LMFDB - Embedded newform 124.3.b.a.63.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.5
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66997 - 1.10055i) q^{2} -3.18220i q^{3} +(1.57758 + 3.67576i) q^{4} +1.05927 q^{5} +(-3.50217 + 5.31417i) q^{6} -9.87284i q^{7} +(1.41085 - 7.87461i) q^{8} -1.12641 q^{9} +O(q^{10})$	\(q+(-1.66997 - 1.10055i) q^{2} -3.18220i q^{3} +(1.57758 + 3.67576i) q^{4} +1.05927 q^{5} +(-3.50217 + 5.31417i) q^{6} -9.87284i q^{7} +(1.41085 - 7.87461i) q^{8} -1.12641 q^{9} +(-1.76894 - 1.16578i) q^{10} -0.537945i q^{11} +(11.6970 - 5.02018i) q^{12} -19.7127 q^{13} +(-10.8655 + 16.4873i) q^{14} -3.37080i q^{15} +(-11.0225 + 11.5976i) q^{16} -3.48549 q^{17} +(1.88107 + 1.23967i) q^{18} +11.6362i q^{19} +(1.67108 + 3.89362i) q^{20} -31.4174 q^{21} +(-0.592036 + 0.898351i) q^{22} -25.0682i q^{23} +(-25.0586 - 4.48962i) q^{24} -23.8780 q^{25} +(32.9195 + 21.6948i) q^{26} -25.0554i q^{27} +(36.2902 - 15.5752i) q^{28} +50.7070 q^{29} +(-3.70974 + 5.62913i) q^{30} -5.56776i q^{31} +(31.1709 - 7.23687i) q^{32} -1.71185 q^{33} +(5.82065 + 3.83595i) q^{34} -10.4580i q^{35} +(-1.77700 - 4.14042i) q^{36} +2.98751 q^{37} +(12.8062 - 19.4321i) q^{38} +62.7297i q^{39} +(1.49447 - 8.34132i) q^{40} +36.6995 q^{41} +(52.4660 + 34.5764i) q^{42} +17.9308i q^{43} +(1.97736 - 0.848652i) q^{44} -1.19317 q^{45} +(-27.5888 + 41.8631i) q^{46} -27.7406i q^{47} +(36.9060 + 35.0758i) q^{48} -48.4729 q^{49} +(39.8754 + 26.2789i) q^{50} +11.0915i q^{51} +(-31.0983 - 72.4591i) q^{52} +73.0615 q^{53} +(-27.5747 + 41.8416i) q^{54} -0.569828i q^{55} +(-77.7448 - 13.9291i) q^{56} +37.0287 q^{57} +(-84.6791 - 55.8056i) q^{58} -23.9095i q^{59} +(12.3903 - 5.31771i) q^{60} +84.2014 q^{61} +(-6.12760 + 9.29798i) q^{62} +11.1209i q^{63} +(-60.0190 - 22.2198i) q^{64} -20.8810 q^{65} +(2.85873 + 1.88398i) q^{66} +19.5503i q^{67} +(-5.49864 - 12.8118i) q^{68} -79.7722 q^{69} +(-11.5095 + 17.4645i) q^{70} +56.5513i q^{71} +(-1.58920 + 8.87004i) q^{72} +52.4675 q^{73} +(-4.98905 - 3.28791i) q^{74} +75.9845i q^{75} +(-42.7719 + 18.3570i) q^{76} -5.31105 q^{77} +(69.0371 - 104.757i) q^{78} -122.069i q^{79} +(-11.6758 + 12.2850i) q^{80} -89.8689 q^{81} +(-61.2869 - 40.3896i) q^{82} +42.9275i q^{83} +(-49.5634 - 115.483i) q^{84} -3.69206 q^{85} +(19.7337 - 29.9438i) q^{86} -161.360i q^{87} +(-4.23611 - 0.758962i) q^{88} -108.163 q^{89} +(1.99255 + 1.31314i) q^{90} +194.620i q^{91} +(92.1449 - 39.5472i) q^{92} -17.7178 q^{93} +(-30.5300 + 46.3260i) q^{94} +12.3258i q^{95} +(-23.0292 - 99.1922i) q^{96} -99.6186 q^{97} +(80.9482 + 53.3469i) q^{98} +0.605947i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.66997	−	1.10055i	−0.834984	−	0.550275i
$2$	−1.66997	−	1.10055i	−0.834984	−	0.550275i
$3$		−	3.18220i		−	1.06073i	−0.847768	−	0.530367i	$-0.822054\pi$
$3$		−	3.18220i		−	1.06073i	0.847768	−	0.530367i	$-0.177946\pi$
$4$	1.57758	+	3.67576i	0.394395	+	0.918941i
$5$	1.05927			0.211853			0.105927	−	0.994374i	$-0.466219\pi$
$5$	1.05927			0.211853			0.105927	+	0.994374i	$0.466219\pi$
$6$	−3.50217	+	5.31417i	−0.583695	+	0.885695i
$7$		−	9.87284i		−	1.41041i	−0.709006	−	0.705203i	$-0.750856\pi$
$7$		−	9.87284i		−	1.41041i	0.709006	−	0.705203i	$-0.249144\pi$
$8$	1.41085	−	7.87461i	0.176357	−	0.984326i
$9$	−1.12641			−0.125157
$10$	−1.76894	−	1.16578i	−0.176894	−	0.116578i
$11$		−	0.537945i		−	0.0489041i	−0.999701	−	0.0244521i	$-0.992216\pi$
$11$		−	0.537945i		−	0.0489041i	0.999701	−	0.0244521i	$-0.00778411\pi$
$12$	11.6970	−	5.02018i	0.974752	−	0.418348i
$13$	−19.7127			−1.51636			−0.758179	−	0.652046i	$-0.773911\pi$
$13$	−19.7127			−1.51636			−0.758179	+	0.652046i	$0.773911\pi$
$14$	−10.8655	+	16.4873i	−0.776111	+	1.17767i
$15$		−	3.37080i		−	0.224720i
$16$	−11.0225	+	11.5976i	−0.688905	+	0.724852i
$17$	−3.48549			−0.205029			−0.102514	−	0.994732i	$-0.532689\pi$
$17$	−3.48549			−0.205029			−0.102514	+	0.994732i	$0.532689\pi$
$18$	1.88107	+	1.23967i	0.104504	+	0.0688706i
$19$			11.6362i			0.612432i	0.951962	+	0.306216i	$0.0990629\pi$
$19$			11.6362i			0.612432i	−0.951962	+	0.306216i	$0.900937\pi$
$20$	1.67108	+	3.89362i	0.0835540	+	0.194681i
$21$	−31.4174			−1.49606
$22$	−0.592036	+	0.898351i	−0.0269107	+	0.0408341i
$23$		−	25.0682i		−	1.08992i	−0.838461	−	0.544962i	$-0.816544\pi$
$23$		−	25.0682i		−	1.08992i	0.838461	−	0.544962i	$-0.183456\pi$
$24$	−25.0586	−	4.48962i	−1.04411	−	0.187067i
$25$	−23.8780			−0.955118
$26$	32.9195	+	21.6948i	1.26613	+	0.834414i
$27$		−	25.0554i		−	0.927976i
$28$	36.2902	−	15.5752i	1.29608	−	0.556257i
$29$	50.7070			1.74852			0.874259	−	0.485459i	$-0.161348\pi$
$29$	50.7070			1.74852			0.874259	+	0.485459i	$0.161348\pi$
$30$	−3.70974	+	5.62913i	−0.123658	+	0.187638i
$31$		−	5.56776i		−	0.179605i
$31$		−	5.56776i		−	0.179605i
$32$	31.1709	−	7.23687i	0.974092	−	0.226152i
$33$	−1.71185			−0.0518743
$34$	5.82065	+	3.83595i	0.171196	+	0.112822i
$35$		−	10.4580i		−	0.298799i
$36$	−1.77700	−	4.14042i	−0.0493612	−	0.115012i
$37$	2.98751			0.0807436			0.0403718	−	0.999185i	$-0.487146\pi$
$37$	2.98751			0.0807436			0.0403718	+	0.999185i	$0.487146\pi$
$38$	12.8062	−	19.4321i	0.337006	−	0.511370i
$39$			62.7297i			1.60845i
$40$	1.49447	−	8.34132i	0.0373618	−	0.208533i
$41$	36.6995			0.895109			0.447555	−	0.894257i	$-0.352295\pi$
$41$	36.6995			0.895109			0.447555	+	0.894257i	$0.352295\pi$
$42$	52.4660	+	34.5764i	1.24919	+	0.823247i
$43$			17.9308i			0.416995i	0.978023	+	0.208498i	$0.0668573\pi$
$43$			17.9308i			0.416995i	−0.978023	+	0.208498i	$0.933143\pi$
$44$	1.97736	−	0.848652i	0.0449400	−	0.0192875i
$45$	−1.19317			−0.0265149
$46$	−27.5888	+	41.8631i	−0.599758	+	0.910068i
$47$		−	27.7406i		−	0.590226i	−0.955462	−	0.295113i	$-0.904643\pi$
$47$		−	27.7406i		−	0.590226i	0.955462	−	0.295113i	$-0.0953574\pi$
$48$	36.9060	+	35.0758i	0.768875	+	0.730745i
$49$	−48.4729			−0.989243
$50$	39.8754	+	26.2789i	0.797508	+	0.525577i
$51$			11.0915i			0.217481i
$52$	−31.0983	−	72.4591i	−0.598045	−	1.39344i
$53$	73.0615			1.37852			0.689259	−	0.724515i	$-0.257936\pi$
$53$	73.0615			1.37852			0.689259	+	0.724515i	$0.257936\pi$
$54$	−27.5747	+	41.8416i	−0.510642	+	0.774845i
$55$		−	0.569828i		−	0.0103605i
$56$	−77.7448	−	13.9291i	−1.38830	−	0.248734i
$57$	37.0287			0.649627
$58$	−84.6791	−	55.8056i	−1.45998	−	0.962166i
$59$		−	23.9095i		−	0.405245i	−0.979257	−	0.202623i	$-0.935054\pi$
$59$		−	23.9095i		−	0.405245i	0.979257	−	0.202623i	$-0.0649465\pi$
$60$	12.3903	−	5.31771i	0.206505	−	0.0886285i
$61$	84.2014			1.38035			0.690176	−	0.723642i	$-0.257533\pi$
$61$	84.2014			1.38035			0.690176	+	0.723642i	$0.257533\pi$
$62$	−6.12760	+	9.29798i	−0.0988323	+	0.149967i
$63$			11.1209i			0.176522i
$64$	−60.0190	−	22.2198i	−0.937797	−	0.347185i
$65$	−20.8810			−0.321246
$66$	2.85873	+	1.88398i	0.0433142	+	0.0285451i
$67$			19.5503i			0.291796i	0.989300	+	0.145898i	$0.0466071\pi$
$67$			19.5503i			0.291796i	−0.989300	+	0.145898i	$0.953393\pi$
$68$	−5.49864	−	12.8118i	−0.0808623	−	0.188409i
$69$	−79.7722			−1.15612
$70$	−11.5095	+	17.4645i	−0.164422	+	0.249492i
$71$			56.5513i			0.796497i	0.917278	+	0.398248i	$0.130382\pi$
$71$			56.5513i			0.796497i	−0.917278	+	0.398248i	$0.869618\pi$
$72$	−1.58920	+	8.87004i	−0.0220722	+	0.123195i
$73$	52.4675			0.718733			0.359367	−	0.933196i	$-0.382993\pi$
$73$	52.4675			0.718733			0.359367	+	0.933196i	$0.382993\pi$
$74$	−4.98905	−	3.28791i	−0.0674196	−	0.0444312i
$75$			75.9845i			1.01313i
$76$	−42.7719	+	18.3570i	−0.562789	+	0.241540i
$77$	−5.31105			−0.0689746
$78$	69.0371	−	104.757i	0.885091	−	1.34303i
$79$		−	122.069i		−	1.54518i	−0.634908	−	0.772588i	$-0.718962\pi$
