LMFDB - Embedded newform 2230.2.a.p.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2230,2,Mod(1,2230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2230.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2230 = 2 \cdot 5 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2230.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:	$17.8066396507$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.67955408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 30x^{2} + 24x + 4 $ x^6 - x^5 - 11x^4 + 30x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.784677$ of defining polynomial
Character	$\chi$	$=$	2230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.784677 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.784677 q^{6} +1.82926 q^{7} -1.00000 q^{8} -2.38428 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.784677 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.784677 q^{6} +1.82926 q^{7} -1.00000 q^{8} -2.38428 q^{9} +1.00000 q^{10} +4.31110 q^{11} +0.784677 q^{12} +5.09537 q^{13} -1.82926 q^{14} -0.784677 q^{15} +1.00000 q^{16} +3.84506 q^{17} +2.38428 q^{18} -5.69498 q^{19} -1.00000 q^{20} +1.43538 q^{21} -4.31110 q^{22} +8.76196 q^{23} -0.784677 q^{24} +1.00000 q^{25} -5.09537 q^{26} -4.22492 q^{27} +1.82926 q^{28} -3.60580 q^{29} +0.784677 q^{30} -5.64853 q^{31} -1.00000 q^{32} +3.38282 q^{33} -3.84506 q^{34} -1.82926 q^{35} -2.38428 q^{36} +1.94230 q^{37} +5.69498 q^{38} +3.99822 q^{39} +1.00000 q^{40} +1.97555 q^{41} -1.43538 q^{42} +5.35537 q^{43} +4.31110 q^{44} +2.38428 q^{45} -8.76196 q^{46} -9.38995 q^{47} +0.784677 q^{48} -3.65379 q^{49} -1.00000 q^{50} +3.01713 q^{51} +5.09537 q^{52} -11.7169 q^{53} +4.22492 q^{54} -4.31110 q^{55} -1.82926 q^{56} -4.46872 q^{57} +3.60580 q^{58} +13.4014 q^{59} -0.784677 q^{60} +12.1210 q^{61} +5.64853 q^{62} -4.36148 q^{63} +1.00000 q^{64} -5.09537 q^{65} -3.38282 q^{66} -7.71903 q^{67} +3.84506 q^{68} +6.87531 q^{69} +1.82926 q^{70} +8.84640 q^{71} +2.38428 q^{72} -2.29231 q^{73} -1.94230 q^{74} +0.784677 q^{75} -5.69498 q^{76} +7.88614 q^{77} -3.99822 q^{78} +13.9264 q^{79} -1.00000 q^{80} +3.83764 q^{81} -1.97555 q^{82} +13.7434 q^{83} +1.43538 q^{84} -3.84506 q^{85} -5.35537 q^{86} -2.82939 q^{87} -4.31110 q^{88} +11.3616 q^{89} -2.38428 q^{90} +9.32078 q^{91} +8.76196 q^{92} -4.43227 q^{93} +9.38995 q^{94} +5.69498 q^{95} -0.784677 q^{96} +6.22626 q^{97} +3.65379 q^{98} -10.2789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 6 q^{10} + 14 q^{11} - q^{12} + 9 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 4 q^{17} - 5 q^{18} + q^{19} - 6 q^{20} + 14 q^{21} - 14 q^{22} + 9 q^{23} + q^{24} + 6 q^{25} - 9 q^{26} - 28 q^{27} - 6 q^{28} - 9 q^{29} - q^{30} + q^{31} - 6 q^{32} - 6 q^{33} - 4 q^{34} + 6 q^{35} + 5 q^{36} - 18 q^{37} - q^{38} - 18 q^{39} + 6 q^{40} + 11 q^{41} - 14 q^{42} - 26 q^{43} + 14 q^{44} - 5 q^{45} - 9 q^{46} + 14 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} + 14 q^{51} + 9 q^{52} + 14 q^{53} + 28 q^{54} - 14 q^{55} + 6 q^{56} + 9 q^{57} + 9 q^{58} + 18 q^{59} + q^{60} + 24 q^{61} - q^{62} + 6 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} + 4 q^{68} + 20 q^{69} - 6 q^{70} + 32 q^{71} - 5 q^{72} - 12 q^{73} + 18 q^{74} - q^{75} + q^{76} + 12 q^{77} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 14 q^{81} - 11 q^{82} + 36 q^{83} + 14 q^{84} - 4 q^{85} + 26 q^{86} - 9 q^{87} - 14 q^{88} + 11 q^{89} + 5 q^{90} + 10 q^{91} + 9 q^{92} + 8 q^{93} - 14 q^{94} - q^{95} + q^{96} - q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 6 * q^10 + 14 * q^11 - q^12 + 9 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 4 * q^17 - 5 * q^18 + q^19 - 6 * q^20 + 14 * q^21 - 14 * q^22 + 9 * q^23 + q^24 + 6 * q^25 - 9 * q^26 - 28 * q^27 - 6 * q^28 - 9 * q^29 - q^30 + q^31 - 6 * q^32 - 6 * q^33 - 4 * q^34 + 6 * q^35 + 5 * q^36 - 18 * q^37 - q^38 - 18 * q^39 + 6 * q^40 + 11 * q^41 - 14 * q^42 - 26 * q^43 + 14 * q^44 - 5 * q^45 - 9 * q^46 + 14 * q^47 - q^48 + 6 * q^49 - 6 * q^50 + 14 * q^51 + 9 * q^52 + 14 * q^53 + 28 * q^54 - 14 * q^55 + 6 * q^56 + 9 * q^57 + 9 * q^58 + 18 * q^59 + q^60 + 24 * q^61 - q^62 + 6 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 + 4 * q^68 + 20 * q^69 - 6 * q^70 + 32 * q^71 - 5 * q^72 - 12 * q^73 + 18 * q^74 - q^75 + q^76 + 12 * q^77 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 14 * q^81 - 11 * q^82 + 36 * q^83 + 14 * q^84 - 4 * q^85 + 26 * q^86 - 9 * q^87 - 14 * q^88 + 11 * q^89 + 5 * q^90 + 10 * q^91 + 9 * q^92 + 8 * q^93 - 14 * q^94 - q^95 + q^96 - q^97 - 6 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.784677	0.453034	0.226517	−	0.974007i	$-0.427266\pi$
$3$	0.784677	0.453034	0.226517	+	0.974007i	$0.427266\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.784677	−0.320343
$7$	1.82926	0.691397	0.345698	−	0.938346i	$-0.387642\pi$
$7$	1.82926	0.691397	0.345698	+	0.938346i	$0.387642\pi$
$8$	−1.00000	−0.353553
$9$	−2.38428	−0.794761
$10$	1.00000	0.316228
$11$	4.31110	1.29984	0.649922	−	0.760001i	$-0.274801\pi$
$11$	4.31110	1.29984	0.649922	+	0.760001i	$0.274801\pi$
$12$	0.784677	0.226517
$13$	5.09537	1.41320	0.706601	−	0.707612i	$-0.250228\pi$
$13$	5.09537	1.41320	0.706601	+	0.707612i	$0.250228\pi$
$14$	−1.82926	−0.488891
$15$	−0.784677	−0.202603
$16$	1.00000	0.250000
$17$	3.84506	0.932565	0.466282	−	0.884636i	$-0.345593\pi$
$17$	3.84506	0.932565	0.466282	+	0.884636i	$0.345593\pi$
$18$	2.38428	0.561981
$19$	−5.69498	−1.30652	−0.653259	−	0.757135i	$-0.726599\pi$
$19$	−5.69498	−1.30652	−0.653259	+	0.757135i	$0.726599\pi$
$20$	−1.00000	−0.223607
$21$	1.43538	0.313226
$22$	−4.31110	−0.919129
$23$	8.76196	1.82700	0.913498	−	0.406844i	$-0.133371\pi$
$23$	8.76196	1.82700	0.913498	+	0.406844i	$0.133371\pi$
$24$	−0.784677	−0.160172
$25$	1.00000	0.200000
$26$	−5.09537	−0.999285
$27$	−4.22492	−0.813087
$28$	1.82926	0.345698
$29$	−3.60580	−0.669581	−0.334790	−	0.942293i	$-0.608666\pi$
$29$	−3.60580	−0.669581	−0.334790	+	0.942293i	$0.608666\pi$
$30$	0.784677	0.143262
$31$	−5.64853	−1.01451	−0.507253	−	0.861797i	$-0.669339\pi$
$31$	−5.64853	−1.01451	−0.507253	+	0.861797i	$0.669339\pi$
