LMFDB - Embedded newform 2001.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
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} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.72479$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72479 q^{2} -1.00000 q^{3} +5.42450 q^{4} -1.02492 q^{5} -2.72479 q^{6} +4.32726 q^{7} +9.33107 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.72479 q^{2} -1.00000 q^{3} +5.42450 q^{4} -1.02492 q^{5} -2.72479 q^{6} +4.32726 q^{7} +9.33107 q^{8} +1.00000 q^{9} -2.79269 q^{10} +2.38338 q^{11} -5.42450 q^{12} +0.754393 q^{13} +11.7909 q^{14} +1.02492 q^{15} +14.5762 q^{16} -1.03913 q^{17} +2.72479 q^{18} -8.17626 q^{19} -5.55967 q^{20} -4.32726 q^{21} +6.49422 q^{22} +1.00000 q^{23} -9.33107 q^{24} -3.94954 q^{25} +2.05557 q^{26} -1.00000 q^{27} +23.4733 q^{28} -1.00000 q^{29} +2.79269 q^{30} -5.92951 q^{31} +21.0551 q^{32} -2.38338 q^{33} -2.83143 q^{34} -4.43509 q^{35} +5.42450 q^{36} +3.05932 q^{37} -22.2786 q^{38} -0.754393 q^{39} -9.56358 q^{40} +1.01080 q^{41} -11.7909 q^{42} +8.18673 q^{43} +12.9287 q^{44} -1.02492 q^{45} +2.72479 q^{46} +8.08697 q^{47} -14.5762 q^{48} +11.7252 q^{49} -10.7617 q^{50} +1.03913 q^{51} +4.09221 q^{52} -0.478182 q^{53} -2.72479 q^{54} -2.44277 q^{55} +40.3780 q^{56} +8.17626 q^{57} -2.72479 q^{58} -8.09543 q^{59} +5.55967 q^{60} -14.8897 q^{61} -16.1567 q^{62} +4.32726 q^{63} +28.2183 q^{64} -0.773191 q^{65} -6.49422 q^{66} -0.830191 q^{67} -5.63679 q^{68} -1.00000 q^{69} -12.0847 q^{70} -1.79880 q^{71} +9.33107 q^{72} +13.2708 q^{73} +8.33601 q^{74} +3.94954 q^{75} -44.3521 q^{76} +10.3135 q^{77} -2.05557 q^{78} +2.46332 q^{79} -14.9394 q^{80} +1.00000 q^{81} +2.75423 q^{82} +4.46805 q^{83} -23.4733 q^{84} +1.06503 q^{85} +22.3072 q^{86} +1.00000 q^{87} +22.2395 q^{88} -5.57787 q^{89} -2.79269 q^{90} +3.26446 q^{91} +5.42450 q^{92} +5.92951 q^{93} +22.0353 q^{94} +8.37999 q^{95} -21.0551 q^{96} -0.684597 q^{97} +31.9488 q^{98} +2.38338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * 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 $

$2$	2.72479	1.92672	0.963360	−	0.268211i	$-0.0864324\pi$
$2$	2.72479	1.92672	0.963360	+	0.268211i	$0.0864324\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.42450	2.71225
$5$	−1.02492	−0.458357	−0.229179	−	0.973384i	$-0.573604\pi$
$5$	−1.02492	−0.458357	−0.229179	+	0.973384i	$0.573604\pi$
$6$	−2.72479	−1.11239
$7$	4.32726	1.63555	0.817776	−	0.575537i	$-0.195207\pi$
$7$	4.32726	1.63555	0.817776	+	0.575537i	$0.195207\pi$
$8$	9.33107	3.29903
$9$	1.00000	0.333333
$10$	−2.79269	−0.883126
$11$	2.38338	0.718616	0.359308	−	0.933219i	$-0.383013\pi$
$11$	2.38338	0.718616	0.359308	+	0.933219i	$0.383013\pi$
$12$	−5.42450	−1.56592
$13$	0.754393	0.209231	0.104616	−	0.994513i	$-0.466639\pi$
$13$	0.754393	0.209231	0.104616	+	0.994513i	$0.466639\pi$
$14$	11.7909	3.15125
$15$	1.02492	0.264633
$16$	14.5762	3.64406
$17$	−1.03913	−0.252027	−0.126014	−	0.992029i	$-0.540218\pi$
$17$	−1.03913	−0.252027	−0.126014	+	0.992029i	$0.540218\pi$
$18$	2.72479	0.642240
$19$	−8.17626	−1.87576	−0.937881	−	0.346957i	$-0.887215\pi$
$19$	−8.17626	−1.87576	−0.937881	+	0.346957i	$0.887215\pi$
$20$	−5.55967	−1.24318
$21$	−4.32726	−0.944286
$22$	6.49422	1.38457
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−9.33107	−1.90470
$25$	−3.94954	−0.789909
$26$	2.05557	0.403130
$27$	−1.00000	−0.192450
$28$	23.4733	4.43603
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	2.79269	0.509873
$31$	−5.92951	−1.06497	−0.532485	−	0.846439i	$-0.678742\pi$
$31$	−5.92951	−1.06497	−0.532485	+	0.846439i	$0.678742\pi$
$32$	21.0551	3.72205
$33$	−2.38338	−0.414893
$34$	−2.83143	−0.485586
$35$	−4.43509	−0.749667
$36$	5.42450	0.904084
$37$	3.05932	0.502948	0.251474	−	0.967864i	$-0.419085\pi$
$37$	3.05932	0.502948	0.251474	+	0.967864i	$0.419085\pi$
$38$	−22.2786	−3.61407
$39$	−0.754393	−0.120800
$40$	−9.56358	−1.51213
$41$	1.01080	0.157861	0.0789304	−	0.996880i	$-0.474850\pi$
$41$	1.01080	0.157861	0.0789304	+	0.996880i	$0.474850\pi$
$42$	−11.7909	−1.81938
$43$	8.18673	1.24846	0.624232	−	0.781239i	$-0.285412\pi$
$43$	8.18673	1.24846	0.624232	+	0.781239i	$0.285412\pi$
$44$	12.9287	1.94907
$45$	−1.02492	−0.152786
$46$	2.72479	0.401749
$47$	8.08697	1.17961	0.589803	−	0.807547i	$-0.299205\pi$
$47$	8.08697	1.17961	0.589803	+	0.807547i	$0.299205\pi$
$48$	−14.5762	−2.10390
$49$	11.7252	1.67503
$50$	−10.7617	−1.52193
$51$	1.03913	0.145508
$52$	4.09221	0.567487
$53$	−0.478182	−0.0656834	−0.0328417	−	0.999461i	$-0.510456\pi$
$53$	−0.478182	−0.0656834	−0.0328417	+	0.999461i	$0.510456\pi$
$54$	−2.72479	−0.370798
$55$	−2.44277	−0.329383
$56$	40.3780	5.39573
$57$	8.17626	1.08297
$58$	−2.72479	−0.357783
$59$	−8.09543	−1.05394	−0.526968	−	0.849885i	$-0.676671\pi$
$59$	−8.09543	−1.05394	−0.526968	+	0.849885i	$0.676671\pi$
$60$	5.55967	0.717751
$61$	−14.8897	−1.90644	−0.953218	−	0.302285i	$-0.902251\pi$
$61$	−14.8897	−1.90644	−0.953218	+	0.302285i	$0.902251\pi$
$62$	−16.1567	−2.05190
$63$	4.32726	0.545184
$64$	28.2183	3.52729
$65$	−0.773191	−0.0959026
$66$	−6.49422	−0.799383
$67$	−0.830191	−0.101424	−0.0507120	−	0.998713i	$-0.516149\pi$
$67$	−0.830191	−0.101424	−0.0507120	+	0.998713i	$0.516149\pi$
$68$	−5.63679	−0.683561
$69$	−1.00000	−0.120386
$70$	−12.0847	−1.44440
$71$	−1.79880	−0.213478	−0.106739	−	0.994287i	$-0.534041\pi$
$71$	−1.79880	−0.213478	−0.106739	+	0.994287i	$0.534041\pi$
$72$	9.33107	1.09968
$73$	13.2708	1.55323	0.776617	−	0.629973i	$-0.216934\pi$
