LMFDB - Embedded newform 6042.2.a.y.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 14x^{5} + 29x^{4} + 48x^{3} - 14x^{2} - 35x - 10 $ x^7 - 3x^6 - 14x^5 + 29x^4 + 48x^3 - 14x^2 - 35x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.835135$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83513 q^{5} -1.00000 q^{6} +0.943730 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83513 q^{5} -1.00000 q^{6} +0.943730 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.83513 q^{10} +0.945380 q^{11} +1.00000 q^{12} -5.72424 q^{13} -0.943730 q^{14} +1.83513 q^{15} +1.00000 q^{16} -1.71116 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.83513 q^{20} +0.943730 q^{21} -0.945380 q^{22} -4.25430 q^{23} -1.00000 q^{24} -1.63228 q^{25} +5.72424 q^{26} +1.00000 q^{27} +0.943730 q^{28} -5.48302 q^{29} -1.83513 q^{30} +5.24958 q^{31} -1.00000 q^{32} +0.945380 q^{33} +1.71116 q^{34} +1.73187 q^{35} +1.00000 q^{36} +3.51711 q^{37} +1.00000 q^{38} -5.72424 q^{39} -1.83513 q^{40} +3.12396 q^{41} -0.943730 q^{42} -9.77701 q^{43} +0.945380 q^{44} +1.83513 q^{45} +4.25430 q^{46} -9.84505 q^{47} +1.00000 q^{48} -6.10937 q^{49} +1.63228 q^{50} -1.71116 q^{51} -5.72424 q^{52} +1.00000 q^{53} -1.00000 q^{54} +1.73490 q^{55} -0.943730 q^{56} -1.00000 q^{57} +5.48302 q^{58} +9.28897 q^{59} +1.83513 q^{60} +7.60557 q^{61} -5.24958 q^{62} +0.943730 q^{63} +1.00000 q^{64} -10.5048 q^{65} -0.945380 q^{66} -11.5835 q^{67} -1.71116 q^{68} -4.25430 q^{69} -1.73187 q^{70} -8.75401 q^{71} -1.00000 q^{72} +0.103642 q^{73} -3.51711 q^{74} -1.63228 q^{75} -1.00000 q^{76} +0.892184 q^{77} +5.72424 q^{78} +13.9413 q^{79} +1.83513 q^{80} +1.00000 q^{81} -3.12396 q^{82} -10.2266 q^{83} +0.943730 q^{84} -3.14021 q^{85} +9.77701 q^{86} -5.48302 q^{87} -0.945380 q^{88} +4.68938 q^{89} -1.83513 q^{90} -5.40214 q^{91} -4.25430 q^{92} +5.24958 q^{93} +9.84505 q^{94} -1.83513 q^{95} -1.00000 q^{96} -11.4165 q^{97} +6.10937 q^{98} +0.945380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.83513	0.820697	0.410349	−	0.911929i	$-0.365407\pi$
$5$	1.83513	0.820697	0.410349	+	0.911929i	$0.365407\pi$
$6$	−1.00000	−0.408248
$7$	0.943730	0.356696	0.178348	−	0.983967i	$-0.442925\pi$
$7$	0.943730	0.356696	0.178348	+	0.983967i	$0.442925\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.83513	−0.580321
$11$	0.945380	0.285043	0.142521	−	0.989792i	$-0.454479\pi$
$11$	0.945380	0.285043	0.142521	+	0.989792i	$0.454479\pi$
$12$	1.00000	0.288675
$13$	−5.72424	−1.58762	−0.793810	−	0.608166i	$-0.791906\pi$
$13$	−5.72424	−1.58762	−0.793810	+	0.608166i	$0.791906\pi$
$14$	−0.943730	−0.252222
$15$	1.83513	0.473830
$16$	1.00000	0.250000
$17$	−1.71116	−0.415017	−0.207509	−	0.978233i	$-0.566536\pi$
$17$	−1.71116	−0.415017	−0.207509	+	0.978233i	$0.566536\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.83513	0.410349
$21$	0.943730	0.205939
$22$	−0.945380	−0.201556
$23$	−4.25430	−0.887084	−0.443542	−	0.896254i	$-0.646278\pi$
$23$	−4.25430	−0.887084	−0.443542	+	0.896254i	$0.646278\pi$
$24$	−1.00000	−0.204124
$25$	−1.63228	−0.326456
$26$	5.72424	1.12262
$27$	1.00000	0.192450
$28$	0.943730	0.178348
$29$	−5.48302	−1.01817	−0.509086	−	0.860716i	$-0.670017\pi$
$29$	−5.48302	−1.01817	−0.509086	+	0.860716i	$0.670017\pi$
$30$	−1.83513	−0.335048
$31$	5.24958	0.942853	0.471426	−	0.881905i	$-0.343739\pi$
$31$	5.24958	0.942853	0.471426	+	0.881905i	$0.343739\pi$
$32$	−1.00000	−0.176777
$33$	0.945380	0.164570
$34$	1.71116	0.293462
$35$	1.73187	0.292740
$36$	1.00000	0.166667
$37$	3.51711	0.578209	0.289105	−	0.957297i	$-0.406642\pi$
$37$	3.51711	0.578209	0.289105	+	0.957297i	$0.406642\pi$
$38$	1.00000	0.162221
$39$	−5.72424	−0.916613
$40$	−1.83513	−0.290160
$41$	3.12396	0.487880	0.243940	−	0.969790i	$-0.421560\pi$
$41$	3.12396	0.487880	0.243940	+	0.969790i	$0.421560\pi$
$42$	−0.943730	−0.145621
$43$	−9.77701	−1.49098	−0.745490	−	0.666517i	$-0.767785\pi$
$43$	−9.77701	−1.49098	−0.745490	+	0.666517i	$0.767785\pi$
$44$	0.945380	0.142521
$45$	1.83513	0.273566
$46$	4.25430	0.627263
$47$	−9.84505	−1.43605	−0.718024	−	0.696018i	$-0.754953\pi$
$47$	−9.84505	−1.43605	−0.718024	+	0.696018i	$0.754953\pi$
$48$	1.00000	0.144338
$49$	−6.10937	−0.872768
$50$	1.63228	0.230839
$51$	−1.71116	−0.239610
$52$	−5.72424	−0.793810
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	1.73490	0.233934
$56$	−0.943730	−0.126111
$57$	−1.00000	−0.132453
$58$	5.48302	0.719956
$59$	9.28897	1.20932	0.604661	−	0.796483i	$-0.293309\pi$
$59$	9.28897	1.20932	0.604661	+	0.796483i	$0.293309\pi$
$60$	1.83513	0.236915
$61$	7.60557	0.973794	0.486897	−	0.873459i	$-0.338129\pi$
$61$	7.60557	0.973794	0.486897	+	0.873459i	$0.338129\pi$
$62$	−5.24958	−0.666697
$63$	0.943730	0.118899
$64$	1.00000	0.125000
$65$	−10.5048	−1.30296
$66$	−0.945380	−0.116368
$67$	−11.5835	−1.41515	−0.707575	−	0.706639i	$-0.750211\pi$
$67$	−11.5835	−1.41515	−0.707575	+	0.706639i	$0.750211\pi$
$68$	−1.71116	−0.207509
$69$	−4.25430	−0.512158
$70$	−1.73187	−0.206998
$71$	−8.75401	−1.03891	−0.519455	−	0.854498i	$-0.673865\pi$
$71$	−8.75401	−1.03891	−0.519455	+	0.854498i	$0.673865\pi$
$72$	−1.00000	−0.117851
$73$	0.103642	0.0121303	0.00606517	−	0.999982i	$-0.498069\pi$
$73$	0.103642	0.0121303	0.00606517	+	0.999982i	$0.498069\pi$
$74$	−3.51711	−0.408856
$75$	−1.63228	−0.188480
$76$	−1.00000	−0.114708
$77$	0.892184	0.101674
$78$	5.72424	0.648143
$79$	13.9413	1.56852	0.784259	−	0.620433i	$-0.213043\pi$
$79$	13.9413	1.56852	0.784259	+	0.620433i	$0.213043\pi$
$80$	1.83513	0.205174
$81$	1.00000	0.111111
