LMFDB - Embedded newform 76.2.k.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	76.71
Dual form			76.2.k.a.15.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647187 - 1.25744i) q^{2} +(0.547993 - 3.10782i) q^{3} +(-1.16230 + 1.62759i) q^{4} +(1.46633 + 1.23040i) q^{5} +(-4.26255 + 1.32228i) q^{6} +(-1.58907 + 0.917452i) q^{7} +(2.79882 + 0.408157i) q^{8} +(-6.53918 - 2.38007i) q^{9} +O(q^{10})$	\(q+(-0.647187 - 1.25744i) q^{2} +(0.547993 - 3.10782i) q^{3} +(-1.16230 + 1.62759i) q^{4} +(1.46633 + 1.23040i) q^{5} +(-4.26255 + 1.32228i) q^{6} +(-1.58907 + 0.917452i) q^{7} +(2.79882 + 0.408157i) q^{8} +(-6.53918 - 2.38007i) q^{9} +(0.598159 - 2.64012i) q^{10} +(2.10674 + 1.21633i) q^{11} +(4.42134 + 4.50412i) q^{12} +(2.49843 - 0.440541i) q^{13} +(2.18207 + 1.40440i) q^{14} +(4.62741 - 3.88286i) q^{15} +(-1.29813 - 3.78350i) q^{16} +(0.818624 - 0.297955i) q^{17} +(1.23929 + 9.76296i) q^{18} +(-4.35874 + 0.0369281i) q^{19} +(-3.70691 + 0.956507i) q^{20} +(1.98048 + 5.44131i) q^{21} +(0.165999 - 3.43628i) q^{22} +(4.69241 + 5.59220i) q^{23} +(2.80221 - 8.47457i) q^{24} +(-0.231990 - 1.31568i) q^{25} +(-2.17091 - 2.85651i) q^{26} +(-6.24660 + 10.8194i) q^{27} +(0.353735 - 3.65272i) q^{28} +(-0.967934 + 2.65938i) q^{29} +(-7.87725 - 3.30574i) q^{30} +(-2.07350 - 3.59141i) q^{31} +(-3.91738 + 4.08095i) q^{32} +(4.93460 - 5.88083i) q^{33} +(-0.904462 - 0.836536i) q^{34} +(-3.45895 - 0.609906i) q^{35} +(11.4743 - 7.87679i) q^{36} +1.48548i q^{37} +(2.86736 + 5.45695i) q^{38} -8.00610i q^{39} +(3.60181 + 4.04217i) q^{40} +(-1.43355 - 0.252774i) q^{41} +(5.56037 - 6.01187i) q^{42} +(-5.26751 + 6.27757i) q^{43} +(-4.42834 + 2.01518i) q^{44} +(-6.66019 - 11.5358i) q^{45} +(3.99497 - 9.51961i) q^{46} +(0.855159 - 2.34953i) q^{47} +(-12.4698 + 1.96103i) q^{48} +(-1.81656 + 3.14638i) q^{49} +(-1.50424 + 1.14320i) q^{50} +(-0.477390 - 2.70741i) q^{51} +(-2.18690 + 4.57848i) q^{52} +(-1.18928 - 1.41733i) q^{53} +(17.6475 + 0.852512i) q^{54} +(1.59262 + 4.37567i) q^{55} +(-4.82200 + 1.91919i) q^{56} +(-2.27379 + 13.5664i) q^{57} +(3.97043 - 0.503998i) q^{58} +(6.43248 - 2.34123i) q^{59} +(0.941293 + 12.0446i) q^{60} +(-8.58916 + 7.20716i) q^{61} +(-3.17403 + 4.93161i) q^{62} +(12.5748 - 2.21728i) q^{63} +(7.66682 + 2.28472i) q^{64} +(4.20558 + 2.42810i) q^{65} +(-10.5884 - 2.39896i) q^{66} +(2.59900 + 0.945959i) q^{67} +(-0.466535 + 1.67870i) q^{68} +(19.9510 - 11.5187i) q^{69} +(1.47167 + 4.74413i) q^{70} +(-6.12140 - 5.13647i) q^{71} +(-17.3306 - 9.33040i) q^{72} +(2.02346 - 11.4756i) q^{73} +(1.86790 - 0.961383i) q^{74} -4.21603 q^{75} +(5.00605 - 7.13719i) q^{76} -4.46368 q^{77} +(-10.0672 + 5.18145i) q^{78} +(-0.908863 + 5.15442i) q^{79} +(2.75173 - 7.14509i) q^{80} +(14.2094 + 11.9231i) q^{81} +(0.609929 + 1.96619i) q^{82} +(8.19927 - 4.73385i) q^{83} +(-11.1582 - 3.10101i) q^{84} +(1.56698 + 0.570334i) q^{85} +(11.3027 + 2.56080i) q^{86} +(7.73445 + 4.46548i) q^{87} +(5.39994 + 4.26416i) q^{88} +(-6.18655 + 1.09085i) q^{89} +(-10.1951 + 15.8406i) q^{90} +(-3.56602 + 2.99225i) q^{91} +(-14.5558 + 1.13755i) q^{92} +(-12.2977 + 4.47601i) q^{93} +(-3.50784 + 0.445277i) q^{94} +(-6.43681 - 5.30885i) q^{95} +(10.5362 + 14.4108i) q^{96} +(-2.11617 - 5.81414i) q^{97} +(5.13204 + 0.247918i) q^{98} +(-10.8814 - 12.9680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.647187	−	1.25744i	−0.457631	−	0.889142i
$2$	−0.647187	−	1.25744i	−0.457631	−	0.889142i
$3$	0.547993	−	3.10782i	0.316384	−	1.79430i	−0.247969	−	0.968768i	$-0.579763\pi$
$3$	0.547993	−	3.10782i	0.316384	−	1.79430i	0.564353	−	0.825534i	$-0.309126\pi$
$4$	−1.16230	+	1.62759i	−0.581149	+	0.813797i
$5$	1.46633	+	1.23040i	0.655765	+	0.550252i	0.908814	−	0.417201i	$-0.136989\pi$
$5$	1.46633	+	1.23040i	0.655765	+	0.550252i	−0.253049	+	0.967453i	$0.581433\pi$
$6$	−4.26255	+	1.32228i	−1.74018	+	0.539817i
$7$	−1.58907	+	0.917452i	−0.600613	+	0.346764i	−0.769283	−	0.638909i	$-0.779386\pi$
$7$	−1.58907	+	0.917452i	−0.600613	+	0.346764i	0.168670	+	0.985673i	$0.446053\pi$
$8$	2.79882	+	0.408157i	0.989533	+	0.144305i
$9$	−6.53918	−	2.38007i	−2.17973	−	0.793356i
$10$	0.598159	−	2.64012i	0.189154	−	0.834880i
$11$	2.10674	+	1.21633i	0.635206	+	0.366736i	0.782765	−	0.622317i	$-0.213809\pi$
$11$	2.10674	+	1.21633i	0.635206	+	0.366736i	−0.147560	+	0.989053i	$0.547142\pi$
$12$	4.42134	+	4.50412i	1.27633	+	1.30023i
$13$	2.49843	−	0.440541i	0.692941	−	0.122184i	0.183924	−	0.982940i	$-0.441120\pi$
$13$	2.49843	−	0.440541i	0.692941	−	0.122184i	0.509017	+	0.860756i	$0.330009\pi$
$14$	2.18207	+	1.40440i	0.583182	+	0.375341i
$15$	4.62741	−	3.88286i	1.19479	−	1.00255i
$16$	−1.29813	−	3.78350i	−0.324533	−	0.945875i
$17$	0.818624	−	0.297955i	0.198545	−	0.0722646i	−0.240833	−	0.970566i	$-0.577421\pi$
$17$	0.818624	−	0.297955i	0.198545	−	0.0722646i	0.439379	+	0.898302i	$0.355199\pi$
$18$	1.23929	+	9.76296i	0.292103	+	2.30115i
$19$	−4.35874	+	0.0369281i	−0.999964	+	0.00847188i
$19$	−4.35874	+	0.0369281i	−0.999964	+	0.00847188i
$20$	−3.70691	+	0.956507i	−0.828890	+	0.213882i
$21$	1.98048	+	5.44131i	0.432175	+	1.18739i
$22$	0.165999	−	3.43628i	0.0353912	−	0.732618i
$23$	4.69241	+	5.59220i	0.978436	+	1.16605i	0.986112	+	0.166084i	$0.0531121\pi$
$23$	4.69241	+	5.59220i	0.978436	+	1.16605i	−0.00767613	+	0.999971i	$0.502443\pi$
$24$	2.80221	−	8.47457i	0.572000	−	1.72987i
$25$	−0.231990	−	1.31568i	−0.0463980	−	0.263136i
$26$	−2.17091	−	2.85651i	−0.425750	−	0.560208i
$27$	−6.24660	+	10.8194i	−1.20216	+	2.08220i
$28$	0.353735	−	3.65272i	0.0668497	−	0.690299i
$29$	−0.967934	+	2.65938i	−0.179741	+	0.493834i	−0.996542	−	0.0830848i	$-0.973523\pi$
$29$	−0.967934	+	2.65938i	−0.179741	+	0.493834i	0.816802	+	0.576918i	$0.195745\pi$
$30$	−7.87725	−	3.30574i	−1.43818	−	0.603543i
$31$	−2.07350	−	3.59141i	−0.372412	−	0.645036i	0.617524	−	0.786552i	$-0.288136\pi$
$31$	−2.07350	−	3.59141i	−0.372412	−	0.645036i	−0.989936	+	0.141516i	$0.954802\pi$
$32$	−3.91738	+	4.08095i	−0.692501	+	0.721417i
$33$	4.93460	−	5.88083i	0.859004	−	1.02372i
$34$	−0.904462	−	0.836536i	−0.155114	−	0.143465i
$35$	−3.45895	−	0.609906i	−0.584669	−	0.103093i
$36$	11.4743	−	7.87679i	1.91238	−	1.31280i
$37$			1.48548i			0.244211i	0.992517	+	0.122106i	$0.0389646\pi$
$37$			1.48548i			0.244211i	−0.992517	+	0.122106i	$0.961035\pi$
$38$	2.86736	+	5.45695i	0.465147	+	0.885234i
$39$		−	8.00610i		−	1.28200i
$40$	3.60181	+	4.04217i	0.569497	+	0.639123i
$41$	−1.43355	−	0.252774i	−0.223883	−	0.0394766i	0.0605811	−	0.998163i	$-0.480705\pi$
$41$	−1.43355	−	0.252774i	−0.223883	−	0.0394766i	−0.284464	+	0.958687i	$0.591816\pi$
$42$	5.56037	−	6.01187i	0.857984	−	0.927652i
$43$	−5.26751	+	6.27757i	−0.803288	+	0.957321i	−0.999731	−	0.0231942i	$-0.992616\pi$
$43$	−5.26751	+	6.27757i	−0.803288	+	0.957321i	0.196443	+	0.980515i	$0.437061\pi$
$44$	−4.42834	+	2.01518i	−0.667598	+	0.303801i
$45$	−6.66019	−	11.5358i	−0.992843	−	1.71965i
$46$	3.99497	−	9.51961i	0.589026	−	1.40359i
$47$	0.855159	−	2.34953i	0.124738	−	0.342714i	−0.861568	−	0.507643i	$-0.830517\pi$
$47$	0.855159	−	2.34953i	0.124738	−	0.342714i	0.986306	+	0.164928i	$0.0527393\pi$
$48$	−12.4698	+	1.96103i	−1.79986	+	0.283050i
$49$	−1.81656	+	3.14638i	−0.259509	+	0.449483i
$50$	−1.50424	+	1.14320i	−0.212732	+	0.161673i
$51$	−0.477390	−	2.70741i	−0.0668480	−	0.379114i
$52$	−2.18690	+	4.57848i	−0.303269	+	0.634921i
$53$	−1.18928	−	1.41733i	−0.163360	−	0.194685i	0.678154	−	0.734919i	$-0.262780\pi$
$53$	−1.18928	−	1.41733i	−0.163360	−	0.194685i	−0.841515	+	0.540234i	$0.818336\pi$
$54$	17.6475	+	0.852512i	2.40152	+	0.116012i
$55$	1.59262	+	4.37567i	0.214748	+	0.590016i
$56$	−4.82200	+	1.91919i	−0.644367	+	0.256463i
$57$	−2.27379	+	13.5664i	−0.301171	+	1.79692i
$58$	3.97043	−	0.503998i	0.521343	−	0.0661782i
$59$	6.43248	−	2.34123i	0.837437	−	0.304802i	0.112530	−	0.993648i	$-0.464105\pi$
$59$	6.43248	−	2.34123i	0.837437	−	0.304802i	0.724907	+	0.688846i	$0.241882\pi$
$60$	0.941293	+	12.0446i	0.121520	+	1.55495i
$61$	−8.58916	+	7.20716i	−1.09973	+	0.922782i	−0.997407	−	0.0719693i	$-0.977072\pi$
$61$	−8.58916	+	7.20716i	−1.09973	+	0.922782i	−0.102322	+	0.994751i	$0.532627\pi$
$62$	−3.17403	+	4.93161i	−0.403102	+	0.626316i
$63$	12.5748	−	2.21728i	1.58428	−	0.279351i
$64$	7.66682	+	2.28472i	0.958352	+	0.285590i
$65$	4.20558	+	2.42810i	0.521639	+	0.301168i
$66$	−10.5884	−	2.39896i	−1.30334	−	0.295291i
$67$	2.59900	+	0.945959i	0.317519	+	0.115567i	0.495863	−	0.868401i	$-0.334852\pi$
$67$	2.59900	+	0.945959i	0.317519	+	0.115567i	−0.178344	+	0.983968i	$0.557074\pi$
$68$	−0.466535	+	1.67870i	−0.0565756	+	0.203572i
$69$	19.9510	−	11.5187i	2.40181	−	1.38669i
$70$	1.47167	+	4.74413i	0.175898	+	0.567032i
$71$	−6.12140	−	5.13647i	−0.726477	−	0.609587i	0.202692	−	0.979243i	$-0.435031\pi$
$71$	−6.12140	−	5.13647i	−0.726477	−	0.609587i	−0.929169	+	0.369656i	$0.879476\pi$
$72$	−17.3306	−	9.33040i	−2.04243	−	1.09960i
$73$	2.02346	−	11.4756i	0.236828	−	1.34312i	−0.601902	−	0.798570i	$-0.705590\pi$
$73$	2.02346	−	11.4756i	0.236828	−	1.34312i	0.838730	−	0.544547i	$-0.183299\pi$
$74$	1.86790	−	0.961383i	0.217138	−	0.111758i
$75$	−4.21603			−0.486825
$76$	5.00605	−	7.13719i	0.574233	−	0.818692i
$77$	−4.46368			−0.508684
