LMFDB - Embedded newform 342.2.x.b.281.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.5
Character	$\chi$	$=$	342.281
Dual form			342.2.x.b.185.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.164003 + 1.72427i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.421448 - 1.15792i) q^{5} +(-1.23397 - 1.21545i) q^{6} +(-0.0757763 - 0.131248i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.94621 + 0.565569i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.164003 + 1.72427i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.421448 - 1.15792i) q^{5} +(-1.23397 - 1.21545i) q^{6} +(-0.0757763 - 0.131248i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.94621 + 0.565569i) q^{9} +(0.421448 + 1.15792i) q^{10} +4.18801i q^{11} +(1.72655 + 0.137905i) q^{12} +(1.93789 + 5.32431i) q^{13} +(0.142413 + 0.0518340i) q^{14} +(2.06568 + 0.536788i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.59461 + 4.38114i) q^{17} +(1.89338 - 2.32704i) q^{18} +(2.66011 - 3.45309i) q^{19} +(-1.06714 - 0.616116i) q^{20} +(0.213880 - 0.152184i) q^{21} +(-2.69200 - 3.20820i) q^{22} +(-6.17539 - 1.08889i) q^{23} +(-1.41126 + 1.00416i) q^{24} +(2.66706 + 2.23793i) q^{25} +(-4.90691 - 2.83301i) q^{26} +(-1.45838 - 4.98730i) q^{27} +(-0.142413 + 0.0518340i) q^{28} +(-1.50415 + 8.53047i) q^{29} +(-1.92745 + 0.916592i) q^{30} -9.03738i q^{31} +(0.939693 - 0.342020i) q^{32} +(-7.22126 + 0.686845i) q^{33} +(-1.59461 - 4.38114i) q^{34} +(-0.183911 + 0.0324284i) q^{35} +(0.0453738 + 2.99966i) q^{36} +3.92690i q^{37} +(0.181845 + 4.35510i) q^{38} +(-8.86272 + 4.21464i) q^{39} +(1.21351 - 0.213975i) q^{40} +(9.15707 - 7.68369i) q^{41} +(-0.0660197 + 0.254059i) q^{42} +(1.09159 + 6.19071i) q^{43} +(4.12439 + 0.727240i) q^{44} +(-0.586789 + 3.64983i) q^{45} +(5.43055 - 3.13533i) q^{46} +(-3.11369 - 0.549027i) q^{47} +(0.435623 - 1.67637i) q^{48} +(3.48852 - 6.04229i) q^{49} -3.48160 q^{50} +(-7.81579 - 2.03101i) q^{51} +(5.57993 - 0.983892i) q^{52} +(-4.00225 - 3.35828i) q^{53} +(4.32296 + 2.88306i) q^{54} +(4.84938 + 1.76503i) q^{55} +(0.0757763 - 0.131248i) q^{56} +(6.39032 + 4.02042i) q^{57} +(-4.33103 - 7.50157i) q^{58} +(1.20629 + 6.84119i) q^{59} +(0.887335 - 1.94109i) q^{60} +(-1.07052 + 0.389637i) q^{61} +(5.80912 + 6.92303i) q^{62} +(0.297483 + 0.343828i) q^{63} +(-0.500000 + 0.866025i) q^{64} +6.98184 q^{65} +(5.09031 - 5.16789i) q^{66} +(7.10819 - 8.47121i) q^{67} +(4.03768 + 2.33116i) q^{68} +(0.864755 - 10.8266i) q^{69} +(0.120039 - 0.143057i) q^{70} +(1.44787 - 1.21491i) q^{71} +(-1.96290 - 2.26870i) q^{72} +(1.66614 + 9.44917i) q^{73} +(-2.52416 - 3.00818i) q^{74} +(-3.42139 + 4.96576i) q^{75} +(-2.93871 - 3.21932i) q^{76} +(0.549669 - 0.317352i) q^{77} +(4.08012 - 8.92545i) q^{78} +(0.210570 - 0.578535i) q^{79} +(-0.792063 + 0.943944i) q^{80} +(8.36026 - 3.33257i) q^{81} +(-2.07574 + 11.7721i) q^{82} +(10.0374 - 5.79511i) q^{83} +(-0.112732 - 0.237057i) q^{84} +(4.40097 + 3.69285i) q^{85} +(-4.81552 - 4.04070i) q^{86} +(-14.9555 - 1.19454i) q^{87} +(-3.62692 + 2.09401i) q^{88} +(0.130167 - 0.738215i) q^{89} +(-1.89656 - 3.17311i) q^{90} +(0.551961 - 0.657801i) q^{91} +(-2.14469 + 5.89249i) q^{92} +(15.5829 - 1.48215i) q^{93} +(2.73813 - 1.58086i) q^{94} +(-2.87730 - 4.53549i) q^{95} +(0.743847 + 1.56419i) q^{96} +(-4.50990 - 5.37468i) q^{97} +(1.21155 + 6.87104i) q^{98} +(-2.36861 - 12.3387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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
$3$	0.164003	+	1.72427i	0.0946870	+	0.995507i
$3$	0.164003	+	1.72427i	0.0946870	+	0.995507i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.421448	−	1.15792i	0.188477	−	0.517837i	−0.809079	−	0.587699i	$-0.800034\pi$
$5$	0.421448	−	1.15792i	0.188477	−	0.517837i	0.997557	+	0.0698623i	$0.0222560\pi$
$6$	−1.23397	−	1.21545i	−0.503767	−	0.496204i
$7$	−0.0757763	−	0.131248i	−0.0286407	−	0.0496072i	0.851350	−	0.524598i	$-0.175785\pi$
$7$	−0.0757763	−	0.131248i	−0.0286407	−	0.0496072i	−0.879991	+	0.474991i	$0.842451\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.94621	+	0.565569i	−0.982069	+	0.188523i
$10$	0.421448	+	1.15792i	0.133274	+	0.366166i
$11$			4.18801i			1.26273i	0.775485	+	0.631366i	$0.217506\pi$
$11$			4.18801i			1.26273i	−0.775485	+	0.631366i	$0.782494\pi$
$12$	1.72655	+	0.137905i	0.498413	+	0.0398098i
$13$	1.93789	+	5.32431i	0.537474	+	1.47670i	0.849997	+	0.526787i	$0.176604\pi$
$13$	1.93789	+	5.32431i	0.537474	+	1.47670i	−0.312523	+	0.949910i	$0.601174\pi$
$14$	0.142413	+	0.0518340i	0.0380614	+	0.0138532i
$15$	2.06568	+	0.536788i	0.533357	+	0.138598i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.59461	+	4.38114i	−0.386749	+	1.06258i	0.581707	+	0.813398i	$0.302385\pi$
$17$	−1.59461	+	4.38114i	−0.386749	+	1.06258i	−0.968456	+	0.249185i	$0.919837\pi$
$18$	1.89338	−	2.32704i	0.446275	−	0.548488i
$19$	2.66011	−	3.45309i	0.610270	−	0.792193i
$19$	2.66011	−	3.45309i	0.610270	−	0.792193i
$20$	−1.06714	−	0.616116i	−0.238621	−	0.137768i
$21$	0.213880	−	0.152184i	0.0466724	−	0.0332092i
$22$	−2.69200	−	3.20820i	−0.573937	−	0.683991i
$23$	−6.17539	−	1.08889i	−1.28766	−	0.227049i	−0.512430	−	0.858729i	$-0.671254\pi$
$23$	−6.17539	−	1.08889i	−1.28766	−	0.227049i	−0.775229	+	0.631680i	$0.782366\pi$
$24$	−1.41126	+	1.00416i	−0.288072	+	0.204974i
$25$	2.66706	+	2.23793i	0.533413	+	0.447586i
$26$	−4.90691	−	2.83301i	−0.962324	−	0.555598i
$27$	−1.45838	−	4.98730i	−0.280665	−	0.959806i
$28$	−0.142413	+	0.0518340i	−0.0269135	+	0.00979571i
$29$	−1.50415	+	8.53047i	−0.279314	+	1.58407i	0.445602	+	0.895231i	$0.352990\pi$
$29$	−1.50415	+	8.53047i	−0.279314	+	1.58407i	−0.724916	+	0.688837i	$0.758122\pi$
$30$	−1.92745	+	0.916592i	−0.351902	+	0.167346i
$31$		−	9.03738i		−	1.62316i	−0.584240	−	0.811581i	$-0.698607\pi$
$31$		−	9.03738i		−	1.62316i	0.584240	−	0.811581i	$-0.301393\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−7.22126	+	0.686845i	−1.25706	+	0.119564i
$34$	−1.59461	−	4.38114i	−0.273473	−	0.751360i
$35$	−0.183911	+	0.0324284i	−0.0310866	+	0.00548140i
$36$	0.0453738	+	2.99966i	0.00756230	+	0.499943i
$37$			3.92690i			0.645578i	0.946471	+	0.322789i	$0.104620\pi$
$37$			3.92690i			0.645578i	−0.946471	+	0.322789i	$0.895380\pi$
$38$	0.181845	+	4.35510i	0.0294992	+	0.706491i
$39$	−8.86272	+	4.21464i	−1.41917	+	0.674883i
$40$	1.21351	−	0.213975i	0.191873	−	0.0338324i
$41$	9.15707	−	7.68369i	1.43009	−	1.19999i	0.484437	−	0.874826i	$-0.339025\pi$
$41$	9.15707	−	7.68369i	1.43009	−	1.19999i	0.945657	−	0.325165i	$-0.105420\pi$
$42$	−0.0660197	+	0.254059i	−0.0101871	+	0.0392021i
$43$	1.09159	+	6.19071i	0.166466	+	0.944074i	0.947540	+	0.319636i	$0.103561\pi$
$43$	1.09159	+	6.19071i	0.166466	+	0.944074i	−0.781075	+	0.624438i	$0.785328\pi$
$44$	4.12439	+	0.727240i	0.621774	+	0.109636i
$45$	−0.586789	+	3.64983i	−0.0874734	+	0.544084i
$46$	5.43055	−	3.13533i	0.800691	−	0.462279i
$47$	−3.11369	−	0.549027i	−0.454178	−	0.0800838i	−0.0581205	−	0.998310i	$-0.518511\pi$
$47$	−3.11369	−	0.549027i	−0.454178	−	0.0800838i	−0.396057	+	0.918226i	$0.629622\pi$
$48$	0.435623	−	1.67637i	0.0628767	−	0.241964i
$49$	3.48852	−	6.04229i	0.498359	−	0.863184i
$50$	−3.48160			−0.492373
$51$	−7.81579	−	2.03101i	−1.09443	−	0.284398i
$52$	5.57993	−	0.983892i	0.773797	−	0.136441i
$53$	−4.00225	−	3.35828i	−0.549751	−	0.461296i	0.325106	−	0.945678i	$-0.394600\pi$
$53$	−4.00225	−	3.35828i	−0.549751	−	0.461296i	−0.874857	+	0.484382i	$0.839045\pi$
$54$	4.32296	+	2.88306i	0.588280	+	0.392335i
$55$	4.84938	+	1.76503i	0.653890	+	0.237996i
$56$	0.0757763	−	0.131248i	0.0101260	−	0.0175388i
$57$	6.39032	+	4.02042i	0.846419	+	0.532518i
$58$	−4.33103	−	7.50157i	−0.568692	−	0.985004i
$59$	1.20629	+	6.84119i	0.157045	+	0.890647i	0.956892	+	0.290443i	$0.0938027\pi$
$59$	1.20629	+	6.84119i	0.157045	+	0.890647i	−0.799847	+	0.600204i	$0.795086\pi$
$60$	0.887335	−	1.94109i	0.114554	−	0.250593i
$61$	−1.07052	+	0.389637i	−0.137066	+	0.0498879i	−0.409642	−	0.912246i	$-0.634346\pi$
$61$	−1.07052	+	0.389637i	−0.137066	+	0.0498879i	0.272576	+	0.962134i	$0.412124\pi$
$62$	5.80912	+	6.92303i	0.737758	+	0.879226i
$63$	0.297483	+	0.343828i	0.0374793	+	0.0433183i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	6.98184			0.865991
$66$	5.09031	−	5.16789i	0.626574	−	0.636123i
$67$	7.10819	−	8.47121i	0.868403	−	1.03492i	−0.130650	−	0.991429i	$-0.541707\pi$
$67$	7.10819	−	8.47121i	0.868403	−	1.03492i	0.999054	−	0.0434943i	$-0.0138490\pi$
$68$	4.03768	+	2.33116i	0.489641	+	0.282694i
$69$	0.864755	−	10.8266i	0.104104	−	1.30337i
$70$	0.120039	−	0.143057i	0.0143474	−	0.0170986i
$71$	1.44787	−	1.21491i	0.171830	−	0.144183i	−0.552817	−	0.833303i	$-0.686447\pi$
$71$	1.44787	−	1.21491i	0.171830	−	0.144183i	0.724647	+	0.689120i	$0.242003\pi$
$72$	−1.96290	−	2.26870i	−0.231330	−	0.267369i
$73$	1.66614	+	9.44917i	0.195007	+	1.10594i	0.912408	+	0.409281i	$0.134220\pi$
$73$	1.66614	+	9.44917i	0.195007	+	1.10594i	−0.717401	+	0.696660i	$0.754669\pi$
$74$	−2.52416	−	3.00818i	−0.293428	−	0.349694i
$75$	−3.42139	+	4.96576i	−0.395068	+	0.573397i
$76$	−2.93871	−	3.21932i	−0.337093	−	0.369281i
$77$	0.549669	−	0.317352i	0.0626407	−	0.0361656i
$78$	4.08012	−	8.92545i	0.461982	−	1.01061i
$79$	0.210570	−	0.578535i	0.0236909	−	0.0650903i	−0.927283	−	0.374360i	$-0.877862\pi$