$73$	13.2708	1.55323	0.776617	+	0.629973i	$0.216934\pi$
$74$	8.33601	0.969041
$75$	3.94954	0.456054
$76$	−44.3521	−5.08754
$77$	10.3135	1.17533
$78$	−2.05557	−0.232747
$79$	2.46332	0.277145	0.138572	−	0.990352i	$-0.455749\pi$
$79$	2.46332	0.277145	0.138572	+	0.990352i	$0.455749\pi$
$80$	−14.9394	−1.67028
$81$	1.00000	0.111111
$82$	2.75423	0.304153
$83$	4.46805	0.490432	0.245216	−	0.969468i	$-0.421141\pi$
$83$	4.46805	0.490432	0.245216	+	0.969468i	$0.421141\pi$
$84$	−23.4733	−2.56114
$85$	1.06503	0.115518
$86$	22.3072	2.40544
$87$	1.00000	0.107211
$88$	22.2395	2.37074
$89$	−5.57787	−0.591253	−0.295626	−	0.955304i	$-0.595528\pi$
$89$	−5.57787	−0.591253	−0.295626	+	0.955304i	$0.595528\pi$
$90$	−2.79269	−0.294375
$91$	3.26446	0.342208
$92$	5.42450	0.565544
$93$	5.92951	0.614861
$94$	22.0353	2.27277
$95$	8.37999	0.859769
$96$	−21.0551	−2.14893
$97$	−0.684597	−0.0695103	−0.0347551	−	0.999396i	$-0.511065\pi$
$97$	−0.684597	−0.0695103	−0.0347551	+	0.999396i	$0.511065\pi$
$98$	31.9488	3.22731
$99$	2.38338	0.239539
$100$	−21.4243	−2.14243
$101$	19.2544	1.91589	0.957943	−	0.286958i	$-0.0926439\pi$
$101$	19.2544	1.91589	0.957943	+	0.286958i	$0.0926439\pi$
$102$	2.83143	0.280353
$103$	−5.09888	−0.502408	−0.251204	−	0.967934i	$-0.580826\pi$
$103$	−5.09888	−0.502408	−0.251204	+	0.967934i	$0.580826\pi$
$104$	7.03929	0.690260
$105$	4.43509	0.432820
$106$	−1.30295	−0.126553
$107$	−13.7603	−1.33026	−0.665131	−	0.746727i	$-0.731624\pi$
$107$	−13.7603	−1.33026	−0.665131	+	0.746727i	$0.731624\pi$
$108$	−5.42450	−0.521973
$109$	−12.0945	−1.15845	−0.579223	−	0.815169i	$-0.696644\pi$
$109$	−12.0945	−1.15845	−0.579223	+	0.815169i	$0.696644\pi$
$110$	−6.65604	−0.634629
$111$	−3.05932	−0.290377
$112$	63.0752	5.96005
$113$	3.66701	0.344963	0.172482	−	0.985013i	$-0.444821\pi$
$113$	3.66701	0.344963	0.172482	+	0.985013i	$0.444821\pi$
$114$	22.2786	2.08658
$115$	−1.02492	−0.0955741
$116$	−5.42450	−0.503653
$117$	0.754393	0.0697437
$118$	−22.0584	−2.03064
$119$	−4.49661	−0.412203
$120$	9.56358	0.873031
$121$	−5.31950	−0.483591
$122$	−40.5715	−3.67317
$123$	−1.01080	−0.0911409
$124$	−32.1646	−2.88847
$125$	9.17255	0.820418
$126$	11.7909	1.05042
$127$	−9.23920	−0.819847	−0.409923	−	0.912120i	$-0.634445\pi$
$127$	−9.23920	−0.819847	−0.409923	+	0.912120i	$0.634445\pi$
$128$	34.7790	3.07406
$129$	−8.18673	−0.720802
$130$	−2.10679	−0.184777
$131$	−6.81925	−0.595800	−0.297900	−	0.954597i	$-0.596286\pi$
$131$	−6.81925	−0.595800	−0.297900	+	0.954597i	$0.596286\pi$
$132$	−12.9287	−1.12529
$133$	−35.3808	−3.06791
$134$	−2.26210	−0.195416
$135$	1.02492	0.0882109
$136$	−9.69623	−0.831445
$137$	4.86061	0.415270	0.207635	−	0.978206i	$-0.433423\pi$
$137$	4.86061	0.415270	0.207635	+	0.978206i	$0.433423\pi$
$138$	−2.72479	−0.231950
$139$	−11.5906	−0.983105	−0.491553	−	0.870848i	$-0.663570\pi$
$139$	−11.5906	−0.983105	−0.491553	+	0.870848i	$0.663570\pi$
$140$	−24.0582	−2.03329
$141$	−8.08697	−0.681046
$142$	−4.90136	−0.411313
$143$	1.79801	0.150357
$144$	14.5762	1.21469
$145$	1.02492	0.0851148
$146$	36.1603	2.99265
$147$	−11.7252	−0.967078
$148$	16.5953	1.36412
$149$	−5.07301	−0.415597	−0.207799	−	0.978172i	$-0.566630\pi$
$149$	−5.07301	−0.415597	−0.207799	+	0.978172i	$0.566630\pi$
$150$	10.7617	0.878688
$151$	9.42334	0.766861	0.383430	−	0.923570i	$-0.374743\pi$
$151$	9.42334	0.766861	0.383430	+	0.923570i	$0.374743\pi$
$152$	−76.2932	−6.18820
$153$	−1.03913	−0.0840090
$154$	28.1022	2.26454
$155$	6.07726	0.488137
$156$	−4.09221	−0.327639
$157$	−17.9873	−1.43554	−0.717772	−	0.696278i	$-0.754838\pi$
$157$	−17.9873	−1.43554	−0.717772	+	0.696278i	$0.754838\pi$
$158$	6.71204	0.533981
$159$	0.478182	0.0379223
$160$	−21.5798	−1.70603
$161$	4.32726	0.341036
$162$	2.72479	0.214080
$163$	−16.3947	−1.28413	−0.642066	−	0.766649i	$-0.721922\pi$
$163$	−16.3947	−1.28413	−0.642066	+	0.766649i	$0.721922\pi$
$164$	5.48310	0.428158
$165$	2.44277	0.190169
$166$	12.1745	0.944925
$167$	22.7384	1.75955	0.879775	−	0.475390i	$-0.157693\pi$
$167$	22.7384	1.75955	0.879775	+	0.475390i	$0.157693\pi$
$168$	−40.3780	−3.11523
$169$	−12.4309	−0.956222
$170$	2.90198	0.222572
$171$	−8.17626	−0.625254
$172$	44.4090	3.38615
$173$	21.4566	1.63132	0.815659	−	0.578533i	$-0.196375\pi$
$173$	21.4566	1.63132	0.815659	+	0.578533i	$0.196375\pi$
$174$	2.72479	0.206566
$175$	−17.0907	−1.29194
$176$	34.7407	2.61868
$177$	8.09543	0.608490
$178$	−15.1985	−1.13918
$179$	−14.9868	−1.12016	−0.560082	−	0.828437i	$-0.689231\pi$
$179$	−14.9868	−1.12016	−0.560082	+	0.828437i	$0.689231\pi$
$180$	−5.55967	−0.414393
$181$	−17.0940	−1.27059	−0.635295	−	0.772269i	$-0.719122\pi$
$181$	−17.0940	−1.27059	−0.635295	+	0.772269i	$0.719122\pi$
$182$	8.89498	0.659340
$183$	14.8897	1.10068
$184$	9.33107	0.687895
$185$	−3.13555	−0.230530
$186$	16.1567	1.18467
$187$	−2.47665	−0.181111
$188$	43.8678	3.19939
$189$	−4.32726	−0.314762
$190$	22.8338	1.65653
$191$	−15.6430	−1.13189	−0.565944	−	0.824444i	$-0.691488\pi$
$191$	−15.6430	−1.13189	−0.565944	+	0.824444i	$0.691488\pi$
$192$	−28.2183	−2.03648
$193$	21.1145	1.51985	0.759927	−	0.650009i	$-0.225235\pi$
$193$	21.1145	1.51985	0.759927	+	0.650009i	$0.225235\pi$
$194$	−1.86538	−0.133927
$195$	0.773191	0.0553694
$196$	63.6034	4.54310
$197$	2.37520	0.169226	0.0846128	−	0.996414i	$-0.473035\pi$
$197$	2.37520	0.169226	0.0846128	+	0.996414i	$0.473035\pi$
$198$	6.49422	0.461524
$199$	−14.1714	−1.00459	−0.502294	−	0.864697i	$-0.667510\pi$
$199$	−14.1714	−1.00459	−0.502294	+	0.864697i	$0.667510\pi$
$200$	−36.8535	−2.60593
$201$	0.830191	0.0585572
$202$	52.4643	3.69138