$78$	−10.0672	+	5.18145i	−1.13988	+	0.586684i
$79$	−0.908863	+	5.15442i	−0.102255	+	0.579918i	0.890026	+	0.455910i	$0.150686\pi$
$79$	−0.908863	+	5.15442i	−0.102255	+	0.579918i	−0.992281	+	0.124008i	$0.960425\pi$
$80$	2.75173	−	7.14509i	0.307652	−	0.798846i
$81$	14.2094	+	11.9231i	1.57882	+	1.32479i
$82$	0.609929	+	1.96619i	0.0673554	+	0.217130i
$83$	8.19927	−	4.73385i	0.899987	−	0.519608i	0.0227911	−	0.999740i	$-0.492745\pi$
$83$	8.19927	−	4.73385i	0.899987	−	0.519608i	0.877196	+	0.480132i	$0.159411\pi$
$84$	−11.1582	−	3.10101i	−1.21745	−	0.338348i
$85$	1.56698	+	0.570334i	0.169963	+	0.0618614i
$86$	11.3027	+	2.56080i	1.21880	+	0.276138i
$87$	7.73445	+	4.46548i	0.829220	+	0.478750i
$88$	5.39994	+	4.26416i	0.575635	+	0.454561i
$89$	−6.18655	+	1.09085i	−0.655773	+	0.115630i	−0.491627	−	0.870806i	$-0.663598\pi$
$89$	−6.18655	+	1.09085i	−0.655773	+	0.115630i	−0.164145	+	0.986436i	$0.552487\pi$
$90$	−10.1951	+	15.8406i	−1.07466	+	1.66974i
$91$	−3.56602	+	2.99225i	−0.373820	+	0.313673i
$92$	−14.5558	+	1.13755i	−1.51755	+	0.118598i
$93$	−12.2977	+	4.47601i	−1.27521	+	0.464140i
$94$	−3.50784	+	0.445277i	−0.361806	+	0.0459268i
$95$	−6.43681	−	5.30885i	−0.660403	−	0.544677i
$96$	10.5362	+	14.4108i	1.07534	+	1.47080i
$97$	−2.11617	−	5.81414i	−0.214865	−	0.590337i	0.784699	−	0.619877i	$-0.212818\pi$
$97$	−2.11617	−	5.81414i	−0.214865	−	0.590337i	−0.999564	+	0.0295408i	$0.990595\pi$
$98$	5.13204	+	0.247918i	0.518414	+	0.0250435i
$99$	−10.8814	−	12.9680i	−1.09362	−	1.30333i
$100$	2.41104	+	1.15163i	0.241104	+	0.115163i
$101$	−0.868620	−	4.92619i	−0.0864309	−	0.490174i	−0.997039	−	0.0769024i	$-0.975497\pi$
$101$	−0.868620	−	4.92619i	−0.0864309	−	0.490174i	0.910608	−	0.413272i	$-0.135614\pi$
$102$	−3.09544	+	2.35249i	−0.306495	+	0.232931i
$103$	7.63840	−	13.2301i	0.752634	−	1.30360i	−0.193907	−	0.981020i	$-0.562116\pi$
$103$	7.63840	−	13.2301i	0.752634	−	1.30360i	0.946542	−	0.322581i	$-0.104551\pi$
$104$	7.17249	−	0.213243i	0.703320	−	0.0209102i
$105$	−3.79096	+	10.4156i	−0.369959	+	1.01645i
$106$	−1.01251	+	2.41272i	−0.0983441	+	0.234344i
$107$	−2.60064	−	4.50444i	−0.251414	−	0.435461i	0.712502	−	0.701670i	$-0.247562\pi$
$107$	−2.60064	−	4.50444i	−0.251414	−	0.435461i	−0.963915	+	0.266209i	$0.914229\pi$
$108$	−10.3492	−	22.7423i	−0.995857	−	2.18838i
$109$	0.530188	−	0.631854i	0.0507828	−	0.0605206i	−0.740055	−	0.672546i	$-0.765201\pi$
$109$	0.530188	−	0.631854i	0.0507828	−	0.0605206i	0.790838	+	0.612026i	$0.209645\pi$
$110$	4.47142	−	4.83449i	0.426333	−	0.460951i
$111$	4.61660	+	0.814031i	0.438188	+	0.0772644i
$112$	5.53400	+	4.82128i	0.522914	+	0.455568i
$113$		−	7.40610i		−	0.696707i	−0.937363	−	0.348353i	$-0.886741\pi$
$113$		−	7.40610i		−	0.696707i	0.937363	−	0.348353i	$-0.113259\pi$
$114$	18.5305	−	5.92087i	1.73554	−	0.554540i
$115$			13.9736i			1.30304i
$116$	−3.20336	−	4.66639i	−0.297424	−	0.433263i
$117$	−17.3862	−	3.06566i	−1.60736	−	0.283421i
$118$	−7.10697	−	6.57322i	−0.654249	−	0.605114i
$119$	−1.02749	+	1.22452i	−0.0941902	+	0.112252i
$120$	14.5361	−	8.97871i	1.32696	−	0.819641i
$121$	−2.54110	−	4.40132i	−0.231009	−	0.400120i
$122$	14.6213	+	6.13595i	1.32375	+	0.555522i
$123$	−1.57115	+	4.31671i	−0.141666	+	0.389224i
$124$	8.25539	+	0.799466i	0.741356	+	0.0717941i
$125$	6.06405	−	10.5032i	0.542385	−	0.939438i
$126$	−10.9264	−	14.3771i	−0.973398	−	1.28081i
$127$	0.543667	+	3.08329i	0.0482426	+	0.273598i	0.999381	−	0.0351659i	$-0.0111959\pi$
$127$	0.543667	+	3.08329i	0.0482426	+	0.273598i	−0.951139	+	0.308764i	$0.900085\pi$
$128$	−2.08897	−	11.1192i	−0.184641	−	0.982806i
$129$	16.6230	+	19.8105i	1.46358	+	1.74422i
$130$	0.331377	−	6.85969i	0.0290637	−	0.601635i
$131$	3.36828	+	9.25428i	0.294288	+	0.808550i	0.995427	+	0.0955253i	$0.0304531\pi$
$131$	3.36828	+	9.25428i	0.294288	+	0.808550i	−0.701139	+	0.713025i	$0.747325\pi$
$132$	3.83613	+	14.8668i	0.333893	+	1.29399i
$133$	6.89248	−	4.05762i	0.597654	−	0.351840i
$134$	−0.492556	−	3.88029i	−0.0425504	−	0.335206i
$135$	−22.4719	+	8.17909i	−1.93407	+	0.703944i
$136$	2.41280	−	0.499795i	0.206895	−	0.0428571i
$137$	13.0208	−	10.9257i	1.11244	−	0.933448i	0.114242	−	0.993453i	$-0.463556\pi$
$137$	13.0208	−	10.9257i	1.11244	−	0.933448i	0.998198	+	0.0600045i	$0.0191115\pi$
$138$	−27.3960	−	17.6323i	−2.33211	−	1.50096i
$139$	−9.34767	+	1.64825i	−0.792859	+	0.139803i	−0.555387	−	0.831592i	$-0.687430\pi$
$139$	−9.34767	+	1.64825i	−0.792859	+	0.139803i	−0.237472	+	0.971394i	$0.576319\pi$
$140$	5.01300	−	4.92087i	0.423676	−	0.415890i
$141$	−6.83330	−	3.94521i	−0.575468	−	0.332246i
$142$	−2.49709	+	11.0215i	−0.209551	+	0.924907i
$143$	5.79939	+	2.11081i	0.484970	+	0.176514i
$144$	−0.516273	+	27.8306i	−0.0430227	+	2.31922i
$145$	−4.69141	+	2.70859i	−0.389601	+	0.224936i
$146$	−15.7394	+	4.88249i	−1.30260	+	0.404078i
$147$	8.78293	+	7.36975i	0.724404	+	0.607847i
$148$	−2.41776	−	1.72657i	−0.198738	−	0.141923i
$149$	−3.22494	+	18.2896i	−0.264198	+	1.49834i	0.507112	+	0.861880i	$0.330713\pi$
$149$	−3.22494	+	18.2896i	−0.264198	+	1.49834i	−0.771310	+	0.636459i	$0.780398\pi$
$150$	2.72856	+	5.30139i	0.222786	+	0.432857i
$151$	5.44123			0.442801			0.221400	−	0.975183i	$-0.428937\pi$
$151$	5.44123			0.442801			0.221400	+	0.975183i	$0.428937\pi$
$152$	−12.2144	−	1.67570i	−0.990720	−	0.135917i
$153$	−6.06228			−0.490107
$154$	2.88884	+	5.61280i	0.232789	+	0.452292i
$155$	1.37843	−	7.81745i	0.110718	−	0.627913i
$156$	13.0307	+	9.30547i	1.04329	+	0.745034i
$157$	9.83579	+	8.25321i	0.784982	+	0.658678i	0.944498	−	0.328518i	$-0.106549\pi$
$157$	9.83579	+	8.25321i	0.784982	+	0.658678i	−0.159516	+	0.987195i	$0.550993\pi$
$158$	7.06957	−	2.19304i	0.562424	−	0.174469i
$159$	−5.05652	+	2.91938i	−0.401008	+	0.231522i
$160$	−10.7654	+	1.16409i	−0.851079	+	0.0920295i
$161$	−12.5872	−	4.58135i	−0.992007	−	0.361061i
$162$	5.79642	−	25.5839i	0.455409	−	2.01006i
$163$	−16.8860	−	9.74913i	−1.32261	−	0.763611i	−0.338468	−	0.940978i	$-0.609909\pi$
$163$	−16.8860	−	9.74913i	−1.32261	−	0.763611i	−0.984145	+	0.177367i	$0.943242\pi$
$164$	2.07763	−	2.03944i	0.162235	−	0.159254i
$165$	14.4716	−	2.55173i	1.12661	−	0.198652i
$166$	−11.2590	−	7.24638i	−0.873867	−	0.562428i
$167$	−17.0859	+	14.3367i	−1.32214	+	1.10941i	−0.336299	+	0.941755i	$0.609175\pi$
$167$	−17.0859	+	14.3367i	−1.32214	+	1.10941i	−0.985846	+	0.167655i	$0.946380\pi$
$168$	3.32209	+	16.0376i	0.256305	+	1.23733i
$169$	−6.16790	+	2.24493i	−0.474454	+	0.172687i
$170$	−0.296970	−	2.33949i	−0.0227766	−	0.179431i
$171$	28.5905	+	10.1326i	2.18637	+	0.774861i
$172$	−4.09493	−	15.8698i	−0.312236	−	1.21006i
$173$	7.49191	+	20.5839i	0.569600	+	1.56496i	0.805132	+	0.593096i	$0.202094\pi$
$173$	7.49191	+	20.5839i	0.569600	+	1.56496i	−0.235532	+	0.971867i	$0.575683\pi$
$174$	0.609432	−	12.6156i	0.0462009	−	0.956385i
$175$	1.57572	+	1.87787i	0.119113	+	0.141954i
$176$	1.86715	−	9.54979i	0.140742	−	0.719843i
$177$	−3.75117	−	21.2740i	−0.281955	−	1.59905i
$178$	5.37554	+	7.07321i	0.402913	+	0.530159i
$179$	4.97474	−	8.61650i	0.371829	−	0.644027i	−0.618018	−	0.786164i	$-0.712064\pi$
$179$	4.97474	−	8.61650i	0.371829	−	0.644027i	0.989847	+	0.142137i	$0.0453973\pi$
$180$	26.5167	+	2.56792i	1.97644	+	0.191402i
$181$	−1.36725	+	3.75648i	−0.101627	+	0.279217i	−0.980077	−	0.198616i	$-0.936355\pi$
$181$	−1.36725	+	3.75648i	−0.101627	+	0.279217i	0.878451	+	0.477833i	$0.158578\pi$
$182$	6.07044	+	2.54750i	0.449971	+	0.188833i
$183$	17.6918	+	30.6430i	1.30781	+	2.26520i
$184$	10.8507	+	17.5668i	0.799927	+	1.29504i
$185$	−1.82773	+	2.17821i	−0.134378	+	0.160145i
$186$	13.5872	+	12.5668i	0.996264	+	0.921443i
$187$	2.08704	+	0.368001i	0.152619	+	0.0269109i
$188$	2.83013	+	4.12271i	0.206409	+	0.300679i
$189$		−	22.9238i		−	1.66746i
$190$	−2.50973	+	11.5297i	−0.182075	+	0.836453i
$191$		−	5.39176i		−	0.390134i	−0.980790	−	0.195067i	$-0.937508\pi$
$191$		−	5.39176i		−	0.390134i	0.980790	−	0.195067i	$-0.0624924\pi$
$192$	11.3019	−	22.5751i	0.815642	−	1.62922i
$193$	−15.2825	−	2.69472i	−1.10006	−	0.193970i	−0.405990	−	0.913878i	$-0.633073\pi$
$193$	−15.2825	−	2.69472i	−1.10006	−	0.193970i	−0.694070	+	0.719908i	$0.744184\pi$
$194$	−5.94136	+	6.42380i	−0.426565	+	0.461202i
$195$	9.85072	−	11.7396i	0.705425	−	0.840692i
$196$	−3.00965	−	6.61366i	−0.214975	−	0.472405i
$197$	2.13117	+	3.69129i	0.151839	+	0.262993i	0.931904	−	0.362706i	$-0.118147\pi$
$197$	2.13117	+	3.69129i	0.151839	+	0.262993i	−0.780064	+	0.625699i	$0.784814\pi$
$198$	−9.26409	+	22.0754i	−0.658370	+	1.56883i
$199$	2.62112	−	7.20146i	0.185806	−	0.510498i	−0.811459	−	0.584410i	$-0.801326\pi$
$199$	2.62112	−	7.20146i	0.185806	−	0.510498i	0.997265	+	0.0739116i	$0.0235483\pi$
$200$	−0.112294	−	3.77704i	−0.00794039	−	0.267077i
$201$	4.36411	−	7.55886i	0.307820	−	0.533161i
$202$	−5.63222	+	4.28040i	−0.396281	+	0.301168i
$203$	−0.901732	−	5.11397i	−0.0632892	−	0.358931i
$204$	4.96144	+	2.36982i	0.347370	+	0.165921i
$205$	−1.79105	−	2.13449i	−0.125093	−	0.149080i
$206$	−21.5795	−	1.04246i	−1.50352	−	0.0726316i
$207$	−17.3747	−	47.7367i	−1.20763	−	3.31793i
$208$	−4.91008	−	8.88094i	−0.340453	−	0.615783i
$209$	−9.22765	−	5.22386i	−0.638290	−	0.361342i
$210$	15.5504	−	1.97393i	1.07308	−	0.136214i
$211$	19.2013	−	6.98869i	1.32187	−	0.481121i	0.417812	−	0.908533i	$-0.362797\pi$
