LMFDB - Embedded newform 8030.2.a.bl.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} - x^{17} + 200 x^{16} - 263 x^{15} - 1900 x^{14} + 3165 x^{13} + 10217 x^{12} + \cdots + 1388 $ x^19 - 9x^18 - x^17 + 200x^16 - 263x^15 - 1900x^14 + 3165x^13 + 10217x^12 - 16393x^11 - 33875x^10 + 44043x^9 + 68537x^8 - 63620x^7 - 79890x^6 + 48388x^5 + 49353x^4 - 17806x^3 - 14287x^2 + 2436*x + 1388
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-1.51882$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.51882 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.51882 q^{6} +3.87973 q^{7} +1.00000 q^{8} +3.34446 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.51882 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.51882 q^{6} +3.87973 q^{7} +1.00000 q^{8} +3.34446 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.51882 q^{12} +1.45016 q^{13} +3.87973 q^{14} +2.51882 q^{15} +1.00000 q^{16} -4.54191 q^{17} +3.34446 q^{18} -2.38124 q^{19} +1.00000 q^{20} +9.77234 q^{21} +1.00000 q^{22} -4.77274 q^{23} +2.51882 q^{24} +1.00000 q^{25} +1.45016 q^{26} +0.867632 q^{27} +3.87973 q^{28} +8.93086 q^{29} +2.51882 q^{30} +8.56554 q^{31} +1.00000 q^{32} +2.51882 q^{33} -4.54191 q^{34} +3.87973 q^{35} +3.34446 q^{36} -3.21657 q^{37} -2.38124 q^{38} +3.65269 q^{39} +1.00000 q^{40} -7.14717 q^{41} +9.77234 q^{42} -3.09761 q^{43} +1.00000 q^{44} +3.34446 q^{45} -4.77274 q^{46} -1.94547 q^{47} +2.51882 q^{48} +8.05228 q^{49} +1.00000 q^{50} -11.4403 q^{51} +1.45016 q^{52} +0.850864 q^{53} +0.867632 q^{54} +1.00000 q^{55} +3.87973 q^{56} -5.99792 q^{57} +8.93086 q^{58} +12.6207 q^{59} +2.51882 q^{60} +10.2345 q^{61} +8.56554 q^{62} +12.9756 q^{63} +1.00000 q^{64} +1.45016 q^{65} +2.51882 q^{66} +10.6071 q^{67} -4.54191 q^{68} -12.0217 q^{69} +3.87973 q^{70} -13.3045 q^{71} +3.34446 q^{72} -1.00000 q^{73} -3.21657 q^{74} +2.51882 q^{75} -2.38124 q^{76} +3.87973 q^{77} +3.65269 q^{78} -10.5068 q^{79} +1.00000 q^{80} -7.84797 q^{81} -7.14717 q^{82} +4.74658 q^{83} +9.77234 q^{84} -4.54191 q^{85} -3.09761 q^{86} +22.4952 q^{87} +1.00000 q^{88} -16.9490 q^{89} +3.34446 q^{90} +5.62621 q^{91} -4.77274 q^{92} +21.5751 q^{93} -1.94547 q^{94} -2.38124 q^{95} +2.51882 q^{96} +17.1882 q^{97} +8.05228 q^{98} +3.34446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) $ 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * 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
$3$	2.51882	1.45424	0.727121	−	0.686509i	$-0.240858\pi$
$3$	2.51882	1.45424	0.727121	+	0.686509i	$0.240858\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.51882	1.02830
$7$	3.87973	1.46640	0.733200	−	0.680014i	$-0.238026\pi$
$7$	3.87973	1.46640	0.733200	+	0.680014i	$0.238026\pi$
$8$	1.00000	0.353553
$9$	3.34446	1.11482
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.51882	0.727121
$13$	1.45016	0.402201	0.201101	−	0.979571i	$-0.435548\pi$
$13$	1.45016	0.402201	0.201101	+	0.979571i	$0.435548\pi$
$14$	3.87973	1.03690
$15$	2.51882	0.650357
$16$	1.00000	0.250000
$17$	−4.54191	−1.10158	−0.550788	−	0.834645i	$-0.685673\pi$
$17$	−4.54191	−1.10158	−0.550788	+	0.834645i	$0.685673\pi$
$18$	3.34446	0.788297
$19$	−2.38124	−0.546294	−0.273147	−	0.961972i	$-0.588065\pi$
$19$	−2.38124	−0.546294	−0.273147	+	0.961972i	$0.588065\pi$
$20$	1.00000	0.223607
$21$	9.77234	2.13250
$22$	1.00000	0.213201
$23$	−4.77274	−0.995186	−0.497593	−	0.867411i	$-0.665783\pi$
$23$	−4.77274	−0.995186	−0.497593	+	0.867411i	$0.665783\pi$
$24$	2.51882	0.514152
$25$	1.00000	0.200000
$26$	1.45016	0.284399
$27$	0.867632	0.166976
$28$	3.87973	0.733200
$29$	8.93086	1.65842	0.829210	−	0.558937i	$-0.188791\pi$
$29$	8.93086	1.65842	0.829210	+	0.558937i	$0.188791\pi$
$30$	2.51882	0.459872
$31$	8.56554	1.53842	0.769208	−	0.638999i	$-0.220651\pi$
$31$	8.56554	1.53842	0.769208	+	0.638999i	$0.220651\pi$
$32$	1.00000	0.176777
$33$	2.51882	0.438470
$34$	−4.54191	−0.778932
$35$	3.87973	0.655794
$36$	3.34446	0.557410
$37$	−3.21657	−0.528801	−0.264400	−	0.964413i	$-0.585174\pi$
$37$	−3.21657	−0.528801	−0.264400	+	0.964413i	$0.585174\pi$
$38$	−2.38124	−0.386288
$39$	3.65269	0.584898
$40$	1.00000	0.158114
$41$	−7.14717	−1.11620	−0.558100	−	0.829774i	$-0.688470\pi$
$41$	−7.14717	−1.11620	−0.558100	+	0.829774i	$0.688470\pi$
$42$	9.77234	1.50790
$43$	−3.09761	−0.472382	−0.236191	−	0.971707i	$-0.575899\pi$
$43$	−3.09761	−0.472382	−0.236191	+	0.971707i	$0.575899\pi$
$44$	1.00000	0.150756
$45$	3.34446	0.498563
$46$	−4.77274	−0.703703
$47$	−1.94547	−0.283776	−0.141888	−	0.989883i	$-0.545317\pi$
$47$	−1.94547	−0.283776	−0.141888	+	0.989883i	$0.545317\pi$
$48$	2.51882	0.363561
$49$	8.05228	1.15033
$50$	1.00000	0.141421
$51$	−11.4403	−1.60196
$52$	1.45016	0.201101
$53$	0.850864	0.116875	0.0584376	−	0.998291i	$-0.481388\pi$
$53$	0.850864	0.116875	0.0584376	+	0.998291i	$0.481388\pi$
$54$	0.867632	0.118070
$55$	1.00000	0.134840
$56$	3.87973	0.518450
$57$	−5.99792	−0.794444
$58$	8.93086	1.17268
$59$	12.6207	1.64308	0.821539	−	0.570153i	$-0.193116\pi$
$59$	12.6207	1.64308	0.821539	+	0.570153i	$0.193116\pi$
$60$	2.51882	0.325178
$61$	10.2345	1.31039	0.655195	−	0.755460i	$-0.272586\pi$
$61$	10.2345	1.31039	0.655195	+	0.755460i	$0.272586\pi$
$62$	8.56554	1.08782
$63$	12.9756	1.63477
$64$	1.00000	0.125000
$65$	1.45016	0.179870
$66$	2.51882	0.310045
$67$	10.6071	1.29586	0.647930	−	0.761700i	$-0.275635\pi$
$67$	10.6071	1.29586	0.647930	+	0.761700i	$0.275635\pi$
$68$	−4.54191	−0.550788
$69$	−12.0217	−1.44724
$70$	3.87973	0.463716
$71$	−13.3045	−1.57895	−0.789477	−	0.613780i	$-0.789648\pi$