$79$	0.210570	−	0.578535i	0.0236909	−	0.0650903i	0.950974	+	0.309270i	$0.100085\pi$
$80$	−0.792063	+	0.943944i	−0.0885554	+	0.105536i
$81$	8.36026	−	3.33257i	0.928918	−	0.370285i
$82$	−2.07574	+	11.7721i	−0.229227	+	1.30001i
$83$	10.0374	−	5.79511i	1.10175	−	0.636096i	0.165070	−	0.986282i	$-0.447215\pi$
$83$	10.0374	−	5.79511i	1.10175	−	0.636096i	0.936680	+	0.350186i	$0.113882\pi$
$84$	−0.112732	−	0.237057i	−0.0123001	−	0.0258650i
$85$	4.40097	+	3.69285i	0.477352	+	0.400546i
$86$	−4.81552	−	4.04070i	−0.519271	−	0.435720i
$87$	−14.9555	−	1.19454i	−1.60340	−	0.128068i
$88$	−3.62692	+	2.09401i	−0.386631	+	0.223222i
$89$	0.130167	−	0.738215i	0.0137977	−	0.0782506i	−0.977131	−	0.212636i	$-0.931795\pi$
$89$	0.130167	−	0.738215i	0.0137977	−	0.0782506i	0.990929	+	0.134386i	$0.0429061\pi$
$90$	−1.89656	−	3.17311i	−0.199915	−	0.334475i
$91$	0.551961	−	0.657801i	0.0578612	−	0.0689563i
$92$	−2.14469	+	5.89249i	−0.223600	+	0.614335i
$93$	15.5829	−	1.48215i	1.61587	−	0.153692i
$94$	2.73813	−	1.58086i	0.282417	−	0.163053i
$95$	−2.87730	−	4.53549i	−0.295205	−	0.465331i
$96$	0.743847	+	1.56419i	0.0759185	+	0.159645i
$97$	−4.50990	−	5.37468i	−0.457910	−	0.545716i	0.486847	−	0.873487i	$-0.338147\pi$
$97$	−4.50990	−	5.37468i	−0.457910	−	0.545716i	−0.944757	+	0.327771i	$0.893703\pi$
$98$	1.21155	+	6.87104i	0.122385	+	0.694079i
$99$	−2.36861	−	12.3387i	−0.238054	−	1.24009i
$100$	2.66706	−	2.23793i	0.266706	−	0.223793i
$101$	2.07554	−	2.47354i	0.206524	−	0.246126i	−0.652833	−	0.757502i	$-0.726420\pi$
$101$	2.07554	−	2.47354i	0.206524	−	0.246126i	0.859357	+	0.511376i	$0.170864\pi$
$102$	7.29275	−	3.46805i	0.722090	−	0.343388i
$103$	0.313047	+	0.180738i	0.0308454	+	0.0178086i	0.515343	−	0.856984i	$-0.327664\pi$
$103$	0.313047	+	0.180738i	0.0308454	+	0.0178086i	−0.484498	+	0.874792i	$0.660998\pi$
$104$	−3.64204	+	4.34042i	−0.357132	+	0.425613i
$105$	−0.0860772	−	0.311793i	−0.00840027	−	0.0304279i
$106$	5.22456			0.507454
$107$	7.90423	−	13.6905i	0.764130	−	1.32351i	−0.176575	−	0.984287i	$-0.556502\pi$
$107$	7.90423	−	13.6905i	0.764130	−	1.32351i	0.940705	−	0.339225i	$-0.110165\pi$
$108$	−5.16477	+	0.570188i	−0.496981	+	0.0548664i
$109$	−7.48615	−	8.92164i	−0.717043	−	0.854539i	0.277297	−	0.960784i	$-0.410561\pi$
$109$	−7.48615	−	8.92164i	−0.717043	−	0.854539i	−0.994340	+	0.106246i	$0.966117\pi$
$110$	−4.84938	+	1.76503i	−0.462370	+	0.168289i
$111$	−6.77103	+	0.644022i	−0.642678	+	0.0611279i
$112$	0.0263168	+	0.149250i	0.00248671	+	0.0141028i
$113$	3.56971	+	6.18292i	0.335810	+	0.581640i	0.983640	−	0.180145i	$-0.0576566\pi$
$113$	3.56971	+	6.18292i	0.335810	+	0.581640i	−0.647830	+	0.761785i	$0.724323\pi$
$114$	−7.47955	+	1.02780i	−0.700524	+	0.0962622i
$115$	−3.86345	+	6.69170i	−0.360269	+	0.624004i
$116$	8.13968	+	2.96260i	0.755750	+	0.275071i
$117$	−8.72069	−	14.5905i	−0.806228	−	1.34889i
$118$	−5.32150	−	4.46527i	−0.489884	−	0.411061i
$119$	0.695851	−	0.122697i	0.0637886	−	0.0112476i
$120$	0.567969	+	2.05733i	0.0518483	+	0.187807i
$121$	−6.53943			−0.594494
$122$	0.569612	−	0.986596i	0.0515702	−	0.0893222i
$123$	14.7505	+	14.5291i	1.33001	+	1.31005i
$124$	−8.90008	−	1.56932i	−0.799251	−	0.140930i
$125$	9.05109	−	5.22565i	0.809554	−	0.467396i
$126$	−0.448893	−	0.0721694i	−0.0399906	−	0.00642936i
$127$	5.46567	+	0.963745i	0.485000	+	0.0855185i	0.410801	−	0.911725i	$-0.365249\pi$
$127$	5.46567	+	0.963745i	0.485000	+	0.0855185i	0.0741985	+	0.997243i	$0.476360\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−10.4954	+	2.89749i	−0.924070	+	0.255109i
$130$	−5.34840	+	4.48784i	−0.469086	+	0.393610i
$131$	1.94547	−	0.343038i	0.169976	−	0.0299714i	−0.0880122	−	0.996119i	$-0.528051\pi$
$131$	1.94547	−	0.343038i	0.169976	−	0.0299714i	0.257988	+	0.966148i	$0.416940\pi$
$132$	−0.577548	+	7.23082i	−0.0502691	+	0.629362i
$133$	−0.654785	−	0.0874721i	−0.0567771	−	0.00758479i
$134$			11.0584i			0.955298i
$135$	−6.38952	−	0.413201i	−0.549922	−	0.0355627i
$136$	−4.59149	+	0.809603i	−0.393717	+	0.0694229i
$137$	1.50058	+	4.12282i	0.128204	+	0.352236i	0.987143	−	0.159841i	$-0.0510982\pi$
$137$	1.50058	+	4.12282i	0.128204	+	0.352236i	−0.858939	+	0.512078i	$0.828876\pi$
$138$	6.29678	+	8.84953i	0.536017	+	0.753322i
$139$	−20.6044	+	7.49938i	−1.74764	+	0.636089i	−0.999619	−	0.0275851i	$-0.991218\pi$
$139$	−20.6044	+	7.49938i	−1.74764	+	0.636089i	−0.748022	+	0.663674i	$0.768996\pi$
$140$			0.186748i			0.0157831i
$141$	0.436017	−	5.45887i	0.0367193	−	0.459720i
$142$	−0.328205	+	1.86135i	−0.0275424	+	0.156201i
$143$	−22.2983	+	8.11590i	−1.86467	+	0.678686i
$144$	2.96196	+	0.476201i	0.246830	+	0.0396834i
$145$	9.24367	+	5.33683i	0.767645	+	0.443200i
$146$	−7.35015	−	6.16750i	−0.608302	−	0.510426i
$147$	10.9907	+	5.02419i	0.906494	+	0.414388i
$148$	3.86724	+	0.681899i	0.317885	+	0.0560518i
$149$	−1.26316	−	1.50537i	−0.103482	−	0.123325i	0.711818	−	0.702364i	$-0.247872\pi$
$149$	−1.26316	−	1.50537i	−0.103482	−	0.123325i	−0.815300	+	0.579039i	$0.803428\pi$
$150$	−0.570992	−	6.00322i	−0.0466213	−	0.490161i
$151$	5.98969	+	3.45815i	0.487434	+	0.281420i	0.723509	−	0.690315i	$-0.242528\pi$
$151$	5.98969	+	3.45815i	0.487434	+	0.281420i	−0.236075	+	0.971735i	$0.575861\pi$
$152$	4.32052	+	0.577173i	0.350440	+	0.0468149i
$153$	2.22020	−	13.8096i	0.179492	−	1.11644i
$154$	−0.217081	+	0.596426i	−0.0174929	+	0.0480614i
$155$	−10.4646	−	3.80879i	−0.840533	−	0.305929i
$156$	2.61162	+	9.45994i	0.209097	+	0.757401i
$157$	17.6475	+	6.42317i	1.40842	+	0.512625i	0.930667	−	0.365867i	$-0.119228\pi$
$157$	17.6475	+	6.42317i	1.40842	+	0.512625i	0.477757	+	0.878492i	$0.341450\pi$
$158$	0.210570	+	0.578535i	0.0167520	+	0.0460258i
$159$	5.13420	−	7.45172i	0.407169	−	0.590960i
$160$		−	1.23223i		−	0.0974165i
$161$	0.325033	+	0.893022i	0.0256162	+	0.0703800i
$162$	−4.26220	+	7.92677i	−0.334870	+	0.622786i
$163$	5.76968	+	9.99338i	0.451916	+	0.782742i	0.998505	−	0.0546590i	$-0.0174072\pi$
$163$	5.76968	+	9.99338i	0.451916	+	0.782742i	−0.546589	+	0.837401i	$0.684074\pi$
$164$	−5.97685	−	10.3522i	−0.466714	−	0.808372i
$165$	−2.24807	+	8.65110i	−0.175012	+	0.673487i
$166$	−3.96409	+	10.8912i	−0.307673	+	0.845324i
$167$	0.762962	−	4.32697i	0.0590398	−	0.334831i	−0.940953	−	0.338536i	$-0.890068\pi$
$167$	0.762962	−	4.32697i	0.0590398	−	0.334831i	0.999993	+	0.00370496i	$0.00117933\pi$
$168$	0.238735	+	0.109134i	0.0184188	+	0.00841984i
$169$	−14.6343	+	12.2796i	−1.12571	+	0.944585i
$170$	−5.74505			−0.440626
$171$	−5.88426	+	11.6780i	−0.449980	+	0.893038i
$172$	6.28621			0.479319
$173$	6.69296	−	5.61606i	0.508856	−	0.426981i	−0.351870	−	0.936049i	$-0.614454\pi$
$173$	6.69296	−	5.61606i	0.508856	−	0.426981i	0.860727	+	0.509068i	$0.170010\pi$
$174$	12.2244	−	8.69814i	0.926731	−	0.659404i
$175$	0.0916248	−	0.519630i	0.00692618	−	0.0392803i
$176$	1.43238	−	3.93544i	0.107970	−	0.296645i
$177$	−11.5982	+	3.20193i	−0.871775	+	0.240672i
$178$	0.374801	+	0.649175i	0.0280925	+	0.0486577i
$179$	−4.37844	−	7.58368i	−0.327260	−	0.566831i	0.654707	−	0.755883i	$-0.272792\pi$
$179$	−4.37844	−	7.58368i	−0.327260	−	0.566831i	−0.981967	+	0.189052i	$0.939459\pi$
$180$	3.49248	+	1.21166i	0.260314	+	0.0903118i
$181$	2.66248	+	7.31510i	0.197900	+	0.543727i	0.998457	−	0.0555303i	$-0.0176849\pi$
$181$	2.66248	+	7.31510i	0.197900	+	0.543727i	−0.800557	+	0.599257i	$0.795463\pi$
$182$			0.858698i			0.0636510i
$183$	−0.847408	−	1.78196i	−0.0626422	−	0.131726i
$184$	−2.14469	−	5.89249i	−0.158109	−	0.434400i
$185$	4.54703	+	1.65498i	0.334304	+	0.121677i
$186$	−10.9845	+	11.1519i	−0.805420	+	0.817695i
$187$	−18.3483	−	6.67823i	−1.34176	−	0.488360i
$188$	−1.08137	+	2.97105i	−0.0788672	+	0.216686i
$189$	−0.544064	+	0.569329i	−0.0395748	+	0.0414126i
$190$	5.11950	+	1.62489i	0.371407	+	0.117882i
$191$	−15.9194	−	9.19105i	−1.15188	−	0.665041i	−0.202539	−	0.979274i	$-0.564919\pi$
$191$	−15.9194	−	9.19105i	−1.15188	−	0.665041i	−0.949346	+	0.314233i	$0.898253\pi$
$192$	−1.57526	−	0.720104i	−0.113685	−	0.0519690i
$193$	−4.94018	−	5.88748i	−0.355602	−	0.423790i	0.558354	−	0.829603i	$-0.311433\pi$
$193$	−4.94018	−	5.88748i	−0.355602	−	0.423790i	−0.913956	+	0.405813i	$0.866989\pi$
$194$	6.90956	+	1.21834i	0.496078	+	0.0874719i
$195$	1.14504	+	12.0386i	0.0819980	+	0.862100i
$196$	−5.34472	−	4.48475i	−0.381765	−	0.320339i
$197$	4.17254	+	2.40902i	0.297281	+	0.171635i	0.641221	−	0.767356i	$-0.278428\pi$
$197$	4.17254	+	2.40902i	0.297281	+	0.171635i	−0.343940	+	0.938992i	$0.611762\pi$
$198$	9.74565	+	7.92951i	0.692593	+	0.563526i
$199$	−11.8378	+	4.30860i	−0.839159	+	0.305429i	−0.725612	−	0.688104i	$-0.758443\pi$
$199$	−11.8378	+	4.30860i	−0.839159	+	0.305429i	−0.113547	+	0.993533i	$0.536221\pi$
$200$	−0.604574	+	3.42871i	−0.0427499	+	0.242447i
$201$	15.7724	+	10.8671i	1.11250	+	0.766508i
$202$			3.22897i			0.227190i
$203$	1.23359	−	0.448990i	0.0865809	−	0.0315129i
$204$	−3.35735	+	7.34437i	−0.235062	+	0.514209i
$205$	−5.03787	−	13.8414i	−0.351860	−	0.966727i
$206$	−0.355984	+	0.0627696i	−0.0248026	+	0.00437336i
$207$	18.8098	−	0.284523i	1.30737	−	0.0197757i
$208$		−	5.66601i		−	0.392867i
$209$	14.4616	+	11.1406i	1.00033	+	0.770608i
$210$	0.266356	+	0.183518i	0.0183803	+	0.0126640i
$211$	10.3352	−	1.82237i	0.711503	−	0.125457i	0.193829	−	0.981035i	$-0.437909\pi$
