LMFDB - Embedded newform 378.2.u.c.43.3

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	378.43
Dual form			378.2.u.c.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.217603 - 1.71833i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-3.75298 - 1.36597i) q^{5} +(-1.27121 + 1.17644i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.90530 - 0.747827i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.217603 - 1.71833i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-3.75298 - 1.36597i) q^{5} +(-1.27121 + 1.17644i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.90530 - 0.747827i) q^{9} +(1.99692 + 3.45877i) q^{10} +(3.33747 - 1.21474i) q^{11} +(1.73001 - 0.0840870i) q^{12} +(-3.57695 + 3.00141i) q^{13} +(0.766044 - 0.642788i) q^{14} +(-3.16385 + 6.15161i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.586324 - 1.01554i) q^{17} +(1.74489 + 2.44036i) q^{18} +(-2.53462 + 4.39010i) q^{19} +(0.693523 - 3.93317i) q^{20} +(1.65444 + 0.512682i) q^{21} +(-3.33747 - 1.21474i) q^{22} +(0.830334 + 4.70906i) q^{23} +(-1.37931 - 1.04761i) q^{24} +(8.38878 + 7.03902i) q^{25} +4.66937 q^{26} +(-1.91721 + 4.82952i) q^{27} -1.00000 q^{28} +(-5.29898 - 4.44637i) q^{29} +(6.37783 - 2.67872i) q^{30} +(-1.09070 - 6.18569i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-1.36108 - 5.99920i) q^{33} +(-0.203628 + 1.15483i) q^{34} +(1.99692 - 3.45877i) q^{35} +(0.231967 - 2.99102i) q^{36} +(-2.00809 - 3.47812i) q^{37} +(4.76354 - 1.73379i) q^{38} +(4.37906 + 6.79948i) q^{39} +(-3.05946 + 2.56719i) q^{40} +(-4.16419 + 3.49417i) q^{41} +(-0.937826 - 1.45619i) q^{42} +(5.72547 - 2.08390i) q^{43} +(1.77583 + 3.07583i) q^{44} +(9.88202 + 6.77515i) q^{45} +(2.39085 - 4.14108i) q^{46} +(-1.48940 + 8.44682i) q^{47} +(0.383222 + 1.68912i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-1.90158 - 10.7844i) q^{50} +(-1.87262 + 0.786511i) q^{51} +(-3.57695 - 3.00141i) q^{52} -8.45795 q^{53} +(4.57303 - 2.46727i) q^{54} -14.1848 q^{55} +(0.766044 + 0.642788i) q^{56} +(6.99208 + 5.31061i) q^{57} +(1.20118 + 6.81223i) q^{58} +(-13.4058 - 4.87933i) q^{59} +(-6.60756 - 2.04757i) q^{60} +(-0.108346 + 0.614463i) q^{61} +(-3.14056 + 5.43961i) q^{62} +(1.24097 - 2.73130i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(17.5241 - 6.37824i) q^{65} +(-2.81356 + 5.47053i) q^{66} +(4.46842 - 3.74945i) q^{67} +(0.898300 - 0.753763i) q^{68} +(8.27239 - 0.402079i) q^{69} +(-3.75298 + 1.36597i) q^{70} +(-5.05446 - 8.75458i) q^{71} +(-2.10029 + 2.14215i) q^{72} +(-3.96326 + 6.86456i) q^{73} +(-0.697403 + 3.95517i) q^{74} +(13.9208 - 12.8830i) q^{75} +(-4.76354 - 1.73379i) q^{76} +(0.616739 + 3.49770i) q^{77} +(1.01607 - 8.02351i) q^{78} +(-11.3279 - 9.50527i) q^{79} +3.99384 q^{80} +(7.88151 + 4.34532i) q^{81} +5.43596 q^{82} +(-5.26811 - 4.42047i) q^{83} +(-0.217603 + 1.71833i) q^{84} +(0.813258 + 4.61222i) q^{85} +(-5.72547 - 2.08390i) q^{86} +(-8.79339 + 8.13783i) q^{87} +(0.616739 - 3.49770i) q^{88} +(2.62533 - 4.54721i) q^{89} +(-3.21509 - 11.5421i) q^{90} +(-2.33469 - 4.04379i) q^{91} +(-4.49333 + 1.63544i) q^{92} +(-10.8664 + 0.528160i) q^{93} +(6.57046 - 5.51327i) q^{94} +(15.5092 - 13.0137i) q^{95} +(0.792183 - 1.54027i) q^{96} +(13.7402 - 5.00102i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-10.6048 + 1.03333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * 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
$3$	0.217603	−	1.71833i	0.125633	−	0.992077i
$3$	0.217603	−	1.71833i	0.125633	−	0.992077i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−3.75298	−	1.36597i	−1.67839	−	0.610882i	−0.685298	−	0.728262i	$-0.740328\pi$
$5$	−3.75298	−	1.36597i	−1.67839	−	0.610882i	−0.993087	+	0.117380i	$0.962550\pi$
$6$	−1.27121	+	1.17644i	−0.518971	+	0.480281i
$7$	−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
$9$	−2.90530	−	0.747827i	−0.968433	−	0.249276i
$10$	1.99692	+	3.45877i	0.631482	+	1.09376i
$11$	3.33747	−	1.21474i	1.00628	−	0.366258i	0.214280	−	0.976772i	$-0.431260\pi$
$11$	3.33747	−	1.21474i	1.00628	−	0.366258i	0.792005	+	0.610515i	$0.209037\pi$
$12$	1.73001	−	0.0840870i	0.499410	−	0.0242738i
$13$	−3.57695	+	3.00141i	−0.992066	+	0.832442i	−0.985866	−	0.167538i	$-0.946418\pi$
$13$	−3.57695	+	3.00141i	−0.992066	+	0.832442i	−0.00620075	+	0.999981i	$0.501974\pi$
$14$	0.766044	−	0.642788i	0.204734	−	0.171792i
$15$	−3.16385	+	6.15161i	−0.816903	+	1.58834i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.586324	−	1.01554i	−0.142204	−	0.246305i	0.786122	−	0.618071i	$-0.212086\pi$
$17$	−0.586324	−	1.01554i	−0.142204	−	0.246305i	−0.928326	+	0.371766i	$0.878752\pi$
$18$	1.74489	+	2.44036i	0.411275	+	0.575198i
$19$	−2.53462	+	4.39010i	−0.581483	+	1.00716i	0.413821	+	0.910358i	$0.364194\pi$
$19$	−2.53462	+	4.39010i	−0.581483	+	1.00716i	−0.995304	+	0.0967995i	$0.969139\pi$
$20$	0.693523	−	3.93317i	0.155077	−	0.879483i
$21$	1.65444	+	0.512682i	0.361027	+	0.111876i
$22$	−3.33747	−	1.21474i	−0.711551	−	0.258983i
$23$	0.830334	+	4.70906i	0.173137	+	0.981907i	0.940273	+	0.340422i	$0.110570\pi$
$23$	0.830334	+	4.70906i	0.173137	+	0.981907i	−0.767136	+	0.641485i	$0.778319\pi$
$24$	−1.37931	−	1.04761i	−0.281551	−	0.213843i
$25$	8.38878	+	7.03902i	1.67776	+	1.40780i
$26$	4.66937			0.915739
$27$	−1.91721	+	4.82952i	−0.368968	+	0.929442i
$28$	−1.00000			−0.188982
$29$	−5.29898	−	4.44637i	−0.983995	−	0.825670i	0.000692110	−	1.00000i	$-0.499780\pi$
$29$	−5.29898	−	4.44637i	−0.983995	−	0.825670i	−0.984687	+	0.174330i	$0.944224\pi$
$30$	6.37783	−	2.67872i	1.16443	−	0.489066i
$31$	−1.09070	−	6.18569i	−0.195896	−	1.11098i	−0.911137	−	0.412105i	$-0.864794\pi$
$31$	−1.09070	−	6.18569i	−0.195896	−	1.11098i	0.715240	−	0.698879i	$-0.246317\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−1.36108	−	5.99920i	−0.236933	−	1.04433i
$34$	−0.203628	+	1.15483i	−0.0349219	+	0.198052i
$35$	1.99692	−	3.45877i	0.337541	−	0.584639i
$36$	0.231967	−	2.99102i	0.0386611	−	0.498503i
$37$	−2.00809	−	3.47812i	−0.330128	−	0.571799i	0.652409	−	0.757867i	$-0.273759\pi$
$37$	−2.00809	−	3.47812i	−0.330128	−	0.571799i	−0.982537	+	0.186069i	$0.940425\pi$
$38$	4.76354	−	1.73379i	0.772748	−	0.281257i
$39$	4.37906	+	6.79948i	0.701210	+	1.08879i
$40$	−3.05946	+	2.56719i	−0.483743	+	0.405909i
$41$	−4.16419	+	3.49417i	−0.650337	+	0.545697i	−0.907173	−	0.420758i	$-0.861764\pi$
$41$	−4.16419	+	3.49417i	−0.650337	+	0.545697i	0.256836	+	0.966455i	$0.417320\pi$
$42$	−0.937826	−	1.45619i	−0.144710	−	0.224695i
$43$	5.72547	−	2.08390i	0.873126	−	0.317792i	0.133694	−	0.991023i	$-0.457316\pi$
$43$	5.72547	−	2.08390i	0.873126	−	0.317792i	0.739433	+	0.673231i	$0.235094\pi$
$44$	1.77583	+	3.07583i	0.267717	+	0.463699i
$45$	9.88202	+	6.77515i	1.47312	+	1.00998i
$46$	2.39085	−	4.14108i	0.352512	−	0.610569i
$47$	−1.48940	+	8.44682i	−0.217252	+	1.23210i	0.659704	+	0.751525i	$0.270681\pi$
$47$	−1.48940	+	8.44682i	−0.217252	+	1.23210i	−0.876956	+	0.480570i	$0.840430\pi$
$48$	0.383222	+	1.68912i	0.0553134	+	0.243804i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	−1.90158	−	10.7844i	−0.268924	−	1.52515i
$51$	−1.87262	+	0.786511i	−0.262219	+	0.110134i
$52$	−3.57695	−	3.00141i	−0.496033	−	0.416221i
$53$	−8.45795			−1.16179			−0.580894	−	0.813979i	$-0.697297\pi$
$53$	−8.45795			−1.16179			−0.580894	+	0.813979i	$0.697297\pi$
$54$	4.57303	−	2.46727i	0.622310	−	0.335753i
$55$	−14.1848			−1.91267
$56$	0.766044	+	0.642788i	0.102367	+	0.0858961i
$57$	6.99208	+	5.31061i	0.926124	+	0.703408i
$58$	1.20118	+	6.81223i	0.157723	+	0.894490i
$59$	−13.4058	−	4.87933i	−1.74529	−	0.635235i	−0.745772	−	0.666201i	$-0.767919\pi$
$59$	−13.4058	−	4.87933i	−1.74529	−	0.635235i	−0.999520	+	0.0309667i	$0.990141\pi$
$60$	−6.60756	−	2.04757i	−0.853032	−	0.264340i
$61$	−0.108346	+	0.614463i	−0.0138723	+	0.0786739i	−0.990958	−	0.134173i	$-0.957162\pi$
$61$	−0.108346	+	0.614463i	−0.0138723	+	0.0786739i	0.977086	+	0.212847i	$0.0682734\pi$
$62$	−3.14056	+	5.43961i	−0.398851	+	0.690831i
$63$	1.24097	−	2.73130i	0.156347	−	0.344112i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	17.5241	−	6.37824i	2.17359	−	0.791124i
$66$	−2.81356	+	5.47053i	−0.346326	+	0.673376i
$67$	4.46842	−	3.74945i	0.545905	−	0.458069i	−0.327647	−	0.944800i	$-0.606256\pi$
$67$	4.46842	−	3.74945i	0.545905	−	0.458069i	0.873551	+	0.486732i	$0.161811\pi$
$68$	0.898300	−	0.753763i	0.108935	−	0.0914072i
$69$	8.27239	−	0.402079i	0.995879	−	0.0484046i
$70$	−3.75298	+	1.36597i	−0.448567	+	0.163265i
$71$	−5.05446	−	8.75458i	−0.599854	−	1.03898i	−0.992842	−	0.119434i	$-0.961892\pi$
$71$	−5.05446	−	8.75458i	−0.599854	−	1.03898i	0.392988	−	0.919544i	$-0.371441\pi$
$72$	−2.10029	+	2.14215i	−0.247521	+	0.252455i
$73$	−3.96326	+	6.86456i	−0.463864	+	0.803436i	−0.999149	−	0.0412352i	$-0.986871\pi$
$73$	−3.96326	+	6.86456i	−0.463864	+	0.803436i	0.535285	+	0.844671i	$0.320204\pi$
$74$	−0.697403	+	3.95517i	−0.0810714	+	0.459779i
$75$	13.9208	−	12.8830i	1.60743	−	1.48760i
$76$	−4.76354	−	1.73379i	−0.546415	−	0.198879i
$77$	0.616739	+	3.49770i	0.0702840	+	0.398600i
$78$	1.01607	−	8.02351i	0.115047	−	0.908483i
