LMFDB - Embedded newform 6018.2.a.bb.1.11

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 41 x^{11} + 179 x^{10} + 540 x^{9} - 2773 x^{8} - 2260 x^{7} + 17621 x^{6} + \cdots + 128 $ x^13 - 4x^12 - 41x^11 + 179x^10 + 540x^9 - 2773x^8 - 2260x^7 + 17621x^6 - 838x^5 - 44478x^4 + 16472x^3 + 29944x^2 - 6856x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.75551$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75551 q^{5} +1.00000 q^{6} +1.74830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75551 q^{5} +1.00000 q^{6} +1.74830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.75551 q^{10} +6.11375 q^{11} +1.00000 q^{12} -5.30745 q^{13} +1.74830 q^{14} +2.75551 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.22416 q^{19} +2.75551 q^{20} +1.74830 q^{21} +6.11375 q^{22} -7.05140 q^{23} +1.00000 q^{24} +2.59286 q^{25} -5.30745 q^{26} +1.00000 q^{27} +1.74830 q^{28} -2.85793 q^{29} +2.75551 q^{30} -0.451851 q^{31} +1.00000 q^{32} +6.11375 q^{33} +1.00000 q^{34} +4.81746 q^{35} +1.00000 q^{36} -2.31891 q^{37} +4.22416 q^{38} -5.30745 q^{39} +2.75551 q^{40} -4.96402 q^{41} +1.74830 q^{42} +11.3298 q^{43} +6.11375 q^{44} +2.75551 q^{45} -7.05140 q^{46} +10.3589 q^{47} +1.00000 q^{48} -3.94346 q^{49} +2.59286 q^{50} +1.00000 q^{51} -5.30745 q^{52} +8.55286 q^{53} +1.00000 q^{54} +16.8465 q^{55} +1.74830 q^{56} +4.22416 q^{57} -2.85793 q^{58} -1.00000 q^{59} +2.75551 q^{60} -7.55793 q^{61} -0.451851 q^{62} +1.74830 q^{63} +1.00000 q^{64} -14.6247 q^{65} +6.11375 q^{66} +5.93189 q^{67} +1.00000 q^{68} -7.05140 q^{69} +4.81746 q^{70} +7.26473 q^{71} +1.00000 q^{72} -4.37263 q^{73} -2.31891 q^{74} +2.59286 q^{75} +4.22416 q^{76} +10.6886 q^{77} -5.30745 q^{78} +7.90719 q^{79} +2.75551 q^{80} +1.00000 q^{81} -4.96402 q^{82} -4.90741 q^{83} +1.74830 q^{84} +2.75551 q^{85} +11.3298 q^{86} -2.85793 q^{87} +6.11375 q^{88} -14.0099 q^{89} +2.75551 q^{90} -9.27899 q^{91} -7.05140 q^{92} -0.451851 q^{93} +10.3589 q^{94} +11.6397 q^{95} +1.00000 q^{96} -3.80339 q^{97} -3.94346 q^{98} +6.11375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * 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
$5$	2.75551	1.23230	0.616152	−	0.787628i	$-0.288691\pi$
$5$	2.75551	1.23230	0.616152	+	0.787628i	$0.288691\pi$
$6$	1.00000	0.408248
$7$	1.74830	0.660794	0.330397	−	0.943842i	$-0.392817\pi$
$7$	1.74830	0.660794	0.330397	+	0.943842i	$0.392817\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.75551	0.871370
$11$	6.11375	1.84336	0.921682	−	0.387945i	$-0.126815\pi$
$11$	6.11375	1.84336	0.921682	+	0.387945i	$0.126815\pi$
$12$	1.00000	0.288675
$13$	−5.30745	−1.47202	−0.736010	−	0.676970i	$-0.763293\pi$
$13$	−5.30745	−1.47202	−0.736010	+	0.676970i	$0.763293\pi$
$14$	1.74830	0.467252
$15$	2.75551	0.711471
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	4.22416	0.969088	0.484544	−	0.874767i	$-0.338985\pi$
$19$	4.22416	0.969088	0.484544	+	0.874767i	$0.338985\pi$
$20$	2.75551	0.616152
$21$	1.74830	0.381510
$22$	6.11375	1.30346
$23$	−7.05140	−1.47032	−0.735159	−	0.677894i	$-0.762893\pi$
$23$	−7.05140	−1.47032	−0.735159	+	0.677894i	$0.762893\pi$
$24$	1.00000	0.204124
$25$	2.59286	0.518571
$26$	−5.30745	−1.04088
$27$	1.00000	0.192450
$28$	1.74830	0.330397
$29$	−2.85793	−0.530705	−0.265352	−	0.964151i	$-0.585488\pi$
$29$	−2.85793	−0.530705	−0.265352	+	0.964151i	$0.585488\pi$
$30$	2.75551	0.503086
$31$	−0.451851	−0.0811548	−0.0405774	−	0.999176i	$-0.512920\pi$
$31$	−0.451851	−0.0811548	−0.0405774	+	0.999176i	$0.512920\pi$
$32$	1.00000	0.176777
$33$	6.11375	1.06427
$34$	1.00000	0.171499
$35$	4.81746	0.814299
$36$	1.00000	0.166667
$37$	−2.31891	−0.381227	−0.190613	−	0.981665i	$-0.561048\pi$
$37$	−2.31891	−0.381227	−0.190613	+	0.981665i	$0.561048\pi$
$38$	4.22416	0.685249
$39$	−5.30745	−0.849872
$40$	2.75551	0.435685
$41$	−4.96402	−0.775249	−0.387625	−	0.921817i	$-0.626704\pi$
$41$	−4.96402	−0.775249	−0.387625	+	0.921817i	$0.626704\pi$
$42$	1.74830	0.269768
$43$	11.3298	1.72778	0.863891	−	0.503678i	$-0.168020\pi$
$43$	11.3298	1.72778	0.863891	+	0.503678i	$0.168020\pi$
$44$	6.11375	0.921682
$45$	2.75551	0.410768
$46$	−7.05140	−1.03967
$47$	10.3589	1.51100	0.755501	−	0.655148i	$-0.227394\pi$
$47$	10.3589	1.51100	0.755501	+	0.655148i	$0.227394\pi$
$48$	1.00000	0.144338
$49$	−3.94346	−0.563351
$50$	2.59286	0.366685
$51$	1.00000	0.140028
$52$	−5.30745	−0.736010
$53$	8.55286	1.17483	0.587413	−	0.809287i	$-0.300147\pi$
$53$	8.55286	1.17483	0.587413	+	0.809287i	$0.300147\pi$
$54$	1.00000	0.136083
$55$	16.8465	2.27158
$56$	1.74830	0.233626
$57$	4.22416	0.559503
$58$	−2.85793	−0.375265
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.75551	0.355735
$61$	−7.55793	−0.967693	−0.483847	−	0.875153i	$-0.660761\pi$
$61$	−7.55793	−0.967693	−0.483847	+	0.875153i	$0.660761\pi$
$62$	−0.451851	−0.0573851
$63$	1.74830	0.220265
$64$	1.00000	0.125000
$65$	−14.6247	−1.81398
$66$	6.11375	0.752551
$67$	5.93189	0.724696	0.362348	−	0.932043i	$-0.381975\pi$
$67$	5.93189	0.724696	0.362348	+	0.932043i	$0.381975\pi$
$68$	1.00000	0.121268
$69$	−7.05140	−0.848889
$70$	4.81746	0.575796
$71$	7.26473	0.862165	0.431082	−	0.902313i	$-0.358132\pi$
$71$	7.26473	0.862165	0.431082	+	0.902313i	$0.358132\pi$
$72$	1.00000	0.117851
$73$	−4.37263	−0.511777	−0.255889	−	0.966706i	$-0.582368\pi$
$73$	−4.37263	−0.511777	−0.255889	+	0.966706i	$0.582368\pi$
$74$	−2.31891	−0.269568
$75$	2.59286	0.299397
$76$	4.22416	0.484544
$77$	10.6886	1.21808
$78$	−5.30745	−0.600950
$79$	7.90719	0.889629	0.444814	−	0.895623i	$-0.353270\pi$
$79$	7.90719	0.889629	0.444814	+	0.895623i	$0.353270\pi$
$80$	2.75551	0.308076
$81$	1.00000	0.111111
$82$	−4.96402	−0.548184
$83$	−4.90741	−0.538658	−0.269329	−	0.963048i	$-0.586802\pi$
$83$	−4.90741	−0.538658	−0.269329	+	0.963048i	$0.586802\pi$
