LMFDB - Embedded newform 378.2.u.e.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	378.43
Dual form			378.2.u.e.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.73154 - 0.0419083i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.354259 - 0.128940i) q^{5} +(1.29950 + 1.14512i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99649 + 0.145132i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.73154 - 0.0419083i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.354259 - 0.128940i) q^{5} +(1.29950 + 1.14512i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99649 + 0.145132i) q^{9} +(0.188497 + 0.326487i) q^{10} +(2.76158 - 1.00513i) q^{11} +(-0.259408 - 1.71251i) q^{12} +(-4.07784 + 3.42171i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(0.608011 + 0.238111i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.02781 - 5.24432i) q^{17} +(-2.20215 - 2.03728i) q^{18} +(0.0148207 - 0.0256701i) q^{19} +(0.0654644 - 0.371267i) q^{20} +(-0.341951 + 1.69796i) q^{21} +(-2.76158 - 1.00513i) q^{22} +(-1.37810 - 7.81558i) q^{23} +(-0.902066 + 1.47861i) q^{24} +(-3.72135 - 3.12258i) q^{25} +5.32324 q^{26} +(-5.18247 - 0.376880i) q^{27} +1.00000 q^{28} +(-4.78964 - 4.01899i) q^{29} +(-0.312709 - 0.573226i) q^{30} +(-0.0693598 - 0.393359i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-4.82392 + 1.62470i) q^{33} +(-1.05155 + 5.96362i) q^{34} +(-0.188497 + 0.326487i) q^{35} +(0.377407 + 2.97617i) q^{36} +(2.75692 + 4.77513i) q^{37} +(-0.0278537 + 0.0101379i) q^{38} +(7.20435 - 5.75395i) q^{39} +(-0.288795 + 0.242327i) q^{40} +(-5.65151 + 4.74218i) q^{41} +(1.35338 - 1.08091i) q^{42} +(-1.46070 + 0.531651i) q^{43} +(1.46941 + 2.54509i) q^{44} +(-1.04282 - 0.437781i) q^{45} +(-3.96807 + 6.87291i) q^{46} +(1.89209 - 10.7306i) q^{47} +(1.64145 - 0.552842i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(0.843561 + 4.78407i) q^{50} +(5.02301 + 9.20766i) q^{51} +(-4.07784 - 3.42171i) q^{52} -4.70930 q^{53} +(3.72775 + 3.61993i) q^{54} -1.10792 q^{55} +(-0.766044 - 0.642788i) q^{56} +(-0.0267384 + 0.0438279i) q^{57} +(1.08572 + 6.15745i) q^{58} +(6.22082 + 2.26419i) q^{59} +(-0.128914 + 0.640122i) q^{60} +(2.33614 - 13.2489i) q^{61} +(-0.199714 + 0.345914i) q^{62} +(0.663262 - 2.92576i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.88580 - 0.686377i) q^{65} +(4.73967 + 1.85617i) q^{66} +(9.08087 - 7.61975i) q^{67} +(4.63887 - 3.89248i) q^{68} +(2.05870 + 13.5908i) q^{69} +(0.354259 - 0.128940i) q^{70} +(2.81563 + 4.87681i) q^{71} +(1.62393 - 2.52247i) q^{72} +(-5.51391 + 9.55037i) q^{73} +(0.957469 - 5.43007i) q^{74} +(6.31282 + 5.56284i) q^{75} +(0.0278537 + 0.0101379i) q^{76} +(-0.510319 - 2.89417i) q^{77} +(-9.21742 - 0.223088i) q^{78} +(-3.32945 - 2.79374i) q^{79} +0.376995 q^{80} +(8.95787 + 0.869773i) q^{81} +7.37752 q^{82} +(8.38962 + 7.03973i) q^{83} +(-1.73154 - 0.0419083i) q^{84} +(0.396428 + 2.24825i) q^{85} +(1.46070 + 0.531651i) q^{86} +(8.12505 + 7.15978i) q^{87} +(0.510319 - 2.89417i) q^{88} +(1.32012 - 2.28652i) q^{89} +(0.517446 + 1.00567i) q^{90} +(2.66162 + 4.61006i) q^{91} +(7.45754 - 2.71432i) q^{92} +(0.103615 + 0.684025i) q^{93} +(-8.34692 + 7.00390i) q^{94} +(-0.00856026 + 0.00718291i) q^{95} +(-1.61279 - 0.631604i) q^{96} +(-8.37922 + 3.04979i) q^{97} +(0.500000 + 0.866025i) q^{98} +(8.42092 - 2.61107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.73154	−	0.0419083i	−0.999707	−	0.0241958i
$3$	−1.73154	−	0.0419083i	−0.999707	−	0.0241958i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.354259	−	0.128940i	−0.158429	−	0.0576636i	0.261588	−	0.965180i	$-0.415754\pi$
$5$	−0.354259	−	0.128940i	−0.158429	−	0.0576636i	−0.420017	+	0.907516i	$0.637976\pi$
$6$	1.29950	+	1.14512i	0.530519	+	0.467493i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.99649	+	0.145132i	0.998829	+	0.0483774i
$10$	0.188497	+	0.326487i	0.0596081	+	0.103244i
$11$	2.76158	−	1.00513i	0.832648	−	0.303059i	0.109703	−	0.993964i	$-0.465010\pi$
$11$	2.76158	−	1.00513i	0.832648	−	0.303059i	0.722945	+	0.690905i	$0.242788\pi$
$12$	−0.259408	−	1.71251i	−0.0748846	−	0.494360i
$13$	−4.07784	+	3.42171i	−1.13099	+	0.949012i	−0.999107	−	0.0422538i	$-0.986546\pi$
$13$	−4.07784	+	3.42171i	−1.13099	+	0.949012i	−0.131881	+	0.991266i	$0.542102\pi$
$14$	−0.766044	+	0.642788i	−0.204734	+	0.171792i
$15$	0.608011	+	0.238111i	0.156988	+	0.0614801i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.02781	−	5.24432i	−0.734352	−	1.27193i	−0.955007	−	0.296583i	$-0.904153\pi$
$17$	−3.02781	−	5.24432i	−0.734352	−	1.27193i	0.220655	−	0.975352i	$-0.429180\pi$
$18$	−2.20215	−	2.03728i	−0.519053	−	0.480192i
$19$	0.0148207	−	0.0256701i	0.00340009	−	0.00588913i	−0.864320	−	0.502942i	$-0.832251\pi$
$19$	0.0148207	−	0.0256701i	0.00340009	−	0.00588913i	0.867720	+	0.497053i	$0.165584\pi$
$20$	0.0654644	−	0.371267i	0.0146383	−	0.0830179i
$21$	−0.341951	+	1.69796i	−0.0746198	+	0.370525i
$22$	−2.76158	−	1.00513i	−0.588771	−	0.214295i
$23$	−1.37810	−	7.81558i	−0.287353	−	1.62966i	−0.696756	−	0.717308i	$-0.745374\pi$
$23$	−1.37810	−	7.81558i	−0.287353	−	1.62966i	0.409403	−	0.912354i	$-0.365737\pi$
$24$	−0.902066	+	1.47861i	−0.184133	+	0.301819i
$25$	−3.72135	−	3.12258i	−0.744270	−	0.624516i
$26$	5.32324			1.04397
$27$	−5.18247	−	0.376880i	−0.997366	−	0.0725306i
$28$	1.00000			0.188982
$29$	−4.78964	−	4.01899i	−0.889415	−	0.746308i	0.0786780	−	0.996900i	$-0.474930\pi$
$29$	−4.78964	−	4.01899i	−0.889415	−	0.746308i	−0.968093	+	0.250593i	$0.919375\pi$
$30$	−0.312709	−	0.573226i	−0.0570926	−	0.104656i
$31$	−0.0693598	−	0.393359i	−0.0124574	−	0.0706494i	0.977945	−	0.208861i	$-0.0669757\pi$
$31$	−0.0693598	−	0.393359i	−0.0124574	−	0.0706494i	−0.990403	+	0.138212i	$0.955865\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−4.82392	+	1.62470i	−0.839737	+	0.282824i
$34$	−1.05155	+	5.96362i	−0.180339	+	1.02275i
$35$	−0.188497	+	0.326487i	−0.0318619	+	0.0551864i
$36$	0.377407	+	2.97617i	0.0629012	+	0.496028i
$37$	2.75692	+	4.77513i	0.453235	+	0.785026i	0.998585	−	0.0531824i	$-0.0169365\pi$
$37$	2.75692	+	4.77513i	0.453235	+	0.785026i	−0.545350	+	0.838209i	$0.683603\pi$
$38$	−0.0278537	+	0.0101379i	−0.00451847	+	0.00164459i
$39$	7.20435	−	5.75395i	1.15362	−	0.921369i
$40$	−0.288795	+	0.242327i	−0.0456624	+	0.0383153i
$41$	−5.65151	+	4.74218i	−0.882617	+	0.740604i	−0.966715	−	0.255854i	$-0.917643\pi$
$41$	−5.65151	+	4.74218i	−0.882617	+	0.740604i	0.0840985	+	0.996457i	$0.473199\pi$
$42$	1.35338	−	1.08091i	0.208831	−	0.166788i
$43$	−1.46070	+	0.531651i	−0.222755	+	0.0810760i	−0.450987	−	0.892531i	$-0.648928\pi$
$43$	−1.46070	+	0.531651i	−0.222755	+	0.0810760i	0.228232	+	0.973607i	$0.426706\pi$
$44$	1.46941	+	2.54509i	0.221521	+	0.383686i
$45$	−1.04282	−	0.437781i	−0.155454	−	0.0652605i
$46$	−3.96807	+	6.87291i	−0.585061	+	1.01335i
$47$	1.89209	−	10.7306i	0.275990	−	1.56522i	−0.459808	−	0.888018i	$-0.652082\pi$
$47$	1.89209	−	10.7306i	0.275990	−	1.56522i	0.735799	−	0.677200i	$-0.236807\pi$
$48$	1.64145	−	0.552842i	0.236923	−	0.0797959i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	0.843561	+	4.78407i	0.119298	+	0.676570i
$51$	5.02301	+	9.20766i	0.703361	+	1.28933i
$52$	−4.07784	−	3.42171i	−0.565494	−	0.474506i
$53$	−4.70930			−0.646872			−0.323436	−	0.946250i	$-0.604838\pi$
$53$	−4.70930			−0.646872			−0.323436	+	0.946250i	$0.604838\pi$
$54$	3.72775	+	3.61993i	0.507282	+	0.492610i
$55$	−1.10792			−0.149391
$56$	−0.766044	−	0.642788i	−0.102367	−	0.0858961i
$57$	−0.0267384	+	0.0438279i	−0.00354159	+	0.00580514i
$58$	1.08572	+	6.15745i	0.142563	+	0.808513i
$59$	6.22082	+	2.26419i	0.809882	+	0.294773i	0.713575	−	0.700579i	$-0.247075\pi$
$59$	6.22082	+	2.26419i	0.809882	+	0.294773i	0.0963068	+	0.995352i	$0.469297\pi$
$60$	−0.128914	+	0.640122i	−0.0166427	+	0.0826394i
$61$	2.33614	−	13.2489i	0.299112	−	1.69635i	−0.350891	−	0.936416i	$-0.614121\pi$
$61$	2.33614	−	13.2489i	0.299112	−	1.69635i	0.650003	−	0.759932i	$-0.274768\pi$
$62$	−0.199714	+	0.345914i	−0.0253637	+	0.0439312i
$63$	0.663262	−	2.92576i	0.0835631	−	0.368611i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.88580	−	0.686377i	0.233905	−	0.0851346i
$66$	4.73967	+	1.85617i	0.583414	+	0.228478i
$67$	9.08087	−	7.61975i	1.10940	−	0.930901i	0.111383	−	0.993778i	$-0.464472\pi$
$67$	9.08087	−	7.61975i	1.10940	−	0.930901i	0.998021	+	0.0628765i	$0.0200274\pi$
$68$	4.63887	−	3.89248i	0.562546	−	0.472032i
$69$	2.05870	+	13.5908i	0.247838	+	1.63614i
$70$	0.354259	−	0.128940i	0.0423421	−	0.0154112i
$71$	2.81563	+	4.87681i	0.334154	+	0.578771i	0.983322	−	0.181874i	$-0.0582162\pi$
$71$	2.81563	+	4.87681i	0.334154	+	0.578771i	−0.649168	+	0.760645i	$0.724883\pi$
$72$	1.62393	−	2.52247i	0.191382	−	0.297276i
$73$	−5.51391	+	9.55037i	−0.645354	+	1.11779i	0.338865	+	0.940835i	$0.389957\pi$
$73$	−5.51391	+	9.55037i	−0.645354	+	1.11779i	−0.984220	+	0.176951i	$0.943376\pi$
$74$	0.957469	−	5.43007i	0.111303	−	0.631233i
$75$	6.31282	+	5.56284i	0.728941	+	0.642342i
$76$	0.0278537	+	0.0101379i	0.00319504	+	0.00116290i
$77$	−0.510319	−	2.89417i	−0.0581563	−	0.329821i
$78$	−9.21742	−	0.223088i	−1.04367	−	0.0252597i
$79$	−3.32945	−	2.79374i	−0.374592	−	0.314320i	0.435983	−	0.899955i	$-0.356401\pi$