$79$	−11.3279	−	9.50527i	−1.27449	−	1.06943i	−0.993978	−	0.109577i	$-0.965051\pi$
$79$	−11.3279	−	9.50527i	−1.27449	−	1.06943i	−0.280514	−	0.959850i	$-0.590505\pi$
$80$	3.99384			0.446525
$81$	7.88151	+	4.34532i	0.875723	+	0.482814i
$82$	5.43596			0.600301
$83$	−5.26811	−	4.42047i	−0.578250	−	0.485209i	0.306122	−	0.951992i	$-0.400969\pi$
$83$	−5.26811	−	4.42047i	−0.578250	−	0.485209i	−0.884372	+	0.466783i	$0.845413\pi$
$84$	−0.217603	+	1.71833i	−0.0237425	+	0.187485i
$85$	0.813258	+	4.61222i	0.0882103	+	0.500265i
$86$	−5.72547	−	2.08390i	−0.617394	−	0.224713i
$87$	−8.79339	+	8.13783i	−0.942751	+	0.872467i
$88$	0.616739	−	3.49770i	0.0657446	−	0.372856i
$89$	2.62533	−	4.54721i	0.278285	−	0.482003i	−0.692674	−	0.721251i	$-0.743568\pi$
$89$	2.62533	−	4.54721i	0.278285	−	0.482003i	0.970959	+	0.239248i	$0.0769009\pi$
$90$	−3.21509	−	11.5421i	−0.338900	−	1.21664i
$91$	−2.33469	−	4.04379i	−0.244742	−	0.423905i
$92$	−4.49333	+	1.63544i	−0.468462	+	0.170506i
$93$	−10.8664	+	0.528160i	−1.12679	+	0.0547677i
$94$	6.57046	−	5.51327i	0.677691	−	0.568651i
$95$	15.5092	−	13.0137i	1.59121	−	1.33518i
$96$	0.792183	−	1.54027i	0.0808518	−	0.157204i
$97$	13.7402	−	5.00102i	1.39510	−	0.507777i	0.468383	−	0.883525i	$-0.344837\pi$
$97$	13.7402	−	5.00102i	1.39510	−	0.507777i	0.926721	+	0.375749i	$0.122615\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	−10.6048	+	1.03333i	−1.06582	+	0.103853i
$100$	−5.47539	+	9.48365i	−0.547539	+	0.948365i
$101$	1.07023	−	6.06957i	0.106492	−	0.603945i	−0.884122	−	0.467256i	$-0.845243\pi$
$101$	1.07023	−	6.06957i	0.106492	−	0.603945i	0.990614	−	0.136689i	$-0.0436461\pi$
$102$	1.94007	+	0.601195i	0.192096	+	0.0595272i
$103$	−0.624625	−	0.227345i	−0.0615462	−	0.0224010i	0.311064	−	0.950389i	$-0.399315\pi$
$103$	−0.624625	−	0.227345i	−0.0615462	−	0.0224010i	−0.372610	+	0.927988i	$0.621537\pi$
$104$	0.810828	+	4.59843i	0.0795082	+	0.450913i
$105$	−5.50876	−	4.18400i	−0.537600	−	0.408317i
$106$	6.47916	+	5.43666i	0.629312	+	0.528055i
$107$	4.25496			0.411343			0.205671	−	0.978621i	$-0.434062\pi$
$107$	4.25496			0.411343			0.205671	+	0.978621i	$0.434062\pi$
$108$	−5.08907	−	1.04945i	−0.489696	−	0.100983i
$109$	−4.93807			−0.472982			−0.236491	−	0.971634i	$-0.575997\pi$
$109$	−4.93807			−0.472982			−0.236491	+	0.971634i	$0.575997\pi$
$110$	10.8662	+	9.11780i	1.03605	+	0.869348i
$111$	−6.41351	+	2.69371i	−0.608743	+	0.255675i
$112$	−0.173648	−	0.984808i	−0.0164082	−	0.0930556i
$113$	2.73104	+	0.994017i	0.256914	+	0.0935092i	0.467267	−	0.884116i	$-0.345239\pi$
$113$	2.73104	+	0.994017i	0.256914	+	0.0935092i	−0.210352	+	0.977626i	$0.567461\pi$
$114$	−1.94265	−	8.56259i	−0.181946	−	0.801960i
$115$	3.31622	−	18.8072i	0.309240	−	1.75378i
$116$	3.45866	−	5.99058i	0.321129	−	0.556211i
$117$	12.6366	−	6.04506i	1.16826	−	0.558866i
$118$	7.13310	+	12.3549i	0.656655	+	1.13736i
$119$	1.10193	−	0.401069i	0.101014	−	0.0367659i
$120$	3.74553	+	5.81578i	0.341918	+	0.530906i
$121$	1.23662	−	1.03765i	0.112420	−	0.0943318i
$122$	0.477967	−	0.401062i	0.0432731	−	0.0363105i
$123$	5.09798	+	7.91578i	0.459670	+	0.713742i
$124$	5.90232	−	2.14827i	0.530044	−	0.192920i
$125$	−11.8832	−	20.5824i	−1.06287	−	1.84094i
$126$	−2.70628	+	1.29462i	−0.241095	+	0.115334i
$127$	−7.08804	+	12.2768i	−0.628962	+	1.08939i	0.358798	+	0.933415i	$0.383187\pi$
$127$	−7.08804	+	12.2768i	−0.628962	+	1.08939i	−0.987760	+	0.155979i	$0.950147\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−2.33494	−	10.2917i	−0.205580	−	0.906134i
$130$	−17.5241	−	6.37824i	−1.53696	−	0.559409i
$131$	0.0855526	+	0.485193i	0.00747477	+	0.0423915i	0.988317	−	0.152412i	$-0.0487041\pi$
$131$	0.0855526	+	0.485193i	0.00747477	+	0.0423915i	−0.980842	+	0.194804i	$0.937593\pi$
$132$	5.67171	−	2.38215i	0.493659	−	0.207339i
$133$	−3.88327	−	3.25845i	−0.336722	−	0.282544i
$134$	−5.83311			−0.503904
$135$	13.7923	−	15.5063i	1.18705	−	1.33457i
$136$	−1.17265			−0.100554
$137$	7.78246	+	6.53026i	0.664900	+	0.557918i	0.911551	−	0.411187i	$-0.134886\pi$
$137$	7.78246	+	6.53026i	0.664900	+	0.557918i	−0.246651	+	0.969104i	$0.579330\pi$
$138$	−6.59547	−	5.00938i	−0.561444	−	0.426427i
$139$	−2.23593	−	12.6806i	−0.189649	−	1.07555i	−0.919835	−	0.392306i	$-0.871678\pi$
$139$	−2.23593	−	12.6806i	−0.189649	−	1.07555i	0.730186	−	0.683249i	$-0.239434\pi$
$140$	3.75298	+	1.36597i	0.317185	+	0.115446i
$141$	14.1903	+	4.39734i	1.19504	+	0.370323i
$142$	−1.75540	+	9.95534i	−0.147310	+	0.835434i
$143$	−8.29201	+	14.3622i	−0.693413	+	1.20103i
$144$	2.98586	−	0.290942i	0.248822	−	0.0242452i
$145$	13.8133	+	23.9254i	1.14714	+	1.98690i
$146$	7.44848	−	2.71103i	0.616441	−	0.224366i
$147$	−0.792183	+	1.54027i	−0.0653381	+	0.127040i
$148$	3.07657	−	2.58155i	0.252893	−	0.212202i
$149$	−17.3442	+	14.5535i	−1.42089	+	1.19227i	−0.470033	+	0.882649i	$0.655758\pi$
$149$	−17.3442	+	14.5535i	−1.42089	+	1.19227i	−0.950860	+	0.309622i	$0.899797\pi$
$150$	−18.9449	+	0.920818i	−1.54685	+	0.0751845i
$151$	3.52349	−	1.28244i	0.286737	−	0.104364i	−0.194647	−	0.980873i	$-0.562356\pi$
$151$	3.52349	−	1.28244i	0.286737	−	0.104364i	0.481385	+	0.876509i	$0.340134\pi$
$152$	2.53462	+	4.39010i	0.205585	+	0.356084i
$153$	0.943994	+	3.38892i	0.0763174	+	0.273978i
$154$	1.77583	−	3.07583i	0.143101	−	0.247857i
$155$	−4.35610	+	24.7047i	−0.349891	+	1.98433i
$156$	−5.93577	+	5.49325i	−0.475242	+	0.439812i
$157$	19.4526	+	7.08017i	1.55249	+	0.565059i	0.968999	−	0.247063i	$-0.0794654\pi$
$157$	19.4526	+	7.08017i	1.55249	+	0.565059i	0.583488	+	0.812122i	$0.301688\pi$
$158$	2.56784	+	14.5629i	0.204286	+	1.15856i
$159$	−1.84048	+	14.5335i	−0.145959	+	1.15258i
$160$	−3.05946	−	2.56719i	−0.241872	−	0.202954i
$161$	−4.78171			−0.376851
$162$	−3.24447	−	8.39485i	−0.254909	−	0.659561i
$163$	−11.4754			−0.898826			−0.449413	−	0.893324i	$-0.648367\pi$
$163$	−11.4754			−0.898826			−0.449413	+	0.893324i	$0.648367\pi$
$164$	−4.16419	−	3.49417i	−0.325168	−	0.272849i
$165$	−3.08665	+	24.3741i	−0.240296	+	1.89752i
$166$	1.19418	+	6.77255i	0.0926866	+	0.525652i
$167$	−4.33607	−	1.57820i	−0.335535	−	0.122125i	0.168758	−	0.985658i	$-0.446024\pi$
$167$	−4.33607	−	1.57820i	−0.335535	−	0.122125i	−0.504293	+	0.863533i	$0.668247\pi$
$168$	1.27121	−	1.17644i	0.0980762	−	0.0907645i
$169$	1.52863	−	8.66929i	0.117587	−	0.666869i
$170$	2.34168	−	4.05592i	0.179599	−	0.311075i
$171$	10.6469	−	10.8591i	0.814187	−	0.830415i
$172$	3.04646	+	5.27662i	0.232290	+	0.402339i
$173$	1.46132	−	0.531877i	0.111102	−	0.0404378i	−0.285871	−	0.958268i	$-0.592283\pi$
$173$	1.46132	−	0.531877i	0.111102	−	0.0404378i	0.396973	+	0.917830i	$0.370061\pi$
$174$	11.9670	−	0.581657i	0.907218	−	0.0440953i
$175$	−8.38878	+	7.03902i	−0.634132	+	0.532100i
$176$	−2.72073	+	2.28296i	−0.205083	+	0.172085i
$177$	−11.3014	+	21.9739i	−0.849468	+	1.65166i
$178$	−4.93401	+	1.79583i	−0.369820	+	0.134603i
$179$	−0.708120	−	1.22650i	−0.0529274	−	0.0916730i	0.838348	−	0.545136i	$-0.183522\pi$
$179$	−0.708120	−	1.22650i	−0.0529274	−	0.0916730i	−0.891275	+	0.453463i	$0.850189\pi$
$180$	−4.95622	+	10.9084i	−0.369415	+	0.813063i
$181$	9.81532	−	17.0006i	0.729567	−	1.26365i	−0.227500	−	0.973778i	$-0.573055\pi$
$181$	9.81532	−	17.0006i	0.729567	−	1.26365i	0.957066	−	0.289869i	$-0.0936116\pi$
$182$	−0.810828	+	4.59843i	−0.0601026	+	0.340859i
$183$	1.03227	+	0.319884i	0.0763077	+	0.0236465i
$184$	4.49333	+	1.63544i	0.331253	+	0.120566i
$185$	2.78532	+	15.7963i	0.204781	+	1.16137i
$186$	8.66363	+	6.58018i	0.635248	+	0.482483i
$187$	−3.19046	−	2.67711i	−0.233309	−	0.195770i
$188$	−8.57713			−0.625551
$189$	−4.42323	−	2.72673i	−0.321743	−	0.198340i
$190$	−20.2458			−1.46878
$191$	12.9012	+	10.8254i	0.933496	+	0.783296i	0.976442	−	0.215781i	$-0.0692297\pi$
$191$	12.9012	+	10.8254i	0.933496	+	0.783296i	−0.0429454	+	0.999077i	$0.513674\pi$
$192$	−1.59692	+	0.670714i	−0.115248	+	0.0484046i
$193$	0.263200	+	1.49268i	0.0189455	+	0.107445i	0.992814	−	0.119667i	$-0.0381827\pi$
$193$	0.263200	+	1.49268i	0.0189455	+	0.107445i	−0.973869	+	0.227112i	$0.927072\pi$
$194$	−13.7402	−	5.00102i	−0.986488	−	0.359052i
$195$	−7.14661	−	31.5000i	−0.511779	−	2.25576i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	4.56571	−	7.90803i	0.325293	−	0.563424i	−0.656279	−	0.754519i	$-0.727870\pi$
$197$	4.56571	−	7.90803i	0.325293	−	0.563424i	0.981572	+	0.191095i	$0.0612037\pi$
$198$	8.78793	+	6.02503i	0.624531	+	0.428180i
$199$	7.82174	+	13.5477i	0.554469	+	0.960368i	0.997945	+	0.0640815i	$0.0204118\pi$
$199$	7.82174	+	13.5477i	0.554469	+	0.960368i	−0.443476	+	0.896286i	$0.646255\pi$
$200$	10.2904	−	3.74539i	0.727639	−	0.264839i
$201$	−5.47044	−	8.49411i	−0.385855	−	0.599128i
$202$	−4.72129	+	3.96163i	−0.332189	+	0.278739i
$203$	5.29898	−	4.44637i	0.371915	−	0.312074i
$204$	−1.09974	−	1.70759i	−0.0769971	−	0.119556i
$205$	20.4011	−	7.42538i	1.42487	−	0.518611i
$206$	0.332356	+	0.575658i	0.0231564	+	0.0401080i
$207$	1.10920	−	14.3022i	0.0770945	−	0.994069i
$208$	2.33469	−	4.04379i	0.161881	−	0.280387i
$209$	−3.12641	+	17.7307i	−0.216258	+	1.22646i
$210$	1.53053	+	6.74610i	0.105617	+	0.465525i
$211$	−9.87338	−	3.59362i	−0.679712	−	0.247395i	−0.0209879	−	0.999780i	$-0.506681\pi$