$84$	1.74830	0.190755
$85$	2.75551	0.298877
$86$	11.3298	1.22173
$87$	−2.85793	−0.306403
$88$	6.11375	0.651728
$89$	−14.0099	−1.48505	−0.742524	−	0.669819i	$-0.766372\pi$
$89$	−14.0099	−1.48505	−0.742524	+	0.669819i	$0.766372\pi$
$90$	2.75551	0.290457
$91$	−9.27899	−0.972703
$92$	−7.05140	−0.735159
$93$	−0.451851	−0.0468548
$94$	10.3589	1.06844
$95$	11.6397	1.19421
$96$	1.00000	0.102062
$97$	−3.80339	−0.386175	−0.193088	−	0.981182i	$-0.561850\pi$
$97$	−3.80339	−0.386175	−0.193088	+	0.981182i	$0.561850\pi$
$98$	−3.94346	−0.398349
$99$	6.11375	0.614455
$100$	2.59286	0.259286
$101$	−10.8784	−1.08244	−0.541221	−	0.840880i	$-0.682038\pi$
$101$	−10.8784	−1.08244	−0.541221	+	0.840880i	$0.682038\pi$
$102$	1.00000	0.0990148
$103$	−12.7785	−1.25911	−0.629554	−	0.776957i	$-0.716762\pi$
$103$	−12.7785	−1.25911	−0.629554	+	0.776957i	$0.716762\pi$
$104$	−5.30745	−0.520438
$105$	4.81746	0.470136
$106$	8.55286	0.830727
$107$	−5.37408	−0.519532	−0.259766	−	0.965672i	$-0.583645\pi$
$107$	−5.37408	−0.519532	−0.259766	+	0.965672i	$0.583645\pi$
$108$	1.00000	0.0962250
$109$	1.84830	0.177035	0.0885173	−	0.996075i	$-0.471787\pi$
$109$	1.84830	0.177035	0.0885173	+	0.996075i	$0.471787\pi$
$110$	16.8465	1.60625
$111$	−2.31891	−0.220101
$112$	1.74830	0.165199
$113$	−12.1954	−1.14725	−0.573624	−	0.819119i	$-0.694463\pi$
$113$	−12.1954	−1.14725	−0.573624	+	0.819119i	$0.694463\pi$
$114$	4.22416	0.395629
$115$	−19.4302	−1.81188
$116$	−2.85793	−0.265352
$117$	−5.30745	−0.490674
$118$	−1.00000	−0.0920575
$119$	1.74830	0.160266
$120$	2.75551	0.251543
$121$	26.3779	2.39799
$122$	−7.55793	−0.684263
$123$	−4.96402	−0.447590
$124$	−0.451851	−0.0405774
$125$	−6.63292	−0.593266
$126$	1.74830	0.155751
$127$	6.62896	0.588225	0.294112	−	0.955771i	$-0.404976\pi$
$127$	6.62896	0.588225	0.294112	+	0.955771i	$0.404976\pi$
$128$	1.00000	0.0883883
$129$	11.3298	0.997536
$130$	−14.6247	−1.28267
$131$	11.8851	1.03841	0.519203	−	0.854651i	$-0.326229\pi$
$131$	11.8851	1.03841	0.519203	+	0.854651i	$0.326229\pi$
$132$	6.11375	0.532134
$133$	7.38508	0.640368
$134$	5.93189	0.512437
$135$	2.75551	0.237157
$136$	1.00000	0.0857493
$137$	−3.13750	−0.268055	−0.134027	−	0.990978i	$-0.542791\pi$
$137$	−3.13750	−0.268055	−0.134027	+	0.990978i	$0.542791\pi$
$138$	−7.05140	−0.600255
$139$	−16.2769	−1.38058	−0.690292	−	0.723531i	$-0.742518\pi$
$139$	−16.2769	−1.38058	−0.690292	+	0.723531i	$0.742518\pi$
$140$	4.81746	0.407149
$141$	10.3589	0.872377
$142$	7.26473	0.609643
$143$	−32.4484	−2.71347
$144$	1.00000	0.0833333
$145$	−7.87507	−0.653989
$146$	−4.37263	−0.361881
$147$	−3.94346	−0.325251
$148$	−2.31891	−0.190613
$149$	−10.9009	−0.893040	−0.446520	−	0.894774i	$-0.647337\pi$
$149$	−10.9009	−0.893040	−0.446520	+	0.894774i	$0.647337\pi$
$150$	2.59286	0.211706
$151$	0.523247	0.0425813	0.0212906	−	0.999773i	$-0.493222\pi$
$151$	0.523247	0.0425813	0.0212906	+	0.999773i	$0.493222\pi$
$152$	4.22416	0.342624
$153$	1.00000	0.0808452
$154$	10.6886	0.861316
$155$	−1.24508	−0.100007
$156$	−5.30745	−0.424936
$157$	13.5324	1.08000	0.540000	−	0.841665i	$-0.318424\pi$
$157$	13.5324	1.08000	0.540000	+	0.841665i	$0.318424\pi$
$158$	7.90719	0.629062
$159$	8.55286	0.678286
$160$	2.75551	0.217842
$161$	−12.3279	−0.971578
$162$	1.00000	0.0785674
$163$	0.0147332	0.00115400	0.000576998	−	1.00000i	$-0.499816\pi$
$163$	0.0147332	0.00115400	0.000576998		1.00000i	$0.499816\pi$
$164$	−4.96402	−0.387625
$165$	16.8465	1.31150
$166$	−4.90741	−0.380889
$167$	−13.7127	−1.06112	−0.530562	−	0.847646i	$-0.678019\pi$
$167$	−13.7127	−1.06112	−0.530562	+	0.847646i	$0.678019\pi$
$168$	1.74830	0.134884
$169$	15.1690	1.16685
$170$	2.75551	0.211338
$171$	4.22416	0.323029
$172$	11.3298	0.863891
$173$	19.7459	1.50125	0.750625	−	0.660729i	$-0.229753\pi$
$173$	19.7459	1.50125	0.750625	+	0.660729i	$0.229753\pi$
$174$	−2.85793	−0.216659
$175$	4.53308	0.342669
$176$	6.11375	0.460841
$177$	−1.00000	−0.0751646
$178$	−14.0099	−1.05009
$179$	−3.47535	−0.259760	−0.129880	−	0.991530i	$-0.541459\pi$
$179$	−3.47535	−0.259760	−0.129880	+	0.991530i	$0.541459\pi$
$180$	2.75551	0.205384
$181$	−17.0838	−1.26983	−0.634913	−	0.772583i	$-0.718964\pi$
$181$	−17.0838	−1.26983	−0.634913	+	0.772583i	$0.718964\pi$
$182$	−9.27899	−0.687805
$183$	−7.55793	−0.558698
$184$	−7.05140	−0.519836
$185$	−6.38980	−0.469787
$186$	−0.451851	−0.0331313
$187$	6.11375	0.447082
$188$	10.3589	0.755501
$189$	1.74830	0.127170
$190$	11.6397	0.844435
$191$	2.50429	0.181204	0.0906020	−	0.995887i	$-0.471121\pi$
$191$	2.50429	0.181204	0.0906020	+	0.995887i	$0.471121\pi$
$192$	1.00000	0.0721688
$193$	23.9106	1.72113	0.860563	−	0.509345i	$-0.170112\pi$
$193$	23.9106	1.72113	0.860563	+	0.509345i	$0.170112\pi$
$194$	−3.80339	−0.273067
$195$	−14.6247	−1.04730
$196$	−3.94346	−0.281676
$197$	−8.45709	−0.602542	−0.301271	−	0.953538i	$-0.597411\pi$
$197$	−8.45709	−0.602542	−0.301271	+	0.953538i	$0.597411\pi$
$198$	6.11375	0.434485
$199$	−1.13729	−0.0806201	−0.0403101	−	0.999187i	$-0.512835\pi$
$199$	−1.13729	−0.0806201	−0.0403101	+	0.999187i	$0.512835\pi$
$200$	2.59286	0.183343
$201$	5.93189	0.418403
$202$	−10.8784	−0.765402
$203$	−4.99652	−0.350687
$204$	1.00000	0.0700140
$205$	−13.6784	−0.955342
$206$	−12.7785	−0.890323
$207$	−7.05140	−0.490106
$208$	−5.30745	−0.368005
$209$	25.8254	1.78638
$210$	4.81746	0.332436
$211$	27.3561	1.88327	0.941636	−	0.336632i	$-0.109288\pi$
$211$	27.3561	1.88327	0.941636	+	0.336632i	$0.109288\pi$
$212$	8.55286	0.587413
$213$	7.26473	0.497771
$214$	−5.37408	−0.367365
$215$	31.2195	2.12915
$216$	1.00000	0.0680414
$217$	−0.789969	−0.0536266
$218$	1.84830	0.125182
$219$	−4.37263	−0.295475
$220$	16.8465	1.13579
$221$	−5.30745	−0.357017
$222$	−2.31891	−0.155635
$223$	8.53493	0.571541	0.285771	−	0.958298i	$-0.407750\pi$