$211$	19.2013	−	6.98869i	1.32187	−	0.481121i	0.904057	+	0.427412i	$0.140575\pi$
$212$	3.68913	−	0.288309i	0.253371	−	0.0198011i
$213$	−19.3177	+	16.2095i	−1.32363	+	1.11066i
$214$	−3.98095	+	6.18536i	−0.272132	+	0.422823i
$215$	−15.4479	+	2.72388i	−1.05354	+	0.185767i
$216$	−21.8992	+	27.7321i	−1.49005	+	1.88693i
$217$	6.58989	+	3.80468i	0.447351	+	0.258278i
$218$	−1.13765	−	0.257751i	−0.0770512	−	0.0174571i
$219$	−34.5553	−	12.5771i	−2.33503	−	0.849881i
$220$	−8.97292	−	2.49370i	−0.604954	−	0.168125i
$221$	1.91402	−	1.10506i	0.128751	−	0.0743343i
$222$	−1.96421	−	6.33192i	−0.131829	−	0.424970i
$223$	7.79705	+	6.54250i	0.522129	+	0.438118i	0.865373	−	0.501128i	$-0.167081\pi$
$223$	7.79705	+	6.54250i	0.522129	+	0.438118i	−0.343244	+	0.939246i	$0.611526\pi$
$224$	2.48093	−	10.0789i	0.165764	−	0.673427i
$225$	−1.61438	+	9.15562i	−0.107626	+	0.610375i
$226$	−9.31270	+	4.79313i	−0.619472	+	0.318834i
$227$	12.9399			0.858848			0.429424	−	0.903103i	$-0.358717\pi$
$227$	12.9399			0.858848			0.429424	+	0.903103i	$0.358717\pi$
$228$	−19.4378	−	19.4690i	−1.28730	−	1.28937i
$229$	14.2432			0.941219			0.470610	−	0.882342i	$-0.344034\pi$
$229$	14.2432			0.941219			0.470610	+	0.882342i	$0.344034\pi$
$230$	17.5709	−	9.04352i	1.15859	−	0.596312i
$231$	−2.44607	+	13.8723i	−0.160939	+	0.912732i
$232$	−3.79452	+	7.04805i	−0.249122	+	0.462727i
$233$	12.3534	+	10.3658i	0.809300	+	0.679083i	0.950441	−	0.310906i	$-0.100633\pi$
$233$	12.3534	+	10.3658i	0.809300	+	0.679083i	−0.141141	+	0.989990i	$0.545077\pi$
$234$	7.39727	+	23.8462i	0.483575	+	1.55887i
$235$	4.14481	−	2.39301i	0.270378	−	0.156103i
$236$	−3.66588	+	13.1907i	−0.238628	+	0.858639i
$237$	15.5210	+	5.64917i	1.00820	+	0.366953i
$238$	2.20474	+	0.499516i	0.142912	+	0.0323788i
$239$	−18.4124	−	10.6304i	−1.19100	−	0.687625i	−0.232468	−	0.972604i	$-0.574680\pi$
$239$	−18.4124	−	10.6304i	−1.19100	−	0.687625i	−0.958534	+	0.284979i	$0.908013\pi$
$240$	−20.6978	−	12.4673i	−1.33603	−	0.804763i
$241$	5.49009	−	0.968052i	0.353648	−	0.0623577i	0.00599789	−	0.999982i	$-0.498091\pi$
$241$	5.49009	−	0.968052i	0.353648	−	0.0623577i	0.347650	+	0.937624i	$0.386980\pi$
$242$	−3.88981	+	6.04375i	−0.250047	+	0.388507i
$243$	16.1305	−	13.5351i	1.03477	−	0.868277i
$244$	−1.74718	−	22.3565i	−0.111852	−	1.43123i
$245$	−6.53500	+	2.37855i	−0.417506	+	0.151960i
$246$	6.44482	−	0.818091i	0.410906	−	0.0521596i
$247$	−10.8738	+	2.01247i	−0.691881	+	0.128050i
$248$	−4.33750	−	10.8980i	−0.275432	−	0.692026i
$249$	−10.2188	−	28.0760i	−0.647592	−	1.77924i
$250$	−17.1317	−	0.827598i	−1.08351	−	0.0523419i
$251$	5.90861	+	7.04161i	0.372948	+	0.444462i	0.919575	−	0.392914i	$-0.128533\pi$
$251$	5.90861	+	7.04161i	0.372948	+	0.444462i	−0.546627	+	0.837376i	$0.684088\pi$
$252$	−11.0069	+	23.0439i	−0.693367	+	1.45163i
$253$	3.08375	+	17.4888i	0.193874	+	1.09951i
$254$	3.52519	−	2.67909i	0.221190	−	0.168101i
$255$	2.63119	−	4.55736i	0.164772	−	0.285393i
$256$	−12.6297	+	9.82295i	−0.789357	+	0.613934i
$257$	6.16751	−	16.9451i	0.384719	−	1.05701i	−0.584626	−	0.811303i	$-0.698759\pi$
$257$	6.16751	−	16.9451i	0.384719	−	1.05701i	0.969345	−	0.245703i	$-0.0790189\pi$
$258$	14.1523	−	33.7235i	0.881084	−	2.09954i
$259$	−1.36285	−	2.36053i	−0.0846836	−	0.146676i
$260$	−8.84009	+	4.02282i	−0.548239	+	0.249485i
$261$	12.6590	−	15.0864i	0.783572	−	0.933824i
$262$	9.45677	−	10.2247i	0.584241	−	0.631681i
$263$	10.7849	+	1.90167i	0.665025	+	0.117262i	0.495963	−	0.868343i	$-0.334815\pi$
$263$	10.7849	+	1.90167i	0.665025	+	0.117262i	0.169062	+	0.985605i	$0.445926\pi$
$264$	16.2114	−	14.4453i	0.997742	−	0.889047i
$265$		−	3.54157i		−	0.217557i
$266$	−9.56292	−	6.04082i	−0.586341	−	0.370387i
$267$			19.8245i			1.21324i
$268$	−4.56045	+	3.13064i	−0.278574	+	0.191234i
$269$	26.9447	+	4.75109i	1.64285	+	0.289679i	0.917213	−	0.398398i	$-0.130434\pi$
$269$	26.9447	+	4.75109i	1.64285	+	0.289679i	0.725638	+	0.688077i	$0.241545\pi$
$270$	24.8282	+	22.9635i	1.51100	+	1.39752i
$271$	15.2661	−	18.1934i	0.927347	−	1.10517i	−0.0668682	−	0.997762i	$-0.521301\pi$
$271$	15.2661	−	18.1934i	0.927347	−	1.10517i	0.994215	−	0.107407i	$-0.0342549\pi$
$272$	−2.18999	−	2.71048i	−0.132788	−	0.164347i
$273$	7.34521	+	12.7223i	0.444553	+	0.769988i
$274$	−22.1653	−	9.30182i	−1.33906	−	0.561944i
$275$	1.11155	−	3.05397i	0.0670292	−	0.184161i
$276$	−4.44118	+	45.8602i	−0.267328	+	2.76046i
$277$	−1.99118	+	3.44882i	−0.119638	+	0.207220i	−0.919624	−	0.392799i	$-0.871507\pi$
$277$	−1.99118	+	3.44882i	−0.119638	+	0.207220i	0.799986	+	0.600019i	$0.204840\pi$
$278$	8.12226	+	10.6874i	0.487141	+	0.640987i
$279$	5.01121	+	28.4200i	0.300013	+	1.70146i
$280$	−9.43204	−	3.11881i	−0.563672	−	0.186385i
$281$	−3.21635	−	3.83310i	−0.191871	−	0.228664i	0.661529	−	0.749920i	$-0.269908\pi$
$281$	−3.21635	−	3.83310i	−0.191871	−	0.228664i	−0.853400	+	0.521256i	$0.825464\pi$
$282$	−0.538427	+	11.1457i	−0.0320628	+	0.663719i
$283$	3.20210	+	8.79770i	0.190345	+	0.522969i	0.997751	−	0.0670271i	$-0.0213514\pi$
$283$	3.20210	+	8.79770i	0.190345	+	0.522969i	−0.807406	+	0.589996i	$0.799129\pi$
$284$	15.4750	−	3.99306i	0.918271	−	0.236945i
$285$	−20.0263	+	17.0953i	−1.18626	+	1.01264i
$286$	−1.09909	−	8.65846i	−0.0649903	−	0.511985i
$287$	2.50993	−	0.913538i	0.148156	−	0.0539245i
$288$	35.3294	−	17.3624i	2.08180	−	1.02309i
$289$	−12.4414	+	10.4396i	−0.731846	+	0.614092i
$290$	6.44210	+	4.14619i	0.378293	+	0.243473i
$291$	−19.2290	+	3.39059i	−1.12722	+	0.198760i
$292$	16.3258	+	16.6314i	0.955393	+	0.973281i
$293$	1.03094	+	0.595211i	0.0602279	+	0.0347726i	0.529812	−	0.848115i	$-0.322263\pi$
$293$	1.03094	+	0.595211i	0.0602279	+	0.0347726i	−0.469584	+	0.882888i	$0.655596\pi$
$294$	3.58280	−	15.8136i	0.208953	−	0.922268i
$295$	12.3128	+	4.48150i	0.716880	+	0.260923i
$296$	−0.606309	+	4.15759i	−0.0352410	+	0.241655i
$297$	−26.3199	+	15.1958i	−1.52724	+	0.881751i
$298$	25.0851	−	7.78161i	1.45314	−	0.450776i
$299$	14.1873	+	11.9045i	0.820472	+	0.688457i
$300$	4.90028	−	6.86198i	0.282918	−	0.396177i
$301$	2.61109	−	14.8082i	0.150501	−	0.853531i
$302$	−3.52149	−	6.84200i	−0.202639	−	0.393713i
$303$	−15.7857			−0.906866
$304$	5.79793	+	16.4434i	0.332534	+	0.943091i
$305$	−21.4623			−1.22893
$306$	3.92343	+	7.62294i	0.224288	+	0.435775i
$307$	3.77412	−	21.4041i	0.215401	−	1.22160i	−0.664810	−	0.747013i	$-0.731487\pi$
$307$	3.77412	−	21.4041i	0.215401	−	1.22160i	0.880210	−	0.474584i	$-0.157402\pi$
$308$	5.18813	−	7.26507i	0.295621	−	0.413966i
$309$	−36.9310	−	30.9888i	−2.10093	−	1.76289i
$310$	−10.7221	+	3.32607i	−0.608972	+	0.188908i
$311$	−28.7054	+	16.5731i	−1.62773	+	0.939773i	−0.642968	+	0.765893i	$0.722297\pi$
$311$	−28.7054	+	16.5731i	−1.62773	+	0.939773i	−0.984767	+	0.173880i	$0.944370\pi$
$312$	3.26775	−	22.4077i	0.185000	−	1.26858i
$313$	29.2682	+	10.6528i	1.65434	+	0.602130i	0.989458	−	0.144821i	$-0.0462607\pi$
$313$	29.2682	+	10.6528i	1.65434	+	0.602130i	0.664880	+	0.746951i	$0.268483\pi$
$314$	4.01229	−	17.7093i	0.226427	−	0.999392i
$315$	21.1671	+	12.2208i	1.19263	+	0.688565i
$316$	−7.33294	−	7.47023i	−0.412510	−	0.420233i
$317$	−11.1921	+	1.97346i	−0.628609	+	0.110841i	−0.478872	−	0.877885i	$-0.658954\pi$
$317$	−11.1921	+	1.97346i	−0.628609	+	0.110841i	−0.149738	+	0.988726i	$0.547843\pi$
$318$	6.94346	+	4.46887i	0.389370	+	0.250602i
$319$	−5.27385	+	4.42529i	−0.295279	+	0.247769i
$320$	8.43100	+	12.7834i	0.471307	+	0.714615i
$321$	−15.4241	+	5.61393i	−0.860892	+	0.313339i
$322$	2.38549	+	18.7926i	0.132938	+	1.04727i
$323$	−3.55717	+	1.32894i	−0.197926	+	0.0739441i
$324$	−35.9216	+	9.26896i	−1.99564	+	0.514942i
$325$	−1.15922	−	3.18494i	−0.0643021	−	0.176669i
$326$	−1.33052	+	27.5426i	−0.0736909	+	1.52544i
$327$	−1.67315	−	1.99398i	−0.0925254	−	0.110267i
$328$	−3.90909	−	1.29258i	−0.215843	−	0.0713710i
$329$	0.796670	+	4.51814i	0.0439219	+	0.249093i
$330$	−12.5744	−	16.5456i	−0.692200	−	0.910807i
$331$	−0.569873	+	0.987049i	−0.0313230	+	0.0542531i	−0.881262	−	0.472628i	$-0.843305\pi$
$331$	−0.569873	+	0.987049i	−0.0313230	+	0.0542531i	0.849939	+	0.526881i	$0.176639\pi$
$332$	−1.82520	+	18.8472i	−0.100171	+	1.03438i
$333$	3.53554	−	9.71381i	0.193746	−	0.532314i
$334$	29.0853	+	12.2059i	1.59148	+	0.667874i
$335$	2.64710	+	4.58491i	0.144626	+	0.250500i
$336$	18.0163	−	14.5567i	0.982869	−	0.794131i
$337$	11.8905	−	14.1706i	0.647718	−	0.771920i	−0.337850	−	0.941200i	$-0.609700\pi$
$337$	11.8905	−	14.1706i	0.647718	−	0.771920i	0.985568	+	0.169280i	$0.0541442\pi$
$338$	6.81465	+	6.30286i	0.370668	+	0.342830i
$339$	−23.0168	−	4.05849i	−1.25010	−	0.220427i
$340$	−2.74957	+	1.88751i	−0.149116	+	0.102365i
$341$		−	10.0882i		−	0.546308i
$342$	−5.76227	−	42.5085i	−0.311588	−	2.29859i
$343$		−	19.5108i		−	1.05348i
$344$	−17.3051	+	15.4198i	−0.933026	+	0.831382i
$345$	43.4274	+	7.65742i	2.33805	+	0.412262i
$346$	21.0343	−	22.7422i	1.13081	−	1.22263i
$347$	−11.4936	+	13.6975i	−0.617008	+	0.735321i	−0.980553	−	0.196255i	$-0.937122\pi$
$347$	−11.4936	+	13.6975i	−0.617008	+	0.735321i	0.363545	+	0.931577i	$0.381566\pi$
$348$	−16.2577	+	7.39832i	−0.871505	+	0.396592i
$349$	−4.75225	−	8.23114i	−0.254382	−	0.440603i	0.710345	−	0.703853i	$-0.248539\pi$