$32$	−1.00000	−0.176777
$33$	3.38282	0.588873
$34$	−3.84506	−0.659423
$35$	−1.82926	−0.309202
$36$	−2.38428	−0.397380
$37$	1.94230	0.319312	0.159656	−	0.987173i	$-0.448961\pi$
$37$	1.94230	0.319312	0.159656	+	0.987173i	$0.448961\pi$
$38$	5.69498	0.923847
$39$	3.99822	0.640228
$40$	1.00000	0.158114
$41$	1.97555	0.308529	0.154264	−	0.988030i	$-0.450699\pi$
$41$	1.97555	0.308529	0.154264	+	0.988030i	$0.450699\pi$
$42$	−1.43538	−0.221484
$43$	5.35537	0.816686	0.408343	−	0.912829i	$-0.366107\pi$
$43$	5.35537	0.816686	0.408343	+	0.912829i	$0.366107\pi$
$44$	4.31110	0.649922
$45$	2.38428	0.355428
$46$	−8.76196	−1.29188
$47$	−9.38995	−1.36967	−0.684833	−	0.728700i	$-0.740125\pi$
$47$	−9.38995	−1.36967	−0.684833	+	0.728700i	$0.740125\pi$
$48$	0.784677	0.113258
$49$	−3.65379	−0.521970
$50$	−1.00000	−0.141421
$51$	3.01713	0.422483
$52$	5.09537	0.706601
$53$	−11.7169	−1.60943	−0.804717	−	0.593659i	$-0.797683\pi$
$53$	−11.7169	−1.60943	−0.804717	+	0.593659i	$0.797683\pi$
$54$	4.22492	0.574939
$55$	−4.31110	−0.581308
$56$	−1.82926	−0.244446
$57$	−4.46872	−0.591896
$58$	3.60580	0.473465
$59$	13.4014	1.74472	0.872358	−	0.488868i	$-0.162590\pi$
$59$	13.4014	1.74472	0.872358	+	0.488868i	$0.162590\pi$
$60$	−0.784677	−0.101301
$61$	12.1210	1.55193	0.775966	−	0.630775i	$-0.217263\pi$
$61$	12.1210	1.55193	0.775966	+	0.630775i	$0.217263\pi$
$62$	5.64853	0.717364
$63$	−4.36148	−0.549495
$64$	1.00000	0.125000
$65$	−5.09537	−0.632003
$66$	−3.38282	−0.416396
$67$	−7.71903	−0.943029	−0.471515	−	0.881858i	$-0.656293\pi$
$67$	−7.71903	−0.943029	−0.471515	+	0.881858i	$0.656293\pi$
$68$	3.84506	0.466282
$69$	6.87531	0.827690
$70$	1.82926	0.218639
$71$	8.84640	1.04987	0.524937	−	0.851141i	$-0.324089\pi$
$71$	8.84640	1.04987	0.524937	+	0.851141i	$0.324089\pi$
$72$	2.38428	0.280990
$73$	−2.29231	−0.268295	−0.134147	−	0.990961i	$-0.542830\pi$
$73$	−2.29231	−0.268295	−0.134147	+	0.990961i	$0.542830\pi$
$74$	−1.94230	−0.225788
$75$	0.784677	0.0906067
$76$	−5.69498	−0.653259
$77$	7.88614	0.898709
$78$	−3.99822	−0.452710
$79$	13.9264	1.56684	0.783420	−	0.621493i	$-0.213474\pi$
$79$	13.9264	1.56684	0.783420	+	0.621493i	$0.213474\pi$
$80$	−1.00000	−0.111803
$81$	3.83764	0.426405
$82$	−1.97555	−0.218163
$83$	13.7434	1.50853	0.754265	−	0.656570i	$-0.227993\pi$
$83$	13.7434	1.50853	0.754265	+	0.656570i	$0.227993\pi$
$84$	1.43538	0.156613
$85$	−3.84506	−0.417056
$86$	−5.35537	−0.577484
$87$	−2.82939	−0.303343
$88$	−4.31110	−0.459564
$89$	11.3616	1.20432	0.602162	−	0.798374i	$-0.294306\pi$
$89$	11.3616	1.20432	0.602162	+	0.798374i	$0.294306\pi$
$90$	−2.38428	−0.251325
$91$	9.32078	0.977084
$92$	8.76196	0.913498
$93$	−4.43227	−0.459605
$94$	9.38995	0.968500
$95$	5.69498	0.584292
$96$	−0.784677	−0.0800858
$97$	6.22626	0.632181	0.316090	−	0.948729i	$-0.397630\pi$
$97$	6.22626	0.632181	0.316090	+	0.948729i	$0.397630\pi$
$98$	3.65379	0.369089
$99$	−10.2789	−1.03307
$100$	1.00000	0.100000
$101$	−1.87705	−0.186774	−0.0933868	−	0.995630i	$-0.529769\pi$
$101$	−1.87705	−0.186774	−0.0933868	+	0.995630i	$0.529769\pi$
$102$	−3.01713	−0.298741
$103$	−10.5699	−1.04148	−0.520741	−	0.853715i	$-0.674344\pi$
$103$	−10.5699	−1.04148	−0.520741	+	0.853715i	$0.674344\pi$
$104$	−5.09537	−0.499642
$105$	−1.43538	−0.140079
$106$	11.7169	1.13804
$107$	1.11375	0.107670	0.0538352	−	0.998550i	$-0.482855\pi$
$107$	1.11375	0.107670	0.0538352	+	0.998550i	$0.482855\pi$
$108$	−4.22492	−0.406543
$109$	3.64865	0.349477	0.174739	−	0.984615i	$-0.444092\pi$
$109$	3.64865	0.349477	0.174739	+	0.984615i	$0.444092\pi$
$110$	4.31110	0.411047
$111$	1.52408	0.144659
$112$	1.82926	0.172849
$113$	−3.35837	−0.315929	−0.157964	−	0.987445i	$-0.550493\pi$
$113$	−3.35837	−0.315929	−0.157964	+	0.987445i	$0.550493\pi$
$114$	4.46872	0.418534
$115$	−8.76196	−0.817057
$116$	−3.60580	−0.334790
$117$	−12.1488	−1.12316
$118$	−13.4014	−1.23370
$119$	7.03364	0.644773
$120$	0.784677	0.0716309
$121$	7.58555	0.689596
$122$	−12.1210	−1.09738
$123$	1.55017	0.139774
$124$	−5.64853	−0.507253
$125$	−1.00000	−0.0894427
$126$	4.36148	0.388552
$127$	11.0984	0.984828	0.492414	−	0.870361i	$-0.336115\pi$
$127$	11.0984	0.984828	0.492414	+	0.870361i	$0.336115\pi$
$128$	−1.00000	−0.0883883
$129$	4.20224	0.369986
$130$	5.09537	0.446894
$131$	19.3359	1.68939	0.844694	−	0.535250i	$-0.179782\pi$
$131$	19.3359	1.68939	0.844694	+	0.535250i	$0.179782\pi$
$132$	3.38282	0.294437
$133$	−10.4176	−0.903322
$134$	7.71903	0.666822
$135$	4.22492	0.363624
$136$	−3.84506	−0.329711
$137$	−9.05027	−0.773217	−0.386608	−	0.922244i	$-0.626353\pi$
$137$	−9.05027	−0.773217	−0.386608	+	0.922244i	$0.626353\pi$
$138$	−6.87531	−0.585266
$139$	−22.7314	−1.92805	−0.964026	−	0.265810i	$-0.914361\pi$
$139$	−22.7314	−1.92805	−0.964026	+	0.265810i	$0.914361\pi$
$140$	−1.82926	−0.154601
$141$	−7.36808	−0.620505
$142$	−8.84640	−0.742373
$143$	21.9666	1.83694
$144$	−2.38428	−0.198690
$145$	3.60580	0.299446
$146$	2.29231	0.189713
$147$	−2.86705	−0.236470
$148$	1.94230	0.159656
$149$	7.95730	0.651887	0.325944	−	0.945389i	$-0.394318\pi$
$149$	7.95730	0.651887	0.325944	+	0.945389i	$0.394318\pi$
$150$	−0.784677	−0.0640686
$151$	−12.4465	−1.01288	−0.506442	−	0.862274i	$-0.669039\pi$
$151$	−12.4465	−1.01288	−0.506442	+	0.862274i	$0.669039\pi$
$152$	5.69498	0.461924
$153$	−9.16771	−0.741166
$154$	−7.88614	−0.635483
$155$	5.64853	0.453701
$156$	3.99822	0.320114
$157$	−12.7720	−1.01931	−0.509657	−	0.860378i	$-0.670228\pi$
$157$	−12.7720	−1.01931	−0.509657	+	0.860378i	$0.670228\pi$
$158$	−13.9264	−1.10792
$159$	−9.19395	−0.729127
$160$	1.00000	0.0790569
$161$	16.0279	1.26318
$162$	−3.83764	−0.301514
$163$	15.4904	1.21330	0.606651	−	0.794968i	$-0.292513\pi$
$163$	15.4904	1.21330	0.606651	+	0.794968i	$0.292513\pi$
$164$	1.97555	0.154264
$165$	−3.38282	−0.263352
$166$	−13.7434	−1.06669
$167$	19.2832	1.49218	0.746090	−	0.665845i	$-0.231929\pi$
$167$	19.2832	1.49218	0.746090	+	0.665845i	$0.231929\pi$
$168$	−1.43538	−0.110742
$169$	12.9628	0.997140
$170$	3.84506	0.294903
$171$	13.5784	1.03837
$172$	5.35537	0.408343
$173$	5.82172	0.442617	0.221308	−	0.975204i	$-0.428967\pi$
$173$	5.82172	0.442617	0.221308	+	0.975204i	$0.428967\pi$
