LMFDB - Embedded newform 6045.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 15 x^{9} + 29 x^{8} + 81 x^{7} - 151 x^{6} - 192 x^{5} + 345 x^{4} + 199 x^{3} + \cdots + 118 $ x^11 - 2x^10 - 15x^9 + 29x^8 + 81x^7 - 151x^6 - 192x^5 + 345x^4 + 199x^3 - 344x^2 - 70x + 118
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.18294$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18294 q^{2} -1.00000 q^{3} +2.76522 q^{4} -1.00000 q^{5} +2.18294 q^{6} +0.121846 q^{7} -1.67042 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18294 q^{2} -1.00000 q^{3} +2.76522 q^{4} -1.00000 q^{5} +2.18294 q^{6} +0.121846 q^{7} -1.67042 q^{8} +1.00000 q^{9} +2.18294 q^{10} -2.69927 q^{11} -2.76522 q^{12} -1.00000 q^{13} -0.265982 q^{14} +1.00000 q^{15} -1.88401 q^{16} +4.36968 q^{17} -2.18294 q^{18} +0.489188 q^{19} -2.76522 q^{20} -0.121846 q^{21} +5.89233 q^{22} -1.37944 q^{23} +1.67042 q^{24} +1.00000 q^{25} +2.18294 q^{26} -1.00000 q^{27} +0.336930 q^{28} +2.76690 q^{29} -2.18294 q^{30} -1.00000 q^{31} +7.45352 q^{32} +2.69927 q^{33} -9.53874 q^{34} -0.121846 q^{35} +2.76522 q^{36} -10.8514 q^{37} -1.06787 q^{38} +1.00000 q^{39} +1.67042 q^{40} +1.31479 q^{41} +0.265982 q^{42} -0.663518 q^{43} -7.46405 q^{44} -1.00000 q^{45} +3.01122 q^{46} +5.38791 q^{47} +1.88401 q^{48} -6.98515 q^{49} -2.18294 q^{50} -4.36968 q^{51} -2.76522 q^{52} +6.09480 q^{53} +2.18294 q^{54} +2.69927 q^{55} -0.203533 q^{56} -0.489188 q^{57} -6.03997 q^{58} +14.3339 q^{59} +2.76522 q^{60} -10.9089 q^{61} +2.18294 q^{62} +0.121846 q^{63} -12.5025 q^{64} +1.00000 q^{65} -5.89233 q^{66} +0.377510 q^{67} +12.0831 q^{68} +1.37944 q^{69} +0.265982 q^{70} +0.664296 q^{71} -1.67042 q^{72} +15.8588 q^{73} +23.6878 q^{74} -1.00000 q^{75} +1.35271 q^{76} -0.328894 q^{77} -2.18294 q^{78} -2.39380 q^{79} +1.88401 q^{80} +1.00000 q^{81} -2.87010 q^{82} -0.171520 q^{83} -0.336930 q^{84} -4.36968 q^{85} +1.44842 q^{86} -2.76690 q^{87} +4.50890 q^{88} -8.62711 q^{89} +2.18294 q^{90} -0.121846 q^{91} -3.81444 q^{92} +1.00000 q^{93} -11.7615 q^{94} -0.489188 q^{95} -7.45352 q^{96} +10.7893 q^{97} +15.2482 q^{98} -2.69927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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 $

$2$	−2.18294	−1.54357	−0.771785	−	0.635884i	$-0.780636\pi$
$2$	−2.18294	−1.54357	−0.771785	+	0.635884i	$0.780636\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.76522	1.38261
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.18294	0.891180
$7$	0.121846	0.0460534	0.0230267	−	0.999735i	$-0.492670\pi$
$7$	0.121846	0.0460534	0.0230267	+	0.999735i	$0.492670\pi$
$8$	−1.67042	−0.590582
$9$	1.00000	0.333333
$10$	2.18294	0.690305
$11$	−2.69927	−0.813859	−0.406930	−	0.913460i	$-0.633401\pi$
$11$	−2.69927	−0.813859	−0.406930	+	0.913460i	$0.633401\pi$
$12$	−2.76522	−0.798249
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.265982	−0.0710866
$15$	1.00000	0.258199
$16$	−1.88401	−0.471004
$17$	4.36968	1.05980	0.529902	−	0.848059i	$-0.322229\pi$
$17$	4.36968	1.05980	0.529902	+	0.848059i	$0.322229\pi$
$18$	−2.18294	−0.514523
$19$	0.489188	0.112227	0.0561137	−	0.998424i	$-0.482129\pi$
$19$	0.489188	0.112227	0.0561137	+	0.998424i	$0.482129\pi$
$20$	−2.76522	−0.618321
$21$	−0.121846	−0.0265889
$22$	5.89233	1.25625
$23$	−1.37944	−0.287632	−0.143816	−	0.989604i	$-0.545937\pi$
$23$	−1.37944	−0.287632	−0.143816	+	0.989604i	$0.545937\pi$
$24$	1.67042	0.340972
$25$	1.00000	0.200000
$26$	2.18294	0.428109
$27$	−1.00000	−0.192450
$28$	0.336930	0.0636737
$29$	2.76690	0.513801	0.256900	−	0.966438i	$-0.417299\pi$
$29$	2.76690	0.513801	0.256900	+	0.966438i	$0.417299\pi$
$30$	−2.18294	−0.398548
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.45352	1.31761
$33$	2.69927	0.469882
$34$	−9.53874	−1.63588
$35$	−0.121846	−0.0205957
$36$	2.76522	0.460869
$37$	−10.8514	−1.78395	−0.891976	−	0.452083i	$-0.850681\pi$
$37$	−10.8514	−1.78395	−0.891976	+	0.452083i	$0.850681\pi$
$38$	−1.06787	−0.173231
$39$	1.00000	0.160128
$40$	1.67042	0.264116
$41$	1.31479	0.205335	0.102668	−	0.994716i	$-0.467262\pi$
$41$	1.31479	0.205335	0.102668	+	0.994716i	$0.467262\pi$
$42$	0.265982	0.0410419
$43$	−0.663518	−0.101185	−0.0505927	−	0.998719i	$-0.516111\pi$
$43$	−0.663518	−0.101185	−0.0505927	+	0.998719i	$0.516111\pi$
$44$	−7.46405	−1.12525
$45$	−1.00000	−0.149071
$46$	3.01122	0.443980
$47$	5.38791	0.785908	0.392954	−	0.919558i	$-0.371453\pi$
$47$	5.38791	0.785908	0.392954	+	0.919558i	$0.371453\pi$
$48$	1.88401	0.271934
$49$	−6.98515	−0.997879
$50$	−2.18294	−0.308714
$51$	−4.36968	−0.611878
$52$	−2.76522	−0.383466
$53$	6.09480	0.837185	0.418593	−	0.908174i	$-0.362524\pi$
$53$	6.09480	0.837185	0.418593	+	0.908174i	$0.362524\pi$
$54$	2.18294	0.297060
$55$	2.69927	0.363969
$56$	−0.203533	−0.0271983
$57$	−0.489188	−0.0647945
$58$	−6.03997	−0.793087
$59$	14.3339	1.86611	0.933056	−	0.359730i	$-0.117131\pi$
$59$	14.3339	1.86611	0.933056	+	0.359730i	$0.117131\pi$
$60$	2.76522	0.356988
$61$	−10.9089	−1.39675	−0.698373	−	0.715734i	$-0.746092\pi$
$61$	−10.9089	−1.39675	−0.698373	+	0.715734i	$0.746092\pi$
$62$	2.18294	0.277233
$63$	0.121846	0.0153511
$64$	−12.5025	−1.56282
$65$	1.00000	0.124035
$66$	−5.89233	−0.725295
$67$	0.377510	0.0461202	0.0230601	−	0.999734i	$-0.492659\pi$
$67$	0.377510	0.0461202	0.0230601	+	0.999734i	$0.492659\pi$
$68$	12.0831	1.46529
$69$	1.37944	0.166065
$70$	0.265982	0.0317909
$71$	0.664296	0.0788374	0.0394187	−	0.999223i	$-0.487449\pi$
$71$	0.664296	0.0788374	0.0394187	+	0.999223i	$0.487449\pi$
$72$	−1.67042	−0.196861
$73$	15.8588	1.85613	0.928067	−	0.372414i	$-0.121470\pi$