$82$	−3.12396	−0.344983
$83$	−10.2266	−1.12251	−0.561256	−	0.827642i	$-0.689682\pi$
$83$	−10.2266	−1.12251	−0.561256	+	0.827642i	$0.689682\pi$
$84$	0.943730	0.102969
$85$	−3.14021	−0.340603
$86$	9.77701	1.05428
$87$	−5.48302	−0.587842
$88$	−0.945380	−0.100778
$89$	4.68938	0.497073	0.248536	−	0.968623i	$-0.420050\pi$
$89$	4.68938	0.497073	0.248536	+	0.968623i	$0.420050\pi$
$90$	−1.83513	−0.193440
$91$	−5.40214	−0.566298
$92$	−4.25430	−0.443542
$93$	5.24958	0.544356
$94$	9.84505	1.01544
$95$	−1.83513	−0.188281
$96$	−1.00000	−0.102062
$97$	−11.4165	−1.15917	−0.579586	−	0.814911i	$-0.696786\pi$
$97$	−11.4165	−1.15917	−0.579586	+	0.814911i	$0.696786\pi$
$98$	6.10937	0.617140
$99$	0.945380	0.0950143
$100$	−1.63228	−0.163228
$101$	−11.8300	−1.17713	−0.588563	−	0.808452i	$-0.700306\pi$
$101$	−11.8300	−1.17713	−0.588563	+	0.808452i	$0.700306\pi$
$102$	1.71116	0.169430
$103$	−12.4760	−1.22929	−0.614647	−	0.788802i	$-0.710702\pi$
$103$	−12.4760	−1.22929	−0.614647	+	0.788802i	$0.710702\pi$
$104$	5.72424	0.561308
$105$	1.73187	0.169013
$106$	−1.00000	−0.0971286
$107$	1.45928	0.141074	0.0705372	−	0.997509i	$-0.477529\pi$
$107$	1.45928	0.141074	0.0705372	+	0.997509i	$0.477529\pi$
$108$	1.00000	0.0962250
$109$	−9.31958	−0.892654	−0.446327	−	0.894870i	$-0.647268\pi$
$109$	−9.31958	−0.892654	−0.446327	+	0.894870i	$0.647268\pi$
$110$	−1.73490	−0.165416
$111$	3.51711	0.333829
$112$	0.943730	0.0891741
$113$	−5.69613	−0.535847	−0.267923	−	0.963440i	$-0.586337\pi$
$113$	−5.69613	−0.535847	−0.267923	+	0.963440i	$0.586337\pi$
$114$	1.00000	0.0936586
$115$	−7.80722	−0.728027
$116$	−5.48302	−0.509086
$117$	−5.72424	−0.529207
$118$	−9.28897	−0.855119
$119$	−1.61487	−0.148035
$120$	−1.83513	−0.167524
$121$	−10.1063	−0.918751
$122$	−7.60557	−0.688576
$123$	3.12396	0.281678
$124$	5.24958	0.471426
$125$	−12.1711	−1.08862
$126$	−0.943730	−0.0840741
$127$	−0.986042	−0.0874970	−0.0437485	−	0.999043i	$-0.513930\pi$
$127$	−0.986042	−0.0874970	−0.0437485	+	0.999043i	$0.513930\pi$
$128$	−1.00000	−0.0883883
$129$	−9.77701	−0.860818
$130$	10.5048	0.921328
$131$	14.9647	1.30747	0.653736	−	0.756722i	$-0.273201\pi$
$131$	14.9647	1.30747	0.653736	+	0.756722i	$0.273201\pi$
$132$	0.945380	0.0822848
$133$	−0.943730	−0.0818318
$134$	11.5835	1.00066
$135$	1.83513	0.157943
$136$	1.71116	0.146731
$137$	8.40272	0.717893	0.358946	−	0.933358i	$-0.383136\pi$
$137$	8.40272	0.717893	0.358946	+	0.933358i	$0.383136\pi$
$138$	4.25430	0.362150
$139$	11.0518	0.937400	0.468700	−	0.883357i	$-0.344723\pi$
$139$	11.0518	0.937400	0.468700	+	0.883357i	$0.344723\pi$
$140$	1.73187	0.146370
$141$	−9.84505	−0.829103
$142$	8.75401	0.734620
$143$	−5.41159	−0.452540
$144$	1.00000	0.0833333
$145$	−10.0621	−0.835611
$146$	−0.103642	−0.00857744
$147$	−6.10937	−0.503893
$148$	3.51711	0.289105
$149$	11.5495	0.946169	0.473084	−	0.881017i	$-0.343141\pi$
$149$	11.5495	0.946169	0.473084	+	0.881017i	$0.343141\pi$
$150$	1.63228	0.133275
$151$	−15.1818	−1.23548	−0.617738	−	0.786384i	$-0.711951\pi$
$151$	−15.1818	−1.23548	−0.617738	+	0.786384i	$0.711951\pi$
$152$	1.00000	0.0811107
$153$	−1.71116	−0.138339
$154$	−0.892184	−0.0718942
$155$	9.63369	0.773796
$156$	−5.72424	−0.458306
$157$	5.37516	0.428984	0.214492	−	0.976726i	$-0.431190\pi$
$157$	5.37516	0.428984	0.214492	+	0.976726i	$0.431190\pi$
$158$	−13.9413	−1.10911
$159$	1.00000	0.0793052
$160$	−1.83513	−0.145080
$161$	−4.01491	−0.316420
$162$	−1.00000	−0.0785674
$163$	−2.06780	−0.161963	−0.0809813	−	0.996716i	$-0.525805\pi$
$163$	−2.06780	−0.161963	−0.0809813	+	0.996716i	$0.525805\pi$
$164$	3.12396	0.243940
$165$	1.73490	0.135062
$166$	10.2266	0.793736
$167$	12.4384	0.962511	0.481255	−	0.876580i	$-0.340181\pi$
$167$	12.4384	0.962511	0.481255	+	0.876580i	$0.340181\pi$
$168$	−0.943730	−0.0728103
$169$	19.7670	1.52054
$170$	3.14021	0.240843
$171$	−1.00000	−0.0764719
$172$	−9.77701	−0.745490
$173$	0.792617	0.0602616	0.0301308	−	0.999546i	$-0.490408\pi$
$173$	0.792617	0.0602616	0.0301308	+	0.999546i	$0.490408\pi$
$174$	5.48302	0.415667
$175$	−1.54043	−0.116446
$176$	0.945380	0.0712607
$177$	9.28897	0.698202
$178$	−4.68938	−0.351484
$179$	16.6202	1.24225	0.621124	−	0.783712i	$-0.286676\pi$
$179$	16.6202	1.24225	0.621124	+	0.783712i	$0.286676\pi$
$180$	1.83513	0.136783
$181$	−18.1589	−1.34974	−0.674869	−	0.737937i	$-0.735800\pi$
$181$	−18.1589	−1.34974	−0.674869	+	0.737937i	$0.735800\pi$
$182$	5.40214	0.400433
$183$	7.60557	0.562220
$184$	4.25430	0.313632
$185$	6.45437	0.474535
$186$	−5.24958	−0.384918
$187$	−1.61770	−0.118298
$188$	−9.84505	−0.718024
$189$	0.943730	0.0686462
$190$	1.83513	0.133135
$191$	−10.1518	−0.734560	−0.367280	−	0.930110i	$-0.619711\pi$
$191$	−10.1518	−0.734560	−0.367280	+	0.930110i	$0.619711\pi$
$192$	1.00000	0.0721688
$193$	−20.6219	−1.48440	−0.742198	−	0.670181i	$-0.766217\pi$
$193$	−20.6219	−1.48440	−0.742198	+	0.670181i	$0.766217\pi$
$194$	11.4165	0.819659
$195$	−10.5048	−0.752261
$196$	−6.10937	−0.436384
$197$	−15.4504	−1.10079	−0.550397	−	0.834903i	$-0.685523\pi$
$197$	−15.4504	−1.10079	−0.550397	+	0.834903i	$0.685523\pi$
$198$	−0.945380	−0.0671853
$199$	0.511182	0.0362367	0.0181184	−	0.999836i	$-0.494232\pi$
$199$	0.511182	0.0362367	0.0181184	+	0.999836i	$0.494232\pi$
$200$	1.63228	0.115420
$201$	−11.5835	−0.817037
$202$	11.8300	0.832353
$203$	−5.17449	−0.363178
$204$	−1.71116	−0.119805
$205$	5.73288	0.400402
$206$	12.4760	0.869242
$207$	−4.25430	−0.295695
$208$	−5.72424	−0.396905
$209$	−0.945380	−0.0653933
$210$	−1.73187	−0.119510