$71$	−13.3045	−1.57895	−0.789477	+	0.613780i	$0.789648\pi$
$72$	3.34446	0.394148
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−3.21657	−0.373919
$75$	2.51882	0.290848
$76$	−2.38124	−0.273147
$77$	3.87973	0.442136
$78$	3.65269	0.413585
$79$	−10.5068	−1.18211	−0.591054	−	0.806632i	$-0.701288\pi$
$79$	−10.5068	−1.18211	−0.591054	+	0.806632i	$0.701288\pi$
$80$	1.00000	0.111803
$81$	−7.84797	−0.871997
$82$	−7.14717	−0.789273
$83$	4.74658	0.521005	0.260503	−	0.965473i	$-0.416112\pi$
$83$	4.74658	0.521005	0.260503	+	0.965473i	$0.416112\pi$
$84$	9.77234	1.06625
$85$	−4.54191	−0.492640
$86$	−3.09761	−0.334024
$87$	22.4952	2.41174
$88$	1.00000	0.106600
$89$	−16.9490	−1.79659	−0.898295	−	0.439392i	$-0.855194\pi$
$89$	−16.9490	−1.79659	−0.898295	+	0.439392i	$0.855194\pi$
$90$	3.34446	0.352537
$91$	5.62621	0.589787
$92$	−4.77274	−0.497593
$93$	21.5751	2.23723
$94$	−1.94547	−0.200660
$95$	−2.38124	−0.244310
$96$	2.51882	0.257076
$97$	17.1882	1.74520	0.872598	−	0.488439i	$-0.162434\pi$
$97$	17.1882	1.74520	0.872598	+	0.488439i	$0.162434\pi$
$98$	8.05228	0.813403
$99$	3.34446	0.336131
$100$	1.00000	0.100000
$101$	−14.0172	−1.39477	−0.697383	−	0.716699i	$-0.745652\pi$
$101$	−14.0172	−1.39477	−0.697383	+	0.716699i	$0.745652\pi$
$102$	−11.4403	−1.13276
$103$	−3.47737	−0.342636	−0.171318	−	0.985216i	$-0.554802\pi$
$103$	−3.47737	−0.342636	−0.171318	+	0.985216i	$0.554802\pi$
$104$	1.45016	0.142200
$105$	9.77234	0.953683
$106$	0.850864	0.0826432
$107$	−5.90939	−0.571282	−0.285641	−	0.958337i	$-0.592206\pi$
$107$	−5.90939	−0.571282	−0.285641	+	0.958337i	$0.592206\pi$
$108$	0.867632	0.0834879
$109$	2.91166	0.278886	0.139443	−	0.990230i	$-0.455469\pi$
$109$	2.91166	0.278886	0.139443	+	0.990230i	$0.455469\pi$
$110$	1.00000	0.0953463
$111$	−8.10196	−0.769004
$112$	3.87973	0.366600
$113$	11.3858	1.07108	0.535541	−	0.844509i	$-0.320108\pi$
$113$	11.3858	1.07108	0.535541	+	0.844509i	$0.320108\pi$
$114$	−5.99792	−0.561756
$115$	−4.77274	−0.445061
$116$	8.93086	0.829210
$117$	4.84999	0.448382
$118$	12.6207	1.16183
$119$	−17.6214	−1.61535
$120$	2.51882	0.229936
$121$	1.00000	0.0909091
$122$	10.2345	0.926586
$123$	−18.0024	−1.62323
$124$	8.56554	0.769208
$125$	1.00000	0.0894427
$126$	12.9756	1.15596
$127$	8.29060	0.735672	0.367836	−	0.929891i	$-0.380099\pi$
$127$	8.29060	0.735672	0.367836	+	0.929891i	$0.380099\pi$
$128$	1.00000	0.0883883
$129$	−7.80233	−0.686957
$130$	1.45016	0.127187
$131$	21.1239	1.84560	0.922800	−	0.385279i	$-0.125895\pi$
$131$	21.1239	1.84560	0.922800	+	0.385279i	$0.125895\pi$
$132$	2.51882	0.219235
$133$	−9.23856	−0.801085
$134$	10.6071	0.916312
$135$	0.867632	0.0746739
$136$	−4.54191	−0.389466
$137$	3.76526	0.321688	0.160844	−	0.986980i	$-0.448578\pi$
$137$	3.76526	0.321688	0.160844	+	0.986980i	$0.448578\pi$
$138$	−12.0217	−1.02335
$139$	−13.9399	−1.18236	−0.591182	−	0.806538i	$-0.701339\pi$
$139$	−13.9399	−1.18236	−0.591182	+	0.806538i	$0.701339\pi$
$140$	3.87973	0.327897
$141$	−4.90029	−0.412679
$142$	−13.3045	−1.11649
$143$	1.45016	0.121268
$144$	3.34446	0.278705
$145$	8.93086	0.741668
$146$	−1.00000	−0.0827606
$147$	20.2823	1.67285
$148$	−3.21657	−0.264400
$149$	−10.1288	−0.829780	−0.414890	−	0.909872i	$-0.636180\pi$
$149$	−10.1288	−0.829780	−0.414890	+	0.909872i	$0.636180\pi$
$150$	2.51882	0.205661
$151$	19.0978	1.55416	0.777080	−	0.629401i	$-0.216700\pi$
$151$	19.0978	1.55416	0.777080	+	0.629401i	$0.216700\pi$
$152$	−2.38124	−0.193144
$153$	−15.1902	−1.22806
$154$	3.87973	0.312637
$155$	8.56554	0.688000
$156$	3.65269	0.292449
$157$	0.955147	0.0762291	0.0381145	−	0.999273i	$-0.487865\pi$
$157$	0.955147	0.0762291	0.0381145	+	0.999273i	$0.487865\pi$
$158$	−10.5068	−0.835877
$159$	2.14317	0.169965
$160$	1.00000	0.0790569
$161$	−18.5169	−1.45934
$162$	−7.84797	−0.616595
$163$	−14.7485	−1.15519	−0.577594	−	0.816324i	$-0.696008\pi$
$163$	−14.7485	−1.15519	−0.577594	+	0.816324i	$0.696008\pi$
$164$	−7.14717	−0.558100
$165$	2.51882	0.196090
$166$	4.74658	0.368406
$167$	−2.24108	−0.173420	−0.0867101	−	0.996234i	$-0.527635\pi$
$167$	−2.24108	−0.173420	−0.0867101	+	0.996234i	$0.527635\pi$
$168$	9.77234	0.753952
$169$	−10.8970	−0.838234
$170$	−4.54191	−0.348349
$171$	−7.96396	−0.609019
$172$	−3.09761	−0.236191
$173$	−11.7394	−0.892530	−0.446265	−	0.894901i	$-0.647246\pi$
$173$	−11.7394	−0.892530	−0.446265	+	0.894901i	$0.647246\pi$
$174$	22.4952	1.70536
$175$	3.87973	0.293280
$176$	1.00000	0.0753778
$177$	31.7893	2.38943
$178$	−16.9490	−1.27038
$179$	7.77300	0.580981	0.290490	−	0.956878i	$-0.406182\pi$
$179$	7.77300	0.580981	0.290490	+	0.956878i	$0.406182\pi$
$180$	3.34446	0.249281
$181$	−14.7422	−1.09578	−0.547890	−	0.836550i	$-0.684569\pi$
$181$	−14.7422	−1.09578	−0.547890	+	0.836550i	$0.684569\pi$
$182$	5.62621	0.417043
$183$	25.7788	1.90563
$184$	−4.77274	−0.351851
$185$	−3.21657	−0.236487
$186$	21.5751	1.58196
$187$	−4.54191	−0.332138
$188$	−1.94547	−0.141888
$189$	3.36617	0.244853
$190$	−2.38124	−0.172753
$191$	0.583705	0.0422354	0.0211177	−	0.999777i	$-0.493278\pi$
$191$	0.583705	0.0422354	0.0211177	+	0.999777i	$0.493278\pi$
$192$	2.51882	0.181780
$193$	20.2509	1.45769	0.728847	−	0.684677i	$-0.240057\pi$
$193$	20.2509	1.45769	0.728847	+	0.684677i	$0.240057\pi$
$194$	17.1882	1.23404
$195$	3.65269	0.261574
$196$	8.05228	0.575163
$197$	−16.2491	−1.15770	−0.578850	−	0.815434i	$-0.696498\pi$
$197$	−16.2491	−1.15770	−0.578850	+	0.815434i	$0.696498\pi$
$198$	3.34446	0.237680
$199$	−0.733206	−0.0519756	−0.0259878	−	0.999662i	$-0.508273\pi$
$199$	−0.733206	−0.0519756	−0.0259878	+	0.999662i	$0.508273\pi$