$349$	−4.75225	−	8.23114i	−0.254382	−	0.440603i	−0.964727	+	0.263251i	$0.915205\pi$
$350$	1.34152	−	3.19671i	0.0717072	−	0.170871i
$351$	−10.8403	+	29.7835i	−0.578614	+	1.58973i
$352$	−13.2167	+	3.83268i	−0.704450	+	0.204283i
$353$	−5.73568	+	9.93449i	−0.305280	+	0.528760i	−0.977324	−	0.211751i	$-0.932083\pi$
$353$	−5.73568	+	9.93449i	−0.305280	+	0.528760i	0.672044	+	0.740511i	$0.265417\pi$
$354$	−24.3230	+	18.4851i	−1.29275	+	0.982472i
$355$	−2.65611	−	15.0636i	−0.140972	−	0.799491i
$356$	5.41514	−	11.3371i	0.287002	−	0.600864i
$357$	3.24253	+	3.86430i	0.171613	+	0.204520i
$358$	−14.0543	−	0.678933i	−0.742793	−	0.0358827i
$359$	8.61799	+	23.6777i	0.454840	+	1.24966i	0.929280	+	0.369376i	$0.120428\pi$
$359$	8.61799	+	23.6777i	0.454840	+	1.24966i	−0.474440	+	0.880288i	$0.657349\pi$
$360$	−13.9323	−	35.0050i	−0.734296	−	1.84493i
$361$	18.9973	−	0.321920i	0.999856	−	0.0169432i
$362$	5.60840	−	0.711918i	0.294771	−	0.0374176i
$363$	−15.0710	+	5.48540i	−0.791023	+	0.287909i
$364$	−0.725389	−	9.28191i	−0.0380207	−	0.486505i
$365$	17.0867	−	14.3374i	0.894356	−	0.750454i
$366$	27.0818	−	42.0781i	1.41559	−	2.19946i
$367$	6.93117	−	1.22215i	0.361804	−	0.0637958i	0.0102088	−	0.999948i	$-0.496750\pi$
$367$	6.93117	−	1.22215i	0.361804	−	0.0637958i	0.351595	+	0.936152i	$0.385639\pi$
$368$	15.0667	−	25.0131i	0.785407	−	1.30390i
$369$	8.77264	+	5.06489i	0.456685	+	0.263667i
$370$	3.92185	+	0.888552i	0.203887	+	0.0461936i
$371$	3.19018	+	1.16113i	0.165626	+	0.0602829i
$372$	7.00849	−	25.2182i	0.363373	−	1.30750i
$373$	−28.1670	+	16.2622i	−1.45843	+	0.842025i	−0.998934	−	0.0461546i	$-0.985303\pi$
$373$	−28.1670	+	16.2622i	−1.45843	+	0.842025i	−0.459496	+	0.888180i	$0.651970\pi$
$374$	−0.887966	−	2.86248i	−0.0459156	−	0.148016i
$375$	−29.3191	−	24.6017i	−1.51403	−	1.27043i
$376$	3.35242	−	6.22688i	0.172888	−	0.321127i
$377$	−1.24675	+	7.07069i	−0.0642111	+	0.364159i
$378$	−28.8253	+	14.8360i	−1.48261	+	0.763082i
$379$	23.4446			1.20427			0.602135	−	0.798394i	$-0.294317\pi$
$379$	23.4446			1.20427			0.602135	+	0.798394i	$0.294317\pi$
$380$	16.1221	−	4.30606i	0.827049	−	0.220896i
$381$	9.88024			0.506180
$382$	−6.77980	+	3.48948i	−0.346885	+	0.178537i
$383$	−3.75733	+	21.3089i	−0.191990	+	1.08883i	0.724650	+	0.689118i	$0.242002\pi$
$383$	−3.75733	+	21.3089i	−0.191990	+	1.08883i	−0.916640	+	0.399714i	$0.869109\pi$
$384$	−35.7012	+	0.398925i	−1.82187	+	0.0203575i
$385$	−6.54525	−	5.49212i	−0.333577	−	0.279904i
$386$	6.50221	+	20.9608i	0.330954	+	1.06688i
$387$	49.3863	−	28.5132i	2.51044	−	1.44941i
$388$	11.9227	+	3.31349i	0.605283	+	0.168217i
$389$	−21.8603	−	7.95648i	−1.10836	−	0.403410i	−0.277968	−	0.960590i	$-0.589661\pi$
$389$	−21.8603	−	7.95648i	−1.10836	−	0.403410i	−0.830391	+	0.557181i	$0.811883\pi$
$390$	−21.1371	−	4.78892i	−1.07032	−	0.242496i
$391$	5.50754	+	3.17978i	0.278528	+	0.160808i
$392$	−6.36846	+	8.06472i	−0.321656	+	0.407330i
$393$	30.6064	−	5.39674i	1.54389	−	0.272230i
$394$	3.26230	−	5.06876i	0.164352	−	0.255361i
$395$	−7.67470	+	6.43984i	−0.386156	+	0.324023i
$396$	33.7540	−	2.63790i	1.69620	−	0.132560i
$397$	24.0948	−	8.76979i	1.20928	−	0.440143i	0.342828	−	0.939398i	$-0.388615\pi$
$397$	24.0948	−	8.76979i	1.20928	−	0.440143i	0.866455	+	0.499255i	$0.166393\pi$
$398$	−10.7517	+	1.36480i	−0.538936	+	0.0684114i
$399$	−8.83332	−	23.6441i	−0.442219	−	1.18369i
$400$	−4.67672	+	2.58566i	−0.233836	+	0.129283i
$401$	0.905379	+	2.48751i	0.0452125	+	0.124220i	0.960244	−	0.279162i	$-0.0900567\pi$
$401$	0.905379	+	2.48751i	0.0452125	+	0.124220i	−0.915032	+	0.403382i	$0.867834\pi$
$402$	−12.3292	−	0.595596i	−0.614924	−	0.0297056i
$403$	−6.76267	−	8.05944i	−0.336873	−	0.401469i
$404$	9.02744	+	4.31194i	0.449132	+	0.214527i
$405$	6.16554	+	34.9665i	0.306368	+	1.73750i
$406$	−5.84691	+	4.44357i	−0.290177	+	0.220531i
$407$	−1.80683	+	3.12951i	−0.0895610	+	0.155124i
$408$	−0.231079	−	7.77242i	−0.0114401	−	0.384792i
$409$	−7.31695	+	20.1032i	−0.361800	+	0.994038i	0.616593	+	0.787282i	$0.288513\pi$
$409$	−7.31695	+	20.1032i	−0.361800	+	0.994038i	−0.978393	+	0.206755i	$0.933710\pi$
$410$	−1.52485	+	3.63356i	−0.0753068	+	0.179449i
$411$	−26.8199	−	46.4535i	−1.32293	−	2.29138i
$412$	12.6552	+	27.8095i	0.623475	+	1.37008i
$413$	−8.07371	+	9.62187i	−0.397281	+	0.473461i
$414$	−48.7812	+	52.7422i	−2.39746	+	2.59214i
$415$	17.8474	+	3.14698i	0.876095	+	0.154479i
$416$	−7.98949	+	11.9218i	−0.391717	+	0.584512i
$417$			29.9541i			1.46686i
$418$	−0.596654	+	14.9840i	−0.0291833	+	0.732892i
$419$		−	3.96184i		−	0.193549i	−0.995306	−	0.0967744i	$-0.969147\pi$
$419$		−	3.96184i		−	0.193549i	0.995306	−	0.0967744i	$-0.0308525\pi$
$420$	−12.5461	−	18.2761i	−0.612187	−	0.891783i
$421$	−39.1951	−	6.91115i	−1.91025	−	0.336829i	−0.912815	−	0.408373i	$-0.866096\pi$
$421$	−39.1951	−	6.91115i	−1.91025	−	0.336829i	−0.997437	+	0.0715443i	$0.977207\pi$
$422$	−21.2146	−	19.6214i	−1.03271	−	0.955154i
$423$	−11.1841	+	13.3287i	−0.543789	+	0.648062i
$424$	−2.75009	−	4.45226i	−0.133556	−	0.216221i
$425$	−0.581925	−	1.00792i	−0.0282275	−	0.0488915i
$426$	32.8846	+	13.8002i	1.59326	+	0.668624i
$427$	7.03658	−	19.3328i	0.340524	−	0.935582i
$428$	10.3541	+	1.00271i	0.500486	+	0.0484679i
$429$	9.73803	−	16.8668i	0.470157	−	0.814335i
$430$	13.4228	+	17.6619i	0.647303	+	0.851731i
$431$	−3.45718	−	19.6067i	−0.166527	−	0.944419i	−0.947476	−	0.319826i	$-0.896376\pi$
$431$	−3.45718	−	19.6067i	−0.166527	−	0.944419i	0.780950	−	0.624594i	$-0.214735\pi$
$432$	49.0442	+	9.58898i	2.35964	+	0.461350i
$433$	−19.0331	−	22.6828i	−0.914675	−	1.09007i	−0.995633	−	0.0933494i	$-0.970243\pi$
$433$	−19.0331	−	22.6828i	−0.914675	−	1.09007i	0.0809587	−	0.996717i	$-0.474202\pi$
$434$	0.519247	−	10.7487i	0.0249247	−	0.515955i
$435$	5.84695	+	16.0644i	0.280340	+	0.770227i
$436$	0.412166	+	1.59733i	0.0197392	+	0.0764984i
$437$	−20.6595	−	24.2017i	−0.988279	−	1.15772i
$438$	6.54883	+	51.5908i	0.312915	+	2.46510i
$439$	0.0910357	−	0.0331343i	0.00434490	−	0.00158141i	−0.339847	−	0.940481i	$-0.610375\pi$
$439$	0.0910357	−	0.0331343i	0.00434490	−	0.00158141i	0.344192	+	0.938899i	$0.388153\pi$
$440$	2.67148	+	12.8968i	0.127358	+	0.614830i
$441$	19.3675	−	16.2512i	0.922260	−	0.773868i
$442$	−2.62827	−	1.69158i	−0.125014	−	0.0804601i
$443$	21.2279	−	3.74305i	1.00857	−	0.177838i	0.355129	−	0.934817i	$-0.384437\pi$
$443$	21.2279	−	3.74305i	1.00857	−	0.177838i	0.653438	+	0.756980i	$0.273326\pi$
$444$	−6.69078	+	6.56781i	−0.317530	+	0.311694i
$445$	−10.4137	−	6.01237i	−0.493658	−	0.285014i
$446$	3.18064	−	14.0385i	0.150607	−	0.664744i
$447$	55.0735	+	20.0451i	2.60489	+	0.948101i
$448$	−14.2792	+	3.40335i	−0.674631	+	0.160793i
$449$	16.9734	−	9.79959i	0.801024	−	0.462471i	−0.0428051	−	0.999083i	$-0.513629\pi$
$449$	16.9734	−	9.79959i	0.801024	−	0.462471i	0.843829	+	0.536612i	$0.180296\pi$
$450$	12.5574	−	3.89542i	0.591963	−	0.183632i
$451$	−2.71266	−	2.27620i	−0.127734	−	0.107182i
$452$	12.0541	+	8.60809i	0.566978	+	0.404890i
$453$	2.98175	−	16.9104i	0.140095	−	0.794518i
$454$	−8.37451	−	16.2711i	−0.393035	−	0.763638i
$455$	−8.91064			−0.417737
$456$	−11.9012	+	37.0420i	−0.557324	+	1.73465i
$457$	9.26419			0.433360			0.216680	−	0.976243i	$-0.430477\pi$
$457$	9.26419			0.433360			0.216680	+	0.976243i	$0.430477\pi$
$458$	−9.21804	−	17.9100i	−0.430731	−	0.836878i
$459$	−1.88992	+	10.7183i	−0.0882138	+	0.500285i
$460$	−22.7433	−	16.2415i	−1.06041	−	0.757262i
$461$	3.95276	+	3.31676i	0.184098	+	0.154477i	0.730179	−	0.683256i	$-0.239437\pi$
$461$	3.95276	+	3.31676i	0.184098	+	0.154477i	−0.546081	+	0.837732i	$0.683881\pi$
$462$	19.0266	−	5.90222i	0.885200	−	0.274596i
$463$	−27.6307	+	15.9526i	−1.28411	+	0.741379i	−0.977596	−	0.210488i	$-0.932495\pi$
$463$	−27.6307	+	15.9526i	−1.28411	+	0.741379i	−0.306510	+	0.951867i	$0.599161\pi$
$464$	11.3182	+	0.209959i	0.525436	+	0.00974712i
$465$	−23.5399	−	8.56781i	−1.09164	−	0.397323i
$466$	5.03931	−	22.2422i	0.233441	−	1.03035i
$467$	20.9939	+	12.1208i	0.971481	+	0.560885i	0.899687	−	0.436535i	$-0.143794\pi$
$467$	20.9939	+	12.1208i	0.971481	+	0.560885i	0.0717935	+	0.997420i	$0.477128\pi$
$468$	25.1976	−	24.7345i	1.16476	−	1.14335i
$469$	−4.99788	+	0.881260i	−0.230780	+	0.0406928i
$470$	−5.69153	−	3.66312i	−0.262531	−	0.168967i
$471$	31.0394	−	26.0452i	1.43022	−	1.20010i
$472$	18.9589	−	3.92722i	0.872656	−	0.180765i
$473$	−18.7328	+	6.81820i	−0.861337	+	0.313501i
$474$	−2.94150	−	23.1727i	−0.135107	−	1.06436i
$475$	1.05977	+	5.72614i	0.0486256	+	0.262733i
$476$	−0.798768	−	3.09560i	−0.0366115	−	0.141887i
$477$	4.40358	+	12.0987i	0.201626	+	0.553963i
$478$	−1.45080	+	30.0324i	−0.0663580	+	1.37365i
$479$	−1.51494	−	1.80544i	−0.0692195	−	0.0824926i	0.730323	−	0.683101i	$-0.239369\pi$
$479$	−1.51494	−	1.80544i	−0.0692195	−	0.0824926i	−0.799543	+	0.600609i	$0.794925\pi$
$480$	−2.28157	+	34.0948i	−0.104139	+	1.55621i
$481$	0.654415	+	3.71137i	0.0298387	+	0.169224i
$482$	−4.77038	−	6.27694i	−0.217285	−	0.285907i
$483$	−21.1357	+	36.6081i	−0.961707	+	1.66573i
$484$	10.1171	+	0.979755i	0.459867	+	0.0445343i
$485$	4.05070	−	11.1292i	0.183933	−	0.505352i
$486$	−27.4590	−	11.5234i	−1.24557	−	0.522710i
$487$	−16.3996	−	28.4049i	−0.743135	−	1.28715i	−0.951061	−	0.309003i	$-0.900005\pi$