$79$		−	122.069i		−	1.54518i	0.634908	−	0.772588i	$-0.281038\pi$
$80$	−11.6758	+	12.2850i	−0.145947	+	0.153562i
$81$	−89.8689			−1.10949
$82$	−61.2869	−	40.3896i	−0.747402	−	0.492556i
$83$			42.9275i			0.517199i	0.965985	+	0.258599i	$0.0832610\pi$
$83$			42.9275i			0.517199i	−0.965985	+	0.258599i	$0.916739\pi$
$84$	−49.5634	−	115.483i	−0.590041	−	1.37480i
$85$	−3.69206			−0.0434360
$86$	19.7337	−	29.9438i	0.229462	−	0.348184i
$87$		−	161.360i		−	1.85471i
$88$	−4.23611	−	0.758962i	−0.0481376	−	0.00862456i
$89$	−108.163			−1.21532			−0.607658	−	0.794198i	$-0.707891\pi$
$89$	−108.163			−1.21532			−0.607658	+	0.794198i	$0.707891\pi$
$90$	1.99255	+	1.31314i	0.0221395	+	0.0145905i
$91$			194.620i			2.13868i
$92$	92.1449	−	39.5472i	1.00158	−	0.429861i
$93$	−17.7178			−0.190513
$94$	−30.5300	+	46.3260i	−0.324787	+	0.492829i
$95$			12.3258i			0.129746i
$96$	−23.0292	−	99.1922i	−0.239887	−	1.03325i
$97$	−99.6186			−1.02700			−0.513498	−	0.858091i	$-0.671651\pi$
$97$	−99.6186			−1.02700			−0.513498	+	0.858091i	$0.671651\pi$
$98$	80.9482	+	53.3469i	0.826002	+	0.544356i
$99$			0.605947i			0.00612068i
$100$	−37.6694	−	87.7697i	−0.376694	−	0.877697i
$101$	151.019			1.49524			0.747620	−	0.664127i	$-0.231197\pi$
$101$	151.019			1.49524			0.747620	+	0.664127i	$0.231197\pi$
$102$	12.2068	−	18.5225i	0.119674	−	0.181593i
$103$			141.381i			1.37263i	0.727304	+	0.686316i	$0.240773\pi$
$103$			141.381i			1.37263i	−0.727304	+	0.686316i	$0.759227\pi$
$104$	−27.8117	+	155.230i	−0.267420	+	1.49259i
$105$	−33.2794			−0.316947
$106$	−122.010	−	80.4078i	−1.15104	−	0.758564i
$107$			146.624i			1.37032i	0.728394	+	0.685159i	$0.240267\pi$
$107$			146.624i			1.37032i	−0.728394	+	0.685159i	$0.759733\pi$
$108$	92.0976	−	39.5268i	0.852755	−	0.365989i
$109$	78.1864			0.717307			0.358653	−	0.933471i	$-0.383236\pi$
$109$	78.1864			0.717307			0.358653	+	0.933471i	$0.383236\pi$
$110$	−0.627124	+	0.951594i	−0.00570113	+	0.00865085i
$111$		−	9.50687i		−	0.0856475i
$112$	114.501	+	108.823i	1.02233	+	0.971635i
$113$	−29.2613			−0.258950			−0.129475	−	0.991583i	$-0.541329\pi$
$113$	−29.2613			−0.258950			−0.129475	+	0.991583i	$0.541329\pi$
$114$	−61.8368	−	40.7520i	−0.542428	−	0.357473i
$115$		−	26.5540i		−	0.230904i
$116$	79.9944	+	186.387i	0.689607	+	1.60679i
$117$	22.2045			0.189782
$118$	−26.3136	+	39.9280i	−0.222996	+	0.338373i
$119$			34.4117i			0.289174i
$120$	−26.5438	−	4.75571i	−0.221198	−	0.0396309i
$121$	120.711			0.997608
$122$	−140.614	−	92.6679i	−1.15257	−	0.759573i
$123$		−	116.785i		−	0.949473i
$124$	20.4658	−	8.78360i	0.165047	−	0.0708355i
$125$	−51.7748			−0.414199
$126$	12.2391	−	18.5715i	0.0971354	−	0.147393i
$127$		−	193.688i		−	1.52510i	−0.646927	−	0.762552i	$-0.723946\pi$
$127$		−	193.688i		−	1.52510i	0.646927	−	0.762552i	$-0.276054\pi$
$128$	75.7757	+	103.160i	0.591998	+	0.805940i
$129$	57.0594			0.442321
$130$	34.8706	+	22.9806i	0.268235	+	0.176774i
$131$		−	148.970i		−	1.13718i	−0.822623	−	0.568588i	$-0.807490\pi$
$131$		−	148.970i		−	1.13718i	0.822623	−	0.568588i	$-0.192510\pi$
$132$	−2.70058	−	6.29236i	−0.0204590	−	0.0476694i
$133$	114.882			0.863777
$134$	21.5161	−	32.6484i	0.160568	−	0.243644i
$135$		−	26.5403i		−	0.196595i
$136$	−4.91751	+	27.4469i	−0.0361582	+	0.201815i
$137$	169.298			1.23576			0.617878	−	0.786274i	$-0.287993\pi$
$137$	169.298			1.23576			0.617878	+	0.786274i	$0.287993\pi$
$138$	133.217	+	87.7933i	0.965340	+	0.636183i
$139$		−	13.1921i		−	0.0949072i	−0.998873	−	0.0474536i	$-0.984889\pi$
$139$		−	13.1921i		−	0.0949072i	0.998873	−	0.0474536i	$-0.0151106\pi$
$140$	38.4410	−	16.4983i	0.274579	−	0.117845i
$141$	−88.2763			−0.626073
$142$	62.2375	−	94.4387i	0.438292	−	0.665062i
$143$			10.6043i			0.0741562i
$144$	12.4158	−	13.0637i	0.0862210	−	0.0907200i
$145$	53.7123			0.370430
$146$	−87.6190	−	57.7431i	−0.600130	−	0.395501i
$147$			154.251i			1.04932i
$148$	4.71304	+	10.9814i	0.0318449	+	0.0741986i
$149$	−24.8848			−0.167012			−0.0835059	−	0.996507i	$-0.526612\pi$
$149$	−24.8848			−0.167012			−0.0835059	+	0.996507i	$0.526612\pi$
$150$	83.6247	−	126.892i	0.557498	−	0.845944i
$151$		−	180.514i		−	1.19546i	−0.801698	−	0.597730i	$-0.796070\pi$
$151$		−	180.514i		−	1.19546i	0.801698	−	0.597730i	$-0.203930\pi$
$152$	91.6306	+	16.4170i	0.602833	+	0.108006i
$153$	3.92609			0.0256607
$154$	8.86927	+	5.84507i	0.0575927	+	0.0379550i
$155$		−	5.89775i		−	0.0380500i
$156$	−230.580	+	98.9611i	−1.47807	+	0.634366i
$157$	−231.318			−1.47336			−0.736681	−	0.676241i	$-0.763608\pi$
$157$	−231.318			−1.47336			−0.736681	+	0.676241i	$0.763608\pi$
$158$	−134.343	+	203.851i	−0.850272	+	1.29020i
$159$		−	232.496i		−	1.46224i
$160$	33.0184	−	7.66578i	0.206365	−	0.0479111i
$161$	−247.495			−1.53723
$162$	150.078	+	98.9052i	0.926408	+	0.610526i
$163$			288.668i			1.77097i	0.464671	+	0.885483i	$0.346172\pi$
$163$			288.668i			1.77097i	−0.464671	+	0.885483i	$0.653828\pi$
$164$	57.8964	+	134.899i	0.353027	+	0.822553i
$165$	−1.81331			−0.0109897
$166$	47.2439	−	71.6875i	0.284602	−	0.431853i
$167$			32.3508i			0.193718i	0.995298	+	0.0968588i	$0.0308795\pi$
$167$			32.3508i			0.193718i	−0.995298	+	0.0968588i	$0.969120\pi$
$168$	−44.3253	+	247.400i	−0.263841	+	1.47262i
$169$	219.589			1.29934
$170$	6.16563	+	4.06330i	0.0362684	+	0.0239018i
$171$		−	13.1071i		−	0.0766499i
$172$	−65.9093	+	28.2873i	−0.383194	+	0.164461i
$173$	77.8910			0.450237			0.225118	−	0.974331i	$-0.427723\pi$
$173$	77.8910			0.450237			0.225118	+	0.974331i	$0.427723\pi$
$174$	−177.585	+	269.466i	−1.02060	+	1.54865i
$175$			235.743i			1.34710i
$176$	6.23889	+	5.92949i	0.0354482	+	0.0336903i
$177$	−76.0848			−0.429857
$178$	180.629	+	119.039i	1.01477	+	0.668758i
$179$		−	29.3270i		−	0.163838i	−0.996639	−	0.0819191i	$-0.973895\pi$
$179$		−	29.3270i		−	0.163838i	0.996639	−	0.0819191i	$-0.0261049\pi$
$180$	−1.88232	−	4.38581i	−0.0104573	−	0.0243656i
$181$	−213.227			−1.17805			−0.589024	−	0.808115i	$-0.700488\pi$
$181$	−213.227			−1.17805			−0.589024	+	0.808115i	$0.700488\pi$
$182$	214.189	−	325.009i	1.17686	−	1.78576i
$183$		−	267.946i		−	1.46419i
$184$	−197.403	−	35.3676i	−1.07284	−	0.192215i
$185$	3.16457			0.0171058
$186$	29.5881	+	19.4993i	0.159076	+	0.104835i
$187$			1.87500i			0.0100268i
$188$	101.968	−	43.7631i	0.542383	−	0.232782i
$189$	−247.367			−1.30882
$190$	13.5652	−	20.5838i	0.0713958	−	0.108336i
$191$		−	289.005i		−	1.51312i	−0.653927	−	0.756558i	$-0.726880\pi$
$191$		−	289.005i		−	1.51312i	0.653927	−	0.756558i	$-0.273120\pi$
$192$	−70.7080	+	190.993i	−0.368271	+	0.994753i
$193$	280.290			1.45228			0.726139	−	0.687548i	$-0.241313\pi$
$193$	280.290			1.45228			0.726139	+	0.687548i	$0.241313\pi$
$194$	166.360	+	109.635i	0.857525	+	0.565130i
$195$			66.4475i			0.340756i
$196$	−76.4699	−	178.175i	−0.390153	−	0.909056i
$197$	−300.952			−1.52767			−0.763837	−	0.645410i	$-0.776687\pi$
$197$	−300.952			−1.52767			−0.763837	+	0.645410i	$0.776687\pi$
$198$	0.666875	−	1.01191i	0.00336805	−	0.00511066i
$199$		−	17.8355i		−	0.0896255i	−0.998995	−	0.0448128i	$-0.985731\pi$
$199$		−	17.8355i		−	0.0896255i	0.998995	−	0.0448128i	$-0.0142691\pi$
$200$	−33.6883	+	188.030i	−0.168441	+	0.940148i
$201$	62.2130			0.309517
$202$	−252.197	−	166.204i	−1.24850	−	0.822793i
$203$		−	500.622i		−	2.46612i
$204$	−40.7698	+	17.4978i	−0.199852	+	0.0857734i
$205$	38.8746			0.189632
$206$	155.597	−	236.102i	0.755325	−	1.14612i
$207$			28.2371i			0.136411i
$208$	217.282	−	228.620i	1.04463	−	1.09914i
$209$	6.25964			0.0299504
$210$	55.5755	+	36.6256i	0.264645	+	0.174408i
$211$			301.769i			1.43018i	0.699031	+	0.715091i	$0.253615\pi$