$174$	2.82939	0.214496
$175$	1.82926	0.138279
$176$	4.31110	0.324961
$177$	10.5158	0.790415
$178$	−11.3616	−0.851585
$179$	−3.84100	−0.287090	−0.143545	−	0.989644i	$-0.545850\pi$
$179$	−3.84100	−0.287090	−0.143545	+	0.989644i	$0.545850\pi$
$180$	2.38428	0.177714
$181$	−0.332970	−0.0247495	−0.0123747	−	0.999923i	$-0.503939\pi$
$181$	−0.332970	−0.0247495	−0.0123747	+	0.999923i	$0.503939\pi$
$182$	−9.32078	−0.690902
$183$	9.51105	0.703077
$184$	−8.76196	−0.645941
$185$	−1.94230	−0.142801
$186$	4.43227	0.324990
$187$	16.5764	1.21219
$188$	−9.38995	−0.684833
$189$	−7.72850	−0.562166
$190$	−5.69498	−0.413157
$191$	6.26411	0.453255	0.226628	−	0.973981i	$-0.427230\pi$
$191$	6.26411	0.453255	0.226628	+	0.973981i	$0.427230\pi$
$192$	0.784677	0.0566292
$193$	−1.42102	−0.102287	−0.0511436	−	0.998691i	$-0.516287\pi$
$193$	−1.42102	−0.102287	−0.0511436	+	0.998691i	$0.516287\pi$
$194$	−6.22626	−0.447019
$195$	−3.99822	−0.286319
$196$	−3.65379	−0.260985
$197$	11.0792	0.789359	0.394680	−	0.918819i	$-0.370856\pi$
$197$	11.0792	0.789359	0.394680	+	0.918819i	$0.370856\pi$
$198$	10.2789	0.730487
$199$	−1.27260	−0.0902119	−0.0451059	−	0.998982i	$-0.514363\pi$
$199$	−1.27260	−0.0902119	−0.0451059	+	0.998982i	$0.514363\pi$
$200$	−1.00000	−0.0707107
$201$	−6.05695	−0.427224
$202$	1.87705	0.132069
$203$	−6.59597	−0.462946
$204$	3.01713	0.211242
$205$	−1.97555	−0.137978
$206$	10.5699	0.736439
$207$	−20.8910	−1.45202
$208$	5.09537	0.353301
$209$	−24.5516	−1.69827
$210$	1.43538	0.0990508
$211$	−9.76156	−0.672014	−0.336007	−	0.941860i	$-0.609077\pi$
$211$	−9.76156	−0.672014	−0.336007	+	0.941860i	$0.609077\pi$
$212$	−11.7169	−0.804717
$213$	6.94157	0.475628
$214$	−1.11375	−0.0761345
$215$	−5.35537	−0.365233
$216$	4.22492	0.287470
$217$	−10.3326	−0.701426
$218$	−3.64865	−0.247118
$219$	−1.79872	−0.121547
$220$	−4.31110	−0.290654
$221$	19.5920	1.31790
$222$	−1.52408	−0.102289
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	−1.82926	−0.122223
$225$	−2.38428	−0.158952
$226$	3.35837	0.223395
$227$	2.03459	0.135040	0.0675201	−	0.997718i	$-0.478491\pi$
$227$	2.03459	0.135040	0.0675201	+	0.997718i	$0.478491\pi$
$228$	−4.46872	−0.295948
$229$	−22.4731	−1.48507	−0.742533	−	0.669810i	$-0.766376\pi$
$229$	−22.4731	−1.48507	−0.742533	+	0.669810i	$0.766376\pi$
$230$	8.76196	0.577747
$231$	6.18807	0.407145
$232$	3.60580	0.236733
$233$	−10.1457	−0.664667	−0.332333	−	0.943162i	$-0.607836\pi$
$233$	−10.1457	−0.664667	−0.332333	+	0.943162i	$0.607836\pi$
$234$	12.1488	0.794192
$235$	9.38995	0.612533
$236$	13.4014	0.872358
$237$	10.9277	0.709831
$238$	−7.03364	−0.455923
$239$	1.40565	0.0909237	0.0454619	−	0.998966i	$-0.485524\pi$
$239$	1.40565	0.0909237	0.0454619	+	0.998966i	$0.485524\pi$
$240$	−0.784677	−0.0506507
$241$	−19.8677	−1.27979	−0.639895	−	0.768463i	$-0.721022\pi$
$241$	−19.8677	−1.27979	−0.639895	+	0.768463i	$0.721022\pi$
$242$	−7.58555	−0.487618
$243$	15.6861	1.00626
$244$	12.1210	0.775966
$245$	3.65379	0.233432
$246$	−1.55017	−0.0988351
$247$	−29.0180	−1.84637
$248$	5.64853	0.358682
$249$	10.7841	0.683415
$250$	1.00000	0.0632456
$251$	29.9649	1.89137	0.945683	−	0.325090i	$-0.105395\pi$
$251$	29.9649	1.89137	0.945683	+	0.325090i	$0.105395\pi$
$252$	−4.36148	−0.274747
$253$	37.7737	2.37481
$254$	−11.0984	−0.696378
$255$	−3.01713	−0.188940
$256$	1.00000	0.0625000
$257$	2.84640	0.177553	0.0887767	−	0.996052i	$-0.471704\pi$
$257$	2.84640	0.177553	0.0887767	+	0.996052i	$0.471704\pi$
$258$	−4.20224	−0.261620
$259$	3.55298	0.220771
$260$	−5.09537	−0.316002
$261$	8.59725	0.532156
$262$	−19.3359	−1.19458
$263$	−13.8873	−0.856331	−0.428165	−	0.903700i	$-0.640840\pi$
$263$	−13.8873	−0.856331	−0.428165	+	0.903700i	$0.640840\pi$
$264$	−3.38282	−0.208198
$265$	11.7169	0.719760
$266$	10.4176	0.638745
$267$	8.91516	0.545599
$268$	−7.71903	−0.471515
$269$	15.3869	0.938154	0.469077	−	0.883157i	$-0.344587\pi$
$269$	15.3869	0.938154	0.469077	+	0.883157i	$0.344587\pi$
$270$	−4.22492	−0.257121
$271$	−9.14494	−0.555515	−0.277758	−	0.960651i	$-0.589591\pi$
$271$	−9.14494	−0.555515	−0.277758	+	0.960651i	$0.589591\pi$
$272$	3.84506	0.233141
$273$	7.31381	0.442652
$274$	9.05027	0.546747
$275$	4.31110	0.259969
$276$	6.87531	0.413845
$277$	−5.38241	−0.323397	−0.161699	−	0.986840i	$-0.551697\pi$
$277$	−5.38241	−0.323397	−0.161699	+	0.986840i	$0.551697\pi$
$278$	22.7314	1.36334
$279$	13.4677	0.806289
$280$	1.82926	0.109319
$281$	26.2120	1.56368	0.781838	−	0.623482i	$-0.214283\pi$
$281$	26.2120	1.56368	0.781838	+	0.623482i	$0.214283\pi$
$282$	7.36808	0.438763
$283$	−14.1074	−0.838600	−0.419300	−	0.907848i	$-0.637724\pi$
$283$	−14.1074	−0.838600	−0.419300	+	0.907848i	$0.637724\pi$
$284$	8.84640	0.524937
$285$	4.46872	0.264704
$286$	−21.9666	−1.29891
$287$	3.61380	0.213316
$288$	2.38428	0.140495
$289$	−2.21549	−0.130323
$290$	−3.60580	−0.211740
$291$	4.88561	0.286399
$292$	−2.29231	−0.134147
$293$	8.66157	0.506014	0.253007	−	0.967464i	$-0.418580\pi$
$293$	8.66157	0.506014	0.253007	+	0.967464i	$0.418580\pi$
$294$	2.86705	0.167210
$295$	−13.4014	−0.780261
$296$	−1.94230	−0.112894
$297$	−18.2141	−1.05689
$298$	−7.95730	−0.460954
$299$	44.6455	2.58191
$300$	0.784677	0.0453034
$301$	9.79639	0.564654
$302$	12.4465	0.716217
$303$	−1.47288	−0.0846147
$304$	−5.69498	−0.326629
$305$	−12.1210	−0.694045
$306$	9.16771	0.524083
$307$	−4.34018	−0.247707	−0.123854	−	0.992300i	$-0.539525\pi$
$307$	−4.34018	−0.247707	−0.123854	+	0.992300i	$0.539525\pi$
$308$	7.88614	0.449354
$309$	−8.29395	−0.471826
$310$	−5.64853	−0.320815
$311$	−15.0527	−0.853560	−0.426780	−	0.904355i	$-0.640352\pi$
$311$	−15.0527	−0.853560	−0.426780	+	0.904355i	$0.640352\pi$
$312$	−3.99822	−0.226355
$313$	30.6330	1.73148	0.865739	−	0.500495i	$-0.166849\pi$
$313$	30.6330	1.73148	0.865739	+	0.500495i	$0.166849\pi$
$314$	12.7720	0.720764
$315$	4.36148	0.245742
$316$	13.9264	0.783420
$317$	−18.5672	−1.04284	−0.521418	−	0.853301i	$-0.674597\pi$
$317$	−18.5672	−1.04284	−0.521418	+	0.853301i	$0.674597\pi$
$318$	9.19395	0.515571
$319$	−15.5450	−0.870351
$320$	−1.00000	−0.0559017
$321$	0.873935	0.0487783
$322$	−16.0279	−0.893203