$223$	8.53493	0.571541	0.285771	+	0.958298i	$0.407750\pi$
$224$	1.74830	0.116813
$225$	2.59286	0.172857
$226$	−12.1954	−0.811227
$227$	−27.5578	−1.82907	−0.914536	−	0.404503i	$-0.867444\pi$
$227$	−27.5578	−1.82907	−0.914536	+	0.404503i	$0.867444\pi$
$228$	4.22416	0.279752
$229$	−20.6731	−1.36612	−0.683059	−	0.730364i	$-0.739351\pi$
$229$	−20.6731	−1.36612	−0.683059	+	0.730364i	$0.739351\pi$
$230$	−19.4302	−1.28119
$231$	10.6886	0.703261
$232$	−2.85793	−0.187633
$233$	−14.8729	−0.974358	−0.487179	−	0.873302i	$-0.661974\pi$
$233$	−14.8729	−0.974358	−0.487179	+	0.873302i	$0.661974\pi$
$234$	−5.30745	−0.346959
$235$	28.5441	1.86201
$236$	−1.00000	−0.0650945
$237$	7.90719	0.513627
$238$	1.74830	0.113325
$239$	−7.67894	−0.496709	−0.248355	−	0.968669i	$-0.579890\pi$
$239$	−7.67894	−0.496709	−0.248355	+	0.968669i	$0.579890\pi$
$240$	2.75551	0.177868
$241$	24.5988	1.58455	0.792275	−	0.610164i	$-0.208896\pi$
$241$	24.5988	1.58455	0.792275	+	0.610164i	$0.208896\pi$
$242$	26.3779	1.69564
$243$	1.00000	0.0641500
$244$	−7.55793	−0.483847
$245$	−10.8663	−0.694220
$246$	−4.96402	−0.316494
$247$	−22.4195	−1.42652
$248$	−0.451851	−0.0286926
$249$	−4.90741	−0.310994
$250$	−6.63292	−0.419503
$251$	12.5029	0.789178	0.394589	−	0.918858i	$-0.370887\pi$
$251$	12.5029	0.789178	0.394589	+	0.918858i	$0.370887\pi$
$252$	1.74830	0.110132
$253$	−43.1105	−2.71033
$254$	6.62896	0.415938
$255$	2.75551	0.172557
$256$	1.00000	0.0625000
$257$	20.5732	1.28332	0.641660	−	0.766989i	$-0.278246\pi$
$257$	20.5732	1.28332	0.641660	+	0.766989i	$0.278246\pi$
$258$	11.3298	0.705364
$259$	−4.05415	−0.251912
$260$	−14.6247	−0.906988
$261$	−2.85793	−0.176902
$262$	11.8851	0.734264
$263$	11.4835	0.708104	0.354052	−	0.935226i	$-0.384804\pi$
$263$	11.4835	0.708104	0.354052	+	0.935226i	$0.384804\pi$
$264$	6.11375	0.376275
$265$	23.5675	1.44774
$266$	7.38508	0.452808
$267$	−14.0099	−0.857393
$268$	5.93189	0.362348
$269$	−5.75648	−0.350979	−0.175490	−	0.984481i	$-0.556151\pi$
$269$	−5.75648	−0.350979	−0.175490	+	0.984481i	$0.556151\pi$
$270$	2.75551	0.167695
$271$	−11.6300	−0.706474	−0.353237	−	0.935534i	$-0.614919\pi$
$271$	−11.6300	−0.706474	−0.353237	+	0.935534i	$0.614919\pi$
$272$	1.00000	0.0606339
$273$	−9.27899	−0.561590
$274$	−3.13750	−0.189543
$275$	15.8521	0.955916
$276$	−7.05140	−0.424445
$277$	20.3152	1.22062	0.610311	−	0.792162i	$-0.291045\pi$
$277$	20.3152	1.22062	0.610311	+	0.792162i	$0.291045\pi$
$278$	−16.2769	−0.976221
$279$	−0.451851	−0.0270516
$280$	4.81746	0.287898
$281$	−30.6094	−1.82600	−0.913002	−	0.407954i	$-0.866242\pi$
$281$	−30.6094	−1.82600	−0.913002	+	0.407954i	$0.866242\pi$
$282$	10.3589	0.616864
$283$	−18.9783	−1.12814	−0.564071	−	0.825726i	$-0.690766\pi$
$283$	−18.9783	−1.12814	−0.564071	+	0.825726i	$0.690766\pi$
$284$	7.26473	0.431082
$285$	11.6397	0.689478
$286$	−32.4484	−1.91871
$287$	−8.67858	−0.512280
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−7.87507	−0.462440
$291$	−3.80339	−0.222958
$292$	−4.37263	−0.255889
$293$	7.30981	0.427044	0.213522	−	0.976938i	$-0.431507\pi$
$293$	7.30981	0.427044	0.213522	+	0.976938i	$0.431507\pi$
$294$	−3.94346	−0.229987
$295$	−2.75551	−0.160432
$296$	−2.31891	−0.134784
$297$	6.11375	0.354756
$298$	−10.9009	−0.631475
$299$	37.4249	2.16434
$300$	2.59286	0.149699
$301$	19.8079	1.14171
$302$	0.523247	0.0301095
$303$	−10.8784	−0.624948
$304$	4.22416	0.242272
$305$	−20.8260	−1.19249
$306$	1.00000	0.0571662
$307$	−17.4609	−0.996545	−0.498273	−	0.867020i	$-0.666032\pi$
$307$	−17.4609	−0.996545	−0.498273	+	0.867020i	$0.666032\pi$
$308$	10.6886	0.609042
$309$	−12.7785	−0.726946
$310$	−1.24508	−0.0707159
$311$	19.9113	1.12907	0.564534	−	0.825410i	$-0.309056\pi$
$311$	19.9113	1.12907	0.564534	+	0.825410i	$0.309056\pi$
$312$	−5.30745	−0.300475
$313$	−17.0137	−0.961674	−0.480837	−	0.876810i	$-0.659667\pi$
$313$	−17.0137	−0.961674	−0.480837	+	0.876810i	$0.659667\pi$
$314$	13.5324	0.763676
$315$	4.81746	0.271433
$316$	7.90719	0.444814
$317$	−23.4314	−1.31604	−0.658020	−	0.753000i	$-0.728606\pi$
$317$	−23.4314	−1.31604	−0.658020	+	0.753000i	$0.728606\pi$
$318$	8.55286	0.479621
$319$	−17.4727	−0.978283
$320$	2.75551	0.154038
$321$	−5.37408	−0.299952
$322$	−12.3279	−0.687009
$323$	4.22416	0.235038
$324$	1.00000	0.0555556
$325$	−13.7614	−0.763348
$326$	0.0147332	0.000815999 0
$327$	1.84830	0.102211
$328$	−4.96402	−0.274092
$329$	18.1104	0.998460
$330$	16.8465	0.927370
$331$	14.4892	0.796397	0.398199	−	0.917299i	$-0.369636\pi$
$331$	14.4892	0.796397	0.398199	+	0.917299i	$0.369636\pi$
$332$	−4.90741	−0.269329
$333$	−2.31891	−0.127076
$334$	−13.7127	−0.750328
$335$	16.3454	0.893045
$336$	1.74830	0.0953774
$337$	−5.54188	−0.301885	−0.150943	−	0.988543i	$-0.548231\pi$
$337$	−5.54188	−0.301885	−0.150943	+	0.988543i	$0.548231\pi$
$338$	15.1690	0.825084
$339$	−12.1954	−0.662364
$340$	2.75551	0.149439
$341$	−2.76250	−0.149598
$342$	4.22416	0.228416
$343$	−19.1324	−1.03305
$344$	11.3298	0.610864
$345$	−19.4302	−1.04609
$346$	19.7459	1.06154
$347$	30.2170	1.62213	0.811067	−	0.584953i	$-0.198887\pi$
$347$	30.2170	1.62213	0.811067	+	0.584953i	$0.198887\pi$
$348$	−2.85793	−0.153201
$349$	−18.1544	−0.971783	−0.485891	−	0.874019i	$-0.661505\pi$
$349$	−18.1544	−0.971783	−0.485891	+	0.874019i	$0.661505\pi$
$350$	4.53308	0.242303
$351$	−5.30745	−0.283291
$352$	6.11375	0.325864
$353$	15.9489	0.848876	0.424438	−	0.905457i	$-0.360472\pi$
$353$	15.9489	0.848876	0.424438	+	0.905457i	$0.360472\pi$
$354$	−1.00000	−0.0531494
$355$	20.0181	1.06245
$356$	−14.0099	−0.742524
$357$	1.74830	0.0925297
$358$	−3.47535	−0.183678
$359$	19.1528	1.01084	0.505422	−	0.862872i	$-0.331337\pi$
$359$	19.1528	1.01084	0.505422	+	0.862872i	$0.331337\pi$
$360$	2.75551	0.145228
$361$	−1.15648	−0.0608676
$362$	−17.0838	−0.897903
$363$	26.3779	1.38448
$364$	−9.27899	−0.486351