$211$	−9.87338	−	3.59362i	−0.679712	−	0.247395i	−0.658724	+	0.752385i	$0.728903\pi$
$212$	−1.46871	−	8.32945i	−0.100871	−	0.572069i
$213$	−16.1431	+	6.78019i	−1.10611	+	0.464571i
$214$	−3.25949	−	2.73504i	−0.222814	−	0.186963i
$215$	−24.3342			−1.65958
$216$	3.22388	+	4.07512i	0.219357	+	0.277277i
$217$	6.28112			0.426390
$218$	3.78278	+	3.17413i	0.256203	+	0.214979i
$219$	10.9331	+	8.30392i	0.738793	+	0.561127i
$220$	−2.46316	−	13.9693i	−0.166066	−	0.941808i
$221$	5.14531	+	1.87274i	0.346111	+	0.125974i
$222$	6.64452	+	2.05902i	0.445951	+	0.138193i
$223$	0.353333	−	2.00385i	0.0236609	−	0.134188i	−0.970689	−	0.240339i	$-0.922742\pi$
$223$	0.353333	−	2.00385i	0.0236609	−	0.134188i	0.994350	+	0.106151i	$0.0338526\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−19.1079	−	26.7238i	−1.27386	−	1.78159i
$226$	−1.45316	−	2.51694i	−0.0966625	−	0.167424i
$227$	−5.35921	+	1.95059i	−0.355703	+	0.129465i	−0.513690	−	0.857976i	$-0.671722\pi$
$227$	−5.35921	+	1.95059i	−0.355703	+	0.129465i	0.157987	+	0.987441i	$0.449500\pi$
$228$	−4.01577	+	7.80804i	−0.265951	+	0.517100i
$229$	−3.35181	+	2.81250i	−0.221494	+	0.185855i	−0.746782	−	0.665069i	$-0.768402\pi$
$229$	−3.35181	+	2.81250i	−0.221494	+	0.185855i	0.525288	+	0.850924i	$0.323958\pi$
$230$	−14.6294	+	12.2756i	−0.964637	+	0.809426i
$231$	6.14440	−	0.298648i	0.404272	−	0.0196496i
$232$	−6.50016	+	2.36586i	−0.426756	+	0.155327i
$233$	4.87709	+	8.44737i	0.319509	+	0.553406i	0.980386	−	0.197089i	$-0.0631487\pi$
$233$	4.87709	+	8.44737i	0.319509	+	0.553406i	−0.660877	+	0.750495i	$0.729815\pi$
$234$	−13.5659	−	3.49188i	−0.886832	−	0.228272i
$235$	17.1278	−	29.6663i	1.11730	−	1.93522i
$236$	2.47730	−	14.0495i	0.161259	−	0.914542i
$237$	−18.7982	+	17.3967i	−1.22107	+	1.13004i
$238$	−1.10193	−	0.401069i	−0.0714274	−	0.0259974i
$239$	3.01319	+	17.0887i	0.194907	+	1.10537i	0.912551	+	0.408963i	$0.134110\pi$
$239$	3.01319	+	17.0887i	0.194907	+	1.10537i	−0.717643	+	0.696411i	$0.754779\pi$
$240$	0.869073	−	6.86273i	0.0560984	−	0.442987i
$241$	−18.5630	−	15.5762i	−1.19575	−	1.00335i	−0.999741	−	0.0227518i	$-0.992757\pi$
$241$	−18.5630	−	15.5762i	−1.19575	−	1.00335i	−0.196009	−	0.980602i	$-0.562798\pi$
$242$	−1.61430			−0.103771
$243$	9.18173	−	12.5975i	0.589008	−	0.808127i
$244$	−0.623942			−0.0399438
$245$	3.05946	+	2.56719i	0.195462	+	0.164012i
$246$	1.18288	−	9.34076i	0.0754178	−	0.595545i
$247$	−4.11029	−	23.3106i	−0.261531	−	1.48322i
$248$	−5.90232	−	2.14827i	−0.374798	−	0.136415i
$249$	−8.74217	+	8.09043i	−0.554013	+	0.512710i
$250$	−4.12700	+	23.4054i	−0.261015	+	1.48029i
$251$	8.51239	−	14.7439i	0.537298	−	0.930627i	−0.461751	−	0.887010i	$-0.652779\pi$
$251$	8.51239	−	14.7439i	0.537298	−	0.930627i	0.999048	−	0.0436170i	$-0.0138881\pi$
$252$	2.90530	+	0.747827i	0.183017	+	0.0471087i
$253$	8.49150	+	14.7077i	0.533856	+	0.924666i
$254$	13.3212	−	4.84851i	0.835844	−	0.304222i
$255$	8.10227	−	0.393810i	0.507384	−	0.0246614i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−12.5982	+	10.5711i	−0.785851	+	0.659408i	−0.944715	−	0.327893i	$-0.893661\pi$
$257$	−12.5982	+	10.5711i	−0.785851	+	0.659408i	0.158864	+	0.987301i	$0.449217\pi$
$258$	−4.82671	+	9.38477i	−0.300498	+	0.584270i
$259$	3.77398	−	1.37362i	0.234504	−	0.0853523i
$260$	9.32437	+	16.1503i	0.578273	+	1.00160i
$261$	12.0700	+	16.8807i	0.747113	+	1.04489i
$262$	0.246339	−	0.426672i	0.0152189	−	0.0263599i
$263$	−2.98233	+	16.9136i	−0.183898	+	1.04294i	0.743464	+	0.668776i	$0.233181\pi$
$263$	−2.98233	+	16.9136i	−0.183898	+	1.04294i	−0.927363	+	0.374164i	$0.877930\pi$
$264$	−5.87599	−	1.82087i	−0.361642	−	0.112067i
$265$	31.7425	+	11.5533i	1.94993	+	0.709716i
$266$	0.880266	+	4.99224i	0.0539726	+	0.306094i
$267$	−7.24231	−	5.50066i	−0.443222	−	0.336635i
$268$	4.46842	+	3.74945i	0.272952	+	0.229034i
$269$	28.9555			1.76545			0.882723	−	0.469893i	$-0.155708\pi$
$269$	28.9555			1.76545			0.882723	+	0.469893i	$0.155708\pi$
$270$	−20.5327	+	3.01297i	−1.24958	+	0.183364i
$271$	5.22070			0.317135			0.158568	−	0.987348i	$-0.449312\pi$
$271$	5.22070			0.317135			0.158568	+	0.987348i	$0.449312\pi$
$272$	0.898300	+	0.753763i	0.0544674	+	0.0457036i
$273$	−7.45660	+	3.13181i	−0.451294	+	0.189546i
$274$	−1.76414	−	10.0049i	−0.106576	−	0.604420i
$275$	36.5479	+	13.3023i	2.20392	+	0.802161i
$276$	1.83246	+	8.07689i	0.110301	+	0.486172i
$277$	−0.778323	+	4.41409i	−0.0467649	+	0.265217i	−0.999221	−	0.0394583i	$-0.987437\pi$
$277$	−0.778323	+	4.41409i	−0.0467649	+	0.265217i	0.952456	+	0.304675i	$0.0985479\pi$
$278$	−6.43811	+	11.1511i	−0.386132	+	0.668800i
$279$	−1.45701	+	18.7869i	−0.0872289	+	1.12474i
$280$	−1.99692	−	3.45877i	−0.119339	−	0.206701i
$281$	−3.51400	+	1.27899i	−0.209628	+	0.0762983i	−0.444700	−	0.895680i	$-0.646690\pi$
$281$	−3.51400	+	1.27899i	−0.209628	+	0.0762983i	0.235072	+	0.971978i	$0.424467\pi$
$282$	−8.04385	−	12.4899i	−0.479004	−	0.743763i
$283$	1.34676	−	1.13007i	0.0800568	−	0.0671757i	−0.601881	−	0.798586i	$-0.705582\pi$
$283$	1.34676	−	1.13007i	0.0800568	−	0.0671757i	0.681938	+	0.731410i	$0.261137\pi$
$284$	7.74388	−	6.49789i	0.459515	−	0.385579i
$285$	−18.9870	−	29.4817i	−1.12469	−	1.74634i
$286$	15.5839	−	5.67207i	0.921494	−	0.335397i
$287$	−2.71798	−	4.70768i	−0.160437	−	0.277885i
$288$	−2.47431	−	1.69640i	−0.145800	−	0.0999612i
$289$	7.81245	−	13.5316i	0.459556	−	0.795974i
$290$	4.79733	−	27.2070i	0.281709	−	1.59765i
$291$	−5.60348	−	24.6984i	−0.328482	−	1.44784i
$292$	−7.44848	−	2.71103i	−0.435890	−	0.158651i
$293$	−1.63879	−	9.29402i	−0.0957389	−	0.542962i	−0.994518	−	0.104561i	$-0.966656\pi$
$293$	−1.63879	−	9.29402i	−0.0957389	−	0.542962i	0.898780	−	0.438401i	$-0.144455\pi$
$294$	1.59692	−	0.670714i	0.0931341	−	0.0391168i
$295$	43.6469	+	36.6241i	2.54122	+	2.13234i
$296$	−4.01618			−0.233436
$297$	−0.532033	+	18.4473i	−0.0308717	+	1.07042i
$298$	22.6413			1.31157
$299$	−17.1039	−	14.3519i	−0.989144	−	0.829991i
$300$	15.1046	+	11.4722i	0.872062	+	0.662347i
$301$	1.05802	+	6.00036i	0.0609835	+	0.345855i
$302$	−3.52349	−	1.28244i	−0.202754	−	0.0737964i
$303$	−10.1966	−	3.15976i	−0.585781	−	0.181524i
$304$	0.880266	−	4.99224i	0.0504867	−	0.286324i
$305$	1.24596	−	2.15807i	0.0713436	−	0.123571i
$306$	1.45522	−	3.20285i	0.0831891	−	0.183095i
$307$	−2.28879	−	3.96431i	−0.130628	−	0.226255i	0.793291	−	0.608843i	$-0.208366\pi$
$307$	−2.28879	−	3.96431i	−0.130628	−	0.226255i	−0.923919	+	0.382588i	$0.875033\pi$
$308$	−3.33747	+	1.21474i	−0.190170	+	0.0692162i
$309$	−0.526574	+	1.02384i	−0.0299557	+	0.0582442i
$310$	19.2168	−	16.1248i	1.09144	−	0.915829i
$311$	6.07768	−	5.09978i	0.344634	−	0.289182i	−0.453997	−	0.891003i	$-0.650002\pi$
$311$	6.07768	−	5.09978i	0.344634	−	0.289182i	0.798631	+	0.601821i	$0.205558\pi$
$312$	8.07805	−	0.392633i	0.457330	−	0.0222285i
$313$	3.14581	−	1.14498i	0.177812	−	0.0647181i	−0.251580	−	0.967836i	$-0.580950\pi$
$313$	3.14581	−	1.14498i	0.177812	−	0.0647181i	0.429392	+	0.903118i	$0.358728\pi$
$314$	−10.3505	−	17.9276i	−0.584113	−	1.01171i
$315$	−8.38821	+	8.55540i	−0.472622	+	0.482042i
$316$	7.39379	−	12.8064i	0.415933	−	0.720417i
$317$	4.40054	−	24.9567i	0.247159	−	1.40171i	−0.568266	−	0.822845i	$-0.692386\pi$
$317$	4.40054	−	24.9567i	0.247159	−	1.40171i	0.815425	−	0.578863i	$-0.196503\pi$
$318$	10.7519	−	9.95029i	0.602934	−	0.557984i
$319$	−23.0864	−	8.40275i	−1.29259	−	0.470463i
$320$	0.693523	+	3.93317i	0.0387691	+	0.219871i
$321$	0.925894	−	7.31142i	0.0516784	−	0.408084i
$322$	3.66300	+	3.07362i	0.204131	+	0.171286i
$323$	5.94444			0.330758
$324$	−2.91070	+	8.51633i	−0.161705	+	0.473129i
$325$	−51.1332			−2.83636
$326$	8.79070	+	7.37627i	0.486872	+	0.408534i
$327$	−1.07454	+	8.48523i	−0.0594223	+	0.469234i
$328$	0.943944	+	5.35337i	0.0521206	+	0.295591i
$329$	−8.05986	−	2.93355i	−0.444355	−	0.161732i
$330$	18.0319	−	16.6876i	0.992622	−	0.918620i
$331$	−1.97996	+	11.2289i	−0.108828	+	0.617196i	0.880794	+	0.473500i	$0.157010\pi$
$331$	−1.97996	+	11.2289i	−0.108828	+	0.617196i	−0.989622	+	0.143696i	$0.954101\pi$
$332$	3.43851	−	5.95568i	0.188713	−	0.326860i
$333$	3.23307	+	11.6067i	0.177171	+	0.636041i
$334$	2.30717	+	3.99614i	0.126243	+	0.218659i
$335$	−21.8916	+	7.96788i	−1.19606	+	0.435332i
$336$	−1.73001	+	0.0840870i	−0.0943797	+	0.00458732i
$337$	−19.8213	+	16.6320i	−1.07974	+	0.906005i	−0.995899	−	0.0904742i	$-0.971162\pi$
$337$	−19.8213	+	16.6320i	−1.07974	+	0.906005i	−0.0838364	+	0.996480i	$0.526717\pi$
$338$	−6.74351	+	5.65848i	−0.366799	+	0.307781i
$339$	2.30233	−	4.47652i	0.125045	−	0.243131i
$340$	−4.40093	+	1.60181i	−0.238674	+	0.0868702i
$341$	−11.1542	−	19.3196i	−0.604034	−	1.04622i
$342$	−15.1361	+	1.47486i	−0.818465	+	0.0797513i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	1.05802	−	6.00036i	0.0570449	−	0.323518i
$345$	−31.5954	−	9.79088i	−1.70104	−	0.527123i
$346$	−1.46132	−	0.531877i	−0.0785610	−	0.0285939i
$347$	−1.79576	−	10.1843i	−0.0964014	−	0.546720i	−0.994309	−	0.106535i	$-0.966024\pi$
$347$	−1.79576	−	10.1843i	−0.0964014	−	0.546720i	0.897907	−	0.440184i	$-0.145087\pi$
$348$	−9.54116	−	7.24668i	−0.511460	−	0.388463i