$200$	1.00000	0.0707107
$201$	26.7173	1.88450
$202$	−14.0172	−0.986248
$203$	34.6493	2.43191
$204$	−11.4403	−0.800979
$205$	−7.14717	−0.499180
$206$	−3.47737	−0.242280
$207$	−15.9622	−1.10945
$208$	1.45016	0.100550
$209$	−2.38124	−0.164714
$210$	9.77234	0.674355
$211$	−21.3304	−1.46845	−0.734223	−	0.678909i	$-0.762453\pi$
$211$	−21.3304	−1.46845	−0.734223	+	0.678909i	$0.762453\pi$
$212$	0.850864	0.0584376
$213$	−33.5117	−2.29618
$214$	−5.90939	−0.403957
$215$	−3.09761	−0.211255
$216$	0.867632	0.0590349
$217$	33.2319	2.25593
$218$	2.91166	0.197202
$219$	−2.51882	−0.170206
$220$	1.00000	0.0674200
$221$	−6.58649	−0.443055
$222$	−8.10196	−0.543768
$223$	−19.7785	−1.32447	−0.662233	−	0.749298i	$-0.730391\pi$
$223$	−19.7785	−1.32447	−0.662233	+	0.749298i	$0.730391\pi$
$224$	3.87973	0.259225
$225$	3.34446	0.222964
$226$	11.3858	0.757369
$227$	3.52074	0.233679	0.116840	−	0.993151i	$-0.462724\pi$
$227$	3.52074	0.233679	0.116840	+	0.993151i	$0.462724\pi$
$228$	−5.99792	−0.397222
$229$	6.32114	0.417712	0.208856	−	0.977946i	$-0.433026\pi$
$229$	6.32114	0.417712	0.208856	+	0.977946i	$0.433026\pi$
$230$	−4.77274	−0.314705
$231$	9.77234	0.642973
$232$	8.93086	0.586340
$233$	27.2322	1.78404	0.892020	−	0.451995i	$-0.149288\pi$
$233$	27.2322	1.78404	0.892020	+	0.451995i	$0.149288\pi$
$234$	4.84999	0.317054
$235$	−1.94547	−0.126908
$236$	12.6207	0.821539
$237$	−26.4648	−1.71907
$238$	−17.6214	−1.14222
$239$	−10.2197	−0.661060	−0.330530	−	0.943795i	$-0.607228\pi$
$239$	−10.2197	−0.661060	−0.330530	+	0.943795i	$0.607228\pi$
$240$	2.51882	0.162589
$241$	−22.2897	−1.43580	−0.717902	−	0.696145i	$-0.754897\pi$
$241$	−22.2897	−1.43580	−0.717902	+	0.696145i	$0.754897\pi$
$242$	1.00000	0.0642824
$243$	−22.3705	−1.43507
$244$	10.2345	0.655195
$245$	8.05228	0.514441
$246$	−18.0024	−1.14779
$247$	−3.45317	−0.219720
$248$	8.56554	0.543912
$249$	11.9558	0.757668
$250$	1.00000	0.0632456
$251$	−3.70947	−0.234140	−0.117070	−	0.993124i	$-0.537350\pi$
$251$	−3.70947	−0.234140	−0.117070	+	0.993124i	$0.537350\pi$
$252$	12.9756	0.817385
$253$	−4.77274	−0.300060
$254$	8.29060	0.520199
$255$	−11.4403	−0.716417
$256$	1.00000	0.0625000
$257$	−31.1405	−1.94249	−0.971246	−	0.238079i	$-0.923482\pi$
$257$	−31.1405	−1.94249	−0.971246	+	0.238079i	$0.923482\pi$
$258$	−7.80233	−0.485752
$259$	−12.4794	−0.775433
$260$	1.45016	0.0899349
$261$	29.8689	1.84884
$262$	21.1239	1.30504
$263$	−28.7510	−1.77286	−0.886432	−	0.462859i	$-0.846823\pi$
$263$	−28.7510	−1.77286	−0.886432	+	0.462859i	$0.846823\pi$
$264$	2.51882	0.155023
$265$	0.850864	0.0522682
$266$	−9.23856	−0.566452
$267$	−42.6915	−2.61268
$268$	10.6071	0.647930
$269$	5.97776	0.364470	0.182235	−	0.983255i	$-0.441667\pi$
$269$	5.97776	0.364470	0.182235	+	0.983255i	$0.441667\pi$
$270$	0.867632	0.0528024
$271$	−5.65162	−0.343311	−0.171656	−	0.985157i	$-0.554912\pi$
$271$	−5.65162	−0.343311	−0.171656	+	0.985157i	$0.554912\pi$
$272$	−4.54191	−0.275394
$273$	14.1714	0.857694
$274$	3.76526	0.227468
$275$	1.00000	0.0603023
$276$	−12.0217	−0.723620
$277$	−25.8136	−1.55099	−0.775493	−	0.631356i	$-0.782499\pi$
$277$	−25.8136	−1.55099	−0.775493	+	0.631356i	$0.782499\pi$
$278$	−13.9399	−0.836058
$279$	28.6471	1.71506
$280$	3.87973	0.231858
$281$	4.62394	0.275841	0.137921	−	0.990443i	$-0.455958\pi$
$281$	4.62394	0.275841	0.137921	+	0.990443i	$0.455958\pi$
$282$	−4.90029	−0.291808
$283$	−25.2895	−1.50330	−0.751652	−	0.659560i	$-0.770743\pi$
$283$	−25.2895	−1.50330	−0.751652	+	0.659560i	$0.770743\pi$
$284$	−13.3045	−0.789477
$285$	−5.99792	−0.355286
$286$	1.45016	0.0857496
$287$	−27.7291	−1.63680
$288$	3.34446	0.197074
$289$	3.62898	0.213469
$290$	8.93086	0.524438
$291$	43.2940	2.53794
$292$	−1.00000	−0.0585206
$293$	−30.7224	−1.79482	−0.897410	−	0.441197i	$-0.854554\pi$
$293$	−30.7224	−1.79482	−0.897410	+	0.441197i	$0.854554\pi$
$294$	20.2823	1.18289
$295$	12.6207	0.734807
$296$	−3.21657	−0.186959
$297$	0.867632	0.0503451
$298$	−10.1288	−0.586743
$299$	−6.92123	−0.400265
$300$	2.51882	0.145424
$301$	−12.0179	−0.692700
$302$	19.0978	1.09896
$303$	−35.3069	−2.02833
$304$	−2.38124	−0.136573
$305$	10.2345	0.586025
$306$	−15.1902	−0.868369
$307$	29.3932	1.67756	0.838779	−	0.544472i	$-0.183270\pi$
$307$	29.3932	1.67756	0.838779	+	0.544472i	$0.183270\pi$
$308$	3.87973	0.221068
$309$	−8.75888	−0.498275
$310$	8.56554	0.486490
$311$	−1.51038	−0.0856456	−0.0428228	−	0.999083i	$-0.513635\pi$
$311$	−1.51038	−0.0856456	−0.0428228	+	0.999083i	$0.513635\pi$
$312$	3.65269	0.206793
$313$	34.6450	1.95825	0.979126	−	0.203254i	$-0.0651516\pi$
$313$	34.6450	1.95825	0.979126	+	0.203254i	$0.0651516\pi$
$314$	0.955147	0.0539021
$315$	12.9756	0.731092
$316$	−10.5068	−0.591054
$317$	−33.1245	−1.86046	−0.930229	−	0.366981i	$-0.880392\pi$
$317$	−33.1245	−1.86046	−0.930229	+	0.366981i	$0.880392\pi$
$318$	2.14317	0.120183
$319$	8.93086	0.500032
$320$	1.00000	0.0559017
$321$	−14.8847	−0.830782
$322$	−18.5169	−1.03191
$323$	10.8154	0.601784
$324$	−7.84797	−0.435998
$325$	1.45016	0.0804402
$326$	−14.7485	−0.816842
$327$	7.33394	0.405568
$328$	−7.14717	−0.394636
$329$	−7.54789	−0.416128
$330$	2.51882	0.138657
$331$	21.6331	1.18906	0.594530	−	0.804073i	$-0.297338\pi$
$331$	21.6331	1.18906	0.594530	+	0.804073i	$0.297338\pi$
$332$	4.74658	0.260503
$333$	−10.7577	−0.589518
$334$	−2.24108	−0.122627
$335$	10.6071	0.579527
$336$	9.77234	0.533125
$337$	23.6684	1.28930	0.644651	−	0.764477i	$-0.277003\pi$
$337$	23.6684	1.28930	0.644651	+	0.764477i	$0.277003\pi$
$338$	−10.8970	−0.592721
$339$	28.6787	1.55761