$73$	15.8588	1.85613	0.928067	+	0.372414i	$0.121470\pi$
$74$	23.6878	2.75365
$75$	−1.00000	−0.115470
$76$	1.35271	0.155167
$77$	−0.328894	−0.0374809
$78$	−2.18294	−0.247169
$79$	−2.39380	−0.269324	−0.134662	−	0.990892i	$-0.542995\pi$
$79$	−2.39380	−0.269324	−0.134662	+	0.990892i	$0.542995\pi$
$80$	1.88401	0.210639
$81$	1.00000	0.111111
$82$	−2.87010	−0.316949
$83$	−0.171520	−0.0188267	−0.00941337	−	0.999956i	$-0.502996\pi$
$83$	−0.171520	−0.0188267	−0.00941337	+	0.999956i	$0.502996\pi$
$84$	−0.336930	−0.0367620
$85$	−4.36968	−0.473959
$86$	1.44842	0.156187
$87$	−2.76690	−0.296643
$88$	4.50890	0.480650
$89$	−8.62711	−0.914472	−0.457236	−	0.889345i	$-0.651161\pi$
$89$	−8.62711	−0.914472	−0.457236	+	0.889345i	$0.651161\pi$
$90$	2.18294	0.230102
$91$	−0.121846	−0.0127729
$92$	−3.81444	−0.397682
$93$	1.00000	0.103695
$94$	−11.7615	−1.21310
$95$	−0.489188	−0.0501896
$96$	−7.45352	−0.760722
$97$	10.7893	1.09549	0.547743	−	0.836646i	$-0.315487\pi$
$97$	10.7893	1.09549	0.547743	+	0.836646i	$0.315487\pi$
$98$	15.2482	1.54030
$99$	−2.69927	−0.271286
$100$	2.76522	0.276522
$101$	−13.6432	−1.35755	−0.678777	−	0.734344i	$-0.737490\pi$
$101$	−13.6432	−1.35755	−0.678777	+	0.734344i	$0.737490\pi$
$102$	9.53874	0.944476
$103$	−16.4058	−1.61651	−0.808254	−	0.588835i	$-0.799587\pi$
$103$	−16.4058	−1.61651	−0.808254	+	0.588835i	$0.799587\pi$
$104$	1.67042	0.163798
$105$	0.121846	0.0118909
$106$	−13.3046	−1.29225
$107$	5.41857	0.523833	0.261917	−	0.965091i	$-0.415645\pi$
$107$	5.41857	0.523833	0.261917	+	0.965091i	$0.415645\pi$
$108$	−2.76522	−0.266083
$109$	5.01652	0.480496	0.240248	−	0.970712i	$-0.422771\pi$
$109$	5.01652	0.480496	0.240248	+	0.970712i	$0.422771\pi$
$110$	−5.89233	−0.561811
$111$	10.8514	1.02997
$112$	−0.229559	−0.0216913
$113$	−16.2066	−1.52459	−0.762297	−	0.647228i	$-0.775928\pi$
$113$	−16.2066	−1.52459	−0.762297	+	0.647228i	$0.775928\pi$
$114$	1.06787	0.100015
$115$	1.37944	0.128633
$116$	7.65108	0.710385
$117$	−1.00000	−0.0924500
$118$	−31.2900	−2.88048
$119$	0.532427	0.0488075
$120$	−1.67042	−0.152488
$121$	−3.71397	−0.337633
$122$	23.8135	2.15598
$123$	−1.31479	−0.118550
$124$	−2.76522	−0.248324
$125$	−1.00000	−0.0894427
$126$	−0.265982	−0.0236955
$127$	2.66148	0.236168	0.118084	−	0.993004i	$-0.462325\pi$
$127$	2.66148	0.236168	0.118084	+	0.993004i	$0.462325\pi$
$128$	12.3852	1.09471
$129$	0.663518	0.0584195
$130$	−2.18294	−0.191456
$131$	−2.38633	−0.208494	−0.104247	−	0.994551i	$-0.533243\pi$
$131$	−2.38633	−0.208494	−0.104247	+	0.994551i	$0.533243\pi$
$132$	7.46405	0.649662
$133$	0.0596055	0.00516845
$134$	−0.824080	−0.0711897
$135$	1.00000	0.0860663
$136$	−7.29919	−0.625901
$137$	18.7011	1.59774	0.798872	−	0.601501i	$-0.205430\pi$
$137$	18.7011	1.59774	0.798872	+	0.601501i	$0.205430\pi$
$138$	−3.01122	−0.256332
$139$	−8.81638	−0.747796	−0.373898	−	0.927470i	$-0.621979\pi$
$139$	−8.81638	−0.747796	−0.373898	+	0.927470i	$0.621979\pi$
$140$	−0.336930	−0.0284758
$141$	−5.38791	−0.453744
$142$	−1.45012	−0.121691
$143$	2.69927	0.225724
$144$	−1.88401	−0.157001
$145$	−2.76690	−0.229779
$146$	−34.6188	−2.86507
$147$	6.98515	0.576126
$148$	−30.0063	−2.46651
$149$	5.66722	0.464276	0.232138	−	0.972683i	$-0.425428\pi$
$149$	5.66722	0.464276	0.232138	+	0.972683i	$0.425428\pi$
$150$	2.18294	0.178236
$151$	1.43625	0.116880	0.0584402	−	0.998291i	$-0.481387\pi$
$151$	1.43625	0.116880	0.0584402	+	0.998291i	$0.481387\pi$
$152$	−0.817148	−0.0662795
$153$	4.36968	0.353268
$154$	0.717955	0.0578545
$155$	1.00000	0.0803219
$156$	2.76522	0.221394
$157$	8.73871	0.697425	0.348712	−	0.937230i	$-0.386619\pi$
$157$	8.73871	0.697425	0.348712	+	0.937230i	$0.386619\pi$
$158$	5.22552	0.415720
$159$	−6.09480	−0.483349
$160$	−7.45352	−0.589253
$161$	−0.168078	−0.0132464
$162$	−2.18294	−0.171508
$163$	11.2819	0.883670	0.441835	−	0.897096i	$-0.354328\pi$
$163$	11.2819	0.883670	0.441835	+	0.897096i	$0.354328\pi$
$164$	3.63567	0.283898
$165$	−2.69927	−0.210138
$166$	0.374417	0.0290604
$167$	1.43019	0.110671	0.0553356	−	0.998468i	$-0.482377\pi$
$167$	1.43019	0.110671	0.0553356	+	0.998468i	$0.482377\pi$
$168$	0.203533	0.0157029
$169$	1.00000	0.0769231
$170$	9.53874	0.731588
$171$	0.489188	0.0374091
$172$	−1.83477	−0.139900
$173$	18.3288	1.39351	0.696757	−	0.717307i	$-0.254626\pi$
$173$	18.3288	1.39351	0.696757	+	0.717307i	$0.254626\pi$
$174$	6.03997	0.457889
$175$	0.121846	0.00921067
$176$	5.08546	0.383331
$177$	−14.3339	−1.07740
$178$	18.8324	1.41155
$179$	−20.1508	−1.50614	−0.753071	−	0.657939i	$-0.771428\pi$
$179$	−20.1508	−1.50614	−0.753071	+	0.657939i	$0.771428\pi$
$180$	−2.76522	−0.206107
$181$	15.9328	1.18427	0.592137	−	0.805837i	$-0.298284\pi$
$181$	15.9328	1.18427	0.592137	+	0.805837i	$0.298284\pi$
$182$	0.265982	0.0197159
$183$	10.9089	0.806412
$184$	2.30423	0.169870
$185$	10.8514	0.797807
$186$	−2.18294	−0.160061
$187$	−11.7949	−0.862531
$188$	14.8987	1.08660
$189$	−0.121846	−0.00886297
$190$	1.06787	0.0774712
$191$	2.10350	0.152204	0.0761020	−	0.997100i	$-0.475753\pi$
$191$	2.10350	0.152204	0.0761020	+	0.997100i	$0.475753\pi$
$192$	12.5025	0.902293
$193$	9.21955	0.663638	0.331819	−	0.943343i	$-0.392338\pi$
$193$	9.21955	0.663638	0.331819	+	0.943343i	$0.392338\pi$
$194$	−23.5524	−1.69096
$195$	−1.00000	−0.0716115
$196$	−19.3155	−1.37968
$197$	3.07085	0.218789	0.109394	−	0.993998i	$-0.465109\pi$
$197$	3.07085	0.218789	0.109394	+	0.993998i	$0.465109\pi$
$198$	5.89233	0.418749
$199$	17.0895	1.21144	0.605722	−	0.795676i	$-0.292884\pi$
$199$	17.0895	1.21144	0.605722	+	0.795676i	$0.292884\pi$
$200$	−1.67042	−0.118116
$201$	−0.377510	−0.0266275
$202$	29.7824	2.09548