$211$	10.3352	−	1.82237i	0.711503	−	0.125457i	0.517674	+	0.855578i	$0.326798\pi$
$212$	−4.00225	+	3.35828i	−0.274875	+	0.230648i
$213$	2.33228	+	2.29727i	0.159805	+	0.157406i
$214$	2.74511	+	15.5683i	0.187652	+	1.06423i
$215$	7.62839	+	1.34509i	0.520252	+	0.0917344i
$216$	3.58994	−	3.75664i	0.244264	−	0.255607i
$217$	−1.18614	+	0.684819i	−0.0805205	+	0.0464885i
$218$	11.4694	+	2.02237i	0.776809	+	0.136972i
$219$	−16.0196	+	4.42257i	−1.08251	+	0.298849i
$220$	2.58030	−	4.46921i	0.173964	−	0.301314i
$221$	−26.4167			−1.77698
$222$	4.77294	−	4.84568i	0.320339	−	0.325221i
$223$	−13.3736	+	2.35813i	−0.895564	+	0.157912i	−0.602442	−	0.798163i	$-0.705805\pi$
$223$	−13.3736	+	2.35813i	−0.895564	+	0.157912i	−0.293122	+	0.956075i	$0.594694\pi$
$224$	−0.116096	−	0.0974161i	−0.00775699	−	0.00650889i
$225$	−9.12343	−	5.08500i	−0.608228	−	0.339000i
$226$	−6.70886	−	2.44183i	−0.446267	−	0.162428i
$227$	3.96772	−	6.87229i	0.263347	−	0.456130i	−0.703782	−	0.710416i	$-0.748507\pi$
$227$	3.96772	−	6.87229i	0.263347	−	0.456130i	0.967129	+	0.254286i	$0.0818403\pi$
$228$	5.06901	−	5.59510i	0.335703	−	0.370545i
$229$	−8.53888	−	14.7898i	−0.564265	−	0.977336i	−0.997118	−	0.0758711i	$-0.975826\pi$
$229$	−8.53888	−	14.7898i	−0.564265	−	0.977336i	0.432852	−	0.901465i	$-0.357507\pi$
$230$	−1.34176	−	7.60952i	−0.0884732	−	0.501757i
$231$	0.637347	+	0.895731i	0.0419344	+	0.0589348i
$232$	−8.13968	+	2.96260i	−0.534396	+	0.194504i
$233$	−14.3087	−	17.0524i	−0.937394	−	1.11714i	−0.992932	−	0.118686i	$-0.962132\pi$
$233$	−14.3087	−	17.0524i	−0.937394	−	1.11714i	0.0555380	−	0.998457i	$-0.482313\pi$
$234$	16.0590	+	5.57142i	1.04981	+	0.364215i
$235$	−1.94799	+	3.37401i	−0.127073	+	0.220096i
$236$	6.94672			0.452193
$237$	1.03208	+	0.268197i	0.0670411	+	0.0174213i
$238$	−0.454185	+	0.541276i	−0.0294404	+	0.0350857i
$239$	−15.6579	−	9.04008i	−1.01282	−	0.584754i	−0.100807	−	0.994906i	$-0.532142\pi$
$239$	−15.6579	−	9.04008i	−1.01282	−	0.584754i	−0.912017	+	0.410152i	$0.865476\pi$
$240$	−1.75751	−	1.21092i	−0.113447	−	0.0781646i
$241$	−8.19302	+	9.76406i	−0.527759	+	0.628958i	−0.962397	−	0.271647i	$-0.912432\pi$
$241$	−8.19302	+	9.76406i	−0.527759	+	0.628958i	0.434638	+	0.900605i	$0.356876\pi$
$242$	5.00950	−	4.20347i	0.322023	−	0.270209i
$243$	7.11735	+	13.8688i	0.456578	+	0.889683i
$244$	0.197824	+	1.12192i	0.0126644	+	0.0718233i
$245$	−5.52625	−	6.58593i	−0.353059	−	0.420760i
$246$	−20.6387	−	1.64848i	−1.31588	−	0.105103i
$247$	23.5403	+	7.47151i	1.49783	+	0.475401i
$248$	7.82660	−	4.51869i	0.496990	−	0.286937i
$249$	11.6385	+	16.3568i	0.737559	+	1.03657i
$250$	−3.57456	+	9.82101i	−0.226075	+	0.621135i
$251$	2.31257	−	2.75602i	0.145968	−	0.173958i	−0.688106	−	0.725610i	$-0.741558\pi$
$251$	2.31257	−	2.75602i	0.145968	−	0.173958i	0.834075	+	0.551652i	$0.186002\pi$
$252$	0.390262	−	0.233258i	0.0245842	−	0.0146939i
$253$	4.56028	−	25.8626i	0.286702	−	1.62597i
$254$	−4.80643	+	2.77499i	−0.301582	+	0.174119i
$255$	−5.64570	+	8.19409i	−0.353547	+	0.513134i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	21.8320	+	18.3192i	1.36184	+	1.14272i	0.975409	+	0.220404i	$0.0707375\pi$
$257$	21.8320	+	18.3192i	1.36184	+	1.14272i	0.386433	+	0.922317i	$0.373707\pi$
$258$	6.17749	−	8.96593i	0.384594	−	0.558194i
$259$	0.515399	−	0.297566i	0.0320253	−	0.0184898i
$260$	1.21238	−	6.87577i	0.0751888	−	0.426417i
$261$	−0.393030	−	25.9832i	−0.0243280	−	1.60832i
$262$	−1.26981	+	1.51330i	−0.0784493	+	0.0934923i
$263$	−1.45543	+	3.99875i	−0.0897454	+	0.246574i	−0.976443	−	0.215777i	$-0.930772\pi$
$263$	−1.45543	+	3.99875i	−0.0897454	+	0.246574i	0.886697	+	0.462351i	$0.152994\pi$
$264$	−4.20545	−	5.91037i	−0.258828	−	0.363758i
$265$	−5.57536	+	3.21894i	−0.342492	+	0.197738i
$266$	0.557821	−	0.353880i	0.0342022	−	0.0216978i
$267$	1.29423	+	0.103374i	0.0792055	+	0.00632639i
$268$	−7.10819	−	8.47121i	−0.434202	−	0.517461i
$269$	−4.10283	−	23.2683i	−0.250154	−	1.41869i	−0.808212	−	0.588891i	$-0.799565\pi$
$269$	−4.10283	−	23.2683i	−0.250154	−	1.41869i	0.558058	−	0.829802i	$-0.311546\pi$
$270$	5.16026	−	3.79057i	0.314043	−	0.230687i
$271$	24.4569	−	20.5218i	1.48565	−	1.24661i	0.585770	−	0.810478i	$-0.300792\pi$
$271$	24.4569	−	20.5218i	1.48565	−	1.24661i	0.899882	−	0.436132i	$-0.143652\pi$
$272$	2.99688	−	3.57154i	0.181712	−	0.216557i
$273$	1.22475	+	0.843847i	0.0741252	+	0.0510720i
$274$	−3.79961	−	2.19371i	−0.229543	−	0.132527i
$275$	−9.37249	+	11.1697i	−0.565182	+	0.673558i
$276$	−10.5120	−	2.73164i	−0.632747	−	0.164425i
$277$	4.30762			0.258820			0.129410	−	0.991591i	$-0.458692\pi$
$277$	4.30762			0.258820			0.129410	+	0.991591i	$0.458692\pi$
$278$	10.9634	−	18.9891i	0.657539	−	1.13889i
$279$	5.11127	+	26.6260i	0.306003	+	1.59406i
$280$	−0.120039	−	0.143057i	−0.00717371	−	0.00854930i
$281$	11.2307	−	4.08763i	0.669966	−	0.243848i	0.0154330	−	0.999881i	$-0.495087\pi$
$281$	11.2307	−	4.08763i	0.669966	−	0.243848i	0.654533	+	0.756033i	$0.272865\pi$
$282$	3.17489	+	4.46201i	0.189062	+	0.265709i
$283$	0.279344	+	1.58424i	0.0166053	+	0.0941731i	0.991984	−	0.126363i	$-0.0403304\pi$
$283$	0.279344	+	1.58424i	0.0166053	+	0.0941731i	−0.975379	+	0.220536i	$0.929219\pi$
$284$	−0.945030	−	1.63684i	−0.0560772	−	0.0971286i
$285$	7.34851	−	5.70508i	0.435288	−	0.337940i
$286$	11.8647	−	20.5502i	0.701572	−	1.21516i
$287$	−1.70236	−	0.619609i	−0.100487	−	0.0365743i
$288$	−2.57509	+	1.53912i	−0.151739	+	0.0906937i
$289$	−3.62890	−	3.04501i	−0.213465	−	0.179118i
$290$	−10.5115	+	1.85346i	−0.617257	+	0.108839i
$291$	8.52777	−	8.65773i	0.499906	−	0.507525i
$292$	9.59493			0.561501
$293$	2.06692	−	3.58001i	0.120751	−	0.209146i	−0.799313	−	0.600915i	$-0.794803\pi$
$293$	2.06692	−	3.58001i	0.120751	−	0.209146i	0.920064	+	0.391768i	$0.128136\pi$
$294$	−11.6488	+	3.21590i	−0.679373	+	0.187555i
$295$	8.42993	+	1.48642i	0.490809	+	0.0865430i
$296$	−3.40080	+	1.96345i	−0.197667	+	0.114123i
$297$	20.8869	−	6.10771i	1.21198	−	0.354405i
$298$	1.93527	+	0.341240i	0.112107	+	0.0197675i
$299$	−6.16965	−	34.9898i	−0.356800	−	2.02351i
$300$	4.29620	+	4.23171i	0.248041	+	0.244318i
$301$	0.729804	−	0.612378i	0.0420652	−	0.0352969i
$302$	−6.81122	+	1.20100i	−0.391942	+	0.0691099i
$303$	4.60544	+	3.17313i	0.264575	+	0.182291i
$304$	−3.68071	+	2.33503i	−0.211103	+	0.133923i
$305$			1.40379i			0.0803806i
$306$	7.17588	+	12.0059i	0.410218	+	0.686331i
$307$	−2.00147	+	0.352914i	−0.114230	+	0.0201419i	−0.230471	−	0.973079i	$-0.574027\pi$
$307$	−2.00147	+	0.352914i	−0.114230	+	0.0201419i	0.116241	+	0.993221i	$0.462916\pi$
$308$	−0.217081	−	0.596426i	−0.0123694	−	0.0339845i
$309$	−0.260300	+	0.569419i	−0.0148079	+	0.0323931i
$310$	10.4646	−	3.80879i	0.594347	−	0.216325i
$311$			16.8651i			0.956333i	0.878269	+	0.478167i	$0.158699\pi$
$311$			16.8651i			0.956333i	−0.878269	+	0.478167i	$0.841301\pi$
$312$	−8.08135	−	5.56802i	−0.457516	−	0.315227i
$313$	−2.98139	+	16.9083i	−0.168518	+	0.955714i	0.776844	+	0.629693i	$0.216819\pi$
$313$	−2.98139	+	16.9083i	−0.168518	+	0.955714i	−0.945362	+	0.326021i	$0.894292\pi$
$314$	−17.6475	+	6.42317i	−0.995906	+	0.362480i
$315$	0.523498	−	0.199555i	0.0294958	−	0.0112437i
$316$	−0.533181	−	0.307832i	−0.0299938	−	0.0173169i
$317$	24.4070	+	20.4799i	1.37083	+	1.15027i	0.972467	+	0.233040i	$0.0748673\pi$
$317$	24.4070	+	20.4799i	1.37083	+	1.15027i	0.398367	+	0.917226i	$0.369577\pi$
$318$	0.856842	+	9.00855i	0.0480493	+	0.505174i
$319$	−35.7257	−	6.29940i	−2.00025	−	0.352699i
$320$	0.792063	+	0.943944i	0.0442777	+	0.0527681i
$321$	24.9025	+	11.3837i	1.38992	+	0.635378i
$322$	−0.823014	−	0.475167i	−0.0458648	−	0.0264800i
$323$	10.8867	+	17.1606i	0.605750	+	0.954843i
$324$	−1.83019	−	8.81195i	−0.101677	−	0.489553i
$325$	−6.74697	+	18.5371i	−0.374254	+	1.02826i
$326$	−10.8435	−	3.94670i	−0.600564	−	0.218587i
$327$	14.1556	−	14.3713i	0.782805	−	0.794735i
$328$	11.2328	+	4.08841i	0.620228	+	0.225745i
$329$	0.163885	+	0.450269i	0.00903525	+	0.0248242i
$330$	−3.83870	−	8.07216i	−0.211313	−	0.444358i
$331$		−	31.2464i		−	1.71746i	−0.512432	−	0.858728i	$-0.671255\pi$
$331$		−	31.2464i		−	1.71746i	0.512432	−	0.858728i	$-0.328745\pi$
$332$	−3.96409	−	10.8912i	−0.217558	−	0.597734i
$333$	−2.22093	−	11.5695i	−0.121706	−	0.634002i
$334$	2.19686	+	3.80508i	0.120207	+	0.208205i
$335$	−6.81324	−	11.8009i	−0.372247	−	0.644751i
$336$	−0.253031	+	0.0698547i	−0.0138040	+	0.00381089i
$337$	−8.41055	+	23.1078i	−0.458152	+	1.25876i	0.468707	+	0.883354i	$0.344720\pi$
$337$	−8.41055	+	23.1078i	−0.458152	+	1.25876i	−0.926859	+	0.375409i	$0.877502\pi$
$338$	3.31732	−	18.8135i	0.180438	−	1.02332i
$339$	−10.0756	+	7.16916i	−0.547230	+	0.389375i
$340$	4.40097	−	3.69285i	0.238676	−	0.200273i
$341$	37.8486			2.04962
$342$	−2.99887	−	12.7282i	−0.162160	−	0.688262i
$343$	−2.11825			−0.114375
$344$	−4.81552	+	4.04070i	−0.259635	+	0.217860i
$345$	−12.1719	−	5.56417i	−0.655313	−	0.299565i
$346$	−1.51717	+	8.60430i	−0.0815636	+	0.462570i
$347$	−7.27206	+	19.9798i	−0.390385	+	1.07257i	0.576442	+	0.817138i	$0.304441\pi$
$347$	−7.27206	+	19.9798i	−0.390385	+	1.07257i	−0.966826	+	0.255435i	$0.917781\pi$
$348$	−3.77339	+	14.5209i	−0.202275	+	0.778400i
$349$	14.0180	+	24.2799i	0.750367	+	1.29967i	0.947645	+	0.319326i	$0.103456\pi$