$323$	−21.8975	−1.21841
$324$	3.83764	0.213202
$325$	5.09537	0.282640
$326$	−15.4904	−0.857934
$327$	2.86301	0.158325
$328$	−1.97555	−0.109081
$329$	−17.1767	−0.946983
$330$	3.38282	0.186218
$331$	15.9972	0.879283	0.439642	−	0.898173i	$-0.355105\pi$
$331$	15.9972	0.879283	0.439642	+	0.898173i	$0.355105\pi$
$332$	13.7434	0.754265
$333$	−4.63099	−0.253777
$334$	−19.2832	−1.05513
$335$	7.71903	0.421736
$336$	1.43538	0.0783065
$337$	−1.95488	−0.106489	−0.0532447	−	0.998581i	$-0.516956\pi$
$337$	−1.95488	−0.106489	−0.0532447	+	0.998581i	$0.516956\pi$
$338$	−12.9628	−0.705085
$339$	−2.63523	−0.143126
$340$	−3.84506	−0.208528
$341$	−24.3513	−1.31870
$342$	−13.5784	−0.734237
$343$	−19.4886	−1.05229
$344$	−5.35537	−0.288742
$345$	−6.87531	−0.370154
$346$	−5.82172	−0.312977
$347$	−34.7332	−1.86458	−0.932288	−	0.361716i	$-0.882191\pi$
$347$	−34.7332	−1.86458	−0.932288	+	0.361716i	$0.882191\pi$
$348$	−2.82939	−0.151671
$349$	29.4373	1.57575	0.787873	−	0.615838i	$-0.211183\pi$
$349$	29.4373	1.57575	0.787873	+	0.615838i	$0.211183\pi$
$350$	−1.82926	−0.0977783
$351$	−21.5276	−1.14906
$352$	−4.31110	−0.229782
$353$	5.96153	0.317300	0.158650	−	0.987335i	$-0.449286\pi$
$353$	5.96153	0.317300	0.158650	+	0.987335i	$0.449286\pi$
$354$	−10.5158	−0.558908
$355$	−8.84640	−0.469518
$356$	11.3616	0.602162
$357$	5.51914	0.292104
$358$	3.84100	0.203003
$359$	28.1780	1.48718	0.743589	−	0.668637i	$-0.233122\pi$
$359$	28.1780	1.48718	0.743589	+	0.668637i	$0.233122\pi$
$360$	−2.38428	−0.125663
$361$	13.4328	0.706988
$362$	0.332970	0.0175005
$363$	5.95221	0.312410
$364$	9.32078	0.488542
$365$	2.29231	0.119985
$366$	−9.51105	−0.497151
$367$	6.84567	0.357341	0.178671	−	0.983909i	$-0.442820\pi$
$367$	6.84567	0.357341	0.178671	+	0.983909i	$0.442820\pi$
$368$	8.76196	0.456749
$369$	−4.71026	−0.245206
$370$	1.94230	0.100975
$371$	−21.4332	−1.11276
$372$	−4.43227	−0.229803
$373$	16.0307	0.830039	0.415019	−	0.909813i	$-0.363775\pi$
$373$	16.0307	0.830039	0.415019	+	0.909813i	$0.363775\pi$
$374$	−16.5764	−0.857147
$375$	−0.784677	−0.0405206
$376$	9.38995	0.484250
$377$	−18.3729	−0.946253
$378$	7.72850	0.397511
$379$	−19.5399	−1.00370	−0.501850	−	0.864955i	$-0.667347\pi$
$379$	−19.5399	−1.00370	−0.501850	+	0.864955i	$0.667347\pi$
$380$	5.69498	0.292146
$381$	8.70870	0.446160
$382$	−6.26411	−0.320500
$383$	−0.990061	−0.0505897	−0.0252949	−	0.999680i	$-0.508052\pi$
$383$	−0.990061	−0.0505897	−0.0252949	+	0.999680i	$0.508052\pi$
$384$	−0.784677	−0.0400429
$385$	−7.88614	−0.401915
$386$	1.42102	0.0723279
$387$	−12.7687	−0.649070
$388$	6.22626	0.316090
$389$	−34.7242	−1.76059	−0.880295	−	0.474427i	$-0.842655\pi$
$389$	−34.7242	−1.76059	−0.880295	+	0.474427i	$0.842655\pi$
$390$	3.99822	0.202458
$391$	33.6903	1.70379
$392$	3.65379	0.184544
$393$	15.1725	0.765350
$394$	−11.0792	−0.558161
$395$	−13.9264	−0.700712
$396$	−10.2789	−0.516533
$397$	5.20747	0.261356	0.130678	−	0.991425i	$-0.458285\pi$
$397$	5.20747	0.261356	0.130678	+	0.991425i	$0.458285\pi$
$398$	1.27260	0.0637894
$399$	−8.17447	−0.409235
$400$	1.00000	0.0500000
$401$	10.3915	0.518926	0.259463	−	0.965753i	$-0.416454\pi$
$401$	10.3915	0.518926	0.259463	+	0.965753i	$0.416454\pi$
$402$	6.05695	0.302093
$403$	−28.7814	−1.43370
$404$	−1.87705	−0.0933868
$405$	−3.83764	−0.190694
$406$	6.59597	0.327352
$407$	8.37344	0.415056
$408$	−3.01713	−0.149370
$409$	11.6534	0.576222	0.288111	−	0.957597i	$-0.406973\pi$
$409$	11.6534	0.576222	0.288111	+	0.957597i	$0.406973\pi$
$410$	1.97555	0.0975653
$411$	−7.10154	−0.350293
$412$	−10.5699	−0.520741
$413$	24.5147	1.20629
$414$	20.8910	1.02674
$415$	−13.7434	−0.674635
$416$	−5.09537	−0.249821
$417$	−17.8368	−0.873472
$418$	24.5516	1.20086
$419$	−8.00039	−0.390845	−0.195422	−	0.980719i	$-0.562608\pi$
$419$	−8.00039	−0.390845	−0.195422	+	0.980719i	$0.562608\pi$
$420$	−1.43538	−0.0700395
$421$	−33.5414	−1.63471	−0.817354	−	0.576136i	$-0.804560\pi$
$421$	−33.5414	−1.63471	−0.817354	+	0.576136i	$0.804560\pi$
$422$	9.76156	0.475185
$423$	22.3883	1.08856
$424$	11.7169	0.569021
$425$	3.84506	0.186513
$426$	−6.94157	−0.336320
$427$	22.1725	1.07300
$428$	1.11375	0.0538352
$429$	17.2367	0.832197
$430$	5.35537	0.258259
$431$	−22.7615	−1.09639	−0.548193	−	0.836352i	$-0.684684\pi$
$431$	−22.7615	−1.09639	−0.548193	+	0.836352i	$0.684684\pi$
$432$	−4.22492	−0.203272
$433$	−30.9591	−1.48780	−0.743899	−	0.668292i	$-0.767026\pi$
$433$	−30.9591	−1.48780	−0.743899	+	0.668292i	$0.767026\pi$
$434$	10.3326	0.495983
$435$	2.82939	0.135659
$436$	3.64865	0.174739
$437$	−49.8992	−2.38700
$438$	1.79872	0.0859464
$439$	12.0336	0.574331	0.287165	−	0.957881i	$-0.407287\pi$
$439$	12.0336	0.574331	0.287165	+	0.957881i	$0.407287\pi$
$440$	4.31110	0.205523
$441$	8.71167	0.414841
$442$	−19.5920	−0.931898
$443$	−26.1897	−1.24431	−0.622154	−	0.782895i	$-0.713742\pi$
$443$	−26.1897	−1.24431	−0.622154	+	0.782895i	$0.713742\pi$
$444$	1.52408	0.0723296
$445$	−11.3616	−0.538590
$446$	−1.00000	−0.0473514
$447$	6.24391	0.295327
$448$	1.82926	0.0864246
$449$	13.2683	0.626169	0.313084	−	0.949725i	$-0.398638\pi$
$449$	13.2683	0.626169	0.313084	+	0.949725i	$0.398638\pi$
$450$	2.38428	0.112396
$451$	8.51678	0.401039
$452$	−3.35837	−0.157964
$453$	−9.76650	−0.458870
$454$	−2.03459	−0.0954878
$455$	−9.32078	−0.436965
$456$	4.46872	0.209267
$457$	4.45288	0.208297	0.104148	−	0.994562i	$-0.466788\pi$
$457$	4.45288	0.208297	0.104148	+	0.994562i	$0.466788\pi$
$458$	22.4731	1.05010
$459$	−16.2451	−0.758256
$460$	−8.76196	−0.408529
$461$	8.24591	0.384050	0.192025	−	0.981390i	$-0.438494\pi$
$461$	8.24591	0.384050	0.192025	+	0.981390i	$0.438494\pi$
$462$	−6.18807	−0.287895
$463$	−8.17780	−0.380054	−0.190027	−	0.981779i	$-0.560858\pi$
$463$	−8.17780	−0.380054	−0.190027	+	0.981779i	$0.560858\pi$
$464$	−3.60580	−0.167395
$465$	4.43227	0.205542
$466$	10.1457	0.469991
$467$	−34.2177	−1.58341	−0.791704	−	0.610905i	$-0.790806\pi$
$467$	−34.2177	−1.58341	−0.791704	+	0.610905i	$0.790806\pi$
$468$	−12.1488	−0.561579
$469$	−14.1201	−0.652008
$470$	−9.38995	−0.433126
$471$	−10.0219	−0.461783
$472$	−13.4014	−0.616850
$473$	23.0875	1.06157
$474$	−10.9277	−0.501926
$475$	−5.69498	−0.261303
