339618
$868$	26.3560	0.894579
$869$	−22.5293	−0.764253
$870$	11.9643	0.405627
$871$	7.34676	0.248935
$872$	−3.85965	−0.130704
$873$	−0.447712	−0.0151528
$874$	−55.8420	−1.88888
$875$	39.3748	1.33111
$876$	8.42134	0.284531
$877$	18.1154	0.611713	0.305856	−	0.952078i	$-0.401057\pi$
$877$	18.1154	0.611713	0.305856	+	0.952078i	$0.401057\pi$
$878$	8.77870	0.296267
$879$	−32.0747	−1.08185
$880$	−9.05791	−0.305342
$881$	14.0626	0.473782	0.236891	−	0.971536i	$-0.423872\pi$
$881$	14.0626	0.473782	0.236891	+	0.971536i	$0.423872\pi$
$882$	3.62744	0.122142
$883$	40.5859	1.36582	0.682912	−	0.730501i	$-0.260713\pi$
$883$	40.5859	1.36582	0.682912	+	0.730501i	$0.260713\pi$
$884$	−0.872188	−0.0293349
$885$	1.69357	0.0569287
$886$	−36.9950	−1.24287
$887$	−12.5256	−0.420567	−0.210283	−	0.977640i	$-0.567439\pi$
$887$	−12.5256	−0.420567	−0.210283	+	0.977640i	$0.567439\pi$
$888$	−5.23414	−0.175646
$889$	42.4326	1.42314
$890$	18.1513	0.608433
$891$	5.34841	0.179179
$892$	4.15974	0.139278
$893$	−17.3285	−0.579878
$894$	−14.2808	−0.477621
$895$	−0.765356	−0.0255830
$896$	3.25998	0.108908
$897$	5.94179	0.198391
$898$	−35.1087	−1.17159
$899$	57.1147	1.90488
$900$	−2.13182	−0.0710608
$901$	−9.00406	−0.299969
$902$	−63.5382	−2.11559
$903$	−28.1685	−0.937390
$904$	2.85200	0.0948560
$905$	−18.6991	−0.621580
$906$	−10.6867	−0.355041
$907$	10.3762	0.344535	0.172268	−	0.985050i	$-0.444891\pi$
$907$	10.3762	0.344535	0.172268	+	0.985050i	$0.444891\pi$
$908$	−8.45801	−0.280689
$909$	−15.2331	−0.505251
$910$	4.81535	0.159627
$911$	15.4998	0.513532	0.256766	−	0.966474i	$-0.417343\pi$
$911$	15.4998	0.513532	0.256766	+	0.966474i	$0.417343\pi$
$912$	8.19698	0.271429
$913$	59.0410	1.95397
$914$	21.7100	0.718103
$915$	23.0263	0.761226
$916$	18.5289	0.612212
$917$	18.9730	0.626545
$918$	−1.00000	−0.0330049
$919$	−30.8058	−1.01619	−0.508095	−	0.861301i	$-0.669650\pi$
$919$	−30.8058	−1.01619	−0.508095	+	0.861301i	$0.669650\pi$
$920$	−11.5374	−0.380378
$921$	4.21824	0.138996
$922$	4.25372	0.140089
$923$	−3.92346	−0.129142
$924$	−17.4357	−0.573592
$925$	−11.1583	−0.366882
$926$	−31.3122	−1.02898
$927$	−13.1296	−0.431232
$928$	7.06454	0.231905
$929$	−46.7723	−1.53455	−0.767275	−	0.641318i	$-0.778388\pi$
$929$	−46.7723	−1.53455	−0.767275	+	0.641318i	$0.778388\pi$
$930$	13.6920	0.448979
$931$	−29.7341	−0.974496
$932$	−0.749085	−0.0245371
$933$	−29.6866	−0.971895
$934$	−17.8953	−0.585553
$935$	−9.05791	−0.296225
$936$	−0.872188	−0.0285084
$937$	20.7990	0.679474	0.339737	−	0.940520i	$-0.389662\pi$
$937$	20.7990	0.679474	0.339737	+	0.940520i	$0.389662\pi$
$938$	−27.4600	−0.896599
$939$	−2.46778	−0.0805331
$940$	−3.58023	−0.116774
$941$	15.5612	0.507281	0.253641	−	0.967299i	$-0.418372\pi$
$941$	15.5612	0.507281	0.253641	+	0.967299i	$0.418372\pi$
$942$	−19.3407	−0.630156
$943$	−80.9314	−2.63549
$944$	1.00000	0.0325472
$945$	5.52099	0.179598
$946$	46.2141	1.50255
$947$	−54.5603	−1.77297	−0.886485	−	0.462756i	$-0.846860\pi$
$947$	−54.5603	−1.77297	−0.886485	+	0.462756i	$0.846860\pi$
$948$	4.21233	0.136810
$949$	7.34499	0.238429
$950$	17.4745	0.566949
$951$	17.5247	0.568278
$952$	3.25998	0.105656
$953$	42.0794	1.36309	0.681543	−	0.731778i	$-0.261309\pi$
$953$	42.0794	1.36309	0.681543	+	0.731778i	$0.261309\pi$
$954$	−9.00406	−0.291517
$955$	−18.3356	−0.593326
$956$	−15.0757	−0.487584
$957$	−37.7841	−1.22139
$958$	−13.5206	−0.436831
$959$	−21.9511	−0.708839
$960$	1.69357	0.0546597
$961$	34.3625	1.10847
$962$	−4.56515	−0.147186
$963$	4.99176	0.160857