$79$	−3.32945	−	2.79374i	−0.374592	−	0.314320i	−0.810575	+	0.585635i	$0.800845\pi$
$80$	0.376995			0.0421493
$81$	8.95787	+	0.869773i	0.995319	+	0.0966414i
$82$	7.37752			0.814710
$83$	8.38962	+	7.03973i	0.920880	+	0.772710i	0.974158	−	0.225869i	$-0.0725222\pi$
$83$	8.38962	+	7.03973i	0.920880	+	0.772710i	−0.0532772	+	0.998580i	$0.516967\pi$
$84$	−1.73154	−	0.0419083i	−0.188927	−	0.00457257i
$85$	0.396428	+	2.24825i	0.0429986	+	0.243857i
$86$	1.46070	+	0.531651i	0.157511	+	0.0573294i
$87$	8.12505	+	7.15978i	0.871097	+	0.767609i
$88$	0.510319	−	2.89417i	0.0544002	−	0.308519i
$89$	1.32012	−	2.28652i	0.139933	−	0.242371i	−0.787538	−	0.616266i	$-0.788645\pi$
$89$	1.32012	−	2.28652i	0.139933	−	0.242371i	0.927471	+	0.373895i	$0.121978\pi$
$90$	0.517446	+	1.00567i	0.0545436	+	0.106007i
$91$	2.66162	+	4.61006i	0.279013	+	0.483265i
$92$	7.45754	−	2.71432i	0.777502	−	0.282988i
$93$	0.103615	+	0.684025i	0.0107443	+	0.0709301i
$94$	−8.34692	+	7.00390i	−0.860919	+	0.722397i
$95$	−0.00856026	+	0.00718291i	−0.000878264	+	0.000736951i
$96$	−1.61279	−	0.631604i	−0.164604	−	0.0644628i
$97$	−8.37922	+	3.04979i	−0.850781	+	0.309659i	−0.730359	−	0.683064i	$-0.760647\pi$
$97$	−8.37922	+	3.04979i	−0.850781	+	0.309659i	−0.120422	+	0.992723i	$0.538425\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	8.42092	−	2.61107i	0.846334	−	0.262423i
$100$	2.42894	−	4.20704i	0.242894	−	0.420704i
$101$	1.73102	−	9.81708i	0.172242	−	0.976836i	−0.769036	−	0.639205i	$-0.779263\pi$
$101$	1.73102	−	9.81708i	0.172242	−	0.976836i	0.941279	−	0.337631i	$-0.109625\pi$
$102$	2.07073	−	10.2822i	0.205032	−	1.01809i
$103$	−10.0456	−	3.65630i	−0.989823	−	0.360266i	−0.204171	−	0.978935i	$-0.565450\pi$
$103$	−10.0456	−	3.65630i	−0.989823	−	0.360266i	−0.785652	+	0.618669i	$0.787672\pi$
$104$	0.924370	+	5.24236i	0.0906420	+	0.514056i
$105$	0.340074	−	0.557427i	0.0331878	−	0.0543993i
$106$	3.60753	+	3.02708i	0.350395	+	0.294016i
$107$	−13.4386			−1.29916			−0.649579	−	0.760294i	$-0.725055\pi$
$107$	−13.4386			−1.29916			−0.649579	+	0.760294i	$0.725055\pi$
$108$	−0.528771	−	5.16918i	−0.0508810	−	0.497404i
$109$	16.7418			1.60357			0.801786	−	0.597611i	$-0.203883\pi$
$109$	16.7418			1.60357			0.801786	+	0.597611i	$0.203883\pi$
$110$	0.848713	+	0.712155i	0.0809216	+	0.0679013i
$111$	−4.57361	−	8.38388i	−0.434108	−	0.795763i
$112$	0.173648	+	0.984808i	0.0164082	+	0.0930556i
$113$	6.34575	+	2.30966i	0.596958	+	0.217275i	0.622787	−	0.782392i	$-0.286000\pi$
$113$	6.34575	+	2.30966i	0.596958	+	0.217275i	−0.0258292	+	0.999666i	$0.508223\pi$
$114$	0.0486548	−	0.0163870i	0.00455694	−	0.00153478i
$115$	−0.519536	+	2.94643i	−0.0484469	+	0.274756i
$116$	3.12622	−	5.41477i	0.290262	−	0.502749i
$117$	−12.7158	+	9.66129i	−1.17557	+	0.893186i
$118$	−3.31003	−	5.73314i	−0.304713	−	0.527778i
$119$	−5.69042	+	2.07114i	−0.521640	+	0.189861i
$120$	0.510216	−	0.407498i	0.0465761	−	0.0371993i
$121$	−1.81045	+	1.51915i	−0.164587	+	0.138105i
$122$	−10.3058	+	8.64761i	−0.933045	+	0.782917i
$123$	9.98457	−	7.97444i	0.900278	−	0.719031i
$124$	0.375339	−	0.136612i	0.0337064	−	0.0122681i
$125$	1.85818	+	3.21847i	0.166201	+	0.287868i
$126$	−2.38873	+	1.81493i	−0.212805	+	0.161687i
$127$	3.95711	−	6.85392i	0.351137	−	0.608187i	−0.635312	−	0.772256i	$-0.719129\pi$
$127$	3.95711	−	6.85392i	0.351137	−	0.608187i	0.986449	+	0.164069i	$0.0524619\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	2.55155	−	0.859362i	0.224651	−	0.0756626i
$130$	−1.88580	−	0.686377i	−0.165396	−	0.0601992i
$131$	1.93831	+	10.9927i	0.169351	+	0.960438i	0.944464	+	0.328615i	$0.106582\pi$
$131$	1.93831	+	10.9927i	0.169351	+	0.960438i	−0.775113	+	0.631823i	$0.782307\pi$
$132$	−2.43768	−	4.46851i	−0.212173	−	0.388934i
$133$	−0.0227066	−	0.0190531i	−0.00196891	−	0.00165211i
$134$	−11.8542			−1.02405
$135$	1.78734	+	0.801739i	0.153830	+	0.0690027i
$136$	−6.05562			−0.519265
$137$	−3.58586	−	3.00889i	−0.306361	−	0.257067i	0.476625	−	0.879107i	$-0.341860\pi$
$137$	−3.58586	−	3.00889i	−0.306361	−	0.257067i	−0.782986	+	0.622039i	$0.786304\pi$
$138$	7.15893	−	11.7344i	0.609408	−	0.998902i
$139$	−0.957111	−	5.42804i	−0.0811811	−	0.460401i	−0.998116	−	0.0613629i	$-0.980455\pi$
$139$	−0.957111	−	5.42804i	−0.0811811	−	0.460401i	0.916934	−	0.399038i	$-0.130656\pi$
$140$	−0.354259	−	0.128940i	−0.0299404	−	0.0108974i
$141$	−3.72594	+	18.5012i	−0.313781	+	1.55808i
$142$	0.977858	−	5.54571i	0.0820600	−	0.465385i
$143$	−7.82200	+	13.5481i	−0.654108	+	1.13295i
$144$	−2.86542	+	0.888480i	−0.238785	+	0.0740400i
$145$	1.17857	+	2.04134i	0.0978747	+	0.169524i
$146$	10.3628	−	3.77174i	0.857628	−	0.312151i
$147$	1.61279	+	0.631604i	0.133020	+	0.0520938i
$148$	−4.22385	+	3.54423i	−0.347198	+	0.291334i
$149$	−7.35921	+	6.17511i	−0.602890	+	0.505885i	−0.892373	−	0.451298i	$-0.850961\pi$
$149$	−7.35921	+	6.17511i	−0.602890	+	0.505885i	0.289483	+	0.957183i	$0.406517\pi$
$150$	−1.26017	−	8.31918i	−0.102893	−	0.679259i
$151$	−7.66062	+	2.78824i	−0.623412	+	0.226903i	−0.634361	−	0.773037i	$-0.718737\pi$
$151$	−7.66062	+	2.78824i	−0.623412	+	0.226903i	0.0109494	+	0.999940i	$0.496515\pi$
$152$	−0.0148207	−	0.0256701i	−0.00120211	−	0.00208212i
$153$	−8.31168	−	16.1540i	−0.671959	−	1.30597i
$154$	−1.46941	+	2.54509i	−0.118408	+	0.205089i
$155$	−0.0261483	+	0.148294i	−0.00210028	+	0.0119113i
$156$	6.91755	+	6.09574i	0.553847	+	0.488050i
$157$	10.7210	+	3.90213i	0.855629	+	0.311424i	0.732333	−	0.680946i	$-0.238431\pi$
$157$	10.7210	+	3.90213i	0.855629	+	0.311424i	0.123296	+	0.992370i	$0.460654\pi$
$158$	0.754725	+	4.28026i	0.0600427	+	0.340519i
$159$	8.15436	+	0.197359i	0.646683	+	0.0156516i
$160$	−0.288795	−	0.242327i	−0.0228312	−	0.0191577i
$161$	−7.93615			−0.625456
$162$	−6.30305	−	6.42429i	−0.495214	−	0.504740i
$163$	23.3555			1.82934			0.914671	−	0.404199i	$-0.132450\pi$
$163$	23.3555			1.82934			0.914671	+	0.404199i	$0.132450\pi$
$164$	−5.65151	−	4.74218i	−0.441308	−	0.370302i
$165$	1.91841	+	0.0464309i	0.149348	+	0.00361464i
$166$	−1.90177	−	10.7855i	−0.147606	−	0.837116i
$167$	−1.79783	−	0.654357i	−0.139120	−	0.0506357i	0.271522	−	0.962432i	$-0.412473\pi$
$167$	−1.79783	−	0.654357i	−0.139120	−	0.0506357i	−0.410642	+	0.911797i	$0.634695\pi$
$168$	1.29950	+	1.14512i	0.100259	+	0.0883478i
$169$	2.66322	−	15.1038i	0.204863	−	1.16183i
$170$	1.14147	−	1.97708i	0.0875466	−	0.151635i
$171$	0.0481355	−	0.0747693i	0.00368101	−	0.00571775i
$172$	−0.777222	−	1.34619i	−0.0592626	−	0.102646i
$173$	−6.68321	+	2.43249i	−0.508115	+	0.184939i	−0.583340	−	0.812228i	$-0.698255\pi$
$173$	−6.68321	+	2.43249i	−0.508115	+	0.184939i	0.0752253	+	0.997167i	$0.476032\pi$
$174$	−1.62193	−	10.7074i	−0.122958	−	0.811725i
$175$	−3.72135	+	3.12258i	−0.281307	+	0.236045i
$176$	−2.25126	+	1.88903i	−0.169695	+	0.142391i
$177$	−10.6767	−	4.18125i	−0.802512	−	0.314282i
$178$	−2.48102	+	0.903017i	−0.185960	+	0.0676840i
$179$	−8.64693	−	14.9769i	−0.646302	−	1.11943i	−0.983999	−	0.178172i	$-0.942981\pi$
$179$	−8.64693	−	14.9769i	−0.646302	−	1.11943i	0.337698	−	0.941255i	$-0.390352\pi$
$180$	0.250046	−	1.10300i	0.0186373	−	0.0822125i
$181$	−6.36372	+	11.0223i	−0.473011	+	0.819280i	−0.999523	−	0.0308884i	$-0.990166\pi$
$181$	−6.36372	+	11.0223i	−0.473011	+	0.819280i	0.526512	+	0.850168i	$0.323500\pi$
$182$	0.924370	−	5.24236i	0.0685189	−	0.388590i
$183$	−4.60036	+	22.8431i	−0.340069	+	1.68861i
$184$	−7.45754	−	2.71432i	−0.549777	−	0.200103i
$185$	−0.360961	−	2.04711i	−0.0265383	−	0.150506i
$186$	0.360310	−	0.590596i	0.0264192	−	0.0433046i
$187$	−13.6328	−	11.4393i	−0.996928	−	0.836522i
$188$	10.8961			0.794682
$189$	−1.27108	+	5.03829i	−0.0924575	+	0.366482i
$190$	0.0111746			0.000810692
$191$	1.15435	+	0.968616i	0.0835260	+	0.0700866i	0.683595	−	0.729862i	$-0.260416\pi$
$191$	1.15435	+	0.968616i	0.0835260	+	0.0700866i	−0.600069	+	0.799948i	$0.704860\pi$
$192$	0.829478	+	1.52052i	0.0598624	+	0.109734i
$193$	2.34333	+	13.2897i	0.168677	+	0.956612i	0.945192	+	0.326514i	$0.105874\pi$
$193$	2.34333	+	13.2897i	0.168677	+	0.956612i	−0.776516	+	0.630098i	$0.783015\pi$
$194$	8.37922	+	3.04979i	0.601593	+	0.218962i
$195$	−3.29412	+	1.10946i	−0.235897	+	0.0794501i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	−7.15804	+	12.3981i	−0.509989	+	0.883327i	0.489944	+	0.871754i	$0.337017\pi$
$197$	−7.15804	+	12.3981i	−0.509989	+	0.883327i	−0.999933	+	0.0115731i	$0.996316\pi$
$198$	−8.12916	−	3.41266i	−0.577715	−	0.242527i
$199$	−3.61010	−	6.25288i	−0.255913	−	0.443255i	0.709230	−	0.704977i	$-0.249043\pi$
$199$	−3.61010	−	6.25288i	−0.255913	−	0.443255i	−0.965143	+	0.261723i	$0.915709\pi$
$200$	−4.56491	+	1.66149i	−0.322788	+	0.117485i
$201$	−16.0433	+	12.8134i	−1.13160	+	0.903786i
$202$	−7.63633	+	6.40764i	−0.537290	+	0.450840i
$203$	−4.78964	+	4.01899i	−0.336167	+	0.282078i
$204$	−8.19554	+	6.54559i	−0.573803	+	0.458283i
$205$	2.61355	−	0.951255i	0.182538	−	0.0664385i
$206$	5.34516	+	9.25808i	0.372415	+	0.645041i
$207$	−2.99516	−	23.6193i	−0.208178	−	1.64165i
$208$	2.66162	−	4.61006i	0.184550	−	0.319650i
$209$	0.0151265	−	0.0857869i	0.00104633	−	0.00593400i
$210$	−0.618819	+	0.208418i	−0.0427025	+	0.0143822i
$211$	15.1581	+	5.51709i	1.04353	+	0.379812i	0.806216	−	0.591622i	$-0.201512\pi$