$476$	7.03364	0.322386
$477$	27.9363	1.27911
$478$	−1.40565	−0.0642928
$479$	−12.4646	−0.569520	−0.284760	−	0.958599i	$-0.591914\pi$
$479$	−12.4646	−0.569520	−0.284760	+	0.958599i	$0.591914\pi$
$480$	0.784677	0.0358155
$481$	9.89674	0.451253
$482$	19.8677	0.904948
$483$	12.5768	0.572263
$484$	7.58555	0.344798
$485$	−6.22626	−0.282720
$486$	−15.6861	−0.711535
$487$	−26.4192	−1.19717	−0.598583	−	0.801061i	$-0.704269\pi$
$487$	−26.4192	−1.19717	−0.598583	+	0.801061i	$0.704269\pi$
$488$	−12.1210	−0.548691
$489$	12.1550	0.549667
$490$	−3.65379	−0.165061
$491$	−23.9779	−1.08211	−0.541053	−	0.840988i	$-0.681974\pi$
$491$	−23.9779	−1.08211	−0.541053	+	0.840988i	$0.681974\pi$
$492$	1.55017	0.0698869
$493$	−13.8645	−0.624428
$494$	29.0180	1.30558
$495$	10.2789	0.462001
$496$	−5.64853	−0.253626
$497$	16.1824	0.725880
$498$	−10.7841	−0.483247
$499$	−29.2840	−1.31093	−0.655466	−	0.755224i	$-0.727528\pi$
$499$	−29.2840	−1.31093	−0.655466	+	0.755224i	$0.727528\pi$
$500$	−1.00000	−0.0447214
$501$	15.1311	0.676007
$502$	−29.9649	−1.33740
$503$	−15.7335	−0.701524	−0.350762	−	0.936465i	$-0.614077\pi$
$503$	−15.7335	−0.701524	−0.350762	+	0.936465i	$0.614077\pi$
$504$	4.36148	0.194276
$505$	1.87705	0.0835277
$506$	−37.7737	−1.67924
$507$	10.1716	0.451738
$508$	11.0984	0.492414
$509$	36.3124	1.60952	0.804760	−	0.593600i	$-0.202294\pi$
$509$	36.3124	1.60952	0.804760	+	0.593600i	$0.202294\pi$
$510$	3.01713	0.133601
$511$	−4.19324	−0.185498
$512$	−1.00000	−0.0441942
$513$	24.0608	1.06231
$514$	−2.84640	−0.125549
$515$	10.5699	0.465765
$516$	4.20224	0.184993
$517$	−40.4810	−1.78035
$518$	−3.55298	−0.156109
$519$	4.56817	0.200520
$520$	5.09537	0.223447
$521$	−11.0837	−0.485586	−0.242793	−	0.970078i	$-0.578064\pi$
$521$	−11.0837	−0.485586	−0.242793	+	0.970078i	$0.578064\pi$
$522$	−8.59725	−0.376291
$523$	16.8965	0.738833	0.369417	−	0.929264i	$-0.379558\pi$
$523$	16.8965	0.738833	0.369417	+	0.929264i	$0.379558\pi$
$524$	19.3359	0.844694
$525$	1.43538	0.0626452
$526$	13.8873	0.605517
$527$	−21.7189	−0.946092
$528$	3.38282	0.147218
$529$	53.7720	2.33791
$530$	−11.7169	−0.508947
$531$	−31.9528	−1.38663
$532$	−10.4176	−0.451661
$533$	10.0662	0.436013
$534$	−8.91516	−0.385797
$535$	−1.11375	−0.0481517
$536$	7.71903	0.333411
$537$	−3.01395	−0.130061
$538$	−15.3869	−0.663375
$539$	−15.7519	−0.678480
$540$	4.22492	0.181812
$541$	1.37716	0.0592089	0.0296045	−	0.999562i	$-0.490575\pi$
$541$	1.37716	0.0592089	0.0296045	+	0.999562i	$0.490575\pi$
$542$	9.14494	0.392809
$543$	−0.261274	−0.0112123
$544$	−3.84506	−0.164856
$545$	−3.64865	−0.156291
$546$	−7.31381	−0.313002
$547$	9.22542	0.394450	0.197225	−	0.980358i	$-0.436807\pi$
$547$	9.22542	0.394450	0.197225	+	0.980358i	$0.436807\pi$
$548$	−9.05027	−0.386608
$549$	−28.8998	−1.23341
$550$	−4.31110	−0.183826
$551$	20.5350	0.874819
$552$	−6.87531	−0.292633
$553$	25.4750	1.08331
$554$	5.38241	0.228677
$555$	−1.52408	−0.0646935
$556$	−22.7314	−0.964026
$557$	−0.373469	−0.0158244	−0.00791219	−	0.999969i	$-0.502519\pi$
$557$	−0.373469	−0.0158244	−0.00791219	+	0.999969i	$0.502519\pi$
$558$	−13.4677	−0.570132
$559$	27.2876	1.15414
$560$	−1.82926	−0.0773005
$561$	13.0072	0.549163
$562$	−26.2120	−1.10569
$563$	26.1605	1.10254	0.551268	−	0.834329i	$-0.314144\pi$
$563$	26.1605	1.10254	0.551268	+	0.834329i	$0.314144\pi$
$564$	−7.36808	−0.310252
$565$	3.35837	0.141288
$566$	14.1074	0.592979
$567$	7.02006	0.294815
$568$	−8.84640	−0.371187
$569$	−45.6418	−1.91340	−0.956702	−	0.291071i	$-0.905988\pi$
$569$	−45.6418	−1.91340	−0.956702	+	0.291071i	$0.905988\pi$
$570$	−4.46872	−0.187174
$571$	−13.6620	−0.571737	−0.285868	−	0.958269i	$-0.592282\pi$
$571$	−13.6620	−0.571737	−0.285868	+	0.958269i	$0.592282\pi$
$572$	21.9666	0.918472
$573$	4.91531	0.205340
$574$	−3.61380	−0.150837
$575$	8.76196	0.365399
$576$	−2.38428	−0.0993451
$577$	−17.3490	−0.722248	−0.361124	−	0.932518i	$-0.617607\pi$
$577$	−17.3490	−0.722248	−0.361124	+	0.932518i	$0.617607\pi$
$578$	2.21549	0.0921521
$579$	−1.11504	−0.0463395
$580$	3.60580	0.149723
$581$	25.1403	1.04299
$582$	−4.88561	−0.202515
$583$	−50.5125	−2.09201
$584$	2.29231	0.0948565
$585$	12.1488	0.502291
$586$	−8.66157	−0.357806
$587$	4.23715	0.174886	0.0874429	−	0.996170i	$-0.472130\pi$
$587$	4.23715	0.174886	0.0874429	+	0.996170i	$0.472130\pi$
$588$	−2.86705	−0.118235
$589$	32.1682	1.32547
$590$	13.4014	0.551728
$591$	8.69358	0.357606
$592$	1.94230	0.0798280
$593$	−20.6298	−0.847165	−0.423583	−	0.905857i	$-0.639228\pi$
$593$	−20.6298	−0.847165	−0.423583	+	0.905857i	$0.639228\pi$
$594$	18.2141	0.747332
$595$	−7.03364	−0.288351
$596$	7.95730	0.325944
$597$	−0.998576	−0.0408690
$598$	−44.6455	−1.82569
$599$	−2.99561	−0.122397	−0.0611987	−	0.998126i	$-0.519492\pi$
$599$	−2.99561	−0.122397	−0.0611987	+	0.998126i	$0.519492\pi$
$600$	−0.784677	−0.0320343
$601$	−7.71797	−0.314823	−0.157411	−	0.987533i	$-0.550315\pi$
$601$	−7.71797	−0.314823	−0.157411	+	0.987533i	$0.550315\pi$
$602$	−9.79639	−0.399271
$603$	18.4043	0.749483
$604$	−12.4465	−0.506442
$605$	−7.58555	−0.308397
$606$	1.47288	0.0598317
$607$	8.70777	0.353437	0.176719	−	0.984261i	$-0.443452\pi$
$607$	8.70777	0.353437	0.176719	+	0.984261i	$0.443452\pi$
$608$	5.69498	0.230962
$609$	−5.17571	−0.209730
$610$	12.1210	0.490764
$611$	−47.8453	−1.93561
$612$	−9.16771	−0.370583
$613$	10.9065	0.440510	0.220255	−	0.975442i	$-0.429311\pi$
$613$	10.9065	0.440510	0.220255	+	0.975442i	$0.429311\pi$
$614$	4.34018	0.175155
$615$	−1.55017	−0.0625088
$616$	−7.88614	−0.317741
$617$	−10.6911	−0.430408	−0.215204	−	0.976569i	$-0.569042\pi$
$617$	−10.6911	−0.430408	−0.215204	+	0.976569i	$0.569042\pi$
$618$	8.29395	0.333632
$619$	−44.3873	−1.78408	−0.892039	−	0.451959i	$-0.850725\pi$
$619$	−44.3873	−1.78408	−0.892039	+	0.451959i	$0.850725\pi$
$620$	5.64853	0.226850
$621$	−37.0186	−1.48551
$622$	15.0527	0.603558
$623$	20.7833	0.832666
$624$	3.99822	0.160057
$625$	1.00000	0.0400000
$626$	−30.6330	−1.22434
$627$	−19.2651	−0.769373
$628$	−12.7720	−0.509657
$629$	7.46827	0.297779
$630$	−4.36148	−0.173766
$631$	−7.06987	−0.281447	−0.140724	−	0.990049i	$-0.544943\pi$