$349$	2.99837	+	2.51593i	0.160499	+	0.134675i	0.719500	−	0.694492i	$-0.244371\pi$
$349$	2.99837	+	2.51593i	0.160499	+	0.134675i	−0.559001	+	0.829167i	$0.688815\pi$
$350$	10.9508			0.585344
$351$	−7.63762	−	23.0293i	−0.407666	−	1.22921i
$352$	3.55166			0.189304
$353$	1.33925	+	1.12376i	0.0712809	+	0.0598118i	0.677732	−	0.735309i	$-0.262963\pi$
$353$	1.33925	+	1.12376i	0.0712809	+	0.0598118i	−0.606451	+	0.795121i	$0.707407\pi$
$354$	22.7819	−	9.56854i	1.21085	−	0.508562i
$355$	7.01077	+	39.7601i	0.372093	+	2.11025i
$356$	4.93401	+	1.79583i	0.261502	+	0.0951789i
$357$	−0.449385	−	1.98075i	−0.0237840	−	0.104832i
$358$	−0.245928	+	1.39472i	−0.0129977	+	0.0737135i
$359$	14.0534	−	24.3412i	0.741711	−	1.28468i	−0.210005	−	0.977700i	$-0.567348\pi$
$359$	14.0534	−	24.3412i	0.741711	−	1.28468i	0.951716	−	0.306980i	$-0.0993185\pi$
$360$	10.8085	−	5.17051i	0.569656	−	0.272510i
$361$	−3.34865	−	5.80002i	−0.176244	−	0.305264i
$362$	−18.4468	+	6.71407i	−0.969540	+	0.352884i
$363$	−1.51393	−	2.35072i	−0.0794606	−	0.123381i
$364$	3.57695	−	3.00141i	0.187483	−	0.157317i
$365$	24.2509	−	20.3489i	1.26935	−	1.06511i
$366$	−0.585149	−	0.908577i	−0.0305862	−	0.0474921i
$367$	−6.64545	+	2.41875i	−0.346890	+	0.126258i	−0.509589	−	0.860418i	$-0.670202\pi$
$367$	−6.64545	+	2.41875i	−0.346890	+	0.126258i	0.162699	+	0.986676i	$0.447980\pi$
$368$	−2.39085	−	4.14108i	−0.124632	−	0.215869i
$369$	14.7112	−	7.03750i	0.765836	−	0.366358i
$370$	8.02000	−	13.8910i	0.416940	−	0.722161i
$371$	1.46871	−	8.32945i	0.0762515	−	0.432444i
$372$	−2.40706	−	10.6096i	−0.124800	−	0.550081i
$373$	−25.6874	−	9.34944i	−1.33004	−	0.484096i	−0.423379	−	0.905952i	$-0.639156\pi$
$373$	−25.6874	−	9.34944i	−1.33004	−	0.484096i	−0.906662	+	0.421857i	$0.861379\pi$
$374$	0.723218	+	4.10157i	0.0373967	+	0.212087i
$375$	−37.9531	+	15.9405i	−1.95989	+	0.823163i
$376$	6.57046	+	5.51327i	0.338846	+	0.284325i
$377$	32.2995			1.66351
$378$	1.63569	+	4.93199i	0.0841306	+	0.253674i
$379$	−9.05781			−0.465268			−0.232634	−	0.972564i	$-0.574734\pi$
$379$	−9.05781			−0.465268			−0.232634	+	0.972564i	$0.574734\pi$
$380$	15.5092	+	13.0137i	0.795604	+	0.667591i
$381$	19.5533	+	14.8511i	1.00174	+	0.760843i
$382$	−2.92446	−	16.5854i	−0.149628	−	0.848585i
$383$	−27.7608	−	10.1041i	−1.41851	−	0.516296i	−0.484895	−	0.874572i	$-0.661142\pi$
$383$	−27.7608	−	10.1041i	−1.41851	−	0.516296i	−0.933615	+	0.358277i	$0.883364\pi$
$384$	1.65444	+	0.512682i	0.0844276	+	0.0261627i
$385$	2.46316	−	13.9693i	0.125534	−	0.711940i
$386$	0.757853	−	1.31264i	0.0385737	−	0.0668116i
$387$	−18.1926	+	1.77269i	−0.924782	+	0.0901108i
$388$	7.31100	+	12.6630i	0.371160	+	0.642868i
$389$	−22.8749	+	8.32578i	−1.15980	+	0.422134i	−0.849027	−	0.528349i	$-0.822811\pi$
$389$	−22.8749	+	8.32578i	−1.15980	+	0.422134i	−0.310776	+	0.950483i	$0.600589\pi$
$390$	−14.7732	+	28.7242i	−0.748070	+	1.45451i
$391$	4.29541	−	3.60427i	0.217228	−	0.182276i
$392$	−0.766044	+	0.642788i	−0.0386911	+	0.0324657i
$393$	0.852337	−	0.0414278i	0.0429947	−	0.00208976i
$394$	−8.58072	+	3.12313i	−0.432290	+	0.157341i
$395$	29.5296	+	51.1468i	1.48580	+	2.57347i
$396$	−2.85913	−	10.2642i	−0.143677	−	0.515796i
$397$	15.4397	−	26.7424i	0.774897	−	1.34216i	−0.159955	−	0.987124i	$-0.551135\pi$
$397$	15.4397	−	26.7424i	0.774897	−	1.34216i	0.934852	−	0.355037i	$-0.115532\pi$
$398$	2.71646	−	15.4058i	0.136164	−	0.772224i
$399$	−6.44410	+	5.96368i	−0.322608	+	0.298557i
$400$	−10.2904	−	3.74539i	−0.514518	−	0.187269i
$401$	−0.106156	−	0.602040i	−0.00530117	−	0.0300644i	0.982042	−	0.188660i	$-0.0604145\pi$
$401$	−0.106156	−	0.602040i	−0.00530117	−	0.0300644i	−0.987344	+	0.158596i	$0.949303\pi$
$402$	−1.26930	+	10.0232i	−0.0633072	+	0.499912i
$403$	22.4672	+	18.8522i	1.11917	+	0.939097i
$404$	6.16320			0.306631
$405$	−23.6436	−	27.0739i	−1.17486	−	1.34531i
$406$	−6.91732			−0.343301
$407$	−10.9269	−	9.16880i	−0.541629	−	0.454480i
$408$	−0.255172	+	2.01499i	−0.0126329	+	0.0997570i
$409$	−3.06906	−	17.4055i	−0.151755	−	0.860647i	−0.961693	−	0.274130i	$-0.911610\pi$
$409$	−3.06906	−	17.4055i	−0.151755	−	0.860647i	0.809937	−	0.586516i	$-0.199501\pi$
$410$	−20.4011	−	7.42538i	−1.00754	−	0.366713i
$411$	12.9146	−	11.9518i	0.637031	−	0.589539i
$412$	0.115426	−	0.654614i	0.00568663	−	0.0322505i
$413$	7.13310	−	12.3549i	0.350997	−	0.607945i
$414$	−10.0430	+	10.2431i	−0.493584	+	0.503422i
$415$	13.7329	+	23.7861i	0.674121	+	1.16761i
$416$	−4.38777	+	1.59702i	−0.215128	+	0.0783003i
$417$	−22.2760	+	1.08272i	−1.09086	+	0.0530211i
$418$	13.7921	−	11.5729i	0.674592	−	0.566050i
$419$	−8.66454	+	7.27041i	−0.423290	+	0.355183i	−0.829413	−	0.558636i	$-0.811325\pi$
$419$	−8.66454	+	7.27041i	−0.423290	+	0.355183i	0.406123	+	0.913819i	$0.366881\pi$
$420$	3.16385	−	6.15161i	0.154380	−	0.300168i
$421$	−10.4725	+	3.81169i	−0.510399	+	0.185770i	−0.584366	−	0.811491i	$-0.698657\pi$
$421$	−10.4725	+	3.81169i	−0.510399	+	0.185770i	0.0739661	+	0.997261i	$0.476434\pi$
$422$	5.25352	+	9.09936i	0.255737	+	0.442950i
$423$	10.6439	−	23.4267i	0.517525	−	1.13905i
$424$	−4.22897	+	7.32480i	−0.205377	+	0.355724i
$425$	2.22989	−	12.6463i	0.108165	−	0.613436i
$426$	16.7246	+	5.18266i	0.810307	+	0.251101i
$427$	−0.586314	−	0.213401i	−0.0283737	−	0.0103272i
$428$	0.738867	+	4.19032i	0.0357145	+	0.202547i
$429$	22.8746	+	17.3737i	1.10439	+	0.838808i
$430$	18.6411	+	15.6417i	0.898951	+	0.754310i
$431$	21.7186			1.04615			0.523074	−	0.852287i	$-0.324785\pi$
$431$	21.7186			1.04615			0.523074	+	0.852287i	$0.324785\pi$
$432$	0.149798	−	5.19399i	0.00720718	−	0.249896i
$433$	39.2759			1.88748			0.943739	−	0.330692i	$-0.107282\pi$
$433$	39.2759			1.88748			0.943739	+	0.330692i	$0.107282\pi$
$434$	−4.81161	−	4.03742i	−0.230965	−	0.193803i
$435$	44.1175	−	18.5296i	2.11527	−	0.888426i
$436$	−0.857488	−	4.86305i	−0.0410662	−	0.232898i
$437$	−22.7778	−	8.29045i	−1.08961	−	0.396586i
$438$	−3.03762	−	13.3889i	−0.145143	−	0.639745i
$439$	1.36260	−	7.72768i	0.0650333	−	0.368822i	−0.934871	−	0.354988i	$-0.884485\pi$
$439$	1.36260	−	7.72768i	0.0650333	−	0.368822i	0.999904	−	0.0138345i	$-0.00440381\pi$
$440$	−7.09239	+	12.2844i	−0.338116	+	0.585635i
$441$	2.47431	+	1.69640i	0.117825	+	0.0807809i
$442$	−2.73776	−	4.74194i	−0.130222	−	0.225551i
$443$	−15.1343	+	5.50845i	−0.719054	+	0.261714i	−0.675524	−	0.737338i	$-0.736083\pi$
$443$	−15.1343	+	5.50845i	−0.719054	+	0.261714i	−0.0435299	+	0.999052i	$0.513860\pi$
$444$	−3.76648	−	5.84832i	−0.178749	−	0.277549i
$445$	−16.0642	+	13.4795i	−0.761516	+	0.638988i
$446$	−1.55872	+	1.30792i	−0.0738075	+	0.0619319i
$447$	21.2336	+	32.9699i	1.00431	+	1.55942i
$448$	0.939693	−	0.342020i	0.0443963	−	0.0161589i
$449$	2.42397	+	4.19843i	0.114394	+	0.198136i	0.917537	−	0.397650i	$-0.130174\pi$
$449$	2.42397	+	4.19843i	0.114394	+	0.198136i	−0.803143	+	0.595786i	$0.796841\pi$
$450$	−2.54021	+	32.7540i	−0.119747	+	1.54404i
$451$	−9.65334	+	16.7201i	−0.454558	+	0.787318i
$452$	−0.504676	+	2.86216i	−0.0237379	+	0.134625i
$453$	−1.43694	−	6.33357i	−0.0675132	−	0.297577i
$454$	5.35921	+	1.95059i	0.251520	+	0.0915458i
$455$	3.23832	+	18.3654i	0.151815	+	0.860984i
$456$	8.09517	−	3.40001i	0.379091	−	0.159220i
$457$	−26.6700	−	22.3788i	−1.24757	−	1.04684i	−0.996893	−	0.0787667i	$-0.974902\pi$
$457$	−26.6700	−	22.3788i	−1.24757	−	1.04684i	−0.250679	−	0.968070i	$-0.580654\pi$
$458$	4.37547			0.204452
$459$	6.02869	−	0.884651i	0.281395	−	0.0412920i
$460$	19.0974			0.890420
$461$	−7.99151	−	6.70567i	−0.372202	−	0.312314i	0.437430	−	0.899252i	$-0.355889\pi$
$461$	−7.99151	−	6.70567i	−0.372202	−	0.312314i	−0.809632	+	0.586938i	$0.800333\pi$
$462$	−4.89885	−	3.72077i	−0.227915	−	0.173106i
$463$	−3.81267	−	21.6227i	−0.177190	−	1.00489i	−0.935586	−	0.353099i	$-0.885128\pi$
$463$	−3.81267	−	21.6227i	−0.177190	−	1.00489i	0.758396	−	0.651794i	$-0.225983\pi$
$464$	6.50016	+	2.36586i	0.301762	+	0.109832i
$465$	41.5028	+	12.8610i	1.92465	+	0.596416i
$466$	1.69380	−	9.60600i	0.0784636	−	0.444989i
$467$	−12.8412	+	22.2416i	−0.594219	+	1.02922i	0.399438	+	0.916760i	$0.369205\pi$
$467$	−12.8412	+	22.2416i	−0.594219	+	1.02922i	−0.993657	+	0.112457i	$0.964128\pi$
$468$	8.14755	+	11.3949i	0.376621	+	0.526731i
$469$	2.91656	+	5.05162i	0.134674	+	0.233262i
$470$	−32.1898	+	11.7161i	−1.48481	+	0.540425i
$471$	16.3990	−	31.8853i	0.755626	−	1.46920i
$472$	−10.9285	+	9.17014i	−0.503027	+	0.422090i
$473$	16.5772	−	13.9099i	0.762220	−	0.639579i
$474$	25.5826	−	1.24344i	1.17505	−	0.0571132i
$475$	−52.1644	+	18.9863i	−2.39347	+	0.871151i
$476$	0.586324	+	1.01554i	0.0268741	+	0.0465473i
$477$	24.5729	+	6.32509i	1.12511	+	0.289606i
$478$	8.67615	−	15.0275i	0.396838	−	0.687343i
$479$	−3.31582	+	18.8050i	−0.151504	+	0.859221i	0.810409	+	0.585864i	$0.199245\pi$
$479$	−3.31582	+	18.8050i	−0.151504	+	0.859221i	−0.961913	+	0.273356i	$0.911866\pi$
$480$	−5.07703	+	4.69853i	−0.231733	+	0.214457i
$481$	17.6221	+	6.41392i	0.803499	+	0.292450i
$482$	4.20790	+	23.8642i	0.191665	+	1.08698i
$483$	−1.04051	+	8.21653i	−0.0473451	+	0.373865i
$484$	1.23662	+	1.03765i	0.0562101	+	0.0471659i
$485$	−58.3980			−2.65172
$486$	−15.1311	+	3.74831i	−0.686361	+	0.170027i