$203$	−4.32726	−0.303714
$204$	5.63679	0.394654
$205$	−1.03599	−0.0723566
$206$	−13.8934	−0.968000
$207$	1.00000	0.0695048
$208$	10.9962	0.762450
$209$	−19.4871	−1.34795
$210$	12.0847	0.833924
$211$	12.8837	0.886950	0.443475	−	0.896287i	$-0.353746\pi$
$211$	12.8837	0.886950	0.443475	+	0.896287i	$0.353746\pi$
$212$	−2.59390	−0.178150
$213$	1.79880	0.123252
$214$	−37.4941	−2.56304
$215$	−8.39073	−0.572243
$216$	−9.33107	−0.634899
$217$	−25.6585	−1.74181
$218$	−32.9551	−2.23200
$219$	−13.2708	−0.896760
$220$	−13.2508	−0.893369
$221$	−0.783916	−0.0527319
$222$	−8.33601	−0.559476
$223$	−3.16955	−0.212249	−0.106124	−	0.994353i	$-0.533844\pi$
$223$	−3.16955	−0.212249	−0.106124	+	0.994353i	$0.533844\pi$
$224$	91.1109	6.08761
$225$	−3.94954	−0.263303
$226$	9.99184	0.664647
$227$	23.4740	1.55802	0.779012	−	0.627009i	$-0.215721\pi$
$227$	23.4740	1.55802	0.779012	+	0.627009i	$0.215721\pi$
$228$	44.3521	2.93729
$229$	12.4848	0.825019	0.412510	−	0.910953i	$-0.364652\pi$
$229$	12.4848	0.825019	0.412510	+	0.910953i	$0.364652\pi$
$230$	−2.79269	−0.184145
$231$	−10.3135	−0.678579
$232$	−9.33107	−0.612615
$233$	−9.55710	−0.626107	−0.313053	−	0.949736i	$-0.601352\pi$
$233$	−9.55710	−0.626107	−0.313053	+	0.949736i	$0.601352\pi$
$234$	2.05557	0.134377
$235$	−8.28849	−0.540681
$236$	−43.9137	−2.85854
$237$	−2.46332	−0.160010
$238$	−12.2523	−0.794201
$239$	2.85259	0.184519	0.0922593	−	0.995735i	$-0.470591\pi$
$239$	2.85259	0.184519	0.0922593	+	0.995735i	$0.470591\pi$
$240$	14.9394	0.964337
$241$	0.712445	0.0458926	0.0229463	−	0.999737i	$-0.492695\pi$
$241$	0.712445	0.0458926	0.0229463	+	0.999737i	$0.492695\pi$
$242$	−14.4946	−0.931745
$243$	−1.00000	−0.0641500
$244$	−80.7694	−5.17073
$245$	−12.0174	−0.767762
$246$	−2.75423	−0.175603
$247$	−6.16811	−0.392468
$248$	−55.3286	−3.51337
$249$	−4.46805	−0.283151
$250$	24.9933	1.58072
$251$	−8.60983	−0.543447	−0.271724	−	0.962375i	$-0.587594\pi$
$251$	−8.60983	−0.543447	−0.271724	+	0.962375i	$0.587594\pi$
$252$	23.4733	1.47868
$253$	2.38338	0.149842
$254$	−25.1749	−1.57962
$255$	−1.06503	−0.0666946
$256$	38.3289	2.39556
$257$	21.7102	1.35425	0.677123	−	0.735870i	$-0.263227\pi$
$257$	21.7102	1.35425	0.677123	+	0.735870i	$0.263227\pi$
$258$	−22.3072	−1.38878
$259$	13.2385	0.822598
$260$	−4.19418	−0.260112
$261$	−1.00000	−0.0618984
$262$	−18.5810	−1.14794
$263$	−18.3399	−1.13089	−0.565443	−	0.824787i	$-0.691295\pi$
$263$	−18.3399	−1.13089	−0.565443	+	0.824787i	$0.691295\pi$
$264$	−22.2395	−1.36875
$265$	0.490097	0.0301064
$266$	−96.4054	−5.91100
$267$	5.57787	0.341360
$268$	−4.50337	−0.275087
$269$	−12.5342	−0.764222	−0.382111	−	0.924116i	$-0.624803\pi$
$269$	−12.5342	−0.764222	−0.382111	+	0.924116i	$0.624803\pi$
$270$	2.79269	0.169958
$271$	11.5839	0.703673	0.351837	−	0.936061i	$-0.385557\pi$
$271$	11.5839	0.703673	0.351837	+	0.936061i	$0.385557\pi$
$272$	−15.1467	−0.918401
$273$	−3.26446	−0.197574
$274$	13.2442	0.800110
$275$	−9.41326	−0.567641
$276$	−5.42450	−0.326517
$277$	−19.8284	−1.19137	−0.595686	−	0.803217i	$-0.703120\pi$
$277$	−19.8284	−1.19137	−0.595686	+	0.803217i	$0.703120\pi$
$278$	−31.5821	−1.89417
$279$	−5.92951	−0.354990
$280$	−41.3841	−2.47317
$281$	−14.0464	−0.837936	−0.418968	−	0.908001i	$-0.637608\pi$
$281$	−14.0464	−0.837936	−0.418968	+	0.908001i	$0.637608\pi$
$282$	−22.0353	−1.31219
$283$	3.86800	0.229929	0.114964	−	0.993370i	$-0.463325\pi$
$283$	3.86800	0.229929	0.114964	+	0.993370i	$0.463325\pi$
$284$	−9.75760	−0.579007
$285$	−8.37999	−0.496388
$286$	4.89919	0.289695
$287$	4.37400	0.258189
$288$	21.0551	1.24068
$289$	−15.9202	−0.936482
$290$	2.79269	0.163992
$291$	0.684597	0.0401318
$292$	71.9877	4.21276
$293$	24.7095	1.44355	0.721774	−	0.692129i	$-0.243327\pi$
$293$	24.7095	1.44355	0.721774	+	0.692129i	$0.243327\pi$
$294$	−31.9488	−1.86329
$295$	8.29715	0.483079
$296$	28.5467	1.65924
$297$	−2.38338	−0.138298
$298$	−13.8229	−0.800740
$299$	0.754393	0.0436277
$300$	21.4243	1.23693
$301$	35.4261	2.04193
$302$	25.6767	1.47753
$303$	−19.2544	−1.10614
$304$	−119.179	−6.83539
$305$	15.2608	0.873829
$306$	−2.83143	−0.161862
$307$	28.6139	1.63308	0.816539	−	0.577290i	$-0.195890\pi$
$307$	28.6139	1.63308	0.816539	+	0.577290i	$0.195890\pi$
$308$	55.9457	3.18780
$309$	5.09888	0.290065
$310$	16.5593	0.940504
$311$	9.41777	0.534033	0.267016	−	0.963692i	$-0.413962\pi$
$311$	9.41777	0.534033	0.267016	+	0.963692i	$0.413962\pi$
$312$	−7.03929	−0.398522
$313$	−2.66933	−0.150880	−0.0754398	−	0.997150i	$-0.524036\pi$
$313$	−2.66933	−0.150880	−0.0754398	+	0.997150i	$0.524036\pi$
$314$	−49.0118	−2.76589
$315$	−4.43509	−0.249889
$316$	13.3623	0.751687
$317$	16.2962	0.915283	0.457642	−	0.889137i	$-0.348694\pi$
$317$	16.2962	0.915283	0.457642	+	0.889137i	$0.348694\pi$
$318$	1.30295	0.0730657
$319$	−2.38338	−0.133444
$320$	−28.9215	−1.61676
$321$	13.7603	0.768027
$322$	11.7909	0.657081
$323$	8.49623	0.472743
$324$	5.42450	0.301361
$325$	−2.97951	−0.165273
$326$	−44.6722	−2.47416
$327$	12.0945	0.668829
$328$	9.43186	0.520787
$329$	34.9945	1.92931
$330$	6.65604	0.366403
$331$	12.7644	0.701597	0.350798	−	0.936451i	$-0.385910\pi$
$331$	12.7644	0.701597	0.350798	+	0.936451i	$0.385910\pi$
$332$	24.2369	1.33018
$333$	3.05932	0.167649
$334$	61.9574	3.39016
$335$	0.850878	0.0464884
$336$	−63.0752	−3.44103
$337$	23.1747	1.26240	0.631202	−	0.775618i	$-0.282562\pi$
$337$	23.1747	1.26240	0.631202	+	0.775618i	$0.282562\pi$
$338$	−33.8716	−1.84237
$339$	−3.66701	−0.199165
$340$	5.77725	0.313315
$341$	−14.1323	−0.765305
$342$	−22.2786	−1.20469