$365$	−12.0488	−0.630665
$366$	−7.55793	−0.395059
$367$	9.85124	0.514230	0.257115	−	0.966381i	$-0.417228\pi$
$367$	9.85124	0.514230	0.257115	+	0.966381i	$0.417228\pi$
$368$	−7.05140	−0.367580
$369$	−4.96402	−0.258416
$370$	−6.38980	−0.332190
$371$	14.9529	0.776318
$372$	−0.451851	−0.0234274
$373$	−26.4295	−1.36847	−0.684233	−	0.729264i	$-0.739863\pi$
$373$	−26.4295	−1.36847	−0.684233	+	0.729264i	$0.739863\pi$
$374$	6.11375	0.316134
$375$	−6.63292	−0.342522
$376$	10.3589	0.534220
$377$	15.1683	0.781209
$378$	1.74830	0.0899227
$379$	−28.3107	−1.45422	−0.727112	−	0.686519i	$-0.759138\pi$
$379$	−28.3107	−1.45422	−0.727112	+	0.686519i	$0.759138\pi$
$380$	11.6397	0.597105
$381$	6.62896	0.339612
$382$	2.50429	0.128131
$383$	−5.16293	−0.263813	−0.131907	−	0.991262i	$-0.542110\pi$
$383$	−5.16293	−0.263813	−0.131907	+	0.991262i	$0.542110\pi$
$384$	1.00000	0.0510310
$385$	29.4527	1.50105
$386$	23.9106	1.21702
$387$	11.3298	0.575928
$388$	−3.80339	−0.193088
$389$	12.3875	0.628069	0.314035	−	0.949412i	$-0.398319\pi$
$389$	12.3875	0.628069	0.314035	+	0.949412i	$0.398319\pi$
$390$	−14.6247	−0.740553
$391$	−7.05140	−0.356605
$392$	−3.94346	−0.199175
$393$	11.8851	0.599524
$394$	−8.45709	−0.426062
$395$	21.7884	1.09629
$396$	6.11375	0.307227
$397$	−10.1713	−0.510485	−0.255242	−	0.966877i	$-0.582155\pi$
$397$	−10.1713	−0.510485	−0.255242	+	0.966877i	$0.582155\pi$
$398$	−1.13729	−0.0570071
$399$	7.38508	0.369717
$400$	2.59286	0.129643
$401$	15.5217	0.775119	0.387559	−	0.921845i	$-0.373318\pi$
$401$	15.5217	0.775119	0.387559	+	0.921845i	$0.373318\pi$
$402$	5.93189	0.295856
$403$	2.39817	0.119462
$404$	−10.8784	−0.541221
$405$	2.75551	0.136923
$406$	−4.99652	−0.247973
$407$	−14.1773	−0.702740
$408$	1.00000	0.0495074
$409$	4.74254	0.234503	0.117252	−	0.993102i	$-0.462592\pi$
$409$	4.74254	0.234503	0.117252	+	0.993102i	$0.462592\pi$
$410$	−13.6784	−0.675529
$411$	−3.13750	−0.154761
$412$	−12.7785	−0.629554
$413$	−1.74830	−0.0860281
$414$	−7.05140	−0.346557
$415$	−13.5224	−0.663790
$416$	−5.30745	−0.260219
$417$	−16.2769	−0.797081
$418$	25.8254	1.26316
$419$	29.0192	1.41768	0.708841	−	0.705368i	$-0.249218\pi$
$419$	29.0192	1.41768	0.708841	+	0.705368i	$0.249218\pi$
$420$	4.81746	0.235068
$421$	−8.03538	−0.391620	−0.195810	−	0.980642i	$-0.562734\pi$
$421$	−8.03538	−0.391620	−0.195810	+	0.980642i	$0.562734\pi$
$422$	27.3561	1.33167
$423$	10.3589	0.503667
$424$	8.55286	0.415364
$425$	2.59286	0.125772
$426$	7.26473	0.351977
$427$	−13.2135	−0.639446
$428$	−5.37408	−0.259766
$429$	−32.4484	−1.56662
$430$	31.2195	1.50554
$431$	−7.34702	−0.353894	−0.176947	−	0.984220i	$-0.556622\pi$
$431$	−7.34702	−0.353894	−0.176947	+	0.984220i	$0.556622\pi$
$432$	1.00000	0.0481125
$433$	2.50996	0.120621	0.0603104	−	0.998180i	$-0.480791\pi$
$433$	2.50996	0.120621	0.0603104	+	0.998180i	$0.480791\pi$
$434$	−0.789969	−0.0379197
$435$	−7.87507	−0.377581
$436$	1.84830	0.0885173
$437$	−29.7862	−1.42487
$438$	−4.37263	−0.208932
$439$	19.1970	0.916222	0.458111	−	0.888895i	$-0.348526\pi$
$439$	19.1970	0.916222	0.458111	+	0.888895i	$0.348526\pi$
$440$	16.8465	0.803126
$441$	−3.94346	−0.187784
$442$	−5.30745	−0.252449
$443$	−16.9969	−0.807547	−0.403774	−	0.914859i	$-0.632302\pi$
$443$	−16.9969	−0.807547	−0.403774	+	0.914859i	$0.632302\pi$
$444$	−2.31891	−0.110051
$445$	−38.6045	−1.83003
$446$	8.53493	0.404141
$447$	−10.9009	−0.515597
$448$	1.74830	0.0825993
$449$	−21.5289	−1.01601	−0.508006	−	0.861354i	$-0.669617\pi$
$449$	−21.5289	−1.01601	−0.508006	+	0.861354i	$0.669617\pi$
$450$	2.59286	0.122228
$451$	−30.3488	−1.42907
$452$	−12.1954	−0.573624
$453$	0.523247	0.0245843
$454$	−27.5578	−1.29335
$455$	−25.5684	−1.19866
$456$	4.22416	0.197814
$457$	27.3756	1.28058	0.640289	−	0.768134i	$-0.278814\pi$
$457$	27.3756	1.28058	0.640289	+	0.768134i	$0.278814\pi$
$458$	−20.6731	−0.965991
$459$	1.00000	0.0466760
$460$	−19.4302	−0.905939
$461$	14.0377	0.653802	0.326901	−	0.945059i	$-0.393996\pi$
$461$	14.0377	0.653802	0.326901	+	0.945059i	$0.393996\pi$
$462$	10.6886	0.497281
$463$	−20.0988	−0.934072	−0.467036	−	0.884238i	$-0.654678\pi$
$463$	−20.0988	−0.934072	−0.467036	+	0.884238i	$0.654678\pi$
$464$	−2.85793	−0.132676
$465$	−1.24508	−0.0577393
$466$	−14.8729	−0.688975
$467$	18.4254	0.852625	0.426312	−	0.904576i	$-0.359812\pi$
$467$	18.4254	0.852625	0.426312	+	0.904576i	$0.359812\pi$
$468$	−5.30745	−0.245337
$469$	10.3707	0.478875
$470$	28.5441	1.31664
$471$	13.5324	0.623538
$472$	−1.00000	−0.0460287
$473$	69.2677	3.18493
$474$	7.90719	0.363189
$475$	10.9526	0.502541
$476$	1.74830	0.0801330
$477$	8.55286	0.391609
$478$	−7.67894	−0.351227
$479$	−2.58706	−0.118206	−0.0591028	−	0.998252i	$-0.518824\pi$
$479$	−2.58706	−0.118206	−0.0591028	+	0.998252i	$0.518824\pi$
$480$	2.75551	0.125771
$481$	12.3075	0.561174
$482$	24.5988	1.12045
$483$	−12.3279	−0.560941
$484$	26.3779	1.19900
$485$	−10.4803	−0.475885
$486$	1.00000	0.0453609
$487$	30.0533	1.36185	0.680923	−	0.732355i	$-0.261579\pi$
$487$	30.0533	1.36185	0.680923	+	0.732355i	$0.261579\pi$
$488$	−7.55793	−0.342131
$489$	0.0147332	0.000666260 0
$490$	−10.8663	−0.490887
$491$	26.2319	1.18383	0.591915	−	0.806001i	$-0.298372\pi$
$491$	26.2319	1.18383	0.591915	+	0.806001i	$0.298372\pi$
$492$	−4.96402	−0.223795
$493$	−2.85793	−0.128715
$494$	−22.4195	−1.00870
$495$	16.8465	0.757195
$496$	−0.451851	−0.0202887
$497$	12.7009	0.569713
$498$	−4.90741	−0.219906
$499$	−18.1992	−0.814710	−0.407355	−	0.913270i	$-0.633549\pi$
$499$	−18.1992	−0.814710	−0.407355	+	0.913270i	$0.633549\pi$
$500$	−6.63292	−0.296633
$501$	−13.7127	−0.612640
$502$	12.5029	0.558033
$503$	−6.30562	−0.281154	−0.140577	−	0.990070i	$-0.544896\pi$
$503$	−6.30562	−0.281154	−0.140577	+	0.990070i	$0.544896\pi$
$504$	1.74830	0.0778753
$505$	−29.9756	−1.33390
$506$	−43.1105	−1.91650