$487$	−41.3701			−1.87466			−0.937328	−	0.348447i	$-0.886709\pi$
$487$	−41.3701			−1.87466			−0.937328	+	0.348447i	$0.886709\pi$
$488$	0.477967	+	0.401062i	0.0216366	+	0.0181552i
$489$	−2.49709	+	19.7186i	−0.112923	+	0.891705i
$490$	−0.693523	−	3.93317i	−0.0313302	−	0.177682i
$491$	38.7294	+	14.0964i	1.74783	+	0.636159i	0.999627	−	0.0273067i	$-0.00869306\pi$
$491$	38.7294	+	14.0964i	1.74783	+	0.636159i	0.748206	+	0.663466i	$0.230915\pi$
$492$	−6.91026	+	6.39509i	−0.311539	+	0.288313i
$493$	−1.40856	+	7.98835i	−0.0634384	+	0.359777i
$494$	−11.8351	+	20.4990i	−0.532487	+	0.922294i
$495$	41.2110	+	10.6078i	1.85230	+	0.476783i
$496$	3.14056	+	5.43961i	0.141015	+	0.244246i
$497$	9.49928	−	3.45745i	0.426101	−	0.155088i
$498$	11.8973	−	0.578269i	0.533132	−	0.0259128i
$499$	−11.7029	+	9.81992i	−0.523895	+	0.439600i	−0.865987	−	0.500066i	$-0.833309\pi$
$499$	−11.7029	+	9.81992i	−0.523895	+	0.439600i	0.342092	+	0.939666i	$0.388864\pi$
$500$	18.2062	−	15.2768i	0.814205	−	0.683199i
$501$	−3.65540	+	7.10736i	−0.163311	+	0.317533i
$502$	−15.9981	+	5.82282i	−0.714029	+	0.259885i
$503$	−6.43121	−	11.1392i	−0.286753	−	0.496671i	0.686280	−	0.727338i	$-0.259243\pi$
$503$	−6.43121	−	11.1392i	−0.286753	−	0.496671i	−0.973033	+	0.230667i	$0.925909\pi$
$504$	−1.74489	−	2.44036i	−0.0777237	−	0.108702i
$505$	−12.3074	+	21.3171i	−0.547673	+	0.948598i
$506$	2.94907	−	16.7250i	0.131102	−	0.743516i
$507$	−14.5640	−	4.51315i	−0.646812	−	0.200436i
$508$	−13.3212	−	4.84851i	−0.591031	−	0.215118i
$509$	7.31637	+	41.4932i	0.324292	+	1.83915i	0.514602	+	0.857429i	$0.327940\pi$
$509$	7.31637	+	41.4932i	0.324292	+	1.83915i	−0.190309	+	0.981724i	$0.560949\pi$
$510$	−6.45983	−	4.90636i	−0.286046	−	0.217257i
$511$	−6.07206	−	5.09506i	−0.268612	−	0.225392i
$512$	−1.00000			−0.0441942
$513$	−16.3427	−	20.6578i	−0.721546	−	0.912064i
$514$	16.4457			0.725390
$515$	2.03366	+	1.70644i	0.0896138	+	0.0751949i
$516$	9.72989	−	4.08661i	0.428334	−	0.179903i
$517$	5.28985	+	30.0002i	0.232647	+	1.31941i
$518$	−3.77398	−	1.37362i	−0.165819	−	0.0603532i
$519$	−0.595950	−	2.62676i	−0.0261593	−	0.115302i
$520$	3.23832	−	18.3654i	0.142010	−	0.805377i
$521$	13.6626	−	23.6643i	0.598568	−	1.03675i	−0.394465	−	0.918911i	$-0.629070\pi$
$521$	13.6626	−	23.6643i	0.598568	−	1.03675i	0.993033	−	0.117839i	$-0.0375967\pi$
$522$	1.60459	−	20.6898i	0.0702309	−	0.905570i
$523$	−3.78237	−	6.55126i	−0.165392	−	0.286467i	0.771403	−	0.636347i	$-0.219555\pi$
$523$	−3.78237	−	6.55126i	−0.165392	−	0.286467i	−0.936794	+	0.349881i	$0.886222\pi$
$524$	−0.462966	+	0.168506i	−0.0202248	+	0.00736121i
$525$	10.2699	+	15.9464i	0.448216	+	0.695957i
$526$	13.1565	−	11.0396i	0.573650	−	0.481349i
$527$	−5.64233	+	4.73447i	−0.245784	+	0.206237i
$528$	3.33084	+	5.17189i	0.144956	+	0.225077i
$529$	0.127135	−	0.0462732i	0.00552759	−	0.00201188i
$530$	−16.8899	−	29.2541i	−0.733648	−	1.27072i
$531$	35.2991	+	24.2012i	1.53185	+	1.05024i
$532$	2.53462	−	4.39010i	0.109890	−	0.190335i
$533$	4.40763	−	24.9969i	0.190916	−	1.08274i
$534$	2.01217	+	8.86902i	0.0870751	+	0.383800i
$535$	−15.9688	−	5.81217i	−0.690392	−	0.251282i
$536$	−1.01291	−	5.74449i	−0.0437510	−	0.248124i
$537$	−2.26162	+	0.949892i	−0.0975961	+	0.0409909i
$538$	−22.1812	−	18.6122i	−0.956298	−	0.802430i
$539$	−3.55166			−0.152981
$540$	17.6657	+	10.8901i	0.760210	+	0.468636i
$541$	−3.78890			−0.162897			−0.0814487	−	0.996678i	$-0.525955\pi$
$541$	−3.78890			−0.162897			−0.0814487	+	0.996678i	$0.525955\pi$
$542$	−3.99929	−	3.35580i	−0.171784	−	0.144144i
$543$	−27.0768	−	20.5653i	−1.16198	−	0.882542i
$544$	−0.203628	−	1.15483i	−0.00873048	−	0.0495130i
$545$	18.5325	+	6.74528i	0.793846	+	0.288936i
$546$	7.72517	+	2.39390i	0.330607	+	0.102450i
$547$	1.96566	−	11.1478i	0.0840454	−	0.476645i	−0.913513	−	0.406809i	$-0.866641\pi$
$547$	1.96566	−	11.1478i	0.0840454	−	0.476645i	0.997559	−	0.0698358i	$-0.0222475\pi$
$548$	−5.07964	+	8.79819i	−0.216991	+	0.375840i
$549$	0.774291	−	1.70417i	0.0330459	−	0.0727324i
$550$	−19.4467	−	33.6827i	−0.829211	−	1.43624i
$551$	32.9509	−	11.9932i	1.40376	−	0.510925i
$552$	3.78798	−	7.36514i	0.161227	−	0.313481i
$553$	11.3279	−	9.50527i	0.481713	−	0.404205i
$554$	3.43355	−	2.88109i	0.145878	−	0.122406i
$555$	27.7493	−	1.34876i	1.17789	−	0.0572515i
$556$	12.0997	−	4.40393i	0.513141	−	0.186768i
$557$	8.13785	+	14.0952i	0.344812	+	0.597231i	0.985320	−	0.170720i	$-0.0546094\pi$
$557$	8.13785	+	14.0952i	0.344812	+	0.597231i	−0.640508	+	0.767952i	$0.721276\pi$
$558$	13.1921	−	13.4551i	0.558468	−	0.569599i
$559$	−14.2251	+	24.6385i	−0.601656	+	1.04210i
$560$	−0.693523	+	3.93317i	−0.0293067	+	0.166207i
$561$	−5.29441	+	4.89970i	−0.223530	+	0.206866i
$562$	3.51400	+	1.27899i	0.148229	+	0.0539511i
$563$	0.148418	+	0.841722i	0.00625508	+	0.0354743i	0.987776	−	0.155883i	$-0.0498222\pi$
$563$	0.148418	+	0.841722i	0.00625508	+	0.0354743i	−0.981520	+	0.191357i	$0.938711\pi$
$564$	−1.86641	+	14.7383i	−0.0785901	+	0.620595i
$565$	−8.89174	−	7.46106i	−0.374078	−	0.313889i
$566$	−1.75808			−0.0738975
$567$	−5.64792	+	7.00721i	−0.237190	+	0.294275i
$568$	−10.1089			−0.424161
$569$	−6.21221	−	5.21266i	−0.260429	−	0.218526i	0.503218	−	0.864159i	$-0.332149\pi$
$569$	−6.21221	−	5.21266i	−0.260429	−	0.218526i	−0.763648	+	0.645633i	$0.776594\pi$
$570$	−4.40555	+	34.7889i	−0.184528	+	1.45715i
$571$	−1.58103	−	8.96648i	−0.0661642	−	0.375236i	−0.999853	−	0.0171501i	$-0.994541\pi$
$571$	−1.58103	−	8.96648i	−0.0661642	−	0.375236i	0.933689	−	0.358086i	$-0.116570\pi$
$572$	−15.5839	−	5.67207i	−0.651595	−	0.237161i
$573$	21.4089	−	19.8128i	0.894368	−	0.827692i
$574$	−0.943944	+	5.35337i	−0.0393995	+	0.223446i
$575$	−26.1817	+	45.3480i	−1.09185	+	1.89114i
$576$	0.805011	+	2.88998i	0.0335421	+	0.120416i
$577$	−13.2059	−	22.8734i	−0.549770	−	0.952230i	−0.998290	−	0.0584572i	$-0.981382\pi$
$577$	−13.2059	−	22.8734i	−0.549770	−	0.952230i	0.448520	−	0.893773i	$-0.351951\pi$
$578$	−14.6826	+	5.34403i	−0.610716	+	0.222282i
$579$	2.62218	−	0.127451i	0.108974	−	0.00529669i
$580$	−21.1633	+	17.7581i	−0.878757	+	0.737365i
$581$	5.26811	−	4.42047i	0.218558	−	0.183392i
$582$	−11.5833	+	22.5219i	−0.480143	+	0.933563i
$583$	−28.2281	+	10.2742i	−1.16909	+	0.425514i
$584$	3.96326	+	6.86456i	0.164001	+	0.284058i
$585$	−55.6825	+	5.42571i	−2.30219	+	0.224325i
$586$	−4.71870	+	8.17302i	−0.194928	+	0.337624i
$587$	1.74432	−	9.89254i	0.0719959	−	0.408309i	−0.927416	−	0.374030i	$-0.877976\pi$
$587$	1.74432	−	9.89254i	0.0719959	−	0.408309i	0.999412	−	0.0342785i	$-0.0109133\pi$
$588$	−1.65444	−	0.512682i	−0.0682278	−	0.0211426i
$589$	29.9203	+	10.8901i	1.23285	+	0.448719i
$590$	−9.89395	−	56.1114i	−0.407327	−	2.31007i
$591$	−12.5951	−	9.56619i	−0.518092	−	0.393501i
$592$	3.07657	+	2.58155i	0.126446	+	0.106101i
$593$	−23.3610			−0.959321			−0.479660	−	0.877454i	$-0.659240\pi$
$593$	−23.3610			−0.959321			−0.479660	+	0.877454i	$0.659240\pi$
$594$	12.2653	−	13.7895i	0.503250	−	0.565789i
$595$	−4.68337			−0.191999
$596$	−17.3442	−	14.5535i	−0.710446	−	0.596135i
$597$	24.9813	−	10.4923i	1.02242	−	0.429421i
$598$	3.87714	+	21.9884i	0.158548	+	0.899171i
$599$	−1.44926	−	0.527488i	−0.0592153	−	0.0215526i	0.312243	−	0.950002i	$-0.398920\pi$
$599$	−1.44926	−	0.527488i	−0.0592153	−	0.0215526i	−0.371458	+	0.928450i	$0.621142\pi$
$600$	−4.19658	−	18.4972i	−0.171325	−	0.755146i
$601$	−5.44543	+	30.8826i	−0.222124	+	1.25973i	0.645984	+	0.763351i	$0.276447\pi$
$601$	−5.44543	+	30.8826i	−0.222124	+	1.25973i	−0.868108	+	0.496375i	$0.834664\pi$
$602$	3.04646	−	5.27662i	0.124164	−	0.215059i
$603$	−15.7860	+	7.55167i	−0.642857	+	0.307528i
$604$	1.87481	+	3.24726i	0.0762849	+	0.132129i
$605$	−6.05843	+	2.20509i	−0.246310	+	0.0896496i
$606$	5.78001	+	8.97478i	0.234797	+	0.364575i
$607$	−5.63213	+	4.72591i	−0.228601	+	0.191819i	−0.749893	−	0.661560i	$-0.769895\pi$
$607$	−5.63213	+	4.72591i	−0.228601	+	0.191819i	0.521292	+	0.853379i	$0.325450\pi$
$608$	−3.88327	+	3.25845i	−0.157487	+	0.132148i
$609$	−6.48724	−	10.0729i	−0.262876	−	0.408175i
$610$	−2.34164	+	0.852289i	−0.0948104	+	0.0345082i
$611$	−20.0249	−	34.6841i	−0.810121	−	1.40317i
$612$	−3.17351	+	1.51813i	−0.128282	+	0.0613669i
$613$	2.08449	−	3.61045i	0.0841918	−	0.145825i	−0.820855	−	0.571137i	$-0.806502\pi$
$613$	2.08449	−	3.61045i	0.0841918	−	0.145825i	0.905047	+	0.425313i	$0.139836\pi$
$614$	−0.794890	+	4.50804i	−0.0320791	+	0.181930i
$615$	−8.31990	−	36.6715i	−0.335491	−	1.47874i
$616$	3.33747	+	1.21474i	0.134470	+	0.0489433i
$617$	−7.08760	−	40.1958i	−0.285336	−	1.61822i	−0.704083	−	0.710117i	$-0.748642\pi$
$617$	−7.08760	−	40.1958i	−0.285336	−	1.61822i	0.418747	−	0.908103i	$-0.362469\pi$
$618$	1.06149	−	0.445832i	0.0426994	−	0.0179340i
$619$	−31.5176	−	26.4464i	−1.26680	−	1.06297i	−0.994923	−	0.100639i	$-0.967911\pi$
$619$	−31.5176	−	26.4464i	−1.26680	−	1.06297i	−0.271877	−	0.962332i	$-0.587644\pi$
$620$	−25.0858			−1.00747
$621$	−24.3344	−	5.01816i	−0.976508	−	0.201372i
$622$	−7.93385			−0.318118
$623$	4.02224	+	3.37506i	0.161148	+	0.135219i
$624$	−6.44053	−	4.89170i	−0.257827	−	0.195825i
$625$	6.97469	+	39.5554i	0.278987	+	1.58222i