$211$	6.33737	0.436283	0.218141	−	0.975917i	$-0.430001\pi$
$211$	6.33737	0.436283	0.218141	+	0.975917i	$0.430001\pi$
$212$	1.00000	0.0686803
$213$	−8.75401	−0.599815
$214$	−1.45928	−0.0997546
$215$	−17.9421	−1.22364
$216$	−1.00000	−0.0680414
$217$	4.95419	0.336312
$218$	9.31958	0.631202
$219$	0.103642	0.00700345
$220$	1.73490	0.116967
$221$	9.79510	0.658890
$222$	−3.51711	−0.236053
$223$	25.9879	1.74028	0.870138	−	0.492809i	$-0.164030\pi$
$223$	25.9879	1.74028	0.870138	+	0.492809i	$0.164030\pi$
$224$	−0.943730	−0.0630556
$225$	−1.63228	−0.108819
$226$	5.69613	0.378901
$227$	1.44464	0.0958841	0.0479420	−	0.998850i	$-0.484734\pi$
$227$	1.44464	0.0958841	0.0479420	+	0.998850i	$0.484734\pi$
$228$	−1.00000	−0.0662266
$229$	3.78065	0.249832	0.124916	−	0.992167i	$-0.460134\pi$
$229$	3.78065	0.249832	0.124916	+	0.992167i	$0.460134\pi$
$230$	7.80722	0.514793
$231$	0.892184	0.0587014
$232$	5.48302	0.359978
$233$	2.74114	0.179578	0.0897891	−	0.995961i	$-0.471381\pi$
$233$	2.74114	0.179578	0.0897891	+	0.995961i	$0.471381\pi$
$234$	5.72424	0.374206
$235$	−18.0670	−1.17856
$236$	9.28897	0.604661
$237$	13.9413	0.905584
$238$	1.61487	0.104677
$239$	12.5178	0.809712	0.404856	−	0.914380i	$-0.367322\pi$
$239$	12.5178	0.809712	0.404856	+	0.914380i	$0.367322\pi$
$240$	1.83513	0.118457
$241$	−29.8382	−1.92205	−0.961024	−	0.276464i	$-0.910837\pi$
$241$	−29.8382	−1.92205	−0.961024	+	0.276464i	$0.910837\pi$
$242$	10.1063	0.649655
$243$	1.00000	0.0641500
$244$	7.60557	0.486897
$245$	−11.2115	−0.716278
$246$	−3.12396	−0.199176
$247$	5.72424	0.364225
$248$	−5.24958	−0.333349
$249$	−10.2266	−0.648083
$250$	12.1711	0.769770
$251$	−8.86513	−0.559562	−0.279781	−	0.960064i	$-0.590262\pi$
$251$	−8.86513	−0.559562	−0.279781	+	0.960064i	$0.590262\pi$
$252$	0.943730	0.0594494
$253$	−4.02194	−0.252857
$254$	0.986042	0.0618698
$255$	−3.14021	−0.196648
$256$	1.00000	0.0625000
$257$	13.3684	0.833901	0.416950	−	0.908929i	$-0.363099\pi$
$257$	13.3684	0.833901	0.416950	+	0.908929i	$0.363099\pi$
$258$	9.77701	0.608690
$259$	3.31920	0.206245
$260$	−10.5048	−0.651478
$261$	−5.48302	−0.339391
$262$	−14.9647	−0.924523
$263$	9.54904	0.588819	0.294409	−	0.955679i	$-0.404877\pi$
$263$	9.54904	0.588819	0.294409	+	0.955679i	$0.404877\pi$
$264$	−0.945380	−0.0581841
$265$	1.83513	0.112731
$266$	0.943730	0.0578638
$267$	4.68938	0.286985
$268$	−11.5835	−0.707575
$269$	31.5725	1.92501	0.962506	−	0.271260i	$-0.0874403\pi$
$269$	31.5725	1.92501	0.962506	+	0.271260i	$0.0874403\pi$
$270$	−1.83513	−0.111683
$271$	18.4055	1.11805	0.559026	−	0.829150i	$-0.311175\pi$
$271$	18.4055	1.11805	0.559026	+	0.829150i	$0.311175\pi$
$272$	−1.71116	−0.103754
$273$	−5.40214	−0.326952
$274$	−8.40272	−0.507627
$275$	−1.54313	−0.0930540
$276$	−4.25430	−0.256079
$277$	−16.2950	−0.979069	−0.489535	−	0.871984i	$-0.662833\pi$
$277$	−16.2950	−0.979069	−0.489535	+	0.871984i	$0.662833\pi$
$278$	−11.0518	−0.662842
$279$	5.24958	0.314284
$280$	−1.73187	−0.103499
$281$	4.86474	0.290206	0.145103	−	0.989417i	$-0.453649\pi$
$281$	4.86474	0.290206	0.145103	+	0.989417i	$0.453649\pi$
$282$	9.84505	0.586264
$283$	−26.6781	−1.58585	−0.792925	−	0.609319i	$-0.791443\pi$
$283$	−26.6781	−1.58585	−0.792925	+	0.609319i	$0.791443\pi$
$284$	−8.75401	−0.519455
$285$	−1.83513	−0.108704
$286$	5.41159	0.319994
$287$	2.94817	0.174025
$288$	−1.00000	−0.0589256
$289$	−14.0719	−0.827761
$290$	10.0621	0.590866
$291$	−11.4165	−0.669248
$292$	0.103642	0.00606517
$293$	−11.7215	−0.684780	−0.342390	−	0.939558i	$-0.611236\pi$
$293$	−11.7215	−0.684780	−0.342390	+	0.939558i	$0.611236\pi$
$294$	6.10937	0.356306
$295$	17.0465	0.992487
$296$	−3.51711	−0.204428
$297$	0.945380	0.0548565
$298$	−11.5495	−0.669042
$299$	24.3527	1.40835
$300$	−1.63228	−0.0942398
$301$	−9.22686	−0.531827
$302$	15.1818	0.873613
$303$	−11.8300	−0.679614
$304$	−1.00000	−0.0573539
$305$	13.9572	0.799190
$306$	1.71116	0.0978205
$307$	9.89391	0.564675	0.282338	−	0.959315i	$-0.408890\pi$
$307$	9.89391	0.564675	0.282338	+	0.959315i	$0.408890\pi$
$308$	0.892184	0.0508369
$309$	−12.4760	−0.709733
$310$	−9.63369	−0.547157
$311$	−17.8694	−1.01328	−0.506642	−	0.862157i	$-0.669113\pi$
$311$	−17.8694	−1.01328	−0.506642	+	0.862157i	$0.669113\pi$
$312$	5.72424	0.324072
$313$	18.7648	1.06065	0.530326	−	0.847794i	$-0.322070\pi$
$313$	18.7648	1.06065	0.530326	+	0.847794i	$0.322070\pi$
$314$	−5.37516	−0.303338
$315$	1.73187	0.0975799
$316$	13.9413	0.784259
$317$	9.00652	0.505857	0.252928	−	0.967485i	$-0.418606\pi$
$317$	9.00652	0.505857	0.252928	+	0.967485i	$0.418606\pi$
$318$	−1.00000	−0.0560772
$319$	−5.18354	−0.290223
$320$	1.83513	0.102587
$321$	1.45928	0.0814493
$322$	4.01491	0.223742
$323$	1.71116	0.0952115
$324$	1.00000	0.0555556
$325$	9.34358	0.518288
$326$	2.06780	0.114525
$327$	−9.31958	−0.515374
$328$	−3.12396	−0.172492
$329$	−9.29107	−0.512233
$330$	−1.73490	−0.0955031
$331$	7.83078	0.430419	0.215209	−	0.976568i	$-0.430957\pi$
$331$	7.83078	0.430419	0.215209	+	0.976568i	$0.430957\pi$
$332$	−10.2266	−0.561256
$333$	3.51711	0.192736
$334$	−12.4384	−0.680598
$335$	−21.2573	−1.16141
$336$	0.943730	0.0514847
$337$	−14.6251	−0.796679	−0.398339	−	0.917238i	$-0.630413\pi$
$337$	−14.6251	−0.796679	−0.398339	+	0.917238i	$0.630413\pi$
$338$	−19.7670	−1.07518
$339$	−5.69613	−0.309371
$340$	−3.14021	−0.170302
$341$	4.96285	0.268753
$342$	1.00000	0.0540738
$343$	−12.3717	−0.668009
$344$	9.77701	0.527141
$345$	−7.80722	−0.420327
$346$	−0.792617	−0.0426114
$347$	12.7027	0.681916	0.340958	−	0.940079i	$-0.389249\pi$