$487$	−16.3996	−	28.4049i	−0.743135	−	1.28715i	0.207926	−	0.978145i	$-0.433329\pi$
$488$	−26.9812	+	16.6658i	−1.22138	+	0.754427i
$489$	−39.5520	+	47.1362i	−1.78860	+	2.13157i
$490$	7.22024	+	6.67799i	0.326177	+	0.301681i
$491$	−13.1877	−	2.32535i	−0.595154	−	0.104942i	−0.132046	−	0.991244i	$-0.542155\pi$
$491$	−13.1877	−	2.32535i	−0.595154	−	0.104942i	−0.463108	+	0.886302i	$0.653266\pi$
$492$	−5.19970	−	7.57449i	−0.234421	−	0.341485i
$493$			2.46543i			0.111037i
$494$	9.56792	+	12.3706i	0.430481	+	0.556581i
$495$		−	32.4039i		−	1.45645i
$496$	−10.8964	+	12.5072i	−0.489264	+	0.561590i
$497$	14.4398	+	2.54613i	0.647714	+	0.114210i
$498$	−28.6903	+	31.0200i	−1.28564	+	1.39004i
$499$	−21.7580	+	25.9301i	−0.974021	+	1.16079i	0.0129539	+	0.999916i	$0.495877\pi$
$499$	−21.7580	+	25.9301i	−0.974021	+	1.16079i	−0.986975	+	0.160876i	$0.948568\pi$
$500$	10.0468	+	22.0777i	0.449306	+	0.987345i
$501$	35.1931	+	60.9563i	1.57231	+	2.72333i
$502$	5.03040	−	11.9869i	0.224518	−	0.535004i
$503$	12.7105	−	34.9217i	0.566731	−	1.55708i	−0.242844	−	0.970065i	$-0.578080\pi$
$503$	12.7105	−	34.9217i	0.566731	−	1.55708i	0.809575	−	0.587016i	$-0.199698\pi$
$504$	36.0997	−	1.07327i	1.60801	−	0.0478072i
$505$	4.78750	−	8.29219i	0.213041	−	0.368998i
$506$	19.9953	−	15.1962i	0.888900	−	0.675551i
$507$	3.59689	+	20.3990i	0.159743	+	0.905949i
$508$	−5.65025	−	2.69883i	−0.250689	−	0.119741i
$509$	6.82338	+	8.13179i	0.302441	+	0.360435i	0.895764	−	0.444529i	$-0.146629\pi$
$509$	6.82338	+	8.13179i	0.302441	+	0.360435i	−0.593323	+	0.804964i	$0.702184\pi$
$510$	−7.43346	−	0.359095i	−0.329159	−	0.0159010i
$511$	7.31289	+	20.0920i	0.323503	+	0.888817i
$512$	20.5255	+	9.52379i	0.907109	+	0.420896i
$513$	26.8278	−	47.3898i	1.18448	−	2.09231i
$514$	−25.2989	+	3.21139i	−1.11589	+	0.141648i
$515$	27.4788	−	10.0015i	1.21086	−	0.440717i
$516$	−51.5644	+	4.02980i	−2.27000	+	0.177402i
$517$	4.65939	−	3.90969i	0.204920	−	0.171948i
$518$	−2.08620	+	3.24141i	−0.0916624	+	0.142419i
$519$	68.0765	−	12.0037i	2.98823	−	0.526905i
$520$	10.7796	+	8.51235i	0.472718	+	0.373291i
$521$	−12.4939	−	7.21337i	−0.547369	−	0.316024i	0.200691	−	0.979655i	$-0.435681\pi$
$521$	−12.4939	−	7.21337i	−0.547369	−	0.316024i	−0.748060	+	0.663631i	$0.769015\pi$
$522$	−27.1629	−	6.15416i	−1.18889	−	0.269360i
$523$	−25.6633	−	9.34069i	−1.12218	−	0.408440i	−0.286732	−	0.958011i	$-0.592569\pi$
$523$	−25.6633	−	9.34069i	−1.12218	−	0.408440i	−0.835447	+	0.549571i	$0.814791\pi$
$524$	−18.9772	−	5.27402i	−0.829021	−	0.230397i
$525$	6.69957	−	3.86800i	0.292393	−	0.168813i
$526$	−4.58862	−	14.7921i	−0.200073	−	0.644965i
$527$	−2.76750	−	2.32220i	−0.120554	−	0.101157i
$528$	−28.6559	−	11.0360i	−1.24709	−	0.480279i
$529$	−5.26005	+	29.8312i	−0.228698	+	1.29701i
$530$	−4.45330	+	2.29206i	−0.193439	+	0.0995606i
$531$	−47.6354			−2.06720
$532$	−1.40695	+	15.9343i	−0.0609992	+	0.690840i
$533$	−3.69299			−0.159961
$534$	24.9280	−	12.8301i	1.07874	−	0.555214i
$535$	1.72886	−	9.80485i	0.0747452	−	0.423901i
$536$	6.88804	+	3.70837i	0.297518	+	0.160177i
$537$	−24.0524	−	20.1824i	−1.03794	−	0.870934i
$538$	−11.4641	−	36.9562i	−0.494253	−	1.59329i
$539$	−7.65406	+	4.41907i	−0.329684	+	0.190343i
$540$	12.8067	−	46.0816i	0.551114	−	1.98304i
$541$	14.6005	+	5.31414i	0.627724	+	0.228473i	0.636240	−	0.771491i	$-0.280489\pi$
$541$	14.6005	+	5.31414i	0.627724	+	0.228473i	−0.00851644	+	0.999964i	$0.502711\pi$
$542$	−32.7570	−	7.42159i	−1.40703	−	0.318784i
$543$	10.9252	+	6.30768i	0.468846	+	0.270688i
$544$	−1.99092	+	4.50796i	−0.0853601	+	0.193277i
$545$	1.55487	−	0.274165i	0.0666032	−	0.0117439i
$546$	11.2437	−	17.4698i	0.481188	−	0.747640i
$547$	−22.9739	+	19.2774i	−0.982292	+	0.824241i	−0.984434	−	0.175757i	$-0.943763\pi$
$547$	−22.9739	+	19.2774i	−0.982292	+	0.824241i	0.00214187	+	0.999998i	$0.499318\pi$
$548$	2.64865	+	33.8915i	0.113145	+	1.44777i
$549$	73.3196	−	26.6861i	3.12920	−	1.13894i
$550$	−4.55956	+	0.578781i	−0.194420	+	0.0246793i
$551$	4.12077	−	11.6273i	0.175551	−	0.495339i
$552$	60.5407	−	24.0957i	2.57678	−	1.02558i
$553$	−3.28468	−	9.02459i	−0.139679	−	0.383765i
$554$	5.62535	+	0.271748i	0.238998	+	0.0115455i
$555$	5.76790	+	6.87391i	0.244834	+	0.291781i
$556$	8.18210	−	17.1300i	0.346998	−	0.726473i
$557$	3.59379	+	20.3814i	0.152274	+	0.863587i	0.961236	+	0.275727i	$0.0889185\pi$
$557$	3.59379	+	20.3814i	0.152274	+	0.863587i	−0.808962	+	0.587861i	$0.799970\pi$
$558$	32.4931	−	24.6943i	1.37554	−	1.04539i
$559$	−10.3950	+	18.0047i	−0.439662	+	0.761516i
$560$	2.18259	+	13.8787i	0.0922311	+	0.586480i
$561$	2.28736	−	6.28448i	0.0965725	−	0.265331i
$562$	−2.73830	+	6.52509i	−0.115508	+	0.275244i
$563$	−4.49016	−	7.77718i	−0.189238	−	0.327769i	0.755759	−	0.654850i	$-0.227268\pi$
$563$	−4.49016	−	7.77718i	−0.189238	−	0.327769i	−0.944996	+	0.327081i	$0.893935\pi$
$564$	14.3635	−	6.53634i	0.604814	−	0.275230i
$565$	9.11247	−	10.8598i	0.383364	−	0.456876i
$566$	8.99020	−	9.72020i	0.377886	−	0.408571i
$567$	−33.5187	−	5.91025i	−1.40765	−	0.248207i
$568$	−15.0362	−	16.8746i	−0.630907	−	0.708041i
$569$			23.6238i			0.990361i	0.868790	+	0.495181i	$0.164898\pi$
$569$			23.6238i			0.990361i	−0.868790	+	0.495181i	$0.835102\pi$
$570$	34.4570	+	14.1180i	1.44324	+	0.591337i
$571$			23.3260i			0.976163i	0.872798	+	0.488082i	$0.162303\pi$
$571$			23.3260i			0.976163i	−0.872798	+	0.488082i	$0.837697\pi$
$572$	−10.1762	+	6.98568i	−0.425486	+	0.292086i
$573$	−16.7566	−	2.95464i	−0.700018	−	0.123432i
$574$	−2.77311	−	2.56484i	−0.115747	−	0.107055i
$575$	6.26895	−	7.47105i	0.261433	−	0.311564i
$576$	−44.6969	−	33.1877i	−1.86237	−	1.38282i
$577$	−15.3325	−	26.5567i	−0.638302	−	1.10557i	−0.985805	−	0.167893i	$-0.946304\pi$
$577$	−15.3325	−	26.5567i	−0.638302	−	1.10557i	0.347503	−	0.937679i	$-0.387030\pi$
$578$	21.1790	+	8.88791i	0.880930	+	0.369688i
$579$	−16.7494	+	46.0187i	−0.696082	+	1.91247i
$580$	1.04433	−	10.7839i	0.0433635	−	0.447777i
$581$	−8.68616	+	15.0449i	−0.360363	+	0.624166i
$582$	16.7082	+	21.9849i	0.692577	+	0.911302i
$583$	−0.781568	−	4.43249i	−0.0323692	−	0.183575i
$584$	10.3471	−	31.2923i	0.428168	−	1.29488i
$585$	−21.7221	−	25.8873i	−0.898096	−	1.07031i
$586$	0.0812321	−	1.68155i	0.00335567	−	0.0694642i
$587$	−5.84762	−	16.0662i	−0.241357	−	0.663123i	−0.999933	−	0.0115389i	$-0.996327\pi$
$587$	−5.84762	−	16.0662i	−0.241357	−	0.663123i	0.758576	−	0.651584i	$-0.225895\pi$
$588$	−22.2034	+	5.72921i	−0.915651	+	0.236269i
$589$	9.17048	+	15.5775i	0.377863	+	0.641858i
$590$	−2.33349	−	18.3830i	−0.0960684	−	0.756814i
$591$	12.6397	−	4.60049i	0.519929	−	0.189239i
$592$	5.62030	−	1.92834i	0.230993	−	0.0792544i
$593$	−4.15251	+	3.48437i	−0.170523	+	0.143086i	−0.724055	−	0.689742i	$-0.757724\pi$
$593$	−4.15251	+	3.48437i	−0.170523	+	0.143086i	0.553532	+	0.832828i	$0.313280\pi$
$594$	36.1417	+	23.2611i	1.48291	+	0.954415i
$595$	−3.01330	+	0.531326i	−0.123533	+	0.0217822i
$596$	−26.0197	−	26.5068i	−1.06581	−	1.08576i
$597$	−20.9445	−	12.0923i	−0.857202	−	0.494906i
$598$	5.78739	−	25.5441i	0.236664	−	1.04458i
$599$	−21.5337	−	7.83764i	−0.879845	−	0.320237i	−0.137698	−	0.990474i	$-0.543970\pi$
$599$	−21.5337	−	7.83764i	−0.879845	−	0.320237i	−0.742147	+	0.670237i	$0.766193\pi$
$600$	−11.7999	−	1.72080i	−0.481729	−	0.0702515i
$601$	−11.7394	+	6.77773i	−0.478859	+	0.276469i	−0.719941	−	0.694035i	$-0.755831\pi$
$601$	−11.7394	+	6.77773i	−0.478859	+	0.276469i	0.241082	+	0.970505i	$0.422498\pi$
$602$	−20.3103	+	6.30041i	−0.827784	+	0.256785i
$603$	−14.7439	−	12.3716i	−0.600418	−	0.503810i
$604$	−6.32432	+	8.85612i	−0.257333	+	0.360350i
$605$	1.68928	−	9.58038i	0.0686789	−	0.389498i
$606$	10.2163	+	19.8496i	0.415009	+	0.806333i
$607$	−7.35854			−0.298674			−0.149337	−	0.988786i	$-0.547714\pi$
$607$	−7.35854			−0.298674			−0.149337	+	0.988786i	$0.547714\pi$
$608$	16.9241	−	17.9325i	0.686365	−	0.727258i
$609$	−16.3875			−0.664054
$610$	13.8901	+	26.9875i	0.562394	+	1.09269i
$611$	1.10149	−	6.24688i	0.0445617	−	0.252722i
$612$	7.04618	−	9.86694i	0.284825	−	0.398847i
$613$	−13.2122	−	11.0863i	−0.533635	−	0.447773i	0.335719	−	0.941962i	$-0.391021\pi$
$613$	−13.2122	−	11.0863i	−0.533635	−	0.447773i	−0.869354	+	0.494189i	$0.835465\pi$
$614$	−29.3569	+	9.10674i	−1.18475	+	0.367518i
$615$	−7.61511	+	4.39659i	−0.307071	+	0.177288i
$616$	−12.4931	−	1.82188i	−0.503359	−	0.0734058i
$617$	26.1889	+	9.53198i	1.05433	+	0.383743i	0.810294	−	0.586024i	$-0.199308\pi$
$617$	26.1889	+	9.53198i	1.05433	+	0.383743i	0.244032	+	0.969767i	$0.421530\pi$
$618$	−15.0652	+	66.4940i	−0.606011	+	2.67478i
$619$	1.02147	+	0.589747i	0.0410564	+	0.0237039i	0.520388	−	0.853930i	$-0.325787\pi$
$619$	1.02147	+	0.589747i	0.0410564	+	0.0237039i	−0.479331	+	0.877634i	$0.659121\pi$
$620$	11.1215	+	11.3297i	0.446650	+	0.455012i
$621$	−89.8161	+	15.8370i	−3.60419	+	0.635517i
$622$	39.4174	+	25.3694i	1.58049	+	1.01722i
$623$	8.83007	−	7.40930i	0.353769	−	0.296848i
$624$	−30.2911	+	10.3930i	−1.21261	+	0.416052i
$625$	15.5381	−	5.65540i	0.621523	−	0.226216i
$626$	−5.54684	−	43.6973i	−0.221696	−	1.74649i
$627$	−21.2915	+	25.8153i	−0.850300	+	1.03096i
$628$	−24.8650	+	6.41600i	−0.992221	+	0.256026i
$629$	0.442605	+	1.21605i	0.0176478	+	0.0484870i
$630$	1.66785	−	34.5254i	0.0664487	−	1.37553i