$211$			301.769i			1.43018i	−0.699031	+	0.715091i	$0.746385\pi$
$212$	115.260	+	268.557i	0.543681	+	1.26678i
$213$	179.958			0.844871
$214$	161.367	−	244.857i	0.754051	−	1.14419i
$215$			18.9935i			0.0883418i
$216$	−197.301	−	35.3494i	−0.913431	−	0.163655i
$217$	−54.9696			−0.253316
$218$	−130.569	−	86.0481i	−0.598939	−	0.394716i
$219$		−	166.962i		−	0.762385i
$220$	2.09455	−	0.898949i	0.00952069	−	0.00408613i
$221$	68.7083			0.310897
$222$	−10.4628	+	15.8762i	−0.0471297	+	0.0715142i
$223$			398.436i			1.78671i	0.449353	+	0.893355i	$0.351655\pi$
$223$			398.436i			1.78671i	−0.449353	+	0.893355i	$0.648345\pi$
$224$	−71.4485	−	307.746i	−0.318966	−	1.37386i
$225$	26.8964			0.119539
$226$	48.8654	+	32.2035i	0.216219	+	0.142493i
$227$			273.396i			1.20439i	0.798350	+	0.602194i	$0.205707\pi$
$227$			273.396i			1.20439i	−0.798350	+	0.602194i	$0.794293\pi$
$228$	58.4158	+	136.109i	0.256210	+	0.596969i
$229$	−204.702			−0.893896			−0.446948	−	0.894560i	$-0.647489\pi$
$229$	−204.702			−0.893896			−0.446948	+	0.894560i	$0.647489\pi$
$230$	−29.2240	+	44.3443i	−0.127061	+	0.192801i
$231$			16.9008i			0.0731637i
$232$	71.5402	−	399.298i	0.308363	−	1.72111i
$233$	86.4348			0.370965			0.185482	−	0.982648i	$-0.440615\pi$
$233$	86.4348			0.370965			0.185482	+	0.982648i	$0.440615\pi$
$234$	−37.0809	−	24.4372i	−0.158465	−	0.104432i
$235$		−	29.3848i		−	0.125042i
$236$	87.8856	−	37.7191i	0.372396	−	0.159827i
$237$	−388.448			−1.63902
$238$	37.8717	−	57.4663i	0.159125	−	0.241455i
$239$		−	275.267i		−	1.15175i	−0.817539	−	0.575873i	$-0.804662\pi$
$239$		−	275.267i		−	1.15175i	0.817539	−	0.575873i	$-0.195338\pi$
$240$	39.0933	+	37.1546i	0.162889	+	0.154811i
$241$	−81.7854			−0.339359			−0.169679	−	0.985499i	$-0.554273\pi$
$241$	−81.7854			−0.339359			−0.169679	+	0.985499i	$0.554273\pi$
$242$	−201.583	−	132.848i	−0.832987	−	0.548959i
$243$			60.4828i			0.248900i
$244$	132.835	+	309.505i	0.544404	+	1.26846i
$245$	−51.3458			−0.209575
$246$	−128.528	+	195.027i	−0.522471	+	0.792794i
$247$		−	229.381i		−	0.928666i
$248$	−43.8440	−	7.85530i	−0.176790	−	0.0316746i
$249$	136.604			0.548611
$250$	86.4622	+	56.9808i	0.345849	+	0.227923i
$251$			7.99583i			0.0318559i	0.999873	+	0.0159280i	$0.00507024\pi$
$251$			7.99583i			0.0318559i	−0.999873	+	0.0159280i	$0.994930\pi$
$252$	−40.8777	+	17.5441i	−0.162213	+	0.0696193i
$253$	−13.4853			−0.0533018
$254$	−213.164	+	323.453i	−0.839227	+	1.27344i
$255$			11.7489i			0.0460741i
$256$	−13.0099	−	255.669i	−0.0508201	−	0.998708i
$257$	−481.528			−1.87365			−0.936826	−	0.349797i	$-0.886251\pi$
$257$	−481.528			−1.87365			−0.936826	+	0.349797i	$0.886251\pi$
$258$	−95.2873	−	62.7967i	−0.369331	−	0.243398i
$259$		−	29.4952i		−	0.113881i
$260$	−32.9414	−	76.7536i	−0.126698	−	0.295206i
$261$	−57.1169			−0.218839
$262$	−163.949	+	248.775i	−0.625759	+	0.949523i
$263$			230.671i			0.877077i	0.898712	+	0.438539i	$0.144504\pi$
$263$			230.671i			0.877077i	−0.898712	+	0.438539i	$0.855496\pi$
$264$	−2.41517	+	13.4802i	−0.00914837	+	0.0510612i
$265$	77.3917			0.292044
$266$	−191.850	−	126.434i	−0.721240	−	0.475315i
$267$			344.197i			1.28913i
$268$	−71.8623	+	30.8422i	−0.268143	+	0.115083i
$269$	419.206			1.55839			0.779193	−	0.626784i	$-0.215629\pi$
$269$	419.206			1.55839			0.779193	+	0.626784i	$0.215629\pi$
$270$	−29.2089	+	44.3215i	−0.108181	+	0.164154i
$271$			164.842i			0.608275i	0.952628	+	0.304137i	$0.0983682\pi$
$271$			164.842i			0.608275i	−0.952628	+	0.304137i	$0.901632\pi$
$272$	38.4187	−	40.4234i	0.141245	−	0.148615i
$273$	619.320			2.26857
$274$	−282.723	−	186.321i	−1.03184	−	0.680005i
$275$			12.8450i			0.0467092i
$276$	−125.847	−	293.224i	−0.455968	−	1.06241i
$277$	421.686			1.52233			0.761165	−	0.648558i	$-0.224628\pi$
$277$	421.686			1.52233			0.761165	+	0.648558i	$0.224628\pi$
$278$	−14.5186	+	22.0304i	−0.0522251	+	0.0792460i
$279$			6.27158i			0.0224788i
$280$	−82.3525	−	14.7547i	−0.294116	−	0.0526952i
$281$	27.1518			0.0966257			0.0483129	−	0.998832i	$-0.484616\pi$
$281$	27.1518			0.0966257			0.0483129	+	0.998832i	$0.484616\pi$
$282$	147.419	+	97.1525i	0.522761	+	0.344512i
$283$		−	6.77145i		−	0.0239274i	−0.999928	−	0.0119637i	$-0.996192\pi$
$283$		−	6.77145i		−	0.0239274i	0.999928	−	0.0119637i	$-0.00380825\pi$
$284$	−207.869	+	89.2142i	−0.731933	+	0.314134i
$285$	39.2233			0.137626
$286$	11.6706	−	17.7089i	0.0408063	−	0.0619192i
$287$		−	362.328i		−	1.26247i
$288$	−35.1113	+	8.15168i	−0.121914	+	0.0283045i
$289$	−276.851			−0.957963
$290$	−89.6978	−	59.1131i	−0.309303	−	0.203838i
$291$			317.007i			1.08937i
$292$	82.7718	+	192.858i	0.283465	+	0.660473i
$293$	−14.8865			−0.0508072			−0.0254036	−	0.999677i	$-0.508087\pi$
$293$	−14.8865			−0.0508072			−0.0254036	+	0.999677i	$0.508087\pi$
$294$	169.760	−	257.593i	0.577417	−	0.876168i
$295$		−	25.3265i		−	0.0858526i
$296$	4.21494	−	23.5255i	0.0142397	−	0.0794781i
$297$	−13.4784			−0.0453819
$298$	41.5567	+	27.3869i	0.139452	+	0.0919024i
$299$			494.162i			1.65272i
$300$	−279.301	+	119.872i	−0.931003	+	0.399572i
$301$	177.028			0.588132
$302$	−198.665	+	301.453i	−0.657831	+	0.998189i
$303$		−	480.574i		−	1.58605i
$304$	−134.952	−	128.260i	−0.443922	−	0.421907i
$305$	89.1918			0.292432
$306$	−6.55644	−	4.32086i	−0.0214263	−	0.0141204i
$307$		−	11.5459i		−	0.0376088i	−0.999823	−	0.0188044i	$-0.994014\pi$
$307$		−	11.5459i		−	0.0376088i	0.999823	−	0.0188044i	$-0.00598598\pi$
$308$	−8.37861	−	19.5222i	−0.0272033	−	0.0633836i
$309$	449.903			1.45600
$310$	−6.49077	+	9.84905i	−0.0209380	+	0.0317711i
$311$			595.929i			1.91617i	0.286486	+	0.958084i	$0.407513\pi$
$311$			595.929i			1.91617i	−0.286486	+	0.958084i	$0.592487\pi$
$312$	493.972	+	88.5024i	1.58324	+	0.283661i
$313$	314.997			1.00638			0.503190	−	0.864176i	$-0.332159\pi$
$313$	314.997			1.00638			0.503190	+	0.864176i	$0.332159\pi$
$314$	386.293	+	254.577i	1.23023	+	0.810754i
$315$			11.7800i			0.0373967i
$316$	448.697	−	192.574i	1.41993	−	0.609410i
$317$	−332.358			−1.04845			−0.524225	−	0.851580i	$-0.675645\pi$
$317$	−332.358			−1.04845			−0.524225	+	0.851580i	$0.675645\pi$
$318$	−255.874	+	388.261i	−0.804635	+	1.22095i
$319$		−	27.2776i		−	0.0855098i
$320$	−63.5761	−	23.5367i	−0.198675	−	0.0735523i
$321$	466.587			1.45354
$322$	413.308	+	272.380i	1.28357	+	0.845901i
$323$		−	40.5579i		−	0.125566i
$324$	−141.775	−	330.337i	−0.437578	−	1.01956i
$325$	470.698			1.44830
$326$	317.693	−	482.065i	0.974518	−	1.47873i
$327$		−	248.805i		−	0.760872i
$328$	51.7776	−	288.994i	0.157858	−	0.881080i
$329$	−273.879			−0.832459
$330$	3.02816	+	1.99563i	0.00917625	+	0.00604738i
$331$			57.5914i			0.173992i	0.996209	+	0.0869961i	$0.0277268\pi$
$331$			57.5914i			0.173992i	−0.996209	+	0.0869961i	$0.972273\pi$
$332$	−157.791	+	67.7216i	−0.475275	+	0.203981i
$333$	−3.36516			−0.0101056
$334$	35.6037	−	54.0248i	0.106598	−	0.161751i
$335$			20.7090i			0.0618179i
$336$	346.297	−	364.367i	1.03065	−	1.08443i
$337$	−287.967			−0.854501			−0.427251	−	0.904133i	$-0.640518\pi$
$337$	−287.967			−0.854501			−0.427251	+	0.904133i	$0.640518\pi$
$338$	−366.707	−	241.669i	−1.08493	−	0.714996i
$339$			93.1154i			0.274677i
$340$	−5.82453	−	13.5712i	−0.0171310	−	0.0399152i
$341$	−2.99515			−0.00878344
$342$	−14.4251	+	21.8885i	−0.0421785	+	0.0640014i
$343$		−	5.20379i		−	0.0151714i
$344$	141.198	+	25.2977i	0.410459	+	0.0735398i
$345$	−84.5001			−0.244928
$346$	−130.075	−	85.7229i	−0.375940	−	0.247754i
$347$			19.4017i			0.0559127i	0.999609	+	0.0279564i	$0.00889995\pi$
$347$			19.4017i			0.0559127i	−0.999609	+	0.0279564i	$0.991100\pi$