$340$	−4.54191	−0.246320
$341$	8.56554	0.463850
$342$	−7.96396	−0.430642
$343$	4.08257	0.220438
$344$	−3.09761	−0.167012
$345$	−12.0217	−0.647226
$346$	−11.7394	−0.631114
$347$	−7.76767	−0.416990	−0.208495	−	0.978023i	$-0.566857\pi$
$347$	−7.76767	−0.416990	−0.208495	+	0.978023i	$0.566857\pi$
$348$	22.4952	1.20587
$349$	21.0708	1.12789	0.563947	−	0.825811i	$-0.309282\pi$
$349$	21.0708	1.12789	0.563947	+	0.825811i	$0.309282\pi$
$350$	3.87973	0.207380
$351$	1.25820	0.0671579
$352$	1.00000	0.0533002
$353$	−0.109688	−0.00583810	−0.00291905	−	0.999996i	$-0.500929\pi$
$353$	−0.109688	−0.00583810	−0.00291905	+	0.999996i	$0.500929\pi$
$354$	31.7893	1.68958
$355$	−13.3045	−0.706130
$356$	−16.9490	−0.898295
$357$	−44.3851	−2.34911
$358$	7.77300	0.410816
$359$	18.5127	0.977060	0.488530	−	0.872547i	$-0.337533\pi$
$359$	18.5127	0.977060	0.488530	+	0.872547i	$0.337533\pi$
$360$	3.34446	0.176268
$361$	−13.3297	−0.701563
$362$	−14.7422	−0.774834
$363$	2.51882	0.132204
$364$	5.62621	0.294894
$365$	−1.00000	−0.0523424
$366$	25.7788	1.34748
$367$	−22.3244	−1.16533	−0.582663	−	0.812714i	$-0.697989\pi$
$367$	−22.3244	−1.16533	−0.582663	+	0.812714i	$0.697989\pi$
$368$	−4.77274	−0.248796
$369$	−23.9034	−1.24436
$370$	−3.21657	−0.167222
$371$	3.30112	0.171386
$372$	21.5751	1.11861
$373$	−1.03562	−0.0536222	−0.0268111	−	0.999641i	$-0.508535\pi$
$373$	−1.03562	−0.0536222	−0.0268111	+	0.999641i	$0.508535\pi$
$374$	−4.54191	−0.234857
$375$	2.51882	0.130071
$376$	−1.94547	−0.100330
$377$	12.9512	0.667018
$378$	3.36617	0.173137
$379$	−34.8294	−1.78906	−0.894532	−	0.447004i	$-0.852491\pi$
$379$	−34.8294	−1.78906	−0.894532	+	0.447004i	$0.852491\pi$
$380$	−2.38124	−0.122155
$381$	20.8825	1.06985
$382$	0.583705	0.0298649
$383$	20.9975	1.07292	0.536461	−	0.843925i	$-0.319761\pi$
$383$	20.9975	1.07292	0.536461	+	0.843925i	$0.319761\pi$
$384$	2.51882	0.128538
$385$	3.87973	0.197729
$386$	20.2509	1.03074
$387$	−10.3598	−0.526620
$388$	17.1882	0.872598
$389$	6.58357	0.333800	0.166900	−	0.985974i	$-0.446624\pi$
$389$	6.58357	0.333800	0.166900	+	0.985974i	$0.446624\pi$
$390$	3.65269	0.184961
$391$	21.6774	1.09627
$392$	8.05228	0.406702
$393$	53.2072	2.68395
$394$	−16.2491	−0.818618
$395$	−10.5068	−0.528655
$396$	3.34446	0.168065
$397$	28.9861	1.45477	0.727386	−	0.686228i	$-0.240735\pi$
$397$	28.9861	1.45477	0.727386	+	0.686228i	$0.240735\pi$
$398$	−0.733206	−0.0367523
$399$	−23.2703	−1.16497
$400$	1.00000	0.0500000
$401$	16.2888	0.813423	0.406711	−	0.913557i	$-0.366675\pi$
$401$	16.2888	0.813423	0.406711	+	0.913557i	$0.366675\pi$
$402$	26.7173	1.33254
$403$	12.4214	0.618753
$404$	−14.0172	−0.697383
$405$	−7.84797	−0.389969
$406$	34.6493	1.71962
$407$	−3.21657	−0.159439
$408$	−11.4403	−0.566378
$409$	−13.8043	−0.682577	−0.341288	−	0.939959i	$-0.610863\pi$
$409$	−13.8043	−0.682577	−0.341288	+	0.939959i	$0.610863\pi$
$410$	−7.14717	−0.352974
$411$	9.48402	0.467812
$412$	−3.47737	−0.171318
$413$	48.9649	2.40941
$414$	−15.9622	−0.784502
$415$	4.74658	0.233001
$416$	1.45016	0.0710998
$417$	−35.1120	−1.71944
$418$	−2.38124	−0.116470
$419$	−16.1650	−0.789710	−0.394855	−	0.918743i	$-0.629205\pi$
$419$	−16.1650	−0.789710	−0.394855	+	0.918743i	$0.629205\pi$
$420$	9.77234	0.476841
$421$	−14.7807	−0.720365	−0.360183	−	0.932882i	$-0.617286\pi$
$421$	−14.7807	−0.720365	−0.360183	+	0.932882i	$0.617286\pi$
$422$	−21.3304	−1.03835
$423$	−6.50654	−0.316359
$424$	0.850864	0.0413216
$425$	−4.54191	−0.220315
$426$	−33.5117	−1.62365
$427$	39.7070	1.92156
$428$	−5.90939	−0.285641
$429$	3.65269	0.176353
$430$	−3.09761	−0.149380
$431$	11.7435	0.565662	0.282831	−	0.959170i	$-0.408726\pi$
$431$	11.7435	0.565662	0.282831	+	0.959170i	$0.408726\pi$
$432$	0.867632	0.0417440
$433$	6.85291	0.329330	0.164665	−	0.986350i	$-0.447346\pi$
$433$	6.85291	0.329330	0.164665	+	0.986350i	$0.447346\pi$
$434$	33.2319	1.59518
$435$	22.4952	1.07856
$436$	2.91166	0.139443
$437$	11.3650	0.543664
$438$	−2.51882	−0.120354
$439$	38.5745	1.84106	0.920530	−	0.390671i	$-0.127757\pi$
$439$	38.5745	1.84106	0.920530	+	0.390671i	$0.127757\pi$
$440$	1.00000	0.0476731
$441$	26.9305	1.28241
$442$	−6.58649	−0.313287
$443$	−11.2042	−0.532327	−0.266163	−	0.963928i	$-0.585756\pi$
$443$	−11.2042	−0.532327	−0.266163	+	0.963928i	$0.585756\pi$
$444$	−8.10196	−0.384502
$445$	−16.9490	−0.803460
$446$	−19.7785	−0.936539
$447$	−25.5125	−1.20670
$448$	3.87973	0.183300
$449$	5.98426	0.282415	0.141207	−	0.989980i	$-0.454902\pi$
$449$	5.98426	0.282415	0.141207	+	0.989980i	$0.454902\pi$
$450$	3.34446	0.157659
$451$	−7.14717	−0.336547
$452$	11.3858	0.535541
$453$	48.1041	2.26013
$454$	3.52074	0.165236
$455$	5.62621	0.263761
$456$	−5.99792	−0.280878
$457$	21.1484	0.989282	0.494641	−	0.869097i	$-0.335300\pi$
$457$	21.1484	0.989282	0.494641	+	0.869097i	$0.335300\pi$
$458$	6.32114	0.295367
$459$	−3.94071	−0.183937
$460$	−4.77274	−0.222530
$461$	−32.2488	−1.50198	−0.750989	−	0.660315i	$-0.770423\pi$
$461$	−32.2488	−1.50198	−0.750989	+	0.660315i	$0.770423\pi$
$462$	9.77234	0.454650
$463$	5.16432	0.240006	0.120003	−	0.992774i	$-0.461710\pi$
$463$	5.16432	0.240006	0.120003	+	0.992774i	$0.461710\pi$
$464$	8.93086	0.414605
$465$	21.5751	1.00052
$466$	27.2322	1.26151
$467$	29.7727	1.37772	0.688859	−	0.724896i	$-0.258112\pi$
$467$	29.7727	1.37772	0.688859	+	0.724896i	$0.258112\pi$
$468$	4.84999	0.224191
$469$	41.1526	1.90025
$470$	−1.94547	−0.0897378
$471$	2.40585	0.110855
$472$	12.6207	0.580916
$473$	−3.09761	−0.142428
$474$	−26.4648	−1.21557
$475$	−2.38124	−0.109259
$476$	−17.6214	−0.807675
$477$	2.84568	0.130295