$343$	20.4472	1.10404
$344$	76.3910	4.11872
$345$	1.02492	0.0551797
$346$	58.4649	3.14309
$347$	−7.87073	−0.422523	−0.211262	−	0.977430i	$-0.567757\pi$
$347$	−7.87073	−0.422523	−0.211262	+	0.977430i	$0.567757\pi$
$348$	5.42450	0.290784
$349$	−20.2614	−1.08457	−0.542284	−	0.840195i	$-0.682440\pi$
$349$	−20.2614	−1.08457	−0.542284	+	0.840195i	$0.682440\pi$
$350$	−46.5687	−2.48920
$351$	−0.754393	−0.0402665
$352$	50.1823	2.67472
$353$	−2.08029	−0.110723	−0.0553614	−	0.998466i	$-0.517631\pi$
$353$	−2.08029	−0.110723	−0.0553614	+	0.998466i	$0.517631\pi$
$354$	22.0584	1.17239
$355$	1.84362	0.0978494
$356$	−30.2572	−1.60363
$357$	4.49661	0.237986
$358$	−40.8359	−2.15824
$359$	24.0681	1.27027	0.635133	−	0.772403i	$-0.280945\pi$
$359$	24.0681	1.27027	0.635133	+	0.772403i	$0.280945\pi$
$360$	−9.56358	−0.504045
$361$	47.8512	2.51848
$362$	−46.5778	−2.44807
$363$	5.31950	0.279201
$364$	17.7081	0.928155
$365$	−13.6015	−0.711936
$366$	40.5715	2.12070
$367$	−7.21883	−0.376820	−0.188410	−	0.982090i	$-0.560333\pi$
$367$	−7.21883	−0.376820	−0.188410	+	0.982090i	$0.560333\pi$
$368$	14.5762	0.759839
$369$	1.01080	0.0526202
$370$	−8.54372	−0.444167
$371$	−2.06922	−0.107429
$372$	32.1646	1.66766
$373$	−20.7310	−1.07341	−0.536704	−	0.843770i	$-0.680331\pi$
$373$	−20.7310	−1.07341	−0.536704	+	0.843770i	$0.680331\pi$
$374$	−6.74837	−0.348950
$375$	−9.17255	−0.473668
$376$	75.4601	3.89156
$377$	−0.754393	−0.0388532
$378$	−11.7909	−0.606458
$379$	12.9895	0.667228	0.333614	−	0.942710i	$-0.391732\pi$
$379$	12.9895	0.667228	0.333614	+	0.942710i	$0.391732\pi$
$380$	45.4573	2.33191
$381$	9.23920	0.473339
$382$	−42.6240	−2.18083
$383$	−35.6863	−1.82349	−0.911743	−	0.410762i	$-0.865263\pi$
$383$	−35.6863	−1.82349	−0.911743	+	0.410762i	$0.865263\pi$
$384$	−34.7790	−1.77481
$385$	−10.5705	−0.538723
$386$	57.5326	2.92833
$387$	8.18673	0.416155
$388$	−3.71360	−0.188529
$389$	1.85642	0.0941243	0.0470622	−	0.998892i	$-0.485014\pi$
$389$	1.85642	0.0941243	0.0470622	+	0.998892i	$0.485014\pi$
$390$	2.10679	0.106681
$391$	−1.03913	−0.0525513
$392$	109.409	5.52597
$393$	6.81925	0.343985
$394$	6.47192	0.326051
$395$	−2.52470	−0.127031
$396$	12.9287	0.649689
$397$	−18.4801	−0.927489	−0.463745	−	0.885969i	$-0.653494\pi$
$397$	−18.4801	−0.927489	−0.463745	+	0.885969i	$0.653494\pi$
$398$	−38.6143	−1.93556
$399$	35.3808	1.77126
$400$	−57.5695	−2.87847
$401$	−24.3126	−1.21411	−0.607056	−	0.794659i	$-0.707650\pi$
$401$	−24.3126	−1.21411	−0.607056	+	0.794659i	$0.707650\pi$
$402$	2.26210	0.112823
$403$	−4.47318	−0.222825
$404$	104.446	5.19637
$405$	−1.02492	−0.0509286
$406$	−11.7909	−0.585173
$407$	7.29151	0.361427
$408$	9.69623	0.480035
$409$	30.3298	1.49971	0.749855	−	0.661602i	$-0.230123\pi$
$409$	30.3298	1.49971	0.749855	+	0.661602i	$0.230123\pi$
$410$	−2.82286	−0.139411
$411$	−4.86061	−0.239756
$412$	−27.6589	−1.36266
$413$	−35.0311	−1.72377
$414$	2.72479	0.133916
$415$	−4.57938	−0.224793
$416$	15.8838	0.778769
$417$	11.5906	0.567596
$418$	−53.0984	−2.59713
$419$	27.8837	1.36221	0.681105	−	0.732186i	$-0.261500\pi$
$419$	27.8837	1.36221	0.681105	+	0.732186i	$0.261500\pi$
$420$	24.0582	1.17392
$421$	14.0024	0.682437	0.341219	−	0.939984i	$-0.389160\pi$
$421$	14.0024	0.682437	0.341219	+	0.939984i	$0.389160\pi$
$422$	35.1054	1.70890
$423$	8.08697	0.393202
$424$	−4.46195	−0.216691
$425$	4.10411	0.199078
$426$	4.90136	0.237472
$427$	−64.4318	−3.11807
$428$	−74.6430	−3.60801
$429$	−1.79801	−0.0868085
$430$	−22.8630	−1.10255
$431$	29.8983	1.44015	0.720075	−	0.693897i	$-0.244108\pi$
$431$	29.8983	1.44015	0.720075	+	0.693897i	$0.244108\pi$
$432$	−14.5762	−0.701299
$433$	−37.3902	−1.79686	−0.898428	−	0.439120i	$-0.855290\pi$
$433$	−37.3902	−1.79686	−0.898428	+	0.439120i	$0.855290\pi$
$434$	−69.9142	−3.35599
$435$	−1.02492	−0.0491411
$436$	−65.6068	−3.14200
$437$	−8.17626	−0.391123
$438$	−36.1603	−1.72781
$439$	−27.9734	−1.33510	−0.667549	−	0.744565i	$-0.732657\pi$
$439$	−27.9734	−1.33510	−0.667549	+	0.744565i	$0.732657\pi$
$440$	−22.7936	−1.08664
$441$	11.7252	0.558343
$442$	−2.13601	−0.101600
$443$	12.5665	0.597051	0.298525	−	0.954402i	$-0.403505\pi$
$443$	12.5665	0.597051	0.298525	+	0.954402i	$0.403505\pi$
$444$	−16.5953	−0.787577
$445$	5.71686	0.271005
$446$	−8.63638	−0.408944
$447$	5.07301	0.239945
$448$	122.108	5.76907
$449$	5.54208	0.261547	0.130774	−	0.991412i	$-0.458254\pi$
$449$	5.54208	0.261547	0.130774	+	0.991412i	$0.458254\pi$
$450$	−10.7617	−0.507311
$451$	2.40912	0.113441
$452$	19.8917	0.935627
$453$	−9.42334	−0.442747
$454$	63.9618	3.00188
$455$	−3.34580	−0.156854
$456$	76.2932	3.57276
$457$	32.2110	1.50677	0.753383	−	0.657582i	$-0.228421\pi$
$457$	32.2110	1.50677	0.753383	+	0.657582i	$0.228421\pi$
$458$	34.0185	1.58958
$459$	1.03913	0.0485026
$460$	−5.55967	−0.259221
$461$	−22.9127	−1.06715	−0.533576	−	0.845752i	$-0.679152\pi$
$461$	−22.9127	−1.06715	−0.533576	+	0.845752i	$0.679152\pi$
$462$	−28.1022	−1.30743
$463$	−1.70309	−0.0791491	−0.0395746	−	0.999217i	$-0.512600\pi$
$463$	−1.70309	−0.0791491	−0.0395746	+	0.999217i	$0.512600\pi$
$464$	−14.5762	−0.676685
$465$	−6.07726	−0.281826
$466$	−26.0411	−1.20633
$467$	28.0758	1.29919	0.649596	−	0.760279i	$-0.274938\pi$
$467$	28.0758	1.29919	0.649596	+	0.760279i	$0.274938\pi$
$468$	4.09221	0.189162
$469$	−3.59245	−0.165884
$470$	−22.5844	−1.04174
$471$	17.9873	0.828812
$472$	−75.5390	−3.47697
$473$	19.5121	0.897167
$474$	−6.71204	−0.308294
$475$	32.2925	1.48168
$476$	−24.3919	−1.11800
$477$	−0.478182	−0.0218945
$478$	7.77272	0.355516