$203$	0.337135	0.0236623
$204$	−12.0831	−0.845987
$205$	−1.31479	−0.0918288
$206$	35.8127	2.49519
$207$	−1.37944	−0.0958774
$208$	1.88401	0.130633
$209$	−1.32045	−0.0913373
$210$	−0.265982	−0.0183545
$211$	−11.2341	−0.773386	−0.386693	−	0.922209i	$-0.626383\pi$
$211$	−11.2341	−0.773386	−0.386693	+	0.922209i	$0.626383\pi$
$212$	16.8534	1.15750
$213$	−0.664296	−0.0455168
$214$	−11.8284	−0.808573
$215$	0.663518	0.0452515
$216$	1.67042	0.113657
$217$	−0.121846	−0.00827143
$218$	−10.9508	−0.741679
$219$	−15.8588	−1.07164
$220$	7.46405	0.503226
$221$	−4.36968	−0.293937
$222$	−23.6878	−1.58982
$223$	13.0897	0.876549	0.438275	−	0.898841i	$-0.355590\pi$
$223$	13.0897	0.876549	0.438275	+	0.898841i	$0.355590\pi$
$224$	0.908180	0.0606803
$225$	1.00000	0.0666667
$226$	35.3781	2.35332
$227$	−15.9459	−1.05837	−0.529184	−	0.848507i	$-0.677502\pi$
$227$	−15.9459	−1.05837	−0.529184	+	0.848507i	$0.677502\pi$
$228$	−1.35271	−0.0895854
$229$	−7.72033	−0.510174	−0.255087	−	0.966918i	$-0.582104\pi$
$229$	−7.72033	−0.510174	−0.255087	+	0.966918i	$0.582104\pi$
$230$	−3.01122	−0.198554
$231$	0.328894	0.0216396
$232$	−4.62188	−0.303441
$233$	13.5052	0.884754	0.442377	−	0.896829i	$-0.354135\pi$
$233$	13.5052	0.884754	0.442377	+	0.896829i	$0.354135\pi$
$234$	2.18294	0.142703
$235$	−5.38791	−0.351469
$236$	39.6363	2.58010
$237$	2.39380	0.155494
$238$	−1.16226	−0.0753378
$239$	−17.3268	−1.12078	−0.560390	−	0.828229i	$-0.689349\pi$
$239$	−17.3268	−1.12078	−0.560390	+	0.828229i	$0.689349\pi$
$240$	−1.88401	−0.121613
$241$	−30.7096	−1.97818	−0.989089	−	0.147317i	$-0.952936\pi$
$241$	−30.7096	−1.97818	−0.989089	+	0.147317i	$0.952936\pi$
$242$	8.10736	0.521161
$243$	−1.00000	−0.0641500
$244$	−30.1656	−1.93115
$245$	6.98515	0.446265
$246$	2.87010	0.182991
$247$	−0.489188	−0.0311263
$248$	1.67042	0.106072
$249$	0.171520	0.0108696
$250$	2.18294	0.138061
$251$	13.6801	0.863477	0.431739	−	0.901999i	$-0.357900\pi$
$251$	13.6801	0.863477	0.431739	+	0.901999i	$0.357900\pi$
$252$	0.336930	0.0212246
$253$	3.72346	0.234092
$254$	−5.80985	−0.364543
$255$	4.36968	0.273640
$256$	−2.03107	−0.126942
$257$	−6.18392	−0.385743	−0.192871	−	0.981224i	$-0.561780\pi$
$257$	−6.18392	−0.385743	−0.192871	+	0.981224i	$0.561780\pi$
$258$	−1.44842	−0.0901745
$259$	−1.32219	−0.0821570
$260$	2.76522	0.171491
$261$	2.76690	0.171267
$262$	5.20920	0.321826
$263$	0.449369	0.0277093	0.0138546	−	0.999904i	$-0.495590\pi$
$263$	0.449369	0.0277093	0.0138546	+	0.999904i	$0.495590\pi$
$264$	−4.50890	−0.277504
$265$	−6.09480	−0.374401
$266$	−0.130115	−0.00797786
$267$	8.62711	0.527971
$268$	1.04390	0.0637661
$269$	14.5125	0.884840	0.442420	−	0.896808i	$-0.354120\pi$
$269$	14.5125	0.884840	0.442420	+	0.896808i	$0.354120\pi$
$270$	−2.18294	−0.132849
$271$	1.52358	0.0925511	0.0462756	−	0.998929i	$-0.485265\pi$
$271$	1.52358	0.0925511	0.0462756	+	0.998929i	$0.485265\pi$
$272$	−8.23255	−0.499171
$273$	0.121846	0.00737444
$274$	−40.8234	−2.46623
$275$	−2.69927	−0.162772
$276$	3.81444	0.229602
$277$	10.7132	0.643692	0.321846	−	0.946792i	$-0.395697\pi$
$277$	10.7132	0.643692	0.321846	+	0.946792i	$0.395697\pi$
$278$	19.2456	1.15428
$279$	−1.00000	−0.0598684
$280$	0.203533	0.0121634
$281$	7.28139	0.434371	0.217186	−	0.976130i	$-0.430312\pi$
$281$	7.28139	0.434371	0.217186	+	0.976130i	$0.430312\pi$
$282$	11.7615	0.700385
$283$	−1.97232	−0.117242	−0.0586211	−	0.998280i	$-0.518670\pi$
$283$	−1.97232	−0.117242	−0.0586211	+	0.998280i	$0.518670\pi$
$284$	1.83692	0.109001
$285$	0.489188	0.0289770
$286$	−5.89233	−0.348421
$287$	0.160201	0.00945638
$288$	7.45352	0.439203
$289$	2.09412	0.123184
$290$	6.03997	0.354679
$291$	−10.7893	−0.632480
$292$	43.8530	2.56630
$293$	−1.70720	−0.0997355	−0.0498677	−	0.998756i	$-0.515880\pi$
$293$	−1.70720	−0.0997355	−0.0498677	+	0.998756i	$0.515880\pi$
$294$	−15.2482	−0.889290
$295$	−14.3339	−0.834551
$296$	18.1263	1.05357
$297$	2.69927	0.156627
$298$	−12.3712	−0.716643
$299$	1.37944	0.0797748
$300$	−2.76522	−0.159650
$301$	−0.0808468	−0.00465993
$302$	−3.13525	−0.180413
$303$	13.6432	0.783784
$304$	−0.921638	−0.0528595
$305$	10.9089	0.624644
$306$	−9.53874	−0.545294
$307$	−31.1631	−1.77857	−0.889285	−	0.457353i	$-0.848798\pi$
$307$	−31.1631	−1.77857	−0.889285	+	0.457353i	$0.848798\pi$
$308$	−0.909463	−0.0518214
$309$	16.4058	0.933291
$310$	−2.18294	−0.123983
$311$	19.4079	1.10052	0.550261	−	0.834993i	$-0.314528\pi$
$311$	19.4079	1.10052	0.550261	+	0.834993i	$0.314528\pi$
$312$	−1.67042	−0.0945687
$313$	−1.91191	−0.108068	−0.0540339	−	0.998539i	$-0.517208\pi$
$313$	−1.91191	−0.108068	−0.0540339	+	0.998539i	$0.517208\pi$
$314$	−19.0760	−1.07652
$315$	−0.121846	−0.00686523
$316$	−6.61938	−0.372369
$317$	29.3446	1.64816	0.824078	−	0.566476i	$-0.191694\pi$
$317$	29.3446	1.64816	0.824078	+	0.566476i	$0.191694\pi$
$318$	13.3046	0.746083
$319$	−7.46860	−0.418161
$320$	12.5025	0.698913
$321$	−5.41857	−0.302435
$322$	0.366905	0.0204468
$323$	2.13760	0.118939
$324$	2.76522	0.153623
$325$	−1.00000	−0.0554700
$326$	−24.6278	−1.36401
$327$	−5.01652	−0.277414
$328$	−2.19624	−0.121267
$329$	0.656494	0.0361937
$330$	5.89233	0.324362
$331$	−11.2128	−0.616309	−0.308155	−	0.951336i	$-0.599711\pi$
$331$	−11.2128	−0.616309	−0.308155	+	0.951336i	$0.599711\pi$
$332$	−0.474289	−0.0260300
$333$	−10.8514	−0.594651
$334$	−3.12201	−0.170829
$335$	−0.377510	−0.0206256
$336$	0.229559	0.0125235
$337$	22.7340	1.23840	0.619200	−	0.785233i	$-0.287457\pi$
$337$	22.7340	1.23840	0.619200	+	0.785233i	$0.287457\pi$
$338$	−2.18294	−0.118736
$339$	16.2066	0.880224
$340$	−12.0831	−0.655299
$341$	2.69927	0.146173