$348$	593.121	−	254.558i	1.70437	−	0.731490i
$349$	−576.667			−1.65234			−0.826171	−	0.563420i	$-0.809485\pi$
$349$	−576.667			−1.65234			−0.826171	+	0.563420i	$0.809485\pi$
$350$	259.447	−	393.683i	0.741277	−	1.12481i
$351$			493.908i			1.40714i
$352$	−3.89304	−	16.7683i	−0.0110598	−	0.0476371i
$353$	−9.56237			−0.0270889			−0.0135444	−	0.999908i	$-0.504311\pi$
$353$	−9.56237			−0.0270889			−0.0135444	+	0.999908i	$0.504311\pi$
$354$	127.059	+	83.7351i	0.358924	+	0.236540i
$355$			59.9029i			0.168741i
$356$	−170.636	−	397.582i	−0.479315	−	1.11680i
$357$	109.505			0.306736
$358$	−32.2759	+	48.9752i	−0.0901560	+	0.136802i
$359$			293.422i			0.817331i	0.912684	+	0.408666i	$0.134006\pi$
$359$			293.422i			0.817331i	−0.912684	+	0.408666i	$0.865994\pi$
$360$	−1.68339	+	9.39574i	−0.00467607	+	0.0260993i
$361$	225.599			0.624927
$362$	356.082	+	234.667i	0.983651	+	0.648251i
$363$		−	384.126i		−	1.05820i
$364$	−715.377	+	307.029i	−1.96532	+	0.843485i
$365$	55.5771			0.152266
$366$	−294.888	+	447.461i	−0.805705	+	1.22257i
$367$		−	41.3093i		−	0.112559i	−0.998415	−	0.0562797i	$-0.982076\pi$
$367$		−	41.3093i		−	0.112559i	0.998415	−	0.0562797i	$-0.0179239\pi$
$368$	290.732	+	276.314i	0.790033	+	0.750854i
$369$	−41.3387			−0.112029
$370$	−5.28474	−	3.48277i	−0.0142831	−	0.00941290i
$371$		−	721.324i		−	1.94427i
$372$	−27.9512	−	65.1263i	−0.0751376	−	0.175071i
$373$	477.326			1.27969			0.639847	−	0.768502i	$-0.278998\pi$
$373$	477.326			1.27969			0.639847	+	0.768502i	$0.278998\pi$
$374$	2.06353	−	3.13119i	0.00551747	−	0.00837217i
$375$			164.758i			0.439354i
$376$	−218.447	−	39.1380i	−0.580975	−	0.104090i
$377$	−999.571			−2.65138
$378$	413.096	+	272.240i	1.09285	+	0.720212i
$379$			378.247i			0.998014i	0.866598	+	0.499007i	$0.166302\pi$
$379$			378.247i			0.998014i	−0.866598	+	0.499007i	$0.833698\pi$
$380$	−45.3069	+	19.4450i	−0.119229	+	0.0511711i
$381$	−616.355			−1.61773
$382$	−318.064	+	482.629i	−0.832629	+	1.26343i
$383$			71.9412i			0.187836i	0.995580	+	0.0939180i	$0.0299392\pi$
$383$			71.9412i			0.187836i	−0.995580	+	0.0939180i	$0.970061\pi$
$384$	328.277	−	241.134i	0.854888	−	0.627952i
$385$	−5.62582			−0.0146125
$386$	−468.074	−	308.473i	−1.21263	−	0.799152i
$387$		−	20.1974i		−	0.0521897i
$388$	−157.156	−	366.174i	−0.405042	−	0.943749i
$389$	624.713			1.60595			0.802973	−	0.596015i	$-0.203250\pi$
$389$	624.713			1.60595			0.802973	+	0.596015i	$0.203250\pi$
$390$	73.1288	−	110.965i	0.187510	−	0.284526i
$391$			87.3751i			0.223466i
$392$	−68.3882	+	381.705i	−0.174460	+	0.973738i
$393$	−474.053			−1.20624
$394$	502.579	+	331.212i	1.27558	+	0.840640i
$395$		−	129.304i		−	0.327351i
$396$	−2.22732	+	0.955930i	−0.00562454	+	0.00241397i
$397$	342.790			0.863451			0.431725	−	0.902005i	$-0.357905\pi$
$397$	342.790			0.863451			0.431725	+	0.902005i	$0.357905\pi$
$398$	−19.6288	+	29.7847i	−0.0493187	+	0.0748358i
$399$		−	365.579i		−	0.916238i
$400$	263.194	−	276.928i	0.657986	−	0.692319i
$401$	−166.748			−0.415832			−0.207916	−	0.978147i	$-0.566668\pi$
$401$	−166.748			−0.415832			−0.207916	+	0.978147i	$0.566668\pi$
$402$	−103.894	−	68.4685i	−0.258442	−	0.170320i
$403$			109.755i			0.272346i
$404$	238.245	+	555.111i	0.589715	+	1.37404i
$405$	−95.1952			−0.235050
$406$	−550.960	+	836.023i	−1.35704	+	2.05917i
$407$		−	1.60712i		−	0.00394869i
$408$	87.3415	+	15.6485i	0.214072	+	0.0383542i
$409$	−380.415			−0.930109			−0.465055	−	0.885282i	$-0.653965\pi$
$409$	−380.415			−0.930109			−0.465055	+	0.885282i	$0.653965\pi$
$410$	−64.9192	−	42.7834i	−0.158340	−	0.104350i
$411$		−	538.742i		−	1.31081i
$412$	−519.683	+	223.040i	−1.26137	+	0.541359i
$413$	−236.054			−0.571560
$414$	31.0764	−	47.1551i	0.0750636	−	0.113901i
$415$			45.4717i			0.109570i
$416$	−614.462	+	142.658i	−1.47707	+	0.342928i
$417$	−41.9799			−0.100671
$418$	−10.4534	−	6.88905i	−0.0250081	−	0.0164810i
$419$		−	255.872i		−	0.610673i	−0.952244	−	0.305337i	$-0.901231\pi$
$419$		−	255.872i		−	0.610673i	0.952244	−	0.305337i	$-0.0987690\pi$
$420$	−52.5009	−	122.327i	−0.125002	−	0.291255i
$421$	−510.367			−1.21227			−0.606136	−	0.795361i	$-0.707281\pi$
$421$	−510.367			−1.21227			−0.606136	+	0.795361i	$0.707281\pi$
$422$	332.111	−	503.944i	0.786994	−	1.19418i
$423$			31.2473i			0.0738708i
$424$	103.079	−	575.331i	0.243111	−	1.35691i
$425$	83.2263			0.195827
$426$	−300.523	−	198.052i	−0.705453	−	0.464911i
$427$		−	831.307i		−	1.94686i
$428$	−538.955	+	231.311i	−1.25924	+	0.540447i
$429$	33.7451			0.0786600
$430$	20.9033	−	31.7185i	0.0486123	−	0.0737640i
$431$		−	521.859i		−	1.21081i	−0.795917	−	0.605405i	$-0.793011\pi$
$431$		−	521.859i		−	1.21081i	0.795917	−	0.605405i	$-0.206989\pi$
$432$	290.583	+	276.172i	0.672645	+	0.639287i
$433$	−11.2973			−0.0260908			−0.0130454	−	0.999915i	$-0.504153\pi$
$433$	−11.2973			−0.0260908			−0.0130454	+	0.999915i	$0.504153\pi$
$434$	91.7975	+	60.4968i	0.211515	+	0.139394i
$435$		−	170.923i		−	0.392927i
$436$	123.345	+	287.395i	0.282902	+	0.659163i
$437$	291.699			0.667504
$438$	−183.750	+	278.822i	−0.419521	+	0.636579i
$439$			241.789i			0.550773i	0.961334	+	0.275387i	$0.0888059\pi$
$439$			241.789i			0.550773i	−0.961334	+	0.275387i	$0.911194\pi$
$440$	−4.48717	−	0.803943i	−0.0101981	−	0.00182714i
$441$	54.6004			0.123810
$442$	−114.741	−	75.6169i	−0.259594	−	0.171079i
$443$		−	110.660i		−	0.249797i	−0.992170	−	0.124898i	$-0.960140\pi$
$443$		−	110.660i		−	0.249797i	0.992170	−	0.124898i	$-0.0398605\pi$
$444$	34.9450	−	14.9979i	0.0787050	−	0.0337790i
$445$	−114.574			−0.257469
$446$	438.499	−	665.375i	0.983181	−	1.49187i
$447$			79.1883i			0.177155i
$448$	−219.373	+	592.558i	−0.489671	+	1.32267i
$449$	−367.458			−0.818392			−0.409196	−	0.912447i	$-0.634191\pi$
$449$	−367.458			−0.818392			−0.409196	+	0.912447i	$0.634191\pi$
$450$	−44.9160	−	29.6008i	−0.0998134	−	0.0657795i
$451$		−	19.7423i		−	0.0437745i
$452$	−46.1621	−	107.558i	−0.102128	−	0.237959i
$453$	−574.433			−1.26806
$454$	300.886	−	456.563i	0.662745	−	1.00564i
$455$			206.155i			0.453087i
$456$	52.2421	−	291.587i	0.114566	−	0.639445i
$457$	−84.4936			−0.184888			−0.0924438	−	0.995718i	$-0.529468\pi$
$457$	−84.4936			−0.184888			−0.0924438	+	0.995718i	$0.529468\pi$
$458$	341.846	+	225.285i	0.746389	+	0.491889i
$459$			87.3302i			0.190262i
$460$	97.6061	−	41.8910i	0.212187	−	0.0910674i
$461$	160.163			0.347425			0.173713	−	0.984796i	$-0.444424\pi$
$461$	160.163			0.347425			0.173713	+	0.984796i	$0.444424\pi$
$462$	18.6002	−	28.2238i	0.0402602	−	0.0610905i
$463$		−	212.442i		−	0.458837i	−0.973328	−	0.229419i	$-0.926318\pi$
$463$		−	212.442i		−	0.458837i	0.973328	−	0.229419i	$-0.0736825\pi$
$464$	−558.917	+	588.081i	−1.20456	+	1.26742i
$465$	−18.7678			−0.0403609
$466$	−144.343	−	95.1258i	−0.309750	−	0.204133i
$467$		−	180.476i		−	0.386458i	−0.981154	−	0.193229i	$-0.938104\pi$
$467$		−	180.476i		−	0.386458i	0.981154	−	0.193229i	$-0.0618960\pi$
$468$	35.0295	+	81.6186i	0.0748493	+	0.174399i
$469$	193.017			0.411550
$470$	−32.3394	+	49.0716i	−0.0688072	+	0.104408i
$471$			736.100i			1.56284i
$472$	−188.278	−	33.7327i	−0.398894	−	0.0714677i
$473$	9.64578			0.0203928
$474$	648.695	+	427.506i	1.36856	+	0.901912i
$475$		−	277.849i		−	0.584945i
$476$	−126.489	+	54.2872i	−0.265733	+	0.114049i
$477$	−82.2972			−0.172531
$478$	−302.945	+	459.687i	−0.633777	+	0.961689i
$479$		−	895.039i		−	1.86856i	−0.356545	−	0.934278i	$-0.616045\pi$
$479$		−	895.039i		−	1.86856i	0.356545	−	0.934278i	$-0.383955\pi$
$480$	−24.3941	−	105.071i	−0.0508210	−	0.218898i
$481$	−58.8918			−0.122436
$482$	136.579	+	90.0089i	0.283359	+	0.186740i
$483$			787.578i			1.63060i