$479$	−25.5753	−1.16856	−0.584282	−	0.811551i	$-0.698624\pi$
$479$	−25.5753	−1.16856	−0.584282	+	0.811551i	$0.698624\pi$
$480$	21.5798	0.984976
$481$	2.30793	0.105232
$482$	1.94127	0.0884223
$483$	−4.32726	−0.196897
$484$	−28.8557	−1.31162
$485$	0.701655	0.0318605
$486$	−2.72479	−0.123599
$487$	34.5635	1.56622	0.783112	−	0.621881i	$-0.213631\pi$
$487$	34.5635	1.56622	0.783112	+	0.621881i	$0.213631\pi$
$488$	−138.937	−6.28939
$489$	16.3947	0.741394
$490$	−32.7449	−1.47926
$491$	14.9939	0.676664	0.338332	−	0.941027i	$-0.390137\pi$
$491$	14.9939	0.676664	0.338332	+	0.941027i	$0.390137\pi$
$492$	−5.48310	−0.247197
$493$	1.03913	0.0468003
$494$	−16.8068	−0.756175
$495$	−2.44277	−0.109794
$496$	−86.4299	−3.88082
$497$	−7.78388	−0.349155
$498$	−12.1745	−0.545553
$499$	1.58115	0.0707819	0.0353909	−	0.999374i	$-0.488732\pi$
$499$	1.58115	0.0707819	0.0353909	+	0.999374i	$0.488732\pi$
$500$	49.7565	2.22518
$501$	−22.7384	−1.01588
$502$	−23.4600	−1.04707
$503$	38.2023	1.70336	0.851679	−	0.524064i	$-0.175585\pi$
$503$	38.2023	1.70336	0.851679	+	0.524064i	$0.175585\pi$
$504$	40.3780	1.79858
$505$	−19.7342	−0.878161
$506$	6.49422	0.288703
$507$	12.4309	0.552075
$508$	−50.1181	−2.22363
$509$	0.866481	0.0384061	0.0192030	−	0.999816i	$-0.493887\pi$
$509$	0.866481	0.0384061	0.0192030	+	0.999816i	$0.493887\pi$
$510$	−2.90198	−0.128502
$511$	57.4264	2.54039
$512$	34.8804	1.54151
$513$	8.17626	0.360991
$514$	59.1558	2.60925
$515$	5.22594	0.230282
$516$	−44.4090	−1.95500
$517$	19.2743	0.847684
$518$	36.0721	1.58492
$519$	−21.4566	−0.941842
$520$	−7.21470	−0.316386
$521$	3.68724	0.161541	0.0807704	−	0.996733i	$-0.474262\pi$
$521$	3.68724	0.161541	0.0807704	+	0.996733i	$0.474262\pi$
$522$	−2.72479	−0.119261
$523$	−41.5135	−1.81526	−0.907628	−	0.419775i	$-0.862109\pi$
$523$	−41.5135	−1.81526	−0.907628	+	0.419775i	$0.862109\pi$
$524$	−36.9910	−1.61596
$525$	17.0907	0.745900
$526$	−49.9724	−2.17890
$527$	6.16155	0.268401
$528$	−34.7407	−1.51189
$529$	1.00000	0.0434783
$530$	1.33541	0.0580067
$531$	−8.09543	−0.351312
$532$	−191.923	−8.32093
$533$	0.762542	0.0330294
$534$	15.1985	0.657705
$535$	14.1032	0.609735
$536$	−7.74657	−0.334601
$537$	14.9868	0.646727
$538$	−34.1530	−1.47244
$539$	27.9456	1.20370
$540$	5.55967	0.239250
$541$	−25.7510	−1.10712	−0.553561	−	0.832809i	$-0.686731\pi$
$541$	−25.7510	−1.10712	−0.553561	+	0.832809i	$0.686731\pi$
$542$	31.5638	1.35578
$543$	17.0940	0.733576
$544$	−21.8791	−0.938058
$545$	12.3959	0.530982
$546$	−8.89498	−0.380670
$547$	28.4992	1.21854	0.609268	−	0.792964i	$-0.291463\pi$
$547$	28.4992	1.21854	0.609268	+	0.792964i	$0.291463\pi$
$548$	26.3664	1.12632
$549$	−14.8897	−0.635478
$550$	−25.6492	−1.09369
$551$	8.17626	0.348320
$552$	−9.33107	−0.397157
$553$	10.6594	0.453285
$554$	−54.0283	−2.29544
$555$	3.13555	0.133097
$556$	−62.8735	−2.66643
$557$	−29.0231	−1.22975	−0.614873	−	0.788626i	$-0.710793\pi$
$557$	−29.0231	−1.22975	−0.614873	+	0.788626i	$0.710793\pi$
$558$	−16.1567	−0.683967
$559$	6.17602	0.261218
$560$	−64.6469	−2.73183
$561$	2.47665	0.104564
$562$	−38.2735	−1.61447
$563$	−30.2427	−1.27458	−0.637288	−	0.770626i	$-0.719944\pi$
$563$	−30.2427	−1.27458	−0.637288	+	0.770626i	$0.719944\pi$
$564$	−43.8678	−1.84717
$565$	−3.75838	−0.158116
$566$	10.5395	0.443009
$567$	4.32726	0.181728
$568$	−16.7847	−0.704272
$569$	−34.0959	−1.42937	−0.714687	−	0.699444i	$-0.753431\pi$
$569$	−34.0959	−1.42937	−0.714687	+	0.699444i	$0.753431\pi$
$570$	−22.8338	−0.956401
$571$	−7.96785	−0.333444	−0.166722	−	0.986004i	$-0.553318\pi$
$571$	−7.96785	−0.333444	−0.166722	+	0.986004i	$0.553318\pi$
$572$	9.75329	0.407805
$573$	15.6430	0.653496
$574$	11.9183	0.497459
$575$	−3.94954	−0.164707
$576$	28.2183	1.17576
$577$	−35.2407	−1.46709	−0.733545	−	0.679640i	$-0.762136\pi$
$577$	−35.2407	−1.46709	−0.733545	+	0.679640i	$0.762136\pi$
$578$	−43.3793	−1.80434
$579$	−21.1145	−0.877488
$580$	5.55967	0.230853
$581$	19.3344	0.802127
$582$	1.86538	0.0773227
$583$	−1.13969	−0.0472011
$584$	123.831	5.12416
$585$	−0.773191	−0.0319675
$586$	67.3284	2.78131
$587$	−6.85699	−0.283018	−0.141509	−	0.989937i	$-0.545195\pi$
$587$	−6.85699	−0.283018	−0.141509	+	0.989937i	$0.545195\pi$
$588$	−63.6034	−2.62296
$589$	48.4812	1.99763
$590$	22.6080	0.930758
$591$	−2.37520	−0.0977025
$592$	44.5933	1.83277
$593$	36.7362	1.50858	0.754288	−	0.656543i	$-0.227982\pi$
$593$	36.7362	1.50858	0.754288	+	0.656543i	$0.227982\pi$
$594$	−6.49422	−0.266461
$595$	4.60865	0.188936
$596$	−27.5186	−1.12720
$597$	14.1714	0.579999
$598$	2.05557	0.0840584
$599$	39.6697	1.62086	0.810430	−	0.585836i	$-0.199234\pi$
$599$	39.6697	1.62086	0.810430	+	0.585836i	$0.199234\pi$
$600$	36.8535	1.50454
$601$	−13.4001	−0.546601	−0.273300	−	0.961929i	$-0.588115\pi$
$601$	−13.4001	−0.546601	−0.273300	+	0.961929i	$0.588115\pi$
$602$	96.5289	3.93423
$603$	−0.830191	−0.0338080
$604$	51.1169	2.07992
$605$	5.45205	0.221658
$606$	−52.4643	−2.13122
$607$	10.1830	0.413313	0.206657	−	0.978414i	$-0.433742\pi$
$607$	10.1830	0.413313	0.206657	+	0.978414i	$0.433742\pi$
$608$	−172.152	−6.98168
$609$	4.32726	0.175350
$610$	41.5824	1.68362
$611$	6.10076	0.246810
$612$	−5.63679	−0.227854
$613$	−9.64274	−0.389467	−0.194733	−	0.980856i	$-0.562384\pi$
$613$	−9.64274	−0.389467	−0.194733	+	0.980856i	$0.562384\pi$
$614$	77.9669	3.14649
$615$	1.03599	0.0417751
$616$	96.2361	3.87746
$617$	−1.00133	−0.0403122	−0.0201561	−	0.999797i	$-0.506416\pi$
$617$	−1.00133	−0.0403122	−0.0201561	+	0.999797i	$0.506416\pi$
$618$	13.8934	0.558875