$347$	12.7027	0.681916	0.340958	+	0.940079i	$0.389249\pi$
$348$	−5.48302	−0.293921
$349$	−11.7061	−0.626612	−0.313306	−	0.949652i	$-0.601437\pi$
$349$	−11.7061	−0.626612	−0.313306	+	0.949652i	$0.601437\pi$
$350$	1.54043	0.0823396
$351$	−5.72424	−0.305538
$352$	−0.945380	−0.0503889
$353$	20.3601	1.08366	0.541829	−	0.840489i	$-0.317732\pi$
$353$	20.3601	1.08366	0.541829	+	0.840489i	$0.317732\pi$
$354$	−9.28897	−0.493703
$355$	−16.0648	−0.852630
$356$	4.68938	0.248536
$357$	−1.61487	−0.0854681
$358$	−16.6202	−0.878403
$359$	2.09184	0.110403	0.0552015	−	0.998475i	$-0.482420\pi$
$359$	2.09184	0.110403	0.0552015	+	0.998475i	$0.482420\pi$
$360$	−1.83513	−0.0967201
$361$	1.00000	0.0526316
$362$	18.1589	0.954409
$363$	−10.1063	−0.530441
$364$	−5.40214	−0.283149
$365$	0.190196	0.00995533
$366$	−7.60557	−0.397550
$367$	6.01599	0.314032	0.157016	−	0.987596i	$-0.449813\pi$
$367$	6.01599	0.314032	0.157016	+	0.987596i	$0.449813\pi$
$368$	−4.25430	−0.221771
$369$	3.12396	0.162627
$370$	−6.45437	−0.335547
$371$	0.943730	0.0489960
$372$	5.24958	0.272178
$373$	15.7044	0.813143	0.406571	−	0.913619i	$-0.366724\pi$
$373$	15.7044	0.813143	0.406571	+	0.913619i	$0.366724\pi$
$374$	1.61770	0.0836491
$375$	−12.1711	−0.628514
$376$	9.84505	0.507720
$377$	31.3862	1.61647
$378$	−0.943730	−0.0485402
$379$	−17.0526	−0.875935	−0.437967	−	0.898991i	$-0.644301\pi$
$379$	−17.0526	−0.875935	−0.437967	+	0.898991i	$0.644301\pi$
$380$	−1.83513	−0.0941404
$381$	−0.986042	−0.0505164
$382$	10.1518	0.519412
$383$	12.3364	0.630360	0.315180	−	0.949032i	$-0.397935\pi$
$383$	12.3364	0.630360	0.315180	+	0.949032i	$0.397935\pi$
$384$	−1.00000	−0.0510310
$385$	1.63728	0.0834434
$386$	20.6219	1.04963
$387$	−9.77701	−0.496993
$388$	−11.4165	−0.579586
$389$	18.5999	0.943052	0.471526	−	0.881852i	$-0.343703\pi$
$389$	18.5999	0.943052	0.471526	+	0.881852i	$0.343703\pi$
$390$	10.5048	0.531929
$391$	7.27980	0.368155
$392$	6.10937	0.308570
$393$	14.9647	0.754870
$394$	15.4504	0.778378
$395$	25.5842	1.28728
$396$	0.945380	0.0475071
$397$	−25.2974	−1.26964	−0.634820	−	0.772660i	$-0.718926\pi$
$397$	−25.2974	−1.26964	−0.634820	+	0.772660i	$0.718926\pi$
$398$	−0.511182	−0.0256232
$399$	−0.943730	−0.0472456
$400$	−1.63228	−0.0816140
$401$	3.70797	0.185167	0.0925837	−	0.995705i	$-0.470487\pi$
$401$	3.70797	0.185167	0.0925837	+	0.995705i	$0.470487\pi$
$402$	11.5835	0.577732
$403$	−30.0499	−1.49689
$404$	−11.8300	−0.588563
$405$	1.83513	0.0911886
$406$	5.17449	0.256806
$407$	3.32501	0.164814
$408$	1.71116	0.0847150
$409$	19.3580	0.957193	0.478597	−	0.878035i	$-0.341146\pi$
$409$	19.3580	0.957193	0.478597	+	0.878035i	$0.341146\pi$
$410$	−5.73288	−0.283127
$411$	8.40272	0.414476
$412$	−12.4760	−0.614647
$413$	8.76628	0.431361
$414$	4.25430	0.209088
$415$	−18.7671	−0.921243
$416$	5.72424	0.280654
$417$	11.0518	0.541208
$418$	0.945380	0.0462401
$419$	16.8689	0.824099	0.412049	−	0.911162i	$-0.364813\pi$
$419$	16.8689	0.824099	0.412049	+	0.911162i	$0.364813\pi$
$420$	1.73187	0.0845067
$421$	8.14734	0.397077	0.198539	−	0.980093i	$-0.436380\pi$
$421$	8.14734	0.397077	0.198539	+	0.980093i	$0.436380\pi$
$422$	−6.33737	−0.308498
$423$	−9.84505	−0.478683
$424$	−1.00000	−0.0485643
$425$	2.79309	0.135485
$426$	8.75401	0.424133
$427$	7.17761	0.347349
$428$	1.45928	0.0705372
$429$	−5.41159	−0.261274
$430$	17.9421	0.865247
$431$	37.8269	1.82206	0.911028	−	0.412344i	$-0.135290\pi$
$431$	37.8269	1.82206	0.911028	+	0.412344i	$0.135290\pi$
$432$	1.00000	0.0481125
$433$	27.1022	1.30245	0.651225	−	0.758885i	$-0.274256\pi$
$433$	27.1022	1.30245	0.651225	+	0.758885i	$0.274256\pi$
$434$	−4.95419	−0.237809
$435$	−10.0621	−0.482440
$436$	−9.31958	−0.446327
$437$	4.25430	0.203511
$438$	−0.103642	−0.00495219
$439$	−30.1404	−1.43852	−0.719261	−	0.694740i	$-0.755519\pi$
$439$	−30.1404	−1.43852	−0.719261	+	0.694740i	$0.755519\pi$
$440$	−1.73490	−0.0827081
$441$	−6.10937	−0.290923
$442$	−9.79510	−0.465905
$443$	−2.76097	−0.131178	−0.0655889	−	0.997847i	$-0.520893\pi$
$443$	−2.76097	−0.131178	−0.0655889	+	0.997847i	$0.520893\pi$
$444$	3.51711	0.166915
$445$	8.60564	0.407946
$446$	−25.9879	−1.23056
$447$	11.5495	0.546271
$448$	0.943730	0.0445870
$449$	−5.32221	−0.251170	−0.125585	−	0.992083i	$-0.540081\pi$
$449$	−5.32221	−0.251170	−0.125585	+	0.992083i	$0.540081\pi$
$450$	1.63228	0.0769465
$451$	2.95333	0.139067
$452$	−5.69613	−0.267923
$453$	−15.1818	−0.713302
$454$	−1.44464	−0.0678003
$455$	−9.91366	−0.464759
$456$	1.00000	0.0468293
$457$	−38.5993	−1.80560	−0.902800	−	0.430060i	$-0.858492\pi$
$457$	−38.5993	−1.80560	−0.902800	+	0.430060i	$0.858492\pi$
$458$	−3.78065	−0.176658
$459$	−1.71116	−0.0798701
$460$	−7.80722	−0.364014
$461$	25.7184	1.19782	0.598912	−	0.800815i	$-0.295600\pi$
$461$	25.7184	1.19782	0.598912	+	0.800815i	$0.295600\pi$
$462$	−0.892184	−0.0415081
$463$	1.37037	0.0636864	0.0318432	−	0.999493i	$-0.489862\pi$
$463$	1.37037	0.0636864	0.0318432	+	0.999493i	$0.489862\pi$
$464$	−5.48302	−0.254543
$465$	9.63369	0.446752
$466$	−2.74114	−0.126981
$467$	−10.7367	−0.496835	−0.248418	−	0.968653i	$-0.579911\pi$
$467$	−10.7367	−0.496835	−0.248418	+	0.968653i	$0.579911\pi$
$468$	−5.72424	−0.264603
$469$	−10.9317	−0.504779
$470$	18.0670	0.833368
$471$	5.37516	0.247674
$472$	−9.28897	−0.427560
$473$	−9.24300	−0.424993
$474$	−13.9413	−0.640345
$475$	1.63228	0.0748942
$476$	−1.61487	−0.0740176
$477$	1.00000	0.0457869
$478$	−12.5178	−0.572553
$479$	−34.1475	−1.56024	−0.780119	−	0.625631i	$-0.784842\pi$
$479$	−34.1475	−1.56024	−0.780119	+	0.625631i	$0.784842\pi$