$626$	−3.14581	−	1.14498i	−0.125732	−	0.0457626i
$627$	29.7869	+	9.23046i	1.18957	+	0.368629i
$628$	−3.59470	+	20.3865i	−0.143444	+	0.813511i
$629$	−2.35478	+	4.07860i	−0.0938913	+	0.162625i
$630$	11.9250	−	1.16198i	0.475105	−	0.0462943i
$631$	14.6464	+	25.3683i	0.583064	+	1.00990i	0.995114	+	0.0987346i	$0.0314795\pi$
$631$	14.6464	+	25.3683i	0.583064	+	1.00990i	−0.412050	+	0.911161i	$0.635187\pi$
$632$	−13.8958	+	5.05765i	−0.552744	+	0.201182i
$633$	−8.32349	+	16.1837i	−0.330829	+	0.643245i
$634$	−19.4129	+	16.2893i	−0.770983	+	0.646932i
$635$	43.3712	−	36.3927i	1.72113	−	1.44420i
$636$	−14.6323	+	0.711203i	−0.580209	+	0.0282010i
$637$	4.38777	−	1.59702i	0.173850	−	0.0632762i
$638$	12.2840	+	21.2765i	0.486328	+	0.842345i
$639$	8.13779	+	29.2145i	0.321926	+	1.15571i
$640$	1.99692	−	3.45877i	0.0789352	−	0.136720i
$641$	−0.386620	+	2.19263i	−0.0152706	+	0.0866038i	−0.991491	−	0.130178i	$-0.958445\pi$
$641$	−0.386620	+	2.19263i	−0.0152706	+	0.0866038i	0.976220	+	0.216782i	$0.0695561\pi$
$642$	−5.40897	+	5.00572i	−0.213475	+	0.197560i
$643$	43.4763	+	15.8241i	1.71454	+	0.624041i	0.997344	−	0.0728323i	$-0.0232038\pi$
$643$	43.4763	+	15.8241i	1.71454	+	0.624041i	0.717194	+	0.696873i	$0.245426\pi$
$644$	−0.830334	−	4.70906i	−0.0327198	−	0.185563i
$645$	−5.29519	+	41.8141i	−0.208498	+	1.64643i
$646$	−4.55371	−	3.82101i	−0.179163	−	0.150336i
$647$	4.39134			0.172641			0.0863206	−	0.996267i	$-0.472489\pi$
$647$	4.39134			0.172641			0.0863206	+	0.996267i	$0.472489\pi$
$648$	7.70391	−	4.65293i	0.302638	−	0.182784i
$649$	−50.6687			−1.98892
$650$	39.1703	+	32.8678i	1.53639	+	1.28918i
$651$	1.36679	−	10.7930i	0.0535688	−	0.423012i
$652$	−1.99269	−	11.3011i	−0.0780398	−	0.442586i
$653$	33.5591	+	12.2145i	1.31327	+	0.477991i	0.901296	−	0.433205i	$-0.142617\pi$
$653$	33.5591	+	12.2145i	1.31327	+	0.477991i	0.411974	+	0.911196i	$0.364840\pi$
$654$	6.27735	−	5.80936i	0.245464	−	0.227164i
$655$	0.341684	−	1.93778i	0.0133507	−	0.0757155i
$656$	2.71798	−	4.70768i	0.106119	−	0.183804i
$657$	16.6479	−	16.9798i	0.649498	−	0.662444i
$658$	4.28856	+	7.42801i	0.167186	+	0.289574i
$659$	−32.0782	+	11.6755i	−1.24959	+	0.454813i	−0.880263	−	0.474487i	$-0.842634\pi$
$659$	−32.0782	+	11.6755i	−1.24959	+	0.454813i	−0.369326	+	0.929300i	$0.620411\pi$
$660$	−24.5398	+	1.19275i	−0.955210	+	0.0464279i
$661$	18.1174	−	15.2023i	0.704686	−	0.591302i	−0.218416	−	0.975856i	$-0.570089\pi$
$661$	18.1174	−	15.2023i	0.704686	−	0.591302i	0.923103	+	0.384554i	$0.125645\pi$
$662$	8.73453	−	7.32914i	0.339477	−	0.284855i
$663$	4.33762	−	8.43381i	0.168459	−	0.327542i
$664$	−6.46229	+	2.35208i	−0.250786	+	0.0912785i
$665$	10.1229	+	17.5334i	0.392549	+	0.679915i
$666$	4.98395	−	10.9694i	0.193124	−	0.425056i
$667$	16.5383	−	28.6452i	0.640365	−	1.10915i
$668$	0.801273	−	4.54424i	0.0310022	−	0.175822i
$669$	−3.36639	−	1.04319i	−0.130152	−	0.0403319i
$670$	21.8916	+	7.96788i	0.845745	+	0.307826i
$671$	0.384810	+	2.18236i	0.0148554	+	0.0842492i
$672$	1.37931	+	1.04761i	0.0532082	+	0.0404126i
$673$	29.6493	+	24.8787i	1.14290	+	0.959004i	0.999530	−	0.0306658i	$-0.00976275\pi$
$673$	29.6493	+	24.8787i	1.14290	+	0.959004i	0.143367	+	0.989670i	$0.454207\pi$
$674$	25.8749			0.996663
$675$	−50.0782	+	27.0185i	−1.92751	+	1.03994i
$676$	8.80303			0.338578
$677$	28.4304	+	23.8559i	1.09267	+	0.916857i	0.996910	−	0.0785481i	$-0.0250284\pi$
$677$	28.4304	+	23.8559i	1.09267	+	0.916857i	0.0957569	+	0.995405i	$0.469473\pi$
$678$	−4.64114	+	1.94930i	−0.178242	+	0.0748625i
$679$	2.53908	+	14.3999i	0.0974411	+	0.552616i
$680$	4.40093	+	1.60181i	0.168768	+	0.0614265i
$681$	2.18557	+	9.63333i	0.0837514	+	0.369150i
$682$	−3.87381	+	21.9695i	−0.148336	+	0.841255i
$683$	−0.976994	+	1.69220i	−0.0373836	+	0.0647503i	−0.884112	−	0.467275i	$-0.845236\pi$
$683$	−0.976994	+	1.69220i	−0.0373836	+	0.0647503i	0.846728	+	0.532026i	$0.178569\pi$
$684$	12.5429	+	8.59947i	0.479590	+	0.328809i
$685$	−20.2873	−	35.1386i	−0.775137	−	1.34258i
$686$	−0.939693	+	0.342020i	−0.0358776	+	0.0130584i
$687$	4.10343	+	6.37151i	0.156556	+	0.243088i
$688$	−4.66745	+	3.91645i	−0.177945	+	0.149313i
$689$	30.2536	−	25.3858i	1.15257	−	0.967122i
$690$	17.9100	+	27.8094i	0.681822	+	1.05868i
$691$	−26.7448	+	9.73431i	−1.01742	+	0.370311i	−0.796278	−	0.604931i	$-0.793201\pi$
$691$	−26.7448	+	9.73431i	−1.01742	+	0.370311i	−0.221142	+	0.975242i	$0.570978\pi$
$692$	0.777552	+	1.34676i	0.0295581	+	0.0511961i
$693$	0.823867	−	10.6231i	0.0312961	−	0.403538i
$694$	−5.17068	+	8.95589i	−0.196277	+	0.339961i
$695$	−8.92996	+	50.6443i	−0.338733	+	1.92105i
$696$	2.65087	+	11.6842i	0.100481	+	0.442889i
$697$	5.99004	+	2.18019i	0.226889	+	0.0825808i
$698$	−0.679676	−	3.85463i	−0.0257261	−	0.145900i
$699$	15.5766	−	6.54227i	0.589162	−	0.247451i
$700$	−8.38878	−	7.03902i	−0.317066	−	0.266050i
$701$	30.7248			1.16046			0.580229	−	0.814453i	$-0.302963\pi$
$701$	30.7248			1.16046			0.580229	+	0.814453i	$0.302963\pi$
$702$	−8.95219	+	22.5508i	−0.337879	+	0.851126i
$703$	20.3590			0.767855
$704$	−2.72073	−	2.28296i	−0.102541	−	0.0860424i
$705$	−47.2493	−	35.8867i	−1.77951	−	1.35157i
$706$	−0.303582	−	1.72170i	−0.0114255	−	0.0647971i
$707$	5.79152	+	2.10794i	0.217812	+	0.0792772i
$708$	−23.6025	−	7.31402i	−0.887037	−	0.274878i
$709$	−2.45604	+	13.9289i	−0.0922386	+	0.523111i	0.903320	+	0.428967i	$0.141122\pi$
$709$	−2.45604	+	13.9289i	−0.0922386	+	0.523111i	−0.995559	+	0.0941437i	$0.969989\pi$
$710$	20.1867	−	34.9644i	0.757594	−	1.31219i
$711$	25.8027	+	36.0870i	0.967678	+	1.35337i
$712$	−2.62533	−	4.54721i	−0.0983884	−	0.170414i
$713$	28.2232	−	10.2724i	1.05697	−	0.384704i
$714$	−0.928951	+	1.80620i	−0.0347651	+	0.0675953i
$715$	50.7382	−	42.5744i	1.89750	−	1.59219i
$716$	1.08490	−	0.910342i	0.0405447	−	0.0340211i
$717$	30.0196	−	1.45910i	1.12110	−	0.0544912i
$718$	−26.4118	+	9.61310i	−0.985679	+	0.358758i
$719$	−22.7837	−	39.4625i	−0.849689	−	1.47170i	−0.881486	−	0.472210i	$-0.843456\pi$
$719$	−22.7837	−	39.4625i	−0.849689	−	1.47170i	0.0317973	−	0.999494i	$-0.489877\pi$
$720$	−11.6033	−	2.98670i	−0.432429	−	0.111308i
$721$	0.332356	−	0.575658i	0.0123776	−	0.0214386i
$722$	−1.16297	+	6.59554i	−0.0432813	+	0.245461i
$723$	−30.8045	+	28.5079i	−1.14563	+	1.06022i
$724$	18.4468	+	6.71407i	0.685569	+	0.249527i
$725$	−13.1539	−	74.5992i	−0.488522	−	2.77055i
$726$	−0.351276	+	2.77389i	−0.0130371	+	0.102949i
$727$	7.11810	+	5.97280i	0.263996	+	0.221519i	0.765171	−	0.643827i	$-0.222654\pi$
$727$	7.11810	+	5.97280i	0.263996	+	0.221519i	−0.501175	+	0.865346i	$0.667099\pi$
$728$	−4.66937			−0.173058
$729$	−19.6486	−	18.5185i	−0.727725	−	0.685869i
$730$	−31.6572			−1.17169
$731$	−5.47327	−	4.59262i	−0.202436	−	0.169864i
$732$	−0.135772	+	1.07214i	−0.00501827	+	0.0396273i
$733$	5.65987	+	32.0987i	0.209052	+	1.18559i	0.890935	+	0.454131i	$0.150050\pi$
$733$	5.65987	+	32.0987i	0.209052	+	1.18559i	−0.681883	+	0.731462i	$0.738839\pi$
$734$	6.64545	+	2.41875i	0.245288	+	0.0892776i
$735$	5.07703	−	4.69853i	0.187269	−	0.173308i
$736$	−0.830334	+	4.70906i	−0.0306065	+	0.173578i
$737$	10.3586	−	17.9417i	0.381565	−	0.660889i
$738$	−15.7931	−	4.06516i	−0.581351	−	0.149641i
$739$	18.8800	+	32.7011i	0.694512	+	1.20293i	0.970345	+	0.241725i	$0.0777132\pi$
$739$	18.8800	+	32.7011i	0.694512	+	1.20293i	−0.275832	+	0.961206i	$0.588954\pi$
$740$	−15.0727	+	5.48600i	−0.554082	+	0.201669i
$741$	−40.9497	+	1.99036i	−1.50432	+	0.0731176i
$742$	−6.47916	+	5.43666i	−0.237858	+	0.199586i
$743$	−30.5592	+	25.6422i	−1.12111	+	0.940720i	−0.998660	−	0.0517548i	$-0.983519\pi$
$743$	−30.5592	+	25.6422i	−1.12111	+	0.940720i	−0.122447	+	0.992475i	$0.539074\pi$
$744$	−4.97579	+	9.67465i	−0.182421	+	0.354690i
$745$	84.9723	−	30.9274i	3.11314	−	1.13309i
$746$	13.6680	+	23.6736i	0.500420	+	0.866753i
$747$	11.9997	+	16.7824i	0.439045	+	0.614036i
$748$	2.08242	−	3.60686i	0.0761409	−	0.131880i
$749$	−0.738867	+	4.19032i	−0.0269976	+	0.153111i
$750$	39.3201	+	12.1846i	1.43577	+	0.444920i
$751$	−31.3669	−	11.4166i	−1.14459	−	0.416598i	−0.301023	−	0.953617i	$-0.597328\pi$
$751$	−31.3669	−	11.4166i	−1.14459	−	0.416598i	−0.843570	+	0.537019i	$0.819550\pi$
$752$	−1.48940	−	8.44682i	−0.0543129	−	0.308024i
$753$	−23.4825	−	17.8354i	−0.855751	−	0.649958i
$754$	−24.7429	−	20.7617i	−0.901083	−	0.756098i
$755$	−14.9754			−0.545010
$756$	1.91721	−	4.82952i	0.0697284	−	0.175648i
$757$	−31.6253			−1.14944			−0.574720	−	0.818350i	$-0.694889\pi$
$757$	−31.6253			−1.14944			−0.574720	+	0.818350i	$0.694889\pi$
$758$	6.93868	+	5.82225i	0.252024	+	0.211474i
$759$	27.1204	−	11.3907i	0.984409	−	0.413457i
$760$	−3.51564	−	19.9382i	−0.127526	−	0.723235i
$761$	−30.2463	−	11.0087i	−1.09643	−	0.399067i	−0.270429	−	0.962740i	$-0.587165\pi$
$761$	−30.2463	−	11.0087i	−1.09643	−	0.399067i	−0.825998	+	0.563673i	$0.809388\pi$
$762$	−5.43259	−	23.9452i	−0.196802	−	0.867442i
$763$	0.857488	−	4.86305i	0.0310431	−	0.176054i
$764$	−8.42065	+	14.5850i	−0.304648	+	0.527666i
$765$	1.08639	−	14.0080i	0.0392783	−	0.506462i
$766$	14.7712	+	25.5845i	0.533706	+	0.924405i
$767$	62.5969	−	22.7834i	2.26024	−	0.822661i