$964$	−23.0265	−0.741633
$965$	0.0164602	0.000529872 0
$966$	−22.2086	−0.714550
$967$	−23.7985	−0.765309	−0.382654	−	0.923892i	$-0.624990\pi$
$967$	−23.7985	−0.765309	−0.382654	+	0.923892i	$0.624990\pi$
$968$	17.6055	0.565863
$969$	8.19698	0.263325
$970$	0.758232	0.0243453
$971$	4.38164	0.140613	0.0703067	−	0.997525i	$-0.477602\pi$
$971$	4.38164	0.140613	0.0703067	+	0.997525i	$0.477602\pi$
$972$	−1.00000	−0.0320750
$973$	37.7891	1.21146
$974$	28.7702	0.921856
$975$	−1.85935	−0.0595469
$976$	13.5963	0.435207
$977$	34.7203	1.11080	0.555400	−	0.831584i	$-0.312565\pi$
$977$	34.7203	1.11080	0.555400	+	0.831584i	$0.312565\pi$
$978$	−11.5555	−0.369503
$979$	−57.3231	−1.83206
$980$	−6.14333	−0.196241
$981$	−3.85965	−0.123229
$982$	−38.9666	−1.24347
$983$	−13.4071	−0.427621	−0.213811	−	0.976875i	$-0.568588\pi$
$983$	−13.4071	−0.427621	−0.213811	+	0.976875i	$0.568588\pi$
$984$	11.8798	0.378715
$985$	39.6859	1.26450
$986$	7.06454	0.224981
$987$	−6.89164	−0.219363
$988$	7.14931	0.227450
$989$	58.8649	1.87180
$990$	−9.05791	−0.287879
$991$	−8.09941	−0.257286	−0.128643	−	0.991691i	$-0.541062\pi$
$991$	−8.09941	−0.257286	−0.128643	+	0.991691i	$0.541062\pi$
$992$	8.08471	0.256690
$993$	2.76351	0.0876975
$994$	14.6647	0.465136
$995$	−23.3616	−0.740612
$996$	−11.0390	−0.349783
$997$	−34.1018	−1.08002	−0.540008	−	0.841660i	$-0.681579\pi$
$997$	−34.1018	−1.08002	−0.540008	+	0.841660i	$0.681579\pi$
$998$	−8.87761	−0.281016
$999$	−5.23414	−0.165601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bc.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bc.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69357 q^{5} -1.00000 q^{6} +3.25998 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69357 q^{5} -1.00000 q^{6} +3.25998 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.69357 q^{10} +5.34841 q^{11} -1.00000 q^{12} -0.872188 q^{13} +3.25998 q^{14} +1.69357 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -8.19698 q^{19} -1.69357 q^{20} -3.25998 q^{21} +5.34841 q^{22} +6.81251 q^{23} -1.00000 q^{24} -2.13182 q^{25} -0.872188 q^{26} -1.00000 q^{27} +3.25998 q^{28} +7.06454 q^{29} +1.69357 q^{30} +8.08471 q^{31} +1.00000 q^{32} -5.34841 q^{33} +1.00000 q^{34} -5.52099 q^{35} +1.00000 q^{36} +5.23414 q^{37} -8.19698 q^{38} +0.872188 q^{39} -1.69357 q^{40} -11.8798 q^{41} -3.25998 q^{42} +8.64072 q^{43} +5.34841 q^{44} -1.69357 q^{45} +6.81251 q^{46} +2.11402 q^{47} -1.00000 q^{48} +3.62744 q^{49} -2.13182 q^{50} -1.00000 q^{51} -0.872188 q^{52} -9.00406 q^{53} -1.00000 q^{54} -9.05791 q^{55} +3.25998 q^{56} +8.19698 q^{57} +7.06454 q^{58} +1.00000 q^{59} +1.69357 q^{60} +13.5963 q^{61} +8.08471 q^{62} +3.25998 q^{63} +1.00000 q^{64} +1.47711 q^{65} -5.34841 q^{66} -8.42336 q^{67} +1.00000 q^{68} -6.81251 q^{69} -5.52099 q^{70} +4.49841 q^{71} +1.00000 q^{72} -8.42134 q^{73} +5.23414 q^{74} +2.13182 q^{75} -8.19698 q^{76} +17.4357 q^{77} +0.872188 q^{78} -4.21233 q^{79} -1.69357 q^{80} +1.00000 q^{81} -11.8798 q^{82} +11.0390 q^{83} -3.25998 q^{84} -1.69357 q^{85} +8.64072 q^{86} -7.06454 q^{87} +5.34841 q^{88} -10.7178 q^{89} -1.69357 q^{90} -2.84331 q^{91} +6.81251 q^{92} -8.08471 q^{93} +2.11402 q^{94} +13.8822 q^{95} -1.00000 q^{96} -0.447712 q^{97} +3.62744 q^{98} +5.34841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} - 14 q^{3} + 14 q^{4} + 2 q^{5} - 14 q^{6} + q^{7} + 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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