$211$	15.1581	+	5.51709i	1.04353	+	0.379812i	0.237310	+	0.971434i	$0.423734\pi$
$212$	−0.817761	−	4.63776i	−0.0561641	−	0.318522i
$213$	−4.67101	−	8.56241i	−0.320052	−	0.586687i
$214$	10.2946	+	8.63816i	0.703722	+	0.590493i
$215$	0.586017			0.0399660
$216$	−2.91762	+	4.29971i	−0.198519	+	0.292558i
$217$	−0.399427			−0.0271149
$218$	−12.8250	−	10.7614i	−0.868615	−	0.728855i
$219$	9.94781	−	16.3058i	0.672211	−	1.10184i
$220$	−0.192388	−	1.09108i	−0.0129708	−	0.0735609i
$221$	30.2915	+	11.0252i	2.03762	+	0.741635i
$222$	−1.88546	+	9.36229i	−0.126544	+	0.628356i
$223$	3.92494	−	22.2594i	0.262833	−	1.49060i	−0.512301	−	0.858806i	$-0.671207\pi$
$223$	3.92494	−	22.2594i	0.262833	−	1.49060i	0.775134	−	0.631797i	$-0.217682\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−10.6978	−	9.89686i	−0.713186	−	0.659791i
$226$	−3.37650	−	5.84827i	−0.224601	−	0.389021i
$227$	7.44318	−	2.70910i	0.494021	−	0.179809i	−0.0829817	−	0.996551i	$-0.526444\pi$
$227$	7.44318	−	2.70910i	0.494021	−	0.179809i	0.577003	+	0.816742i	$0.304222\pi$
$228$	−0.0478051	−	0.0187216i	−0.00316597	−	0.00123987i
$229$	14.3258	−	12.0207i	0.946673	−	0.794353i	−0.0320608	−	0.999486i	$-0.510207\pi$
$229$	14.3258	−	12.0207i	0.946673	−	0.794353i	0.978734	+	0.205133i	$0.0657626\pi$
$230$	2.29192	−	1.92315i	0.151125	−	0.126809i
$231$	0.762351	+	5.03276i	0.0501590	+	0.331131i
$232$	−5.87537	+	2.13846i	−0.385737	+	0.140397i
$233$	−6.34970	−	10.9980i	−0.415983	−	0.720503i	0.579548	−	0.814938i	$-0.303229\pi$
$233$	−6.34970	−	10.9980i	−0.415983	−	0.720503i	−0.995531	+	0.0944346i	$0.969896\pi$
$234$	15.9510	+	0.772572i	1.04275	+	0.0505046i
$235$	−2.05389	+	3.55745i	−0.133981	+	0.232062i
$236$	−1.14956	+	6.51949i	−0.0748301	+	0.424382i
$237$	5.64801	+	4.97701i	0.366877	+	0.323292i
$238$	5.69042	+	2.07114i	0.368855	+	0.134252i
$239$	1.40675	+	7.97805i	0.0909948	+	0.516057i	0.995901	+	0.0904468i	$0.0288295\pi$
$239$	1.40675	+	7.97805i	0.0909948	+	0.516057i	−0.904906	+	0.425610i	$0.860059\pi$
$240$	−0.652783	−	0.0157992i	−0.0421369	−	0.00101983i
$241$	9.64070	+	8.08951i	0.621012	+	0.521091i	0.898121	−	0.439747i	$-0.144932\pi$
$241$	9.64070	+	8.08951i	0.621012	+	0.521091i	−0.277110	+	0.960838i	$0.589376\pi$
$242$	2.36338			0.151924
$243$	−15.4745	−	1.88146i	−0.992690	−	0.120696i
$244$	13.4533			0.861258
$245$	0.288795	+	0.242327i	0.0184504	+	0.0154817i
$246$	−12.7745	−	0.309179i	−0.814472	−	0.0197125i
$247$	0.0273996	+	0.155391i	0.00174339	+	0.00988727i
$248$	−0.375339	−	0.136612i	−0.0238341	−	0.00867489i
$249$	−14.2320	−	12.5412i	−0.901915	−	0.794766i
$250$	0.645340	−	3.65991i	0.0408149	−	0.231473i
$251$	−9.72987	+	16.8526i	−0.614144	+	1.06373i	0.376390	+	0.926461i	$0.377165\pi$
$251$	−9.72987	+	16.8526i	−0.614144	+	1.06373i	−0.990534	+	0.137267i	$0.956168\pi$
$252$	2.99649	+	0.145132i	0.188761	+	0.00914246i
$253$	−11.6614	−	20.1982i	−0.733148	−	1.26985i
$254$	−7.43694	+	2.70682i	−0.466635	+	0.169841i
$255$	−0.592211	−	3.90956i	−0.0370857	−	0.244826i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	14.1241	−	11.8516i	0.881039	−	0.739280i	−0.0853532	−	0.996351i	$-0.527202\pi$
$257$	14.1241	−	11.8516i	0.881039	−	0.739280i	0.966393	+	0.257071i	$0.0827574\pi$
$258$	−2.50698	−	0.981793i	−0.156078	−	0.0611237i
$259$	5.18132	−	1.88585i	0.321951	−	0.117181i
$260$	1.00342	+	1.73797i	0.0622292	+	0.107784i
$261$	−13.7688	−	12.7380i	−0.852269	−	0.788461i
$262$	5.58115	−	9.66683i	0.344804	−	0.597219i
$263$	−1.96417	+	11.1394i	−0.121116	+	0.686884i	0.862423	+	0.506188i	$0.168946\pi$
$263$	−1.96417	+	11.1394i	−0.121116	+	0.686884i	−0.983539	+	0.180695i	$0.942165\pi$
$264$	−1.00493	+	4.98999i	−0.0618492	+	0.307113i
$265$	1.66831	+	0.607216i	0.102484	+	0.0373010i
$266$	0.00514716	+	0.0291910i	0.000315593	+	0.00178982i
$267$	−2.38167	+	3.90388i	−0.145756	+	0.238914i
$268$	9.08087	+	7.61975i	0.554702	+	0.465451i
$269$	−15.6563			−0.954583			−0.477291	−	0.878745i	$-0.658381\pi$
$269$	−15.6563			−0.954583			−0.477291	+	0.878745i	$0.658381\pi$
$270$	−0.853835	−	1.76305i	−0.0519627	−	0.107296i
$271$	7.79979			0.473803			0.236902	−	0.971534i	$-0.423868\pi$
$271$	7.79979			0.473803			0.236902	+	0.971534i	$0.423868\pi$
$272$	4.63887	+	3.89248i	0.281273	+	0.236016i
$273$	−4.41551	−	8.09406i	−0.267239	−	0.489875i
$274$	0.812848	+	4.60989i	0.0491060	+	0.278494i
$275$	−13.4154	−	4.88281i	−0.808980	−	0.294445i
$276$	−13.0268	+	4.38744i	−0.784122	+	0.264093i
$277$	−1.29026	+	7.31740i	−0.0775239	+	0.439660i	0.921197	+	0.389097i	$0.127213\pi$
$277$	−1.29026	+	7.31740i	−0.0775239	+	0.439660i	−0.998721	+	0.0505634i	$0.983898\pi$
$278$	−2.75589	+	4.77334i	−0.165287	+	0.286286i
$279$	−0.150747	−	1.18876i	−0.00902498	−	0.0711693i
$280$	0.188497	+	0.326487i	0.0112649	+	0.0195113i
$281$	22.1181	−	8.05031i	1.31945	−	0.480241i	0.416170	−	0.909287i	$-0.363372\pi$
$281$	22.1181	−	8.05031i	1.31945	−	0.480241i	0.903283	+	0.429046i	$0.141150\pi$
$282$	14.7466	−	11.7778i	0.878146	−	0.701355i
$283$	−14.1578	+	11.8798i	−0.841594	+	0.706181i	−0.957922	−	0.287030i	$-0.907332\pi$
$283$	−14.1578	+	11.8798i	−0.841594	+	0.706181i	0.116328	+	0.993211i	$0.462888\pi$
$284$	−4.31379	+	3.61970i	−0.255977	+	0.214790i
$285$	0.0151235	−	0.0120788i	0.000895838	−	0.000715485i
$286$	14.7005	−	5.35056i	0.869262	−	0.316385i
$287$	3.68876	+	6.38912i	0.217741	+	0.377138i
$288$	2.76614	+	1.16124i	0.162996	+	0.0684266i
$289$	−9.83527	+	17.0352i	−0.578545	+	1.00207i
$290$	0.409312	−	2.32132i	0.0240356	−	0.136313i
$291$	14.6368	−	4.92968i	0.858024	−	0.288983i
$292$	−10.3628	−	3.77174i	−0.606435	−	0.220724i
$293$	−1.78660	−	10.1323i	−0.104374	−	0.591935i	−0.991468	−	0.130347i	$-0.958391\pi$
$293$	−1.78660	−	10.1323i	−0.104374	−	0.591935i	0.887094	−	0.461588i	$-0.152720\pi$
$294$	−0.829478	−	1.52052i	−0.0483762	−	0.0886782i
$295$	−1.91184	−	1.60422i	−0.111311	−	0.0934014i
$296$	5.51384			0.320486
$297$	−14.6906	+	4.16828i	−0.852436	+	0.241868i
$298$	9.60677			0.556505
$299$	32.3623	+	27.1552i	1.87156	+	1.57043i
$300$	−4.38212	+	7.18289i	−0.253002	+	0.414704i
$301$	0.269926	+	1.53083i	0.0155583	+	0.0882355i
$302$	7.66062	+	2.78824i	0.440819	+	0.160445i
$303$	−3.40875	+	16.9262i	−0.195827	+	0.972382i
$304$	−0.00514716	+	0.0291910i	−0.000295210	+	0.00167422i
$305$	−2.53591	+	4.39232i	−0.145206	+	0.251504i
$306$	−4.01646	+	17.7173i	−0.229606	+	1.01283i
$307$	−4.07441	−	7.05709i	−0.232539	−	0.402769i	0.726016	−	0.687678i	$-0.241370\pi$
$307$	−4.07441	−	7.05709i	−0.232539	−	0.402769i	−0.958555	+	0.284909i	$0.908037\pi$
$308$	2.76158	−	1.00513i	0.157356	−	0.0572728i
$309$	17.2412	+	6.75204i	0.980816	+	0.384110i
$310$	0.115353	−	0.0967922i	0.00655158	−	0.00549743i
$311$	10.9893	−	9.22115i	0.623149	−	0.522884i	−0.275643	−	0.961260i	$-0.588891\pi$
$311$	10.9893	−	9.22115i	0.623149	−	0.522884i	0.898791	+	0.438376i	$0.144446\pi$
$312$	−1.38089	−	9.11612i	−0.0781774	−	0.516099i
$313$	13.8251	−	5.03194i	0.781443	−	0.284422i	0.0796686	−	0.996821i	$-0.474614\pi$
$313$	13.8251	−	5.03194i	0.781443	−	0.284422i	0.701774	+	0.712399i	$0.252392\pi$
$314$	−5.70453	−	9.88053i	−0.321925	−	0.557591i
$315$	−0.612214	+	0.950957i	−0.0344943	+	0.0535804i
$316$	2.17314	−	3.76399i	0.122249	−	0.211741i
$317$	0.654977	−	3.71456i	0.0367871	−	0.208630i	−0.960874	−	0.276986i	$-0.910664\pi$
$317$	0.654977	−	3.71456i	0.0367871	−	0.208630i	0.997661	+	0.0683561i	$0.0217754\pi$
$318$	−6.11974	−	5.39271i	−0.343178	−	0.302408i
$319$	−17.2666	−	6.28453i	−0.966745	−	0.351866i
$320$	0.0654644	+	0.371267i	0.00365957	+	0.0207545i
$321$	23.2695	+	0.563189i	1.29878	+	0.0314341i
$322$	6.07944	+	5.10126i	0.338794	+	0.284282i
$323$	−0.179497			−0.00998746
$324$	0.698959	+	8.97282i	0.0388311	+	0.498490i
$325$	25.8596			1.43443
$326$	−17.8913	−	15.0126i	−0.990909	−	0.831472i
$327$	−28.9891	−	0.701620i	−1.60310	−	0.0387997i
$328$	1.28109	+	7.26544i	0.0707365	+	0.401167i
$329$	−10.2390	−	3.72670i	−0.564495	−	0.205459i
$330$	−1.43974	−	1.26870i	−0.0792550	−	0.0698394i
$331$	−3.90834	+	22.1653i	−0.214822	+	1.21832i	0.666393	+	0.745601i	$0.267837\pi$
$331$	−3.90834	+	22.1653i	−0.214822	+	1.21832i	−0.881215	+	0.472716i	$0.843274\pi$
$332$	−5.47594	+	9.48460i	−0.300531	+	0.520535i
$333$	7.56806	+	14.7087i	0.414727	+	0.806033i
$334$	0.956606	+	1.65689i	0.0523431	+	0.0906610i
$335$	−4.19947	+	1.52848i	−0.229442	+	0.0835099i
$336$	−0.259408	−	1.71251i	−0.0141519	−	0.0934254i
$337$	21.9585	−	18.4254i	1.19616	−	1.00369i	0.196424	−	0.980519i	$-0.437067\pi$
$337$	21.9585	−	18.4254i	1.19616	−	1.00369i	0.999731	−	0.0231744i	$-0.00737731\pi$
$338$	−11.7487	+	9.85833i	−0.639045	+	0.536223i
$339$	−10.8911	−	4.26522i	−0.591526	−	0.231655i
$340$	−2.14526	+	0.780810i	−0.116343	+	0.0423454i
$341$	−0.586921	−	1.01658i	−0.0317836	−	0.0550508i
$342$	−0.0849347	+	0.0263357i	−0.00459274	+	0.00142407i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−0.269926	+	1.53083i	−0.0145535	+	0.0825367i
$345$	1.02308	−	5.08010i	0.0550807	−	0.273504i
$346$	6.68321	+	2.43249i	0.359292	+	0.130771i
$347$	−0.459583	−	2.60643i	−0.0246717	−	0.139920i	0.969984	−	0.243170i	$-0.0781872\pi$
$347$	−0.459583	−	2.60643i	−0.0246717	−	0.139920i	−0.994656	+	0.103249i	$0.967076\pi$
$348$	−5.64011	+	9.24490i	−0.302342	+	0.495578i