$507$	15.1690	0.673678
$508$	6.62896	0.294112
$509$	11.9782	0.530925	0.265463	−	0.964121i	$-0.414475\pi$
$509$	11.9782	0.530925	0.265463	+	0.964121i	$0.414475\pi$
$510$	2.75551	0.122016
$511$	−7.64465	−0.338179
$512$	1.00000	0.0441942
$513$	4.22416	0.186501
$514$	20.5732	0.907445
$515$	−35.2115	−1.55160
$516$	11.3298	0.498768
$517$	63.3317	2.78533
$518$	−4.05415	−0.178129
$519$	19.7459	0.866747
$520$	−14.6247	−0.641337
$521$	−6.49326	−0.284475	−0.142237	−	0.989833i	$-0.545430\pi$
$521$	−6.49326	−0.284475	−0.142237	+	0.989833i	$0.545430\pi$
$522$	−2.85793	−0.125088
$523$	−10.7703	−0.470951	−0.235475	−	0.971880i	$-0.575665\pi$
$523$	−10.7703	−0.470951	−0.235475	+	0.971880i	$0.575665\pi$
$524$	11.8851	0.519203
$525$	4.53308	0.197840
$526$	11.4835	0.500705
$527$	−0.451851	−0.0196829
$528$	6.11375	0.266067
$529$	26.7223	1.16184
$530$	23.5675	1.02371
$531$	−1.00000	−0.0433963
$532$	7.38508	0.320184
$533$	26.3463	1.14118
$534$	−14.0099	−0.606269
$535$	−14.8084	−0.640221
$536$	5.93189	0.256219
$537$	−3.47535	−0.149973
$538$	−5.75648	−0.248180
$539$	−24.1093	−1.03846
$540$	2.75551	0.118578
$541$	−19.3553	−0.832150	−0.416075	−	0.909330i	$-0.636595\pi$
$541$	−19.3553	−0.832150	−0.416075	+	0.909330i	$0.636595\pi$
$542$	−11.6300	−0.499552
$543$	−17.0838	−0.733135
$544$	1.00000	0.0428746
$545$	5.09301	0.218160
$546$	−9.27899	−0.397104
$547$	33.5508	1.43453	0.717264	−	0.696801i	$-0.245394\pi$
$547$	33.5508	1.43453	0.717264	+	0.696801i	$0.245394\pi$
$548$	−3.13750	−0.134027
$549$	−7.55793	−0.322564
$550$	15.8521	0.675935
$551$	−12.0724	−0.514300
$552$	−7.05140	−0.300128
$553$	13.8241	0.587861
$554$	20.3152	0.863110
$555$	−6.38980	−0.271232
$556$	−16.2769	−0.690292
$557$	14.0650	0.595952	0.297976	−	0.954573i	$-0.403688\pi$
$557$	14.0650	0.595952	0.297976	+	0.954573i	$0.403688\pi$
$558$	−0.451851	−0.0191284
$559$	−60.1325	−2.54333
$560$	4.81746	0.203575
$561$	6.11375	0.258123
$562$	−30.6094	−1.29118
$563$	15.9081	0.670446	0.335223	−	0.942139i	$-0.391188\pi$
$563$	15.9081	0.670446	0.335223	+	0.942139i	$0.391188\pi$
$564$	10.3589	0.436188
$565$	−33.6046	−1.41376
$566$	−18.9783	−0.797717
$567$	1.74830	0.0734216
$568$	7.26473	0.304821
$569$	−33.0471	−1.38541	−0.692704	−	0.721222i	$-0.743581\pi$
$569$	−33.0471	−1.38541	−0.692704	+	0.721222i	$0.743581\pi$
$570$	11.6397	0.487535
$571$	15.0421	0.629492	0.314746	−	0.949176i	$-0.398081\pi$
$571$	15.0421	0.629492	0.314746	+	0.949176i	$0.398081\pi$
$572$	−32.4484	−1.35674
$573$	2.50429	0.104618
$574$	−8.67858	−0.362237
$575$	−18.2833	−0.762465
$576$	1.00000	0.0416667
$577$	36.9316	1.53748	0.768740	−	0.639561i	$-0.220884\pi$
$577$	36.9316	1.53748	0.768740	+	0.639561i	$0.220884\pi$
$578$	1.00000	0.0415945
$579$	23.9106	0.993692
$580$	−7.87507	−0.326995
$581$	−8.57961	−0.355942
$582$	−3.80339	−0.157655
$583$	52.2900	2.16563
$584$	−4.37263	−0.180941
$585$	−14.6247	−0.604659
$586$	7.30981	0.301966
$587$	29.2270	1.20633	0.603165	−	0.797617i	$-0.293906\pi$
$587$	29.2270	1.20633	0.603165	+	0.797617i	$0.293906\pi$
$588$	−3.94346	−0.162625
$589$	−1.90869	−0.0786462
$590$	−2.75551	−0.113443
$591$	−8.45709	−0.347878
$592$	−2.31891	−0.0953067
$593$	−21.9786	−0.902553	−0.451277	−	0.892384i	$-0.649031\pi$
$593$	−21.9786	−0.902553	−0.451277	+	0.892384i	$0.649031\pi$
$594$	6.11375	0.250850
$595$	4.81746	0.197496
$596$	−10.9009	−0.446520
$597$	−1.13729	−0.0465461
$598$	37.4249	1.53042
$599$	−39.8998	−1.63026	−0.815130	−	0.579278i	$-0.803334\pi$
$599$	−39.8998	−1.63026	−0.815130	+	0.579278i	$0.803334\pi$
$600$	2.59286	0.105853
$601$	−16.8732	−0.688272	−0.344136	−	0.938920i	$-0.611828\pi$
$601$	−16.8732	−0.688272	−0.344136	+	0.938920i	$0.611828\pi$
$602$	19.8079	0.807310
$603$	5.93189	0.241565
$604$	0.523247	0.0212906
$605$	72.6848	2.95506
$606$	−10.8784	−0.441905
$607$	−13.8851	−0.563579	−0.281790	−	0.959476i	$-0.590928\pi$
$607$	−13.8851	−0.563579	−0.281790	+	0.959476i	$0.590928\pi$
$608$	4.22416	0.171312
$609$	−4.99652	−0.202469
$610$	−20.8260	−0.843219
$611$	−54.9793	−2.22423
$612$	1.00000	0.0404226
$613$	−44.3627	−1.79179	−0.895897	−	0.444261i	$-0.853466\pi$
$613$	−44.3627	−1.79179	−0.895897	+	0.444261i	$0.853466\pi$
$614$	−17.4609	−0.704664
$615$	−13.6784	−0.551567
$616$	10.6886	0.430658
$617$	39.1172	1.57480	0.787400	−	0.616443i	$-0.211427\pi$
$617$	39.1172	1.57480	0.787400	+	0.616443i	$0.211427\pi$
$618$	−12.7785	−0.514028
$619$	−2.20185	−0.0885000	−0.0442500	−	0.999020i	$-0.514090\pi$
$619$	−2.20185	−0.0885000	−0.0442500	+	0.999020i	$0.514090\pi$
$620$	−1.24508	−0.0500037
$621$	−7.05140	−0.282963
$622$	19.9113	0.798371
$623$	−24.4935	−0.981311
$624$	−5.30745	−0.212468
$625$	−31.2414	−1.24966
$626$	−17.0137	−0.680006
$627$	25.8254	1.03137
$628$	13.5324	0.540000
$629$	−2.31891	−0.0924611
$630$	4.81746	0.191932
$631$	8.59451	0.342142	0.171071	−	0.985259i	$-0.445277\pi$
$631$	8.59451	0.342142	0.171071	+	0.985259i	$0.445277\pi$
$632$	7.90719	0.314531
$633$	27.3561	1.08731
$634$	−23.4314	−0.930582
$635$	18.2662	0.724871
$636$	8.55286	0.339143
$637$	20.9297	0.829265
$638$	−17.4727	−0.691750
$639$	7.26473	0.287388
$640$	2.75551	0.108921
$641$	34.9422	1.38013	0.690067	−	0.723745i	$-0.257581\pi$
$641$	34.9422	1.38013	0.690067	+	0.723745i	$0.257581\pi$
$642$	−5.37408	−0.212098
$643$	−21.0006	−0.828182	−0.414091	−	0.910235i	$-0.635900\pi$
$643$	−21.0006	−0.828182	−0.414091	+	0.910235i	$0.635900\pi$
$644$	−12.3279	−0.485789
$645$	31.2195	1.22927
$646$	4.22416	0.166197
$647$	11.4818	0.451397	0.225698	−	0.974197i	$-0.427534\pi$
$647$	11.4818	0.451397	0.225698	+	0.974197i	$0.427534\pi$
$648$	1.00000	0.0392837
$649$	−6.11375	−0.239986
$650$	−13.7614	−0.539768
$651$	−0.789969	−0.0309613
$652$	0.0147332	0.000576998 0
$653$	−12.1928	−0.477141	−0.238571	−	0.971125i	$-0.576679\pi$