$480$	−1.83513	−0.0837621
$481$	−20.1328	−0.917977
$482$	29.8382	1.35909
$483$	−4.01491	−0.182685
$484$	−10.1063	−0.459375
$485$	−20.9509	−0.951329
$486$	−1.00000	−0.0453609
$487$	19.4474	0.881244	0.440622	−	0.897693i	$-0.354758\pi$
$487$	19.4474	0.881244	0.440622	+	0.897693i	$0.354758\pi$
$488$	−7.60557	−0.344288
$489$	−2.06780	−0.0935091
$490$	11.2115	0.506485
$491$	−42.4811	−1.91714	−0.958571	−	0.284852i	$-0.908056\pi$
$491$	−42.4811	−1.91714	−0.958571	+	0.284852i	$0.908056\pi$
$492$	3.12396	0.140839
$493$	9.38233	0.422559
$494$	−5.72424	−0.257546
$495$	1.73490	0.0779780
$496$	5.24958	0.235713
$497$	−8.26142	−0.370575
$498$	10.2266	0.458264
$499$	−13.0234	−0.583008	−0.291504	−	0.956570i	$-0.594156\pi$
$499$	−13.0234	−0.583008	−0.291504	+	0.956570i	$0.594156\pi$
$500$	−12.1711	−0.544309
$501$	12.4384	0.555706
$502$	8.86513	0.395670
$503$	−26.7866	−1.19436	−0.597178	−	0.802109i	$-0.703711\pi$
$503$	−26.7866	−1.19436	−0.597178	+	0.802109i	$0.703711\pi$
$504$	−0.943730	−0.0420371
$505$	−21.7096	−0.966063
$506$	4.02194	0.178797
$507$	19.7670	0.877882
$508$	−0.986042	−0.0437485
$509$	19.8557	0.880088	0.440044	−	0.897976i	$-0.354963\pi$
$509$	19.8557	0.880088	0.440044	+	0.897976i	$0.354963\pi$
$510$	3.14021	0.139051
$511$	0.0978097	0.00432685
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−13.3684	−0.589657
$515$	−22.8951	−1.00888
$516$	−9.77701	−0.430409
$517$	−9.30732	−0.409335
$518$	−3.31920	−0.145837
$519$	0.792617	0.0347920
$520$	10.5048	0.460664
$521$	−32.8920	−1.44103	−0.720513	−	0.693442i	$-0.756094\pi$
$521$	−32.8920	−1.44103	−0.720513	+	0.693442i	$0.756094\pi$
$522$	5.48302	0.239985
$523$	20.8556	0.911951	0.455976	−	0.889992i	$-0.349290\pi$
$523$	20.8556	0.911951	0.455976	+	0.889992i	$0.349290\pi$
$524$	14.9647	0.653736
$525$	−1.54043	−0.0672300
$526$	−9.54904	−0.416358
$527$	−8.98287	−0.391300
$528$	0.945380	0.0411424
$529$	−4.90089	−0.213082
$530$	−1.83513	−0.0797132
$531$	9.28897	0.403107
$532$	−0.943730	−0.0409159
$533$	−17.8823	−0.774568
$534$	−4.68938	−0.202929
$535$	2.67798	0.115779
$536$	11.5835	0.500331
$537$	16.6202	0.717213
$538$	−31.5725	−1.36119
$539$	−5.77568	−0.248776
$540$	1.83513	0.0789716
$541$	23.8856	1.02692	0.513462	−	0.858112i	$-0.328363\pi$
$541$	23.8856	1.02692	0.513462	+	0.858112i	$0.328363\pi$
$542$	−18.4055	−0.790582
$543$	−18.1589	−0.779272
$544$	1.71116	0.0733654
$545$	−17.1027	−0.732598
$546$	5.40214	0.231190
$547$	−39.3376	−1.68195	−0.840977	−	0.541070i	$-0.818019\pi$
$547$	−39.3376	−1.68195	−0.840977	+	0.541070i	$0.818019\pi$
$548$	8.40272	0.358946
$549$	7.60557	0.324598
$550$	1.54313	0.0657991
$551$	5.48302	0.233585
$552$	4.25430	0.181075
$553$	13.1568	0.559485
$554$	16.2950	0.692306
$555$	6.45437	0.273973
$556$	11.0518	0.468700
$557$	−22.8447	−0.967963	−0.483981	−	0.875078i	$-0.660810\pi$
$557$	−22.8447	−0.967963	−0.483981	+	0.875078i	$0.660810\pi$
$558$	−5.24958	−0.222232
$559$	55.9660	2.36711
$560$	1.73187	0.0731849
$561$	−1.61770	−0.0682992
$562$	−4.86474	−0.205207
$563$	−11.1696	−0.470743	−0.235372	−	0.971905i	$-0.575631\pi$
$563$	−11.1696	−0.470743	−0.235372	+	0.971905i	$0.575631\pi$
$564$	−9.84505	−0.414551
$565$	−10.4532	−0.439768
$566$	26.6781	1.12137
$567$	0.943730	0.0396329
$568$	8.75401	0.367310
$569$	21.2459	0.890676	0.445338	−	0.895363i	$-0.353084\pi$
$569$	21.2459	0.890676	0.445338	+	0.895363i	$0.353084\pi$
$570$	1.83513	0.0768653
$571$	−43.7289	−1.83000	−0.914998	−	0.403457i	$-0.867808\pi$
$571$	−43.7289	−1.83000	−0.914998	+	0.403457i	$0.867808\pi$
$572$	−5.41159	−0.226270
$573$	−10.1518	−0.424098
$574$	−2.94817	−0.123054
$575$	6.94422	0.289594
$576$	1.00000	0.0416667
$577$	44.5382	1.85415	0.927075	−	0.374876i	$-0.122315\pi$
$577$	44.5382	1.85415	0.927075	+	0.374876i	$0.122315\pi$
$578$	14.0719	0.585315
$579$	−20.6219	−0.857016
$580$	−10.0621	−0.417805
$581$	−9.65112	−0.400396
$582$	11.4165	0.473230
$583$	0.945380	0.0391537
$584$	−0.103642	−0.00428872
$585$	−10.5048	−0.434318
$586$	11.7215	0.484213
$587$	−2.46738	−0.101840	−0.0509198	−	0.998703i	$-0.516215\pi$
$587$	−2.46738	−0.101840	−0.0509198	+	0.998703i	$0.516215\pi$
$588$	−6.10937	−0.251946
$589$	−5.24958	−0.216305
$590$	−17.0465	−0.701794
$591$	−15.4504	−0.635543
$592$	3.51711	0.144552
$593$	8.91795	0.366216	0.183108	−	0.983093i	$-0.441384\pi$
$593$	8.91795	0.366216	0.183108	+	0.983093i	$0.441384\pi$
$594$	−0.945380	−0.0387894
$595$	−2.96351	−0.121492
$596$	11.5495	0.473084
$597$	0.511182	0.0209213
$598$	−24.3527	−0.995855
$599$	−2.55854	−0.104539	−0.0522696	−	0.998633i	$-0.516646\pi$
$599$	−2.55854	−0.104539	−0.0522696	+	0.998633i	$0.516646\pi$
$600$	1.63228	0.0666376
$601$	−15.1690	−0.618757	−0.309379	−	0.950939i	$-0.600121\pi$
$601$	−15.1690	−0.618757	−0.309379	+	0.950939i	$0.600121\pi$
$602$	9.22686	0.376059
$603$	−11.5835	−0.471716
$604$	−15.1818	−0.617738
$605$	−18.5463	−0.754016
$606$	11.8300	0.480559
$607$	16.0599	0.651852	0.325926	−	0.945395i	$-0.394324\pi$
$607$	16.0599	0.651852	0.325926	+	0.945395i	$0.394324\pi$
$608$	1.00000	0.0405554
$609$	−5.17449	−0.209681
$610$	−13.9572	−0.565112
$611$	56.3555	2.27990
$612$	−1.71116	−0.0691695
$613$	−10.6259	−0.429178	−0.214589	−	0.976704i	$-0.568841\pi$
$613$	−10.6259	−0.429178	−0.214589	+	0.976704i	$0.568841\pi$
$614$	−9.89391	−0.399286
$615$	5.73288	0.231172
$616$	−0.892184	−0.0359471
$617$	−19.0461	−0.766768	−0.383384	−	0.923589i	$-0.625241\pi$
$617$	−19.0461	−0.766768	−0.383384	+	0.923589i	$0.625241\pi$
$618$	12.4760	0.501857
$619$	−26.4697	−1.06391	−0.531954	−	0.846774i	$-0.678542\pi$