$349$	14.0180	+	24.2799i	0.750367	+	1.29967i	−0.197278	+	0.980347i	$0.563210\pi$
$350$	0.263823	+	0.456955i	0.0141019	+	0.0244253i
$351$	23.7277	−	17.4297i	1.26649	−	0.930328i
$352$	1.43238	+	3.93544i	0.0763463	+	0.209760i
$353$			9.54763i			0.508169i	0.967182	+	0.254085i	$0.0817742\pi$
$353$			9.54763i			0.508169i	−0.967182	+	0.254085i	$0.918226\pi$
$354$	6.82658	−	9.90801i	0.362829	−	0.526605i
$355$	−0.796562	−	2.18854i	−0.0422771	−	0.116155i
$356$	−0.704396	−	0.256379i	−0.0373329	−	0.0135881i
$357$	0.325685	+	1.17971i	0.0172371	+	0.0624370i
$358$	8.22878	+	2.99503i	0.434905	+	0.158292i
$359$	−1.81305	+	4.98132i	−0.0956893	+	0.262904i	−0.978298	−	0.207205i	$-0.933563\pi$
$359$	−1.81305	+	4.98132i	−0.0956893	+	0.262904i	0.882608	+	0.470109i	$0.155785\pi$
$360$	−3.45424	+	1.31674i	−0.182054	+	0.0693982i
$361$	−4.84768	−	18.3712i	−0.255141	−	0.966904i
$362$	−6.74163	−	3.89228i	−0.354332	−	0.204574i
$363$	−1.07248	−	11.2757i	−0.0562908	−	0.591823i
$364$	−0.551961	−	0.657801i	−0.0289306	−	0.0344781i
$365$	11.6436	+	2.05307i	0.609452	+	0.107463i
$366$	1.79458	+	0.820359i	0.0938039	+	0.0428809i
$367$	−1.61200	−	1.35263i	−0.0841458	−	0.0706067i	0.599744	−	0.800192i	$-0.295269\pi$
$367$	−1.61200	−	1.35263i	−0.0841458	−	0.0706067i	−0.683890	+	0.729585i	$0.739713\pi$
$368$	5.43055	+	3.13533i	0.283087	+	0.163440i
$369$	−22.6330	+	27.8167i	−1.17822	+	1.44808i
$370$	−4.54703	+	1.65498i	−0.236389	+	0.0860385i
$371$	−0.137494	+	0.779766i	−0.00713833	+	0.0404835i
$372$	1.24630	−	15.6035i	0.0646177	−	0.809004i
$373$		−	3.11847i		−	0.161468i	−0.996736	−	0.0807342i	$-0.974274\pi$
$373$		−	3.11847i		−	0.161468i	0.996736	−	0.0807342i	$-0.0257265\pi$
$374$	18.3483	−	6.67823i	0.948767	−	0.345323i
$375$	10.4948	+	14.7495i	0.541951	+	0.761661i
$376$	−1.08137	−	2.97105i	−0.0557675	−	0.153220i
$377$	−48.3337	+	8.52254i	−2.48931	+	0.438933i
$378$	0.0508198	−	0.785849i	0.00261389	−	0.0404197i
$379$			21.1889i			1.08840i	0.838955	+	0.544201i	$0.183167\pi$
$379$			21.1889i			1.08840i	−0.838955	+	0.544201i	$0.816833\pi$
$380$	−4.96622	+	2.04601i	−0.254762	+	0.104958i
$381$	−0.765371	+	9.58234i	−0.0392111	+	0.490918i
$382$	18.1028	−	3.19202i	0.926222	−	0.163318i
$383$	−1.77726	+	1.49130i	−0.0908136	+	0.0762016i	−0.687064	−	0.726597i	$-0.741101\pi$
$383$	−1.77726	+	1.49130i	−0.0908136	+	0.0762016i	0.596251	+	0.802798i	$0.296656\pi$
$384$	1.66959	−	0.460927i	0.0852011	−	0.0235216i
$385$	−0.135811	−	0.770220i	−0.00692155	−	0.0392541i
$386$	7.56880	+	1.33458i	0.385242	+	0.0679285i
$387$	−6.71732	−	17.6217i	−0.341461	−	0.895763i
$388$	−6.07617	+	3.50808i	−0.308471	+	0.178096i
$389$	17.0681	+	3.00957i	0.865389	+	0.152591i	0.588684	−	0.808364i	$-0.299646\pi$
$389$	17.0681	+	3.00957i	0.865389	+	0.152591i	0.276705	+	0.960955i	$0.410758\pi$
$390$	−8.61539	−	8.48606i	−0.436257	−	0.429708i
$391$	14.6179	−	25.3189i	0.739259	−	1.28043i
$392$	6.97703			0.352393
$393$	0.910552	+	3.29825i	0.0459313	+	0.166375i
$394$	−4.74483	+	0.836642i	−0.239041	+	0.0421494i
$395$	−0.581153	−	0.487645i	−0.0292410	−	0.0245361i
$396$	−12.5626	+	0.190026i	−0.631294	+	0.00954916i
$397$	−33.5646	−	12.2165i	−1.68456	−	0.613129i	−0.690635	−	0.723203i	$-0.742669\pi$
$397$	−33.5646	−	12.2165i	−1.68456	−	0.613129i	−0.993923	+	0.110074i	$0.964891\pi$
$398$	6.29876	−	10.9098i	0.315728	−	0.546857i
$399$	0.0434389	−	1.14337i	0.00217466	−	0.0572402i
$400$	−1.74080	−	3.01516i	−0.0870401	−	0.150758i
$401$	0.370485	+	2.10112i	0.0185011	+	0.104925i	0.992660	−	0.120939i	$-0.0385906\pi$
$401$	0.370485	+	2.10112i	0.0185011	+	0.104925i	−0.974159	+	0.225864i	$0.927479\pi$
$402$	−19.0676	+	1.81360i	−0.951006	+	0.0904543i
$403$	48.1178	−	17.5134i	2.39692	−	0.872407i
$404$	−2.07554	−	2.47354i	−0.103262	−	0.123063i
$405$	−0.335428	−	11.0850i	−0.0166675	−	0.550819i
$406$	−0.656379	+	1.13688i	−0.0325755	+	0.0564225i
$407$	−16.4459			−0.815193
$408$	−2.14899	−	7.78418i	−0.106391	−	0.385374i
$409$	0.788381	−	0.939556i	0.0389829	−	0.0464581i	−0.746201	−	0.665721i	$-0.768124\pi$
$409$	0.788381	−	0.939556i	0.0389829	−	0.0464581i	0.785184	+	0.619263i	$0.212569\pi$
$410$	12.7563	+	7.36487i	0.629990	+	0.363725i
$411$	−6.86275	+	3.26356i	−0.338515	+	0.160980i
$412$	0.232352	−	0.276906i	0.0114472	−	0.0136422i
$413$	0.806487	−	0.676723i	0.0396846	−	0.0332994i
$414$	−14.2263	+	12.3087i	−0.699183	+	0.604939i
$415$	−2.48001	−	14.0649i	−0.121739	−	0.690417i
$416$	3.64204	+	4.34042i	0.178566	+	0.212806i
$417$	−16.3101	−	34.2976i	−0.798710	−	1.67956i
$418$	−18.2392	+	0.761569i	−0.892110	+	0.0372496i
$419$	6.61242	−	3.81768i	0.323038	−	0.186506i	−0.329708	−	0.944083i	$-0.606950\pi$
$419$	6.61242	−	3.81768i	0.323038	−	0.186506i	0.652746	+	0.757577i	$0.273617\pi$
$420$	−0.322004	+	0.0306271i	−0.0157122	+	0.00149445i
$421$	−6.62893	+	18.2128i	−0.323074	+	0.887639i	0.666742	+	0.745288i	$0.267688\pi$
$421$	−6.62893	+	18.2128i	−0.323074	+	0.887639i	−0.989816	+	0.142350i	$0.954534\pi$
$422$	−6.74580	+	8.03934i	−0.328381	+	0.391349i
$423$	9.48408	−	0.143459i	0.461132	−	0.00697522i
$424$	0.907236	−	5.14519i	0.0440593	−	0.249872i
$425$	−14.0576	+	8.11617i	−0.681895	+	0.393692i
$426$	−3.26329	−	0.260649i	−0.158107	−	0.0126285i
$427$	0.132259	+	0.110979i	0.00640047	+	0.00537064i
$428$	−12.1100	−	10.1615i	−0.585358	−	0.491173i
$429$	−17.6510	−	37.1172i	−0.852197	−	1.79203i
$430$	−6.70829	+	3.87303i	−0.323503	+	0.186774i
$431$	−4.06994	+	23.0818i	−0.196042	+	1.11181i	0.714885	+	0.699242i	$0.246479\pi$
$431$	−4.06994	+	23.0818i	−0.196042	+	1.11181i	−0.910927	+	0.412568i	$0.864632\pi$
$432$	−0.335328	+	5.18532i	−0.0161335	+	0.249479i
$433$	0.835652	−	0.995891i	0.0401589	−	0.0478595i	−0.745591	−	0.666404i	$-0.767833\pi$
$433$	0.835652	−	0.995891i	0.0401589	−	0.0478595i	0.785750	+	0.618544i	$0.212277\pi$
$434$	0.468444	−	1.28704i	0.0224860	−	0.0617798i
$435$	−7.68615	+	16.8138i	−0.368523	+	0.806161i
$436$	−10.0861	+	5.82319i	−0.483035	+	0.278880i
$437$	−20.1872	+	18.4276i	−0.965686	+	0.881513i
$438$	9.42899	−	13.6851i	0.450535	−	0.653900i
$439$	−3.11911	−	3.71722i	−0.148867	−	0.177413i	0.686457	−	0.727170i	$-0.259165\pi$
$439$	−3.11911	−	3.71722i	−0.148867	−	0.177413i	−0.835325	+	0.549757i	$0.814720\pi$
$440$	0.896129	+	5.08220i	0.0427213	+	0.242284i
$441$	−6.86055	+	19.7748i	−0.326693	+	0.941658i
$442$	20.2364	−	16.9803i	0.962547	−	0.807673i
$443$	9.49902	−	11.3205i	0.451312	−	0.537853i	−0.491632	−	0.870803i	$-0.663600\pi$
$443$	9.49902	−	11.3205i	0.451312	−	0.537853i	0.942944	+	0.332950i	$0.108044\pi$
$444$	−0.541539	+	6.78000i	−0.0257003	+	0.321764i
$445$	−0.799934	−	0.461842i	−0.0379205	−	0.0218934i
$446$	8.72901	−	10.4028i	0.413330	−	0.492588i
$447$	2.38851	−	2.42491i	0.112972	−	0.114694i
$448$	0.151553			0.00716018
$449$	3.14402	−	5.44561i	0.148376	−	0.256994i	−0.782252	−	0.622963i	$-0.785929\pi$
$449$	3.14402	−	5.44561i	0.148376	−	0.256994i	0.930627	+	0.365968i	$0.119262\pi$
$450$	10.2575	−	1.96909i	0.483544	−	0.0928238i
$451$	32.1794	+	38.3499i	1.51527	+	1.80583i
$452$	6.70886	−	2.44183i	0.315558	−	0.114854i
$453$	−4.98045	+	10.8950i	−0.234002	+	0.511891i
$454$	1.37797	+	7.81488i	0.0646716	+	0.366771i
$455$	−0.529058	−	0.916355i	−0.0248026	−	0.0429594i
$456$	−0.286626	+	7.54439i	−0.0134225	+	0.353299i
$457$	−2.08364	+	3.60897i	−0.0974685	+	0.168820i	−0.910636	−	0.413209i	$-0.864408\pi$
$457$	−2.08364	+	3.60897i	−0.0974685	+	0.168820i	0.813168	+	0.582030i	$0.197741\pi$
$458$	16.0478	+	5.84094i	0.749867	+	0.272929i
$459$	24.1756	+	1.56340i	1.12842	+	0.0729734i
$460$	5.91915	+	4.96676i	0.275982	+	0.231576i
$461$	−5.55968	+	0.980321i	−0.258940	+	0.0456581i	−0.301611	−	0.953431i	$-0.597524\pi$
$461$	−5.55968	+	0.980321i	−0.258940	+	0.0456581i	0.0426710	+	0.999089i	$0.486413\pi$
$462$	−1.06400	−	0.276491i	−0.0495018	−	0.0128635i
$463$	2.57234			0.119547			0.0597734	−	0.998212i	$-0.480962\pi$
$463$	2.57234			0.119547			0.0597734	+	0.998212i	$0.480962\pi$
$464$	4.33103	−	7.50157i	0.201063	−	0.348251i
$465$	4.85116	−	18.6684i	0.224967	−	0.865724i
$466$	21.9222	+	3.86547i	1.01553	+	0.179065i
$467$	−16.9075	+	9.76155i	−0.782386	+	0.451711i	−0.837275	−	0.546782i	$-0.815853\pi$
$467$	−16.9075	+	9.76155i	−0.782386	+	0.451711i	0.0548891	+	0.998492i	$0.482519\pi$
$468$	−15.8832	+	6.05459i	−0.734200	+	0.279873i
$469$	−1.65046	−	0.291021i	−0.0762114	−	0.0134381i
$470$	−0.676528	−	3.83678i	−0.0312059	−	0.176978i
$471$	−8.18103	+	31.4825i	−0.376962	+	1.45064i
$472$	−5.32150	+	4.46527i	−0.244942	+	0.205531i
$473$	−25.9268	+	4.57159i	−1.19211	+	0.210202i
$474$	−0.963016	+	0.457960i	−0.0442328	+	0.0210348i
$475$	14.8225	−	3.25648i	0.680101	−	0.149417i
$476$		−	0.706586i		−	0.0323863i
$477$	13.6908	+	7.63065i	0.626858	+	0.349383i
$478$	17.8055	−	3.13959i	0.814404	−	0.143601i
$479$	4.50312	+	12.3722i	0.205753	+	0.565301i	0.999052	−	0.0435309i	$-0.0138607\pi$
$479$	4.50312	+	12.3722i	0.205753	+	0.565301i	−0.793299	+	0.608832i	$0.791638\pi$
$480$	2.12470	−	0.202089i	0.0969788	−	0.00922407i
$481$	−20.9080	+	7.60990i	−0.953324	+	0.346982i
$482$		−	12.7461i		−	0.580568i
$483$	−1.48650	+	0.706903i	−0.0676383	+	0.0321652i
$484$	−1.13556	+	6.44008i	−0.0516164	+	0.292731i
$485$	−8.12414	+	2.95694i	−0.368898	+	0.134268i
$486$	−14.3669	−	6.04917i	−0.651695	−	0.274396i