$478$	−10.2197	−0.467440
$479$	3.69082	0.168638	0.0843189	−	0.996439i	$-0.473129\pi$
$479$	3.69082	0.168638	0.0843189	+	0.996439i	$0.473129\pi$
$480$	2.51882	0.114968
$481$	−4.66453	−0.212684
$482$	−22.2897	−1.01527
$483$	−46.6409	−2.12223
$484$	1.00000	0.0454545
$485$	17.1882	0.780475
$486$	−22.3705	−1.01475
$487$	35.0475	1.58816	0.794078	−	0.607816i	$-0.207954\pi$
$487$	35.0475	1.58816	0.794078	+	0.607816i	$0.207954\pi$
$488$	10.2345	0.463293
$489$	−37.1487	−1.67992
$490$	8.05228	0.363765
$491$	−2.45971	−0.111005	−0.0555026	−	0.998459i	$-0.517676\pi$
$491$	−2.45971	−0.111005	−0.0555026	+	0.998459i	$0.517676\pi$
$492$	−18.0024	−0.811613
$493$	−40.5632	−1.82688
$494$	−3.45317	−0.155366
$495$	3.34446	0.150322
$496$	8.56554	0.384604
$497$	−51.6178	−2.31538
$498$	11.9558	0.535752
$499$	−2.92672	−0.131018	−0.0655090	−	0.997852i	$-0.520867\pi$
$499$	−2.92672	−0.131018	−0.0655090	+	0.997852i	$0.520867\pi$
$500$	1.00000	0.0447214
$501$	−5.64489	−0.252195
$502$	−3.70947	−0.165562
$503$	−35.3345	−1.57549	−0.787743	−	0.616004i	$-0.788751\pi$
$503$	−35.3345	−1.57549	−0.787743	+	0.616004i	$0.788751\pi$
$504$	12.9756	0.577979
$505$	−14.0172	−0.623758
$506$	−4.77274	−0.212174
$507$	−27.4477	−1.21900
$508$	8.29060	0.367836
$509$	−3.40123	−0.150757	−0.0753784	−	0.997155i	$-0.524016\pi$
$509$	−3.40123	−0.150757	−0.0753784	+	0.997155i	$0.524016\pi$
$510$	−11.4403	−0.506584
$511$	−3.87973	−0.171629
$512$	1.00000	0.0441942
$513$	−2.06604	−0.0912179
$514$	−31.1405	−1.37355
$515$	−3.47737	−0.153231
$516$	−7.80233	−0.343479
$517$	−1.94547	−0.0855616
$518$	−12.4794	−0.548314
$519$	−29.5694	−1.29795
$520$	1.45016	0.0635936
$521$	28.0550	1.22911	0.614557	−	0.788873i	$-0.289335\pi$
$521$	28.0550	1.22911	0.614557	+	0.788873i	$0.289335\pi$
$522$	29.8689	1.30733
$523$	−32.7416	−1.43169	−0.715845	−	0.698260i	$-0.753958\pi$
$523$	−32.7416	−1.43169	−0.715845	+	0.698260i	$0.753958\pi$
$524$	21.1239	0.922800
$525$	9.77234	0.426500
$526$	−28.7510	−1.25360
$527$	−38.9039	−1.69468
$528$	2.51882	0.109618
$529$	−0.220927	−0.00960550
$530$	0.850864	0.0369592
$531$	42.2095	1.83174
$532$	−9.23856	−0.400542
$533$	−10.3645	−0.448937
$534$	−42.6915	−1.84744
$535$	−5.90939	−0.255485
$536$	10.6071	0.458156
$537$	19.5788	0.844887
$538$	5.97776	0.257719
$539$	8.05228	0.346836
$540$	0.867632	0.0373369
$541$	24.8012	1.06629	0.533144	−	0.846025i	$-0.321010\pi$
$541$	24.8012	1.06629	0.533144	+	0.846025i	$0.321010\pi$
$542$	−5.65162	−0.242758
$543$	−37.1330	−1.59353
$544$	−4.54191	−0.194733
$545$	2.91166	0.124722
$546$	14.1714	0.606481
$547$	−35.8443	−1.53259	−0.766296	−	0.642488i	$-0.777902\pi$
$547$	−35.8443	−1.53259	−0.766296	+	0.642488i	$0.777902\pi$
$548$	3.76526	0.160844
$549$	34.2288	1.46085
$550$	1.00000	0.0426401
$551$	−21.2665	−0.905985
$552$	−12.0217	−0.511677
$553$	−40.7635	−1.73344
$554$	−25.8136	−1.09671
$555$	−8.10196	−0.343909
$556$	−13.9399	−0.591182
$557$	33.1235	1.40349	0.701745	−	0.712428i	$-0.252405\pi$
$557$	33.1235	1.40349	0.701745	+	0.712428i	$0.252405\pi$
$558$	28.6471	1.21273
$559$	−4.49202	−0.189992
$560$	3.87973	0.163948
$561$	−11.4403	−0.483008
$562$	4.62394	0.195049
$563$	−25.5078	−1.07503	−0.537514	−	0.843255i	$-0.680636\pi$
$563$	−25.5078	−1.07503	−0.537514	+	0.843255i	$0.680636\pi$
$564$	−4.90029	−0.206339
$565$	11.3858	0.479002
$566$	−25.2895	−1.06300
$567$	−30.4480	−1.27869
$568$	−13.3045	−0.558244
$569$	38.3808	1.60901	0.804503	−	0.593948i	$-0.202432\pi$
$569$	38.3808	1.60901	0.804503	+	0.593948i	$0.202432\pi$
$570$	−5.99792	−0.251225
$571$	14.4920	0.606471	0.303236	−	0.952916i	$-0.401933\pi$
$571$	14.4920	0.606471	0.303236	+	0.952916i	$0.401933\pi$
$572$	1.45016	0.0606341
$573$	1.47025	0.0614205
$574$	−27.7291	−1.15739
$575$	−4.77274	−0.199037
$576$	3.34446	0.139352
$577$	28.6530	1.19284	0.596420	−	0.802673i	$-0.296589\pi$
$577$	28.6530	1.19284	0.596420	+	0.802673i	$0.296589\pi$
$578$	3.62898	0.150946
$579$	51.0084	2.11984
$580$	8.93086	0.370834
$581$	18.4155	0.764002
$582$	43.2940	1.79459
$583$	0.850864	0.0352392
$584$	−1.00000	−0.0413803
$585$	4.84999	0.200522
$586$	−30.7224	−1.26913
$587$	−10.8906	−0.449501	−0.224751	−	0.974416i	$-0.572157\pi$
$587$	−10.8906	−0.449501	−0.224751	+	0.974416i	$0.572157\pi$
$588$	20.2823	0.836426
$589$	−20.3966	−0.840427
$590$	12.6207	0.519587
$591$	−40.9286	−1.68358
$592$	−3.21657	−0.132200
$593$	30.7379	1.26226	0.631128	−	0.775679i	$-0.282592\pi$
$593$	30.7379	1.26226	0.631128	+	0.775679i	$0.282592\pi$
$594$	0.867632	0.0355994
$595$	−17.6214	−0.722406
$596$	−10.1288	−0.414890
$597$	−1.84681	−0.0755851
$598$	−6.92123	−0.283030
$599$	3.60766	0.147405	0.0737026	−	0.997280i	$-0.476518\pi$
$599$	3.60766	0.147405	0.0737026	+	0.997280i	$0.476518\pi$
$600$	2.51882	0.102830
$601$	−26.2674	−1.07147	−0.535734	−	0.844387i	$-0.679965\pi$
$601$	−26.2674	−1.07147	−0.535734	+	0.844387i	$0.679965\pi$
$602$	−12.0179	−0.489813
$603$	35.4749	1.44465
$604$	19.0978	0.777080
$605$	1.00000	0.0406558
$606$	−35.3069	−1.43424
$607$	48.7144	1.97726	0.988629	−	0.150378i	$-0.0480491\pi$
$607$	48.7144	1.97726	0.988629	+	0.150378i	$0.0480491\pi$
$608$	−2.38124	−0.0965720
$609$	87.2754	3.53658
$610$	10.2345	0.414382
$611$	−2.82123	−0.114135
$612$	−15.1902	−0.614029
$613$	15.9344	0.643585	0.321792	−	0.946810i	$-0.395715\pi$
$613$	15.9344	0.643585	0.321792	+	0.946810i	$0.395715\pi$
$614$	29.3932	1.18621
$615$	−18.0024	−0.725929
$616$	3.87973	0.156319
$617$	−0.486151	−0.0195717	−0.00978586	−	0.999952i	$-0.503115\pi$
$617$	−0.486151	−0.0195717	−0.00978586	+	0.999952i	$0.503115\pi$