$342$	−1.06787	−0.0577436
$343$	−1.70403	−0.0920090
$344$	1.10835	0.0597583
$345$	−1.37944	−0.0742663
$346$	−40.0106	−2.15099
$347$	−32.0359	−1.71978	−0.859888	−	0.510483i	$-0.829467\pi$
$347$	−32.0359	−1.71978	−0.859888	+	0.510483i	$0.829467\pi$
$348$	−7.65108	−0.410141
$349$	−2.33188	−0.124823	−0.0624113	−	0.998051i	$-0.519879\pi$
$349$	−2.33188	−0.124823	−0.0624113	+	0.998051i	$0.519879\pi$
$350$	−0.265982	−0.0142173
$351$	1.00000	0.0533761
$352$	−20.1190	−1.07235
$353$	3.89368	0.207239	0.103620	−	0.994617i	$-0.466958\pi$
$353$	3.89368	0.207239	0.103620	+	0.994617i	$0.466958\pi$
$354$	31.2900	1.66304
$355$	−0.664296	−0.0352572
$356$	−23.8558	−1.26436
$357$	−0.532427	−0.0281790
$358$	43.9879	2.32484
$359$	15.8758	0.837892	0.418946	−	0.908011i	$-0.362400\pi$
$359$	15.8758	0.837892	0.418946	+	0.908011i	$0.362400\pi$
$360$	1.67042	0.0880387
$361$	−18.7607	−0.987405
$362$	−34.7802	−1.82801
$363$	3.71397	0.194933
$364$	−0.336930	−0.0176599
$365$	−15.8588	−0.830088
$366$	−23.8135	−1.24475
$367$	−1.84039	−0.0960677	−0.0480338	−	0.998846i	$-0.515296\pi$
$367$	−1.84039	−0.0960677	−0.0480338	+	0.998846i	$0.515296\pi$
$368$	2.59888	0.135476
$369$	1.31479	0.0684451
$370$	−23.6878	−1.23147
$371$	0.742625	0.0385552
$372$	2.76522	0.143370
$373$	17.8615	0.924832	0.462416	−	0.886663i	$-0.346983\pi$
$373$	17.8615	0.924832	0.462416	+	0.886663i	$0.346983\pi$
$374$	25.7476	1.33138
$375$	1.00000	0.0516398
$376$	−9.00006	−0.464143
$377$	−2.76690	−0.142503
$378$	0.265982	0.0136806
$379$	−28.5381	−1.46590	−0.732952	−	0.680280i	$-0.761858\pi$
$379$	−28.5381	−1.46590	−0.732952	+	0.680280i	$0.761858\pi$
$380$	−1.35271	−0.0693926
$381$	−2.66148	−0.136352
$382$	−4.59181	−0.234937
$383$	8.41658	0.430067	0.215034	−	0.976607i	$-0.431014\pi$
$383$	8.41658	0.430067	0.215034	+	0.976607i	$0.431014\pi$
$384$	−12.3852	−0.632030
$385$	0.328894	0.0167620
$386$	−20.1257	−1.02437
$387$	−0.663518	−0.0337285
$388$	29.8347	1.51463
$389$	−26.4352	−1.34032	−0.670158	−	0.742219i	$-0.733774\pi$
$389$	−26.4352	−1.34032	−0.670158	+	0.742219i	$0.733774\pi$
$390$	2.18294	0.110537
$391$	−6.02769	−0.304834
$392$	11.6681	0.589329
$393$	2.38633	0.120374
$394$	−6.70347	−0.337716
$395$	2.39380	0.120445
$396$	−7.46405	−0.375083
$397$	9.20077	0.461773	0.230887	−	0.972981i	$-0.425837\pi$
$397$	9.20077	0.461773	0.230887	+	0.972981i	$0.425837\pi$
$398$	−37.3054	−1.86995
$399$	−0.0596055	−0.00298401
$400$	−1.88401	−0.0942007
$401$	11.2048	0.559543	0.279772	−	0.960067i	$-0.409741\pi$
$401$	11.2048	0.559543	0.279772	+	0.960067i	$0.409741\pi$
$402$	0.824080	0.0411014
$403$	1.00000	0.0498135
$404$	−37.7265	−1.87696
$405$	−1.00000	−0.0496904
$406$	−0.735945	−0.0365243
$407$	29.2907	1.45189
$408$	7.29919	0.361364
$409$	0.225184	0.0111346	0.00556731	−	0.999985i	$-0.498228\pi$
$409$	0.225184	0.0111346	0.00556731	+	0.999985i	$0.498228\pi$
$410$	2.87010	0.141744
$411$	−18.7011	−0.922458
$412$	−45.3654	−2.23500
$413$	1.74652	0.0859408
$414$	3.01122	0.147993
$415$	0.171520	0.00841957
$416$	−7.45352	−0.365439
$417$	8.81638	0.431740
$418$	2.88246	0.140986
$419$	−17.2855	−0.844451	−0.422225	−	0.906491i	$-0.638751\pi$
$419$	−17.2855	−0.844451	−0.422225	+	0.906491i	$0.638751\pi$
$420$	0.336930	0.0164405
$421$	10.2320	0.498678	0.249339	−	0.968416i	$-0.419787\pi$
$421$	10.2320	0.498678	0.249339	+	0.968416i	$0.419787\pi$
$422$	24.5233	1.19377
$423$	5.38791	0.261969
$424$	−10.1809	−0.494426
$425$	4.36968	0.211961
$426$	1.45012	0.0702584
$427$	−1.32921	−0.0643249
$428$	14.9835	0.724256
$429$	−2.69927	−0.130322
$430$	−1.44842	−0.0698489
$431$	29.9656	1.44339	0.721695	−	0.692211i	$-0.243363\pi$
$431$	29.9656	1.44339	0.721695	+	0.692211i	$0.243363\pi$
$432$	1.88401	0.0906447
$433$	−23.9444	−1.15069	−0.575347	−	0.817909i	$-0.695133\pi$
$433$	−23.9444	−1.15069	−0.575347	+	0.817909i	$0.695133\pi$
$434$	0.265982	0.0127675
$435$	2.76690	0.132663
$436$	13.8718	0.664337
$437$	−0.674803	−0.0322802
$438$	34.6188	1.65415
$439$	−14.8480	−0.708658	−0.354329	−	0.935121i	$-0.615291\pi$
$439$	−14.8480	−0.708658	−0.354329	+	0.935121i	$0.615291\pi$
$440$	−4.50890	−0.214953
$441$	−6.98515	−0.332626
$442$	9.53874	0.453712
$443$	−26.9768	−1.28171	−0.640854	−	0.767663i	$-0.721420\pi$
$443$	−26.9768	−1.28171	−0.640854	+	0.767663i	$0.721420\pi$
$444$	30.0063	1.42404
$445$	8.62711	0.408964
$446$	−28.5739	−1.35302
$447$	−5.66722	−0.268050
$448$	−1.52338	−0.0719730
$449$	−18.5788	−0.876787	−0.438394	−	0.898783i	$-0.644452\pi$
$449$	−18.5788	−0.876787	−0.438394	+	0.898783i	$0.644452\pi$
$450$	−2.18294	−0.102905
$451$	−3.54896	−0.167114
$452$	−44.8149	−2.10791
$453$	−1.43625	−0.0674810
$454$	34.8089	1.63366
$455$	0.121846	0.00571222
$456$	0.817148	0.0382665
$457$	−40.9029	−1.91336	−0.956678	−	0.291150i	$-0.905962\pi$
$457$	−40.9029	−1.91336	−0.956678	+	0.291150i	$0.905962\pi$
$458$	16.8530	0.787489
$459$	−4.36968	−0.203959
$460$	3.81444	0.177849
$461$	−15.4353	−0.718895	−0.359448	−	0.933165i	$-0.617035\pi$
$461$	−15.4353	−0.718895	−0.359448	+	0.933165i	$0.617035\pi$
$462$	−0.717955	−0.0334023
$463$	10.0704	0.468011	0.234006	−	0.972235i	$-0.424817\pi$
$463$	10.0704	0.468011	0.234006	+	0.972235i	$0.424817\pi$
$464$	−5.21288	−0.242002
$465$	−1.00000	−0.0463739
$466$	−29.4810	−1.36568
$467$	−4.91590	−0.227481	−0.113740	−	0.993511i	$-0.536283\pi$
$467$	−4.91590	−0.227481	−0.113740	+	0.993511i	$0.536283\pi$
$468$	−2.76522	−0.127822
$469$	0.0459980	0.00212399
$470$	11.7615	0.542516
$471$	−8.73871	−0.402658
$472$	−23.9436	−1.10209
$473$	1.79101	0.0823507
$474$	−5.22552	−0.240016
$475$	0.489188	0.0224455
$476$	1.47228	0.0674816
$477$	6.09480	0.279062