$487$	0.979574	+	0.565557i	0.0443887	+	0.0256278i	0.522030	−	0.852927i	$-0.325175\pi$
$487$	0.979574	+	0.565557i	0.0443887	+	0.0256278i	−0.477641	+	0.878555i	$0.658508\pi$
$488$	−0.872696	−	0.732279i	−0.0395051	−	0.0331487i
$489$	−16.2850	+	11.5874i	−0.736435	+	0.524002i
$490$	8.46671	+	1.49291i	0.382487	+	0.0674428i
$491$	−11.3503	−	13.5267i	−0.512231	−	0.610453i	0.446495	−	0.894786i	$-0.352672\pi$
$491$	−11.3503	−	13.5267i	−0.512231	−	0.610453i	−0.958725	+	0.284334i	$0.908228\pi$
$492$	16.8698	−	12.0035i	0.760548	−	0.541159i
$493$	−34.9747	−	20.1926i	−1.57518	−	0.909431i
$494$	−22.8355	+	9.40791i	−1.02742	+	0.423282i
$495$	−15.2855	−	2.45748i	−0.687033	−	0.110456i
$496$	−3.09097	+	8.49236i	−0.138788	+	0.381318i
$497$	−0.269169	−	0.0979694i	−0.0120739	−	0.00439453i
$498$	−19.4295	−	5.04896i	−0.870659	−	0.226249i
$499$	8.69831	+	3.16593i	0.389390	+	0.141726i	0.529294	−	0.848439i	$-0.322457\pi$
$499$	8.69831	+	3.16593i	0.389390	+	0.141726i	−0.139904	+	0.990165i	$0.544679\pi$
$500$	−3.57456	−	9.82101i	−0.159859	−	0.439209i
$501$	7.58599	+	0.605917i	0.338917	+	0.0270704i
$502$			3.59773i			0.160574i
$503$	−6.58007	−	18.0786i	−0.293391	−	0.806084i	−0.995565	−	0.0940790i	$-0.970009\pi$
$503$	−6.58007	−	18.0786i	−0.293391	−	0.806084i	0.702174	−	0.712005i	$-0.252213\pi$
$504$	−0.149022	+	0.429541i	−0.00663799	+	0.0191333i
$505$	−1.98942	−	3.44578i	−0.0885281	−	0.153335i
$506$	13.1308	+	22.7432i	0.583735	+	1.01106i
$507$	−23.5734	−	23.2195i	−1.04693	−	1.03122i
$508$	1.89821	−	5.21528i	0.0842193	−	0.231391i
$509$	−1.95208	+	11.0708i	−0.0865244	+	0.490704i	0.910493	+	0.413525i	$0.135703\pi$
$509$	−1.95208	+	11.0708i	−0.0865244	+	0.490704i	−0.997017	+	0.0771793i	$0.975409\pi$
$510$	−0.942204	−	9.90602i	−0.0417215	−	0.438646i
$511$	1.11393	−	0.934701i	0.0492775	−	0.0413487i
$512$	−1.00000			−0.0441942
$513$	−21.1010	−	8.23082i	−0.931633	−	0.363400i
$514$	−28.4996			−1.25707
$515$	0.341213	−	0.286311i	0.0150356	−	0.0126164i
$516$	1.03096	+	10.8391i	0.0453853	+	0.477166i
$517$	2.29933	−	13.0402i	0.101124	−	0.573505i
$518$	−0.203547	+	0.559241i	−0.00894334	+	0.0245716i
$519$	10.7813	+	10.6194i	0.473245	+	0.466141i
$520$	3.49092	+	6.04645i	0.153087	+	0.265154i
$521$	11.7751	+	20.3951i	0.515876	+	0.893524i	0.999830	+	0.0184307i	$0.00586699\pi$
$521$	11.7751	+	20.3951i	0.515876	+	0.893524i	−0.483954	+	0.875094i	$0.660800\pi$
$522$	17.0028	+	19.6517i	0.744191	+	0.860130i
$523$	3.98784	+	10.9565i	0.174376	+	0.479094i	0.995835	−	0.0911733i	$-0.0290617\pi$
$523$	3.98784	+	10.9565i	0.174376	+	0.479094i	−0.821459	+	0.570268i	$0.806839\pi$
$524$		−	1.97548i		−	0.0862992i
$525$	0.911008	+	0.0727651i	0.0397597	+	0.00317573i
$526$	−1.45543	−	3.99875i	−0.0634596	−	0.174354i
$527$	39.5941	+	14.4111i	1.72474	+	0.627756i
$528$	7.02068	+	1.82439i	0.305536	+	0.0793965i
$529$	15.3369	+	5.58216i	0.666821	+	0.242703i
$530$	2.20188	−	6.04962i	0.0956436	−	0.262779i
$531$	−7.42313	−	19.4733i	−0.322137	−	0.845070i
$532$	−0.199845	+	0.629648i	−0.00866440	+	0.0272987i
$533$	58.6557	+	33.8649i	2.54066	+	1.46685i
$534$	−1.05788	+	0.752725i	−0.0457791	+	0.0325736i
$535$	−12.5213	−	14.9223i	−0.541343	−	0.645147i
$536$	10.8904	+	1.92027i	0.470393	+	0.0829429i
$537$	12.3582	−	8.79336i	0.533297	−	0.379461i
$538$	18.0995	+	15.1873i	0.780326	+	0.654771i
$539$	25.3052	+	14.6099i	1.08997	+	0.629295i
$540$	−1.51645	+	6.22069i	−0.0652577	+	0.267696i
$541$	3.57328	−	1.30057i	0.153628	−	0.0559158i	−0.264062	−	0.964506i	$-0.585062\pi$
$541$	3.57328	−	1.30057i	0.153628	−	0.0559158i	0.417689	+	0.908590i	$0.362840\pi$
$542$	−5.54393	+	31.4412i	−0.238132	+	1.35052i
$543$	−12.1765	+	5.79052i	−0.522545	+	0.248495i
$544$			4.66232i			0.199895i
$545$	−13.4856	+	4.90834i	−0.577658	+	0.210250i
$546$	−1.48063	+	0.140829i	−0.0633650	+	0.00602692i
$547$	−14.4846	−	39.7961i	−0.619316	−	1.70156i	−0.708654	−	0.705556i	$-0.750697\pi$
$547$	−14.4846	−	39.7961i	−0.619316	−	1.70156i	0.0893380	−	0.996001i	$-0.471525\pi$
$548$	4.32076	−	0.761866i	0.184574	−	0.0325453i
$549$	2.93361	−	1.75341i	0.125203	−	0.0748335i
$550$		−	14.5810i		−	0.621736i
$551$	25.4553	+	27.8859i	1.08443	+	1.18798i
$552$	9.80850	−	4.66441i	0.417478	−	0.198530i
$553$	−0.0918880	+	0.0162023i	−0.00390747	+	0.000688993i
$554$	−3.29983	+	2.76888i	−0.140196	+	0.117639i
$555$	−2.10791	+	8.11173i	−0.0894759	+	0.344324i
$556$	3.80754	+	21.5936i	0.161476	+	0.915773i
$557$	3.13180	+	0.552221i	0.132699	+	0.0233984i	0.239603	−	0.970871i	$-0.422983\pi$
$557$	3.13180	+	0.552221i	0.132699	+	0.0233984i	−0.106904	+	0.994269i	$0.534094\pi$
$558$	−21.0303	−	17.1112i	−0.890284	−	0.724376i
$559$	−30.8459	+	17.8089i	−1.30464	+	0.753235i
$560$	0.183911	+	0.0324284i	0.00777165	+	0.00137035i
$561$	8.50589	−	32.7326i	0.359119	−	1.38197i
$562$	−5.97572	+	10.3503i	−0.252071	+	0.436599i
$563$	27.5003			1.15900			0.579501	−	0.814972i	$-0.303248\pi$
$563$	27.5003			1.15900			0.579501	+	0.814972i	$0.303248\pi$
$564$	−5.30023	−	1.37732i	−0.223180	−	0.0579955i
$565$	8.66377	−	1.52766i	0.364488	−	0.0642690i
$566$	−1.23232	−	1.03404i	−0.0517981	−	0.0434638i
$567$	−1.07090	−	0.844741i	−0.0449737	−	0.0354758i
$568$	1.77607	+	0.646438i	0.0745224	+	0.0271240i
$569$	−7.69616	+	13.3301i	−0.322640	+	0.558829i	−0.981032	−	0.193846i	$-0.937904\pi$
$569$	−7.69616	+	13.3301i	−0.322640	+	0.558829i	0.658392	+	0.752675i	$0.271237\pi$
$570$	−1.96213	+	9.09387i	−0.0821847	+	0.380900i
$571$	10.1606	+	17.5988i	0.425210	+	0.736485i	0.996440	−	0.0843049i	$-0.0268670\pi$
$571$	10.1606	+	17.5988i	0.425210	+	0.736485i	−0.571230	+	0.820790i	$0.693534\pi$
$572$	4.12055	+	23.3688i	0.172289	+	0.977099i
$573$	13.2370	−	28.9566i	0.552985	−	1.20968i
$574$	1.70236	−	0.619609i	0.0710552	−	0.0258620i
$575$	−14.0333	−	16.7242i	−0.585230	−	0.697449i
$576$	0.983306	−	2.83427i	0.0409711	−	0.118095i
$577$	1.95568	−	3.38733i	0.0814158	−	0.141016i	−0.822442	−	0.568848i	$-0.807389\pi$
$577$	1.95568	−	3.38733i	0.0814158	−	0.141016i	0.903858	+	0.427832i	$0.140722\pi$
$578$	4.73719			0.197041
$579$	9.34140	−	9.48376i	0.388215	−	0.394132i
$580$	6.86090	−	8.17650i	0.284883	−	0.339511i
$581$	−1.52120	−	0.878263i	−0.0631099	−	0.0364365i
$582$	−0.967563	+	12.1138i	−0.0401068	+	0.502131i
$583$	14.0645	−	16.7615i	0.582493	−	0.694188i
$584$	−7.35015	+	6.16750i	−0.304151	+	0.255213i
$585$	−20.5699	+	3.94871i	−0.850462	+	0.163259i
$586$	0.717834	+	4.07104i	0.0296534	+	0.168173i
$587$	−11.0377	−	13.1543i	−0.455576	−	0.542935i	0.488542	−	0.872540i	$-0.337529\pi$
$587$	−11.0377	−	13.1543i	−0.455576	−	0.542935i	−0.944119	+	0.329605i	$0.893084\pi$
$588$	6.85637	−	9.95124i	0.282752	−	0.410382i
$589$	−31.2069	−	24.0404i	−1.28586	−	0.990567i
$590$	−7.41316	+	4.27999i	−0.305195	+	0.176204i
$591$	−3.46948	+	7.58966i	−0.142715	+	0.312197i
$592$	1.34308	−	3.69008i	0.0552002	−	0.151661i
$593$	−10.5095	+	12.5247i	−0.431573	+	0.514329i	−0.937376	−	0.348320i	$-0.886752\pi$
$593$	−10.5095	+	12.5247i	−0.431573	+	0.514329i	0.505802	+	0.862649i	$0.331197\pi$
$594$	−12.0743	+	18.1046i	−0.495414	+	0.742840i
$595$	0.151192	−	0.857450i	0.00619825	−	0.0351520i
$596$	−1.70185	+	0.982563i	−0.0697104	+	0.0402473i
$597$	−9.37062	−	19.7049i	−0.383514	−	0.806468i
$598$	27.2173	+	22.8380i	1.11300	+	0.933915i
$599$	13.6436	+	11.4483i	0.557462	+	0.467766i	0.877459	−	0.479652i	$-0.159237\pi$
$599$	13.6436	+	11.4483i	0.557462	+	0.467766i	−0.319996	+	0.947419i	$0.603682\pi$
$600$	−6.01117	−	0.480131i	−0.245405	−	0.0196013i
$601$	26.7434	−	15.4403i	1.09089	−	0.629824i	0.157074	−	0.987587i	$-0.449794\pi$
$601$	26.7434	−	15.4403i	1.09089	−	0.629824i	0.933812	+	0.357763i	$0.116460\pi$
$602$	−0.165433	+	0.938218i	−0.00674255	+	0.0382389i
$603$	−16.1511	+	28.9781i	−0.657725	+	1.18008i
$604$	4.44571	−	5.29819i	0.180893	−	0.215580i
$605$	−2.75603	+	7.57214i	−0.112049	+	0.307851i
$606$	−5.56762	+	0.529560i	−0.226169	+	0.0215119i
$607$	2.03226	−	1.17332i	0.0824867	−	0.0476237i	−0.458189	−	0.888855i	$-0.651502\pi$
$607$	2.03226	−	1.17332i	0.0824867	−	0.0476237i	0.540676	+	0.841231i	$0.318168\pi$
$608$	1.31865	−	4.15465i	0.0534785	−	0.168493i
$609$	0.976491	+	2.05340i	0.0395694	+	0.0832081i
$610$	−0.902337	−	1.07536i	−0.0365346	−	0.0435402i
$611$	−3.11079	−	17.6422i	−0.125849	−	0.713726i
$612$	−13.2143	−	4.58448i	−0.534156	−	0.185317i
$613$	−20.2198	+	16.9664i	−0.816670	+	0.685268i	−0.952190	−	0.305507i	$-0.901174\pi$
$613$	−20.2198	+	16.9664i	−0.816670	+	0.685268i	0.135520	+	0.990775i	$0.456730\pi$
$614$	1.30637	−	1.55687i	0.0527208	−	0.0628302i
$615$	23.0401	−	10.9567i	0.929067	−	0.441815i
$616$	0.549669	+	0.317352i	0.0221468	+	0.0127865i
$617$	−20.0298	+	23.8706i	−0.806371	+	0.960995i	−0.999798	−	0.0201193i	$-0.993595\pi$
$617$	−20.0298	+	23.8706i	−0.806371	+	0.960995i	0.193427	+	0.981115i	$0.438040\pi$
$618$	−0.166614	−	0.603518i	−0.00670219	−	0.0242770i
$619$	37.2821			1.49849			0.749247	−	0.662290i	$-0.230415\pi$
$619$	37.2821			1.49849			0.749247	+	0.662290i	$0.230415\pi$
$620$	−5.56807	+	9.64419i	−0.223619	+	0.387320i
$621$	3.57546	+	32.3865i	0.143478	+	1.29963i
$622$	−10.8407	−	12.9194i	−0.434672	−	0.518022i
$623$	−0.106753	+	0.0388549i	−0.00427697	+	0.00155669i
$624$	9.76973	−	0.929241i	0.391102	−	0.0371994i
$625$	0.786556	+	4.46078i	0.0314623	+	0.178431i
$626$	−8.58458	−	14.8689i	−0.343109	−	0.594282i