$618$	−8.75888	−0.352334
$619$	−22.6199	−0.909169	−0.454585	−	0.890704i	$-0.650212\pi$
$619$	−22.6199	−0.909169	−0.454585	+	0.890704i	$0.650212\pi$
$620$	8.56554	0.344000
$621$	−4.14098	−0.166172
$622$	−1.51038	−0.0605606
$623$	−65.7575	−2.63452
$624$	3.65269	0.146224
$625$	1.00000	0.0400000
$626$	34.6450	1.38469
$627$	−5.99792	−0.239534
$628$	0.955147	0.0381145
$629$	14.6094	0.582514
$630$	12.9756	0.516960
$631$	10.5345	0.419373	0.209686	−	0.977769i	$-0.432756\pi$
$631$	10.5345	0.419373	0.209686	+	0.977769i	$0.432756\pi$
$632$	−10.5068	−0.417938
$633$	−53.7275	−2.13547
$634$	−33.1245	−1.31554
$635$	8.29060	0.329002
$636$	2.14317	0.0849824
$637$	11.6771	0.462662
$638$	8.93086	0.353576
$639$	−44.4964	−1.76025
$640$	1.00000	0.0395285
$641$	19.9764	0.789021	0.394510	−	0.918891i	$-0.370914\pi$
$641$	19.9764	0.789021	0.394510	+	0.918891i	$0.370914\pi$
$642$	−14.8847	−0.587452
$643$	31.6424	1.24785	0.623927	−	0.781483i	$-0.285536\pi$
$643$	31.6424	1.24785	0.623927	+	0.781483i	$0.285536\pi$
$644$	−18.5169	−0.729670
$645$	−7.80233	−0.307217
$646$	10.8154	0.425526
$647$	22.9666	0.902909	0.451454	−	0.892294i	$-0.350905\pi$
$647$	22.9666	0.902909	0.451454	+	0.892294i	$0.350905\pi$
$648$	−7.84797	−0.308297
$649$	12.6207	0.495406
$650$	1.45016	0.0568798
$651$	83.7053	3.28067
$652$	−14.7485	−0.577594
$653$	23.3338	0.913121	0.456561	−	0.889692i	$-0.349081\pi$
$653$	23.3338	0.913121	0.456561	+	0.889692i	$0.349081\pi$
$654$	7.33394	0.286780
$655$	21.1239	0.825377
$656$	−7.14717	−0.279050
$657$	−3.34446	−0.130480
$658$	−7.54789	−0.294247
$659$	−34.7058	−1.35195	−0.675973	−	0.736926i	$-0.736276\pi$
$659$	−34.7058	−1.35195	−0.675973	+	0.736926i	$0.736276\pi$
$660$	2.51882	0.0980450
$661$	−5.34811	−0.208017	−0.104009	−	0.994576i	$-0.533167\pi$
$661$	−5.34811	−0.208017	−0.104009	+	0.994576i	$0.533167\pi$
$662$	21.6331	0.840793
$663$	−16.5902	−0.644309
$664$	4.74658	0.184203
$665$	−9.23856	−0.358256
$666$	−10.7577	−0.416852
$667$	−42.6247	−1.65044
$668$	−2.24108	−0.0867101
$669$	−49.8185	−1.92609
$670$	10.6071	0.409787
$671$	10.2345	0.395098
$672$	9.77234	0.376976
$673$	2.46587	0.0950522	0.0475261	−	0.998870i	$-0.484866\pi$
$673$	2.46587	0.0950522	0.0475261	+	0.998870i	$0.484866\pi$
$674$	23.6684	0.911675
$675$	0.867632	0.0333952
$676$	−10.8970	−0.419117
$677$	−0.584797	−0.0224756	−0.0112378	−	0.999937i	$-0.503577\pi$
$677$	−0.584797	−0.0224756	−0.0112378	+	0.999937i	$0.503577\pi$
$678$	28.6787	1.10140
$679$	66.6855	2.55915
$680$	−4.54191	−0.174174
$681$	8.86810	0.339827
$682$	8.56554	0.327991
$683$	−33.2048	−1.27055	−0.635273	−	0.772287i	$-0.719113\pi$
$683$	−33.2048	−1.27055	−0.635273	+	0.772287i	$0.719113\pi$
$684$	−7.96396	−0.304510
$685$	3.76526	0.143863
$686$	4.08257	0.155873
$687$	15.9218	0.607455
$688$	−3.09761	−0.118095
$689$	1.23389	0.0470073
$690$	−12.0217	−0.457658
$691$	−16.5420	−0.629286	−0.314643	−	0.949210i	$-0.601885\pi$
$691$	−16.5420	−0.629286	−0.314643	+	0.949210i	$0.601885\pi$
$692$	−11.7394	−0.446265
$693$	12.9756	0.492902
$694$	−7.76767	−0.294857
$695$	−13.9399	−0.528769
$696$	22.4952	0.852680
$697$	32.4618	1.22958
$698$	21.0708	0.797541
$699$	68.5930	2.59443
$700$	3.87973	0.146640
$701$	21.1673	0.799478	0.399739	−	0.916629i	$-0.369101\pi$
$701$	21.1673	0.799478	0.399739	+	0.916629i	$0.369101\pi$
$702$	1.25820	0.0474878
$703$	7.65942	0.288881
$704$	1.00000	0.0376889
$705$	−4.90029	−0.184555
$706$	−0.109688	−0.00412816
$707$	−54.3830	−2.04528
$708$	31.7893	1.19472
$709$	38.7059	1.45363	0.726816	−	0.686833i	$-0.240999\pi$
$709$	38.7059	1.45363	0.726816	+	0.686833i	$0.240999\pi$
$710$	−13.3045	−0.499309
$711$	−35.1396	−1.31784
$712$	−16.9490	−0.635191
$713$	−40.8811	−1.53101
$714$	−44.3851	−1.66107
$715$	1.45016	0.0542328
$716$	7.77300	0.290490
$717$	−25.7417	−0.961342
$718$	18.5127	0.690886
$719$	−16.2716	−0.606828	−0.303414	−	0.952859i	$-0.598127\pi$
$719$	−16.2716	−0.606828	−0.303414	+	0.952859i	$0.598127\pi$
$720$	3.34446	0.124641
$721$	−13.4913	−0.502440
$722$	−13.3297	−0.496080
$723$	−56.1437	−2.08801
$724$	−14.7422	−0.547890
$725$	8.93086	0.331684
$726$	2.51882	0.0934822
$727$	23.9475	0.888165	0.444083	−	0.895986i	$-0.353530\pi$
$727$	23.9475	0.888165	0.444083	+	0.895986i	$0.353530\pi$
$728$	5.62621	0.208521
$729$	−32.8034	−1.21494
$730$	−1.00000	−0.0370117
$731$	14.0691	0.520364
$732$	25.7788	0.952813
$733$	−29.6278	−1.09433	−0.547164	−	0.837026i	$-0.684292\pi$
$733$	−29.6278	−1.09433	−0.547164	+	0.837026i	$0.684292\pi$
$734$	−22.3244	−0.824010
$735$	20.2823	0.748122
$736$	−4.77274	−0.175926
$737$	10.6071	0.390717
$738$	−23.9034	−0.879897
$739$	−13.2024	−0.485659	−0.242829	−	0.970069i	$-0.578075\pi$
$739$	−13.2024	−0.485659	−0.242829	+	0.970069i	$0.578075\pi$
$740$	−3.21657	−0.118243
$741$	−8.69792	−0.319526
$742$	3.30112	0.121188
$743$	2.23965	0.0821647	0.0410824	−	0.999156i	$-0.486919\pi$
$743$	2.23965	0.0821647	0.0410824	+	0.999156i	$0.486919\pi$
$744$	21.5751	0.790980
$745$	−10.1288	−0.371089
$746$	−1.03562	−0.0379166
$747$	15.8748	0.580827
$748$	−4.54191	−0.166069
$749$	−22.9268	−0.837727
$750$	2.51882	0.0919743
$751$	−6.74486	−0.246123	−0.123062	−	0.992399i	$-0.539271\pi$
$751$	−6.74486	−0.246123	−0.123062	+	0.992399i	$0.539271\pi$
$752$	−1.94547	−0.0709439
$753$	−9.34349	−0.340496
$754$	12.9512	0.471653
$755$	19.0978	0.695042
$756$	3.36617	0.122427
$757$	46.4239	1.68730	0.843652	−	0.536890i	$-0.180401\pi$
$757$	46.4239	1.68730	0.843652	+	0.536890i	$0.180401\pi$
$758$	−34.8294	−1.26506
$759$	−12.0217	−0.436360
$760$	−2.38124	−0.0863766