$478$	37.8234	1.73000
$479$	−28.5368	−1.30388	−0.651940	−	0.758270i	$-0.726045\pi$
$479$	−28.5368	−1.30388	−0.651940	+	0.758270i	$0.726045\pi$
$480$	7.45352	0.340205
$481$	10.8514	0.494779
$482$	67.0371	3.05346
$483$	0.168078	0.00764783
$484$	−10.2699	−0.466815
$485$	−10.7893	−0.489917
$486$	2.18294	0.0990200
$487$	−22.2368	−1.00764	−0.503822	−	0.863807i	$-0.668073\pi$
$487$	−22.2368	−1.00764	−0.503822	+	0.863807i	$0.668073\pi$
$488$	18.2225	0.824893
$489$	−11.2819	−0.510187
$490$	−15.2482	−0.688841
$491$	−4.09089	−0.184619	−0.0923096	−	0.995730i	$-0.529425\pi$
$491$	−4.09089	−0.184619	−0.0923096	+	0.995730i	$0.529425\pi$
$492$	−3.63567	−0.163909
$493$	12.0905	0.544528
$494$	1.06787	0.0480456
$495$	2.69927	0.121323
$496$	1.88401	0.0845948
$497$	0.0809416	0.00363073
$498$	−0.374417	−0.0167780
$499$	−28.6280	−1.28156	−0.640782	−	0.767723i	$-0.721390\pi$
$499$	−28.6280	−1.28156	−0.640782	+	0.767723i	$0.721390\pi$
$500$	−2.76522	−0.123664
$501$	−1.43019	−0.0638960
$502$	−29.8627	−1.33284
$503$	12.4668	0.555869	0.277935	−	0.960600i	$-0.410350\pi$
$503$	12.4668	0.555869	0.277935	+	0.960600i	$0.410350\pi$
$504$	−0.203533	−0.00906609
$505$	13.6432	0.607117
$506$	−8.12808	−0.361337
$507$	−1.00000	−0.0444116
$508$	7.35958	0.326528
$509$	−10.6552	−0.472282	−0.236141	−	0.971719i	$-0.575883\pi$
$509$	−10.6552	−0.472282	−0.236141	+	0.971719i	$0.575883\pi$
$510$	−9.53874	−0.422383
$511$	1.93233	0.0854812
$512$	−20.3367	−0.898765
$513$	−0.489188	−0.0215982
$514$	13.4991	0.595421
$515$	16.4058	0.722924
$516$	1.83477	0.0807712
$517$	−14.5434	−0.639618
$518$	2.88626	0.126815
$519$	−18.3288	−0.804545
$520$	−1.67042	−0.0732526
$521$	41.7195	1.82777	0.913883	−	0.405978i	$-0.133069\pi$
$521$	41.7195	1.82777	0.913883	+	0.405978i	$0.133069\pi$
$522$	−6.03997	−0.264362
$523$	−5.22258	−0.228367	−0.114184	−	0.993460i	$-0.536425\pi$
$523$	−5.22258	−0.228367	−0.114184	+	0.993460i	$0.536425\pi$
$524$	−6.59871	−0.288266
$525$	−0.121846	−0.00531778
$526$	−0.980945	−0.0427712
$527$	−4.36968	−0.190346
$528$	−5.08546	−0.221316
$529$	−21.0972	−0.917268
$530$	13.3046	0.577913
$531$	14.3339	0.622038
$532$	0.164822	0.00714594
$533$	−1.31479	−0.0569498
$534$	−18.8324	−0.814959
$535$	−5.41857	−0.234265
$536$	−0.630599	−0.0272377
$537$	20.1508	0.869572
$538$	−31.6798	−1.36581
$539$	18.8548	0.812133
$540$	2.76522	0.118996
$541$	1.05012	0.0451482	0.0225741	−	0.999745i	$-0.492814\pi$
$541$	1.05012	0.0451482	0.0225741	+	0.999745i	$0.492814\pi$
$542$	−3.32589	−0.142859
$543$	−15.9328	−0.683741
$544$	32.5695	1.39641
$545$	−5.01652	−0.214884
$546$	−0.265982	−0.0113830
$547$	−22.3517	−0.955690	−0.477845	−	0.878444i	$-0.658582\pi$
$547$	−22.3517	−0.955690	−0.477845	+	0.878444i	$0.658582\pi$
$548$	51.7126	2.20905
$549$	−10.9089	−0.465582
$550$	5.89233	0.251250
$551$	1.35354	0.0576625
$552$	−2.30423	−0.0980747
$553$	−0.291675	−0.0124033
$554$	−23.3862	−0.993583
$555$	−10.8514	−0.460614
$556$	−24.3792	−1.03391
$557$	−16.5690	−0.702052	−0.351026	−	0.936366i	$-0.614167\pi$
$557$	−16.5690	−0.702052	−0.351026	+	0.936366i	$0.614167\pi$
$558$	2.18294	0.0924111
$559$	0.663518	0.0280638
$560$	0.229559	0.00970065
$561$	11.7949	0.497982
$562$	−15.8948	−0.670483
$563$	−11.7569	−0.495496	−0.247748	−	0.968824i	$-0.579691\pi$
$563$	−11.7569	−0.495496	−0.247748	+	0.968824i	$0.579691\pi$
$564$	−14.8987	−0.627350
$565$	16.2066	0.681819
$566$	4.30545	0.180972
$567$	0.121846	0.00511704
$568$	−1.10965	−0.0465599
$569$	14.7363	0.617776	0.308888	−	0.951098i	$-0.400043\pi$
$569$	14.7363	0.617776	0.308888	+	0.951098i	$0.400043\pi$
$570$	−1.06787	−0.0447280
$571$	−42.5841	−1.78209	−0.891045	−	0.453914i	$-0.850027\pi$
$571$	−42.5841	−1.78209	−0.891045	+	0.453914i	$0.850027\pi$
$572$	7.46405	0.312088
$573$	−2.10350	−0.0878750
$574$	−0.349709	−0.0145966
$575$	−1.37944	−0.0575264
$576$	−12.5025	−0.520939
$577$	40.5491	1.68808	0.844040	−	0.536280i	$-0.180171\pi$
$577$	40.5491	1.68808	0.844040	+	0.536280i	$0.180171\pi$
$578$	−4.57134	−0.190143
$579$	−9.21955	−0.383151
$580$	−7.65108	−0.317694
$581$	−0.0208990	−0.000867035 0
$582$	23.5524	0.976276
$583$	−16.4515	−0.681351
$584$	−26.4908	−1.09620
$585$	1.00000	0.0413449
$586$	3.72670	0.153949
$587$	−1.69556	−0.0699832	−0.0349916	−	0.999388i	$-0.511140\pi$
$587$	−1.69556	−0.0699832	−0.0349916	+	0.999388i	$0.511140\pi$
$588$	19.3155	0.796556
$589$	−0.489188	−0.0201566
$590$	31.2900	1.28819
$591$	−3.07085	−0.126318
$592$	20.4441	0.840248
$593$	−15.7803	−0.648018	−0.324009	−	0.946054i	$-0.605031\pi$
$593$	−15.7803	−0.648018	−0.324009	+	0.946054i	$0.605031\pi$
$594$	−5.89233	−0.241765
$595$	−0.532427	−0.0218274
$596$	15.6711	0.641912
$597$	−17.0895	−0.699428
$598$	−3.01122	−0.123138
$599$	−36.8172	−1.50431	−0.752156	−	0.658986i	$-0.770986\pi$
$599$	−36.8172	−1.50431	−0.752156	+	0.658986i	$0.770986\pi$
$600$	1.67042	0.0681945
$601$	22.1135	0.902029	0.451015	−	0.892517i	$-0.351062\pi$
$601$	22.1135	0.902029	0.451015	+	0.892517i	$0.351062\pi$
$602$	0.176483	0.00719293
$603$	0.377510	0.0153734
$604$	3.97154	0.161600
$605$	3.71397	0.150994
$606$	−29.7824	−1.20983
$607$	−40.2710	−1.63455	−0.817274	−	0.576249i	$-0.804516\pi$
$607$	−40.2710	−1.63455	−0.817274	+	0.576249i	$0.804516\pi$
$608$	3.64617	0.147872
$609$	−0.337135	−0.0136614
$610$	−23.8135	−0.964182
$611$	−5.38791	−0.217972
$612$	12.0831	0.488431
$613$	−31.6684	−1.27907	−0.639537	−	0.768760i	$-0.720874\pi$
$613$	−31.6684	−1.27907	−0.639537	+	0.768760i	$0.720874\pi$
$614$	68.0270	2.74535
$615$	1.31479	0.0530174
$616$	0.549390	0.0221356
$617$	−14.8514	−0.597894	−0.298947	−	0.954270i	$-0.596635\pi$