$619$	29.4218	1.18256	0.591281	−	0.806466i	$-0.298622\pi$
$619$	29.4218	1.18256	0.591281	+	0.806466i	$0.298622\pi$
$620$	32.9661	1.32395
$621$	−1.00000	−0.0401286
$622$	25.6615	1.02893
$623$	−24.1369	−0.967025
$624$	−10.9962	−0.440201
$625$	10.3466	0.413864
$626$	−7.27338	−0.290703
$627$	19.4871	0.778241
$628$	−97.5723	−3.89356
$629$	−3.17904	−0.126757
$630$	−12.0847	−0.481466
$631$	−46.2853	−1.84259	−0.921294	−	0.388866i	$-0.872867\pi$
$631$	−46.2853	−1.84259	−0.921294	+	0.388866i	$0.872867\pi$
$632$	22.9854	0.914310
$633$	−12.8837	−0.512081
$634$	44.4037	1.76349
$635$	9.46943	0.375783
$636$	2.59390	0.102855
$637$	8.84541	0.350468
$638$	−6.49422	−0.257109
$639$	−1.79880	−0.0711595
$640$	−35.6456	−1.40902
$641$	29.5602	1.16756	0.583780	−	0.811912i	$-0.301573\pi$
$641$	29.5602	1.16756	0.583780	+	0.811912i	$0.301573\pi$
$642$	37.4941	1.47977
$643$	22.8121	0.899621	0.449810	−	0.893124i	$-0.351492\pi$
$643$	22.8121	0.899621	0.449810	+	0.893124i	$0.351492\pi$
$644$	23.4733	0.924976
$645$	8.39073	0.330385
$646$	23.1505	0.910843
$647$	27.7127	1.08950	0.544749	−	0.838599i	$-0.316625\pi$
$647$	27.7127	1.08950	0.544749	+	0.838599i	$0.316625\pi$
$648$	9.33107	0.366559
$649$	−19.2945	−0.757375
$650$	−8.11855	−0.318436
$651$	25.6585	1.00564
$652$	−88.9331	−3.48289
$653$	−18.2397	−0.713774	−0.356887	−	0.934148i	$-0.616162\pi$
$653$	−18.2397	−0.713774	−0.356887	+	0.934148i	$0.616162\pi$
$654$	32.9551	1.28865
$655$	6.98917	0.273089
$656$	14.7337	0.575254
$657$	13.2708	0.517744
$658$	95.3527	3.71724
$659$	18.0505	0.703149	0.351574	−	0.936160i	$-0.385646\pi$
$659$	18.0505	0.703149	0.351574	+	0.936160i	$0.385646\pi$
$660$	13.2508	0.515787
$661$	−9.33849	−0.363225	−0.181613	−	0.983370i	$-0.558132\pi$
$661$	−9.33849	−0.363225	−0.181613	+	0.983370i	$0.558132\pi$
$662$	34.7805	1.35178
$663$	0.783916	0.0304448
$664$	41.6917	1.61795
$665$	36.2624	1.40620
$666$	8.33601	0.323014
$667$	−1.00000	−0.0387202
$668$	123.345	4.77234
$669$	3.16955	0.122542
$670$	2.31847	0.0895702
$671$	−35.4879	−1.36999
$672$	−91.1109	−3.51468
$673$	12.8952	0.497074	0.248537	−	0.968622i	$-0.420050\pi$
$673$	12.8952	0.497074	0.248537	+	0.968622i	$0.420050\pi$
$674$	63.1462	2.43230
$675$	3.94954	0.152018
$676$	−67.4314	−2.59352
$677$	45.6983	1.75633	0.878165	−	0.478358i	$-0.158768\pi$
$677$	45.6983	1.75633	0.878165	+	0.478358i	$0.158768\pi$
$678$	−9.99184	−0.383734
$679$	−2.96243	−0.113688
$680$	9.93784	0.381099
$681$	−23.4740	−0.899525
$682$	−38.5075	−1.47453
$683$	−21.1386	−0.808847	−0.404423	−	0.914572i	$-0.632528\pi$
$683$	−21.1386	−0.808847	−0.404423	+	0.914572i	$0.632528\pi$
$684$	−44.3521	−1.69585
$685$	−4.98173	−0.190342
$686$	55.7144	2.12719
$687$	−12.4848	−0.476325
$688$	119.332	4.54948
$689$	−0.360737	−0.0137430
$690$	2.79269	0.106316
$691$	10.9159	0.415261	0.207630	−	0.978207i	$-0.433425\pi$
$691$	10.9159	0.415261	0.207630	+	0.978207i	$0.433425\pi$
$692$	116.392	4.42455
$693$	10.3135	0.391778
$694$	−21.4461	−0.814084
$695$	11.8795	0.450614
$696$	9.33107	0.353693
$697$	−1.05036	−0.0397852
$698$	−55.2081	−2.08966
$699$	9.55710	0.361483
$700$	−92.7086	−3.50406
$701$	−12.4276	−0.469384	−0.234692	−	0.972070i	$-0.575408\pi$
$701$	−12.4276	−0.469384	−0.234692	+	0.972070i	$0.575408\pi$
$702$	−2.05557	−0.0775824
$703$	−25.0138	−0.943411
$704$	67.2550	2.53477
$705$	8.28849	0.312162
$706$	−5.66837	−0.213332
$707$	83.3189	3.13353
$708$	43.9137	1.65038
$709$	−45.4539	−1.70706	−0.853529	−	0.521046i	$-0.825542\pi$
$709$	−45.4539	−1.70706	−0.853529	+	0.521046i	$0.825542\pi$
$710$	5.02350	0.188528
$711$	2.46332	0.0923817
$712$	−52.0475	−1.95056
$713$	−5.92951	−0.222062
$714$	12.2523	0.458532
$715$	−1.84281	−0.0689171
$716$	−81.2959	−3.03817
$717$	−2.85259	−0.106532
$718$	65.5806	2.44745
$719$	−30.5357	−1.13879	−0.569394	−	0.822065i	$-0.692822\pi$
$719$	−30.5357	−1.13879	−0.569394	+	0.822065i	$0.692822\pi$
$720$	−14.9394	−0.556760
$721$	−22.0642	−0.821714
$722$	130.385	4.85241
$723$	−0.712445	−0.0264961
$724$	−92.7267	−3.44616
$725$	3.94954	0.146682
$726$	14.4946	0.537943
$727$	13.9153	0.516091	0.258045	−	0.966133i	$-0.416922\pi$
$727$	13.9153	0.516091	0.258045	+	0.966133i	$0.416922\pi$
$728$	30.4609	1.12896
$729$	1.00000	0.0370370
$730$	−37.0613	−1.37170
$731$	−8.50711	−0.314647
$732$	80.7694	2.98532
$733$	7.18360	0.265332	0.132666	−	0.991161i	$-0.457646\pi$
$733$	7.18360	0.265332	0.132666	+	0.991161i	$0.457646\pi$
$734$	−19.6698	−0.726027
$735$	12.0174	0.443267
$736$	21.0551	0.776101
$737$	−1.97866	−0.0728849
$738$	2.75423	0.101384
$739$	3.44007	0.126545	0.0632725	−	0.997996i	$-0.479846\pi$
$739$	3.44007	0.126545	0.0632725	+	0.997996i	$0.479846\pi$
$740$	−17.0088	−0.625256
$741$	6.16811	0.226591
$742$	−5.63820	−0.206985
$743$	−6.89471	−0.252942	−0.126471	−	0.991970i	$-0.540365\pi$
$743$	−6.89471	−0.252942	−0.126471	+	0.991970i	$0.540365\pi$
$744$	55.3286	2.02845
$745$	5.19942	0.190492
$746$	−56.4876	−2.06816
$747$	4.46805	0.163477
$748$	−13.4346	−0.491218
$749$	−59.5446	−2.17571
$750$	−24.9933	−0.912627
$751$	44.3395	1.61797	0.808985	−	0.587829i	$-0.200017\pi$
$751$	44.3395	1.61797	0.808985	+	0.587829i	$0.200017\pi$
$752$	117.878	4.29855
$753$	8.60983	0.313760
$754$	−2.05557	−0.0748593
$755$	−9.65815	−0.351496
$756$	−23.4733	−0.853714
$757$	−30.4467	−1.10660	−0.553302	−	0.832981i	$-0.686633\pi$
$757$	−30.4467	−1.10660	−0.553302	+	0.832981i	$0.686633\pi$
$758$	35.3938	1.28556
$759$	−2.38338	−0.0865112
$760$	78.1943	2.83640
$761$	34.4231	1.24784	0.623919	−	0.781489i	$-0.285540\pi$
$761$	34.4231	1.24784	0.623919	+	0.781489i	$0.285540\pi$