$653$	−12.1928	−0.477141	−0.238571	+	0.971125i	$0.576679\pi$
$654$	1.84830	0.0722741
$655$	32.7496	1.27963
$656$	−4.96402	−0.193812
$657$	−4.37263	−0.170592
$658$	18.1104	0.706018
$659$	−22.0212	−0.857825	−0.428913	−	0.903346i	$-0.641103\pi$
$659$	−22.0212	−0.857825	−0.428913	+	0.903346i	$0.641103\pi$
$660$	16.8465	0.655750
$661$	−22.7873	−0.886325	−0.443162	−	0.896441i	$-0.646143\pi$
$661$	−22.7873	−0.886325	−0.443162	+	0.896441i	$0.646143\pi$
$662$	14.4892	0.563138
$663$	−5.30745	−0.206124
$664$	−4.90741	−0.190444
$665$	20.3497	0.789127
$666$	−2.31891	−0.0898561
$667$	20.1524	0.780305
$668$	−13.7127	−0.530562
$669$	8.53493	0.329980
$670$	16.3454	0.631478
$671$	−46.2073	−1.78381
$672$	1.74830	0.0674420
$673$	9.08940	0.350371	0.175185	−	0.984535i	$-0.443948\pi$
$673$	9.08940	0.350371	0.175185	+	0.984535i	$0.443948\pi$
$674$	−5.54188	−0.213465
$675$	2.59286	0.0997991
$676$	15.1690	0.583423
$677$	−19.2308	−0.739099	−0.369549	−	0.929211i	$-0.620488\pi$
$677$	−19.2308	−0.739099	−0.369549	+	0.929211i	$0.620488\pi$
$678$	−12.1954	−0.468362
$679$	−6.64945	−0.255182
$680$	2.75551	0.105669
$681$	−27.5578	−1.05602
$682$	−2.76250	−0.105782
$683$	−35.4334	−1.35582	−0.677911	−	0.735144i	$-0.737115\pi$
$683$	−35.4334	−1.35582	−0.677911	+	0.735144i	$0.737115\pi$
$684$	4.22416	0.161515
$685$	−8.64542	−0.330324
$686$	−19.1324	−0.730479
$687$	−20.6731	−0.788728
$688$	11.3298	0.431946
$689$	−45.3938	−1.72937
$690$	−19.4302	−0.739696
$691$	13.0730	0.497320	0.248660	−	0.968591i	$-0.420010\pi$
$691$	13.0730	0.497320	0.248660	+	0.968591i	$0.420010\pi$
$692$	19.7459	0.750625
$693$	10.6886	0.406028
$694$	30.2170	1.14702
$695$	−44.8511	−1.70130
$696$	−2.85793	−0.108330
$697$	−4.96402	−0.188026
$698$	−18.1544	−0.687154
$699$	−14.8729	−0.562546
$700$	4.53308	0.171334
$701$	−36.8460	−1.39165	−0.695827	−	0.718209i	$-0.744962\pi$
$701$	−36.8460	−1.39165	−0.695827	+	0.718209i	$0.744962\pi$
$702$	−5.30745	−0.200317
$703$	−9.79546	−0.369443
$704$	6.11375	0.230421
$705$	28.5441	1.07503
$706$	15.9489	0.600246
$707$	−19.0187	−0.715271
$708$	−1.00000	−0.0375823
$709$	−4.42879	−0.166327	−0.0831634	−	0.996536i	$-0.526502\pi$
$709$	−4.42879	−0.166327	−0.0831634	+	0.996536i	$0.526502\pi$
$710$	20.0181	0.751265
$711$	7.90719	0.296543
$712$	−14.0099	−0.525044
$713$	3.18618	0.119323
$714$	1.74830	0.0654284
$715$	−89.4120	−3.34382
$716$	−3.47535	−0.129880
$717$	−7.67894	−0.286775
$718$	19.1528	0.714775
$719$	−20.7815	−0.775020	−0.387510	−	0.921866i	$-0.626665\pi$
$719$	−20.7815	−0.775020	−0.387510	+	0.921866i	$0.626665\pi$
$720$	2.75551	0.102692
$721$	−22.3407	−0.832011
$722$	−1.15648	−0.0430399
$723$	24.5988	0.914841
$724$	−17.0838	−0.634913
$725$	−7.41021	−0.275208
$726$	26.3779	0.978977
$727$	−4.12031	−0.152814	−0.0764069	−	0.997077i	$-0.524345\pi$
$727$	−4.12031	−0.152814	−0.0764069	+	0.997077i	$0.524345\pi$
$728$	−9.27899	−0.343902
$729$	1.00000	0.0370370
$730$	−12.0488	−0.445947
$731$	11.3298	0.419049
$732$	−7.55793	−0.279349
$733$	−24.5619	−0.907216	−0.453608	−	0.891201i	$-0.649863\pi$
$733$	−24.5619	−0.907216	−0.453608	+	0.891201i	$0.649863\pi$
$734$	9.85124	0.363616
$735$	−10.8663	−0.400808
$736$	−7.05140	−0.259918
$737$	36.2661	1.33588
$738$	−4.96402	−0.182728
$739$	6.02839	0.221758	0.110879	−	0.993834i	$-0.464633\pi$
$739$	6.02839	0.221758	0.110879	+	0.993834i	$0.464633\pi$
$740$	−6.38980	−0.234894
$741$	−22.4195	−0.823601
$742$	14.9529	0.548940
$743$	43.9652	1.61293	0.806464	−	0.591284i	$-0.201379\pi$
$743$	43.9652	1.61293	0.806464	+	0.591284i	$0.201379\pi$
$744$	−0.451851	−0.0165657
$745$	−30.0377	−1.10050
$746$	−26.4295	−0.967651
$747$	−4.90741	−0.179553
$748$	6.11375	0.223541
$749$	−9.39549	−0.343304
$750$	−6.63292	−0.242200
$751$	−41.0344	−1.49737	−0.748683	−	0.662928i	$-0.769314\pi$
$751$	−41.0344	−1.49737	−0.748683	+	0.662928i	$0.769314\pi$
$752$	10.3589	0.377750
$753$	12.5029	0.455632
$754$	15.1683	0.552398
$755$	1.44182	0.0524730
$756$	1.74830	0.0635849
$757$	3.21947	0.117014	0.0585069	−	0.998287i	$-0.481366\pi$
$757$	3.21947	0.117014	0.0585069	+	0.998287i	$0.481366\pi$
$758$	−28.3107	−1.02829
$759$	−43.1105	−1.56481
$760$	11.6397	0.422217
$761$	12.4382	0.450883	0.225442	−	0.974257i	$-0.427618\pi$
$761$	12.4382	0.450883	0.225442	+	0.974257i	$0.427618\pi$
$762$	6.62896	0.240142
$763$	3.23137	0.116983
$764$	2.50429	0.0906020
$765$	2.75551	0.0996258
$766$	−5.16293	−0.186544
$767$	5.30745	0.191641
$768$	1.00000	0.0360844
$769$	13.2952	0.479438	0.239719	−	0.970842i	$-0.422945\pi$
$769$	13.2952	0.479438	0.239719	+	0.970842i	$0.422945\pi$
$770$	29.4527	1.06140
$771$	20.5732	0.740925
$772$	23.9106	0.860563
$773$	−20.5187	−0.738007	−0.369003	−	0.929428i	$-0.620301\pi$
$773$	−20.5187	−0.738007	−0.369003	+	0.929428i	$0.620301\pi$
$774$	11.3298	0.407242
$775$	−1.17158	−0.0420845
$776$	−3.80339	−0.136534
$777$	−4.05415	−0.145442
$778$	12.3875	0.444112
$779$	−20.9688	−0.751285
$780$	−14.6247	−0.523650
$781$	44.4147	1.58928
$782$	−7.05140	−0.252158
$783$	−2.85793	−0.102134
$784$	−3.94346	−0.140838
$785$	37.2886	1.33089
$786$	11.8851	0.423928
$787$	20.5141	0.731249	0.365625	−	0.930762i	$-0.380855\pi$
$787$	20.5141	0.731249	0.365625	+	0.930762i	$0.380855\pi$
$788$	−8.45709	−0.301271
$789$	11.4835	0.408824
$790$	21.7884	0.775196
$791$	−21.3212	−0.758095
$792$	6.11375	0.217243
$793$	40.1133	1.42446
$794$	−10.1713	−0.360967
$795$	23.5675	0.835854
$796$	−1.13729	−0.0403101
$797$	40.2596	1.42607	0.713035	−	0.701129i	$-0.247320\pi$
$797$	40.2596	1.42607	0.713035	+	0.701129i	$0.247320\pi$
$798$	7.38508	0.261429
$799$	10.3589	0.366472
$800$	2.59286	0.0916713
$801$	−14.0099	−0.495016
$802$	15.5217	0.548092
$803$	−26.7331	−0.943392
$804$	5.93189	0.209202
$805$	−33.9698	−1.19728
$806$	2.39817	0.0844721
$807$	−5.75648	−0.202638
$808$	−10.8784	−0.382701
$809$	10.0850	0.354568	0.177284	−	0.984160i	$-0.443269\pi$