$484$	190.431	+	443.704i	0.393452	+	0.916743i
$485$	−105.523			−0.217573
$486$	66.5643	−	101.004i	0.136964	−	0.207828i
$487$		−	59.9511i		−	0.123103i	−0.998104	−	0.0615515i	$-0.980395\pi$
$487$		−	59.9511i		−	0.123103i	0.998104	−	0.0615515i	$-0.0196048\pi$
$488$	118.796	−	663.054i	0.243434	−	1.35872i
$489$	918.598			1.87852
$490$	85.7458	+	56.5086i	0.174991	+	0.115324i
$491$			338.755i			0.689929i	0.938616	+	0.344965i	$0.112109\pi$
$491$			338.755i			0.689929i	−0.938616	+	0.344965i	$0.887891\pi$
$492$	429.275	−	184.238i	0.872509	−	0.374468i
$493$	−176.739			−0.358497
$494$	−252.445	+	383.058i	−0.511022	+	0.775421i
$495$			0.641860i			0.00129669i
$496$	64.5729	+	61.3706i	0.130187	+	0.123731i
$497$	558.321			1.12338
$498$	−228.124	−	150.340i	−0.458081	−	0.301887i
$499$		−	245.137i		−	0.491256i	−0.969364	−	0.245628i	$-0.921006\pi$
$499$		−	245.137i		−	0.491256i	0.969364	−	0.245628i	$-0.0789941\pi$
$500$	−81.6789	−	190.312i	−0.163358	−	0.380624i
$501$	102.947			0.205483
$502$	8.79981	−	13.3528i	0.0175295	−	0.0265992i
$503$		−	465.778i		−	0.926000i	−0.886358	−	0.463000i	$-0.846773\pi$
$503$		−	465.778i		−	0.926000i	0.886358	−	0.463000i	$-0.153227\pi$
$504$	87.5725	+	15.6899i	0.173755	+	0.0311308i
$505$	159.970			0.316772
$506$	22.5201	+	14.8413i	0.0445061	+	0.0293306i
$507$		−	698.777i		−	1.37826i
$508$	711.952	−	305.559i	1.40148	−	0.601494i
$509$	−85.6030			−0.168179			−0.0840894	−	0.996458i	$-0.526798\pi$
$509$	−85.6030			−0.168179			−0.0840894	+	0.996458i	$0.526798\pi$
$510$	12.9302	−	19.6203i	0.0253534	−	0.0384711i
$511$		−	518.003i		−	1.01371i
$512$	−259.651	+	441.277i	−0.507130	+	0.861870i
$513$	291.549			0.568322
$514$	804.137	+	529.946i	1.56447	+	1.03102i
$515$			149.760i			0.290797i
$516$	90.0158	+	209.737i	0.174449	+	0.406467i
$517$	−14.9229			−0.0288645
$518$	−32.4610	+	49.2561i	−0.0626660	+	0.0950889i
$519$		−	247.865i		−	0.477582i
$520$	−29.4600	+	164.430i	−0.0566538	+	0.316211i
$521$	540.107			1.03667			0.518337	−	0.855176i	$-0.326551\pi$
$521$	540.107			1.03667			0.518337	+	0.855176i	$0.326551\pi$
$522$	95.3834	+	62.8600i	0.182727	+	0.120421i
$523$			786.199i			1.50325i	0.659591	+	0.751625i	$0.270730\pi$
$523$			786.199i			1.50325i	−0.659591	+	0.751625i	$0.729270\pi$
$524$	547.579	−	235.012i	1.04500	−	0.448497i
$525$	750.182			1.42892
$526$	253.865	−	385.213i	0.482634	−	0.732345i
$527$			19.4064i			0.0368242i
$528$	18.8688	−	19.8534i	0.0357364	−	0.0376012i
$529$	−99.4168			−0.187933
$530$	−129.242	−	85.1734i	−0.243852	−	0.160704i
$531$			26.9319i			0.0507191i
$532$	181.236	+	422.280i	0.340669	+	0.793760i
$533$	−723.445			−1.35731
$534$	378.806	−	574.798i	0.709375	−	1.07640i
$535$			155.314i			0.290307i
$536$	153.951	+	27.5826i	0.287222	+	0.0514601i
$537$	−93.3246			−0.173789
$538$	−700.060	−	461.357i	−1.30123	−	0.857540i
$539$			26.0758i			0.0483781i
$540$	97.5559	−	41.8695i	0.180659	−	0.0775361i
$541$	713.597			1.31903			0.659516	−	0.751690i	$-0.270761\pi$
$541$	713.597			1.31903			0.659516	+	0.751690i	$0.270761\pi$
$542$	181.417	−	275.281i	0.334718	−	0.507899i
$543$			678.531i			1.24960i
$544$	−108.646	+	25.2240i	−0.199717	+	0.0463677i
$545$	82.8203			0.151964
$546$	−1034.24	−	681.592i	−1.89422	−	1.24834i
$547$			891.978i			1.63067i	0.578987	+	0.815337i	$0.303448\pi$
$547$			891.978i			1.63067i	−0.578987	+	0.815337i	$0.696552\pi$
$548$	267.082	+	622.301i	0.487376	+	1.13559i
$549$	−94.8453			−0.172760
$550$	14.1366	−	21.4508i	0.0257029	−	0.0390014i
$551$			590.037i			1.07085i
$552$	−112.547	+	628.175i	−0.203889	+	1.13800i
$553$	−1205.17			−2.17932
$554$	−704.201	−	464.086i	−1.27112	−	0.837700i
$555$		−	10.0703i		−	0.0181447i
$556$	48.4911	−	20.8116i	0.0872141	−	0.0374309i
$557$	578.550			1.03869			0.519345	−	0.854565i	$-0.326176\pi$
$557$	578.550			1.03869			0.519345	+	0.854565i	$0.326176\pi$
$558$	6.90219	−	10.4733i	0.0123695	−	0.0187694i
$559$		−	353.464i		−	0.632314i
$560$	121.288	+	115.273i	0.216585	+	0.205844i
$561$	5.96664			0.0106357
$562$	−45.3427	−	29.8819i	−0.0806809	−	0.0531707i
$563$			713.303i			1.26697i	0.773756	+	0.633484i	$0.218376\pi$
$563$			713.303i			1.26697i	−0.773756	+	0.633484i	$0.781624\pi$
$564$	−139.263	−	324.483i	−0.246920	−	0.575324i
$565$	−30.9955			−0.0548594
$566$	−7.45232	+	11.3081i	−0.0131666	+	0.0199790i
$567$			887.261i			1.56483i
$568$	445.319	+	79.7855i	0.784013	+	0.140467i
$569$	−4.65375			−0.00817882			−0.00408941	−	0.999992i	$-0.501302\pi$
$569$	−4.65375			−0.00817882			−0.00408941	+	0.999992i	$0.501302\pi$
$570$	−65.5017	−	43.1672i	−0.114915	−	0.0757320i
$571$		−	315.374i		−	0.552319i	−0.961112	−	0.276159i	$-0.910938\pi$
$571$		−	315.374i		−	0.552319i	0.961112	−	0.276159i	$-0.0890618\pi$
$572$	−38.9790	+	16.7292i	−0.0681452	+	0.0292468i
$573$	−919.672			−1.60501
$574$	−398.760	+	605.076i	−0.694704	+	1.05414i
$575$			598.578i			1.04101i
$576$	67.6060	+	25.0286i	0.117371	+	0.0434525i
$577$	122.118			0.211643			0.105822	−	0.994385i	$-0.466253\pi$
$577$	122.118			0.211643			0.105822	+	0.994385i	$0.466253\pi$
$578$	462.333	+	304.689i	0.799884	+	0.527143i
$579$		−	891.938i		−	1.54048i
$580$	84.7355	+	197.434i	0.146096	+	0.340403i
$581$	423.816			0.729460
$582$	348.881	−	529.391i	0.599453	−	0.909606i
$583$		−	39.3031i		−	0.0674153i
$584$	74.0240	−	413.161i	0.126753	−	0.707468i
$585$	23.5205			0.0402061
$586$	24.8600	+	16.3833i	0.0424231	+	0.0279579i
$587$		−	1025.99i		−	1.74785i	−0.486064	−	0.873923i	$-0.661568\pi$
$587$		−	1025.99i		−	1.74785i	0.486064	−	0.873923i	$-0.338432\pi$
$588$	−566.989	+	243.343i	−0.964267	+	0.413848i
$589$	64.7876			0.109996
$590$	−27.8731	+	42.2945i	−0.0472425	+	0.0716855i
$591$			957.689i			1.62046i
$592$	−32.9298	+	34.6481i	−0.0556247	+	0.0585271i
$593$	311.311			0.524977			0.262488	−	0.964935i	$-0.415457\pi$
$593$	311.311			0.524977			0.262488	+	0.964935i	$0.415457\pi$
$594$	22.5085	+	14.8337i	0.0378931	+	0.0249725i
$595$			36.4511i			0.0612624i
$596$	−39.2577	−	91.4705i	−0.0658686	−	0.153474i
$597$	−56.7561			−0.0950688
$598$	543.850	−	825.234i	0.909448	−	1.37999i
$599$			1032.78i			1.72417i	0.506767	+	0.862083i	$0.330841\pi$
$599$			1032.78i			1.72417i	−0.506767	+	0.862083i	$0.669159\pi$
$600$	598.348	+	107.203i	0.997247	+	0.178672i
$601$	−878.643			−1.46197			−0.730984	−	0.682394i	$-0.760939\pi$
$601$	−878.643			−1.46197			−0.730984	+	0.682394i	$0.760939\pi$
$602$	−295.631	−	194.828i	−0.491081	−	0.323634i
$603$		−	22.0217i		−	0.0365202i
$604$	663.528	−	284.776i	1.09856	−	0.471484i
$605$	127.865			0.211347
$606$	−528.895	+	802.542i	−0.872764	+	1.32433i
$607$		−	710.389i		−	1.17033i	−0.810915	−	0.585164i	$-0.801030\pi$
$607$		−	710.389i		−	1.17033i	0.810915	−	0.585164i	$-0.198970\pi$
$608$	84.2097	+	362.711i	0.138503	+	0.596565i
$609$	−1593.08			−2.61590
$610$	−148.947	−	98.1600i	−0.244176	−	0.160918i
$611$			546.842i			0.894995i
$612$	6.19372	+	14.4314i	0.0101205	+	0.0235807i
$613$	73.0735			0.119206			0.0596032	−	0.998222i	$-0.481016\pi$
$613$	73.0735			0.119206			0.0596032	+	0.998222i	$0.481016\pi$
$614$	−12.7068	+	19.2813i	−0.0206952	+	0.0314027i
$615$		−	123.707i		−	0.201149i
$616$	−7.49311	+	41.8224i	−0.0121641	+	0.0678936i
$617$	632.245			1.02471			0.512354	−	0.858774i	$-0.328774\pi$
$617$	632.245			1.02471			0.512354	+	0.858774i	$0.328774\pi$
$618$	−751.323	−	495.141i	−1.21573	−	0.801198i
$619$		−	932.513i		−	1.50648i	−0.657744	−	0.753241i	$-0.728489\pi$
$619$		−	932.513i		−	1.50648i	0.657744	−	0.753241i	$-0.271511\pi$
$620$	21.6787	−	9.30418i	0.0349657	−	0.0150067i
$621$	−628.094			−1.01142
$622$	655.849	−	995.181i	1.05442	−	1.59997i
$623$			1067.88i			1.71409i