$762$	25.1749	0.911992
$763$	−52.3362	−1.89470
$764$	−84.8555	−3.06997
$765$	1.06503	0.0385062
$766$	−97.2378	−3.51335
$767$	−6.10714	−0.220516
$768$	−38.3289	−1.38308
$769$	−34.2773	−1.23607	−0.618035	−	0.786151i	$-0.712071\pi$
$769$	−34.2773	−1.23607	−0.618035	+	0.786151i	$0.712071\pi$
$770$	−28.8024	−1.03797
$771$	−21.7102	−0.781874
$772$	114.536	4.12223
$773$	−10.4729	−0.376682	−0.188341	−	0.982104i	$-0.560311\pi$
$773$	−10.4729	−0.376682	−0.188341	+	0.982104i	$0.560311\pi$
$774$	22.3072	0.801814
$775$	23.4188	0.841229
$776$	−6.38802	−0.229316
$777$	−13.2385	−0.474927
$778$	5.05837	0.181351
$779$	−8.26457	−0.296109
$780$	4.19418	0.150176
$781$	−4.28723	−0.153409
$782$	−2.83143	−0.101252
$783$	1.00000	0.0357371
$784$	170.909	6.10390
$785$	18.4355	0.657993
$786$	18.5810	0.662764
$787$	43.2021	1.53999	0.769995	−	0.638050i	$-0.220259\pi$
$787$	43.2021	1.53999	0.769995	+	0.638050i	$0.220259\pi$
$788$	12.8843	0.458983
$789$	18.3399	0.652917
$790$	−6.87929	−0.244754
$791$	15.8681	0.564205
$792$	22.2395	0.790245
$793$	−11.2327	−0.398885
$794$	−50.3544	−1.78701
$795$	−0.490097	−0.0173820
$796$	−76.8731	−2.72469
$797$	−22.4875	−0.796549	−0.398274	−	0.917266i	$-0.630391\pi$
$797$	−22.4875	−0.796549	−0.398274	+	0.917266i	$0.630391\pi$
$798$	96.4054	3.41272
$799$	−8.40345	−0.297293
$800$	−83.1580	−2.94008
$801$	−5.57787	−0.197084
$802$	−66.2468	−2.33926
$803$	31.6294	1.11618
$804$	4.50337	0.158822
$805$	−4.43509	−0.156316
$806$	−12.1885	−0.429321
$807$	12.5342	0.441224
$808$	179.664	6.32057
$809$	14.7365	0.518108	0.259054	−	0.965863i	$-0.416589\pi$
$809$	14.7365	0.518108	0.259054	+	0.965863i	$0.416589\pi$
$810$	−2.79269	−0.0981252
$811$	53.4867	1.87817	0.939086	−	0.343682i	$-0.111674\pi$
$811$	53.4867	1.87817	0.939086	+	0.343682i	$0.111674\pi$
$812$	−23.4733	−0.823750
$813$	−11.5839	−0.406266
$814$	19.8679	0.696368
$815$	16.8032	0.588591
$816$	15.1467	0.530239
$817$	−66.9368	−2.34182
$818$	82.6423	2.88952
$819$	3.26446	0.114069
$820$	−5.61973	−0.196249
$821$	21.2503	0.741640	0.370820	−	0.928705i	$-0.379077\pi$
$821$	21.2503	0.741640	0.370820	+	0.928705i	$0.379077\pi$
$822$	−13.2442	−0.461944
$823$	−11.6892	−0.407459	−0.203730	−	0.979027i	$-0.565306\pi$
$823$	−11.6892	−0.407459	−0.203730	+	0.979027i	$0.565306\pi$
$824$	−47.5780	−1.65746
$825$	9.41326	0.327728
$826$	−95.4524	−3.32121
$827$	−36.0442	−1.25338	−0.626690	−	0.779269i	$-0.715591\pi$
$827$	−36.0442	−1.25338	−0.626690	+	0.779269i	$0.715591\pi$
$828$	5.42450	0.188515
$829$	11.0806	0.384846	0.192423	−	0.981312i	$-0.438366\pi$
$829$	11.0806	0.384846	0.192423	+	0.981312i	$0.438366\pi$
$830$	−12.4779	−0.433113
$831$	19.8284	0.687839
$832$	21.2877	0.738019
$833$	−12.1841	−0.422153
$834$	31.5821	1.09360
$835$	−23.3050	−0.806503
$836$	−105.708	−3.65599
$837$	5.92951	0.204954
$838$	75.9775	2.62460
$839$	40.9744	1.41459	0.707296	−	0.706917i	$-0.249915\pi$
$839$	40.9744	1.41459	0.707296	+	0.706917i	$0.249915\pi$
$840$	41.3841	1.42789
$841$	1.00000	0.0344828
$842$	38.1538	1.31487
$843$	14.0464	0.483783
$844$	69.8876	2.40563
$845$	12.7406	0.438292
$846$	22.0353	0.757591
$847$	−23.0189	−0.790938
$848$	−6.97009	−0.239354
$849$	−3.86800	−0.132750
$850$	11.1828	0.383568
$851$	3.05932	0.104872
$852$	9.75760	0.334290
$853$	20.2611	0.693726	0.346863	−	0.937916i	$-0.387247\pi$
$853$	20.2611	0.693726	0.346863	+	0.937916i	$0.387247\pi$
$854$	−175.563	−6.00766
$855$	8.37999	0.286590
$856$	−128.399	−4.38858
$857$	12.5526	0.428789	0.214395	−	0.976747i	$-0.431222\pi$
$857$	12.5526	0.428789	0.214395	+	0.976747i	$0.431222\pi$
$858$	−4.89919	−0.167256
$859$	−49.7481	−1.69738	−0.848692	−	0.528887i	$-0.822609\pi$
$859$	−49.7481	−1.69738	−0.848692	+	0.528887i	$0.822609\pi$
$860$	−45.5155	−1.55207
$861$	−4.37400	−0.149066
$862$	81.4666	2.77476
$863$	29.3777	1.00003	0.500015	−	0.866017i	$-0.333328\pi$
$863$	29.3777	1.00003	0.500015	+	0.866017i	$0.333328\pi$
$864$	−21.0551	−0.716309
$865$	−21.9913	−0.747727
$866$	−101.881	−3.46204
$867$	15.9202	0.540678
$868$	−139.185	−4.72424
$869$	5.87102	0.199161
$870$	−2.79269	−0.0946811
$871$	−0.626290	−0.0212210
$872$	−112.855	−3.82175
$873$	−0.684597	−0.0231701
$874$	−22.2786	−0.753585
$875$	39.6920	1.34184
$876$	−71.9877	−2.43224
$877$	47.3882	1.60019	0.800093	−	0.599876i	$-0.204783\pi$
$877$	47.3882	1.60019	0.800093	+	0.599876i	$0.204783\pi$
$878$	−76.2218	−2.57236
$879$	−24.7095	−0.833432
$880$	−35.6064	−1.20029
$881$	−46.1479	−1.55476	−0.777382	−	0.629029i	$-0.783453\pi$
$881$	−46.1479	−1.55476	−0.777382	+	0.629029i	$0.783453\pi$
$882$	31.9488	1.07577
$883$	−17.8622	−0.601111	−0.300556	−	0.953764i	$-0.597172\pi$
$883$	−17.8622	−0.601111	−0.300556	+	0.953764i	$0.597172\pi$
$884$	−4.25235	−0.143022
$885$	−8.29715	−0.278906
$886$	34.2410	1.15035
$887$	34.0136	1.14207	0.571033	−	0.820927i	$-0.306543\pi$
$887$	34.0136	1.14207	0.571033	+	0.820927i	$0.306543\pi$
$888$	−28.5467	−0.957964
$889$	−39.9805	−1.34090
$890$	15.5773	0.522151
$891$	2.38338	0.0798462
$892$	−17.1933	−0.575673
$893$	−66.1212	−2.21266
$894$	13.8229	0.462307
$895$	15.3602	0.513436
$896$	150.498	5.02778
$897$	−0.754393	−0.0251885
$898$	15.1010	0.503928
$899$	5.92951	0.197760
$900$	−21.4243	−0.714144
$901$	0.496895	0.0165540
$902$	6.56437	0.218570
$903$	−35.4261	−1.17891
$904$	34.2171	1.13804
$905$	17.5200	0.582385
$906$	−25.6767	−0.853050
$907$	1.99413	0.0662141	0.0331070	−	0.999452i	$-0.489460\pi$
$907$	1.99413	0.0662141	0.0331070	+	0.999452i	$0.489460\pi$
$908$	127.335	4.22575
$909$	19.2544	0.638629
$910$	−9.11662	−0.302213