$617$	−14.8514	−0.597894	−0.298947	+	0.954270i	$0.596635\pi$
$618$	−35.8127	−1.44060
$619$	−27.5876	−1.10884	−0.554419	−	0.832237i	$-0.687060\pi$
$619$	−27.5876	−1.10884	−0.554419	+	0.832237i	$0.687060\pi$
$620$	2.76522	0.111054
$621$	1.37944	0.0553548
$622$	−42.3662	−1.69873
$623$	−1.05118	−0.0421145
$624$	−1.88401	−0.0754210
$625$	1.00000	0.0400000
$626$	4.17359	0.166810
$627$	1.32045	0.0527336
$628$	24.1644	0.964265
$629$	−47.4170	−1.89064
$630$	0.265982	0.0105970
$631$	4.59055	0.182747	0.0913734	−	0.995817i	$-0.470874\pi$
$631$	4.59055	0.182747	0.0913734	+	0.995817i	$0.470874\pi$
$632$	3.99865	0.159058
$633$	11.2341	0.446515
$634$	−64.0574	−2.54404
$635$	−2.66148	−0.105618
$636$	−16.8534	−0.668282
$637$	6.98515	0.276762
$638$	16.3035	0.645461
$639$	0.664296	0.0262791
$640$	−12.3852	−0.489569
$641$	−42.4201	−1.67549	−0.837746	−	0.546059i	$-0.816127\pi$
$641$	−42.4201	−1.67549	−0.837746	+	0.546059i	$0.816127\pi$
$642$	11.8284	0.466830
$643$	47.3537	1.86745	0.933725	−	0.357992i	$-0.116539\pi$
$643$	47.3537	1.86745	0.933725	+	0.357992i	$0.116539\pi$
$644$	−0.464773	−0.0183146
$645$	−0.663518	−0.0261260
$646$	−4.66624	−0.183591
$647$	−20.9100	−0.822057	−0.411028	−	0.911623i	$-0.634830\pi$
$647$	−20.9100	−0.822057	−0.411028	+	0.911623i	$0.634830\pi$
$648$	−1.67042	−0.0656202
$649$	−38.6910	−1.51875
$650$	2.18294	0.0856218
$651$	0.121846	0.00477551
$652$	31.1970	1.22177
$653$	−39.3594	−1.54025	−0.770127	−	0.637891i	$-0.779807\pi$
$653$	−39.3594	−1.54025	−0.770127	+	0.637891i	$0.779807\pi$
$654$	10.9508	0.428208
$655$	2.38633	0.0932415
$656$	−2.47708	−0.0967137
$657$	15.8588	0.618711
$658$	−1.43309	−0.0558675
$659$	−11.9564	−0.465757	−0.232878	−	0.972506i	$-0.574814\pi$
$659$	−11.9564	−0.465757	−0.232878	+	0.972506i	$0.574814\pi$
$660$	−7.46405	−0.290538
$661$	−7.70130	−0.299546	−0.149773	−	0.988720i	$-0.547854\pi$
$661$	−7.70130	−0.299546	−0.149773	+	0.988720i	$0.547854\pi$
$662$	24.4768	0.951317
$663$	4.36968	0.169704
$664$	0.286510	0.0111187
$665$	−0.0596055	−0.00231140
$666$	23.6878	0.917885
$667$	−3.81676	−0.147786
$668$	3.95477	0.153015
$669$	−13.0897	−0.506076
$670$	0.824080	0.0318370
$671$	29.4461	1.13675
$672$	−0.908180	−0.0350338
$673$	−33.3811	−1.28675	−0.643374	−	0.765552i	$-0.722466\pi$
$673$	−33.3811	−1.28675	−0.643374	+	0.765552i	$0.722466\pi$
$674$	−49.6269	−1.91156
$675$	−1.00000	−0.0384900
$676$	2.76522	0.106354
$677$	−30.6606	−1.17838	−0.589191	−	0.807993i	$-0.700554\pi$
$677$	−30.6606	−1.17838	−0.589191	+	0.807993i	$0.700554\pi$
$678$	−35.3781	−1.35869
$679$	1.31463	0.0504509
$680$	7.29919	0.279911
$681$	15.9459	0.611049
$682$	−5.89233	−0.225629
$683$	27.7642	1.06237	0.531184	−	0.847257i	$-0.321747\pi$
$683$	27.7642	1.06237	0.531184	+	0.847257i	$0.321747\pi$
$684$	1.35271	0.0517222
$685$	−18.7011	−0.714533
$686$	3.71979	0.142022
$687$	7.72033	0.294549
$688$	1.25008	0.0476587
$689$	−6.09480	−0.232193
$690$	3.01122	0.114635
$691$	9.39922	0.357563	0.178782	−	0.983889i	$-0.442784\pi$
$691$	9.39922	0.357563	0.178782	+	0.983889i	$0.442784\pi$
$692$	50.6831	1.92668
$693$	−0.328894	−0.0124936
$694$	69.9323	2.65459
$695$	8.81638	0.334424
$696$	4.62188	0.175192
$697$	5.74520	0.217615
$698$	5.09034	0.192672
$699$	−13.5052	−0.510813
$700$	0.336930	0.0127347
$701$	−42.0495	−1.58819	−0.794095	−	0.607794i	$-0.792055\pi$
$701$	−42.0495	−1.58819	−0.794095	+	0.607794i	$0.792055\pi$
$702$	−2.18294	−0.0823897
$703$	−5.30835	−0.200208
$704$	33.7477	1.27191
$705$	5.38791	0.202920
$706$	−8.49965	−0.319889
$707$	−1.66237	−0.0625199
$708$	−39.6363	−1.48962
$709$	5.85662	0.219950	0.109975	−	0.993934i	$-0.464923\pi$
$709$	5.85662	0.219950	0.109975	+	0.993934i	$0.464923\pi$
$710$	1.45012	0.0544219
$711$	−2.39380	−0.0897746
$712$	14.4109	0.540070
$713$	1.37944	0.0516603
$714$	1.16226	0.0434963
$715$	−2.69927	−0.100947
$716$	−55.7213	−2.08240
$717$	17.3268	0.647083
$718$	−34.6559	−1.29335
$719$	26.9893	1.00653	0.503266	−	0.864132i	$-0.332132\pi$
$719$	26.9893	1.00653	0.503266	+	0.864132i	$0.332132\pi$
$720$	1.88401	0.0702131
$721$	−1.99897	−0.0744456
$722$	40.9534	1.52413
$723$	30.7096	1.14210
$724$	44.0575	1.63739
$725$	2.76690	0.102760
$726$	−8.10736	−0.300892
$727$	−15.0359	−0.557649	−0.278825	−	0.960342i	$-0.589945\pi$
$727$	−15.0359	−0.557649	−0.278825	+	0.960342i	$0.589945\pi$
$728$	0.203533	0.00754344
$729$	1.00000	0.0370370
$730$	34.6188	1.28130
$731$	−2.89936	−0.107237
$732$	30.1656	1.11495
$733$	35.0045	1.29292	0.646461	−	0.762947i	$-0.276248\pi$
$733$	35.0045	1.29292	0.646461	+	0.762947i	$0.276248\pi$
$734$	4.01746	0.148287
$735$	−6.98515	−0.257651
$736$	−10.2817	−0.378987
$737$	−1.01900	−0.0375353
$738$	−2.87010	−0.105650
$739$	0.756091	0.0278132	0.0139066	−	0.999903i	$-0.495573\pi$
$739$	0.756091	0.0278132	0.0139066	+	0.999903i	$0.495573\pi$
$740$	30.0063	1.10305
$741$	0.489188	0.0179708
$742$	−1.62110	−0.0595126
$743$	−25.8315	−0.947665	−0.473832	−	0.880615i	$-0.657130\pi$
$743$	−25.8315	−0.947665	−0.473832	+	0.880615i	$0.657130\pi$
$744$	−1.67042	−0.0612405
$745$	−5.66722	−0.207631
$746$	−38.9905	−1.42754
$747$	−0.171520	−0.00627558
$748$	−32.6155	−1.19254
$749$	0.660230	0.0241243
$750$	−2.18294	−0.0797096
$751$	9.88333	0.360648	0.180324	−	0.983607i	$-0.442285\pi$
$751$	9.88333	0.360648	0.180324	+	0.983607i	$0.442285\pi$
$752$	−10.1509	−0.370165
$753$	−13.6801	−0.498529
$754$	6.03997	0.219963
$755$	−1.43625	−0.0522705
$756$	−0.336930	−0.0122540
$757$	26.3947	0.959330	0.479665	−	0.877452i	$-0.340758\pi$
$757$	26.3947	0.959330	0.479665	+	0.877452i	$0.340758\pi$
$758$	62.2969	2.26273
$759$	−3.72346	−0.135153
$760$	0.817148	0.0296411