$627$	−16.8376	+	26.7627i	−0.672428	+	1.06880i
$628$	9.39004	−	16.2640i	0.374703	−	0.649005i
$629$	−17.2043	−	6.26186i	−0.685981	−	0.249677i
$630$	−0.272752	+	0.489366i	−0.0108667	+	0.0194968i
$631$	−27.1796	−	22.8064i	−1.08200	−	0.907908i	−0.0859172	−	0.996302i	$-0.527382\pi$
$631$	−27.1796	−	22.8064i	−1.08200	−	0.907908i	−0.996086	+	0.0883941i	$0.971826\pi$
$632$	0.606311	−	0.106909i	0.0241178	−	0.00425261i
$633$	4.83725	+	17.5217i	0.192263	+	0.696427i
$634$	−31.8611			−1.26537
$635$	3.41943	−	5.92263i	0.135696	−	0.235033i
$636$	−6.44696	−	6.35018i	−0.255639	−	0.251801i
$637$	38.9314	+	6.86465i	1.54252	+	0.271987i
$638$	31.4166	−	18.1384i	1.24380	−	0.718106i
$639$	−3.57861	+	4.39824i	−0.141568	+	0.173992i
$640$	−1.21351	−	0.213975i	−0.0479682	−	0.00845810i
$641$	−6.63111	−	37.6069i	−0.261913	−	1.48538i	−0.777683	−	0.628656i	$-0.783605\pi$
$641$	−6.63111	−	37.6069i	−0.261913	−	1.48538i	0.515770	−	0.856727i	$-0.327506\pi$
$642$	−26.3937	+	7.28655i	−1.04168	+	0.287577i
$643$	−33.2793	+	27.9247i	−1.31241	+	1.10124i	−0.324552	+	0.945868i	$0.605213\pi$
$643$	−33.2793	+	27.9247i	−1.31241	+	1.10124i	−0.987856	+	0.155373i	$0.950342\pi$
$644$	0.935897	−	0.165024i	0.0368795	−	0.00650285i
$645$	−1.06822	+	13.3740i	−0.0420612	+	0.526600i
$646$	−19.3703	−	6.14799i	−0.762115	−	0.241889i
$647$			28.4430i			1.11821i	0.829097	+	0.559104i	$0.188855\pi$
$647$			28.4430i			1.11821i	−0.829097	+	0.559104i	$0.811145\pi$
$648$	7.06622	+	5.57392i	0.277587	+	0.218964i
$649$	−28.6510	+	5.05194i	−1.12465	+	0.198306i
$650$	−6.74697	−	18.5371i	−0.264638	−	0.727086i
$651$	−1.37534	−	1.93291i	−0.0539039	−	0.0757569i
$652$	10.8435	−	3.94670i	0.424663	−	0.154565i
$653$		−	32.2060i		−	1.26032i	−0.776467	−	0.630158i	$-0.782990\pi$
$653$		−	32.2060i		−	1.26032i	0.776467	−	0.630158i	$-0.217010\pi$
$654$	−1.60609	+	20.1081i	−0.0628033	+	0.786288i
$655$	0.422703	−	2.39727i	0.0165164	−	0.0936689i
$656$	−11.2328	+	4.08841i	−0.438567	+	0.159626i
$657$	−10.2530	−	26.8969i	−0.400006	−	1.04935i
$658$	−0.414971	−	0.239583i	−0.0161772	−	0.00933993i
$659$	−25.4267	−	21.3355i	−0.990484	−	0.831115i	−0.00484638	−	0.999988i	$-0.501543\pi$
$659$	−25.4267	−	21.3355i	−0.990484	−	0.831115i	−0.985638	+	0.168873i	$0.945987\pi$
$660$	8.12930	+	3.71617i	0.316432	+	0.144652i
$661$	27.9136	+	4.92192i	1.08571	+	0.191440i	0.687740	−	0.725957i	$-0.258603\pi$
$661$	27.9136	+	4.92192i	1.08571	+	0.191440i	0.397972	+	0.917397i	$0.369714\pi$
$662$	20.0848	+	23.9361i	0.780617	+	0.930303i
$663$	−4.33241	−	45.5496i	−0.168257	−	1.76900i
$664$	10.0374	+	5.79511i	0.389527	+	0.224894i
$665$	−0.377244	+	0.721324i	−0.0146289	+	0.0279717i
$666$	9.13804	+	7.43513i	0.354092	+	0.288105i
$667$	18.5775	−	51.0411i	0.719322	−	1.97632i
$668$	−4.12875	−	1.50274i	−0.159746	−	0.0581428i
$669$	−6.25936	−	22.6730i	−0.242001	−	0.876588i
$670$	12.8047	+	4.66053i	0.494689	+	0.180052i
$671$	−1.63181	−	4.48335i	−0.0629951	−	0.173078i
$672$	0.148931	−	0.216157i	0.00574516	−	0.00833844i
$673$		−	46.3630i		−	1.78716i	−0.448902	−	0.893581i	$-0.648185\pi$
$673$		−	46.3630i		−	1.78716i	0.448902	−	0.893581i	$-0.351815\pi$
$674$	−8.41055	−	23.1078i	−0.323962	−	0.890079i
$675$	7.27164	−	16.5652i	0.279886	−	0.637595i
$676$	9.55184	+	16.5443i	0.367378	+	0.636318i
$677$	−15.8097	−	27.3832i	−0.607617	−	1.05242i	−0.991632	−	0.129096i	$-0.958792\pi$
$677$	−15.8097	−	27.3832i	−0.607617	−	1.05242i	0.384015	−	0.923327i	$-0.374541\pi$
$678$	3.11009	−	11.9684i	0.119442	−	0.459642i
$679$	−0.363675	+	0.999190i	−0.0139566	+	0.0383454i
$680$	−0.997618	+	5.65777i	−0.0382569	+	0.216966i
$681$	12.5004	+	5.71434i	0.479016	+	0.218974i
$682$	−28.9937	+	24.3286i	−1.11023	+	0.931592i
$683$	−9.45932			−0.361951			−0.180975	−	0.983488i	$-0.557925\pi$
$683$	−9.45932			−0.361951			−0.180975	+	0.983488i	$0.557925\pi$
$684$	10.4788	+	7.82272i	0.400666	+	0.299109i
$685$	5.40631			0.206565
$686$	1.62268	−	1.36159i	0.0619541	−	0.0519857i
$687$	24.1012	−	17.1489i	0.919516	−	0.654271i
$688$	1.09159	−	6.19071i	0.0416164	−	0.236019i
$689$	10.1246	−	27.8172i	0.385717	−	1.05975i
$690$	12.9008	−	3.56154i	0.491125	−	0.135586i
$691$	19.7618	+	34.2285i	0.751775	+	1.30211i	0.946962	+	0.321346i	$0.104135\pi$
$691$	19.7618	+	34.2285i	0.751775	+	1.30211i	−0.195187	+	0.980766i	$0.562531\pi$
$692$	−4.36852	−	7.56650i	−0.166066	−	0.287635i
$693$	−1.43996	+	1.24586i	−0.0546994	+	0.0473263i
$694$	−7.27206	−	19.9798i	−0.276044	−	0.758424i
$695$			27.0188i			1.02488i
$696$	−6.44325	−	13.5491i	−0.244231	−	0.513578i
$697$	19.0614	+	52.3709i	0.722004	+	1.98369i
$698$	−26.3452	−	9.58888i	−0.997182	−	0.362944i
$699$	27.0563	−	27.4687i	1.02336	−	1.03896i
$700$	−0.495825	−	0.180466i	−0.0187404	−	0.00682096i
$701$	7.11248	−	19.5414i	0.268634	−	0.738067i	−0.729880	−	0.683576i	$-0.760424\pi$
$701$	7.11248	−	19.5414i	0.268634	−	0.738067i	0.998514	−	0.0544916i	$-0.0173538\pi$
$702$	−6.97290	+	28.6038i	−0.263175	+	1.07958i
$703$	13.5599	+	10.4460i	0.511423	+	0.393977i
$704$	−3.62692	−	2.09401i	−0.136695	−	0.0789208i
$705$	−6.13718	−	2.80550i	−0.231139	−	0.105661i
$706$	−6.13710	−	7.31391i	−0.230973	−	0.275263i
$707$	−0.481925	−	0.0849763i	−0.0181246	−	0.00319586i
$708$	1.13928	+	11.9780i	0.0428168	+	0.450162i
$709$	−32.8925	−	27.6001i	−1.23530	−	1.03654i	−0.997876	−	0.0651374i	$-0.979251\pi$
$709$	−32.8925	−	27.6001i	−1.23530	−	1.03654i	−0.237427	−	0.971405i	$-0.576304\pi$
$710$	2.01697	+	1.16450i	0.0756954	+	0.0437027i
$711$	−0.293180	+	1.82358i	−0.0109951	+	0.0683894i
$712$	0.704396	−	0.256379i	0.0263984	−	0.00960822i
$713$	−9.84070	+	55.8094i	−0.368537	+	2.09008i
$714$	−1.00779	−	0.694366i	−0.0377157	−	0.0259860i
$715$			29.2400i			1.09351i
$716$	−8.22878	+	2.99503i	−0.307524	+	0.111930i
$717$	13.0196	−	28.4810i	0.486226	−	1.06364i
$718$	−1.81305	−	4.98132i	−0.0676625	−	0.185901i
$719$	2.15331	−	0.379686i	0.0803048	−	0.0141599i	−0.133351	−	0.991069i	$-0.542574\pi$
$719$	2.15331	−	0.379686i	0.0803048	−	0.0141599i	0.213656	+	0.976909i	$0.431463\pi$
$720$	1.79972	−	3.22902i	0.0670715	−	0.120339i
$721$		−	0.0547825i		−	0.00204021i
$722$	15.5223	+	10.9571i	0.577680	+	0.407781i
$723$	−18.1795	−	12.5256i	−0.676104	−	0.465833i
$724$	7.66630	−	1.35178i	0.284916	−	0.0502383i
$725$	−23.1023	+	19.3851i	−0.857997	+	0.719945i
$726$	8.06948	+	7.94834i	0.299486	+	0.294991i
$727$	1.10262	+	6.25329i	0.0408940	+	0.231922i	0.998404	−	0.0564793i	$-0.0179875\pi$
$727$	1.10262	+	6.25329i	0.0408940	+	0.231922i	−0.957510	+	0.288401i	$0.906876\pi$
$728$	0.845653	+	0.149111i	0.0313420	+	0.00552644i
$729$	−22.7463	+	14.5467i	−0.842454	+	0.538768i
$730$	−10.2392	+	5.91159i	−0.378969	+	0.218798i
$731$	−28.8630	−	5.08933i	−1.06754	−	0.188236i
$732$	−1.90204	+	0.525099i	−0.0703015	+	0.0194082i
$733$	22.0942	−	38.2683i	0.816068	−	1.41347i	−0.0924913	−	0.995713i	$-0.529483\pi$
$733$	22.0942	−	38.2683i	0.816068	−	1.41347i	0.908559	−	0.417757i	$-0.137184\pi$
$734$	2.10432			0.0776718
$735$	10.4496	−	10.6089i	0.385439	−	0.391313i
$736$	−6.17539	+	1.08889i	−0.227628	+	0.0401370i
$737$	35.4775	+	29.7692i	1.30683	+	1.09656i
$738$	−0.542385	−	35.8570i	−0.0199655	−	1.31991i
$739$	2.11001	+	0.767982i	0.0776181	+	0.0282507i	0.380537	−	0.924766i	$-0.375739\pi$
$739$	2.11001	+	0.767982i	0.0776181	+	0.0282507i	−0.302919	+	0.953016i	$0.597961\pi$
$740$	2.41943	−	4.19057i	0.0889399	−	0.154048i
$741$	−9.02222	+	41.8152i	−0.331440	+	1.53612i
$742$	−0.395898	−	0.685715i	−0.0145339	−	0.0251734i
$743$	−5.63425	−	31.9534i	−0.206701	−	1.17226i	−0.894741	−	0.446585i	$-0.852640\pi$
$743$	−5.63425	−	31.9534i	−0.206701	−	1.17226i	0.688041	−	0.725672i	$-0.258471\pi$
$744$	9.07502	+	12.7541i	0.332706	+	0.467588i
$745$	−2.27546	+	0.828198i	−0.0833663	+	0.0303428i
$746$	2.00452	+	2.38889i	0.0733905	+	0.0874634i
$747$	−26.2948	+	22.7504i	−0.962075	+	0.832395i
$748$	−9.76291	+	16.9099i	−0.356968	+	0.618286i
$749$	−2.39581			−0.0875410
$750$	−17.5203	−	4.55282i	−0.639751	−	0.166246i
$751$	18.5335	−	22.0874i	0.676299	−	0.805981i	−0.313328	−	0.949645i	$-0.601444\pi$
$751$	18.5335	−	22.0874i	0.676299	−	0.805981i	0.989627	+	0.143664i	$0.0458884\pi$
$752$	2.73813	+	1.58086i	0.0998493	+	0.0576480i
$753$	5.13139	+	3.53551i	0.186998	+	0.128841i
$754$	31.5476	−	37.5970i	1.14890	−	1.36920i
$755$	6.52860	−	5.47814i	0.237600	−	0.199370i
$756$	0.466204	+	0.634661i	0.0169557	+	0.0230824i
$757$	−6.92406	−	39.2683i	−0.251659	−	1.42723i	−0.804505	−	0.593946i	$-0.797569\pi$
$757$	−6.92406	−	39.2683i	−0.251659	−	1.42723i	0.552846	−	0.833284i	$-0.313542\pi$
$758$	−13.6200	−	16.2317i	−0.494700	−	0.589561i
$759$	45.3420	+	3.62161i	1.64581	+	0.131456i
$760$	2.48919	−	4.75956i	0.0902926	−	0.172647i
$761$	23.2754	−	13.4381i	0.843734	−	0.487130i	−0.0147980	−	0.999891i	$-0.504711\pi$
$761$	23.2754	−	13.4381i	0.843734	−	0.487130i	0.858532	+	0.512761i	$0.171377\pi$
$762$	−5.57310	−	7.83247i	−0.201892	−	0.283740i
$763$	−0.603679	+	1.65859i	−0.0218546	+	0.0600451i
$764$	−11.8158	+	14.0815i	−0.427480	+	0.509451i
$765$	−15.0547	−	8.39084i	−0.544304	−	0.303372i
$766$	0.402871	−	2.28480i	0.0145563	−	0.0825531i
$767$	−34.0869	+	19.6801i	−1.23081	+	0.710608i
$768$	−0.982705	+	1.42629i	−0.0354603	+	0.0514666i
$769$	14.5643	+	12.2209i	0.525203	+	0.440698i	0.866441	−	0.499279i	$-0.166402\pi$