$349$	−10.2651	−	8.61344i	−0.549478	−	0.461067i	0.325286	−	0.945616i	$-0.394539\pi$
$349$	−10.2651	−	8.61344i	−0.549478	−	0.461067i	−0.874764	+	0.484549i	$0.838984\pi$
$350$	4.85788			0.259664
$351$	22.4228	−	16.1960i	1.19684	−	0.864481i
$352$	2.93881			0.156639
$353$	−0.153428	−	0.128741i	−0.00816613	−	0.00685219i	0.638695	−	0.769460i	$-0.279474\pi$
$353$	−0.153428	−	0.128741i	−0.00816613	−	0.00685219i	−0.646862	+	0.762607i	$0.723919\pi$
$354$	5.49119	+	10.0659i	0.291854	+	0.534996i
$355$	−0.368647	−	2.09070i	−0.0195658	−	0.110963i
$356$	2.48102	+	0.903017i	0.131494	+	0.0478598i
$357$	9.94001	−	3.34780i	0.526081	−	0.177184i
$358$	−3.00305	+	17.0311i	−0.158716	+	0.900123i
$359$	14.6220	−	25.3260i	0.771717	−	1.33665i	−0.164904	−	0.986310i	$-0.552731\pi$
$359$	14.6220	−	25.3260i	0.771717	−	1.33665i	0.936621	−	0.350344i	$-0.113935\pi$
$360$	−0.900539	+	0.684218i	−0.0474626	+	0.0360614i
$361$	9.49956	+	16.4537i	0.499977	+	0.865985i
$362$	11.9599	−	4.35304i	0.628597	−	0.228791i
$363$	3.19855	−	2.55460i	0.167880	−	0.134082i
$364$	−4.07784	+	3.42171i	−0.213737	+	0.179346i
$365$	3.18477	−	2.67234i	0.166699	−	0.139877i
$366$	18.2074	−	14.5418i	0.951715	−	0.760112i
$367$	31.2450	−	11.3722i	1.63097	−	0.593626i	0.645546	−	0.763721i	$-0.276630\pi$
$367$	31.2450	−	11.3722i	1.63097	−	0.593626i	0.985428	+	0.170095i	$0.0544074\pi$
$368$	3.96807	+	6.87291i	0.206850	+	0.358275i
$369$	−17.6229	+	13.3897i	−0.917412	+	0.697038i
$370$	−1.03934	+	1.80020i	−0.0540329	+	0.0935878i
$371$	−0.817761	+	4.63776i	−0.0424561	+	0.240780i
$372$	−0.655641	+	0.220820i	−0.0339934	+	0.0114490i
$373$	26.4031	+	9.60994i	1.36710	+	0.497584i	0.918242	−	0.396019i	$-0.129608\pi$
$373$	26.4031	+	9.60994i	1.36710	+	0.497584i	0.448859	+	0.893603i	$0.351831\pi$
$374$	3.09030	+	17.5260i	0.159796	+	0.906246i
$375$	−3.08264	−	5.65079i	−0.159187	−	0.291806i
$376$	−8.34692	−	7.00390i	−0.430460	−	0.361199i
$377$	33.2832			1.71417
$378$	4.21225	−	3.04252i	0.216655	−	0.156490i
$379$	−6.08047			−0.312333			−0.156166	−	0.987731i	$-0.549914\pi$
$379$	−6.08047			−0.312333			−0.156166	+	0.987731i	$0.549914\pi$
$380$	−0.00856026	−	0.00718291i	−0.000439132	−	0.000368475i
$381$	−7.13915	+	11.7020i	−0.365750	+	0.599513i
$382$	−0.261670	−	1.48401i	−0.0133882	−	0.0759284i
$383$	16.2277	+	5.90638i	0.829194	+	0.301802i	0.721528	−	0.692385i	$-0.243440\pi$
$383$	16.2277	+	5.90638i	0.829194	+	0.301802i	0.107666	+	0.994187i	$0.465662\pi$
$384$	0.341951	−	1.69796i	0.0174501	−	0.0866487i
$385$	−0.192388	+	1.09108i	−0.00980498	+	0.0556068i
$386$	6.74735	−	11.6868i	0.343431	−	0.594840i
$387$	−4.45413	+	1.38109i	−0.226416	+	0.0702048i
$388$	−4.45849	−	7.72233i	−0.226346	−	0.392042i
$389$	−23.4555	+	8.53711i	−1.18924	+	0.432848i	−0.859457	−	0.511208i	$-0.829198\pi$
$389$	−23.4555	+	8.53711i	−1.18924	+	0.432848i	−0.329784	+	0.944056i	$0.606976\pi$
$390$	3.23659	+	1.26752i	0.163891	+	0.0641835i
$391$	−36.8148	+	30.8913i	−1.86180	+	1.56224i
$392$	−0.766044	+	0.642788i	−0.0386911	+	0.0324657i
$393$	−2.89559	−	19.1156i	−0.146063	−	0.964254i
$394$	13.4527	−	4.89639i	0.677738	−	0.246676i
$395$	0.819263	+	1.41901i	0.0412216	+	0.0713979i
$396$	4.03368	+	7.83958i	0.202700	+	0.393954i
$397$	−8.95530	+	15.5110i	−0.449454	+	0.778476i	−0.998350	−	0.0574137i	$-0.981715\pi$
$397$	−8.95530	+	15.5110i	−0.449454	+	0.778476i	0.548897	+	0.835890i	$0.315048\pi$
$398$	−1.25377	+	7.11051i	−0.0628460	+	0.356418i
$399$	0.0385189	+	0.0339428i	0.00192836	+	0.00169927i
$400$	4.56491	+	1.66149i	0.228245	+	0.0830746i
$401$	−0.907094	−	5.14439i	−0.0452981	−	0.256898i	0.953746	−	0.300614i	$-0.0971916\pi$
$401$	−0.907094	−	5.14439i	−0.0452981	−	0.256898i	−0.999044	+	0.0437155i	$0.986080\pi$
$402$	20.5261	+	0.496791i	1.02375	+	0.0247777i
$403$	1.62880	+	1.36673i	0.0811363	+	0.0680814i
$404$	9.96852			0.495952
$405$	−3.06126	−	1.46315i	−0.152115	−	0.0727046i
$406$	6.25244			0.310303
$407$	12.4131	+	10.4158i	0.615295	+	0.516293i
$408$	10.4856	+	0.253781i	0.519113	+	0.0125640i
$409$	3.82054	+	21.6674i	0.188914	+	1.07138i	0.920823	+	0.389980i	$0.127518\pi$
$409$	3.82054	+	21.6674i	0.188914	+	1.07138i	−0.731910	+	0.681402i	$0.761371\pi$
$410$	−2.61355	−	0.951255i	−0.129074	−	0.0469791i
$411$	6.08298	+	5.36031i	0.300051	+	0.264404i
$412$	1.85635	−	10.5279i	0.0914560	−	0.518673i
$413$	3.31003	−	5.73314i	0.162876	−	0.282109i
$414$	−12.8878	+	20.0187i	−0.633399	+	0.983865i
$415$	−2.06440	−	3.57564i	−0.101337	−	0.175521i
$416$	−5.00221	+	1.82065i	−0.245253	+	0.0892649i
$417$	1.42980	+	9.43901i	0.0700176	+	0.462230i
$418$	−0.0667304	+	0.0559934i	−0.00326389	+	0.00273873i
$419$	2.89950	−	2.43297i	0.141650	−	0.118859i	−0.569209	−	0.822193i	$-0.692751\pi$
$419$	2.89950	−	2.43297i	0.141650	−	0.118859i	0.710859	+	0.703334i	$0.248306\pi$
$420$	0.608011	+	0.238111i	0.0296679	+	0.0116186i
$421$	−12.9632	+	4.71822i	−0.631788	+	0.229952i	−0.638009	−	0.770029i	$-0.720242\pi$
$421$	−12.9632	+	4.71822i	−0.631788	+	0.229952i	0.00622128	+	0.999981i	$0.498020\pi$
$422$	−8.06545	−	13.9698i	−0.392620	−	0.680038i
$423$	7.22699	−	31.8795i	0.351388	−	1.55003i
$424$	−2.35465	+	4.07837i	−0.114352	+	0.198063i
$425$	−5.10829	+	28.9705i	−0.247788	+	1.40528i
$426$	−1.92561	+	9.56165i	−0.0932963	+	0.463264i
$427$	−12.6420	−	4.60129i	−0.611787	−	0.222672i
$428$	−2.33359	−	13.2344i	−0.112798	−	0.639711i
$429$	14.1119	−	23.1313i	0.681329	−	1.11679i
$430$	−0.448915	−	0.376684i	−0.0216486	−	0.0181653i
$431$	−38.9069			−1.87408			−0.937039	−	0.349226i	$-0.886445\pi$
$431$	−38.9069			−1.87408			−0.937039	+	0.349226i	$0.886445\pi$
$432$	4.99883	−	1.41836i	0.240506	−	0.0682407i
$433$	12.8732			0.618647			0.309324	−	0.950957i	$-0.399897\pi$
$433$	12.8732			0.618647			0.309324	+	0.950957i	$0.399897\pi$
$434$	0.305979	+	0.256747i	0.0146875	+	0.0123243i
$435$	−1.95519	−	3.58406i	−0.0937443	−	0.171842i
$436$	2.90718	+	16.4874i	0.139229	+	0.789605i
$437$	−0.221051	−	0.0804561i	−0.0105743	−	0.00384874i
$438$	−18.1016	+	6.09664i	−0.864930	+	0.291309i
$439$	1.98380	−	11.2507i	0.0946817	−	0.536967i	−0.900163	−	0.435554i	$-0.856553\pi$
$439$	1.98380	−	11.2507i	0.0946817	−	0.536967i	0.994844	−	0.101413i	$-0.0323363\pi$
$440$	−0.553958	+	0.959484i	−0.0264089	+	0.0457416i
$441$	−2.76614	−	1.16124i	−0.131721	−	0.0552971i
$442$	−16.1177	−	27.9168i	−0.766643	−	1.32786i
$443$	−31.8873	+	11.6060i	−1.51501	+	0.551419i	−0.959896	−	0.280356i	$-0.909548\pi$
$443$	−31.8873	+	11.6060i	−1.51501	+	0.551419i	−0.555114	+	0.831774i	$0.687325\pi$
$444$	7.46231	−	5.95997i	0.354146	−	0.282848i
$445$	−0.762489	+	0.639804i	−0.0361454	+	0.0303296i
$446$	−17.3148	+	14.5288i	−0.819878	+	0.687960i
$447$	13.0016	−	10.3841i	0.614954	−	0.491150i
$448$	−0.939693	+	0.342020i	−0.0443963	+	0.0161589i
$449$	−13.2499	−	22.9495i	−0.625301	−	1.08305i	−0.988483	−	0.151335i	$-0.951643\pi$
$449$	−13.2499	−	22.9495i	−0.625301	−	1.08305i	0.363182	−	0.931718i	$-0.381690\pi$
$450$	1.83340	+	14.4578i	0.0864272	+	0.681549i
$451$	−10.8406	+	18.7764i	−0.510463	+	0.884147i
$452$	−1.17265	+	6.65041i	−0.0551566	+	0.312809i
$453$	13.3815	−	4.50691i	0.628720	−	0.211753i
$454$	−7.44318	−	2.70910i	−0.349326	−	0.127144i
$455$	−0.348483	−	1.97634i	−0.0163371	−	0.0926524i
$456$	0.0245868	+	0.0450701i	0.00115138	+	0.00211060i
$457$	−19.9148	−	16.7105i	−0.931576	−	0.781685i	0.0445233	−	0.999008i	$-0.485823\pi$
$457$	−19.9148	−	16.7105i	−0.931576	−	0.781685i	−0.976100	+	0.217323i	$0.930268\pi$
$458$	−18.7010			−0.873839
$459$	13.7150	+	28.3196i	0.640163	+	1.32185i
$460$	−2.99189			−0.139497
$461$	−0.900787	−	0.755850i	−0.0419538	−	0.0352035i	0.621570	−	0.783359i	$-0.286495\pi$
$461$	−0.900787	−	0.755850i	−0.0419538	−	0.0352035i	−0.663523	+	0.748155i	$0.730940\pi$
$462$	2.65100	−	4.34535i	0.123336	−	0.202164i
$463$	−4.68123	−	26.5486i	−0.217555	−	1.23382i	−0.876417	−	0.481553i	$-0.840073\pi$
$463$	−4.68123	−	26.5486i	−0.217555	−	1.23382i	0.658861	−	0.752264i	$-0.271038\pi$
$464$	5.87537	+	2.13846i	0.272757	+	0.0992755i
$465$	0.0514917	−	0.255682i	0.00238787	−	0.0118570i
$466$	−2.20523	+	12.5065i	−0.102155	+	0.579351i
$467$	9.32723	−	16.1552i	0.431613	−	0.747575i	−0.565400	−	0.824817i	$-0.691278\pi$
$467$	9.32723	−	16.1552i	0.431613	−	0.747575i	0.997012	+	0.0772421i	$0.0246114\pi$
$468$	−11.7226	−	10.8449i	−0.541877	−	0.501307i
$469$	−5.92712	−	10.2661i	−0.273689	−	0.474043i
$470$	3.86005	−	1.40494i	0.178051	−	0.0648053i
$471$	−18.4004	−	7.20600i	−0.847844	−	0.332035i
$472$	5.07126	−	4.25529i	0.233424	−	0.195866i
$473$	−3.49946	+	2.93640i	−0.160905	+	0.135016i
$474$	−1.12746	−	7.44308i	−0.0517860	−	0.341872i
$475$	−0.135310	+	0.0492488i	−0.00620845	+	0.00225969i
$476$	−3.02781	−	5.24432i	−0.138779	−	0.240373i
$477$	−14.1114	−	0.683471i	−0.646115	−	0.0312940i
$478$	4.05056	−	7.01578i	0.185268	−	0.320894i
$479$	2.12310	−	12.0407i	0.0970069	−	0.550153i	−0.897107	−	0.441813i	$-0.854335\pi$
$479$	2.12310	−	12.0407i	0.0970069	−	0.550153i	0.994114	−	0.108340i	$-0.0345535\pi$
$480$	0.489905	+	0.431704i	0.0223610	+	0.0197045i
$481$	−27.5814	−	10.0388i	−1.25760	−	0.457730i
$482$	−2.18537	−	12.3938i	−0.0995408	−	0.564524i
$483$	13.7418	+	0.332590i	0.625273	+	0.0151334i
$484$	−1.81045	−	1.51915i	−0.0822934	−	0.0690523i
$485$	3.36165			0.152645