$761$	9.30414	0.337275	0.168637	−	0.985678i	$-0.446063\pi$
$761$	9.30414	0.337275	0.168637	+	0.985678i	$0.446063\pi$
$762$	20.8825	0.756495
$763$	11.2964	0.408958
$764$	0.583705	0.0211177
$765$	−15.1902	−0.549204
$766$	20.9975	0.758671
$767$	18.3020	0.660848
$768$	2.51882	0.0908901
$769$	−46.3377	−1.67098	−0.835490	−	0.549505i	$-0.814816\pi$
$769$	−46.3377	−1.67098	−0.835490	+	0.549505i	$0.814816\pi$
$770$	3.87973	0.139816
$771$	−78.4374	−2.82485
$772$	20.2509	0.728847
$773$	20.9174	0.752345	0.376172	−	0.926550i	$-0.377240\pi$
$773$	20.9174	0.752345	0.376172	+	0.926550i	$0.377240\pi$
$774$	−10.3598	−0.372377
$775$	8.56554	0.307683
$776$	17.1882	0.617020
$777$	−31.4334	−1.12767
$778$	6.58357	0.236032
$779$	17.0191	0.609774
$780$	3.65269	0.130787
$781$	−13.3045	−0.476072
$782$	21.6774	0.775182
$783$	7.74870	0.276916
$784$	8.05228	0.287582
$785$	0.955147	0.0340907
$786$	53.2072	1.89784
$787$	5.19602	0.185218	0.0926091	−	0.995703i	$-0.470479\pi$
$787$	5.19602	0.185218	0.0926091	+	0.995703i	$0.470479\pi$
$788$	−16.2491	−0.578850
$789$	−72.4187	−2.57817
$790$	−10.5068	−0.373815
$791$	44.1736	1.57063
$792$	3.34446	0.118840
$793$	14.8416	0.527041
$794$	28.9861	1.02868
$795$	2.14317	0.0760105
$796$	−0.733206	−0.0259878
$797$	29.1140	1.03127	0.515636	−	0.856808i	$-0.327556\pi$
$797$	29.1140	1.03127	0.515636	+	0.856808i	$0.327556\pi$
$798$	−23.2703	−0.823759
$799$	8.83615	0.312600
$800$	1.00000	0.0353553
$801$	−56.6852	−2.00287
$802$	16.2888	0.575177
$803$	−1.00000	−0.0352892
$804$	26.7173	0.942248
$805$	−18.5169	−0.652636
$806$	12.4214	0.437524
$807$	15.0569	0.530028
$808$	−14.0172	−0.493124
$809$	−53.1902	−1.87007	−0.935033	−	0.354560i	$-0.884631\pi$
$809$	−53.1902	−1.87007	−0.935033	+	0.354560i	$0.884631\pi$
$810$	−7.84797	−0.275750
$811$	35.8944	1.26042	0.630212	−	0.776423i	$-0.282968\pi$
$811$	35.8944	1.26042	0.630212	+	0.776423i	$0.282968\pi$
$812$	34.6493	1.21595
$813$	−14.2354	−0.499258
$814$	−3.21657	−0.112741
$815$	−14.7485	−0.516616
$816$	−11.4403	−0.400489
$817$	7.37616	0.258059
$818$	−13.8043	−0.482655
$819$	18.8166	0.657507
$820$	−7.14717	−0.249590
$821$	−43.9304	−1.53318	−0.766591	−	0.642136i	$-0.778048\pi$
$821$	−43.9304	−1.53318	−0.766591	+	0.642136i	$0.778048\pi$
$822$	9.48402	0.330793
$823$	−8.02404	−0.279701	−0.139850	−	0.990173i	$-0.544662\pi$
$823$	−8.02404	−0.279701	−0.139850	+	0.990173i	$0.544662\pi$
$824$	−3.47737	−0.121140
$825$	2.51882	0.0876941
$826$	48.9649	1.70371
$827$	−16.1865	−0.562859	−0.281429	−	0.959582i	$-0.590809\pi$
$827$	−16.1865	−0.562859	−0.281429	+	0.959582i	$0.590809\pi$
$828$	−15.9622	−0.554726
$829$	−38.7480	−1.34577	−0.672887	−	0.739746i	$-0.734946\pi$
$829$	−38.7480	−1.34577	−0.672887	+	0.739746i	$0.734946\pi$
$830$	4.74658	0.164756
$831$	−65.0197	−2.25551
$832$	1.45016	0.0502751
$833$	−36.5728	−1.26717
$834$	−35.1120	−1.21583
$835$	−2.24108	−0.0775559
$836$	−2.38124	−0.0823569
$837$	7.43173	0.256878
$838$	−16.1650	−0.558409
$839$	41.9714	1.44901	0.724507	−	0.689267i	$-0.242067\pi$
$839$	41.9714	1.44901	0.724507	+	0.689267i	$0.242067\pi$
$840$	9.77234	0.337178
$841$	50.7603	1.75036
$842$	−14.7807	−0.509375
$843$	11.6469	0.401140
$844$	−21.3304	−0.734223
$845$	−10.8970	−0.374870
$846$	−6.50654	−0.223699
$847$	3.87973	0.133309
$848$	0.850864	0.0292188
$849$	−63.6997	−2.18617
$850$	−4.54191	−0.155786
$851$	15.3519	0.526255
$852$	−33.5117	−1.14809
$853$	−17.3906	−0.595443	−0.297721	−	0.954653i	$-0.596227\pi$
$853$	−17.3906	−0.595443	−0.297721	+	0.954653i	$0.596227\pi$
$854$	39.7070	1.35874
$855$	−7.96396	−0.272362
$856$	−5.90939	−0.201979
$857$	−26.7253	−0.912918	−0.456459	−	0.889744i	$-0.650883\pi$
$857$	−26.7253	−0.912918	−0.456459	+	0.889744i	$0.650883\pi$
$858$	3.65269	0.124701
$859$	−32.5481	−1.11053	−0.555263	−	0.831675i	$-0.687383\pi$
$859$	−32.5481	−1.11053	−0.555263	+	0.831675i	$0.687383\pi$
$860$	−3.09761	−0.105628
$861$	−69.8446	−2.38030
$862$	11.7435	0.399984
$863$	−33.4170	−1.13753	−0.568765	−	0.822500i	$-0.692578\pi$
$863$	−33.4170	−1.13753	−0.568765	+	0.822500i	$0.692578\pi$
$864$	0.867632	0.0295174
$865$	−11.7394	−0.399152
$866$	6.85291	0.232872
$867$	9.14074	0.310436
$868$	33.2319	1.12797
$869$	−10.5068	−0.356419
$870$	22.4952	0.762660
$871$	15.3819	0.521197
$872$	2.91166	0.0986012
$873$	57.4852	1.94558
$874$	11.3650	0.384428
$875$	3.87973	0.131159
$876$	−2.51882	−0.0851031
$877$	−2.67878	−0.0904561	−0.0452280	−	0.998977i	$-0.514401\pi$
$877$	−2.67878	−0.0904561	−0.0452280	+	0.998977i	$0.514401\pi$
$878$	38.5745	1.30183
$879$	−77.3842	−2.61010
$880$	1.00000	0.0337100
$881$	43.4184	1.46280	0.731401	−	0.681948i	$-0.238867\pi$
$881$	43.4184	1.46280	0.731401	+	0.681948i	$0.238867\pi$
$882$	26.9305	0.906798
$883$	−7.77175	−0.261540	−0.130770	−	0.991413i	$-0.541745\pi$
$883$	−7.77175	−0.261540	−0.130770	+	0.991413i	$0.541745\pi$
$884$	−6.58649	−0.221528
$885$	31.7893	1.06859
$886$	−11.2042	−0.376412
$887$	11.2366	0.377289	0.188645	−	0.982045i	$-0.439591\pi$
$887$	11.2366	0.377289	0.188645	+	0.982045i	$0.439591\pi$
$888$	−8.10196	−0.271884
$889$	32.1653	1.07879
$890$	−16.9490	−0.568132
$891$	−7.84797	−0.262917
$892$	−19.7785	−0.662233
$893$	4.63263	0.155025
$894$	−25.5125	−0.853267
$895$	7.77300	0.259823
$896$	3.87973	0.129613
$897$	−17.4333	−0.582082
$898$	5.98426	0.199697
$899$	76.4976	2.55134
$900$	3.34446	0.111482
$901$	−3.86455	−0.128747
$902$	−7.14717	−0.237975
$903$	−30.2709	−1.00735
$904$	11.3858	0.378685
$905$	−14.7422	−0.490048
$906$	48.1041	1.59815
$907$	37.6164	1.24903	0.624515	−	0.781013i	$-0.285297\pi$
$907$	37.6164	1.24903	0.624515	+	0.781013i	$0.285297\pi$