$809$	10.0850	0.354568	0.177284	+	0.984160i	$0.443269\pi$
$810$	2.75551	0.0968189
$811$	−34.1850	−1.20040	−0.600198	−	0.799851i	$-0.704912\pi$
$811$	−34.1850	−1.20040	−0.600198	+	0.799851i	$0.704912\pi$
$812$	−4.99652	−0.175343
$813$	−11.6300	−0.407883
$814$	−14.1773	−0.496912
$815$	0.0405976	0.00142207
$816$	1.00000	0.0350070
$817$	47.8590	1.67437
$818$	4.74254	0.165819
$819$	−9.27899	−0.324234
$820$	−13.6784	−0.477671
$821$	32.3707	1.12974	0.564872	−	0.825179i	$-0.308926\pi$
$821$	32.3707	1.12974	0.564872	+	0.825179i	$0.308926\pi$
$822$	−3.13750	−0.109433
$823$	−48.4311	−1.68820	−0.844101	−	0.536184i	$-0.819865\pi$
$823$	−48.4311	−1.68820	−0.844101	+	0.536184i	$0.819865\pi$
$824$	−12.7785	−0.445162
$825$	15.8521	0.551898
$826$	−1.74830	−0.0608310
$827$	38.6456	1.34384	0.671920	−	0.740624i	$-0.265470\pi$
$827$	38.6456	1.34384	0.671920	+	0.740624i	$0.265470\pi$
$828$	−7.05140	−0.245053
$829$	25.5050	0.885824	0.442912	−	0.896565i	$-0.353945\pi$
$829$	25.5050	0.885824	0.442912	+	0.896565i	$0.353945\pi$
$830$	−13.5224	−0.469371
$831$	20.3152	0.704726
$832$	−5.30745	−0.184003
$833$	−3.94346	−0.136633
$834$	−16.2769	−0.563621
$835$	−37.7856	−1.30763
$836$	25.8254	0.893192
$837$	−0.451851	−0.0156183
$838$	29.0192	1.00245
$839$	−29.6052	−1.02208	−0.511042	−	0.859556i	$-0.670740\pi$
$839$	−29.6052	−1.02208	−0.511042	+	0.859556i	$0.670740\pi$
$840$	4.81746	0.166218
$841$	−20.8322	−0.718352
$842$	−8.03538	−0.276917
$843$	−30.6094	−1.05424
$844$	27.3561	0.941636
$845$	41.7984	1.43791
$846$	10.3589	0.356146
$847$	46.1165	1.58458
$848$	8.55286	0.293706
$849$	−18.9783	−0.651333
$850$	2.59286	0.0889342
$851$	16.3516	0.560525
$852$	7.26473	0.248886
$853$	−24.6258	−0.843170	−0.421585	−	0.906789i	$-0.638526\pi$
$853$	−24.6258	−0.843170	−0.421585	+	0.906789i	$0.638526\pi$
$854$	−13.2135	−0.452157
$855$	11.6397	0.398070
$856$	−5.37408	−0.183682
$857$	18.6781	0.638031	0.319016	−	0.947749i	$-0.396648\pi$
$857$	18.6781	0.638031	0.319016	+	0.947749i	$0.396648\pi$
$858$	−32.4484	−1.10777
$859$	26.1135	0.890980	0.445490	−	0.895287i	$-0.353030\pi$
$859$	26.1135	0.890980	0.445490	+	0.895287i	$0.353030\pi$
$860$	31.2195	1.06458
$861$	−8.67858	−0.295765
$862$	−7.34702	−0.250241
$863$	43.6170	1.48474	0.742370	−	0.669990i	$-0.233702\pi$
$863$	43.6170	1.48474	0.742370	+	0.669990i	$0.233702\pi$
$864$	1.00000	0.0340207
$865$	54.4100	1.84999
$866$	2.50996	0.0852918
$867$	1.00000	0.0339618
$868$	−0.789969	−0.0268133
$869$	48.3426	1.63991
$870$	−7.87507	−0.266990
$871$	−31.4832	−1.06677
$872$	1.84830	0.0625912
$873$	−3.80339	−0.128725
$874$	−29.7862	−1.00753
$875$	−11.5963	−0.392027
$876$	−4.37263	−0.147737
$877$	−6.72907	−0.227224	−0.113612	−	0.993525i	$-0.536242\pi$
$877$	−6.72907	−0.227224	−0.113612	+	0.993525i	$0.536242\pi$
$878$	19.1970	0.647867
$879$	7.30981	0.246554
$880$	16.8465	0.567896
$881$	49.7499	1.67612	0.838058	−	0.545581i	$-0.183691\pi$
$881$	49.7499	1.67612	0.838058	+	0.545581i	$0.183691\pi$
$882$	−3.94346	−0.132783
$883$	32.0109	1.07725	0.538626	−	0.842545i	$-0.318943\pi$
$883$	32.0109	1.07725	0.538626	+	0.842545i	$0.318943\pi$
$884$	−5.30745	−0.178509
$885$	−2.75551	−0.0926256
$886$	−16.9969	−0.571022
$887$	11.3447	0.380918	0.190459	−	0.981695i	$-0.439002\pi$
$887$	11.3447	0.380918	0.190459	+	0.981695i	$0.439002\pi$
$888$	−2.31891	−0.0778176
$889$	11.5894	0.388695
$890$	−38.6045	−1.29403
$891$	6.11375	0.204818
$892$	8.53493	0.285771
$893$	43.7576	1.46429
$894$	−10.9009	−0.364582
$895$	−9.57638	−0.320103
$896$	1.74830	0.0584065
$897$	37.4249	1.24958
$898$	−21.5289	−0.718428
$899$	1.29136	0.0430693
$900$	2.59286	0.0864285
$901$	8.55286	0.284937
$902$	−30.3488	−1.01050
$903$	19.8079	0.659166
$904$	−12.1954	−0.405614
$905$	−47.0746	−1.56481
$906$	0.523247	0.0173837
$907$	−32.2266	−1.07007	−0.535034	−	0.844831i	$-0.679701\pi$
$907$	−32.2266	−1.07007	−0.535034	+	0.844831i	$0.679701\pi$
$908$	−27.5578	−0.914536
$909$	−10.8784	−0.360814
$910$	−25.5684	−0.847584
$911$	16.9541	0.561716	0.280858	−	0.959749i	$-0.409381\pi$
$911$	16.9541	0.561716	0.280858	+	0.959749i	$0.409381\pi$
$912$	4.22416	0.139876
$913$	−30.0027	−0.992944
$914$	27.3756	0.905506
$915$	−20.8260	−0.688485
$916$	−20.6731	−0.683059
$917$	20.7787	0.686173
$918$	1.00000	0.0330049
$919$	−43.5259	−1.43579	−0.717894	−	0.696152i	$-0.754894\pi$
$919$	−43.5259	−1.43579	−0.717894	+	0.696152i	$0.754894\pi$
$920$	−19.4302	−0.640596
$921$	−17.4609	−0.575356
$922$	14.0377	0.462308
$923$	−38.5572	−1.26912
$924$	10.6886	0.351631
$925$	−6.01261	−0.197693
$926$	−20.0988	−0.660489
$927$	−12.7785	−0.419702
$928$	−2.85793	−0.0938163
$929$	12.1966	0.400158	0.200079	−	0.979780i	$-0.435880\pi$
$929$	12.1966	0.400158	0.200079	+	0.979780i	$0.435880\pi$
$930$	−1.24508	−0.0408278
$931$	−16.6578	−0.545937
$932$	−14.8729	−0.487179
$933$	19.9113	0.651867
$934$	18.4254	0.602897
$935$	16.8465	0.550940
$936$	−5.30745	−0.173479
$937$	21.0281	0.686957	0.343479	−	0.939161i	$-0.388395\pi$
$937$	21.0281	0.686957	0.343479	+	0.939161i	$0.388395\pi$
$938$	10.3707	0.338616
$939$	−17.0137	−0.555223
$940$	28.5441	0.931006
$941$	−45.6548	−1.48830	−0.744152	−	0.668010i	$-0.767146\pi$
$941$	−45.6548	−1.48830	−0.744152	+	0.668010i	$0.767146\pi$
$942$	13.5324	0.440908
$943$	35.0033	1.13986
$944$	−1.00000	−0.0325472
$945$	4.81746	0.156712
$946$	69.2677	2.25209
$947$	−15.1126	−0.491092	−0.245546	−	0.969385i	$-0.578967\pi$
$947$	−15.1126	−0.491092	−0.245546	+	0.969385i	$0.578967\pi$
$948$	7.90719	0.256814
$949$	23.2075	0.753347
$950$	10.9526	0.355350
$951$	−23.4314	−0.759817
$952$	1.74830	0.0566626
$953$	7.42899	0.240648	0.120324	−	0.992735i	$-0.461607\pi$
$953$	7.42899	0.240648	0.120324	+	0.992735i	$0.461607\pi$
$954$	8.55286	0.276909
$955$	6.90060	0.223298
$956$	−7.67894	−0.248355