$631$	30.4723	+	36.3155i	1.21308	+	1.44570i	0.860144	+	0.510052i	$0.170374\pi$
$631$	30.4723	+	36.3155i	1.21308	+	1.44570i	0.352941	+	0.935646i	$0.385182\pi$
$632$	−4.64756	+	14.0553i	−0.184870	+	0.559092i
$633$	−11.1974	−	63.5038i	−0.445058	−	2.52405i
$634$	9.72487	+	12.7961i	0.386224	+	0.508199i
$635$	−2.99648	+	5.19006i	−0.118912	+	0.205961i
$636$	1.12561	−	11.6232i	0.0446332	−	0.460888i
$637$	−3.15246	+	8.66130i	−0.124905	+	0.343173i
$638$	8.97769	+	3.76755i	0.355430	+	0.149159i
$639$	27.8038	+	48.1577i	1.09990	+	1.90509i
$640$	10.6179	−	18.8747i	0.419710	−	0.746089i
$641$	7.60426	−	9.06241i	0.300350	−	0.357944i	−0.594669	−	0.803970i	$-0.702717\pi$
$641$	7.60426	−	9.06241i	0.300350	−	0.357944i	0.895020	+	0.446027i	$0.147161\pi$
$642$	17.0415	+	15.7616i	0.672573	+	0.622062i
$643$	25.5305	+	4.50172i	1.00683	+	0.177531i	0.652659	−	0.757652i	$-0.273653\pi$
$643$	25.5305	+	4.50172i	1.00683	+	0.177531i	0.354167	+	0.935182i	$0.384765\pi$
$644$	22.0866	−	15.1619i	0.870334	−	0.597463i
$645$			49.5019i			1.94913i
$646$	3.97321	+	3.61284i	0.156324	+	0.142145i
$647$			16.7243i			0.657501i	0.944417	+	0.328751i	$0.106628\pi$
$647$			16.7243i			0.657501i	−0.944417	+	0.328751i	$0.893372\pi$
$648$	34.9031	+	39.1703i	1.37112	+	1.53876i
$649$	16.3992	+	2.89163i	0.643727	+	0.113506i
$650$	−3.25463	+	3.51890i	−0.127657	+	0.138023i
$651$	15.4355	−	18.3953i	0.604964	−	0.720968i
$652$	35.4942	−	16.1522i	1.39006	−	0.632567i
$653$	−3.05595	−	5.29306i	−0.119588	−	0.207133i	0.800016	−	0.599978i	$-0.204824\pi$
$653$	−3.05595	−	5.29306i	−0.119588	−	0.207133i	−0.919605	+	0.392845i	$0.871491\pi$
$654$	−1.42447	+	3.39436i	−0.0557011	+	0.132730i
$655$	−6.44744	+	17.7142i	−0.251922	+	0.692151i
$656$	0.904567	+	5.75197i	0.0353174	+	0.224577i
$657$	−40.5445	+	70.2251i	−1.58179	+	2.73974i
$658$	5.16569	−	3.92585i	0.201379	−	0.153045i
$659$	−8.40615	−	47.6737i	−0.327457	−	1.85710i	−0.491812	−	0.870701i	$-0.663665\pi$
$659$	−8.40615	−	47.6737i	−0.327457	−	1.85710i	0.164355	−	0.986401i	$-0.447446\pi$
$660$	−12.6671	+	26.5197i	−0.493065	+	1.03228i
$661$	14.9228	+	17.7843i	0.580430	+	0.691729i	0.973736	−	0.227678i	$-0.0731134\pi$
$661$	14.9228	+	17.7843i	0.580430	+	0.691729i	−0.393307	+	0.919407i	$0.628669\pi$
$662$	1.60997	+	0.0777740i	0.0625731	+	0.00302277i
$663$	−2.38546	−	6.55399i	−0.0926435	−	0.254536i
$664$	24.8805	−	9.90262i	0.965549	−	0.384296i
$665$	15.0992	+	2.53069i	0.585521	+	0.0981359i
$666$	−14.5027	+	1.84094i	−0.561967	+	0.0713349i
$667$	−19.4137	+	7.06601i	−0.751702	+	0.273597i
$668$	−3.47556	−	44.4724i	−0.134473	−	1.72069i
$669$	24.6057	−	20.6466i	0.951310	−	0.798244i
$670$	4.05207	−	6.29585i	0.156545	−	0.243230i
$671$	−26.8614	+	4.73638i	−1.03697	+	0.182846i
$672$	−29.9640	−	13.2335i	−1.15589	−	0.510492i
$673$	22.5139	+	12.9984i	0.867848	+	0.501052i	0.866633	−	0.498947i	$-0.166280\pi$
$673$	22.5139	+	12.9984i	0.867848	+	0.501052i	0.00121569	+	0.999999i	$0.499613\pi$
$674$	−25.5140	−	5.78057i	−0.982762	−	0.222659i
$675$	15.6841	+	5.70853i	0.603680	+	0.219721i
$676$	3.51510	−	12.6481i	0.135196	−	0.486467i
$677$	38.3495	−	22.1411i	1.47389	−	0.850952i	0.474324	−	0.880351i	$-0.342693\pi$
$677$	38.3495	−	22.1411i	1.47389	−	0.850952i	0.999568	+	0.0293990i	$0.00935935\pi$
$678$	9.79290	+	31.5688i	0.376094	+	1.21239i
$679$	8.69695	+	7.29761i	0.333758	+	0.280056i
$680$	4.15291	+	2.23584i	0.159257	+	0.0857405i
$681$	7.09095	−	40.2148i	0.271726	−	1.54103i
$682$	−12.6853	+	6.52897i	−0.485745	+	0.250007i
$683$	37.9898			1.45364			0.726819	−	0.686829i	$-0.240998\pi$
$683$	37.9898			1.45364			0.726819	+	0.686829i	$0.240998\pi$
$684$	−49.7225	+	34.7566i	−1.90119	+	1.32895i
$685$	32.5359			1.24313
$686$	−24.5336	+	12.6271i	−0.936696	+	0.482106i
$687$	7.80519	−	44.2654i	0.297787	−	1.68883i
$688$	30.5891	+	11.7805i	1.16620	+	0.449128i
$689$	−3.59573	−	3.01717i	−0.136986	−	0.114945i
$690$	−18.4769	−	59.5630i	−0.703405	−	2.26753i
$691$	−0.0712585	+	0.0411411i	−0.00271080	+	0.00156508i	−0.501355	−	0.865242i	$-0.667165\pi$
$691$	−0.0712585	+	0.0411411i	−0.00271080	+	0.00156508i	0.498644	+	0.866807i	$0.333832\pi$
$692$	−42.2100	−	11.7308i	−1.60458	−	0.445937i
$693$	29.1888	+	10.6239i	1.10879	+	0.403567i
$694$	24.6623	+	5.58760i	0.936167	+	0.212102i
$695$	−15.7348	−	9.08450i	−0.596856	−	0.344595i
$696$	19.8247	+	15.6550i	0.751454	+	0.593400i
$697$	−1.24886	+	0.220207i	−0.0473038	+	0.00834093i
$698$	−7.27454	+	11.3027i	−0.275346	+	0.427815i
$699$	38.9845	−	32.7119i	1.47453	−	1.23728i
$700$	−4.88787	+	0.381991i	−0.184744	+	0.0144379i
$701$	6.42635	−	2.33900i	0.242720	−	0.0883428i	−0.217796	−	0.975994i	$-0.569887\pi$
$701$	6.42635	−	2.33900i	0.242720	−	0.0883428i	0.460516	+	0.887652i	$0.347664\pi$
$702$	44.4667	−	5.64450i	1.67829	−	0.213038i
$703$	−0.0548558	−	6.47482i	−0.00206893	−	0.244202i
$704$	13.3730	+	14.1387i	0.504014	+	0.532871i
$705$	−5.16572	−	14.1927i	−0.194552	−	0.534528i
$706$	16.2041	+	0.782784i	0.609848	+	0.0294605i
$707$	5.89984	+	7.03116i	0.221886	+	0.264434i
$708$	38.9854	+	18.6213i	1.46516	+	0.699831i
$709$	−3.47480	−	19.7066i	−0.130499	−	0.740096i	−0.977889	−	0.209125i	$-0.932938\pi$
$709$	−3.47480	−	19.7066i	−0.130499	−	0.740096i	0.847390	−	0.530971i	$-0.178173\pi$
$710$	−17.2225	+	13.0888i	−0.646348	+	0.491215i
$711$	18.2111	−	31.5425i	0.682969	−	1.18294i
$712$	−17.7603	+	0.528025i	−0.665595	+	0.0197886i
$713$	10.3542	−	28.4478i	0.387766	−	1.06538i
$714$	2.76059	−	6.57820i	0.103312	−	0.246183i
$715$	5.90671	+	10.2307i	0.220898	+	0.382607i
$716$	8.24205	+	18.1118i	0.308020	+	0.676870i
$717$	−43.1273	+	51.3972i	−1.61062	+	1.91946i
$718$	24.1958	−	26.1605i	0.902980	−	0.976302i
$719$	16.0253	+	2.82569i	0.597642	+	0.105380i	0.464282	−	0.885687i	$-0.346312\pi$
$719$	16.0253	+	2.82569i	0.597642	+	0.105380i	0.133360	+	0.991068i	$0.457423\pi$
$720$	−34.9998	+	40.1738i	−1.30437	+	1.49719i
$721$			28.0315i			1.04395i
$722$	−12.6996	−	23.6795i	−0.472630	−	0.881261i
$723$		−	17.5927i		−	0.654280i
$724$	−4.52488	−	6.59147i	−0.168166	−	0.244970i
$725$	3.72344	+	0.656543i	0.138285	+	0.0243834i
$726$	16.6513	+	15.4008i	0.617988	+	0.571576i
$727$	1.48698	−	1.77212i	0.0551491	−	0.0657242i	−0.737765	−	0.675058i	$-0.764119\pi$
$727$	1.48698	−	1.77212i	0.0551491	−	0.0657242i	0.792914	+	0.609334i	$0.208563\pi$
$728$	−11.2020	+	6.91927i	−0.415172	+	0.256445i
$729$	−5.40168	−	9.35598i	−0.200062	−	0.346518i
$730$	−29.0867	−	12.2064i	−1.07655	−	0.451779i
$731$	−2.44168	+	6.70845i	−0.0903087	+	0.248121i
$732$	−70.4375	−	6.82129i	−2.60345	−	0.252122i
$733$	7.32768	−	12.6919i	0.270654	−	0.468786i	−0.698376	−	0.715732i	$-0.746093\pi$
$733$	7.32768	−	12.6919i	0.270654	−	0.468786i	0.969029	+	0.246945i	$0.0794268\pi$
$734$	−6.02255	−	7.92455i	−0.222296	−	0.292501i
$735$	3.81096	+	21.6131i	0.140570	+	0.797210i
$736$	−41.2034	−	2.75727i	−1.51878	−	0.101634i
$737$	4.32482	+	5.15412i	0.159307	+	0.189855i
$738$	0.691236	−	14.3090i	0.0254447	−	0.526721i
$739$	−1.64645	−	4.52359i	−0.0605657	−	0.166403i	0.905719	−	0.423878i	$-0.139332\pi$
$739$	−1.64645	−	4.52359i	−0.0605657	−	0.166403i	−0.966285	+	0.257475i	$0.917109\pi$
$740$	−1.42087	−	5.50653i	−0.0522322	−	0.202424i
$741$	0.295650	+	34.8965i	0.0108610	+	1.28196i
$742$	−0.604595	−	4.76292i	−0.0221954	−	0.174852i
$743$	−39.1760	+	14.2589i	−1.43723	+	0.523108i	−0.938993	−	0.343935i	$-0.888240\pi$
$743$	−39.1760	+	14.2589i	−1.43723	+	0.523108i	−0.498233	+	0.867043i	$0.666018\pi$
$744$	−36.2461	+	7.50814i	−1.32885	+	0.275262i
$745$	−27.2323	+	22.8506i	−0.997716	+	0.837183i
$746$	38.6780	+	24.8935i	1.41610	+	0.911416i
$747$	−64.8834	+	11.4407i	−2.37396	+	0.418593i
$748$	−3.02471	+	2.96912i	−0.110594	+	0.108562i
$749$	8.26522	+	4.77193i	0.302005	+	0.174362i
$750$	−11.9601	+	52.7889i	−0.436721	+	1.92758i
$751$	−10.4064	−	3.78761i	−0.379734	−	0.138212i	0.145099	−	0.989417i	$-0.453650\pi$
$751$	−10.4064	−	3.78761i	−0.379734	−	0.138212i	−0.524833	+	0.851205i	$0.675872\pi$
$752$	−9.99955	−	0.185497i	−0.364646	−	0.00676438i
$753$	25.1219	−	14.5042i	0.915494	−	0.528561i
$754$	9.69784	−	3.00835i	0.353174	−	0.109558i
$755$	7.97866	+	6.69489i	0.290373	+	0.243652i
$756$	37.3107	+	26.6443i	1.35698	+	0.969044i
$757$	0.827186	−	4.69120i	0.0300646	−	0.170505i	−0.966078	−	0.258249i	$-0.916855\pi$
$757$	0.827186	−	4.69120i	0.0300646	−	0.170505i	0.996143	+	0.0877439i	$0.0279657\pi$
$758$	−15.1731	−	29.4802i	−0.551111	−	1.07077i
$759$	56.0420			2.03419
$760$	−15.8486	−	17.4858i	−0.574891	−	0.634275i
$761$	−1.17846			−0.0427193			−0.0213597	−	0.999772i	$-0.506800\pi$
$761$	−1.17846			−0.0427193			−0.0213597	+	0.999772i	$0.506800\pi$
$762$	−6.39436	−	12.4238i	−0.231643	−	0.450066i
$763$	−0.262813	+	1.49048i	−0.00951446	+	0.0539592i
$764$	8.77559	+	6.26682i	0.317490	+	0.226726i
$765$	−8.88934	−	7.45904i	−0.321395	−	0.269682i
$766$	29.2262	−	9.06622i	1.05599	−	0.327576i
$767$	15.0397	−	8.68318i	0.543053	−	0.313532i
$768$	23.6070	+	44.6338i	0.851843	+	1.61058i
$769$	−16.7613	−	6.10062i	−0.604429	−	0.219994i	0.0216350	−	0.999766i	$-0.493113\pi$
$769$	−16.7613	−	6.10062i	−0.604429	−	0.219994i	−0.626064	+	0.779772i	$0.715335\pi$
$770$	−2.66999	+	11.7847i	−0.0962198	+	0.424690i
$771$	−49.2826	−	28.4533i	−1.77487	−	1.02472i
$772$	22.1487	−	21.7417i	0.797151	−	0.782500i