$761$	3.08563	0.111854	0.0559269	−	0.998435i	$-0.482189\pi$
$761$	3.08563	0.111854	0.0559269	+	0.998435i	$0.482189\pi$
$762$	5.80985	0.210469
$763$	0.611242	0.0221284
$764$	5.81663	0.210438
$765$	−4.36968	−0.157986
$766$	−18.3729	−0.663839
$767$	−14.3339	−0.517567
$768$	2.03107	0.0732901
$769$	39.1161	1.41056	0.705282	−	0.708927i	$-0.250820\pi$
$769$	39.1161	1.41056	0.705282	+	0.708927i	$0.250820\pi$
$770$	−0.717955	−0.0258733
$771$	6.18392	0.222709
$772$	25.4940	0.917551
$773$	−52.7305	−1.89659	−0.948293	−	0.317398i	$-0.897191\pi$
$773$	−52.7305	−1.89659	−0.948293	+	0.317398i	$0.897191\pi$
$774$	1.44842	0.0520623
$775$	−1.00000	−0.0359211
$776$	−18.0226	−0.646974
$777$	1.32219	0.0474334
$778$	57.7063	2.06887
$779$	0.643178	0.0230443
$780$	−2.76522	−0.0990106
$781$	−1.79311	−0.0641625
$782$	13.1581	0.470532
$783$	−2.76690	−0.0988810
$784$	13.1601	0.470005
$785$	−8.73871	−0.311898
$786$	−5.20920	−0.185806
$787$	−40.3012	−1.43658	−0.718291	−	0.695743i	$-0.755075\pi$
$787$	−40.3012	−1.43658	−0.718291	+	0.695743i	$0.755075\pi$
$788$	8.49156	0.302499
$789$	−0.449369	−0.0159980
$790$	−5.22552	−0.185916
$791$	−1.97471	−0.0702126
$792$	4.50890	0.160217
$793$	10.9089	0.387388
$794$	−20.0847	−0.712779
$795$	6.09480	0.216160
$796$	47.2562	1.67495
$797$	−36.9470	−1.30873	−0.654366	−	0.756178i	$-0.727064\pi$
$797$	−36.9470	−1.30873	−0.654366	+	0.756178i	$0.727064\pi$
$798$	0.130115	0.00460602
$799$	23.5435	0.832908
$800$	7.45352	0.263522
$801$	−8.62711	−0.304824
$802$	−24.4595	−0.863694
$803$	−42.8071	−1.51063
$804$	−1.04390	−0.0368154
$805$	0.168078	0.00592398
$806$	−2.18294	−0.0768907
$807$	−14.5125	−0.510862
$808$	22.7899	0.801746
$809$	−14.8086	−0.520641	−0.260320	−	0.965522i	$-0.583828\pi$
$809$	−14.8086	−0.520641	−0.260320	+	0.965522i	$0.583828\pi$
$810$	2.18294	0.0767006
$811$	−17.1093	−0.600790	−0.300395	−	0.953815i	$-0.597118\pi$
$811$	−17.1093	−0.600790	−0.300395	+	0.953815i	$0.597118\pi$
$812$	0.932251	0.0327156
$813$	−1.52358	−0.0534344
$814$	−63.9397	−2.24109
$815$	−11.2819	−0.395189
$816$	8.23255	0.288197
$817$	−0.324585	−0.0113558
$818$	−0.491562	−0.0171871
$819$	−0.121846	−0.00425763
$820$	−3.63567	−0.126963
$821$	13.7331	0.479288	0.239644	−	0.970861i	$-0.422969\pi$
$821$	13.7331	0.479288	0.239644	+	0.970861i	$0.422969\pi$
$822$	40.8234	1.42388
$823$	−12.9716	−0.452162	−0.226081	−	0.974109i	$-0.572591\pi$
$823$	−12.9716	−0.452162	−0.226081	+	0.974109i	$0.572591\pi$
$824$	27.4045	0.954679
$825$	2.69927	0.0939763
$826$	−3.81255	−0.132656
$827$	−49.6296	−1.72579	−0.862896	−	0.505382i	$-0.831352\pi$
$827$	−49.6296	−1.72579	−0.862896	+	0.505382i	$0.831352\pi$
$828$	−3.81444	−0.132561
$829$	49.2193	1.70946	0.854729	−	0.519075i	$-0.173724\pi$
$829$	49.2193	1.70946	0.854729	+	0.519075i	$0.173724\pi$
$830$	−0.374417	−0.0129962
$831$	−10.7132	−0.371636
$832$	12.5025	0.433448
$833$	−30.5229	−1.05756
$834$	−19.2456	−0.666421
$835$	−1.43019	−0.0494936
$836$	−3.65132	−0.126284
$837$	1.00000	0.0345651
$838$	37.7331	1.30347
$839$	−29.4112	−1.01539	−0.507694	−	0.861538i	$-0.669502\pi$
$839$	−29.4112	−1.01539	−0.507694	+	0.861538i	$0.669502\pi$
$840$	−0.203533	−0.00702256
$841$	−21.3443	−0.736009
$842$	−22.3358	−0.769744
$843$	−7.28139	−0.250785
$844$	−31.0646	−1.06929
$845$	−1.00000	−0.0344010
$846$	−11.7615	−0.404368
$847$	−0.452531	−0.0155492
$848$	−11.4827	−0.394317
$849$	1.97232	0.0676898
$850$	−9.53874	−0.327176
$851$	14.9687	0.513122
$852$	−1.83692	−0.0629319
$853$	39.1970	1.34208	0.671040	−	0.741421i	$-0.265848\pi$
$853$	39.1970	1.34208	0.671040	+	0.741421i	$0.265848\pi$
$854$	2.90158	0.0992899
$855$	−0.489188	−0.0167299
$856$	−9.05127	−0.309366
$857$	−6.49242	−0.221777	−0.110888	−	0.993833i	$-0.535370\pi$
$857$	−6.49242	−0.221777	−0.110888	+	0.993833i	$0.535370\pi$
$858$	5.89233	0.201161
$859$	−34.1952	−1.16672	−0.583362	−	0.812212i	$-0.698263\pi$
$859$	−34.1952	−1.16672	−0.583362	+	0.812212i	$0.698263\pi$
$860$	1.83477	0.0625651
$861$	−0.160201	−0.00545965
$862$	−65.4129	−2.22797
$863$	1.55668	0.0529898	0.0264949	−	0.999649i	$-0.491565\pi$
$863$	1.55668	0.0529898	0.0264949	+	0.999649i	$0.491565\pi$
$864$	−7.45352	−0.253574
$865$	−18.3288	−0.623198
$866$	52.2691	1.77618
$867$	−2.09412	−0.0711201
$868$	−0.336930	−0.0114361
$869$	6.46151	0.219192
$870$	−6.03997	−0.204774
$871$	−0.377510	−0.0127914
$872$	−8.37969	−0.283772
$873$	10.7893	0.365162
$874$	1.47305	0.0498268
$875$	−0.121846	−0.00411914
$876$	−43.8530	−1.48166
$877$	−28.5056	−0.962566	−0.481283	−	0.876565i	$-0.659829\pi$
$877$	−28.5056	−0.962566	−0.481283	+	0.876565i	$0.659829\pi$
$878$	32.4123	1.09386
$879$	1.70720	0.0575823
$880$	−5.08546	−0.171431
$881$	49.2471	1.65918	0.829589	−	0.558375i	$-0.188575\pi$
$881$	49.2471	1.65918	0.829589	+	0.558375i	$0.188575\pi$
$882$	15.2482	0.513432
$883$	−44.2567	−1.48936	−0.744679	−	0.667423i	$-0.767397\pi$
$883$	−44.2567	−1.48936	−0.744679	+	0.667423i	$0.767397\pi$
$884$	−12.0831	−0.406399
$885$	14.3339	0.481828
$886$	58.8887	1.97841
$887$	28.1236	0.944297	0.472149	−	0.881519i	$-0.343479\pi$
$887$	28.1236	0.944297	0.472149	+	0.881519i	$0.343479\pi$
$888$	−18.1263	−0.608278
$889$	0.324290	0.0108764
$890$	−18.8324	−0.631265
$891$	−2.69927	−0.0904288
$892$	36.1958	1.21192
$893$	2.63570	0.0882004
$894$	12.3712	0.413754
$895$	20.1508	0.673567
$896$	1.50909	0.0504150
$897$	−1.37944	−0.0460580
$898$	40.5563	1.35338
$899$	−2.76690	−0.0922813
$900$	2.76522	0.0921738
$901$	26.6323	0.887252
$902$	7.74716	0.257952
$903$	0.0808468	0.00269041
$904$	27.0719	0.900397
$905$	−15.9328	−0.529623
$906$	3.13525	0.104162
$907$	19.0593	0.632855	0.316427	−	0.948617i	$-0.397517\pi$