$624$	−727.516	−	691.437i	−1.16589	−	1.10807i
$625$	542.105			0.867369
$626$	−526.035	−	346.670i	−0.840311	−	0.553786i
$627$		−	19.9194i		−	0.0317694i
$628$	−364.922	−	850.269i	−0.581087	−	1.35393i
$629$	−10.4129			−0.0165548
$630$	12.9644	−	19.6722i	0.0205785	−	0.0312256i
$631$			391.832i			0.620970i	0.950578	+	0.310485i	$0.100492\pi$
$631$			391.832i			0.620970i	−0.950578	+	0.310485i	$0.899508\pi$
$632$	−961.245	−	172.221i	−1.52096	−	0.272502i
$633$	960.289			1.51704
$634$	555.028	+	365.777i	0.875438	+	0.576935i
$635$		−	205.168i		−	0.323099i
$636$	854.602	−	366.782i	1.34371	−	0.576701i
$637$	955.530			1.50005
$638$	−30.0204	+	45.5527i	−0.0470539	+	0.0713992i
$639$		−	63.6999i		−	0.0996868i
$640$	80.2667	+	109.274i	0.125417	+	0.170741i
$641$	1095.34			1.70880			0.854398	−	0.519618i	$-0.173926\pi$
$641$	1095.34			1.70880			0.854398	+	0.519618i	$0.173926\pi$
$642$	−779.185	−	513.502i	−1.21368	−	0.799848i
$643$		−	945.580i		−	1.47058i	−0.677755	−	0.735288i	$-0.737047\pi$
$643$		−	945.580i		−	1.47058i	0.677755	−	0.735288i	$-0.262953\pi$
$644$	−390.443	−	909.732i	−0.606278	−	1.41263i
$645$	60.4411			0.0937072
$646$	−44.6359	+	67.7303i	−0.0690959	+	0.104846i
$647$		−	462.162i		−	0.714315i	−0.934044	−	0.357158i	$-0.883746\pi$
$647$		−	462.162i		−	0.714315i	0.934044	−	0.357158i	$-0.116254\pi$
$648$	−126.792	+	707.683i	−0.195666	+	1.09210i
$649$	−12.8620			−0.0198182
$650$	−786.050	−	518.027i	−1.20931	−	0.796964i
$651$			174.924i			0.268701i
$652$	−1061.07	+	455.396i	−1.62741	+	0.698461i
$653$	−184.463			−0.282485			−0.141242	−	0.989975i	$-0.545110\pi$
$653$	−184.463			−0.282485			−0.141242	+	0.989975i	$0.545110\pi$
$654$	−273.822	+	415.496i	−0.418689	+	0.635315i
$655$		−	157.799i		−	0.240915i
$656$	−404.519	+	425.627i	−0.616645	+	0.648822i
$657$	−59.0999			−0.0899543
$658$	457.369	+	301.417i	0.695089	+	0.458081i
$659$			896.791i			1.36084i	0.732824	+	0.680418i	$0.238202\pi$
$659$			896.791i			1.36084i	−0.732824	+	0.680418i	$0.761798\pi$
$660$	−2.86064	−	6.66529i	−0.00433430	−	0.0100989i
$661$	−577.087			−0.873051			−0.436526	−	0.899692i	$-0.643791\pi$
$661$	−577.087			−0.873051			−0.436526	+	0.899692i	$0.643791\pi$
$662$	63.3822	−	96.1758i	0.0957436	−	0.145281i
$663$		−	218.644i		−	0.329779i
$664$	338.037	+	60.5644i	0.509093	+	0.0912115i
$665$	121.691			0.182994
$666$	5.61971	+	3.70353i	0.00843801	+	0.00556086i
$667$		−	1271.14i		−	1.90575i
$668$	−118.914	+	51.0361i	−0.178015	+	0.0764013i
$669$	1267.90			1.89522
$670$	22.7913	−	34.5833i	0.0340168	−	0.0516169i
$671$		−	45.2958i		−	0.0675049i
$672$	−979.309	+	227.363i	−1.45730	+	0.338338i
$673$	24.8487			0.0369223			0.0184611	−	0.999830i	$-0.494123\pi$
$673$	24.8487			0.0369223			0.0184611	+	0.999830i	$0.494123\pi$
$674$	480.895	+	316.922i	0.713494	+	0.470211i
$675$			598.271i			0.886327i
$676$	346.420	+	807.158i	0.512455	+	1.19402i
$677$	87.9473			0.129907			0.0649537	−	0.997888i	$-0.479310\pi$
$677$	87.9473			0.129907			0.0649537	+	0.997888i	$0.479310\pi$
$678$	102.478	−	155.500i	0.151148	−	0.229350i
$679$			983.518i			1.44848i
$680$	−5.20896	+	29.0736i	−0.00766023	+	0.0427552i
$681$	870.002			1.27754
$682$	5.00181	+	3.29631i	0.00733403	+	0.00483331i
$683$		−	609.159i		−	0.891888i	−0.895061	−	0.445944i	$-0.852868\pi$
$683$		−	609.159i		−	0.891888i	0.895061	−	0.445944i	$-0.147132\pi$
$684$	48.1787	−	20.6776i	0.0704367	−	0.0302304i
$685$	179.332			0.261799
$686$	−5.72703	+	8.69015i	−0.00834844	+	0.0126679i
$687$			651.404i			0.948186i
$688$	−207.955	−	197.642i	−0.302260	−	0.287270i
$689$	−1440.24			−2.09033
$690$	141.112	+	92.9965i	0.204511	+	0.134778i
$691$			828.209i			1.19857i	0.800537	+	0.599283i	$0.204548\pi$
$691$			828.209i			1.19857i	−0.800537	+	0.599283i	$0.795452\pi$
$692$	122.879	+	286.309i	0.177571	+	0.413741i
$693$	5.98242			0.00863263
$694$	21.3526	−	32.4002i	0.0307674	−	0.0466862i
$695$		−	13.9740i		−	0.0201064i
$696$	−1270.65	−	227.655i	−1.82564	−	0.327091i
$697$	−127.916			−0.183523
$698$	963.015	+	634.651i	1.37968	+	0.909242i
$699$		−	275.053i		−	0.393495i
$700$	−866.536	+	371.904i	−1.23791	+	0.531291i
$701$	499.471			0.712512			0.356256	−	0.934388i	$-0.384053\pi$
$701$	499.471			0.712512			0.356256	+	0.934388i	$0.384053\pi$
$702$	543.570	−	824.810i	0.774316	−	1.17494i
$703$			34.7633i			0.0494499i
$704$	−11.9531	+	32.2869i	−0.0169788	+	0.0458621i
$705$	−93.5082			−0.132636
$706$	15.9688	+	10.5239i	0.0226188	+	0.0149063i
$707$		−	1490.99i		−	2.10889i
$708$	−120.030	−	279.670i	−0.169534	−	0.395014i
$709$	−376.981			−0.531708			−0.265854	−	0.964013i	$-0.585654\pi$
$709$	−376.981			−0.531708			−0.265854	+	0.964013i	$0.585654\pi$
$710$	65.9261	−	100.036i	0.0928537	−	0.140896i
$711$			137.500i			0.193389i
$712$	−152.602	+	851.743i	−0.214329	+	1.19627i
$713$	−139.574			−0.195756
$714$	−182.870	−	120.516i	−0.256120	−	0.168789i
$715$			11.2328i			0.0157102i
$716$	107.799	−	46.2658i	0.150558	−	0.0646170i
$717$	−875.956			−1.22170
$718$	322.925	−	490.005i	0.449757	−	0.682458i
$719$		−	153.462i		−	0.213439i	−0.994289	−	0.106719i	$-0.965965\pi$
$719$		−	153.462i		−	0.213439i	0.994289	−	0.106719i	$-0.0340346\pi$
$720$	13.1517	−	13.8379i	0.0182662	−	0.0192193i
$721$	1395.83			1.93597
$722$	−376.743	−	248.283i	−0.521804	−	0.343882i
$723$			260.258i			0.359969i
$724$	−336.383	−	783.771i	−0.464617	−	1.08256i
$725$	−1210.78			−1.67004
$726$	−422.749	+	641.477i	−0.582299	+	0.883577i
$727$		−	789.080i		−	1.08539i	−0.839929	−	0.542696i	$-0.817404\pi$
$727$		−	789.080i		−	1.08539i	0.839929	−	0.542696i	$-0.182596\pi$
$728$	1532.56	+	274.580i	2.10516	+	0.377170i
$729$	−616.352			−0.845475
$730$	−92.8120	−	61.1654i	−0.127140	−	0.0837882i
$731$		−	62.4975i		−	0.0854960i
$732$	984.906	−	422.706i	1.34550	−	0.577468i
$733$	−959.428			−1.30891			−0.654453	−	0.756103i	$-0.727101\pi$
$733$	−959.428			−1.30891			−0.654453	+	0.756103i	$0.727101\pi$
$734$	−45.4630	+	68.9852i	−0.0619386	+	0.0939853i
$735$			163.393i			0.222303i
$736$	−181.416	−	781.401i	−0.246489	−	1.06169i
$737$	10.5170			0.0142700
$738$	69.0342	+	45.4952i	0.0935423	+	0.0616467i
$739$		−	209.239i		−	0.283138i	−0.989928	−	0.141569i	$-0.954785\pi$
$739$		−	209.239i		−	0.283138i	0.989928	−	0.141569i	$-0.0452148\pi$
$740$	4.99237	+	11.6322i	0.00674645	+	0.0157192i
$741$	−729.935			−0.985068
$742$	−793.853	+	1204.59i	−1.06988	+	1.62343i
$743$			828.987i			1.11573i	0.829932	+	0.557865i	$0.188379\pi$
$743$			828.987i			1.11573i	−0.829932	+	0.557865i	$0.811621\pi$
$744$	−24.9971	+	139.520i	−0.0335983	+	0.187527i
$745$	−26.3596			−0.0353820
$746$	−797.119	−	525.321i	−1.06852	−	0.704184i
$747$		−	48.3540i		−	0.0647309i
$748$	−6.89207	+	2.95797i	−0.00921399	+	0.00395450i
$749$	1447.59			1.93270
$750$	181.324	−	275.140i	0.241766	−	0.366854i
$751$			194.602i			0.259123i	0.991571	+	0.129562i	$0.0413570\pi$
$751$			194.602i			0.259123i	−0.991571	+	0.129562i	$0.958643\pi$
$752$	321.726	+	305.771i	0.427827	+	0.406610i
$753$	25.4444			0.0337906
$754$	1669.25	+	1100.08i	2.21386	+	1.45899i
$755$		−	191.213i		−	0.253262i
$756$	−390.242	−	909.264i	−0.516193	−	1.20273i
$757$	457.841			0.604810			0.302405	−	0.953180i	$-0.402210\pi$
$757$	457.841			0.604810			0.302405	+	0.953180i	$0.402210\pi$
$758$	416.280	−	631.661i	0.549182	−	0.833326i
$759$			42.9131i			0.0565390i
$760$	97.0613	+	17.3900i	0.127712	+	0.0228815i
$761$	−94.2418			−0.123839			−0.0619197	−	0.998081i	$-0.519722\pi$
$761$	−94.2418			−0.123839			−0.0619197	+	0.998081i	$0.519722\pi$
$762$	1029.29	+	678.330i	1.35078	+	0.890196i
$763$		−	771.922i		−	1.01169i
$764$	1062.31	−	455.929i	1.39046	−	0.596765i
$765$	4.15878			0.00543631