$773$	−28.7474	+	5.06894i	−1.03397	+	0.182317i	−0.664783	−	0.747037i	$-0.731476\pi$
$773$	−28.7474	+	5.06894i	−1.03397	+	0.182317i	−0.369190	+	0.929354i	$0.620365\pi$
$774$	−67.8157	−	43.6468i	−2.43758	−	1.56885i
$775$	−4.24412	+	3.56124i	−0.152453	+	0.127923i
$776$	−3.54971	−	17.1365i	−0.127427	−	0.615164i
$777$	−8.08295	+	2.94195i	−0.289974	+	0.105542i
$778$	4.14290	+	32.6372i	0.148530	+	1.17010i
$779$	6.25782	+	1.04884i	0.224210	+	0.0375785i
$780$	7.65790	+	29.6779i	0.274197	+	1.06264i
$781$	−6.64858	−	18.2668i	−0.237905	−	0.653638i
$782$	0.433964	−	8.98330i	0.0155185	−	0.321242i
$783$	−22.7266	−	27.0846i	−0.812184	−	0.967923i
$784$	14.2625	+	2.78856i	0.509374	+	0.0995913i
$785$	4.26781	+	24.2039i	0.152325	+	0.863875i
$786$	−26.5942	−	34.9930i	−0.948582	−	1.24816i
$787$	−0.668131	+	1.15724i	−0.0238163	+	0.0412510i	−0.877688	−	0.479233i	$-0.840915\pi$
$787$	−0.668131	+	1.15724i	−0.0238163	+	0.0412510i	0.853872	+	0.520484i	$0.174248\pi$
$788$	−8.48497	−	0.821699i	−0.302265	−	0.0292718i
$789$	11.8201	−	32.4754i	0.420807	−	1.15616i
$790$	13.0647	+	5.48267i	0.464820	+	0.195065i
$791$	6.79474	+	11.7688i	0.241593	+	0.418451i
$792$	−25.1622	−	40.7363i	−0.894099	−	1.44750i
$793$	−18.2844	+	21.7905i	−0.649298	+	0.773803i
$794$	−26.6213	−	24.6220i	−0.944755	−	0.873802i
$795$	−11.0066	−	1.94075i	−0.390362	−	0.0688314i
$796$	8.67455	+	12.6364i	0.307461	+	0.447884i
$797$		−	36.9364i		−	1.30835i	−0.756341	−	0.654177i	$-0.773015\pi$
$797$		−	36.9364i		−	1.30835i	0.756341	−	0.654177i	$-0.226985\pi$
$798$	−24.0142	+	26.4095i	−0.850094	+	0.934887i
$799$		−	2.17818i		−	0.0770585i
$800$	6.27801	+	4.20728i	0.221961	+	0.148750i
$801$	43.0513	+	7.59110i	1.52114	+	0.268218i
$802$	2.54194	−	2.74834i	0.0897589	−	0.0970473i
$803$	18.2210	−	21.7149i	0.643004	−	0.766302i
$804$	7.23036	+	15.8886i	0.254995	+	0.560349i
$805$	−12.8201	−	22.2050i	−0.451849	−	0.782625i
$806$	−5.75753	+	13.7196i	−0.202800	+	0.483253i
$807$	29.5311	−	81.1359i	1.03954	−	2.85612i
$808$	−0.420453	−	14.1421i	−0.0147915	−	0.497516i
$809$	−13.2530	+	22.9549i	−0.465951	+	0.807050i	−0.999244	−	0.0388803i	$-0.987621\pi$
$809$	−13.2530	+	22.9549i	−0.465951	+	0.807050i	0.533293	+	0.845930i	$0.320954\pi$
$810$	39.9780	−	30.3827i	1.40468	−	1.06754i
$811$	−1.61077	−	9.13515i	−0.0565619	−	0.320778i	0.943378	−	0.331719i	$-0.107629\pi$
$811$	−1.61077	−	9.13515i	−0.0565619	−	0.320778i	−0.999940	+	0.0109405i	$0.996517\pi$
$812$	9.37156	+	4.47630i	0.328877	+	0.157087i
$813$	−48.1761	−	57.4140i	−1.68961	−	2.01360i
$814$	5.10452	+	0.246589i	0.178913	+	0.00864292i
$815$	−12.7652	−	35.0720i	−0.447144	−	1.22852i
$816$	−9.62378	+	5.32078i	−0.336900	+	0.186265i
$817$	22.7279	−	27.5568i	0.795149	−	0.964092i
$818$	30.0139	−	3.80990i	1.04941	−	0.133210i
$819$	30.4406	−	11.0795i	1.06368	−	0.387148i
$820$	5.55583	−	0.434192i	0.194018	−	0.0151627i
$821$	−7.41970	+	6.22587i	−0.258949	+	0.217284i	−0.763015	−	0.646381i	$-0.776282\pi$
$821$	−7.41970	+	6.22587i	−0.258949	+	0.217284i	0.504065	+	0.863666i	$0.331837\pi$
$822$	−41.0548	+	63.7885i	−1.43195	+	2.22488i
$823$	−14.8508	+	2.61860i	−0.517666	+	0.0912785i	−0.426376	−	0.904546i	$-0.640210\pi$
$823$	−14.8508	+	2.61860i	−0.517666	+	0.0912785i	−0.0912898	+	0.995824i	$0.529099\pi$
$824$	26.7785	−	33.9110i	0.932873	−	1.18135i
$825$	−8.88207	−	5.12806i	−0.309234	−	0.178536i
$826$	17.3241	+	3.92503i	0.602783	+	0.136569i
$827$	9.22703	+	3.35836i	0.320855	+	0.116782i	0.497427	−	0.867506i	$-0.334278\pi$
$827$	9.22703	+	3.35836i	0.320855	+	0.116782i	−0.176571	+	0.984288i	$0.556501\pi$
$828$	97.8905	+	27.2052i	3.40193	+	0.945445i
$829$	−42.6296	+	24.6122i	−1.48059	+	0.854817i	−0.999758	−	0.0219971i	$-0.992998\pi$
$829$	−42.6296	+	24.6122i	−1.48059	+	0.854817i	−0.480829	+	0.876814i	$0.659664\pi$
$830$	−7.59349	−	24.4787i	−0.263574	−	0.849668i
$831$	9.62718	+	8.07816i	0.333963	+	0.280228i
$832$	20.1616	+	2.33067i	0.698976	+	0.0808016i
$833$	−0.549604	+	3.11696i	−0.0190426	+	0.107996i
$834$	37.6654	−	19.3859i	1.30425	−	0.671280i
$835$	−42.6936			−1.47747
$836$	19.2276	−	8.94720i	0.665000	−	0.309445i
$837$	51.8094			1.79079
$838$	−4.98177	+	2.56406i	−0.172092	+	0.0885738i
$839$	−1.74578	+	9.90080i	−0.0602710	+	0.341814i	−1.00000		0.000106438i	$-0.999966\pi$
$839$	−1.74578	+	9.90080i	−0.0602710	+	0.341814i	0.939729	+	0.341920i	$0.111077\pi$
$840$	−14.8614	+	27.6040i	−0.512767	+	0.952429i
$841$	16.0799	+	13.4926i	0.554479	+	0.465264i
$842$	16.6762	+	53.7582i	0.574701	+	1.85263i
$843$	−13.6751	+	7.89534i	−0.470996	+	0.271930i
$844$	−10.9428	+	39.3748i	−0.376667	+	1.35534i
$845$	−11.8064	−	4.29717i	−0.406152	−	0.147827i
$846$	23.9982	+	5.43714i	0.825074	+	0.186933i
$847$	8.07599	+	4.66267i	0.277494	+	0.160211i
$848$	−3.81862	+	6.33951i	−0.131132	+	0.217700i
$849$	29.0964	−	5.13048i	0.998587	−	0.176078i
$850$	−0.890787	+	1.38405i	−0.0305537	+	0.0474725i
$851$	−8.30709	+	6.97048i	−0.284763	+	0.238945i
$852$	−3.92955	−	50.2817i	−0.134624	−	1.72262i
$853$	21.0381	−	7.65726i	0.720332	−	0.262180i	0.0442655	−	0.999020i	$-0.485905\pi$
$853$	21.0381	−	7.65726i	0.720332	−	0.262180i	0.676067	+	0.736840i	$0.263683\pi$
$854$	−28.8638	+	3.66391i	−0.987699	+	0.125376i
$855$	29.4561	+	50.0356i	1.00738	+	1.71118i
$856$	−5.44021	−	13.6686i	−0.185943	−	0.467183i
$857$	7.26265	+	19.9540i	0.248087	+	0.681615i	0.999756	+	0.0220739i	$0.00702692\pi$
$857$	7.26265	+	19.9540i	0.248087	+	0.681615i	−0.751669	+	0.659541i	$0.770751\pi$
$858$	−27.5112	−	1.32901i	−0.939218	−	0.0453716i
$859$	−4.83618	−	5.76354i	−0.165008	−	0.196649i	0.677204	−	0.735795i	$-0.263192\pi$
$859$	−4.83618	−	5.76354i	−0.165008	−	0.196649i	−0.842212	+	0.539146i	$0.818747\pi$
$860$	13.5216	−	28.3088i	0.461084	−	0.965323i
$861$	−1.46369	−	8.30102i	−0.0498825	−	0.282898i
$862$	−22.4167	+	17.0364i	−0.763516	+	0.580261i
$863$	12.1124	−	20.9793i	0.412311	−	0.714143i	−0.582831	−	0.812593i	$-0.698055\pi$
$863$	12.1124	−	20.9793i	0.412311	−	0.714143i	0.995142	+	0.0984500i	$0.0313885\pi$
$864$	−19.6833	−	67.8759i	−0.669638	−	2.30918i
$865$	−14.3408	+	39.4009i	−0.487600	+	1.33967i
$866$	−16.2042	+	38.6130i	−0.550642	+	1.31212i
$867$	25.6265	+	44.3864i	0.870322	+	1.50744i
$868$	−13.8519	+	6.30351i	−0.470164	+	0.213955i
$869$	−8.18419	+	9.75354i	−0.277630	+	0.330866i
$870$	16.4159	−	17.7488i	0.556550	−	0.601741i
$871$	6.91017	+	1.21845i	0.234142	+	0.0412856i
$872$	1.74180	−	1.55205i	0.0589848	−	0.0525589i
$873$			43.0564i			1.45724i
$874$	−17.0615	+	41.6411i	−0.577114	+	1.40853i
$875$			22.2539i			0.752319i
$876$	60.6339	−	41.6237i	2.04863	−	1.40633i
$877$	−23.2095	−	4.09245i	−0.783728	−	0.138192i	−0.232555	−	0.972583i	$-0.574708\pi$
$877$	−23.2095	−	4.09245i	−0.783728	−	0.138192i	−0.551173	+	0.834391i	$0.685820\pi$
$878$	−0.100581	−	0.0930276i	−0.00339446	−	0.00313953i
$879$	2.41476	−	2.87779i	0.0814477	−	0.0970656i
$880$	14.4879	−	11.7059i	0.488388	−	0.394604i
$881$	12.5493	+	21.7361i	0.422797	+	0.732306i	0.996212	−	0.0869589i	$-0.0277149\pi$
$881$	12.5493	+	21.7361i	0.422797	+	0.732306i	−0.573415	+	0.819265i	$0.694382\pi$
$882$	−32.9693	−	13.8358i	−1.11013	−	0.465875i
$883$	−16.9886	+	46.6758i	−0.571712	+	1.57077i	0.230085	+	0.973171i	$0.426100\pi$
$883$	−16.9886	+	46.6758i	−0.571712	+	1.57077i	−0.801797	+	0.597596i	$0.796123\pi$
$884$	−0.426070	+	4.39965i	−0.0143303	+	0.147976i
$885$	20.6750	−	35.8102i	0.694983	−	1.20375i
$886$	−18.4451	−	24.2703i	−0.619674	−	0.815376i
$887$	5.78998	+	32.8366i	0.194408	+	1.10255i	0.913259	+	0.407380i	$0.133558\pi$
$887$	5.78998	+	32.8366i	0.194408	+	1.10255i	−0.718850	+	0.695165i	$0.755331\pi$
$888$	12.5888	+	4.16263i	0.422452	+	0.139689i
$889$	−3.69270	−	4.40078i	−0.123849	−	0.147598i
$890$	−0.820545	+	16.9857i	−0.0275047	+	0.569364i
$891$	15.4331	+	42.4022i	0.517029	+	1.42053i
$892$	−19.7110	+	5.08611i	−0.659974	+	0.170295i
$893$	−3.64066	+	10.2726i	−0.121830	+	0.343759i
$894$	−10.4374	−	82.2244i	−0.349078	−	2.74999i
$895$	17.8964	−	6.51375i	0.598210	−	0.217731i
$896$	13.5208	+	15.7527i	0.451700	+	0.526259i
$897$	44.7717	−	37.5679i	1.49488	−	1.25436i
$898$	−23.3073	−	15.0008i	−0.777776	−	0.500583i
$899$	11.5579	−	2.03797i	0.385478	−	0.0679702i
$900$	−13.0253	−	13.2691i	−0.434175	−	0.442304i
$901$	−1.39587	−	0.805907i	−0.0465032	−	0.0268487i
$902$	−1.10657	+	4.88413i	−0.0368448	+	0.162624i
$903$	−44.5904	−	16.2296i	−1.48388	−	0.540087i
$904$	3.02285	−	20.7283i	0.100539	−	0.689415i
$905$	−6.62681	+	3.82599i	−0.220283	+	0.127180i
$906$	−23.1935	+	7.19481i	−0.770552	+	0.239031i
$907$	−17.9605	−	15.0706i	−0.596367	−	0.500412i	0.293908	−	0.955834i	$-0.405044\pi$
$907$	−17.9605	−	15.0706i	−0.596367	−	0.500412i	−0.890276	+	0.455422i	$0.849488\pi$
$908$	−15.0400	+	21.0608i	−0.499118	+	0.698928i
$909$	−6.04460	+	34.2806i	−0.200487	+	1.13702i
$910$	5.76685	+	11.2046i	0.191169	+	0.371428i
$911$	−35.7961			−1.18598			−0.592989	−	0.805211i	$-0.702052\pi$
$911$	−35.7961			−1.18598			−0.592989	+	0.805211i	$0.702052\pi$
$912$	54.2802	−	9.00810i	1.79740	−	0.298288i
$913$	23.0316			0.762236
$914$	−5.99566	−	11.6491i	−0.198319	−	0.385319i
$915$	−11.7612	+	66.7009i	−0.388812	+	2.20506i
$916$	−16.5549	+	23.1822i	−0.546988	+	0.765962i
$917$	−13.8428	−	11.6155i	−0.457130	−	0.383577i