$619$	−26.4697	−1.06391	−0.531954	+	0.846774i	$0.678542\pi$
$620$	9.63369	0.386898
$621$	−4.25430	−0.170719
$622$	17.8694	0.716499
$623$	4.42550	0.177304
$624$	−5.72424	−0.229153
$625$	−14.1743	−0.566970
$626$	−18.7648	−0.749994
$627$	−0.945380	−0.0377549
$628$	5.37516	0.214492
$629$	−6.01834	−0.239967
$630$	−1.73187	−0.0689994
$631$	−41.7838	−1.66339	−0.831693	−	0.555236i	$-0.812628\pi$
$631$	−41.7838	−1.66339	−0.831693	+	0.555236i	$0.812628\pi$
$632$	−13.9413	−0.554555
$633$	6.33737	0.251888
$634$	−9.00652	−0.357695
$635$	−1.80952	−0.0718086
$636$	1.00000	0.0396526
$637$	34.9716	1.38562
$638$	5.18354	0.205218
$639$	−8.75401	−0.346303
$640$	−1.83513	−0.0725401
$641$	22.4676	0.887417	0.443709	−	0.896171i	$-0.353662\pi$
$641$	22.4676	0.887417	0.443709	+	0.896171i	$0.353662\pi$
$642$	−1.45928	−0.0575934
$643$	−24.3747	−0.961244	−0.480622	−	0.876928i	$-0.659589\pi$
$643$	−24.3747	−0.961244	−0.480622	+	0.876928i	$0.659589\pi$
$644$	−4.01491	−0.158210
$645$	−17.9421	−0.706471
$646$	−1.71116	−0.0673247
$647$	−44.0818	−1.73303	−0.866517	−	0.499147i	$-0.833647\pi$
$647$	−44.0818	−1.73303	−0.866517	+	0.499147i	$0.833647\pi$
$648$	−1.00000	−0.0392837
$649$	8.78161	0.344709
$650$	−9.34358	−0.366485
$651$	4.95419	0.194170
$652$	−2.06780	−0.0809813
$653$	44.6871	1.74874	0.874371	−	0.485259i	$-0.161275\pi$
$653$	44.6871	1.74874	0.874371	+	0.485259i	$0.161275\pi$
$654$	9.31958	0.364424
$655$	27.4623	1.07304
$656$	3.12396	0.121970
$657$	0.103642	0.00404345
$658$	9.29107	0.362204
$659$	−6.18492	−0.240930	−0.120465	−	0.992718i	$-0.538439\pi$
$659$	−6.18492	−0.240930	−0.120465	+	0.992718i	$0.538439\pi$
$660$	1.73490	0.0675309
$661$	23.8786	0.928770	0.464385	−	0.885634i	$-0.346275\pi$
$661$	23.8786	0.928770	0.464385	+	0.885634i	$0.346275\pi$
$662$	−7.83078	−0.304352
$663$	9.79510	0.380410
$664$	10.2266	0.396868
$665$	−1.73187	−0.0671591
$666$	−3.51711	−0.136285
$667$	23.3265	0.903204
$668$	12.4384	0.481255
$669$	25.9879	1.00475
$670$	21.2573	0.821240
$671$	7.19016	0.277573
$672$	−0.943730	−0.0364052
$673$	12.7962	0.493256	0.246628	−	0.969110i	$-0.420677\pi$
$673$	12.7962	0.493256	0.246628	+	0.969110i	$0.420677\pi$
$674$	14.6251	0.563337
$675$	−1.63228	−0.0628265
$676$	19.7670	0.760268
$677$	46.0768	1.77088	0.885438	−	0.464757i	$-0.153858\pi$
$677$	46.0768	1.77088	0.885438	+	0.464757i	$0.153858\pi$
$678$	5.69613	0.218759
$679$	−10.7741	−0.413473
$680$	3.14021	0.120422
$681$	1.44464	0.0553587
$682$	−4.96285	−0.190037
$683$	−35.8332	−1.37112	−0.685559	−	0.728017i	$-0.740442\pi$
$683$	−35.8332	−1.37112	−0.685559	+	0.728017i	$0.740442\pi$
$684$	−1.00000	−0.0382360
$685$	15.4201	0.589172
$686$	12.3717	0.472354
$687$	3.78065	0.144241
$688$	−9.77701	−0.372745
$689$	−5.72424	−0.218076
$690$	7.80722	0.297216
$691$	40.5981	1.54443	0.772213	−	0.635364i	$-0.219150\pi$
$691$	40.5981	1.54443	0.772213	+	0.635364i	$0.219150\pi$
$692$	0.792617	0.0301308
$693$	0.892184	0.0338913
$694$	−12.7027	−0.482188
$695$	20.2815	0.769321
$696$	5.48302	0.207834
$697$	−5.34559	−0.202479
$698$	11.7061	0.443081
$699$	2.74114	0.103680
$700$	−1.54043	−0.0582229
$701$	−22.6026	−0.853687	−0.426843	−	0.904326i	$-0.640374\pi$
$701$	−22.6026	−0.853687	−0.426843	+	0.904326i	$0.640374\pi$
$702$	5.72424	0.216048
$703$	−3.51711	−0.132650
$704$	0.945380	0.0356304
$705$	−18.0670	−0.680442
$706$	−20.3601	−0.766261
$707$	−11.1643	−0.419876
$708$	9.28897	0.349101
$709$	−15.2967	−0.574479	−0.287239	−	0.957859i	$-0.592738\pi$
$709$	−15.2967	−0.574479	−0.287239	+	0.957859i	$0.592738\pi$
$710$	16.0648	0.602900
$711$	13.9413	0.522839
$712$	−4.68938	−0.175742
$713$	−22.3333	−0.836389
$714$	1.61487	0.0604351
$715$	−9.93099	−0.371398
$716$	16.6202	0.621124
$717$	12.5178	0.467487
$718$	−2.09184	−0.0780667
$719$	33.9949	1.26779	0.633897	−	0.773417i	$-0.281454\pi$
$719$	33.9949	1.26779	0.633897	+	0.773417i	$0.281454\pi$
$720$	1.83513	0.0683914
$721$	−11.7739	−0.438485
$722$	−1.00000	−0.0372161
$723$	−29.8382	−1.10970
$724$	−18.1589	−0.674869
$725$	8.94984	0.332389
$726$	10.1063	0.375078
$727$	−8.16836	−0.302948	−0.151474	−	0.988461i	$-0.548402\pi$
$727$	−8.16836	−0.302948	−0.151474	+	0.988461i	$0.548402\pi$
$728$	5.40214	0.200217
$729$	1.00000	0.0370370
$730$	−0.190196	−0.00703948
$731$	16.7300	0.618783
$732$	7.60557	0.281110
$733$	−15.7424	−0.581460	−0.290730	−	0.956805i	$-0.593898\pi$
$733$	−15.7424	−0.581460	−0.290730	+	0.956805i	$0.593898\pi$
$734$	−6.01599	−0.222054
$735$	−11.2115	−0.413543
$736$	4.25430	0.156816
$737$	−10.9508	−0.403378
$738$	−3.12396	−0.114994
$739$	−2.37951	−0.0875318	−0.0437659	−	0.999042i	$-0.513936\pi$
$739$	−2.37951	−0.0875318	−0.0437659	+	0.999042i	$0.513936\pi$
$740$	6.45437	0.237267
$741$	5.72424	0.210285
$742$	−0.943730	−0.0346454
$743$	−30.5583	−1.12107	−0.560537	−	0.828129i	$-0.689405\pi$
$743$	−30.5583	−1.12107	−0.560537	+	0.828129i	$0.689405\pi$
$744$	−5.24958	−0.192459
$745$	21.1948	0.776518
$746$	−15.7044	−0.574979
$747$	−10.2266	−0.374171
$748$	−1.61770	−0.0591489
$749$	1.37717	0.0503207
$750$	12.1711	0.444427
$751$	16.6357	0.607046	0.303523	−	0.952824i	$-0.401837\pi$
$751$	16.6357	0.607046	0.303523	+	0.952824i	$0.401837\pi$
$752$	−9.84505	−0.359012
$753$	−8.86513	−0.323063
$754$	−31.3862	−1.14302
$755$	−27.8606	−1.01395
$756$	0.943730	0.0343231
$757$	−24.4587	−0.888966	−0.444483	−	0.895787i	$-0.646613\pi$
$757$	−24.4587	−0.888966	−0.444483	+	0.895787i	$0.646613\pi$
$758$	17.0526	0.619379
$759$	−4.02194	−0.145987
$760$	1.83513	0.0665673
$761$	−35.3591	−1.28177	−0.640883	−	0.767639i	$-0.721431\pi$