$766$	79.1749	−	120.139i	0.103361	−	0.156840i
$767$			471.319i			0.614497i
$768$	−813.591	+	41.4002i	−1.05936	+	0.0539066i
$769$	−605.863			−0.787858			−0.393929	−	0.919141i	$-0.628884\pi$
$769$	−605.863			−0.787858			−0.393929	+	0.919141i	$0.628884\pi$
$770$	9.39493	+	6.19149i	0.0122012	+	0.00804090i
$771$			1532.32i			1.98745i
$772$	442.179	+	1030.28i	0.572771	+	1.33456i
$773$	−1024.39			−1.32522			−0.662609	−	0.748965i	$-0.730551\pi$
$773$	−1024.39			−1.32522			−0.662609	+	0.748965i	$0.730551\pi$
$774$	−22.2283	+	33.7290i	−0.0287187	+	0.0435775i
$775$			132.947i			0.171544i
$776$	−140.547	+	784.458i	−0.181118	+	1.01090i
$777$	−93.8598			−0.120798
$778$	−1043.25	−	687.528i	−1.34094	−	0.883712i
$779$			427.043i			0.548193i
$780$	−244.245	+	104.826i	−0.313135	+	0.134393i
$781$	30.4215			0.0389520
$782$	96.1606	−	145.914i	0.122968	−	0.186590i
$783$		−	1270.48i		−	1.62258i
$784$	534.292	−	562.171i	0.681495	−	0.717055i
$785$	−245.027			−0.312137
$786$	791.652	+	521.719i	1.00719	+	0.663764i
$787$		−	438.904i		−	0.557692i	−0.960336	−	0.278846i	$-0.910048\pi$
$787$		−	438.904i		−	0.557692i	0.960336	−	0.278846i	$-0.0899519\pi$
$788$	−474.776	−	1106.23i	−0.602507	−	1.40384i
$789$	734.043			0.930346
$790$	−142.305	+	215.933i	−0.180133	+	0.273333i
$791$			288.892i			0.365224i
$792$	4.77160	+	0.854902i	0.00602474	+	0.00107942i
$793$	−1659.83			−2.09311
$794$	−572.448	−	377.257i	−0.720967	−	0.475135i
$795$		−	246.276i		−	0.309781i
$796$	65.5590	−	28.1369i	0.0823606	−	0.0353479i
$797$	375.964			0.471724			0.235862	−	0.971787i	$-0.424209\pi$
$797$	375.964			0.471724			0.235862	+	0.971787i	$0.424209\pi$
$798$	−402.338	+	610.505i	−0.504183	+	0.765043i
$799$			96.6897i			0.121013i
$800$	−744.298	+	172.802i	−0.930373	+	0.216002i
$801$	121.836			0.152105
$802$	278.464	+	183.515i	0.347213	+	0.228822i
$803$		−	28.2247i		−	0.0351490i
$804$	98.1460	+	228.680i	0.122072	+	0.284428i
$805$	−262.163			−0.325668
$806$	120.791	−	183.288i	0.149865	−	0.227405i
$807$		−	1334.00i		−	1.65303i
$808$	213.066	−	1189.22i	0.263695	−	1.47180i
$809$	718.273			0.887852			0.443926	−	0.896063i	$-0.353585\pi$
$809$	718.273			0.887852			0.443926	+	0.896063i	$0.353585\pi$
$810$	158.973	+	104.767i	0.196263	+	0.129342i
$811$			164.904i			0.203334i	0.994818	+	0.101667i	$0.0324176\pi$
$811$			164.904i			0.203334i	−0.994818	+	0.101667i	$0.967582\pi$
$812$	1840.17	−	789.772i	2.26622	−	0.972626i
$813$	524.562			0.645218
$814$	−1.76871	+	2.68384i	−0.00217287	+	0.00329710i
$815$			305.776i			0.375185i
$816$	−128.635	−	122.256i	−0.157641	−	0.149824i
$817$	−208.646			−0.255381
$818$	635.280	+	418.665i	0.776626	+	0.511816i
$819$		−	219.222i		−	0.267670i
$820$	61.3277	+	142.894i	0.0747899	+	0.174261i
$821$	−666.985			−0.812406			−0.406203	−	0.913783i	$-0.633147\pi$
$821$	−666.985			−0.812406			−0.406203	+	0.913783i	$0.633147\pi$
$822$	−592.912	+	899.681i	−0.721304	+	1.09450i
$823$		−	176.822i		−	0.214851i	−0.994213	−	0.107426i	$-0.965739\pi$
$823$		−	176.822i		−	0.214851i	0.994213	−	0.107426i	$-0.0342607\pi$
$824$	1113.32	+	199.468i	1.35112	+	0.242073i
$825$	40.8755			0.0495461
$826$	394.203	+	259.790i	0.477243	+	0.314515i
$827$		−	819.060i		−	0.990400i	−0.868779	−	0.495200i	$-0.835095\pi$
$827$		−	819.060i		−	0.990400i	0.868779	−	0.495200i	$-0.164905\pi$
$828$	−103.793	+	44.5463i	−0.125354	+	0.0537999i
$829$	−263.605			−0.317979			−0.158990	−	0.987280i	$-0.550824\pi$
$829$	−263.605			−0.317979			−0.158990	+	0.987280i	$0.550824\pi$
$830$	50.0439	−	75.9363i	0.0602938	−	0.0914895i
$831$		−	1341.89i		−	1.61479i
$832$	1183.13	+	438.012i	1.42204	+	0.526457i
$833$	168.952			0.202823
$834$	70.1051	+	46.2010i	0.0840589	+	0.0553969i
$835$			34.2682i			0.0410397i
$836$	9.87509	+	23.0090i	0.0118123	+	0.0275227i
$837$	−139.502			−0.166669
$838$	−281.600	+	427.298i	−0.336038	+	0.509902i
$839$			1467.95i			1.74964i	0.484448	+	0.874820i	$0.339020\pi$
$839$			1467.95i			1.74964i	−0.484448	+	0.874820i	$0.660980\pi$
$840$	−46.9523	+	262.062i	−0.0558956	+	0.311979i
$841$	1730.20			2.05732
$842$	852.296	+	561.684i	1.01223	+	0.667083i
$843$		−	86.4026i		−	0.102494i
$844$	−1109.23	+	476.064i	−1.31425	+	0.564057i
$845$	232.604			0.275271
$846$	34.3892	−	52.1820i	0.0406492	−	0.0616809i
$847$		−	1191.76i		−	1.40703i
$848$	−805.319	+	847.340i	−0.949668	+	0.999222i
$849$	−21.5481			−0.0253806
$850$	−138.985	−	91.5947i	−0.163512	−	0.107758i
$851$		−	74.8917i		−	0.0880044i
$852$	283.898	+	661.481i	0.333213	+	0.776387i
$853$	210.670			0.246976			0.123488	−	0.992346i	$-0.460592\pi$
$853$	210.670			0.246976			0.123488	+	0.992346i	$0.460592\pi$
$854$	−914.895	+	1388.26i	−1.07131	+	1.62559i
$855$		−	13.8840i		−	0.0162385i
$856$	1154.61	+	206.865i	1.34884	+	0.241665i
$857$	471.554			0.550238			0.275119	−	0.961410i	$-0.411283\pi$
$857$	471.554			0.550238			0.275119	+	0.961410i	$0.411283\pi$
$858$	−56.3533	−	37.1382i	−0.0656798	−	0.0432846i
$859$			686.837i			0.799577i	0.916607	+	0.399789i	$0.130916\pi$
$859$			686.837i			0.799577i	−0.916607	+	0.399789i	$0.869084\pi$
$860$	−69.8156	+	29.9638i	−0.0811809	+	0.0348416i
$861$	−1153.00			−1.33914
$862$	−574.332	+	871.488i	−0.666279	+	1.01101i
$863$			702.758i			0.814319i	0.913357	+	0.407160i	$0.133481\pi$
$863$			702.758i			0.814319i	−0.913357	+	0.407160i	$0.866519\pi$
$864$	−181.322	−	780.999i	−0.209864	−	0.903934i
$865$	82.5073			0.0953842
$866$	18.8662	+	12.4333i	0.0217854	+	0.0143571i
$867$			880.997i			1.01614i
$868$	−86.7190	−	202.055i	−0.0999067	−	0.232783i
$869$	−65.6664			−0.0755655
$870$	−188.110	+	285.436i	−0.216218	+	0.328088i
$871$		−	385.389i		−	0.442467i
$872$	110.310	−	615.688i	0.126502	−	0.706064i
$873$	112.211			0.128535
$874$	−487.128	−	321.029i	−0.557355	−	0.367311i
$875$			511.164i			0.584188i
$876$	613.714	−	263.396i	0.700587	−	0.300681i
$877$	−559.485			−0.637953			−0.318977	−	0.947763i	$-0.603339\pi$
$877$	−559.485			−0.637953			−0.318977	+	0.947763i	$0.603339\pi$
$878$	266.101	−	403.780i	0.303077	−	0.459887i
$879$			47.3718i			0.0538929i
$880$	6.60865	+	6.28092i	0.00750983	+	0.00713740i
$881$	935.168			1.06148			0.530742	−	0.847533i	$-0.321913\pi$
$881$	935.168			1.06148			0.530742	+	0.847533i	$0.321913\pi$
$882$	−91.1808	−	60.0904i	−0.103380	−	0.0681297i
$883$		−	1394.76i		−	1.57957i	−0.613384	−	0.789785i	$-0.710192\pi$
$883$		−	1394.76i		−	1.57957i	0.613384	−	0.789785i	$-0.289808\pi$
$884$	108.393	+	252.555i	0.122616	+	0.285696i
$885$	−80.5941			−0.0910668
$886$	−121.787	+	184.799i	−0.137457	+	0.208576i
$887$			468.687i			0.528395i	0.964469	+	0.264198i	$0.0851071\pi$
$887$			468.687i			0.528395i	−0.964469	+	0.264198i	$0.914893\pi$
$888$	−74.8629	−	13.4128i	−0.0843051	−	0.0151045i
$889$	−1912.25			−2.15102
$890$	191.334	+	126.094i	0.214982	+	0.141679i
$891$			48.3446i			0.0542588i
$892$	−1464.56	+	628.565i	−1.64188	+	0.704669i
$893$	322.796			0.361473
$894$	87.1507	−	132.242i	0.0974840	−	0.147922i
$895$		−	31.0652i		−	0.0347097i
$896$	1018.48	−	748.121i	1.13670	−	0.834957i
$897$	1572.52			1.75309
$898$	613.643	+	404.406i	0.683344	+	0.450341i
$899$		−	282.325i		−	0.314043i
$900$	42.4312	+	98.8647i	0.0471458	+	0.109850i
$901$	−254.655			−0.282636
$902$	−21.7274	+	32.9690i	−0.0240880	+	0.0365510i
$903$		−	563.338i		−	0.623852i
$904$	−41.2834	+	230.421i	−0.0456675	+	0.254891i
$905$	−225.864			−0.249574
$906$	959.285	+	632.193i	1.05881	+	0.697784i
$907$			1174.62i			1.29506i	0.762039	+	0.647531i	$0.224198\pi$
$907$			1174.62i			1.29506i	−0.762039	+	0.647531i	$0.775802\pi$
$908$	−1004.94	+	431.305i	−1.10676	+	0.475005i
$909$	−170.110			−0.187139