$631$	−7.06987	−0.281447	−0.140724	+	0.990049i	$0.544943\pi$
$632$	−13.9264	−0.553961
$633$	−7.65968	−0.304445
$634$	18.5672	0.737396
$635$	−11.0984	−0.440428
$636$	−9.19395	−0.364564
$637$	−18.6174	−0.737650
$638$	15.5450	0.615431
$639$	−21.0923	−0.834399
$640$	1.00000	0.0395285
$641$	14.0747	0.555917	0.277958	−	0.960593i	$-0.410342\pi$
$641$	14.0747	0.555917	0.277958	+	0.960593i	$0.410342\pi$
$642$	−0.873935	−0.0344915
$643$	19.8330	0.782138	0.391069	−	0.920361i	$-0.372105\pi$
$643$	19.8330	0.782138	0.391069	+	0.920361i	$0.372105\pi$
$644$	16.0279	0.631590
$645$	−4.20224	−0.165463
$646$	21.8975	0.861548
$647$	−33.8826	−1.33206	−0.666031	−	0.745924i	$-0.732008\pi$
$647$	−33.8826	−1.33206	−0.666031	+	0.745924i	$0.732008\pi$
$648$	−3.83764	−0.150757
$649$	57.7748	2.26786
$650$	−5.09537	−0.199857
$651$	−8.10779	−0.317770
$652$	15.4904	0.606651
$653$	−35.9915	−1.40846	−0.704228	−	0.709974i	$-0.748707\pi$
$653$	−35.9915	−1.40846	−0.704228	+	0.709974i	$0.748707\pi$
$654$	−2.86301	−0.111953
$655$	−19.3359	−0.755517
$656$	1.97555	0.0771322
$657$	5.46551	0.213230
$658$	17.1767	0.669618
$659$	4.14324	0.161398	0.0806989	−	0.996739i	$-0.474285\pi$
$659$	4.14324	0.161398	0.0806989	+	0.996739i	$0.474285\pi$
$660$	−3.38282	−0.131676
$661$	6.61936	0.257463	0.128732	−	0.991679i	$-0.458909\pi$
$661$	6.61936	0.257463	0.128732	+	0.991679i	$0.458909\pi$
$662$	−15.9972	−0.621747
$663$	15.3734	0.597054
$664$	−13.7434	−0.533346
$665$	10.4176	0.403978
$666$	4.63099	0.179447
$667$	−31.5939	−1.22332
$668$	19.2832	0.746090
$669$	0.784677	0.0303374
$670$	−7.71903	−0.298212
$671$	52.2547	2.01727
$672$	−1.43538	−0.0553711
$673$	−8.16975	−0.314921	−0.157460	−	0.987525i	$-0.550331\pi$
$673$	−8.16975	−0.314921	−0.157460	+	0.987525i	$0.550331\pi$
$674$	1.95488	0.0752993
$675$	−4.22492	−0.162617
$676$	12.9628	0.498570
$677$	45.6888	1.75596	0.877982	−	0.478694i	$-0.158890\pi$
$677$	45.6888	1.75596	0.877982	+	0.478694i	$0.158890\pi$
$678$	2.63523	0.101206
$679$	11.3895	0.437088
$680$	3.84506	0.147451
$681$	1.59649	0.0611777
$682$	24.3513	0.932461
$683$	−35.2184	−1.34759	−0.673797	−	0.738916i	$-0.735338\pi$
$683$	−35.2184	−1.34759	−0.673797	+	0.738916i	$0.735338\pi$
$684$	13.5784	0.519184
$685$	9.05027	0.345793
$686$	19.4886	0.744078
$687$	−17.6341	−0.672785
$688$	5.35537	0.204172
$689$	−59.7017	−2.27445
$690$	6.87531	0.261739
$691$	−30.3517	−1.15463	−0.577317	−	0.816520i	$-0.695900\pi$
$691$	−30.3517	−1.15463	−0.577317	+	0.816520i	$0.695900\pi$
$692$	5.82172	0.221308
$693$	−18.8028	−0.714258
$694$	34.7332	1.31845
$695$	22.7314	0.862251
$696$	2.82939	0.107248
$697$	7.59611	0.287723
$698$	−29.4373	−1.11422
$699$	−7.96110	−0.301116
$700$	1.82926	0.0691397
$701$	18.5074	0.699013	0.349507	−	0.936934i	$-0.386349\pi$
$701$	18.5074	0.699013	0.349507	+	0.936934i	$0.386349\pi$
$702$	21.5276	0.812505
$703$	−11.0614	−0.417187
$704$	4.31110	0.162481
$705$	7.36808	0.277498
$706$	−5.96153	−0.224365
$707$	−3.43362	−0.129135
$708$	10.5158	0.395208
$709$	7.11656	0.267268	0.133634	−	0.991031i	$-0.457335\pi$
$709$	7.11656	0.267268	0.133634	+	0.991031i	$0.457335\pi$
$710$	8.84640	0.331999
$711$	−33.2044	−1.24526
$712$	−11.3616	−0.425793
$713$	−49.4922	−1.85350
$714$	−5.51914	−0.206548
$715$	−21.9666	−0.821506
$716$	−3.84100	−0.143545
$717$	1.10298	0.0411915
$718$	−28.1780	−1.05159
$719$	−22.3609	−0.833919	−0.416960	−	0.908925i	$-0.636904\pi$
$719$	−22.3609	−0.833919	−0.416960	+	0.908925i	$0.636904\pi$
$720$	2.38428	0.0888569
$721$	−19.3351	−0.720078
$722$	−13.4328	−0.499916
$723$	−15.5897	−0.579788
$724$	−0.332970	−0.0123747
$725$	−3.60580	−0.133916
$726$	−5.95221	−0.220907
$727$	−27.1183	−1.00576	−0.502881	−	0.864356i	$-0.667727\pi$
$727$	−27.1183	−1.00576	−0.502881	+	0.864356i	$0.667727\pi$
$728$	−9.32078	−0.345451
$729$	0.795581	0.0294660
$730$	−2.29231	−0.0848422
$731$	20.5917	0.761613
$732$	9.51105	0.351539
$733$	25.4499	0.940013	0.470006	−	0.882663i	$-0.344252\pi$
$733$	25.4499	0.940013	0.470006	+	0.882663i	$0.344252\pi$
$734$	−6.84567	−0.252678
$735$	2.86705	0.105753
$736$	−8.76196	−0.322970
$737$	−33.2775	−1.22579
$738$	4.71026	0.173387
$739$	−36.6806	−1.34932	−0.674659	−	0.738129i	$-0.735709\pi$
$739$	−36.6806	−1.34932	−0.674659	+	0.738129i	$0.735709\pi$
$740$	−1.94230	−0.0714004
$741$	−22.7698	−0.836469
$742$	21.4332	0.786838
$743$	−19.8081	−0.726687	−0.363343	−	0.931655i	$-0.618365\pi$
$743$	−19.8081	−0.726687	−0.363343	+	0.931655i	$0.618365\pi$
$744$	4.43227	0.162495
$745$	−7.95730	−0.291533
$746$	−16.0307	−0.586926
$747$	−32.7681	−1.19892
$748$	16.5764	0.606095
$749$	2.03735	0.0744430
$750$	0.784677	0.0286524
$751$	39.3882	1.43730	0.718648	−	0.695374i	$-0.244761\pi$
$751$	39.3882	1.43730	0.718648	+	0.695374i	$0.244761\pi$
$752$	−9.38995	−0.342416
$753$	23.5128	0.856853
$754$	18.3729	0.669102
$755$	12.4465	0.452975
$756$	−7.72850	−0.281083
$757$	−10.8352	−0.393812	−0.196906	−	0.980422i	$-0.563089\pi$
$757$	−10.8352	−0.393812	−0.196906	+	0.980422i	$0.563089\pi$
$758$	19.5399	0.709723
$759$	29.6401	1.07587
$760$	−5.69498	−0.206579
$761$	−41.3946	−1.50055	−0.750276	−	0.661124i	$-0.770080\pi$
$761$	−41.3946	−1.50055	−0.750276	+	0.661124i	$0.770080\pi$
$762$	−8.70870	−0.315483
$763$	6.67435	0.241628
$764$	6.26411	0.226628
$765$	9.16771	0.331459
$766$	0.990061	0.0357724
$767$	68.2852	2.46564
$768$	0.784677	0.0283146
$769$	−3.29142	−0.118692	−0.0593459	−	0.998237i	$-0.518901\pi$
$769$	−3.29142	−0.118692	−0.0593459	+	0.998237i	$0.518901\pi$
$770$	7.88614	0.284197
$771$	2.23350	0.0804377
$772$	−1.42102	−0.0511436
$773$	23.2709	0.836996	0.418498	−	0.908218i	$-0.362557\pi$
$773$	23.2709	0.836996	0.418498	+	0.908218i	$0.362557\pi$
$774$	12.7687	0.458962
$775$	−5.64853	−0.202901
$776$	−6.22626	−0.223510
$777$	2.78794	0.100017
$778$	34.7242	1.24492
$779$	−11.2507	−0.403098
$780$	−3.99822	−0.143159
$781$	38.1377	1.36467
$782$	−33.6903	−1.20476
$783$	15.2342	0.544427
$784$	−3.65379	−0.130493
$785$	12.7720	0.455851
$786$	−15.1725	−0.541184
$787$	−40.1094	−1.42975	−0.714874	−	0.699254i	$-0.753516\pi$
$787$	−40.1094	−1.42975	−0.714874	+	0.699254i	$0.753516\pi$
$788$	11.0792	0.394680
$789$	−10.8971	−0.387947
$790$	13.9264	0.495478