$768$	−0.937826	−	1.45619i	−0.0338409	−	0.0525457i
$769$	−2.45303	+	2.05833i	−0.0884584	+	0.0742254i	−0.685945	−	0.727654i	$-0.740611\pi$
$769$	−2.45303	+	2.05833i	−0.0884584	+	0.0742254i	0.597486	+	0.801879i	$0.296166\pi$
$770$	−10.8662	+	9.11780i	−0.391589	+	0.328583i
$771$	15.4232	+	23.9481i	0.555454	+	0.862468i
$772$	−1.42430	+	0.518402i	−0.0512616	+	0.0186577i
$773$	−3.18696	−	5.51998i	−0.114627	−	0.198540i	0.803004	−	0.595974i	$-0.203234\pi$
$773$	−3.18696	−	5.51998i	−0.114627	−	0.198540i	−0.917631	+	0.397434i	$0.869901\pi$
$774$	15.0758	+	10.3360i	0.541889	+	0.371521i
$775$	34.3916	−	59.5679i	1.23538	−	2.13974i
$776$	2.53908	−	14.3999i	0.0911478	−	0.516925i
$777$	−1.53909	−	6.78383i	−0.0552146	−	0.243369i
$778$	22.8749	+	8.32578i	0.820105	+	0.298494i
$779$	−4.78509	−	27.1376i	−0.171444	−	0.972305i
$780$	29.7805	−	12.5080i	1.06631	−	0.447857i
$781$	−27.5036	−	23.0783i	−0.984158	−	0.825806i
$782$	−5.60725			−0.200515
$783$	31.6331	−	17.0669i	1.13048	−	0.609921i
$784$	1.00000			0.0357143
$785$	−63.3340	−	53.1435i	−2.26049	−	1.89677i
$786$	−0.679557	−	0.516136i	−0.0242390	−	0.0184100i
$787$	4.38150	+	24.8487i	0.156184	+	0.885761i	0.957696	+	0.287782i	$0.0929180\pi$
$787$	4.38150	+	24.8487i	0.156184	+	0.885761i	−0.801512	+	0.597978i	$0.795971\pi$
$788$	8.58072	+	3.12313i	0.305676	+	0.111257i
$789$	28.4142	+	8.80509i	1.01157	+	0.313469i
$790$	10.2555	−	58.1620i	0.364875	−	2.06931i
$791$	−1.45316	+	2.51694i	−0.0516683	+	0.0894920i
$792$	−4.40749	+	9.70065i	−0.156613	+	0.344698i
$793$	−1.45671	−	2.52309i	−0.0517292	−	0.0895977i
$794$	−29.0172	+	10.5614i	−1.02978	+	0.374810i
$795$	26.7597	−	52.0300i	0.949069	−	1.84532i
$796$	−11.9836	+	10.0554i	−0.424748	+	0.356406i
$797$	−17.7137	+	14.8636i	−0.627451	+	0.526494i	−0.900136	−	0.435609i	$-0.856533\pi$
$797$	−17.7137	+	14.8636i	−0.627451	+	0.526494i	0.272684	+	0.962104i	$0.412089\pi$
$798$	8.76984	−	0.426258i	0.310449	−	0.0150894i
$799$	9.45138	−	3.44002i	0.334366	−	0.121699i
$800$	5.47539	+	9.48365i	0.193584	+	0.335298i
$801$	−11.0279	+	11.2477i	−0.389651	+	0.397418i
$802$	−0.305664	+	0.529425i	−0.0107934	+	0.0186947i
$803$	−4.88859	+	27.7246i	−0.172515	+	0.978379i
$804$	7.41513	−	6.86232i	0.261511	−	0.242015i
$805$	17.9457	+	6.53169i	0.632502	+	0.230212i
$806$	−5.09290	−	28.8833i	−0.179390	−	1.01737i
$807$	6.30081	−	49.7550i	0.221799	−	1.75146i
$808$	−4.72129	−	3.96163i	−0.166094	−	0.139370i
$809$	3.15576			0.110951			0.0554754	−	0.998460i	$-0.482333\pi$
$809$	3.15576			0.110951			0.0554754	+	0.998460i	$0.482333\pi$
$810$	0.709284	+	35.9376i	0.0249217	+	1.26272i
$811$	−26.8439			−0.942617			−0.471308	−	0.881969i	$-0.656218\pi$
$811$	−26.8439			−0.942617			−0.471308	+	0.881969i	$0.656218\pi$
$812$	5.29898	+	4.44637i	0.185958	+	0.156037i
$813$	1.13604	−	8.97088i	0.0398427	−	0.314622i
$814$	2.47694	+	14.0474i	0.0868166	+	0.492362i
$815$	43.0672	+	15.6752i	1.50858	+	0.549077i
$816$	1.49068	−	1.37955i	0.0521844	−	0.0482940i
$817$	−5.36339	+	30.4173i	−0.187641	+	1.06417i
$818$	−8.83700	+	15.3061i	−0.308979	+	0.535167i
$819$	3.75890	+	13.4944i	0.131346	+	0.471531i
$820$	10.8552	+	18.8017i	0.379079	+	0.656585i
$821$	0.143222	−	0.0521285i	0.00499848	−	0.00181930i	−0.339520	−	0.940599i	$-0.610265\pi$
$821$	0.143222	−	0.0521285i	0.00499848	−	0.00181930i	0.344518	+	0.938780i	$0.388042\pi$
$822$	−17.5756	+	0.854263i	−0.613021	+	0.0297958i
$823$	31.7860	−	26.6716i	1.10799	−	0.929714i	0.110054	−	0.993926i	$-0.464898\pi$
$823$	31.7860	−	26.6716i	1.10799	−	0.929714i	0.997936	+	0.0642116i	$0.0204532\pi$
$824$	−0.509199	+	0.427269i	−0.0177388	+	0.0148846i
$825$	30.8107	−	59.9066i	1.07269	−	2.08568i
$826$	−13.4058	+	4.87933i	−0.466449	+	0.169774i
$827$	−4.29231	−	7.43450i	−0.149258	−	0.258523i	0.781695	−	0.623661i	$-0.214355\pi$
$827$	−4.29231	−	7.43450i	−0.149258	−	0.258523i	−0.930954	+	0.365138i	$0.881022\pi$
$828$	14.2775	−	1.39120i	0.496177	−	0.0483476i
$829$	7.81062	−	13.5284i	0.271274	−	0.469860i	−0.697914	−	0.716181i	$-0.745888\pi$
$829$	7.81062	−	13.5284i	0.271274	−	0.469860i	0.969188	+	0.246321i	$0.0792217\pi$
$830$	4.76938	−	27.0485i	0.165548	−	0.938867i
$831$	7.41548	+	2.29793i	0.257240	+	0.0797144i
$832$	4.38777	+	1.59702i	0.152119	+	0.0553667i
$833$	0.203628	+	1.15483i	0.00705529	+	0.0400126i
$834$	17.7603	+	13.4893i	0.614990	+	0.467096i
$835$	14.1174	+	11.8459i	0.488553	+	0.409945i
$836$	−18.0043			−0.622690
$837$	31.9651	+	6.59172i	1.10487	+	0.227843i
$838$	11.3108			0.390723
$839$	−5.37955	−	4.51398i	−0.185723	−	0.155840i	0.545186	−	0.838315i	$-0.316459\pi$
$839$	−5.37955	−	4.51398i	−0.185723	−	0.155840i	−0.730909	+	0.682475i	$0.760903\pi$
$840$	−6.37783	+	2.67872i	−0.220056	+	0.0924248i
$841$	3.27316	+	18.5630i	0.112867	+	0.640103i
$842$	10.4725	+	3.81169i	0.360907	+	0.131359i
$843$	1.43307	+	6.31652i	0.0493575	+	0.217553i
$844$	1.82453	−	10.3474i	0.0628028	−	0.356172i
$845$	−17.5790	+	30.4476i	−0.604734	+	1.04743i
$846$	−23.2121	+	11.1041i	−0.798049	+	0.381768i
$847$	0.807148	+	1.39802i	0.0277339	+	0.0480366i
$848$	7.94787	−	2.89279i	0.272931	−	0.0993388i
$849$	−1.64877	−	2.56009i	−0.0565856	−	0.0878620i
$850$	−9.83708	+	8.25429i	−0.337409	+	0.283120i
$851$	14.7113	−	12.3442i	0.504296	−	0.423155i
$852$	−9.48041	−	14.7205i	−0.324793	−	0.504316i
$853$	−13.5250	+	4.92269i	−0.463086	+	0.168550i	−0.563018	−	0.826445i	$-0.690360\pi$
$853$	−13.5250	+	4.92269i	−0.463086	+	0.168550i	0.0999316	+	0.994994i	$0.468138\pi$
$854$	0.311971	+	0.540350i	0.0106754	+	0.0184904i
$855$	−54.7908	+	26.2106i	−1.87381	+	0.896384i
$856$	2.12748	−	3.68491i	0.0727158	−	0.125948i
$857$	−1.54217	+	8.74606i	−0.0526794	+	0.298760i	−0.999752	−	0.0222590i	$-0.992914\pi$
$857$	−1.54217	+	8.74606i	−0.0526794	+	0.298760i	0.947073	+	0.321019i	$0.104025\pi$
$858$	−6.35537	−	28.0125i	−0.216969	−	0.956330i
$859$	−20.5997	−	7.49767i	−0.702852	−	0.255817i	−0.0342240	−	0.999414i	$-0.510896\pi$
$859$	−20.5997	−	7.49767i	−0.702852	−	0.255817i	−0.668628	+	0.743597i	$0.733118\pi$
$860$	−4.22558	−	23.9645i	−0.144091	−	0.817182i
$861$	−8.68077	+	3.64597i	−0.295840	+	0.124254i
$862$	−16.6374	−	13.9605i	−0.566673	−	0.475495i
$863$	21.9518			0.747249			0.373625	−	0.927580i	$-0.378115\pi$
$863$	21.9518			0.747249			0.373625	+	0.927580i	$0.378115\pi$
$864$	−3.45339	+	3.88254i	−0.117487	+	0.132087i
$865$	−6.21084			−0.211175
$866$	−30.0871	−	25.2460i	−1.02240	−	0.857895i
$867$	−21.5516	−	16.3689i	−0.731932	−	0.555916i
$868$	1.09070	+	6.18569i	0.0370209	+	0.209956i
$869$	−49.3531	−	17.9631i	−1.67419	−	0.609355i
$870$	−45.7066	−	14.1637i	−1.54960	−	0.480195i
$871$	−4.72965	+	26.8232i	−0.160258	+	0.908869i
$872$	−2.46904	+	4.27650i	−0.0836122	+	0.144820i
$873$	−43.6592	+	4.25416i	−1.47764	+	0.143981i
$874$	12.1198	+	20.9922i	0.409959	+	0.710070i
$875$	22.3332	−	8.12861i	0.754999	−	0.274797i
$876$	−6.27925	+	12.2090i	−0.212156	+	0.412504i
$877$	19.3594	−	16.2444i	0.653720	−	0.548536i	−0.254477	−	0.967079i	$-0.581903\pi$
$877$	19.3594	−	16.2444i	0.653720	−	0.548536i	0.908197	+	0.418543i	$0.137459\pi$
$878$	−6.01107	+	5.04389i	−0.202864	+	0.170223i
$879$	−16.3268	+	0.793562i	−0.550688	+	0.0267662i
$880$	13.3293	−	4.85148i	0.449332	−	0.163543i
$881$	29.1873	+	50.5539i	0.983346	+	1.70321i	0.649068	+	0.760731i	$0.275159\pi$
$881$	29.1873	+	50.5539i	0.983346	+	1.70321i	0.334278	+	0.942474i	$0.391507\pi$
$882$	−0.805011	−	2.88998i	−0.0271061	−	0.0973105i
$883$	11.4132	−	19.7683i	0.384086	−	0.665257i	−0.607556	−	0.794277i	$-0.707850\pi$
$883$	11.4132	−	19.7683i	0.384086	−	0.665257i	0.991642	+	0.129020i	$0.0411833\pi$
$884$	−0.950815	+	5.39234i	−0.0319794	+	0.181364i
$885$	72.4299	−	67.0301i	2.43470	−	2.25319i
$886$	15.1343	+	5.50845i	0.508448	+	0.185060i
$887$	4.07111	+	23.0884i	0.136694	+	0.775232i	0.973665	+	0.227984i	$0.0732134\pi$
$887$	4.07111	+	23.0884i	0.136694	+	0.775232i	−0.836970	+	0.547248i	$0.815675\pi$
$888$	−0.873935	+	6.90112i	−0.0293273	+	0.231586i
$889$	−10.8595	−	9.11221i	−0.364216	−	0.305614i
$890$	20.9703			0.702927
$891$	31.5827	+	4.92840i	1.05806	+	0.165108i
$892$	2.03476			0.0681290
$893$	−33.3073	−	27.9481i	−1.11459	−	0.935249i
$894$	4.92681	−	38.9051i	0.164777	−	1.30118i
$895$	0.982196	+	5.57031i	0.0328312	+	0.186195i
$896$	−0.939693	−	0.342020i	−0.0313929	−	0.0114261i
$897$	−28.3831	+	26.2671i	−0.947684	+	0.877032i
$898$	0.841834	−	4.77428i	0.0280924	−	0.159320i
$899$	−21.7243	+	37.6275i	−0.724545	+	1.25495i
$900$	22.9998	−	23.4582i	0.766659	−	0.781939i
$901$	4.95910	+	8.58940i	0.165211	+	0.286155i
$902$	18.1423	−	6.60328i	0.604074	−	0.219865i
$903$	10.5408	−	0.512335i	0.350776	−	0.0170495i
$904$	2.22636	−	1.86814i	0.0740477	−	0.0621334i
$905$	−60.0592	+	50.3956i	−1.99643	+	1.67521i
$906$	−2.97038	+	5.77544i	−0.0986844	+	0.191876i
$907$	−45.3315	+	16.4993i	−1.50521	+	0.547851i	−0.957403	−	0.288755i	$-0.906759\pi$
$907$	−45.3315	+	16.4993i	−1.50521	+	0.547851i	−0.547805	+	0.836606i	$0.684536\pi$
$908$	−2.85157	−	4.93907i	−0.0946328	−	0.163909i
$909$	−7.64832	+	16.8336i	−0.253679	+	0.558334i
$910$	9.32437	−	16.1503i	0.309100	−	0.535376i
$911$	6.03848	−	34.2459i	0.200064	−	1.13462i	−0.704957	−	0.709250i	$-0.749034\pi$