$761$	−35.3591	−1.28177	−0.640883	+	0.767639i	$0.721431\pi$
$762$	0.986042	0.0357205
$763$	−8.79517	−0.318406
$764$	−10.1518	−0.367280
$765$	−3.14021	−0.113534
$766$	−12.3364	−0.445732
$767$	−53.1724	−1.91994
$768$	1.00000	0.0360844
$769$	10.6235	0.383093	0.191547	−	0.981483i	$-0.438650\pi$
$769$	10.6235	0.383093	0.191547	+	0.981483i	$0.438650\pi$
$770$	−1.63728	−0.0590034
$771$	13.3684	0.481453
$772$	−20.6219	−0.742198
$773$	20.2413	0.728029	0.364014	−	0.931393i	$-0.381406\pi$
$773$	20.2413	0.728029	0.364014	+	0.931393i	$0.381406\pi$
$774$	9.77701	0.351427
$775$	−8.56879	−0.307800
$776$	11.4165	0.409829
$777$	3.31920	0.119076
$778$	−18.5999	−0.666838
$779$	−3.12396	−0.111927
$780$	−10.5048	−0.376131
$781$	−8.27587	−0.296134
$782$	−7.27980	−0.260325
$783$	−5.48302	−0.195947
$784$	−6.10937	−0.218192
$785$	9.86413	0.352066
$786$	−14.9647	−0.533773
$787$	−41.3319	−1.47332	−0.736661	−	0.676262i	$-0.763599\pi$
$787$	−41.3319	−1.47332	−0.736661	+	0.676262i	$0.763599\pi$
$788$	−15.4504	−0.550397
$789$	9.54904	0.339955
$790$	−25.5842	−0.910243
$791$	−5.37561	−0.191135
$792$	−0.945380	−0.0335926
$793$	−43.5362	−1.54601
$794$	25.2974	0.897771
$795$	1.83513	0.0650855
$796$	0.511182	0.0181184
$797$	40.0557	1.41885	0.709423	−	0.704782i	$-0.248955\pi$
$797$	40.0557	1.41885	0.709423	+	0.704782i	$0.248955\pi$
$798$	0.943730	0.0334077
$799$	16.8465	0.595985
$800$	1.63228	0.0577098
$801$	4.68938	0.165691
$802$	−3.70797	−0.130933
$803$	0.0979808	0.00345767
$804$	−11.5835	−0.408518
$805$	−7.36791	−0.259685
$806$	30.0499	1.05846
$807$	31.5725	1.11141
$808$	11.8300	0.416177
$809$	5.14694	0.180957	0.0904783	−	0.995898i	$-0.471160\pi$
$809$	5.14694	0.180957	0.0904783	+	0.995898i	$0.471160\pi$
$810$	−1.83513	−0.0644801
$811$	−45.2585	−1.58924	−0.794620	−	0.607108i	$-0.792330\pi$
$811$	−45.2585	−1.58924	−0.794620	+	0.607108i	$0.792330\pi$
$812$	−5.17449	−0.181589
$813$	18.4055	0.645507
$814$	−3.32501	−0.116541
$815$	−3.79469	−0.132922
$816$	−1.71116	−0.0599026
$817$	9.77701	0.342054
$818$	−19.3580	−0.676838
$819$	−5.40214	−0.188766
$820$	5.73288	0.200201
$821$	−19.1781	−0.669319	−0.334659	−	0.942339i	$-0.608621\pi$
$821$	−19.1781	−0.669319	−0.334659	+	0.942339i	$0.608621\pi$
$822$	−8.40272	−0.293078
$823$	50.8563	1.77274	0.886369	−	0.462979i	$-0.153220\pi$
$823$	50.8563	1.77274	0.886369	+	0.462979i	$0.153220\pi$
$824$	12.4760	0.434621
$825$	−1.54313	−0.0537248
$826$	−8.76628	−0.305018
$827$	−20.0808	−0.698277	−0.349138	−	0.937071i	$-0.613526\pi$
$827$	−20.0808	−0.698277	−0.349138	+	0.937071i	$0.613526\pi$
$828$	−4.25430	−0.147847
$829$	−10.6810	−0.370968	−0.185484	−	0.982647i	$-0.559385\pi$
$829$	−10.6810	−0.370968	−0.185484	+	0.982647i	$0.559385\pi$
$830$	18.7671	0.651417
$831$	−16.2950	−0.565266
$832$	−5.72424	−0.198452
$833$	10.4541	0.362214
$834$	−11.0518	−0.382692
$835$	22.8261	0.789930
$836$	−0.945380	−0.0326967
$837$	5.24958	0.181452
$838$	−16.8689	−0.582726
$839$	−45.1309	−1.55809	−0.779045	−	0.626968i	$-0.784296\pi$
$839$	−45.1309	−1.55809	−0.779045	+	0.626968i	$0.784296\pi$
$840$	−1.73187	−0.0597552
$841$	1.06356	0.0366744
$842$	−8.14734	−0.280776
$843$	4.86474	0.167551
$844$	6.33737	0.218141
$845$	36.2751	1.24790
$846$	9.84505	0.338480
$847$	−9.53758	−0.327715
$848$	1.00000	0.0343401
$849$	−26.6781	−0.915591
$850$	−2.79309	−0.0958023
$851$	−14.9629	−0.512920
$852$	−8.75401	−0.299907
$853$	54.2290	1.85677	0.928383	−	0.371625i	$-0.121199\pi$
$853$	54.2290	1.85677	0.928383	+	0.371625i	$0.121199\pi$
$854$	−7.17761	−0.245613
$855$	−1.83513	−0.0627603
$856$	−1.45928	−0.0498773
$857$	11.0392	0.377091	0.188545	−	0.982064i	$-0.439623\pi$
$857$	11.0392	0.377091	0.188545	+	0.982064i	$0.439623\pi$
$858$	5.41159	0.184749
$859$	−22.1238	−0.754853	−0.377427	−	0.926039i	$-0.623191\pi$
$859$	−22.1238	−0.754853	−0.377427	+	0.926039i	$0.623191\pi$
$860$	−17.9421	−0.611822
$861$	2.94817	0.100473
$862$	−37.8269	−1.28839
$863$	37.8195	1.28739	0.643696	−	0.765282i	$-0.277400\pi$
$863$	37.8195	1.28739	0.643696	+	0.765282i	$0.277400\pi$
$864$	−1.00000	−0.0340207
$865$	1.45456	0.0494565
$866$	−27.1022	−0.920971
$867$	−14.0719	−0.477908
$868$	4.95419	0.168156
$869$	13.1798	0.447095
$870$	10.0621	0.341137
$871$	66.3068	2.24672
$872$	9.31958	0.315601
$873$	−11.4165	−0.386391
$874$	−4.25430	−0.143904
$875$	−11.4863	−0.388306
$876$	0.103642	0.00350173
$877$	−5.84907	−0.197509	−0.0987545	−	0.995112i	$-0.531486\pi$
$877$	−5.84907	−0.197509	−0.0987545	+	0.995112i	$0.531486\pi$
$878$	30.1404	1.01719
$879$	−11.7215	−0.395358
$880$	1.73490	0.0584835
$881$	45.7867	1.54259	0.771296	−	0.636477i	$-0.219609\pi$
$881$	45.7867	1.54259	0.771296	+	0.636477i	$0.219609\pi$
$882$	6.10937	0.205713
$883$	6.02749	0.202841	0.101421	−	0.994844i	$-0.467661\pi$
$883$	6.02749	0.202841	0.101421	+	0.994844i	$0.467661\pi$
$884$	9.79510	0.329445
$885$	17.0465	0.573012
$886$	2.76097	0.0927568
$887$	22.6750	0.761354	0.380677	−	0.924708i	$-0.375691\pi$
$887$	22.6750	0.761354	0.380677	+	0.924708i	$0.375691\pi$
$888$	−3.51711	−0.118026
$889$	−0.930557	−0.0312099
$890$	−8.60564	−0.288462
$891$	0.945380	0.0316714
$892$	25.9879	0.870138
$893$	9.84505	0.329452
$894$	−11.5495	−0.386272
$895$	30.5002	1.01951
$896$	−0.943730	−0.0315278
$897$	24.3527	0.813112
$898$	5.32221	0.177604
$899$	−28.7836	−0.959986
$900$	−1.63228	−0.0544094
$901$	−1.71116	−0.0570070
$902$	−2.95333	−0.0983350
$903$	−9.22686	−0.307051
$904$	5.69613	0.189450
$905$	−33.3240	−1.10773
$906$	15.1818	0.504381
$907$	16.6776	0.553772	0.276886	−	0.960903i	$-0.410698\pi$