$486$	10.6448	+	11.3881i	0.482857	+	0.516575i
$487$	−25.1513			−1.13971			−0.569856	−	0.821744i	$-0.693001\pi$
$487$	−25.1513			−1.13971			−0.569856	+	0.821744i	$0.693001\pi$
$488$	−10.3058	−	8.64761i	−0.466522	−	0.391459i
$489$	−40.4410	−	0.978788i	−1.82881	−	0.0442623i
$490$	−0.0654644	−	0.371267i	−0.00295738	−	0.0167721i
$491$	28.7773	+	10.4741i	1.29870	+	0.472689i	0.896574	−	0.442894i	$-0.146048\pi$
$491$	28.7773	+	10.4741i	1.29870	+	0.472689i	0.402128	+	0.915583i	$0.368271\pi$
$492$	9.58709	+	8.44813i	0.432220	+	0.380871i
$493$	−6.57473	+	37.2872i	−0.296111	+	1.67933i
$494$	0.0788939	−	0.136648i	0.00354960	−	0.00614809i
$495$	−3.31986	−	0.160794i	−0.149217	−	0.00722716i
$496$	0.199714	+	0.345914i	0.00896741	+	0.0155320i
$497$	5.29165	−	1.92600i	0.237363	−	0.0863931i
$498$	2.84100	+	18.7552i	0.127308	+	0.840443i
$499$	18.3813	−	15.4237i	0.822859	−	0.690460i	−0.130781	−	0.991411i	$-0.541748\pi$
$499$	18.3813	−	15.4237i	0.822859	−	0.690460i	0.953640	+	0.300951i	$0.0973040\pi$
$500$	−2.84690	+	2.38883i	−0.127317	+	0.106832i
$501$	3.08560	+	1.20839i	0.137854	+	0.0539870i
$502$	18.2862	−	6.65562i	0.816152	−	0.297055i
$503$	9.15993	+	15.8655i	0.408421	+	0.707406i	0.994713	−	0.102694i	$-0.0327462\pi$
$503$	9.15993	+	15.8655i	0.408421	+	0.707406i	−0.586292	+	0.810100i	$0.699413\pi$
$504$	−2.20215	−	2.03728i	−0.0980917	−	0.0907478i
$505$	−1.87904	+	3.25459i	−0.0836162	+	0.144827i
$506$	−4.04997	+	22.9685i	−0.180043	+	1.02108i
$507$	−5.24445	+	26.0414i	−0.232914	+	1.15654i
$508$	7.43694	+	2.70682i	0.329961	+	0.120096i
$509$	−6.97626	−	39.5643i	−0.309217	−	1.75366i	−0.602958	−	0.797773i	$-0.706012\pi$
$509$	−6.97626	−	39.5643i	−0.309217	−	1.75366i	0.293741	−	0.955885i	$-0.405100\pi$
$510$	−2.05936	+	3.37556i	−0.0911899	+	0.149473i
$511$	8.44780	+	7.08854i	0.373709	+	0.313579i
$512$	−1.00000			−0.0441942
$513$	−0.0864822	+	0.127449i	−0.00381828	+	0.00562701i
$514$	−18.4377			−0.813254
$515$	3.08730	+	2.59056i	0.136043	+	0.114154i
$516$	1.28938	+	2.36356i	0.0567617	+	0.104050i
$517$	−5.56051	−	31.5352i	−0.244551	−	1.38692i
$518$	−5.18132	−	1.88585i	−0.227654	−	0.0828593i
$519$	11.6742	−	3.93188i	0.512441	−	0.172590i
$520$	0.348483	−	1.97634i	0.0152820	−	0.0866684i
$521$	8.61711	−	14.9253i	0.377522	−	0.653888i	−0.613179	−	0.789944i	$-0.710109\pi$
$521$	8.61711	−	14.9253i	0.377522	−	0.653888i	0.990701	+	0.136056i	$0.0434428\pi$
$522$	2.35972	+	18.6083i	0.103282	+	0.814463i
$523$	−11.3191	−	19.6053i	−0.494951	−	0.857280i	0.505032	−	0.863101i	$-0.331481\pi$
$523$	−11.3191	−	19.6053i	−0.494951	−	0.857280i	−0.999983	+	0.00582037i	$0.998147\pi$
$524$	−10.4891	+	3.81773i	−0.458219	+	0.166778i
$525$	6.57454	−	5.25093i	0.286936	−	0.229169i
$526$	8.66490	−	7.27071i	0.377808	−	0.317018i
$527$	−1.85289	+	1.55476i	−0.0807133	+	0.0677265i
$528$	3.97732	−	3.17660i	0.173091	−	0.138244i
$529$	−37.5712	+	13.6748i	−1.63353	+	0.594557i
$530$	−0.887690	−	1.53752i	−0.0385588	−	0.0667858i
$531$	18.3120	+	7.68747i	0.794673	+	0.333608i
$532$	0.0148207	−	0.0256701i	0.000642557	−	0.00111294i
$533$	6.81956	−	38.6756i	0.295388	−	1.67523i
$534$	4.33384	−	1.45964i	0.187543	−	0.0631647i
$535$	4.76074	+	1.73277i	0.205825	+	0.0749142i
$536$	−2.05847	−	11.6741i	−0.0889122	−	0.504246i
$537$	14.3449	+	26.2956i	0.619027	+	1.13474i
$538$	11.9934	+	10.0637i	0.517074	+	0.433876i
$539$	−2.93881			−0.126584
$540$	−0.479190	+	1.89941i	−0.0206211	+	0.0817375i
$541$	−14.0869			−0.605641			−0.302821	−	0.953048i	$-0.597928\pi$
$541$	−14.0869			−0.605641			−0.302821	+	0.953048i	$0.597928\pi$
$542$	−5.97498	−	5.01361i	−0.256648	−	0.215353i
$543$	11.4810	−	18.8189i	0.492696	−	0.807595i
$544$	−1.05155	−	5.96362i	−0.0450847	−	0.255688i
$545$	−5.93093	−	2.15868i	−0.254053	−	0.0924678i
$546$	−1.82029	+	9.03864i	−0.0779011	+	0.386818i
$547$	−6.14342	+	34.8411i	−0.262674	+	1.48970i	0.512904	+	0.858446i	$0.328570\pi$
$547$	−6.14342	+	34.8411i	−0.262674	+	1.48970i	−0.775578	+	0.631251i	$0.782542\pi$
$548$	2.34050	−	4.05387i	0.0999814	−	0.173173i
$549$	8.92305	−	39.3611i	0.380826	−	1.67989i
$550$	7.13819	+	12.3637i	0.304374	+	0.527190i
$551$	−0.174154	+	0.0633868i	−0.00741920	+	0.00270037i
$552$	12.7993	+	5.01250i	0.544775	+	0.213346i
$553$	−3.32945	+	2.79374i	−0.141583	+	0.118802i
$554$	5.69193	−	4.77610i	0.241827	−	0.202917i
$555$	0.539228	+	3.55979i	0.0228890	+	0.151105i
$556$	5.17938	−	1.88514i	0.219655	−	0.0799478i
$557$	−2.07280	−	3.59020i	−0.0878275	−	0.152122i	0.818765	−	0.574129i	$-0.194659\pi$
$557$	−2.07280	−	3.59020i	−0.0878275	−	0.152122i	−0.906593	+	0.422007i	$0.861326\pi$
$558$	−0.648643	+	1.00754i	−0.0274592	+	0.0426527i
$559$	4.13734	−	7.16608i	0.174991	−	0.303093i
$560$	0.0654644	−	0.371267i	0.00276638	−	0.0156889i
$561$	23.1264	+	20.3789i	0.976396	+	0.860398i
$562$	−22.1181	−	8.05031i	−0.932994	−	0.339582i
$563$	−5.09962	−	28.9214i	−0.214923	−	1.21889i	−0.881040	−	0.473042i	$-0.843156\pi$
$563$	−5.09962	−	28.9214i	−0.214923	−	1.21889i	0.666116	−	0.745848i	$-0.267955\pi$
$564$	−18.8671	−	0.456638i	−0.794450	−	0.0192279i
$565$	−1.95023	−	1.63644i	−0.0820468	−	0.0688455i
$566$	18.4817			0.776843
$567$	2.41208	−	8.67075i	0.101298	−	0.364137i
$568$	5.63126			0.236282
$569$	13.6326	+	11.4391i	0.571510	+	0.479554i	0.882147	−	0.470975i	$-0.156098\pi$
$569$	13.6326	+	11.4391i	0.571510	+	0.479554i	−0.310637	+	0.950529i	$0.600542\pi$
$570$	−0.0193493		0.000468309i	−0.000810455		1.96153e-5i
$571$	−2.41904	−	13.7191i	−0.101234	−	0.574125i	−0.992658	−	0.120955i	$-0.961404\pi$
$571$	−2.41904	−	13.7191i	−0.101234	−	0.574125i	0.891424	−	0.453170i	$-0.149707\pi$
$572$	−14.7005	−	5.35056i	−0.614661	−	0.223718i
$573$	−1.95822	−	1.72558i	−0.0818057	−	0.0720871i
$574$	1.28109	−	7.26544i	0.0534718	−	0.303253i
$575$	−19.2764	+	33.3877i	−0.803882	+	1.39236i
$576$	−1.37256	−	2.66760i	−0.0571898	−	0.111150i
$577$	−16.0803	−	27.8519i	−0.669431	−	1.15949i	−0.978063	−	0.208308i	$-0.933204\pi$
$577$	−16.0803	−	27.8519i	−0.669431	−	1.15949i	0.308632	−	0.951182i	$-0.400129\pi$
$578$	18.4843	−	6.72772i	0.768844	−	0.279836i
$579$	−3.50063	−	23.1099i	−0.145481	−	0.960413i
$580$	−1.80567	+	1.51514i	−0.0749764	+	0.0629127i
$581$	8.38962	−	7.03973i	0.348060	−	0.292057i
$582$	−14.3812	−	5.63200i	−0.596119	−	0.233454i
$583$	−13.0051	+	4.73347i	−0.538617	+	0.196040i
$584$	5.51391	+	9.55037i	0.228167	+	0.395197i
$585$	5.75041	−	1.78303i	0.237750	−	0.0737192i
$586$	−5.14430	+	8.91018i	−0.212509	+	0.368076i
$587$	−0.594572	+	3.37198i	−0.0245406	+	0.139177i	−0.994616	−	0.103626i	$-0.966956\pi$
$587$	−0.594572	+	3.37198i	−0.0245406	+	0.139177i	0.970076	+	0.242802i	$0.0780667\pi$
$588$	−0.341951	+	1.69796i	−0.0141018	+	0.0700227i
$589$	−0.0111255	−	0.00404937i	−0.000458420	−	0.000166851i
$590$	0.433378	+	2.45781i	0.0178419	+	0.101186i
$591$	12.9140	−	21.1678i	0.531213	−	0.870729i
$592$	−4.22385	−	3.54423i	−0.173599	−	0.145667i
$593$	34.9302			1.43441			0.717206	−	0.696861i	$-0.245421\pi$
$593$	34.9302			1.43441			0.717206	+	0.696861i	$0.245421\pi$
$594$	13.9330	+	6.24985i	0.571677	+	0.256435i
$595$	2.28294			0.0935913
$596$	−7.35921	−	6.17511i	−0.301445	−	0.252943i
$597$	5.98900	+	10.9784i	0.245113	+	0.449317i
$598$	−7.33594	−	41.6042i	−0.299989	−	1.70132i
$599$	−32.6735	−	11.8922i	−1.33500	−	0.485902i	−0.426769	−	0.904361i	$-0.640348\pi$
$599$	−32.6735	−	11.8922i	−1.33500	−	0.485902i	−0.908236	+	0.418459i	$0.862571\pi$
$600$	7.97397	−	2.68564i	0.325536	−	0.109641i
$601$	1.95844	−	11.1069i	0.0798865	−	0.453059i	−0.918457	−	0.395521i	$-0.870564\pi$
$601$	1.95844	−	11.1069i	0.0798865	−	0.453059i	0.998343	−	0.0575375i	$-0.0183249\pi$
$602$	0.777222	−	1.34619i	0.0316772	−	0.0548665i
$603$	28.3166	−	21.5146i	1.15314	−	0.876141i
$604$	−4.07613	−	7.06006i	−0.165855	−	0.287270i
$605$	0.837249	−	0.304734i	0.0340390	−	0.0123892i
$606$	13.4912	−	10.7751i	0.548041	−	0.437708i
$607$	−21.7905	+	18.2844i	−0.884449	+	0.742141i	−0.967089	−	0.254439i	$-0.918109\pi$
$607$	−21.7905	+	18.2844i	−0.884449	+	0.742141i	0.0826400	+	0.996579i	$0.473665\pi$
$608$	0.0227066	−	0.0190531i	0.000920873	−	0.000772704i
$609$	8.46191	−	6.75833i	0.342894	−	0.273861i
$610$	4.76595	−	1.73466i	0.192968	−	0.0702345i
$611$	29.0013	+	50.2318i	1.17327	+	2.03216i
$612$	14.4653	−	10.9905i	0.584723	−	0.444265i
$613$	−20.3552	+	35.2563i	−0.822140	+	1.42399i	0.0819452	+	0.996637i	$0.473887\pi$
$613$	−20.3552	+	35.2563i	−0.822140	+	1.42399i	−0.904085	+	0.427352i	$0.859447\pi$
$614$	−1.41503	+	8.02503i	−0.0571059	+	0.323864i
$615$	−4.56535	+	1.53761i	−0.184092	+	0.0620024i
$616$	−2.76158	−	1.00513i	−0.111267	−	0.0404980i
$617$	5.08261	+	28.8249i	0.204618	+	1.16045i	0.898040	+	0.439915i	$0.144991\pi$
$617$	5.08261	+	28.8249i	0.204618	+	1.16045i	−0.693421	+	0.720532i	$0.743898\pi$
$618$	−8.86738	−	16.2548i	−0.356698	−	0.653863i
$619$	−1.20334	−	1.00972i	−0.0483665	−	0.0405843i	0.618284	−	0.785955i	$-0.287828\pi$
$619$	−1.20334	−	1.00972i	−0.0483665	−	0.0405843i	−0.666650	+	0.745370i	$0.732273\pi$
$620$	−0.150582			−0.00604752
$621$	4.19641	+	41.0234i	0.168396	+	1.64621i
$622$	−14.3456			−0.575205
$623$	−2.02254	−	1.69712i	−0.0810315	−	0.0679935i
$624$	−4.80191	+	7.87097i	−0.192230	+	0.315091i
$625$	3.97452	+	22.5406i	0.158981	+	0.901624i