$911$	6.03848	−	34.2459i	0.200064	−	1.13462i	0.905021	−	0.425368i	$-0.139855\pi$
$912$	−8.38675	−	2.59891i	−0.277713	−	0.0860586i
$913$	−22.9519	−	8.35380i	−0.759596	−	0.276470i
$914$	6.04561	+	34.2863i	0.199971	+	1.13409i
$915$	−3.43715	−	2.61058i	−0.113629	−	0.0863030i
$916$	−3.35181	−	2.81250i	−0.110747	−	0.0929276i
$917$	−0.492678			−0.0162697
$918$	−5.18689	−	3.19749i	−0.171193	−	0.105533i
$919$	45.7531			1.50926			0.754628	−	0.656153i	$-0.227817\pi$
$919$	45.7531			1.50926			0.754628	+	0.656153i	$0.227817\pi$
$920$	−14.6294	−	12.2756i	−0.482318	−	0.404713i
$921$	−7.31003	+	3.07025i	−0.240874	+	0.101168i
$922$	1.81153	+	10.2737i	0.0596595	+	0.338346i
$923$	44.3557	+	16.1441i	1.45998	+	0.531391i
$924$	1.36108	+	5.99920i	0.0447761	+	0.197359i
$925$	7.63710	−	43.3122i	0.251106	−	1.42409i
$926$	−10.9781	+	19.0147i	−0.360764	+	0.624862i
$927$	1.64471	+	1.12762i	0.0540193	+	0.0370358i
$928$	−3.45866	−	5.99058i	−0.113536	−	0.196650i
$929$	24.1789	−	8.80041i	0.793285	−	0.288732i	0.0865839	−	0.996245i	$-0.472405\pi$
$929$	24.1789	−	8.80041i	0.793285	−	0.288732i	0.706701	+	0.707513i	$0.250183\pi$
$930$	−23.5261	−	36.5296i	−0.771451	−	1.19785i
$931$	3.88327	−	3.25845i	0.127269	−	0.106791i
$932$	−7.47214	+	6.26987i	−0.244758	+	0.205376i
$933$	−7.44056	−	11.5532i	−0.243593	−	0.378234i
$934$	24.1335	−	8.78388i	0.789673	−	0.287417i
$935$	8.31687	+	14.4052i	0.271991	+	0.471102i
$936$	1.08314	−	13.9662i	0.0354035	−	0.456499i
$937$	−15.4599	+	26.7773i	−0.505052	+	0.874775i	0.494931	+	0.868932i	$0.335193\pi$
$937$	−15.4599	+	26.7773i	−0.505052	+	0.874775i	−0.999983	+	0.00584292i	$0.998140\pi$
$938$	1.01291	−	5.74449i	0.0330727	−	0.187564i
$939$	−1.28291	−	5.65468i	−0.0418663	−	0.184533i
$940$	32.1898	+	11.7161i	1.04992	+	0.382138i
$941$	7.88423	+	44.7137i	0.257019	+	1.45763i	0.790837	+	0.612026i	$0.209645\pi$
$941$	7.88423	+	44.7137i	0.257019	+	1.45763i	−0.533819	+	0.845599i	$0.679244\pi$
$942$	−33.0578	+	13.8845i	−1.07708	+	0.452380i
$943$	−19.9119	−	16.7081i	−0.648421	−	0.544090i
$944$	14.2662			0.464325
$945$	12.8757	+	16.2754i	0.418846	+	0.529438i
$946$	−21.6400			−0.703577
$947$	−0.380439	−	0.319226i	−0.0123626	−	0.0103735i	0.636585	−	0.771206i	$-0.280346\pi$
$947$	−0.380439	−	0.319226i	−0.0123626	−	0.0103735i	−0.648948	+	0.760833i	$0.724791\pi$
$948$	−20.3967	−	15.4917i	−0.662454	−	0.503146i
$949$	−6.42704	−	36.4495i	−0.208630	−	1.18320i
$950$	52.1644	+	18.9863i	1.69244	+	0.615997i
$951$	−41.9262	−	12.9922i	−1.35955	−	0.421302i
$952$	0.203628	−	1.15483i	0.00659962	−	0.0374283i
$953$	5.00862	−	8.67519i	0.162245	−	0.281017i	−0.773428	−	0.633884i	$-0.781460\pi$
$953$	5.00862	−	8.67519i	0.162245	−	0.281017i	0.935674	+	0.352867i	$0.114793\pi$
$954$	−14.7582	−	20.6404i	−0.477815	−	0.668258i
$955$	−33.6307	−	58.2501i	−1.08826	−	1.88493i
$956$	−16.3058	+	5.93483i	−0.527368	+	0.191946i
$957$	−19.4623	+	37.8414i	−0.629128	+	1.22324i
$958$	14.6277	−	12.2741i	0.472598	−	0.396557i
$959$	−7.78246	+	6.53026i	−0.251309	+	0.210873i
$960$	6.90938	−	0.335830i	0.222999	−	0.0108389i
$961$	−7.94269	+	2.89090i	−0.256216	+	0.0932549i
$962$	−9.37652	−	16.2406i	−0.302311	−	0.523618i
$963$	−12.3619	−	3.18198i	−0.398358	−	0.102538i
$964$	12.1162	−	20.9858i	0.390235	−	0.675907i
$965$	1.05118	−	5.96153i	0.0338386	−	0.191908i
$966$	6.07857	−	5.62540i	0.195575	−	0.180994i
$967$	−26.9223	−	9.79893i	−0.865764	−	0.315112i	−0.129313	−	0.991604i	$-0.541277\pi$
$967$	−26.9223	−	9.79893i	−0.865764	−	0.315112i	−0.736450	+	0.676492i	$0.763500\pi$
$968$	−0.280320	−	1.58977i	−0.00900981	−	0.0510972i
$969$	1.29353	−	10.2145i	0.0415542	−	0.328137i
$970$	44.7354	+	37.5375i	1.43637	+	1.20526i
$971$	25.9260			0.832006			0.416003	−	0.909363i	$-0.363431\pi$
$971$	25.9260			0.832006			0.416003	+	0.909363i	$0.363431\pi$
$972$	14.0005	+	6.85471i	0.449065	+	0.219865i
$973$	12.8762			0.412793
$974$	31.6913	+	26.5922i	1.01546	+	0.852068i
$975$	−11.1268	+	87.8636i	−0.356342	+	2.81389i
$976$	−0.108346	−	0.614463i	−0.00346808	−	0.0196685i
$977$	−29.5244	−	10.7460i	−0.944568	−	0.343795i	−0.176600	−	0.984283i	$-0.556510\pi$
$977$	−29.5244	−	10.7460i	−0.944568	−	0.343795i	−0.767968	+	0.640488i	$0.778732\pi$
$978$	14.5877	−	13.5002i	0.466464	−	0.431689i
$979$	3.23829	−	18.3653i	0.103496	−	0.586956i
$980$	−1.99692	+	3.45877i	−0.0637893	+	0.110486i
$981$	14.3466	+	3.69283i	0.458051	+	0.117903i
$982$	−20.6075	−	35.6932i	−0.657611	−	1.13902i
$983$	−35.2050	+	12.8136i	−1.12286	+	0.408689i	−0.835697	−	0.549191i	$-0.814936\pi$
$983$	−35.2050	+	12.8136i	−1.12286	+	0.408689i	−0.287168	+	0.957880i	$0.592714\pi$
$984$	9.40426	−	0.457093i	0.299797	−	0.0145716i
$985$	−27.9372	+	23.4421i	−0.890153	+	0.746927i
$986$	6.21383	−	5.21402i	0.197889	−	0.166048i
$987$	−6.79465	+	13.2111i	−0.216276	+	0.420515i
$988$	22.2427	−	8.09569i	0.707635	−	0.257558i
$989$	14.5673	+	25.2313i	0.463212	+	0.802307i
$990$	−24.7509	−	34.6159i	−0.786636	−	1.10017i
$991$	2.52440	−	4.37239i	0.0801902	−	0.138893i	−0.823141	−	0.567837i	$-0.807781\pi$
$991$	2.52440	−	4.37239i	0.0801902	−	0.138893i	0.903332	+	0.428943i	$0.141114\pi$
$992$	1.09070	−	6.18569i	0.0346299	−	0.196396i
$993$	18.8641	+	5.84566i	0.598633	+	0.185506i
$994$	−9.49928	−	3.45745i	−0.301299	−	0.109664i
$995$	−10.8491	−	61.5284i	−0.343940	−	1.95058i
$996$	−9.48558	−	7.20447i	−0.300562	−	0.228282i
$997$	45.0534	+	37.8043i	1.42686	+	1.19728i	0.947542	+	0.319632i	$0.103559\pi$
$997$	45.0534	+	37.8043i	1.42686	+	1.19728i	0.479315	+	0.877643i	$0.340885\pi$
$998$	15.2771			0.483588
$999$	20.6476	−	3.02983i	0.653261	−	0.0958595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.43.3	✓	24
27.22	even	9	inner	378.2.u.c.211.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.43.3	✓	24	1.1	even	1	trivial
378.2.u.c.211.3	yes	24	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.217603 - 1.71833i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-3.75298 - 1.36597i) q^{5} +(-1.27121 + 1.17644i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.90530 - 0.747827i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.217603 - 1.71833i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-3.75298 - 1.36597i) q^{5} +(-1.27121 + 1.17644i) q^{6} +(-0.173648 + 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.90530 - 0.747827i) q^{9} +(1.99692 + 3.45877i) q^{10} +(3.33747 - 1.21474i) q^{11} +(1.73001 - 0.0840870i) q^{12} +(-3.57695 + 3.00141i) q^{13} +(0.766044 - 0.642788i) q^{14} +(-3.16385 + 6.15161i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.586324 - 1.01554i) q^{17} +(1.74489 + 2.44036i) q^{18} +(-2.53462 + 4.39010i) q^{19} +(0.693523 - 3.93317i) q^{20} +(1.65444 + 0.512682i) q^{21} +(-3.33747 - 1.21474i) q^{22} +(0.830334 + 4.70906i) q^{23} +(-1.37931 - 1.04761i) q^{24} +(8.38878 + 7.03902i) q^{25} +4.66937 q^{26} +(-1.91721 + 4.82952i) q^{27} -1.00000 q^{28} +(-5.29898 - 4.44637i) q^{29} +(6.37783 - 2.67872i) q^{30} +(-1.09070 - 6.18569i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-1.36108 - 5.99920i) q^{33} +(-0.203628 + 1.15483i) q^{34} +(1.99692 - 3.45877i) q^{35} +(0.231967 - 2.99102i) q^{36} +(-2.00809 - 3.47812i) q^{37} +(4.76354 - 1.73379i) q^{38} +(4.37906 + 6.79948i) q^{39} +(-3.05946 + 2.56719i) q^{40} +(-4.16419 + 3.49417i) q^{41} +(-0.937826 - 1.45619i) q^{42} +(5.72547 - 2.08390i) q^{43} +(1.77583 + 3.07583i) q^{44} +(9.88202 + 6.77515i) q^{45} +(2.39085 - 4.14108i) q^{46} +(-1.48940 + 8.44682i) q^{47} +(0.383222 + 1.68912i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-1.90158 - 10.7844i) q^{50} +(-1.87262 + 0.786511i) q^{51} +(-3.57695 - 3.00141i) q^{52} -8.45795 q^{53} +(4.57303 - 2.46727i) q^{54} -14.1848 q^{55} +(0.766044 + 0.642788i) q^{56} +(6.99208 + 5.31061i) q^{57} +(1.20118 + 6.81223i) q^{58} +(-13.4058 - 4.87933i) q^{59} +(-6.60756 - 2.04757i) q^{60} +(-0.108346 + 0.614463i) q^{61} +(-3.14056 + 5.43961i) q^{62} +(1.24097 - 2.73130i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(17.5241 - 6.37824i) q^{65} +(-2.81356 + 5.47053i) q^{66} +(4.46842 - 3.74945i) q^{67} +(0.898300 - 0.753763i) q^{68} +(8.27239 - 0.402079i) q^{69} +(-3.75298 + 1.36597i) q^{70} +(-5.05446 - 8.75458i) q^{71} +(-2.10029 + 2.14215i) q^{72} +(-3.96326 + 6.86456i) q^{73} +(-0.697403 + 3.95517i) q^{74} +(13.9208 - 12.8830i) q^{75} +(-4.76354 - 1.73379i) q^{76} +(0.616739 + 3.49770i) q^{77} +(1.01607 - 8.02351i) q^{78} +(-11.3279 - 9.50527i) q^{79} +3.99384 q^{80} +(7.88151 + 4.34532i) q^{81} +5.43596 q^{82} +(-5.26811 - 4.42047i) q^{83} +(-0.217603 + 1.71833i) q^{84} +(0.813258 + 4.61222i) q^{85} +(-5.72547 - 2.08390i) q^{86} +(-8.79339 + 8.13783i) q^{87} +(0.616739 - 3.49770i) q^{88} +(2.62533 - 4.54721i) q^{89} +(-3.21509 - 11.5421i) q^{90} +(-2.33469 - 4.04379i) q^{91} +(-4.49333 + 1.63544i) q^{92} +(-10.8664 + 0.528160i) q^{93} +(6.57046 - 5.51327i) q^{94} +(15.5092 - 13.0137i) q^{95} +(0.792183 - 1.54027i) q^{96} +(13.7402 - 5.00102i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-10.6048 + 1.03333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

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