$918$	14.7007	−	4.56026i	0.485194	−	0.150511i
$919$	24.2681	−	14.0112i	0.800530	−	0.462186i	−0.0431266	−	0.999070i	$-0.513732\pi$
$919$	24.2681	−	14.0112i	0.800530	−	0.462186i	0.843656	+	0.536884i	$0.180399\pi$
$920$	−5.70342	+	39.1096i	−0.188036	+	1.28940i
$921$	−64.4520	−	23.4586i	−2.12376	−	0.772987i
$922$	1.61244	−	7.11691i	0.0531029	−	0.234383i
$923$	−17.5568	−	10.1364i	−0.577888	−	0.333644i
$924$	−19.7355	−	20.1050i	−0.649249	−	0.661405i
$925$	1.95441	−	0.344616i	0.0642607	−	0.0113309i
$926$	37.9416	+	24.4195i	1.24684	+	0.802476i
$927$	−81.4375	+	68.3341i	−2.67476	+	2.24439i
$928$	−7.06101	−	14.3679i	−0.231789	−	0.471648i
$929$	−7.13749	+	2.59784i	−0.234174	+	0.0852322i	−0.456442	−	0.889753i	$-0.650876\pi$
$929$	−7.13749	+	2.59784i	−0.234174	+	0.0852322i	0.222268	+	0.974986i	$0.428654\pi$
$930$	4.46122	+	35.1449i	0.146289	+	1.15245i
$931$	7.80175	−	13.7814i	0.255692	−	0.451666i
$932$	−31.2296	+	8.05828i	−1.02296	+	0.263958i
$933$	35.7758	+	98.2932i	1.17125	+	3.21798i
$934$	1.65420	−	34.2429i	0.0541272	−	1.12046i
$935$	2.60751	+	3.10750i	0.0852746	+	0.101626i
$936$	−47.4097	−	15.6766i	−1.54964	−	0.512405i
$937$	0.989598	+	5.61229i	0.0323288	+	0.183345i	0.996696	−	0.0812214i	$-0.0258821\pi$
$937$	0.989598	+	5.61229i	0.0323288	+	0.183345i	−0.964367	+	0.264567i	$0.914771\pi$
$938$	4.34269	+	5.71417i	0.141794	+	0.186574i
$939$	49.1457	−	85.1228i	1.60381	−	2.77788i
$940$	−0.922656	+	9.52747i	−0.0300937	+	0.310752i
$941$	11.9414	−	32.8089i	0.389280	−	1.06954i	−0.578046	−	0.816004i	$-0.696185\pi$
$941$	11.9414	−	32.8089i	0.389280	−	1.06954i	0.967326	−	0.253534i	$-0.0815931\pi$
$942$	−52.8385	−	22.1740i	−1.72157	−	0.722469i
$943$	−5.31325	−	9.20283i	−0.173023	−	0.299685i
$944$	−17.2082	−	21.2980i	−0.560080	−	0.693192i
$945$	28.2055	−	33.6140i	0.917525	−	1.09346i
$946$	20.6971	+	19.1427i	0.672921	+	0.622384i
$947$	57.4378	+	10.1278i	1.86648	+	0.329110i	0.988694	−	0.149946i	$-0.0479101\pi$
$947$	57.4378	+	10.1278i	1.86648	+	0.329110i	0.877784	+	0.479057i	$0.159021\pi$
$948$	−27.2345	+	18.6958i	−0.884537	+	0.607212i
$949$		−	29.5625i		−	0.959638i
$950$	6.51440	−	5.03848i	0.211355	−	0.163470i
$951$			35.8644i			1.16298i
$952$	−3.37557	+	3.00783i	−0.109403	+	0.0974845i
$953$	14.1731	+	2.49911i	0.459113	+	0.0809540i	0.398421	−	0.917203i	$-0.369558\pi$
$953$	14.1731	+	2.49911i	0.459113	+	0.0809540i	0.0606917	+	0.998157i	$0.480669\pi$
$954$	12.3635	−	13.3674i	0.400282	−	0.432785i
$955$	6.63402	−	7.90612i	0.214672	−	0.255836i
$956$	38.7027	−	17.6123i	1.25174	−	0.569622i
$957$	10.8630	+	18.8152i	0.351150	+	0.608210i
$958$	−1.28977	+	3.07340i	−0.0416707	+	0.0992971i
$959$	−10.6671	+	29.3077i	−0.344460	+	0.946396i
$960$	44.3487	−	19.1968i	1.43135	−	0.619574i
$961$	6.90118	−	11.9532i	0.222619	−	0.385587i
$962$	4.24329	−	3.22484i	0.136809	−	0.103973i
$963$	6.28519	+	35.6451i	0.202537	+	1.14865i
$964$	−4.80553	+	10.0608i	−0.154776	+	0.324037i
$965$	−19.0937	−	22.7550i	−0.614648	−	0.732509i
$966$	59.7111	+	2.88452i	1.92117	+	0.0928078i
$967$	−9.26769	−	25.4628i	−0.298029	−	0.818827i	−0.994829	−	0.101562i	$-0.967616\pi$
$967$	−9.26769	−	25.4628i	−0.298029	−	0.818827i	0.696800	−	0.717265i	$-0.254606\pi$
$968$	−5.31566	−	13.3557i	−0.170852	−	0.429268i
$969$	2.18080	+	11.7833i	0.0700574	+	0.378534i
$970$	−16.6159	+	2.10918i	−0.533503	+	0.0677218i
$971$	−25.5203	+	9.28864i	−0.818986	+	0.298087i	−0.717331	−	0.696733i	$-0.754636\pi$
$971$	−25.5203	+	9.28864i	−0.818986	+	0.298087i	−0.101656	+	0.994820i	$0.532414\pi$
$972$	3.28122	+	41.9857i	0.105245	+	1.34669i
$973$	13.3419	−	11.1952i	0.427723	−	0.358902i
$974$	−25.1038	+	39.0047i	−0.804376	+	1.24979i
$975$	−10.5335	+	1.85733i	−0.337341	+	0.0594823i
$976$	38.4181	+	23.1412i	1.22973	+	0.740733i
$977$	−23.9247	−	13.8130i	−0.765420	−	0.441916i	0.0658183	−	0.997832i	$-0.479034\pi$
$977$	−23.9247	−	13.8130i	−0.765420	−	0.441916i	−0.831238	+	0.555916i	$0.812368\pi$
$978$	84.8683	+	19.2282i	2.71379	+	0.614849i
$979$	−14.3603	−	5.22671i	−0.458956	−	0.167046i
$980$	3.72431	−	13.4009i	0.118969	−	0.428077i
$981$	−4.97085	+	2.86992i	−0.158707	+	0.0916296i
$982$	5.61094	+	18.0877i	0.179052	+	0.577201i
$983$	21.7373	+	18.2398i	0.693313	+	0.581759i	0.919863	−	0.392241i	$-0.128300\pi$
$983$	21.7373	+	18.2398i	0.693313	+	0.581759i	−0.226549	+	0.974000i	$0.572745\pi$
$984$	−6.15927	+	11.4404i	−0.196350	+	0.364707i
$985$	−1.41676	+	8.03485i	−0.0451418	+	0.256012i
$986$	3.10012	−	1.59559i	0.0987280	−	0.0508141i
$987$	14.4782			0.460845
$988$	9.36306	−	20.0372i	0.297879	−	0.637467i
$989$	−59.8228			−1.90225
$990$	−40.7458	+	20.9714i	−1.29499	+	0.666514i
$991$	−5.06926	+	28.7492i	−0.161030	+	0.913248i	0.792033	+	0.610478i	$0.209023\pi$
$991$	−5.06926	+	28.7492i	−0.161030	+	0.913248i	−0.953064	+	0.302770i	$0.902089\pi$
$992$	22.7791	+	5.60706i	0.723236	+	0.178024i
$993$	2.75529	+	2.31196i	0.0874363	+	0.0733678i
$994$	−6.14367	−	19.8050i	−0.194865	−	0.628176i
$995$	12.7041	−	7.33473i	0.402748	−	0.232527i
$996$	57.5737	+	16.0005i	1.82429	+	0.506997i
$997$	−28.5953	−	10.4078i	−0.905623	−	0.329620i	−0.153119	−	0.988208i	$-0.548932\pi$
$997$	−28.5953	−	10.4078i	−0.905623	−	0.329620i	−0.752504	+	0.658588i	$0.771154\pi$
$998$	46.6870	+	10.5776i	1.47785	+	0.334829i
$999$	−16.0720	−	9.27919i	−0.508497	−	0.293581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.71.3	yes	48
3.2	odd	2		684.2.cf.a.451.6		48
4.3	odd	2	inner	76.2.k.a.71.4	yes	48
12.11	even	2		684.2.cf.a.451.5		48
19.15	odd	18	inner	76.2.k.a.15.4	yes	48
57.53	even	18		684.2.cf.a.91.5		48
76.15	even	18	inner	76.2.k.a.15.3	✓	48
228.167	odd	18		684.2.cf.a.91.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.15.3	✓	48	76.15	even	18	inner
76.2.k.a.15.4	yes	48	19.15	odd	18	inner
76.2.k.a.71.3	yes	48	1.1	even	1	trivial
76.2.k.a.71.4	yes	48	4.3	odd	2	inner
684.2.cf.a.91.5		48	57.53	even	18
684.2.cf.a.91.6		48	228.167	odd	18
684.2.cf.a.451.5		48	12.11	even	2
684.2.cf.a.451.6		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647187 - 1.25744i) q^{2} +(0.547993 - 3.10782i) q^{3} +(-1.16230 + 1.62759i) q^{4} +(1.46633 + 1.23040i) q^{5} +(-4.26255 + 1.32228i) q^{6} +(-1.58907 + 0.917452i) q^{7} +(2.79882 + 0.408157i) q^{8} +(-6.53918 - 2.38007i) q^{9} +O(q^{10})\)	\(q+(-0.647187 - 1.25744i) q^{2} +(0.547993 - 3.10782i) q^{3} +(-1.16230 + 1.62759i) q^{4} +(1.46633 + 1.23040i) q^{5} +(-4.26255 + 1.32228i) q^{6} +(-1.58907 + 0.917452i) q^{7} +(2.79882 + 0.408157i) q^{8} +(-6.53918 - 2.38007i) q^{9} +(0.598159 - 2.64012i) q^{10} +(2.10674 + 1.21633i) q^{11} +(4.42134 + 4.50412i) q^{12} +(2.49843 - 0.440541i) q^{13} +(2.18207 + 1.40440i) q^{14} +(4.62741 - 3.88286i) q^{15} +(-1.29813 - 3.78350i) q^{16} +(0.818624 - 0.297955i) q^{17} +(1.23929 + 9.76296i) q^{18} +(-4.35874 + 0.0369281i) q^{19} +(-3.70691 + 0.956507i) q^{20} +(1.98048 + 5.44131i) q^{21} +(0.165999 - 3.43628i) q^{22} +(4.69241 + 5.59220i) q^{23} +(2.80221 - 8.47457i) q^{24} +(-0.231990 - 1.31568i) q^{25} +(-2.17091 - 2.85651i) q^{26} +(-6.24660 + 10.8194i) q^{27} +(0.353735 - 3.65272i) q^{28} +(-0.967934 + 2.65938i) q^{29} +(-7.87725 - 3.30574i) q^{30} +(-2.07350 - 3.59141i) q^{31} +(-3.91738 + 4.08095i) q^{32} +(4.93460 - 5.88083i) q^{33} +(-0.904462 - 0.836536i) q^{34} +(-3.45895 - 0.609906i) q^{35} +(11.4743 - 7.87679i) q^{36} +1.48548i q^{37} +(2.86736 + 5.45695i) q^{38} -8.00610i q^{39} +(3.60181 + 4.04217i) q^{40} +(-1.43355 - 0.252774i) q^{41} +(5.56037 - 6.01187i) q^{42} +(-5.26751 + 6.27757i) q^{43} +(-4.42834 + 2.01518i) q^{44} +(-6.66019 - 11.5358i) q^{45} +(3.99497 - 9.51961i) q^{46} +(0.855159 - 2.34953i) q^{47} +(-12.4698 + 1.96103i) q^{48} +(-1.81656 + 3.14638i) q^{49} +(-1.50424 + 1.14320i) q^{50} +(-0.477390 - 2.70741i) q^{51} +(-2.18690 + 4.57848i) q^{52} +(-1.18928 - 1.41733i) q^{53} +(17.6475 + 0.852512i) q^{54} +(1.59262 + 4.37567i) q^{55} +(-4.82200 + 1.91919i) q^{56} +(-2.27379 + 13.5664i) q^{57} +(3.97043 - 0.503998i) q^{58} +(6.43248 - 2.34123i) q^{59} +(0.941293 + 12.0446i) q^{60} +(-8.58916 + 7.20716i) q^{61} +(-3.17403 + 4.93161i) q^{62} +(12.5748 - 2.21728i) q^{63} +(7.66682 + 2.28472i) q^{64} +(4.20558 + 2.42810i) q^{65} +(-10.5884 - 2.39896i) q^{66} +(2.59900 + 0.945959i) q^{67} +(-0.466535 + 1.67870i) q^{68} +(19.9510 - 11.5187i) q^{69} +(1.47167 + 4.74413i) q^{70} +(-6.12140 - 5.13647i) q^{71} +(-17.3306 - 9.33040i) q^{72} +(2.02346 - 11.4756i) q^{73} +(1.86790 - 0.961383i) q^{74} -4.21603 q^{75} +(5.00605 - 7.13719i) q^{76} -4.46368 q^{77} +(-10.0672 + 5.18145i) q^{78} +(-0.908863 + 5.15442i) q^{79} +(2.75173 - 7.14509i) q^{80} +(14.2094 + 11.9231i) q^{81} +(0.609929 + 1.96619i) q^{82} +(8.19927 - 4.73385i) q^{83} +(-11.1582 - 3.10101i) q^{84} +(1.56698 + 0.570334i) q^{85} +(11.3027 + 2.56080i) q^{86} +(7.73445 + 4.46548i) q^{87} +(5.39994 + 4.26416i) q^{88} +(-6.18655 + 1.09085i) q^{89} +(-10.1951 + 15.8406i) q^{90} +(-3.56602 + 2.99225i) q^{91} +(-14.5558 + 1.13755i) q^{92} +(-12.2977 + 4.47601i) q^{93} +(-3.50784 + 0.445277i) q^{94} +(-6.43681 - 5.30885i) q^{95} +(10.5362 + 14.4108i) q^{96} +(-2.11617 - 5.81414i) q^{97} +(5.13204 + 0.247918i) q^{98} +(-10.8814 - 12.9680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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