$791$	−6.14334	−0.218432
$792$	10.2789	0.365244
$793$	61.7609	2.19319
$794$	−5.20747	−0.184806
$795$	9.19395	0.326076
$796$	−1.27260	−0.0451059
$797$	28.6602	1.01520	0.507599	−	0.861594i	$-0.330533\pi$
$797$	28.6602	1.01520	0.507599	+	0.861594i	$0.330533\pi$
$798$	8.17447	0.289373
$799$	−36.1050	−1.27730
$800$	−1.00000	−0.0353553
$801$	−27.0892	−0.957149
$802$	−10.3915	−0.366936
$803$	−9.88237	−0.348741
$804$	−6.05695	−0.213612
$805$	−16.0279	−0.564911
$806$	28.7814	1.01378
$807$	12.0737	0.425015
$808$	1.87705	0.0660345
$809$	51.0170	1.79366	0.896831	−	0.442374i	$-0.145863\pi$
$809$	51.0170	1.79366	0.896831	+	0.442374i	$0.145863\pi$
$810$	3.83764	0.134841
$811$	−2.71907	−0.0954794	−0.0477397	−	0.998860i	$-0.515202\pi$
$811$	−2.71907	−0.0954794	−0.0477397	+	0.998860i	$0.515202\pi$
$812$	−6.59597	−0.231473
$813$	−7.17582	−0.251667
$814$	−8.37344	−0.293489
$815$	−15.4904	−0.542605
$816$	3.01713	0.105621
$817$	−30.4987	−1.06701
$818$	−11.6534	−0.407450
$819$	−22.2234	−0.776547
$820$	−1.97555	−0.0689891
$821$	7.40885	0.258571	0.129285	−	0.991607i	$-0.458732\pi$
$821$	7.40885	0.258571	0.129285	+	0.991607i	$0.458732\pi$
$822$	7.10154	0.247695
$823$	−41.0846	−1.43212	−0.716060	−	0.698039i	$-0.754056\pi$
$823$	−41.0846	−1.43212	−0.716060	+	0.698039i	$0.754056\pi$
$824$	10.5699	0.368220
$825$	3.38282	0.117775
$826$	−24.5147	−0.852977
$827$	−4.33225	−0.150647	−0.0753236	−	0.997159i	$-0.523999\pi$
$827$	−4.33225	−0.150647	−0.0753236	+	0.997159i	$0.523999\pi$
$828$	−20.8910	−0.726012
$829$	−19.8767	−0.690346	−0.345173	−	0.938539i	$-0.612180\pi$
$829$	−19.8767	−0.690346	−0.345173	+	0.938539i	$0.612180\pi$
$830$	13.7434	0.477039
$831$	−4.22345	−0.146510
$832$	5.09537	0.176650
$833$	−14.0491	−0.486771
$834$	17.8368	0.617638
$835$	−19.2832	−0.667323
$836$	−24.5516	−0.849135
$837$	23.8646	0.824881
$838$	8.00039	0.276369
$839$	29.0616	1.00332	0.501659	−	0.865065i	$-0.332723\pi$
$839$	29.0616	1.00332	0.501659	+	0.865065i	$0.332723\pi$
$840$	1.43538	0.0495254
$841$	−15.9982	−0.551662
$842$	33.5414	1.15591
$843$	20.5679	0.708397
$844$	−9.76156	−0.336007
$845$	−12.9628	−0.445935
$846$	−22.3883	−0.769725
$847$	13.8760	0.476784
$848$	−11.7169	−0.402358
$849$	−11.0698	−0.379914
$850$	−3.84506	−0.131885
$851$	17.0184	0.583382
$852$	6.94157	0.237814
$853$	−12.4039	−0.424701	−0.212350	−	0.977194i	$-0.568112\pi$
$853$	−12.4039	−0.424701	−0.212350	+	0.977194i	$0.568112\pi$
$854$	−22.1725	−0.758726
$855$	−13.5784	−0.464372
$856$	−1.11375	−0.0380672
$857$	3.16633	0.108160	0.0540798	−	0.998537i	$-0.482777\pi$
$857$	3.16633	0.108160	0.0540798	+	0.998537i	$0.482777\pi$
$858$	−17.2367	−0.588452
$859$	−6.26942	−0.213910	−0.106955	−	0.994264i	$-0.534110\pi$
$859$	−6.26942	−0.213910	−0.106955	+	0.994264i	$0.534110\pi$
$860$	−5.35537	−0.182617
$861$	2.83567	0.0966392
$862$	22.7615	0.775261
$863$	24.9822	0.850405	0.425203	−	0.905098i	$-0.360203\pi$
$863$	24.9822	0.850405	0.425203	+	0.905098i	$0.360203\pi$
$864$	4.22492	0.143735
$865$	−5.82172	−0.197944
$866$	30.9591	1.05203
$867$	−1.73844	−0.0590406
$868$	−10.3326	−0.350713
$869$	60.0380	2.03665
$870$	−2.82939	−0.0959254
$871$	−39.3313	−1.33269
$872$	−3.64865	−0.123559
$873$	−14.8452	−0.502432
$874$	49.8992	1.68786
$875$	−1.82926	−0.0618404
$876$	−1.79872	−0.0607733
$877$	29.9573	1.01159	0.505793	−	0.862655i	$-0.331200\pi$
$877$	29.9573	1.01159	0.505793	+	0.862655i	$0.331200\pi$
$878$	−12.0336	−0.406113
$879$	6.79653	0.229241
$880$	−4.31110	−0.145327
$881$	−40.8335	−1.37572	−0.687858	−	0.725845i	$-0.741449\pi$
$881$	−40.8335	−1.37572	−0.687858	+	0.725845i	$0.741449\pi$
$882$	−8.71167	−0.293337
$883$	−45.5042	−1.53134	−0.765669	−	0.643235i	$-0.777592\pi$
$883$	−45.5042	−1.53134	−0.765669	+	0.643235i	$0.777592\pi$
$884$	19.5920	0.658951
$885$	−10.5158	−0.353484
$886$	26.1897	0.879859
$887$	−51.0109	−1.71278	−0.856389	−	0.516332i	$-0.827297\pi$
$887$	−51.0109	−1.71278	−0.856389	+	0.516332i	$0.827297\pi$
$888$	−1.52408	−0.0511447
$889$	20.3020	0.680907
$890$	11.3616	0.380841
$891$	16.5445	0.554260
$892$	1.00000	0.0334825
$893$	53.4756	1.78949
$894$	−6.24391	−0.208828
$895$	3.84100	0.128391
$896$	−1.82926	−0.0611114
$897$	35.0323	1.16969
$898$	−13.2683	−0.442768
$899$	20.3675	0.679293
$900$	−2.38428	−0.0794761
$901$	−45.0520	−1.50090
$902$	−8.51678	−0.283578
$903$	7.68700	0.255807
$904$	3.35837	0.111698
$905$	0.332970	0.0110683
$906$	9.76650	0.324470
$907$	55.3224	1.83695	0.918475	−	0.395480i	$-0.129422\pi$
$907$	55.3224	1.83695	0.918475	+	0.395480i	$0.129422\pi$
$908$	2.03459	0.0675201
$909$	4.47542	0.148440
$910$	9.32078	0.308981
$911$	29.6248	0.981513	0.490757	−	0.871297i	$-0.336720\pi$
$911$	29.6248	0.981513	0.490757	+	0.871297i	$0.336720\pi$
$912$	−4.46872	−0.147974
$913$	59.2490	1.96086
$914$	−4.45288	−0.147288
$915$	−9.51105	−0.314426
$916$	−22.4731	−0.742533
$917$	35.3705	1.16804
$918$	16.2451	0.536168
$919$	50.6922	1.67218	0.836091	−	0.548591i	$-0.184835\pi$
$919$	50.6922	1.67218	0.836091	+	0.548591i	$0.184835\pi$
$920$	8.76196	0.288873
$921$	−3.40564	−0.112220
$922$	−8.24591	−0.271565
$923$	45.0757	1.48368
$924$	6.18807	0.203573
$925$	1.94230	0.0638624
$926$	8.17780	0.268739
$927$	25.2016	0.827729
$928$	3.60580	0.118366
$929$	23.9588	0.786061	0.393031	−	0.919525i	$-0.371427\pi$
$929$	23.9588	0.786061	0.393031	+	0.919525i	$0.371427\pi$
$930$	−4.43227	−0.145340
$931$	20.8083	0.681963
$932$	−10.1457	−0.332333
$933$	−11.8115	−0.386691
$934$	34.2177	1.11964
$935$	−16.5764	−0.542108
$936$	12.1488	0.397096
$937$	35.8216	1.17024	0.585120	−	0.810947i	$-0.301048\pi$
$937$	35.8216	1.17024	0.585120	+	0.810947i	$0.301048\pi$
$938$	14.1201	0.461039
$939$	24.0370	0.784418
$940$	9.38995	0.306267
$941$	12.7360	0.415182	0.207591	−	0.978216i	$-0.433438\pi$
$941$	12.7360	0.415182	0.207591	+	0.978216i	$0.433438\pi$
$942$	10.0219	0.326530
$943$	17.3097	0.563681
$944$	13.4014	0.436179
$945$	7.72850	0.251408
$946$	−23.0875	−0.750640
$947$	−44.1718	−1.43539	−0.717696	−	0.696357i	$-0.754803\pi$
$947$	−44.1718	−1.43539	−0.717696	+	0.696357i	$0.754803\pi$
$948$	10.9277	0.354916
$949$	−11.6802	−0.379155
$950$	5.69498	0.184769
$951$	−14.5692	−0.472440