$907$	16.6776	0.553772	0.276886	+	0.960903i	$0.410698\pi$
$908$	1.44464	0.0479420
$909$	−11.8300	−0.392375
$910$	9.91366	0.328634
$911$	−1.14044	−0.0377844	−0.0188922	−	0.999822i	$-0.506014\pi$
$911$	−1.14044	−0.0377844	−0.0188922	+	0.999822i	$0.506014\pi$
$912$	−1.00000	−0.0331133
$913$	−9.66800	−0.319964
$914$	38.5993	1.27675
$915$	13.9572	0.461412
$916$	3.78065	0.124916
$917$	14.1226	0.466371
$918$	1.71116	0.0564767
$919$	−14.5640	−0.480421	−0.240210	−	0.970721i	$-0.577216\pi$
$919$	−14.5640	−0.480421	−0.240210	+	0.970721i	$0.577216\pi$
$920$	7.80722	0.257396
$921$	9.89391	0.326015
$922$	−25.7184	−0.846989
$923$	50.1101	1.64939
$924$	0.892184	0.0293507
$925$	−5.74091	−0.188760
$926$	−1.37037	−0.0450331
$927$	−12.4760	−0.409765
$928$	5.48302	0.179989
$929$	34.1670	1.12098	0.560491	−	0.828160i	$-0.310612\pi$
$929$	34.1670	1.12098	0.560491	+	0.828160i	$0.310612\pi$
$930$	−9.63369	−0.315901
$931$	6.10937	0.200227
$932$	2.74114	0.0897891
$933$	−17.8694	−0.585019
$934$	10.7367	0.351316
$935$	−2.96869	−0.0970866
$936$	5.72424	0.187103
$937$	−7.21300	−0.235639	−0.117819	−	0.993035i	$-0.537590\pi$
$937$	−7.21300	−0.235639	−0.117819	+	0.993035i	$0.537590\pi$
$938$	10.9317	0.356932
$939$	18.7648	0.612367
$940$	−18.0670	−0.589280
$941$	−49.7419	−1.62154	−0.810770	−	0.585365i	$-0.800951\pi$
$941$	−49.7419	−1.62154	−0.810770	+	0.585365i	$0.800951\pi$
$942$	−5.37516	−0.175132
$943$	−13.2903	−0.432790
$944$	9.28897	0.302330
$945$	1.73187	0.0563378
$946$	9.24300	0.300516
$947$	−23.9521	−0.778340	−0.389170	−	0.921166i	$-0.627238\pi$
$947$	−23.9521	−0.778340	−0.389170	+	0.921166i	$0.627238\pi$
$948$	13.9413	0.452792
$949$	−0.593270	−0.0192584
$950$	−1.63228	−0.0529582
$951$	9.00652	0.292057
$952$	1.61487	0.0523383
$953$	7.72995	0.250398	0.125199	−	0.992132i	$-0.460043\pi$
$953$	7.72995	0.250398	0.125199	+	0.992132i	$0.460043\pi$
$954$	−1.00000	−0.0323762
$955$	−18.6300	−0.602851
$956$	12.5178	0.404856
$957$	−5.18354	−0.167560
$958$	34.1475	1.10326
$959$	7.92990	0.256070
$960$	1.83513	0.0592287
$961$	−3.44190	−0.111029
$962$	20.1328	0.649108
$963$	1.45928	0.0470248
$964$	−29.8382	−0.961024
$965$	−37.8439	−1.21824
$966$	4.01491	0.129178
$967$	−48.9783	−1.57504	−0.787518	−	0.616292i	$-0.788634\pi$
$967$	−48.9783	−1.57504	−0.787518	+	0.616292i	$0.788634\pi$
$968$	10.1063	0.324827
$969$	1.71116	0.0549704
$970$	20.9509	0.672691
$971$	21.0298	0.674877	0.337439	−	0.941348i	$-0.390439\pi$
$971$	21.0298	0.674877	0.337439	+	0.941348i	$0.390439\pi$
$972$	1.00000	0.0320750
$973$	10.4299	0.334367
$974$	−19.4474	−0.623134
$975$	9.34358	0.299234
$976$	7.60557	0.243448
$977$	26.5421	0.849156	0.424578	−	0.905391i	$-0.360423\pi$
$977$	26.5421	0.849156	0.424578	+	0.905391i	$0.360423\pi$
$978$	2.06780	0.0661209
$979$	4.43324	0.141687
$980$	−11.2115	−0.358139
$981$	−9.31958	−0.297551
$982$	42.4811	1.35562
$983$	−54.7889	−1.74750	−0.873748	−	0.486379i	$-0.838317\pi$
$983$	−54.7889	−1.74750	−0.873748	+	0.486379i	$0.838317\pi$
$984$	−3.12396	−0.0995881
$985$	−28.3535	−0.903418
$986$	−9.38233	−0.298794
$987$	−9.29107	−0.295738
$988$	5.72424	0.182112
$989$	41.5944	1.32262
$990$	−1.73490	−0.0551387
$991$	45.1709	1.43490	0.717450	−	0.696610i	$-0.245309\pi$
$991$	45.1709	1.43490	0.717450	+	0.696610i	$0.245309\pi$
$992$	−5.24958	−0.166674
$993$	7.83078	0.248502
$994$	8.26142	0.262036
$995$	0.938088	0.0297394
$996$	−10.2266	−0.324041
$997$	−48.8274	−1.54638	−0.773190	−	0.634174i	$-0.781340\pi$
$997$	−48.8274	−1.54638	−0.773190	+	0.634174i	$0.781340\pi$
$998$	13.0234	0.412249
$999$	3.51711	0.111276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.y.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.y.1.6	✓	7	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83513 q^{5} -1.00000 q^{6} +0.943730 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.83513 q^{5} -1.00000 q^{6} +0.943730 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.83513 q^{10} +0.945380 q^{11} +1.00000 q^{12} -5.72424 q^{13} -0.943730 q^{14} +1.83513 q^{15} +1.00000 q^{16} -1.71116 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.83513 q^{20} +0.943730 q^{21} -0.945380 q^{22} -4.25430 q^{23} -1.00000 q^{24} -1.63228 q^{25} +5.72424 q^{26} +1.00000 q^{27} +0.943730 q^{28} -5.48302 q^{29} -1.83513 q^{30} +5.24958 q^{31} -1.00000 q^{32} +0.945380 q^{33} +1.71116 q^{34} +1.73187 q^{35} +1.00000 q^{36} +3.51711 q^{37} +1.00000 q^{38} -5.72424 q^{39} -1.83513 q^{40} +3.12396 q^{41} -0.943730 q^{42} -9.77701 q^{43} +0.945380 q^{44} +1.83513 q^{45} +4.25430 q^{46} -9.84505 q^{47} +1.00000 q^{48} -6.10937 q^{49} +1.63228 q^{50} -1.71116 q^{51} -5.72424 q^{52} +1.00000 q^{53} -1.00000 q^{54} +1.73490 q^{55} -0.943730 q^{56} -1.00000 q^{57} +5.48302 q^{58} +9.28897 q^{59} +1.83513 q^{60} +7.60557 q^{61} -5.24958 q^{62} +0.943730 q^{63} +1.00000 q^{64} -10.5048 q^{65} -0.945380 q^{66} -11.5835 q^{67} -1.71116 q^{68} -4.25430 q^{69} -1.73187 q^{70} -8.75401 q^{71} -1.00000 q^{72} +0.103642 q^{73} -3.51711 q^{74} -1.63228 q^{75} -1.00000 q^{76} +0.892184 q^{77} +5.72424 q^{78} +13.9413 q^{79} +1.83513 q^{80} +1.00000 q^{81} -3.12396 q^{82} -10.2266 q^{83} +0.943730 q^{84} -3.14021 q^{85} +9.77701 q^{86} -5.48302 q^{87} -0.945380 q^{88} +4.68938 q^{89} -1.83513 q^{90} -5.40214 q^{91} -4.25430 q^{92} +5.24958 q^{93} +9.84505 q^{94} -1.83513 q^{95} -1.00000 q^{96} -11.4165 q^{97} +6.10937 q^{98} +0.945380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * q^99

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