$957$	−17.4727	−0.564812
$958$	−2.58706	−0.0835840
$959$	−5.48528	−0.177129
$960$	2.75551	0.0889338
$961$	−30.7958	−0.993414
$962$	12.3075	0.396810
$963$	−5.37408	−0.173177
$964$	24.5988	0.792275
$965$	65.8861	2.12095
$966$	−12.3279	−0.396645
$967$	15.1910	0.488509	0.244254	−	0.969711i	$-0.421457\pi$
$967$	15.1910	0.488509	0.244254	+	0.969711i	$0.421457\pi$
$968$	26.3779	0.847819
$969$	4.22416	0.135700
$970$	−10.4803	−0.336502
$971$	20.4268	0.655528	0.327764	−	0.944760i	$-0.393705\pi$
$971$	20.4268	0.655528	0.327764	+	0.944760i	$0.393705\pi$
$972$	1.00000	0.0320750
$973$	−28.4568	−0.912282
$974$	30.0533	0.962971
$975$	−13.7614	−0.440719
$976$	−7.55793	−0.241923
$977$	27.4372	0.877794	0.438897	−	0.898537i	$-0.355369\pi$
$977$	27.4372	0.877794	0.438897	+	0.898537i	$0.355369\pi$
$978$	0.0147332	0.000471117 0
$979$	−85.6531	−2.73749
$980$	−10.8663	−0.347110
$981$	1.84830	0.0590116
$982$	26.2319	0.837094
$983$	−25.1747	−0.802947	−0.401474	−	0.915871i	$-0.631502\pi$
$983$	−25.1747	−0.802947	−0.401474	+	0.915871i	$0.631502\pi$
$984$	−4.96402	−0.158247
$985$	−23.3036	−0.742515
$986$	−2.85793	−0.0910151
$987$	18.1104	0.576461
$988$	−22.4195	−0.713259
$989$	−79.8912	−2.54039
$990$	16.8465	0.535418
$991$	15.6222	0.496257	0.248128	−	0.968727i	$-0.420184\pi$
$991$	15.6222	0.496257	0.248128	+	0.968727i	$0.420184\pi$
$992$	−0.451851	−0.0143463
$993$	14.4892	0.459800
$994$	12.7009	0.402848
$995$	−3.13381	−0.0993485
$996$	−4.90741	−0.155497
$997$	25.1421	0.796258	0.398129	−	0.917329i	$-0.369660\pi$
$997$	25.1421	0.796258	0.398129	+	0.917329i	$0.369660\pi$
$998$	−18.1992	−0.576087
$999$	−2.31891	−0.0733672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.bb.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.bb.1.11	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75551 q^{5} +1.00000 q^{6} +1.74830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75551 q^{5} +1.00000 q^{6} +1.74830 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.75551 q^{10} +6.11375 q^{11} +1.00000 q^{12} -5.30745 q^{13} +1.74830 q^{14} +2.75551 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.22416 q^{19} +2.75551 q^{20} +1.74830 q^{21} +6.11375 q^{22} -7.05140 q^{23} +1.00000 q^{24} +2.59286 q^{25} -5.30745 q^{26} +1.00000 q^{27} +1.74830 q^{28} -2.85793 q^{29} +2.75551 q^{30} -0.451851 q^{31} +1.00000 q^{32} +6.11375 q^{33} +1.00000 q^{34} +4.81746 q^{35} +1.00000 q^{36} -2.31891 q^{37} +4.22416 q^{38} -5.30745 q^{39} +2.75551 q^{40} -4.96402 q^{41} +1.74830 q^{42} +11.3298 q^{43} +6.11375 q^{44} +2.75551 q^{45} -7.05140 q^{46} +10.3589 q^{47} +1.00000 q^{48} -3.94346 q^{49} +2.59286 q^{50} +1.00000 q^{51} -5.30745 q^{52} +8.55286 q^{53} +1.00000 q^{54} +16.8465 q^{55} +1.74830 q^{56} +4.22416 q^{57} -2.85793 q^{58} -1.00000 q^{59} +2.75551 q^{60} -7.55793 q^{61} -0.451851 q^{62} +1.74830 q^{63} +1.00000 q^{64} -14.6247 q^{65} +6.11375 q^{66} +5.93189 q^{67} +1.00000 q^{68} -7.05140 q^{69} +4.81746 q^{70} +7.26473 q^{71} +1.00000 q^{72} -4.37263 q^{73} -2.31891 q^{74} +2.59286 q^{75} +4.22416 q^{76} +10.6886 q^{77} -5.30745 q^{78} +7.90719 q^{79} +2.75551 q^{80} +1.00000 q^{81} -4.96402 q^{82} -4.90741 q^{83} +1.74830 q^{84} +2.75551 q^{85} +11.3298 q^{86} -2.85793 q^{87} +6.11375 q^{88} -14.0099 q^{89} +2.75551 q^{90} -9.27899 q^{91} -7.05140 q^{92} -0.451851 q^{93} +10.3589 q^{94} +11.6397 q^{95} +1.00000 q^{96} -3.80339 q^{97} -3.94346 q^{98} +6.11375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 4 q^{5} + 13 q^{6} + 11 q^{7} + 13 q^{8} + 13 q^{9} + 4 q^{10} + 7 q^{11} + 13 q^{12} + 6 q^{13} + 11 q^{14} + 4 q^{15} + 13 q^{16} + 13 q^{17} + 13 q^{18} + 9 q^{19} + 4 q^{20} + 11 q^{21} + 7 q^{22} + 2 q^{23} + 13 q^{24} + 33 q^{25} + 6 q^{26} + 13 q^{27} + 11 q^{28} + 14 q^{29} + 4 q^{30} - 5 q^{31} + 13 q^{32} + 7 q^{33} + 13 q^{34} + 24 q^{35} + 13 q^{36} + 4 q^{37} + 9 q^{38} + 6 q^{39} + 4 q^{40} + 28 q^{41} + 11 q^{42} + q^{43} + 7 q^{44} + 4 q^{45} + 2 q^{46} + 12 q^{47} + 13 q^{48} + 32 q^{49} + 33 q^{50} + 13 q^{51} + 6 q^{52} + 22 q^{53} + 13 q^{54} - 7 q^{55} + 11 q^{56} + 9 q^{57} + 14 q^{58} - 13 q^{59} + 4 q^{60} - 9 q^{61} - 5 q^{62} + 11 q^{63} + 13 q^{64} + 34 q^{65} + 7 q^{66} + 26 q^{67} + 13 q^{68} + 2 q^{69} + 24 q^{70} + 8 q^{71} + 13 q^{72} + 4 q^{73} + 4 q^{74} + 33 q^{75} + 9 q^{76} + 38 q^{77} + 6 q^{78} - 17 q^{79} + 4 q^{80} + 13 q^{81} + 28 q^{82} + 14 q^{83} + 11 q^{84} + 4 q^{85} + q^{86} + 14 q^{87} + 7 q^{88} + 19 q^{89} + 4 q^{90} - 5 q^{91} + 2 q^{92} - 5 q^{93} + 12 q^{94} + 25 q^{95} + 13 q^{96} - 5 q^{97} + 32 q^{98} + 7 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 4 * q^5 + 13 * q^6 + 11 * q^7 + 13 * q^8 + 13 * q^9 + 4 * q^10 + 7 * q^11 + 13 * q^12 + 6 * q^13 + 11 * q^14 + 4 * q^15 + 13 * q^16 + 13 * q^17 + 13 * q^18 + 9 * q^19 + 4 * q^20 + 11 * q^21 + 7 * q^22 + 2 * q^23 + 13 * q^24 + 33 * q^25 + 6 * q^26 + 13 * q^27 + 11 * q^28 + 14 * q^29 + 4 * q^30 - 5 * q^31 + 13 * q^32 + 7 * q^33 + 13 * q^34 + 24 * q^35 + 13 * q^36 + 4 * q^37 + 9 * q^38 + 6 * q^39 + 4 * q^40 + 28 * q^41 + 11 * q^42 + q^43 + 7 * q^44 + 4 * q^45 + 2 * q^46 + 12 * q^47 + 13 * q^48 + 32 * q^49 + 33 * q^50 + 13 * q^51 + 6 * q^52 + 22 * q^53 + 13 * q^54 - 7 * q^55 + 11 * q^56 + 9 * q^57 + 14 * q^58 - 13 * q^59 + 4 * q^60 - 9 * q^61 - 5 * q^62 + 11 * q^63 + 13 * q^64 + 34 * q^65 + 7 * q^66 + 26 * q^67 + 13 * q^68 + 2 * q^69 + 24 * q^70 + 8 * q^71 + 13 * q^72 + 4 * q^73 + 4 * q^74 + 33 * q^75 + 9 * q^76 + 38 * q^77 + 6 * q^78 - 17 * q^79 + 4 * q^80 + 13 * q^81 + 28 * q^82 + 14 * q^83 + 11 * q^84 + 4 * q^85 + q^86 + 14 * q^87 + 7 * q^88 + 19 * q^89 + 4 * q^90 - 5 * q^91 + 2 * q^92 - 5 * q^93 + 12 * q^94 + 25 * q^95 + 13 * q^96 - 5 * q^97 + 32 * q^98 + 7 * q^99

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