$769$	14.5643	+	12.2209i	0.525203	+	0.440698i	−0.341238	+	0.939977i	$0.610846\pi$
$770$	0.599125	+	0.502725i	0.0215910	+	0.0181170i
$771$	−28.0067	+	40.6486i	−1.00864	+	1.46392i
$772$	−6.65589	+	3.84278i	−0.239551	+	0.138305i
$773$	8.41729	−	47.7368i	0.302749	−	1.71698i	−0.331166	−	0.943572i	$-0.607442\pi$
$773$	8.41729	−	47.7368i	0.302749	−	1.71698i	0.633915	−	0.773403i	$-0.281447\pi$
$774$	16.4728	+	9.18122i	0.592103	+	0.330012i
$775$	20.2250	−	24.1033i	0.726505	−	0.865815i
$776$	2.39967	−	6.59303i	0.0861430	−	0.236676i
$777$	0.597610	+	0.839885i	0.0214392	+	0.0301307i
$778$	−15.0095	+	8.66572i	−0.538115	+	0.310681i
$779$	−2.17372	−	52.0596i	−0.0778817	−	1.86523i
$780$	12.0545	+	0.962831i	0.431621	+	0.0344749i
$781$	5.08804	+	6.06369i	0.182064	+	0.216976i
$782$	5.07674	+	28.7916i	0.181544	+	1.02959i
$783$	44.7376	−	4.93901i	1.59879	−	0.176506i
$784$	−5.34472	+	4.48475i	−0.190883	+	0.160170i
$785$	14.8750	−	17.7274i	0.530912	−	0.632716i
$786$	−2.81760	−	1.94131i	−0.100500	−	0.0692444i
$787$	18.3251	+	10.5800i	0.653221	+	0.377137i	0.789689	−	0.613507i	$-0.210242\pi$
$787$	18.3251	+	10.5800i	0.653221	+	0.377137i	−0.136468	+	0.990644i	$0.543575\pi$
$788$	3.09697	−	3.69083i	0.110325	−	0.131480i
$789$	−7.13362	−	1.85374i	−0.253963	−	0.0659949i
$790$	0.758641			0.0269912
$791$	0.540999	−	0.937038i	0.0192357	−	0.0333172i
$792$	9.50136	−	8.22065i	0.337616	−	0.292108i
$793$	−4.14910	−	4.94470i	−0.147339	−	0.175592i
$794$	33.5646	−	12.2165i	1.19116	−	0.433548i
$795$	−6.46468	−	9.08551i	−0.229279	−	0.322230i
$796$	2.18754	+	12.4061i	0.0775351	+	0.439724i
$797$	−3.34795	−	5.79881i	−0.118590	−	0.205404i	0.800619	−	0.599174i	$-0.204504\pi$
$797$	−3.34795	−	5.79881i	−0.118590	−	0.205404i	−0.919209	+	0.393769i	$0.871171\pi$
$798$	0.701669	+	0.903796i	0.0248388	+	0.0319940i
$799$	7.37047	−	12.7660i	0.260748	−	0.451630i
$800$	3.27164	+	1.19078i	0.115670	+	0.0421004i
$801$	0.0340123	+	2.24855i	0.00120177	+	0.0794486i
$802$	−1.63438	−	1.37141i	−0.0577121	−	0.0484262i
$803$	−39.5732	+	6.97782i	−1.39651	+	0.246242i
$804$	13.4409	−	13.6457i	0.474023	−	0.481248i
$805$	1.17103			0.0412735
$806$	−25.6029	+	44.3456i	−0.901825	+	1.56201i
$807$	39.4479	−	10.8904i	1.38863	−	0.383362i
$808$	3.17992	+	0.560705i	0.111869	+	0.0197255i
$809$	−0.239238	+	0.138124i	−0.00841116	+	0.00485619i	−0.504200	−	0.863587i	$-0.668212\pi$
$809$	−0.239238	+	0.138124i	−0.00841116	+	0.00485619i	0.495789	+	0.868443i	$0.334879\pi$
$810$	7.38226	+	8.27600i	0.259386	+	0.290789i
$811$	−15.6274	−	2.75553i	−0.548752	−	0.0967597i	−0.107603	−	0.994194i	$-0.534318\pi$
$811$	−15.6274	−	2.75553i	−0.548752	−	0.0967597i	−0.441148	+	0.897434i	$0.645429\pi$
$812$	−0.227958	−	1.29281i	−0.00799976	−	0.0453689i
$813$	39.3961	+	38.8047i	1.38168	+	1.36094i
$814$	12.5983	−	10.5712i	0.441570	−	0.370521i
$815$	14.0032	−	2.46913i	0.490509	−	0.0864900i
$816$	6.64979	+	4.58168i	0.232789	+	0.160391i
$817$	24.2808	+	12.6986i	0.849479	+	0.444267i
$818$			1.22650i			0.0428837i
$819$	−1.25416	+	2.25019i	−0.0438238	+	0.0786280i
$820$	−14.5060	+	2.55779i	−0.506570	+	0.0893220i
$821$	−11.6506	−	32.0098i	−0.406609	−	1.11715i	−0.958961	−	0.283538i	$-0.908492\pi$
$821$	−11.6506	−	32.0098i	−0.406609	−	1.11715i	0.552352	−	0.833611i	$-0.313730\pi$
$822$	3.15939	−	6.91133i	0.110197	−	0.241060i
$823$	−0.805170	+	0.293058i	−0.0280665	+	0.0102154i	−0.356015	−	0.934480i	$-0.615865\pi$
$823$	−0.805170	+	0.293058i	−0.0280665	+	0.0102154i	0.327949	+	0.944696i	$0.393643\pi$
$824$			0.361476i			0.0125926i
$825$	−20.7967	−	14.3288i	−0.724047	−	0.498866i
$826$	−0.182816	+	1.03680i	−0.00636097	+	0.0360749i
$827$	25.1865	−	9.16712i	0.875819	−	0.318772i	0.135298	−	0.990805i	$-0.456801\pi$
$827$	25.1865	−	9.16712i	0.875819	−	0.318772i	0.740521	+	0.672033i	$0.234579\pi$
$828$	2.98609	−	18.5735i	0.103774	−	0.645473i
$829$	−11.5202	−	6.65117i	−0.400112	−	0.231005i	0.286420	−	0.958104i	$-0.407535\pi$
$829$	−11.5202	−	6.65117i	−0.400112	−	0.231005i	−0.686532	+	0.727099i	$0.740868\pi$
$830$	10.9405	+	9.18018i	0.379751	+	0.318649i
$831$	0.706461	+	7.42749i	0.0245068	+	0.257657i
$832$	−5.57993	−	0.983892i	−0.193449	−	0.0341103i
$833$	20.9093	+	24.9188i	0.724465	+	0.863384i
$834$	34.5403	+	15.7895i	1.19603	+	0.546746i
$835$	−4.68874	−	2.70704i	−0.162260	−	0.0936811i
$836$	13.4825	−	12.3073i	0.466303	−	0.425658i
$837$	−45.0721	+	13.1799i	−1.55792	+	0.455565i
$838$	−2.61145	+	7.17489i	−0.0902110	+	0.247853i
$839$	15.3043	+	5.57032i	0.528364	+	0.192309i	0.592408	−	0.805638i	$-0.298177\pi$
$839$	15.3043	+	5.57032i	0.528364	+	0.192309i	−0.0640435	+	0.997947i	$0.520400\pi$
$840$	0.226982	−	0.230442i	0.00783163	−	0.00795099i
$841$	−43.2553	−	15.7436i	−1.49156	−	0.542884i
$842$	−6.62893	−	18.2128i	−0.228448	−	0.627655i
$843$	8.89004	+	18.6943i	0.306189	+	0.643867i
$844$		−	10.4946i		−	0.361239i
$845$	8.05121	+	22.1205i	0.276970	+	0.760969i
$846$	−7.17301	+	6.20614i	−0.246613	+	0.213372i
$847$	0.495534	+	0.858290i	0.0170267	+	0.0294912i
$848$	2.61228	+	4.52460i	0.0897061	+	0.155376i
$849$	−2.68584	+	0.741482i	−0.0921776	+	0.0254476i
$850$	5.55179	−	15.2534i	0.190425	−	0.523188i
$851$	4.27596	−	24.2502i	0.146578	−	0.831284i
$852$	2.66736	−	1.89793i	0.0913824	−	0.0650221i
$853$	−29.0217	+	24.3521i	−0.993685	+	0.833801i	−0.986097	−	0.166171i	$-0.946860\pi$
$853$	−29.0217	+	24.3521i	−0.993685	+	0.833801i	−0.00758781	+	0.999971i	$0.502415\pi$
$854$	−0.172652			−0.00590804
$855$	11.0423	+	11.7352i	0.377637	+	0.401334i
$856$	15.8085			0.540322
$857$	23.6263	−	19.8248i	0.807059	−	0.677203i	−0.142845	−	0.989745i	$-0.545625\pi$
$857$	23.6263	−	19.8248i	0.807059	−	0.677203i	0.949904	+	0.312542i	$0.101181\pi$
$858$	37.3799	+	17.0876i	1.27613	+	0.583360i
$859$	−3.46278	+	19.6384i	−0.118149	+	0.670054i	0.866994	+	0.498318i	$0.166049\pi$
$859$	−3.46278	+	19.6384i	−0.118149	+	0.670054i	−0.985143	+	0.171736i	$0.945062\pi$
$860$	2.64931	−	7.27892i	0.0903408	−	0.248209i
$861$	0.789180	−	3.03694i	0.0268952	−	0.103499i
$862$	−11.7189	−	20.2978i	−0.399148	−	0.691345i
$863$	−1.51655	−	2.62674i	−0.0516240	−	0.0894154i	0.839059	−	0.544041i	$-0.183106\pi$
$863$	−1.51655	−	2.62674i	−0.0516240	−	0.0894154i	−0.890683	+	0.454626i	$0.849773\pi$
$864$	−3.07618	−	4.18773i	−0.104654	−	0.142469i
$865$	−3.68221	−	10.1168i	−0.125199	−	0.343981i
$866$			1.30004i			0.0441773i
$867$	4.65526	−	6.75659i	0.158101	−	0.229466i
$868$	0.468444	+	1.28704i	0.0159000	+	0.0436849i
$869$	2.42291	+	0.881868i	0.0821916	+	0.0299153i
$870$	−4.91978	−	17.8207i	−0.166796	−	0.604178i
$871$	58.8782	+	21.4299i	1.99501	+	0.726125i
$872$	3.98330	−	10.9440i	0.134891	−	0.370611i
$873$	16.3268	+	13.2843i	0.552580	+	0.449604i
$874$	3.61926	−	27.0925i	0.122423	−	0.916417i
$875$	−1.37172	−	0.791961i	−0.0463725	−	0.0267732i
$876$	1.57359	+	16.5442i	0.0531668	+	0.558978i
$877$	27.1041	+	32.3014i	0.915240	+	1.09074i	0.995575	+	0.0939729i	$0.0299567\pi$
$877$	27.1041	+	32.3014i	0.915240	+	1.09074i	−0.0803345	+	0.996768i	$0.525599\pi$
$878$	4.77876	+	0.842624i	0.161275	+	0.0284372i
$879$	6.51188	+	2.97679i	0.219640	+	0.100405i
$880$	−3.95325	−	3.31717i	−0.133264	−	0.111822i
$881$	−39.3323	−	22.7085i	−1.32514	−	0.765069i	−0.340595	−	0.940210i	$-0.610629\pi$
$881$	−39.3323	−	22.7085i	−1.32514	−	0.765069i	−0.984543	+	0.175141i	$0.943962\pi$
$882$	−7.45552	−	19.5583i	−0.251040	−	0.658561i
$883$	−25.2236	+	9.18064i	−0.848842	+	0.308953i	−0.729568	−	0.683908i	$-0.760279\pi$
$883$	−25.2236	+	9.18064i	−0.848842	+	0.308953i	−0.119274	+	0.992861i	$0.538057\pi$
$884$	−4.58722	+	26.0154i	−0.154285	+	0.874993i
$885$	−1.18046	+	14.7792i	−0.0396809	+	0.496799i
$886$			14.7779i			0.496472i
$887$	−37.8367	+	13.7714i	−1.27043	+	0.462400i	−0.887257	−	0.461276i	$-0.847392\pi$
$887$	−37.8367	+	13.7714i	−1.27043	+	0.462400i	−0.383176	+	0.923675i	$0.625170\pi$
$888$	−3.94326	−	5.54187i	−0.132327	−	0.185973i
$889$	−0.287678	−	0.790389i	−0.00964841	−	0.0265088i
$890$	0.909651	−	0.160396i	0.0304916	−	0.00537649i
$891$	13.9568	+	35.0129i	0.467571	+	1.17298i
$892$			13.5799i			0.454690i
$893$	−10.1786	+	9.29137i	−0.340613	+	0.310924i
$894$	−0.271001	+	3.39289i	−0.00906362	+	0.113475i
$895$	−10.6266	+	1.87375i	−0.355207	+	0.0626326i
$896$	−0.116096	+	0.0974161i	−0.00387849	+	0.00325444i
$897$	59.3201	−	16.3766i	1.98064	−	0.546798i
$898$	1.09191	+	6.19252i	0.0364375	+	0.206647i
$899$	77.0931	+	13.5936i	2.57120	+	0.453372i
$900$	−6.59201	+	8.10182i	−0.219734	+	0.270061i
$901$	21.0951	−	12.1793i	0.702781	−	0.405751i
$902$	−49.3017	−	8.69322i	−1.64157	−	0.289452i
$903$	1.17559	+	1.15795i	0.0391213	+	0.0385340i
$904$	−3.56971	+	6.18292i	−0.118727	+	0.205641i
$905$	9.59239			0.318862
$906$	−3.18791	−	11.5474i	−0.105911	−	0.383637i
$907$	−53.2911	+	9.39665i	−1.76950	+	0.312011i	−0.961013	−	0.276502i	$-0.910825\pi$
$907$	−53.2911	+	9.39665i	−1.76950	+	0.312011i	−0.808488	+	0.588513i	$0.799714\pi$
$908$	−6.07890	−	5.10080i	−0.201735	−	0.169276i
$909$	−4.71602	+	8.46141i	−0.156421	+	0.280647i
$910$	0.994303	+	0.361897i	0.0329608	+	0.0119968i
$911$	21.1475	−	36.6286i	0.700648	−	1.21356i	−0.267591	−	0.963533i	$-0.586228\pi$
$911$	21.1475	−	36.6286i	0.700648	−	1.21356i	0.968239	−	0.250026i	$-0.0804392\pi$
$912$	−4.62987	−	5.96358i	−0.153310	−	0.197474i
$913$	24.2700	+	42.0368i	0.803219	+	1.39122i