$910$	226.883	−	344.271i	0.249322	−	0.378320i
$911$			1790.47i			1.96539i	0.185236	+	0.982694i	$0.440695\pi$
$911$			1790.47i			1.96539i	−0.185236	+	0.982694i	$0.559305\pi$
$912$	−408.149	+	429.446i	−0.447531	+	0.470883i
$913$	23.0927			0.0252932
$914$	141.102	+	92.9894i	0.154378	+	0.101739i
$915$		−	283.826i		−	0.310193i
$916$	−322.934	−	752.437i	−0.352548	−	0.821438i
$917$	−1470.76			−1.60388
$918$	96.1112	−	145.838i	0.104696	−	0.158865i
$919$		−	434.097i		−	0.472358i	−0.971710	−	0.236179i	$-0.924105\pi$
$919$		−	434.097i		−	0.472358i	0.971710	−	0.236179i	$-0.0758951\pi$
$920$	−209.102	−	37.4637i	−0.227285	−	0.0407215i
$921$	−36.7414			−0.0398929
$922$	−267.467	−	176.267i	−0.290094	−	0.191179i
$923$		−	1114.78i		−	1.20777i
$924$	−62.1234	+	26.6624i	−0.0672332	+	0.0288554i
$925$	−71.3357			−0.0771197
$926$	−233.803	+	354.771i	−0.252487	+	0.383122i
$927$		−	159.253i		−	0.171794i
$928$	1580.59	−	366.960i	1.70322	−	0.395431i
$929$	1069.25			1.15097			0.575484	−	0.817813i	$-0.304814\pi$
$929$	1069.25			1.15097			0.575484	+	0.817813i	$0.304814\pi$
$930$	31.3417	+	20.6549i	0.0337007	+	0.0222096i
$931$		−	564.041i		−	0.605844i
$932$	136.358	+	317.714i	0.146307	+	0.340895i
$933$	1896.36			2.03255
$934$	−198.623	+	301.389i	−0.212658	+	0.322686i
$935$			1.98613i			0.00212420i
$936$	31.3273	−	174.852i	0.0334694	−	0.186808i
$937$	−287.842			−0.307195			−0.153597	−	0.988134i	$-0.549086\pi$
$937$	−287.842			−0.307195			−0.153597	+	0.988134i	$0.549086\pi$
$938$	−322.332	−	212.425i	−0.343637	−	0.226466i
$939$		−	1002.38i		−	1.06750i
$940$	108.011	−	46.3568i	0.114906	−	0.0493158i
$941$	1012.35			1.07583			0.537913	−	0.843001i	$-0.319213\pi$
$941$	1012.35			1.07583			0.537913	+	0.843001i	$0.319213\pi$
$942$	810.114	−	1229.26i	0.859994	−	1.30495i
$943$		−	919.992i		−	0.975601i
$944$	277.293	+	263.542i	0.293743	+	0.279175i
$945$	−262.028			−0.277279
$946$	−16.1081	−	10.6157i	−0.0170276	−	0.0112216i
$947$			671.318i			0.708889i	0.935077	+	0.354445i	$0.115330\pi$
$947$			671.318i			0.708889i	−0.935077	+	0.354445i	$0.884670\pi$
$948$	−612.808	−	1427.84i	−0.646422	−	1.50616i
$949$	−1034.27			−1.08986
$950$	−305.786	+	463.998i	−0.321880	+	0.488419i
$951$			1057.63i			1.11213i
$952$	270.978	+	48.5498i	0.284641	+	0.0509977i
$953$	1438.62			1.50957			0.754784	−	0.655973i	$-0.227742\pi$
$953$	1438.62			1.50957			0.754784	+	0.655973i	$0.227742\pi$
$954$	137.434	+	90.5722i	0.144060	+	0.0949394i
$955$		−	306.134i		−	0.320559i
$956$	1011.82	−	434.256i	1.05839	−	0.454243i
$957$	−86.8029			−0.0907031
$958$	−985.034	+	1494.68i	−1.02822	+	1.56021i
$959$		−	1671.46i		−	1.74292i
$960$	−74.8987	+	202.312i	−0.0780194	+	0.210742i
$961$	−31.0000			−0.0322581
$962$	98.3475	+	64.8134i	0.102232	+	0.0673736i
$963$		−	165.159i		−	0.171504i
$964$	−129.023	−	300.624i	−0.133841	−	0.311850i
$965$	296.902			0.307670
$966$	866.769	−	1315.23i	0.897276	−	1.36152i
$967$			655.956i			0.678341i	0.940725	+	0.339170i	$0.110146\pi$
$967$			655.956i			0.678341i	−0.940725	+	0.339170i	$0.889854\pi$
$968$	170.305	−	950.549i	0.175935	−	0.981972i
$969$	−129.063			−0.133192
$970$	176.219	+	116.133i	0.181670	+	0.119725i
$971$		−	1381.59i		−	1.42285i	−0.702761	−	0.711426i	$-0.748050\pi$
$971$		−	1381.59i		−	1.42285i	0.702761	−	0.711426i	$-0.251950\pi$
$972$	−222.320	+	95.4165i	−0.228725	+	0.0981651i
$973$	−130.243			−0.133858
$974$	−65.9792	+	100.116i	−0.0677405	+	0.102789i
$975$		−	1497.86i		−	1.53626i
$976$	−928.109	+	976.537i	−0.950931	+	1.00055i
$977$	−1039.06			−1.06352			−0.531760	−	0.846895i	$-0.678469\pi$
$977$	−1039.06			−1.06352			−0.531760	+	0.846895i	$0.678469\pi$
$978$	−1534.03	−	1010.96i	−1.56854	−	1.03370i
$979$			58.1859i			0.0594340i
$980$	−81.0021	−	188.735i	−0.0826552	−	0.192587i
$981$	−88.0700			−0.0897757
$982$	372.817	−	565.710i	0.379651	−	0.576079i
$983$			604.601i			0.615057i	0.951539	+	0.307529i	$0.0995019\pi$
$983$			604.601i			0.615057i	−0.951539	+	0.307529i	$0.900498\pi$
$984$	−919.638	−	164.767i	−0.934591	−	0.167446i
$985$	−318.788			−0.323643
$986$	295.148	+	194.510i	0.299339	+	0.197272i
$987$			871.538i			0.883017i
$988$	843.149	−	361.866i	0.853389	−	0.366261i
$989$	449.493			0.454493
$990$	0.706399	−	1.07188i	0.000713534	−	0.00108271i
$991$		−	851.190i		−	0.858920i	−0.903086	−	0.429460i	$-0.858704\pi$
$991$		−	851.190i		−	0.858920i	0.903086	−	0.429460i	$-0.141296\pi$
$992$	−40.2932	−	173.552i	−0.0406181	−	0.174952i
$993$	183.268			0.184560
$994$	−932.378	−	614.460i	−0.938006	−	0.618169i
$995$		−	18.8925i		−	0.0189875i
$996$	215.504	+	502.124i	0.216369	+	0.504141i
$997$	−871.723			−0.874346			−0.437173	−	0.899377i	$-0.644020\pi$
$997$	−871.723			−0.874346			−0.437173	+	0.899377i	$0.644020\pi$
$998$	−269.785	+	409.370i	−0.270326	+	0.410191i
$999$		−	74.8532i		−	0.0749281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.5	✓	30
4.3	odd	2	inner	124.3.b.a.63.6	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.5	✓	30	1.1	even	1	trivial
124.3.b.a.63.6	yes	30	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66997 - 1.10055i) q^{2} -3.18220i q^{3} +(1.57758 + 3.67576i) q^{4} +1.05927 q^{5} +(-3.50217 + 5.31417i) q^{6} -9.87284i q^{7} +(1.41085 - 7.87461i) q^{8} -1.12641 q^{9} +O(q^{10})\)	\(q+(-1.66997 - 1.10055i) q^{2} -3.18220i q^{3} +(1.57758 + 3.67576i) q^{4} +1.05927 q^{5} +(-3.50217 + 5.31417i) q^{6} -9.87284i q^{7} +(1.41085 - 7.87461i) q^{8} -1.12641 q^{9} +(-1.76894 - 1.16578i) q^{10} -0.537945i q^{11} +(11.6970 - 5.02018i) q^{12} -19.7127 q^{13} +(-10.8655 + 16.4873i) q^{14} -3.37080i q^{15} +(-11.0225 + 11.5976i) q^{16} -3.48549 q^{17} +(1.88107 + 1.23967i) q^{18} +11.6362i q^{19} +(1.67108 + 3.89362i) q^{20} -31.4174 q^{21} +(-0.592036 + 0.898351i) q^{22} -25.0682i q^{23} +(-25.0586 - 4.48962i) q^{24} -23.8780 q^{25} +(32.9195 + 21.6948i) q^{26} -25.0554i q^{27} +(36.2902 - 15.5752i) q^{28} +50.7070 q^{29} +(-3.70974 + 5.62913i) q^{30} -5.56776i q^{31} +(31.1709 - 7.23687i) q^{32} -1.71185 q^{33} +(5.82065 + 3.83595i) q^{34} -10.4580i q^{35} +(-1.77700 - 4.14042i) q^{36} +2.98751 q^{37} +(12.8062 - 19.4321i) q^{38} +62.7297i q^{39} +(1.49447 - 8.34132i) q^{40} +36.6995 q^{41} +(52.4660 + 34.5764i) q^{42} +17.9308i q^{43} +(1.97736 - 0.848652i) q^{44} -1.19317 q^{45} +(-27.5888 + 41.8631i) q^{46} -27.7406i q^{47} +(36.9060 + 35.0758i) q^{48} -48.4729 q^{49} +(39.8754 + 26.2789i) q^{50} +11.0915i q^{51} +(-31.0983 - 72.4591i) q^{52} +73.0615 q^{53} +(-27.5747 + 41.8416i) q^{54} -0.569828i q^{55} +(-77.7448 - 13.9291i) q^{56} +37.0287 q^{57} +(-84.6791 - 55.8056i) q^{58} -23.9095i q^{59} +(12.3903 - 5.31771i) q^{60} +84.2014 q^{61} +(-6.12760 + 9.29798i) q^{62} +11.1209i q^{63} +(-60.0190 - 22.2198i) q^{64} -20.8810 q^{65} +(2.85873 + 1.88398i) q^{66} +19.5503i q^{67} +(-5.49864 - 12.8118i) q^{68} -79.7722 q^{69} +(-11.5095 + 17.4645i) q^{70} +56.5513i q^{71} +(-1.58920 + 8.87004i) q^{72} +52.4675 q^{73} +(-4.98905 - 3.28791i) q^{74} +75.9845i q^{75} +(-42.7719 + 18.3570i) q^{76} -5.31105 q^{77} +(69.0371 - 104.757i) q^{78} -122.069i q^{79} +(-11.6758 + 12.2850i) q^{80} -89.8689 q^{81} +(-61.2869 - 40.3896i) q^{82} +42.9275i q^{83} +(-49.5634 - 115.483i) q^{84} -3.69206 q^{85} +(19.7337 - 29.9438i) q^{86} -161.360i q^{87} +(-4.23611 - 0.758962i) q^{88} -108.163 q^{89} +(1.99255 + 1.31314i) q^{90} +194.620i q^{91} +(92.1449 - 39.5472i) q^{92} -17.7178 q^{93} +(-30.5300 + 46.3260i) q^{94} +12.3258i q^{95} +(-23.0292 - 99.1922i) q^{96} -99.6186 q^{97} +(80.9482 + 53.3469i) q^{98} +0.605947i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

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