$907$	19.0593	0.632855	0.316427	+	0.948617i	$0.397517\pi$
$908$	−44.0939	−1.46331
$909$	−13.6432	−0.452518
$910$	−0.265982	−0.00881720
$911$	24.7807	0.821022	0.410511	−	0.911856i	$-0.365350\pi$
$911$	24.7807	0.821022	0.410511	+	0.911856i	$0.365350\pi$
$912$	0.921638	0.0305185
$913$	0.462977	0.0153223
$914$	89.2884	2.95340
$915$	−10.9089	−0.360638
$916$	−21.3484	−0.705370
$917$	−0.290764	−0.00960186
$918$	9.53874	0.314825
$919$	−33.9403	−1.11959	−0.559793	−	0.828632i	$-0.689119\pi$
$919$	−33.9403	−1.11959	−0.559793	+	0.828632i	$0.689119\pi$
$920$	−2.30423	−0.0759683
$921$	31.1631	1.02686
$922$	33.6944	1.10966
$923$	−0.664296	−0.0218656
$924$	0.909463	0.0299191
$925$	−10.8514	−0.356790
$926$	−21.9831	−0.722408
$927$	−16.4058	−0.538836
$928$	20.6232	0.676988
$929$	−21.0728	−0.691376	−0.345688	−	0.938350i	$-0.612354\pi$
$929$	−21.0728	−0.691376	−0.345688	+	0.938350i	$0.612354\pi$
$930$	2.18294	0.0715813
$931$	−3.41705	−0.111989
$932$	37.3447	1.22327
$933$	−19.4079	−0.635386
$934$	10.7311	0.351132
$935$	11.7949	0.385735
$936$	1.67042	0.0545993
$937$	8.16147	0.266624	0.133312	−	0.991074i	$-0.457439\pi$
$937$	8.16147	0.266624	0.133312	+	0.991074i	$0.457439\pi$
$938$	−0.100411	−0.00327852
$939$	1.91191	0.0623929
$940$	−14.8987	−0.485943
$941$	31.9175	1.04048	0.520241	−	0.854020i	$-0.325842\pi$
$941$	31.9175	1.04048	0.520241	+	0.854020i	$0.325842\pi$
$942$	19.0760	0.621531
$943$	−1.81367	−0.0590611
$944$	−27.0053	−0.878946
$945$	0.121846	0.00396364
$946$	−3.90966	−0.127114
$947$	34.5003	1.12111	0.560554	−	0.828118i	$-0.310588\pi$
$947$	34.5003	1.12111	0.560554	+	0.828118i	$0.310588\pi$
$948$	6.61938	0.214987
$949$	−15.8588	−0.514799
$950$	−1.06787	−0.0346462
$951$	−29.3446	−0.951563
$952$	−0.889375	−0.0288248
$953$	51.4641	1.66709	0.833543	−	0.552455i	$-0.186309\pi$
$953$	51.4641	1.66709	0.833543	+	0.552455i	$0.186309\pi$
$954$	−13.3046	−0.430751
$955$	−2.10350	−0.0680677
$956$	−47.9124	−1.54960
$957$	7.46860	0.241426
$958$	62.2941	2.01263
$959$	2.27865	0.0735815
$960$	−12.5025	−0.403518
$961$	1.00000	0.0322581
$962$	−23.6878	−0.763726
$963$	5.41857	0.174611
$964$	−84.9186	−2.73504
$965$	−9.21955	−0.296788
$966$	−0.366905	−0.0118050
$967$	24.7033	0.794404	0.397202	−	0.917731i	$-0.369981\pi$
$967$	24.7033	0.794404	0.397202	+	0.917731i	$0.369981\pi$
$968$	6.20388	0.199400
$969$	−2.13760	−0.0686695
$970$	23.5524	0.756220
$971$	19.2616	0.618133	0.309067	−	0.951040i	$-0.399983\pi$
$971$	19.2616	0.618133	0.309067	+	0.951040i	$0.399983\pi$
$972$	−2.76522	−0.0886943
$973$	−1.07424	−0.0344385
$974$	48.5415	1.55537
$975$	1.00000	0.0320256
$976$	20.5526	0.657873
$977$	−41.9354	−1.34163	−0.670817	−	0.741623i	$-0.734056\pi$
$977$	−41.9354	−1.34163	−0.670817	+	0.741623i	$0.734056\pi$
$978$	24.6278	0.787509
$979$	23.2869	0.744251
$980$	19.3155	0.617010
$981$	5.01652	0.160165
$982$	8.93015	0.284972
$983$	−58.7429	−1.87361	−0.936804	−	0.349854i	$-0.886231\pi$
$983$	−58.7429	−1.87361	−0.936804	+	0.349854i	$0.886231\pi$
$984$	2.19624	0.0700137
$985$	−3.07085	−0.0978454
$986$	−26.3928	−0.840517
$987$	−0.656494	−0.0208964
$988$	−1.35271	−0.0430354
$989$	0.915280	0.0291042
$990$	−5.89233	−0.187270
$991$	11.4117	0.362504	0.181252	−	0.983437i	$-0.441985\pi$
$991$	11.4117	0.362504	0.181252	+	0.983437i	$0.441985\pi$
$992$	−7.45352	−0.236650
$993$	11.2128	0.355826
$994$	−0.176690	−0.00560428
$995$	−17.0895	−0.541775
$996$	0.474289	0.0150284
$997$	−36.8973	−1.16855	−0.584275	−	0.811556i	$-0.698621\pi$
$997$	−36.8973	−1.16855	−0.584275	+	0.811556i	$0.698621\pi$
$998$	62.4931	1.97818
$999$	10.8514	0.343322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.w.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.w.1.2	✓	11	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18294 q^{2} -1.00000 q^{3} +2.76522 q^{4} -1.00000 q^{5} +2.18294 q^{6} +0.121846 q^{7} -1.67042 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18294 q^{2} -1.00000 q^{3} +2.76522 q^{4} -1.00000 q^{5} +2.18294 q^{6} +0.121846 q^{7} -1.67042 q^{8} +1.00000 q^{9} +2.18294 q^{10} -2.69927 q^{11} -2.76522 q^{12} -1.00000 q^{13} -0.265982 q^{14} +1.00000 q^{15} -1.88401 q^{16} +4.36968 q^{17} -2.18294 q^{18} +0.489188 q^{19} -2.76522 q^{20} -0.121846 q^{21} +5.89233 q^{22} -1.37944 q^{23} +1.67042 q^{24} +1.00000 q^{25} +2.18294 q^{26} -1.00000 q^{27} +0.336930 q^{28} +2.76690 q^{29} -2.18294 q^{30} -1.00000 q^{31} +7.45352 q^{32} +2.69927 q^{33} -9.53874 q^{34} -0.121846 q^{35} +2.76522 q^{36} -10.8514 q^{37} -1.06787 q^{38} +1.00000 q^{39} +1.67042 q^{40} +1.31479 q^{41} +0.265982 q^{42} -0.663518 q^{43} -7.46405 q^{44} -1.00000 q^{45} +3.01122 q^{46} +5.38791 q^{47} +1.88401 q^{48} -6.98515 q^{49} -2.18294 q^{50} -4.36968 q^{51} -2.76522 q^{52} +6.09480 q^{53} +2.18294 q^{54} +2.69927 q^{55} -0.203533 q^{56} -0.489188 q^{57} -6.03997 q^{58} +14.3339 q^{59} +2.76522 q^{60} -10.9089 q^{61} +2.18294 q^{62} +0.121846 q^{63} -12.5025 q^{64} +1.00000 q^{65} -5.89233 q^{66} +0.377510 q^{67} +12.0831 q^{68} +1.37944 q^{69} +0.265982 q^{70} +0.664296 q^{71} -1.67042 q^{72} +15.8588 q^{73} +23.6878 q^{74} -1.00000 q^{75} +1.35271 q^{76} -0.328894 q^{77} -2.18294 q^{78} -2.39380 q^{79} +1.88401 q^{80} +1.00000 q^{81} -2.87010 q^{82} -0.171520 q^{83} -0.336930 q^{84} -4.36968 q^{85} +1.44842 q^{86} -2.76690 q^{87} +4.50890 q^{88} -8.62711 q^{89} +2.18294 q^{90} -0.121846 q^{91} -3.81444 q^{92} +1.00000 q^{93} -11.7615 q^{94} -0.489188 q^{95} -7.45352 q^{96} +10.7893 q^{97} +15.2482 q^{98} -2.69927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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