$914$	−0.723640	−	4.10397i	−0.0239359	−	0.135747i
$915$	−2.42051	+	0.230225i	−0.0800195	+	0.00761100i
$916$	−16.0478	+	5.84094i	−0.530236	+	0.192990i
$917$	−0.192443	−	0.229345i	−0.00635504	−	0.00757364i
$918$	−19.5245	+	14.3421i	−0.644405	+	0.473361i
$919$	6.68902	−	11.5857i	0.220650	−	0.382178i	−0.734355	−	0.678765i	$-0.762515\pi$
$919$	6.68902	−	11.5857i	0.220650	−	0.382178i	0.955006	+	0.296588i	$0.0958487\pi$
$920$	−7.72690			−0.254749
$921$	−0.936765	−	3.39320i	−0.0308675	−	0.111810i
$922$	3.62882	−	4.32466i	0.119509	−	0.142425i
$923$	9.27435	+	5.35455i	0.305269	+	0.176247i
$924$	0.992797	−	0.472122i	0.0326606	−	0.0155317i
$925$	−8.78814	+	10.4733i	−0.288952	+	0.344360i
$926$	−1.97053	+	1.65347i	−0.0647555	+	0.0543363i
$927$	−1.02452	−	0.355441i	−0.0336497	−	0.0116742i
$928$	1.50415	+	8.53047i	0.0493762	+	0.280026i
$929$	−1.45195	−	1.73037i	−0.0476370	−	0.0567715i	0.741700	−	0.670732i	$-0.234020\pi$
$929$	−1.45195	−	1.73037i	−0.0476370	−	0.0567715i	−0.789337	+	0.613960i	$0.789575\pi$
$930$	8.28359	+	17.4191i	0.271630	+	0.571193i
$931$	−11.5847	−	28.1193i	−0.379675	−	0.921572i
$932$	−19.2781	+	11.1302i	−0.631474	+	0.364581i
$933$	−29.0800	+	2.76593i	−0.952037	+	0.0905523i
$934$	6.67730	−	18.3457i	0.218488	−	0.600290i
$935$	−15.4657	+	18.4313i	−0.505782	+	0.602768i
$936$	8.27540	−	14.8476i	0.270490	−	0.485309i
$937$	−4.45373	+	25.2583i	−0.145497	+	0.825154i	0.821470	+	0.570252i	$0.193154\pi$
$937$	−4.45373	+	25.2583i	−0.145497	+	0.825154i	−0.966967	+	0.254902i	$0.917957\pi$
$938$	1.45139	−	0.837963i	0.0473897	−	0.0273604i
$939$	−29.6434	−	2.36771i	−0.967377	−	0.0772674i
$940$	2.98449	+	2.50428i	0.0973433	+	0.0816807i
$941$	−33.0440	−	27.7272i	−1.07720	−	0.903880i	−0.0815167	−	0.996672i	$-0.525976\pi$
$941$	−33.0440	−	27.7272i	−1.07720	−	0.903880i	−0.995686	+	0.0927920i	$0.970421\pi$
$942$	−13.9695	−	29.3756i	−0.455151	−	0.957110i
$943$	−64.9152	+	37.4788i	−2.11393	+	1.22048i
$944$	1.20629	−	6.84119i	0.0392613	−	0.222662i
$945$	0.429942	+	0.869924i	0.0139860	+	0.0282986i
$946$	16.9225	−	20.1674i	0.550198	−	0.655700i
$947$	9.35571	−	25.7046i	0.304020	−	0.835287i	−0.689772	−	0.724027i	$-0.742289\pi$
$947$	9.35571	−	25.7046i	0.304020	−	0.835287i	0.993791	−	0.111260i	$-0.0354887\pi$
$948$	0.443342	−	0.969833i	0.0143991	−	0.0314987i
$949$	−47.0815	+	27.1825i	−1.52833	+	0.882381i
$950$	−9.26144	+	12.0223i	−0.300481	+	0.390055i
$951$	−31.3101	+	45.4430i	−1.01530	+	1.47359i
$952$	0.454185	+	0.541276i	0.0147202	+	0.0175429i
$953$	−0.280284	−	1.58957i	−0.00907930	−	0.0514913i	0.979932	−	0.199334i	$-0.0638780\pi$
$953$	−0.280284	−	1.58957i	−0.00907930	−	0.0514913i	−0.989011	+	0.147843i	$0.952767\pi$
$954$	−15.3926	+	2.95485i	−0.498355	+	0.0956669i
$955$	−17.3517	+	14.5598i	−0.561487	+	0.471144i
$956$	−11.6217	+	13.8502i	−0.375873	+	0.447948i
$957$	5.00276	−	62.6338i	0.161716	−	2.02466i
$958$	−11.4023	−	6.58312i	−0.368391	−	0.212691i
$959$	0.427405	−	0.509361i	0.0138016	−	0.0164481i
$960$	−1.49771	+	1.52054i	−0.0483385	+	0.0490752i
$961$	−50.6742			−1.63465
$962$	11.1249	−	19.2689i	0.358682	−	0.621256i
$963$	−15.5445	+	44.8055i	−0.500916	+	1.44384i
$964$	8.19302	+	9.76406i	0.263879	+	0.314479i
$965$	−8.89926	+	3.23906i	−0.286477	+	0.104269i
$966$	0.684339	−	1.49703i	0.0220183	−	0.0481660i
$967$	0.795759	+	4.51297i	0.0255899	+	0.145127i	0.994926	−	0.100612i	$-0.0320802\pi$
$967$	0.795759	+	4.51297i	0.0255899	+	0.145127i	−0.969336	+	0.245740i	$0.920969\pi$
$968$	−3.26972	−	5.66332i	−0.105093	−	0.182026i
$969$	−27.8041	+	21.5859i	−0.893196	+	0.693440i
$970$	4.32276	−	7.48724i	0.138796	−	0.240401i
$971$	−34.5382	−	12.5709i	−1.10838	−	0.403419i	−0.277984	−	0.960586i	$-0.589666\pi$
$971$	−34.5382	−	12.5709i	−1.10838	−	0.403419i	−0.830401	+	0.557167i	$0.811888\pi$
$972$	14.8940	−	4.60093i	0.477725	−	0.147575i
$973$	2.54560	+	2.13602i	0.0816083	+	0.0684775i
$974$	−1.11393	+	0.196416i	−0.0356926	+	0.00629357i
$975$	−33.0695	−	8.59344i	−1.05907	−	0.275210i
$976$	1.13922			0.0364657
$977$	7.00219	−	12.1282i	0.224020	−	0.388014i	−0.732005	−	0.681299i	$-0.761415\pi$
$977$	7.00219	−	12.1282i	0.224020	−	0.388014i	0.956025	+	0.293285i	$0.0947486\pi$
$978$	5.02681	−	19.3443i	0.160740	−	0.618563i
$979$	3.09165	+	0.545141i	0.0988096	+	0.0174228i
$980$	−7.44550	+	4.29866i	−0.237838	+	0.137316i
$981$	27.1015	+	22.0511i	0.865286	+	0.704036i
$982$	17.3896	+	3.06626i	0.554925	+	0.0978483i
$983$	3.85511	+	21.8634i	0.122959	+	0.697334i	0.982499	+	0.186267i	$0.0596388\pi$
$983$	3.85511	+	21.8634i	0.122959	+	0.697334i	−0.859540	+	0.511068i	$0.829250\pi$
$984$	−5.20730	+	20.0389i	−0.166003	+	0.638817i
$985$	4.54795	−	3.81619i	0.144910	−	0.121594i
$986$	39.7717	−	7.01283i	1.26659	−	0.223334i
$987$	−0.749508	+	0.356427i	−0.0238571	+	0.0113452i
$988$	11.4457	−	21.8853i	0.364137	−	0.696263i
$989$		−	39.4187i		−	1.25344i
$990$	13.2890	−	7.94280i	0.422353	−	0.252439i
$991$	15.9705	−	2.81603i	0.507319	−	0.0894541i	0.0858707	−	0.996306i	$-0.472633\pi$
$991$	15.9705	−	2.81603i	0.507319	−	0.0894541i	0.421449	+	0.906852i	$0.361522\pi$
$992$	−3.09097	−	8.49236i	−0.0981383	−	0.269633i
$993$	53.8771	−	5.12449i	1.70974	−	0.162621i
$994$	0.269169	−	0.0979694i	0.00853751	−	0.00310740i
$995$			15.5231i			0.492114i
$996$	18.1293	−	8.62134i	0.574449	−	0.273178i
$997$	−7.49456	+	42.5038i	−0.237355	+	1.34611i	0.600242	+	0.799819i	$0.295071\pi$
$997$	−7.49456	+	42.5038i	−0.237355	+	1.34611i	−0.837597	+	0.546289i	$0.816040\pi$
$998$	−8.69831	+	3.16593i	−0.275340	+	0.100216i
$999$	19.5846	−	5.72691i	0.619630	−	0.181191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.b.281.5	yes	48
9.5	odd	6		342.2.bf.b.167.3	yes	48
19.14	odd	18		342.2.bf.b.299.3	yes	48
171.14	even	18	inner	342.2.x.b.185.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.185.5	✓	48	171.14	even	18	inner
342.2.x.b.281.5	yes	48	1.1	even	1	trivial
342.2.bf.b.167.3	yes	48	9.5	odd	6
342.2.bf.b.299.3	yes	48	19.14	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.164003 + 1.72427i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.421448 - 1.15792i) q^{5} +(-1.23397 - 1.21545i) q^{6} +(-0.0757763 - 0.131248i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.94621 + 0.565569i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.164003 + 1.72427i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.421448 - 1.15792i) q^{5} +(-1.23397 - 1.21545i) q^{6} +(-0.0757763 - 0.131248i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.94621 + 0.565569i) q^{9} +(0.421448 + 1.15792i) q^{10} +4.18801i q^{11} +(1.72655 + 0.137905i) q^{12} +(1.93789 + 5.32431i) q^{13} +(0.142413 + 0.0518340i) q^{14} +(2.06568 + 0.536788i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.59461 + 4.38114i) q^{17} +(1.89338 - 2.32704i) q^{18} +(2.66011 - 3.45309i) q^{19} +(-1.06714 - 0.616116i) q^{20} +(0.213880 - 0.152184i) q^{21} +(-2.69200 - 3.20820i) q^{22} +(-6.17539 - 1.08889i) q^{23} +(-1.41126 + 1.00416i) q^{24} +(2.66706 + 2.23793i) q^{25} +(-4.90691 - 2.83301i) q^{26} +(-1.45838 - 4.98730i) q^{27} +(-0.142413 + 0.0518340i) q^{28} +(-1.50415 + 8.53047i) q^{29} +(-1.92745 + 0.916592i) q^{30} -9.03738i q^{31} +(0.939693 - 0.342020i) q^{32} +(-7.22126 + 0.686845i) q^{33} +(-1.59461 - 4.38114i) q^{34} +(-0.183911 + 0.0324284i) q^{35} +(0.0453738 + 2.99966i) q^{36} +3.92690i q^{37} +(0.181845 + 4.35510i) q^{38} +(-8.86272 + 4.21464i) q^{39} +(1.21351 - 0.213975i) q^{40} +(9.15707 - 7.68369i) q^{41} +(-0.0660197 + 0.254059i) q^{42} +(1.09159 + 6.19071i) q^{43} +(4.12439 + 0.727240i) q^{44} +(-0.586789 + 3.64983i) q^{45} +(5.43055 - 3.13533i) q^{46} +(-3.11369 - 0.549027i) q^{47} +(0.435623 - 1.67637i) q^{48} +(3.48852 - 6.04229i) q^{49} -3.48160 q^{50} +(-7.81579 - 2.03101i) q^{51} +(5.57993 - 0.983892i) q^{52} +(-4.00225 - 3.35828i) q^{53} +(4.32296 + 2.88306i) q^{54} +(4.84938 + 1.76503i) q^{55} +(0.0757763 - 0.131248i) q^{56} +(6.39032 + 4.02042i) q^{57} +(-4.33103 - 7.50157i) q^{58} +(1.20629 + 6.84119i) q^{59} +(0.887335 - 1.94109i) q^{60} +(-1.07052 + 0.389637i) q^{61} +(5.80912 + 6.92303i) q^{62} +(0.297483 + 0.343828i) q^{63} +(-0.500000 + 0.866025i) q^{64} +6.98184 q^{65} +(5.09031 - 5.16789i) q^{66} +(7.10819 - 8.47121i) q^{67} +(4.03768 + 2.33116i) q^{68} +(0.864755 - 10.8266i) q^{69} +(0.120039 - 0.143057i) q^{70} +(1.44787 - 1.21491i) q^{71} +(-1.96290 - 2.26870i) q^{72} +(1.66614 + 9.44917i) q^{73} +(-2.52416 - 3.00818i) q^{74} +(-3.42139 + 4.96576i) q^{75} +(-2.93871 - 3.21932i) q^{76} +(0.549669 - 0.317352i) q^{77} +(4.08012 - 8.92545i) q^{78} +(0.210570 - 0.578535i) q^{79} +(-0.792063 + 0.943944i) q^{80} +(8.36026 - 3.33257i) q^{81} +(-2.07574 + 11.7721i) q^{82} +(10.0374 - 5.79511i) q^{83} +(-0.112732 - 0.237057i) q^{84} +(4.40097 + 3.69285i) q^{85} +(-4.81552 - 4.04070i) q^{86} +(-14.9555 - 1.19454i) q^{87} +(-3.62692 + 2.09401i) q^{88} +(0.130167 - 0.738215i) q^{89} +(-1.89656 - 3.17311i) q^{90} +(0.551961 - 0.657801i) q^{91} +(-2.14469 + 5.89249i) q^{92} +(15.5829 - 1.48215i) q^{93} +(2.73813 - 1.58086i) q^{94} +(-2.87730 - 4.53549i) q^{95} +(0.743847 + 1.56419i) q^{96} +(-4.50990 - 5.37468i) q^{97} +(1.21155 + 6.87104i) q^{98} +(-2.36861 - 12.3387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

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