$952$	−7.03364	−0.227962
$953$	−7.62082	−0.246862	−0.123431	−	0.992353i	$-0.539390\pi$
$953$	−7.62082	−0.246862	−0.123431	+	0.992353i	$0.539390\pi$
$954$	−27.9363	−0.904470
$955$	−6.26411	−0.202702
$956$	1.40565	0.0454619
$957$	−12.1978	−0.394298
$958$	12.4646	0.402712
$959$	−16.5553	−0.534600
$960$	−0.784677	−0.0253253
$961$	0.905856	0.0292212
$962$	−9.89674	−0.319084
$963$	−2.65550	−0.0855722
$964$	−19.8677	−0.639895
$965$	1.42102	0.0457442
$966$	−12.5768	−0.404651
$967$	39.1152	1.25786	0.628930	−	0.777462i	$-0.283493\pi$
$967$	39.1152	1.25786	0.628930	+	0.777462i	$0.283493\pi$
$968$	−7.58555	−0.243809
$969$	−17.1825	−0.551982
$970$	6.22626	0.199913
$971$	45.5572	1.46200	0.731000	−	0.682378i	$-0.239054\pi$
$971$	45.5572	1.46200	0.731000	+	0.682378i	$0.239054\pi$
$972$	15.6861	0.503131
$973$	−41.5817	−1.33305
$974$	26.4192	0.846524
$975$	3.99822	0.128046
$976$	12.1210	0.387983
$977$	−7.49467	−0.239776	−0.119888	−	0.992787i	$-0.538253\pi$
$977$	−7.49467	−0.239776	−0.119888	+	0.992787i	$0.538253\pi$
$978$	−12.1550	−0.388673
$979$	48.9808	1.56543
$980$	3.65379	0.116716
$981$	−8.69941	−0.277751
$982$	23.9779	0.765165
$983$	−18.5311	−0.591051	−0.295526	−	0.955335i	$-0.595495\pi$
$983$	−18.5311	−0.591051	−0.295526	+	0.955335i	$0.595495\pi$
$984$	−1.55017	−0.0494175
$985$	−11.0792	−0.353012
$986$	13.8645	0.441537
$987$	−13.4782	−0.429015
$988$	−29.0180	−0.923187
$989$	46.9235	1.49208
$990$	−10.2789	−0.326684
$991$	44.5754	1.41599	0.707993	−	0.706220i	$-0.249601\pi$
$991$	44.5754	1.41599	0.707993	+	0.706220i	$0.249601\pi$
$992$	5.64853	0.179341
$993$	12.5526	0.398345
$994$	−16.1824	−0.513275
$995$	1.27260	0.0403440
$996$	10.7841	0.341708
$997$	49.3103	1.56167	0.780837	−	0.624735i	$-0.214793\pi$
$997$	49.3103	1.56167	0.780837	+	0.624735i	$0.214793\pi$
$998$	29.2840	0.926969
$999$	−8.20607	−0.259628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2230.2.a.p.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2230.2.a.p.1.4	✓	6	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:	\( N \)	\(=\)	\( 2230 = 2 \cdot 5 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2230.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.784677 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.784677 q^{6} +1.82926 q^{7} -1.00000 q^{8} -2.38428 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.784677 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.784677 q^{6} +1.82926 q^{7} -1.00000 q^{8} -2.38428 q^{9} +1.00000 q^{10} +4.31110 q^{11} +0.784677 q^{12} +5.09537 q^{13} -1.82926 q^{14} -0.784677 q^{15} +1.00000 q^{16} +3.84506 q^{17} +2.38428 q^{18} -5.69498 q^{19} -1.00000 q^{20} +1.43538 q^{21} -4.31110 q^{22} +8.76196 q^{23} -0.784677 q^{24} +1.00000 q^{25} -5.09537 q^{26} -4.22492 q^{27} +1.82926 q^{28} -3.60580 q^{29} +0.784677 q^{30} -5.64853 q^{31} -1.00000 q^{32} +3.38282 q^{33} -3.84506 q^{34} -1.82926 q^{35} -2.38428 q^{36} +1.94230 q^{37} +5.69498 q^{38} +3.99822 q^{39} +1.00000 q^{40} +1.97555 q^{41} -1.43538 q^{42} +5.35537 q^{43} +4.31110 q^{44} +2.38428 q^{45} -8.76196 q^{46} -9.38995 q^{47} +0.784677 q^{48} -3.65379 q^{49} -1.00000 q^{50} +3.01713 q^{51} +5.09537 q^{52} -11.7169 q^{53} +4.22492 q^{54} -4.31110 q^{55} -1.82926 q^{56} -4.46872 q^{57} +3.60580 q^{58} +13.4014 q^{59} -0.784677 q^{60} +12.1210 q^{61} +5.64853 q^{62} -4.36148 q^{63} +1.00000 q^{64} -5.09537 q^{65} -3.38282 q^{66} -7.71903 q^{67} +3.84506 q^{68} +6.87531 q^{69} +1.82926 q^{70} +8.84640 q^{71} +2.38428 q^{72} -2.29231 q^{73} -1.94230 q^{74} +0.784677 q^{75} -5.69498 q^{76} +7.88614 q^{77} -3.99822 q^{78} +13.9264 q^{79} -1.00000 q^{80} +3.83764 q^{81} -1.97555 q^{82} +13.7434 q^{83} +1.43538 q^{84} -3.84506 q^{85} -5.35537 q^{86} -2.82939 q^{87} -4.31110 q^{88} +11.3616 q^{89} -2.38428 q^{90} +9.32078 q^{91} +8.76196 q^{92} -4.43227 q^{93} +9.38995 q^{94} +5.69498 q^{95} -0.784677 q^{96} +6.22626 q^{97} +3.65379 q^{98} -10.2789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 6 q^{10} + 14 q^{11} - q^{12} + 9 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 4 q^{17} - 5 q^{18} + q^{19} - 6 q^{20} + 14 q^{21} - 14 q^{22} + 9 q^{23} + q^{24} + 6 q^{25} - 9 q^{26} - 28 q^{27} - 6 q^{28} - 9 q^{29} - q^{30} + q^{31} - 6 q^{32} - 6 q^{33} - 4 q^{34} + 6 q^{35} + 5 q^{36} - 18 q^{37} - q^{38} - 18 q^{39} + 6 q^{40} + 11 q^{41} - 14 q^{42} - 26 q^{43} + 14 q^{44} - 5 q^{45} - 9 q^{46} + 14 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} + 14 q^{51} + 9 q^{52} + 14 q^{53} + 28 q^{54} - 14 q^{55} + 6 q^{56} + 9 q^{57} + 9 q^{58} + 18 q^{59} + q^{60} + 24 q^{61} - q^{62} + 6 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} + 4 q^{68} + 20 q^{69} - 6 q^{70} + 32 q^{71} - 5 q^{72} - 12 q^{73} + 18 q^{74} - q^{75} + q^{76} + 12 q^{77} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 14 q^{81} - 11 q^{82} + 36 q^{83} + 14 q^{84} - 4 q^{85} + 26 q^{86} - 9 q^{87} - 14 q^{88} + 11 q^{89} + 5 q^{90} + 10 q^{91} + 9 q^{92} + 8 q^{93} - 14 q^{94} - q^{95} + q^{96} - q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 6 * q^10 + 14 * q^11 - q^12 + 9 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 4 * q^17 - 5 * q^18 + q^19 - 6 * q^20 + 14 * q^21 - 14 * q^22 + 9 * q^23 + q^24 + 6 * q^25 - 9 * q^26 - 28 * q^27 - 6 * q^28 - 9 * q^29 - q^30 + q^31 - 6 * q^32 - 6 * q^33 - 4 * q^34 + 6 * q^35 + 5 * q^36 - 18 * q^37 - q^38 - 18 * q^39 + 6 * q^40 + 11 * q^41 - 14 * q^42 - 26 * q^43 + 14 * q^44 - 5 * q^45 - 9 * q^46 + 14 * q^47 - q^48 + 6 * q^49 - 6 * q^50 + 14 * q^51 + 9 * q^52 + 14 * q^53 + 28 * q^54 - 14 * q^55 + 6 * q^56 + 9 * q^57 + 9 * q^58 + 18 * q^59 + q^60 + 24 * q^61 - q^62 + 6 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 + 4 * q^68 + 20 * q^69 - 6 * q^70 + 32 * q^71 - 5 * q^72 - 12 * q^73 + 18 * q^74 - q^75 + q^76 + 12 * q^77 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 14 * q^81 - 11 * q^82 + 36 * q^83 + 14 * q^84 - 4 * q^85 + 26 * q^86 - 9 * q^87 - 14 * q^88 + 11 * q^89 + 5 * q^90 + 10 * q^91 + 9 * q^92 + 8 * q^93 - 14 * q^94 - q^95 + q^96 - q^97 - 6 * q^98 + 16 * q^99

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