$908$	3.52074	0.116840
$909$	−46.8800	−1.55491
$910$	5.62621	0.186507
$911$	13.3509	0.442335	0.221168	−	0.975236i	$-0.429013\pi$
$911$	13.3509	0.442335	0.221168	+	0.975236i	$0.429013\pi$
$912$	−5.99792	−0.198611
$913$	4.74658	0.157089
$914$	21.1484	0.699528
$915$	25.7788	0.852221
$916$	6.32114	0.208856
$917$	81.9548	2.70639
$918$	−3.94071	−0.130063
$919$	−19.4685	−0.642205	−0.321103	−	0.947044i	$-0.604053\pi$
$919$	−19.4685	−0.642205	−0.321103	+	0.947044i	$0.604053\pi$
$920$	−4.77274	−0.157353
$921$	74.0362	2.43958
$922$	−32.2488	−1.06206
$923$	−19.2936	−0.635057
$924$	9.77234	0.321486
$925$	−3.21657	−0.105760
$926$	5.16432	0.169710
$927$	−11.6299	−0.381977
$928$	8.93086	0.293170
$929$	1.11246	0.0364988	0.0182494	−	0.999833i	$-0.494191\pi$
$929$	1.11246	0.0364988	0.0182494	+	0.999833i	$0.494191\pi$
$930$	21.5751	0.707474
$931$	−19.1744	−0.628416
$932$	27.2322	0.892020
$933$	−3.80437	−0.124549
$934$	29.7727	0.974193
$935$	−4.54191	−0.148536
$936$	4.84999	0.158527
$937$	3.45790	0.112965	0.0564823	−	0.998404i	$-0.482012\pi$
$937$	3.45790	0.112965	0.0564823	+	0.998404i	$0.482012\pi$
$938$	41.1526	1.34368
$939$	87.2646	2.84777
$940$	−1.94547	−0.0634542
$941$	−43.9117	−1.43148	−0.715740	−	0.698367i	$-0.753911\pi$
$941$	−43.9117	−1.43148	−0.715740	+	0.698367i	$0.753911\pi$
$942$	2.40585	0.0783867
$943$	34.1116	1.11083
$944$	12.6207	0.410769
$945$	3.36617	0.109502
$946$	−3.09761	−0.100712
$947$	53.8777	1.75079	0.875394	−	0.483409i	$-0.160602\pi$
$947$	53.8777	1.75079	0.875394	+	0.483409i	$0.160602\pi$
$948$	−26.4648	−0.859536
$949$	−1.45016	−0.0470741
$950$	−2.38124	−0.0772576
$951$	−83.4347	−2.70556
$952$	−17.6214	−0.571112
$953$	−52.0558	−1.68625	−0.843126	−	0.537716i	$-0.819287\pi$
$953$	−52.0558	−1.68625	−0.843126	+	0.537716i	$0.819287\pi$
$954$	2.84568	0.0921323
$955$	0.583705	0.0188882
$956$	−10.2197	−0.330530
$957$	22.4952	0.727168
$958$	3.69082	0.119245
$959$	14.6082	0.471723
$960$	2.51882	0.0812946
$961$	42.3684	1.36672
$962$	−4.66453	−0.150391
$963$	−19.7637	−0.636876
$964$	−22.2897	−0.717902
$965$	20.2509	0.651900
$966$	−46.6409	−1.50064
$967$	−15.0255	−0.483186	−0.241593	−	0.970378i	$-0.577670\pi$
$967$	−15.0255	−0.483186	−0.241593	+	0.970378i	$0.577670\pi$
$968$	1.00000	0.0321412
$969$	27.2420	0.875140
$970$	17.1882	0.551879
$971$	26.5355	0.851566	0.425783	−	0.904825i	$-0.359999\pi$
$971$	26.5355	0.851566	0.425783	+	0.904825i	$0.359999\pi$
$972$	−22.3705	−0.717535
$973$	−54.0829	−1.73382
$974$	35.0475	1.12300
$975$	3.65269	0.116980
$976$	10.2345	0.327598
$977$	−27.2439	−0.871610	−0.435805	−	0.900041i	$-0.643536\pi$
$977$	−27.2439	−0.871610	−0.435805	+	0.900041i	$0.643536\pi$
$978$	−37.1487	−1.18789
$979$	−16.9490	−0.541692
$980$	8.05228	0.257221
$981$	9.73792	0.310908
$982$	−2.45971	−0.0784926
$983$	52.7984	1.68401	0.842004	−	0.539471i	$-0.181376\pi$
$983$	52.7984	1.68401	0.842004	+	0.539471i	$0.181376\pi$
$984$	−18.0024	−0.573897
$985$	−16.2491	−0.517739
$986$	−40.5632	−1.29180
$987$	−19.0118	−0.605151
$988$	−3.45317	−0.109860
$989$	14.7841	0.470107
$990$	3.34446	0.106294
$991$	−26.9453	−0.855944	−0.427972	−	0.903792i	$-0.640772\pi$
$991$	−26.9453	−0.855944	−0.427972	+	0.903792i	$0.640772\pi$
$992$	8.56554	0.271956
$993$	54.4898	1.72918
$994$	−51.6178	−1.63722
$995$	−0.733206	−0.0232442
$996$	11.9558	0.378834
$997$	26.4842	0.838764	0.419382	−	0.907810i	$-0.362247\pi$
$997$	26.4842	0.838764	0.419382	+	0.907810i	$0.362247\pi$
$998$	−2.92672	−0.0926436
$999$	−2.79080	−0.0882970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.16	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.16	✓	19	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.51882 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.51882 q^{6} +3.87973 q^{7} +1.00000 q^{8} +3.34446 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.51882 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.51882 q^{6} +3.87973 q^{7} +1.00000 q^{8} +3.34446 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.51882 q^{12} +1.45016 q^{13} +3.87973 q^{14} +2.51882 q^{15} +1.00000 q^{16} -4.54191 q^{17} +3.34446 q^{18} -2.38124 q^{19} +1.00000 q^{20} +9.77234 q^{21} +1.00000 q^{22} -4.77274 q^{23} +2.51882 q^{24} +1.00000 q^{25} +1.45016 q^{26} +0.867632 q^{27} +3.87973 q^{28} +8.93086 q^{29} +2.51882 q^{30} +8.56554 q^{31} +1.00000 q^{32} +2.51882 q^{33} -4.54191 q^{34} +3.87973 q^{35} +3.34446 q^{36} -3.21657 q^{37} -2.38124 q^{38} +3.65269 q^{39} +1.00000 q^{40} -7.14717 q^{41} +9.77234 q^{42} -3.09761 q^{43} +1.00000 q^{44} +3.34446 q^{45} -4.77274 q^{46} -1.94547 q^{47} +2.51882 q^{48} +8.05228 q^{49} +1.00000 q^{50} -11.4403 q^{51} +1.45016 q^{52} +0.850864 q^{53} +0.867632 q^{54} +1.00000 q^{55} +3.87973 q^{56} -5.99792 q^{57} +8.93086 q^{58} +12.6207 q^{59} +2.51882 q^{60} +10.2345 q^{61} +8.56554 q^{62} +12.9756 q^{63} +1.00000 q^{64} +1.45016 q^{65} +2.51882 q^{66} +10.6071 q^{67} -4.54191 q^{68} -12.0217 q^{69} +3.87973 q^{70} -13.3045 q^{71} +3.34446 q^{72} -1.00000 q^{73} -3.21657 q^{74} +2.51882 q^{75} -2.38124 q^{76} +3.87973 q^{77} +3.65269 q^{78} -10.5068 q^{79} +1.00000 q^{80} -7.84797 q^{81} -7.14717 q^{82} +4.74658 q^{83} +9.77234 q^{84} -4.54191 q^{85} -3.09761 q^{86} +22.4952 q^{87} +1.00000 q^{88} -16.9490 q^{89} +3.34446 q^{90} +5.62621 q^{91} -4.77274 q^{92} +21.5751 q^{93} -1.94547 q^{94} -2.38124 q^{95} +2.51882 q^{96} +17.1882 q^{97} +8.05228 q^{98} +3.34446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * q^99

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