$626$	−13.8251	−	5.03194i	−0.552563	−	0.201117i
$627$	−0.0297875	+	0.147910i	−0.00118960	+	0.00590695i
$628$	−1.98116	+	11.2357i	−0.0790569	+	0.448354i
$629$	16.6949	−	28.9164i	0.665668	−	1.15297i
$630$	1.08025	−	0.334952i	0.0430380	−	0.0133448i
$631$	−22.6871	−	39.2952i	−0.903159	−	1.56432i	−0.823370	−	0.567505i	$-0.807909\pi$
$631$	−22.6871	−	39.2952i	−0.903159	−	1.56432i	−0.0797892	−	0.996812i	$-0.525425\pi$
$632$	−4.08417	+	1.48652i	−0.162460	+	0.0591305i
$633$	−26.0157	−	10.1883i	−1.03403	−	0.404950i
$634$	−2.88941	+	2.42450i	−0.114753	+	0.0962894i
$635$	−2.28559	+	1.91783i	−0.0907007	+	0.0761069i
$636$	1.22163	+	8.06475i	0.0484408	+	0.319788i
$637$	5.00221	−	1.82065i	0.198195	−	0.0721369i
$638$	9.18737	+	15.9130i	0.363731	+	0.630001i
$639$	7.72921	+	15.0219i	0.305763	+	0.594259i
$640$	0.188497	−	0.326487i	0.00745101	−	0.0129055i
$641$	−1.87275	+	10.6209i	−0.0739693	+	0.419501i	0.925227	+	0.379414i	$0.123874\pi$
$641$	−1.87275	+	10.6209i	−0.0739693	+	0.419501i	−0.999196	+	0.0400865i	$0.987237\pi$
$642$	−17.4635	−	15.3888i	−0.689228	−	0.607347i
$643$	19.4855	+	7.09214i	0.768433	+	0.279687i	0.696341	−	0.717711i	$-0.254810\pi$
$643$	19.4855	+	7.09214i	0.768433	+	0.279687i	0.0720922	+	0.997398i	$0.477032\pi$
$644$	−1.37810	−	7.81558i	−0.0543047	−	0.307977i
$645$	−1.01471	−	0.0245590i	−0.0399543	−	0.000967009i
$646$	0.137502	+	0.115378i	0.00540996	+	0.00453949i
$647$	−10.1465			−0.398902			−0.199451	−	0.979908i	$-0.563916\pi$
$647$	−10.1465			−0.398902			−0.199451	+	0.979908i	$0.563916\pi$
$648$	5.23218	−	7.32286i	0.205540	−	0.287669i
$649$	19.4551			0.763680
$650$	−19.8096	−	16.6222i	−0.776997	−	0.651978i
$651$	0.691626	+	0.0167393i	0.0271070	+	0.000656066i
$652$	4.05564	+	23.0007i	0.158831	+	0.900775i
$653$	−23.4464	−	8.53380i	−0.917530	−	0.333954i	−0.160275	−	0.987072i	$-0.551238\pi$
$653$	−23.4464	−	8.53380i	−0.917530	−	0.333954i	−0.757255	+	0.653119i	$0.773460\pi$
$654$	21.7560	+	19.1713i	0.850726	+	0.749658i
$655$	0.730733	−	4.14419i	0.0285521	−	0.161927i
$656$	3.68876	−	6.38912i	0.144022	−	0.249453i
$657$	−17.9084	+	27.8173i	−0.698674	+	1.08526i
$658$	5.44807	+	9.43633i	0.212388	+	0.367866i
$659$	14.3717	−	5.23089i	0.559844	−	0.203766i	−0.0465711	−	0.998915i	$-0.514829\pi$
$659$	14.3717	−	5.23089i	0.559844	−	0.203766i	0.606415	+	0.795149i	$0.292607\pi$
$660$	0.287402	+	1.89732i	0.0111871	+	0.0738532i
$661$	21.3040	−	17.8762i	0.828629	−	0.695303i	−0.126347	−	0.991986i	$-0.540325\pi$
$661$	21.3040	−	17.8762i	0.828629	−	0.695303i	0.954976	+	0.296684i	$0.0958807\pi$
$662$	17.2416	−	14.4674i	0.670112	−	0.562291i
$663$	−51.9889	−	20.3601i	−2.01908	−	0.790719i
$664$	10.2914	−	3.74576i	0.399383	−	0.145364i
$665$	0.00558731	+	0.00967751i	0.000216667	+	0.000375278i
$666$	3.65712	−	16.1322i	0.141711	−	0.625110i
$667$	−24.8101	+	42.9724i	−0.960652	+	1.66390i
$668$	0.332226	−	1.88415i	0.0128542	−	0.0728998i
$669$	−7.72906	+	38.3787i	−0.298823	+	1.48381i
$670$	4.19947	+	1.52848i	0.162240	+	0.0590504i
$671$	−6.86547	−	38.9360i	−0.265039	−	1.50311i
$672$	−0.902066	+	1.47861i	−0.0347979	+	0.0570385i
$673$	26.8501	+	22.5299i	1.03500	+	0.868465i	0.991437	−	0.130586i	$-0.0416859\pi$
$673$	26.8501	+	22.5299i	1.03500	+	0.868465i	0.0435589	+	0.999051i	$0.486130\pi$
$674$	−28.6648			−1.10413
$675$	18.1089	+	17.5852i	0.697013	+	0.676854i
$676$	15.3368			0.589879
$677$	−2.64111	−	2.21615i	−0.101506	−	0.0851737i	0.590622	−	0.806948i	$-0.298882\pi$
$677$	−2.64111	−	2.21615i	−0.101506	−	0.0851737i	−0.692128	+	0.721774i	$0.743327\pi$
$678$	5.60147	+	10.2680i	0.215123	+	0.394342i
$679$	1.54842	+	8.78151i	0.0594228	+	0.337003i
$680$	2.14526	+	0.780810i	0.0822669	+	0.0299427i
$681$	−13.0017	+	4.37899i	−0.498227	+	0.167803i
$682$	−0.203836	+	1.15601i	−0.00780527	+	0.0442659i
$683$	−6.67743	+	11.5656i	−0.255505	+	0.442547i	−0.965032	−	0.262130i	$-0.915575\pi$
$683$	−6.67743	+	11.5656i	−0.255505	+	0.442547i	0.709528	+	0.704677i	$0.248908\pi$
$684$	0.0819920	+	0.0344207i	0.00313504	+	0.00131611i
$685$	0.882357	+	1.52829i	0.0337131	+	0.0583929i
$686$	0.939693	−	0.342020i	0.0358776	−	0.0130584i
$687$	−25.3095	+	20.2141i	−0.965616	+	0.771215i
$688$	1.19077	−	0.999177i	0.0453978	−	0.0380933i
$689$	19.2038	−	16.1139i	0.731605	−	0.613889i
$690$	−4.04915	+	3.23396i	−0.154149	+	0.123115i
$691$	−24.4734	+	8.90761i	−0.931014	+	0.338861i	−0.762611	−	0.646857i	$-0.776083\pi$
$691$	−24.4734	+	8.90761i	−0.931014	+	0.338861i	−0.168403	+	0.985718i	$0.553861\pi$
$692$	−3.55606	−	6.15928i	−0.135181	−	0.234141i
$693$	−1.10913	−	8.74639i	−0.0421323	−	0.332248i
$694$	−1.32332	+	2.29205i	−0.0502324	+	0.0870051i
$695$	−0.360826	+	2.04634i	−0.0136869	+	0.0776222i
$696$	10.2631	−	3.45661i	0.389021	−	0.131022i
$697$	41.9812	+	15.2799i	1.59015	+	0.578768i
$698$	2.32691	+	13.1966i	0.0880748	+	0.499497i
$699$	10.5339	+	19.3096i	0.398428	+	0.730357i
$700$	−3.72135	−	3.12258i	−0.140654	−	0.118023i
$701$	16.4226			0.620275			0.310137	−	0.950692i	$-0.399625\pi$
$701$	16.4226			0.620275			0.310137	+	0.950692i	$0.399625\pi$
$702$	−27.5875	−	2.00622i	−1.04122	−	0.0757200i
$703$	0.163438			0.00616417
$704$	−2.25126	−	1.88903i	−0.0848476	−	0.0711956i
$705$	3.70549	−	6.07380i	0.139557	−	0.228752i
$706$	0.0347792	+	0.197243i	0.00130893	+	0.00742333i
$707$	−9.36735	−	3.40944i	−0.352295	−	0.128225i
$708$	2.26374	−	11.2406i	0.0850764	−	0.422448i
$709$	0.514281	−	2.91664i	0.0193142	−	0.109537i	−0.973627	−	0.228148i	$-0.926733\pi$
$709$	0.514281	−	2.91664i	0.0193142	−	0.109537i	0.992941	+	0.118611i	$0.0378442\pi$
$710$	−1.06148	+	1.83853i	−0.0398365	+	0.0689989i
$711$	−9.57119	−	8.85461i	−0.358948	−	0.332074i
$712$	−1.32012	−	2.28652i	−0.0494737	−	0.0856909i
$713$	−2.97875	+	1.08418i	−0.111555	+	0.0406027i
$714$	−9.76642	−	3.82475i	−0.365499	−	0.143138i
$715$	4.51790	−	3.79097i	0.168960	−	0.141774i
$716$	13.2479	−	11.1163i	0.495096	−	0.415435i
$717$	−2.10150	−	13.8733i	−0.0784818	−	0.518108i
$718$	−27.4803	+	10.0020i	−1.02555	+	0.373271i
$719$	−7.75675	−	13.4351i	−0.289278	−	0.501044i	0.684360	−	0.729145i	$-0.260082\pi$
$719$	−7.75675	−	13.4351i	−0.289278	−	0.501044i	−0.973638	+	0.228100i	$0.926749\pi$
$720$	1.12966	+	0.0547140i	0.0420999	+	0.00203907i
$721$	−5.34516	+	9.25808i	−0.199064	+	0.344789i
$722$	3.29916	−	18.7105i	0.122782	−	0.696332i
$723$	−16.3543	−	14.4114i	−0.608222	−	0.535964i
$724$	−11.9599	−	4.35304i	−0.444485	−	0.161779i
$725$	5.27431	+	29.9121i	0.195883	+	1.11091i
$726$	−4.09230	−	0.0990452i	−0.151879	−	0.00367591i
$727$	13.6895	+	11.4868i	0.507714	+	0.426022i	0.860324	−	0.509748i	$-0.170261\pi$
$727$	13.6895	+	11.4868i	0.507714	+	0.426022i	−0.352610	+	0.935770i	$0.614706\pi$
$728$	5.32324			0.197292
$729$	26.7159	+	3.90634i	0.989479	+	0.144679i
$730$	−4.15743			−0.153873
$731$	7.21087	+	6.05064i	0.266704	+	0.223791i
$732$	−23.2950	−	0.563804i	−0.861006	−	0.0208388i
$733$	−0.360823	−	2.04633i	−0.0133273	−	0.0755829i	0.977419	−	0.211312i	$-0.0677735\pi$
$733$	−0.360823	−	2.04633i	−0.0133273	−	0.0755829i	−0.990746	+	0.135729i	$0.956662\pi$
$734$	−31.2450	−	11.3722i	−1.15327	−	0.419757i
$735$	−0.489905	−	0.431704i	−0.0180704	−	0.0159236i
$736$	1.37810	−	7.81558i	0.0507974	−	0.288086i
$737$	17.4187	−	30.1700i	0.641625	−	1.11133i
$738$	22.1066	+	1.07071i	0.813757	+	0.0394135i
$739$	−11.0155	−	19.0793i	−0.405210	−	0.701844i	0.589136	−	0.808034i	$-0.299468\pi$
$739$	−11.0155	−	19.0793i	−0.405210	−	0.701844i	−0.994346	+	0.106190i	$0.966135\pi$
$740$	1.95333	−	0.710954i	0.0718058	−	0.0261352i
$741$	−0.0409314	−	0.270214i	−0.00150365	−	0.00992656i
$742$	3.60753	−	3.02708i	0.132437	−	0.111128i
$743$	−3.91011	+	3.28097i	−0.143448	+	0.120367i	−0.711688	−	0.702496i	$-0.752069\pi$
$743$	−3.91011	+	3.28097i	−0.143448	+	0.120367i	0.568240	+	0.822863i	$0.307625\pi$
$744$	0.644191	+	0.252280i	0.0236172	+	0.00924903i
$745$	3.40329	−	1.23869i	0.124687	−	0.0453823i
$746$	−14.0488	−	24.3332i	−0.514363	−	0.890903i
$747$	24.1177	+	22.3121i	0.882421	+	0.816355i
$748$	8.89817	−	15.4121i	0.325349	−	0.563521i
$749$	−2.33359	+	13.2344i	−0.0852674	+	0.483576i
$750$	−1.27082	+	6.31024i	−0.0464036	+	0.230417i
$751$	−26.2861	−	9.56735i	−0.959193	−	0.349118i	−0.185476	−	0.982649i	$-0.559383\pi$
$751$	−26.2861	−	9.56735i	−0.959193	−	0.349118i	−0.773717	+	0.633531i	$0.781605\pi$
$752$	1.89209	+	10.7306i	0.0689976	+	0.391305i
$753$	17.5540	−	28.7733i	0.639702	−	1.04856i
$754$	−25.4964	−	21.3940i	−0.928525	−	0.779125i
$755$	3.07336			0.111851
$756$	−5.18247	−	0.376880i	−0.188484	−	0.0137070i
$757$	−32.3950			−1.17742			−0.588708	−	0.808346i	$-0.700363\pi$
$757$	−32.3950			−1.17742			−0.588708	+	0.808346i	$0.700363\pi$
$758$	4.65791	+	3.90845i	0.169183	+	0.141961i
$759$	19.3458	+	35.4628i	0.702208	+	1.28722i
$760$	0.00194045	+	0.0110049i	7.03876e−5	+	0.000399188i
$761$	7.25518	+	2.64067i	0.263000	+	0.0957242i	0.470155	−	0.882584i	$-0.344198\pi$
$761$	7.25518	+	2.64067i	0.263000	+	0.0957242i	−0.207155	+	0.978308i	$0.566420\pi$
$762$	12.9908	−	4.37531i	0.470608	−	0.158501i
$763$	2.90718	−	16.4874i	0.105247	−	0.596886i
$764$	−0.753450	+	1.30501i	−0.0272589	+	0.0472137i
$765$	0.861597	+	6.79440i	0.0311511	+	0.245652i
$766$	−8.63456	−	14.9555i	−0.311979	−	0.540364i