$911$	3.41787	0.113239	0.0566196	−	0.998396i	$-0.481968\pi$
$911$	3.41787	0.113239	0.0566196	+	0.998396i	$0.481968\pi$
$912$	119.179	3.94641
$913$	10.6491	0.352432
$914$	87.7683	2.90312
$915$	−15.2608	−0.504505
$916$	67.7239	2.23766
$917$	−29.5087	−0.974462
$918$	2.83143	0.0934510
$919$	5.56763	0.183659	0.0918296	−	0.995775i	$-0.470729\pi$
$919$	5.56763	0.183659	0.0918296	+	0.995775i	$0.470729\pi$
$920$	−9.56358	−0.315302
$921$	−28.6139	−0.942858
$922$	−62.4325	−2.05610
$923$	−1.35700	−0.0446663
$924$	−55.9457	−1.84048
$925$	−12.0829	−0.397283
$926$	−4.64056	−0.152498
$927$	−5.09888	−0.167469
$928$	−21.0551	−0.691167
$929$	−32.3923	−1.06276	−0.531379	−	0.847134i	$-0.678326\pi$
$929$	−32.3923	−1.06276	−0.531379	+	0.847134i	$0.678326\pi$
$930$	−16.5593	−0.543000
$931$	−95.8683	−3.14196
$932$	−51.8425	−1.69816
$933$	−9.41777	−0.308324
$934$	76.5007	2.50318
$935$	2.53836	0.0830134
$936$	7.03929	0.230087
$937$	−1.53335	−0.0500925	−0.0250462	−	0.999686i	$-0.507973\pi$
$937$	−1.53335	−0.0500925	−0.0250462	+	0.999686i	$0.507973\pi$
$938$	−9.78870	−0.319612
$939$	2.66933	0.0871104
$940$	−44.9609	−1.46646
$941$	−4.27935	−0.139503	−0.0697514	−	0.997564i	$-0.522221\pi$
$941$	−4.27935	−0.139503	−0.0697514	+	0.997564i	$0.522221\pi$
$942$	49.0118	1.59689
$943$	1.01080	0.0329162
$944$	−118.001	−3.84060
$945$	4.43509	0.144273
$946$	53.1664	1.72859
$947$	55.7160	1.81053	0.905263	−	0.424851i	$-0.139673\pi$
$947$	55.7160	1.81053	0.905263	+	0.424851i	$0.139673\pi$
$948$	−13.3623	−0.433987
$949$	10.0114	0.324985
$950$	87.9903	2.85478
$951$	−16.2962	−0.528439
$952$	−41.9581	−1.35987
$953$	60.9052	1.97291	0.986457	−	0.164019i	$-0.0524459\pi$
$953$	60.9052	1.97291	0.986457	+	0.164019i	$0.0524459\pi$
$954$	−1.30295	−0.0421845
$955$	16.0328	0.518809
$956$	15.4739	0.500461
$957$	2.38338	0.0770437
$958$	−69.6873	−2.25150
$959$	21.0332	0.679196
$960$	28.9215	0.933437
$961$	4.15904	0.134163
$962$	6.28863	0.202753
$963$	−13.7603	−0.443421
$964$	3.86466	0.124472
$965$	−21.6406	−0.696636
$966$	−11.7909	−0.379366
$967$	27.2667	0.876839	0.438420	−	0.898770i	$-0.355538\pi$
$967$	27.2667	0.876839	0.438420	+	0.898770i	$0.355538\pi$
$968$	−49.6366	−1.59538
$969$	−8.49623	−0.272938
$970$	1.91187	0.0613863
$971$	44.4273	1.42574	0.712870	−	0.701297i	$-0.247395\pi$
$971$	44.4273	1.42574	0.712870	+	0.701297i	$0.247395\pi$
$972$	−5.42450	−0.173991
$973$	−50.1558	−1.60792
$974$	94.1785	3.01767
$975$	2.97951	0.0954206
$976$	−217.036	−6.94716
$977$	0.396649	0.0126899	0.00634496	−	0.999980i	$-0.497980\pi$
$977$	0.396649	0.0126899	0.00634496	+	0.999980i	$0.497980\pi$
$978$	44.6722	1.42846
$979$	−13.2942	−0.424884
$980$	−65.1883	−2.08236
$981$	−12.0945	−0.386149
$982$	40.8552	1.30374
$983$	−2.59076	−0.0826323	−0.0413161	−	0.999146i	$-0.513155\pi$
$983$	−2.59076	−0.0826323	−0.0413161	+	0.999146i	$0.513155\pi$
$984$	−9.43186	−0.300677
$985$	−2.43438	−0.0775658
$986$	2.83143	0.0901710
$987$	−34.9945	−1.11389
$988$	−33.4590	−1.06447
$989$	8.18673	0.260323
$990$	−6.65604	−0.211543
$991$	55.7666	1.77148	0.885742	−	0.464178i	$-0.153650\pi$
$991$	55.7666	1.77148	0.885742	+	0.464178i	$0.153650\pi$
$992$	−124.846	−3.96388
$993$	−12.7644	−0.405067
$994$	−21.2095	−0.672724
$995$	14.5246	0.460460
$996$	−24.2369	−0.767977
$997$	−4.99638	−0.158237	−0.0791184	−	0.996865i	$-0.525211\pi$
$997$	−4.99638	−0.158237	−0.0791184	+	0.996865i	$0.525211\pi$
$998$	4.30830	0.136377
$999$	−3.05932	−0.0967925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.11	✓	11
3.2	odd	2		6003.2.a.m.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.11	✓	11	1.1	even	1	trivial
6003.2.a.m.1.1		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+2.72479 q^{2} -1.00000 q^{3} +5.42450 q^{4} -1.02492 q^{5} -2.72479 q^{6} +4.32726 q^{7} +9.33107 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.72479 q^{2} -1.00000 q^{3} +5.42450 q^{4} -1.02492 q^{5} -2.72479 q^{6} +4.32726 q^{7} +9.33107 q^{8} +1.00000 q^{9} -2.79269 q^{10} +2.38338 q^{11} -5.42450 q^{12} +0.754393 q^{13} +11.7909 q^{14} +1.02492 q^{15} +14.5762 q^{16} -1.03913 q^{17} +2.72479 q^{18} -8.17626 q^{19} -5.55967 q^{20} -4.32726 q^{21} +6.49422 q^{22} +1.00000 q^{23} -9.33107 q^{24} -3.94954 q^{25} +2.05557 q^{26} -1.00000 q^{27} +23.4733 q^{28} -1.00000 q^{29} +2.79269 q^{30} -5.92951 q^{31} +21.0551 q^{32} -2.38338 q^{33} -2.83143 q^{34} -4.43509 q^{35} +5.42450 q^{36} +3.05932 q^{37} -22.2786 q^{38} -0.754393 q^{39} -9.56358 q^{40} +1.01080 q^{41} -11.7909 q^{42} +8.18673 q^{43} +12.9287 q^{44} -1.02492 q^{45} +2.72479 q^{46} +8.08697 q^{47} -14.5762 q^{48} +11.7252 q^{49} -10.7617 q^{50} +1.03913 q^{51} +4.09221 q^{52} -0.478182 q^{53} -2.72479 q^{54} -2.44277 q^{55} +40.3780 q^{56} +8.17626 q^{57} -2.72479 q^{58} -8.09543 q^{59} +5.55967 q^{60} -14.8897 q^{61} -16.1567 q^{62} +4.32726 q^{63} +28.2183 q^{64} -0.773191 q^{65} -6.49422 q^{66} -0.830191 q^{67} -5.63679 q^{68} -1.00000 q^{69} -12.0847 q^{70} -1.79880 q^{71} +9.33107 q^{72} +13.2708 q^{73} +8.33601 q^{74} +3.94954 q^{75} -44.3521 q^{76} +10.3135 q^{77} -2.05557 q^{78} +2.46332 q^{79} -14.9394 q^{80} +1.00000 q^{81} +2.75423 q^{82} +4.46805 q^{83} -23.4733 q^{84} +1.06503 q^{85} +22.3072 q^{86} +1.00000 q^{87} +22.2395 q^{88} -5.57787 q^{89} -2.79269 q^{90} +3.26446 q^{91} +5.42450 q^{92} +5.92951 q^{93} +22.0353 q^{94} +8.37999 q^{95} -21.0551 q^{96} -0.684597 q^{97} +31.9488 q^{98} +2.38338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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