$767$	−33.1149	+	12.0528i	−1.19571	+	0.435203i
$768$	−1.35338	+	1.08091i	−0.0488358	+	0.0390040i
$769$	37.6770	−	31.6147i	1.35867	−	1.14006i	0.382274	−	0.924049i	$-0.375141\pi$
$769$	37.6770	−	31.6147i	1.35867	−	1.14006i	0.976392	−	0.216007i	$-0.0693034\pi$
$770$	0.848713	−	0.712155i	0.0305855	−	0.0256643i
$771$	−24.9532	+	19.9296i	−0.898669	+	0.717746i
$772$	−12.6809	+	4.61546i	−0.456394	+	0.166114i
$773$	0.798212	+	1.38254i	0.0287097	+	0.0497266i	0.880023	−	0.474931i	$-0.157527\pi$
$773$	0.798212	+	1.38254i	0.0287097	+	0.0497266i	−0.851314	+	0.524657i	$0.824194\pi$
$774$	4.29981	+	1.80508i	0.154553	+	0.0648823i
$775$	−0.970184	+	1.68041i	−0.0348500	+	0.0603621i
$776$	−1.54842	+	8.78151i	−0.0555849	+	0.315238i
$777$	−9.05071	+	3.04828i	−0.324692	+	0.109357i
$778$	23.4555	+	8.53711i	0.840921	+	0.306070i
$779$	0.0379733	+	0.215357i	0.00136053	+	0.00771597i
$780$	−1.66462	−	3.05142i	−0.0596031	−	0.109258i
$781$	12.6774	+	10.6376i	0.453634	+	0.380644i
$782$	48.0583			1.71856
$783$	23.3075	+	22.6334i	0.832942	+	0.808852i
$784$	1.00000			0.0357143
$785$	−3.29487	−	2.76473i	−0.117599	−	0.0986773i
$786$	−10.0691	+	16.5046i	−0.359154	+	0.588701i
$787$	5.59324	+	31.7209i	0.199378	+	1.13073i	0.906045	+	0.423181i	$0.139086\pi$
$787$	5.59324	+	31.7209i	0.199378	+	1.13073i	−0.706668	+	0.707546i	$0.749802\pi$
$788$	−13.4527	−	4.89639i	−0.479233	−	0.174427i
$789$	3.86788	−	19.2060i	0.137700	−	0.683752i
$790$	0.284527	−	1.61363i	0.0101230	−	0.0574105i
$791$	3.37650	−	5.84827i	0.120055	−	0.207941i
$792$	1.94920	−	8.59827i	0.0692619	−	0.305526i
$793$	35.8075	+	62.0204i	1.27156	+	2.20241i
$794$	16.8305	−	6.12578i	0.597290	−	0.217396i
$795$	−2.86331	−	1.12134i	−0.101551	−	0.0397697i
$796$	5.53099	−	4.64105i	0.196041	−	0.164498i
$797$	−35.7966	+	30.0369i	−1.26798	+	1.06396i	−0.273196	+	0.961958i	$0.588081\pi$
$797$	−35.7966	+	30.0369i	−1.26798	+	1.06396i	−0.994784	+	0.102004i	$0.967475\pi$
$798$	−0.00768919	−	0.0507612i	−0.000272194	−	0.00179693i
$799$	−62.0036	+	22.5675i	−2.19353	+	0.798379i
$800$	−2.42894	−	4.20704i	−0.0858759	−	0.148741i
$801$	4.28758	−	6.65993i	0.151494	−	0.235317i
$802$	−2.61187	+	4.52390i	−0.0922285	+	0.159744i
$803$	−5.62771	+	31.9163i	−0.198598	+	1.12630i
$804$	−15.4046	−	13.5745i	−0.543278	−	0.478736i
$805$	2.81145	+	1.02329i	0.0990907	+	0.0360661i
$806$	−0.369219	−	2.09394i	−0.0130052	−	0.0737560i
$807$	27.1096	+	0.656130i	0.954303	+	0.0230969i
$808$	−7.63633	−	6.40764i	−0.268645	−	0.225420i
$809$	8.71526			0.306412			0.153206	−	0.988194i	$-0.451040\pi$
$809$	8.71526			0.306412			0.153206	+	0.988194i	$0.451040\pi$
$810$	1.40457	+	3.08858i	0.0493514	+	0.108522i
$811$	−7.14643			−0.250945			−0.125473	−	0.992097i	$-0.540045\pi$
$811$	−7.14643			−0.250945			−0.125473	+	0.992097i	$0.540045\pi$
$812$	−4.78964	−	4.01899i	−0.168084	−	0.141039i
$813$	−13.5057	−	0.326876i	−0.473665	−	0.0114640i
$814$	−2.81382	−	15.9580i	−0.0986244	−	0.559327i
$815$	−8.27389	−	3.01145i	−0.289822	−	0.105486i
$816$	−7.86929	−	6.93440i	−0.275480	−	0.242753i
$817$	−0.00800098	+	0.0453758i	−0.000279919	+	0.00158750i
$818$	11.0008	−	19.0540i	0.384634	−	0.666206i
$819$	7.30644	+	14.2003i	0.255308	+	0.496197i
$820$	1.39064	+	2.40866i	0.0485633	+	0.0841142i
$821$	3.95083	−	1.43798i	0.137885	−	0.0501859i	−0.272156	−	0.962253i	$-0.587737\pi$
$821$	3.95083	−	1.43798i	0.137885	−	0.0501859i	0.410041	+	0.912067i	$0.365514\pi$
$822$	−1.21429	−	8.01630i	−0.0423532	−	0.279600i
$823$	26.6232	−	22.3395i	0.928026	−	0.778706i	−0.0474361	−	0.998874i	$-0.515105\pi$
$823$	26.6232	−	22.3395i	0.928026	−	0.778706i	0.975462	+	0.220168i	$0.0706606\pi$
$824$	−8.18925	+	6.87160i	−0.285286	+	0.239384i
$825$	23.0247	+	9.01702i	0.801619	+	0.313932i
$826$	−6.22082	+	2.26419i	−0.216450	+	0.0787814i
$827$	14.0148	+	24.2743i	0.487342	+	0.844101i	0.999894	−	0.0145548i	$-0.00463310\pi$
$827$	14.0148	+	24.2743i	0.487342	+	0.844101i	−0.512552	+	0.858656i	$0.671300\pi$
$828$	22.7404	−	7.05111i	0.790282	−	0.245043i
$829$	22.4680	−	38.9157i	0.780347	−	1.35160i	−0.151393	−	0.988474i	$-0.548376\pi$
$829$	22.4680	−	38.9157i	0.780347	−	1.35160i	0.931740	−	0.363126i	$-0.118291\pi$
$830$	−0.716958	+	4.06607i	−0.0248860	+	0.141135i
$831$	2.54079	−	12.6163i	0.0881392	−	0.437656i
$832$	5.00221	+	1.82065i	0.173420	+	0.0631198i
$833$	1.05155	+	5.96362i	0.0364340	+	0.206627i
$834$	4.97199	−	8.14976i	0.172166	−	0.282203i
$835$	0.552525	+	0.463624i	0.0191209	+	0.0160444i
$836$	0.0871103			0.00301277
$837$	0.211206	+	2.06471i	0.00730034	+	0.0713669i
$838$	−3.78503			−0.130752
$839$	28.9283	+	24.2738i	0.998717	+	0.838023i	0.986806	−	0.161906i	$-0.0517641\pi$
$839$	28.9283	+	24.2738i	0.998717	+	0.838023i	0.0119109	+	0.999929i	$0.496209\pi$
$840$	−0.312709	−	0.573226i	−0.0107895	−	0.0197782i
$841$	1.75263	+	9.93963i	0.0604354	+	0.342746i
$842$	12.9632	+	4.71822i	0.446742	+	0.162601i
$843$	−38.6357	+	13.0125i	−1.33069	+	0.448176i
$844$	−2.80110	+	15.8858i	−0.0964179	+	0.546813i
$845$	−2.89095	+	5.00728i	−0.0994518	+	0.172256i
$846$	−26.0279	+	19.7757i	−0.894859	+	0.679902i
$847$	1.18169	+	2.04675i	0.0406033	+	0.0703271i
$848$	4.42529	−	1.61068i	0.151965	−	0.0553108i
$849$	25.0127	−	19.9771i	0.858434	−	0.685611i
$850$	22.5351	−	18.9092i	0.772947	−	0.648579i
$851$	33.5211	−	28.1275i	1.14909	−	0.964200i
$852$	7.62122	−	6.08689i	0.261099	−	0.208533i
$853$	50.9402	−	18.5407i	1.74416	−	0.634822i	0.744690	−	0.667410i	$-0.232597\pi$
$853$	50.9402	−	18.5407i	1.74416	−	0.634822i	0.999469	+	0.0325883i	$0.0103750\pi$
$854$	6.72664	+	11.6509i	0.230181	+	0.398685i
$855$	−0.0266932	+	0.0202811i	−0.000912887	+	0.000693600i
$856$	−6.71930	+	11.6382i	−0.229661	+	0.397784i
$857$	9.16022	−	51.9502i	0.312907	−	1.77458i	−0.270816	−	0.962631i	$-0.587293\pi$
$857$	9.16022	−	51.9502i	0.312907	−	1.77458i	0.583723	−	0.811953i	$-0.301596\pi$
$858$	−25.6789	+	8.64866i	−0.876662	+	0.295260i
$859$	−23.4218	−	8.52484i	−0.799142	−	0.290864i	−0.0900112	−	0.995941i	$-0.528690\pi$
$859$	−23.4218	−	8.52484i	−0.799142	−	0.290864i	−0.709131	+	0.705077i	$0.750913\pi$
$860$	0.101761	+	0.577114i	0.00347001	+	0.0196794i
$861$	−6.11949	−	11.2176i	−0.208552	−	0.382296i
$862$	29.8044	+	25.0088i	1.01514	+	0.851805i
$863$	25.8796			0.880952			0.440476	−	0.897764i	$-0.354810\pi$
$863$	25.8796			0.880952			0.440476	+	0.897764i	$0.354810\pi$
$864$	−4.74103	−	2.12666i	−0.161293	−	0.0723504i
$865$	2.68123			0.0911646
$866$	−9.86145	−	8.27474i	−0.335106	−	0.281187i
$867$	17.7441	−	29.0850i	0.602622	−	0.987778i
$868$	−0.0693598	−	0.393359i	−0.00235423	−	0.0133515i
$869$	−12.0026	−	4.36860i	−0.407161	−	0.148194i
$870$	−0.806025	+	4.00232i	−0.0273268	+	0.135691i
$871$	−10.9577	+	62.1442i	−0.371287	+	2.10568i
$872$	8.37089	−	14.4988i	0.283474	−	0.490992i
$873$	−25.5509	+	7.92255i	−0.864765	+	0.268138i
$874$	0.117619	+	0.203722i	0.00397852	+	0.00689100i
$875$	3.49224	−	1.27107i	0.118059	−	0.0429701i
$876$	17.7855	+	6.96521i	0.600916	+	0.235333i
$877$	−12.8839	+	10.8108i	−0.435057	+	0.365056i	−0.833856	−	0.551982i	$-0.813872\pi$
$877$	−12.8839	+	10.8108i	−0.435057	+	0.365056i	0.398799	+	0.917038i	$0.369427\pi$
$878$	−8.75149	+	7.34338i	−0.295349	+	0.247827i
$879$	2.66894	+	17.6194i	0.0900212	+	0.594287i
$880$	1.04110	−	0.378930i	0.0350955	−	0.0127737i
$881$	−8.45027	−	14.6363i	−0.284697	−	0.493110i	0.687839	−	0.725864i	$-0.258560\pi$
$881$	−8.45027	−	14.6363i	−0.284697	−	0.493110i	−0.972536	+	0.232754i	$0.925226\pi$
$882$	1.37256	+	2.66760i	0.0462164	+	0.0898228i
$883$	−3.26702	+	5.65865i	−0.109944	+	0.190429i	−0.915747	−	0.401755i	$-0.868401\pi$
$883$	−3.26702	+	5.65865i	−0.109944	+	0.190429i	0.805803	+	0.592183i	$0.201734\pi$
$884$	−5.59764	+	31.7458i	−0.188269	+	1.06773i
$885$	3.24320	+	2.85790i	0.109019	+	0.0960673i
$886$	31.8873	+	11.6060i	1.07127	+	0.389912i
$887$	0.881131	+	4.99714i	0.0295855	+	0.167788i	0.996021	−	0.0891231i	$-0.0284065\pi$
$887$	0.881131	+	4.99714i	0.0295855	+	0.167788i	−0.966435	+	0.256911i	$0.917295\pi$
$888$	−9.54746	−	0.231076i	−0.320392	−	0.00775439i
$889$	−6.06265	−	5.08716i	−0.203335	−	0.170618i
$890$	0.995358			0.0333645
$891$	25.6121	−	6.60191i	0.858039	−	0.221172i
$892$	22.6028			0.756799
$893$	−0.247414	−	0.207605i	−0.00827939	−	0.00694723i
$894$	−16.6345	−	0.402603i	−0.556342	−	0.0134651i
$895$	1.13213	+	6.42064i	0.0378430	+	0.214618i
$896$	0.939693	+	0.342020i	0.0313929	+	0.0114261i
$897$	−54.8987	−	48.3767i	−1.83302	−	1.61525i
$898$	−4.60164	+	26.0972i	−0.153559	+	0.870874i
$899$	−1.24870	+	2.16281i	−0.0416464	+	0.0721337i
$900$	7.88886	−	12.2538i	0.262962	−	0.408461i
$901$	14.2589	+	24.6971i	0.475032	+	0.822779i
$902$	20.3736	−	7.41539i	0.678367	−	0.246905i
$903$	−0.403235	−	2.66201i	−0.0134188	−	0.0885861i
$904$	5.17310	−	4.34075i	0.172055	−	0.144371i
$905$	3.67561	−	3.08421i	0.122182	−	0.102522i
$906$	−13.1478	−	5.14900i	−0.436808	−	0.171064i
$907$	20.8557	−	7.59087i	0.692503	−	0.252051i	0.0282967	−	0.999600i	$-0.490992\pi$
$907$	20.8557	−	7.59087i	0.692503	−	0.252051i	0.664207	+	0.747549i	$0.268769\pi$
$908$	3.96043	+	6.85967i	0.131432	+	0.227646i
$909$	6.61174	−	29.1655i	0.219298	−	0.967359i
$910$	−1.00342	+	1.73797i	−0.0332629	+	0.0576130i
$911$	5.93733	−	33.6723i	0.196713	−	1.11561i	−0.713246	−	0.700913i	$-0.752776\pi$
$911$	5.93733	−	33.6723i	0.196713	−	1.11561i	0.909959	−	0.414699i	$-0.136113\pi$
$912$	0.0101359	−	0.0503298i	0.000335633	−	0.00166659i
$913$	30.2445	+	11.0081i	1.00095	+	0.364315i
$914$	4.51433	+	25.6020i	0.149321	+	0.846839i
$915$	4.57511	−	7.49922i	0.151248	−	0.247917i
$916$	14.3258	+	12.0207i	0.473337	+	0.397177i
$917$	11.1623			0.368611
$918$	7.69718	−	30.5100i	0.254045	−	1.00698i
$919$	40.7088			1.34286			0.671429	−	0.741069i	$-0.265681\pi$
$919$	40.7088			1.34286			0.671429	+	0.741069i	$0.265681\pi$
$920$	2.29192	+	1.92315i	0.0755623	+	0.0634043i
$921$	6.75927	+	12.3904i	0.222726	+	0.408278i
$922$	0.204192	+	1.15803i	0.00672470	+	0.0381377i
$923$	−28.1687	−	10.2526i	−0.927184	−	0.337468i
$924$	−4.82392	+	1.62470i	−0.158695	+	0.0534487i
$925$	4.65126	−	26.3786i	0.152933	−	0.867324i
$926$	−13.4791	+	23.3464i	−0.442950	+	0.767212i
$927$	−29.5709	−	12.4140i	−0.971235	−	0.407729i
$928$	−3.12622	−	5.41477i	−0.102623	−	0.177749i
$929$	−45.0244	+	16.3875i	−1.47720	+	0.537658i	−0.950046	−	0.312110i	$-0.898964\pi$
$929$	−45.0244	+	16.3875i	−1.47720	+	0.537658i	−0.527157	+	0.849768i	$0.676742\pi$
$930$	−0.203794	+	0.162766i	−0.00668268	+	0.00533730i
$931$	−0.0227066	+	0.0190531i	−0.000744178	+	0.000624439i
$932$	9.72831	−	8.16302i	0.318661	−	0.267389i
$933$	−19.4150	+	15.5063i	−0.635618	+	0.507653i
$934$	−17.5295	+	6.38020i	−0.573581	+	0.208766i
$935$	3.35456	+	5.81027i	0.109706	+	0.190016i
$936$	2.00903	+	15.8428i	0.0656672	+	0.517839i
$937$	−7.76367	+	13.4471i	−0.253628	+	0.439296i	−0.964522	−	0.264003i	$-0.914957\pi$
$937$	−7.76367	+	13.4471i	−0.253628	+	0.439296i	0.710894	+	0.703299i	$0.248291\pi$
$938$	−2.05847	+	11.6741i	−0.0672113	+	0.381174i
$939$	−24.1497	+	8.13363i	−0.788096	+	0.265431i
$940$	−3.86005	−	1.40494i	−0.125901	−	0.0458242i
$941$	2.70285	+	15.3286i	0.0881104	+	0.499699i	0.996642	+	0.0818828i	$0.0260933\pi$
$941$	2.70285	+	15.3286i	0.0881104	+	0.499699i	−0.908532	+	0.417816i	$0.862796\pi$
$942$	9.46356	+	17.3476i	0.308340	+	0.565217i
$943$	44.8512	+	37.6346i	1.46056	+	1.22555i
$944$	−6.62006			−0.215465
$945$	1.09993	−	1.62097i	0.0357806	−	0.0527301i
$946$	4.56822			0.148526
$947$	−20.9966	−	17.6182i	−0.682296	−	0.572515i	0.234380	−	0.972145i	$-0.424694\pi$
$947$	−20.9966	−	17.6182i	−0.682296	−	0.572515i	−0.916676	+	0.399631i	$0.869138\pi$
$948$	−3.92064	+	6.42645i	−0.127336	+	0.208721i
$949$	−10.1938	−	57.8118i	−0.330904	−	1.87665i
$950$	0.135310	+	0.0492488i	0.00439003	+	0.00159784i
$951$	−1.28979	+	6.40447i	−0.0418243	+	0.207679i
$952$	−1.05155	+	5.96362i	−0.0340808	+	0.193282i
$953$	−28.3137	+	49.0408i	−0.917172	+	1.58859i	−0.113481	+	0.993540i	$0.536200\pi$
$953$	−28.3137	+	49.0408i	−0.917172	+	1.58859i	−0.803690	+	0.595048i	$0.797133\pi$
$954$	10.3706	+	9.59418i	0.335761	+	0.310623i
$955$	−0.284046	−	0.491983i	−0.00919153	−	0.0159202i
$956$	−7.61257	+	2.77075i	−0.246208	+	0.0896124i
$957$	29.6345	+	11.6056i	0.957948	+	0.375154i
$958$	−9.36600	+	7.85900i	−0.302602	+	0.253913i
$959$	−3.58586	+	3.00889i	−0.115793	+	0.0971622i
$960$	−0.0977953	−	0.645609i	−0.00315633	−	0.0208369i
$961$	28.9806	−	10.5481i	0.934856	−	0.340260i
$962$	14.6757	+	25.4191i	0.473165	+	0.819546i
$963$	−40.2686	−	1.95037i	−1.29764	−	0.0628498i
$964$	−6.29252	+	10.8990i	−0.202668	+	0.351032i
$965$	0.883423	−	5.01014i	0.0284384	−	0.161282i
$966$	−10.3130	−	9.08783i	−0.331817	−	0.292396i
$967$	12.0885	+	4.39986i	0.388740	+	0.141490i	0.528994	−	0.848626i	$-0.322570\pi$
$967$	12.0885	+	4.39986i	0.388740	+	0.141490i	−0.140254	+	0.990116i	$0.544792\pi$
$968$	0.410397	+	2.32747i	0.0131906	+	0.0748079i
$969$	0.310806	+	0.00752240i	0.00998453	+	0.000241654i
$970$	−2.57518	−	2.16083i	−0.0826839	−	0.0693800i
$971$	36.2113			1.16207			0.581037	−	0.813877i	$-0.302647\pi$
$971$	36.2113			1.16207			0.581037	+	0.813877i	$0.302647\pi$
$972$	−0.834243	−	15.5661i	−0.0267584	−	0.499283i
$973$	−5.51178			−0.176700
$974$	19.2670	+	16.1669i	0.617354	+	0.518022i
$975$	−44.7771	−	1.08373i	−1.43401	−	0.0347072i
$976$	2.33614	+	13.2489i	0.0747780	+	0.424087i
$977$	25.9233	+	9.43530i	0.829359	+	0.301862i	0.721596	−	0.692315i	$-0.243409\pi$
$977$	25.9233	+	9.43530i	0.829359	+	0.301862i	0.107763	+	0.994177i	$0.465631\pi$
$978$	30.3505	+	26.7448i	0.970501	+	0.855204i
$979$	1.34737	−	7.64131i	0.0430621	−	0.244217i
$980$	−0.188497	+	0.326487i	−0.00602133	+	0.0104292i
$981$	50.1666	+	2.42977i	1.60169	+	0.0775766i
$982$	−15.3121	−	26.5213i	−0.488628	−	0.846329i
$983$	−3.78959	+	1.37930i	−0.120869	+	0.0439928i	−0.401747	−	0.915751i	$-0.631597\pi$
$983$	−3.78959	+	1.37930i	−0.120869	+	0.0439928i	0.280878	+	0.959744i	$0.409375\pi$
$984$	−1.91379	−	12.6341i	−0.0610093	−	0.402761i
$985$	4.13441	−	3.46918i	0.131733	−	0.110537i
$986$	29.0043	−	24.3375i	0.923684	−	0.775063i
$987$	17.5731	+	6.88204i	0.559359	+	0.219058i
$988$	−0.148272	+	0.0539666i	−0.00471716	+	0.00171691i
$989$	6.16815	+	10.6835i	0.196136	+	0.339717i
$990$	2.43980	+	2.25714i	0.0775420	+	0.0717366i
$991$	28.6184	−	49.5685i	0.909094	−	1.57460i	0.0937675	−	0.995594i	$-0.470109\pi$
$991$	28.6184	−	49.5685i	0.909094	−	1.57460i	0.815326	−	0.579002i	$-0.196558\pi$
$992$	0.0693598	−	0.393359i	0.00220218	−	0.0124892i
$993$	7.69638	−	38.2164i	0.244237	−	1.21276i
$994$	−5.29165	−	1.92600i	−0.167841	−	0.0610891i
$995$	0.472666	+	2.68062i	0.0149845	+	0.0849815i
$996$	9.87931	−	16.1935i	0.313038	−	0.513111i
$997$	−28.9793	−	24.3165i	−0.917782	−	0.770111i	0.0558011	−	0.998442i	$-0.482229\pi$
$997$	−28.9793	−	24.3165i	−0.917782	−	0.770111i	−0.973584	+	0.228331i	$0.926673\pi$
$998$	−23.9950			−0.759550
$999$	−12.4880	−	25.7860i	−0.395103	−	0.815832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.43.1	✓	36
27.22	even	9	inner	378.2.u.e.211.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.43.1	✓	36	1.1	even	1	trivial
378.2.u.e.211.1	yes	36	27.22	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.73154 - 0.0419083i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.354259 - 0.128940i) q^{5} +(1.29950 + 1.14512i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99649 + 0.145132i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.73154 - 0.0419083i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.354259 - 0.128940i) q^{5} +(1.29950 + 1.14512i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99649 + 0.145132i) q^{9} +(0.188497 + 0.326487i) q^{10} +(2.76158 - 1.00513i) q^{11} +(-0.259408 - 1.71251i) q^{12} +(-4.07784 + 3.42171i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(0.608011 + 0.238111i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.02781 - 5.24432i) q^{17} +(-2.20215 - 2.03728i) q^{18} +(0.0148207 - 0.0256701i) q^{19} +(0.0654644 - 0.371267i) q^{20} +(-0.341951 + 1.69796i) q^{21} +(-2.76158 - 1.00513i) q^{22} +(-1.37810 - 7.81558i) q^{23} +(-0.902066 + 1.47861i) q^{24} +(-3.72135 - 3.12258i) q^{25} +5.32324 q^{26} +(-5.18247 - 0.376880i) q^{27} +1.00000 q^{28} +(-4.78964 - 4.01899i) q^{29} +(-0.312709 - 0.573226i) q^{30} +(-0.0693598 - 0.393359i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-4.82392 + 1.62470i) q^{33} +(-1.05155 + 5.96362i) q^{34} +(-0.188497 + 0.326487i) q^{35} +(0.377407 + 2.97617i) q^{36} +(2.75692 + 4.77513i) q^{37} +(-0.0278537 + 0.0101379i) q^{38} +(7.20435 - 5.75395i) q^{39} +(-0.288795 + 0.242327i) q^{40} +(-5.65151 + 4.74218i) q^{41} +(1.35338 - 1.08091i) q^{42} +(-1.46070 + 0.531651i) q^{43} +(1.46941 + 2.54509i) q^{44} +(-1.04282 - 0.437781i) q^{45} +(-3.96807 + 6.87291i) q^{46} +(1.89209 - 10.7306i) q^{47} +(1.64145 - 0.552842i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(0.843561 + 4.78407i) q^{50} +(5.02301 + 9.20766i) q^{51} +(-4.07784 - 3.42171i) q^{52} -4.70930 q^{53} +(3.72775 + 3.61993i) q^{54} -1.10792 q^{55} +(-0.766044 - 0.642788i) q^{56} +(-0.0267384 + 0.0438279i) q^{57} +(1.08572 + 6.15745i) q^{58} +(6.22082 + 2.26419i) q^{59} +(-0.128914 + 0.640122i) q^{60} +(2.33614 - 13.2489i) q^{61} +(-0.199714 + 0.345914i) q^{62} +(0.663262 - 2.92576i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.88580 - 0.686377i) q^{65} +(4.73967 + 1.85617i) q^{66} +(9.08087 - 7.61975i) q^{67} +(4.63887 - 3.89248i) q^{68} +(2.05870 + 13.5908i) q^{69} +(0.354259 - 0.128940i) q^{70} +(2.81563 + 4.87681i) q^{71} +(1.62393 - 2.52247i) q^{72} +(-5.51391 + 9.55037i) q^{73} +(0.957469 - 5.43007i) q^{74} +(6.31282 + 5.56284i) q^{75} +(0.0278537 + 0.0101379i) q^{76} +(-0.510319 - 2.89417i) q^{77} +(-9.21742 - 0.223088i) q^{78} +(-3.32945 - 2.79374i) q^{79} +0.376995 q^{80} +(8.95787 + 0.869773i) q^{81} +7.37752 q^{82} +(8.38962 + 7.03973i) q^{83} +(-1.73154 - 0.0419083i) q^{84} +(0.396428 + 2.24825i) q^{85} +(1.46070 + 0.531651i) q^{86} +(8.12505 + 7.15978i) q^{87} +(0.510319 - 2.89417i) q^{88} +(1.32012 - 2.28652i) q^{89} +(0.517446 + 1.00567i) q^{90} +(2.66162 + 4.61006i) q^{91} +(7.45754 - 2.71432i) q^{92} +(0.103615 + 0.684025i) q^{93} +(-8.34692 + 7.00390i) q^{94} +(-0.00856026 + 0.00718291i) q^{95} +(-1.61279 - 0.631604i) q^{96} +(-8.37922 + 3.04979i) q^{97} +(0.500000 + 0.866025i) q^{98} +(8.42092 - 2.61107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

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